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EPA 600/9-76-016
JULY 1976
PROCEEDINGS OF THE
CONFERENCE
ON
ENVIRONMENTAL
MODELING AND SIMULATION
APRIL 19-22, 1976
CINCINNATI, OHIO
Sponsored by:
Office of Research and Development
and
Office of Planning and Management
U.S. ENVIRONMENTAL PROTECTION AGENCY
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EPA REVIEW NOTICE
These Proceedings have been reviewed by the U.S. Environmental Protection Agency
and approved for publication. Approval does not signify that the contents necessarily
reflect the views and policies of the Environmental Protection Agency, nor does mention
of trade names or commercial products constitute endorsement or recommendation for
use.
This document is available to the public for sale through the National Technical
Information Service, 5285 Port Royal Road, Springfield, Virginia 22161.
Monitoring Technology Division
Office of Monitoring and Technical Support (RD-680)
Office of Research and Development
U.S. Environmental Protection Agency
401 M. Street, S.W.
Washington, D.C. 20460
11
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Proceedings of
the EPA Conference on
ENVIRONMENTAL MODELING AND SIMULATION
Editor
Wayne R. Ott
Editorial Board
Oscar Albrecht, economics
Robert Clark, water supply
Robert Kinnison, statistics
Albert Klee, solid waste
Elijah Poole, simulation
Harry Torno, water pollution
Bruce Turner, air pollution
Ronald Venezia, planning
Production Manager
Vernon J. Laurie
Acknowledgement
Appreciation is expressed to Booz.Allen Applied Research, a division of Booz-Allen &
Hamilton Inc., for assistance in preparing the Proceedings.
111
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FOREWORD
Although many mathematical models have existed for some time in air pollution,
water pollution, ecology, and other environmental areas, there previously have been few
attempts to bring these models together to create one scientific field unto itself. This
conference, the EPA Conference on Environmental Modeling and Simulation, is a first
attempt to bring together the many diverse environmental modeling efforts in order to
form a unified discipline—environmental modeling.
The Conference Proceedings are believed to be the most complete single resource
document currently available covering the state-of-the-art of environmental modeling hi a
variety of environmental fields.
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TABLE OF CONTENTS
Page
Number
CONFERENCE BACKGROUND
Elijah L. Poole
CONFERENCE GOALS
Albert C. Trakowski
KEYNOTE ADDRESS:
TOWARD A COMMON LANGUAGE, Andrew W. Breidenbach
LUNCHEON ADDRESS:
A RESOURCE AND ENVIRONMENTAL MANAGEMENT EXCHANGE, Ira L. Whitman
1* MANAGEMENT I
Session Leader: Ed Schuck
FUTURE ENVIRONMENTAL QUALITY MANAGEMENT USING MODELS, D.W. Duttweiler and
W.M. Sanders, III
A SYSTEMATIC APPROACH TO REGIONAL WATER QUALITY PLANNING, G.P. Grimsrud and
E.J. Finnemore
A REVIEW OF EPA's GREAT LAKES MODELING PROGRAM, W.L. Richardson and N.A. Thomas
2 AIR QUALITY MANAGEMENT
Session Leader: Francis S. Binkowski
THE DEVELOPMENT AND IMPLEMENTATION OF USER ORIENTED AIR QUALITY MODELS,
J.J. Walton
A GENERIC SURVEY OF AIR QUALITY SIMULATION MODELS, G.D. Sauter
AIR QUALITY MODELING-A USER'S VIEWPOINT, R.H. Thuillier
3 MANAGEMENT H
Session Leader: David Duttweiler
SPACE: A CLOSER LOOK AT THE IMPACT OF ENVIRONMENTAL POLICY, E. Heilberg
RIBAM, A GENERALIZED MODEL FOR RIVER BASIN WATER QUALITY MANAGEMENT PLANNING,
R.N. Marshall, S.G. Chamberlain and C.V. Beckers, Jr.
COMPARISON OF EUTROPHICATION MODELS, J.S. Tapp
MANAGEMENT IN COMPETITIVE ECOLOGICAL SYSTEMS, D.R. Falkenburg
PLANNING IMPLICATIONS OF DISSOLVED OXYGEN DEPLETION IN THE WILLAMETTE RIVER,
OREGON, D.A. Rickert, W.G. Hines and S.W. McKenzie
URBANIZATION AND FLOODING-AN EXAMPLE, R.P. Shubinski and W.N. Fitch
PLANNING MODELS FOR NON-POINT RUNOFF ASSESSMENT, H.A. True
10
14
20
26
30
35
40
45
50
57
62
69
74
'Sessions are numbered in the same order as in the conference, and the papers are grouped according to the sessions.
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4 AIR QUALITY SIMULATION & APPLICATIONS
Session Leaders: Robert Jurgens and Roger S. Thompson
DESIGN AND APPLICATION OF THE TEXAS EPISODIC MODEL, J.H. Christiansen 77
AIR MODELING IN OHIO EPA, J.C. Bun and A.B. Clymer 82
DESIGNING A REGIONAL AIR POLLUTION MONITORING NETWORK: AN APPRAISAL OF
A REGRESSION EXPERIMENTAL DESIGN APPROACH, P.R. Gribik, K.O. Kortanek and J.R. Sweigart 86
SAMPLED CHRONOLOGICAL INPUT MODEL (SCIM) APPLIED TO AIR QUALITY PLANNING IN
TWO LARGE METROPOLITAN AREAS, R.C. Koch, D.J. Pelton and P.H. Hwang 92
MODELING OF PARTICULATE AND SULFUR DIOXIDE IN SUPPORT OF TEN-YEAR PLANNING,
R.A. Porter and J.H. Christiansen 97
5 WATER QUALITY
Session Leaders: Roger Shull and William P. Sommers
A MATHEMATICAL MODEL OF DISSOLVED OXYGEN IN THE LOWER CUYAHOGA RIVER,
A.E. Ramm 101
A WATER RESIDUALS INVENTORY FOR NATIONAL POLICY ANALYSIS, E.H. Pechan and R.A. Luken 106
A MULTI-PARAMETER ESTUARY MODEL, P.A. Johanson, M.W. Lorenzen and W.W. Waddel 111
MATHEMATICAL MODEL OF A GREAT LAKES ESTUARY, C.G. Delos 115
COST-EFFECTIVE ANALYSIS OF WASTE LOAD ALLOCATIONS, J. Kingscott 120
WASTE ALLOCATIONS IN THE BUFFALO (NEW YORK) RIVER BASIN, D.H. Sargent 126
STREAM MODELING AND WASTE LOAD ALLOCATION, J.Y. Hung, A. Hossain and T.P. Chang 129
PATUXENT RIVER BASIN MODEL RATES STUDY, T.H. Pheiffer, L.J. Clark and N.L. Lovelace 133
6 WATER RUNOFF I (TRANSPORT)
Session Leaders: Richard Field and Lee Mulkey
EFFICIENT STORAGE OF URBAN STORM WATER RUNOFF, J.R. Doyle, J.P. Heaney, W.C. Huber and
S.M. Hasan 139
JOINT USE OF SWMM AND STORM MODELS FOR PLANNING URBAN SEWER SYSTEMS, H.L. Kaufman and
Fu-Hsiung Lai 144
SIMULATION OF AGRICULTURAL RUNOFF, A. Donigian, Jr. and N.H. Crawford 151
MODELING THE EFFECT OF PESTICIDE LOADING ON RIVERINE ECOSYSTEMS, J.W. Falco and L.A. Mulkey 156
RADIONUCLIDE TRANSPORT IN THE GREAT LAKES, R.E. Sullivan and W.H. Ellett 161
FEDBAK 0 3-A COMPUTER FOR THE MODELING OF FIRST ORDER CONSECUTIVE REACTIONS WITH
FEEDBACK UNDER A STEADY STATE MULTIDIMENSIONAL NATURAL AQUATIC SYSTEM, G.A. Nossa 166
MODELING THE HYDRODYNAMIC EFFECTS OF LARGE MAN-MADE MODIFICATIONS TO LAKES, J.F. Paul 171
AN EMPIRICAL MODEL FOR NUTRIENT ACCUMULATION RATES IN LAKE ONTARIO, P.A.A. Clark,
D.J. Casey, A. Solpietro and J.P. Sandwick 176
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7 RADIATION AND HEALTH
Session Leader: Mary J. White
MODELS FOR EXTRAPOLATION OF HEALTH RISK, W.M. Upholt 182
USE OF MATHEMATICAL MODELS IN NONIONIZING RADIATION RESEARCH, C.M. Weil 186
AIR POLLUTANT HEALTH EFFECTS ESTIMATION MODEL, W.C. Nelson, J.H. Knelson and V. Hasselblad 191
MORTALITY MODELS: A POLICY TOOL, W.B. Riggan, J.B. Van Bruggen, L. Truppi and M. Hertz 196
A RADIOACTIVE WASTE MANAGEMENT ASSESSMENT MODEL, S.E. Logan and S.M. Goldberg 199
FOOD-AN INTERACTIVE CODE TO CALCULATE INTERNAL RADIATION DOSES FROM
CONTAMINATED FOOD PRODUCTS, D.A. Baker, G.R. Hoenes and J.K. Soldat 204
AER QUALITY AND INTRA-URBAN MORTALITY, J.J. Gregor 209
EVALUATION OF HEALTH DATA IN TERMS OF ENVIRONMENTAL FACTORS, M. Katzper and N.P. Ross 214
8 ENERGY
Session Leader: Oscar Albrecht
INTEGRATED ASSESSMENT: CONCEPT AND LIMITATIONS, L. Smith, R.H. Ball, P.M. Cukor,
S. Plotkin and F. Princiotta 218
AN INTEGRATED TECHNOLOGY ASSESSMENT OF ELECTRIC UTILITY ENERGY SYSTEMS,
P. Cukor, S. Cohen, G. Kendall, T. Johnston, S. Gage and L. Smith 223
ENVIRONMENTAL IMPACT MODELING FOR PROJECT INDEPENDENCE, R.A. Livingston, G.R. Kendall,
R.W. Menchen and H.P. Santiago 230
AN ENVIRONMENTAL RESIDUAL ALLOCATION MODEL, F.Lambie and M. Allen 236
HITTMAN REGIONAL ENVIRONMENTAL COEFFICIENTS FOR THE PROJECT INDEPENDENCE
EVALUATION SYSTEMS (PIES) MODEL, W.R. Menchen, M.S. Mendis, Jr. and H.L. Schultz, III 241
INTEGRATED ECONOMIC-HYDROSALINITY-AIR QUALITY ANALYSIS FOR OIL SHALE AND COAL
DEVELOPMENT IN COLORADO, C.W. Howe, J.F. Kreider, B. Udis, R.C. Hess, D.V. Orr and J.T. Young 247
9 SIMULATION I
Session Leader: Theodore R. Harris
CSMP CONCEPT AND APPLICATIONS TO ENVIRONMENTAL MODELING AND SIMULATION, C.L. Wang and
G. Chang 252
GASP IV CONCEPTS APPLICABLE TO ENVIRONMENTAL MODELING AND SIMULATION, A.A.B. Pritsker 259
RADIONUCLIDE REMOVAL BY THE pH ADJUSTMENT OF PHOSPHATE MILL EFFLUENT WATER,
D.L. Norwood and J.A. Broadway 264
AN APPLICATION OF BIASED ESTIMATION THEORY TO ITERATIVE MAXIMUM LIKELIHOOD
SEARCH STRATEGIES, D.J. Svendsgaard 269
10 ECONOMICS I
Session Leader: Oscar Albrecht
ECONOMIC AND DEMOGRAPHIC MODELING RELATED TO ENVIRONMENTAL MANAGEMENT,
A.V. Kneese 274
ECONOMIC IMPLICATIONS OF POLLUTION-INTENSIVE EXPORTS BY DEVELOPING
COUNTRIES, P.A. Petri 282
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A TAXONOMY OF ENVIRONMENTAL MODELS, R.U. Ayres 288
A STOCHASTIC MODEL FOR SUBREGIONAL POPULATION PROJECTION, P.M. Meier 293
11 AIR QUALITY (LONG TERM MODELS AND SENSITIVITY TESTING)
Session Leaders: John H. Christiansen and Richard H. Thuillier
USE OF THE CLIMATOLOGICAL DISPERSION MODEL FOR AIR QUALITY MAINTENANCE
PLANNING IN THE STATE OF RHODE ISLAND, P.H. Guldberg, T.E. Wright and A.R. McAllister 298
IMPROVEMENTS IN AIR QUALITY DISPLAY MODEL, C. Prasad 303
AIR POLLUTION MODELING IN THE DETROIT METROPOLITAN AREA, A. Greenberg, B. Cho and
J.A. Anderson 308
SENSITIVITY TESTS WITH A PARAMETERIZED MIXED-LAYER MODEL SUITABLE FOR
AIR QUALITY SIMULATIONS, D. Keyser and R.A. Anthes 313
PREDICTION OF CONCENTRATION PATTERNS IN THE ATMOSPHERIC SURFACE LAYER,
S. Hameed and S.A. Lebedeff 318
A TIME-DEPENDENT, FINITE GAUSSIAN LINE SOURCE MODEL, J.C. Burr and R.G. Duffy 322
12 WATER QUALITY H
Session Leader: Don Lewis
WATER QUALITY MODELING IN TEXAS, J.J. Beal, A.P. Covar and D.W. White 326
A DYNAMIC WATER QUALITY SIMULATION MODEL FOR THE THAMES RIVER, D.G. Weatherbe 330
DISPERSION MODEL FOR AN INSTANTANEOUS SOURCE OF POLLUTION IN NATURAL STREAMS AND
ITS APPLICABILITY TO THE BIG BLUE RIVER (NEBRASKA), M.K. Bansal 335
SELECTING THE PROPER REAERATION COEFFICIENT FOR USE IN WATER QUALITY
MODELS, A.P. Covar 340
RECEIV-II, A GENERALIZED DYNAMIC PLANNING MODEL FOR WATER QUALITY MANAGEMENT,
C.V. Beckers, P.E. Parker, R.N. Marshall and S.G. Chamberlain 344
MODIFICATIONS TO QUAL-II TO EVALUATE WASTEWATER STORAGE, J.S. Tapp 350
13 WATER RUNOFF II
Session Leader: Paul Wisner
WATER POLLUTION MODELING IN THE DETROIT METROPOLITAN AREA, M. Selak, C. Harlow,
J. Anderson and R. Skrentner 353
GENERALIZED METHOD FOR EVALUATING URBAN STORM WATER QUALITY MANAGEMENT
STORAGE/TREATMENT ALTERNATIVES, J.P. Heaney, W.C. Huber, S.M. Hasan and P. Murphy 358
MODELING HYDROLOGIC - LAND USE INTERACTIONS IN FLORIDA, P.B. Bedient, W.C. Huber and
P. Heaney 362
MODELING URBAN RUNOFF FROM A PLANNED COMMUNITY, E.V. Diniz, D.E. Holloway and
W.G. Characklis 367
14 SOLID WASTE
Session Leader: Albert Klee
MODELING IN SOLID WASTE MANAGEMENT: A STATE-OF-THE-ART REVIEW, D.H. Marks 372
WRAP: A MODEL FOR REGIONAL SOLID WASTE MANAGEMENT PLANNING, E.B. Berman 377
ST. LOUIS: AN APPLICATION OF WRAP, D.M. Krabbe 381
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DEVELOPMENT OF A MODEL FOR AN ORGANIC SOLID WASTE STABILIZATION PROCESS ON A
PILOT PLANT, D.S. Whang and G.F. Meenaghan 386
15 PLANNING I
Session Leader: Ronald Venezia
EVALUATION AND SELECTION OF WATER QUALITY MODELS: A PLANNER'S GUIDE,
E.J. Finnemore and G.P. Grimsrud 391
A LANDSCAPE PLANNING MODEL AS AN AID TO DECISION-MAKING FOR COMMUNITY GROWTH
AND MANAGEMENT, J. Gy. Fabos and S.A. Joyner, Jr. 396
A RESOURCE ALLOCATION MODEL FOR THE EVALUATION OF ALTERNATIVES IN SECTION 208
PLANNING CONSIDERING ENVIRONMENTAL, SOCIAL AND ECONOMIC EFFECTS, D. Hill 401
REGIONAL RESIDUALS-ENVIRONMENTAL QUALITY MANAGEMENT MODELS: APPLICATIONS
TO EPA's REGIONAL MANAGEMENT PROGRAMS, W.O. Spofford, Jr. and C.N. Ehler 407
A COMPUTER MODELING STUDY TO ASSESS THE EFFECTS OF A PROPOSED MARINA ON A
COASTAL LAGOON, Kuang-Mei Lo, T.G. King, A.S. Cooper 414
16 SIMULATION U
Session Leader: Gary Liberson
DIGITAL COMPUTER SIMULATION OF SECONDARY EFFLUENT DISPOSAL ON LAND,
Kuang-Mei Lo and D.D. Adrian 419
COMPUTER SIMULATION OF LONG-TERM SECONDARY IMPACTS OF WATER AND WASTEWATER
PROJECTS, G.A. Outer, T.C. Ryan and J.F. Westermeier 424
A CRITICAL APPRAISAL OF MATHEMATICAL MODELS FOR LAND SUBSIDENCE SIMULATION,
E.J. Finnemore and R.W. Atherton 429
UNSTEADY-STATE, MULTI-DIMENSIONAL ANALYTICAL MODELING OF WATER QUALITY
IN RIVERS, R.W. Cleary 434
SIMUALTION MODELING OF ENVIRONMENTAL INTERACTION EFFECTS, E.T. Smith 439
17 ECONOMICS II
Session Leader: Oscar Albrecht
TOWARD A DYNAMIC ECONOMIC MODEL FOR REGULATING FLUOROCARBON EMISSIONS,
R.C. D'Arge, J. Harrington and L. Eubanks 446
ENVIRONMENTAL, FISCAL, AND SOCIO-ECONOMIC IMPACT OF LAND USE POLICIES: TOWARD AN
INTERACTIVE ANALYSIS, J. Kuhner, M. Shapiro, R.J. deLucia and W.C. Lienesch 453
A TOTAL CONCEPT SYSTEM FOR MUNICIPAL WASTE DISPOSAL, L.L. Nagel 458
ECONOMIC FORECASTING FOR VIRGINIA'S WATER RESOURCE PROGRAMS, C.P. Becker,
A.M. Griffin, Jr. and C.S. Lown 466
18 AIR QUALITY (NEW TECHNIQUES AND PHYSICAL MODELING)
Session Leaders: Richard A. Porter and Terry Clark
MODELING RADIATIVE TRANSFER IN THE PLANETARY BOUNDARY LAYER: PRELIMINARY
RESULTS, F.S. Binkowski 473
ADAPTIVE FORECASTING OF BACKGROUND CONCENTRATIONS USING FEEDBACK CONTROL
AND PATTERN RECOGNITION TECHNIQUES, R. Carbone and W.L. Gorr 478
SOURCE-ORIENTED EMPIRICAL AIR QUALITY MODELS, K.L. Calder and W.S. Meisel 483
EPA FLUID MODELING FACILITY, R.S. Thompson and W.H. Snyder 488
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PLUME BEHAVIOR IN THE LEE OF A MOUNTAIN RIDGE-A WIND TUNNEL STUDY, A.H. Huber,
W.H. Snyder, R.S. Thompson and R.E. Lawson, Jr. 493
A NOTE ON THE SEA BREEZE REGIME, S.T. Rao and P.J. Samson 499
A NUMERICAL MODEL FOR STABLY STRATIFIED FLOW AROUND COMPLEX TERRAIN
J.J. Riley, E.W. Geller and Hsien-Ta Liu 503
19 WATER QUALITY IH (TRANSPORT)
Session Leaders: Donald Dean Adrian and Larry Roesner
HYDRODYNAMIC AND WATER QUALTIY MODELING IN THE OPEN OCEAN USING MULTIPLE
GRID SIZES, P.J. Wickramaratne, J.W. Demenkow, S.G. Chamberlain and J.D. Callahan 508
BLACK RIVER THERMAL ANALYSIS, D.R. Schregardus and G.A. Amendola 512
WATER MODELING IN OHIO EPA, R.G. Duffy and A.B. Clymer 517
THREE-DIMENSIONAL MODEL DEVELOPMENT FOR THERMAL POLLUTION STUDIES,
R.A. Bland, S. Sengupta and S. Lee 522
SOME OBSERVATIONS ON MODELING DISPERSION OF POLLUTANTS IN NEAR-SHORE WATERS
OF LAKE MICHIGAN, R.H. Snow 527
A RIVER BASIN PLANNING METHODOLOGY FOR STREAMS WITH DISSOLVED OXYGEN AND
EUTROPHICATION CONSTRAINTS, T.M. Walski and R.G. Curran 532
MODELING POLLUTANT MIGRATION IN SUBSURFACE ENVIRONMENTS, A.A. Metry 537
A MODEL OF TIDAL FLUSHING FOR SMALL COASTAL BASINS, A.Y. Kuo 543
20 WATER RUNOFF III AND DATA AND VERIFICATION
Session Leaders: Wayne Huber and Harry Torno
EVALUATION OF MATHEMATICAL MODELS FOR THE SIMULATION OF TIME-VARYING RUNOFF AND
WATER QUALITY IN STORM AND COMBINED SEWERAGE SYSTEMS, A. Brandstetter, R. Field and H.C. Torno 548
USE OF MATHEMATICAL MODELS FOR HYDROLOGIC FORECASTING IN THE NATIONAL WEATHER
SERVICE, J.C. Schaake, Jr. 553
TESTING OF THE STORM WATER MANAGEMENT MODEL OF U.S. EPA, J. Marsalek 558
APPLICATION OF STORM & SWMM FOR ASSESSMENT OF URBAN DRAINAGE ALTERNATIVES
IN CANADA, P.E. Wisner, A.F. Roake and A.F. Ashamalla 563
ON THE VERIFICATION OF A THREE-DIMENSIONAL PHYTOPLANKTON MODEL OF LAKE
ONTARIO, R.V. Thomann and R.P. Winfield 568
MATHEMATICAL MODEL FOR THE EXCRETION OF 14CO2 DURING RADIO RESPIROMETRIC
STUDIES, R. Dtis 573
ESTIMATION OF THE OPTIMAL SAMPLING INTERVAL IN ASSESSING WATER QUALITY
OF STREAMS, L.J. Hetling, G.A. Carlson and J.A. Bloomfield 579
FIELD DATA FOR ENVIRONMENTAL MODELING-ADJUNCT OR INTEGRAL?, P.E. Shelley 583
DATA DEFICIENCIES IN ACID MINE DRAINAGE MODELING, V.T. Ricca 586
21 SOLID WASTE
Session Leader: Albert Klee
A MODELING TECHNIQUE FOR OPEN DUMP BURNING, M. Rosenstein and V.J. Descamps 591
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DEVELOPMENT AND USE OF A FIXED CHARGE PROGRAMMING MODEL FOR REGIONAL SOLID
WASTE PLANNING, W. Walker, M. Aquilina and D. Schur 595
INCENTIVES FOR WASTE COLLECTION BASED ON WORK CONTENT MODELING, R.L. Shell and D.S. Shupe 600
PLANNING FOR VARIATIONS IN SOLID WASTE GENERATION, D. Grossman 605
MODEL OF THE MOVEMENT OF HAZARDOUS WASTE CHEMICALS FOR SANITARY LANDFILL SITES,
E. Elzy and F.T. Lindstrom 609
22 ECOLOGY
Session Leader: John A. Burckle
PHYTOPLANKTON BIOMASS MODEL OF LAKE HURON AND SAGINAW BAY, D.M. Di Toro and
W.F. Matystik, Jr. 614
COMPARISON OF PROCESSES DETERMINING THE FATE OF MECURY IN AQUATIC SYSTEMS,
R.R. Lassiter, J.L. Malanchuk and G.L. Baughman 619
ASPECTS OF MATHEMATICAL MODELS AND MICROCOSM RESEARCH, J.W. Haefner and J.W. Gillett 624
AN ECOLOGICAL MODEL FOR THE GREAT LAKES, D. Scavia, B.J. Eadie and A. Robertson 629
23 WATER SUPPLY I
Session Leader: Robert Clark
SIMULATION AND MATHEMATICAL MODELING OF WATER SUPPLY SYSTEMS-STATE-OF-THE-ART
R.A. Deininger 634
CAPACITY EXPANSION FOR MUNICIPAL WATER AND WASTEWATER SERVICES: INCORPORATION
OF UNCERTAINTY, R.G. Curran, D.H. Marks and D.S. Grossman 639
ADAPTIVE SHORT-TERM WATER DEMAND FORECASTING, D.H. Budenaers 646
HYDROLOGIC IMPACT STUDIES OF ALTERNATIVES TO MEET WATER NEEDS IN SOUTH-
CENTRAL PENNSYLVANIA, J.C. Schaake, Jr., D.H. Marks, B.M. Harley and G.J. Vicens 651
THE OPERATIONAL WATER QUALITY MODEL, A.N. Shahane, P. Berger and R.L. Hamrick 657
24 STATISTICS I
Session Leader: Robert Kinnison
HOW TO MAKE SIMULATIONS MORE EFFECTIVE, G.S. Fishman 664
THE FACTUAL BACKGROUND OF ECOLOGICAL MODELS: TAPPING SOME UNUSED RESOURCES,
E.C. Pielou 668
TIME SERIES ANALYSIS AND FORECASTING FOR AIR POLLUTION CONCENTRATIONS WITH
SEASONAL VARIATIONS, Der-Ann Hsu and J.S. Hunter 673
METEOROLOGICAL ADJUSTMENT OF YEARLY MEAN VALUES FOR AIR POLLUTANT
CONCENTRATION COMPARISONS, S.M. Sidik and H.E. Neustader 678
THE APPLICATION OF CLUSTER ANALYSIS TO STREAM WATER QUALITY DATA, J.A. Bloomfield 683
APPLICATION OF PATH ANALYSIS TO DELINEATE THE SECONDARY GROWTH EFFECTS OF
MAJOR LAND USE PROJECTS, T. McCurdy, F. Benesh, P. Guldberg and R. D'Agostino 691
PREDICTION OF PHYTOPLANKTON PRODUCTIVITY IN LAKES, V.W. Lambou, R.W. Thomas,
L.R. Williams, S.C. Hern and J.D. Bliss 696
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25 AIR (POINT SOURCE)
Session Leader: Bruce Turner
APPLICATIONS OF THE SINGLE SOURCE (CRSTER) MODEL TO POWER PLANTS: A SUMMARY,
J.A. Tikvart and C.E. Mears 701
MODIFIED DISPERSION MODELING PROCEDURES FOR INDIANA POWER PLANTS, H.D. Williams,
S.K. Mukherji, D.R. Maxwell, M.W. Bobb and C.R. Hansen 706
SEVERITY OF STATIONARY AIR POLLUTION SOURCES-A SIMULATION APPROACH, B.C. Eimutis,
B.J. Holmes and L.B. Mote 710
26 AIR QUALITY (NEW TECHNIQUES)
Session Leaders: Joseph A. Tikvart and George D. Sauter
ATMOSPHERIC POLLUTANT DISPERSION USING SECOND-ORDER CLOSURE MODELING OF THE
TURBULENCE, W.S. Lewellen and M. Teske 714
POINT SOURCE TRANSPORT MODEL WITH A SIMPLE DIFFUSION CALCULATION FOR ST. LOUIS,
T.L. Clark and R.E. Eskridge 719
THE CHANGE IN OZONE LEVELS CAUSED BY PRECURSOR POLLUTANTS: AN EMPIRICAL
ANALYSIS, L. Breiman and W.S. Meisel 725
QUALITY ASSURANCE AND DATA VALIDATION FOR THE REGIONAL AIR MONITORING SYSTEM
OF THE ST. LOUIS REGIONAL AIR POLLUTION STUDY, R. Jurgens and R.C. Rhodes 730
QUANTITATIVE RISK ASSESSMENT FOR COMMUNITY EXPOSURE TO VINYL CHLORIDE,
A.M. Kuzmack and R.E. McGaughy 736
27 WATER (WASTEWATER AND CONVEYANCE)
Session Leader: Robert Smith
NEW MODELS FOR OPTIMAL SEWER SYSTEM DESIGN, B.C. Yen, H.G. Wenzel, Jr., W.H. Tang and
L.W. Mays 740
THE USE OF LITHIUM CHLORIDE FOR AERATION TANK PERFORMANCE ANALYSIS, T.J. Olenik,
R.C. Ahlert and R. Gesumaria 745
SWAN-A SEWER ANALYSIS MODELING SYSTEM, B.C. Tonias and P.C. King 750
ON-LINE MODELS FOR COMPUTERIZED CONTROL OF COMBINED SEWER SYSTEMS, J.W. Labadie,
N.S. Grigg and P.O. Trotta 755
MATHEMATICAL MODELS FOR CALCULATING PERFORMANCE AND COST OF WASTEWATER
TREATMENT SYSTEMS, R.G. Eilers 760
28 WATER (ECOLOGY)
Session Leader: Mutafa Shirazi
THE ECOLOGICAL MODEL AS APPLIED TO LAKE WASHINGTON, C.W. Chen and D.J. Smith 764
A LIMNOLOGICAL MODEL FOR EUTROPHIC LAKES AND IMPOUNDMENTS, R.G. Baca and R.C. Arnett 768
MATHEMATICAL MODELING OF PHYTOPLANKTON DYNAMICS IN SAGINAW BAY, LAKE HURON,
V.J. Bierman, Jr. and D.M. Dolan 773
THE APPLICATION OF A STEADY-STATE WATER QUALITY MODEL TO THE PERMIT WRITING
PROCESS, LAKE MILNER, IDAHO, J.R. Yearsley 780
BUOYANT SURFACE JET, M.A. Shirazi and L.R. Davis 784
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29 ECOLOGY AND NOISE
Session Leader: John O. Burckle
AGROECOSYSTEM-A LABORATORY MODEL ECOSYSTEM TO SIMULATE AGRICULTURAL
FIELD CONDITIONS FOR MONITORING PESTICIDES, M.L. Beall, Jr., R.G. Nash and P.C. Kearney 790
A CONCEPTUAL MODEL FOR ECOLOGICAL EVALUATION OF POWER PLANT COOLING SYSTEM
OPERATION, M.W. Lorenzen and C.W. Chen 794
REVIEW OF THE STATUS OF MODELING ENVIRONMENTAL NOISE, W.J. Galloway 799
COMMUNITY NOISE MODELING, B. Manns 803
30 WATER SUPPLY D
Session Leader: Robert Clark
THE COST OF WATER SUPPLY UTILITY MANAGEMENT, R.M. Clark and J.I. Gillian 808
MATHEMATICAL MODELING OF DUAL WATER SUPPLY SYSTEMS, A.K. Deb and K.J. Ives 814
DATA COLLECTION FOR WATER QUALITY MODELING IN THE OCCOQUAN WATERSHED OF
VIRGINIA, C.W. Randall, T.J. Grizzard and R.C. Hoehn 819
WATER SUPPLY SYSTEMS PLANNING, MANAGEMENT AND COMMUNICAITON THROUGH AN
INTERACTIVE RIVER BASIN SIMULATION MODEL, R.A. Hahn 824
FUTURE DIRECTIONS IN URBAN WATER MODELING, M.B. Sonne, L.A. Roesner and R.P. Shubinski 829
31 STATISTICS II
Session Leader: Robert Kinnison
TRANSPORT MODELING IN THE ENVIRONMENT USING Tifji DISCRETE-PARCEL-RANDOM-WALK
APPROACH, S.W. Ahlstrom and H.P. Foote * 833
AN INTERACTIVE SYSTEM FOR TIME SERIES ANALYSIS AND DISPLAY OF WATER QUALITY
DATA, S. Buda, R.L. Phillips, G.N. Cederquist and D.E. Geister 838
CONFERENCE COMMITTEES 844
AUTHOR INDEX 845
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CONFERENCE BACKGROUND
Elijah L. Poole
Office of Planning and Management
U.S. Environmental Protection Agency
It is my unique pleasure to welcome you to the "EPA Conference on Environmental Modeling and Simulation."
This is the first EPA conference where modeling and simulation will be discussed in so many diverse topic
areas: air, water, pesticides, solid waste, noise, radiation, health, energy, ecology, planning, management,
economics, and others.
The Environmental Protection Agency was established in 1970 to permit coordinated and effective governmental
action in order to protect the environment. Two of its roles are to perform research and to transmit research
results to the users. In general, mathematical modeling and simulation are widely used for performing research,
and this appears to be particularly true for environmental research.
We were overwhelmingly pleased to receive 220 abstracts as a result of our call for papers, and 164
papers are scheduled for presentation at this conference. These papers indicate considerable and extensive
environmental modeling efforts in EPA, State and local governments, universities, and private industry. Some
papers also were contributed by modelers from Canada. We feel that we are indeed fortunate at this conference
to have so many distinguished speakers and attendees - many of whom are well known experts in their fields.
Some major objectives of the Conference are: to perform a state-of-the-art review of predictive modeling
and simulation in the environmental decisionmaking process, to share modeling expertise within and across
various media, and to better understand computer requirements and other resources needed in the development
and use of models.
Considerable efforts are expended in formulating and developing mathematical models, and a large share
of computer time is spent running modeling programs. This conference should serve to enhance communication
among modelers and users of models, thereby decreasing development and operating costs and also eliminating
some redundancies. With the expertise represented here, I feel that many of the Conference objectives will
be accomplished.
The Conference has been in the planning stages for more than a year. It was some 18 months ago that
Dr. Wayne Ott of the Office of Research and Development and I discussed the feasibility of structuring a
conference on environmental modeling and simulation. Prior conversations with many of the Agency modelers
and users of models supported the usefulness and desirability of such a conference, and so now the concept
has come to fruition.
Many people have been involved working to make the Conference a success. The list is rather long so I
will not take the time to try and name everyone. In the back of your program guide you will see an extensive
list of primary contributors beginning with Vern Laurie, the Conference Coordinator, and Delores Platt for
logistics. And, of course, there are many others whose efforts are appreciated.
In general, the program is organized according to subject matter. The Program Committee felt that some
papers were of considerable interest and should be presented, although no topic category may have existed.
Because it was decided not to have a miscellaneous session, you will occasionally find a paper in a session
where it may not seem to belong. This happens rarely, however.
It is our hope that all attendees find the Conference stimulating and discover new techniques and
contacts for future references in developing, operating, and using models.
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CONFERENCE GOALS
Albert C. Trakowski
Deputy Assistant Administrator for
Monitoring and Technical Support
U.S. Environmental Protection Agency
Conference Moderator
I believe we have opened a new chapter in the environmental sciences by holding this conference. For the
first time we are bringing together, under one roof, all the many varied and diverse environmental topics where
mathematicians, statisticians, operations research specialists, systems analysts, engineers, and others with
quantitative backgrounds share a common interest.
It is unfortunate, I believe, that modelers working in air pollution seldom have a chance to become fully
acquainted with water pollution modeling approaches. Similarly, computer models in solid wastes seldom are
brought to the attention of persons developing models for economic studies of air pollution. Models developed
for noise applications probably are not widely known among the air or water pollution modeling communities, and
models concerned with ecological processes do not often appear in the literature alongside papers on environmen-
tal statistics.
There is, however, a commonality of approach among modelers. This commonality should enable them to communi-
cate freely and effectively once they are brought together in a forum such as the present conference. Although
mathematics and statistics form the foundation for this commonality, the universality does not end there; there
is also a commonality of purpose among the modeling community.
Most models are based on, or make use of, environmental data in some form—particularly monitoring data. Also
most modelers, by developing abstractions of reality, attempt to simulate reality. By examining the behavior of
their model under a variety of situations and with different inputs, they often make predictions about reality.
The "rightness" or ''wrongness" of these predictions is, of course, model validation. Models also share many
similarities in terms of applications and uses. Some of the more common uses are to (1) project future environ-
mental phenomena and variables; (2) develop more optimal control systems and technology; (3) gain insights into
underlying physical, chemical, or biological processes; (4) evaluate the consequences of various environmental
management decisions and regulatory strategies; (5) assist in the planning process; (6) aid in the interpretation
and analysis of monitoring data intended to depict the state of the environment; (7) estimate the risks of
adverse effects of environmental pollution on human health, plants, and animals; (8) assess the economic and
social costs arising from environmental pollution.
Our goal in planning this conference was not, however, merely to bring modelers from different environmental
media together for them to share thoughts about the nature of models. Rather, our goal was to seek a confronta-
tion between the model users and the model developers. Thus, you will see that the Conference Program contains
some very interesting papers discussing the practical experience of environmental managers with models. In
several instances, we have included papers from state and local environmental control officials who will tell us
the problems and successes they have had with particular kinds of environmental modeling efforts. We hope that
the question and answer periods in the technical sessions will stir some lively debate on these matters. Hope-
fully, by bringing model users and model developers together we can accomplish a better understanding of the
potential uses and limitations of models at the same time that the developers receive some constructive feedback
from the users.
This brings me to some comments about the role of the Environmental Protection Agency in the modeling areas.
EPA's Office of Research and Development serves as the major scientific and technical arm of the Agency, carry-
ing forward a broad and varied research program covering air, water, energy, ecology, and many other facets of
the environmental sciences. This research program includes both in-house and contractual work directed toward
the development, testing, evaluation, and refinement of models for all environmental media. Within the Office
of Research and Development, the Office of Monitoring and Technical Support is the primary organizational entity
responsible for transferring the technology produced by the research community into the hands of the user com-
munity. We view this conference, which is cooperatively supported by EPA's Office of Planning and Management,
as one of the more important means by which the results of scientific research (in this case, environmental
modeling approaches) can be effectively transferred to the user community. Thus, we hope the conference will
help facilitate a productive dialogue between the developers of models and the environmental managers faced with
the need to make decisions using the results of these models.
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TOWARD A COMMON LANGUAGE
KEYNOTE ADDRESS
Dr. Andrew W. Breidenbach
Assistant Administrator, Office of
Water and Hazardous Material
U.S. Environmental Protection Agency
As a scientist and a decisionmaker within the Environmental Protection Agency, I am struck by the fact that
this conference is long overdue. It is the first conference on modeling and simulation to bring all the various
media of the environmental community together. In looking over the schedule for the next two and a half days, I
note that at least 15 distinct areas are represented, including air, water, energy, solid waste, ecology, noise,
health, and radiation. Five years ago, before EPA existed, this conference would not have been possible, but
today it seems quite natural to consider multi-media approaches.
This conference is important to me because scientists and modelers are playing a very active role in decision-
making today. As our decisions become more complicated, scientists are working more closely with the decision-
maker. By visiting with you, I hope to learn more about modeling. At the same time, I hope I can convey to you
some of my thoughts, so we can establish a basis for communication between modelers and decisionmakers.
GETTING DEFINITIONS STRAIGHT
Good communication begins with a common language. I ask you to recall the situation not too many years ago
when Congressmen and Administrators shuddered at such terms as "Biochemical Oxygen Demand," "Total Suspended
Particulates," "polychlorinated biphenyls," and "oxides of nitrogen." These words probably sounded more like
Greek than English. But let us look at how far we have come in just a few years. Most Congressmen know that
"BOD" has something to do with sewage treatment plants. Even such terms as "ozone layer" and "catalytic con-
verter" are household terms. I think we have come a long way toward bringing the language of the scientist
within the province of the decisionmaker.
But the language of models is another story. Take the simple word "model." How often has someone come into
my office and mentioned that he has a model, and I wait expectantly for her to come into the room. Or for a
large display case to be carried in with a miniature replica of a waste treatment plant. These are not unusual
reactions when hearing the word model. We have become accustomed from childhood to such concepts as "model T,"
"toy models," or "you should model yourself after that person." All of these examples imply that a model is a
physical representation.
The dictionary's definition seems to focus on this physical aspect. Webster defines a model as "a standard
for imitation or comparison; a pattern. A representation, generally in miniature, to show the construction or
serve as a copy of something." Actually this is not a quote from Webster, but from the Random House Dictionary,
which I thought would be more appropriate for this conference.
Nowhere does the dictionary, or for that matter, the decisionmaker's general experience, really depict the
idea of a mathematical model. Yet from what I can gather, almost all of the models you will hear about this
week are mathematical models of one sort or another.
Even if the decisionmaker understands the concept of mathematical model, he is likely to be confused and
overwhelmed by the variety and complexity of available models. This confusion could lead to a serious breakdown
in communication. For instance, the decisionmaker may have in mind a simple, deterministic model, but the
scientist may actually be using a statistical model, or a stochastic model, or a simulation, or an analog computer
model.
It is important to get our definitions straight and agree on a common language. Since the language of
modeling is unknown to the public and to many managers, the subject seems to cause some fear, or at least a
feeling of distrust. It is only human nature to be a little afraid of something new or something you do not
understand.
A COMMON LANGUAGE
A simplified and clarified language of modeling will go a long way in advancing the cause of modeling. Mana-
gers and the public will better appreciate modeling, and as appreciation and understanding of models grow, so will
the use of models.
A careful and consistent language of modeling can also help communication between modelers. As you listen
over the next few days to the many talks on models, think of how many different ways you hear the word "model" .
used. In the titles of the papers to be presented, the words "modeling" or "model" occur 107 times. One would
expect that for such a common word, each of us would be well acquainted with its meaning. Yet, when you listen
to papers being presented, ask youself whether you really know what the authors mean by the word "model." Better
yet, consider whether you think your neighbors on either side of you have the same concept of "model" that you
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have, and that the authors have. I suspect there may be a good deal of fuzziness in the definitions commonly
used.
Another major reason for my concern about definitions is that we are frequently being sued over our deci-
sions, both by industry and by environmentalists. Courts must listen to both plaintiff and defendant discuss
modeling. Since neither the plaintiffs, the defendants, nor the courts can define their terms exactly, I can
almost guarantee that opposing sides will disagree on what they mean by "model."
Thus, development of a consistent and understandable modeling language is becoming extremely important to
the manager, the scientist, and the public.
We will not, however, be able to develop a common language overnight, and even if we attack the problem over
the next two and a half days, we may not get very far. But there are some reasonable first steps we can take.
As the keynoter for this conference, let me propose some questions from my perspective as a decisionmaker to help
define what I mean by a common language. As you hear about models in your area of concern, whether it be water
quality, ecology, or economics, keep in mind what decisionmakers like me need to know.
CURIOSITY OR DECISION TOOL?
One question might be, "Is this model a mathematical curiosity or is it a tool for making decisions?" I
know that we have advanced well beyond the mathematical curiosity stage but I am not sure whether we have arrived
at the decisionmaking end of the spectrum as yet.
To help find out where we stand in the evolution of models, let me describe the results of my own model
which I commissioned solely for this conference. The model is called A Statistical System to Evaluate Symposium
Success, also known as ASSESS. My staff assures me that it is a state-of-the-art model, with nothing but the
best data inputs, and the most rigorous of validation techniques.
We performed a keyword analysis on the titles of all 164 papers to be presented here this week. Then we
classified the papers into three categories: Policy-Oriented, State-of-the-Art Review, and Technical.
We called a paper Policy-Oriented if the title of the paper had the slightest hint of policy orientation,
such as by using the words "planning," or "management," or "policy." Of course I hoped that 95 percent would
be Policy-Oriented papers. In reality, we found that only 17 percent of the papers fell in this category. So
I doubt that we have reached the stage of model evolution where all models are being directed at policy questions.
The next category is State-of-the-Art Review. These papers perform a valuable service to modelers and
decisionmakers by comparing and analyzing models. Twelve percent of the papers fell in this category. I hope
we will see more of this kind of paper in the future.
The third category is Technical papers. If the title of a paper did not mention policy, and did not appear
to be a review, we called it a technical paper. By now you will not be surprised to learn that the majority of
papers—71 percent—appear to be Technical papers. These figures suggest we may have too many models which are
still in the mathematical curiosity phase. I hope not.
I do not wish to imply that all technical papers are irrelevant to the decisionmaker. I know that many are
very relevant. My point is that the modeler must become more sensitive to decisionmakers1 needs, and must know
how they intend to use the model.
So much for the ASSESS model. I know the conference will be a success in spite of it.
ASSUMPTIONS
Another question I ask as a decisionmaker concerns the model's assumptions. Assumptions do for a model what
gasoline does for an automobile—they make it run, and they determine how far it can go. The person who developed
the model probably knows precisely what assumptions are important. It is the user—the decisionmaker—who will
feel the effects of these assumptions.
The decisionmaker must be told if there are assumptions which are simply not true and which completely in-
validate the model. Unfortunately, modelers can become so involved in making the model work that they forget
to distinguish between things that are true and things that are convenient simplifying assumptions. The user
must know, for instance, if a model is only for lakes, or if it assumes complete mixing, or if it is valid only
for summer months. Stating the assumptions is a key part of the common language of modeling.
SENSITIVITY
I also like to ask about the sensitivity of the model to input variables. The decisionmaker must be told
which variables are critical to the results, and which variables do not impact the results. One of the most
useful outputs of models is thi-s ability to distinguish between what is important, and what is unimportant. So
sensitivity analysis should also be a part of the language of modeling.
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VALIDATION
One of my favorite questions is, "Has this model been validated?" Sometimes it may be impossible to validate
a model completely. For instance, a global economic growth model may be difficult to validate. But to use a
model in making a decision, I must have some proof that the model works, or at least have something which convinces
me I can rely on it.
The only sure way to validate a model is to test it using new data—that is, test it using data which were
not used to develop the model. In the water program, we have often found models which people claimed were valid,
but were really just tested with the same data used to develop and calibrate the model. This is like using a
pocket calculator to verify that x+y y+x, for all the possible values of x and y. When you test a model with
new data, you are also helping to determine how robust the model is—that is,-how applicable the model is under
varying situations.
Validation is not something to be afraid of. Validation techniques can improve your models in the long run,
even if they show that your present model is incorrect for the task at hand. And I guarantee that decisionmakers
will use your model more willingly if you have solid evidence to validate it.
DATA INPUTS
One final question I often ask is" What data did you use? Did you collect the data yourself, or did someone
collect it for you? Are the data valid today, or are they obsolete? What variables were measured?" I can assure
you these are not empty questions. We have found treatment models which use temperatures as a key independent
variable, but which were based on input data collected at a constant temperature. We have also found a water
quality model for a particular river, where all the so-called ambient monitoring data were collected just down-
stream from industrial outfalls. A good corollary to the "garbage in-garbage out" rule is that a model is only
as good as its data.
The quality of data used is probably one of the restraining forces for the modeling community today. The
high costs of collecting data are enough to make some managers shudder at the word "model." Yet, it is the
modeler's responsibility to insist on good data, even if it means higher cost. If good data are not available,
the modeler should point out how this limits the validity of the results.
DECISIONMAKING AND RISK
Why ask these questions? Why worry about who uses the model? About assumptions and sensitivity? About
validation? About data? The reason is that as a decisionmaker, I cannot afford to use a model which is wrong.
For once a manager uses a model which turns out to be wrong, he will probably never want to use a model again.
Consider the county executive or State governor who makes a decision based on an urban transportation model
for air pollution, or a stream loading model for water pollution. What will be his reaction after the new parking
plan is implemented, and the air is still dirty? Or after the new treatment plant is built, and pollution does
not improve? Not only will the modeler's reputation suffer, but the momentum of the entire environmental movement
could suffer seriously.
The public manager wants to minimize his risk of making wrong decisions. And that, in a sense, is one of the
primary justifications for developing models in the first place. It is your job and responsibility as modelers
to reduce the manager's risk.
THE BIG PROBLEMS
In the water program, decisions are made routinely using models, or so I am told. Models are used to help
determine effluent guidelines, determine water quality standards, and evaluate the impact of effluent reductions
on water. We could not set standards for "best available technology," for instance, without the use of models,
since in many cases the technology does not exist in widespread use. Water quality criteria could not be
established for many materials without using mathematical models. Mathematical models are well known in toxico-
logy and help the scientist determine the relationships between doses for animals, aquatic life, and human
beings. Models help us determine what amount of pollutant in the water will yield a cummulative toxic dose
in aquatic organisms. Effluent loading models can help determine the impact of our multi-bill ion dollar clean-
up programs.
It was my intention when preparing this paper to give examples of modeling success stories. Yet with all of
these models in my program, we could not find one which was universally acclaimed for solving what we call a "Big
Problem." A Big Problem is a problem that makes the press, that causes Congress to come screaming and yelling at
our doors. To be sure, we have many examples where a model was used to help make a local decision. Yet many of
these models were unreliable or controversial and, in the final analysis, decisions were sometimes made on the
basis of common sense as much as they were on the model.
I interpret this to mean that modeling has been in an embryonic state. I hope that you, the modelers, through
this conference and your interaction, will help modeling come of age for the Big Problem.
I believe that models have a lot to offer the manager. That is why I would like to see both managers and
scientists start working with more urgency on the problem of developing a common language. If a dialog is
5.
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initiated, the modeler will begin to get a better idea of what the decisionmaker faces. Models to solve the Big
Problems could begin to be developed. And the decisionmaker will have better Information to confirm or deny his
common-sense beliefs. As environmental problems become more complex, the decisionmaker depends more and more on
technical knowledge. Models can help focus this knowledge, and help us solve some of these problems.
CONCLUSION
The organizers of this conference have done an excellent job of bringing together many diverse entities.
The program is so diverse, and the time is so short, that you will only be able to hear a small portion of the
papers to be presented, even if you spend all of your time at conference sessions, and not at the bar downstairs
or watching the World Champion Cincinnati Reds. All of these papers, and the stimulating dialog with your counter-
parts should ensure that we meet the major objectives of this conference. These objectives are, and I quote:
"To perform a state-of-the-art review of predictive modeling and simulation in the environmental
decisionmaking process; to share modeling expertise within and across various media; and to examine
the adequacy of computer and other resources in the development and use of models."
As we embark on this conference, I give you the task of creating a common language that both modelers and
decisionmakers can readily understand. This language will also help convey our decisions to the general public.
I also give you the task of creating a consistent methodology for verifying models and describing their capabilities,
so that managers will have a standard with which they can measure the usefulness and accuracy of models. Armed
with these, the modeler will be able to convince more and more managers to use models in environmental decisions.
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A RESOURCE AND ENVIRONMENTAL MANAGEMENT EXCHANGE
LUNCHEON ADDRESS
Dr. Ira L. Whitman
Environmental Engineering and Management
Columbus, Ohio
The conference coordinators advise me that this meeting is dedicated to the users of modeling efforts, to
individuals in government and industry whose management and planning efforts will determine the future course of
resource and environmental management.
What I have to say should be of interest to anyone concerned about the future of environmental management —
and should particularly concern you modelers and analysts who care about the results of your efforts and the
impact that you have on the environment. I will plead my case for an awakening, a humanization of technical
persons working in the environmental professions. Also, I will offer a plan to create leadership in the environ-
mental field, leadership capable of dealing with real-world problems founded upon a solid scientific and techni-
cal base.
I can personally recall that day, almost 15 years ago, when I first interviewed with my graduate advisor to
be, and learned that in exchange for tuition and stipend I would be transforming unit operations of sanitary en-
gineering into analog computer simulations. However, it wasn't until several months later that I learned what
an analog computer was. It took even longer to recognize the fantastic potential for discovery that existed
with the use of models, simulation and with computers. My efforts were modest by comparison with yours, yet they
were sufficient to crank out that all-important Master's thesis, and send me off to the cruel hard world where
there is no equation for reality, and no model that tells us when and how to make the right decisions.
I decided to leave the models and computers to others, and attempted to build upon their expertise in envi-
ronmental modeling to bring about more rational environmental policies and better managed environmental programs.
In 1971, in Ohio, we introduced the concept of effluent charges to the Citizen's Task Force on Environmental Pro-
tection, a concept that was endorsed by a coalition of environmentally oriented citizens and businessmen above
the protests of the industrial community. In 1972, we quietly commissioned a study of an industrial cost sharing
approach based on computer modeling of major air pollution sources in one of our industrial cities. Also in that
year, we hired some of the State's first environmental modelers, who have distinguished themselves by presenting
no less than three papers here at this conference. Yet, in 1974, a major enforcement case we were pursuing was
hopelessly lost, due considerably to our failure to validate critical air quality monitoring data.
The lesson learned from these experiences is this: There is an undeniable linkage between the major ele-
ments of a national program of resource and environmental management. I see four such elements, each being a
link in the process of achieving our national environmental goals. These elements are:
1. Scientific monitoring and understanding of the components of the environment.
2. Integration and analysis of these components into understanding of environmental systems, through model-
ing and other systematic tools.
3. Formulation of environmental policies, and administrative and legislative actions in order to manage our
environmental systems.
4. Implementation of environmental programs including design and construction of facilities.
Scientific monitoring and research allows us to identify and describe the components of our environment. We
must know what these are before such systems can be modeled and analyzed. Much of your work has been restricted
by limitations in our basic data and our knowledge of natural processes. Ecological modeling, for example, is
only as good as our knowledge of the basic ecological processes themselves, many of which we understand in only a
primitive fashion. Millions of dollars now go into basic environmental data collection — from ships, balloons,
space satellites, and from complex and very simple monitoring equipment here on earth. The outputs from this
first phase of environmental inquiry are the raw inputs needed by you, the modelers, mathematicians, and analysts.
Environmental modeling and simulation are integrating processes, by which relationships are tested and ex-
plored. Through modeling, we can integrate the biological and chemical factors that describe a polluted waterway
with the cost and benefit factors that describe the results of improving that waterway, thus gaining economic in-
sights into the impacts of physical phenomenon. The horizons of your models have become elasticized by new gen-
erations of computers and new generations of modelers who have ingeniously learned how to represent a physical
world by an electronic world.
But what of the results of your modeling efforts? Where do they lead and where have they gone? How many
"optimal" solutions have become "acceptable" solutions? How many "least cost" alternatives have become "most
used" alternatives? Where have your models taken us?
You have led us, I believe, to the doorstep of that next element in our environmental programs, the formula-
tion of policies, and administrative and legislative actions. But have you taken us across the threshold?
Rarely! It is this realm of policy and administration that concerns me the most, for this is the real world —
the world of people and their problems; it is the place where push comes to shove —not just in our models, but
in our city halls and board rooms and anywhere that real power is being bartered and brokered.
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Ah--but you say that it is your job to provide the data and the alternatives, and that it is the decision-
makers who must make the choices. But who are the decisionmakers — and why is it they who are playing chess with
our resources and our lives while you, who have the tools of understanding at your command, are playing second
fiddle?
So the question I ask is this — how do we integrate the rationality which you, as modelers and analysts, can
provide into the real world of the political pro and the board room Machiavelli?
Can we bring the decisionmaker to you and convince him of your wisdom? Can we wrap you up in a nice neat
shiny package and bring you to his world? Will he listen? Will he understand you?
NO!!
How do your models, and what they have to offer, get across that doorstep into the real world where the
action is? My friends, you take them across. Hand-carry them—special delivery. And how do you guarantee that
they are actually delivered, and that they find their way into the thought processes that lead to action? You
must be there on the other side waiting to receive them1, and willing to put them to use.
Become the decisionmakers! Not through your models, but through yourselves — your talents, your words, your
actions, your interests. Prepare yourselves to put behind you the world of computers and to professionally in-
habit the world of people. You will find a vacuum there waiting for your leadership, and the vacuum created in
your wake will soon be filled by new generations of modelers waiting and following behind you.
If you expect the leaders, the decisionmakers, to understand and embody the work which you are performing,
then you must prepare to provide the leadership. I am suggesting that you, the mathematicians, modelers, and en-
gineers, become humanized to the point where your concerns are with the use, the impacts, and the practicality of
your plans and the results of your modeling efforts. In short, no environmental policies and programs in this
country, nor any public policy, can grow and evolve towards the achievement of their goals unless the persons
best trained and equipped to understand and implement those policies grow with it. Grow!
I believe that many of you must set out to reorient yourselves and grow, in two directions which will enable
you to become a part of the decisionmaking process. Grow in the direction of your personal actions and behavior,
and grow in the direction of your professional interests and career.
Grow by communicating! How often have you heard the word communicate thrown up to you — at professional
meetings, in your office, and anywhere where people are concerned about the results of your labors?
Communicate! But do you really? Can you describe your work and its applications to your wives? How many
of you are understood by them well enough so that they would be able to describe to others what you do?
What about your kids? Do they understand what you do? Have you ever spoken to their classes in school? If
you have, did you get your point across well enough so that your kids were glad you came? Do you think you could
explain to a 6th grade class what you do, and why it will help fight pollution in some way? What about an 8th
grade class? 10th grade? 12th grade? Could you, in fact, successfully speak before a class of college sopho-
mores? Could you do it without writing equations on the board?
Several years ago, my kids, very young at the time, were confused by the fact that certain people called me
Dr. Whitman, yet whenever they were ill their mother would have to take them to visit the pediatrician (and usu-
ally complain about the cost as well). What kind of a doctor was I that I couldn't treat sick kids? After much
attempted explanation, it all crystalized when I explained that I was a ''doctor of sick rivers," and not a doctor
of sick children. Children's perceptions of pollution are very vivid, and very real. Cleanliness is usually the
first concept driven home to kids by their parents — and violation of public cleanliness, pollution, is not an
abstraction to them by any means. It is what you and I are doing to clean up the pollution that becomes the ab-
straction. In their simplified world, mother always has an immediate solution for the pollution problems which
concern them. Yet we, whose business and profession it is to clean up on a larger scale, seldom produce results,
or even take actions which the kids can comprehend. Well, if they in their enthusiasm cannot know what we do,
what makes you think that the public at .large will?
If your kids, or the ones down the block, can't understand what you're doing, what about your parents? Have
you ever tried to explain your professional activities to your parents and to members of their generation? They
want to know that the country which they fought for 35 years ago, and which they helped rebuild after a disastrous
depression, is being left in good shape for their grandchildren. They don't care too much about our generation —
if things are a mess they figure it's our own fault. But they surely care about our children! What have you done
lately to assure our senior citizens that you are helping to produce a healthful and safe environment for future
generations? Do they understand you? Do you talk to them at all?
Communication is just the beginning! How about involvement in community problems — environmental or other-
wise? I know that many of us "working stiffs" in this field are getting involved, be we modelers, or lawyers, or
technicians. Much of the acceptance of public involvement in environmental policies and programs has come about
because some of us have been involved, and are beginning to understand what citizen action really means.
How about involvement in the political process? How many of you (federal employees excluded!) have ever
seriously participated in the election of a candidate? Have you passed petitions from door to door and tried to
explain why your man was better than the other guy? Have you ever cornered and interrogated a local candidate to
find out what he really stood for? Have you sat in on legislative hearings — only to wonder what was really de-
cided behind closed doors before the hearing ever began?
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Why am I dwelling upon the theme of communication and involvement? Because they are part of personal growth.
Unless you share experiences with other people, experience their interests, their feelings, their views, their
preferences, their philosophy of government, it will be impossible for you as an economist or mathematician or
scientist to take your efforts into the real world where it all happens. I'm talking about the world beyond the
doorstep where so many of our academic exercises come to rest.
But self-help is not always enough! There are those of you out there, and colleagues of yours around the
country, who would like nothing better than to have the opportunity to take your talents to the board room, and
to city hall, and to apply yourselves not just to the description and modeling of the environment, but to partic-
ipate in the decisions and the actions which lead to the management and protection of the environment.
To enable this professional growth to happen, I am proposing a Resource and Environmental Management Ex-
change, for the purpose of developing responsible, well rounded, experienced men and women capable of exercising
leadership in the private and public sectors in dealing with environmental and resource issues. This is the
first public announcement of this concept which has been brewing for months, and which will be put before leading
governmental and private organizations concerned with our ability to manage and protect our natural and environ-
mental resources. The objective of the Exchange is not to take technocrats and let them manage our resources,
but rather to build upon persons who have strong technical experience in the environmental field and help them
become fully rounded, sensitive, alert participants in the management and policy-making processes.
The Resource and Environmental Management Exchange would, with the commitment of the individuals and organi-
zations involved, establish over a five-year span the capability we need to manage our environment and our re-
sources intelligently and democratically. Just what commitment do we need?
At the start, I would envision an Exchange which has the backing of some 75 to 140 organizations, involving
200 individuals. These individuals would be presently employed, as many of you are, by large and small corpora-
tions, states, universities, units of our federal government, think tank and research centers, local and regional
agencies, and professional societies. Each organization participating would be committed to the following:
1. Selecting and sponsoring one or more of its staff for involvement in the Exchange over a five-year
period.
2. Underwriting part of the cost of its employees' participation in the Exchange, including seminar and
involvement programs held regularly over the five-year period.
3. A willingness to exchange personnel with other participating organizations for periods of 6 to 18 months.
4. A commitment to build management opportunities for Exchange graduates.
I estimate the cost of this program to be from $3,000 to $4,000 per year per person, which accounts for all
costs above the normal salary and other costs of employment for Exchange participants over a five-year period.
For a complete Exchange group of 200 individuals, this results in a total cost of $4 million over the five-year
period.
But what are the potential benefits by which this cost can be measured? What is the price of leadership?
Corporations now spend thousands of dollars in training and upgrading their management team members, and in relo-
cating them throughout their organizations. The cost of hiring new management talent into their organizations is
even higher. The current value of environmental programs — public and private, is in the billions of dollars a
year, and still growing!
We have spent millions on environmental monitoring, and data collection, and more millions on models and
computer analyses to try to generate some sense of these data. Yet, by and large, we deliver the results of our
efforts to persons in organizations, private and public, untrained in management and unaware of the benefits
which national resource management can really produce. And, even more alarming, policy and management actions
lead to programs costing billions of dollars in the construction of waste treatment facilities, in the prevention
of adverse environmental impacts, and in the cancellation of facilities that might otherwise be built. As various
need surveys show, the total cost of meeting our environmental goals lies somewhere between our annual federal
budget and our gross national product, both of which are very large amounts, to say the least. Can you imagine
what the value of improved management and alert leadership in these programs will be? That is why this program
is being proposed — to bring us the professional growth and leadership that i.s needed.
Through modeling and simulation we have been able to integrate many factors within our environmental and
economic systems. We can make trade-offs leading toward solutions that offer us the most for our money. Through
your efforts we can study the response of air sheds to new development, the change in river quality as we pro-
gress with our pollution cleanup efforts, and we can electronically track garbage trucks as they find their way
around a large city over assorted hypothetical routes.
But now we must do more than model the environment and simulate our management systems. We must harness the
talent which has been used to develop these magnificent tools and give it the opportunity to grow and to prepare
for the responsibilities of leadership. We must steer ourselves toward people, for it is they, and not our ma-
chines, who will determine whether, and to what degree, our environmental goals will be met. And, in building
this leadership, we should consider the institution of efforts to expose our talent to new situations, new expe-
riences, new pressures, and new responsibilities. In short, we need to consider something like a Resource and
Management Exchange, which will allow us to build upon our scientific and technical skills and develop this lead-
ership for the future. With it, we all grow!
I hope you agree! Please let me have your ideas, and your response to these ideas.
9
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FUTURE ENVIRONMENTAL QUALITY MANAGEMENT
USING MODELS
David W. Duttweiler
Director
US Environmental Protection Agency
Environmental Research Laboratory
Athens, Georgia
Walter M. Sanders, III
Acting Associate Director for
Water Quality Research
US Environmental Protection Agency
Environmental Research Laboratory
Athens, Georgia
Introduction
The purpose of this paper is threefold: 1) to show
environmental pollution control officials and managers
the potential of models for enhancing the efficiency
and effectiveness of their efforts, 2) to suggest to
modelers that their products can be more useful in
environmental protection, and 3) to outline a future
mode of action for environmental protection that could
be superior, in its accomplishments and costs, to the
present approach.
The concept of the environment as a system will be
outlined and "pollution control" compared with
"environmental quality management." Steps to realize
environmental quality management through use of models
will be described and the potential benefits of
instituting environmental quality management will be
discussed.
Environment
A useful concept of the environment is a system
composed of sources of materials linked by transport
and reaction processes to biological receptors or sinks
where the materials are sequestered from further
significant environmental activity. The materials are
usually residuals (wastes) of human activity,
occasionally materials intentionally injected into the
environment like pesticides, and often the products of
geochemical processes. They become pollutants when,
for reasons such as health, ecology, economics, or
aesthetics, they are undesirable constituents of one or
more abiotic environmental components (media), such as
air, water, or land. The atmosphere, for example,
transports a pollutant from its source to receptors or
to sinks, which may be organisms, another environmental
component, or man-made objects. During transport the
pollutant may participate in chemical or physical
reactions that may transform it into other materials
that may also be pollutants or that may give further
rise to pollutants. Pollution occurs when adverse
effects attributable directly or indirectly to the
pollutants are discerned in receptors, or when the
"quality" of the medium is degraded to a level that
impairs its utility. Fishkills and saline agricultural
irrigation water, respectively, are two obvious
examples.
Pollution Control
The contemporary approach to eliminating or
preventing the undesirable effects of pollutants
focuses, logically, on their sources, but virtually
ignores the rest of the environmental system or treats
it piecemeal. Pollution control is based on
technological or managerial modification of pollutant
sources that either emit greater amounts of pollutants
than society deems reasonable for such sources, or that
cause pollutants to appear in air or water in amounts
that society finds unacceptable. Pollution control is
generally confined to sources that affect a single
medium; rarely are effects in other media considered.
Environmental System Management
A superior approach to solving society's environ-
mental pollution problems, employing a holistic view of
both the environment and society, would allow the
environment to be managed to achieve the objectives
society chooses. Advocated by both environmental
technologists and social scientists (for example,
McGauhey, 1968; Freeman, et_ al., 1973), a system
management approach could devise means of attaining
society's objectives most effectively and efficiently.
Management of the environmental system, rather than its
individual components, should prevent the unanticipated
adverse effects that result when the solution of one
environmental problem creates several more serious
ones.
The systems approach forces recognition of the
interconnectedness of environment and society, and
provides a means of evaluating the impact of projected
social changes on the environment, and of environmental
changes on society. Unfortunately, social systems are
understood as poorly as environmental systems.
Environmental Management Functions
We recognize six major steps in the systems
approach to environmental management. First, the
community's objectives must be clearly identified, and
criteria must be developed to judge their satisfactory
attainment.
Second, the system to be managed must be defined.
Its components must be identified at a. useful level of
resolution. The boundaries of the system must be
delineated and all significant inputs and
the boundaries must be quantified.
linking the components must be
quantified.
outputs at
The processes
identified and
Third, the functional relationships between the
objectives and the environmental (and social) system
must be adequately quantified.
Fourth, strategies must be formulated that permit
sufficient variety of alternative decisions to be
a
examined for
consequences and
objectives.
decisions to be
their environmental and social
for their ability to achieve the
Fifth, an effective means of
decisions must be established.
implementing the
10
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Finally, a means of measuring the results of
implementing the decisions must be provided, and data
on environmental and social impact must be made
available for use in any of the preceding steps.
Each of the above steps, so easily stated,
represents technical, as well as managerial and
political, challenges that are not likely to be met
satisfactorily without considerable rational
simplification. For example, one could not possibly
define every input and output of a watershed, since
measuring every component of mass transport across the
shed boundaries in the real world would be an
insurmountable task. However, the dominant processes
of the environmental system can be measured
sufficiently well to account for much of the system's
behavior. Although such incomplete information about
the system will prevent full explanation of many of its
phenomena, nevertheless it can usually allow rational,
system-wide decisions. Simultaneously, areas of
ignorance that must be addressed to improve system
management will be identified.
Even the simplest of environmental processes is
affected by a complex of interacting environmental
factors whose net effect is difficult to analyze
mentally. Systematic study of these factors and their
relations to the process can yield insight that can be
experienced by the knowledgeable environmental
scientist as a mental picture of the process. Even
better, these insights can be expressed as a
quantitative mathematical model. Models of individual
processes combined into larger models of the
environmental system can be studied more economically
and more comprehensively than can the real environment.
Outputs of model studies can be analyzed for system
response to various input strategies and for insights
that would be impossible to gain from study of the
prototype.
Modeling
Systems science offers some concepts (see for
example, McFarlane, 1964) that help understand the
potential and limitations of environmental models. An
environmental system is a real-world physical system
which can be studied only through a measuring system.
The output of the measuring system is a set of
observations that is used to construct a mathematical
model of the physical system. Observations of the
physical system can be compared to the model's
description, giving a set of errors that guide
refinement of the model. This iterative process
continues until the errors become acceptably small.
The model is then accepted as adequate to represent or
simulate the prototype physical system for the
intended purpose.
Some models can be formulated in a way that allows
them to be used analytically for detecting interesting
features of the system and its behavior. Especially
for management purposes, they can find optima, that is,
find a set of conditions that will cause an objective
function (an objective stated mathematically as a
function of one or more system variables) to take on a
desired maximum or minimum. For example, the minimum
value of the cost function for a set of pollution
control procedures can be found through mathematical
manipulation. Some models can only be formulated in a
way that requires the objective function to be searched
for the optima. Even with this restriction, however,
searches using models are usually much more efficient
for finding the optima than are searches in the real
world.
Models must not be confused with their real-world
prototypes, and conclusions drawn from them must be
applied with caution. A model built with one objective
in mind will likely be inappropriate to simulate the
system for a different objective. Models built without
clearly defined objectives may have no practical use in
solving environmental problems. Models that are not
periodically compared with their prototypes can become
treacherously inaccurate if the prototypes or
constraints change without detection.
Mathematical models are perhaps the only feasible
means of accomplishing the six major steps outlined for
system management. The setting of social objectives is
an especially complicated process in a democratic
society. Models of this process and the interactions
between society's various objectives can suggest
efficient means of optimizing its results. Objectives
set by any process, however, may be unanimously
desirable, but not feasible. Models that relate
objectives to the systems to be managed can give
insight into their feasibility that might otherwise
await actual failure of attainment. An imprecise or
non-feasible objective can often be recognized and an
equivalent feasible objective substituted as a result
of such modeling.
The quantitative descriptive power of models is
essential to define a system to be managed, and to
focus attention on its significant features. For a
given objective, these features can be described
quantitatively so that the variables having the
greatest relevance to the objectives can be modeled.
Functional relationships between objectives and
the system to be managed obviously can be quantified
only through mathematical representations. These
functions, known with sufficient resolution and
precision, are crucial to the rational application of
system management.
Development of alternative management strategies
for environmental systems can use the powerful
techniques of operations research, mostly based on
models, that have been applied so successfully in
most other modern industrial and commercial activ-
ities. (See, for example, Churchman, et al. , 1957.)
If the means of implementing decisions is
considered separately, models can be used to design
efficient decision-implementing systems and guide their
operation. Again, operations research and modern
management science offer powerful techniques.
Finally, the design of systems to monitor the
results of environmental management decisions should be
based on the models used to reach the decisions.
Models of the monitoring system itself are useful for
optimizing its operation.
The six steps involve a variety of disciplines
that traditionally are not accustomed to the team
effort that is needed to make system management
effective. Semantic and philosophical differences can
find a common ground in models and their symbolism.
Environmental System Models
Construction of predictive environmental models is
a complex scientific challenge. Recent successes have
been confined mainly to models for managing specific
materials or controlling the quality of a single medium
(see, for example, Loucks, 1972; Thomann, 1972;
Deininger, 1973; Hill et_ al., 1976; Lassiter, 1975;
Bloomfield et_ al., 1973) . Environmental modelers are
adopting a modular approach that permits any number of
11
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subsystem models to be assembled into larger, more
comprehensive environmental system models. Such models
will never be able to predict reliably every variable
and parameter that might be of interest, but they
should provide sufficient basic information to meet the
environmental manager's needs. Models that offer
insight into ecosystem functions that impact
environmental quality (Chen et al., 1975), and in the
behavior of pollutants in ecosystems (Gillett, 1974;
Sanders, 1975) are available in various stages of
utility. Models that describe an operationally
significant water quality parameter, dissolved oxygen,
have been available in useful form for fifty years
(Streeter and Phelps, 1925) and are in general use for
making water pollution control decisions. Models of
the concentration and distribution of atmospheric
pollutants are being used for planning and operating
air pollution control programs (Singpurwalla, 1974).
Social System Models
Modeling society is as great a scientific
challenge as is modeling the environment. The simpler
social subsystems, e.g. community activities for solid
waste disposal (Liebman, 1974), have been successfully
modeled. The social subsystem that has received the
greatest attention of modelers is, of course, the US
economic system, which continues to challenge
econometricians. Models are available for such social
functions as community health services (Palmer, 1974),
law enforcement (Gass, 1974), educational systems
(Weiss, 1974).
Management Models
Logical decision making has benefited greatly from
the quantitative analytical techniques developed by
operations research. Both processes and organizations
for decision making have been modeled for a variety of
purposes and in numerous settings. A large body of
knowledge on decision making under uncertainty (see,
for example, Raiffa, 1968) is available for application
by social institutions responsible for managing
environmental quality. Regional models that can help
identify decisions which minimize the cost of
"managing" residuals are available (see, for example,
Kneese, et al., 1970; Spofford, 1973).
Implementation
The development and application of realistic
environmental management models have been hindered by
the difficulty in defining or isolating specific
systems to be managed and by the discontinuity of the
social institutions having the responsibility for
planning and implementing management strategies.
Logical geographic subdivisions for one medium seldom
coincide with those for another medium; none of the
subdivisions match the various state and local
governmental boundaries. EPA has had difficulty in
focusing on true intermedia programs since its
authority and funding are provided by eight separate
laws which are either media, material, or source
specific.
The future of environmental system management
looks much brighter, however, with the creation of the
150 "Designated Area" planning agencies, established
under the authority of Section 208, Public Law 92-500,
for water quality planning and management. More
recently, they have been given increased responsibility
for planning air, solid waste, thermal, and noise
pollution control strategies (Mellencamp, 1976). The
designation of these subregional or sub-basin
management areas has greatly increased the degree of
resolution that can be achieved compared to the
regional or national scale. Given clearly stated
objectives and the proper criteria and tools, these
planning institutions can devise true multimedia
environmental management alternatives that will permit
local officials to explore and strike optimum
strategies for achieving both environmental protection
and other social benefits simultaneously. Using well
developed systems models, such agencies can quickly
explore many alternative decisions that could not only
reduce the cost of managing the environment for social
good but also achieve a level of environmental quality
not otherwise attainable.
Based on such model strategies and continual
feedback from the local area, these agencies could
influence the allocation of costs so that they would be
shared equitably and could evaluate progress towards
goals and provide course-correcting stimuli. We
believe that these same benefits can also be attained
on a wider scale when the 208 program shifts from the
designated area to the state-wide emphasis as
stipulated in the law.
In order to achieve these desired environmental
and social benefits, the scientific community must
greatly increase its efforts to move systems modeling
concepts from the realm of scientific research to
practical applications. Social and governmental
institutions are developing, but well evaluated
comprehensive modeling tools, especially those linking
environmental and socio-economic systems, are currently
not available for their use.
One obstacle has been the system approach's huge
appetite for data. Obviously the effectiveness of
system management depends on sufficient pertinent data
to construct, test, and use the models needed for each
step. The formidable complexity of social and environ-
mental systems might suggest that enough data of the
right kind is so costly as to be unattainable. We do
not believe that data now available, or data that could
feasibly be obtained, is insufficient to meet the
present needs of models if a relatively gross level of
resolution is accepted. Environmental management
decisions based on meager comprehension of the entire
system will be, we believe, superior to decisions based
on near-perfect understanding of one system component
and ignorance of the others. Acceptance, initially, of
a grosser level of resolution will facilitate the
application and subsequent development of system
management techniques. The allocation of society's
resources to environmental system management can then
grow, if necessary, toward an optimum for achieving the
stated objectives.
Obviously, we believe that the systems approach to
environmental quality management is a desirable option
for improving American social action in environmental
protection and one that deserves more consideration,
development, application and evaluation.
References
Bloomfield et al. 1973. Aquatic Modeling in the
Eastern Deciduous Forest Biome, US I.E.P. In:
Modeling the Eutrophication Process, Workshop
Proceedings. Utah Water Research Laboratory, Utah
State University, Logan, Utah.
Chen, C. C. et al. 1975. Ecologic Simulation for
Aquatic Environments. In: Systems Analysis and
Simulation in Ecology, Volume III, Patten, B. C.
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Academic Press, Inc., New York. p. 476-
Churchman, C. W., R. L. Ackoff, E. L. Arnoff. 1957.
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and Sons, Inc., New York. 645 p.
Deininger, R. A. (ed.). 1973. Models for Environ-
mental Pollution Control. Ann Arbor Science
Publishers, Inc., Ann Arbor, Michigan. 448 p.
Freeman, A. M., III, R. H. Haveman, and A. V. Kneese.
1973. The Economics of Environmental Policy.
John Wiley and Sons, Inc., New York. 184 p.
Gass, S. I. 1974. Models in Law Enforcement and
Criminal Justice. Chapter 8 in: A Guide to Models
in Governmental Planning and Operations. EPA
Report Number 600/5-74-008. p. 233-275.
Gillett e_t al. 1974. A Conceptual Model for the
Movement of Pesticides Through the Environment.
US EPA, ORD, NERC, Corvallis, Oregon. EPA Report
Number EPA-660/3-74-024, December. 79 p.
Hill, J., IV, H. P. Kollig, D. F. Paris, N. L. Wolfe,
and R. G. Zepp. 1976. Dynamic Behavior of Vinyl
Chloride in Aquatic Ecosystems. US EPA, ORD,
Environmental Research Laboratory, Athens,
Georgia. EPA Report Number EPA-660/3-76-001. 63
P-
Kneese, A. V., R. U. Ayres, and R. C. d'Arge. 1970.
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Balance Approach. Resources for the Future, Inc.
Washington, DC.
Lassiter, R. R. 1975. Modeling Dyanmics of Biological
and Chemical Components of Aquatic Ecosystems. US
EPA, ORD, NERC, Corvallis, Oregon. EPA Report
Number EPA-660/3-75-012. 54 p.
Liebman, J. C. 1974. Models in Solid Waste Manage-
ment. Chapter 5 in: A Guide to Models in Govern-
mental Planning and Operations. EPA Report Number
600/5-74-008. p. 141-164.
Loucks, 0. L. 1972. Systems Methods in Environmental
Court Actions. Systems Analysis and Simulation in
Ecology, Volume II, Patten, B. C. (ed.). Academic
Press, New York. 592 p.
McFarlane, A. G. J. 1964. Engineering Systems
Analysis. Addison-Wesley Publishing Company,
Inc., Reading, Massachusetts. 272 p.
McGauhey, P. C. 1968. Engineering Management of Water
Quality. McGraw-Hill Book Company, New York. 295
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Mellencamp, G. L. 1976. Personal Communication,
Director, Waste Management Program, Chattanooga
Area Regional Council of Governments, Chattanooga,
Tennessee.
Palmer, B. Z. 1974. Models in Planning and Operating
Health Services. Chapter 11 in: A Guide to Models
in Governmental Planning and Operations. EPA
Report Number 600/5-74-008. p. 349-374.
Raiffa, H. 1968. Decision Analysis. Addison-Wesley
Publishing Company, Inc., Reading, Massachusetts.
309 p.
Sanders, W. M., III. 1975. A Strategy for Aquatic
Pollutants, Fate and Transport Determination.
Presented at the International Conference on
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Nevada, September. (Proceedings in press).
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Planning and Operations. EPA Report Number 660/5-
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Quality Management Models. Chapter 19 in: Models
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A SYSTEMATIC APPROACH TO REGIONAL WATER QUALITY PLANNING
G. Paul Grimsrud and E. John Finnemore
Systems Control, Inc.
Palo Alto, California
This paper describes the methodologies developed
for regional water quality management planning on the
Snohomish and Stillaguamish River Basins in the State
of Washington. These methodologies were specially
designed to be responsive to future changes in state
and federal legislation, land use, economics, popula-
tion, employment, geographical and political boundaries,
technological development, and changes in the natural
or man-made conditions of the water bodies. Computer
models were developed and utilized to project future
sewage and runoff flows, determine the assimilative
character of water bodies, plan and cost various alter-
native wastewater management plans and provide other
information on the cost-effectiveness of alternatives
necessary for the completion of the Water Quality
Management Plans. The modeling and programming elements
are the principal factors allowing the development of a
dynamic and easily updated Water Quality Plan.
The approach is applied to river basin planning on
the Snohomish and Stillaguamish Basins, demonstrating
its application and results. The methodologies are
presently used by planners in Snohomish County for on-
going water quality planning.
-Introduction
Planners and managers responsible for the perfor-
mance of water quality planning programs must usually
deal with the complex engineering, economic, financial,
legal, institutional and environmental aspects of water
quality. They must face the need to develop or acquire
a systematic approach to planning which can take all of
these factors into account. This paper presents a
water quality planning methodology which includes most
up-to-date technology for computer-based modeling, yet
great flexibility for practical use. The methodology
is designed for the selection of most cost-effective
wastewater management schemes in a region, and the
time-phased design of such schemes over many years in
the future. The methodology was developed under con-
tract with EPA, and used on the Snohomish and Stilla-
guamish River Basins in Washington State.
Planning Procedure
The planning steps followed in the quest for a
cost-effective water quality management plan^for river
basins include the selection of alternative configura-
tions for treatment facilities, carrying out assimi-
lation analyses for receiving waters, costing the
alternative configurations, and making cost-effective-
ness comparisons. The methodologies employed in these
steps are a compromise of computer-oriented quantita-
tive procedures and planner-oriented qualitative
activities.
Figure 1 summarizes and clarifies the interdepend-
encies of the tasks in this planning methodology and
illustrates the flow of events - prerequisites, bottle-
necks, critical paths, progressions. The starting-
point data or inputs to the planning process are listed
in Column 1 (left hand side). The flow paths to the
right from these starting points show the impacts of
the input data on subsequent tasks.
Throughout the formulation of planning method-
ologies, weaknesses in present available information
were found. It was evident that certain plan inputs,
such as the water quality standards, were likely to
change in the near future, thus causing a need for plan
updating. These problems were given foremost consider-
ation in the development of plan methodologies. Future
updates to the inputs (data or assumptions) should only
be made directly to items in Column 1 of Figure 1.
Thus, whenever any input to the plan development process
is significantly changed at some future date, the flow
paths of Figure 1 will identify the downstream tasks in
need of review and possible re-execution.
Of prime concern in the development of an effective
water quality plan are the concentrations of pollutants
in the receiving waters of the basins. Since the
natural movements of these waters, and hence their
transportive and diluting effects, are ever-changing
and variable, some specific flow regime must be
selected for planning purposes to make possible the
comparison of alternatives.
Flow Regimes
A specific flow regime, for analysis purposes, is
required to provide the basis for the computation of
receiving water qualities. Although the regime should
approximate "worst-case" conditions to provide the
fullest protection against water quality violations,
any conditions, however conservative, can be exceeded
with some (possibly very small) frequency or proba-
bility. To plan to control events which occur on the
average only once in a. thousand years, say, would be
to incur inordinate expenses. Thus, the selected flow
regime must be in a sense an arbitrary design condition,
corresponding to flow magnitudes which are adequate for
design purposes a large majority of the time.
Waste load dilutions are, in Western Washington
areas, lowest during summer low-flow conditions. The
seven-day/ten-year low-flow conditions have been
specified' for the State of Washington. These were
determined for many points on streams around the basin
using available U.S.G.S. data, and a set of streamflow
analysis and synthesis programs (see Reference 1 for
details).
Pollutant concentrations may be even greater,
however, when materials which have accumulated on
urban and agricultural areas over a dry period are
washed off by a summer storm. Storms during the
summer months are very common in the Pacific Northwest.
Storm occurrence averages at least three measurable
storms every summer. Due to this relatively high
frequency of storms, runoff of non-point pollutants can
be expected to occur during the worst-case design
conditions.
The design storm selected for the purposes of
including non-point runoff was a typical summer storm.
It was assumed to have occurred after twelve dry days,
which, based on historical data, was found to be the
average period between summer storms. Runoff resulting
from the average summer storm was input as a uniform
flow over the 24 hour modeling period in the upper
basins. A runoff pollutograph resulting from the storm
was used in the Snohomish Estuary.
14
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In addition to the above conditions, for the
estuary a tidal condition corresponding to the typical
monthly low swing was incorporated into the flow
regime. This provided a conservative estimate of tidal
flushing.
Because of the somewhat arbitrary nature of this
flow regime, the above-mentioned flow conditions were
presented for consideration to the Snohomish County
Advisory Committee, and they were accepted.
Determination of Alternatives
Considerations included in the selection of
alternative wastewater treatment configurations for
the basins were:
• Locations of existing treatment plants;
• Suitability of existing facilities;
• Probable locations of future treatment
plants;
• Optional locations for outfalls;
• Types of treatment plants, including
storage facilities;
• Spatial distribution, and relationship
to river and estuary system;
• Topography; and
• Soil conditions.
In developing alteratives, at all times only
systems that would be hydraulically sound and that
showed a potential to be simple, least cost, and
reliable, were considered. To accomplish this,
gravity systems were used whenever possible.
The list of alternative treatment plant and out-
fall locations, and types of treatment, for possible
inclusion in the alternative plans was derived from
previous studies, from discussions with local treat-
ment plant operators, engineers and elected officials,
and from the personal familiarity of Snohomish County
Staff members. The alternatives chosen represent
those most likely to be effective, based on the best
engineering judgment of these sources and current EPA
cost-effectiveness guidelines.3
Alternative configurations involving the possible
combination of industrial and municipal flows were not
considered acceptable when the industrial flows would
be greater than about one-third of the municipal flows.
This was due to the fact that the biological processes
involved in treatment plants need a reasonably steady
wastewater quality; this characteristic of municipal
wastewater is easily upset by flow and quality varia-
tions in effluents from industrial sources beyond the
control of the municipal treatment plant. The alter-
native of industry responsibility for the operation of
the "combination" treatment plant was not considered
at this time to be desirable.
The general objective of the various regionalized
configurations was to achieve overall cost reductions
through the economies of scale obtained from combining
several local wastewater treatment plants. The addi-
tional costs of required interceptor sewers and/or
force mains were included.
Wasteload Allocation
The execution of a cost-effective waste load
allocation in the river basins required consideration
of different types of sources (point, drainage district,
and non-point), different time horizons with their
varying water quality standards required by law,
different receiving waters (rivers, estuary) and alter-
native regionalization schemes for wastewater treatment
facilities. Many of these were interdependent.
In order to approach the identification of a most
cost-effective basin configuration in an organized and
effective manner, a working procedure was developed in
advance of undertaking the task. This procedure is
summarized in Figure 2 (supplemented by Table 1), which
outlines the alternative "routes" which were considered
demanding of investigation, in some cases conditional
upon the findings from earlier phases. The following
assumptions were used in this procedure:
1. Straightforward structural solutions were to be
attempted first. Only if they were found un-
successful would non-structural solutions be
considered.
2. Where regionalized treatment plants were expanded
existing plants, the same outfall locations would
be used.
Assimilation Analysis
A very large number of computations are needed to
determine water quality levels which result from a
variety of wasteloads with complex hydrodynamic and
natural constituent processes. Therefore, computer
modeling of receiving waters for the analyses of waste
assimilation was selected as appropriate. Computer
modeling also allows rapid recomputation for various
alternative cases, once the basic model has been
established, thus facilitating comparisons.
The water quality computer models may also be used
to investigate which estuary and river segments are
"water quality limited," and which are "effluent lim-
ited". ^ Given conditions where all point sources
just meet effluent standards, the former designation
applies where receiving water standards are violated
and the latter applies where they are met.
Waste Load Forecasts
In addition to specifying the receiving water
geometry and the design flow regime, the water quality
models require, as input, data on waste loads. Waste
loads may, now or in the future, be directly subject to
effluent standards, and may also be limited, indir-
ectly, by receiving water quality standards. The ob-
jective of an assimilation analysis is to determine
what may be discharged where, and yet meet the various
pertinent standards.
Federal guidelines for effluent standards for
municipal and industrial wastewaters have been, or are
in the process of being, established. The standards
become more stringent with time, varying in requirement
from the "best practicable control technology currently
available" or secondary treatment, to the "best avail-
able technology economically achieveable" or "zero
discharge."
Proposed EPA standards for many industrial efflu-
ents are published in the Federal Register. ' For
each quality constituent, two effluent limitations are
provided: (1) a maximum for any one day, and (2) a
maximum average of daily values for any period of
15
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thirty consecutive days. The latter lower value was
selected as the basis for computing industrial waste
loads, since use of the former would be compounding
worst-case events having a very small joint probability
of occurrence.
The pollutant concentrations employed in the
models as existing in effluent from secondary treatment
in municipal wastewater treatment plants are given in
Table 2. Where these values were uncertain, they were
chosen to err on the high side, so as to provide a
"worst-case" safety margin. Chlorine in secondary
municipal effluent was modeled as a conservative (non-
decaying) constituent. The various representative
types and levels of secondary treatment employed in
this study included:
• Oxidation Process (aerated ponds or ditches
with 3 to 4 days retention capacity and
effluent chlorination) meeting secondary
standards (assumed maximum flow capacity
of 2 mgd).
• High Rate Trickling Filters (primary
sedimentation, H.R. filters with re-
circulation, secondary clarification,
effluent chlorination).
• Conventional Activated Sludge (primary
sedimentation, aeration, secondary
clarification, effluent chlorination).
The municipal wastewater flows were predicted
using a computer forecasting model, SNOQUAL, which
determines flows on the basis of population dynamics.
The details of this program are given in Reference 1.
One other important potential source of pollution
is storm runoff from urban areas (in storm or combined
sewers) or from agricultural lands (non-point sources).
The manner in which these were computed and input to
the models is discussed in Reference 1.
Rivers. A steady-state river water quality model
(SNOSCI) as described in Reference 1, a specially
modified version of DOSAG, was used for the river
assimilation analysis. Numerous runs were made to
test various boundary conditions. These consisted of
point sources (municipal and industrial), non-point
sources (agricultural runoff), and tributary streams.
The scheme of Figure 2 was used as a guide for
running the alternative test conditions. First, runs
were made with (a) zero point loads (representing 100%
treatment) and full non-point loads, and (b) vice-versa.
Point source treatment would be achieved by traditional
structural means (sources and treatment plants); non-
point "treatment" would be effected (at least partially)
by "non-structural" measures such as by restricted land
use and agricultural practices.
Next, with secondary treatment of municipal and
industrial point sources, a number of runs were required
to identify the locations and sizes required for reduc-
tions in non-point sources in order to meet receiving
water quality standards.
The effects of various regionalized wastewater
treatment schemes were then investigated, combining
municipal and industrial effluents at certain appro-
priate outfall locations.
These investigations were repeated for present,
1980 and year 2000 waste flows.
Estuary. The transient estuary water quality
model (SRMSCI) as described in Reference 1, a specially
modified version of RECEIV7 'for this study, and pre-
viously calibrated to the extent possible, was used for
the estuary assimilation analysis. The design flow
conditions included river inputs as per the output from
the river model.
Numerous runs were made to test alternative muni-
cipal and industrial treatment schemes, again using
the scheme of Figure 2 as a guide. An additional
category of source, the Drainage District (treatable
"non-point"), was included to represent two such
extensive areas.
First, runs were made with no storm and non-point
sources, and with point sources at secondary treatment.
Next, the storm and non-point sources were included in
the estuary model, and a number of runs were required
to determine the locations and magnitudes of coliform
reductions required to meet standards.
The "most stringent" regionalization scheme for
the lower basin was run, with year 2000 municipal and
industrial loads. This included municipal flows from
Seven Lakes, Tulalip, Marysville, Lake Stevens,
Mukilteo and Everett, all given secondary treatment
at the present Everett Site.
Cost of Alternatives
The objective of these alternative costing proce-
dures was to develop appropriate procedures for esti-
mating costs for the large number of plan alternatives
considered, each with its numerous facility components
and with time phasing.
A computer model, \SUSCI2, was developed by Systems
Control, Inc., to design, time-phase, and cost sewers,
force mains, pumping stations, and treatment plants.
More details of this model are.provided in Reference 1.
Given the alternative sewer networks, and locations
and types of treatment plants, together with the fore-
cast flows, SUSCI2 designs the facilities needed and
computes the capital and M&O expenditures required,
indicates the timing of costs over the planning period
(1976-2000), and also determines a discounted total
cost (present worth) for each alternative scheme. All
the alternatives were costed with this model, taking
advantage of common components (typically local sewer
systems) which need not be repeated. Care was taken
to ensure that the same total area was serviced under
each alternative, regardless of the manner of servicing.
After making preliminary investigations into com-
parative costs of minor local alternatives, it was
determined to be most efficient to analyze and select
from the major alternatives first, then proceed to the
intermediate and finally to the outermost and most
minor and localized alternatives. The lesser costing
alternatives were thus considered as variations of
the preferable major (central) alternative. This
approach was acceptable, since the effects of the
minor alternatives were relatively small enough not
to affect the selection between the major alternatives;
this results principally from the fact that a small
change in treatment capacity has less effect on the
unit cost of treatment in larger plants than it does
in smaller plants. As a result of this procedure,
large numbers of cost evaluations of unattractive
alternative combinations were avoided.
Costs for the chlorination of drainage waters in
controllable drainage districts were computed manually.
16
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The capital cost of a contact tank and chemical feed
equipment was based on a formula by Smith assuming
dosage at 8 mg/L with a 15 minute contact time, and
updating this to a 1976 dollar cost with an ENR
Construction Cost Index curve for Seattle9. The M&O
cost for chlorine, etc., was derived from a cost curve
of operating costs of sewage tanks, after Engineering
Science Inc., and making allowances for the recent
large cost increases experienced for chlorine.
Cost-Effectiveness Comparisons
Alternative plans which met receiving water stan-
dards, as determined by the assimilation analysis, were
compared for cost and effectiveness. Besides comparing
the total discounted costs, their components (e.g., M&O
vs. capital) were compared, since the M&O costs con-
tained more uncertainty than the capital costs. Under
effectiveness, such factors as reliability were con-
sidered. Thus, among schemes of similar costs, those
with more force mains were less attractive than those
with fewer (more reliable gravity sewers). If the
differences in cost and effectiveness between two
schemes was not sufficiently great, no preference
between them was expressed on those grounds alone, and
more detailed engineering would be necessary to deter-1
mine the less expensive alternative. Differences
between environmental impacts of alternatives were also
considered.
Time-Phased Facility Schedule
A time-phased facility construction schedule,
required to satisfy the demands of the basin management
plan selected for the two basins, had to be determined.
As part of the assimilation analysis the receiving
water quality models SNOSCI and SRMSCI, for the upper
and lower portions of the basins respectively, were
applied to investigate a number of alternative cases
(see Figure 2). Computer runs for the projected year
2000 point loads treated at the secondary level deter-
mined that generally no problems occurred in the
receiving waters, besides those due to non-point sources.
Therefore, a schedule for the additional facilities
required by the plan was simply, and practically auto-
matically, governed by (1) the extra facilities needed
by the year 2000, and (2) the dates when demands would
exceed the capacities of existing facilities, or when
the useful lives of existing facilities would expire.
The scheduling of facilities expansions was
computed by the sewerage system planning and costing
model named SUSCI2. Given the alternative sewer net-
works and locations and types of treatment plants,
together with the forecast sewage flows, SUSCI2
designs the facilities needed and computes the capital
and M&O expenditures required, indicates the timing of
costs over the planning period (1976-2000, in four-
year incremental planning periods), and also determines
a discounted total cost for each scheme. Besides
determining the needs for new facilities, SUSCI2 also
computes extensions and updates needed to augment
existing facilities; based on present capabilities, it
estimates from input demand forecasts the dates when
capacities will become inadequate. Since the designs
are automatically optimized with respect to cost
within SUSCI2, the results are automatically the most
cost-effective.
The resulting time-phased development schedule
was presented at local public meetings and at the
technical advisory meetings. These meetings were
specifically set up to enable the provision of practical
inputs to plan scheduling.
The allocation of cost data over the implementation
schedule was done by preparing the schedule in table
form, and indicating therein the distribution of costs
over the various incremental planning periods.
References
1. Systems Control, Inc. , and Snohomish County Planning
Dept. Water Quality Management Plan for the Snoho-
mish and Stillaguamish River Basins; Volumes I-VI.
Everett, Washington, November 1974.
2. Washington State Dept. of Ecology. Guidelines for
the Development of Water Pollution Control and Ab-
atement Plans for Sewage Drainage Basins, Second
Edition. Olympia, Washington, September 1, 1970.
3. Environmental Protection Agency. EPA Cost-Effect-
iveness Proposed Analysis Guidelines. Federal Regi-
ster, Volume 38, No. 127. Washington, D.C., July 3,
1973.
4. 92nd Congress. Water Pollution Control Act Amend-
ments of 1972: PL92-500. October 1972.
5. Environmental Protection Agency. Proposed Guide-
lines and Standards: Pulp, Paper, and Paperboard
Manufacturing Point Source Category. Federal Regi-
ster, Volume 39, No. 10, Part II, p. 1912, Subpart
A. Washington, B.C., January 15, 1974.
6. Environmental Protection Agency. Proposed Effluent
Guidelines and Performance and Pretreatment Stand-
ards for New Sources: Timber Products. Federal
Register, Volume 39, No. 2, Part III, pp. 944-5,
Subparts A,B. Washington, D.C., January 3, 1974.
7. Metcalf & Eddy, Inc., University of Florida, and
Water Resources Engineers, Inc. Storm Water Manage-
ment Model, Volumes 1-4 (EPA Report No. 11024DOC).
Superintendent of Documents, Washington, D.C., July-
October 1971.
8. Smith, Robert. Preliminary Design of Wastewater
Treatment Systems. J.S.E.D., Proc. A.S.C.E., pp.
117-145. February 1969.
9. George S. Nolte and Associates and Snohomish County
Planning Dept. Snohomish County, Washington, Rural
Water Sewer Facilities Study. Everett, Washington,
December 1973.
Table 1.
Types of Sources Included In the
Pour Cases of Figure 2
Types of Sources Present
PTS
Case
1
2
3
4
Segment
Location
Above DD's
Below DD's
Below DD's
Above DD's
Point
Y
Y
Y
Y
Treatable
Non-Point
(Drainage
Districts)
N
Y
Y
N
Elusive
(Non-Treatable)
Non-Point
N
N
Y
Y
Partially treatable by non-structural means.
Definitions (also for Figure 2):
AWT - Advanced Wastewater Treatment
DD - Drainage District. These are agricultural
areas where rain runoff is routed through
systems of drainage ditches to adjacent rivers.
HPT - Highest Practicable Treatment
NP - Non Point Sources
PTS - Point Sources
2° - Secondard (Treatment)
Y - Yes
N - Ho
17
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Table 2. Concentrations Resulting from
Secondary Treatment of Municipal
Wastewater, as Employed in
Receiving Water Quality Models
Constituent
Concentration
BOD
DO
NH -N
N02-N
O-PO.-P
ci2
Cu
Pb
Fecal Coli
Total Coli
Temperature
30.0 mg/L
5.0 mg/L
9.8 mg/L
0.0 mg/L
10.0 mg/L
10.0 mg/L
1.0 mg/L
1.0 mg/L
0.05 mg/L
200 MPN/100 mL
2000 MPN/100 mL
25°C
Figure 1. WATER QUALITY MANAGEMENT PLANNING
T T T \ I .-
—rivsf i
-------
FIGURE 2
SCHEME FOR DEVELOPMENT OF ALTERNATIVES
®
1
DESCRIBE SUITABLE
2° TREATMENT
RUN ALL SOURCES FOR YR.
2000, ASSUMING 2° TREATMENT
19
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A REVIEW OF EPA'S GREAT LAKES MODELING PROGRAM
W.L. Richardson
U.S. Environmental Protection Agency
Large Lakes Research Station
Grosse lie, Michigan
N.A. Thomas
U.S. Environmental Protection Agency
Large Lakes Research Station
Grosse lie, Michigan
The Large Lakes Research Station at Grosse lie,
Michigan, is responsible for implementing the EPA,
Office of Research and Development's research program
for the Great Lakes. The objective is to be able to
describe the transport and fate of pollutants.
Mathematical models provide the researcher with the
necessary tools for accomplishing this task and, once
calibrated and verified, they can be used by water
quality managers confronted with making policy
decisions. Several levels of modeling research have
been initiated which address water quality issues
ranging from lake-wide to nearshore effects, and from
eutrophication to hazardous materials. Concurrent
surveillance and experimentation programs are being
conducted for model calibration and verification. An
overview of the EPA Great Lakes modeling program is
presented including results from some specific
models.
Introduction
The Environmental Protection Agency, Office of
Research and Development, is conducting a research
program to address many of the complex water quality
issues on the Great Lakes. The Federal Water
Pollution Control Act and the 1972 Amendments specify
that the agency ... "shall conduct research and
technical development . . . with respect to the
quality of waters of the Great Lakes, including an
analysis of the present and projected future water
quality of the Great Lakes under varying conditions
of waste treatment and disposal." The U.^.-Canada
Agreement on Great Lakes Water Quality further
provides impetus for this research effort.
In response to these directives, the
Environmental Research Laboratory—Duluth, Large
Lakes Reasearch Station (LLRS) is implementing a
modeling research program to improve the
understanding of complex limnological processes in
the Great Lakes. The program has been implemented
primarily through grants to academic institutions and
by a small in-house effort. This research dovetails
with a concurrent water quality survey and
experimentation program which provides information
necessary for model calibration and verification.
The models are providing decision makers in EPA and
other water management agencies with quantitative
tools for evaluating alternative courses of action
concerning water quality. Because the limnological
processes are so complex and interrelated; because
the Great Lakes include such a large geographical
area; and because of the long detention times;
simple, empirical and intuitive approaches are not
adequate. This is critical for the Great Lakes where
billion dollar decisons can affect the entire system.
Though the cost of modeling one Great Lake may be on
the order of a million dollars, the billions spent
for remedial actions justifies the effort. As a
model for each of the lakes is developed, less data
and experimentation are required which reduces the
cost of each subsequent lake modeling program. In
addition, the model structure, kinetics, and software
can be used for smaller lakes which would not
necessarily be modeled without having the Great
Lakes modeling experience.
Models are not expected to answer every question,
however, and the researchers would be the first to
agree that there are major deficiencies which are
difficult to overcome. These include the imprecise
scientific knowledge of specific processes and
interactions and further computational restrictions
imposed by available computer technology and cost of
computer operation. Models are intended to enhance
the managers' experience and judgement and
improve their insight into cause and effect. In
addition, the modeling research provides secondary
benefits by (1) systematizing and quantifying complex
interrelationships between the physical, chemical and
biological elements in limnology and (2) by
identifying the weakest areas in our knowledge and,
in fact, defining research needs.
This paper presents an overview of the general
modeling process along with a summary of specific
model results.
Great Lakes Model-Management Process
The general modeling-management process for the
Great Lakes is shown in Figure 1. Modeling
is the focus for understanding limnological processes
and for translating them into terms necessary for
management's use. The process as shown includes:
1. Monitoring material inputs.
2. Surveillance of material pools.
3. Experimentation to define biochemical
processes.
4. Establishment and management of
water quality standards.
5. Establishment of abatement programs.
6. Action to reduce material loads.
Development of a model entails both calibration
and verification. Calibrating a. model involves
comparing computed results to measured data and
adjusting model parameters until the computed
variables match the measured. Verification is
obtained when computed results match data from an
independent data set without parameter adjustment.
Once calibrated and verified, the model is used
to simulate the effect of possible modifications to
the system (e.g., reductions in phosphorus loads) on
the concentration of materials in the water body.
The simulated concentrations are compared to those
desired (water quality standards). The results can
be used as a basis to establish long-range planning
goals, to determine effluent allocations, or to
reestablish water quality standards.
Model Development
Water quality models are structured to predict
the effect of material discharges (loads) on material
concentrations in the receiving water body. Two
20
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modeling approaches are in general use. They are 1)
empirical and 2) deterministic. The empirical or
statistical approach involves correlations of cause-
factors to effect factors. For example, Vollenweider
has compiled total phosphorus loading data on several
lake systems and correlated these to the measured
peak chlorophyll a_ levels. Since a range of
conditions has been incorporated, predictions of the
effect of phosphorus reductions are made by
interpolation.
The disadvantage of this approach is that there
are several assumptions which may limit its use
particularly for the Great Lakes: 1) it assumes the
phosphorus loadings are known and correct, 2) it
assumes the chlorophyll a_ is in equilibrium with the
loads (ie., there is no time lag in response to the
loads), and 3) it assumes average conditions are
sufficiently precise.
The deterministic approach is based on basic
principles and incorporates equations representing
the actual limnological processes. These models
account for and trace each variable through the
system and conserve mass, energy, and momentum in
space and time.
For the deterministic models the calibration or
data "fitting" process is based on knowledge of the
system parameters in contrast to the empirical
approach which forces a least squares fit to the
data. If the deterministic model output from initial
simulations does not match the data, a limnological
rationale for parameter adjustment is necessary. If
a rationale is not available then further
experimentation is required. Any interim results are
qualified to reflect the range of possible solutions.
The disadvantage of the deterministic approach,
however, is that it requires much more research time
and computer resources.
The modeling process includes, but is not
necessarily limited to, the following steps:
A. Assessment Phase
1. Define issues.
2. Define objectives.
3. Conceptualize model.
4. Assess general data availability.
5. Determine capabilities and requirements
of various model approaches.
b. Assess model accuracy.
a. Describe information the model can provide.
c. Determine time required to develop and
implement.
d. Determine computer resources required.
B. Decision Phase
1. Determine resources available.
a. Computer time.
b. Research resources.
2. Determine priorities.
3. Determine accuracy required.
4. Determine deadline.
5. Choose a course of action based on the above
assessments.
C. Implementation Phase
1. Develop and implement model.
2. Compile existing data.
3. Design and implement surveillance
and experimental programs.
4. Calibrate model.
5. Determine success of approach and modify
accordingly.
6. Verify model.
7. Evaluate the success of the model.
8. Present results to the scientific community.
9. Document models.
D. Management Phase
1. Conduct management simulations.
2. Make model available for management use.
3. Modify and refine model as required.
Great Lakes Issues
The issues concerning the Great Lakes can be
categorized by water quality parameters and the time
and space scales involved. The most urgent issue is
eutrophication. The problem is the effect of
phosphorus and nitrogen on levels of algal biomass
and the degree of control required to restore and/or
maintain adequate water quality. This issue requires
knowledge of lake-wide phenomena and even phenomena
involving the interaction between lakes. The time
scale is on the order of years to decades.
A second level issue also involves eutrophication
but in the nearshore regions and embayments. Because
of the shorter response time in these localized
areas, time and space scales are smaller (seasons and
kilometers).
A third level issue involves immediate effects on
even smaller scales (hours and meters) of materials
or heat in the discharge plume. For example, the
material distribution in an effluent plume may be
critical to nearby water intakes or recreational
sites. Specific questions have been asked such as
Where to locate the discharge structure? What size
mixing zone is allowed so not to interfere with water
uses? and What local and short-lived biological
responses are expected?
Great Lakes Models
General
The first phase in modeling each of the Great
Lakes (except Superior) involves development,
calibration and verification of the phytoplankton-
zooplankton-nutrient model first structured by
O'Connor , for the San Joaquin Delta.
The general system scheme of this approach is
depicted in Figure 2.
Phytoplankton biomass is represented by
chlorophyll a_ which is used primarily because of the
ease of measurement and availability of data. Phy-
toplankton carbon is obtained by specifying a carbon-
chlorophyll stoichiometry and is the element
zooplankton consume along with the nutrients
contained in the phytoplankton. The nutrients,
phosphorus and nitrogen are also accounted for and
traced through the phytoplankton and zooplankton by
specifying stoichiometry relationships with carbon.
Phytoplankton growth rate is a function of
temperature, light, and nutrients and follows
Michaelis-Menten product kenetics. The model
includes nutrient recycling, phytoplankton settling,
nutrient sedimentation, and material loadings.
Because of the large time and space scales involved,
the lake is represented by a. few segments, each
assumed to be homogeneous. The model output
respresents the average concentration in each seg-
ment.
Lake Ontario
Lake Ontario was the first Great Lake to be
modeled using this approach. This was initiated for
the International Field Year on the Great Lakes
(IFYGL) by a grant to Manhattan College. This work
culminated in a two volume EPA Ecological Research
Series Report?». In summary, the Lake Ontario effort
involved the calibration of the
phytoplankton/nutrient structure for the three layer
segmentation scheme (Lake-1) shown in Figure 3. The
results have been reported to the International Joint
Commission (IJC) for management considerations.
The results, depicted in Figure 4, indicate that
the chlorophyll a. levels are not in equilibrium with
the nutrient loads. This is evident because the
21
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simulated peak chlorophyll a^ continues to increase
for about 6 to 8 years before reaching an equilibrium
level. Further, even with reducing the phosphorus
loads to levels set by the Water Quality Agreement,
chlorophyll a^ levels are predicted to increase to a
new equilibrium.
With Lake-1 having been substantially calibrated,
work continues at Manhattan College to refine the
Lake Ontario model by 1) addition of spacial detail
(Figure 5); and, 2) addition of biological detail
(multi-species). The limiting factors in this work
are not the expansion of the model structure itself,
but with data availability and the overwhelming task
of data reduction for model verification. In
addition, there is the matter of interpreting model
output. The analyst soon becomes overwhelmed by the
reams of computer output even if these have been
reduced to graphical form. To overcome these
limitations, the model researchers have been relying
to a great extent on the EPA STORET system for data
archiving, manipulation, and statistical analysis.
Also, more work is underway to output both data and
model computations in graphical form. The Manhattan
College staff has even produced movies of model ouput
to reduce the effort in interpreting their results.
Research is now proceeding with the development of
statistical techniques to determine how well these
complex models represent the data.
Lake Huron
The Lake Huron modeling effort is also being
conducted by Manhattan College under the direction of
the EPA Large Lakes Research program. The modeling
research is being conducted in conjunction with the
IJC Upper Lakes Reference Study and the results will
have direct input to this management level report.
Essentially, the same model structure is being
applied with a 5-segment scheme shown in Figure 6.
The unique aspect of this system is the high material
gradients evident in and extending from Saginaw Bay.
This is an excellent case to test the general
applicability of this model structure.
Lake Erie
The Lake Erie eutrophication model includes
similar nutrient-biological systems applied to a 5-
segment scheme (Figure 7) except that the process of
dissolved oxygen depletion and resulting nutrient
regeneration must be incorporated. Manhattan College
is progressing with this task while concurrent field
effort is being conducted by Ohio State University
and State University College of New York at Buffalo.
Lake Erie is also the site of an issue involving
the effect of power plants on fish populations. To
address this issue a research program has been
initiated involving both data collection and model
development for fish in the western basin. The model
will incorporate data collected on the number of fish
larvae passing through a power plant and the number
observed in the western basin. The effect on the
adult populations in time will be computed.
Saginaw Bay
Modeling research on Saginaw Bay, Lake Huron, is
being conducted by the LLRS at Grosse lie.
Eutrophication is the primary issue in Saginaw Bay
evidenced by the highest chlorophyll a. levels
recorded in the Great Lakes system. A sub-issue is
the effect of blue-green algae on taste and odor in
municipal water supplies.
Two parallel modeling efforts are progressing.
First, the Manhattan model structure is being applied
to a five segment scheme7. This application research
has benefitted the program by not only providing
insight into cause and effect but also by familiariz-
ing EPA personnel with the details of the Manhattan
models and computer programs. This has enhanced
relationships with the grantee and has resulted in
better program management. In this way, the LLRS has
or will have the capability of operating any of the
models developed by Manhattan College.
The second in-house modeling effort on Saginaw
Bay involves development of the next generation of
verified ecosystem models. Bierman has structured a
four class phytoplankton model which includes more
detailed interaction kinetics in place of Michaelis-
Menten kinetics. Model results are being used in the
IJC Upper Lakes Reference Study report.
The Saginaw Bay modeling research is also being
expanded to include the fate and transport of
hazardous materials. A preliminary model structure is
being formulated and surveillance and experimental
research is being implemented.
Transport Models
Another modeling effort being conducted with sup-
port of the LLRS is devoted to describing the
detailed transport processes in the Great Lakes. The
primary objective is to develop a general approach to
describing pollutant transport on relatively fine
time and space scale in the near-shore region. The
work is being done at Case Western Reserve
University^.
The models use the first principle conservation
equations for mass, momentum, and energy. Winds and
solar radiation drive these equations which result in
computed current velocities, current direction, and
thermal structure in three dimensions. Verification
of this type model is difficult and requires synoptic
data at many points. The application is being
demonstrated along the Lake Erie shore near Cleveland
and will describe the course of the Cuyahoga River
discharge into the lake.
The transport models are also being used to
evaluate the potential effect of the proposed
Cleveland Jetport on water quality and temperature
structure. By varying the model geometry to
represent the proposed configuration of the jetport,
it is possible to predict the circulation patterns
and the subsequent distribution of material
concentrations (Figure 8).
Using the same general approach, Paul10 has
developed thermal plume models which have been
substantially verified at the Point Beach Power Plant
on Lake Michigan.
Conclusions
The experience gained thus far in implementing
the Great Lakes modeling effort has led to a number
of conclusions which may be helpful to others
initiating similar modeling programs.
First, the structuring and calibrating of a model
derives benefits long before a final verified model
is obtained. The modeling process requires a
systematic approach to data collection and analysis.
Intermim results reveal gaps in knowledge for a
particular system or process and are useful in
defining and directing new study and research.
Second, most of the effort in the modeling
process is involved with data reduction. Relatively
little effort is required to generate reams of
theoretical computer output. The primary concern is
to structure a model with sufficient bio-chemical
detail to be realistic, but simple enough so as not
to be data limited.
22
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Third, considerable effort is required to
calibrate and verify large scale models even with
existing model structure and computer programs. For
this reason, this process appears to be in the realm
of applied research rather than engineering
application. A modeling program of necessity should
not be separated from a total research program. This
program involves the entire range of model
structuring, experimentation, and research
surveillance.
Finally, because of the resource commitments made
to the total research effort, once a model has been
implemented, i.e., calibrated and verified, a
continuing effort should be made to document the
model, and to keep it operational. In this manner,
models could be used to assist in answering the many
short-term, day-to-day questions facing the EPA and
other environmental regulatory agencies. Only after
calibration and verification for a specific system
can a model be turned over to an engineering staff
for general management application.
One continuing question remains, however, and
that concerns the confidence placed on model results
by managers. Progress in gaining managerial
confidence is being made as more rigorous techniques
are developed to evaluate how well model results
match the data. In the final analysis confidence
will come as model predictions accurately forecast
actual water quality. For Saginaw Bay, with its
short response time, verification data will soon be
available to test predictions of the eutrophication
models. A good fit there could go a long way toward
convincing managers of the utility of the other Great
Lakes models.
References
1. Public Law 92-500,92nd Congress, S2770,
An Act To Amend the Federal Water Pollution
Control Act. October 18, 1972.
2. Great Lakes Water Quality Agreement
Between the United States of America and
Canada, Signed at Ottawa, April 15, 1972.
3. Vollenweider, R.A. and P.J. Dillon. The
Application of the Phosphorus Loading Concept to
Eutrophic Research. National Research Council
Canada, Associate Committee on Scientific Criteria
for Environmental Quality June 1974.
4. O'Connor, D.J., R.V. Thomann, and D.M.
DiToro, 1973. Dynamic Water Quality Fore-
casting and Management. Environmental
Protection Agency. Ecological Research
Series EPA-660/3-73-009.
5. Thomann, R.V., D.M. DiToro, R.P. Winfield
and D.J. O'Connor. Mathematical Modeling
of Phytoplankton in Lake Ontario, 1. Model
Development and Verification. U.S. Envir-
onmental Protection Agency,Corvallis,
Oregon. 660/3-75-005.
March 1975. 177p.
6. Thomann, R.V., R.P. Winfield, D.M. DiToro
and D.J. O'Connor. Mathematical Modeling
of Phytoplankton in Lake Ontario, 2. Sim-
ulations Using Lake-1 Model. U.S. Environmen-
tal Protection Agency, Duluth, Minnesota. In
Press.
7. Richardson, W.L. and V.J. Bierman, Jr.
A Mathematical Model of Pollutant Cause and
Effect in Saginaw Bay, Lake Huron. U.S.
Environmental Protection Agency, Environmental
Research Laboratory—Duluth, Duluth, Minn.
In press.
8. Bierman, V.J., Jr. and W.L. Richardson.
Mathematical Model of Phytoplankton Growth
and Class Succession in Saginaw Bay, Lake
Huron. U.S. Environmental Protection Agency
Environmental Research Laboratory—Duluth,
Duluth, Minn. In press.
9. Lick, Wilbert. Numerical Models of Lake
Currents. Case Western Reserve University,
Dept. of Earth Sciences, for U.S.E.P.A.,
Environmental Research Laboratory—Duluth.
In press.
10. Paul, J.F. and W. Lick. A Numerical Model
for Thermal Plumes and River Discharges.
Proceedings, 17th Conference on Great Lakes
Research, 1974, I.A.G.L.R.
23
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GREAT LAKES
MODELING-MANAGEMENT PROCESS
INPUT MONITORING
Waste loads
Tributary loads
Atmospheric loads
Meteorological conditions
Figure 1. Great Lakes Model-Management Process.
NUTRIENT INPUTS
NIAGARA RIVETT
TRIBUTARIES
MUNICIPAL
INDUSTRIAL WASTES
ENVIRONMENTAL INPUTS
SOLAR RADIATION
WATER TEMPERATURE
LIGHT EXTINCTION
SYSTEM PARAMETERS
1 VERTICALEPILIMNION
XCHANGE TRANSPOR
Figure 3. Lake Ontario (Lake-1) Model Segmentation?
UPPER TROPHIC
LEVEL 02
CARBON
T
UPPER TROPHIC
LEVEL #1
CARBON
t
CARNIVOROUS
;'.OOPI.ANKT')S'
CARBON
1
HERBIVOROUS
7.00 PLANKTON
CARBON
t
1'HYTOPl.ANKTW;
UII.OROI'HYI.I.
| NITROGEN CYCI.F
1
1 ORCANK: AM: ONIA
[" SI'i'HOCI^: NITROCKN
! t i
N 1 TRATE
NITKOCKS
w
' PHOSPHOROUS CYCLE
1 OI-'CA'irC AVAI
| PHOSPHOROUS PflOSPH
1 t
1
1
1
AUM-: i
UKOUS .
1
HIOI.OCIfjM.
SUfl-MODKI.
_l
Figure 2. General Eutrophication Model Structure.
o
IE
3
Z
o -r
Z »-
O a
Pr*Mnt Condition
WQA Condition
•toral Condition
I I I i L
J I I i
I 10 12
YEARS
16 18 20 22 24
Figure 4. Projected Peak CJorophyll a Concentrations
for Lake Ontario?
24
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Figure 5. Lake Ontario (Lake-3) Model Segmentation.
LAKE HURON
Figure 6. Lake Huron Model Segmentation.
Figure 7. Lake Erie Model Segmentation.
HORIZONTAL SURFACE VELOCITIES
•Cuvahoqa Rl»»r
CONSTANT CONCENTRATION
Figure 8. Simulated Currents and Conservative Material
Concentrations for Alternative Jetport
Configurations.
25
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THE DEVELOPMENT AND IMPLEMENTATION OF USER ORIENTED AIR QUALITY MODELS
John J. Walton
Lawrence Livermore Laboratory
University of California
Livermore, CA 94550
Abstract
Implementation of the Clean Air Act and its
amendments requires that decisions be made, at various
levels of government, on many complex questions. In
order to facilitate the work of decision- and policy-
makers, readily useable air quality models must be
developed. Such models can have quite different require-
ments and constraints than those developed primarily for
research purposes. These needs will be identified and
past experience will be drawn upon to illustrate how
some of them have or have not been met.
Introduction
The National Science Foundation, through Its
Research Applied to National Needs (RANN) program, has
sponsored an interagency program at the University of
California Lawrence Livermore Laboratory (LLL) , the
NASA-Ames Research Center (ARC) and the Bay Area Air
Pollution Control District (BAAPCD) to develop and vali-
date a regional air pollution model which can be applied
to the air quality problems of the San Francisco Bay
Area. This work resulted in the Livermore Regional Air
Quality (LIRAQ) model.1'2 The model calculates in the
two horizontal dimensions the transport, dispersion and
chemical changes undergone by the most significant
photochemically reactive and non-reactive air pollutants
in the San Francisco Bay Area. Through the approxi-
mately three year duration of this project a wide
variety of problems were encountered and handled with
varying degrees of success. This experience has given
us a feeling for the various, often interrelated,
factors which must be considered by both user and
modeler in order that an appropriate and useable air
quality model be developed. It is our purpose here, to
share our thoughts on this subject with the attendees
of the EPA Conference on Modeling and Simulation.
Just as the atmosphere itself exhibits many complex
and interrelated features, so does the process of user/
modeler communication and compromise needed to cope with
the diverse requirements and constraints governing model
development. We have chosen to break these into three
broad categories:
I. The needs of the user group or agency.
II. The inherent physical complexities and constraints
of the specific problem.
III. The various resources which the user has at his
di sposal.
It should be emphasized that these are not independent
factors and frequently compromises need be made between
them. In the balance of this paper we will describe in
more detail the various aspects of each of these factors.
I . User Needs
We see the user as any group or agency which may
come to the modeler seeking to address questions related
to air quality. The user's needs will provide the
framework required for model development. Here we can
identify five basic considerations, each one of which
is related to some degree to the others.
Model Application. Unlike the modeler, for whom
the model is a tool with which to explore the nature of
pollution, its origins and evolution, the user will in
general be charged with a specific responsibility and a
model directed to this end will be required. Some
examples of specific applications are: the study of
pollution episodes, support in legal action, assessments
required in land use planning, study of the efficacy of
of various pollution abatement strategies and regulation
needed to implement mandated standards. It should be
pointed out, that while there may be overlap between
several of these areas, an agency charged with more
than one responsibility may, in fact, require more than
one model.
Pollutant Characteristics. Depending upon the
time and space scales of concern, the pollutants of
interest may be anything from inert to highly reactive,
or they may have properties which make them subject to
specific scavenging processes. For example, nuclear
releases are considered inert but may consist of par-
ticulates which will settle out at some known rate.
Hydrogen sulfide, stored at a geothermal sight can,
depending upon concentration, be anything from lethal
gas to an unpleasant odor. Further, if the time scale
of interest is of sufficient length (approximately one
day) the gas will oxidize to produce sulfates which may
precipitate out as an "acid rain". The pollutants
associated with combustion range from effectively inert
carbon monoxide to hydrocarbons and the oxides of
nitrogen and sulfur which lead to the secondary pollu-
tants ozone/oxidant and particulate sulfates. The
effects may not be direct, for example, the Department
of Transportation sponsored Climatic Impact Assessment
Program (CIAP),3 which,among other things considered,
explored the effect of ozone reduction in the strato-
sphere, due to effluent from supersonic aircraft, upon
ultraviolet radiation at the earth's surface.
Spatial Domain. The area of interest can be any-
thing from the region immediately downwind from a power
plant stack to the entire globe. Local models would,
for example, be employed to treat processes going on in
the vicinity of industrial facilities. The LIRAQ. model
mentioned above is concerned with regions of character-
istic dimension of one-hundred to two-hundred kilometers.
The question of the sulfate budget in the eastern United
States would be of subcontinental proportions. Finally
the CIAP project employed global models of one, two and
three-dimensions. It should be clear that the size of
the domain will influence the degree of spatial detail
which can be achieved. Spatial domain relates also to
26
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vertical extent. Although It will depend strongly upon
the application, we can say roughly that local and
regional problems may be addressed with models focusing
on a well mixed layer below an inversion, if it exists
(less than a kilometre), subcontinental models may go
through the convective cloud layer (three to four kilo-
metres) and global models may be expected to extend into
the stratosphere (thirty to thirty-five kilometres).
Temporal Scale. The time periods of interest may
be anything from hours to years. As mentioned above,
the time period treated by the model may influence those
physical characteristics of the pollutants which must be
emphasized in the model calculation. In turn, the time
scales of interest are roughly related to the spatial
domain under consideration extending from local problems
simulating hours to global scales which may be concerned
with processes evolving over periods of years.
Confidence Level. Any model, however complex, is
only an approximation of physical reality. As will be
discussed in the following sections of this paper, the
modeler is limited in the number of processes which he
can describe and even these are sometimes not fully
understood or must be treated with approximations. The
question then is, to what degree can the model be
expected to reproduce the physical picture which is
observed? Further, because of the demands put upon him,
what degree of accuracy does the user need in order to
make meaningful judgements? This criterion is fre-
quently related to domain of interest. For local pro-
blems one might expect to achieve results with accuracy
of ten percent while regional and subcontinental pro-
blems might be considered reliable when giving results
within tens of percent. For global calculations, some-
times order of magnitude or even the sign of a change
may be sufficient.
The user will, in general, have a well defined
application, including the pollutants of interest,
while temporal and spatial scales may be less specific.
The modeler will be -able to provide guidance in deter-
mining what confidence level can be realistically
expected from model results. Communication between the
user and the modeler is vital during this foundation
stage of model development, in order that both parties
be aware of and appreciate the various requirements and
constraints and the compromises which must be made
between them. The definition of possible constraints
will lie primarily in the purview of the modeler and
rests upon the second factor governing the model.
II. Physical Processes and Constraints
Under this heading the modeler must consider any
process or condition, either natural or man-made which
might contribute to the state of the physical system
which he is trying to describe. He must always make
compromises between what he would wish to treat and
what lies within the capacity of the state-of-the-art
or of his resources to handle. Discussed here are
those factors which most commonly will play a part in
the problem.
Sources. Man and nature both provide the atmo-
sphere with effluents through a variety of sources.
Some of the natural sources which contribute to our
"ambient" atmosphere are; forests (hydrocarbons), soil
micro-organisms (methane, nitrous oxide, hydrogen
sulfide), fires (carbon monoxide and particulate),
volcanoes (sulfur, fluorine, particulate, hydrochloric
acid) and oceans (chlorides, calcium and sulphates).
The pollutants we consider from man's activity are
particulates and species such as carbon monoxide,
hydrocarbons and oxides of nitrogen and sulfur result-
ing from combustion processes in transportation and
power generation. In parts of the United States 50-2
from space heating is significant. By-products such as
hydrogen sulfide, flourine, trace metals and volatile
hydrocarbons from various industries may present pro-
blems in some areas. Pesticides form another class of
pollutant which we may wish to follow, while industrial
accidents and leaking storage vessels provide a whole
spectrum of problems of local concern.
Chemi stry. The above are considered primary
pollutants and their reactions with other species pre-
sent and their response to the diurnal solar cycle help
to define the level of chemical complexity required in
the model. If these pollutants alone are of interest
it may be possible to treat their reactions with simple
chemistry or decay terms. However, as mentioned
earlier, depending upon time scale these may lead,
through a chain of more complex reactions to secondary
pollutants. Among these secondary pollutants are ozone
or oxidant resulting from the presence of hydrocarbons
and the oxides of nitrogen in the presence of sunlight.
Similarly, oxides of sulfur lead to sulfate thence to
sulfuric acid in the presence of water.
Meteorology. Here we mean all of the natural pro-
cesses in the atmosphere which can affect the pollu-
tants being considered. Turbulent winds will transport
and disperse the pollutants. The presence of water
vapor will promote heterogeneous transformation; water
vapor in the form of clouds will affect photodissocia-
tion processes, while rainfall provides a mechanism for
the scavenging of certain pollutants (e.g., sulfates
and nitrates).
Radiation. As mentioned in the above sections,
photochemical reactions may play a role in the problem
and hence the significance of solar radiation trans-
port. Generally, for models on scales less than global,
radiation is a, possibly time-dependent, input quantity.
It is however clear that feedback mechanisms may exist
which can play a significant part in the evolution of
the chemically active species and the radiation balance.
Topography. The character of the terrain in the
region can affect, directly or indirectly, source input,
chemistry and transport. For example, a source elevated
due to the terrain may emit above an inversion, which
will inhibit its transport to the surface. Surface
characteristics can affect heating, modifying the
chemistry and possible convective activity. Complex
terrain such as that seen in the San Francisco Bay
Area has strong channeling effects, giving rise to
characteristic flow and pollution patterns. Finally,
the character of the terrain will affect the level of
turbulence and hence dispersion rate.
Boundary Conditions. Since there will usually be
conditions outside the model domain which can affect
what occurs within, a set of boundary conditions must
be supplied to the model to account for these. These
consist of pollutant background values, possible up-
wind sources and transport across the domain boundaries.
As the model becomes more complex, more information
Will be required. Pollutant background is usually
available from observations in unperturbed regions.
Information on upwind sources may be more difficult to
acquire, frequently being outside the region of influ-
ence of the user. Recourse must then be had to some,
hopefully realistic, artiface. Transport at the domain
boundaries is of course the mechanism by which condi-
tions outside the region affect processes within. This
information is generally available through the same
process that provides wind fields for transport within
the region.
27
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Through this second stage the modeler has had to
determine those physical characteristics and processes
which are required to provide a model which will meet
the user's needs. This is a phase during which actual
numerical experiments will be carried out, in order to
test new ideas and also to see if already existing pro-
grams or subprograms can be adapted to address the
user's problem. There are, in fact, a number of "off-
the-shelf" models of varying complexity which are avail-
able to the potential user and it is to be hoped that as
the process of developing user oriented air quality
models continues, readily adaptable programs will become
increasingly available.
One might expect that once the model requirements
have been defined and the pertinent physical processes
identified it would simply be a matter of writing a
computer program, handing it over to the user and going
on to other things. However, anyone who has had to
function within a budget will be well aware that further
compromises must be made, because there never seems to
be sufficient money to do all those things desired.
This brings us to the final factor.
III. User Resources
Here we are concerned with any factor which may
tend to facilitate or impede the process of addressing
the user's problem. Here the user and modeler must
work in concert to apply available funds in the most
efficient way possible.
Computer Availability. User and modeler demands
must be compatible with the available computational
facilities. A computer offers, at a price, some degree
of computational speed, a certain amount of storage for
coding and data, and some form of input/output facili-
ties. The modeler, in developing a large, complex pro-
gram will be constrained by the size of the computer
available although some tradeoffs between speed and
storage are possible. The user, on the other hand, is
more concerned about the speed with which the computer
can run his problem and provide him with useable output.
This question of "turn around" time depends to a certain
extent upon the user's mission. A .land use planner can
afford to wait several days for his answers, while an
agency which must respond to sudden emergencies will
require immediate answers albeit, in less detail than
those of the former. With a given computer system, the
actual time (cost) involved in computation rests upon
the model complexity. Compromise is almost invariably
required between the modeler who wishes to include as
much physics and chemistry as possible and the user who
finally pays the bill.
Data Avallabi1ity. User and modeler both are
plagued by the lack of data and as more and more complex
models are developed the need for data is correspond-
ingly increased. We wish to have data for all physic-
ally pertinent aspects of our problem, at least over
the domain of interest. Source data for the model are
often not available at all from direct measurement and
must be estimated from indirect measures such as popu-
lation, industrial and traffic flow patterns. Meteoro-
logical data are generally sparse, entailing the use of
various types of interpolative schemes to provide infor-
mation over the entire domain. Pollutant data, required
for model validation are often incomplete or difficult
to measure with accuracy.
Response Time. There are two kinds of response
time which concern the user and constrain the modeler.
The first is the time available for model development.
This is imposed upon the modeler by the user in order
that the user may meet his commitments. As mentioned
in Section II of this paper, there is an increasing
number of existing air quality models which help to
alleviate this problem. On the other hand, we tend to
make increasing demands upon our models which involves
the inclusion of more physical mechanisms and the use of
more sophisticated numerical techniques. The second
time constraint was alluded to in the first part of this
section, that is the model/computer response time, which
is imposed by the user's mission upon the computer choice
and model design.
Personnel. Finally, in order that an air quality
model be appropriate for a given problem and provide
useable results, communication links must exist at all
levels of development and application. In general,
the responsibilities and background of user personnel
will be quite different from those of the modeler. The
modeler is expected to be aware of the relative impor-
tance of the many physical characteristics of the pro-
blem and how they may be addressed, while a local air
quality agency, for example, may be expected to supply
decision and policy makers with information pertaining
to the impact of changing population patterns and pollu-
tion abatement strategies. As models become more com-
plex, the user may find that a third party or model
operator is required to provide direct operation of the
model and to interpret its raw results.
During model development direct user/modeler links
are necessary for the reasons mentioned earlier in this
paper. They are: to reconcile the user requirements
with the modeler's ability to produce a functional
model within the constraints imposed by the physics and
chemistry, data availability and computational facili-
ties, and to make the user aware of the model's features
and limitations. Once the problem has been defined,
continued communication will help to keep the project on
track to its desired goal. To this end there are
several options available. First, formal and informal
reports always have a place, particularly in providing
documentation of the work in progress and of the model
upon completion. They do not, however, provide very
direct user/modeler interaction. In the ILL project a
"user advocate" was employed to meet this need. This
person is a member of the developer agency who acts as
the user's representative with the modeling group.
The role is demanding in that it requires not only a
full knowledge of the user's needs but also a knowledge
of the limitations under which the modeler must function.
Perhaps the best approach, if it is economically feas-
ible, is to have direct user participation in model
development. Though the BAAPCD did not participate
directly in the LIRAQ model development, they did play
a major role in data acquisition.
The most important communication link is the last,
that between the finished model and the user. The user
should be able to formulate a problem in his own terms
and have it executed. Computed results must then be
provided to the user, again in his own terms. As an
example of how this was achieved in one case we can use
the LLL LIRAQ model. The name LIRAQ refers specifically
to the air quality program itself. In order to facili-
tate the use of this model by the BAAPCD several other
programs have been provided. The "Problem Formulator"
is a program which provides an interface between the
actual running code (LIRAQ) and the user. Through a
series of questions to the user the Problem Formulator
determines the type of problem to be run, physical con-
ditions, spatial domain, etc. This in turn provides a
series of instructions to an "Executive Routine" which
selects, and modifies if necessary, the appropriate
input data, runs the LIRAQ model and directs the com-
puted results to the desired output medium. Although
this does isolate the user from the workings of the
model it was felt necessary because of the model's very
complexity and the large amounts of data which must be
manipulated.
28
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Conclusion
In conclusion, we might say that development and
implementation of a complex air quality model can be
reduced to a process of Communication and Compromise.
The user and modeler are hopefully knowledgeable in their
diverse fields. There must be a mutual understanding of
the existing requirements and constraints. The modeler
must make many compromises in his effort to describe
the real world with the various facilities available to
him. He must remain aware of the possibility that no
viable compromise exists, since it would be most unfor-
tunate to learn this only after the expense of model
development. The user, for his part, must recognize the
limitations which do exist and be able to operate within
them. Finally, there must be interfaces which permit
the user to communicate with the model in his own terms.
Acknowledgements
The author is indebted to a number of his fellow
workers in the Atmospheric and Geophysical Sciences
Division of Lawrence Livermore Laboratory, for their
many helpful comments. He wishes to express special
thanks to Drs. H. W. Ellsaesser, M. C. MacCracken and
G. L. Potter for their help in preparation of this paper.
This work was performed under the auspices of the U. S.
Energy Research and Development Administration under
contract No. W-y
References
1. M. C. MacCracken and G. D. Sauter, editors:
"Development of an Air Pollution Model for the San
Francisco Bay Area," Final report to the National
Science Foundation, UCRL-51920, 1975.
2. M. C. MacCracken et al.: "The Livermore Regional
Air Quality Model: I. Concept and Development,"
UCRL-77if75, submitted to the Journal of Applied
Meteorology.
3. CIAP Monographs I-VI, Department of Transportation,
1975. Available through the National Technical
Information Service, Springfield, VA 22151.
k. D. V. Lamb, F. I. Badgley and A. J. Rossano, Jr.:
"A Critical Review of Mathematical Diffusion Modeling
Techniques for Predicting Air Quality with Relation to
Motor Vehicle Transportation," Washington State
Department of Highways P. B. 224656, June 1973- Avail-
able through NTS.
29
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A GENERIC SURVEY OF AIR QUALITY SIMULATION MODELS*
G. D. Sauter
University of California Lawrence Livermore Laboratory
Livermore, California 9^550
Abstract
This survey of the generic types of models which
have "been developed for numerical simulation of air
quality compares and contrasts them on the "basis of
such criteria as the simplifying assumptions made in
the solution of the general continuity equation, the
problems to which each model type is applicable and
not applicable, the requirements for input data, and
computational speed.
Introduction
A variety of generic types of numerical models
for simulation of air quality have been or are being
developed. The various types can be described in
terms such as the assumptions on which each is based,
the applications to which each is suitable and not
suitable, the amount and quality of input data each
requires, and the demands which each places on users
(e.g., operational costs, computer capacity, expertise
of operational personnel). Successful use of any air
quality simulation model requires a satisfactory
matching of the user's needs and resources with the
model's capabilities and requirements. Therefore, in
deciding whether to use air quality simulation models,
Het rate of change of
the average concentration
in an arbitrary, well-mixed
volume element
2. The net transport out of the element due to
dispersion and diffusion. These transport
mechanisms result from turbulent fluctuations
in the mean winds.
3. The emission of the pollutant into the
element by sources within or on the lower
boundary of the element.
k. Creation or destruction of the species within
the element by chemical reactions between
species and photochemical reactions triggered
by incident solar radiation. The strength of
any particular reaction is generally propor-
tional to the product of the concentrations
of the species involved. This means that for
chemically reactive species, the total concen-
tration cannot be determined by adding
together the contributions from all signifi-
cant sources.
5. Physical loss or destruction mechanisms such
as surface deposition, decay, or rainout.
In principle, one can write a mathematical de-
scription of each of these processes and combine the
various terms in a continuity (conservation of mass)
equation, for each species of interest, of the form:
net rate of advection into element
+ net rate of diffusion into element
+ rate of source emission into element
rate of physical loss out of element
+ net rate of chemical production
within element
and if so which ones are most suited to his needs, a
potential user must not only realistically assess the
goals he wishes to obtain via modeling and his re-
sources for accomplishing them, but also understand
the capabilities and requirements of the various
candidate models.
This paper is devoted to a brief survey of the
capabilities and requirements of the generic types of
numerical air quality simulation models presently
available. As a general rule, the more that one
requires of a model (e.g., good spatial and temporal
resolution, the ability to treat simultaneously a
number of pollutants, accurate description of relevant
physical and chemical processes), the greater the
resources (e.g., computer capacity and cost, quality
and quantity of input data) he must make available.
The Basis for numerical Simulation of Air Quality
Numerical air quality simulation models are
designed to simulate, with varying degrees of sophis-
tication, the physical and chemical processes which
govern the mixing, modifying, and transporting of
atmospheric pollutants from their sources to other
points of interest, often designated as receptors.
The important processes which determine the variation
with time of the average concentration over an
arbitrary volume element of a pollutant species of
interest are:
1. The net transport of the pollutant into the
element by advection; i.e., due to divergence
of the pollutant flux, the product of concen-
tration and the local average wind vector.
*Work performed under auspices of U. S. Energy Research
The series of equations can then be solved to deter-
mine the spatially and temporally varying concentra-
tions of all pollutants of interest. In practice,
it is not possible to write down and solve the
continuity equation in all generality for even a
single non-reactive species; among other things
diffusion and loss mechanisms are not fully understood.
The situation for reactive species is even more
ambiguous; not only do the chemical reaction terms
couple the continuity equations for many species and
make the equations non-linear, but also many of the
significant reactions are poorly understood. Even if
all the physical and chemical processes were well
known, available meteorological and source emissions
data are invariably of insufficient quality and
quantity to allow an accurate simulation.
Thus in any practical numerical air quality
simulation, a simplified form of the continuity
equation is solved. The simplifications are generally
of three types:
1. Approximation or neglect of spatial
dependences
2. Approximation or neglect of temporal
variations
3. Approximation or neglect of one or more of
the terms in the continuity equation.
In practice, most models incorporate simplifications
of all three types. For example, one can assume that
all meteorological parameters and source emission
rates remain constant over a time interval (say 3 hr)
and then change to new but constant values over the
next interval, etc. Or one might use a highly
simplified set of chemical reactions in formulating
and Development Administration contract W-7
30
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the chemical production term. Depending on the
simplifications involved, different air quality
simulation models are applicable to different prob-
lems or situations. Ho single model is applicable to
all problems. Although no model represents any
practical problem with total accuracy, veil-
formulated and applied air quality simulation models
can be used to gain, at reasonable levels of effort
and cost, insights into air quality problems which it
would not be feasible to obtain by any other means.
Highly Simplified Models
Rollback Models
Rollback models are the simplest air quality
simulation models. Their real objective is the
determination of the degree to which source emissions
must be reduced if some desired air quality is to be
obtained. In their simplest form, rollback models
are based on the assumption that the local concentra-
tion of a pollutant above its background level is
directly proportional to the strength of all
neighboring source emissions of that pollutant. Such
an assumption only applies to stable pollutants which
do not undergo significant production or removal via
chemical reactions. The proportional assumption
applies only if the same fractional degree of control
is applied to all sources. The fact that nearby
sources make a larger contribution than those further
away is not recognized. In non-linear rollback
models, only selected emission sources are reduced,
often with different fractional reductions for
different sources. Some attempts have been made to
use the rollback technique for ozone by applying it
to oxides of nitrogen and hydrocarbons, the precursors
of ozone, but the results have been inconsistent and
not particularly encouraging.
In addition to their not being useful for
reactive pollutants, the applicability of rollback
models is limited by other factors. According to
these models the spatial and temporal variations in
air quality will be the same in the future as observed
now. Changing spatial and temporal distributions of
source emissions and meteorological patterns do not
impact on air quality; source strengths are all-
important. The models do have two important
advantages. First, from an operational point of view,
they are very easy to apply. Second, and more
important, rollback models are one of the two types
(Gaussian plume models are the other) which are
officially sanctioned by the EPA for use in develop-
ing implementation plans for the satisfaction of
ambient air quality standards.
Gaussian Plume Models
The most frequently used air quality simulation
model is the semi-empirical Gaussian plume formula-
tion. In its basic form the model assumes a time and
spatially independent horizontal wind field, a time
independent point source, and no chemical reactions ,
or loss mechanisms. Turbulent diffusion in the
direction of the wind is assumed negligible, and
diffusion in the cross-wind and vertical directions
is assumed to produce a Gaussian (bell-shaped) con-
centration profile about the plume centerline. The
resulting downwind concentration of the plume can
then be expressed in closed form as a function of the
source strength, the average wind velocity, and two
diffusion parameters whose values have been determined
empirically for the various classes of atmospheric
stability. The plume is assumed to expand indef-
initely in the upward vertical direction and to be
totally reflected at the surface of a flat topography.
The basic plume equation is sometimes multiplied by a
decay factor to simulate a simple loss mechanism.
The basic plume equation can be used to treat
the case of multiple point sources by summing the
pollutant concentration contributions of the individual
sources. In the same way, continuous linear or area
sources can be decomposed into an appropriate set of
source elements and handled as multiple point sources.
If the emissions are uniform over the linear or area
source, a closed form, analogous to the basic point
source form, can readily be developed. In any event,
the size of the complex source region should be
limited to one over which the meteorology can be
assumed reasonably uniform. Also, the summation
technique restricts the applicability of the Gaussian
plume model to non-reactive species.
The major advantages of the Gaussian plume models
are their simplicity and ease of application; the
closed-form solutions can readily be converted to
graphical, tabular, or nomogram form. This advantage
is lost, however, if the model is applied to a many
source, many receptor situation. Other advantages are
that these models require very little input data and
that there is considerable experience in their use.
The major limitation in the applicability of
plume models is the assumption that the wind field is
constant and uniform. In practice this limits their
use to time periods on the order of an hour and spa-
tial distances on the order of 10 km. Quasi-steady-
state applications can be made by periodically
updating the source emissions and meteorology, but
this does not alleviate the spatial limitation.
Further, since the predicted pollutant concentration
is inversely proportional to the wind speed, the model
is not applicable on calm or nearly calm days.
Finally, the model is not applicable in situations
with complex topography or low altitude inversions.
Gaussian Puff Models
The Gaussian puff model was developed to overcome
some of the limitations of the plume equation, par-
ticularly the time independence. In its basic form,
the model tracks a puff of pollutant emitted from a
point source as it is blown downwind and diffused in a
Gaussian manner. The puff is allowed to expand in
volume so that all of the original pollutant mass is
retained within it. In the quasi-time dependent case,
the wind field and source emission rate are periodi-
cally updated and assumed constant over each time
interval. In the steady-state limit, the puff model
is equivalent to the plume model. As with the plume
model, multiple source situations are treated by
summation, with due consideration taken of the time
for puffs from the various source elements to reach
the receptor. The cross-axis distribution within the
puff need not be assumed to be Gaussian; in one refine-
ment, cross-axis diffusion is determined from turbulent
eddy diffusion (k) theory.
Although it does permit some degree of time
dependence, the puff model suffers from some of the
other limitations of the plume model; i.e., only non-
reactive pollutants can be treated for cases of
relatively flat topography (some rather unsuccessful
attempts have been made to incorporate a simplified
treatment of reactive species). It can be used in
light wind situations. The time dependent puff model
is not as easy to apply as the plume model. Time
dependent source data are required, and time dependent
trajectories must be determined. These more difficult
operational problems tend to outweigh the added
31
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advantages of the puff model, and it is not widely
used. It is test applied to cases of a few sources
and a few nearby receptors. Even here a computer is
generally required. For widely distributed sources
and multiple receptors, the large number of trajec-
tories required makes the use of the puff model
prohibitive.
One Box Models
These models are based on the assumption that
pollutants are uniformly mixed throughout a fixed
volume (box) of air. For air quality simulation (as
opposed to simulation of smog chambers), the box is
usually taken to extend vertically from the terrain
surface to the inversion base; horizontally the box
should cover an entire region of distributed sources.
In the simplest applications no transport of pollutants
into or out of the box is allowed. The resulting
concentrations are then proportional to the total
rates of source emissions of pollutants into the box
and inversely proportional to the average residence
time and the inversion base height. Since pollutant
clouds must generally travel distances on the order
of 5-10 km before uniform mixing can occur, simple
box models should only be used to estimate average
concentrations over large area sources (e.g., whole
cities) or to simulate background concentrations at
points with no large local sources nearby.
Models which are essentially a special type of
box model have been developed by Gifford and Hanna at
NOAA's Atmospheric Turbulence and Diffusion Laboratory.
For non-reactive pollutants, the simple ATDL dispersion
model can be expressed as c = A Q/u, where c is the
average pollutant concentration in the box, Q is the
average source emission rate per unit area, and u is
the mean wind speed. The dimensionless parameter A is
assumed to be a constant for a given atmospheric
stability; analyses of air quality data for a number
of urban areas suggest that, over long averaging times
(month, season, year), A = 225 is a reasonable value.
The ATDL dispersion model is a reasonable one to use
in determining average concentrations of non-reacting
pollutants over large areas and long averaging times.
If the area considered is too small, the effects of
sources outside the region under study may be signif-
icant; if the averaging time is too short, the model
will not effectively account for significant short-
term deviations from average source emission rates and
meteorology. Operationally, the ATDL model is very
easy to apply, and it requires a minimum of input data.
Its major drawback is the lack of spatial resolution
over large areas.
Hanna has also applied the ATDL model to several
reactive pollutants by incorporating a very simplified
set of chemical reactions. For example, all reactive
hydrocarbons are lumped together as a single species.
The resulting model has five parameters (instead of
just one for the non-reactive model) which can be
adjusted to give the best results for a particular
situation. The chemical mechanism is not general; a
different mix of sources and/or significantly different
meteorology would necessitate a retuning of the model.
As with the non-reactive version, this model is
designed to determine average concentrations over a
large area under typical meteorological conditions.
More Complex Models
The models described above stress ease of
application at the expense of physical and chemical
fidelity. They are either analytic or require very
limited numerical computer capabilities, and the input
data requirements are modest. (An exception is the
use of the puff model with a large number of trajec-
tories.) However their applicability is limited;
e.g., simulation of a steady-state or quasi-steady-
state point source (Gaussian plume model) or air
quality averaged over a large area (ATDL). The models
described below are designed to yield air quality
simulations which include both spatial and temporal
dependences. As a result, their operation is con-
siderably more demanding, requiring extensive computer
capability and quite large amounts of spatially and
temporally resolved meteorological and source emissions
data.
Eulerian Grid Multibox Models
An Eulerian multibox model consists of a number of
constant size volume elements in a fixed spatial grid
which covers the entire region of interest. Pollutants
are allowed to flow through the boundaries of each
element as a result of advection, diffusion, sources,
and sinks. Within each element, the pollutants are
assumed to be mixed; they may be chemically reactive.
Time dependence is introduced by periodically
(typically every hour) updating the source emission
rates and the prevailing meteorology (wind speed and
direction, inversion base height, and for reactive
pollutants, incident sunlight) for each grid element.
Thus the multibox simulations produce time histories
of (hourly) average pollutant concentrations with
spatial resolutions determined by the size of the grid
elements. The minimum size of the elements is limited
by one or both of two factors: the quality of the
available source emission and meteorological input
data and the memory capacity of the computer to be
used. For a given computer, the minimum grid element
size is determined by a combination of factors: the
size of the region to be simulated, the number of
pollutant species considered, the number of vertical
layers of elements, the degree of sophistication of
the numerical technique used, and the complexity of
the chemical reaction set (if any). Increasing one
or more of these factors increases the minimum grid
size. Typically, the horizontal dimensions of a grid
element are a few kilometers. A significant data
gathering and preprocessing effort is necessary to
produce realistic source emission and meteorological
input data with this resolution, particularly in
regions with complex topography, which tends to make
both the meteorology and the source distribution less
uniform.
The usual approach in calculating the flow of
pollutants across the boundary of an Eulerian grid
element is to use a technique based on the finite
difference between the pollutant concentrations on
either side of the boundary. The assumption that each
element is well-mixed gives rise to errors, referred
to as numerical diffusion, in the simulation of
pollutant transport. These errors can be controlled
reasonably well, at the expense of additional compu-
tational complexity, with higher order differencing
schemes, especially for distributed rather than
localized sources. Two of the most prominent examples
of such models are the Systems Applications, Inc.
(SAI) and Livermore Regional Air Quality (LIRAQ)
models.
The SAI model, originally developed for the Los
Angeles basin, uses a grid with several vertical
layers, thus simulating the solution of the continuity
equation in three dimensions, and in turn requiring
sufficient meteorological data to adequately represent
a three-dimensional wind field. The model contains a
reaction set of 16 reactions covering 13 species (all
hydrocarbons lumped together) which probably should be
tuned for each area of application. A more extensive
32
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chemical reaction set is now being incorporated into
the model.
The LIRAQ model, originally developed for
application to the San Francisco Bay Area, uses a
single layer of grid elements between the terrain
surface and the "base of the inversion layer. Only
horizontal pollutant transport is simulated; within
each element, the vertical pollutant distribution is
represented in terms of a, simplified profile. Two
versions of the model exist. The non-reactive version
(LIRAQ-l), when used on a CDC-7600 computer, can treat
up to four species simultaneously on a ^5 by 50
element grid, more than adequate to treat the entire
Bay Area with 5 km resolution or subregions with finer
resolution. About 15 min. of computer time are required
for a 2k hr simulation. LIRAQ-2, for reactive species,
incorporates a set of k& reactions to treat 19 species,
including three hydrocarbon classes. This limits a.
CDC-7600 simulation to a maximum of 20 by 20 elements,
still enough to cover most of the Bay Area with 5 km
resolution. A 2k hr simulation requires about 60 min.
of computer time.
These Bulerian grid multibox models represent the
most comprehensive approach to simulating air quality
on a regional basis; they are applicable to such air
quality problems as regional compliance with air
quality standards and evaluation of the impact on
regional air quality of various land use alternatives.
However, because all emissions within a grid element
are lumped together, these models should not be used
to simulate the effect of a strong local source on
nearby (within a few grid elements) receptors. Sub-
stantial input data and computer capability are
required to operate these complex models, and appli-
cations are limited to simulations of a few days for
"typical" or "worst case" conditions.
Particle -in-Cell (PIC) Models
These time dependent models combine the use of an
Eulerian grid and marker particles, each marker
representing a fixed mass of pollutant. The markers
are introduced into the grid where emissions occur and
are tracked as they are transported and dispersed
throughout the three-dimensional grid by the specified
wind field. At the end of any time interval, the
concentration of a pollutant in any grid element can
be determined by summing the masses represented by the
particles then in the element. This technique virtu-
ally eliminates transport errors due to numerical
diffusion.
The limitation on the PIC technique is the large
number of particles which must be tracked to adequately
represent pollutant concentrations and concentration
gradients over a large grid. Available computer memory
sizes limit a simulation to a combination of about
particles and 10^ grid elements (about 30 min of
CDC-7600 computer time would be required for an 8 hr
simulation). This makes it extremely difficult to
represent large gradients and small changes in concen-
trations of several species with sufficient accuracy
to adequately characterize chemical reactions, so the
PIC technique is best applied to non-reactive species.
PIC models are perhaps the best choice for accurate
three-dimensional simulations of the pollutant concen-
trations produced by localized sources of non-reactive
species. The major effort in applying the PIC
technique to urban air quality simulation has been the
application of the NEXUS model by Sklarew to CO and
ozone in Los Angeles.
^
Lagrangian Box Models
In contrast to Eulerian box models, which
simulate the time history of pollutant concentrations
within a volume element fixed in space, Lagrangian box
models (sometimes called trajectory models) simulate
the time history of pollutant concentrations within
boxlike elements of constant volume as they flow along
wind streamlines. A box may have one or several layers
(cells) between the terrain surface and the base of the
inversion height. As the box flows across a source,
pollutants may flow in through the bottom of the box
and diffuse vertically into other cells (if any), but
usually no horizontal transport of pollutants across
the boundary of the box is allowed, so numerical dif-
fusion problems are eliminated. Within each cell the
air is assumed to be well-mixed, and chemical reactions
can occur. The horizontal dimensions of the box,
typically on the order of a few kilometers, determine
the spatial resolution of the calculated concentrations
and of the required input data. Both source emissions
and meteorology can be time dependent. As with
Eulerian multibox models, they are usually updated on
an hourly or few hourly basis.
Lagrangian box models are primarily source-
receptor oriented; that is, they relate the pollutant
concentration at a receptor area to specific upwind
emission sources via one or more wind trajectories.
Thus the user can identify the source areas respon-
sible for observed pollutant concentrations at selected
points along specific trajectories. Air quality simu-
lations on a regional basis can be treated by tracking
boxes along enough different trajectories to adequately
represent the sources and meteorology of the region and
interpolating between calculated trajectories. This
procedure works best in areas with relatively uniform
source distributions and meteorology, where the number
of trajectories needed to characterize the region is
reasonably small. For regions with complex meteorology
and/or source distributions, the number of trajectories
needed may make the computer requirements prohibitive.
The ratio of time simulated to computer time required
is on the order of 500 to 1 for each trajectory con-
sidered (e.g., about 30 min of computer time would be
required to follow 25 trajectories over a 10 hr period).
Thus, as is the case for Eulerian multibox models,
simulations are limited to a day or so for typical or
worst-case conditions.
Representative of Lagrangian box models is the
DIFKIK model, developed at General Research Corporation,
which has been applied to both the Los Angeles and
San Francisco Bay regions. The model uses five vertical
layers and vertical diffusivity rates that depend on
atmospheric stability. The simplified chemical reaction
set employs l6 reactions encompassing 13 species, with
all hydrocarbons lumped together. Other models may
combine more sophisticated chemistry and simpler
meteorological treatments.
Conclusion
Although it has of necessity been very brief, this
generic survey of numerical air quality simulation
models should be sufficient to show that a variety of
these models is now available. These models differ
widely in the level with which they treat the important
physical and chemical processes involved, in the
applications for which they are designed, and in the
input data and computational capacity they require.
No single model is adequate for all types of air quality
simulations. In selecting an air quality simulation
model, a potential user should seek a good match of
his resources and modeling needs with the capabilities
and resource requirements of the model.
33
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Selected References
The references listed here "by no means comprise
an exhaustive list. Rather, they have "been selected
to be representative of the air quality simulation
models currently in use. The references generally
contain further references to generically similar
models.
Rollback Models:
Gaussian Models:
ATDL Models:
Eulerian Multi-
"box Models:
PIC Models:
Langrangian Box
Models:
N. de Nevers and J. R. Morris,
"Rollback Modeling: Basic and
Modified," J. Air Poll. Control
Assoc. 25, 9^3 (1975).
D. B. Turner, Workbook of Atmos-
pheric Dispersion Estimates, EPA
Office of Air Programs Publication
AP-26 (19TO).
S. R. Hanna, "A Simple Dispersion
Model for the Analysis of Chemically
Reactive Pollutants," Atm. Envir. J_,
803 (1973).
M. C. MacCracken and G. D. Sauter,
"Development of an Air Pollution
Model for the San Francisco Bay
Area: Final Report to the NSF,
Vol 1," Lawrence Livermore Laboratory
Report UCRL-51920 (1975).
S. D. Reynolds, et al., "Mathemati-
cal Modeling of Photochemical Air
Pollution. Ill: Evaluation of the
Model," Atm. Envir. 8, 563 (197^).
R. C. Sklarew, et al., "Mathemati-
cal Modeling of Photochemical Smog
Using the PICK Method," J. Air Poll.
Control Assoc. 22, 865 (1972).
J. R. Martinez, et al., "User's
Guide to Diffusion/Kinetics (DIFKHJ)
Code: Final Report EPA Contract
No. 68-02-0336," General Research
Corporation (1973).
34
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AIR QUALITY MODELING A USER'S VIEWPOINT
Richard H. ThuiTlier
Chief of Research and Planning
Bay Area Air Pollution Control District, San Francisco, California
A requirement for modeling has developed out of
the Clean Air Act amendments of 1970. In spite of
this requirement and the existence of a variety of
modeling techniques, there is a prevailing reluctance
toward the use of modeling as a decisioranaking tool.
Based on experience with regional application of a
variety of models, the Bay Area Air Pollution Control
District encourages the use of appropriate techniques
in a coordinated regional context. The District feels
that much can be gained from simplified approaches at
minimal cost and recommends that regional resources be
pooled for effective, efficient, and standardized
application.
Introduction
The Bay Area Air Pollution Control District
(BAAPCD) has regulated air pollutant emissions in the
nine-county San Francisco Bay Area over a period of
20 years. Traditionally, such regulation has been
accomplished, by and large, through best effort tech-
nological control of point sources, with air quality
improvement as a general goal. Control program effec-
tiveness has been measured against the yardstick of
air monitoring data from community-representative
sites.
With the advent of the Clean Air Act amendments
of 1970 and ensuing Federal regulations, there devel-
oped a requirement for a more structured approach to
air quality control. The promulgation of ambient air
quality standards and associated compliance schedules
has given rise to a concept of air quality control
and analysis based on more precise relationships be-
tween source emissions and their resulting air quality
impact. The activities involved in establishing such
relationships and using them effectively in an air
quality control context comprise the challenging field
of air quality modeling.
Notwithstanding the existing requirement for
modeling, relatively little has been done in exploit-
ing the potential of this emerging technology. The
evident reluctance to use modeling is engendered by
such factors as esoteric techniques, required re-
sources for model use, and a general confusion re-
garding appropriate application.
Immediately after the promulgation of the Clean
Air Act amendments, the BAAPCD made an extensive com-
mitment to modeling in all its facets. In a region as
extensive as the Bay Area, air quality standards can
be achieved only if planning decisions properly con-
sider air quality. We feel that modeling can provide
appropriate air quality input to decisionmaking and
is, therefore, a very useful tool for planning and
regulating air quality. We are grateful for this
opportunity to discuss our philosophy and experience
in this regard, with a view toward stimulating greater
interest within the user community.
Institutional Framework for Modeling Application
In attempting to fulfill the requirements of the
Clean Air Act, control measures must be conceived and
applied on a coordinated, regionwide basis with con-
sideration of all sources of pollution in terms of
their combined, impact upon receptors. A control pro-
gram of such scope cannot proceed effectively toward
desired levels of air quality without the unifying
guidance of a regional air quality model. Throughout
this presentation, the term "model" should be con-
strued to refer not to a single algorithm or computer
code but rather to an integrated and compatible set
of analytical tools which, together, supply the nec-
essary quantitative relationship between regionwide
sources and receptors in the context of defined air
quality standards.
One of the principal problems associated with
modeling in a regional context arises from a broad
spectrum of source categories and a variety of juris-
dictional responsibilities. Incompatible data bases,
divergent institutional resources, and special in-
terest bias can serve to place air quality control
more in the context of an adversary proceeding than
in the context of a coordinated technical effort.
Since such controversy has a tendency to divert ener-
gies and obscure goals, the interest of air quality
attainment and maintenance can best be served by
resolution of such conflicts. In this regard, two
possible approaches suggest themselves: One approach
would be the vesting of all responsibility for air
quality analysis in a single agency with regionwide
jurisdiction. An alternative approach would be to
continue with a decentralized analysis responsibility
under a unified code of procedures involving, for
effectiveness, an integrated, complementary use of
diversified resources and compatible techniques. The
latter appeals to the author from the standpoint of
political acceptability as well as technical feasi-
bility. Ideally, such an approach would proceed
under the guidance of a highly qualified multidisci-
plinary technical committee, group, or team, with
sole responsibility for the development, dissemi-
nation, and coordination of standardized procedures
for the region. Such a team could also be responsible
for interpretation of modeling results.
In the Bay Area, a combination of the two ap-
proaches prevails. In 1972, the BAAPCD created a
multidisciplinary Research and Planning Section with-
in the District's Technical Services Division with
responsibility for air quality model development and
application. Over a 3-year period, the group has
developed a sizeable inventory of techniques. As
an agency with regional jurisdiction and in view of
its experience with air quality models, the District
has been able to exercise regional leadership in air
quality modeling activity. We have, however, been
greatly assisted in our efforts by other regional
agencies possessing specialized resources and ex-
pertise not available in-house. The District, in
35
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turn, provides guidance and assistance to a variety of
agencies and individuals who wish to do their own anal-
ysis in a way which is mutually acceptable to the ana-
lyst and the District. Current efforts in air quality
maintenance planning should serve to further the inter-
est of a coordinated institutional effort in the re-
gional solution of air quality problems.
The Relationship of Modeling to Decisionmaking
In addition to technical and institutional prob-
lems as discussed above, another barrier to the effec-
tive use of modeling technology is a confusion or mis-
understanding of the relationship of modeling to the
decisionmaking process. It is important to realize
that decisionmaking is inherently subjective. The con-
cept of a decision implies a choice among alternatives
involving an element of uncertainty. Decisionmakers
deal with the reality of uncertainty and their deci-
sions are conditioned by but not necessarily dependent
upon the amount or quality of available information.
These factors are frequently overlooked when mod-
eling is proposed as an air quality analysis tool. One
of two alternative, contradictory, and equally unwar-
ranted arguments will frequently be lodged against the
adoption of a modeling program. On the one hand.it is
argued that the uncertainties in the models will render
them useless as input to the decisionmaking process.
On the other hand, it is argued that the valued judg-
ment of the decisionmaker will be replaced by the model
itself as an objective but utterly inscrutable and pos-
sibly flawed arbiter. With regard to these arguments,
we note that mandated decisions relating to air quality
must be made on the basis of available information.
Modeling results may or may not influence a decision
but as added information cannot conceivably detract
from the quality of that decision. The alternative to
|LAND USE/TRANSPORTATION |.
i
1 EMISSIONS MODELS 1
I
EMISSIONS INVENTORIES |
METEOROLOGICAL AND/OR •
CLIMATOLOGICAL DATA
1 1
REGIONAL ' • LOCAL
DISPERSION DISPERSION
MODELING MODELING
AIR QUA
DAT
1
PROJECT /ELEMEN1
MODELING AND
ANALYSIS
N. 1
^
LITY
t
1
STATISTICAL
DISTRIBUTION
ANALYSIS
/
[SYSTEM VERIFICATION AND CALIBRATION STUDIES 1
1
ESTIMATED ESTIMATED
REGIONAL . LOCAL
AIR QUALITY ' AIR QUALITY •
BACKGROUND VARIABILITY
(COARSE RESOLUTION) (MEDIUM RESOLUTION)
\
( COMPREHENSIVE REGIONAL
AIR
1
ESTIMATED
AIR QUALITY AT
SENSITIVE
RECEPTOR SITES
(PINE RESOLUTION)
/
QUALITY ANALYSIS 1
INTERPRETATION AND
SUMMARIZATION
[REPORTS AND PRESENTATIONS
consideration of modeling information, whatever the de-
gree of uncertainty, is all too often a complete disre-
gard of the air quality issue. In our experience, the
contribution of modeling is a positive one, serving to
clarify the decisionmaking process and to make deci-
sions less arbitrary in nature. With regard to the in-
stallation of a model as an objective arbiter, we feel
this is rather unlikely in view of the very imperfec-
tions used as a basis for the first argument. In real-
ity, modeling output must invariably be subject to in-
terpretation before a decision can be based in any way
upon it. In the interest of efficiency, however, stan-
dardization of routine procedures and the development
of criteria based on accepted modeling techniques may
be desirable.
In summary, modeling results should be viewed as
nothing more than information input to the primarily
judgmental process of decisionmaking. Such information
may be weighed with other factors in arriving at the
decision. Modeling uncertainties, whatever their na-
ture or extent, should be considered simply as part of
the general store of uncertainty inherent in the deci-
sionmaking process. If this viewpoint is taken, then
there is nothing to fear from modeling except, of
course, fear itself. Within a carefully structured,
institutionally integrated and professionally adminis-
tered program, we feel that modeling can be a very ef-
fective decisionmaking tool.
Model Selection and Application
To be most effective, models should be selected to
complement available resources and flexibly address the
problem area in which they will be applied. Applica-
tions in the Bay Area run the gamut from regional plan-
ning to project review. To meet our needs, we have
adopted the modular system outlined schematically in
Figure 1. Modeling is done on three spatial scales of
BAYMOD Local
Scale Domain
• - Project/Element \
Scale Domain I \
>BAYMOD Count;
Source Area
(One of nln.
r*Reglonal
Wind Pattern
(One of forty)
BAY AREA
AIR POLLUTION CONTROL
DISTRICT
Figure la. Flow Chart of Regional Air Quality Modeling
Activity in the San Francisco Bay Area.
Figure Ib. Setting for Regional Air Quality Modeling
Application in the San Francisco Bay Area.
36
-------
resolution using techniques of the simplest type con-
sistent with physical setting and application require-
ments of the scale in question. A statistical model
supplements and links the temporal resolutions of the
various modeling techniques. Meteorological, clima-
tological, and source emissions data bases are avail-
able in various formats as input to the modeling. The
system is designed to provide air quality estimates at
three spatial scales, independently, in a manner that
enables successively coarser scales to be treated as
background. The statistical model enables us to ad-
dress the air quality problem directly in terms of the
ambient air quality standards over appropriate averag-
ing times.
The modular, multifaceted nature of our system
allows us to deal effectively with a variety of appli-
cations at appropriate levels of time and cost with
our own in-house resources or in collaboration with
outside agencies or individuals. We feel that exist-
ing techniques, judiciously employed, enable us to
provide useful input to decisionmaking in virtually
all of our air quality problem areas.
Figure 2 illustrates photochemical modeling out-
put within the regional scale domain in Figure 1. The
model LIRAQ-21 estimates concentrations of ozone, ni-
trogen oxides, hydrocarbons, and carbon monoxide at a
regional resolution of 25 km^. Finer resolutions of
4 km2 and 1 knr are available for subregional analysis
and a less complex version of the model, LIRAQ-1, is
available for nonreactive analysis alone. The model
accounts for the perturbed airflow through complex
terrain providing a field of concentrations hour by
hour or a time history at selected points based on
emissions and meteorological data input chronologi-
cally. The principal use of this model will be in the
evaluation of regionwide planning or regulatory alter-
natives. The frequency of model application, using a
CDC 7600 computer, is somewhat limited by cost.
For the purpose of local scale analysis, the Dis-
trict has developed a gaussian model, BAYMOD.^ This
model provides annual average concentration estimates
for nonreactive pollutants over a 690 km? local area
at a resolution of 1 km?. Annual average emissions
and wind speed data are input as a 690 element (30x23)
grid of 1 km squares. A local wind rose is utilized
for annual weighted average transport from upwind grid
squares treated as point sources. Concentrations from
sources within the same grid square are calculated as
an integrated line source average. The model may be
made to treat local sources alone or to include
county-scale regional background through use of a box
model in conjunction with transport by regional wind
patterns. Larsen's statistical model is used in con-
junction with historical monitoring data to relate an-
nual averages to averaging times associated with air
quality standards.3 BAYMOD is run routinely on the
District's in-house Hewlett-Packard 3000 minicomputer.
Typical applications are air quality analysis of local
plan alternatives and the estimation of pollutant
background concentration for use with more localized
analyses. Individual local analyses may be assembled
in mosaic form to provide larger regional coverage at
fine (1 km2) resolution. Figure 3 is sample output
from BAYMOD in the vicinity of the city of Santa
Rosa, within the local scale domain in Figure 1.
10 11 II IJ 14 15 16 1' IB 19 1U it 1
//// xxxx
//// 0.60 - 0.74 XXXX 2.00 - 2.49
//// XXXX
0.75 - 0.99 **«* 2.50 - 2.99
III!
MM 1.00 - 1.49
_ CARBON MONOXIDE (PARTS PER MILLION)
ANNUAL AVERAGE l KM RESOLUTION
SANTA ROSA AREA 1973
MODEL: BAYMOD (GAUSSIAN)
Figure 2. Estimated Distribution of Ozone Concentra-
tions at 1400 PST, 26 July 1973 by LIRAQ-2 Regional
Photochemical Model. Concentration Units Are Parts
Per Million With an Isopleth Spacing of 0.02 PPM.
Figure 3. Estimated Distribution of Carbon Monoxide
Concentration (Annual Average) in the Vicinity of
Santa Rosa, California, by the BAYMOD Regional Gaussian
Model.
The final module in the District system is at the
project/element scale. Standard gaussian, single and
multiple point, and line source techniques are em-
ployed to estimate the air quality impact of stacks,
roads, housing developments, shopping centers, air-
ports, and a variety of other projects and project
37
-------
source elements, as illustrated by Figure 4. Princi-
pal applications are for permit review, variance hear-
ings, and the review of environmental impact reports.
Modeling is done using either computerized codes de-
veloped in-house or by manual or nomographic methods,
depending on the scope and time frame of the analysis.
To fill a large number of requests for assistance in
project-level air quality analyses by non-District in-
dividuals and agencies, the District has prepared a
comprehensive set of guidelines involving manual tech-
niques in "cookbook" format.4 The popularity of this
publication is indicative of an existing need for user
assistance.
Figure 4. Illustration of a Typical Setting for Mod-
eling Application on the Project/Element Scale.
Simplifications, Assumptions, and Parameterizations
Perhaps one of the greatest drawbacks to effec-
tive model application is the esoteric nature of many
techniques. There is an allure associated with so-
phistication perpetuated by the aesthetic appeal of
complex technology and by an intuitive feeling that
complex problems can be solved only by complex
methods. As a general rule, we feel that sophistica-
tion should be sought only when there is true com-
plexity in the nature of the problem solution and when
the quality of the input data is commensurate with the
requirements of the model. The photochemical process
will normally require modeling complexity while non-
reactive modeling is amenable to considerable simpli-
fication. The principal benefit to simplicity, aside
from cost, is the increased breadth of application
through frequent and multiple use. If the outputs of
various models are compared in the context of the in-
formation required, the merits of simplification may
be readily assessed.
Frequently, the modeling process can be simpli-
fied through proper definition of the problem and ap-
propriate parameterization of the modeling scheme.
For example, in assessing carbon monoxide levels in a
local area, we might initially consider a model which
would provide point values of concentration at multi-
ple locations and at discrete time intervals. With
such a model we could then evaluate the highest point
concentration in the area during the period of peak
traffic flow under the most adverse meteorological
conditions. If, however, we determined that point
values were not of interest in our study area due to
spatial mobility of receptors (people), more appro-
priate spatial averages might be obtained by a far
simpler and less costly approach.
An argument against the application of simplified
techniques in air quality regulatory situations is
based on the premise that the social and economic con-
sequences of such decisions are too important to be
based upon analyses exhibiting less than state-of-the-
art accuracy and precision. While the premise is un-
doubtedly correct, care must be taken to avoid a
never-ending search for the perfect model. Simplifi-
cation is consistent with the premise if "state-of-
the-art" is defined to include considerations of data
base condition, problem definition, and required in-
formation, in addition to the conceptual and algorith-
mic structure of the analysis scheme itself. When the
choice of model includes such considerations, useful
estimates can frequently be made with available tech-
niques at minimal cost. The District makes liberal
use of such techniques and recommends them to others
for a wide range of applications. Our efforts in this
regard have resulted, we feel, in a greatly increased
willingness to include air quality considerations
among the many factors normally involved in land use
and other decisions.
Monitoring, Modeling, and Regulatory Relationships
Historically, disparate motivations have in-
fluenced the formulation of air quality regulations,
the setting of air quality standards, the establish-
ment of air monitoring programs, and the development
of air quality models. Regulations have normally been
source-oriented, focusing on equipment or performance
characteristics with a view toward, ease of enforce-
ment. Air quality standards are receptor-oriented
focusing on time-averaged ambient concentrations re-
latable to effects on health or welfare. Air monitor-
ing has been site-oriented with a view toward repre-
sentative sampling under economic and facility con-
straints, and finally, model development has been
guided by computations technology under data con-
straints.
In complying with the comprehensive requirements
of Clean Air Act legislation, efforts in modeling,
monitoring, and regulation should ideally be inte-
grated in a compatible and complementary systems ap-
proach to air quality analysis. While complete com-
patibility may never be achieved, many improvements
are possible over the present conditions. In the in-
terest of such improvements, we offer the following
comments:
1. Spatial averaging should be incorporated
wherever possible in the definition and interpretation
of air quality standards as well as monitoring
38
-------
programs. Thus, for example, the standard for pollut-
ant X might be defined as Y parts per million as a
spatial average over Z square kilometers. Similarily,
air monitoring using statistical/mobile techniques
might provide estimates of existing air quality as a
spatial average on the same scale. An appropriate
spatial definition would accommodate the resolution
limitations of modeling input as well as the spatial
mobility of human receptors over the averaging times
inherent in the dosage-oriented air quality standards.
In addition, modeling output could be compared, for
validation, with air .monitoring data on a compatible
spatial scale.
2. Modeling should be incorporated in source
performance regulations to achieve consistency between
emission limitation and desired air quality. Thus, a
regulation might limit source emissions to a rate
which, on the basis of a given dispersion algorithm,
would maintain ground-level concentrations at a speci-
fied level.
3. Air monitoring should be performed at places
other than the traditional downtown urban locations to
better define regional gradients. Data from nonurban
sites would facilitate the validation of modeling
techniques and would provide needed information on
background levels of pollutants from natural sources.
Conclusions and Recommendations
Our experience has convinced us that air quality
modeling is a very useful tool for air quality regula-
tion and planning. Specifically, modeling has given
us a consistent rationale for decisionmaking and en-
abled us to provide technically-supportable solutions
to a great variety of problems. We feel that under
the guidance of appropriate expertise and with suffi-
cient ingenuity, very simple techniques can be applied
effectively at minimal cost. We realize that air
quality problems and appropriate modeling techniques
often substantially differ from region to region, and
for that reason, no single technique or set of tech-
niques can be applied universally, with success. We
feel, however, that the store of existing techniques
is flexible enough to provide useful solutions to air
quality problems in almost any set of circumstances.
Finally, we feel that, notwithstanding the demon-
strable limitations of modeling technology, decisions
based on modeling results, professionally interpreted,
will better serve the interests of air quality than
those based on intuition alone.
We highly recommend that the framework for a com-
prehensive and standardized program of model applica-
tion be established in each region with existing or
potential air quality problems. A small interdisci-
plinary staff dedicated to the task of regional model-
ing can provide appropriate guidance for the solution
of air quality problems and the efficient utilization
of resources. In the interest of establishing such
regional capabilities,we would suggest that considera-
tion be given to state and Federal encouragement as
well as funding. Our own experience in this regard
has been very positive, and we have welcomed the op-
portunity of sharing our feelings and ideas at this
conference.
References
1. MacCracken, M.C. and G.D. Sauter, Eds., Develop-
ment of an Air Pollution Model for the San
Francisco Bay Area, Final Report to the National
Science Foundation, Lawrence Livermore Labora-
tory, Livermore, California, Vol. 1, 221 p., 1975.
2. Thuiller, R.H., A Regional Air Pollution Modeling
System for Practical Application in Land Use Plan-
ning Studies, Bay Area Air Pollution Control Dis-
trict, Information Bulletin 5-17-76, 22 pp., 1973.
3. , Air Quality Statistics in Land Use
Planning Applications, Preprints, Third Conference
on Probability and Statistics in Atmospheric
Sciences, Boulder, Colorado, June 1973, pp. 139-
144, 1973.
4. Bay Area Air Pollution Control District, Guide-
lines for Air Quality Impact Analysis of Projects.
BAAPCD Information Bulletin 6-01-75, 1975.
39
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SPACE: A CLOSER LOOK AT THE IMPACT OF ENVIRONMENTAL POLICY
Ernest Heilberg
Chase, Rosen § Wallace, Inc.,
Alexandria, Virginia
Abstract
The Spatial Pollution Analysis §
Comparative Evaluation (SPACE) System is a
computer-based model system designed to
indicate the impact of local policy deci-
sions on the environmental quality within
metropolitan areas. This system was deve-
loped as an adjunct to the Strategic
Environmental Analysis System (SEAS) and
relies heavily on data produced by SEAS.
Major features of SPACE include:
1. The determination of net emissions
and ambient levels of pollution resolved to
a grid system covering the analyzed region.
2. The ability to introduce a broad
variety of local environment-related policy
changes.
Introduction
Contrary to what the acronym may at
first suggest, the SPACE System deals with
matters very close at hand pollution within
metropolitan areas. The actual name, The
Spatial Pollution Analysis and Comparative
Evaluation System, was intended to point out
that the system is concerned with the spatial
distribution of pollution, rather than just
cumulative or average values for the region
considered. This is the concept of "space"
you should associate with this system.
There are several important aspects of
the SPACE System which are not indicated by
the name. First, as suggested before, the
"space" in question is that within a metro-
politan area, specifically an SMSA (Standard
Metropolitan Statistical Area). Second, the
system has been designed to be sensitive to a
broad range of local environment-related poli-
cies. Finally, the system has been developed
as an extention of SEAS (the Strategic En-
vironmental Assessment System).1 All of
these features will be discussed in more
detail later.
Putting these features together, the in-
tended applications of SPACE should begin to
become apparent. The SPACE model system is
essentially a planning tool, for use by both
national and local planners, in screening en-
vironment-related policy options. Three spe-
cific categories of application were con-
sidered during the system design efforts:
1) Use by local planners to compare the
relative effectiveness and efficiency
of local environmental quality im-
provement plans.
2) Use by EPA planners (in conjunction
with SEAS) to determine the impact
of national policies on metropolitan
areas.
3) Use by EPA planners, in their de-
velopment of guidelines for local
planners, to compare the effects of
specific local policies on various
types of metropolitan areas.
To provide for these applications, SPACE
was designed to consider a broad range 'of po-
licies as well as a variety of impacts of
such policies. As a result, SPACE can be
used as a policy screening tool with appli-
cations far beyond those initially intended,
e.g. inclusion of an energy submodel would
permit studies involving both pollution and
energy policies. Some of the other possible
applications will be alluded to later.
Background
Before proceeding with the discussion of
SPACE, it will be useful to review SEAS,
especially those elements of SEAS which are
most pertinent to SPACE. SEAS is a large,
complex collection of forecasting models
which relate the national economy to the
generation of pollution residuals and the
associated costs of pollution control. It
provides a framework within which a
decision-maker can assess the impact of
alternative national policies related to the
economy and the environment.
SEAS is driven by a Leontief-type econo-
mic (input-output) model which forecasts the
expected levels of the various economic sec-
tors in the U.S. over a 15 year period. These
projections are converted to pollution fore-
casts, by considering the technologies in-
volved for operation, production and abate-
ment. The economic and pollution forecasts
are then disaggregated to various sub-regions
of the nation, e.g. states, SMSA's, etc.,
by considering the relative characteristics
of the subregions. To insure completeness,
pollution sources not directly related to the
economic sectors (e.g. related to households
and transportation) are introduced at the
disaggregated levels and aggregated upwards.
Using SEAS it is thus possible to esti-
mate the amount of the various pollution re-
siduals that can be expected to be generated
nationwide or within specified sub-regions of
the nation, and to note the possible changes
in these estimates that result from imple-
menting various national policies. It should
be obvious that the results obtained are most
meaningful when considering the nation as a
whole or the larger subregions. As consider-
ation turns to the smaller sub-regions, e.g.
SMSA's, local policy decisions can be ex-
pected to have a significant impact not
reflected in the SEAS analysis.
40
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The desire to provide for the more
meaningful use of the disaggregated pro-
jections led to the conception of the SPACE
System. To demonstrate the feasibility of
this concept, the Washington Environmental
Research Center of EPA let a contract to
Chase, Rosen § Wallace, Inc. (CRW)' and Alan
M. Voorhees § Assoc., Inc. (AMV) to develop
the SPACE Test System. It is this test sys-
tem, completed in mid-1975, that is the sub-
ject of this presentation.
SPACE System Applications
SPACE is a working system which can be
of value in problem solving. Its main
utility is as a tool in comparing the rela-
tive impact of various local policy options
on pollution in a metropolitan area. Thus,
for a locality attempting to meet specific
environmental goals, SPACE could be useful
in screening policy alternatives.
The policy alternatives that can be
treated are essentially unconstrained by
the SPACE System. These include: (1) di-
rect pollution control programs, such as
improving the capacity and/or quality of
solid waste management systems or water
treatment systems, setting stricter emis-
sion standards for factories or motor
vehicles; (2) land use controls, such as
zoning, limiting emissions in specific
locations, designating open land, select-
ing specific sites for major facilities
(e.g. airport, sports arena, etc.);
(3) auto use deterrents, such as establish-
ing auto free zones, designating special
bus and car pool lanes, improving mass
transit, increasing fuel and parking costs;
and (4) other indirect means, such as pro-
viding economic incentives for private
emission control actions, establishing con-
straints on use of specific fuel types.
This listing is by no means exhaustive; but
rather, illustrates the broad range of pos-
sible considerations.
The metropolitan areas that can be
considered are limited only by the availa-
bility of data. As will be discussed later,
EPA has taken steps that should ultimately
eliminate this limitation. With data avail-
able for sufficient SMSA's, it will be pos-
sible for EPA to determine the differing
impact of specific policies on different
types of cities. Guidance provided by EPA
to local planners could thus be tailored to
the specific locality.
By design, SPACE measures the impact
of policy options in terms of pollution.
In the process of making such determina-
tions, the system becomes involved in ana-
lyses related to local economic activity,
land use, transportation, and energy. With
minor modifications, mainly related to the
massaging and display of intermediate
results, the possible applications of
SPACE can be extended to include the mea-
surement of policy impact in a variety of
forms. For example, SPACE could indicate
the trade-off between pollution generated
and fuel consumed resulting from policies •
that encourage or discourage use of specific
fuels; or it could indicate the inability
of the region to meet the SEAS economic pro-
jections as a result of policies constrain-
ing factory emissions. The combination of
the wide range of policies that can be
treated and the variety of impact measures
possible, results in a highly flexible model
for local policy screening.
SPACE System Overview
The metropolitan area under study is
initially a flat, relatively empty rectangu-
lar grid system. It contains rivers, high-
ways, railroad tracks, but little else. For
each analysis year the SEAS projections in-
dicate the amount of residential, industrial,
commercial, and other developments that are
expected to exist in the region. These
are distributed over the grid system by
considering the attractions and constraints
associated with individual grid squares,
the features of neighboring grid squares,
and the historical land use patterns. This
distribution is intended to be represen-
tative, not predictive. Each activity
thus located becomes a single stationary
pollution source.
In addition to any pollution generated
directly by these activities, each activity
has the potential of attracting pollution
through the motor vehicles that come to or
leave its facilities. These mobile pollution
sources are given location in the grid system
by associating trip ends directly with the
located activities and by distributing the
trip routes over the implied transportation
network.
With both stationary and mobile pollu-
tion sources located, gross pollution gener-
ated in each grid square is determined, based
on size and type of each source. The actual
pollution emitted to the environment is next
determined by considering two types of pollu-
tion modification transformation and trans-
portation.
Pollution transformation generally in-
volves some technological process for con-
verting the polluting substances into other
substances. These other substances may also
be considered pollution, as in the case of
burning solid waste to produce a smaller
volume of ash plus air pollution. Some of
the new substances may, however, be useful
materials, as in the conversion of some
solid waste to fertilizer.
Pollution transportation refers to the
physical movement of the residuals from one
location to another, generally with no sig-
nificant change in the substances transport-
ed. This includes the piping of sewage
waste to treatment plants and the hauling of
solid waste to land fills and incinerators.
At their destination this transported pollu-
tion may be transformed.
The transportation of pollution resid-
uals to activities which may in turn trans-
form them introduces a special concept.
Each category of activity is designated as
being either "exogenous" or "endogenous".
41
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Exogenous activities are those whose
operating levels are determined external
to the region, e.g. steel mills operate at
levels determined by national and inter-
national demands. Endogenous activities,
on the other hand, are those whose operat-
ing levels are determined within the
region, e.g. water treatment plants. This
distinction is important, as the pollution
generated is more a function of the operat-
ing level than the actual size of the
activities.
The operating levels of endogenous
activities are taken to be proportional to
the demands placed on them by other acti-
vities in the region, both exogenous and
endogenous. In SPACE these demands are
measured in terms of the pollution trans-
ported to the endogenous activities. Not
all endogenous activities can be character-
ized as receiving and processing pollution
residuals, however. Thus, for electric
power generating stations, and other such
endogenous activities, dummy pollutants must
be defined. These dummy pollutants are
simply the demands, e.g. electric power de-
mand. Like actual transported pollutants,
these dummy pollutants are used primarily to
determine the operating level of the receiv-
ing activities.
Through these various considerations,
net pollution emitted in each grid square is
determined. The final consideration in SPACE
is the possible dispersion of the emitted
residuals in air or water. This yields
ambient levels of the residuals in each grid
square.
As suggested by the foregoing discus-
sion, SPACE, starting with an empty region
grid for each analysis year, essentially
creates a snapshot of the region for an
average day during the year. This does not,
however, mean that each year is analyzed in-
dependently. The carryover from one ana-
lysis year to the next is provided for in
three ways. First, the data obtained from
SEAS already reflects the impact of time on
such items as economic productivity and
growth, technological advances, population
growth, changes in demand for industrial
output, etc. Second, user designated policy
changes remain in effect unless again
changed. In particular, auto emission stan-
dards specified for- one year, influence auto
emissions for cars of that model year when
analyzing subsequent years. Finally, land
use patterns determined for one analysis
year are a major consideration in specific
activity location in subsequent analysis
years. This approach in considering changes
over time is most meaningful if the interval
between analysis years is at least 3 years,
and preferably 5 years or more.
SPACE System Structure
SPACE was originally conceived as a
patchwork of existing models and data bases.
It was not possible to strictly adhere to
this concept, however, since existing ele-
ments were not always sufficiently com-
patible. As an alternative, the system was
designed in modular form with usable exist-
ing elements adapted as modules and missing
links developed specifically for the test
version of SPACE. This design provides for
relatively easy replacement of components
as better models or data files become avail-
able.
The resulting modular system can be con-
sidered to consist of 13 components. Each of
these will be discussed briefly.
SEAS Files
Reference has already been made to the
use of SEAS data as the basis for SPACE anal-
yses. Although much of the SEAS data is used
in some form, two SEAS files are read direct-
ly by SPACE. These are the disaggregated
economic projections and the pollution resi-
dual coefficients for the various economic
sectors. The residual coefficients are esti-
mates of pollution produced per unit of the
activity, reflecting operating and/or pro-
duction processes used, and, optionally,
abatement processes used.
Modal City Files
The Modal City Files refer to the col-
lection of data required as input to SPACE to
describe the specific SMSA's being analyzed.
Lest the idea of developing such files for
each application scare off potential users,
the original design of SPACE included the
concept of Modal Cities (or Modal Regions).
This concept envisions the development of a
typology for the SMSA's, such that a small
number of (actual or composite) SMSA's would
be used to represent all SMSA's. These
representative SMSA's would constitute the
Modal Cities. A Modal City File would then
be developed for each, and made part of the
SPACE System. Efforts towards this end have
been initiated recently, through an EPA con-
tract with Urban Systems Research § Engi-
neering, Inc. Currently SPACE contains only
a single Modal City File, developed speci-
fically for the test system.
Permanent Data Piles
The major portion of the remaining in-
puts for SPACE will be referred to as the
Permanent Data Files. These include data
reflecting generalized behavior patterns,
national averages, etc. Perhaps the most
important items in these files are the des-
criptions of the economic sectors, including
employment information, area requirements,
etc. Other important data included in these
files are pollution transformation factors
and auto emissions standards.
MSPACB
The main program for the SPACE model is
referred to as MSPACE. Its functions are to
read the input data files, create a working
data base, sequence the analysis through the
designated analysis years, sequence the exe-
cution of assessment modules for each analy-
sis year and create history files for pos-
sible future use. The design of this program
is such as to permit relatively independent
42
-------
design and operation of the other component
modules.
OVRIDE
A major design feature of SPACE is the
means for introducing environment related
policy. Subroutine OVRIDE serves this func-
tion. At the start of each analysis year,
following the automatic updating of the
working data base, SPACE allows the user
to specify a broad spectrum of modifica-
tions reflecting new policies. These range
from simple speed limit changes to more com-
plex land use constraints.
Activity Allocation
The first of the major submodels exe-
cuted each analysis year is the activity
allocation module. This submodel distributes
units of the various activities (population,
specific industries, commercial activities,
etc.) among the grid squares of the region.
In dispersing a given activity an attrac-
tiveness index, relative to that type of
activity, is calculated for each grid square.
Within the constraints of minimum activity
size, available land, and local policy, each
activity is distributed in proportion to the
size of the index. The total number of units
distributed is essentially that implied by
the SEAS projections. Where the minimum
size is relatively small in comparison to
total sector size, as in the case of housing,
the resulting allocation will be highly dis-
persed. Where the minimum size is large,
such as with heavy industry, the allocation
will be more concentrated.
The attractiveness indices, which are
the major bases for the allocation process,
consider a wide range of grid square cha-
racteristics. These include accessibility,
historical land use, distance from the
central business district, the proximity
of related activities and, if pertinent,
the proximity of an employment base. The
importance assigned each such attraction
factor is varied with the type of activity
being allocated.
Transportation
The transportation module operates di-
rectly on the results of the activity allo-
cation module. Associated with each located
activity are a number of trip ends, based on
the activity type and size. These trip ends
include those for work trips, business trips,
shopping and recreation trips, freight pick-
up and delivery, etc. The trips associated
with each pair of trip ends are then catego-
rized by type auto, bus, rail transit, etc.
through consideration of the local modal
split. This modal split is determined from
existing facilities, established patterns
and local policies which encourage or dis-
courage use of specific modes.
The trips themselves, specifically the
vehicle miles traveled (VMT), are then dis-
tributed over the grid squares in a manner
similar to the distribution of activities.
Grid square attractiveness for trip miles is
based on facilities available in the grid
square (e.g. highway lane-miles, bus seat-
miles, etc.), plus the number of trip ends
located in or adjacent to the grid square.
Finally the transportation module determines
the average vehicle speeds in each grid
square by considering legal speed limits and
congestion implied by the ratio of the VMT
distribution to highway capacity.
Pollution
The SPACE pollution module has been
built around the Georgetown University IMMP
Model. Its main function is to convert data
in the SPACE data base so as to be compatible
with IMMP input requirements. This module
controls the execution of IMMP, but the IMMP
model, as modified, for SPACE, controls the
execution of other submodels within the
pollution module.
IMMP
The IMMP Model primarily takes care of
the pollution analysis and accounting, in-
cluding the considerations of pollution
transformation, transportation and dis-
persion. In addition it determines the
operating levels of the endogenous activi-
ties. Some modifications have been made to
the IMMP program for its use in SPACE. These
primarily involve the use of IMMP to control
the execution of other components, specific-
ally MOBILE, STORM and MAPS.
The only significant modification made
to the analysis in IMMP relates to the de-
termination of net pollution emissions by
endogenous activities. The basic IMMP Model
treats such emissions as being directly pro-
portional to the operating level of the acti-
vity. As modified for SPACE, the net emis-
sions from endogenous activities also reflect
the mix of pollutant residuals received.
MOBILE
Subroutine MOBILE was developed to
compliment IMMP, since the basic IMMP Model
is limited in its ability to treat mobile
pollution source emissions. This routine
determines net emissions from motor vehicles
in each grid square, and then passes the
results to IMMP for inclusion in grid square
totals. MOBILE considers both trip end and
running emissions. It considers the mix of
vehicle types, fuels used and average speeds.
It further reflects emission standards and
age distributions of the vehicles, which
affect emission control quality.
STORM
One source of water pollution, not
reflected in the other components dis-
cussed is the runoff from rain or melting
snow. Since other analyses in SPACE re-
flect an average day during each analysis
year, direct integration of this type pol-
lution would not be meaningful. To handle
this consideration, the Corps of Engineers'
STORM Model3 was adapted. This model analy-
zes the precipitation history in a region
for a full year. It isolates precipitation/
runoff events and determines the pollution
content of the runoff for each event. It
43
-------
further considers treatment of the runoff
(in a quantitative sense only) and possible
storage and overflow of runoff awaiting
treatment.
For purposes of SPACE analyses, STORM
has been modified to isolate the results for
an average rain day and a worst rain day.
The levels of overflow and treatment thus
determined are passed back to IMMP as amounts
of pollution residuals dumped directly into
streams and amounts transported to water
treatment plants, respectively.
To accommodate this use of STORM, IMMP
was further modified. IMMP now determines
the remaining capacity of the water treat-
ment plants, which it passes to STORM. Upon
receiving the results of the STORM analysis,
IMMP produces three sets of water pollution
results one for an average dry day, one
for an average rain day and one for a worst
rain day.
MAPS
The output formats incorporated in the
basic IMMP and STORM models were not felt
to adequately meet the needs of SPACE System
users. As a result a general purpose rou-
tine was developed to produce rectangular
grid displays, showing appropriate data for
each grid square in the region. This rou-
tine, referred to as MAPS, is used to dis-
play a wide variety of SPACE output, includ-
ing the net emissions and ambient levels of
individual pollution residuals in each grid
square.
History Files
The last of the major SPACE System com-
ponents are the History Files. Following
the analysis for each year, the working data
base is copied to a semi-permanent History
File. This feature allows the user to effi-
ciently analyze variations of previous runs.
Thus following a run involving 5 analysis
years, the user may desire to rerun the
situation with specific policy modifications
introduced at the start of the third analysis
year. This would be accomplished by using
the History File created at the end of the
second year to recreate the data base as it
existed. The policy modifications would
then be entered, and SPACE would be executed
for only the last three analysis years.
SPACE Run Preparation
The mechanics of actually using the
SPACE System can be very simple or relatively
complex, depending on the degree of complex-
ity associated with the policy options to be
analyzed. Because of the variety of perma-
nent files incorporated in the system, the
use of SEAS Files and the anticipated exis-
tence of the Modal City Files, required user
input, other than policy descriptions, is
minimal. These include designation of ana-
lysis years, the Modal City File to be used
and, if pertinent, the History File to be
used for restart runs.
User specified policies are entered by
modifying data in the working data base.
The complexity involved in entering such
policies is somewhat reduced by using a
variable format approach for designating
modifications. Thus, the user need only be
concerned with the specific items to be
changed. It is in the determination of
items to be changed and, to a lesser degree,
the new values to be introduced that the
complexities arise. The test system has
been designed to give the user maximum free-
dom in selecting policies to be analyzed.
Thus there is no shopping list of options
for the user to select from. Rather there
is a list of factors that can be changed,
e.g. speed limits, auto emission stan-
dards, abatement process effectiveness, etc.
The user must translate his policy choice
into value changes for one or more of the
factors.
The various computer files that con-
stitute the SPACE Test System all exist on
a single EPA disk volume located at the
Optimum Systems, Inc. (OSI) facility in
Rockville, Maryland. To further aid users
in run preparation, all pertinent files, in-
cluding sample JCL instructions, have been
stored so as to permit data input and job
execution from remote terminals using the
WYLBUR language. A draft users guide4 for
the test system is available for those de-
siring more details on this aspect of the
system.
Summary
This, then, is the SPACE System a
collection of computer models and data
bases capable of further disaggregating the
determinations from SEAS, in such a way as
to allow analysis of the impact on SMSA's of
various local policies. It is a highly
flexible system which, although intended
primarily for the study of environmental
pollution, can be used to study a variety
of environment-related phenomena.
References
U.S. Environmental Protection Agency,
"Strategic Environmental Assessment
System," Draft Report, Washington, D.C.,
December 16, 1975.
Paik, Inja K., et al., "The Integrated
Multi-Media Pollution Model,"
EPA-600/5-74-020, Office of Research
and Development, U.S. Environmental
Protection Agency, Washington, D.C.,
February 1974.
The Hydrologic Engineering Center,
"Urban Storm Water Runoff STORM,"
Draft 723-S8-L2520, U.S. Army Corps of
Engineers, Davis, California,
October 1974.
Chase, Rosen § Wallace, Inc., "Spatial
Pollution Analysis and Comparative
Evaluation (SPACE) System Users' and
Operators' Guide," Draft Report,
Alexandria, Virginia, July 1975.
44
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RIBAM, A GENERALIZED MODEL FOR
RIVER BASIN WATER QUALITY MANAGEMENT PLANNING
Richard N. Marshall, Stanley G. Chamberlain, Charles V. Beckers, Jr.
Environmental Systems Analysis
Oceanographic & Environmental Services
Raytheon Company
Portsmouth, Rhode Island
ABSTRACT
To meet water quality objectives in streams
and rivers, a need arises for systematic
analysis of alternative pollution abatement
strategies. The computerized mathematical
model, RIBAM (River BAsin Model), predicts
water quality for 17 constituents, including
DO, carbonaceous BOD, and parameters that
represent nitrification and photosynthetic
processes. Predicted water quality profiles
throughout the basin for varying sets of
waste loads and flow regimes can be compared
with each other and with desired water
quality goals. RIBAM is suited for determin-
ing the waste load allocations necessary
for achieving water quality standards in
rivers. A unique calibration method, based
on open-channel hydraulic equations, for an
exponential relationship between stream
velocity and flow is presented.
The basic assumptions of RIBAM are that
steady-state conditions exist and that the
concentrations of water quality parameters
are well mixed, varying only in the longitud-
inal direction of the stream. The applica-
tion of RIBAM to the Beaver River Basin,
including the Mahoning River, in Ohio and
Pennsylvania is discussed.
BACKGROUND
RIBAM was developed by Raytheon Company
under a project sponsored by the US Environ-
mental Protection Agency to provide a veri-
fied, computerized mathematical model of the
water quality in selected portions of the
Beaver River Basin. RIBAM is a major modifi-
cation of the DOSAG model.1 In most cases,
predicted values of water quality parameters
at several Basin locations agreed with
previously measured values during three simu-
lated time periods.
RIBAM can be used by EPA, state and local
agencies, and consulting firms for basin-
wide water quality planning, in accordance
with PL 92-500, the Federal Water Pollution
Control Act Amendments of 1972. Raytheon
held a model training seminar for the rele-
vant agencies in Ohio. RIBAM is presently
being used by the EPA Region V Michigan-Ohio
District Field Office in Cleveland in an on-
going project to determine waste load con-
ditions that most favorably meet water
quality objectives in the Mahoning River,
Ohio.
MODEL ASSUMPTIONS
In RIBAM, it is assumed that steady-state
consitions exist in which the basin condit-
ions are invariant with time. The basin
conditions include the various effluent
waste loads, stream flow, velocity, depth,
and the model parameters, such as reaction
rates and coefficients. Basin conditions
can vary spatially, but only along the longi-
tudinal direction of the stream. The water
quality constituents modeled in RIBAM are
assumed to have uniform values throughout
any cross section of the stream at any given
basin location.
BASIN NETWORK
RIBAM analyzes a river basin as a network
consisting of the following four basic
components:
Junction- confluence between two
streams within the river basin.
Stretches - length of river between two
junctions.
Headwater Stretches - length of river
from a headwater to its first junction
with another stretch (either headwater
or normal).
Segments or Reaches - subunits of
length that comprise a stretch
(either headwater or normal).
In RIBAM, segments are defined such that the
model parameters are assumed to be invariant
throughout the length of the entire segment.
At the head of each segment, new values of
model parameters can be defined and addition-
al flows and waste loads may enter the
stream. Figure 1 demonstrates the modeling
network for the RIBAM application to the
Beaver River Basin.
SOLUTION TYPES IN RIBAM
The in-stream reactions that effect the con-
centrations of the 17 water quality parame-
ters in RIBAM are represented by differen^
tial equations.
All of the differential equations have
analytical solutions, which are computed in
a piecewise continuous manner along the en-
tire length of the river basin network. More
specifically, a mass balance is computed as
additional flows and waste loads enter the
stream at the head of a segment. The solu-
tion for concentration of each water quality
parameter is then computed for the length of
the segment. The concentration at the down-
stream end of the segment is then an input
to the mass balance at the head of the next
down-stream segment.
45
-------
Figure 1. RIBAM Segmentation Network for
Beaver River Basin
The differential equations and analytical
solutions of the water quality parameters
can be categorized into three types:
conservative
non-conservative, non-coupled
non-conservative, coupled
The conservative solution defines the concen-
tration of the water quality parameter as
being constant throughout the segment. The
conservative equation is:
dC _
3t ~
where C
(1)
concentration of water
quality parameter (usually
mg/1)
t = time (days)
The conservative solution is:
C(t) = C
(2)
where CQ is concentration at the head
of the segment after the mass balance
is computed (i.e., at time equal to
zero) and t is time of travel through
the segment.
The conservative parameters, or those param-
eters whose concentrations are defined by
the conservative solution, are:
Sulfates
Manganese
Iron
Total Nitrogen
Dissolved Solids
Lead
Chlorides
In RIBAM, the mass exchange at the head of a
segment is categorized according to three
source types; 1) tributary sources, 2)
municipal sources (discharge of treated
municipal sewage), and 3) industrial sources.
For each source type and each segment, the
RIBAM user may select one flow value and one
concentration value for each water quality
parameter. If multiple sources of a single
type are located at a segment head, flow and
concentration must be combined externally
for use in RIBAM. Tributary and municipal
source types are similar because they repre-
sent flow and mass additions to the system.
They are distinguished mainly to facilitate
easier model use and interpretation of
results. The tributary source type can be
used to represent a withdrawal, by specifying
a negative flow value. The industrial source
type represents the mass added to water that
is circulated through a facility for use in
its industrial processing. The mass balance
equation is:
VQ1+Q2
where:
Q = stream flow entering from the
s upstream reach (cfs)
flow added by tributary sources
(cfs)
flow added by municipal wastewater
sources (cfs)
Q,
1
Q-
Q,
flow passing through industrial
sources (cfs)
C = concentration of parameter at
s downstream end of the upstream
segment (usually mg/1)
C, = concentration of parameter in
tributary streams (usually mg/1)
C2 = concentration of parameter in
municipal wastewater sources
(usually mg/1)
C., = net change in concentration
between intake and discharge of
industrial process water
(usually mg/1)
The equation for the non-conservative, non-
coupled solution is :
dC
-KG
(4)
where K is the reaction rate of the
constituent.
The solution to equation (4) is:
C(t) = CQe "Kt
(5)
In RIBAM, the following constituents are
defined by the non-conservative, non-coupled
solution:
Phosphorous
Ammonia Nitrogen
Cyanides
Phenols
Carbonaceous BOD
Coliforms
The non-conservative, coupled parameter
equation links the constituent in concern
with one or more other constituents. A
unique equation and analytical solution
exists for each of the following coupled
parameters:
Nitrite Nitrogen
Nitrate Nitrogen
Chlorophyll a
Dissolved Oxygen (DO)
46
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The relationships among constituents for the
coupled parameters is shown in Table 1.
TABLE 1. RELATIONSHIPS AMONG COUPLED
PARAMETERS
for simulations using the calibrated model
parameter values for one or more previously
observed time periods.
K1VCB DIM* MUM UULTJI1- IIMUST
HONING BlVtft UCHOH Of MirtH BlytD
«,OT ro* o.o,
COUPLED PARAMETER
COUPLED TO
Nitrite Nitrogen
Ammonia Nitrogen
Nitrate Nitrogen
Nitrite Nitrogen
Ammonia Nitrogen
Chlorophyll a
Phosphorous
Nitrate Nitrogen
Nitrite Nitrogen
Ammonia Nitrogen
Dissolved Oxygen
Iron
Nitrite Nitrogen
Ammonia Nitrogen
Carbonaceous BOD
Chlorophyll a
The mathematical relationships among coupled
parameters represent the natural processes
of nitrification, bacterial oxidation of
organic material, and photosynthesis. The
equation for DO also includes terms for
reaeration and benthic demand. Reference 2
presents the mathematical form for each
coupled parameter.
The reaeration coefficient, K.,y, may be
specified for each reach, or it may be
computed by:
K
17
A*VB
(6)
D
where V = stream velocity (fps)
D = stream depth (feet)
and A, B, and C are coefficient values,
which have been determined for previous
field studies3. RIBAM also predicts
reaeration at dams2.
CALIBRATION OF THE MODEL
In simulating water quality in a river basin
for a previously observed time period, the
predicted values of the model are compared
with measured values. The model is cali-
brated to the river basin when agreement is
attained between predicted and measured
values.
Each reach of the stream has a unique set of
model parameters, reaction rates and co-
efficient values, that affect the predicted
values. The model is calibrated by adjusting
the model parameter values. The sensitivity
of model predictions to the model parameters
describes the relative change in predicted
values due to variations in the model
parameter values. Figure 2 demonstrates the
comparison between predicted and measured
values for the calibration of dissolved
oxygen in the Mahoning River, Ohio for a time
period in July-August 1971. The calibrated
model is usually verified with a favorable
comparison of predicted and measured values
Figure 2. Comparison of Predicted and
Measured Values of Dissolved
Oxygen, Mahoning River
The stream velocity is an important term in
RIBAM, because it is inversely related to t,
the time of travel through a reach. For
non-conservative, non-coupled parameters,
the amount of reactant removed by natural
processes is exponentially related to t
(see equation (5)). Similarly, the mass lost
or gained by coupled parameters is sensitive
to the value to t.
The velocity of a reach is estimated by:
V = aQL
(7)
where Q = stream flow (cfs)
and a, b are coefficient values. The
values may be determined from a statistical
analysis of several flow-velocity observa-
tions within the reach. Frequently, obser-
vations are limited to a time of travel
measurement over a length of stream for one
flow condition.
Consequently, a method is developed to deter-
mine the coefficients from limited data.
This method applies the basic hydraulic
equations for open channel flow to obtain
several pairs of velocity and flow values
for each reach. A statistical regression is
then applied to these values to determine
the coefficients of equation (7). The first
hydraulic equation"* is :
Q = 1.49
AR 2/3S
(8)
47
-------
where: 2
A = cross sectional area (ft )
R = cross sectional area divided by
wetted perimeter
(hydraulic radius, ft)
S = slope or energy gradient
n = Manning coefficient
In this method, rectangular stream cross-^
sections are assumed, yielding the following
definitions:
R = DW
W+2D (9)
where W = stream width (ft)
and A = DW (10)
Upon substitution, equation (8) becomes
-K3W5D5+4Q3D2+4WQ3D+Q3W 2 = 0 (11)
where K = 1.49
1/2
n
Depth is the only unknown quantity in
equation (11).if Q is defined as a measured
flow value or treated as an independent
variable. Equation (11) is a polynomial in
D, which can be solved numerically using
Newton's method.
When depths have been determined by solving
equation (11), the velocities are computed
using the hydraulic equation1* .
V = 1.49
R 2/3 S
(12)
To determine flow-velocity pairs, equation
(11) and (12) must be solved a sufficient
number of times for accuracy in the statisti-
cal regression. The independent variable,
flow, should be varied over the expected
range of values. Widths, which are assumed
to be invariant over the range of flows, and
the slopes must be estimated from detailed
maps or other sources. If a measurement of
average velocity (or time of travel) has
been made for the reach, the value of n can
be found by iteratively computing equations
(11) and (12) and determining which value is
in the best agreement with the measured
velocity. In the absence of velocity
measurements, an engineering estimate of n
must be made.
The flow-velocity pairs generated from
equations (11) and (12) are fitted to the
curve defined by equation (7) by statistical
regression techniques. The resulting co-
efficients can be used for velocity predic-
tions in RIBAM simulations. The method
offers the advantage of a simple velocity
prediction equation that is based on the
physical characteristics of the reach and
that requires limited or no observational
data on velocity.
SENSITIVITY ANALYSIS
Results of a sensitivity analysis demonstrate
the numerical significance of model param-
eters to the RIBAM predictions. For example,
the percent change of a predicted value may
be compared with similar percent changes in
model parameter values that affect the pre-
diction. RIBAM sensitivity analysis results
for the Beaver River Basin are reported in
reference 2.
MODEL APPLICATIONS
Upon calibration of RIBAM to a particular
basin, the model can be used to predict
water quality for projected conditions.
RIBAM is a simple, effective tool for deter-
mining waste load allocations for point
sources in a river basin. The model can
estimate water quality profiles for varying
effluent loadings, which may be due to
changing sewered population, increased treat-
ment, or addition of a new discharge facility.
The water quality can be simulated for dif-
ferent environmental conditions, such as
stream flow and water temperature. RIBAM
has been used by USEPA personnel to predict
water quality for projected conditions in
the Mahoning River.
USER-COMPUTER INTERFACE
RIBAM, like other computer models, requires
the user to learn data deck input formats
and model outputs. The RIBAM input/output
is straightforward, and.fully documented2.
Figure 3 presents a typical printout for
RIBAM water quality predictions. The compu-
tation time and costs for RIBAM are rela-
tively low compared to water quality models
that require numerical solutions, such as
finite difference techniques.
FINAL SUMMARY FOR AMMONIA
DURING THt MONTH OF MAR
CONCENTRATIONS I
.FLOWS IN CFS
CONC. COHC.
AT AT
HEAD fHD
30
.80
.80
.riO
:S
0 -,
D *0
1*1
3
362
-0
12
•
O <>2
(,8 6B
0 fi
3 3
6 59
8 7B
6 5&
2 95
<. 2
26 1
62 *6
05 90
53 51
349 4l
65 62
67 65
Figure 3. Typical RIBAM Final Summary
Table for a Non-Conservative,
Non-Coupled Parameter.
CONCLUSIONS
RIBAM is useful for the basin-wide water
quality planning function. Predicted water
quality profiles for different basin con-
ditions can be analyzed to aid in determining
the waste load conditions that are most suit-
able to the water quality objectives of the
48
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basin. Coefficients for the velocity
prediction equation can be determined by a
method that considers the physical charact-
eristics of the stream and requires minimal
observational data.
REFERENCES
[1] Texas Water Development Board. DOSAG-1,
Simulation of Water Quality in Streams
and Canals, Program Documentation and
User's Manual. Report No. PB 202974.
September 1970.
[2] Raytheon Company, Oceanographic &
Environmental Services. BEBAM A
Mathematical Model of Water Quality for
the Beaver River Basin. Four volumes.
US Environmental Protection Agency.
December 1973 February 1974.
[3] Churchill, M.A., H.K. Elmore and
R.A. Buckingham. Prediction of Stream
Reaeration Rates. Proc. ASCE, Jour.
San. Eng. Div. SA4. July 1962.
[4] Streeter, V.L., Fluid Mechanics.
McGraw-Hill Book Company, Inc. 1962.
49
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COMPARISON OF EUTROPHICATION MODELS
By: John S. Tapp
Environmental Protection Agency
Technical Support Branch
Water Division
Region IV
Atlanta, Georgia
A complex mathematical model for simulating
an aquatic ecosystem was compared with less complex
models of the type developed by Vollenweider to see
if utilizing the sophisticated mathematical approach
adds to the decision making ability in comparison
to the less complex models. The reservoir used for
comparison was Lake Harding on the Chattahoochee
River in Georgia and Alabama. Data collected by
the EPA National Eutrophication Survey on 66 South-
eastern water bodies were used to test the Vollen-
weider type models. Results indicate that for Lake
Harding either approach would give comparable results
in terms of the decision to limit point source
phosphorus to the reservoir.
Introduction
The problem of eutrophication has traditionally
been a difficult one for regulatory agencies. The
complex interactions that occur in a reservoir or
lake generally cannot be easily defined to the point
where assessing the impact of a point or nonpoint
wastewater source discharge on a lake can be made
with detailed accuracy. Over the years, three basic
approaches have evolved for use by agencies in order
to make decisions concerning limitations of nutrients,
namely nitrogen and phosphorus, into aquatic systems.
The three approaches are (1) complex reservoir
models which try to simulate the complex inter-
actions that occur within a water body; (2) a more
simplistic approach which relates the input of phos-
phorus to a water body or the concentration of phos-
phorus in a water body with its physical properties;
and (3) a very simplistic mass balance approach.
Realizing the limitations of the very simplistic
mass balance, the two approaches in general use
today are the complex reservoir model and the
approach relating an input or in-lake concentration
of phosphorus to some physical characteristics of
the water body (commonly called the Vollenweider
approach).
From a scientific standpoint, the best approach
would be the complex modeling approach which, if
carried to an extreme, would attempt to represent
accurately the complex interactions that occur
within a lake or reservoir. However, in practical
terms, the ability to represent these complex
interactions is limited because some interactions
have not yet been identified and some that are
known cannot readily be measured. Very extensive
and expensive research and data collection programs
could attempt to accurately represent all identified
and measurable constituents and interactions
occurring in the complex ecologic system. However,
the collection of this massive amount of data is
usually infeasible within budgetary restrictions;
therefore, a common approach used is to define the
major interactions and base the model upon these
interactions. A minimum data collection program to
calibrate one of these complex models representing
only the major interactions is still very expensive.
The question is whether going to a relatively
sophisticated mathematical approach really adds to
the decision making ability as compared with the
less complex Vollenweider approach. This paper
attempts to address this question in relation to
one reservoir in a Southeastern United States
setting.
Complex Reservoir Model-EPAECO
An example of a reservoir model currently in
use today is one developed for EPA by Water Re-
sources Engineers-'- and is known by the acronym
EPAECO. The model was originally developed for the
Office of Water Resources Research (USDI) and
simulates the temporal variation of vertical water
quality and biologic profiles over an annual cycle
in response to meterologic conditions, tributary
conditions, and reservoir releases. In reality, an
aquatic ecosystem has a delicate and stable balance
of many different aquatic organisms and water
quality constituents. The reservoir ecologic model
solves a set of equations which represent only the
more significant interactions of the reservoir biota
with water quality. The reservoir ecologic model
EPAECO simulates the hydrodynamic water quality and
biological responses of reservoirs to tributary
inputs and environmental energy exchanges in
reservoir releases.
Vollenweider Approach
The other basic type of model in use today is
a nutrient budget model for phosphorus derived by
Vollenweider2. As indicated in Figure 1, Vollen-
weider plotted phosphorus loading in grams per
square meter per year versus the mean depth divided
by the retention time of a lake. Vollenweider then
empirically defined a basic loading tolerance for
the case where the mean depth divided by the reten-
tion time was much less than one. Using the solu-
tion to the equation, the loading tolerance lines
were projected throughout the commonly encountered
ranges of mean depth divided by retention time.
The lower line was called the permissible limit and
the upper line was called the dangerous limit and
was defined as twice the permissible limit. The
permissible limit was said to separate oligotrophic
and mesotrophic lakes and the dangerous limit was
to separate mesotrophic and eutrophic lakes.
Vollenweider and Dillon3 furthered the Vollenweider
approach using the steady state solution to the
model. If dangerous and permissible lines are
drawn as shown in Figure 2, the trends represent
equal predictive phosphorus concentrations. This
model indicates that the prediction of the trophic
state of the lake is based on a measure of the
predictive phosphorus concentration in the lake
rather than on the phosphorus loading and is called
the Dillon model.
Larsen and Mercier^ expressed Vollenweider's
mass balance model in terms of concentration. The
Larsen-Mercier curves relate the steady state lake
and mean input phosphorus concentrations. Larsen
and Mercier selected values of 10 and 20 micrograms
50
-------
o
z
o
U)
o:
O '.0
X
0.
tn
O
X
a.
' l ' ' ""1 '
VOLLENWEIDER MODEL
st » a
Symbolt
A . ..KXTROPHIC
D " EUTBOPHIC
31 M SZ D at
" D 0 „• °0»
R .D«a«
„. ., °i« .f
"„ 'V5' Xi
0 J, D^' a X ,*
D D «> /
OLISOTROPHIC"
LlOl'OjlO. —•
L101-OJ5
.3.
I 1
10.
FIGURE 1. The Vollenweider Model and Data from
Southeastern Lakes and Reservoirs
LARSEN-MERCIER MODEL
o
"EUTROPHIC" 7 M4jM
&
//
"" S,
i1
1C U "
^s °°
fl i,
Symbols
A = MESOTROPHIC
O = 'EUTROPHIC
I 1
OLIGOTROPHIC
J L
O.I 0.2 0.3 0.4 O.S 0.6 0.7 0.8 0.9 IO
•e»p
E
k_
o>
a:
i
j
FIGURE 3.
The Larsen-Mercier Model and Data from
Southeastern Lakes and Reservoirs
Z(m)
FIGURE 2. The Dillon Model and Data from Southeastern
Lakes and Reservoirs
of phosphorus per liter to delineate the oligothopic,
mesotrophic and eutrophic states. These values were
selected based on studies in the literature suggesting
that springtime concentrations of total phosphorus
in excess of 20 Mg/1 were likely to produce average
summer chlorophyll concentrations of 10 ng/I or
greater. Larsen and Mercier's curves are shown in
Figure 3.
Physical Setting-Lake Harding
The reservoir used to compare the models
described above was Lake Harding, also known as
Bartlett's Ferry Reservoir, and is located on the
Chattahoochee River about 120 river miles downstream
from Atlanta, Georgia and approximately 286 river
miles upstream from the confluence of the Chatta-
hoochee and Flint Rivers. The general location is
shown in Figure 4. This reservoir was chosen because
Water Resources Engineers^ under contract to EPA had
calibrated the reservoir ecologic model EPAECO on the
reservoir.
From a eutrophication standpoint, Lake Harding
is very advanced, i.e., anaerobic conditions prevail
in the lower depths of the reservoir during the sum-
mer months, productivity is high, and the water is
turbid. Since the time EPAECO was calibrated on Lake
Harding, a new reservoir immediately upstream has
been impounded. Therefore, the projections utilized
in this paper are merely to compare the results from
the various models and essentially have no application
in terms of real effluent limitations to be established,
except where parallels can be drawn between Lake Harding
and the new upstream reservoir.
GENERAL LOCATION OF LAKE HARDING
A
LAKE SIDNEY
LANIER
O FRANKLIN
D WEST POINT
LAKE HARDING
FIGURE 4. The Location of Lake Harding
51
-------
Results and Discussion
Vollenweider Type Models
Gakstatter et al.^ sunnnarized the results of
the 3 Vollenweider type models in relation to data
collected by the National Eutrophication Survey on
23 water bodies most of which were located in the
Northeastern and North Central United States. The
study concluded that based on the trophic state
classification developed by the National Eutrophi-
cation Survey, the models developed by Dillon and
Larsen-Mercier fit the data much better than
Vollenweider's model. The Vollenweider model was
probably less precise because unlike the Dillon and
Larsen-Mercier models it only considers total
phosphorus loading without regard to in-lake
processes which reduce the effective phosphorus
concentration.
Gakstatter and Allum^ also compared the Vollenweider,
Dillon and Larsen-Mercier models with data collected
by the National Eutrophication Survey from 53 water
bodies in the states of Georgia, North Carolina,
South Carolina and Alabama. The data of Gakstatter
and Allum for the 53 water bodies and additional
data from 13 other Southeastern water bodies also
collected by the National Eutrophication Survey in
the states of Kentucky, Florida and Mississippi are
shown in Figures 1, 2 and 3. The trophic state
index used for these data was that developed by the
National Eutrophication Survey. Figures 1, 2 and 3
indicate that for the 66 water bodies all three of
the Vollenweider type models generally fit the data.
The names of the water bodies and the hydraulic
retention time of each are shown in Table i .
TAEt-E 1. KEY TO LAKES SHOW IH riCURrS 3, 1 AMD 5.
y c r t tiff .tare
La)-e Ho. HRT Lake Mo. HUT Lahc No. IIRT
A
n .
B
an
un
oona
: :shear
Ridge
Hill
Falls
cy
ole
air
T f, George
na
ry
nock
see
e 2
a uska 2
Loo1:mit Shoals 23 H.fi2 Hantt H5
:'t. Island 20 ".03 P rkwick IP
>JorPifin 25n.PS P r<*y "7
Tillory 2R n.f>0 L y 50
K. C. nowon 31 - w IS.T 5?
"oultrie 36 0.11 D«lc Hollow Kl
SalnHa 39 o.Ol Herring ton K4
Secession 10 - .Snrctia PI
7 Banhhead 43 0.02 Enid Ml
4 Uolt 44 0, 02 Arfcabuhla MS
n2
02
30
US
nn
nij
03
60
70
50
10
12
29
To investigate the effect of hydraulic retention
time on the fit of the data for the 66 Southeastern
water bodies, those with hydraulic retention times
of less than or equal to 0.08 years (30 days) were
compared with the Vollenweider, Dillon, and Larsen-
Mercier models as shown in Figures 5, 6 and 7. Those
with hydraulic retention times of greater than 0.08
years were compared with the 3 models as shown in
Figure 8, 9 and 10. The results indicate that the
three models are generally applicable for water
bodies with both long and short mean hydraulic
retention times.
Lake Harding was one of the water bodies sampled
by the EPA National Eutrophication Survey^, Charac-
teristics of the reservoir determined by the National
Eutrophication Survey are shown in Table 2. Annual
phosphorus loads are shown in Table 3. The survey
found that for the most part Lake Harding was phos-
phorus limited, although the most upstream station
in the lake which was nearer the relatively small
point source wastewater discharges tended to be
nitrogen limited. Because the National Eutrophica--
tion Survey considered only point sources within
a 25-mile radius, a majority of the nonpoint phos-
phorus load in the Chattahoochee River as shown in
'Table 3 is from wastewater treatment plants in the
Atlanta metropolitan area.
Marlar and Herndon^ have estimated the
Atlanta area point source input of phosphorus to
the Chattahoochee River as 1,006,992 kilograms
per year, which indicates that Atlanta point
sources account for approximately 76 percent of
the total phosphorus load in the Chattahoochee
River tributary and 72 percent of the total phos-
phorus input to Lake Harding. Nonpoint source
inputs to the Chattahoochee River tributary rep-
resent 22 percent of the total phosphorus in the
river. The yearly average phosphorus loading
to Lake Harding from the National
2
Q
O
_J
O
X
Q.
VOLLENWEIOER MODEL
Tl^-0.08 YEARS
an
Symbols
£ • MESOTnOPHIG
O - EUTROPHIC
O • DEPENDS ON
TIME OF YEAR
LCOI-0.20
L(0)-O.I5
s
OLIGOTROPHIC
10.0
T.'TW
FIGURE 5. The Vollenweider Model and Data
from Southeastern Lakes and Reservoirs with
Hydraulic Retention Times Less than or Equal
to 0.08 Years
E
•s.
O>
Z (m)
FIGURE 6. The Dillon Model and Data from
Southeastern Lakes and Reservoirs with
Hydraulic Retention Times Less than or Equal
to 0.08 Years
52
-------
Kl D
a o
LARSEN-MERCIER MODEL
JV^o.oe YEARS
"EUTROPHIC" .-,
/ '
.'' / -*
/
/
OLIGOTROPHIC
Symbols
• MCSOTROPHIC
O.O O.I 0.2 O.I 0.4 0.3 0.6 O.T O.t 0.9 1.0
Rexp
FIGURE 7. The Larsen-Mercier Model and Data
from Southeastern Lakes and Reservoirs with
Hydraulic Retention Times Less than or Equal
to 0.08 Years
•^
X
«**
.£
at
^, 10.0
0
Q
3
3
CE 1.0
O
I
Q.
ta
o
X
a.
: VOLLENWEIDCR MODEL
T»'>o.oa YEARS.
"EUTROPHIC"
f DO,
: " /
I *-••* a f ° f X
a • MESOTROPHIC o Da & / 4T
O a CUTROPHIC D G / ' ,
O • OCKNOt ON 4 jf /
TIME Of YCAB fT *a vs.*^ /
__
• '^'^'^ ' Es^
•** "^S" "* SsC
[ HOl-0.30 — —""""Si-"''' A^^^
LIOLOJfl. — "-- ,--^ "OLIGOTROPHIC-
HOJ-OJS — — -^^-^
LtO)-O.IOi bj_thj.— -."""T , .....I . . 1 i
1.1 i.O 10-0 100.0
1
-
:
—
i
-
~
_
III!
IOOO
FIGURE 8. The Vollenweider Model and Data
from Southeastern Lakes and Reservoirs with
Hydraulic Retention Times Greater than 0.08
Years
Z (m)
"FIGURE 9. The Dillon Model and Data from Southeastern
Lakes and Reservoirs with Hydraulic Retention Times
Greater than 0.08 Years
LARSEN-MERCIER MODEL
Tw^O.OB YEARS
EUTROPHIC
a
O
o5:
If
'A?
/
"OLIGOTROPHIC"
Symbols
& ' MESOTROPHIC
O « EUTROPHIC
• • DEPENDS ON TIME
OF TEAR
O.O O.I O.2 0.3 0.4 O.t 0.6 0.7 0.8 O.9 1.0
Rexp
FIGURE 10. The Larsen-Mercier Model and Data from1
Southeastern Lakes and Reservoirs with Hydraulic
Retention Times Greater than 0.08 Years
TABLE
CHARACTERISTICS OF LAKE HARDING
MORPttOHETRY
Surface Areai 23.67 square kilometers
Mean Deptht 9.4 meters
Maximum Depthi 33.8 meters
Volume. 222.»98xl06 cubic meters
Mean Hydraulic Retention Time: 1« days
TRIBUTARY.
Chattahoochee River
All Others
TOTAL I
MEAH OUTLET FLOW
DRAINABE AREA (Km2) HEAH FLOW Im3/sec)
9,479.1 165.2
1,478.9 20.6
10,958.1 185.8
ISS.a
Eutrophication survey data was 58.74 grams/m^/year
based on total input. The calculated allowable
loadings in grams/m2/year to maintain dangerous and
permissible in-lake concentrations based on the
models of Vollenweider, Dillon, and Larsen-Mercier
are shown in Table k.
If 90 percent of the Atlanta point source con-
tribution of phosphorus to Lake Harding were removed,
the loading rate would be reduced to 20.45 grams/
m2/year, which is about twice the dangerous loading
indicated by the Larsen-Mercier and Dillon models
and about 3 times that indicated by the Vollenweider
model. If 99 percent of all of the Atlanta point
source phosphorus to Lake Harding were removed, the
loading rate would be 15.36 grams/m2/year which is
53
-------
beginning to approach the dangerous level of the
Dillon and Larsen-Mercier models, but is still
about 2.5 times that of the Vollenweider model. A
cursory attempt was made to analyze other South-
eastern water bodies sampled by the National
Eutrophication Survey with phosphorus loadings in
the 15 grams/m2/year range and with physical charac-
teristics similar to Lake Harding to see if this
loading indicated an impairment of use of the water
body. However, the analysis failed to reveal
sufficient data upon which to base a conclusion.
TABLE j . AVERAGE ANNUAL TOTAL PHOSPHORUS LOADING
TO LAKE HARDIHG
INPUTS
Chattahoochee River (nonpoint)
Other major tributaries (nonpoint)
Minor tributaries and immediate
drainage {nonpoint)
Municipal STP's (point)
Industrial
Septic tanks
Direct precipitation
TOTAL
OUTPUTS
Lake Outlet
NET ACCUMULATION
Kq P/yr % of Total
1,318,550 94. <*
36,430 2.b
j,480 0.3
31,190 2.3
Unknown
325 0.1
415 0.1
1,390,390
618,575
741,815
TABLE 4. CALCULATED LAKE HARDING PHOSPHORUS
LOADINGS (gr/m2/year)
Present Loadings=58. 74 gr/m^/year
Permissible
Dangerous
VOLLENWEIDER
3.1
6.2
DILLON
5.5
11.0
LARSEN-MERCIER
5.2
10.4
EPAECO
The reservoir model EPAECO utilizes concentra-
tions of water quality constituents in the tribu-
taries as input to the model. For the Lake Harding
calibration, the only tributary considered was the
Chattahoochee River because this was the only tribu-
tary on which any water quality data were available
during the simulation period (July through Decem-
ber, 1973). Also, as shown in Table 3, the
Chattahoochee River provides the majority of the
phosphorus input to Lake Harding. The tributary
water quality data available on the Chattahoochee
River consisted of one sample per month for the six
month study period. Daily tributary input concen-
trations to EPAECO were obtained by linear inter-
polation of the monthly data. Tributary concen-
trations of water quality constituents that were
not measured during the monthly sampling were
estimated based on the past experience of Water
Resources Engineers.
In order that EPAECO simulate conditions with
various phosphorus removal rates from point sources
in Atlanta, a routine was written into the model to
reduce the daily tributary concentrations to reflect
point source removals. This was accomplished by
taking the daily tributary concentration of phos
phorus and daily flow and converting to pounds of
phosphorus. The pounds of phosphorus assumed to
be removed by 90% removal from the Atlanta point
sources (based on yearly average loadings converted
to daily average loadings) were subtracted from the
instream pounds and the resulting number was
converted back to concentration for input to the
reservoir. On several days this calculation left
no phosphorus for input to the reservoir. However,
this was not believed significant due to the nature
of the various estimates such as estimated yearly
average point source loadings and interpolated
daily instream concentrations.
The model is designed to simulate the reservoir
for a one year period. The Lake Harding simulation
included only day 202 (July 21) through day 365
(December 31). Accordingly, the same period was
used in this study. As noted earlier, the average
hydraulic retention time was approximately 20 days
during the simulation period. Therefore, for the
period of study the lake water theoretically
exchanged about eight times, which should be enough
to wash out initial conditions and allow the impact
of the 90 percent point source phosphorus removal
to be assessed.
The temperature stratification in the reservoir
as calculated by EPAECO is shown in Figure 11 and the
corresponding dissolved oxygen stratification is
shown in Figure 12. Rather pronounced temperature
stratification existed throughout much of the
'simulation period. Supersaturated surface dissolved
oxygen concentrations and very low bottom dissolved
oxygen concentrations were also exhibited throughout
the majority of the simulation period. The simula-
tion denoted by "1973 conditions" represents the
best calibration of the model for the study period
and is used as the base for evaluating conditions
with phosphorus removal.
cc.
Ul
a.
BOTTOM
SURFACE
1 I '
250
' I '
275
300
TIME (days)
FIGURE 11. Temperature Stratification in Lake
Harding as Calculated by the Reservoir Ecologic
Model EPAECO
The changes in surface dissolved oxygen con-
centrations between 1973 conditions and the same
conditions with 90 percent point source phosphorus
removal are shown in Figure 13. Throughout the
simulation period the dissolved oxygen concentration
at the surface remained- essentially the same after
removal of point source phosphorus. The same was
true for dissolved oxygen concentrations at the
bottom of the reservoir. The orthophosphorus (as P)
54
-------
0>
z
UJ
X
o
D
UJ
O
v)
ZOO ZZS ZSO 279 300 ~ 329
TIME (days)
FIGURE 12. Dissolved Oxygen Stratification in
Lake Harding as Calculated by the Reservoir
Ecologic Model EPAECO
concentrations at the surface are shown in Figure 14
and the corresponding concentrations of green and
blue-green algae at the surface are shown in
Figures 15 and 16, respectively. As would be
expected, lowering the orthophosphorus concentration
to the reservoir resulted in an eventual lowering of
surface orthophosphorus concentrations. The same
trend was noted for orthophosphorus concentrations
at the reservoir bottom. Phosphorus removal reduced
the peaks in surface green algae concentration which
would indicate lowering of concentrations during
periods of algal blooms. The area differential
under the two curves in Figure 15 indicates a 20
percent reduction in green algal biomass after point
source phosphorus removal. Peaks in surface blue-
green algae concentrations are also reduced indica-
ting lower bloom concentrations and indicating a
357, reduction in biomass after point source phos-
phorus removal. The zooplankton concentrations at
the surface were the same before and after point
source phosphorus removal.
Figure 17 displays the total weight of the 3
types of fish on an areal basis throughout the
simulation period and indicates that phosphorus
removal would reduce the .total weight of fish in
the reservoir. The decline in total fish was due
to a decline in the warmwater fish which cannot be
readily explained based on model output. Also shown
is a large growth of fish from day 250 to day 310
which is probably of the correct magnitude but not
at the proper time.
in
0
Id
O
>-
g
O
Ul
o
05
o>
o
90 X I- REMOVAL
1973 CONDITIONS
' I '
Z25
TIME (doyt)
FIGURE 13. The Dissolved Oxygen Concentrations
Before and After Point Source Phosphorus
Removal as Calculated by EPAECO for Lake Harding
x
v,
O
l-
x
o
05
U.
90% f REMOVAL .
1973 CONDITI 1NS-
I
220
I
240
1
260
T ^ \ ' T
280 300 320
1
340
55
TIME (days)
FIGURE 17. The Combined Weight of the Three
Classes of Fish Before and After Point Source
Phosphorus Removal as Calculated by EPAECO
for Lake Harding
-------
Conclusions
References
Based on the data collected by the EPA National
Eutrophication Survey on 66 water bodies in the
Southeastern United States, the Vollenweider model,
the Dillon model, and the Larsen-Mercier model all
have some merit when examining eutrophication
problems. Since the Vollenweider model considers
total phosphorus input to a water body and does not
account for phosphorus in the outflow from the water
body, it is the most conservative of the three for
establishing load restrictions to a water body. The
Vollenweider model should therefore be used as a
first cut analysis in the absence of data. Where
data exist to establish a phosphorus retention
coefficient, the Larsen-Mercier and Dillon models
should be used as a first cut to establish load
restrictions to a water body.
The EPAECO model simulations indicate that with
90 percent point source phosphorus removal, yearly
green and blue-greeen algal biomass would decrease
by 20 percent and 35 percent, respectively. This
should result in some improvement in the water
quality in the reservoir even though the simulations
showed no differences in dissolved oxygen before
and after phosphorus removal. The results from
using the Vollenweider, Dillon, and Larsen-Mercier
models indicate that even with point source phos-
phorus removal the reservoir would still remain
eutrophic. However, a closer examination indicates
that 99 percent point source removal would reduce
the loading rate to the same range as the dangerous
rate calculated by the Dillon and Larsen-Mercier
models. Therefore, intuitively, some improvement
should result over a long term.
To make the Vollenweider type approach truly
applicable to Southeastern water bodies, further
work needs to be done to relate the trophic state
of a given water body to an actual present or future
impairment of water use in the water body. The
trophic state classification presently used by the
National Eutrophication Survey weighs heavily
chemical parameters and turbidity. In Southeastern
water bodies, these parameters are greatly influenced
by the interactions with the clay based soils
typical in the Southeast and may not give a true
indication of the actual trophic state.
In terms of Lake Harding, either approach,
EPAECO or the Dillon and Larsen-Mercier models,
supports the conclusion that control of upstream
point sources of phosphorus would be of benefit
to the overall water quality in the lake. The
conclusion is valid for the specific case examined,
i.e., a relatively small lake with an extremely high
phosphorus loading and a relatively small hydraulic
retention time. Other lakes where sophisticated
lake models have been constructed should be
similarly tested to see if this conclusion is
valid for the majority of impounded reservoir
situations encountered in the United States.
1. Water Resources Engineers. "Computer Program^
Documentation for the Reservoir Model EPAECO,"
U. S. Environmental Protection Agency, Wash-
ington, D. C., February, 1975.
2. Vollenweider, R.A., Input-Output Models.
Schweiz. A. Hydrol. (In Press).
3. Vollenweider, R.A., and Dillon, P.J., "The
Application of the Phosphorus Loading Concept
to Eutrophication Research." Prepared for the
Associate Committee on Scientific Criteria
for Environmental Quality. Burlington,
Ontario, June, 1974.
4. Larsen, D.P., and Mercier, H.T., "Lake
Phosphorus Loading Graphs: An Alternative."
U. S. Environmental Protection Agency National
Eutrophication Survey Working Paper No. 174,
July, 1975.
5. Water Resources Engineers. "Simulation of
Measured Water Quality and Ecologic Responses of
Bartletts Ferry Reservoir Using the Reservoir
Ecologic Model EPAECO." U. S. Environmental
Protection Agency, Washington, D.C., March, 1975.
6. Gakstatter, J.H., et al.,"Lake Eutrophication:
Results from the National Eutrophication Survey."
Presented at the 26th Annual AIBS Meeting, Oregon
State University, Corvallis, Oregon, August
17-22, 1975.
7. Gakstatter, J.H., and Allum, M.O., Data Pre-
sented at the EPA-Region IV Seminar on
Eutrophication, Atlanta, Georgia, December 3,
1975.
8. EPA National Eutrophication Survey. "Revised
Preliminary Report on Lake Harding, Georgia."
National Environmental Research Center, Las
Vegas, Nevada, July, 1975.
9. Marlar, J.T. and Herndon, A.B., "Evaluation
of Available Data: Lake Jackson and West Point
Reservoir." Internal EPA-Region IV Working
Paper, August 20, 1974.
List of Symbols
z = mean depth (meters)
TW hydraulic retention time (years)
L = phosphorus loading (grams per square meter
per year)
R or Rexp phosphorus retention coefficient
(fraction retained)
P = hydraulic washout coefficient (J_/T , years )
w
[P] = mean influent phosphorus concentration
(micro grams per liter)
56
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MANAGEMENT IN COMPETITIVE ECOLOGICAL SYSTEMS
Donald R. Falkenburg
School of Engineering
Oakland University
Rochester, Michigan 48063
1. Abstract
A competitive ecology is an essentially unbalanced
system in which a weaker species is driven out of ex-
istence by a stronger competitor. Management policies
which include selective harvest and replenishment al-
ter the equilibrium states of such a system so that
both the stronger and weaker members of the competi-
tive system can coexist.
2. The Competition Equation
The Volterra competition model describes the
growth dynamics of several species competing for the
same environmental resource. Volterra reasoned that
if the depletion of the resource increases linearly
with population size which in turn .reduces the growth
rate , and if each species has a different efficiency
for utilizing the resource, then the growth equations
have the following form:
dxi
N
1,2 N (1)
Although this quadratic interaction model may be sim-
plistic, it does possess sufficient "richness'' to
predict the replacement of a "weaker" species by a
"stronger" competitor the so called competitive ex-
2
elusion principle of Cause. Volterra's competition
model is one of a class of eco-system models which
describe the interaction among several species.
g
Scudo presents an excellent summary of these models
along with a well selected list of references to Vol-
terra's work.
In order to understand the assumptions which un-
derlie the Volterra and related competition models
let us examine a situation in which two species are in
a competitive environment. Let N and N be the size
of the two populations which compete for a food supply
F. The assumption that the growth of N and N are
independent of the age structure of those populations
renders to the model a significant simplification. It
is important to realize that the preceeding statement
does not imply age structure is absent from the popu-
lation, but rather the population has attained a sta-
h
ble age configuration ; under such conditions the pop-
ulation can be modeled by an ordinary differential
equation. The second important assumption is that the
model is fundamentally deterministic. We know that
the dynamic model of a population system reflects an
aggregate interaction among individual members of the
population an interaction which arises from random
encounters. If there are very few individuals then we
must model such a system from a probabilistic perspec-
tive. If, on the other hand, there are many indivi-
duals within the population, it is often reasonable to
construct a macroscopic model - a model which we use
to project the size of a population and not the prob-
ability density function for the population size. The
assumption that the model is macroscopic does not pre-
clude that such a model may itself be subject to ran-
dom disturbances.
The third and perhaps the most restrictive as-
sumption is that the competing species which are being
modeled are isolated. Simply stated it is not likely
that one can ever observe a pure two-species interac-
tion in nature; the complex ecological webs which ex-
ist attest to this. In fact, the growth of a single
species may be affected by hundreds of other species.
One way of dealing with this situation is to add dis-
turbance inputs to the describing equations in an at-
tempt to include the influence of species which are not
explicitly represented in the model.
The competition model involves these three species
the two competitors and the resource (in this case,
a food base) for which they compete. A dynamic model
for such a three-species system is given in equation
(2).
dN
~dt -1 -1 -1 -1
dN
at
(2)
_
dt ' V
pF2 - a1F
- "2FN2
The last of these equations describes the dynamics of
the food base. The coefficient of growth k_ for the
food base is assumed to be positive. The second term
on the right hand side of this equation accounts for
the reduction in the population growth due to the pres-
sure of increasing population size. The remaining two
terms account for the consumption of the resource by
the two species. Here it is assumed that the per capi-
ta consumption increases linearly with the available
food. In the first two equations, consumption of the
food base leads to a linear increase in the per capita
growth rate (this may occur through the reduction of
the mortality rate, an elevation in the reproductive
capacity or through, a combination of both). Now, it is
not necessary to assume that the relationships des-
cribed above are linear; in fact within the last sec-
tion of this paper an analysis is presented which is
applicable to a generalized population interaction mo-
del. Finally, if one assumes that the characteristic
response time of the food base is much smaller than the
response times for the competing species, i.e.,
k_»k , k , then the dynamic equation representing the
growth of the food base can be replaced by the quasi-
static equation
pF
0.
(3)
Using equation (3) to eliminate F from the first two
equations in (2) yields the Volterra competition model
dN
dt
dN
dt~
where
. q./p ,
Vi - ki > °
3. Management with Proportionate Harvest
The Volterra competition model presented in equa-
tion (>O contains six parameters. It is easy to show,
57
-------
however, that the essential character of the response
depends only upon the single non-dimensional parameter
-r = A./A where A. t./y.. There are three singular
points or equilibrium states that the system can at-
tain. If the equilibrium levels of population are de-
fined as 0^ and Q , these states are given by:
(a) Q1 = 0
(b) Q1 - 0
(c) Qi ej/V'l
By normalizing population size X
E2/a2Y2
(5)
N2/Q2,
and scaling time T
ations.
e..t we obtain the following equ-
^ X[l X - Y/r]
q -
rX Y]
where
(6)
X.
These results demonstrate that the species with the
largest value of A.
E./-Y- wil1 attain a stable equi-
librium configuration at a finite, non-zero population
level, while the weaker competitor is driven to extinc-
tion at the stable equilibrium configuration. This ex-
cursion variable analysis is born out globally in the
phase portrait for the non-linear competition equations
(see figure 1). Here it becomes evident that the
stronger -member drives out or replaces the weaker com-
petitor.
In the interest of preserving a balance between
the two species allowing each to coexist with the oth-
er, one might choose a management policy in which har-
vest of the stronger species and/or replenishment of
the weaker competitor is instituted; the intent here
being to remove the competitive advantage of the
stronger member of the system. Suppose that spe-
cies Y is the stronger competitor and that the rates of
harvest and replenishment are given by H and R respec-
tively. Defining normalized, time scaled rates of
0 = a Y R and V = oijTj11 ("nere a$_ and ^ are the coef-
ficients appearing in (4))then the competition equa-
tions become:
= X [1 X Y/r] + U
(8)
y0=0)_
The equilibrium points associated with (6) are of
course (xo=Q> yo=0)> (xo=0> yo=1) and ^
In order to examine the nature of these equilibria, we
assume that X and Y experience small excursions x and
y from their respective equilibrium levels . The line-
arized differential equations which arise from this
excursion analysis are presented in equation (7) below.
Az
where
(7)
(1 2X° Y°/r)
-X°/r
-rY°/q
- 2Y° rX°)/q
Now, the roots of the characteristic equation
det[sl A] 0 determine the nature of the singular
points. These roots are computed for each equilibrium
state (X ,YU) and are summarized in Table I.
equilib.
point
X°=0, Y°=0
X°=0, Y°=l
X°=l, Y°=0
roots of
characteristic
equation
si=1>V t
V T'S2=(1T>
n _ _(l-r)
°1 1>02' q
nature of equilb.
point
unstable node
stable node (rl)
stable node (r>l)
saddle point (r< 1)
Table I. Characterization of
Equilibrium Points
Let us consider first the harvest strategy. Our first
thought is to institute a program of proportionate har-
vesting, that is, a program in which a specified frac-
tion of Y is removed. This is, perhaps, the simplest
approach to take, since if a constant effort is made
to harvest Y, then the yield will increase with larger
numbers of species Y producing an approximately pro-
portionate harvest. This is contrasted with the con-
cept of an absolute harvest in which M members must be
selected. In the absolute harvest the effort is ad-
justed to target the desired yield. In the propor-
tionate harvest, then V f • y and U 0. The effect
of such a strategy is to shift one of the singular
points of the differential equation producing the fol-
lowing equilibrium configuration.
equilib.
points
X°=0,Y°=0
X°=0,Y°=(l-f)
X°=1,Y°=0
roots of
characteristic
equation
s1=i
S2=(l-f)/q
S1=-(l-f)/q
S2=(r+f-l)/r
s1=-i
S2=(l-r-f)/q
nature of
equilb . point
unstable node
stable node
r + f < 1
saddle r+f>l
saddle r+f < 1
stable node
r + f > 1
Table II. The Effect of Proportionate
Harvesting on Equilibria (f< 1)
If the harvest fraction is sufficiently large, the orig-
inally weaker species will dominate the ecology. If
this management policy is continued indefinitely, the
harvested species, once the dominant competitor, will
be driven toward extinction. If one desires a scheme
whereby both species can co-exist, it is possible to
institute a program in which a period of harvest is
58
-------
followed by a period of "natural growth". This strat-
egy would render alternating advantages to the two
species producing (if properly implemented) a limit cy-
cle or closed periodic solution in the phase plane.
Since neither species is permitted to dominate the
ecology for a sufficiently long period of time, both
can coexist.
4. Management with Absolute
Harvest and Replacement
An alternate procedure for controlling the growth
in this ecological system is to impose an absolute
harvest. Contrasted to the proportionate policy, the
absolute harvest involves the setting of a target har-
vest level; the harvesting of the stronger species is
continued until this target is achieved. In a similar
fashion we could consider a constant replenishment pro-
gram for the weaker species. If U and V are the con-
stant levels of replacement and harvest, the equations
which describe the growth within the competitive sys-
tem are
- f(X, Y, U)
qg= g(X, Y, V)
(9)
where
f(X, Y, U) X[l - X Y/r] + U
g(X, Y, V) Y[l rX - Y] - V
Setting f and g to zero yields a pair of simultaneous
equations in X and Y; for any level of harvest V and
replacement U these equations can be solved to obtain
the equilibrium points. Graphically, one can inter-
pret f=0 and g=0 as families of curves parameterized
in U and V respectively. These curves are illustrated
in figure 2. The intersection of any f=0 curve with
another g=0 curve yield these equilibria. A few equi-
librium points are illustrated in the figure.
Once the equilibrium point is established, we must
determine the character of the equilibrium point - does
it represent a stable or an unstable configuration?
We proceed' to obtain the characteristic equation from
the linearized form of the describing equations
dx 3 f 3 f
- — -—-y 4- TJ
dT 3lr 3 Y y
dy_ = L6_ x + LS_
qdT 3 X 3 Y y
(10)
obtaining
det[sl A] sz + as + b 0
The nature of the singular point depends upon the co-
efficients a and b; this dependence is illustrated in
figure 4. We know immediately that the equilibrium
point must be stable; if in addition it is possible
to demonstrate that a2 > 4b then we would know that
the equilibrium configuration would be a stable node.
Using the fact that Sf -(3 f/3 X)/(3 f/3 Y) and
S = -(3g/3 X)/(3 g/3 Y) we can write this inequality as
i£ _ I iS.
3X q 3 Y
.
q 3 Y 3X
(12)
Since 3 f /3 Y and 3 g/3 X have the same sign a2 > 4b and
from figure 4 we see that the singular point is a
stable node. Similar reasoning leads to the conclu-
sion that for equilibrium point lib < 0. Again fig-
ure 4 can be used to establish this to be a saddle
point. Both species can coexist at the stable equili-
brium point; the motion of this system toward the
equilibrium point is illustrated in the phase portrait
of figure 5.
It is interesting to consider the special case in
which the replacement rate U - 0 while the harvest
rate V > 0. Under these conditions no such stable
equilibrium point exists such that both X > 0 and
Y > 0. Thus an absolute harvest policy with no re-
placement will not achieve our stated objectives fail-
ing to produce a balance within the system (see figure
S). The compliment of this strategy in which replace-
ment is instituted without harvest does produce a de-
sired stable equilibrium point; this conclusion can
be reached using the geometric arguments presented
above.
5. Summary
In the unmanaged Volterra competition system, the
stronger species will replace the weaker competitor.
Proportionate harvest alters the balance within the
ecology, and can effect a competitive advantage to the
originally weaker species. A continuous application
of such a management strategy merely shifts the com-
petitive advantage; again the system is driven to-
ward dominance by a single member. Absolute harvest
alone does not produce a stable equilibrium configura-
tion in which both species can coexist. A combined
policy which implements both an absolute harvest of
the stronger member and the replacement of the weaker
competitor can induce a balance within the system.
The design of such a strategy is based upon the
control curves presented in figure 2. Although these
curves were developed for the Volterra competition
equations, they can be modified if any of the as-
sumptions of linearity presented in the model develop-
ment are deemed inappropriate. Levels of harvest and
replacement are then selected such that X > Y . and
min
where
Y > Y . at the equilibrium .
mm ^
3f/3Y
b = — — -"•
q 3Y 3Y
Now S and Sf are slopes of the curves g=0 and f=0 at
the equilibrium point. Consider the illustration in
figure 3. At equilibrium point I the geometry of the
curves is such that the partial derivatives of both f
and g with respect to each coordinate are negative,
thus a > 0 and since S > S_ the coefficient b > 0.
g f
6. References
1. Volterra, V.,"Variazioni efluttuazioni del numero
(11) d'individui in specie animali conviventi," R. Comit.
, Talass. Italiano, Memoria 131 (Venesia, 19277!
2. Cause, G. F., The Struggle for Existence , Williams
and Wilkins (Baltimore, Md., 1934).
3. Scudo, F. H., "Vito Volterra and Theoretical Ecol-
ogy", Theoretical Population Biology, Vol. 2 (1971).
4. Lotka, A. J.,"The Stability of the Normal Age Dis-
tribution", Proc. Nat. Acd. Sciences, Vol.8 ,(1922).
5. Minorsky, N.,Nonlinear Oscillations, Krieger (Hunt-
ington, N.Y., 1974)..
59
-------
o.
§
1.0
X (weaker competitor)
Figure 1. Urananaged Competition
X (weaker competitor)
Figure 2. Control Curves for Selecting
Harvest and Replacement Rates
f=o
X (weaker competitor)
Figure 3. Representative Control Curves
STABLE
FOCUS
CENTER"?
UNSTABLE
FOCUS
Figure U. Nature of Roots of Characteristic
Equation
60
-------
X (weaker competitor)
Figure 5. Competition with both Harvest and
Replenishment
X (weaker competitor)
Figure 6. Competition with Harvest Management
o l
X (weaker competitor)
Figure 7. Competition with Replacement Management
61
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PLANNING IMPLICATIONS OF DISSOLVED OXYGEN DEPLETION IN THE WILLAMETTE RIVER, OREGON
David A. Rickert, Walter G. Hines, and Stuart W. McKenzie
U.S. Geological Survey
Portland, Oregon
ABSTRACT
Basinwide secondary treatment of municipal and indus-
trial wastewaters has resulted in a dramatic increase
of summertime dissolved-oxygen (DO) concentrations in
the Willamette River. Rates of carbonaceous decay
(ki) are very low (0.03 to 0.06/day), and point-source
BOD loading now accounts for less than one-third of the
satisfied oxygen demand. Nitrification is now the
dominant DO sink. DO concentrations met the state
standards in all reaches of the Willamette during the
low-flow period of 1974. Mathematical modeling shows
that low-flow augmentation from storage reservoirs was
largely responsible for the standards being met.
Future achievement of DO standards will require con-
tinued low-flow augmentation in addition to pollution
control. Summertime flows above 6000 ft^/s will be
needed even with increased treatment removals of oxygen
depleting materials. The greatest immediate incremen-
tal improvement in DO can be made through reduction in
point-source ammonia loading. The pros and cons of
upgrading treatment efficiencies for BOD removal would
best be determined after ammonia loadings have been
reduced to reasonable levels and the possibility of
controlling a benthal-oxygen demand in Portland Harbor
has been fully assessed.
(KEY TERMS: river-quality planning; dissolved-oxygen
standards; dissolved-oxygen modeling; biochemical-
oxygen demand; nitrification; low-flow augmentation.)
INTRODUCTION
Historically, dissolved-oxygen (DO) depletion has been
the critical water-quality problem in the Willamette
River. During summer low-flow periods, DO concentra-
tions of zero were sometimes observed in Portland
Harbor (see figure 1), and for years, low DO levels
inhibited the fall migration of salmon from the
Columbia River.1
In recent years, summer DO levels have increased
dramatically. The improvement has resulted primarily
from the basinwide advent of secondary wastewater
treatment, coupled with streamflow augmentation from
storage reservoirs. With an average annual flow of
35,000 ft3/s, the Willamette is now the largest river
in the United States on which all known point sources
of wastewaters receive secondary treatment. The
Willamette thus offers a unique opportunity to docu-
ment the impacts of secondary treatment on a large
river and also to predict the amount of further
improvement likely to result from different alter-
natives of river-basin management.
PHYSICAL SETTING
Willamette River Basin
The Willamette River basin, a watershed of almost
11,500 sq mi (figure 1), is located in northwestern
Oregon between the Cascade and Coast ranges. Within
the basin are the state's three largest cities,
Portland, Salem, and Eugene, and approximately 1.4
million people, representing 70 percent of the
state's population (1970 census). The Willamette
River basin supports an important timber, agricultural,
industrial, and recreational economy and also
extensive fish and wildlife habitats.
The basin is roughly rectangular, with a north-south
dimension of about 150 mi and an east-west width of
75 mi. Elevations range from less than 10 ft near the
mouth of the Willamette River to 450 ft on the valley
floor near Eugene and to more than 10,000 ft in the
Cascade Range. Average annual precipitation in the
basin is 63 inches.
Hydrology
Channel Morphology.—The Willamette River main stem
forms at the confluence of its Coast and Middle forks
south of Eugene and flows northward for 187 mi through
the Willamette Valley floor. The river is composed of
three morphological reaches (figure 1 and table 1).
Each reach has a unique hydraulic regime and, there-
fore, different velocities, sediment-transport
characteristics, and patterns of biological activity.
The Upstream Reach, stretching from above Eugene to
near Newberg, is shallow and fast-moving. The river-
bed is composed largely of cobbles and gravel which
provide ample opportunity for attachment of periphytic
biological growths. During the summer low-flow period,
mean velocity in this reach is about seven times that
observed in the Newberg Pool and 18 times greater than
in the Tidal Reach. Morphologically, this section of
the river is an "eroding" reach.
Between a point just above Newberg and the Willamette
Falls is a deep, slow-moving reach known as the
Newberg Pool. Hydraulically, the Pool can be charac-
terized as a large stilling basin behind a weir
(Willamette Falls). Travel time in this 25.5-mi reach
is relatively long during low-flow conditions.
Morphologically, the Pool is a depositional reach.
The lower 26.5 mi of the river is affected by tides
(nonsaline water) transmitted from the Pacific Ocean
via the Columbia River and, during April to July, by
backwater from the Columbia. The Tidal Reach is
dredged to maintain a 40-ft-deep navigation channel up
to river mile (RM) 14. During low flows, net down-
stream movement in the Tidal Reach is slow, but tidal
flow reversals can cause large instantaneous changes
in velocity. Low-flow hydraulics are most complex in
the lower 10 mi where, depending on hourly changes in
tidal conditions, Willamette River water may move
downstream or Columbia River water upstream. Owing
to morphological characteristics and the hydraulic
conditions, the subreach below RM 10 is the primary
depositional area of the Willamette River.
Flow.—Most of the flow in the Willamette occurs in
the November to March period as a result of persistent
winter rainstorms and spring snowmelt. Each summer
there is a naturally occurring low-flow period, the
timing, duration, and magnitude of which are now
largely controlled by reservoir releases. Since 1954,
when large-scale reservoir regulation began, discharge
during the low-flow period of July-August has been
maintained at a minimum of about 6000 ft3/s (Salem
gage) by reservoir augmentation. In comparison, for
the unusually dry year of 1973, the calculated (from
a deterministic model) naturally occurring low flow
for this period would have been 3260 ft3/s. The
summertime flow releases are made for purposes other
than river-quality enhancement, but, as subsequently
described, the augmentation has a profound impact on
the DO regime.
Temperature.—Water temperatures in the Willamette
River and in all tributaries reach a maximum during
62
-------
the annual July-August low-flow period. Temperatures
during July average about 20° C in the Newberg Pool
and about 22° C in the Tidal Reach; these are
controlled primarily by ambient air temperatures.
DATA PROGRAM
Review of existing data indicated that an appreciable
DO deficit occurs in the Willamette only below RM 86
and during the yearly low-flow period of July through
August. The DO-data-collection program was developed
to formulate a mathematical model for simulating
conditions below RM 86 for the critical summer period.
Emphasis was placed on direct intensive measurement
of waste loads and model coefficients to avoid
reliance on published values, engineering estimates,
and the development of model coefficients through
computerized curve fitting (optimization). Details
of sampling approaches and analytical techniques are
reported in other papers. >^>
DISSOLVED-OXYGEN REGIME
Dissolved-Oxygen Profiles
Basinwide secondary treatment has had a profound
impact on the major deoxygenation processes and
consequently on the DO regime of the Willamette
River. During the summer low-flow period of 1974,
average daily DO concentrations met state standards
for all reaches of the river at flow conditions
between 6500 and 7000 ft /s and water temperatures
between 22° and 25° C.
Figure 2 compares the 1973 DO profile of the river
below RM 86 to historic conditions. In 1956, there
was a DO-concentration "plateau" between Salem and
Newberg, followed by a sharp decrease in DO through
the Newberg Pool. These conditions were consistent
with large loadings of carbonaceous biochemical
oxygen demand (BOD) in the vicinity of Salem, a rapid
travel time between Salem and Newberg, and a large
amount of carbonaceous deoxygenation in the slow-
flowing Newberg Pool.
The 1959 data show an increase in DO concentration
below Willamette Falls and a sharp decrease in DO
through the Tidal Reach. These observations were
consistent with known reaeration at the falls, inflow
of cool high-DO water from the Clackamas River, and
the decay of carbonaceous wastes which entered the
river just below the falls and throughout Portland
Harbor.
The 1973 profile shows a rapid decrease of DO from
RM 86 to Newberg, a DO "plateau" in the Newberg Pool,
a DO increase over Willamette Falls, a gradual
decline in DO between RM's 24 and 13, a sharp decrease
in DO between RM's 13 and 5, and recovery of DO
below RM 5. The DO decrease between RM 86 and
Newberg contrasts with a "plateau" in 1956 and
results from nitrification that did not occur at the
earlier date. The 1973 DO "plateau" in the Newberg
Pool indicates that carbonaceous deoxygenation is
now occurring at a rate slow enough to be balanced
by DO inputs from atmospheric reaeration. The DO
decrease between RM's 24 and 13 is consistent with
measured river loads of ultimate BOD (BODuit), but
the sharp decrease between RM's 13 and 5 cannot be
accounted for by known sources of BOD. (See section
entitled "Benthal-Oxygen Demand.") The DO profile
of the Willamette during July-August 1974 was
essentially the same as that presented in figure 2
for 1973.
Nitrification
During the summers of 1973 and 1974, nitrification
was the dominant control on DO in the shallow, swift-
flowing subreach between RM's 85 and 55. Examination
of historical data indicates that this reach began to
receive appreciable ammonia loading from a pulpmill
in 1956. Dissolved-oxygen data from the 1950's and
1960's are sketchy, but suggest that nitrification did
not become a significant oxygen sink until the advent
of secondary treatment at pulp and paper mills.
Secondary treatment incurred the use of ammonium
hydroxide for neutralizing wastewaters prior to
treatment, and resulted in continuous discharge of
effluents to the Willamette rather than the previously
used program of summer lagooning and winter discharging,
Figure 3 shows the average instream concentrations of
ammonia, nitrite, and nitrate nitrogen from RM 120 to
7 for August 12-14, 1974. The curves reflect a
prominent ammonia source near RM 116 and rapid in-
stream oxidation of ammonia to nitrite and nitrate
downstream to RM 86. During the study period, the
subreach below RM 86 received about 5800 Ib/d
ammonia nitrogen from upstream sources, 16,200 Ib/d
from an ammonia-base pulp and paper mill at RM 85,
and about 1700 Ib/d from a municipal sewage plant at
RM 78. The instream data show a rapid conversion of
the ammonia to nitrite and nitrate between RM's 85
and 55. The deep, relatively slow-moving Newberg
Pool begins at RM 52 and, although residual ammonia
entered this reach, no further nitrification could
be detected from nitrogen-species analysis.
The occurrence of nitrification in a shallow, surface-
active reach and the contrasting absence in a deep,
slow-moving reach is consistent with a recent hypo-
thesis proposed by Tuffey, Hunter, and Matulewich.^
According to the hypothesis, nitrification in shallow,
swift-flowing reaches would occur by virtue of an
attached, rather than a suspended population of
nitrifying organisms. To test the hypothesis,
enumerations of nitrifying bacteria were made on
water samples and on biological slimes scraped from
rocks. Nitrosomonas concentrations were <1 most
probable number (MPN)/ml in all water samples from -
throughout the river. In slimes, Nitrosomonas
concentrations were <1 MPN/mg above RM 86 and 1-4 MPN/
mg in samples collected between RM's 85 and 55 (the
active zone of nitrification). The Newberg Pool is a
deep depositional reach and few rocks are available
for attachment. In comparison, Nitrobacter concen-
trations in the zone of nitrification ranged from
<1 to 4 MPN/ml in water samples and from 6-50 MPN/mg
in slimes. The bacteriological data thus support the
hypothesis that nitrification occurred in slimes
attached to rocks rather than in flowing water.
Based on observed river concentrations of nitrate
(figure 3), an in-river rate of nitrification was
calculated for the affected subreach. Assuming first-
order decay, the rate, kn (log^o)» was about 0.7/d.
Applying this rate to the measured loadings of
ammonia indicates that, for the August 12-14 period,
nitrification removed about 55,000 Ib/d DO from the
30-mi subreach. This satisfied demand was responsible
for most of the decrease observed in DO concentration
(figure 2).
Carbonaceous Deoxygenation
Present-day (1974) BOD-loading patterns and rates of
exertion contrast sharply with those observed during
the mid-1950's.
63
-------
BOD Loading.—During the dry-weather period of 1954,
the estimated point-source loading of BODu^t to the
Willamette River was approximately 350,000 Ib/d.
This total included chemical demands resulting from
sulfite wastes, soluble and suspended carbonaceous
demands from pulp and paper mills, and the carbona-
ceous demands of raw sewage and primary effluents.
In contrast, the point-source BODuj^ loading during
August 1974 was about 92,000 Ib/d (table 2). The
decrease resulted from secondary treatment of all
carbonaceous wastes, chemical recovery of sulfite
wastes, and the routing of sewage effluents from
metropolitan Portland into the Columbia River instead
of the Willamette.
During the 1974 low-flow period, nonpoint sources
contributed about 77,000 Ib/d BODuit to the
Willamette, or about 46 percent of the total basin-
wide loading (table 2). Because of the design of
the nonpoint-sampling program, it appears that
almost all of the estimated loading from diffuse
sources represents natural background demand from
essentially pristine streams. Thus, only about
one-half the observed total BODu^t loading to the
Willamette River is potentially amenable to removal
by future pollution-control programs.
Concentrations and Rates.—During the low-flow period
of 1954, five-day BOD's (BOD5) in the Willamette
River varied from about 1.0 mg/1 at sites far removed
from waste inputs to about 2.5 mg/1 below large waste
outfalls. During 1974, measured BOD5 concentrations
were about 1.0 mg/1 throughout the river. The
apparent anomaly of the comparative concentrations
arises from marked differences between 1954 and 1974
in the river rates of deoxygenation (k^). The value
throughout the river in 1954 was probably 0.1/d
(log^o) or greater. The measured k-^'s in 1974 were
clustered around 0.04/d. Thus in 1954, a minimum of
about 68 percent of BODu^t was exerted in five days,
whereas in 1974 the comparative value was 39 percent
(see Velz for discussion of BOD exertion).^ This
comparison underscores the need for determining ki
values and BODul(. (rather than BOD5 alone) as a basis
for accurately modeling DO under conditions of
secondary treatment.
The in-river concentrations of BODu^t during 1973
and 1974 averaged about 2.5 mg/1.
Benthal-Oxygen Demand
During 1970, benthal respirometer studies (written
communication, John Sainsbury, 1970) of the
Willamette documented a benthal-oxygen demand of
27,000 to 54,000 Ib/d in the subreach between RM's 13
and 7. The river at that time still received some
raw sewage in the form of combined sewer overflows
and a moderate loading of settleable solids from
pulp and paper mills. Because these sources of solids
are now largely controlled, it was anticipated that
the benthal demand would be greatly reduced by 1973.
However, during preliminary calibration of our model,
predicted DO concentrations between RM's 13 and 5
were higher than those measured in the river, whereas
predicted BODu,t concentrations were considerably
lower. Refined modeling tests suggested an
unaccounted-for oxygen demand of about 27,000 Ib/d
in the subreach.
DO Modeling
The model chosen for the study was the one developed
and used for more than 30 years by C. J. Velz. The
basic model, described in detail in Applied Stream
Sanitation,7 is applicable to conditions of steady
(invariable), nonuniform (changing cross-sectional
geometry), plug (nondispersive) flow. The computer
program as formulated for the present study is
called the WIRQAS (Willamette Intensive River Quality
Assessment Study) model.
The model was calibrated against 1974 streamflow and
temperature conditions and verified against the
slightly lower flow and higher temperature conditions
of 1973. For conditions representing 1974 summer low,
the model indicates that an oxygen demand of 164,000
Ib/d was satisfied between RM's 86 and 5. Of the
total, about 22 percent resulted from background
carbonaceous-oxygen demand, 28 percent from point-
source carbonaceous demand, 34 percent from point-
source ammonia, and 16 percent from the unaccounted-
for demand in Portland Harbor.
PLANNING IMPLICATIONS
As an aid to river-quality planning, the WIRQAS model
has been used to test management alternatives
concerning (1) BOD loading, (2) ammonia loading, (3)
low-flow augmentation, and (4) the effects of possible
removal or reduction of the benthal-oxygen demand.
This section describes the major implications of
tested alternatives by comparing measured DO profiles
with profiles generated by the verified model. A
fact the reader should bear in mind in examining the
following illustrations (figures 4-8) is that, for
ease of presentation, the DO profiles are plotted as
a function of river location. Thus the slopes of
curves in specific subreaches do not represent the
actual rates at which oxygen is added to or lost from
the river. For example, the profiles in figures 4-8
suggest a rapid rate of oxygen depletion below
Willamette Falls. Actually, the steepness of the
curves is caused by the slow time-of-travel in the
Tidal Reach (see table 1) rather than by an
accelerated rate of oxygen depletion.
BOD Loading
The effect of BOD loading on summertime DO is
reflected in figure 4. The curve labeled 100 percent
represents the average DO profile of the river at
the flow, water temperatures, ammonia loading, and
BOD loading actually measured during the low-flow,
steady-state period of mid-August 1974. The upper
and lower curves represent the predicted DO profiles
at 50 percent and 200 percent of the measured point-
source BOD loading with all other variables held
constant at observed levels. These curves are
calculated on the basis that all point-source BOD
receives secondary treatment and decays at rates of
0.06/d above RM 55 and 0.03/d below this point.
The upper curve in figure 4 indicates that only a
slight improvement in DO can be obtained by a 50
percent decrease of BOD loading from each point
source in the basin. The predicted increase in DO
would be <5 percent of saturation at the bottom of
the Newberg Pool (RM 28) and 5 percent at RM 5, the
low DO point in the river.
In contrast, a doubling of BOD loading from each
point source would depress DO by 5 percent of
saturation at RM 28 and by 10 percent at RM 5. This
decrease in DO would cause violation of the state DO
standard in the subreach between RM's 62 and 50.
Figure 5 compares the DO profile observed in mid-
August 1974 with the predicted profile assuming a
BOD5 standard of 10 mg/1 for all municipal wastewater
effluents. Such a standard, attainable by high-level
64
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secondary treatment, is presently being considered by
Oregon and several other states throughout the
country. Application of the 10 mg/1 standard in the
Willamette River basin would decrease municipal
summertime loading of BODult from 37,600 Ib/d to
17,400 Ib/d. The largest individual decrease would
be about 7000 Ib/d at Salem (RM 78). The modeling
results (figure 5) indicate that, over the investigated
reaches, the reduced loading would have no effect on
river DO. The lack of an effect stems from (1) the
small reduction attainable in total loading of BODuit
(about 12 percent; see table 2), (2) the low rate at
which BODuit is exerted in the river, and (3) the
locations within the basin of the largest municipal
wastewater treatment plants.^
Ammonia Loading
Figure 6 illustrates the effect of ammonia loading on
summertime DO in the Willamette. Compared to the
observed DO profile (the 100 percent curve), a 50
percent reduction in ammonia-nitrogen loading from
each point source would increase the DO by 7 percent
of saturation near the bottom of the Upstream Reach
(RM 60), by 5 percent at RM 28, and by <5 percent at
RM 5. In contrast, a doubling of ammonia-nitrogen
loading in each point source would decrease the DO
by 13 percent at RM 60, by 11 percent at RM 28, and
by 7 percent at RM 5. These results illustrate two
important points. First, ammonia loading has its
greatest effect on DO in the active zone of nitri-
fication between RM's 85 and 55. Thereafter,
measurable nitrification ceases to occur and the
upstream effects of the process are gradually
diminished by atmospheric reaeration. Second,
comparison of figures 4 and 6 indicates that point-
source ammonia loading has a greater influence on
Willamette River DO than point-source BOD loading.
At the observed relative point-source loadings
(43,000 Ib/d ammonia-nitrogen; 92,000 Ib/d BODult),
this occurs primarily as a result of (1) the greater
oxygen demand per unit weight of ammonia as compared
to the organic matter in secondary effluents, and
(2) the much greater rate at which ammonia is
oxidized (ki 0.03 to 0.06/d; kn = 0.7/d).
The upper curve in figure 6 shows the impact of
applying a standard of 10 mg/1 ammonia-nitrogen to
all municipal and industrial effluents.
Most of the ammonia that enters the Willamette below
RM 86 is discharged from a large pulp and paper mill
at RM 85 (see "Nitrification"). Control of ammonia
from this one source would greatly reduce the impact
of nitrification on the DO regime of the river.
Low-Flow Augmentation
The effect of flow augmentation on DO is illustrated
in figure 7. The observed flow at Salem during mid-
August 1974 was 6760 ft3/s. For comparison,
computed DO profiles are presented for Salem flows
of 9000, 5000, and 3260 ft3/s. The latter value is
near the lowest minimum monthly average flow ever
observed for July under natural (nonaugmented)
conditions. As previously noted, predictions from
a deterministic model indicate this flow would have
occurred during July of the unusually dry year of 1973.
The impact of flow augmentation is marked. At a flow
of 3260 ft3/s, the 1974 BOD and ammonia-nitrogen
loadings would cause violation of state DO standards
by a wide margin at most locations. The predicted
DO saturation levels at 3260 ft3/s are nearly 30
percent less than the observed values (6760 ft-Vs) at
RM's 60, 28, and 5.
At a flow of 5000 ft3/s, the state DO standard would
have been violated between RM's 67 and 50 and just
have been met in the Newberg Pool.
In contrast to the marked decrease predicted in DO
at decreased flows, an increase to 9000 ft3/s would
cause a relatively small improvement in saturation
percentages. The effects of augmentation on
Willamette River DO result from a complex interaction
of flow with (1) the loading and rate of BOD exertion,
(2) ammonia loading and the rate of nitrification,
(3) time of travel, and (4) atmospheric reaeration.
The most significant interactions at different levels
of flow have not been delineated, but it appears
under the combined conditions observed in 1974 that
flow augmentation to discharges above 7000 ft-Vs
would provide little incremental increase in DO
concentrations. However, 'under future-conditions,
flows in excess of 7000 ft3/s might be a desirable
alternative to expensive, energy-consuming advanced-
waste treatment processes.
Figure 8 illustrates the combined effects of
nitrification and flow augmentation. Curve B is the
average DO profile observed during the steady, low-
flow period of July-August 1973. Curve D is the
predicted DO profile at a flow of 3260 ft3/s and the
observed ammonia loading. In comparing curves B and
D, note that without augmentation, the state DO
standards would have been violated at most points in
the river. Curves A and C represent predicted DO
profiles at the same two flows, but with ammonia-
nitrogen loading reduced to 10 mg/1 in all point-source
discharges. With such an effluent limitation, the DO
profile predicted at 6000 ft3/s is considerably above
the observed profile (curve B) throughout most of the
river. However, curve C portrays the most important
finding for 1973 conditions. Even with basinwide
secondary treatment and a reasonable limitation on
ammonia loading, low-flow augmentation would be
necessary to achieve DO standards in the Newberg Pool
and the Tidal Reach.
Benthal-Oxygen Demand
As previously noted, the WIRQAS model indicates the
presence of an unaccounted-for oxygen demand of
27,000 Ib/d between RM's 13 and 7. Field investigations
suggest that most of the demand is benthal in origin,
but the exact causes are unknown. Possible factors
that may either cause or affect the oxygen demand
include:
1. Unknown sources of raw sewage'.
2. Combined-sewer overflows.
3. Urban storm runoff.
4. Bilge water and refuse from ships.
5. A net oxygen loss caused by algal respiration
exceeding algal production owing to limited
light penetration of the water column.
6. A turbid, high-oxygen demanding, estuarine-like
"null zone" resulting from tidally influenced
hydraulic conditions.
7. Sedimentation and decomposition of natural
organics such as leaves and algae.
These possibilities are presently the focus of further
study. Hopefully, all or at least part of the demand
can be related to controllable sources. If so,
management control of these sources will provide a
means for improving summertime DO by up to 8 percent
of saturation at RM 5.
65
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SUMMARY AND CONCLUSIONS
REFERENCES
Future achievement of DO standards in the Willamette
River will require continued low-flow augmentation in
addition to pollution control. Minimum flows of
6000 ft^/s (Salem gage) are presently (1974) needed to
meet the standards at existing BOD and ammonia
loadings and with the occurrence of an unidentified
(probably benthal) oxygen demand in Portland Harbor.
As basin development continues, it is likely that
summertime flows above 6000 ft^/s will be needed even
with increased treatment removal of oxygen-depleting
materials.
Point-source loading of ammonia is presently the major
cause of oxygen depletion below RM 86. Because most
of the ammonia comes from one source, reduction of
ammonia loading offers a relatively simple alternative
for achieving a large improvement in summertime DO.
Removal or partial reduction of the oxygen demand in
Portland Harbor would improve the summer DO
concentrations between RM's 10 and 5. However, the
feasibility of reducing the demand is yet to be
determined.
BOD loading from municipal wastewater treatment plants
presently exerts a relatively small impact on DO.
Increased efficiency of BOD removal at the largest
municipal plants and at selected industrial plants
might be desirable in the future. The benefits to be
gained from this alternative would best be determined
after ammonia loadings have been reduced to reasonable
levels and the possibility of controlling the
suspected benthal demand has been fully assessed.
1. Gleeson, G. W., 1972. The return of a river, the
Willamette River, Oregon. Advisory Committee on
Environmental Science and Technology and the
Water Resources Research Institute, Oregon State
University, Corvallis, 103 pp.
2. Rickert, D. A., Hines, W. G., and McKenzie, S. W.,
1975. Methods and data requirements for river-
quality assessment. Water Resources Bulletin,
Vol. 11, No. 5, pp. 1013-1039.
3. Hines, W. G., Rickert, D. A., McKenzie, S. W.,
and Bennett, J. P., 1975. Formulation and use
of practical models for river-quality assessment.
USGS Survey Circular 715-B, 16 pp.
4. Hines, W. G., McKenzie, S. W., and Rickert, D. A.
(in press). Dissolved oxygen regime of the
Willamette River, Oregon, under conditions of
basinwide secondary treatment. USGS Survey
Circular 715-1.
5. Tuffey, T. J., Hunter, J. V., and Matulewich, V. A..
1974. Zones of nitrification. Water Resources
Bulletin, Vol. 10, No. 3, pp. 555-564.
6. Velz, C. J., 1951. Report on natural purification
capacities, Willamette River. National Council
for Stream Improvement of the Pulp, Paper, and
Paperboard Industries, Inc., School of Public
Health, Michigan University, Ann Arbor, 80 pp.
7. Velz, C. J., 1970. Applied stream sanitation.
John Wiley & Sons, Inc., New York, 619 pp.
This paper was originally published by the American
Water Resources Association in the Proceedings of the
Urbanization and Water Quality Control Symposium, 1975,
pp. 70-84.
TABLE 1. Physical Characteristics of the Main Stem Willamette River
(for discharge at Salem = 6000 ft3/s).
Reach
1 Tidal
2 Newberg
Pool
3 Upstream
Length,
miles
26.5
25.5
135
Approxi-
mate
bed slope,
ft /mile
0.1
.12
2.8
Bed
material
Clay, sand,
and gravel
do
Cobbles and
gravel
Represen-
tative
midchannel
water
depth,
ft
40
25
7
Average
velocity,
ft/s
0.16
.40
2.9
Approxi-
mate
travel
time
in reach,
days
10
3.9
2.8
TABLE 2. Dry-Weather 1974 Ultimate BOD Loading, Willamette River, Oregon
Sources
Loading, Ibs/day
Percent
Nonpoint
Point
Municipal
Industrial
Total:
77,100
37,600
54,400
169,100
46
22
_32
100
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Willamette Portland
Newberg Falls |— Harbor
DISTANCE. IN RIVER MILES ABOVE MOUTH
Figure 1. — Map and profile representing the Willamette River,
Oreg., (A) distinctive morphologic reaches, (81 elevation
profile.
80 60 40 20
RIVER MILES ABOVE MOUTH
Figure 2. — Comparison of 1973 and historical DO profiles in the
Willamette River for steady, low-flow conditions.
LOCATION (River Mile)
Albany Salem Newberg
120 86 50
1.4
Newberg
Willamette Portland
Falls |— Harbor
< 80
EXPLANATION
State DO standards
468
TIME OF PASSAGE, DAYS
Figure 3. — Inorganic nitrogen concentrations in the Willamette
River during mid-August 1974.
RIVER MILES ABOVE MOUTH
Figure 4 — DO profiles for selected percentages of the measured
point-source BOD loading during mid-August 1974. Flow and
ammonia loading held constant at observed levels.
67
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Salem
1
Newberg
Willamette Portland
Falls |— Harbor -*|
EXPLANATION
Observed
A Predicted for a BODg municipal
effluent standard of 10 mg/1
State DO standards
Newberg
Willamette Portland
Falls i*— Harbor -+
60 40
RIVER MILES ABOVE MOUTH
EXPLANATION
State DO standards
60 40
RIVER MILES ABOVE MOUTH
Figure 5 — DO profiles: observed during mid-August 1974 and
predicted for a BOD^ municipal effluent standard of 10 mg/1.
Flow and ammonia loading held constant at observed levels.
Figure 6 — DO profiles for an effluent standard of 10 mg/1
NH4-N and for selected percentages of the measured point-
source ammonia loading during mid-August 1974. Flow and
BOD loading held constant at observed levels.
Newberg
Willamette Portland
Falls I*— Harbor *|
1 1
EXPLANATION
State DO standards
60 40
RIVER MILES ABOVE MOUTH
Salem
1
Newberg
Willamette Portland
Falls I*— Harbor -
EXPLANATION
State DO standards
Figure 7 — DO profiles for selected flows with BOD and ammo-
nia loadings held constant at levels measured during mid-
August 1974. Observed flow was about 6,760 ft3/s.
o so eo 40 20
RIVER MILES ABOVE MOUTH
Figure 8. — DO profiles for selected conditions of flow and
ammonia loading. BQD loading held constant at levels ob-
served during July-August, 1973. Curves A C and D are pre-
dicted; curve B is observed.
68
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URBANIZATION AND FLOODING AN EXAMPLE
Robert P. Shubinski, Vice President and William N. Fitch, Principal Engineer
Water Resources Engineers, Inc.
Springfield, Virginia
The Four Mile Run watershed in Northern Virginia
is a classical example of the development of flood
problems with urbanization. The Corps of Engineers has
planned $29,000,000 in channel improvements to
alleviate the problem, but the Congress, concerned that
future development in the basin will create the problem
again, required that a land management program be
developed. The selected approach to land management
is designed to determine effective structural and
nonstructural methods of flood abatement. Emphasis is
on the nonstructural. The technical portions of the
program rely on two stormwater models. The models are
STORM, a Corps model which is useful as a screening
tool, and SWMM, a more detailed model sponsored by
EPA. The paper describes the application of these
models, using historic and design hydrology, to
determine the plans and policies for further basin
development.
Introduction
This paper describes the application of two
complementary stormwater models to an urbanizing
watershed. The first model, STORM (Storage, Treatment,
Overflow, Runoff Model),1 is a simple model based on
the rational method. It was used to develop a
statistical analysis of the basin's hydrology, thereby
defining the design storm. The sophisticated model,
WREM (Water Resources Engineers Model),2 was then
applied, using the design hydrology developed in STORM,
to determine the response of the watershed to various
control alternatives. Later, in work now underway,
these results will be used to assign design shares for
future development to each of the political subdivisions
in the basin.
The Overview Model, STORM
The Four Mile Run Basin, located in Northern
Virginia, has a total watershed area of 19.5 square
miles. Figure 1 is a map of the basin. There are
five major tributaries, all of which have steep slopes
and in general have rapid and very peaked runoff
characteristics. The base flow of Four Mile Run, for
the purposes of this study defined as the dry weather
flow, varies from 3 to 7 cfs. This discharge is
insignificant compared to peak discharge rates for
flooding events and was therefore not included in the
flood flow analysis.
Three types of hydrologic data were prepared as
input to STORM: areal and temporal distribution of
rainfall, stream flood stage and evaporation rate.
Rainfall distribution data were analyzed to identify
significant long term trends in the major storm events
and the type of storm which creates major floods, and
to define reliable isohyetal patterns for the major
storm events. Data for this study were taken from
recording and nonrecording rainfall gages operated
in 60 different locations in and around the watershed
by the United States Geological Survey (US6S), the
National Weather Service (NWS), and Arlington and
Fairfax Counties.
Temporal data indicated that higher intensity
rainfalls occurred during thunderstorms rather than
during hurricanes or slow-moving storms and the time
at which peak intensities occur for different stations
was found to be less variable for thunderstorms than
for slow-moving storms. Analysis of the areal
distribution showed a large variability of total rain-
fall between stations, particularly for thunderstorms.
Average rainfall for the basin was determined by
weighting the average rainfall between successive
isohyetals by the area between isohyetals, totalling
these products and dividing by the total area. Figure
2 presents the isohyetals for the largest peak dis-
charge (July 23, 1969).
Stream flow stage data are available from nine
gages in the watershed operated by the USGS. However,
records are sketchy for the purposes of this study due
to the destruction of the gages during extreme flooding
and delays in replacing the gages. Discharge rates for
all of seven primary locations are available for only
one of the seven flood events selected for the study.
Evaporation directly affects the available
depression storage and therefore affects the proportion
of rainfall which occurs as runoff. The evaporation
rate used as input to STORM is the pan coefficient for
the Washington area (0.76) published by the NWS
extrapolated for winter months.
Definition of the Rainfall/Runoff Relationship
The hydrologic data described above for six
storm events were used with data for present land use
conditions to adjust the runoff coefficients used in
STORM until the model reproduced field conditions
within a preset margin. This procedure resulted in
the definition of the rainfall/runoff relationship for
the Four Mile Run Watershed and a calibrated simulation
model that can be used to generate extended runoff
records from the long term rainfall records at
National Airport. The six storm events were selected
for the calibration procedure on the basis of flood
magnitude, recentness, and availability of rainfall and
runoff data. All six storms had a recurrence interval
greater than five years.
Land use data were transformed into percent
surface imperviousness for each of five land use
classifications: single family residential and schools,
multi-family residential, commercial/office/institu-
tional, industrial and open space. While the residen-
tial and open space classifications occupy 15.5 square
miles of the total 19.5 square miles of the watershed,
the percent impervious for residential usage ranges
from 13 to 71 percent.
Determination of the runoff coefficient for
pervious and impervious areas is the essence of the
calibration process in STORM. The runoff coefficient
is the fraction of the total rainfall which becomes
surface runoff, and is thus directly related to the
infiltration capacity of the surface. The runoff
69
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coefficients determined during the STORM calibration
were, for pervious areas, 0.39 and, for impervious
areas, 0.90. These values were then used in simulating
the flood which would result from the design storm
event. It should be noted that all six calibration
storms caused major flooding; therefore the runoff
coefficients are defined, in the strict sense, for
flooding events only.
The model was calibrated using the complete
hydrographs of two of the six major storm events and
peak discharge measurements for the other four
available for a downstream gage. Complete hydrographs
for these four storms were not available due to the
loss of the key downstream gage during the storms. As
shown in Figure 3, the calibration simulations for
discharges of five of the six storms showed agreement
within ± 12 percent of measured flows. The discrep-
ancy can be caused by several factors, most importantly
that the model assumes that infiltration capacity of
the surface is constant through the duration of a storm
and that depression storage is constant for all storm
magnitudes.
A sensitivity analysis was made for the model in
order to determine the relative effects of varying
key parameters, i.e., ratio of basin rainfall to
National Airport rainfall, pervious and impervious
runoff coefficients, depression storage, percent
impervious for low density land use category and
percent impervious for the vacant land use category.
The sensitivity analysis showed that:
1. The predicted discharge rates are highly
sensitive to inaccuracies in the average rainfall
patterns for the basin,
2. Large changes in land use produce a signifi-
cant change in peak discharge for major storm events,
3. The effects of land use changes over the
calibration period (1963-1973) are overshadowed by
inaccuracies in stream flow measurement, and
4. The sensitivity of the model to changes in
land use is relatively independent of the runoff
coefficients determined in the calibration process.
Analysis of Design Flood Frequencies
Flood frequency analysis was used to determine
the probable extreme flow which the flood control
project must accommodate. The specific flood frequency
which serves as the basis of the project design must
be selected through economic analyses and policy
decisions. The expected flood frequency for flood
events is determined by analyzing the statistical
variation of historical flow records. Since the
project design is based on present land use conditions,
these historical flow records must be adjusted to
account for the effects of urbanization. Figure 4
presents a comparative flood frequency curve developed
by two methods—the unit hydrograph method with external
flow adjustment (USAGE method)3 and rainfall runoff
analysis for present land use (STORM method)
The USAGE method for adjusting flow records was
to increase historical flows by fixed annual
percentages. The method used in the present study is
based on discharges predicted by STORM, calibrated for
present land use, and historical rainfall records. A
comparison of the two methods shows a significant
difference, but flow frequency curves for the methods
cross near the 100-year recurrence interval which was
the point selected as the design frequency. For
intervals of less than 90 years STORM predicts higher
annual flows and for intervals greater than 90 years
it predicts lower peak annual flows. Since the
predicted peak annual flows for these high recurrence
intervals are projected from available records, the
difference in the two methods for recurrence intervals
greater than 60 years is a direct result of differences
of predicted flows in the less frequent events. At a
design recurrence interval of 100 years the peak annual
flow based on the model STORM anlaysis is only 2.4
percent lower than the USAGE design flow. That differ-
ence was judged to be insignificant for project design.
It should be noted that the STORM method was based
on calibration to only flood events. Therefore, STORM
overestimates minor annual floods.
Development of the Design Storm
A design storm event was developed in order to
evaluate the effects of urbanization and runoff control
on the USAGE project. The channel design portion of
the project was selected as the focal point of the
study because it has a lower design capacity than
any of the other flood control structures in the flood
control project. Since the basis of the channel
design is the 100-year flood, the design storm must
generate such an event when it is applied to the
existing watershed land use pattern.
The design storm event was developed by the method
of Kiefer and Chu.1* This method uses the rainfall
intensity-duration curve to yield the fraction of the
rainfall before the time of peak intensity which is
equal to the ratio observed for the area. It gives
a design storm consistent with the measured rainfall
patterns and the results of several previous studies.
The actual design storm used in STORM is a stepped
hyetograph developed from the continuous function
produced by the Kiefer and Chu method. Figure 5
presents the design storm that was adopted.
The design capacity of the channel proposed by
the USAGE is 22,500 cfs. The model. STORM predicted
a 100-year flow of 21,950 cfs using historical data.
Using the Kiefer and Chu 100-year design storm, only
19,500 cfs was predicted. Therefore, the design
storm rainfall was increased by a constant percentage
to generate a peak runoff of 22,500 cfs. The frequency
of the design storm thus produced therefore exceeds
the 100-year rainfall return frequency by some small
amount. Justification for this adjustment can be
inferred from the distinction between rainfall
frequency and flood frequency. The analyses in STORM,
although they are based ostensibly on runoff, are
really based on rainfall because of the limitations
of the rational method. It is logical, therefore, to
modify the design storm to reflect flow records
instead of rainfall.
The Detailed Model, WREM
Unlike STORM, which does not include routing and
considers the collection system only indirectly, the
model WREM routes flow using the Navier-Stokes
equation and requires a detailed description of the
watershed, the sewer system and the stream network.
A drainage area receives rainfall which is reduced by
infiltration losses and by intercepted runoff
(depression storage). Infiltration is estimated by
equations relating the infiltration rate to the
antecedent moisture conditions and to soil type.
Standard SCS soil classifications are used and the
infiltration rate modified according to rainfall
intensity and timing. Infiltration occurs both on
70
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pervious and impervious areas, but at different rates.
Residential runoff from both pervious and
impervious areas is further modified by retaining a
small portion of the runoff on the surface. Retention
depths ranging from 0.05 inch to 0.20 inch are used.
Runoff is then routed from each subcatchment
using the Manning equation to portray overland flow.
The average flow length of the pervious and impervious
areas is estimated and the flow velocity estimated.
Runoff is collected at an inlet and conveyed by
storm sewer or gutter downstream through the collection
system. Manning's equation for open channel flow is
solved by finite difference techniques to maintain
continuity using average flows over a time interval
usually ranging from 5 to 30 minutes.
Hydrographs are routed through the stream system
by shortening the time step to 40 seconds and solving
the transient flow equations at that time step by
finite difference approximations. Tidal effects on
the lower reaches are included.
The WREM Network
The watershed was subdivided into 177 drainage
areas connected by 97 minor pipes. The main channel
and minor tributaries are conveyed through an addi-
tional 90 channels and major pipes. The rainfall
interval used is 15 minutes with records developed
from 4 to 8 continuous gages depending on the storm
event simulated. Nine major land use categories are
used for the impervious/pervious estimation. The
impervious/pervious data by land use category are
developed for 49 zones within the watershed to
incorporate geographic locational differences in lot
coverage. Soils data revealed that 3 of the 4 SCS
classifications occur in the watershed. These soil
classifications are assigned to each of the 177
drainage areas. Intensive data collection was
undertaken to define:
Rainfall variations (temporal and area!)
Soil type
Land use (past, current and future)
Soil cover (impervious/pervious data)
Storm sewers
Natural channels.
points. The USGS gaging station at Shirlington is
Transport Model Conduit #401 which drains 14.3 square
miles of the watershed's total of 19.5 square miles.
Agreement was good there for the two most recent
storms (1969 and 1972). The other conduits are in
tributary streams usually draining smaller tributary
areas. The exceptions are 470 and 408 which are the
box culverts under the RFP Railroad and the Mt. Vernon
Avenue Bridge, i.e., downstream from the mouth. Peak
flow estimates were available there.
Conclusion
This project has demonstrated the conjoint use
of two models to utilize the best features of each.
They have been used individually by many investigators
throughout the country; this is the first time, so far
as the authors are aware, that the models have been
used together. WREM has provided the capability to
examine the response of the system to a single design
event in great detail. STORM has provided the
hydrologic background to insure that the single event
used is significant. Taken together, the models give
the best of both continuous simulation and single
event simulation.
References
1. "Urban Runoff: Storage, Treatment and Overflow
Model 'STORM'," Hydrologic Engineering Center,
U.S. Army Corps of Engineers, Davis, California,
September 1973.
2. Kibler, D.F., J.R. Monser and L.A. Roesner, San
Francisco Stormaatev Model: User's Manual and
Program Documentation, Water Resources Engineers,
prepared for the City and County of San Francisco
(undated).
3. Baltimore District, Corps of Engineers, Fourmile
Run: Local Flood-Protection Project, Design
Memorandum No. 1, Hydrology and Hydraulic Analyses,
June 1972.
4. Keifer, C.J., and H.H. Chu, "Synthetic Storm
Pattern for Drainage Design," J. Hydraulics Div.,
Proa. ASCE, HY4, Vol. 83, August 1957, p. 1332.
Calibration Storms
The watershed experienced major flooding events
in 1963, 1966, twice in 1969, 1970, 1972 and 1975.
The rainfall hyetographs were prepared for each of
these storms from the rain gage network data.
Streamflow data are unfortunately lacking as the 1969
storm destroyed the stream gage. Therefore, only
peak flow measurements are available for the 1969
storms and all storms thereafter.
Surveying the available hydrologic data and
comparing it to the available land use data resulted
in the selection of 1963, (July) 1969 and 1972 floods
as calibration storms. The land use breakdowns for
each calibration year shown in Table 1 were prepared
as were details of channel/storm sewer modifications.
Antecedent moisture conditions were determined for
each storm. The model was then used to simulate these
three events. The model results are presented in
Table 2 and compared to measured flow at defined
FOUR MILE RUN LAUD USE
TYPE DESC.
OPEN SPACE
Low DENSITY
MEDIUM DENSITY
HIGH DENSITY
SCHOOLS
INSTITUTIONAL
COMMEP.CIAL
INDUSTRIAL
SHIRLEY HIGHWAY
1963
1.0901
8,3191
0.9751
2,3318
0,7207
0.8319
1.3053
0,5593
0,2019
1969
1.0395
8.2631
0.9751
2.1133
0,7311
0.8109
1.3053
0.5693
0.2019
1972
3.9125
8.2G81
0.9751
2,1661
0,7996
0.3166
1.3053
0.5693
0,2019
1975
3.3318
8.2652
0.9751
2.5171
0.7996
0.3195
1.3058
0.5693
0,2019
FUTURE
LAND
3.3119
8,3789
1.0212
2.3377
0.7996
0.8S68
1.3356
0.5693
0,2019
71
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TABLE 2
FLOH CAL1B8ATIOII RESULTS AT USGS GAG DIG STATIONS
r-1...-
TR*:;SPOST KODEL
CoiJDun 3
218
217
219
310
308
101
306
116
115
108
170
1972
USGS
FLO*
--
980
700
1,250
10,000
--
--
"
KODEL
FLOW
1,107
795
5,550
651
813
9,372
8,853
1,697
781
10,861
6,121
DlFF.
(18.9
--
|7.0
(32.5
|6.2
"
--
--
"
1969
USGS
FLOW
1,330
1,280
1,800
1,600
1,900
11,600
2,200
1,700
17,000
5,500
MODEL
FLOH
1,611
1,287
6,317
1,279
1,775
11,213
13,183
3,010
1,308
17,263
6,250
DT.
I23.1
|0.5
(31.6
(20.0
1 6'5
|2.G
(38.2
(23.1
fl.5
(13.1
1963
USGS
FLOW
830
"
--
11,700
"
--
"
I'ODEL
FLOW
1,290
911
5,393
772
779
9,290
8,802
2,196
1,018
11,780
5,752
D,jf.
|13.7
—
--
-
(20.6
--
"
"
—
-- INDICATES VALUE NOT DETERMINED
20CO 0 2000 4000
SCALE IN FEET
FIGURE 1
Four Mile Run Watershed Map
FIGURE 2 o I 2MILES
Area] Distribution of Total Rainfall for BASIN BOUNDARY
700 EST July 22 to 1800 EST July 23, 1969
-10% OF Q MEASURED
-Q MODEL - Q MEASURED
FIGURE 3
'(72)
Variation Between Observed and
Model Peak Discharge Bates For
Model Calibration
NOTE -
DEPRESSION STORAGE = ,23"
RUNOFF COEFFICIENT (PERVIOUS)" 39
RUNOFF COEFFICIENT (IMPERVIOUS) e 90
HIMKRB IN WHENTHESIS INDICATE
1-EAR DF OCCURRENCE OF
CALIBRATION STORM
7,500 lopoo 12,500 I5.OOO
0 Mooiurtd ( eft )
72
-------
Maximum Annual Flow \
Frequency Curve From
STORM (1922-1973 Rainfall)
Omlting Flows with Recurrence
Irtervoi Less Than 5 Years
Maximum Annual Flow Usng STORM
Maximum Annual Flow Using USACE Method
Flow Frequency Curves at USGS
Gaging Station Using USACE Method
and Model STORM
\
Maximum Annual Flow Frequency Curve Using USACE Method
(Adjusted For Urbanisation J 1951-1972
1000 200 IOO 50 20 D 5 2
RECURRENCE INTERVAL .YEARS
ADOPTED DESIGN STORM
AT NATIONAL AIRPORT
TIME FROM PEAK INTENSITY-MNUTES
73
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PLANNING MODELS FOR NON-POINT RUNOFF ASSESSMENT
Howard A. True
Computer Systems Analyst
Ambient Monitoring Section
Surveillance and Analysis Division
E. P. A., Region IV, Athens, Georgia
ABSTRACT
Several computer based processes were developed for
assessing the potential magnitudes of constituents
from non-point sources. These processes have evolved
from application of diverse procedures and literature
data to solving specific problems in Environmental Im-
pact Statement preparation and review, National Pollu-
tant Discharge Elimination System*permit load alloca-
tions, and preparation of water quality field survey
reports. The availability of workable processes used
in industrial operations research and anticipated
needs in the Section 208 areawide studies have led to
the development of some very useful calculating pro-
cedures. The coverage of much of the vast spectrum
of gross assessments amply justify the efforts ex-
pended to date. Major benefits can be derived by re-
petitive use of these processes to calculate relative
numerical measures of effects resulting from changes
in treatment level percentages, land use allocation
percentages, population densities, loading rates, and
rainfall event intensities.
These grouped processes are referred to as planning
models and their formulation and data requirements are
given in separate documentation. They are not excess-
ively complex or costly to run and simple problems can
be handled with a minimum of effort. Flexible inputs
and external user controls allow maximum exercise of
judgment by the user and presents the opportunity for
imaginative and innovative problem formulation. Re-
port exhibits and resource requirements are contained
in the handout material.
BACKGROUND
An early review of P.L. 92-500, FWPCA** amendments, in-
dicated that major emphasis would be placed on assess-
ment of areawide pollutant sources. Historically, wa-
ter quality planners have given primary attention to
point sources and have developed few procedures for
assessing impacts from diffused sources. Environmental
Impact Statement (EIS) requirements have imposed a man-
date on those responsible for preparation and review of
Environmental Impact Statements to Insure adequate cov-
erage for all significant environmental impacts. EPA,
Region IV, which covers eight southeastern states, has
calculated the magnitude of non-point constituents for
a number of federally prepared Environmental Impact
Statements. These operational needs forced the devel-
opment of assessment procedures for producing quick
answers and have resulted in a fair degree of success.
Analytical requirements have varied enough to require
the development of several discrete calculating pro-
cesses. In response to the requirements of the Section
208 areawide planning program, these procedures have
been collected and formalized into a few processes cap-
able of serving as planning models. No attempt has
been made to duplicate existing stream, reservoir, es-
tuary, and storm water management models.
* NPDES
** Federal Water Pollution Control Act
GENERAL CHARACTERISTICS
The individual planning models discussed here are: (A)
"Urban, Commercial, and Industrial Runoff," (B) "Ero-
sion, Sedimentation, and Rural Runoff" and (C) "Total
Loadings from Point and Non-Point Sources to Waterbod-
ies." Models (A) and (B) produce independent reports
and can also provide loading factors for model (C).
Model (C) provides a composite report for multiple
point and non-point sources for a single parameter.
Urban areas can be split into twenty sub-areas and up
to forty parameters can be calculated for single storm
events within a metropolitan area using model (A).
Large or small areas, such as entire river basins or
single-acre plots, can be analyzed, using model (B) ,
for soil loss, sediment delivered, and the usual rural
parameters (Nitrogen, Phosphorous, Potassium, BOD, TOC,
and Acid drainage). Best combinations of treatment
requirements and land use alternatives can be deter-
mined by multiple runs with model (C). The hydrologic,
transport, and calculating mechanisms differ in all
processes, and each process is designed to best ful-
fill its intended purpose.
The "Urban, Commercial, and Industrial Runoff" Model
.(A)
This planning model is designed for a single rainfall
event and will calculate the "first flush" slug load
in pounds or coliform counts along with runoff concen-
trations for up to forty parameters at a time. These
runoff slugs from up to twenty sub-areas are routed to
a water body mixing zone, and the resulting stream or
stillwater constituent concentrations are calculated
after each slug arrives. Runoff water quantity is cal-
culated In a manner similar to the "Rational Method"
and all parameter calculations use deterministic meth-
ods.
Key parameter inputs to the model are: parameter name,
units, waterbody background concentration, curb mile
and per acre loading factors. Waterbody input infor-
mation includes acre-feet for stillwater or ft-Vsec flow
and velocity for moving streams. Other inputs include
routing distances, runoff velocities, area, rainfall
intensity, area type runoff factors, and either popu-
lation for suburban areas or percent imperviousness
for industrial and commercial areas. Multiple rain-
fall event intensities are allowed to give multiple
reports for all areas in a single run.
Model features are:
(1) Utilization of the first fifteen minutes of
rainfall only.
(2) Calculated curb miles and percent impervious-
ness, utilizing regression equations and pop-
ulation density, for suburban areas only.
(3) Summarization of curb mile loaded suburban
areas with areal loaded commercial and in-
dustrial areas.
74
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(4) Still water or moving stream mixing depend-
ing on receiving water input data.
Productive uses are:
(1) Gross assessment of current and projected
area non-point pollution potential.
(2) Reasonably accurate calculation of urban
type non-point loads after load factor ad-
justment consistent with sampling and local
characterization of pollutants.
(3) Supplies refined, non-point loadings to
Model (C) for consolidating point and non-
point single parameter loads to waterbodies.
The "Erosion, Sedimentation, and Rural Runoff" Model
IB)
This planning model is primarily of the periodic type
and can be run for a single month or any group of con-
secutive months not exceeding one year. It is essen-
tially nonhydrologic since the calculating mechanism
is the "Universal Soil Loss Equation" developed by
USDA. It will handle a single storm for erosion and
sedimentation only, but special input requirements ap-
ply in this case. The model calculates tons of soil
loss, sediment delivery to waterbodies and sediment
downstream migration. Forest litter, nitrogen, phos-
phorous, potassium, BOD, TOC, and acid drainage are
calculated and reported in pounds. Excluding acid
drainage, the remaining common parameters are calcu-
lated from sediment, litter (leaves, twigs, etc.),
and from animal and fowl droppings.
This is a probabilistic process using a random number
generator to obtain a better representation of highly
variable conditions. The process can easily be made
into a pure deterministic process by using mean values
and zero deviations in the input data. Some users
have operated in this manner successfully. The inter-
nal design of this process is quite complex and chan-
ges other than report line formats are likely to lead
to disaster and are not recommended.
No provisions exist for handling pesticides; however,
model (A) will calculate these parameters when oper-
ated with areal loading factors for pesticides. Model
(B) is designed to give the user almost total control
of results through localized input data and its flex-
ibility allows a minimum of input with a default to
national distributions and loading factors contained
internally or in the master deck preceding local data.
Key inputs to this system include: report headings,
time period, multiplier starting value for the random
number generator, standard state FIPS numbers, and
number of units. Each sub-area requires: acres,
blowup factor (plot size), one to five soil types,
percent slope and slope length range, one to five crop
management practices, one to five erosion control
practices, load factors for sediment and litter, ani-
mal and fowl counts, and loading factors for acid
drainage.
Model features are:
(1) Multiple sub-areas within each state for de-
tailed definition.
(2) Multiple number of states for handling entire
river basins.
(3) Gross assessments for large areas with mini-
mum local input data needed.
(4) Very detailed assessments for areas of in-
terest by using many small units and compre-
hensive localized data.
Productive uses include:
(1) Projections of effects of land use changes
and erosion control practices with minor
changes to input data.
(2) Refining load factors for model (C) for use
in consolidating point and non-point single
parameter loads to waterbodies.
The "Total Loadings from Point and Non-Point Sources
to Waterbodies" Model (C)
This planning model uses some concepts from R. A. Vol-
lenweider's "Export Process" and has no hydrologic
characteristics. The time period can be from one day
to any number of days, such as a one-hundred-and-fifty
day growing season. All loading factors are on an an-
nual basis and are modified by the factor (period in
days/365). The model is designed to handle a single
parameter for three point sources and five non-point
sources for each of an unlimited number of sub-areas.
The composite report gives three columns of loading
information composed of minimum expected, most prob-
able, and maximum expected. The minimum and maximum
quantities are calculated from loading factor limits.
Probabilistic methods, utilizing a random number gene-
rator, are used to calculate the most probable quanti-
ty from each source.
This model is a relatively simple process and the com-
puter program can be modified by users if desired.
Any parameter that is quantifiable on a weight basis
can be handled. Simple attenuation processes are
built into the system.
Key inputs to this system include: report headings,
time period, modification to multiplier starting value
for the random number generator, population, acres,
treatment level percentages for point sources, land
use distribution percentages for non-point sources,
loading factor limits (national and localized) and at-
tenuation factors.
Model features are:
(1) Unlimited number of sub-areas.
(2) A set of national loading factor limits for
default use in the absence of local loading
factor limits.
(3) Capabilities for producing a composite re-
port from multiple point and non-point sour-
ces for a single parameter.
Productive uses include:
(1) Determining load allocations for issuing
NPDES permits by making multiple runs using
modified point source treatment levels and
setting each sewage treatment plant up in a
separate sub-area.
(2) Making long range projections by changing
population, treatment level percentages and
land use distribution percentages for cer-
tain sub-areas.
(3) Gross assessments to determine if a more de-
tailed study is needed requiring use of mod-
els (A) and (B) .
75
-------
(4) Producing progress reports.
SUMMARY
The main objective in assessing non-point runoff is to
estimate constituent loads for some representative
time period for a defined drainage area. No absolute-
ly accurate answers appear economically feasible now
or in the near future, and getting a handle on the
many facets of the problem is very difficult. These
planning models are generalized tools designed for in-
itial gross assessments with refinement capabilities
to provide ball park numbers for decision making. Nu-
merical values such as these, systematically arrived
at, provide a basis for estimating the relative ef-
fects of changes to physical features. Control of run-
off constituents through process and/or structural
changes would settle, filter, or otherwise reduce con-
centrations rather than eliminate runoff. This is of-
ten in direct conflict with some forms of flood con-
trol where speeding up the runoff from land is the
paramount objective.
The accuracy of output from these planning models is
directly related to the quality of input data supplied
by the user. These models are tools for planners and
are being made available to anyone willing to learn
how to use them.
All computer programming is in the universally used
FORTRAN-4 language. Source programs and test case run
decks for all three planning models are in library
files on the EPA-OSI computer system and may be repro-
duced on 80-column cards if a request is made through
normal EPA channels. Run modules for each planning
model can be accessed by EPA-OSI users through Job
Control Language procedures. Concise documentation
for problem definition and data coding is contained
in the exhibit handout.
All libraries are located on EPA-OSI disk RIV004.
Source programs and exhibit run decks (approximately
1,450 cards) are in a library named CNMD01.HAT.NPPP.OG
and the exhibit run decks only (256 cards) are in a
library named CNMD01.HAT.NPRUN. Compiled modules are
in a library named CNMD01.HAT.ASSESS and program names
are EPAURA, EPARRB, and EPATLC for planning models A,
B, and C.
76
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DESIGN AMD APPLICATION OF THE TEXAS EPISODIC MODEL
John H. Christiansen
Data Processing Section
Texas Air Control Board
Austin, Texas
The Texas Episodic Model (TEM)is a new short-term
air pollution dispersion computer model being used ex-
tensively by the Texas Air Control Board.
Design innovations make the TEM several times
faster than models of comparable sophistication and
accuracy. The TEM uses steady-state bivariate Gaussian
plume point source logic, but solves the dispersion
equation by interpolating in a table of precalculated
coefficients, rather than time-consuming explicit cal-
culations of the exponentials involved. Area sources
are handled by a very fast algorithm based on work of
S.R. Hanna and F.A. Gifford.
The model calculates plume rise via one of six
equations (all due to G.A. Briggs), choosing the appro-
priate equation on the basis of 1) downwind distance,
2) atmospheric stability, and 3) whether the rise of
the plume is dominated by thermal buoyancy or momentum.
It also takes into account pollutant decay, variation
of wind speed with height, and atmospheric inversion
layers. Plumes may be trapped below an inversion or
may penetrate it and escape. The degree of penetrabil-
ity is variable, and is specified by the user, allowing
simulation of "weak" or "strong" inversions.
Concentrations are calculated for one or two pollu-
tants at up to 2500 locations in -a. uniform grid of
arbitrary dimensions and spacing, for a wide range of
sample times from 10 minutes to 2k hours.
The versatility provided by a. wide variety of input
options and graphic output options allows the TEM to
serve the needs of several different user groups within
the Texas Air Control Board. Four examples of current
TEM applications are discussed.
Introduction
The Texas Episodic Model, or TEM, is a. FORTRAN com-
puter program which may be used to predict air pollu-
tion concentrations for short time periods. An emis-
sions inventory and a set of meteorological conditions
are used to create scenarios simulating the dispersion
of airborne pollutants in the lower atmosphere. The
TEM was developed to fulfill the requirements of the
Texas Air Control Board (TACB) for a model of high
enough efficiency, sophistication, and versatility to
make it a worthwhile analytical tool for a wide range
of applications.
This paper will first describe several design fea-
tures of the TEM. The input data required and the
types of output available will also be discussed. The
remainder of the paper will deal with some of the TEM's
current areas of application within the TACB.
Model Design
Point Source Algorithm
The TEM employs the steady-state Gaussian plume
hypothesis for calculation of concentrations due to
point sources. This hypothesis makes use of the
following assumptions:
1. The emission rate of the source is constant, and no
dispersion occurs in the downwind direction. The
pollutant is simply transported downwind at the
appropriate wind speed. The TEM uses the wind
speed at the physical source height.
2. In both the crosswind and vertical directions, the
pollutant is dispersed by turbulent eddy diffusion.
The concentration patterns in these directions take
the form of Gaussian distributions about the center
line of the plume. The standard deviations of the
two Gaussian distributions increase with downwind
distance or time elapsed since release. In the TEM,
the standard deviations are power law functions of
downwind distance.
3. The plume is reflected at the earth's surface. This
means that none of the pollutant is lost to reac-
tion or deposition at the surface.
Pollutants are assumed to be essentially non-reactive.
For concentrations at ground level, the Gaussian plume
equation may be written:
exp
(1)
viiere x is the concentration, in micrograms per cubic
meter;
Q is the source emission rate, in grams per second;
U is the wind speed at physical source height, in
meters per second;
H is the effective source height, equal to the physical
source height plus the plume rise, in meters;
x,y,z are the downwind, crosswind, and vertical direc-
tions respectively, in meters.
The standard deviations o~v and o~_ vary with down-
wind distance x and atmospheric stability class S
according to the following formulae:
a = a(S) x
z
cr.= c(s) x
b(S)
d(S)
(2)
(3)
Values of the stability-dependent coefficients a,b,c,
and d are derived from Turner and Busse and Zimmerman .
Vertical Wind Profile. The mean wind speed in the
lower atmosphere typically increases with height in a
way that can be approximated by a power'3aw. The quan-
tity U in equation (l) represents the wind speed at the
physical height of the source. The TEM derives this
wind speed for each source from the input "ground level"
wind speed by a formula featuring exponential increase
with height, with the exponent dependent on atmospheric
stability.
Plume Rise. The effective source height, H, in
equation (l) is the sum of the physical source height,
h, and the plume rise, Ah. Calculation of the plume
rise is handled quite rigorously by the TEM. The plume
may emerge into "stable" (stability classes E and F) or
"unstable" (classes A through D) air. The dimensions,
exit velocity, and exit temperature of the source and
the ambient temperature will indicate whether the up-
ward motion of the plume is dominated by momentum or
thermal buoyancy. The TEM employs a separate set of
plume rise equations for each of the four possible
situations: stable/buoyant, stable/momentum, unstable/
buoyant, and unstable/momentum. The atmospheric stabil-
ity is an input parameter for each TEM weather scenario,
so for each source the program has only to decide
whether the plume rise is momentum- or buoyancy-domin-
ated. Peak plume rise is calculated using both the
momentum and buoyancy plume rise equations for the
77
-------
atmospheric stability in question. If the momentum
equation yields a higher plume rise than the buoyancy
equation, the plume is assumed to be momentum-dominated^
and the momentum plume rise is used. If the buoyancy
plume rise is higher, it is used instead.
An additional equation is used to calculate plume
rise as a function of the downwind distance out to the
distance at which the plume reaches maximum height.
The six plume rise equations used by the TEM are all
due to Briggs-^.
TEM Solution of the Dispersion Equation. The TEM
is able to solve equation (1) very quickly for each
source-receptor combination due to a numerical trick
first introduced in the Texas Climatological Model^-
Let K and K be defined by
= 1000 exp -y'
V o-y L 2
and
f-H2
I " "_
K = 1000
Z ™z U2
/ \
Then, from equation (1),
x =
(It)
(5)
(6)
Note that Ky and Kz are independent of emission rate Q
and wind speed U.
In a separate program, Ky values were generated for
twenty downwind distances, x, eight angular distances
from the plume centerline, 6 (y=xtan 0), and seven
stability classes, S. The Ky values for each of these
1120 combinations (20x8x7) are stored as data tables
in the TEM. Similarly, Kz values were generated for
the same twenty downwind distances, fourteen effective
source heights, H, and seven stability classes, giving
I960 values. The downwind distance values chosen were
x=2, 3, »t, 5, 6, 7, 8, 10, 12, lit, IT, 20, 23, 27, 31, 36,i*l,l*T, 53 and
60 km. The effective source heights were H= 10,20,30,
50,70,100,150,200,300,lt50,700,1000,lltOO and 2000 meters.
The seven stability categories are commonly referred to,
in increasing order of stability, as classes A,B,C,D
(day), D(night), E, and F. Finally, the angular dis-
tance from the centerline were 9=0, $,26,.. .,76, where
the increment S is a function of stability class, rang-
dng from 5° for A stability to just 1° for F stability.
This means that the Ky data table is good to an angle
of 35° from the plume centerline in A stability, but
only 7° in F stability. The 6 values were chosen so
that the concentration at an angle of 76 from the
centerline vould be 1.0 percent or less of the center-
line concentration at all downwind distances. As
stability decreases, the effectiveness of turbulent
diffusion increases, so that the plume spreads out more
and a larger 6 is required.
For downwind distances greater than 2.0 kilometers,
the TEM calculates point source concentrations from
equation (6) instead of equation (l). Ky and Kz are
found by linear interpolation in the Ky and Kz tables.
This procedure is much faster than the explicit calcu-
lation of the exponentials in equation (l), and is
chiefly responsible for the high speed of the model.
For downwind distances of less than 2.0 kilometers, the
TEM uses equation (l) instead of equation (6). This is
because the accuracy of the linear interpolation is
inadequate at such short distances.
When interpolating for a Kz value, it is assumed
that the plume has completed its rise, so that the
effective source height is constant in the distance
range under consideration. The rise of the plume is
considered to be complete before the plume gets 2.0
kilometers downwind of its source, a. valid assumption
in nearly every case.
Mixing Height. The "mixing layer" of relatively
turbulent air near the ground is very frequently
bounded by a layer of stable air aloft. The distance
from the ground to the bottom of the stable layer is
the "mixing height". The effect of the stable layer is
i virtually to prevent vertical dispersion above the
mixing height. Pollutants emitted into the mixing
layer will be trapped there, eventually becoming
totally mixed in the vertical direction. On the other
hand, pollutants emitted directly into the stable layer
will remain there, and not disperse downward to any
extent. The TEM can simulate either of these possibil-
ities. If the physical source height exceeds the mix-
ing height, the plume will obviously emerge into the
stable layer, and the source is neglected. If the
maximum effective source height is less than the mixing
height, the plume is trapped in the mixing layer, and
the expression for vertical dispersion (Kz) will have
to be modified to account for it .
The TEM treats restricted vertical mixing as sug-
gested by Turner1. Uniform vertical mixing impends at
some downwind distance x^j (a function of az), and is
considered complete at 2xm.
may be written
For xJ2xm, equation (l)
exp
(7)
with mixing height =L, and the Gaussian distribution in
z replaced by a uniform distribution in z, 0< z LI.
For the weakest possible inversion, 1=1. For n strong
inversion, I> 2. A recent paper by Briggs' addresses
the inversion penetration problem in considerable
detail. If LI $H> L, then H is set equal to L, and the
plume does not escape.
Pollutant Decay. Removal of pollutants from a
plume by various processes such as adsorption and chem-
ical reaction may be simulated (albeit simplistically)
by assigning a decay half-life to each pollutant. The
TEM adds a decay term to the dispersion' equation (6):
X =
QK K
y z
U
exp
•-0.692X
L UT.
1/2
(8)
where T ^. is the half-life, in seconds. Since half-
lives of many pollutants may be dependent on meteoro-
logical conditions, separate half-life values are input
to the model for each pollutant in each weather
scenario.
Area Source Algorithm
The TEM's area source logic is based on an algo-
rithm of Gifford and HannaS. It uses the standard
formalism of a, grid of square area sources of the same
size, but varying emission rates. The concentration
due to area sources in a given square is due to the
emissions in that square and in the N squares upwind.
78-
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The concentration is given by
x=
where A x is the area source grid spacing in meters,
Q^ is the area emission rate of the square containing
the receptor, in gm/km2/sec,
Q. are the area emission rates of the N upwind sources,
U is the surface wind speed, in meters/sec,
and a(S) .and b(S) are as defined in equation (2).
The stability class index S is decreased by one (index
for stability class A=l, B=2,...,F=7) to simulate urban
surface roughness. In the TEM, the value of If is four,
so each area source square affects itself and the four
squares downwind of it.
TEM Inputs and Outputs
Input Structure
Input to tne TEM can be divided into four sections,
as listed below:
1. Control Parameters (U cards). Control parameters
remain constant throughout the run regardless of
changes in weather in different scenarios. They
specify such items as input and output options and
dimensions and spacing of the grid of receptors at
which concentrations are calculated.
2. Scenario Parameters (l to 8 cards). From one to
eight weather scenarios may be created in each run.
Each scenario uses the same sources and receptors,
but different weather conditions. Each card con-
tains the necessary weather parameters for one
scenario.
3. Area Sources (0 to 200 cards). Each area source
card contains the location, dimensions and
emission rates of one area source.
14. Point Sources (0 to 300 cards). Each point source
card contains the location, height, diameter, exit
temperature, exit velocity, emission rates and
identification for one point source.
The control parameters give the user considerable
flexibility in deciding what the model should calculate
and in what form the results should be presented. A
few of the more important ones will be mentioned here.
The TEM will calculate pollutant concentrations
for one or two pollutants at up to 2500 locations
("receptors") in a rectangular grid of arbitrary dimen-
sions and arbitrary but uniform spacing between rows
and columns. The "receptor grid" is completely speci-
fied by five parameters: the coordinates of the south-
west corner of the grid, the number of rows and columns
(maximum of 50 each), and the spacing between rows and
columns. An option allows the user to let the TEM cal-
culate the grid parameters itself, choosing them so as
to ensure that the point of maximum concentration for
the entire source distribution, as well as the individ-
ual maximum for each source, will fall within the
boundaries of a receptor grid of maximum allowable
resolution.
The values of o~v and 0"z in the dispersion equation
were derived for a sample time of 10 minutes. The
concentrations calculated by the TEM are thus 10-min-
ute values, but they may be converted to 30-minute,
1-hour or 3-hour readings by a statistical formula
dependent on atmospheric stability^ > . In addition,
a 2it-hour time period can be simulated using eight
scenarios representing 3 hours of weather\each.
The user has a choice of formats and units for
source and weather data.
The concentrations of each pollutant at each
point in the receptor grid can be displayed in any of
the following forms-, or in virtually any combination
of them:
1. List of the coordinates and concentrations at each
receptor. This is the standard form for most air
quality models.
2. Map of the receptor grid. The concentrations
across the receptor grid are displayed in two di-
mensions with coordinates along the edges of the
page. Spatial concentration distributions are
immediately apparent with this option.
3. Control list. As an aid in formulating control
strategies, a list is printed of the identifica-
tions and contributions of the five point sources
contributing the most to the total concentration
at each receptor, for a maximum of 625 receptors
(a 25x25 grid).
k. Finally, the coordinates and concentrations at
each receptor can be output on punched cards for
input to a contour plotting routine.
Notes on TEM Performance
To assess the relative speed of the TEM, several
timing tests were conducted against the other two
short-term models available to the TACB, with each
model operating on identical sources and receptors.
The two models, both of which are substantially less
sophisticated than the TEM, are the Argonne Steady-
State Model (ASSM), and the Small Area Model MK IV,
developed some years ago by the TACB. The TEM proved
three to five times faster than both models. The
larger the area covered by the simulation, the
faster the TEM will be, since it uses a faster
algorithm for downwind distances over 2.0 kilo-
meters . The error introduced by K and K inter-
v z
polation is typically on the order of 1.0 to 5-0
percent.
TEM Applications
The TEM has found several areas of application
within the Texas Air Control Board. Although the bulk
of all TEM run requests come from the Meteorology and
Permits Sections, each modeling study cited here orig-
inated in a different section of the TACB.
In the discussion of each application, the empha-
sis will be on the subject of the analysis, the TEM's
role in the analysis, and the impact of the model
results.
Permits Section
The TACB's Permits Section employs the TEM routine-
ly as part of its analysis of new construction permit
applications from Texas industries. Action taken on a
permit application involving any potentially signifi-
cant air pollution sources is governed by four basic
criteria:
1. State and Federal allowable in-stack pollutant
concentrations.
2. State allowable ground-level concentrations based
on emissions from a single company or companies
with contiguous properties.
3. Federal allowable ground-level concentrations based
on all emissions in the area and background con-
centrations, if any.
h. Ground-level concentration of one percent of the
threshold limiting value (TLV) for any compound
having a TLV. These include about 500 compounds
considered to have harmful health effects.
79
-------
The TEM is used to evaluate the impact of the
proposed new facility against the second and third
criteria, and may in the future he used for the fourth
as well.
The pollutants usually modeled are sulfur oxides
(SOX), and less frequently, total suspended particulate
matter (TSP). Area sources are not used, and point
source and receptor grid parameters are input in
English units. The number of sources and the dimen-
sions of the receptor grid vary greatly. For studies
of a single plant (criterion two), there are generally
from one to thirty sources, and a spacing between ad-
jacent receptors in the receptor grid of 100 to 500
feet. For studies of the impact of the plant on the
air quality of an entire region (criterion three),
there may be from 30 to 300 sources, with a grid spac-
ing of 500 to 2000 feet. An example of the latter is
the basic inventory of 268 sources for the Houston
Ship Channel, Texas'most heavily industrialized area.
A typical receptor grid for this region would consist
of 50 rows and 25 columns spaced 2000 feet apart, giv-
ing an area of roughly 10 by 20 miles, uniformly
covered by 1250 receptors.
For each permit study, the Meteorology Section
provides an ensemble of weather scenarios representing
reasonable worst-case conditions for the area in ques-
tion. From k to 100 scenarios (run up to eight at
a. time by the TEM) are usually necessary to complete a
study. The number of scenarios run is largely depen-
dent on the complexity of the source distribution.
Also, if the TEM predicts a violation of an air quality
standard, more runs will be made in order to assess the
magnitude of the problem, and still more runs may be
made using source inventories altered to reflect alter-
nate approaches and control strategies for preventing
the violation. If a. significant violation of state or
Federal standards is predicted, the permit application
will be denied unless the necessary abatement proce-
dures are instituted. If a minor violation is pre-
dicted, the applicant will be required to take precau-
tions against its occurrence. The granting or denial
of a permit on the basis of criteria two or three is
thus very strongly dependent on the results of TEM
predictions.
Air Quality Evaluation Division
The TEM is also being applied in a. study under-
taken by the TACB's Air Quality Evaluation Division
(AQE). The study is attempting to establish culpabil-
ity for violations of the 24-hour ambient air quality
standard for total particulate by making use of the
TEM's control list output option. The methodology is
as follows:
1. A computer program searches the AQE master file of
measured pollutant concentrations for receptors
reporting a violation of the 24-hour standard. In
general, when a region shows a violation, roughly
five to eight receptors exceed the standard. The
program then retrieves the weather data for the
same day at a reliable weather station in the
region. The weather data is in the form of eight
3-hour readings.
2. A 2U-hour simulation is run with the TEM, using
eight 3-hour scenarios drawn from the weather
data and the best available inventory of point and
area sources of TSP for the region in which the
violation occurred. The control list option is
used, giving the five sources contributing the
most to the total concentration at each of up to
625 locations. Grid spacing is typically 0.5 to
2.0 kilometers. The source inventories for the
Dallas and Houston areas contain roughly 100 area
and 250 point sources each.
3. The predicted and observed concentrations are com-
pared. If the predictions are within +_ 30 percent
of the measurements, the control list is consulted
to see if any sources stand out as major polluters.
If any such sources are found, consideration will be
given to rewriting the local emissions regulations
to prevent future violations. If the TEM grossly
underpredicts the concentration, a search is made
for poorly sited receptors (wind flow obstructions,
etc.) and for unreported sources. Most of these
searches have been successful.
This study is thus providing a. check on the validity of
receptor data and the completeness of the emissions
inventory as well as determining culpability for viola-
tions of air quality standards.
Meteorology and Planning Sections
Texas' control strategy work for EPA's 10-year
Air Quality Maintenance Plan (AQMP) is being undertaken
by the Meteorology and Planning Sections of the TACB.
The necessary dispersion modeling of sulfur oxides and
particulates in designated Air Quality Maintenance
Areas is performed by the TEM and the Texas Climatolog-
ical Model (TOM), a long-term companion to the TEM with
compatible inputs and outputs. The basic goal of the
AQMP is to assure acceptable air quality through 1985,
despite industrial growth, population growth, and
changes expected in land use and availability of dif-
ferent fuels. The emissions inventories for each Air
Quality Maintenance Area are extrapolated for future
years, and the TEM is run with the control list option
and an ensemble of possible short-term, worst-case
weather scenarios to predict future air quality, to
identify potential trouble spots and to aid in formu-
lating control strategies.
Laboratory Division
The TACB's Laboratory Division is currently
involved in a project which uses an extensive field
study and TEM modeling to investigate the relationships
between gaseous and particulate pollutants. In June
and September of 1975, over sixty high-volume particu-
late samplers in the Houston area took readings simul-
taneously on nine different days. X-ray fluorescence
analysis of the particulate matter collected yielded
concentrations of chlorine, ammonium, nitrates, sul-
fates, total sulfur, benzine-soluble hydrocarbons, and
several metals.
A substantial amount of sulfur in the form of sul-
fates and sulfites appears in the particulate samples.
It is suspected that much of the sulfur was actually
emitted in the form of sulfur dioxide. Since S02 is
acidic, the sulfur could be tied up in the form of
sulfites on contact with any alkaline particulate.
TEM modeling is being used to help test this hypothesis.
The TEM is making 24-hour predictions of S02 and TSP
concentrations across the Houston area for each of the
nine days of the field study. If the hypothesis is
valid, one would expect to find receptors where pre-
dicted TSP is less than measured TSP, predicted S02 is
high, and the TSP collected contains large amounts of
sulfur. The extent of conversion of S02 to particu-
lates is probably dependent on travel time from source
to receptor. Travel times can be approximated, since
the wind speed is supposedly known and the TEM control
list can identify the major contributing sources at
each receptor.
Results of this project could have great impact in
at least two areas. First, control of sulfur oxide
80'
-------
emissions might be necessary to meet particulate
standards. This should be reflected in the local
regulations. Second, if the phenomenon mentioned
above exists, it should be taken into account in dis-
persion models, at least in terms of adjusted decay
rates and/or "calibration factors" if no better
method can be found.
References
1. D.B. Turner, Workbook of Atmospheric Dispersion
Estimates, Public Health Service Publ. Ho. 999-
AP-26, 1970.
2. A.D. Busse and J.R. Zimmerman, User's Guide for the
Climatological Dispersion Model, U.S. Environmental
Protection Agency, Research Triangle Park, H.C.
(EPA-Rlt-73-02l(), 1973.
3. G.A. Briggs, Plume Rise, U.S. Atomic Energy
Commission, Division of Technical Information,
Oak Ridge, Tenn., 1969.
It. J.H. Christiansen and R.A. Porter, "Ambient Air
Quality Predictions with the Fast Air Quality
Model," Proceedings of the Conference of Ambient
Air Quality Measurements, APCA Southwest Section,
Austin, Texas, 1975.
5. G.A. Briggs, Plume Rise Predictions, AMS Workshop
on Meteorology and Environment Assessment, Boston,
Mass., 1975-
6- F.A. Gifford, Jr. and S.R. Hanna, "Urban Air
Pollution Modelling", paper No. ME-320, Second
International Clean Air Congress, Washington, D.C.,
1970.
7- I.A. Singer, Journal of the APCA 21_, Jjk, 1961.
8- J.C. Caraway, private communication, 1975-
8V
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AIR MODELING IN OHIO EPA
John C. Burr
Environmental Assessment Section Chief
Ohio EPA
Columbus, Ohio
A. Ben Clymer
Consulting Engineer
Columbus, Ohio
Annual Mean S02 and TSP Over Flat Terrain
Modeling for Ambient Network Design
The term ambient network is intended to mean that
network which is used for assessing long-term concen-
trations as, e.g., annual mean concentrations for
comparison with annual air quality standards. Urban
background carbon monoxide concentrations are another
example.
In this case one wants to know the mean concen-
tration distribution of a pollutant over some area of
concern. In other words we want to determine a three-
dimensional concentration surface. The design problem
then becomes one of determining the number and location
(geographic) of sensors adequate to define such a
surface with a specified degree of confidence. The
design theory of such a network has been developed by
the authors.^'^ It utilizes a parametric representa-
tion of concentration as a function of distance. For
pollutants originating from point sources a polar
coordinate system is used, and the concentration repre-
sentation is a gaussian function of the coordinate. , 3
The theory has been applied to three cities in Ohio.
The number and distribution of sensors, so determined,
is reasonable.
Existing Models for Design of Regulations
Annual models currently being used by us are the
Modified Climatological Dispersion Model (MCDM),4 and
the Ohio County Annual Maximum (OCAM) model.5 Both
MCDM and OCAM are steady-state, uniform wind, gaussian
dispersion models. MCDM is a revision of COM6 which
has been modified to generate a source contribution
table.
We use MCDM because it has been shown, when prop-
erly applied, to produce reasonable correlation
coefficients (range of 0.75 to 0.85). It is being
modified to produce "coupling coefficients" which are
merely row vectors of relative source contribution at
each receptor. Thus a simple matrix multiplication of
emission rate and "coupling coefficient" will predict
the concentration at the receptor. In this manner we
can easily examine the effect of altering various
emission rates.
The OCAM model was developed to permit efficient
and realistic modeling of maximum annual concentrations
in smaller metropolitan areas. It treats both area and
point sources. Area sources are modeled by the method
of Miller and Holzworth.7 It has been found8 for point
sources, that maximum annual concentration, normalized
for emission rate, is related to mean plume height by
a power law. The law is deduced from hypothetical
source COM modeling. OCAM includes a quantitative
means of how a given source is to be modeled, i.e., as
a point source or as part of the area sources.
Early application of OCAM for modeling sulfur
dioxide yielded a correlation coefficient of 0.78 when
based upon modeling in 36 Ohio Counties.5 When extended
by a Larson Transform^ the OCAM model predicted second-
highest 24-hour concentrations in these same 36
counties with a correlation coefficient of 0.66.
Matrix Model of Concentration by Source Category
This is a model with which we are experimenting.
The emission rates, are categorized according to a
column vector, E,(m x 1) by Source Industrial Classi-
fication (SIC) codes. A matrix of constants, D,(n x m)
relates SIC classified emission rates to an observed
concentration column vector, C(n x 1):
D
n x m
The n x m matrix D can, in principle, be determined
from a least squares fit of historical data. Alterna-
tively it could be synthesized from the "coupling
coefficients" between sources (by SIC code) and recep-
tors.
If the emissions are projected by SIC code, then
the above matrix equation gives a forecast for the
concentrations. It is also possible to invert the
equation, in order to solve for a unique set of
emissions, {E} which will yield a given set of concen-
trations {C}.
This is a highly condensed city pollution model.
Its simplicity and potential ability for short-
circuiting disperson modeling commend it for consider-
ation.
Annual Mean S02 and TSP Over Nonflat Terrain
Phenomena of Concern
Nonflat terrain gives rise to a remarkable number
of micro-and mesoscale meteorological phenomena
affecting the dispersion of pollutants.10'12 It
would be valuable to be able to deal with the majority
of these effects upon concentration at an arbitrary
surface point. Among these effects are the following:
1. Channeling of wind by a valley, causing a
strongly bimodal wind rose;
2. Boundary layer instability effects, such
as vortex (eddy) and downwash generation
on the lee side of a ridge;
3. Plume impingement on a ridge or plateau;
4. Increase of turbulence aloft due to surface
roughness over a wide range of scales;
5. Downflow of colder air in a valley;
82
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6. Irregular distribution of updrafts due to
insolation of rough terrain;
7. Several possible effects of the thermal
structure T(z) of the atmosphere,
including an elevated or ground-level
inversion;
8. Extra turbulence due to wind shear;
9. Bending of plume by variation of wind
direction with altitude;
10. Nonuniform wind speed and direction
due to potential flow over rough terrain;
11. Possibility of a Coriolis effect in a large
valley;
12. Reduction of wind speed in a valley relative
to geostrophic wind;
13. Elevation of a "cloud" of pollution which
is caused by inflow of cooler cleaner air
below.
Analytical Approaches
The simplest assumption is to ignore terrain
unevenness, as in all flat-earth models. The resulting
errors are not well understood in cause or magnitude.
If the terrain is very rough, the annual average con-
centrations predicted by a flat-earth model cannot be
"calibrated" satisfactorily to observed data at a set
of monitoring sites, because the scatter is so bad.
The next simplest assumption useful in the case
of a ground level receptor which is elevated relative
to the base of a source stack, is that the effect of
nonflat terrain may be taken into account by deducting
from stack height the elevation of the receptor above
the stack base. In effect, this assumption is that
the elevated ground is permeable to the wind and that
the wind field is not distorted by the terrain. A
somewhat more rational correction to plume height above
rough terrain is made in the PSDM program.1'
Since roughness of terrain greatly increases the
diffusion coefficients ay and az, an appealing model
assumption would be that there is perfect mixing within
some specified box, with flowthrough being determined
by the wind. The authors have found that such a model,
even with substantial dilution by exchange of air at
the top, gives much too high a concentration at the
ground, when applied to the valley area of Steubenville,
Ohio.
Part of the modeling problem is to describe the
wind vector field for each of a set of wind speed and
direction classes. There are many approaches for
finding the wind field, such as the shallow fluid
model!3, closed-form approximations in simple
geometries^, and various numerical methods based on
the Navier-Stokes equations14>15 or modified potential
flow.16
After having the wind field, one can apply one of
the existing models, such as COM6, as a subroutine in
a program which deals with pollution transport,
diffusion, and decay in a nonuniform wind.l' the
authors are currently investigating this approach.
Diurnal Scale Problems
Modeling for Episode Network Design
An episode network has the purpose of detecting an
incipient episode of high pollutant concentration over
a period of days. The detection is only possible with
some particular degree of confidence when performed by
a given number of sensors, because the "signal" is
"noisy". The statistical theory involved has been
worked out by Clarenburg.18 One of us (JCB) has
extended the theory,2 and we have applied it to two
cities in Ohio.3,19 The numbers of monitors thus
determined are reasonable.
Diurnal Phenomena
The most disastrous air pollution episodes are
those which last only a few days and which importantly
involve short-term phenomena. These phenomena must be
modeled, in order to understand how an area's pollu-
tion compares with short-term standards under various
conditions. The modeling problems associated with
these diurnal phenomena may be summarized as follows:
1. Inversions. The creation, persistence,
and the diurnal rise and fall of an
inversion are basic in pollution episodes,
since they limit the mixing volume. More-
over, the production and maintenance of an
inversion are correlated with low wind speed,
which further increases pollutant concentra-
tions. The modeling problem is to represent
the vertical transient thermal structure of
the atmosphere T(z,t) over a period of days,
usually in a valley.
2. Valley Minds. An episode can be compounded
by the intensification of an inversion by
cold drainage winds sliding underneath at
night.
3. Lake Breezes. A large dammed river, such as
the Ohio River, is essentially a lake. It
is conceivable that a two-cell cylindrical
circulation could develop on a clear day,
with downflow in the middle and rising air
on both shores, trapping pollutants in the
circulation field.
4. Urban Thermal Circulation. This toroidal
circulation, which is driven by the heat
release of a city, can also trap and
recirculate pollutants.
The authors have not yet brought these phenomena
into a short-term model of such a city as Steubenville,
Ohio.
"Urban Plume" Modeling for Ozone
The State of the Art of Ozone Modeling
Regression models for ozone as a function of some
environmental variables, such as temperature and wind
ed 20,21
speed,
are available.
The diurnal curve of ozone concentration versus
time is approximately a sinusoid plus a constant.
This curve is the solution of the following differen-
tial equation:
83
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d[03]
dt
KI
[03]
where I is illumination intensity (a sinusoidal func-
tion of time) and where K and T are constants. The
authors have derived this equation from published sets
of kinetic equations by making some reasonable simpli-
fications.
The next most complicated model would take account
of vertical movement (by diffusion or by transport in
a lake breeze) and the vertical distribution of ozone
over the diurnal cycle.22 Then it would be desirable
to model the growth and decay of ozone concentration in
an urban plume extending into a rural area.23 Until
such models are available, further complication of the
kinetics model seems unwarranted.
Considerations for Statewide Ozone Network
As a necessary preliminary to modeling ozone in
Ohio, the monitoring network is being expanded. At
present virtually all 28 monitors are urban. Hence
it is desirable that all monitors added in the near
future have rural sites. Each rural site should be
within about 50 miles of at least one city and prefer-
ably at the centroid of several cities, in order that
urban plumes can be studied.22
The Automotive Source Problem
Metropolitan Carbon Monoxide Modeling
All of this work has been done in cooperation with
the Ohio Department of Transportation (ODOT). We
initially thought to use the APRAC24 model for this
purpose. We approached ODOT to obtain the traffic-
grid and vehicle load factors for the Columbus, Ohio
area. It was quickly found that ODOT's number of
traffic grid links exceeded the capacity of APRAC by
about a factor of ten. Although an APRAC compatible
grid for Columbus was eventually produced, it was
concluded that such an approach was impractical for
all Ohio cities.
A greatly simplified model called COPOLLUT25 was
developed for survey purposes. In the emission rate
algorithm, only traffic links are assumed to produce
the pollution pattern. Turning movements are not
included. In the dispersion algorithm, wind direction
is assumed to be at the same relative angle for each
traffic link, and, therefore actual meteorological
conditions are not used. Emission factors are taken
from reference 28.
Thus the model emphasizes the emission character-
istics of carbon monoxide pollution. Sophisticated
dispersion relationships are not used. Such assump-
tions are compatible with measured concentration
patterns27 Of carbon monoxide. The principal short-
coming of the model is its inability to handle the
influence of street canyons upon dispersion. Such
effects would be important, principally in the Central
Business District. The model produces realistic
patterns of pollution in the sense that they are
neither largely better than nor worse than the air
quality standards for Columbus.
Finite Line Source Model
A model described elsewhere in this conference2^
has been developed for modeling finite line sources.
A closed-form, time-dependent solution has been
derived. The dispersion function explicitly incorpor-
ates ground roughness and vertical heat flux. The
incorporation of ground roughness and the functional
form of the time dependence are thought to be quite
characteristic of carbon moxoxide dispersion from
roadways in a variety of areas of varying degrees of
urban development. It is intended to be applied to
analyses of proposed roadway development. It can also
be readily adapted to Indirect Source complexes.
Conclusions
Our use of air quality models emphasizes their
use for assessing environmental situations and for
regulation development. We emphasize that models be
theoretically realistic and hopefully simple. We
further require them to be representative of the real
world as attested by measurement comparisons.
Existing models which we have acquired deal with
only an extremely limited number of real situations.
Such models are restricted theoretically to flat
terrain, steady-state, uniform wind, non-reactive
pollutant situations. We are seeking and developing
additional models which incorporate topography,
kinetics, thermal structure (both vertical and
horizontal), and diurnal phenomena such as valley
winds, heat islands, and lake breeze.
The major air pollution problems in Ohio generally
occur where some or all of these variables are present.
We will not feel confident in defining the situation
or devising control remedies until we can confidently
model where and when these variables occur.
References
1. Burr, J. C., Jr., "Air Quality Monitoring Require-
ments for Cleveland with Extensions to Cuyahoga
County: A Quantitative Evaluation Based on
Existing Data and Sources", Research Report,
City of Cleveland, Division of Air Pollution
Control, Cleveland, Ohio, 1972.
2. Burr, John, and Clymer, Ben, "Geographical
Distribution of Sensors in Urban Air Monitoring
Networks", Third Conference on Energy and the
Environment, Hueston Woods, Ohio, 1975.
3. Clymer, A. Ben, "Design of Episode and Ambient
Networks for Monitoring Particulates and Sulfur
Dioxide in Metropolitan Columbus", Ohio EPA,
November 1974.
4. PEDCo-Environmental Specialists, Inc., "Modifica-
tion of the Climatological Dispersion Model",
Contract No. 68-02-1375, Task Order No. 21,
Prepared for U.S. EPA, Region V.
5. Ohio EPA, "Air Quality Summary Report", submitted
to the Ohio Energy Emergency Commission,
November 1975.
6. Busse, Adrian D., and Zimmerman, John R., "User's
Guide for the Climatological Dispersion Model",
Report EPA-R4-73-024, U.S. EPA, Research Triangle
Park, N.C. 27711, December 1973.
7. Miller, M. E., and G. C. Holzworth, "An Atmos-
pheric Diffusion Model for Metropolitan Areas",
APCA Journal, 17_, pp 46-50(1967).
84
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8. Blaszak, T., private communication, Region V,
U. S. EPA, 230 South Dearborn Street, Chicago,
Illinois.
9. Larsen, R. I., "A Mathematical Model for Relating
Air Quality Measurements to Air Quality Standards",
U. S. EPA, No. AP-89(November 1971).
10. Munn, "Descriptive Micrometeorology", Academic
Press, New York, 1966.
11. Scorer, "Air Pollution", Pergamon Press, London,
1968.
12. Egan, Bruce A., "Turbulent Diffusion in Complex
Terrain", Lecture Notes, Workshop on Meteorology
and Environmental Assessment, Environmental
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"Diffusion Model Calculations of Long-Term and
Short-Term Ground-Level S02 Concentrations in
Allegheny County, Pennsylvania:, H. E. Cramer
Co., Inc., Salt Lake City, Utah 84108, Report
PB-245262, March 1975.
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Pollution Transport in Street Canyons",
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Research and Monitoring, June 1973.
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Model for Use in Numerical Evaluation of Air
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17. Rosenblum, Harvey S., Egan, Bruce A., Ingersoll,
Claire S., and Keefe, Michael J., "Adaptation
of Gaussian Plume Model to Incorporate Multiple
Station Data Input", Environmental Research and
Technology, Inc., Concord, Mass. 01742, ERT
Document No. P-1121, vol. 1, June 1975.
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System to Predict Unfavorable Weather Conditions",
APCA Paper 68-55, presented at St. Paul, Minn.,
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19. Burr, John C., and Clymer, A. Ben, "Design of
Episode and Ambient Networks for Monitoring
Particulates and Sulfur Dioxide in Metropolitan
Cincinnati", Ohio EPA, Columbus, Ohio, October
1975.
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85
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DESIGNING A REGIONAL AIR POLLUTION MONITORING NETWORK:
AN APPRAISAL OF A REGRESSION EXPERIMENTAL DESIGN APPROACH
P. R. Gribik
Graduate School of industrial Administration
Carnegie-Mellon University
Pittsburgh, Pennsylvania 15213
J. R. Sweigart
School of Urban and Public Affairs
Carnegie-Mellon University
Pittsburgh, Pennsylvania 15213
K. 0. Kortanek
Department of Mathematics
Carnegie-Melion University
Pittsburgh, Pennsylvania 15213
ABSTRACT
The problem of allocating measuring resources
to aid in accurately estimating ground level
pollution concentrations throughout a region
is examined. Application of optimal regres-
sion experimental design makes the uncertain-
ty in the estimates small for a given
measurement effort and suggests where the
measurements should be taken. Design cri-
teria are surveyed for this problem as well
as the assumptions that underlie the applica-
tion of this technique. The allocation and
location problem is illustrated with a hypo-
thetical example.
1. INTRODUCTION
Generally, the effectiveness of an air qual-
ity management program depends greatly upon
the ability to estimate accurately the ambi-
ent air pollution levels throughout a given
region. in turn, the ability to make ac-
curate estimates depends upon the design of
the monitoring network, specifically, upon
the locations of the measuring equipment.
in this paper we discuss the problem of al-
locating pollution measuring resources to
satisfy the need for accurate estimation of
the ground level concentration of a pollutant
throughout a region. The techniques can be
viewed as being source-oriented in that they
give estimates of the pollution contribution
of each source, which is important for use in
an air quality management program. Results
from a diffusion model are used to determine
the form of a response surface with which one
estimates the pollutant concentration at each
point in the region, including those points
where measurements are not made. Multivari-
ate regression analysis can be used to fit
the response surface to the measurements ob-
tained from a monitoring network by computing
numerical values of unknown parameters, such
as the emission distribution of point sour-
ces. Before actually taking measurements and
solving for these parameters, one first seeks
to allocate the measurement resources to
points throughout the region and thus deter-
mine sampling sites.
in this paper mathematical methods are sur-
veyed which treat the problem of allocating
these resources in some optimal way. The ba-
sic problem is one of regression experimental
design, where the goal is to obtain good esti-
mates of unknown parameters. Beginning with
Section 2, the underlying experimental regres-
sion design model is presented. Basic as-
sumptions are stated. in Section 3, design
criteria are examined for the model which
tend to make the uncertainty in the estimates
of the parameters as small as possible in an
economically efficient manner. The problem
of resource allocation is treated under the
assumption of a fixed weather state.
The basic assumptions introduced in
Sections 2 and 3 are examined in Section 4.
Finally, in Section 5 our conclusions are
presented with a view towards implementation.
2. THE ESTIMATION OF UNKNOWN PARAMETERS:
EMISSION RATES
Given a control region R, consider the prob-
lem of estimating the ground level concentra-
tion of a single pollutant throughout R by
using measurements collected at a finite num-
ber of points in R. in R there are n
known sources of pollutant and this pollutant
is assumed not to react with any others. It
is clear that pollution concentrations are
highly dependent upon weather state as speci-
fied by wind direction, wind speed, mixing
height, stability class and so forth. Con-
sider a single weather state during which the
need for accurate estimation of air pollution
concentrations is acute.
For a particular weather state a diffusion
model may be used to approximate the pollu-
tion concentration at any point x in R
due to source i. This approximation is of
the form 9.u.(x) where 6. may be interpre-
ted as the emission rate of source i and
u.(x) is the pollution transfer function of
i J_T
the i source as determined by the dif-
fusion model (with a unitary emission rate) .
Assuming unknown "background" pollution, 6 ,
the pollution concentration at any point x
in R can be written as
9o +
n
2 6,1
(1)
In fitting (1) to actual measurements, linear
regression analysis can be used to estimate
86
-------
,
^ j
8n. Call these computed estimates
resulting function
particular criterion function. in the next
section we discuss the allocation problem in
more detail and the problem of choosing a
criterion function.
is then used to estimate the concentration of
pollutant at any point in R.
Assume that measurements of the pollutant are
made at the points x.
3.
..,...
k.
in R with
measurements taken at x. and that any
observation can be written in the form,
n
9o +
.
eiui(x)
Here e (x)
the result of the
by g-, j = 1,..
N = £ k.
1=1 1
is a random error term.
j
Denote
measurement at x.
and set
M = £
1=1
ki T
-Tr u(x.)u(x.)
b = £ k.u. (x)g.
k.
(the total number
of measurements
taken in R)
(the information
matrix for the
given measure-
ment scheme)
and
(the average pol-
lution reading
at x . f o r
measurements) .
k .
u(x.) is the column vector
1 m
u(x)) . if the information matrix M
(l,u_ (x. ),...,
is
non-singular, the least squares estimator of
6= (90,91,..., 9n)T is S = ^ M"^. Since
the total number of measurements that may be
made in a period is fixed, the measurements
should be allocated to points in R so that
H is a good estimate of 6.
THE PROBLEM OF ALLOCATING MEASUREMENT
RESOURCES
The problem here is to determine the points
in R where measurements are to be taken and
the proportion of the total measurement ef-
fort to be expended at each location. Let
x, , . . . ,x denote the points where measure-
1m
ments are to be taken and
the respective proportions.
is not only to determine
p.,...,p
denote
The problem here
and p. but
also the number of monitors, m. We define a
design denoted by e as follows:
x.
e = [(PI»XI),...,(p^jxj}, where
and where
that
€(x) =
e is actually a function such
O if x
I if x = x±
nr
The problem can then be restated as one of
finding a design which provides "good" esti-
mates of pollution concentrations throughout
R. As mentioned previously this can be done
by making some function of the covariance ma-
trix of §, call it $(M), small. We thus
propose the following non-linear optimization
task, governed by a design criteria as speci-
fied by i(M) .
Program P_
Compute min $(M)
for all M e R
L' and
R1 x R
subject to the constraints
m T
M = £ p u(x.)u(x )
1=1 1 1 i
We consider the allocation problem under two
standard assumptions that will be used in de-
fining what is meant by 6 being a "good"
estimate.
Al The random errors in the observations
are independent among all observations.
A2 The mean of e (x) is 0 and the vari-
ance of e (x) is Ac where c is
known while A may be known or unknown.
Under these two assumptions, the covariance
matrix of
is (Ac/NjM"
Since the co-
variance matrix of gives an indication of
the uncertainty in our estimates and we wish
to make this uncertainty small in some sense,
we consider the problem of allocating the
measurement resources so as to "make the co-
variance matrix small" with respect to a
and
p± ^ O; i = 1, . . . ,m
x± ^ x. for i jt j
m is an arbitrary positive integer.
The solution to Program P, { (p^,x. ),...,
(p ,x )), will be called an optimal design.
Another assumption is required.
A3 There is at least one design whose in-
formation matrix is non- singular for
the given weather state.
Under assumptions A1-A3 the properties of
Program P and its optimal designs will be
examined for two design criteria. The func-
tions that will be considered are
87
-------
-log det(M) and tr(GM ) for some specified
positive definite matrix G (det = determi-
nate, tr = trar-3) . The designs optimal for
Program P under these two criteria are termed
D- optimal and L- optimal designs, respectively.
Fundamental contributions to the study of
these problems have been made by Kiefer and
Wolfowitz [8] . Mathematical properties of
these problems and also some numerical algo-
rithms for their solution are discussed in
Fedorov [4] .
Relying on a designn e to estimate 6, the
variance of
+ E .u. (x) for any xeR
0
is given by ^ u (x) TM~ ^ (e) u (x) . M~1(e) de-
notes the inverse of the information matrix
M which depends upon the design e. Kiefer
and Wolfowitz [8] have shown that a design
e* is D-optimal if and only if its associ-
ated information matrix M(e*) solves
T - 1
min max u(x) M u(x)
Men xeR
where
0 = [Me R(*+D*(n+l), there is a de-
sign e for Program P such
that M = £ e (x)u(x)u(x)T
xeR
and det (M) ^ 0) .
Thus the D-optimal design minimizes the maxi-
mum variance of the best linear unbiased
estimates (BLUE) of ground level pollution
concentrations in the region R.
The L-optimal design is related to the expec-
ted error in
Let
be the vector
of the true source strengths in equation (1) .
Since 6 is unbiased E(8) = 9fc (E =
Expected value operator) . If the design e
is used to collect data during a given weather
state, then
E((6-etrue)TG(e-etrue))=
tr[GM~:L(€)].
(3)
Thus the L- optimal design problem is equiva-
lent to finding the design for which the LHS
of (3) is minimized. An important special
case occurs when G is chosen to be the
identity matrix. Then the L-optimal design
seeks to minimize the expected sum squared of
errors in the BLUE of 8.
Another important choice of G is
r T
G = j u(x)u (x) 6 (dx)
R
where 6 is a probability measure on R for
which G is non-singular. It can be shown
in this case that the L-optimal design prob-
lem seeks to minimize the weighted average of
the variance of the BLUE of the ground level
pollutant concentrations in the region R
where <5 ( • ) is the weighting term. One pos-
sible choice of 5 ( • ) is to set 6 (A) =
"°" where pop (A) = population of region
pop R
A, for A some subset of R. In this case,
Program P would determine an allocation that
yields better estimates of the pollution in
the more densely populated sections of R.
The final choice of the design criterion will
depend upon the intended use of the estimated
coefficients &•. If the estimated coeffici-
ents are to be used to estimate total concen-
tration at points throughout R, any of the
design criteria suggested is appropriate.
However, if the purpose is to use the esti-
mates of 6 as estimated emission rates of
sources to be used as a basis for regulatory
policy, then the L-optimal design with G = I
should be taken.
4. DISCUSSION OF ASSUMPTIONS Al THROUGH A3
The previous results depend upon the assump-
tions that were made. Assumption Al is like-
ly to be difficult to satisfy and deserves
further discussion. This assumption depends
upon the accuracy of the diffusion
model and the interpretation and
implementation of the optimal design. Sup-
pose that we use one of the previous models
and obtain { (p*,x*) , . . . , (p* ,x*) } as an opti-
mal design. Also suppose that we are to take
N measurements and that we interpret the op-
timal design to mean that we are to take
ptN observations at x* with all measure-
ments taken at the same time. Under this in-
terpretation, the assumption that the devi-
ations of the measurements from the model are
independent (Al) may well be violated. For
assumption Al to be valid under this inter-
pretation, we would need a diffusion model
that was accurate down to very small scale
effects. Since the diffusion models avai-
lable at present are not this accurate, this
interpretation is not adequate.
Assume that the diffusion model used can ac-
curately model effects as small as d meters
in diameter and t minutes in duration. Let
T = t- (
max
p*N)
and assume that the weather state remains un-
changed and that the emission rates of the
sources and other parameters of the point
sources remain constant for a period of T
minutes. If we take a measurement at point
x^ every T/(p*N) minutes during this period
of T minutes and if min||x* - x*|| ;>_ d
where || • )| is the Euclidean norm on R ,
then the deviations of the measurements from
the model will be independent.
If min|lxt -
< d, we can alter the pre-
vious programs to insure that the points in a
design are far enough apart. one way would
be to add the constraints
x. - x .
1 i 3 i
for
to a program. However these constraints are
nonconvex and so increase the difficulty of
solving the program. There is another way
-
to insure that
minx- - x*
d which is
88
-------
consistent with the practicalities of the
problem.
In a practical problem, the optimal design
would probably not be exactly implemented but
only used as a guide since factors not pre-
cisely modeled would also be considered. For
example, a monitoring station would not be
placed in the lee of a large building or next
to a minor pollution source that was only
considered in the aggregate background pol-
lution 9 . Hence, if a sufficiently fine
grid H on R is chosen, the resulting op-
timal design would be adequate for our
purposes.
If the grid H satisfies
min IJx - y|| 1 d
x,yeH
(4)
then no two points in an optimal design can
be closer than d and so assumption Al will
be satisfied. in U.S. regional air pollution
studies, grid squares are typically one to
ten kilometers on a side. if the region R
is such that max ||x - y|| » lo kilometers,
x,yeR
which is the case in most problems of in-
terest, and if d is on the order of one to
ten kilometers or smaller, H can be chosen
to be a grid sufficiently fine to yield use-
ful results while satisfying (4). Also, a
grid H will insure that no further assump-
tions on the transfer functions and the
region R are needed.
5. CONCLUSIONS: INTERPRETATIONS AND
IMPLEMENTATION
The previous models consider the problem of
allocating measurement resources to collect
pollution concentration data during the time
that a specified weather state holds. Since
the optimal allocation depends upon the
transfer functions obtained from a diffusion
model and these functions depend upon the
weather state, the models developed may give
different optimal allocations for different
weather states. We do not suggest propor-
tionally dividing the equipment among the
allocations optimal for the different weather
states since the result may not be a good al-
location to the overall problem.
One way to approach this problem is to extend
the methods of this paper to more than one
weather state. in this case, it is necessary
to choose a set of weather states
S = [s^,...,s,] which is of interest. We
then wish to design a monitoring network for
the region R so that good estimates of the
parameters 8. can be made, on the average,
when the weather state is in the set S. Let
w be a random variable which denotes the
weather state at some time in the future
where frequency data can be used to estimate
the conditional probability that w is in
S. The details of this extension have been
completed in P. R. Gribik's Thesis [6].
The methods of this paper are directly appli-
cable if one is willing to choose a prevail-
ing or typical weather condition for the
region and design on it. Another direct ap-
proach would require the utilization of a
long-term diffusion model and a prespecified
frequency distribution on wind direction and
wind speed. Then, the measurements would be
used to develop long-term averages at the
given set of design points and the p. would
be interpreted as the proportion of measure-
ment effort to be expended at point x. to
develop this average. The main use of the
estimated parameters computed in this situ-
ation would be for the calibration of the
diffusion model results.
It is highly desirable that a regional moni-
toring network provide information on air
quality both in the short-run and the long-
run. The above alternatives suggest a vari-
ety of ways in which this goal may be accom-
plished. For example, a monitoring network
which is for all practical purposes station-
ary, can be established to satisfy the needs
for long term estimation. If this network is
not satisfactory in the short-run it would be
necessary to determine a set of "critical"
weather states where the probability of ex-
ceeding ambient air quality standards is
high. For critical states designs could be
computed and for short periods of time dur-
ing these critical states mobile monitoring
equipment could be placed at the previously
designated locations.
The methods described in the paper are per-
haps more attractive if mobile monitoring
equipment is available, but the application
of the methods is still reasonable if all
equipment is stationary. The actual imple-
mentation plan will of course depend upon the
resources available as well as individual
characteristics'of the region under consider-
ation.
6.
AN ILLUSTRATION OF THE ALLOCATION
PROCEDURE
In this section we consider a small example
which illustrates the allocation procedure
and indicates a sample allocation of resour-
ces. Suppose we have a region with four
major polluters and an unknown background
source. The four sources are described as
fo1lows:
Source
HP
(m)
TS
(deg
K)
VS
(m/
sec)
D
(m)
VF
(m3/
sec)
R
(mi)
S
(mi)
1 61.0 600. 6.1 2.6 32.4 5.7 3.9
2 34.7 727. 1.6 1.5 2.8 6.5 4.7
3 113.0 546. 9.3 5.2 197.5 2.9 5.7
4 50.0 460. 7.0 2.5 34.4 7.0 2.9
and
HP: physical stack height
TS: stack gas temperature
VS: stack gas exit velocity
D: inside diameter of stack
VF: stack gas volumetric flow rate
R: x-coordinate of stack
S: y-coordinate of stack.
89
-------
The EPA computer program DBT51 which calcu-
lates concentrations for multiple point sour-
ces was used to calculate concentrations at
729 grid points (1 mile grid) for a single
weather state. A typical weather state was
defined by Pasquill's stability class D,
wind speed 5 m/sec, mixing lid - 1219 m,
ambient air temperature - 284 deg K, and with
wind from the southwest. For purposes of il-
lustration we choose a non-uniform grid of 80
points which reflect the changes in individu-
al contributions of the sources involved.
Figure 1 indicates the diffusion coefficients
x 10O at the 80 points considered. The lo-
cations of the sources are also indicated in
Figure 1. For each of those locations con-
tributions from each of these sources are
computed and stored.
Initial Design
Location
(grid point #)
Mass (p.)
223 226 251 3O5 368
.2 .2 .2 .2 .2
Location 223 226 251 305 368 307 249
(grid
point #)
Mass (pi) .195 .198 .009 .009 .199 .196 .194
Even without termination it appears that a
design is emerging with monitors at grid
points 223, 226,, 368, 3O7, and 249 and with
approximately the same measurement effort to
be expended at each of these points. It is
informative to note the individual contribu-
tions of the sources at each of these loca-
tions.
®
®
©
®
,1
.1
14
1.3
4.2
0
2.7
45
.2
5.4
1.1
.1
16
195
83
.1
30
147
2
1.6
.7
6.7
.1
1.9
114
8.4
60
92
1.4
7,1
.8
40
25
16
65
2
6.9
2.2
36
33
18
6.6
4
31
34
16
.1
.3
2.7
5.7
27
32
15
.5
2,9
5.9
24
29
14
1.1
5,7
8.1
22
27
13
1.7
.1
462 516 570 624
Figure 1:
Total concentrations at
80 locations in R
Let us choose our design criteria as the one
which minimizes the maximum variance of the
best linear unbiased extimate (BLUE) of
ground level pollution over the chosen grid,
i.e., we propose to compute a D-optimal
design. Using an algorithm proposed by
Fedorov [4] (p. 102) we specify an initial
design and proceed to obtain a solution to
Program P. The initial design as well as an
"approximate optimal design" are given below.
Monitor
1
2
3
4
5
Location
223
226
249
307
368
Sources
#1
46.62
0
O
39.4
0
#1
181.64
O
0
74.46
0
#1
0
0
0
0
7.07
#i
0
0
82.3
0
0
in this problem it can be projected that 1
and 4 monitor sources 1 and 2, 2 monitors the
background pollution, 3 monitors source 4,
and 5 monitors source 3. We also note that
an initial design with points 196, 202, 335,
424, and 648 led to a comparable outcome.
The implication to the estimation problem
goes as follows. Locate monitors at 223,
226, 249, 307, and 368 and take approximately
the same number of measurements at each lo-
cation during the weather state specified.
Use the average of these measurements,
g.,...,g5 to fit the measurements to the dif-
fusion model estimates and then use
4
9O + £ @^u^(x) to estimate concentrations at
the remaining 75 grid points. We can then
guarantee that these estimates are "best" in
the sense described earlier in this section.
REFERENCES
[1] Atwood, C. L., "Sequences Converging to
D-optimal Designs of Experiments", Ann.
Math. Stat. !_ (1973) , 342-352.
[2] Escudero, L. F., "The Air Pollution
Abatement MASC-AP Model", Proceedings gf_
the international Conference on Mathe-
matical Models for Environmenta1 Prob-
lems . September, 1975, University of
Southampton, United Kingdom.
[3] Federer, W. T. and L. N. Balaam, Bibli-
ography on Experiment and Treatment
Design, Oliver and Boyd, Edinburgh, 1973.
[4] Fedorov, V. V., Theory of Optimal Experi-
ments (translated by w. j. Studden and
E. M. Klimko), Academic Press, New York,
1972.
90
-------
[5] Fortak, H. G., "Potential Applications
of Mathematical Meteorological Diffusion
Models to the Solution of Problems of
Air Quality Maintenance", Proceedings of
the Fifth NATO/CCMS Expert Panel on Air
Pollution Model chapter 1_, Research Tri-
angle Park, North Carolina, 1974.
[6] Gribik, P. R., "Semi-infinite Program-
ming Equivalents and Solution Techniques
for Optimal Experimental Design and
Geometric Programming Problems with An
Application to Environmental Protection'1 ,
Ph.D. Thesis, Graduate School of Indus-
trial Administration, Carnegie-Mellon
University, December, 1975.
[7] Gustafson, S.-A. and K. 0. Kortanek,
"Determining Sampling Equipment Loca-
tions by Optimal Experimental Design
with Applications to Environmental Pro-
tection and Acoustics", Proc. Comp. Sci.
and Stat. Seventh Annual Symposium on
interface, W. J. Kennedy, ed., Iowa
State University, Ames, Iowa, 332-338,1973.
[8] Kiefer, J. and J. Wolfowitz, "The Equiva-
lence of Two Extremum Problems", Canadi-
an J. Math. 12_ (I960), 363-366.
[9] Seinfeld, John, "Optimal Location of Pol-
lutant Monitoring Stations in an Air-
shed", Atmospheric Environment 6_ (1972) ,
847-858.
[10] Sommer, G. and M. A. Pollatchek, "A Fuz-
zy Programming Approach to an Air Pol-
lution Regulation Problem", Technical
Report 76/01 Lehrstuhl filr Unternehmens-
forschung. Aachen, West Germany.
91
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SAMPLED CHRONOLOGICAL INPUT MODEL (SCIM) APPLIED TO AIR QUALITY
PLANNING IN TWO LARGE METROPOLITAN AREAS
R.C. Koch, D.J. Pelton and P.H. Hwang
GEOMET, Incorporated
Gaithersburg, Maryland
SCIM is a multiple-source urban diffusion model
based on the Gaussian plume equation and has been used
to analyze S0? control regulations in Boston and San
Francisco. Maximum 3-hour, 24-hour, and annual mean con-
centrations are calculated from NEDS emission or fuel
use data and standard National Climatic Center data.
Model validation results for Boston show a model to
measurement correlation of 0.97 for annual means and
0.81 for maximum 24-hour concentrations of SOo based on
comparisons at 14 stations. The analysis showed that
fuel regulations which permit increasing fuel-sulfur to
1 percent in the Boston core area will not meet National
Ambient Air Quality Standards (NAAQS). In San Francisco
the analysis showed that limiting SOp emissions from
large sources is more critical for meeting NAAQS than is
limiting the sulfur content of fuels.
Introduction
Projected shortages of low-sulfur fuels have caused
many states to reexamine their regulations for control-
ling sulfur emissions. Areas where present regulations
are more stringent than necessary to meet air quality
standards may be suitable for more lenient S0« emission
regulations. Proper evaluation of this questfon in
large metropolitan areas, which contain large power
plants and chemical processing plants and where sub-
stantial quantities of fuel are used for space heating,
requires the use of a computer simulation model to
account for the effects of many sources and to determine
both the long-term and maximum short-term air quality
levels resulting from these sources. The recent require-
ment to develop air quality maintenance plans for many
urban areas also requires the use of a dispersion model
capable of evaluating air quality levels from many
simultaneous sources. The multiple-source Gaussian
plume dispersion model can be used to make these evalu-
ations. This paper describes the application of such a
model, the Sampled Chronological Input Model (SCIM), to
evaluate alternative SCL control strategies in Boston
and San Francisco.
Model Description
SCIM is based on the Gaussian plume equation with
the origin at a receptor point of interest and the x-
axis pointed upwind into the mean wind direction.
Assuming an impervious ground surface and an exponential
depletion constant (k) to account for physical and
chemical removal processes, the ground-level concentra-
tion from a point source is given by:
- M «y dx
XA
The integration operation is simplified by the
"narrow plume" assumption, that:
•±- f q exp J- W/
y *• y
dy
As long as the spatial distances between variations in
area-source emission rate are large compared to the
horizontal diffusion parameter, it may be assumed that:
q (x)wq(x.o)
As a result,
'•*- I - jj*- } dx
This equation is evaluated using a variation of the
trapezoid rule in which small increments in x are
gradually increased with increasing x to a uniform
increment. Area sources may be defined for up to five
area source heights.
The effects of the two types of sources (area and
point) are analyzed separately and added together to
give a resultant concentration.
Limited Mixing
The marked reduction in vertical diffusion which is
caused by a stable layer aloft is approximated using a
suggestion by Pasquill (1962) that a uniform vertical
distribution will be approximately achieved at a down-
wind distance from the source at which a is equal to
the height of the mixing layer. At half this height no
effect due to limited mixing needs to be considered.
Using linear interpolation between these distances and
assuming a is represented as a simple power law of x:
• x
L, x
IT V O
exp
2a
kx
v
2a
'ft)
Let q(dx)(dy) be the total amount of pollutant
emitted per unit time in a horizontal element of area
(dx)(dy). Assuming that the total concentration at
a receptor is the sum of concentration contributions
from all individual area source elements with an ef-
fective area source height h., the concentration x.
at the receptor location due to the area source is:
Plume Rise
The effective height of point sources is repre-
sented as the stack height plus a plume rise calculated
using Briggs (1969) equations for leveled off plume
heights. For stable conditions (Pasquill stability
class E) assuming a potential temperature gradient of
0.02°c/m:
92
-------
AH = 2.9
F T
0.03034 u
\ 0.33
For neutral and unstable conditions (Pasquill stability
classes A through D):
3-75F0.33x0.67
AH
.67.3F
.0.4
,HS <_ 305 ,
,HS'> 305,
Wind Speed
The wind speed is estimated for each effective
point or area source height using the following power
law (e.g. , Munn 1966):
M(h)
'1
Three values of "a" are input to SCIM correspond-
ing to unstable (classes A, B, and C), neutral (class D)
and stable (classes E and F) conditions.
Diffusion Parameters
Diffusion parameter values either for rural con-
ditions (Pasquill 1962) or for urban conditions (McElroy
and Pooler 1968) are used to characterize a and a by
power law functions. y
=
az = bx^
The rural parameters are given in Table 1, and the
urban parameters are given in Table 2.
Table 1. Fitted Constants for the Pasquill
Diffusion Parameters
Stability
CIu
A
B
C
D
E
Crosswlnd
Co=W>
a
0.40
0.295
0.20
0.13
0.098
Constants tor Vertical Diffusion Parameter, »
"S",
b
0. US
0.119
0.111
0.105
0.100
q
1.03
0.986
0.911
0.827
0.778
*1
(Meter4
250
1000
1000
1000
1000
«,<*S-*2
b
0. 00883
0. OS79
0.111
0.392
0.373
4
1.51
1.09
0.911
0.636
0.587
"2
( Meten)
500
10,000
10,000
10,000
10,000
*2<«
b
0. 000226
0.0579
0. Ill
0.948
2.85
1
2.10
1.09
0.911
0.540
0. 366
(1) * • ax t where x li downwind distance from Che source; a and x are In roeten.
(2) * » tut ; * and x ore in meters.
Table 2. Fitted Constants for Urban Parameters
Based on Turner Stability Classifications
Stability
Index
A'3'
B
C
D
C
Crojswlnd
Constants ( D
a
_
1.42
1.26
1.13
0.992
P
.
0.745
0.730
0.710
0.650
Constants for Vertical Diffusion Parameter (2*
x£600
b
.
0.0926
0.0891
0.083S
0.0777
1
.
1.18
1.11
1.08
0.9SS
x>600
b
.
0.0720
0.169
1.07
1.01
<1
.
1.22
1.01
0.6S2
0.554
(1) *„ • »XP( where x Is downwind distance from source; a and X are In meten.
(2) • s • bxP; «t and i an ID meters.
(J) Not available from McElroy and Pooler data; use Clasl B values.
The stability classification used in SCIM is based
on the Pasquill classes of atmospheric stability using-
a system suggested by Turner (1964). The Turner sta-
bility categories are determined from routine airport
weather observations.
Mixing Height
The procedure which is used to define the height
of the mixing layer is the following: Determine the
vertical temperature profile from the nearest appropri-
ate (same air mass) radiosonde, or by interpolation of
two or more nearby radiosondes. Estimate minimum
morning and maximum afternoon air temperatures which
are representative of the urban area. The afternoon
temperature may be obtained directly from airport
observations or other available data. In most cases
the morning urban temperature will exceed the rural
temperature. Construct adiabatic temperature profiles
from the urban temperatures which intersect the rural
temperature profile. The heights of these intersect-
ions are assumed to be the minimum and maximum mixing
heights. The method of interpolating between these
values to give hourly estimates is:
1. Use the morning minimum from midnight to
6 a.m.
2. Linearly interpolate between the minimum and
maximum between 6 a.m. and 2 p.m.
3. Use the afternoon maximum between 2 p.m. and
midnight.
Validation
Validation in San Francisco
The average ratio of predicted to observed 20-day
mean concentration for 20 stations is 1.0, which is an
excellent agreement. The ratios obtained for each of
three regions are more instructive.
The Martinez (northeast) and Richmond (north) re-
gions are the areas of most interest since most of the
large sources are located in those regions. In the Rich-
mond region the model tends to overpredict the concen-
tration and the regional average ratio is 1.4. In the
Martinez region the station to station ratios are more
uniform than in the Richmond region, however the regional
average predicted to observed ratio is 0.4, which is
not quite as good in the Richmond region. There is a
consistent and general underprediction in the Martinez
region but the ratios are fairly uniform. Validation
results were not as favorable in the San Francisco region
where the predicted to observed ratio is 3.9. Because
the observed concentrations in this area'were consis-
tently below the sensing threshold of the monitors, no
particular significance is attached to this result.
Overall, the performance of the model on the 24-hour
average S02 concentrations from 20 stations for a 20-day
sample was judged to be acceptable.
Validation in Boston
Annual Means. S02 concentrations measured using
gas bubblers were compared to model calculations based
on 8 hourly calculations, one for every third hour of
the measurement day (Koch, 1975). The calculated values
generally exceeded the measured values by a small
amount varying from about 5 vig/m3 when the measured
value is 10 yg/m3 to about 7 ug/m3 when the measured
value is 50 yg/m3. The correlation coefficient for the
15 pairs of values is 0.97.
93.
-------
Maximum 24-Hour Concentration. S02 concentrations
were calculated for all days for which a measurement
was available for 1972. The maximum measured and cal-
culated values do not necessarily correspond to the
same day. The calculated values deviate from the
measured value by a maximum of 50 yg/nH for a measured
value of 150 yg/m3 and by 35 yg/m3 for a measured value
of 75 yg/m^. The correlation coefficient is 0.81 for
the 14 values for which comparisons were made. The
mean difference of measured minus calculated concentra-
tion is 2.4 ug/m3. and the standard deviation of the
differences is 26 yg/m3.
Maximum 3-Hour Concentration. Hourly concentra-
tions of S02 were measured at four monitoring sites.
Calculations were made for every third hour for days on
which concentrations were measured. Three of the four
calculated maximums are within 10 percent of the maxi-
mum measured values. At one site the calculated value
exceeded the measured value by 50 percent. However,
since the calculations for two of the sites are sus-
pected to be subject to errors in the emission inventory,
these results are not conclusive regarding the model
validity in estimating maximum 3-hour concentrations.
Distribution of 24-Hour Concentrations. The char-
acteristics of the frequency distribution of paired,
measured, and calculated 24-hour concentrations at 14
stations were determined (see Table 3).
Table 3. Summary of Correlations Between Parameters of
Paired, Measured, and Calculated 24-Hour SO. Concentrations
Distribution C haracteristlcj
Maximum Value
95th Percenttle
Mean
Geometric Mean
Standard Deviation
Geometric Standard Deviation
Correlation Coefficients
14 Monitoring Sites
0. 81
0. 89
0.97
0.97
0.89
0.21
The measured and calculated values were sorted and
ranked from high to low value, independently, and the
percentiles were determined by linear interpolation of
the ranked arrays. The paired percentile values do not
necessarily correspond to any specific day.
The measured distribution is well represented by
the model calculations, although the individual day-to-
day comparisons are not as well correlated as the ranked
percentiles might lead one to expect. The correlation
coefficients for calculated and measured values at a
single station vary from 0 to 0.6 and average about 0.3.
The chief reasons why day-to-day variations in S02
concentrations are not simulated in chronological se-
quence are:
Only annual fuel consumption by point sources
is accurately estimated. Seasonal, weekly,
and daily variations are not represented.
. The allocation of residual and distillate oil
to area sources is only an approximation.
. While temperature is the best known basis for
estimating variations in fuel consumption for
space heating, the sensitivity of different
fuel users is not well known.
. Meteorological data obtained from a single
site may not be representative of a metro-
politan-area-wide average on some days.
The uncertainties cited above have plagued all
urban modeling studies. The result is that, over
a significant period of time (a year or more) the
average concentrations on a given day may vary sig-
nificantly from the model estimate. This is due to
randomly distributed errors balancing out over a long
period of time.
Evaluation of Alternative Fuel-Sulfur
Regulations in the Boston AqcR"
The SCIM model was used to analyze the impact of
eight fuel scenarios (described in Table 4) on the
ambient concentrations of SOg in the Metropolitan
Boston area. Sulfur dioxide concentrations were cal-
culated for every third hour of every sixth day of 1972
at 135 receptor .locations (Koch, 1975).
Table 4. Fuel Sulfur Content for Boston AQCR Fuel
Regulation Strategies
Strategy Number
1
2
3
4
5
6
7
8
Maximum Fuel Sulfur Content (Percent)
Distillate
Oil
0.3
0.3
0.
0.
0.
0.
0.
0.5
Residual Oil and Coal
Borton Cora A*ea
0.
1.
0.
1.
0,
1.
a
'•
Outride Con Aroa
1.0
1.0
2.0
2.0
1.0
1.0
2.0
2.0
if 13 town*, Including Arlington, Selmont, Boston, Brookllne, Cambridge,
Chelsea, Everett, Maiden, Medford, Newton, SommervlUe, Waltham and VVatertown.
Emission Inventory
Sulfur dioxide emissions for point and area sources
were estimated from the 1972 state emission inventory
which included sulfur dioxide emissions, amount and
type of fuel used, and data related to the effective
height of emissions for 356 point sources and 1718 area
sources.
The point source data were used without attempting
to account for seasonal or diurnal variations in the
rate of sulfur dioxide emissions. Area source emissions
which have a greater impact on ground-level concentra-
tions than point sources, because they are released at
lower heights and have less buoyancy, are mostly due to
space heating. It is reasonable to generalize on the
seasonal and diurnal variations in their emissions
using the relationship:
QI FD,
s-E
(H.. - T.J), annual sum.
The parameters Di and H-J (Table 5) were previously
determined by the best fit between model calculations
and sulfur dioxide measurements in New York City. A
value for F (the fraction of emissions which are sen-
sitive to temperature) of 0.8 was adopted for the
Boston area based on correlations between model cal-
culations using experimental values of F and sulfur
dioxide measurements at some 20 sites.*
94
*It was later reported to M. Rosenstein of EPA Region I
by the Better Home Heating Council that 85 percent of
fuel usage by a typical Boston home is for space heat-
ing.
-------
Table 5. Hourly Values of Fuel Demand Parameters
for Estimating Space Heating
Hour of
1
I
3
1
1
1
1
I
1
1
ie
19
20
21
22
Z3
24
Hi
Heating
Threshold
55
55
55
S6
SB
59
61
63
64
65
55
65
65
65
55
65
65
65
65
65
54
6Z
60
56
Heat
Demand
!343
.434
.340
.416
.685
.123
.US
.046
.936
.936
.998
.003
.039
.152
.243
.313
.339
.306
.200
0.316
Q.J87
0.386
The five meteorological parameters required as in-
put to SCIM are: (1) wind direction, (2) wind speed,
(3) temperature, (4) atmospheric stability, and (5) mix-
ing height. Measurements of wind speed and direction,
cloud cover, and air temperature observed at Logan Air-
port in Boston every third hour of the day during 1972
were obtained on magnetic tape fron the National Climat-
ic Center (NCC) in Asheville, North Carolina. The wind
speed, total amount of cloud cover in tenths, and the
height of the cloud ceiling were used in the SCIM model
to determine the atmospheric stability class. A special
program was used to calculate the mixing height for each
12-hour radiosonde observation time using the radiosonde
data for Portland, Maine, and the surface temperature ob-
served at Logan Airport. The mixing height is defined
as the greatest height to which a parcel of air at \
the surface can be lifted before it becomes 1°C or more
colder than atmospheric temperatures as indicated by the
radiosonde temperature profile. Temperature changes in
the displaced parcel are computed assuming adiabatic
expansion of the air and adsorption of any latent heat
due to condensation as the parcel is lifted. The 12-
hour mixing heights are interpolated to hourly values.
Annual Mean Concentrations of SOg
The annual mean concentrations computed by the
model show that the highest concentrations for each
scenario occur in three locations which form a belt
stretching from South Boston through the Boston Hub to
.Everett. This belt runs through the center of the prin-
cipal sources of SOg as shown in Figure 1.
The primary National Ambient Air Quality Standard
for annual mean concentrations of S02 (80 pg/m3) is
exceeded in the belt of high concentrations in scenarios
2, 4, 6, and 8. These are the scenarios in which fuels
other than distillate oil are allowed to contain 1.0
percent sulfur in the Boston core area. Furthermore,
the gradient around the high belt zone is intensified
as compared to the present situation (scenario 1). In
scenarios 3, 5, and 7 the increases are much more uni-
form and dispersed. In scenario 7, in which both the
sulfur content of all distillate oil and the sulfur
content of other fuels outside the core area are raised,
the maximum concentration in the belt zone is very
close to the NAAQS.
Maximun Short-Term Concentrations of SO,
The calculations for each receptor were used, assum-
ing a log-normal distribution, to estimate the 99.73
percentile (i.e., 364/365 of the distribution) and the
99.97 percentile (i.e., 2919/2920 of the distribution),
respectively. The geometric mean and standard deviation
for 24-hour values were determined from the average of
eight 3-hour values for every sixth day. All values
were used to determine a geometric mean and standard
deviation of 1-hour values. The 1-hour and 24-hour
values were converted to 3-hour values using the rela-
• tionships suggested by Larsen (1971). The minimum of
the two estimates was selected.
The percentile values were determined as follows:
Using this procedure, the 24-hour NAAQS was found
to be exceeded at several locations for every scenario.
The distribution of calculated 24-hour concentrations
was plotted on log-probability scales for each location
'which exceeded the NAAQS and for sufficient additional
locations to identify the maximum concentration associ-
ated with each scenario. At most of the locations
examined, it was found that the distribution leveled off
near the high values and the calculated log-normal dis-
tribution was a poor fit. However, the high end of the
distribution could be fitted by eye to a straight line
which was consistent with the data. An extrapolation
of this visually fitted line was used to derive a new,
more reasonable estimate of the concentrations not
exceeded more than once per year.
When the top part of the distribution is extrapo-
lated graphically to determine the annual maximum con-
centration, it is estimated that for scenarios 1, 3, 5,
and 7 none of the sites will exceed the 24-hour standard.
When this procedure is repeated for 3-hour concentra-
tions, it is estimated that for scenarios 1, 3, 5, and
7 none of the sites will exceed the 3-hour standard.
With regard to the scenarios 2, 4, 6, and 8, it is
estimated that both the 3-hour and 24-hour standards
will be exceeded at several locations due to the
potentially large increase of S02 emissions from
point sources in the core area.
Table 6. Maximum Concentrations For Each Scenario
Figure 1. Locations of Principal Point and Area Sources
of SO-, Belt of High Computed S02 Concentrations,
and Receptors Used for Model Calculations
K.,.
*fol«S«««. I >!<*/•«>
CD AMI Sourct ( >3|Jt/IH /MC)
Scenario
1
2
3
4
5
6
7
8
Annual
Receptor
69
69
1,69
69
69
69
1
69
Concentration
toS/rn3)
60
110
60
110
65
115
70
115
24-Hour
Receptor
69
69
10,93
69
74
69
10
76
ConcenD^ation
(wsM3)
260
500
290
500
290
500
330
510
3-Hour
Receptor
40
40
40
40
40
40
10
40
Concentration
(CS/m3)
800
1500
800
1500
800
1500
860
1500
95
-------
Evaluation of Alternative SO? Emission
Limitations in San Francisco
The impact of control strategies which limit pro-
cess source emissions to no greater than 300, 500, 1000,
or 2000 ppm or which limit the sulfur content of the
fuel in combustion sources to 0.3, 0.5, 0.7, and 0.9
percent sulfur were evaluated for the San Francisco
Bay Area. As a further consideration, an alternative
to limit power-generating plants to consumption of 0.5
percent sulfur fuel oil and prohibit their use of nat-
ural gas was evaluated. These nine alternatives, plus
the present emission situation, form the ten strategies
evaluated in this study.
Source Emission Inventory
Data were obtained for point and area sources from
the Bay Area Air Pollution Control District (BAAPCD).
The data for 41 points were updated by reviewing sev-
eral sets of supplementary data to select those which
are complete and are most representative. No sea-
sonal or diurnal variations were applied to the point
source emissions. The area source emissions were
represented by uniform 5 km squares over the whole
area. Seasonal and diurnal variations in emissions
were furnished by BAAPCD for each grid square.
Meteorolgical Data
Meteorological data used in this study included
surface observations from San Francisco and Oakland
International Airports, upper air observations from
Oakland International Airport, and surface wind speed
and direction from seven sites operated by private
companies. A vector average of wind speed and direction
was computed for each of three regions, which pro-'
vides a reasonable spatial variation of the wind
throughout the area.
Analysis
Monthly variations in the power plant emissions
and hourly variations of the area source emissions were
represented in the model. Due to the complex wind pat-
terns in the Bay Area three separate regions represent-
ing meteorological and geographical groupings of the
S02 sources were used. Winds for each source region
are used to advect SO- into neighboring regions. 24-
hour average concentrations were made for every other
day in 1973 by averaging eight 1-hour concentrations.
The annual mean and the highest predicted 24-hour
average concentration for each of the ten strategies
were determined for each of 120 locations based on
hourly evaluations for about 1300 hours. The annual
maximum 24-hour concentration was estimated by sta-
tistical extrapolation of the geometric mean and the
geometric standard deviation, assuming a log-normal
distribution.
It was found that the national standard for annual
means is not exceeded at any point under all ten of the
strategies. However, the 24-hour standard will be
exceeded if a strategy is developed which allows non-
combustion emissions of SO, which exceed 2500 ppm.
Based on this finding, it is recommended that both a
concentration-emission limit for process industries
(e.g., 2000 ppm) and a fuel-sulfur limit (e.g., 1.0
'percent) be adopted for the Bay Area.
Symbols
a, b, p, q - Empirical parameters for diffusion functions
(cry and az)
Cp, x» XA - Concentration
q Point source emission rate
Area source emission rate per unit area
Q,., Qt
Di'Hi
Space heat demand factor and temperature
threshold
F Fraction of emissions due to, space heating
D , H , T , V Stack diameter, height, temperature,
s s s s and velocity
h, hA Effective stack height
AH - Plume rise
v (or y,) - Wind speed (y, means height h^)
k - Exponential pollutant decay constant
L - Mixing height
m , s - Geometric mean and standard deviation
x, y Alongwind and crosswind rectangular
coordinates
y~ Distances to upwind and crosswind edges of
area source
T - Air temperature
V 'V
a , a - Horizontal and vertical diffusion parameters.
Z - Standard deviation corresponding to
P percentile p
References
Briggs, G.A., Plume Rise, U.S. Atomic Energy Commission,
Oak Ridge, Tennessee, 1969.
Koch, R.C., and S.D. Thayer, Validation and Sensitivity
Analysis of the Gaussian Plume Multiple-Source Urban
Diffusion Model. Contract No. CPA 70-94, 1971.
Prepared for Environmental Protection Agency, Research
Triangle Park, N.C., by GEOMET, Incorporated, Gaithers-
burg, Md. Available in PB 20691 from NTIS, Spring-
field, Va;
Koch, R.C., and G.E. Fisher, Evaluation of the Multiple-
Source Gaussian Plume Diffusion Model, Phase I Report,
Contract No. 68-02-0281, 1973. Prepared for Environ-
mental Protection Agency, Research Triangle Park,
N.C., by GEOMET, Incorporated, Gaithersburg, Md.
Koch, R.C. Impact of Proposed Revisions in Fuel-Sulfur
Regulations on SOg Concentrations in the Metropolitan
Boston Area, Task 3, Final Report, Contract No. 68-02-
1442, 1975. Prepared for Environmental Protection
Agency, Research Triangle Park, N.C., by GEOMET,
Incorporated, Gaithersburg, Md.
McElroy, J.L., and F. Pooler, St. Louis Dispersion
Study, Vol. II Analysis. Publication No. AP-53,
1968, Environmental Protection Agency, Research
Triangle Park, N.C.
Munn, R.E., Descriptive Meteorology, Advances in Geo-
physics, Supplement No. 1, Academic Press, New
York, 1966.
Pasquill, F., Atmospheric Diffusion, D. Van Nostrand
Co., Ltd., London, 1962.
Turner, D.B., "A Diffusion Model for an Urban Area."
Journal of Applied Meteorology, 3, 83-91, 1964.
96.
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MODELING OF PAHTICULATE AND SULFUR DIOXIDE IN SUPPORT OF TEH-YEAR PLANNING
Richard A. Porter, P.E.
Meteorology
Texas Air Control Board
Austin, Texas
John H. Christiansen
Data Processing
Texas Air Control Board
Austin, Texas
Urban air pollution modeling is a vital part of the
planning for attainment and maintenance of ambient air
quality standards. A Gaussian plume model based on
annual climatology and an accurate emissions inventory
can be made to represent adequately the ambient condi-
tions in an urban area through calibration with am-
bient air quality data. A model such as the Texas
Climatological Model that incorporates options for use
in control strategy development allows the analyst to
identify sources of current and projected violations
of ambient air quality standards.
,Introduction
Mathematical modeling is an important tool for re-
lating emitted pollutants to ambient air quality for
air quality maintenance planning and analysis. As
such, there are three important elements in the model-
ing process: emissions inventory, the computer model
algorithm, and air quality data from ambient air moni-
tors. This paper discusses the modeling process as
it applies to support for Air Quality Maintenance
Planning and Analysis (AQMPA) for the pollutants sul-
fur dioxide (SOa) and total suspended particulate
(TSP). A method of obtaining and maintaining an emis-
sions inventory for modeling is discussed. The Texas
Climatological Model (TCM) computer algorithm and its
use is outlined. The use of ambient air quality data
for model calibration is illustrated. Finally, model
projections of ambient air quality for future years
are discussed.
Emissions Inventory
The emissions inventory for Air Quality Maintenance
Planning and Analysis (AQMPA) modeling is divided into
emission from point sources and emissions from area
sources. For a typical Gaussian plume model, the in-
formation required for point sources is location,
emission rate, and stack parameters (stack height,
stack diameter, exit gas flow rate, and exit gas
temperature). Area sources are formed as squares of
various sizes. The information required for area
sources is location of the southwest corner, length of
a side of the square, and the emission rate. Point
sources are usually the major sources of pollution;
therefore, a major effort should be made to be as
accurate and detailed in the point source inventory
as possible. Area sources are appropriate for aggre-
gating the relatively nma.il numerous sources such as
residential space heating and vehicle traffic. Guid-
ance for establishing emission inventories is pro-
vided by the Environmental Protection Agency (EPA).9
In a major urban area the cost of gathering a special
one-time emissions inventory is prohibitive. For-
tunately the information gathered by the states for
97
the National Emissions Data System (NEDS) can be pro-
cessed to provide a point source emissions inventory
for modeling; however, such data are not available as
one of the regular reports from NEDS. Once an in-
ventory base has been established, it is desirable to
establish a system for updating the inventory so that
in successive years a current inventory will be avail-
able for modeling. The Texas Air Control Board has
devised a method of inventory maintenance that com-
bines the use of annual inventory of specified indus-
trial sources with onsite inspection and permit moni-
toring to continually update the emission inventory.
A base year emissions inventory for 1973 was estab-
lished by mailing questionaires to all known major
sources of pollution. In future years questionaires
will be mailed to all accounts that have more than 500
tons/year emissions of any pollutant. In addition,
inventories will be updated any time an operating per-
mit application is approved for new or expanded facili-
ties ; and all visits to facilities by investigators
from the State or Regional offices of the Texas Air
Control Board will include a check for changes to the
emissions inventory for that account.
Computer Dispersion Algorithm
The primary computer algorithm used for AQMPA plan-
ning by the Texas Air Control Board is the Texas
Climatological Model (TCM).5 The TCM combines the
familiar Gaussian dispersion algorithm for point
sources with a simple area source algorithm suggested
by Hanna and Gifferd11 to compute pollution concen-
trations in an urban environment. The TCM is similar
in concept to the Climatological Dispersion Model
(CDM)1* in that botli models are based on the same point
source and plume rise equations; however, the TCM
differs significantly in execution from the CDM be-
cause the point source equation is solved by inter-
polating in a table of precalculated coefficients and
a simple equation is used to calculate concentrations
due to area sources. As a result of these changes,
the TCM is much faster than the CDM (roughly two
orders of magnitude); but both models predict essen-
tially the same concentrations given the same input
data.
The TCM is suitable for non-reactive pollutants such
as S02, TSP, and carbon monoxide (CO). Input to the
model consists of: (l) a stability wind rose for a
year or a season; (2) point source and area source
parameters for two pollutants; (3) air quality monitor
data for calibration (optional).
Model output from the version of the TCM used in
AQMPA planning differs significantly from the pub-
lished version of the model (known originally as the
Fast Air Quality Model).5 These, changes are tailored
to the needs of the analyst charged iritjr control
strategy development. In addition to the listing of
expected concentrations and a punched card output op-
tion for isopleth mapping, the control strategy ver-
sion of the TCM provides a print plot grid suitable
for hand isoplething and a culpability list of the
five high contributors to the concentration at each
grid point.
-------
Model Calibration
n = 'the number of data points,
A mathematical model can, at best, only account for
those physical phenomena which are described by the
mathematical algorithm. Gaussian urban models such
as the TCM, CDM, and Air Quality Display Model (AQDM)1"
contain algorithms that account for steady-state emis-
sions from discrete sources defined in the inventory
with veil-defined meteorological conditions that change
in discrete increments. The TCM and the CDM do account
for some pollutant reactivity with a. decay half-life
term, but in practice neither model seems adequately to
account for the transformation of S02 to sulfates .
There are many important transformations which affect
the concentration of pollutants in an urban environ-
ment that these urban models do not attempt to address.
These transformations include meteorological condi-
tions that vary continuously and often cannot be char-
acterized by a single value at a.n altitudes of con-
cern: reentrainment and background levels of pollution
(especially important in TSP studies), pollutant re-
activity (especially important in the SOz to sulfate
conversion), and absorption by sinks (important in CO
removal). The ideal solution is to modify existing
models or create new models that include all important
transformations of pollution in an urban environment.
This is a difficult ideal to fulfill.
Reactivity, reentrainment, background, and meteorology
all change drastically from urban area to urban area,
and there is no simple algorithm known at this time
that adequately accounts for all these important fac-
tors. There is a statistical technique, regression
analysis, which can be used to relate the results of
urban models to observed pollution levels. The use
of regression analysis for such a purpose is generally
termed model calibration. It would be much better to
build a model that needs no calibration, since model
calibration is easily misused. However, regression
analysis is the best available method at this time
to account for important transformations of the pol-
lutant that are not adequately covered by the model
algorithm.
Linear Regression
Model calibration by linear regression involves creat-
ing a scatter diagram of points (See Figure l) that
represent the observed pollutant concentration
(vertical axis) versus the predicted concentration
(horizontal axis). A best-fit straight line is es- .
tablished for the data points by the method of least
squares. The equations of interest are:2
(1)
(2)
(3)
where:
X = the calibrated concentration
x^ = the predicted concentration at the i point
y^ = the observed concentration at the i point
a0 = the intercept of the line of regression
ai = the slope of the line of regression
A measure of how well changes in the observed data are
accounted for by the model is given by the correlation
coefficient :
I
/
V
The number of data points and the magnitude of r
(ranging from 0 = no relation to 1 = perfect correla-
tion) combine to give an estimate of the confidence
we can have in the calibration of the model . l 3
where
1+r
ll-r.
(5)
Z = the abscissa value of the normal
probability curve.
TABLE 1: Confidence Level for Z Values
1.96 2.575 2.8l
Confidence Level
99.'.
Ambient Air Data
Ambient air quality data from monitors in the urban
area being modeled are important elements in the cali-
bration procedure. The monitors used should represent
ambient conditions at the location being modeled. It
is important that the ambient air monitor be sited
properly (no wind flow obstructions), that the method
used be sensitive enough to measure ambient levels,
and that a large enough sample be taken to charac-
terize the annual mean value adequately. Recommenda-
tions for monitor siting6 and data evaluation10 are
detailed in the EPA guideline series. Because pol-
lutant distributions at urban ambient air monitors
have been found to be log-normal12, the annual geo-
metric mean should be used in model calibration. The
problem of zero values in the computation can be
avoided by assigning a value equal to one-half the
minimum detectable level to measurements that fall be>-
'low the minimum detectable level. However, any moni-
tor that has recorded more than 25 percent of its values
for the year below the minimum detectable level should
not be used for model calibration.
Examples of Model Calibration
Figure 1 is a scatter diagram of observed and pre-
dicted values for TSP in the Dallas-Fort Worth metro-
politan area for 1972. The model used is the TCM.
All TSP ambient air monitors in the area were surveyed
and only those monitors that were not wind flow ob-
structed were used to construct the calibration curve
of Figure 1. Correlation and confidence level are
very high for these data. The intercept of the line of
regression is about 2k ug/m3 which is a reasonable
(perhaps low) number for a background TSP level.
The slope of the regression line is 1.9. A possible
interpretation of the slope is that TSP in the busy
98
-------
Industrial areas is feeing reentrained because of the
higtL level of human activity. This interpretation is
strictly conjecture and requires support by independent
tests before acceptance.
L>
UJ
IT
LJJ
99.99%
10 20 30 40
CALCULATED TSP (M9/m3)
FIGURE 1. Dallas-Fort Worth, 1972, Observed versus
Predicted TSP (jj.g/m3)
Figure 2 is a scatter diagram of the same urban area
•with all monitors in the area used for calibration
without regard to wind flow obstructions. The data
points referring to the sites with wind flow obstructed
monitors are indicated by x's, and the rest of the
monitors are shown with dots. The solid line is the
same regression line as Figure 1. The dashed line is
a result of a least-squares fit to all the monitor
data. Although there is a dramatic drop in the cor-
relation coefficient when all sites are considered,
there is very little difference in the confidence level
because as r becomes smaller n increases. Since includ-
ing data points whose physical relation to the model is
questionable results in almost no change in the confi-
dence level, the concept of confidence level is called
into question. The critical assumption in the confi-
dence level equation is that the n observations are
independent. The independence of the observations is
questionable because the means were generated from
samples taken on the same days of the year (thereby
experiencing the same meteorology and background) and
because some of the monitors are located close enough
together to be dominated by the same sources. There-
fore, because of temporal and (in some cases) spatial
correlation between the observations a high confidence
level generated by equation (5) should be suspect.
Conversely, a low confidence level generated by equa-
tion (5) can be believed. If the data will not support
a Z value of at least 1.96 (95% confidence), the validity
of the emissions inventory, the computer algorithm, and
the air quality data should be carefully examined.
100
H
D
cc
UJ
I/I
DASHED LINE
(ALL DATA POINTS)
30
20 30
CALCULATED (M9/m3)
40
FIGURE 2. Comparison of Calibration Curves
In terms of designating an area as being in violation
of the annual standard, it makes very little differ-
ence which calibration curve in Figure 2 is used.
.Based on the first calibration curve, all points for
which the uncalibrated model predictions exceed
27 pg/m3 would exceed the annual standard (75pg/m3)
when calibrated. Using the second calibration curve,
only those points whose uncalibrated value exceed
32 i^g/m3 would be above the annual standard. This
shows a degree of robustness in the calibrated model
predictions with respect to the quality of ambient air
monitor data and illustrates the point that the model
predictions are not precision estimates. At best, the
calibrated urban air pollution model indicates "ball-
park" figures for projected ambient air quality.
99
-------
Predicting Future Ambient Air Quality
Mathematical modeling allows the air quality planner
to consider the impact of urban growth on future am-
bient air quality. It is necessary to project the
future emissions inventory for the area being
modeled.6'7 A joint frequency distribution of meteo-
rological elements (stability wind rose) for a period
of several years should be used for climatological in-
put to the model. The model algorithm can then be
exercised using projected emissions and average meteo-
rology. Linear regression for model calibration can-
not be performed because ambient air quality data are
not available for future years. The calibration
equation that was established for a year of known
emissions inventory and sampled air quality data must
be used. Future year model projections can be accu-
rate only to the degree that the projected emissions
inventory is accurate; the future year meteorology
will conform to the average climatology, and the local
conditions that influenced the model calibration
equation remain the same.
12. Larsen, R.I., "A Mathematical Model for Relating
Air Quality Measurements to Air Quality Standards,"
Report AP-89, USEPA, RTF, NC, November 1971-
13. Miller, I., and Freund, J.E., Probability and
Statistics for Engineers, Prentice-Hall Inc.,
Englewood Cliffs, N.J. , 1965-
Ik. TRW Systems Group, Air Quality Display Model,
National Air Pollution Control Administration,
Washington, B.C., 19&9-
References
"Air Quality Monitoring Site Description Guide-
lines," USEPA, RTF, NC, OAQPS, Number 1.2-019.
Bevington, P.R., Data Reduction and Error Analysis
for the Physical Sciences, McGraw-Hill, New York,
1969.
Brier, G.W. , Validity of the Air Quality Pis-play
Model Calibration Procedure, USEPA, RTF, NC,
(EPA-Rl*-73-017), January 1973.
Busse, A.D., and Zimmerman, J.R. , User's Guide
for the Climatological Dispersion Model, USEPA,
RTF, NC, (EPA-Rl*-T3-02lt), 1973.
Christiansen, J.H., and Porter, R.A., "Ambient
Air Quality Predictions with the Fast Air Quality
Model," Proceedings of the Conference on Ambient
Air Quality Measurements, Southwest Section,
APCA, March 1975.
Guidelines for Air Quality Maintenance Planning
and Analysis, Vol. 13, "Allocating Projected
Emissions to Subcounty Areas," EPA h'yO/k-Th-Olk,
USEPA, TRP, NC, November 197^.
Guidelines for Air Quality Maintenance Planning
and Analysis, Vol. 12, "Applying Atmospheric
Simulation Models to Air Quality Maintenance
Areas," EPA-h50/k-lk-013, USEPA, RTF, NC,
September 19Jh.
10.
11.
Guidance for Air Quality Monitoring Network Design
and Instrument Siting. USEPA, RTF, NC, OAQPS,
Number 1.2-012, January 197*t.
Guidelines for Compiling an Emission Inventory.
Report NO. APTD-1135, USEPA, RTF, NC , 27711,
March 1973.
Guidelines for the Evaluation of Air Quality Data,
USEPA, RTF, NC, OAQPS, Number 1.2-015, February
Hanna, S.R. , "A Simple Method of Calculating
Dispersion from Urban Area Sources," Journal of
APCA 21, Ilk, December 1971.
TOO
-------
A MATHEMATICAL MODEL OF DISSOLVED
OXYGEN IN THE LOWER CUYAHOGA RIVER
Alan E. Ranun
Cleveland Environmental Research Group
Cleveland State University
Cleveland, Ohio
ABSTRACT
A computer model was developed to rapidly simulate
dissolved oxygen content in the Cuyahoga River under
varying conditions of flow and biochemical oxygen de-
mand. The model, which has been used to simulate pres-
ent and projected dissolved oxygen levels for the navi-
gation channel of the Cuyahoga River, shows that de-
spite the fact that industrial and municipal discharges
may be completely eliminated, other factors are signif-
icant enough to cause a severe oxygen sag in the navi-
gation channel.
BACKGROUND
Because of its recreational potential and the vast
industrial complexes which span its banks depend
upon it as a route for transporting raw and finished
goods, the Cuyahoga River is an important river. Its
importance, however, is being overshadowed by its pol-
lution.
The current pollution problem in the Cuyahoga
River is twofold:
1) The natural contour of the mouth and delta have
been altered by man in an effort to make this section
navigable to large vessels. These alterations have
decreased the velocity of water, which has in turn
decreased the river's capacity for natu*ral aeration of
water in this section; and
2) Industries and municipalities have become dependent
upon the river as a receptacle for their discharged
waste. This waste, which had generally been improperly
treated or untreated, has created a condition of anoxia
and physical degradation in certain sections of the
river.
Both of the above conditions have resulted in decreased
dissolved oxygen in sections of the river.
Because dissolved oxygen is vital to maintaining
a homeostatic environment in stream ecosystems, one is
justifiably concerned about the low dissolved oxygen
content in sections of the Cuyahoga River. This con-
cern is not only for the effect that low dissolved ox-
ygen may have upon the plant and animal life in the
river, but also for the effect that it may have upon
the near shore water quality in Lake Erie.
In order to determine the effect of discharged
waste upon dissolved oxygen in the river and the effect
of river dissolved oxygen upon dissolved oxygen at the
confluence of Lake Erie, a mathematical simulation com-
puter model was developed. A model is advantageous for
resolution of problems of this nature because param-
eters can be manipulated and hypothetical situations
can be tested.
This model addresses itself to the problems of
dissolved oxygen, and is designed specifically for use
in the Cuyahoga River; however, minor alterations could
make it adaptable to any stream possessing similar
physical-hydraulic conditions.
The navigation channel is the dredged portion of
the lower Cuyahoga River which extends from its mouth
to mile point 6. Dredging maintains the navigation
channel at a depth of approximately 25 feet. While
lake water intrusion is generally restricted to the
lower one mile of the navigation channel, the hydraulic
effect of lake level fluctuations is suspected to exist
throughout much of the channel. This hydraulic effect
tends to increase longitudinal mixing within the chan-
nel much as tidal flux increases longitudinal mixing in
estuaries. In the case of estuaries the dispersive ef-
fects of tidal fluxing are generally experienced well
above that point where there is a measurable salinity
change. Within the navigation channel, then, one might
expect dispersion to influence water quality to varying
degrees. The most significant influence is observed
during periods of low flow.. Because the magnitude of
mixing and its significance to water quality was not
previously determined, a model of the navigation chan-
nel was developed to incorporate dispersion.
METHODS
MODEL FORM
Many forms of models have been developed for estuaries
in which dispersion is important and must be incorpor-
ated. Of the many forms available, the finite differ-
ence approach was selected because of its logical par-
allelism to the Cuyahoga River and its amenability to
computeri zation.
Conceptually, the navigation channel was divided into
twenty sections, each having a length of 0.3 miles.
The choice of the number of sections was dictated by
the hydrology and geometry of the channel and by the
amount of computer time required to obtain a solution.
Since the solution methodology requires inversion of
a matrix of order N, (where N equals the number of sec-
tions in the river) as N increases the time to obtain
a solution increases significantly. Each section is
considered completely mixed, and hence it is assumed
that no vertical or horizontal variations within a
section of the river exist.
Mass balances were developed for each section with re-
spect to DO deficit and CBOD. The balances incorporate
flow from section to section and dispersion and advec-
tion between adjacent sections. Any input to or output
from a given section was included in the mass balance
equations for that section, as were source and sink
terms for processes occurring within a section. The
approach has been described in detail by Thomann, 1972
(1). The model simulates steady state conditions.
DATA REQUIREMENTS
The data required as inputs to the model may be classi-
fied under three headings: (1) coefficient determina-
tion data, (2) field data and (3) simulation run data.
Coefficient determination data and field data are nec-
essary to adapt the model's parameters to those of the
Cuyahoga River system. Simulation run data is neces-
sary to exercise the model utilizing various sets of
system conditions.
101
-------
The coefficients considered in the model include longi-
tudinal dispersion, flow, benthal uptake, deoxygenation
and reaeration.
Longitudinal Dispersion (D ) within the channel
was estimated from chloride distributions. Within the
lower one mile, where lake intrusion is dominant, re-
gression techniques produced estimates of longitudinal
mixing coefficients on the order of 1.0-2.5 mi /day.
It was observed that mixing effects were most intense
within this region but became less intense as one pro-
ceeded upstream. Since longitudinal dispersion had
never been measured upstream, the rate of decrease in
magnitude of dispersion was not known. However, rea-
sonable estimates were obtained from historical data
on upstream chloride distributions. As will be noted
in the following discussion, such errors as those in-
volved in 'educated guessing' were found to be rela-
tively unimportant to the system's general behavior.
Benthal Uptake (Sb) has never been measured within
the navigation channel and consequently no data was
available regarding the magnitude of this sink in the
river. A decision not to design a study to measure
benthal uptake was based upon current investigations
being conducted at Cleveland State University. These
investigations are attempting to evaluate the design
of benthal respirometers of the bell jar variety.
Preliminary results of the above mentioned investiga-
tions indicate numerous problems resulting from the
use of this type respirometer and tend to cast doubt
upon measurements obtained from its use. Additionally,
the model did not appear to be very sensitive to
changes in benthal uptake (see section on Sensitivity
Analysis). Since it was felt that the cost and time
required to conduct such a study were not justifiable,
a study of benthal uptake was not undertaken. Litera-
ture estimates of benthal uptake in rivers such as the
Cuyahoga indicate a range of values from 2-10 gm/m/day.
An estimated uptake from the channel of 5 gm/m2/day
was used.
trification, to result in depletion of DO within the
navigation channel.
Reaeration was estimated from the empirical re-
lationship formulated by O'Connor (3).
Flow data were taken from USGS records.
RESULTS AND DISCUSSION
SENSITIVITY ANALYSES
One of the more useful applications of water quality
models is to test the response of the water quality
parameters under observation to changes in system pa-
rameters. By holding all but one parameter constant,
it is possible to determine the relative effects of
each parameter on DO. Loadings used in the sensitivity
analyses were taken from Table 1, with the exception of
flow which was 850 cfs in the channel.
2
3
4
5
6
7
8
9
11
12
14
15
17
18
19
20
25
25
25
25
25
25
25
25
25
25
25
25
23
25
4200 3
4400 3
4300 3
9000 3
4700 3
5100 3
4900 3
7400 3
4200 3
6200 3
6200 3
6500 3
4500 3
7000 3
5 0
5 0
5 0
5 0
5 0
5 0
5 0
5 0
5 0
5 0
5 0
5 0
5 0
5 1
22
22
22
22
22
22
22
22
22
22
22
60
BO
00
0 5
510 5
9990 5
0 5
0 5
1602 5
0 5
0 5
0 5
0 5
0 5
0 5
0 5
0 5
0 5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5 30
5 30
5 30
5 31
5 31
5 31
5 31
5 30
5 30
5 30
5 30
5 28
5 28
5 28
5 28
21
D - depth (ft)
A - area (ft2)
F - flow (cfs)
D - dispersion <
*
w - waste load Ubs/day)
Sb - benthal uptake (gm/m2/day)
TEMP - temperture (°c)
Deoxygenation coefficients(K )in the lower Cuya-
hoga River were estimated from previous Cuyahoga River
studies. Values utilized by Dal ton, Dalton and Little
(2) ranged from 0.2 to 0.07 liters per day (base e).
These estimates were derived from an empirical equation
developed by O'Connor (3) which utilized a combination
of parameters, including river depth, to estimate K .
Small variations in the value of K were found to have
fairly large effects upon dissolved oxygen steady-state
concentrations in the navigation channel (see section
on Sensitivity Analysis).
Nitrogenous Demand (Nitrification) was assumed to
be negligible. Some investigators have assumed the
process to be important, while others (2) considered
it unlikely that nitrification occurs. O'Connor (4)
suggests that nitrification is typically observed when
dissolved oxygen exceeds 1-2 mg/1. This is generally
true for rivers which do not receive a high concentra-
tion of various industrial wastes which inhibit bacter-
ial growth; however, the navigation channel, because
of its high industrial waste load, does not necessarily
meet the conditions for this assumption. The basic ar-
guments against nitrification are based upon the as-
sumption that river and water quality conditions exist-
ing at critical low flow periods are not suitable for
growth of nitrifying bacteria. No reliable experi-
mental study of the nitrification process within the
lower Cuyahoga exists despite the fact that loadings of
ammonia are significant enough, through potential ni-
Dispersion. The effect of variations in disper-
sion coefficients is illustrated in Figure (1A). Dou-
bling the dispersion coefficients while holding flow
and temperature constant had very little effect upon
the results. This suggests that a 2- or 4- fold error
in dispersion estimates would not appreciably affect
the simulation output.
Benthal Uptake. Figure (IB) indicates that the
maximum difference in DO which results from a 4- fold
change in benthal uptake is only about 1 mg/1. Al-
though benthal uptake has not been measured in the
river, it is doubtful that it is greater than
10 gm/m /day. Hence an error in estimating benthal up-
take by 2- to 4- fold was also not critical to the sim-
ulation of the DO sag in the channel.
Deoxygenation. Figure (1C) illustrates the re-
sults of varying the deoxygenation coefficient (K ) in
the channel. It is immediately apparent that the mag-
nitude of the sag is quite sensitive to relatively
small changes in KI- For example, decreasing K from
0.15 to 0.07 resulted in an increase of nearly 1.5 mg/1
in the minimum DO. Literature values of K in the Cuy-
ahoga River ranged from 0.25 to 0.07. For critical
tuning of the model a study of deoxygenation coeffici-
ents in the channel during critical low flow conditions
is necessary.
102
-------
Upstream Conditions. Figure (ID) illustrates the
effect upon DO concentration of improving the quality
of the water entering the channel. The effect of im-
proving water quality by 1 mg/1 at the head of the
channel increases the minimum DO near mile point 2.0
by approximately 0.5 mg/1. To obtain water having 1
mg/1 of DO at mile point 2.0 would require upstream
water of better than 5 mg/1 DO.
o
O
V)
5
B '
5432106543210
MILE POINT
Figure 1. Sensitivity Analyses.
MODEL VERIFICATION
Because there was no data available for simultaneous
DO at several locations within the channel, a sampling
run was conducted in the channel on August 28, 1974 to
supply this information. On this date the flow within
the channel was 715 cfs. By slightly adjusting dis-
persion coefficients for the upper reach of the chan-
nel, it was possible to obtain a stable simulation for
the river conditions on August 28, 1974. This minor
adjustment of dispersion coefficients can be justified
since the sensitivity analysis indicated the system to
be relatively insensitive to this parameter.
The major trend in dissolved oxygen fluctuations was
simulated by the model (Figure 2). From upstream to
downstream the general shape of the observed data was
successfully modeled. It is assumed that biological
and random influences which were not incorporated in
the model, resulted in the slight variations at each
sample point.
Figure (2) indicates that the model is valid and, if
properly utilized, can provide significant insight and
understanding into DO behavior in the lower Cuyahoga
River.
SIMULATION RUNS
General. A variety of simulation runs was con-
ducted. These runs incorporated variations in waste
load allocations, and input values were altered to re-
flect changes in waste load conditions (BOD and flow).
The simulation runs were used to assess the influence
of alternate waste quality control measures on the
overall dissolved oxygen quality in the system.
o
2 5
UJ 4
O
S'
s •
1,
(fl
(0 „
5 '
I I I I
6 5 4 3 2 I 0
MILE POINT
Figure 2. Verification Run.
The program was developed for input of values for
cross-sectional area, flow and BOD. Cross-sectional
areas at the interface of adjacent sections, where
dispersion is considered, were obtained from U. S. Army
Corps of Engineers' dredging maps. Where necessary,
water levels were adjusted to late-summer, early-fall
depths.
Flow within the navigation channel is relatively con-
stant with respect to distance. Small increases in
flow occur near the upper end of the channel due to
the Ohio Canal return, and to a much lesser degree,
Morgan Run and Burke Brook. Flow data utilized in the
simulations conducted within the navigation channel
were averages obtained from Havens and Emerson (5) and
from the United States Geological Survey Water Re-
sources Data for Ohio (6) (7). A low flow of 345 cfs
and an average flow of 850 cfs were used.
Photosynthesis, a major biological source of DO, was
considered to be insignificant within the navigation
channel. Water is turbid and it is doubtful that any
significant photosynthesis occurs except at the sur-
face. Chlorophyll analyses of both surface and bottom
water within the lower channel indicated no measurable
chlorophyll.
BOD loadings were determined from Ohio EPA records.
Records indicated that the majority of industries
within the navigation channel which discharge signifi-
cant amounts of waste are located above section 10
(m.p. 3.15). The results of simulation runs utilizing
these data are presented and compared in the following.
Simulation 1. This baseline simulation illus-
trates the effect of present municipal and industrial
discharges on water quality during low flow conditions.
It was assumed that if all other water quality param-
eters remained constant or improved, this simulation
would represent the poorest expected water quality pro-
file for the navigation channel. System parameters
for this simulation are presented in Table 1.
The results (Figure 3A) of this simulation show that
discharges into Sections 2, 4 and 5 degrade water
quality until the DO reaches zero in Section 5 (m.p.
4.65). More waste is discharged into Section 8 (m.p.
3.75), but its effect is not observed since DO has al-
ready reached zero. Based upon this simulation run,
one would expect the river to be anoxic from Section 5
to Section 19 (m.p. .45). At Section 19 water quality
improves slightly due to lake water intrusion.
The following simulation runs manipulate flow, BOD and
DO to illustrate how the model can be used as a manage-
ment tool. A summary of simulation runs and the vari-
103
-------
ables manipulated is given in Table 2.
Table 2. Summary of Parameters used in Simulations
Simulation Flow
No (cfs)
1 345
2 850
3 345
4 345
5 850
Loading
Source
1973-OEPA
1973-OEPA
1978-OEPA
50% 1973
1978-OEPA
Boundary
Upstream
BOD
8
8
6
4
6
DO
3
3
3.5
4
5
Conditions
Downstream
BOD
6
e
6
6
6
DO
6
6
6
6
6
Simulation 2. The effect of flow upon DO was
tested in Simulation (3). An average flow of 850 cfs
was used as the flow in the navigation channel. Fig-
ure (3B) shows that DO begins to drop slowly until zero
DO is reached in Section 10 (m.p. 3.15).
When comparing Simulations (1) and (2), it is apparent
that for identical conditions, river water quality dur-
ing low flow is greatly reduced. This is primarily due
to the low velocity and high holding time in each sec-
tion during low flow. In general, it could then be
assumed that water quality in the Cuyahoga River could
be improved if the concentration of waste being dis-
charged during low flow periods is reduced. This could
be accomplished by temporarily storing the waste and
releasing it when river flow is high or by storing
water in large reservoirs and releasing it as dilution
water when river flow is low.
Simulation 5. If the best practical treatment
guidelines are met by 1978, it is expected that the
DO in the navigation channel will improve. Projected
1978 waste load reductions were obtained from the Ohio
EPA in Columbus. These values were input to illustrate
the degree of improvement which could be anticipated.
D
210 54
MILE POINT
Figure 3. Simulation Runs.
3210
Results are shown in Figure (3C). Since all other con-
ditions are identical to Run #1, the trend in DO is ex-
pected to be somewhat similar. As expected, DO drops
to zero in Section 5. While water quality improves
slightly as Ib/day of waste load decreases, the im-
provement does not appear to be very significant.
Simulation 4. Simulation (4) was conducted to ob-
serve how dissolved oxygen is affected when all waste
loads are decreased to 50% of 1973 values. The results
of this simulation are compared in Figure (3D) with
those of Simulations (1) and (3). It is apparent from
the figure that water quality is only slightly improved
by waste load reductions. Despite the reduced load-
ings, benthal uptake, upstream loadings, low rates or
reaeration and long channel residence times combine to
produce anoxia within much of the channel. Since the
model does not reflect reduced benthal uptake rates,
which might in time result from reduced loadings, these
results may be somewhat pessimistic.
Simulation 5. Simulation (5) was conducted to
test the combined effects of improved upstream water
quality (entering DO 5 mg/1, BOD = 6 mg/1), reduced
loadings (1978 projections) and augmented flow (850
cfs.) Under these combined conditions DO dropped slow-
ly, reaching a low of 0.35 mg/1 at mile point 1.35
(Section 16) (see Figure 3E). Thus a combination of
improved upstream water quality, reduced waste loading
and increased flow produced a significant improvement
in DO concentrations within the. channel.
UTILIZING THE TRANSFER MATRIX
As the model calculates the DO deficit response for
each section, the DO drop for each section is computed
and listed in tabular format. The changes in DO from
one section to another resulting from variations in
waste load allocations can thus be directly and quickly
determined from the matrix shown in Table 3. (Only half
of the complete matrix is shown.)
As an example of the use of this matrix, consider the
DO profile for the channel shown in Figure (3F) as
"1973 channel loadings". This profile results from a
flow of 900 cfs in the channel, a DO of 4.4 mg/1 and
a BOD of 8.0 mg/1 for water entering the channel, and
the waste loadings shown in Table 1.
Suppose that Republic Steel and U. S. Steel were to re-
duce their waste loadings to zero. This would result
in a removal of approximately 10,000 Ibs/days of waste
from Section 5 (Republic Steel) and a removal of ap-
proximately 1,600 Ibs/day from Section 8 (U. S. Steel).
Table 3 indicates the decrease in DO (Sections 1-20)
resulting from waste inputs to Sections 1-10. It also
can be interpreted to read the increase in DO in Sec-
tions 1-20 resulting from waste reductions in Sections
1-10. Thus a 10,000 Ib/day waste removal from Section
5 would result in the increases in DO shown under 'Sec-
tion 5' (Table 3). A removal of 1600 Ibs/day of waste
from Section 8 would produce the response obtained by
taking the values from Table 3 (under 'Section 8') and
multiplying each by 1600/10000 .16).
The total response is the sum of the two responses and
indicated by the line labeled 'improved conditions' in
Figure (3F).
These operations allow a decision-maker to assess im-
mediately the results of hypothetical waste load allo-
cations without running the model. In addition, the
matrix indicates that Section 16 is the most sensitive
region of the channel and will receive its maximum ef-
fect (a drop in DO of 0.59 mg/1) when 10,000 Ibs/day of
waste is discharged into Section 5.
104
-------
The transfer matrix must be recalculated (i.e., the
model must be run) for different river conditions.
Once the matrix is available, however, any set of
waste load allocations may be applied (without rerun-
ning the model) to observe the corresponding DO re-
sponse.
Table 3. Transfer Matrix.
Section
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
1
0.12
0.15
0.17
0.19
0.22
0.24
0.27
0.28
0.31
0.32
0.34
0.36
0.36
0.34
0.26
0.18
-
2
0.
0.
0.
0.
0.
0.
0.
0.
0.
0
0,
0
0.
0
0
0.
0.
11
15
.17
.20
.23
.26
.29
.31
.34
.36
.38
.40
.41
.39
.29
.20
.10
3
0 .
0.
0.
0.
0.
0
0
0.
0
0
0
0
0
0
0
0
.13
.15
.19
.22
.26
.29
.32
.35
.37
.40
.42
.43
.41
.31
.22
.11
4
0.04
0.09
0.12
0.16
0.19
0.23
0.26
0.29
0.32
0.35
0.38
0.40
0.41
0.40
0.30
0.21
0.10
5
0.08
0.12
0.18
0.24
0.29
0.35
0.39
0.45
0.49
0.53
0.57
0.59
0.57
0.44
0.30
0.15
6
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
03
.08
.14
.20
.26
.32
.37
.43
.46
.51
.56
.58
.56
.43
.30
.15
7
0.
0.
0
0
0
0.
0
0
0.
0.
0
0
0,
0.
.05
.09
.14
.18
.22
.26
.29
.32
.36
.58
.37
.28
.20
.10
8
0
0
0
0
0
0
0
0
0
0
0
0
0
.05
.09
.14
.18
.23
.26
.30
.34
.36
.35
.27
.19
.09
9
-
0.05
0.10
0.14
0.19
0.23
0.27
0.31
0.33
0.33
0.26
0.18
0.09
10
-
0.07
0.12
0.19
0.23
0.28
0.34
0.37
0.37
0.29
0.20
0.10
managing water quality?
Answer 3: The Transfer Matrix (Table 12) provides an
excellent tool for determining the optimal
locations for outfalls and the optimal
waste load inputs because this matrix
points out the sections which can least
tolerate and most tolerate a. waste load.
Through an understanding of the complex physical,
chemical and biological events occurring simultaneous-
ly within the system, the model has demonstrated its
ability to simulate the dissolved oxygen profile in
the river. The oxygen profiles resulting from use of
the model, when compared with field measurements, pro-
vided a reasonable fit. The model, therefore, allows
a water planner to assess the impact of alternate
water quality control measures on the river system by
varying the treatment levels at each discharge point
and the water quality conditions in Lake Erie at its
mouth. By increasing flow, while holding discharge
constant, the model can also estimate the volume of
dilution water required to meet dissolved oxygen stand-
ards in the river.
REFERENCES
SUMMARY
By utilizing the model it is possible to answer sever-
al types of questions which must be addressed by man-
agement :
Question 1: How can the model determine the upstream
water quality required to achieve the
water quality standards set for the Cuya-
hoga River's navigation channel?
Answer 1: In order to maintain the standards set
for the river, water quality in sections
14-16 must be controlled. Therefore, up-
stream flow, BOD, DO and waste inputs
must be manipulated until an acceptable
DO is obtained in Sections 14-17. Simu-
lations 1-5 demonstrate the expected
changes which would occur when manipulat-
ing each of these parameters. Additional
manipulations require only changing the
input data.
Question 2: How can the model be utilized to deter-
mine the best physical system for achiev-
ing that water quality?
Answer 2: Once the desired DO level is obtained in
Sections 14-16, one must then determine
the most economic or most efficient means
for effecting the required changes. For
example, if flow is doubled and BOD is
decreased by half, then one must decide
how to double the flow and decrease the
BOD. Such alternatives as storing dilu-
tion water to augment flow, eliminating
all discharges, etc., must be approached
from an economical point of view; how-
ever, the response to using combinations
of the different alternatives can be ob-
served from the model.
Question 3: How can the model assist in determining
the optimal system for administering and
6.
Thomann, R. V. System Analysis and Water Quality
Management. New York. Environmental Science
Services Division, 1972. 286 p.
Dalton, Dalton 5 Little. Industrial Waste Survey
Program for the Lower Cuyahoga River. Cleveland,
Ohio. January 1971.
O'Connor, D. J. Estuarine Distribution of Non-
Conservative Substances. Jour. San. Eng. Div.
ASCE. Vol 91. No. SA 1. February 1965. p. 23.
O'Connor, D. J., et al. Dynamic Water Quality
Forecasting and Management. Environmental Pro-
tection Agency. Publication Number 600/3 73
009. August 1973.
Havens 5 Emerson. Master Plan for Pollution
Abatement. City of Cleveland, Ohio. July 1968.
U. S. Department of Interior, Water Resources
Data for Ohio. 1973.
U. S. Department of Interior, Water Resources
Data for Ohio. Part 1. Surface Water Records.
1974.
105
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A WATER RESIDUALS INVENTORY FOR NATIONAL POLICY ANALYSIS
Edward H. Pechan*
Consultant
National Academy of Sciences
Washington, D.C.
ABSTRACT
A computer based water residuals generation and dis-
charge inventory was developed to assist in the
evaluation of regional and national implications of
the uniform effluent requirements of the Federal
Water Pollution Control Act Amendments of 1972
(PL 92-500) and in the evaluation of alternative
residuals control policies.
The completed system, termed the National Residuals
Discharge Inventory (NRDI), has been used in a number
of applications including the investigation of costs,
residuals discharge, and residuals dilution effects
of three alternative policies to national uniform
effluent standards.
BACKGROUND
The Federal Water Pollution Control Act Amendments of
1972 (hereafter referred to as P.L. 92-500 or the
1972 Act) marked a decisive shift in the nation's
approach to restoring and maintaining the physical,
chemical, and biological integrity of its waters.
That shift is best reflected in the major change in
enforcement mechanisms. Under prior legislation,
ambient water quality standards were set as the control
mechanism. The use of the waters for such activities
as drinking, recreation, and manufacturing determined
the kinds and amounts of residuals to be discharged,
the degree of residual abatement required, and the
rapidity with which dischargers were to install the
necessary abatement technology. Under the 1972 Act,
effluent limitations were set as the control mechanism.
The existence and availability of water pollution
control technology determined the kinds and amounts
of residuals to be discharged, and legislatively man-
dated compliance dates determined the rapidity with
which dischargers must install the necessary abate-
ment technology.
The overwhelming Congressional support for the 1972
Law resulted from disillusionment with the lack of
progress under more than two decades of Federal
legislation. Contributing problems to the failure
of previous efforts were the tardiness of the States
in setting water quality standards, the complex
procedures which delayed enforcement actions against
polluters, and the failure to fully implement the
Federal construction grant program for municipal
sewage treatment facilities.
The 1972 Act attempted to respond to these limitations
with three essential elements; uniformity, finality,
and enforceability. Uniformity is mandated by the
requirement that each residual discharger within a
category or class of industrial sources and all
municipal sources must meet stipulated effluent
limitations regardless of geographic location.
Categories or classes of industrial sources will be
required to meet unique, nationally uniform, effluent
limitations based on "best practicable control
technology currently available" (BPT) by 1977, and
to meet even more stringent nationally uniform
effluent limitations based on "best available
technology economically achievable" (BAT) by 1983.
All municipal sources (publicly owned treatment works)
will be required to meet effluent limitations based
on secondary treatment (ST) by 1977 and based
Ralph A. Luken**
Consultant
National Academy of Sciences
Washington, D.C.
on "best practicable wastewater treatment technology"
(BPWTT) by 1983.
Finality is mandated by the requirement to meet more
stringent effluent limitations by point sources
(municipal and industrial activities) at specific
dates in the future. While prior legislation did
not set specific dates for meeting water quality
goals, the 1972 Act requires dischargers to meet one
set of effluent limitations in 1977, a more stringent
set of effluent limitations in 1983, and looks toward
achieving a final goal of zero discharge of pollutants
into navigable waters by 1985. In addition, an
interim goal of achieving waters fit for fishing and
swimming by 1983 is established. The concept of
finality is intended to remove the uncertainty on the
part of industrial and municipal dischargers about
the nation's (or at least Congress') commitment to
maintaining and restoring the quality of the nation's
waters.
Enforceability is assured through the provisions of
the permit program and the new enforcement authorities
given to the EPA. The 1972 Act is based on the
assumption that violations of permit conditions
would be easier to determine than violations of
water quality standards, assuming the ability to
design an adequate compliance monitoring program and
to inspect the operations of residual dischargers.
EPA not only has the authority, but is required to
issue an abatement order whenever there is a violation
of the conditions of a permit and a state fails to
move against the violator in a timely fashion.
Furthermore, a citizen may bring suit against EPA if
it fails to issue a necessary order.
Although the 1972 Act received Congressional support
in its final form sufficient to override a Presiden-
tial veto, there were many compromises in the develop-
ment of the final version as it moved through the
procedures of the Congress. Thus, while the three
major innovative provisions of the Senate version
survived in the legislation agreed to by the
Conference Committee, a provision was inserted to
establish a National Study Commission to "make a
full and complete investigation and study of all of
the technological aspects of achieving, and all
aspects of the total economic, social and environmen-
tal effects of achieving or not achieving the
effluent limitations and goals set forth for 1983
..." (P.L. 92-500) looking toward recommendations not
later than October 18, 1975 as to any needed "... mid-
course corrections that may be necessary ..."
(H.R. 92-1465).
In implementing its study program, using the efforts
of almost 100 contractors, the National Commission
on Water Quality (NCWQ) appeared to accept the
uniformity provisions of the Act and defined its
contract studies to concentrate primarily on the
finality provisions and secondarily on the
enforceability provisions. None of the studies
* Mr. Pechan is currently with the U.S. Energy Research
and Development Administration in Washington, D.C.
** Dr. Luken is currently with the United Nations in
Bangkok, Thailand.
106
-------
questioned the benefits or costs of requiring uniform
treatment of similar classes of residual discharges
regardless of geographic location.
Early in the course of its study program, the NCWQ
contracted with the National Academy of Sciences/
National Academy of Engineering/National Research
Council under the provisions of Section 315 for
assistance in particular areas of concern.
In order to provide the assistance needed, the
Environmental Studies Board of the National Research
Council created the Study Committee on Water Quality
Policy (CWQP). In connection with its accomplish-
ments of the tasks assigned by NCWQ, CWOP determined
that an independent assessment of residual reduction
technologies was essential to provide perspective on
its assignment. In the absence of a breakdown by
NCWQ of national totals by geographic regions,
primarily due to inability of the Strategic Environ-
mental Assessment System (SEAS) to accurately compute
and display (by region) data fron the contractor
studies, CWQP engaged consultants and directed them
to devise a system which could provide it with a
basis for an independent analysis of the effects of
'achieving or not achieving the goals of the Act.
NATIONAL RESIDUALS DISCHARGE INVENTORY
To provide a basis for handling the immense amount
of data available from the NCWQ contractor's reports,
from the U.S. Environmental Protection Agency (EPA)
and from other available sources, the consultants
devised a system for computerized analysis called
the National Residuals Discharge Inventory (NRDI).
The NRDI analysis was to provide a basis for the
CWQP's comments on the NCWQ's contractor and staff
draft reports. - It was also hoped that the analysis
would be of value to the NCWQ as it moved toward
preparation of its own final report.
To carry out this assignment, the CWQP consultants
were requested to:
• document the distribution of residual generation
and discharges by region;
• document the distribution of residual generation
by activity;
• describe the relative importance of activity
categories by region;
• document the distribution of residual reduction
technology cost by region;
• indicate the sensitivity of estimates of residuals
generation, discharge, and reduction technology
costs to various assumptions;
• evaluate the quality of basic data on residual
generation, discharge, and technology used by
NCWQ contractors and describe other possible data
sources.
NRDI is a quantitative assessment of residual genera-
tion and discharges and of residual reduction techno-
logy costs in each of the 3,111 counties or county
approximations in the contiguous U.S. Data for
industrial, municipal, urban runoff, and non-irriga-
ted agriculture sources are available for each county.
However, the data are not displayed at the county
level, but rather are aggregated for purposes of
analysis by the Water Resources Council's 99 aggrega-
ted sub-areas (ASAs), the 18 Water Resource Regions
(WRRs) and by the nation. The ASAs and WRRs are
often generically referred to in this report as
river basins.
The purposes of NRDI are: (a) to provide a compre-
hensive measure of biological oxygen demand (BOD),
total suspended solids (TSS), nitrogen (N), and
phosphorus (P) residual generation and discharge
aggregated for the nation and for each of the 18
WRRs and 99 ASAs, (b) to indicate the relative
importance of various activities as sources of
residuals after the effluent limitations for 1977 and
1983 are met; (c) to provide a comprehensive measure
of the costs of residual reduction technologies
required to meet the 1977 and 1983 technological
objectives of the 1972 Law aggregated for the nation,
the 18 WRRs, and the 99 ASAs, and (d) to estimate the
cost savings to the nation of pursuing alternative
policies. The NRDI analyses include point sources,
which'are defined as discharges from municipal and
industrial activities, and areal sources, which are
defined as urban runoff and drainage from non-irri-
gated agricultural activities.
Thus, NRDI is a conceptually simple but systematic
computational procedure for evaluating various
aspects of the 1972 Law. The inventory has the
capacity to predict potential reductions in residuals
discharged into the ambient environment and the
associated costs of the application of uniform
residual reduction technologies stipulated by EPA for
municipal and industrial residual generators. It can
compare the resulting reductions in discharges from
these sources with those from other sources, primarily
urban storm water runoff and non-irrigated agriculture,
by river basins. More importantly, NRDI allows for an
evaluation of policy alternatives to the uniform
application of residual reduction technologies to
legislatively defined (P.L. 92-500) point sources.
These policies reflect alternatives where in a given
river basin, achievement of the 1983 effluent limita-
tions would not make a significant improvement in
total residual reductions and ambient water quality,
and where a given level of residual reduction could
be achieved at a lower cost without the uniform appli-
cation of residual reduction technology to point sources.
NRDI consists of (a) inventories of production and
consumption activities which generate and discharge
residuals, (b) a system for analyzing the effects
of increased industrial production and population
growth, (c) an index of potential water quality
changes, and (d) residual discharge reduction policies
which include the BPT/ST and BAT/BPWTT technology
goals in the Act.
ACTIVITY INVENTORIES
The purposes of the activity inventories are twofold.
First, the inventories relate process/production
data to residual generation coefficients for calcula-
tion of residual generation for a particular activity.
Second, the inventories assign an appropriate
residual reduction technology, as specified under
the policy alternatives, thereby enabling the
computation of abatement costs and of residuals dis-
charged into the ambient environment. The specifi-
city of the individual activity inventories for the
above process depends upon the importance of each
sector as a residual generator and upon the
availability of data.
The data input files for activity inventories contain
information on identifiable point and areal source
residual generating activities. The point and areal
activities combined cover most major waterborne
107
-------
residual generating activities. Information included
about these activities, where appropriate and avail-
able, are location of activity, measures of production
(physical output, employees, land area, or population)
type of production process, and current residual
reduction technologies being used.
There are several activity inventories for the muni-
cipal, industrial, and areal categories. The muni-
cipal category includes a sewage treatment plant inven-
tory based on the 1974 EPA Needs Survey1. The indus-
trial category includes an in depth industry inventory
for the significant process water users and a general
industry inventory for the vast majority of other
residual generating industries (Table 1).
TABLE 1 NRDI INDUSTRY STUDY CATEGORIES
INDUSTRIES STUDIED IN DEPTH
Pulp and Paper
Petroleum Refining
Textiles
Iron £ Steel
Plastics 6 Synthetics
Organic Chemicals
Inorganic Chemicals
Steam Electric
INDUSTRIES STUDIED IN GENERAL
Ore Mining
Coal Mining
Petroleum £ Gas
Mineral Mining
Meat Processing
Dairy Products
Grain Mills
Cane Sugar
Beet Sugar
Seafood
Builders Paper
Fertilizer
Paving £ Roofing
Rubber
Leather
Glass
Cement
Pottery
Asbestos
Ferroalloys
Non-ferrous Metals
Electroplating
Fruits £ Vegetables
Other Organic Chemicals
Industrial plant data for the in-depth industries
was developed from numerous sources as described in
the NRDI report2. Plant data for the general indus-
tries was obtained from Census data3. Residuals
generation and water use information was obtained
from both EPA Development Documents and Census data4.
Residual generation coefficients for industries
studied in depth are specified for each production
process within an activity category. For the indus-
tries studied in general, total residual generation
for a four-digit SIC category is used. The coeffi-
cients are given as weights of residuals per produc-
tion output unit (for example, pounds of organic
residuals generated per ton of pulp or per barrel of
crude oil processed). The residuals included are BOD,
TSS, and wastewater flow.
The input file also specifies the various residual
reduction technologies available for each of the
activities. Information specified for each technology
or unit process includes costs and residual reduction
rates or removal efficiencies.
Areal sources include urban runoff and non-irrigated
agriculture, both analyzed by county. Information
for the urban runoff was obtained from the Needs
Survey, Census data5, and an NCWQ contractor report6.
Counties were included which were (1) part of an
SMSA and (2) had an average resident population
density of .6 persons per acre or more.
Non-irrigated agriculture activities were defined on a
county-by county basis by acres under cultivation,
soil types, etc. Residuals were computed by
successive application of the uniform soil loss
equation, sediment delivery ratios, and residuals
carried by sediment. The single control policy was
developed by simulating the application of soil conser-
vation measures as outlined in the 1967 Conservation
Needs Inventory.
Estimated residual delivery and costs of control were
obtained from the NCWQ contractor?. The sediment
delivery ratios were back-computed and residual load-
ings were adjusted to correspond with Iowa State
Sediment delivery ratios8.
The costs of residual reduction technologies are com-
puted for the capital or initial investment cost.
GROWTH ANALYSIS
The purpose of the growth analysis is to project
future levels of residual generation and discharge.
The projected growth for industry is based on increas-
es in physical output growth while that for municipal-
ities is based on population growth rates. Growth
is not projected for urban runoff or non-irrigated
agriculture activities. While the growth analysis
design permitted either national or ASA averages for
industrial and municipal sectors, as a first approx-
imation, only the former have been used to date.
The growth assumption does not generally influence the
results of the analysis presented here which is based
only on 1973 data.
Inputs into the growth analysis are projected
industrial production and population increases. The
projected growth for industry is available either from
the Wharton Economic Forecasting Analysis used by
NCWQ9 or the U.S. Department of Commerce, OBERS Series
filO. The projected growth for municipalities is
based on U.S. Department of Commerce, Census Series E
population growth rates.
RESIDUALS DILUTION RANKING INDEX
The purpose of the water quality indexing procedure is
to convert the information on residuals discharged into
an approximate measure of water quality. The procedure
is essentially a mechanism for ranking the basins
according to relative average water quality, i.e.,
"average" conditions are determined for each basin and
the basins ranked accordingly. Such a. ranking may then
be used to identify those ASAs which are relatively well
off or have problems under current conditions and
which may be significantly affected by different water
quality management policies. Since the "average"
conditions do not reflect a real situation at any given
location or time, they cannot be used to attempt to
pinpoint specific water quality problems in a sub-basin
or stream segment.
At this time, the only water quality related data
unique to each river basin are approximations of low
and average flow conditions and number of stream
miles.
OUTCOME SUMMARIES
The outputs resulting from each policy alternative are:
• residual generation;
• residual discharge;
• abatement costs;
• residuals dilution index.
108
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These outputs must be taken together to evaluate a
given policy, because no one output is by itself an
adequate evaluation measure. However, even the
combination is no substitute for basin specific evalua-
tion. At that level of detail, data are available for
assessing actual changes in physical, chemical and
biological parameters and for measuring the damages
which are sustained directly by human beings or
indirectly by plants and animals of value to man.
ALTERNATIVE POLICIES
A variety of alternative policies can be selected for
solution in the NKDI. These policies include both
uniform and non-uniform abatement policies and can
simulate controls on areal as well as point sources.
In using the model, a target year for analysis is
selected. Standard years are 1973 (base case), 1977,
and 1983.
The model has been exercised with a variety of abate-
ment policies. Due to the simplicity of the model, it
is relatively easy to add new policies. The basic
policies used to date are discussed below:
a. No control - This policy estimates risiduals
discharge if no control technology is used.
b. 1973 controls - This policy estimates discharge
and costs based on control technology in place in 1973.
c. BPT/ST - This policy estimates effects of the 1977
standards of the Act: Best Practicable Treatment for
industry and Secondary Treatment for municipalities.
d. BAT/BPWTT - This policy estimates effects of the
1983 standards for industry and secondary treatment
for municipalities supplemented with tertiary facil-
ities when requested in the Needs Survey.
e. BAT/BPWTT+- This policy is identical to (d) for
industrial sources but includes filtration for all
municipalities not requesting treatment more stringent
than secondary in the Needs Survey.
f. Non-irrigated agricultural control - Costs and
residual implications of implementing practices out-
lined in the 1967 Conservation Needs Inventory are
included.
g. Urban storm control Costs and residual implica-
tions of one of five urban storm control strategies
(combined, separate storm, and unsewered) is simulated.
h. Ocean discharges - Effects of discharge and costs
for ocean counties are excluded. This function is
used to simulate lower levels of treatment for ocean
discharges based on using a specified set of counties.
i. New Source Performance Standards - In this policy,
residual discharges and costs for industrial growth
are based on new source performance standards (approx-
imated by BAT).
j• Limited technology - Simulation of stringent
effluent limitation policies can be limited to ASAs
with relatively bad water quality.
k. Cost effective strategy - This policy used data on
cost per quantity of residuals removed to identify
cost-effective solutions in each ASA.
Combinations of these policy components can be
combinned in a single run if desired.
RESULTS
Illustrative results and conclusions are presented in
this paper. The results presented show the costs of
uniform application of BAT/BPWTT, as well as three
policy alternatives.
Table 2 presents summary results of the policies.
The results of the illustrative alternatives to
the uniform application of BAT/BPWTT are discussed
below.
TABLE 2 - COMPARISONS OF ALTERNATIVE POLICIES
BOD Removed Total Capital
Technology 109 Ibs/yr 10? 1975 $
Uniform BPT/ST 7.4
Uniform BAT/BPWTT 8.8
Alternative I 8.0
Alternative II
Cost-eff. BPT/ST 7.4
Cost-eff. BAT/BPWTT 8.8
Alternative III
EPA counties 8.7
Potential counties 8.6
38.5
55.6
43.2
23.0
37.0
55.2
52.9
Alternative I: Limit BAT/BPWTT Technology Investment
to Areas with Relatively Poor Water Quality
One alternative is to require that the BAT/BPWTT
technology objectives be met only in those areas
(ASAs) which have relatively severe water quality
problems. This alternative limits the application
of BAT/BPWTT technologies to ASAs which have a BOD
dilution index equal to or greater than 3.0 mg/1.
The result of this alternative is that if uniform
water quality is a policy objective, it can be
obtained for only $5.. 7 billion more than BPT/ST,
a reduction of $12.5 billion from the costs of
uniform BAT/BPWTT. This is achieved by applying the
more stringent effluent limitation to 21 instead of
all 99 ASAs. The results suggest that in the re-
maining areas (78 ASAs) BAT/BPWTT may not really be
necessary because they generally may have met water
quality standards after BPT/ST. Areas (ASAs) with
no additional cost, in this case, would be located
in the New England, Tennessee, Upper Mississippi,
Lower Mississippi, Upper Colorado, and Pacific North-
west WRRs. This alternative illustrates that if the
ultimate goal of the law is to restore the nation's
water quality, then it can be achieved at lesser cost
Alternative II; Invest Only in Cost Effective Options
The second alternative is to require only those
sources which have the least cost to invest in more
stringent technology in order to achieve the residual
reduction accomplished by uniform BAT/BPWTT. This
alternative is based on considering all major sources
of residuals, including urban runoff and non-irrigated
agriculture,and applying both BPT/ST and BAT/BPWTT
non-uniformly in order to achieve a given level of
residual reduction for the least cpsts.
The results showed that a 33 percent reduciton in
total BPT/ST and BAT/BPWTT costs, 41 percent for
BPT/ST and 12 percent for BAT/BPWTT, can be obtained,
and the same quantities of residuals removed, by
substituting a nonuniform cost effective policy
109
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approach for uniformity. The five regions (WRRs) that
benefit the most from a cost effective approach include
the Upper Mississippi, Lower Mississippi, Missouri,
Rio Grande and Arkansas-White-Red Water Resource Regions.
This alternative suggests that if the quantities of
residuals removed after uniform BPT/ST and BAT/BPWTT
are policy objectives, then they can be achieved at
lesser costs.
Alternative III; Do Not Invest in BAT Technology in
Areas with Potential for Ocean Discharge
The last alternative is to not require point source
dischargers in all counties which have the potential
for ocean discharge to meet the BAT/BTWPP technology
objectives. This alternative is based on computing
a lower bound, which excluded point dischargers in
selected counties in only three regions with generally
recognized assimilative capacity, and an upper bound
which excluded point source dischargers in selected
counties in regions with potential tidal dilution
capacity. The lower bound resulted in a national
cost saving of $0.4 billion or only two percent of
the NRDl estimated BAT/BPWTT costs while the upper
bound considered 172 counties and resulted in a
national cost savings of $2.7 billion. Savings
included fifteen percent of the uniform BAT/BPWTT
costs for the California region and twenty-eight
percent for the Pacific Northwest. This alternative
illustrates that if the nation is willing to use the
natural assimilative capacity of the oceans, a few
regions would achieve a significant reduction in BAT/
BPWTT costs.
In summary, we examined three illustrative alternatives
to the uniform application of the technology standards.
These alternatives could conceivably yield savings of
between 2 percent and 70 percent of the costs of meet-
ing uniform standards without a significant deterior-
ation of either the residual reductions or the water
quality gains achieved using the uniform policy. Since
these alternatives are not mutually exclusive, all or
some of them could be adapted simultaneously and
result in a significant percent reduction of the costs
of uniform standards. Of course, more detailed
analysis would be needed including consideration of
institutional issues and methods of implementation
before a new approach is adopted.
CONCLUSIONS
Analysis done to date with the NRDI has shown it to
be a powerful tool which can be used to examine the
effects of various abatement policies at a regional
level. The model is unique in its capability of
simultaneously estimating costs, residuals discharge,
and residuals dilution effects of alternative policies.
Major limitations of the system include its omission
of some important sources i.e. silviculture, construc-
tion, its limited coverage of residuals, and our
limited faith in the "water quality" estimates.
REFERENCES
1.
2.
3.
U.S. Environmental Protection Agency, Joint State-
EPA Survey of Needs for Municipal Waste water
Treatment Facilities, computer tape, March, 1975.
Luken, Basta, and Pechan, The National Residuals
Discharge Inventory, National Research Council,
Washington, D.C. January, 1976.
U.S. Department of Commerce, Bureau of the Census,
1972 County Business Patterns, Washington, D.C.
4. U.S. Department of Commerce, Bureau of the Census
1972 Census of Manufacturers, Water Use in
Manufacturing, Washington, D.C.
5. U.S. Department of Commerce, Bureau of the Census,
1972 City County Data Book, Washington, D.C.
6. Black, Crow, and Eidsness, Study and Assessment
of Capabilities and Costs of Technology for
Control of Pollutant Discharges from Urban
Runoff, NCWQ Contract, November, 1975.
7. Midwest Research Institute, Cost and Effective-
ness of Control of Pollution from Selected Non-
point Sources, NCWQ Contract, July, 1975.
8. Wade, James, C., Iowa State University, letter
communication, May, 1975.
9. Wharton Econometric Forecasting Associates,
Wharton Econometric Forecasting Estimates, Mark IV,
Solution of March 4, 1975.
10. U.S. Water Resources Council, 1972 OBERS Project-
ions, April, 1974.
no
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A MULTI-PARAMETER ESTUARY MODEL*
Paul A. Johanson
Tetra Tech, Inc.
Lafayette, California
Marc W. Lorenzen
Tetra Tech, Inc.
Lafayette, California
William W. Waddel
Washington Public Power
Supply System
Richland, Washington
ABSTRACT
To obtain information needed in the development of a
water quality plan for Grays Harbor, in Washington
State, the mathematical water quality model EXPLORE
was modified for application to the harbor and the
lower Chehalis River. This report describes the model
selection criteria and the procedures used in applying
the model to a tidally influenced estuary and river.
Results of the study show that model calculations and
observed data correlate well, confirming that the
model is a valuable tool for evaluating the effects
of various waste discharge schemes on the quality
of a water body and thus for helping to select a plan
for managing water resources. The study also indi-
cates that further information about rates of benthic
oxygen demand and the oxygen content of incoming sea-
water would improve the accuracy of the model calcula-
tions.
INTRODUCTION
The need for high quality water to maintain natural
productivity and the need to assimilate waste mater-
ials often conflict in estuarine areas (1). Careful
management of water resources is essential in these
areas, and one tool which can be of immense help to
the engineer/planner is mathematical simulation.
Through the use of computer models it is possible to
describe quantitatively the behavior and interactions
of various water quality parameters and thereby pre-
dict the effects of various management schemes.
This report describes the modification of a mathemati-
cal model for application to a particular estuary
system. Water quality problems and conflicting water
uses in the estuary have indicated the need for more
careful resource management, and water quality model-
ing can be of obvious benefit.
PURPOSE AND CONCLUSIONS OF THE STUDY
Application of the Battelle-Northwest EXPLORE water
quality model to Grays Harbor and the lower Chehalis
River in Washington State was the major task of a
recently completed program. The purpose of the study
was to provide specific information needed to develop
a water quality management plan for Grays Harbor
County. It was felt that mathematical modeling tech-
niques would provide the best method of evaluating
the effects of various waste discharge schemes on the
water quality of Grays Harbor.
This report reviews the characteristics of a water
quality model needed for this task and discusses
calibration and use of the model. Results are in
reasonable agreement with observed data and show the
utility of the model as a water management tool.
*This work was completed under partial support of Con-
tract 68-01-1807 of the Environmental Protection Agen -
cy in Oct. 1974, while the participants were employed
at Battelle Northwest Laboratories, Richland, WA.
The assistance of Charles R. Cole of BNW is grate-
fully acknowledged.
Results of this study indicate that further informa-
tion is needed about rates of benthic oxygen demand
and the oxygen content of incoming seawater, and field
measurements of these parameters are suggested.
CAPABILITIES REQUIRED OF THE MODEL
Water quality modeling in an estuarine system requires
the determination of water flows, depths, and veloci-
ties in order to properly transport the quality para-
meters through the system. Thus, hydrodynamic calcu-
lations are prerequisite to any quality calculations.
Once the physical transport of water has been deter-
mined, biological and chemical reactions can be
superimposed to calculate water quality at any loca-
tion and time.
The primary quality parameter of concern in Grays Har-
bor is dissolved oxygen (DO). Low oxygen concentra-
tions have been observed in the estuary during periods
of low flow. DO is predominantly a function of bio-
chemical oxygen demand (BOD) discharged to the system,
benthic oxygen demand, surface reaeration, and algal
growth and decay. BOD and benthic oxygen demand de-
pend on wastes discharged to the system. Surface
reaeration depends on water and wind velocities as well
as oxygen deficiencies. Algal growth and decay rates
depend on nutrient concentrations, light penetration,
temperature and possibly toxic substances discharged
to the system.
The EXPLORE model is derived from a hydrodynamic code
developed by Water Resources Engineers (WRE) (2).
Whereas standard approaches to the solution of un-
steady flow equations generally represent varying
methods of making the equations numerically discrete,
the approach adopted by WRE involves a discretization
of the physical system being modeled. The region is
subdivided into a number of nodes with channels con-
necting adjacent nodes. The continuity equation is
solved at junctions or node points while the momentum
equation is solved along connecting channels. This
approach has been applied successfully to the simula-
tion of estuarine networks of the Sacramento-San
Joaquin Delta by WRE and to the Columbia River by the
Environmental Protection Agency. The general purpose
computer program originally written by WRE was later
modified, updated and refined by the Federal Water
Pollution Control Administration and is reported by
Callaway, Byram and Ditsworth (3) and Feigner and
Harris (4). More generalized versions of the code
have been incorporated into the Storm Water Manage-
ment Model (5) and the Battelle-Northwest EXPLORE
Program (6).
MODEL SELECTION
The Battelle-Northwest EXPLORE hydraulic code was
chosen for use in the Grays Harbor-Chehalis River
estuary for three reasons: it has been successfully
tested and used for a number of different simulations;
it can be effectively applied to an estuary with the
physiographic features of Grays Harbor; and a number
of water quality programs have been written for use
111
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with this code.
The three most widely used of these water quality
models are discussed in references 4, 5 and 6. The
EXPLORE quality code was selected because it is the
most comprehensive and versatile of the three programs
and because it was written for maximum compatibility
with the EXPLORE hydraulic code.
The water quality models used were developed by Bat-
tell e-Northwest for the Environmental Protection Agen-
cy to serve as a management tool in the study of
water resources and pollution abatement programs. The
models afford an overall perspective of the synergis-
tic effects of various proposed plans.
Not all of the water quality models were used in the
present modeling effort due to a lack of data for cal-
ibration, but other constituents can be studied when
more data become available.
A detailed description of the procedure for using the
EXPLORE code has been given elsewhere (7). Briefly:
the study area is divided into nodes and channels.
Surface area and depth are determined for each node,
while length and width are measured for each channel.
The process of dividing the area into nodes requires
experience, three considerations being paramount:
areas of great concern (such as waste discharges,
municipal areas, or regions characterized by low water
quality) or requiring great detail will generally re-
quire a large number of nodes; channels must be longer
than a limit which is determined by the timestep used;
and more detailed systems involve greater expense in
data preparation and computational time.
Tributary stream flows are added as either time-varying
or constant values, upstream control points andtidally
controlled nodes are established and the tidal regime
is chosen. The hydraulic code then calculates flows
and velocities for each channel and water surface ele-
vations and volumes for each node as functions of time.
The code is allowed to run for a number of tidal cycles
until steady-state conditions are established. Although
the code can handle transient conditions, only average
diurnal variations are considered for specific condi-
tions such as low flow periods. This is so because
the effect on the predicted water quality of transient
conditions caused by variations in tidal cycles and
river flows is usually small for the short period of
time for which the simulation is performed. By aver-
aging the variations the computational time is reduced,
which significantly reduces costs without compromising
the usefulness of the results.
Utilizing the output from the hydraulic code in con-
junction with the quality of the waste sources and
initial conditions of each water quality parameter,
the quality code calculates the concentrations of
all the parameters as functions of time and location.
The values of constants which are not known are set
so that the computer output simulates field observa-
tions. Once the model is calibrated, the locations
and magnitudes of waste sources can be varied to
evaluate the effects of different management schemes.
CALIBRATION AND VERIFICATION
Hydrodynamic Model
In order to calibrate the hydrodynamic portion of the
model, stream flow and tidal data were needed. August
15-20, 1971, was chosen for calibration because quali-
ty data for this period were available. High and low
water predictions from Department of Commerce Tide
Tables were chosen to describe the time-stage curve,
and river flow data for the same period were taken
from Water Resources Data for Washington.
Water Quality Model
Because sufficient data were not available with regard
to chemical concentrations, algal nutrients, and
photosynthetic processes in Grays Harbor, only BOD,
benthic oxygen demand, and surface reaeration were
considered in the model calculations. Information
about sources of major BOD discharge were obtained
from the State Department of Ecology.
The dissolved oxygen concentrations measured in the
Harbor for 1970, 1971 and 1972 were taken from
Interim Reports and from raw data supplied by the
Department of Ecology.
Initial calculations showed that waste discharges
alone would not account for the low observed DO. It
became apparent that a benthic oxygen demand would
have to be assumed in areas where waste discharges
occurred, a reasonable assumption since organic matter
would be expected to settle to the bottom in such
areas and create an oxygen demand. The values used
were chosen to correctly simulate the observed oxygen
concentrations in the estuary for 1971 and were not
changed for the 1970 and 1972 verification periods
other than to examine the effect of eliminating ben-
thic demand. There is probably.some benthic oxygen
demand throughout the estuary, but assumption of
values was considered to be warranted only in the
areas where oxygen data were available for calibration.
In the process of analyzing the oxygen field data it
was observed that although less BOD was discharged
to the North Channel during 1970 than in 1971, the
measured oxygen concentrations were lower in 1970
than in 1971. The most logical explanation for this
observation is that incoming ocean water must have
been lower in dissolved oxygen in 1970 than in 1971.
For this reason the 1970 incoming ocean water oxygen
concentration was fixed at 6.0 mg/1. In 1971 and
1972 the incoming oxygen concentration was set at 7.0
mg/1.
Figures 1, 2, and 3 show computer predictions (curves)
and data for five consecutive days (points) for 1970,
1971, and 1972. DO is plotted against Department of
Ecology station numbers (lower axis) and node numbers
(upper axis)
NODE NUMBER M-
9-10 10-11 11-12 D 14 15 15 16 17-18 18 20
AUG 1970 CALIBRATED MODEL
• FIELD DATA
53 52 51 50
D.O.E. STATION NUMBER
685 49 33 47 45 « 71
Figure 1.
112
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NODE NUMBER 14-
9-10 10-11 11-12 13 M 15 15 16 17-18 18 20
AUG 1171
-CALIBRATED MODEL
FIELD DATA
t !
53 52 51 50 685 49 33 47 45 44 71
D.O E. STATION NUMBER
NODE NUMBER 14-
9-10 10-11 11-12 13 14 15 15 16 17-18 18 20
CASE1
1970 FLOW CONDITIONS
CALIBRATED MODEL
NO BENTHIC DEMAND
53 52 51 50 685 49 33 47 45 44 71
D.O.E. STATION NUMBER
Figure 2.
Figure 4.
NODE NUMBER M-
9-10 10-11 11-12 13 M 15 15 16 17-18 18 20
-CALIBRATED MODEL
FIELD DATA
53 52 51 50 685 49 33 47 45 44 71
D 0 E. STATION NUMBER
NODE NUMBER
9-10 10-11 11-12 13
14 15 15 16 17-18 18 20
CASE 2
1970 FLOW CONDITIONS
CALIBRATED MODEL
NO BENTHIC DEMAND
+1/2 REAERATION RATE
3.0
38
52 51 50
0.0.E. STATION NUMBER
685 49 33 47 45 44 71
Figure 3.
SENSITIVITY ANALYSIS
In each of the sensitivity studies lowest DO was found
to occur in the same general area, so the figures show
only this region.
The importance of benthic oxygen demand in 1970 is
illustrated in Figure 4. The model predictions, with
the elimination of benthic oxygen demand, are shown
with the calibrated model predictions for 1970. It is
readily apparent that the benthic demand used in the
model contributes significantly to the predicted ox-
ygen sag. Figure 5 shows the predicted oxygen concen-
trations with no benthic demand and a reduced
reaeration coefficient. It is apparent that some
other combination of lower benthic BOD and reaeration
coefficients could have simulated the data. However,
it was felt that the values used were the most ap-
propriate.
Figure 6 illustrates the effect of removing the ben-
thic oxygen demand for the 1972 flow conditions. With
no benthic demand, the predicted oxygen concentrations
are significantly higher than the calibrated model had
predicted. A comparison of Figures 4 and 6 reveals
that the benthic oxygen demand was more important in
producing the oxygen sag during the 1972 period than
during 1970. This result is consistent with the fact
that industrial discharges were lower in 1972 than in
1970. As the discharged BOD is decreased, the contri-
bution of benthic demand becomes more important in
the total oxygen balance
Figure 5.
NODE NUMBER
9-10 10-11 11-12 13
14 15 15 16 17-1! 18 20
CASE 3
1972 FLOW CONDITIONS
-CALIBRATED MODEL
-NO BENTHIC DEMAND
53 52 51 50
D.O.E. STATION NUMBER
685 49 33 47 45 44 71
Figure 6.
The effect of eliminating industrial discharges of
BOD is shown in Figure 7. The model was run with
ocean DO set at 6.0 and 7.0 mg/1. Minimum DO occurs
in approximately the same point for each of these
cases and ranges from 5.8 mg/1 to 6.2 mg/1. Benthic
demand would be expected to gradually decrease under
these conditions but the rate of change is not known.
113
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5.0
3.0
NODE NUMBER 14-
9-10 10-11 11-12 13 14 15 15 16 17-18 18 20
CASES 4 & 5
1972 FLOW CONDITIONS
OCEAN D.O. -7.0 mg/1
OCEAN D.O. =6.0 mg/1
CALIBRATED MODEL
NO INDUSTRIAL LOADING
53 52 51 50
D.O.E. STATION NUMBER
49 33 47 45 44 71
9-10 N°DEUU-Tl6ERll-1213 14 is'15 16 17-18 18 20
_ 7.0
t
CASES
1972 FLOW CONDITIONS
CALIBRATED MODEL
OCEAN D.O. -7.0mg/l
PROPOSED D.O.E. LOADINGS
BOTH IN NODE 28
OCEAN D.O. -6.0mg/l
53 52 51 50 685 49 33 47 45 44 71
D.O.E. STATION NUMBER
Figure 7.
The effects of the proposed Department of Ecology
discharge limits were simulated with ocean DO of 6.0
mg/1 and 7.0 mg/1, as shown in Figure 8. The observed
1972 conditions do not differ greatly from the pro-
posed limits. The results show that proposed limits
will probably not be sufficient to meet quality
standards.
NODE NUMBER 14-
9-10 10-11 11-12 13 14 15 15 16 17-1818 20
Figure 9.
o 5.0
3.0
CASE 6
1972 FLOW CONDITIONS
OCEAN D.O. -7.0 mg/1
OCEAN 0.0. • 6.0 mg/1
CALIBRATED MODEL
PROPOSED D.O.E. DISCHARGES
53 52 51 50
D.O.E. STATION NUMBER
49 33 47 45 44 ' 71
Figure 8.
Figure 9 shows the predicted results of combining the
pulp mill discharges. The model predictions show
virtually no difference between results of the separ-
ate and combined discharges (Figures 8 and 9).
The last alternative placed the entire industrial dis-
charge much closer to the estuary mouth. The results
for the proposed discharge levels and a benthic oxygen
2
demand of 2.0 g/m /day between the discharge and the
estuary outlet indicated essentially no oxygen deple-
tion. The calculations show that for these conditions
DO in the estuary may be very nearly equal to the
concentration in incoming seawater. However, this
result should be interpreted cautiously because there
is presently no information about tidal exchange co-
efficients.
Study of saltwater intrusion based on 1972 hydraulic
conditions showed that water similar to ocean water
extends nearly up to the region of DO sag examined
earlier, corroborating the small DO change up to this
point.
MONITORING SYSTEM IMPROVEMENTS
It is suggested that future effort be devoted to field
measurements of benthic oxygen uptake rates and the
determination of ebb and flood tide water quality at
the seaward boundary of Grays Harbor. The benthic
measurements should be made in the North and South
Channels and up the Chehalis River to Cosmopolis.
Other monitoring system improvements, such as the
measurement of nutrient concentration and photo-
synthetic rates, would be valuable but of secondary
importance compared to the above suggestions.
REFERENCES
Odum, E.P., Fundamentals of Ecology. 3rd ed. W.B.
Saunders Co., Philadelphia, 1971. pp. 352-362.
A Hydraulic Hater Quality Model of Suisun and San
Pablo Bays. Water Resources Engineers report of an
investigation conducted for FWPCA. 35 pp., March,
1966.
Call away, R.J., K.V. Byram and 6.R. Ditsworth, Mathej
matical Model of the Columbia River from the Pacific
Ocean to Bonneville Dam - Part I. Federal Water
Pollution Control Administration, Pacific Northwest
Water Laboratory. 155 pp., November, 1969.
Feigner, K.D., and H.S. Harris, Documentation Report,
FWQA Dynamic Estuary Model. July, 1970.
Storm Water Management Model, Volumes 1-4. Metcalf
& Eddy, Inc., Palo Alto, California; University of
Florida, Gainesville, Florida; and Water Resources
Engineers, Inc., Walnut Creek, California.
Baca, R.G., W.W. Waddel, C.R. Cole, A. Brandstetter
and D.B. Cearlock, EXPLORE I: A River Basin Water
Quality Model. Report to the U.S. Environmental
Protection Agency, Battelle-Northwest, Richland, WA.,
1973.
Lorenzen, M.W., W.W. Waddel, and P.A. Johanson,
Development of a Mathematical Water Quality Model
for Grays Harbor and the Chehalis River, Washington.
Report to the U.S. Environmental Protection Agency.
4 vols. Battelle-Northwest, Richland, WA., 1974.
Interim Reports I and II, Cooperative Grays Harbor
Surveillance Program. Washington State Department
of Ecology, 1970-1971.
114
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MATHEMATICAL MODEL OF A GREAT LAKES ESTUARY
Charles G. Delos
U.S. Environmental Protection Agency
Chicago, Illinois
Abstract
A one dimensional steady state finite section
estuary model was applied successfully to the lower 11
miles of the Black River of Ohio. The approach used
was necessitated by the fact that water quality in the
lower portion of the river is strongly influenced by
Lake Erie waters. The one dimensional estuary model
represents a compromise between conventional stream
models, which are fundamentally inadequate to simulate
this type of system, and multi-dimensional models,
which require considerably greater resources to apply
successfully. The approach used is likely applicable
to the lower reaches of nearly all rivers tributary to
the Great Lakes.
General Considerations
The Black River of Ohio drains an area of 467
square miles to Lake Erie . Water quality of the lower
11 miles of the river is severly degraded by discharges
from U.S. Steel Lorain Works and the cities of Elyria
and Lorain sewage treatment plants. In order to assess
the degree of waste treatment required to attain
acceptable levels of dissolved oxygen in the river,
field data collection and mathematical modeling was
initiated by U.S. Environmental Protection Agency.
The study area shown diagramatically in Figure 1,
encompassed 11.3 miles of waterway, extending from
above Elyria STP (River Mile 10.8) down through the
river-harbor interface (R,M. 0.0), out to the harbor-
lake interface (R.M. -0.5). Above approximately
River Mile 6.5, the Black River is a free flowing
stream. Below this point water level and quality are
influenced by backwaters of Lake Erie; thus, although
it is not saline, the system conforms to an accepted
definition of an estuary.1' 2 Following the last
glacial retreat the stage of Lake Erie has been hy-
pothesized to have risen significantly due to gradual
upwarp of the outlet sill in response to removal of the
ice loading.1' 3 The river valley formed by downcut-
ting during the low water period was thereby drowned,
forming the present backwater.1' 2 Additional en-
largement of the lower 3 miles of channel has been done
by man to expedite navigation.
While the free flowing portion of the river (R.M.
10.8 - 6.5) is shallow and of moderate velocity and
slope, the estuary portion is quite deep and slow
moving. Here current measurements and water quality
data indicate stratification with intrusion of cleaner,
cooler Lake Erie waters beneath the warmer effluent
waters .
Vertical concentration gradients were not found to
be excessive, however. The variation of dissolved
oxygen with depth averaged about 1 mg/1 in the lower
portion of the river. Consequently, it is appropriate
to describe the system one dimensionally using the
average concentration (from top to bottom) at each
station as commonly applied to pollution analysis of
estuaries. In this case, the transport of material
caused by the rather complex hydrodynamic behavior in
the estuary portion of the river is described in terms
of advective and dispersive transport along the
longitudinal axis, as discussed by Harleman.4
The hydrograph of the Black River at Elyria in-
dicated that a. very low and relatively steady flow
regime had been maintained for about two weeks
preceding the July 1974 survey and continued throughout
the survey period. Under such conditions, the system
is likely to approach a steady state.
The mathematical description of water quality be-
havior in a one dimensional estuary under steady state
conditions is well developed and is elucidated else-
where.5 Furthermore, a. number of computer programs
are available to expedite solution. The program
utilized, the AUTO-SS version of AUTO-QUAL, incor-
porates a finite section approach.6 The river,
between R.M. -0.6 - 10.8 was divided into a large
number of equal length segments within which mixing
was assumed to be complete. Concentrations were
determined by advective and dispersive transport into
and out of each section and by the sources and sinks
of material within each section.
For a system thus discretized the dissolved
oxygen concentration in section j , located upstream of
section j-1 and downstream of section j+1, is defined
by
= (-QjDOj+1
O. -qoutjOOj +qin.jDOin . ) /V .
CBODj -KN NBOD-; +KA (DOsat .-DO . ) +P .-R.-SOO;
j J j J j 3 3 J J J
where
A = cross sectional area (L )
DO = dissolved oxygen concentration (M/L )
E = dispersion coefficient (L2/T)
K^ = reaeration coefficient (1/T)
K(-, = carbonaceous BOD decay coefficient (1/T)
KN = nitrogenous BOD decay coefficient (1/T)
P = photosynthetic oxygen production (M/L3/T)
Q = river flow (L3/T)
qin = effluent or tributary flow (L3/T)
qout = diversion flow (L3/T)
R = algal respiration (M/L3/T)
SOD = sediment oxygen demand (M/L3/T)
V = section volume (L3)
X = section length (L)
The primary difference between the finite section
estuary model and the finite section stream model
(e.g., QUAL-II^) is that the downstream boundry con-
dition must be fixed in order to model the estuary.
This reflects the obvious fact that the water quality
of Lake Erie (a large system) is relatively unaffected
by conditions in the Black River (a small system) .
Model Calibration
The calibration is based on a rather comprehen-
sive field survey performed on July 23-26, 1974.
Hydraulic Characteristics
Flow conditions comparable to the once in 10 year
7 day low flow were observed in the river during the
115
-------
t
o-
oo
<
UJ
ce
CO
8
C£
O
O
0
_l
5 ^ FIGURE 1: BLACK RIVER DIAGRAM
\\ ^ ~ --_
HARBOR ESTUARY PORTION FREE FLOWING PORTION 1 FT DEPTH
1 31 FT DREDGLD UNUktUULU ^ — A
PFPTH ™ FT 2-15 FT,,, _.- '
s — fi~~lr vi ELYRIA STP
^L^STP 1U_ I *™™«»«
U.S. STEEL
RIVER MILE
012 34 56 789 10
I i i i i i i 1 1 1 1
July 1974 survey. Net flow traveling past the steel
mill averaged 25.4 cfs. This low flow is dwarfed by
the 266 cfs cycled through the steel mill intakes and
outfalls.
Hydraulic slope in the free flowing portion of
the river (above R.M. 6.5) averaged 4.7 ft/mile. At
R.M. 6.5 the Lake Erie water elevation essentially
intercepts the river elevation and the river bed slope
of 3-4 ft/mile results in increasing depth. Below
R.M. 2.9, the channel is dredged to a depth of 30 ft.
Channel dimensions are shown in Figure 1.
Current measurements were made at two cross
sections (R.M. 2.3 and 3.1) in the estuary portion of
the river. Four times in three days, current direc-
tion and velocity were measured at 3 foot depth
intervals at 3-5 points along each transect. The
longitudinal component of velocity, averaged laterally
and temporally, is shown in Figure 2. Intrusion of
lake water beneath the effluent waters is clearly in-
dicated in both cases. Flow was more sharply strati-
fied at the more upstream cross-section. Also
noteworthy at this cross-section is the small current
traveling downstream along the river bed, possibly
originating from cool upstream water which escaped
entrainment in the upstream water intake.
The net advective velocity, computed for the
simulation from flow and channel dimensions, was only
0.02 and 0.001 ft/sec at the upper and lower cross
sections respectively. These very low velocities
sharply contrast the maximum stratified current velo-
cities (shown in Figure 2) of 0.25 and 0.2 ft/sec at
the upper and lower cross sections respectively. The
necessity for a high degree of longitudinal dispersion
in a one dimensional model is thus apparent.
0.0 -0.1 -0.2 0.2 0.1
VELOCITY (FT/SEC)
FIGURE 2: MEASURED CURRENT VELOCITIES
0.0 -0.1
The longitudinal dispersion coefficient, E, was
determined from conservative materials profiles, using
the trial and error fit procedure described by Thomann
for use with finite difference computation.5 The value
of E is shown as a function of river mile in Figure 3.
Comparison of observed and predicted dissolved solids
profiles is shown in Figure 4. Fluoride, chloride,
and sulfate displayed analogous profiles and comparable
fits.
The observed level of dispersive mixing is believ-
ed to be a manifestation primarily of the stratified
flow conditions which result from gravitational insta-
bility of the lighter effluent waters and heavier lake
waters. The 3-4 °C vertical temperature differentials
represent density differentials of approximately 0.001
g/ml. It is also likely of importance that the steel
mill withdraws water from some distance beneath the
surface and discharges heated effluent at the surface.
The dispersion coefficient, highest below the steel
mill, decreases in the harbor towards values expected
for near shore and open lake waters.
Wind effects, in the form of seiches, may also
constitute a portion of the dispersive energy. Lunar
tides, on the other hand, are not observed on the Great
Lakes.
Dissolved Oxygen Balance
Reaeration capacity, Ka, was calculated using the
O'Connor formula modified as recommended by O'Connor?'
KA = KL/H
and
KL = 12.9
constrained by KL > 2
where KL is the surface transfer coefficient, H
depth, and U is net velocity.
~ 1000
750
o
cj
500
250
FIGURE 3:
2468
RIVER MILE
LONGITUDINAL DISPERSION COEFFICIENT
116
-------
FIGURE 4:
OBSERVED AND PREDICTED
DISSOLVED SOLIDS
JULY 23-26, 1974
600
400h
o
00
JLJL
10
RIVER MILE
The Tsivoglou formula was considered for
application to the free flowing portion but was found
to significantly underestimate reaeration capacity.
The Churchill formula, on the other hand, was consid-
ered to be inapplicable for this situation as it was
developed for streams with velocities considerably
higher than found anywhere in the study reach, and
depths greater than those found in the free flowing
portion.11 Its use would also underestimate reaera-
tion capacity.
The bulk of the oxidizable nitrogen consisted of
ammonia. As the rate limiting step under this condi-
tion can be expected to be ammonia oxidation, a single
first order kinetic reaction will closely approximate
the three or four stage reaction (depending on whether
starting with ammonia or organic nitrogen):8' 12
Org-N —NH3 —N02 —N03
Nitrogenous BOD (NBOD) was calculated based on total
Kjeldahl nitrogen concentration.
Differences in decay rates were expected to exist
between the estuary and free flowing portions of the
river, due to differences in benthai character, ratio
of volume to benthal surface, and rate of replacement
of fluid elements at the benthal interface.8 In the
free flowing portion (above R.M. 6.5) the decay co-
efficient was found to be 0.15 day"1 (base e) based on
the observed rate of disappearance. Such a low rate
is characteristic of a system dominated by gross levels
of carbonaceous BOD.8
The decay coefficient in the estuary portion of
the river was estimated to be 0.05 day"1, based on fit
to the observed NBOD levels. This unusually low rate
is attributed to insufficient levels of dissolved
oxygen existing through much of the estuary.8' 9» 12
Carbonaceous BOD (CBOD) was determined from the
long term BOD (20 or 30 day BOD) less the NBOD. The
decay coefficient, estimated from observed CBOD levels
and rates of disapperance, was found to be 0.7 day"1
in the first mile below Elyria STP, 0.5 day"1 through
the remainder of the free flowing portion of the river,
and 0.14 day"1 in the estuary portion.
BOD loading is summarized in Table 1.
Table 1: Oxygen demanding effluent loads (Ibs/day)
Source CBOD NBOD
Elyria STP 9800
U.S. Steel (net) 14000
Lorain STP 2600
5000
8700
2800
The diurnal dissolved oxygen variation at all
stations in the estuary portion of the river was either
small or inconsistant with photosynthetic activity.
Negligible algal productivity is likely a consequence
of rapid light extinction in the water column.
Sediment oxygen demand (SOD) measurements were
made at various locations. When converted to mg/l/day,
the SOD was found to be minor relative to the oxygen
uptake of BOD dissolved and suspended in the water
column (Kc x CBOD + % * NBOD, in mg/l/day).
Thus, without incurring significant error, the
accumulation of organic matter in the sediments could
be assumed to have attained a steady state, with the
rate of decay within the sediments balanced by the
rate of deposition. 3 The small sediment oxygen demand
found was therefore implicitly accounted for in the BOD
decay, as originally suggested by Streeter.1^
FIGURE 5:
OBSERVED AND PREDICTED
DISSOLVED OXYGEN
JULY 23-26, 1974
4 6
RIVER MILE
10
117
-------
Comparison of observed and predicted dissolved
oxygen concentrations for the July 1974 survey is shown
in Figure 5.
Verification
Water quality data collected in September 16, 1975
was used to test the predictive capability of the model.
Net flow past U.S. Steel was approximately four times
greater, and temperatures 3-4 °C less than those found
during the July 1974 survey.
As the U.S. Steel effluents were not monitered at
this time, previously measured net loads (concentra-
tion deltas between intakes and outfalls) were assumed.
However, due to the high degree of recirculation
through the river by the steel mill, the plant's intake
and effluent qualities are interdependent upon each
other. Subsequent to using a tedious manual conver-
gence method involving several computer runs to
determine the correct intake and outfall concentrations
for a given set of conditions, the computer program was
modified to couple each intake to the outfall it feeds
(as shown in Figure 1) . Effluent BOD was computed
from the given change in BOD between intake and outfall,
added to the intake BOD computed during the previous
iterative step in the solution.15
Effluent dissolved oxygen (DO) was handled in
analogous manner; however, the relationship between
the intake and outfall DO is more complex. The follow-
ing simplification of the process is expected:
(1) Water is pumped from intake with DO concentra-
tion Cj_.
(2) Temperature is raised to outfall temperature;
DO saturation is depressed to CSO; deficit is
(3) Water undergoes reaeration in returning to
lake elevation, resulting in new deficit Do;
DQ/D-J^ = e-KAt, where KA is a reaeration
coefficient.
The product K^t (or ratio DO/D^) was determined from
the July 1974 data. Since the reaeration coefficient
can be expected to be temperature dependent, an
Arrhenius rate dependency was assumed.
Comparison of observed and predicted dissolved
oxygen concentrations for the September 1975 survey are
shown in Figure 6.
Sensitivity Analysis
The sensitivity of dissolved oxygen predictions
to changes in system parameters under low flow condi-
UJ
CJ
X
o 4
Q
o 2
5
0
0246
RIVER MILE
FIGURE 6: OBSERVED AND PREDICTED DO, SEPT. 16, 1975
tions was investigated. The analysis was based on
conditions expected following implementation of
improved treatment by dischargers.
Predicted dissolved oxygen levels were most sensi-
tive to changes in the reaeration and dispersion
coefficients and Lake Erie BOD (downstream boundary
condition). They were less sensitive to CBOD and NBOD
decay coefficients and Lake Erie dissolved oxygen, and
were quite insensitive to river flow and upstream
boundary conditions.
The great difference in sensitivity to dispersion
and flow of course reflects the previously discussed
magnitude of difference between stratified flow
velocities and net advective velocity.
Conclusion
Intrusion of Lake Erie waters into the Black River
estuary is brought about primarily by thermally induced
density differences between Lake and effluent waters.
Under low flow conditions net advection downstream
plays little role in the transport of pollutants out of
the estuary. Rather, transport brought about by oppos-
ing vertically stratified flows may be simulated as
longitudinal dispersion in a one dimensional, steady
state estuary model. The magnitude of the dispersion
coefficient used is somewhat smaller than found for
many ocean estuaries, but greater than normally applied
to streams or lakes.
The approach taken is adequate for planning and
enforcement purposes.
Additionally, due to the sluggish flow in the
backwater, reaeration is best calculated from basic
surface transfer considerations (surface to volume
ratio), with minimum values of surface transfer co-
efficient chosen independently of flow turbulence
(velocity, depth, slope) considerations.
The observed influence of the lake on water quality
in the lower reaches of the river also has an important
implication to the modeling of Great Lakes. Loads to
Lake Erie calculated by multiplying the observed
concentration by the net advective flow will signifi-
cantly underestimate the true load being delivered to
the lake (by dispersive transport). Using concentra-
tions observed further upstream will by-pass this
effect but will also fail to include major waste
sources.
References
1. Brant, R.A., and Herdendorf, C.E., "Delineation of
Great Lakes Estuaries", Proceedings 15th Conference
of Great Lakes Research, page 710, 1972.
2. Pritchard, D.W., "What is an Estuary: Physical
Viewpoint", in Estuaries, edited by G.H. Lauff,
American Association for Advancement of Science,
Washington, D.C., 1967.
3. Hough, J.L., Geology of the Great Lakes, University
of Illinois Press, Urbana, 1958.
4. Harleman, D.R.F., "Diffusion Processes in Stratified
Flow", in Estuary and Coastline Hydrodynamics,
edited by A.T. Ippen, McGraw-Hill Book Co., New York,
1966.
5. Thomann, R.V., Systems Analysis and Water Quality
Management, Environmental Science Services Division,
New York, 1972.
-------
6. Crim, R.L., and Lovelace, N.L. "AUTO-QUAL Modelling
Systems" EPA-440/9-73-003, U.S. EPA, Washington
D.C., March, 1973.
7. Water Resources Engineers, Inc., "Computer Program
Documentation for the Stream Quality Model QUAL-
II", prepared for U.S. EPA, May, 1973.
8. O'Connor, D.J., Thomann, R.V., DiToro, D.M. and
Brooks, N.H., "Mathematical Modeling of Natural
Systems", Manhattan College, New York, 1974.
9. Hydroscience, Inc., "Water Quality Analysis for the
Markland Pool of the Ohio River", prepared for
Malcolm Pirnie Engineers and the Metropolitan Sewer
District of Greater Cincinnati, October, 1968
10. Tsivoglou, E.C., and Wallace, J.R., "Characteriza-
tion of Stream Reaeration Capacity" EPA-R3-72-012,
U.S. EPA, October, 1972.
11. Churchill, M.A. Elmore, H.L., and Buckingham, R.A.,
"The Prediction of Stream Reaeration Rates",
Journal SEP, ASCE, Volume 88, Number 4, SA4, July,
1962.
12. O'Connor, D.J., Thomann, R.V., and DiToro, D.M.,
"Dynamic Water Quality Forecasting and Management",
EPA-660/3-73-009, U.S. EPA, August, 1973.
13. Velz, C.J., "Significance of Organic Sludge
Deposits", Oxygen Relationships in Streams, Public
Health Technical Report W58-2.
14. Streeter, H.W., "Modern Sewage Disposal", Federa-
tion of Sewage Works Association, page 198, 1938.
15. Schregardus, D. , U.S. EPA Michigan-Ohio District
Office, unpublished communication.
119
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COST-EFFECTIVE ANALYSIS OF WASTE LOAD ALLOCATIONS
John Kingscott, Environmental Protection Agency, Washington, D.C.
Introduction
The Federal Water Pollution Control Act
Amendments of 1972 require the States to identify
those waters for which the minimum legislated
effluent limitations are not stringent enough to meet
applicable water quality standards. Roughly 2000
segments have been identified as being water quality
limited for a variety of reasons. The waste load
allocation procedure is used to determine effluent
limitations based on water quality considerations
rather than uniform applications of technology.
State Basin Planning under Section 303 of the Act and
currently Water Quality Management Planning under
Section 208 is attempting to ensure that the 1983
goals of fishable and swimmable water uses will be
achieved in these segments. The potential investment
of large sums of money for advanced waste treatment
justifies a close look at the practical implications
of the waste load allocations. Much of the current
attention being given to nonpoint sources is the
result of a concern that these sources will negate
the upgrading of water uses despite increased levels
of point source control. However, many segments do
have predominately point source problems or the non-
point problems can be independently addressed for
periods of high flow.
Common stream analysis practice consists of the
application of verified deterministic models to pre-
dict the water quality response during critical or
design conditions. The behavior of any water segment
can most reasonably be approximated as a probabilistic
system since the flow, temperature, waste load, and
initial instream concentrations all vary over time.
The state of the art in model development is far be-
yond the availability of basic data and insight into
biological processes needed to broadly apply more
sophisticated methods. This emphasizes the need for
judgment in interpreting the results of the simpler
deterministic models.
This paper considers the relative consequences
of some procedures used in the application of determi-
nistic models, in particular the choice of design
conditions and seasonal application of waste load
allocations. It was desired that the analysis be
general and applicable to a number of situations and
issues. It was also necessary not to be hypothetical
but to address real situations. The resulting
analysis considers the costs of advanced waste treat-
ment and the effects in terms of a risk for the
violation of dissolved oxygen stream standards. An
effluent analysis was undertaken to define an empirical
procedure for generating effluent loading factors.
The waste treatment costs were considered by combining
flow dependent unit processes to form viable treatment
systems. Five water quality limited segments were
analyzed using historical U. S. Geological Survey
streamflow records. Cost-effective curves were gen-
erated to define feasible treatment options for
nitrogenous and carbonaceous BOD removal. The optimal
investment strategy for levels of treatment higher
than secondary was then used to study issues related
to waste load allocations.
Effluent Analysis
A number of factors can be expected to affect
treatment efficiency and the variability of effluent
loadings. The need existed to produce a generally
applicable procedure to generate BOD loadings for dif-
ferent treatment schemes.
Daily effluent BOD concentrations were analyzed
for nine Michigan and five Texas3 secondary plants.
The mean, variance, and coefficient of skewness were
obtained for one year of operation of each of the
plants. The distributions were assumed to be log
normal and a method was sought to generate synthetic
daily mean concentrations given an annual mean effluent
load.
Matalas6,1* has suggested a procedure for pre-
serving the moments of a distribution when log values
are generated. If "a" is the lower bound of random
daily BOD represented by x» then y - log (x a) is
normally distributed. If the x parameters represent
the daily mean concentration of BOD, they are related
to the y parameters as follows:
v(x) = a + exp Ca2(y)/2 + v(y}H
exp f2 LV(y)
- exp
(1)
+ 2,(fJ]_
- 3
+ 2
U /2
where y is the mean, a2 is the variance,
and Y is the coefficient of skewness.
To preserve the statistics of the generated BOD
values, the mean, variance, and coefficient of skew-
ness are determined for the historic distribution
(the x variables); substituted into equations 1, 2,
and 3; and solved for y(y), n2(y) and "a." These are
the parametric values that are used in the generation
process to give a series of synthetic normally distri-
buted logarithms y-| , y^—y^- Tne generated BOD's
are then calculated back through the transformation
by the relation:
XT = exp(yi) + a
The independent variables chosen to describe the
distribution were the wastewater discharge Q, in mgd,
and yearly average effluent BOD concentration y(x) in
mg/1. The following empirical relationships were
developed by stepwise regression:
a2(x) 4.06 y(x)i.27q-.2S (4)
multiple correlation coefficient = .83
Y(X) 5.81 yCx)--"3 (5)
multiple correlation coefficient = .47
Thus normally distributed logs could be generated
and transformed into daily mean concentrations of
effluent BOD. The standard deviations for distribu-
tions thus generated are related to those for the
historical operation of the treatment plants in
figure 1. The response of the generated distributions
to variations of the independent variables is given in
figure 2.
120
-------
• MICHIGAN
O TEXAS
20r
5 10 15
GENERATED
Fig. 1. Comparison of generated and
observed standard deviations.
FLOW=25 m.g.d.
41
BOD (mg/1)
BOD-30 (««n)
21
4<
BOD (mg/1)
Fig. 2. Response of the generated BOD distribution
to changes in waste flew and mean BOD.
This technique serves as a crude approximation of
reality and does not consider numerous important fac-
tors. However, the procedure is very general and can
be applied with a minumum amount of information.
Cost Analysis
Costs were calculated using combinations of
various unit processes for wastewater treatment and
sludge disposal.10 Consideration was given to those
processes which remove oxygen demanding material for
what might be considered secondary and advanced sys-
tems. The various combinations of processes were
classified according to characteristic effluent quality
assuming a typical influent waste stream. Compatible
unit processes were combined as building blocks con-
sidering basic design criteria, equipment sizing, and
quantities and characteristics of sludges so that
compatible combinations were formed.
The total cost for each unit process was
determined based on wastewater flow and includes cap-
ital, operation, and maintenance. These costs were
developed based on unit sizing as determined by
standard design criteria, process loading capabilities,
solids generation, chemical and energy consumption,
and manpower requirements. The values were trended
to a common cost level representative of February 1973.
Figure 3 traces the combinations of unit wastewater
processes and the effluent values which are character-
istic of the combined systems.
Figure 3
WASTEWATER TREATMENT
UNIT PROCESS COMBINATIONS
15 15 15 15 15 15
Al CONVENTIONAL PRIMARY
A3 PRIMARY WITH SINGLE STAGE LIME ADDITION
A4 PRIMARY WITH ALUM ADDITION
A5 PRIMARY WITH FERRIC CHLORIDE ADDITION
Bl,2,3 TRICKLING FILTER
Cl,2,3 ACTIVATED SLUDGE
C4 ACTIVATED SLUDGE WITH ALUM ADDITION
C5 ACTIVATED SLUDGE WITH FERRIC CHLORIDE
C6 HIGH RATE ACTIVATED SLUDGE
D FILTRATION
E ACTIVATED CARBON
Gl,2 BIOLOGICAL NITRIFICATION
J BREAK POINT CHLORINATION
121
-------
Segment Analysis
The fundamental equation which describes the
longitudinal distribution of dissolved oxygen can be
developed from the principles of mass balance and
continuity. An advective system with carbonaceous
and nitrogenous oxygen sinks and first order kinetic
relationships takes the following form:
JC=_ |_L (QC) + Ks(Cs-C)-KdL(x)KnN(x) (6)
where: C = concentration of dissolved oxygen
Cs - saturation concentration of D.O.
K, = reaeration rate constant
iq carbonaceous BOD oxidation rate
constant
L(x) concentration of carbonaceous BOD
K_ nitrogenous BOD oxidation rate
constant
N(x) concentration of nitrogenous BOD
Q river volumetric flow
A river cross-sectional area
x = longitudinal distance
Equations of this nature have been solved by Li5 for
the case where boundary conditions are arbitrary func-
tions of time and by DiToro and 0'Conner2 for the case
where boundary conditions are functions of time and
the flow is time-variable. The steady state solution
to equation 6 for constant boundary conditions and
coefficients is:
State
Basin
K u
D(x)=Cs-C(x)=D N
d ' exp
where: D(x)
o' Q'
u = Q/A
N,
(7)
= distribution of D.O. deficit
= initial concentrations
A " = stream velocity
Historical daily streamflows were considered
along' with randomly generated waste loads and charac-
teristic monthly temperatures to calculate a minimum
dissolved oxygen value with equation 7. This method
implies that the stream flow and velocity are constant
for one day and then abruptly change to another con-
stant value the subsequent day and so on. It is
important to note that equation 7 describes a profile
derived from steady state conditions for constant
streamflow, waste load, and reaction rate coefficients.
However, the equation was applied by assuming the
parameters are constant for one day and then immedi-
ately change. Limitations to this approach1 imply
that the solution is valid only for one day's travel
time below the waste source. This will be significant
for relatively small reaction rate coefficients which
cause the minimum D.O. to occur some time after one
day from the time of input. The significance of this
fact on the analysis is unknown but could conceivably
be small if D.O. standards violations are occurring
during relatively steady flow periods on the recession
tail of the hydrograph.
Five stream segments that are water quality
limited for dissolved oxygen were analyzed. The seg-
ments have been modeled through the EPA National
River Basin Modeling Program and represent a variety
of hydrologic conditions.
Flint
Cache La Poudre
Schuylkill
Reedy
Upper Miss.
Ga.
Colo.
Pa.
S.Car.
Minn.
Chattahoochee
S. Platte
Delaware
Santee
Mississippi
Average
Flow (cfs)
345
130
1740
85
12090
The stream hydraulic descriptions were simplified
and assumed to be constant for the entire segment.
Municipal and industrial waste sources were combined
for the simulation so either one or two point sources
were included depending on the existence of industrial
discharges. The distribution of daily loadings for an
industrial source was assumed to have the same charac-
teristics as a municipal source but generated
independently. The nitrogenous BOD component was
assumed to also have the same log normal
characteristics.
U. S. Geological Survey stream gaging stations
exist on all segments, and daily flows for the last
twenty years of record were obtained from STORET
(except the Colorado stream where twelve years are
available). The daily stream flows were used to calcu-
late the hydraulic response and the reaeration rate
constant. Daily waste loadings were produced by
assuming a constant waste flow and randomly generated
daily mean concentrations. Consequently, the load-
ings were assumed to be independent of the time of
year and streamflow. Representative monthly water
temperatures were determined from the U. S. Geological
Survey Water Resources Data-Water Quality Records.
Representative boundary conditions were determined from
the original model validation studies and assumed to be
constant. The power functions for velocity, depth,
and reaeration coefficient determination and reaction
rate constant temperature adjustments were applied over
the wide range of flows and temperatures. Table I
shows the values which were used for the simulations.
The simulation procedure was used to calculate the
cost-effective curves unique to each segment system
shown in figure 4. For each classification of effluent
quality a simulation was made from the historical daily
streamflow records to determine the number of times the
average daily oxygen was below a standard of 4 mg/1.
This standard has tentatively been identified8 as pro-
viding a low level of protection; that is, it should
permit populations of tolerant species and successful
passage of most migrants while there may be a reduced
production or elimination of sensitive fish. The cor-
responding costs were determined as the least costly
combination of unit processes capable of achieving the
effluent values (including sludge disposal). The
ammonia removal points were determined by considering
an average of four alternatives—trickling filter and
break point chlorination, trickling filter and biological
nitrification, activated sludge and break point chlori-
nation, and high rate activated sludge with biological
nitrification. The averaging was done to generalize the
procedure as biological nitrification was less costly
but potential seasonal operating problems and perhaps
land requirements would not always make it the more
reasonable choice. Ammonia removal was considered on
increments of one quarter of the waste flow to aid the
construction of a continuous plot. This possibility
is not unreasonable and might be compared to split
treatment in a water softening operation. The result-
ing cost-effective curves provide a guide to the
selection of advanced treatment schemes that minimize
the total cost associated with a given frequency of
oxygen standard violation. The curves map the optimal
122
-------
UPPER MISSISSIPPI
21
~ 15
o
o
o
O CBOD Removal
X NBOD Removal
CBOD=30
NH3=15
1 2 3
VIOLATION OCCURRENCE
CACHE LA POUDPE
30
t
O CBOD Removal
X NBOD Removal
31
• 1234
VIOLATION OCCURRENCE (%)
REEDY
choice of advanced treatment schemes and clearly define
the point at which ammonia removal should be considered.
In some segments there is a strong indication that an
understanding of the process of stream nitrification is
important to waste load allocation decisions and
efforts should be made to assess the likelihood of its
occurrence.9,10 The adequacy of first order kinetic
relationships should probably also be confirmed against
possible nonlinear approaches that may more reasonably
represent the autotrophic bacteria activity.
Haste Load Allocation Analysis
The implications of a seven-day ten-year low flow
for allocations have been questioned as the practice
is based on tradition rather than substantive justifi-
cation. The effects of the choice of alternative crit-
ical conditions and varying modes of operation deserve
further investigation.
For each of the five segments a 3% annual growth
rate was assumed and allocations calculated for a
twenty-year flow projection. Seven-day two-, five-,
and ten-year low flows were calculated from the his-
torical record and allocations determined with the
maximum monthly temperature. The occurrence of oxygen
violations and corresponding total costs for secon-
dary treatment (carbonaceous BOD 30 and ammonia
15) and low flow dependent allocations under present
waste flow conditions are given in figure 5. The
occurrence is expressed as a percent and calculated
by dividing the number of days having a mean D.O.
below 4.0 mg/1. by the number of historical daily
average flows. The segments show varying degrees of
sensitivity to the choice of critical flow conditions.
The increased liklihood of an instream violation
as point source flows increase to the twenty-year
projected level while concentrations are held con-
stant is given in figure 6. Simulations were also
made at the twenty-year projected flow with the car-
bonaceous reaction rate decreased by 2556 as an indi-
cation of a possible safety factor resulting from a
biologically more stable waste from advanced treatment
processes.
The result of adherence to the load allocation
for specified months of the year is shown in figure
7. A four-month effluent standard (July, August, Sep-
tember, & October) and six-month standard (June, July,
August, September, October, & November) are compared to
yearly operation at the allocated level. The Georgia
21
O CBOD Removal
X NBOD Removal
o
o
o
2411
VIOLATION OCCURRENCE (%)
Fig. 4. Cost-effective curves for three
river segments.
Secondary
7-dy. 2-yr.
7 dy. 10 yr.
Mss
Cache Reedy Schuyl. Flint
Fig. 5. Cost and corresponding frequency of a
D.O. less than 4 mg/1 for secondary treatment
and allocations based on 7-day 2 and 10-year
low flows.
123
-------
TABLE I
Values of Constants and Boundary Conditions used for Simulation
SEGMENT
Municipal
Flow (mgd)
Industrial
Flow (mgd)
Velocity Depth
(ft/sec) (ft)
K.
Upper Mississippi 250
Reedy 15
Schuylkill 25
Cache La Poudre
.000133Q 10.7 12.96u-5
1.5 .35
.038Q-716 .292Q'41 7.6u
D1.33 .6
.06Q-4
.8Q'23 7.6u
D
.0855Q'17 .44Q'335 2.833u
1.33 .55
Q = stream-flow, in cfs
Ah change in water surface elevation, in feet
tf time of travel, days
D = mean depth of stream, in feet
u = mean velocity of stream, in ft/sec
.25
.2
Flint
10 1 .09Q'31
D
.45Ah
tf .4 .5
2 0.0
and South Carolina segments show some difference bet-
ween four- and six-month standards, while the Minne-
sota and Pennsylvania streams exhibit the practicality
of a four-month requirement. The capital and annual
operation and maintenance costs for secondary and the
increment for advanced treatment are given. Relative
to secondary treatment, a greater proportion of the
total cost associated with the load allocation is for
operation and maintenance. This is due in part to
the higher cost of operating break point chlorination
which was averaged with biological nitrification to
form the means of ammonia removal.
Ol
00
°
11
dP
• —
M
o 12
w
PH
K
D
U 1
O
o
o
H 4
E-i
5
o
H
> 1
-M
r s
d1 S
Q] ^ .— ,. "!J
• ^ c
^ 5 G -a
y en q LJ*
H a) o >^
'Q 03 fN ^
..T"
o
o
CO
(U 1 o
CL| (J 1
L t£ PL
I— 1 o ^
\0
3 ^ \
-^
n
-i n
.-,
^
n
1 n 1
-Th
Miss. cache Reedy Schuyl. Flint
Fig. 6. Frequency of a D.O. less than 4 mg/1 at
present wastewater flow and 20 year projection
at a 3% increase per year.
-l29
Miss. Cache Reedy Schuyl. Flint
Fig. 7. Amortized capital costs and annual
operation and maintenance costs for a 7-day
10-year WLA and corresponding instream
violations for time dependent operation.
M
O
D
B3
o
O
H
o
o
o
Miss.
Cache Reedy Schuyl.
Flint
Fig. 8. Costs and instream D.O. violations for
7 day-2year allocation and 6 months operation
at 7-day 10—year allocation.
124
-------
Figure 8 is a comparison of seven-day two-year
based effluent limits with seven-day ten-year based
limits which are practiced for six months with secon-
dary treatment the remaining months. The costs for
the seasonal treatment option were calculated by as-
suming the operation and maintenance costs for the
advanced treatment processes were less by one half
for six months of operation. The figure shows the
advantage of a seasonal effluent limit for all segments.
Conclusions
The assumptions made in this analysis imply that
the absolute values for the cost and violation occur-
rence are of secondary importance to their relative
values. Assuming the existence of a verified deter-
ministic stream model the procedure given may be used
to produce cost-effective curves which guide the
choice of advanced wastewater treatment schemes.
With the minimum legislated levels of treatment it is
probable that stream nitrification will become increas-
ingly important and should be given close attention
during model calibration and verification. The waste
load allocation procedure is an effective means for
controlling the risk of a stream standards violation
and absorbing the effects of increased waste flow. In
some segments the significant difference in the risk
associated with the two-year and ten-year recurrence
interval for the design condition indicates the advan-
tage of using the more stringent requirement. Cost-
effective considerations imply the practicality of im-
plementing variable effluent limits such as on a sea-
sonal basis.
This work was stimulated by practical concerns.
The assumptions made were necessary to produce results
which could provide some insight into policy decisions
which must be made soon due to legislated deadlines.
Additional work is needed to assess the implications
of the various application-oriented procedures and
decisions which must be addressed by those involved
with all phases of related water quality
planning.
8.
9.
10.
References
Ditoro, D. M., O'Connor, D. J., Thoman, R. V.,
"Discussion to Risk Evaluation in Sewage Treat-
ment Plant Design," Journal of the Sanitary Engi-
neering Division, ASCE, No. SA6, December 1967,
pp. 268-271.
DiToro, D. M., O'Connor, D. J., "The Distribution
of Dissolved Oxygen in a Stream with Time Varying
Velocity," Water Resources Research, 4(3), June
1968, pp. 639-646.
"Evaluation of Factors Affecting Discharge Quality
Variation," Texas A&R, Environmental Engineering
Division.
Fiering, M. , Jackson, B., Synthetic Streamflows,
American Geophysical Union, Water Resources
Monograph Series 1, Washington, D.C., 1971.
Li, Wen-Hsiung, "Unsteady Dissolved-Oxygen Sag
in a Stream," Journal of the Sanitary Engineering
Division. ASCE, Vol. 88, No. SA3, Proc. Paper
3129, May 1962, pp. 75-85.
Matalas, N. C., "Mathematical Assessment of
Synthetic Hydrology," Water Resources Research,
3(4), 1967, pp. 937-945.
O'Connor, D. J., "The Temporal and Spatial Distri-
bution of Dissolved Oxygen in Streams," Water
Resources Research, 3(1), 1967, p. 65.
Quality Criteria for Water, U. S. Environmental
Protection Agency, preliminary draft.
Tuffey, T. J., Hunter, J. V., Whipple, W., Yu,
S.L., Instream Aeration and Parameters of Stream
and Estuarine Nitrification, Rutgers University,
Water Resources Research Institute, November
1974, p. 59.
Van Note, R. H., Hebert, P. V., Putel , R. M.,
Chupek, C., Feldman, L., A Guide to the Selection
of Cost-Effective Wastewater Treatment Systems,
EPA-430/9-75-002, July 1975.
125
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WASTE ALLOCATIONS IN THE BUFFALO (NEW YORK) RIVER BASIN
Donald H. Sargent
Versar Inc.
Springfield, Virginia
Abstract
A water quality simulation model, VERWAQ, was
developed for the corplex hydraulic and waste load
characteristics of the Buffalo River. These character-
istics include very low water velocities, oscillating
flow, upstream flow, inter-basin transfer of water,
many critical conservative and non-conservative water
quality parameters, thermal pollution, and important
non-point as well as point sources of wastes. The
developed and verified model was used to project water
quality and to allocate waste loads.
Description of the Study Area
The Buffalo River was the subject of a compre-
hensive evaluation of waste loadings and water quality,
performed by Versar Inc. in 1973 (under EPA Contract
68-01-1569) as part of the U.S. Environmental Pro-
tection Agency's conmitments to abate and control
water pollution under the 1972 Great Lakes Water Qual-
ity Agreement between the U.S. and Canada.1 This river
in western New York was identified as one of several
concentrated areas of municipal and industrial activity
which have had poor water quality and which contributed
to the waste loads of the Great Lakes.
The Buffalo River discharges into the easternmost
end of Lake Erie, just at the head (southern) end of
the Niagara River. It extends only 13 kilometers
(8 miles) upstream from its mouth, and is located in
the City of Buffalo and in surrounding Erie County.
The watershed of the Buffalo River and its three tribu-
taries (Cazenovia Creek, Buffalo Creek, and Cayuga
Creek) is roughly triangular in shape, extending to the
south and east of Buffalo, and has a drainage area of
446 square miles. Except for a few miles just above
their confluence with tie Buffalo River, the tribu-
taries are fast-flowing streams with primarily agri-
cultural drainage areas and with several small
communities. The lower reach of Cayuga Creek passes
through the large urban residential coiritiunities of
Lancaster and Depew, and bears little resemblance to
its upper reaches or to the other two tributaries.
Buffalo River itself is characterized by heavy
industrial development in the midst of a large munici-
pality. Its waste load and water quality problems
dominate any such concerns for the entire watershed.
There are 43 individual industrial discharges into the
Buffalo River. Very heavy waste loads into this reach
are imposed by frequent overflows, from numerous out-
falls, from the combined storm/sanitary sewer system.
The problems are aggravated by the hydraulic character-
istics of this reach and by large heat loads. As a
result, the water quality deficiencies in the Buffalo
River were (until recently) typified by a summertime
dissolved oxygen concentration of less than one mg/1
and by the almost complete absence of aquatic life.
Characterization of Present Conditions
Hydraulics of the Buffalo River
The industrialized reach of the Buffalo River is
maintained as a shipping channel to a depth of 6.7
meters (22 feet), and has a very low slope, less than
0.2 meters per kilometer. Most of the river's volu-
metric flow is due to industrial discharges whose in-
take source is not the River but in the Buffalo Outer
Harbor. These industrial flows amount to more than
twice the natural discharge at average summertime con-
ditions and to twenty times the natural discharge at
critical flow conditions; resulting in a relatively
stable total flow rate in summertime. Because of the
very large man-made river cross-section, however, the
calculated average velocity is very low, less than 0.02
meters per second, and the calculated residence time in
this short reach is greater than five days.
Oscillating flow in the upstream as well as down-
stream direction (driven by oscillations in the level
of Lake Erie) of significantly higher velocities than
the calculated average, was observed and measured in
the industrialized reach of the Buffalo River. In-
dependent sets of time-varying water-level data for
Lake Erie at the mouth of the Buffalo River and for the
Buffalo River itself also exhibited significant oscil-
lations. A dynamic analysis, which converted observed
water level oscillations to flow rate oscillations,
resulted in a calculated R.M.S. velocity of 0.096
m/sec, which is in general agreement with the R.M.S.
velocity (from direct measurements of velocity) of
0.082 m/sec, and which is five times the calculated
time-average downstream velocity of 0.018 m/sec. An
extension of the dynamic analysis resulted in a calcu-
lated longitudinal movement of water of ± 200 meters
superimposed upon the time-average movement.
Water Quality
Except for the lower reach of Cayuga Creek and
for the short Buffalo River itself, most of the Buffalo
River watershed (including all of Buffalo Creek and
the upper reaches of Cayuga Creek) is typified by good
water quality. This is consistent with an agricul-
tural, wooded, and vacant land use pattern, dotted with
small residential communities and scattered park and
recreational areas.
Table 1 summarizes the water quality data for
the industrial (dredged) reach of the Buffalo River.
Specific contraventions of water quality standards in
this reach are an average summertime dissolved oxygen
concentration of 0.9 mg/1 (compared to the minimum
allowable of 3.0 mg/1) and an average iron concentra-
tion of 3.1 mg/1 (compared to the maximum allowable
of 0.8 mg/1). Although many of the other parameters,
including temperature, are at high levels compared to
the natural waters, no other specific water quality
contraventions were found.
Chemical analysis of bottom deposits from the
industrialized reach of the Buffalo River indicate
high levels of oxygen demand, oil, grease, and iron.
Biological sampling of these bottom deposits indicate
that this reach of river is essentially devoid of
bottom organisms; a finding consistent with the meas-
ured dissolved oxygen level of less than 1 mg/1.
Waste Loads
The Buffalo River receives the waste loads of
its upstream tributaries, a very heavy concentration of
industrial discharges, and frequent overflows from com-
bined sewers. ?
The waste load to the Buffalo River from the
three upstream tributaries is based upon the measured
water quality and flow data for these tributaries
126
-------
under two conditions of flow: the average summertime
flow, equivalent to the 70 per cent duration point;
and the minimum average seven-day critical discharge
with a recurrence interval of ten years (MA7CD/10),
equivalent to the 99 per cent duration point, and
specified as critical flow by the New York State De-
partment of Environmental Conservation. The heat flux
of the upstream discharge is defined as zero, with the
choice of a baseline temperature equivalent to the
temperature of this discharge (19.0°C in summer).
The waste load from industrial point discharges
is based upon NPDES permit applications on file at EPA
Region II as of July 1973. The dissolved oxygen con-
tent of the industrial discharges, not included in the
NPDES permit applications, was based upon data inde-
pendently supplied by the major dischargers. The heat
flux was calculated from the temperature difference
between each industrial effluent and the baseline
temperature.
The combined sewer overflows into the Buffalo
River were, for the purposes of this study, judged to
be quite evenly distributed in time and in distance.
Overflows from the Buffalo combined sewer system occur
on the average of once every five days, and are quite
evenly distributed over the year. There are 70 over-
flow outfalls from more than 250 overflow chambers.
The fact that much of this waste is deposited on the
bottom of the industrialized reach of the Buffalo
River and affects water quality as a benthal load is
further justification for approximating the combined
sewer waste load as a distributed (non-point) load.
This combined sewer overflow waste load was quantified
from two studies of overflow quantity in Buffalo, from
the difference between runoff and influent at the
sewage treatment plant, and from two studies which
characterized the constituents of combined sewer over-
flows in places other than Buffalo.
A comparison of the various waste loads at aver-
age summer flow, using BOD-5 as the parameter of com-
parison, indicates that the combined sewer overflow
accounts for 31 per cent of the wastes to the Buffalo
River.
Simulation Model
In general, the widely-used steady-state uniform
flew stream models, which are essentially computerized
versions of the Streeter-Phelps analysis for the BOD-DO
relationship, are limited to the very simplest appli-
cations of point sources of wastes to a constant-
temperature, non-dispersive, free-flowing stream.
VERWAQ, a computerized model, was developed by extend-
ing the capabilities of existing models to accomodate
the complex nature of the industrialized reach of the
Buffalo River.
Features of VERWAQ
Hydraulics. The industrialized reach of the
Buffalo River exhibited longitudinally homogeneous
water quality measurements of virtually every parameter.
The independent measurement and analysis of oscillating
flow in the upstream as well as the downstream direc-
tion (driven by oscillations in the level of Lake Erie)
strengthened the hypothesis that this reach may be a
well-mixed body of water as opposed to a free-flowing
stream. The simulation model therefore was required
to test this hypothesis; e.g., VERWAQ is useful as
either a plug-flow model (no longitudinal dispersion)
or a completely-mixed model (complete dispersion of all
constituents including heat). The same VERWAQ com-
puter program is used for both; the desired approach
is selected with an input key word.
Water Quality Parameters. A total of 26 water
quality parameters were specifically identified by EPA
for careful attention in this study (and in other
Great Lakes studies). The water quality data and the
waste load data for the Buffalo River revealed that 57
constituents were deserving of analysis in this heavily-
industrialized reach. The simulation model was re-
quired to track these many parameters, both conserva-
tive and non-conservative. In addition to the con-
ventional treatment of carbonaceous BOD as non-
conservative, the model was required to similarly treat
nitrogenous BOD, ammonia, organic nitrogen, and
phenols. Three distinct deoxygenation rate constants
are used in the model.
Reaeration. The industrialized reach of the
Buffalo River has extremely low linear velocities.
Moreover, the prevailing winds off Lake Erie are per-
sistent and of high velocity. Consequently, the model
calculates the reaeration coefficient in two ways: as
determined by stream velocity, and as determined by
wind velocity. The program selects the larger of the
two coefficients for each river segment.
Thermal Analysis. The very large heat loads
from industrial sources into the Buffalo River, plus
the high residence times for water in this reach and
the high wind velocities, required that the model
simulate effects upon the river water temperature. The
thermal analysis of VERWAQ includes the heat flux from
discharges, tributaries, and non-point sources, con-
vection and conduction between the stream and the
ambient air, and solar radiation to the stream. Rate
constants are then appropriately adjusted for temper-
ature.
Non-Point Waste Loads. The combined sewer over-
flows (and benthal loads) constitute almost one-third
of the total waste loads. The model was required to
treat non-point sources as distributed waste loads
simultaneously as it treats point sources of other
wastes. The Streeter-Phelps equations in differential
form were augmented by a distributed waste model
(chemical and thermal constituents) and then reinte-
grated.
In the conventional Streeter-Phelps analysis, the
steady-state BOD balance around a differential longi-
tudinal segment of the river (between point-source
additions) is composed of three terms: the upstream
waste input, the downstream waste output, and the
reaction (oxidation) loss in the segment. The analysis
for VERWAQ adds a fourth term, the non-point source
(distributed) waste input in the distance interval dx:
(QL/R)dx; where Q, L, and R are respectively the non-
point-source total flow rate, the non-point-source
BOD concentration, and the longitudinal distance (reach)
over which the non-point discharge is evenly distri-
buted.
As in the conventional Streeter-Phelps analysis,
the sum of the terms is set equal to zero (for steady-
state) and integrated over a longitudinal river
distance x. In this analysis, however, the extra non-
point-source term is included in the sum and in the
integral. The result is solved for the BOD concentra-
tion which is then substituted into the equation for
deoxygenation rate. Integration of this equation
yields the expression for oxygen deficit as a function
of longitudinal distance.
Testing of the Model in the Buffalo River
Plug-Flow Model. The plug-flow model was applied
extensively to the dredged portion of the Buffalo
River, using various values and combinations of values
for the constants. Satisfactory simulation of the
127
-------
ernpiricaHy-determined non-conservative water quality
parameters was not achieved, confirming the prior
conclusion of significant longitudinal mixing based
upon the river hydraulics and upon the empirical water
quality data. Typically, the dissolved oxygen profile
calculated with the plug-flow model is a decrease in
DO from about 7 ppm to near zero in the two-mile reach
with the heaviest waste loads. The experimentally-
determined dissolved oxygen content, however, was
uniformly low (0.0 to 1.8 mg/1) throughout this reach.
Despite high values (consistent with high temperatures
but still reasonable) for the deoxygenation coeffi-
cients , the plug-flow model could not approximate the
measured step change in dissolved oxygen content with
distance.
Completely-Mixed Model. The completely-mixed
modeling option of VERWSQ resulted in excellent
agreanent (as shown in Table 1) with experimentally-
determined data, for conservative parameters and non-
conservative parameters (dissolved oxygen, BODg,
NH3-N, and phenols), using for the most part constants
independently published by others. For all except
fluoride and nickel, the calculated values came well
within the range of measurements. It is possible
that slightly-soluble salts such as fluorides, whose
ions originate from different industrial discharges,
may exceed their solubilities and precipitate in the
river. The model was then adequately verified by
comparing its water quality predictions with measured
winter time data in a completely different flow rate
regime from the upstream tributaries (two to seven
times the average summer time flow).
Water Qiality Projections
Projected Waste Loads
The projected waste loads into the Buffalo River
were based upon implementation of Best Practicable
Control Technology Currently Available (BPCTCA). It
was projected that three sewage treatment plants cur-
rently discharging into Cayuga Creek would be phased
out during dry weather as the sewage is incorporated
into the Buffalo system. The projected industrial
waste loads were based upon existing permits,
effluent limitation guideline development documents,
interim effluent guidance documents, or Region II
permit summary tables; as these were available in
October 1973. Several independent judgements were
made in the absence, at that time, of promulgated
effluent limitations guidelines or of issued permits.
It was also judged that several low-volume industrial
discharges would be incorporated into the municipal
sewer system. It was projected that the combined
sewer overflow waste load would remain the same as the
present load.
Projected Water Quality and Waste Load Allocations
The developed and verified model was utilized to
predict water quality from the projected BPCTCA waste
loads. These projected water quality data, for both
the average summer time and critical flow conditions,
are listed in Table 1. The projected water quality,
at critical flow conditions, marginally came within
the standards for temperature and dissolved oxygen.
However, more stringent waste allocations were recon-
mended for iron. Upon implementation of BPCTCA, which
would be effective in reducing most waste loads, the
oxygen-demanding waste load of the combined sewer over-
flows would then become the dominant constraint for
achieving good water quality in the Buffalo River.
References
1. Sargent, Donald H., Waste Allocations in the
Buffalo (New York) River Basin, Final Report,
EPA-905/9-74-010 (February 1975).
Table 1
Water Quality, Dredged Portion of the Buffalo River
Concentrations in mg/1
Dissolved Oxygen
BOD-5
NH3-N
N03-N
Cyanide
P-Total
Sulfate
Chloride
Fluoride
Oil & Grease
Phenols
Arsenic
Barium
Cadmium
Chromium
Copper
Iron
Lead
Mercury
Nickel
Selenium
Zinc
Water
Quality,
Criteria^
3.0*
—
2.0*
4
0.1*
25
500
250
1.5
7
0.2
1.0
5.0
0.3*
0.05
0.2*
0.8
0.1
0.006
0.7
2.5
0.3*
Measured
No. Data Pts. Max.
76
41
29
17
28
28
33
33
17
29
29
12
11
15
27
24
10
21
27
12
21
10
4.0
14.0
1.26
0.59
0.05
0.85
68
70
0.69
7.2
0.266
0.03
0.20
0.00
0.08
0.06
5.65
0.23
0.017
0.00
0.004
0.178
Data
Min.
0.0
0.6
0.14
0.0
0.0
0.07
49
46
0.44
0.1
0.008
0.00
0.0
0.00
0.00
0.00
0.68
0.00
0.000
0.00
0.001
0.024
Average
0.94
4.22
0.69
0.13
0.01
0.29
57
57
0.53
2.6
0.027
0.02
0.0
0.00
0.02
0.02
3.11
0.06
0.001
0.00
0.003
0.084
Calculated
Present
Data (b)
1.03
4.22
0.69
0.42
0.034
0.60
60.5
51.7
1.14
3.89
0.02
0.011
0.001
0.004
0.057
0.034
3.066
0.071
0.001
0.027
0.000
0.098
Projected Data
Avg. Summer Critical
FlcwW Flow(C>
3.79
1.89
0.22
0.39
0.03
0.45
58.6
43.2
1.09
2.23
0.010
0.010
0.0
0.001
0.015
0.030
2.054
0.037
0.000
0.026
0.000
0.087
3.06
1.73
0.21
0.28
0.038
0.55
58.6
44.6
1.40
2.40
0.013
0.014
0.0
0.001
0.020
0.037
2.729
0.048
0.000
0.036
0.000
0.116
(a) Criteria Labelled * are explicit in N.Y. State Standards
Others are implied by "fish survival" criterion.
(b) Average Summer Flow, Completely-Mixed Model.
(c) Critical Flow, Completely-Mixed Model
128
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STREAM MODELING AND WASTE LOAD ALLOCATION
James Y. Hung, Aolad Hossain and T. P. Chang
Water Pollution Control Division
Indiana State Board of Health
Indianapolis, Indiana
ABSTRACT
The Indiana Stream Pollution Control Board conducted
an intensive stream modeling program for Indiana's
major rivers during the past three years. These
stream models were used primarily for the purpose of
waste load allocation. This paper describes the
stream self-purification system models for BOD, DO and
ammonia. In addition to the analysis of model compo-
nents, problems of evaluating system parameters are
examined. The formulation of the waste load alloca-
tion methodology and the issues in allocation imple-
mentations are reviewed. The paper is concluded by a
discussion of the limitations in using stream models.
INTRODUCTION
The Federal Water Pollution Control Act Amendments of
1972 have established improved river quality as a ma-
jor goal of overall river basin planning. The tasks
of setting water quality standards and determining
waste load allocations for dischargers are bestowed
upon the State Water Pollution Control Agencies in
conjunction with the U. S. Environmental Protection
Agency (USEPA). During the past three years, the In-
diana Stream Pollution Control Board (ISPCB) has been
in the process of building stream quality models for
Indiana's rivers.1 Because dissolved oxygen (DO) is
traditionally the main indicator of pollution, a ma-
jor effort was made to model DO as well as the oxygen
consuming parameters such as biochemical oxygen demand
(BOD) and nitrogenous oxygen demand (NOD).
In the Indiana Water Quality Management Plan, Indiana
streams are divided into ninety-nine segments with
forty-two segments classified as water quality limited
segments. The criteria of segment classification was
based mainly on the projected condition of dissolved
oxygen deficiency and the need of advanced waste
treatment. Of the ninety-nine segments classified,
eighteen segments have been modeled, including the Wa-
bash River, White River,3 Grand Calumet River,
Little Calumet RiverS and the Mississinewa River."
The model was designed mainly for waste load alloca-
'tion purposes and therefore emphasis was placed on a
critical condition at low stream flow period.
Objectives of this paper are (1) to describe the ra-
tionale, considerations and procedures of ISPCB's
stream modeling and waste load allocation processes;
and (2) to summarize ISPCB's experience, in particu-
lar, the types of problems they encountered during
this entire endeavor.
STREAM MODELING
In the selection of model components, it is necessary
to consider the local climate and stream conditions as
well as the purpose of modeling. Indiana climate is of
the humid, continental, warm summer type. It is chai—
acterized by definite winter and summer seasons accom-
panied by wide temperature ranges. Occasionally,
stream temperature in the summer months, May to Sept-
ember, can be above 30°C. Annual precipitation aver-
ages approximately 38 inches and stream runoff is a-
bout 12 inches. Indiana adopts the average seven-con-
secutive-day, once in ten years low flow in the defin-
ition of its water quality criteria. Dry seasons are
usually between August and October. Therefore, stream
nitrification can be significant during the summer
months with low stream flow and high water temperature.
As described earlier, the purpose of modeling is to
determine BOD and NOD allocations for municipal and
industrial dischargers. Only daily average DO stand-
ards were tested against the load allocation, and thus
photosynthetic and respiration factors were not con-
sidered which cause diurnal DO variations. In view of
the fact that the sludge deposit in the stream bed is
expected to be reduced due to increasing pollution
control measures, benthal demand was also neglected
for most segments modeled.
In the ISPCB study, a modified version of the
Streeter-Phelps equation for DO deficits was utilized
which includes both carbonaceous and nitrogenous bio-
chemical oxygen demands and atmospheric reaeration.
The revised Streetei—Phelps equations are as follows:
K1Lo , -K2t "Kit KnN0 -K2t -Knt)
D(t) --K-J7 (e - ) -— (e -
(e
-K2t
n
D0e
N = N0e"Knt
where:
D(t) = DO deficit at time t.
D0 = Initial DO deficit, mg/1
L0 = Initial carbonaceous BOD, mg/1
L = Carbonaceous BOD at time t, mg/1
N0 = Initial NOD, mg/1
N = NOD at time t, mg/1
(D
(2)
(3)
K1
Kn
KZ
ion rate constant
= Carbonaceous deoxygenati
(base e) , day
= Nitrogenous deoxygenat ion rate constant
(base e) , day ~1
= Reaeration rate constant (base e) , day
The carbonaceous deoxygenat ion rate, K-| , and the
nitrogenous deoxygenation rate, Kn, were determined by
the slope of the BOD and N03~N profiles respectively
when plotted on a semi log paper. The stream reaera-
tion coefficient, K2, was computed by one of the emp-
irical equations' which are functions of stream temp-
erature, stream flow velocity and mean depth. The
hydraulic data usually available for flow velocity and
depth are taken at the gaging stations. These stations
are often located at the control sections of the stream
where the flow velocity tends to be higher and mean
depth to be smaller than that of the normal stream
reaches. Using the above mentioned hydraulic data
would tend to produce an overestimated K2 value. An-
other source of the hydraulic data is the dye travel
129
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study which provides the time of travel information.
However, dye studies taken at critical low flow period
are very rare. Previous investigators '>° have found
that general hydraulic equations developed at various
ranges of flow can be quite different and that the
actual travel time at low flow period is longer than
that computed by hydraulic equations for high flows.
When stream DO profile data were available, the model
verification was made to compare the computed stream
DO profile with the measured profile. In this way, an
appropriate equation of K2 was decided for a particu-
lar stream segment. However, complete sets of stream
profile data for DO, BOD and N03-N are often difficult
to obtain. In this case, the choice of a stream re-
aeration equation would be difficult because various
proposed equations^ could produce quite different re-
sults. Frequently, individual judgement must be used
in the selection of equations.
Further complications resulted from the fact that our
purpose of modeling was waste load allocation. Bio-
chemical characteristics are expected to be different
in the effluent and in the stream when additional
treatment and additional quantity of wastewater are
realized. The deoxygenation rates, both K-j and Kn,
computed from existing measurements can serve only as
a reference for predicting future stream deoxygenation
rates. The problem of deoxygenation rate prediction
is unresolved in the current state of art. Further-
more, there is evidence in our Wabash River study that
stream deoxygenation rates are functions of dilution
ratio and therefore dependent upon the stream dis-
charge rate, in addition to stream temperature.
The one dimensional modeling of DO, BOD and NOD, such
as that represented by equations (1), (2), and (3), may
yield poor results in a short reach immediately below
the effluent outfall because of the incomplete mixing
problem. This is particularly true when the dilution
ratio is large. Stream survey data used for ISPCB
model verifications were mainly composite samples
taken in a twenty-four hour intensive survey. For
each stream cross section, samples were taken at cen-
ter, left side and right side of the stream width.
These samples were analyzed separately and their aver-
age values were used for model verification.
WASTE LOAD ALLOCATION FORMULATIONS
PL 92-500 requires all dischargers to provide, at the
minimum, a secondary wastewater treatment (such as an
activated sludge process) for municipal wastewater
plants and the best practicable treatment (BPT) for
industrial wastewater plants. However, if the pre-
determined stream water quality standard in the
affected segment cannot be achieved as a result of
this minimum treatment (defined as a water quality
limited segment), then various levels of advanced
wastewater treatment (AWT) would be required for some
or all dischargers. Methods for determination of each
polluter's treatment level (or waste load allocation)
in this affected segment then becomes a question for
consideration. The problem would be simple if only
one discharger was responsible for the affected stream
quality. The answer becomes somewhat cloudy when more
than one discharger is involved. Proposed solutions
to this problem follow two basic approaches^; the
cost effectiveness approach and the equity approach.
The cost effectiveness approach is a typical mathe-
matical programming problem of the form;
minimize: total treatment costs
subject to:
quality standard, physical and tech-
nical constraints
Due to the usually nonlinear nature of the cost func-
tion associated with the treatment levels, a nonlinear
programming solution is generally required.^ However,
the major difficulty in implementing this cost effec-
tiveness approach is the inequality which results from
discrimination in treatment requirements. Difficul-
ties may also be encountered when new waste sources
enter into this segment and complete readjustments may
then be required. In addition, this approach assumes
that optimal solution in the stream segment being
considered is independent of the influences from both
upstream and downstream segments. This, however, is
usual ly untrue.
The second proposed solution is an equity approach in
the form;
TI = T2 T,
Subject to; quality goal satisfied, physical and
technical constraints
Where Tj = the degree of treatment for the i-th plant.
Again, the so-called "degree of treatment" is diffi-
cult to define, especially when comparing a privately-
owned industrial plant with a publically-owned munic-
ipal plant. The present practice in Indiana is to a-
dopt a combination of the two above mentioned ap-
proaches. An example is the waste load allocation for
the Grand Calumet River Basin.
Academicians have proposed a third but not yet prac-
ticed approach,'" which is to treat the stream assimi-
lative capacity as a commodity and to offer it in a
competively open market. The allocations would be
settled purely by the balance of supply and demand
subject to certain constraint. However, this approach
neglects historical factors and would require institu-
tional changes.
Allocation computation in all three approaches re-
quires the predetermination of the relationships be-
tween the effluent quality (such as biochemical oxygen
demand and ammonia concentration). These relation-
ships can be established through either regressional
analysis or simulational analysis (such as the
Streeter-Phelps equation for dissolved oxygen). How-
ever, the simulational method is generally preferred
because it provides better capability in generating
alternative solutions such as by-pass piping and
timing adjustments.
ALLOCATION RELATED PROBLEMS
Compared to wastewater treatment technology and stream
modeling techniques, studies related to wasteload
allocation methodology are still in their infancy. No
established pattern or criteria exist as to the selec-
tion of boundary conditions and loading frequencies in
a load allocation computation. For example, the head-
water source for a stream segment represents a multi-
parametric loading which consists of flow rate, temp-
erature and pollutant concentrations such as DO, BOD
and ammonia. However, these parameters are not con-
stant but rather stochastic processes. Each parameter
follows a given statistical distribution. The problem
is one of selecting statistically a reasonable combin-
ation of loading concentrations in performing waste-
load allocation analysis. The situation becomes more
complex when one takes into account simultaneously the
stochastic loadings of tributaries as well as treat-
ment plant effluents.
The present I SPCB practice in the selection of bound-
ary conditions and loading frequencies is on a case-
by-case basis and the factors considered include di-
lution ratio, loading characteristics and stream qual-
130
-------
Ity criteria for that segment.
The increasing uses of biological treatment processes
in treating municipal and industrial wastewater have
made it necessary to include stream nitrification in
the stream DO analysis, especially where the summer
temperature range covers the optimal temperatures of
nitrification, that is, between 25°C to 30°C. Under
this condition, the conventional concept of a single
valued stream assimilative capacity of BOD becomes in-
adequate because NOD is also involved, and because the
carbonaceous deoxygenation rate (K'j) and the nitro-
genous deoxygenation rate (Kn) are not necessarily e-
qual. The recent USEPA recommendation to use total
oxygen demand, which is defined as the summation of
ultimate BOD, NOD and DO, as a single-valued loading
allocation would have the same problem. Instead, the
analysis would have to provide an optimal combination
of allocated BOD, DO and ammonia loadings for an ef-
fluent source. The definition of stream assimilative
capacity becomes more elusive when multiple point
sources scattered over different locations are exist-
ent in the same stream segment.
Traditionally, one assumes that critically low DO con-
centration in the stream occurs at extremely low flow
This was not always found to be,true in the case of
multiple sources distributed at different locations,
particularly when presented with both BOD and NOD sag
curves. This phenomena occurs because the stream
DO profile is formed by the superposition of all indi-
vidual sag curves. The alternation of the shape and
location of each individual DO sag due to the change
of stream velocity and temperature can create such an
overlapping that the critical DO can take place at a
flow rate higher than a seven day, once in ten year
stream flow.
IMPLEMENTATION PHASE
Stream modeling and waste load allocation of BOD, NOD
and DO are parts of the National Pollutant Discharge
Elimination System as well as the State Continuing
Planning Process. Once the allocation is determined,
it enters into the permit as an effluent limitation.
The duration of the permit is usually five years. At
the end of the permit duration, ISPCB reevaluates the
status of the stream water quality and the program of
wastewater treatment technology. It then reevaluates
waste load allocations for that stream segment.
A majority of the waste load allocations are presently
designed on a year round basis. In some cases, sepa-
rate allocation values are given for summer months and
for winter months. Eventually, the waste allocation
may require a detailed operational schedule for efflu-
ent limits on a monthly basis or directly tied to
daily climate and stream flow conditions. This pro-
cess would require a higher degree of scientific so-
phistication and management which could become an
overwhelming administrative task under the present
understaffed condition in the ISPCB.
DISCUSSION AND SUMMARY
Computer modeling of stream self-purification systems
is a useful tool for water quality management, espe-
cially in a dynamic program like waste load allocation.
However, when applying this tool one has to be mindful
of its limitations and a certain degree of flexibility
and precaution are required. First, not all aspects of
stream self-purification systems are understood at the
present stage of development. The first order differ-
ential equation currently used for describing the
self-purification systems has its shortcomings, nota-
bly in dealing with stream nitrification, which is a
two-stage process. Furthermore, the K rates in the
Streeter-Phelps equation are not constants and their
predictabilities are uncertain. As a result, model
verification can be difficult. Secondly, complete
sets of climate and stream quality information are
often not available in the calibration of model char-
acteristics and individual judgement has to be substi-
tuted. Thirdly, due to the incompleteness of the
allocation criteria relative to boundary and loading
frequencies, case-by-case negotiations and compromises
based on local circumstances are unavoidable in load
allocation determinations.
Although the problems discussed in this paper are for
BOD, NOD and DO, similar problems also exist for ther-
mal and conservative pollutants. The situation cou]d
become even more complex if effects of nonpoint source
pollutants are taken into consideration.
ACKNOWLEDGMENTS
The authors wish to express their appreciation to Mr.
Samuel L, Moore for his support and encouragement in
the preparation of this paper. Messrs. Burt Jacobs,
Richard Moss, and Patrick O'Connell have contributed
significantly to the Indiana Stream Pollution Control
Board waste load allocation programs.
AFFILIATIONS OF AUTHORS
Drs. James Y. Hung, Aolad Hossain and T. P. Chang are
presently serving as Acting Chiefs of the Engineering
System Section, the Computer Modeling Section and the
Program Support Branch, respectively, Water Pollution
Control Division, Indiana State Board of Health, Indi-
anapoli s, Indiana.
REFERENCES
1. Chang, T.P., "Computer Applications in Water Pol-
lution Control", Proc. 1975 International Computer
Symposium. Vol. II, pp. 24-32, Taipei, Taiwan,
China, August 1975
2. Water Pollution Control Division, "Wabash River
Models and Load Allocations", Tech. Report, Indi-
ana Stream Pollution Control Board, Indianapolis,
Indiana, 1975.
3. Water Pollution Control Division, "West Fork,
White River Models and Load Allocations", Tech.
Report, Indiana Stream Pollution Control Board,
Indianapolis, Indiana, 1974.
k. Combinatorizs, Inc., "Load Allocation Study of the
Grand Calumet River and Indiana Harbor Ship Canal",
Combinatorizs, Inc., Lafayette, Indiana, 1974.
5. Henry Steeg and Associates, "Load Allocation
Study - Little Calumet River Basin in Indiana",
Henry B. Steeg and Associates, Indianapolis, Indi-
ana, 1974.
6. Water Pollution Control Division, "Middle Missis-
sinewa River Models and Load Allocations", Tech.
Report, Indiana Stream Pollution Control Board,
Indianapolis, Indiana, 1973.
7. Stall, J.B., and Yu-Si Fok, "Hydraulic Geometry of
Illinois Streams", University of Illinois Water
Resources Center, Urbana Research Report no. 15,
1968.
8. Stall, J.B., and D.W. Hiestand, "Provisional Time-
of-Travel for Illinois Streams", Illinois State
Water Survey Report of Investigation 63, 1969.
9. Cleary, E.J., "Effluent Standards Strategy: Re-
131
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juvenation of an Old Game Plan". Jour. Water Pol-
lution Control Federation, Vol. k6, pp. 9-17,
10. Mar, B.W. , "A System of Waste Discharge Rights for
the Management of Water Quality", Water Resour.
Res., Vol. 7, No. 5, pp. 1079-1086, 1971.
132
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PATUXENT RIVER BASIN MODEL
RATES STUDY
Thomas H. Pheiffer
Leo J. Clark
U. S. Environmental Protection Agency
Region III
Annapolis Field Office
Annapolis, Maryland
Norman L. Lovelace
Water Division
Water Planning & Standards Branch
U. S. Environmental Protection Agency
Region IX
San Francisco, California
ABSTRACT
During the summer seasons of 1973 and 1975, inten-
sive water quality surveys were carried out in
the Patuxent River Basin for the purposes of
mathematical model calibration and validation. In
the summer of 1973, the Patuxent was receiving
secondary effluent from eight major municipal
treatment plants. No significant industrial waste
discharges are present in the Patuxent system. A
steady state water quality model was calibrated
and validated using the data collected from the
1973 field surveys. During 1975, a major treat-
ment plant was upgraded to include high BOD re-
moval and nitrification; new field surveys were
conducted and the model was recalibrated and
validated to reflect changes in the instream re-
action rates* as a result of the changed effluent
characteristics. This paper discusses the field
studies, data results, model application procedures
and perhaps most importantly, how the procedures
that were used could be improved.
BACKGROUND
The state-of-the-art of modelling is such that
mathematical expressions can be written and trans-
lated into computer programs to represent complex
environmental interactions. However, too little
effort is being directed towards defining the
numerous variables and/or biological coefficients
required to make these mathematical expressions
either descriptive or predictive. Much effort is
being devoted to studying the mathematical behavior
of these equations and expressions, but not enough
is being given to real world applications.
A basic, but essential problem confronting many
modellers is what instream reaction rates to assume
for carbonaceous decay and nitrification when
treatment is upgraded above the conditions that
existed when field data was collected. To date,
estimates of reaction rates for highly treated
municipal effluents are based solely on the best
judgement of modelling experts, not on well docu-
mented field data. With this in mind, the Annapolis
Field Office (AFO), Region III, EPA, has attempted
to define changes in instream reaction rates re-
sulting from the upgrading of a major wastewater
treatment plant, in particular, the Parkway Plant
of the Washington Suburban Sanitary Commission,
located near Laurel, Maryland.
STUDY AREA
The Patuxent River, located entirely within the
State of Maryland, has a drainage area of approxi-
mately 930 square miles. Its two major tributaries
are the Little Patuxent River and the Western Branch
with drainage areas of 160 and 110 miles,
respectively. The tidal portion extends to
Hardesty, Maryland, a distance of 54 miles from the
mouth of the estuary.
The headwaters of the Patuxent are impounded above
Laurel, Maryland in the Triadelphia Reservoir and
the T. Howard Duckett Reservoir (Rocky Gorge). The
Rocky Gorge Dam provides for a generally regulated
flow in the mainstream of the Patuxent downstream
to the confluence of the Little Patuxent with the
mainstem, a distance of 17.5 river miles. During
the summer months, this regulated flow amounts to
approximately 10 million gallons per day (mgd) or
15 cubic feet per second (cfs). It is in this
critical reach (17.5 miles) that stream quality was
improved by upgrading the Parkway Wastewater
Treatment Plant.
The Little Patuxent is not regulated by dams and
exhibits irregular flow patterns following thunder-
storm activity. Surging flows into the estuary
during the summer are attributed mainly to the
Little Patuxent. Total annual precipitation in the
basin is estimated at 30-44 inches per year with the
maximum precipitation occurring in July or August.
DESCRIPTION OF STUDY
For the purpose of obtaining data for model
application, 52 water quality sampling stations
were located in the Patuxent River Basin. Twenty-
seven of these stations were located in the estuary
between river mile 0.0 and 54.0. Fourteen stations
were located in the free flowing mainstream of the
Patuxent between r.iver mile 54.0 and river mile
81.0 at Laurel, Maryland downstream from Rocky
Gorge Dam. Eleven sampling stations were estab-
lished in the Little Patuxent from its confluence
with the mainstem upstream to Savage, Maryland,
river mile 18.0.
Water quality surveys were carried out in the Basin
during April 3-5, June 4-7, July 9-12, and
October 9-12, 1973. The June and July intensive
surveys encompassed the entire Basin. The April
and October surveys were confined to the estuary
with the April survey designed to determine rough
salinity gradients for estimating dispersion co-
efficients. The October survey measured surface
and bottom dissolved oxygen concentrations for model
verification. Data collected in the estuary were
obtained during slack water conditions.
* Reaction rates refer to first order rate constants
The models used in these studies use first order
rate expressions to represent the nitrification
and carbonaceous deoxygenation processes. The
question of whether a first order representation
of these processes is the most realistic is not
a point of discussion for this paper.
133
-------
Curing the period of July 28-31, 1975, an intensive
water quality survey was carried out in the
critical reach of the free-flowing Patuxent from
below the dam of the Rocky Gorge Reservoir
(mile 81) downstream to the head of tide (mile 54).
The purpose of this survey was to obtain data for
recalibration of the existing model. The Parkway
Plant located at river mile 74.5 had gone on line
during January, 1975 with advance waste treatment
(AWT). Next, a survey was initiated from October
14-16, 1975, to obtain data to validate the reaction
rates determined from the July 28-31, 1975 survey
data.
Flows for the studies were obtained from stream
discharge gages located in the free-flowing
portion of the Basin. The United States Geological
Survey made current meter discharge measurements at
each site during the June and July, 1973 studies
and again prior to the 1975 surveys. This enabled
the USGS to furnish stream discharges for the gage
heights read at the time of sampling. The samples
were analyzed at the Annapolis Field Office labora-
tory during the 1973 and 1975 surveys for the
following parameters: DO, BOD5, TOC, TC, TKN, NH3,
N02+N03, Pi, TP and Ciiloro a_. Salinity,
conductivity, temperature and pH were routinely
measured in the field.
Special studies during 1973 included long-term BOD
measurements at specified estuarine and stream
stations for the purpose of attempting to measure
in-stream carbonaceous and nitrogenous oxygen
demand rate constants. Methyl blue, an inhibitant
to the bacterial oxidation of ammonia nitrogen, was
injected into duplicate samples to determine the
second stage oxygen demand (nitrogenous BOD).
Again, during July 28-31, 1975, in the critical
reach below the Parkway AWT Plant, an attempt was
made to follow a specific parcel of water based
on time-of-travel data obtained during the week of
June 30, 1975. Long-term BOD and the nitrogen
series were run on samples from the selected
stations below the discharge of the Parkway AWT
Plant.
Twenty-four hour composite samples of wastewater
treatment plant effluents were obtained from the
major plants in the basin during the June and July,
1975 surveys. Composite treatment plant data were
also available from a survey by the Annapolis Field
Office during October, 1972. The nine plants
shown in Figure 1 account for approximately 96% of
the treated wastewater discharged in the entire
basin. During the 1975 surveys, only the waste-
water treatment plants in the critical reach of the
mainstem of the Patuxent were sampled. These
included the Maryland City, Parkway and Bowie-
Bel air Plants.
DATA ANALYSIS
This discussion and those that follow will focus
on the critical reach of the free flowing Patuxent,
i.e., from below the Rocky Gorge Dam (mile 81)
downstream to the head of tide (mile 54). As
previously mentioned, the Parkway Plant is located
at river mile 74.5 in this segment.
The data comparisons discussed below will concern
the water quality data collected during the
July 9-12, 1973 and July 28-31, 1975 surveys. The
low flow conditions were essentially the same,
36 cfs in 1973 and 31 cfs in 1975, at the
Baltimore-Washington Parkway (mile 75) just above
PATUXENT RIVER BASIN
the Parkway Plant. Likewise, stream temperatures
were similar in the segment, i.e., 23°C in 1973
and 24°C in 1975.
Figure 2 illustrates the improvement in D.O. levels
between the 1973 and 1975 July surveys. The
average D.O. concentration at mile 71.5 for the
4 day survey periods increased from 5.1 mg/1 (7/9-
7/12, 1973) to approximately 5.9 mg/1 (7/28-7/31,
1975). The minimum observed concentration in-
creased from 3.1 mg/1 to 5.5 mg/1 for the same
periods.
At this point, it is important to note the recent
modifications to the Parkway Plant. Its design
flow has been expanded from a 2.4 mgd secondary
facility to a 7.5 mgd AWT plant. The AWT plant
went on line during January, 1975. The current
monthly average flow through the plant is 4.5 mgd.
It should be noted that the secondary facility was
overloaded during the 1973 studies. In 1973, the
flow was about the same as the current 4.5 mgd.
Prior to expansion, the Parkway Plant was a
secondary facility utilizing trickling filters.
The expanded plant encompasses the trickling
filters plus an activated sludge system which
achieves high BOD removal and the nitrification of
ammonia nitrogen to nitrate nitrogen. Micro-
strainers have been added to further reduce the
suspended solids. The effluent then goes through
a chlorine contact chamber and is aerated prior to
discharge to the Patuxent (1). This added aeration
process has resulted in D.O. levels of 7-8 mg/1
in the AWT effluent. In July, 1973, D.O. effluent
134
-------
a.
u
g
8
5
S2
S
3
IS.O-
12.0-
IIJJ'
10 JO
IJB
t.Q
t.O
4.0
3.0
LITTLE PATUXENT
RIVER
PARKWAY
PLANT
levels were 4-5 mg/1 in the absence of aeration
and with secondary treatment.
During July, 1973, the typical wastewater reduc-
tions achieved at the Parkway Plant amounted to
83% for BOD5 and 17 mg/1 for TKN. The ammonia
levels comprised about 90% of the TKN in the July,
1973 effluent. The AWT effluent during July, 1975
showed good levels of BOD removal, averaging 5.5
mg/1 BOD5, while TKN averaged 7.1 mg/1, the re-
moval rate being 98% for BOD5 and 72% for TKN.
During August, 1975, the plant achieved an 85.8%
removal of TKN. A 95% BOD5 reduction is the norm
at the Parkway AWT Plant.
With the above background information in mind,
one would naturally expect accompanying reductions
in BOD and TKN downstream from the Parkway Plant.
The average ammonia levels for the July 9-12, 1973
and the July 28-31, 1975 periods decreased from
2.7 to 0.5 mg/1 at river mile 73.7, a mile below
the plant, and from 0.5 to 0.09 mg/1 at mile 66.4,
about 8 miles below the Parkway discharge and
just above the Bowie-Belair discharge. The
N02+N03 levels at the same two stations for the
two periods increased from 1.3 to 3.5 mg/1 and
from 1.4 to 3.0 mg/1 for 1973 and 1975, respective-
ly. The N02+N03 1973 data indicate no instream
nitrification of NH3 to N02+N03, even though there
was evidence that nitrification was occurring (see
NH3 results above). The large increase in
N02+N03 during July, 1975 was due to the Parkway
Plant effluent containing around 10-12 mg/1
N02+N03. The apparent loss of nitrogen from the
system will be addressed later in this paper.
Also, there were corresponding reductions in
instream BOD5 concentrations. For example, the
July, 1973 BOD5 averaged 5.0 mg/1 below the plant
(mile 73.7) and 3.0 mg/1 at the end of the reach
(mile 66.4). July, 1975 data showed a general
average of 1.0 mg/1 BOD5 throughout the reach.
MODEL APPLICATION
Two models from the CMS (Comprehensive Modelling
System), a system of mathematical models developed
by Crim and Lovelace, were applied to the Patuxent
River System. The two models used were AUTOSS and
AUTOQD (2).
Both AUTOSS and AUTOQD contain a hydraulic
component, that computes the streamflow profile,
and a water quality component that computes concen-
tration profiles. The models are one-dimensional,
single channelled models that use first order
kinetics to represent instream bio-chemical
processes. AUTOSS is a steady state model while
AUTOQD is a quasi-dynamic model. AUTOQD represents
flow patterns as step shaped patterns in time, and
water quality concentrations as continuous patterns,
Data on the free flowing portion (for the period
July 15-19, 1968) were available from a cooperative
study with the Maryland Department of Water
Resources. Both the 1968 and the 1973 data show
the mainstem to contain high concentrations of TKN
nitrogen. These high nitrogen concentrations were
attributed to wastewater treatment plant discharges
of excessive amount of TKN and NH3 forms of
nitrogen.
AUTOSS was calibrated to simulate DO conditions in
the mainstem for the periods July 15-19, 1968 and
June 4-7, 1973. Ultimate carbonaceous (CBOD) and
nitrogenous (NBOD) BOD loadings from the treatment
paints were entered into the model at the appro-
priate river miles. The ultimate CBOD and NBOD
loadings were calculated from the commonly used
literature values where ultimate CBOD 1.45 BOD5*
and ultimate NBOD = 4.57 TKN. Relatively steady
state low flow conditions occurred during July,
1968 and medium flow conditions occurred during
June, 1973. The out flow at the downstream junc-
tion of the model was 120.1 cubic feet per second
(cfs) and 458.3 cfs, respectively. Stream
velocities used in model calibration were obtained
from 1968 and 1975 studies by the Annapolis Field
Office of time-of-travel and from depth measure-
ments made during 1973 studies.
During the period of July 9-12, 1973, an average
net flow of 152.3 cfs was recorded in the mainstem
of the Patuxent. The calibrated coefficients
obtained from the July, 1968 and June, 1973 model
runs were used in the model validation runs.
Treatment plant discharge values for carbonaceous
and nitrogenous oxygen demand loadings used in the
model reflected the results of the composite
sampling of July 10-11, 1973. Observed DO values
were assigned to major inflows while a DO of 5.0
mg/1* was used for treament plant effluents. The
model verification curve for this flow oeriod and
* D.O. data were not taken for the final effluent
just prior to its discharge to the stream. This
was an unfortunate oversight since effluents
comprise a substantial portion of the total
flow in the Patuxent above confluence with the
Little Patuxent.
135
-------
the June 4-7, 1973 calibration are shown in
Figure 3. Documentation of the 1973 studies in-
cluding model application to the estuary is set
forth in Technical Report 58, by Pheiffer and
Lovelace (3).
9 JO-
10
7,0-
.
•
O
4.0'
XO-
U
|t/4 - 8/7 , l»73| \ AVERAGE RANGE
^
fl
o
4(4>505tMMUMM«4
|7/» - 7/B , H73| | WERAGE 1 RANGE
TO 71 74 T« T»
50 32 54 M M BO M <4 M •« TO 72 T4 Te 71
RIVER MILE
MODEL RECALIBRATION
As stated earlier, the Parkway AWT Plant went on
line in January, 1975. This necessitated adjust-
ments to the existing model which had been cali-
brated and verified on instream reaction to the
discharge of secondary treated effluent from the
Maryland City (mile 77.5), Parkway (mile 74.5),
and the Bowie-Belair Plants (mile 64.5). With
this knowledge, the July 28-31, 1975 intensive
survey was planned to encompass the critical reach
from below Rocky Gorge Dam (mile 81) downstream to
the head of tide (mile 54). The Washington
Suburban Sanitary Commission maintained a low flow
similar to the July 9-12, 1973 flow condition, at
the Rocky Gorge Reservoir for the study period.
Instream temperatures resembled July, 1973 water
temperatures.
Utilizing the July, 1973 and the July, 1975 stream.
data, two independent methods were employed to
determine reaction rates for the carbonaceous bio-
chemical oxygen demand (CBOD) and the nitrogenous
biochemical oxygen demand (NBOD). First, a semi-
logarithmic graphic solution of plotting stream
station loadings (Ibs/day) versus travel time in
days was used. Next, the reaction rates obtained
from the semi-log plots were tested in the model.
Only through model testing of the rates and a
knowledge of the stream can the modeller select
the best values which work in the model and yet do
not compromise the field data.
The above methods for rate determination were
employed for the calibration of the 1973 version
of the model, i.e., the one validated when the
critical stream segment was receiving secondary
effluent only. The existing version of the model
was recalibrated from rate determinations based on
the July 28-31, 1975 stream data. This calibration
reflects the effect of the Parkway AWT Plant
discharge from mile 74.5 downstream to mile 64.5.
CONCLUSIONS
Figures 4 and 5 are semi-log plots of the July,
1973 and July, 1975 CBOD and NBOD loadings at
stream sampling stations in the critical reach
below the Parkway Plant, mile 73.7 to 66.4. These
plots are intended to graphically show the reduced
loadings for both CBOD and NBOD due to improved
treatment at the Parkway Plant. As previously
discussed, the stream flow conditions and stream
temperatures are nearly identical for the two
study periods.
Figure 4 shows a reduction in the CBOD decay rate
of 51% due to higher BOD5 removal at the Parkway
Plant. The K rates determined were 0.61
(I/day base e) for the period July 9-12, 1973 and
0.30 (I/day base e) during July 28-31, 1975. It
should be noted that only two reliable data points,
mile 73.7 and 66.4, were obtained from the lona
term BOD studies. The grab samples were not
dechlorinated as were the long term samples,
thereby giving low, erratic BOD5 values.
136
-------
The conclusion drawn from Figure 5 is that the K
rate for NBOD has been reduced 37% with the
addition of nitrification at the Parkway Plant.
The determined K rates for NBOD-decreased from
0.76 (I/day base e) in 1973 to 0.48 in 1975.
higher DO levels in the lower part of the critical
reach. The discussion section which follows, will
address the need for further field studies and
model adjustments. However, the calibrated decay
rates were tested with an independent set of data
for October 15-16, 1975, and the model predicted
DO quite accurately in the sag area at the dis-
charge ooint of the Parkway AWT Plant.
FIGURE 5
13.0
11.0
7/26-7/31 If AVERAGE 1 RANGE
O 1973 MODCl RATES
(SECONDARY TREATMENT)
A 1975 MODEL CALIBRATION
O 1975 GRAPHC RATES
(SEMI-LOG PLOTS)
2 X
o o A o
*+*+-*•
~T- 3 T"i ~ i LO
TRAVEL TIME FROM PARKWAY (DAYS)
The rate that best fit the 1973 version of the
model for the decay of CBOD was 0.62 (I/day base e)
in the critical reach below the Parkway Plant. The
CBOD rate tested in the 1975 model was 0.40
(I/day base e). Even with the restriction of
limited BOD data for the July, 1975 period, the
rates used in the model pretty much paralleled
those determined graphically.
For NBOD, a K rate of 0.65 was used in the upper
half of the critical reach in the 1973 model,
while a rate of 0.45 worked best in the lower end
of the reach. The calibrated rates for the 1975
model were 0.50 and 0.27 in the same segments.
Figure 6 represents a sensitivity analysis of the
model decay rates discussed above. Three
separate model runs were made. First, the 1973
rates were used to predict the July, 1975 DO field
data. These rates gave a better fit in the lower
half of the critical reach, but not at the sag
point. Next, the 1975 graphic rates were plugged
into the model. Thirdly, the graphic rates were
increased for NBOD decay in an attempt to get the
best calibration. However, no rates were adjusted
to the point where the TKN and BOD field data were
compromised. As indicated by Figure 6, the model
prediction with the calibrated rates predicted
The general conclusion to be drawn in this paper
is that modifications to model rates due to
changes in stream loadings, changes in discharge
locations, etc., should be based on estimates from
actual field data. The best way to estimate these
decay rates for free flowing streams is not by
curve fitting with the existing model. Rather,
free flowing stream rates should be obtained by
plotting semi-logarithmically the actual stream
segment loadings versus travel time. These rates
can then be adjusted to calibrate the model (but
not to the degree that the BOD and nitrogen data
are compromised) so that DO prediction profile
matches the field data.
DISCUSSION
The investigators realize that there are short-
comings in the studies both in terms of data
requirements and model simulation. The contribution
of this paper to the state-of-the-art review of
modelling might best be described as the basic
awareness of the investigators of the need to up-
date a model when the conditions on which that
model had previously been validated have changed
137
-------
and the realization that field studies must be
carried out to define changes in model coefficients
due to modifications in wastewater inputs to the
model.
Additional studies seem warranted to further
define instream changes in the decay of CBOD and
NBOD below the Parkway AWT Plant. Field studies
should again be carried out during a steady state,
low flow condition accompanied by warm weather
stream temperatures. The nature of effluents from
the Maryland City, Parkway and the Bowie-Belair
Plants must be better defined. The results of
24 hour composite samples might not truly represent
the proper numbers for BOD and nitrogen to use as
a steady state input. Either hourly grab samples
or a daily grab sample at discrete plant flow
periods should be obtained. A weighted average
of these samples results could give more reliable
numbers for model usage. In addition, a firm fix
on the DO level of the final pi ant (s) effluent
should be established for a typical warm weather
condition.
Future studies should delineate the effluent plume
in order to determine the extent of instream
mixing, the rate of decay by the microbial popula-
tion within the plume area, and the configuration
of the plume so that the stream sampling below the
point of discharge can be designed to represent a
composite analysis of stream quality in that
segment. In addition, oxygen sediment demand
should be measured at and below the point of dis-
charge in an attempt to quantify the affects of
any sludge deposits on the oxygen content of the
overlying water. Benthic oxygen demand should be
quantified throughout the entire critical segment
in order to substantiate any assumption made
regarding background oxygen demand or depletion.
The investigators strongly feel that more visual
observations are needed in the critical area where
they are trying to define instream reaction rates.
As noted earlier, the data for 1973 indicate that
nitrification of NH3 to N03 appears to occur.
However, the reduction of NH3 does not result in a
corresponding increase in N03. Rather, the data
indicates a loss of nitrogen from the system. The
loss of nitrogen through instream denitrification
does not appear probable, since DO levels do not
approach anoxic conditions. Algae cannot account
for this decrease, since chlorophyll a_ levels are
and have been extremely low, i.e., 1-10 yg/1 in the
free flowing Patuxent. Rooted aquatic plants, or
other shoreline vegetation ,if present in sufficient
quantities, could account for the nitrogen loss
from the water column by plant utilization of the
inorganic forms of nitrogen as well as affecting
the DO budget on a diurnal basis. This possibility
should definitely be investigated, since field
biologists with the State of Maryland have indica-
ted the presence of rooted aquatic plants in the
study area.
It is recognized that BOD is not the ideal
parameter for determining rates. One reason is
that laboratory error is often high. In the
Patuxent, chlorine in the stream samples gave
erroneous values in some instances, though once the
chlorine was detected, it was destroyed in the
laboratory before BOD was run. But, if BOD is to
be used for rate determinations, sufficient BOD
measurements should be taken to make the rate
determination statistically valid.
It should be noted that the models discussed in
this paper were used by the State of Maryland
in 1973 to evaluate effluent limitations proposed
for wastewater treatment plants in the Patuxent
River Basin Water Quality Management Plan (4).
The recalibrated model (1975) of the free flowing
mainstem was also given to Maryland at the request
of the Maryland Water Resources Administration.
REFERENCES
(1) Schell, T. "Parkway Wastewater Treatment
Plant", Washington Suburban Sanitary
Commission, (unpublished manuscript),
April, 1974.
(2) Crim, R. L. and Lovelace, N. L. "AUT0-QUAL
Modelling System", Annapolis Field Office,
Region III, U. S. Environmental Protection
Agency, Technical Report No. 54, March, 1973.
(3) Pheiffer, T. H. and Lovelace, N. L.
"Application of AUT0-QUAL Modelling System
to the Patuxent River Basin", Annapolis Field
Office, Region III, U. S. Environmental
Protection Agency, Technical Report No. 58,
December, 1973.
(4) "The Patuxent River Basin Water Quality
Management Plan", Maryland Environmental
Service, (draft copy), April, 1974.
138
-------
EFFICIENT STORAGE OF URBAN STORM WATER RUNOFF
J. Robert Doyle
US Environmental Protection Agency
Denver, Colorado 80201
James P. Heaney, Wayne C. Huber and Sheikh M. Hasan
Department of Environmental Engineering Sciences
University of Florida
Gainesville, Florida 32611
A mixed integer linear programming model is used to
evaluate alternatives for use of storm water detention
in flood plains and developing areas. This model is
suitable where a refined analysis is needed. Mixed
integer programming is appropriate when it is necessary
to handle fixed charge problems. This added feature
significantly increases the computational complexity
of the model as compared to standard linear program-
ming procedures. Given an inventory of available
storage sites, both in and out of the flood plain, and
costs for other flow reduction measures, the optimi-
zation model determines the least costly combination
of storage reservoirs. Application to the Hogtown
Creek drainage basin in Gainesville, Florida is
included to demonstrate the techniques.
«
Introduction
Storage facilities for controlling the quantity and
quality of urban runoff are becoming increasingly
popular.* Urban areas have numerous storage options
available such as natural depressions, rooftops and
parking lots within the drainage basin in addition to
storage in the flood plain itself. The model presen-
ted in this paper addresses one part of the analysis
regarding selecting the number and capacity of reser-
voir sites. The objective is to find the least costly
way of providing a specified level of service. Other
considerations regarding environmental impacts,
implementation problems, etc., are not considered here.
Hasan presents procedures for examining these other
considerations•
The Decision Model
A mixed integer programming model was used to evaluate
alternatives for storing urban runoff.3 The objective
is to minimize the cost of storing water for a specified
level of runoff control. The model provides the
engineer or urban planner with a method for evaluating
the complete drainage system and utilizes simplified
information from each subsystem to test the consequences
of instituting various land use or water management
plans.
The objectives of the runoff control model are:
1. to synthesize hydrologic, land use, and
runoff control cost data from all parts
of an urban watershed in order to evaluate
a storm water runoff alternative;
2. to find the least cost solution to the
problem of maintaining natural stream
flows within an urbanizing watershed,
thus deriving certain water quality
benefits; and/or
3. to assign the responsibility for control
of urban storm water quality to land
developers and owners by specifying
an allowable rate of runoff from their
lands.
The complete mixed integer programming model is listed
below with each equation or function discussed subse-
quently.
Minimize Z = £(S u + X.D ) +
(1)
subject to
EX.. + S.
where Z
i
S
S
\
IX , R = 0 for all i
m mi i
Tk + \ = pk for all k
S - S A. <_ 0 for all i
1.0 for all k
(2)
(3)
(4)
(5)
(6)
= the total fixed and variable cost of
storm water storage in the flood plain
and all sub-basins,
= number designating a node; flood plain
storage site or stream junction,
. = units of water stored at flood plain
1 site ±,
= total capacity of storage site i,
= unit cost of water stored at site i,
= 1 if storage site i is used, 0 otherwise,
D fixed cost of site i,
k = number designating a sub-basin,
1 number designating a sub-basin storage
alternative or alternative combination
in sub-basin k,
T = volume of water stored in sub-basin k,
k
v, = unit cost of water stored in sub-basin k,
k '
$, .. 1 if sub-basin storage alternative 1 in
sub-basin k is used, 0 otherwise,
C fixed cost of storage alternative 1 in
sub-basin k,
139
-------
X = volume of water which flows from node i
to downstream node j,
X = volume of water which flows from upstream
m node m into node i,
R. = volume of water entering flood plain
1 site i (R± = Rk),
& = volume of water leaving sub-basin k,
P = volume of runoff entering sub-basin k, and
storage capacity of alternative 1 in
kl
sub-basin k.
The objective function, equation (1), is minimized in
order to obtain the least total cost, subject to cer-
tain constraints. The first summation in the objective
function is the total variable cost, (S^Uj)> and fixed
cost, (X.D ), of flood plain storage throughout the
watershed. The second summation in the objective
function is the total cost associated with use of all
sub-basin storage alternatives, the first term being
the variable cost, (T v ) , and the second term being
the fixed cost (klckl) •
Determination of the least cost is subject to the
physical laws of continuity. Continuity constraints
are written for stream flows in the flood plain and
flows within each sub-basin as shown by equations (2)
and (3), respectively. Continuity of stream flow must
be maintained at every point or node in the network
where two or more streams join or where storage is
permitted. These constraints specify that the dif-
ference between the water volume which flows into and
out at a given point must be stored at that point.
Therefore, equation (2) requires that storage at node
i, (S ), equals the difference between the storm water
inflow, (XX . + R ), and downstream releases, (ZX ).
m m j
Equation (3) states simply that within sub-basin k,
storage plus releases to the flood plain, (T + IL ) ,
must equal the total runoff volume entering the sub-
basin, (P ) .
The variables X and $ of the objective function can
only take on values of either 0.0 or 1.0. When one
of these variables is set equal to 1.0, a fixed charge
is incurred; when the value is 0.0, no charge is in-
curred. Each of these zero-one variables is associated
with a possible storage site, such that if any amount
of water is stored there, the zero-one variable should
be set to 1.0. In fact, when solving for the optimal
continuous solution, it is very possible that many of
the zero-one variables will be set at values between
0.0 and 1.0. If this is the case, a branch and bound
procedure is used to determine the optimal mixed
integer solution in which all zero-one variables take
on integer values. The functional inequalities (4)
and (5) are zero-one inducement constraints.
The first of these zero-one constraints, inequality (4),
is related to flood plain storage sites and performs two
functions in the decision model. The first function is
to force at least a portion of the fixed cost to be
incurred at a used storage site when solving the problem
for the optimal continuous solution. This is necessary
to ensure the proper behavior of the model. The second
function is to increase the efficiency of the branch and
bound procedure in finding the optimal mixed integer
solution. For all flood plain storage sites, the
storage volume used, (S.) , must be less than equal to
the site's storage capacity, (S^i.
The second zero-one inducement constraint set,
inequality (5), is required for sub-basins which have
fixed cost storage alternatives. These storage alter-
natives are actually combinations of potential storage
sites which might be utilized within a single sub-basin.
Therefore, these alternatives are mutually exclusive.
Equation (6) specifies this mutually exclusive condition
by requiring that the sum of all terms (one term
associated with each alternative) within a sub-basin
equal 1.0. The branch and bound integer solution pro-
cedure will require that the $ terms equal either 0.0
or 1.0. Therefore, inequality (5) actually specifies
the relationship between the variables R. and ((i^.
For a. given value of R,. the <(>,- term associated with
the alternative with the lowest fixed cost and suffi-
cient storage capacity, (t ), to satisfy the continuity
conditions specified by equation (3), will be set equal
to 1.0. Within sub-basin k, all other $ terms will be
set equal to 0.0.
All variables of the decision model must take on non-
negative values. The variables which represent stream
flow volumes and storage volumes also have a specified
upper bound. The stream flow variables have an upper
bound, (X ), equal to the estimated natural stream flow
ij *
volume over a set time period. This upper bound is cal-
culated through simulation of the natural hydrograph
representing conditions prior to urbanization, thus con-
straining urban storm water runoff to rates which
existed under natural conditions. The upper bound on
storage volume for each facility is set by the feasible
limitations of storing water in each facility.
The mixed integer programming model was run using the
IBM MPSX package. It is relatively expensive to
utilize and is not widely available. If the fixed
charge part of the problem is eliminated, then one can
use standard linear programming codes which are widely
available. Thus, this approach is appropriate for more
refined investigations.
The Study Area
Hogtown Creek is the major natural drainage system for
the western portion of Gainesville, Florida, where the
University of Florida is located. The drainage basin
has an area of around 13,000 acres and is made of two
predominately different land forms. The southern part
of the basin is primarily low lands in which water col-
lected throughout the watershed is eventually recharged •
to the ground water system.
In contrast, the northern part of the basin comprises
uplands which have been extensively developed in some
areas with more outlying areas currently undergoing
suburban development. However, a significant amount of
natural and agricultural land still exists.
Increasingly severe downstream flooding problems asso-
ciated with upstream development led to the passage of
a flood plain ordinance which included provisions to
retain runoff peak flows and volumes at their pre-
development levels. As a result of'this ordinance
numerous detention facilities are in operation in the
basin. This modeling application was made to provide
some guidance in comparing the suitability of alter-
native sites.
The decision model is set up by partitioning the entire
drainage basin into the twenty subcatchments shown in
network form in Figure 1. The appropriate continuity
equations are written according to this network
140
-------
utilizing the general form shown by equations (2) and
(3). Constraints established by estimating natural
hydrologic conditions and storage capacities are used
in equation (3), and inequalities (4) and (5).
DETENTION V7
Ri^lM V
GROUND WATER
BASIN
RUNOFF
|9 INPUT
JUNCTION
NODES
PREPARED BYI8M-AS
POINT OF O
CONCENTRATION
ONLY
good drainage characteristics, the use of grass-lined
swales in residential areas was assumed. Runoff coef-
ficients were calculated for the projected residential
areas by taking into account the use of grass-lined
svales for drainage. For each hydrograph the volume of
water which flowed from the respective sub-basins during
a 75 hour time period, assuming no sub-basin storage,
was used as the input variable, (P ), the total runoff
volume into sub-basin k.
Capacity of Storage Sites, S. and t,.
1 K..L
and Streamflow Volumes, X. .
The study area was surveyed to determine potential _
storage sites for storage within the flood plain, (S ) ,
and to estimate each site's storage capacity and land
area. Within each sub-basin, significant available
sites, e.g., wetlands, were inventoried to determine
t
Figure 1. Hogtown Creek Network
Flow Diagram
Variables for which input values must be determined
prior to running the model are discussed below.
Fixed and Variable Costs, D , C, , u v
The fixed cost of flood plain storage at site i, D ,
and of storage alternative 1 in sub-basin k, C , were
assumed to be $1,500 per acre of land. The unit costs
of water stored at site i, u , or in sub-basin k, v ,
3
were assumed to be $350 per 1,000 ft .
Runoff Volume, P
Soils information, along with assumptions about the
natural vegetative and hydrologic conditions of the
watershed, were used to calculate natural stream flow
hydrographs. ** 5 All hydrographs were calculated
utilizing a design event with a recurrence interval
of 3 years and a rainfall intensity of 0.31 inches
per hour for a duration of 15 hours. These hydrographs
were used to establish stream flow constraints for use
in the decision model and were calculated using a com-
puter simulation model which required runoff coeffi-
cients and times of concentration as inputs.
In order to examine ultimate urban conditions, the study
area was first categorized into developed and undeveloped
areas. The developed area was further broken down into
land use types to determine runoff coefficients.7 The
undeveloped area was categorized by projected land use,
which was predominantly residential. The same runoff
coefficients used for existing land use categories were
used for future land uses, with the exception of resi-
dential use. In areas where soils were known to have
ukl'
Sub-basin storage capacity was limited to the
An upper limit on stream
runoff entering the sub-basin
flow volume,
(X..), was determined based on maintaining
bank stability.
Results
In solving the problem, the model allocates the
specified total potential runoff volumes from each sub-
basin among the sub-basin and flood plain storage sites,
while allowing only a specified volume of runoff to flow
downstream. The model results for this example are
shown in Tables 1 and 2.
Table 1 shows how the flow volumes were allocated to
flood plain storage sites while maintaining as a maximum
flow volume the natural stream flow conditions. In
order to minimize storage costs, the flow volumes are set
near to the natural flow conditions. However, only for
a few stream reaches are the flow volumes equal to the
maximum limit. These stream reaches form a constraint
for upstream flows. Two reaches show a zero flow which
should be changed by specifying a minimum allowable flow
volume different than zero. Depending on the minimum
volumes specified for each reach, this added constraint
could significantly alter the results given for this
example.
As shown in Table 1, almost all of the flood plain
storage sites were utilized to capacity. The cost of
utilizing these sites was calculated from the land area
required for each site if filled to capacity. The cost-
effectiveness of the various sites is not the same
because the capacity/area relationship (and therefore
capacity/cost relationship) differed for each site.
However, almost all sites were fully utilized because
the cost of flood plain storage was generally much less
than storage within the sub-basins.
Table 2 summarizes all storage allocations and costs.
Only in sub-basin 7 was the total storage capacity
utilized. This is because this sub-basin contained the
natural depression sites which were estimated to cost
much less than constructing storage facilities. In all
other sub-basins, storage was assumed to be available
only by providing special storm water holding facilities
at $350 per 1,000 ft of storage which was the most
expensive alternative considered.
The fixed costs of providing storm water storage is
the sum of the flood plain storage costs and sub-basin
7 storage costs, or $440,000. This figure is less than
3 percent of the total optimal storage cost of approxi-
mately $15 million. However, storage within the flood
plain alone represents more than 50 percent of the total
storm water volume stored.
141
-------
Table 1. Summary of Model Results - Flood Plain Allocations
Flow and Storage Volumes 100,000 ft
Link
i.J
1.J1*
2,J2
4.J1
J1.J2
J2,3
3,7*
14,7
7,8*
8,J5
10,11
11, J3
12, J3*
J3.13
13,15
15, J4
16, J4*
J4,17
17,9
9,18
18, J5*
J5.19
19, J6*
20, J6*
J6,Sink*
XU
56.4
0.0
25.1
81.5
81.5
169.0
3.5
251.0
267.0
0.0
59.2
63.4
123.0
145.0
125.0
17.8
143.0
178.0
298.0
334.0
602.0
643.0
426.0
685.0
Xij
56.4
45.3
25.7
82.0
127.0
169.0
22.5
251.0
288.0
63.6
96.1
63.4
159.0
183.0
201.0
17.8
218.0
238.0
314.0
334.0
617.0
643.0
426.0
685.0
Sub -basin
i
1
2
3
4
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Ri
186.0
7.5
136.0
25.5
96.1
39.1
121.0
3.5
61.0
99.0
80.3
6.8
49.0
35.9
52.4
61.7
40.9
58.5
Si
130.0
7.4
48.2
0.0
17.0
23.3
0.0
3.5
1.8
35.6
57.4
3.4
69.7
18.1
17.3
25.7
0.0
16.0
Si
130.0
7.4
48.2
0.0
17.0
28.3
0.0
3.5
1.8
35.6
57.4
3.4
69.7
18.1
17.3
25.7
3.1
16.0
*Xij * Xij
Table 2. Summary of Model Results Sub-basin Storage and Costs
Sub-basin
1
2
3
4
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Flood Plain
Total
Storage Volume Used
(100,000 ft3)
13.8
86.6
0.0
37.4
37.9
0.0
0.0
106.0
0.0
34.8
11.8
28.2
0.0
13.2
0.0
0.0
0.0
87.6
483.0
940.3
Storage Capacity
(100,000 ft3)
200.0
94.0
136.0
62.9
37.9
39.3
121.0
110.0
61.0
134.0
92.1
35.1
49.0
49.1
52.4
61.7
40.9
146.0
475.0
1997.4
Storage Cost
($)
484,000
3,030,000
0
1,310,000
45,000
0
0
3,720,000
0
1,220,000
412,000
989,000
0
462,000
0
0
0
3,060,000
395,000
15,127,000
142
-------
These results are given only as an example of how the
model can be utilized. In actual practice, the model
should be run several times to evaluate the effects of
different land use projections and different design
storm events. Several runs with varied inputs would
provide insight into the sensitivity of the storage
allocations and resulting costs. For example, sub-
basin 1 at the very top of the drainage system has a.
greater total potential runoff volume than any other
sub-basin (more than twice the average for any sub-
basin) . What would be the effect of a decision to
maintain that area in a more natural state rather than
allowing residential development? The resulting cost
difference could be significant due to the location
of sub-basin 1 and the large increase in potential run-
off volume caused by development. Also of interest may
be the cost difference of providing the necessary
storage for a one year storm rather than the three year
event considered in this example.
For this example, the model was run utilizing limited
information on the availability and cost of storage.
Presently, a great deal more information is available
on the cost of storage alternatives. Also, as indi-
cated by the model results, utilization of the flood
plain water detention sites and marsh land may provide
the most cost-effective solution to controlling storm
water runoff. Therefore, more emphasis should be
given to considering the availability of natural
storage areas within the various sub-basins. Certainly,
the model is better utilized when the sub-basin alter-
native storage costs differ, as they would in
evaluating various natural depression sites which might
exist throughout the watershed.
The results for this example show that the fixed costs
for providing storage within the flood plain and in
sub-basin 7 are a small percentage of the total costs.
For other situations, this may not be the case. How-
ever, if fixed costs are not considered significant,
or if they can be reasonably estimated as variable
cost, the model can be greatly simplified and more
easily solved. The model presented can be easily
altered for considering only variable costs by elimi-
nating the integer variables and zero-one inducement
constraints.
Conclusions
The mixed integer programming model provides an
efficient method for allocating urban storm water run-
off among alternative storage sites and can also be
used to compare land use and drainage options within an
urbanizing watershed where it is important to include
fixed charges. The effort required to utilize the
decision model as a planning tool is weighted heavily
towards data collection; e.g., storage site locations
and capacities, hydrologic simulation, land use, and
can be used most easily where existing planning has
already developed much of the input data requirements.
Unless a significant portion of the cost associated
with storage alternatives are fixed, the use of a
mixed-integer model as presented appears to make the
solving of the model more difficult than is necessary.
Where all costs can be assumed to be a variable, the
model can be greatly simplified by dropping the zero-
one variables and constraints. This type of decision
model should be used after more simplified approxi-
mations have been developed. These simpler approxi-
mations should be adequate for most planning studies.
More refined procedures such as this mixed integer
programming model can be used in specialized cases.
References
1. Poertner, H. G. , On-Site Detention of Urban Storm-
water Runoff, OWRR, USDI, 1973.
2. Hasan, S. M., Integrated Approach to Urban Waste-
water Quality Management, PhD Dissertation,
University of Florida, Gainesville, 1976.
3. Doyle, J. R. , Evaluation of Land Use Alternatives
to Control Urban Storm Water Quality, ME Thesis,
University of Florida, Gainesville, 1973.
4. United States Department of Agriculture, Soil Map
for Alachua County, Florida, University of Florida
Agriculture Experiment Station, 1954.
5. Soil Conservation Service, SCS National Engineering
Handbook, Section 4—Hydrology, USDA, Washington,
DC, 1972.
6. Herrera, S. D., "Floodplain Definition in a
Developing Urban Area," Masters Thesis, University
of Florida, Gainesville, 1973.
7. Vargas, C., "Evaluation of Area Parameters Con-
trolling Stormwater Runoff in the Hogtown Drainage
Basin," Masters Thesis, University of Florida,
Gainesville, 1972.
8. Planning Division, Department of Community Develop-
ment, "Land Use Plan, Gainesville Urban Area,"
Gainesville, Florida, 1970.
143
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JOINT USE OF SWMM AND STORM MODELS
FOR PLANNING URBAN SEWER SYSTEMS
Herbert L. Kaufman
Partner
Clinton Bogert Associates
Fort Lee, New Jersey
Fu-Hsiung Lai
Group Supervisor and Project Engineer
Clinton Bogert Associates
Fort Lee, New Jersey
A joint use of the SWMM and STORM models was
demonstrated to provide a tool for sewer system plan-
ning which effectively alleviates urban flooding and
prevents pollution in the receiving waters. Techniques
were developed for projection of runoff characteristics
from one drainage district to others for citywide
sewer planning.
A concept making use of the characteristics of
runoff quantity and quality and interceptor capacity
for cost-effective pollution control is described.
The pollutants discharged to receiving waters for
various interceptor capacities have been comparatively
quantified.
Introduction
In the past, concern with storm runoff was mainly
over the street and basement flooding and sewers were
installed to correct the problem. With the recognition
of the pollution problems associated with storm runoff,
reduction of pollution reaching natural water bodies
has become increasingly desirable.
Elimination of all pollution from wet weather
flow could be prohibitively expensive nor is it nec-
essary to prevent damage to the environment. The
marginal benefit received by society usually diminish-
es with each additional increment of pollution abate-
ment facility provided. Hence, there exists an opti-
mal level of expenditure for pollution control that
society should plan to provide. The determination of
this optimal level depends upon many factors, includ-
ing (1) the degree of flood protection justified, (2)
the characteristics of real storm runoff, (3) the
combined sewage quantity and quality and the character
of the receiving waters.
Because of the complex nature of the urban rain-
fall-runoff and pollutant accumulation-washout-trans-
port processes, and the many management alternatives,
reliance on computer models to assist in the system
simulation becomes advantageous. There are at least
16 mathematical models developed which permit the
planning of sewer systems to alleviate urban flooding,
and prevent pollution in the receiving waters.^>2,3
Of these models, the EPA Storm Water Management
Model,"4 frequently abbreviated "SWMM" and the Corps of
Engineers' Storage, Treatment, and Overflow Model^.
abbreviated as "STORM", are probably the most useful
and comprehensive for urban sewer system design and
planning. These two models consider both runoff
quantity and quality.
The SWMM Model can simulate rainfall-runoff
processes in fine scale, both spatially and temporally,
and route storm runoff quantity and quality from
individual catchments and subcatchments through a
sewer pipe network. It can be used to analyze or
design a sewer system for an actual or synthetic storm
event. It can also be adapted for planning studies.
The STORM Model can economically analyze hourly runoff
quantity and quality for long-term precipitation
records, based on such parameters as percent imper-
viousness and land use. It has been used to evaluate
the effectiveness of storage and treatment facilities
for overflow pollution control6. Unlike the SWMM
Model, which considers overland and sewer flow rou-
ting, no such routing is made in the STORM Model.
The existing SWMM Model requires the use of short
time intervals (minutes) for routing runoff quantity
and quality. It cannot be used for simulation or
analysis based on long-term precipitation data. The
STORM Model, while it can provide a time history of
overflows for a given storage and treatment capacity
for continuous rainfall data recorded hourly, does not
model the collection and conveyance system which is an
essential part in a cost-effective study.
The advantage of joint use of the SWMM and STORM
Models has been demonstrated in the current study to
establish the optimum design for possible alternative
sewer systems for the City of Elizabeth, New Jersey.
This paper will attempt to demonstrate the advantage
of using these two models, somewhat modified, jointly
for flood control and pollution abatement.
The design of sewer system components was based
on (1) protecting the urban area from flooding by a
storm with a 5-year return frequency, and (2) provid-
ing interceptor, storage and treatment facilities to
optimally minimize the frequency of, and the pol-
lutants in, the untreated overflows. The amount and
frequency of overflow that can be tolerated would
depend upon the characteristics of the overflow and
the assimilating capacity of receiving waters. As far
as the environmental effects are concerned, the more
frequently occurring rainfalls appear to cause greater
impact on the receiving waters than the more intensive
storms with return frequencies greater than one-year.
Hence, design of storage and treatment facilities and
interceptor sewers would be based on real rainstorms
which could be no more intense than a one-year return
frequency storm.
Description of Study Area
The study area consists of the City of Elizabeth,
New Jersey. Data developed through modeling of Drain-
age District A was through correlation of STORM and
SWMM applied to planning for the entire City. Figure
1 shows the location of the study area.
The 4400 acres of urban development are served by
25 drainage districts. The population of the City is
close to saturation and is expected to have only a
moderate future growth. The land uses in District A
are predominantly residential (about 90 percent),
with some neighborhood commercial (about 5 percent)
and small industrial areas (about 3 percent). The
relevant land use data are shown in Table 1. The
district has an estimated population of 16,500, or
about 25 persons per acre. Its impervious area equals
47 percent of the total.
The existing sewer system in the City is of the
combined type. The sewers are old and undersized, as
144
-------
FIGURE 1. Study Area
forwarded to the Hydrologic Engineering Center (EEC)
of the Army Corps of Engineers for incorporation in
the new version of STORM to be released.
Quantity and Quality Considerations
Differences between SWUM and STORM in the consid-
eration of storm runoff quantity and quality are worth
noting.
Quantity
In STORM, runoff volume from the watershed is
calculated on an hourly basis as a function of rain-
fall plus snowmelt. Losses of rainfall and/or snow-
melt volume due to infiltration in the watershed are
accounted for by the use of a runoff coefficient C. C
is derived from two basic coefficients, C^ and C2- GI
represents the runoff coefficient for pervious areas
and C2 for impervious areas. For a given watershed,
knowing the land uses, the amount of depression storage
averaged over the watershed and the amount of rainfall
and snowmelt, C can be calculated from C^ and C2 to
determine the amount of runoff. There is no runoff
from the watershed until the detention storage, which
is uniformly applied to the entire watershed, is
filled.
TABLE 1
DRAINAGE DISTRICT A LAND USE DATA
Land Use
Single Family
Multiple Family
Commercial
Industrial
Open Space
% of
Area
71.7
18.2
5.3
2.8
2.0
% Imper- Curb Length
vious (Ft/Acre)
43
50
80
80
19
413.
298.
283.
216.
296.
is the Westerly Interceptor which parallels the Eliza-
beth River. There are numerous complaints of street
and basement flooding. Overflows to the Elizabeth
River are frequent.
Secondary treatment facilities are now under con-
struction at the Joint Meeting Plant. The City has
allocated to it a peak wet weather flow capacity of 40
million gallons per day (mgd). The Corps of Engineers
has also planned a diked storage area, with a total
capacity of about 21 million gallons, along the Eliza-
beth River near the Joint Meeting Plant.
The Elizabeth River is tidal from its mouth to
the Penn Central Railroad. The river, which drains
about 23 square miles, does not provide adequate dilu-
tion for the untreated initial overflows of combined
sewage.
Modification of SWMM and STORM Programs
In addition to continuous updating of the models
as revisions become available, both models were modi-
fied. The SWMM program was modified to allow design
capability with gutter pipes surcharged. This elimi-
nated revising the input sewer dimension for the
elimination of such surcharge.
The STORM program was modified to include a dry
weather flow routine for simulation of combined sewage
overflows. Input data allow diurnal hourly variation
of dry weather flow quantity and quality for various
land uses. A copy of the program changes has been
In SWMM, runoff volume over a fine time interval
is made by using a number of overland flow elements to
simulate the initial collection processes. The
amount of runoff from pervious and impervious areas is
separately considered. Infiltration loss from per-
vious areas is computed using Morton's equation. In
addition, rainfall on a certain percent of impervious
areas results in immediate runoff and enters the sewer
system without time delay and loss of volume. This is
true regardless of the amount of rainfall since dwell-
ings, such as those in Elizabeth with pitched roofs,
have roof drains directly connected to a street gutter.
SWMM uses a more valid concept of the hydraulics
of rainfall-runoff processes than STORM. Parameters
required for SWMM Model can be reasonably estimated.
The model has been applied to a number of watershed
in the United States' >8 and the accuracy of the runoff
quantity computations has been relatively good. If a
watershed is segmented properly, SWMM can be used for
runoff prediction in urban areas.
The significant advantage of STORM is its ability
to analyze input from long-term rainfall records to
evaluate overall rainfall pattern effects.
Neglecting land surface erosion and dry weather
flow, both SWMM and STORM compute street pollutant
washout by storm runoff according to the amount of
dust and dirt accumulated along the street curbs prior
to the occurrence of a storm. From the total pounds
of dust and dirt washout, the pollutant components
such as suspended solids (SS) and BOD are computed
either for the available local data or from specified
default values. In study areas where quantity and
quality data are not available for evaluating pollutant
parameters, default values specified to either program
could be used.
Both SWMM and STORM use the same default values
for most of the pollutant calculations except for SS
and BOD. The value used by SWMM for suspended solids
is about ten times and for BOD, about 5 times that
used by STORM. More discussions and comparisons of
runoff quality computation can be found in the re-
ference^.
145
-------
As SWMM is an event simulator and STORM an
analytical tool for long-term rainfall records, the
computations of street dust and dirt accumulation with
dry days and street sweeping are different. Figure 2
shows that pollutant accumulation as computed by SWMM
increases monotonically with the number of antecedent
dry days for an assumed seven-day street sweeping
interval. The pollutant accumulation calculated by
STORM indicated periodical fluctuation of S3 accumula-
tion at the street curb reflecting the effect of
street cleaning frequency and the number of dry days
since the last street cleaning. In SWMM, additional
accumulation of dust and dirt on the street curb is
assumed to be equal to the maximum accumulation for
the period between successive street sweeping. It
does not credit the cleaning effects of street sweeping.
Recognition of this difference is significant when
making comparison of runoff quality from a single
storm event with two models.
£ looo-
I
DRAINAGE AREA = 55 ACRES
STREET SWEEPING INTERVAL =
SWEEPING EFFICIENCY -075
CURVE I - SWMM USING SWMM DEFAULT \fflLUES
CURVE 2- STORM USING SWMM DEFAULT VALUES
CURVE 3- SWMM USING STORM DEFAULT VALUES
CURVE 4- STORM USING STORM DEWULT VALUES
-.**^\ --.-~~ \^---s
10 15 20
NUMBER OF DRY DAYS
The following assumptions were made in the cali-
bration of Cj and C2-
1, Surface runoff data was generated by a program
adapted from the SWMM RUNOFF Block without gutter
routing. This is consistent with the STORM
program, in which the effect of gutter flow is
not considered.
2. The depression storage capacities for pervious
and impervious areas used in SWMM were 0.25 and
0.062 inches, respectively. 25 percent of the
impervious area was assumed to have no detention
storage. The equivalent depression storage for
District A was computed as 0.155 inches, based
upon 47 percent of the area being impervious.
3. The infiltration capacity curve shown in Figure 3
was used in SWMM to account for the infiltration
loss. A maximum rate of infiltration of 3.0
in/hr, a minimum of 0.28 in/hr, and a decay rate
of 0.00138/sec was used. The antecedent condi-
tions for rainfall events were such that the
infiltration curve specified applied. Assumption
for STORM is that the depression storage capacity
of 0.155 inches is available prior to the begin-
ning of the rainfall event.
TIME IN MINUTES
FIGURE 3. 5-Year Storm Hyetograph and Infiltra-
tion Curve
FIGURE 2. Street SS Accumulation, SWMM Vs. STORM
As the use of SWMM generally requires fine time
interval for rainfall input and flow routing, rainfall
intensity during the course of a rainstorm may be
greater than hourly rainfall intensity required for
STORM. Higher intensity of rainfall would mean greater
pollutant washout from streets.
Calibration of STORM Runoff Coefficient
Runoff coefficients, C-^ and C2 respectively, for
pervious and impervious areas, used in STORM, were
calibrated using data generated by SWMM in District A.
These coefficients were applied to other drainage
districts in the City to obtain runoff volume from
synthetic or real rainstorms.
For use of SWMM, District A was subdivided into
279 subcatchments with an average area of 2.3 acres.
The surface runoff from these subcatchments drains
into 139 gutter pipes and subsequently to 32 trunk
sewers. The downstream end of the sewer system con-
nects to the Westerly Interceptor.
4. A typical rainfall event is assumed to have
three-hour duration and an intermediate pattern
similar to the 5-year design storm with hourly
interval as shown in Figure 3. In fact, use of
2-minute hyetograph or of 1-hour hyetograph
results in little difference in total surface
runoff volume from 3-hour rainfall event. The 5-
year storm has the average 1-hour, 2-hour, and 3-
hour rainfall intensities of 1.6, 1.05 and 0.81
inches' per hour respectively.
5. The runoff coefficient, C^, for the impervious
area, was set equal to 1.0, since there is no
infiltration loss for an impervious area and the
depression storage is accounted for separately.
The runoff coefficient for pervious area C^ is
calibrated so that the 3-hour storm runoff volume
computed with the adapted SWMM program is the same as
that computed with the STORM program. The calibrated
Ci values are shown in Figure 4 as a function of 3-
hour rainfalls. As anticipated, C^ increases with an
increase in the amount of rainfall (or average rain-
fall intensity) over the specified duration. For the
146
-------
5-year design storm used in the study, with a total
rainfall of 2.43 inches or an average intensity of
0.81 inches per hour, a C-^ value of 0.55 would be
appropriate. For other rainfall amounts, such as 0.6,
1.38, and 4.86 inches (or intensities 0.2, 0.46 and
1.62 inches per hour respectively), the appropriate C±
values are 0.25, 0.3 and 0.78. 0.6 and 1.38 inches of
rainfall respectively correspond to a storm return
interval of 1.3 month and 1 year, based on the analysis
of hourly rainfall data recorded at the Newark
International Airport from 1963 to 1974. 85 percent
of rainfall during that period has an amount less than
0.6 inches.
X DATA POINT
RUNOFF COEF. FOR IMPERVIOUS AREA'1.0
3-HR. RAINFALL (INCHES)
FIGURE 4. STORM Runoff Coefficient Vs. Rainfall
Considering that the runoff coefficient, C^,
increases with the amount of rainfall and STORM assumes
a constant runoff coefficient for the entire time span
of records to be simulated regardless of the rainfall
volume or intensity, a C;L value of 0.25 was proposed
for the simulation of long-term rainfall records for
overflow pollutional evaluation. Reducing C^ value to
0.15 results in a nine percent reduction in the mass
volume of overland flow from District A using 12-year
data. The amount of pollutant washout from streets is
independent of Ci^. It therefore is apparent that the
selected C-^ value of 0.25 should provide sufficiently
consistent results from the STORM program to permit
valid engineering evaluation.
Generation of 5-Year Design Storm Runoff Hydrograph
As mentioned earlier, the City has 25 drainage
districts with District A the largest in area.
Cltywlde planning requires development of a runoff
hydrograph and pollutograph from each drainage basin
for storms of interest. These runoff hydrographs and
pollutographs are required for cost effective sizing
of intercepting sewers, storage and treatment facili-
ties. Upstream collection sewers in each drainage
district are adequately sized so that street and/or
basement flooding would be prevented for a design
storm with a 5-year return interval.
A 5-year storm runoff hydrograph for all drainage
districts could be obtained by making a. detailed sewer
layout and by segmenting the catchment and preparing
land use data in each district. The amount of work
involved is usually more than required or justified
for master planning. An alternative is to make a
detailed study in one district for projection to other
drainage districts.
Storm runoff and sewer routing in District A were
analyzed using SWMM. Overland and gutter flows were
analyzed with the SWMM RUNOFF Block and trunk sewer
flow with or without sanitary wastes with the SWMM
TRANSPORT Block. Catchment and land use data were
prepared to the necessary detail for accuracy.
Although there are existing combined sewers in District
A, they are totally inadequate in size. The new sewer
system was designed to convey the total 5-year storm
runoff. Existing sewer data, however, were used in
preparing sewer layout, slope, and other pertinent
sewer information.
The two primary factors governing the shape and
rate of the routed hydrograph for a given drainage
basin are area and percent of imperviousness. The
area affects mainly the extent of flow attenuation and
the peaking time of a hydrograph. The land use, and
consequently percent of imperviousness, affects mainly
the runoff volume. Normalized hydrographs, based on
information developed for District A, were used to
determine hydrographs for other drainage districts.
Comparison of the normalized hydrographs within
the range of drainage areas to be analyzed showed the
effect on the hydrograph shape of percent of imper-
viousness or equivalently, the land uses to be insig-
nificant. To represent the variation of hydrograph
shape with drainage area, five normalized hydrographs
were used. Two of the normalized hydrographs are shown
in Figure 5, one for a drainage area greater than 500
acres and one for a drainage area less than 150 acres.
Figure 5 also shows the larger drainage area to have a
hydrograph with greater spread and delayed peaking
time.
DRAINAGE AHErt > 300 ACRES
0 20 40 GO 80 100 I2O I4O 160 180
FIGURE 5. Normalized Hydrographs
The 5-year storm runoff volume in drainage
districts other than District A was obtained with the
STORM program, using the calibrated runoff coefficient
0.55 for pervious area and 1.0 for impervious area and
the available land use data. Dividing the runoff
volume by the integrated area enclosed by the appro-
priate normalized hydrograph permitted estimation of
the outflow hydrograph.
Figure 6 shows three computed outflow hydrographs
expressed in cubic foot per second per acre. It
illustrates the effect of drainage area combined with
the percent of imperviousness on the shape and peak
runoff rate per acre.
Planning Interceptors For Pollution Control
Conveyance of 5-year storm runoff by interceptors
to storage for later treatment would not only be
prohibitively costly but also is not required to
prevent pollution. Pollutional effects from a storm
occurring, on the average, once in five years, would
not cause as much damage as a storm occurring monthly.
147
-------
CURVE I—655 ACRES, 47% IMR
CURVE 2— 229 ACRES, 57 % IMR
CURVE 3—[22 ACRES,73%IMR
30 40 50 60 70 80 90 IOC
TIME SINCE START OF STORM
130 140 150 160
FIGURE 6. Computed Outflow Hydrographs
To determine the quantity of runoff to be stored and
treated, the characteristics of storm runoff and
combined sewage quantity and quality were investigated.
SWMM was used to obtain the storm runoff and
combined sewage quantity and quality from District A.
Average conditions of four antecedent dry days, a
seven-day street sweeping interval and 75 percent
sweeping efficiency were assumed. Quantity and
quality of dry weather flow used are in conformance
with the EPA Studyl°. In computing suspended solids
from street dust and dirt washout, STORM default
values were used.
In addition to the 5-year storm, runoff from a 1-
year and a 1.3-month storm was analyzed. The rainfall
characteristics of these two storms were obtained
using a partial duration series analysis of hourly
data for a 12 year period. They were also assumed to
have the same pattern as the 5-year storm. Figure 7
shows the 5-year storm hydrograph and pollutographs
from District A. Runoff from 1-year and 1.3-month
storms has characteristics similar to the 5-year storm,
with the difference basically in the magnitude of flow
and pollutant loading.
Curve A of Figure 7 is the outflow hydrograph
which maintains a relative low value until one hour
after the rainfall starts. Curves B and C respect-
ively show the suspended solids (SS) concentration
(mg/1) and rate (pounds per minute) of combined sewage
outflow. The SS concentration of storm runoff without
sanitary wastes is shown in Curve D.
Curve C illustrates the existence of two flushes
in a combined sewer. The first flush ends about 50
minutes from the start of the storm when the flow rate
is computed at 207 cfs and the concentration of sus-
pended solids is 25 mg/1. This flush is mainly
attributed to the deposit of solids in combined sewers
from sanitary wastes during dry days. The second
flush ends about 40 minutes later when the flow rate
is estimated at 850 cfs. This flush represents
mainly the street pollutant washout. To contain the
first flush, a storage volume equivalent to 0.063
inches of rainfall over the entire area of District A
is required. For containment, of the second flush,
however, 0.906 inches of storage would be necessary.
Curve B, which sets forth the concentration of
the pollutant discharge, permits drawing significant
conclusions. There is only one peak polluting dis-
charge which ends about 56 minutes from the beginning
of rainfall. The peak polluting discharge is defined
as one containing a SS concentration of more than 20
mg/1. The flow rate is computed as 249 cfs at that
time. The storage volume required to contain this
first flush is 0.098 inches over the entire drainage
22-i
10
20
FIGURE 7.
30 40 50 60
TIME SINCE START OF STORM (MINUTES)
5-Year Storm Hydrograph and Pollutographs
70
80
90
148
-------
basin. Hence, because of the low concentration of
pollutants found in the second flush shown in Curve C,
its containment does not appear justified.
For containment of the first flush (as previously
defined), from the 1-year storm, the magnitude of
intercepted flows from District A was computed as 549
cfs and the required storage equal to 0.144 inches.
If the criteria for the first flush limit is increased
to 22 mg/1 of SS, the design requirement reduces to
153 cfs and 0.055 inches. For the 1.3-month storm,
the computed flows are 213 cfs and a storage of .103
inches for the defined first flush limitation.
Dividing regulated flows of 35, 153, 207, 249,
and 549 cfs by the unregulated 5-year storm peak
outflow of 1406 cfs, the ratios of regulated peak out-
flow to unregulated 5-year storm peak outflow are
0.0249, 0.1088, 0.1472, 0.1771, and 0.3905 respec-
tively. Applying these ratios to the 5-year storm
runoff hydrographs for other drainage districts, the
inflow hydrographs to interceptors were obtained for
various degrees of runoff control.
Runoff from the City's twenty-five drainage
districts was assumed to drain into interceptors at 14
inlet locations. The SWMM Transport Block was used
for sizing of interceptors for conveyance of regulated
flow to a storage basin near the treatment plant.
STORM was also used for Drainage District A to
analyze the 12-year (1963-1974) hourly precipitation
data to obtain annual statistics of overflow events
and pollutional loadings for various amounts of flow
intercepted for treatment.
Figure 8 shows at various ratios of interceptor
capacity the (1) combined sewage SS concentration
discharged to receiving waters, (2) annual number of
overflow events from District A, and (3) cost of
pumping facilities for storage and interceptor
facilities. Data for storms with a return frequency
of 5 years, 1 year and 1.3 months is shown. Other
costs do not vary with the ratio of interceptor ca-
pacity to peak design storm flow.
OVERFLOW CONCENTRATION (SWUM)
OVERFLOW EVENT (STORM)
0,-REGULATED 5-YR. STORM PEAK OUTFLOW
02-UNREGULATED 5-YR. STORM PEAK OUTFLOW
o^
££
-10 z^
gS
is
0.2 0.3 0.4
QI/OZ
FIGURE 8. Cost-Effective Pollution Control
Considerations
For interceptor capacity to peak flow ratio of
0.0249, inadequate control of pollution would be
experienced.
At a ratio of 0.1088, the cost is estimated at
$39.4 million, with discharge SS concentration of 40,
22, and 30 mg/1 respectively for the 5-year, 1-year
and 1.3-month storms. The number of annual overflow
events extending one hour or more is 6.6. These
events would discharge a total of 2702 Ibs. of SS and
620 Ibs. of BOD. An increase of the ratio to 0.1472
increases costs by 15 percent to $45.5 million, but
reduces the overflow SS concentrations to 25, 21.4 and
26.7 mg/1 for the three storms respectively and the
number of annual overflow events of one hour or more
duration to 3.8. These would contain a total of 1150
Ibs. of SS and 260 Ibs. of BOD. However, short duration
overflows would still occur with the 1.3-month storm.
Further increase of the ratio to 0.1991 would increase
cost by less than 5 percent to $47.6 million but would
eliminate overflow from 1.3-month storm. The number
of annual overflow events of one hour or more would be
2.3. Further increase in the ratio and its capital
cost increment would result in insignificant return in
pollution control. Conveyance of uncontrolled 5-year
storm runoff would cost as much as $121 million.
Based on the above discussions, the range of cost-
effective interceptor flows for pollution control
would be from 10 to 18 percent of the peak 5-year
storm runoff with the planned storage and treatment
capacity available in Elizabeth.
Conclusions
A joint use of the SWMM and STORM models was
demonstrated to provide a useful tool for planning
sewer systems for cost-effective flood control and
pollution abatement.
The study shows that intercepting flows from 10
to 18 percent of the peak 5-year design storm runoff
would be within the range of being cost-effective and
would adequately intercept the most significant part
of runoff pollutants.
Acknowledgements
The study described in this paper was undertaken
for the City of Elizabeth, New Jersey and financed in
part with Federal funds from the Environmental Protec-
tion Agency under Demonstration Grant No. S-802971.
The writers wish to acknowledge the valuable
suggestions during the course of the study by Messrs.
Richard Field and Anthony N. Tafuri, Chief and Project
Officer respectively, Storm and Combined Sewer Section,
Advanced Waste Treatment Research Laboratory, U.S.
Environmental Protection Agency. Dr. Brendan M.
Harley, Dr. Guillermo J. Vicens and Mr. Richard L.
Laramie of Resource Analysis, Inc., Cambridge, Mass-
achusetts and Mr. Gerald G. Gardner of Clinton Bogert
Associates have provided considerable input during the
course of the study.
References
1. ASCE Urban Water Resources Research Program Tech.
Memo. No. IHP1, "Urban Mathematical Modeling and
Catchment Research in the U.S.A.", 345 East 47th
Street, N.Y., N.Y. 10017, June, 1975.
2. Huber, Wayne C, "Modeling for Storm Water Strate-
gies", APWA Reporter, May 1975.
3. Torno, Harry C., "Storm Water Management Models"
Conference Proceedings, Urban Runoff Quantity and
149
-------
Quality, held at Franklin Pierce College, Rindge,
New Hampshire, August 11-16, 1974.
4. Metcalf and Eddy, Inc., University of Florida and
Water Resources Engineers, Inc. "Storm Water
Management Model" Four Volumes, Environmental
Protection Agency, Water Quality Office, Report
No. 11024DOC07/71 to 11024DOC10/71 , 1971.
5. Hydrologic Engineering Center, Corps of Engineers,
"Urban Storm Water Runoff: STORM", Generalized
Computer Program 723-S8-L2520, October 1974.
6. Water Resources Engineers, the Hydrologic Engi-
neering Center and Dept. of Public Works, City of
San Francisco, "A Model for Evaluating Runoff-
Quality in Metropolitan Master Planning.", ASCE
Urban Water Resources Research program, Tech.
Memo No. 23, ASCE, 345 East 47th Street, N.Y.,
N.Y. 10017, April 1974.
7. Environmental Protection Agency and University of
Massachusetts, "Application of Stormwater Manage-
ment Models-1976"; A short course held at Pacific
Grove, California, January 5-9, 1976.
8. Jewell, T.K., P.A. Mangarella, and F.A. DiGiano,
"Application and Testing of the EPA Stormwater
Management Model to Greenfield, Massachusetts",
Proceedings, National Symposium on Urban Rainfall
and Runoff and Sediment Control, Lexington,
Kentucky, July 26-31, 1974.
9. Huber, Wayne C., "Differences Between Old and New
Runoff Quality Models", Memo to N682 File, Grant
R802411, May 28, 1974.
10. Environmental Protection Agency, "Water Quality
Studies", Water Program Operations Training
Program, PB-237 586, May 1974.
150
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SIMULATION OF AGRICULTURAL RUNOFF
Anthony S. Donigian, Jr.
Hydrocomp, Inc. Palo Alto, CA
Norman H. Crawford
Hydrocomp, Inc. Palo Alto, CA
Abstract
The Agricultural Runoff Management (ARM) Model described
in this paper simulated runoff, snow accumulation and
melt, sediment loss, pesticide-soil interactions, and
soil nutrient transformations on small agricultural
watersheds. The results of Model testing for simulation
of runoff, sediment, and pesticide loss are presented to
demonstrate possible uses of the ARM Model as a tool for
evaluating the water quality impact of agricultural
practicies.
Introduction
The development of models to simulate the water quality
impact of nonpoint source pollutants is receiving
considerable attention by the engineering and scientific
community. One of the major reasons for this interest
is the passage of the Federal Water Pollution Control
Act Amendments of 1972, specifically requiring the
evaluation of the contribution of nonpoint source
pollution to overall water quality. This paper
describes a modeling effort whose goal is the simulation
of water quality resulting from agricultural lands. The
beginnings of this research modeling effort date from
1971 when the U.S. Environmental Protection Agency,
through the direction of the Environmental Research
Laboratory in Athens, Georgia (ERL-Athens), sponsored
the development and initial testing of the Pesticide
Transport and Runoff (PTR) Model (1). The Agricultural
Runoff Management (ARM) Model discussed in this paper is
the combined result of further model testing and
refinement, algorithm modifications, and inclusion of
additional capabilities not present in the PTR Model.
The ultimate goal of the continuing ARM Model
development effort is the establishment of a methodology
and a tool for the evaluation of the efficacy of
management practices to control the loss of sediment,
pesticides, nutrients, and other nonpoint pollutants
from agricultural lands.
Modeling Philosophy
The guiding philosophy of the modeling effort is to
represent, in mathematical form, the physical processes
occurring in the transport of nonpoint pollutants. The
hydrologic and water quality related processes occurring
on the land surface (and in the soil profile) are
continuous in nature; hence, continuous simulation is
critical to the accurate representation of these
physical processes. Although nonpoint source pollution
from the land surface takes place only during
runoff-producing events, the status of the soil moisture
and the pollutant prior to the event is a major
determinant of the amount of runoff and pollutants that
can reach the stream during the event. In turn, the
soil moisture and pollutant status prior to the event is
the result of processes that occur between events.
Cultivation and tillage practices, pesticide and
fertilizer applications, pesticide degradation and
nutrient transformations, all critically affect the mass
of pollutant that can enter the aquatic environment
during a runoff-producing event. Models that simulate
only single events cannot accurately evaluate
agricultural land management practices since
between-event processes are ignored. Although all
between-event processes cannot be precisely described at
the present state of technology, continuous simulation
provides a sound framework for their approximation and
for further research into their quantification.
When modeling nonpoint source pollution, the above
stated philosophy is joined by the fact that the
transport mechanisms of such pollutants are universal.
Whether the pollutants originate from pervious or
impervious lands, from agricultural or urban areas, or
from natural or developed lands, the major transport
modes of runoff and sediment loss are operative. (Wind
transport may be significant in some areas, but its
importance relative to runoff and sediment loss is
usually small.) In this way, the simulation of nonpoint
source pollution is analogous to a three-layered
pyramid. The basic foundation of the pyramid is the
hydrology of the watershed. Without accurate simulation
of runoff, modeling nonpoint pollutants is practically
impossible. Sediment loss simulation, the second layer
of the pyramid, follows in sequence the hydrologic
modeling. Although highly complex and variable in
nature, sediment modeling provides the other critical
transport mechanism. The pinnacle or final layer of the
pyramid is the interaction of various pollutants with
sediment loss and runoff, resulting in the overall
transport simulation of nonpoint source pollutants.
The Agricultural Runoff Management (ARM) Model
The ARM Model simulates runoff (including snow
accumulation and melt), sediment, pesticides, and
nutrient contributions to stream channels from both
surface and subsurface sources. No channel routing
procedures are included. Thus, the Model is applicable
to watersheds that are small enough that channel
processes and transformations can be assumed negligible.
Although the limiting area will vary with climatic and
topographic characteristics, watersheds greater than one
to two square miles are approaching the upper limit of
applicability of the ARM Model. Channel processes will
significantly affect the water quality in larger
watersheds.
Figure 1 demonstrates the general structure and
operation of the ARM Model. The major components of the
Model individually simulate the hydrologic response
(LANDS) of the watershed, sediment production (SEDT),
pesticide adsorption/desorption (ADSRB), pesticide
degradation (DEGRAD), and nutrient transformations
(NUTRNT). The executive routine, MAIN, controls the
overall execution of the program; calling subroutines at
proper intervals, transferring information between
routines, and performing the necessary input and output
functions.
e 1 ARM model structure and operation
INPUT
OUTPUT-
MAIN
nEcunvc
-CHECKR CHic« »pn s[oi[«ci
-NUTRIO HID MIIIIiNI MPUI
-OUTMON, OUTYR oiim somuns
PEST——
ADSRB
P(STICID[ AD
AND mom
SORPTION
151
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In order to simulate vertical movement and
transformations of pesticides and nutrients in the soil
profile, specific soil zones (and depths) are
established so that the total soil mass in each zone can
be specified. Total soil mass is a necessary ingredient
in the pesticide adsorption/desorption reactions and
nutrient transformations. The vertical soil zones
simulated in the ARM Model include the surface, upper,
lower, and groundwater zones. The depths of the surface
and upper soil zones are specified by the Model input
parameters, and are generally 3-6 mm and 75-150 mm,
respectively. The upper zone depth corresponds to the
depth of incorporation of soil-incorporated chemicals.
It also indicates the depth used to calculate the mass
of soil in the upper zone whether agricultural chemicals
are soil-incorporated or surface-applied. The depths of
the surface and lower zones are important because the
active surface zone is crucial to the washoff and
degradation of agricultural chemicals, while the extent
of the lower zone determines to what degree soluble
pollutants will contaminate the groundwater. The lower
zone depth is presently specified as 1.8 meters (6
feet). However, the zonal depths will vary with the
geology and topography of the watershed. Further
evaluation of these zones is presently in progress.
The transport and vertical movement of pesticides and
nutrients, as conceived in the ARM Model, is indicated
in Figure 2. Pollutant contributions to the stream can
occur from the surface zone, the upper zone, and the
groundwater zone. Surface runoff is the major transport
mechanism carrying dissolved chemicals, pesticide
particles, or sediment and adsorbed chemicals. The
interflow component of runoff can transport dissolved
pesticides or nutrients occurring in the upper zone.
Vertical chemical movement between the soil zones is the
result of infiltrating and percolating water. From the
surface, upper, and lower zones, uptake and
transformation of nutrients and degradation of
pesticides is allowed. On the watersheds tested, the
groundwater zone has been considered a sink for deep
percolating chemicals since the groundwater flow
contribution has been negligible. However, on larger
watersheds this contribution could be significant.
Figure 2 Pesticide and nutrient movement in the ARM model
Model Algorithms
The algorithms, or equations, used to describe the
processes simulated by the ARM Model are fully discussed
in the final project report (2). A brief presentation
of the general methodology is included here.
Hydrology
Hydrologic simulation by the LANDS subprogram is derived
from modifications of the Stanford Watershed Model (3)
and the Hydrocomp Simulation Program (4). Through a set
of mathematical functions, LANDS simulates continuously
the major components of the hydrologic cycle, including
interception, surface runoff, interflow, infiltration,
and percolation to groundwater. In addition, energy
balance calculations are performed to simulate _the
processes of snow accumulation and melt. Various
publications have previously described the hydrologic
(1, 3, 4, 5) and snowmelt algorithms (2, 4, 5).
Sediment
The algorithms for simulating soil loss, or erosion,
were initially derived from research by Negev at
Stanford University (6) and have been subsequently
influenced by the work of Meyer and Wischmeier (7),
Onstad and Foster (8), and Fleming and Fahmy (9).
Although Negev simulated the entire spectrum of the
erosion process, only sheet and rill erosion were
included in the ARM Model. The two component processes
of sheet and rill erosion pertain to (1) detachment of
soil fines (generally the silt and clay fraction) by
raindrop and impact, and (2) pick-up and transport of
soil fines by overland flow. These processes are
represented as follows:
Soil fines detachment: 1PFD
RER(t) (1 - COVER(T))*KRER*PR(t)JKtK
(1)
Soil fines transport: ,-.-D
SER(t) KSER*OVQ(t)di>tK, for SER(t)±SRER(t) (2)
SER(t) = SRER(t), for SER(t) > SRER(t) (3)
ERSN(t) SER(t)*F (4)
where
RER(t) soil fines detached during time
interval t, tonnes/ha
COVER(T)= fraction of vegetal cover as a function
of time, T, within the growing season
KRER detachment coefficient for soil properties
PR(t) precipitation during the time interval, mm
JRER exponent for soil detachment
SER(t) fines transport by overland flow, tonnes/ha
JSER exponent for fines transport by overland flow
KSER coefficient of transport
SRER reservoir of soil fines at the beginning of
time interval, t, tonnes/ha
OVQ(t) overland flow occurring during the time
interval, t, mm
F fraction of overland flow reaching the stream
during the time interval, t
ERSN(t) sediment loss to the stream during the time
interval, t, tonnes/ha
In the operation of the algorithms, the soil fines
detachment (RER) during each time (5 or 15 minutes)
interval is calculated by Equation 1 and added to the
total fines storage or reservoir (SRER). Next, the
total transport capacity of the overland flow (SER) is
determined by Equation 2. Sediment is assumed to be
transported at capacity if sufficient fines are
available, otherwise the amount of fines in transport is
limited by the fines storage, SRER (Equation 3). The
sediment loss to the waterway in the time interval is
calculated in Equation 4 by the fraction of total
overland flow that reaches the stream. A land surface
flow routing technique (1, 4, 5) determines the overland
flow contribution to the stream in each time interval.
After the fines storage (SRER) is reduced by the actual
sediment loss to the stream (ERSN), the algorithms are
ready for simulation of the next time interval. Thus,
the sediment that doesn't reach the stream is returned
to the fines storage and is available for transport in
the next time interval. The methodology attempts to
represent the major processes of importance in soil
erosion so that the impact of land management practices
(e.g. tillage, terracing, mulching, etc.) can be
specified by their effects on the sediment parameters.
152
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Pesticides
The process of pesticide adsorption/desorption onto
sediment particles is a major determinant of the amount
of pesticide loss that will occur. This process
establishes the division of available pesticide between
the water and sediment phases, and thus specifies the
amounts of pesticide transported in solution and on
sediment. The algorithm employed to simulate this
process in the ARM Model is described as follows:
X/M KC
1/N
+ F/M
(5)
where X/M
F/M
pesticide adsorbed per unit soil, ug/gm
pesticide adsorbed in permanent fixed
state per unit soil. F/M is less than
or equal to FP/M, where FP/M is the
permanent fixed capacity of soil in ug/gm
for pesticide. This can be approximated by
the cation or anion exchange capacity for
that particular soil type.
equilibruim pesticide concentration in
solution, mg/1
exponent
coefficient
Basically this algorithm is comprised of an empirical
term, F/M, plus the standard Freundlich single-valued
(SV) adsorption/desorption isotherm (solid line in
Figure 3). The empirical term, F/M, accounts for
pesticides that are permanently adsorbed to soil
particles and will not desorb under repeated washing.
As indicated in Figure 3, the available pesticide must
exceed the capacity of the soil to permanently adsorb
pesticides before the adsorption/desorption equilibrium
is operative. Thus the pesticide concentration on soil
particles must exceed FP/M before the equilibrium soil
and solution pesticide concentrations are evaluated by
the Freundlich curve. An in-depth description and
discussion of the underlying assumptions is presented in
the PTR Model report (1).
" T
1 _FP
SINGLE-VALUED (SV)
NON-SINGLE-VALDE(HSV)
1-ADSORPTION
2-DESORPTION
3-NEVI ABSORPTION
(-DEWOESORP1ION
PESTICIDE SOLUTION CONC.(C) MC/l
Figure 3 Adsorption/desorption algorithms in the ARM model
The ARM Model includes an option to use a
non-single-valued (NSV) adsorption/ desorption function
because research has indicated that the assumption of
single-valued adsorption/desorption (Figure 3) is not
valid for many pesticides (10, 11, 12). In these cases,
the adsorption and desorption processes would follow
different curves, as indicated by the dashed lines in
Figure 3. The NSV algorithm utilizes the above SV
algorithm (solid line) as a base from which different
desorption curves are calculated. The form of the
desorption curve is identical to Equation 5 except that
K and N values are replaced by K' and N1 respectively.
The prime denotes the desorption process.. The user
specifies the N' value as an input parameter (NP), and
the ARM Model calculates K1 as a function of the
adsorption/desorption parameters (K, N, N1) and the
pesticide solution concentration (12). The calculation
is performed whenever the desorption process is
initiated. The end result is desorption curves
emanating from the base SV adsorption curve as shown in
Figure 3. Thus the NSV function simulates higher
pesticide concentrations on sediment than the SV
function in order to represent the irreversibility of
the adsorption process.
Attenuation of the applied pesticide, through volatil-
ization and degradation processes, is also critical to
the accurate simulation of pesticide transport from the
land surface. These processes are not well understood
and are topics of continuing research. The ARM Model
includes a simple daily first-order degradation factor
(user input) to approximate the reduction in the amount
of pesticide that can be transported anytime during the
growing season. More sophisticated degradation models
are presently being investigated for addition to the ARM
llodel.
Nutrients
Nutrient simulation in the ARM Model attempts to
represent the reactions of nitrogen and phosphorus
compounds in the soil profile as a basis for predicting
the nutrient content of agricultural runoff. The
nutrient model assumes first-order reaction rates and is
derived from work by Mehran and Tanji (13), and Hagin
and Arnberger (14). The processes simulated include
immobilization, mineralization, nitrification/denitrifi-
cation, plant uptake, and adsorption/desorption. The
model is presently being refined and tested on field
data. The final project report (2) includes a complete
description of the nutrient model and discussions of the
component processes.
ARM Model Testing and Simulation Results
The ARM Model development effort is supported by an
extensive data collection and analysis program sponsored
by the Environmental Protection Agency's Environmental
Research Laboratory in Athens, Georgia (ERL-Athens).
Test watersheds located in Georgia and Michigan, ranging
from 0.6 to 2.7 hectares, have been instrumented for the
continuous monitoring and sampling of runoff and
sediment. Collected samples are refrigerated on site
and later analyzed for pesticide and nutrient content.
In addition, meteorologic conditions are continuously
monitored and soil core samples are taken and analyzed
immediately following application and periodically
throughout the growing season.
Model testing for runoff, sediment loss, and pesticide
loss was completed on one year of data (January
1973-December 1973) from the PI and P3 watersheds in
Watkinsville, Georgia. PI (2.70 ha) is a natural
watershed while P3 (1.26 ha) is a terraced watershed
with a grass waterway. Both watersheds received
identical management practices during 1973: minimum
tillage was employed, soybeans were planted, and the
herbicides paraquat (l,l'-dimethyl-4,4-bipyridinium
ion), diphenamid (N, N-dimethyl-2, 2-diphenylacetamide),
and trifluralin ( a, a, a -trifluoro-2, 6-dinitro-N,
N-dipropyl-p-toluidine) were applied at 1.1, 3.4 and 1.1
kg/ha, respectively. Pesticide simulations were
performed for paraquat and diphenamid.
The monthly simulation results on the PI watershed
(Figures 4 and 5) were obtained from one continuous
simulation run for 1973. The simulated runoff values
(Figure 4) agree quite well with recorded data except
for the spring period. The hydrology parameters were
calibrated on 7.5 months of data in 1972; the
calibration results were reported in the PTR Model
report (1). Additional trial runs have indicated that
the hydrologic characterisitcs appear to vary on a
seasonal basis. During the dry summer- fall period, the
watershed is highly responsive, producing short-duration
sharp-peaked hydrographs from the thunderstorms that
153
-------
occur in the area. In the wetter winter-spring period,
the watershed response is much more moderate with less
erratic hydrographs extending over a longer duration.
Since most pesticide loss occurs during the summer
months, the simulation studies were concentrated on the
critical summer.
-|—r
• RECORDED
- SIMULATED
IFMtMl IISOKD
TIME. MONTHS
Figure 4 1973 monthly rainfall, runoff and sediment loss
for the P1 watershed
The monthly sediment simulation in Figure 4 indicates
the impact of tillage operations. Major storms occurred
in May and June immediately following tillage of the
watersheds. In fact, the recorded monthly sediment loss
in May and June was estimated due to equipment
malfunctions resulting from the high sediment load.
Except for these two months, the simulated and recorded
sediment loss are reasonably close. Since the sediment
algorithms were modified during this study, the
simulation shown in Figure 4 was obtained through
calibration of the sediment parameters. More experience
with the sediment algorithms on different watersheds is
needed to truly verify the methodology.
The monthly pesticide simulation results are shown in
Figure 5 for paraquat and diphenamid. The simulation
values were obtained with parameters evaluated from
laboratory data and the literature; calibration of
pesticide parameters was minimized in order to evaluate
the applicability of the algorithms using parameters
from the literature. The agreement between the
simulated and recorded monthly values is fair. The
following points are indicated:
RECORDED
NSV SIMULATION
SV SIMULATION
* PESTICIDE ANALYSIS
DISCONTINUED
AFTER 9/9/73
s o
TIME. MONTHS
Figure 5 Monthly paraquat and diphenamid loss from
the P1 watershed for the 1973 growing season
(1) Since paraquat is entirely (and essentially
irreversibly) adsorbed onto sediment particles,
pesticide loss closely parallels sediment loss.
Both the recorded and simulated values demonstrate
this behavior. Thus more accurate simulation of
sediment loss would improve the paraquat
simulation.
(2) Diphenamid is transported both in solution and on
sediment particles; thus an initial comparison of
the SV and NSV adsorption/desorption algorithms was
possible. Although the diphenamid simulation in
Figure 5 agrees well with the recorded values,
results for various and other watersheds indicate
that further investigation is warranted. The SV
function performs better for some storms, while the
NSV function performs better for others.
(3) The importance of attenuation processes is
demonstrated by both the paraquat and diphenamid
data. The large majority of pesticide loss occurs
within one to two months following application
(June 13, 1973 for the PI watershed). Thus the
first storm events immediately following
application are the critical ones for pesticide
transport from the land surface.
Numerous storm events were simulated during 1973.
Figures 6 and 7 present the results for the storm of
June 21, 1973. This storm occurred one week after
planting and is one of the better simulated storms
during the summer period. The original report (2)
includes similar figures for various events to indicate
the variability of the simulation results. The storm
runoff and sediment loss for the June 21st storm is well
simulated. The pesticide loss for both paraquat (Figure
6) and diphenamid (Figure 7) is plotted in terms of mass
removal, i.e. pesticide mass per unit time. This
representation demonstrates the close association
between pesticide loss and the transport mechanisms of
runoff and sediment loss. Although the SV function more
closely represents the recorded diphenamid loss in
Figure 7, as mentioned above the NSV function performed
better for other storms. In essence, Figures 6 and 7
demonstrate the type of comparisons that must be made
for storm events when analyzing the ability of a model
to represent agricultural runoff.
0.25
0.20
RECORDED
SIMUUTED
Figure 6 Runoff, sediment and paraquat loss from the P1
watershed on June 21.1973
154
-------
i OE
X
3
~ I I T
RfCOIOtD
HSV SIHIIUTION
SV SIMULATION
Figure 7 Diphenamid loss in water and on sediment from the
P1 watershed on June 21,1973
Conclusions
The testing of the ARM Model has indicated that the
hydrology and sediment simulations reasonably represent
the observed data while the pesticide simulations can
show considerable deviation from recorded values. This
is especially true for pesticides that move by both
runoff and sediment loss. The effects of tillage
operations and management practices need to be further
evaluated for hydrology and sediment production.
Parameter changes as a result of agricultural practices
need to be quantified. Although the results of sediment
simulation have been promising, certain deviations in
the results indicate a lack of understanding of certain
aspects of the physical process. Other processes in the
soil erosion mechanism, such as natural compaction of
the surface following tillage and the effect of rainfall
intensity on the transport capacity, need to be
evaluated for possible inclusion in the Model. Although
the hydrology model has been applied to hundreds of
watersheds in the United States, the accompanying
sediment model has been applied to only a few. If the
ARM Model is to be generally applicable, the most
immediate need is to evaluate the sediment simulation
capability in varying climatic and edaphic regions.
For pesticide simulation, the results demonstrate the
need to further investigate the processes of pesticide
degradation and pesticide-soil interactions. Both the
SV and NSV adsorption/desorption functions require
further research. A non-equilibrium approach should be
investigated to determine its applicability. The
interactions in the active surface zone appear to
control the major portion of pesticide loss especially
for highly sediment-adsorbed pesticides like paraquat.
The depth of the active surface zone and the extent of
pesticide degradation in that zone are critical to the
simulation of pesticide loss for any storm event. The
need for testing the ARM Model in other regions also
pertains to both the pesticide and nutrient functions.
The processes recommended above for further research
should be studied and evaluated in many regions of the
country to determine the impact of soil and climatic
conditions.
The final version of the ARM Model will be designed for
use by state and local agencies across the country.
This work has demonstrated that simulation models can be
developed to represent the processes important to the
quality of agricultural runoff. Moreover, continuous
simulation models can be employed to develop probability
distributions for sediment, pesticide, and nutrient loss
as a basis for economic evaluation (15). In this way,
models, like the ARM Model, can provide a valuable tool
for planning and evaluation of pesticide regulations,
fertilizer application, and other agricultural
management practices.
Acknowledgments
The authors gratefully acknowledge the financial support
of the U.S. Environmental Protection Agency, Office of
Research and Development. Coordination and direction
was provided by the Environmental Research Laboratory in
Athens, Georgia.
References
1. Crawford, N.H., and A.S. Donigian, Jr. Pesticide
Transport and Runoff Model for Agricultural Lands.
Office of Research and Development, U.S.
Environmental Protection Agency, Washington D.C.
EPA 660/2-74-013. December 1973. 211 p.
2. Donigian, A.S., Jr., and N.H. Crawford. Modeling
Pesticides and Nutrients on Agricultural Lands.
Office of Research and Development. U.S.
Environmental Protection Agency. September 1975.
263 p. (in press)
3. Crawford, N.H. and R.K. Linsley. Digital
Simulation in Hydrology: Stanford Watershed Model
IV. Department of Civil Engineering, Stanford
University. Stanford, California. Technical
Report No. 39. July 1966. 210 p.
4. Hydrocomp Simulation Programming: Operations
Manual. Hydrocomp Inc. Palo Alto, California, 2nd
ed. 1969. p.1-1 to 1-27, p. 3-5 to 3-16.
5. Donigian, A.S., Jr., and N.H. Crawford. Modeling
Nonpoint Pollution from the Land Surface. Office
of Research and Development, U.S. Environmental
Agency. February 1976. (draft final
10.
11.
12.
13.
14.
15.
Protection
report)
Negev, M.A.
Department
University.
Report No.
Sediment Model on a Digital Computer.
of Civil Engineering, Stanford
Stanford, California. Technical
76. March 1967. 109 p.
Meyer, L.D., and W.H. Wischmeier. Mathematical
Simulation of the Process of Soil Erosion by Water.
Trans. Am. Soc. Agric. Eng. 12(6) :754-758,762,
1969.
Onstad, C.A., and G.R. Foster. Erosion Modeling
on a Watershed. Trans. Am. Soc. Agri. Eng.
18(2)=288-292, 1975.
Fleming, G., and M. Fahmy, Some Mathematical
Concepts for Simulating the Water and Sediment
Systems of Natural Watershed Areas. Department of
Civil Engineering, Strathclyde University. Glasgow
Scotland. Report HO-73-26. 1973.
Davidson, J.M., and J.R. McDougal. Experimental
and Predicted Movement of Three Herbicides in a
Water-Saturated Soil. J. Environ. Qua!.
2(4):428-433, October-December 1973.
Van Genuchten, M.Th., J.M. Davidson, and P.J.
Wierenga. An Evaluation of Kinetic and Equilibrium
Equations for the Prediction of Pesticide Movement
through Porus Media. Soil Sci. Soc. Amer. Proc.
38:29-35, January-February 1974.
Davidson, J.M., R.S. Mansell, and D.R. Baker.
Herbicide Distributions within a Soil Profile and
their Dependence Upon Adsorption-Desorption. Soil
Crop Sci. Soc. Florida Proc. 1973. 26p.
Mehran, M., and K.K. Tanji. Computer Modeling of
Nitrogen Transformations in Soils. J. Environ.
Qua!. 3(4):391-395, 1974.
Hagin, J., and A. Amberger. Contribution of
Fertilizers and Manures to the N- and P- Load of
Waters. A Computer Simulation. Report Submitted
to Deutsche Forschungs Gemeinschaft. 1974. 123 p.
Donigian, A.S., Jr., and W.H. Wagcjy. Simulation:
A Tool for Water Resource Management. Water Res.
Bull. 10(2):229-244, April 1974.
155
-------
MODELING THE EFFECT OF PESTICIDE LOADING
ON RIVERINE ECOSYSTEMS
J. W. Falco
Research Chemical Engineer
US Environmental Protection Agency
Environmental Research Laboratory
Athens, Georgia 30601
L. A. Mulkey
Agricultural Engineer
US Environmental Protection Agency
Environmental Research Laboratory
Athens, Georgia 30601
Abstract
A mathematical model for predicting the fate and
transport of malathion in riverine ecosystems has been
developed. The model predicts the concentration of
malathion down the length of a river reach as a
function of time and non-point source loading. Model
simulations predict that standing crops of various fish
species and other organisms decrease with increasing
malathion concentration. Mass die-offs were predicted
at critical malathion loadings and concentrations.
Introduction
Under Section 208 of Public Law 92-500,
approximately 150 designated areas of the country will
require area-wide waste treatment management plans. In
light of a recent court test (National Resources
Defense Council versus the US Environmental Protection
Agency), many other areas will also require basin-wide
plans. There are numerous problems which must be
considered in area-wide planning. One can broadly
classify these problems into two areas, evaluation of:
(1) point source related problems, and (2) non-point
source (NPS) related problems. Furthermore, NPS
problems can be divided into urban and non-urban runoff
related problems.
In evaluating potential water pollution impacts
from non-point sources, mathematical models and
statistical correlations provide a powerful analytical
tool, particularly when limited data exist. These
models provide the means to determine major potential
NPS impacts; e.g., sediment loads created by
agricultural practices in a given area. Secondly,
these models provide the means to estimate the
consequences of management decisions on a basin scale.
A number of models and correlations are available
in the public domain for NPS pollution evaluation. For
estimation of pollutant loads from single storm events,
the "Storm watershed Management Model (SWMM),"
developed by Metcalf and Eddy, Inc.; University of
Florida; and Water Resources Engineers, Inc., can be
used.1 For long-term pollutant loads based on annual
average loadings, statistical correlations developed by
McElroy et^ al_._ can be used.2
For continuous simulation of multiple storm
events, two models are available. STORM is a runoff
model developed by Water Resources Engineers, Inc., and
revised by the US Army Corps of Engineers.3 This model
accounts for variation in surface water storage but
does not account for water storage in subsurface
compartments of watersheds. Consequently, it does not
accurately simulate water movement in the watershed
during dry periods between storm events. Both SWMM and
STORM are particularly suited for and used extensively
in analyzing urban NPS problems.
Hydrocomp Corporation has done a great deal of
research on continuous simulation models which predict
runoff continuously from multiple storm events. Unlike
STORM, these models account for subsurface water
movement, and are more comprehensive in terms of
estimating water movement on the watershed between
storm events. Two models which have recently been
developed by Hydrocomp have potential application for
basin-scale planning. The "Agricultural Runoff Model
(ARM)"1* is a continuous simulation runoff model which
simulates pesticide and nutrient loads. In addition to
simulating pesticide-soil interactions, the model also
simulates soil nutrient transformations. The NPS
Model5 simulates pollutant contributions to
streamchannels from both urban and non-urban sources.
The model is keyed to the transport of sediments over
the watershed. Potential basin applications include
analysis of BOD-DO, temperature, and suspended solids
related problems.
Similarly, there are a number of water quality
models which can be used in non-point source pollution
analysis. QUAL I,6 QUAL II,7 DOSAG,9 and, to a lesser
extent, AUTO-QUAL,9 are river models which are
applicable for analysis. It should be noted that most
of these models require lumping of non-point sources
into a small number of equivalent point sources. In
addition, many variants of the previously referenced
river models are also available. The most significant
of these is the EXPLORE-I model.10 In addition to the
mass balance equations incorporated into the above
mentioned models, EXPLORE-I also contains a momentum
balance which permits flood routing during storm
events.
This paper focuses on NPS problems associated with
non-urban areas. Specifically, it deals with the
impact on rivers of application of malathion, an
organo-phosphorus pesticide, on agricultural
watersheds. We have chosen this problem as a
demonstrative example because it clearly illustrates
the unique nature of non-point source problems and
because a sufficient amount of data was available on
this compound.
For evaluation purposes, ranges of malathion loads
were inputted into a river quality model to show the
effects on different species of fish. These loads were
pulses in time along the entire length of the river
section of interest. Eventually we intend to link ARM
with the water quality model and simulate a series of
storm events which were actually observed on
experimental watersheds. Based on biological and
chemical processes for which we have data, a time
series of malathion concentration profiles down the
length of the river reach were calculated and potential
reduction in the standing crops of Carp, Striped Bass,
and Bluegills were estimated.
Mathematical Development
The receiving water model used to predict the
impact of malathion loads is a modification of a
pesticide transport model developed by Falco et_ al.11
It is essentially a material balance which accountsTor
the transport and transformation of chemical and
156
-------
biological constituents which are involved in the
chemical and biological degradation processes. With
one exception, the continuity equation used for each
constituent is as follows:
where Iq second-order rate coefficient
CQ,, concentration of hydroxide ion
Cu concentration of malathion
at
ax2
v 8Ci
3x
Si
Since the two competing reactions have been combined,
the rate constant kj is the sum of the individual rate
constants for each of the competing reactions; i.e.,
where
Ci
concentration of constituent i
dispersion coefficient
rate of production or elimination of
constituent i by pathway j
source strength of component i
time
distance in the direction of flow
kelim + khydrol
(4)
Using the data provided,12 the variation of these two
rate coefficients can be fit to an exponential
function,
This form of the continuity equation assumes that flow
is one dimensional and that the cross-sectional area of
the river reach is constant. We have assumed that, in
the case of fish which are adversely affected by
malathion, these organisms are stationary; i.e.,
kelim
Al
A2
T
(5)
8t
(2)
*hydro!
exp
(6)
where R = rate of reduction of the standing crop
of organism i due to the presence of
malathion
Equation 2 assumes that there is no net transport of
organisms over the length of the stream. This is not a
particularly realistic assumption. The reason we have
used it is to clearly illustrate the deleterious
effects of high malathion concentrations on a test set
of organisms. It should be noted that this assumption
eliminated the possibility of using this version of the
model to predict natural restocking of fish by invasion
from unaffected areas.
Two processes which are responsible for malathion
degradation in aquatic ecosystems have been included in
the model. The chemical degradation pathway modeled is
alkaline hydrolysis. A detailed discussion of the
chemical reactions involved in this pathway has been
presented by Wolfe.12 Wolfe's12 results indicate two
competing temperature dependent reactions occur. The
first reaction, favored at low temperatures, results in
the formation of an intermediate malathion monoacid
product. An elimination reaction, favored at high
temperatures, results in production of diethyl
furmarate and 0,0-dimethyl-phosphoro-dithioic acid.
In modeling these two reactions, we have assumed
that the overall chemical degradation of malathion is a
second order reaction; i.e.,
At temperatures usually associated with natural
environments, the hydrolosis reaction is favored.
Thus, it was assumed in the model that chemical
degradation of malathion and the appearance of a-
malathion monoacid are stoichiometrically related.
Consequently,
a- monoacid
(7)
where
yield of a- monoacid from malathion
For microbial degradation, Paris13 proposed two
models. The first used was the standard Monod
expression for growth of organisms and limiting
substrate utilization. The second model assumed second
order reaction between malathion and bacteria. The
standards of deviation calculated for least squares
fits of the data to both models indicated that the
second order reaction model gave the best fit. In the
model constructed by Falco,11 a Monod expression was
used to approximate the growth of bacteria on a readily
degradable carbon source, and a second order rate
equation was used to describe the degradation of
malathion by bacteria; i.e.,
hydrolysis
"klCOHCM
(3)
R,
Bacteria
k3-CB
(8)
(9)
157
-------
inal
where RBacteria
-k2 CDCU
(10)
B
Ci
net rate of increase of
bacteria
microbial degradation rate of
malathion
rate of carbon utilization
concentration of bacteria
concentration of carbon source
growth rate of
on specified carbon
"Sn
maximum
bacteria
source
half-saturation constant for
bacterial growth on specified
carbon source
specific microbial degradation
rate for malathion
specific bacterial death rate
bacteria growth yield
It should be noted that equation 8
k3CD> to account for the death
D
starvation conditions.
includes a term,
of bacteria under
Paris observed that the major product of bacterial
mediated malathion degradation was B- malathion
monoacid.13 Consequently, malathion degradation and
formation of g- monoacid are stoichiometrically
related; i.e.,
R
6- monoacid
Y2k2-C3-C
M
(11)
where y2
yield of B- monoacid from malathion
In this paper, the bacterial degradation model used
the one developed by Falco.11
is
To summarize briefly, the water quality model used
accounts for transport of chemical constituents:
malathion, a- monoacid, 6- monoacid, and degradable
carbon and bacteria by equation 1. The degradation of
malathion which appears as a sink term (^ R-J) in
J ' J
equation 1 is accounted for by equations 3 and 5. The
growth and death of bacteria are accounted for in the
transport equation for bacteria by inclusion of
equation 8. The uptake of degradable carbon is
accounted for in its transport equation by substitution
of equation 9 for (. R. .) in equation 1. The source
J IJ
terms in the equations which describe the transport of
a- and 6- monoacids are defined by equations 7 and 11,
respectively. Lastly, the toxic effects of malathion
on standing crops of fish are modeled according to
equation 2, where it is also assumed that
Ri
~ K L. U i. u i-
(12)
and CF = concentration of organisms effected by
malathion
kt = specific death rate
The only required relationships which we have not
discussed are the boundary and initial conditions which
are applicable to the river system. These, along with
a description of the nature of the sources of pollutant
loads (S.) are specific to the particular problem being
investigated.
Results and Discussion
The equations discussed in the previous section
were coded into a Fortran program described by Falco.11
The appropriate, coefficients used for each simulation
are listed in Table 1.
ymax ^ mg org"1 hr"^
7.2 x 10"10
km (mg T1)
6.3
k, (M"1 hr'1)
1.43 x 10"
k2 (i org'1 hr"1)
1.21 x 10'12
k3 (hr'1)
5.16 x 10'3
Yi (mg/mg)
0.915
Yz (mg/mg)
0.915
Y (org/mg)
5.73 x 109
Table 1. VALUES OF RATE COEFFICIENTS AND YIELD
FACTORS USED IN ALL SIMULATIONS.
For all simulations shown, it was assumed that a
significant point source of readily available carbon
was located 16 km from the upstream reference point
with a discharge rate of 10.9 kg/day of usable carbon.
For simulations in which reduction in fish populations
were projected, it was assumed that malathion degraded
via alkaline hydrolysis at a rate which would
correspond to a pH 8. This is an extremely high pH
which is not very likely to occur in streams. We have
used it here because it predicts a rapid decay in
malathion. As it will be shown, in spite of this rapid
decay, standing crops of fish are severely affected
under moderate malathion loads. The point is, even
under the most favorable conditions for malathion
degradation, material entering the system can be
present long enough to have an adverse impact.
The physical characteristics of the system we have
simulated are shown in Table 2.
River cross-
sectional area
30 m2
River
length
129 km
Surface area
of basin
25.8 km?
Average
river
velocity
9 m/min
Table 2. PHYSICAL CHARACTERISTICS OF THE SYSTEM.
For simulations in which fish population reductions
were projected, the following specific death rates were
used:
1. For Carp, let = 1.44 x 10"3 i mg'1 hr'1 , .
2. For Striped Bass, kt = 3.28 x 10"2 f mg- hr
3. For Bluegill, k,, = 0.135 i mg-1 hr-1
These values were obtained by fitting toxicity data for
24, 48, and 96 hr TL_
Ferguson1"
to an exponential
concentration and time; i.e.,
concentrations
function
reported by
in malathion
158
-------
where
0.5
"TL
exp -k,.CTL -tTL (13)
exposure time
measured toxicity of malathion
Figure 1 shows the steady state concentration
profile which would exist if the loading rate for
malathion were 0.126 gin/acre day. The contribution of
microbial and chemical degradation are also shown along
with the concentration profile that would exist if
neither of these two processes occurred. Under the
conditions simulated, both alkaline hydrolysis and
microbial degradation are important processes for the
elimination of malathion.
Base Line
Microbial Activity
Hydrolysis, pH =
Total Degradation
Length (km)
Figure 1. Comparison of steady-state malathion
concentration profiles in response to
a load of 0.126 gm/acre day.
Figures 2 and 3 show the response of the river to
a pulse of malathion loaded over a period of two days
in the amount of 700 nig/acre. Figure 2 shows the
concentration profiles for malathion as the pesticide
is degraded and diluted out of the river. Figure 3
shows the concentration profiles of a- malathion
monoacid as it is formed and diluted out of the river.
Comparing the two graphs, it can be seen that the
monoacid persists in the river for longer periods of
time than malathion. Because of its relative
persistence, more information is needed on this
degradation product.
Figures 4 and 5 show the relative standing crops
of Carp, Bass and Bluegill before and after a storm
event in which malathion is loaded into the river.
Figure 4 shows the impact of runoff amounting to 700
mg/acre and Figure 5 shows the impact of runoff
loads were chosen to demonstrate the variation in
species response to a range of malathion inputs. Based
upon recommended application rates of malathion, the
range of loads used in these examples are possible.
However, neither field data nor simulation loading
model results are available to determine the
probability of occurence of such loads or to delineate
the actual physical conditions under which they may
occur. The projections indicate that severe damage
could occur to both Bass and Bluegill at the higher
loading. At low loading rates, only Bluegills are
adversely affected.
16 32 48 64 80 96 112 128
0.1
Figure 2. Response of a stream to a pulse of malathion
of 700 mg/acre.
0.30 p
0.25 ~
J= 0.20 -
0.15 -
0.10 ~
0.05 -
16
32
Figure 3.
159
Length (km)
Concentration profiles of a- malathion
monoacid as a function of time in response
to a 700 mg/acre pulse of malathion.
-------
40 -
» 20 -
16
48 64 80
Length (km)
96
112 128
Figure 4. Response of three species of fish to a pulse
of malathion of 700 mg/acre.
100
80
60
i 1 1 1 7
4 20
Bluegill
16
32 48
64
80 96 112 128
Length (km)
Figure 5. Response of three species of fish to a pulse
of malathion of 44 mg/acre.
In summary, we have presented an analysis and
projected the impact of a pesticide on three species of
fish. We have indicated the types of information
necessary for this analysis. Although the absolute
values of coefficients and parameters may vary from one
problem to another, the procedure should be applicable
to many situations. The use of this model and
eventually more sophisticated ones as they are
published should provide insight into a broad range of
NPS pollution problems.
References
1. Metcalf & Eddy, Inc., University of Florida, and
Water Resources Engineers, Inc. Storm Water
Management Model, Volume II—Verification and
Testing. US EPA Water Pollution Control Research
Series, 11024DOC08171.
2. McElroy, A. D., S. Y. Chiu, J. W. Nebgen, A.
Aleti, and F. W. Bennett. Interim Report on
Loading Functions for Assessment of Water
Pollution from Nonpoint Sources. US EPA Report,
Project 68-01-2293. 1976.
3. Hydrologic Engineering Center. Urban Storm Water
Runoff "STORM". US Army Corps of Engineers
Report. 1975.
4. Donigian, A. S., Jr. and N. H. Crawford. Modeling
Pesticides and Nutrients on Agricultural Lands.
US EPA Report, EPA-600/2-76-043. 1976.
5. Donigian, A. S., Jr. and N. H. Crawford. Modeling
Nonpoint Pollution From the Land Surface. US EPA
Report. In press.
6. Masch, F. D. and Associates and the Texas Water
Development Board. Simulation of Water Quality in
Streams and Canals, Theory and Description of the
QUAL-I Mathematical Modeling System. The Texas
Water Development Board, Report 128. 1971.
7. Roesner, L. A., J. R. Monser, and D. E. Evenson.
Computer Program Documentation for the Stream
Quality Model QUAL-II. US EPA Intermediate
Technical Report, Contract No. 68-01-0739. 1973.
8. Texas Water Development Board. DOSAG-1 Simulation
of Water Quality in Streams and Canals Program
Documentation and Users Manual. Texas Water
Development Board Report. 1970.
9. Crim, R. L. and N. L. Lovelace. AUTO-QUAL Model-
ing System. US EPA Report 440/9-73-003. 1973.
10. Baca, R. G., W. W. Waddel, C. R. Cole, A. Brand-
stetter, and D. B. Cearlock. EXPLORE-I: A River
Basin Water Quality Model. Battelle Pacific
Northwest Laboratories Report. 1973.
11. Falco, J. W., D. L. Brockway, K. L. Sampson, H. P.
Kollig, and J. R. Maudsley. Models for Transport
and Transformation of Malathion in Aquatic
Systems. Proceedings of the American Institute
for Biological Sciences Symposium, Freshwater
Quality Criteria Research of the Environmental
Protection Agency, Con/all is, 1975. In press.
12. Wolfe, N. L., R. G. Zepp, J. A. Gordon, and G. L.
Baughman. The Kinetics of Chemical Degradation of
Malathion in Water. Environmental Research
Laboratory, Athens, Georgia. In press.
13. Paris, D. F., D. L. Lewis, and N. L. Wolfe. Rates
of Degradation of Malathion by Bacteria Isolated
From an Aquatic System. Environmental Sciences
and Technology. £(2):135-138. 1975.
14. Ferguson, T. L. and R. von Rumker. Initial
Scientific and Minieconomic Review of Malathion.
US EPA Report, Contract No. 68-01-2448. 1975.
.160
-------
RADIONUCLIDE TRANSPORT IN THE GREAT LAKES
R. E. Sullivan, Ph.D.
Environmental Protection Agency
Office of Radiation Programs
Washington, D. C.
W. H. Ellett, Ph.D.
Environmental Protection Agency
Office of Radiation Programs
Washington, D. C.
Summary
A mathematical model has been developed to
predict radionuclide levels in the Great Lakes due to
nuclear power generation in the United States and
Canada. The calculations have been used to verify
the feasibility of proposed International water
quality objectives for radioactivity in the Lakes.
Dose rates and doses to reference-man from the inges-
tion of Lake waters are predicted based on expected
future power generation in this region.
Introduction
A recent bipartite agreement between the United
States and Canada on water quality in the Great
Lakes mandated establishment of a radioactivity
objective for the Lakes. The liquid effluents
discharged into the Great Lakes from, nuclear power
plants and other nuclear facilities, such as fuel
reprocessing plants, are of particular interest in
this regard since some of the entrained
radionuclides have relatively long half-lives.
1 2
Previous work in this area ' has been
concerned mainly with fallout from nuclear weapons
tests. Since in this study we are primarily
concerned with predicting the concentrations of
specific radionuclides emitted in the nuclear fuel
cycle and the resultant doses to reference-man, the
contribution from fallout has been neglected.
However, such source terms may be included by
specifying appropriate initial concentrations for
these radionuclides.
A simplified model of the Great Lakes system
has been employed which assumes perfect mixing but
allows for the periodic establishment of a
thermocline by varying the mixing volume.
Corrections are made, where necessary, for removal
of radionuclides by sedimentation and equilibration.
The results are given in terms of radionuclide
concentrations in each lake and the dose rates and
doses ensuing from continuous, long-term ingestion
of system waters. With the model described, it is
possible to obtain analytical solutions for the
coupled differential equations describing these
quantities as a function of time. However, a
FORTRAN computer program has been employed to reduce
the calculational effort required.
In succeeding sections, we present a
description of the physical and mathematical models
developed, the rationale employed in specifying
source terms for various types of facilities, and
details of the dose calculation. A sample problem,
projecting the future effects of radioactive
contamination of the Great Lakes due to projected
nuclear plant operations, is described in some
detail. Results from .this and similar problems have
been used to verify the feasibility of the water
quality objectives set by the U.S.-Canada agreement.
Physical Model Analysis
Radionuclide Concentrations
The physical model of the Great Lakes comprises
a set of five bodies of water characterized by
constant total volume, inflow, outflow, and surface
area. The lakes are interconnected so that, with
the exception of Lakes Superior and Michigan, each
may contribute radioactivity to succeeding members
of the chain as indicated in Figure 1.
'Figure 1. Physical Model of the Great Lakes
The governing differential equation for models of
this type, for the ith lake and a single nuclide is:
dC,
where
C^ = concentration for ith lake [Ci/cm3]
Ri = input rate into ith lake [Ci/yjr]
Vj_ = mixing volume of ith lake [cm3]
\r = radioactive decay constant for this
nuclide
\p = decay constant for physical removal
(sedimentation, equilibration) [yr"1]
q^ = volumetric flow out of ith lake [cm3/yt]
Because of the summation on j, a major difficulty in
solving the equation arises in that each Cj term
embodies the complete differential equation for all
preceeding lakes, thus complicating the expressions
for the lower lakes.
161
-------
We have chosen to apply the Laplace transform
in order to obtain solutions to these equations.
the transformed equation for Ci is
c? + •
+ (s+ki)
(2)
where kj^ = ( \r + \p + y ) depends on both the
characteristics of the lake (i) and the physical
properties of the radionuclide. Cj is the initial
lake concentration. For Lakes Superior and
Michigan, which have no lake tributaries, the Cj
term vanishes and the equation (2) reduces to
(3)
C§
The general equation becomes increasingly more
complex as we proceed down the chain of lakes.
However, the transformed solutions to these general
equations comprise only terms of the form
c(s) =
f(s)
g(s)
in which f (s) is constant and g(s) is the product of
linear, non-repeated factors,
(4)
g(s) = (s+k1)(s+k2)•
To reduce the effort required in solving such
expressions, a variation of Heavisides' partial
fraction expansion3,
(5)
_
eU )
n=l
is applied. Here, g(kn) denotes the product of all
the factors except the factor (s-kj^) . Using (5) , the
solution to equation (3) for Lake Michigan or Lake
Superior is
(6)
For the next lake (Huron) equation (2) includes
expressions for the preceeding lakes
Hi
Vi
(7)
ifj: _ IfinC 1 "I
j |(s+ki )j V-, [g (s+kO J
where the summation over j indicates the presence of
two terms, one for Lake Superior and the other for
Lake Michigan, the c(s) terms for these lakes
corresponding to the Cj (s) terms in equation (2).
It is evident that as the differential equation
for each lake in the progression is transformed,
each term will contain an additional factor
(s + k) Again, solutions are found by means of the
inverse transform of equation (5), which yields the
concentration of a specified radionuclide as a
function of time.
Dose Rate and Dose to Reference-Man
The concentrations of radioactivity in
lake water can be used to find the annual dose rate
due to ingestion of lake water by reference-man.
Because the radioactivity in the lakes is expected
to be a strongly varying function of time, due to
the rapid projected growth of nuclear power, dose
estimates cannot be based on a constant intake of
activity over the time necessary to reach
equilibirum in the body except for nuclides having a
relatively short effective half-life. Nor can the
dose over a 50-year period be determined using the
conventional models given in ICRP Publication 2.4
Rather, in this study the dose rate and dose
calculations are based on equations and data
presented in ICRP 105 and ICRP IDA6. However, for
organ burden, b(t), and cumulated activity , B(T),
the equations have been revised slightly to conform
to program usage. Both dose and dose rate are
predicated, at present, solely on an assumed
consumption by reference - man of 2.2 liters of
drinking water per day. This quantity is somewhat
larger than that usually consumed as drinking water
to account for the contribution to the body burden
from food pathways.
Over a time interval short enough to allow
treating the average concentration as constant, the
intake, I(t), is directly proportional to the lake
concentration. Integration of the ICRP equations
for organ burden and cumulated activity are
straightforward if the retention function, R(t),
contains only exponential terms. For the isotopes
of interest here retention functions of this form
are given in reference 5. For ingestion at a
constant average intake, I,
b(t) = I
(8)
R(t-r) dr
and
(9)
B(T)
Jo Jo
R(t-r) dr dt
Since the retentibn function, R(t), is the sum
of a series of exponentials,
(10)
R(t) =
n=l
162
-------
each term in the integral defining the organ burden
will be of the form
are assumed to be removed only by radioactive
and, where applicable, sedimentation.
decay
(11)
bn(t) =
There are two solutions for
first yields the organ burden
bn(t) =
dr
this equation. The
(12)
_
Pn
at any time during the period, beginning at time tj_,
of ingestion. The second solution gives the organ
burden at any time subsequent to t-21 the end of the
ingestion period.
(13)
3-pn(t-t2) . e-
The instantaneous dose rate depends only on the organ
content at some time t. However, cumulated activity
and, therefore, the dose depend on the whole time
history of ingestion so that the sum of equations
(12) and (13) must be used in evaluation of the
total dose over a period T. The cumulated activity
is then
(14)
-Pn(t-t2) -
H
where T^, T2, and T are analogous to the t values
used in the organ burden equations. Performing the
integration and collecting terms,
.(15)
with A similar term for each exponential needed in
the retention function. Note that, since intake is
directly proportional to lake concentration (which
comprises only constant and exponential terms),
equations (8) and (9) may be solved analytically.
However, for the short time intervals considered
here (one year) the use of an average I is
sufficient.
Computer Program Analysis
The basic program uses three loops to account
for the dependence on time, lake and isotope. The
time loop is usually solved in one - year increments
and, to account for the existence of a thermocline,
mixing during the first half year is based on the
total lake volume while in the last half year a 17-
meter depth (thermocline) is presumed and the
product of this depth and the lake surface area
define the mixing volume. The model assumes that
lake outflows remain constant in the epilimnion,
with equilibration dependent on the concentration
above the thermocline. Nuclides in the hypolimnion
Several options are available for defining the
source terms, R. Specification of reactor type is
required since the liquid discharges vary
significantly between the various (BWR, PWR) types.
These releases also depend on the sophistication of
the liquid radwaste system employed by each type of
reactor. Since detailed examination of the radwaste
system for each operating reactor may not be
practical and is not possible for plants scheduled
for future operation, it has been necessary to make
some assumptions regarding these releases. We have
utilized the results of an in-depth environmental
analysis' which presented typical releases expected
from four classes each of BWR and PWR liquid waste
system representing a range of treatment from
minimum to maximum. This data is incorporated into
the computer program for use in a source input
option. Thus, the simplest input consists of
specifying the number of BWRs and PWRs (nominal 1000
MWe) on each lake along with the appropriate choice of
radwaste system type (1 through 4) and allowing the
program to internally generate source terms for each
lake and isotope. Alternatively, the actual source
terms for each lake and isotope may be directly
entered or the two options may be combined.
The data required to obtain solutions for five
isotopes (H3, Co60, Sr90, Cs134, Cs137) is
presently stored in the program, but other
radionuclides may easily be added. At present, this
data includes correction factors, in the form of the
effective decay constants indicated in equation (2),
to account for equilibration of tritium8 and
sedimentation of cesium9.
The standard output consists, for each isotope,
of the average radionuclide concentrations for each
year and Great Lake. A summary table giving annual
dose rates and cummulative doses by year for each
lake is also printed out. The critical organ
assumed for each isotope is identified at the head
of each column.
Problem Description
The underlying purpose of this analysis and the
resulting computer program was to estimate the
effect on the Great Lakes of nuclear power plant
operation through the year 2050. These estimates
were needed in order to establish reasonable
estimates of water quality for the lakes. To obtain
a valid assessment it is necessary to consider not
only the effluent from the plants themselves, but
also that from any reprocessing plants located on
the lakes. Separate determinations were made for
each of the sources described below in order to
compare the relative effects of each.
Sources
U.S. Nuclear Power Stations
The total number of nuclear power plants in the
United States has been estimated by interpolation of
data contained in a compilation issued by the
10
AEC.-LU The apportionment of reactors to the Great
Lakes basin and to the individual lakes was taken to
have the same ratio to the total number as the known
1980 values.
U.S. Fuel Reprocessing Plants
Only one reprocessing operation, the Nuclear
163
-------
Fuel Services plant, is presently scheduled for the
Great Lakes basin. The source terms for this
facility were taken from the associated
Environmental Impact Statement.H One additional
facility, located inland but contributing to the
tritium concentration in Lake Michigan by rainout,
has been postulated.
Canadian Power Stations
Source terms for the Canadian heavy water
reactors expected to be in use during this period
have been estimated from current data furnished by
facility operators.12 It should be noted that
these values are very conservative and may
overestimate the activity entering the Lakes from
Canadian reactors. In particular, tritium
discharges are expected to be reduced in the future
due to the economic incentive to conserve heavy
water.
Results
Using the general procedure described in the
text, the nuclide concentrations, dose rates, and
cumulative doses have been determined for the period
1962-2050. Two sets of operating conditions have
been used: in the first, the nuclear facilities
operating in the year 2000 have been assumed to
continue operation at a constant level until 2050.
In the second, all sources have been presumed to be
removed after the year 2000 in order to estimate the
time required for radioactive decay and lake
turnover to clear the lakes. The only operational
reactors in the period 1969-1970 were on Lake
Michigan. Nuclide concentrations in the remaining
lakes during this period are due to flow from
Michigan through connecting rivers. Subsequent to
this period,generating stations begin to come on
line in the other lakes until, by 1980, operating
reactors are projected for all lakes but Superior.
Lakes Erie and Ontario, which not only have large
numbers of facilities but receive the effluent from
other lakes, have roughly twice the nuclide
concentrations of the other lakes. Radioactivity
concentrations are rather insignificant until after
1980 when there is a sharp rise through the year
2000.
To indicate the overall effect of nuclear power
generation on radionuclide levels in the Great
Lakes, the dose rates from each isotope considered
are given in Table 1 for each lake. Table 2 shows
the cumulative doses, by lake, incurred from inges-
tion of each nuclide through the year 2050. Both
sets of results are for operation at a constant
level through the year 2050 assuming the number of
installations is constant after the year 2000.
Based on the model described in the text, by
far the largest cumulative dose is due to the
concentration of tritium in Lake waters. The vast
majority of the tritium present is from fuel
reprocessing activities and is in the effluent from
Canadian heavy water reactors. However, the maximum
seventy-year dose — from about 1980 to 2050 — is
only 23 millirem, due to ingestion of Lake Ontario
water. The remaining isotopes contribute less than
1 millirem to the total dose.
It should be noted that the results presented
may be altered when refinements to the model (i.e.,
hydrographies, source, equilibration, sedimentation,
etc.) are possible. In particular, the effects of
localized near-shore currents may variably affect
the concentration of isotopes in the drinking water
intakes of cities adjacent to effluent discharges.
On a long-term basis, however, in which relatively
perfect mixing may be assumed, these results should
not be affected drastically. Moreover, these results
indicate that nuclide concentrations arising from
currently projected nuclear fuel cycle operations
yield radiation doses which lie within the proposed
objective for Great Lakes Water Quality.
References
1. Machta, L., Harris, D. L., and Telegados, K.,
"Strontium-90 Fallout Over Lake Michigan," J^_
Geophys. Res., 75, 1092-1096, 1970.
2. Lerman, A., "Strontium-90 in the Great Lakes:
Concentration - Time Model," J. Geophys. Res.,
77, 3256-3264, 1972.
3. Churchill, R. V., "Modern Operational
Mathematics in Engineering," p.44, McGraw-Hill,
New York, 1944.
4. INTERNATIONAL COMMISSION ON RADIOLOGICAL
PROTECTION. Permissible Dose for Internal
Radiation, ICRP Publication 2, Pergammon Press,
N.Y., N.Y. (1959).
5. INTERNATIONAL COMMISSION ON RADIOLOGICAL
PROTECTION. Evaluation of Radiation Doses to
Body Tissues from Internal Contamination due to
Occupational Exposure, ICRP Publication 10,
Pergamon Press, N.Y., N.Y. (1968).
6. INTERNATIONAL COMMISSION ON RADIOLOGICAL
PROTECTION. The Assessment of Internal
Contamination Resulting from Recurrent or
Prolonged Uptakes, ICRP Publication 10A,
Pergamon Press, N.Y., N.Y. (1971).
7. U.S. ENVIRONMENTAL PROTECTION AGENCY.
"Environmental Analysis of the Uranium Fuel
Cycle Part II, Nuclear Power Reactors, EPA-
520/9-73-003-C, Office of Radiation Programs,
Environmental Protection Agency, Washington, D.C.
(1973) .
8. Strom, Peter 0., "Method for Estimating Tritium
(HTO) in the Great Lakes," USNRC, Unpublished.
9. Wahlgren, M. A., and Nelson, D. M., "Residence
Times for 239Pu and 137Cs in Lake Michigan
Water," ANL-8060, Part III, 85-89, Argonne
National Laboratory, Argonne, Illionis (1973).
(Residence time estimates updated by telephone
communication.)
10. U. S. ATOMIC ENERGY COMMISSION. "Nuclear Power
Growth 1974-2000," WASH-1139, p.6, Case D,
USAEC, February 1974.
11. NUCLEAR FUEL SERVICES. Environmental Report,
Docket Number 50-201, p.8.2-3, NFS Inc. (1973).
12. Personal Communication, K. Y. Wong, Supv.,
Central Health Physics Services, Ontario
Hydroelectric, to A. H. Booth, Director,
Radiation Protection Bureau, Department of
Health and Welfare (Canada) dated November 26,
1975.
164
-------
TABLE 1
DOSE EQUIVALENT RATE IN THE YEAR 2050*
(mi crorem/year)
Isotope and
Critical Organ
Tritium
(Body Water)
Cobalt-60
(Total Body)
Strontium-90
(Bone)
Cesium-134
(Total Body)
Cesium-137
(Total Body)
*After 50 years
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
Lake
Michigan
6.402
55.38
0.007
2.633
0.635
0.995
Lake
Huron
5.205
22.48
137.8
0.004
0.041
2.434
0.283
0.199
0.478
0.907
Lake
Erie
13.36
55.92
15.91
97.91
0.017
0.028
5.189
4.865
2.097
0.176
0.064
2.842
0.140
0.393
Lake
Ontario
11.34
110.8
8.797
257.7
0.012
0.082
5.121
10.71
0.874
0.195
0.447
1.452
0.178
1.956
operation at constant source level.
1. U. S. Nuclear Power
2. NFS Fuel
Isotope and
Critical Organ
Tritium
(Body Water)
Cobalt-60
(Total Body)
Strontium-90
(Bone)
Cesium-134
(Total Body)
Cesium-137
(Total Body)
Reactors
Reprocessing Plant
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
DOSE
Lake
Michigan
332.0
2791.7
0.372
100.6
40.06
61.81
3
4
TABLE 2
EQUIVALENT BY THE
(microrem)
Lake
Huron
247.9
954.5
7646.5
0.226
2.39
79.89
279.3
16.68
12.42
27.74
55.74
. Postulated H-3
Canadian Power
YEAR 2050*
Lake
Erie
727.5
3852.0
644.7
5236.5
0.998
1.55
218.7
565.0
124.3
12.27
3.93
167.2
9.723
23.69
Rainout into Lake Michigan
Reactors
Lake
Ontario
584.1
7245.4
317.4
14464. S
0.691
4.76
209.6
51.76
13.53
27.59
84.43
12.21
119.02
*After 50 years operation at constant source leveli lifetime dose.
1. Nuclear Power Stations
2. NFS Reprocessing Plant
3. Postulated H-3 Rainout into Lake Michigan
4. Canadian Power Stations
165
-------
FEDBAK03 - A COMPUTER PROGRAM FOR .THE, MODELLING OF FIRST ORDER CONSECUTIVE REACTIONS WITH
FEEDBACK-UNDER A'STEADY STATE'TOLTffilMENSrONAL. NATflRAL AQUATIC SYSTEM
George A. Nossa
Environmental Engineer
Data Systems Branch
U.S. Environmental Protection Agency
New York, N.Y.
ABSTRACT
The computer model described is used to compute the
steady-state distribution of water quality variables
undergoing consecutive reactions with feedback and
following first order kinetics. The program has
been developed in a general form but is specifically
applicable to the reactions observed by nitrogenous
species and the associated dissolved oxygen uptake
in the natural environment.
The basis for this model is the theory of conserva-
tion of mass. The approach used to solve the equa-
tions is a finite difference scheme developed by
Thomann (%'$> , which has been shown to be a very
effective tool in the field of water quality manage-
ment.
INTRODUCTION
A computer model has been developed to serve as a
useful tool in the prediction of water quality para-
meters which react under first order kinetics and as
a system of consecutive reactions.where any parameter
can react in .a feedback fashion. The problem setting
assumes an aquati'c environment' in which steady state:
conditions can be applied
Lets consider a system of five reactants:
FIGURE 1
SCHEMATIC OF FIVE REACTANT SYSTEM
In the above system, the consecutive feedfoward and
feedback reaction rates are presented. All the
possible reaction loops for the first reactant have
also been included. This particular system will be
used in the theory development.
THEORY
The general estuarine advection/dispersion equation
may be written as:
where:
N concentration of constituent
t = time, in tidal cycles
E = tidally averaged dispersion coefficient
which includes the dispersive effects of
tidal motion
U = net advective velocity
K = first order decay coefficient of constitu-
ent N
direct discharge? of N
W(x) =
Assuming steady state conditions: dN/dt
equation (1) becomes:
0 and
0 = E d2N
U dN
dY
KN + W(x) (2)
Direct solutions for the above equation have been
computed by O'ConnorO .2), a computer program has
been documented by EPA, Region II(3) which uses this
technique to solve for water quality parameters.
A second solution approach developed by Thomann^4'5'
solves the above differential equation directly by
replacing the derivatives with finite-difference
approximations. This approach is used by computer
program HAR03; documented by EPA, Region ll(°> to
analyze systems of consecutive reactions. The
Thomann solution technique will also be the approach
followed in program FEDBAK03.
If we take the first reactant N-] on figure 1 and we
incorporate all the feedback loops, equation (2)
becomes:
(3)
K51N5+W1
where K-JJ are the appropriate first order reaction
rate constants. The incorporation of the reaction
term KH allows for the first order decay of this
first component out of the system.
For the other remaining reactants equation (2) would
be written as:
Q E d2N2 _ U dN2 _ K22N2+K12N2+K32N3+K42N4+
K52N5+W2 ........ (4)
K53N5+W3 ........ (5)
U 6N_ - KN +
6x
WN(x)
(1)
166
-------
0 =
U £^A - K44N4+K14Ni+K24N2+K34N3+
dx
|/_,N +U.
^54^5 W4
(6)
E d2Nr U dNc
0 —T5- j-5- "
dx2 dx
The Thomann solution approach divides the system
into completely mixed segments, as illustrated for a
one dimensional estuary in figure 2.
FIGURE 2
SEGMENTED ONE DIMENSIONAL ESTUARY
where segments 1 and 'n' each form an interface with
the boundaries. Equation (3) for the "i" segment on
figure (2) can be written as:
EiAiiid2Nlsi _ Qiii
dx
(8)
The derivatives on the equation above can be replaced
by finite-difference approximations giving:
Q-
i.i+1
where:
-l,iNl,i) (9B)
(9C)
i i = subscripts used to denote the
interface between adjacent segments
i and j
i -i = average length of segments i and
1>J
a- • and 3-j j are weight factors to
correct the concentrations from
equation 9B
xi i
1 >J
(10)
(n)
In order for the final concentrations to be positive,
it is required that:
Substituting equations (9A) and (9B) into equation
(8) yields:
Grouping terms in the above equation yields:
Letting:
i ,i
(u)
1,1+1
The general equation for the ith segment becomes:
ai ,i-!
, ^5. . (18)
The use of this finite difference approximation
scheme has a numerical dispersion, which can be
approximated as (5)
Enum Ul(a-l/2) (ISA)
Where Eoun,is the numerical dispersion. This is par-
ticularly important to stream applications where
advective velocities may be high and this effect may
lead to distorted results.
Extension to multi-dimensional analysis:
If we consider a grid of orthogonally straped
sections such as the one illustrated in figure 3:
kl
k2
i
k4
k3
FIGURE 3
HYPOTHETICAL TWO DIMENSIONAL SYSTEM
167
-------
Following the convention that flows entering a sec-
tion is negative and flow out of a section is posi-
tive, a mass balance due to the transport and disper-
sion of material from section i to all surrounding
sections k(s) is:(4>5>8)
vidN1.i
(19)
This equation is the equivalent to equation (13) for
the one dimensional case. The generalization of the
advection term is possible since:
-Qikaik =
and
-Qikgik =
(2°)
(21)
Using equation (19), if the terms containing the de-
pendent variable NT t-\ are grouped on the left hand
side and the direct loads of this component and the
terms for the formation of NT due to other components
are placed on the right hand side, one obtains: (8 )
where
aik
(22)
(22A)
(22B)
For sections where flow enters a section from the
boundary with a concentration c^
... (23)
and the forcing function at the boundary is added to
the direct loads at that section by:
(24)
For sections forming a boundary, where flow leaves
this section to an area with a concentration c,:
... (25)
and
(26)
The set of equations for component N]for n number of
spacial sections in the system described in figure 1
would be:
,4+- • -+alnNl ,rT
N5,l (27)
a21Nl ,l+a22Ni ,2+a23Nl ,3+a24N-| >4+. • •+a2nN1 >n=
wl,2+V2K2l,2N2>2+V2K31>2N3)2+...+V2K51>2
N5,2 (28)
,i+a32Nl ,2+a33Nl ,3+- • • -+a3nNl ,n=Wl ,3+
V3K21,3N2)3+V3K31)3N3>3+...+V3K51,3
N-5,3
an!Nl ,l+an2Nl ,2+an3+- • -+annNl ,n=wl ,n+vnK21 ,n
(29)
(30)
In matrix notation equations (27) thru (30) can be
written as:
[A1](N1)=(W1)+[VK21](N2)+[VK31J(N3)+[VK41J
(N4)+[VK51](N5) ........................ (31)
where:
[A]J is a square matrix of n order, containing the
a's as defined on equations (22A) and (22B),
note that the main diagonal has the reaction
rate constant KIT
(N-] ) ,(N2) ,. . .(Ms) are nxl vectors of the reactant
over all sections
(Wl) is an nxl vector of the waste loads for react-
ant N-|for all sections
[VK2l],[VK31],[VK4i] and [VK51].each of these is an
nxn diagonal matrix of the section volume and
the first order reaction coefficient at that
segment.
A similar analysis as above for the second reactant
N2 on figure 1 yields:
[A2](N2)=(W2)+[VK12](N1)+[VK32](N3)+[VK42]
(N4)+[VK52](N5) ........................ (32)
where:
[A2] is an nxn matrix similar to [A-|J, but the
main diagonal contains the reaction rate
constant K22
(W2) is an nxl vector of direct waste loads for
component N2 over the n sections
For the other reactants N3, N4, NS similar equations
are generated:
[A3](N3)=(W3)+[VK13](N1)+[VK23](N2)+[VK43]
(N4H[VK53](N5) ........................ (33)
[A4](N4)=(W4)+[VK14](N1)+[VK24](N2)+[VK34]
(N3MVK54](N5) ........................ (34)
CA5](N5) = (W5)+[VK15](N1)+[VK25](N2)+[VK35]
(N3)+[VK45](N4) ........................ (35)
The above matrix equations (31) thru (35) can be
written as a matrix of Matrices: (5, 8)
168
-------
[A] ] -[VK21HVK31]-[VK41J-[VK5l]
•[VK12] [A2 ]-[VK32]-[VK42]-[VK52]
-[VK13] -[VK23] [A3 ]-[VK43]-[VK35]
-[VK14J -[VK24J-[VK34J [A4 J-[VK54]
-[VK25]-[VK35]-[VK45] [A5 ]
(NT
(N2
(N3
(N4
(N5
W2)
W3)
or
CA] (N)
(w).
(37)
wjiere [A] is the 5n x 5n matrix above and (N) and
(W) are 5n x 1 vectors. The solution of the five
reactants over all the spacial sections are given by
(N) = [A]'1 (W) (38)
Application of the theory by the computer program
The program described follows a modular approach in
which the user specifies to the main line program the
options desired, and subroutines are called accord-
ingly to perform specific tasks.
The steps to be accomplished can be summarized as:
a) Input the physical characteristics of the system;
namely, the geometry, temperature, hydro!ogic
characteristics, reaction schemes and correspond-
ing reaction rates.
b) Calculate E1 and «'s for all the sections as
described on equations (9C) and (10). In order to
handle the constraint stated on equation (12), the
program tests the expression:
1-EWQ4
(39)
and if such is the case a^- is recalculated as:
-ij l-E'ij/2Qij (40)
which places "ij well within the tolerable range.
c) Set up the system matrix [A-,-] by computing its
elements as given on equations (22A) and (22B).
It should be noted that the difference between the
[Ai] matrices in equations (31) thru (35) is the
addition of a separate main diagonal term KjKjj^.
In order to conserve space, this matrix is set up
without this term and during the creation of the
matrix of matrices [A], the appropriate VfKjj^-
term is added.
d) Set up the matrix of matrices [A], this is done by
combining an offline disk file containing all the
ViKi terms for the system and the [Ai] matrix.
e) Input of direct discharges into the system and
boundary concentrations, and from these compute
the system source vector (W) as described on equa-
tions (24) and (26).
f) Solve for the reactants concentrations at all seg-
ments by inverting the matrix [~R] and multiplying
it by the waste vector (W).
Optionally, the program can also perform system sen-
sitivity analysis by varying the waste vector (W) and
re-multiplying by [A]'1 and/or changing the reaction
rate constants for any reactants and repeating step
(f). A second option is the computation of dissolved
oxygen deficit and the corresponding dissolved oxygen
concentration by selecting the reaction schemes pro-
ducing the deficit and the associated stochiometric
coefficient.
The computer program has been written for the IBM 370
with a Fortran (IV) 6 or H level compiler. The pro-
gram occupies 140K of core to execute and takes 35
CPU seconds to solve a 10 segment, 8 component system.
As presently written, the program can accommodate a
multi-dimensional system of up to sixty sections and
each section can have a maximum of six interfaces.
The maximum number of reactants is such that when
multiplied by the number of sections cannot exceed
120. This present limitation can be easily expanded.
Application to nitrification
Figure 4 is a schematic representation of the nitro-
gen cycle:
FIGURE 4
MAJOR FEATURES OF THE NITROGEN CYCLE
Since waste loads are usually in the form of organic
nitrogen or ammonia, these species will consume oxy-
gen by the bacterial reactions:(7)
NH4+ +3/2 02 Nitrosomas>NO?+2H++HoO
Bacteria
followed by
N02 + 1/2 0? Nitrobacte^NOj
Bacteria
(41;
(42)
From the stochiometry of the reaction on equation
(41), it takes 3.43 grams of oxygen for the oxidation
of one gram of ammonia as nitrogen to nitrite. The
second reaction takes 1.14 grams of oxygen for the
oxydation of one gram of nitrite as nitrogen to nit-
rate. The entire oxydation process therefore takes
4.57 grams of oxygen per gram of ammonia nitrogen.
Letting:
NT = organic nitrogen
N2 = ammonia nitrogen
N3 = nitrite nitrogen
N4 = nitrate nitrogen
Ng = plant and animal nitrogen
The system to be solved would be:
K25
K36=1.14 K
34
K26=3.43 K23
FIGURE 5
NITROGEN CYCLE WITH DEFICIT COMPONENT
169
-------
If we assume these reactions to follow first order
kinetics, the system can readily be solved using
program FEDBAK03. The computation of dissolved oxy-
gen deficit can be accomplished two ways. A deficit
"species" can be defined (noted Ng above), the decay
of which is the reaeration rate, Ka. The reaction
schemes producing deficit are then defined, and the
corresponding reaction rate would be the product of
the stochiometric coefficient by the reaction rate
of the reaction using up oxygen. A second method
to compute deficit concentrations as done for com-
ponent NI in equations (22) thru (31), one obtains
[B](D)i=3.43[VK23](N2)+1.14[VK34](N3) (43)
where [B] is a matrix similar to the [AjJ matrices
of equations (31) thru (35), except that the main
diagonal term has the reaeration rate Ka instead ^f
K-J-J, (N2) and (N^) are nxl vectors of the steady-
state concentration of these reactants. (D)-j is an
nxl vector of the deficit concentrations over all
segments due to the oxydation of ammonia and nitrite.
The solution to the deficit concentration over all
space is given by:
(D)i=3.43[VK23](N2)[B]-'1+1.14[VK34](N3)[B]-l.(44)
This method is used to compute deficit in program
FEDBAK, by using the optional subroutine.
The application to nitrification and dissolved oxygen
deficit assumed first order kinetics for the bacter-
ial reactions. This should be confirmed by laboratory
studies, or the nature of the system should be care-
fully considered. This computer model has been found
to be very useful as a predictive tool and in provi-
ding insights to the behavior of nitrogen species in
the aquatic environment. On new applications this
will ultimately depend on the applicatively of the
underlying assumptions to the system of interest.
ACKNOWLEDGEMENTS
The author is grateful to Steve Chapra of the Great
Lakes Environmental Research Laboratories and Richard
Winfield of the Manhattan College Department of Envi-
ronmental Engineering and Science for their review
and comments on this paper.
The data for test applications of this model were made
available by Dr. Richard Tortoriello of the Delaware
River Basin Commission. His input to this project is
gratefully acknowledged.
REFERENCES
(1) O'Connor, D.J., "Oxygen Balance of an Estuary".
Jour. San. Eng. Div. ASCE, Vol 86, May 1960, pp 35-55
(2) O'Connor, D.J., "The Temporal and Spacial Distri-
bution of Dissolved Oxygen in Streams". Water Resour-
ces Research, Vol 3, No. 1, 1967, pp 65-79.
(3) Chapra, S.C. and Gordimer S., ES001 A Steady Sta-
te, One Dimensional, Estuarine Water Quality Model,
USEPA,Region II, New York, N.Y. September 1973.
(4) Thomann, R.V., "Mathematical Model for Dissolved
Oxygen". Jour. San. Eng. Div., ASCE, Vol 89, No. SA5,
October 1963, pp 1-30.
(5) Thomann, R.V., System Analysis and Water Quality
Management, Environmental Science Division, New York,
1971.
(6) Chapra, S.C. and Nossa, G.A. HAR03 A Computer
Program for the Modelling of Water Quality Parameters
in Steady State Multidimensional Natural Aquatic Sys-
tem.. USEPA, Region II, New York, N.Y. October 1974
(7) Stratton, F.E. and Me Carty, P.L., "Prediction of
Nitrification Effects on the Dissolved Oxygen Balance
of Streams" Env. Sci. and Tech., Vol. 1, No. 5, May
1967, pp 405-410.
(8) O'Connor, D.J., Thomann, R.V., and Di Toro, D.M.,
Dynamic Water Quality Forecasting and Management,
USEPA, Office of Research and Development, Wash.,D.C.
Report No. EPA-660/3-73-009, August 1973
170
-------
MODELING THE HYDRODYNAMIC EFFECTS OF LARGE MAN-MADE
MODIFICATION TO LAKES
John F. Paul
Department of Earth Sciences
Case Western Reserve University
Cleveland, Ohio 44106
currently at
Large Lakes Research Station
Environmental Research Laboratory-Duluth
' Grosse lie, Michigan 48138
A three dimensional hydrodynamic model is des-
cribed which can be used as a predictive tool for as-
sessing the possible effects of large man-made modi-
fications to lakes. The example of the proposed jet-
port island in Lake Erie is used as a sample applica-
tion of the model.
Introduction
The real value of numerical models is in their
predictive capability. By this is meant their abil-
ity to be used for physical situations that are dis-
tinctly different from those for which they have been
developed. The major use of models has so far been
in the verification sense, that is, they have been
developed to agree with existing sets of data. The
purpose of this paper is to present an example of
the predictive use of one particular hydrodynamic
numerical model.1'2'3
A new jetport has been proposed to be built in
the vicinity of Cleveland, Ohio. One possible site
being considered is a to-be-built dyked area in Lake
Erie near Cleveland. As part of the feasibility
studies for the proposed lake jetport, a numerical
model describing the hydrodynamics of the Lake Erie
area near Cleveland was developed to help determine
the possible effects of such a jetport on the summer
temperature structure in the lake.
A numerical model for a situation such as the
proposed jetport has several advantages. First, once
the model is developed, simulations are relatively
inexpensive to produce, compared to building and run-
ning a physical model or conducting field surveys.
For example, the numerical model to be discussed re-
quires approximately twenty minutes of CPU time for
one day of real-time simulation. Second, it is ex-
tremely easy to simulate different physical condi-
tions on the lake, e.g., different wind directions
and speeds, and different thermal structure. Third,
it is a simple task to alter the model geometry to
simulate the effect of different jetport configura-
tions. In this way the model could be considered as
a design tool.
Another advantage of a numerical model is that
it may be the only alternative for assessing a pro-
posed modification to a lake. For this jetport ex-
ample, field data can only be used to tell what is
happening in the lake at the present time, not what
happens after a jetport is built in the lake. One
conception of the jetport is a two mile by three mile
island located five miles off Cleveland. No previous
experience with modifications of this scale to large
lakes is available. A physical model of this situa-
tion would be extremely expensive, and even if it
were built, its results may be questionable due to
the extreme distortion required in the model and the
inability to properly represent some of the physical
mechanisms occurring in the lake.
Description of the Numerical Model
The equations for the numerical model are de-
rived from the time-dependent, three-dimensional
equations of motion for a viscous, heat-conducting
fluid. The basic assumptions used in the model are:
(a) The Boussinesq approximation is valid. This as-
sumes that density variations are small and can be
neglected in the.equations of motion except in the
gravity term. The coupling between the energy and
momentum equations is retained. (b) Eddy coefficients
are used to account for turbulent diffusion effects
in both the momentum and energy equations. The hori-
zontal eddy coefficients are assumed constant but the
vertical eddy coefficients vary depending on the ver-
tical temperature gradient and other parameters. (c)
The rigid-lid approximation is valid, i.e., the ver-
tical velocity at the undisturbed water surface is
zero. This approximation is used to eliminate sur-
face gravity waves and the small time scales associ-
ated with them, greatly increasing the maximum time
step possible in the numerical computations. In this
approximation, only the high frequency surface varia-
tions associated with gravity waves are neglected.
(d) The pressure is assumed to vary hydrostatically.
The model equations, as described in detail by
Paul and Lick3, are:
1. the three-dimensional, imcompressible
continuity equation,
2. two time-dependent, three-dimensional
horizontal momentum equations,
3. the time-dependent, three-dimensional
temperature equation,
4. the equation of state,
5. the Poisson equation for the pressure.
The boundary conditions used with the above
equations are as follows. The bottom and shore are
taken as no-slip, impermeable, insulated surfaces.
A heat transfer condition proportional to a temper-
171
-------
SCALE:
20 40 MILES
J
TOLEDO
KILOMETERS
BUFFALO
CLEVELAND
AREA CONSIDERED
FOR MODEL APPLICATION
ERIE
FIGURE 1. AREA OF LAKE ERIE CONSIDERED FOR APPLICATION OF THE MODEL
ature difference1 and a wind-dependent stress are
imposed at the water surface. The pressure boundary
conditions are derived from the appropriate horizon-
tal momentum equation. Along the open water bound-
aries either velocity and temperature values are
specified or normal derivatives of the velocity and
temperature are set to zero.
The equations and boundary conditions are put
into appropriate finite differences form in both
space and time. A strictly conservative numerical
scheme is used in the model. In addition, a stretch-
ing of the vertical coordinate proportional to the
local depth is used. With this transformation, the
same number of vertical grid points are present in
the shallow as in the deeper parts of the lake. This
ensures that in the shallow areas there is no loss
of accuracy in the computations due to lack of ver-
tical resolution. Refer to the report by Paul and
Lick3 for details.
Application of the Numerical Model to the Jetport
The section of Lake Erie considered is a sixteen
mile by sixteen mile area near Cleveland (Figure 1).
The jetport configuration used in this example is a
two mile by three mile island five miles from Cleve-
land in approximately fifty feet (15.2 m) of water.
The numerical model has been run with and without the
jetport island. Sample results are presented for
14.8 hours after the start of a 12 mph (5.4 m/sec)
wind from the south. The lake is initially stratified
with a thermocline depth of 30 ft (9.15 m), epilimnion
temperature of 75°F (24°C), and hypolimnion tempera-
ture of 55°F (13°C). Figures 2 through 5 show results
without the jetport island and Figures 6 through 9
show results with the jetport island.
Comparing the horizontal isotherm plots (Figures
2, 3, 6, 7) for the two cases, it is apparent that the
jetport island influences the temperature of the lake
over a large distance (about 6 to 8 miles) from the
island. The velocity plots (Figures 4, 5, 8, 9) also
indicate a large region of influence. This effect is
due to the upwelling of cold water on the eastern
edge of the island and downwelling of warm water on
the western edge. These upwellings and downwellings
result in changes to the stratification structure in
that area of the lake. Since this is a variable-den-
sity model, changes in the temperature structure do
cause changes in the velocity pattern. Using a con-
stant-density, free surface model, Sheng found that
the jetport island only exerted an influence over a
distance of one to two miles into the lake.
The results presented are for only one parti-
cular wind direction. As the wind shifts, the up-
welling and downwelling regions change their posi-
tions around the island. Thus, it can be seen that
the effect of the proposed jetport island during the
summer season would be to erode the thermocline in
that area of the lake. The mixing of epilimnion and
hypolimnion waters may be considered in one way to
be beneficial since it will keep the area of the
lake affected from going anoxic in the late summer,
but in another way it may not be considered benefi-
cial because of the increased nutrient input to the
epilimnion. Also, this forcing of warm water to the
bottom may be detrimental to aquatic species depend-
ent upon colder waters for their existence or repro-
ductive activities.
The model also could be used to predict the ef-
fect of different jetport configurations, for example,
a jetport peninsula instead of a jetport island. The
results presented are qualitative and indicate how a
numerical model might be used to predict the effects
of large man-made modifications to lakes.
Acknowledgement
This work was supported by the U. S. Environ-
mental Protection Agency and the U. S. Army Corps of
Engineers. I would like to thank Dr. W. J. Lick for
his advice while this work was being performed.
Bibliography
1. J. F. Paul and W. J. Lick. A numerical model for
three-dimensional, variable-density jet. Techni-
cal Report, Division of Fluid, Thermal and Aero-
space Sciences, Case Western Reserve University,
Cleveland, Ohio, 1973.
172
-------
W I II D
SCALE
0 1
MILES
ISOTHERM LEGEND
73 . 9°F
72 . 6°F
71 . 3°F
70 . 0°F
68 . 7°F
67 . 1°F
66 . 1°F
61 . 8°F
63 . B°F
62 . 2°F
60 . 9°F
S9 . 6°F
5 8 , 1 ° F
57 . 1°F
(23
(22
(21
(21
(20
(19
(19
(18
(17
(16
(16
(15
(11
(13
3°C)
6°C)
8°C)
7°C)
0°C)
2°C)
5°C)
8°C)
6°C)
9°C)
WIND
SCALE
0 1 IB CM/ S E C
MILES
FIGURE 2 . SURFACE ISOTHERMS FOR MODEL WITHOUT JETPORT
FIGURE4. SURFACE VELOCITIES FOR MODEL WITHOUT JETPORT
SCALE
0 1
WIND MILES
ISOTHERM
73
72
71
70
68
67
66
61
63
62
60
59
58
57
9°F
,6°F
.3°F
. 0°F
.7°F
. 1°F
,1°F
. 8°F
B°F
. 2°F
. 9°F
,6°F
, 1°F
.1°F
LEG
(23
(22
(21
(21
(20
(19
(19
(18
(17
(16
(16
(IB
(11
(13
END
, 3°C )
.6°C)
, 8°C)
.1°C)
1 ° C )
!7°C)
. 0°C )
.2°C)
.B°C)
. 8°C)
.1°C)
, 1°C )
. 6°C)
, 9°C)
N SCALE
/ / \\ 15C./SEC
HIND n I Ltb
*. v \
FIGURE 3 . ISOTHERMS AT HO FT FOR MODEL UITHOUT JETPORT
FIGURES. VELOCITIES AT 10 FT FOR MODEL WITHOUT JETPORT
-------
WIND
SCALE
0 1
MILES
A
B
C
D
E
F
f,
H
I
J
K
L
PI
N
I SOTI
73 .
72 ,
71 .
70 .
68 .
67 .
66 ,
61 .
63 .
62 .
60 .
59 .
58 ,
57 .
HERM
9°F
6°F
3°F
0°F
7°F
1°F
1°F
8°F
5°F
2°F
9°F
6°F
1°F
1°F
LEGEND
(23
(22
(21
(21
(20
(19
(19
(18
(17
(16
(16
(15
( 1 1
(13
. 3°C)
. 6°C)
. 8°C)
. 1 ° C )
, 1 ° C )
. 7°C)
. 0°C)
. 2°C)
. 5°C)
. 8°C)
. 1 ° C )
, 1 ° C )
, 6°C)
. 9°C)
N SCALE
-ft 1\ I 1 -*
/ / 01 1 5 CM/S EC
WIND MILES
FIGURE 6. SURFACE ISOTHERMS FOR MODEL WITH JETPORT
FIGURES. SURFACE VELOCITIES FOR MODEL WITH JETPORT
WIND
SCALE
0 1
MILES
SCALE
A
B
C
D
E
F
fi
H
I
J
K
L
M
N
ISOTHERM
73 .
72 .
71 ,
70 .
68 .
67 .
66 ,
61 .
63 .
62.
60 .
59 .
58 .
57 .
9°F
6°F
3°F
0°F
7°F
1°F
1°F
8°F
5°F
2°F
9°F
6°F
1°F
1°F
LEGEND
(23
(22
(21
(21
(20
(19
(19
(18
(17
(16
(16
(15
(11
(13
, 3°C)
, 6°C)
, 8°C)
,7°C)
, 0°C)
, 2°C)
, 5°C)
, 8°C)
, 6°C)
,9°C)
WIND
0 1
MILES
15 CM/SEC
FIGURE 7 ISOTHERMS AT 10 FT FDR MODEL WITH JETPORT
FIGURE9. VELOCITIES AT 10FT FOR MODEL WITH JET
PORT
-------
2. J. F. Paul and W. J. Lick. A numerical model for
thermal plumes and river discharges. Proc. 17th
Conf. Great Lakes Res., IAGLR, 1974, pp. 445-455.
J. F. Paul and W. J. Lick. Application of a
three-dimensional hydrodynamic model to study the
effects of a proposed jetport island on the ther-
mocline structure in Lake Erie. Report 17-6 of
the Lake Erie International Jetport Model Feasi-
bility Investigation. U.S. Army Engineer Water-
ways Experiment Station, Vicksburg, Miss. 1975.
4. Y. P. Sheng. The wind-driven currents and con-
taminant dispersion in the near-shore of large
lakes. Report 17-6 of the Lake Erie International
Jetport Model Feasibility Investigation. U. S.
Army Engineer Waterways Experiment Station, Vicks-
burg, Miss. 1975.
175
-------
AN EMPIRICAL MODEL FOR NUTRIENT ACCUMULATION RATES IN LAKE ONTARIO
Patricia A.A. Clark
U.S. Environmental Protection Agency
Rochester, New York
Jane P. Sandwick
U.S. Environmental Protection Agnecy
Rochester, New York
Abstract
Based on the chemical concentration data collected
during the International Field Year for the Great Lakes
(IFYGL)--May 1972 through June 1973, monthly average
rates of chemical accumulation have been determined
for total phosphate (TP), nitrite-nitrate (N02-N03),
ammonia (NHs), total Kjeldahl nitrogen (TKN), total
organic carbon (TOC), and ($04). The accumulation
rates are the consequence of such processes as biochem-
ical transformation processes, sediment exchanges, etc.
The model relates the accumulation rate of a particular
substance with the rate of exchange of the total mass
of that substance in the lake and with the total net
loading rate to the lake (tributaries, direct indus-
trial, direct municipal and on-lake precipitation).
The total masses of each chemical substance for each of
the 11 cruises (Figures 1-6) have been calculated using
the numerical integration computer program SPLOTCH
(Boyce 1973) with the input of concentration measure-
ments which were collected from about 75 stations on
the lake at depths of 1,5,10,20,25,30,40,50,100,150
meters and at the lake bottom.3 This study is de-
scribed by Casey, Clark and Sandwick (1976) together
with the U.S. tributary loading rates and the direct on-
lake precipitation loading rates.4 Canadian tributary
loading rates for the same period were presented by
Casey and Salbach (1975).5 The mass balance equation
relating these quantities and the accumulation rate will
now be derived. All quantities in the equation can be
evaluated directly on the basis of the measured lake
concentrations and loading rates so that the equation
can be solved for the accumulation rate in each case.
In addition, analysis of the equation will provide a
means for the assessment of certain assumptions which
are commonly made in large lake limnology.
Accumulation Rate Equation
It is convenient to begin with the hydrodynamic equation
for the conservation of mass in the integral form (see,
for example, Batchelor 1967),
(1)
where e, is the concentration of chemical species i, v_
is the flow velocity and r, is the rate of accumulation
(or loss) per unit volume of the same species. V is the
volume of the fluid (in this case the volume of Lake
Ontario). S is the total surface bounding the volume of
the lake.
The term on the left-hand side of eq. (1) can be written
as
Donald J. Casey
U.S. Environmental Protection Agency
Rochester, New York
Anthony Solpietro
U.S. Environmental Protection Agency
Rochester, New York
where m. is the total mass of chemical species i in
the lake at time t. Cn- designates the second term on
the right of eq. (2). This term can be neglected
whenever (Ap/p )» (AV/V). The-U.S. Army Corps of
Engineers measured a change of about 1 meter in the
level of Lake Ontario (Monthly Bulletin of the Lake
Levels, 1972 and T973).''1 This corresponds to a volume
increment of about 20 km3 so that Av/v^-012. If this
is compared with (Ap/p)~.20 for total phosphate (see
Table 1), which has about the smallest concentration
variation of any of the chemical substances studied,
it is apparent that (Ap/p)» (AV/V) will hold for all
substances.
The second term in eq. (1) is the net loading rate
where Ln-T is the net loading rate (inflow minus out-
flow) due to tributary stream flow, L-JR is the load-
ing rate due to rainfall directly on the lake surface
and L-jS is the net loading due to sediment (sediment
release sediment adsorption). LjTand L^R are shown
in Tables 1, 3, 4, 6, 7, 9. Calculations of LiR are
based on precipitation chemistry measurements re-
ported by Shiomi and Kuntz (1973) and by Casey et al.,
(1975) and monthly total of lake precipitation measured
by Bolsenga and Ragman (1975).'0'4'2 L^ must be
either estimated or calculated.
The third term in eq. (1) is the total net rate of
production of species i
(4)
where T-j is a function of time.
Substituting eqs. (2), (3), and (4) into eq. (1) re-
sults in the following equation.
All quantities in eq. (5) can be determined from mea-
surements except the sum, L-J + T-j = S-j so this sum can
be obtained from equation (5). Eq. (5) may be re*-
written as
dm — LJ +Sj (6)
where , . _ , .T^, ,R
Equation (6) is similar to that obtained by
Vollenweider (1969),
dmw — J— Q
dt ~ ~v~
(7)
176
-------
where mw is the total amount of substance w in the lake
at time t, J is the rate of tributary loading of sub-
stance w to the lake, Q is the mean discharge out of
the lake, V is the mean volume of the lake and a is
the sedimentation rate coefficient.'2
In comparing eqs. (6) and (7) L-j is the net loading
rate (inflow-outflow) obtained directly from measure-
ment. The comparable terms in eq. (7), J-Qm /V, in-
volve an assumption about the outflow. The actual out-
flow and the Qn^/V assumed form are compared. The in-
clusion of a surface contribution in the source term
in these equations seems prudent in view of the dis-
cussion by Dillon and Kirchner (1975), Kirchner and
Dillon (1975), Dillon (1975) and Chapra (1975) with re-
gard to phosphate. 8'9<7-6
dmw/dt is obtained from a numerical differentiation of
mi (t) calculated by means of the SPLOTCH program. It
is assumed that the chemical masses so obtained are
characteristic of the average chemical masses in the
lake for the month during which the cruise occurred.
The assumption seems justified on the basis of the
relatively smooth progression of mass determinations
from cruise to cruise. For those months for which no
cruises took place, linearly interpolated values have
been obtained. The monthly variations in chemical mass
contents of the lake are plotted in Figures 1-6 and
will be discussed in the accumulation rates section.
Numerical differentiation of m-j with respect to t is
performed by passing a parabola through 3 successive
monthly mass values, m,, mz, m3. The derivative at
the mid point is given by
and 1973 and early winter 1972, reflecting seasonal
perturbations from the mean (see Figure 1). Thus
d m
dT
m3-mjl +0(h2)
2 h
(8)
where h t -t _1 (see, for example, Wylie, 1951). In
this case h = month, however, dm/dt is expressed in
units of metric tons/day. The monthly values of dm/dt
for each substance are provided in Tables 2, 5, 8.
These tables also include the total monthly loading
rate L and the calculated value of the monthly source
term S for each substance.
Nutrient Accumulation Rates
For each substance studied, the variation of the mass
content is shown and described. A numerical time dif-
ferentiation of the monthly mass content has been per-
formed and is tabulated. This quantity together with
the monthly loading rates to the lake have been sub-
stituted into eq. (6) to yield the source term. The
nature of the source term variation is discussed in
order to extract information regarding the nature of
the physical processes.
Using the IFYGL data we have examined the Vollenweider
model which assumed a source term of the form, -crmw
(eq. (7)). For each of the 6 substances of this study,
the model proved inadequate since the structures of the
functions S and m (or mw) for each substance are very
different. The assumed form of the outflow term in eq.
(7), Qmw/V, when compared with the measured St.
Lawrence loading proves a useful model for nitrite-
nitrate, total Kjeldahl nitrogen, sulfate and organic
carbon while in the cases of total phosphate and ammo-
nia, the model predictions deviate considerably from
the measured value.
Total Phosphate
The total phosphate content of the lake shows an aver-
age pf 9.5% from the mean with a maximum deviation of
19%. The maximum deviations occurred in spring 1972
. — . — mxlCP Melr
FIGURE 1 THE MASS CONTENT (ra) AND THE PRODUCTION RATE CS) OF TOTAL PHOSPHATE
DURING THE FIELD YEAR.
dm/dt will be small. Table 1 lists the various contri-
butions and the net total loading rate of total phos-
phate by month. The total net loading rate to the lake
varied by a factor of 10 reaching a maximum in the
December 1972 through March 1973 period and a minimum
in the August through October 1972 period. Having
Table 1 Total phosphate loading rates to Lake Ontario
(metric tons/day)
Month
Apr 1972
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Jan 1973
Feb
Mar
Apr
May
Mean
N 1 agara
River
19.2
12.5
2 It. 0
20. It
22.1
17.2
15. If
19.3
31.5
18. G
23.5
28.9
17. 8
lit. 5
20. ll
U.S.
Tr 1 butar 1 es
18.it
12.5
11.1
12. 7
It. 6
2.9
It. 8
9.0
11|.9
12.5
8.9
18.7
11|.2
7.7
10.9
Direct municipal and
Industrial
Month
Apr 1972
May
Jun
July
Aug
Sep
Oct
Nov
Dec
Jan 1973
Feb
Mar
Apr
May
Mean
U.S.
.16
.lit
.111
.15
.13
.15
.lit
.111
.18
.18
.19
.17
.16
.15
.1C
Canada
8.3
7.3
7.1
7.7
6.7
7.9
7. It
7.3
9.1
9.6
9.9
9.0
8.3
7.9
8.1
Canad 1 an
Tr 1 butar 1 es
5.1
3.9
3.6
5.8
1.9
1.3
2. 0
2. 2
It. 8
3-D
2.6
5.7
3.9
2.7
3.5
Dl rect
Preclp.
It. 9
6.0
7.9
It. 8
6. It
5.1
5.8
7.9
8.2
2.8
k.O
7.5
7.7
5.8
6.1
St. Lawrence
Rl ver
20.7
19.8
21.7
27.2
33.6
21. G
16.9
15.8
13.3
12.9
20. It
25. If
27.0
28.0
21.7
Net loading
rate
35. it
22.5
32.1
2l4.lt
8.2
13.0
18.6
30.0
55.lt
31|.6
28. 7
It It. 6
25.1
10.8
27.lt
obtained the mean monthly numerical derivative, dm/dt,
and the total net loading rate L, eq. (6) yields the
source term. All of these quantities are listed in
Table 2.
177
-------
Total phosphate and nitrite-nitrate mass balance
equation terms (metric tons/day)
Table3 -
Nitrite-nitrate loading rates to lake Ontario
(metric tons/day)
Total Phosphate
Ni trIte-NItrate
Month dm/dt/lO*
May 1972 1 1.8
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Jan 1973 -1
Feb
Mar 1
Apr
May
88
33
13
19
65
55
02
25
07
19
92
08
Mean ,39
•L/10*
2.25
3.21
2. 1.1.
.82
1.30
1.6G
3.00
5.51.
3.4G
2.87
4.46
2.51
1.08
2. 68
s/io*
.77
-2.33
-2.11
.69
-1.11
-1.21
-2.45
-5.52
-I..71
-2.80
-3.27
-1.59
-1.00
-2.27
dra/dt/10
-5.60
.87
• .28
-3.19
-1.C3
-1.11
-1.C1
.03
3.0C
3.14
• .34
-2.50
-2.31
.88
L/10J
.09
.28
.03
.01
.06
.06
.14
.17
.15
.07
.09
.11
.10
.10
S/10*
-5.69
.59
• .31
-3.20
-1.69
-1.17
-1.75
.14
2.91
3.07
.43
-2.61
-2.41
-.115
Throughout the field year, there is a loss rate for
phosphate, -S, which averages 2.27 metric tons/day.
This monthly loss rate varies by a factor of about 7
during the field year with maximum losses occurring in
the winter. The August through October period shows a
minimum loss rate.
Nitrite-Nitrate
The total nitrite-nitrate content of the lake shows
very definite seasonal variation (see Figure 2). Max-
imum mass content is characteristic of the early summer
1972 and spring 1973 periods with a low occurring in
. — . — mxlO5 Melrrc Tom
S xlO3 Metric Tom/day
FIGURE 2 THE MASS CONTENT (m) AND THE PRODUCTION RATE (S) OP NITRITE-NITRATE
DURING THE PIELD YEAR.
the late summer through fall period. The range of
variation is a factor of about 2.3. In Table 3 a
compilation of the partial and net total loading
rates for NOo-NO., is provided. This net total
loading rate varied by a factor of more than 20
during the field year, but is typically more than
an order of magnitude smaller than either dm/dt or S.
This indicates that a major source of nitrite-nitrate
variation is due to the biochemical transformation
rather than loading rate variations.
In contract to total phosphate, the source term
changed sign during the year so that losses of NOg-NOa
occurred in the spring and summer and production was
noted during the winter months.
Month
Apr 1972
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Jan 1973
Feb
Mar
Apr
May
Mean
Niagara
River
116.2
112.7
182.9
122.1
93.9
24.6
1(1.2
93.6
130.5
175.lt
133.8
153.3
137.2
218.7
121.. 0
U.S.
Tributaries
85.7
57.3
62.6
63.9
16.5
8.3
13.3
46.5
73.1
611.7
57.8
98.1
77.5
36.6
5ll.lt
Canad 1 an
Tr 1 butar I es
17.3
11.9
15.lt
17. C
3.5
1.5
2.2
9.7
16.1
111. 2
llt.S
22.2
17.1
8.5
12.3
St. Lawrence
River
100.0
158.6
62.6
222.5
169.7
29.0
60.3
90.9
103.2
136. 2
181.7
258.lt
198.9
226.5
li|3.1
Direct municipal and
Industrial
Month
Apr 1972
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Jan 1973
Feb
Mar
Apr
May
Mean
Ammonia
U.S.
.47
.4it
.1)2
.39
.35
.35
.38
. UO
.Sit
.It 9
.53
.5I|
.5"t
.48
.45
Canada
2.3
2.2
2.1
1.9
1.7
1.7
1.9
2.0
2.7
2. It
2.6
2.7
2.7
2. It
2.2
Direct
Precl p.
49.2
60.7
79. It
It8. 5
6".. 3
51.7
58.0
80.1
58.0
28.7
1.0.2
75.9
78.1
58.0
59. U
Net loading
rate
171.2
8G.6
280.2
31.9
11.1
59.2
56.7
lltl.lt
172.7
149.7
67.7
94.2
1111.2
98.2
109.6
The total ammonia content of the lake shows a strong
seasonal variation (Figure 3). Highest mass content
,- — , — m x 10 Metric Tom
" Sx]Q2 Meirie Ton i/day
FIGVRE 3 THE MASS CONTENT (m) AND THE PRODUCTION RATE (S) OP AMMONIA
DURING THE FIELD YEAH.
occurred in the late summer through fall of 1972.
After reaching a midwinter minimum, the mass content
climbed with onset of spring 1973. Provided in Table
4 are the loading rate contributions of ammonia, which
show a variation by a factor of about 3 during the
field year.
178
-------
Table A
Ammonia loading rates to Lake Ontario
(metric tons/day)
Month
Apr 1972
May
Jun
Jul
Aug
iep
Oct
Nov
Dec
Jan 1973
feb
Mar
Apr
May
Mean
Month
Apr 1972
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Jan 1973
Feb
Mar
Apr
May
Mean
N 1 agar«
Klver
27.8
16.0
U7.5
33.3
27.6
17.7
17.2
60.7
lii.lt
30.5
9.5
20.8
15. It
12.0
25.0
Direct
U.S.
3.5
2.9
3.0
2.6
2.5
2. It
2.5
3.5
3.5
2.8
3.0
3.3
3. it
3.0
3.0
3 U.S.
Tributaries
16.2
9.9
13.7
10.1
3.9
2.6
6.1
17.6
19.0
15. It
13.5
18.6
lit, 6
9.8
12.2
municipal and
1 ndustr 1 al
Canada
31.it
25.9
25.9
23.7
22.6
20.7
22.6
31.8
31.1
25.6
27.1
30. 0
30.6
27.0
26.9
Canad 1 an
Tr I butar I es
it. 5
2.7
it. 7
3. It
1.3
.85
2.2
C.5
6.5
5.1
It. 7
5.7
It. 3
3. It
it.O
Dl rect
Precl p.
31.0
38.3
50.0
30.6
U0.9
33.7
36,6
50,5
52.2
18.1
25.it
U7.9
It9.2
36.6
38.6
St. Lawrence
River
3.3
it. It
12.5
29.2
32.8
13.0
11.3
11.1
13.0
19.2
26.5
36. It
27.8
16.5
18.lt
Net loading
rate
111.1
91.3
132.3
7it.5
66.0
65.0
75.9
159.5
113.7
78.3
56.7
89.9
89.7
75.3
91. It
Because of the comparable sizes of the 3 terms in eq.
(6) (see Table 5), loadings as well as such processes
as biochemical transformation and sediment exchange are
important to changes in the ammonia mass content of the
lake.
Table5 Ammon I a and total Kjeldahl nitrogen - mass balance
equat I on terms (r.ietr I c tons/day)
Ammonla Total Kj e1dah 1 NItrogen
Month dm/dt/101 L/10* S/10*
May 1972
Jun 3
Jul
Aug
Sep
Oct -1
Nov -3
Dec -2
Jan 1973
Feb
Mar 1
Apr 1
May
93
b2 1
81
10
25
10
15 1
38 1
Sit
13
01
17
Sli
91 .02
32 2.30
75 .07
66 .70
65 .140
76 -l.CG
CO -14.75
lit -3.52
78 -1.C2
57 .It It
90 .11
90 .27
75 .19
dm/dt/103 L/10* S/lo'
-1
_1
_ 1
53
r.i4
00
»7
10
75
31
10
18
22
76
2!
4S
18
01
13
14 -1
1)2 -1
01 -1
17 -1
23
16
13
19
21
18
35
75
13
01
12
76
"4«
33
02
35
95
42
30
Total Kjeldahl Nitrogen
Figure 4 shows the seasonal variation of the total
Kjeldahl nitrogen content of Lake Ontario during the
field year. High values were characteristic of the
summer 1972 followed by low levels during the winter
and spring 1973. A variation by a factor of 20 oc-
curred in the total net loading rate (see Table 4), L.
1 S x 10^ Metric ToTivday
FIGURE 4 THE MASS CONTENT (m) AND THE PRODUCTION RATE (S) OF TOTAL tUELDAHL NITROGEN
DURING TKF, FIELD YEAR.
As is indicated in Table 6 a considerable difference in
the relative sizes of dm/dt, L and S was noted during
the field year. In spring 1972, winter and spring 1973
the magnitudes of the three terms are comparable while
during the summer and fall L is smaller in order of
magnitude than dm/dt and S. Thus the biochemical
transformations and sediment exchange processes are the
Table 6 • Total Kjeldahl nitrogen loading rates to Lake Ontario
(metric tons/day)
Month
Apr 1972
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Jan 1973
Feb
Mar
Apr
May
Mean
Month
Apr 1972
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Jan 1973
Feb
Mar
Apr
May
Mean
NI agara
Klver
117.3
89.8
91.6
110.0
138.0
m.s
85.9
92.9
109.2
93.9
106.5
107.6
115.8
113.5
106.9
U.S.
Tr 1 butar 1 es
6lt.3
It It. 3
146.8
U2.C
18.9
10.3
18.0
It2.l|
55.8
51.8
39.1
60.8
U9.2
31.3
Ul.O
Direct municipal and
1 ndustr 1 a)
U.S. Canada
5.2
it. it
U. 5
3.9
3.7
3.6
3.7
5.3
5.2
ll.3
It. 5
5.1
5.1
It. 5
It. 5
111. 8
35.0
35.6
31.5
29.6
29.0
28.1
30.1
U0.9
3lt.5
36.6
Il0.lt
U1.2
36.0
35.0
Canad Ian
Tr I butar 1 es
36.0
36.6
i|2.9
U5.0
18.5
10.5
18.1
36.0
l|2.i|
ill. 3
33.2
33.5
26.5
28.2
32.1
Direct
Precl p.
It7.lt
58.5
76.5
H6.8
62.5
51.5
55.9
77.2
79.7
27.6
38.8
73.2
75.3
55.9
59.1
St. Lawrence
Rl ver
98.1)
85. 7
2011.6
153.2
128.lt
211.3
197.9
117.5
106.3
99.1
130.1
132.lt
98.7
89.7
132. It
Net loading
rate
213.6
182.9
93 3
126.6
lltl.8
18.1
11.8
166. It
226.9
15U.9
128.6
188.2
2lk.lt
179.7
11(6.2
179
-------
dominant sources for changes in the TKN content of the
lake during the summer-fall period while loading con-
tributions became more important in the winter.and
spring. The TKN source term, S, in eq. (6) changes
sign during the year with losses indicated in the late
summer through winter periods and production in both
spring 1972 and 1973.
Sulfate
May, June and July measurements are missing because of
difficulties in the chemical analysis of these samples.
Sulfate mass content of the lake remained fairly uniform
,. _ . _ mxlO'Meirk Tor
1973
M J J
S O N D
F M A M
FIGURE 5 THE MASS CONTENT (.) AND PRODUCTION RATE (S) 0? SULPATE
DURING THE FIELD YEAR.
throughout the field year so that dm/dt « 0. This then
required a balance between S and L. On the basis of the
Month
Aor 1972
May
Jun
Ju]
AUP
Sep
r>ct
Nov
nee
Jan 1973
Feh
Mar
Apr
May
'Van
Month
Apr 1972
May
Jun
Jul
AUK
S*p
net
Nov
nee
Jan 1973
Feb
Mar
Apr
May
Table/ Sulfate
(m
loading rate to Lake Ontario
etrlc tnns/day)
Niagara U.S.
P.lver Tributaries
...
...
6609
68U3
11507
16120
15822
U163
H259
11(732
114961
151149
13016
...
...
...
1327
731
9148
2815
4080
3605
2855
14373
3260
269«
2P60
nlrert municipal and
i ndus tr 1 al
U.S. Canada
...
...
27.3
27.0
27.5
38.9
38.5
31.6
32.lv
37.1
37.6
33.0
...
...
...
132
130
132
187
186
153
157
179
181
159
Cana-1 Ian
Trlhutarlps
...
...
656
358
lilq
12U3
1822
16014
1311
1786
1262
13148
1181
nirert
Prect n.
...
...
5PS
1491
533
736
760
263
370
6H8
717
53?
St. Lawrence
D|Ver
...
---
...
1839U
20110
210143
21U146
1752"
163140
17795
19521
20680
10771
19263
Met loading
rate
...
---
— .
- 90U7
-11530
- 7l4?7
- 306
5180
ill 80
118P
2105
- 261
150
source term, Table 7 shows sulfate utilization in the
summer through fall period and sulfate production in
the winter.
Tahle 8 Sul
Month dm/rtt/10
Hay 1972
Jun ----
Ju)
AUK
Sen 0
net 0
Nov 0
nee 0
Jan 1973 0
Feb 0
Mar 0
Apr 0
May 0
Mean 0
Sulfate
L/105
....
- .09
- .12
.07
.00
.05
.03
.01
.02
.00
.00
.01
S/104
....
....
....
.09
.12
.07
.00
.05
.03
.01
.02
.00
.00
.01
dm/rft/10
1,35
11.63
2.76
.23
.31
-1.39
-3.69
-14.66
-2.76
.89
1.1*8
.89
1.85
.10
L/104
.20
.Oil
.15
.18
-.02
-.11
.03
.23
.2.14
.18
.32
,2I|
.19
.111
S/104
1.15
l|.59
2.61
.05
• .29
-1.28
-3.72
-11.89
-3.00
.70
1.16
.65
1.67
.116
Total Organic Carbon
Strong seasonal variations in the total organic carbon
content of the lake are illustrated in Figure 6.
Peakinq in the summer-fall 1972 period, the TOC content
Sx10d Metric Toni/doy
FIGUHE 6 THE MASS CONTENT (m) AND THE PRODUCTION RATE (S) OF TOTAL ORGANIC CARBON
DURING THE FIELD YEAR.
fell to a midwinter minimum before beginning a gradual
spring rise. A comparison of the terms in eq. (6) as
shown in Table 9 indicates that the main balance was
between dm/dt and S since L was an order of magnitude
smaller. Thus changes in the TOC content of the lake
are mainly a consequence of biochemical transformations
rather than loading rate differences.
33.1
isn
sol
-1B52
180
-------
Table 9
Total organic carbon loading rates to Lake Ontario
(metric tons/day)
Month
Apr 1972
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Jan 1973
Feb
Mar
Apr
May
Mean
Month
Apr 1972
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Jan 1973
Feb
Mar
Apr
May
Niagara
.(Iver
U78
2075
1323
1925
2557
1871)
1051
298
1067
18811
1838
2102
2382
21(00
1732
Dl rect
1
U.S.
1*8.9
U0.3
1.1.7
36.7
31). 5
33.5
31). 6
1*9.1
50.1
39.5
1)1.9
K6.7
1(6.9
1)1.5
U.S.
Tr 1 butar 1 es
711)
525
369
379
325
281
317
1*22
519
377
255
1)68
36>)
280
UOO
munlcl pal and
ndustr 1 al
Canada
5i). 2
1)1). 2
U5.7
1(0.5
37.9
37.2
37.9
51). 2
53.7
1)3.6
1)6.2
51.8
51.6
1)5.5
Canadl an
Tributaries
930
716
1)80
531
502
1)50
1)87
717
672
1)58
302
509
397
376
538
Dl rect
Precl p.
1)1(8
552
722
1(1)1
590
1)86
528
729
753
261
366
691
710
528
St. Lawrence
River
1667
1921
2601)
1891)
2233
3320
3562
1935
813
051
1002
61)7
1591
1812
1832
Net loading
rate
2006
2032
377
11)59
1813
- 158
-1107
33I(
2302
2U12
181)7
3222
2361
1859
8. Dillon, P.J. and W.B. Kirchner, 1975, Reply, Water
Resour. Res. Y\_, p. 1035-1036.
9. Kirchner, W.B. and P.J. Dillon, 1975, An empirical
method of estimating the retention of phosphorus
in lakes, Water Resour. Res. V\_, p. 182.
10. Shiomi, M.T. and K.W. Kuntz, 1973, Great Lakes
precipitation chemistry: Part 1. Lake Ontario
basin. Proc. of the 16th Conference on Great
Lakes Research, pp. 581-602.
11. U.S. Army Corps of Engineers, 1972 and 1973,
Monthly Bull, of the Lake Levels, Detroit, Mich.
12. Vollenweider, R.A., 1969, Moglichkeiten und
Grenzen elementarer Model!e der stoffbilanz von
Seen, Arch. Hydrobiol., pp. 1-36.
13. Wylle, C.R., Jr., 1951, Advanced Engineering
Mathematics, McGraw Hill Book Co., New York.
1)1.9
558
11)83
References
1. Batchelor, G.K., 1967, An Introduction to Fluid
Dynamics, p. 74, Cambridge University Press,
New York, 1967.
2. Bolsenga, S.J. and J.C. Ragman, 1975, IFYGL
Bulletin #16, pp. 57-62, National Oceanic &
Atmospheric Administration, Rockville, Maryland
20852.
3. Boyce, P.M., 1973, A computer routine for calcu-
lating total volume contents of a dissolved
substance from an arbitrary distribution of a
dissolved substance from an arbitrary distribu-
tion of concentration profiles, Technical Bull.
No. 83, CCIW, Burlington, Ontario.
4. Casey, D.J., P.A. Clark and J. Sandwick, 1976,
Comprehensive IFYGL materials balance study of
Lake Ontario (preprint).
5. Casey, D.J. and S.E. Salbach, 1975, IFYGL stream
materials balance study, Proceedings 17th
Conference on Great Lakes Research, Inter-
national Association for Great Lakes Research,
pp. 668-681.
6. Chapra, S.C., Comment on "An Empirical Method of
Estimating the Retention of Phosphorus in Lakes"
by W.B. Kirchner and P.J. Dillon, Water Resour.
Res. 11, p. 1033-1034.
7. Dillon, P.J., 1975, The application of the
phosphorus-loading concept to eutrophieation
research, Scientific Series No. 46, Inland
Waters Directorate, CCIW, Burlington, Ontario.
181
-------
MODELS FOR EXTRAPOLATION OF HEALTH RISK
William M/ Upholt
Environmental Protection Agency
Washington, B.C.
Extrapolation models for estimating the risk
of adverse effects on human health resulting from
low dosages of radiation to which man may be exposed
may assume a threshold dosage below which the risk
becomes vanishingly low. Aside from theoretical
considerations such an assumption is not particu-
larly helpful unless there is a reasonable basis
for estimating at what dosage that threshold
exists. Moreover, to be most useful in consider-
ing the balance between risk and social cost of
regulation, the model should provide both a best
estimate of risk and an estimate of confidence in
that estimate.
Background
Historically, it has been the practice for
regulatory agencies to attempt to assure the
public that they can promise safety from adverse
health effects caused by the toxicants they are
regulating. This concept was challenged in the
case of ionizing radiation in the first instance
and in the case of chemical carcinogens more
recently. In both cases it was claimed that there
is no reason to assume a threshold and, therefore,
there can be no safe dosage. The regulators of
radiation realized very early that there was no
way to completely eliminate all exposure to ion-
izing radiation and so they were forced to regu-
late at exposure levels of acceptable risk rather
than no risk. In the case of chemical carcino-
gens, there is still a strong opinion that no
preventable exposure is acceptable and thus com-
plete elimination of all exposure to any control-
lable carcinogen is the only regulation that is
acceptable. Nevertheless, for a number of years
some scientists have recognized the difficulties
of completely eliminating all exposure to certain
carcinogens and so they attempted to define an
acceptable risk as one that is mathematically
"virtually zero." This "virtual zero" may be 1CT9>
10~H, or some other figure depending, presumably,
on the size of the population at risk.
A more recent school of regulatory decision-
makers insists that the determination of an "ac-
ceptable risk" depends in part upon the cost of
achieving a lower risk. Thus, according to this
school, some form of cost/benefit balancing is
necessary to rational decision-making. For pur-
poses of this paper the latter position is taken.
Cost/Benefit Balancing
It is not within the scope of this paper to
discuss the many models for decision-making.
Neither is the use of the term cost/benefit bal-
ancing intended to refer necessarily to costs and
benefits in common units and thus arrive at a
critical equation for making the regulatory deci-
sion. Rather it implies only that both costs and
benefits must be considered by the decision-maker
before he arrives at his final decision. No spe-
cific units are prescribed nor is it necessary to
use the same units for both costs and benefits.
In fact, it may be undesirable to use dollars or
equivalents because of the psychological implica-
tion of equating human health to dollars. It is
even possible in some cases to describe costs or
benefits or both in non-numerical but quantitative
terms such as "less than background" or to compare-
them with other more familiar but similar costs
or benefits. Nevertheless, for modeling pur-
poses, at least, it is desirable to strive for
understandable numerical terms.
Of course, both costs and benefits may be
reversed depending upon the viewpoint of the
observer. Even the same observer may reverse the
terms from time to time depending upon how he
views the decision he is about to make or the
audience to which he is addressing his argument.
To avoid needless confusion in this paper I have
arbitrarily chosen the viewpoint that one purpose
of the Environmental Protection Agency is to
reduce risk of adverse health effects and thus any
reduction in risk that can be attributed to a
regulatory action is a benefit. To complete this
rationale, the deprivation sustained by society in
having to do without the product in question or
the increased cost of the product associated with
complying with the regulation is the cost to so-
ciety of achieving the reduced risk.
Threshold Concepts
Accepting the rationale that costs of regu-
lating a product must be justified in terms of
reduction in risk does not eliminate the useful-
ness of the concept of a threshold.
A threshold is normally defined as the lowest
dosage at which a given effect is produced. If
the effect is one commonly found in the population
even in the absence of the substance in question
then the threshold becomes the lowest dosage at
which the frequency of the effect rises above the
background level. Such a point is difficult or
impossible to determine experimentally because of
the principles of variability and the empirical
limits to the size of experimental populations.
Thus, it can best be approximated by using a suit-
able model for extrapolation from points more
easily determined experimentally. Though it is
always simpler to build a model based upon a
smooth continuous curve, it is more important that
the model approximate the empirical evidence.
Thus, if there is adequate evidence of an unex-
plained or unanticipated break or other irregular-
ity in the slope of the curve, the model should be
modified to accommodate such empirical evidence if
it is to be of maximal usefulness in the very
practical world of regulation.
There is a concept of long standing in toxi-
cology that effect of a toxicant depends upon dos-
age. This does not mean that higher dosages nec-
essarily produce more severe or more frequent
effects, though this is often true. For instance,
if the effect in question is delayed in its devel-
opment, higher dosages may produce a more serious
effect such as death which prevents the develop-
ment of the effect in question. Actually, it is
quite common for a substance to have a reversal in
type of effect at extremely low dosages as compared
to much higher dosages. Thus it is well known
that odors that are strongly attractive at very
low dosages may be very repugnant at higher dos-
182
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ages. It is also true that substances such as
vitamins that are essential to good health at low
dosages may be toxic at high dosages. For such
substances it is reasonable to assume that a
dose/response curve will go through an inflection
point where the slope changes from negative to
positive if frequency of adverse effect is shown
on the ordinate and dosage on the abscissa. Such
a point might well be considered as a threshold
even though there is a background of effects from
other causes which means that the curve never
crosses the x-axis. Since, in such cases, the
adverse effect from very low dosages is apt to be
different, and possibly independent of the adverse
effect at higher dosages, it is probably more
reasonable to consider this point an intersection
of two curves relating effects of the substance
caused by different mechanisms.
Clearly there may also be theoretically
sound mechanisms for a positive intersect with the
X-axis and also for inflection points showing a
sharp change in slope. Thus, the observed effect
of a substance may require a two-stage metabolic
reaction within the body or a natural defense
mechanism may be far more effective at very low
dosages than at even slightly higher dosages. For
instance, the normal organism may have an excess
of cholinesterase that prevents cholinergic symp-
toms at relatively low dosages of cholinesterase
inhibitors, but once the excess is exhausted, the
development of cholinergic symptoms occurs over a
very narrow range of increased dosages. The ob-
served symptoms may thus have an apparent threshold
even though the cholinesterase inhibition
curve may have quite a different slope with no
distinct threshold.
Models for Extrapolation of Risk
Traditional Threshold Model
Faced with the need for estimating risk at
the relatively low dosages to which human popula-
tions are exposed, and the frequent necessity to
conduct toxicity testing at much higher dosages, a
regulatory agency has no alternative but to rely
upon extrapolation by means of some model relating
dosage to effect, unless it finds it possible to
completely stop all exposure to the substance
being regulated (or alternatively decides to'
take no regulatory action). Faced with this prob-
lem and the social demands for "safety," regula-
tory agencies have long found it convenient to
assume that there is a threshold or true "no
effect" level for any particular adverse health
effect and that levels producing no observed
effects in experimental animals are a reasonable
approximation to that true threshold. Recognizing
the realities of experimental variance and limited
numbers of experimental subjects, a compensatory
"safety" factor was introduced to assure that the
standard for regulation was at or below the true
threshold. The size of this factor depends upon
the same factors that affect experimental variance
(size and uniformity of test population and vari-
ability between replications in the same and dif-
ferent laboratories). In addition, another factor
was added to cover the undetermined physiological
differences between man and the experimental
organism. The size of this factor might depend
upon whether or not there is evidence of human
exposure and other aspects of our knowledge of
Che comparative physiology and toxicology between
the species involved.
This model for estimating risk to human popu-
lations has been satisfactory in those cases where
the cost to society from the resulting regulations
has not been exorbitant and the adverse effects
have rarely been observed in man. It does not
provide a quantitative estimate of risk, nor of
benefit of the regulation in terms of reduced
risk, and therefore is not very helpful in deter-
mining whether or not the societal cost of the
regulation is reasonable. Thus, it encourages
over-regulation when the adverse effect is easily
detected and immediate but it encourages under-
regulation when the adverse effect is delayed or
otherwise difficult to associate with human expo-
sure.
It is the latter aspect of this type of
extrapolation model that has led to a demand that
a different model, namely a model which postulates
no threshold, be used for regulating substances
suspected of causing cancer or other adverse
effects that may have an obscured cause. Unfor-
tunately, many individuals have combined this very
rational demand for a "no threshold" model with
the less rational desire for absolute safety and
concluded that the only acceptable standard for
such effects is zero exposure or as near to that
as can be achieved in the real world.
Interestingly, the other aspect of the tradi-
tional "threshold" model (that it encourages over-
regulation of substances causing readily apparent
adverse effects) also should have led to demand
for a more realistic model that would provide a
more quantitative estimate of risk, thus reducing
societal cost of needless over-regulation.
No Threshold Models
The assumption of no threshold demands
more emphasis on the shape of the dose/response
curve and its position as related to the axes. It
also requires a clearer description of the
effect to be assessed and the time at which the
effect is to be observed. In the case of a de-
layed effect such as cancer, it may be a problem
to maintain the experimental animals alive long
enough for the cancer to be observed. This period
often approaches the life expectancy of the unex-
posed animals. Even at such a termination of
observation, the effect seen may not be an obvious
cancer but rather a neoplasm that must be care-
fully examined and classified by an experienced
pathologist. If some other effect such as a
benign tumor can be described as a precursor to
the adverse effect of principal concern (such as
cancer) then it is possible to consider this as
the effect to be observed. On the other hand,
there should be a clear distinction made between
various effects in describing the extrapolation
model. Thus, if the experimental end point is to
be cancer at 24 months of exposure, then a benign
tumor that might become malignant at 30 months
does not meet the definition. If, on the other
hand, benign tumors at 24 months is the end point
then that could well include frank cancers (pre-
sumably developed from the benign tumors) as well
as earlier deaths if benign tumors were present at
death. Some statisticians have attempted to de-
velop extrapolation models that take "time-to-
cancer" into account since there is experimental
evidence that the latent period of cancer is
longer at lower levels of exposure. Even in the
case of relatively acute effects, the presence of
precursors to the adverse end effect must be
183
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clearly recognized and considered in developing an
extrapolation model. For instance, in the case of
cholinesterase inhibition, mentioned above, the
adverse health effect of major concern may be
serious cholinergic symptoms. Such symptoms,
though clearly recognizable, may not be defined
easily. It is common to use depression of cholin-
esterase activity in peripheral blood as a more
reproducible end point. However, significant
depression in such activity may be detected in the
absence of symptoms, and, because cholinesterase
can be readily regenerated in. the normal body, a
low but detectable level of cholinesterase may be
of no particular concern.
It is possible to carry this argument to the
extreme in which it can be claimed that any for-
eign substance reaching a living cell will produce
some reaction in that cell and thus there is no
possible "no-effect" level of exposure that re-
sults in such contact with a cell. The conclusion
is simply that the end effect of concern must be
clearly defined as well as the point in time at
which it is to be observed.
Having agreed upon the definition of the
effect to be observed and the period of observa-
tion, the simplest extrapolation model is a
straight line on an arithmetic scale intersecting
the origin (in the case of a "no threshold" model)
and some observable or experimentally determined
point. This model recognizes the principle that
frequency of effect usually increases as dosage
increases. It ignores experience that shows that
the most common curve relating observed effects to
dosage is sigmoid in shape. C.I. Bliss developed
a widely acclaimed model for use in the experimental
range that used probability units (standard deviation
using five as the arbitrary unit for 50 percent
effect) as the ordinate and the logarithm of the
dosage as the abscissa. This model often produces
a satisfactory straight line in the usual experimental
range of 30 percent to 70 percent effects. Mantel
and Bryan used this relationship as the basis for
their model but they chose to use a slope of one
regardless of the experimental slope (which is
frequently greater than one) on the basis that
extrapolation is always dangerous so one should be
conservative in the sense of minimizing the risk
of underestimating the probability of effect at
any given dosage. For the same reason,they chose
as a determinant point for their model the upper
99 percent confidence limit for the estimate of
probability of effect at the highest dosage tested
at which no effect was observed.
Numerous other models have been designed in
an effort to accommodate certain other observed
and theoretical characteristics of the dosage/
response relationship. Most of these models agree
quite well with observed points (which are usually
in the range of 30 percent to 70 percent response,
except for those that are either 0 percent or 100
percent) but diverge considerably at very low
levels—those levels of greatest concern to the
regulatory agencies.
It is perhaps surprising that most modelers
have chosen to adopt a series of assumptions, as
did Mantel and Bryan, described as conservative
and designed to avoid underestimating the risk at
any particular dosage. Probably this can be
explained on the basis that they have been more
concerned with the risk of adverse effects than
they have been with cost to society. This is per-
haps characteristic of an affluent society that is
accustomed to buying what it wants with little
concern for cost. It appears less desirable in a
regulatory agency charged with protecting society
from adverse effects without upsetting the economy.
Thus over-conservatism as expressed above can
result in major economic problems and even in
reducing availability of certain products that
society has come to consider essential. This
becomes more dramatic when societal cost is
expressed in terms of more expensive automobiles,
more expensive energy, less plastics, and less
ease and rapidity of mobility. Since these are
factors that are a part of societal cost which may
be required to reduce incidence of cancer and
other adverse health effects, and since society
does not seem to be willing to pay such costs
needlessly, it becomes increasingly important for
regulatory agencies to be realistic in their
extrapolations rather than "conservative" as that
term is used to describe a bias.
Conclusions
It is becoming more important that regulatory
agencies consider societal cost of their regula-
tions as well as benefits to society in terms of
less risk of adverse health effects. Since the
risk can seldom be estimated directly from experi-
mental data based upon relatively high dosages, it
is essential that such agencies make judicious use
of extrapolation models, always bearing in mind
the obvious dangers of extrapolation.
Extrapolation models should provide estimates
of two parameters just as is expected of many
statistical models. First they should provide a
best estimate of the probability of adverse effect
at the dosage under consideration. These dosages
should include the dosages to which various seg-
ments of the population are exposed in the absence
of regulation and they should also include dosages
that would be expected if various alternative reg-
ulatory actions were in fact taken.
It should be borne in mind that such alterna-
tives are typically discrete; that is to say that
they are, in the last analysis, dependent upon
some form of technology which will reduce pollu-
tion to a fixed degree rather than to a continu-
ously variable range. Thus, the dosages that
should be considered are a discontinuous set or a
step function. They are, therefore, the inde-
pendent variable, and the probability of adverse
effect is the dependent variable. There is little
value in selecting arbitrarily a "safe" probability
of risk and then designing the technology and
regulations to match it. The value or benefits
attributable to each alternative regulatory option
is thus the reduction of risk that can be expected
therefrom.
Secondly, the model should provide an esti-
mate of the degree of uncertainty associated with
the estimate of risk. Since, by definition, there
is no experimental data in the region of extrapo-
lation, there can be no experimental second moment
about the mean and thus no standard deviation in
the classical sense. To assume some such figures
may well lead to a false confidence in extrapola-
tion. It is most reasonable, then, to be content
with a verbal description of uncertainty of the
estimated risk. This can be done, possibly by
indicating what estimates would have resulted from
other assumptions such as the "conservative"
assumptions now commonly used. With more experi-
ence it may be possible to develop other estimates
of uncertainty that are more meaningful to the
decision-maker. In any case a "best estimate" of
184
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risk or reduction in risk coupled with meaningful
disclaimers of accuracy, preferably in terms of
describing some of the estimates from alternative
assumptions, is preferable to purely subjective
guesses either by the decision-maker, or by some
expert who very likely has already made up his
mind as to the degree of regulation that is justi-
fied.
References
1. Bliss, C.I. Calculation of the Dosage-
Mortality Curve. Ann. Appl. Biol. 22:134-137,
1935.
2. Mantel, M. , and Bryan, W.R. Safety Testing of
Carcinogenic Agents. National Cancer Institute
27:455-470, 1961.
185
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USE OF MATHEMATICAL MODELS IN NONIONIZING RADIATION RESEARCH
Claude M. Weil
Experimental Biology Division
Health Effects Research Laboratory
U.S. Environmental Protection Agency
Research Triangle Park, NC 27711
Abstract
Mathematical models are described which provide an
improved understaniing of the interaction with bio-
logical objects of electromagnetic energy in the
radio frequency-microwave spectrum. Significant
dosimetric data are derived for the absorption
characteristics and internal dose distribution, using
a rrulti-layered sphere model exposed to plane wave
radiation over the frequency range 0.1 to 10 GHz.
Using such data, some generalized conclusions are
presented which provide useful dosage estimation
methods to those involved in the health effects of
nonionizing radiation research.
Introduction
There is increasing concern regarding the potentially
harmful effects of exposure to nonionizing electro-
magnetic radiation in the radio frequency (RF) -
microwave spectrum (wavelengths range of approx. 3000
to 0.1 cms). Such concerns have been prompted by two
factors: the increasing proliferation of high-
powered RF and microwave sources, such as radio and
TV broadcast transmitters, radar transmitters,
domestic and industrial cooking and drying ovens,
diathermy devices, etc., leading to the potential for
excessive human exposure to man-made radiation. The
other factor is the thousand fold difference which
now exists between the ANSI recommended protection
guide of 10 irW/on^ maximum exposure rate in the United
States and the more conservative protection standard
adopted in the Soviet Union and Eastern Europe
(exposures greater than 2 hours). Much research has
been done in this country on the short-term, high
level heating effects of microwave energy. This
work has been well documented in a number of recent
review papers.1'2,3 work on the chronic effects of
long term, low level exposure has been pursued by
Soviet workers for many years and is now being
strongly emphasized in this country.^ Findings are
frequently contradictory and often not repeatable,
leading to much controversy and speculation regarding
the effects of low level exposure. This is un-
doubtedly due, in large part, to the difficulties
involved in measuring or estimating absorbed energy
dose for the subject undergoing irradiation.
Johnson ' has emphasized that observed biological
effects or phenomena can only be related to the
absorbed dose and not to the incident power density.
The- degree to which electromagnetic energy is coupled
into the irradiated subject is a very complex function
of size, shape, dielectric composition and orientation
of the subject as well as the wavelength, spatial
characteristics and polarization of the incident
radiation. Furthermore, the internal distribution
of absorbed energy is never uniform, except when the
incident wavelength is nuch larger than object size,
and is frequently concentrated into localized "hot
spot" regions. This means that for the same exposure
conditions the absorbed dose and internal dose
distribution for a small object such as an experi-
mental animal will be very different from that for a
much larger object such as a human.
Because of the general complexity of the electromagnetic
interaction problem, much use has been made of very
simplified mathematical models in order to obtain a
better understanding of the nature of this inter-
action. Such models consist of objects having a
simple planar, spherical or cylindrical shape that
are generally exposed to the simplest form of rad-
iation; i.e., the electromagnetic plane wave. These
objects are composed of various layers of homogeneous
and dissipative dielectrics which approximate the
known dielectric properties of various biological
tissues such as muscle, fat, bone, skin, etc.
Solutions for the planar model are very simple-*'' but
the results are not really applicable to any closed
object with curved boundaries except when the incident
wave length is verv short,compared to object size.
The sphere model ''' ' has been popular because it
better approximates a curved object and because the
solution is well known and can be readily handled using
high speed machine techniques. Such a model can be
considered to be a crude representation of animal and
human heads, but the analogy is obviously approximate
and very limited. Some work has also been done on the
interaction of cylindrical and spherical models with
the more complex radiation from a direct-contact
aperture source.10'I1 Models of prolate spheroid and
ellipsoid shape which better approximate the char-
acteristically elongated bodies of laboratory animals
as well as humans, are presently being investigated.
To date, solutions have only been obtained for the
case where incident wavelength is much greater than
object size. The results have underlined the
important dependency of energy absorption on object
orientation with respect to the polarization of the
incident electric field. Several workers13 are
presently attempting to solve problems involving models
of arbitrary shape and homogeneity, using finite
element methods and numerical solutions, but such
methods are relatively costly and limited by the total
number of elements that a computer can handle.
Detailed results for the multi-layered sphere model
exposed to plane wave radiation are now presented.
Some results for the prolate spheroid are also
included.
Formulation of Sphere Model Problem
Figure 1 shows the six-layered model used in this
study, with a plane wave, polarized in the x-direction
and propagating in the z-direction, incident upon it.
The outer most region (p = 7) or sixth layer repre-
sents air. The dielectric properties and layer thick-
ness of the remaining regions ( p = 1,2,3,4,5,6),
consisting of a core of brain-like matter and five
concentric layers, are summarized in Table 1 for
three different sized spheres (6.6, 12 and 20 cms
diameter).
Region
(P)
1
2
3
4
5
6
Tissue
Modeled
Brain
CSF
Dura
Bone
Fat
Skin
Electrical Properties
of Tissue at 109 Hz
Relative
Perm1tt1v1tv
60
76
45
8.5
5.5
45
Conductivity
(ohm-m) "1
0.9
1.7
1.0
0.11
0.08
1.0
Core Size and
Layer Thicknesst cms
Outer Radius rfi B
3.3cms 6ons lOcms
r,=2.68 r.-5.27 r,-9.10
1 0.2 ' 0.2 ' 0.2
0.05 0.05 0.05
0.2 0.28 0.4
0.07 0.1 0.15
0.1 0.1 0.1
186
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Tissue electical properties were obtained fron values
published by Schwan7 and others5. Variations of +30%
or more can exist in the figures quoted. The changes
of electrical characteristics with frequency are
significant and were incorporated into all aspects of
this work; sets of curves giving average permittivity
and conductivity changes with frequency for the various
tissues modeled, were prepared and stored in a data
bank.
Expansion of the incident and secondary (scattered
an3 internally induced) fields into vector spherical
harmonics is based on Stratton's formulation^ (See
Fig 1). Tangential components of E and H-fields
sized spheres ranging from 2 to 12.5 ons outer radii
are shown in terms of the frequency of incident
radiation over the spectral range 100 to 10,000 MHz
(A = 300 to 3 cms). This representation readily shows
that combination of model size and incident frequency
for which the energy absorption is greatest. Two
major "ridge" lines running diagonally across the plot
are clearly identifiable; these represent regions of
resonant absorption. The third ridge line to the
right of the plot represents a resonant coupling of
energy into the core of the model by the outer tissue
layers. Note that the absorption coefficient can
considerably exceed unity in the resonant absorption
regions.
2.0
200 250 300
500 600 700 800 1000 1500 2000 2500 3000
FREQUENCY, MHz
4000 5000
10,000
Fig. 1. Plane wave incident upon spherical model with six concentric
shells.
Spherical Harmonic Expansions for Electric Fields
Incident:
Reflected:
fi»i
Induced within sphere:
n-i
Scattering cross section:
= 2" V
' n«l
Total cross section:
Abjoiption cross section, fia = Qt ~ Qr
are then equated at the six regional boundaries in
order to determine the unknown expansion coefficients.
Absorption Properties and Dose Distribution
Par a simple object having a well known geometric
cross-section, such as a sphere, the absorption
characteristics are conveniently defined in terms of
an absorption coefficient, given by the actual
absorption cross section, Qa divided by the shadow
cross section. This coefficient is a measure of how
efficiently the incident energy is coupled into the
object being irradiated. In the contour plot of
Fig 2, the absorption characteristics for different
Fig, 2. Radius versus frequency diagram for multi-
layered sphere; the contours represent lines of
constant absorption coefficient.
The internal distribution of absorbed energy (dose)
in the brain-like core of a 6 ons radius sphere
(roughly equivalent to infant sized head)is
illustrated in Figs 3 and 4 for two different
frequencies. The distributions are shown in the
plane ( = 0) of the incident electric field vector
(E-plane) and the contours are normalized iso-dose
rate lines (constant absorbed dose rate, normalized
to E0 = 1 volt/neter peak). At the resonant absorp-
tion frequency of 800 MHz (see Fig 3), a major "hot
spot" concentration is found to exist immediately in
front of the sphere center, due to focusing of energy
into the center, as well as standing wave effects.
Ohe greatest internal field concentration was found
to exist at 1650 MHz (see Fig 4) where the original
hot spot has now split into two separate and more
intense concentrations that are located behind the
sphere center on both sides of the z-axis. At still
higher frequencies microwave energy is decreasingly
able to penetrate very far into the sphere owing to
the greatly increased conductivrly values of the core
dielectric (conductivity at 3 GHz has increased three
fold over its value at 100 MHz). Consequently most
of the incident energy is now deposited in the front
hemisphere and the Internal concentrations collapse.
By programming the computer to methodically scan
throughout the E-plane of the model and to select the
maximum field strength both inside and on the surface
of the sphere, comprehensive data are obtained for both
peak and average absorbed dose rates. Fig 5 shows such
data as a function of frequency for the 6 cms radius
sphere exposed to an incident power density of 10 mW/an2.
At low frequencies (<500 MHz), absorption is relatively
poor and the internal distribution is seen to be
relatively even. In the resonant region (500-2500 MHz),
187
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absorption is strong arid most of the energy is
internally deposited. At frequencies above 2500 MHz,
surface heating strongly predominates and the overall
absorption gradually diminishes with frequency.
Similar data were obtained for both a smaller (3.3 cms
radius and a larger (10 cms radius) sphere, equivalent
to a monkey and a human head respectively.
40.0
Fig. 3. Iformalized dose rate distribution in core of
6 cms radius sphere at 800 MHz, E-plane.
6.0 cms
1650 MHz
E-PLANE
.in 180 iin
2!
VALUES ON CONTOUR LINES REPRESENT
Fig. 4. E-plane distribution in core of 6 cms
sphere at 1650 MHz.
— OUTER RADIUS = 6.0 cms
INCIDENT FLUX = 10 MW/cmZ
100 150 200 300 WO 500 700 1000 1500 2000 3000 40005000 ?COO 10,000
FREQUENCY, MHz
Fig. 5. Average and peak (localized) absorbed dose
rate versus incident frequency for 6 cms radius
sphere.
Prolate Spheroid Model
Problems involving the interaction of plane wave
radiation with prolate spheriod and ellipsoid
models have recently received some attention.
Solutions have, so far, only been obtained for
the below-resonance approximation where incident
wavelength is still much longer than the model
dimensions. Dumey et al.-^ have obtained data
on the absorption characteristics of a large man-
size prolate spheriod, composed of muscle-
equivalent dielectric, exposed to relatively
low frequency radiation in the 1-30 MHz band.
Diese results have shown a significant dependency
of energy absorption on the orientation of the
spheroid with respect to the polarization of the
incident field. Durney's results are reproduced
in Figs 6 and 7; maximum absorption is seen to
occur for the electric polarization case when the
major axis of the spheriod (length 2a) is oriented
parallel to the electric field vector (see Fig 6).
For the two other polarization cases, when the major
axis is oriented parallel to either the magnetic field
vector or along the direction of propagation (cross
polarization), absorption is seen to be less than
that for an equivalent sphere model of the same
volume. In Fig 7, total absorption of a constant
volume spheriod, normalized with respect to that of
the equivalent sphere model is plotted against the
eccentricity a/b of the spheriod. Ihe orientational
effects are seen to be further accentuated as the
spheriod eccentricity increases; note that for the
electric polarization case, energy absorption has
increased to a level some seven times greater than
that for the sphere model.
Solutions for the prolate spheroid problem in the
resonant region, where absorption is greatest, are
now being attempted. Preliminary results have shown
that a man-size model will exhibit resonant absorption,
under free-space conditions, in the frequency range
65-75 MHz.
188,
-------
Fr.qu.nt, In MHi
Pig. 6. Average absorbed dose rate of a muscle^
equivalent prolate spheroid for three different
polarizations, electric Pe, magnetic Pft and cross Pc;
incident power density = 1 mW/cm , spheroid volume =
0.07 m3, a = 1 m, a/b = 7.73. The dotted line labeled
Ps represents the absorption by an equivalent sphere
of equal volume.
(Reproduced by permission of the authors and the IEEE.)
Fig. 7. Total power absorbed by an C.07 m muscle
equivalent prolate spheroid, relative to that absorbed
by a sphere of equal volume, versus spheroid
eccentricity a/b for the three basic polarizations
considered.
(Reproduced by permission of the authors and the IEEE.)
Conclusions
Using the various nodel data, it is possible to draw
some generalized conclusions regarding the inter-
action of microwaves with biological objects: a) All
objects exhibit a resonant behavior, marked by a
significant increase in absorbed energy when the
incident wavelength is comparable to the object
dimensions. Large objects respond uniformly to a
broad spectrum of relatively low frequencies while
small objects have a narrow and more peaked response
at higher frequencies. The response of a specific
subject will obviously depend on the subject's
anthropomorphic form as well as the other factors
already mentioned, b) For larger objects, where
path lengths are relatively long, hot spot effects
are not significant and at low frequencies the
deposited energy is relatively evenly distributed.
At higher frequencies virtually all the energy is
frontally deposited, c) For small and medium sized
objects, hot spot effects are significant over
essentially the same frequency range for which res-
onance absorption occurs. As the object becomes
smaller, peak internal fields can reach prohibitively
high values at frequencies close to resonance.
d) The higher the frequency, the poorer the energy
penetration, so that microwaves at frequencies above
about 5 GHz are incapable of penetrating even the
smallest experimental object usually considered.
Finally, it is worth repeating again the conclusions
reached by numerous other investigators in this field:
that any effects seen during microwave exposures of
experimental animals are not necessarily extrapola-
table to man, owing to the widely differing absorption
characteristics and internal distributions existing
for man compared to that of the animal at the same
frequency and same incident field level. This is
clearly supported by the results of this study, which
show that much greater local and average thermal
burdens exist in a small object or animal than is the
case for the large object (incident power density and
frequency remaining the same). Great care must
therefore be taken in the interpretation of results
obtained during animal experimentation.
References
1. S.F. deary: "Biological Effects of Microwave
and Radiofrequency Radiation," CRC Critical
Reviews in Environmental Control, pp. 257-306,
(July 19701.
2. S.M. Michaelson: "Effects of Exposure to
Microwaves: Problems and Perspectives,"
Environmental Health Perspectives, Vol. 8,
•specti-y
W.
pp. 133-156, (August 1974
3. D.I. MdRee: "Environmental Aspects of Micro-
wave Radiation," Environmental Health
Perspectives, Vol. 6, pp. 41-53,(October
1972).
4. C.H. Dodge: "Clinical and Hygienic Aspects
of Exposure to Electromagnetic Fields,"
Proceedings of Symposium on Biological
Effects and Health Implications of Microwave
Radiation held in Richmond, Va., September
1969, pp. 140-149, NTIS Doc. No. PB 193 898.
5. C.C. Johnson and A.W. Guy: "Nonionizing
Electromagnetic Wave Effects in Biological
Materials and Systems," Proc. IEEE, Vol. 60,
pp. 692-718, (June 1972).
189
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6. C.C. Johnson: "Research Needs for Establish-
ing a Radio Frequency Electromagnetic Radiation
Safety Standard," J. Microwave Power, Vol. 8,
(3/4), pp. 367-388, (1973). 10.
7. H.P. Schwan: "Radiation Biology, Medical
Applications and Radiation Hazards," in
Microwave Power Engineering, Vol. 2, ed. by
B.C. Okress, Academic Press, NY, 1968,
pp. 215-234. 11.
8. A.R. Shapiro, R.F. Lutomirski and H.T. Yura:
"Induced Heating within a Cranial Structure
Irradiated by an Electromagnetic Plane Wave,"
IKKK Trans. Microwave Theory and Techs, 12.
MTT-19, pp. 187-196, (Feb 1971).
9. C.M. Weil: "Absorption Characteristics of
Multilayered Sphere Models Exposed to UHF/
Microwave Badiation," IEEE Trans. Biomed. Bng.,
BME-22, pp. 468-476, (Nbv 1975).
H.S. Ho, A.W. Guy, R.A. Sigelmann and J.F.
Lehmann: "Microwave Heating of Simulated
Human Liiribs by Aperture Sources," TRRR
Trans Microwave Theory and leans, MTT-19,
pp. 224-231 (Feb 1971
H.S. Ho: "Contrast of Dose Distribution in
Phantom Heads due to Aperture and Plane Wave
Sources," Annals N.Y. Acadony Sciences, Vol. 247,
pp. 454-472, (Feb 1975).
C.H. Durney, C.C. Johnson and H. Massoudi:
"Long Wavelength Analysis of Plane Wave
Irradiation of a Prolate Spheroid Model of
Man," IKW; Trans. Microwave Theory and Techs.,
MTT-23, pp. 246-253, (Feb 1975).
DISCLAIMER
This report has been reviewed by the Office of
Research and Development, EPA, and approved for
publication. Approval does not signify that the
contents necessarily reflect the views and policies
of the Environmental Protection Agency, nor does
mention of trade names or commercial products
constitute endorsement or recotinendation for use.
190
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AIR POLLUTANT HEALTH EFFECTS ESTIMATION MODEL
William C. Nelson, John H. Knelson, Victor Hasselblad
Health Effects Research Laboratory
Environmental Protection Agency
Research Triangle Park, North Carolina
A computerized system has been developed which
sequentially utilizes estimates of air pollutant emis-
sions, ambient levels, health damage functions, and
populations at risk to provide an aggregate estimate of
health effect. Emissions estimates should be pollutant
specific for a base year (and any additional years),
can be source specific such as stationary and mobile
or power plant and nonpower plant, and can be geo-
graphic area specific. Ambient levels should be
pollutant specific for a base year. Levels for addi-
tional years can either be provided or estimated from
the emissions estimates. Arithmetic means are used
to estimate chronic health effects. Geometric means
and standard geometric deviations are used for acute
health effects. Daily or hourly averages are esti-
mated assuming the log normal distribution. The
model can consider compound effects such as the
variable short-term contribution of mobile and sta-
tionary sources. Health damage functions have been
developed separately for input to the model for
sulfates, photochemical oxidants, carbon monoxide,
and nitrogen dioxide. Various specific health ef-
fects were considered including mortality, aggrava-
tion of asthma, acute lower respiratory disease in
children, aggravation of chronic heart and lung dis-
ease in the elderly, chronic respiratory disease,
and transient irritation symptoms. Age and disease
status specific populations at risk were considered.
Aggregate estimates were developed for each health
effect and pollutant damage function. All estimates
,are in terms of an excess above a baseline since none
of these effects are caused by air pollution alone.
Although the resulting estimates are admittedly
very rough approximations, this first level of quanti-
fication is valuable for comparison of differing con-
trol strategies and for establishing ranges of uncer-
tainty, which can be considered more fully in future
research.
Introduction
Environmental control policymakers require
knowledge of the complex relationships between air
pollutant emissions, air quality, human exposures, and
health damages for a variety of pollutant categories.
This need is particularly critical for two of our
largest and most important industry groups, the electric
power industry and the motor vehicle transportation
industry. The necessity for trade-offs is obvious as
our national shortage of low-sulfur fossil fuel is
superimposed on our commitment to the implementation
of the Clean Air Act amendments.
Difficult decisions must be made involving consid-
eration of benefit-cost relationships. Figure 1 shows
the cyclical relationship of emissions, air quality,
effects, and control decisions. The pollutants emitted
By stationary sources and by motor vehicles are sub-
jected to meteorological factors and to physical and
chemical forces which produce an ambient air quality
level. With knowledge of damage functions and of the
exposure of a target "population," human or otherwise,
one can estimate physical effects. These physical
effects would include effects on human health, vegeta-
tion, animals, and materials. Policy decisions might
be made on the basis of these physical effects.
Population
at Risk
Physical
Effects
<;>
/*
Economic
Damage
Function
Figure 1. Schematic Relationship of Emissions, Air
Quality, Effects, and Control Measures
Our computerized model presently assumes that this
is the case. In fact, the only physical effects con-
sidered to date are effects on human health.
For completeness, damage functions might also be
used to estimate economic damage. A control policy
must be made and enacted into law. The resulting
control measures will exert their effect on emissions
and the cycle shall continue.
Unfortunately, the research information base for
determining these critical relationships is fragmentary
rather than complete. Nevertheless, these available
fragments must be utilized to provide the best possible
estimates for these relationships.
This model considers the elements of Figure 1
through the physical (health) damage stage. Since the
resulting estimates of health effects from various
"scenario" assumptions have been presented elsewhere,
this paper will stress the methodology of the model and
its flexibility as an estimation tool. The following
sections describe the components of the model in some
detail.
Emissions
The model requires emissions and air quality
information for some base period, ideally a year. The
simplest relation between emissions and air quality is
based on the assumption that the change in air quality
due to man-^nade pollution sources is proportional to
tfie change in man-made emissions in tne region of
interest. Therefore if emission estimates~are provided
for additional years, resulting air quality for the ith
year is estimated by the formula
(AQrBAQ.)/(AQ-BAO) E^E
where AQ, BAQ, and E represent total air quality,
natural background air quality, and emissions for a
base year, and where the subscripted variables repre-
sent these same quantities for the ith year.
191
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It should be noted that this model assumption does
not relate air quality to emissions but only relates
changes in air quality to changes in emissions. This
assumption provides a reasonable estimate if the
meteorologic and topographic characteristics of the
area and the temporal and spatial distribution of
emissions remain stable over the time period of inter-
est.
Emissions have also been classified into compart-
ments such as mobile and stationary sources or power
plant and non.power plant sources. Various "growth"
scenario assumptions can be considered for the various
cases. For each, the simple assumption of a linear
relation between changing emissions and air quality is
made.
Emissions estimates have also been classified by
geographic area. The contiguous United States has been
divided into seven regions representing approximately
the Northeast, the Southeast, the Eastcentral, the
Midwest, the Southcentral, the Northern Plains, and the
West. State boundaries have been maintained.
Air Quality
As mentioned earlier, air quality information for
some base time period is required. For our model we
utilized the data base of the National Aerometric Data
Bank (NADB). We developed air quality data for each
of the seven geographic areas mentioned previously.
Additionally, each region was divided into four strata,
depending on population, based on the 1970 Census.
These four strata were classified as rural (including
towns of less than 2500, urban places of less than
100,000, urban areas larger than 100,000 but less than
2,000,000, and urban areas larger than 2,000,000. Air
quality data were derived from NADB representing each
of the 28 population and geographic classes.
Obviously the inclusion of these 28 classes adds
a little more realism to the model since it permits
consideration of different control options for differ-
ent population size areas and for different regions of
the country. Additional subdivision is desirable for
certain problems. For example, the south coast air
basin of California was considered separately for the
oxidant problem. The model can be easily modified to
permit consideration of other individual regions,
cities, or states.
To date, information on ambient levels has been
obtained and used for suspended sulfates, oxidants,
carbon monoxide, and nitrogen dioxide. More monitoring
data are obviously available for some of these pollu-
tants than for others.
The particular aerometric parameter used to esti-
mate health damage is dependent on the type of effect.
Annual arithmetic means are used to estimate health
effects which are attributable to long-term pollutant
exposure. Averages or maxima for shorter time periods
are required for estimating acute health effects.
Daily or hourly averages are calculated from the annual
geometric mean and standard geometric deviation, assum-
ing a log normal distribution. The acute health ef-
fects from these shorter exposures are aggregated so
that all damage estimates are expressed on an annual
basts.
Health Damage Functions
The health information base for pollutant effects
was reviewed in careful detail. Although a great
number of research studies have been carried out, the
total information available is limited. Methodology
variations in the individual studies usually prevent
•strict comparability of study results. The significant
effects observed in many studies despite differences in
the health end point, target population, and pollutants
measured, ensure that pollutant effects are widespread.
The data base, therefore, provides far more qualitative
information than quantitative information. However,
there are a relatively few pollutants and health
effects for which enough reliable quantitative data
exist from multiple studies to allow estimation of
health damage functions.
These functions are now discussed for each rele-
vant pollutant. Each function has been determined on
the basis of excess risk of illness or death above a
baseline level since none of these effects are due to
air pollution alone. The specific characteristics of
each function are also displayed in Table 1.
Carbon Monoxide
The effect of low-level carbon monoxide exposure
on the cardiovascular system has been investigated by
several investigators.5 There is evidence from
laboratory animal studies and from human volunteer
studies of less severe cardiac effects,that carbon
monoxide exposure can increase risk of death for indi-
viduals suffering myocardial infarctions.6 While
adverse effects might occur at very low carboxyhemoglo-
bin levels, the damage function was constructed assum-
ing no adverse effect could be demonstrated below a
carboxyhemoglobin level of 2 percent. A linear
increase in adverse effect was assumed up to a
carboxyhemoglobin level of 10 percent.
There also is evidence that carbon monoxide ex-
posure can decrease the time to onset of chest pain
and increase the duration of the pain for persons with
stable coronary artery disease.7 Studies with human
volunteers were conducted at 2.9 percent carboxyhemo-
globin and at 4.5 percent carboxyhemoglobin. The
total mean time of increased disability (decreased
activity plus increased duration of chest pain) was 87
seconds at 2.9% COHb and 144 seconds at 4.5% COHb.
Linear damage functions were estimated for these data
points assuming an effects threshold ranging from 0.5%
COHb to 2.0% COHb. The most reasonable point estimate
of the threshold has been determined to be 1.5% COHb
and this is the value shown in Table 1.
Suspended Sulfates
Exposure to elevated levels of sulfur oxides,
particularly suspended sulfate aerosols, has been shown
to cause or aggravate several health effects. A
problem is that these effects were observed in communi-
ty studies where levels of sulfur dioxide, acid-sulfate
aerosol, and suspended particulate matter were usually
simultaneously elevated. Another limitation is that
for some studies, suspended sulfate levels had to be
estimated from measured sulfur dioxide concentrations.
Despite these difficulties, it is likely that
short-term elevated exposure to sulfates is largely
responsible for the perceptible increases in daily mor-
tality observed during air pollution episodes in New
York,?.10 London,11 and Oslo.12 Data points
from these studies were plotted and a linear regression
equation was estimated. An effects threshold for a 24-
hour average sulfates concentration was estimated to be
25 yg/m3.
Elevated short-term exposures also cause aggrava-
tion of asthma and of preexisting heart and lung
diseases. The studies of volunteer asthmatics were
done in the United States8 and Japan.13 The
studies of elderly volunteers with chronic heart or
lung disease were done in Chicago14 and New York.8
Results indicated that each of these susceptible
groups were more likely to experience an attack or a
worsening of their chronic symptoms on high sulfate
days. Data points from these studies allowed plots to
be constructed and, as with the mortality data, linear
regression equations to be estimated. For the asthma
damage function, a threshold was estimated to occur at
a daily average sulfate concentration of 6 vg/m3 and
for the aggravation of preexisting heart and lung
192
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Table 1. Summary of Damage Function Characteristics
Pollutant and
Health Effect
Carbon Monoxide
Mortality
Angina
Pectoris
Oxidants
Aggravation of
Heart and Lung
Disease in
Elderly
Aggravation of
Asthma
Eye Discomfort
Cough
Chest Discomfort
Headache
Nitrogen Dioxide
Lower Respiratory
Disease in
Children
Days of Restricted
Activity from
Lower Respiratory
Disease
Population at Risk
One-sixth of persons
suffering myocardial
infarctions or sudden
coronary death (0.26
percent of population)
Two percent of the
population
The prevalence of
chronic heart and
lung disease among the
11 percent of the pop-
ulation older than 65
years is 27 percent
The prevalence of
asthma in the general
population is 3
percent
Healthy Population
(Excludes persons
with asthma or
heart and lung disease)
Healthy Population
(Excludes persons
with asthma or heart
and lung disease)
Healthy Population
(Excludes persons
with asthma or heart
and lung disease)
Healthy Population
(Excludes persons
with asthma or heart
and lung disease)
All children in the
population or 23.5
percent of population
Children with a
lower respiratory
disease
Assumed Baseline
Frequency of
Disorder within
Population at Risk
Prevalence of one
out of 200 of
population at risk
One attack per day
lasting 254 seconds
per attack or
- 0.07 person-hours
per day
One out of five of
population at risk
complain of symptom
aggravation on any
given day
One out of 50
asthmatics experience
an attack each day
Five percent per day
Ten percent per day
Two percent per day
Ten percent per day
Fifty percent of
children have one
attack per year
2.66 days per
attack
Pollutant
Concentration
Threshold
For Effect
2.0 % COHb or
13.1 mg/m3
8-hour average
CO
1.50% COHb or
9.5 mg/m3
8-hour average
CO
400 yg/m3 for
one hour or
more
400 yg/m3 for
one hour or
more
260 yg/m3 for
one hour or
more
400 yg/m3 for
one hour or
more
420 yg/m3 for
one hour or
more
100 yg/m3 for
one hour or
more
50 yg/m3 annual
average
50 yg/m3 annual
average
Effect Increase as %
of Baseline Per
Pollutant Unit Above
Threshold
5.0% per % COHb
18.75% per % COHb
1.75% per 100 yg/m3
1.75% per 100 yg/m3
3.25% per 100 yg/m3
1.75% per 100 yg/m3
1 .0% per 100 yg/m3
.35% per 100 yg/m3
5.0% per 25 yg/m3
5.0% per 25 yg/m3
193
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Table 1. (Continued)
Pollutant and
Health Effect
Sul fates
Mortality
Aggravation of
Heart and Lung
Disease in Elderly
Aggravation of
Asthma
Lower Respiratory
Disease in Children
Chronic Respiratory
Disease
Nonsmokers
Smokers
Population at Risk
Total Population
Same as above for
oxidants function
Same as above for
oxidants function
Same as above for
nitrogen dioxide
function
62 percent of
population age 21
or older
38 percent of
population age 21
or older
Assumed Baseline
Frequency of
Disorder within
Population at Risk
Daily death rate of
2.58 per 100,000
Same
Same
Same
Two percent
prevalence
Ten percent
prevalence
Pollutant
Concentration
Threshold
For Effect
25 yg/m3 for
one day or
more
9 yg/m3 for
one day or
more
6 yg/m3 for
one day or
more
13 yg/m3 for
several years
10 yg/m3 for
several years
15 yg/m3 for
several years
Effect Increase as %
of Baseline Per
Pollutant Unit Above
Threshold
2.5% per 10 pg/m3
14.1% per 10 yg/m3
33.5% per 10 yg/m3
76.9% per 10 yg/m3
134% per 10 yg/m3
73.8% per 10 yg/m3
disease function the threshold was estimated to be 9
yg/m3.
Long-term exposures or repeated shortrterm expo-
sures to suspended sulfates have also been linked with
increased acute respiratory disease in normal healthy
children. Epidemiologic studies which have related ob-
served increases in 3-year incidence rates of acute
lower respiratory disease in children 12 years old
and younger to increases in annual average concentra-
tions of suspended sulfates have been carried out in
the United StatesS and England.15'16 These
studies permit the estimation of a damage function.
Another health parameter linked to sulfur oxide
exposure is chronic respiratory disease. Commmunity
questionnaire surveys in several United States cities^
have consistently shown differences in prevalence
of chronic respiratory disease symptoms in adults
attributable to annual average exposure to suspended
sulfates. In these studies, a very important codeter-
minant of chronic respiratory disease is individual
cigarette smoking. The available data showed that
cigarette smokers were slightly less affected by ambi-
ent sulfates than were their nonsmoking neighbors.
The relatively large sample size of these studies made
it possible to estimate a separate damage function for
smokers and for nonsmokers.
Oxidants
Exposures to elevated photochemical oxidant levels
have been associated with increases in minor irritation
symptoms in otherwise healthy adults. A volunteer
panel of student nurses in Southern California main-
tained daily diaries in their health symptoms.'7
Significant associations were found with daily fre-
quency rates for headache, chest discomfort, eye irri-
tation and cough and daily oxidant level. The inves-
tigators had estimated segmented regression lines,
known as "hockey stick" functions, for each of these
four health effects. The functions were used as the
basis of the damage functions for our model, requiring
the ordinates to be converted from observed frequency
rates to percent excess above baseline frequencies.
In addition to the previously described relation-
ships with sulfates, it is also believed that oxidants
can aggravate asthma and symptoms of chronic heart and
lung disease. As an estimate of a lower boundary for
this functional relationship for the susceptible popu-
lation at risk, the slope of the regression line for
cough in a healthy population was used. As can be seen
from Table 1, the baseline frequency and the target
population are different for each health end point.
Nitrogen Dioxide
A damage function relating increased incidence
of acute lower respiratory disease in children with
annual average concentrations of nitrogen dioxide has
Been developed. This function and a related one esti-
mating days- of restricted activity resulting from
these illnesses have been obtained from data of a study
conducted in Chattanooga, Tennessee.'" Although
tSe survey was conducted during a period of rapidly
decreasing nitrogen dioxide exposures, it is possible
to form reasonable assumptions about the causes of the
observed effects.19 A regression equation was esti-
mated for three different threshold estimates; however,
the estimate providing the intermediate effect of the
three appears to be most reliable and is therefore
shown in Table 1. Several different estimates were
also considered for the baseline annual incidence of
lower respiratory disease, ranging from a per child
rate of 0.5 to 2.0 attacks per year. In order to be
conservative, the smallest of these, 0.5, has been
incorporated into the model.
Population at Risk
As mentioned previously, the appropriate popula-
tion at risk must be determined for each individual
damage function and obviously will be matched as close-
ly as possible to the target population used in the
194
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studies upon which the damage function is based. The
specific populations at risk which the model considers
are shown in Table 1. For each function except
mortality attributable to elevated daily average
sulfates, some subset of the total population is used.
The model incorporates these population subsets in
two different ways. First, the specific population
subsets are calculated for each of 28 population
density and geographic region categories described
previously in the Air Quality section. These cate-
gories are necessary for the model to determine aggre-
gated national estimates of health impact. However,
there are some situations in which national estimates
are not appropriate and estimates are required for
smaller regions. To provide flexibility for these
situations, all population subclasses have also been
calculated on the basis of a standard million popula-
tion.
Health Effects
As stated in the introduction, the purpose of this
paper is not to provide specific numbers for excess
illnesses or premature deaths, but rather to summarize
the development and methodology of the computerized
model. Therefore the effects estimated, which obvious-
ly depend heavily on the region (population) and time
period (air quality) of interest, will be covered only
very briefly.
The magnitude of most effects is very large, if
considered for an area of moderate or large population.
An exception is mortality attributable to carbon
monoxide for which the assumption of a threshold level
of 2 percent carboxyhemoglobin (or equivalently an 8-
hour average carbon monoxide level of approximately
13 mg/m3) ensures a small estimated effect. However,
for effects attributable to sulfates, the set of damage
functions estimate that the annual national public
health toll is on the level of millions of excess
diseases and thousands of premature deaths. The
estimated figures for effects attributable to oxidants
and nitrogen dioxide are also very large as is the
estimate of increased disability from angina pectoris
attributable to carbon monoxide.
Conclusion
The fact that the national estimates of health
effects attributable to air pollutant exposure are very
large brings out several major points.
First, it must be stressed that the damage func-
tions documented in this model provide very rough
estimates of reality. Although these functions are
believed to be the best available from the present
health information base, their limitations must con-
stantly be remembered. These functions should be
frequently reevaluated and revised.
Second, the commitment to performing new research
studies must be renewed. These studies must have the
proper research design and methodology to permit valid
quantitative results. Too often in the past, only
qualitative information has been obtained of air pollu-
tion's effect on health. Also, investigators must
increase their efforts to extract quantitative results
from their available data by use of improved statistical
analysis procedures.
Third, the existence of this computerized model at
least provides a flexible mechanism for systematic
assessment of the magnitude of environmentally related
public health problems. Its use can aid in the specific
definition of feasible alternatives and hence in the
making of many of our present difficult environmental
decisions.
References
1. Chapman, L. D. et al, Electricity Demand: Project
Independence and the Clean Air Act, ORNL-NSF-EP-89,
Oak Ridge National Laboratory, pp. 14-31, November
1975.
2. Finklea, J. F. et al, Health Effects of Increasing
Sulfur Oxides Emissions, EPA In-house Report,
March 1975.
3. Draft Report of the Air Quality, Noise and Health
Panel, Department of Transportation Interagency
Task Force, 1975.
4. Finklea, J. F. et al, Estimates of the Public
Health Benefits and Risks Attributable to Equipping
Light Duty Motor Vehicles with Oxidation Catalysts,
EPA In-house Report, February 1975.
5. Air Quality Criteria for Carbon Monoxide, N. 10,
NATO Committee on Challenges of Modern Society,
pp. 7-51 to 7-68, June 1972.
6. EPA Memo Knelson to Finklea, December 26, 1974,
entitled "Excess Cardiac Deaths Related to CO
Exposure: Extrapolation from Animal Dose-Response
Data."
7. Knelson, J. H., General Population Morbidity
Estimates from Exacerbation of Angina Pectoris
Related to Low-Level Carbon Monoxide Exposure, EPA
In-house Report, August 1975.
8. Health Consequences of Sulfur Oxides: A Report
from CHESS, 1970-71, EPA 650/1-74-004, Environmen-
tal Protection Agency, May 1974.
9. Buechley, R. W. et al, S02 Levels and Perturbations
in Mortality, Archives of Environmental Health
27, pp. 134-137, September 1973.
10. Glasser, M. and L. Greenburg, Air Pollution
Mortality and Weather: New York City 1960-64,
(presented at the Epidemiology Section of the
American Public Health Association Annual Meeting,
Philadelphia, November 1969.
11. Martin, A. E. and W. Bradley, Mortality Fog and
Atmospheric Pollution, Monthly Bulletin of the
Ministry of Health (London) 36, pp. 341-344, 1963.
12. LindeBerg, W., Air PollutionTn Norway III:
Correlations Between Air Pollutant Concentrations
and Death Rates in Oslo, Smoke Damage Council,
Oslo, 1968.
13. Sugita, O.M. et al, The Correlation Between
Respiratory Disease Symptoms in Children and Air
Pollution, Report No. 1: A Questionnaire Health
Survey, Taiki Osen Kenkyu 5_, p. 134, 1970.
14. Carnow, B. W. et al, The Role of Air Pollution
in Chronic Obstructive Pulmonary Disease, J.
American Medical Association 214, pp. 894-899,
November 1970.
15. Douglas, J. W. B. and R. E. Waller, Air Pollution
and Respiratory Infection in Children, British
Journal of Preventive Social Medicine 20, pp. 1-8,
1966.
16. Lunn, J. E. et al, Patterns of Respiratory Illness
in Sheffield Infant School Children, British
Journal of Preventive Social Medicine 21, pp. 7-16,
19.67.
17. Hammer, D. I. et al, Los Angeles Student Nurse
Study, Archives of Environmental Health 28, pp.
225-260, May 1974. ~~
18. Hammer, D. I. et al, Air Pollution and Childhood
Lower Respiratory Disease: Exposures to Oxides
of Nitrogen, EPA In-house Report, February 1975.
19. Knelson, J. H. et al, Impact on Public Health
of Low-Level Long-Term N02 Exposure, EPA In-house
Report, July 1975.
195
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MORTALITY MODELS: A POLICY TOOL
Wilson B. Riggan, Ph.D., John B. Van Bruggen, Larry Truppi, Marvin Hertz, Ph.D.
Environmental Protection Agency, Research Triangle Park, N.C.
Summary
The recent Pittsburgh air pollution epi-
sode in November 1975 presents a striking need
to use daily mortality models as a policy
tool. In this preliminary study we found 16
deaths when the episode period was compared to
the same four days of the week before, and the
same four days of the week following the epi-
sode. Estimated excess deaths of 23 were
found when the period of the episode was com-
pared to the same month and period in the
years 1962 through 1972. However, after
fitting the model which accounted for tempera-
ture and other covariates we found only 14
deaths. In the preceding comparison the ef-
fect of temperature had been assigned to air
pollution.
Mortality Models: A Policy Tool
With the great improvement in air quality
monitoring technology, there is a strong ac-
companying need to quantify the health impact
from environmental pollution. The recent
Pittsburgh episode in November 1975 is a
striking example of this present need. The
Donora, Meuse Valley, New York, and London
episodes of previous decades, which were
handicapped by a lack of pollution exposure
data, also provide glaring examples of this
present need for more air monitoring data
which can be related to observed health
changes.
An important tool for improving the
assessment of the total health effects of
pollution is the use of daily mortality
models. Although man reacts to pollution
through a full spectrum of biological re-
sponses ranging from subtle physiologic
changes to death, mortality is currently the
best documented and defined health indicator
available. It is extremely noteworthy to
recall that statistically strong effects were
not obvious at the time of some of the his-
toric pollution episodes. The adverse health
effects in the 1952 London episode, for ex-
ample, became clear only when mortality
records became vital statistics.
This paper will describe the use of
daily mortality models based on single fore-
cast equations that can apply to metropolitan
areas in the Northeastern United States.
Specifically the Pittsburgh pollution episode
of November 17-20, 1975, will be discussed,
using the model to draw mortality inferences.
The models enable epidemiologists to estimate
deaths caused by high concentration of air
pollution. Mortality models are very useful
to prospective pollution control in that they
enable authorities to forecast the probable
effect of a specific control action and later
to assess the effectiveness of controls.
Why use a model rather than the real
world • Admittedly, a model is a crude "Alice
In Wonderland" simplification of the real
world. But it provides information on rela-
tionships between measurable factors which
may be adjusted for, or controlled. The model
must be scientifically valid in that it must
approximate a microcosm of the real world.
The validity of various models can be compared
by how closely they approximate the actual
observation data.
Materials and Methodology
For the recent Pittsburgh episode we have
three major sources of mortality data:
National Center for Health Statistics; Depart-
ment of Vital Statistics, the State of Penn-
sylvania, and Allegheny County Health Depart-
ment. The National Oceanic and Atmospheric
Administration supplied the meteorological
data. Aerometric data were supplied by the
Allegheny County Air Pollution Control Board.
Background of the Pittsburgh Episode
The National Weather Service Forecast
Office at Pittsburgh Airport issued an Air
Stagnation warning at noon, Monday, November
17, 1975. The areas covered included western
Pennsylvania, several eastern Ohio and nor-
thern West Virginia counties. A large high
pressure system became stationary over the
State of West Virginia, causing strong sur-
face temperature inversions which trapped
cooler air at the ground, particularly in
valleys such as are common around Pittsburgh.
Pittsburgh's location also brought very light
surface winds causing poor dispersion. Wind
speeds at the Pittsburgh Airport averaged
6.8 kph on November 17, fell to 4.2 kph on
November 18, 4.0 kph on November 19, and rose
to 13.7 kph on November 20, the last day of
the episode. Table 1 presents daily maximum
and minimum temperatures, departure from
normal average temperature, afternoon mixing
depths, average wind speed, resultant wind
direction and speed, and average relative
humidity.
Table 1
Daily Weather Conditions
Nov. 17 to Nov. 20, 1975
17 18 19 20
Temperature (C)
Maximum 16.7 17.2 17.2 18.3
Minimum 1.7 2.2 1.7 1.7
Departure from
Normal (C)
+ 4.4 +5.. 6 +5.0 +6.12
Afternoon Mixing
Depth (m) 926 1,061 869 927
Average Windspeed
(kph) 6.8 4.2 4.0 13.7
Resultant Wind
Direction (deg) 230 270 160 160
Resultant Wind
Speed (kph) 6.3 3.4 1.6 13.2
Avg. Rel. Humidity(%) 60 63 60 56
196
-------
Approach
We secured death certificates from Alle-
gheny County Health Department. We compiled
mortality figures for the four days of the
Pittsburgh pollution episode, and the corre-
sponding four days in the preceding and fol-
lowing weeks. These records were not complete,
comprising 85-90 percent of ultimate recorded
deaths. This variation is due to a number of
residents who died outside the county; and
will be added to the county records at a later
time. Table 2 gives this comparison, reveal-
ing 16 excess deaths during the episode.
Table 2 ,
Mortality Figures From Allegheny County
for the Four Days of the Pittsburgh Air
Pollution Episode, and the Corresponding
Four Days in the Preceding and
Following Week
Deaths
During
Episode
181
Average Deaths
of Individuals
for Preceding
and Following
Week
163.5
Excess Deaths
During Episode
17.5
Discussion
By using the same four days of the pre-
ceding and the following week as a control,
we have removed the day of week. However,
the last day of the corresponding four-day
period of the following week was Thanksgiving
which normally has the higher holiday death
rate. This suggests that without the holiday
the excess deaths may have been greater than
17.
We adjusted for incomplete mortality
records for November 1975 in the following
manner. First we checked for an annual trend
and found none. We divided the average daily
deaths of the 11 years of November (47.3) by
the average daily deaths of November 1975
(40.4). We used this factor of 1.17 to ad-
just the daily deaths upward for November
1975.
Table 3 compares the average number of
deaths for November 17 through 20 for years
1962 through 1972 with the deaths during the
Pittsburgh episode of November 17 through 20.
This comparison gives an excess of 23 deaths.
Table 3
Day of
Month
17
18
19
20
Comparison of Deaths
1975
Average
1962-1972
60
52
47
54
49
47
47
47
Excess
Deaths
11
5
0
7
Total 23
Probability = .048
effect has been removed, we selected for each
year Monday through Thursday of the week pre-
ceding Thanksgiving for comparing with Monday
through Friday of the episode.
Table 4
Comparison of Deaths by Day of Week
Day of Week
Monday
Tuesday
Wednesday
Thursday
1975
Deaths
60
52
47
54
Average
1962-1972
49
48
44
49
Excess
Deaths
11
4
3
5
Total 23
Probability = .048
The above comparison has removed the
seasonal effect; to be sure the day of week
Hence, the difference is not due to the
day of the week or the annual cycle.
Application of Model
Daily fluctuations in mortality rates
are primarily determined by four major
factors:
1. Annual cycles
2. Epidemic influenza-pneumonia
3. Temperature
4. Environmental pollution.
Annual cycles of mortality are important
in determining mortality rates because the
highest death rates are in the winter and the
lowest in the summer. Epidemic influenza-
pneumonia is important because during an epi-
demic, death rates rise far above those due to
annual cycle. Temperature has an effect as
well as the annual cycle, in that a sharp
drop in temperature associated with the move-
ment of a weather front reduces mortality.
Heat waves also have an extreme effect on
mortality. Environmental pollutants increase
mortality, but their effects are small com-
pared to the others except in air pollution
episodes. Temperature and annual cycle may
have 15 to 20 times the effect of air pollu-
tion. Environmental pollution has a signifi-
cant additional effect, assessable only when
the other, strong effects are adequately
measured.
Application
Our first step in developing an empiri-
cal forecast model for Allegheny County was
to divide the 11 years of mortality data into
two periods: 5 years, 1962-1966; and 6 years,
1967-1972. The first period was used to de-
velop the model and estimate the coefficients
while the second period was used to test the
model.
First, daily total mortality observa-
tions were corrected to eliminate major
influenza epidemics. Next, mortality data
were checked for trend, and adjustable daily
mortality ratios were computed as the daily
observations divided by the average of the
11 years. We estimated coefficients for the
following model:
197
-------
X(2) X(3)
a5ti+a6ti+a7ti
where Y^ = Daily mortality ratio of observed
deaths on the itn day multiplied.
by 100 and divided by the average
number of deaths per day for the
11 years.
X(l) = Lagged function distributes
temperature effect over 3 days
However, Figure 1 presents graphically the
results using deviations from expected deaths
generated by the model which adjusted for
annual cycle, temperature, etc.
20-
(used
._,
as distributed lagged
function) .
t.t2t3
""" """ """
Exponential polynomial function,
third power of observed maximum
temperature in degrees Celsius
for the given day.
X(2) = Observed temperature minus the
average temperature for the
preceding seven days.
X(3) = Precipitation during the day in
millimeters .
X(4) = Holiday effect - Thanksgiving,
Christmas, etc.
Mortality is given as "mortality ratio
expected. "
This standardized ratio allows direct
comparison between places and times, and
statements about percent change in mortality
per unit change in the pollution variable.
We used 1962-1966 data to estimate a set
of coefficients. We also estimated a set of
coefficients using 1967-1972 data. Estimated
expected deaths for 1967 through 1972 with
coefficients generated from the same data
gave a sum of squares of deviation from
expected of 98.3. Sum of squares of devia-
tion from expected deaths for 1967-1972 using
coefficients generated from data for 1962-1966
was 98.7. Therefore, the relationship found
in the first period holds for the second
period.
We felt justified in using the coeffi-
cients from 1962-1966 to calculate the expected
mortality ratios for November 1975. The air
pollution episode was the only observable
unusual condition in November 1975 that could
have caused expected mortality to deviate so
widely.
After adjusting deaths during the epi-
sodes and for the same days of the week in
the previous and following weeks for tempera-
ture, precipitation, annual cycle, and day of
week, we still show at least 14 excess deaths
during the episode. There seems little
possibility that this result could be due
to random chance.
Aerometric Data
With aerometric data for only three
weeks from seven stations, we have not in
this preliminary report attempted to estimate
coefficients for a dose-response function.
14-
•H
4J
(0
•H
a> 2-|
Q 0
-2
SO,
COH
Week before
episode
70
1.09
Week after
episode
93
0.99
Week of
episode
152
3.00
Figure 1. Comparison of Deviations from
Expected Deaths Generated by the Model
The above results indicate that using
deaths without considering temperature and
other covariates in the Pittsburgh episode
tends to inflate the number of deaths.
Comment and Conclusion
One may ask if the excess deaths would
have occurred within a few days or weeks
rather than during the episode. We simply
do not know. However, mortality rates were
higher the week following the episode than
the week preceding. At least, there is no
evidence that the excess deaths would have
occurred during the week following the epi-
sode.
This preliminary study also found a need
for more timely aerometric data, especially
in pollution episodes.
1. Goldberger, Arthur S., Econometric Theory,
John S. Wiley and Sons, Inc., New York,
1964, pp. 274-278.
198
-------
A RADIOACTIVE WASTE MANAGEMENT ASSESSMENT MODEL
S.E. Logan
Department of Chemical and Nuclear Engineering
The University of New Mexico
Albuquerque, New Mexico
S.M. Goldberg
Office of Radiation Programs
U.S. Environmental Protection Agency
Washington, D.C.
One of the major environmental concerns associated
with the projected increase in nuclear power genera-
tion is the treatment and storage or disposal of high-
level and transuranic radioactive waste. This model
provides a detailed assessment methodology for the
short-term as well as long-term quantitative effects
on the environment resulting from the release of
radionuclides during all phases of radioactive waste
management operations. This model includes a fault
tree for determination of release probabilities and
their resultant magnitudes, an environmental model
for calculating transport of radionuclides to man by
environmental pathways and an economic model for an
evaluation of associated damages. Full implementa-
tion of this technology assessment model will aid
EPA and others in evaluating the radioactive high-
level and transuranic waste management programs.
Background
Assessment methodology, that is both independent and
flexible, is urgently needed for the evaluation of
the various long-term waste disposal methods and
management options. High-level and transuranic radio-
active waste must eventually be placed in long-term
repositories for hundreds of thousands of years to
prevent the entry of these wastes into the environ-
ment. Management of these wastes must be accom-
plished in a fashion which ensures a minimum public
health hazard and a minimum risk to the environment
from the detrimental effects of radioactive contami-
nation.
In this regard, a technology assessment model is being
developed to perform parametric risk calculations for
high-level and transuranic wastes for a variety of
geologic disposal concepts, fixation processes, and
reprocessing and repository operations. The model is
specifically designed to translate probabilities and
consequences of risk occurrences so that they can be
considered in a cost-effectiveness methodology.
During FY 1976, this assessment model is being
utilized initially for a specific demographic and
geographic site and a specific geologic concept, i.e.,
bedded salt in the Los Medanos area of Southeast New
Mexico.3 This model could be applied later to other
specific concepts and sites that are considered or
proposed by ERDA as part of their terminal storage
program.
The source terms for the environmental model are the
quantities of the significant radionuclides that will
be part of the inventory of commercial reprocessing
plants and will be transported to a Federal repository.
A screening method has been developed and applied to
select significant radionuclides.'* These include
fission product isotopes and heavy metal isotopes.
The radionuclide concentrations versus time were
obtained utilizing the ORIGEN isotope generation and
depletion code developed at ORNL^ and up-to-date fuel
and power conditions. The waste form is assumed to
be a borosilicate glass with 25 wt% waste calcine
content.
Fault trees have been constructed to provide the
relationships between various geologic, meteorological,
and man-caused events which are potential mechanisms
for release of radioactive material to the environ-
ment.2'3'8'9 The fault tree model within AMRAW
evaluates the probability for release by each of numer-
ous potential release mechanisms (such as diapirism,
tectonic process, fractures of underlying rock,
groundwater transport resulting from aquifers, etc.),
and the fraction of the inventory released by each
such occurrence during a specific increment of time.
Each path through a fault tree which leads to a
release represents a set of conditions existing at a
given time which together can permit a release to
occur (Figure 2). Each such path comprises a "cut
set" and has associated probability factors and
release fractions or transfer coefficients. A flex-
ible system has been programmed in AMRAW for the fault
tree data. For each environmental release category,
any number of cut sets can be accommodated, subject
only to an adequate DIMENSION statement. Each cut set
may consist of a number of component probability
factors, which could provide a parametric survey for a
single or a group of initial release conditions.
Further, each component probability can be represented
by any or all of the following built-in functions;
constant, step change, ramp change, and exponential
change. Thus, for example, the geologic process of
basin-range crustal extension is expected to occur
(and simultaneously represented by the code) with zero
probability at the present time and gradually increas-
ing probability ramp function in the future.
Model Application
Model Development
The University of New Mexico has been developing an
environmental model entitled AMRAW. (Assessment Method
for Radioactive Waste Management). This radioactive
waste management systems model has four parallel paths
(Figure 1); each path represents a phase in the waste
management sequence and includes a release or fault
tree model, an environmental model, and an economic
model. Presently, the major effort is being applied
to the terminal or long-term storage branch for a
site-specific environment. It is planned that the
repository operations branch will be implemented
during the next phase of work on the model.
The environmental model determines the transport to and
accumulations at various receptors in the biosphere.
These receptors are: air, ground surface, surface
water, and groundwater (Figure 3). The model does
adjust each release amount to account for environmental
removal and/or fixation processes. The environmental
model is also used to determine pathways from environ-
mental input concentrations to radiation dose to man.
Pathways include: immersion in air, inhalation, inges-
tion of groundwater, submersion in water, ingestion
of contaminated food and drink, and direct surface
exposure. The release increments to the four recep-
tors in the environment are represented from all
release events in the geologic condition of deep rock-
melt disposal for a variety of transuranic material
199
-------
at several decay times (Table 1) . Transfer coeffi-
cients for environmental transport and radiation dose
is obtained by applying results from other available
environmental codes such as Percol (groundwater
transport model); INREM and EXREM (radiation dose
codes); and AQUAMOD, AIRDOS, and TERMOD (environmen-
tal receptor
The economic model will calculate detailed total
damage and marginal damage costs. These damages will
be evaluated from the appropriate residual effects
that are associated with the release of radionuclides
in the waste management process. A study of rela-
tionships between long-term costs associated with
radioactivity and long-term costs associated with
other environmental pollutants will be started for
the purpose of placing residuals effects in a proper
perspective. These costs are presented in a para-
metric format, utilizing simplified sensitivity
analysis to allow a cost -effectiveness perspective
to be utilized in any decisionmaking process.
The AMRAW code is structured to allow incorporation
of many of the existing or newly developed nuclear
fuel cycle and environmental sciences codes as sub-
routines, thus allowing the main program to be as
simple and straightforward as possible to avoid any
""black "box1' mysteries. By this means, AMEAW serves
as a vehicle to bring together data from several
disciplines in an organized -manner.
Conclusions
Application of this technology assessment model is
planned by EPA for the following uses: (1) to com-
pare and assess possible and proposed future storage
and/or disposal concepts and methods for high-level
waste; (2) to help develop the technical bases and
guidelines for establishing environmental policy
relative to the control of commercial alpha wastes
and high-level wastes; (3) to apply information from
the model to EPA's continuing effort to develop the
generic ability to evaluate the environmental accept-
ability of presently operating and proposed fuel cycle
facilities that produce, treat, store, and dispose of
transuranic and high-level waste; and (4) to assist
EPA in developing criteria and standards relating to
transuranic and high-level waste management activities.
Implementation of this model is possible for a whole
range of both radioactive as well as non -radioactive
hazardous materials which require perpetual care.
This model provides the capability to evaluate feed-
back effects from the results, to handle changes in
any of the treatment or processing operations of
these hazardous waste products, in order to minimize
environmental impact . These feedback effects could
serve to identify options which could act as incen-
tives to transform these wastes into less hazardous
forms, such as the application of transmutation to
modify the very long-term hazard potential of trans-
uranic wastes .
3. H. C. Claiborne and F. Gera, "Potential Contain-
ment Failure Mechanisms and Their Consequences
at a Radioactive Waste Repository in Bedded Salt
in New Mexico," ORNL-TM-4639, Oak Ridge National
Lab., October 1974.
4. S. E. Logan and G. H. Whan, "Selection of Signifi-
cant Elements and Radionuclides for Waste Manage-
ment Assessment," Trans. Am. Nucl. Soc., 19, 204,
1974.
5. M. J. Bell, "ORIGEN--The ORNL Isotope Generation
and Depletion Code," ORNL-4628, Oak Ridge
National Lab., May 1973.
6. Generic Environmental Statement on Mixed-Oxide
Fuel, WASH-1327, January 1976.
7. Nuclear Power 1974-2000, WASH-1175, February 1974.
8. F. Gera and D. G. Jacobs, "Considerations in the
Long-Term Management of High-Level Radioactive
Wastes," ORNL-4762, Oak Ridge National Lab.,
February 1972.
9. D. H. Denham, D. A. Baker, J. K. Soldat and J. P.
Corley, "Radiological Evaluations for Advanced
Waste Management Studies," BNWL-1764, Battelle
Pacific Northwest Labs., September 1973.
10. R. C. Routson and R. J. Serne, "One-Dimensional
Model of the Movement of Trace Radioactive Solute
Through Soil Columns: The PERCOL Model," BNWL-
1718, Battelle Northwest Labs. (1972).
11. R. E. Moore, "AIRDOS--A Computer Code for Estimat-
ing Population and Individual Doses Resulting
From Atmospheric Releases of Radionuclides from
Nuclear Facilities," ORNL-TM-4687, Oak Ridge
National Lab., January 1975.
12. D. K. Trubey and S. V. Kaye, "The EXREM III
Computer Code for Estimating External Radiation
Doses to Populations from Environmental Releases,"
ORNL-TM-4322, Oak Ridge National Lab., December
1973.
13. G. S. Killough, P. S. Rohwer and W. D. Turner,
"INREM--A Fortran Code Which Implements (ICRP 22
Models for Internal Radiation Dose to Man," ORNL-
5003, Oak Ridge National Lab., February 1975.
References
S. E. Logan, "A Technology Assessment Methodology
Applied to High-Level Radioactive Waste Manage-
ment," Ph.D. Dissertation, The University of New
Mexico, May 1974.
K. J. Schneider and A. M. Platt, Ed., "Advanced
Waste Management Studies, High-Level Radioactive
Waste Disposal Alternatives," USAEC Report
BNWL-1900 (4 volumes), May 1974.
200
-------
w - 1
w - 2
w - 3
w - 4
REPROCESSING
PLANT
J
RESIDUALS
GENERATION
RESIDUALS
TREATMENT
WASTE
TRANSPORT
*k 1 x" 1
REPOSITORY
OPERATIONS
xkl
LONG TERM
STORAGE
xkl
ACTIVITY
TRANSFER CDEFF.
DAMAGE CHARGES
ASSESSED
AGAINST RESIDUALS
-------
WASTE TRANSPORT
TO SHALLOW DEPTH
VOLCANISM DIAPIRISM
MELT
MIGRATION
TRANSPORT OF WASTE DEPOSIT
ACCIDENTAL HEAT GROUND
PENETRATION BARRIER WATER
DECAY
o
Q
D
0
CAUSE OF RELEASE
MIXING ZONE
TRANSPORT MECHANISM
RELEASE MEDIA
MATRIX
COMBINING POINT
Figure 2. A Simplified Version of a Possible Release Cutset For Deep Rock-Melt Disposal
RELEASE TO
ENVIRONMENT
T
RELEASE TO
AIR
RELEASE TO
SURFACE WATER
T
RELEASE TO
GROUND WATER
RELEASE TO
LAND SURFACE
A
Figure 3. Categorical Breakdown of Environmental Receptors in Biosphere for AMRAW
202
-------
TABLE 1. Concentrations of Selected Significant Transuranic Waste Material Per
Increment of Fuel for a Simulated Case of Deep-Rock Melt Disposal
TIME
RECEPTOR CONCENTRATIONS (Ci)
1. RADIONUCLIDE Pu-239
1.
3.
10.
30.
100.
300.
1000.
3000.
10000.
30000.
100000.
300000.
1000000.
AIR
O.OOE-01
O.OOE-01
O.OOE-01
O.OOE-01
5.51E-09
1.88E-08
9.95E-08
5.37E-07
3.73E-06
1.42E-05
2.87E-05
1.13E-05
1.36E-07
GROUND
SURFACE
O.OOE-01
O.OOE-01
O.OOE-01
O.OOE-01
3.94E-07
1.34E-06
7.11E-06
3.84E-05
2.67E-04
1.01E-03
2.05E-03
8.11E-04
9.72E-06
SURFACE
WATER
O.OOE-01
O.OOE-01
O.OOE-01
O.OOE-01
5.28E-11
1.80E-10
9.54E-10
5.15E-09
3.58E-08
1.36E-07
2.75E-07
1.09E-07
1.30E-09
GROUND
WATER
O.OOE-01
O.OOE-01
O.OOE-01
O.OOE-01
6.85E-12
2.34E-11
1.24E-10
6.68E-10
4.64E-09
1.76E-08
3.57E-08
1.41E-08
1.69E-10
2. RADIONUCLIDE Np-237
AIR
GROUND
SURFACE
1.
3.
10.
30.
100.
300.
1000.
3000.
10000.
30000.
100000.
300000.
1000000.
0
0
0
0
7
2
8
2
9
2
9
2
8
.OOE-01
.OOE-01
.OOE-01
.OOE-01
.31E-10
.20E-09
.48E-09
.65E-08
.66E-08
.83E-07
.90E-07
.71E-06
.26E-06
0.
0,
0
0,
5.
1,
6,
1,
6.
2,
7,
1,
5.
.OOE-01
.OOE-01
.OOE-01
.OOE-01
.22E-08
.57E-07
.06E-07
.89E-06
.90E-06
.02E-05
.07E-05
.94E-04
.90E-04
SURFACE
WATER
0
0
0
0
7
2
8
2
9
2
9
2
7
.OOE-01
.OOE-01
.OOE-01
.OOE-01
.OOE-12
.11E-11
.13E-11
.54E-10
.26E-10
.71E-09
.49E-09
.60E-08
.92E-08
GROUND
WATER
0
0
0
0
9
2
1
3
1
3
1
3
1
.OOE-01
.OOE-01
.OOE-01
.OOE-01
.08E-13
.74E-12
.05E-11
.29E-11
.20E-10
.51E-10
.23E-09
.38E-09
.03E-08
3. RADIONUCLIDE AM-243
1.
3.
10.
30.
100.
300.
1000.
3000.
10000.
30000.
100000.
300000.
1000000.
AIR
O.OOE-01
O.OOE-01
O.OOE-01
O.OOE-01
2.85E-07
8.06E-07
2.71E-06
6.87E-06
1.68E-05
1.93E-05
9.47E-06
4.71E-08
1.58E-10
GROUND
SURFACE
O.OOE-01
O.OOE-01
O.OOE-01
O.OOE-01
2.04E-05
5.76E-05
1.93E-04
4.91E-04
1.20E-03
1.38E-03
6.77E-04
3.36E-06
1.13E-08
SURFACE
WATER
O.OOE-01
O.OOE-01
O.OOE-01
O.OOE-01
2.73E-09
7.72E-09
2.59E-08
6.S9E-08
1.61E-07
1.85E-07
9.08E-08
4.51E-10
1.51E-12
GROUND
WATER
O.OOE-01
O.OOE-01
O.OOE-01
O.OOE-01
3.54E-10
l.OOE-09
3.37E-09
8.55E-09
2.09E-08
2.40E-08
1.18E-08
5.85E-11
1.96E-13
203
-------
FOOD - AN INTERACTIVE CODE TO CALCULATE INTERNAL
RADIATION DOSES FROM CONTAMINATED FOOD PRODUCTS
D. A. Baker, G. R. Hoenes and J. K. Soldat
Battelle
Pacific Northwest Laboratory
Richland, Washington 99352
Summary
An interactive code, FOOD, has been written in BASIC
for the UNIVAC 1108 to facilitate calculation of
internal radiation doses to man from radionuclides in
food products. In the dose model, vegetation may be
contaminated by either air or irrigation water con-
taining radionuclides. The model considers two mecha-
nisms for radionuclide contamination of vegetation:
1) direct deposition on leaves and 2) uptake from soil
through the root system. The user may select up to
14 food categories with corresponding consumption
rates, growing peri9ds, and either irrigation rates or
atmospheric deposition rates. These foods include
various kinds of produce, grains, and animal products.
At present, doses may be calculated for the
total body and six internal organs from 190 radio-
nucl ides. Dose summaries can be displayed at the
local terminal. Further details on percent contribu-
tion to dose by nuclide and by food type are avail-
able from an auxiliary high-speed printer. This out-
put also includes estimated radionucl ide concentrations
in soil, plants, and animal products.
Introduction
The computer program FOOD is designed to calculate
radiation doses to man from ingestion of foods, such
as produce, milk, eggs, and meat contaminated by
radionuclides. These radionuclides may be deposited
on vegetation and the ground by water used for irriga-
tion or directly from the air. A total of 14 food
categories may be selected with corresponding con-
sumption rates, growing periods, and irrigation rates
or atmospheric deposition assigned by the user. At
present, doses to the total body, and six internal
organs from 190 radionuclides may be calculated.
Dose summaries are displayed at the local terminal.
Additional detains on percent contribution to dose ,
by nuclide and by food type are available from an
auxiliary high-speed printer. This latter output
also includes estimated radionuclide concentrations
in soil, plants, and animal products.
The program is designed to be compatible with files
of releases and dose factors which are used by a
program, ARRRG, which calculates doses to man from
ingestion of drinking water and aquatic foods and
from aquatic recreation. The program ARRRG has been
described in detail previously.^
Model
The model presented for estimating the transfer of
radionuclides (except for H-3 and C-14) from irriga-
tion water or from air to plants through both leaves
and soil to food products was derived by Soldat2 for
a study of the potential doses to people from a
nuclear power complex in the year 2000.
Deposition on Food Products
The source of the radionuclide contamination of the
foods may be either deposition with water used for
sprinkler irrigation or deposition of airborne radio-
nuclides. In the absence of specific data, sprinkler
irrigation is normally assumed, rather than surface
irrigation, because the aerial spray produced by the
sprinkler leads to foliar deposition resulting in
higher radionuclide concentrations in the plants (and
animals consuming them) than would irrigation via fur-
rows or drip. These latter systems can be simulated,
if desired, by setting the factor for foliar retention
in the program to zero.
Deposition by Irrigation Hater. The deposition rate
di from irrigation water is defined by the relation
d. C. I (water deposition)
(la)
where:
d. deposition rate or flux [pCi/(m -d)] of
radionuclide i
C. concentration of radionuclide i in water used
1W for irrigation (pCi/J.)
I irrigation rate [&/(m -d)]. Amount of water
sprinkled on unit area of field in one day.
Deposition Directly from Air. The deposition rate onto
the foilage from airborne radionuclides is defined as:
d. 86,400 x.. \IA. (air deposition)
Mi
where:
86,400 dimensional conversion factor (sec/d)
V.. deposition "velocity" of radionuclide i
dl (m/sec)
o
^. annual average air concentration (pCi/m ) of
1 radionuclide i.
Concentration in Vegetation
The concentration of radioactive material in vegetation
resulting from deposition onto the plant foliage and
uptake from the soil of prior depositions on the ground
is given in Equation (2).
Civ di
r V1
YVXEi
BivO -
-A.t.
PA,
(2)
where:
C
iv
concentration of radionuclide i in edible
portion of plant v (pCi/kg)
fraction of deposition retained on plant
(dimensionless), taken to be 0.25
factor for the translocation of externally
deposited radionuclide to edible parts of
plants (dimensionless). For simplicity it
is taken to be independent of radionuclide
204
-------
and set to 1 for leafy vegetables and fresh
forage, and 0.1 for all other produce,
including grain. (Reference 2 lists values
of this parameter which vary with nuclide.)
The second set of terms in the brackets in Equation (3)
is omitted if the animal does not drink contaminated
water. Animal consumption rates normally assumed are
given in Table 1 .
A. = radiological decay constant for radionuclide
1 i (
-------
hv'
(4) Dose Calculations for Man
where:
C
, concentration of tritium in the environmental
lw water (pCi/a)*
concentration in irrigation water (for water
release)
pCi H/m air * absolute humidity U/m3) (for
airborne release)
1/9 - fraction of the mass of water which is
hydrogen
Fhu = fraction of hydrogen in total vegetation
(see Table 3).
The concentration of tritium in the animal product is:
'la
Cnc Qr + C, Q i
1F yF 1 aw yaw
hF
ha
(5)
where
C
IF
concentration of tritium in feed or forage
(pCi/kg) calculated by Equation (4) above,
where now C
IF
- fraction of hydrogen in animal feed.where
now F.
hf
Fhy (grain)
F, = fraction of hydrogen in animal product (see
"a Table 3)
concentration tritium in animal drinking
water (set to 0 unless there is a release
to water).
"law
Similarly, the concentration of carbon-14 in
vegetation is:
C *F
U r
cv
(6)
where
C
3w
Concentration of carbon-14 in the environ-
mental mediums carbon concentration in that
medium. (pCi ^C/kg carbon)
pCi C/a v carbon concentration in irri-
gation water (kg/n) for water release
cv
pCi c/m T carbon concentration in air
(kg/m3) for air release
fraction of carbon in total vegetation.
The concentration of carbon-14 in the animal
product is:
The dose, Rvr, in mrem to a person consuming vegetation
is:
'vr
iv v ir
(9)
Similarly the dose from consuming a particular animal
product is:
-ar
CiaUaDir
(10)
where:
U ,U = annual consumption of contaminated vegetable
v a or animal products in kg
D. = a factor which converts intake in pCi of
ir
nuclide i to dose in mrem to organ r.
Normally the exposure mode is assumed to be a 1-year1
chronic ingestion at a uniform rate. Dose factors are
available for calculating the dose during the year of
ingestion or for calculating a 50-year dose commit-
ment. Additional factors are also available for 1-
and 50-year doses from single acute intakes and for
ages other than adults. However, these have not been
entered into the routine program. The dose and dose
commitment factors employed have been derived from
the ingestion and inhalation models given in ICRP
Publication 2.5 \
Dose Calculations for Biota
Since the program output lists the radionuclide con-
centrations in the final product from the consumption
by animals of both contaminated feed and drinking
water, the internal radiation dose to animals can be
estimated in a manner analogous to calculation of
internal dose to man. If the assumption were made
that the concentration of the radionuclides in meat
were similar to the average concentration in the whole
animal, then the total body dose would be similar to
that in the meat. The following equations can be used
to calculate the dose rate in mrad/yr to an animal con-
taining a constant concentration of a radionuclide.
18'7 Ma Cia
(11)
where:
e. effective absorbed energy of nuclide i in
13 the animal (MeV/dis)
18.7 conversion factor calculated as follows:
"3a
Cor Qr + Cn Q
3F XF 3aw ya
ca
(7)
For an air release C3aw= 0 and since Fcw is very small
compared to Fcf, Equation (7) reduces to:
C3a C3F
fe)
(8)
(1.17 x 106 dis-yr^-pCi"1) (1.6 x 10"5 g-mrad-MeV"1)
_ 1R 7 dis-g-mrad
I0'/ pCi-yr-MeV
ia = concentration of nuclide i in the animal
(pCi/g).
The subscript 1 refers to tritium which is the first
nuclide in the isotope listing; similarly the sub-
script 3 in Equation (6) refers to '^C.
206
-------
TABLE 1. Consumption Rates of Feed and Water
by Farm Animals
Feed or Forage
( kg/day )
Milk Cow
Beef Cattle
EJemerrt
Be
N
F
Na
P
Ca
Sc
Cr
Hn
Fe
Co
Ni
Cu
Zn
Se
Br
Rb
Sr
Y
Zr
Nb
Mo
Tc
Ru
Rh
Pd
Ag
Cd
Sn
Sb
Te
I
Cs
Ba
La
Ce
Pr
Nd
Pm
Sm
Eu
Tb
Ho
W
Pb
Bi
Po
Ra
Ac
Th
Pa
U
Np
Pu
Am
Cm
Cf
Pig
Poultry
TABLE 2
Plant/Soil
(chickens)
Water
(i/day
1
Qc Q
yF xaw
55 (fresh forage) 60
68 (dry feed) 50
4.2 (dry
0.12 (dry
feed)
feed)
Plant Concentration Factors and
Transfer
Egq/Feed
(Dimerisionless) (day/kg)
H
Biv
4.7E-04
7.5E+00
2.0E-02
5.0E-02
5.0E+01
4.0E-02
1.1E-03
2.5E-04
3.0E-02
4.0E-04
9.4E-03
1.9E-02
1.3E-01
4.0E-01
1.3E+00
7.6E-01
1.3E-01
2.0E-01
2.5E-03
1.7E-04
9.4E-03
1.3E-01
2.5E-01
l.OE-02
1.3E+01
5.0E+00
1.5E-01
3.0E-01
2.5E-03
1.1E-02
1.3E+00
2.0E-02
2.0E-03
5.0E-03
2.5E-03
5.0E-04
2.5E-03
2.4E-03
2.5E-03
2.5E-03
2.5E-03
2.6E-03
2.6E-03
1.8E-02
6.8E-02
1.5E-01
9.0E-03
1.4E-03
2.5E-03
4.2E-03
2.5E-03
2.5E-03
2.5E-03
2.5E-04
2.5E-04
2.5E-03
2.5E-03
2.0E-02
9.9E-04*
9.9E-04
2.0E-01
l.OE+01
l.OE+00
9.9E-04
9.9E-04
l.OE-01
l.OE-01
l.OE-01
l.OE-01
2.0E-01
4.0E-03
2.1E+00
1.6E+00
3.0E-00
4.0E-01
5.0E-04
1.2E-03
1.2E-03
4.0E-01
9.9E-04
4.0E-03
4.0E-03
4.0E-03
9.9E-04
9.9E-04
9.9E-04
7.0E-02
4.0E-01
1.6E+00
6.0E-01
4.0E-01
2.0E-03
3.0E-03
4.0E-03
2.0E-04
7.0E-03
7.0E-03
7.0E-03
7.0E-03
7.0E-03
9.9E-04
9.9E-04
9.9E-04
9.9E-04
2.0E-05
2.0E-03
2.0E-03
2.0E-03
3.4E-01
2.0E-03
2.0E-03
2.0E-03
2.0E-03
2.0E-03
Coefficients
Milk/Grass
(day/£)
2.0E-06
1.1E-02
7.0E-03
4.0E-02
1.2E-02
8.0E-03
2.5E-06
1.1E-03
l.OE-04
6.0E-04
5.0E-04
3.4E-03
7.0E-03
6.0E-03
2.3E-02
2.5E-02
l.OE-02
1.5E-03
5.0E-06
2.5E-06
1.2E-03
4.0E-03
1.2E-02
5.0E-07
5.0E-03
5.0E-03
2.5E-02
6.2E-05
1.3E-03
7.5E-04
5.0E-04
l.OE-02
5.0E-03
4.0E-04
2.5E-06
l.OE-05
2.5E-06
2.5E-06
2.5E-06
2.5E-06
2.5E-06
2.5E-06
2.5E-06
2.5E-04
l.OE-05
2.5E-04
1.2E-04
2.0E-04
2.5E-06
2.5E-06
2.5E-06
6.0E-04
2.5E-06
2.5E-08
2.5E-06
2.5E-06
7.5E-07
Beef/Feed
(day/kg)
- - ^ -
bia
8.0E-04
9.9E-04
2.0E-02
5.0E-02
5.0E-02
3.3E-03
6.0E-03
9.9E-04
5.0E-03
2.0E-02
l.OE-03
l.OE-03
l.OE-02
5.0E-02
l.OEtOO
2.0E-02
1.5E-01
3.0E-04
5.0E-03
5.0E-04
5.0E-04
l.OE-02
9.9E-04
l.OE-03
l.OE-03
l.OE-03
9.9E-04
1.6E-02
9.9E-04
3.0E-03
5.0E-02
2.0E-02
3.0E-02
5.0E-04
5.0E-03
l.OE-03
5.0E-03
5.0E-03
5.0E-03
5.0E-03
5.0E-03
5.0E-03
5.0E-03
9.9E-04
9.9E-04
9.9E-04
9.9E-04
9.9E-04
5.0E-03
5.0E-03
5.0E-03
5.0E-03
5.0E-03
5.0E-03
5.0E-03
5.0E-03
5.0E-03
10
0.3
Animal Product
Pork/Feed
(day/kg)
l.OE-02
9.9E-04
9.0E-02
l.OE-01
5.4E-01
3.3E-03
l.OE-02
9.9E-04
2.0E-02
5.0E-03
5.0E-03
5.0E-03
1.5E-02
1.4E-01
4.5E-01
9.0E-02
2.0E-01
7.3E-03
5.0E-03
l.OE-03
l.OE-03
2.0E-02
9.9E-04
5.0E-03
5.0E-03
5.0E-03
9.9E-04
1.6E-02
9.9E-04
7.0E-03
l.OE-02
9.0E-02
2.6E-01
l.OE-02
5.0E-03
5.0E-03
5.0E-03
5.0E-03
5.0E-03
5.0E-03
5.0E-03
5.0E-03
5.0E-03
9.9E-04
9.9E-04
9.9E-04
9.9E-04
9.9E-04
l.OE-02
l.OE-02
l.OE-02
6.0E-04
l.OE-02
l.OE-02
l.OE-02
l.OE-02
l.OE-02
Poultry/Feed
(day/kg)
4.0E-01
9.9E-04
9.9E-04
l.OE-02
1.9E-01
3.3E-03
4.0E-03
9.9E-04
1.1E-01
l.OE-03
1 .OE-03
l.OE-03
2. OE-03
2. OE-03
3.7E-01
4. OE-03
2.0E+00
9.0E-04
5.0E-04
1 .OE-04
l.OE-04
2. OE-03
9.9E-04
3. OE-04
3. OE-04
3. OE-04
9.9E-04
1 .6E-02
9.9E-04
6. OE-03
1 .OE-02
4. OE-03
4.5E+00
5. OE-04
4. OE-03
6. OE-04
l.OE-03
4. OE-03
l.OE-04
4. OE-03
4. OE-03
4. OE-03
4. OE-03
9.9E-04
9.9E-04
9.9E-04
9.9E-04
9.9E-04
4. OE-03
4. OE-03
4. OE-03
1.2E-03
4. OE-03
4. OE-03
4. OE-03
4. OE-03
4.CE-03
* Where value unknown, a default value of 9.9E-04 was used.
207
-------
TABLE J3. Calculation of Fractions of Hydrogen and Carbon
in Environmental Media, Vegetation, and Animal
Products
Food or Fodder
Fresh Fruits, Vegetables and
Grass
Grain and Stored Animal Feed
Eggs
Milk
Beef
Pork
Poultry
Absolute Humidity
Water
fw
0.80
0.12
0.75
0.88
0.60
0.50
0.70
Carbon
(dry)
0.45
0.45
0.60
0.58
0.60
0.66
0.67
Hydrogen
(dry)
fh
0.062
0.062
0.092
0.083
0.094
0.10
0.087
0.008 H/m3
Carbon(a)
(wet)
Fcv ' Fca
0.090
0.40
0.15
0.070
0.24
0.33
0.20
Hydrogen^ '
(wet)
FhV Fha
0.10
0.068
0.11
0.11
0.10
0.11
0.10
Concentration of carbon in water 2.0 x 10" kg/Vc'
-4
Concentration of carbon in air 1.6 x 10 kg/m
w'
(*) Fcv or Fca = fc (1 f,
Fhv or Fha = V9 + fh (1 fw>
(c) Assumes a typical bicarbonate concentration of 100 mg/i
(d) Assumes a typical atmospheric COp concentration of 320 ppmy.
References
1. Soldat, J. K., et al., Models and Computer Codes
for Evaluating Environmental Radiation Doses,
USAEC Report BNWL-1754, Pacific Northwest Labora-
tory, Richland, WA, February 1974.
2. Fletcher, J. F. and W. L. Dotson (compilers),
HERMES - Digital Computer Code for Estimating
Regional Radiological Effects from the Nuclear
Power Industry, USAEC Report HEDL-TME-71-168,
Hanford Engineering Development Laboratory,
Richland, WA, 1971.
3. Mraz, F. R., et al., "Fission Product Metabolism
in Hens and Transference to Eggs," Health Physics,
no. 10, pp. 77-782, 1964.
4. Ng, Y. C., et al., Prediction of the Maximum
Dosage to Man from the Fallout of Nuclear
Devices - IV, Handbook for Estimating the Maximum
Internal Dose from Radionuclides Released to the
Biosphere, USAEC Report, UCRL-50163, Lawrence
Radiation Laboratory, University of California,
Livermore, CA, 1968.
5. International Commission on Radiological Protec-
tion, Report of ICRP Committee II on Permissible
Dose for Internal Radiation, ICRP Publication 2,
Pergamon Press, New York, 1959.
6. Annenkov, I. K., et al., "The Radiobiology and
Radioecology of Farm Animals," USAEC Report
AEC-tr-7523, April 1974.
208
-------
AIR QUALITY AND INTRA-URBAN MORTALITY
John J. Gregor
Center for the Study of Environmental Policy
The Pennsylvania State University
University Park, Pennsylvania
The effect of air pollution on white mortality
for Allegheny County, Pennsylvania is examined for the
years 1968-1972 through the use of eighteen weighted
regressions. The mortality rates are characterized by:
age (less than 45, 45-64, and 65 and over); sex (male
and female); and, cause grouping (overall, pollution-
related, and all other). Air pollution is demonstrated
to have a greater effect on men than women in the two
younger age groups and approximately the same effect
on both sexes for the 65 and over age group.
The possibility that extremely high levels of air
pollution can shorten lives and affect the quality of
human life was painfully brought to the attention of
individuals in the United States by the 1948 episode
of Donora, Pennsylvania. Today few people would argue
that the existence of pollution concentrations of
Donora's magnitude do not have significant health
effects. There is substantially less agreement, how-
ever, on the significance of the effects of smaller
levels of air pollution on health.
Background
The health effects of air pollution have been
given increased attention in recent years. A growing;
number of experimental, episodic, and epidemiological
studies have shown inverse relationships between air
quality and various measures of health. This paper
makes use of the insights developed by these earlier
works in an attempt to quantify the relationship
between ambient air quality and intra-urban mortality
differentials. Some of the experimental studies with
animals have shown the existence of synergistic
effects of sulfur dioxide (S0?) and various types of
particulates (4, 5, 10 and 21). These, and other ex-
perimental studies have shown changes in vital functions
and mortality in animals, but only changes in pulmonary
functions could be studied in man. For this reason,
experimental studies have shed only limited light on
the relationship between levels of air pollution and
mortality in man.
Episodic studies conducted by Schrenk
23
17
Scott
18
and Wilkins ^ have shown the existence of direct rela-
tionships between high levels of air pollution and
23
mortality. Wilkins estimated that the five-day
London fog of December 1952, caused at least 4,000
deaths. Similar, but not so drastic, estimates of
excess mortality were also presented by Schrenk con-
-1 Q
earning the 1948 Donora episode and by Scott for the
1962 London episode. As can be seen from these
episodic studies, they have the advantage of being able
to study mortality but are hindered in that they deal
only with specific episodes of abnormally high
pollution. Hence, such studies are not applicable to
the everyday pollution levels faced by individuals in
our urban areas. As Anderson notes:
Although the deleterious effects of acute
exposures to air pollution are well estab-
lished, it is not possible to extrapolate
from these data to the low levels of air
pollution to which persons are exposed in
a modern urban society (Anderson p. 585).
For these reasons, epidemiological studies have
grown in popularity since, in theory, they allow one
to isolate the effects of lower levels of pollution on
mortality. Most of these studies have also shown an
inverse relationship between air quality and mortality.
The procedure usually consists of calculating different
mortality rates or partial correlation coefficients for
populations exposed to different air quality conditions,
after controlling for socioeconomic class by dividing
the area under study into four or five socioeconomic
groups (Griffith9, Winkelstein24, and Zeidberg25).
There are, however, other factors which affect
mortality which are correlated with air pollution.
Freeman , for example, has shown that air quality
levels of white neighborhoods are higher than those of
non-white neighborhoods. These relationships have led
Lave and Seskin to note:
If the explanatory variables were orthogonal
to each other, the inability to get measures
on all variables would not be important. If
they were independent, one could find the
effect of any variable on the mortality rate
by a univariate regression. However, ortho-
gonality is not a reasonable assumption . . .
This colinearity among explanatory variables
means that univariate regression, or simple
cross tabulations (which constitutes the
preponderance of evidence), are not likely
to produce results that one could interpret.
(Lave and Seskin14 p. 295).
In an attempt to circumvent these limitations,
Lave and Seskin estimated their own relationships using
mortality data for 117 Standard Metropolitan Statis-
tical Areas (SMSA's) for the period 1959-1961. They
used multiple regressions to explain the variance in 35
different mortality rates (characterized by age: under
28 days, under 1 year, 14 years and younger, 15-44,
45-64, and 65 and older; by race: white and non-white;
and by sex: male and female). Their independent vari-
ables were minimum sulfates, mean particulates, minimum
particulates, percent poor, population per square mile,
percent of population 65 or older, and percent non-
white, all of which do not appear in any of their
specific linear regressions since only the "best"
results were presented. The results of their linear
regressions show a predominantly inverse relation-
ship between mortality and ambient air quality.
Their analysis, however, was severely restricted
by data limitations, the most important of these for
the purpose of isolating ambient air quality's effects
on mortality being the use of only one monitoring
stations' readings for an entire SMSA. As they note,
"it is a heroic assumption to regard these figures as
representative of an entire SMSA in making comparisons
across areas'1 (Lave and Seskin p. 286).
It should also be noted that the disaggreagated
mortality rates they used are probably not accurate
since as Lave and Seskin note:
These age specific death rates were derived
by dividing the number of people who died
by the total population. If the age dis-
tribution of people differs across cities,
these approximate death rates will not
even be proportional to the true rates.
14
(Lave and Seskin p. 318).
The errors in the measurement of these dependent
209
-------
variables could be a reason for the low coefficients
of determination for their disaggregated (age, age-sex-
specific) mortality rates.
Even with these limitations, Lave and Seskin have
significantly advanced our insights into the epidemic-
logical association between ambient air quality and
mortality to a new peak. They have shown that after
controlling for other factors which may affect mor-
tality, air quality does exhibit a significant associ-
ation with mortality. Their experiments with alterna-
tive specifications have given results not signifi-
cantly different from the general linear model (Lave
and Seskin ). Whether these associations are causal
is still an unsettled question. The experimental and
episodic works mentioned earlier, however, strengthen
the arguments for the existence of at least an
aggrevation effect.
Objectives and Significance
Recognizing the probable existence of ambient air
quality's aggravation effects on mortality, it is sur-
prising that only a few attempts have been made iso-
lating these effects in the epidemlological laboratory.
If the energy crisis continues as appears likely, this
isolation will become increasingly important as primary
air quality standards come under closer scrutiny; since
these standards are the fundamental impediments to the
use of alternative energy sources (coal and high-sulfur
oil).
As noted earlier, with the exception of Lave and
Seskin's work, few attempts have been made to control
for the collinearity among independent variables in
explaining the variance in mortality rates for areas
of different air quality. However, due to data con-
straints, their results are subject to some debate,
especially for the disaggregated mortality rates.
In an attempt to overcome these data constraints
the current analysis examines long-term (1968-1972)
mortality functions for small groupings of census
tracts within Allegheny County, Pennsylvania.
Allegheny County is particularly well suited for this
type of analysis since it has neighborhoods of both
good and bad air quality. Moreover, the relatively
rich microcounty data base (i.e., census and ain
quality data) enabled the circumvention of some of the
problems that beset Lave and Seskin. Specifically,
the existence of a multitude of monitoring stations'
readings for air quality removes reliance on a single
monitoring station. The relatively accurate infor-
mation of population at risk by age, sex, and race
from the 1970 census ensures that the mortality rates
calculated will be representative of their population
even in disaggregated form.
By approaching the problem of isolating air
quality's effect on mortality at the intra-urban level
through the'.use of multiple regression analysis, it was
possible to control for a majority of "other" factors
which were believed to influence an individual's
probability of'death. This procedure allowed isolation
of air quality'^ influence on mortality in such a way
that relatively accurate shift parameters in the
various mortality, functions could be estimated.
Thie Mortality Model
Dependent Variables ,
Any attempt to provide a more reliable estimate
of the effects of air quality on mortality, via intra-
urban, cross-sectional mortality analysis, must recog-
nize that other factors besides air quality influence
the risks of death. Specifically, since many variables
are collinear to air quality, it is necessary to isolate
the affect of ambient air quality on mortality. The
best procedure for controlling some of the most
important factors is by using age-sex-race-cause-
specific mortality rates. The following narrative pro-
vides a brief explanation of mortality differentials
according to each classification:
Age. In general, children are not subject to the
same hazards as adults. This result coupled with a
decreasing ability of the body to protect itself after
a certain age leads to the expectation of differentials
in mortality with respect to age.
Sex. Differentials in the risk of death can also
be expected on the basis of sex. Although females do
experience lower mortality rates, whether or not these
differentials are biological or social is still an
unsettled question.
Race. Differential mortality is also exhibited by
different races within any age-sex group. With the
exception of those causes of death related to inherent
generic deficiencies such as sickle cell anemia, this
result is probably due to social class differences.
Cause. Finally, it must be recognized that air
quality would be expected only to accentuate the risks
of death from certain causes (bronchitis, emphysema,
asthma, etc.). Therefore, deaths should be separated
into various causes to enable the isolation of air
quality's influence on mortality.
Thus, by controlling for age, sex and race, as
well as examining cause-specific mortality rates, it is
possible partially to isolate the effects of air qual-
ity on mortality. This analysis was conducted using
five-year average age-sex-cause-specific mortality
rates for the white population as the dependent vari-
ables in the multiple regression analysis. Another
advantage of using these specific mortality rates (par-
ticularly age and sex) as dependent variables is that
such variables provide valuable indicators of the pri-
mary etiological effects of air pollution. Specifically,
by isolating housewives the analysis avoids complica-
tions associated with work-related pollution exposures.
Individual five-year average mortality rates were
calculated by distributing the 87,349 descendants of
Allegheny County during 1968-1972 to their correspond-
ing 1970 census tract. This procedure resulted in
occasional census tract groupings since place of resi-
dence was originally coded based on 1960 census tracts.
Following this step, all groups were deleted for which
complete census information was not available due to
confidentiality suppressions. This deletion, in
addition to the exclusion of individuals with no coded
residence, reduced the file to 84,034 (approximately
96 percent of the original file). The remaining census
tracts were then reaggregated in order to obtain a
minimum of 300 deaths per area resulting in 175 group-
ings. It should be recognized that those groupings
were constructed to minimize the variance of certain
key soicoeconomic variables (i.e., family income,
education, percent white) while maintaining the con-
tiguous nature of each group.
The reason for reducing the number of areas for
which mortality rates are calculated as well as using
a five-year average mortality rate is that such pro-
cedures will help reduce the variance caused in these
rates by small and differing sample sizes (population
of the census tracts). This is an important consid-
eration since we are concerned with the stability of
these mortality rates and not their absolute size.
Consider, for example, a census tract with twenty
individuals, one of which dies during our five-year
period. In this case the five-year average mortality
rate will be 1/100 while the yearly rates will be
highly unstable ranging from 1/20 to zero (undefined).
This non-constant variance is also the motive for using
weighted multiple regression analysis. Since these
.mortality rates are a proportion (or a proportion
multiplied by a constant), the variance of the observed
210
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2 2
mortality rates will be 0 /N where CT is the variance
of a proportion and N is the sample size. Assuming
2
that 0 is appropriately the same for all samples for
a given age group, then the variance of the observed
mortality rates are inversely proportional to the
sample size. In the weighted regression, instead of
2
minimizing the sum of squares of errors, IE where E
is the difference between observed mortality rates and
estimated mortality rates. The objective is to mini-
2 2
mize ZE. /(a /N.), which, assuming CT is constant, will
2
be minimized when IE N. is minimized or when
2
E(E.N 1/2) is minimized. In essence, this means the
errors should be weighted by a factor equal to the
20
square root of the sample size. (See Smith, W. and
also Draper and Smith .)
Independent Variables
The rationale for using multiple regression
analysis is that there exist important factors other
than age, sex, race,and air quality which influence an
individual's probability of death. Some of these
factors may be colinear to other independent vari-
ables. These variables include income, education,
social status, occupation, residence, housing, climate,
availability and access to quality medical care,
quantity and quality of food consumed, tobacco consump-
tion, sanitation, and marital status (Kosa , Shryock
19
and Siegel ). Unfortunately, measurement or observa-
tion of many of these factors is extremely difficult.
Certain proxies can, however, be used while estimates
can be made of other variables. The following
independent variables are used in the model:
Percentage of Adult White Population With High
School Education. "Higher levels of education may be
associated with relatively more medical care at preven-
tive stages" (Auster, et al., p. 415). It may also be
associated with the possession of better knowledge of
preventive care and willingness to seek and follow a
doctor's advice. In general, people with higher
education also tend to have higher incomes (correlation
coefficient of .83 for Allegheny County) and thus con-
sume higher quality goods which should favorably affect
their health. Due to this high colinearity only
education (as opposed to education and income) is used.
Negative association between education and mortality
12 8
have been shown by Kitagawa and Hauser , Fuchs , and
Auster, et al. The estimates of this variable for
each of the 175 Allegheny County groupings were taken
from 1970 census data.
Total Particulates Multiplied by Sulfur Dioxide.
These variables represent two of the most available air
quality measurements. Although each variable was
originally employed- separately, the most consistent
results were obtained when the measurements interacted
multiplicatively. In essence, this procedure allowed
for the possible synergistic effects mentioned previous-
ly. The five-year average for each of these variables
•was calculated from monitoring data obtained from the
Allegheny County Department of Public Health. Missing
values for each monitoring station were assigned the
mean value for the years when such observations were
available. These monitoring stations were located on a
map by their USGS coordinates and, using a computerized
napping program, estimates were made for the remaining
points in Allegheny County using "standard" mapping
procedures. Specifically, the calculation method was
a weighted average of slopes and values of nearby data
points developed from a gravity-type model and modified
to consider distance and direction.
The resulting interpolated values were then
plotted on a map of Allegheny County to facilitate the
estimation of average values of S0_ and total partic-
ulates for each census tract grouping. A clear overlay
was placed over this computer-generated map and
weighted averages of the air quality variables were
calculated for each census tract grouping.
Number of Days With .1 Inch or More Precipi-
tation and Number of Days With A Maximum Temp.erature
Less Than 32 Degrees. These variables are the two most
consistent and significant of the fourteen climatologi-
cal variables originally considered. Although climate
has been recognized as an important factor in mortality
(Hirsch11, Petersen16 and Berke & Wilson3), the
literature on the cause-effect mechanism has not
developed to the level where it can be a_ priori deter-
mined which climatological variables are of major
importance. The average values for these variables
were estimated using the same procedure outlined for
total particulates and SO .
Population Per .156 Residential Acres.
Proximity to other individuals can influence exposure
to various diseases. This variable was calculated by
dividing the total population of the area by its
residential acreage.
Results
The results of applying weighted regression
analysis to the white male and female five-year average
mortality rates for Allegheny County are presented in
Table 1. It should be recognized that the inclusion of
additional independent variables for each mortality
function did not significantly increase the equations
overall explanatory power. The dichotomy of mortality
rates into overall, pollution-related and all other is
based on the a priori explanation's previously dis-
cussed. Specifically, the contention is that air
quality will only influence the probability of death
from certain causes (e.g., respiratory diseases) while
having no discernable effect on others (e.g., motor
vehicle accidents).
The interactive air quality term (Total Particu-
lates Multiplied by SO,) is consistently positive and
significant for the pollution-related causes of death.
Moreover, size of the coeffiecient increases with age,
as expected, although it differs little between sexes
for the 65 and above age group. For the less than 45
and 45-64 age groups the coefficient is at least twice
as large for males as females, suggesting the existence
of higher exposures at work.
The air quality term is negative only for the less
than 45 overall and the all other causes mortality
irates. Probable explanations of this result are that:
1) individuals in this age group die from non-pollution
related causes, 2) the ability of the body to withstand
the influence of pollution on health decrease with age,
and, 3) there exists a cumulative-type influence of
pollution on mortality. Since the coefficient in the
overall mortality function will be, optimally, the sum
of the pollution-related and all other causes coeffi-
cients, the relatively large negative sign for all
other causes in the less than 45 age group also causes
the overall coefficient to be negative.
The signs of the remaining coefficient are pre-
dominantly significant and of the expected sign where
ji priori values could be expected (percentage of adult
white population with a high school education and
population per .156 residential acres). For the number
of days that precipitation exceeds .1 inch the sign is
continually positive and significant while for number
of days with a maximum temperature less that 32 degrees
the sign is predominantly negative and significant.
211
-------
TABLE 1. 1968-1972 White Male and Female
Age-Cause-Specific Mortality Functions
PART A - OVERALL MORTALITY FUNCTIONS
Variable
Percent of Adult White
Population with High School
Education (1)
Total Participates
Multiplied by S02 (2)
Number of Days
Precipitation > .1" (3)
Number of Days Maximum
Temperature < 32 degrees (4)
Population per .156'
Residential Acres (5)
Constant (6)
I2
Less than 45
Male Female
-1-449 AA -0.639
(5.206) (3.041)
-0.001 -0.001
(0.327) (0.378)
2.824 1.713
(5.371) (4.527)
-1.471 -1.462
(1.368) (1.935)
0.023 0.012
(0.773) (0.555)
3056.927 2168.157
(4.620) (4.622)
.281 .185
*
All mortality rates (dependent variables) are in deaths
**
The values in parenthesis are the corresponding student
PART
Variable
Percent of Adult White
Population with High
School Education (1)
Total Particulates
Multiplied by SO (2)
Number of Days
Precipitation >.l" (3)
Number of Days Maximum
Temperature < 32 degrees (4)
Population per .156'
Residential Acres (5)
45-64
Male Female
-14.941
(7.121)
0.045
(2.257)
19.455
(4.354)
-0.729
(0.079)
0.647
(2.733)
16862.343
(4.830)
.404
per 100,000.
t values.
-5.690
(5.490)
0.026
(2.779)
6.996
(3.152)
4.246
(0.943)
0.205
(1.958)
7492.812
(4.109)
.404
65
Male
-39.621
(6.238)
0.112
(1.757)
111.159
(7.121)
-49.172
(1.553)
0.283
(0.471)
29326.868
(3.534)
.539
and over
Female
-10.752
(2.047)
0.110
(2.120)
60.013
(4.699)
-27.657
(1.070)
-0.365
(0.779)
31072.048
(4.467)
.491
***
B - POLLUTION RELATED CAUSE-SPECIFIC MORTALITY FUNCTIONS
Less than 45 45-64
Male Female Male Female
-0.406 -0.059 -9.
(3.721) (0.651) (6.
0.002 0.001 0.
(1.656) (1.515) (2.
0.271 0.154 13.
(1.313) (0.961) (4.
0.606 -0.311 -2.
(1.439) (0.971) (0.
0.004 0.014 0.
(0.351) (1.574) (1.
706 -4.351
431) (6.639)
031 0.014
180) (2.395)
494 3.991
198) (2.844)
702 2.777
406) (0.975)
338 0.138
983) (2.082)
65 and over
Male Female
-27.284 -8.494
(5.476) (2.123)
0.095 0.097
(1.906) (2.452)
77.549 43.159
(6.333) (4.436)
-30.882 -20.563
(1.243) (1.044)
0.015 -0.301
(0.032) (0.843)
Constant (6)
R2
281.944 697.898
(1.087) (3.514)
11738.581 3815.604
(4.674) (3.309)
19207.563 22439.555
(2.956) (4.241)
.156
.019
.348
.357
.498
.465
These mortality rates are based on total deaths from tuberculosis of the respiratory system,
malignant neoplasms of bruccal cavity, pharynx and respiratory system, major cardiovascular
disease, acute and chronic bronchitis and bronchiolitis, emphysema and asthma.
212
-------
PART C - MORTALITY FUNCTIONS - ALL OTHER CAUSES
Variable
Percent of Adult White
Population with High
School Education (1)
Total Particulates
Multiplied by S02 (2)
Number of Days
Precipitation > .1" (3)
Number of Days Maximum
Temperature < 32 degrees
Population per .156
Residential Acres (5)
Constant (6)
—9
Less than 45
Male Female
45-64
Male Female
65 and over
Male Female
-1.043
(4.353)
-0.003
(1.134)
2.553
(5.641)
-2.077
(4) (2.244)
0.019
(0.738)
2774.988
(4.871)
.234
-0.581
(3.013)
-0.002
(1.110)
1.559
(4.489)
-1.151
(1.659)
-0.002
(0.122)
1470.260
(3.414)
.193
-5.236
(5.729)
0.014
(1.580)
5.960
(3.062)
1.973
(0.489)
0.309
(2.999)
5123.750
(3.369)
.315
-1.339
(2.289)
0.012
(2.240)
3.005
(2.399)
1.469
(0.542)
0.067
(1.137)
3677.218
(3.574)
.332
-12.336
(5.471)
0.017
(0.739)
33.610
(6.065)
-18.290
(1.627)
0.268
(1.254)
10119.306
(3.435)
.415
-2.258
(1.927)
0.013
(0.701)
16.854
(3.661)
-7.095
(0.761)
-0.064
(0.378)
8587.513
(3.430)
.360
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213
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EVALUATION OF HEALTH DATA IN TERMS OF ENVIRONMENTAL FACTORS
Meyer Katzper
Systems and Information Analysis
Rockville, Maryland
N. Phillip Ross
Bureau of Quality Assurance, DHEW
Rockville, Maryland
Presently, improved health data is becoming available
in terms of hospital records which are to be part of
a national computerized data base. Simultaneously,
the more comprehensive environmental monitoring which
is being implemented provides measures of environ-
mental pollutants. The question that our models
address is whether stress due to environmental factors
can be detected in hospital data. To the extent that
hospital data reflects environmental stress, a dis-
criminating tool is available for determining the most
probably significant pollutants from a health view-
point.
Background
A major underlying motivation for environmental studies
is the recognition that environmental factors affect
man's health. In carcinogenesis research, efforts
have been undertaken to establish a direct link, be-
tween an environmental factor such as might exist in
a special work environment and the development of
cancer.1>2 However, there have been few systematic
attempts to establish a relationship between data on
incidence of illness and broad-range environmental
monitoring data. Epidemiological studies generally
cover severe episodes of environmental pollution. In
such cases, changes in morbidity and mortality patterns
have been related to pollution in the community
environment.3,4 Part of the difficulty in the past of
relating health and environmental factors has been a
a lack of good data. Another difficulty has been
insufficient realization of the practical significance
of large-scale studies and a resulting lack of high-
level committment to their support. These drawbacks
are presently being overcome.5,6
This paper examines the potential use of a large-scale
health data base in defining standards for levels and
exposure times to environmental pollutants known to
have deleterious effects on human health. In 1972,
Congress passed legislation creating Professional
Standards Review Organizations (PSRO). The PSRO
program provides the unique opportunity to collect
uniform hospital discharge records on a national
basis. For the first time there will exist a com-
prehensive data base containing health information
on an entire population. The necessity for statisti-
cal inference will be eliminated. The population
data which will be available could be used to validate
suspected relationships as well as to uncover rela-
tionships heretofore only hinted at in sample data
sets. Once this data base is established, linkage
to local and national environmental data bases will
provide a new and powerful capacity for analysis of
health data as it relates to environmental conditions.
In order to utilize this potential, there is a need
to develop a conceptual base from which meaningful
analysis of the data will be possible. Our appoach
will be to develop a series of models which will
present a conceptual framework on which to build
more complex and realistic models enabling researchers
to realize the potential of this new data base.
A series of models is considered, starting with the
simplest and proceeding to introduce complicating
factors. All models consider dose levels of
deleterious substances and the length of time of
human exposure. Within the framework of the model,
we seek to answer the question of whether a response
would be detectable by examination of clinical
records. When results are detectable, the model
presents a basis for setting human health hazard
levels in terms of human health effects. As a
canonical example we consider a population subjected
to an ongoing environmental stressor. An attempt is
made to describe possible effects of the continued
stress on the population. Underlying assumptions
must be made as to the characteristics of the
resultant illness. These assumptions form the frame-
work of the model which is then mathematically and
logically formulated. These results can then be used
to set up a quantitative methodology for establishing
acceptable stressor levels. The direct and immediate
benefit of the modeling is development of the metho-
dology which will yield insight into the nature of
the problem if not its actual solution.
Model Development
Background
There is no doubt that environmental pollution has
adverse affects on human health. The episodes of
Donora, Pennsylvania (1948) and London (1952) provide
indisputable evidence that in extreme cases environ-
mental pollution can result in considerable loss of
life and in serious illness. Acute episodes of pollu-
tion represent abrupt and unusual exposure to high
concentrations of pollutants, and produce the most ob-
vious health effects. However, human populations are
continually exposed to varying levels of pollutants
during their lifetimes. Recent studies have shown
that chronic exposure to moderate concentrations of
pollutants do adversely affect human morbidity and
mortality.7
Chronic exposure of human populations to low levels of
pollutants is an inevitable consequence of man's
technological development and has become a political
and economic fact of life. The problem of developing
standards for acceptable levels of pollutants is
complex. In principle, a "dose-response" relationship
can be established if the exposure levels are high and
the cause and effect relationship clear; however, with
low-level chronic exposure the setting of standards
becomes very complex.
The models developed in this paper focus on long-term
exposure of populations to low-level concentrations of
environmental pollutants with known cause and,effect
relationships to human health. The models are simpli-
fied by design, and as stated in the introduction, are
intended to provide a structural framework from which
continued probing and analysis of the data will lead
to more realistic models and the development of
objective methodologies for the setting of standards.
214
-------
In all the models discussed, the basic underlying
premise is that although chemical substances are
toxic at some concentration, a concentration exists
for all substances from which no injurious effects
will result no matter how long the exposure.8
Using this conceptual basis, the models are developed
in such a manner as to provide for the generation of
dose-response curves which will allow for estimation
of standards for pollution levels based on analysis
of clinical data. Even though the state-of-the-art
is such that the generation of a complete set of
dose-response curves for all pollutants for differ-
ent types of populations is not technically feasible,
the models can provide a basis for initial generation
of dose-response curves which will provide the basis
for decisionmaking in setting standards for individual
pollutant levels in the environment.
Models
The simplest model relates effects on health to long-
term chronic exposure at low levels of a single pol-
lutant. Exposure is assumed to result in a cumulative
effect over time with the resultant onset of clinical
symptoms when the cumulative dose reaches a critical
level. The effect may be espressed as follows:
Y.J = LT Q Onset of Clinical Symptoms (1)
where
Y-J is the cumulative effect value for the ith
observation
L is the level of pollutant which is assumed to be
constant over time
T is the time of continuous exposure to the pollutant
Q is the critical value for the cumulative effect.
This model assumes all individuals in the exposed
population are identical in their reaction from
exposure to the pollutant. The model implies a
binary situation in which the ith individual does
not demonstrate any clinical symptoms until the
cumulative exposure effect equals or exceeds the
critical value Q
P (of Clinical Symptoms) 0 when LT < Q
P (of Clinical Symptoms) 1 when LT ^.Q
Validation of this model required the examination of
the clinical records of a cohort population (i.e.,
a group of individuals all exposed to level L of a
pollutant at the same time for the same period of
time (T)). If the model is valid, the clinical records
for the cohort will show onset of symptoms for all
members of the cohort at the same time. Determination
of Q in turn allows for the establishment of accept-
able standards for pollutant levels.
Unfortunately, humans rarely respond in such a uni-
form fashion as is assumed by this model. Biolog-
ical variations within the cohort population will
result in variations in response to constant exposure.
It is not unreasonable to assume that the variations
in dose-response times will be a function of biologi-
cal variability resulting in the dose-response times
being distributed as a random normal variate. It is
possible to modify model one to accommodate this
concept.
As in model one the modified model relates health
effects to chronic exposure at low levels of a
single pollutant; however, this model provides for
individual biological variations in the members of
the exposed population. This model may be expressed
as follows:
LT +
(2)
where
ei normally distributed variable representing the
individual biological variability component for the
ith individual. The expected value of e-j is 0.
Using this model one would expect to find in a cohort
population exposed to a single pollutant at level L
for a given time T (such that LT = Q) that only a
portion of the cohort population would exhibit
clinical symptoms as a result of exposure rather than
the entire population as would be expected under
model one. If we accept the assumption that e is a
random variable normally distributed with an expected
value of 0, then the portion of the cohort population
exhibiting clinical symptoms after exposure to level L
of the pollutant for time T would be one half (.50).
The concept of a cumulative critical value still
holds; however, each individual reacts differently to
the same exposure effectively having an individual-
ized Q level .
YT = LT + ei
If LT Q for the single pollutant, then
Q +
If
0 for (Q
1 for (Q
+ ej
-------
Y.J = The cumulative effective value for the ith in-
dividual
al=Weight factor for exposure to the first pollutant
a2 = Weight factor for exposure to the second
pollutant
LI =Level of concentration of first pollutant
1-2 = Level of concentration of second pollutant
T-j =Time of exposure to first pollutant
T2 =Time of exposure to second pollutant
I =Synergistic or antagonistic effect of interaction
between the two pollutants
e-j =Measure of biological variation for ith
individual
If a cohort population is exposed to constant levels
of the first (Li) and second^ (L2) pollutants for a
specified time (T) where
T = T] T2
such that T( a-|b| + a2L2^ ^12
where
Q]2 a cumulative critical value for exposure to
LI and L2
then Y,-
Q12
I + e.
Validation of the model from clinical records becomes
a matter of detecting the existence of an interactive
effect. If I 0, then the model is simply a
linearly additive function and one would expect to
detect clinical symptoms in approximately one half
the cohort population after exposure to the two
pollutants for time T. However, if I ^ 0, one must
examine the data to determine the presence of
synergistic or antagonistic effects due to the
interactive process. For example, there have been
synergistic effects observed from exposure to sulfur
oxides in the presence of undifferentiated parti -
culate matter.' Laboratory studies have shown that
a combination of sulfur oxides and particulates may
produce an effect that is greater than the sum of
effects produced by the pollutants individually.
The degree of potentiation is dependent on the mix
of pollutants and varies across different concentra-
tion. A three-to four-fold potentiation of the
irritant response to sulfur dioxide is observed in
the presence of particulate matter capable of
oxidizing sulfur dioxide to sulfuric acid.10 In
situations where two pollutants are involved, the
validation of interactive effects through examination
of clinical records is straightforward. Interactive
synergistic effects would result in more than one
half the cohort population exhibiting clinical
symptoms after exposure to the pollutants for a time
equal to T. The greater the proportion of records
showing clinical symptoms, the greater the synergism.
Interactive antagonistic effects would result in
less than one half the cohort population exhibiting
clinical symptoms after exposure to both pollutants
for a time equal to T. The greater the antagonistic
effect, the lower the proportion of records showing
clinical symptoms.
Expansion of this model to involve more than two
different pollutants is possible; however, the
216
complications produced by the possibilities of_
secondary, tertiary, quaternary . . . interactions
are limitless and present methodological problems of
extreme complexity in relating such models to actual
clinical data.
Further Modeling Consideration
In reality, individuals are exposed to a variety of
pollutants at varying concentrations and for differ-
ent periods of time during their lifetime. Those
exposed do not necessarily suffer from a single
specific pollution-induced disease, but rather
experience an aggregation of clinical symptoms in
part due to pollutant exposure, aggravation of a
previous weakness due to prior illness, etc.
An approach to the multifactor problems of pollution-
induced illness offered by the availability of clini-
cal information on a national basis is the capability
of grouping disease entities relative to the presence
of environmental stressors for specified populations
(populations defined by geographic groups or logical
groupings). Consider a patient exposed over time to
a variety of pollutants. In such a case it would be
very difficult to determine which pollutant or
combination of pollutants were responsible for the
illness. If there is available a large accumulation
of clinical and associated environmental records for
different populations, it would be possible to set
up a three-dimensional matrix in which we set out
environmental stressors versus clinical symptoms and
population. By examining the matrix it would be
possible through logical elimination to determine
which stressors were not related to special disease
syndromes. For example, consider two populations
have identical clinical symptoms and in population one,
environmental stressors A and B are present and in
population two environmental stressors A and C are
present. It is reasonable to conclude that factor
A is a critical environmental stressor in contrib-
uting to the presence of the observed clinical
symptoms. Analytical techniques such as cluster
analysis applied to such matrices could provide key
information in relating specific pollutants or
clusters of pollutants to specific disease entities
in the population. Once identified, appropriate
models can be developed to aid in the establishment
of pollutant level standards for different populations.
The models developed in this paper do not address the
complexity inherent in real-world situations. Obvious-
ly the conditions and assumptions of these models are
not frequently met in real-world situations. The
models are indicators of analytic approaches which must
be undertaken. The basic models must be augmented
and modified to accomodate the specific situation
addressed by the available data. For example, one of
the aspects of environmental stress that must be
accounted for in evaluating health effects is the
level at which permanent damage to the organism
occurs. A complementary aspect of this study is the
modeling of recuperation under improved conditions. A
case in point is an area with good air quality which
at frequent intervals gets a peak of some pollutant.
The physiological effects may then be reversible; the
large dose received being compensated for by the long
recovery time available between peaks. These observa-
tions can form the basis for a recuperative model of
environmental effects where the cumulative critical
value is never reached even though exposure time
exceeds that which is necessary to produce illness.
Another situation which must be addressed is the
possibility that the clinical records may show stress
symptoms which cannot be directly related to any
-------
given environmental stressor. Studies by Martinll
in London showed direct relationships between levels
of smoke and sulfur dioxide and respiratory and
cardiac morbidity. Empirical evidence indicates that
environmental stress is producing clinical symptoms
in individuals with prior weaknesses. In cases
where it is suspected that environmental stressors
have exacerbated prior weaknesses, the extended
clinical records must be examined. In some cir-
cumstances it may be desirable to carry out
retrospective studies to ascertain whether environ-
mental factors are the underlying stressors. Such
studies require an extra level of data and extra
inductive steps which are not presently considered
by our models.
All of the models which we have discussed can be
programmed and simulated. With increasing com-
plexity when analytic formulations cannot be
solved, the logical modeling structure can still be
established and simulated to determine results.
Conclusion
The models which we have presented illustrate our
perceptions of environmental effects and indicate
how health data can provide a basis for testing of
the hypotheses underlying the models. Presently,
the system for gathering data is being established.
With the initial gathering of data, the appropriate
ranges of parameters to be used in the models will
be determined. At this point, simulation will be
used to indicate the effects across the empirically
determined ranges. Results will be compared with
data and improvement will be made as our understanding
increases.
The main reason for formulation of basic models
using a minimum of hypotheses and advanced tech-
niques is that our present level of information is
insufficient to support intricate theories. With
the basic models as a guide, fundamental questions
can be addressed and appropriate data collected
for their resolution. Based on the new informa-
tion obtained, the models can be revised, refined,
and expanded. In this stepwise manner with the
interaction of theoretical constructs with data,
a firm foundation can be laid for understanding
the environmental effects on health.
References
Morris, J. N., Uses of Epidemiology, Williams and
Wilks Co., 1964.
Ember, L., "The Spector of Cancer," Environmental
Science and Technology, 116, December 1975.
National Air Pollution Control Administration, Air
Quality Criteria for Sulfur Oxides, Department
of Health, Education, and Welfare, Publication
AP-50, 1969, (Part of a series of publications
on air pollutants).
Health Hazards of the Human Environment, World
Health Organization, Geneva, 1972.
Goran, M.J., et al., "The PSRO Hospital Review
System," Supplement to Medical Care, 13, No. 4,
April 1975.
6. International Conference on Environmental Sensing
and Assessment (ICESA), Report in Environmental
Science and Technology, December, 1975.
7. Purdom, W. P., Environmental Health, Academic
Press, New York, 1972.
8. IBID, number 4, p. 133.
9. National Air Polution Control Administration, Air
Quality Criteria for Particulate Matter,
Department of Health, Education, and Welfare,
Publication AP-49, 1969.
10. IBID, number 3.
11. Martin, A. E., and Bradley, W., "Mortality and
Morbidity Statistics and Air Pollution",
Proceedings Royal Society of Medicine, 57,
969-975, 1964.
217
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INTEGRATED ASSESSMENT: CONCEPT AND LIMITATIONS
Lowell Smith, Richard H. Ball, Steve Plotkin, and Frank Princiotta
U.S. Environmental Protection Agency
Washington, D.C.
and
Peter M. Cukor
Teknekron, Inc.
Berkeley, California
Introduction
The Integrated Assessment (IA) program conducted by
the Environmental Protection Agency (EPA) is a multi-
agency, interdisciplinary effort to define and eval-
uate the various environmental and socioeconomic ef-
fects which result from energy extraction, processing,
transportation, conversion and end use activities.
Integrated Assessment at EPA traces its genesis to
the early socioeconomic and modeling work performed
within the EPA's Washington Environmental Research
Center, where research was conducted on environmental
assessment methodology, on environmental benefit deter-
minations, and on linking environmental protection
strategies with models of the U.S. economy.
In early 1974, following release of the Ray report
(reference 1), the Office of Management and Budget
established an interagency task force on "Health and
Environmental Effects of Energy Use," chaired by Dr.
Donald King, Department of State, and Dr. Warren Muir
of the President's Council on Environmental Quality.
The task force's objectives were to:
• Examine the existing Federal research program
relating to the human health and environmental
effects of energy use; and to
• Recommend mutually supporting multi-agency
research programs, including a programmatic
allocation of Federal research funds, to deve-
lop a clearer understanding of the health and
environmental effects of energy use.
An important conclusion of the task force was that the
social and economic consequences of alternative energy
and environmental policies needed to be considered
along with, and in coordination with, the health and
environmental impacts of such policies. The authors
of the task force report (reference 2) recommended the
formation of a research program to identify "environ-
mentally, socially, and economically acceptable
(energy development) alternatives" by integrating re-
sults from the two research areas, socioeconomic and
health/ecological, as well as from research on cost/
benefit/risk evaluation and policy implementation
alternatives. In response to these recommendations,
the Office of Energy, Minerals, and Industry (OEMI)
established its IA program, which is further described
herein in terms of its modeling requirements.
Problem Statement
The problem addressed by the IA program is one that
has become painfully apparent to society over the past
several decades. The development of new technologies,
or the extension of technologies to undeveloped geo-
graphical areas, carries with it a chain of impacts
extending throughout the physical, economic, and social
systems. Many of these impacts are initially unfore-
seen, yet they may have far-reaching consequences which
run counter to, and even overshadow, the intended
benefits brought by a technology.
The traditional research programs of the EPA have in-
cluded in their analyses of energy technologies an
examination of a broad range of environmental effects.
This range of research effort spans the measurement of
pollutants discharged from stacks, outflows, etc.,
determination of their ecosystem and health impacts,
control technologies for controlling or mitigating
these impacts, and computations of the associated
control costs. The IA cuts across these several
areas of research interest, emphasizing their inter-
connectedness for policy analysis purposes.
Additionally, the IA program attempts to carry these
analyses further, by focusing on the secondary and
higher order impacts of the technologies themselves
and of the environmental controls applied to them.
The higher order effects considered include the
possible social and economic consequences of techno-
logies on land use and population migration, and the
measures of the associated impacts on: the social struc-
ture (e.g. changes from rural to urban society, in-
flux of workers with different social values leading
to conflict), the environment (e.g., influx of popu-
lation creating sewage problems, destruction of
natural habitats), and on the economy (e.g., demand
for new construction and operation workers which may
create labor shortages for previously established
industry and agriculture, and capital requirements and
their associated economic and environmental implica-
tions). The program also attempts to trace in depth
the effects of environmental controls on the environ-
ment, society, and the economy.
An obvious prerequisite to incorporating social and
economic analysis into the health and environmental
effects research program is that of insuring that the
more focused portions of the Federal energy research
program are complete with regard to investigating in
sufficient depth all of the impact areas of concern.
The IA program is responsible for identifying gaps in
the overall research effort that prevent a complete
assessment of optimal development and environmental
control alternatives. Thus, work conducted within the
program consists mainly of integrative analysis rather
then original research or data collection. When
further original research or data collections are iden-
tified as being necessary to allow a complete analy-
sis, the program will generally turn to the other
research programs of the EPA and the other Federal
agencies for assistance.
Program Objectives
The IA program is responsive to the national need of
developing a well-coordinated set of energy policies
which will foster the joint attainment of energy and
environmental goals. Further, it provides a mecha-
nism whereby implementation strategies for these coor-
dinated energy policies can be conceptually tested as
to their full range of socioeconomic and environmental
consequences. Objectives of the IA program include:
218
-------
o Identification of energy supply and con-
version alternatives which are acceptable
when judged jointly by environmental, social
and economic criteria and constraints;
o Evaluation of the cost/risk/benefit trade-
offs of energy production, conservation,
and pollution control alternatives, especial-
ly as these prevent environmental damage and
secure related benefits;
• Assistance to the nation, and EPA in parti-
cular, in the selection of optimized policies
for the attainment of environmental quality
goals; and
• Identification of critical gaps in current
energy-related research programs, and of
other priority research topics, which must
be addressed in order to support direct EPA
responsibilities.
Program Methodology
The primary analysis tool used by the IA program is the
Technology Assessment (TA). Coates (reference 3) de-
fines TA as "the systematic study of the effects on
society that may occur when a technology is introduced,
extended, or modified with a special emphasis on the
impacts that are unintended, indirect, and delayed."
By this definition, TA precisely fits the analysis re-
quirements defined above. The TA's incorporated in the
IA program will focus on regional energy development
problems and emerging energy technologies.
The appropriate way to conduct a TA remains a matter
for extended debate. TA methodologies range from
highly formal structures modeled by decision analysis
techniques•, event trees, and quantitative cost/risk/
benefit analyses that stress intense interaction
within one or more interdisciplinary teams. These
various techniques for conducting Technology Assess-
ments are described at length in the literature (see
references 4 through 7). The IA program is delibe-
rately neutral with respect to favoring any TA meth-
odology, at least at this early stage of the program.
This attitude is subject to change as further ex-
perience is acquired, or as special situations are
encountered.
Although selection of an appropriate methodology is ob-
viously critical, the successful conclusion of a TA may
be even more closely linked to choices made regarding
the scope or boundaries of the assessment. These
choices are linked to:
o Identification of the decision-maker(s);
o Resources available to the assessment team; and
o Nature of the assessment subject.
For instance, local decision-makers will usually make
decisions based on the impacts on their jurisdications
alone. However, a TA addressed to this type of deci-
sion-maker must consider what actions outside juris-
dictions might take if the client chooses a course of
action which is antithetical to the interests of these
outside jurisdictions. Would a state cut off finan-
cial assistance if a locality insisted on pursuing a
course of action which hurt its neighbors? A TA that
did not consider these aspects would be of limited
value.
When the decision-maker to be addressed is the Federal
Government, as is the case to a great extent within the
IA program, the definition of project scope becomes
quite different. The Federal decision-maker is nor-
mally placed in the rather ambiguous position of having
to incorporate simultaneously the viewpoints and in-
terests of the Nation as a whole, as well as the States
and other regional or local interest groups. This type
of "global" perspective can rarely be fully accommo-
dated in a TA, and thus each assessment is forced, re-
luctantly, to make critical choices as to the geo-
graphical boundaries of impacts considered, the time
frames to be examined, the types of impacts to be fo-
cused on, parts of fuel cycles to be stressed, etc. In
multi-year assessments, such choices are particularly
critical to the success of the first year efforts.
Modeling Requirements
The IA program attempts to utilize research results
and specific models for relating a wide range of causes
with environmental and socioeconomic effects. Some of
these include:
• Source emission characterization of specified
operations as a function of operating load,
fuel input, etc.;
• Operating effectiveness, economic costs,
effects on reliability, etc., of pollution
control technologies;
• Pollutant transport within and between media;
• Pollutant chemical transformation processes
which occur within a given medium;
• Pollutant uptake and concentration in food
webs;
• Acute and chronic responses of organisms to
pollutant exposures;
• Pollutant effects on human welfare, including
as yet poorly quantifiable impacts;
• Acute and chronic human health responses to
ambient pollutant concentrations;
• Economic damage expected from pollutant re-
leases;
• Local socioeconomic effects of energy develop-
ment;
• Individual, corporate and institutional re-
sponse mechanisms to changes in driving forces;
• Cost/risk/benefit analysis disaggregated to
specific classes of parties at interest; and
• Net energy analysis for entire fuel cycles from
extraction through transportation and conver-
sion to pollution control and waste disposal.
Results of these analyses are integrated, through the
TA mechanism, into several possible cross-cuts or di-
mensions of comparative analysis'. Of greatest interest
are analyses which articulate the range of environmen-
tal and socioeconomic consequences for:
• Differing levels of pollutant control within a
given energy technology;
• Alternative energy technologies within a spec-
ific geographical region;
• Selected energy technologies applied to all
geographical regions; and
• Differing strategies for development of a
specified, energy resource, including factors
such as institutional constraints, time phasing
and method of extraction.
Because of their generally wide-ranging nature, which
attempts to draw results from a number of disparate
disciplines into a policy-oriented decision structure,
the TA's within the IA program are referred to as Inte-
grated Technology Assessments (ITA's) Each ITA at-
tempts to integrate its results across two or more of
the above listed analysis dimensions.
Current Projects
The IA program currently has two TA's fully underway, a
third about to be launched, and two more in the active
planning phase. The first three of these are described in
some detail in order to indicate the range of model-
219
-------
ing requirements and opportunities within the IA program.
1. An Integrated Technology Assessment of Western
Energy Resource Development: The objectives of
the Western Energy ITA are to:
• Assist the EPA in developing environmental con-
trol policies and implementation strategies for
mitigating the adverse impacts of Western energy
resource development;
• Assist EPA's Office of Research and Development
in evaluating that portion of its environmental
research program dealing with the problems of
Western energy development;
• Provide a balanced assessment of the full range
of costs and benefits stemming from alternative
energy resource developments in the Western
United States in order to assist Federal and
State planning for such development.
This ITA is being conducted jointly by the University
of Oklahoma's Science and Public Policy (S&PP) Program
and the Radian Corporation. The Project Director is
Dr. Irvin (Jack) White, professor of political science
at Oklahoma University and assistant director of the
S&PP Program.
The ITA focuses on the impacts of developing coal, oil
shale, oil, natural gas, geothermal and uranium re-
sources in 13 western states (reference 8). Develop-
ment of these resources, and especially of coal and
oil shale, has become a source of extreme contention
among interest groups both within and outside of the
region, largely because the impacts, positive and
negative, are separated spatially and temporally. For
example, the development will satisfy demand for
energy largely in the Midwest and the Pacific coastal
states, while environmental damage will largely accrue
to the resource rich states inside the region. Al-
though in the long term the overall financial position
of the resource states may possibly improve from the
expanded tax base created by development, short term
demands for services such as education, housing, and
other services associated with a rapidly expanding
population will create an initial severe strain on
local finances.
The Western Energy ITA team does not favor a highly
structured approach to TA, and thus there is a de-
emphasis of formal decision analysis and cost/risk/
benefit tools and model building. Impact analysis
will focus on a series of site-specific and regional
scenarios. Energy development levels are set by as-
suming levels of national energy demand based on pre-
vious forecasts and allocating shares of the supply
responses to the region (possibly by utilizing the
Gulf-SRI energy model). During the first year of the
study, the "boundaries" can be specified as follows:
• All portions of the fuel cycle (excluding end
use) are considered except that the uranium
fuel cycle is examined only to the milling
stage;
• The focus of attention in impact analysis will
be the eight major resource states. Impacts
outside the region are not considered in depth
with the possible exception being at electri-
city demand centers in the Midwest; and
• Exogenous variables affecting development
rates are not examined in depth.
The implication of these boundaries is that the ITA
focuses, in the first year, on the question of how to
cope with development if it occurs. The parallel ques-
tions that a "complete" TA would attempt to answer
whether or not development should occur, and how to
promote the level of development desired (or, at least,
how to predict the level likely to occur) require
analyses considerably beyond the first-year study
boundaries.
2. An Integrated Technology Assessment of
Electric Utility Energy Systems: The Electri-
cal Utility ITA has as its objectives;
• To provide a means of testing pollution con-
trol policies and strategies which affect the
electric utility industry, and which must be
formulated in response to current and near
terms issues.
• To identify those issues, especially environ-
mental issues, which are likely to require po-
licy decisions in the future, and to identify
the research programs which should be initiated
in order to provide a sound basis for future
decisions regarding these issues.
The ITA is being conducted by the Energy and Environ-
mental Engineering Division of Teknekron, Inc.,
Berkeley, California. The Principal Investigator is
Dr. Peter M. Cukor; the Project Director is
Mr. Glen R. Kendall.
The Electric Utility ITA focuses on the energy con-
version and pollution control technology alternatives,
health and ecological effects, and resultant national
economic impacts associated with activities of the
electrical utility industry (reference 9). Rapid
depletion of the readily accessible fluid state dom-
estic energy resources for electrical power generation,
coupled with international concerns about the quantity
and security of imported oil and gas, have produced a
major tilt in the industry in favor of nuclear fission
and coal combustion as the electricity-producing tech-
nologies of choice over the next decade. Additionally,
factors such as the decreasing availability of natural
gas supplies are continuing to produce a shift towards
increasing electrical demand at the expense of the more
traditional energy sources, even as the total national
energy demand has decreased over the past two years.
The future development implied by these forces, invol-
ing development of new mining areas and increased pro-
duction in established areas, development of extensive
new transmission and storage facilities, construction
of extremely large fossil and nuclear generating faci-
lities, and a vast quantity of supporting development,
may result in the creation of new (and the exacerbation
of existing) environmental, social and economic problems
that demand the close attention of the Federal govern-
ment .
In contrast to the Western Energy ITA, which is con-
siderably broader in terms of the "actors" who play
significant roles in affecting the course of develop-
ment, the Electric Utility ITA is structured so as to
consider the actions and effects of one industry as it
is affected by external forces. Thus, Teknekron's
approach to conducting this ITA relies heavily on
creating models to predict the behavior of the electric
utility industry. These models are to be exercised to-
wards the end of the first year by analyzing a set of
scenarios which are designed to display the results on
the industry, environment and society of implementing
alternative policy options. A parallel effort will be
conducted to critically review and analyze the data
and models available to measure the impacts of alter-
native courses of development, and to analyze the sen-
sitivity of current industry practices to emerging pol-
itical and social changes. A particularly important
part of Teknekron's work involves a thorough review of
the mechanisms of atmospheric transport and transfor-
220
-------
matlon of sulfur oxides and their associated health
impacts on human and other receptors. Currently, this
area is rich with possibilities for modeling the rela-
tionship between regional sulfur oxide emissions and
the adverse effects of aerosol sulfates on public
health, welfare and ecological systems.
During the first year, the boundaries of the ITA are
such that it will:
• Focus primarily on existing coal technologies
and secondarily on other fossil fuel technolo-
gies;
• Focus on the power plant portion of the fuel
cycle;
• In terms of environmental impacts focus on air
pollutants and, more specifically, on long dis-
tance transport and associated chemistry of
atmospheric aerosols; and
o Generally confine air impact analysis to defin-
ing exposure of populations to pollutants with-
out calculating health effects, aesthetic or
economic damages.
A description of the individual models being con-
structed during the first year to simulate the economic
decision making practices of the utility industry and
the resulting exposure of receptors to pollutant re-
leases is contained in the following paper.
3. Ohio River Basin Energy Facility Impact Study:
Congress, in a rider to EPA's FY 76 appropriation bill
has required the Office of Research and Development to
conduct a study of the Lower Ohio River Basin, to "be
comprehensive in scope, investigating the impacts from
air, water and solid residues on trie natural environ-
ment and residents of the region" which might result
from an increasing concentration of power plants in
the Ohio River Basin. The IA program has developed a
plan for this study which casts it in the form of a
regionally-focused ITA (reference 10). The scope is
broadened to consider the accelerated deployment of
both conventional power plants and coal-based syn-
thetic fuel plants in the Basin, (includes portions of
the states of Ohio, Illinois, Indiana, and Kentucky).
The major focus will be on an in depth examination of
the impacts of coal development and conversion pro-
cesses on the region, its people, social infrastructure,
agricultural lands and natural environments. Mech-
anisms to mitigate potential adverse impacts and to
shape future development along environmentally and
socially acceptable lines will be analyzed. Addition-
ally, attention will be paid to extra-regional con-
cerns, e.g., the role of Basin development in meeting
national energy demands, and the issue of how much
impact the long distance transport of sulfur dioxide
and the resulting sulfate aerosols may have on the
urbanized Northeast.
This ITA will be conducted over a two and a half year
period by several teams of academic researchers who
have been selected from Mid-west universities. It wil]
be one of the most ambitious TA'« yet attempted in
terms of the number of separate research groups and
institutions participating.
4. Other Planned Studies:
A regionally-oriented Appalachian ITA will commence in
the fall of this year. It will round out the major
regional ITA's which focus on accelerated coal deve-
lopment and utilization. A fifth ITA, to be oriented
towards a thorough assessment of advanced coal combus-
tion and conversion technologies, will begin in the
early spring of 1977.
ITA studies are also planned to address pollution
control issues for industries, other than primary
energy producing industries. These studies will
emphasize inter-industry interactions and aggregate
effects of pollution from all industries. Initial
methodological studies will begin in the fall of 1976.
5.
Strategic Environmental Assessment System
(SEAS):
Although it is not a TA in any sense, SEAS is an im-
portant enough analysis tool to merit a brief dis-
cussion here. SEAS, originally developed within the
old Washington Environmental Research Center of EPA, is
a system of interdependent models designed to forecast
' the economic, environmental and energy consequences of
alternative Federal environmental policies under vary-
ing assumptions about the future. The core of SEAS is
an input/output model of the United States economy
(INFORUM) which models the interactions between differ-
ent economic sectors.
SEAS is capable of developing estimates to 1985 of:
• Economic projections in terms of physical out-
put for 350 industries and processes;
• Pollution control costs for 500 control tech-
nologies; and
• Projections of environmental residuals and
energy use for each of 350 industries.
A detailed description of SEAS is available in re-
ference 11.
SEAS represents a potentially important tool for tech-
nology assessment and is thus being maintained and de-
veloped further under the IA program. For instance,
SEAS offers the potential to measure the national im-
pacts of new energy development to complement the fo-
cus on in-region impacts of the regional TA's (such as
the Western Energy ITA). This type of measurement is
crucial if Federal decision-makers are to take into
account all of the potential impacts of development
alternatives.
Work currently in progress to modify SEAS includes the
development of additional capability to predict energy
demand in the transportation, residential and com-
mercial, and industrial sectors. For instance, a new
transportation model will forecast activity (vehicle
miles traveled), emissions and energy demand, with
feedbacks to the input/output model to account for
changes in automobile mix and transportation efficiency.
Another important part of current work is the inte-
gration into SEAS of the Brookhaven National Labora-
tory's ESNS energy supply model. Addition of ESNS will
allow the study of new energy sources including coal
gasification and liquefaction, oil shale, off-shore
oil drilling, and geothermal and solar energy. Finally,
consideration is being given to extending the SEAS
economic models to the year 2000, and to improving the
completeness and accuracy of the regional data bases.
Although the TA is the heart of the IA program, other
types of projects are undertaken in support of the
general program objectives. These projects may be
categorized as:
Supplementary Studies- research projects that will
supplement the TA's either by providing results that
will fill research gaps identified by a TA, or by
providing increased coverage of issues associated with
a TA, as these become identified in the course of as-
sessment as being crucial to EPA's fulfilling its re-
sponsibilities. This category also includes integrative
studies that fall short of full TA's on topics of con-
221
-------
cern to the EPA. Frequently, detailed modeling work
will be funded, at it supports the direct needs of an
ongoing TA. Examples of this model development might
include:
• A detailed economic model of a pollution abate-
ment technology for a specified energy conver-
sion process, taking into account variable
characteristics of input fuel types, several
levels of required control, technological
approach, etc.;
• Models which transform pollutant releases into
ambient concentrations, especially for reactive
pollutants on a regional scale; and
• A generalized model for displaying socioecono-
mic impacts on idealized local communities for
particular energy technologies.
Integrated Assessment Methodology - projects that will
develop new methods of conducting TA's and other inte-
grative analyses. These are projects that integrate
and adapt the results of research being conducted by
the Office of Technology Assessment, the National
Science Foundation, other Federal agencies and the
private sector on TA methodology (e.g., cost/benefit/
risk analysis, multivariate decision analysis, etc.)
into a framework which is suitable for EPA's decision-
making processes. Case studies conducted by these
projects will be chosen so as to be supportive of on-
going TA's. This portion of the program includes
maintenance and further development of the Strategic
Environmental Assessment System (SEAS) model.
"Pass-Through Programs"- projects supporting the IA
program that are conducted by other Federal agencies
under EPA funding. Agencies participating in this
portion of the program include USDA, TVA, ERDA, HUD,
and Commerce.
Conclusions
Although the Integrated Assessment program is in its
infancy, the two TA's are well enough along to have
surfaced several important issues for the program.
First, the TA's tend to deal with issues that go well
beyond the traditional interests of the EPA. Thus,
coordination with interested Federal agencies and
other entities is vital not only for information ex-
change purposes but also to prevent questions of the
"propriety" of the research from hindering its pro-
gress. Second, it has become clear that the object-
ive of incorporating social and economic concerns into
the decision-making process is extremely ambitious.
Defining useful but realistic analytical boundaries is
clearly one of the most crucial-if not the most
crucial-problems facing the program. The danger here
is that these boundaries may be set so wide that the
level of analysis will become too shallow to be
credible.
Third, a fundamental limitation to the value of policy
analysis studies such as those just described is the
availability of necessary inputs in the form of tested
research results from the physical, biological and
medical sciences, and from economics, political and the
social sciences. The uncertainties are large in much
of this desired information. We are limited by an
ability to model many of the interactions which cri-
tically affect, or drive, policy decisions. The error
bars on these uncertainties grow progressively wider
as we progress in our examination of the availability
of models and supporting data for pollutant releases
at one end of the analysis structure through the media
transport processes to consider the effect of pollu-
tants upon distributions of receptors at the other end
of the analysis structure.
Fourth, systematic methodologies to evaluate these
several forms of impact within a common base of com-
parison are not available at present. Finally,
modeling the behavior of individuals' perceptions,
social structures and institutions is in an embryonic
stage of development. Yet, it is these factors which,
in the end, determine how we treat the environment,
what economic impacts and costs are to be internalized,
how much economic activity the environment must sustain.
There are challenges here to engage our best efforts
for some time to come.
REFERENCES
1. The Nation's Energy Future, A Report to the
President of the United States. December 1973,
submitted by Dr. Dixy Lee Ray, Chairman, U.S.
Atomic Energy Commission.
2. Report to the Interagency Work Group on Health and
Environmental Effects of Energy Use. November 1974
Prepared for the Office of Management and Budget:
Council on Environmental Quality, Executive Office
of the President.
3. Coates, Joseph F., "Technology Assessments: The
Benefits ... the Costs...The Consequences." The
Futurist; December, 1971.
4. Arnstein, Sherry R., and Alexander N.
Christakis (1975) Perspectives on Technology
Assessment, based on a workshop sponsored by the
Academy for Contemporary Problems and the National
Science Foundation. Columbus, Ohio: Academy for
Contemporary Problems.
5. Coates, Joseph F. (1974) "Technology Assess-
ment," in McGraw-Hill Yearbook of Science and
Technology.
6. Coates, Vary T. (1972) Technology and Public
Policy: The Process of Tbchnology Assessment
in the Federal Government. Washington, D.C.:
Studies in Science and Technology, 2 vols.
7. Jones, Martin V. (1973) A Comparative State-
of-the-Art Review of Selected U.S. Technology
Assessment Studies, Tbe Mitre Corporation,
M73-62.
8. White, Irvin L., et_ al_ (1976) First Year Work Plan
for a Technology Assessment of Western Energy
Resources Development. Washington, D.C.: EPA-
600/5-76-001.
9. First Year Work Plan, An Integrated Technology
Assessment of Electric Utility Energy Systems,
December 15, 1975, Prepared for EPA by Teknekron
under EPA Contract No. 68-01-1921.
10. Work Plan for an Impact Assessment of Energy
Conversion Facilities in the Ohio River Basin,
Phase I, March 30, 1976 draft, Office of Energy
Minerals, and Industry, U.S. Environmental
Protection Agency, Washington, D.C.
11. Strategic Environmental Assessment System (Draft),
U.S. Environmental Protection Agency, December 16,
1975. Can be obtained from Technical Information
Division, Office of Research and Development, EPA
Washington, D.C. 20460.
222
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AN INTEGRATED TECHNOLOGY ASSESSMENT OF ELECTRIC UTILITY ENERGY SYSTEMS
Peter M. Cukor
Sanford Cohen
Glen R. Kendall
Tom L. Johnston
Teknekron, Inc.
2118 Milvia Street
Berkeley, California
Stephen J. Gage
Lowell Smith
Office of Energy, Minerals and Industry
Office of Research and Development
U.S. Environmental Protection Agency
Washington, D.C.
Introduction
Teknekron, Inc., under the sponsorship of the Office of
Energy, Minerals and Industry; U.S. Environmental Protection
Agency, is conducting an Integrated Technology Assessment
(ITA) of Electric Utility Energy Systems. The ITA has two
primary goals. The first goal is to provide EPA with the
capability to assess the environmental, economic, institu-
tional and social effects of the generation of electricity and
those activities which supply the fuels used to produce
electricity. These effects will be quantified for a number of
scenarios. The scenario elements include alternative futures
for utility development, pollution control and siting regula-
tions. The second goal is to assist EPA in developing research
and development programs whose results are necessary in
order to conduct these impact assessments. The time frame
for the assessments is the period 1975-2000.
The ITA is being conducted over a three-year period. The
scope and direction of the first year's effort have been
defined such that the results will be responsive to the key
policy issues which are likely to be faced by EPA over the
next 6-18 months. As a result, the first year's work
emphasizes:
• Fossil fuel electricity generation
• Primary and secondary air pollutants
• Short-range and long-range dispersion of air pollu-
tants
• Human populations exposed to air pollutants
This paper provides a description of the models, data bases
and analytical techniques which are being employed in the
development of the overall ITA model. This model will
simulate the environmental effects associated with elec-
tricity generation and the economic impacts of alternative
policies for pollution control on the utility industry and
electricity consumers. It must be emphasized, however, that
impact prediction is not the only product of the Integrated
Technology Assessment. Rather, impact prediction provides
the quantitative information which serves as input to the
technology assessment exercise in which the feasibility and
impact of alternative environmental policies are appraised.
Thus, this paper focuses on only one part of the conceptual
framework for conducting the ITA.
Modeling Methodology
The basic analytical framework for assessment of alterna-
tives with respect to a single module of an electrical energy
fuel cycle is displayed in Figure I. Although this framework
is appropriate for assessing alternative regulations for pollu-
tion control and siting for any fuel cycle module, quantifica-
tion of results rests upon the assumption that such a module
will actually be constructed and operated (or continued in
operation, if now existing) at a definite level of production.
The electric utility industry can develop in alternative ways
over the coming decades. Future developments will include
alternative fuel cycles, fuel cycle configurations, facility
sites, pollution control technologies, regulatory policies,
demand growth rates, etc. Control levels and siting limita-
tions will affect not only production costs and environmental
impacts, as indicated by Figure I, but will also affect the
decisions made within the utility industry with regard to
employing or not employing these technologies under various
conditions.
It is therefore necessary to integrate the modular analysis
within a more comprehensive framework which allows assess-
ment of the fundamental industry decisions with regard to
utilization of modules. This comprehensive framework is
displayed in Figure 2. The diagram is intended to show the
major technical and economic areas and interrelationships
which must be integrated. It demonstrates the key role, as a
driving force, of policy analysis and scenario development
(represented by the exogenously specified inputs to each
model component). Potential demand for electricity and
costs of alternative methods for meeting this demand under
environmental and other constraints are shown to be the basis
of utility decisions. These decisions determine the course of
industry development and the consequences which may flow
from this course, including effects on human populations and
ecosystems as well as socioeconomic effects.
Figure 2 has been constructed in two sections. The section
above the dotted line shows the configuration of components
and information flows for simulation of the development and
operation of an electric utility system. By proper definition
of the system, it is possible (with some important limitations)
to conduct simulations on a regional, multiregional or
national basis. Inspection of the components in the upper
part of Figure 2 reveals that only economic, technical and
environmental policy decisions are involved. The simulation
of physical, chemical and biological phenomena, which must
be addressed on a site-specific basis, is described by the
configuration of components below the dotted line. This
method of display has been selected in order to demonstrate
clearly how economics and policy affect decisions concerning
the type, quantity and location of power production facilities
and the manner in which they are operated. A realistic
assessment of how future developments in the electric utility
industry will affect environmental quality must include an
estimate of industry response to alternative policies as well
as simulation of the production, dispersion, transformation
and effects of environmental pollutants.
The lower portion of Figure 2 shows the configuration of
components and information flows for simulation of the
release, transport and transformation of air pollutants and
determination of populations exposed. The modeling effort
must be carried out on a site-specific basis. Thus, the
information developed by the system simulation in the upper
223
-------
INPUT
Facility & Control Selections
Selected fuel-cycle
module with
alternative levels
of control
RESIDUALS
&
COSTS
rri Production costs (including
"^ distribution & control )
0 Residuals by pollutant
for each control level
Site Selections
Distance to consumers
Dispersion parameters
Potential receptors
IB—
TRANSPORT
—-rj
Ambient concentrations
(by pollutant)
for each selected
control level
»EJ
Exposures of receptors
to ambient concentrations
Value assignments
for selected damages
GQ — •
DAMAGES
Q) Monetized damages
|T| Non-monetized damages
i b
LJUIUJ — •
TRADE OFF-
ANALYSIS
Ranking of Site/Control
alternatives
Ranking of Implemen-
tation alternatives
Possible re-ordering of
Site/Control alternatives
Figure 1. Elements in Scenario Specification
ADDITION ANO
CAPITAL REQUIREMENTS
SOCIO/PDLITICAL
CONSTRAINTS SITES
JL
POLICY
_i_
CHARACTERISTICS W
UI STING CAfACITT
AS OF JANUADT l.tlM
unr
flf
SfAiDN
-££,—
DLHUtO
DCr
B
SEA
KHhr OCMAW1
PUUWIMG
hr
Y
VON
6 AND M COSTS
ACTUAL CAPACITY
AMI TICKS AND
COXVMtSIONS
K
FUEL COST PER mur L^
- 1
EXPiKSE AW
DISPATCHING
COSIi
FUEL CONSUMPTIOH
(Ogtput)
, 4
HtGOLATWr
COSTS. PRICES
AhO RCVtMJLS
OF CAPACITY
CONTROL ADDITIONS AM) GENERATION HUT RAW* niNUf [HKV
TECIMLOGT RETROFITTED UNITS Mil AM* FUEL TIKI WKT
CHARACTERISTICS OF
EXISTING CAPACITY
COST Of CLIAM FlKtS L^ L^
r r
C L
CAPITAL REQU1REHEHTS
FM CAPACITY ADDITIONS.
CONVERSIONS. ETC.
CANCELLAT lOHS/OEFCRRALS
FIH.UICIAL
r
CAPITAL REOUIRUCKTS IHVENTMf Of
TOR CONTROLS 6UCRATIW UNITS
CAPITAL
REQUIREHENTS
(Output)
INCOME
STATEMENTS
(Outputs)
G{NEA*II*G iMIT
ChAfcACIUlSIICS
(fix- GeneriLfM Mil)
3 !y Module)
l CAPACITY
| AIR POLLUTANT ^ if
RESIDUALS
AND
UATCR
CONUM-TION
r-,
DISPERSION
PQLLUTAKT
ISOPlETHS
tf
evosuftc
umuus
^ GENERATING UNIT
RESIDUAL LOADINGS CHARACTERISTICS
TO AIR AKD UNO (fro* Gcntrttloa
MU Hodyli)
Figure 2. Module Diagram and Information Flows
in the ITA Model
224,
-------
portion of Figure 2 must be disaggregated so as to drive the
site-specific models shown in the lower portion of the figure.
Scenario Development
The exogenously specified inputs to the components displayed
in Figure 2 are elements of the various scenarios which are
being addressed in the ITA.
By the term "scenario" we mean a specification of future
events or conditions which is sufficiently complete to allow
an evaluation of principal costs to the industry and consum-
ers, effects on air quality, cost effectiveness of pollution
control alternatives, and resource consumption that will
occur if these events or conditions do, in fact, come about.
Our focus is on the pollutants released and resulting human
exposures. Releases depend on a number of diverse factors
which may be grouped under the headings of economics,
technology and policy.
For example, the chemical species and quantities of pollu-
tants released depend on the fuels used, the design of
generating units and the total amount of electricity produced.
These, in turn, are dependent upon general economic condi-
tions and the market prices for the fuels which compete for
usage by utilities. Given production levels, generating unit
characteristics and the properties of fuels, pollutant releases
depend upon the technology employed for electricity produc-
tion and the effectiveness of any control technology em-
ployed. Environmental policies such as mandated emission
limits affect pollutants released from any one source. Energy
policy affects production insofar as the price and availability
of fuels are concerned. More direct effects on production
may results from efforts toward conservation, electrification
or load management.
Exposures also depend on when and where pollutants are
released and on demographic patterns. Timing of releases
depends on the temporal pattern of demand which may be
affected by policies of demand management. Siting of
sources is affected by economic, technological and policy
constraints. Siting flexibility depends on the existence of
cost-effective technology for long distance transmission.
Environmental controls may take the form of siting restric-
tions.
Table I presents, in outline form, the principal elements to be
considered in specifying a scenario. Elements to be consid-
ered are grouped under the four headings of Economics,
Technology, Siting and Policy. Complete specification of a
scenario requires hypothesizing specific occurrences under
each of the headings.
For the first year's effort, an initial list of 25 scenarios has
been prepared by postulating specific occurrences for the
scenario elements identified in Table I. This list will be
subject to further refinement as the modeling effort pro-
ceeds.
Figure 3 exhibits the 25 selected scenarios in event tree
format. In selecting these scenarios, the first criterion was
the elimination of the less probable combination of elements
and the second was selection of those most clearly focused on
the environmental problems associated with usage of coal. In
the second and third years, greater emphasis will be placed on
other scenarios.
The 25 scenarios displayed in the figure have been grouped in
five sets for convenience in discussion. The lettered
elements correspond to the list provided in Table I. The
rationale for each group is as follows:
Group A. This group provides a basis for comparison of
.policies on a more or less "business as usual" basis. A high
economic growth rate with responsiveness to utility needs in
price setting is postulated with no major effective programs
for conservation. These conditions have been typical of the
last two decades, although not representative of the very
recent past. A high degree of dependence on either nuclear
power or coal for baseload additions is postulated with
conversion of gas fired power plants to oil. The policy
options of baseline and relaxed controls (P. and P^) and
maximum controls (P^) with one intermediate level (P.,)
provide a range with which to evaluate possible costs and
benefits of alternate levels of control. These policy options
are combined with two siting alternatives in order to reflect
differences in the populations subjected to, or protected
from, exposure to pollutants.
Group B. This group provides a contrast to Group A in
terms of showing how air pollution may be reduced from the
Group A baseline by factors other than control policies. A
slow economy is predicted with emphasis on conservation
together with a high degree of dependence of nuclear power.
Group C. This group provides a contrast to Group A
with respect to costs. A slow economy, emphasis on
conservation and nonresponsive regulatory policies are pre-
dicted. Extensive dependence on coal is assumed. Control
options are imposed under these conditions of financial
adversity for utilities.
Group D. Group D includes an electrification policy so
that growth in electricity usage is greater than in Group A.
This growth could result from the occurrence of several
events such as deployment of electric automobiles, increased
use of electric space conditioning and extensive curtailment
of natural gas supplies. Extensive dependence on either
nuclear or coal for baseload additions is investigated under
conditions of natural gas curtailment (which would contribute
to the need for electrification). The more stringent control
policy, P^, is used together with the baseline control level,
rather than Po, as being more consistent with the increase in
pollutant releases that would be a result of the thrust toward
electrification.
Group E. Group E provides a contrast to Group D by
isolating the impact of the movement toward electrification.
It posits continued effective emphasis on conservation with
other elements the same as for Group D.
This listing of scenarios is subject to change throughout the
ITA. Individual scenarios may be dropped and others added.
The basic framework is expected to remain unchanged. Of
course, all the elements require extensive analysis to develop
the quantitative specifications.
Description Of Components In The Simulation Framework
Specification of scenario elements provides the driving force
for the individual components in the simulation framework
displayed in Figure 2. The role of each component and the
inputs to and outputs from each component are described
below.
Electricity Demand
Demand for electricity in future years is the fundamental
determinant of utility growth. Demand is thus a determinant
of all economic and social costs and benefits actually
accruing under any control policy. Forecasts used in the ITA
are being . carefully evaluated. Forecasting alternatives
include extrapolation of past trends (including factoring
judgments of expert individuals or bodies), econometric
predictions and technology forecasts.
The Demand Component specifies electricity demand by
season for each year and region of interest. Demand by
season is specified using a typical daily load shape curve for
each season and region of interest.
225
-------
Table 1. Elements in Scenario Specification
Economics
Group I: High growth rate,
favorable conditions for
utility financing and:
e-| No significant
effect on pattern
or level of demand
through policy
initiatives.
&2 Continuing and ef-
fective conserva-
tion efforts aimed
at both pattern and
level of demand.
e3 Effective measures
toward increased
electrification.
Group II: Low economic
growth rate with emphasis
on conservation and:
e^ A regulatory policy
responsive to needs
to attract invest-
ment to the industry.
eg A regulatory policy
of restrained and
delayed price in-
creases which
translates into a
curtailment of
earnings.
Technology
t-| Extensive depend-
ence on nuclear
power for base-
load additions.
Natural gas plants
convert to oil .
t£ Extensive depend-
ence on coal for
baseload additions.
Natural gas plants
convert to oil .
Siting
s-| No change in the
current balance of
considerations re-
garding remote
versus near load
center siting.
$2 An increase in re-
mote siting due to
technical break-
throughs or policy
decisions.
Policy
Pi Baseline controls;
air quality stan-
dards are attained
by limiting emis-
sions.
P2 Relaxed controls;
air qual ity stan-
dards are attained
utilizing tall
stacks and inter-
mittent constrols.
P3 More stringent con-
trols on precursors
of sul fates.
p^ More stringent con-
trols on all air
pollutants.
Figure 3. Scenarios for First Year ITA
226
-------
Inputs—Growth rates in energy demand for each region,
"regional" average load factor and load shape curves for each
season.
Outputs—Energy and peak demand by region and season
(to Planning, Production Expense, Dispatching and Regulatory
Components).
Future capacity additions and conversions are being deter-
mined in accordance with announced plans of electric utilities
and modified to reflect different postulated growth rates,
capital requirements, and siting and sociopolitical con-
straints. Control policies as well as economic rationale are
being considered both with regard to environmental protec-
tion and programs aimed at national energy self-sufficiency.
Inputs
• Demand (from Demand Component).
• Conversions, i.e., from oil to coal, from gas to
coal, etc.; Planned Capacity Additions; Capital
Costs; Socio/Political Constraints; Generating
Unit Sites (exogenous inputs).
Outputs to Control Technology and Generation Mix
Components:
• Planned conversions (oil to coal, gas to oil).
• New units by type brought on-line in a given year.
Outputs to Financial and Regulatory Components:
• Capital requirements for construction of units and
control devices.
• Cancellation, deferral or acceleration of units
scheduled to come on-line in future years.
Control technology
Alternative methods for air pollution control are being
specified in terms of costs and capabilities. Modeling
reflects both the consequences of pollutant shifts from one
medium to another and the possibility for creation of new
pollutants as a by-product of control.
The Control Technology Component specifies costs, effi-
ciency and impact on plant operation of pollution control
alternatives for SO?
thermal effluents.
NO , particulates, and chemical and
Inputs
Capacity additions and conversions (from Planning
Component).
Characteristics of existing capacity (from Gen-
eration Mix Component).
Degree of control required (exogenous input).
Cost of clean fuels (from Primary Energy Supply
Component).
• Costs for meeting a given emission or effluent
standard (to Financial Component).
• Characteristics of capacity additions and retro-
fitted units (to Generation Mix Component).
• Degree of pollution control (to Residuals Com-
ponent).
Generation Mix
Most recently available characteristics of existing capacity
are being specified on the basis of Federal Power Commission
data as updated by information from utilities. Component
input includes the characteristics of planned capacity addi-
tions and modifications to existing capacity to reflect fuel
conversions and retrofits for pollution controls. The Genera-
tion Mix Component is essentially a file which contains the
characteristics of generating units for any particular year of
interest to the 1TA.
The Generation Mix Component specifies the capacity profile
as of 1974. It is updated during the simulation to show the
"state of the system" for each year of interest in the future.
Inputs—characterization of existing capacity as of
January I, 1974 (data available from FPC) according to:
Size
Age
Type and composition of fuel(s)
Heat rate
Type of air pollution controls
Type of cooling
Stack height
Location
Ownership
Status of Section 3l6(a) application
Capacity factor
0 & M expense
Source of fuel
puts—data available from other sources:
Characteristics of additions to generating capac-
ity according to size, fuel type and composition,
type of pollution control, etc. (from Planning
Component).
Retirements and re-rates (from Planning Compo-
nent).
• Inventory of generating units (output).
• Generating unit characteristics (to Residuals
Component and Control Technology Component).
• Heat rates and fuel types for each class of facility
(to Primary Energy Supply Component).
• O & M costs (to Production Expense and Dispatch-
ing Component).
Primary Energy Supply
The chemical and physical characteristics and delivered costs
of primary fuels are being specified according to source of
supply. This facilitates the identification and assessment of
environmental and socioeconomic impacts associated with
fuel extraction and processing to be conducted in years two
and three of the ITA.
The Primary Energy Supply Component specifies the cost of
available fuels for each generating unit.
Heat rates and fuel types for each facility (from
Generation Mix Component).
• Fuel cost per kilowatt hour generated for each
facility (to Production Expense and Dispatching
Component).
• Cost of clean fuels (to Control Technology Com-
ponent).
Production Expense and Dispatching
Generating units are not operated in isolation; they function
as part of an integrated system in which production is
227
-------
allocated to units to meet demand which varies by time of
day and by season. Introduction of pollution controls which
affect efficiency will cause shifts of load among units. In
coming years, there may be attempts to change load curve
shapes through special pricing regulations. Changes in
allocation of load (e.g., between peaking and base load units)
may radically change pollutant characteristics. Seasonal
production patterns, of course, fundamentally affect the
release of pollutants and, consequently, exposures. The
dispatching of load plus the operating characteristics of a
generating unit determine the expense incurred by the utility
and, thus, the costs borne by the consumer. The ITA utilizes
a simple dispatching model to determine capacity factors and
production expenses.
The Production Expense and Dispatching Component calcu-
lates generating costs for each class of unit and specifies
capacity factors such that the demand is met at least cost.
investor owned utilities require that simulation of the
financial impacts of future environmental policies treat the
two types of firms separately.
The Financial Component calculates financial flows and
updates balance sheets and income statements each year.
Initial balance sheet (exogenous input).
Profit and loss items (exogenous input).
Rate schedules (from Regulatory Component).
Production costs and revenues (from Regulatory
Component).
Capital requirements (from Planning Component)
for new capacity, transmission, distribution and
plant conversions.
Capital requirements for pollution control equip-
ment (from Control Technology Component).
Fuel cost for each class of unit (from Primary
Energy Supply Component).
0 & M costs for each class of unit (from
Generation Mix Component).
Demand by season (from Demand Component).
• Fuel consumption for each class of unit (output).
• Capacity factors for each class of unit (to Re-
siduals Component).
• Production expenses (to Regulatory Component).
Regulatory
The effects of regulatory policies on the financial and
operating characteristics of utilities are being considered.
This includes consideration of alternative pricing schemes and
regulatory lag. The methods of treating production cost pass-
through and financing of construction work-in-progress will
affect the rate of utility response to needs for pollution
controls, capacity additions and fuel conversions.
The Regulatory Component specifies electricity rates consis-
tent with recovery of production costs and a return on rate
base.
• Production expenses (from Production Expense
and Dispatching Component).
• Demand for electricity (from Demand Compo-
nent).
• Regulatory environment (exogenous input).
• Rate base and financial needs (from Financial
Component).
• Updated balance sheets and income statements
for each year (output).
• Aggregate capital requirements (output).
Residuals And Water Consumption
Existing data bases for the residual releases from power plant
operation are being refined and assigned to existing and new
facilities. Generating unit characteristics and fuel properties
are being considered in order to define residual release rates
as functions of these independent variables. The residuals
model not only considers the removal efficiencies of control
equipment, but also reflects increased residual releases due
to reduction in plant efficiency resulting from control
technology application. The first year's effort focuses on air
pollutants, especially SC^, NOX, and primary particulates.
Other residuals considered will include trace elements and
waste heat. Cross-media effects are also considered.
Since calculation of evaporative water consumption requires
some of the same inputs as residuals generation, it is included
in this component.
Unit capacity factors (from Production Expense
and Dispatching Component).
Properties of the fuels (from Primary Energy
Supply Component).
Characteristics of the generating unit (from Gen-
eration Mix Component).
Characteristics of control devices (from Genera-
tion Mix Component).
• Electricity rates (output).
• Production costs, prices and revenues (to Finan-
cial Component).
Financial
Costs of both new facilities and of pollution control equip-
ment are being evaluated in the context of utility financing.
Needs for capital, ability to finance capital expansion,
earnings and the ability to recover capital and operating costs
in revenues are basic considerations in industry decisions with
regard to development. The impact of control policies is
being measured in terms of effects on needs for capital,
earnings, prices and return on investment. The fundamentally
different financial structures of investor owned and non-
• Air pollutant release rates from each generating
unit (to Dispersion Component and output).
• Water consumption rate for condenser cooling
(output).
• Solid waste generation rates (output).
• Waste heat discharged (output).
Dispersion
Pollutants are being traced from release at the power plant
to eventual impact on sensitive receptors. Chemical trans-
formations and interaction with other materials in the
environment will be included in the assessment. The first
year's study considers the dispersion of air pollutants only. In
view of the results of very recent research, a major emphasis
must be placed on transport of pollutants on an inter-regional
scale (i.e., 100 to 1000 miles from the source).
228
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The Dispersion Component calculates changes in local air
quality due to releases of pollutants calculated in the
Residuals Component. Separate models are provided for
short range and long range atmospheric transport.
Inputs
Release rates for each air pollutant (from Resid-
uals Component).
Stack parameters for each generating unit (from
Generation Mix Component).
Location of each generating unit (from Generation
Mix Component).
Local meteorological parameters (exogenous in-
put).
Outputs
Ambient concentrations of air pollutants at dis-
tances less than 50 km from the generating unit.
Concentrations are specified according to location
parameters, e.g., census tract, zip code, county
(to Exposure Component and output).
Contributions to sulfate concentrations in se-
lected impact areas greater than 100 miles down-
wind from the generating units (to Exposure
Component and output).
Exposure
Populations at risk to air pollutants for specific geographical
regions are being identified such that projected patterns of
demographic growth correspond to growth in regional demand
for electricity. The demographic modeling reflects changes
in national fertility rates as well as secular economic trends.
Since populations at risk are defined in terms of the spatial
relationship between sources and receptors and the conditions
of pollutant transport, the interaction of siting, residuals and
air dispersion models is crucial to exposure model develop-
ment.
The Exposure Component calculates populations exposed to
increments in ambient pollutant concentrations.
Inputs
Pollutant isopleths (from Dispersion Component)
according to locationol parameter (census tract,
zip code, etc.).
Outputs
Populations exposed to specified levels of pollu-
tant concentrations.
229
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ENVIRONMENT IMPACT MODELLING FOR PROJECT INDEPENDENCE
R. A. Livingston
Office of Planning and Evaluation
U. S. Environmental Protection Agency
Washington, D.C.
R. W. Menchen
Hittman Associates, Inc.
Columbia, Maryland
G. R. Kendall
Teknekron, Inc.
Berkeley, California
H. P. Santiago
Office of Planning and Analysis
Federal Energy Administration
Washington, D.C.
I. SUMMARY
An application of the environmental residuals tech-
nique for evaluating the environmental implication of
energy policy studies is described. This paper covers
the adaptation of the techniques to the particular
needs of the Project Independence Evaluation Systems,
some typical results of the analysis, and its limita-
tions. Several different methods of scenario and
residual comparison are investigated. The conclusions
are that the residuals approach can be a useful tool
in comparing alternative scenarios, but a tradeoff
must be made between degree of detail and compre-
hension of results. Areas for further work include
extension of residuals to cover more items of interest,
introduction of time dependency, and development of
aggregate measures for comparison.
II. BACKGROUND
This project arose from Environmental Protection
Agency's participation in the Project Independence
interagency effort initiated in March of 1974 to
evaluate national energy problems and provide a
framework for developing a national energy policy.
The effort assembled a comprehensive energy data base,
developed a methodology for analyzing future energy
supply and demand alternatives, and investigated the
impacts and implications of major energy strategies.
The results of the initial study were presented to the
President in December 1974. Subsequent studies uti-
lizing the Project Independence Evaluation System
(PIES) were published in connection with the Draft
Environmental Impact Statement for the Energy Inde-
pendence Act, March 1975,2 and the current version of
the Project Independence Report.
EPA was given the responsibility of assessing the
environmental impacts of the energy scenarios pro-
duced by PIES. The assessment had to be performed
rapidly, repetitively and in a consistent fashion.
The assessment of the scenario had to be done using
quantitative techniques as much as possible.
III. CONSTRAINTS ON ANALYSIS
A. PIES Model and Scenario Constraints
The Project Independence Evaluation System (PIES) is
a set of computer models of the technologies, demand
and the markets through which energy commodities are
extracted, transported, transformed and consumed.
Regional production, processing and conversion activ-
ities are represented within the energy network as
nodes, with links depicting transportation and dis-
tribution possibilities. The PIES model simulates a
market system which takes into account prices,
resource requirements and capacity constraints, and
constricts a set of energy flows that satisfies the
final demands for energy. It is a least cost linear
program. PIES models energy supply side and adjusts
prices (thus demands) until the system achieves an
equilibrium balance at which no consuming sector
would be willing to pay more for an additional unit
of any energy product, and no supplies would provide
an additional unit of any energy product for less
than the prevailing prices.^
An individual energy scenario is developed on the PIES
model by inputting a set of supply and demand data
representing particular energy policies or conditions,
including the world price of oil. The system then
computes a least cost solution and provides the out-
put in terms of quantities produced and consumed,
with associated prices. The solution applies only to
one point in time and for one world price of oil.
The PIES system is not a dynamic model.
B. glES Output Constraints
The PIES output becomes the data base for the environ-
mental assessment. However, it was designed to suit
the objectives and data availability of t^ie energy
analysis, and these did not necessarily correspond to
the needs of the environmental analysis. The infor-
mation content and structure of the PIES output thus
constrained the scope of the subsequent environmental
information.
On the supply side, the PIES output gave production
statistics on an individual region basis for coal,
oil, natural gas, and U235 extraction. However, the
regions for each energy source were based upon
traditional boundaries, as defined by the relevant
source of statistics. For example, coal was organi-
zed by the Bureau of Mines coal provinces, petroleum
and natural gas by NPC petroleum provinces and so on.
Similarly, oil refining was broken down by Petroleum
Administration Districts (PAD) and electricity by
Electric Reliability Council regions. Generally,
the regional boundaries of one activity did not
coincide with that of another, which prevented a
direct comparison of energy scenarios on a geo-
graphical basis.
Second, the PIES output specified only the total
quantity of activity for a particular region, without
specifying the size of the facilities or their geo-
graphic location within the region. For example, oil
refining activity was described as total barrels of
throughput in a PAD. This production could be dis-
tributed in any number of locations from Delaware
to Florida, and in any size facility from 10,000 to
greater than 250,000 barrels per day.
Finally, source factors significant from an environ-
mental viewpoint, such as sulphur content of coal,
were not given in the output.
C. Environmental Data Constraints
In addition to the limitations imposed on the envi-
ronmental analysis by the PIES output, the analysis
was further constrained by the availability of
quantitative environmental data, and methodological
230
-------
problems of environmental analysis. Warner and
Preston in their 1974 review of environmental impact
assessment methodologies, identified 17 different
approaches to environmental impact assessment and
concluded that there was "no universally applicable
procedures for conducting an adequate analysis."5
Similarly, a number of studies have attempted to
compile the environmental data related to energy on a
systematic basis. >'>°>9 They differed among each
other in sources of data, assumptions, pollutants
covered and method of aggregation. 10 For the purposes
of the Project Independence analysis, it was decided
to use the data base prepared by Hittman Associates
for the Council on Environmental Quality. It was felt
that this provided the most thorough, flexible and
widely utilized set of data available at the time.
However, in making this choice, the environmental
analysis was then limited to the set of pollutants
as specified in the CEQ study. This covered seven
water pollutants, and six air pollutants, as well as
land use, solid waste, and occupational health.
D. Constraints of Project Independence Organization
The scope of the environmental analysis was also
limited to a certain extent by the role of EPA's task
force within the overall structure of Project Indepai-
dence. In total there were 21 interagency task forces
set up to address various aspects of energy supply
and demand. In particular, questions related to water
use and availability were assigned to the Water
Resources Council and some socio-economic matters
were assigned to a Manpower Task Force headed by the
Labor Department. H
The other aspect of the Project Independence organi-
zation that limited the scope of the environmental
analysis was the schedule, which originally allotted
two months for the entire process of development and
analysis of energy scenarios. This ruled out the
development of any major new environmental techniques,
and required that the environmental analysis involved
be capable of being done in a short time.
IV. OBJECTIVE OF ENVIRONMENTAL ANALYSIS
Given the constraints outlined above, several objec-
tives were chosen as a basis for designing a
methodology for doing the environmental evaluation.
These were:
A. Emphasis on Interscenario Comparison
The primary purpose of the environmental evaluation
was to enable energy policy makers to appreciate the
relative environmental ranking of different strategies
to solve energy problems. However, this does not
require that absolute environmental quality be pre-
dicted for a given scenario.
B. Level of Analytical Detail Consistent with PIES
Output
The PIES Model operated on an aggregated regional
basis, and looked at macroeconomic questions. The
general lack of site specific information for energy
production or consumption ruled out dispersion
modelling or health effects calculation for measuring
environmental impact. To do so would have produced
spurious accuracy, not supported by the quality of
information available.
C. No Environmental Constraints in PIES Model
A theoretically rigorous energy model should take
into account the effect of environmental regulations
and limitations on energy supply and consumption.
However, this was not an objective for the Project
Independence evaluation for two reasons. The first
was the problem described of accurately' calculating
environmental quality with the data available.
The second was the economic basis of the PIES model.
Entering environmental variables into the model's
calculation would have required coverting environ-
mental impacts into external social costs. While
theoretical models exist for calculating external
costs, a satisfactory practical method was not
available.
D. No Preemption of Environmental Impact Statement
The environmental analysis performed in this project
was not intended to satisfy the requirements of the
EIS. This was partly because the Project Indepen-
dence effort was a policy study, not involving
specific physical activities which could be identi-
fied as requiring an EIS. Another reason was to
avoid the possibility that by doing an EIS for
Project Independence as a whole, individual projects
could be relieved of the responsibility of having to
do specific EIS.
E. Rapid Response
Since the environmental evaluation came at the end of
the process of generating energy scenarios, it would
inevitably have a very short timeframe for analysis
before the final report would be written. Therefore,
it became essential to be able to do the evaluation
on short notice, in a rapid fashion.
V. ANALYTICAL APPROACH
Given the constraints and objectives outlined above,
the environmental evaluation evolved into a compari-
son of energy scenarios using discrete residuals
on a consistent regional basis.
A. Residuals
The term "residuals" means any measurable quantity
which is associated with a given activity, and which
results in environmental impacts. Air pollutants
and water pollutants are included in this definition,
as well as things such as land use, solid waste,
water use, and manpower, which are not usually con-
sidered pollutants. Unquantifiable items like
esthetics are not considered to be residuals.
It should also be noted that residuals are the pre-
cursors of environmental impacts and not the impacts
themselves. For instance, the S02 emitted by a power
plant is a residual, but the health effects caused by
that S02 are an environmental impact. The number of
acres of land disrupted by strip mining is a residual,
but the loss of the ecosystem on that land is an
environmental impact, and so on. Thus, the defini-
tion of residuals avoids the problems and uncertain-
ties of calculating transport of pollutants and
their effects.
Finally, by eliminating any reference to local
environmental conditions, such as terrain, meteorot-
ogy , population, etc. it becomes possible to con-
ceptualize and compare representative energy activi-
ties rather than being forced to speak in terms of
a particular coal mine or a particular power plant.
This aspect is important when analyzing future energy
choices, when the exact location of an activity is
unknown, thus making it impossible to calculate the
changes in ambient environmental conditions such as
air quality or water quality. However, it is
possible to compare the residuals associated with
the alternatives since these are independent of
231
-------
location.
B. Regional Allocation System
Thus, the advantages of residuals are that they deal
in measurable, predictable quantities, in an objec-
tive way. Subjective elements, such as the
ultimate environmental impact, or the relative
weighting of different pollutants, are not con-
sidered. However, if one wishes to proceed to this
kind of analysis, it is still necessary to know the
residuals as the first step.
Furthermore, this makes it possible to trace back
through all the steps involved in producing and trans-
porting, converting, and consuming energy. Thus
residuals analysis can account for all the associated
pollution that may not occur at the power plant
or other energy facility, itself, but that must also
be charged to the production and consumption of a
unit of energy.
In practice, the residuals technique involves a
matrix of coefficients. One dimension of the matrix
is energy activities, the other the residuals of
interest. Each element in the matrix thus relates
the production of a given residual to the throughput
of energy involved in a specific activity. Separate
matrices are developed for each major energy type.
A sample coefficient matrix for coal is presented
in Figure 1. It is necessary to define a vector,
E^, composed of a set of variables e -^j which
describes a quantity of energy in a specific series
of steps, or trajectory, from mining or extraction,
to end use. The subscripts thus describe the
jth step, eg. mining, in the ith energy source eg.
coal. Then by multiplication, the total set of
residuals, rik associated with this trajectory can
be calculated:
(1)
ik
"ij
"ijk
However, since more than one energy trajectory is
usually involved, each with its characteristic
residuals matrix, the total residuals for an energy
scenario are:
(2)
rilc
However, equation (2) should be modified in the case
of Project Independence analysis to take into account
the regional nature of the energy reserves. Thus
for region 1, the residuals are:
(3)
rkl
"ijkl
Since each type of energy production specified in the
PIES output had its own set of regions, it was also
necessary to introduce an allocation factor a
such that:
Iql
(4)
J
mijiq
Thus in order to arrive at a quantitative measure
of the residuals associated with a given energy a set
of regionalized , energy specific residual matrices
had to be generated as well as a set of allocation
factors to convert from energy regions into a con-
sistent set of regions for residuals analysis. The
residuals matrices were developed under contract by
Hittman Associates, Inc., utilizing residuals
matrices developed under a previous contract for
CEQ13, and modified to suit the specification of
PIES. This effort is described in a separate
paper.
From equation (4) it can be seen that the set of uni-
form regions into which the various energy regions are
allocated, must be a common subset of each energy
region. These uniform regions must also make sense
from an environmental standpoint. This task was
assigned to another contractor ERGO (Energy Resources
Co.).
The basic question to be decided was which type of
region should be used. Air Quality Control Regions
(AQCR) were not used originally because their
boundaries were drawn along political subdivisions
rather than topographically separate regions, and
because in some cases, they covered too broad an area.
Instead it was decided to use river basins, as defined
by the National Oceanographic and Atmospheric Adminis-
tration. These basins represented national regions
for water quality analysis, and their physical
boundaries also provided a. fairly good basis for air
sheds.
The development of the river basins model and the
allocation procedure is described in more detail in a
separate paper.15 Subsequently, a subroutine was
added to the model which provides the ability to
allocate the residuals to AQCRs.
C. Other Considerations of Residuals Analysis
1. Energy End Use—In the initial Project Independence
effort, the environmental evaluation associated with
the end use of energy was not considered, although
impacts associated with electrical generation were
included. End uses were not considered primarily
because the Project Independence effort concentrated
on supply options to meet a given level of demand.
Thus the level of demand was essentially not within
the control of policy measures under consideration.
The environmental evaluation was intended to bring
home the effect of conscious decisions on the part of
policy makers. Secondly, the amount of effort
required to produce end use residuals matrices and
allocation models was not available in this phase of
the project. However, in subsequent efforts, the
end use environmental evaluation was implemented and
used.
2. Nuclear Energy—A set of residual coefficients were
derived to describe the non-radiological aspects of
nuclear energy, primarily U-235 extraction and opera-
tional releases of radioactivity from power plants.
No overall analysis of radioactivity was made. This
was because of the difficulties of comparing the
production and decay over time of radioactivity with
other residuals. Also, the level of nuclear power
usage was relatively constant among energy scenarios,
and thus would have little effect on their relative
ranking.
3. Environmental Control Standards—It was assumed
that all environmental control regulations and
standards promulgated up to the time of the Project
Independence study could be in full effect in 1985,
the point of time chosen for the analysis. This had
the effect of reducing some water pollutants to zero,
and minimized land use impacts from strip mining.
4. Socio-Economic Factors—No evaluation of the usual
socio-economic factors was made, nor were analysis of
environmental impacts of secondary development con-
sidered. This was done both because it was not
within the scope of the environmental task force's
responsibility and because it involved data which was
not readily available.
232
-------
D. Scenario Comparison
Once the residuals had been calculated and compiled
on a consistent regional basis, it was necessary to
find a technique to compare scenarios. A number of
different techniques were considered.
1. Single Index— The use of a measure which would
aggregate all the individual residuals into a. single
index was considered and rejected. Although it
would have provided a simple means of ranking the
scenarios, it would have involved the use of weighting
factors to be applied to the residuals. The state
of the art has not advanced to the point where
objective weighting factors are available, and
judgemental ones would have introduced a subjective
factor into the analysis. Moreover, it was felt that
as much information as possible should be presented
concerning the environmental impacts, and thus it was
better to display the entire list of residuals,
rather than a single number.
2. Overlays—An attempt was made to display the
residuals as overlays on a national map. However, it
proved impossible to present more than two pollutants
at a time, or, alternatively, to compare more than
two scenarios at a time (Figure 2). Moreover, the
river basins introduced too much detail.
3. Tabular Presentation—The most successful approach
on a regional basis was in the form of tables of
residuals. In order to make the data manageable,
the data from the river basins were aggregated into
14 major regions, corresponding to the demand
regions used by FEA. An example of this format is
presented in Figure 3. Here the method of comparison
is simly to match the products to a particular
residual from one scenario to another.
4. Graphical—The regional tabular method is the most
straightforward. However, it tends to take up a lot
of space and major trends are difficult to extract
from the details. Consequently, in its publication
on Project Independence, FEA resorted to presenting
the residuals on a national basis in the form of
bar charts. This is illustrated in Figure 4.
While definitely simplifying the presentation and
making it more comprehensible, this has the effect
of discarding the information on regional impacts,
which is one of the major objectives of the PIES
approach.
5. Differential Comparison—As a way of overcoming
some of the difficulties of the regional tabular
approach, a matrix was prepared showing the
differentials in residuals between two selected
scenarios, one dimension are the individual residuals
The matrix is presented in Figure 5. While it does
provide a concise detailed comparison, its dis-
advantage is that it cannot be simply extended to
comparison of three or more alternatives.
VI. RESULTS
It is not the intent of this paper to cover in a
comprehensive fashion the results of the various
scenario analyses, these can be found in the reports
published by FEA,I6 and ERGO17'18 and Hittman.
However, there were some findings that kept
recurring.
One is that on a national basis energy related
pollutant loadings will either decline or remain
constant between 1972 and 1985. This indicates the
effect of meeting pollution control standards, and
emphasizes the importance of accurate assumptions
concerning the efficiency and degree of use of
controls.
A second find, on a national basis, is that residual
loadings variations among scenarios in 1985, tends to
be less than the 'change between 1972 and 1985. From a
national policy viewpoint, this suggests that the most
useful effort should be on making sure that environ-
mental standards are met, rather than attempting fine
tune energy supplies to determine the most environ-
mentally acceptable scenario.
Third, for some residuals, such as particulates, the
loadings associated with different supply scenarios,
are small in comparison with the quantities from end
use activities. This suggests that more thought
should be given to controlling end use emissions, and
to energy conservation.
Fourth, some scenarios involving accelerated develop-
ment had the effect of reducing some residuals over
the business-as-usual scenarios in 1985. This
apparently results from the more rapid retirement
of older facilities with less stringent pollution con-
trols, as well as switching away from coal to oil.
Finally, individual regions may show widely
different environmental impacts within a given
scenario and between scenarios. This indicates that
comparing residuals solely on a national basis is not
sufficient for evaluating environmental impacts.
VII. CONCLUSIONS AND RECOMMENDATIONS
The primary conclusion is that residuals analysis can
be useful as a practical tool in comparing environ-
mental impacts of energy alternatives. While it is
not a substitute for a thorough study of particular
regional or local impacts associated with a definite
activity, it does provide quick "broad-brush"
answers more in keeping with the generalized informa-
tion produced in policy studies like Project Inde-
pendence. It can be used as a way of identifying
problem regions which should receive more indepth
analysis. Care must be taken however to use residuals
on a comparative rather than absolute basis.
There appears to be a definite tradeoff between the
amount of detail involved in the analysis and the
comprehensibility of the results. Although the
environmental evaluation actually produces information
for over three hundred subregions of the U.S., it
becomes extremely difficult to relate this to the
overall implications of energy policy. Consequently,
a more aggregated comparison technique, at 10 sub-
regions of the U.S. had to be carried out. Even then,
it proved difficult to comprehend, and for the FEA
reports, it proved necessary to resort to national
summaries.
Areas for further work include developing a better
methodology for comparing and presenting residuals
and scenarios, so that the full capacity of the
techniques can be utilized. Additional residual
coefficients need to be developed for items like
trace metals. Some more extensive emissions and moni-
toring data is needed before a simple and practical
technique for converting residuals information into
air and water quality results can be developed.
Finally, the residual coefficients should be modified
to reflect problems that are not at steady state with
energy throughputs. These would include efforts that
are cumulative over time, such as acid mine drainage,
land use or radioactive wastes, or that are site
sensitive, such as impacts due to construction.
233
-------
Improvements in residuals modelling also implies
improvements in energy modelling. This includes
better regional descriptions, better characteriza-
tion of industrial energy facilities, additional
energy resource characteristics, and introduction of
dynamic elements into the model.
REFERENCES
1. FEA, Project Independence Report, November 1974,
Pg- 1.
2. FEA, Draft Environmental Impact Statement for
Energy Independence Act, March 1975.
3. FEA, National Energy Outlook (in draft).
4. FEA, Project Independence Report, November 1974,
Appendix, p^ 204
5. M.L. Warren & E.H. Preston, A Review of Environ-
mental Impact Assessment Methodologies, U. S. Environ-
mental Protection Agency, April 1974, p. 1.
6. Battelle Columbus, Environmental Considerations
in Future Energy Growth, April 1973.
7. Teknekron, Inc., Residuals from Electric Power
Generation Fuel Cycles, December 1974.
8. Atomic Energy Commission, WASH-1224, Risk-Cost-
Benefit Analysis of Alternate Sources of Electrical
Energy, December 1974.
9. Hittman Associates, Inc., Environmental Impacts
Efficiency and Cost of Energy Supply and End Use
Final Report HIT 593, Council on Environmental
Quality, November 1974.
10. Peter Cukor, "Comparison of Residuals Analysis,"
Teknekron, Inc., internal communication, January 1975.
11. Joel Haverman & J. G. Phillip, "Project Inde-
pendence ," National Journal Reports, November 2,
1974, Vol. 6, No. 44, p. 1637.
12. A. V. Kneese, B. T. Bower, ed. Environmental
Quality Analysis. Johns Hopkins Press, Baltimore,
1972.
13. Council on Environmental Quality, MERES and the
Evaluation of Energy Alternatives, May 1975.
14. W. R. Menchen, M. S. Mendis, D. F. Becker,
H.L. Schultz, Hittman Environmental Coefficients for
Regional Pollutant Loading Analysis, in press.
15. F. Lambie "Environmental Residual Allocation
Model," Energy Resources Co., in press.
16. FEA, op. cit.
17.Energy Resources Co., Project Independence Blue-
print: Environmental Quality Analysis Final Report -
Phase I. December 1974.
18. Energy Resources Co., Assessment of the Environ-
mental Implication of Project Independence, in draft.
19. Hittman Associates Project Independence Final
Report, in draft.
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234
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SSt}" lsi^^«B». - • I>».K*S
SSSS,,,™! ^•^^•B >»»f:-xl
J |_, , , , , , , . . | . . . . i . . . . . ... i ' i < i |
.m..,o. "°°° ""'ffilSWHf"'"
^;0, w////m i i "., -».r -..„,
\;,;:;,"' " i::MBH^BBBH:::::;^:::::l t^/l ..,:-,,r-.,,
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:t:;'t» l kiH^MI^HHRiiR-:*!
S?:;:.".,,,, I^^H^HH^Hkjk^^d
i i i i i i i i i i 1 i i i i i i i i i ' ' ' ' |
i5000 iULyiiR dTir>r^
ict««ioi '"" "r "'"'
™'m v/y////////////M \ \ »•••"-' =••
i^""™"! S»\S~!%« fen™.,,.
is;;:1" u i •*.,...-.-.i^i ky '•"««»
»CCILMA«D ~— KT^^^J^/^
SSt? | m*..?.jix//M
SSK.™. «..^^:.a^^
P 1 1 1 1 1 1 1 1 1 1 1 ' 1 1 1 ' ' ' i ' ' ' ' i ' ' ' ' i ' • '(
! J« ••"*•• !™sa™--- "!to
•ill-' '"""•- -«—-"""'
COMPARISON OF $H SCENARIOS
DEMAND REGIONS
POLLUTANT 123156789 10 Nat.
Acids
Bases A A A - A
TDS A A BAB A
SS A A A B A
Organics B B B B B B
Thermal A
NOX A A A A - A
SOX A A A - A A
HC A B B B
CO AAAAAA A
Aid. A A BAB
Solids A A A A - B B
F-Land
I-Land A A A A A A
TOTAL NO.
A 23 11 8913200 7
B 101000511!! 3
12 12 3 7 6 H 7 12 11 H 5
A Accelerated Supply has less loading
B = Business as Usual has less loading
If difference between strategies is
less than 5? or if difference be-
tween strategies is less than \% of
the National total of that pollutant
in Business as Usual
P~~~T^h?<$
V \ " 1 \ 4/w — Iv
\ \ J \r^~2, ^
^Vj1 f ' / s r^ */*
^^— — ^-J 7 ( 1 (
'" « < — ~-v\\ ^t-^^-^ \
D -Sr 10 \ \ // \ \
._ J^^Vi M [ """^ ^
FIGURE 5. EXAMPLE OF DIFFERENTIAL COMPARISON
TOTAL NO.
(less Nat. )
A B
0 0 10
307
325
3 1 6
055
109
1) 0 6
1) 0 6
127
6 0 I
325
1 1 5
0 0 10
505
39
13
98
FIGURE 4. EXAMPLE OF GRAPHICAL COMPARISON
235
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AN ENVIRONMENTAL RESIDUAL ALLOCATION MODEL
M. Allen F. Lambie
Energy Resources Co. Inc.
Cambridge, Massachusetts
Summary
An environmental residuals technique was develop-
ed to quantitatively evaluate the environmental impli-
cations of Project Independence. Three models are
discussed that compare the regional impacts of differ-
ent scenarios of energy development: a Residual Allo-
cation Model to predict the quantity and distribution
of 15 energy-associated pollutant loadings, a Water
Use Model to assess the compatibility of water avail-
able and water required for projected energy use, and
an Air Quality Model to compare the impacts of the
scenarios on ambient air quality. The approach is
useful for scenario comparison, but is limited in
degree of detail and absolute accuracy. It is con-
cluded that the level of control technology achieved
is more critical environmentally than the choice of
scenarios. Further work should include a refinement
and extension of the residuals studied and a more de-
tailed sensitivity analysis, especially with respect
to control technology and facility siting assumptions.
Introduction
The viability of any long-range planning for
national energy development rests in part on the
critical nature of the environmental component. Al-
though national strategies for developing energy re-
sources must be chosen ultimately from the set of
alternatives that are economically and technically
practicable, the pressing nature of environmental
problems dictates that, among such alternatives, the
optimal choice should consider the relative environ-
mental impacts of the strategies. Precisely this
reasoning led to the formulation of a model by which
to compare the environmental implications of the
various scenarios generated by the Federal Energy
Administration's (FEA) Project Independence Evaluation
System (PIES) model1'2'3. This Residual Allocation
Model, developed by Energy Resources co., assesses
energy scenarios on the basis of the allocated levels
and geographic distribution of pollution loadings
associated with energy supply and the resulting end
use patterns. In addition, a Water Use Model indi-
cates for each scenario the general compatibility of
energy-associated water demands with regional projec-
tions of water supply. Finally, an Air Quality Model
evaluates emissions predicted by the Residual Alloca-
tion Model in terms of their impact on regional am-
bient air quality. (See Figure 1.)
The purpose of these models is to allocate pre-
dicted pollution loadings into common geographic areas
so that the relative impacts of these loadings can be
analyzed. The study considers 15 impact categories,
or residuals, defined by the Environmental Protection
Agency (EPA):
Air Pollutants
Particulates
Nitrogen Oxides
Sulfur Oxides
Hydrocarbons
Carbon Monoxide
Aldehydes
Water Pollutants
Acids
Bases
Total Dissolved Solids
Suspended Solids
Organics
Thermal Discharge
COAL
ROOUCTION
NATURAL
GAS S OIL
PRODUCTION
'
DISAGGREGATION TO
FOSSIL FUEL REGIONS
SYNTHETICS
PRODUCTION
POUER
PLANT
PRODUCTION
DISAGGREGATION TO
RIVER BASINS OR AQCR
REFINERY
THROUGHPUT
V
'S **
END USE CONSUMPTION:
INDUSTRIAL
TRANSPORTATION
RESIDENTIAL S
COMMERCIAL
1
'
UATER
USE
MODEL
1
WATER USE
RIVER BASIN AND
AQCR LOADINGS
AND PRODUCTION
1
1
RESIDUALS BY
DEMAND REGION
\
'
AIR
QUALITY
MODEL
i
AIR QUALITY
Land Use Parameters
Solid Wastes
Fixed Land
Maximum Incremental Land
Figure 1 FLOW CHART FOR ENVIRONMENTAL ASSESSMENT
Projected regional levels of these residuals serve
as the basic indicators of environmental quality. The
analysis consists of five distinct stages:
1. The PIES Model predicts levels of energy activities
and resulting pollution loadings for a given scenario.
Unfortunately, the geographic regions used for each
activity are different.
2. The Residual Allocation Model allocates these pro-
duction and consumption levels and the associated pol-
lution loadings among a consistent set of smaller
regions.
3. Impacts of pollution loadings are analyzed at
various levels of geographic aggregation.
4. The Water Use Model estimates regional energy-
related water demand on the basis of scenario produc-
tion levels; this demand is compared to projected re-
gional water supply.
5. The Air Quality Model assesses scenario-related
ambient air quality on the basis of regional loadings
predicted by the Residual Allocation Model.
The models were developed with the particular aim
of aiding time-constrained EPA and FEA analysts in the
comparison of the environmental impacts of various
scenarios. The need to guarantee realistic output
useful to decision-makers required feedback between
the conceptual formulation and the feasible approaches.
Thus, a "paper" model was conceived, the required
supporting data were sought, and the model was revised
to accept the best data found to be available. As
with most working models, the critical factor in this
process was the availability of meaningful, reliable
data at level of detail sufficient to support the
236
-------
allocation. Since, as a practical matter, some data
bases are finely partitioned along one variable
(e.g. industrial category) and others along another
(e.g. plant location), a number of data bases often
had to be combined or used in series to determine an
activity's distribution.
It should be noted that the Residual Allocation
Model and the peripheral air and water models are
comparative as opposed to predictive models. Reliable
predictions of absolute pollution levels which will
result from various energy strategies are extremely
difficult, if not impossible, to make on the basis of
currently available information. Accordingly, the
model's results are valid only to the extent that they
provide a means of comparison between the forseeable
impacts that different scenarios can be expected to
have on the environment or between the relative en-
vironmental impacts of a single scenario on different
regions in the analysis.
Residual Allocation Model
The allocation of energy production and associ-
ated residuals is performed by two computer models,
called the Supply Model and the End Use Model. As
their names suggest, the Supply Model allocates the
production and residuals directly corresponding to the
extraction and refinement of energy resources, whereas
the End Use Model allocates the activities and resid-
uals associated with the consumption of these re-
sources for various end uses. Because the most cur-
rent and complete data is available for 1972, that
year is taken as the base year for the projections
made by the present models. The models' target year
for the Project Independence Blueprint3 is 1985.
The geographical format of the allocation con-
sists of disaggregating energy production and resid-
uals, predicted on a broad geographical scale by the
PIES model, down to the scale of 335 River Basins, de-
fined by the National Oceanographic and Atmospheric
Administration, and 243 Air Quality Control Regions
(AQCR's), defined by the EPA. The production and re-
siduals assigned to these smaller levels are then
available for reaggregation up to the larger regions
necessary for analysis of a wider scope.
In the Supply Model, the residual allocation
scheme is based on the known location and production
of natural energy resources, as well as the location
and capacities of existing or planned conversion fa-
cilities. Specifically, the allocation proceeds
according to the following rules:
1. Production and residuals from existing coal mines
which were active in 1972 are allocated on the basis
of 1972 production levels.
2. P-roduction and residuals from coal mines predict-
ed to come onstream by 1985 are allocated according to
the size, type, and location of known coal deposits.
3. Production and residuals associated with oil and
natural gas production and the extraction of oil from
oil shale are allocated on the basis of known reserves.
4. Production from coal gasification and liquefac-
tion is assigned on the basis of the sizes and loca-
tions of proposed plants.
5. Power plant and refinery activity is allocated
according to the location and capacities of facilities
projected to be onstream in 1983.
The form of the allocation is quite simple: for
each energy activity, the amount of residual k allo-
cated to River Basin (AQCR) j is
where S. is the 1972 level of a surrogate quantity as-
sociated with the activity in PIES region i containing
River Basin (AQCR) j, S. is the 1972 level of that sur-
rogate in River Basin (AQCR) j, E. is the forecasted
level of the activity in PIES region i; and It . is
the coefficient, specific to region i, of the amount
of residual k generated per unit of activity . The
choice of surrogates is dependent upon the availability
of measures well correlated to the activity, for which
data can be obtained reliably at the geographic level
required. Once the residuals for each activity have
been assigned to River Basins or AQCR's, the model
sums the levels of each residual over all activities,
thereby arriving at the total River Basin and AQCR
loadings for all residuals^.
The End Use Model follows essentially the same
scheme. Activity levels in this segment of the Allo-
cation Model refer to fuel consumption forecasts for
various fuels grouped by use categories. The PIES
model generates forecasts for these fuel consumption
levels for each Demand Region defined by the Census
Bureau. The 11 categories treated by the PIES model
are:
Industrial Sector
Coal
Natural Gas
Distillate Oil
Residual Oil
Transportation Sector
Gasoline
Jet Fuel
Distillate Oil
Residual Oil
Residential and Commercial Sector
Natural Gas
Distillate Oil
Residual Oil
The variety of activities included in the consideration
of end use patterns is extensive, and for most of these
activities no comprehensive fuel consumption data are
readily available. As a consequence, many different
surrogates had to be tabulated in order to effect the
disaggregation of consumption levels to River Basins
and AQCR's. The End Use Model currently uses the
following surrogates:
Fuel Category
All Industrial Fuels
Gasoline
Jet Fuel
Transportation
Distillate
Transportation Residual
All Residential and
Commercial Fuels.
Surrogates (1972 data)
Number of employees in each
major industry category.
State fuel consumption by
2-digit SIC. National fuel
consumption by 4-digit SIC.
State consumption data and
population.
Number of jet takeoffs.
Primary rail track mileage,
interstate highway mileage,
population, and vessel bunk-
ering data.
Residual consumption at U.S.
ports.
Population.
237
-------
Although more appropriate measures of these consumption
levels exist, none were found that were reliable and
available at the geographic level required.
After the disaggregation phase, the model converts
the consumption predictions into residual loadings for
the six air pollution parameters using a set of end
use pollutant coefficients developed for fossil fuels
(No water or land use residuals were considered since
the only direct environmental impact of the end uses of
energy is on air quality.) The output then consists of
total levels for each of 6 air residuals in every
River Basin and AQCR'.
As with any model, the Allocation Model depends
on several specific assumptions and limitations in
scope. One of the most critical of these is the
assumed level of pollution control technology. In
converting 1985 production and consumption levels to
residual loadings predictions, the PIES model supposes
that existing and promulgated control standards are
enforced and that surface mine reclamation laws will be
implemented. Table 1 compares the effect of control
technology on the loadings associated with energy
supply for one scenario. Moreover, in allocating the
new facilities required for the realization of specif-
ic scenarios, the model assumes that facility siting
patterns will obey the distribution defined by facili-
ties projected to be onstream in 1983. This assump-
tion is consistent with the objectives set forth in
the Non-Significant Deterioration legislation now under
consideration. Of course, the model also contains the
inherent assumptions involved in the use of surrogate
quantities for the disaggregation and the suppositions
regarding economic and demographic development that
are imposed by the choice of 1972 as the base year.
Table 1
EFFECT OF CONTROL TECHNOLOGY3
WATER POLLUTANTS
197! Control
Technology
U/tll with
Advanced Control
Technology
Major Rcgulaeod
Activities «
ACIDS
l.«53
0
Coal
mining
BASES D
(tons/day)
23.30
36.67
Coal
Blnlng
TDS SS OROANICS THERMAL c
(100 tons/day) (tons/day) {100 tono/dey) {E9Btu/day)
531.5 14.389 5-97 35.301
5*. 4 165 !.«» 24.021
Coal power
AIH POLLUTANTS
AS/Hl «llh
1972 Control
AS/ill with
Advanced Control
(UJor Regulated
ARTICULATES
Oil
refining
HO(X)
generation
SO(X) HC CO ALDEKIDES
Oil
Oil Coal power
refining generation
LAND USE
1972 Control
Technology
AS/111 kith
TechnoloE*
Kftjor Regulated
Activities
SDLICS
1.69?- 9
5*1.2
Surface
cotl BlnlnB
FIXED LAMD HAX. 1HCKE.1ENTAL LAND
367,551 23.910
356.210 ;i,*6o
Surface
eo«l nlnlne
E9 IB 1,000,000,001
The Allocation Model does not attempt to disag-
grate the loadings in curies expected to result from
the mining, processing, reprocessing, and waste
management associated with the uranium fuel cycle.
Curies are a measure of the activity of radionuclides,
and as dimensions of residual loadings they do not
indicate accurately the quality of radiation in terms
of human health risks. Furthermore, the pollution
loadings which are analyzed include only those direct-
ly attributable to the extraction, processing, conver-
sion, and end use of energy resources, i.e. those
which can be quantized per unit of energy in some rea-
sonable fashion. This restriction excludes from the
model's scope any pollutants resulting from the con-
struction of energy facilities or from secondary de-
velopment induced by the exploitation of energy re-
sources. Finally, the model does not take into account
pollution loadings, such as spills from pipelines,
trains, tankers, etc., that result from the transpor-
tation or transmission of energy. The End Use Model
does account, however, for vehicle emissions associated
with the transport of fuels.
Water Use Model
Ideally, a model to indicate energy impacts on am-
bient water quality would provide the basis on which to
evaluate scenario water use implications. Unfortunate-
ly, the physical and chemical dynamics of hydrological
phenomena occur on such a small scale that nationwide
and even basin-wide predictions of water quality are
hardly possible. A river which is anaerobic 30 yards
downstream from a paper mill can rid itself of a sig-
nificant amount of BOD in 30 miles, defying any analy-
sis which looks no closer than the River Basins used
for this model. Because of this difficulty of scale,
a model to predict water use patterns was developed
instead.
The Water Use Model uses an accounting scheme to
assess the impacts of scenario-related energy develop-
ment on water use patterns. The model consists of two
sections. The first takes as input the energy produc-
tion levels predicted by the Supply Model and from
these computes energy-associated water withdrawal and
consumption for each River Basin. The second section
evaluates the resulting energy use predictions in re-
lation to the amount of water available for energy-
associated activities (i.e. total water supply minus
non-energy use).
More specifically, once all relevant energy acti-
vity levels are known for every River Basin, the model
converts them to water demand estimates using a set of
water use coefficients . Summing the results of this
conversion over all energy activities within a basin
gives the total energy-related withdrawal and consump-
tion of water for that River Basin. The total water
available for all uses in each region is just the sum
of inflows from other watersheds, groundwater supply,
and indigenous supply from natural runnoff, minus ex-
ports to other regions. The water available for energy
use is then simply the total water available minus non-
energy associated water consumption^.
Air Quality Model
Although comparison of air pollution loadings
among scenarios provides a useful means for evaluating
major environmental impacts on a geographical basis,
the comparison of the effects these loadings will have
on ambient air quality is much more meaningful to de-
cision makers. Unlike hydrological phenomena, atmos-
pheric mixing occurs on a large enough scale to enable
rough estimates of the general air quality in the
AQCR's. In order to accomplish such an analysis, the
Air Quality Model relates 1972 air quality to emissions
and then applies this relationship to the emissions
predicted for a given scenario. Using such a process,
comparisons may be made among scenarios of their
relative impacts on regional air quality.
238
-------
Input to the Air Quality Model consists of energy-
associated emissions generated in AQCR's by the Resi-
dual Allocation Model for particulates and SO (The
x
lack of adequate monitoring data to evaluate 1972 air
quality for other pollutants precluded their consider-
ation.) The model converts the emissions for a single
AQCR to an air quality measure and range using con-
version factors based on the ratio of indices- of 1972
quality to 1972 emissions data. The indices of 1972
air quality are generally the minimum, median and maxi-
mum of the 1972 average annual concentrations for all
monitoring stations in each AQCR. However, since not
all AQCR's were monitored for both pollutants in 1972,
some of the data used in the present model are taken
from 1974 data, or, in some cases, from data for AQCR's
judged to possess similar topographic, atmospheric,
demographic, and industrial characteristics.
The crucial assumption in the Air Quality Model is
that the relationship between emissions and ambient
quality is linear and time independent in every AQCR.
This is justifiable only insofar as no drastic changes
occur in the distribution or overall quantity of par-
ticulates and SO emitted between 1972 and 1985. It
also requires that each AQCR experience no drastic
climatological changes during the interim. Moreover,
because the analysis is conducted on a basin-wide
scale, no distinction is made between point and area
sources of residuals or between stack heights at which
pollutants are emitted. Site-specific air quality
models cannot be applied in this context because pro-
jections of the location of energy activities cannot be
accurate beyond the AQCR level. At this point in time,
attempts at formulating a more precise functional rela-
tionship between emissions and quality are also hamper-
ed by the fact that monitoring of emissions and air
quality only now approaches a comprehensive network.
Until a substantial history of comprehensive monitor-
ing in all AQCR's becomes available, roll-back approxi-
mations like that used in the Air Quality Model will
be the best empirical relationships obtainable for this
level of analysis. For this reason, it is imperative
that the output of the model be used for comparison
purposes only. The air quality estimates do not nec-
essarily provide realistic predictions of 1985 air
quality. However, since the same analysis is used re-
gardless of the scenario being considered, the model
is useful as a basis for comparison among scenario
impacts on air quality7.
Conclusions and Recommendations
The results of the model are useful for comparison
of the environmental impacts of energy alternatives and
as indicators of specific regions needing further study
on the effects of energy development. The output can-
not be used as a definitive indicator of environmental
"hotspots." The major conclusion drawn from the analy-
sis performed up to now stems from the model's sensi-
tivity to assumptions regarding pollution control tech-
nology. The degree to which control technology will be
implemented between now and 1985 is the single most
influential factor of the impacts which various scenar-
ios exert on the environment.
Most of the important general limitations of the
model have been outlined earlier. The model is clearly
not site-specific in its methodology; the allocation
of residuals goes no further than the River Basin
level, with no explicit consideration of topography,
climate, or severity of particular point sources. The
model also inherits all of the limitations of its vari-
ous inputs, including the PIES Model output, the resid-
ual and water use coefficients, and the data taken from
the many other sources. Another crucial concept whose
limitations must be taken into account is that of a
"residual." The fifteen residuals allocated by the
model define relatively broad classes of environmental
impact. For example, predictions of loadings in organ-
ics, measured in hundreds of tons per day, do not dis-
tinguish between chemically different hydrocarbons.
Loadings extimates for solids, measured in thousands of
tons per day, lump together all residuals which do not
enter the air or water. They include such different
wastes as spent shale from oil shale processing and
scrubber sludge from coal-fired power plants. Resid-
uals provide a convenient, allocable set of impact cat-
egories by which the overall effects of energy develop-
ment can be compared.
Several areas needing further study or attention
have become evident through the development and appli-
cation of the Residual Allocation Model. There is an
obvious need for more extensive environmental monitor-
ing. Also, if energy planning is to advance, better
regional census data must be gathered. Much of the un-
certainty imposed by the use of surrogates could be
mitigated if a more complete inventory of regional and
local energy consumption patterns were available. A
sensitivity analysis of the model should be conducted
to include variations in the method of projecting
facility siting, along with an investigation into the
degree of control technology that one realistically
can expect to be implemented by 1985.
The analysis should be expanded to include at
least three additional areas of environmental impact.
To begin with, some assessment ought to be made of the
ramifications of facility construction on surrounding
areas. The construction of water-diverting facilities
for a hydroelectric plant, for example, may take ten
or more years. The resulting temporary and long-term
changes in the surrounding water quality are not in-
cluded in the present model. Further study should
also be conducted into the possibility of presenting
radioactivity and trace metal loadings on a regional
basis in terms that relate to potential human health
hazards. Finally, it might be useful to introduce an
energy accounting scheme which would examine Btu pro-
duction and consumption on both the regional and na-
tional levels. Such a program would indicate the
relative energy productivity and demand distributions
among River Basins or AQCR's and would help measure
the degree of environmental damage export. The out-
put of the model then could be used to examine the
questions of who is producing the'energy for whom
and at what environmental cost.
References
Federal Energy Administration, Draft Environmen-
tal Impact Statement: Energy Independence Act of 1975
and Related Tax Proposals, March 1975.
Federal Energy Administration, Environmental
Report on Modifications to the Mandatory Oil Import
Program: A $3 Import Fee, January, 1975.
Federal Energy Administration, Project Indepen-
dence Report, Washington, D.C.: Government Printing
Office, November, 1974.
4
U.S. Environmental Protection Agency, Summary
Report of the Pollutants Associated with the Resource
Activities of the Hittman Environmental Coefficient
Matrices. Prepared by Hittman Associates, December,
1974.
U.S. Environmental Protection Agency, Project
Independence Blueprint: Environmental Quality Anal-
239
-------
ysis Final Report, Phase I. Prepared by Energy Re-
sources Co. Inc., December, 1974.
U.S. Environmental Protection Agency, Environ-
mental Pollutant Coefficients for Fossil Fuel End Use
in the Transportation, Industrial and Residual/Commer-
cial Sectors. Prepared by Hittman Associates, 1975.
U.S. Environmental Protection Agency, Assess-
ment of the Environmental Implications of Project
Independence. Prepared by Energy Resources Co. Inc.
(in draft).
Q
U. S. Environmental Protection Agency, Final
Water Withdrawal and Consumption Coefficients for the
Project Independence Energy Production Activities.
Prepared by Hittman Associates, 1975.
Acknowledgements:
We wish to acknowledge Richard Livingston and Glen
Kendall. Without their initiative and subsequent help
this model would not exist.
240
-------
HITTMAN REGIONAL ENVIRONMENTAL COEFFICIENTS FOR THE
PROJECT INDEPENDENCE EVALUATION SYSTEMS (PIES) MODEL
Matthew S. Mendis, Jr.
William R. Menchen
H. Lee Schultz, III
Energy Systems Department
Hittman Associates, Inc.
Columbia, MD
The development and utilization of environmental
coefficients for the environmental/policy analysis of
energy strategies is described in this paper. The
paper outlines Hittman Associates' efforts as a mem-
ber of the Project Independence Blueprint Environ-
mental Task Force. The extensive environmental data
bank developed for the Project Independence Evaluation
Systems (PIES) model is described along with its
utility in the policy analysis decision stream. The
limitations of the data bank are discussed, and
suggested modifications recommended. The technique
for determining environmental residuals as accom-
plished by the PIES Environment Report is also
described. The conclusion is that the Hittman en-
vironmental coefficients can be utilized effectively
in a first-cut comparative environmental analysis of
energy scenarios.
Introduction
The Hittman Regional Environmental Coefficients
were developed for the environmental analysis of the
Project Independence Blueprint (PIB). The purpose of
PIB was to analyze the economic, environmental and
social impacts of different possible Government
policies on future energy supply and demand. In or-
der to achieve this, the Federal Energy Administra-
tion, in an interagency effort, developed the Project
Independence Evaluation Systems (PIES) model to fore-
cast energy supply and demand for different sets of
assumed government policies and imported oil prices.
Attached to the PIES model was an "Environment
Report" submodel which was developed by the Environ-
mental Cross-Cut Task Force headed by the Environ-
mental Protection Agency (EPA).
As a member of the PIB Environmental Task
Force, Hittman Associates, Inc. (HAI) was assigned
the task of: 1) defining the environmental indicators
to be used in the energy assessment; 2) establishing
the environmental data requirements; 3) defining the
pollution abatement technologies; 4) identifying en-
vironmental constraints to be included in the price
equilibrium mode; and 5) developing environmental
data for quantitative analysis of each of the PIES
generated scenarios.
The principal and most important task was the
development of regional environmental coefficients
for the quantitative analysis of PIB. To accomplish
this task, HAI aggregated into the PIES model an
extensive environmental data bank previously developed
under contract with the Council on Environmental
Quality . Where necessary, the earlier coefficients
were updated and revised or new coefficients de-
veloped. The coefficients represent units of pollu-
tants (i.e., air and water pollutants solid waste,
land use and occupational health) per unit of energy
supplied, converted or consumed. The environmental
coefficients were also regionalized according to the
energy activity considered. For example, environ-
mental coefficients for coal supply were developed
for the twelve coal supply regions shown in Figure
1. The regional coefficients reflect variations
in the characteristics of the energy resource, ex-
traction, processing, storage and utilization.
The environmental coefficients developed for the
PIB were integrated into PIES as a subprogram. The
subprogram utilizes the output of the supply/demand
portion of PIES and the Hittman Regional Environmental
Coefficients to generate the PIES Environment Report.
This report presents the environmental residuals
(i.e., total quantity of each pollutant) associated
with each energy supply, conversion and end use acti-
vity. The environmental residuals were determined by
taking the product of the level of an energy activity
(i.e., tons of coal supplied per day) and that energy
activity's environmental coefficients (i.e., Ibs of
pollutant per ton of coal supplied). A flow diagram
of the Environment Report algorithm is presented in
Figure 2.
A generalized discussion of the Hittman Regional
Environmental Coefficients is presented in the
following sections. A detailed presentation of these
coefficients is available in Reference 2.
Data Development
Basis for the Environmental Coefficient Matrices
The basic references used in preparing the en-
vironmental coefficient matrices supplied to the FEA
Project Independence model were two reports pre-
pared by Hittman Associates for the Council on Environ-
mental Quality (CEQ) on the environmental impacts,
efficiency, and cost of energy supply and end useJ
These reports, issued in final November 1974, pre-
sented quantified data on the broad range of environ-
mental impacts to land, water, and air for each step
in the fossil fuel supply and end use chain. The
reports covered the fossil fuel supply system com-
ponents, all electric power plant conversion for
coal, oil, and natural gas and some of the future
supply activities including high and low Btu coal
gasification, oil shale, and coal liquefaction. New
data was obtained by HAI for the nuclear fuel cycle,
hydroelectric power plants, transportation of
energy resources and energy end use (transportation,
residential/commercial, and industrial) activities.
The format of the data presented in the CEQ
reports was at a lower level of aggregation than
that required for the Project Independence model.
Since the CEQ impact data was derived for each step
in the energy supply trajectory, it was necessary
to aggregate the environmental impacts from several
steps in order to arrive at a set of coefficients
consistent with the level of aggregation specified
in the PIB model. Also, the CEQ data is presented
241
-------
in terms of impacts per trillion Btu input to each
process, and it was desired tO'put these impacts on
a physical units basis (tons of coal, bbl of oil,
etc.) to be consistent with the energy flow format
of the PIB model.
Coal production provides an illustrative example.
The PIB model specifies the tons of coal produced,
ready-for shipment, from each of twelve coal supply
regions. To get to this point, several unit opera-
tions or activities must be performed on the coal
resource in the ground. First the coal must be ex-
tracted. It must then be transported locally to a
preparation site and stored. It may then be prepared
by washing to remove impurities or just sized for
shipment. Each of these activities may, in turn, be
performed by one or more specific processes. Ex-
traction of coal in the Hittman data base is comprised
of underground (room and pillar, and longwall) and
surface (auger, strip, and contour) mining techniques
or processes. Local transportation of the coal can
be performed by mine rail, conveyor, or trucks.
Preparation of the coal may involve washing (dense
media) or simple breaking and sizing.
As a concrete illustration of the methodology
employed to manipulate the Hittman data for use with
the PIB model, consider coal production from existing
underground mines in Northern Appalachia. From Bureau
of Mines' data for this region it was determined that
75 percent of the coal extracted from the ground re-
ceived some type of mechanical cleaning and that the
remaining 25 percent was just mechanically crushed or
sized. Bureau of Mines' data further showed that 95
percent of the coal from this region was extracted by
room and pillar operations, while 5 percent was ex-
tracted by the longwall method. These relative
fractions were the basis for determining the combina-
tion and weighting of processes used from the data
base.
The procedure used was to work backward from the
point of coal ready for shipment and determine, using
the respective process efficiencies, the Btu input
needed to deliver this amount of coal. The Btu input
numbers (recall that the data base is on a trillion
Btu input basis) represent the multipliers used with
the data base environmental coefficients to deter-
mine the environmental impact from that respective
operation. A summation of impacts over all opera-
tions then gives the coefficients for use with the
PIB model. Table 1 and Figure 3 illustrate the
derivation of one (of 18) PIB environmental coeffi-
cients for underground coal production from the
Northern Appalachian region.
Table 1.
Derivation of PIES Coefficient
From CEQ Data
Room and Pillar
Extraction
Longwall Extraction
Mine Rail Transport
Steam Coal Preparation
Breaking and Sizing
Data Base Solid
Waste Impact/
1012 Btu Input
1.19+03
1.78+03
0
5.97+03
2.54+00
6.78+03 tons solid waste x ID12 Btu
1012 Btu for delivery
42.4x103 tons
coal
Btu Input
Multipliers
1.71
.06
1.028
.778
.25
Total
1.59+02 tons
Tons Solid
Waste per
1012 Btu
2.03+03
1.07+02
0
4.64+03
6.35-01
6.78+03
solid waste
Additional data were obtained through a litera-
ture search for those energy activities not in-
cluded in the CEQ report. Specifically, environ-
mental matrices were developed independent of the
CEQ report for the nuclear fuel cycle, hydroelectric
power plants, energy transportation, and all the end
use activities.
Data Format
The Hittman environmental data was designed to
facilitate its incorporation and utilization in the
PIES model or any other similar energy model. En-
vironmental coefficients are given on the basis of
unit of pollutant produced per unit of energy input
or output associated with an energy activity. For
example, the nitrogen oxides (NOX) associated with
the extraction of natural gas was determined to be
2.75x10"
tons N0x per 10
SCF natural gas. Thus,
if a region produces 250x10 SCF of natural gas per
day, the associated environmental residual can be
determined as:
250x1 0
x 2.75x10
-3 tons N0x
106 SCF
-1
6.875x10" tons-
day
The environmental data for each energy activity is
presented in a matrix where the energy activity and
regions make up the rows and the environmental pollu-
tants make up the columns. An example matrix can
be found in Figure 4.
A discussion of the energy activities, the en-
vironmental pollutants and the regional delineations
that make up the Hittman Environmental Coefficient
Matrices is presented below.
Data Description
Definitions
In order to describe the environmental impacts
associated with energy supply, conversion and end
use, a number of definitions were adopted:
Term Example/Definition
Pollutant SO- emission from the combustion
of coal for steam generation
Process Combustion of coal for steam gen-
eration (results in a set of
pollutants)
Activity A combination of processes (i.e.,
electricity generation by coal-
fired power plants)
Environmental Unit of pollutant per unit of
Coefficient energy into an activity (i.e., «
Ibs of SO emitted per ton of coal
into a coal-fired power plant)
103 tons coal for
delivery
242
-------
Environmental The total quantity of a pollutant
Residual for a given time period resultant
from an energy activity (i.e.,
tons of SO emitted per day)
Controlled Vs. Uncontrolled
All environmental coefficients incorporated in
the PIES model were designated controlled. "Con-
trolled" implies that impacts are consistent with the
use of control technology which will probably be re-
quired and/or available in 5 to 10 years. As an
illustration, past laws that governed the reclamation
of surface mined lands minimally required that effort
be made to restore the land. This included partial
backfilling and an attempt at revegetation. However,
since the degree and success of reclamation were not
mandatory, (for the ''uncontrolled" condition) reclama-
tion was not assumed for area stripping operations,
and only partial backfilling was assumed for contour
mines. In the controlled situation, contour backfill-
ing and revegetation were assumed required for either
type of stripping operation. The attainment of this
high level of reclamation will require such practices
as stockpiling and redistribution of the topsoil,
segregation of toxic overburden, and seed bed prepara-
tion. Generally speaking, the controlled condition
incorporates the environmental standards proposed or
soon to be implemented by the EPA. A more detailed
explanation of controlled as it is related specifi-
cally to each process in the energy activity chain
is to be found in the writeups preceding each energy
activity environmental matrix in Reference 2.
Uncontrolled environmental coefficient matrices
were developed for comparison of a "base case" to
the PIES scenarios. "Uncontrolled," according to
the ground rules adopted in this study, means that
impacts are the current national or regional aver-
age value. In the absence of current (1972-73)
data, impacts typify the use of least stringent
environmental controls. The uncontrolled environ-
mental coefficients are not presented in Reference
2. However, uncontrolled environmental coefficients
in the CEQ format are presented for fossil fuel
energy activities in Reference 1.
Energy Activities
The energy related activities evaluated for
environmental residuals in the PIES data base were:
• Coal Supply:
• Underground
» Surface
• Coal Gasification:
• Low Btu
• High Btu
• Coal Liquefaction
• Shale Oil Supply:
• Underground
• Surface
• In-Situ
• Natural Gas Supply:
• Extraction
• Processing
• Crude Oil Supply:
•- Domestic Onshore
• Domestic Offshore
• U235 Extraction
• Energy Transportation:
» Coal:
Ra11 road
- Barge
Pipeline Slurry
• Crude & Syncrude Oil:
Pipeline
* Crude Oil:
Barge
Railroad
• Crude & Refined 011:
Tanker
• Oil Products:
- Barge
Truck
- Rail
Pipeline
• Natural & Synthetic Gas:
- Pipeline
• Liquefied Natural Gas:
Tanker
• Deep Draft Port Facility:
Monobuoy Mooring System
Power Plants:
Coal Fired
Oil Fired
Gas Fired
Gas Turbine Simple Cycle
Low Btu Gas/Steam Turbine
Combined Cycle
Hydroelectri c
Nuclear
El ctricity Transmission & Distribution
Oi Refineries
Existing
New (Fuel Oil)
New (Gasoline)
Transportation Energy End Use
Residential/Commercial Energy End Use
Industrial Energy End Use
The energy activities analyzed for environ-
mental residuals are only those directly attributable
to energy material extraction, processing, and utili-
zation on a per unit of energy basis. Because
residuals from other energy-related activities cannot
be estimated on the basis of a per unit of energy in-
put or output, environmental coefficients were not
developed for pollutants resulting from:
• Construction of energy facilities
• Conjunctive development induced by
energy development
• Secondary pollutants resultant from
interaction of primary pollutants
with the environment
Environmental Pollutants
The environmental pollutants considered in the
PIES data base were:
• Water Pollutants:
Acids, Bases, Total Dissolved Solids,
Suspended Solids, Organics, Thermal
• Air Pollutants:
Particulates, Nitrogen Oxides, Sulfur
Oxides, Hydrocarbons, Carbon Monoxides,
Aldehydes
• Land Impacts:
Solid Waste, Permanent Land Use
(Fixed Land), Temporary Land Use
(Maximum Incremental Land)
• Occupational Health:
Deaths, Injuries, Man-days Lost
The water and air pollutants are aggregated in
broad categories such as acids, bases, particulates,
etc. The constituent pollutants (i.e., sulfuric
acid, calcium carbonate, trace metals, etc.) are not
identified for two reasons. First, the time allo-
cated for development of the environmental coeffi-
cients for PIES precluded any further breakdown.
Secondly, the level of information on the energy
activities generated by PIES was such that accuracy
would not be enhanced if any further breakdown in the
243
-------
pollutant categories was attempted. The broad pollu-
tant categories had the advantage of facilitating
qualitative environmental analysis of the PIES
scenarios.
Solid wastes are considered to be all residuals
not entering the air or water that result from the
basic fuel resource, or from the system processes
that make fuels useful for consumption.
The land impacts include areas required for ex-
traction, structures, disposal of solid wastes, roads,
ports, pipelines, storage, and buffer zones. Both
fixed and incremental land effects are considered.
Fixed land effects are those associated with facili-
ties such as processing plants, pipelines and storage
tanks, whereas incremental land effects are those
associated with excavation, such as strip mining,
and solid waste disposal.
Occupational health is considered on the basis
of deaths, injuries, and man-days lost due to in-
juries.
Regionalization
In order to be compatible with the PIES output,
environmental coefficients for each energy activity
were determined regionally to reflect variations in
the characterization of the energy activities. PIES
regions for each energy activity were defined to
"correspond to natural data divisions appropriate to
each resource, conversion facility and demand."
The results of this regional division are shown in
Table 2.
Table 2. PIES Energy Regions
Energy Activity
Coal Supply
High Btu Gasification
Low Btu Gasification
Coal Liquefaction
Oil Production
Natural Gas.Production
Natural Gas Processing
Energy Transportation
All Electric Generating
Power Plants
Oil Refineries
Oil Shale Recovery
U-235 Extraction
Electricity Transmission
and Distribution
Residential/Commercial End Use
Industrial End Use
Transportation End Use
Number and Region Definition
12 FEA Coal Supply Regions
(See Figure 1)
14 NPC Petroleum Provinces of
the U.S.
National
9 Census Regions
7 Petroleum Administration for
Defense (PAD) Districts
National
9 Census Regions
Environmental coefficients were developed for the
PIES regions utilizing a weighting system to reflect
the variation within a given region of:
• Energy resource characteristics
• Energy production, conversion and
utilization
• Regulatory requirements on energy.
supply, conversion and end use
(i.e., environmental constraints)
• Energy consumption patterns
Environmental Coefficient Matrices
The result of the HAI/PIES effort was the develop-
ment of a comprehensive set of environmental coeffi-
cient matrices for energy supply, conversion and end
use. Thirty-three matrices were developed encompassing
the energy activities, pollutants, and regions dis-
cussed above. These environmental matrices, the
associated assumptions, the methodology for their
utilization and a sensitivity analysis are presented
in Reference 2.
Data Application
General
The Hittman Regional Environmental Coefficients
developed for the PIES model have potential for a
wide range of applications. The present format of
units of pollutant per unit of energy input or output
1?
has the advantage (over the CEQ format of 10 Btu's
into a system) of compatible application to most
existing data bases. The use of consistent environ-
mental coefficients also enables energy policy makers
to obtain relative environmental rankings of various
energy strategies. The regional characteristics of
most of the coefficients allow for the focusing of en-
vironmental analysis to specific regions without a
loss of resolution. Environmental coefficients and
the subsequent environmental residuals analysis has
the advantage of allowing the comparison between
energy alternatives without getting into the site
specific nature of the energy facilities. Thus, it
becomes possible to discuss representative energy
activities rather than specific facilities (i.e.,
a particular power plant). Additionally, the
residual analysis has a further advantage in that it
is required as a primary step if one wants to proceed
to an environmental quality analysis and subsequent
environmental impact assessment.
Application to PIES
The output of PIES for the Environment Report
is a series of energy activity levels relating to
energy supply, conversion, transportation and end
use within a given region. The environmental evalua-
tion of each PIES scenario requires explicit con-
sideration of the entire set of energy activities
and the environmental residuals that are generated
by these activities. The Hittman Environmental
Coefficients, as utilized in PIES for residual analy-
sis, are described below.
Consider the following: -i energy activities;
3 regions; and k environmental pollutants. Then we
can define the following:
E.. the level of the ith energy activity
in the jth region
Piik ~ the ^tn environmental coefficient
for the ith energy activity in the
j'th region
Utilizing the definitions above, we can determine
various aggregations of environmental residuals (ER)
as is done in PIES by the following operations:
ER.., =
1-3k
P..£ : the residuals associated
with a regional energy
activity
244.
-------
£(E..
-
x P
--
1-3 K-
x p
tne residuals associated
with all regional energy
activities
: the residuals
associated with
total national
energy activities
The procedure of product summations to determine
environmental residuals allows for incorporation into
other regional or national energy models.
Conclusions and Recommendations
The immediate conclusion is that the Hittman
environmental coefficients can be utilized as an
effective tool in the policy analysis of energy
strategies. The relative environmental residuals
comparison of various energy strategies can aid in
pointing out environmental problem areas of future
energy development. The environmental residuals
technique allows for a rapid, broad analysis of
energy strategies and can indicate those strategies
or regions that should be studied in more depth.
However, the environmental residuals technique can
be utilized only as a means of comparison between
strategies, and not as a statement of environmental
quality.
Several recommendations for refinement of the
environmental coefficients technique can be identi-
fied. These include:
(1) Development of additional environmental
coefficients for pollutants not considered
in PIES such as specific trace metals, etc.
(2) Consideration of secondary pollutants that
result from the interaction of primary
pollutants with the environment
1.
2.
3.
4.
(3) Development of techniques to reflect resi-
duals that are time variant with energy
throughputs (i.e., acid mine drainage,
reclamable land use, radioactive waste,
etc.).
(4) Development of more uniform regions so
as to optimize coefficient resolution
within the available data base
(5) Finally, better techniques should be
developed to utilize the residuals data
for a generalized environmental quality
analysis (i.e., building in quality indi-
cators for each type of pollutant in order
to reflect the sensitivity of any given
region to an increase in a given environ-
mental residual)
References
Environmental Impacts. Efficiency and Cost of
Energy Supply and End Use, Vol. I and II,
Final Report, HIT-593, Hittman Associates, Inc.,
November 1974.
Hittman Associates Project Independence Final
Report, in draft, due for publication April
1976.
Federal Energy Office Memorandum from William
W. Hogan - Balancing Task Force, to Gorman
Smith May 2, 1974.
Environmental Impact Modeling for Project
Independence, Richard A. Livingston, G.R.
Kendall and W.R. Menchen.
1. Northern Appalachla
2. Appalachia
3. Southern Appalachla
4. Midwest
5. Central West
6. Gulf
7. Eastern Northern
Great Plains
8. Western Northern
Great Plains
9. Rockies
10. Southwest
11. Northwest
12. Alaska
Figure 1. PIES Coal Supply Regions
245
-------
PIES Supply/Demand
Integration Model
Regional
Energy Conversion
Hittman Regional
Energy Supply
Environmental
Coefficients
Hittman Regional
Energy Conversion
Environmental
Coefficients
Regional
Environmental Residuals
[PIES Environment Report]
FIGURE 2. Environment Report Generation
CEQ Room and Pillar Mining
Variables (Land Impact):
Coal Neat Value
Coal Density
Seam Thickness
Mine Depth
Angle of Draw
% Subsides
Mine Life
Process Efficiency
etc.
CEQ Room and
Pillar Mining
Land Impact
Coefficient
CEQ Longwal 1 M1 nlng
Variables (Land Impact):
Coal Heat Value
Coal Density
Seam Thickness
Mine Depth
Angle of Draw
Mine Life
Process Ef f 1c1 ency
etc.
CEQ Longwal 1
Mining
Land Impact
Coefficient
CEQ Steam Coal Plant
Variables (Land Impact):
Process Efficiency
Clean Coal Recovery
Raw Coal Feed
Magnetite Losses
Tramp Iron Losses
etc.
CEQ Steam Coal
Plant Land
Impact Coeffi-
cient
FIGURE 3. Flow Diagram of CEQ Data Conversion
to PIES Coefficients
HATER IMPACTS (TONS/UNIT)
/AIR IMPACTS (TONS/UNIT)/
REGION VIII-W.N. GT. PLAINS-OLD-U
REGION VIII-W.N. GT. PLAINS-NEW-U
REGION VIII-W.N. GT. PLAINS-OLD-S
REGION VIII-W.N. GT. PLAINS-NEW-S
REGION IX - ROCKIES - OLD - U
REGION IX - ROCKIES - NEW U
REGION IX ROCKIES - OLD S
REGION IX • ROCKIES - NEW - S
REGION X SOUTHWEST - OLD - U
REGION X - SOUTHWEST - NEW - U
REGION X - SOUTHWEST OLD - S
REGION X - SOUTHWEST - NEW - S
REGION XI NORTHWEST OLD-U
REGION XI - NORTHWEST NEW-U
REGION XI NORTHWEST - OLD-S
REGION XI - NORTHWEST - NEW-S
REGION XII - ALASKA NEW - U
REGION XII ALASKA NEW-S
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1.39-02
1.44-02
0
g
1.94-02
1.97-02
0
0
1.67-02
1.70-02
0
0
1.44-02
1.44-02
9.47-03
7.72-03
0
0
4.66-01
4.85-01
0
0
6.51-01
6.62-01
0
0
5.63-01
5.72-01
0
0
4.83-01
4.83-01
3.19-01
2.60-01
0
0
6.92-03
6.48-02
0
0
4.62-02
7.65-02
0
0
3.99-02
6.62-02
0
0
6.48-02
6.48-02
5.08-02
3.86-03
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
o'
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1.64-02
1.64-02
0
0
6.48-02
6.48-02
0
0
5.61-02
5.61-02
0
0
1.57-03
1.34-03
0
1.81-03
U
0
2.74-02
2.74-02
0
0
2.40-02
2.40-02
0
0
2.07-02
2.07-02
0
0
4.47-02
3.80-02
0
5.15-02
U
0
2.02-03
2.02-03
0
0
1.75-03
1.75-03
0
0
1.51-03
1.51-03
0
0
3.29-03
2.78-03
0
3.76-03
FIGURE 4. Environmental Coefficient
Matrix for Coal Supply
246
-------
INTEGRATED ECONOMIC-HYDROSALINITY-AIR QUALITY ANALYSIS
FOR OIL SHALE AND COAL DEVELOPMENT IN COLORADO
Charles W. Howe
Bernard Udis
Robert C. Hess
Douglas V. Orr
Jeffrey T. Young
Department of Economics
University of Colorado
Jan F. Krelder
Environmental Consulting Services
Boulder, Colorado
The objective of this study was to analyze the
economic, hydrologic, water quality, and air quality
implications of establishing a shale oil industry and
expanding coal mining in Colorado. The main tools of
analysis consisted of (1) the Colorado State Univer-
sity input-output (1-0) model of the State; (2) the
University of Colorado (l-O) models of the Upper Main
Stem of the Colorado (UMS) and Green River Basin
economies; (3) the C.U. hydro-salinity model cali-
brated to the UMS, White, and Yampa basins; (4) the
C.U. air quality model; and (5) state 1970 date on
employment by industry and skill, the latter reduced
to a set of employment coefficients per million dol-
lars of output for the various sectors of the State
economy. The strategy was to analyze three steady-
state scenarios: a shale oil scenario, an under-
ground coal mining expansion scenario, and a strip
mining coal expansion scenario. Changes in outputs
and employment due to oil shale and coal expansion
were estimated.
The coal scenario consisted of 6 underground
expansions totaling 10.35 million tons per year in
the UMS Basin and 5 strip mining operations totaling
12.45 million tons per year in the Green River Basin.
The shale oil scenario consisted of 4 operations
totaling 134,000 bbls/day in the UMS Basin and 3
operations totaling 146,000 bbls/day in the Green
River Basin. The steady-state increase in statewide
output levels due to shale oil was about $1.6 billion.
Increased payments to households totaled $134 million
statewide. The statewide increase in employment was
16,670.
The underground coal expansion induced an expan-
sion in statewide output levels of $171 million, in-
creased payments to Colorado households of $27 mil-
lion, and direct and indirect increases in employment
of 4964 persons.
The strip mining expansion increased statewide
output levels $47 million, increased payments to
Colorado households by $3.8 million statewide, and
increased employment by 1300 persons.
The water implications included direct and in-
direct consumptive uses of 31,668 acre-feet per year
in the UMS, 34,164 per year in the White River Sub-
basin, and 8520 in the Yampa. Added salt loadings
were 3576, 5568, and 3204 tons per year in the 3
basins, assuming that brine and spent shale problems
will be totally controlled. Shale oil production is
the major air polluter. Some 17 phases of the shale
oil process contribute significantly to air pollution.
It is predicted that a significant degradation of air
quality will occur in Garfield and Rio Blanco Coun-
ties from the postulated 280,000 bbl/day industry on
the assumption that processes similar to TOSCO II
will be used. Occasional conditions of poor disper-
sion could lead to much more severe short term
episodes. Ambient air quality impacts in the vicinity
of the plant itself are seen to be critically depen-
dent on plant location with respect to topographic
features.
Methods of Analysis
The scenarios analyzed are given below in Tables
1 and 2. They represented the best available esti-
mates of likely developments as of June, 1975. It
should be noted that only the direct and indirect
efforts of coal and shale oil production have been
analyzed. The coal and oil produced have been
treated as exports from Colorado, even though some
are intended for use within the State.
Table 1.
Coal Scenario
Company /Location
Ultimate
Tonnage
Meth
-od
Uses
Colorado River Basin ,.
1.
2.
3.
4.
5.
6.
Colo. Consol. (Colum-
bine Glass) Paonia
Adolph Coors
Bowie-Paonia
Pittsburgh/Midway
Paonia
Atlantic Richfield
Somerset
Western Slope Carbon
Somerset
Public Service Co.
Cameo
TOTAL
Green River Basin
1.
2.
3.
4.
5.
Empire Energy
Moffat City
Utah International
Craig (Mttffat C.)
W. R. Grace
Moffat County
Peabody
Routt County
Energy Fuel
Routt County
TOTAL
2.0x10
5
4.0x10
f.
1.0x10
6
2.0x10
6
0.6x10
6
0. 75x10
10.35x10°
/:
2.0x10
g
2.6x10
g
3.0x10
g
0.85x10
C.
4.0x10
12.45xl06
UG
UG
UG
UG
UG
UG
UG
S
S
S
S
S
Export from
State
To Golden
Export from
State
Export (?)
To Pueblo
Thermal,
Cameo
Slurry Pipe
to Texas*
Thermal,
Craig
Slurry Pipe
to Texas*
Thermal,
Hayden #2
To Denver
* requires
water &
power
The basic tool of economic analysis used was in
the input-output (1-0) type of model. Excellent ex-
positions of this type of model are available in the
literature (e.g. Baumol-1- or Miernyk^) but, in brief,
such a model shows the linkages which exist among the
various economic sectors of a region by virtue of
247
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Company/Location
Table 2.
Shale Oil Scenario
bbls/day
Retorting-, Mining
Tech. - Tech.
TOSCO II
Union
Underfeed
In Situ
Paraho
Superior
3 Minerals
TOSCO II
TOSCO II
UG
UG
UG
UG
UG
UG
Colorado River Basin—
Colony 46,000
Union 50,000
Occidental 30,000
(Garrett Res.)
Earaho 8,000
TOTAL 134,000
Green River Basin
Superior 50,000
Rio Blanco (C-a) 50,000
Shell Oil (c-b), 46,000
(formerly ARCO)
TOTAL 146,000
I/ Omitting all Utah developments.
2/ We will assume TOSCO II for all plants.
supplying one another with inputs. The linked sectors
include households and a local-state government sector.
When one sector expands its output (say to satisfy a
new national demand for an energy commodity like coal),
it demands more inputs from other economic sectors of
the region, and they, in turn, demand more from their
suppliers (including households which supply the labor
inputs required). Some inputs are imported from out-
side the region, and such "leakages" finally cause the
total regional requirements to converge to new equili-
brium levels of output for each regional economic
sector.
Should it be desired to know how much of a pollut-
ant will be generated by the regional economy or how
much of some natural resource like water will be re-
quired, it is then possible to multiply the output
levels by corresponding coefficients representing the
generation of the waste or use of the resource to ar-
rive at a total. This .procedure is followed, for
example, in determining non-agricultural consumptive
water uses, the total level of wastes generated, and
employment by sector. More complex models are needed
to determine the water use of agriculture and the pat-
terns by which air-borne wastes are distributed at
ground levels.
The regions for which 1-0 models exist are: the
Green River Basin, the Upper Main Stem of the Colorado
River (UMS), the San Juan River Basin, and the State
of Colorado. The first two were used to represent the
economic structures of their respective portions of the
State of Colorado. The Green and UMS 1-0 models were
used in conjunction with Gray's 1-0 model^ of the en-
tire State to analyze statewide and regional economic
effects.
To trace water use in greater detail and to anal-
yze the salinity (total dissolved solids) effects on
water quality of the energy developments under study,
the hydro-salinity model (Udis, Howe, and Kreider^) was
calibrated to three separate sub-basins: the Colorado
UMS below Glenwood Springs (excluding the Gunnison-
Uncompaghre systems); the White River; and the Yampa
River. The outputs of the models include monthly and
annual river basin outflows, and total dissolved solids
loadings by month and year.
The air pollution model does not cover regions but
calculates ground level concentrations of particulates,
sulphur dioxide, oxides of nitrogen, carbon monoxide,
and unburned hydrocarbons for areas surrounding im-
portant point and diffuse sources. A point source
would be, for example, a coal mine or a thermal elect-
ric plant. A diffuse source would be a town where
there are many small point and mobil sources.
The strategy of applying these models to the
analysis of the coal and shale oil scenarios consisted
of the following steps:
1. use the state-wide 1-0 model to get total
state output and employment effects;
2. use the UMS 1-0 model to get the output and
employment effects occurring in the UMS region
(roughly Garfield, Mesa, Delta, and Montrose Counties)
as a result of the coal and shale oil developments;
3. use the Green River Basin 1-0 model to esti-
mate the output and employment effects of the coal and
shale oil developments assumed for that region (Rio
Blanco, Moffat, and Routt Counties);
4. assume that the ''rest of the State" effects
are given by the quantities in (1) less those in (2)
and (3);
5. apply the hydro-salinity models to the im-
mediate basins where the developments are occurring,
since that is where any critical water problems will
arise;
6. apply the air pollution model to the import-
ant new point sources.
For shale oil and the new strip and underground
coal mining processes, the major problem was to create
the column of technical coefficients showing the in-
puts from the regional (or state) sectors. Each en-
try requires two facts: (1) the technologically re-
quired input from the particular sector and (2) the
portion of that input likely to be supplied by the
regional (state) sector (the remainder being the
amount imported. It was decided that the rows correr
spending to the new energy activities and showing the
distribution of their output would all be zeroes, the
output being completely exported from the State. (This
is not the case for all coal output; see the Coal
Scenario in Table 1).
The major sources consulted during the construc-
tion of the shale oil column were references 5 thru
10. Reference 11 would have been extremely useful had
it been known in time. Interviews with officials of
the Shale Oil Corporation provided new information and
verification of data from other sources.
The final data used to characterize the oil shale
sector were stated in terms of the annual inputs into
a 50,000 bbl/day plant, the output of which was eval-
uated at $12 per barrel. These are given in Table 3.
Table 3.
Major Inputs Into a 50,000 bbl/Day
Shale Oil Plant (1970 dollars)
Electric power
Payments to state and
federal government
Wages and salaries
Imports (out of state)
Depreciation
Water
Water use (consumptive)
$ 9,300,000
9,500,000
15,000,000
165,200,000
20,000,000
7,200 acre-feet
32.87 acre feet/$106 output
In retrospect, other "guesstimates" of additional in-
puts could have been attempted and probably some of
the "imports" (e.g. ceramic balls for retorting)
should have been allocated to Colorado. In sum, the
economic impacts are biased downward by omitting other
positive inputs, but the amount of this bias is diffi-
cult to estimate.
Coal mining was characterized as new underground
or new strip. For the former, data were obtained from
industry sources and a promise of confidentality was
made. However, the following classes of inputs were
included: wages and benefits, chemicals and explor
aives, fuel and power, supplies, and other. In the
248
-------
caae of chemicals and explosives, it was assumed that
they were available within the State, but not in the
UMS or Green BasiCna-. Consumptive water use was esti-
mated to be 6.8 acre-feet per million dollars of out-
put (at $7/ton).
The new strip mining sector was estimated from
U.S. Bureau of Mines data, Circular 1972 1C 8535.
Estimates were based on a 5 million ton per year oper-
ation and are given in Table 4.
Table 4.
Major Inputs Into a 5 Million Ton/Year
Western Strip Mining Operation
Wages and salaries $850,800
Local taxes 250,000
Federal taxes 314,400
Chemicals & explosives 850,600
Oil and gas 111,000
Electric power 126,000 ,
Water use (consumptive) 326.8 acre-feet/$10
output
The same assumption was made regarding the source of
the "chemicals and explosives" input. In all cases,
strip coal was valued at $2/ton and underground coal,
being of much higher quality and heat content suited
primarily for metalurgical uses, at $7/ton.
Water
Water "use" must be specified both in terms of
how much is withdrawn from the source and how much is
actually consumed. Return flows - the difference be-
tween withdrawals and consumptive use - can represent
a large part of the water diverted (1/2 to 2/3 for
residential uses, as much as 1/2 for irrigation) and
are quite important to the maintenance of flows for
downstream users. It is also necessary to distinguish
between direct and indirect water uses.
Water quality in this study is defined as total
dissolved solids (TDS), either in tons of total salt
load or in concentration. TDS is affected by natural
sources, the contents of return flows, and the concen-
trating effects of consumptive water uses. A change
in economic activity will induce both direct and in-
direct salt loadings and both are computed by the
hydro-salinity model.
It is not yet known whether or not serious salt
problems will follow from shale oil development. Pro-
blems might relate to the use or disposal of brines
recovered with the shale and the possible leaching of
salts from the spent shale. Industry sources have
asserted that these will not be significant sources of
pollution. The calculations in this study cover only
TDS additions from sanitary and clean-up water uses
typical of industry.
Air Pollution
The impacts of the three energy development sce-
narios include possible degradation of air quality in
Rio Blanco, Routt, Moffat, Garfield, Gunnison, and
Delta counties. An attempt was made to calculate the
dispersion or diffusion of airborne pollutants through
the region by use of a mathematical simulation model.
In this section, only the direct air pollution impacts
of energy growth are considered. Although the input-
output framework provides a mechanism by which both
direct and indirect effects can be calculated, the
scope of this section includes only direct air quality
impacts.
All energy extraction scenarios considered here
are centered in Northwestern Colorado. This area is
typified by a proliferation of ridges, valleys and
mesas and is generally quite variable in form and con-
tour. This type of conformation results in local
micro-climates influenced less by synoptic (mesoscale)
climatic events and more by local (microscale) char-
acteristics. As a result, dispersion of airborne pol-
lutants varies from site to site and can only be mod-
eled approximately by the best of air pollution models
now extant.
Mean temperatures for a year range from 40°-60°F
and insolation is about 1500 Btu/(ft )(day) on a hori-
zontal surface. Precipitation averages from 8 to 16
inches per year in the region. In this arid, sunny
coimate, fugitive dust emissions require more control
effort than in other areas of the United States. High
surface winds associated with the passages of cold
fronts may exacerbate the fugitive dust problem at
mine sites and temporarily unvegetated areas.
With the exception of the aerological environment
of large municipalities, air quality in the region is
excellent. However, few data on air quality exist for
the area other than measurements of particulate con-
centrations made near the towns of Meeker, Grand
Valley, Rio Blanco and Rangely by the Colorado Depart-
ment of Health. There are indications that natural
particulate hazes from windblown dust may exceed ac-
ceptable air quality standards periodically at the
present time with no industrial development in the
region. Airborne hydrocarbons may exist in some areas
of the region resulting from emissions from vegetation
(sagebrush).
An air pollutant dispersion model APGDM has been
developed at the University of Colorado's Bureau of
Economic Research. The model is of the Gaussian type
and is described in Udis, et al^. This simulation
model includes the effects of the following primary
variables upon the diffusion of pollutants from a
given source into the atmosphere: (1) stack height,
exit temperature, exit velocity and plume rise; (2)
wind speed, wind direction, ambient temperature,
atmospheric stability, temperature gradient, and inso-
lation; (3) inversion depth; (4) background air qual-
ity; (5) arbitrary receptor location; (6) terrain
variations downwind; (7) arbitrary time period.
Since the behavior of plumes in the present im-
pact areas may not conform to all Gaussian model as-
sumptions, the dispersion results presented in the
shale oil impact analysis must be viewed as approxi-
mate.
Direct airborne emissions from underground coal
mining are negligible. The transportation, storage
and distribution phases of underground-mined coal are
also very clean since conveyors or trains are used
for transport. Surface mining of coal can result in
significant air pollution from the mining and trans-
port phases.
Unlike the two coal extraction scenarios con-
sidered in this report, the development of the postu-
lated 280,000 bbl/day shale oil extraction industry
will have major impacts on the air quality in Rio
Blanco and Garfield Counties. Since sufficient tech-
nical data were available only on the TOSCO II pro-
cess , it has been assumed that all plants are to use
that process so that the related calculation can be
demonstrated. Estimates of emissions from a steady
state TOSCO II plant with underground shale mining
have been based on the Environmental Impact Statement
prepared by the Colony Development Operation-^ for
their proposed 50,000 bbl/day facility to be located
at Parachute Creek, Colorado. Significant emissions
arise from some 17 phases of the operation includ-
ing shale transport and crushing, retorting, power
plant operation, and on-site kerogen storage. Cemen-
tation reactions and revegetation are assumed to con-
trol fugitive dust from large spent shale disposal
areas. The total annual emissions from one 50,000
bbl/day TOSCO II plant and from the seven plants
postulated in the present scenario are shown in
Table 5.
The calculated emissions agree with those pre-
sented in the FEA Project Independence Oil Shale Task
Force Report with the exception of NOX emissions. The
FEA report, inexplicably, does not include the domi-
nant NOjr emitter of the TOSCD II process (raw shale
249
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preheat system). Fugitive dust emissions are expected
to be much smaller C46TPY for 50000 B/D plant) than
those associated with. the. procession plant13.
TaEle 5
Annual Direct Emissions Prom Shale Oil
Extraction (tons/year)* Assuming TOSCO II Technology-
Production Level
Pollutant 50,000 B/D 280,000 B/D
Particulates 3075 17220
SO, 6950 38920
NO| 24600 137760
CO 250 1400
Hydrocarbons 1700 9520
* These figures are based on the assumption that all
shale oil projects would be using the TOSCO II process
and experiencing a 90% load factor at each plant.
Model outputs are in terms of incremental pollu-
tion increases for the region surrounding each of the
seven postulated plants considered. The physical dis-
tributions of long term average pollution are presented
on isopleth (constant pollutant quantity) maps which
are a convenient visual means of determining the nature
of pollutant distribution in the areas around a given
source. Incremental isopleth maps for S02 and NO^
are illustrated in Figure 1.
Results
Selected results are given in Tables 6-11 below.
Table 6
Total Output Impacts of Energy Developments
(millions of 1970 dollars)
Shale Oil UG Coal Strip Coal Total
UMS Basin
Green Basin
Statewide
% 1970
722
800
1,654
4.3%
120
-
171
0.4%
-
33
47
0.1%
842
833
1,872
4.9%
Table 7
Total Increases in Income Payments to
Colorado Households
(millions of 1970 dollars)
Shale Oil UG Coal Strip Coal Total
UMS Basin
Green Basin
Statewide
% 1970
64
72
136
1.7%
24
-
27
0.3%
--
3.9
3.9
0.05%
88
76
167
2.1%
Table 8
Total Increases in Employment
Shale Oil UG Coal Strip Coal
Total
6,480
7,525
16,670
2.0%
4,326
- 1,206
4,964 1,300
0.6% 0.2%
10,806
8,731
22,934
2.7%
UMS Basin
Green Basin
Statewide
% 1970
Table 9
UMS Increases in Annual Consumptive Use
and Salt Loadings
Shale Oil New UG Coal Both
Increased consumptive
use (AF/yr) 31,320 348 31,668
Increased salt
loading (ton/yr) 3,444 132 3,576
Table 10
White River Increases in Annual Consumptive
Use and Salt Loadings
Shale Oil
Increased consumptive use (AF/yr) 34,164
Table 11
Yampa River Increases in Annual
Consumptive Use and Salt Loadings
Coal &
New Strip Coal Spillovers*
Increased consumptive
use (AF/yr) 8,148 8,520
Increased salt loading
(tons/yr) 2,172 3,204
*Economic spillovers from shale oil development in
White River Basin.
(a)
58
Increased salt loading (tons/yr)
5,568
(b)
Figure 1. Longterm Average tsopletB. Maps for Rio
Blanco (c-a Tract) (50,000 bbl/day) for S02
and NO ; 250,000 s-erles map, contour inter-
vals 2:xand 10 meg/cubic -meter, respectively.
250.
-------
References
1. Baumol, William J., Economic Theory and Operations
Analysis, Prentice-Hall, Englewood Cliffs, N.J.,
1972.
2. Miernyk, William H., The Elements of_ Input-Output
Analysis. Random House, New York, 1965.
3. Gray, S. L. , J. R. McKean, and D. D. Rohdy,
"Estimating the Impact of Higher Education from
Input-Output Models: A Case Study," Rocky
Mountain Social Science Journal, V. 12, No. 1,
January 1975.
4. Udis, B. , C. W. Howe, and J. F. Kreider, The
Interrelationship of Economic Development and
Environmental Quality in the Upper Colorado
River Basin, National Technical Information
Service Accession No. COM-73-11970, Springfield,
Va., 1974.
5. Udis, Bernard et^ al^, "An Interindustry Analysis
of the Colorado River Basin in 1960 with
Projections to 1980 and 2010, Appendix, Part II",
June 1968. Prepared under Contract No. WA 67-4
with Federal Water Pollution Control Adminis-
tration, U. S. Department of Interior, June 1968
(unpublished).
6. Colorado, Office of the Governor, Oil Shale Plan-
ning and Coordination, IMPACT: An Assessment
of the Impact of Oil Shale Development —
Colorado Planning and Management Region 11.
Vol. I_, Executive Summary, December 1974.
7. Colorado, Legislative Council, Committee on Oil
Shale. Coal, and Related Minerals: Report to
the Governor and the Colorado General Assembly,
Leg. Co. Research Publication No. 208,
December 1974.
8. Colorado West Area Council of Governments, Oil
Shale and the Future of a_ Region — A Summary
Report. September 1974.
9. U. S. Federal Energy Administration, Project Inde-
pendence Blueprint Final Task Force Report:
Potential Future Role of Oil Shale, Prospects
and Constraints, Interagency Task Force on Oil
Shale, Department of Interior, November 1974.
10. Sladek, Thomas A., "Recent Trends in Oil Shale,
Parts 1 and 2," Mineral Industries Bulletin,
Colorado School of Mines Research Institute,
November 1974 January 1975.
11. Just, J. , B. Borko, W. Parker, and A. Ashmore,
New Energy Technology Coefficients and Dynamic
Energy Models, Vol. 1, The Mitre Corp.,
January 1975.
12. Colony Development Corporation, An Environmental
Impact Analysis for a. Shale Oil Complex At
Parachute Creek. Colorado, 3 Vols., 1974.
13. Federal Energy Administration, Project Indepen-
dence — Potential Future Roles of Oil Shale,
USGPO No. 4118-00016, Washington, D. C. 1974.
251
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CSMP CONCEPT AND APPLICATIONS TO
ENVIRONMENTAL MODELING AND SIMULATION
Grace Chang and C. Lindsay Wang
Systems Architects, Inc.
Arlington, Virginia
ABSTRACT
The Continuous System Modeling Program (CSMP) is a
continuous system simulation language that allows
models to be prepared directly and simply from
either a block diagram representation or a set of
differential equations. A CSMP program is
constructed from three types of statements:
Structure Statements which define the model, Data
Statements which assign numerical values to
parameters, constraints and initial conditions, and
Control Statements which specify the execution and
report generation options. CSMP accepts most
FORTRAN statements to supply the user with logic
and algebraic capability. Computer graphics and
interactive execution capabilities are also
available in CSMP.
In this paper, the fundamental concepts of CSMP
that are related to environmental modeling and
simulation are summarized. Procedures for applying
the concept to environmental models are described.
Sample cases for environmental problems are
presented.
CSMP OVERVIEW
Continuous System Modeling Program III (CSMP III)
is an IBM program product which aids development
and execution of simulation models for continuously
changing systems. Tt. is written in FORTRAN TV
language and ASSEMBLER language, and has been
installed at many IBM 360/370 facilities.
CSMP III is a continuous system simulation
language (CSSL) that allows the digital simulation
of continuous processes on large-scale digital
machine.
The program provides an application-oriented
language which permits models to be prepared
directly and simply from either a block diagram
representation or a set of ordinary differential
equations. It includes a basic set of functional
blocks (also called functions) which can represent
the components of a continuous system and accepts
application-oriented statements defining the
connections between these functional blocks.
A CSMP III program is constructed from three types
of statements:
Structure Statements which define the model.
They consist of FORTRAN statements and functions,
and functional blocks (also called functions)
designed for CSMP.
Data Statements which assign numerical values to
parameters, constants and initial conditions.
Control Statements which specify options for the
execution of the program and the choice of output.
It accepts FORTRAN statements, thus supplying the
user with logical and algebraic capability. Hence
the user can readily handle complex nonlinear and
time-variant problems.
This program is specifically designed to satisfy
the needs of scientists and engineers, who wish to
simulate physical phenomenon without having to
spend time and resources learning the intricacies of
sophisticated computer programming.
Applications in which CSMP III can be used include
studies of nuclear reactors, control system design,
parameter estimation, studies of blood circulation
and other physiological processes, studies of
chemical refineries, natural gas transmission,
process control, investigation of aircraft landing
and take-off, plant growth, natural resources
management, simulation of corporate financial
policies and industrial dynamics.
CSMP III has the following basic functional
capabilities:
• Powerful Standard Functions The CSMP III
language contains 42 powerful simulation
functions for performing such operations as
integration, differentiation, signal and
function generation, Laplace transformation,
switching and logical operations.
• Capability to Develop Additional Functions
By combining standard CSMP III functions and/or
FORTRAN statements, the user may build larger,
more powerful functions specifically suited to
his particular field of study. These functions
become part of his CSMP III language and they
may be used in a manner identical to the
252
-------
standard CSMP III functions.
pen at the appropriate point on the curve.
• Extensive Function Generation Capability The
user may incorporate arbitrary or experimental
data into his model. Such data may be the
function of one or two variables. Interpolation
between data points is handled automatically,
including interpolation of functions of two
variables.
• Powerful Array-Handling Capability The
storage, manipulation, and printing of arrays is
easily performed. Integrator arrays are also
easily specified and handled.
• FORTRAN-Based System FORTRAN statements can be
intermixed (with a few minor exceptions) with
CSMP III statements, thereby placing the logic
and algebraic capability of the FORTRAN
language at the user's disposal.
• Extensive Library Facilities The library
facilities of CSMP III allow the user to
develop and maintain libraries of functions,
sub-models, arbitrary or experimental data,
tables, and complete models.
• Wide Selection of Integration Algorithms The
user has a wide range of integration algorithms
from which to choose both single and double
precision; fixed and variable step, including
one specifically designed for "stiff" equations.
• Numerous Output Options The values of one
through 55 selected variables may be printed
during the simulation run.
t Improved Coding and Debugging Aids The CSMP III
language including FORTRAN when used in
conjunction with CSMP III is free-form.
Extensive debugging aids are available to the
user to check out his CSMP III and his FORTRAN
coding.
• Flexible Installation CSMP III may be tailored
to the user's particular hardware configuation.
The CSMP III graphic feature provides the
following capabilities:
• Interactive Interrogation of Results Using the
graphic device (such as IBM 2250 graphic display
terminal), the user may quickly display and
analyze the results of the simulation run and
select those variables which are to be printed
or print-plotted for later reference and
evaluation.
One to four grids may be simultaneously displayed,
with one to four variables plotted per grid.
Graphic plots to logarithmic scales are readily
available.
The value of a plotted variable may be obtained
merely by touching the display with the light
• On-Line Reference Manual Whenever the user is
in doubt about the user of a CSMP III statement,
he can immediately obtain a graphical display
of instructional messages relating to rules and
proper usage.
• Interactive Simulation Run Control By
dynamically displaying selected variables
during a simulation run, the user can monitor
the simulation and interrupt the run at will to
change the model, model data, execution
specifications or to vary the display itself.
• Interactive Model Development With its highly
versatile set of editing features, Graphic
CSMP III makes it easy for the user to develop
simulation models, completely "on-line".
With merely a few touches of the light pen, the
user may store and retrieve data, sub-models,
or entire models using the CSMP III library.
This assures continuity of model development
and helps the individual user to quickly
incorporate commonly used sub-models and data
into his model.
CSMP OPERATION OVERVIEW
CSMP III uses five phases, in the following order,
to build and execute a CSMP III model: Input
Processor, Translator, FORTRAN, Linkage Editor,
and Execution.
1. The Input Processor phase reads the next
CSMP III model from the Input file, accesses
and retrieves any data referenced in the
symbolic library by INCLUDE statements, and
builds the input for the Translator phase.
2. The Translator phase analyzes the CSMP III
statements from the Translator input file and
builds two separate files: a FORTRAN input
file containing FORTRAN subprograms representing
the logic of the CSMP III model's structure,
and an Execution input file containing the
CSMP III data and execution control statements.
3. The FORTRAN phase converts the FORTRAN
subprograms from the Translator phase to a
machine-language object module.
4. The Linkage Editor phase combines the machine-
language object module produced by the FORTRAN
phase with the precompiled CSMP III load
module library (for integration, plotting, etc.)
to produce the Execution phase load module.
5. The Execution phase (built by the Linkage
Editor phase) first interprets the data and
execution control statements from the
Translator phase for the next run and then
proceeds to execute that simulation run,
storing simulation results on the Prepare
253
-------
data set when required. This is repeated until
all the execution runs have been exhausted.
Print documents are generated during each exe-
cution run, while output documents are
generated at the end of each execution case.
STRUCTURE OF THE MODEL
The CSMP formulation of a model is divided into
three segments INITIAL, DYNAMIC and TERMINAL
that describe, respectively, the computations to be
performed before, during and after each solution.
INITIAL Segment which is intended exclusively
for the computation of initial condition values
and those parameters that the user prefers to
express in terms of the more basic parameters.
This segment is optional.
DYNAMIC Segment which is the most extensive in
the model. It contains the complete description
of the systems dynamics, together with any other
computations required during the solution of the
system. The structure statements within this
segment are generally a mixture of CSMP and
FORTRAN statements.
The DYNAMIC segment is required. This segment
may be declared explicitly by a DYNAMIC statement
or implicitly by the absence of INITIAL, DYNAMIC,
or TERMINAL statements.
TERMINAL Segment which is used for these
computations required at the end of the run, after
completion of the solution. This segment is
optional.
These segments represent the highest level of the
structure hierarchy. Each of the segments may
include one or more sections which represent
rational groupings of the structure statements
and may be processed as either paralleled or
procedural entities.
SEGMENT
INITIAL /
DYNAMIC A
TERMINAL \
. SECTION «^
/
SECTION -^
X.
\
\ SECTION ^
SORT ^
NOSORT
STATEMENTS
•^ STATEMENTS
-^ STATEMENTS
STATEMENTS
-"""' STATEMENTS
-\ STATEMENTS
STATEMENTS
r±T STATEMENTS
"\ STATEMENTS
Structure of the CSMP TV Model
These sections contain the structure statements
that specify model dynamics and associated
computations.
ELEMENTS OF THE CSMP III
The basic elements in the preparation of CSMP
statements are:
1. NUMERICAL CONSTANTS which are unchanging
quantities specified in numeric form in
the input statements.
2. SYMBOLIC NAMES which represent quantities
that may either change during a run or be
changed by the program between successive runs
of the same model structure.
3. OPERATORS which are used instead of
functional blocks to indicate basic arithema-
tical functions or relationships. As in
FORTRAN, these operators are +, -, *, /, **,
+ and ( ).
4. FUNCTIONAL BLOCKS which are used for more
complex mathematical operations, such as:
integration, time delay, quantization and
limiting.
BLOCK REPRESENTATION
•*-*,
INPUTS
OUTPUTS
V Y2 ..... Yn
MATHEMATICAL EXPRESSION
. XL X2...XB)
EQUIVALENT CSMP III STATEMENT
Y1,Y2,....YM=DEVICE(P1,P2,...P5,X1,X2 ..... XN)
Example:
Y = 1NTERICIC,X)
which states the output, Y, is obtained by
integrating X, with Y at the starting time
is equal to 1C.
5, LABELS - which are the first word of CSMP
data and control statements that tell the
program the purpose of the statement. Some
254
-------
statements contain only the label, such as
INITIAL, NOSORT, and NEDMAC. Other contain a
label and appropriate data.
Example:
TIMER
DELT = 0.025
FINTIM = 100
which specifies the integration interval and the
"finish time" for a run.
PROBLEM DESCRIPTION
Oxygen balance studies of a polluted stream
usually result in one or more dissolved oxygen
profiles along the course of the stream. Dissolved
oxygen is a very commonly used water quality
criterion; it is an important general index of
quality albeit not all-pervasive.
Following is a general equation describing dissolved
oxygen relations in a stream receiving oxygen-
consuming waste:
— - -(K +
dt L
K )B +
*
R
CD
where
S = The rate of change of BOD [Biochemical
Oxygen Demand) with respect to time
B BOD present
R The rate of BOD addition due to runoff and
scour
K.= The rate constant for deoxygenation
K,= The rate constant for sedimentation
A related expression, using dissolved
oxygen deficit, D, rather than BOD, B is
the rollowing:
dD _ „
ar - Ki
K2D
A
(2)
where
dD _ The rate of change of dissolved
dT oxygen deficit with respect to time
D The existing oxygen deficit (the
difference between the saturation
concentration and the existing dissolved
oxygen concentration)
A The net rate of oxygen production due to
photosynthesis and respiration of phyto-
planton and/or waterweeds
K. = The rate constant for reaeration
Integrating these two equations, we get:
"t •
-------
0.XVGEN. BALANCE IN.. P.OLUJ.TfcD »AJE«S
K1
On the oxygen sag curve. C is dissolved oxgen (DO)
saturation; D is initial DO deficit; D is
critical DO deficit; C is critical DO level
MODEL DESCRIPTION
Figure 2 shows a complete listing of the CSMP III
statements for the sample problem.
The INCON and PARAMETER statements assign the
values of initial conditions and parameters.
K, = (0.26, 0.27) means that two simulation runs
will be made; each with a different K. value.
DYNAMIC card indicates the end of the initializa-
tion statements, and the beginning of the dynamic
portion of the simulation. The INTGRL function is
used to perform integration. TIMER FINTIM specifies
the finish time for terminating this simulation.
OUTDEL indicates the time interval of output
printing and plotting. PRINT statement presents
the variables which are printed during execution
of the run. TITLE allows the user to specify
the text of a heading to appear at the top of each
page of the print document. OUTPUT statement
lists the variables to be print-plotted after
completion of the case. LABEL specifies the text
of a heading appearing at the top of each page of
the print-plot document. PAGE MERGE indicates
that two curves, B and D, are to be merged on a
single output print-plot. The END and STOP
statements define the end of the model.
INCON
PARAMETER
PARAMETER
DYNAMIC
B0=5.2.
I = (0.26i0.27) .
AsO.,«Ji
00=6,9
K2aO.Hi
K3=0.36
OR=-(K1»K?)>B»R
On=KI»B-K2*D-A
8=INT6RU(BO.DB)
0 = I NTSR L_ ^ 10 D)
TIMER
PRINT
fl NT IMC 2 5._. Q U IDE. Lj 0 ,5
OBfDD.BiO
TITLE
OUTPUT
LABEL
OXYGEN BALANCE IN POLLUTED HATERS
8,0
PAGE
EttQ
VERGE
OXYGEN DEFICIT CURVE AND BOD CURVE
FIGURE 2 SAMPLE INPUT
RESULT
Figures 3, 4, 5 and 6 show the tabular printing
output and merged print-plotting output for the
run with a K-^ = 0.26 and 0.27 respectively. From
these outputs we can find the critical time is 3.0
and critical oxygen deficit is 7.0585 for 1C. = 0.26,
and the critical time is 4, critical oxygen deficit
is 7.1567 for K = 0.27, respectively.
,0
1.00000
1.50000
08
on
B _ -
-.12400 ,16300 5,2000
-.31096 ,10823 5. OL77 —
-.22809 6.B660E-02 4.8840
-.16729 1.0214E-02 4.7660
2.00000 -.12270
I, 50000 -«._9.9?3E-.02__
3.00000 -6.6004E-02
3,50000 -I.eiJiOE-.p.Z
4". 00000 -3.5506E-02
U. 50000 -2.6041t-0_2
5.00000
5.50000
6.00000
6.500JO
7.00000
7.50000
8.00000
8.5000.0
9.00000
9j50000
10.0000
lOjSOOO
1 1,0000
11.5000
12,0000
12.5000
13.0000
13.5000
14.0000
11.5000
15.0000
15,5000
16,0000
16,5000
17.0000
17.5000
18.0000
18.5000
19.0000
19,5000
20.0000
20,5000
21 .0000
21.5000
22.0000
22.5000
23.0000
23.5000
21.0000
21.5000
25.0000
-1.9099E-02
-1 ._4.009E.-02_ _
-1.0274E-02
-5.5265E-03
-4.0531E-OJ
-2.9716E-03
-2,I801E-03
-1 .5971E-03
•1.171 1E-03
•8.5831E-01
-6.2913E-01
-4.6158E-04
-3.3855E-04
•2.1700E-04
-1.8120E-04
•1.3256E-04
-9.6321E-05
-7.0572E-05
-5.1498E-05
-3.7193E-05
-2.7657E-05
-2.0027E-05
-1.4305E-05
-1.0490E-05
-7.6294E-06
-4.7684E-06
-2.8610E-06
-1.9073E-06
-9.5367E-07
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
J.9693E-02
5.S029E-03.
-4.5652E-03
-K6132Y-02
•J.9125E-02
• 2.0930F.-02
•2.2234E-02
-2.216IE-OE.
-2.1793E-02
-2.a2E7.EjJi
1.7140
4.661J
4.6226
1.5.9.12
1.5734
1.5169
1.J38.7
1.5327
"..52.83
4.5250
4.5227
-2.05J1E-02 4.5209
- .9756E-02. 4,5196
- .8935E-02 4.5187
- .8096E-02 4.5180
- .7254E-02
- .6424E-02
- .5614E-02
• .4B2BE-02
- .4072E-02
- .3346E-02
- .2652E-02
- .1989E-02
- .13S8E-02
• .0757E-02
-1.01BBE-02
-9.6464E-03
-9.I328E-03
-8.6468t-03
-B.1859E-03
-7.74S7t-03
-7.3348E-03
-6,_9431E-03
-6.57I5E-03
-6.2206E-03
-5.8876E-03
-5.5724E-03
-5.274PE-03
-4.9919t-03
-4.7217E-03
-1.471BE-03
-4.2324E-03
• 4.0058I--03
-3.79HE-03
-3.5884E-03
-3.39631-03
4.5175
4.5171
4.5169
4.5(67
4.5165
1.5163
4.5163
4.5162
4.5162
4.5162
1.5162
4.5162
4.5162
1.5161
1.5161
1.5161
' 1.5161
4.5161
4.5161
4.5161
. .".516 1_
4.5161
. ".5161 .
4,5161
4.5161
4.5161
4.5161
4.5161
4.5161
4.5161
6,9000
6.9671
7.0107
7.0376
7.0523
7.0564.
7.0585
1.0.5.41.
7.0474
7.0385
7.0285
7.0177.
7.0067
6.9956
6.9846
6.9738
6.9634
6.9533.
6.9436
6.9344
6.9255
6.9171
6.9091
6.9015
6.8943
6.8871
6.8809
6.8748
6.6689
6.8634
6.R56?
6.6532
6.8465
6.8441
6.8398
6.6359_
6.8321
6.8285
6.8251
6.6P19
6.6189
6,8161
6.8133
6,6)06
6.6083
6.8060
6.6039
6.6016
6.7999
6.7960
6.7963
FIGURE 3 TABULAR PRINTING OUTPUT
0.26)
REFERENCES
1. CSMP III Program Reference Manual (SH19-7001-2)
IBM Corporation (1972)'
2. CSMP III and Graphic Feature General Information
(GH19-7000-1), IBM Corporation fl97iy
3, CSMP III Operations Guide (SH19-7002-1) , IBM
Corporation (1972)
4. CSMP III Graphic Feature Program Reference
Manual (SH19-7005~1) . IBM Corporation (1972)
S, CSMP III Graphic Feature Operations Guide
(SH19- 7004-1) IBM Corporation CLdT^
6. Gordon, Geoffrey, "System Simulation,"
Prentice-Hall, Inc. (1969)
7. Leonard, Caiccio, Water and Water Pollution
Handbook, Volume 1, Marcel Dekker, Inc., New
York (1971)
8. Thomas R. Camp, Water and Its Impurities, Reinhold
Publishing Corporation, (1963)
256
-------
Kl
.26000
TIME
.0
.50000
l.onoo
1 ,5000
2.0000
2,5000
3.0000
3.5000
1,0000
1,5000
5.0000
5.5000
6.0000
6.5000
7,0000
7,5000
6.0000
8.5000
9,0000
9.5000
10.000
10.500
11,000
11.500
12,000
12.500
13.000
13.500
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11.500
15,000
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5.2000
5.0177
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1.7860
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1.6226
1,5912
1.5731
1.5581
1.5169
1.5387
1.5327
1.5283
1,5250
1,5227
1.5209
1.5196
1.5187
1.5160
1.51 75
1.5171
1.5169
1,5167
1.5165
1.5161
1.5163
1.5163
1.5162
1.5162
1,5162
1.5162
1,5162
1.5162
1.5161
1.5161
1.5161
1,5161
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257
-------
0)
-------
GASP IV CONCEPTS APPLICABLE TO ENVIRONMENTAL MODELING AND SIMULATION
A. Alan B. Pritsker
Purdue University and Pritsker & Associates, Inc.
Lafayette, Indiana
Abstract
Environmental modeling and simulation involves the
characterization of a system in order to determine the
dynamic performance of the system over a specified
period of time. To obtain this dynamic portrayal of
the system variables, it is necessary to identify and
model the state variables of the system and the points
in time at which logical decisions are made to change
the status of the system. There has been a growing
trend to model systems that involve continuous variables
with discrete events superimposed in order to alter the
behavior of the system status. This paper presents the
fundamental concepts of the GASP IV simulation language
that are used to obtain combined simulations. Speci-
fically the paper includes definitions and explanations
of the following basic simulation concepts : system
status representation; time-events and state-events;
time advance procedures; and data collection and
analysis. Two exaoples of combined models are pre-
sented that illustrate the concepts as applied to en-
vironmental modeling and simulation:
1) Simulation of electroplating operations to evalu-
ate different operating procedures and control
policies regarding metal flow and concentration
levels; and
2) A model of an urban area with discrete events
superimposed.
This paper presents new modeling and simulation
concepts that are useful for resolving environmental
problems.
Description of GASP IV 8.9.10,17
GASP IV is a FORTRAN based simulation language
that can be used for discrete, continuous, or combined
simulation.* The interactions between discretely and
continuously changing variables are easily modeled in
GASP IV. Extensive use and applications have been
made of GASP IV.
In GASP IV a system is modeled in two dimensions,
the time dimension and the state-space dimension.
These dimensions are further decomposed into manageable
elements. In the time dimension this involves the de-
fining of events and the potential changes to the
system when an event occurs. The user must specify the
causal mechanisms by which events can occur. GASP IV,
however, sequences these events in simular time. Thus,
the user must define only the mathematical-logical re-
lations that transpire at an event occurrence, and he
is not required to model the timing of the events
during the simulation.
In the state-space dimension the system is decom-
posed into its entities which are described by attri-
butes. The attributes are further classified as dis-
crete or continuous. The value of a discrete attribute
remains constant between event times. The value of a
continuous attribute, hereafter referred to as a state
variable, may change between event times according to a
prescribed dynamic behavior. Special storage arrays
are provided by GASP IV for storing values of state
* GASP PL/I is a PL/I version of GASP IV.
11
variables and, if required, their derivatives and im-
mediate past values.
A dynamic simulation is then obtained by modeling
the events of the system and by advancing time from one
event to the next. Events usually cause changes in the
status of the system or in the equations defining the
state variables of the system. However, change, either
discrete or continuous, need not occur at an event time.
Events could occur at decision points where the decision
is not to change the status of the system. Conversely,
the system status may change continuously without an
event occurring as long as these status changes have
been prescribed in a well-defined manner.
Those events that occur at a specified projected
point in time are referred to as time-events. They are
commonly thought of in conjunction with next-event sim-
ulation. Those events that occur when the system
reaches a particular state are called state-events.
Unlike time-events, they are not scheduled in the
future but occur when state variables meet prescribed
conditions. In GASP IV, state-events can initiate
time-events and time-events can initiate state-events.
The behavior of a system model is simulated by
computing the values of the state variables at small
time steps and by computing the values of the attributes
at event times. The time step increment is automatical-
ly determined by GASP IV based on the equation form for
the state variables, the time of the next event, and
accuracy and output requirements.
When an event occurs, it can change the system's
status in three ways: it can alter the value of state
variables or the attributes of the entities; it can
alter the relationships that exist among entities or
state variables; or it can change the number of enti-
ties present. Any of these changes can result from the
occurrence of an event. Between event times, only the
values of the state variables can change and such
changes must be in accordance with prescribed equations.
At each time step, the state variables are evalu-
ated to determine if the conditions prescribing a.
state-event have occurred. If a state-event was passed,
the step size was too large and is reduced. If a
state-event occurs, the model status is updated accord-
ing to the user's state-event subroutines. Step size
is automatically set so that no time-event will occur
within a step. This is accomplished by setting the
step size so that the time-event ends the step.
Since time-events are scheduled happenings, certain
attributes are associated with them. At the minimum, a
time-event must have attributes that define its time of
occurrence and its type.
In addition to the just described functions of pro-
viding automatic time advance, event scheduling and con-
trol, continuous variable integration with variable step
size and user specified accuracy requirements, and
discrete-continuous interaction procedures; GASP IV also
provides subprograms that accomplish statistical data
collection, random deviate generation, program monitoring
259
-------
and error reporting, information storage and retrieval,
automatic statistical computation and reporting, stan-
dardized simulation reports, tabular and plotted
histograms, automatic plotting routine, and built-in
flexibility in output reports and other provided func-
tions. Table 1 presents a list of the GASP IV subpro-
grams and user-written subprograms that are used to
accomplish these functional capabilities.
Table 1. Categorization of GASP IV and User-Written
Subprograms According to Functional Capability
Function
GASP IV Provided
User-written*
Time advance
and status
update
GASP
Initialization DATIN, CLEAR, SET
Data storage FILEM, RMOVE, CANCL,
and retrieval COPY, NPRED, NSUCR,
NFIND
Location of KROSS
state-events
STATE, SCOND,
EVNTS, and
specific event
subprograms
Main program,
INTLC
Monitoring
of system
simulation
Error reporting
Data collection
and reporting
Miscellaneous
support
Random deviate
generation
MONTR
ERROR
COLCT, TIMST, TIMSA,
HISTO, GPLOT, PRKTQ,
PRNTS, SUMRY
SUMQ, PRODQ, GTABL,
GDLAY
DRAND, UNFRM, TRIAG,
RNORM, ERLNG, GAMA,
BETA, NPSSN, EXPON,
WEIBL, DPROB, RLOGN
UMONT
UERR
SSAVE, OTPUT
* Only those subprograms required by a specific appli-
cation need be provided by the user.
Through the use of these subprograms, a GASP IV
simulation model is developed. The model includes a
set of event programs or state variable equations or
both that describe the system's stochastic/dynamic be-
havior; lists and matrices that store information; an
executive routine that directs the flow of information
and control within the model; and various support
routines.
GASP IV concepts provide a view of the world that
simplifies model building. These concepts facilitate
the representation of the relevant aspects of system
behavior. As a programming language, GASP IV gives the
computer programmer a set of FORTRAN subprograms de-
signed to carry out the most important functions in
simulation programming. Modeling concepts are trans-
lated by GASP IV into FORTRAN routines that can be
easily used. GASP IV provides the link between the
modeling and programming activities that is so important
to a successful simulation study, as well as providing
a common basis for modeling diverse systems and a well-
developed framework which fosters communication between
simulation modelers.
In the following sections, two examples are given
that illustrate the combined modeling capabilities in-
herent in GASP IV as applied to environmental problems.
Simulation of Electroplating Operations 2»3>"Ml3.m
Cadmium is used in the electroplating industry to
provide iron and steel products with protection against
corrosion. A cadmium coating also provides an attrac-
tive appearance and good solderability. The discharge
of cadmium into the nation's waterways, however, poses
an environmental threat in that cadmium has been associ-
ated with several chronic and acute effects in man and
other species even when present in only trace amounts.
The barrel plating line simulated in this paper is
represented in Figure 1. Parts to be plated are placed
in large perforated barrels. Using an overhead crane,
an operator lowers a barrel into the plating bath. The
parts in the barrel become the cathode and attract cad-
mium ions from cadmium anodes which are periodically
replenished by the plater. The electrolyte is composed
of sodium cadmium-cyanide, excess sodium cyanide, and
sodium hydroxide plus additional agents and brighteners.
After a specified time, the barrel is lifted out of the
bath. The parts in the barrel retain a certain volume
of bath liquid at the very high cadmium concentration
of the bath. This is called dragout volume and dragout
concentration. The barrel is then immersed in a running
rinse. Running rinses are supplied with fresh water at
the bottom of the tank and empty via the overflow at
the top of the tank. The dipping of a barrel causes an
increase in the rinse concentration while the flowing
water decreases this concentration. The next rinse is
an acid bath designed to brighten plated parts with an
Barrel
Barrel + Dragout
Barrel + Dragout
PLATING BATH
RUNNING RINSE
Effluent
Stream
Barrel + Dragout
ACID i RINSE
Barrel + Dragout
RUNNING RINSE
Fresh
Water
Dumped
Monthly
Effluent
Stream
Fresh
Water
Figure 1. A Barrel Plating Line.
260
-------
attractive finish. The final rinse is another running
rinse. The barrels are then emptied, washed and reused.
The discharge of cadmium is due to the continuous ef-
fluent flow from the running rinses and the periodic
dumping of the acid rinse.
The process is modeled in terms of the events at
which cadmium concentrations or equations describing
these concentrations can be altered in the various
parts of the process.
The insertion and removal of barrels in the rinse
tanks and the dumping of tank contents are the time-
events of the process. Each barrel has attributes as-
sociated with it that characterize the type of parts in
the barrel, the dragout volume in the barrel, the con-
centration of this dragout volume, and codes denoting
the next processing point (next event type) for the
barrel and the time of occurrence of this event. When
a barrel is placed in a running rinse, it causes a
surge of effluent equal to the displacement of the
barrel. The effluent due to the surge is assumed to
have the current cadmium concentration of the rinse and
occurs Instantaneously. The barrel then Immediately
causes an Increase in rinse concentration dependent
upon the current amount of cadmium in the rinse, the
volume of the rinse, and the volume and concentration
of the dragout in the barrel.
The barrel stays in the rinse until it is scheduled
to be withdrawn. During this stay in the rinse, the
concentration of the rinse decreases due to the fresh
water supply. Immediately after withdrawal, the tank
begins to refill, and the concentration decreases in «
different manner than when the barrel was in the tank.
This is because fresh water is entering the tank but no
effluent is leaving. When the tank is completely re-
filled, the effluent again starts pouring from the tank.
Other tanks of the system are modeled in a similar
fashion.
In Figure 2, a plot for one of the simulation runs
of the GASP IV model of the electroplating line is pre-
sented. Time, in three minute intervals, is plotted on
the independent axis. Cadmium concentration, in parts
per million, and also cadmium amounts in ounces are
represented on the dependent axis. The symbol 1 repre-
senting cadmium concentration in rinse tank 1 has a
sawtooth behavior pattern. Increases in this variable
are the result of barrel inserts into the tank. The
die-away curves following the increases are the result
of fresh water diluting the concentration as it enters
the tank. The total process effluent is plotted using
the symbol 9. As expected, the plot shows a continual
Increase in cadmium released as the process continues.
Figure 3 shows a statistical summary of dragout volume
observations made during the simulation. A histogram
!• COM 1
I- COUC »
I* CONS 1
•-TOTAL ff
oo os ti ti n
curlicues
ii 11
Figure 2. Plot of State Variables for Plating Line Simulation.
5I»*ut»TtON •I*OJ*CT
OATS z/ «/ ivi
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Figure 3. Statistical Summary for Plating Line Simulation.
261
-------
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Figure A. Histogram of Peak Cadmium Concentration of Rinse 1.
of interest to the modeler and not currently available
from direct measuring procedures used is shown in
Figure 4. It represents observations on peak concen-
tration values (occurring immediately after a barrel
insertion) of rinse concentration of rinse 1.
An interesting feature of this model is the trade-
off between production rate and amount of pollution in
the effluent. One way to decrease the amount of cadmium
in the effluent is to decrease the amount of cadmium in
the dragout from the plating bath. This can be accom-
plished by decreasing the process flow by requiring a
dwell time over the plating bath. Simulation runs were
made to evaluate the tradeoffs between the increased
cost due to production slow down as a basis for meeting
EPA standards on cadmium concentrations in the effluent.
GASP IV Model of Cadmium Flow in an Urban Area 15
In this example, the sixty square mile region of
extreme northwestern Indiana which includes the cities
of Gary and East Chicago was modeled. There are several
hundred sources of cadmium emissions in the region which
can be to either air or water or both. The impact of
each source on the various ecosystems in the region is
unclear. Questions that were raised and for which the
model was designed are: 1) what are the flow patterns
and characteristics of cadmium in the urban area under
study?; 2) what are the levels of cadmium on urban
structures?; and 3) what control policies may be useful
in meeting pollution standards?
The major compartments for one portion of the
model developed are shown in Figure 5. In this flow-
chart, the rectangles represent compartments (or levels
in systems dynamics terminology), the circles represent
generation rates, and the lines between circles and/or
rectangles represent transfers. Equations relating the
compartments to one another were developed, and these
were used to define the state variables for the system.
Source emission data was used in order to obtain the
input components for the model. The inputs along with
the equations for the state variables constitutes the
continuous portion of the model. Superimposed on this
continuous model are rainfall events which wash down
the urban structures and provide inputs of cadmium to
Sediment
1
Water Out
Sludge
Figure 5. Major Compartments for Urban Submodel.
262
-------
the municipal plant. These discrete events are sign!- 12. Schooley, R. W., "Simulation in the Design of a
fleant in that they can cause overflow conditions to Corn Syrup Refinery," 1975 Winter Computer
occur at the municipal plant. Such overflow conditions Simulation Conference, December 18-19, 1975,
occurring at the time when cadmium and other particulate Sacramento, California.
matter is washed from the urban structures could be a
significant component to the levels of pollution in the 13. Sigal, C. E., "Designing a Production System with
waterways to which the overflow is directed. Environmental Considerations," Proceedings of the
AIIE Fall Institute Conference. New York, 1973.
The time behavior for each level of each compart-
ment was obtained during the simulation. In addition, 14. Sigal, C. E., "Modeling Cadmium Discharge from an
the peak values for particulate matter on the urban Electroplating Line with the GASP IV Simulation
structures was collected along with the percent of time Language," Proceedings of the First Annual NSF
that the municipal plant was bypassed and the amount of Trace Contaminants Conference, Oak Ridge National
pollution in the effluent that was bypassed. Sensltivi- Laboratory, pp. 89-107.
ty studies were performed for assessing the different
rates of increase (or decrease) of total emissions and 15. Talavage, J., and M. Triplett, "GASP IV Urban
their effects on the levels of the state variables Model of Cadmium Flow," Simulation, Vol. 23, No. 4
describing the system. Results from this study have (October 1974), pp. 101-108.
been published previously.15
16. Wong, G., "A Computer System Simulation with
Summary GASP IV," 1975 Winter Computer Simulation Con-
ference, December 18-19, 1975, Sacramento,
The basic concepts of combined simulation inherent California.
in the GASP IV simulation language have been presented.
The interaction between state variables, time-events, 17. Wortman, D. B., "The Anatomy of GASP IV,"
and state-events has been demonstrated through examples. Slmuletter, Vol. 6, No. 1 (October 1974), pp. 60-
The two examples presented in this paper illustrate the 64.
types of environmental systems that can be studied and
analyzed using GASP IV.
References
1. Fishman, G. S., Concepts and Methods in Discrete
Event Digital Simulation, New York: John Wiley &
Sons, Inc., 1973.
2. Grant, F. H., and A. A. B. Pritsker, "Models of
Cadmium Electroplating Processes," NSF(RANN) Grant
No. GI-35106, Purdue University, December 1974.
3. Grant, F. H., and A. A. B. Pritsker, "User's
Manual for the Electroplating Simulation Program
(ESP)," NSF(RANN) Grant No. GI-35106, Purdue
University, December 1974.
4. Grant, F. H., and A. A. B. Pritsker, "Technical
Description of the Electroplating Simulation
Program (ESP),", NSF(RANN) Grant GI-35106, Purdue
University, December 1974.
5. Green, R., "AN-PTC-39 Circuit Switch Simulation,"
1975 Winter Computer Simulation Conference,
December 18-19, 1975, Sacramento, California.
6. Mihram, G. A., Simulation: Statistical Foundations
and Methodology, New York: Academic Press, 1971.
7. Nagy, E. A., "Intermodal Transshipment Facility
Simulation: A Case Study," 1975 Winter Computer
Simulation Conference, December 18-19, 1975,
Sacramento, California.
8. Pritsker, A. A. B., The GASP IV Simulation Language,
New York: John Wiley & Sons, Inc., 1974.
9. Pritsker, A. A. B., "Three Simulation Approaches to
Queueing Studies Using GASP IV," Computers &
Industrial Engineering, Vol. 1, No. 1, 1976.
10. Pritsker, A. A. B., "GASP IV Simulation for
Scientists of Systems," Proceedings of the Annual
Meeting of the Society for General Systems
Research, January 27-30, 1975, New York.
11. Pritsker, A. A. B., and R. E. Young, Simulation
With GASP PL/I, New York: John Wiley & Sons, Inc.,
1975.
263
-------
RADIONUCLIDE REMOVAL BY THE pH ADJUSTMENT OF PHOSPHATE MILL EFFLUENT WATER
David L. Norwood and Jon A. Broadway
Eastern Environmental Radiation Facility
Montgomery, Alabama 36109
Abstract
Application of the GASP IV simulation system to
the waste water treatment process in a phosphate ore
milling industry has been presented. Specific
attention has been directed to a quantitative evalua-
tion of precipitation of radionuclides due to the
liming treatment (pH adjustment) used in a wet process
plant and the residual radionuclides in effluent water.
The variation in output radionuclide concentrations
was studied as a function of important system parame-
ters such as flow rate, liming rate, and pH. Extension
of this modeling capability to other large industrial
applications has been discussed and implications for
further study have been indicated.
Introduction
A study of effluents from the phosphate mining
and milling industry in Florida has been underway since
1974 by the Eastern Environmental Radiation Facility
(EERF) in Montgomery, Alabama. One goal of this study
has been to develop a simulation of the liming process
used to treat waste water before its discharge into
the environment. This liming treatment is used to
adjust the pH of the waste water for the removal of
flouride and phosphorous. It was shown by the EERF
that radionuclides are also removed by this process.
Results from further field work which will pro-
vide information on the parameters important in the
radionuclide removal process will be incorporated into
the model presented in this report. The objective of
this study is to establish a computer model which will
be helpful in estimating the radionuclides, flouride,
and phosphorous which will be present in phosphate
industry effluents.
Field measurements made during 1974 produced data
99 ft
which indicate that the liming process reduces Ra
concentrations over a range of 95% to greater than 997«.
The data used in this report were collected at an
operating wet process phosphoric acid plant in central
Florida. An effort was made,,however, to see that the
model presented here is sufficiently general that it
could easily*be adapted to other plants which also use
the liming method of pH adjustment. The parameters
which characterize this model are all defined in one
subroutine, which sets all initial conditions, or are
set up as input values to the model.
Overview of the Effluent Treatment
The wet processing of phosphate ore involves the
addition of sulfuric acid to the phosphate ore to
produce gypsum and phosphoric acid. The gypsum is
removed from the process water by allowing it to settle
out. The process water is retained in a lake for con-
tinued sedimentation and reuse in the plant. Due to
rainfall into this lake it is sometimes necessary to
release some process water to the general environment.
Prior to this release, the process water is routed
,through a series of ponds where it is treated with a
lime slurry to effect pH adjustment. These ponds also
allow for settling out of solids precipitated when the
pH is raised. Both the raising of pH and adequate
settling time are necessary for effective removal of
flourides, phosphorous and radioactivity.
plant in central Florida. This process consists of
adding lime to the process water as it enters the
system of ponds. The process water contained in the
holdup pond is typically at pH of 1.5 3.0 before
the liming treatment begins. For the purpose of the
modeling process contained in this paper, the process
water was assumed to be a pH of approximately 2.5 at
the start of the first liming stage. Contact with
the lime causes sedimentation and pH increase until
the second liming occurs. The second liming stage
starts at a pH of approximately 4.0 and continued con-
tact with the lime solution causes increased sedimen-
tation and the pH is increased to a. range of 7 to 10
at the point of release to the surface water system.
Laboratory Measurement of Sedimentation Rates
One portion of this study involved a series of
laboratory experiments to characterize the sedimenta-
996
tion rate of Ra from the process water treated by
the lime as a function of time for given values of
starting pH levels. The actual process water and
lime slurry as used by the phosphate plant were used
in the laboratory study.
A process water sample of six liters was stirred
continuously while lime was added to reach the pH
value for the sedimentation study. Lime addition was
stopped at a pH of 2.5 and a timer was then started
to measure sedimentation rates. Samples of the super-
nate were removed at t = 0, 5, 10, 100, and 400
9 9 ft
minutes for Ra analysis by the radon emanation
method as described in the American Public Health
Association's Methods for the Examination of Water
2
and Waste Water. A similar experiment was performed
for the second sedimentation process with a second
process water sample with adjustment of the solution
to an initial pH of 4.0, in order to approximate the
conditions at the start of the second liming step in
the industrial process. Measured concentrations of
9 9ft
Ra at the two initial pH levels are given in Table
1. Total Ra in this case is the sum of the
dissolved and undissolved
226
Ra.
226
Table 1
Ra Concentrations in Process Water After Liming as
Measured in Laboratory Experiment
Total Ra for
r\ r\ /•
Total Ra for
The treatment under consideration in this study
is the double liming process used at a wet process
Sedimentation
time after .„.
initial pH is initial pH - 2.5 initial pH = 4.0
obtained (min.^ (gCi/1) (gCi/1)
0 5.5 6.6
5 2.1 8.42
10 2.94 6.62
100 1.54 0.54
400 2.16 0.42
For a given pH we have assumed that the
retention rate of the radionuclides in the effluent
water after treatment is dependent solely on the time
spent in the liming ponds before release to the out-
side environment, and since the settling rate at any
time is proportional to the amount of radionuclides
present in the process water, we are led to an
equation of the form :
264
-------
where:
C = C e'
o
t = time
C = concentration at time t,
C = initial concentration,
and X = settling factor to be determined.
Using a stepwise Gauss-Newton iteration procedure
on the parameters X and C a non linear least square
curve of the form (1) was calculated. This was facili-
tated by running the BMD07R program from the Bio-Medical
Statistical package of programs developed by the UCLA
Health Sciences Computing Facility on an IBM 370 com-
puter operated by the Optimum Systems Incorporated, of
Bethesda, Maryland. This program was run once with
each of the two sets of data given in Table 1. The
complete results of the two runs are given in the
Appendix. For an initial pH of 2.5, the procedure pro-
duced a value of X = 0.0018, and for an initial pH of
4.0 the procedure produced a value of X= 0.020. Al-
though these two values need further refinement, they
do give a reasonable approximation of the results ob-
tained in actual field measurements. Further experi-
ments can be run with an assortment of pH values in an
effort to develop a single, reliable equation relating
the concentration at time t to both the pH and the time
spent in the liming ponds. When this final equation is
determined, the model will provide a simple mechanism
for estimating the effects of various combinations of
liming practices at the two liming points.
GASP IV
A decision to use GASP IV as the modeling
language was made because of its combined
discrete/continuous modeling capabilities and because
of the authors' familiarity with FORTRAN, the host
language of GASP IV. Actually, the initial system
presented here could have been modeled with a strictly
continuous language, but future embellishments will be
more easily implemented if we also have the discrete
event case available.
GASP IV is a combined discrete/continuous FORTRAN
based simulation language which comes to the user as a
set of FORTRAN subroutines . Because of its complex-
ity, it requires more effort to use successfully than
some of the other strictly discrete or strictly
continuous simulation languages, however, if a model
has both discrete and continuous components, then
GASP IV can be well worth the extra effort. The fact
that it is FORTRAN based simplifies the writing of
subroutines required to customize GASP IV for the
user's application and generally obviates the need to
learn another high level computer language. The user
has to provide subroutines (in FORTRAN) to process
and schedule events and to initialize his continuous
and non-GASP variables, and to allow for any addition-
al output and/or error messages which are desired but
not supplied by GASP itself.
The GASP Model
The basic model which is described in this report
is an attempt to simulate the flow of liquid effluents
from the process water pond through the liming ponds.
We assume that the initial liming occurs at the
entrance to the liming system, and that the second
liming occurs somewhere between entry into the system
and exit from it. For simplification, we have
initially made the assumption that the system we are
dealing with has reached equilibrium in the sense
that the volumetric flow rate of the effluents through
the system is essentially constant. As more precise
information about the topography of the liming ponds
is obtained we will easily be able to incorporate this
into the model, but for now, only small errors will
probably be induced by the assumption of constant
volumetric flow rate. We have also made the assump-
tion that the cross-section of the liming pond system
at any point is a segment of a circle. This does not
seem like an unreasonable assumption and it allows us
to calculate the cross-sectional area from other known
4
parameters.
In setting up the GASP model for the flow of the
effluents through the liming ponds it seemed that
distance traversed through the liming pond system
would be a more natural independent variable than
actual time spent in the liming pond system. Thus,
for purposes of this simulation the GASP variable
TNOW was used to represent the distance that the
effluent had traveled through the system. This is
one indication of the adaptibility of the GASP TV
simulation language. In fact, no inconsistencies at
all are introduced by using distance instead of time
as the independent variable. Thus, in addition to
TNOW, the GASP variables TTBEG, TTLAS, TTNEX and TTFIN
refer to distance from entry into the liming pond
system at initial liming, the last update point, the
projected next update point, and exit from the system,
respectively.
The state variables SS(1) and SS(2) are used to
denote the concentration at distance TNOW from entry
into the liming system, and the time, in minutes, that
it took to traverse the distance TNOW.
Other variables introduced into the program are
VF = Volumetric Flow Rate of the effluent through the
system (recall our assumption of a constant VF
throughout the system), TM = elapsed time from last
state event, DLIM2 = the distance from entry into the
system that the second liming occurs, and a few
variables which are used only in the user added
FUNCTION AREA which calculates the cross-sectional
area of the pond as a function of distance from entry
point.
For our purposes at EERF, we have modified the
original GASP IV software somewhat to achieve faster
throughput and turn around of our runs, at the expense
of storage for the rather large arrays which are pro-
vided with the stock version of GASP IV. A list of
the arrays which can be conveniently reduced in size
in this manner is provided on pages 77 and 80 of Dr.
Pritsker's book, The GASP IV Simulation Language.
Following is a brief discussion of each of the user
written subprograms used in this model. A block
diagram of their interrelationship to each other and
GASP IV is given in Figure 1.
Subroutine STATE
Subroutine STATE first calculates the time
increment since the last update of the concentration.
Since distance is the independent variable, DTNOW
gives us the distance traveled since the last update.
Thus, if we know the volumetric flow rate and the
average cross-sectional area of the ponds over that
distance we can easily calculate the time lapse, (TM)
by
TM = DTNOW*AREA(X)/VF (2)
where AREA(X) cross-sectional area at
distance X from initial liming
and TTLAS
-------
Function Area
The basic assumptions made in calculating the
cross-sectional area of the pond system is that the
cross-section is a segment of a circle. We are then
able to get the cross-sectional area if we can get
the chord of this segment of a circle and the
perpendicular distance from the chord to the arc of
the segment by using the law of cosines to get the
radius and applying the standard formula for area of
a segment of a circle.^ The chord is just the width
of the liming pond at that point and since the ponds
are kept dredged to a depth of about 7 feet, that
suffices as the other measurement.
Subroutine INTLC
The initial conditions subroutine is used to
input the initial values for the volumetric flow rate
(VF), distance at which the second liming occurs
(DLIM2), and the initial concentration (SS(1)), and
the initial time (SS(2)).
Subroutine SSAVE
This subroutine is used to tell the GASP IV
executive which variables (in this case distance,
TNOW, and time, SS(2)) are to be plotted by the GASP
IV provided plot routine.
Conclusions
Three simulations have been run at this time using
three different volumetric flow rates. The results of
3
using a typical low VF of 10.6 m /min, and "average"
3 3
VF of 16.0 m /min and a high VF of 38.9 m /min are
shown in Figure 2. From these three outputs the
effect of modifying the volumetric flow rate is
obvious. The higher the flow rate, the less time the
water spends in the liming system and consequently
the more radionuclldes that are released to the
environment. Obviously there is an optimal VF some-
where since a stagnant liming pond system (VF = 0) is
clearly not ideal. As more information is gathered
concerning the phosphate plant release to the process
water pond and their behavior in that pond, this model
can be used to determine the optimal VF.
This model is only a first step in the process of
simulation removal of radionuclides from the effluents
of a phosphate plant. However, with this basic model
and the discrete/continuous capabilities of GASP IV
more complex functions such as seasonal effects and
discrete lime addition can be included. Such refine-
ments will increase the model's effectiveness as a
tool in the evaluation of the release of radionuclides
into the environment from phosphate plants using the
liming procedure.
References
1. Guimond, R. J. and Windham, S. T., Radioactivity
Distribution in Phosphate Products, By-Products,
Effluents and Wastes, Technical Note, Environmental
Protection Agency, Office of Radiation Programs,
August 1975.
2. American Public Health Association, Methods for
the Examination of Water and Waste Water.
3. Pritsker, A. A. B., The GASP IV Simulation
Language, New York, John Wiley & Sons, 1974.
4. Standard Mathematical Tables, 14th Edition,
Chemical Rubber Company, 1964.
5. BMD Biomedical Computer Programs, University of
California Press, Berkeley, California, 1973.
lilitin il Sibpnirms li mill.
HQ —^-[T1 = SHkprifrm A cills $lkpri|ni I.
Sikttitlii tASP li tki SASP IV pr«»llil incitiii tiknitlii
111 Slkriltln DATIN Is tkl SASP IV rrllllll lltl ilMt tllcilllii
Fifirl I.
OUTPUT OF 6»SP SIMULATION
USINC V»mi)US VF FACTOKS
Actllll Fllltf
Hlliu ninllli
111 201 JM 4M500 110
Flfirt i. Olltlltl Fril Flrtt Llllll |llt|[l|
266
-------
APPENDIX
Ai. t
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23 *
24.
23.
26.
27.
28.
29,
30.
31.
32,
33.
34.
35.
36.
37.
38.
39.
40,
41,
•42,
43.
44,
45.
46.
47.
BMDX85 - NON LINEAR LEAST SQUARES - REVISED NOVEMBER 19?1971
HEALTH SCIENCES COMPUTING FACILITY, UCLA
PROBLM CODE
NUMBER OF VARIABLES
INDEX OF THE DEPENDENT VARIABLE
INDEX OF THE WEIGHTING VARIABLE
NUMBER OF CASES
NUMBER OF PARAMETERS
TOLERANCE
EPSILON
MAXIMUM NUMBER OF ITERATIONS
NUMBER OF VARIABLE FORMAT CARDS
ALTERNATE INPUT TAPE NUMBER
REWIND OPTION
VARIABLE FORMAT
MINIMA
PH4,
0.000010
0.000010
100
1
5
NO
(2F6,2)
MAXIMA
ITERATION
•-1.0000E
l.OOOOE
20
20
,OOOOE 20
, OOOOE 20
0
1
2
3
4
b
6
7
8
9
10
0
0
0
0
0
0
0
0
0
0
0
ERROR
MEAN
SQUARE
2.3969E 00
1.2664E 00
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8625E
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-1 .5000E--02
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THE PARAMETERS
8.0854E-01
ASYMPTOTIC CORRELATION
1
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MATRIX OF THE
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2
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85512
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0.80854
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0
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54000
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267
-------
BMDX85
NON LINEAR LEAST SQUARES - REMISED NOVEMBER :l 9 r 19 71
3. HEALTH SCIENCES COMPUTING FACILITY? UCLA
4. PROBL.M CODE Pl-l 2.5
5, NUMBER OF VARIABLES 2
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268
-------
AN APPLICATION
OF BIASED ESTIMATION THEORY
TO ITERATIVE MAXIMUM LIKELIHOOD SEARCH STRATEGIES
David J. Svendsgaard
Mathematical Statistician
Health Effects Research Laboratory
U. S. Environmental Protection Agency
Research Triangle Park, North Carolina
In scientific investigations, bias is generally
regarded as something that is not wanted. In theoret-
ical statistics, biased estimation has been studied
with a view toward obtaining improved estimators.
Often times, such improved estimators require sub-
jective input from the investigator — another
something that is not generally accepted in scientific
investigations. This paper documents a situation
where the use of biased estimation works better than
unbiased estimation. Although we believe the
situation is important in its own right, we consider
it as evidence that biased estimation theory deserves
serious consideration in environmental modelling work.
Here, we describe a modification to an existing
iterative scheme for obtaining the maximum likelihood
estimators of the parameters of the cumulative
logistic function adjusted for natural responsiveness.
This modification incorporates the concept of biased
estimation, while the original scheme is viewed as
using unbiased estimation. Empirical results indicate
that a higher percentage of successful convergences
occur when the modification is used. We believe that
the modification is less dependent on the starting
values, and that the modification requires subjective
input in a form that is easy for most potential users
to specify.
We conclude our discussion with comments on the
fitted dose-response model.
Introduction
Background
Parametric dose-response models have great
utility in quantifying the relationship between an
agent and a health effect of that agent. Knowledge
of such relationships is key information for the
determination of air quality standards.
The parameters of such models are estimated from
observed data. The maximum likelihood estimators
(MLE) of these parameters have good statistical
attributes, and so the MLE is often calculated.
Even for simple mathematical models, this calculation
usually involves the use of iterative methods. Such
iterative schemes do not always successfully converge
to the MLE.
We have attempted to determine the MLE for the
cumulative logistic function adjusted for natural
responsiveness. The data was obtained in an epidem-
ic! ogical panel study. Generally, there are no
control groups for such studies and existing iterative
methods can perform poorly under such circumstances.
Difficulty in using one such method was experienced
in this case.
The success of the iterative method we used
depended heavily on our ability to start the iteration
with good starting estimates of the parameters
(starting values). If one set of starting values
doesnht result in convergence, one tries another set.
Complex subjective judgments may be required to obtain
good starting values. Since starting with the MLE
as a set of starting values will usually result in
convergence, one can always be accused of using poor
starting values when the iterative scheme fails.
Statement of the Problem
There are a couple of ways that an iterative
scheme can fail. When very poor starting values are
used, convergence to a relative maximum may take
place, or the specified number of iterations may be
used up before convergence to the MLE has occurred.
Another type of failure results when the revised
estimates overshoot the MLE and get progressively
worse.. This type of failure occurs when a certain
matrix requiring inversion is ill-conditioned. It is
this type of failure that was experienced in our case,
and it is this type of problem that our modification
is designed to handle.
Biased Estimation
This type of failure can be viewed as the fault
of unbiased estimation. At each iteration the
revised estimates are derived from a solution vector.
This solution vector can be considered the least
squares estimator of the parameters of a particular
linear model. Although the least squares estimator
attains minimum variance among unbiased estimators,
this variance can be large.
The theory of biased estimation is based on the
fact that mean squared error (bias plus variance) can
be smaller for a slightly biased estimator with much
smaller variance, than for an unbiased estimator.
This theory is applied to develop a class of
estimators appropriate for this problem. The result
is an iterative maximum likelihood search strategy
in which the user of the method simply specifies a
bound on the difference between the MLE and the
starting value for the proportion of natural responses.
The method using the least squares estimator can be
viewed as considering this difference to be unbounded.
Thus, the user can specify a very crude bound and
expect to do better by incorporating this bound into
the modified method.
Overview
First, we present the theory involved. This
includes a description of the dose response model, a
description of the iterative method, the development
of a modification to this iterative method, and a
discussion on the subjective input required to use
the modification.
Second, we do an empirical evaluation of this
modification. The data used in the evaluation is
described. Next, we describe the evaluation, list
the results, and draw conclusions.
Finally, we make some comments on the application
of this model when it is fitted to epidemiological
panel studies.
269
-------
Theoretical Development
Description of the Cumulative Logistic Adjusted for
Natural Responsiveness Dose-Response Model
Consider a dose-response experiment where dose
levels I. at N different levels are applied to n.
subjects and at each dose level r. subjects respond.
If the administration of a dose Z causes a pro-
portion P(Z) of the test subjects to respond and other
independent factors acting on the test subjects during
the experiment causes a proportion C to respond, then
the total expected proportion responding will be
P'(Z) P(Z) + C P(Z)C C + (1 C) P(Z).
This equation is called Abbott's Formula. If
P(Z) is the cumulative logistic function
(1)
P(Z)
1
1 + exp - (A+BZ)
then P'(Z) is known as the cumulative logistic
adjusted for natural responsiveness.
Tolerance Concept
This model is motivated by the concept of a
tolerance. An individual's tolerance is defined as
that level of dose Z such that doses higher than Z
always cause a response. The purpose of the model is
to make inferences about the distribution of tolerances
in a target population.
Sampling Considerations
In fitting such models, it is usual to assume
that the n^ subjects exposed to a dose level Zi were
randomly selected from the target population. Assume
in addition that the proportion of tolerances less
than Z is P(Z) for each Z. When these two assumptions
are correct the probability of observing r, responses
from the n^ subjects dosed at level Z. for i=l,2,...,N
N
* ("]) PCZ/1' (l-P^))"1"^.
is
KA.B.C) =
In general, L(A,B,C) is called the-likelihood
function. Those choices of A, B, and C (denoted by
A, B, and C) that maximize L(A,B,C) are the MLE.
Description of an Existing Iterative Method
Based on an approximation to the first derivative
of the log likelihood evaluated at the MLE by the first
order terms of the Taylor-Maclaurin expansion,
Finney1 has derived the expressions used in iterative-
ly solving for the MLE of the parameters of the probit
dose-response model adjusted for natural responsive-
ness. These expressions can be easily applied to the
logistic model described in (1). When AS, B$ and C$
are the starting values for the parameters A, B, and
C respectively, at the iteration number S, the
revised estimates (X , B .,, C .,) are
s+i
The formulae for aQ, al and a2 are algebraically
the same as the formulae for the least squares
estimator of the parameters of the linear model
yi aQXoi + ajXi.. + a2X2i + £. (2)
for 1=1,2 N;
where the e^ are uncorrelated random variables with
tJ D
and
The x
zero mean and common variance a-, me Aoi,
x2i are all determined from AS, B$ and GS, and the
formula for the y. also involves ri. The formulae
and
below define the x-n- and
j=0,l and 2.
Ii -c
n. s
P
for i=l ,2 N and
1 - C
P. =
i 1 + exp - (As + Bsz.) '
i - P,-;
Wf
wi =
(A
Pi-Pi,
Wi '
..
and
:T
If Cj 1s obtained from inspection of the data,
Aj can be obtained by iteration to maximize the
likelihood for this value of Cj. The appropriate
expressions involved in this first stage of iteration
are algebraically equivalent to the least squares
estimators
[:;]=[:;]
for the parameters of the model
y, = ax, + alXl, + e., 1=1,2,..., N; (3)
[ 001 I I
which is obtained from (2) by setting «2 to zero.
Of course, starting values for A and B are required
even for this first stage of iteration, and for B one
could use zero and set
In
P-Ci
1-P"
where P" =
This choice of starting value for A maximizes
the likelihood function for these values of B and
0
Cj. Having obtained revised estimates for A and B
after a number of iterations from this first stage,
one could proceed to the second stage of iteration
using (2) and these revised estimates as starting
270
-------
values.
Based on empirical results, it appears that the
success of such a two stage scheme depends on how well
Cj is chosen and on what criterion is used to deter-
mine when to stop first stage iterations and go to
the second stage. A very stringent criterion is
wasteful of computer time if Ct is chosen close to C.
When a very loose criterion is employed, e.g. omitting
the first stage entirely, failure rates are high.
The failures are usually the result of high correla-
tions among the x.- resulting in a singularity in the
matrix requiring inversion. Invariably, such a
singularity is preceded by an unreasonably large
overestimation of the magnitude of a2.
When we regard (2) as the true model whose
parameters are to be estimated, the problems mentioned
in the last paragraph are a familiar weakness of
least squares estimation. That is, even though the
least squares estimator achieves minimum variance
among unbiased estimators, this variance can be very
large when the independent variables are highly
correlated. In those cases cited above, we view this
variance as being intolerably large. Possibly a
slightly biased estimator with much smaller variance
can achieve small enough mean squared error (bias
plus variance) to usually avoid those type of
problems.
Development of an Alternative Estimator via the
Consideration of Biased Estimation Theory
Consider the class of biased estimators of the
form
(4)
where kp, KI and k2 are constants, we shall consider
using the a- in place of the a. in a single phase
iteration scheme. Note if the k^ are zero then the
a.j are the least squares estimators of the model
described in (3) which are biased when a2 is nonzero.
It is also possible to obtain the u. from (4) by
letting the ki take on certain values.
We shall use an error criterion that seems
appropriate for this problem and show how the k^ can
be chosen so that for a wide range of a2 values,
better performance in terms of this criteria is
attained by an estimator using the chosen k^ 's than
is attained by using either of the estimators
mentioned in the above paragraph. The choice of the
k.. is made by specifying an upperbound on a2/cr .
It turns out that the formula for the k. that we
suggest using involves the specified upperbound and
the correlation between the x... Generally, this
correlation changes from one iteration to the next,
so that even though only one bound is used, the ki
vary between iterations. In those cases where
successful convergence takes place, the estimators
are similar to those that were suggested for the two
Initially, the x.. are highly
stage scheme.
In later iterations,
the correlations become smaller and the a-'s approach
the u.. 's. Thus, instead of selecting a criteria for
deciding when to jump from the first to second stage
of iterations, the use of the proposed estimator
eliminates the need to make this decision by
automatically incorporating it into the computation
process based on the value of the specified upper-
bound.
Let the true model at each iteration be
and consider approximating n over an interval of
interest ? £X<5i with
ri=a X
0 0
where (a , aj, a2) is a vector of estimated regres-
sion coefficients. A reasonable measure of the
closeness of n to n is integrated mean square error
,-Nn
E (n-n)2
dx
where ft
••i;
where
M ('
a2 J,
dx. Note that J=B+V,
(E(n)-n)2 dx,
and
_Nn f
°2J£
Var n dx.
Let Y be the vector whose ith element is y.
and denote the design matrix whose ith row is
(xo-j.x^.Xz.) by
x = [X! ; x2]
Nx3 Nx2 Nxl '
then
and Var Y = a2IN.
We shall consider the class K of estimators of
the general form in (4)
where
and
where H=IN-X1(XiX1)"1Xi.
N
Now
271
-------
where .- -,
"1
- (X{Xi)"X1X2
and E(a2)=a2.
Denote W ~
3x3
2x2
1x2
and k=
2x1
W3
Ixl"
.-(
dx,
The integrated mean square error of estimators
in K is
trace
-a' '--.--
+N trace W k'CX^HXz)"1^
When k=y, the estimator is unbiased and when k=0, V is
smallest for any estimator in K. Differentiating
J(k) with respect to k and setting the derivatives
to zero yields that the minimum J estimator in K is
a
-o
<*1
0
•A If*
A
+ k* o2
ai/a2
ai/a2+(X2HX2)2 '
This value of k requires that one know a|/a2, but
using
+ /
k = maxlO,
y
it can be shown that
J(k+)< min (J(0),J(v))
-i
when
M-(X2HX2)
M(X2HX2)+3
(5)
(6)
So if k is obtained by specifying any value for
M such that (6) is true, smaller J will be achieved
using (a , aj, a2) with k=k+ then when k=0 or y.
Considerations on Choosing M
One way to choose a value M that bounds a§/a2 is
to find an upper bound for a| and a lower bound for
a2. Therefore, first consider a2 as being C-CS>
since C = a2 + Cs- Partial justification for
considering a2 C-C can be based on a result from
large sample theory: "...if first approximations are
of nonzero efficiency, one cycle of computation will
yield fully efficient estimates".1 By (1), C is a
proportion so if we agree to set Cj tc some value
between zero and one then (C-Cj)23 a2, will be less
than one.
Considering only the variability contributed
to y.j by P^ we have
(1-C) (C+(
Var
yi
When we assume that the starting values are equal to
the respective true parameters of the model, we have
2
that a
M=l.
is one. For these reasons we suggest using
Smaller values for M such as Pj might be used,
but we have only shown that (6) is true when (5)
is true for the case where k is deterministic. The
use of any information gained from the data in fixing
k would require that k be treated as random.
Actually, considering the error criterion we are
using, even when M is carefully chosen the error may
be unacceptably large. So if the iteration routine
fails one should consider varying M, however choosing
M larger. than 1 seems unnecessary.
Empirical Evaluation of Modification
Description of the Data Used in Evaluating the Itera-
Methods
Hammer et al reported on data from student nurses
in Los Angeles wFio completed daily symptom diaries
during the period of their training. The total number
of yes/no responses of four symptom categories pooled
over days having the same range of maximum hourly oxi-
dant levels were computed from Table 3 of this refer-
ence. The doses were the midpoints of these oxidant
ranges. The symptom categories are Headache, Eye Dis-
comfort, Cough and Chest Discomfort with no accompany-
ing fever, chills or temperature. Due to the restric-
tions, the positive responses are indicators of only
mild personal discomfort.
Assuming independence between days of responses
from the same student nurse, the number of positive
responses are taken to be binomially distributed with
parameters P! and n. where
P. - C + (l-C)/(l+exp-(A+BZ.) for i=l,2,.,.,9.
The MLE's for the parameters (A, B, C) of this model
are listed in Table I for each symptom. The i's are
ordered so that Z1 is the lowest oxidant range and
Z9 is the highest.
272
-------
Description of Evaluation
Iterations were run using three different start-
ing values for C and four different bounds on a£/a2.
The starting values for C were:
(a) The observed proportion of total responses
corresponding to the lowest oxidant level. For all
four symptom categories this proportion turned out to
differ from the MLE for C by less than 0.01. The min-
imum observed proportion was used as a starting value
for C in the case of Chest Discomfort in order to
avoid the computation of the logarithm of a negative
number in the process of getting a starting value for
A.
(b) One half the proportion used in (a).
(c) Zero.
The starting value for B was zero and the start-
ing value for A was
In
where F - (zr. )/sn. .
The four different values for M used were Pf,
P§, 1, and ». Infinity corresponds to using the least
squares estimator for (2).
Iterations were continued until the change in the
likelihood was zero (to the accuracy of the computer),
or until 30 iterations, or until the program faulted.
The maximum number of iterations was 25.
Table I
Maximum Likelihood Estimates for Each Symptom
Symptom
B
Headache
Eye Discomfort
Cough
Chest Discomfort
-4.6269
-5.0457
-9.9495
-13.2602
.0407
.0931
.1690
.2243
.0954
.0417
.0944
.0177
Results
Table II lists the occurences of successful con-
vergence. From this table it can be seen that the
percent of successful conversions was higher in all
cases when a finite bound on a£/a2 was used. When
Pf was specified as a bound, the failure was due to
convergence to the MLE of A and B for the starting
value Cj. The highest percent of successful conver-
sions when a starting value for C of either 0 or
l/2Pj was used occurred when M was set equal to one.
Conclusions
If good starting values are used, convergence can
always take place using Finney's formula. However,
how good these starting values must be depends on the
data.
The modification of Finney's formula developed
here yields successful convergence for starting values
that are too poor to be used directly in Finney's
formula. When very poor starting values for C are
used neither the modification nor Finney's formula
works all the time. However, for some values of M,
a higher success rate can be obtained using the modi-
fication. Moreover, when seemingly adequate C start-
ing values are used, successful convergence is ob-
tained using the modification in cases where the use
of Finney's formula had failed.
The use of smaller M values seems to yield poorer
success rates for poor choices of C starting values,
but can achieve improved success rates for seemingly
adequate C starting values.
It is recommended that a number of C starting
values be used with this modification. When no other
information is available, M should be taken to be one.
If convergence fails due to a singularity, a tighter
bound should be tried. A plot of the likelihood
obtained at the final iteration versus the correspond-
ing C value is helpful for deciding if more starting
values should be tried and what values to use.
Table II
Successful (S) and Failing (F) Iteration Attempts
Symptom
Starting Value for C
p?
PI
1
Eye Discomfort
Headache
Cough
Chest Discomfort
% Success
Eye Discomfort
Headache
Cough
Chest Discomfort
% Success
Eye Discomfort
Headache
Cough
Chest Discomfort
% Success
Eye Discomfort
Headache
Cough
Chest Discomfort
% Success
S
F
F
F
25
S
F
F
F
25
S
S
F
F
50
F*
F*
F*
F*
0
S
F
F
F
25
S
F
F
F
25
S
S
F*
F*
50
F*
F*
F*
F*
0
S
S
S
S
100
F
S
S
F*
50
F
S
S
F*
50
F*
F*
S
F*
25
* Indicates failure occurred due to program default.
Some Comments on Applications of Dose-Response Model
When Fitted to Data From Panel Studies
Both the logistic and the probit models were fit
to the Nurse eye discomfort data. The fit of both
models was almost identical. The Probit fit just a
little better, but the difference in fit provided no
substantial grounds for choosing between the models.
The adjustment for natural responsiveness was signifi-
cantly different from zero (p<_0.05). There was also
significant lack of fit (p<_ 0.05) for both models. A
test of equal proportions reporting eye discomfort on
days having the same maximum oxidant reading was also
rejected.
It is felt that these models when adjusted for
natural responsiveness adequately describe the rela-
tionship between eye discomfort and oxidant measure-
ments for these nurses. The fact that there was
significant lack of fit for these models is attribut-
ed to dose error resulting probably from spatial
variation. That is, the fixed air sampler is only a
crude indicator of dose for these nurses.
For purposes of selecting an air quality stan-
dard, it is felt that this modelling effort is
sufficient.
References
[1] Finney, D. J. (1971). Probit Analysis. Univer-
sity Press, Cambridge. Chapters 4 and 7.
[2] Hammer, D. I.; Hasselblad, V.; Portnoy, B.; and
Wehrle, P. F. Los Angeles Student Nurse Study.
Arch. Environ. Health 28, 255-260.
273
-------
ECONOMIC AND DEMOGRAPHIC MODELING RELATED TO ENVIRONMENTAL MANAGEMENT
Allen V. Kneese, Professor, Department of Economics
University of New Mexico, Albuquerque, New Mexico 87131
I will select a few main modeling issues for dis-
cussion. First, economic-social-environmental problems
are accumulating at a great rate. As a consequence, I
fear that there will be a great temptation to apply
models to complex issues when, in fact, they are not
well designed to deal with them, and then to base poli-
cy on conclusions which may be quite unrealistic.
Second is the old but still very important issue of how
far one should carry the explicit incorporation of
interdependencies in models, and the related question
of whether one is better advised to use optimization or
simulation approaches and under what circumstances.
I will conclude the paper by discussing an optimi-
zation model designed to test a number of hypotheses
about quantitative modeling and the environment. From
these hypotheses I will single out one which I feel is
currently of particular importance to the Environmental
Protection Agency. When EPA was formed, a main ratio-
nale was that the environmental media, the land, the
water, the air, should be treated simultaneously in the
policymaking and administrative process. This has not
occurred, and I wish to indicate evidence concerning
its importance and to discuss the role of a formal quan-
titative model in generating this evidence.
Introduction
"But I deeply fear a much worse outcome. We are
seeing a proliferation of costly attempts to establish
environmental management 'data banks' containing every-
thing up to and including the kitchen sink. These are
to be linked by some forms of vaguely specified models
constructed by loosely organized interdisciplinary and
interuniversity teams. When these huge jerry-built
structures come crashing down, as many of them surely
must, we may well see a backlash on the part of spon-
soring agencies deeply embarrassed by their inability
to show useful results from enterprises which have run
into the millions of dollars. This may mean that all
economic ecological modeling enterprises become dis-
credited, even sober and well thought through ones. If
this happens, it could greatly retard the further suc-
cessful application of management science to this impor-
tant area of national concern."!
The paper from which the above quote is taken was
published in 1973 but was written in 1970. It was in
response to the euphoria and enthusiasm about mathemati-
cal modeling applied to social problems which character-
ized the latter part of the 1960's. Most unfortunately,
the fears expressed in this paper have come true. Today,
to mention mathematical modeling in proposals going to
the NSF-RANN program for funding is the end of the pro-
posal. We hold this conference in an atmosphere char-
acterized by enormous skepticism about mathematical
modeling in general and about large quantitative models
in particular. The skepticism is a reaction to a number
of things: the exaggerated claims which have been made
for modeling, modeling without data, indulging in the
circular reasoning of drawing conclusions about the real
world from assumed relationships in models, specifica-
tion of irrelevant objective functions, the definition
of "systems" which correspond to no present or potential
decisionmaking unit, and so forth. One result has been
the creation of a number of models which, at worst, pro-
duced results that are deceptive or, at most, are use-
less and costly. This is not to say that there have not
been some notable successes, but at the moment we are
suffering heavily from past mistakes.
Asking Models Questions
They Were Not Designed To Analyze
Attitides toward models in the natural resources
and environmental area tend to fall at polar extremes;
on the one hand are the totally skeptic and on the other
those who uncritically accept whatever data a model pro-
duces. As an example of the latter, the recent Ford
Foundation Energy Report is a case in point. Among
other things, the Ford Energy Report incorporated a
mathematical projections model to answer questions about
the economic effects of reduced rates of energy use.
Before discussing projections, a quote from Mark Twain
creates the proper mood for attempting a long-range look
into the future.
"In the space of one hundred and seventy-six years
the Lower Mississippi has shortened itself 242 miles.
That is an average of a trifle over one mile and a third
per year. Therefore, any calm person who is not blind
or idiotic, can see that in the old Oolitic Silurian
Period, just a million years ago next November, the
Lower Mississippi River was upward of one million three
hundred thousand miles long. By the same token any per-
son can see that seven hundred and forty-two years from
now the Lower Mississippi will be only a mile and three
quarters long. There is something fascinating about
science. One gets such wholesale returns of conjecture
out of such a trifling investment of fact."
The language of the Ford Foundation Report with
respect to its model is revealing. "An economic model
developed for the project by Data Resources Incorporated
provides a broad-based measure of the impact of reduced
energy growth and concludes that a transition to a
slower growth—even zero energy growth—can indeed be
accomplished without major economic cost or upheaval.
The study indicates that it is economically efficient as
well as technically possible over the next 25 years to
cut rates of energy growth at least in half. Energy
consumption levels would be 40 to 50 percent lower than
continued historical growth rates would produce at a
very moderate cost of GNP--scarcely 4 percent below the
cumulative total under historial growth in the year 2000,
but still more than twice the level of 1975." No quali-
fying statements are made.2
First, as all of us here are painfully aware, the
degree of accuracy of all quantitative models of the
economy is questionable, especially when they are used
for projecting for long periods into the future. The
idea that they could identify a 4 percent difference in
cumulative GNP over many years is incredible. If there
are not problems with the structure of the model, there
are data problems. For example, the parameters of the
model used in the Ford Foundation study were estimated
from data from the period covering 1950 to 1970. In
many respects we have moved entirely outside the range
of variation covered during that period, especially in
the areas pertinent to the model, such as fuel prices,
domestic energy sources, and international trade condi-
tions.
Second, one may have questions about the specific
structure of the model. It is, for example, highly
aggregated; it contains only nine sectors of which five
are energy sectors. Is it really possible to address
274
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the problem at hand with so few production sectors?
Moreover, it appears that the basic structure of the
model will predetermine one of the main results that it
is said to have found, i.e., that energy usage does not
have much to do with economic growth. The relationship
between energy input and economic output and energy
cost is based on the assumption that the increasing use
of energy per unit output during the period when energy
costs were falling can be extrapolated to a future
situation in which energy costs rise. That is, the
energy output relationship is reversible given a re-
versal of the historical trend in real prices. Aside
from the question of whether dynamics of the real eco-
nomic system permit such reversibility, there is the
question of relationships between energy input and man-
hour productivity. One may reasonably hypothesize that
one factor in the increase in man-hour productivity in
the post-war period is the substitution of inanimate
energy for human energy. If this substitution effect
is important, then a reversal of the situation would
surely result in a reduction in productivity and a
slower rate of economic growth. In the model, however,
the factors determining aggregate output appear to be
entirely uncoupled from any relations of this sort.
Productivity is exogenously given. Should we then be
surprised that the cost and rate of growth of energy
use do not much affect the rate of GNP growth? That
they do not is one of the principal conclusions of the
study, but whether it is a conclusion or whether it is
built into the assumptions of the model is questionable.
This problem concerning the appropriateness of
asking models to answer policy-type questions is unan-
swered. It may be wise, at least when such models are
used by public agencies and particularly Federal agen-
cies, to create a model review board. Its duty would
be to assess and pass judgment on the suitability of
various models to address agencies' problems.
Models of Economic Environmental Systems
To try to understand the results of policy actions,
different institutional structures for decisionmaking,
alternative technologies, etc., a number of models of
economic-ecological systems have been built. Since
these are of more direct interest to our session than
the energy model discussed in the last section, a few
generalizations about this type of modeling would be
useful before moving on to a specific application.
It is often said that the first principle of ecol-
ogy is that everything is connected to everything else.
This is perhaps true but somewhat unhelpful; however,
it does bring into focus the question of how far mod-
elers should go in the explicit incorporation of inter-
dependencies. This is a general problem in systems
analysis but it takes on additional force in connection
with environmental problems because of the prominence
of "ecological thinking" in the field. The "frog in the
hole in the bottom of the sea" chain of reasoning of
some ecologists has led to visions of the environmental
management problem which push it beyond the bounds of
successful modeling. Years ago, when operations re-
search was first being explored by economists, Robert
Dorfman wrote a fine article stating the general point
very well.3 In it, he said:
"As a result of complexity the operations analyst,
like every other worker, lives always near the end of
his tether. He simplifies his problem as much as he
dares (somewhat more than he should dare), applies the
most powerful analytical tools at his command, and with
luck just squeaks through. But if all established
methods fail, either because the problem cannot be
forced into one of the standard types or because after
all acceptable simplifications it is still so large or
complicated, the equations describing it cannot be
solved. When he finds himself in this fix, the opera-
tions analyst falls back on simulation or gaming."
One result of the ability of simulation to treat
relationships beyond those manageable in optimization
problems is that much discipline and order is lost, and
the problem of choosing among alternative outcomes of
the simulation can easily become impossible.
Consider a small simulation model in which there
are 28 variables (an actual environmental model may
easily have many hundreds), each of which may be set at
any one of three levels. There are then 328 possible
designs of the system. This is approximately 23 thou-
sand billion. If it takes 2 minutes of computer time
to simulate each design, about 100 million years could
be required to complete the simulation. Of course no
simulator would attempt the complete enumeration of out-
comes in a large problem, but this calculation does
suggest the complexities involved. This and the paucity
of data available for defining relationships specifying
coefficients have been among the problems which doomed
some of the more ambitious ecological modeling efforts
to costly failure.
The elementary set of needs in economic-ecological
modeling is that (1) the model must be persuasive, i.e.,
it must represent something in the real world with
sufficient fidelity that a decisionmaker could with some
confidence base a decision on it and (2) that some
reasonably straightforward and efficient criteria must
exist for choosing among vast numbers of alternative
results.
Of course simulations can be very useful if in-
formed judgment readily yields a few alternative systems
for analysis. But it seems this is an unusual situation
when large environmental systems are at issue. Simula-
tion models can also be supplied with objective func-
tions and one or another form of sampling can be used to
generate a "response surface." The principles of sam-
pling for this kind of problem are not well understood,
however, and providing an adequate sample may be an
extremely large problem in itself if the number of vari-
ables and alternative scales is great and the response
surface is irregular. Otherwise, the process may come
to a halt at the top of a gentle rise while totally
ignoring the neighboring mountain peak.
Perhaps it is essential that we accept some form of
optimization models, with all their limitations, as the
only ones likely to be useful for decisionmaking in
large problems like environmental management--although
our experience is not so extensive that this conclusion
can be drawn with certainty. Optimization models can,
of course, incorporate simulation submodels to provide
descriptive linkages in a set of nested models. But
they do not sacrifice specifying a criterion function
and require an orderly approach to the optimal solution.
Selected parameters of the optimization model can be
varied and new solutions found. This would almost
always oe desirable in any real decision situation. The
device of an objective function with constraints and a
specific solution procedure is not abandoned, however.
Clearly it is necessary to recognize that these
models can never be "comprehensive" in the sense that
they consider all linkages and all alternatives. Great
care must therefore be taken to specify what aspects of
reality are and are not included. In this connection, a
well functioning market system can be of great help,
which is often ignored in the more ecologically oriented
models. We may exclude many aspects of resource use
from explicit consideration in our environmental policy
or management models on the grounds that they are appro-
priately handled by the market exchange system. The
interface between these processes and the model as such
275
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is through the system of values generated by the market,
that is, prices. The model itself can then focus ex-
pi ic^'tly on those aspects of resource use where the
market exchange is known to fail seriously as an allo-
cative device, e.g., with respect to allocating common-
property environmental resources of air, water, and
associated ecological systems.
Static and dynamic elements are likely to be par-
ticularly difficult to handle adequately in optimiza-
tion models, and these are important deficiencies.
Sensitivity analysis and the like can help, but the
wise modeler will never let himself think that his
models will provide a complete basis for decisionmaking
either on conceptual or empirical grounds in a field as
complex as environmental quality. Models must be
viewed as potentially helpful tools which constitute an
element, albeit a major one, in the decisionmaking pro-
cess. They are tools which can reveal obscure impacts
of common-sense policies and quantify them to some
extent. They must be built and used because of the in-
herent logic demands of the problem and because we have
nothing better.
The Regional Residual Model
I would like to conclude this introductory paper
by discussing in general terms an environmental modeling
enterprise which took place in the Quality of the En-
vironment program at Resources for the Future while I
was program director. The specific form and structure
of the model was very much a result of the preceding
type of consideration. It was developed by a team of
researchers representing several disciplines and is
often called the Russell-Spofford model, or more fully,
the Regional Residuals Management model. It isa static
optimization type model built for application to the
Delaware Estuary Region for several purposes. For ex-
ample, it could help test the impact on the cost of en-
vironmental management of introducing exotic technolo-
gies, such as stream reaeration, into the system. It
could play out economic, in the sense of efficiency and
distributional, implications of setting ambient stan-
dards at various levels in the region. In a politicized
version it was useful in testing certain hypotheses on
how the structure of legislative processes would affect
decisions on environmental quality, e.g., referenda
versus COGS versus small district representation in
legislative assemblies. (For a relatively full report,
see Reference 4.)
Here I wish only to say something about the struc-
ture of the model and particularly the light it sheds
on one of the main hypotheses we sought to test with
it--that there are important nonmarket linkages among
the environmental media of land, water, and air, and
that treating each in isolation as is done in current
legislation and administrative practice is likely to
lead to unanticipated and probably inefficient results.
This is what might be called the basic EPA hypothesis.
The Russell-Spofford Model*
The Russell-Spofford model is, as already implied,
designed to deal simultaneously with the three major
general types of residuals—airborne, waterborne, and
solid--and reflects the physical links among them in a
regional context. It "recognizes," for example, that
the decision to remove waterborne organic wastes by
standard sewage treatment processes creates a sludge
which, in turn, represents a solid residuals problem;
*This portion of the paper is based largely on material
prepared by my former associates at RfF, Clifford
Russell and Walter Spofford.
the sludge must either be disposed of on land or burned,
the latter alternative creating airborne particulates
and gaseous residuals.
The model also can incorporate the nontreatment
alternatives available (especially to industrial firms)
for reducing the level of residuals generation. These
include: input substitution (as natural gas for coal);
change in basic production methods (as in the conver-
sion of beet sugar refineries from the batch to contin-
uous-diffusion process); recirculation of residual-
bearing streams (as in recirculation of condenser
cooling water in thermal-electric generating plants);
and materials recovery (as in the recovery and reuse of
fiber, clay, and titanium from the "white water" of
paper-making machines). These alternatives are included
by means of industrial linear programming submodels.
The model uses environmental diffusion models but
it is also capable of incorporating environmental simu-
lation submodels. In practice, the latter takes the
form of an aquatic ecosystem model which translates re-
siduals discharges into impacts upon various species of
concern to man.
In addition to these features, the model incor-
porates a unique political (collective choice) feature.
I think it is fair to say that this model is at the
frontier of quantitative research in environmental eco-
nomics.
The model containing these features is shown sche-
matically in Figure 1. The three main components of the
overall framework may be described as follows:
A Linear Programming Model. This model relates in-
puts and outputs of selected production processes and
consumption activities at specified locations within a
region, including: the unit amounts and types of resi-
duals generated by the production of each product, the
costs of transforming these residuals from one form to
another (gaseous to liquid in the scrubbing of stack
gases), the costs of transporting the residuals from one
place to another, and the cost of any final discharge-
related activity such as several types of landfill opera-
tions.
The programming model, which actually consists of
an array of submodels pertaining to individual industrial
plants, landfill operations, incinerators, and sewage
treatment plants, permits a wide range of choices among
production processes, raw material input mixes, by-
product production, materials recovery, and in-plant
adjustments and improvement. All these choices can re-
duce the total quantity of residuals to be disposed of.
That is, the residuals generated are not assumed fixed
either in form or in quantity. This model also allows
for choices among treatment processes and hence among
the possible forms of the residual to be disposed of in
the natural environment and, to a limited extent, among
the locations at which discharge is accomplished.
Environmental Models-Physical, Chemical and Bio-
logical . These component models describe the fate of
various residuals after their discharge into the natural
environment. Essentially, they may be thought of as
transformation functions operating on the vector of re-
siduals discharges and yielding another vector of am-
bient concentrations at specific locations throughout
the environment (these are the now familiar diffusion
models) and, in some instances, impacts on living things
(these are aquatic ecosystem models reaching beyond the
Streeter Phelps formulation). In aquatic ecosystem
models, living creatures which participate in these pro-
cesses are explicitly included in the model and the out-
put is stated in terms of impact on living things (e.g.,
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plankton and fish) rather than on physical parameters
such as dissolved oxygen.
A Set of Receptor-Damage Functions. These func-
tions relate the concentration of residuals in the en-
vironment and the impact on living things to the re-
sulting damages, whether these are sustained directly
by humans or indirectly through impacts on material
objects or on such receptors as plants or animals in
which man has a commercial, scientific, or aesthetic
interest. Ideally, for a full-scale overall efficiency
version of the model, the functions relating concentra-
tions and impacts on species to damage should be in
monetary terms. In fact, the model as finally imple-
mented is designed to meet environmental standards.
However, its solution technique is based upon "penalty
functions" and, therefore, proceeds as though violations
of the standards carried a price. Since the objective
is to meet environmental standards the price of viola-
tion is set very high.
The linkage between the components of the model
and the method of optimum seeking may be illustrated as
follows: Solve the linear programming model initially
with no restrictions or prices on the discharge of re-
siduals. Using the resulting initial set of discharges
as inputs to the models of the natural environment, and
the resulting ambient concentrations and impacts on
living things as the arguments of the penalty functions,
the marginal penalties can be determined as the change
in penalties associated with a unit change ina specific
discharge. These marginal penalties may then be applied
as interim effluent charges on the discharge activities
in the linear model, and that model solved again for a
new set of production, consumption, treatment, and dis-
charge activities. With appropriate bounds constraining
consecutive solutions, the procedure is repeated until
a position close to the optimum is found. This process
can be looked upon as a steepest ascent technique for
solving a nonlinear programming problem.
The Russell-Spofford model was designed for the
analysis of residuals management in regions where the
scale and severity of the problems justify a consider-
able investment in data and analysis. The model is
still in the process of being applied to the Delaware
Valley, which is discussed in the next section.
The Lower Delaware Valley Region
The Lower Delaware Valley region, chosen for this
application, is a complex region with many individual
point and nonpoint sources of residuals discharges. It
is defined by county boundaries, shown in Figure 2. The
grid superimposed on the figure is used for locating
air pollution sources and receptors in the model. It
is related to the Universal Mercator grid.
The region consists of Bucks, Montgomery, Chester,
Delaware, and Philadelphia counties in Pennsylvania;
Mercer, Burlington, Camden, Gloucester, and Salem
counties in New Jersey; and New Castle County in Dela-
ware. The major cities in the area are Philadelphia
(coterminous with Philadelphia County); Trenton in Mer-
cer County; Camden in Camden County; and Wilmington in
New Castle County. Overall, the population of the area
in 1970 was a little more than 5.5 million1. Of this,
35 percent is accounted for by Philadelphia alone, with
a further 5 percent found in Trenton, Camden, and Wil-
mington. However, other parts of the region are also
heavily urbanized.
The region as a whole contains an abundance of
manufacturing plants. In fact, it is one of the most
heavily industrialized areas in the United States. It
has, for example, 7 major oil refineries, 5 steel plants,
16 major pulp and paper or paper mills, 15 important
thermal power generating facilities, numerous large and
small chemical and petrochemical plants, foundaries, and
large assembly plants for the auto and electronic indus-
tries. This, of course, made the task of identifying
sources of residuals discharges, estimating the costs of
discharge reduction for them, and including them in the
regional model an enormous one. The model used contains
125 industrial plants, 44 municipal sewage treatment
plants, and 23 municipal incinerators, which are all
dealt with as point sources. In addition, there are 57
home and commercial heating sources with controllable
discharges, each of which is treated as an area source,
i.e., not tied to a specific stack location. Other
point and nonpoint sources distinguished in the region
are incorporated as background discharges.
The large population of the region naturally pro-
duces vast quantities of residuals from consumption
activities requiring correspondingly large facilities
for their handling and disposal. There are 7 municipal
sewage treatment plants with flows greater than 10 mil-
lion gallons per day (mgd) and 17 with flows greater
than 1 mgd, counting only those discharging directly to
the Delaware Estuary. On the major tributaries to the
estuary and the Schuylkill River, there are more than
120 municipal treatment plants of widely varying sizes.
For the disposal of solid residuals there are 17 incin-
erators currently operating with an aggregate capacity
of about 6,000 tons per day, and many major and minor
landfill operations. Together, on an annual basis, the
heating of homes and commercial buildings is responsible
for about one-quarter of the total discharges of SOg and
10 to 15 percent of the particulate discharges in the
region.
The major recipient of waterborne residuals in this
area is the Delaware Estuary itself. The Estuary is
generally taken to be the stretch of river between the
head of the tide at Trenton and the head of the Delaware
Bay at Listen Point, Delaware. For analysis purposes •
the estuary was divided into the same 22 reaches shown
in Figure 3.
The low flow of the river varies widely from month
to month and year to year. For aquatic ecosystem model-
ing purposes, a relatively low flow period was selected.
For the modeling of air quality, the atmospheric
conditions used represent the annual joint probability
distribution of wind speed, wind direction, a.nd stability
conditions for 1968, assumed uniform throughout the
region. Conditions representing rare events were not
used in the model for either air or water quality analy-
ses. Ideally, explicit attention would also be given to
this aspect of the modeling, but mathematical program-
ming models do not lend themselves well to the ideal
analysis of systems in which random events occur. As I
mentioned earlier, this is one of their weaknesses.
Contents of the Model
The model framework was discussed in general terms
earlier in this paper in connection with Figure 1. Here
the discussion is more detailed in order to grasp the
nature of the actual application of the concepts out-
lined there. The model is designed to provide the mini-
mum-cost method of simultaneously meeting several sets
of exogenously determined standards. Two of them are of
interest here.
Minimum Production Requirements. This means bills
of goods for the individual industrial plants, heat re-
quirements for home and commercial space heating, and
specified quantities of liquid and solid residuals re-
quiring some disposal action by municipalities.
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Levels of Ambient Environmental Quality. This is
represented, for example, by maximum concentrations of
SOg and suspended particulates at a number of receptor
locations in the region, minimum concentrations of dis-
solved oxygen and fish biomass in the estuary, maximum
concentrations of algae in the estuary, and restrictions
on the types of landfill operations which can be used
in the region.
In Figure 4, more detail is given on how the model
functions. In the upper left of the diagram is found
the basic driving force for the entire model, the linear
programming model of residuals generation and discharge.
It is in this part of the model that minimum "produc-
tion" constraints are found. A key output of this
part, as mentioned in connection with Figure 1, is a
vector of residuals discharges, identified by substance
and location. These discharges feed into the environ-
mental models--the model of the aquatic ecosystem and
the dispersion model for-the suspended particulates and
S02 discharges. This section of the overall model, in
turn, produces as output a vector of ambi-ent environ-
mental quality levels (for example, S02 concentrations)
at numerous designated points in the region. These con-
centrations are then treated as input to the "evalua-
tion" submodel found in the lower right of the diagram.
Here the concentrations implied by one solution of the
production submodel are compared with the constraints
imposed for the model run, and the penaty function pro-
cedure is used to iterate the model until all constraints
are met, within some specified tolerance.
The Production Model
In fact, as was also indicated in connection with
Figure 1, the production model consists of a number of
sets of linear programs with each set arranged in a
module. The modules reflect the chronological develop-
ment of the model as it was expanded over time to en-
compass more and more of the activities in the region.
A summary of this part of the model is shown in Table 1.
The modules are shown in the first column. The designa-
tion MPSX derives from the particular computational
routine used in the analysis. The next three columns
give the dimensions of the LP matrix for each module
and the number of discharges. Residuals generated by
the linear programs for these activities reflect opera-
ting conditions as of about 1970, and represent genera-
tion under steady-state conditions. Variability of
residuals generation in the various activities was not
considered. It will be noted that the overall program
has over 3,000 rows and nearly 8,000 columns. Included
are 306 sources of discharges, with options for reducing
discharges. For the number of discharges and types of
residuals being considered, there are nearly 800 speci-
fied residuals being discharged to the various environ-
mental media. The next column gives the type of acti-
vities in each module.
Only the powerful capacity of contemporary compu-
ting machines makes it feasible to solve a problem of
this size. Even so, scaling down the model to fit the
capability of even a large computer was a difficult
practical problem.
The Environmental Models
The overall model incorporates a 22-reach nonlinear
ecosystem model of the Delaware Estuary. Inputs of li-
quid residuals discharges to this model include: or-
ganics (BOD), nitrogen, phosphorus, toxics, suspended
solids, and heat (Btu). Outputs are expressed in terms
of ambient concentrations of algae, bacteria, zoo-
plankton, fish, oxygen, BOD, nitrogen, phosphorus,
toxics, suspended solids, and temperature. Three of
these outputs--algae, fish, and oxygen—are constrained
(all can be constrained in the model). In addition, the
model includes two 57 x 251 (57 receptor locations and
251 dischargers) air dispersion matrices, one for sulfur
dioxide and one for suspended particulates. These re-
late ambient ground-level concentrations to residuals
discharges (S02 and particulates).
Results
At the time of this writing, production runs with
the large model have just gotten underway. A few pre-
liminary results, however, can be presented with respect
to the "EPA hypothesis."
First, the model shows that in this realistic set-
ting of an actual case there are significant linkages
among the management aspects of the different residuals
types. Tighter ambient standards for the atmosphere do:
significantly affect the cost of maintaining water qual-
ity standards and vice versa. This can be seen by con-
sidering the following example results from production
runs with the model.
Air
Easy ambient
standards
Tight ambient
standards
Easy
ambient
standards
Water
Tight
ambient
standards
$395,640
$422,031
1,064,892
1,309,271
High quality landfill required for all runs.
All the numbers in the table refer to total addi-
tional costs to the region for meeting environmental
standards in dollars per day. The sample runs show that
going from easy (relatively low) water standards to tight
(relatively high) water standards costs about $26,000
per day when only easy air standards are imposed. If,
however, tight air standards are required, going from
easy to tight water standards costs about $244,000, or
almost ten times as much. Thus, the model tends to
support the EPA hypothesis that, taken in a realistic
regional context, there are linkages among the different
environmental media in the realistic setting of an im-
portant region and that they are of substantial magni-
tude. Policymaking, planning, and administration which
ignore them are likely to encounter untoward surprises.
Perhaps even more important, the Delaware applica-
tion indicates that it is possible to develop an inte-
grated residuals management model for a large region at
a manageable cost. The cost of this model (granted that
much of the basic data had been collected already) was
about 10 man-years of effort on the part of the senior
researchers, some research assistance, and perhaps
$100,000 worth of computer time at commercial rates. In
dollars, the cost could be put at roundly $1 million, or
about 1 day's worth extra cost to the region of operating
with tight environmental standards.
Conclusion
In conclusion, it seems appropriate to return to
the question of the choice of models. Mathematical
models for analysis of environmental and other resources
problems must be designed for specific purposes if they
are to be useful. There is no such thing as a general
model. If models are regional in character, it is
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usually even difficult to transfer them to another re-
gion. Such models must not be asked questions they
were not designed to answer. This seems obvious but
there are important instances in which this is happening.
On the matter of optimization versus simulation
models, the question may be discussed by summarizing
the considerations which enter into the choice in rela-
tion to residuals-management-type models. It should be
remembered that, as illustrated by the Russell-Spofford
model, combinations of simulation and optimization are
possible.
1. Mathematical optimization imposes a valuable
discipline on the modeler and the modeling process.
2. If ambient standards are the targets to be
achieved by a control strategy and there are a large
number of dischargers, a large number of receptors, and
a large number of possible discharge reduction options,
mathematical optimization is usually the reasonable way
to proceed.
3. If there are only a few major dischargers and
a few options for reducing residuals discharges, simula-
tion may be easier and sufficiently efficient.
4. If there are many similar sources of residual
discharges, but only one or two options for reducing
discharges at each source, and the objective is defined
in terms of required reductions or percent reduction at
the sources rather than in terms of ambient conditions,
simulation again may be easier and sufficently efficient.
5. Large mathematical optimization models are ex-
pensive and difficult, unless they are linear.
6. Large, nonlinear mathematical optimization
models frequently have multiple "optima" and it is
usually difficult to identify and deal with this situa-
tion when it exists.
7. The linearity assumptions may or may not do
great violence to the real world.
8. Synergistic and antagonistic effects are more
difficult to handle in mathematical optimization than
in simulation models.
9. Economies of scale or analogous increasing-
return situations cannot be handled satisfactorily by
any mathematical optimization technique.
10. Time-dependent phenomena are difficult to
handle in optimization models.
The balance of these considerations will usually
point to optimization as the preferred approach of the
problem is large and complex.
Finally, it should be remembered that any approach
to analyzing a complex environmental management problem
involves obtaining, arranging, and handling large amounts
of empirical data. In many cases the major problem is
that of obtaining empirical data on activities—produc-
tion process, residuals generation, and residuals dis-
charge reduction options and their costs--and on the
effects of discharges on ambient conditions.
References
1- Allen V. Kneese, "Management Science Economics and
and Environmental Science," Management Science,
Vol. 19, No. 10, June 1973, p. 1126.
2. Energy Policy Project of the Ford Foundation, A
Time To Choose: America's Energy Future, Cambridge,
Mass.: Ballinger Publishing Company, 1974, p. 135.
Robert Dorfman, "Operations Research," American
Economic Review, Vol. 50, No. 4, 1960.
Blair Bower and Allen V. Kneese, Residuals Environ-
mental Quality Management, to be published by
Resources for the Future, Inc. Also a publication
by the modeling team is in preparation.
Regional linear
programming model—
industrial, house-
hold and governmental
activities
Effluent
restrictions
or charges
Evaluation section
ambient standards,
damage function
Figure 1. Schematic of Regional Residuals Management
Model
- COUNTY LINE
- STATE LIN I
- REGION BOUNDARY
Note: The grid is in kilometers and is based on the Universal Transverse
Mercator (UTM) grid system.
Figure 2. Lower Delaware Valley Region
279
-------
Source: FWPCA, Delaware Estuary Comprehensive Study.
Figure 3. Map of the Delaware Estuary Showing
Analysis Sections
LINEAR PROGRAMMING MODEL OF
PRODUCTION, RESIDUALS DISPOSAL, ETC.
Marginal
COSTS OF PRODUCTION,
MODIFICATION, ETC.
Models of
Generation &
Modification
of Residuals
In Production
Processes
Generation
& Modification
if Consumption
Residuals
Constraints o
E.G: Increase In Munlcl
Increase In elect
Modification
Costs of
Recycling
Recycling
Alternatives
(Residential
Commercial,
Industrial
Waste Paper)
i the Distribu
pal Sewer and
ricity and Hoi
TRIAL "EFFLUENT CHARGES"
Instream
Aeration
"Discharge
of
Oxygen
Discharge of
Residuals.
Differentiated by
Type and Location
of Discharge)
tlon of Costs
Water Bills, percentage
e-heating costs.
Local and | (Horsepower
R.gional Options ACTIVITY LEVZLS
Discharges
V . S
VIA
CONSTRAINT LEVELS
Penalties
Attributed to
Individual
__Dlscharger3
§o«>w c
•H -n O
E u tna-H
•H UI-HC u
C 3 W-H-H
1J-0
§> m
we
3 tH«0-H O
E tu 3-H
•H • C U
c a> o--^-"
•H ecu —
g *i
•H «a-H
13 *> U U
O 3 ^ O
3^1 >**J-H
O-^ J3-H-C
A
t
T
J
ENVIRONMENTAL MODELS
ENVIRONMENTAL
EVALUATION
SECTION
Physical Dispersion Models
for suspended parclculates .Ambient Concentrat-
«nd sulfur dioxide ' ion, o[ residuals
Biological Systems Models .Ambient Concentrations
Aquatic Ecosystem «' Residuals, Biomass
«°DH- pianito-n/18"' *°°'
\
)
•^
Constraints
(vith penalty functions).
on Ambient Concentrations,
Species Populations, etc.
Figure 4. Schematic Diagram of the Regional Residuals
Management Model
280.
-------
Table 1. Delaware Valley Model
Residuals Generation and Discharge Modules
Module
Identifi-
cation
MPSX 1
MPSX 2
MPSX 3
MPSX 4
MPSX 5
MPSX 6
Total
Size of Linear Program
Rows
286
741
564
468
923
228
3210
Columns
1649
1474
1854
570
1778
394
7719
Discharges
130
114
157
180
86
116
783
Description
Petroleum Refineries (7)
Steel Mills (5)
Power Plants (17)
Home Heat (57)
Commercial heat (57)
"Over 25 ^agms/m3"
dischargers (75)
Delaware Estuary
Sewage Treatment
plants (36)
Paper plants (10)
Municipal Incinerators (23)
Municipal solid resid-
uals handling and
disposal activities
Delaware Estuary industrial
dischargers (22)*
Instream aeration (22)
Extra
Cost
Constraints
57 Electricity
(percent
extra cost)
57 fuel
(percent
extra cost)
57 fuel
(percent
extra cost)
36 sewage
disposal
(5 per house-
hold per
year)
57 solid re-
siduals
disposal
(percent
extra cost)
57 instream
aeration
(absolute
extra cost)
* Twelve of the Delaware Estuary Industrial Wastewater discharges in MPSX 6 are
also represented by SO.and/or particulate discharges in MPSX 3.
281
-------
ECONOMIC IMPLICATIONS OF POLLUTION-INTENSIVE EXPORTS BY DEVELOPING COUNTRIES
Peter A. Petri
Department of Economics
Brandeis University
Waltham, Massachusetts
SUMMARY
A new, detailed world model is described and used
to identify some economic implications of exports of
pollution-intensive products by so-called "fourth
world" countries. For these nations, pollution-
intensive exports are found to be unattractive
relative to conventional types of exports from the
viewpoint of various economic criteria. Still,
pollution-intensive exports are found to generate
net earnings of foreign exchange, a factor critical
to the development prospects of resource-poor, low-
income regions.
1. Introduction
At the request of the United Nations, a team of
economists at Brandeis and Harvard Universities has
recently assembled a comprehensive, disaggregated,
multi-regional model of the world economy.* The
purpose of the model is to shed light on the alter-
native paths the world economy could follow over the
next three decades. To this end, the model contains
a large amount of detailed information on natural
resources, agriculture, industry, and the environ-
ment. It is used here to assess the economic conse-
quences of certain alternative export strategies for
a group of developing nations.
In a series of projections described elsewhere,
the model has shown that the attainment of reasonable
growth targets for a large part of the developing
world will require substantial improvements in their
export capabilities. If the export positions of
these nations were to evolve along historically
established trends, the sharp disparities in income
that now prevail would widen in the future. The
prospects for developing countries without sub-
stantial resource endowments (the so-called "fourth
world") are especially vulnerable to the projected
external payments imbalances. These problems
motivate the search for alternative export strategies
for these nations—including two particular approaches
investigated in this paper.
The first of these strategies would involve
stepped-up exports of commodities that are conven-
tionally thought to represent the comparative advan-
tages of a developing economy. The second strategy
would focus on exports of products manufactured by
relatively pollution-intensive processes. This latter
approach rests on the assumption that the absorptive
capacities of the environment are greater in areas
that have not yet experienced extensive industrializa-
tion, and that this fact might obviate the need for
costly abatement measures. It is not our purpose to
test the validity of these assumptions. Rather, we
concentrate on the purely economic (in contrast to
environmental) implications of the two alternatives.
An important secondary objective of this paper is
to provide a direct, though simple, example of how the
new world model can be used to study questions in
international policy. The next section offers a general
overview of the model's structure, though obviously its
precise technical details cannot be adequately described
in so short an essay.^
2. The Model
The world model consists of 15 sub-models, each
representing (in terms of some 175 equations and 229
variables) the economic structure of a particular
region. The sub-models are linked by a network of
trade, that is, by detailed inter-regional flows of
goods, services, and various types of capital.
The parameters of the system, that is, the
quantitative descriptions of the regional units, were
first estimated for 1970, and then projected forward
to 1980, 1990, and 2000. These four parallel systems,
describing the state of the world economy at the end
of each decade, are linked in turn by the growth (in
the case of capital) and depletion (in the case of
resources) of certain detailed stocks.
Figure 1 illustrates, albeit in highly simplified
form, the critical interdependencies within a given
regional sub-model. Figure 2 gives some indication of
how the sub-models are linked. The system is in fact
a good deal more flexible than Figure 1 indicates.
New variables or equations can be readily added. Also,
the direction of the logical flow can be changed by
varying which variables are prespecified and which are
endogenously determined in a given application.
Figure 1 presents the basic specification used in the
analyses of later sections; this structure reflects
one of many possible specifications of the system.
Officially, this project was described as the "Study on the Impact of Prospective Environmental Issues and Poli-
cies on the International Development Strategy." The senior research team was headed by W. Leontief, and included
A. P. Carter, J. J. Stern and the author. The model used in this paper is, of course, a joint product of the group;
however, the other members of the team do not necessarily share the particular conclusions and views expressed here.
P. A. Petri and A. P. Carter, "Resources, Environment, and the Balance of Payments: Application of a Model of
the World Economy," delivered at the Third Reisenburg Symposium on the Stability of Contemporary Economic Systems,
forthcoming in the Conference volume.
Preliminary "Technical Report" prepared for CDPPP, United Nations, May 1975, describes the model more fully. A
final version will be published by United Nations shortly.
282
-------
Figure 1. Internal Structure of a Region
/^Development^
\^ Targets J
X -,
Consumption J Gross Dom.
Level fi | Product /^
l!^ '
ffinvironmentalj
\ Standards^/
„ r~
Abatement'
Levels /£
T_
Net
Emissions/^
^
X k
Intel
De
N
44
r>
\j -\,
v
"^N
£>
I
mands /^
— (5) —
)
Investment
Levels f$
_
1 1
si/ >
M
Final
Demands
Tot
Dem
— (
^
ii
:al
rnds
fa
— Production,
Extraction/^
T ,
— © — ' v
\f
GrosS Capital
Emissions /£ Required /£
t. J
Key
^HE
x 16"
0
to Symbols
?)
—
&>
< —
(<§S
Labor
Required /J"
Government _
Purchases^
-7-[ I f
^
Apopulat ion7\
~\JJrban Pop^/
Export ^ Impc
Level (i Leve
Detailed ,-
Exports fa ^
J I
Extraction
Limits /£
^
Resource
Depletion/^"
(
•, Detailed
Imports fa
/
* \
\
Tri
Bal.
\
/ PRICE \ Pr
\ MODEL J ^Proje
\
/
'" ^
«i ^r
^ j
.^world
y
-------
Figure 2
Interaction of Regions
World Trade Pools
GDP
/Region A
\ Structure f- '
GDP
Region B's
Structure
I
Excess or\
dereraployment/
Bal. of Pay
Surplus/Def
The first full row of variables in Figure 1 shows
how the overall level of consumption is determined.
Here exogenous targets for gross domestic product
(GDP) are given and the endogenously determined levels
of investment, government expenditures, and foreign
trade follow from them. The GDP targets in this case
were supplied by the United Nations, and are consis-
tent with the goals of the U.N.'s Second Development
Decade. Government expenditures are determined
partly by the GDP, and partly by the size of the
urban population as it influences the requirements for
urban services. Investment and import levels are
determined by relationships further along the flow-
chart .
Exports are exogenous to a given region but
endogenous to the world system as a whole. Figure 2
describes the trade model that links the 15 regional
sub-models. The trade model leaves the determination
of each region's imports to the structural equations
describing that region. Import requirements are then
summed across regions, and the resulting world
demands are allocated to the regions as exports. The
allocations are accomplished by export share coeffi-
cients specific to each traded commodity. These
regional export shares, initially projected with
regression studies based on historical and cross-
section data, can be readily changed to accomodate
alternative assumptions, as is done later in this
paper.
Given the detailed list of exported commodities,
and the levels of consumption, government expenditures
and investment, it is now possible to specify the
detailed final demands facing each regional economy.
The transformations from overall demand levels to
demands for specific commodities are accomplished by
various converter coefficients representing the compo-
sition of consumption, investment, etc. These co-
efficients depend on the region's per-capita income,
and also reflect, in some cases, region-specific
influences on the commodity breakdown of demand. The
detailed final demands are added to intermediate
demands (the input requirements of producers) to arrive
at the total domestic demands facing the regional
economy.
284
Unlike most input-output based models, the system.
treats several key commodities and activities in their
natural physical dimensions. Five agricultural commo-
dities, nine exhaustible resource commodities, as well
as eight pollutants are measured in metric tons or
other relevant physical units. This feature makes it
possible to use physical quantity data and to check
the results against other detailed projections.
Domestic demands can be satisfied either by
imports or by local production. Depending on the
commodity, two different approaches are used to effect
these allocations. In the case of exhaustible resource
commodities, importing regions are assigned output
levels consistent with the amount of regional resource
reserves still available, and imports are used to fill
all remaining unsatisfied demands. In the case of
manufactured products, import dependency ratios are
specified using, once again, regressions based on
historical and cross-section data. These regressions
indicate that a region's import coefficients generally
vary inversely with economic size, and depending on
the commodity, either increase or decrease as a
function of the region's development level relative
to the development levels of its foreign competitors.
With one or the other of these approaches, the
domestic demand for each commodity was apportioned
between imports and domestic production.
In turn, the domestic output levels determine the
demand for intermediate inputs and the requirements
of various types of capital and labor. These require-
ments are calculated using input-output coefficients
that vary with the region's development level, with
time, and in some instances, with certain region-
specific conditions.
The capital requirements of producers, along with
the capital requirements of households and of the
abatement activities are next used to determine the
economy-wide level of total investment. These compu-
tations begin with the capital stocks available at
the beginning of each decade, and arrive at the
investment levels that provide for the replacement of
worn-out plant and equipment and for the required net
expansion of capacity.
As shown on the left side of Figure 1, production
also results in "gross emissions" of various specific
pollutants. A set of abatement activities, e.g.,
various levels of waste-water treatment, is specified
as a means of controlling the pollutants generated in
production and by households. Untreated emissions
plus the residuals emitted by the abatement processes
are summed to show the net emissions released into the
environment. The usefulness of this information is
limited, of course, by the present inability of the
model to determine specific local concentrations
within its large geographical areas.
On the right side of Figure 1, the detailed
export and import levels are valued at projected prices
in order to arrive at projected trade balances. The
price model is independent of the physical system dis-
cussed so far, though it is based on many of the same
assumptions, relationships, and structural coefficients.
The price model relies on the inter-industry
structure of an advanced developed economy to examine
the price implications of the various projected changes
in the structural coefficients. The prices obtained
are normalized to keep the value of a bundle of con-
sumption goods constant throughout the projection
period, and should therefore be interpreted as rela-
tive rather than absolute price projections.
The inputs structures of the resource industries
played an important role in the estimation of future
prices. As each region exhausted its high-grade
reserves of a specific resource it was assumed to move
-------
to lower quality deposits. This meant, in turn, that
extraction would entail higher input requirements
(per unit of usable resource output) and hence higher
costs. Specific (though obviously tentative) data
about the quantity and quality of deposits in each
region were used to trigger the changes in extraction
input requirements. Of the relative price changes
projected, a large part, can be traced to the successive
exhaustion of high-grade reserves of a number of
resource commodities. Other, smaller effects arise
because labor productivities are projected to grow at
unequal rates in different sectors, and because
various kinds of input substitution are expected to
take place.
Our description has, so far, dealt with a
particular structural specification based on exo-
genous GDP targets. Alternative specifications
make it possible to ask rather different types of
questions. For example, it might be useful to know
what GDP levels might be attained given, say, limits
on the available labor force. Figure 2 shows a
schematic approach that assigns a unique specifica-
tion to each regional sub-model, depending on the
particular factors that are expected to govern that
region's future development. In Region A, the supply
of labor is assumed to limit the level of GDP. Con-
ceptually, the appropriate level of GDP could be found
by trial-and-error, as the level that (through the
interactions described in Figure 1) results in
"correct" labor requirements. In the case of Region B,
balanced (or appropriately imbalanced) trade might be
viewed as the relevant target. The computations do
not in fact need to depend on a trial-and-error pro-
cedure: the results of the new specification can be
obtained directly by modifying and solving the original
simultaneous equation system used to describe the
region.
A further implication of this approach is that
several different instruments could be used to achieve
the same ultimate outcome for any given target vari-
able. In order to obtain balanced international
accounts, for example, the region's share of world
exports might be assumed to increase even though its
GDP is held constant. Alternately, its import-
dependency coefficients might be changed, or new
assumptions might be introduced concerning inter-
national aid and capital flows.
3. The Experiment
The two hypothetical trade development programs
(representing the conventional and pollution-intensive
export strategies) will be examined in the context of
the'GDP-target specification shown in Figure 1.
Earlier projections based on this structure have
generally shown sizeable and deteriorating balance of
payments deficits for developing regions without sub-
stantial resource endowments. These deficits are due
to the rising prices of imported resource commodities,
to the high import-intensity of capital formation in
developing regions, and to the relatively slow growth
of markets for the key exports of the developing
world.
Against this background we turn now to examine
the Implications of a pollution-intensive export pro-
gram for three developing regions: Latin America ^
(Medium Income) , Asia (Low Incomg , and Arid Africa.
It is clear, of course, that any strategy that results
in a vigorous expansion of exports will also improve
the exporter's balance of payments position. In
order to identify the specific characteristics of
the pollution-intensive program, we perform a con-
trolled experiment; one that contrasts the effects
of this strategy with the implications of more tradi-
tional approaches to export development.
In Experiment A,export increases are assumed to
occur in five sectors (textiles and apparel, wood
products, furniture and fixtures, printing, and
miscellaneous manufactures) characterized by labor-
intensive and relatively standardized production
technologies. In Experiment B,the same amount of
exports is assumed to be produced by a different
group of sectors (primary metal processing, paper,
industrial chemicals, rubber, and other chemicals),
industries that are generally recognized as the most
pollution-intensive among manufacturing processes.
Both programs are constructed to generate (by
the year 2000) $50 billion of new exports for the
three regions taken together. The $50 billion is
divided among the regions in proportion to the
currently projected exports. The increases are further
assigned to specific products—within the industry
group relevant to each experiment—in proportion to
overall world trade in these products. The hypotheti-
cal export increases calculated this way are shown in
Table 1.
Table 1. Alternative $50 bill. Export Strategies
($ bill. , 2000 relative prices)
A. Conventional Exports**
Latin Arid
America Asia Africa
Textiles, Apparel 13.0 20.5 1.69
Wood Products 1.7 2.7 .23
Furniture, Fixtures .3 .4 .03
Printing 1.2 1.8 .15
Miscellaneous Mfg. 2.3 3.6 .30
Totals (Z - 50.0) 18.5 29.1 2.40
B. Pollution-Intensive Exports
Primary Metals 6.0 9.4 .78
Paper 4.0 6.3 .52
Rubber 1.0 1.6 .13
Ind'l Chemicals 4.4 7.0 .57
Other Chemicals 3.0 4.7 .39
Totals (£ = 50.0) 18.5
**
29.1 2.40
Detail may not add due to rounding.
K
These three regions include (a) Argentina, Brazil,
Mexico, Chile, Cuba; (b) Bangladesh, Pakistan, India,
Indonesia; (c) Egypt, Ethiopia, Morocco, Sudan, plus
in each case smaller countries.
The experiments were implemented by inflating
each region's export share coefficients so as to
generate the export increases of Table 1. Both pro-
grams are assumed to be phased in gradually over the
1970-2000 period, reaching the specified increases in
the year 2000.
In the context of fixed GDP targets, the export
increases have two immediate effects: first, exports
displace consumption goods in production and, second,
the export increases reduce the region's trade deficit.
Secondary consequences follow from the fact that the
input structures of the export-oriented sectors may be
quite different from the input structures of the con-
sumption-oriented activities that they replace. These
precise consequences depend, of course, on the sectoral
mix of the export program, and shall be examined
shortly.
285
-------
While using the fixed-GDP specification, we shall
not be able to measure directly the growth-generating
consequences of either program. To do so, we would
have to identify a specific limit on each region's
development (as is done schematically in Figure 2)
and experiment with the alternative export strategies
under that particular constraint. To the extent that
the programs affect the limiting factor differently,
they would generate different rates of long-term growth.
At this stage, however, the fixed-GDP context
offers a more general way of assessing the effects of
each strategy on a set of different factors that
potentially limit growth (including foreign exchange,
capital, and labor)—without prejudging which of these
factors is most acutely limiting. This is done in
Section 4. The next logical step, the quantification
of the ultimate development impacts of these effects,
is left to future work.
4. Comparison of Alternative Export Strategies
Table 2 presents the balance of trade implica-
tions of the two strategies. In neither case is the
net improvement (for the three regions taken together)
as great as the $50 billion export increase; both
export strategies involve leakages in the form of
added import requirements. The import leakages of
pollution-intensive exports are some $5.5 billion
higher than those of the conventional strategy.
Pollution-intensive industries tend to have above-
average raw material and capital requirements, and
these two kinds of commodities are heavily imported.
In addition, the inter-industry purchases of
pollution-intensive industries tend to favor the
least developed and therefore most import-dependent
sectors of a developing economy.
Table 2. Balance of Trade Results, 2000
A. Improvement of LDC Balances
($ bill., 2000 relative prices)
Central
Projection
Latin America -84.6
Asia -81.6
Arid Africa - 7.9
Subtotal: -174.1
Improvements over
Central Projection:
Export Strategy
A B
-65.5 -69.1
-58.8 -60.9
- 6.4 - 6.2
-130.7 -136.2
+43.4
+37.9
B. Regional Distribution of the Losses Offsetting
the LDC Improvements (percentages)
Western Europe (High Income)
North America
Japan
Soviet Union
Eastern Europe
Western Europe (Medium)
Middle East
Asia, Centrally Planned
Latin America (Low Income)
Tropical Africa
Southern Africa
Total Losses
Total Losses in $
The rest of the world is differently affected
by the two export alternatives. As the second part
Export
A
44
9
16
4
10
6
3
3
1
1
1
100%
-43.4
Strategy
B
41
27
9
10
4
1
2
3
1
1
1
100%
-37.9
of Table 2 shows, the predominant effect of both
strategies is to reduce the trade surpluses (or to
increase the deficits) of advanced developed
countries. The conventional exports are apparently
diverted more sharply from Europe and Japan, while
the pollution-intensive products are obtained more at
the expense of North America and the Soviet Union.
The internal consequences of the trade alterna-
tives are summarized in Table 3. The most striking
differences emerge in the overall capital stock re-
quired in production. In Experiment A, the diversion
of gross product from consumption-oriented activities
to conventional exports has in fact saved capital in-
puts. In contrast, the pollution-intensive program
imposes added capital requirements on the regional
economy. While the $34.4 billion difference between
the programs is small relative to the total capital
stocks of the three economies, it is large when com-
pared to the capital requirements of the programs
themselves. It would take about 40% more capital to
implement the pollution-intensive strategy than it
would to produce equally valued conventional exports.
Table 3. Additional Requirements
of Pollution-Intensive Strategy
over the $50 bill. Conventional Strategy
($ bill., 1970 prices except as noted)
Building & Plant Capital
Equipment Capital
Subtotal: All Fixed Capital
As % of Economy-wide Stock (%)
Annual Investment
Employment (mill, myr.)
All Three
Developing Regions
18.1
16.3
34.4
1.2
2.3
1.5
The employment differences between the programs
are small and mixed. Quite surprisingly, both pro-
grams tend to generate about the same amount of
employment when all indirect effects are taken into
account. Differences might be found if employment
were further itemized by skill categories, but this
refinement has not yet been implemented on the world
system.
The environmental implications are shown in
Table 4. While the economic differences between the
alternative programs are found to be small relative
to overall economic magnitudes, this is not the case
with respect to the net emissions of specific pollu-
tants. These added pollutant loadings are not easily
interpreted in the absence of geographically detailed
projections. Nevertheless, they suggest that a
pollution-intensive export program that is large
enough to affect the balance of trade will also have
non-negligible environmental consequences.
If the difficulty of achieving one or the other
of the export targets is related to the extent of the
required structural transformation of the economy,
our solutions can also shed light on the relative
feasibility of the two programs. Table 5 shows the
output changes implied by each of the programs
relative to the standard projections for 2000.
The structural changes implied by the pollution-
intensive alternative are typically larger than those
for the conventional program, and especially so for
the two poorest regions, Asia (Low Income) and
Tropical Africa. This was to be expected, of course,
286
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since the conventional export bundle was designed to
emphasize the strengths of a developing economy. The
radically different output profiles obtained under
Experiment B suggest that major changes would have to
take place (in terms of new infra-structure, manpower
training, and the establishment of supplying indus-
tries) before the new activities can be absorbed in
the economic fabric.
Table 4. Additional Net Emissions
with Pollution-Intensive Export Strategy. 2000
(percentages relative to projected emissions)
Pesticides
Particulates (Air)
BOD
Nitrogen (Water)
Suspended Solids
Dissolved Solids
Latin
America
-1
68
12
8
16
8
Asia
-2
11
5
0
23
8
Arid
Africa
-1
9
3
0
U
3
In sum, several economic criteria mitigate in
favor of the conventional and against the pollution-
intensive strategy—provided, and this is quite
important, that a choice exists at all. Even the
pollution-intensive approach, relying as it does on
some resources that are especially scarce to a
developing economy, does generate foreign exchange,
and would, in the absence of other earning oppor-
tunities, most likely contribute to the development
process.
Table 5. Additional Output Required
to Implement Export Strategies in 2000
(percentages relative to projected output)
A. Conventional Exports
Textiles, Apparel
Wood Products
Furniture, Fixtures
Printing
Miscellaneous Mfg.
Five Industries
Together
Latin
America
27
16
-2*
8
24
15
Asia
20
32
-2*
37
23
17
B. Pollution-Intensive Exports
Primary Metals
Paper
Rubber
Ind'l Chemicals
Other Chemicals
Five Industries
Together
19
26
11
20
17
22
67
75
41
35
33
49
Arid
Africa
19
50
0
40
18
16
42
40
33
17
30
30
Since in our computation exports displace consump-
tion in (fixed) GDP, and since furniture is important
in consumption and not so in the export package,
furniture output would decline if the strategy were
implemented.
5. Conclusions
By postulating two hypothetical export programs,
we have attempted to identify some economic conse-
quences involved in the choice between conventional
and pollution-intensive export strategies. The
pollution-intensive approach is found to be more
expensive in terms of capital, and requires more
imports. Moreover, this approach would imply size-
able shifts in the output mix of the developing
economy, and might create non-negligible environmental
repercussions. Also, at least initially, the pollution-
intensive sectors would tend to operate as an enclave
within the regional economy.
Some dynamic theories of development suggest that
the early establishment of basic industries—as the
pollution-intensive sectors typically are—can
actually hasten development through a variety of
backward and forward linkages with other sectors
of the economy. These effects would have to be
large in order to offset the static disadvantages
cited above.
287
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A TAXONOMY OF ENVIRONMENTAL MODELS
Robert U. Ayres
International Research and Technology Corporation, 1501 Wilson Boulevard, Arlington, Virginia
22209
The Role of Models
Problems of the environment are essentially pro-
blems of production and consumption, as concerned with
Teal physical materials and energy. These real physi-
cal materials must be derived from the natural envi-
ronment where they are distributed unevenly. Their
usage involves successive stages of processing and
transformation which inevitably result in social costs
(externalities), ranging from noise to the discharge
of toxic waste materials. Similary, so-called "Final"
consumption—that convenient abstraction from classi-
cal economics—is not final at all in terms of dis-
position of real materials and energy. On the con-
trary, consumption of material goods means in practical
terms that the goods have lost their utility value and
become wastes. But these still have to be disposed of
and are still capable of causing very serious harm to
the natural environment and to man, depending upon
the location and method of discharge or disposal.
In short, a whole collection of new problems
associated with stocks and flows of physical materials
and energy has come to the fore. They were with us
all along, but in the 1930's other problems associated
with organizing the economy and fully utilizing its
resources were far more urgent. Natural resources, on
the other hand, are becoming painfully scarce in the
industrialized world. Many of the most abundant
natural resources of the earth have already been dis-
sipated, not to say wasted. The surface of the earth
still has abundance to offer, but we must dig deeper,
scrape the bottom of the ocean, or look at more remote
areas of mountains, deserts, and jungles. Extracting
these resources is creating newer and more serious
problems also. Delicate ecosystems such as the Arctic
tundra or the tropical oceans are beginning to show
adverse"effects from this intensification of digging,
drilling, and quarrying. Mine wastes, oil leakage,
combustion products of a vast variety of types and
kinds of pollution are fouling our environment, and
making survival impossible for many harmless species
of plants and animals which formerly shared the earth
with us. Some have even questioned whether human life
itself can survive for long amidst this environmental
carnage.
No doubt, some of the immediate fears of resource
exhaustion are overblown, but it is not our purpose
here to evaluate their validity. It is enough to say
simply that the ''new" problems facing economists in
the 1970's and 1980's are intimately associated with
the real properties of physical materials and energy,
and above all, with their stocks and flows—that is
with their physical quantities. To deal with these
problems we need first of all an appropriate economic
theory. The conventional paradigm addresses the
economy as a set of relationships between production,
investment and consumption expressed in monetary terms,
and defines its concerns as determining conditions for
maximizing consumer utility and social welfare by
optimizing these relationships. But another paradigm
is needed in which the economy is viewed as a set of
transformations of physical materials from the raw
state through successive stages of extracting and pro-
cessing to goods and services, and finally to waste
flows. Even physical dispersion and biological impacts
must be considered. The problem of optimization is
correspondingly broadened. This broader theory must
address the problem of production of externalities as
well as economic services, and the allocation of such
externalities. It must deal with the problem of defin-
ing and maximizing social welfare subject to resource
supply pervasive constraints, laws of thermodynamics,
and the existence of externalities resulting from
waste residuals; and it must provide theoretical tools
to facilitate our understanding of the appropriate
mechanisms for managing the economy.
One characteristic of the "new" problems in
environmental economics is that they are increasingly
at the "micro", rather than the "macro" level of ag-
gregation. Resource and environmental concerns tend
to involve consideration of technological particulars,
as contrasted with interrelationships among broad ag-
gregates such as population or Gross National Product.
This increasing concern with detail is character-
istic of the development of any science. In the early
stages of development of theoretical chemistry, it was
convenient to proceed by lumping all the chemical
elements together, calling them "matter" and looking
for generalized "laws of matter". But the number of
valid inferences that can be made from this simple
model is quite limited. Each element is different,
each has different properties, each reacts differently
from the others. Sooner or later the chemist is
forced to recognize and take into account these dif-
ferences by developing a more elaborate model.
However, the chemist continues to consider mole-
cules essentially as complete entities. These are the
objects of his research. It is precisely the combina-
tions between atoms (of similar or dissimilar species),
which are governed by electromagnetic forces, that
chemistry is all about.
Note that the analytical methods of chemistry are
of no value in studying reactions that occur within
the nucleus of a single atom. These are governed by
different—stronger but shorter range—forces which
have essentially no influence on the interactions be-
tween atoms and molecules. Conversely, the electrical
forces which.govern inter-atomic relations have no
measurable effect on the probabilities or rates of
nuclear reactions. The two classes of phenomena are
virtually independent of each other, though neverthe-
less governed by the same fundamental physical laws.
On the other extreme, consider the gravitational
forces that control the motions of stars and planets.
These are the only forces in the universe that are ef-
fective at truly long distances. But, by the same
token, the gravitational forces are incredibly weak by
comparison to electromagnetic forces. Only when
enormous numbers of particles are collected together
as "mass" is the gravitational effect significant--
whereas the electrical forces are cancelled out at a
distance by the fact that positive and negative charges
are present in equal numbers. The laws of chemistry,
then, have little to say about the motions of cosmo-
logical objects. Similarly, astrophysics contributes
little to chemistry.
Each branch of science lumps together and aggre-
gates "over" the objects and forces that are too weak
or too short range to influence the phenomena with
which it concerns itself. However, it also aggregates
into categories those objects and forces with which it
is concerned. Chemistry aggregates atoms and molecules
by species. It does not examine single atoms. Similar-
ly, other sciences such as physics, astronomy, and
biology tend to classify their objects in such a way as
to distinguish differences that matter from differences
that do not matter at that level of aggregation.
Aggregation, ther, is at the heart of theoretical
science. If an investigator examines only individual
cases, in an individual way, patterns are indistin-
guishable and one is soon lost in a sea of particulars
to which no general significance can be attached. On
the other hand, if aggregation is carried too far,
unlike elements are lumped together, essential
288
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differences are obscured and again, the expansion of
knowledge is limited.
The environmental or social scientist's problem
in this respect is obviously more complex than that of
the chemist, who has to deal with a very limited num-
ber of clearly defined elements, with known atomic
structure, which he combines or separates in endless
ways. The environmental or social scientist, on the
other hand, has no "unit" of absolutely fixed value or
quantity. Measures of utility or value are ambiguous.
Even physical measures of the quantity of a commodity
(tons or cubic feet) fail to take account of physical
transformations, not to mention variations in the
quality. Not only is everything influenced by every-
thing else, but everything fluctuates in relation to
everything else.
In order to find answers to many of the pressing -
problems of an era of rapid technological change, an'
environmental economist must be able to carry out
analysis at a level of aggregation that is appropriate
to take into account the widely different resources,
mater-Lais, forms of energy and production processes to
which technological changes specifically apply.
A list of examples of "new" problems facing
economists arising from the resource-environment-
technology interface could be made arbitrarily long.
Almost every major technological decision has a
resource/environmental dimension. The controversy
over the SST is an excellent illustration. To build
and operate such an aircraft will result in increased
demands for hydrocarbon fuels, and it will result in
physical disturbances to the stratosphere that may ul-
timately affect the intensity of both ultraviolet and
visible solar radiation on the Earth's surface. All
of these impacts have potential economic consequences
of significant magnitude, which require assessment.1
Similarly, problems arising initially out of perceived
resource-needs immediately reveal technological and
environmental aspects. Thus, the exploitation of
Alaska's north slope involved building an enormous
north-south pipeline across Alaska, with immense
potential for environmental disturbance. Proposals to
exploit Colorado oil shale or Wyoming-Montana coal are
seen to require diversion of large amounts of scarce
water away from traditional agricultural uses. The
proposals to solve a resource problem by relying more
heavily on nuclear power, especially "breeder reactors"
and plutonium reprocessing, are also evidently fraught
with environmental risks.
The history of the last few years has been—and
undoubtedly of the next decades will be—increasingly
preoccupied by the need to choose among and between
complex, expensive and uncertain technological pro-
grams; each of which involves large potential environ-
mental risks and hazards as well as possible benefits.
The cheap alternatives and easy choices are no longer
available.
And the factors which must be weighted to arrive
at rational choices are intrinsically concerned with
detailed technological and environmental questions.
What is the marginal impact on the human environment
of one unit more (or less) of mercury? or PVC? What
is the net environmental benefit of electric cars using
nuclear power vis-a-vis ICE powered cars using gasoline?
What if we burn coal to make electricity in large power
plants in remote areas vis-a-vis converting it to gas
and burning it in local "total energy" installations?
How much will it cost to desulfurize coal? oil? What
are the potential markets for by-product sulfur? Etc.,
etc.
Lawrence Klein has defined a model as a "schema-
tic simplification that strips away the non-essential
aspects to reveal the inner workings, shape, or design
of a more complicated mechanism".2 Aggregation is the
key to model design, just as it is the key to theoreti-
cal science in a more general sense. The fact that a
model cannot hope to reproduce "all" the details—even
the more important ones—of a complex reality is an
inherent limitation on what can be accomplished by it.
Yet its comparative simplicity is also a strength. An
excessively detailed model would be cumbersome to
handle and expensive to maintain, yet still imperfect.
On the other hand, the simplification of reality im-
plicit in a model can be a trap, for if the model omits
key factors that may have a determining effect on
possible outcomes, it can depart too far from reality
and lead to false conclusions. It is all too common
for even experienced investigators (who should know
better) to be hypnotized by the neat rows of figures
emerging from a computer and mistake them for a por-
trayal of real facts.
Central to the design problem,too, is the decision
of what factors the model should explicitly take into
account. This judgment is determined by the questions
the model is designed to answer. If the investigator
wants to know how fast DDT is building up in the ocean,
he may project DDT use in cotton farming and malaria
control. This can be useful, although it does not tell
him where the effects will be concentrated or which
species will be affected. Its predictive accuracy, of
course, hangs on the accuracy of the projections of the
two aggregates: cotton production and public health
use. If the tradeoff between malaria control and over-
population is to be explored—by country—a much more
detailed analysis of alternate strategies is needed.
To accomplish the practical purposes of applied
environmental analysis, clearly, we must build com-
puterized accounting and optimization models to reflect
a wide variety of such factors.
Qualitative vs. Quantitative Models
The first and most important distinction that
needs to be made is between qualitative and quantita-
tive models. The term "qualitative" may seem inappro-
priate as applied to models, but it is not. Diagrams
and pictures—said to be "worth a thousand words" —
are clearly models, by Klein's definition. (Even a
photograph is a "model", since it represents a 3-
dimentional dynamic reality in a 2-dimentional static
form.) For that matter, a verbal description of a real
event is also a kind of model. Qualitative models can
be highly precise and rigorous in expressing certain
types of information. A classic example is the famous
periodic table of the elements, developed by Mendeleyev.
It is clearly a model, and clearly qualitative. There
are no measures involved.
Despite the obvious importance of qualitative
models, the remainder of this paper will be concerned
explicitly with quantitative models.
Simulation vs. Optimization Models
A second fundamental dichotomy can be drawn be-
tween simulation (or forecasting) models and optimiza-
tion models. While both types are applicable in
economics, the latter type is more fundamental to the
discipline, whereas physical models are more likely to
be of the former kind. Indeed, economics has generally
been defined as the study of optimal allocation of
scarce (limited in availability) resources among com-
peting ends or uses (in ordinary language, this pro-
cess is often simply called "economizing").
In particular, classifical economics is concerned
with the allocation of investment capital among compet-
ing projects and localities, the allocation of income
among competing expenditive categories (or means of
achieving satisfaction), and so on. The newer pro-
blems of economics, as already noted, concern optimal
allocation of natural resources among sectors of
society, selection of technologies to maximize desired
outputs and minimize costly inputs and/or costly wastes;
selection of optimal pollution abatement strategies,
investment schedules, etc.
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Static vs. Dynamic Models
A third key distinction is between static and
dynamic models. The static/dynamic distinction con-
cerns the treatment of time. In a static model, time
is not a variable: the solution is valid either for a
particular point in time (only), or for all time, de-
pending on whether the exogenous variables of the pro-
blem are themselves time dependent or not. "Cross-
sectional" survey data is often used. In a dynamic
model, time is an explicit variable and the solution
evolves with time. Longitudinal (time-series) data is
appropriate. Clearly the dynamic optimizing case is
most general, but is also most difficult to formulate
(and to compute). Static non-optimizing models are of
comparatively little importance. The only significant
example I know of in economics is the input-output
model. I know of no good examples in the physical
sciences. Combining the two dimensions, there are four
major categories:
• static simulation
• dynamic simulation (forecasting) models
t static optimizing models
• dynamic optimizing models.
Causation vs. Correlation Models
Quantitative models may also be divided along
another axis, depending on the use of phenomenological
causality. This is not a distinction that can always
be made cleanly by an outside observer, since it some-
times depends on the modeller's intentions. There is a
wide spectrum. At one extreme one finds "blind" ex-
trapolation of exponential curves as straight lines on
log-paper--where no strict causality is even suggested
and the forecaster assumed (in effect) that the curve
has a kind of independent life. At the other extreme
is the completely analytic model where everything is
explained in terms of a fundamental physical theory,
such as the "laws of gravitation". Obviously even
fundamental theories are not unchangeable. (Too many
have been upset during the present century for us to
feel confident that we know all the basic laws govern-
ing matter and energy, still less living organisms.)
Thus dependence on "causality" is always relative.
Econometric models, based on correlative relation-
ships between variables determined by statistical
analysis of time-series data, tend to be weak in
causality. In a sense, the use of sophisticated
statistical methods can be a substitute for understand-
ing underlying mechanisms and relationships. (This is
not necessarily the case: a good theoretical model can
be improved by the application of refined statistical
techniques for empirical estimation of key parameters.
But often statistical means are employed to select
relationships between variables precisely because
fundamental theory is lacking; indeed, the theory may
develop more rapidly as a consequence of such analysis.)
Realistic vs. Abstract Models
Causal models, based on fundamental theory—as
opposed to correlative models developed by statistical
analysis of empirical data—may be either realistic or
abstract. In the latter case they are intended to
represent real phenomena and to assist either in fore-
casts or in determining optimum arrangements. On the
other hand, abstract (data-free) models are intended
only to generate "theorems", elucidate limiting cases,
and so forth. They tend to be deliberately oversimpli-
fied. Much of theoretical resource environmental
economics in recent years has been concerned with ex-
ploring the properties of very simple models that
(presumably) exemplify more general principles.
Short-term vs. Long-term Models
An important subsidiary distinction, applicable to
realistic forecasts only, must be made between short-
term and long-term dynamic simulation models. The
distinction is extremely important in practice, yet
often overlooked (or not understood) even by many
practitioners. The difference hinges on how data is
used in the model and how the results are interpreted.
Briefly, long-term models are concerned with moving
averages or trends, in which temporary departures from
equilibrium are deliberately ignored. Indeed, the more
precisely calibrated the model is for use in short-term
forecasts, the faster it will depart from the long-term
trends. Conversely the more closely it is tied to
long-term trends the lower the correlation with short-
term fluctuations. Hence fluctuations in the input
(i.e. historical) data are regarded as "noise" and are
normally smoothed over. On the other hand, short-term
models are precisely concerned with the fluctuations
away from equilibrium. Hence they tend to utilize all
historical data, with the smallest possible time incre-
ments—usually quarterly—and, as a rule, recalibrate
and recompute after each new set of data points are
added to the series. And because the non-equilibrium
aspect is vital, multiple correlation regression
analysis is heavily used in developing the equations.
The important point here is that short-term models
are predictions because they take off from an actua-l
set of initial conditions, such that all values of
variables and parameters are guaranteed to be realistic,
at least, at time zero. The predictive value declines
fairly rapidly as the forecast horizon is extended, of
course, because the starting point is always off-
equilibrium.
Long-term models, on the other hand, do not give
predictions, but are used instead to make projections
usually in sets of possible alternatives). A long-term
model has no predictive value even in the short-run,
because it is concerned with trends and smoothed
averages. These are seldom in agreement with actual
current values of the model variables. And because
equilibrium conditions are mainly of concern, it is
reasonable to depend heavily on accounting identities
(e.g., input-output relationships, materials, energy
balances, etc.) which can be relied upon to change
fairly slowly, if at all. The purpose of a long-term
model is to examine the quantitative consequences of
changes in exogenous trends in parametric relationships
or in constraints. Conclusions drawn from long-term
models should always be explicitly contingent on the
particular set of starting assumptions. (A contingent
statement is always of the type: "if ... then ..."'.
The assumptions are an intrinsic part of the statement.)
Because short-term and long-term models are used
for different purposes (and supported by different
institutional sponsors) the developers are often out of
touch with each other and—at times—unjustifiably
contemptuous of each other's methodologies. In parti-
cular, there is a tendency for each to encroach on the
others' domain, rather than to develop a synergistic
dialog. But it is becoming increasingly urgent that
such a dialog be initiated, both to minimize duplica-
tion of effort and rediscovery of the wheel and for
more fundamental reasons. The latter have to do with
the need to develop realistic long-term dynamic opti-
mizations in which short-run departures from equili-
brium play an explicit role.
For the moment it is worth noting, simply, that
realistic optimization models currently tend to draw
more on engineering and physical information than on
statistical (time-series) analysis—which may explain
why econometricians have largely ignored this area in
the past.
Levels of Aggregation
Considerations noted earlier suggest that one use-
ful way of further subdividing realistic models is by
level of aggregation. There exists a natural hierarchy
of aggregation levels in economics, each level useful
for some particular purpose. Most highly aggregated
290
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(call this Level 1) is the model based primarily on
such broad measures as total population, total labor
force, unemployment rate, gross national product, gross
capital formation, private consumption expenditures,
wholesale and consumers' price indexes, rate of price
inflation and so on. Non-economic models at the same
level would introduce total energy flow, biomass, etc.
Some of these aggregates, notably population and labor
force, can be estimated for a number of years ahead
because birth and death rates change relatively slowly,
and age distributions of the population can be pro-
jected with fair accuracy.
Beyond these pivotal aggregates, forecasts of
economic quantities become increasingly difficult and
have to be based on a priori assumptions, such as the
proportionality of inputs to outputs or the assumption
that relationships between the various quantities that
have held true during past periods of time will con-
tinue to hold true in the future. Such relationships
often take the form of equations, by which, if certain
macro-variables such as population, labor force and
productivity are assumed, the other quantities can be
estimated. The trends projected by such techniques
are more reliable for short-term forecasts than for
long-term ones; and therefore, as forecasts extend
further and further into the future, they are likely
to become increasingly unrealistic.
A special problem with long-term forecasts at
this level of aggregation is that the key elements af-
fecting long-term changes in the economy are not
necessarily the same as those affecting the short term.
For the long-term, the key elements include technologi-
cal changes, possible raw material shortages, rising
energy costs, material substitutions, changes in social
customs, changes in the educational level of the popu-
lation, environmental deterioration, and many other
factors not explicitly accounted for in the aggregates
generally used in Level 1.
A second level of aggregation (call it Level 2)
involves dividing up the economy by industry sector
and/or region. A familiar example of this is the
input-output model which takes the form of a matrix
recording the pattern of flow of materials and energy
(or the pattern of purchases and sales) between indus-
try sectors, between each sector and the government,
and between each sector and the final customer. Such
a table does not identify the particular commodities
or energy forms that flow into and out of the sectors,
nor the transformations that take place in the produc-
tion processes, but it accounts for all inflows and
outflows in total. These inflows and outflows must
balance, both for the system as a whole and for each
individual sector after accounting for waste and for
materials drawn from the environment.
The development of input-output models provided
for the first time a comprehensive view of the struc-
ture of the economy, like a still photograph that
catches an action in mid-motion. These models
facilitated studies to be made that had formerly been
extremely tedious, if not impossible. With them one
could determine the effects a change in one sector
might be expected to have on the other sectors. For
example, if automobile size and weight are reduced,
the direct effects on the iron and steel, coal mining,
petroleum refining, glass, nonferrous metals, synthe-
tic rubber, chemical, machine tools, and many other
sectors can be traced. But beyond these direct effects
are secondary and tertiary effects: the reduced demand
for intermediate products entering into the automobile
industry affects communications, transportation, elec-
tric power, and so on. The effects ripple through a
maze of inter-relationships.
For some industries the level of aggregation used
in published input-output tables—even if regionalized--
is still much too broad for accurate analysis. For
example, the sector "Industrial Chemicals" includes a
wide variety of products made from different raw
materials by different processes and used in differ-
ent sectors. Thus benzene is derived both from coal and
from petroleum. It is used in petroleum refining (to
gasoline), in manufacturing synthetic rubber, in making
the plastic styrene, and in many other chemicals. A
shift in the proportions of these products within the
sector can alter significantly the inputs and outputs
for the sector.
At the commodity level of disaggregation, it is
apparent that the same commodity can, in many cases, be
produced by several alternative processes. An example
is the production of PVC bottles. At least 20 differ-
ent processes may be involved in PVC manufacture and
these can be combined in more than 60 different ways-
each with different environmental impacts. In other
words, there are over 60 possible chains of processes
leading from raw materials to finished PVC, all requir-
ing different inputs and yielding different wastes. A
study of the environmental consequences of regulations
affecting process technology or energy would need to
take these alternative chains of processes into account.
To deal with problems where this level of detail is un-
avoidable requires a still higher level of disaggrega-
tion (Level 3).
Determinism vs. Uncertainty
A final distinction of utmost importance must be
made between models that are endogenously deterministic
with fixed inputs (in the clockwork sense) and models
that explicitly provide for stochastic or irregularly
variable inputs. Variable inputs may be distributed
according to different rules, ranging from normal
(Gaussian) or log-normal distributions to ad hoc
heuristic "scenarios" based on extra-model intelligence.
In the case of physical models stochastic or normal
distributions are common. For instance, the "mix" of
local weather conditions, genetic variability, or other
factors is likely to be subject to a normal type of
distribution. Apart from this, however, indeterminacy
is not a serious limitation for physical models since
it comes into play only at the atomic or sub-atomic
level of disaggregation. [Indeterminacy Principle,
formulated by Heisenberg, states that the product of
uncertainties of complementary variables such as momen-
tum and position will always exceed a specified minimum
value (called Planck's constant, h).]
In the case of economic, social or political
models the situation is significantly less favorable
for the modeller, however. Here the indeterminacy
principle becomes a factor if one attempts to predict
the behavior of individuals, committees or structured
organizations (including governments) having a small
number of effective decision-makers. This is a logical
implication of the free-will of the individual. But,
even if humans were actually instinctually pre-pro-
grammed, in the same sense as insects, an indeterminacy
principle would still be applicable because it is
clearly impossible to monitor an individual human's
behavior (including thoughts) closely enough to pre-
dict his or her actions without disturbing the object
of the surveillance to the point of affecting those
actions significantly.
To deal with indeterminacy in the realm of human
behavior it is convenient to introduce "policy"
variables (or parameters) in the models. Rather than
trying to predict what human behavior will be, which
is impossible where a small number of effective
decision-makers are involved, the model must be formu-
lated to explore the implications of alternative
decisions or "policy options".
Mapping Model Types to Issues
Space limitations do not permit a detailed ex-
ploration of this topic. A few brief comments must
suffice to conclude this paper. How can one decide
what type of model is most appropriate to a given
policy issue? The foregoing taxonomy constitutes a
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kind of hierarchical checklist for the classification 1.
of models. In effect it defines a large number of
possible "pigeon holes". On reflection, it is clear
that the same screening process can also be applied to
problems by examining the relevant variables and rela-
tionships:
• Are the pertinent data quantitative?
• Is the question one of prediction? Or is it a
question of characterizing the best (optimal) 2.
solution?
• Is time an explicit variable?
t Is there an underlying phenomenological theory
available? Or must one rely on observed correla- 3.
tions between independent observations?
• Is realism desired? Or is it the object of the
exercise to deepen ones understanding of the ^
fundamentals by systematic simplification?
• If time is a variable and realistic simulation is
desired, is the time-scale short or long?
• What is the level of aggregation at which the key 5.
phenomena are observable (viz. National? sectoral?
regional? commodity? process?).
• Are there stochastic or random elements in the pro-
blem? Is the behavioral response by individual
decision-makers or small groups of decision-
makers a factor in the problem?
Disregarding the last three items for quantitative
models there are 12 possible combinations of the
various characteristics noted above, of which 8 or 9
(at least) seem to be relevant (i.e. the boxes are
occupied). For two of the categories a further short/
long subdivision seems called for. Any of the cases
may be at any level of aggregation and may involve
stochastic or human choices.
REALISTIC NON-REALISTIC
Non-causal
(Statistical)
Static ?
Simulation
Dynamic Short
Simulation Long
Static
Optimization
Dynamic
Optimization
Causal -
Empirical
X
Short
Long
X
Causal -
Abstract
X
X
X
X
As noted above, classifications are not always unam-
biguous. For instance, an "equilibrium" air pollution
dispersion (e.g. "plume") model would certainly be
classed as a causal-empirical, but it is not quite
clear whether the term "static" or "dynamic" is appli-
cable. A pollution forecasting model utilizing
empirically determined pollution coefficients for
highly aggregated sectors would certainly be classed
as static-simulation, but there might be a question as
to whether truly causal relationships are used. If
the pollution output for a sector were developed based
on more detailed process-level analysis, explicitly
incorporating materials and energy balances, there
would be no ambiguity, of course.
As a matter of possible interest, SEAS belongs in
the causal-empirical-dynamic simulation (long-term)
category.3 The Materials-Process-Product Model (IR&T)1*
and the Russell-Spofford Model (RFF)5 probably belong
in the causal-empirical static optimization. Examples
of abstract models in the field of biology, ecology,
and environmental economics are quite plentiful. How-
ever, realistic dynamic optimization models have not
yet been developed to my knowledge.
A team of investigators composed of Wassily Leon-
tief, Anne Carter, Peter Petri, and Joseph Stern,
"Technical Report on the Study on the Impact of
Prospective Environmental Issues and Policies on the
International Development Strategy", prepared for
the UN Center for Development Planning Projections
and Policies Office, forthcoming.
Lawrence R. Klein, "What is a Model"
(unpublished).
U.S. Environmental Protection Agency, Strategic
Environmental Assessment System, Prototype Documen-
tation, Phase III, 1975.
Robert LI. Ayres, James Saxton and Martin Stern,
"Materials Process-Product Model", International
Research and Technology Corporation, July 1974.
C.S. Russell and W.O. Spofford, "A Quantitative
Framework for Residuals Management Decisions", in
A.V. Kneese and B. Bower, Environmental Quality
Analysis: Theory and Method in the Social Saienaes,
Resources For the Future, Inc., Johns Hopkins
University Press, 1972.
292
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A STOCHASTIC MODEL FOR SUBREGIONAL POPULATION PROJECTION
Peter M. Meier
Energy Policy Analysis Division
Dept. of Applied Science
Brookhaven National Laboratory
Upton, New York 11973
ABSTRACT
A stochastic method for the projection of subregional
population is developed, to be used in conjunction
with regional OBERS projections. The model is based
on a Monte Carlo simulation and numerical integration
technique to generate probability distributions of
future population , given some analytical formulation
of population density in urban areas, and is addres-
sed particularly to consulting engineers who must
make decisions on design capacity for waste treatment
facilities.
INTRODUCTION
Projections of population, and the associated speci-
fication of service area, waste flows and pollutant
loadings, lie at the very heart of the current nat-
ional effort to reduce water pollution. Yet, as the
recent controversy over excess capacity in intercep-
tors has amply demonstrated, the level of competency
current in the environmental engineering profession
in matters of socioeconomic planning is far from
adequate. This deficiency is all the more serious
in light of some of the very sophisticated optimi-
zation and design techniques employed in the engineer-
ing of the pollution abatement facilities themselves;
it clearly makes little sense to devote substantial
resources to detailed design and engineering optimi-
zation if the initial premise of design capacity and
expected loadings is in substantial error. In view
of the crude methods used to project population,^ and
the rigid use of design standards derived decades
ago, it should come as no surprise that a number of
recent investigations have found fault with current
facility planning practices. Indeed, it is a sorry
reflection on the profession that the current EPA
guidelines for planning treatment facilities find it
necessary to provide sample calculations of a present
worth analysis.
In this paper, we focus on one particular area of
socioeconomic planning, population projection. The
intent here is to illustrate some lines of analysis
that might profitably be applied to any large public
sector capital investment, but with particular em-
phasis on the planning of waste treatment facilities.
Experts in mathematical modelling will find little in
the way of sophisticated analytical formulation, but
then its content is addressed to the practicing pro-
fessional. Indeed, the most important criterion for
the successful development of a modelling technique
is the degree to which it is consonant with the
ability of the consulting profession to apply it, and
the ability of the public and the political process
to understand its assumptions. Highly complex models
will not aid the planning process if only their
originators can fully use them or fully understand
them.
THE OBERS PROJECTIONS
The OBERS projections of population and economic ac-
tivity, prepared by the U.S. Department of Commerce
and the U.S. Department of Agriculture for the Water
Resources Council,* are now in fairly broad use as a
basis for planning activities by Federal Agencies.
And the U.S. Environmental Protection Agency (EPA)
now requires that plans prepared under Section 201 of
PL 92-500 relate the proposed facility capacity, and
the forecast population to be served, to the applica-
ble OBERS projection. Unfortunately, the smallest
spatial unit for which an independent OBERS projection
is available is the Standard Metropolitan Area (SMSA),
yet the service area of even many large regional
wastewater treatment facilities often cover far less
than an entire SMSA. There thus seems some need to
develop a rational method of sub-regional population
projection within the framework of the regional OBERS
forecast.
The classical solution to this problem is the so-
called step-down projection technique, in which the
total regional growth is assigned to sub-regional
areas on the basis of some deterministic allocation
scheme. Unfortunately, such simple allocation for-
mulae tend to be quite inadequate for the level of
disaggregation necessary, say, for interceptor sizing,
which requires minor civil divisions or census tracts
as the basic spatial unit. Moreover, the most obvious
deficiency in current methods of population projection
is their deterministic nature, even despite the widely
known and accepted circumstance that most population
projections prove to be in error.& The urgent prior-
ity, then, is to formalize the notion of the probabil-
istic population projection in terms suitable for use
in design algorithms.' That, of course, demands ex-
pression of a population projection as a probability
distribution, rather than as the currently adopted
expedient of specifying a "high" and a "low" projec-
tion, with a "most likely" case somewhere in between.
Indeed, given a probabilistic expression of population
and a corresponding probability distribution of ex-
pected flows, a number of algorithms developed in the
Operations Research field can quickly identify the
correct investment strategy, taking into account scale
economies, interest rates, and planning horizons.
This approach, however, can only be used if
probabilistic projections are available; and
until that occurs, one can hardly fault those who
adopt the traditional hedge against uncertainty that
rests on overdesign.
The two major objectives of this paper, then, are to
develop a probabilistic approach to step-down pro-
jections, and to suggest a step-down procedure that
rests not on simple arithmetic allocation ratios but
on the overall patterns of regional population dis-
tribution, obtaining the subregional population of
interest by integration of the chosen functional re-
presentation over the appropriate spatial limits.
In the interest of clarity, we shall use a simple
exponential model of urban population density as the
basis for exposition; more complex analytical repres-
entations would pose only additional computational
effort, without change to approach itself.
293
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THE DETERMINISTIC CASE
In order to develop the sub-regional integration pro-
cedure, consider first the deterministic case of the
classic exponential model of urban population
density,^ given by
(1)
where d(r,t) is the population density at time t at
distance r from the city center, d(o,t) is the pop-
ulation density at the city center, and a(t) is the
density gradient at time t. The total number of in-
habitants within some radius R is then given by the
integral R 6
P(R,t) =|Jd(o,t) e'O^^r-dr-de (2)
9d(o,t)
cc(t)
a(t))e-a(t)RJ (3)
where
ians. 1
is the sectoral angle of the city, in rad-
Given this model, we note that changes in population
can only be accommodated by changes in the density
gradient
-------
cannot solve Eq. (3) explicitly for a(t), one can
again turn to a numerical solution procedure, and
a(t) is in fact given by the root of
9d(o,t) r -,
y(a(0)=P(R,t) - _|l - (1 + a(t))e-a(t)R|= 0
a(t) (9)
In general, for a model of spatial population distri-
bution of g parameters, g-1 parameters must be pro-
jected into the future, the g-th being determined by
the specified parameters and the OBERS projection
P(R,t).
At this point, then, having a projection for cr(t) ;
d(o,t),t=l,..n, we can apply Eq. (5) to project the
population of any subarea j. The beauty of the
approach, of course, lies in the fact that one can
generate projections for an entire set of subregions
(by merely changing the limits of integration in Eq.
(5)) , projections which are not only all consistent
with the overall SMSA projection, but also with each
other. This is in contrast to the procedure followed
in most regional plans for wastewater or water supply,
where the population of each community tends to be
projected separately, with total regional population
given as the total (which may or may not agree with
an independent projection for the region as a whole).
THE STOCHASTIC CASE
In addition to the measurement and model specification
error discussed above, the most obvious source of
uncertainty lies in the OBERS projection itself. These
projections are based on certain expectations regard-
ing national birth and death rates, inter-regional
migration patterns, and shift-share analysis of region-
al economic activity; and, although the OBERS project-
ions are generally regarded as methodologically sound,
even their most avid proponents do not claim perfect
foresight. To be realistic, then, even the OBERS
projections must be expected to show error, once we
have the benefit of hindsight. However, for purposes
of this paper (and indeed for facilities planning
under current EPA Guidelines) , we can assume that the
OBERS projections are the best in existence, and we
shall simply assume that any uncertainty is sufficient-
ly small in comparison to other sources that they may
be ignored. Indeed, it should be intuitively obvious
that the uncertainty associated with the projection of
large spatial units is much less than projections of
small regions, a notion fully supported by statistical
evaluations of projection accuracy.
Given the premise, then, that the major source of un-
certainty lies in our ability to accurately predict the
distribution of population within the SMSA, what does
this imply for our model? In terms of the exponential
representation used in this paper, it simply means that
the projection of d(o,t) into the future (or, alter-
natively, of a(t)), is a stochastic rather than a
deterministic procedure. Thus, rather than specifying
a single set of values d(o,t),t=l,..n (which in turn
specifies a single series of a(t), and subsequently
a single deterministic projection for Pj(t)), we admit
that for each time point, the value of d(o,t) is in
fact given by some probability distribution. This, in
turn, implies that ct(t) is also a random variable, as
is Pj(t). Thus, by generating a probabilistic state-
ment for d(o,t), one can also generate the desired
probabilistic projection for Pj(t).
Unfortunately, even using a model as simple as the one
used here, analytical solution is quite intractable.
That is, given a known probability distribution for
d(o,t), it is not possible to easily derive an ex-
pression for the probability distribution of Pj(t).
Indeed, even the relationship between the mean and
variance of d(o,t) and Pj is not easy to determine
analytically, in view of the difficulty of explicit
solution of Eq. (3). But even in the event that a
model were chosen that allowed explicit solution of
parameters, the effort of analytical solution would
be beyond the capabilities of most non-mathematicians.
This type of situation, however, is almost ideal for
applying the so-called Monte Carlo, or stochastic
simulation technique. This technique simply repeats
the projection procedure defined for the deterministic
case some number of times, say q times; but each time
the projection is repeated, a value for d(o,t) is
drawn from an urn which contains a set of d(o,t)
values that corresponds to the probability distribu-
tion chosen. The result is that the procedure genera-
tes q projections for Pj(t); but since each projection
depends on a different value of d(o,t), P^(t) will
also differ from projection to projection. In turn,
the q projections for Pj(t) define a probability
distribution, whose moments can readily be calculated.
Of course, the urn in a computer program is simply a
subroutine that generates successive random values in
accordance with the desired probability distribution.
A sample calculation will illustrate the procedure.
Figures 2, 3, and 4 show the result of such a Monte
Carlo simulation projection for part of the Trenton,
N.J. SMSA. Figure 2 shows the distribution of
d(o,1985) and d(o,2000), as generated by the random
value subroutine; Figure 3 shows the distribution of
a(1985), a(2000), and finally Figure 4 shows the dis-
tribution of sample projection values for Pj(1985)
and Pj(2000). From this distribution of sample
values, we compute the desired lower moments of the
projection; the expected values in this case compute
to
E{Pj(1985)}= 19600
E{Pj(2000>]= 21200
d(o,1985)=d(o,2000)
26000
Figure 2:
30000 36000
Distribution of d(o,1985)
295
-------
2000
.42
.46
.50
1985
.52
•42 .46 .50
Figure 3: Distribution of a(t)
.52
2000
18000
20000
23000
1985
18000 20000
Figure 4: Distribution of P.(t)
23000
This particular series was generated by assuming a
normal distribution for d(o,t); we note that the dis-
tribution of a(t), however, is skewed, as is the
resulting distribution of Pj(t).
Depending on the assumptions made for the distribution
of d(o,t), different types of probability distribution
would be generated for Pj(t).
It could be argued that the procedure here is some-
what arbitrary, given the infinite number of possible
probability specifications for d(o,t). However, a
closer examination indicates that the definition of
d(o,t) is little different from the definition of most
of the parameters selected, say, in designing a treat-
ment facility; the engineer applies his Judgement and
experience in selecting the major design variables,
and, as he runs through the entire process chain,
returns to make adjustments to previously selected
design parameters so that the final design product
has overall consistency. In a similar manner, then,
an experienced planner makes judgements on the ex-
pected development of central population density, a
judgement that would be based on analysis of land use
developments in the region, likely trends in zoning,
urban renewal, and central city revitalization efforts
and so on. Different developments can readily be
associated with different assessments of likelihood,
from which a probability distribution of outcomes can
readily be generated. The use of the model, then,
forces the decision-maker to think about the factors
that determine the distribution of population, a pro-
cess that is not engendered by the more crude methods
of fitting regression lines to historical data, or
simply drawing arbitrary extrapolations.
CONCLUSIONS
In this brief exposition we have suggested some
approaches to sub-regional population projections
that should lie within the bounds of comprehension of
the average consulting firm. The emphasis has been
on developing the theme of the stochastic population
projection, and the imposition of a planning frame-
work that forces the individual who makes decisions
on design capacity of treatment facilities to give
more detailed thought to the underlying forces of
urban and regional population growth patterns than is
now customary. More complex representations of urban
spatial growth than the one employed here could
readily be incorporated, and indeed the computer pack-
age is designed in such a way as to encourage the
planner to experiment with alternative formulations.
Hopefully by such experimentation and simulation, the
decision-maker gains a better understanding of the
relationships between planning assumptions and the
sensitivity of population projections used as a basis
for large capital investments, in addition to pro-
viding the design engineer with a rigorous definition
of uncertainty in terms of well-defined probability
distributions.
ACKNOWLEDGEMENT
This paper is based on work supported by the Division
of Biomedical and Environmental Research, U.S. Energy
Research and Development Administration, as part of
the Brookhaven Regional Energy Studies Program.
The content of the paper, however, reflects the per-
sonal judgements of the writer, and should not neces-
sarily be viewed as the position of either the
Brookhaven National Laboratory, or the U.So Energy and
Research Administration.
NOTES
1. See e.g., Urban Systems Research and Engineering,
"Interceptor Sewers and Suburgan Sprawl: the Impact
of Construction Grants on Residential Land Use",
Report to CEQ, Sept., 1974; and e.g. editorial comment
in recent issues of the WPCF Journal, especially Vol.
47, No. 7, p. 1823 (July 1975).
2. One need only scan the most recent texts in the
field, e.g. Metcalf and Eddy's recent book, or recent
296
-------
editions of Fair, Geyer, and Okun, to ascertain the
primitive nature of current techniques of population
projection in comparison to the remaining facets of
engineering design.
3. For example, R. Zanoni and R. Rutkowski, in,"Per
Capita Loadings of Domestic Wastewater", J. WPCF.
Vol. 44, No. 9, p.1757 (Sept.1972), point out that
the per capita loading factors of BOD and Suspended
Solids, still prescribed by many state standards for
facility design, are based on wastewater characteris-
tics of two and three decades ago, and often quite
different to currently encountered values.
4. U.S. Water Resources Council, Washington, D.C.,
"OBERS Projections of Regional Economic Activity in
the U.S., Series E Population, Vol.5, Standard
Metropolitan Statistic Areas", April, 1974.
5. For an overview of these methods, see e.g. W.
Isard et al., "Methods of Regional Analysis: An
Introduction to Regional Science", MIT Press, Cam-
bridge, Mass., 1960, Chapter 2.
6. P. M. Berthuouex, in "Some Historical Statistics
Related to Future Standards", Journal. Env. Engr. Div.
ASCE. Vol. 100, No. EE2, p.423, April, 1974, includes
a very interesting analysis of the error distribution
of population projections made by consulting engineers
over the past few decades.
7. See e.g. Berthuouex and L. B. Polkowski, "Optimum
Waste Treatment Plant Design under Uncertainty", J.
WPCF. Vol. 43, No.9,p.1589 (Sept.,1970) for an illus-
tration of engineering optimization given an input of
specified probabilistic characteristics.
data base runs to several hundred dollars for an
average SMSA.
15. Meier and McCoy, Note 10, supra, at p. 14.
16. Many firms, for example, have access to the
national computing networks of the Boeing and McDonnell
Douglas Companies via remote batch station, especially !
firms active in structural engineering.
17. The use of Monte Carlo Simulation in population
projection is developed in Meier, Note 8, supra.
8. For further details on probabilistic population
projections and their use in Environmental Engineering
Design, see P. M. Meier, "Population Projection at
Design Level", Journal. San. Engr. Div.. ASCE. Vol.98,
No. SA6, p.883 (Dec., 1972). The relationship be.tween
interest rate, scale economies, and projection uncer-
tainty is given in P. Berthuouex and L. Polkowski,
"Design Capacities to Accommodate Forecast Uncertain-
ties", Journal. Sanitary Engr. Div.. ASCE, Vol. 96,
No. SA5, p.1183-1210.
9. This, of course, is the classic model of R. Clark,
"Urban Population Densities", Journal of the Royal
Statistical Society. Series A, Vol. 114, No. 4, p.490,
(1951). Countless further empirical studies have
confirmed the general validity of this model for all
but oriental cities.
10. For definition and discussion of the spatial geo-
metry of SMSA's, see P. M. Meier and M. McCoy, "An
Analytical Approach to the Determination of Urban
Population Density Gradients and its Application to
Energy Planning Problems", Energy Policy Analysis
Group, Brookhaven National Lab., Report BNL 20916,
Jan, 1976.
11. H. Winsborough, "City Growth and Urban Structure",
Journal of Regional Science. Vol. 4, No. 2, p.
(1962).
12. A.Guest, "Urban Growth and Population Densities",
Demography. Vol. 10, p. 53 (1973).
13. See Meier and McCoy, Note 10, supra. Chapter VIII.
14. The National Planning Data Corporation of
Rochester, N.Y« has made census tract area determin-
ations for all SMSA's using advanced electronic
planimetry; however, use of this proprietary computer
297
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USE OF THE CLIMATOLOGICAL DISPERSION MODEL
FOR AIR QUALITY MAINTENANCE PLANNING
IN THE STATE OF RHODE ISLAND
Peter H. Guldberg
Walden Research Division of Abcor, Inc.
Cambridge, Mass.
Thomas E. Wright
Rhode Island Division of Air Pollution Control
Providence, R.I.
Audrey R. McAllister
Environemental Protection Agency
Boston, Mass.
An air quality modeling analysis was performed
in preparation of an Air Quality Maintenance Plan
(AQMP) for the State of Rhode Island.1 The Climato-
logical Dispersion Model (CDM), developed by ERAS
was used to project future air quality levels and to
test maintenance strategies for the years 1978, 1980,
and 1985.
The choice of the CDM for maintenance analysis
over the Air Quality Display Model3 (AQDM) is dis-
cussed. The accuracy of the CDM is demonstrated,
and suggestions for improvement of the model are made.
Introduction
state of
RHODE ISLAND
In June, 1973, EPA published regulations4 re-
quiring all states to identify areas that might, as
a consequence of current air quality and/or of the
projected growth rate of the area for the next 10
years, have the potential for exceeding any National
Ambient Air Quality Standard (NAAQS). States were
also required to submit a detailed analysis of the
impact on air quality of projected growth in each
such designated Air Quality Maintenance Area (AQMA).
Where NAAQS maintenance problems are identified by
analysis, the states must submit a long-term Air
Quality Maintenance Plan (AQMP) containing measures
to ensure maintenance of NAAQ'S for a 10-year period
from the date of submission of the plan. The sub-
mittal of long-term plans will be made according
to time schedules to be published by the Administra-
tor no later than July 1976. In the interim,
EPA Region I is requiring states in their jurisdiction
to submit attainment and short-term maintenance (i.e.,
1975 to 1978) plans for Set I pollutants (S02 and TSP)
only.
Based upon information supplied to EPA in 1974
by the Rhode Island Department of Health, Division
of Air Pollution Control (DAPC), one AQMA in Rhode
Island was identified by the Administrator as having
the potential for violating NAAQS in the 10-year
period between 1975 and 1985$. The boundaries of
this AQMA are shown by the shaded area in Figure 1;
they include 21 municipalities centered around
Metropolitan Providence. The pollutants for which
the Metropolitan Providence AQMA has been identified
are Sulfur Dioxide (S02), Total Suspended Parti-
culates (TSP), and Photochemical Oxidants.
The Metropolitan Providence
Air Quality Maintenance Area
Figure 1. AQMA with Potential for Violating
NAAQS Between 1975 and 1985
Objectives of Study
Technical assistance was provided to the State
of Rhode Island DAPC to develop an AQMP for the
Metropolitan Providence AQMA.. As a result of this
work, the state submitted a draft summary of their
short-term plan to EPA in January 1976. Air quality
projections and control strategy analyses were per-
formed for the years of 1978, 1980, and 1985 to:
Determine areas in the Metropolitan Provi-
dence AQMA where annual NAAQS for S02 and
TSP will be exceeded
298
-------
• Evaluate control strategies which will ensure
maintenance of standards in these areas
through 1985.
An investigation of photochemical oxidants was
not undertaken as part of this study.
Technical Approach
Air quality modeling analyses were performed
to project future air quality levels and to test
maintenance strategies. The work effort entailed
the execution of the following tasks:
• The Rhode Island point source emissions
inventory was updated to the base year of
1974, and the information was submitted to
the NEDS data bank at EPA.
• Modifications to the COM were made to allow
for representation of stable atmospheric
dispersion conditions.
• Utilizing the base-year point and area source
emission inventories as inputs to the COM,
a validation of the model was performed by
comparing predicted annual S02 and TSP
levels for 1974 with measured air quality
data in the AQMA from EPA's Storage and
Retrieval of Aeormetric Data (SAROAD) system.
• The COM was calibrated using the statistical
relationship between measured and predicted
pollutant concentrations derived in the
model validation.
• Using data from the State of Rhode Island
Land Use Plan6 and methodologies outlined
in EPA's AQMP Guidelines, growth factors
were developed for projecting point and
area source S02 and TSP emissions for 1978,
1980, and 1985.
• The above growth factors were applied to the
base-year (1974) emissions inventories for
1978, 1980, and 1985. These projected base
case emissions incorporate the effects of
Federal New Source Performance Standards (NSPS)
and the Providence Transportation Control Plan
and assume full compliance with current state
air pollution control regulations.
• Utilizing the projected inventories as inputs
to the COM, future annual S02 and TSP levels
in the Metropolitan Providence AQMA were pro-
jected for the years 1978, 1980, and 1985.
Based on these modeling projections, areas in
the AQMA where annual NAAQS for S02 and TSP
will be exceeded were identified.
• Control strategies were entered into the
future air quality predictions through ad-
justments to the projected point and area
source emission inventories. The COM was
used to evaluate the effectiveness of the
various control strategies in maintaining
annual NAAQS for SD2 and TSP through 1985.
Description of Atmospheric Diffusion Model
Model Choice
Successful application of generalized models to
specific emission sources requires definition of the
source characteristics. The air quality maintenance
analysis undertaken in the current study required an
atmospheric transport and diffusion model capable
of predicting annual average S02 and TSP concen-
trations at specified receptor points due to an
array of both point and area emissions sources. In
addition, the reactive nature of S02 necessitated
the use of a model which could simulate pollutant
decay processes as a function of atmospheric resi-
dence time. The two most widely used and accepted
atmospheric diffusion models which met the above
criteria are the Air Quality Display Model3 (AQDM)
and the COM2. Both models are based on the Gaussian
plume configuration, i.e., they simulate atmospheric
transport and diffusion processes by assuming the
concentrations of pollutants downwind within a plume
generated by point and area source emissions can be
represented by a Gaussian distribution in both the
crosswind and vertical directions. Emissions sources
are assumed to be continuous for the time analyzed.
As the plume expands due to diffusion and turbulence,
it is diluted and transported downwind, principally
by the mean wind. The rate of expansion is charac-
terized by a series of empirical dispersion curves
which are dependent on the stability of the atmos-
phere, as determined in studies made by Pasquill^
and reported by Turner^. A stability-dependent mix-
ing height is also used to simulate diffusion pro-
cesses in the atmospheric mixing layer.
The COM differs in some respects from AQDM,
which has been used extensively for simulation
purposes. Although both predict long-term pollu-
tant concentrations, the COM determines emission
contributions from area sources more accurately than
AQDM, using numerical integration techniques. Ef-
fective emission heights for point sources are cal-
culated in both models using the well accepted
Briggs* plume rise formulaelO,!!, and both models
make use of an exponential decay term to simulate
the reactivity of S02 with other atmospheric con-
stituents. However, the COM allows a realistic
atmospheric stability-dependent power law increase
in wind speed with height that is lacking in EPA's
AQDM.
Finally, a validation study conducted at the
National Environmental Research Center^2 has shown
that the CDM yielded smaller errors than the AQDM,
with concentration maxima and means nearer those
of the measured data. For these reasons, the CDM
was judged to be the model best suited to air
quality maintenance analysis and therefore, was
chosen for use in this study.
*The original version of EPA's AQDM described in
the user's manual? has been subsequently modified
to replace the Holland plume rise equations with
those developed by Briggs.
299
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Model Modifications
The COM model computes concentrations at re-
ceptor points which are assumed to be located in
urban areas. The lower layer of the urban atmosphere
is generally more unstable than the corresponding ad-
jacent rural atmosphere. In fact, the turbulence
and heating present in the lower urban atmosphere
precludes the occurrence of stable atmospheric con-
ditions associated with nighttime radiational cool-
ing in the rural environment. To account for this
effect, the COM uses empirical dispersion coeffici-
ents associated with less stable atmospheric con-
ditions in computirg pollutant concentrations. While
this procedure is correct when both receptor and
source are located within the urban environment, it
was felt that some adjustment was necessary in order
to model the rural portion of the Metropolitan
Providence AQMA. Rural receptors are by definition
located far from the urban core, and the travel time
from the source to the receptor is dominated by the
rural component. Thus, in calculating pollutant
concentrations at rural receptor sites, the dis-
persion of emissions was determined using the em-
pirical dispersion coefficients of Pasquill8 directly
without adjustments for the urban environment. This
allowed modeling of stable atmospheric conditions
when applicable in the rural environment. In
addition, the Briggs plume rise formulae used in the
COM were updated to include equations for plume rise
under stable atmospheric conditions.
Model Input
The COM accepts as input the joint frequency
distribution of meteorological conditions, the
average afternoon and nocturnal mixing heights,
the locations and emission rates of both area and
point sources, and the locations of the desired re-
ceptor points. At each receptor, the concentration
due to each point and area source is calculated.
These calculations assume transport and diffusion
processes which represent the frequency distribution
of meteorological conditions input to the model.
The basic meteorological input to the model con-
sisted of standard "Day/Night STAR" data from the
National Climatic Center in Asheville, North Carolina.
Weather observations for Providence, Rhode Island
(Station #14765} are taken hourly by the National
Weather Service at Green Airport. These data, aggreg-
ated to eight observations per day and distributed as
STAR data, are representative of the meteorological
conditions for the State of Rhode Island. The result
is a joint frequency distribution which gives the joint
frequency of occurrence of a wind direction sector,
wind speed class, and stability class. There are 16
different wind direction sectors, 6 wind speed classes,
and 6 atmospheric stability classes. The COM is well
suited for AQMP evaluation since the NCC can provide
"Day/Night STAR" data for any year at any station in
the U.S. where daily weather observations are taken.
Measured data in the joint frequency distribution are
divided into two classes indicating their occurrence
during either the day or night. This information is
used along with factors input to the COM, which esti-
mate the diurnal variation of emissions, to more
accurately predict ambient pollutant concentrations.
The effects of seasonal variations in emissions on
ambient concentrations can also be accounted for through
the use of quarterly emissions data in COM with
quarterly "Day/Night STAR" data available from NCC.
For the model validation, in which predictions
of annual concentrations of S02 and TSP in 1974 were
made, the 1974 annual STAR data were used as input
to the COM model. To model future years, a 10-year
climatological average STAR data set for 1964 to 1973
was used. Although use of STAR data from a parti-
cular year may have yielded higher predicted con-
centrations at some points in the AQMA, it was not
possible to objectively determine the annual worst
case meteorological conditions for the entire AQMA
due to complex source-receptor relationships in the
urban area studied. Therefore, climatological aver-
age meteorological data were judged to be the best
representation of possible future conditions.
Model Validation and Calibration
For the purpose of verifying the accuracy of CDM
in predicting annual average SO? and TSP concentra-
tions for the State of Rhode Island, a model valida-
tion exercise was performed. This validation
consisted of comparing air quality model predictions
for 1974 with actual 1974 annual concentrations
measured at 22 intermittent and continuous-monitoring
stations throughout the AQMA. The measured data
were obtained from EPA's SAROAD data file at the
National Aerometric Data Bank.
Scatter diagrams of measured versus predicted
1974 annual average concentrations of SO, and TSP
are shown, respectively, in Figures 2 ana 3.
loo _
„ eo
60
40
I
20 40 60 80
X_: Predicted S02 Concentration (ng/m3)
100
Figure 2. Comparison of Measured and Predicted 1974
Annual S02 Concentrations in the Metropolitan
Providence AQMA
300.
-------
I
+J
£ 60
s
I
a.
£
•v 40
20
I
I
20 40 60 80
-Xp: Predicted TSP Concentration (pg/m3)
Figure 3. Comparison of Measured and Predicted 1974
Annual TSP Concentrations in the Metropolitan
Providence AQMA
The correlation coefficients (r) between measured
and predicted concentrations are 0.86 and 0.78, re-
spectively, for SOp and TSP. These results indicate
good correlation between these quantities and demon-
strate the accuracy of the COM in predicting air
quality levels throughout the AQMA. The correlations
may also be interpreted quantitatively, since r2 is
equal to the percentage of the variance of the meas-
ured concentrations that can be accounted for by a
linear relationship with the predicted concentrations.
These values are 74% and 61%, respectively, for S02
and TSP. The standard errors of estimate for the
linear regression relationships were found to be
10.0 yg/m3 and 8.3 yg/m3, respectively, for S0? and
TSP.
The purpose of a calibration is to adjust model
estimates based on the relationship between measured
(X } and predicted (X ) concentrations determined
fr8m the model validation. This is accomplished by
a linear regression on the validation data of which
slope and intercept are then used as correction
factors in making future predictions. Referring to
the scatter diagram for S02 in Figure 2, the linear
regression line of best fit was found to be Xm
0.52X + 9.9 by the method of least squares.
Referring to Figure 3 for TSP, the linear regression
line was found to be Xm 0.67X + 31.9.
These equations were used to calibrate the
model for all future modeling predictions. Mote that
both lines have a positive intercept. There are
three possible physical interpretations of these in-
tercepts: (1) background pollutant concentrations,
(2) systematic bias in the measured data, and (3)
systematic bias in the model predictions. For par-
ticulate matter, 31.9 yg/nr is within the normal
background level range due to road dust, pollen, and
other fugitive dust sources, supported by the lowest
measured annual average TSP value in the State in
1974 of 23 yg/m3 in Washington County. For SOp, the
background level of 9.9 yg/m3 is supported by the
lowest measured annual average value in the State
in 1974 of 11 yg/m3. in the town of Westerly.
Future Base Case Air Quality
Calibrated modeling predictions of future air
quality levels indicate that the annual primary
standard for SO? of 80 yg/m3 will not be exceeded
in the Metropolitan Providence AQMA through 1985.
The maximum predicted concentration was 54 yg/m3,
occurring in the city of Providence in 1985. Even
if the standard error of estimate of the S0p_ model
predictions of 10.0 yg/m3 is added .to this value,
the result is still well within the standard*.
Future TSP levels are also predicted not to
exceed the annual primary standard of 75 g/m . How-
ever, TSP levels are predicted to exceed the annual
secondary standard of 60 yg/m3 by 1.4 yg/m3 in the
city of Providence in 1985. It should be noted that
this increment is less" than the standard error of
estimate of the model calibration of 8.3 yg/m .
Concentration isopleths and the predicted area of
violation for this case are shown in Figure 4 as an
example of results obtainable from the COM.
Figure 4. Predicted Base Case 1985 Annual Average
TSP Concentrations in Rhode Island ( g/m3)
The annual secondary TSP standard of 60 g/m3
is to be used only as a guide in assessing imple-
mentation plans to achieve the 24-hour secondary
TSP standard of 150 g/m3. Therefore, an analysis
was undertaken to extrapolate statistically the
future base case annual average TSP concentrations
predicted by COM to 24-hour maximum values, using
the techniques of Larsenl3. The purpose of this ana-
lysis was to verify that the predicted TSP levels ex-
*The State of Rhode Island has adopted air quality
standards which are identical to the NAAQS.
301
-------
ceeding the annual secondary TSP standard in the AQMA
imply violations of the 24-hour secondary standard
and hence the need for air quality maintenance
measures to further control parti cul ate emissions.
Note that the secondary 24-hour TSP standard is
not to be exceeded more than once per year. Thus,
in order for a violation of the standard to occur,
the second highest 24-hour TSP concentration in a
given year must exceed 150 yg/nr. Larsen's statisti-
cal techniques were used to extrapolate such values,
and the results show a predicted violation of the
24-hour standard in the Metropolitan Providence area,
with valtres as high as 188 yg/m in downtown Provi-
dence through 1985. The output from the COM is
easily used in this extrapolation, and one possible
improvement to the model would be to add a Larsen
subroutine to the computer code so that both annual
average and 24-hour maximum concentrations could be
output simultaneously.
Thus, the modeling results indicate that further
control of particulate emissions in the Metropolitan
Providence AQMA will be necessary to maintain am-
bient air quality standards for TSP through 1985.
Evaluation of Air Quality Maintenance Strategies
The particulate control strategies tested for
air quality maintenance were:
• An annual inspection and periodic maintenance
program for all large industrial, commercial,
and institutional boilers included in the
point source inventory, including electric
generating power plants
• Use of unleaded gasoline by all 1975 and
newer light-duty motor vehicles included
in the area source inventory.
These strategies were evaluated by making appropriate
adjustments to the future projected emission inven-
tories and then rerunning the COM to predict future
air quality. The results indicate only the use of
the second strategy will maintain annual TSP levels
in the AQMA below the secondary standard through
1985. Projected effects of the first strategy are to
reduce future TSP levels, at most, by 1 yg/m^.
Al'though predicted concentrations output by
the COM show the split between total area and total
point source contributions, a detailed source-
contribution file* is not produced. We consider this
omission to be the principal weakness of the COM
used in this study as such data would eliminate the
need to adjust emission inventories and constantly
rerun the model in order to test different control
strategies. By compiling source contributions at
all receptor points, alternative maintenance strate-
gies can be quickly evaluated through the application
of appropriate scaling factors to only those sources
affected by the strategy. Since this work was done,
a version of COM with this capability has been de-
veloped for EPA Region V.
Conclusions
The CDM was used to identify areas in the
Providence AQMA where annual NAAQS for S02
and TSP are likely to be exceeded, and to test
control strategies to maintain air quality standards.
The CDM was found to be an accurate model, well
suited to air quality maintenance analysis. The
principal weakness of the CDM was its inability
to produce a source-contribution file that would
allow a more analytical approach to the evaluation
of maintenance strategies. We note that subsequent
to this study, a version of CDM has been developed
for EPA Region V which includes this capability.
The usefulness of the CDM in AQMP evaluation could
also be improved upon by the addition of a Larsen
subroutine to statistically extrapolate annual
levels to 24-hour maximum concentrations.
References
1. Guldberg, P.M., Kemerer, B.L., and Shah, M.C.,
Technical Support to the State of Rhode Island
on Development of an Air Quality Maintenance
Plan, Publication No. EPA901/9-75-001, pre-
pared by Hal den Research Div. of Abcor, Inc.,
Cambridge, Ma., under contract No. 68-02-1377,
Task Order 6, September 1975.
2. Busse, A.D., and Zimmerman, J.R., User's Guide
for the Climatological Dispersion Model, U.S.
Environmental Protection Agency, Publication
No. EPA-R4-73-024, Research Triangle Park, N.C.,
December 1973.
3. Air Quality Implementation Planning Program,
prepared for the Environmental Protection
Agency, Washington, D.C. by TRW Systems Group,
1970.
4. Federal Register, Vol. 38, pg. 15834; as amended
by Vol. 30, pg. 16343, May 8, 1974, and by Vol.
40, pg. 25814, June 19, 1975.
5. Federal Register, Vol. 40, pg. 18726.
6. State Land Use Policies and Plan, Rhode Island
Statewide Planning Program, Report No. 22,
Providence, January 1975.
7. Guidance for Air Quality Maintenance Planning
and Analysis, Volume 5. 7. and 11. U.S. Environ-
mental Protection Agency, Publication Nos. EPA-
450/4-74-006, -014, and-008, Research Triangle
Park, N.C.
8. Pasquill, F., Atmospheric Diffusion, D. Van
Nostrand Company, Ltd., London, 1962.
9. Turner, D.B., Journal of Applied Meteorology,
February 1964.
10. Briggs, G.A., "Some Recent Analyses of Plume
Rise Observation," Proceedings of the Second
International Clean Air Congress, New York,
Academic Press, 1971.
11. Briggs, G.A., "Discussion on Chimney Plumes in
Neutral and Stable Surroundings," Atmos. En-
viron., 6: 507-510, 1972.
12. Turner, D.C., Zimmerman, J.R., and Busse, A.D.,
An Evaluation of Some Climatological Dispersion
Models, presented at the 3rd meeting of the
NATO/CCMS Panel on Modeling.
13. Larsen, R.I., A Mathematical Model for Relating,
Air Quality Measurements to Air Quality
Standards, U.S. Environmental Protection Agency,
Office of Air Programs, Publication Mo. AP-89,
Research Triangle Park, November 1971
urn> the source-contribution file produced
by EPA s Implementation Planning Program. 3
302
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IMPROVEMENTS IN AIR QUALITY DISPLAY MODEL
Chandrika Prasad, Ph.D., P.E.
State Air Pollution Control Board
Richmond, Virginia 23219
The Air Quality Display 'Model (AQDM) is widely
used to predict the concentration of sulfur dioxide
and suspended particulates in the ambient air. This
paper describes some of the difficulties encountered
in the use of this model and the modifications to im-
prove the model.
It is suggested that (l) in calibrating the model
the line of the best fit be determined on the basis of
the measured minus the background concentration and
the calculated concentration, (2) the actual number of
samples (which were used to compute the standard geo-
metric deviation) be used in computing the highest and
the second highest concentrations, (3) in computing the
source contributions to a receptor the y-intercept and
a part of the background not be apportioned in the in-
dividual source contribution and (k) a. few modifica-
tions to the input and output formats be made. These
modifications add to the usefulness of the model and
the ease in reviewing the results.
Nomenclature
A = y-intercept
B = slope of the regression line
Ci = uncalibrated concentration due to source i at
a receptor
C = uncalibrated total calculated concentration at
a receptor
D = standard geometric deviation
E = a variable (see Appendix A)
F = plotting position frequency
G = background concentration
i = a subscript
N = number of samples
R = rank order (highest, second highest, etc.)
S^ = concentration contribution (calibrated) from
source i to a receptor
S = concentration contribution (calibrated) from all
sources to H, receptor
T = total concentration (calibrated) at a receptor
(annual arithmetic mean)
^max = highest concentration (short-term)
u = uncertainty
y - measured air quality concentration
z = number of standard deviations from the mean .
Introduction
Atmospheric simulation models are frequently used
to relate pollutant emissions to pollutant concentra-
tions. Some of the models most readily available to
air pollution control agencies and representative of
the state-of-the-art of atmospheric simulation models
are given in Reference 1.
The models estimate the concentration for a 1-hour
period or for seasonal or annual averages. The long-
term models such as AQDM2* and COM3 are widely used
to predict the concentration of sulfur dioxide and sus-
pended particulates. The AQDM is preferred and is the
minimum acceptable1* by the Environmental Protection
Agency for air quality analysis for these two pollu-
* Numbers in superscripts denote references cited.
tants in developing the air quality, maintenance plans.
The AQDM is essentially a. long-term model. The
model determines the impact of a variety of sources at
a given receptor for a given set of meteorological con-
ditions. It then weighs this concentration by the fre-
quency with which that particular set of meteorological
conditions occurs and then sums up over all meteorolog-
ical conditions, thus producing a long-term average
concentration. Basic input to the model is a compre-
hensive emission inventory on both point and area
sources. The meteorological input to the model is a
joint frequency distribution of wind speed, direction,
and stability classes along with an average mixing
depth.
Through a mathematic simulation of the atmospher-
ic diffusion process, the model determines the arith-
metic average of ground level concentrations over an
annual period. To provide a comparison with the Nation-
al Ambient Air Quality Standards the program includes a
statistical model? which is used to relate the annual
arithmetic mean to annual geometric mean and the high-
est concentration for a selected number of receptors.
Climatological Dispersion Model (CDM) is another
long-term model frequently used. The AQDM and CDM have
differences in calculation techniques; however, the two
require basically the same inputs and have same types
of outputs. A significant difference between the two is
a. source contribution table generated by the AQDM
which allows the impact of each source on air quality
to be evaluated. Such a source contribution table is
highly desirable, especially when developing a strategy
to maintain the standards. Such a table is also useful
in evaluating the impact of a new source or the impact
of a control program for an existing source.
Modifications To The AQDM
Several difficulties were encountered in the use of
the AQDM. These are discussed in the paragraphs which
follow. Also discussed are the methods to overcome
these difficulties by modifying the model. These modi-
fications cover the following areas:
Calibration procedure, used to compute y-
intercept and slope of the line of the best
fit during calibration of the model
Statistical model, used to compute annual geo-
metric mean and highest concentration
Source contribution table, used to generate
individual source contribution to selected
receptors
Input and output formats, used for data input
and results output.
Existing Calibration Procedure
Before using the AQDM to estimate regional air
quality, the model is first calibrated using existing
air quality data. This is accomplished by making an
AQDM run using the emission, meteorological, and mea-
sured air quality data for a specific year. The cali-
bration procedure begins with the use of the model to
calculate concentration values at each of the monitor-
303
-------
ing stations for which measured air quality data are
available. The line of the best fit (which describes
the relationship between the measured and calculated
concentration) is obtained using the least-square tech-
nique. One of the following two procedures is used to
handle the background concentration.
Use Of Background Concentration As Input. If
an accurate value of the background concentration is
available, it is included in the input data. The AQDM
program adds the background concentration to the calcu-
lated concentration before attempting to determine the
line of the best fit as shown in Figure 1. The regres-
sion line in this case can be described by the equation:
y = A + B( C + G
(1)
In this case, since the accurate value of the
background concentration, G, was used as input, the y-
intercept. A, can be considered as the unknown and
might be attributed to natural sources and/or /
man-made sources outside the area being modeled, or it
may be considered as an uncertainty due to uncertain-
ties in the input data on emissions, meteorology, and
measured air quality. For the sake of brevity, let it
be called the uncertainty and denote it by 'U'. Hence,
in this case, U = A.
100
80
ho
=1
td
-------
Figure 1, 2, and 3.
Computation Of Calibrated Concentration
Once the model is calibrated, the y-intercept and
the slope of the regression line are used to calibrate
or adjust the calculated concentrations at all the re-
ceptors. The model (without modifications) uses the
following relation to compute the calibrated concen-
tration:
T=A+B(C+G) (2)
In the modified version of the program, this is
done by using the relation:
T A + G + B C (3)
Existing Procedure In The Statistical Model
The air quality standards for sulfur dioxide and
suspended particulates are in terms of annual mean con-
centrations. In addition, the standards include a 21*-
hour value not to be exceeded more than once per year.
The AQDM program includes a statistical model to
convert the annual arithmetic mean to the annual geo-
metric mean and the highest concentration. To do this,
the model requires the value of standard geometric devia-
tions for all the receptors which are selected for the
statistical output.
It should be noted that the standard geometric de-
viations are available only from the past historical
data on measured air qualities and are available only
for those receptors where there is a monitoring station.
At this time there is no technique available to project
standard geometric deviations for future years. At the
same time, the standard geometric deviations are based on
a limited number of samples, the prevalent sampling fre-
quency being every third to every sixth day, with the
sample size ranging from 60 to 120 per year. In comput-
ing the highest concentration the model assumes a sample
size of 365 (continous sampling). It is further realiz-
ed that to obtain 365 samples (2U-hour samples) using a.
Hi-Vol sampler will require at least two samplers side
by side. The mathematical relations used in the model
to compute the highest concentrations are given in
Appendix A with the only difference that the model uses
the number of samples to be 365 in all cases.
If the standard geometric deviation, which is based
on a limited number of samples, is assumed to be the
same for continous sampling (or 365 samples)it introduces
significant errors in the computed values of the high-
est concentrations. Figure k shows the ratio of the
highest concentration to the annual arithmetic mean as
a function of sample size for several values of the
standard geometric deviation.
At the same time the model does not compute the
second highest concentration which is actually desired
for a. comparison with the air quality standards.
Modified Procedure For The Satistical Model
It is suggested that for direct comparison with
the standards,the second highest concentration be com-
puted using the actual number of samples (which were
used to compute the standard geometric deviation) for
the selected receptors using the procedures given in
Appendix A. Figure 5 shows the ratio of the second
highest concentration to the annual arithmetic mean as
a function of the number of samples for several values
of the standard geometric deviations.
Existing Procedure For Source Contribution Table
The AQDM provides a table which gives the contri-
bution from each source to each of five selected recep-
tors. If the five receptors are not selected by the
Number of Samples, N
Figure k-.,Ratio of the Highest Concentration to the
Annual Arithmetic Mean as function of
sample size and standard geometric
deviation.
65
125
185 2l*5
Dumber of Samples,
305
365
N
Figure 5. Ratio of the Second Highest Concentration
to the Annual Arithmetic Mean as function
of sample size and standard geometric
deviation.
user, the program automatically selects five receptors
with the highest, second, third, fourth, and fifth high-
est concentrations. The source contribution is given
both as a concentration and a percentage of the total
concentration for that receptor.
The model starts with computing the uncalibrated
form of the total concentration for the specific recep-
tor under consideration by using the following relation
(which is derived from Equation 2):
c ^ o (U)
The model also calculates the concentration due to
each source at this receptor. Let C^ be the concentra-
tion contribution due to source i to this receptor. The
source contribution, S^, due to source i to this recep-
tor is calculated using the following relation:
305
-------
r -i c-i
3± + [ A + ( B 1 ) Gj —-1
(5)
The total contribution from all sources to this
receptor is given by the summation of equation 5 over
all sources.
2* C.
2, B c. + TA+(B-I)G (6)
S = I Si
C
or,
S=BC+A+
1 )
(7)
Adding the background, Gs to the total source con-
tribution, S, gives the total calibrated concentration
at this receptor as
T=S+G=A+B(C+G) (8)
which is the same as Equation 2.
Modified Procedure For Source Contribution Table
A close examination of Equation 5 indicates that a
part of the background, G, and the y-intercept, A, are
apportioned in the ratio of the individual source con-
tribution, C^ , to the total concentration, C . If
there is a change in the total concentration, C, due to
emissions data changes in sources other than i, the con-
tribution from source i to the same receptor will change
even though all other conditions are unchanged. This
presents problems when comparing the results of one
AQDM run with the other.
The procedure described below overcomes this diffi-
culty and gives consistent results in each case.
The source contribution from source i to a given
receptor should only be adjusted for the slope of the
regression line and should be computed as follows:
Si B Ci (9)
The total source contribution , S , will be the sum-
mation of Equation 9 over all sources as given by
S = B C
(10)
Adding the background , G , and the y-intercept, A ,
will give the total concentration
T=A+G+BC (11)
which is same as Equation 3.
assembled together. Similarly all the PLUME cards are
assembled together in the same order as the SOURCE
cards,and are usually placed behind the last SOURCE
card. In processing these emission data (Source and
Plume Data), the Plume Data read from the first PLUME
card are assigned to the first SOURCE card, the data on
the second PLUME card are assigned to the data on the
second SOURCE card,and so on. The model (without modi-
fications) makes no comparison to ascertain that Plume
Data are assigned to the correct Source Data.
TABLE 1. An Example Of SOURCE Data Input
Column 1°
SOURCE =
LOCATION
HORIZ
20
290.2
351*. 3
223.0
223.0
221.5
221.5
VERT.
30
1*21*3.0
It267.7
1*321*. 6
1(321*. 6
1*312.3
1*312.3
AREA
1*0
0.0
0.0
0.0
0.0
0.0
0.0
EMISSION (TPY)
S02
50
53.818
72.1*67
0.000
0.000
12.657
8.1*38
TSP
60
2.037
9.267
l*.2l+7
0.767
38.062
11.671
STACK
HT.
70
122.0
122.0
15.0
16.7
58.2
58.2
SOURCE
ID*
80
'9952'
•99531
'5701'
'5703'
'1+751'
•1*752'
* Source ID Is Additional Input Under Modified Program.
The modified program reads the source identifica-
tion number entered in columns 75 to 80 of SOURCE and
PLUME cards. For each point source,identical identifi-
cation numbers are used on both the SOURCE and PLUME
cards.
TABLE 2. An Example Of PLUME Data Input
ColumnlO
PLUME =
GAS VEL.
20
12.1*
21.6
53.3
12.5
12.8
21.5
STACK DIA.
30
5.0
7-9
i*.o
i*.o
i*.o
1*.3
GAS TEMP
1*0
392.0
391.0
1*19.0
,. 1*52.0
1*01.0
395-0
50-70
PLUME ID*
80
'9952'
'9953'
'5701'
'5703'
'1*751'
'1*752'
* Plume ID Is Additional Input Under Modified Program,
For area sources the PLUME cards are internally
generated by the program. The modified program compares
the source identification number with the plume identi-
fication number and if a mismatch is found, further
processing of the data is stopped and the mismatch in-
formation is printed as shown in Table 3.
Modifications To The Input And Output Format
Source Data. One of the basic inputs to the
model is a comprehensive emission inventory on both
point and area sources. The emission data for each
emission point are entered on two cards. The first
card (designated as SOURCE =) contains the data on
source location, emission rates and stack height,as
shown in Table 1. The second card (designated as PLUME
=) contains stack diameter, exit gas velocity and tem-
perature, as shown in Table 2. All the SOURCE cards are
Sampling Station Data. Input format for the
measured air quality data has been modified (as shown
in Table 1*) to include an identification number for
data from each sampling station,and the program is modi-
fied to read these additional data. In the 'CORRELATION
DATA' output these identification numbers are reprinted.
At the same time,the modified program prints out cali-
brated concentrations. This is helpful in reviewing the
Correlation Data output, an example of which is shown
in Table 5.
TABLE 3. An Example Of Source Data Output
SOURCE
NO.
1
2
3
1*
5
6
SOURCE LOCATION
(KM)
HORIZ .
290.2
351*. 3
223.0
223.0
221.5
221.5
VERT.
1*21*3.0
1*267-7
1*321*. 6
1*321*. 6
1*312.3
1*312.3
SOURCE
AREA
0.0
0.0
0.0
0.0
0.0
0.0
EMISSION RATE
(TON/DAY)
S02
53.818
72.1*67
0.000
0.000
12.657
8.1*38
TSP
2.037
9.267
l*.2l*7
0.767
38.062
11.671
STACK DATA
HT.
(m)
122.0
122.0
15.0
16.7
58.2
.58.2
DIA.
(m)
5-0
7-9
i*.o
lt.0
i*.o
1*.3
VEL.
(m/s)
12.1*
21.6
12.5
53.3
12.8
21.5
TEMP.
(°K)
392.0
391.0
1*52.0
1*19-0
1*01.0
395.0
ID NO.
S*
9952
9953
5701
5703
1*751
1*752
P*
9952
9953
5703
5701
!*751
1*752
S/P MISMATCH
S/P MISMATCH
* Additional output generated by the modified program.
This AQDM run was unsuccessful due to source/plume data mismatch.
306
-------
TABLE 1*. An Example Of SAMPLING STATION Data Input
Acknowledgement
Column 10
FAROE =
HORIZ.
COORD.
20
386.0
386.5
381*. 5
381*. 5
328.0
VERT.
COORD.
30
1*075.0
1*075.1
1*069.7
1*071.1*
1*060.8
MEASUARD ANNUAL
ARTHMETIC MEAN
1*0
71*. o
85-0
81*. 0
97.0
65.0
STATION
ID*
50
'176A1
'176D'
'176E1
'176F'
'178B'
* Additional Data Input Under Modified Program.
TABLE 5- An Example Of CORRELATION Data Output
SITE
HO.
1
2
3
1*
5
RECEPTOR
LOCATION
HORIZ.
386.0
386.5
381*. 5
381*. 5
328.0
VERT.
1*075-0
1*075.1
1*069.7
1*071.'*
1*060.8
PARTICULATE COHC.
OBSERVED
71*. o
85.0
81*. 0
97.0
65.0
CALCULATED
59-0
1*3.0
63.0
66.0
23.0
ID
NO. »
176A
17 6D
17 6E
17 6F
178B
CALI- *
BRATED
COHCEN.
81*. 8
72.7
87.7
89.8
57.0
* Additional Output Generated By The Modified Program.
Source Contribution Table. The AQDM program
has been modified so that all sources (point or area)
contributing more than ~L% to any of the five receptors
are identified and their source identification numbers
be printed as shown in Table 6. At the same time the
maximum percentage contribution to any of the five re-
ceptors are printed. This makes the output very useful.
TABLE 6. An Example Of SOURCE CONTRIBUTION TO
FIVE MAXIMUM RECEPTORS Output
SOURCE
HUMBER
367
368
369
370
371
RECEP.
21*1*
0.0635
0.12$
0.0361
0.07$
0.0065
0.01$
0.0022
0.00$
0.0281*
0.05$
RECEP.
60
0.01*70
0.09$
0.0301
0.06$
0.001*5
0.01$
0.0015
0.00$
0.0230
o.oi*$
RECEPT .
213
1.3050
2.33$
0.01*12
0.07$
0.0196
o.oi*$
0.0065
0.01$
15-5961*
27.88$
RECEP.
1*9
0.0719
O.ll*$
0.01+15
0.08$
0.0057
0.01$
0.0025
0.00$
0.0319
0.06$
. RECEP.
225
0.2610
0.50$
0.1118
0.22$
0.1100
0.21$
0.0373
0.07$
0.0866
0.17$
ID *
CODE
1701
1771
1801
1802
1811
$ *
FLAG
>2$
>27$
* Additional Output Generated By The Modified Program.
Conclusions
The various modifications described above can be
grouped together under the following two categories:
Modifications To The Mathematical Logics
Under this category it was suggested that
(l) During calibration of the model the line
the best fit be determined by comparing the computer
calculated concentrations with the measured minus the
background concentration
(2) The second highest concentration "be computed
using the actual number of samples to compare the re-
sults with the short-term National Ambient Air Quality
Standards
(3) The y-intercept and the "background not
be apportioned while computing the source contributions
from individual sources to a receptor.
The only additional input required to carry out the
modifications under this category is the data on the
number of samples for those receptors which are select-
ed for the statistical output.
Modifications To The Input And Output Formats
Under this category the additional input data re-
quired are (l) the SOURCE and PLUME identification
numbers and (2) the sampling station identification
numbers. These data are reproduced in the outputs on
SOURCE DATA, CORRELATION DATA and SOURCE CONTRIBUTION
TO FIVE RECEPTORS.
These modifications are helpful in reviewing the
output results and avoid a lot of cross-referencing.
The modifications to the Input and Output formats
as described previously were incorporated into the
model by Erik Hougland (presently with the Tennessee
Valley Authority) while working at Virginia Polytechnic
Institute and State University on a contract from the
Virginia State Air Pollution Control Board. His work in
this area is acknowledged. The author also wishes to
thank his colleague Limon E. Fortner for first pointing
out the problem associated with generation of the
Source Contribution Table.
References
1. "Guidelines For Air Quality Maintenance Planning
and Analysis, Vol. 12, Applying The Atmospheric
Simulation Models To Air Quality Maintenance Areas,"
EPA-l*50/l*-7l*-013, U.S. EPA., Research Triangle Park,
N.C., Sept. 1971*.
2. "Air Quality Display Model," TRW Systems Group Man-
ual for NAPCA, HEW, Contact No. PH-22-68-60,
Washington, D.C., Nov. 1969.
3. "User's Guide For The Climatological Dispersion
Model," Environmental Monitoring Series, EPA-RU-73-
021* (mis PB 2273l*6AS) NERC, EPA., Research
Triangle Park, N.C., Dec. 1973.
1*. "Maintenance of Ambient Air Quality Standards, Re-
quirements For Preparation, Adoption and Submittal
of Implementation Plans ," Federal Register, Oct. 20,
1975-
5. R. I. Larsen, "A Mathematical Model For Relating Air
Quality Measurements To Air Quality Standards," U.S.
EPA., Publication No. AP-89, Research Triangle Park,
N.C., Nov. 1971.
Appendix A
Computation Of Highest And Second Highest Concentration
First compute the plotting position frequency, F ,
using Larsen's technique5 as given below:
F = 100
R-O.i*
N
(A-l)
Next compute the number of standard deviations from
the mean from the relations:
Z = E -
E= {in (A
2.52 + 0.80 E + 0.01 E2
1 + 1.1*3 E + 0.19 E2 + 0.001 E3
(A-2)
(A-3)
Finally, compute the highest concentration by the
relation given below:
Tmax Tg
(A-l*)
where the annual geometric mean, Tg , is related to the
annual aritmetic mean, T, by the relation:
T
T =
g EXP (0.5 ln2D)
(A-5)
In the procedure described above use R = 1 and
R = 2 for computing the highest and the second highest
concentrations respectively.
307
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AIR POLLUTION MODELING IN THE DETROIT METROPOLITAN AREA
A. Greenberg
B. Cho
Air Pollution Control Division
Wayne County Department of Public Health
Detroit, Michigan
James A. Anderson, P.E.
Wayne State University and
Physical Dynamics, Inc.
Detroit, Michigan
SUMMARY
The Air Quality Display Model (AQDM) and the Climato-
logical Dispersion Model (COM) have been used by the
Air Pollution Control Division of the Wayne County
Department of Public Health and Wayne State Univer-
sity to simulate annual averages of suspended
particulate and sulfur dioxide in the Detroit Metro-
politan area. Several meteorological models includ-
ing the STAR program were evaluated to determine the
effect of meteorological input data on predicted con-
centrations. The Briggs and Holland' plume rise
formulas were similarly evaluated. Correlations of
predicted concentrations with observations by the
Wayne County Air Pollution Control Division range
from .75 to above .90, depending on the combination
of models used.
Applications of air pollution modeling at the Wayne
County Air Pollution Control Division have dealt with
developing a better understanding of how sulfur
dioxide and particulate controls should be applied
and in evaluating the impact of new sources on air
quality. In addition, several divisions of Wayne
State University are using the air pollution diffu-
sion models in a variety of applications. The College
of Engineering is developing algorithms for determin-
ing optimal air pollution control strategies with
limited energy resources. The College of Lifelong
Learning uses the models in an environmental simula-
tion game called ENVIRO-ED as part of an educational
effort to develop better public awareness of the en-
vironmental problems in the Detroit region. The
Ethnic Studies Division of the Center for Urban Stud-
ies uses the same models for analyzing the socio-
economic impact of air pollution on Detroit area
residents.
As a result of the success with the AQDM and COM, dif-
fusion models have become a primary tool in the
Detroit area for predicting the future impact of pol-
lutant sources on ambient air quality and for criti-
cal decisionmaking such as locating major emission
sources, assessing fuel and/or process changes,
locating air monitoring stations, and reviewing
emission standards.
INTRODUCTION
The Detroit metropolitan area, with a population of
approximately 4.7 million people, is the major
industrial center of Michigan. The region consists
of seven Michigan counties: Livingston, Macomb,
Monroe, Oakland, St.Clair, Washtenaw, and Wayne,
covering 4500 square miles and a portion of Ontario,
Canada. The city of Detroit and Wayne State Uni-
versity are both located in Wayne County. The Air
Pollution Control Division is responsible for the
enforcement of applicable air pollution regulations
in Wayne County which in part are designed to meet
the National Ambient Air Quality Standards (NAAQS).
The Division operates a basic air monitoring network
of 14 continuously recording sampling stations that
telemeter data back to a central processing station,
plus three additional manually operated high volume
air samplers. Sulfur dioxide concentrations are re-
corded continuously at the 14 stations and suspended
particulate is measured at all 17 stations on a 24-
hour sample - 6 days per week schedule. This system
provided the ambient air quality data for verifying
and calibrating the AQDM and CDM. Two major airports
in the region are National Weather Service stations
and provide local climatological data (LCD) for the
meteorological needs of the models.
The 1974 emission inventory of sulfur dioxide and
suspended particulate that was used in this study
identified 506 point sources, 395 of which were in
Wayne County. To qualify as a point source, the
source must have emitted at least 5 tons per year and
be part of a plant that emitted at least 25 tons per
year. The remaining known emissions were included
in the area source inventory.
MODEL INPUT DATA
The two major input data sets required for diffusion
modeling are an emission inventory for point and area
sources, and the various meteorological parameters.
The sensitivity of the model to this data is such that
every effort should be made to obtain the most ac-
curate data possible.
EMISSION INVENTORY
The total inventory of emissions for the year 1974 was
divided into three major categories: point sources
(public utilities and major industrial, institutional,
and governmental facilities); area sources (resident-
ial, commercial,and small industrial); and mobile
sources (automobiles, aircraft, and vessels).
Point source emission data is determined by the amount
of fuel consumed and the manufacturing process. Area
source emissions are based on the fuel consumption
in the residential neighborhoods, small-size domestic
and commercial incinerators, and on small manufactur-
ing processes,
Mobile source emissions primarily depend on the gas-
oline consumption data for passenger and commercial
vehicles, but these emissions were neglected in this
study because their contributions to the total mass
emission rate of sulfur dioxide and suspended parti-
culates throughout Wayne County were approximately 2%
and 6%, respectively. In addition, these sources,
distributed throughout the County, mathematically con-
tribute negligible quantities at the receptor sites.
We did not feel that collecting the total mobile
source emissions for a grid square and placing them
at some point in the grid square is a proper proced-
ure. Rather, they should be treated as moving line
sources.
Area source information was only available from Wayne
County at the time. Using the UTM system, a grid of
5000-meter squares was established over Wayne County
to arrive at the area source emissions. Unfortunate-
308
-------
ly, our area source information was originally based
on grid squares one mile in length. The layout of
Detroit and Wayne County made the choice of the mile
grids very logical at the time. However, grid sizes
of kilometer integers are the only size acceptable to
the CDM. Since 5 kilometers is very close to 3 miles,
this was the smallest grid square we could use.
METEOROLOGICAL INPUT DATA
The various meteorological data such as wind speed,
wind direction, sky cover, etc., were available in
LCD form from the Wayne County Detroit Metropolitan
Airport which is about 20 miles southwest of Detroit,
or from the Detroit City Airport which is in the
northeast part of the city (and Wayne County). Neither
of these weather stations are in the immediate vicin-
ity of the major pollution sources, but Metropolitan
Airport seemed to provide better overall correlation
and was used in most cases.
Over a period of one year, 2920 atmospheric observa-
tions are recorded at each weather station. A meteor-
ological model then statistically calculates a joint
frequency distribution of wind direction, wind speed,
and atmospheric stability. The Day-Night STAR program
which was developed by the National Climatic Center
and is a part of the CDM, uses 16 sectors for direct-
ion, 6 classes of wind speed and 6 stability cate-
gories. (5) For the 1974 Metropolitan Airport data,
this model aggregated the 2920 three-hour readings
into a distribution of 153 district probabilities
which were used for the CDM simulations.
A similar model developed at Wayne State Univer-
sity, that enables the user to aggregate the meteoro-
logical data into intervals as fine as the original
data, was used to evaluate the STAR program. The
LCD data was originally collected in speed intervals
of 1 knot and directional intervals of 10 degrees.
Using the conventional 6 stabilities, and 10 degree
directional intervals, the number of distinct prob-
abilities in the joint frequency distribution varies
from 316 to 857, as shown in Table 1.
Speed Intervals
(Meters per second)'
1
2
3
4
5
Number of District
Probabilities
857
582
448
372
316
TABLE 1. Joint Frequency Distribution
The five different distributions summarized in Table 1
were used as input to the AQDM to evaluate the useful-
ness of this approach. In all cases, more data are
provided compared to the STAR model (which requires
more computer time) , but as the "fineness" of the
distribution increased, the correlation of simulated
versus observed data Increased. These results suggest
that further work is needed in this area.
Both the CDM and the AQDM used the curves of Pasquill-
Gifford (4) to approximate stabilities in Detroit.
The only difference between the two is the CDM uses
an empirical power law to approximate the functions
where the AQDM uses a table.
Four CDM computer simulations were made (Table 2). The
first included only Wayne County sources in the emis-
sion inventory. We then hoped to improve the linear
regression analysis in the second CDM simulation by
Including sources outside of Wayne County that could
affect Wayne County air quality. These were few in
number, but an increase in estimated concentrations at
most stations of 1 to 2 micrograms per cubic meter
for suspended particulate and 2 to 6 micrograms per
cubic meter for sulfur dioxide was found. For CDM
simulation number 3, the principal change was to
increase the sulfur dioxide half-life to 3 hours.
Half-life in simulations 1 and 2 were both 1.25 hours.
Because of this increase in half-life, estimated
sulfur dioxide concentrations increased at most sta-
tions by 3 to 6 micrograms per cubic meter.
The fourth CDM simulation used a sulfur dioxide half-
life of 3 hours, but the meteorological data was rep-
resentative of Detroit City Airport which is located
in a residential section of Detroit, while the previ-
ous simulations all used a joint frequency distribu-
tion from Metropolitan Airport. The correlation of
the regression analysis for particulate did not im-
prove by using Detroit City Airport data, but the cor-
relation for sulfur dioxide did improve.
PARTICULATE
Simulation Intercept
Correlation Coefficient
0.70
0.84
0.84
0.77
15.7
12.3
9.0
6.6
SULFUR DIOXIDE
1.38
1.36
1.26
1.49
CONDITIONS
0.76
0.75
0.73
0.81
Wayne County Sources Only
All Sources In or Near County
Sulfur Dioxide Life of 3 Hours
(previously 1.25 Hours)
City Airport Meteorological Data
(previously Metropolitan Airport)
TABLE 2.
Linear Regression Analysis of CDM
Simulations
As can be seen in the table, the best correlation for
particulates was simulation number 2, due to the add-
ition of sources outside the county. For sulfur di-
oxide, the best correlation was achieved with simula-
tion number 4 using a half-life of 3 hours and in-
cluding sources outside the county. With a background
defined by the y intercept, the high particulate
background, as will be seen, is justified and under-
standable. The sulfur dioxide background is accept-
ably low in the area of only 0.003 parts per million.
CONCLUSIONS
The different simulations point out important practi-
cal aspects that must be considered when using the
state of the art diffusion models for decision making
purposes.
The emission inventory is extremely critical and
should be arrived at very carefully. The Wayne County
Air Pollution Control Division determined the point
source emission inventory with data gathered princi-
pally by stack tests and emission factors (2) based
309
-------
on fuel consumption and the manufacturing process.
A significant amount of time was devoted to the emis-
sion inventory, yet the accuracy of the suspended
particulate inventory is still being questioned.
Stack tests are performed under ideal conditions not
always representative of day-to-day emissions. Con-
sequently, the data supplied by industry had to be
carefully scrutinized before it was used to estimate
emissions. For example, collector efficiency is
frequently supplied from the designer blueprints, but
it is unlikely the claimed efficiency is the normal
operative efficiency. Even the particulate inventory
does not represent only the emission of suspended
particulates, but includes varying amounts of settle-
able matter, dependent on the type and efficiency
of the collector and the resulting size distribution
of the emissions. Finally, the particulate emission
inventory certainly represents only a portion of the
total suspended particulate burden in the atmosphere.
Much of the uninventoried suspended particulate is
not the so-called natural background, but includes
man-made background, i.e., suspended particulate
emitted not from intended points of emission such as
smoke stacks, but from wind-blown factory dust, coke
piles, ventilation air, ground-up street dust from
mobile sources, etc. The Wayne County Air Pollution
Control Division undertook a program, sampling the
ventilation air from an iron foundry and a casting
plant which are considered point sources based on the
quantity of emissions from their stacks. We found a
greater particulate emission rate from the ventilator
ducts than from the respective smoke stacks. It is
mistakenly believed that except for the natural
background,a conventional particulate emission in-
ventory can account for essentially all of the atmo-
sphere's particulate burden.
Because the man-made or unaccountable particulate
background depends largely on the type of industry
involved, the total particulate background (man-made
plus natural) will vary across the study area. The
heavy industrialized regions of Wayne County contain-
ing large power plants, iron foundries, steel mills,
coke ovens, cement plants, slag piles, etc., use
many processes which are dirty operations in the sense
that there are many chances for the evolution of
particulate matter at low heights above grade into
the open air. It takes a source with excellent house-
keeping practices and "total enclosure" controls to
avoid these fugitive types of emissions. It is the
nature of the processes in a heavy industrialized
area that makes this a very difficult task to ac-
complish.
As the above regression analyses indicate, the CDM is
doing a very acceptable job of estimating particulate
concentrations. The y intercept (which is total
background) is approximately 65 micrograms per cubic
meter county-wide. As expected, the total background
is higher in those county areas recording the heaviest
suspended particulate concentrations. By taking the
difference between the uncalibrated CDM estimated
particulate concentrations and the measured particu-
late concentrations, the result is total estimated
background concentrations. This is done for each
receptor site. (While this may not be an exact method,
it gives a feeling as to the magnitude of the unac-
countable sources.) If natural background remains
constant throughout the area (not too bad an assump-
tion) the varying concentrations are due to man-made
unaccounted sources. It turns out, as expected, that
we can draw isopleths of total background (Figure 1).
Figure 1, Total Particulate Background (
Wayne County, Michigan
We find that a section of the heavy industrialized
area has an annual mean background of over 100 micro-
grams per cubic meter. Put another way, if somehow
we were able to plug up all well inventoried and
intended sources of emission, the measured particu-
late concentrations in certain areas of the county
would be well over. 75 micrograms per cubic meter, the
primary standard. The importance of this cannot be
overstated. It relates to the practicality of ever
achieving the suspended particulate NAAQS as they
presently stand, and the importance of enforcement
officials focusing on and paying careful attention to
all possible points of emission.
In Wayne County, we have seen the importance of fugi-
tive-type emissions on air quality as a result of a
comprehensive control program at the large industrial
park of the Ford Motor Company Rouge Complex. It
contains basic oxygen furnaces, coke ovens, power
plant, blast furnaces, large material storage piles,
etc. A substantial part of the control program was to
reduce or end the fugitive type of emissions attend-
ant to a large array of processes through different
types of good housekeeping practices. The once high
suspended particulate concentrations measured im-
mediately downwind of the complex and less than a
quarter of a mile from the border have been reduced
in two years by 30%.
CONTROL STRATEGY DEVELOPMENT APPLICATIONS
Air pollution diffusion models are also being used in
the Detroit area to develop and evaluate alternative
air pollution abatement strategies. The State of Mich-
igan is a long way from being "energy independent."
Estimates of the basic fuels imported to the state
range as high as 95% of demand, but the state obvious-
ly has a good supply of water, which suggests that it
will continue to be a major manufacturing center and
perhaps even an energy converting center. As the
supplies of oil and gas dwindle and prices increase,
however, greater emphasis will surely be placed on
using more coal, which raises at least two questions.
First, would it be possible, practical, or desirable
to convert many of the boilers that once burned coal
310
-------
back to coal? If the answer is yes, the second
question is, which sources-should be burning coal
and how should emissions be controlled so as to reach
or maintain the NAAQS in the "best" way. Many algo-
rithms have been developed recently in an attempt to
find the "optimal" solution to this problem (1).
However, the existing models usually have not in-
cluded fuel availability as a variable, and more
importantly, the effect of a new set of fuel demands
on price. Consequently, the "optimal" solution
often suggests a large-scale conversion from coal to
gas or oil, neither of which are in great supply.
Even if the fuels were available, the new set of de-
mands could very easily affect the prices to the
point where the "optimal" solution is no longer
optimal. This problem is being examined at Wayne
State University by coupling an energy supply-demand
model with an air pollution dispersion model similar
to the AQDM. Basically, the energy model assumes
that the quantity of a particular fuel available is
a function of price up to the ultimate reserves of
the mine or well. The model has a primary energy
system that simulates the extraction of basic fuel
resources and the conversion of these basic fuels to
coal, oil, or natural gas. For example, coal should
be converted to natural gas in the primary energy
model. A secondary energy model then simulates the
conversion of the basic fuels to other energy forms
such as electricity and/or the transportation to the
final end user, where the final energy conversion
takes place. The air pollution diffusion model is
used to predict the impact of all energy conversions,
hence pollutant generation, on the local environment.
The overall model is structured to operate in simu-
lation or optimization mode. When the system operates
in simulation mode, the air pollution model attempts
to find the combination of manufacturing levels and
energy end uses that will enable a set of pollution
constraints, such as the NAAQS, while maximizing the
net benefit to the region from energy utilization.
The net benefit is defined as production profits
minus the total cost of energy to the region, in-
cluding industrial uses. Total cost of energy is
determined by adding the cost of the basic fuels at
various levels of extraction and all later conversion
and transportation costs. The entire model is cur-
rently being tested on a small scale with a hypo-
thetical community of 40,000 people. In the future,
we hope to extend the model to a major metropolitan
area such as Detroit.
One of the problems encountered in any project of
this scope is handling the large quantities of input
and output data. The AQDM and COM models are quite
satisfactory for experienced users who are dealing
with a specialized air pollution problem. However,
when working on a more generalized problem where air
pollution is one of many constraints, such as the
energy-environment dilemma, a data management system
is needed to integrate those models with other sim-
ulation programs and the many sources of input data.
In addition, graphic display of the simulated output
data is very useful when examining regional patterns.
In response to these needs, we have developed an Air
Quality Information System (AQIS) that integrates
the CDM, AQDM, and other related simulation models
developed at Wayne State University with the U.S.
Census, Census of Manufacturers, Local Climatological
Data, apd health data for the Detroit area. The
system also includes a capability that enables the
user to generate, among others, contour maps of air
quality. The output from the mapping program can
then be examined live on a graphic display terminal
or routed to a plotter for hard copy.
EDUCATIONAL APPLICATIONS
ENVIRONED is a computer-assisted instruction package
that deals with the involvement of the individual in
problems of energy consumption, resource depletion,
and environmental pollution (3). Part I of ENVIRO-
ED introduces the user to air pollution, water pol-
lution, and solid waste disposal problems and is
usually the first program used. Once the individual
becomes familiar with the problems, he/she is asked
to clean up the air over Detroit by imposing various
controls on emissions, allocating fuels, or limiting
certain industrial and residential activities. Once
a control strategy is identified, a.simulation of air
quality in the region and the control strategy costs
is done with the AQIS. If the NAAQS are not met, the
student is required to continue adding constraints
until the standards are met. The simulation data can
be displayed live on graphic display terminals such
as the TEKTRONIX, but few of the users to date have
had that type of hardware.
ENVIRO-ED has been used by the College of Engineering
at Wayne State University with excellent success and
the College of Lifelong Learning is experimenting
with the programs in its new General Studies degree
program.
OTHER APPLICATIONS
The Ethnic Studies Division of the Center for Urban
Studies, Wayne State University, is researching the
dynamics of ethnic neighborhoods in the Detroit area
to identify factors causing changes in these com-
munities and to attempt to predict future patterns.
Since many of these communities originally formed
near major manufacturing facilities, not too surpris-
ingly, air pollution has always been identified as a
major problem by the residents. In order to quantify
the situation, the Ethnic Studies Division has used
the AQIS to simulate particulate and sulfur dioxide
concentrations in these ethnic neighborhoods. When
these data are coupled with the 1970 U.S. Census data,
they provide a cross-tabulation of pollutant concentra-
tions with various population characteristics of
Detroit, such as ethnic group, age,and income dis-
tributions.
FUTURE WORK
In the future, we plan to continue evaluating the
effect of certain input data and program sub-models
on the estimated concentrations of sulfur dioxide and
particulate matter. We will attempt to continue
updating and improving our emissions inventory with
emphasis on area sources since they had a greater
impact than point source emissions on selected re-
ceptor sites. Size distributions of suspended part-
iculate and the half-life of sulfur dioxide in the
Detroit area will also be investigated, which should
improve the accuracy of the simulations. In addi-
tion, our efforts to evaluate alternative control
strategies will receive special emphasis in case the
need for large-scale conversion to coal becomes
necessary in the region. The AQDM and CDM models
have been found quite satisfactory for long-term sim-
ulations of sulfur dioxide and particulate. However,
similar success has not been enjoyed in our efforts
to model these same pollutants on a short-term basis.
Consequently, we are currently developing a real-time
simulation model for sulfur dioxide and particulate
311
-------
matter and will continue this work in the future.
REFERENCES
1. Atkinson, S.E. and Lewis, D. H., A Cost Evalua-
tion of Alternative Air Quality, U. S. Environ-
mental Protective Agency, 1974.
2. "Compilation of Air Pollutant Emission Factors,"
(AP-42), U. S. Environmental Protection Agency,
Research Triangle Park, North Carolina, 1975.
3. Anderson, J.A., Harlow, C.D., and Bartalucci, S.,
"ENVIRO-ED, A CAI Experiment in Developing Public
Awareness," Energy, Ecology and Society, Mich-
igan Academy of Science, Arts and Letters, 1974.
4. Pasquill, F., "The Estimation of the Dispersion
of Windborne Material," Meteorological Magazine,
Vol. 90, 1961.
5. Busse, A.D. and Zimmerman, J. R., User's Guide
for the Climatological Dispersion Model, U. S.
Environmental Protection Agency, 1973.
312
-------
SENSITIVITY TESTS WITH A PARAMETERIZED
MIXED-LAYER MODEL SUITABLE FOR AIR QUALITY SIMULATIONS
Daniel Keyser
Richard A. Anthes
The Pennsylvania State University
University Park, Pennsylvania
Several modifications to the one-layer tnesoscale
numerical model which Lavoie developed and applied to
Great Lake snowstorms are formulated and tested. The
model atmosphere consists of a parameterized constant-
flux layer of fixed depth, a well-mixed layer capped by
an inversion, and a deep layer of stable air overlying
the mixed layer. Time-dependent calculations of the
horizontal components of the wind velocity, potential
temperature and the height of the base of the inversion
are performed over a mesoscale grid. Since the mixed-
layer assumption eliminates the dependence of the prog-
nostic variables on height, the low-level mean flow can
be predicted far more cheaply than with multi-layer
models.
The major refinements introduced in this paper lie
in the parameterization of the effects of the stable
layer on the mixed-layer, the entrainment of mass, heat
and momentum Into the mixed-layer by subgrid-scale
eddies, and the erosion of the inversion by heating.
The sensitivity of the model solutions to the initial
inversion height and strength, the stability of the
upper layer, the vertical shear of the geostrophic
wind, and the height of the undisturbed level in the
overlying stable layer is investigated. These tests
are performed for an east-west cross-section for mod-
erate flow over complex terrain.
The Mixed-Layer Model
Multi-level primitive equation models can simulate
complex, mesoscale flow patterns realistically. How-
ever, high-resolution, multi-level models require such
large amounts of computer storage and time that they
currently are not practical tools for everyday opera-
tional use. A simpler numerical model which requires
far less computing power, but at the same time can
duplicate the main results of a complicated model,
would be a desirable alternative.
Since meteorologists universally recognize the im-
portance of terrain patterns in "tuning" the local
weather conditions, it is necessary to design a meso-
scale model which can resolve topographic detail. Var-
iations in surface heating and roughness also cause or
"force" mesoscale circulations. Since these three
effects act at the surface, one intuitively might ex-
pect them to be most important in the planetary bound-
ary layer (PEL).
Under conditions of moderate flow or strong sur-
face heating, the PEL can be considered well-mixed; the
turbulent eddies distribute heat, moisture, and momen-
tum uniformly in the vertical. Under such conditions,
one may treat the PEL as a single layer and consider
only horizontal variations in the flov. Lavoie devel-
oped a prototype mixed-layer model and applied it to
mesoscale studies of Great Lake snowstorms and convec-
tive precipitation over Hawaii.3>^ We contend that
this type of model may be relevant in modeling low-level
flow in more general situations.
Because the model explicitly predicts the atmos-
phere's behavior for the mixed-layer only, the behavior
of the rest of the atmosphere must be parameterized.
In the remainder of this section, we present the model
and discuss its assumptions and parameterizations.
Structure of the Model Atmosphere
The lowest layer of the model consists of a thin
(50m) surface layer which contains most of the wind
shear and a super-adiabatic lapse rate, and follows the
variable terrain (Fig. 1). The elevation of the terrain
is denoted by ZQ; the height of the top of the surface
layer is denoted by Zs. The main layer extends from Zs
to the base, h, of a stable upper layer. This second
layer is assumed to be well-mixed so that potential
temperature, 8, and the horizontal wind velocity, V,
are approximately constant in the vertical. The upper
stable layer is marked by a zero or first order discon-
tinuity in 8 at its base and contains a lapse rate that
is vertically constant. The winds in the stable layer
are assumed to be geostrophic and may include a constant
shear in the vertical.
1. Hypotk&ttcal. cjiot>ts-t>e.c£ion
0(5 mixed-tayeji modeJt.
313
-------
The height, h, of the mixed-layer is a material
surface with the exception that subgrid-scale eddies
may entrain mass, heat and momentum from the stable
layer above. The entrainment depends on the surface
fluxes of heat and momentum. The height, H, is the
level at which the mesoscale perturbation in the poten-
tial temperature structure induced by heating or the
terrain pattern is assumed to vanish.
Fig. 1 shows a. cross section view of possible var-
iations of the potential temperature structure permitted
in the model. The 9^ isentrope.intersects h as a first-
order discontinuity in potential temperature, while the
82 isentrope intersects h as a zero-order discontinuity.
iThe vertical isentropes between h and Zg are character-
istic of a well-mixed layer. The 8-pattern between h
and H indicates the response of a stable layer to a
mesoscale perturbation in the PEL.
Y, in the stable layer. The fourth term represents a
restoring force associated with horizontal deformations
in the height of the mixed layer. The fifth term re-
presents the modification to the pressure gradient force
due to the baroclinity of the PEL. The last three terms
represent the effects of surface friction, horizontal
mixing, and entrainment of u-momentum across h. The
parameterized contribution of entrainment to the u-ten-
dency is denoted by (-5^)
1 3 V3t'entrainment
The v-equation is simpler because in the one-dimen-
sional case north-south gradients in v, 8, 8^, and h
vanish. The mesoscale pressure gradient terms do not
appear.
Thermodynamic equation. The thermodynamic equation
governs the local time rate of change of 8 in the bound-
ary layer,
Model Equations
The derivation of the system of equations describ-
ing the physical behavior of a mixed-layer is not pre-
sented here. Instead, we present the final system of
equations and discuss some of its basic properties. In
order to simplify the discussion further, we only con-
sider variations in the west to east direction. Since
the vertical variations in the mixed-layer are sup-
pressed, only horizontal variations are permitted and
the model is effectively one-dimensional. The one-
dimensional version retains the essential physics, but
simplifies the interpretation of the results of the
sensitivity tests that follow later.
Equations of motion. The partial differential
equations governing the evolution of the west-east, (u),
and north-south, (v), components of the horizontal wind
velocity in the mixed-layer are as follows:
li - _ 38
3t U 3x p c (h - Z )"
36
'•St'entrainment
In (3) FH(ZS) is the flux of sensible heat by eddy mo-
tions into the mixed-layer through Zg; ps is the air
density at Zs, cp is the specific heat for dry air at
constant pressure, KH is the eddy coefficient for the
horizontal transport of heat, and (•§£)entrainment repre-
sents the effect of entrainment across h. The neat flux
term must be non-negative; otherwise, the mixed-layer
assumption might be violated.
Mixed-layer height equation. The prognostic equa-
tion controlling the development of h is
3h
3t
= -uf +W(h)
+ s
(4)
where W(h) is the vertical velocity at the height h, and
S is the time rate of change of h due to entrainment of
mass from the stable layer into the mixed layer.
jm
3x
gft-y
29
li
3x
h - Z
— + r—•>
-2 V3t'entrainment
3x
(1)
Diagnostic equations and parameterizations. The
vertical velocity is determined by neglecting local
density variations and integrating the continuity equa-
tion from Z to h.
W(h) = - W(Zs) -
h
(h
Z t —
V 3x
h - Z
3v
3t entrainment
(2)
where W(Zg) is the vertical velocity at Zg. The first
term represents the effect of sloping terrain,
3Z
w(zs)
o
3x
(6)
In (1) and (2), x is distance and t is time. The
Coriolis parameter, f, is 10~^ s~ and is constant in
the x-direction; g is gravity, ug(H) and vg(H) are the
west-east and north-south components of the geostrbphic _ 0.1 FH(ZS)
wind at the height, H; 8 denotes the potential tempera- p c +
ture in the mixed-layer; 8^ is the potential tempera- P p
ture in the stable layer at h, the height of the top of
the mixed-layer; y is the lapse rate of 8 in the stable
The entrainment term, S, follows a parameterization
introduced by Tennekes:?
g(h-Zs)
)/A84
(7)
layer; CD is the bulk-aerodynamic drag coefficient, and
KM is the coefficient of eddy-viscosity for horizontal
momentum.
where 90 is the potential temperature at the earth's
surface and the friction velocity, u*,is the downward
flux of momentum through Zs. For a neutral boundary
layer u* is given by
The first term on the right side of (1) is the ad-
vection of u. The second term represents the linear
acceleration associated with the departure of the mixed-
layer wind from the large-scale, geostrophic wind at H.
The third term represents contributions to the pressure-
gradient force from baroclinity and the static stability,
u. = C.
1/2
(8)
o Deardorff1
(7) may be defined by
the inversion strength,
314
-------
A9. = maximum
(9)
0.09(h - Z
Equation (7) states that entrainment of mass depends on
the surface heat and momentum fluxes. The entire term
is modulated by A6j which represents the resistance of
the overlying stable layer to penetration by turbulent
eddies.
components are time-dependent and are determined by
their values in the interior^of the domain in a manner
prescribed by Anthes, et al. The solutions are
smoothed in space and time once each hour during the
integration to suppress non-linear instability.
Experimental Results
The following experiments indicate the sensitivity
of the model solutions to changes in input parameters.
Such information is useful if the parameter cannot be
specified accurately by atmospheric measurements, or if
the applicability of the parameterization is question-
able.
The height of the undisturbed level, H, is arbi-
trarily assumed to be proportional to the depth of the
perturbation induced in the h field.
H
h + a(h - h)
max max
(10)
where h^x and h are the maximum and average values of
h on the domain at a given time and a is a constant of
order one.
Airflow over a Mountain
Before discussing the results of the sensitivity
tests, we present a model simulation of moderate air-
flow over complex terrain. This case demonstrates
some of the physical capabilities of the model and
serves as a control experiment for the following sensi-
tivity tests.
The experiment contains the following specifications:
The potential temperature lapse rate or static
stability, Y> in the stable layer is given by
9H-9h
(11)
' H - h '
where 6 is determined by
n
9H 6 (hi) + Y1 (H - hi) . (12)
In (12), the superscript, i, indicates the initial
value of the variable.
The geostrophic wind at H is determined by assum-
ing the following profile:
3V
V (H) V (h1) +
"
(H - h1)
(13)
The parameters Vg and
g
2
must be specified since they
are external large-scale variables.
The effects of entrainment on the momentum and po-
tential temperature in the PEL are calculated with the
assumption of conservation of mass and enthalpy. If
Ah = S At is the change in the inversion height due
to entrainment over a time step, At, then Oh, 6, u,
and v are calculated from
8h(t + At)
. , .
VV ^'
6h(t) + YSAt
(h* - ZS) d>*
2Ah
Ah]
(14)
(15)
h* + 2Ah -
where <)> is u, v, or 6, and an asterisk indicates the
value of a variable before the effects of entrainment
are considered. The factor of 2 before Ah in (15) is
a consequence of using centered time- differencing.
Numerical Procedure
Time and space derivatives in the preceding equa-
tions are approximated by centered- in-time and cen-
tered- in-space finite differences. The system is inte-
grated forward from a specified set of initial condi-
tions over a staggered grid that is "stretched" at the
boundaries. The grid increment, Ax, increases near the
boundaries in order to minimize their effect on the
solutions in the interior of the domain. The variables,
9, 9, , and h are fixed at the boundaries; the velocity
Ax
min
20 km
Terrain profile: smoothed west-east Appalachian profile
at approximately 38°N latitude.
-3 -3
C = 1.5 x 10 over water; 7.0 x 10 over land
u = 10 ms , v
g g
Oms ,Yf
Z + 500 m = 1426.59 m
omax
= 5° K km
6 = 290°K,
"1
293°K
~3
ps = 1.21 kg m
No surface heating
H: a 1 in (10)
1.03 kg m
"3
8V
Ky = KJJ = [5 x 104 + 0.08 (Ax)2 |^| ] (|*- )2 [m2 s'1]
min
The superscript, i, indicates the initial value of
a variable; the subscripts max and min denote maximum
and minimum values, respectively. The formulation for
KM and KH increases the damping near the boundaries
where Ax is larger than in the interior of the domain.
The initial u and v are calculated assuming a steady-
state balance between frictional, Coriolis, and pressure-
gradient forces. This procedure helps minimize the ini-
tial shock of starting the model. 1 For this set of
specifications :
u = 8.61 ms
u1 = 9.92 ms"1
= 3.38 ms
= 0.83 ms
"1
over land.
over water.
The model is integrated for 12 h using a 240 s-time
step. The solutions contain transient oscillations over
the integration period; these oscillations result from
initial imbalances that the terrain produces in the flow.
Additional experiments indicate that about 18 h of inte-
gration time are needed to attain a steady state. This
adjustment time corresponds closely with the inertial
period of 17.5 h associated with f
~^ "-*-.
Inertial
gravity waves apparently effect the adjustment process
towards a steady state; after one cycle the model var-
iables are in balance.
315
-------
We desire a quasi-steady state for the sensitivity
testing because we would like to investigate the model s
physical response to the fixed terrain profile with its
associated surface drag, and the synoptic-scale pressure
gradient force. Although the final steady-state is not
reached until after about 18 h, the solutions at 12 h
are quite similar to the ultimate steady-state solu-
tions. For example, Fig. 2 depicts the 12 h and steady-
state solutions of u, W(h) and h. The steady solution
is the time average between 18 h and 24 h. Because of
the qualitative agreement between the 12 h and steady-
state solutions, the results from the sensitivity tests
will be compared at 12 h.
roughly parallels the terrain profile and the perturba-
tion in W(h) has helped produce a perturbation at the
coast.
Sensitivity Tests
The fields of mixed-layer height, h, at 12 h will
be compared since they represent an integrated response
to the velocity components and entrainment. Fig. 3 con-
tains the results of the tests.
W(h)
(cmi-l)
I2h
— ie-24h AVERAGE
200 4 ,-Ln the. JinJL-
k<-, e£- 6-*-, y'S a. a^d
3.
3z '
Variation of h . Two experiments were run; one
with h1 - Zomax = 250 m, the other with h1 - Zomax =
1000 m. The h curves are plotted so that their end-
points coincide despite differences in the numerical
values. This presentation demonstrates their relative
changes. The greatest effect of changing the initial
height of the inversion occurs at the mountain, and the
least variation occurs over the water. Kntrainment is
the factor causing the differences . In these adiabatic
experiments, it is inversely proportional to the PEL
depth, and is stronger over land where the roughness is
greater.
Variation of initial inversion strength, Sh1 - 9 .
316
-------
Experiments were run for inversion strengths of 1.5°K
and 6.0°K. The case with the weaker initial inver-
sion strength shows the greater growth in h at 12 h.
As in the preceding case, the changes are negligible
over water where entrainment is weak. The perturbation
in h at the coast is more accentuated in the less
stable case <6hi - 61 = 1.5°K).
Variation of y . Experiments with
-1
2.5°K km
and 10.0°K km"1 are performed. The results indicate
that for weaker y*, stronger perturbations in h develop
at the mountain. Weaker perturbations develop when the
upper layer is more stable. Qualitatively, a large re-
storing force from the upper layer causes weaker upward
motions and less growth in h. Also, entrainment is
weaker when y* is large.
Variation of H. We change H by varying the para-
meter a in (10) from 0.5 to 2.0. At 12 h for a equal
to 0.5, H equals 2330 m; for a equal to 1.0, H equals
2510 m; and for a equal to 2.0, H equals 3100 m. In-
creasing a by a factor of 4 increases H by about 1/3.
The h fields coincide very closely, so the variations
in H have little effect on the model dynamics through
the restoring force. This case does not contain shear
of the geostrophic wind, so Vo(H) is independent of the
value of H.
The one-dimensional mixed-layer model data can be
used as input for a cross-sectional air quality model
of the mixed layer. We have designed such an air quality
model that considers sources, sinks and vertical diffu-
sion on an Eulerian grid, and treats the advective trans-
port with a par tide-in-cell technique. Fig. 4 depicts
the meteorological state predicted by the mixed-layer
model and the associated concentration pattern of a pas-
sive contaminant in the PEL. This example demonstrates
the potential of combining mixed-layer model data with
a typical air quality model.
H
~g
Vertical shear of ug. In our final test we intro-
duce a vertical shear in the geostrophic wind; -^^
equal to 10 ms"-'- km"-*-. This value corresponds to a
north-south potential temperature gradient of -2.96°K
(100 km)~l a value characteristic of frontal zones.
At 12 h the h pattern exhibits a maximum at the
mountain ridge which is 500 m higher than in the case
without shear. The perturbation at the coast is ampli-
fied. Including shear dramatically increases the kine-
tic energy in the model. The geostrophic wind, ug(H),
is higher causing stronger horizontal winds and verti-
cal velocities which intensify the perturbation in the
h-field. In turn, H rises increasing ug(H). At 12 h,
H = 3096 m and ug(H) =26.7 ms~1. The model results
are reasonable for this strong a pressure gradient; how-
ever, in physically realistic experiments shears would
be weaker and there would be limits on H and ug(H).
To summarize, changing h , 8j, 9 , y and Of
cause relatively small differences in the model's be-
havior while changing ug(H) produces a significant
effect. The geostrophic wind represents synoptic-
scale forcing while the other parameters represent
mesoscale processes. These model results indicate that
in the absence of surface heating, the mesoscale motions
are most sensitive to variations in synoptic-scale pres-
sure gradients under moderate to strong wind conditions.
Application to Air Quality Simulations
Because the one-dimensional model results are en-
couraging, we intend to conduct further tests with di-
abatic heating as an additional forcing term. We then
plan experiments with a two-dimensional version of the
model that will utilize real data in order to determine
how realistically a simple model can depict mean bound-
ary-layer behavior.
The output of u, v, W, 6, and h can serve as input
for a regional scale air quality model of a well-mixed
boundary layer, where to a first approximation the con-
centration of a pollutant is vertically uniform. In or-
der to maintain large horizontal gralients, particle-
in-cell techniques can be used in simulating the advec-
tion of concentration patterns. If sources and sinks
can be modeled realistically, reasonable estimates of
pollutant concentrations should be obtainable from such
a model.5 We feel that mixed-layer models can generate
i V\ »-* --*_
10
90
190 290 390
Land I Wot.,
490
4. Cn.o&&-&e.(Ltion de.pi.cJMQ 12 k-mi.-iad-lja.yeM.
modeJt output and c.onc.e.nt^ation o£ a paw-tve. contaminant
deJii.ve.d ^fiom the. aJui quaLity modeJL. \JwtLc.aJL OMLOM at
x 50 km ie.pn.eJt,ante c.e.nteA od 20 km-wide. ajina. coatee otf
Atte.ngth 35 \ig m~2 &~>. Ve.po&-ition iA &imuJLate.d ea&t o-f,
the. c.oat>t (* >_ 2SO km); the. de.po&i£ion velocity iA 3 ami"'.
kKAom >ie.p>ieJ>znt uiind diA.e.ctLon -in the. mixed-layex.. Dot-
ted ti.ne& an.e.-it,optethi,o(i contaminant c.onc.ent>iation in
unitA oj, ug m"3. Va&hed tine* ate. iAen&wpeA. ?ote.ntiaJi
te.mpeAatufi& at 12 h in the. mi.x.e.d-iayeA \xvu.M> ^lorn
290.55°K to 2<)0.90°K.
Acknowledgements
This research was supported by the Environmental
Protection Agency through Contract 800-397-03. Daniel
Keyser holds a National Science Foundation Graduate
Fellowship in Meteorology. Gail Maziarz capably typed
the manuscript.
Sources
1. Anthes, R. A., N. Seaman, J. Sobel, and T. T. Warner,
1974. The Development of Mesoscale Models Suitable
for Air Pollution Studies," Select Research Group
in Air Pollution Meteorology, Second Annual Pro-
gress Report: Vol. 1, Environmental Protection
Agency, Research Triangle Park, N.C. 27711.
2. Deardorff, J. W., 1972, "Parameterization of the
Planetary Boundary Layer for Use in General Circu-
lation Models," Mon. Wea. Rev., 100, 2, 93-106.
3. Lavoie, R. L., 1972, "A Mesoscale Numerical Model of
Lake-Effect Storms, J_. Atmos. Sci., 29, 6, 1025-1040.
4. Lavoie, R. L., 1974, "A Numerical Model of Trade Wind
Weather on Oahu," Mon. Wea. Rev.. 102, 9, 630-637.
5. Nordlund, G. G., 1975, "A Quasi-Lagrangian Cell Method
for Calculating Long-Distance Transport of Airborne
Pollutants," J_. Appl. Meteor., 14, 6, 1095-1104.
6. Queney, P., 1948, "The Problem of Air Flow over Moun-
tains," Bull. Amer. Meteor. Soc., 20, 16-26.
7. Tennekes, H., 1973, "A Model for the Dynamics of the
Inversion Above a Convective Boundary Layer," J_.
Atmos. Sci., 30, 4, 558-567. ~
the meteorological data such a model requires.
317
-------
PREDICTION OF CONCENTRATION PATTERNS IN THE ATMOSPHERIC SURFACE LAYER
S. Hameed
Laboratory for Planetary Atmospheres Research
Department of Mechanics
State University of New York
Stony Brook, N. Y. 11794
S. A. Lebedeff
Institute for Space Studies
NASA, 2880 Broadway
New York, N. Y. 10025
Abstract
We present a study of turbulent diffusion in the
atmospheric surface layer under conditions of neutral
stability. The two-dimensional semi-empirical diffu-
sion equation is solved using the integral method,
previously described by us [3-6]. Concentration dis-
tributions at the ground are obtained for area sources
and for line sources situated perpendicular to the mean
wind direction. It is found that the concentration
distributions are represented by simple formulas for
downwind distances x » zo, where zo is the roughness
length. Also, at such large distances, the equation
for the shape of the boundary of the polluted layer
obtained by the integral method is found to be the same
as given by Lagrangian Similarity Theory. This equa-
tion yields the value A = 0.65 for the ratio of the
mean vertical velocity to the friction velocity in the
neutral surface layer, which compares well with the
value A = 0.75 found by Kazanskii and Monin [7] from
experiment.
Introduction
Prediction of pollutant concentration patterns
requires solution of the diffusion equation in which
the mean wind velocities and eddy diffusion coeffi-
cients appear as input quantities. In practice the
mean wind velocity as a function of height is obtained
from measurements while the diffusivity function is
estimated with the help of a boundary layer model.
Usually models of the boundary layer are based on
simplifying assumptions, such as existence of steady
state conditions and homogeneity in the horizontal
direction, which do not correspond realistically to the
urban problem where pollution dispersion is of the
greatest interest. Such simplified models are, none-
theless, of interest in dispersion studies because,
hopefully, they lead to an understanding of the basic
processes involved. Also, methods developed for study-
ing such simple models could be of use in the future
when more realistic models of the urban boundary layer
become available. In this paper we will focus our
attention on perhaps the simplest dispersion problem,
that is, the prediction of concentration distributions
from area and line sources in the atmospheric surface
layer. The surface layer is the lowest part of the
planetary boundary layer in which Reynold stresses are
found to be nearly constant with height. According to
Monin-Obukhov similarity theory the turbulent transport
processes in the surface layer are completely charac-
terized by only two parameters, namely, the friction
velocity u* = (T0/p)T, where To is the constant value
of turbulent stress and Q3is the air density, and the
length scale L = IH* , where k is the
Mg/T0) (q/Cpp)
von Karman constant, g is the gravitational accelera-
tion, TQ the air temperature, q the vertical heat flux
and Cp is the specific heat capacity of air. In
neutral conditions q = 0 and |L = °°; in stable condi-
tions q<0 and L>0 and when unstable conditions prevail
q>0 and L<0. In particular, the mean wind velocity
u(z) and the eddy diffusivity K(z) can be represented
in terms of a function \
~ l I1 »T ' Z *7 ' J l^'
where zo is the roughness length characterizing the
ground roughness which is assumed to be uniform in the
x,y directions. The determination of the function
4>(Z/L) has been the subject of several theoretical and
experimental investigations [l]; in particular,
Businger et al. [2] have found from observations that:
and
= 1 + 4.7 z/L ,- L>0,
_ 1
(1 15 z/L)''
L<0
(3)
It may be noted that these forms of 0 is speci-
fied by the boundary condition:
K(z) = -Q
(5)
Also,
c(x,z) = 0
and c(x,z) = 0
With u(z) and K(z) given by equations (1,2), the dif-
fusion equation becomes:
x = 0,
z = <*>.
(6)
—
k2
3c
dx = 3z
(7)
This equation can, of course, be solved by numerical
methods but we will apply an integral method to obtain
its solution. We have studied application of the
integral method to the diffusion equation in our
previous work [3, 4, 5, 6] and we find that it is con-
siderably simpler than numerical integration and also
gives accurate solutions for the concentration distri-
bution at the surface. In the present problem we find
that the method becomes particularly simple and yields
interesting results for the surface layer under condi-
tions of neutral stability. In the following, there-
fore, we will solve equation (7) for the neutral sur-
face layer; the treatment of stable and unstable
318
-------
surface layers is somewhat more involved and will be
presented elsewhere [6].
For neutral stability L = <*>, $ (Z/L) = 1 and f =
log z. Hence equation (7) becomes
^log(z/z0) |f=|^z|| (8)
and the boundary condition (5) reduces to:
ku*z -°- = -Q ; z = ZQ (9)
Let us define dimensionless variables:
5 = ^r1 ,5 = f- and N(5,?) = ^£-
Then equations (8,9) become:
3N _ 3 9_N
09 ^ 85 " 3? ^ fit, '
(10)
(8a)
(9a)
The increase in the depth of the pollutant cloud with
distance according to equation (16) is compared with
the approximation (17) in Fig. 1, and the corresponding
increase in the surface concentration over an area
source No(5,l), according to equations (14) and (14a)
is shown in Figure 2. It may be noted that this solu-
tion is for a uniform area source which extends from
x = 0 to x = °°. Concentration distributions for
sources of finite extent or spatially varying emission
strengths can be constructed from this basic solution
by superposition, as shown in [3,6]. Furthermore, if
M(5,C) is the concentration distribution due to an
infinitely long line source situated at right angles to
the mean wind direction, then, as explained in [6],
(18)
We differentiate equation (14) and consider the case
6»1 and obtain:
d&_
In the integral method it is assumed that the distribu-
tion of the contaminant above the area source is limi-
ted to a finite depth £ = 6(5) and the contaminant
concentration and its flux vanish for larger values of
N(?,O = o , ? = 6(5),
(19)
- z0 (5 + 11 6)
18
This result is shown as the dash-dot curve in Fig. (2).
S = 6(5),
(11)
Thus 6(5) represents the top of the polluted layer. We
have found [5,6] that the integral method yields an
accurate solution of a problem characterized by a
linear diffusivity function, such as equation (8a), if
we assume the solution to be of the form:
N(5,?) = no(5)U f-)2 log (I)
o o
(12)
Substitution of this expression in the boundary condi-
tion, equation (9a), gives: 2
(13)
no(5) -
(6-1)(6-1+2 log 6)
Concentration at the surface z = ZQ is obtained by
using equation (13) with equation (12) and taking C. =
1; ,*,>•,*
»i if n \ (o-i) log o n/u
"o^'1) = (6-1+2 log 6) ( '
We now integrate the diffusion equation (8a) from
? 1 to £ = 6 to obtain:
.6
(log ?) (1-1)'
o
log ()dC = ?
= 1 (15)
(16)
where we have used conditions (9a) and (11) on the
right hand side. Integration over 5 then gives:
'l§ <"'3+^2~2 + g^log *-* ~54~ 63+262-^- + y7
(6-1) (6-1 + 2 log 6)
This is an algebraic relationship for determining 6(5)
which together with equation (14) gives the concentra-
tion distribution at z = ZQ.
With reference to the definitions (10) we note
that 6 has been expressed in units of z0. Since ZQ is
usually small (~1 cm) we have 6»1, except in a small
region very close to the upwind edge of the area source.
Hence we may use the approximation
18
and replace equation (14) by:
if 6 >
(17)
N (5,1) = log 6
o
(14a)
Shape of the Contaminated Layer
Calculation of the shape of the boundary of the
contaminated layer due to a source located on the
ground has been the subject of several investigations
on the basis of the Lagrangian Similarity Theory [1].
Also, Kazanskii and Monin [7] have experimentally
observed the dispersion of smoke from a maintained line
source in the surface layer in near-neutral conditions.
They have explained the observed shape by arguing that,
since the friction velocity u* is the only velocity
scale in the surface layer, the mean vertical velocity
of particles at the top of the contaminated layer
should be:
|| = Au» (20)
where Z represents the top of the layer and X is a
constant. Also, neglecting the effect of horizontal
diffusion, the smoke particles may be taken to move
along the horizontal direction with the mean velocity
of the wind:
- log
\
(21)
Thus, combining equations (20,21) one obtains for the
shape of the boundary:
i
(22)
In the integral method used in the previous sec-
tion, the shape of the boundary is given by equation
(16) which yields for 6»1:
M = 11 log 6 26 .
d6 18 27
(23)
With reference to the definitions (10), writing 6 = —,
zo
and neglecting the constant term asymptotically, equa-
tion (23) becomes: ,
3v 1 1 -7
(24)
which on comparison with equation (22) shows that the
shape of the pollutant layer obtained by the integral
method is in essential agreement with that obtained by
Lagrangian similarity arguments in the region suffi-
319
-------
140
ieo
— x Downwind Distance
Z0
Figure 1. Variation of the depth 6 with the downwind distance . The error in equation (17) is 1.6 percent at
6 = 100.
" . ^ne Source Eq. (19)
180
— * Downwind Distance
zo
Figure 2. Variation of ground level concentation with the downwind distance £• Area Source, equation (14).
Area Source, equation (14a). Line Source, equation (19). The error in equation (14a) is nearly 10
percent at 5 = 100.
320,
-------
ciently removed from the upwind edge of the source. If 7. Kazanskii, A. B. and A. S. Monin: (1957). The form
the right hand sides of equabions (22,24) are equated of smoke jets. Izves. Akad. Nauk. SSSR, Ser. Geofiz.
we obtain: No. 8, 1020. See also A. S. Monin (1959) Smoke propa-
\ — ^"^ = o 65 (25) gation in the surface layer of the atmosphere. Adv.
11 " Geophys. 6, 331.
which may be compared with the value A = 0.75 obtained
by Kazanskii and Monin from estimates of u* and (dz/dt)
in their experiments. Considering the necessarily
ambiguous definition of the top of the contaminated
layer this agreement is encouraging because it shows
the essential validity of the integral method.
Conclusions
We have analyzed the dispersion process in the
atmospheric surface layer under steady state conditions.
By applying the integral method to the case of neutral
stability we find that for a semi-infinite area source
the concentration distribution at the surface z = zo is
given by:
ca(x,z ) = _S_ log (!_)
ku* z
where
i|~zlog
-------
A TIME DEPENDENT, FINITE GAUSSIAN LINE SOURCE MODEL
John C. Burr
Environmental Evaluation Section Chief
Ohio EPA
Columbus, Ohio
Robert G. Duffy
Water Quality Surveillance Section Chief
Ohio EPA
Columbus, Ohio
Introduction
Mathematical models of atmospheric diffusion range
between two extremes. On the one hand there exist
models which depend upon the facility with which com-
puters are able to crunch numbers. In some situations
they are the only means of obtaining a worthy answer.
However, cause and effect are difficult to trace.
On the other hand are models which rely upon sim-
plifying assumptions to yield a closed-form solution.
These solutions represent a limited number of turbulent
conditions. To extend their applicability, ad hoc
assumptions are often introduced to represent
additional conditions.
The model presented here lies somewhere between
these extremes. It expresses the concentration in
terms of the more readily observed physical parameters
and does so in a realistic and continuous manner. The
dispersion sub-model further extends the model to
explicitly incorporate mechanical and thermal
turbulence.
The Field Equations
The field equation for concentration c of a
conservative material at a point in a flow of uniform
velocity u is
, ,
—
at
3x
— (K?3?/3y) + —
3y
.The speed u is parallel to the x axis, z is the vertical
axis, and the transfer coefficients in each direction
are represented by K^, K2, 1(3. In general
K~K(x,y,z,t).
Looking toward the dispersion sub-model, we adopt
a representation which satisfied Taylor's Hypothesis.1
That is, for times, t, which are small compared to the
Lagrangian time scale of the diffusion process, the rms
dispersion z is given by z = at, where a is the disper-
sion speed. We then represent the transfer coefficients
by K.J = a.jai, where ai is the instantaneous scale of
dispersion.
We now assume that a is invariant in space and
time, i.e., a-o^ = a2^t and solve equation (1) for the
boundary conditions c(x ut, y, z, t2/2)
<5(x ut, y, z, t2/2) where 6 is the Dirac delta
function, whence
-3
(2)
ala2a3
exp {(x ut)2/2a!2t2
y2/2a2t2
z2/2a32t2}
This equation represents the concentration due to an
instantaneous release at t = 0, x = 0, y = 0, z = 0
for fixed dispersion speeds. It may be integrated in
closed form for various conditions of interest. Two of
these, the unsteady plume, and the infinite, unsteady
line source have been dealt with by Lissaman.'
The Unsteady Line Source
Consider a temporally varying line source
(Figure 1) of strength Q(t), and_ length L, oriented at
an angle to the x-axis, with tt, as before, parallel
to the x-axis. A receptor located at (x,y) has coor-
dinates (x - ? cos ) relative to an arbi-
trary point (£;,<)>) of the source. At the point (x,y,z)
the concentration for a time period T = T2 Tj, may
be written
S(x,y,z,T)=CL(x,y,z,T)/0(T)
T? L
- ut
(3)
cos<|>,y-Csin, z,t)d?dt
for a constant emission rate, Q(T) over the period T.
After introduction of the explicit form of c(x,y,z,t)
from equation (2), equation (3) may be integrated to
yield
C(d,£,z,T)
,z2u2sin2
2an2av2r
x[erf{2-^[(d/ah2r)u sin- r/T2]}x
>- erf {2'^ a1 [u
erf{2-5s[(d/an2r)usin
(erf{2"J'2ah"1[u cos
-erf{2"!sah"1[u
where an H ai = 32, av = 33 and x,y have been trans-
formed to trie source coordinates:
d x sin ((>
with r2 = 2
and where erf(X)
y cos $ , L x cos § + y sin
= z2/av2 + d2/ah2
X'
,IT / exp(-x2)dx.
Note that erf(-X) = -erf(X). Substitution of L/a? for
L/an, u/aj for u/ah, [(x/aJsin (y/a2) cos <(>)]
for d/ah, and [(x/ai) cos $ + (y/a2) sin <)>)] for l/a.,
removes the restriction that ai = a2.
Characteristics
The solution appears rather complicated. However,
when one notes that certain combinations of variables
appear more than once, it doesn't seem quite so
formidable.
One is tempted to simplify the equation by taking
the limit as TI approaches zero. However, this produces
a discontinuity at t 0, L although it yields
solutions having the proper form when 0 < £ < L or for
£ outside this range. The difficulty arises when one
attempts to evaluate terms such as lim{£/T}
322
-------
Time
as t and T both approach zero
because there is no "right" way to evaluate the limit.
For this reason we recommend retaining Ti finite,
though small .
In order to gain some insight into this solution
it is helpful to examine how it represents various
limiting cases such as: symmetric conditions;
parallel, perpendicular, and zero wind; infinite line
source (L,l+°°); and steady state (To -> °°) conditions.
For ease of examining these cases we'll work with the
form in which T^ -»• 0 and restrict the receptor to the
range 0 < l< L:
c(d,£,z,T)
z2u2sin2
exp -
"Vz
x(2 + erf {2"z[(d/ah2r)u sin - r/T]}
(5)
x |erf i2~\~ 1 [u cos 4. + (L-£)/T] }-erf {2'^tu cos - 1/1} }] )
Wind Vector
A most satisfying feature of this model is that
the expression retains its significance as the wind
vector approaches zero; that is, as u and/or approach
zero. The terms u sin 41 and u cos 4> represent the
perpendicular and parallel components of the wind
respectively. When the wind is perpendicular ( - 90°)
to the line source the third term reduces to:
The concentration is symmetric about L 1/2 as
may be seen by substituting £ = L/2 t A£. It is a
maximum at the midpoint, and decreases toward either
end.
If the source may be considered to have infinite
extent, i.e., £/(/TahT) Z 4, this term reduces to a
value of 2. Thus for an infinite source with perpen-
dicular wind, equation (6) reduces to:
, (7)
exp -
a a
erf{2^2[ah-2du/r r/T]}]
which agrees with the expression derived by Lissaman.1
When the wind is parallel to the source the second
term reduces to 2 - erf{2-JSr/T}. This term represents
the process whereby the emitted "cloud" diffuses to a
receptor located at a distance d from the source with
no advection occurring.
The zero-wind speed solution is seen to be:
erf{2~SYT}]
F} + erf{2-^ /anT}]
with the entire, foregoing discussion about symmetry,
diffusion, and advection being applicable.
Subject to the initial restriction regarding
Lagrangian time scales, and a periodically steady
source, the model provides a realistic representation
of temporal effects. A very important benefit of the
explicit representation of time in this model is the
elimination of the question of what sampling time is
represented by the model.
Equation (5) yields a steady-state solution
/„ ; — \~1 ,
(2ainavr/2?) exp - {
z2u2sin2
(9)
The infinite source, steady-state solution, (c.f.
Equation (6)), on the other hand is:
-1
? (2ahavrT^?) exp
"Ss
erf{2"s(d/an2r)u sin
(10)
Both equation (9) and (10) are independent of
source extent which, in fact, they should be. The
two different forms illustrate the problem of taking
simultaneous limits of time and geometry.
The approach to a steady-state solution in the
special cases of perpendicular, parallel, and zero
wind may be inferred from the previous discussion.
In all cases the concentration increases as the
steady-state is approached.
Dispersion Relations
The dispersion speeds are evaluated from the
Monin-Obukhov3 similarity theory of turbulence in the
lower boundary layer of the earth. This model states
that a steady self-similar two-dimensional boundary
layer can be described by ground roughness, ZQ, tem-
perature, T, and the height invariant heat and momen-
tum fluxes. These fluxes are characterized by u*, the
friction velocity, and H, the convective heat flux.
The Monin-Obukhov scale length is defined by
L = -u*3PCpT/kgH
where p is the density, Cp is the specific heat at
constant pressure, k is von Karmans constant, and g
is the gravitational constant. Both turbulent and
mean speeds are expressible as u/u* = f(z/z0,z/L)
where the form of f is a function of the type of
velocity. Lumley and Panofsky^ express the mean
horizontal speed as:
u u*[ln z/zo ^(z/L)]/k (U)
where t|i, the non-adiabatic part of the profile is
plotted in reference 4.
According to the theory, the vertical fluctuation
velocity, av, is given by an equation of the form
av u*F(Z/l). Panofsky and McCormick5 postulated
that av should be a function of height, z, the rate
of energy supply by mechanical turbulence,
EI = u*23u/8z
and the rate of supply of convective energy
e2 = gH/pCpT.
323
-------
They derive an expression for av which may be written
as
1/3
av 1.05(u*3S/k + 2.4 zgH/pCpT)1'
where S,the wind shear.is given by S (kz/u*)3u/3z.
The effect of the convective heat flux, H, on the
dispersion speed is much smaller than the effect of
the wind speed and, consequently it doesn't require
as great preceision in its determination. Measured
values of H may be used, or, near the ground, it may
be estimated from temperature and insolation data.
The wind shear, S, may be derived from measure-
ments of the variation of wind speed along the vertical
axis. In the more common case where S is not known,
additional relationships are needed among S, L, and ij;
in order to fit the observed wind speed by means of
equation (11) and subsequently to solve for av from
equation (12).
equation
4
and, by taking
We make use of Ellison's6 interpolation
S" 18(z/L)S3 = 1
z/L
(13)
(14)
By solving for £ and d£ from equation (13) and using
partial fractions the integral may be evaluated in
closed form. Equation (13) is solved for S by use of
a Maclaurin series expansion for values of S near the
origin, and by two iteration forms for z/L positive or
negative. They converge in five or six cycles.
Ellison's interpolation equation represents well
the wind shear for unstable, neutral, and slightly
stable conditions. However, neither it nor any other
equation known to the authors does a good job of
representing more stable conditions. Therefore this
model should be used in stable cases with caution.
Temporal Effects
Since the model contains an explicit representa-
tion of time one would hope to be able to describe the
effect of step changes in emission rate, wind vector,
and dispersion speed. Important temporal changes
immediately come to mind such as varying vehicle speeds
and/or varying vehicle-to-capacity ratios. Another
important practical condition occurs when pollution
is caused to shift back and forth across a receptor
under light and variable wind conditions.
The principal problem of describing these effects
is that of either (a) representing the change in the
concentration after the step change of a variable or
(b) matching concentrations at the time of a step
change of a variable.
We wish to consider the representation of concen-
tration produced by step changes in the emission rate,
Q, the wind, u, and the dispersion speed, a. Thus
C(u,a,T)
f.'.
will be the general expression for the concentration at
time T.
Change of Emission Rate
Imagine that a source operating under conditions
ui,ai, undergoes a step change in emission rate from
Ql for times T < TI to Q2 for times T > Tl. The con-
centration at time T > Ti may be calculated by adding
a differential source, of emission rate (Q2 QI).
which commences at time T}, to the continuing, old
source:
C(u,a,T)
(Q2 Q1)c(u1,a1,T
For T sufficiently large, c(u,a,T TI) becomes equal
to s(u,a,T) so that if Q2 = 0, the concentration even-
tually decays to zero.
Wind Change
The wind, u, or its components u sin $ along d,
and u cos cf> along L, in equation (4) acts merely to
transport (advect) the pollutant from the source to the
receptor located at {d,£,z}. Imagine that a source
operating at a rate QI with dispersion speed a^, is
subject to a step change of wind from uj at times
T < TI to U2 at times T > TJ. Since the wind acts only
to transport the pollutant all we need do is describe
how the wind changes from u^ to u2 at times T » TI.
This is given by:
= U(T
(u2 UI)TI/T.
Thus, if the wind undergoes a step change from ui at
times T < TI to u2 at times T>Tj, the concentration
at any time T > TJ becomes:
C(u,a,T)
This is equivalent to what Lissaman^ calls the
standard solution for a moving receptor . . . .
If the emission rate also changes from Qj at times
T <
ential
commences at time Tj but which now is subject to a
wind u2. In this case the concentration at time
T > T]^ is given by
Ti to Q2 at times T > TJ one again adds a differ-
ial source, of emission rate (Q2 Qi), which
C(u,a,T) Q1C(u,a1,T)+(Q2 Q1)c(u2,a1J
Change of Dispersion Speed
The foregoing are exact solutions for the concen-
tration existing at times T > T^ when, at T TI, the
emission rate changes from Qi to Q2 and/or the wind
changes from uj to u2. It is not clear that changes
in the dispersion speed, a, may be treated exactly.
Physically the dispersion speed serves to specify,
as a function of time, the distance of a "labeled"
parcel of the dispersing "cloud" from an observer
moving with the "cloud". Thus, a reasonable approxi-
mation would appear to be to treat step changes in
the dispersion speed, a, in the same manner as step
changes in wind speed are treated. Thus if a source,
operating at a rate Q} under a wind u^, is subject to
a step change from a-, for times T < T^ to a2 at times
T >
define:
a = a(T
a2 + (a2
324.
-------
then the concentration at any time T > Tj becomes:
C(u,a,T) = Q1C(u1,a,T)
Within the constructs outlined here the effect of
combinations of step changes in emission rate, disper-
sion speed, or wind may be calculated.
Validation
We have not had the opportunity to validate the
model. However, Panofsky and McCormick5 present
validation data for the dispersion speed sub-model.
Lissaman^ found that concentrations of carbon monoxide
predicted by the infinite line source model correlated
well with measured concentrations without any adjustment
of the predicted values.
Conclusions
A reasonably simple, closed-form model of the
finite line source has been found. The model produces
finite solutions in a continuous manner for the limit-
ing conditions of steady-state, infinite source, and
zero-wind. It predicts reasonable concentrations at
any point relative to the source. The entire model,
including the dispersion relation, incorporates the
important parameters of wind, surface roughness, and
heat flux in a rational manner. It can be extended to
model unsteady conditions. The simple analytical form
of the model makes it suitable for construction of
network roadway models.
Figure I
Source-Wlnd-Receptor Geometry
References
1. Taylor, G. I., "Diffusion by Continuous Movements",
Proc. London Mathematical Soc., 20, pp 196-212
(1921).
2. Lissaman, P.B.S. "A Simple Unsteady Concentration
Model Explicitly Incorporating Ground Roughness
and Heat Flux", Paper #73-129, 66th Annual Meeting
of the Air Pollution Control Association (1973).
3. Monin, A. S. and A. M. Obukhov, "Basic Laws of
Turbulent Mixing in the Ground Layer of the
Atmosphere" translated from Akademiia Nauk SSSR,
Leningrad, Geofizicheskii Institut, Trudy, 151,
#24. PP 163-187 (1974).
4. Lumley, J. L. and H. A. Panofsky, "The Structure
of Atmospheric Turbulence", Interscience Publishers,
John Wiley and Sons, New York (1964).
5. Panofsky, H. A. and R. A. McCormick, "The Spectrum
of Vertical Velocity Near the Surface", Quart. J.
Roy. Meteorol. Soc., 86, p 495 (1960).
6. Ellison, T. H., "Turbulent Transport of Heat and
Momentum From an Infinite Rough Plane", J. Fluid
Mech., 2, p 456 (1957).
325
-------
WATER QUALITY MODELING IN TEXAS
Joseph J. Beal, P.E.; Andrew P. Covar; and Dale W. White, P.E.
Engineering Analysis and Modeling Section
Texas Water Quality Board
Austin, Texas
Abstract
The State of Texas, acting through the Texas Water
Quality Board, has been intensely interested in water
quality modeling for the last three years. In the
past, this effort has dealt mainly with the waste load
evaluation program, made necessary for the allocation
of point source waste discharges by Public Law 92-500.
A considerable amount of water quality modeling will
be required for the evaluation of treatment alterna-
tives which will be developed under Section 208 of the
same law. This modeling effort will consider the ef-
fects of point and nonpoint waste sources on receiving
water quality, both under steady-state and time
variable conditions.
Introduction
As far back as 1968, mathematical modeling studies in
the State of Texas were being conducted to determine
how much to restrict the discharge of pollutants. Dis-
solved oxygen is the parameter most often evaluated by
our modeling studies. Other parameters ranging in
difficulty from conservative substances to eutrophica-
tion processes have been studied. The objective of
this paper is to show how applied models are used in
planning problems and water quality management deci-
sions in the State of Texas. The various types of
models currently in use are discussed along with the
State's future need for models.
The Role of Modeling in Water Quality
Management Prior to Public Law 92-500
Prior to Public Law 92-500, the Texas Water Quality
Act was the basic legal authority for the Texas Water
Quality Board's surface water protection program. The
Act directed the agency as follows: It is the policy
of this state and the purpose of this Act to maintain
the quality of the water in the state consistent with
the public health and enjoyment, the propogation and
protection of terrestrial and aquatic life, the opera-
tion of existing industries, and the economic develop-
ment of the state; . . . and to require the use of all
reasonable methods to implement this policy." The
agency under the "all reasonable methods" clause uses
a permit system as its basic regulatory device to con-
trol the point discharge of pollutants. Obviously, if
you restrict the discharge of pollutants, the Act will
require the expenditure of public and private funds for
wastewater treatment systems. Therefore, you must know
the degree of pollutant discharge restriction in order
to avoid wasting resources and whether or not the per-
mits are accomplishing their objective. This was
accomplished with descriptive studies of water quality
and later with mathematical modeling.
The first modeling endeavors by the Texas Water Quality
Board were conceptual models prepared by consultants.
During these early endeavors, the reports or users
manuals were complicated with technical language. The
model limitations were often not explained. This re-
quired the users to contact the consultants for assis-
tance. Due to these early problems, many people at the
state level failed to accept mathematical models of
water quality as useful decision making tools.
Planning Aspects of Public Law 92-500
The Federal Water Pollution Control Act Amendments of
1972 (FWPCAA) established numerous requirements the
States would need to satisfy in order to be eligible
for construction grant and program grant funds from
the Environmental Protection Agency.
The period of 1973-1977 is generally referred to as
Phase I of the Act's implementation. In Phase I, the
emphasis has been on issuing discharge permits and
making construction grants in order to control point
sources of pollution which are easily identifiable
and correctable. For many areas of the nation, the
achievement of this requirement will be all that is
necessary for attainment of the 1983 goal.
In Phase II (1978-1983), the emphasis will be on solv-
ing the more severe and complex problems produced by
point and nonpoint sources of pollution. The identi-
fication of the programs necessary in achieving the
1983 goal in complex problem areas is to be accom-
plished through the preparation of plans required by
Section 208 of the Act.
Section 303 of the Act sets forth requirements for
each State to establish water quality standards and
implementation plans. Under this section each State
is required to have a continuing planning process
which will result in plans for all navigable waters
within the State. These plans are required to contain
certain items including the following: 1) total maxi-
mum daily load of pollutants for waters which cannot
achieve water quality standards using the minimum
wastewater treatment levels set forth in the Act,
2) adequate implementation for revised or new water
quality standards, and 3) controls over the disposi-
tion of all residual waste from any water treatment
processing.
Pursuant to Section 303, the EPA issued regulations on
State Continuing Planning Process (40 CFR Part 130)
and Preparation of Water Quality Management Basin
Plans (40 CFR Part 131). These regulations require
that revisions to basin plans after July 1, 1975,
shall "reconsider current actions with respect to the
most recent data or analysis and shall concentrate, if
appropriate, on the identification and evaluation of
methods and procedures (including land use require-
ments) to control, to the extent feasible, non-point
sources of pollution". The current 40 CFR 130 and 131
guidelines also include the planning requirements of
Section 208 of the Act.
For each stream segment with water quality problems
caused by nonpoint source discharges, the following
minimal information is required: 1) type of problem;
2) identification of waters affected; 3) identifica-
tion of nonpoint discharges contributing to problem;
and 4) alternative procedures and methods (including
land use requirements) to feasibly control significant
nonpoint source discharges (this evaluation should
consider the technical, legal, institutional, economic,
and environmental feasibility). The 40 CFR Part 131
regulations further specify that controls over resid-
ual wastes be included in basin plans. Residual
326
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wastes to be considered include all residual waste from
any municipal, industrial or other water or wastewater
treatment processing. The regulations also, address
land and subsurface disposal practices. Basin plans
are required to establish a process to control the
disposal of pollutants on land or in subsurface excava-
tions wherever such disposal causes or may cause viola-
tion of water quality standards or materially affect
groundwater quality.
There are two types of areawide planning in which the
TWQB is involved - Designated Areawide Planning and
Planning in Non-Designated Areas.
Designated Areawide Planning is the planning
required in areas designated by the Governor
as having substantial water quality problems
as a result of urban-industrial concentrations
or other factors. Eight areas have been des-
ignated as 208 areas.
Planning in Non-Designated Areas is the planning
required in all other areas of the State that
are not considered to have substantial water
quality problems. These are considered to be
State planning areas in which the Texas Water
Quality Board is the Planning Agency.
The level of detail of planning for each State planning
area will be contingent upon the type and complexity of
problems in the planning area, and consequently, the
planning tools that are required differ from one area
to another.
The purpose of 208 type planning is to: 1) develop
methods of achieving or maintaining adequate water
quality in the Nation's streams, and 2) insure that
construction grant funds spent on construction of
domestic sewage treatment plants are spent in a cost
effective manner.
In other words, through this planning process should be
determined such things as whether or not any particular
stream has the ability to meet 1983 stream standards
through the application of effluent limitations on
dischargers or whether that particular stream is beyond
the point of ever meeting existing stream standards
for current designated uses. In fact, the most current
EPA regulations (40 CFR 130) indicate that a State may
establish less restrictive uses than those contained in
existing water quality standards by demonstrating one
of the following: 1} existing designated use is not
attainable because of irretrievable man-induced condi-
tions, 2) existing designated use is not attainable
because of natural background, or 3) the application
of effluent limitations for existing sources more
stringent than those required pursuant to the EPA
Effluent Limitation Guideline program in order to
attain the existing designated use would result in
substantial and widespread adverse economic impact
(of course, in order to make these kinds of determina-
tions, both point source and nonpoint source modeling
efforts will be required in these determinations).
The nonpoint source pollution program is an integral
part of the basin planning and areawide planning pro-
grams. The FWPCAA requires a nonpoint source program
element in all areawide plans conducted in areas desig-
nated pursuant to Section 208(a)(2). In developing the
nonpoint source planning element in the Basin Plan, the
nonpoint program in the designated 208 areas can be
more closely coordinated with the other nondesignated
areas. Basin planning regulations require a nonpoint
source program element for each water quality segment
in which nonpoint source discharges contribute to the
water quality problem.
The nonpoint source discharge program will also provide
valuable input to, or require input from, other State
programs:
1. Water quality standards must reflect achievable
goals. At such time as these standards are revised
consideration will be given to the impact of non-
point source discharges on water quality and the
feasibility of controlling such discharges.
2. Waste load evaluations should reflect the contri-
bution of nonpoint source discharges to the total
load. Detailed information on the origin, magni-
tude, and frequency of nonpoint source discharges
will improve the accuracy and reliability of water
quality models.
3. The feasibility of controlling nonpoint source dis-
charges will influence treatment level requirements
for point source discharges.
4. In some cases, waste control orders (discharge
permits) will be required for nonpoint source
discharges.
5. Monitoring programs should be adequate to assess
the magnitude and frequency of significant nonpoint
source discharges. Either routine monitoring or
special surveys may be required to fulfill this
requirement.
As indicated earlier, both traditional steady-state
point source modeling as well as non-steady state run-
off type modeling is required to achieve the integra-
tion of a viable point and nonpoint source control
program.
The Role of Modeling in Water Quality
Management After Public Law 92-500
Each year the Texas Water Quality Board is called upon
to develop a statewide water quality management program
which can successfully provide guidance in the imple-
mentation of the Texas Water Quality Act and the
FWPCAA. The aim of this program is to: first, bring
about an improvement in water quality in areas where
violations of the Texas Water Quality Standards are
known to exist and secondly, to preserve the existing
quality of the navigable waters of the state where
conditions are already acceptable, and further, to
implement the necessary requirements for areawide and
basin plans in order to insure good water quality in
the future.
One of the main efforts toward meeting these objectives
lies in preparation of waste load evaluations as re-
quired by the FWPCAA Section 303(d)(l)(C). These waste
load evaluations as previously mentioned become a part
of the Basin plans, as basin planning strategy. They
are taken into account during consideration of permit
applications as well as determination of new stream
standards.
Routinely waste load evaluations will be updated or
revised as necessary to accomplish national water
quality objectives in conformity with the requirements
of the Act and the Continuing Planning Process. For
critical segments within each 208 Designated Area,
these updates are currently underway.
Texas has twenty-three designated river basins which
have been further divided into 297 discrete hydrologic
segments. Of these, 230 or 78 percent are considered
as "effluent limited" where the minimum treatment re-
quired by law will accomplish our stream standards.
The remaining 67 segments or 22 percent are considered
327
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"water quality limited" where a higher level of treat-
ment is required to meet the desired stream standard.
Since the start of implementation of the FWPCAA, 89
waste load evaluation reports have been prepared. Of
these, 59 segments were water quality limited while 30
were effluent limited.
A determination of the assimilative capacity of a
stream segment requires the quantitative assessment of
the effects on the environment of various alternative
measures. This is the forte' of mathematical modeling.
As such, modeling plays a significant role in the deci-
sion making process of several facets of Texas Water
Quality Board activities, especially the formulation
of waste load evaluations and the issuing of waste
discharge permits.
The assimilative capacity of a stream is determined
in some cases by complex mathematical models utilizing
digital computers; while in other situations, simple
engineering calculations are used. This leads us to
a categorization, or hierarchy of available steady-
state models to be used in the management process.
The first type of model, the type that has the greatest
weight in the decision making process, is the model
that is completely calibrated and verified for a par-
ticular stream segment. This type of model would have
been verified during several different flow conditions
with predictions closely approximating known conditions.
The second level of model is somewhat similiar to the
first, but lacks verification while being adequately
calibrated. This type of model may have been partially
verified for only one flow condition.
The third level in the hierarchy of models is that
model which has neither been calibrated nor verified,
but has been developed with "text-book" or assumed
values. This type of model would not have had its
predictions matched with actual conditions, nor would
it have utilized actual load input conditions but only
estimations of what the loads might have been at a
given time.
The fourth and lowest level of modeling, although fre-
quently used for the first rough cut at solving dis-
solved oxygen problems, is the model that does not
actually mathematically account for the transport of
waste materials, but computes the assimilative capacity
of a body of water assuming the body of water is a com-
pletely mixed reactor. This type of model is useful
for identifying a target load for a stream segment and
gives the user an idea of the magnitude of the problem
which must be solved.
An example of the first level of modeling would be the
Houston Ship Channel model prepared during the Galves-
ton Bay Project. This model was verified numerous
times for steady-state conditions. Very few other
bodies of water have been modeled to this extent. The
second level of modeling is typified by the well-known
QUAL-I or QUAL-II type models when flow and loading
data is somewhat limited. The third level might be
OUAL-I with assumed values for much of the input data.
The fourth level is based on the amount of oxygen that
can enter through the water surface.
Each level of modeling is useful, for different pur-
poses, and has a place in sound water quality manage-
ment. For instance, relatively great reliance can be
put on the predictive capacity of a level 1 model for
analyzing alternative water quality management actions.
Treatment levels can be closely evaluated for waste
load allocations with only limited additional input
required for management decisions, these additional
inputs being principally cost of treatment and benefits
of maintenance of water quality. For a level 2 model-
ing situation, less reliance can be placed on model
output, and consequently, other factors may take on
more weight when considering possible alternatives.
These factors include overall water quality considera-
tions as well as cost of control measures. When a 3 or
4 type modeling effort is employed, the management de-
cision is usually of the nature of requiring step wise
reductions in waste loading, followed by an evaluation
of stream quality response, and then a further control
action should the initial step prove unsuccessful.
It should be noted here that the Quality Board does not
rely solely on model predictions during the planning
process. This would be not only unsound, but also un-
warranted. Indeed, all information available should be
considered. Consequently, public hearings are conduct-
ed by the Texas Water Quality Board after dissemination
of engineering reports concerning the modeling and
water quality management decisions under consideration
for implemention. These hearings work in two ways.
That is to say, the Texas Water Quality Board gains
additional pertinent information, and at the same time,
provides the interested public with a better knowledge
of what has gone on during the decision making process.
Problems more complex than determining the total as-
similative capacity of a stream segment are: 1) How
should the total assimilative capacity be divided
among the various waste discharges, and 2) How much
allowance for expansion should be provided? '
In dividing the assimilative capacity among dischargers
we have strived for an equal effort among all dis-
chargers. Some dischargers, however, feel that we have
picked on them or that the assimilative capacity has
been divided inequitably. In some areas where the
majority of pollutant loadings comes from municipal
discharges, we have taken a position that the larger
plants which account for the majority of the total load
should be required to improve their wastewater treat-
ment. An example of this is the Dallas-Fort Worth Area
where 4 large wastewater treatment plants account for
approximately 90 percent of the total organic load
while the remaining 5 small plants account for approx-
imately 10 percent of the loading. The four large
plants are required to discharge an effluent with a
BOD5 of not more than 10 mg/1 on a monthly average
basis while the five small plants may discharge an
effluent BOD5 of 20 mg/1 on a monthly average basis.
In areas dominated by industrial discharges, we gen-
erally use as a starting point the U.S. Environmental
Protection Agency's industrial effluent guidelines.
Federal law has required the EPA to define for most
industrial categories what are known as: 1) Best
Practical Treatment, and 2) Best Available Treatment.
These guidelines were developed to impose an equal
effort in waste treatment on each type of industry.
In the most complex waste load allocation performed
by this Agency, the Houston Ship Channel, where 165
wastewater treatment plants and 206 industrial dis-
charges were involved, the assimilative capacity was
divided up among the various industries by requiring
each to provide treatment such that all discharges are
an equal percentage of the differential between best
practical and best available treatment. This is illus-
trated mathematically by the following equation:
Allowable Discharge BPT - * (BPT - BAT)
where:
BPT best practical treatment
328
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BAT best available treatment
X percent reduction required
Over a period of time, the waste loading to any given
stream is constantly changing. Therefore, as a waste
load allocation is developed, a buffer for growth of
existing waste dischargers and the addition of new dis-
chargers to a stream segment is included. This buffer
is to insure that as additional loads are imposed upon
the stream, the stream is not immediately out of com-
pliance. However, as this buffer is consumed and as
the quantity of waste loads approaches the calculated
assimilative capacity of the stream, the staff of TWQB
must be aware so that further action (either continued
monitoring if the water quality is acceptable and not
deteriorating or additional waste load allocations)
can be taken. Consequently, the TWQB has developed
an automatic data processing system to account for the
current waste load conditions on a stream segment and
to compare existing conditions of loading to the waste
load allocation. By using this system, it is possible
to quickly determine potential problem areas and to
establish priorities for analysis of stream segments
utilizing limited engineering resources.
The modeling work previously discussed covers Phase I
of the FWPCAA. The Texas Water Quality Board is pre-
sently in the development of methodology stage of
modeling for the 208 areawide planning program. The
types of models that will be used are discussed briefly
under modeling inventory.
Modeling Inventory
Over the last four years, the Texas Water Quality Board
has acquired a number of computer models for use in the
various water quality management tasks given to us. The
models vary in complexity from simple one-dimensional
steady-state river models to two-dimensional and time
variable estuarine models.
Our general purpose models include: 1) the QUAL models
- developed by the Texas Water Development Board and
modified by Water Resources Engineers, Inc., 2) the
AUTO-QUAL models developed by the Environmental
Protection Agency, and 3) the ESTPOL models developed
by Texas A&M University. The primary use of these mod-
els is in the waste load evaluation work performed by
the Texas Water Quality Board. These are basically
steady-state applications.
In time variable applications, the TWQB is now applying
or evaluating 1) the AUTO-QUAL model; 2) the STORM mod-
el - developed by Water Resources Engineers, Inc.; 3)
the STORM WATER MANAGEMENT model - developed by Metcalf
& Eddy, Inc., the University of Florida, and Water
Resources Engineers, Inc.; and 4) RECEIV II - developed
by Ratheon for the EPA. One or more of these models
will be used in the upcoming 208 program dealing with
nonpoint waste loadings.
The TWQB has acquired two general purpose lake models.
These are 1) EPARES, and 2) RIVER-RESERVOIR, both
developed by Water Resources Engineers, Inc. We have
not yet had the opportunity to use either of these
models, but we have tried to become familiar with their
basic features.
At times the TWQB has turned to basin specific models
to solve particular water quality management problems.
The largest example of this type of work has been the
Galveston Bay Project. In this project, a two-dimen-
sional model of Galveston Bay was developed along with
a one-dimensional steady-state model of the Houston
Ship Channel. The development of these models was
accomplished by Tracer and Hydroscience, Inc. The ship
channel model was used in the waste load evaluation of
that segment. Hydroscience, Inc. has also developed a
basin specific model for the Trinity River and they are
presently under contract to develop an eutrophication
model of Lake Livingston, a 82,600 acre lake northeast
of Houston. The TWQB continues to look for new models
and for new applications of existing models.
329
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A DYNAMIC WATER QUALITY SIMULATION MODEL FOR THE THAMES RIVER
D. G. Weatherbe
Water Resources Branch
Ontario Ministry of the Environment
Toronto, Ontario
The Thames River basin is experiencing
problems of water quality and flooding, heightened
by intensive agricultural use and an expanding
urban population. A study was initiated to
provide solutions to these problems as well as
problems of erosion, unsatisfied recreational
demand, and conflicts in reservoir use. In order
to provide a suitable tool for the analysis and
projection of the water quality problem, a dynamic
water quality simulation model was developed and
applied to the major growth center, the City of
London. This paper describes the major objectives
of the water quality modelling, the model structure
and processes, as well as model input and output
summaries. The application of the model to
evaluate various water quality management options
is described.
Need for a Study
The river experiences water quality impairment
problems caused by excessive inputs of nutrients,
oxygen demanding materials, bacteria and suspended
solids from urban and rural sources. The largest
city in the basin, the City of London, is expected
to grow from a population of 220,000 in 1971, to
500,000 in 2001, with a proportional increase in
sewage discharges to the river. Options for
controlling present and future problems for the
City of London consisted of increased levels of
sewage treatment, sewage diversion directly to
Lake Erie by pipeline, low flow augmentation from
proposed reservoirs and urban growth restrictions.
This part of the study was initiated primarily to
evaluate these water quality options.
FIGURE 1
THAMES RIVER DRAINAGE BASIN
Province of Ontario
Scale of Miles
LAKE
ERIE
Thames River Study
Basin Description
The Thames River in southwestern Ontario (Fig.
1), drains 2,250 square miles of mainly agricultural
land with a total 1971 population of 415,000,
334,000 in urban areas and 81,000 in rural.
Major surface water uses include those for
sewage disposal, recreation and fish and wildlife
habitats. Municipal water supplies are either of
ground water origin or are imported from the
Great Lakes by pipeline. Three multiple use
reservoirs in the basin, with a maximum combined
storage volume of 72,500 acre-feet, are used for
flood control, low flow augmentation and recreation.
Study Objectives
General - The overall objective of the study was
"to develop guidelines for the management of the
basin's water resources to ensure that adequate
quantities of water of satisfactory quality are
available for the recognized uses at the lowest
possible cost, and that erosion and flood protection
are provided consistent with appropriate benefit-
cost criteria"!.
Water Quality Objective The general water
quality objective defined during the study was to
maintain existing water quality where it is
satisfactory for fish and aquatic life and
recreation, and to improve quality to that level
in those areas where it is presently degraded.
Appropriate dissolved oxygen criteria to
achieve this objective were identified for major
sections of the river, based on published Ontario
330
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guidelines^
These criteria were redefined in
statistical terms to allow comparison with model
output summaries. For example. Criteria C, which
represents an acceptable quality of water with
some stress, to be applied for warm water fish
species in non-spawning periods, is stated as
follows: "the dissolved oxygen concentration
should be above 5 mg/1 95 percent of the time in
a given month. Concentrations may range between
5 mg/1 and 4 mg/1 for periods up to four hours in
length within any 24 hour period, provided that
water quality is favourable in all other respects".
Dynamic Water Quality Simulation Model
Model Description
The dissolved oxygen model used in the
Thames River Study takes account of the effects
of carbonaceous and nitrogenous oxygen demand,
atmospheric aeration, aeration at weirs, respir-
ation in bottom sludges, photosynthetic oxygen
production, and respiration of aquatic plants and
algae. Model parameters are adjusted to account
for the effect of changes in temperature and
channel flow.
The model expressed as a differential equation,
in terms of the oxygen deficit D, is given below
as a function of time, t, and distance, x. The
oxygen deficit D is the difference between the
oxygen saturation concentration and the actual
concentration.
jD + V3D
8t 8x
-KaD+KdL(x)+KnN(x)+S P(t)+R
where:
D
V
t
x
Ka
=oxygen deficit, mg/1
=velocity of stream, ft/sec
=time, days
=distance, ft
,,-1
=aeration coefficient, day •*• (O'Connor and
Dobbins, 1958)3
Kd =deoxygenation coefficient, day~^
L(x) =carbonaceous oxygen demand as a function of
x, given by L(x)=Lo e~Kni'x/v'l
=initial concentration of carbonaceous
oxygen demand, mg/1
=oxygen demand removal coefficient, day~l
=nitrogenous oxygen demand as a function of
x., given by N(x)=No e"*-" (X/V)
=Initial nitrogenous oxygen demand, mg/1
=nitrogenous oxidation coefficient, day"!
=benthic bacterial respiration, mg/l/day
P(t) =photosynthetic oxygen source as a function
of time, of the form P(t)=Pm Sin | (TT/p)
(t-ts) | for daylight hours. A step function
approximation F (t), of the function P(t) is
used which assumes a constant rate of
photosynthesis over a time step, h (two
hours)
=maximum rate of photosynthetic production,
mg/l/day
=period of sunlight, days (fraction)
=time of sunrise, days (fraction)
=algal respiration, mg/l/day
Lo
Kr
N(x)
No
Kn
S
Pm
P
ts
R
This formulation and solution are as expressed
by O'Connor and DiToro (1970)4 except for the
step function, F(t).
Gl
W2,
H10 N
W3
L2_V
H13
H14
W5
Slj North Thames River
City o
London
-S31
Thames
H3
LEGEND
1-17 = Junction Points
S1-S5 = Sewage Treatment
Plants
G1-G3 = Generated Flows
H1-H15 = Local Inflows
W1-W5 = Withdrawal Flows
= City of London
16
Figure 2: Thames River water quality simulation
model geometry of river system.
River System Geometry
The dissolved oxygen levels throughout a
river are described by treating the river as a
collection of reaches with constant conditions in
each reach, calculating the effect of all input
and withdrawals at the head of the reach and
using the model formulation to calculate the
concentrations of dissolved oxygen and waste
constituents at the end of the reach. Weir
aeration is assumed to take place at the head of
the reach . Figure 2 shows the geometry of the
river system modelled, indicating the reach
junctions, sewage treatment plant inputs, local
inflows (tributaries), withdrawal flows and
upstream flows.
Input Variations
The dynamic water quality simulation model
was developed to take account of the variations
of natural and man-made conditions that affect
water quality, to provide increased information
about the possible effects of water management
planning alternatives in the river basin. The
inputs to the system vary with time to reproduce
the variations in conditions that occur in the
real system. Causes of variation in water
quality accounted for in the dynamic simulation
model, include:
331
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i Streamflow from the upstream main channel
and from tributaries. Daily streamflows
were generated for the upstream gauge
locations, based on the historical record.
The method generates extensive traces of
Streamflow data from available historical
records using stochastic techniques and thus
allows the water quality simulation model to
be run for as long a period as required
(Singer, 1974)6. Channel flow velocities,
aeration rates, respiration rates and
photosynthetic rates are affected by changes
in Streamflow.
ii Water quality from upstream and from tributaries.
Probability distributions based on observed
water quality are used in the model to
reproduce daily variations in dissolved
oxygen (DO), carbonaceous (CARBOD) and
nitrogenous oxygen demand (NOD). Diurnal
variations of dissolved oxygen are also
included.
iii Waste treatment plant loads. Observed daily
mean effluent flows are reproduced by
mathematically describing seasonal and
within-week trends and adding a random
component. Within-day variations in treatment
plant flows are also included. Daily mean
water quality parameter concentrations (DO,
NOD, CARBOD) are randomly chosen from
probability distributions based on observed
data. Table 1 describes the probability
distributions for the water quality of the
main channel flows and sewage treatment
plants.
iv Sunlight energy. A probability distribution
of sunlight energy for each month is used to
calculate variations in the average photosynthetic
rates of plants and algae for each reach,
and each day.
Model Application
Model Runs
Computer simulation runs were undertaken to
evaluate various cases defined by input conditions.
Each run consisted of the simulation of dissolved
oxygen, carbonaceous and nitrogenous oxygen
demand at each reach node, every two hours, for
thirty years, for each month simulated. Typically,
the critical months of May, June, July and August
were simulated.
Input conditions for Streamflow, sewage
treatment quality, sewage flow, and sewage
outfall location were altered to define various
management possibilities as outlined below:
Streamflow - Cases modelled consisted of unregulated
flows generated from historic records, regulated
flows from the operation of three existing reservoirs
and regulated flows from the addition of two
proposed reservoirs.
Sewage Treatment Quality Cases modelled consisted
of existing quality as described in Table 1,
based on 1972 data, improved quality consisting
of nitrified secondary effluent approximated by
the quality of Greenway STP, shown in Table 1 and
zero pollutants defined by negligible concentration
of pollutants and high effluent dissolved oxygen.
Sewage Flow - Cases modelled were existing (1972)
flow rate with a. total of 27.6 MIGD (51.2 cfs) on
the average and 1991 project sewage flow rate of
49.5 MIGD (92 cfs).
Sewage Outfall Location - Cases modelled were
existing (1972) with 1991 flows distributed to
existing STP's on a proportional basis, a new
plant downstream accepting all flow increases and
complete sewage diversion to Lake Erie.
Temperature. Mean daily water temperatures
are calculated in the model according to
observed trends. Oxygen saturation concentrations,
aeration rates and respiration rates depend
on temperature.
TABLE 1: Thames River Simulation, Water Quality Inputs, Description of Probability
Distributions and Mean Sewage Flows
Model Output For each month and each reach, the
model printout tables consisting of the number of
violations of dissolved oxygen criteria, the
distribution of and average duration of violations,
Carbonaceous O.D.
Input Location
Adelaide STP
Pottersburg STP
Vauxhall STP
Greenway STP
Oxford STP
North Thames R.
Thames R. (S. Branch)
10%c
(mg/1)
13.4
12.0
15.8
8.0
10.0
1.2
1.0
Median
(mg/1)
30.0
35.0
40.0
20.0
20.0
1.8
1.6
90%
(mg/1)
68.0
109.0
98.0
54.0
44.0
5.2
3.3
Nitrogenous
10%
(mg/1)
59.4
11.2
20.3
4.7
60.7
2.4
2.6
Median
(mg/1)
98.0
45.0
64.0
7.0
123.0
3.2
3.2
O.D. Daily Mean Flow
90%
(mg/1)
125.0
114.0
98.0
23.0
180.0
6.6
4.9
1972
(cfs)
5.1
6.6
6.3
32.0
1.4
Notes:
a Carbonaceous oxygen demand, (CARBOD) estimated by multiplying BODc data by the
CARBOD/BODs ratio determined through laboratory analysis. Ratio of 2 for the
STP'i= and 1 for the stream inputs were used.
b Nitrogenous oxygen demand, (NOD) determined by multiplying Kjeldahl nitrogen
data by 4.57, the ratio of NOD to unoxidized nitrogen, determined by
stoichiometric balance.
c 10 percent of observations did not exceed value.
d Based on the period from May to October 1972
332
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._ 2
78 9 10 11 12
MAIN THAMES
13 14 15 16
THAMES south .branch
Reach number (end of reach)
r—
I
%
\
I I
D
1
^
i
I
77.
^
i
i
i
i
t
%
\
cz
»
•
S
•I
1
Sewaj
|
m
5e
-
I
%
i
%
i
LEGEND
DO less than 5 mg/1
DO less than 4 mg/1
DO less than 3 mg/1
DO less than 2 mg/1
DO less than 1 mg/1
Treatment Plant
(-,
5% criteria
condition
i n
& Z U
Figure 3: Thames River water quality simulation model
dissolved oxygen output summary for the month of July
based on inputs for existing conditions (1972).
12 34 56 78 9 10 11 12 13 14 15 16
NORTH I THAMES I MAIN THAMES
THAMES south branch
Reach number (end of reach)
Figure 4: Thames River water quality simulation model
dissolved oxygen output summary for the month of
i^uly, based on input conditions of improved quality
effluent, existing sewage flow, existing dam operation,
existing outfall location.
and the total time in violation. Optional output
consists of cross tabulations of output parameters
(dissolved oxygen, carbonaceous and nitrogenous
oxygen demand) with streamflow for each reach,
and a plot of output parameters.
Existing Conditions - The output table showing
the percent time in violation is shown graphi-
cally in Figure 3 for the existing conditions,
defined by the model input combination of regu-
lated flow, existing sewage quality, existing
sewage flow and existing outfall locations. The
criteria condition that allows occurrences of
dissolved oxygen less than 5 mg/1 for 5 percent
of the time is also shown. From this, it can be
seen that significant criteria violations occur
in eight of the sixteen reaches.
Model Verification - The model is constructed
with calibrated parameters based on actual
surveys and actual data are used in the input
variations. Consequently, results are thought to
represent the real conditions. Intensive survey
data, and long term monitoring data confirm that
a dissolved oxygen problem exists; however,
continuous data comparable to model output are
presently not available for verification. The
model provides the "best" estimate of water
quality, but the absolute values predicted cannot
be verified. Consequently, the model is most
useful for comparing the relative effectiveness
of optional control measures.
Conclusions Derived from Model Applications
Existing Conditions - Dissolved oxygen conditions
presently represent an unacceptable quality.
Urban expansion without improvement should not be
allowed.
Nitrification - Improvement of sewage quality by
nitrification of effluents significantly improves
water quality in the river. Figure 4 shows the
predicted water quality resulting from nitri-
fication of effluents. The model predicts an
insignificant negative effect from increased
sewage flows when only nitrified effluents are
discharged.
Zero Pollutants - Treatment to a zero pollutant
level further improves water quality, however,
violations are still predicted by the model.
This is due to the combined effects of upstream
quality and algal and sludge respiration.
333
-------
Flow Augmentation The addition of upstream
reservoirs operated to provide flow augmentation
would significantly improve water quality.
Outfalls The location of sewage outfalls within
the city causes no significant difference in
water quality. Diversion of sewage to Lake Erie
would improve quality, but not to the level
provided by treatment to a "zero pollutant"
level. This is because diversion of sewage
reduces both the waste load and the flow to the
river.
Verification Dissolved oxygen data of a continuous
nature are required for proper verification of
the model (a continuous monitor was installed in
1974).
Urban Runoff The model parameters and input
variations include the indirect effects of urban
runoff which were present in the stream during
intensive surveys; however, the urban runoff
effect is inseparable from other effects.
Consequently, studies are being undertaken to
determine the significance of this source.
Eutrophication - The effects of nutrient controls
on dissolved oxygen could not be estimated, since
no quantification was available for the nutrient
plant growth dissolved oxygen relationship.
Studies are being undertaken to investigate this
phenomena.
Waste Loading Guidelines
Conclusions derived from model runs were
used in the statement of allowable waste dis-
charge rates for each reservoir construction
alternative. These statements, called waste
loading guidelines, are based on loading rates
which produce marginally acceptable water quality.
The loading rate, which produced the model output
shown in Figure 4 was considered marginally
acceptable, in spite of the predicted criteria
violations, because of the lack of model veri-
fications and since treatment to the zero pol-
lutant level or diversion still produced criteria
violations. An arbitrary limit on the dilution
ratio acceptable at low flow was also incorporated
in the identification of allowable waste discharge
rates as follows: tertiary treatment (to stream
quality - approximately 15 mg/1 total oxygen
demand) should be initiated when the dilution
ratio of stream flow to sewage reaches 1.5:1, and
increases in discharge should stop when the
dilution ratio reaches 1:1.
"System Options", which were combinations of
a waste disposal option and a reservoir construction
option were defined on the basis of the above
analysis. Water quality benefits were assumed to
be constant for all options. The present value
of costs for each option was estimated at various
interest rates, including the negative costs
(i.e. benefits) from flood control. A least cost
ordering of the options then provided input to a
subsequent analysis of unquantified costs and
benefits for various options.
References
Thames River Basin Water Management Study,
Ontario Ministry of the Environment and the
Ontario Ministry of Natural Resources, 1975,
Toronto, Ontario.
Guidelines and Criteria for Water Quality
Management in Ontario, Ontario Ministry of
the Environment, 1974, Toronto, Ontario.
O'Connor, D.J.; Dobbins, W.E., Mechanism
of Reaeration in Natural Streams, ASCE,
123, 641, 1958.
O'Connor, D.J.;, DiToro, D.M., Photosyn-
thesis and Oxygen Balance in Streams ,
ASCE, J. Sanitary Engineering Div., 90,
April, 1970.
Thackston, E.L. and Spence, R.E., Review
of Supplemental Reaeration of Flowing
Streams. J. WPCF, 38(10), October 1968.
Singer, S., Daily Streamflow Simulation
on the Thames River Basin. Water Resources
Paper 7, Ontario Ministry of the Environment,
1974, Toronto, Ontario.
334
-------
DISPERSION MODEL FOR AN INSTANTANEOUS SOURCE OF POLLUTION
IN NATURAL STREAMS AND ITS APPLICABILITY TO THE
BIG BLUE RIVER (NEBRASKA)
Mahendra K. Bansal, Ph.D., P.E.
Nebraska Natural Resources Commission, Lincoln, Nebraska
Mathematical Model of Dispersion
Dispersion behavior in natural streams depends
upon dispersion rates, channel configuration, turbu-
lent flow characteristics, and biochemical changes
taking place in the stream environment. This is true
for an instantaneous source of pollution for all times.
This also holds good for a continuous source of pollu-
tion during transition periods when mixing is not com-
plete in the reach. Therefore, the prediction of
turbulent dispersion coefficients is important in the
determination of water quality constituent concentra-
tion in natural streams. However, the longitudinal
dispersion rates predicted by the QUAL model are low,
which results in higher concentration peaks of short
durations. In steady-state conditions, for a. continu-
ous plane source of pollution, the dispersion behavior
in natural streams does not depend upon the dispersion
rates. Under these conditions, an exact solution of
the dispersion equation is available, and as such a
finite-difference approximation technique should not
be used. One- and three-dimensional mathematical models
of dispersion are presented in this study. The tur-
bulent dispersion coefficients calculated were tested
for the Big Blue River in Nebraska. The dispersion
model developed is not dependent on channel size or
regional location of the stream.
Introduction
A pollutant,whether agricultural or domestic,
municipal or industrial, hot or cold, when discharged
into a stream, will mix and disperse according to tur-
bulent flow characteristics of the stream. Presently,
significant advances have been made in the understand-
ing of the basic mechanism of dispersion, but the
problem of predicting the time-concentration distri-
bution of a water quality constituent still remains to
be settled. There are some dispersion models avail-
able, but their applicability is often limited.
The U. S. Environmental Protection Agency, in its
effort to deal with the stream pollution under Section
303 of the Federal Water Pollution Control Act Amend-
ments of 1972, adopted the QUAL-I and QUAL-II models
to help in formulation of the water quality management
plans for various river basins in Nebraska and other
states. The water quality model, QUAL-I ' , was
designed to simulate the dynamic behavior of conser-
vative minerals, water temperature, carbonaceous BOD,
and dissolved oxygen levels in various segments of
natural streams. The QUAL-II model,which is a modi-
fied version of the QUAL-I model, additionally
simulates benthal oxygen demand, nitrogenous BOD,
phosphorous, coliforms, chlorophyll-A, and radioactive
constituents in natural streams. The simulation of the
dispersion component are identical in the QUAL-I and
QUAL-II models.
The Nebraska Natural Resources Commission,on
request from the State Department of Environmental
Control,tested the suitability of QUAL-I and QUAL-II
models in simulating the dynamic behavior of conserva-
tive minerals in the Big Blue River in Nebraska. The
time-of-travel data1*, gathered by the U. S. Geological
Survey on the Big Blue River during August 1973 and
May 1974, were analyzed to respond to the turbulent
dispersion dynamism in natural streams.
The concentration distribution of a water quality
constituent in turbulent streams is governed by the
law of conservation of mass. The diffusive mass-trans-
port equation for a conservative pollutant, where there
are no bio-chemical changes taking place in the stream
environment, assuming longitudinal flow and no other
sources and sinks in the reach, is:
3
3
where c = local mean concentration; x, y, z = spatial
coordinates in longitudinal, lateral, and vertical
directions, respectively, measured from the center of
stream surface as datum; u = mean flow velocity in
longitudinal direction;
D, Dz
turbulent diffu-
sion coefficients in x, y, z directions, respectively;
and t = time elapsed since injection of the pollutant
or dye in a natural stream. Equation 1 is based on
the Fick's law of diffusion where the transport asso-
ciated with the turbulent fluctuations is proportional
to the concentration gradient. For one-dimensional
flow, the diffusive mass-transport equation reduces to:
3t
.(2)
where D^ = longitudinal dispersion coefficient; and
V - average velocity of flow in the reach. Equations
1 and 2, assuming dispersion coefficients are constant
in a reach, correspond to:
e
32c,
,32c
.(3)
For sampling stations far downstream of the injection
site, where mixing in the lateral and vertical direc-
tions is almost completed, it can be assumed that
DL = DX, because:
32c >;> 3?c 32c _
3x 3y 3y
Otherwise, DL would remain a function of Dx, Dy, Dz,
32c/3x2, 32c/3y2,32c/3z2, and non-linearity of flow.
In this study,
and u/V.
is taken to be a function of D
Instantaneous Source
Let M be the amount of conservative constituent
injected as a plane source at any point of the stream.
The initial and boundary conditions are:
c(x,0) = 0 for all x,
f
•'—a
A(x) c(x,t)dx = M - constituent losses in the
reach for all t,
c(°°,t) = 0 for all t,
-Jj0- ->• 0, as t -»• °°.
OX
The solution of Eq. 3 that satisfies the above condi-
tions , is well known and is given by,
335
-------
c(x,t) =
r (x-vt)21
exp - -i '—
L 40^ J
losses in the
reach (4)
m dt1
The one-dimensional mathematical model of dispersion,
which is also a solution of Eq. 3, adopted in this
study is :
The resulting concentration at time t due to the
water quality constituent dumped continuously at
origin from time 0 to t, is given by,
exp
r (*-vt>2 kovti
- - •• ---
L 4DLt L J
/ -\
~F= I o ^P l *-x"u^t"t > 7-772 »
^4TTDLJ { 4DL(t-t') J(t-t')A
or
where kg is a loss factor and L is some characteristic
length. In this study, k0 is kept unity, and L is
taken equal to x. If the value of DL is known for a
reach, the concentration distribution can be computed
from Eq. 5.
The three-dimensional model of dispersion, which
is a solution of Eq. 1, adopted in this study is:
2DL
dn
where n
.(10)
c(x,y,z,t)=
exp
,7TDLt
2H
exp
The exact solution of Eq. 10 is not available,
but it can be approximated as,
c - 5 erfc (-*
.(11)
To use Eq. 6, three of the four unknowns c, DL, Dy,
and Dz must be known. The value of DL is first deter-
mined from the one-dimensional model of dispersion,
and Dy and D2 are considered inter-related. Based on
past work, the empirical relationship is taken as,
where p is an undefined constant, and erfc is a com-
plementary error function. The value of x must not
exceed the characteristic length L after which the
mixing in lateral and vertical directions is almost
completed. The length L can be taken a multiple of
16DL/V. For steady- state conditions, when t •>• <*> ,
.(7)
Ox A
where u = ^, V -fr, H = ^; Q, A, B are discharge,
cross-section area, and top width of flow; x is the
reach length; and tp is the time to peak arrival of
the constituent concentration at a sampling station.
The value of Dz which gives the best fit between the
computed and measured time-concentration curves, is
taken to be the approximate value of Dz for that
stream reach.
c - ^ for all
u
(12)
If M units are the total amount of the constituent
concentration dumped in the stream per unit time,
then,
•jp t or c Q * constant, therefore,
c Q
where cj,
(13)
incoming constituent concentration and
The empirical equations used in the evaluation of discharge in the stream; c,,, Q, - effluent concentra-
turbulent dispersion coefficients, DL, Dy, Dz, in the
longitudinal, lat '
on past work ^,6,
teral, and vertical directions, based
'** are:
5 DL
$^) = 6.45 -
0.762 log(-
£—) = -8.1 + 1.558 log(-
.(8)
.(9)
where p, \i, and v are the density, coefficient of
viscosity, and kinematic viscosity of flow at stream
water temperature; and K is a regional dispersion
factor assumed to be unity for the Big Blue River.
Equations 7, 8, and 9 reveal that the dimension-
less dispersion parameters are a function of the
Reynolds number of flow, and channel configuration of
the stream. Knowing the dispersion coefficients, the
concentration distribution for an instantaneous
source of pollution can be computed at any point of
the stream.
Continuous Plane Source
tion and flow discharged into the stream; and c, Q
resulting outgoing constituent concentration and dis-
charge downstream of the injection site under steady-
state conditions.
Dispersion Component in the QUAL-Model
The diffusive mass-transport equation used in the
QUAL-I and QUAL-II models is the same as Eq. 2. A
finite-difference method is used for its solution. To
avoid instability of solution, an implicit technique
of backward-difference approximation is used to solve
Eq. 3. The linear equation adopted at time step n + 1
when its spatial distribution for all distance steps
i at time step n are known, is:
-n+1
where
and
W cn+1
i i+1
Gn
.(14)
Zi"aiGi-l
Let m units per unit area of a conservative con-
stituent be dumped at the origin for times t>0 in a
stream moving with a uniform velocity u in x-direc-
tion. The concentration at any point (x,t) due to the
constituent m dt1 injected during a time element dt'
at time t ' is :
+ •££.
Ax2
V
336
-------
Ax
ui = I<
dl „ zl
For a head reach, W, = —, GI —, and
bl bl
n AQx^ ACx-L At
Zl = cl
In Eq. 14, c^_|_j is unknown, therefore, the solution
starts backward from the last reach, given by,
n+1
(15)
where G. ^i, and Z. = c° +
AQx Acx At
This is possible when Wj_ = 0. The assumption of Wj_ in
the last reach to be zero for all time increments is
questionable. During initial periods, when mixing is
not complete, W^ should not be zero.
A perusal of numerical values of a, b, d, and z
would reveal that d is approximately zero for all
times, and the resulting concentration can be approx-
imated as,
n+1
= G for
times
(16)
It is not true for the last reach only as it has been
adopted in the QUAL model given by Eq. 15.
It is to be further noted that the QDAL-I and
QUAL-II models are designed for a continuous source of
pollution. This is evident from the values of Z-^
which are computed cumulatively for constituent in-
creaments, Acx£, injected at origin at time intervals
of At integrated over 0 to t. However, under steady
state conditions, an exact solution is available for a
linear uniform flow, given by Eq. 13. In this case,
the resulting concentration is not dependent on the
dispersion coefficient. Equation 13 is important
because steady-state solutions are often required to
be studied in evaluation of the water quality manage-
ment plans.
In the case of a continuous source of pollution,
the finite-difference approximate solution is there-
fore valid only for the transition period during which
the mixing is not completed. It should also hold good
for an instantaneous source of pollution, where the
concentration distribution is dependent on the disper-
sion rates for all times.
The QUAL model uses the Elder's equation9 to
evaluate the longitudinal dispersion coefficient,
described by,
DL 5.93 U^ D
where U* is the bed shear velocity, given by^/S^e.
and Se is the energy slope calculated from the Man-
ning's equation. The resulting dispersion equation
is expressed as ,
The mean velocity and depth of flow are calculated
from the relationships,
u' = aQ^, and D = yQ6
where a, 6, J,6 are constants of proportionality pre-
determined from the velocity- and stage-discharge
rating curves.
The values of longitudinal dispersion coeffi-
cients calculated from Eq. 17 and Eq. 8 differ con-
siderably. It is later found that Eq. 17 cannot be
used for all the hydraulic flow conditions in natural
streams.
Dispersion Simulation in the Big Blue River
A summary of the time-of-travel data and dis-
charge measurements collected by the D. S. Geological
Survey between the Seward and Barneston stations on
the Big Blue River during August 1973 is given in
Table 1. A fluorescent dye, Rhodamine WT, 20 percent
solution in acetic acid, 'was injected at three loca-
tions along the river and the fluorescence was moni-
tored at regular intervals for about ten days at
fifteen sampling stations, as shown in Fig. 1. It is
well known that a natural stream profile is not uni-
form. Its configuration changes from section to
section. There are some dead pockets present in a
stream reach, where the dye is detained temporarily
and is released at later times. In some cases, the
measured concentration curve has two or more peaks.
To make the hydraulic data as consistent as possible,
the observed top-width and area of cross section of
flow are plotted against the measured discharge for
each gaging station. Such a plot for the Big Blue
River at Crete is shown in Fig. 2, which indicates
that the cross-section area is not zero for a zero
discharge, and the effective cross section is then
determined.
To verify the dispersion model for the Big Blue
River, the time-concentration distribution curves were
computed from the longitudinal dispersion rates adopt-
ed in the QDAL model (Eq. 17) and also from the one-
and three-dimensional models of dispersion, Eqs. 5 and
6. They are shown plotted against the site measure-
ments in Figs. 3 and 4, respectively, for the sampling
site near Seward. The dispersion coefficients evalu-
ated from Eqs. 7, 8, 9, and 17 are also given in
Table 1. It is evident from Fig. 3 and Table 1 that
the longitudinal dispersion coefficients computed in
the QUAL model are much less than those required to
simulate the observed time-concentration distribution.
The concentration distribution resulting from the
QUAL model, therefore, consists of higher peaks span-
ning for short durations only. The adoptability of
the Elder's equation in simulation of the dispersion
component in the QUAL model, therefore, needs further
investigations.
In order to verify the applicability of the
longitudinal dispersion coefficient predicted from
Eq. 8, a test was made to check the response of peak
concentration at different locations along the stream.
Variations in the computed peak concentrations and the
site measurements are shown in Fig. 5 for the stream
reach between the Seward and Crete stations on the Big
Blue River. Figure 5 indicates that the one-dimen-
sional model of dispersion, Eq. 5, behaved satisfac-
torily. And the values of longitudinal dispersion
coefficients predicted from Eq. 8 agree well with the
turbulent dispersion characteristics of the stream.
22.6 Nu D°'833
(17)
where N is the Manning's coefficient for the reach.
337
-------
TABLE 1
TIME-OF-TRAVEL MEASUREMENTS
BIG BLUE RIVER (NEBRASKA)
1973
SI.
No.
Dye
1
2
3
4
5
Distance
Traversed
(miles)
Flow
(cfs)
Dumped at Highway 34 at
1.20 25.50
5.36
20.46
25.26
31.06
25.00
25.00
25.00
25.00
X-section
Area
Cft2)
Seward (amount
24.20
59.00
36.10
40.00
22.00
Top
Width
(ft)
6 Ib)
36.00
38.00
32.00
36.00
24.00
Water
Temp.
25
25
24
24
24
Time
to
Peak
(hrs)
3.80
28.60
91.00
197.20
232.90
QUAL model
Disp. Coeff.
(ft2/sec)
0.92
0.91
0.91
0.91
0.91
Estimated
Dispersion Coefficients
DL
90.
28.
52.
36.
74.
84
60
95
32
99
(ft^/sec)
0.0368
0.0031
0.0103
0.0279
0.1046
DZ
0.000013
0.000037
0.000027
0.000032
0.000032
Dye Dumped at Site Below Dam Southeast of Milford (amount 20 Ib)
6 5.80 32.30 27.10 26.00 28 17.00 0.65 123.66 0.0210 0.000027
7 19.76 132.40 103.00 85.00 28 37.00 1.69 171.99 0.1122 0.000029
8 49.00 152.00 85.00 50.00 26 87.00 1.87 293.33 0.0973 0.000057
9 54.15 156.00 100.00 82.00 26 94.10 1.90 227.53 0.1785 0.000031
Dye Dumped at Damsite at DeWitt (amount 35 Ib)
10
11
12
13
14
15
5.15
23.07
29.25
32.70
38.50
48.00
194.00
210.00
200.00
192.00
295.00
300.00
161.00
96.40
112.00
112.00
190.00
148.00
110.00
79.00
110.00
127.00
126.00
86.00
28
28
28
28
28
28
6.30
32.50
45.00
67.00
90.50
161.20
2.21
2.23
1.78
1.73
2.27
2.29
200.31
380.74
271.15
218.86
210.29
269.21
0.0586
0.3572
0.4411
0.9610
0.6905
1.5992
0.000031
0.000034
0.000024
0.000022
0.000049
0.000081
1.
References
Simulation of Water Quality in Streams and Canals,
Texas Water Development Board, Austin, Texas,
Report 128 (Aug. 1971).
2. QUAL-I Simulation of Water Quality in Streams and
Canals: Program Documentation and User's Manual,
Texas Water Development Board, Austin, Texas,
(Sept. 1970).
3. Computer Program Documentation for the Stream
Quality Model QUAL-II, Water Resource
Engineers, Inc., Walnut Creek, California,
(May 1973).
4. "Time-of-Travel Measurements on the Big Blue
River, August 1973 and May 1974". Unpublished
Report, Water Resources Div., U. S. Geological
Survey, Lincoln, Nebraska. Letters to Mr. Dayle
Williamson, Exec. Sec., Nebraska Natural
Resources Comm. of Feb. 5, 1974 and Nov. 8,
1974.
5. Bansal, Mahendra K., "Dispersion and Reaeration in
Natural Streams", Ph.D. Thesis, Univ. of Kansas,
Lawrence, Kansas (May 1970).
6. Bansal, Mahendra K., "Dispersion in Natural
Streams". Jour, of Hydr. Div., ASCE, HY-11,
1867 (Nov. 1971).
7. Bansal, Mahendra K., "Turbulent Dispersion in
Natural Streams and Laboratory Channels". Proc.
XV Cong., Int. Assoc. of Hydr. Res., Istanbul,
Turkey, vol. 2, B-6, 39 (Sept. 1973).
8. Bansal, Mahendra K., Simulation of Dispersion
Component in Water Quality Model, Big Blue
River (Nebraska), Tech. Publ., Nebraska
Natural Resources Comm., Lincoln, Nebraska,
(July 1975) .
9. Elder, J. W., "The Dispersion of a Marked Fluid
in Turbulent Shear Flow". Jour. Fluid Mech.
Vol. 5, pt. 4 (1959).
Fig. 1 Time-of-Travel Sampling Stations
along the Big Blue River
(Nebraska)
338
-------
DISCHARGE MEASUREMENTS
• X-SBCTON AREA
. TOPWtDTH
CD
0.
0.
1500
OBSERVED CONC DtST •-—•—-.
COMPUTED OUAL MODEL: • . •
500
CO 2OO 30O 4OO
DISCHARGE IN CFS
Fig. 2 Discharge Measurements on the
Big Blue River near Crete
(Nebraska)
300
Ol
O 4 8 12
TIME ELAPSED SINCE INJECTION OF DYE
IN HOURS
Fig. 3 QUAL-I Computed versus Measured
Time-Concentration in the Big
Blue River near Seward (Nebraska)
N =
WT. MO SUM: OOOM4*
irr. VMTCM SUM= OUOOOIM
9 - 9OM ft
sm NO i
TIMC OF DUMP: *OO »-«-73
TUM or curorr. aD
OTOM
Fig. 4 Simulated versus Measured Time-
Concentration in the Big Blue
River near Seward (Nebraska)
0 3 D 19 20 29 30
DISTANCE TRAVELED IN MILES FROM WJfCTKDN SITE
Fig. 5 Peak Concentration Variation in
the Big Blue River between
Seward and Crete (Nebraska)
339
-------
SELECTING THE PROPER REAERATION COEFFICIENT FOR
USE IN WATER QUALITY MODELS
Andrew P. Covar
Administrative Operations
Texas Water Quality Board
Austin, Texas
Abstract
Various methods for calculating atmospheric reaeration
coefficients for use in mathematical water quality
models are reviewed, and a rational engineering method
is developed to guide the engineer in the selection of
a proper predictive equation.
Introduction
The waste assimilation capacity for oxygen demanding
materials of a body of water is primarily a function
of three parameters; the volume of the water body, the
allowable dissolved oxygen deficit, and the rate at
which oxygen enters the water body from the atmosphere.
The first two are simple concepts and are easily cal-
culated, but the third, the reaeration coefficient, is
more complex and more difficult to obtain. Many for-
mulae have been developed for the water quality analyst
to use in estimating this important coefficient, and
in the past, it has been the practice to use whichever
of these formulae produced the best "fit" to available
dissolved oxygen data. While this may be an acceptable
practice in some circumstances, it does leave the esti-
mation of a very important parameter open to personal
interpretation and bias. For this reason, a more
objective method is suggested.
Review
Streeter and Phelps1 (1925)
Streeter and Phelps in 1925 developed the classic oxy-
gen sag equation for the prediction of the oxygen
profile in a flowing stream. The equation was
dD
dt
K2D
(1)
where dD/dt is the rate of change of the dissolved
oxygen deficit, L is the amount of oxygen demanding
material in the stream, D is the dissolved oxygen
deficit, and KI and l<2 are the rate constants of
decay and reaeration.
The prediction equation for K2, the reaeration rate
constant, was
m
x 2.31 (2)
ZU
N2 ~ (H')2
NOTE: (all equations give
K2 to the base e)
where U is the stream velocity, H' is the depth above
minimum low water, Z is an irregularity factor, and m
is a function of the mean change in velocity per change
in gage height. Several of the variables in this ex-
pression must be empirically evaluated. This work did
set the precedent for equations of this type and much
of the subsequent research has been on the evaluation
of constants to use in similar equations.
O'Connor-Dobbins2 (1958)
This work was based on the theories of turbulent flow
and the rate of renewal of saturated surface waters. A
theoretical development was presented along with cer-
tain lab findings which tend to support some of the
assumptions made. The predictive equation developed
for streams displaying isotropic turbulence was
_
1(2 "
, .
( '
where Dm is the molecular diffusion coefficient and H
is the average stream depth. An additional equation
was developed for streams with nonisotropic turbulence
but O'Connor has since recommended using only the form
shown. Based on field data reported by others and some
rather rough estimates of system geometry, a comparison
was made of reported values vs_ computed values. The
authors reported good agreement.
Part of the criticism of their work has centered on the
somewhat arbitrary manner in which they classified
streams as isotropic ys_ nonisotropic. This is not sig-
nificant in lieu of the O'Connor recommendation that
only the "isotropic" equation be used. Other criticism
involves some of the theoretical assumptions made in
the development of the equation, and the estimates of
stream geometry in the field area. Churchill, et al .3
(1962) imply that the field data were for polluted
streams which would interfere with verification. There
is general agreement that the equation fairly accurate-
ly predicts reaeration coefficients for many different
systems.
Churchill -El more-Buckingham3 (1962)
This work was based on observed reaeration rates below
dams from which oxygen-deficient water was released at
a constant flow during the course of the experiment.
This work is generally felt to be the most extensive
and reliable set of field data available for the calcu-
lation of reaeration rates. Many different equations
were tested and one important finding was that the
reliability of the equation was not significantly im-
proved by the addition of terms for slope, viscosity,
surface tension, or any other of the many factors which
could have an effect on the reaeration process. The
equation suggested for use
_ 5.026 U
-
.969
H
1.673
x 2.31
(4)
is of the same general form as the O'Connor-Dobbins
equation.
Owens-Edwards-Gibbs4 (1964)
This study involved the deaeration of six English
streams with sodium sulfite and monitoring the oxygen
recovery. Combining their data with that of Gameson,
340
-------
et al.5 (1955) resulted in
_ 9.41
x 2.31
(5)
The streams involved in this study were generally less
than 2.0 feet deep.
Langbien-Durum6 (1967)
Langbien and Durum combined the field data of O'Connor
and Dobbins (1958) and of Churchill, et al_. (1962)
with the lab data of Krenkel and Orlob (1963) and of
Streeter, et al.7 (1936) and obtained
= _1,3U x 2.31
(6)
Not all of Churchill's data were included in the analy-
sis. The grouping of vastly dissimilar data to derive
a single equation could be questioned. A better ap-
proach might have been to apply the separate equations
only for stream conditions similar to those used in
these derivation.
Isaacs-Gaudy8 (1968)
Using a circular trough with recirculating water, a
regression analysis on reaeration data yielded
3.053 U
H1-5
x 2.31
(7)
The applicability of this equation has been criticized
due to differences in stream flow characteristics in
circular tanks and those found in natural streams.
Negulescu-Rojanski (1969)
Similar to the work of Isaacs and Gaudy, this study
involved a recirculating flume to yield
K = 4.74
(8)
Due to the type of apparatus, the depths were limited
to less than 0.5 feet.
Thackston-Krenkel-Orlob10'11'12 (1963, 1966, 1969)
Much work has been done by these investigators using
laboratory flumes and some field data. There is a
lack of agreement among the various equations derived,
and, as in similar work, the applicability of labora-
tory flume data to wider and deeper channels can be
questioned. The reaeration process is clearly related
to stream turbulence and similarities between turbu-
lent flow in a laboratory flume and the turbulence in
a more geometrically complex natural channel may not
be as great as was assumed.
Tsivogloul3.14 (1967, 1972)
Using a gas tracer technique developed in 1966, the
author was able to directly measure the rate of gas
transfer between a stream and the atmosphere.
Tsivoglou concludes the "reaeration rate coefficient
is directly proportional to the rate of energy expen-
diture in nontidal freshwater streams." In other
words, K2 equals the change in water elevation per
unit time times some constant of proportionality.
The equation suggested was
0.054
at 25°C
(9)
with typical units for Ah and t being feet and days.
Using 0.054 as the constant all the observed values for
K2 fell within ±50% of that value predicted by the
equation. The author further concluded that flow
changes by a factor of 2 or 3 do not significantly
affect K2. While the tracer technique offers the first
reliable method for directly measuring the rate of gas
transfer in natural streams, there was considerable
"scatter" in the data.
Review Summary
In general, the laboratory studies involved flow re-
gimes much different than those found in natural
streams. These studies are useful in testing some of
the conceptual models which strive to explain the re-
aeration process but their applicability to natural
streams can be questioned. The investigators using
field data used the best techniques available at that
time to measure or estimate the reaeration coefficient.
For a more detailed critique of previous work than has
been presented here, see Lau15 (1972) and Bennett and
Rathbunl6 (1972).
A Suggested Method
The arbitrary selection of an equation to predict the
reaeration coefficient can significantly bias the re-
sults of an analysis. This is illustrated in Figure 1.
The only difference in the three dissolved oxygen sags
shown is in the reaeration coefficient as predicted by
the three equations suggested by O'Connor-Dobbins;
Churchill, et^ aj_.; and Owens, e_t ]»!_. As you can see,
the O'Connor-Dobbins curve predicts a minimum dissolved
oxygen concentration of 5.0 mg/1 while the Churchill,
et al. curve predicts a minimum of 2.3 mg/1 and a zone
oT dissolved oxygen less than 5.0 mg/1 extending for
80 miles. It would obviously make a great deal of
difference in an analysis which equation was used to
predict this coefficient. Some of these differences
might be eliminated given a good set of data and a
proper calibration procedure but adequate data are
frequently not available.
Of the several equations available to the water quality
analyst, the two suggested by O'Connor and Dobbins and
Churchill, et^ al_. have much in their favor. The two
equations are similar in form and have each been used
extensively. Considerable effort was made to verify
1
a *
' Saturation Dissolved Oxygen
Churchill, et al.
40 60 i
River Mile
lOO 120
FIGURE 1. Effects of Different K2 Equations on Dissolved Oxygen Sag
341.
-------
each with available data. Figure 2 illustrates the
data used by O'Connor and Dobbins in the field veri-
fication of their equation and the data used by
Churchill, et al_. in their field work. Also shown
is the data~~used" by Owens, et_ al_. in their work. It
is evident that each equation was derived from or veri-
fied using streams with significantly different flow
characteristics. There is very little overlap in the
data. Since each of the authors cautioned against the
use of their equation for streams with vastly different
hydraulic characteristics, the figure has been divided
into three regions each of which roughly includes most
of the data used in one of the studies mentioned. The
"A" line which divides the data of O'Connor and Dobbins
from that of Churchill, et^ aj_. is also a line where the
two equations suggested by these authors yield identi-
cal answers. The fact that this equivalence line sep-
arates the data so neatly tends to support the work of
both groups. The "B" line was arbitrarily set at a
depth equal to 2.0 feet to define the region containing
most of the Owens, jrb aj_. data.
It is suggested that each of these three works cited
is the most appropriate for combinations of depth and
velocity similar to that used in the original research.
For depths less than 2.0 feet, the equation suggested
by Owens, £t al_. seems to have the strongest backing.
For streams with depths greater than 2.0 feet, the
selection of a proper equation would depend on which
area of Figure 2 best describes the hydraulic proper-
ties of the stream in question.
The effect of such a selection method is shown in
Figure 3. For each of the three areas, the reaeration
coefficient has been calculated and plotted on the
graph using the proper equation. Note the exact agree-
ment between the O'Connor and Dobbins equation and the
Churchill, et^ jH_. equation at all points along the
upper line. There is fair agreement between the upper
and lower areas of the graph at either end of the line
drawn at a depth of 2.0 feet with progressively less
agreement toward the center.
Conclusions
1. Much research has been done concerning the evalua-
tion of the reaeration rate coefficient and its appli-
cation to the field of water quality management.
2. With some notable exceptions there is generally
poor agreement between the various equations derived.
3. Equations derived from very shallow laboratory
flume data should not be applied to natural streams
which probably have entirely different hydraulic
characteristics.
4. Equations derived from field studies are best
applied in instances where stream conditions are
similar to those from which the equations were derived.
•<> .5 .6 .7
Velocity (feet per second)
.G .5 .6 .7 .8 .9 1
Velocity (feet per second)
FIGURE 2. Field Data Considered By Three Different Investigators.
FIGURE 3. K2 vs Depth and Velocity Using The Suggested Method.
342
-------
References
1. Streeter, H. W., and Phelps, E. B., 1925. A Study
of the Pollution and Natural Purification of the
Ohio River. U.S. Public Health Service, Bull. 146.
2. O'Connor, D. J. and Dobbins, W. E., 1958. "Mech-
anism of Reaeration in Natural Streams." Am. Soc.
Civil Engineers Trans., v. 123, p. 641-684.
3. Churchill, M. A., Elmore, H. L., and Buckingham,
R. A., 1962. "The Prediction of Stream Reaeration
Rates." Am. Soc. Civil Engineers Journ., v. 88,
no. SA-4, p. 1-46.
4. Owens, M., Edwards, R. W., and Gibbs, J. W., 1964.
"Some Reaeration Studies in Streams." Int. Jour.
Air and Water Pollution, v. 8, p. 469-486.
5. Gameson, A. L. H., Truesdale, G. A., and Downing,
A. L., 1955. "Reaeration Studies in a Lakeland
Beck." Inst. Water Engineers Jour., v. 9, no. 7,
p. 571-594.
6. Langbein, W. B., and Durum, W. H., 1967. The
Aeration Capacity of Streams. U.S. Geological
Survey, Circ. 542.
7. Streeter, H. W., Wright, C. T., and Kehr, R. W.,
1936. "Measures of Natural Oxidation in Polluted
Streams." Sewage Works Journal, v. 8, no. 2.
8. Isaacs, W. P., and Gaudy, A. F., 1968. "Atmospher-
ic Oxygenation in a Simulated Stream." Am. Soc.
Civil Engineers Jour., v. 94, no. SA-2, p. 319-344.
9. Negulescu, M., and Rojanski, V., 1969. "Recent
Research to Determine Reaeration Coefficient."
Water Research, v. 3, no. 3, p. 189-202.
10. Krenkel, P. A., and Orlob, G. T., 1963. "Turbu-
lent Diffusion and the Reaeration Coefficient."
Am. Soc. Civil Engineers Trans., v. 128, p. 293-
334.
11. Thackston, E. L., 1966. "Longitudinal Mixing
and Reaeration in Natural Streams." Vanderbilt
University, Ph.D. dissertation.
12. Thackston, E. L., and Krenkel, P. A., 1969.
"Reaeration Prediction in Natural Streams." Am.
Soc. Civil Engineers Jour., v. 95, no. SA-1,
p. 65-94.
13. Tsivoglou, E. C., 1967. Tracer Measurement of
Stream Reaeration. Federal Water Pollution
Control Administration, June, 86 p.
14. Tsivoglou, E. C., and Wallace, J. R., 1972.
Characterization of Stream Reaeration Capacity.
U.S. Environmental Protection Agency, Rept.
R3-72-012.
15. Lau, Y. L., 1972. A Review of Conceptual Models
and Prediction Equations for Reaeration in Open-
Channel Flow. Dept. of Environment, Canada.
Technical Bull. no. 61.
16. Bennett, J. P. and Rathbun, R. E., 1972.
Reaeration in Open-Channel Flow. U.S. Geological
Survey, Professional Paper 737.
343
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RECEIV-II, A GENERALIZED DYNAMIC PLANNING MODEL FOR WATER QUALITY MANAGEMENT
Charles V. Beckers, Peter E. Parker*, Richard N. Marshall and Stanley G. Chamberlain
Raytheon Company
Oceanographic and Environmental Services
Portsmouth, Rhode Island 02871
Introduction
Under funding by the US Environmental
Protection Agency , Raytheon has developed
the RECEIV-II Water Quantity and Quality
Model2. In this paper, we discuss the
background of the model development ^work
and describe the model in some detail.
To illustrate model applications, we
present results from its use on the
Pawtuxet River (RI)3 and Norwalk Harbor (CT) .
We conclude the paper with a brief discussion
of some of the apparent limitations of the
model and areas in which improvements have
already been made by Raytheon.
Background
The need for RECEIV-II stems primarily
from Public Law 92-500, the Federal Water
Pollution Control Act Amendments of 1972.
Several sections of the law call for the
states or their designated agencies to pro-
duce plans, commonly designated "303e" and
"208" plans, for achievement of the stream
water quality standards through selective
application of discharge limitations and
other institutional controls on the quality
of water reaching the streams. In each case,
accurate forecasting of stream quality is
needed to determine the potential of the
proposed plans for achieving these goals.
Such forecasting is best done using comput-
erized, mathematical models of water quality5,
allowing rapid assessment of expected water
quality under rarely observed conditions,
e.g. the 7-day, 10-year low flow.
Anticipating the need to produce such
plans on a number of New England waterways,
USEPA awarded Raytheon a contract to develop
and calibrate water quality models for some
18 waterways in Rhode Island and
Connecticut1. The calibrated models were to
be capable of representing the following
appropriately linked water quality
constituents in each waterway:
• phosphorus
• coliforms
• ammonia nitrogen
•nitrite nitrogen
•nitrate nitrogen
• total nitrogen
* Now at Institute of Paper Chemistry, 1043
East South River, Appleton, Wisconsin 54911.
• carbonaceous biochemical oxygen
demand (BOD)
• chlorophyll a_
• dissolved oxygen
• salinity
• a non-conservative metal ion to
be selected by Raytheon.
While the waterways to be modeled are
extremely diverse, ranging from upland
streams through shallow lakes and impound-
ments to estuaries, it was concluded that
overall project constraints could best be
satisfied through use of a single, general-
ized set of coding. The generalized model
had to be capable of representing the
following basin features:
• Time-varying to handle tidal
conditions and the chlorophyll a
growth-death cycle.
• Two-dimensional to permit
modeling the broad, vertically
homogeneous areas of the
vertically well-mixed estuaries.
• Multiple ocean inlets to cover
such cases as New Haven Harbor
and Narragansett Bay, where there
are multiple inlets at the ocean
boundary.
• Multiple shallow dams to deal with
the multiplicity of mill ponds
found on the New England rivers.
(In the State of Rhode Island alone,
there are nearly 400 dams, most
dating from the nineteenth century
textile industry.)
• Conservative and non-conservative
constituents to handle the variety
of water quality constituents
considered in the project.
In addition, contractual clauses required
that the models be capable of running on a
variety of computers and of employing metric
units.
Since no existing model satisfied all
the requirements, it was decided to modify
the Receiving Water Block (RECEIV) of the
USEPA1s Storm Water Management Model (SWMM)6.
RECEIV was selected because it already included
many of the necessary features, particularly
the time-varying property, and could be
straightforwardly modified to incorporate
the others. It also had the incidental
advantage of providing previously unavail-
344
-------
able capability to SWMM. To clearly indicate
its lineage, the new model was named
RECEIV-II.
Description of RECEIV-II
RECEIV-II is a generalized,stand-alone
model intended for use in forecasting water
quality on a basin-wide scale, under alterna-
tive conditions of point and non-point
discharge, stream flow and desired waterway
usage. The emphasis is on forecasting the
far-field effects of an individual discharge
or assembly of discharges. Examples include
the installation of additional treatment
capacity at a municipal or industrial dis-
charge, development of a new industrial site,
population growth, institution of new zoning
regulations, or establishment of a new
control policy for flow regulation.
Fundamentally, RECEIV-II consists of two
separated models coupled together. Hydraulic
conditions are modeled first, using the
QUANTITY section of RECEIV-II. Data on the
temporal and spatial distribution of flow are
then automatically transferred to the QUALITY
section, in which water quality conditions
are computed.
The analytical framework used to describe
the waterway discretizes space and time, per-
mitting numerical integration of the partial
differential equations of hydrodynamics and
water quality. The spatial framework uses the
discrete element method7 in which state
variables such as surface elevation and con-
stituent concentration are computed at nodes
and transport (flow and velocity) is computed
in channels linking the nodes. The temporal
framework consists of discrete, uniform
timesteps, with step duration selected in-
dependently in the QUANTITY and QUALITY
sections. (For computational reasons, the
QUALITY timestep must always be greater than
or equal to the QUANTITY timestep.)
Fundamental Equations
The fundamental equations of the QUANTITY
model are the reduced, one-dimensional form of
the equation of motion for uniform, incompress-
ible flow in the open channels between the
nodes:
= -v . .
3t 3x
011 _ F
8x f
(1)
and the continuity equation expressing conser-
vation of mass for an incompressible fluid in
the open-topped nodes:
(2)
where:
v = velocity (m/s)
t = time (s)
x = distance along the channel (m)
H = water surface elevation
referenced to datum plan
of the model (m)
g = gravitational acceleration
(= 9.8 m/s2)
Ff = acceleration due to fluid
resistance (m/s2)
F = acceleration due to wind
stress (m/s2)
Q = the net flow out of the node (m3/s)
A = the surface area of the node (m2)
The acceleration due to fluid resistance is
estimated by the Manning formula:
*,r (3)
where n = Manning's roughness factor (s/m )
R = hydraulic radius (m)
The acceleration due to wind stress is
estimated by the Ekman formula:
F = — ' a
w R p
cos
(4)
where K = windstress coefficient (=0.0026)
—— = ratio of air density to water
pw density (=1.165-10~3)
U = wind speed (m/s)
¥ = angle between the wind direction an
and the axis of the channel
The numerical technique used to integrate
equations (1) and (2) is detailed in the
RECEIV-II Documentation Report2.
The fundamental form of the equations
describing volumetric average water
quality constituent concentration in a
node is:
dC
ar
1 dM
v ar
M dV
V2" dt
(5)
where C = volumetric average constituent
concentration (typically,
gm/m3)
M = constituent mass in node
(typically, gin)
V = volume of node (m3)
Equation (5) expresses the concept of
conservation of mass in a control volume,
frequently called a continuously stirred
tank reactor (CSTR)8. The derivatives
on the right can be evaluated in terms
of the flows and constituent masses
crossing the boundaries of the node,
and in terms of the bio-chemical reactions
345,
-------
taking place in the node:
dC
(c±-c)
where Q . = flows entering node from up-
J stream nodes (m3/s)
(6)
Q.
1
flows entering node from point
and non-point sources (mVs)
C. = concentration of constituent
1 entering node from upstream
nodes (typically, gm/m3)
C. = concentration of constituent
1 entering node from point and
non-point sources (typically,
gm/m 3)
M = rate of constituent mass
^ gained due to biological,
physical or chemical processes
in the node (typically, gm/s)
M, = rate of constituent mass lost
due to biological, physical or
chemical processes in the
node (typically, gm/s)
The interactions among the eleven water quality
constituents modeled in RECEIV-II are pre-
sented in the (£M + EM,) terms. For example,
the rather complex interactions affecting
the dissolved oxygen are formulated as:
= k,(C*-C9) - k7C7 - a9
- a9,5k5C5 + a9,e(G8-D8)C8 -(b/R)
(7)
nodal concentration of DO
saturation concentration
of DO
DO reaeration rate
nodal concentration of
carbonaceous BOD
rate of oxidation of
carbonaceous BOD
nodal concentration of
ammonia nitrogen
rate of oxidation of
ammonia nitrogen to
nitrite nitrogen
stoichiometric ratio of
oxygen in nitrite
nodal concentration of
nitrite nitrogen
rate of oxidation of
nitrite nitrogen to
nitrate nitrogen
where
C9
C*
k9
C7
C.,
k.
CB
ks
a9,5 = stoichiometric ratio of
oxygen in nitrate
C8 = nodal concentration of
chlorophyll a
Ge = "growth" rate of
chlorophyll a
De = adjusted "death" rate of
chlorophyll a
a9(8 = stoichiometric ratio of
oxygen produced per unit
"growth" of chlorophyll a.
b =
benthic oxygen demand
All reaction rates (k's) are adjusted for
the effects of temperature during computation.
Equations for computation of BOD oxidation
rate, DO surface reaeration, DO reaeration
at dams, saturation DO and exchange at the
tidal boundaries are detailed in the RECEIV-II
Documentation Report? along with the
numerical integration procedures used in
the QUALITY section.
Program Structure
RECEIV-II is written in ANSI-standard
FORTRAN9 to assure inter-computer compat-
ibility and has been successfully tested on
the CDC 6700, CDC Cyber 73, IBM 370/155 and
Honeywell 6000/60 computers. It consists
of a main program and 14 subroutines that
perform various computational, input and
output functions. The program can be
modularized to minimize the total computer
memory requirements, with the QUANTITY and
QUALITY sections typically loaded and run
independently. Information transfer among
the program modules is via mass storage,
either mag tape or disk. The coding of
RECEIV-II has been carefully structured to
preserve compatibility with the present
SWMM, but the two models have not yet been
integrated.
Model Input and Output
In order to compute the primary model
outputs, RECEIV-II requires a wide range of
information on the river basin being
modeled. Since the equations used in
RECEIV-II constitute our concept of how
the waterway "works", the data required
by RECEIV-II would be required under any
circumstances to provide an adequate
description of the waterway. Table 1
summarizes the necessary input data, and
characterizes it according to the spatial
and temporal intensity needed.
The primary computational outputs of
RECEIV-II are:
• Stage or tidal height at each node
(m above datum)
• Flow in each channel (m3/s)
• Velocity in each channel (m/s)
• Constituent concentration in each
node (typically, mg/1)
346
-------
Results
The frequency of output for each of these
results is under user control and an integer
multiple of the basic timestep of the model.
TABLE 1. RECEIV-II DATA REQUIREMENTS.
CHARACTERISTIC
DATA REQUIRED
<5 O P
H O
H 00 PC H
H !3 U Cd
i o <: w
I O W FM
GEOGRAPHICAL
Source location
Node location
Node-channel connectivity
Dam location
Ocean interface location
Surface area
Bottom elevation
Length
Width
METEOROLOGICAL
Wind speed and direction
Evaporation rate
Precipitation rate
HYDRAULIC
Tidal height
Stage height
Velocity
Manning coefficient
Dam height, width & shape
Background flow
WATER QUALITY
Water temperature
Temperature compensation
coefficient
Constituent concentration
Background concentration
Ocean concentration
Ocean exchange rate
Reaction rate
Benthic oxygen demand
Reaeration constants
Sunrise
Sunset
Maximum light intensity
Saturation light intensity
Extinction coefficient
Growth coefficient
Respiration rate
Michaelis-Menton
constants
Nutrient ratios
Grazing rate
gOURCE CONDITIONS
Flow
Constituent concentration
(or mass rate)
W
O
WQ
Q 2
H O
t£ O
U W \
O I
P £i W i
00 H 5 P •
^gggi
w
o
"^
j pq
u
o
Under the original USEPA funding,
Raytheon calibrated RECEIV-II to 18 New
England waterways, with varying degrees
of success using the data available in
197310'11. The calibration results ranged
from good to unusuable, with streams and
rivers typically turning our better than
bays and harbors. In at least one case,
the Quinnipiac River, state officials have
used the Raytheon-calibrated model to
develop 303e waste load allocations, with
only minor updating to reflect more recent
data. Load allocations on other rivers and
harbors have subsequently been achieved
using improved data bases.
Availability of data was invariably the
single most important factor controlling the
success of the calibration effort in each
waterway. In several cases, we were unable to
find the minimum two sets of data needed for
calibration. The data on bays and harbors
were substantially weaker than on streams and
rivers. Despite the heavy use of the bays and
harbors for navigation, basic data on tides
and currents were noticeably absent. As
discussed above, the data necessary to RECEIV-
II calibration are fundamental to an under-
standing of the processes active in a waterway.
Failure to develop adequate RECEIV-II calibra-
tions for a number of the 18 waterways is
indicative of the state of knowledge of those
waterways.
Another factor contributing to difficulty
in calibration is a fundamental limitation of
the model in representing the stream bed as a.
rectangular channel. RECEIV was originally
developed as a stormwater model, representing
relatively high-flow conditions. In contrast,
application of RECEIV-II in the context of
303e load allocations requires modeling of
very low flow conditions. In many cases, the
use of a rectangular channel approximation
breaks down under low flow, due either to
reduction in stream dimensions or separation
of the flow due to stream bed bathymetry.
However, in those waterways for which
sufficient data were available, RECEIV-II has
performed quite well. The Quinnipiac River is
one example, and Raytheon has recently complet-
ed preliminary waste load allocations using
RECEIV-II on Norwalk Harbor and the Pawtuxet
River, under contract to Connecticut and Rhode
Island, respectively. In each case, addition-
al refinement of the basic calibration was
required to achieve satisfactory results.
This was accomplished through additional data
collection and detailed analysis of available
data. The results of these two wasteload
allocations illustrate the desirability of
using a dynamic quantity and quality model
for 303e planning.
Pawtuxet River
The preliminary results of the load
allocation work on the Pawtuxet River
illustrate the importance of nitrogenous
oxygen demand in achieving water quality
standards for rivers. A single unit of
ammonia nitrogen discharged at the Cranston
Treatment Plant (approximately 14.4 MGD) has
the equivalent effect on dissolved oxygen at
-------
the Broad Street Dam of 5.5 units of carbon-
aceous BOD. While the necessary removal of
carbonaceous BOD is thought to be achiev-
able by Cranston's consulting engineers,
there is concern for the ability to maintain
the equivalent nitrogen allocation necessary
to maintain water quality standards, espec-
ially during the colder months of the year
when biological nitrification processes are
difficult to maintain. For this reason, the
dynamic capabilities of RECEIV-II have been
exercised to determine the sensitivity of
the Pawtuxet River to nitrogenous demand
under varying flow and temperature conditions.
It is of interest to note that, with
respect to the total treatment plant-river
system, winter conditions may turn out to be
the "critical period" for maintenance of the
water quality standards, not the summer
months as commonly assumed.
Norwalk Harbor
A similar conclusion concerning the
"critical period" has been reached in the
case of Norwalk Harbor, but for entirely
different reasons. Algal growth in Norwalk
Harbor appears to play a major role in the
oxygen cycle, especially as it affects the
carbonaceous and nitrogenous BOD assimilation
capacity. During cold, dry weather, algal
oxygen production is sufficiently reduced
to constitute the maximum restriction on
total BOD discharged into the harbor. In
cold, wet weather, higher nutrients loadings
tend to be offset by increased algal oxygen
production. While warm, wet weather is
relatively non-restrictive on total BOD, it
is most restrictive on carbonaceous BOD
removal at the Norwalk STP. The dynamic
features of RECEIV-II permit detailed
analysis of each of these cases without the
need to recalibrate the model for changing
conditions. In addition to allowing study
of the seasonal variations, RECEIV-II also
allows confirmation of such details of the
oxygen cycle as the early morning minimum,
which results from algal respiration through
the nighttime hours. Sensitivity analyses
also indicate Norwalk Harbor dissolved oxygen
levels to be very sensitive to variations in
sunlight intensity, as might be expected
from the strong dependency on algal popu-
lation. A similarly strong dependency on
tidal range is exhibited, due to reduced ex-
change with Long Island Sound during neap
tides.
Discussion
Thus, when sufficient data are avail-
able to adequately describe the waterway,
RECEIV-II has proven itself to be a useful
and dependable approach to forecasting water
quality. Its unique dynamic features have
allowed the examination of aspects of water
quality that might otherwise have escaped
notice. Because of the dynamic formulation,
it is preferred for application to estuaries,
for use in cases of un-steady discharge (e.g.
stormwater runoff), for extrapolation to low
flow conditions, and for examination of
seasonal, daily or tidal variations in water
quality.
As with all models, experience in the
use of RECEIV-II has highlighted areas in
which the model can be improved. When those
improvements have related to features of the
model developed under USEPA contract, Raytheon
has publicized corrections and changes
through release of Program Modification
announcements. The objective is to assure
the integrity of Raytheon's model in its use
by the many agencies and firms now holding
copies. To date, nine Program Modifications
have been distributed to the user group
through the USEPA.
In addition, Raytheon has found it nec-
essary to further expand the model's capa-
bility beyond that originally required for
RECEIV-II. To satisfy various contractual
commitments, Raytheon has developed the
proprietary RECEIV-III model. Among the
numerous improvements incorporated in RECEIV-
III are coding to model water temperature and
organic nitrogen (coupled to chlorophyll
-------
5. Jon B. Hinwood and Ian G. Wallis . "Clas-
sification of Models of Tidal Waters",
Jour. Hydr. Div. , Proc. ASCE; 101 (HY10) :
1315-1331. October 1975. - -
6. Metcalf & Eddy, Inc., University of
Florida, and Water Resources Engineers,
Inc . Storm Water Management Model. US
Environmental Protection Agency, Wash-
ington, DC. Report Nos . 11024 DOC 07/71,
11024 DOC 08/71, 11024 DOC 09/71, 11024
DOC 10/71. July-October, 1971. 1132p.
7. R.P. Shubinski, J.C. McCarthy and M.R.
Lindorf . "Computer Simulation of
Estuarial Networks", Jour. Hydr. Diy. ,
Proc. ASCE, 91 (HY5) : 33-49. September
1965.
8. C.W. Chen and G.T.Orlob. Final Report r
Ecological Simulation for Aquatic Envir-
onments . Office of Water Resources Res-
earch, US Department of the Interior,
Washington, DC. Report No. OWRR C-2044.
December 1972. 155p.
9. ASA Sectional Committee on Computers and
Information Processing. American
National Standard FORTRAN. American
National Standards Institute , Inc . , New
York, NY. Standard ANSI X3. 9-1966.
March 7, 1966.
10. Raytheon Company. New England River
Basins Modeling Project Final Report,
Volume III - Documentation Report, Part 2
- Appendix D: Connecticut River Basins
p
ib
Calbrations . US Environmental Protection
Agency, Washington, DC. January 1975.
254p.
11. Raytheon Company. New England River
Basins Modeling Project Final ReporE,
Volume III - Documentation Report, Part
3 - Appendix E: Rhode Island River
Basins Calibrations. US Environmental
Protection Agency, Washington , DC .
February 1975. 182p.
349
-------
MODIFICATIONS TO QUAL - II TO
EVALUATE WASTEWATER STORAGE
John S . Tapp
Technical Support Branch
Water Division
EPA, Region IV
Atlanta, Georgia
To help evaluate the feasibility of storing waste-
water to alleviate adverse effects on receiving water
quality during low flow conditions, the water quality
model QUAL - II was modified. The general modifica-
tions are described and situations which lend them-
selves to application of the modified model are
discussed.
Introduction
Effluent limitations for wastewater discharges are
commonly established based on maximum temperature at
some critical statistical low stream flow condition,
normally defined by water quality standards. Thus,
commonly utilized procedures of arriving at effluent
limitations based on water quality standards in some
situations do not take into account, (a) water temp-
erature changes, (b) flow rate fluctuations, or
(c) other seasonal variations. For situations where
assimilative capacity is limited and the storage of
effluent from a wastewater treatment facility is
feasible, the normal seasonal changes in water temp-
erature and flow rates can be utilized to allow in-
stream water quality standards to be maintained, at
a cost less than by utilizing treatment alone.
Under extremely critical conditions, even the possi-
bility of no discharge could be investigated.
To use the wastewater storage approach requires
curves of stream flow versus wastewater flow at a
given quality to maintain some instream constituent
concentration, generally dissolved oxygen. To estab-
lish the curves of stream flow and allowable waste-
water flow, a mathematical model is very useful.
However, most dissolved oxygen models are not con-
structed such that these curves can be determined
without much trial and error input and manipulation.
This paper describes the modifications to a
commonly used model to allow easy generation, without
trial and error manipulation, of curves of stream
flow versus wastewater flow (at a given oxygen demand
concentration) to maintain a given instream dissolved
oxygen concentration.
The Model
The model selected for modification was QUAL - II as
developed by Water Resources Engineers1. QUAL-II is
a modification of QUAL I originally developed for
the Texas Water Quality Board. As developed, QUAL-II
can simulate the dynamic behavior of conservative
materials; temperature; carbonaceous biochemical ox-
ygen demand; chlorophyll A; the nitrogen forms of
ammonia, nitrite, and nitrate; phosphorus; benthic
oxygen demand; dissolved oxygen; and coliforms. All
constituents except temperature can also be simulated
directly in the steady state mode. The general model
constituent layout is shown in Figure 1.
Figure 1
The General Model Constituent Layout for QUAL-II
QUAL - II is structed as one main program supported by
19 subroutines. The general structure of the model
is shown in Figure 2. The description of the various
subroutines and their functions are described by
Water Resources Engineers-*- and need not be repeated
here. The main focus of the modifications to QUAL-II
was to take advantage of subroutine FLOAUG to check
for a prespecified instream dissolved oxygen target
level. If that level was not met all flows would
be incrementally increased based on drainage area con-
tribution to arrive at a flow in a prespecified head-
water which would allow the dissolved oxygen target
to be met in all reaches below the discharge under
study. All data necessary to utilize the modified
model is read in subroutine INDATA and model control
is maintained by the main program QUAL - II•
The detailed modifications made to QUAL-II are descri-
bed by Tapp . Basically, the model was modified such
that a drainage area and a drainage area factor would
be assigned to each reach, to each direct input trib-
utary, and to each headwater. A range of wastewater
350
-------
flows for the specific discharge to be studied is
specified. For a given wastewater flow the model uses
subroutine FLOAUG to check for a minimum instream dis-
solved oxygen concentration. If the dissolved oxygen
concentration is less than the minimum, then subrou-
tine FLOAUG increases the flow in each reach, direct
input tributary, and headwater in proportion to the
drainage area and drainage area factor. When the
dissolved oxygen concentration below the discharger
under study is above the specified minimum, the seq-
uence returns to the main program where a new waste-
water flow is taken through the same procedure. The
output from the model is a series of wastewater flows
with corresponding stream flows for the headwater
above the discharger under study at a given tempera-
ture and given wastewater effluent quality. The
modifications were developed for the steady state mode
and have not been tested in the dynamic mode.
Figure 2
The General Model Structure of QUAL - II
Model Utility
The type of curve which can be platted from the info-
rmation developed by the modified QUAL-II model is
shown in Figure 3. For any stream flow in the head-
water above the discharger under study, an allowable
wastewater flow to meet a given dissolved oxygen tar-
get level can be determined at a given stream tempera-
ture and effluent quality. Knowing the hydrology of
the headwater above the discharge, the storage volume
necessary to maintain the dissolved oxygen target can
be determined. This can be accomplished for a dis-
charger and a given effluent quality by generating
a curve of wastewater flow versus stream flow to meet
a given instream dissolved oxygen concentration for
the water temperature associated with each month of
stream flow records. A temperature simulation model
based on meterological data could be linked with the
hydrologic data to provide daily water temperatures,
if desired. Knowing the water temperature and a
daily stream flow value, one could go to the waste-
water flow versus stream flow curve for that tempera-
ture and effluent concentration and arrive at an allow-
able wastewater flow. The average daily flow of the
discharger would then be compared with the allowable
wastewater flow and if the flow from the discharger
was greater than the allowable flow the difference
would be put into storage. If the discharger flow was
less than the allowable flow then the difference would
be taken from storage and put into the stream along
with the flow from the discharger. For the period of
hydrologic records under evaluation, this procedure
could be utilized to arrive at the maximum storage
volume required for the given effluent quality and
would be one point on a storage volume versus effluent
quality curve. Where large amounts of hydrologic
records are to be utilized the wastewater flow versus
stream flow curves can be defined by fitted equations
and a curve at one temperature can be related to a
curve at another temperature by the use of tempera-
ture coefficients . Once these relationships are estab-
lished the storage volume can easily be calculated by
simple digital computer routines.
Utilizing the above procedure, other storage volumes
are then determined for varying effluent concentrations
and a curve of effluent quality as measured by ulti-
mate oxygen demand (UOD) versus the storage volume
necessary to maintain a given instream dissolved oxy-
gen level can be determined as shown in Figure 4.
From the information of oxygen demand in the effluent
versus storage volume, costs of wastewater treatment
and storage costs can be used to develop the curves
shown in Figure 5. The minimum point on the total
cost curve would give the least cost combination of
storage and treatment.
AT A GIVEN
TEMPERATURE
AND EFFLUENT
CONCENTRATION
STREAM FLOW
Figure 3
An Example of the Curve Which Can be Plotted from
Points Generated by the Modified QUAL-II Model
351
-------
LU
^J
_l
u.
u.
UJ
Q
O
STORAGE VOLUME
Figure 4
A Curve of Oxygen Demand in the Effluent Versus
Storage Volume
UOD IN EFFLUENT
STORAGE VOLUME
by a straight line with a slope and a Y-intercept.
The slopes and Y-intercepts at different temperatures
were related by coefficients such that for each
instream dissolved oxygen level investigated the
allowable wastewater flow was only a function of the
stream flow and the temperature. A digital computer
program was written to read in over 30 years of <•
stream flow records, assign the proper temperature,
and calculate and accumulate the storage volume of
wastewater. Based on this output, an equation for
operation of the storage pond to meet the required
instream dissolved oxygen concentration was developed,
References
^Water Resources Engineers, Inc., "Computer Program
Documentation for the Stream Quality Model QUAL-II,"
Prepared for the Environmental Protection Agency,
Systems Analysis Branch, Washington, D. C., 1973.
2Tapp, J.S., "User's Manual For Wastewater Storage
Option, QUAL-II", Environmental Protection Agency
Region IV, Technical Support Branch, Atlanta, Georgia,
February, 1976.
J. S., "In Plant Wastewater Storage and
Release for Water Quality Control: A Case Study",
Presented at the ASCE Environmental Engineering
Division Second Annual National Conference on
Environmental Engineering Research, Development,
and Design, Gainesville, Florida, July 20-23, 1975.
Figure 5
The Curves Showing the Least Cost Combination
of Storage and Treatment
Another example where the modified QUAL-II model could
prove useful would be a situation where instream dis-
solved oxygen standards could not be met with an indus-
try discharging at an effluent quality defined as Best
Available Treatment (BAT). In this instance,
effluent concentration would be left constant and stor-
age volumes tested against allowable instream dissolv-
ed oxygen concentrations. A study of this type was
conducted by Tapp^ where the curves of allowable waste-
water flow versus stream flow were developed by trial
and error, thus pointing to the need for the modified
model. In this study an industry which was the defi-
nition of BAT for its class had an existing storage pond
of a given volume. An idea of what instream dissolved
oxygen concentration could be maintained based on over
30 years of past hydrologic records on the stream was
desired. A curve of allowable wastewater flow versus
stream flow for each average monthly water temperature
was plotted and broken into two sections each fitted
352
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WATER POLLUTION MODELING IN THE DETROIT METROPOLITAN AREA
Michael Selak
Robert Skrentner, P.E.
City of Detroit
Detroit Water and Sewerage Dept.
Detroit, Michigan
Carl Harlow
James Anderson, P.E.
College of Engineering
Wayne State University
Detroit, Michigan
SUMMARY
The EPA Storm Water Management Model (SWMM) has
been used by the Detroit Water and Sewerage
Department and Wayne State University to simulate
waste water flow in the Oakwood Sewer District of
the City of Detroit. This District is a 1,500-acre
(3,705-hectares) residential/industrial area with
combined sewers from which flow is pumped to the
Detroit waste water treatment plant and/or to the
Rouge River during periods of high rainfall. After
several minor modifications to the SWMM, the
simulation results from the Runoff and Transport
blocks of SWMM compared favorably with observa-
tions by the computerized monitoring system of the
Detroit Water and Sewerage Department.
The output from the SWMM Transport block is routed
to a computer simulation of the Detroit waste water
treatment plant called STPSIM, which was developed
at Wayne State University. This model enables the
user to evaluate the effect of storm flow on plant
performance and to compare various strategies for
treating the stored waste water. The simulated
results from STPSIM appear to be quite represen-
tative of the actual treatment plant performance.
However, model calibration has been difficult due
to a shortage of real-time data from the plant.
All of the water pollution simulation models operate
on Wayne State University's 360/67 computer system
in time sharing or batch mode through an executive
program called the Detroit Water Quality Informa-
tion System (DWQIS). The DWQIS was developed at
Wayne State University with assistance from the
Detroit Water and Sewerage Department. In
addition to the above models, the DWQIS contains
census and local climatological data for the
Detroit area which was used to provide some of the
necessary input data for the SWMM.
INTRODUCTION
Ninety-seven communities of the Detroit metropol-
itan area are supplied with potable water and
seventy-four communities receive waste water
collection and treatment services from the Detroit
Water and Sewerage Department (DWSD). As of
July 1975, the waste water service area under
DWSD contract was 1075 square miles (2784 sq. km.).
The collection system contains separate sanitary
and combined sewers that normally flow to the DWSD
regional treatment plant located at the confluence
of the Detroit and Rouge Rivers. This plant
provides advanced secondary treatment to a flow
of ISO million gallons per day (19.7 cms). Total
plant flow averages 800 MGD (35.0 cms). Seventy-
six possible points of overflow to the Detroit and
Rouge Rivers exist to relieve the system during
periods of extreme flow. The plant is currently
undergoing a major improvement program including
the installation of a computer system that will
monitor and aid in the control of the treatment
unit processes.
The DWSD, with an EPA research and demonstration
grant, installed a system-monitoring and remote
control network to better integrate the waste water
collection and treatment operations. The data
collected by the network is transmitted to the DWSD
System Control Center and provides operators with
information to remotely control dry weather and
storm pump stations, flow regulating devices,
inflatable dams, and the entire water distribution
network. The DWSD computers monitor events as
they occur, but they are not capable of predicting
system response to storm events and the resulting
changes in waste water quality and quantity. For
these reasons, the DWSD has begun a program of
utilizing computer models to predict system
behavior, which is a primary goal for optimizing
the performance of an existing system. The
objective of the DWSD is to implement methods that
will provide system response information in an
attempt to utilize the storage capabilities of the
sewer system more efficiently, improve upon the
system operation to prevent overflows, and
operate the treatment plant more efficiently. To
meet these objectives, the DWSD is applying the EPA
model SWMM and the Wayne State University treatment
plant simulation model STPSIM to the Detroit system.
APPLICATION OF SWMM TO THE OAKWOOD SEWER DISTRICT
The Oakwood Sewer District of the City of Detroit
was selected to test and evaluate SWMM because:
a) it is relatively isolated from the balance of
Detroit, b) its land use is typical of the City,
and c) it is of a manageable size. The district
has a population of 17,250 and an area of 1500
acres (607.5 hectares). 46% of the land area is
classified as residential, 44% as industrial, 3%
as commercial, and 7% parkland. A combined sewer
system collects and transports sanitary flow,
industrial wastes, and storm water to a single
pump station. Under normal conditions, a 20.0 cfs
(0.6 cms) pump transports the dry weather flow to
the main plant. During periods of high flow due
to storm water, additional pumps with a total
capacity of up to 488 cfs (13.8 cms) can be used to
relieve the system into the Rouge River near its
confluence with the Detroit River. As part of the
353
-------
system-monitoring network, the pump station is
equipped with a weighing bucket and a tipping bucket
rain gage. An additional tipping bucket rain gage
is located in the near vicinity. In addition, three
level sensors are operating in the major sewers of
the district. During periods of rainfall, the
system-monitoring network is capable of collecting
rainfall data with time intervals as small as five
minutes. The level sensors provide flow data on a
continuous basis.
The major blocks of the SWMM that were utilized in
this study include RUNOFF, Version I and TRANSPORT,
Version II. Version II of the RUNOFF block is
currently being evaluated. The dual-stage pump
capacity built into the TRANSPORT block was found to
be inadequate for the conditions at Oakwood and had
to be modified to allow for multiple pumps of
different capacities. Several storms with rainfalls
of up to 2 inches extending over 40 hours were used
to evaluate the models.
RUNOFF BLOCK
The Oakwood district was initially divided into 150
subcatchments with an average size of 10 acres
CM-.05 hectares). Land use divisions, sewer maps,
U. S. Census data, previous DWSD reports, and
topographic maps all played an important role in
this selection process. Pipes up to 24 inches
(61 cm.) in diameter were included in the RUNOFF
block. Due to the long computer times needed for
this configuration, later analyses used as few as
50 subcatchments of up to 80 acres. Storm durations
ranged from 3 to 40 hours with a maximum of 120
time steps of 15 minutes used for the 40-hour storm.
Although this is in excess of the SWMM recommenda-
tions, it was about the smallest that could be used
without altering the RUNOFF block, and no serious
difficulties were encountered.
TRANSPORT BLOCK
The output from RUNOFF becomes the input to the
TRANSPORT block. The combined sewers of the
Oakwood district are circular or egg-shaped,
monolithic concrete or brick, and range in diameter
from 3 to 10 feet (.92 - 3.05 meters). Most of the
necessary input data for this block was taken from
DWSD sewer maps, the U. S. Census, and DWSD water
use data. The major sewers were divided into 138
elements, and as in RUNOFF, 120 time steps of 15
minutes each were used for the simulation. The
Oakwood pump station has four pairs of pumps with
capacities of 20 cfs (0.6 cms), 40 cfs (1.1 cms),
98 cfs (2.8 cms), and 106 cfs (3.0 cms), respectively.
Under normal conditions, one 20-cfs (0.6-cms) pump
handles dry weather flow. As the level in the wet
well rises, additional pumps are activated as
needed. For the storms modeled in this study, the
20-cfs (0.6-cms) pump handled dry weather flow and
two 40-cfs (1.1-cms) pumps were used during the
overflow condition.
The dry weather flow, infiltration, inflow, and
insystem storage option of TRANSPORT were used in
this study, but the insystem storage model was
found to be inadequate for the conditions in
Oakwood. Consequently, DWSD computer programs
were used to determine the storage potential of the
Oakwood sewers which was then utilized in TRANSPORT
as an "irregular reservoir".
SWMM RESULTS
In general, the results generated by SWMM correlate
satisfactorily with observations and it seems that
SWMM is capable of predicting the waste water systerc
behavior. Figure 1 shows the relationship between
the rainfall hyetograph and the resulting runoff
hydrograph. No data was collected to verify this
relationship, but the pattern is clearly represen-
tative. Figure 2 is a plot of the actual and
simulated overflow from the Oakwood pump station.
3:0 6X> *O I2» 15.-O B» 21:0 24* 3:0 6:0 9:0 12:0
FIGURE 1-HAINFALL HYETOGRAPH & RUNOFF HYDROGRAPH VS. TIME
c
F
S
80 •
60-
40-
20 •
i
A
•*••-
r~
STORM -^
, — SANITARY
1
1 J
• 2
C
M
S
• I
3:0 SO *0 12:0 15:0 IS'-O 21:0 24:0 3:0 SO SO 12*
FIGURE 2-PUMP FLOW VS. TIME
SOLID-MODEL DASHED-REAL
The quantity of waste water that overflowed was
predicted within the accuracy of the measured data.
However, the time that the pump was predicted to
have gone on deviated from the actual pump records
by approximately two hours. Based on an elapsed
time of 20 hours from the beginning of the simula-
tion, this represents a deviation of approximately
10%. Considering the accuracy of the input data and
the state-of-the-art of the models, this deviation
seems quite reasonable.
354
-------
WASTE WATER TREATMENT PLANT SIMULATION
STPSIM is a dynamic waste water treatment plant
model which uses the digital computer to simulate
plant behavior. The computer program is written in
Fortran and consists of various subroutines totaling
approximately 1500 lines. STPSIM currently has the
capability of modeling; 1) settleable solids, 2)
suspended solids, 3) dissolved solids, 4) B.O.D.,
and 5) chlorides. The output from STPSIM is
displayed in tabular and graphical forms with the
graphical display being optional. Through STPSIM,
the user can study plant behavior by adjusting
various operation parameters such as tanks in
service, recycling, chemical feeds, etc.
There are many reasons for studying the dynamic
behavior and operational characteristics of waste-
water treatment processes, including optimizing the
treatment of processes by properly adjusting opera-
tional controls. Some of the possible benefits that
could be derived from this optimization are:
1. Reduced costs: savings on chemicals and
electrical energy.
2. Better treatment of dry weather flow:
higher removal efficiencies might be
obtainable during normal plant operation.
3. Higher treatment capacities: through
better control it might be possible to
treat higher capacities during high runoff
periods while maintaining water quality
standards.
However, treatment processes are usually operated
as steady-state systems with general operating
procedures based on flow quantity rather than flow
quality. Furthermore, to report the efficiency of a
given process, the samples are usually extracted
from the inlet and the outlet at approximately the
same time. This obviously assumes that the process
is at steady state.
STPSIM REQUIRED INPUT DATA
STPSIM requires the following types of information:
1. Time information: time step and length
of analysis.
2. Quality information: influent concentra-
tions for the pollutants that will be
analyzed for each time period.
3. Quantity information: flow rates for each
time period.
4. Plant operating information: which tanks
will be in service, initial concentrations
of tanks, routing schemes, recycle schemes.
5. Calibration information: (optional) reaction
coefficients, reactor behavior type.
6. Desired output: graphical, tabular, or both.
The quality and quantity data can be the output from
the TRANSPORT block of SWMM or from plant observa-
tions .
A dynamic model is needed since waste water treat-
ment systems are rarely at steady-state due to
significant variations in flow quantity and quality
during a given day (1). This can be seen in
Figure 3 where the concentration of suspended solids
of the influent was measured hourly for the Detroit
waste water treatment plant on February 23 and 24,
1975.
260 -r
210 •
160 • .
10
e:o
ie:o 24:0
TIME (MRS)
FIGURE 3-OBSERVED PLANT INFLUENT FEB. 23-24
(SS-SUSPENDED SOLIDS, MG/L )
BASIC ALGORITHM
The basic reactor type used for modeling the various
processes is the "complete mixed" reactor. Some of
the processes act as plug flow reactors while others
have complete mix characteristics (5). Plug flow is
usually approximated in long tanks with a high
length-to-width ratio in which longitudinal disper-
sion is absent or at least minimal. This condition
is usually characteristic of primary sedimentation
tanks. Complete mixing occurs when the pollutant
entering the tank is immediately dispersed throughout
the tank. Round or square tanks are generally rep-
resentative of this condition. Aeration tanks, for
the activated sludge process are usually operated
under complete mix conditions (1,2). However, in
many instances, the reactors cannot be properly
characterized by either of the above ideal types and
therefore are classified as non-ideal reactors.
The complete mix reactor was chosen as the basic
reactor for STPSIM since it is possible to model
plug flow and non-ideal reactors with this model in
parallel and series combinations.
For a single complete mix reactor, a mass balance
yields, for a given time,
Mass in = Mass out + Disappearance by reaction +
Accumulation
= QC - RV + V (dC/dt) where
= flow - constant for a given tank
= volume of the tank, constant over time
= concentration of pollutant in tank
incoming concentration of pollutant
QC.
x in
Q
V
c
c.
in
355
-------
R
t
reaction mechanism
time
This basic differential equation is solved numerically
at each time step for each pollutant and for each
reactor.
The various reactor types are handled in the follow-
ing manner:
1. Complete Mix use of the basic algorithm
2. Plug Flow - use of "N" complete mix sub-
reactors in series. As "N" approaches
infinity, the behavior will approach that of
plug flow, Figure 4.
1
INFLUENT MIXED
T 1 f
1
i-
c
T
3
REACTOR
i
S
1
c
4-
3
EFFLUENT
'
330
250
170 •
90
10
s:o
-f-
s:o
ie:o 24 :o
TIME (MRS)
FIGURE 6-SIMULATED d OBSERVED ( + ) PLANT EFFLUENT
FEB. 23-24 ( SS- SUSPENDED SOLIDS, MG/L )
FIGURE 4- PLUG FLOW REACTOR
3. Non-ideal types - using complete mix (CM) and
plug flow (PF) reactors in parallel and series
combinations along with recycle schemes,
Figure 5.
r
I J
FIGURE 5- NON-IDEAL REACTOR
RESULTS
STPSTM has been used to model the Detroit Waste Water
Treatment Plant. The analysis chosen for presenta-
tion is for suspended solids for the 23rd and 24-th
of February, 1975. Suspended solids were measured on
an hourly basis during this period for plant influent
and effluent. On this date, the activated sludge
system was not in operation which permitted the sedi-
mentation processes to be modeled alone. If the
activated sludge system had been in operation,
additional information would have been required. As
seen in Figure 6, there appear to be questionable
data points for the effluent measured at 2:00 P.M. on
the 23rd and at 4:00 A.M. on the 24th. The approxi-
mate residence times during this period were on the
order of one hour. Therefore, if peaks in the
effluent did occur, similar peaks should have existed
in the influent earlier, but none were observed.
Several possible explanations exist. One is that the
measured points are in error, which is impossible to
check at this time. A second explanation might be
that the measured effluent points were correct and
internal operations, such as recycling, were respon-
sible. However, this information also was not
available. Finally, a third explanation could be
that the influent peaks did occur prior to the
effluent peaks, but were missed. This alternative is
examined below.
For this analysis, two influent points were adjusted
to creat 'artificial' influent peaks prior to the
two effluent peaks in question. The measured influent
at 12:00 P.M. on the 23rd was changed from 100 mg/1
to 270 mg/1 and the measured influent at 3:00 A.M. on
the 24th was changed from 90 mg/1 to 320 mg/1. All
tanks in operation, which were basically sedimentation
tanks, were modeled as plug flow reactors. Initial
suspended solids concentrations for all reactors
were assumed to be 10 mg/1.
It appears, by observing Figure 6, that the initial
concentrations were set too low and that it took
approximately three hours before simulated values
agree with measured values. From this time until
about 12 hours later, simulated values agree reason-
ably well with observed data. This period of agree-
ment was also evidenced in other analyses of this
same data where adjustments in the influent points
were not made. An interesting point is that these
artificial influent peaks were still unable to explain
the 'questioned' effluent peaks,and the correlation
of observed with simulated concentrations was lower.
Therefore, it appears either that these effluent
peaks did not occur, or that internal operations were
responsible.
As additional plant operating data becomes available,
it should be possible to calibrate STPSIM for other
pollutants over a range of flow conditions. These
preliminary results indicate that STPSIM can be
developed to the point where it will be a useful tool
for operating the plant.
356
-------
DETROIT WATER QUALITY INFORMATION SYSTEM
The efficient use of all of these models, especially
if real-time plant operating information is expected
in a short time frame, requires a relatively sophis-
ticated computer management system that provides for
easy access to, and updating of,the input data along
with assignment of I/O devices and proper sequencing
of the programs. The Detroit Water Quality Informa-
tion System (DWQIS) is a time sharing/batch mode
Fortran program designed to meet these needs. In
addition to SWMM, STORM, and STPSIM, the DWQIS
manages the execution of the Wayne State University
Air Quality Information System (AQIS) and the Detroit
Metropolitan Area Data System (DMADS). Efforts are
currently underway to use the ai-n pollution simula-
tion data as input to SWMM-RUNOFF to determine the
effect of air pollution washout on water quality.
The data system, DMADS, provides much of the socio-
economic input data for SWMM and STORM. The EWQIS
also stores, retrieves and updates data files on disc
and tape, using language familiar to engineers and
technicians. A program to check for probable errors
in the input data for the various models is also
being implemented as part of the DWQIS. These
features are very important if a large staff of
people with or without strong computer capabilities
are to be working on the project.
MANAGEMENT AND MODELING
Based on DWSD's experience with the Oakwood sewer
district, modeling costs for overflow quantity could
range up to $3 $5 per acre ($1.2 $2.0 per hectare)
depending on the accuracy required. These costs
include salary, fringe benefits, overhead,and computer
time. Sampling costs are expected to be a maximum of
$15,000 per outfall for a detailed sampling program
to obtain data for diurnal and seasonal variations
in quality for dry and wet weather flow. Total
sampling costs will also depend on the desired model
accuracy, quality variations among outfalls, and
sampled parameters. For the wastewater treatment
plant, a $30,000 to $50,000 sampling program should
provide sufficient model calibration data. The
estimated total modeling cost is about 0.25% of the
DWSD's estimated overflow abatement and plant expan-
sion construction costs through the year 1990.
As more overflow abatement facilities are added to the
system, a means must be found to operate the system
in a more coordinated and efficient manner. Because
of the large number of potential operational modes,
computerized analysis is perhaps the only viable
alternative to optimize waste water collection system
operations. System response model output could
provide the input data to the optimization models.
Modeling of the treatment plant will allow for
alternative nodes of operation to be simulated. Con-
sidering that DWSD treatment plant chemical and
utility costs for 1975 exceeded $6 million, an
increase in operational efficiency of as little as 1%
or 2% could easily justify the cost of modeling.
Since environmental modeling and simulation is a
relatively new tool available to assist managers in
decision making related to the planning, design, and
operation of their systems, its use is limited. To
encourage the expanded use of modeling techniques, it
is recommended that a series of mini-seminars be held
with EPA sponsershiD to explain the ramifications of
modeling to managers. The seminars should stress the
anticipated costs of modeling and the expected
benefits.
It is further recommended that additional EPA funds
be committed to research and demonstration grant
projects related to modeling and to improving the
state of the art in both waste water sampling and
flow measurement. These funds should be at least
0.5% of the monies committed for construction grants.
In addition, the grants should be 100% federally
funded for projects which will utilize models or
measurement devices within urban watersheds and in
conjunction with the municipalities or agencies
having jurisdiction over the waste water system.
In summary, modeling appears to be a viable means to
analyze waste water collection/treatment systems.
Thus, a major objective of EPA must be to encourage
model development, usage,and calibration.
REFERENCES
1. Andrews, J., "Dynamic Models and Control Strate-
gies for Wastewater Treatment Process," Water
Research, 1973.
2. Chudoba, J., Ottova, V., Madera, V., "Control of
Activated Sludge Filamentous Bulking - I. Effect
of the Hydraulic Regime or Degree of Mixing in an
Aeration Tank," Water Research, 1973.
3. DiGiano, F.A., Mangarella, P.A. , Ed., Applications
of Stornwater Management Models, Environmental
Protection Agency, EPA-670/2-75-065, June 1975.
4. Huber, W.C. , Heaney, J.P., Medina, M.A., Peltz,
W.A., Sheikh, H., Smith, G.F., Stormwater Manage-
ment Model User's Manual Version II, Environ-
mental Protection Agency, EPA-670/2-75-017,
March 1975.
5. Metcalf 6 Eddy, Inc., Wastewater Engineering,
McGraw-Hill Book Company, 1972.
6. Metcalf £ Eddy, Inc., University of Florida,
Water Resources Engineers, Inc., Storm Water
Management Model-Volumes I-IV, Environmental
Protection Agency, 1971.
7. Wisner, P.E., Marsalek, J., Perks, A.R., Belore,
H.S., "Interfacing Urban Runoff Models", Pre-
sented at the American Society of Civil Engineers
Speciality Conference on Environmental Engineering
Research, Development, and Design, Gainesville,
Florida, July 20-23, 1975.
357
-------
GENERALIZED METHOD FOR EVALUATING
URBAN STORM WATER QUALITY MANAGEMENT STORAGE/TREATMENT ALTERNATIVES
James P. Heaney, Wayne C. Huber and Sheikh M. Hasan
Department of Environmental Engineering Sciences
University of Florida
Gainesville, Florida 32611
Michael P. Murphy
William M. Bishop, Consulting Engineers
Tallahassee, Florida 32302
We are nearing completion of an EPA-sponsored study in
conjunction with the American Public Works Association
to estimate the nationwide cost of controlling pollu-
tion from combined sewer overflows and storm sewer
runoff.1 Two models, the USEPA Storm Water Management
Model (SWMM) and the Corps of Engineers' STORM, were
used extensively in this study to estimate pollutant
loading rates and evaluate various storage/treatment
alternatives.2 3 ** Detailed modeling studies were
performed in Atlanta, Denver, Minneapolis, San Fran-
cisco, and Washington, DC. This paper describes the
results of continuous simulation of hourly rainfal.1
and runoff in these cities for a wide variety of
assumed availabilities of storage and treatment combi-
nations. Results of these simulation studies are
presented as isoquants showing the technologically
efficient combinations of storage and treatment to
obtain a specified per cent pollution control. This
information is combined with cost data developed in
this study to determine the optimal combination of
storage and treatment for any desired level of control
for each of the five cities. The results are presen-
ted in a normalized form which enables engineers and
planners to derive preliminary estimates of control
costs for other cities. This information is useful
for early phases of 208 planning and for NEEDS sur-
veys. A more complete description of this procedure
is presented elsewhere.^
Simplifying Assumptions
In order to devise such a general procedure, numerous
simplifying assumptions were made. A constant per
cent BOD removal was assumed for the treatment units.
In actuality, performance would vary widely due to the
dynamic nature of the inflows. No account is taken
of the equalizing effects and treatment which occur in
storage. Cost functions are based on relatively few
actual installations. The tradeoff between treatment
plant size and pipelines is not considered explicitly.
Approximate curves fit to the results for the five
cities are extrapolated to the other 243 urbanized
areas.
Multipurpose waste management schemes are not con-
sidered. Actual costs for a given city could be quite
different than the estimates obtained using this
highly simplified procedure. However, the methodology
is general. Thus, the user needs only to substitute
more accurate local data to obtain refined estimates.
Control Technology and Associated Costs
A wide variety of control alternatives are available
for improving the quality of wet weather flows.6 7 8
Rooftop and parking lot storage, surface and under-
ground tanks and storage in treatment units are the
flow attenuation control alternatives. Wet weather
quality control alternatives can be subdivided into
two categories: primary devices and secondary devices.
Primary devices take advantage of physical processes
such as screening, settling and flotation. Secondary
devices take advantage of biological processes and
physical-chemical processes. These control devices
are suitable for treating stormwater runoff as well as
combined sewer overflows. However, the contact stabi-
lization process is feasible only if the domestic
wastewater facility is of an activated sludge type.
The quantities of wet weather flows that can be treated
by this process are limited by the amount of excess
activated sludge available from the dry weather plant.
At the present time, there are several installations
throughout the country designed to evaluate the
effectiveness of various primary and secondary devices.
Based on these data, the representative performance of
primary devices is assumed to be 40 percent 8005
removal efficiency and that of secondary devices to be
85 percent BODs removal efficiency. No treatment is
assumed to occur in storage. Hasan has synthesized
available information regarding stormwater pollution
control costs. ^ The results are shown in Table 1.
Table 1. Cost Functions for
Wet Weather Control Devices
a,b,i
Total Annual Cost: $/yr
TC - wTZ or wSZ
Control Alternative
Primary
Swirl Concentrator0' 'e
Micros trainer c'
Dissolved Air Flotation6
Sedimentation11
2,555.0
9,179.8
10,198.1
40,792.5
0.70
0.76
0.84
0.70
Representative Primary Device Total Annual Cost
$3,000 per mgd
Secondary
Storage
Contact Stabilizations
Physical-Chemical"1
24,480.4
40,792.5
0.85
0.85
Representative Secondary Device Total Annual Cost
$15,000 per mgd
High Density (15 per/ac)
Low Density (5 per/ac)
Parking Lotn
Rooftop"
51,000.0 1.00
10,200.0 1.00
10,200.0 1.00
5,000.0 1.00
Representative Annual Storage CostJ ($ per ac-in) •*
$122
0.16(PD)
T = Wet Weather Treatment Rate in mgd; S K Storage Volume in I
ENR » 2200. Includes land costs, chlorination, sludge handling,
engineering and contingencies.
Sludge handling costs based on data from Battelle Northwest, 1974.
CFleld and Moffa, 1975.10
dBenjes, et al., 1975.n
"T-ager and Smith., 1974.7
fMaher, 1974.12
8Agnew, et al., 1975.13
lit
Agnew, et al. . 197513 and Wiswall and Robbins, 1975.
For T <_ 100 mgd. No economies of scale beyond 100 mgd.
PD c gross population density, persons per acre.
358
-------
Optimal Mix of Storage and Treatment
The evaluation procedure for the nationwide assessment
consisted of relatively detailed studies of five cities:
Atlanta, Denver, Minneapolis, San Francisco, and
Washington, DC. For each city, a single storm event
for a selected catchment was simulated using the USEPA
Storm Water Management Model (SWMM). Also, one year of
hourly precipitation, runoff, and discharge rates were
estimated using the HEC STORM model.1* STORM estimates
the total volume of storm water which is treated for a
specified size of storage unit and treatment rate.
Numerous combinations were tested for each of the five
cities to derive storage/treatment isoquants as shown
in Figure 1 for Atlanta. Given the storage/treatment
isoquants and knowing the relative costs of storage and
treatment, one can determine an optimal expansion path
in terms of control costs versus percent BOD removal.
The optimal expansion path is determined by comparing
the costs of the various alternatives as shown in
Figure 1, or
.016 020
024 .026
Figure 1. Storage/Treatment Isoquants for
Various BOD Control Levels - Atlanta
(1)
where CT = unit cost of treatment,
c = unit cost of storage, and
b
MRS
ST
marginal rate of substitution of
storage for treatment.
The above problem can be expressed in the more compact
mathematical form shown below:
minimize Z - cg(S) + CT(T)
subject to f(R ;S,T) - 0
RI,S,T >. o
(2)
where Z = total annual control costs per acre,
c CS) storage costs,
c (T) = treatment costs,
S = storage volume, inches,
T = treatment rate, inches per hour,
R, = percent pollutant control, and
f(R^;S,T) = production function relating the level
of pollution control attainable with
specified availabilities of storage (S)
and treatment (T).
The storage/treatment isoquants are of the form:
_
- T1)e
(3)
where T = treatment rate at which isoquant becomes
asymptotic to the ordinate, inches per
hour,
T = treatment rate at which isoquant intersects
the abscissa, inches per hour, and
K = constant, inch
Substituting equation (3) into equation (2) and
assuming linear costs, this constrained optimization
problem can be solved by the method of Lagrange multi-
pliers to yield the optimal mix of storage,S*, and
treatment,!*, or
S*
max ( In --
] , 0)
and
T* = T +
-KS*
(4)
(5)
Note that T* is expressed as a function of S*, so it is
necessary to find S* first. Knowing S* and T*. the
optimal solution is
Z*
cgS* + CTT*.
(6)
The above optimization procedure was programmed to
generate curves (e.g., Figure 2) showing percent
pollutant removed versus total annual costs for primary
and secondary treatment in conjunction with storage.
The results indicated that the secondary treatment/
storage curves could be used to estimate control costs
over the entire range of interest. Note that, for wet
weather control, marginal costs are increasing because
of the disproportionately large sized control units
needed to capture the less frequent larger runoff
volumes. The curves shown in Figure 2 can be
approximated by functions of the form:
ke
(7)
where Z = total annual cost, dollars per acre per
year,
k,n = parameters,
R = percent pollutant removal, 0 <_ R. <_ R. ,
and
RI = maximum percent pollutant removal.
The five secondary cost curves and associated cost
functions are shown on Figure 3. Note that the control
costs per unit of runoff are much higher for San Fran-
cisco and Denver. This difference appears to be
359
-------
PERCENT POLLUTANT CONTROL, R,
Figure 2. Control Costs for Primary and Secondary Units as a
Function of Percent BOD Removal, Atlanta
WASHINGTON, D.C. - 18.49 in/yr
(50.0 cm/yr)
SAN FRANCISCO- 9.68 in/yr
(25.1 cm/yr)
ATLANTA - 16.93 in/yr
(43.0 cm/yr)
DENVER-5.90 in/yr
(15.0 cm/yr)
MINNEAPOLIS - 10.99 In/yr
(27.9 cm/yr)
10
Figure
i ~r
20 4O 60 80
PERCENT BOD CONTROL
24.7
100
3. Control Cost for Secondary Units as a
Function of Percent BOD Removal for the
Five Regions (Preliminary Results, see
Heaney, Huber, et al., 1976 for Final
Results)
attributable to the different precipitation pattern in
this part of the country. Thus, the five cities were
aggregated into two major categories. The resulting
preliminary estimating equations are shown below:
THIRTEEN WESTERN STATES
0.05R,
Z = (5.6 + 0.18AR)e
w s
0 < R, < 85 (8)
~" J- ~~
7.
e. s
1.8e
EASTERN STATES
(0.09AR + O.OSR.^
< 85
(9)
where Z , Z
e s w s
annual cost using secondary control
devices, dollars per acre, in the
eastern (e) and western (w) US,
AR = annual runoff, inches per year, and
R^ = level of BOD removal.
These equations are used for estimating the control
costs for all of the urbanized areas in the US. One
only needs to input the annual runoff, AR, and the
desired level of control, R .
Runoff Prediction for Nationwide Assessment
Techniques for predicting runoff quantities vary from
very simple methods of the Rational Method type to
sophisticated models of the nature of SWMM. The tech-
nique used in STORM is relatively simple, relying on
weighted average runoff coefficients and a simple loss
function to predict hourly runoff volumes. Nonetheless,
because of the nature of the continuous simulation in-
volved, it is at a considerably higher level, and
therefore more complex, than earlier, desk-top tech-
niques. Due to the complexities and data requirements
of STORM, it was not possible to run the model on all
cities of the nationwide assessment, or even a majority.
These considerations lead directly to the use of a
simple runoff coefficient method in which runoff is
merely a fraction of rainfall. STORM computes a runoff
coefficient, CR, weighted between pervious and imper-
vious areas by:
CR = 0.15 (1-1)+ 0.90 I
= 0.15 + 0.75 I
(10)
360
-------
where I is fraction Imperviousness and the coefficients
0.15 and 0.90 are the default values used in STORM for
runoff coefficients from pervious and impervious areas,
respectively. Note that the effect of demographic fac-
tors (e.g., land use, population density) is incorpo-
rated into the imperviousness. An equation developed
by Stankowski16 for New Jersey catchments was used to
determine imperviousness as a function of population
density, i.e. ,
I =
100
PD
0.573 - 0.039 log.,, PD
(ID
where I fraction imperviousness, and
PD population density, persons per acre.
Thus, annual runoff, AR, from precipitation of P
inches per year is
AR = CRCP) •
(12)
The generalized estimating equation will be applied to
the Cincinnati, Ohio, urbanized area to illustrate the
procedure. The requisite data are presented below1:
Demographic Data
1970 population = 1,110,000
developed area, A = 125,000 acres
population density, PD 8.88 persons per acre.
Annual Runoff, AR
precipitation, P = 34 inches per year.
Using equation (12),
AR = CR(P)
= (0.15 +
0.75[0.0963(PD)
AR = 13.0 inches per year.
0.573 - 0.039 log1Q PD
Control Costs for 60% BOD Control, R,
60%
From equation (9)
(0.09AR + 0.05R )
Z = 1.8e
e s
Z = $116 per acre per year
e s
Total annual costs
Z (A) = $116 (125,000)
e s
Conclusions
A simple procedure for evaluating urban stormwater
quality control costs is presented. This work is a
condensation of the methodology used to develop a
nationwide cost estimate for USEPA.1 A detailed des-
cription of a more refined desk-top procedure for such
evaluations will be released later this year.5
The reader is cautioned that the estimating equations
(8 and 9) are preliminary. Final results will be
presented in Heaney and Huber, et al., 1976.
10.
11.
12,
13,
$14,500,000 per year. 14.
15,
16.
References
Heaney, J. P., W. C. Huber, et al., Nationwide
Evaluation of Combined Sewer Overflows and Storm-
water Discharges: Vol. Ill, Cost Assessment and
Impacts, USEPA, 1976.
Environmental Protection Agency, "Storm Water
Management Model," Water Pollution Control Research
Series, Washington, DC, 1971.
a. Volume I, "Final Report," No. 11024DOC07/71
b. Volume II, "Verification and Testing,"
No. 11024DOC08/71
c. Volume III, "User's Manual," No. 11024DOC09/71
d. Volume IV, "Program Listing," No. 11024DOC10/71
Heaney, J. P., W. C. Huber, et al., "Urban Storm
Water Management Modelling and Decision Making,"
USEPA Contract EPA-670/2-75-022, May 1975.
Hydrologic Engineering Center, "Urban Stormwater
Runoff: STORM," US Army Corps of Engineers,
Generalized Computer Program 723-58-L2520, 1975.
Heaney, J. P., W. C. Huber and S. Hasan, "Storm
Water Management Model Level I, Desktop Analysis,"
USEPA, 1976.
Field, R. I. and E. J. Struzeski, Jr., "Management
and Control of Combined Sewer Overflows," JWPCF
Vol. 44, No. 7, pp. 1393-1415, 1973.
Lager, J. and W. Smith, "Urban Stormwater Manage-
ment and Technology: An Assessment," USEPA Report
EPA-670/2-74-040, NTIS-PB 240 697/AS, 1974.
Becker, B. C. et al., Approaches to Stormwater
Management, Hittman and Assoc., USDI Contract
14-31-001-9025, 1973.
Hasan, S., Integrated Strategies for Urban Water
Quality Management, PhD Dissertation, University of
Florida, Gainesville, 1976.
Field, R. I. and P. E. Moffa, Treatability Deter-
minations for a Prototype Swirl'Combined Sewer
Overflow Regulator/Solids Separator, IAWPR Workshop
on Design-Operator Interactions at Large Wastewater
Treatment Plants, Vienna, Austria, 1975.
Benjes, H. et al., "Estimating Initial Investment
Costs and Operation and Maintenance Requirements of
Stormwater Treatment Processes, USEPA Contract
EPA-68-03-2186 (unpublished), 1975.
Mahar, M. B., Microstraining and Disinfection of
Combined Sewer Overflows - Phase III, USEPA Report
No. EPA-670/2-74-049, 1974.
Agnew, R. W. et al., "Biological Treatment of
Combined Sewer Overflow at Kenosha, Wisconsin,"
USEPA Report EPA-670/2-75-019, NTIS-PB 242 120/AS,
1975.
Wiswall, K. C. and J. C. Robbins, Implications of
On-Site Detention in Urban Watersheds, ASCE Hyd.
Div. Conf., Seattle, Washington, 1975.
Battelle Northwest, "Evaluation of Municipal
Sewage Treatment Alternatives," Council on Environ-
mental Quality, 1974.
Stankowski, S. J., Magnitude and Frequency of Floods
in New Jersey with Effects of Urbanization, Special
Report 38, USGS, Water Resources Div., Trenton,
New Jersey, 1974.
361,
-------
MODELING HYDROLOGIC-LAND USE INTERACTIONS IN FLORIDA
Philip P. Bedient
Asst. Professor
Envi. Sci. & Engr.
Rice University
Houston, Tex. 77001
Wayne C. Huber
Assoc. Professor
Envi. Eng. Sci.
Univ. of Florida
Gainesville, Fla. 32611
James P. Heaney
Assoc. Professor
Envi. Eng. Sci.
Univ. of Florida
Gainesville, Fla. 32611
A technique is developed to describe and quantify
various hydrologic-land use interactions within a Flor-
ida river basin. Surface runoff quantity and quality
are estimated as a function of land use and drainage
patterns at several levels of resolution including the
river basin, tributary watersheds, lake basins, and
marsh areas. A hydrologic-land use model based on a
daily water balance is applied to each soil-land use
complex in the watershed to estimate soil storage and
total runoff. The overall basin response seems to be
more sensitive to the land drainage pattern than to
the condition of the narrow river flood plain.
Potential nutrient loading rates are calculated
using measured concentrations of total P and predicted
runoff volumes. The drainage density index correlates
with observed concentrations and loading rates for the
tributary watersheds. The detention time parameter
for various hydrologic components in the basin indi-
cates the potential for control of runoff quantity and
quality through on-site storage in marsh, pond, and
lake areas. Excessive drainage activities have led to
higher nutrient loads and decreased detention times in
the river basin.
Introduction
Traditional approaches to watershed analysis have
placed little emphasis on linkage mechanisms which re-
late land use and drainage conditions to resulting hy-
drologic and water quality responses in a watershed.
Measured changes in land use and drainage patterns pro-
vide a useful starting point for estimating the impact
of alternative future levels of development. Environ-
mental responses which can be measured or predicted
include the volume of surface runoff and streamflow,
and associated pollutant concentrations or loadings
which stimulate aquatic plant growth.
The main objective of this research is to describe
and quantify various hydrologic-land use interactions
which occur within a river basin, in order to estimate
the historical, present, and projected environmental
responses in the basin. This requires that a techni-
que be devised to characterize surface runoff quantity
and quality as a function of land use and drainage
patterns. Influences of soil storage, vegetative cov-
er, drainage intensity, land use, topography, and cli-
mate are directly considered in the formulation.
It is important to consider these interactions at
several levels of resolution or detail in order to
better understand the overall response of the water-
shed. Various levels which are investigated include
the river basin, lateral tributary systems, lake units,
and marsh drainage areas. Analyzing the response of
these different components allows quantification of
storage and transport mechanisms through the system.
Description of the Study Area
The Kissimmee River Basin, located in central Flor-
ida, is undergoing pressure for both agricultural and
urban expansion, while vast, undeveloped marsh areas in
the basin provide a valuable environmental resource.
This basin provides a convenient study area because of
the quantifiable land use changes and water quality
responses which have been observed over the recent
past.
The original river began near the Orlando area and
passed through a series of shallow lakes before emerg-
ing south of Lake Kissimmee as a meandering river. It
then flowed south to Lake Okeechobee through a rela-
tively narrow marsh flood plain (Figure 1). Presently,
the upper portion of the basin consists of a chain of
large lakes undergoing rapid urbanization from the sur-
rounding Orlando area. The lower basin is undergoing
transition from its undeveloped state as a marsh/swamp
system to a regime dominated by improved pasture with
lateral drainage canals. In addition to the land use
changes, an extensive flood control project has been
implemented by the Corps of Engineers with control
structures at the outlet of the lakes and along the
channelized main river.
Water quality degradation in the form of high nutri-
ent loading in one of the upper lakes and along the
river channel has been increasing over the last two
decades. There is concern for protecting water quality
since the Kissimmee River is the main inflow to Lake
Okeechobee, which provides water supply to all of south
Florida and the Everglades. Objections have been
raised by ecologists and conservation groups over the
destruction of a unique, natural meandering river and
its rich marshes, the decline of fish and waterfowl
resources, and the effect of degraded water quality on
the eutrophication of Lake Okeechobee.1 During the
past two years, intensive studies by several groups
have been underway to examine the environmental re-
source problems in Lake Okeechobee and the Kissimmee
River Basin. The development and application of envi-
ronmental simulation models along with pertinent re-
sults are discussed in the following sections.
Land Use Analysis
Land use in the Kissimmee River Basin has undergone
rapid and significant changes in the last 15 years.
Past activities in the upper part of the basin (1958)
were dominated by urban interests, especially around
the Orlando area, and agricultural interests involved
in citrus on the eastern ridge, small amounts of im-
proved pasture throughout the remainder of the basin.
The dominant undeveloped category was freshwater marsh
and swamp around the large lakes and adjacent to the
Kissimmee flood plain. The 1972 land use patterns show
about 40 percent of the land which was formerly unim-
proved pasture has been improved through diking or
drainage procedures. Large areas of marsh and swamp
have been converted to improved or unimproved pasture.
In addition, urban expansion is evident south of Or-
lando , around lake borders, and in the Disney World
area of western Orange County.
Future patterns of land use in the Kissimmee River
Basin have been projected using estimates of the Soil
Conservation Service (SCS) and the U.S. Department of
Agriculture in conjunction with a linear programming
model developed in the study. The results of this
analysis are projections, to the years 1980, 2000 and
2020, of what land use could be.
A more complete description of the land use method-
ology is available, and the results of the analysis
serve as direct input to the hydrologic-land use model
discussed below.2 The observed shifts in land use and
drainage practices have already created a series of
effects which have begun to jeopardize the region's
ability to cope with increasing runoff volumes and
degraded water quality from waste loads.
362
-------
Hydrologic-Land Use Interactions
Introduction
Relatively little research has been done on prob-
lems associated with watersheds dominated by marsh and
lake storage, extremely flat slopes, and long-term
seasonal rainfall and flooding. These are termed de-
pressional watersheds, and are most commonly found
along the Coastal Plain of the southeastern United
States. South Florida watersheds including the Kissim-
mee-Everglades region fall into this category.
Because the hydrologic response of the drainage
basin is the controlling link for land use and water
quality considerations, a hydrologic-land use model
(HLAND) has been developed which directly incorporates
land use changes and drainage practices. The model is
based on the daily water balance technique of Thorn-
thwaite and the Soil Conservation Service runoff curve
number method applied to each soil-land use type in
each subwatershed.3»4 jhe technique places primary
emphasis on soil storage and potential evapotranspira-
tion (PE) dynamics to determine surface and subsurface
runoff volumes on a daily basis. The approach is
ideally suited for modeling depressional watersheds.
Hydrologic-Land Use Model Description
The climatic water balance was first developed in
an effort to characterize the moisture condition of an
area based on a balance between precipitation (P)
which adds moisture to soil storage and evapotranspir-
ation (ET) which removes it. Knowledge of the rela-
tionship between P and ET provides information on
periods of moisture surplus (S) and moisture deficit
(D), which in turn provides data on irrigation require-
ments, surface runoff, groundwater recharge, and soil
moisture storage.
The various terms and relationships involved in the
water balance are shown in Figure 2. The budget can
be run on a monthly, weekly, or daily basis depending
on the desired accuracy. Measured values of precipi-
tation (P) and calculated potential evapotranspiration
(PE), which can be determined for a region by any one
of the available techniques, provide the initial value
of excess precipitation (P-PE).5 If this value is
positive, then soil moisture storage (ST) is increased
up to the maximum level (SM), and actual evapotranspir-
ation (AE) equals PE. A water surplus (S) is gener-
ated above the ground surface if (P-PE) exceeds (SM-ST)
for a given time increment. For this condition,
S = (P-PE) - (SM-ST)
(D
If the value of (P-PE) is negative, then a loss
occurs from soil moisture storage. The loss is not
linear, because as the soil dries, plants are less
able to remove water via evapotranspiration due to cap-
illary forces. Thornthwaite assumes that the actual
amount of removal is proportional to the level of soil
moisture content. This condition can be expressed by
an exponential relation of the form
ST = (SM) e
-(DHL x AWL)
(2)
where DWL = depletion coefficient, and
AWL = accumulated water loss.
Resulting curves for various levels of SM are plotted
in Figure 2. Thus, for the case of curve A, if the
accumulated water loss is 50 mm, the resulting soil
moisture retained (ST) is 62 mm. Because ST is less
than SM, the AE term is no longer equal to PE for the
case of negative (P-PE). Instead,
AST available moisture which can be removed
from the soil, over one time step.
The difference between PE and AE is termed the water
deficit (D).
The water balance technique is a powerful predictive
tool for areas undergoing land use and vegetative
changes, increased drainage, and/or urbanization.
Drainage of land generally causes a reduction in soil
storage, an increase in surface runoff, and a decrease
in groundwater levels, all of which can be quantified
using the water balance. Increases in irrigation re-
quirements can also be predicted based on increasing
moisture deficits from drainage.
The HLAND Model computerizes the Thornthwaite water
balance for calculation of daily runoff using daily
rainfall values from each soil-land use type in the
study area. Several additional components have been
incorporated to better represent the hydrologic re-
sponse. A more detailed description of the model and
input data is available.6
The SCS runoff curve number CN(J,K) for land use J
and soil group K is used to estimate maximum soil mois-
ture storage SM(J,K) by the equation
SM(J.K) = 1000 - 10
CN(J,K)
(A)
where
AE = P + AST
(3)
Typical values of SM in the Kissimmee River Basin range
from 2 inches for drained improved pasture to 23 inches
for some of the marsh areas.
Predicted surplus volumes do not become runoff in-
stantaneously. Rather, overland flow is delayed by
specifying that a fraction CDET(J,K) of the available
surplus will remain on the land per day. These deten-
tion constants are estimates derived from Thornthwaite
and Mather and the SCS, and vary from 0.60 for drained
improved pasture to 0.90 for marshes and swamps.7,4
These constants allow the surplus to become runoff at
an exponential rate, or in direct proportion to the
amount available. Average detention time in days can
be derived from the detention coefficients for each
soil-land use type.
Base flow contributions as a function of soil mois-
ture storage have been specifically determined for the
Kissimmee River Basin.8 The relation was obtained
through the technique of hydrograph separation for 15
years of streamflow 'data for the Kissimmee River. Base
flow is incorporated into HLAND by fitting an equation
to Langbein's relation, and partitioning the subsur-
face flows to each soil-land use complex in each plan-
ning unit. In this way, base flow is calculated as a
function of soil moisture storage on a given day, and
then subtracted from soil storage at the end of the day
If another type of base flow relation is preferred, it
can easily be incorporated into the model.
Flood Routing and Model Calibration
Extensive and costly flooding occurred under natural
conditions in the Kissimmee River Basin due to prolong-
ed seasonal rainfall, inadequate secondary drainage,
and limited outlet capacity. Tropical hurricanes,
which usually occur during the rainy season, also
served to intensify the problems. The existing flood
control project was implemented in the 1960's and pro-
vided for channelization and control structures on the
Kissimmee River and below the large upper basin lakes.
A comparison of flood hydrographs with and without
the flood control project indicates significant differ-
ences regarding both the shape and magnitude of the
response. The 1969 hydrograph is characteristic of a
developed drainage system with higher peak flows,
shorter lag times, and shorter recession times; compar-
ed to flood events prior to channelization and upland
drainage.
363
-------
The model HLAND was verified for the Kissimmee
River Basin using both 1958 and 1972 land use condi-
tions and a series of historical daily rainfall pat-
terns over the basin. HLAND calculates the contribu-
tion of total runoff to the river, and a flood routing
procedure is used to simulate either the original mean-
dering river or the present channelized regime. In
this way, it is possible to determine the relative
effects of river channelization vs. upland tributary
drainage on observed outflow hydrographs.
While sophisticated flood routing methods are avail-
able, the linear Muskingum method is ideally suited
for modeling the daily response in depressional water-
sheds where long-term seasonal effects are of primary
concern.9 Storage and travel time parameters are ad-
justed to the original river or channelized regime.
A series of calibration years, 1965-1970, was se-
lected based on the availability of data and the fact
that this sequence includes both drought and extreme
flood conditions, which provides a good test of the
accuracy of the model. A comparison of measured and
predicted streamflows for 1972 land use conditions is
depicted in Figure 3 at the gaging station near Lake
Okeechobee (S65-E). It can be seen that the model
provides a generally accurate representation of the
basin response during conditions of floods (1969-1970),
droughts (1965-1967), and average flows (1968).
Based on calibration runs using 1958 land use and
the original flood plain, the basin response seems to
be much more sensitive to the land drainage character-
istics than to the condition of the narrow river flood
plain. Overall travel times in the system were slower
under the 1958 regime because upland marsh and slough
detention provided additional storage capacity during
the wet season. The present regime induces excess
water into drainage canals at a faster rate, and HLAND
results indicate increasing percentages of surface
runoff compared to subsurface flows as upland drainage
activity increases. Thus, lateral subwatersheds domi-
nated by drainage canals tend to produce more surface
runoff than those in a more natural drainage condition,
while subsurface contributions are less under drained
conditions due to decreased soil moisture levels.
Water Quality Considerations
Monitoring Program
Water quality data have been collected in the
Kissimmee River for the past several years, and in
tributary inflows for the 1973-74 period. The monitor-
ing program was begun by the U. S. Geological Survey,
and has been continued and expanded by the Central and
South Florida Flood Control District (FCD).2
An analysis of available water quality data from
the FCD indicates that total and inorganic phosphorus
levels are the most responsive parameters compared to
nitrogen variation. Phosphorus tends to adsorb to
soil particles and is readily available for surface
transport via runoff and erosion.
Samples were taken monthly for one year for the
lower river stations and the major upper lakes in the
basin. A plot of average wet season total P concentra-
tions along the extent of the basin indicates a rapid
decline through the lake system and a further increase
along the channelized portion of the river (Figure 4).
The high levels in the upper lakes are primarily due
to nutrient loading from treated sewage effluent, and
it appears that the lakes are serving as nutrient
sinks at the present time.
The water entering the channelized Kissimmee River
is of fairly good quality, but concentrations increase
rapidly below structure S65-C. Detailed analyses of
tributary inflow quality by the FCD indicate progres-
sively higher P concentrations, especially south of
S65-C, which correlates with the observed trend in the
river. There is a need, then, to explain the observed
distribution of surface runoff and nutrient loading in
the basin as a function of land use and drainage activ-
ities.
Drainage Density and Pollutant Loading
While the hydrologic model estimates source areas
which contribute runoff volumes, non-point sources of
nutrients are primarily a function of land use, with
agricultural lands contributing relatively high loads
due to fertilization of cattle density. Loehr has
surveyed the available literature to determine relative
loading rates from various land uses.l" Potential
nutrient loading rates can be calculated for each sub-
watershed in the basin using measured concentrations of
total phosphorus and predicted runoff volumes from
HLAND. Higher loading tends to be associated with
higher runoff rates in areas of intense drainage.
Detailed analyses of land use and drainage patterns
along the lower river system indicate the importance of
the drainage density index, measured in miles of drain-
age network per square mile of land area. Drainage
density provides a useful general indicator of land use
intensity, runoff volumes, and nutrient concentration
associated with the various tributaries in the Kissim-
mee River Basin.H
When drainage density measurements are compared with
measured inflow concentrations of average total P dur-
ing the wet season, positive correlations are obtained.
Converting to phosphorus loading rates as a function of
tributary drainage density yields the significant rela-
tionship in Figure 5, Although only a limited number
of data points are available for the lower basin, the
results compare favorably with values reported in the
literature for agricultural loading rates.12 it is
reasonable to expect this result since drainage density
is inversely related to the average length of overland
flow, an indicator of potential runoff and pollutant
transport.
Storage-Treatment Concepts
Characteristics of hydrologic and nutrient cycles
can be placed into the general framework of reservoir
storage and control. Various hydrologic components in
a river basin system are distinguished by a set of
specific inflows, outflows, storages, and losses which
contribute to the overall response. The detention time
parameter, T, defined as the ratio of storage volume to
outflow rate, can be used to characterize various com-
ponents of the hydrologic system, e. g., soil, marsh,
pasture, lake, subwatershed or river.
Detention time also plays a key role in nutrient cy-
cling as it relates to treatment rates for runoff on
the land, in the soil, and in lakes or streams. In
general, the longer the detention time, the greater the
potential for nutrient uptake and/or deposition of sed-
iments. Thus, water quality control through the system
can be characterized by the length of time available
for physical, biological and chemical uptake mechanisms.
Calculated detention times from the HLAND results
average about 130 days in the soil system, and range
from 1.5 to 9.5 days for surface runoff from various
land uses. Subwatersheds characterized by intensive
drainage activity tend to have lower average detention
times, 2.2 days compared to 4.5 days for naturally
drained areas.
The flood routing technique in the river channel
uses a travel time or detention time of 3.5 days com-
pared to a possible upper limit of 9.0 days for the
original flood plain condition. These relatively short
detention times result in a low potential for nutrient
uptake in the river or flood plain alone.
Since nutrient uptake requires long detention times,
the greatest potential would occur in lakes and marsh
storage areas, which also provide a measure of flood
storage capacity. Average detention times in Lake
364
-------
Tohopekaliga south of Orlando varies from 4.0 to 6.0
months in wet and dry seasons, and can drop as low as
1.0 month during extreme floods. Although nutrient
loading is excessive to the lake, long detention times
allow for up to 85% uptake by the time the water
leaves the lake (Figure 4). If future developments
around the lake basin should cause a reduction in de-
tention time from 4.0 to 2.0 months, then uptake po-
tential could drop to 67%.
The detailed study of a marsh area above S65-D re-
veals a definite potential for flood attenuation and
nutrient uptake. Results from a marsh routing model
indicate that detention times from 3.0 to 5.0 days
provide from 30 to 55% uptake of total P, based also
on field data. Thus, marsh areas provide a signifi-
cant potential as long as routed runoff volumes
through them do not reduce detention times below 3.0
days. These concepts are presently being tested in
the basin.
In general, marsh and lake detention times are
comparable on a per acre basis to the soil system.
However, both the surface runoff and river system are
distinguished by considerably smaller values of T,
around 5.0 days for the entire river. Thus, the
potential for control of runoff quantity and quality
in the basin exists through on-site storage in marsh,
pond, and lake areas. Excessive drainage activities
have led to higher nutrient loads and decreased
detention times.
LIST OF REFERENCES
Marshall, A. R. , J. H. Hartvell, D. S. Anthony, ej al. , The Kiaaimmee-
Okeechobee Baeln. Report to the Florida Cabinet, Tallahassee,
Florida, 1972.
Heaney, J. P., U. C. Huber, P. B. Bedlent, and J. P. Bovden. Environ-
mental ReaourceB Management Studlea In the Kisslmmee River Baaln,
Final Report to the Central and Southern Florida Flood Control
District, West Palm Beach, Florida, 1975.
Thornthwalte , C. W. "An Approach Toward a Rational Claaalf Icatlon of
Cll»ata." Ceogr. Rev.. 38, 1948, pp. 55-94.
Soil Conaervatlon Service
jidbook; Hydrology,
9.
10.
Sec. 4, U. S. Dept. of Agrlc., Waahington, D. C., 1969.
Tanner, C. B. "Measurement of Bvapotranaplration," In Irrigation of
Agricultural Lands. R. H. Began et al.. eds., Amer. Soc. Agron.,
Hadlaon, Wla., 1967, pp. 534-574.
Bedlent, P. B., Hydrologlc-Land Uae Interactions In a Florida River
Baaln. Ph.D. Diaaertatlon, University of Florida, June, 1975.
Thornthwalte, C. V., and J. R. Mather. The Water Balance. Drexel
Institute of Technology, Publications in Climatology, 8(3), 1955.
Langbein, W. B. "Hydrologlc Studies," In U. S. Gaol. Survey Water
Supply Paper 1255. G. G. Parker, G. E. Ferguson, et al., 1955,
pp. 511-551.
Unsley, R. 1., M. A. Kohler, and J. L. B. Paulhus. Hydrology for
Engineers. McGraw-Hill Book Co., Nev York, 1975.
Loehr, R. C. "Characteristics and Comparative Magnitude of Non-Point
Sourcea." Water Pollution Control Fed., 46(8), 1974,
pp. 1849-1872.
Gregory, K. J., end D. B. Walling. Drainage Basin Form and Procesa.
John Wiley and Sons, New York, 1973.
Uttoraark, P, D. , J. D. Captln, and K. M. Green. Estimating Nutrient
Loading of Lakea from Non-Point Sources. Environmental Protection
Agency. Washington, D. C., 1974.
KISSIMMEE
RIVER
BASIN
Figure 1. Location Map
THE WATER BALANCE
Surplus Conditions
ACCUMULATED WATER LOSS
^
DETERMINE ST
FROM DEPLETION CURVES
\
AST
\
AE = PE II
AE = P + |AST
^
f
P-PE 2 0
IF P-PE <, O
f
D = PE - AE
\
S - (P-PE) - (SM-ST)
IF (P-PE) > (SM-ST)
Soil Moisture Depletion Cur
100
25 50 75
AWL(mm)
Figure 2. The Water Balance
365
-------
Figure 3. Calibration Curves in the Kissimmee
River Basin
I [9 16 K | 13 10 | 9
^ TOKO. -j CYPRESS K HATCI
SAMPLING STATION
s-65A s-ETTSmTTLj
KISSIUMEE RIVER J
Figure 4. Observed Phosphorus Concentrations in the
Kissimmee River Basin
34 66
DRAINAGE DENSITY (MI/SO HI)
Figure 5. Phosphorus Load vs. Drainage Density
366
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MODELING URBAN RUNOFF FROM A PLANNED COMMUNITY
Elvidio V. Diniz, Espey-Huston and Associates, Austin, TX
Don E. Holloway, Espey-Huston and Associates, Houston, TX
William G. Characklis, Rice University, Houston, TX
A management strategy for utilization of water
resources in the planned community of The Woodlands,
near Houston, Texas, is being developed by modifica-
tion and application of the EPA Storm Water Management
Model (SWMM). Selected sites on Panther Branch,
which flows through The Woodlands, and on Hunting
Bayou, a completely developed watershed within the city
limits of Houston, Texas were modeled for testing and
verification of the modifications to the SWMM.
The capacity of the SWMM to model urban runoff quantity
has been improved to include the "natural" drainage
concepts of The Woodlands and the infiltration compu-
tation model in the SWMM is now capable of operating
with a rainfall record which includes periods of zero
rainfall. Three new subroutines have been written to
operate in conjunction with the SWMM. The three sub-
routines generate normalized area-discharge curves
for natural sections, model baseflow conditions, and
model the operation of porous pavements, respectively.
Verification of the SWMM with regard to suspended
solids and BODg was attempted and modifications to
predict COD, Kjeldahl nitrogen, nitrates and phosphates
were performed.
Scope of Study
Increased runoff rates and increased pollutant loads
are two of the major effects of urbanization on the
hydrologic regime of a previously undeveloped water-
shed. The increase in impermeable areas due to urban-
ization results in high velocity surface flows which
tend to increase the potential for capture of pollut-
ants by the storm water and reduce natural infiltration
processes.
The planned new community of The Woodlands is designed
to minimize the detrimental effects of urbanization
upon the runoff characteristics of the watershed in
which it is located. Several extensive changes to the
U.S. Environmental Protection Agency Storm Water
Management Model (SWMM) had to be performed to allow
modeling of storm water runoff in The Woodlands by use
of the SWMM. The necessary changes to the SWMM
include modified computations for infiltration volumes
and pollutographs and three new subroutines to develop
normalized area-discharge curves for natural channel
sections, to model baseflow conditions, and to model
runoff from porous pavements. This paper discusses the
changes that were performed to the SWMM, the new sub-
routines that were developed, and the concurrent
modeling effort in The Woodlands. An urban Houston
watershed, Hunting Bayou, was also modeled because its
drainage characteristics are similar to those of
The Woodlands.
The Woodlands Study Area
The Woodlands is a planned urban community being de-
veloped approximately 28 miles north of Houston,
Texas in a heavily forested 17,800 acre tract in
Montgomery County. A total of 33,000 dwelling units
with a projected population of 112,000 is programmed
at project completion in 1992. A concern for nature
and convenience for people are two of the major
criteria used in the development of the General Plan
for The Woodlands, consequently, all development in
The Woodlands is based on a comprehensive ecological
inventory conducted from 1971 to 1973 . Approximately
33 percent of the total area, including all flood-
prone land, is planned for open space uses. Some of
the open space will be retained in its original state
to provide wildlife habitat, while other areas will
be maintained for park and similar recreational uses.
The Woodlands site is located in the Spring Creek
Watershed. Panther Branch, an intermittent tributary
to Spring Creek, is the major drainage channel as
shown in Figure 1. Drainage channels tributary to
Panther Branch and Spring Creek are characterized by
broad and shallow swales having very mild slopes.
^^.
;J<\ / '"'S .-V'%A,
I NK-? / ;\\\.&-r\
,—x S/'" j ki7,f.--.
WATtRSHCD DivtfC
. SUBCATCKUCNT DIVIDE
THE WOODLANDS BOUND-
' ^-4 N-V
-^;-r\
;;^-J
FIGURE I
.THE WOODLANDS DEVELOPMENT
A detailed soil survey by the U.S. Department of
Agriculture Soil Conservation Service and the Texas
Agricultural Experiment Station determined that the
soils in The Woodlands site are highly leached, acid
in reaction, sandy to loamy in texture and low in
organic content. The vegetation is typical for a
mixed woodlands of the Southern Piney Forest charac-
terized by loblolly and short-leaf pines in associa-
tion with hardwood species, including oak, sweet gum,
hickory and magnolia , The dense vegetation, sandy
soils and mild slopes result in high retention and
infiltration losses from rainfall.
The design of all drainage channels in The Woodlands
is based on the premise that typically narrow and
deep drainage ditches are undesirable. Therefore, the
existing drainage channels are utilized to the fullest
extent possible and any new channels are constructed
as wide, shallow swales and lined with native' vegeta-
tion to emulate the existing channels. Storm sewers
and drains are used in high density and activity areas
to conduct the excess runoff to the nearest drainage
channel with sufficient capacity to safely carry the
flow. To minimize increases in runoff volumes and
peaks, retention ponds are utilized whenever practical.
The net effect of this "natural" drainage system is an
increase in infiltration and storage capacity in the
channels, thereby reducing the impact of urbanization
upon the runoff regime.
Data Sampling and Sources
There are two stream stage recorders located on
367
-------
Panther Branch: Panther Branch near Conroe (P-10) and
Panther Branch near Spring (P-30) as shown in Figure 1.
Station P-10, located below the confluence of Panther
and Bear Branches, measures runoff from 25.1 sq mi of
undeveloped forest land. Station P-30 has a drainage
area of 33.8 sq mi with the developing areas of The
Woodlands (Phase I) immediately upstream.
The Hunting Bayou study area is located northeast of
downtown Houston and within the metropolitan confines
of the city. As seen in Figure 2, there are two gaging
stations: Hunting Bayou at Cavalcade Street (H-10)
and Hunting Bayou at Falls Street (H-20). The drainage
areas of Stations H-10 and H-20 are 1.03 and 3.08 sq mi,
respectively. Land use is primarily residential with
some commercial and industrial areas. There are very
few storm sewers and the major portion of the drainage
system is made up of grass-lined swales comparable to
those of The Woodlands.
where:
LEGEND
DRAINAGE DIVIDE
DRAINAGE SUBDIVIDE
DRAINAGE DITCH
FIGURE 2—THE HUNTING BAYOU WATERSHED
fc
fi
fo
k
t*
infiltration rate at time t*
initial infiltration rate
final infiltration rate
decay coefficient
time from start of rainfall to the
midpoint of the time interval At; or
t* = t + 0.5 At
The RUNOFF Block of the SWMM was structured such that
Horton's time dependant infiltration rate decay
equation would become operative from the start of
modeling time. Consequently, if the time of start of
rainfall did not coincide with the start of modeling
time, the infiltration rate would have decayed to a
lower rate by the time rainfall had begun. This may
be one reason why early investigators determined that
the starting infiltration rate was not a significantly
p
sensitive parameter . A second problem with the com-
putation of infiltration volume resulted from the in-
put of two or more high intensity rainfall events
separated by time periods of zero or low intensity
rainfall that was not capable of satisfying the infil-
tration rate. The infiltration rate would decay with-
out regard to the availability of rainfall for infil-
tration. Modeling runoff under these conditions was
difficult and consequently the infiltration computa-
tion method in the SWMM was modified.
The new computation scheme uses an integral form of
Horton's Equation and a time parameter to monitor the
progress of infiltration only.
Horton's Equation is:
The integral of
M- f0t
(1 - e'kt)
where: M accumulated infiltration volume in
inches at the end of time t
The other variables are as defined previously
During each time interval (At), the volume of water
capable of infiltrating (M
t+At
is calculated and
compared to the total volume of water available for
infiltration determined as
During storm events, streamflow quality sampling was
conducted in conjunction with flow gaging. The
samples were analyzed for a large number of parameters
including suspended solids, COD, nitrates, phosphates
and Kjeldahl nitrogen. Reconstitution of the observed
hydrographs and pollutographs to calibrate the SWMM
were attempted in the modeling effort.
Modifications to the SWMM
The SWMM was originally developed to model the hydro-
logic effects of older urban areas where an artificial
drainage system was imposed upon, and in most cases
entirely replaced, the original drainage system. In
the application of SWMM to The Woodlands, several
deficiencies in the model were encountered. The major
modifications are discussed in the following sections.
Modification to Infiltration Volume Computation
Infiltration rates are computed in the RUNOFF Block of
the SWMM by means of Horton's Equation defined as
follows:
fc (fi f0) e'kt* + f0
Dt = S, + Rt At
where: D. water volume after rainfall during
time interval At
St water volume remaining from the previous
At
R^ intensity of rainfall during At
When the available volume is greater than the infiltra-
tion volume, the excess is calculated as the volume
of water available for runoff. The results are com-
parable to those previously computed by the SWMM.
If the infiltration volume is greater than the
available volume, the time increment, At* < At, is
computed such that the infiltration volume is equal to
the available volume:
M
where:
t+At*
M.
- M.
t+At*
't ul
volume of infiltration at time t+At*
volume of infiltration at time t
volume of water available for
infiltration
and no runoff is generated for that At.
368
-------
The infiltration rate at time (t + At*) then becomes
the starting infiltration rate for the next computa-
tional time interval beginning at time (t + At).
Therefore, the elapsed time for infiltration rate
decay by Horton's Equation will not necessarily coin-
cide with the elapsed runoff computation time.
Subroutine NATSEC
In the TRANSPORT Block of the SWMM, normalized area-
discharge curves are required for flow routing.
Thirteen uniform channel shapes (circular, rectangu-
lar, trapezoidal, etc.) have their respective curves
preprogrammed through Block Data, but those for
natural sections have to be independently computed
and input to the model. Because of the large volume
of work required in preparing these curves for a
"natural" drainage system, Subroutine NATSEC was
written and incorporated into the SWMM. This sub-
routine generates normalized area-discharge curves
for irregularly shaped cross sections and for cross
sections with varying values of Manning's roughness
coefficient, n. The cross section is input to the
subroutine by means of a two-dimensional linear coor-
dinate system. Three Manning's n values, one for each
overbank and one for the channel, may also be used.
Depth increments for equal increments of area are
calculated by an iterative process.
When the depth of flow is below bank elevations, a
single application of Manning's equation is sufficient.
If the channel capacity is exceeded, the flows in
each overbank as well as flows in the channel are
computed by independent applications of Manning's
equation to each flow area. The total discharge is
equated to the sum of the individual discharges.
The output from subroutine NATSEC is a tabular ver-
sion of the normalized area-discharge curves for
natural channels and is comparable to the other
area-discharge curves in Block Data of the SWMM.
Subroutine BASFLO
The SWMM computational scheme considers all infiltra-
tion volume as permanently removed from the runoff
volume. The volume of rainfall that soaks into
vegetation debris and surface soils and which drains
out at a very delayed rate is not accounted for
because in most urban areas this interflow volume is
negligible. But, again, in the "natural" drainage
system of The Woodlands, interflow does become a
significant factor. In vegetated areas, the volume of
infiltration as computed in the SWMM includes evapo-
transpiration losses and losses to groundwater.
Interception losses may be accounted for in either
the infiltration or surface depression storage.
The portion of the hydrograph beyond the point of in-
flection (where dQ/dt -»• °°) is generally considered as
depletion of runoff volume stored in the drainage
system or watershed. As for most depletions in
nature, the rate of depletion approximates an
exponential decay and is often referred to as baseflow
recessions of the form:
Wt+At - wt e
where: Qt+At flow at end of time interval At
Qt flow at start of time interval At
k recession coefficient
The recession coefficients and their associated flow
ranges are user-supplied to Subroutine BASFLO. One
theory of varying recession coefficients for a single
hydrograph is the concept of drainage of different
n
storage units in the hydrologic system . In The Wood-
lands, both stations P-10 and P-30 exhibit 2 recession
ranges. The recession coefficients (determined from
observed hydrographs) are plotted against the flow at
start of recession and the corresponding regression
equations are derived. The coefficients of the regres-
sion equations are input to Subroutine BASFLO. All
flow rates beyond the point of inflection are determined
by consecutive applications of the recession coefficient
regression equations and the baseflow recession
equations.
Subroutine BASFLO also provides for inclusion of the
groundwater component of runoff. The groundwater flow
rate may be input as a constant, linearly varying, or
logarithmic function. All computed groundwater flow
rates are added to the runoff hydrograph with respect
to time resulting in a corresponding upward shift in
the runoff hydrograph.
The baseflow rates are substituted into the runoff
hydrograph prior to addition of groundwater flow rates.
The specific water quality loading rates are applied to
the new flow rates and the corresponding pollutographs
are computed.
Subroutine PORPAV
The Woodlands Development Corporation has envisaged an
extensive use of porous pavements in the place of
conventional impermeable pavements. Subroutine PORPAV
was developed to model the effects of porous pavements
on the runoff volume and peak flows because the SWMM
did not have this capability.
The modeling scheme consists of delineating the porous
pavement and the subgrade as two hydraulically
connected control volumes for which the inflow and out-
flow conditions are established by the equation for
continuity or conservation of mass:
ds
dt
ui T n
-rr -I 0
where:
dt
I
0
change in storage during time interval
dt
time average inflow
time average outflow
Inflow to the porous pavement area is determined as the
sum of direct rainfall onto the pavement and the over-
land flow hydrograph as computed by Izzard's method .
The outflow is the sum of vertical seepage losses, hori-
zontal seepage losses, surface runoff when the porous
pavement storage capacity is exceeded, and evaporation
losses. Vertical seepage losses are computed by the
variable head permeability equation. A modified Darcy
Equation is used to model the horizontal seepage losses
and Manning's Equation is used to establish the surface
runoff rate. The instantaneous evaporation loss rate
is computed from a time-lagged sine curve approximation
of diurnal evaporation loss rates.
Unfortunately, no data on existing porous pavements are
available. Therefore, all testing of Subroutine PORPAV
has been done on a hypothetical area.
Storm Water Quality Modeling
A thorough analysis of the available water quality data
from The Woodlands was conducted in an attempt to
define a methodology to predict runoff quality, speci-
fically nitrates, phosphates, Kjeldahl nitrogen, and
369
-------
COD. The present version of the SWMM considers these
as percentages of the dust and dirt volume. Recog-
nizing that in The Woodlands the dust and dirt genera-
tion rates are not typical of other urban areas, re-
lationships between quantity and quality of flow were
sought. Plots of cumulative pounds of pollutant
versus cumulative volume of flow indicate a strong
relationship as shown in Figure 3.A for COD. In some
cases, if availability of the pollutant is exceeded,
the upper portion of the straight line will curve up-
wards indicating that the rate of pollutant loading is
decreasing with increasing flow. Also, it was deter-
mined that total pollutant loading in units of pounds
per acre is a function of total inches of runoff as
shown in Figure 3.B for COD. The slopes of the
straight lines tend to increase with urbanization, in-
dicating an increase of pollutant loading for the same
volume of runoff. The relative magnitude of the
urbanization effects may be determined by the increase
in slope.
DISCHARGE VOLUME (ft3 x 10s)
FIGURE 3.A—DOUBLE MASS ANALYSES
FOR THE STORM OF 12/05/74 AT GAGE P-30
P-IO
P-30
RUNOFF (in)
FIGURE 3.B—TOTAL POLLUTANT LOADING RATES
The pollutant loading relationship may be used to de-
termine total pollutant mass and the cumulative
pollutant mass relationship can provide a flow depen-
dent mass transport rate. A combination of the two
functions can be used to develop a pollutograph.
This methodology to determine quality of runoff is
unrelated to the dust and dirt accumulation approach
as used in the SWMM. Consequently, the quality of
runoff computations in the SWMM would have to be com-
pletely rewritten to incorporate the new methodology.
A simpler modification involves the input of user
supplied pollutant loading rates. Initial modeling
attempts using this approach are now being conducted.
Application of SWMM to The Woodlands and Hunting Bayou
The 33.8 sq mi of drainage area upstream of Station
P-30 was divided into 57 subcatchments with an average
size of 380 acres. Physical parameters were deter-
mined from topographic maps obtained from the U.S.
Geological Survey and The Woodlands Development Cor-
poration. Certain parameters such as width of sub-
catchment and retention depths cannot be directly
determined for natural watersheds. Therefore, these
parameters can be adjusted within reason so that a
good fit exists between observed and computed hydro-
graphs. Width of subcatchment values were first esti-
mated using the method described in the SWMM User's
Manual. These values had to be reduced by approximately
40 percent because overland flow will not occur as
sheet flow over the entire subcatchment.
The parameters for infiltration modeling at Stations
P-10 and P-30 are listed in Table 1. Table 2 lists
the observed and computed peak flows and volumes and
Figures 4 and 5 compare the observed and computed
hydrographs and suspended solids pollutographs for the
storm of 12/05/74 at Stations P-10 and P-30, respec-
tively. The SWMM predicts suspended solids transport
very well at the P-10 gage, but the prediction at the
P-30 gage is not as successful. One reason may be
the transient state of construction and development in
the drainage area between the two gages. Accounting
for all construction areas and their credibility prior
to the storm event being modeled proved to be difficult.
Consequently, it is presumed that several construction
areas where the natural ground had been disturbed and
stripped of the protective vegetative cover contributed
more suspended solids than the SWMM could predict from
the available input data.
TABLE 1 — INFILTRATION PARAMETERS FOR
PANTHER BRANCH WATERSHED
STORM
DATE
10/28/74
11/10/74
11/24/74
12/05/74
12/10/74
INFILTRATION RATES
Initial Final Decay
in/hr in/hr /sec
P-10
P-30
P-10
P-30
P-10
P-30
P-10
P-30
P-10
P-30
3.5
3.5
0.3
0.3
2.0
2.0
0.5
0.5
0.2
0.2
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
.0005
.0005
.00115
.00115
.00115
.00115
.00115
.00115
.00115
.00115
TABLE 2 — SUMMARY OF MODELING RESULTS
FOR PANTHER BRANCH
STORM
DATE
10/28/74
11/10/74
11/24/74
12/05/74
12/10/74
PEAK FLOW
OBS. COMP.
P-10
P-30
P-10
P-30
P-10
P-30
P-10
P-30
P-10
P-30
cfs
342
376
979
897
680
774
273
329
464
517
cfs
360
410
600
705
645
735
315
37C
380
425
RUNOFF VOLUME
OBS. COMP.
106cu.ft.. 106cu.ft.
24.40
39.34
64.48
72.87
52.24
73.70
36.06
45.52
44.42
51.73
29.03
36.16
53.44
73.61
57.72
78.97
32.66
48.55
33.61
43.02
The 3.42 sq mi of drainage area upstream of Station
H-20 was divided into 24 subcatchments with an average
size of 91 acres. Physical parameters were determined
in a manner similar to that for Stations P-10 and P-30.
The infiltration parameters and the observed and com-
puted peak flows and volumes at Stations H-10 and
H-20 are listed in Tables 3 and 4, respectively. The
observed and computed hydrograph and suspended solids
pollutograph for the storm of 5/08/74 at Station H-20
are shown in Figure 6. During the initial phases of
the modeling program it was determined that due to
testing difficulties, BODg modeling could not be
verified.
As seen in Figures 4, 5, and 6, the computed hydro-
graphs are reasonably acceptable, but the suspended
solids pollutographs for urban areas are severely de-
ficient. Other investigators have arrived at a similar
conclusion .
370
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TABLE 3 — INFILTRATION PARAMETERS FOR
HUNTING BAYOU WATERSHED
FIGURE 4--GAGE P-10, STORM OF 12/05/74
L
TIME (hrs)
\\ OBSERVED
COMPUTED
K) 203O40506O7O60
TIME (hrs)
FIGURE 5--GAGE P-30, STORM OF 12/05/74
1r
TIME (hrs)
FIGURE 6--GAGE H-20, STORM OF 5/08/74
Future Directions
The modifications and additions to the SWMM which are
discussed in this paper indicate that the modeling of
storm water runoff quantity by the SWMM has been con-
siderably improved. The new infiltration and baseflow
models allow a closer parallel to the observed hydro-
graph.
The modeling of smaller subcatchment areas with more
definitive hydrologic regimes will provide a method
of evaluation of the capabilities of the new subroutines
and computational methods in the SWMM. This type of
data are presently being accumulated in The Woodlands.
Storm water quality modeling in the SWMM is constantly
being improved but the results are still less than
satisfactory as shown in the preceding section. The
Present size and structure of the SWMM limits the
STORM
DATE
9/08/68
9/17/68
11/09/70
3/26/74
5/08/75
STATION
H-10
H-20
H-10
H-20
H-10
H-20
H-20
H-20
INFILTRATION RATES
Initial Final Decay
in/hr in/hr /sec
1..00
1..00
0.75
0.75
2.50
2.50
0.10
0.30
0.10
0.10
0.10
0.10
0.10
0.10
0.02
0.10
.0005
.0005
.0005
.0005
.0005
.0005
.0005
.0005
TABLE 4 -- SUMMARY OF MODELING RESULTS
FOR HUNTING BAYOU
STORM
DATE
9/08/68
9/17/68
PEAK FLOW
STATION
H-10
H-20
H-10
H-20
DBS.
11/09/70 H-10
H-20
3/26/74 H-20
5/08/75 H-20
121
325
144
333
85
161
40
73
COttP.
cfs
160
355
155
365
125
220
RUNOFF VOLUME
OBS.
COMP.
10°cu ft 106cu ft
1.43 1.85
4.48 4.69
2.82 2.24
8.37 6.02
1.50 0.97
3.50 2.65
1-46 1.93
1.38 1.32
application of the new methodology described in this
paper. Therefore, it is expected that any significant
improvement in water quality modeling by the SWMM will
necessitate a complete revision of the present method-
ology.
In conclusion, the SWMM has been a valuable tool in
determining the storm water runoff characteristics of
The Woodlands. The quantity of flow has been pre-
dicted satisfactorily and the quality of flow from
undisturbed areas is also satisfactory. The modeling
of quality of flow from disturbed areas is very complex
and further detailed data and study are necessary.
Acknowledgements
This study was supported by Grant No. 802433 from the
Storm and Combined Sewer Section, EPA. Partial funds
for data collection were provided by The Woodlands
Development Corporation.
List of References
1. Wallace, Mcharg, Roberts and Todd, Woodlands New
Community Phase One: Progress Report on Land
Planning and Design Principles, April 1973.
I
2. Metcalf and Eddy, Inc., University of Florida, and
Water Resources Engineers, Inc., Storm Water
Management Model, Vol. II--Verification and
Testing, EPA 11024DOC 08/71, August 1971.
3. Onstad, C.A. and D.G. Jamieson, "Subsurface Flow
Regimes of a Hydrologic Watershed Model," Pro-
ceedings Second Seepage Symposium, ARS 41-147,
Phoenix, Arizona, March 1968.
4. Holtan, H.N. and N.C. Lopez, USDAHL-73 Revised
Model of Watershed Hydrology, ARS Plant Physio-
logy Institute Report No. 1, 1973.
5. Izzard, C.F., "Hydraulics of Runoff from Developed
Surfaces," Proceedings Highway Research Board,
Vol. 26, 1946.
6. Colston, N.V., Characterization and Treatment of
Urban Land Runoff, EPA-620/2-74-096 December
1974.
371
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MODELING IN SOLID WASTE MANAGEMENT: A STATE-OF-THE-ART REVIEW
David H. Marks
Professor of Civil Engineering
Room 1-163
Massachusetts Institute of Technology
Cambridge, Massachusetts 02139
The application of modeling for the prediction of
cause and effect relationships for policy change and
for the analysis of decisions in choosing policy levels
in solid waste management is discussed in five major
subsystems: 1) the organization of individual collec-
tion systems (routing, scheduling, distributing, crew
assignment; 2) the choice of collection technology;
3) the organization of city-wide or regional systems
(facility location); 4) the choice of process and
disposal technology; 5) estimation of waste generation
for short-term and long-term policy changes. Selected
listings of models in each area and an appraisal of the
transfer of modeling to practice are presented as well.
Introduction
The large scale system by which residential solid
waste is generated, stored, collected, transported,
processed, recovered and disposed of is a complicated
and expensive system to successfully manage. There are
many points within the system where policy decisions
about the types of technology used, level of service
offered and organization of services provided can be
made which can strongly effect the cost of the system
as well as impacts on other important objectives such
as environmental quality. However, there has been only
moderate success in gaining an overall perspective of
decision possibilities. For a detailed discussion of
structure of the solid waste management system and our
level of knowledge about cause and effect relationships
in each component, the recently completed National
Science Foundation study on Solid Waste Management
(Hudson, et al, 1974) is suggested. The purpose of
this paper is to provide some order and summary of
analytic methods available for gaining insights about
policy decisions to be made in the system. The word
model is used to imply the representation of a complex
real phenomena by a conceptual analog which is easier
to manipulate to gain understanding about the real
system. Generally in application, such models take two
forms: predictive models and decision models. Predic-
tive models are used to gain insight about the magni-
tude and direction of changes in system performance
measures brought about by changes in policy variables.
While it is possible in theory to derive such models
for Solid Waste Management inductively from assumptions
of the basic underlying mechanisms of the system, most
predictive models are deductive. That is, based on
observed data taken on system variables and outputs,
relationships are built usually using statistical
techniques or for more complex systems simulation.
Decision models on the other hand assume a knowledge
of the underlying cause and effect relationships be-
tween policy variables and system output and attempt
to address the choice of level of policy variables
based on their impacts on stated objectives. Such
models are optimization techniques such as linear
programming, dynamic programming, or search. Through-
out the discussion of models in this paper, the trade-
offs between the detailed nature of the model and the
cost of data and solution, as well as the acceptability
of the assumptions of the theoretical model in real
practice must always be kept in mind.
Modeling activity in the field of environmental
activities over the last few years has been extensive,
and solid waste management has been no exception. While
the development of the computer and its introduction as
a routine tool of practice in engineering has been an
important motivating factor in the design and adoption
of models to aid management, not all modeling efforts
need to be computer based as will be shown later. Fur-
ther, a complex model may be more difficult to transfer
than a simple one. To present in these few briefly al-
lowed pages some overview and assessment of the types
of problems in solid waste management where models have
been developed, the paper will be structured by pre-
senting major subsystems and the modeling work appro-
priate to each. An apology is made in advance that
due to space and time limitation, the author has se-
lected only five major topics, where considerable work
has been done, although there is evidence of work in
others. Also, with each major topic, either because of
lack of space or lack of knowledge of all possible con-
tributions , not all modeling work done in that area has
been presented. The five major areas discussed are:
The organization of individual collection systems
(routing, scheduling, crew assignment), The choice of
collection technology, The organization of city-wide
or regional systems (facility location problems), The
choice and design of process technology, and Estimates
of waste generation for short-term and long-range plan-
ning. This is followed by an appraisal of how well
these models have transferred from development to ap-
plication. In general, the success of transfer has not
been great because of the general difficulty encounter-
ed in several areas. One is that a strong enough effort
to transfer these models from academic and governmen-
tal research groups to actual practioners has not been
make nor is such a transfer easily designed. Even
more important, many of the models are not general
enough to transfer easily or require huge amounts of
data that are expensive to collect. Finally, many
of the decision models are based on regional cost and
do not realistically address other important issues
such as subarea cost and impact distribution.
Models for Organizing Local Collection Systems
Models for dividing up communities into tasks for
individual crews, and for efficiently routing the crews
over the street network have been developed by a number
of researchers. The work is applicable to almost any
collection system, and seems to be both complete and
thorough.
The routing problem for solid waste collection is
actually a combination of a large number of problems,
each of which can be solved with reasonable effort. At
one level, "routing" involves taking the area to be col-
lected by a crew on a day, and finding an efficient path
which will enable them to do the collection with the least
travelling. Another side of "routing" involves deciding
which crew should collect from what set of demands, and
dividing up the work to be done into task assignments.
Shuster and Schur (1974) call the former problem
microrouting and the latter districting or route-balancing;
372
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this seems to be a reasonable terminology. Microrout-
ing generally takes two forms. A node-routing problem
involves an attempt to pick up waste from a set of fix-
ed points, while travelling the least. In the litera-
ture, this is often referred to as the "travelling-
salesman problem" or the "trick-dispatching problem"
when many trucks are used. An arc-routing problem
involves travelling down all the streets, collecting
whatever is there, and again attempting to minimize the
amount of travel. This problem is known as the
"Chinese Postman's Problem," or the "m-postmen's prob-
lem" for the case with more than one route at a time.
In any routing study, the decision of what makes
a reasonable route is the important first stage. Routes
should require an equal amount of work, where possible,
and some method must be available for choosing a fair
assignment. The choice of such a fair day's work is
closely related to waste generation (see later section
in this paper), topography and demography, productivity,
level of service, and the trade-off between overtime
and incentive time. If the estimation of the work re-
quired to collect individual blocks is poor, than it
will be impossible to form balanced task assignments,
and the routing study will be useless. The best com-
pendium of methods for estimating work involved in col-
lection is that by Shuster (1973). Shell and Shupe
(1973) also discuss this issue. Hudson (1975) describes
the use of census data, which are readily available,
for estimating waste generation and collection time.
Lofy (1971) has developed a simple model for the task-
balancing problem which attempts to minimize lost time
at the end of the day.
Districting or Route Balancing
Several methods have been proposed for taking the
data on the work required in any specific area and con-
verting these work requirements into routes. These
methods may be computerized (see Hudson, 1973), but
they may also be manual. Shuster (1973) discusses man-
ual procedures for this method in detail.
Microrouting
The problem of microrouting is how to take a set
of districts, and generate detailed collection routes
from them, minimizing mileage and left-hand turns, go-
ing the correct way on one-way streets and grades, and
meeting other similar objectives.
Shuster and Schur (1974) develop a manual method
for reducing the number of left-hand turns in a route,
by making clockwise (right-hand) loops whenever pos-
sible.
More advanced methods of minimizing mileage in
collection have been developed by Strieker, (1971),
Hudson, et al (1973) and by Liebman and Male (1973).
The M.I.T. approach involves manual routing techniques,
preceded by districting; the basic output is the choice
of which streets should be traveled twice and which only
once, to minimize travel. The approach developed by
Liebman is somewhat different. Analysis is done first
on how mileage in collection can be minimized for the
whole collection area. Then the whole collection area
is subdivided into balanced districts and rerouted.
For all practical applications, the node-routing
problem reduces to an application of the Clark and
Wright algorithm developed about 12 years ago (1964).
There are other techniques available, but the Clarke
and Wright approach is both easy to understand, and
available in packaged form from most computer companies
(e.g., IBM's VSP — Vehicle Scheduling Program (1968).
It can also be applied by hand fairly easily. Beltrami
and Bodin (1974) have extended the basic algorithm to
problems involving containers with different frequencies
of collection, such as schools and restaurants on the
same route, with some success. The Clark and Wright
algorithm does not work well if the starting and ending
points of the route are widely separated, but route mod-
ification after the analysis is fairly easy.
Several companies have developed and marketed
routing packages and have made claims of tremendous
savings. In a well managed moderate sized system, some
savings can probably be realized by the implementation
of these methods. However, claims of large savings from
computerized routing usually include all savings from
the major redesign of an inefficient system. The actual
amount saved by the modeling procedures are probably
smaller.
For crew scheduling, Bodin (1972), Heller, et al
(1973), and Ignall, et al (1972) have proposed models
for making shift and day assignments. Lofty (1971) pro-
poses a model for assigning crews to routes based on
their productivity.
Models for Choice of Collection Technology
Research on the choice of vehicles for collection
has concentrated on the issues of truck capacity and age
of replacement. Techniques have been developed for
choosing vehicle capacity to minimize cost, and for esti-
mating the age at which a truck should be replaced.
Degner (1971) presents a detailed breakdown of vehicle
costs by a variety of measures such as capacity, turning
radius, type of loading, etc. After listing and analyzing
all these attributes, his work provides about the only
available detailed discussion of a method for choosing
a particular type of vehicle out of the available set of
packer bodies and chassis manufactured. The technique
used is DARE, (Decision Alternative Ration Evaluation)
which is a. performance scoring tool: a number of ob-
jectives are stated, along with their relative impor-
tance to the decision-maker. Then the available choices
are evaluated according to the objectives, and a gener-
alized score is created, giving information about which
is best. See Klee (1970) for a good description of the
DARE technique. Clark and Helms (1972) develop a model
for choice of vehicle size using data from Buffalo. They
relate capacity to cost and residences served per truck
per day and use an optimization technique to solve for
truck size. A similar model is proposed by Cardile and
Verhoff (1974). Clark and Gillean (1974) developed a
simulation model to test system configurations in terms
of truck capacity and crew size for Cleveland. Quon,
et al (1970) presents a model to show the effect of
truck age on collection efficiency. Douglas (1973), and
Degner (1971) also consider models for estimating the
economic life of a collection vehicle.
The Organization of City-Wide or Regional Systems
At issue here is an evaluation of where facilities
for transfer and processing should be located and what
form they should take, as well as the assignment of
subareas to facilities. Most of the techniques provided
for this task are optimization models based on minimiza-
tion of regional cost of facilities and transportation.
There are numerous examples such as Hekimian (1973),
Berman (1974), Weston (1973), Fuertes, et al (1974),
Helms and Clark (1970), Morse and Roth (1970), Marks
and Liebman (1971), Skelly (1968), Schultz (1968),
Wersan, et al (1971), and Vasan (1974). The two papers
on the EPA SWAMP program for regional solid waste
management presented at this conference are based on
the Skelly model. Table 1 gives a comparison of the
models according to what factors are included in costs
and the type of optimization techniques used for solution.
373
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Minimization of total cost is not, however, the only
objective in planning solid waste management systems.
Local costs allocation and impacts are also important
but not considered.
Currently, a major effort is underway in systems
analysis research on models to include social and poli-
tical objectives with a least cost economic analysis.
Examples are Fuertes, et al (1974), Kuhner, et al (1974)
and Hekimian (1973). Klee (1971) developed DISCUS, a
solid waste management game which is capable of calcu-
lating total transfer, transportation, processing and
disposal costs for a given system design. This is used
in an interactive process to help decision makers aware
of the tradeoffs involved in different decisions about
the system.
Numerous other simulation models of city-wide
organization are available including Truitt, et al
(1969), and Wersan (1965).
Models for the Choice and Design of Processes
Methods exist whereby the alternative processing
options may be evaluated so that the least-cost alter-
native can be selected. Unfortunately, the cost data
available, especially on the relatively new processes,
are often tentative, limited, or unreliable.
One method for ranking alternatives is DARE
(Decision Alternative Ration Evaluation) developed by
Klee (1970). The process requires the user to make a
number of comparisons between pairs of different eval-
uating criteria in order to develop a weighting system
for those criteria. This provides the ability to es-
tablish a uniform scoring procedure for all alterna-
tives. It has also been applied for collection tech-
nology as previously noted.
Another approach is to use mathematical program-
ming techniques in order to minimize the net present
cost of establishing a processing facility. Such a
model has been developed by Clark (1972). Clark's model
can provide an estimate of what a facility will cost
over time including borrowing costs for facility con-
struction, assuming the model given is fair representa-
tion of the taxing, borrowing, and spending policies
currently in municipal practice.
Wenger and Rhyner (1972) and Popovich, et al
(1973) use a cost-effectiveness analysis approach to
evaluate solid waste disposal systems. Essentially,
this involved first stating a set of objectives for the
system and then ranking the various candidate alterna-
tives according to this set of objectives.
Models for Estimating Waste Generation
The prediction of the quantity and composition of
solid waste is important both for short-term planning
such as route design and for long-term facility plan-
ning and technology choice. The first type of model
is concerned with the detailed local prediction of
quantities expected per collection. Alpern (1972)
developed a model using Los Angeles data relating waste
production to housing type, income and topography.
Hudson (1975) uses aggregate cross-section data to
investigate waste load changes with changes in system
policies such as frequency of collection and place of
collection, as does Quon (1968). McFarland (1972) did
simular work for income level, Clark and Toftner (1972)
worked from land use (zoning) data and DeGeare and
Ongerth (1971) describe commercial establishments.
Long range modeling is more difficult. Stern (1973)
uses an input output methodology for industrial waste
generation as does Steiker (1973).
Having described these models for different manage-
ment subcategories, it is important to consider how
well they have been transferred to real use in local
and regional planning. There are considerable barriers
to model transfer in environmental planning which must
be carefully accounted for and eased before tools such
as these will be widely used. One important barrier is
that most of these models have been developed without
much input from the users. Thus, while they may be of
academic interest, they address the wrong problem or do
not give enough information about the most important
aspects to the local users. A good example are the
regional least cost facility location models which
promise to choose the optimal system configuration for
solid waste facilities from among feasible sites on the
basis of facility and transportation costs. To most local
planners, the high external costs (real or imagined) of
such facilities make no site feasible because of local
opposition. Thus, they do not seek optimal location
but any location where they can build the facility.
Mention has been made of improving optimality criteria
for such models to include social factors which may be
one way out of this dilemma. But a better way might be
through considerable interaction with the local planner
to see what information he can use to help design plans
that have a broad base of public support and, therefore,
can be implemented. At a minimum, this would include an
estimate of disaggregated local impacts. Such inter-
action is not easy nor inexpensive. Considerable time
must be spent in establishing a good dialogue between
theoreticians who think in terms of models and computers
and local planners who are possibly distrustful of them.
We have been guilty in the past of over selling the com-
puter as a panacea that could automate planning proce-
dures and solve all our problems. However, the tools
developed just can't and probably won't ever capture all
the nuances of a specific application. For truck routing
algorithms, it is hard to input to models that some
crews are better performers than others or that some
streets are hard to access from particular directions.
Thus, we must be more careful to emphasize the use of
models to aid our intuition about the problem and to
educate planners about system tradeoffs. With local users
as partners in the development and fine tuning of models
to real use, transfer can take place. It might well
be necessary to work through a rather lengthy local case
study with each local area to which the model is to be
transferred before such tools will be widely used.
In summary, I feel at this point in time that
theoretical development must be focused on the task of
producing with interaction from local planners on simple
to use models which can use readily available data and
produce information focused on specific local situations.
More elegant algorithms developed without local input
are not needed at this point and doomed to gather dust
on the shelf and in the journals without much chance of
implementation. Rather focusing on issues such as impact
prediction, assessment of objectives of local interest
groups and means for showing graphically what the inher-
ent conflict is between differing objectives for the
solid waste system will make a more positive step toward
better model application.
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374
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Beltrami, E. J. and L. D. Bodin. "Networks and Vehicle
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-------
Barman, E. B. A Model for Selecting, Sizing, and
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Bodin, L. "Towards a General Model for Manpower Sched-
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Clarke, G. and J. W. Wright. "Scheduling of Vehicles
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Department of Civil Engineering, Massachusetts
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Hekimian, K. K. A Systems Engineering Approach to
Environmental Quality Management with Emphasis on
Solid Waste Management. Unpublished Ph.D. Thesis,
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Hudson, J. F. (Thesis).
D. J. Grossman, L. Fuertes, D. Marks. Analysis of
_Solid Waste Collection. Research Report R73-47,
Department of Civil Engineering, Massachusetts Institute
of Technology, Cambridge, Ma.: 1973.
Hudson, J. F., F. Gross, D. G. Wilson and D. H. Marks.
Evaluation of Policy Related Research in the Field of
Municipal Solid Municipal Solid Waste Management. MIT
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Cambridge, Ma.
Ignall. E., P. Kolesar, and W. Walker. "Linear Program-
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375
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SMC2(5): 664-666, November 1972.
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Klee, A. J. "DISCUS — A Solid Waste Management Game."
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125-129, July 1970.
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The American City 86(2): 100-103, February 1970.
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Klee, A. J. "The Role of Decision Models in the Eval-
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Management Science 18(2): B-52 to B-67, October 1971.
Kuhner, J. Centralization and Decentralization for
Regional Solid Waste Management: Toward Paretian
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Environmental Systems Program, Harvard University,
Cambridge, Ma. 1974.
Liebman, J. C. and J. W. Male. Optimal Routing of Solid
Waste Collection Vehicles. Department of Civil Engineer-
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Lofy, R. J. Techniques for the Optimal Routing and
Scheduling of Solid Waste Collection Vehicles. Un-
published Ph.D. Thesis, University of Wisconsin, 1971.
(UM 71-25485).
Marks, D. H. and J. C. Liebman. "Location Models: Solid
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April, 1971.
Marks, D. H. and R. Strieker. "Routing for Public Ser-
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McFarland, J. M., C. R. Glassey, P. H. McGauhey,
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Popovich, M. L., and L. Duckstein, and C. C. Kisiel.
"Cost-Effectiveness Analysis of Disposal Systems."
J. Env. Eng. Div.. Proc. ASCE 99 (EE5): 577-591,
October 1973. 7.1
Quon, J. E., R. Martens, and M. Tanaka. "Efficiency of
Refuse Collection Crews." J. San. Eng. Div., Proc.
ASCE 96CSA2): 437-454, April 1970. 4.3, 4.7, 5.1
Quon, J. E., M. Tanaka, and A. Charnes. "Refuse
Quantities and Frequency of Service." J. San Eng. Div.,
Proc. ASCE 94(SA2): 403-420, April 1968. 3.6
Quon, J. E., A. Charnes, and S. J. Wersan. "Simulation
and Analyses of a Refuse Collection System." J. San.
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Quon, J. E., M. Tanaka, and S. J. Wersan. "Simulation
Model of Refuse Collection Policies." J. San Eng. Div.,
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Schultz, G. P. Managerial Decision-Making in Local
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"Facility Planning for a Public Service System:
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-------
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Shell, R. L. and D. S. Shupe. "Work Standards for Waste
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Shuster, K.A. Districting and Route Balancing for
Solid Waste Collection. Cincinnati: U.S.E.P.A., 1973.
(To be published)
Shuster, K.A. A Five-Stage Improvement Process for
Solid Waste Collection Systems. Cincinnati: U.S.E.P.
A., 1974.
Skelly, M. J. Planning for Regional Refuse Disposal
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Ithaca, New York, 1968.
Steiker, G. Solid Waste Generation Coefficients:
Manufacturing Sectors. RSRI Discussion Paper 70,
Regional Science Research Institute, Philadelphia,1973.
Stern, H.I. "Regional Interindustry Solid Waste Fore-
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Truitt, M. M., J. C. Liebman, and C. W. Kruse. "Simula-
tion Model of Urban Refuse Collection." J. San. Eng.
Div.. Proc. ASCE 95(SA2): 289-298, April 1969. " "
Vasan, K. S. Optimization Models for Regional Public
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Research Center, 1974. (PB-231 309). 6.3
Wenger, R. B. and C. R. Rhymer. "Evaluation of Alterna-
tives for Solid Waste Systems." J. Env. Systems 2(2):
89-108, June 1972.
Wersan, S., J. E. Quon, and A. Charnes. Mathematical
Modeling and Computer Simulation for Designing Munici-
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U.S.E.P.A., 1971. (SW-6rg; PB-208 154).
Roy F. Weston, Inc., Environmental Scientists and
Engineers. Development of a Solid Waste Allocaiton
Model. West Chester, Pa.: Roy F. Weston, July 1973.
572, December 1973
Requirements
Aggregate Generation
Household Generation
Haul Distances
Coordinates
Linear Haul Costs
Haul Cost Functions
Facility Capacities
Limits on Capacity
Linear Operating Costs
Operating Cost Functions
Given Haul Routes
Reduction Factors
Fixed Costs
Growth Rates
Limitations
Local Optimum
Limited Alternatives
Linear Costs
Short-Term
No Capacity Limit
Well Defined System
Capital Costs
Extensive Data Input
Development
Weak
Probable Application
Many Authors
Simulation Model
X
X
?
X
?
X
7
X
X
X
Hekimian
X
X
X
X
X
X
X
X
X
X
X
Berman
X
X
X
X
X
X
X
X
X
X
X
X
Weston
X
X
X
X
X
X
X
X
X
X
X
Fuertes, et al
X
X
X
X
X
X
X
X
X
X
X
si
rt>
(-•
1
tp
n
H"
V
S-
X
X
X
X
X
X
X
X
X
X
y
V
Moorse & Roth
X
x
X
X
X
X
X
X
X
x
x
Marks & Liebman
X
X
X
X
X
X
X
X
V
%
(D
M
3
s
c-i
X
x
X
X
X
X
X
X
X
W
W
f^
(t>
n
t-|
w
X
x
x
X
X
X
x
V
x
O3
M
&
X.
x
x
X
X
X
x
Y
Schultz
X
X
X
X
X
x
x
X
x
x
x
x
x
s
1-1
01
B
w
0>
rt
B
M
x
x
X
Y
x
x
Y
Vasan
X
X
X
X
X
X
X
X
X
X
X
Authorship
TABLE 1: COMPARISON OF LEAST-COST FACILIIY LOCATION TECHNIQUES
376
-------
WRAP: A MODEL FOR REGIONAL SOLID WASTE MANAGEMENT PLANNING
Edward B. Herman
The MITRE Corporation
Bedford, Massachusetts 01730
An optimizing model called WRAP (Waste Resources
Allocation Program) has been developed for the
generation of minimum cost regional solid waste
management plans.
This model is addressed to the state, regional,
and local planner who is responsible for sorting out
the confusing array of alternatives available to him,
and for finding a solution which is both economically
viable and politically acceptable.
The model was originally designed in eighteen
alternative modes of operation (nine static modes and
nine dynamic modes) under a MITRE sponsored research
project.-*- WRAP is a fixed-charge linear programming
model, using an algorithm developed by Dr. Warren
Walker.2
In 1974, a basic static mode of the model was used
for a program of operational runs in support of
regional design analysis for the Commonwealth of
Massachusetts. This program used manually-generated
inputs to the algorithm, and a manual interpretation
of outputs. ^
The Office of Solid Waste Management Programs,
U.S. Environmental Protection Agency, has supported
the further development of the model. The EPA program
includes:
• the development of a computerized front end and
back end for one static mode and one dynamic mode of
the model;
• an operational test program on the Greater St.
Louis Region (the City of St. Louis and seven
surrounding counties);
• a parametric exercise program on a region of 53
communities of Massachusetts and New Hampshire; and
• documentation and dissemination.
This paper describes the model in brief and the
philosophy of its application programs. The focus of
the discussion is on the use of the model to
illuminate political and technical issues, using the
original Massachusetts application as an example. The
paper concludes with a description of a model
improvement program now underway at MITRE.
The following paper by Ms. Donna M. Krabbe of EPA
describes an analytical evaluation of the St. Louis
operational test program.
Background
Economies of scale available from two processes
from the point of view of a potential processing site
in Haverhill, Massachusetts are illustrated in figures
1 and 2. The costs are based on MITRE preliminary
haul and processing costs for the two processes. Note
that the decline in processing costs in Figure 1
compensates for rising haul costs as the region is
enlarged, and the minimum cost available is attained
at the maximum region size considered, including all
14 zones (representing 53 communities and 3600 TPD).
In figure 2, there are less economies of scale
available, so that the minimum cost is obtained with
the inclusion of only 4 zones (representing 20
communities and 1700 TPD).
Figure 1. Economies of Scale 1n Dried Shredded Fuel/Residue Recovery
Figure Z. Economies of Scale in Gas Pyrolysls (MITRE Preliminary Estimates)
Economies of scale in processing are a driving
force towards regionalization, but from
regionalization two problems are generated:
• a complexity of system design, and
• a problem of political consensus.
WRAP is addressed to both of these problems. It
is intended to:
• sort out the many alternatives on siting,
sizing, linking, and process selection for transfer
stations, primary processing, secondary processing,
and disposal; and to generate the minimum cost plan
which will meet all requirements; and
377
-------
• illuminate political issues and hence help
their resolution.
Brief Description of the Model
Figure 3 presents an overview of the model, its
inputs and its outputs. Note that both fixed and
variable costs are input. The output is a
comprehensive regional solid waste management plan,
including the selection of sites for transfer,
processing, and disposal, the selection of a process
at each site, the sizing of each site, and the
selection of links and flows connecting sources,
transfer sites, processing sites, and disposal sites.
The plan is preferred in the sense that it is the
minimum cost plan that meets all requirements, given
the sites, processes, and links that were made
available.
ZONES PROCESSING
SITES
HASTE AT EACH LOCATION
CENTROID LOCATION POSSIBLE PROCESSES
COSTS: F + V
FLOW COEFFICIENTS
MAX TONNAGE
LOCATION
COSTS: F + V
LAND AVAILABLE
OPTIMIZER
FIXED CHARGE LINEAR PROGRAMMING MODEL
.OUTPUTS:
COMPREHENSIVE REGIONAL SOLID WASTE
MANAGEMENT PLAN
A key capability of the model is its ability to
trade off the economies of scale in processing,
obtainable through centralized processing, as against
the haul costs implied by such centralization.
Essential to this trade-off capability is the ability
to represent economies of scale in process costs.
Figure 5 illustrates a concave total cost function,
typical of solid waste processing, as represented by
several linear segments. Since the model is cost-
minimizing, it will seek out the lowest cost segment
at any level of tonnage. Thus the capability of
treating cost in two parameters (fixed and variable,
or intercept and slope) permits the model to represent
economies of scale at any level of accuracy desired.
In the actual WRAP applications, three-segment
representations have been used for nearly all
processes.
INTERCEPT 3---
INTERCEPT 2
INTERCEPT 1
SLOPE:
LINEAR SEGMENT 3
Figure 5. P1ecew1se L1nMr Approximation of a Concave Function
(Representing Economies of Scale)
I LOWEST COST
• MEET ALL REQUIRMENTS
/SITE SELECTION
( TECHNOLOGY SELECTION
) SIZING
BLINKS AND FLOWS
F - FIXED
V " VARIABLE
Figure 3. Model Overview
Figure 4 describes the five levels in the model
and allowable linkages among levels. Note that
linkage from one A-level process to another A-level
process is permitted. In the St. Louis application,
this capability was used to allow a packer-to—van
transfer process to link to a truck—to-rail transfer
process. Similarly the dual C-level capability
permits the model to carry two differential residue
commodities (incinerator residue and air
classification heavy-end) into secondary processing
through dummy secondary recovery processes in which
differentiated revenues are generated. This
capability was used in the Massachusetts/New Hampshire
exercise program.
LEVEL
SOURCE
A. TRANSFER STATION
B. PRIHftnr PROCESSING
C. SECONDARY PROCESSING
D. SANITARY LANDFILL
Figure 4. Model: Levels of Processing
The model has three essential components:
Structure - which assures that each alternative
considered is feasible, handles all wastes, processes
all residues, and so forth;
Cost - which assures that each alternative is
properly costed, including economies of scale where
appropriate; and
Procedure - which is an organized search for the
best solution.
Figure 6 illustrates the operation of the model.
The basic structure is rectangular, which means that
there are more variables than equations, and hence
that the problem is underdetermined. Thus there are
many solutions. Among the many solutions to the
system of equations, only that subset of solutions
which have no negative solution values is considered
to be feasible (for a negative solution value implies
grinding up the outputs of the process and generating
its inputs). The optimal solution is that particular
feasible solution which is lowest in cost.
The structure is a system of equations that
assures that each of the solutions examined is
feasible in the sense that (1) all wastes generated
are entered into transportation; (2) all wastes
arriving at a site are processed; (3) all residues
generated are processed at the site or entered into
transportation; and (4) no process exceeds indicated
tonnage maximums.
378
-------
RECTANGULAR
•D
UNDETERMINED CASE
• FEASIBLE SOLUTION: NON-NEGATIVE
• OPTIMAL SOLUTION: LOWEST COST
SEARCH PROCEDURE
FIXED CHARGE
• WHICH STEPS IMPROVE SOLUTION
t KNOWING THAT WE HAVE ARRIVED
• DOUBLE COST ROW F + V
• ALTERED SEARCH PROCEDURE
Figure 6. Operation of the Model
The search procedure requires:
• that those steps which improve the solution can
be separated from those that make it worse; and
• that the procedure knows when it can go no
further (i.e., when it has arrived at the optimum).
The "steps" are transitions from one feasible
solution to another.
In the fixed-charge linear programming procedure,
the algorithm adds the fixed cost (to the system cost)
whenever the corresponding solution value goes from
zero to positive, and subtracts the fixed cost
whenever the corresponding solution value goes from
positive to zero. The fixed-charge algorithm
considers both fixed and variable costs in determining
whether a transition is an improvement.
The fixed-charge algorithm also requires one or
another kind of forcing to make sure that the solution
domain is searched out thoroughly, thus avoiding a
"local optimum" solution. This step is unnecessary in
standard linear programming, in which there are no
local optima. The operational runs of WRAP have used
"single forcing," in which each column outside of the
solution is forced in, and the new solution is
evaluated for improvement over the best previous
solution. The Walker algorithm also includes a double
forcing procedure in which all possible pairs of
columns outside of the solution are forced in, and the
new solution evaluated for improvement; but this
procedure is practical only for very small problems.
A new "group" forcing procedure has been designed, and
is described in the final section of this paper.
Applications: Illuminating Political and Technical
Issues
An application, which is a set of runs, is
designed to illuminate political and technical issues.
Each run in the set will:
• handle all wastes,
• meet all environmental standards (since only
processes which do meet relevant standards
are offered),
• provide the lowest cost solution for its
The "case" is a defined state of
political/technical feasibility. WRAP will generate a
plan and a system cost for each case. The incremental
costs of moving from case to case are calculated, and
in particular the costs of moving from less political
acceptability to greater political acceptability.
Figure 7 illustrates a hypothetical plan set.
D E r
POLITICAL ACCEPTABILITY -
Figure 7. The Plan Set
Figure 8 summarizes issues which have been
illuminated in the three applications which have been
completed at this writing.
REGION SIZE
MASS: LARGE REGION: HOW DOES IT BREAK DOWN
ST. LOUIS: REGION VS STATE BY STATE
PROCESS AVAILABILITY
POLITICAL
LANDFILL IN MASS. & ST. LOUIS
TECHNICAL
GAS PYROLYSIS IN MASS.
SITE AVAILABILITY
ST. LOUIS PROCESSING AT PLANT
MASS. SOUTH ESSEX SITE
MARKET AVAILABILITY
ST. LOUIS ILLINOIS POWER CO.
SENSITIVITY
TONNAGE, MARKET PRICES, PROCESS COSTS
Figure 8. Illumination of Issues
379
-------
The Massachusetts Application
Model Improvement Program
A region of 47 communities in Northeastern
Massachusetts and 6 in New Hampshire was evaluated
primarily to determine how the region would break down
under varying circumstances. The region was divided
into 13 zones for tonnage generation.
Process options were transfer station, dried
shredded fuel, gas pyrolysis, sanitary landfill, and
residue recovery.
The residue recovery process in Lowell East was
given a reduction in all intercept costs of $634.1 per
day to represent the amortized value of an EPA grant
which was obtainable only if that process was selected
at that location.
The seven basic runs in the Masschusetts
application, runs E through K, are described in Figure
9. (Runs A through D were experimental.)
Bone Run
(Optioru Available!
E Trarafor Slat ions.
Shredded Fuel,
Ga Pyrolyiii
RetiduB Recovery,
Landfill
F Tranifar Stalionj,
Shredded Fusl,
Residua Recovery,
Landfill
G Tranrfor Stations.
Shredded Fuel,
fl endue Recovery
Structure of BBEC
Run Solution
South Eitti Pyrolyiii
Lsvwence Py'olyiis
Gloucester Tranrfer Station
Lonall Eul Residue Recovery
$d.3B/(on
Landfill! in: Neviburypnrt.
E M,ddlESS)i, New Hampshire,
S.W, Central Era*. Lowell
East H endue Recovery
S7.34/ton
South Ecui Shredded Fuel
South Erax ReiiduE Recnvsry
Trenifer Ststiuns in
N ewta ury po rt . G 1 o ucaiter,
Lowell Eat, Lewrence
SI 1 23/ton
Modification of
Boiic Run
H
Double tonnage
K
Double Intercept
of Pyroiyas
1
Double tonnage
in ell zones
J
Roman South
Eioii Shredded
Fuel from
consideration
Solution to Modification Run
(Change in Baac Solution)
Additional Transfer
Stationi m;
Newburyport, Lowell E.
OtherwisB the fame $3.45/lon
Pyrolysii in Liwrenci only
Additional Transfer
Otherwiie the ume SB.85/ton
S. EBei,Newburyport,
Lowei! East, Gloucester,
Lowell Eeit Residue
Recovery SS.Wton
Lawrence Shredded Fuel,
TraniferStetiomin.
S. Etwx. Gtouctsta..
Lowell E. Reiidue
Rncovery$10.fl6/tDn
Figurg 9 Summary ol Mttuchuutt] Rum
Note that:
• with all options (run E) gas pyrolysis was
selected in two locations;
• with gas pyrolysis removed (run F) landfill
was selected in six locations for an incremental $3
per ton (gas pyrolysis was not quite in the state-
of-the-art as of the time of the analysis);
• with landfill removed (run G) (it is of
questionable political acceptability in Northeastern
Massachusetts) shredded fuel was selected in one
location for an incremental $4 per ton (or an
incremental $3=50 per ton with a Lawrence location
as in run J); and
• doubling the pyrolysis intercept (run K)
reduced the number of processing locations from two
to one, and added a transfer station.
Ms. Krabbe will present an analytical evaluation
of the St. Louis operational test in the following
paper.
The Massachusetts exercise program has been
described in an earlier paper.4
As the EPA-supported model development program
neared completion, opportunities for improvement of
WRAP were identifed. MITRE internal funds have been
made available for the initiation of two of these, as
follows:
• A marketing version of WRAP, called RAMP
(Recovery and Market Planning Model) has been designed
and carried through initial development, a stage in
which it can be used by MITRE in its operational solid
waste planning work. The model has been run several
times in support of a an ongoing planning study for
the Commonwealth of Massachusetts. RAMP provides a
marketing capability, with multiple commodities,
multiple -market locations, and multiple marketing
segments, with upper bounds. The model traces the
effects of market saturation, and determines the
impact on the preferred solution that results
therefrom. RAMP generates specific transportation
activities linking the various processing centers with
the various markets.
• An improved forcing procedure called "group
forcing" has been designed, and program specifications
for it have been developed. Group forcing will take
advantage of the structural features of WRAP and RAMP
to generate a better solution (i.e., a reduced
probability of a local optimum) in less running time.
An essential aspect of group forcing is the necessity
to define forcing groups of columns which are adjacent
extreme points relative to one another; and it is this
aspect of the technique that is model-specific (i.e.,
relates to WRAP and RAMP only). Forcing groups will
be forced both in and out, whereas the Walker
Algorithm forces in only, and only one or two columns
at a time.
Through use of group forcing, it will be possible
to explore the solution domain with both greater
effectiveness and less running time.
The two improvements together should provide a
substantial improvement in the capability to define
preferred solutions to real problems.
Notes
1. This design was reported in MITRE Report M73-111,
Edward B. Herman, A Model for Selecting, Sizing, and
Locating Regional Solid Waste Processing and Disposal
Facilities, October 1973.
2. Warren Walker, Adjacent Extreme Point Algorithms
for the Fixed Charge Problems, Dept. of Operations
Research, College of Engineering, Cornell University,
January 30, 1968.
3. The runs were reported in , Edward B. Berman and
Harold J. Yaffe, MITRE Report MTR-2945, Regional
Design Analysis for Regional Resource Recovery System
for Northeastern Massachusetts, November 1974.
4. Edward B. Berman and William M. Stein, The MITRE
Solid Waste Management Planning Model: A Status
Report, Presented at the Sixth Annual Northeastern
Regional Antipollution Conference, College of
Engineering, University of Rhode Island, July 8-9,
1975. A MITRE report by the author, WRAP - A Model
for Regional Solid Waste Management Planning:
Documentation of Operational and Exercise Runs, is in
final stages of preparation.
380
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ST. LOUIS: AN APPLICATION OF WRAP
Donna M. Krabbe
Operations Research Analyst
Office of Solid Waste Management Programs
U.S. Environmental Protection Agency
Washington, D.C. 20460
ABSTRACT
A mathematical model called WRAP, Waste Resources
Allocation Program, was developed to aid regional
solid waste planners in sorting through the myriad of
problems and possible solutions that they find con-
fronting them. The true purpose of the model is not
to find the optimum solution, but to use it to find a
structured series of solutions which will clearly show
the impact of decisions made concerning major issues.
This paper discusses the series of model runs
done for the East-West Gateway Coordinating Committee
to illuminate some of the major issues confronting
the decision makers in the St. Louis area.
BACKGROUND
States, regions, counties, cities and towns
across the country are facing critical questions
about what to do with solid waste. How can we plan
systems that dispose of these wastes? Which of the
many disposal options is the best? Which will meet
environmental objectives as well as provide the least
expensive solution? These questions are particularly
difficult to answer when a plan must be developed for
a region consisting of a number of municipalities, a
large area, and a complex transportation network.
Many options are available today, or are rapidly
emerging for consideration. In addition to new tech-
niques in landfilling and incineration, there are
numerous resource recovery technologies, which can,
for example, process mixed waste to produce energy
products like steam or dry fuel as well as recover
additional materials for marketing. Within the next
several years, more technologies will become avail-
able.
Each of these technologies has distinct economic
advantages and disadvantages, and the suitability to
a particular area is dependent upon a number of
factors. Among these are the existence and proximity
of markets for the various reclaimed products, the
existence of sufficient amounts of waste to warrant a
particular processing technology and to utilize the
economies of scale inherent in that process, and the
availability of land.
The array of options is confusing yet deci-
sion makers must be informed about the full system
cost of the major options available to them. Most
importantly, decision makers must be able to determine
the economic effects of varying and changing elements
of the system, according to specific desires and
needs.
A computer model called WRAP, Waste Resources
Allocation Program, has been developed in order to
assist decision makers with these and other compli-
cated considerations. The model enables its users
to sort out all the various options and generate and
cost a number of solid waste management plans. Plans
are expressed in terms of location and capacity of
sites and processes, and the total flow of waste in
the transportation network. Total annual cost of the
system and cost per ton are computed. One of the
most important features of the model is that it can
be used to guide the decision making process in the
selection of alternative systems and translate the
impact of this selection into cost figures.
APPLICATION OF WRAP
Although WRAP is an economic, optimizing model,
its power lies not in selecting the solution for a
regional area, but in allowing a decision maker to
analyze the impact of his decisions. This is accomp-
lished by structuring and executing a series of runs
which will induce the model to react to changes of
basic assumptions or decisions by generating and
costing an alternate set of plans. The incremental
cost of one plan over another is the cost of that
decision or change of conditions.
What this approach to WRAP offers is an effec-
tive combination of optimization and gaming. One uses
the model iteratively to examine issues and decisions
(gaming) but at each step many options can be made
available, with the best combination being selected
(optimization).
ST. LOUIS
Under the sponsorship of the Office of Solid
Waste Management Programs, the model was applied to
identify and illuminate issues in Greater St. Louis,
where the Union Electric Co. is proposing to install
an 8,000 ton per day resource recovery system using
the shredded fuel process developed by them. The
proposed system included the marketing of the re-
covered fuel to Union Electric's power generating
stations within Greater St. Louis. A local regional
planning agency, the East-West Gateway Coordinating
Council, requested EPA to fund an application of the
model to provide further insights into the advan-
tages to the communities of participating in such a
plan.
WRAP IN ST. LOUIS
Preparation of the WRAP application was a joint
effort among the East-West Gateway Coordinating Coun-
cil, the Union Electric Co., the Mitre Corporation
and EPA.
The WRAP model was used to analyze the 450 square
mile area of Greater St. Louis, encompassing 185 muni-
cipalities, and roughly two and one-half million peo-
ple, producing an estimated 8,000 tons per day of
residential, commercial and industrial waste. 185
landfills and dumps, and two incinerators currently
provide inadequate disposal services to the area,
often in violation of environmental regulations.
The Union Electric Company is proposing a large
resource recovery system using the shredded fuel
381
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process (shredding, air classification, magnetic
separation of ferrous metals) developed by them,
including the marketing of the fuel to Union
Electric's steam generating stations within the
region.
THE ISSUES
The solid waste planners at the East-West Gate-
way Coordinating Council identified the following
primary issues which needed to be investigated:
1) Will the Union Electric shredded fuel
process be competitive with landfill?
2) Should processing for shredded fuel be at
the utility sites or at other locations?
3) What would be the impact of restrictions
upon interstate flow of refuse and
and shredded fuel?
4) What would be the effect of the loss of
the Illinois Power company as a potential
market?
5) How would a refusal by some large com-
mercial haulers to participate affect the
system?
SETTING UP THE APPLICATION
Data for the application was drawn largely from
an earlier report prepared for the East-West Gateway
Coordinating Council. The data comprised costs of
the proposed Union Electric process, the Bureau
of Mines residue recovery process, transfer sta-
tions, landfills, and truck and rail haul, as well
as revenues from the sale of recovered material and
energy, and waste generation rates. The region was
divided into 29 districts for waste generation and
possible transfer and processing sites were located.
Structuring of the model runs was, of course,
the critical step in obtaining insight about the
issues to be examined. The number and purpose of
the runs needs to be defined in order to give struc-
ture to the analysis process, but the modeler
must remain flexible about eliminating and adding
runs dynamically as the runs progress.
Originally six runs were anticipated for the
St. Louis problem. During the course of the analy-
sis, one run was dropped as irrelevant, but three
more were added to examine collateral issues. These
runs are listed in Table 1.
Table 1. Summary of St. Louis Runs
A
A-l
B
B-l
C
D
E
F
F-l
Base Case (Off-Site)
B. C. with rail haul
Landfill available
L. A. with rail haul
No Interstate Flow
Loss of Illinois Power
Reduced Tonnage
On-Site Processing
On-Site Expanded
$1.253 per ton
1.440 per ton
1.249 per ton
1.610 per ton
1.840 per ton
Not Run
1.750 per ton
1.950 per ton
1.590 per ton
For each of the above runs, WRAP generated a
solution consisting of system costs, process and site
selections, and transportation activities.
ANSWERS TO ISSUES
Is Shredded Fuel Competitive with Landfill?
This first question is answered by a comparison
of the A and B runs. The cost of a total resource
recovery system (Run A) is $1.253 per ton. When
landfill was offered (Run B), it was selected to
handle only .5% of the waste of the entire region
and cost was reduced by only $.004 per ton.
The systems selected in A and B were almost
identical and were off-site processing for shredded
fuel. Included in these runs was the assumption that
fuel produced at off-utility sites would be trucked to
the closest utility location from each site that was
chosen for processing. The solutions in A and B
resulted in all of the fuel being trucked to the same
utility site (there are two in the region), exceeding
the capacity of that site. This then raised a col-
lateral issue of the method of haul for fuel pro-
duced off-site.
Should Fuel Be Hauled by Truck or Rail?
Runs A-l and B-l were added to the planned se-1
ries of runs to correct the capacitation problem of
A and B by changing the truck haul of fuel to rail
haul. This change did indeed have the desired effect.
Rail haul caused the waste to be sent to both utility
sites. Comparison of the A-l and B-l runs show that
the availability of landfill does not benefit the
region. We can safely conclude that resource
recovery is competitive with landfill for the region.
Should Processing Be At The Utility Sites?
This question is really answered by the fact that
the base case (A-l) which offers both on-site and off-
site processing selected off-site processing. What,
then, would be the incremental cost of on-site
processing? To answer this question Run F was used to
force a selection of on-site processing. Cost in-
creased by $.51 per ton. The solution'in F, however,
showed a curious selection of only one utility site
for shredded fuel processing. Thus, another issue
was raised.
Should Only One Utility Site Be Used for Shredded Fuel
Processing?
The utility site which was not selected in Run F
was actually closer to many of the waste centers, but
it was constrained to a maximum input of 2,000 tons
per day of raw refuse. Was this capacitation con-
straint the cause of its rejection? What would
happen if it was expanded? Run F-l raised the con-
straint to slightly more than 4,000 tons per day.
The result was the selection of processing at that
site at full capacity with the remainder of waste
going to the second utility site, and a cost reduc-
tion of $.36 per ton.
The comparison of F and F-l tells us that enough
transport cost can be saved to justify the capital
expenditure at the first utility site if the capacity
is at least 4,000 tons per day, but not if the size
of the facility is too greatly restricted (i.e.,
2,000 tons per day). The fact that the model
selected full utilization of the facility also
indicates that greater savings might be achieved if it
were expanded further.
382
-------
Because F-l has a more desirable solution than F,
it should be used in answering the question of on-
site vs. off-site processing. Comparison of A-l
and F-l show, of course, that off-site processing is
still more desirable, and that,the cost of on-site
processing is $.15 greater than off-site processing.
Figures 1 and 2 show the geographical ramification of
the on-site/off-site controversy. Both flows from
generation point to initial offload point, and the
transfer network of flow from initial offload point
are shown.
Figures 3 and 4 depict the comparison of on-site
processing at one site only and the better system of
processing at both sites.
What Impact Would Interstate Restriction Have?
The impact of interstate restictions on the flow
of refuse was assessed by comparing Run C with the
base case (A-l). There was no interstate transport
of raw refuse in the base case solution, so the
changes in the system and the incremental cost, $.40
per ton, are the result of the restriction on trans-
port of primary processing residue which had to be
shipped to a central secondary processing site in
Missouri. The secondary process is beneficial enough
that the model decided to construct a facility for
this process in both Missouri and Illinois when resi-
due flow was restricted.
What Mould Be The Effect of Only One Market for
Shredded Fuel ?
In the base case run, the model had available to
it markets both in Missouri (Union Electric) and
Illinois (Illinois Power). The model selected only
use of the Missouri market and, therefore, this ques-
tion is irrelevant.
What Effect Would A Drastic Change in Volume of
Raw Refuse have on the System?
To examine the impact of a reduction of raw
refuse entering into the system, Run E was
designed. Such a question is relevant because
much of the waste in the region is controlled by large
private collection companies. It is essential to know
what impact their nonparticipation, for whatever rea-
son, would have upon the system. Comparison of the
Run E solution to the base case indicates that the
location of primary processing should be shifted fur-
ther out from the city center if less waste is anti-
cipated. This is due to the fact that much of the
waste to be lost would be the commercial waste con-
centrated in the downtown business centers. Loss of
of this waste would increase the system cost $.31
per ton.
CONCLUSION
Perhaps one of the greatest insights obtained
by using WRAP in the St. Louis region is that the
incremental cost of most decisions is going to be
small compared to experiences of other areas in the
country. The model shows the decision makers that
they can have a great deal of flexibility in re-
ordering the design of their system when confronted
with unchangeable real-world situations. For in-
tance if off-site processing is unacceptable to
the community, on-site processing is a viable
alternative for only a $.15 per ton higher cost.
While all of the unfavorable alternatives and con-
straints examined for the region increase the cost of
operation, none has so drastic an effect that it
mandates radical changes or abandonment of the
resource recovery system planned. This provides
decision makers with the required framework in
which to confidently proceed in the final design
of a workable solid waste management system.
The work in the St. Louis area illustrates how
WRAP can be used effectively to sort out the best
solutions from a staggering array of possibilities.
Decisions that would oftentimes be made on political
considerations can be based on solid analytical tech-
niques when using such a sophisticated tool. A model
such as WRAP can help decision makers discover the
best, minimum cost system, as well as the cost of
deviating from that system. Realization of the
true impact of their decisions will lead decision
makers to wiser choices.
BIBLIOGRAPHY
WRAP, Waste Resource Allocation Program. Washington,
U.S. Environmental Protection Agency Publication (in
preparation).
WRAP, User's Guide. Washington, U.S. Environmental
Protection Agency Publication (in preparation).
WRAP, Programmer's Manual. Washington, U.S. Environ-
mental Protection Publication (in preparation).
WRAP. Operational and Exercise Runs. Mitre Corpora-
tion; Bedford, Massachusetts (in preparation).
383
-------
FIGURE 1: SHREDDED FUEL PROCESS: OFF UTILITY SITE
FLOWS TO INITIAL OFFLOAD POINT • THE ST. LOUIS REGION, RUN A-l $1.44 PER TON FLOWS FROM INITIAL OFFLOAD POINT THE ST. LOUIS REGION, RUN A-l
DISTRICT
DISTRICT BOUNDARY
CITY/COUNTY BOUNDARY
DISTRICT CENTROID .
CITY/COUNTY CENTROID
SANITARY LANDFILL
TRUCK TRANSFER
TRUCK CONTAINER TRANSFER
®
GO
00
FIGURE 2: SHREDDED FUEL PROCESS:
FLOWS TO INITIAL OFFLOAD POINT : THE ST. LOUIS REGION, RUN F-l $1,59 PER TON
OlSTllCT
CUT/COUNTY •OUNDAXY
OlSTllCT CtNTIOICT
CITY/COUNTY CINTtOlO
SANHAtY IANOMU
O DISTRICT CENTROID
•(f CITY/COUNTY CENTROID
(S) SANITARY LANDFILL
(C) TRUCK CONTAINER TRANSFER
UTILITY SITE
FLOWS FROM INITIAL OFFLOAD POINT • THE ST. LOUIS REGION, RUN F-l
DIITBICT
DISTRICT BOUNDAKY
---- CITT/COUNTY 60UNOAIY
O DrSTRICT CENTROID
-------
FIGURE 3: CAPACITY CONSTRAINED AT MERAMEC (U.)
FLOWS TO INITIAt OFFLOAD POINT : THE ST. LOUIS REGION, RUN F $1.95 PER TON FLOWS FROM INITIAL OFFLOAD POINT : THE ST. LOUIS REGION, RUN f
DISTRICT
DISTRICT BOUNDARY
CITY/COUNTY BOUNDARY
DISTRICT CENTROID
CITY/COUNTY CENTROID
SANITARY LANDFILL
TRUCK TRANSFER
TRUCK CONTAINER TRANSFER
p nucK TtAwrn now
UTIIITY
RAIL TBANIFIR
DISTRICT.
DISTRICT BOUNDARY
CITY/COUNTY BOUNDARY
DISTRICT CENTROID
CITY/COUNTY CENTROID
SANITARY LANDFILL
TRUCK TRANSFER
TRUCK CONTAINER TIAN5FE*
UTILITY
RAIL TRANSFER
4: CAPACITY EXPANDED AT MERAMEC (U.)
FLOWS TO INITIAL OFFLOAD POINT • THE ST. LOUIS REGION, RUN F-l
DISTRICT CCNIHOID
cnY/couNir CENTROID
JANUARY LANDFILL © UTILITY
TRUCK TRANSFER 0 RAIL TRANSFE'
TRUCK CONTAINER TRANSFER
$1.59 PER TON
FLOWS FROM INITIAL OFFLOAD POINT THE ST. LOUIS REGION, RUN F-l
4
* ClIY/COUNTY CENTHOID
® SANITARY LANDFILL (Tj)
® TRUCK TRANSFER 0
© TRUCK CONTAINER TRANSFER
-------
DEVELOPMENT OF A MODEL FOR AN ORGANIC SOLID WASTE
STABILIZATION PROCESS ON A PILOT PLANT
D.S. Whang
Division of Water Resources
New Jersey Department of Environmental Protection
Trenton, New Jersey
G.F. Meenaghan
Office of Research Services
Texas Tech University
Lubbock, Texas
Abstract
The expansion of commercial production of fed
cattle has resulted in a severe source of pollution and
hazard to health. The bio-stabilization of organic
solid waste is one of the few disposal processes which
recover the organic fraction of the wastes. In spite
of the potential value of this process, lack of engine-
ering information has hindered its utilization and ap-
plication. For this reason, an investigation was in-
stituted to ascertain the kinetic and generalized model
of the system.
A small pilot plant was used for the purpose of
this study. The data obtained from this unit was anal-
yzed with a computer model called COMPOST. The result
of this analysis and modeling indicated that the be-
havior of bio-stabilization model was consistent with
the reaction model of forming an intermediate organism-
substrate complex under a quasi-equilibrium condition.
A mathematical model of the overall process was devel-
oped, which could be used for optimizing the design
of the process. The culmination of this research re-
sulted in the development of a system model which pre-
dicts the behavior of the bio-stabilization process.
The kinetic model obtained may be used as a. model to
study the bio-stabilization process on an industrial
scale. Particular attention should be devoted to
scale-up factors for industrial application.
Introduction
The treatment and disposal of waste from the op-
eration of livestock industry has come to the fore as
a matter of considerable importance in pollution con-
trol. The problem is attributable to the increasing
concentration and quantity resulting from the mass pro-
duction of fed cattle. There are two major factors
that must be considered in attempting to solve a pol-
lution problem: a treatment process must be economic-
ally feasible for operation and it must satisfy the
conservational criteria for the receiving environment.
As emphasized by the Federal legislation concerning
solid waste management, the ideal scheme of a pollution
control process would be ultimate recycling of all
wastes generated.1 The bio-stabilization of the organic
wastes, commonly called composting, is an excellent
example of a pollution control process which recycles
wastes.
Even though the composting has a long history in
its application, there is no published work in the area
of the kinetics and modeling of the process which, from
a chemical engineering point of view, may be a control-
ling factor in the design and optimization of the pro-
cess. Once the kinetic behavior of the process has
been defined, a mathematical model for the overall
system could be used for the optimization of the entire
process.
A small composting pilot plant was used to ob-
tain the kinetic data for this study. The enzymatic
kinetic theory has been applied for the analysis of the
kinetic data obtained. A mathematical model for the
system has been developed and verified using the results
of the kinetic analysis to simulate the bio-stabiliza-
tion process of the organic waste treatment. The pur-
pose of this investigation was to ascertain a kinetic
model of an organic solid waste stabilization process
and to develop a generalized system model in an attempt
to provide rational information for the optimization of
the process.
Theoretical Considerations
The Optimum Reaction Conditions
Approximately half of all urban wastes and some
industrial wastes can be bio-stabilized to a sanitary,
humus-like material?• As the reaction proceeds, the
causative organisms use nutrients in the organic
wastes and develop all of the protoplasm and energy
necessary for the metabolism. Approximately one-third
of the carbon in the organic wastes serves as a source
of energy. The conversion of the substrates into
energy causes a rise in temperature. The magnitude of
the temperature rise is an indication of the intensity
of the microbial activity, accelerating the reaction
rate.
The activity of the micro-organisms is highly
dependent upon the environmental conditions to which
they are subjected. Among these are temperature,
moisture, pH, aeration and nutrients.3 The optimum
temperature range for most cases has been found to be
50 to 70° C. It has been known that aerobic assimila-
tion can occur at any moisture content between 30 and
100 percent. Aeration can be used to reduce excess
moisture in the decomposing material and at the same
time provide the required oxygen for the microbial
activity. Particle size also effects the efficiency
of the areation. Among the elemental requirements of
nutrients, carbon and nitrogen are of major concern,
especially the carbon to nitrogen ratio .4
The end product of the bio-stabilization is a
humus material by which the organic wastes are re-
turned to the ecological cycle in a productive form.
The organic wastes usually consist of carbon, hydrogen,
nitrogen and oxygen. Despite the differences in reac-
tion mechanisms, the overall reaction is similar to
that of a catalyzed oxidation reaction of organic
elements.
Development of the System Equations
The enzymatic kinetic theory, developed by
Michaelis and Menten,5has been applied for the develop-
ment of a system equation, i.e.
k2c
(D
where,
ki + c
ki= kinetic constant
r = reaction rate
c = concentration of substrate.
386
-------
On the other hand, based on an inert material, namely
ash, and for a batch operation of the system under con-
sideration (see Figure 1), a material balance of the
substrate for the system results in the following equa-
tion:
dt
(2)
where,
w = weight of ash in the system
t = time.
Combining Equations (1) and (2), since w is a time-
independent constant in the system, one obtains
and
Y (Z) = ±. (6)
CD
Then, the initial condition, c (o) = CQ) becomes
Y (0) = 1 (7)
and Equation (A) becomes
Z = Jin Y + ~ ( Y-l ) (8)
Kl
Equation (8) is a dimensionless system equation with
a dimensionless initial condition, Equation (7). This
equation competely describes the behavior of the com-
post system under investigation.
(3)
Th,e initial condition of the Equation (3) is c(0) = co.
Solving Equation (3) using the initial condition,
t = T-
( C-C-)
(4)
Equation (4) completely defines the behavior of the
system under consideration if the kinetic constants,
ki and kz, are known.
Transformation of the System Equation
If one defines the dimensionless time and concen-
tration as follows;6
"
fr
(5)
Experimentation
Description of the Pilot Plant
A small pilot plant as shown in Figure 1 was
used for the purpose of this investigation. The pilot
plant consisted of an oxygen supply system, a humidi-
fier, and a reactor. Humidified air was supplied to
the reactor by a perforated pipe which was attached to
the bottom of the reactor. The reactor was insulated
with a coating of Eagle Pitcher cement to prevent bio-
logical energy loss. The reactor was rotated by a
gear-reduction-motor to provide mixing and aeration of
the reactants.
An opening was made on the top of the reactor to
facilitate manual filling and emptying of the reactant
material. An exhaust port welded onto this opening pro-
vided access to the inside of the reactor for the
sampling for the elemental analysis of carbon. The
maximum capacity of the pilot plant was 60 kilograms
per batch.
Humidified gas
Air
Pressure
gauge
Pressure
regulator
Safety Vdlve
2" •
a
o
a
0
a
o>
1
33
O
22
Vent Water
Figure
The Pilot Plant
387
-------
Raw Material
Cattle manure from the Texas Tech University Ex-
perimental feedlot was used as the raw material for this
investigation. In general, the fresh manure contained
85 percent moisture and 15 percent volatile and fixed
solids. Grab samples from the surface of the feedlot
were directly loaded to the reactor. The age of the
manure ranged from three to ten days.
Chemical Analysis
Grab samples were taken from the reactor to anal-
yze the change of elemental carbon concentration with
respect to time. A CHN analyzer, Model 185, manufac-
tured by Hewlett Packard, Avondale, Pennsylvania, was
used to analyze carbon content of the samples. The
content of carbon, measured as grams of carbon per
gram of ash, was used as a system parameter for the
development of the system model.
The samples for chemical analysis were dried in
a Bleeder-Vacuum chamber under a vacuum of 20" mer-
cury at a room temperature for 72 hours. The dried
samples crushed to 48 mesh for the analysis. Cyclo-
hexane 2, 4-dinitrophenylhydrazone (CeHioiN.NH.CeHs
(N0z)2) was used as a standard reference sample to pro-
vide calibration data.
Operating Conditions
Samples were loaded manually to the reactor
through the opening. The sample weight ranged from
34.5 kg to 49.5 kg. The supply gas for oxygen was
saturated with water. The pilot plant reactor was
turned one to three times every day to provide proper
mixing and aeration of the reactants. All experiments
were conducted on a batch basis. A summary of the
operating conditions of the experimental scheme is
shown in Table 1.
Table 1. The Operating Conditions of Reactor for
the Stabilization Reaction
Experiment No.
Sample weight, kg
Source of oxygen
Frequency of mixing,
per day
Gas flow rate, 1/min
Moisture, percent
49.5
Air
1
3
63
34.5
Oxy.
3
6
52
34.5
Oxy.
1
6
52
Results and Discussion
The results of the chemical analysis and the
change of carbon concentration with respect to time
are shown in Figure 2. The reaction rates were deter-
mined by measuring the tangent of the curve for each
experiment. The "symmetric mirror technique" has been
applied to measure this tangent. The kinetic con-
stants, k^ of Equation (1), may be determined by the
application of the Lineweaver-Burke method. The Line-
weaver-Burke plot involves transforming Equation (1)
into the following form and the kinetic constants are
determined graphically using the paired values of
1/r vs. 1/c:
k2
(9)
In this analysis, a regression technique has been
o Data for Experiment No.4
D ii i. No.5
A it ii No.6
Simulated model for Exp No.5
0.25
10
Time , Days
Figure 2 . Experimental Data and Simulated Model
388
-------
used to preclude human prejudice In the determination of
the values of k±. The results of this analysis, which
was obtained from a subroutine of a main computer pro-
gram, are summarized in Table 2.
Table 2. Kinetic Constants of the Proposed Kinetic Malel
Experiment No.
k2,
g C/g Ash
g C/g Ash-day
1.062
0.011
1.136
0.033
1.224
0.029
A computer simulation model of the system, called
COMPOST, has been developed and used for the processing
of all experimental data obtained for this investiga-
tion.7 The COMPOST enables to predict the behavior of
the bio-stabilization system during the decomposition
of the material. One advantage of the model is its
capability to describe the system behavior in a dimen-
sionless form. This generalization of the model in
system analysis may be directly applicable to scale-up
of the process.
In Equation (3), kt is a dissociation constant of
an enzyme-substrate complex and is a measure of the
affinity of the enzyme for the substrate. As shown in
Table 2, all values of kj found in this Investigation
have the same order of magnitude within experimental
error range while those obtained for kj> vary consider-
ably depending on the experimental conditions. The
consistency of k, in magnitude indirectly verifies that
ki is a characteristic constant of the system. An in-
crease in the magnitude of ka would result in a higher
reaction rate. Its contribution to the reaction rate
is directly proportional to its magnitude.
It should be noted that approximately 300 percent
increase was found in the magnitude of ka when pure
oxygen was used as the oxygen source. This increase
compares favorably with the data reported for the
activated sludge process in which the process was
found to be more effective. It should be noted,
however, that the magnitude of ki in this study was in-
dependent of the oxygen source.
The system equation, Equation (4), was developed
based on the mass balance and Michaelis-Menten kinetic
theory. The curve in Figure 2, which simulates the be-
havior of the system during the decomposition reaction,
is a plot of Equation (4) using kinetic constants given
in Table 2 for Experiment No. 5. As can be seen from
the figure, the mathematical model is consistent with-
in the experimental error range.
Equations (5) and (6) define dimensionless time
and concentration, respectively. The use of dimension-
less variables allowed for the system to be interpreted
more easily. Figure 3 shows the results of these trans-
formations. It should be noted that the slope of the
curve depends upon the initial concentration only as
can be seen from the Equation (8). It was expected that
the type of the curve is similar to that of the curve
in Figure 2.
The system model may provide basic analytical in-
formation for control and optimization of the process
for commercial application. However, the control of the
bio-stabilization process is still based on experience
due to lack of analytical information in the design
procedure. Further investigation may be necessary for
optimizing the entire process in industrial applica-
tion. The kinetic data and model herein reported should
be used as a model to study the bio-stabilization pro-
cess on an industrial scale. Particular attention
should be devoted to scale-up factors from pilot scale
to industrial operation. In conclusion, the proposed
model does predict the behavior of the system.
1.0
2 0.8
o
.0
k
o
o
0.6
0 0.2
0
0.2 0.4 0.6 0.8 1.0
Dimenslonless time, Z
1.2
1.4
1.6
Flgurt 3 . Change of Carbon Concentration with Respect to
Time In Dimenslonless Form for Experiment No. 5
389
-------
References
1. Breidenbach, A.W. & Floyd, E.P. Needs for Chemical
Research in Solid Waste Management. U.S. Dept of
HEW, Washington, B.C. 1970.
2. "Solid Waste Disposal." Chemical Engineering
78., 14:155-59.
3. Spohh, E. "Composting by Artificial Aeration."
Compost Science 11, 3:22-24.
4. McGauhey, P.H. American Composting Concept.
Solid Waste Management Office, Environmental Pro-
tection Agency, Washington, D.C. 1971.
5. Rainer, J.W. Behavior of Enzyme Systems. Van
Nostrand Reinhold Co., New York, N.Y. 1969.
6. Smith, C.L., et^ al. Formulation and Optimization
of Mathematical Models. International Textbook
Co., Scranton, Penna. 1970.
7. Whang, D.S. A Kinetic Study on an Organic Solid
Waste Stabilization Process on a Pilot Plant Unit.
Dept. of Chemical Engineering, Texas Tech Univer-
sity, Lubbock, Texas. 1972
8. Albertsson, J.G. et_ ail. Investigation of the Use
of High Purity Oxygen Aeration in the Conventional
Activated Sludge Process. Federal Water Quality
Administration, Washington, D.C. 1970
390
-------
EVALUATION AND SELECTION OF WATER QUALITY MODELS: A PLANNER'S GUIDE
E. John Finnemore and G. Paul Grimsrud
Systems Control, Inc.
Palo Alto, California
As part of a management guide for planners, Sys-
tems Control, Inc., recently developed for the Environ-
mental Protection Agency systematic procedures for
evaluating and selecting receiving water quality models.
Using these procedures, each model is evaluated on the
basis of many considerations, which include both the
technical principles and capabilities of the models
and such resource needs and constraints as additional
labor, specialized technical expertise, time and funds,
and computer limitations. All these considerations
are combined into a single performance index. A pro-
cedure is also prescribed for combining the various
component costs of applying the model into a single
overall cost. A comparison of this overall application
cost with the model's performance index may then be
used as a guide to model selection. The selection
procedure is organized into phases of increasing level
of detail, each of which may or may not be required
depending upon the nature of the planning problem
being confronted.
Background
The priority given to the accomplishment of the
nation's commitment to the goal of clean water is
evidenced by the size of the investment being made for
abatement and prevention of water pollution. This com-
mitment makes management decisions affective receiving
water quality of the utmost importance. With such major
decisions being made daily as part of numerous planning
programs, it is incumbent on planners to assure that the
expenditures they recommend are justified and that the
courses adopted will fully achieve the expected results.
But the selection of water quality planning method-
ologies, one of the first major decisions facing plan-
ners and managers, requires a good understanding of the
difficult technical problems which may be involved, be-
sides the limitations of time and funds.
Since the number of wastewater management alterna-
tives which exist and require evaluation may be large,
the complexity of water quality analysis has stimulated
the development of a variety of tools to assist plann-
ing, ranging from simple graphical techniques to sophis-
ticated computerized models. While these tools freq-
uently enable types and numbers of analyses which
would otherwise be impractical, they can also be
costly and time consuming. It is therefore essential
that planners give careful attention to insuring that
their use is cost-effective.
The model evaluation and selection procedures
described here are specifically oriented to water
quality and water resources planners and managers.
They are designed to enable a planner without previous
experience in water quality modeling to determine
whether a receiving water quality model could and
should be used in a particular planning program, and
which specific model would be most cost-effective.
The two primary purposes of this work were to
develop a technique which would assist planners in
selecting and using water quality analysis methods
which are cost-effectively matched to their planning
responsibilities, and to summarize the technique into
handbook form. The handbook is designed to provide
planners with a sufficient introduction to water qual-
ity modeling to enable effective communication with
systems analysts and administrators regarding water
quality modeling. Besides model selection and evalua-
tion the handbookl also provides guidance on the manage-
ment of modeling and the use of contractual services.
Method
A systematic way of evaluating water quality
models was sought. Clearly, the evaluation procedure
would require answers to many specific questions about
the models and so a tabular format for presenting
these questions and answers was clearly preferred.
Tables represent the condensation of large quantities
of descriptive text, enable far more rapid information
retrieval, and greatly facilitate the comparison of
different models. This tabular method of evaluation
was used directly in the procedures developed for both
model cost-effectiveness analysis and for final model
selection.
Information on the models may be obtained from
program documentation and user's manuals, published
articles about model development and applications,
and if necessary by direct communication with the
developers and users. Most available water quality
models can be located at the following institutions:
the Environmental Protection Agency, the Army Corps of
Engineers, the U.S. Geological Survey, state water
quality planning offices, and colleges and universities
active in the water quality area. The models chosen
to develop and demonstrate this technique are all use-
ful for the prediction of water quality and provide
a wide range of capability and applicability. At
the time (1974-75), they seemed to represent a large
portion of the models expected to be in use in the
near future. This does not imply that another model,
not initially included, might not be preferable in a
particular case. The primary function of the selected
models was to provide a vehicle for development and
demonstration, rather than to draw any conclusions
about them. The chosen models for these demonstration
purposes are all deterministic simulation models of
varying complexity. They were arranged into the follow-
ing six groups, in accordance with their areas of
applicability:
Group I
Steady-state Stream Models
Group II Steady-state Estuary Models
Group III Quasi-dynamic Stream Models
Group IV Dynamic Estuary and Stream Models
Group V Dynamic Lake Models
Group VI Near-field Models
The models used to simulate only stream conditions
are least complex due to the one-dimensional character-
istics of flow. Models for simulating stratified lakes
and reservoirs fall next in line of complexity, followed
by estuarine models. Estuary models are more complex
because the prototype flow is usually in at least two
dimensions, and the boundary conditions, such as tides,
vary rapidly compared with those in lakes. The costs
of model application tend to be proportional to their
complexity.
The "quasi-dynamic" model category (Group III)
have been so named since only their weather (meteorolog-
ical) inputs may be dynamic. Their solutions have
steady-state hydraulics, but dynamic water quality.
The near-field category (Group VI), is the only one in
which very localized effects, such as plume entrain-
ment, are simulated.
There exist many other models different from the
391
-------
models chosen for this development and demonstration,
as well as other versions of those employed here.
A number of these were treated in a. similar but Iess2
extensive manner in an earlier study by the authors.
Probably much the same questions would be used in the
evaluation of other models, and only different answers
would be obtained in some areas.
Types of models notably different from those
evaluated herein include: ecologic modeling of receiv-
ing waters, in which the life forms are of prime inter-
est; truly two-dimensional flow models, in which
velocity components are determined in two perpendicular
directions over a grid of points covering the water
body: three-dimensional models which are still more
complex and presently are far from being ready for
wide use in planning; "continuous" deterministic
models, whose output can be statistically analyzed for
probability studies, but which need much longer records
of water quality data and far longer computer run times;
and stochastic models, which provide an alternative
approach to the question of probabilities.
Results
The resulting model evaluation and selection
technique divides naturally into two stages; model
evaluation, and cost-effectiveness evaluation. The
latter depends heavily upon the former.
Model Evaluation
The questions to be answered in the evaluation of
the models were organized according to their purposes
and contents into the fourteen categories listed in
Table 1. For each of these categories, a table was
prepared which contained from two to six columns, one
for each of the specific questions in the category.
Table 2 is an example of such a table, in this case for
the thirteenth category of Table 1. In each row of
Table 2 the answers are entered for each model chosen
for evaluation. These tabulations of answers then
Table 1
MODEL EVALUATION CATEGORIES
MODEL CAPABILITIES
Applicable Situations
Constituents Modeled
Model Factors Accounted for
DATA REQUIRED
For Model Inputs
Additional, for Calibration and Verification
MODEL COSTS
Initiation Costs
Utilization Costs
MODEL ACCURACY
Representation
Numerical Accuracy
Sensitivity to Input Errors
EASE OF APPLICATION
Sufficiency of Available Documentation
Output Form and Content
Updateability of Data Decks
Modification of Source Decks
provide the information which is used to measure the
suitability of the models for a particular purpose
(its performance index), and the total cost of oper-
ating the models.
Cost-effectiveness Evaluation
A form of cost-effectiveness evaluation was deter-
mined to provide the most appropriate basis for model
selection. The procedure developed to evaluate the
cost-effectiveness of each model requires making a com-
parison of its performance index (PI; a measure of
the model's suitability for a particular purpose) with
the total cost of operating it.
Clearly the process of selecting a water quality
model for any wastewater management planning project
may involve numerous complex considerations. Therefore
the procedure had first to identify the important
factors which influence the selection of models by
planners, and then to structure the consideration of
these factors in such a manner that confusion is
minimized. Of great importance, the procedure does not
tell planners what decisions on models to make: in-
stead it provides them with the essential questions and
thought structure upon which they or their assistants
can make the decisions.
The model selection process is designed to give
users a choica of several different levels of detail
they may want to consider. The process is therefore
divided into four phases, each going into progressively
more detail and requiring progressively more effort.
These phases are:
Phase I: Model Applicability Tests
Phase II: Cost Constraint Tests
Phase III: Performance Index Fating - Simplified
Phase IV: Performance Index Rating - Advanced
The rejection of candidate models in one phase reduces
the number of models to be evaluated in the next phase,
and phases are designed accordingly. All considerations
in the selection process are based upon the results of
the model evaluations discussed previously.
After having identified the problem and inventoried
the data available for a particular planning program,
the basic decision must first be made whether any water
quality model at all should be used. This decision must
task into account whether a model would be helpful in
plan formulation and whether a suitable model and suf-
ficient data are available. (Any additional data gather-
ing should be postponed until after the models are
selected.) Generally, water quality models are useful
in any area where the quantitative relationship be-
tween varying wasteloads and resulting water quality
must be known. However, In "Effluent Limited" areas,
waste treatment alternatives will often be specified by
Federal Effluent Standards, thus eliminating the need
for a water qaulity model. Where there is some doubt
whether water quality modeling is inappropriate or
inefficient in a particular planning application, the
model selection process will soon make this fact
apparent.
A set of candidate models must be identified before
the model selection process can be initiated. Although
the models chosen for demonstration purposes (see Table
2) could be used as the candidate set, many other models
are available which should be considered. The planner
chould select his set of candidate models using as many
sources as possible. Since model titles are frequently
descriptive of their capabilities, the planner should
first use the titles to screen out those obviously not
applicable to his particular problem. For the purposes
of model selection, there is obviously no need to com-
plete the extensive (fourteen category) model evaluation
392
-------
Table 2
MODEL SUMMARY: EASE OF APPLICATION, UPDATEABILITY OF DATA DECKS
I
II
[II
IV
V
VI
MODEL
DOSAG-I
SNOSCI
Simplified Stream
(SSM)
ES001
Simplified Estuary
(SEM)
QUAL-I
QUAL-II
(DEM)
Tidal Temperature
(TTM)
RECEIV
SKMSCI
Deep Reservoir
(DRM)
LAKSCI
Outfall PLUME
CARD CHANGES
(Column 1)
Few.
Few.
None.
Few.
None.
Very small, except for changes of
weather data which may involve
many cards.
"
Few in most cases.
Small, except for weather inputs.
Small, except for transient waste
inputs .
••
Small, except for weather data.
Small, except for weather and
inflow quality data.
Minor changes, of at most a few
cards .
RECOMPUTATION
TIME
{"rnlumn 71
Very small.
Very small.
Relatively large.
Small.
Relatively large.
Small.
Small.
Small.
Small.
Small.
Small.
Small.
Small.
Very small.
HELPFULNESS OF
AVAILABLE DOCUMENTATION
(Column _31
Good.
Good.
Good. Needs thorough study
and good understanding, before
using charts.
Good.
Good. Needs thorough study
and good understanding,
before using charts.
Good.
Good.
Good.
Good.
Poor.
Good.
Generally good. The three
comprising documents are less
convenient to use.
Good.
Adequate .
for models which are rejected by applicability or con-
straint tests (Phase I or II) of the cost-effectiveness
evaluation. Therefore, the model evaluations should be
accomplished concurrently with, and only to the extent
needed by, the various tests and ratings of the cost-
effectiveness phases.
For similar reasons, no model should be processed in a
subsequent phse until all aspects of the preceeding
phase are complete.
The detailed procedure for selecting a water qual-
ity model is discussed in the following subsections,
one for each phase. A flowchart guide to the procedure
has been prepared for each phase. At the end of any
phase the user should decide whether to select a model
on the basis of the factors he has considered thus far,
or whether to refine his analysis further in the next
phase. Worksheets, similar in form to Table 2 but
containing columns for the entries indicated in Table
3, are required to record the cost-effectiveness evalu-
ations for each phase worked. The more phases the
planner uses, the more confidence he can have in his
selection. However, there will be trade-offs between
selection effort and selection confidence, and for
many applications adequate confidence in the selection
will be attained after completing only the first one
or two phases of the process.
Applicability Tests (Phase I). These tests ask
questions about the appropriateness of the models for
the problem at hand, and inappropriate models are
rejected from further study. This first phase of the
selection process is therefore very important, because
of its rapid narrowing down of the field of candidates.
Results of the applicability tests should be re-
corded as a "yes" or "no" in the appropriate columns of
the worksheet; the categories to be tested are given
under Phase I of Table 3. As the various tests proceed,
rejected ("no") models should be deleted from subsequent
worksheets to avoid unneeded further work.
The ability of a model to simulate the behavior of
the correct type of water body is of prime importance.
The user can usually determine this capability of a.
model from the general description in the model documen-
tation. For a deeper understanding, the scale of
interest and the extent of concentration and/or flow
variability should be analyzed. The time variability
test determines whether the needed time-varying model
variables are provided by the model. The time varying
requirements are established by the length of the
simulation period, and by the variability of the flow,
quality and weather inputs. The discretization test
determines whether a model can simulate the level of
spatial detail required for the proposed application;
special features such as the presence of tidal flats,
flow augmentation sources, and storm loadings may
influence this requirement. The constituents capability
test simply requires comparing the model capability to
simulate water quality constituents with the user's
needs; some models have specific constituent capa-
bilities, others can be used for whole classes of
constituents which have certain types of kinetic
reaction, such as first order decay. The driving forces
and boundary factors test involves checking that the
model is capable of simulating all the important driving
forces in the prototype; some of these may need to be
time varying boundary inputs. The various tests of
393,
-------
Table 3
SUMMARY OF COST-EFFECTIVENESS EVALUATION TABULATIONS
COST-EFFECTIVENESS EVALUATION CATEGORIES
APPLICABLE SITUATIONS
Water Body
Time Variability
Discretization, etc.
CONSTITUENTS MODELED
Constituents Modeled
Driving Forces, Boundary Factors
DATA REQUIREMENTS FOR MODEL INPUTS
Hydrologic and Geologic
Water Quality
Effluent
Other
DATA REQUIREMENTS FOR CALIBRATION AND VERIFICATION
Hydrologic and Hydrodynamic
Water Quality
Overall Data Rating
INITIATION COSTS
Model Acquisition
Equipment Requirements
Data Acquisition
UTILIZATION COSTS
Machine Costs
Manpower Costs
Total Costs
Cost Constraint Tests
ADVANCED PI RATING
Internal Factors Accounted For
Model Representation Accuracy
PI RATING, STAGE 2
Numerical Accuracy
Sufficiency of Available Documentation
Output Form and Content
Updateability
Ease of Modification
OVERALL PI RATING
PHASE
I II III IV ALL
U)
c
o
-H
•U
a!
4J
•H
si * - - %
•5 T t^ M Tl
So <2 °° y y a £ «
i ,_j ^^ p »C G f*-i to
J Jj HJ4J4J 0)4J -H 60 -HOD fij
fills 1 1 3 S 3 S B
A R w
A R W
A R W
A, R W
A R W
A A R
A A R
A A R
A A R
A A R
A A R
R W
A A
A A
A A
A A
A A R W
A A
A A
R W
R W
R W
R W
R W
R W
R W
R
A = Answer (yes, no, $, weeks, etc.); R = Rating on scale 0-10; W Weight, normalized about 1.0.
data requirements are designed to ensure that the quan-
ity and quality of the available prototype data are
satisfactory for the needs of the model. While per-
forming these tests, hoever, it is important to consid-
er whether additional data can be specifically acquired
during the project, or whether the model will be used
over a number of years during which data collection
will probably improve. Entries under the "Applicability
Limitations" column of Table 3 should be briefly
descriptive.
Any models deemed marginally applicable in the
Phase I tests may be maintained for further considera-
tion in Phase III, when their level of applicability
will be given a rating.
Cost Constraint Tests (Phase II). In this phase
of the cost-effectiveness evaluation both elapsed
project time and dollar costs are considered as cost
items, which must be compared for each model with user
constraints. Answers to most of these tests (see Phase
III of Table 3) probably will be either in weeks or in
dollars, obtained from the preceding model evaluation
(similar to Table 2).
Model acquisition costs will frequently be nominal,
though delivery time may be a factor, and some may
include a surcharge for each run made. Other models
may require a lease or purchase agreement. Equipment
requirements for calculators and computers with their
peripheral equipment must be compared with the avail-
394
-------
able capabilities, although many services are available
through remote terminals. Data acquisition costs
summarize the costs of acquiring any additional data,
as discussed under Phase I. Machine costs include
charges for computation plus the use of various
peripheral equipment. Computation time is about pro-
portional to the number of constituents modeled, dis-
crete segments modeled, time steps used, and runs made.
Manpower costs include considerations of the number of
personnel and the level of expertize needed for a model,
possible recruitment and/or training time, model set up
time, run time, time to analyze the results, and, of
course, personnel salaries and overhead costs.
From the above, estimates of the total cost and
time requirements for a model can be obtained. In the
final cost constraint tests these are compared with the
project resource constraints, and grossly unacceptable
models rejected. Marginally unacceptable models
probably should not be rejected in this phase because
of the approximations undoubtedly necessary in making
the many cost and time estimates.
Simplified Performance Index Rating (Phase III).
This portion of the model selection process gives a
method for estimating the effectiveness of the candi-
date models. The effectiveness is obtained through
a "Performance Index Rating", which is divided into
two parts. The first, "simplified" part (Phase III)
accounts for the more basic, and usually more important
model attributes which have previously been discussed
in the Phase I and Phase II tests. The second "advanc-
ed part of the Performance Index (PI) rating, performed
in Phase IV, involves much more detailed and usually
somewhat less important considerations of the models.
In most cases, Phase III will give the planner a very
good idea of which model is best for his particular
planning problem. A brief review of the contents of
the second part (Phase IV) will then usually indicate
whether those further considerations are necessary.
The same categories of model attributes treated in
Phase I are now rated more quantitatively, if they have
not been previously rejected. This is shown in Table
3; each category now requires a "rating" and many
require a "weight" for Phase III.
The user must select attribute ratings based upon
his knowledge of the model capabilities and the appli-
cation needs for the category considered. The rating
should fall on the following scale from zero to fen:
10 is excellent, 8 - good, 6 - fair, 4 - poor, 2 very
poor, and 0 - completely inadequate.
The "weights" are used to adjust the impact of each
attribute rating on the overall Performance Index, based
upon their relative importance. For example, if the
"Time Variability" capability of a model is much more
important than the "Constituents Modeled" capability,
then it should have a larger weight. Weights must be
assigned by the planner based upon his judgement of the
importance of each attribute to his planning problem.
In assigning weights the most significant factor is the
relative importance of the various attributes. There-
fore they are normalized about a value of 1.0; typical
weight ranges are given in Ref. 1. For a particular
application a single set of weights should be used for
all candidate models. But they will probably vary with
each application to a different prototype situation.
The user will probably find it more convenient to assign
the ratings and weights at the same time as he performs
the Phase I tests.
When all Phase III ratings required in Table 3 are
complete, the planner should decide whether or not to
proceed with more detailed ratings in Phase IV. If the
Phase III ratings are deemed adequate for model selec-
tion, then the overall performance index of the jth-
model can be computed using the equation:
[Rating (i,j)] [Weight (i) ]
1=1
> Weight (i)
1=1
where i = the attribute numbers
n = number of attributes considered
Advanced Performance Index Rating (Phase IV).
This final phase enables far more intensive probing into
details of various candidate models. Most of the rat-
ings in this phase follow the procedures of Phase III
but require extensive user insight and experience in
water quality analysis and modeling. For this reason
it is included as optional in the overall selection pro-
cess, and it is not discussed in detail here. The eval-
uation categories for Phase IV are listed in Table 3,
and an overall PI rating for both Phases III and IV
could be obtained in the same manner; full details are
given in Reference 1.
Final model selection simply requires making a
tabulation of the total dollar costs (Phase II) and the
overall PI ratings for each model. Table 4 is the re-
sult of an example application. The user can make his
selection by either comparing costs and expected per-
formance, or by using the Pi/cost ratio.
Table 4
COST EFFECTIVENESS COMPARISON
Model
A
B
C
D
PI Rating
(From Phases
III & IV)
6.0
6.1
6.9
7.1
Total Cost
of Application
(From Phase II)
$ 50,740
56,040
53,650
52,740
PI*104
Dollar
1.18
1.09
1.28
1.36
Rank
3
4
2
1
References
1. Grimsrud, G. P., E. J. Finnemore, and H. J. Owen,
"Evaluation of Water Quality Models: A Manage-
ment Guide for Planners," Systems Control, Inc.,
Palo Alto, California (EPA Contract No. 68-01-
2641), 177 p., July 1975.
2. Systems Control, Inc., "Use of Mathematical Models
for Water Quality Planning," State of Washington,
Department of Ecology, WRIS Technical Bulletin No.3,
Olympia, Washington, June 1974.
Acknowledgements
This work was supported by the U.S. Environmental
Protection Agency, Office of Research and Development,
and by the State of Washington Department of Ecology.
The guidance and contributions of the EPA Project
Officer, Mr. Donald H. Lewis, and the DOE Project Offic-
er, Dr. Robert Milhous, are particularly appreciated.
The assistance of Dr. Roger D. Shull, Mr. William P.
Somers, and Mr. John Kingscott, all with the EPA, is
acknowledged.
395
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A LANDSCAPE PLANNING MODEL AS AN AID TO DECISION-MAKING
FOR COMMUNITY GROWTH AND MANAGEMENT
J. Gy. Fabos
Department of Landscape Architecture
and Regional Planning
University of Massachusetts
Amherst, Massachusetts
S. A. Joyner, Jr.
Department of Civil Engineering
University of Massachusetts
Amherst, Massachusetts
Abstract
A landscape planning model for assessing special
resources, hazards and development suitabilities is de-
scribed. Computer mapping aids in the quantitative and
spatial mapping of resultant assessments. A framework
for incorporating economic evaluations of resources,
hazards and development suitabilities into land use de-
cisions is proposed. Application of the model to a
town in the Boston Metropolitan Area showing the results
of 20 years of Metropolitanization is illustrated.
The rationale of the METLAND team has been that the
attention of decision makers could be better and more
easily brought to focus on these landscape issues if the
magnitude of the negative effects resulting from their
actions were clearly pointed out. Our research to date
has demonstrated an attempt to place economic values on
several resource variables. The continuation of this
research, however, will investigate other evaluations
based on energy use analysis and the perception of
various interest groups such as conservationists and
developers.
Background
An interdisciplinary landscape research team was
established at the University of Massachusetts in 1971.
Since that time, over 30 people have contributed to the
development of a Metropolitan Landscape Planning Model
(acronym, METLAND). The team has responded to the per-
ceived problem that the "metropolitanization" of eastern
Massachusetts has caused a needlessly high depletion of
its environmental/landscape resources, has increased
hazards, and development has often occurred on margin-
ally suitable lands. Furthermore, metropolitanization
has impaired the vital ecological stability of large
landscape units. If these phenomena could be quanti-
fied, it was argued, an important step would be taken
to placing them on equal footing with other quantified
"values" and thereby integrating them into the decision
making process.1
It is well recognized that highways and other major
public installations have been the major growth gener-
ators; their planners have seldom taken into account
the factors described above. The model presented here
is designed to provide a procedure to assess special
resource, hazard and development suitability potentials,
which could complement and benefit existing decision
making. The model presented here has been applied to
the town of Burlington in the larger Boston Metropolitan
region. The Boston metropolis has gradually engulfed
2500 square miles (see Figure 1). Application of the
model demonstrates the consequences of this metropoli-
tanization on the town of Burlington. Approximately
eighty percent of this town has been developed with
modern industries, shopping centers and low density
housing.
Post-1960
Suburban
- Growth
Burlington
Study Area
Major Suburban
Growth During
1960s
Pre-Suburban
1950 Growth
Figure 1. Boston Metropolitan Area
Framework of the METLAND Model
To deal quantitatively with environmental issues
of the "metropolitanized" landscape, the METLAND study
has proposed a three-phase planning model including
assessment, evaluation and implementation phases (see
Figure 2). The assessment phase, which is the focus of
this paper, will be outlined in detail below. The re-
maining two phases are in the early stage of develop-
ment at the time of this writing.
Figure 2. METLAND Conceptual Model
ASSESSMENT - PHASE 1
SPECIAL VALUE RESOURCE COMPONENT.
VARIABLES: water, agricultural and wildlife pro-
ductivity, earth resources, visual quality
ECOLOGICAL STABILITY COMPONENT.
VARIABLES: ecological functions, transaction
functions, regional closure
HAZARD COMPONENT.
VARIABLES: air and
pollution
Combined Resource and Hazard values to
J influence development restriction or
resource conservation
DEVELOPMENT SUITABILITY
COMPONENT. VARIABLES:
physical, topoclimate,
visual
Analysis of conflicts between restrictive a'reas
and those which are suitable for development
Ecological Stability as a function of land uses '.
and use distribution ._
EVALUATION - PHASE 2
Trade-off analysis of alternative use types,
densities and distributions in regard to VALUES,
NEEDS and OBJECTIVES, as expressed by interest
groups or measured by professionals
IMPLEMENTATION — PHASE 3
Identification of existing devices and development
of new devices for implementation and application
of those devices
The assessment phase consists of a selection of
variables analyzing the intrinsic value of those en-
vironmental characteristics which may produce benefits
or result in harm to society. These several resource
and hazard analyses are mapped and organized into four
groups, called components. While each individual vari-
able has a specific value, this grouping helps to
identify complementary relationships and environmental
issues and to provide combined values which are useful
396
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in making decisions. The four components of the assess—
ment phase are referred to as: (1) special resources,
(2) hazards, (3) development suitability, and (4) ecol-
ogical stability.
METLAND Assessment Components
(Refer to Figure 2)
The special resource component of the assessment
phase addresses the issue of environmental resources and
specifically deals with three types of resources. These
are: (1) renewable physical resources (e.g., water),
(2) non-renewable physical resources (e.g., sand and
gravel), and (3) "aesthetic-cultural" resources (e.g.,
views). Both renewable and non-renewable physical re-
sources are critical to the metropolitan region. Aes-
thetic-cultural resources, while not critical, are
nonetheless important because their presence enhances
the quality of life. Presently comprising the special
resource component are five individual special resources
or "variables." Representing the first type of environ-
mental resource are the variables known as agricultural
productivity, wildlife productivity (including openland,
woodland, and wetland wildlife subvariables), and water
resources (including water quality and water supply
subvariables) . Representing the second type of resource
is, at the present time, only the variable of sand and
gravel supply. Representing the third.resource type is
visual landscape quality, which refers to such special
landscape features as quality wetland areas, views and
historical sites, and the visual contrast, diversity
and compatibility of land uses.
The assessment of this component is based on the
premise that if a portion of a landscape possesses a
high quality and quantity of one or more of these re-
sources , those areas should receive special planning
consideration and various degrees of protection from
development. If immediate need for the resources is
not apparent, they should be protected or conserved
much as capital resources are saved in a bank until
they are needed.
Assessment procedures have been developed for each
of the special resource variables and subvariables. In
addition, a composite resource assessment procedure has
been developed to evaluate all special resources to-
gether. Although such a composite assessment can be
based on any one of several resource value sets, as it
was mentioned earlier, METLAND has to date used only an
economic evaluation of relative resource significance
in compositing individual special resource assessments.
(This is also the case in the composite assessments
made for other METLAND model components.)
' The hazard component of the assessment phase
focuses on the issue of environmental dangers or unde-
sirabilities. Presently comprising the hazard com-
ponent are three environmental variables: air pollution,
noise pollution and flooding. The individual assess-
ment of these three hazard component variables provides
spatial information on both the type and the magnitude
of hazards. The composite assessment of hazards com-
bines this information.
The development suitability component addresses
the issue of environmental opportunities for alterna-
tive types of development. These opportunities are
landscape resources which can minimize the cost of
development while increasing human comfort and user
amenities. Included in the component are three vari-
ables—a physical variable, a. topoclimate variable and
a visual variable—which enhance the suitability and
the attractiveness of an area for development. To date
only the physical variable is operational.
The ecological stability component, which is being
developed, will deal with the issue of ecological im-
Paot, ecosystem structure and function, and the impli-
cations of such structures and functions in land use
decisions.
The variables and subvariables comprising these
four assessment components are the elements designed
to perform the specific analyses required for applica-
tion of the assessment phase of the model. They are
also the elements which provide the basic assessment
procedures.
METLAND Assessment Procedure and Application
The essential element of the METLAND assessment
procedure is a mapped depiction, at a common scale, of
the results of the variable assessment. A map, there-
fore, is prepared for each subvariable and variable.
These variable assessment maps are then overlaid to
form composite special resource, hazard or development
suitability maps for the study area.
With the expansion of the assessment phase of the
METLAND model to include special resources, environ-
mental hazards, opportunities for development, and
ecological stability, the need for a tool to rapidly
digest and manipulate large amounts of data collected
on the regional scale, and to prepare these individual
and composite variable assessment maps, became impera-
tive. On the basis of a study undertaken to select
such a tool, the Computer Mapping for Land Use Planning
(COMLUP) system (developed by Dr. Neil Allen of the
U.S.D.A. Forest Service) was chosen as most appropriate
for the METLAND study.3 This selection by METLAND of a
computerized mapping system reflected the fact that
computerized data banks are today becoming available
for use by metropolitan regions and communities. It
was assumed that this availability would continue to
increase in the near future. Below, the capabilities
of the COMLUP mapping system are summarized.
The COMLUP Mapping System
The COMLUP system is essentially a computer map-
ping package of some twenty-five programs with provision
for inventory, overlay (including weighting), and line
plotting of spatially located source data.4 For the
purposes of the METLAND study, its function has been
expanded, by METLAND computer specialist Dorothy
Grannis, to that of a landscape planning tool. As such,
it not only provides an inventory of existing environ-
mental values and combinations of values, but is also
able to estimate or simulate the cause-effect relation-
ship of proposed alternative environmental land use
patterns and decisions.
Capabilities of COMLUP
COMLUP is a second generation grid system which
followed the first generation or manually applied over-
laying of grids, most often referred to as SYMAP.5 But
because remote sensing and other land use survey infor-
mation is becoming available at a finer scale, a more
accurate data storing and manipulating system was
needed. The advantage of the second generation COMLUP
computer geographic technique over the earlier tech-
nology is that any shape and size polygon can be
directly input and stored in the computer, by image
digitizer, without subdividing the polygon into grid
cells.6 For data manipulation, the digitized area
still must be subdivided into cells, but this is now
done in a second step by the computer automatically,
instead of as a manual first step.7
Application of the COMLUP system can be described
in a simple three step procedure, as follows. In step
1, the COMLUP program takes the digitized data in line
segment form and overlays the grid of fine granularity
(500 X 1000 cells) on these data. In step 2, maps are
overlaid on one another one at a time by the computer.
Step 3 re-converts the grid data back to line format so
that it may be plotted on a drum or flat-bed plotter.
397
-------
The plotted output constitutes a mapped depiction of
the results of the applied variable assessment proce-
dure.
Composite assessment maps are prepared in a similar
way. The source maps in these cases are the already
prepared individual variable assessment maps. The as-
sessment maps of variables belonging to a single as-
sessment component are' internally overlaid and weighted
as desired. The plotted output is a mapped depiction
of the composited variable assessments belonging to the
component in question.
The rest of this paper briefly summarizes the
application of the assessment phase. The assessment
procedure at the variable level will be shown only by
one example. An overall assessment is also shown which
is produced by the combination of the first three com-
ponents (special resource, hazard and suitability) shown
in Figure 2. The final portion of the paper will sum-
marize the conceptual framework of the evaluation and
implementation phases.
Application of METLAND Assessment Phase
In Figure 2, there is an implied difference among
the various components. Special resource and hazard
components are developed so that development restric-
tion or resource conservation can be achieved. The
third or development suitability component, however, is
designed to show opportunities for development, from the
point of view of physical and topoclimatic suitability
and visual amenity values. To describe an assessment
procedure of a variable, the physical development suit-
ability variable is selected for illustration. The
combined or component assessment incorporates the re-
sults of all variables of each component. In this ini-
tial study, variables are weighted by economic evalua-
tion.
Physical Development Suitability
Assessment Procedure
Q Q
Surficial geologists, soil scientists, civil
engineers and landscape architects-'-"'-'-^ have studied
for decades aspects of physical development suitability.
The significance of this variable can be supported by
the findings of these researchers. Our investigation
identified six subvariables of significance supported
by scientific results and estimated added development
costs needed to overcome development constraints, when
suitability is less than ideal.
12
These subvariables
are as follows in the order of their importance: (1)
depth to bedrock, (2) depth to water table, (3) drain-
age (this often overlaps with water table characteris-
tics) , (4) slope, (5) topsoil, and (6) bearing capacity.
To assess composite suitability based on these six sub-
variables a simple four step procedure is used:13
Step 1: An interpretation of soil types for each of the
six physical factor subvariables.
This interpretation is based on (1) the three-part
symbols by which the SCS identifies all soil types, and
(2) information provided by the SCS Engineering Tech-
nical Guide which identifies the dimensions of physical
factors (e.g., 0-2' depth to bedrock).
Step 2: An assignment of estimates of expected added
development costs to physical subvariable di-
mensions interpreted from soil types.
On the basis of METLAND research, it has become
possible to directly assign actual dollar estimates
representing added development costs. The upper limits
of these added development costs per acre (assuming
that two houses are built with basements on each acre)
for each subvariable are as follows: depth to bedrock
up to $20,000; depth to water table up to $5,000;
drainage up to $5,000 (it should be noted that correct-
ing high water table or poor drainage characteristics
can be done together at little extra cost); slope up to
$1,300 (but development on slopes greater than 15% is
prohibitive for the average development); topsoil up to
$1,500; and bearing capacity up to $1,500.
Step 3: A determination of the estimated total added
development costs for each soil type.
This is accomplished simply by combining the added
costs per physical subvariable for each soil type, with
the exception of the depth to water table and drainage
variables, in which case only the higher cost is
counted for both.
Step 4: An aggregation of total added development costs
into A-B-C-D classes for physical development
suitability (as shown in Table 1 below).
Table 1
A-B-C-D Classes for Physical Development Suitability
Total Added Costs
$ 0 - $2000
$2001 - $4000
$4001 - $9000
$9001 +
Aggregation Class
A
B
C
Undevelopable (or Class D)
As in each assessment procedure, this type of
aggregation serves to categorize soil types in terms of
high, moderate and low potential suitability for a typi-
cal housing development. In this case. A, B and C
classes are based on what total added development costs
actually mean in terms of housing square footage. Also
in this case, a fourth category referred to as "undevel-
opable" (or Class D) is considered. The inclusion of
this fourth category reflects the fact that there is a
significant practical difference between sites that
have a low development suitability and those that are
entirely unsuitable for development.
Once appropriate A, B, C and "undevelopable," or
D classes are assigned to each soil type, the COMLUP
system is used as before to produce the desired assess-
ment map for physical development suitability. Figure
3 shows the COMLUP map results of this physical develop-
ment suitability assessment technique as it was applied
to the town of Burlington.
Combined Assessment of All Components
and a Preliminary Evaluation
At this writing the majority of assessment proce-
dures for the variables have been developed. The five
special resource variables listed in Figure 2 were
applied to the study town of Burlington, Massachusetts.
The composite assessment of all special value resources
and a composite assessment of two of the three hazard
variables was prepared. Each of the variables was
weighted using economic evaluation. The third map used
in this combined assessment procedure was the physical
development suitability assessment map. Topoclimate
and visual suitability assessments were not included
since satisfactory economic evaluations have not yet
been incorporated into these procedures.
The specific purpose of this combined assessment
procedure is to show the consequences of twenty years of
suburban development in Burlington with regard to the
three components for which assessment procedures have
been developed to date. The town of Burlington has
undergone large-scale suburbanization over the past two
decades which is typical of the growth trends of many
metropolitan.communities. In the case of Burlington,
this growth is undoubtedly a combined result of the
town's proximity to Boston and of the large-scale high-
way construction activity, which has taken place in the
town over the last twenty-five years. For the sake of
visual clarity at the present scale, a simplified ver-
sion of these combined overlays is shown. In addition,
since original estimates of resource values, hazard
398
-------
Burlington Physical
Development
Suitability Map
Burlington Composite
Evaluation Map
i KM
A" quality areas: added development costs
from $0 $2000/acre
nrn "B" quality areas: added development costs
^^ from $2001 - $4000/acre
p^ "C" quality areas: added development costs
1=3 from $4001 - $9000/acre
r—I "D" quality or undevelopable areas: prohibitive
^—^ added costs ($9000+)
Figure 3. Burlington Physical Development
Suitability Map
value losses, and added development costs were based on
generalized in irmation unconfirmed by site-specific
investigation ombined landscape values are broadly
expressed by .lar value ranges. (It should be noted,
however, that ,ie COMLUP system can easily compute
specific coirf ations of value and value loss for any
desired land ipe unit. Also, it should be noted that
all economic aightings of values have been substan-
tiated by tht team's resource economists. The argu-
ments which support these values are described in the
Part II Research Bulletin of the METLAND Research.14)
The consequences of twenty years of metropolitan
suburbanization illustrated in Figure 4 are probably
obvious. However, a highlighting of these consequences
as they are seen by the METLAND research team is thought
to be in order.
First, it should be pointed out that each of the
three types of areas identified in Figure 4 indicates
the presence of significant land use constraints. These
mapped constraints may represent special resource areas
which are valuable to people in general, hazard areas
which are harmful or undesirable to people and property,
or other areas which due to their physical landscape
characteristics are especially costly to develop. In
Burlington, parcels of land exhibiting one or more of
these constraints occupy actually about half the town,
or five square miles.
As can be seen, areas having significant land use
constraints are concentrated primarily in the south-
western portion of the town. Unfortunately, when one
inspects the existing land uses of the town, it becomes
evident that post-war land use decisions resulting in
land use changes in Burlington were in no way respon-
sive to the presence of these land use constraints.
Instead, residential development, particularly single
family Bousing, has been established fairly evenly in
128
1962 Composite Special Resource Assess-
ment Value ($18,000 - $150,000)/acre
1971 Air and Noise Pollution Hazards
Assessment ($1280+/acre damages)
jjjjjjjj Development Constraint Assessment
($4000/acre added development costs)
Figure 4. Composite evaluation map of special
resource values, hazard potentials,
and development constraints
all sectors of the town (regardless of the character of
the landscape), while major shopping centers and indus-
trial uses have been located almost exclusively along
the Burlington stretches of the Route 128 and Route 3
highways.
These growth-generating highways have themselves
been located in that part of the town which has some of
the most valuable natural resources together with some
of the worst natural conditions for development. As a
matter of fact, about two-thirds of the area which is
particularly valuable in terms of special resources is
also particularly unsuitable for development, requiring
average added development costs of as much as $9000 or
more per acre to overcome natural constraints for even
low density development. These constraints are primar-
ily a result of a very high water table and/or poor
load bearing capacity. By glancing again at Figure 4,
one is reminded that despite such drawbacks, most of
this unsuitable area is not only developed, but is
actually developed with massive commercial and indus-
trial structures for which the assessed constraints and
compensatory costs are undoubtedly much greater. The
irony of this whole land use situation lies in the fact
that there is a great deal of land in the town which is
distinguished neither for its special resources nor for
its natural constraints to development.
Despite these facts, development in Burlington over
the past two decades did not follow what appears from
all points of view to be the most rational course.
There are two principal reasons for this. First, most
decision makers during the greater part of the post-war
era knew very little about landscape values and con-
straints as they have been assessed here. Second, even
for decision makers who might have known, there were no
commonly accepted devices available for implementing
protection and conservation planning decisions while
satisfying the rights of land owners and developers in
an equitable fashion. As a result, land use changes
followed and were induced by the location of major
transportation routes—a phenomenon which is well-
399
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demonstrated here by the Burlington case study.15
Considering the magnitude of the resource loss,
hazard increase, and development cost to society pro-
ceeding from this pattern of suburban growth, it is
firmly believed by the METLAND team that the long-term
public interest for planners and decision makers is to
take as much account as possible of the natural charac-
teristics of the landscape. Despite the general nature
of the results shown in Figure 4, this type of assess-
ment information is absolutely essential to wise land-
scape planning. At the very least, development deci-
sions should be postponed until estimates of potential
landscape value have been confirmed at the site level.
According to the conservative estimates of the
team, over 20 million dollars worth of resources were
destroyed, hazards increased substantially, and unneces-
sary development costs soared. The team also developed
two alternative growth patterns, one similar to the
existing one and another using a P.U.D. type develop-
ment concept. It was concluded that each growth pat-
tern could easily have accommodated the 25,000 existing
population without impairing or loosing landscape re-
sources or exposing so many residents to unhealthy air
and noise pollution, or incurring unnecessary construc-
tion and site improvement costs. Had either of these
plans been adopted originally, the town would today
find itself in significantly better shape. Instead of
polluted or highly salted local supplies of water, the
town would have numerous sources of clean ground water.
Instead of having to import sand and gravel from distant
sources at ever increasing costs, the town would have
accessible local aggregate supplies for development or
maintenance projects for many years to come. Instead
of being virtually without wetlands and the visual-
cultural benefits associated with them, the town would
have preserved its major wetland which was filled in to
accommodate the sprawling Burlington Mall.
It is realized that economic evaluation has limita-
tions. In broadening the framework of evaluation and
developing specific steps for implementation, it is
thought important to consider other interpretations
based on energy analysis and on the perceptions of
various special interest groups (such as conservation-
ists and developers). In addition the team is attempt-
ing to propose a procedure which would help an effec-
tive participation both of decision makers and of the
public in general. These activities are planned to be
undertaken in Part III of the research during 1976 and
1977.
While expanding and improving this landscape plan-
ning process, the team is convinced that the Burlington
case study should provide an impetus for landscape
assessment and planning prior to metropolitan invasions.
We do not have all the answers, but there is sufficient
supporting evidence which shows the utility of this
approach.
ENDNOTES
IRIS-Illinois Resource Information System.
Feasibility Study Final Report, Center for Advanced
Computation, University of Illinois at Urbana, Urbana,
Illinois, 1972.
Ferris and Fabos.
While METLAND is presently using a "second
generation" technology, computer programmers are
rapidly refining third generation technology designed
to overlay polygon areas directly without reconversion
to grid cells for manipulation. The Canadian Geo-
graphic Information System developed by the Canadian
National Government is an example of a completed third
generation system (see Ferris and Fabos, 1975) .
Q
Flawn, Peter F. Environmental Geology. Harper's
Geoscience Series, Harper and Row, New York, 1970.
9Bartelli, L.J.; Klingebiel, A.A.; Baird, J.V.;
and Heddleson, M., (ed.). Soil Surveys and Land Use
Planning. The Soil Science Society of America and the
American Society of Agronomy, Madison, Wisconsin, 1966.
The MIT Press,
Lynch, Kevin. Site Planning.
Cambridge, Massachusetts, 1974.
Way, Douglas. Terrain Analysis; A Guide to Site
Selection Using Aerial Photographic Interpretation.
Stroudsburg, Pennsylavania, Dowden, Hutchinson and
Ross, 1973.
Fabos, Julius Gy., and Caswell, Stephanie J.
Part II of the "Metropolitan Landscape Planning Model"
(METLAND), Agricultural Experiment Station Research
Bulletin, Amherst, Massachusetts, 1976 (in press).
The initial physical suitability procedure was
developed by Robert Reiter of the METLAND team. The
assessment shown here is a revised procedure based on
the development cost estimates of our resource
economists Robert Torla and John Foster. The adapta-
tion of those costs to this revised procedure was done
by Stephanie Caswell and the authors of this paper.
14.
'Fabos and Caswell.
Fabos et al.
Assessment.
Model for Landscape Resource
Credit to be given to the following agencies:
This study has been primarily supported by the
Massachusetts Agricultural Experiment Station, Uni-
versity of Massachusetts at Amherst, Paper No. 2013;
additional support has been received from the U.S.D.I.
Office of Water Resources Research and the U.S.D.A.
Forest Service, Pinchot Institute of Environmental
Forestry.
Fabos, Julius Gy., et al. Model for Landscape
Resource Assessment. Agricultural Experiment Station
Bulletin No. 602, Amherst, Massachusetts, 1973.
All graphics prepared by Richard Rosenthal.
Ferris, Kimball, and Fabos, Julius Gy.. The
Utility of Computers in Landscape Planning. Agricul-
tural Experiment Station Bulletin No. 617, Amherst,
Massachusetts, 1974.
4
Allen, Neil. Computer Mapping for Land Use
Planning: COMLUP. Intermountain Region: U.S. Forest
Service, 1973.
400
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A RESOURCE ALLOCATION MODEL FOR THE EVALUATION
OF ALTERNATIVES IN SECTION 208 PLANNING CONSIDERING
ENVIRONMENTAL, SOCIAL AND ECONOMIC EFFECTS
Douglas Hill
Grumman Ecosystems Corporation
Bethpage, New York
Modeling for 208 planning should be designed to fac-
ilitate participation by planners and representatives
of the affected public. Intangibles and incommensur-
ables must be considered, and the ultimate need for
value judgments to assess the importance of environ-
mental, social, and economic effects must be accommo-
dated without obscuring the factual analysis.
Ideally, population groups that are affected differ-
ently should be accounted for separately.
Model building should therefore proceed in successive
stages of greater precision. An initial qualitative
analysis leads to a conceptual model that identifies
the differential impacts of the alternatives, making
only the judgment that the impacts are beneficial or
detrimental. With land use decisions among the
alternatives for satisfying water quality goals, a
resource allocation model is useful to account for
other costs and benefits. This can be solved for the
minimum dollar cost mix of activities as a datum;
alternative plans can then be generated by assigning
additional importance to intangible and incommensur-
able values, with the plan selection informed by knowl-
edge of its incremental dollar cost.
Criteria For Modeling in Planning
The nation is embarked on something new in the way of
planning making use of models. Under Section 208 of
PL 92-500, 150 local agencies are engaged in two-year
programs to prepare areawide waste treatment manage-
ment plans to meet water pollution abatement require-
ments with "a total resources perspective." In its
guidelines for conducting this planning, the EPA(l)
emphasizes land use considerations, nonpoint pollution
sources, and environmental, social and economic impact
evaluation in the comparison of alternatives and
selection of a. plan.
Almost without exception, the preparation of these
plans is in the hands of regional planning agencies,
not the departments of public works who have tradi-
tionally done water quality planning. As never before,
land use planners and water quality engineers are
being thrown together to combine their talents. It
remains to be seen whether in 208 environmental
modeling will provide the organizing structure that
focuses interdisciplinary planning or whether it will
remain an arcane art practiced by a few professionals.
To the ordinary planner, a mathematical model is a
black box which is mysterious if not frightening. If
ha is trapped in a situation where he must use the
results of models, he can no doubt be intimidated into
doing so by the authority of his consultants or their
peers, but he will be acting as much on faith as if
someone were reading entrails. When the contract ends,
he will be in no position to judge how his plans should
change as conditions change.
Moreover, not only professionals are engaged in 208
planning. The requirement for regular meetings of a
citizens' advisory committee seems to be leading to
genuine public participation. This may be regarded
as a monumental nuisance or as the opportunity to add
the dimension that has been missing from most environ-
mental decisions in the past: proper consideration of
value judgments.
Environmental decisions necessarily involve both facts
and value judgments, and at some philosphical risk,
emphasized by Walker\2), a distinction can be made
between them.
o Fact: whether and to what extent as effect
occurs
o Value judgment: whether it is good or bad,
and whether that matters
Environmental phenomena described by scientific state-
ments that are subject to test are facts; so are the
tangible products of engineering decisions. Whether
it is important that certain areas of a bay be safe
for swimming is a value judgment. Granted that in the
domain of aesthetics where one's very perceptions are
determined by one's tastes the distinction may not be
.clear.
A sequence of analytical steps showing the relation-
ships of facts and values is given in Table 1. The
sequence starts with a planned action, shown at the
bottom of the diagram, which may have direct environ-
mental, social, or economic effects as indicated by
the lower box in each of the respective columns.
The first step in the analysis is to determine whether
such an effect occurs (yes/no). If so, the next step
is to identify the kind of effect. Identifying the
kind of environmental effect may lead to the identifi-
cation of a social effect (horizontal arrow) not
previously identified as a direct social effect.
Similarly, identification of the kind of social effect
may lead to the identification of an economic impact
(horizontal arrow) not previously identified as a
direct economic impact.
The next fact that may be determined is the direction
of the effect (more/less). On the basis of these
facts, a value judgment can be made (horizontal arrows)
as to whether the change is beneficial or detrimental
to the environment or to man, some of the latter con-
sisting of economic effects. As we illustrate below, :
401
-------
ENVIRONMENTAL EFFECTS
FACTS
VALUE JUDGMENTS
SOCIAL EFFECTS
FACTS
VALUE JUDGMENTS
ECONOMIC EFFECTS
FACTS
I
VALUE JUDGMENTS
FIG. I SEQUENCE OF ANALYTICAL STEPS IN ENVIRONMENTAL MODELING
carrying the analysis only to this point may provide
considerable insight into the implications of alterna-
tive environmental decisions.
The final step in the sequence of analysis of fact is
the quantification of the amount of the change, an
example of which is water quality modeling. This may
assist in the quantification of social effects on man
(diagonal arrow) which may further lead to the mone-
tization of economic effects (diagonal arrow). The
monetization of economic effects may be accomplished
by the marketplace in terms of market prices. In
the case of public goods or bads, however, monetiza-
tion must be accomplished by other analytical means,
i.e., cost-benefit analysis.
Two important classes of effects that cannot be mone-
tized are those that are intangible or incommensurable.
Nevertheless, the direction, more or less, of these
effects may be determined, and a value judgment made
as to whether such an effect is beneficial or detri-
mental to man. There may be some difference of opin-
ion among individuals as to how aesthetic effects, for
example, may become more pleasing; on the other hand,
there is likely to be considerable consensus on what
is displeasing.
The difficulties in treating aesthetics are great
enough that they are usually ignored in environmental
analyses, yet we are told by Kneese and Bower(3) that:
The limited evidence from the studies
and analysis...leads to the virtually
inescapable conclusion that higher
water quality must be justified pri-
marily on aesthetic and recreational
grounds, if it is to be justified at
all.
Similarly, Ridker^' observed that psychic costs are
likely to be a large portion of the total cost of air
pollution. If anything, the aesthetic sensibilities
of the public have probably become more acute since
these studies were made. In the absence of adequate
quantitative methods, assessing the importance of
aesthetic effects and psychic costs is largely a
matter of judgment.
Between the facts of the matter and their effect on
public policy, in short, stands a screen of value
judgments. Most properly, these are the concern of
the affected public. In environmental studies, they
are often ignored or - worse - estimated by technicians
as "importance factors." Of the numerous objections
to this practice, as Andrews(5) points out, it may in
particular obscure the choices to be made by "burying
usable information about impacts on specific para-
meters beneath a layer of questionable value judgments."
The expense that may be justified in raising the
fidelity of models of the facts in the presence of the
noise of value judgments is another question.
In summary, if environmental models for planning are
to be Improved, they should meet several criteria:
They should be comprehensible to other
planning professionals and the lay public
402
-------
o They should identify what is Important
and what is not, preferably early enough
to avoid large scale data collection of
little relevance
o They should distinguish between facts
and value judgments
o They should provide a mechanism that
reflects the uncertainty in value judg-
ments and represents the views of the
affected public
o They should therefore distinguish sections
of the public that are affected in different
ways
In attempting to meet these criteria, the modeling
procedure proposed here will be described by two
examples: (l) a qualitative model to be used near
the beginning of the 208 process to determine what is
important, and (2) a quantitative model to be used at
the end to facilitate making the value judgments
needed to select a plan.
Qualitative Model
To discover profound truths about
man and his relations with the world
about him, we are well advised to
follow two simple rules:
Rule 1. Take a simple idea.
Rule 2. Take it seriously.
Garrett
The qualitative analysis is based upon the simple idea
that a relatively non-controversial judgment can be
made as to whether the environmental, social, and
economic effects of a planned action are beneficial
or detrimental. Taking this idea seriously consists
of organizing the results of this analysis and pre-
senting them in a way that clearly illustrates the
differential beneficial and detrimental effects of
alternative plans on geographical areas or interest
groups .
Qualitative analysis is the process of finding how
many and what elements or ingredients are present,
as in chemistry. The model for planning appropriate
to this initial stage of analysis is a conceptual
model which although a preliminary and tentative
representation of reality should nevertheless consist
of the right variables in their correct relationships.
A particular value of a model at this stage is its
heuristic use as an instrument of discovery to explore
the structure of the problem.
As pointed out by Ackoff and Sasieni (?', differences
in the degree of obscurity of a problem have produced
different patterns of model construction. Inevitably,
however, the model builder must decide how to simplify
reality in the most satisfactory way. In environ-
mental modeling, this has often led to omitting rele-
vant variables: the intangibles and incommensurable s.
In simplifying, the model builder is faced with con-
flicting objectives: (l) to make the model easy to
solve and (2) to make it accurate. At this initial
stage, the emphasis should be on making it easy to
solve, if possible easy enough for the nonmathematical
planner. This can best be accomplished not by dropping
variables but by backing off on the requirement for
accuracy to only the first step in quantification:
whether it is more or less. Moreover, since value
judgments provide the final weighting of environ-
mental impacts anyway, the process of "solving" the
model at this stage can be short-circuited by the
judgment that a given effect will make things better
or worse.
This methodology has previously been applied to an
environmental analysis of alternatives to dredging a
harbor on Long Island, as reported in Wells and Hill("),
Reference will be made to tables originally presented
in that paper for illustration.
Procedure for Qualitative Analysis
The procedure for qualitative analysis is as follows:
1. Establish the comparison of alternatives
on a valid cost-effectiveness basis,
e.g.5 by comparing the environmental,
social, and economic costs of alternatives
of equal effectiveness, say, in disposing
of equal amounts of wastewater.
2. Determine the geographical areas or interest
groups that are affected differentially
by the alternatives considered.
3. Identify comprehensively the environmental,
social, and economic parameters possibly
affected by each alternative.
h. Summarize in tabular form the nature of
the impact on each parameter of each
alternative.
5. Evaluate whether each of these impacts is
beneficial (+) or detrimental (-) to each
geographical area or interest group, as
illustrated in Table 2, nil owing for counter-
vailing effects (+) and uncertainty in the
judgment (/). At this stage, th'is judgment
is made regardless of whether the information
available is precisely quantitative or
merely subjective.
6. Present the pattern of beneficial, detri-
mental, and countervailing impacts in a
matrix of alternatives vs. geographical
areas or interest groups. (The summary
of all impacts on Port Jefferson, Table 2,
is shown as Row k of Table 3.)
7. Superimpose on this matrix the identifi-
cation of the parameters affected benefici-
ally or detrimental 1y, aggregating those
that are affected similarly and noting those
that vary identically with an arrow as
shown in Table 3.
This final table provides a useful display of the con-
sequences of the choices to be made. It does not make
the decision, but it clarifies the decision structure.
The beneficial or detrimental implications of the
hard scientific and engineering facts are exposed.
To choose among the alternatives, further judgments
must then be made as to the environmental, social,
or economic importance of these consequences, a step
best left to the end of the quantitative analysis.
The results of the qualitative analysis consist of
the following:
o Geographical areas (and thus population
groups) and interest groups affected
differentially
403,
-------
TABLE 2 - SUMMARY OF AREA IMPACTS
IMPACT AREA: PORT JEFFERSON HARBOR AND VICINITY
"\ PARAMETERS
\, AFFECTED
"•v
\.
ALTERNATIVES X.
I \
No Modification
Dredge Channel, Basin
Offshore Platform (Harbor)
(Long Island Sound)
(Truck)
Transship from (Barge)
Northvllle: 3
(Pipeline)
Pipeline from
New York Harbor
Ma
Qu
ter
ality
Wate
Shellfish
i
o/-
o/-
H
4
4
4
Fin
Fish
' 1 '
o/-
o/-
4
4
4
t-
0
0
0
0
0
0
0
Gro
rfowl Wa
Other
Wildlife
1
•
-
H
H
V
-t-
Oil
Pollution
, I \
0
0
0
0
0
0
0
i
±
+
+
01
und Plea
er Boa
Air
Quality
i
ase
o/-
0
0
0
0
0
Spoil
Disposal
' 1 '
line C
0
0
0
0
+
0
0
0
0
0
sure pi
ing Haz
Road
Traffic
'
0/+
0/+
o/-
0/+
0/ +
Waves,
Surges
1 w
0
0
0
0
H
4
h
o/-
o/-
0
0
0
0
0
re
ard
SUMMARY
OF ALL
IMPACTS
ON
Aesthetics PT. JEF
4-
4-
Land Use
Conflicts
\ •
o/-
-
H
+
0
0
0
0
+
±
±
;
t
TABLE 3 CONCEPTUAL MODEL: ENVIRONMENTAL EFFECTS BY ALTERNATIVE AND AREA
PLATFORM
IN PORT
JEFF
HARBOR
TRANSHIP
BY PIPELINE
FROM
NORTHVILLE
Oil Poll'n
Aesthetics '
Grd. Water "
Land Use Conf.
Poll'n.
Aesthetics
Grd. Water ^
«Road Traffic
"Water Quality^
/Waterfowl s
Oil Poll'n =
/Aesthetics
Water Quality!
Waterfowl =
Oil Poll'n =
Aesthetics EEEE
Water Quality^,
Waterfowl ^.
Oil Poll'n J~
.Aesthetics _
// // - <&
— N
plater Quality
^Haterfo
Oil Poll'n
^Aesthetics ^
*Grd. Water"
?Lani^ Use Conf.
Nfoaf Traffic^
Water Quality
Waterfowl
Oil Poll'n
Aesthetics II
iGrd. Water
Land Use Conf
Road Traffic
Water Qual1ty_
Waterfowl =
Oil Poll'n ==
Aesthetics =
Grd. Water ^=1
Land Use Conf.=
ad
_Water Quality .
"Waterfowl »
'Oil Poll'n = "
Aesthetics =
*Land Use Conf*
NORTHVILLE t, VICINITY
EWater Quality
=Waterfowl
Oil Poll'n
Aesthetics
lating
Water Quality'
Waterfowl
Oil Poll'n
esthetics
oating
l/ater Quality!
tlaterfowl
011 Poll'n „
Aesthetics ,
Water Quality
waterfowl ~
011 Poll'
PORT JEFFERSON HARBOR
S VICINITY
OTHER L.I. HARBORS
NEW YORK BIGHT g
BENEFICIAL
o Direction of the environmental, social,
and economic impacts: beneficial or
detrimental
o Determination of identical impacts among
areas
o Identification of the environmental, social,
and economic parameters affected on which
data are therefore needed.
For each of the impacts thus identified as discrimina-
ting among the subplans and alternatives considered,
404
-------
a further evaluation can then be made as to whether
these impacts are :
o Long or short term
o Avoidable or unavoidable
o Reversible or irreversible
Where these distinctions are important in discrimin-
ating among alternatives, the information presented
in the tabular summaries can be suitably coded. For
example, irreversible adverse consequences can be
highlighted in the table. We believe that this format
is especially suitable to display and discuss the
evaluations and methodologies with a nontechnical
audience.
This qualitative analysis can be performed very early
in the 208 program, since one does not usually begin
in a state of complete ignorence of the possibilities.
Forcing a preliminary identification of subplans
early in the plan development should have the useful
effect of focusing the main part of the work on real
possibilities. Moreover, the results of this quali-
tative analysis of the impacts will be available early
enough to assure that information needed for the final
evaluation is not unknowingly overlooked until the
final months of the planning program.
Quantitative Model
The qualitative model identifies the trade-offs to be
made; the quantitative model should inform them with
data insofar as possible. The purpose of the quanti-
tative model is to define rigorously the information
needed to compare subplans, to compile them as mixes
into alternative plan packages, and to show the conse-
quences of alternative decisions.
Linear programming models have been used previously
to determine" efficient degrees of wastewater treatment
to achieve specified levels of receiving water quality.
With the emphasis on nonpoint sources of pollution,
nonstructural water quality controls, and land uses
in 208 planning, however, the problem is not simply
to minimize dollar costs. Alternative land uses have
varying environmental and social as well as economic
value, and alternative plans are appropriately cast
in the framework of a resource allocation model. On
the basis of the qualitative analysis, the resource
allocation can be decomposed into geographical areas
that can be analyzed as more or less homogeneous units
with the local environmental and social impacts of
various activities.generally judged to be either bene-
ficial or detrimental. An illustration for one such
area, a hypothetical estuary in which the use of wet-
land is at issue, is shown in Table k. Further details
of this model are given in Hill(9).
The use of a linear program to describe in part natural
processes which are characteristically nonlinear
perhaps deserves some defense. The linear model was
used here because it is inexpensive to solve using
standard computer software, and because i£s economic
interpretation has been well established. Certainly
it will be important to verify that the use of linear
coefficients does not do violence to the known facts.
The more serious question may be whether enough is
known about the natural systems to justify modeling
at all, however, not how closely the model simulates
reality. Probably the principal value of the model
is its identification of the data needed to make an
informed decision.
The model is formulated with an economic objective
function (Row A) using market values and costs to
identify as a datum the mix of activities meeting the
constraints at minimum monetary cost. While it is
not generally possible to define environmental and
TABLE 4. DATA FOR RESOURCE ALLOCATION IN AN ESTUARY
* Product
- Consumt
CONSTflAIIITS
1 Tall Fringing S^_ a_H. (000 Acres)
2. Other Sfiartina (000 Acres)
3 Clam Beds (Acres)
4. Mussel Beds (Acres)
o Sea Worm Bottom (Acres)
6 Detritus 1n fay (000 Ib per year)
/. Haste Water (HGD)
6. D.O. Level (rog/1)
9. Nitrogen Load (000 Ib per day)
1C. Flounders (000 Ib)
11. Cod (000 Ib)
12. Fish Aatto
13. ftartnas {*)
OBJECTIVE FUNCTIONS
A Annual Net Income (SOOO)
B. Envtronaental Value
,C. Social Value
«E
B Sg
-0.003
-0.007
-0.001
-0.00?
M H I
-1000 -100
+0.20? +0.214 +0.35
s s
0
+27.5
> 0.12
t- 1.68
> 650
> 140
-.0026 +'
,.05 (I
405
-------
social functions quantitatively, the signs of the
coefficients can be judged (Rows B and C). These may-
be viewed as the direction of corrections that should
be made to market prices to allow for nonmarket exter-
nal effects. Preserving salt marsh (Columns 1 and 2)
is estimated to have a market value of only $35 per
acre per year, for example, an amount representing
rental of hunting rights. This understates the true
value of wetlands in their natural state because of
their many attributes as a public good: providing
habitat and food for fish and wildlife, serving as a
nutrient trap for waste water, providing open space
that offers aesthetic values, etc. Because of these
positive environmental and social values, the amount
of $35 per acre per year should be increased'.in deter-
mining the best use of wetland, but it is not known
by how much.
The program is therefore exercised parametrically with
the value of wetland increasing to determine how
environmental and social factors will affect the mix
of activities as they are assigned additional impor-
tance . For each such change in the program mix, the
incremental monetary cost can be determined. This
establishes the break-even cost at which one alterna-
tive plan gives way to another because of its additional
environmental and social value. Part of this incre-
mental cost can be attributed to those benefits that
can be quantified. Whether the remainder is sufficient
to account for unquantifiable intangibles can be decided
with the participation of representatives of the public
that will pay the additional dollar cost.
The results of the model are illustrated in Table 5
in which the allocation^ of wetland is determined in
part by their environmental and social value. The
minimum monetary cost allocation is described by the
bottom row of the table where the market value of wet-
lands is $35 per year and environmental and social
values of wetlands are taken to be zero. Under these
circumstances, the allocation of wetlands consists of
preserving 120 acres of tall Spartina alterniflora and
380 acres of other marsh grass, while 1,300 acres of
the other marsh grass is filled for development. If
the positive environmental and social values of wet-
lands are recognized, however, an alternative plan
determined by the model consists of the preservation
of all marsh grass as shown in the top row of the table.
This is determined by the program to have an incre-
mental cost of $247,000 per year which in this case is
the opportunity cost of not filling marsh land for
commercial purposes.
Thus, the decision makers are presented with the
information that if they choose to preserve al1 wet-
lands, they are in effect indicating that the community
is willing to pay an additional quarter million dollars
per year to preserve its environmental and social
values. Notice that this result does not state that
the environmental and social values of wetland in these
circumstances are $247,000; it states that the value
must be_ worth $247,000 for the decision to be made to
preserve all wetlands because of their environmental
and social values. Thus it is left to the decision
makers to decide on behalf of the community whether
this expenditure is justified. Although this kind of
result does not give the- decision makers the "answer",
it narrows the range in which judgment just be exer-
cised.
Environmental decision analysis is largely economic
in nature, but it is ultimately political. Models for
environmental planning can therefore be no more deter-
minate than the political processes. They will perform
a service if they provide the political decision making
processes with information on the consequences of
alternative decisions. Whether an ordinal comparison
TABLE 5. WETLAND ALLOCATION vs.
ENVIRONMENTAL & SOCIAL VALUE
ALTERNATIVE
PLAN
MINIMUM
MONETARY
COST
WETLAND
VALUE
MARKET
$35
$35
ENVL a
SOCIAL
f
(190)
0
WETLAND ALLOCATION (ACRES)
PRESERVE
TALL
S.ALT
120
120
OTHER
1680
380
FILL
TALL
S.ALT
0
0
OTHER
0
1300
INCREMENTAL
COST
+$247,000
that ranks alternatives is sufficient for political
decision making or.whether a cardinal measure of
utility is needed has been a matter of dispute, as
debated in HookU°). Haefelei11' has pointed out that
it is the importance of the issue as well as one's
preference as to its outcome that makes vote trading
possible. Certainly the price that we are willing to
pay is a familiar measure of the importance we assign
to things as well as the way we reveal our preference.,
Moreover, recognizing population groups that are
Impacted differentially, as we have proposed, while
not likely to lead to a Pareto optimum in which no one
suffers, at least identifies the gainers and losers.
The equity with which this trade-off may be made in the
larger political context may depend upon the model used
for planning.
References
1. U. S. Environmental Protection Agency. 1975.
Guidelines for areawide waste treatment management
planning. Washington.
2. Walker, Richard A. 1973. Wetlands preservation
and management on Chesapeake Bay: the role of
scinece in natural resource policy. Coastal Zone
Management Journal l(l): 75-101.
3. Kneese, Allen V. and Blair T. Bower. 1968.
Managing water quality: economics, technology,
institutions. The Johns Hopkins Press, Baltimore.
328 p.
4. Ridker, Ronald G. 1967. Economic costs of air
pollution. Frederick A. Praeger, New York 214 p.
5. Andrews, Richard N. L. 19714.. Comments on 'An
Environmental Evaluation System for Water Resource
Planning1 by Norbert Dee et al. Water Resources
Research 19(2): 376-378.
6. Hardin, Garrett. 1972. Preserving quality on
spaceship Earth. Transactions of the 37th North
American Wildlife and Natural Resources Confer-
ence, Wildlife Management Institute, Washington.
472 p.
7: Ackoff, Russell L. and Maurice W. Sasieni.
Fundamentals of operations research. John Wiley
and Sons, New York. 455 p.
8. Wells, James and Douglas Hill. 1974. Environ-
mental values in decision making: Port Jefferson
as a case study. Journal of Environmental Sciences
12(4): 19-28.
9. Hill, Douglas. 1976. A modeling approach to
evaluate tidal wetlands. Transactions of the 4lst
North American Wildlife and Natural Resources
Conference, Wildlife Management Institute,
Washington, (in press)
10. Hook, Sidney (Ed.) 1967. Human values and
economic policy. New York University Press,
New York. 268 p.
11. Haefele, Edwin T. 1973. Representative govern-
ment and environmental management. The Johns
Hopkins University Press, Baltimore. 188 p.
406
-------
REGIONAL RESIDUALS-ENVIRONMENTAL QUALITY MANAGEMENT MODELS-
APPLICATIONS TO EPA'S REGIONAL MANAGEMENT PROGRAMS
Walter 0. Spofford
Quality of the Environment Program
Resources for the Future
Washington, D.C.
Charles N. Ehler
Office of Air, Land and Water
Office of Research and Development
U.S. Environmental Protection Agency
Washington, D.C.
ABSTRACT
The paper describes the elements of a regional inte-
grated residuals-environmental quality management model
developed at Resources for the Future to assist govern-
ments in establishing public policy on regional environ-
mental quality--air, water and land—through the
explicit analysis of the linkages among gaseous, liquid
and solid residuals, and among the various environmental
media. Within an optimization framework, the model
evaluates a large number of residuals management options
including non-treatment alternatives, so that least-cost
ways of achieving various levels of ambient environ-
mental quality, subject to constraints on the geographic
distribution of costs of achieving these levels, can be
identified. The overall management model is made up of
three parts: a linear programming model of regional
residuals generation and discharge, environmental models
(air dispersion and aquatic ecosystem models), and an
environmental evaluation section. A summary of results
from a test application of the model in the Lower Dela-
ware Valley is presented.
Lessons learned from the development of the Delaware
model are related to the objectives and analytic
requirements of EPA's current regional management
programs, Air Quality Maintenance and Areawide Waste
Treatment Management (208) plans.
INTRODUCTION
While it has long been known that the physical environ-
ment is an interconnected system, we have traditionally
analyzed and regulated it by each of its component
media--air, water, and land—ignoring intermedia link-
ages and possible interform transformations of wastes.
The management of wastes, or residuals, from society's
production and consumption activities requires decisions
regarding environmental quality and economic trade-offs
implied in the discharge of residuals into one or more
of the environmental media. For example, "clean" air is
more likely to result if we choose to discharge
residuals to water bodies or place them on the land;
clean" water is highly probable if we choose to
discharge residuals to the atmosphere and/or land; and
so on. However, if we choose to have high levels of
both air and water quality, as well as high quality
landfills, then the management decisions become increas-
ingly more complex, requiring information on the
physical and economic effects of achieving specified
levels of environmental quality simultaneously. The
development of this information requires analytical
methods that are more sophisticated than those generally
In practice today. The purpose of this paper is to
discuss regional environmental quality management models
in general, and to describe one model, developed over
the past four years at Resources for the Future, that
potentially has great utility in providing this type of
information to decision-makers.
Before discussing the model, however, we will briefly
discuss the needs of one possible group of users of this
type of model--sub-Federal units of government charged
with implementation of two of EPA's regulatory programs,
Air Quality Maintenance and Areawide Waste Treatment
Management (208) plan development.
EPA'S REGIONAL ENVIRONMENTAL QUALITY MANAGEMENT PROGRAMS
Under the 1970 Clean Air Act Ammendments, in April 1971,
EPA promulgated primary and secondary National Ambient
Air Quality Standards (NAAQSs) for hydrocarbons, carbon
monoxide, nitrogen doxide, sulfur oxides and particulate
matter. In addition, standards have been set for photo-
chemical oxidants, even though they are not directly
emitted to the air, but are a product of atmospheric
reactions between nitrogen oxides and reactive hydro-
carbons. National primary ambient air quality standards
are specified at a level of air quality necessary to
protect the public health. National secondary ambient
air quality standards define levels of air quality which
are necessary to protect the public welfare from any
known or anticipated adverse effects.
After the Federal air quality standards were established,
all States were required to submit plans by which they
would insure that the standards would be attained by
1975. In May 1972 EPA published its approvals and
disapprovals of State Implementation Plans (SIPs) and
shortly thereafter promulgated substitute regulations
for deficient State plans. However, the Natural
Resources Defense Council, Inc. (NRDC) and various other
petitioners challenged EPA's approvals on several
grounds, including the contention that the plans approved
were not adequate to ensure maintenance of the NAAQSs
over time once they were attained. No plan was found
that had adequately analyzed the impact of growth on air
quality maintenance for any significant period into the
future. Subsequently, in March 1973, EPA disapproved
all SIPs with respect to maintenance of standards. In
June 1973, EPA promulgated regulations requiring States
to develop Air Quality Maintenance (AQM) plans for areas
with the potential for exceeding a NAAQS between 1975
and 1985. From June 1973 until very recently, EPA and
the States have been designating AQM areas. EPA guide-
lines specified that, at a minimum, the States should
consider all Standard Metropolitan Statistical Areas
(SMSAs). To date, 168 AQM areas have been designated
for at least one airborne residual.
The AQM plan is simply an extension of the SIP. Many of
the strategies in the SIP to insure attaineent of the
standards can also serve to insure maintenance. Tradi-
tional strategies such as the review of new and modified
stationary sources and the prevention of their construc-
tion if air quality standards will be violated, new
source performance standards, and standards for emissions
from new motor vehicles might be sufficient to maintain
standards in many areas of the country. In most areas,
however, these strategies will not be sufficient to
407
-------
maintain standards and it will be necessary to incor-
porate air quality considerations into the overall
context in which decisions regarding metropolitan
development are based.
EPA is currently requiring that the plans be submitted
as soon as possible for areas that will fail to meet the
NAAQSs in the near future; for areas that will not fail
to maintain standards until the more distant future, EPA
will usually require the AQM plan to be submitted at
least 3 to 5 years before measures are actually needed
to maintain the standards. While EPA is flexible on the
time horizon of the AQM plan, it is encouraging a period
of 10 to 20 years as appropriate for most areas. The
regulations will require States to reassess, at
intervals of not more than 5 years, all areas to deter-
mine whether any areas need plan revisions.
Beyond demonstrating that the strategies proposed in the
plan are effective in maintaining NAAQSs, the plan must
also demonstrate that the State or a substate entity has
adequate legal authority to implement the measures con-
tained in the plan. Where measures are included that
local governments have traditionally enforced, e.g.,
minimum thermal insullation requirements for new
construction, the AQM plan must demonstrate that a local
government has the legal authority to enforce such
measures. The plan must also describe the relationships
between air quality management and State, local and
regional programs for land use, transportation, water
quality and solid waste management. Of particular
interest are the physical, technological, economic and
institutional relationships between AQM and Areawide
Waste Treatment Management (208) planning.
The Federal Water Pollution Control Act Ammendments of
1972 (FWPCAA) call for the development of ambient water
quality standards " whenever the State revises or
adopts a new standard such revised or new water
quality standard shall consist of the designated uses of
navigable waters involved and the water quality criteria
for such water based upon such uses. Such standards
shall be such as to protect the public health or welfare
enhance the quality of water, and serve the purposes of
the Act." The "purposes" of the Act are defined to
include "....an interim goal of (ambient) water quality
which provides for the protection and propagation of
fish, shellfish, and wildlife and provides for recrea-
tion in and on the water be achieved by July 1, 1983."
Section 208 of the FWPCAA calls for Areawide Waste
Treatment Management Planning in areas with substantial
water quality management problems due to urban-
industrial concentrations or other factors. Particular
emphasis is being placed in 208 planning on the "soft-
ware" or implementation aspects of water quality manage-
ment (e.g., economic incentives, land use management
measures, etc.), in addition to the traditional
technological options. 208 planning also places
particular importance upon the development of management
strategies for non-point sources.
To date, 149 areas have been designated as 208 planning
areas, but it is anticipated that eventually most SMSAs,
approximately 250, will be covered by 208 plans. In
addition, all 50 States must prepare plans for
non-designated areas of their respective States. Plans
must be submitted to EPA two years after the work plan
is declared operational, but not later than November 1,
1978. The planning time horizon for 208 planning is
20 years.
Specific plan outputs include the identification of
anticipated municipal and industrial treatment works
over a 20 year period, identification of urban storm-
water management systems, a program for the management
of residuals generated in treatment (secondary
residuals), and a program for non-point source manage-
ment. As in Air Quality Maintenance plans, the 208 plan
must demonstrate that the strategies proposed are
enforceable and must identify agencies authorized to
construct, operate and maintain facilities required by
the plan, and otherwise implement the plan.
While AQM and 208 plans have slightly different planning
requirements, both will perform essentially the same
analytical tasks:
1. a survey of existing emissions/effluents,
their sources, ambient environmental quality,
and an initial assessment of existing and
potential problems;
2. a projection of population and economic
activities over the planning period;
3. a projection of future emission/effluent
discharges, from 2;
4. a projection of future ambient environmental
quality, from 3.
5. comparison of results of 4 with standards and
a determination of the reduction required;
6. development of alternative strategies to
achieve and maintain standards;
and 7. evaluation and selection of a "best" strategy
for implementation.
STRUCTURING MANAGEMENT MODELS
Regional residuals-environmental quality management
models can be used to analyze the simultaneous impacts
on costs and on environmental quality of alternative
residuals management strategies. Their basic purpose
is to generate information upon which to base public
decisions regarding the levels of use and/or protection
of the natural environment.
Management models are used primarily to rank sets of
strategies according to a given criterion, such as
least cost to the region. For this use, the intent is
to locate the optimal, or in some sense "best" strategy.
In addition, these models are used to explore the range
of technologically, economically and politically
feasible alternative strategies for the region.
Basically, there are three approaches to seeking an
"optimal" strategy for any given objective and set of
constraints: 1) response surface sampling using
simulation; 2) optimization (mathematical programming)
techniques; and 3) a combination of 1) and 2). An
example of the latter is exogenous treatment of various
levels of low flow augmentation in a water quality
optimization model. However, the costs (and damages,
if they occur) of providing the various augmented flows
are included in the overall ranking of the various
management alternatives.
Each approach has its advantages and disadvantages.
Simulation models, in general, are able to provide a
more realistic representation of real-world conditions,
and their outputs are generally easier to obtain than
optimization models are to solve. They are conceptually
straightforward, and nonlinearities, discontinuous
functions, non-steady-state (transient) behavior, and
stochastic aspects are much easier to include than with
optimization models. However, there are two major
disadvantages. First is the general difficulty of
selecting a priori that combination of raw material
inputs, production processes, recycling and by-product
production opportunities, and residuals modification
activities and levels that optimizes a given'objective
function. Exhaustive sampling of a finite number of
combinations can be used. But because the total number
of combinations is usually extremely large, random
sampling techniques appear to be a more reasonable approach.
408
-------
The second major disadvantage with simulation-type
management models is the extreme difficulty of exploring
the economically and politically feasible range of
management strategies, even when least cost strategies
are not being sought. For regional analyses, economic
and political feasibility becomes relevant when it is
desired to constrain costs, either the regional aggre-
gate, or the distribution of costs among dischargers,
consumers in geographic subregions, and/or among income
groups; or the levels of ambient environmental quality
at designated locations throughout the region; or both
costs and environmental quality simultaneously.
The two major advantages of optimization models are:
1) the direct determination of the activity levels that
optimize a given objective function; and 2) the ability
to simultaneously satisfy sets of constraints,
especially inequality constraints (e.g., upper and lower
bounds on activities), and thus the possibility for
exploring the range of technologically, economically
and politically feasible management strategies. Their
major disadvantages, given the magnitude of the regional
residuals management problem, are that they are
generally difficult to construct and then to solve,
even when formulated as linear programming problems.
Furthermore, they may not be sufficient representations
of the actual (real world) situation. For some cases,
a combination of simulation and optimization techniques
provides the logical approach to residuals management
problems. The use of one technique or the other or a
combination would depend upon each individual situation.
There are two basic types of programming models:
1) linear programming (LP) models, and 2) nonlinear
programming (NLP) models. Linear programming models
are particularly useful when the environmental models
(e.g., water quality, air dispersion, and ecosystem
models) are formulated as a set of linear relationships.
This form of management model is in widespread use
today, especially for applications involving the
management of regional water quality.1
Unfortunately, linear programming models cannot always
be used for analyzing regional management strategies,
especially if ecosystem models are incorporated within
the analytical framework. Ecosystem models are often
expressed as a set of nonlinear relationships, and for
these situations, nonlinear programming models are
necessary.2
The regional model and application described in the next
section is of this general nonlinear form. The
nonlinear programming algorithm used for the analysis is
based on the gradient method of nonlinear programming.
Unlike the more classical linear management models, the
environmental models are not incorporated in the con-
straint set, but dealt with in the objective function.
This modification requires the use of penalty functions
for exceeding ambient standards.3 All nonlinear
programming algorithms start from a trial feasible
solution and using an iterative search process, select
increasingly better solutions until the best possible,
or optimal, solution is found. In the application
described in the next section, a linear program
is used to select better and better solutions.
Details of the algorithm and solution procedure may be
found in [10,12,13 and 17].
A.REGIONAL RESIDUALS-ENVIRONMENTAL QUALITY MANAGEMENT
JtUfcL APPLICATION
In this section we describe the essential elements of a
regional integrated residuals management model developed
at Resources for the Future by an interdisciplinary team
representing the fields of political science, economics,
ecology, and engineering.1* This illustrative application
409
to the eleven-county Lower Delaware Valley region
represents the final phase--a real world application--
of a research effort at RfF which has concentrated on
the development of regional residuals management models
to aid government in establishing public policy for
regional environmental quality management. Publications
describing various stages in the development of the
model are available [10-16]. In addition, a fairly
detailed description of the regional application,
results of analyses using the regional model, policy
and research implications, and lessons learned from the
application have been prepared [17-19].
The Research Objectives
The major objectives of the RfF research effort and
regional application can be stated, briefly, as follows:
1. to investigate the importance of including
within a single analytical structure the
the linkages among gaseous, liquid, and
solid residuals, and the three environmental
media;
2. to explore the feasibility of incorporating
within a regional optimization model a complex,
nonlinear aquatic ecosystem model. An
assessment of this objective is not included
in this paper, but may be found in [19];
and 3. to explore the ways of designing regional
residuals management models to provide
distributional information on costs and
environmental quality such that these models
would be useful in a legislative, as well as
executive, setting. The distribution of costs
and environmental quality is often the central
issue in regional environmental quality manage-
ment, with efficiency considerations (e.g.,
least cost strategies) of secondary importance.
The Region
The region that the RfF group selected for their illus-
trative case study is one of the most densely populated
and heavily industrialized in the U.S. The region
surrounds the well-studied Delaware Estuary, covers
portions of Delaware, Pennsylvania, and New Jersey, and
includes the major cities of Philadelphia, Wilmington,
Camden and Trenton. For the sake of brevity, let it
suffice to note that 5.6 million people resided in the
region in 1970. A major concentration of industrial
activity spews out enormous quantities of liquid and
gaseous residuals to the watercourses and atmosphere
in the region, and generates various types and quantities
of solid residuals.
The Regional Model
The model, applied to the Lower Delaware Valley region,
is designed to provide the minimum cost way of producing
1970 production levels, or "bills of goods," at the
individual industrial plans; of meeting electricity, and
home and commercial space heating, requirements for the
region; of handling, treating, and disposing of specified
quantities of municipal wastewater and solid residuals,
subject to two sets of exogenously imposed constraints:
1. the distribution of environmental quality--
i. in the 22 reaches of the Delaware Estuary:
minimum levels of dissolved oxygen and
fish biomass, and maximum concentrations
of algae;
ii. at 57 selected "receptor" locations through-
out the region: maximum annual average
ground level concentrations of sulfur
dioxide and suspended particulates;
-------
iii. at landfill sites throughout the region:
restrictions on types of landfill opera-
tions which can be employed.
2. the distribution of consumer costs in the 57
political "jurisdictions" of the region5--
i. increases in the costs of electricity
(by utility service area) implied by
constraints on regional environmental
quality (the first constraint set);
ii. increases in home heating costs implied
by constraints on regional environ-
mental quality;
iii. increases in municipal sewage disposal
costs implied by constraints on
regional environmental quality;
iv. increases in municipal solid residuals
handling and disposal costs implied
by constraints on regional environ-
mental quality.
The regional management model is shown schematically
in Figure 1 below. Because the aquatic ecosystem is
nonlinear, an iterative nonlinear programming algorithm
was employed to search for "optimal" solutions. There
are three main parts of the overall regional model: a
linear programming model of regional residuals genera-
tion and discharge (comprising both production and
consumption activities); the environmental models; and
an environmental evaluation section. These three major
components of the regional model are discussed in more
detail below. But first, we should indicate the
linkages among these major parts, and the iterative
scheme that is used to converge on an "optimal"
solution.
A key output of the LP model is a vector of residuals
discharges. This vector is input to the environmental
models. The output of the environmental models are
vectors of ambient environmental quality at designated
points in the region. The ambient concentrations
implied by a given solution of the LP model are then
compared with exogenously imposed environmental "stan-
dards." Marginal penalities, based on penalties for
exceeding the environmental standards and on the
environmental models, are computed and returned to the
LP model as prices, or effluent charges, on residuals
discharges. This iterative process is continued (in
principle) until no better value of the objective
function can be obtained.6
The LP Regional Activity Model: The LP residuals gen-
eration and discharge model describing the major
activities in the Lower Deleware Valley region is
quite large. It consists of roughly 8,000 columns
(variables), over 3,000 rows (constraining relation-
ships), and maintains information on about 800 indi-
vidual residuals discharges. The following regional
activities are included in this model:7 7 petroleum
refineries, 5 steel mills, 17 thermal electric power
plants, 57 home heating activities (one for each
political jurisdiction), 57 commercial heating activi-
ties (one for each political jurisdiction), 75 large
dischargers of gaseous residuals, 36 Deleware Estuary
sewage treatment plants, 10 paper plants, 23 municipal
Figure 1: SCHEMATIC DIAGRAM OF THE DELAWARE VALLEY RESIDUALS-ENVIRONMENTAL QUALITY MANAGEMENT MODEL
LINEAR PROGRAMMING MODEL OF PRODUCTION,
RESIDUALS GENERATION-MODIFICATION-DISPOSAL, ETC
Marginal Penalties Attributed to Individual
i !
1 1
\l/ \1/
COSTS OF PRODUCTION,
MODIFICATION, ETC.
Generation
and
Modification
of Residuals '
from
Production
Processes
Generation
and
Modification
of Consumption
Residuals
(including
landfill,
incineration,
etc.)
COSTS OF
RECYCLING
Recycl i ng
Alternatives
(municipal ,
commercial ,
industrial,
waste paper)
COSTS OF
DIRECT E.Q.
MODIFICATION
Instream
Aeration
("discharge"
of
oxygen)
TRIAL
"EFFLUENT CHARGES"
Discharge of Residuals
(differentiated by
type and location
of discharge)
Constraints on the distribution of consumer costs, e.g., increase
in municipal sewerage bills, percentage increase in electricity,
home-heating, and solid residuals disposal costs
Production,
Modification,
etc.
Extent of
Modification:
Local and
Regional
Options
Extent
of
Recycling
*
ACTIVITY LEV
ENVIRONMENTAL MODELS
Regional Atmc
Disperson f
Aquatic Ecos}
Model of De
Estuary
Aeration
Horsepower
(oxygen
injected)
ELS
Residuals
Discharges
\/
ode! pended Pa
Dioxide
leware Residuals
Biomass o
Zooplankt
sncentration of Sus-
'ticulates and Sulfur
jncentrations of
Dissolved Oxygen;
f Fish, Algae,
jn
Residual
T
\ \
s Discharges and Oxygen Injected
YPES OF CONSTRAINTS
Minimum
Production Levels
Mass Continuity
Conditions
Minimum
Residuals
Modification
Levels
Upper Limit on
Consumer Costs
by Type and
by Political
Jurisdiction
r
/\
ENVIRONMENTAL
EVALUATION
SECTION
' on Ambient Concentrations
and Species Biomass
(ambient standards
with penalty functions)
1
1
J
410
-------
Incinerators, 57 municipal solid residuals handling and
disposal activities (one for each political jurisdic-
tion), 23 Deleware Estuary industrial dischargers, and
22 in-stream aeration activities (one for each Estuary
reach).
The Environmental Models: Two environmental models are
incorporated in the regional model: a nonlinear
ecosystem model of the Deleware Estuary [14,15,16]
and a linear air dispersion model. The eleven "com-
partment" ecosystem model, developed at RfF, is based
on the trophic level approach. The model was calibrated
on conditions that existed in the Estuary in September
1970. Inputs of residuals to the ecosystem model
include: organics (BOD), nitrogen, phosphorus, toxics
(phenols), suspended solids, and heat. As reported
above, target outputs include ambient concentrations of
algae, fish, and dissolved oxygen.
The Gaussian plume-type air dispersion model was
adapted from the U.S.E.P.A.'s Implementation Planning
Program (IPP). Residuals discharges and meteorlogical
conditions in 1970 were used to calibrate the model.
The model accepts as inputs discharges of sulfur
dioxide and particulates, and provides as output ground
level, annual average ambient concentrations of sulfur
dioxide and suspended particulates.
Model Studies and Results of Analyses
The regional model described briefly above has been
run under a number of combinations of air and water
quality standards, solid waste disposal restrictions,
and assumptions about the availability of two regional
residuals management alternatives: in-stream aeration
(in the Estuary) and regional sewage treatment plants.
For the model runs, the following alternative environ-
mental quality restrictions were imposed:
Total regional costs ($ million per year)
Ambient
Air Quality
S02 i
TSP i
Ambient
Water Quality
DO 2
Algae <;
Fish s
Standard
Set (E)
120 ygms/m3
120 ygms/m3
Standard
Set (T)
j: 80 ygms/m3
i 75 ugms/m3
3.0 mg/n.
3.0 nig A,
0.01 mg/i
i 5.0
* 2.0 mg/4
a 0.03 mg/i
Landfill Quality
(3 levels)8 High(H) Medium(M) Low(L)
Implications for the Lower Delaware Region: For the
production runs completed so far, we have found two
general implications for the region: 1) the attainment
of the national primary air quality standards for
sulfur dioxide and suspended particulates will be
costly to the region—over $400 million per year
(compared with $100 million per year for the less
restrictive E level air quality set, and $50 million
per year for the most restrictive T level water quality
set for the Estuary); and 2) that both the regional
management alternatives (in-stream aeration and
regional sewage treatment) appear to hold promise for
reducing the total regional costs of meeting given
ambient quality standards. The total regional costs,
and savings due to these regional alternatives, are
Illustrated in the following table (for T level water
quality standards, E level air quality standards, and
H level landfills):
Regional treatment
plants
no
yes
In-stream aeration
no
$190
$170
yes
$155
$143
Notice that employing both in-stream aeration and
regional sewage treatment plants results in a savings
to the region of about $47 million per year.
Research Objectives and Lessons: In addition to these
general policy implications for the Lower Delaware
Valley region, the model results to date have also shed
light on the three major objectives of the research with
which we started: the inter-media tradeoff question;
the use of the nonlinear, aquatic ecosystems models in
regional analyses (again, not discussed in this brief
paper); and the generation of information on, and the
ability to constrain, the distribution of costs as well
as physical and biological indicators of environmental
quality.
A. Inter-media Linkages: Ample evidence for the impor-
tance of linkages and tradeoffs among the qualities of
the three environmental media are provided by the results
of the analyses, and examples have been provided else-
where [17,18]. Not enough space exists to repeat all
these examples here, but to provide some quantitative
evidence of these linkages, the increase in total costs
(in $ millions) to the region of improving Estuary
quality for specified levels of air quality, given high
quality landfills, is shown in the following table:
Air Quality Standards*
Water
Quality
Standards*
0
E
T
0
$12.3
$39.8
-.( A - "\1 ~\\-
$52.9
E
$ 96.7
-(A 35.4)-
$132.1
( A - 9"5 fi ^
$155.1
*For definitions of E and T levels of air
and water quality, see earlier table;
"0" level indicates no ambient standards
applied in the analysis.
For the 0 level air quality standards, the increase in
total regional cost of moving from the 0 to the E level
water quality standards amounts to $27.5 million per
year. For the E level air quality standards, this
difference amounts to $35.4 million per year. If there
had been no inter-media linkages, these differences
would have been the same. The difference in total
regional costs between the E and T level water quality
standards are even more pronounced. For the 0 level
air quality standards, the difference amounts to $13.1
million per year; at the E level air quality standards,
the difference jumps to $23 million per year.
B. Distributional _Information: Distributional infor-
mation on both environmental quality and certain con-
sumer costs is available as output of the Lower Delaware
Valley regional model, and has been presented in detail
411
-------
elsewhere [17]. For the sake of brevity, we will not
present this information again here. Rather, we will
take this opportunity to discuss the problems we had in
trying to obtain certain kinds of distributional infor-
mation that we desired. In the next section, we will
explain in more detail why we think this information
would be particularly useful in the preparation of Air
Quality Maintenance -and Areawide Waste Treatment
Management (208) plans.
Distributional information, especially on costs, can be
used in two ways, depending on the analysis and on the
type of management model employed: 1) it can be used in
the unconstrained mode to provide information on the
environmental and cost implications of alternative
residuals management strategies; and 2) it can be used
in the constrained mode to help shape the set of eco-
nomically and politically feasible residuals management
strategies that are selected for consideration. Both
programming (optimization) and simulation management
models can be used for the former analyses, but only
programming models are useful for the latter analyses.
Since in most regions the distribution of costs and
environmental quality will be a more important issue
than regional efficiency, we feel it is important to
address the analytical problems associated with
attempting to provide information based on constrained
costs and environmental quality.
We have had relatively little difficulty using the
Lower Delaware Valley regional model in constraining
levels of regional environmental quality and generating
information on the implied costs. And, of course, it
would have been still easier, and certainly less expen-
sive, to merely provide information on the implied costs
and implied levels of regional environmental quality for
various alternative residuals management strategies
(however selected). But the real difficulty arose when
we attempted to constrain both the levels of regional
environmental quality and the distribution of costs
simultaneously. There are two primary reasons for this
difficulty:
1. when costs and levels of regional environ-
mental quality are constrained simul-
taneously, infeasible solutions are
commonplace (as one would expect a priori);
2. the "real world" tradeoffs among distribu-
tions of cost, among levels of regional
environmental quality and the environ-
mental media, and between levels of
environmental quality and costs, are
extremely subtle and many, and occur at
the very top, and flattest portion, of
the regional total cost response surface.
The first difficulty poses a problem for both linear
and nonlinear programming formulations. (Simulation
models, except in very simple situations, are of very
limited use in this type of analysis.) If the run
turns out to be infeasible, it may be obvious (from the
dual values) which constraints need to be relaxed, but
it is not at all obvious by how much these constraints
should be relaxed. Clearly, we need much more opera-
tional experience here before we perfect this use of the
regional model.
Regarding the second difficulty, current nonlinear
programming algorithms are simply not practical,
especially for the large regional applications, and may
not be practical for the smaller (less complex) ones.
Most nonlinear programming algorithms become less and
less efficient as the optimum is approached. Thus, when
the regional efficiency criterion is employed, it makes
sense to stop these algorithms short of an optimum
Only modest cost savings (as a percentage of total
regional costs) are at stake anyway. But in examining
the tradeoffs among the distribution of costs and envi-
ronmental quality, the important information is not only
in the total regional cost dimension, but in a variety
of other dimensions as well. It is the range of alterna-
tives (or management strategies) for satisfying broadly
stated societal objectives, and of course the resulting
implications for individuals' costs and environmental
quality, that become of major importance. And here is
where the current crop of nonlinear programming algo-
rithms lets us down.9 Unfortunately, for these very
important kinds of regional environmental quality man-
agement strategy analyses, our only choice, at this
point in time, is to resort to linear programming
techniques. And we are currently in the process of
restructuring the Lower Delaware Valley regional model
as an LP model by removing the nonlinear ecosystem model
of the Delaware Estuary and replacing it with the Dela-
ware River Basin Commission's linear dissolved oxygen
model.
CONCLUSIONS. ISSUES AND FUTURE RESEARCH
In this paper, we have addressed the use of integrated
regional residuals-environmental quality management
models in the development of Air Quality Maintenance
and Areawide Waste Treatment Management (208) plans.
The structure and usefulness of different kinds of
regional management models were discussed, and a con-
siderable portion of the paper dealt with an application
of such a model to the Lower Delaware Valley region.
Admittedly, there are limitations to the use of the RfF
model, but the research clearly shed light on two
important issues associated with the development of AQM
and 208 plan development and strategy evaluations:
1. linkages among the three major forms of
residuals and among the three environ-
mental media do exist, and evidence
suggests that these linkages are impor-
tant both in physical and economic terms.
Since both of these programs involve
significant public investments and imply
major effects upon their implementation,
to the extent possible, the tradeoffs
among residuals and media should be
explicitly analyzed;
and 2. ambient environmental quality standards can
be met through varying combinations of
strategies which can imply substantially
different distributions of costs among
the public and private sectors, among
the residents of the various subregions,
and among different income groups. It
is clear that at the local level, at
least, the distribution of the costs of
improving and/or maintaining environmental
quality will be the central issue in
determining the political feasibility of
different strategies, with total regional
costs of secondary importance. Thus, to
the extent possible, information on cost
distributions of each strategy should be
generated and presented.
Finally, a model as sophisticated as the Delaware
application is beyond the resources of most environ-
mental quality management agencies. However, the
insights like those described above can guide research
to develop simpler analytic techniques that may be of
more immediate application to AQM and 208 planning
requirements. An effort to develop a range of techni-
ques in an operational handbook for regional environ-
mental quality management is currently planned at RfF.
412
-------
NOTES AND REFERENCES
1. Examples of the linear programming formulation for 9.
wastewater management purposes can be found in M.J.
Sobel, "Water Quality Improvement Programming
Problems," Water Resources Research, 1 (4), 1965,
pp. 477-487; C.S. Revelle, D.P. Loucks, and W.R.
Lynn, "Linear Programming Applied to Water Quality
Management," Water Resources Research, 4 (1), 1968,
pp. 1-9; and R.V. Thomann, "Systems Analysis and
Water Quality Management," Environmental Science
Services Division of Environmental Research and
Applications, Inc., New York, 1972. 10.
2. In terms of the complexity involved in incorporating
steady-state environmental models within an opti-
mization framework, we find it useful to distin-
guish among four broad categories: 1) linear
relationships where ambient concentrations, R, are
expressed as explicit functions or residuals dis-
charges, X, i.e., R = AX; 2) linear, implicit 11.
functions, i.e., X = AR (note that this equation
set can be rearranged by inverting the matrix of
coefficients, i.e., R : A~lX); 3) nonlinear,
explicit functions, R f(X); and 4) nonlinear,
implicit functions, i.e., X f(R). Classical
water quality models fall in the first two cate- 12.
gories and aquatic ecosystem models in the last
category. For more details, see [13].
3. For the use of penalty functions in nonlinear
programming, see A.V. Fiacco and G.P. McCormick,
Nonlinear Programming: Sequential Unconstrained 13.
Minimization Techniques (New York, John Wiley &
Sons, Inc., 1968); and/or W.I. Zangwill, Nonlinear
Programming: A Unified Approach (Englewood Cliffs,
N.J., Prentice-Hall, Inc., 1969).
4. The RfF modelling team consisted of Walter 0. 14.
Spofford, Jr., Clifford S. Russell, Robert A. Kelly,
and Edwin T. Haefele with the assistance of Louanne
Sawyer, Pathana Thananart, Blair T. Bower, and James
W. Sawyer, Jr. Edwin Haefele developed a legislative
bargaining and vote-trading model which is not 15.
described in this paper. However, the management
model reported here is designed to operate in con-
junction with Haefele's political model.
5. To provide information on the geographic distribution
of environmental quality and consumer costs through-
out the region, the Lower Delaware Valley was 16.
divided into 57 political jurisdictions of roughly
100,000 people each. To form these jurisdictions,
some of the 379 cities, towns, boroughs, and town-
ships that are located in this region were aggregated,
and some were subdivided. 17.
6. For details, see [10,12,13, and 17].
7. For details, see Appendix B of reference [17].
8. The three landfill qualities used in the analysis
include: low—open dump, but no buring allowed;
medium—good quality sanitary landfill; high—good
sanitary landfill with shredder, impervious layer
to protect groundwater, wastewater treatment of
leachate, aesthetic considerations such as fences,
trees, etc.
18.
19,
Regional environmental quality management models
represent only one example of a large set of
natural resource allocation problems that would
benefit greatly from the development of nonlinear
programming algorithms that could deal efficiently
with practical, large-scale applications. We hope
that these opportunities will one day be recognized
by the applied mathematician and operations
researchers.
C.S. Russell and W.O. Spofford, Jr., "A Quantita-
tive Framework for Residuals Management Decisions,"
in Allen V. Kneese and Blair T. Bower, eds.,
Environmental Quality Analysis: Theory and Method
in the Social Sciences (Baltimore, Md.: The Johns
Hopkins University Press for Resources for the
Future, 1972).
C.S. Russell, W.O. Spofford, Jr., and Edwin T.
Haefele, "The Management of the Quality of the
Environment," in Jerome Rothenberg and Ian G.
Heggie, eds., The Management of Water Quality and
the Environment (New York: Halsted Press, 1974).
W.O. Spofford, Jr., C.S. Russell, and R.A. Kelly,
"Operational Problems in Large-Scale Residuals
Management Models," in Edwin S. Mills, ed.,
Economic Analysis of Environmental Problems (New
York: National Bureau of Economic Research, 1975).
W.O. Spofford, Jr., "Total Environmental Quality
Management Models," in Rolf A. Deininger, ed.,
Models for Environmental Pollution Control (Ann
Arbor, Mich.: Ann Arbor Science Publishers, Inc.,
1973).
R.A. Kelly, "Conceptual Ecological Model of the
Delaware Estuary," in Bernard C. Patten, ed.,
Systems Analysis and Simulation in Ecology, Vol . IV
(New York: Academic Press, forthcoming).
R.A. Kelly and W.O. Spofford, Jr., "Application of
an Ecosystem Model to Water Quality Management:
The Delaware Estuary," in Charles A.S. Hall and
John W. Day, Jr., eds., Models as Ecological Tools:
Theory and Case Histories (New York: Wlley-
Interscience, Inc., forthcoming, 1976).
R.A. Kelly, "The Delaware Estuary," in C.S. Russell,
ed., Ecological Modeling in a Resource Management
Framework (Washington, D.C.: Resources for the
Future, 1975).
W.O. Spofford, Jr., C.S. Russell, and R.A. Kelly,
Integrated Residuals Management: A Case Study of
the Lower Delaware Valley Region (Washington, D.C.:
Resources for the Future, forthcoming, 1976).
C.S. Russell, W.O. Spofford, Jr., and R.A. Kelly,
"Interdependences Among Gaseous, Liquid, and Solid
Residuals: The Case of the Lower Delaware Valley,"
The Northeast Regional Science Review, Vol. 5, 1975.
C.S. Russell and W.O. Spofford, Jr., "A Regional
Environmental Management Model: An Assessment," a
paper prepared for presentation at the First Annual
Meeting of the American Association of Environ-
mental Economists, Dallas, Texas, December 28, 1976.
413
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A COMPUTER MODELING STUDY TO ASSESS THE EFFECTS OF A PROPOSED MARINA ON A
COASTAL LAGOON
Kuang-Mei Lo, Ph.D., P.E., Project Manager
Thomas G. King, P.E., Project Engineer
Arthur S. Cooper, P.E., Vice President
of
Connell/Metcalf & Eddy, Coral Gables, Florida
ABSTRACT
A water quality and hydrographic study was conducted
to determine the effects of a proposed marina on the
water quality of Old Pass Lagoon, located on the
northwest coast of Florida.
Utilizing field data, the flushing characteristics of
the lagoon were determined using two methods. An
estimate of pollutants discharged from engines of
boats using the marina was made based on information
in the literature. Based on the flushing charac-
teristics and the estimate of pollutants, the post-
construction water quality was predicted using a
steady state water quality model.
BACKGROUND
The proposed marina at the Sandpiper Cove develop-
ment is located at the eastern end of Old Pass
Lagoon. Old Pass Lagoon is close to Destin and is at
the western end of a spit causing the enclosure known
as Choctawhatchee Bay. A map showing the location is
presented as Figure 1.
As may be seen from Figure 1, Old Pass Lagoon is open
at the western end to Choctawhatchee Bay and the Gulf
of Mexico.
The mouth is quite narrow 150 feet at the narrowest
point - and this causes considerable bottling-up of
the waters of the lagoon. A further bottling effect
occurs toward the eastern end of the lagoon where the
lagoon narrows to a width of 150 feet at Norreigo
Point before widening out in the area where it is
proposed that the marina be located.
Tidal motion plays the most important role in water
movement and the flushing action in a lagoon. In the
Gulf of Mexico the range of tide is uniformly small,
but the type of tide varies considerably at different
locations. At Pensacola there is usually but one high
and one low water each day, while at Galveston the
inequality is such that the tide is semi-diurnal when
the moon is on the equator and diurnal at times of a
maximum north or south declination of the moon.
Consequently, in the Gulf of Mexico, the principal
variations in the tide are due to the changing de-
clination of the moon.
FIELD SURVEY
A field survey was conducted in order to determine the
existing quality of the waters of Old Pass Lagoon. At
each of eight stations samples were taken for the
measurement of dissolved oxygen, BOD, nitrogen, ammonia
orthophosphate. total phosphate, and oil and grease.
The analyses were performed at the Connell/Metcalf &
Eddy laboratory in Miami, according to procedures in
Standard Methods (1). The physical characteristics of
the lagoon were determined by measuring nine cross
sections.
A dye test was conducted in the proposed marina area
in order to determine the longitudinal dispersion
coefficient. The dye material used was a solution of
50 grams of Rhodamine-B. The solution was diluted in
the field with lagoon water and released at mid-depth.
Approximately 150 feet down-current of the point of
release, water samples were collected at intervals
following the release of the dye. The water samples
containing the Rhodamine-B were analyzed with an
Aminco-Bowman Spectrophoto-Fluorometer (SPF) capable
of detecting and differentiating Rhodamine-B concen-
trations as low as 5 ppb. The dispersion coefficient
was determined to be 4 ft /sec based on the solution
of the one-dimensional advection and dispersion dif-
ferential equation (2,3,4).
COMPUTATION OF FLUSHING PERFORMANCE
The flushing performance of the lagoon was computed by
two methods. A digital computer model was used to
solve the partial differential equations describing
longitudinal advection and dispersion by numerical
methods and then to compute the reduction in concen-
tration of pollutants due to tidal flushing action.
The flushing performance was also computed using the
tidal prism theory - a simplistic approach which
nonetheless serves as a useful check on the results
obtained using the computer model.
Flushing of a tidal water body is primarily controlled
by mixing and translation of the tides. When a mass of
dye or pollutant is introduced into the lagoon, it is
distributed through the water body by the mechanisms of
advective and dispersive transport. Advective transport
is generally determined by the velocity of the water
due to tides and the addition of fresh water. Dis-
414
-------
SITE OF PROPOSED
MARINA
OLD PASS LAGOON
_NORREIGO//,
POINT //
CLUBHOUSE-^
Vi PROJECT
SITE/
500 0 500 1000 FT
2
SCALE
GULF OF MEXICO
LOCATION MAP
Fig. 1 Map of Old Pass Lagoon Showing the Site of Sandpiper Cove Marina
persive transport is controlled by diffusion which, in
turn, is affected by wind, turbulence, and is also
considered by many investigators to be a function of
the tidal velocity. By assuming that the water is well
mixed, vertically and laterally, the flushing of a
conservative pollutant can be described by the fol-
lowing partial differential equation:
!£.= ! . 3 (AD3c)
3t A ' 3x 3x
3x
(1)
where: c: concentration of the pollutant
U: mean flow velocity in the cross
section
D: longitudinal dispersion coefficient
A: cross sectional area
x; longitudinal distance along the canal
t: time.
In order to solve this equation by numerical methods,
the following initial and boundary conditions are
required:
c(x,0) = C0
c(0,t) 0°
(2)
Thus it is assumed that the initial concentration of
lagoon water is C0 at time t=0, and the concentration
at the tidal source is assumed to be zero at all times.
The mean velocity, U, represents the average of the
velocities resulting from tidal action and fresh water
flow at a given cross section in the lagoon. Since
flow due to the addition of fresh water in this
instance is minimal, the mean velocity is the
average tidal velocity.
To determine this velocity it was assumed that, for a
station in the lagoon, the amount of water flowing
through the station in a time period At was equal to
the change in water elevation, AH, multiplied by the
surface area between the station and the deadend.
This relationship can be described by the following
equation:
AU = SAH
At
(3)
In order to use the above equation to describe the
average velocity throughout the lagoon, it is
necessary to assume that the tide is uniform with
no significant difference in range or phase.
If a mathematical formulation known as the tidal
function, H(t), is used to describe the average
tidal cycle then Equation (3) may be rewritten.
The tidal function, H(t), used in this study is
chosen from the report entitled "Storm Water
Management Model," prepared by the Environmental
Protection Agency, October 1971 (5) :
H(t) = A! + A2Sin(w) + A3Sin(2w) + AASin(3w)
+ A5Cos(w) + A6Cos(2w) + A?Cos(3w)
where w = ^^, n= 1, 2, ... n
and
24
A^, A2, . . .A? are coefficients.
415
-------
A computer program employing a least squares procedure
was developed to calculate the coefficients in the
above equation. Using the computed coefficients, the
tidal function for average tidal conditions at Old
Pass Lagoon may be written as:
H(t) = 0.32 + 0.084 Sin(w) + 0.002 Sin(3w)
+ 0.261 Cos(w) - 0.003 Cos(2w)
0.003 Cos.(3w)
(6)
The cross section information necessary for determining
the mean tide velocity was obtained from field measure-
ments and from information presented in Nautical Chart
870-SC published by the U.S. Department of Commerce (6).
To solve Equation (1), the effective longitudinal
dispersion coefficient, D, is also required. This
coefficient was obtained from the dye test con-
ducted as described above. The value 4 ft /sec
was used as the average dispersion coefficient
throughout the lagoon.
Tidal prism theory was also used to compute the
flushing performance of the lagoon. The average
turnover rate (or flushing rate) can be computed
from the following equation assuming that the
concentration, C, of a pollutant in the lagoon is
GO at time zero, and that the bay is free of the
pollutant. The concentration of the pollutant
after N tidal cycles is given by:
= C0(:
N
-)
(7)
where:
a: mixing coefficent
P: volume of water in tidal prism
V: volume of water in lagoon at low tide.
The volume of water in the lagoon at low tide was
calculated from the measured cross sections to be
79,600,000 cubic feet.
An average value for the tidal fluctuation at East Pass
Destin was computed to be 0.55 feet from tidal predic-
tions published by the U.S. Department of Commerce (7).
By considering this depth of water over the entire area
of Old Pass Lagoon, the volume of water entering the
lagoon during the rising tide was estimated to be
4,200,000 cubic feet.
It is difficult to accurately assess the degree to
which Gulf water is mixed with the lagoon water. It is
known that the mixing coefficient is dependent on the
tidal and wind velocities as well as the geometric
configuration of the lagoon.
An estimate of the mixing coefficient was made by com-
paring the salinity of Gulf water with that of Old
Pass Lagoon. Although no obvious source of freshwater
entering Old Pass Lagoon was evident, the salinity in
the lagoon was below that in the Gulf of Mexico. By
comparison of the salinity in the lagoon before and
after the flood tide an estimate of 0.6 was made for
the mixing coefficient. With the above information,
it is possible to compute the flushing performance of
the lagoon using Equation (7).
Since C/CQ is the fraction of conservative pollutant
remaining in the lagoon, (1-C/CO) expressed as a per-
centage indicates the degree to which flushing has been
achieved.
The results of the flushing calculations are pre-
sented in Figure 2. They indicate that the time for 50
percent flushing performance is about 30 days for the
area in the middle of the lagoon. In other words,
this is the time required to reduce the concentration
of a conservative material initially distributed uni-
100
50
o
E
V)
:D
olO
UJ
o
cc
UJ
Q.
AVERAGE FLUSHING IN LAGOON-v
BY TIDAL PRISM METHOD *-
•FLUSHING IN MID-LAGOON
AS GIVEN BY THE
COMPUTER MODEL
10 15
TIME (DAY)
20
25 30
Fig. 2.
Computed Flushing Performance of Old Pass
Lagoon as Computed by the Tidal Prism
Method and the Computer Model
formly over the canal system to 50 percent of the
initial concentration.
ESTIMATE OF POLLUTANTS FROM THE PROPOSED MARINA
Little data is available regarding the quantities of
pollutants that are discharged from the engines of
pleasurecraft of the type anticipated to use Sandpiper
Cove Marina.
Jackivicz and Kuzminski (8) have presented information
on the various compounds found in the exhaust from
outboard motors.
The sizes and types of craft expected to use the marina
were reported as follows:
Number of Boats
30
18
14
Boat Length
20 ft.
31 ft.
40 ft.
Engine Type
Outboard
Inboard
Inboard
Also, the following conditions are anticipated to be
enforced:
-The general public will not be allowed to use
the marina.
-An onshore waste disposal system will be available
to receive sanitary and other wastes from boats.
Using the information available and making the following
assumptions, an estimate was made of the amount of oil
that will be deposited in Old Pass Lagoon from out-
board engines. The assumptions are:
-Average oil: gasoline ratio 1:50.
-Discharge of both volatile and nonvolatile oil
per boat - 6 gms/liter of fuel comsumed.
-Average usage twice per week.
-Speed - 15 knots.
-Fuel consumption - 3 nautical miles/gallon.
416
-------
The distance from the marina to the bridge at the mouth
of Old Pass Lagoon is approximately 10,000 feet. Thus,
the fuel consumed on two trips in and out of the lagoon
may be computed to be 8.32 liters. Consequently, the
oil discharged per boat per week is A9.92, say 50
grams and the total oil discharged from the thirty
outboard boats is 1500 grams/week.
The biochemical oxygen demand (BOD) and chemical oxygen
demand (COD) may also be computed. Under the above
assumptions, the time spent per boat operating in Old
Pass Lagoon is 26.4 minutes. This may be rounded up to
30 minutes to take into account slower speeds used in
the immediate vicinity of the marina. For boats in
operation for one hour,the rates at which BOD and COD
are generated are 1.05 and 2.50 grams/liter of fuel
consumed respectively. Since 8.32 liters of fuel are
consumed and there are thirty outboard boats the total
weekly demands are 262 and 624 grams respectively.
The above computations have analyzed the effects from
outboard engines. Inboard-engined boats do not utilize
an oil:gasoline mixture and no data were located that
analyze the pollutional aspects of inboard boats. The
potential problem from inboard boats centers around
discharges from the bilges. However, such discharges
are illegal and it must be assumed that stringent
enforcement of the law will severely limit such dis-
charges.
For the purposes of this analysis assume that oil is
discharged at half the rate as that from an inboard
motor, and that BOD and COD are created at the same
rates. Thus, the pollutants from 32 inboard boats are:
Oil:
BOD:
COD:
507.
x 50 x 32
8.75 x 32
20.80 x 32
800 grams/week
280 grams/week
665 grams/week
The total discharges from all boats at the marina are:
Oil: 2,300 grams/wk
BOD: 542 grams/wk
COD: 1,290 grams/wk
0.73 Ibs/day
0.17 Ibs/day
0.40 Ibs/day
WATER QUALITY MODELING ANALYSES
In order to evaluate the effects of the pollutants
generated by boats from the marina, a water quality
modeling analysis was conducted using a steady state
estuary model developed by Connell/Metcalf & Eddy, Inc.
and Hydroscience, Inc.,(9).
The results of the modeling study indicated that the
boats using the marina will cause a practically un-
detectable increase in BOD loading in the lagoon.
Since pollution from oil and grease was the major cause
for concern a more detailed analysis of oil and grease
pollution was conducted according to the following
steps:
(1) The existing oil and grease level in the waters
of the lagoon was simulated using a computer model.
The results of the simulated oil and grease profile
are presented in Table 1.
(2) In order to provide a conservative analysis it was
assumed that the oily waste generated by the 62 boats
is discharged as a point source at the marina. Ini-
tially, the 0.73 Ib/day of oil computed above were
considered to be generated at the marina. The results
of this waste input on the lagoon water are also shown
in Table 1. The indication is that the effect on the
overall oil/grease level in the lagoon waters is almost
undetectable.
(3) Finally, 22 Ib/day of oil loading were considered
as a point source in the marina area. This figure
represents the loading that is applied during a period
of 60 days assuming that 50% flushing takes place. It
should be noted that this flushing time is much higher
than the flushing performance of the lagoon as computed
in the previous section and, therefore, the results are
conservative.
The above calculation was based on the following assump-
tions :
TABLE 1 . RESULTS OF THE WATER QUALITY MODELING STUDY FOR OLD PASS LAGOON
Location from Measured Oil/
Hwy. 98 Bridge Grease Values
Simulated Existing
Oil/Grease Condition
(mg/1) (11
Oil/Grease Profile of the
Lagoon after inputting
0.73 Ib/day Oil/Grease
at Proposed Marina (2)
Oil/Grease Profile of the
Lagoon after inputting
22 Ib/day Oil/Grease at
Proposed Marina (3)
600 9.33
870
1400
1945
2480
2955
3555
4000 3.37
4215
4825
5220 0.42
5300
5750
6335
6670 5.81
7020
7770
8190 0.11
8270
8570
9195 0.11
9740 0.64
7.455
6.770
6.373
6.076
5.894
5.703
5.480
5.252
5.085
4.878
4.640
4.309
3.741
2.951
2.280
1.609
7.484
6.804
6.409
6.114
5.943
5.744
5.523
5.297
5.132
4.927
4.691
4.363
3.802
3.026
2.356
1.159
7.706
7.106
6.759
6.500
6.341
6.175
5.981
5.783
5.639
5.460
5.255
4.969
4.481
3.806
3.222
2.180
417
-------
(1) 4 ft /sec was used as the dispersion coefficient.
This value was determined from the field dye test
conducted near the site of the proposed marina.
(2) It is assumed that the oily waste will be mixed
only in the top one foot of water in the lagoon. This
is not unreasonable since oil floats but wind and wave
action will create mixing.
(3) No freshwater contribution was considered through-
out the lagoon.
(4) Oil and grease are considered to be conservative
materials. The above modeling analysis indicates that
oil and grease discharged from the 62 boats at the
marina would result in an increase of the oil/grease
content of the lagoon water by about 1 mg/1 near the
proposed marina site, and about 0.3 mg/1 near the
outlet of Old Pass Lagoon. The quantity of the in-
crease is considered insufficient to cause deteriora-
tion of the lagoon water.
Even though the quantity may not be sufficient to
degrade the water quality, oil in such quantity as to
be visibly apparent is aesthetically objectionable.
Oil films of microscopic thickness are responsible for
the bright bands of color that may be observed on the
surface of water in canals or on wet roads.
Based on the information contained in a manual on
Disposal of Refinery Wastes published by the American
Petroleum Institute (10), the amount of oil that will
result in a barely visible film on the surface of the
water near the proposed marina may be determined.
The American Petroleum Institute reports that an
oil film of thickness 0.0000015 inches is barely
visible under the most favorable light conditions.
Considering the small lagoon area east of Norreigo
Point, which has a surface area of 792,000 ft ,
the amount of oil in the film is:
0.0000015 x 792000 x 7.48
12
= 0.74 gal.
6.18 Ib.
Assume that the oily waste discharged into the water
due to the marina operations will have disappeared from
the surface within 24 hours due to mixing induced by
wind, boat traffic and tidal action. Then the 6.18
Ibs/day of oil required to maintain a film of oil is
over eight times larger than the volume of oil and
grease that was estimated to be generated by the 62
boats using the marina.
The assumption that the oily waste will have disap-
peared from the surface within 24 hours is a conserva-
tive estimate. According to the American Petroleum
Institute, experiments have indicated that oil films up
to 0.0000003 inches in thickness generally do not
persist more than 5 hours on an agitated water surface.
Tested at sea, less than 24 hours are required to
dissipate a film of 0.00004 inches thickness. In
general, the thinner the film, less time is required
for dispersion.
Furthermore, the 0.73 Ib/day oil waste estimated to be
generated from the boats will be spread over the entire
area of Old Pass Lagoon. In order to be conservative,
we have assumed that this waste is discharged near the
marina site as a point source.
It should be pointed out that the above calculation is
based on the assumption that the oil is evenly distri-
buted on the surface of the water at the vicinity of
the proposed marina. It is possible that wind may
drive the film to the shore or an inlet and result in a
film thick enough 4s to be visible. There is a tendency
for winds to come from the north or from the south,
while least wind activity is from the west. This would
indicate that there is less likelihood of wind action
pushing an oil film toward the deadend of the lagoon
and the vicinity of the proposed marina as opposed to
driving it out of Old Pass Lagoon.
CONCLUSION
The study indicated that existing water quality in the
lagoon is very good. The computations indicate that
the lagoon has a relatively poor flushing performance,
causing the water to be sensitive to the effects of
pollution. However, based on the analysis, it is
concluded that the proposed marina and the 62 boats
berthed there will have little effect on the water
quality of the lagoon.
LITERATURE,CITED
1. Am. Public Health Assoc., Am. Water Works
Assoc., Water Pollution Control Fed. Standard
Methods for the Examination of Water and
Wastewater, Thirteenth Edition, 1971.
2. Feurstein, D. L. and R. E. Selleck, Aug.
1963. Fluorescent Tracers for Dispersion
Measurements. Journal of the Sanitary
Division, ASCE, Vol 89, No. SA4. pp. 1-21.
3. Fischer, H. B., Nov. 1967. The Mechanics of
Dispersion in Natural Streams. Journal of the
Hydraulics Division, ASCE, Vol. 93. No. HY6,
pp. 187-216.
4. Fischer, H. B. , Oct. 1968. Dispersion Pre-
dictions in Natural Streams. Journal of the
Sanitary Division, ASCE, Vol. 90, No. SA6.
pp. 124-130.
5. Metcalf & Eddy, Inc. , University of Florida,
and Water Resources Engineers, Inc., Oct.
1971. Storm Water Management Model, Vol. IV
Program Listing, Environmental Protection
Agency.
6. U.S. Department of Commerce, National Oceanic
and Atmospheric Administration. Nautical
Chart 870-SC.
7. U.S. Department of Commerce, National Oceanic
and Atmospheric Administration. Tide Tables
1974 High and Low Water Predictions, East
Coast of North and South America, 1973.
8. Jackewicz, T. P., Jr., and L. N. Kuzminski,
Aug. 1973. A Review of Outboard Motor Effects
on the Aquatic Environment. Water Pollution
Control Fed., Vol. 45, No. 8, pp. 1759-1770.
9. Connell/Metcalf & Eddy, Inc., and Hydroscience,
Inc., Water Quality Modeling Study for State
of Florida Department of Pollution Control,
1974.
10. American Petroleum Institute, 1969. Manual
on Disposal of Refinery Wastes, Chapter 2.
418
-------
DIGITAL COMPUTER SIMULATION OF SECONDARY EFFLUENT DISPOSAL ON LAND
Kuang-Mei Lo, Phd., PE, Project Manager and Connell/Metcalf
Donald Dean Adrian, PhD., PE, Professor, Department of Civil
A computer simulation study was conducted to
determine the required field area for an infiltration
type of land disposal system based on weather condi-
tions and soil properties. The input information in-
cluded local evaporation data, average monthly rain-
fall and average number of days during the month on
which it rained, and characteristics of soil's in-
filtration and drying rates.
The results of this 20-year simulation were
used to determine the liquid loading rate under
various weather and soil conditions. The liquid
loading rate was used to determine the necessary field
area for a particular disposal system at a given lo-
cation.
Introduction
Land disposal of domestic and industrial waste-
waters has received a great deal of publicity in
recent years. In the Southeast, where climatic con-
ditions are favorable for this type of disposal, wide-
spread interest has been expressed both among
professionals in the wastewater management field and
the general public.
In general, land disposal is practiced in three
ways: spray irrigation, overland flow, and infiltra-
tion percolation. Large land areas are required
for all three methods. Over the years, controversy
surrounding the long-term effects of the land disposal
of effluent, together with the lack of design criteria
to determine the land area required, has in many cases
forced engineers or planners to disregard this treat-
ment method as a feasible method of disposal. The net
result is either failure to consider a viable solu-
tion to effluent disposal or creation of additional
controversy because many people or groups consider
land disposal as the most promising solution for
wastewater management.
This paper is primarily concerned with the devel-
opment of rational design criteria for land disposal,
from which an engineer or planner could determine the
required land area based on the soil infiltration and
drying rates and local climatic conditions. Considera-
tion of chemical and biological changes in the applied
wastewater is beyond the scope of this paper. This
paper is confined to the study of the Infiltration-
Percolation type of land disposal. The best example
of this method is the Flushing Meadows Project near
Phoenix, Arizona .
Description of the System
A.hypothetical land disposal system is shown in
Figure 1, in which a series of infiltration basins are
constructed with soil banks surrounding each basin to
prevent entry of surface water runoff. Secondary
effluent from a treatment plant is pumped from a
storage pond into the basin to a predetermined depth,
the basin is kept flooded until a certain amount of
effluent has infiltrated, then the basin is dried out
prior to the next application. Generally, three major
stages are involved in the disposal process. The
first stage is called the ponding stage because during
this stage effluent is ponded on the surface of the
basin and is removed from the basin by infiltration
and evaporation. Also, in this period, the volume
of the effluent to be disposed of is increased by the
rainfall on the surface of the basin. As the disposal
process progresses, the second stage is reached when
there is no more ponding water in the basin. In this
419,
& Eddy, Inc., Miami, Florida
Engineering, Uni. of Mass/Amherst
RAINFALLl
fEFFLUENT LOSSES THROUGH
EVAPORATION OR DRYING
EFFLUENT LOSSES THROUGH
INFILTRATION OR
REDISTRIBUTION
<7 GROUNDWATER TABLE
Figure 1. Infiltration Basin
stage, the soil water beneath the basin undergoes a
redistribution process which percolates the excessive
water from the upper layer to the lower layer of the
soil. The rate of redistribution normally decreases
rapidly or becomes negligible when the water content
in the soil reaches the field capacity. During the
re-distribution process, water in the soil is also
lost through evaporation. After the soil reaches
field capacity, the disposal process progresses
to the final stage, drying, during which evaporation
proceeds at a rate lower than evaporativity, and the
actual rate is dictated by the ability of the soil
profile to deliver moisture toward the evaporation
zone. The drying process is very important for land
disposal because it not only restores the infiltration
rates of the soil, it also provides a necessary
period for the soil mass to renovate the effluent.
During the redistribution and drying periods, the
process is also affected greatly by rainfall, which
increases the soil water and prolongs the redistribu-
tion or drying period. Sometimes when the rainfall is
high, ponding water results. Consequently, the process
may return to the first stage.
Approach
Because of the stochastic nature of rainfall and
its resultant effect on effluent disposal rates, a
simulation approach was used in this study to test how
a particular design would perform under conditions
representative of a given area of the county. To
achieve this simulation, mathematical equations to
describe the infiltration and drying processes were
adopted from the literature to relate soil characteris-
tics to the amount of water lost by infiltration and
drying. Input data also included rainfall and evap-
oration information. Since actual rainfall records are
cumbersome to use, synthetic rainfalls were generated
for this study. Mean monthly evaporation from a free
water surface published by the U.S. Weather Bureau was
used to represent water loss to the air during the
infiltration and redistribution stages for a given
area.
Synthetic Rainfall
A rainfall probability function was utilized to
sequentially generate rainfall data using the Monte
Carlo Simulation Technique. The generated rainfall
data could not be distinguished from historical rain-
fall data by means of the statistical tests of
significance.
The modified Poisson distribution was used by
2
Bagley to represent the frequency distribution of
daily rainfall for San Francisco, Sacramento and
Spokane. The modified Poisson distribution contains a
persistence characteristic so the likelihood of rain
occurring on a given day increases if it has rained on
the previous day. The Poisson and modified Poisson
distribution are compared in Table 1. The modified
-------
Table 1. Comparison of the Poisson and Modified
Poisson Distribution
Probability
of units of
rain
(p.)
Poisson
distribution
Modified Poisson Distribution
l/(Hd)x/d
xe
-x/1 !
Pi
-x/i!
ix (x+d)...(x+(i-1) d)
Poisson distribution is a function of two parameters,,
x and d,which represents the degree of dependence of
one event upon another. When d is zero, the modified
Poisson distribution approaches the Poisson distribu-
tion as a limit. The procedure by which to calculate
X and d follows an example by Lo which uses Amherst,
Massachusetts rainfall records.
From 1961 to 1965 there were 1224 observation days
for the interval March to October of each year. In
this period, 377 days were considered as having measur-
able rainfall. The average rainfall in this period was
0.087 inch/day.
If one lets M total no. of days in the period,
N total no. of days with rain, and U = average daily
rainfall for the whole period, then the probability of
ho rain was (M-N)/M, which must be equal to P as
shown in Table 1.
(M-N)/M
or
(1225-377)/1225 I/ (l+d)X/d
(2)
The expected value of the modified Poisson distribution
must be equal to U, the average daily rainfall for the
entire period. With the unit increment of rainfall of
0.05 inch, the relationship is:
U
2 X (x + d)
0.05
(Hd)
X/d+1
(l+d)
X/d
i X (x + d) . . . . (x + (i I)1 d)
i ! (1 * d)x/d + 1- !
rearranging Equation (1) as
x -[d log( (M - N) / M ) / M )]/ log (1 + d)
(3)
(4)
and solving Equations (3) and (4) simultaneously, we get
d 13.8, and X = 0.094.
From the probability distribution function,it is
then possible to generate synthetic rainfall to repre-
sent real-world precipitation. This was done by means
of the Monte Carlo simulation technique, in which a
subroutine available at the University of Massachusetts
Computer Center was used to generate a uniformly distri-
buted random number sequence. Then,by applying a table
interpolation method for the inverse probability inte-
gral transformation, the random samples of daily rain-
fall were obtained. Comparison of the generated and
recorded rainfall is shown in Figure 2.
SYNTHETIC RAINFALL
Location ' Boston, Moss.
M
M
A .S
J J
MONTH
Figure 2. Comparison of the Generated
.and Recorded Rainfall
Infiltration and Redistribution of Soil
Moisture Following Infiltration
Infiltration
Passage of water from a basin to the ground fre-
quently occurs under unsaturated conditions because of
the distance between the groundwater table and the
ground surface. The movement of water in the unsatu-
rated soil can be described as:
36 _ 36 ,n
8t ' X (D
36v
3K
3l
where x is the volumetric water content, D(x) is the
soil water diffusivity, K is the hydraulic conductivity
Z is the distance downward, and t is the time.
A
Philip developed the above differential equation's
solution which describes cumulative infiltration as:
St1/2 + (A2+Ko)t + A3 t3/2 +
(6)
Subject to t
0, Z>0, e=e.; and t>0, Z=0, e =e
Philip suggested use of the first two terms to describe
approximately the infiltration:
I(t) St1/2 + At (7)
For a larger t, Hillel5 stated that the cumulative
infiltration can be expressed as:
1/2
I St"" + Kt
which yields the infiltration rate as:
i C ^~ I / ^ i i/
"o" O L T K
(8)
(9)
where K is the hydraulic conductivity of the soil's
upper layer. S was defined by Philip as sorptivity;
it can be determined in the laboratory.
Equation (9)describes the infiltration rate of the
soil for this study. The infiltration rates used in this
study'are shown in Figure 3. The rates describe a
loamy soil.
Redistribution
The infiltration process then comes to an end
when the applied effluent is depleted by evaporation
and infiltration. The movement of water within the
soil after end of infiltration is called redistribu-
tion, since its effect is to redistribute soil water
from upper layers of soil, wetted to near-saturation, to
the lower layers. The rate of distribution depends on
the soil properties, the groundwater depth, and the
420
-------
,. 30
I
u
ui 20
2 10
10
20
DAY
30
4O
Figure 3.
Infiltration Rate as a
Function of Time
moisture content of the soil. The redistribution pro-
cess also involves hysteresis, which complicates the
redistribution process and makes it difficult to des-
cribe mathematically.
For this study, the redistribution process deter-
mines the time required for draining the excessive
water in the soil. The faster the soil drains the
excessive water, the earlier it can start the drying
process. Normally, whether the infiltration basin is
ready for next effluent application depends on the
moisture content of the top soil. As a result,
only the redistribution process of top soil is con-
sidered for this study. The depth of the top soil can
be considered as root zone or tillage zone normally
observed in the field. For this reason, we
assumed that the redistribution in the top soil will
become negligible when the soil water content reaches
field capacity. Field capacity is defined as the
amount of water that a well drained soil retains about
148 hours after being thoroughly wet. Thus, we con-
sidered that the redistribution process would take two
days after infiltration ceases. We further se-
lected 0.3 volumetric water content as the field ca-
pacity for this study, after which we assumed that the
redistribution process ceases and drying process starts.
Evaporation and Drying
Evaporation
The loss of water through evaporation occurs
during the period when effluent is ponded in the in-
filtration basin. U.S. Weather Bureau publications
were used for the mean monthly rate of evaporation.
In the simulation, evaporation ceased as soon as the
ponding water was depleted. Water losses to the air
were then considered to be from drying.
Dryi ng
Drying occurs in two distinct stages. First,
when there is ample water in the soil, the drying rate
is constant and is determined by external and soil-
surface conditions, rather than conductive properties
of the soil profile. Constant-rate drying generally
occurs while the soil water undergoes the redistribu-
tion process. After the soil reaches field capacity,
the drying process enters into second stage, which
proceeds at a rate lower than the constant rate and
is controlled by the conductive properties of the soil
profile. The second stage is called falling-rate
drying. A study of evaporation from bare soil was
reported by Gardner and Hi 11 el5, who stated that the
drying rate can be expressed as:
E = D(e) Wir2/ 4L2 (10)
where E is drying rate in cm/day, D(e) is the diffu-
sivity corresponding to the average water content of
p
soil columns in cm /day, and W is the volumetric water
content in cm for a soil column L cm long.
We confined ourselves to investigating the top 30-
cm layer of soil because, in practice, this is the
layer that dictates whether the basin is dried to a
degree ready for next application of effluent. As
shown in Figure 4, we assumed that the drying process
VOLUMETRIC WATER CONTENT
°'2 °'3
Figure 4. Illustration of Drying Process
in the Soil
starts when the soil is at field capacity, after
which the water loss through drying would follow
Equation (10) until a 0.1 volumetric water content is
reached for the top 30 cm of soil. We assumed that
the constant drying rate is equal to drying rate deter-
mined by Equation (10) at volumetric water content '
0.3, or the evaporation rate, whichever is smaller
Diffusivity of the soil is generally measured
experimentally. Testing procedures are available from
many technical papers and soil and water textbooks.
Figure 5 presents the diffusivity used in this study
as a function of water content, while Figure 6 presents
the drying rates determined by Equation (10) for soil'
water content ranges pertinent to the drying period.
30
20
« 10
0.1 0.2 0.3
VOLUMETRIC WATER CONTENT
0.4
Figure 5. Diffusivity-Water
Content Relationship
0.5
g 0.3
£
2 0.2
i
a.
0.1 0.2 0.3
VOLUMETRIC WATER CONTENT
0.4
Figure 6. Drying Rate-Water
Content Relationship
421
-------
Simulation
Procedure
Once the mathematical equations for the various
components of the land disposal process were formula-
ted, simulation of secondary effluent disposal on an
infiltration basin was initiated. Input data were
local daily rainfall and evaporation, and parameters
to describe the infiltration and drying properties of
the soil, including sorptivity, conductivity, and
diffusivity.
After obtaining the necessary input data and para-
meters, the simulation was conducted on a digital
computer according to the following steps:
• The simulation started at the beginning of each
day with the addition of the daily rainfall on
the surface of the applied effluent. If it was
not raining, a zero amount of rainfall was
added. The depth of effluent on the next day was
obtained by subtracting the amount of water lost
by infiltration and-evaporation during the pre-
vious day. This procedure was repeated until
•no more ponding effluent remained on the surfacee
of the basin.
- After infiltration ceased, two days were added for
redistributing excessive water in the top 30 cm of
soil to the field capacity. In case rain occurred
within the two days, the amount of the total rain-
fall was compared with the water lost through con-
stant-rate drying and infiltration. If it was
larger than that lost by drying and infiltration,
the excessive rainwater was considered to be
ponded on the surface, and the simulation returned
to Step 1. If it was smaller, then an extra
'day was added to account for the additional
infiltration process. The water lost through dry-
ing was determined utilizing the drying equation
at a volumetric water content of 0.3.
• After reaching field capacity, loss of soil water
through drying occurred. If rain occurred during
this period, the amount of rainfall was compared
with the existing water content of the soil to
determine whether it would increase the soil
moisture content, or return the soil water to
Step 2, or even to Step 1. The entire process
stopped when the volumetric water content of the
top 30 cm of soil reached 0.1.
After completion of the above three steps, efflu-
ent was applied to the basin again and the above steps
were repeated. This process was repeated until
the simulation progressed to 20 years.
Five locations were chosen to represent different
meteorological conditions: Phoenix, San Francisco,
Miami, Boston, and Duluth. In recognition of the dif-
ficulty in applying effluent on land in freezing
weather, the normal freezing period for Boston and
Duluth was excluded from simulation. As a result, 8
months out of a year were used for disposal in Boston,
and 6 months for Duluth.
The total effluent to be disposed of for each
application was chosen as 200, 500 and 1,000 cm per
unit area for all locations.
The output of this simulation was a random vari-
able, the time required for disposing the effluent
on the basin, and its associated frequency of
occurrences for the simulation period of 20 years. A
sample output is shown in Table 2. It shows that if
applying 500 cm of effluent on the basin in Miami,
once in 20 years it would be possible to dispose of
the effluent within 35 days, 6 times it would be '.
possible within 42 days, and so on. The mean period
between two successive applications is shown to be
64.2 days. The output for the simulation in other
areas are summarized in Table 3.
Table 2. Simulation Output for Miami for Applied
Depth 500 cm.
Time reqd. No.of Time reqd. No. of
day Occurrences day
35.0
42.0
43.0
46.0
52.0
57.0
58.0
Table 3.
Location
1.0
6.0
2.0
1.0
1.0
2.0
4.0
59.0
60.0
71.0
80.0
81.0
82.0
83.0
Occurrences
80.0
20.0
1.0
3.0
2.0
Mean Disposal Time for Effluent Applied on
Infiltration Basin
Mean Disposal Time (Days)
Application Depth (cm)
1000
Boston
Duluth
Miami
San Francisco
Phoenix
103,
109,
136,
128,
91.
.3
.7
.6
.1
.5
500
56
54
64
71
40
.9
.6
.2
.2
.4
200
27.
26.
33.
33.
18.
0
5
0
2
0
100
18,
18,
24,
26,
.2
.8
.8
.7
50
16,
14,
22,
22.
-
.6
.2
.4
,4
Applications
The major application for the output of this
simulation was to determine the liquid loading rate,
which in turn was used to size the required field area
in which the disposal process actually takes place.
For example, Table 3 shows that in the Miami area it
takes an average of 64.2 days to dispose of 500 cm of
effluent, therefore the liquid loading per year is:
x 500 = 2843 cm/yr 93 ft/yr
(ID
and the field area required based on the liquid loading
is:
Field area(acres) ' "° ^
where Q flow rate of plant effluent, MGD; L = annual
liquid loading, ft/yr. Therefore, for a 1-MGD plant,
the required field area would be 12 acres. The actual
system may be constructed as a series of infiltration
basins. The effluent would be pumped into the first
basin to a predetermined depth. The basin would be
kept flooded until the total effluent reaches 500 cm.
Then the basin would be left to dry out. The effluent
would be applied to the basin again when the volumetric
water content in the basin reaches 0.1. The design
for this particular example seems quite adequate, be-
cause based on the 20-year simulation, the actual dis-
posal time is larger than the average value of 64.2
days only nine times.
The liquid loading rates for other areas are
presented in Tables 4 to 6, which also list the
required field area for a 1-MGD plant.
Discussion of Results
The results indicate that the required field area
for an infiltration type of land disposal system
differs depending on the weather conditions and soil
properties. For example, under the same conditions,
an infiltration basin in the Miami area requires about
50% more area than one located in Phoenix.
The study also indicates that the required field
area decreases if the basin is kept flooded longer.
For example, the required field areas for a 1-MGD
plant in the Miami area are 12.8, 12.0, and 15.4 acres
422
-------
Table 4. Liquid Loading Rates and Required Field
Areas for 1-MGD Plant at Various Locations
Effluent Depth per Application: 100 cm (32.8 ft)
Location
Boston
Duluth
Miami
San Francisco
Phoenix
Liquid
Loading
Rate
(ft/yr)
76.2
53.8
87.7
93.5
130.9
Field
Area
(Acre)
14.7
20.7
12.8
12.0
8.5
Storage*
Area
(AC-ft)
368
552
Not required
Not required
Not required
Storage area for effluent during the freezing period. 5.
Table 5. Liquid Loading Rates and Required Field fi
Areas for 1-MGD Plant at Various Locations
Effluent Depth
Location
Boston
Duluth
Miami
San Francisco
Phoenix
per Appl
Liquid
Loading
Rate
(ft/yr)
69.2
54.1
93.3
84.1
149.3
i cation:
Field
Area
(Acre)
16.0
20.7
12.0
13.3
7.5
500 cm (16.4 ft)
Storage*
Area
(AC-ft)
368
552
Not required
Not required
Not required
Storage area for effluent during the freezing period.
Table 6. Liquid Loading Rates and Required Field
Areas for 1-MGD Plant at Various Locations
Effluent Depth per Application:
Liquid
Loading Field
Rate Area
location (ft/yr) (Acre)
200 cm (6.6 ft)
Storage*
Area
(AC-ft)
Boston
Duluth
Miami
San Francisco
Phoenix
58.3
44.6
72.6
72.1
133.1
19.2
25.1
15.4
15.5
8.4
368
552
Not required
Not required
Not required
Storage area for effluent during the freezing period.
corresponding to effluent depth per application of
1000, 500, and 200 cm. In other words, the longer the
basin is flooded, the more effluent is infiltrated in-
to the ground, and consequently, smaller field area is
required. However, this does not mean that we should
select the longest flooding time in order to have
the highest liquid loading rate, because the liquid
loading rate alone is not sufficient to design the
system. The ability of soil to renovate the effluent
and to avoid excess nitrogen loadings on the ground -
water should be considered. The determination of
water quality loading rates is beyond the scope of
this paper.
Acknowledgment
The junior author acknowledges the support of
Office of Water Research and Technology grant WR-B038-
MASS, U.S. Forestry Service Pinchot Institute grant
USDA-23-591, and the senior author acknowledges sup-
port of Metcalf & Eddy, Incorporated, Miami.
References
Herman Bouwer, R. C. Rice, and E. D.Escarlega,
"High-rate Land Treatment I: Infiltration and
Hydraulic Aspects of the Flushing Meadows Project,"
Journal WPCF: Vol. 46, No. 5, May 1974.
Bagley, J. M., "An Application of Stochastic Pro-
cess," Technical Report No. 35, Department of Civil
Engineering, Stanford University, 1964.
Lo, K. M., "Digital Computer Simulation of Water
and Wastewater Sludge Dewatering on Sand Beds,"
Civil Engr. Dept. Tech. Rept. EVE 26-71-1
(July 1971), Univ. of Mass.
Philip, J. R., "The Theory of Infiltration:
4. Sorptivity and Algebraic Infiltration
Equation," Soil Science, 85, 1958.
Hillel Daniel, Soil and Water: Physical Principles
and Processes, Page 138 to 140, Academic Press,
1971.
Gardner, W. R., and Hillel, P.I., "The Relation
of External Evaporation Conditions to the Drying
of Soils," J. Geophys. Res., 67, 1962.
423.
-------
COMPUTER SIMULATION OF LONG-TERM SECONDARY IMPACTS
OF WATER AND WASTEWATER PROJECTS
Gerald A. Guter, Ph.D.
Director of Environmental Studies
Boyle Engineering Corporation
Newport Beach, California
John F. Westermeier
Biologist
Boyle Engineering Corporation
Newport Beach, California
Thomas C. Ryan
Environmental Planner
Boyle Engineering Corporation
Newport Beach, California
Applications of the KSIM technique were made in the
course of environmental studies for water and waste-
water projects. The National Environmental Policy Act
mandates a systematic interdisciplinary approach which
will insure the integrated use of natural and social
sciences and the environmental design arts in planning
and in decisionmaking which will have an impact on
man's environment. KSIM is being employed as a part
of this interdisciplinary approach. This application
of KSIM requires modification of published techniques
for water resource planning and adaptation to the cases
discussed.
The computer simulation, as applied to three water and
wastewater projects, are discussed herein. These proj-
ects include an Areawide Facilities Plan for the Las
Virgenes Municipal Water District in Los Angeles and
Ventura Counties, California; a Master Plan of Water
and Reclamation Facilities for Los Alisos Water Dis-
trict, Orange County, California; and an irrigation
project on the Colorado River Indian Reservation in
western Arizona. In considering the application of
KSIM to the above projects, major advantages, accept-
ability to reviewers and agencies, types of projects
to which KSIM appears applicable, and further research
on the methods are discussed.
Background
Section 102 of the National Environmental Policy Act
sets forth broad and sweeping policies for all agencies
of the Federal government to:
(A) Utilize a systematic, interdisciplinary approach
which will insure the integrated use of natural and
social sciences and the environmental design arts in
planning and decisionmaking which may have an impact
on man's environment.
(B) Identify and develop methods and procedures, in
consultation with the Council on Environmental Quality
established by Title II of this Act, which will insure
that presently unquantified environmental amenities
and values may be given appropriate consideration in
decisionmaking along with economic and technical
considerations.
(C) Include in every recommendation or report on pro-
posals for legislation and other major Federal actions
significantly affecting the quality of the human envi-
'ronment, a detailed statement which is now commonly
referred to as an Environmental Impact Statement.
Litigative activity over past years has centered
around implementation of Section 102 (C). Case law and
guidelines prepared by the Council on Environmental
Quality and by the Federal agencies have left little
doubt about certain aspects of Environmental Impact
Statement (EIS) preparation. They deal mainly in sub-
ject matter or required contents, format, and proce-
dures of review, however; and give little guidance for
implementing Sections 102(A) or (B).
Section 102(A) mandates the use of the interdisciplin-
ary approach which insures integration of the disci-
plines. This implies the numerous expertise must be
communicable to an integrator or one trained as a
generalist, or the experts must learn to communicate
among themselves. In either case, communication
interdisciplinary in nature is necessary within the
decisionmaking body. The use of several disciplines,
however, is a difficult and time-consuming task.
Section 102 (B) mandates an additional difficult task
for the agencies preparing environmental documents.
This section requires that "unquantifiable environ-
mental amenities and values may be given appropriate
consideration in decisionmaking." The Tenth Circuit's
decision in Trout Unlimited vs. Morton (7 ERC 1321)
touched upon the importance of the unquantifiable.
This court said that in most projects, "the ultimate
decision to proceed ... is not strictly a mathemati-
cal determination. Public affairs defy the control
that precise quantification of its issues would impose,"
The preparation of environmental documents pursuant to
NEPA and the so-called "little NEPA" legislation
adopted by states requires the development of method-
ologies to effectively implement the above NEPA sec-
tions. The Environmental Studies Department of Boyle
Engineering Corporation is pioneering the use of a
computer simulation procedure for EIS preparation which
was developed for integration of the disciplines. The
methodology described in this paper allows for a struc-
tured and sophisticated consideration of the numerous
complex relationships of a project or alternative and
its environment, yet is so structured to allow the
integration of both "hard" and "soft" data.
Description of Simulation Model
Because of their mathematical nature, most simulation
models tend to be excessively numerical. Variables
which are readily quantified exclude variables which
are subjective or intuitive but which may be just as
important. For example, wastewater collection network
parameters, treatment plant capacity, and discharge
requirements are included in the scope of planning a
wastewater treatment system. However, subjective or
semi-quantitative considerations such as local planning
policy, environmental quality, and stimulus to land
development can easily become the controlling factors
in the choice of an alternative system.
The methodology of the simulation,taking into consid-
eration both quantitative and qualitative variables and
applied to cases described below,was developed by Kane,
Vertinsky, and Thomson1 and applied to water resource
planning. For a detailed account of the mathematical
treatment of the model, the reader is referred to the
above basic reference, as well as reports by Kruzic2
and Suta3. One of the advantages of the Kane Simula-
tion Model (KSIM) is that a detailed mathematical
knowledge of the model is not required to use the
model. Thus, a barrier is removed between the disci-
plines who jointly participate in the construction of
the model variables and the simulation modeling by use
of a simplified simulation language.
424
-------
KSIM mathematics has the following properties:
(1) System variables are bounded. It is assumed that
any variable of human significance cannot increase
indefinitely; there must be distinct limits. In an
appropriate set of units these can always be set to one
and zero.
(2) A variable increases or decreases according to
whether the net impact of the other variables is posi-
tive or negative.
(3) A variable's response to a given impact decreases
to zero as that variable approaches its upper or lower
bound. It is generally found that bounded growth
and decay processes exhibit this sigmoidal character.
(4) All other things being equal, a variable will
produce greater impact on the system as it grows larger.
(5) Complex interactions are described by a looped
network of binary interactions.
Representative previous applications of KSIM include
Impact of Canadian Water Sales to the United States
(Kane), Implications of a U.S. Deep Water Port Policy
(U.S. Army Corps of Engineers), Sensitivity of Alter-
native Manpower Policies (U.S. Office of Naval Re-
search) , and Effects of a "Make or Buy" Research Policy
(Policy and Planning Directorate, Canada).
We use the following procedure to apply KSIM as a part
of the environmental impact reports or statements.
The most appropriate portions of a study are those in
which long-term relationships between the proposed
project, its alternatives, and unquantifiable values
must be analyzed. The steps are as follows:
Step 1: Assignment and Preparation of Team Members.
Normally all specialists who participate in the pre-
paration of the draft statement are assigned to the
KSIM team. These are staff scientists, engineers,and
planners of varying backgrounds and expertise involved
in the major subject areas of the EIS. The individ-
uals work together in various studies in support of the
EIS and meet frequently to discuss the results of their
studies. Thus, each is familiarizing himself with the
proposed project, the environment of the project, and
the alternatives under consideration. He is also
learning to communicate with his team members. These
researchers represent a core group. Other experts also
familiar with the project area may join the core group
at a later date. These may be lead agency staff members
or the decisionmakers themselves.
Step 2: Identification of Variables. Critical long-
term variables are identified and defined as precisely
as possible. One variable must represent the proposed
project or alternative. The definition of the vari-
able is separated into its quantitative and qualitative
components.
Step 3. Set Initial Values. A well defined variable
will lend itself to setting an initial value. An
estimate is made of the maximum growth level the vari-
able could achieve. For example, if the variable is
population, the initial value is the present fraction
of the ultimate population.
Step 4. Cross-Impact Analysis. KSIM requires that
two matrices be completed for the simulation. One of
the matrices represents the long-term (Alpha) relation-
ship between variables and the other represents the
short-term (Beta) relationship. The matrices are con-
structed with each variable listed as a row and a col-
umn heading of a table. A basic assumption is that
when one variable changes, it may increase or decrease
each of the other valuables or it may have no relation-
ship at all. Thus, "0," "+," "-" is assigned to each
square of the matrices. Numerical values are assigned
as a refinement.
Step 5. Computer Projection of Variables. Variables,
initial values, and cross-impact values are typed into
a computer with the KSIM program. The computer per-
forms the interactive calculations and displays the
projected changes in each variable over time. Team
members may now modify and refine their model by chang-
ing variable definitions, initial values, and numerical
cross-impact values or by choosing an alternative proj-
ect. This refinement is repeated until the team mem-
bers are satisfied that their projections and inputs
are reasonable.
Step 6. Interpretation of the Projection. Major trends
which appear in the projections and some analyses of
the key factors,and issues which bring about those
trends, can now be discussed using the projections as a
basis for the discussion. Differences in the long-term
impacts between the various alternatives can also be
analyzed and discussed.
Examples of Applications of KSIM
To Environmental Studies
The application of the KSIM procedure to preparation of
environmental studies has been demonstrated in three
water and wastewater management related projects in the
past year. A fourth study application is currently
under way. Described briefly below is the manner in
which KSIM methodologies were applied to the various
studies.
An EIS was initiated to evaluate an Areawide Facilities
Plan of wastewater collection, treatment, and disposal
facilities for the Las Virgenes Municipal Water Dis-
trict. The 118,000-acre service area of the District
included coastal Malibu, portions of the Santa Monica
Mountains, and inland areas of western Los Angeles and
eastern Ventura Counties, California. The issues of
population growth and land use presented unusual prob-
lems due to conflicting philosophies within the region.
Population growth had been rapid and was considered
desirable in the inland urban areas, whereas the
coastal portions of the study area had defeated sewer
bond issues (presumably on alleged growth-inducing
impact) three times since 1966. KSIM was employed to
model the long-term effects of implementing the Area-
wide Facilities Plan.
The KSIM team consisted of the staff of the Depart-
ment of Environmental Studies. Staff members included
specialists trained and experienced in the fields of
water quality and reclamation, public health, social
services, local and regional planning, ecology, and
environmental geology.
Nine variables were defined and initial values set by
the team according to procedures outlined in the pre-
vious section. They;are given below:
Population (POP) represents the number of people
living in the study area. An initial value of 15
percent was established.
Pollution (POL) indicates the level of air, water
and noise pollution in the study area. The initial
value of 45 percent represents the ratio of the pres-
ent measured levels of the three pollutants to the
regulatory standards set for maximum limits.
Desirability (DES) denotes the general attrac-
tiveness of the study area based on such factors as
425
-------
aesthetics, amenity, and quality of life. Largely a
qualitative determination, the study area was given an
initial value of 70 percent.
Urban Services (US) measures the quality
and quality of public services such as schools, police,
fire protection, and utilities provided to area inhabi-
tants. Services were judged more than adequate as
indicated by an initial value of 20 percent (5 percent
above population).
Resource Consumption (RC) represents the total
amount of energy and water consumed in the study area.
The initial value of 11 percent is the ratio of present
usage to that required by the ultimate population
anticipating the effect of current and future energy
conservation measures.
Residential Density (RD) indicates the ratio of
high density urbanization to developed land, initially
estimated at 25 percent.
Employment Dispersal (ED) is the relationship of
distance between places of employment and residence.
The initial value of 27 percent is the quantitative
estimate of the ratio between maximum and existing
distance driven to work.
Wastewater System Capacity (WSC) represents the
proposed project. The initial value of 9 percent is
the existing fraction of ultimate projected wastewater
treatment capacity.
Cost of Living (COL) is probably the most quali-
tative of all variables. The initial value of 20 per-
cent was based on the assumption that the cost of
living would not exceed five times its present value.
Through cross-impact analysis, the Alpha and Beta
matrices were completed and checked for obvious errors.
The derived values were tested on the computer and
subsequent refinements were made. Tables 1 and 2 show
the Alpha and Beta matrices which produced the regional
model depicted in Figure 1.
Table 1. Alpha Matrix of Long-Term Impacts
VARIABLE INITIAL VALUE
1.0
POP
WSC
COL
POP
DES
POL
US
RC
RES
ED
WSC
COL
POP
DES
POL
US
RC
RES
ED
WSC
COL
+2
-1
+2
-1
+1.5
+2
0
+1.5
0
Table
POP
0
+ .5
+ 2
-1
+1.5
-1
0
-1
+ .5
+ 1
+ .
0
+1
0
-1
+ ,
+ .
2.
5 -1.
+ .
0
0
+
.5 0
.2 0
.8 0
Beta
5 +1
5 +1.5
5 + .5
0
+1
5 -1
0
+ .5
+ .9
Matrix
DES POL US
0
+
0
0
0
+
0
0
0
.1 -1
+ 1
+ 1
0
.1 0
0
0
0
.2 0
.5 + .3
0
0
0
0
0
0
+ .5
0
0
+2.2
0
+ .5
.3
0
+1
+ .6
.1
-1
-1
-1
.5
+ .5
.2
.5
-1
of Short-Term
RC
0
0
+1.6
.5
-1
0
0
.5
+ .7
RES
0
.8
.4
0
0
+ .3
0
+ .5
0
-1
-1
+ 1.2
0
+1.5
0
0
0
+ .5
+ .25
+1.7
.7
0
+1
0
0
0
+ .6
-1
.5
.5
+ .8
-1
+1
.5
.5
0
Impacts
ED
.3
0
+1
0
+1
0
0
0
0
WSC
0
+ .1
-l.S
0
0
0
0
0
0
COL
0
.2
0
0
-1.3
0
.1
0
0
Figure 1. Regional Model, Areawide Facilities Plan
The simulation indicates continued urbanization in the
study area, shown by the increases in population, urban
services, and residential density. The fact that urban
services increase slightly is an indication that the
area may be able to retain much of its rural character.
Resource consumption increases at a rate slightly
greater than the population, indicating a slight in-
crease in per capita consumption. The continued rise
in pollution can be directly tied to its strong rela-
tionship with both population and resource consumption.
The steady decrease in employment dispersal indicates
an increase in the number of employment centers in the
project area. (The area has virtually none at present.)
Joining employment dispersal in an overall decline over
the planning period is desirability. The decline is
attributable mainly to increases-in population and
pollution. Cost of living does interact here,also
tending to reduce desirability. The increases in popu-
lation, resource consumption, and urban services indi-
cate future growth, which are accommodated by in-
creased wastewater system capacity. The demand for
wastewater treatment facilities for the year 1987 in
the simulation does not rise above the capacity that
would be provided by the proposed project.
KSIM was again employed in association with an environ-
mental impact report for the Master Plan of Water and
Reclamation Facilities of the Los Alisos Water District,
a 5,400-acre district located within a rapidly growing
area of Orange County, California. Several constraints
on growth exist within the district, including land use
restrictions associated with the flight path of a
military air base and lack of regional wastewater treat-
ment and disposal facilities.
Team members participating in the KSIM analysis in-
cluded members of the Department of Environmental
Studies. District staff and the Board of Directors
reviewed initial KSIM models and offered suggestions
for refinement of the models. Nine variables defined
for this study include the following:
Population (POP) is a quantitative variable of the
number of people residing within the district.
426
-------
Nonrenewable Resources (NRR) represents consump-
tion levels of nonrenewable resources within the dis-
trict including energy consumption and use of con-
struction materials.
Public Services (PUB) reflects levels of public
services including schools, parks, solid waste col-
lection, police protection, public transportation, and
social services.
Pollution (POL) variable is a semi-quantitative
variable reflecting levels of water and air quality
within the district.
Natural Resources (NAT) reflects both qualitative
and quantitative, ecological, agricultural, mineral,
and archaeological resources of the district.
Economic Resources (ECO) reflects both quanti-
tative and qualitative aspects of economic activity
within the district including property values, busi-
ness activity, family income, and employment.
Desirability (DBS) is a qualitative variable
reflecting the characteristic which may cause people
to desire living in an area. Examples of these char-
acters include levels of public services; closeness
to work, shopping, and friends; quality of schools;
and aesthetic qualities.
Reclamation (REC) is a quantitative variable
representing the amount of wastewater generated within
the district that must be reclaimed.
Water Consumption (WAT) is a quantitative vari-
able representing the amount of water used within the
district.
Three KSIM models were generated to reflect possible
changes in land use and in wastewater treatment and
disposal. The first model (Case 1) was the more con-
servative case reflecting current land use restraints
and wastewater treatment and reclamation near or with-
in district boundaries. Case 2 reflected the addition
of some capacity in regional treatment and disposal
facilities. Case 3 reflected a situation where land
use restraints associated with the flight path of the
military air base were liberalized and regional waste-
water treatment was available.
Alpha and Beta matrix values for Case 1 are in Tables
3 and 4. Alpha and Beta values for Cases 2 and 3 were
similar; however, the initial value for reclamation
was lowered to reflect capacity in regional wastewater
treatment and disposal in Cases 2 and 3. The initial
value for population was also lowered in Case 3 to
reflect a potential higher ultimate population.
Table 4. Beta Matrix for Case 1
POP
NRR
PUB
.POL
NAT
ECO
DES
REC
WAT
POP
+2
+ .8
+1.5
+ .5
-2
+2
.5
+ .3
+ 2.5
NRR
.5
+ .5
+ .5
+1.5
.5
.5
.4
+ 1
+ 1
PU
+2
+
+
+1
+1
+ 1
5
5
S
2
1
2
POL NAT
.5 + .3
+1 -1
+1 .2
+ .1 .1
.4 + .5
.5 .5
.5 + .5
+1.5 .3
.3 .3
EC
+ 2
+1
+1
+ 1
-1
+
+1
+1
+ 1
3
5
5
5
S
5
5
DE
+2
+1
+
+
+
+1
+
+ 1
+
3 REC
+ 2
+1.5
8 + .5
1 + .5
2 -1
-1
8 .5
5 + .5
7 .8
«IAT
.1
.3
.5
.1
.1
.5
.3
2.5
.5
Computer projections of each variable for Case 1 are
shown in Figure 2. Population rises to the approxi-
mate levels predicted by current land use elements.
Nonrenewable resource consumption increases in the dis-
trict, reflecting increased urbanization. Public ser-
vice levels rise slightly. Pollution levels increase
over time reflecting air quality degradation in the
region. As urbanization increases, natural resources
decrease in the district. Economic resources rise
steadily over time. Desirability remains at approxi-
mately the same level. Reclamation and water consump-
tion increase in relation to population increase.
Computer projections of variables for the other two
cases were similar to Case 1 with higher population,
reclamation, and water consumption, and a sharper
decline in natural resources.
VARIABLE INITIAL VALUE
1.0 i—
1985
YEAR
Figure 2. Regional Model for Case 1
Table 3. Alpha Matrix for Case 1
POP
NRR
PUB
POL
NAT
ECO
REC
WAT
POP
NRR
PUB
POL
NAT
ECO
DES
REC
HAT
+2
+2.5
+ .5
+2
.4
+2
.2
+3.5
+2.5
.2
+ .5
+ .5
+1
.4
.3
.1
+1
+1
+1
+
f
+ 1
+2
+ 1
5
2
3
3
2
5
+ .2
+1
+1
+ .3
.4
.4
.5
+1.5
.3
+ .3
.5
.2
.3
+ .S
.2
+ .5
.3
.1
+2.5
+1.5
+1
+ .5
.5
+ .8
+1
+2
+1.5
+2
+ 1
+1.5
+ .2
+ .1
+1.5
+1
+1
+ .7
-1
+1
+1
+
+
-1
S
3
5
8
4
5
.1
.4
.3
.1.
.l'
.5
.3
2.5
.5
A brief description of KSIM and the results of the
computer simulations were included in the environ-
mental impact report for the district's Master Plan.
Public agencies, organizations and individuals review-
ing the EIR had no adverse comments to offer in regard
to the use of KSIM.
Use of KSIM by the Department of Environmental Studies
has not been limited to wastewater projects. KSIM has
provided valuable assistance in analyzing environ-
mental impacts associated with expanded agricultural
development on the Colorado River Indian Reservation in
western Arizona. Team members were limited to the
staff of the Department of Environmental Studies.
Variables selected for the analysis included: Indian
Self-determination (ISO), Agriculture (AG), Resource
427
-------
Consumption (RC), Scientific Relationships (SR) ,
Pollution (POL), CRIT System Procedures (CSP), Quality
of Social Services (QSS), Employment (BMP), and Tribal
Income (TI).
Computer projection of these variables is shown in
Figure 3. Several trends are apparent in this simu-
lation. Indian self-determination rises possibly in
response to higher tribal income brought about through
increased agriculture and employment. Resource con-
sumption also increases in response to increased
agricultural development. Increased agriculture also
appears to result in increased pollution levels and
lowering of scientific relationship values. Quality
of social services is projected higher although govern-
ment role (CRIT System Procedures) in the reservation
is decreased.
VARIABLE INITIAL VALUE
1.0
Figure 3. Model for Colorado River Indian Reservation
The Department of Environmental Studies is currently
applying KSIM to the evaluation of environmental
aspects of a water-oriented recreational development.
Variables including recreation, resource consumption,
environmental quality and jurisdictional framework
have been defined for this simulation.
Operational Aspects and Implications of Use
The application of KSIM to appropriate projects has
distinct functional advantages. It allows a multi-
disciplinary interchange as mandated by current
environmental legislation, and provides a sound basis
to decisionmaking through the interactions of the
panel approach. Its use of cross-impact analysis
encourages disciplined inquiry and allows decision-
makers to appreciate the magnitude and complexity of
factors affecting planning decisions. As it provides
a model of the future, it may be periodically checked
to determine if adopted policies are having the effects
initially perceived. Future changes in goals and
policies can be readily integrated into the KSIM model
through ongoing refinement.
Additionally, KSIM has advantages related to EIR/EIS
processes. Evaluation of long-term, secondary,envi-
ronmental impacts as required by NEPA and other acts
is greatly facilitated by the KSIM projection.
Displaying the projections at work sessions or public
hearings and soliciting comment on the models can pro-
vide decisionmakers with a unique way of involving the
public in the planning process.
KSIM is attractive to many reviewers and public agen-
cies as participation in cross-impact analysis does
not require a highly technical background. Because of
this relative simplicity in use, decisionmakers and
other interested parties can actively participate in
the formation of the simulations. However, use of
KSIM for many agencies is limited due to the avail-
ability of necessary data processing equipment. Active
participation by many decisionmakers is also hampered
by the time required for completion of both Alpha and
Beta matrices by the KSIM panel.
We believe KSIM has wide applicability for environ-
mental studies on many types of projects in addition to
those discussed in this paper. Generally, KSIM can be
applied to projects where impacts of a project go well
beyond the immediate time frame. It is particularly
well suited for projects requiring master planning
techniques, as KSIM itself is a planning exercise. We
believe KSIM will be more commonly used for projects
which require a decision about implications of future
growth.
We are currently researching methods to modify, monitor,
and refine the KSIM procedure so that it can be more
easily implemented. One approach is to reduce the
time required to formulate and run a simulation. Ways
in which this may be accomplished include: the com-
posing of checklists of typical variables for specific
types of projects, standardizing and refining methods
for setting variable limits and determining initial
values, and adjusting the program and procedure to
require only the Alpha cross-impact matrix.
It may be possible to save much panel discussion time
by bringing the decisionmakers into the exercise at a
later stage of the simulation. Decisionmakers would
then have more of an evaluative function since a core
group would have already defined variables and set'
initial values. The use of questionnaires is also
being investigated as a way to document the input of
KSIM team members who cannot participate in the dis-
cussion in person.
Future research of the KSIM procedure is needed to sub-
stantiate the accuracy and validity of the model. This
can only be done through long-term monitoring and
evaluating of a KSIM model, and subsequent revision of
the procedure. As with any planning tool, however,
KSIM's real benefit is not in predicting the future
but in facilitating the formulating of policy which
will at least set a rational course of action towards
the future.
References
1. Kane J.; I. Vertinsky; and W. Thomson.,"KSIM: A
Methodology to Interactive Resource Policy Simulation,
Water Resources Research 9(1): 65-79, 1973.
2. Kruzic, P.G./'Cross-Impact Simulation in Water
Resource Planning," U.S. Army Engineers Institute,
Fort Belvoir, Virginia, 1974.
3. Suta, B.E.,"KSIM Theoretical Formulation, A Para-
metric Analysis," Stanford Research Institute, Menlo
Park, California, 1974.
428
-------
A CRITICAL APPRAISAL OF MATHEMATICAL MODELS
FOR LAND SUBSIDENCE SIMULATION
E. John Finnemore and Robert W. Atherton
Systems Control, Inc.
Palo Alto, California
Land subsidence can have a major environmental im-
pact resulting from the withdrawal of geofluids: oil,
gas, groundwater, or geothermal water and steam.
While mathematical models for simulating land subsid-
ence caused by pore fluid withdrawal are still in a re-
latively early stage of development and are not yet
very numerous, the subject is drawing increasing atten-
tion. Documentation is available on two simple and
nine advanced models of this type, and additional mod-
els under various stages of development were identified.
The appraisal of such models reported here required an
examination of the physics included, the model equa-
tions, the numerical methods, and the practical applic-
ability of each. The status of this field and the need
for further work are reviewed.
Background
Examples of major subsidence resulting from
the withdrawal of petroleum, groundwater, and geo-
thermal fluids are respectively: 8.8m vertical and
3.6m horizontal movement over the Wilmington oil field,
Long Beach, California; 8.8m vertical movement in the
San Joaquin Valley, California; and 4.5m vertical and
0.8m horizontal movement at the Wairakei geothermal
field in New Zealand. Numerous instances of lesser
subsidence have occurred around the world.1
The total environmental impact of subsidence ob-
viously depends upon the geographic and economic devel-
opment of the site. In populated areas, roads, railroad
tracks, sewers and drains, power lines, pipelines,
wells, airfields, houses, and buildings may be damaged.
In rural areas, dams and levees, irrigation chan-
nels, agricultural drains, wells, electric transmission
towers, vegetation patterns, and crop irrigation pat-
terns may be affected. Along coastlines and rivers the
areas subject to flooding may be altered and increased,
and drainage paths may be changed. In any location,the
incidence of minor earthquakes may be affected. Within
the producing field itself, wells and well casings,
pipelines, and plant (if any) may be damaged, and the
storage and transmissivity of the producing porous med-
ium (fluid reservoir) may be reduced. It must be noted
that the resulting bowl-shaped surface depressions
which usually form may be significantly offset from the
producing wellfield, as occurred at Wairakei. Also,
for a number of the impacts just mentioned, horizontal
ground motion (not predictable by one-dimensional sub-
sidence models) can have far more serious effects than
vertical motion.
Models are employed for two reasons: they provide
a mechanism with which to improve our understanding of
the nature and behavior of a producing field, and they
provide a means for predicting subsidence and for in-
vestigating alternative schemes for subsidence mitiga-
tion. As early as 1925, while providing an understand-
ing of the consolidation of soils for the first time,
Terzaghi deemed theories of models to be among the most
important and indispenslble engineering tools.
The work reported here was performed as part of a
study of subsidence associated with geothermal develop-
ment, supported by the National Science Foundation.
The models reviewed in that study also included certain
other non-subsidence models, which have frequently been
incorporated into the subsidence models. The work was
accomplished by a review and analysis of the published
and unpublished literature on models for subsidence
caused by any type of geofluid withdrawal. This was
supplemented by discussions and interviews with re-
searchers in the field of subsidence modeling, and by
attendance at numerous seminars and symposia where these
topics were considered.
Model Appraisal
Formulating a mathematical model for land subsid-
ence is no small undertaking. As usual in modeling geo-
physical processes, the accuracy of the model is limited
by the ability to describe the detailed structures pro-
vided by nature. Even when the scope of the modeling
effort is reduced, two major problems remain: the
question of data availability and the problem of com-
putational tractability. It is not clear whether the
data base for a large-scale model is available at this
time. With regard to computational tractibllity, a com-
prehensive three-dimensional reservoir subsidence model
would tax even today's large computers.
Despite the drawbacks listed above, models are in-
valuable as a means of studying a phenomenon, correlat-
ing data, identifying the most crucial data needs, or
extrapolating to unknown conditions. In studying sub-
sidence, we have been compelled to rely on a hierarchy
of models rather than a single definitive model. Our
appraisal has consisted of three parts: (1) a study of
the simplest class of subsidence models, (2) an investi-
gation of the form of an advanced subsidence model which
would provide the minimum predictive capability, and (3)
a study of the state-of-the-art in subsidence modeling.
Simplified Subsidence Models
Simplified models serve two purposes. First, they
provide models which can be used independently of large
computers and program decks. Thus, they provide an in-
expensive means of making a first estimate of subsid-
ence, and they provide a vehicle for the non-expert in
solid mechanics to obtain an understanding of the sub-
sidence process. Second, the site data required to use
a simple model are limited and more likely to be avail-
able.
Simplified subsidence models have been developed
by adapting the work of Geertsma.3 These simplified
models will be a key portion of a subsidence handbook
being developed to provide a guide to the analysis of
potential subsidence associated with geothermal develop-
ment . ^
The simplest compaction model can be expressed
as follows:
AH = H C Ap
m
This simple equation illustrates the fundamentals of
compaction. The compaction AH is the product of the
reservoir thickness H, the reduction in pore pressure
Ap, and the compaction coefficient C . Therefore, as
Geertsma pointed out, compaction can occur in well con-
solidated reservoirs, if they are thick and experience
a large decrease in pore pressure.3 Slightly more
sophisticated models have also been presented in which
C is calculated using an integral over total effective
stress.
429
-------
This compaction equation alone does not account
for response of the overburden to reservoir compaction;
it is the surface deformation that is evident as sub-
sidence. A simple overburden model is also available.
Description of an Advanced Subsidence Model
In modeling subsidence, we are interested in de-
scribing the sinking of the earth's surface due to ad-
justments in the subterranean material stimulated by
the withdrawal of geothermal fluids. Since the fluid
withdrawal is the subsidence stimulus, the first re-
quirement is for a well-bore model and a reservoir mod-
el to relate the pore-pressure distribution in the res-
ervoir to the rate of withdrawal at the surface.
Since reservoir compaction is the precursor of subsid-
ence, a second need is a constitutive equation, a model
for mechanical behavior, for the reservoir material.
These two models must be coupled (interactive), as com-
paction affects the porosity and permeability of the
reservoir.
Two additional distinct material models will be
required: one for clays and one for the overburden.
Clays in communication with the reservoir will also
undergo reduction in pore pressure, and consequently
will compact, though usually with considerable time de-
lay. The overburden, experiencing a change in stress
at the reservoir boundary, will deform; the deformation
of the overburden can be treated as an elastic material.
The all-important reservoir will likely require treat-
ment as a plastic material in order to account for the
well.known irreversible nature of compaction. The
same argument holds for clays. The exact form of the
required two plastic constitutive relations is yet to
be determined.
To summarize, an advanced subsidence model must
include computer subroutines to generate the character-
istic physical properties of the site. It should con-
tain a well-bore model, a reservoir model, and three
models of material behavior, i.e., for the reservoir,
communicating clays, and the overburden. All models
should be implemented using the best available numeric-
al methods.
Survey of Subsidence Models
The recent interest in environmental aspects of
land subsidence, and the increased availability of
large computers, have provided incentives to the devel-
opment of models for subsidence. A considerable number
of these models are presently under continuing develop-
ment. In addition, more subsidence models will be in-
troduced by the plans to incorporate deformation models
into many of the reservoir models (fluid flow, or fluid
heat flow only) presently under development also; these
future possibilities are not discussed here.
The survey reported here identified two simple and
fourteen advanced models designed to simulate subsid-
ence caused by geofluid withdrawal. The developers of
these models and the applications for which they were
designed are listed in Table 1. In the miscellan-
eous category, the first model has a general capability
for any type of man-induced subsidence, and the second
simulates natural geological subsidence in a basin ex-
periencing sedimentary deposition. While much has been
learned about the effects of groundwater withdrawal
since Terzaghi described his consolidation theory in
1925, advanced models for simulating resulting ground
deformation are seen to have appeared only after 1972.
Mathematical models for computing land subsidence
caused by the extraction of oil and/or gas from the
ground were probably first formulated in the 1950's.
The early models were all analytical models; a number
of the more recent numerical subsidence models have
been developed by petroleum company personnel, so that
they remain proprietary. The recent upsurge of inter-
est in alternate energy sources has stimulated the de-
velopment of models for geothermal resources. However,
only two geothermal subsidence models are, as of
February 1976 near first-version completion, and neither
of them has been tested in applications yet.
Table 1
MATHEMATICAL MODELS OF LAND SUBSIDENCE
CAUSED BY PORE FLUID WITHDRAWAL
TYPE
Miscellaneous
Groundwater
Oil and Gas
Geothermal
DEVELOPER(S)
Sandhu and Wilson (1970)
Jacquin and Poulet (1970)
Gambolati,et al. (1973, 1974)
Helm (1974)
Narasimhan (1975)
*McCann and Wilts (1951)
*Geertsma (1966)
Geertsma and van Opstal (1973)
Frazier (1973), Archambeau (1974
Finol and Farouq Ali (1975)
Paris and Farouq Ali (ongoing)
Kosloff and Scott (ongoing)
Oil Companies (proprietary)
Pritchett, Garg, Brownell (1975)
Lippmann ,and Narasimhan (ongoing)
Safai and Finder (ongoing)
*Simple models (remainder are advanced models)
Each of the models listed in Table 1 is discussed
in the following paragraphs, in the same order.
Sandhu and Wilson developed a finite element method
for the general analysis of land subsidence. It per-
mits the consideration in two or three dimensions of
complex geometry, arbitrary time-varying boundary con-
ditions, non-homogeniety as well as anisotropy, and
non-linear and time-dependent material behavior includ-
ing viscoelasticity, creep, temperature effects, resid-
ual stresses and plastic behavior.
Jacquin and Poulet developed a two-dimensional
(axi-symmetric) computer model to study the hydrodynam-
ic patterns in a naturally subsiding sedimentary basin;
With time and deposition of successive sand and clay
strata, the depth of the conical-shaped basin increased
and water was expelled from the clay. Fluid flow was
horizontal in the sands and vertical in the clays.
Gambolati et al. developed a two-step mathematical
model to analyze subsidence in the complex, unconsolid-
ated aquifer-aquitard system underlying Venice, Italy.8^
The hydraulic pressures were calculated in a two-
dimensional vertical cross section in radial coordin-
ates in the first step by a model based on the diffus-
ion equation, which was solved with a finite element
technique. The values of the hydraulic heads in the
aquifers were then used in the second step as time-
dependent boundary conditions in a set of one-
dimensional vertical consolidation models, which were
solved with a finite difference technique. The com-
paction models are based on the one-dimensional form
of the classic diffusion equation, written in terms of
one unknown, the fluid potential, and employing only
one elastic constant, the vertical compressibility, a.
While the compressibility, a, of any layer may be a
non-linear and irreversible function of the pressure
head, at Venice the non-linearity was considered neg-
ligible. The irreversibility was provided by using
two a values for each layer, one for compaction (pre-
consolidation) and another (about one-tenth as large)
for expansion.
430
-------
Although model calibration was hampered by the
sparseness of the available data, the study was able to
predict the results of alternative mitigation measures?
The main disadvantage of this model lay in the limita-
tions imposed by the requirement of radial symetry.
When using the two-oc-vaiue method described above, it
is very important that the computer code should keep
track of the past maximum effective stress at every
point, and use the smaller (expansion) value for com-
pression when the effective stress does not exceed the
past maximum (preconsolidation) stress.
Helm has developed two one-dimensional mathemati-
cal subsidence models for groundwater withdrawal.10-12
Cumulative compaction and expansion in a series of
aquifers and aquitards was computed from the known
applied stress history and from two storage coeffi-
cients (compressibility values), one for recoverable
and the other for non-recoverable compression. By dis-
tinguishing between present effective stress and past
maximum effective stress at any depth, these models em-
ployed the two storage coefficients in a manner very
similar to that used in the model of Gambolati, et al?>^
Non-recoverable compaction occurred only when the past
maximum effective stress at any point was exceeded.
Helm's two models are also both based on the one-
dimensional diffusion equation. One model assumes
linear (not stress-dependent) coefficients, and the
other assumes non-linear (stress-dependent) coeffi-
cients. Two transformations of applied stress enabled
the non-linear formulation to be represented by an
equivalent linear homogeneous formulation. Both models
were solved by finite difference techniques.
The models were applied to a series of 21 aqui-
tards at Pixley, in the San Joaquin Valley, California.
There, continuous records of hydraulic head and com-
paction revealed 3.19 feet of compaction between 1959
and 1971, although there was no long-term decline of
the groundwater level which experienced seasonal fluct-
uations of about 100 feet. The maximum error in the
predictions of the non-linear model was 2.9% compared
with 17. for the linear model.
Narasimhan has developed a subsidence model named
TRUSTT3TRUST will simulate transient groundwater
motion in variably saturated, deformable, heterogen-
eous, isotropic, multidimensional, porous media. It in-
corporates a one-dimensional subsidence model employing
Terzaghi's consolidation theory into a general three-
dimensional, isothermal, groundwater flow model. The
non-linear governing equation employs the pore-pressure
head as the dependent variable; it is solved using an
integrated finite difference method.
TRUST was tested and verified on nine different
problems. Applications involving deformation included:
• One-dimensional, time-varying consolidation of
clay under a foundation load
• One-dimensional shrinkage of an active (benton-
ite) clay slurry, in which large volume changes
can occur in very short times
• One-dimensional drainage (partially saturated
flow) of a deformable sand
• Two-dimensional draining (both fully and part-
ially saturated) flow in a deformable sand
• Two-dimensional drainage and deformation around
a fresh excavation in soft clay.
McCann and Wilts developed two analytical models
as part of a mathematical study of the oil-field sub-
sidence in the Long Beach area.1^ At the time (c.
1950), it was decided that the only physical model
which could logically describe the general known pro-
perties of the soil and be amenable to mathematical
solution was one of a three-dimensional, homogeneous,
isotropic elastic medium of semi-infinite (downward)
extent. Solutions were obtained for motions (vertical
and horizontal, as functions of depth) and stresses
developed in such a medium under the action of general
distribution of the two alternative types of ideal-
ized subsurface disturbance forces. These forces were
intended to represent the effect of drops in the re-
servoir oil pressures, and ways were devised to obtain
the forces from the pressure drops.
The first type of disturbance force was called a
"tension center" (or "tension sphere"), and the second
type consisted of a pair of equal vertical forces act-
ing in opposite directions a short distance apart, con-
sequently named a "vertical pincer."
Analysis yielded the stresses and deformations
caused by such a single disturbance force. Employing
the principle of superposition, arrays of tension cen-
ters and vertical pincers were sought which would yield
the deformation observed at that time. The assumption
of an elastic material is essential for the use of
superposition, and McCann and Wilts themselves stated
that the most serious difficulty with their analysis
was the failure of the earth to behave like an elastic
material. They found that the tension center model
could be arrayed to fit all the observed deformation
data to the accuracy with which they could be measured,
while the vertical pincer model could fit none, and so
they concluded that only the tension center model
should be considered further.
Geertsma developed a three-dimensional analytical
subsidence model for poro-elastic displacements around
a contracting oil reservoir in a semi-infinite, homo-
geneous, isotropic rock medium. It employed a "nu-
cleus of strain" concept, and it integrated the result-
ing displacement function over the volume of a hori-
zontal, disc-shaped producing reservoir. The same lin-
ear elastic properties were specified within and out-
side the reservoir, into which no natural recharge was
allowed as the contained pore pressure was reduced,
causing changes to both internal and external stresses
and strains. Results of evaluations with this model
indicated that notable subsidence (as opposed to com-
paction) can be expected only above large reservoirs
consisting of highly compressible sediments and exper-
iencing substantial pore-pressure reductions.
Geertsma's model (poro-elastic theory) described
here, and McCann and Wilts' model (elastic theory) de-
scribed previously, were reviewed, compared, related,
and improved by Gambolati.1° In particular, Gambolati
demonstrated that Geertsma'« model can be easily ex-
tended to incorporate heterogeneity of the reservoir
(reservoir material more easily deformed than its
overburden).
Geertsma and van Opstal evaluated conceivable nu-
merical methods for calculating subsidence above oil
or gas reservoirs of arbitrary three-dimensional shape
and change in pressure distribution. They concluded,
in 1973, that the simplest method, which still pro-
vided a good overall impression of the spatial subsid-
ence distribution, was one based on the linear elastic
theory of nucleus of strain in the half space.. Then
tested a suitable three-dimensional finite element pro-
gram named ASKA for such purposes, and obtained results
which agreed quite satisfactorily with their analysis.
They also developed another computer program to help
integrate their nucleus-of-strain theory over a com-
pacting reservoir of arbitrary shape, by dividing it
up into a finite number of small parts. This latter
approach they used to predict subsidence and horizontal
displacement patterns over the Groningen gas field from
1975 to 2100.
Frazier and Archambeau developed an elastic re-
servoir model with interactive fluid flow and rock
strain equations, which they applied to the Long Beach
431
-------
oil field with both production and injection.18'19 It
is an axi-symmetric or planar (two-dimensional) finite
element model, which reduces to an implicit time-step
scheme.
Finol and Farouq Ali developed a two-phase, two-
dimensional black oil model for simulating reservoir
production behavior and simultaneous ground deforma-
tion.^ Reservoir compaction was described on the ba-
sis of reported experimental data, from which the sur-
face subsidence was calculated using Geertsma's theory
of poro-elasticity and nucleus-of-strain concept.15
Fair results are obtained with a simulation of the pro-
duction and subsidence history of an oil field on the
Bolivar Coast of Western Venezuela.
Paris and Farouq Ali are presently extending the
work of Finol and Farouq Ali described above, but no
results have been published as yet.
Kosloff and Scott are developing a deformation
model for the Wilmington oil field, which requires pore
pressure histories as input data. This procedure has
the advantage of removing uncertainties in the fluid-
flow patterns caused by large variations in permeabil-
ity, but it makes the model more difficult to use
with future production schemes. They consider that
soils exhibit plastic behavior from the start, and with
stress they strain harden and eventually become elas-
tic. Accordingly, they have used the plastic cap model
as the basis of their constitutive relations. A two-
dimensional, axi-symmetric version of this deformation
model appears to have given good results for subsid-
ence at Wilmington, in spite of the block-shaped zones
in the reservoir formed by faults. They are now at-
tempting to check these results with a three-
dimensional version of the model.
Oil Companies are known to have various models for
simulating subsidence over oil and gas fields and in
permafrost. Because of their proprietary nature, few
details are available.
Pritchett, Garg, Brownell and others are in the
process of developing probably the first multi-
dimensional, deformable, geothermal reservoir model?1""
They have constructed and tested separate two-phase
fluid-heat flow and deformation models, and presently
are in the process of coupling these. The multi-
dimensional deformation model is designed to make
possible the use of a variety of elastic and/or :
plastic constitutive relations. They plan first to>
apply the model to the Wairakei geothermal field in
New Zealand, and wish thereafter to apply it to a site
in the Imperial Valley of California.
Lippmann and Narasimhan are presently working to
incorporate heat drive and temperature dependencies
into the formerly described isothermal groundwater
model of Narasimhan.13 The resulting model will be a
one-phase, three-dimensional geothermal reservoir flow
model, combined with a. one-dimensional deformation
model based on the Terzaghi consolidation theory. It
will therefore be unable to simulate horizontal ground
movements.
Safai and Finder are presently developing a
single-phase, two-dimensional axi-symmetric geothermal
deformation model. For this, Biot's three-dimensional
elastic theory is being extended to a three-dimensional
visco-elastic theory in such a way that the elastic
part can be weighted to control the amount of deforma-
tion irreversibility obtained.
Discussion and Conclusions
We have discussed subsidence models in three
categories: simplified models, advanced subsidence
models, and the state-of-the-art.
The status of the current modeling efforts may be
summarized as follows: at least ten subsidence models
have been developed for pore-fluid withdrawal, and
another five are known to be under development with
three nearing completion. Firm plans for at least four
more are known to the authors.
Compared with the requirements of an advanced sub-
sidence model, the present status of subsidence model-
ing is seen to be in its infancy. With regard to spa-
1 tial coverage, one-and two-dimentional capabilities are
most common in the current modeling efforts; the few
three-dimensional capabilities have, as yet, been little
tested. With regard to mechanical properties of reser-
voir materials, most of the earlier models employed
elastic deformation or Terzaghi's one-dimensional con-
solidation theory. More recently a few have provided a
capability for deformation irreversibility by incorpor-
ating two different elastic coefficients, a larger one
for compaction and a smaller one for expansion. Devel-
opment of models employing plasticity is just beginning.
With regard to numerical methods, finite differ-
ence methods have generally been employed in the flow
models, and finite element methods in the deformation
models. There are, of course, a few variations upon
this theme.
The need for further work is evident from a com-
parison of the above discussion and the previously
stated requirements for an advanced model. The most
challenging problem lies in the modeling of the rheo-
logical behavior (deformation properties) of the geo-
logical materials. A second problem lies in deter-
mining the best way to model the reservoir flow-
reservoir compaction interaction. Overall, there are
also several difficult problems of numerical analysis in
reducing the run time of multi-dimensional simulators to
an acceptable level.
Acknowledgements
This work was supported by the National Science
Foundation-RANN, under NSF Grant No. AER 75-17298; the
guidance and contributions of the NSF Program Manager,
Dr. Ralph Perhac, are particularly appreciated. The
authors also wish to express their gratitude to many of
the cited modelers who have contributed to the work
through their helpful discussions.
References
1. Poland, J. F. and G. H. Davis, "Land Subsidence Due
to Withdrawal of Fluids," ^n D. J. Varnes and
George Kiersch, eds. , Reviews in Engineering Geo-
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ica, pp. 187-269, 1969.
2. Terzaghi, Charles, "Principles of Soil Mechanics:
VIII - Future Development and Problems," Engineer-
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December 31, 1925.
3. Geertsma, J., "Land Subsidence above Compacting Oil
and Gas Reservoirs," J. Pet. Tech., pp. 734-744,
June 1973.
4. Systems Control, Inc., "Handbook for the Analysis
of Subsidence Associated with Geothermal Develop-
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preparation.
5. Nystrom, G. A., "A Review of Soil Models for Sub-
sidence Analysis," Technical Memorandum 5139-400-
10, Systems Control, Inc., Palo Alto, California,
November 1975.
Continued on next page.
432
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6. Sandhu, R. and E. L. Wilson, "Finite Element
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Paris, Vol. 2, pp. 393-400, 1970.
7. Jacquin, C. and M. T. Poulet, "Study of the Hydro-
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Houston, Texas, 1970.
8. Gambolati, G. and R. A. Freeze, "Mathematical
Simulation of the Subsidence of Venice, 1: Theory,"
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733, June 1973.
9. Gambolati, G. , P. Gatto and R. A. Freeze, "Math-
ematical Simulation of the Subsidence of Venice, 2:
Results," Water Resources Research, Vol. 10, No. 3,
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10. Helm, D. C. , "Evaluation of Stress-Dependent Aqui-
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from Known Stress History," Ph.D. dissertation,
University of California, Berkeley, California,
175 pp., 1974.
11. Helm, D. C. , One-Dimensional Simulation of Aquifer
System Compaction Near Pixley, California: 1.
Constant Parameters," Water Resources Research, Vol.
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Saturated - Unsaturated Groundwater Flow," Ph.D.
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ity of California, Berkeley, California, 244 p.,
February 1975.
14. McCann, G. D. and C. H. Wilts, "Mathematical Anal-
ysis of the Subsidence in the Long Beach - San
Pedro Area," California Institute of Technology,
Pasadena, California, 117 p., November 1951.
15. Geertsma, J. , "Problems of Rock Mechanics in Petro-
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First Congress of the International Society of Rock
Mechanics, Lisbon, Portugal, Vol. 1, pp. 585-594,
September 1966.
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pute Land Subsidence, " Bulletin of the Interna-
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No. 2, pp. 219-226, 1972.
17. Geertsma, J. and G. van Opstal, "A Numerical Tech-
nique for Predicting Subsidence above Compacting
Reservoirs, Based on the Nucleus of Strain Concept','
Verhandelingen Kon. Ned. Geol. Mijnbouwk. Gen. Vol.
28, pp. 63-78, 1973.
18. Rlney, T. D., et al., "Constitutive Models and Com-
puter Techniques for Ground Motion Predictions,"
Systems, Science and Software Report SSS-R-73-1490,
La Jolla, California, March 1973.
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USGS Fluid Injection Waste Disposal Research Pro-
gram," California Institute of Technology, Pasa-
dena, California, 340 p., February 1974.
\
20. Finol, A. and S. M. Farouq Ali, "Numerical Simula-
tion of Oil Production with Simultaneous Ground
Subsidence," Journal of the Society of Petroleum
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1975.
21. Brownell, D. H., S. K. Garg, and J. W. Pritchett,
"Computer Simulation of Geothermal Reservoirs,"
paper No. SPE 5381, presented at the 45th Annual
California Regional Meeting of the SPE of AIME,
at Ventura, California, April 2-4, 1975.
22. Pritchett, J.W.j et all., "Geohydrological Envi-
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Phase I," Systems, Science and Software report
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September 1975.
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433
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UNSTEADY-STATE, MULTI-DIMENSIONAL ANALYTICAL MODELING OF WATER QUALITY IN RIVERS
Robert W. Cleary
Water Resources Program
Princeton University
Princeton, New Jersey
The unsteady-state, two-and three-dimensional, convec-
tive-dispersive mass transport partial differential
equations which describe the concentration distribu-
tion of a contaminant released as a line, point or
general source have been solved analytically using in-
tegral transform methods. General two-and three-
dimensional modular solutions are presented in closed-
form which may be used to obtain the exact solution to
a variety of particular boundary conditions and source/
sink formulations. Several exact solutions for un-
steady-state, two and three-dimensional water quality
problems subject to finite geometry boundary condi-
tions are derived from these modular solutions and pre-
sented in closed form.
The solutions may be used to model many water quality
variables including: BOD, temperature, chlorides, and
dye tracers. They are in the form of rapidly-conver-
ging infinite series and error functions and are
easily and inexpensively applied. In addition to
their value as simulation tools, these closed-form ex-
pressions may be used to verify multi-dimensional,
digital computer numerical models which in many cases
could not previously be independently checked.
Introduction
In recent years the modeling of water quality in rivers
has advanced from simple one-dimensional analyses to
the more accurate and also more complicated two-and
three dimentsional approaches^«2,3,4,5,6,7. in gen-
eral, most of the multi-dimensional models presented
in the literature have been solved by numerical tech-
niques. Analytical solutions in two and three dimen-
sions are notably lacking. Those closed-form expres-
sions which are available are generally based on in-
finite geometry systems and have largely been borrowed
from the air pollution literature. Boundary effects
have either been ignored or in special cases been
accounted for using the method of images. The method
of images works well for homogeneous first and second
type boundary conditions but for cases of a non-homo-
geneous boundary concentration (e.g., concentration
varies as a function of time) or a boundary flux (e.g.,
benthic deposits of phosphorus diffuse into overlying
waters), the method fails.
Despite the wide availability of numerical models for
multi-dimensional water quality problems, it is the
opinion of the author that a need exists for analy-
tical models. In a given water quality situation the
selected model should be commensurate with the ques-
tions being asked. Very often these questions can be
answered by a closed-form analytical model without re-
sorting to the complexities, computation problems, and
expenses of a large numerical mode. To be sure, the
analytical model often requires coefficients to be
average constants while the numerical model is more
flexible, allowing for coefficients to vary through-
out time and space. However, in most field situations
one does not know how these coefficients vary spatially
and the numerical modeler often must use average con-
stants over a given large region. Numerical models are
also often plagued by maladies inherent in approxi-
mating derivatives by numerical analogs. The most
serious of these are numerical dispersion (in cases of
convective flows), stability and convergence. Anyone
who has worked with numerical models can appreciate
the unbelievable frustrations these digital computer
maladies can give. It is particularly bothersome when
the digital program is extremely large (over a few
thousand cards) and one is trying to track down the
bug which is causing the program to blow up when a
different range of a parameter is used. Numerical
models may often require large memories which may only
be available on certain computers. Or they may re-
quire inordinate amounts of time to complete a simu-
lation and are thus expensive to operate over a long
period of real time. They also require skilled oper-
ators to set-up, run,and interpret the output. This
may preclude their use by small consulting companies
or public agencies with limited budgets.
It is the opinion of the author that in many cases,
if one considers the questions being asked, the ex-
pense and complexities of applying a numerical model,
and the ease of applying an analytical expression, one
will opt for the analytical solution and will find it
adequate for estimating the expected water quality
under the given circumstances.
Multi-Dimensional Analytical Solutions
It has been noted that multi-dimensional analytical
solutions to the convective-dispersive transport
equation for rivers with finite depths and widths are
significantly absent in the literature. There arefi
many solutions to the straight diffusion equation.
However, modifying this equation to account for con-
vective fluid motion complicates its analytical solu-
tion. Additional complications are also introduced
by the presence of boundaries, in that the final analy-
tical expression must satisfy the operating boundary
conditions. If these boundary conditions are non-
homogeneous functions of space and time, the problem
is immensely complex, when standard methods are used.
The purpose of this paper is to present the solution
technique and analytical solutions to the two-and
three-dimensional, unsteady-state, non-homogeneous
convective-dispersive, general transport equations
which describe the spatial and temporal distribution
of a water quality variable in a river The solution
technique is a systematic integral transform approach
which easily handles non-homogeneous source/sink terms
and non-homogeneous boundary conditions which are
functions of space and/or time.
The River Coordinate System
The river is modeled by rectangular geometry as shown
in Figure 1. The average width of the river is W, the
average height is H,and the flow is predominantly in
the longitudinal direction and is described by the
cross-sectionally, time-averaged constant velocity U.
Water Quality Transport Equation
Multi-dimensional river water quality is mathemati-
cally described by the convective-dispersive trans-
port equation modified for general source/sink
activity. This equation may be written in vector nota-
tion as follows:
434
-------
C F(X,Z)
t = 0
(2d)
X - 00
Figure 1. River Coordinate System
3t
3X
= v(D • vC) + G
(1)
where C represents the concentration of a given water
quality variable, U is a constant, averaged velocity,
D represents effective dispersion coefficients in the
appropriate dimensions, t represents time and 6 rep-
resents a non-homogeneous source or sink function.
In the case of first order biological decay in the
river, one would add -KC to the right-hand side of
equation (1). We will not carry such a modification
through our analyses, as the final results are easily
modified to account for such decay. It should be
noted at this point that the assumptions of constant
velocity and constant (but numerically different)
effective dispersion coefficients place important
limitations on the solutions. Velocity can vary
spatially in a river and there is some evidence that
the vertical dispersion coefficient may have a para-
bolic distribution.9 Notwithstanding these limi-
tations, the solutions represent a significant im-
provement over present "boundary-less" solutions
(which also assume a constant, averaged velocity and
constant dispersion coefficients). They also are
commensurate with many of the questions being asked
by decisionmakers and in cases where a numerical
model must be used, they can serve as an important
and necessary check on the accuracy of the numerical
scheme, for the particular case of constant coeffi-
cients.
General Two-Dimensional Solution
In two dimensions, equation (1) reduces to:
(2)
To maintain complete generality, equation (2) will be
solved subject to non-homogeneous third type boundary
conditions. In this way, first type (concentration
specified) and second type (flux specified) boundary
conditions are automatically included in the final
solution. A general non-homogeneous initial condi-
tion as well as an arbitrary source/sink function will
also be used. Under such specifications, the final
solution will be modular in form and can be used to
solve a host of non-homogeneous boundary value prob-
lems of the first, second, or third type with non-
homogeneous generation or depletion. The boundary
and initial conditions are:
— + h r
^7 II^U
°L 3
f3(X,t)
Z = 0
Z = H
(2a)
(2b)
(2c)
If C does not approach zero as X approaches infinity,
but instead approaches a predictable constant value,
one may define a new variable which represents the
concentration in excess of this constant value. An
example source term, G (X,Z,t), might be a line source,
which would describe the release of a contaminant
from a diffuser pipe. An instantaneous release would
be modeled by three Dirac delta functions:
GL = g^ fiU-X^ 6(Z-Z1) s(t-tQ) (3)
where g^ represents the instantaneous line source
strength (e.g., grams/foot of stream width), X, is the
longitudinal source location, and Z, is the vertical
source location; t is the time of release.
Equation (2) and associated initial and boundary con-
ditions may be further simplified by introducing the
following dimensionless variables:
XU
p -
2 " DxDz
f -
4 D
Z
H
G =
U2t
= n
GD
f3H
h3H
H -
H4 "
(4)
Introducing these variables into equation (2) results
in a straight diffusion equation:
3C 3C
~
32C
(5)
subject to the following dimensionless initial and
boundary conditions:
5 = 0
5 1
C *- 0
c = F(c,e)
(5a)
(5b)
(5c)
(5d)
Method of Solution
If one attempts to solve equation (5) by the common
separation of variables method, severe difficulties
are encountered due to the spatial and temporal non-
homogeneities introduced by the functions: G, f, and
f,. After separation of variables, the resulting
equation in the finite space variable does not meet
Sturm-Liouville requirements for the equation or
boundary conditions. Such problems may explain the
notable lack of analytical solutions for multi-
dimensional, non-homogeneous, partial differential
equations in the literature. One of the purposes of
this paper is to illustrate a general integral trans-
form solution technique which may be used to solve prob-
lems like equation (5), regardless of how non-homo-
geneous they are. The ease with which the technique
handles spatial and temporal non-homogeneities makes
such an approach very powerful and useful in modeling
water quality in rivers. Indeed,the methods may be
used to solve a host of unresolved problems in many
areas of environmental and water resources engineering.
435.
-------
To avoid keeping the analysis too esoteric, more de-
tails of the solution method will be presented than
is customary. Essentially, the method is based on in-
tegrally transforming all spatial derivatives out of
the equation, leaving only an ordinary differential
equation in time. This equation is solved directly
and the transformed water quality variable is then
inverted back by previously defined inversion formu-
las to obtain the desired solution. In Cartesian
coordinates, the usual integral transforms will be
the Fourier (semi-infinite space variables), complex
Fourier (infinite) and Finite Fourier (finite). Con-
sidering only first (Dirichlet), second (Neumann) and
third (Robin or mixed) type boundary conditions, there
are three possible kernels for the Fourier transform
and nine possible kernels for the Finite Fourier
transform. The appropriate kernel to use depends, of
course, on the type of boundary conditions present.
In the case of the Finite Fourier transform, there are
also nine associated eigenvalue relationships. The
kernels and associated eigenvalue expressions come
from solving the homogeneous analogs of the original,
variable-separated partial differential equation.
Since the kernels depend only on the type of boundary
condition present, once they have been tabulated, they
can be used in a variety of different water quality
problems for which the only similarity is the type
(first, second,or third) of boundary conditions pre-
sent (the particular non-homogeneous function associ-
ated with each type boundary condition does not
affect the analytical form of the kernel: it is only
the type itself which is important).
Equation (5) has one finite (vertical) and one in-
finite (longitudinal) dimension. These space vari-
ables may be transformed out of the equation by a
Finite Fourier and a complex Fourier transform, re-
spectively. The result will be an ordinary differen-
tial equation in time, which may be integrated
directly for the transformed concentration variable.
This transformed variable is then inverted twice by
previously defined inversion formulas to yield the
solution to equation (5).
To remove the two space variables the following double
integral transform and corresponding double inver-
sion formulalO>H>12 for the concentration func-
tion C (C,C,T) in the ranges: -
-------
To use solution (10), one simply substitutes into the
total expression his particular G, F, f,, f. and ap-
propriate, kernels and carries out the indicated in-
tegrations.
General Three-Dimensional Solution
In three dimensions,equation (1) becomes:
222
+ U = D + D + D * + G(X,Y,Z,t)
(12)
CO 00
3X
Once again,to maintain complete generality, only
third type boundary conditions will be used:
To remove all three space variables, we define a
triple integral transform and corresponding triple
inversion formula:
JQ J0
(15)
C(e,C,£,T) = -+-
m=0 N=0
exp(-i>e)K(ein,c)K(vN,e)
- Q |y + h,C f,(X,Y,t) Z = 0 (12a)
Z oL O O
Dz|§+ h4C f4(X,Y,t) Z = H (12b)
- Dyf£ + h5C = f5(Z,X,t) Y 0 (12c)
D« W+ hfic - ffiU.X.t) Y W (12d)
Y o T v D
C > 0 X >- + » (12e)
C - F(X,Y,Z) t - 0 (12f)
The dimensionless variables given by equations (4) as
well as the following additional variables will be
incorporated into equation (12) to further generalize
It:
Y p . U2W2 - f5W
; W 'l D D 6 '' " l T5 Dv
" i y
hrW f.u h,W
H - — f - 6W u - 6
5 Dy 6 " °y 6 ' °y
Equation (12) then becomes a straight diffusion
tion:
3C 32C 1 32C 1 32C
— - = _ + ' • • • • + — -f- filp r F T]
2— y D p p O — ^^V^J'aJS*1-/
3e 1 8c 2 35
subject to:
"H + H5C = f5(S,e,T) 5 = 0
}^H6C=f6(c,e,T) , = 1
-f + H3C = fgU.c.O 5 = 0
H + H4C = f4(E'C,T) 5 = 1
C — ». o E ». + -
C-F(e,c,0 T 0
equa-
(14)
(Ha)
(14b)
(14c)
(14d)
(He)
(Hf)
00 OO
c I I K(B
m=0 N=0 n
•(f(*B v)
where: „ ?
28 V..
+ m+ ™
Pl P2
and:
and n T
f r f f
= Loo I L e)
• C(i|), B ,vN,T)di|i (16)
As in the two-dimensional case, the integral transform
defined by equation (15) is applied to equation (14)
and its associated initial and boundary conditions.
The resulting ordinary differential equation is inte-
grated to obtain the triple-transformed concentration
variable which is inverted by equation (16) to yield
the following general modular solution:
K(sm,?)K(vN,e) 27 exp(-1i|ie)exp(-yT)
exptur1
(17)
(17a)
, ,
"(K(em'c)
exp(i>E')K(vN,s'
K(vN,e)
V£
,,)
-o
exp(i>e')K(Bm,c':
exp(l>e1)K(em,c')K(vN,C')F
Applications
(17b)
(17c)
To illustrate the comprehensive flexibility built into
the modular solutions given by equations (10) and (17),
selected closed-form solutions, based on these general
equations, will be presented. Due to space limitations
typical solution details cannot be presented.here but
may be found elsewhere.3'6'13
Two-Dimensional, Instantaneous Tracer Line Source
For this case, the two-dimensional transport equation
is subject to a Dirac delta instantaneous line source
437
-------
function and two second type,no-flux boundary con-
ditions at Z = 0 and Z H. The details are given in
(G). Applying modular solution (10), the solution
with dimensions is:
f (X-X -Ut)]
- 4Dt
S=*—-I
C(X,Z,t) — *= '-^- J|l+2 I exp(-DTu*Nt>
t)
1/2
(18)
Three-Dimensional, Instantaneous Tracer Point Source
In this case, the three-dimensional transport equation
is subject to an instantaneous Dirac delta point
source function and four second type no-flux boundary
conditions at Z=0, Z=H, Y=0, and Y=W. The details may
be found in Reference 6. Applying modular solution
Equation 17, the solution with dimensions is:
(X-X-j-Ut)2"
C(X,Y,Z,t) =
r (x-xrut)-[
I 4Dxt J
+2
exp(-vlDzt)cosyNZcosuNZ1
1C + M 8C = D
at u 3X ux
a2C
+ D
KC
3Y
az
+ gpT 6{X-X1)6(Y-Y1)6(Z-Z1) (20)
The BOD is released as a continuous point source and is
subject to no-flux conditions on all four boundaries.
Initially there is zero BOD. The solution may easily
be obtained by using equation (17) to derive the solu-
tion to the first order decay, instantaneous point
source case (similar to equation (19)) and then inte-
grating this solution over time to obtain the contin-
uous point source solution with dimensions:
gpT EXP(XU/2Dx)
4 W H (Dx)1/2
• EXP{-X(k2/Dx)1/2}
ERFC{X/(4DYt)1/2-(k,t)1/2
,1/2
ERFC{(kt)1/2+X/(4Dt)1/2}
• EXP{X(k2/Dx
COSyNZCOSyNZ1
N=l
(
(21:
1/2
EXP{-X(k,/D)l/':}ERFC{X/(4DYt)1/2-(k,t)1/2}
O A A J
EXP{X(k3/Dx)1/2}ERFC{(k3t)1/2+X/(4Dxt)1/2} J
- COSS YCOSB Y, / , /0
+ 2 Jl (k>/2 m ] (^-Xtk^)1/2)
• ERFC{X/(4DYt)1/2-(k/lt)1/2}
EXP{X(k4/Dx)1/2}ERFC{(k4t)1/2+X/(4Dxt)1/2} J
COSBJ
1/2
N=l m=l (k5)
• (EXP{- X(k5/Dx)1/2}ERFC{X/(4Dxt)1/2-(k5t)1/2}
EXP{X(k5/Dx)1/2}ERFC{(k5t)1/2+X/(4Dxt)1/2}J
where:
and
ihree-Dimensional, Biochemical Oxygen Demand Transport 4
The unsteady-state, three-dimensional, first order de- 5
cay, transport model for BOD in rivers is given by:
0 ; X > 0
References
1. Ahlert, R.C., Biguria, G., and Tarbell, J.. Hater
Resources Research. Vol. 6, No. 2, 1970, pp. 614-
621.
2. Bansal, M.K.. Journal of the Hyd. Div.. ASCE, Vol.
97, No. HY11, 1971, pp. 1867-1886.
3. Cleary, R.W., T.J. McAvoy and W.L. Short, Uater-
1972, Amer. Inst. of Chem. Eng., Symposium Series,
Vol. 69, No. 129, pp. 422-431.
Ruthven, P.M.. Water Research, Vol. 5, 1971, pp.
343-352.
5. Wnek, W.J., and Fochtman, E.G., Envir. Sci. and
Tech.. Vol. 6, No. 4, 1972, pp. 331-337.
6. Cleary, R.W., and Adrian, D.D., Journal of the
Envir Eng. Div^, ASCE, Vol. 99, No. EE3, 1973,
pp. 213-227.
7. Leendertse, J.J. and S-K Liu, Symposium on Model -
ing Techniques, 2nd Annual Symposium of the Water-
ways, Harbors and Coastal Engineering Div. of
ASCE, Sept. 1975, Vol. 1, pp. 625-642.
8. Carslaw, H.S., and Jaeger, J.C., Conduction of
Heat in Solids, 2nd ed., Oxford University Press,
London, England, 1959.
9. Al-Saffar, A.M., thesis presented to the Univer-
sity of California, at Berkeley, Calif., in 1964.
10. Sneddon, I.N., The Use of Integral Transforms,
McGraw-Hill Book Company, New York, N.Y., iy/2,
pp. 423-439.
11. Sneddon, I.N., Fourier Transforms, McGraw-Hill
Book Company, New York, N.Y., 1951, pp. 71-82,
166-202.
12. Tranter, C.J., Integral Transforms 1n Mathematical
Physics, 3rd ed., MetTiuen and Co., Ltd., London,^
England, 1966, pp. 84-85.
13. Cleary, R.W., D.D. Adrian and R.J. Kinch, The
Journal of the Environ. Enq. Div., ASCE, Vol. 100,
No. EE1, pp. 187-200.
438
-------
SIMULATION MODELING OF ENVIRONMENTAL INTERACTION EFFECTS
Ethan T. Smith
Program Analyst
2014 Golf Course Drive
Reston, Virginia
Abstract
The present research addresses the air-water-
land problem simultaneously by means of a
series of mathematical models. A steady-
state water quality model is used to simulate
the effect of biochemical oxygen demanding
wastes on the dissolved oxygen concentrations
in an estuarine system. A Gaussian plume air-
quality model is similarly utilized to relate
the particulate and sulfur oxide emissions of
waste sources to the concentration of these
contaminants in the regional airshed. A ma-
terials balance model is formulated which
simulates the impact of pollution control for
a given medium in exacerbating environmental
pollution in another medium. A strategy mod-
el is formulated that derives removal per-
centages for air loads and waste water dis-
charges, while simultaneously minimizing the
flows of material to solid waste disposal.
The constraints on the optimizing strategy
model are given by equations which require
that ambient quality standards must be at-
tained for dissolved oxygen, particulates,
and sulfur oxides.
The set of models is applied to an eleven-
county study area centering on the city of
Philadelphia, Pa. The results of applying the
models indicate that present ambient quality
standards can be achieved.
Planning for Environmental
Resource Management
The management of the environment, like
any activity undertaken by man, requires some
method of approach which can be thought of as
a plan. On the one hand, this may refer to
some rather formal approach involving a se-
quence of steps arranged in time to achieve
some objective. In the absence of a formal
approach, actions can still be undertaken
which, by default, will tend to be rather in-
dependent of one another. In either case,
effort will be expended on some mixture of
data collection, analysis, negotiation, and
modification of the physical world.
A pervasive problem is associated with
the nature of cause-effect linkages, or
causal chains. The name is perhaps somewhat
of a misnomer, since cause-effect interactions
related to the environment are seldom simple
one or two step processes. Indeed, a much
"lore accurate picture would be that of a
multi-branched tree or network structure with
numerous feedback loops. Under these circum-
stances even well-conceived scientific ap-
proaches to pollution control have encoun-
tered severe problems.
It is now possible to discern the essen-
tial characteristics of many environmental
Problems. Attempts to address these problems
often fall into the error of suboptimization.
Under these circumstances, solutions may be
successful to a greater or lesser degree in
dealing with the matter immediately at hand
(e.g., Biochemical Oxygen Demand, or BOD, in
the water). More relevant however is the fact
that secondary effects resulting from the in-
itial solution act to exacerbate other envir-
onmental problems, or even to cause new pro-
blems.
The concept of materials balance appears
to offer a promising route toward the resolu-
tion of these kinds of difficulties.l In
this approach, the principle of conservation
of mass is applied to material goods as they
pass through the system, undergoing of course
many changes in form. If successful, this
kind of analysis should identify the residual
materials that are byproduct from the process-
ing steps which are designed to yield the
economic products of society. This makes it
possible at least in principle to specify the
links in the causal network in quantitative
terms. This study is focused on just a small
part of the general materials balance model,
specifically the routing available to control
some of the major contaminants of air, water,
and land.
Even in the present rather modest form,
this work significantly transcends tradition-
al concepts of pollution control, and is per-
haps best described as resource management.
This process begins to explore the tradeoffs
possible among (a) the level of technology,
(b) the spatial needs for land use, (c) the
concentration of contaminants in the ambient
environment. There are also important impli-
cations for the use of natural resources such
as water and fisheries for many purposes
(e.g., recreation), and at a further remove,
the use of mineral and energy resources re-
quired to achieve pollution control by tech-
nology. Ultimately, this type of research
is capable of contributing to a definition in
quantitative terms of the carrying capacity
of regions for human activity.2
First, it is important to include se-
condary effects within the set of decisions
variables. Thus, to take one example, the
increase of treatment which removes BOD from
wastewater must be reflected as some combina-
tion of routing to land and air. Organic
sludge either is sent to a disposal site or
is incinerated, and in the latter case it
acts to lower air quality. The incineration
can be accomplished either on site or at a
municipal incinerator. Simultaneously, con-
trols applied to industrial stacks will re-
sult in either ash .to be sent to a landfill
(if dry removed) or solids in the sewerage
system (if wet scrubbed). At least some part
of these solids will be removed at a sewage
treatment plant and will cycle through the
system. Second, the foregoing description,
when applied to a large number of treatment
439
-------
plants, firms, incinerators, power plants, and
landfills, leads to complicated spatial inter-
action as materials are routed from point to
point. This is especially true in a relative-
ly large region like the present eleven county
study area encompassing the Trenton-Philadel-
phia-Wilmington SMSA's. Superimposed on this
interaction is a requirement for segregating
political jurisdictions and accounting for
physical barriers which would preclude par-
ticular paths in a real case. Next, there is
a requirement for state-of-the-art air and
water quality dispersion models with the best
possible validation procedures. Without
field-testing, there is small probability that
conclusions reached by these models will be
acceptable. In order to accomplish these ob-
jectives, the following residuals control and
routing processes have been analyzed:
a. Treatment at sewage treatment plants
(STP's),
b. Treatment at firms possessing indi-
vidual wastewater facilities,
c. Control of particulates and S02 at
individual STP's, firms, power plants,
and municipal incinerators,
d. Control of particulates and 302 by
area sources,
e. Routing of area source solid waste to
land disposal,
f. Routing of sludge from STP's and
firms to municipal incinerators,
g. Routing of wet scrubbed particulates
and S02 to sewerage system, STP's and
river,
h. Routing of sludge from STP's and
firms to land disposal,
i. Routing of dry removed particulates
and S02 to land disposal.
These processes are shown in Table 1. To fa-
cilitate modeling these processes, a series
of decision variables is defined, which are
common to each process. These decision var-
iables are as follows:
DW = BOD allocated to the water,
D = BOD allocated (in transformed form)
to the air, by incineration of
sludge solids,
D = BOD allocated to solid waste dis-
posal, as removed sludge solids,
E& = Particulates allocated to the air,
E = Particulates allocated to the water,
by wet scrubbing,
E = Particulates allocated to solid
waste disposal, by dry removal,
F& = S02 allocated to the air,
FW = S02 allocated to the water, by wet
scrubbing with limestone,
F = S02 allocated to solid waste dis-
posal, by dry removal with lime-
stone.
These decision variables act to allocate the
various residual streams among three possible
media: air, water, and land. The variables
are applied in each of the control and rout-
ing processes, at the completion of which the
total residuals discharged to the media as a
result of these processes are obtained. All
allocation variables are in terms of percent-
ages of untreated (or raw) waste load, and
hence are dlmensionless. It is essential to
realize that all percentages for a given re-
sidual sum to one, i.e., DW + Da + °s = 1.0.
The allocation variables are readily related
to familiar quantities: for example, the per-
cent removal of BOD at a wastewater treatment
plant is 1.0 - DW. Similarly, the percent re-
duction of particulates to the air at a spe-
cific facility is 1.0 - Ea. The other alloca-
tion variables are defined in parallel manner.
Results of Routing Processes
The results of the routing processes
shown in Table 1 can be summarized as follows,
with special reference to mass discharged to
the air, water, or land as residuals:
Sources (k) which discharge directly to
surface water (including STP's), discharge
BOD as a function of DW, as well as solids
resulting from the scrubbing of stack gases
as a function of Ew and Fw. Particulates and
S02 are emitted to the air, both from sludge
incineration and industrial processes. Land
disposal is provided for treatment plant
sludge and solids.
Controls are used (Ea and Fa) to reduce
the emission of particulates and S02 at
sources of the industrial (m), municipal in-
cinerator(i), and power plant (j) types.
Solids which are scrubbed out are routed to
collection systems and to land disposal by
Ew, ES, FW, and FS except for sources having
access to surface water, such as power plants.
Area sources (n), which cover perhaps
five to 25 square miles each, contain a het-
erogeneous assortment of emissions, often
with large contributions from residential and
commerical land uses. The space heating and
refuse incineration aspects of these sources
are included, by allocating part of the solid
waste to land disposal. In the case of these
sources, it is reasonable to assume that re-
duction of air emissions occurs through fuel
switching and the restriction of local incin-
eration practices.
The routing of materials according to the
spatial configuration of the study area re-
quires some assumption for choice among alter-
native destinations. It is assumed that under
long-term average conditions the physically
nearest destination will be selected. In
reality, service areas are probably better de-
terminants for selection of destinations,
e.g., which landfill will service which source;
however, such information is usually not read-
ily available. In addition, destinations are
required to be in the same political jurisdic-
tion (Del., N.J., Pa., or Philadelphia) as the
source being serviced. This constraint adds
reality to decisions under consideration, and
helps to demonstrate the consequences of such
a restriction.
In the case of landfills, the selected
site is checked to determine whether the
acreage required is available; if not, sites
progressively further away are examined until
all conditions are met. If no landfill meets
all conditions, the unmet demand is recorded
as a requirement for further acreage.
440
-------
Water Quality Model Formulation
A one-dimensional, steady-state, finite-
difference model of the Delaware Estuary is
employed for the coupled variables BOD-DO.
Similar formulations may be found in Thomann3
who has worked extensively with the coupled-
system approach. Figure 1 is a map of the
Delaware Estuary showing the 30 segments or
sections of the mathematical model. This es-
tuary constitutes the receiving surface water
in this study. For each of these model sec-
tions a mass-balance equation can be written
for the BOD in the system, and another for
the DO in the system. This results in linear
differential equations based on the physical,
hydrologic, and biochemical characteristics
of each section.
This model, expressed in matrix form, is:
(1)
The atmospheric characteristics are simu-
lated in the mathematical model under speci-
fic assumptions. The first of these is that
the discharge emitted from each source will
take the form of a Gaussian plume. This means
that the dispersion of the plume at a distance
downwind is assumed to follow a Gaussin distri-
bution in directions perpendicular to the wind
vector. The concentration of pollutant can
then be calculated by applying a normal pro-
bability function. In the form used here
this is usually termed the Martin-Tikvart
model . 6
In this case, the model takes the form
sr
Sduv Xs
(5)
(c) = (oa) -
(GJ) = (A)(J)
(cp) = (BMP)
*
The model has been calibrated for the
study area by EPA using 1968 data for par-
ticulates and 303. Regression and correlation
yields r values of 0.87 and 0.88, respectively.
Variation around the annual average predic-
tions of the model is on the order of ± 15 to
(c)
- (c,) ± (cn)
j p
(A)(AJ).
The model has been verified by the Dela-
ware Estuary Comprehensive Study, based on
research conducted from 1961 to 1969.^ In
addition, time-series studies by Thomann make
it possible to calculate a variance of about
1.56 mg/1 around the summer mean values of DO
computed by the model.5
Since (AJ) is a function of the alloca-
tion variable DW, it is possible to evaluate
the DO profile in equation ^ by specifying DW,
and to compare the vector (c) against water
quality standards.
Air Quality Model Formulation
Mathematical models of air quality re-
present a relationship between the sources of
air pollution and the result as measured in
the ambient aif. With the establishment of
air quality standards it becomes necessary to
employ some such relationship to determine
what modification of the source emission
loads is required if the ambient standards
are to be met.
The source emission Qs is a function of
the allocation variable Ea or Fa, depending on
pollutant. Therefore, equation 6 can be
evaluated for each receptor point r as func-
tion of Ea and Fa, i.e., Xr = f(Ea,Fa). Con-
tour maps of Xr can be compared to ambient
air quality standards.
Ambient Quality Data
The initial conditions for the analysis
are given by the present state of the system.
A part of this state is measured in terms of
the numerical values of ambient environmental
quality. In the case of water quality, the
dissolved oxygen concentrations are based on
the work of the Delaware Estuary Comprehen-
sive Study. An initial verification of the
water model was carried out for 1964 data.
Subsequently, the data were updated to 1968
and to 1970, principally by accounting for
the growth of effluent discharges.^,8,9
The DO standards and initial DO profile
for the Delaware Estuary are given in detail
in Figure 6. The DO standards are those of
the Delaware River Basin Commission (DEBC).IO
The data base for particulate and S02
concentration is taken from the EPA Implemen-
tation Planning Program work on the Philadel-
phia Air Quality Control Region.7 The exist-
ing air quality in this reference is based on
measurements from 1968. Figure 2 shows the
1968 annual average pattern of particulate
concentration in the study area, and Figure 3
shows the pattern for S02- This data base
441
-------
has been used by EPA to validate the Gaussian
plume air quality model used in this study.
The air quality standards sought in this
study are an annual geometric mean of 75
ug/m3 for participates, and an annual arith-
metic mean of 80 ug/m3, for sulfur oxides. 11
Discharge Loads to the Environment
In order to carry out analysis of the
study area, numerical measures of the dis-
charges to the environment are necessary.
Ideally, the discharge data should be for the
same year as the ambient quality date (in this
case 1968) so as to permit prediction of im-
provement in environmental quality as a re-
sult of modifying the discharges.
Discharge data for effluents to the Del-
aware Estuary are available in terms of BOD. 8, 9
All values are in terms of first stage car-
bonaceous BOD discharged at the outfall, for
1968. The present research includes 2^ sew-
age treatment plant effluents, which comprise
about 98$ of the BOD discharged to the es-
tuary by municipal waste sources. In addi-
tion, 29 industrial firms are included which
possess wastewater discharges from company-
owned treatment facilities. These sources
account for about 96$ of the BOD discharged
to the estuary by industrial waste sources.
Discharge data for air emissions to the
study area are available as part of the data
base used by EPA in the Implementation Plan-
ning Program.? For the year of 1968 both
particulate and S02 emissions exist for each
stack in the source data file for the Phila-
delphia Air Quality Control Region. The
following set of air emission sources is in-
put to the model:
a. 58 industrial sources accounting
for about 85$ of the S02 and Qk%
of the particulates from all such
sources,
b. 16 municipal incinerators account-
ing for about 97$ of the S02 and
of the particulates from all such
sources,
c. 10 steam-electric generating plants
accounting for about 82$ of the 302
and 89$ of the particulates from all
such sources.
d. 55 area sources accounting for about
63$ of the S02 and 55$ of the par-
ticulates from all such sources.
The most recent National Survey of Solid
Waste Practices is for the year 1968, which
makes it possible to obtain landfill data
contemporary with the rest of the research. 12
Forty-nine landfills and available acreage at
each site (located by Cartesian coordinates)
are used in this study.
problem is to determine the values of the de-
cision variables that will enable all quality
goals to be satisfied.
Recognizing the possible tradeoffs in the
construction of optimization models, the ap-
proach selected in this study relies on an as-
sumption that the percent removal of a given
material must be equal for all waste sources
of one type. This approach has the following
characteristics:
a. It is mathematically simpler than a
linear or nonlinear programming ap-
proach ,
b. The assumption of equal percent re-
moval is often administratively fa-
vored, even though less flexible
than an approach allowing sources to
be individually adjusted,
c. It does permit all ambient standards
to be achieved simultaneously,
d. Damage (cost) functions are not ex-
plicitly represented in the model,
although such functions are implicit
in the ambient quality standards,
since meeting the standards is often
taken as equivalent to minimizing
damages.
Mathematically, the strategy model can be
described as follows:
MIN
subject to (A)(AJ) > (c ) 6 = i'm»J'n
o
where
and
(°owk - Dw) Tk
X ( A Q ) £ X__ for particulates
r s rg and S02
where AQ_ = (E - E ) P for particu-
s oas a s lates
(Foas - Pa> Us
D« + D» + DO = 1-0,
S02'
"w a
was
F + F + F
was
= 1.0,
= 1.0.
Equation 7 shows the minimization of volumes
V of mass allocated to land disposal for all
source types; this process is constrained by
modification of the A Jjj loads so as to meet
the incremental DO goal (eg). Dowk is the
initial percentage allocated to the water,
and Tk is sum of BOD residuals generated.
Similarly, modifications of air source emis-
sions AQS must meet the ambient air stand-
ards Xrg. This depends on initial percentage
allocations E0as
oas
each source s,
and on Pg and Us, the sum of particulate and
S02 residuals generated (see Table l).
Model Results
Strategy Model
There are nine decision variables repre-
sented by the allocation variables which di-
vide residuals among water, air, and land.
The ambient environmental standards have been
specified for both airborne and waterborne
contaminants, and models developed to predict
changes in ambient concentrations as a func-
tion of materials routing. The remaining
The derived values of the allocation per-
centages indicate that 91$ Carbonaceous BOD
removal is required for all sources discharg-
ing into the Delaware Estuary. Similarly,
75$ removal of particulates and 12% removal of
S02 is called for in the case of sources hav-
ing air emissions. In all cases these are
percentages of untreated waste discharges.
At this point it should be noted that one re-
sult of recent EPA work on this river called
442
-------
for a yy$> reduction in Nitrogenous BOD dis-
charges to be superimposed on these conclu-
sions. 9 Other conclusions are that 30$ of
the sludge produced should be incinerated,
and 61% of it consigned to land disposal.
The effect of the treatment levels can
be seen in the predicted improvement in the
quality of the environment. The resultant
dissolved oxygen profile is shown in Figure
6. Except in the three sections containing
the "Bristol Sag" (5 through 7) the DO stand-
ards for summer average conditions are at-
tained everywhere. The primary annual aver-
age air quality standards of 75 ug/m3 for
participates and 80 ug/m3 for S02 are also
achieved. Figure 4 shows the resultant par-
ticulate concentration pattern for the study
area. Figure 5 shows the S02 pattern re-
sulting from the strategy. These figures
clearly show the effect of load reduction in
breaking up the region-wide pattern into a
few peaks of high concentration which tend to
be centered on dense urban and/or industrial
sources within the study area.
The routing of residuals to land ulti-
mately results in the consumption of space at
the sanitary landfills in the study area.
The model will attempt to utilize all avail-
able space in accordance with the routing and
jurisdiction rules, and will route any re-
maining solid waste to another category which
represents the amount by which demand exceeds
supply. The demand excess is as follows:
New Jersey
Pennsylvania
Philadelphia
Delaware
309 acres
239 acres
739 acres
zero
These figures represent demands generated by
this study alone, and are in addition to any
other acreage requirements.
The significance of this analysis is:
a. Numerous air-water-land interactions
can be simulated so as to produce quantita-
tive, non-intuitive results. If desired,
ambient standards can be easily altered and
sensitivity analysis performed on these and
other variables.
b. Numerical results show that required
controls are probably within the range of
current technology. This implies that
changes in land resources; e.g., changes in
density, can be avoided or at least post-
poned.
c. The attainment of water quality
standards implies optimum utilization of,
e.g., recreation and fisheries resources, as
defined by the standards for the region.
d. The emerging problem of solids dis-
posal is quantitatively defined as it would
impact land use if land disposal is used.
e. The methodology is transferable to
other study areas where discharge loads, am-
bient air/water quality data, land disposal
data, and model parameters are available.
Assembling such data should become easier as
a result of recent public laws.
References
1. Kneese, A., Ayres, R. , and D'Arge, H. ,
"Economics and the Environment. " Resources
for the Future, Washington, D.C. (1970).
2. Smith, E.T., "Mathematical Models for En-
vironmental Quality Management. " Rutgers
University (Doctoral dissertation), New
Brunswick, N.J. (197^).
3.
5.
6.
7.
8.
9.
10.
11.
12.
Thomann, H. , "Systems Analysis and Water
Quality Management. " Environmental Research
& Applications, Inc., New York,N.Y. (1972).
"Delaware Estuary Comprehensive Study,
Preliminary Report and Findings." U.S.
Dept. of the Interior, Philadelphia, Pa.
(1966).
Thomann, R.V. , "Time-Series Analysis of
Water Quality Data. "J. San Eng. Div. .ASCE.
(.1967).
"Air Quality Implementation Planning Pro-
gram, " EPA Office of Air Programs, APTD-
0640, Vol. 1, Research Triangle Park,
N.C. (1970).
"Application of Implementation Planning
Program (IPP) Modeling Analysis, Metro-
politan Philadelphia Interstate Air Quality
Control Region. " Environmental Protection
Agency, Research Triangle Park, N.C. (1972).
"The Delaware River - Where Man and Water
Meet." U.S. Dept. of the Interior, Phila-
delphia, Pa. (1969).
"Delaware Estuary Water Quality Standards
Study. 1 Environmental Protection Agency,
New York.N.Y., and Philadelphia, Pa. , (1973).
"Water Quality Standards for the Delaware
River Basin." Resolution No. 67-7, Sec-
tion X, Delaware River Basin Commission
(April, 1967).
"A Citizen's Guide to Clean Air." Conser-
vation Foundation, Washington, D.C.
(Jan., 1972).
Muhich, A., et al, "National Survey of
Community Solid Waste Practices, Region
2, Vol. 1 and 2." U-. S. Dept. of HEW,
Cincinnati, Ohio (1969).
443
-------
TC
FROK
DIRECT-
DISCHABGERS
(STPs i IND.)
k
MUNICIPAL
INCINERATORS
1
INDUSTRIAL
SOURCES
POWER PLANTS
1
AREA SOURCES
DIRECT-
DISCHARGERS
(STPs 4 IND.I
k
SOLIDS
SOLIDS
I '
MUNICIPAL
INCINERATORS
i
SLUDGE
LAND
DISPOSAL
1
SLUDGE,
SOLIDS
SOLIDS
SOLIDS
SOLIDS
SOLID
WASTE
AIB
PASTICULATES ,
so2
PABTICULATES,
so2
PAHTICULATES ,
so2
PABTICULATES,
so2
JARTICULATES,
so2
SURFACE
HATER
BOD,
SOLIDS
SOLIDS
METROPOLITAN PHILADELPHIA INTERSTATE AIR QUALITY CONTROL REGION
Table 1 - Residuals Routing Process
DELAWARE ESTUARY
COMPREHENSIVE STUDY
SECTIONS FOR
MATHEMATICAL MODEL
Figure 1 - Segmented Water Quality Model of
the Delaware Estuary
COUNTY LINE
STATE LINE
REGION BOUNDAI
Figure 2 - 1968 Annual Average Participate
Concentration (ug/m3)
METROPOLITAN PHILADELPHIA INTERSTATE AIR QUALITY CONTROL REGION
- COUNTY LINE
- STATE LINE
- REGION BOUNDA
Figure 3 - 1968 Annual Average 803
Concentration (ug/m3)
444.
-------
METROPOLITAN PHILADtLPHIA INTERSTATE AIR QUALITY CONTROL REGION
METROPOLITAN PHILADELPHIA INTERSTATE AIR QUALITY CONTROL REGION
COUNTY LINE
STATE LINE
REGION BOUNDAH
Figure
Resultant Annual Average
Particulate Concentration lug/ no)
COUNTY LINE
STATE LINE
REGION BOUNDARY
Figure 5 - Besultant Annual Average 302
Concentration (ug/m3)
FBESENT WATEB QUALITY.
STANDARDS
(SUBTRACT 0.5 TO COWUTE
HlNinUK DAILY AVEBAOE)
DELAWARE ESTOAH1 SECTIONS
Figure 6 - Summer Average Dissolved Oxygen
Profiles by Estuary Model Section
(mg/1)
445
-------
TOWARD A DYNAMIC ECONOMIC MODEL FOR REGULATING
FLUOROCARBON EMISSIONS
Ralph d'Arge, Larry Eubanks, Joseph Harrington
Department of Economics
University of Wyoming
Laramie, Wyoming 82071
Abstract
A sequence of benefit-cost models is examined to deter-
mine economically feasible and optimal regulatory stra-
tegies for the production of chlorofluorocarbons by the
United States. Estimates of environmental costs and
market losses (consumer surplus) are developed to esti-
mate at the margin where these costs balance each other.
The implications of a dynamic regulatory model are
briefly outlined.
Introduction
During the past decade, there has been a growing recog-
nition that economic decisions might yield major im-
pacts on global commons property resources, including
the oceans, atmosphere, and even the electro-magnetic
spectrum. Most recently, concern has been expressed as
to the impact of chlorofluorocarbons on the ozone con-
centration in the stratosphere-'- and on the Impact of
these same compounds on world climate. According to
the IMOS report,
"Although the theory of possible ozone reduction
(in the stratosphere) by fluorocarbons 11 and 12
(F-ll and F-12) cannot be presently supported by
direct atmospheric measurements, the matter has
been carefully studied independently by many
scientists. Thus far, the validity of the theory
and the predicted amounts of ozone reduction have
not been seriously challenged. More research is
required and will be undertaken, but there seems
to be legitimate cause for serious concern."2
An extremely simplified sketch of this concern might be
as follows: chlorofluorocarbons after or during econom-
ic use escape and ultimately collect in the stratos-
phere, a distinct air layer 11-60 kilometers above the
surface of the earth. In the stratosphere these chem-
icals interact with 'ozone and other chemical constitu-
ents, initiating a reduction In ozone and perhaps a
change to plants and animals, including humans. The
climatic changes are presumed to induce another set of
adjustments to organic life. The major question is
whether, on balance, these changes in organic life are
beneficial or adverse to humans. This is also the cen-
tral question addressed, from an economic perspective,
by the researchers authoring this report. Secondarily,
a set of policy alternatives is examined as to the eco-
nomic feasibility of alternative regulatory strategies.
Typically such examinations are done with the aid of a
cost-benefit analysis of the problem, and the results
of such an analysis will be briefly summarized. In ad-
dition, possible steady state solutions to the question
of optimal emissions is also examined. Finally, since
the above two analyses do not indicate the optimal path
to the optimal emission levels, and since there are
differential emission rates for various uses of F-ll
and F-12, a dynamic model of emissions is also outlined
and discussed in an attempt to gain insight into the
nature of the optimal path of emission reduction over
time.
Cost-Benefit Analysis
The strategic point of the analysis was to examine mar-
ket relationships for F-ll and F-12 and consumer prod-
ucts utilizing them and also to attempt to partially
estimate the societal costs and benefits involved in
their production and ultimate emission into the atmos-
phere.
Fluorocarbons for the most part are not purchased di-
rectly by households but are utilized as inputs to pro-
duce consumer products or services. In consequence,
the observed demand relationships for fluorocarbons do
not directly relate to consumer valuation but rather
indirectly through demand for products utilizing fluor-
ocarbons. Under some specialized circumstances, final
product demand and consumer surplus will be exactly re-
presentable by the derived demand and surplus for flu-
orocarbons, such that observed losses in "derived" sur-
plus would be equivalent to loss in consumer surplus in
final goods markets. Unfortunately, observed data on
prices and quantities sold historically may not ade-
quately reflect actual dependencies between final prod-
uct demand and surplus and derived demand and surplus.
In order to obtain reasonable,valid bounds on "consumer
surplus," both derived surplus and consumer surplus
losses had to be estimated.
Measures of "derived surplus1' loss for restrictions in
fluorocarbon production were developed for F-ll and
F-12 along with measures of consumer surplus loss for
the major final products using these fluorocarbons in
their production. Other fluorocarbons were not exam-
ined in detail by the authors. Included in the list of
final products were: refrigerators, aerosol deodorants,
auto air conditioners, polyurethane foam mattresses,
and mobile vehicle refrigeration systems. According to
the IMOS report, these products accounted for about 9($
of utilization of major fluorocarbons and more than 98^
of F-ll and F-12 use in 1972.3
Table 1 summarizes the empirical development of derived
and final product demand relationships. Due to the re-
lationship between derived and final product demand, it
was believed to be the case that we were estimating de-
mand relationships which were part of a simultaneous
system of equations, and as a result the regression
procedure known as two-stage-least squares was utilized
as opposed to ordinary least squares in order that con-
sistent coefficient estimates could be obtained. 4
Table 2 presents the set of willingness to pay estimat-
ing equations which were derived from the estimated de-
rived and final product demand relationships in Table !•
In Table 3 are recorded estimates of the present value
of derived surplus for F-ll and F-12 and consumer sur-
plus for major consumer products using F-ll and/or F-12
in their production. Such estimates were derived using
the equations in Table 2. As is readily apparent from
the estimates, "derived surplus" estimates amount to
about $3 billions, while consumer surplus for the major
products using them amount to more than $84 billion8•
Of course, these estimates would tend to bound the ac-
tual value of consumer surplus. On one extreme, if no
-446
-------
substitutes existed for producing the final product,
then the appropriate measure of economic loss would be
the sum of consumer surplus losses in the final markets
Impacted. Whereas, if there were such substitution
possibilities it would appear appropriate to utilize
the "derived surplus" estimates.
It has been hypothesized that F-ll and F-12 emissions
will induce two global effects:
1) reduction in stratospheric ozone and increase
in UV-B light at the earth's surface
2) a slight rise in surface temperature due to an
increased transparency of the stratosphere re-
sulting from ozone depletion.
Both of these global effects, if they occurred at a
significant level, would have large scale ramifications
on biological life and thereby on the U.S. and other
nations' economies. It would seem to be impossible to
empirically estimate the thousands of interrelated im-
pacts of changes in surface microclimates. In the par-
tial analysis which was undertaken, costs and benefits
are estimated for some major sectors of the U.S. econo-
my from ozone depletion or enhancement and for slight
long increases in surface temperature. The U.S. sec-
tors and/or components of them included:
1) Ozone depletion
1.1 Non-melanoma skin cancer
1.2 Materials weathering (polymeric materials)
2) Temperature change (induced by ozone depletion)
2.1 Marine resources (13 economic species)
2.2 Forest products
2.3 Agricultural crops (corn and cotton pro-
duction
2.4 Urban resources (fossil fuel, electricity,
housing, clothing and government expendi-
tures) .
Estimated environmental costs and benefits by category
for 1973 levels of emissions continuing into perpetuity
are recorded in Table 4.
The major question is whether, given the evidence, F-ll
and F-12 should be regulated as to production and/or
emissions and to what degree. It is clear from a sim-
ple comparison of Tables 3 and 4 that the present value
of net benefits of a complete ban on fluorocarbons
production is positive if "derived surplus" is used as
a measure of social cost and negative if the sum of
"consumer surpluses" is used as the relevant measure.
These conclusions are summarized in Table 5.
From Table 5 several general conclusions can be infer-
entially drawn. These are:
1) A complete ban on F-ll and F-12 may or may not
be economically feasible depending on the
availability of substitutes. The benefit-cost
ratio for a complete ban may range from 0.2 to
more than 6.0.
2) A partial ban on F-ll and F-12 use in products
other than as a refrigerant appears to be eco-
nomically feasible, although a major end use,
hair sprays,^ has not been included in the
benefit-cost comparisons.
3) If the hypothesis that fluorocarbon emissions
affect temperature through altering the amount
of ozone and thereby light reduction is not
true, then the economic feasibility of a total
ban is questionable.
Steady State Analysis
The benefit-cost analysis in the preceeding section in-
dicated the circumstances under which a complete or
partial ban on F-ll and F-12 might be economically fea-
sible. This analysis is supplemented in this section
by an examination of the optimum "steady state" per*-
centage reduction in the production of fluorocarbons.
The optimum "steady state1' percentage reduction in the
production of fluorocarbons can be defined as occurring
when total costs, including surplus losses and environ-
mental costs, is at a minimum. This optimization prob-
lem can be written as:
min. S(Q) + EC(Q)
(1)
where S(Q) denotes consumer surplus losses which are a
function of the percentage of 1973 production of F-ll
and F-12, Q, and EC(Q) denotes the environmental costs
as a function of Q also. The necessary and sufficient
conditions for an optimum are given by:
S'(Q) + EC' (Q) =0 or S'(Q) =
S"(Q) + EC"(Q) > 0
EC' (W)
(2)
where (') and (") denote first and second derivatives
respectively.
For the purposes of this optimization, both S(Q) and
EC(Q) have been estimated. The best estimator of S(Q)
appears to be by a parabolic function. Three possible
S(Q)'s were estimated for various measures of consumer
surplus. The estimated S(Q) functions are presented in
Table 6. The first function uses derived surplus as
the measure of surplus loss, the second function uses
consumer surplus, and the final function uses consumer
surplus utilizing the assumption that substitutes for
refrigerants exist after ten years and substitutes for
propellants and foams are available immediately.
It was observed that the relationship between environ-
mental cost by category in present value terms and U.S.
production of F-ll and F-12 approximated a straight
line over the range of interest. Thus, the estimation
of the chain of events of production to emissions,
emissions to changes in UV light and temperature,
changes in UV light on materials life and skin cancer,
and temperature on urban plus natural resources, and
finally conversion of these physical-biological impacts
into discounted (at a constant rate) economic costs can
apparently be approximated by a linear relationship.
The approximate linear relationship occurred for both
temperature and UV related environmental costs. These
estimated linear relationships are presented in Table
7. In order for the environmental cost functions to be
comparable with the surplus loss functions at given
"steady state" long run reductions in U.S. production,
those occurring in the distant future had to be dis-
counted back to the present then annualized. Thus the
estimated EC(Q) presented in Table 7 represents annual-
ized environmental costs for the various discount rates
(3%, 5%, and 8%).
The results of the minimization problem represented by
(1) are summarized In Table 8. It is important to note
that Q is only defined over the interval [0,100] since
it represents percentage of 1973 production of F-ll and
F-12. As such, any solution presented in Table 8 for
which either Q_<0 or QxLOO represents a "corner solution1'
and corresponds to either a 100% optimal reduction in
production or no reduction in production, respectively.
Since Q denotes percentage of 1973 production of fluor-
ocarbons, the optimal reduction in fluorocarbons is
given by 100-Q. The important conclusion of this
"steady state" optimization analysis is that the deter-
447
-------
initiation of the optimum is dependent both on the pos-
sibility of substitutes for fluorocarbons in final
products as well as whether the environmental impacts
are likely to be associated with UV increase or also
with climatic change.
The possible policy alternative would be to assume
that discretionary power existed which would allow
regulators of fluorocarbons to specify which final
products would be allowed to utilize F-ll and F-12 in
their production. For purposes of making such policy
decisions, one reasonable strategy might be to elimi-
nate use of F-ll and F-12 first in those products
which provide the smallest loss in consumer surplus per
pound of fluorocarbons used in the production of the
product. If crude estimates are made of average con-
sumer surplus generated in dollars per pound of fluor-
ocarbon by type of consumer product, one obtains a
range of from 18c per pound for deodorants to $272 per
pound for refrigerators. Figure 1 illustrates the op-
timal "steady state" under this assumption of discre-
tionary power where the loss in consumer surplus func-
tion is derived by assuming complete elimination of
final products utilizing fluorocarbons where the prod-
ucts are eliminated from smallest value of consumer
surplus per pound of fluorocarbon to greatest value.
In this case, a rather narrow optimum range of from 42
to 48% reduction in F-ll and F-12 is estimated as
optimal. The products that could not be allowed to
use F-ll and F-12 are: deodorants using propellants;
perhaps hair spray; foam mattresses, and perhaps some
type of refrigeration systems. It is to be noted that
unlike the previous cases, the optimum strategy is
highly insensitive to the discount rate applied to
environmental costs.
bons. If one denotes emissions by product Z ,Z and
Zr for propellants, foams, and refrigerants respective-
ly, structural equations for a model might be of the
following form: V
Zf(t) = BfQft
Zr(t+6)
(4)
(5)
(6)
where the Q's would represent quantity of fluorocarbons
used as foams, propellants, and refrigerants, and the
6's give the emissions per unit of fluorocarbons in
each use. Z (5+6) was calculated as a>weighted average
of emission rates for refrigerants, using the assump-
tion that all emissions are released at the end of the
economic lifetime of the refrigeration final product in
question; and the economic lifetime was assumed com-
plete after 70% of the refrigerant had been emitted at
given emission rates for the type of refrigeration
final product being considered. For example, after a
refrigerator had emitted 70% of its original charge it
was assumed that the refrigerator was "scrapped" and as
a result all remaining refrigerant was assumed emitted.
This is an extremely simplified approach which does not
include a more realistic representation of the depre-
ciation process of the refrigerator nor its consequent
source of emissions when it is no longer useful as a
refrigerator. Total emissions' of F-ll and F-12 can
then be represented by:
Zt =
(7)
A Prelude to Dynamic Analysis
The analysis of the preceeding section has indicated
possible optimal "steady state'' reductions in the prod-
uction of F-ll and F-12, but such an analysis does not
indicate the optimum path through time for regulation,
i.e., it might pay to slowly approach the steady state
optimum and only achieve it in two or three decades.
The importance of this possibility is perhaps suggest-
ed by the observation that there are differential
emission rates for each of the possible categories of
final product uses of fluorocarbons, and also by the
fact that at current emission rates an appreciable
(2-4%) ozone depletion may not occur for 10 to 20
years and biological impacts 10 to 30 years after
that. In addition, time lags in approaching the
"steady state" would permit the development of ade-
quate substitutes for some or all final products now
dependent on F-ll and F-12. The dynamic model which
is developed below will perhaps aid in an analysis
attempting to discover optimal time paths toward the
optimal steady state.
Development of the model best begins with a discussion
of differential emission rates. There are, as was
noted earlier, three major categories of fluorocarbon
use: propellants, foaming agents, and refrigerants.
Each of these uses causes emission of fluorocarbons
into the atmosphere, but the rate of release is dif-
ferent in each case. Foaming agents release their
emissions immediately upon use, while the assumption
which is usually made with regard to propellants is
that their emissions are released within six months of
their production.6 On the other hand, refrigerant
uses release emissions at a much slower rate that var-
ies from about two percent to 30% annually depending
upon the type of refrigerant use.7 Thus the dynamic
aspect of the fluorocarbon emission problem which is
of particular interest is the rate at which the emis-
sions occur for the various product uses of fluorocar-
where =Q represents the quantity of fluorocarbons lost
to the environment during production, transport, and
storage.
Estimated values for the parameters in the above equa-
tions have been derived from the IMOS report and imply
the following relationships:"
Zf(t) =
Zp(t+.5) =
Z (t+6)
• 94Q.
ft
rt
(8)
(9)
(10)
A representation for the production relationships be-
tween the total quantity of F-ll and F-12 and the
quantities used as foams, propellants and refrigerants
needs to be derived. A very simple relationship of
this form would be:
rt
(ID
Such a relationship essentially represents a fixed
coefficient production function which would not ade-
quately reflect actual production decisions that would
vary according to the relative profitability of apply-
ing fluorocarbons in the production of foams, propel-
lants, and refrigerants. The following relationship
was estimated using 1973 production data:9
Qt = .
.10Qft + .25Qrt
Utilizing (8), (9), (10), and (12), a simple "mass
balance" relationship is derivable:
Z(t) = .711Q(t) + .25Q(t-6) + .039Q(t-l) (13
Assuming the remainder of propellants escape into the
stratosphere in the following year.
448
-------
The next aspect, and perhaps the most difficult to deal
with adequately, is describing the relationship between
the production and use of fluorocarbons and environmen-
tal costs. Earlier in the paper it was indicated that
the sort of causal chain involved is from production to
emissions of fluorocarbons, from emissions to ozone de-
pletion, from ozone depletion to increases in UV light
and changes in climate, and from these changes to envi-
ronmental cost impacts. However, this simple delinea-
tion of a causal chain has abstracted from the time
element involved. For example, the impact of an in-
crease in UV light on the incidence of skin cancer does
not occur immediately with the change in UV light but
rather may reach the new steadv state incidence rate
after approximately 80 years.
The problem is one of relating environmental costs to
ozone depletion because of its consequent impact on UV
light and climate. Ideally, it would be desirable to
estimate the following sets of relationships:
and EC (0
t-z,.
o3(t)
03(t-l)
(14)
(15)
where 0 denotes ozone concentrations in the stratos-
1 2
phere, EC and EC denote environmental costs associat-
ed with UV changes and climatic changes respectively,
f(zt) denotes the functional relationship between ozone
depletion and emissions of fluorocarbons, and t-z. and
t-z. represent the appropriate time profiles for UV
induced and climatic induced environmental costs. Un-
fortunately, such complete relationships have not been
adequately estimated. The problem arises because esti-
mates of ozone depletion resulting from F-ll and F-12
production presume "steady state" production levels
into the indefinite future.
A3 a first approximation to the problem, environmental
costs can be specified as a function of emissions. Re-
calling the discussion of "steady state" optimum in
the previous section, it was observed that the rela-
tionship between production and annualized environmen-
tal costs was very nearly linear. It seems reasonable
to assume that the relationship between environmental
costs and emissions would also be approximately linear.
Net economic benefits from fluorocarbon production can
be estimated as consumer surplus. The objective func-
tional for this model could then be represented as the
maximization of net benefits which is the difference
between consumer surplus and environmental costs:
rate which is directly related to the rate of reduced
emissions from this source.
An estimate of the environmental loss in present value
to the United States of a one year delay (from 1977 to
1978) in achieving a reduction of 90% in production is
$826 millions (at 5%). Alternatively, a one year delay
would yield a gain of about $89 millions if measured by
derived surplus or $2,471 millions if measured by final
goods markets. These results further confirm the con-
clusions above. Continued research will hopefully
identify, given alternative assumptions regarding the
time rate of discovery of substitutes and recycling
possibilities, a feasible dynamic path for regulation.
Footnotes
H.J. Molina and F.S. Rowland, "Stratospheric Sink
for Chlorofluoromethanes: Chlorine Atom-Catalysed
Destruction of Ozone," Nature, Vol. 249 (June 28, 1974).
Fluorocarbons and the Environment, Report of
Federal Task Force on Inadvertent Modification of the
Stratosphere (IMOS), Council on Environmental Quality
and Federal Council for Science and Technology (June
1975).
3
Fluorocarbons and the Environment (op. cit.)
p. 88.
4
For a discussion of simultaneous equation bias
and estimation of simultaneous equations, see Jan
Kmenta (1971), Elements of Econometrics, McMillan
Co.; New York, or Henri Theil (1970) Principles of
Econometrics, John Wiley and Sons, Inc.: New York.
Hair sprays were not incorporated in the analy-
sis due to an unavailability of adequate price data.
Fluorocarbons and the Environment (op. cit) and
Arthur D. Little, Preliminary Economic Impact Assess-
ment of Possible Regulatory Action to Control Atmos-
pheric Emissions of Selected Halocarbons, Draft Report,
Vol. 1, EPA Contract No. 68-02-1349, Task 8 (July 1975)
7Arthur D. Little (ibid).
Fluorocarbons and the Environment (op. cit),
T, B(Q,.)n -
EC(Z
(16)
p. 91.
g
Fluorocarbons and the Environment (op. cit.)
p. 88.
Pythagoras Cutchis, Estimates of Increase in
Skin Cancer Incidence with Time Following a Decrease'
in Stratospheric Ozone, Paper P-1089, Department of
Transportation, Climatic Impact Assessment Program,
Washington, D.C.
where n is a discount factor and the planning interval
one to y is given.
With these assumptions and solving this simple model
utilizing the previously described relationships, two
results are obtained regardless of the discount rate
employed. First, if "derived surplus" measures of
consumer surplus are used, it is optimal to immediately
love to the optimum steady state. Second, if the sum
°f final product consumer surpluses is utilized (with
the consequent assumption of no future substitutions),
then it will never pay to alter 1973 U.S. production
levels. Finally, if reductions in emissions can be
achieved through improved recycling and reduced losses
for refrigerants, then (with this model) production of
U.S. F-ll and F-12 should be reduced through time at a
449
-------
. 502.136 - 463.632(Pn) - 194.898(P ;) - 2948,898(FCO) - .065(PN.
(133.592)**(521.080) (654.021) (1422.507)* (.014)*'
- 10.167 (P^)** - -004 (P)
(2.706) (.655)
2503.286 - 14.6160"^) + 2.304(1)
1316.320)* (4-957)** (.197)***
.9973 4.560 2.677
8(P-) + 1.340(1)
.9720 20.585 1.253
=-3073.343 - 35.262(PH) + 47368(PSH)
(1364. 501)* (16. 499)* (21.657)*
1.237(1)
(.213)***
6}
(3199. 545)*(16. 680)
qMR "5811-897 17-625(PMR}
(103007. 750)(18. 671)
(.709)***
(30.649)
.1L5L J01. JIJ. i.OJ-3
Where
ollowing meanings:
11 = fluorocarbon 11 R = refrigerator
12 = fluorocarbon 12 D = aerosol deodoi
iding coefficient
tistics for the estimated coefficients may be obtained by dividing the coefficient by
tandard error and can be used to test the hypothesis that the value of the estimated
icient is statistically different from zero. The follovins superscripts placed on the
*i9y/. level of confident
Table 1. Summary of Two-Stage Least Squares
Regression Analysis
Willingness to Pay Equatioi
Annual Willingness to P»y
1973 Steady State
CMilliona of 1967 Dollati)
-.001(QU> + [1.083-.4aoO'12)-6.359(Pco)-.001(PN)-.022(
- .00001(Pq)] Qu
-.00015{Q12)2 + [.498-.290(Pi:i)-.00005(Px>-.001(PQ)J QJ2
-.024(QR)2 4- fl71.27(3+.158(i)] QR
-•00025(Q^)2 + [-.839+.383(FJ,T1)+.0007(1)] QD
-.014(QH)2 + [-87.157+1.343(PSH)+.035(1)] QM
-.036(()A)2 + [-479.493+.342(1)] QA
••029(Qm)2 + [-329.752+1.863(1)] QMR
144.300
128.057
2,780.303
649.060
73.777
1,906.729
217.740
Symbols: IJTP - wtllingni
aerosol deodorants
mines:
M - polyur.
: conditioners
-chicle refrige-
Relevant 1973 Values:
Q., = 325 million pounds
•= 487 million points
i •
• 5,940,000* unit
= 1,722,000* units
Q. = 6,462 units
QMR = 68,992 units
QD - 439,400,000 unit:
r11 - $.168 per pound*
P - $.011 per pound
« $709.31 per mil-
lion cubic feet
P.... = $3.49 per 1000
NA gallons (STP)
I • $2945
Px - 6*.8*
PSM - 38.00*
PSD " 95.20
(incli
Mattr,
Indus
jn Equipment
-ties HA-35H
j M25E
Soap, Cosmetics and Chemical Specialties
Consumer Price Index
U.S. Department of Commerce, _Survey of Current Business (1974)
and Environment!
No. 93-110, (USCPO, Washington, D.C., 1975).
U.S. International Trade Commission
Table 2. Willingness to Pay (WTP) Estimation
Equations and Estimated Annual Will-
ingness to Pay Assuming 1973 as Steady
State Values
Present Value 1973, 5 Percent Discount Rate.
In Millions of Dollars
Commodity
Type
F-ll
F-12
Refrigerators
Polyurethane foam
mattresses
Aerosol deodorants
Auto air conditioners
Mobile vehicle refrigera-
tion systems
Estimated 3973
Expenditures
by Commodity**
40
96
1,386
39
729
489
97
Consumer Surplus
or Derived Surplus
(present value)
2,201
740
39,727
1,007
1,174
16,473***
3,349
*Area under the derived demand curve less equilibrium purchases
in 1973.
**Expenditures are estimated from the demand relationships rather than
actual data since actual price may deviate slightly from predicted price
as given by the estimated demand relationship.
***See Chapter II for explanation of the size of this estimate.
Table 3. Estimates of Consumer Surplus and
Derived Surplus* For Selected Products,
United States, 1971 Dollars
450
-------
Category of
Impact
1. Ozone Depletion
1.1 Non-melanoma skin cancer
1.2 Materials weathering
1.3 Biomass productivity
2. Temperature Change (ozone induced)
2.1 Marine resources
2.2 Forest products
2.3 Agricultural crops
2.3.1 corn
2.3.2 cotton
2.4 Urban resources
2.4.1 fossil fuel use
2.4.2 electricity use
2.4.3 housing & clothing
expenditures
2.4.4 public expenditures
TOTAL
Cost or
Benefit*
52 -206
569
-661***
-11,060
269
-16
-5,719
45,617
-11,377
-696
16,357
*Costs are expressed as a present value of all future
costs and benefits resulting from the emission of F-ll and F-12
produced in the year 1973 and maintained at that level into
perpetuity. A five percent rate of discount was utilized to
convert to present values. Estimated costs applying three and
eight percent discount rates are tabulated in Chapter VI of
this report.
**Non-melanoma skin cancer costs are estimated at $325
per case and $1,292 per case. See Chapter IV and Appendix 6
for justification.
***Negative sign denotes benefit.
A. Derived Surplus ?
S(Q) = 147.004 - 2.935Q + .0146Q
S'(Q) = -2.935 + .029Q2
S"(Q) = .029
B. Consumer Surplus
S(Q) = 4086.704 - 81.755Q + .40°Q
S1 (Q) = -81.755 - 818Q
S"(Q) = .818
C. Consumer Surplus with Substitution Assumption
S(Q) = 3977.708 - 79.550Q + .398Q2
S'(Q) = -79.55 + .796Q
S"(Q) = .796
aQ 5 "percentage 1973 production of F-ll and F-12
S(Q) surplus loss function
Q is defined only over the range [0,100]
c
The assumption about substitution is that there
are immediate substitutes for foams and propellants
and substitutes for refrigerants after ten years.
Table 6. Estimated Surplus Loss Functions
ab
Table 4. Estimates of Environmental Costs by
Category Due to Current Levels of F-ll
and F-12 Emissions, United States, 1973
into Perpetuity (Million of 1971 dollars)
Measure of Benefit*
Cost and Benefit Estimates
Derived Surplus 16,978-17,132
Final Product
Consumer Surplus 16,978-17,132
Derived Surplus
(plus omission
of temperature
impacts) 621-775
Final Product
Consumer Surplus
(Refrigerators,
mobile regrige-
ration systems
and automobile
air condition-
ing uses exclud-
ed) 9,508-^,594
Cost Benefit-
Estimate Cost Ratio
2,941 5.8
81,720 .2]
2,942 .21-. 26
2,181 4.4
*Measured by savings in environmental costs of 1973 level
production of F-ll and F-12 in present value terms.
**Loss in consumer or derived surplus at 1973 use rates in
present value terms.
***Approximation based on a 56% reduction in steady state
emissions obtained from Fluorocarbons in the Environment (op. cit.
Table VI-12
Table 5. Benefit-Cost Comparisons for a Ban On
Production of Fluorocarbons 11 and 12
United States, 5 Percent Discount Rate
(Millions of U.S. 1971 dollars)
Discount Rate Intercept
Total Environmental Cost
3% 184.94
(55.36)
57, 96.08
(36.57)
8% 23.23
(22.77)
Skin Cancer and
Materials Weathering Costs
3% 6.29
(0.78)
57. 5.89
(0.46)
8% 3.88
(0.20)
Slope
15.87
(1.04)
7.8J
(0.68)
1.96
(0.43)
0.46
(.015)
0.33
(.01)
0.16
(-01)
2
r
.98
.96
.81
.99
.99
.99
*The estimated equation was y = a + bx where y equaled annual
costs commencing in 1973 in millions of 1971 U.S. dollars and x
equaled the percentage of 1973 U.S. production of F-ll and F-12.
Table 7. Equations Used to Approximate the
Relationship Between Environmental Costs
and U.S. Production Level of Fluoro-
carbons 11 and 12
451
-------
I. Optimization Using Derived Surplus
UV Related EC(Q)d Total EC(Q)"
Discount
Race for
EC(Q)
37.
57.
100
100
10(1
o
0
49
II. Optimization Using Consumer Surplus
UV Related EC(Q) Total EC(Q)e
Discount
Rate for
EC(Q)
37.
57.
8%
q = 99
Q - 99
Q * 99
Q - 80
Q = 90
Q - 97
III. Optimization Using Consumer Surplus and Substitution Assumption
UV Related EC(Q)d Total
Discount
Rate for
EC(Q)
37.
57,
8%
Q - 99
Q = 99
Q = 99
q - 99
q 90
q = 97
Solutions are obtained by solving the necessary conditions
S'(Q) = -EC'(Q) for Q. Note that the sufficient conditions, S"(Q) > -V.C' (Q),
hold in every case. Since EC(Q) is linear EC'(Q) = 0, and from Table 6
it can readily be seen that S"(Q) > 0 in every case.
Q = percentage of 1973 F-ll and F-12 production
EC(Q) E environmental costs
Q <_ 0 or Q >_ 100 represents a "corner solation" and corresponds to
Q = 0 and Q ° 100 respectively.
UV related environmental costs represent skin cancer and materials
weathering costs, and the appropriate relationships can be found in Table 7.
Total environmental costs included both UV and climate related
costs. For appropriate relationships see Table 7.
Table 8. Solutions for Optimum "Steady State"
Reduction in F-ll and F-12 Production
4500
Millions
of 1971
U.S.
Dollars 4000
i Consumer Surplus*
\Lo89 (annual)
Environmental
Costs**
(annual)
A(3X)
80X 100%
% 1973 Production
Level— F-ll 6 F-12
"Consumer surplus loss where products are removed according to rank
order or loss per pound of f luorocarbons.
"Total environmental costs including both UV and temperature effects
Cases A, B, and C refer to application of 3, 5, and 8 percent social rates
oi discount! respectively.
Figure 1. Annual Consumer Surplus Losses With
Product Ranking and Environmental
Costs, United States, 1973
452
-------
ENVIRONMENTAL, FISCAL AND SOCIO-ECONOMIC
IMPACT OF LAND USE POLICIES: TOWARD AN INTERACTIVE ANALYSIS
J. KUhner, M. Shapiro, R.J. deLucia
Meta Systems Inc
Cambridge, Massachusetts
W.C. Lienesch
Water Planning Division
Environmental Protection Agency
Washington, D.C.
Effective implementation of recent environmental
quality legislation requires planning tools which give
quantitative estimates of the various impacts of land
use and environmental controls. A literature review
revealed that no adequate comprehensive tools are
available. Three models have been developed by Meta
Systems Inc for EPA in a recent study. They evaluate:
(1) impact of urban nonpoint sources on water quality;
(2) sewer and treatment plant capacity; and (3) distri-
bution of costs borne by different groups in response
to new development and environmental controls.
Introduction
Federal, state, regional and local environmental
and land use policies have impacts on the physical
environment and on local governments' economic and
fiscal conditions. The impacts have been recognized
in a qualitative manner, but there are few appropriate
tools to quantify them. If land use and emission
controls are to be used effectively in implementing
environmental policies, it is necessary to consider
the dynamics of the local environment in which these
controls are being imposed. The availability of inter-
active computer models would permit local and regional
planners and decision makers to look at the inter-
actions and impacts described above. Ideally, such
models should enable planners to consider all re-
ceiving media (air, water, land) and take into account
the processes which transfer residuals from one medium
to another.
Meta Systems recently completed a project for
EPA which emphasized urban land use/environmental
quality relationships.1 Figure 1 is a conceptual
INPUT
Soclo-Economic and Demographic; Land
Uses; Hydrology/Hydraulic; Meteorology;
etc.
OUTPUT
I) Emissions and Ambient Quality
2) Costs to> Federal and State Government;
Community, Household; Private Firms; etc.
3} Cost Incidence
Figure 1: Conceptual Model for Urban Land Use
Environmental Quality Relationships
model of the interactions between land use and environ-
mental quality. This model provided a general frame-
work for analyzing relationships and for organizing
a review of literature on models and emissions (see
deLucia, et^ al^. ) . However, the project concentrated
on the development of three types of models:
(1) models for assessing the environmental impact of
urban stormwater runoff, (2) a model for evaluating
the capacities of sewers and wastewater treatment
plants; and (3) a cost distribution model for asses-
sing the cost to be covered by different groups in
response to new urban and suburban development. In.
addition, an extensive evaluation of air pollutant
emissions was undertaken. In this paper we briefly
describe the models developed during the course of the
study and outline their potential applications.
Descriptions of the Models
Urban Runoff and Washoff
Urban runoff produces about the same order of
magnitude of pollutant as secondary effluent from
separately treated sanitary sewage, with the exception
that it is somewhat lower in total nitrogen and higher
in sediment.2 Thus maintenance and improvement of
water quality requires methods for predicting the
impact from runoff associated with urban land uses.
We have combined a dynamic water quality model with a
rainfall-runoff-model; the resulting program can be
used for investigating the impact of land uses and
urban land management (such as street sweeping) on the
quantity and quality of stormwater runoff, and on the
propagation of waves and pollutants in the receiving
water body. After an intensive literature review1'2,
we decided to link together STORM^ and the dynamic
receiving water body model of SWMM4, two publicly avail-
able computer models. STORM, a. continuous model, is
attractive because of its relative simplicity of use.
The data required for the model are not very detailed
and appear to be available in most areas. These data
include land use categories, terrain description,
pollutant loading, runoff coefficients, antecedent
conditions, available storage and treatment, erosion
potential and precipitation record. The major draw-
back of the model is its simplified approach to the
runoff coefficient; it uses an adjusted rational
formula containing a composite runoff coefficient.
STORM is designed to compute urban as well as non-
urban runoff and washoff. For every hour of runoff,
hydrographs as well as pollutographs are generated.
Pollutants included are suspended solids, settleable
solids, BOD, N, P04, and coliforms (MPNs). STORM
does not have any routing routines so that the appli-
cation is limited to areas of less than approximately
10 square miles.
SWMM has two distinct phases (hydrodynamic and
quality) which may be simulated together or separately.
In the first phase, the equations of motion and
continuity are applied to derive the hydrodynamics of
the system for each time step, while in the second
phase concentrations of conservative and non-
conservative quality constituents are computed by using
453
-------
the first phase results and equations for conservation
of mass. Information requirements are similar to
those of the steady-state models.
A considerable amount of time and effort has gone
into restructuring STORM and SWMM to link the two pro-
grams and make them compatible. The major modifi-
cations completed are presented in Table 1.
Table 1
Changes in STORM (A) and SWMM (B)
for an Efficient Linkage
(A) — H GPH* files have been created to pass results
from STORM to SWMM
— Rain interval is used instead of rain event for
file generation
— Erosion is calculated hourly
— Erosion is accumulated over the rain interval
— Eroded material can be added to suspended
solids
— Coliforms are included as sixth pollutant
— Program calculates amount of dust and dirt
accumulated at the beginning of rain interval,
and amount left over after the rain event
— Numerous bugs in the original program have been
corrected (logic, core, program, files, de-
fault) .
TT
(B) — GPH files are accepted as sequential input
— One or more of the six pollutants can be
selected for individual runs
— Quality phase can be run independently of
hydrodynamic phase
— Adjusting factors introduced for GPHs.
GPH means hydrograph and pollutograph.
The linkage provides two points of interaction for the
planner. First, he can choose specific rain intervals
from the continuous simulation period of STORM. Then
he can select those intervals from STORM1s output of
pollutographs and hydrographs, to be passed on to
SWMM. This option significantly reduces the computing
costs, but still allows for simulation of all the
events if computation of a frequency distribution of
conditions is desired. Water quality computations
for specific pollutants can be done separately from
the hydrodynamic computations by varying pollutograph
inputs generated for each point discharge of runoff.
This permits intensive testing of quality related
parameters and thereby facilitates calibration of the
quality model.5
The following types of output can be generated by
STORM and SWMM: (1) hydrographs and pollutographs
as total/year/sub-basin or as total/rain interval/
sub-basin or as total/hour/sub-basin; (2) the amount
of dust and dirt on impervious areas at the beginning
and end of rain intervals; (3) total erosion for
selected rainfall events and the amount finally
reaching channels (stream) after application of a
sediment delivery ratio; (4) stage of water level
at each selected node of the river system for every
rainfall event; (5) water level at every node of the
river system for each day; (6) velocity and flow in
every channel of the river system for each day; and
(7) hourly concentration of selected pollutants at
every selected node.
Capacity Evaluation Model
The capacity evaluation model enables planners to
predict when and where new sanitary sewer and waste-
water treatment plant capacity will be needed to accom-
modate projected development. This capability enables
planning to begin on relief sewers before environmen-
tally disruptive back-ups of main sewers occur. In
addition, the information provided by the capacity
evaluation model provides one of the elements needed
to project the fiscal impact of development. It is
not the purpose of the model to replace the detailed
engineering services provided by public works depart-
ments and engineering consultants. Rather it serves
to warn planners when additional detailed (and expen-
sive) engineering studies are required and indicates
where the most significant problems are likely to
occur.
The evaluation model works from two types of input
data. One set of data contains land use and planning
information, including land use projections and waste-
water generation characteristics. The data set is
organized by cells, which are geographic sub-regions
of the planning area. Cells may be specified from
rectangular grids, census tracts, or other classifi-
cations for which planning data are available.
The second set of data characterizes the collec-
tion network and employs a. classification scheme adop-
ted from a previous Meta Systems study.6 The collec-
tion system is divided into a series of arbitrary
links. Each link is assigned an identification number,
and characterized by link type and by the number of
the next downstream link.-*- This characterization
enables the program to "reconstruct" the sewer network
and evaluate link flows in a straightforward fashion.
The program logic makes it possible to characterize
virtually any realistic collection network, and allows
for the inclusion of force mains and relief sewers.
The major output of the capacity evaluation model
is a tabulation of maximum flows for each link in the
network. This information is presented for four time
periods: a base year and 10, 25, and 50 years from
the base year. The projected flows are compared with
maximum design flows of the links and the percent
utilization and overflows (if any) are indicated.
An additional program option allows similar results
to be computed and listed for treatment plants located
in the system.
The model uses steady state hydraulics; the
ability of upstream links to store back-up from
an overloaded line is not taken into account. Thus
actual overflows are likely to be less than those
predicted. However, the model is intended only to
signal possible problems. More detailed evaluations
should be performed when overflows are indicated.
Cost and Fiscal Impact Model
Because of the multiplicity of financing arrange-
ments and the importance of considering the temporal
aspects of financing, it is often difficult for a
planner to work through the financial aspects of new
development, particularly where many alternative
development patterns and financing arrangements must
be considered. The fiscal impact model is designed
to help planners trace how the environmental infra-
structure costs incurred by new development are reflec-
ted in fiscal demands upon the community and in charges
to the individual consumer.
The structure of the impact model is depicted in
Figure 2. Input data includes three types of infor-
mation :
454
-------
1. Socio-economic data describing the size and
growth of the residential, commercial, and industrial
land uses served by the facility; and data on the
property values associated with these uses.
2. Facility data specifying the type and size of
facility. Currently the program handles eight types
of facilities: septic tanks, sanitary sewer laterals,
sanitary sewer house-connections, sanitary sewer mains
and trunks, storm sewer laterals, stormwater detention
basins, storm sewer mains, and sewage treatment plants.
3. Cost allocation data specifying the mechanisms
(e.g., user charges) used to finance the facilities
and the cost shares allocated to each mechanism.
r
BOND
ISSUE
»
GENERAL
PROPERTY
TAX
[
»
_ LOCAL
GOV'T
USER
CHARGE
OUTPUT
DEVELOPER/
RESIDENT
SPECIAL
ASSESS-
MENTS
1
J
$/YEAR
$/ 1000$ ASSESSED VALUE
$/ GAL. TREATED
FINAL INCIDENCE!
i OF COSTS J"
Figure 2: Logic of Cost and Fiscal Impact Model
Cost sub-models compute the capital and OSM costs
for each facility type. These costs are then alloca-
ted to federal and state subsidies, local government,
and developers or residents. The local government
expenditures are further broken down into those
financed through long term debt (mostly capital
expenditures) and those financed through current
revenues (mostly O&M expenditures). Finally the
local expenditures are converted to assessments and
user charges according to the input specification.
Output from the program includes several measures
of fiscal impact: the time sequence of aggregate
expenditures required by federal, state and local
governments and the private sector, the time sequence
of property taxes and user charges needed to finance
the local costs, and measures of total costs borne
by the consumer. The latter are computed by summing
all charges (including private sector) paid by the
consumer and converting to a constant base to yield
an implied tax rate or user charge, i.e., the tax
rate or user charge which would be required if all
local and private expenditures were financed by a
single mechanism.
A final desirable element of the model which has
not yet been developed, is a sub-model for computing
final cost incidence. This sub-model would provide
the tax impacts of federal and state subsidies and the
amount of commercial and industrial expenditures which
are passed on to consumers inside and outside of the
service area.
Examples of the Results
Results from the three models are not based on
the same case study, but are drawn from different
examples that best demonstrate the models' usefulness.
Stormwater Runoff Model
Results from the first model (Figure 3 and Table
2) are based on the analysis of the Mill River Basin,
Hamden, Connecticut.
36.8
36.7
UJ
ID
U.
? 36.6
I
a.
UJ
o
36.5
36.4
f'\—1985
A
I
18 21 24 3 6 9
TIME IN HOURS
Figure 3: Stage Graph at Dam for 1974 and 1985
conditions: 3 hour rainfall interval with
.51 inches of rain; low base flow
Table 2
Ratio of Coliforms from 1985 to 1974 Land Uses
conditions:
Junction
nH
1-1
td
c •
•H
&
Time
(hour)
! 19:00
20
21
22
23
24
2
6
14
:00
:00
:00
:00
:00 (M)
:00
:00
:00
1
(dam)
1
1.
1.
1.
1.
1.
1.
1.
1.
14
03
4
5
55
57
43
59
1
1
1
1
1
1
1
1
3
.95
.28
.38
.44
.47
.67
.68
.66
6
1.38
1.
1.
1.
3.
2.
1.
2.
41
60
89
04
44
27
24
19
Number
1.
2.
4.
1.
1
1
1
8
.46
.18
.06
.9
.81
.97
11
1.72
.
1
1
1
1
86
97
92
88
,L2
(up-
stream)
.51
1
1
1
1
1
1
1
1
The river has a drainage area (above the dam at Whitney
Lake) of 37.7 square miles and is of triangular shape,
about 13.5 miles long and about 5.5 miles wide at the
upper end. During the 40-year period from 1918 to
1957 the average flow at the dam was 42 mgd. For the
analysis we have divided the basin in 11 sub-basins.
Mixed urban and non-urban land uses exist in the 11
sub-basins; 5,030 acres are considered developed in
1974 and 6,300 developed acres are projected for 1985.
455
-------
In Figure 3 the peak stages at the dam are higher in
1985 than 1974, indicating the impact of increased
development on runoff in the basin. In Table 2 the
ratios of 1985 to 1974 coliform concentrations indi-
cate that, at most junctions, additional development
results in higher concentrations. However, due to
the increased runoff, at some junctions and times
coliform concentrations are actually reduced.
Capacity Evaluation Model
Table 3 illustrates the output from the capacity
evaluation model for a hypothetical 12 link sewer
network and associated treatment plant. The Table
indicates that link 6 is likely to back-up under the
proposed development scenario and that the efficiency
of treatment will be somewhat reduced, as the capacity
of the tertiary treatment facilities will be exceeded.
As a next stage in the analysis, the planner could
evaluate proposed relief sewers by adding appropriate
links and re-running the model.
Table 3
Link Capacities and Flows for
Hypothetical Sewer Network
Full and/or Overcapacity Flows:
Link 6 flow exceeded the maximum capacity
by 12.7 percent (1.58 cfs)
Flow in Links (cfs)
Table 4
Selected Costs of New Residential Development
(590 townhouse units; 10 garden
apartments (30 du each))
Max.
Link ID
Total
1
2
3
4
5
6
7
8
9
10
11
12
Flow
1.
1.
1.
1.
1.
12.
5.
12.
1.
5.
3.
1.
20
20
96
20
20
42
77
42
20
77
55
96
Flow Entering
Actual
Flow
1
0
1
0
1
12
1
3
0
0
0
1
.11
.10
.53
.19
.02
.42
.35
.73
.51
.76
.76
.50
Treatment
Treatment
Plant
Percent Cumulative
Utilization Overflow
92
8
78
16
85
100
23
30
42
13
21
76
Plant
.6
.4
.3
.0
.0
.0
.5
.0
.7
.2
.4
.7
(cfs) = 12
0.
0.
0.
0.
0.
1.
0.
0.
0.
0.
0.
0.
0
0
0
0
0
58
0
0
0
0
0
0
.42
Capacity
Maximum
Stage
Capacity
Primary
Secondary
Tertiary
30.
20.
10.
(cfs)
00
00
00
Percent
Utilization
41.4
62.1
124.2
Cost Impact Model
Table 4 represents one of the summary outputs
available from the cost impact model. It lists
aggregate expenditures for four infrastructure types
required by a proposed new development of 890 dwelling
units. The cost allocations employed are hypothetical
and are not intended to correspond to existing prac-
tices. Costs are assigned to developers and local,
state and federal governments. Within the local
government category expenditures are further classi-
fied by revenue sources.
Cost++
Type
Sanitary
Sewer
Laterals
Capital
O&M
Sanitary
Sewer
Interceptor
Capital
O&M
Storm Sewer
Laterals
Capital
O&M
Storm Sewer
Interceptor
Capital
O&M
Dev- Local Gov't
elo
303
0
278
0
26
0
290
0
per A
.7 0.0
.0 0.0
.0 222.4
.0 0.0
.5 13.2
.0 0.0
.2 0.0
.0 0.0
B
60.
1.
0.
0.
0.
0.
90.
0.
7
5
0
2
0
0
7
0
C
182.
0.
0.
0.
0.
0.
272.
0.
2
0
0
6
0
8
1
'8
State
Gov1
60.
0.
5.
0.
10.
0.
72.
0.
t
7
4
6
2
6
2
5
2
U.S.
Gov't
0.
0.
0.
0.
2.
0.
0.
0.
0
0
0
0
6
1
0
0
(+) All values are in thousand base year dollars.
An entry of zero indicates the group or mechanism was
not chosen for financing cost type.
(++) Capital costs are in thousand dollars per group
or mechanism. OSM costs are in thousand dollars per
year per group or mechanism.
(+++) A = Special Assessment; B = User Charge;
C = Property Tax.
Conclusion
The impact of federal, state, regional, and local
environmental and land use policies on environmental
quality is receiving increasing attention. Section 208
of the Federal Water Pollution Control Act Amendments
of 1972, for example, requires the development and
implementation of plans which include regulatory
programs to control both point and nonpoint sources
of pollution on an areawide basis.7 Section 208
also mandates that land use controls be considered
as measures to be included in the regulatory programs.
In addition, the 208 plans are to include a
determination of the cost of the plan and a financial
program to ensure that sufficient funds are available.
It will be necessary, as part of the financial program,
to determine the sources of funding, such as federal
grants, user charges, property tax revenues, etc.
There is a need within the 208 and similar programs
to determine more specifically the relationship between
land use and environmental quality. Because many 208
agencies lack a quantitative understanding of the
land use-water quality relationships for their parti-
cular areas, they may find it useful to follow the
approach presented in this paper. Approaches such
as this one do not provide definitive answers, but
they do provide quantitative data that are more precise
456
-------
than the data which are generally available. This
type of quantitative analysis will be necessary input
to decisions which affect environmental quality.
References
1. Meta Systems Inc, "Land Use Environmental Quality
Relationship," Prepared for the U.S. Environ-
mental Protection Agency under contract no.
68-01-2622, November, 1975.
2. deLucia, R. J. , Kiihner, J. , and Shapiro, M. ,
"Models for Land Use/Water Quality: Some
Observations on What Exists and What is
Needed," Presented at the 47th National ORSA/
TIMS Meeting, Chicago, April 30, 1975.
3. U.S. Army Corps of Engineers, "Urban Runoff:
Storage, Treatment and Overflow Model,
STORM," U.S. Army Davis, California
Hydrologic Engineering Center, Computer
Program 723-S8-L2520, May, 1974.
4. Metcalf and Eddy, Inc.; University of Florida,
Gainesville; and Water Resources Engineers,
Inc.; "Stormwater Management Model, Final
Report," four volumes, prepared for U.S.
Environmental Protection Agency, July, 1971.
5. deLucia, R.J., and Chi, Tze-wen; "Water Quality
Management Models: Specific Cases and
Some Broader Observations," Paper presented
at the joint USSR/USA Symposium on the "Use
and Limitations of Mathematical Models to
Optimize Water Quality Management," Khorkov,
USSR, December, 1975.
6. Meta Systems Inc, "A Program for Simulation of
Acid Mine Drainage in a River Basin,"
Prepared for the Appalachian Regional Com-
mission, 1969.
7. Emison, G.A., and Lienesch, W.C., "Areawide
Water Quality Management Under Section 208:
Conflicts in Planning for Implementation,"
Paper presented at the 1975 American Insti-
tute of Planners National Conference, San
Antonio, Texas, October, 1975.
Acknowledgements
A number of individuals made significant
contributions to the work described in this paper.
The authors would like to thank, in particular,
Eric Schwarz, David Magid, Larry Russell and Ingrid
Dichsen.
457
-------
A TOTAL CONCEPT SYSTEM FOR MUNICIPAL WASTE DISPOSAL
Lester L. Nagel
Senior Project Engineer
Facilities Technology Division
Federal Facilities Office
U. S. Environmental Protection Agency Region II
New York, New York
ABSTRACT
A review of the past and present means of waste
disposal practices is given with individual
evaluations of each.
The negative vs the positive mode of thinking with
respect to waste disposal uses are discussed.
Based on the positive aspect element, two total
concept systems are technically developed. Existing
and proposed useful end product concepts are examined
and evaluated.
Continuity is maintained by proceeding to examine the
economic aspects of the respective systems proposed
and how each relate, in its resultant cost estimate
and to the ultimate financial impact on the community,
to a system's capacity as well as on a per capita
basis.
A summary of the success of the proposed systems to
the basic criteria, as outlined in the "positive
aspect" approach to the disposal problem, is given
for each of the eight conditions initially cited.
BACKGROUND
The body of information presented in this paper is
directed to those public officials and individuals
concerned with the disposal of municipal wastes of
all types and the design, development and economics
of such a system.
The multi-disciplines involved require extensive
knowledge in such divergent areas that individuals
and/or responsible public agencies do not usually
have compatible expertise such that the end result
of such a comprehensive system can be evaluated.
It therefore seems appropriate for an individual,
having extensive experience in such areas to propose
this concept.
The author's approach is therefore directed to these
technical individuals and officials involved in and
responsible for a community's waste disposal problems.
GENERAL CONSIDERATIONS
The problems of todays living are both complicated
and often dangerous to our existence. None however
vex us more than those problems related to the dispos-
al of the products of our daily waste. As we become
more numerous, this waste problem increases in
magnitude and at the same time becomes restrictive in
the available means of its disposal.
According to our 1970 census statistics there were
916 communities in the United States having a popula-
tion of over 25,000. Sixty-five (65) percent of them
are concentrated in twelve states. At present there
are more than 150 over 100,000 each; 26 of them exceed
500,000. These figures do not include any of their
surrounding suburbs.
The need for a modern practical method of waste dis-
posal has long been sought. Numerous papers and
articles have been previously presented on the subject.
(5,8,9,11,15,19,20,22,28,29,30,31,532). In no instance
however, has the solution encompassed the entire prob-
lem in terms of the domestic concept requirements.
This paper therefore, presents such means for a
complete system for the disposal of all of a communitys
daily waste matter.
Additionally it focuses attention on the advantages of
combining any existing sewage treatment and/or munic-
ipal incinerator facilities at a single location.
Regardless of the type of wastewater treatment facili-
ties available the flash evaporation of the wastewater
effluent is not affected by the overall system's
operations nor the number of treatment stages prior to
the flash evaporator unit.
For simplification only, two wastewater systems are
illustrated. In practical applications any waste-
water treatment system is suitable to the proposed
concepts presented.
BASIC PROBLEMS
The use of fire to dispose of wastes has long prevail-
ed. We have designed, built and operated incinerators
that are initially expensive, inefficient in operation
wasteful in the utilization of the energy produced,
and are one of the major causes of air pollution in
areas of concentrated population. (1)
We do not recognize the fact that what appears to be
an acceptable solution in foreign concepts may not be
the most practical answer to our domestic problems of
waste disposal (5,8,15,19, 20 § 22).
Reviewing these waste disposal problems, their magni-
tude, the present methods used and our future require-
ments, we can summarize them as follows:
Each of us presently creates approximately 5 Ibs, of
waste refuse each day (6) (7). In addition we also
create daily 0.2 Ibs. of sewage matter. Both present
a disposal problem. Means of disposal are limited and
can be broadly classified as follows:
Landfill (all types)
Incineration
Energy §/or Materials Resource Recovery
Burning or dumping at sea
Sewage treatment
1.
2.
3.
4.
5,
6. Septic systems
Numerous installations have attempted and are util-
izing, to some extent, the heat value in the burning
of refuse. (5,9,11,15,19,20 § 22). Its use, in most
instances, is limited to the production of steam and/
or electrical power for incinerator plant use. EPA
has made demonstration grants for various other uses
such as: refuse derived fuel, methane recovery etc.
458
-------
Our utility systems' efficient production of electric
power makes the use of this heat energy for such
purposes expensive and wasteful except for metro-
politan size installations. Efforts to utilize sewage
waste matter have proved largely unsuccessful (13)
and economically impractical.
Incinerator designs have changed little since their
inception. Todays designs basically consist of a
firebox with intricate grate designs. They are batch
or continuous fed and, until the early 1960's were
lacking sophisticated fire combustion controls. We
have visited and been briefed by others on the success
of foreign installations using low excess air firing
concepts, apparently without any significant changes
to our own methods on existing installations. (8,14)
European grate designs (8,15,19) have proven far more
effective than ours but are only lately incorporated
into our incinerator units.
Our past control of stack emissions have been either
non-existant or inadequate in design and/or effective-
ness. (1) The installation of efficient APC equip-
ment has been installed and evaluated only within the
past few years. (21,23, 24)
Past and present trends seem more concerned with the
architectural aspects of functional disguise and,
after the initial operational fanfare, settle into
their normal inefficient dirty routine operations.
The present status of disposal procedures cannot
continue to prevail; otherwise, the threat of disease
could reach a level detrimental to the public's
health. Barring further opposition to change some
hope for a practical solution is possible.
The Total Concept Solution
Consider the problem without the chains of conven-
tional ways and existing techniques. Let us review
the asset possibilities of the two discarded products
of our daily lives, refuse and sewage wastes. Both
consist of organic and inorganic substances which
are useless to us individually and are therefore
collected and disposed of for us by central means.
At this point the most useful utilization of this
matter must be considered. Economic evaluation pre-
sents the following considerations:
1. Steam and Elec. Power Generation
2. Composting
3. Fertilizer Production
4. Land Reclaimation
5. Pyrolysis
6. Water Distillation
The production of steam and/or electric power cannot
be domestically justified economically except for
large installations. Power can be purchased at a
lower cost than produced in limited capacities.
Composting has been tried and also found not commer-
cially competitive. (22) Fertilizer production has
also failed both economically and because of odor
problems. (16)
Land reclaimation is limited by available sites and
creates gas and pestilence problems unless the fill
consists of inert matter.
Pyrolysis has yet to achieve economic success.
The sixth consideration, that of water distillation,
presents interesting possibilities. Few will dispute
the creation of clean water, when processed by the
utilization of waste products. Water distillation
fuel costs range from 30 to 40 percent of the total
process product costs. (2) (3) The development of a
low cost distillation system utilizing. "Industrial
Waste Heat" has been proposed (4) and other proposals
also utilizing waste heat have previously been made
(5). Prime consideration to the solution of such
systems demand that it be functionally self-sufficient
and at least partially self-supporting from an eco-
nomic standpoint.
Two versions of the suggested "Total Concept System
for Municipal Waste Disposal" are shown in Figures I
and II.
Each fulfills the economic and engineering require-
ments as previously stated. The ultimate concept
system, given in Figure II however will be shown to
have several advantages over that of the system shown
in Figure I and will also fulfill all of the engin-
eering and economic requirements previously stated.
The common advantages of both systems are reasonably
obvious.
Consolidation of the refuse and sewage services at
the same geographical location results in lower over-
all initial plant site costs, personnel requirements
and plant operating expenses. Incineration of all
solids increases the potential heat energy available,
helps stabilize the refuse heat value and produces a
reasonably inert fill residue greatly reduced in
volume and weight. The disposal problem is thereby
diminished to a considerable extent. The use of the
chemically treated sewage water to produce clean
water for the various system functions shown plus the
surplus available for outright sale, achieves the
objective of the system's partial economic self-
sufficiency. Auxiliary fuel costs are practically
non-existant and the electric power purchased for
either system costs less than when in-plant produced.
Additionally the system of Figure II will operate at
a higher net economic efficiency by utilization of all
of the resultant heat to produce clean water plus
elimination of all boiler maintenance on the non-
existant steam boiler.
Each system would utilize an incinerator unit of 300
tons per day capacity, however whereas the Figure I
system unit would utilize a conventional incinerator-
steam boiler arrangement, shown in Figure III, the
Figure II system would consist of a three stage
incinerator having as the final stage a kiln type
rotating barrel (Volund) design direct gas discharge
unit (19,22,26) as shown in Figure IV. Firing
temperature of both systems would be in the order of
1800-2300F which insures elimination of stack odor
possibilities.
The rotary kiln exit gases of the Figure II system
would be precleaned by a cyclone collector and then
directly utilized in a flash type water distillation
unit (17). The ultimate production of clean water
would be 2.4 x 106 GPD for the Figure I system and 2.7
x 10& GPD for the Figure II system. Each system would
provide approximately 15,000 GPD for use in dissolving
sewage treatment chemicals. Some small additional
amount would be required for makeup for the Figure I
system steam boiler. The balance in either system
would be available for sale as boiler feed water or to
supplement the community's water needs.
459
-------
Both systems have the advantage of allowing for wide
variations in the quantity of water produced, depend-
ent upon the seasonal or even daily change in heat
energy value of the incinerated matter.
The systems presented are representative of the size
required for a community or group of communities hav-
ing a total population of 100,000. Multiples of the
system's units could be installed at a lower unit cost
with a resultant increase in total investment return
in the distilled water product produced for use and/
or sale.
Table I presents the respective capital costs of
equipment and plant investment for both systems.
Annual costs and investment return value for each
system are also included. All values are predicated
on a single 300 ton per day unit (100,000 population)
system. Based upon the data presented in Table I-A
the net annual cost per ton of matter incinerated is
$4.00 and $3.84 respectively.
These net costs are derived upon the basis of a total
of 300 tons/day or 110,000 tons per year generated on
a 365 day basis and being incinerated on a 345 day
schedule of continuous operation each day at a 90/100%
capacity level.
Refuse collection costs are not included, however they
would normally be lower reflecting the savings in
shorter hauling distances with the use of such a
centralized system for small communities. Included
are removal costs of the incinerated residue for use
as adjacent landfill.
Credit for the distillate water produced has been
calculated at the lowest prevailing rate of producing
boiler feed water, $2 per 1000 gals. Present day
costs of treated boiler feed water is in the order of
$2 to $3 per 1000 gallons. No additional credit has
been included in the Table I calculations over the
lower cost figure.
For comparison purposes the relative costs for the
same systems shown in Figures I and II are given in
Table I-B where an activated Sludge Type of Sewage
Process is utilized.
Three additional aspects of the system functions given
in this paper should also be noted.
They are all economic in nature and are therefore of
primary importance when the following conditions may
prevail:
1. In metropolitan areas having an urban-suburban
population of 1,000,000 or greater, the generation of
electrical energy from the heat output of a 3,000 Ton
per day incinerator-steam boiler unit (System Fig. I)
becomes economically feasible.
In this modification the flash evaporator unit would
be eliminated, however the treated sewage water would
then become the condensing cooling water for the
steam turbine.
2. Most communities, having a basic population of
25,000 or more, have installed, on a regional basis,
sewage treatment facilities and in some instances a
municipal incinerator.
Where either or both of these exist the initial
investment for either of the basic systems proposed
is substantially reduced.
3. A raw refuse waste classification system above and
beyond the reclamation of the metals in the ash residue
can be added to any of the proposed systems discussed.
The economic advantages however must be carefully
examined on an individual installation basis before
inclusion as part of the basic systems proposed.
CONCLUSION
As a result of the concepts and economic data as
presented the following criteria has been established:
1. Current methods of refuse disposal only, indicates
an annual per capita cost range of $3.50 to $8.00 (7,
24). With reference to Table I, the comparable net
annual per capita costs, after proportionate value
credit for the useful products produced is made,
would be 63
-------
6. The Environment Gilberston Spring 1966 Issue
Engineering Joint Council Publication Engineer.
7. Refuse Study for the Capitol Region Planning
Agency (Conn.) February 1963 UPA Project P-27.
8. An appraisal of Refuse Incineration in Western
Europe Rogus, C.A. ASME National Incinerator
Conference 1966.
9. Navy to Incinerate Rubbish for Power
Removal Journal 1967.
Refuse
29. Megawatts from Municipal Waste IEEE Spectrum
Nov. 1975.
30. Garbage-to-Energy Conversion Fuels Bond-Sector
Interest. Wall Street Journal Aug. 11, 1975
31. Wheelabrator to Sell Refuse-Produced Power to
General Public Unit Wall Street Journal May 20, 1975
32. Turning Trash into Energy
October 20, 1975
US News § World Report
10. Solid Waste Disposal Part II Fleming, R. R.
The American City 1966.
11. An Incinerator With Power and Other Unusual Fea-
tures Heeding, Velzy § Landman December 1964
American Society of Mechanical Engineers.
12. Brisbane, California Proposed 2000 Ton Inciner-
ator (Reported Late 1967),
13. Something in the Air-A Suburb in Michigan Stinks
to High Heaven Wall Street Journal May 16, 1968.
14. Air Pollution from Incinerators Causes and Cures
Flood, L. P. December 1965 American Society of
Chemical Engineers,
15. European Developments in Refuse Incineration
Magazine Public Works May 1966 Rogus, C.A.
16. Florida Garbage Plant Makes its Presence Known
too Strongly Wall Street Journal February 12, 1968.
17. Gas Turbines Show Promise in Water Desalting
Plants Power Engineering November 1966 and July
1967.
18. Key West Desalination Plant Goes on Stream
Magazine Public Works October 1967.
19. European Practice in Refuse Burning Stabenow,
G. National Incinerator Conference -1964.
20. Survey of European Experiences with High Pressure
Boiler Operation Burning Wastes and Fuel Stabenow,
G. National Incinerator Conference 1966.
21. What Price Incineration Air Pollution Control
National Incinerator Conference 1966. Fife fj Boyer.
22. European Practice in Refuse § Sewage Sludge
Disposal by Incineration Eberhardt, H. National
Incinerator Conference 1966.
23. New Precipitators for Old Incinerators Refuse,
Collection § Disposal 1968.
24. City of Baltimore Rehabilitation § Renovation
of Incinerator No. 4 (1975)
25. Garbage Collection and Incinerator Study Depart-
ment of Public Works Study Committee City of Hack-
ensack, New Jersey.
26. Combustion Profile of a Grate-Rotary Kiln Incin-
erator Woodruff, P. H. $ Larson, G. P. National
Incinerator Conference 1968.
27. Municipal Incineration U.S. Environmental
Protection Agency AP-79 June 1971.
28. Energy Report IEEE Spectrum Nov. 1975.
SUMMARIES TABLE I, I-A § I-B
PLANT CAPITAL COSTS
with
PRIMARY TREATMENT PLANT
Equipment Investment
Plant Investment
System I
9,545,000
1,570,000
Total Investment $11,115,000
Net Annual Costs (Credit) 63,000
NET ANNUAL COSTS CHARGEABLE TO EACH
Function Percent
Incineration/Ton 25
Distillation/M.gal 35
Sewage Treat- 40
ment/106 gal
Unit
System I
$4.00
74.4(f
19. 3£
System II
9,020,000
1,535,000
$10,555,000
($216,000)
FUNCTION
Costs
System II
$3.84
63. 5*
18.5*
PLANT CAPITAL COSTS
with
ACTIVATED SLUDGE PLANT
Equipment Investment
Plant Investment
Total Investment
11,715,000
1,670,000
$13,385,000
11,220,000
1,635,000
$12,855,000
TABLE I
PLANT CAPITAL COSTS
EQUIPMENT INVESTMENT (INSTALLED)
PRIMARY TREATMENT PLANT TYPE
Item
1 Incinerator § Boiler
(300 TPD) (incl. Fans)
1A Incinerator (only)
(300 TPD) (incl. Fans)
2 Mechanical collector
3 Figure I Distillation
Plant (2.4 x 10 GPD)
3A Figure II Distillation
Plant (2.7 x 10 GPD)
4 Sewage Process Plant
(10 x 10 GPD)
5 APC Unit (ESP)
6 Heating § Air Condi-
tioning System
7 Odor Unit (not required)
8 System Coordination
(10% of Equipment costs
and Installation)
Figure I
1,700,000
80,000
3,000,000
3,500,000
300,000
70,000
865,000
Figure II
850,000
80,000
3,400,000
3,500,000
300,000
70,000
820,000
Total Equipment Investment $9,545,000 $9,020,000
All figures have been rounded to nearest $1,000.
461
-------
PLANT INVESTMENT
Item Figure I
Waste Land (100 acres @ 100,000
$1000/acre)
Architectural § Engin- 720,000
eering Fees (7% of T.E.I. § Bldg)
Office 6 Operations 750,000
Building for Items #1,
3 or 3A 6 4
Total Plant Investment $1,570,000
Grand Total $11,115,000
ANNUAL COSTS
A Fixed Charges 8.024% 892,000
(5% - 20 years)
B Electric Power
(a) Sewage Plant 300 KW
(b) Distillation 110 KW 90,000
(c) Incineration 600 KW
C Chemicals
(a) Distillation Plant 50,000
(H2 S04 @ 2.50
-------
TABLE I-B
ACTIVATED SLUDGE TYPE PLANT
Item
1
1A
2
7
J
3A
4
5
6
8
(a) Equipment Investment
Equipment Figure
Incinerator § 1,700,
Boiler
300 TPD-Including
Fans
Incinerator only
300 TPD-Including Fans
Mechanical Collector 80,
r\^ „ 4. J T 1 .3-1-4 rt-n Plant* ^ Oflfl
UlSClJ-ldL-LLHl rJ. dfl L O 3 UUU >
2.4 x 106 GPD
Distillation Plant
2.7 x 106 GPD
Sewage Plant 5,500,
10 x IQo GPD
Precipitator 300,
Heat £, Cooling
System 70,
System Coordination 1,065,
10% of Equipment §
Installation Costs
Total Equipment $11,715,
Investment
CAPITAL COSTS
Installed
I Figure II
nfin
-
000
CiCiCl
3
000 5
000
00
000 1
000 $11
PLANT INVESTMENT
Land
A § E
100 Acres @ $l,000/Acre
Fees 7% of T.E.I.
rigure I
100,000
820,000
850,000
80,000
,400,000
,500,000
300,000
70,000
,020,000
,220,000
Figure II
100,000
785,000
and Building
Building Item 1, 3, § 4 750,000 750,000
Total Plant Investment $1,670,000 $1,635,000
Grand Total $13,385,000 $12,855,000
463
-------
MS FLOW
SYSTEM I
STACK
FIGURE I
TOTAL CONCEPT SYSTEM FOR MUNICIPAL WASTE DISPOSAL
(INCINERATOR-HEAT RECOVERY BOILER UTILIZATION)
SYSTEM II
EMERGENCY
GAS FLOW
REFUSE
TO SYSTEM
ItOT/O
AIR INLET
EMERGENCY BY-PASS
300 TPO
INCINERATOR
UNIT
GAS
FLOW
MECHANKAL
COLLECTOR
\ ASH ASH
\ DISPOSAL/ \DISPOSAL
FRE
cm
COMPACTED SOUOS TO INCINEK
EXCESS
FRESH
WATER
1
GAS FLOW
FLUSH WATEf
\
'• GAS FLOW
WATER
DISTILLATION
UNIT
2.7«108
GPD
SH PROCESSED
WATER FOR
WAL DILUTION
SEWAGE
PROCESSED
WATER
ESP
TUBULAR
COLLECTOR
IWETI
\ SETTLING/
rOip
SOLIDS
DISPOSAL
APCCOU
FLUSH 1
RETU
EXCE
STACK
GAS FLOW 1 1
PU"1 HiTM 1
HEAW. *|^J |
ICTOR
MTER
W
SS PROCESSED SEWAGE WATER TO
RIVER OR OCEAN SOURCE
SEWAGE PROCESS UNIT
IOII06 GPD
ATOR HTT/D
SEWAGE FU1W TO SYSTEM
FIGURE II
TOTAL CONCEPT SYSTEM FOR MUNICIPAL WASTE DISPOSAL
(ROTARY KILN WITH DIRECT GAS UTILIZATION)
464
-------
Figure 3. Boiler With Reciprocating Stroker
IGNITION GRATES
BY-PASS
MIXING CHAMBER
TO WASTE
HEAT
BOILER
SCRUBBER
Figure 4. Section Through Incinerator Unit
465
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ECONOMIC FORECASTING FOR VIRGINIA'S
WATER RESOURCE PROGRAMS
Charles P. Becker, Allender M. Griffin, Jr.,
Carol S. Lown
ABSTRACT
Water resource and water quality management planning
depend, to a large degree, on forecasts of industrial
activity and population projections. A flexible eco-
nomic data base is especially important where planning
follows varying formats of geographical and industrial
detail. Records of employment and payroll are collect-
ed in the administration of Unemployment Insurance
(U.I.) programs and are available from State Employ-
ment Agencies. These statistics have been collected
over a long period of record (thrity-five years).
Many years of record are available on punched-cards
or magnetic tape and may be arrayed and manipulated by
computer. This basic approach has been followed in
Virginia. Historical U.I. payroll and employment re-
cords for the period 1956 through 1970 were procured
on magnetic tape. This data was arrayed by major
hydrologic area and by regional planning district.
Projections of manufacturing activity were then gener-
ated by fitting several exponential equations to annu-
al payroll data in two-digit Standard Industrial
Classifications. These exponentials were then ex-
trapolated to provide a range of industrial projec-
tions. Other parameters of manufacturing activity
were then correlated to the payroll data to generate
projections of indexes such as employment, value-added,
and gross manufacturing output. U.I. payroll data is
now being correlated to parameters in non-manufactur-
ing categories. Projections for industries such as
trade and services will link extrapolated payroll data
with benchmark correlations of payroll and sales re-
ceipts.
(KEY TERMS: water resource planning; unemployment
insurance (U.I.) statistics; value-added; exponential
forecasting; population projections)
\
Economic data has played an important role in water
resource planning and water quality management plan-
ning.' Parameters such as population, employment and
value-added in manufacturing have been correlated to
watei—use and waste generated. Water resource planning
engineers and sanitary engineers are able to make pre-
dictive estimates of future water-use and waste levels
by making correlations with various population and in-
dustrial projections. Water demand, expressed in mil-
lions of gallons per day (MGD) has been related to
value-added in selected manufacturing categories.
Watei—use coefficients are also available for other
heavy water-using industries such as mining. Domestic
water demand can be predicted by applying per capita
water-use factors to population forecasts. Parameters
of water quality such as biological oxygen demand (BOD)
and chemical oxygen demand (COD) have been correlated
to economic indexes in major water-using industries.
Relationships between per capita population and domes-
tic waste generated have also been expressed quantita-
tively in terms of BOD and COD.
In order to produce valid economic forecasts for vary-
ing size planning units, the water resource economist
must have a flexible and comprehensive data base.
Traditional data sources, such as the Bureau of the
Census — U. S. Department of Commerce, publish data'
which provides a valuable overview to the water re-
source planner.
Often, however, more detailed, unpublished data is
necessary where planning units follow a hydrologic
format. Data by reporting establishment must be sorted
and manipulated to produce a valid benchmark or fore-
cast base for hydrologic planning areas of river basins.
Of course, this same data may be sorted by county or
city and further aggregated into economic planning
regions.
The State Employment Security Agencies have collected
and stored an impressive record of payroll and employ-
ment data for administering Unemployment Insurance
programs. This data has been collected in all of the
'Between 19o6 and 1972, the Virginia Division of Water Resources of the Department of Conservation and
Economic Development was responsible for comprehensive water resource planning for the State of Virginia.
On July 1, 1972, the Division of Water Resources was merged with the Virginia State Water Control Board.
Since 1946, the Board has been responsible for water quality management in Virginia. The combined agency is
now operating as the Virginia State Water Control Board.
"Value-added of an industry consists of labor compensation, proprietors' income, profits, interest,
depreciation, and indirect business taxes.1' (U. S. Department of Labor, B.L.S., 1970).
•>ln addition to an every-five year Census of Manufactures, the U. S. Department of Commerce. Bureau
of the Census also conducts Annual Surveys of Manufacturing during interim years.
The State Employment Security Agencies are affiliated with the Manpower Administration (formerly the
Bureau of Employment Security of the U. S. Department of Labor.
466
-------
states, in the territories of Puerto Rico and in.the
Virgin Islands. Unemployment Insurance (U.I,) laws
vary somewhat from state to state in such areas as
program detail and reporting coverage. Some states
have, for example, full coverage in unemployment-in-
sured industries. Other states have required U.I.
reports from firms with four or more employees. Sup-
plementary employment data may be obtained from the
Federal Bureau of Old Age and Survivors Insurance
(B.O.A.S.I.) of the Social Security Administration to
bring coverage up to a universal or "100 percent" in
these "partial coverage" states.
The State of Virginia provides a good illustration
where U.I. coverage was partial for years (required
of firms with four or more employees) in unemployment
insured industries. An amendment (effective January
1, 1972) to the Virginia U.I. law extended coverage to
firms with one or more employees in unemployment in-
sured industries. Certain types of employers are
still excluded from U.I. coverage. Federal and local
government, railroads, churches and state government
(except non-teaching staffs of hospitals and institu-
tions of higher learning) remain exempt from U.I.
coverage.
All states, Puerto Rico and the Virgin Islands submit
U.I. employment and payroll data to the Manpower
Administration under the report designation Employment
Security (E.S.) 202. The E.S. 202 report is forwarded
in the form of a computer print-out. This record
(E.S. 202) is assembled using individual establishment
reports, i.e., the Employers Quarterly Contribution
Report (see facsimile — Figure 1). The Contribution
Reports are audited for completeness and accuracy,
and then key-punched. Each Contribution Report
contains the following identification:
1. A four-digit Standard Industrial Classification
(S.I.C.) Code
2. A three-digit area code designating the county or
city in which the reporting establishment is
physically located
3. A six-digit serial or identification number unique
to each establishment
As was mentioned, U.I. Contribution Reports are filed
quarterly and contain (in Virginia) the following data
1. Monthly Employment
2. Gross Quarterly Payroll
3. Gross Quarterly Payroll subject to Unemployment
Insurance
It. Quarterly contribution, i.e., U.I. tax
5. Quarter and year liability (to U.I.) started
6. Report date (quarter and year)
MANUFACTURING DATA
Of these items above, employment (item #1) and gross
quarterly payroll (item #2) are of particular impor-
tance to the water resource planner. Payroll is of
special relevance, since when cumulated by quarter to
an annual figure it is a major component of value-
added. This index, value-added, has been and is
currently used extensively as an economic indicator
(past, present and future) of water-use and waste
generated. The U.I. payroll in manufacturing is also
an important component of gross manufacturing output
or value-of-product.
a prerequisite for access to the E.S. 202 — U.I.
it is necessary that the requesting agency be
aware of the publication restraints and c*^ta non-
Figure 1. Contribution Report
VIRGINIA EMPLOYMENT COMMISSION
EMPLOYERS QUARTERLY CONTRIBUTION REPORT
&OX 1358 FOR QUARTER ENDING_
Richmond, Vo. 23211
2nd MO—
3rd M0._
INSTRUCTIONS AM ON
IACK OF EMPLOYERS
COPY OF CONTRIBU-
TION REPORT
ALSO:
Numb*t ol HI
Notk* .f Chang*
G Nornt cKar>9<
G Maibng Xddnni chonat
Q D,iiol*«i, no luunior
n ^£!d ^iTL™,
H •" -hoi.
Indrcat* n«w nom» and/or
oddrtu ,„ thl. tpac. If
btiiineil indie ot» lucctiwr
narn* and addrni in thu
^ ^ZZ- C^lMH 1. 1, 4 I J, uf, 'OM! rvurn
PAYROLL DATA
1. TOTAL WAGES for Quarter, including remuneration other
per individual (over $3,000 prior to January 1 , 1 972).
January 1, 1972).
CALCULATION OF CONTRIBUTION
4. CONTRIBUTION - Multiply total of Lin* 3 by tax rate ihown
above.
3. CREDIT MEMO NO. ( ) DEDUCT
(Alwayt attach white copy ol Credit Memoi.)
4. INTEREST (computed on contribution - - Lin* 4 • - at rat* of 1%
p«r month from du* dot* to date of payment.)
PENALTY -• $« INSTRUCTIONS
7. TOTAL AMOUNT DUE for which remittance ii encloiod.
s
s
s
s
$
$
$
I, (or we) certify thai the information contained in thil report, required In accordance wilh the Virginia Unemploy-
ment Compensation Act, it true and correct and that no part of the contribution reported wot, or n to be. deducted
from worker's wagei.
OKIOINAL - BFTUBN TO COMMISSION
VEC-FC-30 (R-ll-7-74) (200M 11-7-74)
disclosure requirements. In Virginia the publication
criteria are as follows:
1. The industry group must include at least three
independent reporting firms (i.e., companies —
not establishments).
2. The industry's employment must be sufficiently
dispersed so that the combined employment of the
two largest firms does not exceed 80 per cent of
the group total.
3. Individual firm data may not be published or dis-
closed verbally under any circumstances.
^4. E.S. 202 data may not be used for law enforcement
purposes, except in the administration of the U.I.
law under which the data is required.
In most states, other detailed economic data germane
to water resource planning is available in both pub-
lished and unpublished form. In many instances, the
unpublished data by firm or reporting establishment is
an extremely flexible planning tool. The data usually
has been collected by reporting unit and contains
identification which is similar to and compatible
with the U.I. reports discussed above. In Virginia,
an Annual Survey of Manufacturers is conducted by the
State Department of Labor and Industry. This survey
is based on a selected sample and represents about 75
per cent of all manufacturing activity in the State.
Firms which participate in the survey are assigned the
following identification data:
467
-------
1. A four-digit Standard Industrial Classification
code
2. A three-digit county or city code
3. A five-digit serial or identification number
The Annual Survey of Manufacturing is conducted by a
mailed questionnaire referred to as the S-l form.
Questionnaire data items include:
1. Total employment
2. Production worker employment
3. Salaries and wages (total payroll)
4. Wages paid to production workers
5. Net selling value-of-product
6. Cost of materials
7. Contract work
8. Physical volume-of-product
9. Capital expenditures
10. Anticipated capital expenditures
had an address indicating a physical location well
.within a particular river basin. The more difficult
hydrologic address determinations were those where a
firm was located near a ridge line. In these in-
stances, a good deal of map detail was necessary.
These "ridge-line" address (hydrologic) determinations
could be accomplished by field trip or by correspon-
dence with knowledgeable people within the "ridge-
line" locality itself. This latter, -less expensive
alternative was chosen.
A number of forecasting methodologies" (or combinations
thereof) are compatible with the data base discussed
above. The behavior of price-adjusted, annual payroll
data was quite encouraging when subjected to several
exponential growth curves. This experience, coupled
with the availability and continuity of U.I. payroll
data, indicated that growth curve fitting and extra-
polation would be fairly valid as a general forecasting
technique. Asymptotic growth curves describe an in-
dustry passing through the following stages:
1.
Period of initial industrial development and
limited production — a phase characterized by
slow growth
Stage of accelerated industrial development, in-
creasing production and rapid expansion
Period of relative stability where the growth rate
levels off with the main emphasis on operating
efficiency and cost minimization
Curves fitted using the Gompertz equation adhered
closely to most historical payroll data in the study
areas (River Basins and Planning Districts). A
Gompertz curve has the shape of a nonsymmetrical "S"
when graphed on arithmetic paper. Its nonsymmetrical
nature results from a difference in behavior on
opposite sides of the points of inflection. The
Gompertz equation generates a curve in which the growth
increments of the logarithms are declining by a con-
stant percentage. The general equation of the Gompertz
curve is:
whe re:
Yc=Ka(bx)
11. Cost and quantity (KWH) of electric power consumed
Value-added is not surveyed directly as a question-
naire item. It can be easily computed, however, as
follows:
Value-added=(Net selling value of products)
-(Cost of materials)-(Contract Work)
The same publication and disclosure restrictions as
outlined regarding the E.S. 202—U.I. data apply to
the Annual Survey of Manufacturing records, (i.e.,
S-l data).
In Virginia, extensive water resource and water quality
management plans are being developed for the nine major
river basins (see River Basin Map—Figure 2). These
studies were begun by the Virginia Division of Water
Resources in 1966 and are being completed by the
Virginia State Water Control Board (see footnote 1).
This planning is being approached in a six volume foi—
mat.5 Within Volume II — Economic Base Study, con-
siderable emphasis is placed on the analysis of manu-
facturing data. This priority reflects the signifi-
cance of high water-use and related high waste poten-
tial of many manufacturing categories.
Much water resource planning is conducted on a hydro-
logic format. In order to express benchmark manufac-
turing data on a hydrologic basis, a major rearrange-
ment of E.S. 202 — U.I. data and S-l data (Annual
Survey of Manufacturing) was necessary. This realign-
ment of the data went beyond the normal county and
city format. The county and city codes were useful,
however, as a broad hydrologic sort routine. As a pre-
liminary step, the punched cards for both the E.S.
202 file and the S-l file were interpreted and sorted
by county and city. Obviously, many counties and
cities are completely within the major hydrologic
areas. In those counties or cities which are situated
in two or more hydrologic areas, however, detailed
address determinations of individual firms had to be
made. It was necessary, therefore, to have address
data for each reporting firm or establishment which
was as specific as possible regarding physical location.
Usually the firm's mailing address coincided closely
with the firm's physical location. Based on this ad-
dress, a valid hydrologic address determination could
be made. This task was especially easyjvhen the firm
Volume I Introduction; Volume II Economic Base Study; Volume III - Hydrologic Analysis;
Water Resource Problems and Requirements; Volume V Engineering Development Alternatives; Volume
tation of Development Alternatives.
^Other forecasting techniques have utilized standard growth rate tables such as those based on the com-
pound interest rate formula. Industrial projections have also been inferred from predictions of population trends.
x =Time interval
K =Asymptote or limit which the trend value
approaches as x approaches infinity
a =The distance from the asymptote to the Y-inter-
cept
b =The base of the exponential equal to the constant
ratio between successive first differences of
the log Y
Two other growth trends which are useful as forecasting
equations are the Modified Exponential and the Pearl-
Reed (logistic). These equations may be categorized
with the Gompertz trend in the broad family of ex-
ponential curves. The general equations for the Pearl-
Reed and the Modified Exponential may be written as
follows:
Modified Exponential
Pearl-Reed
K_
1+10a+bx
Yc=K+abx
Volume IV -
VI Implemen-
468
-------
Figure 2. Major River Basins in Virginia.
RIVER BASINS IN VIRGINIA
• r
I POTOMAC-SHENANDOAH
2 JAMES
3 RAPPAHANNOCK
k ROANOKE
5 CHOUAN AND DISMAL SWAMP
6 TENNESSEE AND BIG SANDY
7 SMALL COASTAL BASINS AND
CHESAPEAKE 6AY
6 YORK
TENN.
N. C.
The Pearl-Reed curve traces a pattern in which the
first differences of the reciprocals of the Yc values
are declining by a constant percentage. The Modified
Exponential curve describes a trend where the amount
of growth declines by a constant percentage.
Figure 3 provides an illustration of a typical expo-
nential growth curve. As is evident, the trend line
(TT1) increases, but at a decreasing rate on the right
of the point of inflection. The horizontal line (KK1)
(narks the upper limit of growth or the horizontal
asymptote.
Asymptotic growth curves approaching horizontal limits
were fitted to the price adjusted U.I. payroll data.
Whenever a valid "data fit" was established, an equa-
tion resulted. An extension of the curve marked a
trend of possible growth. Several growth curves fit-
ted to various intervals of data in the same histori-
cal series were used to create a range of projections.
Value-added, gross manufacturing output and employment
were correlated to payroll data for the forecast re-
ference points.
Prior to growth curve fitting, it is well to look
critically at several aspects of the data and the
study area:
1. An appraisal should be made to determine if
historical growth experience by the industry
under study is actually a valid trend.
2- Is the available data record of sufficient length
to present a representative trend in the area
and industry under study?
3. Is the historical record of sufficient magnitude to
represent a data base wide enough to portend
future industrial development?
Our experience indicates that price adjusting U.I.
Payroll data is an absolute necessity prior to
growth curve fitting. Price adjusting, of course,
eliminates the fluctuations of inflation or deflation,
leaving "real" changes. Unfortunately, there is no
"ideal" price index for price adjusting payroll or
labor costs.
The Wholesale Price Index? (published by the Bureau of
Labor Statistics (B.L.S.), U.S. Department of Labor)
has proven quite satisfactory when applied to manu-
facturing payroll data. Most applications have been
on the two-digit S.I.C. level using the 196? base
converted to 1970.
The Bureau of Water Resources of the Virginia State
Water Control Board now has available 15 years (1956-
1970) of U.I. employment and payroll data. An IBM 360
computer is currently being used for the exponential
curve fitting routines. Previously, an Olivetti Pro-
gramma 101 (a programmable calculator) and an IBM 1130
computer were used. The IBM 360 has, of course, great-
ly expedited curve fitting and extrapolation routines.
Utilizing the "360" program, fifteen years of histori-
cal payroll data were fitted to three exponential
curves — Gompertz, Modified Exponential and Logistic
(Pearl-Reed). The data was analyzed in 6, 9, 12 and
^The Wholesale Price Index "...is an index of the prices at the primary market levels where the first
important commercial transaction for each commodity occurs." (Tuttle, 1957). "Wholesale1, as used in the title
of the index, refers to sales in large quantities, not to prices received by wholesalers, jobbers, or
distributors." (U. S. Department of Labor, B.L.S. Handbook, 1971)-
469
-------
Figure 3-
U.I. Payroll estimates and projections in
transportation, communications and public utilities
for the Southeastern Virginia Planning District
(data expressed in constant 1970 dollars).
400n
350
300
250
o
o
200
CO
z
° 150
100
50
I960 1970 1980 1990 2000 2010 2020
YEARS
15-year intervals. For fifteen consecutive years of
data, this method resulted in twenty-two possible
curve fits for each two-digit S.I.C. Since there were
several different forms which the exponential curves
could take, constraints were built into the program to
eliminate the curves which did not fit a pattern of
normal growth. The desired shape of the growth curve
was that which sloped upward to the right, approaching
some horizontal limit, while increasing at a decreas-
ing rate (see figure 3).
Fifteen years of annual payroll data (1956-1970) were
read in for each industry. The first six-year period
(1956-1961) was analyzed, and the exponential equation
was developed. If the equation did not violate the
built-in constraints, then the program extrapolated
the historical data from the initial year of the fit
period (in this case 1956) to the year 2020. If the
equation violated the constraints, a message was
printed out indicating that there was no fit for that
series. The second group of consecutive years of
payroll data (1957-1962) was then analyzed. This con-
tinued through the twenty-two possible combinations
until the final serial (1956-1970) had been analyzed.
The extrapolated universe payroll values, payrol1-per-
employee, S-l value-added, S-l gross manufacturing
output and S-l payroll were used in a Programming
Language 1 (PL1) program which generated a table of
projections for value-added, gross manufacturing out-
put, payroll and employment, The tables were structur-
ed for photographic reproduction directly from the
printout, thus eliminating virtually all typing and
proofing. The value-added projections were developed
by computing the ratio of S-l payroll and S-l value-
added for the benchmark year. This ratio was applied
to the extrapolated payroll figures to develop the
universe value-added projections. The gross manufac-
turing output projections were developed in much the
same way. The ratio of S-l payroll to S-l gross
manufacturing output was computed for the benchmark
year, and this was applied to the extrapolated payroll
values to give gross manufacturing output projections.
The extrapolated payroll values were divided by the
extrapolated payrol1-per-employee figure to develop
employment projections for each S.I.C. group.
Because of the large volume of output from the exponen-
tials, another method of analysis has been devised
which expedites the evaluation of the extrapolations.
A curve plotting routine has been added to the expo-
nential programs so that each curve that extrapolates
is also graphed. This enables the analyst to pick
the best fit from the plots without having to analyze
reams of computer print-outs. A FORTRAN IV8 program
has been written to utilize the plotter capability of
the IBM 360. This plotter routine will graph the
price-adjusted historical payroll data and all possible
extrapolations. By employing transparent plotting
paper and a uniform scaling factor, an overlay effect
is created for the graphic extrapolations within each
S.I.C. The three exponentials -- Rompertz, Pearl-Reed
and Modified Exponential -- are thereby grouped and
the trend selection process is greatly facilitated.
A clustering effect is a "reasonable" indication of a
medium range projection.
A COBOI.9 routine is used at this point to expand the
extrapolated U.I. payroll to a universe. This universe
payroll figure will include U.I. payroll, B.O.A.S.I.
payroll and non-covered payroll. Universe employment
data can then be estimated by dividing the universe
payroll projections by extrapolations of payrol1-per-
employee. Value-added and gross manufacturing output
(Value-of-product) can be projected through correla-
tion of benchmark payroll to value-added and payroll
to gross manufacturing output (G.M.O.).
POPULATION STATISTICS
In Virginia, the Division of State Planning and
Community Affairs (D.S.P.C.A.) has been designated as
the agency responsible for the State's population
projections. This Division (D.S.P.C.A.) has recently
published population forecasts for all counties and
cities in Virginia. These projections are on an every
ten year basis to the year 2020.
The planning guidelines of the Virginia Division of
Water Resources required a range of population fore-
casts. The range of projections (high, medium and
low) reflect varying demographic assumptions. The
low projections assume a very subdued rate of in-
dustrial development and continued out-migration of
the resident population. The medium forecast is based
on a rather vigorous industrial development program.
"FORTRAN IV is a computer language which is used most frequently in scientific and engineering applications.
The term FORTRAN relates to the primary use of the language: FORmula TRANslating.
-"COBOL is a computer language which is used extensively in business and commercial data processing. The
term COBOL is derived from the expression COmmon Business Oriented Language.
470
-------
An extremely accelerated rate of economic growth is
implicit in the high projection. High and low pro-
jections were generated by fitting the compound in-
terest rate formula above and below the D,S,P.C.A.
forecast (medium). This trend fitting was accomplish-
ed using a FORTRAN IV program on an IBM 1130 computer.
County and city population projections developed by
the Virginia Division of State Planning and Community
Affairs were used by the Division of Water Resources
as the medium range on which the high and low pro-
jections were based.
The following high and low control totals (in thou-
sands) were assumed for the entire state:
Virginia Population (X1000)
1970 1980 1-330. 2020
High
(Medium)
Low
4,648
5,632
5,415
5,198
6,9J9 12,100
6,284 9,340
5,629 7,100
The average annual rate of change was computed for
each ten-year period using the compound interest rate
formula:
Average annual rate of change= R =
e.g. Xt = 5,629,000
X, = 5,198,000
n = 10 (years)
R = 0.00799
t_
X]
1990 State low
1980 State low
A set of ten constants were then computed, five high
(Hj) and five low (L;). These can be defined for
each ten-year period as the differences between R
for the high projection (RHj) and R for the medium
(RM|), and the difference between RM; and for the low
(RLj):
H; = RH;
Li = RM:
RMj
RL:
i = 1,5
i = 1,5
These constants were then applied to each county and
city in developing the high and low projections.
RCi was computed for each county and city for each
ten-year period, using D.S.P.C.A.'s medium projections:
RC. =
For a given county or city, then, the high projections
were computed as follows:
Hi(1980)
Hi(1990)
and the low:
10
(1970 Pop!'n) (1.0 + H] + RC,)
Hi (1980) (1.0 + H2 + RC2)10. etc.
10
Lo(198o) = (1970 Popl'n) (1.0- L, + RC,)
Lo(1990) = Lo (1980) (1.0 - L2 + RC2)1°, etc.
BITUMINOUS COAL MINING
An analysis of Virginia's bituminous coal mining in-
dustry was made in Volume II —Economic Base Study of
the Tennessee and Big Sandy River Basins. Three basic
economic indicators — production, employment and pro-
ductivity — were presented. Production in the coal
industry is measured in mine tonnage and has experienc-
ed an increasing trend in Virginia since the late 19th
century. Record keeping has been quite good in this
industry and a comprehensive set of historical data^is
available from the Virginia Department of Labor and
Industry. Based on the availability and continuity
of this data, growth curve fitting and extrapolation
were selected as reasonable forecasting techniques.
Asymptotic growth curves describe a mineral industry
passing through the following stages:
1. Period of initial exploration, market development
and limited production, a phase characterized by
slow growth
2. Stage of sharply increasing production and rapid
expans ion
3- Period of relative stability where the growth
rate levels off with the main emphasis on operat-
ing efficiency and cost minimization
The three exponential curves (Gompertz, Pearl-Reed and
Modified Exponential) discussed on the above pages
were used in this analysis.
The medium range projection represented the rates of
growth believed to be the most probable. High and low
projections were also developed. These three forecasts
provided a range of data wherein certain water re-
source planning alternatives could be tested.
Basically the same approach (asymptotic growth curves)
was used to project the future low employment trend
in the coal industry. Because of the historically
declining employment series, a low range curve with a
negative trend and a lower limit was fitted and ex-
trapolated.
CURRENT PROJECTS
Recent emphasis in Virginia has been on Metropolitan/
Regional Plans to the State's Water O.uality Manage-
ment Plan. The Metropolitan/Regional Plans are being
developed for Virginia's twenty-two planning districts.
Since the planning districts are aggregations of entire
counties and cities, the data base, described above,
was arrayed and manipulated using the three-digit
county or city codes. The basic economic parameters
developed in the river basin plans, discussed above,
were also generated for the Metropolitan/Regional
Plans.
Data has recently been developed for a special water
quality management study for the lower James River
Basin. The project (The Lower James River Basin Com-
prehensive Management Study), often referred to as the
l:3c" Study, was authorized under Section 3(c) of the
1965 Federal Water Pollution Control Act. The purpose
of the 3(c) Study is to develop a viable water quality
management plan for one of the most intensively
developed sections of Virginia's largest river basin.
'^Annual Reports, Virginia Department of Labor and Industry, 1951-69
471
-------
The data assembled for the "3c" Study includes stan-
dard parameters for all industries and follows a county
and city format. Economic data for the "3cM Study
was generated in terms of a 1970 benchmark and ten-
year projections to the year 2020. Those indexes
requiring price adjustments were expressed in constant
1970 dollars.
The forecasting methodology for the "3c" Study data
generally paralleled the techniques discussed re-
garding the manufacturing data. Again, extrapolations
of "growth curves" fitted to price adjusted payroll
data were correlated to other parameters such as
employment and sales. The major exception was in a
shift from the B.L.S. Wholesale Price Index to the
B.L.S. Consumer Price Index for price adjusting his-
torical payroll data. The "3c" Study places consider-
able emphasis on "real" income of the Study area in
relation to the proposed expenditures for water quali-
ty management. Payroll data (for all industries)
price adjusted with the Consumer Price Index should
produce a fairly realistic indication of how local
income can meet expenditure recommendations. Certain
non-payroll data, however, such as manufacturing
value-added, gross manufacturing output and wholesale
trade receipts was adjusted with the Wholesale Price
Index.
CONCLUSIONS
Economic data adds an important dimension to water
resource and water quality management planning.
Payroll and employment statistics collected to ad-
minister State Unemployment Insurance programs have a
multitude of applications in economic analysis and
forecasting. U.I. data is a continuous, carefully
maintained and relatively extensive set of historical
records. It has been accumulated under national
guidelines of the U. S. Department of Labor, Manpower
Administration and is quite uniform in format. U.I.
records have, for years, been structured for data
processing applications. Further manipulation of
this data such as price adjusting and trend fitting
are thus facilitated. Most of the standard economic
parameters of water resource and water quality manage-
ment planning such as value-added and gross manufac-
turing output have been correlated to U.I. payroll
and employment benchmarks. The Annual Survey of
Manufacturing (Virginia Department of Labor and
Industry) provides value-added and gross manufactur-
ing output data. County and city detail and a data
processing format is an important feature of the
Annual Survey (S-l). Both the U.I. and S-l data have
been further formated by hydrologic area in Virginia.
On balance, the U.I. and S-l data have become valuable
tools for water resource and water quality management
planning in Virginia.
LITERATURE CITED
Tuttle, Alva M. 1957. Elementary Business and Economic Statistics. New York, N. Y,: McGraw-Hill
Book Company, Inc.
U. S. Department of Labor, Bureau of Labor Statistics, 1971. Handbook of Labor Statistics. Bulletin 1705-
Washington, D. C.
U. S. Department of Labor, Bureau of Labor Statistics, 1970. Patterns of U. S. Economic Growth. Bulletin
1672. Washington, D. C.
Virginia Department of Labor and Industry. 1951-68. Annual Reports. Richmond, Virginia.
472
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MODELING RADIATIVE TRANSFER IN THE PLANETARY BOUNDARY LAYER: PRELIMINARY RESULTS
Francis S. Binkowski, NCAA*
Meteorology and Assessment Division
Environmental Sciences Research Laboratory
Environmental Research Center
Research Trianqle Park, N.C. 27711
Abstract
Long wave radiative fluxes and cooling rates
are calculated using a statistical band model. The
vertical quadratures are sums of analytic integrals
of the transmission functions. The calculated cool-
ing rates and fluxes compare very favorably with ob-
servations. '
Introduction
The prediction of pollutant dispersion conditions
in the lower troposphere for use in air quality simu-
lation models requires information about the tempera-
ture profile, since atmospheric thermal stability
strongly influences the character of dispersion.
Thus, the problem becomes to predict the temperature
profile in a realistic way. One of the major in'flu-
ences on the temperature profile especially at night,
but also in the'late afternoon is the rate of change
of the net long wave (infrared) flux with height (or
pressure).
This paper will discuss a method for calculating
the upward, downward and net fluxes for clear skies
(no clouds) and clean air (no aerosol) cases. When
methods for treating clouds and aerosol are introduced
into the calculation method, comparisons with the
benchmark case (clear skies- clean air) as well as
with real atmospheric data will be possible.
Many methods have been proposed for calculating
these fluxes. The most flexible methods are those
which divide the terrestrial spectrum into finite
intervals and calculate the transmission of infrared
radiation within each spectral interval and sum over
the contributions of each interval. Atwater (1966),
Rodgers and Walshaw (1966), Ellingson (1972) and Fels
and Schwartzkopf (1975) have all used this method.
All these authors also used a random band model for
the transmission function. That is, the transmission
for each spectral interval was obtained by consider-
ing the absorption lines within the spectral interval
to be randomly spaced and to have intensity specified
by some probability distribution. The random band
model approach is used here as well as a transmission
function model which has a more realistic probability
distribution for water vapor (Malkmus, 1967) and has
a^simpler mathematical form than previous transmis-
sion models. This transmission function has not been
used for this purpose in the open literature before.
Since our interest is in the lower troposphere,
we shall consider only those absorbers which are most
important in this part of the atmosphere. Thus, wa-
ter vapor and carbon dioxide are the only absorbers
considered. Ozone which has a strong absorbtion band
at 9.6p, and is in the water vapor "window" of 8 to
13 p was not considered in the present work. The
quantitative effects of this ommission are unknown
* On assignment from the National Oceanic and Atmos-
pheric Administration, U.S. Department of Commerce
since real-time tropospheric ozone profiles were un-
available for the comparisons discussed below. Quali-
tatively, the most important effect of ignoring ozone
is that the downward flux at the surface is smaller
than it would be if ozone were considered. Ozone will
be added in future calculations. All other gases pres-
ent in trace amounts are also ignored. As mentioned
previously, the band model approach used here is flexi-
ble enough to permit additional absorbers to be treat-
ed relatively easily. Other absorbers will be consid-
ered when it becomes apparent from comparison with
measurements that it's necessary to include them.
Method of Calculation
We start with the equation of radiative transfer
in integrated form is given by Rodgers and Walshaw
(1966)(with slight modification,^
+F(z)=B(z)+{+F(H)-B(H)}T(U.
KF(z)=B(zM+F(g)-B(0)}T(Ub)+
^,(u')T(u')du' (la)
Sr,(u')T(u')du' (Ib)
where for each spectral interval +F(z), tF(z) and
B(z) are respectively the downward, upward and black-
body fluxes at the reference level z and +F(H), +F(g)
and B(0) are respectively, the downward flux at the
top of the computational domain H, the upward flux at
the ground, g, and the blackbody flux at the bottom of
the atmosphere. The definite integrals are taken over
the amount of absorber (water vapor) u' between z and
levels above z in (la) and between z and levels be-
neath z in (Ib). The total absorber amounts from z
to H and from z to the ground are U£ and U. respec-
tively. The transmission function T(u') is defined
such that T(0) 1 and T-K) as u'->-<». The integral
I
f (ul)T(u')du'
Jo
may be written without approximation as the sum
! -V C 'dBdi1:
where U, which may represent U. or U. has been di-
vided into n increments Ausu. - u._,. If we rep-
resent dB(u')/du' by an average value for each in-
crement of Au such that
then
dB_
du1
B(U,;
B(u. .)
l-l
AU
= AB
AU
(2)
Both of the definite integrals in (1) may be ap-
proximated in this way. This approximation of dB/du'
by AB/Au is strictly valid only when B varies linearly
over u'. In practice only discrete values of B and u'
are available, either from radiosonde measurements in
the atmosphere or from grid point calculations. The
473
-------
approximation in (2) says that between these discrete
values B varies linearly with u1. This is the sim-
plest approximation which allows B to vary between
levels. This may be viewed as a next step from con-
sidering an isothermal slab between the discrete
points. The approximation is invoked in order to ob-
tain the form (2) which contains the integral of the
transmission function, T, over absorber amount u1. If
the precise form of T specified is analytically inte-
grable, then the definite integrals in (1a,b) may be
given by simple sums.
We shall use the transmission function of MaVkmus
(1967) discussed by Rodgers (1967):
T(u')= exp{-a(l+bu1)'i+a}
(3a)
which may be integrated as
f T(u')du'= 2a'V2{(Yra-1)exp(Yi)-(Yi_.-a-l
i)} (3b)
where Y.= -a(l+bu.)2 +a, and the parameters a and b
to be discussed below, are held constant. Thus the
approximation dB/du' by AB/Au, combined with (3b) in-
dicates a simple efficient computation scheme.
The band parameters a and b are defined by (Rod-
gers, 1967) as
4k
irap
or for notational convenience
a = ap ,
where k, a, and & are respective by average line in-
tensity, half width (at one atmosphere) and line spac-
ing which are representative of the spectral interval
considered; and P is an average pressure (discussed
below) for the layer defined by Au. The expressions
a, 6 may be obtained from the wave length, half width
and intensity of individual spectral lines within each
interval. Rodgers and Walshaw (1966) discuss the use
of line data for determining a, 6, and also recommend
the use^of the Curtis-Godson approximation to correct
the a, b for changes in temperature and pressure
along an atmospheric path. This approximation defines
a corrected absorber amount u, and a mean pressure V
between two levels say i, j as:
P.
dp_
J r !•
E h
£=i J H-1
1.66 r
.-1
*
oo
(5a)
(5b)
where r is the mixing ratio, P is pressure, P is
101.325 kPa and 1.66 is the diffusivity factor°for cal-
culating the diffuse fluxes from beam transmission
functions (Armstrong, 1969; Ellingson, 1972). The
* and o> functions are obtained by calculating values
of a, b at three temperature values and fitting empir-
ical functions of the form (Rodgers and Walshaw.
1966):
)= exp{A(e-e
= exp{A'(e-e
B(e-
}
(6a)
(6b)
This representation recovers values of a, 6 with-
in the temperature range considered with a relative
error of 1% or less. The line data of McClatchey et.
al., (1973) were used to calculate a,6,A',B' with a
reference temperature e of 275K. With values of A,
B, A1, B' (6) may be used in (5) to evaluate_the cor-
rected absorber amount u, and mean pressure p. Then,
if the corrected absorber amount is_ used as the vari-
able of integration in (3b), with p constant for each
layer, a and b are constant for the integration. The
temperature and pressure effects,^are included in the
AB/Au term through the factor 2a~ b in (3b), thus
AU is an increment of corrected absorber amount. The
six calculated band parameters were favorably compared
with Rodgers and Walshaw (1966) for consistency where
possible. The line data of McClatchey et.al., how-
ever, includes information which was not available to
Rodgers and Walshaw (1966). This procedure was used
to calculate the transmission function for water vapor
for intervals from 0-760cm and 1200-2500cm .
The 8-13p window was treated differently. The
absorption in this spectral region is of somewhat dif-
ferent character than that treated previously. The
absorption appears as a "continuum" (Bignall, 1970),
that is a region of nearly constant absorption. The
transmission function may be given as
T= exp{-Kstl}
where K is a constant and u is a corrected absorber
amount aefined as
•i " ^
--— f 1.66(0.005P + 0.995e) * r ^2-
where the pressure, p, term represents the broadening
of the individual lines by collision with other species,
and the water vapor pressure, e, term represents self
broadening by water vapor (Bignall, 1970; McClatchey
et.al., 1972). The temperature correction term
4> exp{l745/6 5.90}
is an empirical correction term due to Lee (1973).
When corrected absorber amount u is used as a variable
of integration, this transmission function may be
analytically integrated. This transmission function
and its integral were used for the two intervals 760-
1000cm'1 and 1000-1200cm''.
Carbon dioxide is treated in a highly parameter-
ized way. For one spectral interval 560-760cm~l,
which includes the entire 15p CO^ band an empirical
transmission function due to Rodgers and Walshaw
(1966) is used. This transmission function, T(c), is
also integrable in terms of the carbon dioxide amount
c. The overlap of C02 and water vapor for the one
spectral interval 560-760cm is treated by calculat-
ing a mean transmission T given by
T =
T(c) dc
where C, is the carbon dioxide amount at the same lev-
el as U,. The water vapor Iransmission functions in
(3) are then multiplied by T in the integrals and by
T(C) where C is the total C02 above or beneath z as
appropriate. This parameterization is used for two
reasons: first, it seems to yield good results in com-
parisons with cases when no CO^ is used; second, it is
simple, efficient, and economical compared with a more
comprehensive scheme such as used by Pels and Schwartz-
kopf (1975) in which a detailed line by line integra-
tion is used. A band model approach for COp such as
used by Ellingson(1972) is quite costly since he used
15 intervals for the C02 alone and the present model
474
-------
only considers 12 intervals in total.
Planck functions, B, were calculated by a Gauss-
Laguerre numerical quadrature scheme due to Johnson
and Branstetter (1974). A simple 5 point formulation
gave 6 decimal place accuracy, which is certainly suf-
ficiently accurate for the present needs. This is to
be contrasted with the 96 point Gaussian quadrature
of Ellingson (1972) which also gave 6 place accuracy.
As mentioned above, 12 intervals were used. This
is to be compared with 20 intervals used by Rodgers
and Walshaw (1966); 125 intervals used by Atwater
(1966) and 100 intervals used by Ellingson (1972).
Calculations with as many as 18 intervals were indis-
tinguishable from calculations with 12 intervals, but
calculations with 7 intervals were markedly poorer,
especially in the calculated cooling rates as com-
pared with observed cooling rates. Only results from
the 12 interval model will be presented here.
Equations (la,b) together with approximations
(2a,b) and the appropriate transmission functions are
used to calculate the upward and downward fluxes.
The downward flux at the top is taken to be blackbody
flux times an emissivity of 0.01 which gives the right
order of magnitude for the downward flux at 20 kPa.
The bottom surface, at present, is taken to have an
emissivity of 1.0. The cooling rates are obtained
from the divergence of the net flux, that is
31- J_ !!n _l!!n
3t pC 3Z C 3p
where F is the net flux (F = tF 4-F). At present,
the vertical p-derivative is approximated by a finite
difference.
Results of Validation Calculations
four values are significant at the 5% level. The low-
est three altitudes of downward flux and the lowest
value of the net flux. The relative error for the
downward flux are of the order of 8%, while the rela-
tive error of the net flux is quite large because of
the small value of the flux.
We may compare these errors to the differences
that exist among simultaneous measurements. Gille and
Kuhn (1973) show comparisons of the U.S. radiometer-
sonde with a German and a Japanese instrument. For
the 90 kPa altitude there was a 2% difference in down-
ward flux between the U.S. measurement and the mean of
all three (U.S., German, Japanese), which is signifi-
cant at the 5% level. Further the model calculations
of Ellingson used by Gille and Kuhn showed an under-
estimate of the order of 5% for the same altitudes.
These differences are also significant at the 5% level
(t^4.0). Gille and Kuhn also give some tentative evi-
dence of a systematic overestimate of downward flux
and systematic underestimate of net flux by the U.S.
radiometer-sonde when compared with surface measure-
ments from a Linke-Feussner instrument. Thus the er-
rors, that is, differences between the observed and
calculated fluxes, taken on a case by case basis are
real and significant, but of the same order of magni-
tude as differences among radiometer-sondes, and of
the same order of magnitude as other calculations.
The cooling rate differences show no significant
difference at the 5% level between calculations and
measurements. This is encouraging, since the cooling
rate is the dynamical variable needed for prediction
of the temperature profile.
Conclusions
To assess the validity of the method of calcula-
tion the clear skies measurements discussed by Gille
and Kuhn (1973) were used for comparison with calcula-
tions presented here. Temperature and mixing ratio
at 5 kPa (50mb) increments from 100 to 20 kPa were
used as input data. Upward, downward and net fluxes
were calculated at the input levels and compared with
the in situ measurements of Gille and Kuhn. Results
of this comparison are shown in Figure 1. The in situ
data shown are from over water ascents of the U.S.
Radiometer-sonde in the vicinity of Panama on four
clear skies evenings (OOOOGMT +_ 20 minutes). Figure
1 displays the means of the measurements and the means
of the calculations for the upward, downward and net
calculations, while Figure 2 displays the means of the
measured and calculated cooling rates. Visual inspec-
tion of the figures indicates a good correspondence
between observations and calculations. Table 1 shows
"student t" values (Weatherburn, 1961) for the com-
parison of these means. The table indicates that for
5% significance level with 3 degrees of freedom
(t=3.18) the means do not differ for any of the fluxes or
cooling rates. The interpretation is that a set of
sample calculations is indistinguishable from a set
of measurements. This is consistent with the findings
of Gille and Kuhn (1973) who used results of Elling-
son's (1972) model for calculations.
A somewhat more demanding test of model perform-
ance is a comparison of case by case predictions for
the clear skies cases. The relative error of the
calculation compared with the observation, (OBSERVED-
CALCULATED)/OBSERVED, for each case was calculated and
averaged. A perfect model would have this average
relative error equal to zero. The "t" values for this
comparison are displayed in Table 2, where we see that
The 12 interval model presented here is capable
of calculating useful estimates of the upward, down-
ward and net fluxes and cooling rates in the lower
troposphere for the clear skies, clean air case.
Acknowledgements
The author wishes to thank his colleagues Dr. J.
T. Peterson, Dr. J. H. Shreffler, and Dr. J. K. S.
Ching for their comments, criticisms, and suggestions.
He also wishes to thank his supervisor Dr. K. L.
Demerjian for his encouragement and support.
References
Armstrong, B.H., 1969: The Radiative Diffusivity Fac-
tor for the Random Malkmus Band. J_. Atmos. Sci., 26,
741-743.
Atwater, M.A., 1966: Comparison of Numerical Methods
for Computing Radiative Temperature Changes in the
Atmospheric Boundary Layer. J. Appl. Meteor. (5) 824-
831. ~
Signal!, K.J., 1970: The Water-Vapor Infra-Red Con-
tinuum. Quart. J_. £. Meteor. Soc_., 96, 390-403.
Ellingson, R.G., 1972. A New Longwave Radiative Trans-
fer Model: Calibration and Application to the Tropi-
cal Atmosphere. Dept. of Meteorology. Florida State
University. Report 72-4 June 1972. 348 pp.
Pels, S.B., and M.D. Schwartzkopf, 1975: The Simpli-
fied Exchange Approximation: A New Method for Radia-
tive Transfer Calculations. J_. Atmos. Sci., 32, 1474-
1488.
Gille, J.C. and P.M. Kuhn, 1973. The International
Radiometersonde Intercomparison Programme (1970-1971).
475
-------
WMO Tech. note. No. 128 Geneva.
Goldman, A. and T.G. Kyle, 1968: A Comparison Be-
tween Statistical Model and Line Calculation With Ap-
plication to the 9.6y Ozone and 2.7y Water Vapor
Bands. Appl. Optics, 7, 1167-1177.
Johnson, R.B. and E.E. Branstetter; 1974: Integration
of Planck's Equation by the Laguerre-Gauss Quadrature
Method. J_. Optical Soc. of America., 64, 1445-1449.
Lee, A.C.L., 1973: A Study of the Continuum Absorp-
tion Within the 8-13y Atmospheric Window. Quart. J_.R_.
Meteor. Soc., 99, 490-505.
Malkmus, W., 1967: Random Lorentz Band Model with
Exponential-Tailed S Line Intensity Distribution
Function. J_. Optical Soc. America, 57, 323-329.
McClatchey, R.A., W.S. Benedict, S.A. Clough, D.E.
Burch, R.F. Calfee, K. Fox, L.S. Rothman, J.S. Garing,
1973: AFCRL Atmospheric Absorption Line Parameter
Compilation. AFCRLTR-72-0096 23 January 1973
Environmental Research Paper No. 434. Air Force Cam-
bridge Research Laboratories, L.G. Hanscom Field, Bed-
ford, Massachusetts. 78 pp.
Rodgers, C.D., 1968. Some Extensions and Applications
of the New Random Model for Molecular Band Transmis-
sion. Quart. J_.j*. Meteor. Soc.. 94, 99-102.
Rodgers, C.D. and C.D. Walshaw, 1966: The Computation
of Infrared Cooling Rate in Planetary Atmospheres.
Quart. J_.Ji. Meteor. Soc., 92, 67-92.
Weatherburn, C.E., 1961: A First Course in Mathemati-
cal Statistics, Cambridge University Press. 277 pp.
The t values for comparison of mean of calculations
with iwan of measurements for upward, downward, and
net fluxes and the cooling rates.
Pressure
(kPa)
100
90
80
70
60
50
40
30
20
Upward
0.35
2.47
1.81
1.73
1.82
1.65
1.25
0.58
0.35
Downward
2.21
1.84
1.27
1.36
0.47
0.68
0.55
0.22
0.29
Net
-3.04
-1.29
-0.99
-0.97
-0:66
-0.26
0.05
-0.27
0.61
Cooling r;
1.52
0.06
0.28
0.71
0.91
0.62
1.13
0.95
1.89
Negative value indicate an over-estimate in the calculations.
TABLE 2
The t values for relative error of calculation
Pressure
(kPa)
100
70
60
50
40
30
20
Upward
1.09
3.00
3.02
1.56
1.86
1.81
1.39
0.81
0.60
with measurements on a
r upward, downward, and
ing rates.
)ownward
6.55*
5.56*
3.96*
2.69
1.91
0.84
0.88
0.20
-1.78
Net
-3.83*
-2.35
-1.69
-1.81
-1.16
-0.68
-0.08
0.35
0.93
case by case
net fluxes ai
Cooling ral
1.25
-0.44
0.05
0.47
0.29
-1.17
1.33
1.11
-0.09
* Significant at the 5% confidence levels for 3 degrees of
freedom. t= 3.18
476
-------
X Measurements
• Calculations
30
43
50
60
SO
90
100
0 100 200 300 400 500
DO'.iN'.iARD FLUX (UM~2)
I
200 300 400 500
UPWARD FLUX (HH~2)
0 100 200 300
NET FLUX (WM"2)
Figure 1 : Comparison of mean measured with mean
calculated fluxes for upward, downward,
and net fluxes.
X Measurements
. Calculations
20
30
40
50
60
70
80
90
100
V
\
X
*
A
A
\
\ .
.
012345
COOLING RATE ( K DAY "')
Figure 2 : Comparison of mean measured and mean
calculated cooling rates.
477
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ADAPTIVE FORECASTING OF BACKGROUND CONCENTRATIONS USING FEEDBACK CONTROL AND PATTERN RECOGNITION TECHNIQUES
R. Carbone
Academic Faculty of Management Sciences
The Ohio State University
Columbus, Ohio
W.L. Gorr
School of Public Administration
The Ohio State University
Columbus, Ohio
Abstract
This paper develops and tests an empirically-based
model for tracking and forecasting background concen-
trations of air pollutants. A set of variables (e.g.,
meteorological, locational, economic activity levels,
etc.) and a functional form relating the variables con-
stitute the model. The technique for estimating the
parameters of the model is derived from recent develop-
ments in adaptive feedback and pattern recognition.
Time-varying characteristics of the parameters are
"tracted"; and thus, automatically adapted to structural
changes in the air pollution system. The model and
estimation technique are applied to total suspended
particulates background in Allegheny County,
Pennsylvania, as a pilot test.
1. Introduction
The clean air program for attainment and mainte-
nance of air quality standards (AQS's) has given rise
to a number of modeling requirements for the time se-
ries of pollutant concentrations. (See Rhoads [1] for
a concise review of programs.) Program planning for
regulation of pollutant emissions, capacity expansion,
facilities location etc. requires models relating con-
trol variables to the controllable component of air
quality. These models are common; see for example [2],
[3], and [4]. In addition, it is necessary to model
the uncontrollable component in order to obtain total
or ambient concentrations. Planning tends to involve
special, "once only" studies in a decision process that
yields a regulated time series of concentrations de-
signed to fall within target levels.
Program evaluation of plans and their implementa-
tion requires, on the other hand, routine modeling of
the time series for tracking, detection of disparities
with targeted levels, diagnosis of cause, and correc-
tion. Large numbers of variables and massive quanti-
ties of data are involved in the clean air program so
that a staged modeling approach is desirable with the
early stages being automated and suggestive of the lat-
er, specialized stages.
Tracking models should provide robust and up-to-
date estimates of ambient concentrations so that sig-
nificant changes can be detected. Such models may also
form the basis for simple forecasts through extrapola-
tions of the tracked time series. If there is a dis-
parity between current or forecasted concentrations and
targeted levels, then it is required to advance to a
second stage of automated modeling for preliminary di-
agnostics.
First, tracking and forecasting should be extended
to separate the controllable and uncontrollable compo-
nents of the time series to determine which is the
problem. Second, a sufficient number of explanatory
variables (e.g., meteorological, economic activity lev-
el, regulatory activity level etc.) should be correlat-
ed to concentrations through multivariate statistical
models so that analysts can theorize as to the causes
of the problem. From this basis, analysts could pro-
ceed if necessary to a third stage of analysis which
would be non-routine and involve further measurements
experiments, or other special studies. The results of
diagnostic work would serve the decision process for
modifications of plans or targets.
This paper presents an approach, the adaptive
statistical diffusion model (ASDM), which is promising
for many of the program requirements outlined above.
The ASDM is a. multivariate time series model based on
a "time-varying parameters'1 principle and feedback es-
timation procedures leading to a highly flexible and
automated modeling capability. Section 2 formulates
the ASDM and its estimation procedure, and Section 3
provides program applications. Sections A and 5 give
a specific application to total suspended particulates
(TSP) background in Allegheny County (Pittsburgh),
Pennsylvania. Finally, Section 6 outlines future work.
2. Adaptive Estimation and Forecasting of Pollutant
Concentration Over Time: a General Approach
2.1 Model Formulation
The ASDM consists of a set of explanatory vari-
ables and time-varying parameters combined in a func-
tional, form for pollutant concentrations. An impor-
tant aspect of the ASDM is that all parameters are as-
sumed to be time-varying, and in the estimation proce-
dure discussed below, parameter estimates are updated
sequentially as each observation of the explanatory
variables occurs. This leads to the potential for au-
tomatically capturing the effects on concentration of
missing variables and system structural changes. For
example, suppose an air pollution source to the west
of a concentration monitor has major impacts on the
monitor, but pollutant emission strength is a missing
variable. If wind direction (from which the wind
blows) sectors are represented by a set of indicator
variables, then the time-varying parameter for the
variable "west" might account for effects on concen-
tration of trends or cycles in emissions.
The explanatory variables can be arbitrarily
classified as "quantitative" which refers to dimen-
sioned qualities such as wind speed, or "qualitative"'
which leads to 0/1 indicators for nominal classes of
the qualitative variable; e.g., north, east, south,
and west for wind direction; no, mild, and heavy for
precipitation. A general first-order equation pre-
sented in [6] portrays a useful interaction phenomenon
between quantitative and qualitative variables in a
time-varying framework. Applied to the air pollution
problem, this becomes the ASDM:
y(t) = n a±(t)
1=1
2 . (t)
[ I 3 (t)x (t)] +
u(t)
(1)
1,2,...
where a. specific averaging time, pollutant spe-
cies, and point p in geographic region R are as-
sumed; and
y(t) = pollutant concentration at time t,
z.(t) = the i-th qualitative indicator which
takes values of 0 or 1 depending on
478
-------
whether or not the i-th nominal class
occurs at t,
= the parameter for the t-th observa-
tion associated with the i-th quali-
tative indicator,
x.(t) = the t-th observation for the j-th
quantitative variable,
B.(t) = the parameter for the t-th observa-
tion associated with the j-th quanti-
tative variable, and
u(t) = an undefined error term.
ai(t)
A normalization process is employed for the quali-
tative variables: one nominal class, a "z.(t)" indica-
tor, is suppressed in the ASDM for each qualitative
variable; e.g., "north" for wind direction and "no pre-
cipitation" for precipitation. The collection of sup-
pressed nominal classes for all qualitative variables
becomes the "standard" qualitative condition. An ob-
servation of this standard would then result in the
value of 0 for all remaining, non-standard z.(t)'s in
the product portion of the ASDM. Thus the product
would take the value 1 and the ASDM for the standard
condition would simply be:
y(t)
g.(t)x.(t)
u(t)
(2)
Observations with non-standard conditions result in a
product greater or less than 1 reflecting the relative
effect on the standard concentration model as in (2).
2.2 Estimation Algorithm
Our purpose is to obtain updated estimates of the
a(t) and 6(t) parameters for each observation in order
to capture and track the changing effects of the vari-
ables on concentration. Due to the nature of our prob-
lem, the algorithm used should possess certain desir-
able properties:
a. It should be designed to minimize over-reac-
tions to pollutant measurement and other tran-
sient errors, and thus, provide robust estima-
tors.
b. Estimates of the parameters should be updated
without requiring any a priori knowledge of
the kind of processes which may govern their
time variation. This aspect is crucial since
changes in uncontrollable conditions that may
occur in the future are seldom known or accu-
rately predicted in advance.
c. From an operational point of view, the high
rate of observations occurring over time re-
quires the use of an algorithm which involves
sequential processing of information as op-
posed to batch processing. It should be com-
putationally tractable and implementable on
widely available computers.
An approximation method for estimating time-vary-
ing parameters, Adaptive Estimation Procedure (AEP),
recently developed by Carbone and Longini, see [5] and
[6], lends itself to the nature of our formulation and
problem. In this methodology, robust time-varying es-
timators are generated without using any a priori know-
ledge by recursively updating values via the following
two formulas:
e..(t) =
and
+ |B. (t-i)
V(t) - y(t) x (t)
y(t)
for all j
(3)
a±(t-l)
TZ\ W
for all i = l,...,n
where
y(t) predicted concentration for time t
based on B(t-l) and a(t-l) estimators,
D = damping parameter > 1,
S, = the number of qualitative variables (or
groups of nominal indicator variables) ,
and
x.(t) = updated average for the j-th quanti-
-1 tative variable.
An exponential smoothing scheme is used to calculate
this latter average as follows :
x = S0x (t) + (l-S0)x (t-1)
where 0 < SQ < 1
3. Applications
The problem of attainment and maintenance of AQS's
is to determine values of control variables (e.g., fuel
quality, emission-control-device efficiences, stack
heights, etc.) affecting the controllable component of
concentration, C (t), so that
Ap(t)
C (t) + B (t) < 6 (t) for all p in R (5)
P P P
where A (t) = total or ambient concentration aver-
aged over a period of specified
length (e.g., a year) ending at t,
C (t) = controllable component,
B (t) = background component, and
Sp(t>
AQS.
In order to calculate estimates or forecasts of A (t)
P
and its components, it is necessary to average the ASDM
estimate, y(t), over the relevant period by calculating
simple averages, or by developing a joint probability
distribution of all explanatory variables for calculat-
ing expected values as done in [2] and [3]. Several
approaches have been used or proposed for constraints
(5); from maximum technically feasible controls [7], to
satisficing with some tradeoffs in cost versus air
quality achievement [8], and to cost-effectiveness [9],
[10].
An estimate, A (t), of ambient concentration is
P
obtainable through samples at any p through the ASDM.
For remote regions, R , with no significant controll-
able sources of pollutants, it is reasonable to assume
that concentration is uniform over p but not t; i.e.,
Ap(t)
A ^(t) for all p in R
(6)
where p* is the location of any properly mounted moni-
479
-------
tor in R . It is also common to assume that model (6)
r
provides an estimate for background concentration oc-
curring in developed or urban regions R (see [11]):
B (t) = A . (t) for all q in R
(7)
Thus the ASDM has direct use for tracking, forecasting,
and diagnosing concentrations through models (6) and
(7) using concentration samples from p*.
For attainment, the federal AQS's are a constant
over p and t; i.e., S (t) = 6. However, proposals for
maintenance of air quality have the following defini-
tion [12]:
6 (t) = A (1974) + y (t)
P P P
(8)
where y (t) is a specified series of allowable incre-
ments of degradation of air quality. If the region is
rural, then model (6) suffices for S (t). If the set
of urban monitoring sites is extensive or representa-
tive of air quality, then A (t) as modeled by the ASDM
for all available monitoring sites may be sufficient
for 6 (t). I
P
toring sites.
for 6 (t). Interpolation may be required between moni-
Background concentration is often estimated as the
concentration advected into R as sampled by "back-
ground monitors" located at the boundaries of R ; see,
for example, Pooler [13], Rubin and Bloom [14], and
Samson e_t a^. [15], Here the ASDM extends the concept
of a pollution rose (see Munn [16]) where background is
identified by the wind directions corresponding to ad-
vection into R . Sections 4 and 5 develop the ASDM
background model in detail; where for example, one mod-
el is
B (t) = BdA(t) for all p in R
(9)
where d* represents a dummy site. This "site" is a
composite of all background monitor sites such that
only samples from wind directions corresponding to ad-
vection are utilized.
For program evaluation purposes, it is possible to
estimate the controllable, or more accurately, the lo-
cal component of concentration by difference:
cp(t)
Ap(t) - Bp(t)
(10)
where Ap(t) and B (t) are estimated by the ASDM ap-
proach. In this way, tracking and forecasting may re-
veal the effects of controls by separating out back-
ground.
4. A Demonstration
We now focus our attention on an empirical study
to demonstrate and test out the ASDM approach. The
study is mainly directed at forecasting and tracking
changes in total suspended partlculate (TSP) background
concentration over time in Allegheny County, Pennsyl-
vania. It involves the analysis of some 800 observa-
tions of daily average particulate concentration re-
corded from 1970 to 1975 at two monitors located at op-
posite boundaries of the county. The location of the
two "background" monitors chosen and surrounding major
point sources is found in a map of the county presented
In Figure 1.
In addition to daily average particulate concen-
tration monitored (by hi-vol) by the Allegheny County
Bureau of Air Pollution Control, six variables were
used in the study to reflect meteorological and struc-
tural conditions. They are the 24 hour resultant wind
direction, average wind speed, precipitation, inver-
sion; and finally, two factors reflecting general ac-
tivity level, weekend or weekday and cooling or heating
day. Information on these various conditions for each
observation were obtained from the U.S. Department of
Commerce, Local"GliTuatblogl'cal data for the Greater
Pittsburgh Airport and the Denardo & McFarland Weather
Services, West Mifflin, Pennsylvania.
The next task was to determine how to enter the
variables into the ASDM structure. Both inversion and
wind speed were defined as quantitative aspects; where-
as, the remaining were considered as qualitative.
Here, only a ground level inversion of strength greater
than 2 C determined an inversion, which corresponds to
air-pollution-emergency "watch" conditions in Allegheny
County. Also, the inverse of average wind speed was
the measure utilized. Wind direction was broken down
into eight classes (0-45 degrees, 45-90 and so on) and
precipitation into four (no precipitation; low, 0-.10
inches; mild, .10-.35 inches; and heavy, .35 and over).
Having identified the predictors and how to incorporate
them, the study then proceeded according to the follow-
ing steps.
step !_: a third input file, herein referred to as Mon-
itor III, containing only observations with
background wind directions (315-360 and 0-135
degrees for Monitor I and 135-315 degrees for
Monitor II) was created.
step 2: AEP was applied to the three sets of input da-
ta in the following way.
a. The initial value for all the parameters
was set equal to 1.
b. A standard qualitative condition was de-
fined as weekend, cooling day, 315-360 de-
grees resultant wind direction, and no
precipitation. This implies that the pa-
rameters associated with these character-
istics were held equal to 1 when running
the procedure.
c. SQ = .04 was used for updating mean values
for the quantitative aspects.
d. A dampling parameter of D = 50 was ini-
tially assumed and subsequently readjusted
(?) FUEL COMBUSTION
(?) INDUSTRIAL PROCESS
© MASS EMISSION RATE OF LARGE
POINT SOURCES, Q TOKS/DAY
Figure 1. Major Partlculate Source
Monltora.
in Allegheny County add Background
480
-------
via a recycling procedure (see 16]). The
recycling of the observations was neces-
sary here because of the small number of
observations over the years covered (370
for Monitor I, 410 for Monitor II, and All
for Monitor III), so as to converge to ex-
perienced patterns of change.
5. Results
Some descriptive measures of predictive perform-
ance of ASDM are presented in Table 1. The measures
contained in the table are first, average actual (AC)
and predicted (PC) concentration, and also their stan-
dard deviations, (SAC) and (SCP). The table further
contains the root mean square prediction error (RMSPE),
the simple correlation coefficient (r) between pre-
dicted and observed values, the mean absolute percent-
age deviation (MAPD), and the serial correlation coef-
ficient (p) of a first-order autoregressive scheme.
By carefully examining Table 1, we observe that
the results are promising in terms of the RMSPE, r, and
MAPD; and comparable to diffusion modeling results of
others (see for example, Slade [17] p. 142, McCollister
and Wilson [18], and Bankoff and Hanzevack [19]). The
ASDM results have little or no error in central tenden-
cy detected; and also, we note no evidence of first-or-
der serial correlation in our results for the three
monitors. What may appear somewhat disturbing is that
the standard deviation of the predicted concentrations
Table 1
Some Descriptive Measures of ASDM Performances
AC
PC
SAC
SPC
HMSPE
r
MAPD
P
I
86.81
88.10
43.34
32.98
33.49
.6458
34.33
-.124
Monitors
II
67.35
69.64
36.26
21.94
32.65
.4622
33.97
.020
III
65.74
66.95
35.68
18.83
32.64
.4194
35.77
-.001
is consistently smaller than for the observed values.
However, it can easily be argued that because of the
expected large measurement errors present in TSP data,
the spread of true concentration should be smaller than
that of observed concentration. The AEP is specifical-
ly designed to track true measurements (see [6]) rather
than observed values.
Table 2 presents ASDM parameter estimates for Mon-
itor I at two points in time—the start and end of the
five year study period. Attention is focused on this
monitor since it has had the greatest degree of time-
variation in the parameter estimates. The values in
Table 2 give results as theoretically expected; for ex-
ample, the results reveal that concentration on a week-
day is about 24% greater than on weekends at the begin-
ning of the period and 12% at the end which provides
some measure of the general effectiveness of control
policies; that a low precipitation level reduces con-
centration by approximately 12% in contrast to no pre-
cipitation over the period; that a resultant wind di-
rection from the major point sources (225-270 degrees)
located next to the monitor (see Figure 1) leads to
about 79% greater concentration than the standard di-
rection assumed which Is of a background nature; and
that total concentration given the standard qualitative
condition assumed for no-inversion-high-wlnd-speed days
decreased from 68 ug/m3 to 50 pg/m3.
A value of 35 pgm/m3 annual geometric mean for TSP
background was assumed for Allegheny County in the 1971
state implementation plan. More recently, the U.S. EPA
assumed a 1972 value of 30 ugm/m3 falling to 20 ygm/m3
between 1975 and 1980; and Rubin and Bloom [14] esti-
mated 45 to 50 ygm/m3 based on a pollution rose of
Monitor II (1971-72). Thus, TSP background has been
found to be a significantly large component of ambient
TSP air quality in Allegheny County. Our estimates
show, however, that the background component is even
larger than in the previous estimates.
Figure 2 presents two plots of expected total con-
centration using Monitor III weights (background moni-
tor) . The plots presented illustrate the acute TSP
background problem in Allegheny County: under the con-
Table 2
ASDM Parameter Estimates for Monitor I: Start and End of Period.
Variables
Degree Day
Heating
Cooling
Day
Weekend
Weekday
Precipitation
None
Low
Mild
Heavy
Percent
or
Mean Value
Parameter Estimate
Start End
Variables
Percent
or
Mean Value
Parameter Estimate
Start End
Wind Direction
28.
71.
26.
73.
43.
20.
15.
10.
3.1
89
22
78
51
27
95
27
0.859
1.000
1.000
1.249
1.000
0.881
0.841
0.926
0.
1.
1.
1.
1.
0.
0.
0.
842
000
000
127
000
855
813
907
00
45
90 -
135 -
180 -
225 -
270 -
315 -
Wind Speed"
Inversion
Constant
45
90
135
180
225
270
315
360
1
4.
5.
8.
7.
10.
34.
17.
12.
0.
30.
1.
05
41
65
57
27
32
30
43
12
00
00
0.760
0.931
0.845
1.342
1.539
1.796
1.410
1.000
53.08
7.98
67.59
0.744
0.931
0.853
1.259
1.576
1.773
1.328
1.000
46.79
18.57
49.91
481
-------
DQ. 00 65. 00 170.00 ?S5.00 3WO.00 42S.00
Observation Serial Nunber
Figure 2(fi), Wind Direction fran (MS*.
°O.OD " 65.00 170.00 e«.OD 34D.OO 4ZS.OD
Observation Ferial Xxrbcr
Figure 2(b). Wind Direction From 225-270*.
rre 2. /SD-I TUB Set ic<; of TSr Concentration for 'fonitor III and tlic
Omditions; ttoolinc, Kccldaj , No IVccipJiEitaon, No Inversion,
and 10 niilcs/luwr Wind Speed.
ditions specified, there is a nearly constant trend of
high background concentration. This observation is
consistent with the fact that the updated mean TSP
background over all conditions computed via an exponen-
tial smoothing scheme varied from 75 ygm/m3 at the be-
ginning of the period to 68 ygm/m3 at the end. It ap-
pears, from current evidence, that attainment of the
federal secondary annual TSP standard of 60 ygm/m3 is
impossible regardless of local control policies.
6. Future Work
It is desirable to model a pollutant sampled more
frequently and with a short averaging time than the
case in this paper. It appears that a 24 hour averag-
ing time provides overly aggregated data with respect
to variation in the underlying phenomenon. In future
work, it is also desirable to further investigate the
functional form used in the ASDM; e.g., as to which
variables should be multiplicative, transformed etc.
Finally, we wish to pursue the relationship of adaptive
modeling to the decision framework of the clean air
program, and to determine the requirements of the de-
cision maker.
1.
2.
3.
4.
References
Ehoads, R.G. , "The Nationwide Program for Mainte-
nance of Air Quality," JAPCA. Vol. 25 (1975). pp
1203-1206. -
National Air Pollution Control Administration, Air
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PH-22-68-60, 1969.
Busse, A.D. and J.R. Zimmerman, User's Guide for
the Climatological Dispersion Model. NTIS Report
No. EPA-R4-73-024, Wash., D.C., 1973,,
Gifford, F.A. and S.R. Hanna, "Modeling Urban Air
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5. Carbone, R., "The Design of an Automated Mass-Ap-
praisal System Using Feedback," unpublished Ph.D.
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6. Carbone, R. and R.L. Longini, "An Adaptive Sto-
chastic Approximation Algorithm for Estimating
Time-Varying Parameters," Administrative Science,
Ohio State Univ. Paper WPS 75-56 (1975).
7. Sussman, V.H., "A Critique: New Priorities in Air
Pollution Control," JAPCA. Vol. 21 (1971), pp.
201-203.
8. Dunlap, R.W., W.L. Gorr, and M.J. Massey, "Desul-
furization of Coke Oven Gas: Technology, Econo-
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The Steel Industry and the Environment, Marcel
Dekker, N.Y., 1973.
9. Kohn, R.E., "Application of Linear Programming to
a Controversy on Air Pollution Control," Manage-
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10. Gorr, W.L., S.A. Gustafson, and K.O. Kortanek,
"Optimal Control Strategies for Air Quality Stand-
ards and Regulatory Policy," Environment and Plan-
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11. Environmental Protection Agency, "Guidelines for
Air Quality Maintenance Planning and Analysis Vol-
ume 12," EPA-450/4-74-013, Research Triangle Park,
N.C., 1974.
12. Federal Register, "Maintenance of National Ambient
Air Quality Standards," Vol. 40 (203): 49048
(Oct. 20, 1975).
13. Pooler, F. Jr., "Network Requirements for the St.
Louis Regional Air Pollution Study," JAPCA, Vol.
24 (1974), pp. 228-231.
14. Rubin, E.S. and H.T. Bloom, "Maintenance of Ambi-
ent Particulate Standards in an Industrialized Re-
tion," 68th Annual Meeting of the Air Pollution
Control Association, Boston, Mass. (June, 1975).
15. Samson, P.J., G. Neighmond, and A.J. Yencha, "The
Transport of Suspended Particulates as a Function
of Wind Direction and Atmospheric Conditions,"
JAPCA. Vol. 25 (1975), pp. 1232-1237.
16. Munn, R.E., Biometeorological Methods, Academic
Press, N.Y., 1970.
17. Islitzer, N.F. and D.H. Slade, "Diffusion and
Transport Experiments," in D.H. Slade [ed.] Meteo-
rology, and Atomic Energy 1968, U.S. Atomic Energy
Commission, TID-24190, Springfield, Va., 1968.
18. McCollister, G.M. and K.R. Wilson, "Linear Sto-
chastic Models for Forecasting Daily Maxima and
Hourly Concentrations of Air Pollutants," Atmos.
Envir., Vol. 9 (1975), pp. 417-423.
19. Bankoff, S.G. and E.L. Hanzevack, "The Adaptive-
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482
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SOURCE-ORIENTED EMPIRICAL AIR DUALITY MODELS
Kenneth L. Calder
Environmental Protection Agency
Environmental Sciences Research Laboratory
Research Triangle Park, N.C.
William S. Meisel
Technology Service Corporation
Santa Monica, CA. 90403
ABSTRACT
Meteorological dispersion functions in multiple-source
simulation models for urban air quality are usually
specified on the basis of the analysis of data from
special field experiments, usually involving isolated
sources. In the urban environment, individual sources
cannot be isolated. One may, however, ask for a source-
receptor relationship which, when summed (or integrated)
over all the sources, would minimize the average squared
error in prediction of measured values. The feasibility
of this approach is demonstrated by application to model-
generated data, where the source-receptor relationship
is known.
INTRODUCTION
In commenting on the lack of acceptance of empirical/
statistical models in air quality modeling in 1973, one
of the authors called attention to "the historical be-
lief that air quality models based on statistical re-
gression type of analysis are not source-oriented and,
therefore, are largely useless for control strategy in
terms of the contribution of individual sources to the
degradation of air quality"[i]. He went on to ask
"whether, with an appropriate analysis, a source-
oriented statistical-type of air quality model could
be developed which did not involve prior specification
of meteorological dispersion functions per se and in-
corporation of these as in present air quality models.
My thought here is that for given 'meteorological con-
ditions' these dispersion functions play the role of
transfer functions between the air quality distribution
and the distribution of pollutant emissions, and if one
were smart enough might, therefore, conceivably be ob-
tained empirically by a mathematical inversion tech-
nique (as, for example, by numerical solution of sets
of integral equations) utilizing accumulated data on
the distributions of air quality and emissions. If this
could be accomplished then maybe a major shortcoming of
the current statistical mode.ls could be removed and we
should then in effect have an alternative to the custo-
mary meteorological-dispersion type of modeling." These
comments suggest the motivation for the study reported[2].
The difficulties in developing a source-oriented empi-
rical model can be stated from a statistical point of
view. The spatial distribution of pollutant concentra-
tions over a region is determined by emissions and
meteorological conditions. The number of variables
determining the concentration at a given point is
tremendous, particularly since emissions arise from a
large number of point sources and area sources. Con-
sequently the number of emission variables alone can
easily be in the hundreds. If an empirical model were
to be developed in the most obvious manner, there
should be an attempt to relate the pollutant concentra-
tion at a given point to all the possible emission
variables and meteorological variables affecting the
*
This work was supported in part by Contract No.
68-02-1704 with the Environmental Protection Agency.
concentration at that point. Since the determination
of the relationship between emission/meteorological
variables and concentration requires examples of that
relationship over a very wide range of emission and
meteorological variables, a tremendous amount of data
would be required to adequately determine this relation-
ship.
If we could, however, isolate a given emissions source
and we had a number of receptor locations scattered
about the source, the variation in wind speed and di-
rection would cause a wide variation in measured con-
centration at the receptor locations. With enough
examples of the source-receptor relationship, the varia-
tion of the concentration with distance from the point
source could be determined empirically.
In the urban environment, of course, individual sources
cannot be isolated. Measurements are the result of
contributions from a number of sources. However, be-
cause of the wide diversity of meteorological conditions,
the concentration will vary widely at a given point,
and the sources which contribute to the concentration
at that point will similarly vary. One may then ask for
a consistent source-receptor relationship which, when
summed (or integrated) over all the sources, would
explain best on the average the observed concentrations.
More specifically, one could choose the source-receptor
function which minimized the average squared error in
prediction of the measured values. This concept is the
core of the ideas tested.
The data used to test these ideas are model-created
data. Model data were chosen for three major reasons:
1. With model data, the source-receptor function is
known and can be compared with the function extracted
from the data. With measurement data, "truth" is un-
known.
2. Area sources and point sources can be isolated and
studied separately as well as jointly.
.3. The cost of verifying and organizing measurement
data would have been beyond the scope of the present
study.
MATHEMATICAL FORMULATION
We work with a rectangular coordinate system with x-axis
along the mean horizontal wind direction, with y-axis
crosswind, and with the z-axis vertical. Then in urban
air quality models it is customary to consider the pol-
lutant emissions in terms of a limited number (say 0)
of elevated point-sources together with horizontal area-
sources, the latter being possibly located at a few
distinct heights cs (say, for example, for s 1,2,3).
The total concentration x(x«yi°) at ground level at the
receptor location (x,y,0) will be the sum of the con-
centration contribution from the point-source distri-
bution, say xp(x,y,0) and that from the area-source
distribution \(x,y,0)t i-e.,
483
-------
x(x,y,o) = xD(x,y,o) + xA(x,y,o)
where
XD(x,y,0) £ QD(4)K(x-5Jl,y-pJl;0,ct)
r ft = 1 r
(D
(2)
(x.y.O) ^ ././ VA
s=l A
.//QA(5,n,cs) •
K(x,c,y-n;0.cJd?dn
(3)
and
Q (l) = emission rate of Jl-th elevated
p point-source, located at position
QA(5.n,?s) emission rate of horizontal area-
source distribution located at
height ?s, and A denotes the total
integration domain of the area-
source distribution
K(x-?,y-n.;0,c) source-receptor function; it gives
the ground level concentration at
the receptor location (x,y,0)
resulting from a point-source of
unit strength at (?,n,?).
Note that this formulation includes the assumption of
horizontal homogeneity, namely, that the impact of a
given source upon a given receptor depends only upon
their relative and not absolute coordinates. This
assumption is true for an urban environment only in
an average sense. A single wind direction is simi-
larly valid only in an average sense. Finally, it
should be noted that the above formulation assumes
steady-state conditions and is thus only applicable
for relatively short time periods (of the order of one
hour), when this may be an adequate approximation
providing the emissions and meteorological conditions
are not rapidly changing.
In equations (2) and (3) above it is convenient to
use "source-oriented" position coordinates, and to
consider a typical ground-level receptor location as
Let
y'=
rS
i-n
dx'= -d? ,
dy'= -dn ,
Then
xp(xi,yi,0) £ QpU)K(xrryr)l; o,q)
(4)
(5)
,0)
K(x',y';0,cs)dx'dy'
(6)
In the following several different source-receptor
functions [K(x',y';0,?)] will be considered, includ-
ing the classical Gaussian form that is the basis for
the RAM-model [3]. For the latter, and with the
meteorological condition of infinite mixing depth
exp
K(x',y';0,c)=
exp
(7a)
ay(x')o-z(x')
where U denotes the mean wind speed, and we assume
simple power-law dependencies for the standard devia-
tion functions, say
oy(x') = ay(x') y
') = az(x') y.
(7b)
(7c)
Also, as in the RAM-model we will assume that the
narrow-plume hypothesis may be employed in order to
reduce the double integral of equation (6) to a one-
dimensional integral. Thus, under this hypothesis, if
J K(x',y';0£s)dy' G(x',es),
—00
then in place of equation (6) we have
(8)
3 f
XA(x1,yi,0) £ J QA(xi,x',yi,?s)6(x',i;s)dx>
(9)
which only involves values of the area-source emission
rates in the vertical plane through the wind direction
and the receptor location.
For the special case of a Gaussian plume
G(x',?s)
exp
V1-
"w I
U02(x')
(10)
The basic equations (5) and (6) (or (5) and (9)), with
the Gaussian forms for K(x',y'; 0,5) and G(x".?)
involve four unspecified parameters through the equa-
tions (7b) and (7c), namely, a ,b ,az and bz. More
generally, any functional form chosen for K (and there-
fore G) may have unspecified parameters;.we will de-
note the set of unspecified parameters by the vector
a. Thus for the special Gaussian form
o (ay,by,az,bz) (U)
The explicit dependence of the calculated concentra-
tion values on these parameters could be indicated by
the notation x(xi ,y.j,0;a).
The basic method employed in this study is that of
choosing a. to minimize the error between calculated
-------
and observed values of concentrations. In order to ex-
press this statement formally, we must elaborate our
notation to indicate explicitly the dependence on wind
direction; thus x(x,- ,y. ,0;9; a). For each wind direc-
tion 6j(j=l ,2...R) there is a~concentration observation
for each receptor location (monitoring station). The
receptor locations are denoted (x^.y.) for i=l,2...N,
and are assumed to be at ground level so that we may
omit the symbol 0 in the x-n°tation. Then the mean
square error over all observations is
2 ] N R r -.2
e (l) OT £ £ LWx1,y1,ej)-xcalc(x1,y1;ej;a)J
, N R
I v« y-
™ £ fi
(12)
where XD and
and (9)).
are given by Eqs. (5) and (6) (or (5)
The problem of minimizing e with respect to a is a
standard optimization problem. Chambers provTdes a
good recent survey of available techniques[4]. The
particular technique we employed was "structured ran-
dom search" [5]; this is a rather inefficient technique,
but one which does not require calculation of deriva-
tives and which converges under difficult conditions
(given enough time). This technique's main advantage
was that we could modify the form of the source-
receptor function without modifying the search tech-
nique. The results of applying this methodology to the
best data are discussed following; however, we first
turn to a description of the test data.
TEST DATA
For a realistic distribution of point-sources, area-
sources and receptor locations, use was made of unpub-
lished information from a 1968 air pollution study
conducted in St. Louis, Missouri[6], The area sources
were gridded into over 600 square regions; there were
60 point sources and errors were calculated at 40 re-
ceptors for the 16 wind directions. (See Reference [1]
for more details.) The corresponding concentration
data were generated by the EPA-developed RAM algo-
rithm[3], which is a specific implementation of the
classical Gaussian plume formulation, that considers
both point- and area-sources, with three possible
heights for the latter, and which uses the "narrow-
plume" hypothesis (i.e., Eq. (9)) to calculate the
area-source concentration contribution x/\. A constant
wind speed U of 5 meters per second was employed, and
sixteen wind directions at the points of the compass
were simulated. Infinite mixing depth and a neutral
atmospheric stability category were assumed. For the
latter, in Eqs. (7b) and (7c), we have
a = 0.072
az = 0.038
by = 0.90
bz = 0.76 .
(13)
"Observed" in the present case is model-created test
data; the technique is, of course, intended for prac-
tical use on measured data.
For this data, these values and the indicated equations
are optimal and would produce zero mean-square error.
It is this result we hope to be able to recover from
the data by the optimization procedure.
OPTIMIZING PARAMETERS FOR THE GAUSSIAN FORM OF THE
SOURCE-RECEPTOR FUNCTION
The data base described earlier contains concentration
values at forty receptors and sixteen wind directions,
a total of 640 values (referred to as "actual" values).
The contribution to the concentration from point and
area sources was available separately, as well as in
toto.
Equations (5) and (7a) provide a prediction of the
point-source pollutant concentration at any given re-
ceptor location once the four parameters are specified.
A comparison of values predicted by these equations ver-
sus actual values allows calculation of the root-mean-
square value of the error with a given choice of param-
eter values. (See Eq. (12), with area sources at zero.)
With initial guesses of a =a =0.1 and b =b =1.0, the
search routine described arrived at values of
ay = 0.74, by = 0.92,
0.039, bz = 0.77
when the "true" values (those used to create the data)
were
a = 0.72, b = 0.90, az = 0.38,
= 0.76.
The root-mean-square (RMS) error initially was 157 yg/m
and the maximum error over the 640 values was 1205 yg/m ;
the parameter values after 100 iterations yielded an 3
RMS error of 14 yg/m-* and a maximum error of 175 yg/m .
(Table 1 summarizes these results.) To place the size
of the final error in perspective, we note that the
actual values (due to point sources alone) were as high
as 1545 yg/m3.
Employing Eq. (9) for area sources and using only the
area-source contribution in the "actual" data, we get
similarly promising results (Table 2). Actual values
of concentrations due to area sources reach maximums of
over 800 yg/m3.
The results of treating point and area sources simul-
taneously, representative of the case which would be
encountered with measurement data, are listed in
Table 3; the algorithm once again closely approaches
the optimum values in 100 iterations. Actual values
of the total concentrations from both point and area
sources go above 1600 yg/m3.
While the initial parameter values we chose in these
cases converged toward the values used in creating the
data, experimentation indicated that this was not al-
ways the case. Small RMS errors could be achieved with
combinations of parameters significantly different in
value from those used in creating the data. As indi-
cated in Figure 1, rather different combinations of a
and b yield very similar values of ax° over the range
of x in which we are interested. It is clear that an
essentially equivalent combination of values should
not be deemed erroneous, since they yield an accurate
empirical model. We regard this a characteristic of
the formulation chosen for calculating a and do not re-
gard it a difficulty of the methodology proposed. Fur-
ther, in practice, initial values for the parameters
would be chosen from the literature, and the solution
obtained would be a set of values similar to the ini-
tial values, but which minimized the prediction error.
485
-------
Table 1. Point sources only; parameter values at initial, mid, and final iteration
during search.(tfindspeed is fixed at 5.0 m/sec.)
Iteration
0 (initial)
50 (mid)
100 (final)
ACTUAL
VALUES:
a
y
0.100
0.049
0.074
(0.072)
b
" —
1.00
0.85
0.92
(0.90)
az
0.100
0.050
0.039
(0.038)
bz
1.00
0.71
0.77
(0.76)
RMS Error
(yg/ms)'
157
85
14
(P)
Max. Error
(uq/ms)
1205
711
175
(0)
Table 2. Area sources on!
during search.
not affect area
y; parameter values at
fftindspeed is fixed at
source values. )
initial , mid
5.0 m/sec.
, and final iteration
Values a and b do
RMS Error Max. Error
Iteration
0 (initial)
50 (mid)
100 (final)
bz
0.100 1.00
.028 0.89
.037 0.79
(yg/m3)
157
15
6
(yg/m3)
1205
69
24
ACTUAL
VALUES:
(0.038) (0.76)
(0)
Table 3. Point and area sources together; parameter values at
iteration during
Iteration
!y
0 (initial) 0.100
50 (mid)
0.055
100 (final) 0.074
ACTUAL
VALUES:
i
(0.072)
.22
.20_
Ifi
—
14 ^
D
.12
0
search. (Windspeed is
^y_ az
1.00 0.100
0.79 0.044
0.89 0.036
(0.90) (0.038)
n 7s
a .038 x °'76
n CQ
a .028 x Ulby
a .044 x °'67
fixed at 5.0
L
bz
1.00
0.67
0.74
(0.76)
A
at
A'
//
(0)
initial, mid, and final
m/sec. )
Both Point and Area
RMS Error Max.
( g/m3) (
Sources
Error
9/m3)
157 1205
79
24
(0)
583
194
(0)
0 '°H // /
.03_
.06_
.04_
.02-
n^r^
/
//
/y
/° ^ '
^^'
/ '
f
/
Figure 1. Plot of ax for several values of a and b. (The variable x
is plotted on a log scale.)
486
-------
This aspect of implementation also suggests that a
good initial guess would be employed and, thus, that
convergence to an "optimum" solution would be rapid.
Forty receptors (i.e., air quality monitoring stations)
are more than are available in many monitoring systems.
How many stations are required for this methodology to
be effective? The answer to this question is heavily
dependent on the number and distribution of sources,
but the indications from experiments with our test data
suggest that a considerably smaller number of stations
may suffice. Table 4 indicates errors due to changes
in parameter values, one at a time, from the optimum
values, for a selection of the individual stations.
The errors are sufficiently large that one would expect
that optimum parameter values could be extracted from
a small number of stations at well-chosen locations.
MORE GENERAL SOURCE-RECEPTOR FUNCTIONS
More complex source-receptor functions (such as multi-
variate polynomials and piecewise quadratic functions)
were tested with success[l], but broad conclusions
about alternative forms will not be forthcoming through
the analysis of the present test data. Analysis of
measurement data may allow meaningful comparison of
the Gaussian and more general parameterized forms.
CONCLUSION
A methodology for empirically testing alternative forms
and extracting optimal parameters for source-receptor
dispersion functions has been described. Feasibility
was demonstrated on data for which the "true" source-
receptor function was known; the methodology recovered
parameter values very close to true values. This
approach shows promise as a means for calibrating
Gaussian-form models for particular urban environments
and in testing alternative forms.
REFERENCES
1. Calder, Kenneth L., Quoted by Niels Busch in the
proceedings of the fourth meeting of the NATO/CCMS
Panel on Air Pollution Modeling, from a letter
written in March 1973.
2. Calder, Kenneth L., W. S. Meisel, and M. D. Teener,
"Feasibility Study of a Source-Oriented Empirical
Air Quality Model", (Part II of "Empirical Tech-
niques for Analyzing Air Quality and Meteorological
Data"), Final Report on EPA Contract No. 68-02-1704,
December 1975.
3. Hrenko, Joan M. and D. B. Turner, "An Efficient
Gaussian-Plume Multiple Source Air Quality
Algorithm", Paper 75-04.3, 68th Annual APC Meeting,
Boston, June 1975.
4. Chambers, John M., "Fitting Nonlinear Models:
Numerical Techniques," Biometreka, Vol. 60, No. 1,
1973, pp. 1-13.
5. Meisel, W. S., Computer-Oriented Approaches to
Pattern Recognition, Academic Press, New York,
1972, pp. 51-53.
6. Turner, D. B. and N. G. Edmisten, Unpublished manu-
script of National Air Pollution Control Adminis-
tration, "St. Louis SO- Dispersion Model Study,"
November 1968.
Table 4. Sensitivity Analysis. Root-mean-square and maximum error due to change in each parameter
from nominal values at selected receptors. Concentrations are from both point and area
sources.
Parameter
ay
by
az
bz
U
M'cX.
^%
Change \£
From Tp_
.072 .079
.90 .99
.038 .042
.76 .836
5.0 5.2
Error (in ^g/m1) at Selected. Receptors.
1
RMS MAX
9 32
15 59
24 49
32 66
15 25
10
RMS MAX
67 260
23 63
32 102
44 111
18 30
13
RMS MAX
17 46
22 69
24 45
29 62
19 44
21
RMS MAX
10 32
20 62
27 51
37 80
18 33
22
RMS MAX
11 33
20 66
16 52
23 69
16 39
24
RMS MAX
14 52
10 31
33 109
27 65
14 37
35
RMS MAX
44 175
46 175
47 177
52 178
45 177
Error for
All 40
Receptors
RMS MAX
16 175
24 234
27 151
35 230
18 177
487
-------
EPA FLUID MODELING FACILITY
Roger S. Thompson and William H. Snyder*
Meteorology and Assessment Division
Environmental Sciences Research Laboratory
U.S. Environmental Protection Agency
Research Triangle Park, N.C.
A meteorological wind tunnel and a water channel-
towing tank as used by EPA scientists for laboratory
studies of air pollution dispersion in the vicinity
of buildings and over complex terrain are described.
In these fluid modeling studies, simulated atmospheric
boundary layer flow patterns are created over special-
ly constructed scale models of structures or geoaraphic
areas. Modeling theory provides similarity criteria
to ensure that flow behavior in the model simulates
real processes in the atmosphere. Visualization of
dispersion from modeled emission sources is obtained
by releasing an oil fog in the wind tunnel and dye
in the water channel. Simulated pollutant concentra-
tion levels are determined by emitting a tracer,
which is sampled and measured at locations of interest
around the model site. Neutral atmospheric conditions
are modeled in the wind tunnel and in the water
channel-towing tank in the recirculating mode of
operation. Dispersion under thermally stratified
atmospheric conditions is modeled by filling the
water channel-towing tank with stratified layers of
salt water and towing models through the motionless
fluid. Results of some recent projects are presented
as examples of the types of information gained at the
Fluid Modeling Facility.
*0n assignment from the National Oceanic and Atmospheric Administration.
Introduction
In-house research in fluid modeling of atmos-
pheric dispersion is conducted at the Environmental
Protection Agency's Fluid Modeling Facility (FMF)
located in Research Triangle Park, N.C. The FMF,
which is a part of the Meteorology and Assessment
Division of the Environmental Sciences Research
Laboratory, opened in June 1974 with the installa-
tion - including instrumentation, shop equipment, and
a minicomputer - of the meteorological wind tunnel
(Figure l). In a major expansion of the facility,
the installation of a water channel-towing tank
(Figure 2) was completed in December 1975.
Fluid modeling involves placing a scale model
of a topographic region or an urban area, for example,
in a moving fluid to simulate meteorological effects
at the site. In a towinq tank, the model is moved
through motionless fluid. By following scaling laws,
full scale atmospheric flow can be accurately simu-
lated in the laboratory. In addition, quantitative
measurement of the concentrations of a tracer at
various points in the diffusion field over the model
can be used to provide estimates of pollutant con-
centrations in real (full scale) situations.
Figure 1. EPA meteorological wind tunnel,
488
-------
Figure 2. EPA water channel-towing tank.
Theoretical and Practical Considerations
Discussions of similarity considerations appli-
cable to fluid modeling have been presented in the
literature and will not be repeated here. Compro-
mises often must be made because all similarity cri-
teria can not be satisfied simultaneously. It is
evident that each laboratory has its own set of cri-
teria, which may differ or even conflict with those
of another laboratory. Also, other aspects of model-
ing, such as the minimum Reynolds number limit for
similarity of plume rise, have not been completely
established. A primary goal of the FMF, therefore,
is to test the limits, determine the proper similar-
ity criteria, and set the standards for fluid model-
ing of atmospheric dispersion.
Both air and water are suitable fluids to use
p
as media for modeling atmospheric dispersion . In
principle, a factor of 15 in the Reynolds number may
be gained by modeling with water as the medium. How-
ever, because of structural and pumping requirements,
water facilities are normally much smaller and run
at much lower speeds than wind tunnels. Thus, the
full potential for obtaining larger Reynolds numbers
using water flows is seldom realized.
Water has some advantages over air as the model-
Ing medium. Flow visualization - using different
colors of dyes, hydrogen bubbles, and neutrally buoy-
ant particles - is generally much easier in water.
Salts, acids, and dyes are used as tracers to deter-
mine pollutant concentrations when modeling dispersion
characteristics in water. Water is also rather easily
stratified using salt water layers of varying density;
whereas, stratification in a wind tunnel requires
rather elaborate heating and cooling systems.
Wind tunnels, however, have been used in many
applications to simulate atmospheric motions. Flow
visualization, velocity measurement, and concentration
detection techniques have been developed and advanced
to a level of high reliability and accuracy. Models
used in wind tunnels need not be as solidly construct-
ed or as firmly supported as those for use in water
channels, where pressure forces are generally much
larger. In addition, connections to probes do not
require as much care with electrical insulation in air
as in water, and there is less corrosion o* metal.
Because both a wind tunnel and water channel-
towing tank are available at the FMF, EPA scientists
can use the one most suited to a particular research
project.
Meteorological Hind Tunnel
The meteorological wind tunnel is an open-
circuit, low-speed wind tunnel desianed for simulating
neutral atmospheric flows. The test section -
18 meters (m) long, 3.7 m wide, and 2.0 m high - has
an adjustable ceiling to compensate for blockage when
large models are used. Five subsections with inter-
changeable windows and floor units comprise the test
section. A removable, 3.4 m diameter turntable can
be placed in any of the five sections. The portion
of a model installed on the turntable can be easily
rotated to change the effective wind direction.
A 75 kilowatt (k!J) a.c. motor driving a 1.8 m
diameter fan through a speed controller (eddy current
coupler) produces a top air speed of 10 meters per
second (m/sec.). A carefully designed entrance-
contraction section contains a honeycomb and four
screens to produce a low turbulence flow at the
entrance to the test section. The fan is downstream
of the test section and is housed within a sound-
deadening enclosure. Acoustic silencers in the flow
both upstream and downstream of the fan provide for
quiet operation.
An instrument carriage mounted on rails can
position a probe anywhere in the test section.
Controls to move the carriage in three dimensions are
489
-------
located on an operator's console near the tunnel.
Diaital readout Indicates the position of the probe
to the nearest millimeter.
Many methods have been devised for developing
simulated atmospheric boundary layer air flow in wind
tunnel test sections. Tha FMF has slightly modified
a method devised by Counihan at the Central Elec-
tricity Research Laboratories, England, to create
power law wind profiles. Elliptical vortex-generating
fins are placed just downwind of a castellated barrier
at the entrance to the test section (Fiaure 3). The
fins initiate a boundary layer with a thickness equal
to their heiqht. Two-dimensional roughness elements
are placed on the tunnel floor downstream of the
vortex generators to maintain the boundary layer char-
acteristics over the length of the test section. Mean
velocity and turbulence intensity profiles occurring
4 1/2 heights downwind of 1.8 m fins are shown in
Figure 4. The mean velocity profile generated by this
fin/roughness combination is close to a l/5th power
law, which is typical of flat country with low shrub-
bery. The turbulence intensity profile compares
favorably with atmospheric data reported by Harris ,
which are shown in the figure for comparison. The
FMF has 5 sets of these fins ranging from 15 to 180
centimeters (cm) in height. The fins may be easily
inserted in the wind tunnel to obtain a boundary layer
appropriate to the scale and characteristics of the
model under test.
Fiqure 3. Elliptical vortex generating fins for
developing simulated atmospheric boundary layers in
meteorological wind tunnel test section.
each layer of different density. Atmospheric temper-
ature gradients are modeled by the density gradients
of the salt water. Models are affixed to a turntable,
suspended from a towing carriage into the fluid, and
towed the length of the test section, making possible
the study of flow and dispersion around buildings and
over complex terrain and urban areas, under stably-
stratified atmospheric conditions. The carriage speed
is continuously variable from 0 to 0.5 m/sec. A
filling system, consistina of a brinemaker and five
large tanks, provides the capability of fillina the
test section with a desired stably-stratified salt-
water mixture in approximately 4 hours.
In the water channel mode of operation, the
facility is used in a manner similar to the wind
tunnel procedure, with models fastened to the floor
of the test section. A 1.5 m diameter pump, driven
by a 75 kW a.c. motor throuah a speed controller
(eddy current coupler), produces a top speed of
1.0 m/sec. The channel is supported on jacks that
can be adjusted to tilt the entire unit to compensate
for the pressure drop through the test section.
O 4.5 H DOWNWIND OF VORTEX GENERATING
- FINS
O 4.5 H DOWNWIND OF VORTEX
~ GENERATING FINS —
ATMOSPHERIC DATA
f
0.2 0.3 0.1 0.5 0.6 0.7 0.8 0.9 1.0
U/U,,
10 15 20
!T I U . 100*
Figure 4. Vertical profiles of mean velocity (A) and local turbulence
intensity (B) downwind of vortex generating fins (H=fin height-
1.83m). Atmospheric data6 are included for comparison.
Water Channel-Towing Tank
The water channel-towing tank was added to the
FMF to make possible the study of dispersion under
stably-stratified atmospheric conditions. As the
name implies, it is a dual-purpose facility. Fiaure 2
shows its closed-circuit desion, with the pump in the
return leg on the bottom and the test section (free
surface) on the top. The test section - 2.4 m wide,
1.2 m deep, and 25 m lono - is constructed with floor
and sidewalls of acrylic plastic in an aluminum
framework.
In the towing tank mode of operation, the ends
of the test section are blocked with gates and the
test section is filled layer by layer with salt water,
Instrumentation
The FMF has a Digital Equipment Corporation
POP 11/40 minicomputer located within the facility
to process all laboratory data. The system includes
3 maanetic tape drives, 3 disk drives, an 80K memory
bank, a 16-channel analog-to-diaital converter, a
refresh-graphics terminal, and an electrostatic
printer/plotter. It operates under RSX-11D, which is
a multi-task, multi-user operatina system. Real-time
analysis of the outputs of electronic data gathering
instruments provides instant feedback to the experi-
menter on the results of data being taken. The
maanetic tape drives provide for economical storaae
of digitized data for future analysis.
490
-------
Velocity measurements in the wind tunnel and
water channel-towinq tank are made with Thermo-
Systems Inc. constant temperature hot-film anemometers.
The outputs of the anemometers are digitized, linear-
ized, and analyzed on the computer according to
previously determined calibrations for each hot-film
probe. Mean velocity and turbulence intensity values
are printed out immediately after the last sample has
been digitized for the scrutiny of the technician.
Fast Fourier Transform techniques are used to obtain
spectra and correlations of turbulence from signals
recorded on magnetic tape. Programs have been
written to calculate Reynolds stresses and velocity
fluctuations in two coordinate directions from the
output of cross-film probes.
In the wind tunnel, pollutant dispersion is
studied by releasing a dilute tracer-gas-in-air mix-
ture from the model source, collecting samples throuah
a sampling tube, and measuring the concentration of
tracer in the sample. Two Beckman model 400 Hydro-
carbon Analyzers (flame ionization detectors) are
used to determine the concentration of tracer in the
sample. The output of the analyzer is also processed
by the minicomputer. The response time of this
system is too lona to obtain statistics on concentra-
tion fluctuations, however.
Qualitative evaluations of dispersion patterns
are made using flow visualization techniques. An oil
fog generator produces a paraffin oil mist that is
released from model sources in the wind tunnel;
organic dyes are released in the water channel. By
observing plume behavior and touchdown points, sam-
pling locations for tracer measurements are deter-
mined. Still and motion picture cameras are used to
photograph the experiments for a permanent record.
A metal and woodworking shop located within the
FMF contains equipment and tools for constructina
detailed models from metal, wood, and plastics.
Minor modifications and additions to the facility
are also performed in-house.
The FMF also houses an electronics shop for the
repair and maintenance of instruments and other
electronic equipment and for the development of new
instrumentation.
Applications
Because the water channel-towing tank has only
recently been installed, specific applications are
in the plannina stages. Basic characteristics of
the system are being studied, and modeling and
measurement techniques are being developed for use in
future projects. Some applications of the meteor-
ological wind tunnel will be discussed.
The first study completed in the meteorological
wind tunnel was an analysis of the flow behind a
two-dimensional mountain ridge to determine l:rules
of thumb" for the placement of smoke stacks. A
cavity of recirculating flow was found in the lee of
the ridge with a height equal to approximately twice
the ridge height and a length equal to ten ridge
heights. A summary paper on this work will be
presented at this conference.
Wind tunnels are often used to evaluate aero-
dynamic influences of buildings on smokestack plumes.
Unique characteristics of specific emission sites or
building shapes may require exact modeling of individ-
ual cases. The FMF is more involved with the analysis
of general cases from which general conclusions or
"rules of thumb" can be obtained.
o
One such study was performed to test the notion
that a stack must be 2 1/2 times as high as the
tallest nearby building to avoid plume downwash
resulting from building effects. Two buildings were
5(a) building width twice its height
5(b) building width l/3rd its height
5(c) stack without building
Figure 5. Plume visualization for a stack 1 1/2 times
as hiqh as nearby buildino. Buildino heiahts, stack
heinhts, and boundary layer and effluent character-
istics are identical in all three photoaraphs.
used; one with its width twice its heiaht and one with
its width one-third its height. The 2 1/2 times rule
was found to be unnecessarily conservative for the thin
building. Smoke visualization photooraphs are present-
ed in Figure 5 for a stack that is 1.5 times the
491
-------
building height for the wide building, the thin
building, and no building. Comparison of the photo-
graphs shows that, even though the stack heights and
building heights are identical, the wide building
produces strong plume downwash, whereas the thin
building has essentially no influence on the plume.
Quantitative concentration measurements verified the
visualization results.
The influence of buildinas on stack emissions
was more thoroughly investigated in a cooperative
study performed in response to a request by the EPA
Office of Air Quality Planning and Standards (see
Figure 6). One building with width equal to twice its
height, HR, was used. The stack was located at the
center of the downwind side of the building. Emphasis
was placed on quantifying the building influence on
around level concentrations as a function of stack
height, HL, stack diameter, D, exit velocity, H, and
buoyancy. Many combinations of these parameters were
examined both with and without the building in place.
Figure 6 presents ground level concentrations meas-
ured under the plume centerline for a stack that is
1 1/2 times as high as the building. Measured con-
centrations for a ground release in the building wake
are also presented. A mathematical model based upon
a Gaussian plume formulation with a correction for
increased dispersion behind the building has been
found to approximate the data reasonably well.
theories will be evaluated to establish guidelines for
proper modeling methods.
as 12.0 us is.o
Figure 6. Nondimensionalized ground level concentration for neutral-
ly buoyant plurjie. D/HB = 0.063, W/U = 0.7.
Another model constructed for study in the
meteorological wind tunnel involved moving l:32-scale-
model vehicles to simulate highway traffic (Figure 7).
The vehicles are pulled across the test section by a
chain imbedded in the floor of the turntable. Char-
acteristics of the turbulent wake region downwind of
moving vehicles are to bs determined. Preliminary
results show that the vehicle-induced mechanical tur-
bulence has a strong influence on the dispersion of
vehicle exhaust close to the highway.
Through studies of this type, a general under-
standing of the mechanisms of atmospheric dispersion
can be gained. EPA Fluid Modeling Facility scientists
intend to concentrate efforts on this type of project
as opposed to evaluating specific case studies involv-
ing circumstance peculiar to a given topographical
location or building design. In conjunction with
these studies, modeling techniques and similarity
Figure 7. Hiahway model with moving vehicles on
meteorological wind tunnel turntable.
References
1. Snyder, W.H., R.S. Thompson, and R.E. Lawson, Jr.,
The EPA Meteorological Wind Tunnel: Design, Con-
struction, and Operating Details. Environmental
Protection Agency, Research Triangle Park, N.C.
(In preparation.)
2. Snyder, W.H., "Similarity Criteria for the
Application of Fluid Models to the Study of Air
Pollution Meteorology", Boundary-Layer Meteorology,
v. 3, no. 2, 1972, pp. 113-34.
3. Cermak, J.E., "Laboratory Simulation of the
Atmospheric Boundary Layer", AIAA Journal, v. 9,
no. 9, Sept. 1971, pp. 1746-1754" ~~
4. Sundaram, T.R., G.R. Ludwin, and G.T. Skinner,
"Modeling of the Turbulence Structure of the
Atmospheric Surface Layer", AIAA Journal, v. 10,
no. 6, June 1972, pp. 743-750.
5. Counihan, J., "An Improved Method of Simulating
and Atmospheric Boundary Layer in a Wind Tunnel",
Atm. Env.. v. 3, 1969, pp. 197-214.
6. Harris, R.I., "Measurement of Wind Structure at
Heiahts up to 598 ft. above Ground Level", Symp. Hind
Effects on Buildings and Structures, Louahborouah
Univ. Tech. (Dept. of Transport Technology), 1969.
*
7. Huber, A.M., W.H. Snyder, R.S. Thompson, and
R.E. Lawson, Jr., "Plume Behavior in the Lee of a
Mountain Ridge -- A Wind Tunnel Study", Presented at
the EPA Conference on Modeling and Simulation,
Cincinnati, Ohio, April 1976.
8. Snyder, W.H. and R.E. Lawson, Jr., "Determination of
a Necessary Height for a Stack Close to a Building --
A Wind Tunnel Study". Atm. Env. (In press.)
9. Huber, A.H. and W.H. Snyder, "Building Wake Effects
on Short Stack Effluents". (To be presented at the
Third Symposium on Atmospheric Turbulence, Diffusion
and Air Duality, Raleinh, N.C., October, 1976.)
Mention of trade names or commercial products does
not constitute endorsement or recommendation for use
by the Environmental Protection Agency.
492
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PLUME BEHAVIOR IN THE LEE OF A MOUNTAIN RIDGE — A WIND TUNNEL STUDY
Alan H. Huber
Monitoring and Data Analysis Division
Office of Air Quality Planning and Standards
William H. Snyder*
Roger S. Thompson
Meteorology and Assessment Division
Environmental Sciences Research Laboratory
and
Robert E. Lawson, Jr.
Northrop Services, Inc.
Work Performed In
Fluid Modeling Facility
Meteorology and Assessment Division
U.S. Environmental Protection Agency
Research Triangle Park, N. C. 27711
A wind tunnel study of the concentration field
resulting from a stack placed in the highly turbulent
region downwind of a two-dimensional mountain ridge
is presented. This highly turbulent region, often
referred to as the "cavity," was found to consist
of a large semipermanent eddy. The general cir-
culation was in the main flow direction along the
upper edge, opposite the main flow direction
along the ground surface, and up the slope along
the leeward ridge surface. The eddy is a result of
the main flow separating at the apex of the ridge.
A stack was positioned to emit an air-methane mix-
ture into the cavity in the lee of the ridge.
Longitudinal, lateral, and vertical concentration
profiles showed that a tall stack placed near the
upper boundary of the cavity resulted in higher
ground level concentrations near the downwind end
of the cavity than did a short stack. The high-
est ground level concentrations, however, were
found to occur near the base of the short stack.
Application of the "2.5 times rule" with respect
to the ridge height was found to be sufficient
for avoidance of the highly turbulent region.
Introduction
Aerodynamic effects induced by local terrain
features can have a major influence upon the
dispersion of locally emitted effluents. Even with
the best demonstrated control technology applied,
most plume concentrations at the stack exit are at
levels far in excess of ambient air quality standards.
The plume may frequently be entrained in the tur-
bulent eddies created by air flow over local terrain
features and be brought to the ground before the
concentrations are sufficiently reduced to levels
below ambient air quality standards. These effects
are often referred to as "plume downwashing."
This paper discusses the results of a set of
experiments designed to examine the highly turbulent
region that can be found on the leeward side of a
steeply sloping mountain ridge. The study was con-
ducted in the meteorological wind tunnel at the Fluid
Modeling Facility of the U. S. Environmental Protec-
tion Agency (EPA). Fluid modeling is ideally suited
* On assignment from the National Oceanic and
Atmospheric Administration.
for investigations of the complex plume behaviors
that result from aerodynamic effects because essential
variables can be controlled and examined at will.
For neutral (neutrally stable) atmospheric
flows, aerodynamic effects evolve from interacting
frictional forces and pressure gradients induced
by local surface roughness and terrain features.
Adverse effects exist when surface friction and
pressure gradients combine to retard the surface
layer flow enough to produce separation of the
boundary layer. Separation in a neutral flow
generally occurs near the apex of the terrain feature
resulting in development of a stagnation region on
the leeward side, often referred to as a "cavity."
At the point of separation, the main stream of flow
is vertically raised, resulting in the development of
a stagnation region (cavity) below, where mean
velocities are reduced and the flow is highly
turbulent. The flow reattaches itself somewhere
downstream of the obstacle. In the region of re-
attachment, a portion of the flow is deflected up-
stream, forming a zone of recirculation. The
dividing "streamline" that separates the recircula-
ting flow from the main stream encloses the cavity,
as shown in Figure 1. The "wake region," which is de-
fined as that region of the flow field that is dis-
turbed by the obstacle, can extend far downwind. The
"envelope" is the upper boundary of the wake region.
Far enough downwind, of course, the flow readjusts
itself to a boundary layer appropriate to local
surface roughness.
Figure 1. Diagrammatic sketch of envelope and cavity regions behind
a two-dimensional ridge.
493
-------
Literature Review
1-11
A review of published field studies,
supports the assertion that, on the leeward side
of a mountain ridge, a recirculating flow region with
strong downwash and enhanced dispersion exists.
Consistent information that could define the point
of separation and the size and extent of the cavity
was not found, however. The point of separation
appears to be very much a function of mean flow speed
and direction, atmospheric stability, both the down-
slope and upslope angle of the ridge sides, and the
location of the ridge with respect to surrounding
terrain.
For a particular situation, the cavity will be
largest when separation occurs at the ridge apex. Ob-
structions with sharp edges should exhibit definite
separation at those edges under all atmospheric condi-
tions. The size of the cavity region is greatest for
isolated ridges with steep sloping sides. Stable at-
mospheric conditions act to restrict the size and ex-
tent of the cavity region.
Experimental Plan
Terrain features that most adversely affect
the flow are two-dimensional in nature. Lateral
air motion around a hill results in a smaller cavity
size than would be observed for a two-dimensional
ridge. A study of neutral flow with separation
occurring at the apex of a two-dimensional mountain
ridge best demonstrates the extent to which stagna-
tion regions can influence the dispersion of locally
emitted effluents.
There were three major phases to this study.
Phase I involved a Gaussian ridge and a triangular
ridge. Velocity and cavity size measurements were
made in order to demonstrate that the basic flow
structure is independent of the detailed shape of
the ridge. Phase II involved mapping of the concen-
tration field resulting from a source placed within
the cavity. Phase III examined the effect of
variations in the approach flow on the cavity size
and shape. This presentation emphasizes the results
of the second phase. The complete description of
12
these studies is given in Huber, et al.
Experimental Details
Similarity Criteria
In order to ensure that the flow in the model
simulates that in the atmosphere, it is necessary
to meet certain similarity criteria. Various
nondimensional parameters characterizing the flow
in the atmosphere must be matched in the model.
Because this study is concerned only with neutral
atmospheric flows, non buoyant effluents, and rela-
tively small scales, the Richardson, Froude and
Rossby numbers may be ignored (Snyder ). The
remaining parameters of significance are as follows:
H D
W. U H
W.D.
L ns US 5 U (u") !l X. a H SUS
H'H 'H 'H 'U ' U ' U ' v ' anQ T~'
to S
Where: L - characteristic width of ridge
H
height of ridge
HS = height of stack
D = inside diameter of stack
6 = boundary layer thickness
U = mean wind speed (a function of
elevation)
1/2
(u ) = root-mean-square of longitudinal
velocity fluctuations
W stack effluent speed
U wind speed at top of stack
v kinematic viscosity of air
The first four of these parameters (length
ratios) are easily matched by constructing a
scale model, but because no particular field situa-
tion was modeled, idealized ridge shapes and re-
presentative values were chosen. The fifth and
sixth parameters characterize the boundary layer
approaching the ridge. Two different boundary
layers were used. A vortex generator-roughness
14
element combination similar to that of Counihan
was used to provide a 60-cm atmosphere-like
boundary layer. The other was the natural (<5=15-cm)
boundary layer developed over the smooth wind
tunnel floor.
The effluent speed to wind speed ratio was
maintained at 3:2 in all tests. This value is the
minimum necessary to avoid downwash in the immediate
lee of the stack itself (Sherlock and Stalker15).
Plume rise or downwash from the model stack placed
in the lee of the ridge are, therefore, associated
with disturbances induced by the ridge. The diameter
to ridge height ratio was kept at a value equal to
0.03 in reference to the 30 cm model ridge.
The last two parameters are the ridge
Reynolds number (Reu =U H/v) and the effluent
H 00
Reynolds number (ReD = W D /v). For exact
similarity, the model ridge Reynolds number must
equal the actual ridge Reynolds number. This was
not possible for the model scales used and, for-
tunately, is not necessary (Snyder ) because the flow
fields become independent at sufficiently large
Reynolds number. For a mountain ridge with a sa-
lient edge near the peak, the boundary layer may be
expected to separate at the edge (Scorer2). If the
point of separation on the model occurs at its apex,
similarity of the two flow patterns should result.
The plume behavior should be independent of the ef-
fluent Reynolds number provided the flow is fully
turbulent at the stack exit. Internally serrated
washers were placed inside the stack to ensure fully
turbulent flow at the exit.
Equipment
The wind tunnel test section measures 3.7 m x
2.1 m x 18.3 m. The flow speed within the wind tun-
nel can be controlled between 0.3 and 10 meters per
second (m/sec). The ceiling of the wind tunnel.can
be adjusted to compensate for blockage effects of
the models. In this study, the ceiling was adjusted
to obtain a nonaccelerating free-stream flow above
the mountain ridge. Further details of the wind
tunnel may be obtained from Snyder, et al.16
Three model ridges were constructed. One
ridge was triangular in shape with a 30.5 cm high
494
-------
apex and sloping sides of 30°; the other two had
sides with idealized shapes. The ridges were sym-
metrical about a center line, each side of which
could be divided into three sections. The center
section had a constant slope of 30°. The upper and
lower sections were respectively convex and concave
outward. This model shape appears to be very close
to a Gaussian probability distribution and is re-
ferred to as the Gaussian model ridge in order to
distinguish it from the triangular model ridge..
The two similar Gaussian ridges had apexes of
30.5 cm and 15.2 cm, respectively. The three
models will be referred to in the remainder of this
report as the 30-cm triangular ridge, the 30-cm
Gaussian ridge, and the 15-cm Gaussian ridge.
For mean velocity and turbulence intensity
profiles, a Thermo-Systems Inc. Model 1054 A
anemometer was used in conjunction with their
Model 1210-20 hot-film probes. Smoke visualization
studies made use of an oil-fog generator.
An air-methane mixture was ejected from the
stack as a tracer gas. This effluent simulated a
neutrally buoyant plume because the amount of methane
in the gas mixture was only 1 percent and the stack
gas temperature was equal to the ambient air tempera-
ture.
Concentration profiles were obtained by sampling
a stream through a Beckman Model 400 Hydrocarbon
Analyzer, which is a flame ionization detector.
Its response time of 0.5 second is too long to
examine any dispersion micro-structure. Time averages
can be related to steady-state averages occurring
in similar full scale situations, however. A 2.5
minute averaging time was found to yield stable
values of concentration.
Experimental Concentrations
Concentrations measured in the model may be
related to steady-state averages that would be
measured in the field. The stack gas concentration,
C , is related to the emission rate by
Q"Cs[(ir/.4)(D~)]Ws.
(1)
The field concentration, Cp, is linearly related to
the model concentration, CM, to the emission rates,
2 2
Qp, and to the dilution ratio, UMH M/UpHp. These
basic relations result in the expression
CF=(CM)(Qp/QM)(UM/UF)(HM/HF)2, or (2)
(C/CS)F=(C/CS)M[(WS/US)F/(WS/US)M][(DS/H)2/(DS/H)2].
With identical effluent speed to wind speed ratios
and stack diameter to ridge height ratios, the model
concentration ratios are equal to the field concen-
tration ratios,
(C/CS)M = (C/CS)F. (3)
Experimental Results
Phase I
Smoke Visualization. For flow separation to
occur at the apex of the 30.5-cm Gaussian ridge,
a tripping device was required. A small square rod
was placed along the ridge apex to induce flow
separation. With flow separation at the apex, the
cavity depth and length were two times larger than
for the cases without and were independent of the
mean flow speed. Flow visualization measurements
behind the 30-cm triangular ridge resulted in similar
size and shape of both the cavity and envelope as
those for the tripped 30-cm Gaussian ridge (Figure 2).
Mean Velocity and Turbulence Intensity.
The mean velocity and turbulence intensity pro-
files for both upstream and downstream positions
from the tripped 30-cm Gaussian ridge are present-
ed in Figure 3. The 60-cm atmosphere-like boundary
layer was used as the approach flow. The mean velo-
city, U, is defined as the 1-minute average flow
speed in the longitudinal direction, x. The turbu-
lence intensity is defined as the standard deviation
of the velocity fluctuation in the longitudinal
direction, normalized with the local mean velocity.
Measurements in regions having mean flow reversals are
not quantitatively valid because the hot-film cannot
distinguish flow direction. Smoke visualization
quite clearly revealed upstream flow near the
surface level. The data presented, however, should
permit valid qualitative comparisons.
The degree of disruption of the approach flow
was found to be small in extent for the untripped
ridge. The profiles around the 30-cm triangular
ridge were found to compare quite well with those
of the tripped 30-cm Gaussian ridge. For those cases
in which flow separation occurred at the apex of the
model, the profiles were found to be independent of
the free-stream velocity.
I I
O ENVELOPE; U«= 7.62 m/j«
D ENVELOPE; U°°= 3.05 m/uc
• ENVELOPE; U«= 7.S2 m/*c
(SEPARATION NOT FORCED)
OCAVITY; U~=7.62m/s«c
QCAVITY; U°°O.05ni/[K
• CAVITY; U"=7.62m/Mi:
(SEPARATION NOT FORCED)
H * 30,5 cm
Figure 2. Cavity and envelope size in lee of 30.5-cm Gaussian ridge.
Figure 3. Mean velocity and turbulence intensity profiles for the
30.5-cm, tripped Gaussian ridge, Uoo = 3.05 m/s.
495
-------
Phase II
Concentration measurements are presented in the
figures in order to assist in describing plume be-
havior within the cavity region in the lee of the
30-cm tripped Gaussian ridge. To present the data
in a form for easy comparison, the measured concen-
trations have been nondimensionalized with the stack
gas concentration, C . Thus, the value "C, percent"
in the figures is the measured concentration expressed
as the percentage of stack gas concentration.
This value can be directly related to average field
concentrations as discussed earlier. A field situa-
tion with the stack emission concentration equal
to 2000 ppm would result in the air quality measure-
ment of 1 ppm under circumstances similar to those
of the model where C percent is equal to 0.05.
Concentration Measurements. The concentration
values in Figure 4 were detected by a ground level
probe located near the base of the 30-cm tripped
Gaussian ridge. The stack was positioned at four
different downwind locations and raised to various
heights while the probe sampled at the fixed position.
The stack height where no ground concentrations were
detected defined the limit of the cavity. The fact
that significant ground level concentrations are
found at a distance of 5 H upwind of the stack
demonstrates the existence of a strong recirculating
flow within the cavity region. The size of the
cavity determined from the tracer gas measurements
(Figure 4) showed a maximum depth and horizontal
extent of 2 H and 8.5 H, respectively. The horizon-
tal extent was only slightly smaller than that found
by smoke visualization (10 H) for the same situation
(Figure 2).
Figure 5 gives the resulting ground level con-
centrations downwind from a stack placed at the
leeward base of the tripped ridge for three stack
heights. Maximum concentrations are found very
close to the stack base. The peak concentration
decreases and is shifted downwind as the stack
height increases. This pattern is typically found
to occur over flat terrain. Beyond two ridge heights
downwind from the stack, however, the concentrations
are highest for the tallest stack, which is not at
all typical of plume behavior over flat terrain.
0 It U 0 0.1 0-2 0 0.1 IU 0 0.1 U
Figure 5. Longitudinal ground level concentration profiles
downwind from stack placed at base (x/H = 2.7 from cen-
ter) of 30.5-cm tripped Gaussian ridge.
Figure 4. Ground level concentrations measurements with sampling
probe fixed near base (x/H = 3 from ridge center, z/H = O) of 30.5-
cm, tripped Gaussian ridge (stack was placed at four downwind
locations and its height was varied).
Figure 6a presents some vertical concentration
profiles in the lee of the tripped ridge. The stack
was fixed at the ridge base with the height of the
stack measuring one-half the ridge height. Because
of nearly stagnant mean flow in the lee of the ridge
and the general upward flow in the cavity region
along the ridge surface, a substantial plume rise
occurs -- as is indicated by the vertical con-
centration profiles. The concentrations on the
leeward side of the cavity are more uniform than
those farther upstream, but little spreading occurs
into the region above the cavity (z/H>2). The
lateral concentration profiles in Figure 7a show
that the lateral plume width changes only slightly
in the downwind direction..
Additional concentration measurements for the
same stack and location, but with stack height 1.5
times the ridge height, were also made. Figure 6b
presents a few vertical concentration profiles for
the elevated stack and shows the plume rise to be
essentially zero. Zero plume rise now occurs because
the elevated stack is above the region of mean flow
stagnation. The elevation of the point of maximum
concentration decreases with downwind distance,
showing evidence of the recirculation within the
cavity. The highly uniform concentrations below
z/H = 1 are also evidence of the recirculation.
Even for this elevated stack, little dispersion
into the region above the cavity occurs. The
lateral ground level concentration profiles in
Figure 7b show essentially identical spread with
only minor differences in their values near the
center (y/H = 0). From these results, it is evident
that instead of the strong immediate downwash, which
occurred for the shorter stack, the taller stack
emissions are caught in the outer recirculation
region within the cavity. The direction of the re-
circulation is down the leeward side of the cavity
and upstream along the ground. Concentrations
measured near the reattachment point were highest
for the 1.5 H stack. This occurs because emissions
near the upper boundary of the cavity region are
caught in the general recirculation that downwashes
the plume towards the reattachment point. Because
emissions from a shorter stack at the same location
as above are more rapidly downwashed and dispersed,
a lower concentration will occur at the reattachment
point. This is one instance in which increasing
the stack height does not decrease ground level con-
centration.
496
-------
Phase III
Conclusions
The goal was to determine the effect of the
approach boundary layer conditions on the size and
shape of the leeward cavity region. The cavity
size and envelope for the 60-cm atmosphere-like
boundary layer approaching the 15-cm Gaussian
ridge were found to be similar to those for the
15-cm natural boundary layer. The turbulence
levels of the approaching natural boundary layer
may be expected to be much lower than those of the
simulated atmospheric boundary layer.
Changes in the size of the cavity and the
envelope were found when the mean flow approached
the ridge along a plane elevated to the height of
the ridge apex. Both the wake and envelope size
were reduced in comparison with the cases for an
Isolated ridge. The effect of changing the boundary
layer conditions appears to be minor in comparison
with effects of upwind terrain changes.
For the 30 cm Gaussian ridge with separation
occurring at the apex, the maximum depth and hori-
zontal extent of the cavity region were found to be
2 H and 10 H, respectively. The flow patterns in
the lee of ridges that exhibited separation at their
apex were found not to be sensitive to the detailed
shape of the slopes. The cavity sizes and shapes
were found to be only slightly affected by the
thickness and turbulence intensity of the approach
boundary layer, but were dependent upon the upwind
slope of the terrain.
Near the downwind end of the cavity (that is,
near the reattachment point), the flow is difficult
to characterize. Part of the main flow recirculates
within the cavity, and the rest continues downwind
forming a newly developing boundary layer. This
region can best be characterized by the increased
vertical and lateral spreading of a plume over that
occurring for a flow without the mountain ridge
disruption. The above assertions are generalizations
drawn from a limited amount of smoke visualization
and mean velocity and turbulence intensity data taken
downwind of the reattachment point. Further studies
of the behavior of plumes from stacks placed down-
wind of the reattachment point are needed to
characterize dispersion there.
• i/H • 0, «/H • US FROM STACK
* i/H - 1 . K/H - U5 FROM STACK
* i/H • 0 , K/H • 4.76 FROM STACK
o i/H - 1, x/H • 4.7S FROM STACK
H-M.Bcm
•i/H - D, i/H - US FROM STACK
• i/H - 0, K/H • 111 FROM STACK
_ *i/H • 0. «/H -4.76 FflDM STACK
H - 30.6 cm
1 I
Figure 6. Vertical concentration profiles for stack placed at base
(x/H = 2.7 from center) of 30.5-cm tripped Gaussian ridge.
= 0.5;B-Hs/H= 1.5.
Figure 7. Lateral concentration profiles from stack placed at base
(x/H = 2.7 from center) of 30.5-cm, tripped Gaussian ridge.
A- HS/H = 0.5; B - HS/H = 1.5.
497
-------
The cavity region leeward of the model ridge was
found to be highly turbulent with significant plume
downwash. The plume downwash results in ground
level concentrations within the cavity region that
are greater than 0.05 percent of the stack effluent
concentration. These concentrations are undoubtedly
significantly higher than would occur in the absence
of the mountain lee effects examined in this study.
For similar actual situations, it would be good
engineering practice to avoid placement of any
significant source within the expected cavity region.
The general engineering "rule of thumb," as
found repeatedly throughout the literature, for
avoiding plume downwash in the lee of an obstruction
is to keep the height of the stack "2.5 times" the
height of the obstruction. According to Sutton,
the rule was probably derived by Sir David Brunt
from a study on the height of disturbances over a
long ridge in connection with a British airship
disaster investigation. It, therefore, is not sur-
prising that the general rule is applicable to the
results of this study. Although the maximum depth
of the cavity was found to be 2 H, some margin of
safety is well advised, because strong downwashing
occurs in the upper regions of the cavity. The
maximum horizontal extent of the cavity was found
to be 10 H. Part of a plume emitted above a cavity
can, in this distance, spread downward and thus be-
come entrained within the cavity.
References
1. Scorer, R.S. Theory of Airflow Over Mountains.
IV-Separation of Flow from the Mountain Surface
Quart. Journal Royal Met. Society. 81:340-350,
1955. ~
2. Scorer, R.S. Air Pollution. Oxford, England,
Pergamon Press, 1968
3. Buettner, K.J.K. Orographic Deformation of
Wind Flow. Final Report USAEDRL Project Number
1AO-11001-B-021-01. University of Washington,
Seattle, WA. Contract Number DA.36-039-SC-89118.
May, 1964. 70 p.
4. Start. G.E., N.R. Ricks, and C.R. Dickson.
Effluent Dilutions Over Mountainous Terrain.
Air Resources Laboratory. Idaho Falls, Idaho.
NOAA Technical Memo ERL-ARL-51. 1975. p. 168.
5. Gloyne. R.W. Some Characteristics of the Nat-
ural Wind and Their Modification by Natural and
Artificial Obstruction. Scientific Horticulture.
XVn_:7-19, 1964-1965.
6. Pooler, F.,Jr. and L.E. Niemeyer. Dispersion
from Tall Stacks:An Evaluation. Paper No.ME-14D
(presented at 2nd International Clean Air Con-
gress. Washington, D.C. December 6-11, 1970)
7. Corby, G.A. Airflow Over Mountains:A Review of
Current Literature. Quart. Journal Royal
Met. Society. 80_:491-521, 1954.
8. The Airflow Over Mountains. World Meteorologi-
cal Organization. Geneva, Switzerland. WMO No.98
1967. 43 p.
9. Davidson, B. Some Turbulence and Wind Variabil-
ity Observations in the Lee of Mountain Ridges.
J. Applied Meteorology. 2_(4) :463-472, 1963.
10. Halitsky, J., G.A. Magony, and P. Halpern.
Turbulence Due to Topographical Effects.
New York Univ., N.Y., Geophysical Sciences
Laboratory Report TR66-5, 1965, 75 p.
11. Orgill, M.M., J.E. Cermak, and L.O. Grant.
Laboratory Simulation and Field Estimates of
Atmospheric Transport - Dispersion Over
Mountainous Terrain. Colorado State Univer-
sity, Fort Collins, CO. Technical Report.
CER 70-71 MMO-JEC-LOG40.
12. Huber, A.H., W.H. Snyder, R.S. Thompson, and R.E.
Lawson.Jr. Stack Placement in the Lee of a
Mountain Ridge. Environmental Protection
Agency, Research Triangle Park, NC. (To be pub-
lished).
13. Snyder, W.H. Similarity Criteria for the
Application of Fluid Models to the Study
of Air Pollution Meteorology. Boundary-Layer
Meteorology. 3_(2) :113-134, 1972.
14. Counihan, J. An Improved Method of Simulating
an Atmospheric Boundary Layer in a Wind Tunnel.
Atmospheric Environment. 3_: 197-214, 1969.
15. Sherlock, R.H. and E.A. Stalker. The Control of
Gases in the Wake of Smoke Stacks. Mechanical
Engineer. 62.: 455-458, 1940.
16. Snyder, W.H., R.S. Thompson, and R.E. Lawson, Jr.
The EPA Meteorological Wind Tunnel :Design,
Construction, and Operating Details. Environ-
mental Protection Agency, Research Triangle Park,
NC. (In preparation).
17. Sutton, O.G. Discussion before Institute of
Fuels. Journal Institute Fuel(London).
33:495, 1960.
Mention of trade names or commercial products
does not constitute endorsement or recommendation for
use by the Environmental Protection Agency.
498
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A NOTE ON THE SEA BREEZE REGIME
S. Trivikrama Rao
Division of Air Resources
New York State Department of Environmental Conservation
Albany, New York
Perry J. Samson
Department of Meteorology
University of Wisconsin
Madison, Wisconsin
ABSTRACT
Rotary spectrum analysis is applied to the wind field
over Long Island, New York, to delineate the clock-
wise and counterclockwise turning associated with
various spectral frequencies. On the south shore and
at higher elevations elsewhere over the island, the
diurnal oscillation is found to be a predominantly
clockwise rotation derived from sea breeze. At lower
levels, mid-island and on the north shore, there is no
dominant rotation in the diurnal oscillation. This
may be attributed to the interaction between the
sound breeze from Long Island Sound and the sea breeze
from the Atlantic Ocean.
INTRODUCTION
The sea breeze regime is mainly driven by the
difference between the air temperature over land and
that over water. The diurnal variation of solar
radiation sets up a temperature contrast between the
two surfaces because of their different heat capaci-
ties. Because of the influence of the Coriolis accel-
eration, the rotation of the sea breeze is predomi-
nantly clockwise.
The Long Island Sound to the north and the Atlantic
Ocean to the south of Long Island produce sound
breezes and sea breezes, respectively, resulting in
complex circulation patterns over the island. Rotary
spectrum analysis provides a means of distinguishing
the presence of clockwise and counterclockwise rota-
tion components in the horizontal wind field and is
an excellent tool to study •such interactions.
This paper reports the results of rotary spectrum
analysis of the wind data collected on the north and
south shores and in the center of Long Island, New
York.
SOURCE OF DATA
Data from wind direction and speed sensors were
obtained from towers located on the south shore of
Long Island at Tiana Beach, on the north shore at
Shoreham and Jamesport, and in the center at Brook-
haven National Laboratory (BNL). These locations are
shown in Fig. 1. Hourly values were collected from
sensors at 75 ft. at Tiana Beach, 355 ft. at BNL,
33 ft. and 150 ft. at the Shoreham tower and 400 ft.
at Jamesport tower. Data for the period July-August
1975, representative of summer, are used in this
study. Data for December 1974-January 1975 at 355 ft.
level at BNL, representative of winter, are also
analyzed to explore the seasonal variation of the
different spectral components.
METHOD OF ANALYSIS
Gonnella used the rotary spectrum to study internal
waves in the ocean. This type of analysis has since
been applied to the study of the sea breeze regime
along the coast of Oregon by O'Brien and Pillsbury2.
Basically, the method hinges on the fact that the
spectral decomposition gives at each frequency (f) a
sinusoidal wave for each horizontal velocity componert
The east and north component sinusoids together form
an ellipse at each frequency. Four quantities emerge
in the rotary spectrum analysis: the mean kinetic
energy or the total spectrum, the rotary coefficient,
and the orientation and stability of the ellipse. All
these quantities, except the orientation of the
ellipse, are invariant under coordinate rotation.
If P
are the auto-spectra and P
are the
cross and quadrature spectra of the east and north
components, u(t) and v(t), of the horizontal velocity,
the following mathematical relationships exist:
The total spectrum:
Sf = Cf + Af = 1/4 (Puu + P^)
where the clockwise spectrum:
Cf = 1/8 (Puu + PVV - 2 Quv)
and the anti clockwise spectrum:
Af = 1/8 (Puu + PVV + 2 Quv)
The rotary coefficient:
CR cf - Af = -2 Quv
sf puu + pw
The orientation of the ellipse:
tan 2 0 = 2 puv
P - P
uu w
and the stability of the ellipse:
|p|2 _ (P + P }2 - 4 (P P - p2 )
111 = *.ruu rw-' H ^ruu rw r uv'
^2
The rotary coefficient, CR, varies as (1 -£) where £
is the eccentricity of the ellipse. Its numerical
value ranges from 0, indicating unidirectional motion,
to unity, a pure rotary motion. Further descriptions
of the spectrum may be found in Gonnella .
For the statistical analysis presented here, a fast
Fourier transform algorithm is used to partition the
sample variance among frequency bands. The total
length of the data is divided into 5 non-overlapping
segments each consisting of 256 data points (N = 256),
499
-------
so that the spectral estimates have 10 degrees of
freedom. This technique is discussed by Hinich and
Clay3. To avoid end effects, the N points are
smoothed by use of a weighting function of the form
1/2 (1 - cos lUS), n = 1, 2 N. In addition, the
N
trend is removed by subtracting a linear function from
the data values. These data are Fourier-transformed to
derive the complex Fourier coefficients from which the
clockwise and anticlockwise spectra are computed for
each segment, and then averaged over all segments.
Furthermore, these spectral estimates are subjected to
a "Double-Banning" smoothing procedure (Jenkins and
Watts^-) which increases the reliability of the spec-
tral estimates.
RESULTS
The variance spectra for the wind field at Tiana Beach,
Fig. 2a, shows the dominance of the clockwise rotation
at the diurnal and semi-diurnal frequencies. The
spectra at BNL and Jameaport, Fig. 2b and 2d respec-
tively, do not reveal any anticlockwise rotation at
the diurnal frequency. The peak corresponding to
f = 0.04 cycles/hr at these elevated sensors is pre-
dominantly a clockwise rotating oscillation, a sea-
breeze phenomenon. The spectra at the 33 ft. level at
Shoreham (Fig. 2e) show no clear dominance of rotation
However, at the 150 ft. level (Fig. 2f) the dominance
of clockwise rotation is again seen. Also included
is the spectrum for winter season at BNL 355 ft. level
(Fig. 2c). Note the complete absence of diurnal and
semi-diurnal peaks suggesting that the influence of
the large-scale weather features, dominant in the
winter season, overshadows the sea-breeze circulation
generated by the land and water temperature difference
The rotary spectral statistics are presented in Table
1. The lower bound on values of the ellipse stability
at the 1% confidence level is 0.63 (Panofsky and
Brier^). This implies that the chances are 1 in 100
that a stability coefficient of 0.63 or more will be
found by accident. It is evident from the table that
the ellipse stabilities at Shoreham 150 ft., Tiana
Beach 75 ft., BNL (summer) 355 ft., and Jamesport
400 ft. exceed this limiting value. Also, CR values
of 0.73 at the BNL (summer) and 0.66 at Jamesport
indicate a strong rotary motion at the upper levels.
At the Shoreham 33 ft. level a CR value close to zero
and insignificant ellipse stability coefficient imply
no dominance of any particular direction in the
oscillation. At the upper levels, an average value
of the orientation of the major axis of the ellipse
is found to be 76° (from true north) which corresponds
to the orientation of the Long Island coastline. This
indicates that on eastern Long Island, local circu-
lation patterns are generally aligned in axes parallel
to the shoreline.
TABLE 1
Rotary Spectral Statistics for the Diurnal Oscillation
Station Height of
0'
oserva-
tion(ft)
Shoreham
Shoreham
Jamesport
BNL (Summer)
Tiana Beach
BNL (Winter)
33
150
400
355
75
355
Orientation Rotary
of the
ellipse(0)
275°
83°
70°
75°
78°
347°
uoerr-
ic(clf
0.07
0.32
0.66
0.73
0.42
0.24
Ellipse Cf
Stabil-
ity^)
0.31
0.88
0.77
0.72
0.80
0.20
* A
Af
1.25
1.81
3.88
4.77
2.45
1.68
The effect of friction on the sea breeze hodograph
tends to render the ellipse smaller and considerably
more eccentric. Large eccentricity values for the
diurnal oscillation found at lower levels can be
attributed to the influence of friction at the lower
boundary. It should be recalled that the rotary co-
efficient values vary as (1- C) where C is the eccen-
tricity. The decreasing values of eccentricity (in-
creasing CR) with height reflect the decrease in
frictional influence. The eccentricity found at Tiana
Beach is less than that at the Shoreham 150 ft. level.
This may be explained by the interaction of sound
breeze and sea breeze on the north shore.
Haurwitz' described the relationship between the max-
imum temperature difference between land and water as
a function of coefficient of friction. He suggested
that without friction the time difference between max-
imum sea-breaze velocity and maximum land and water
temperature contrast is 6 hours. With increasing fric-
tion, the time difference between the maximum of the
sea breeze velocity and that of temperature difference
decreases. The average shape of the diurnal wave
can be obtained through superposition of several diurnal
cycles in the record, and then averaging the specific
value for each phase of the wave. When this is done,
it is found that the wind speed maximum occurs around
17:00-18:00 EST at Tiana Beach and at the Shoreham
33 ft. level; and around 20:00 EST at Shoreham 150ft.,
BNL 355 ft., and Jamesport 400 ft. levels. With such
values of friction as have been determined from
observations on land, the maximum sea breeze should
occur about three hours after the temperature differ-
ence between land and water has reached a maximum.
Usually, the maximum temperature difference occurs
about 14:00-15:00 EST. The decrease of frictional
effects with height could explain the larger time
difference between maximum wind speed at Shoreham
150 ft., BNL 355 ft., and Jamesport 400 ft. levels
and maximum land and water temperature difference,
consistent with the rotary coefficient values.
A study of the characteristics of the Atlantic sea
breeze and Long Island sound breeze (LILCO^) concluded
that the sound breezes are generally morning phenomena
and have onset times between 09:00 EST and 12:00 EST.
The average duration of the sound breezes was about
three hours after which they were generally destroyed
by the strengthening of the Atlantic sea breeze. They
also found that the stronger Atlantic sea breeze is
capable of overrunning the sound breeze completely,
resulting in a flow reversal from on-shore to off-shore
near Shoreham. Dominance of clockwise rotating os-
cillation in the rotary spectra at upper levels lends
support to their observation. The dynamics of the in-
teraction of the sea and sound breezes at Shoreham
probably account for the lack of an easily discernable
rotation pattern.
SUMMARY AND CONCLUSIONS
A relatively new descriptive technique to analyze
vector time series, the so-called rotary spectrum, has
been applied to study the sea-breeze circulation over
eastern Long Island, New York. The results indicate
a clear dominance of the sea breeze at levels above
150 ft. The hodographs show a pronounced eccentricity
at lower levels, a manifestation of friction. The
observed phase differences between occurence of max-
imum wind speed over land and maximum land and water
temperature difference are consistent with the sea-
breeze dynamic theories. Furthermore, as to be ex-
pected, during the winter season the local sea-breeze
pattern set up by the land and water temperature con-
trast has been completely overshadowed by large-scale
weather features. In future studies, it would be in-
teresting to compute the trajectories of the wind
field over Long Island to obtain more quantitative
500
-------
information on the nature of sound and sea breezes.
ACKNOWLEDGEMENTS
Thanks are due to Mr. Geroge Martin of the Long Island
Lighting Company and Ms. Constance Nagle of the Brook-
haven National Laboratory for providing us with the
necessary data.
REFERENCES
1. Gonnella, J. (1972) A rotary-component method
for analyzing meteorological and oceanographic
vector time series. Deep Sea Res. 19, 833-846.
2. O'Brien, J. J. and Pillsbury, R. D. (1974)
Rotary wind spectra in a sea breeze regime.
J. App. Meteor., 13, 830-825.
3. Hinich, M. J. and Clay, C. S. (1968) The appli-
cation of the discrete Fourier transform in the
estimation of power spectra, coherence and bi-
spectra of geophysical data. Rev. Geophys. 6,
347-363.
4. Jenkins, G. W. and Walts, D. G. (1968) Spectral
analysis and its applications. Holden-Day,
San Francisco.
5. Gossard, E. E. and Noonkester, V. R. (1968) A
guide to digital computation and use of power
spectra and cross-power spectra. Naval Electron-
ics Laboratory Center for command control and
communications, NELC Technical Document 20,
San Diego.
6. Panofsky, H. A. and Brier, G. W. (1965) Some
applications of statistics to meteorology. First
ed., the Pennsylvania State University, University
Park, Pennsylvania. 224 pp.
7. Haurwitz, B. (1947) Comments on the sea-breeze
circulation. J. Meteor., 1, 1-8.
8. LILCO (1975) Jamesport Nuclear Power Station -
Applicant's Environmental Report.
Fig. 1 Location of the specific measurement sites
used for this study on Long Island, New York.
501
-------
Fig. 2 Rotary Spectral Density Estimates:
a) Spectrum of the horizontal wind during
summer at Tiana Beach at the 75 ft. level.
b) Spectrum of the horizontal wind during
summer at Brookhaven National Laboratory
at the 355 ft. level.
c) Spectrum of the horizontal wind during
winter at Brookhaven National Laboratory
at the 355 ft. level.
d) Spectrum of the horizontal wind during
summer at Jamesport at the 400 ft. level.
e) Spectrum of the horizontal wind during
summer at Shoreham at the 33 ft. level.
f) Spectrum of the horizontal wind during
summer at Shoreham at the 150 ft. level.
The solid lines represent the anticlockwise spectrum
and the dashed lines the clockwise spectrum. If S(f)
is the true spectral estimate and Sf is the estimated
value, then there is a 90% confidence (for 10 degrees
of freedom set by a chi-squared distribution) that
0.55 Sf
-------
A NUMERICAL MODEL FOR STABLY STRATIFIED FLOW AROUND COMPLEX TERRAIN*
James J. Riley
Hsien-Ta Liu
Edward W. Geller
Flow Research, Inc.
Kent, Washington
A computer program has been developed, based on an ex-
pansion suggested by Drazin (1961)1 and Lilly (1973)2
to compute three-dimensional stratified flow around
complex terrain for the case of very strong stratifica-
tion (small internal Froude number). Also, laboratory
experiments were performed for strongly stratified flow
past three different terrain models. Preliminary com-
parisons of the results of the computer program and the
laboratory modeling indicate that the computed results
are in fair agreement with the experiments. Discre-
pancies are probably attributable mainly to the separa-
ted wake in the lee of the models. Other possible
sources of error are discussed in some detail.
1. Introduction
Assessment of the environmental impact of the release
of pollutants into the atmosphere involves the estima-
tion of diffusion patterns under atmospheric conditions
ranging from average to extreme. A detailed knowledge
of the wind field is important in the estimation of dif-
fusion patterns, especially if the region of release is
characterized by complex terrain. Thus, in the assess-
ment of pollution effects, the understanding and pre-
diction of local wind fields is often very important.
One approach to understanding and predicting local wind
fields is numerical simulation. However, the numerical
simulation of three-dimensional stratified flow over
complex terrain is a very difficult task. This diffi-
culty is a result of numerical complications associated
with stratification effects and complex boundaries, and
also of the limitations imposed by the core size and
cycle time of present day computers. Thus, exploration
of certain limiting conditions under which the physical,
mathematical and numerical problems can be simplified
is useful. One such limit is that of very large inter-
nal Froude number, i.e., weak stratification, where the
tools of three-dimensional potential-flow theory are
often available. Another limit is very small internal
Froude number, or strong stratification.
When fluid is strongly stably stratified, vertical mo-
tions are heavily constrained and fluid elements tend
to remain in their horizontal planes. The degree to
which they do remain is measured by the ratio of their
initial kinematic energy, —p U , to the potential energy
required to lift the fluid element over or around the
obstacle, .. dp_
the square of the internal Froude number, where
ch2.
2 5 dx
j
Here, h is the characteristic vertical scale of the
obstacle, g is the acceleration due to gravity, and
j— is a characteristic ambient stratification. The
dX3
ratio is
o"2 /o_f_
PC .2 \Nh/
dp
dx_
"•This work is supported by the Environmental Protection
Agency, Research Triangle Park, North Carolina, Con-
tract No. 68-02-1293.
Vdp
JL_c
p_ dx,,
N =
is a characteristic Brunt-Vaisala frequency of the am-
bient fluid. For strongly stratified flows (F + O),
Drazin (1961)1 and, later, Lilly (1973)2have proposed a
2
formal expansion in F , which predicts that to the low-
est order, the flow resembles two-dimensional (hori-
zontal) flow around contours of terrain at a given
level. The deviations from this two-dimensional flow
can be determined from the higher order terms in a
power series.
In the work discussed in this presentation, we have
developed computer programs to solve the equations re-
sulting from the expansion suggested by Drazin and
Lilly. We have also performed laboratory studies of
stratified flows past simple terrain configurations to
validate the numerical programs. Finally, we have made
preliminary comparisons of theory and experiment.
2. Brief Description of the Theory
Consider the steady-state flow past a three-dimensional
terrain feature with a typical vertical scale, h, and
horizontal scale, L. We assume the oncoming (free-
stream) flow has characteristic velocity, U, and char-
acteristic stratification, dp /dx_, which is a constant.
(The coordinate system is oriented with positive x.j
vertically upwards). We will also make the Boussinesq
approximation and will neglect viscous (turbulent) ef-
fects. The equations of motion are (see Phillips,
1966)3:
g (0,0,-g)
and
u- = 0
u • Vp + u, -4P- = 0.
3 dx.
(2.1)
(2.2)
(2.3)
Here, u is the velocity vector, p is the density fluc-
tuation about the ambient p, and p is the pressure per-
turbation about the ambient. The vertical displacement
of a fluid element,
-------
balance in the vertical momentum equation. Then,
p - . P (2.5e)
(o)
To scale u_, we assume that u -j*- and either u. -T&- or
3 3 dx3 1 3X-L
G -4P- (or both) are in approximate balance in equation
2
(2.3), which results in „
U3
a3 ~~
where
U F
Nh
2 '
(2.5f)
(2.6a)
is the Froude number,
Vdp
_S_ _£.
P dx_
(2.6b)
o 3
is the characteristic Brunt-Vaisala frequency, and
where we scale the ambient stratification (assumed)
horizontally uniform as
dp
From (2.4), the scaling for ty is
(2-6c)
(2'6d)
hF
Substituting (2.5) into the horizontal component of
(2.1), we find
?H ' V!±H + F* U3 ^ "H = - V" <2
The vertical component of (2.1) becomes
Continuity is now expressed as
2 3u3
v -^ + F -° •
and the incompressibility condition is
(2.9)
Finally, the equation for ijj, the displacement, becomes
(2.11)
= v
Next, we expand the independent variables in the powers
2
of the small parameter, £ = F , i.e.,
n=0
The resulting equations to the lowest order are
a,<0) • V" V<0) •
- o.
(2.12)
(2.13)
(2.14)
- P
(o)
and
(o) . (o) = u (o)
1 J
(2.15)
(2.16)
(2.17)
Combining (2.16) and (2.17) gives
Assuming p _and ijj are zero in the free stream,
-r-^-
(o) ,
or with (2.15)
3x,
dx
(2.18)
Note that, from equations (2.13) and (2.14), the equa-
tions for UH and p are those for an inviscid,
two-dimensional flow in a horizontal plane. In parti-
cular, if the incoming (horizontal) flow is irrotational,
then the entire horizontal flow field is irrotational.
Thus, in this case the tools of the potential-flow
theory can be employed to compute the flow. In a given
horizontal plane, the resulting solution would be that
of a two-dimensional flow about an obstacle defined by
the contour of the terrain at the vertical level of
that terrain. The vertical displacement can be com-
puted from (2.18), where it is a result of the pressure
difference in the flow between two adjacent horizontal
layers. A calculation of the vertical displacement can
also be used to estimate the region of validity of the
results.
Equations (2.13), (2.14) and (2.18) were programmed on
the computer for flow past somewhat arbitrarily shaped
terrain features. The free-stream flow was assumed
irrotational, and standard numerical procedures for
computing the two-dimensional potential flow past ar-
bitrarily shaped bodies were used.
3. Description of the Experiment
The experimental setup was basically the same as that
discussed in Flow Research Report No. 57 (Liu and Lin,
1975)4. In addition to "the idealized terrain model,
which has been used for detailed studies in the past
(see Flow Research Report No. 29)5 and is defined by
= 17
.SJ
exp -.0008513(x. 61)"
.01197 (x2 - 18.82)
7 2
exp | -.0008513(3^- 61) - .01197(x2 +18.82)
+ 16 , (3.1)
1(
we used a conically shaped model
30 f 1 - jj) r £ 15
0 r > 15,
(3.2)
504
-------
and a Gaussian shaped model,
the experiments was roughly from .05 to .5.
,) - 30 exp | - fa
a/2
(3.3)
/ 2 2\1/2
Here, r = Ix + x_ I and all distances are measured
in centimeters.
The two latter (new) models were designed to be inter-
changeable with the idealized model. Neutrally buoyant
dyes, each of a different color, were released through
small stainless-steel tubes (.3 mm I.D.) at three levels
upstream of the model. Three plumes spaced in the hori-
zontal were released in each level. The plume trajec-
tories were photographed, and then analyzed for later
comparisons with analytical results. Figure 1 shows a
typical side view of the streak-line patterns for flow
past the Gaussian peak.
Figure 1. The Flow Patterns Traced by Neutrally
Buoyant Dye in the Vicinity of a
Three-Dimensional Gaussian-Shaped
Model. N = .135 Hz, U = 4 cm/s,
F, = .97.
Note that in each horizontal plane, three streak lines
were released. However, in the side view, the three
are difficult to distinguish, especially in the lowest
Froude number cases. This difficulty is somewhat com-
pounded by the slight vertical spread of each streak
line. However, in a given horizontal plane, the Inner-
most streak line is displaced more than the others, so
that its displacement is easily detectable in the photo-
graphs. Thus, when comparisons were made, we used the
innermost streak line.
The choice of the model conditions was based on the
following criterion. The expansion can only remain
valid as long as streamlines do not cross in the verti-
cal. This crossing would occur, for^example, if
$(x->)> J (x +Ax )+Ax . Thus, -Ax. > i^(x,+Ax-)-iJ)(x-), or
-'333 ' J j-> -5
in the limit, as Ax, -* 0,
3x, —
When one considers both upward and downward displace-
ments, this condition generalizes to
dip
> 1.
Thus, in nondimensional terms, a necessary condition for
the validity of the expansion is
< 1.
(3.4)
We selected the various parameters in the experiments so
that (3.4) was satisfied over a large portion of the
vertical region of interest. The Froude number range of
4. Comparisons of Experimental and Numerical Results
The general behavior of the streak lines can be seen
by examination of figure 1 . In the middle horizontal
plane, consider the inner streak line, which exhibits
the largest vertical displacement. As a fluid element
approaches the model, it slows down in a manner similar
to an element in a two-dimensional flow about a
cylinder. Simultaneously, the element experiences an
upward pressure force, causing it to rise upward (see
equation 2.18). As the element starts around the
mountain, it accelerates, the vertical pressure force
changes direction, and the element is displaced down-
ward. The flow separates near the point of maximum
lateral extension of the model. Past the midpoint of
the mountain, the elements return to their equilibrium
levels, and are entrained into the wake of the model.
For the Froude number range in the experiments, the
wake flow in the lee of the model appeared to consist
of turbulent, quasi-horizontal eddies, whose vertical
velocity fluctuations were rapidly decaying with down-
stream distance.
The incoming flow was slightly unsteady. We observed
that the inner streak lines slowly oscillated from one
side of the mountain to the other. This oscillation
often produced an inner streak-line pattern as sketched
in figure 2.
^^HM*******^ £.
Figure 2. Sketch of the Instantaneous Streak-
Line Pattern
One possible explanation of this phenomenon is the
following. For two-dimensional flow past a cylinder,
turbulent vortex streets are observed in the Reynolds
number range of about 60 £ R £ 5000, where the Reynolds
number R is UD/v, D is the diameter of the cylinder,
and v is the kinematic viscosity. For our case, R is
typically
R «
.01 cm /sec
~ 4000
which is in this range. The vortex motion is accom-
panied by movement of the stagnation points, which in
turn causes the incoming flow to oscillate slightly.
For R in this range, the Strouhal number, defined by
S = nD/U, where n is the vortex shedding frequency in
radians/sec, is approximately .21. Thus,
n ^ .21 x 4 cm/sec
2TT ~ 2IT x 10 cm
X .014 cycles/sec.
This value corresponds roughly to the frequency of the
oscillations noted in the experiments.
Figure 3 shows streak lines in the horizontal plane,
x, = 13.2 cm (the middle plane) for the Gaussian model
505
-------
with F = .152. Also shown are the numerical predic-
tions. In addition, the contour of the model at the
free-stream level of the plumes is displayed. Note that
the numerical calculation tends to underpredict streak-
line displacement. This discrepancy is probably the re-
sult of mainly two effects. The first is the displace-
ment effect of the boundary layer, which is not taken
into account in the inviscid numerical model. The
second and more important effect is the displacement
effect of the separated wake. These two effects to-
gether produce an "apparent" body, as sketched in
figure 4a.
NUMERICAL RESULTS
_. NUMERICAL (WITH SIMPLIFIED WAKE MODEL)
^__c-^—~ EXPERIMENTAL RESULTS
20 X,(CM)
COMPARISON OF EXPERIMENTAL E NUMERICALLY COMPUTED
STREAK LINES IN THE HORIZONTAL PLANE DEFINED BY X,= I4CM
FOR CASE TTC (GAUSSIAN MODEL Ff -.9?)
APPARENT" BODY
CONTOUR
Figure 4a. Apparent Body Shape
Reynolds numbers will usually be several orders of mag-
nitude larger than the critical value, separation is
likely to occur just past the point of maximum lateral
extent.
When viscous terms are added to ^he scaling arguments
presented in section 2, one finds that the lowest order
solution is no longer two-dimensional. Thus, the con-
clusions drawn above could be modified somewhat because
of the three-dimensional nature of the boundary layer.
The displacement effect of the separated wake was crude-
ly modeled by extending the body, as shown in figure 4b.
Figure 3 also shows the results of a calculation using
this body shape instead of the circular shape. The mod-
ification of the streak lines, especially the outermost
ones, is noticeable. However, from the discussion
above, the model suggested in figure 4b is probably more
adequate for the full-scale case than the laboratory
case. Also, the effect of the boundary layer may have
to be taken into account to obtain close agreement be-
tween the numerical and experimental results.
The width of the tank is approximately 120 cm, so it is
possible that the sidewalls influence the flow field
near the models. Sidewalls were not included in the
numerical calculations for the Gaussian and conical
models. However, the horizontal displacement of the
streamline whose free-stream position is at the side-
walls was computed. For the Gaussian and conical models
the displacement of this streamline was negligible for
the cases computed. Thus, for these cases, we can as-
sume that the effect of sidewalls is unimportant.
Figure 5 shows the experimentally determined vertical
displacement for the conical model with F = .109. Also
shown in this plot is the numerical prediction for the
innermost plume in the middle level. The numerical
calculation predicts a very slight rise in the plume as
it approaches the mountain, which is also discernible in
the experiments. The distance that the plume drops is
also predicted fairly well. However, the asymmetry of
the experimental results is missed entirely. This dis-
crepancy is again probably attributable to the neglect
of the boundary layer and wake effects.
SOLID LINES-EXPERIMENTAL RESULTS
DOTTED LINE "KUMSRICAL RESULTS
Figure 4b. Model for the Separated Wake
Note that for a two-dimensional flow past a circular
cylinder, if the Reynolds number is subcritical (i.e.,
below approximately 3 x 10 ), the boundary layer is
laminar, and it separates at about 80° from the front
stagnation point (Schlichting, I960)6. Since the Rey-
nolds numbers for the experiments were an order of mag-
nitude less than the critical value, it is reasonable
to assume that the boundary layer was laminar and sepa-
rated before the point of maximum lateral extension of
the body. For two-dimensional flow past a circular cy-
linder, if the Reynolds number is supercritical, the
boundary layer is turbulent, and separation probably
occurs just past the point where the cross section
starts to converge. Thus, in the full-scale case, where
FIGURE 5 COMPARISON OF EXPERIMENTAL 8 NUMERICALLY COMDUTED RESULTS
FOR VERTICAL DISPLACEMENT FOR CASE TX. b
(CONICAL MODEL &-.7-;)
Figure 6 shows similar experimental plots for the Gaus-
sian model at F .152. Also shown are the numerical
predictions for the innermost plume for each of the
three levels. The agreement and explanation of the re-
sults are very similar to the previous case.
Finally, figure 7 shows comparisons of experimentally
observed and numerically computed streak lines for the
idealized terrain case, with F = .218. The dye was
released at approximately x, = 11.5 cm. Note that the
506
-------
SHADED AREAS* EXPERIMENTAL RESULTS
- NUMERICAL RESULTS
• 10 CM
FIGURE 6. COMPARISON OF EXPERIMENTAL £ NUMERICALLY COM PUTED
RESULTS FOR VERTICAL DISPLACEMENT FOP, CASE 7 C
(GAUSSION MODEL, ft • .97)
IWB1CAL RESULTS
EXPERIMENTAL RESULTS
FIGURE 7. cmnlSOIl OF EXPERIBOITAL t «I|«E«!CALLY CWUTETJ STREAK
HUES IN THE IIOHIZOIiTAL PLANE DEFINED BY L • U 5 ffl
(ILEALI2EJ) TERRAIN MILL, F,, - 1,37) '
calculation included separation in the wake, as discus-
sed above. Comparisons for this case are much better
than for the previous cases because the crude wake
modeling for the potential flow calculation closely
matched the real flow. In the calculations for the pre-
vious cases, the assumption that the separation stream
line is straight and parallel to the upstream flow di-
rection was not supported by the experimental results
which indicate a diverging wake region.
An examination of the side view shows sizeable vertical
displacement as the stream lines traverse the ridge.
This is accompanied by some motion towards the ridge,
resulting in the inner plume appearing to cut through
the terrain in the top view. As the fluid comes over
the ridge, it tends to fall below its ambient level,
thus forcing the fluid laterally away from the ridge,
and producing the slight bulge seen in the figure above
the ridge. This bulge may also be attributable to a
boundary layer separation bubble. According to the
potential flow calculation, the boundary layer is sub-
jected to an adverse pressure gradient near the most
upstream point on the model. Therefore, separation of
the laminar boundary layer is likely.
Finally, calculations of the streamline at the location
of the tank sidewall show that its lateral displacement
is significant. Thus sidewall effects, which were
neglected in the calculation, could be of some impor-
tance in this case.
5. Conclusions and Suggestions for Future Studies
This study was intended to be a very preliminary examin-
ation of the use of the scaling suggested by Drazin
(1961)1 and Lilly (1973)6 for the case of very low
Froude-number, three-dimensional flow over complex ter-
rain. Preliminary results indicate the following:
(i) For the Froude number regime studied, the basic
scaling suggested was appropriate, and the flow did
resemble two-dimensional flow around contours of the
terrain model at the appropriate level.
(ii) To improve the numerical model, the inclusion of
at least two effects is of primary importance. They
are: (a) the displacement effect of the boundary layer,
and, more importantly, (b) the displacement effect of
the separated wake.
(iii) The prediction of vertical displacement was
roughly valid for the case computed, considering that
the effects discussed in (ii) were not modeled.
(iv) The accuracy of the lowest order solution depends
strongly on the type of terrain feature considered, as
well as the vertical level, the lateral distance from
the terrain feature, and, of course, the Froude number.
For a given Froude number, the agreement between the
numerical model and experiment was much better for the
idealized complex peak than for the Gaussian and coni-
cal models.
(v) The computed vertical displacement'can be used to
estimate regions of applicability of the lowest order
solution.
(vi) Slight unsteadiness in the oncoming flow may be a
result of turbulent vortex shedding in the lee of the
models.
One obvious improvement can be made in the numerical
model. The separated wake can be crudely modeled by
standard techniques used in aerodynamics to compute
flow past two-dimensional bodies. (Note, however,
that one may have to take into account the three-
dimensional nature of the boundary layer).
Several other improvements are also possible. First,
one could include the vertical and horizontal shearing
of the free-stream flow. Second, the atmospheric
boundary layer could be modeled. This modeling can be
accomplished most simply by using the computed invis-
cid flow to derive a turbulent boundary layer model. A
more sophisticated approach would allow the computed
boundary layer to react back on the inviscid flow.
Third, the scaling analysis could include the effect of
atmospheric compressibility, although this effect
shouldn't be too important because the vertical motions
are weak. Fourth, Coriolis forces could be included.
Fifth, as discussed by Drazin and Lilly, the scaling
breaks down near the model peaks (because the local
scale height is very small, and, therefore, the local
Froude number is very large). An investigation of the
coupling of the present numerical model with some other
model near the mountain peaks could be performed.
Sixth, turbulent diffusion could be modeled in the
plume dispersion process with the turbulent diffusivity
related to the local Richardson number._ Finally, it is
implicit in the scaling analysis that dpc/dx3 character-
ize the complete density profile. For example, in re-
gions where dp/dx3 is very small compared to dpc/dxj,
the expansion will probably break down. So the case of
a two-layer fluid (each layer having a different constant
density) cannot be treated with the present scaling.
Thus, rescaling the equations to include these more
general cases would be useful.
References
1. Drazin, P. G. (1961), Tellus 13. 239-251.
2. Lilly, D.K. (1973) Flow Research Note No. 40.
3. Phillips, O.M. (1966), The Dynamics of the Upper
Ocean, Cambridge University Press.
4. Liu, H.T. and Lin, J.T. (1975), Flow Research
Report No. 57.
5. Lin, J.T., Liu, H.T. and Pao, Y.H. (1974), Flow
Research Report No. 29.
6. Schlichting, H. (1960), Boundary Layer Theory, McGraw
507
-------
HYDRODYNAMIC AND WATER QUALITY MODELING
IN THE OPEN OCEAN USING MULTIPLE GRID SIZES
Priya J. Wickramaratne, James W. Demenkow,
Stanley G. Chamberlain and Janice D. Ca.-llah.an
Environmental, Systems Analysis
Oceanographic & Environmental Services
Raytheon Company
Portsmouth, Rhode Island
ABSTRACT
This paper discusses the problems and limita-
tions of the application of hydrodynamic and
water quality models to open ocean areas in
which varying degrees of resolution are re-
quired. In applications involving power plant
or wastewater treatment discharge into large
bodies of water, a higher degree of spatial
resolution is often required near the dis-
charge location. The models have been execu-
ted using two different grids sizes in order
to obtain the desired resolution while re-
ducing overall computer costs. The grids were
intermeshed using a technique in which the
length scale of the larger grid was an even
multiple of the smaller grid. The results
obtained using the larger grid were used to
generate boundary conditions for the smaller
grid. This was easily accomplished since the
length scale of the larger grid was taken
to be an even multiple of the smaller grid.
INTRODUCTION
The modeling of environmental problems per-
taining to water pollution frequently requires
a greater level of detail in certain geograp-
hical regions, while not requiring as much in
the rest of the study area. For example, a
model of a discharge plume would require con-
siderably more detail in the vicinity of the
outfall, where the concentration gradients are
the steepest, and less detail as one moves
away from the outfall, where the gradients are
considerably less steep.
Many of these water quality models use a
finite difference technique, where the study
area is overlaid by a grid of constant cell
size. Computer costs and core storage size
often make the modeling of the entire area
with a grid fine enough to obtain the desired
details both costly, and impractical. Hence,
the need exists to mesh together a fine and
coarse grid structure which will provide both
the desired detail of the fine grid and the
economic advantages of the coarse grid.
This paper describes a technique to accomplish
the intermeshing of coarse and fine grid
structures in far-field models for any well-
mixed waterway An application of the tech-
nique is given to illustrate how it can be
performed for an open ocean situation.
TECHNIQUES
Circulation Model
A circulation model used extensively by
Raytheon is a two-dimensional long wave pro-
pagation model based on Leendertse1.
The model consists of a digital computer
algorithm which yields a numerical solution
to the vertically averaged hydrodynamic
equations of motion. The equations of motion
describe water currents which are driven by
horizontal pressure gradients produced by
tidally induced changes in surface elevation.
They include a "continuity equation"
and the momentum equations
3u , 3u
3u
5t
8t 3x
where :
u =
. o
3y
3y
v(u2+v2)1/2
vertically-averaged velocity in x direc-
tion .
v = vertically-averaged velocity in y direc-
tion.
r\ = incremental tide height about mean value.
h = water depth to reference plane (mlw) .
C = Chezy coefficient.
g = acceleration of gravity.
t = time .
These equations are solved numerically by the
multi-operation method : which possesses the
good stability attributes of a pure implicit
scheme and the computational efficiency of an
explicit scheme.
Boundary Conditions . A key to running
the circulation model is the generation of the
appropriate driving forces on the boundaries.
This paper will concentrate on the generation
of boundary conditions at the boundaries
between the coarse and fine grid regions.
(The outer boundary conditions for the coarse
grid region are specified in the usual way) .
If the fine grid region is entirely within the
coarse grid region, as in Figure 1, then the
fine grid boundary conditions can be found
from the coarse grid simulation. Boundary
condition data for the fine grid is obtained
by first executing the coarse grid model and
saving the computed water levels in the cells
which form the boundaries of the fine grid,
at every time step over the desired simula-
tion time period. The values thus obtained,
are linearly interpolated between spatial
points (at every time step) , as shown in
Figure 1, to give the desired boundary
508
-------
conditions. The time step is determined from
the grid size and water depth, with computer
costs being used as constraints, to satisfy
the accuracy criterion,
At < 2AL (gh)"1/2
where At is the time step, and AL is the
length of a grid square.
The basic equation which describes the de-
pendence of the concentration (C) on the dis-
tance variables (x,y), time (t), depth (h),
currents (U,V), constituent decay coefficient
(k), diffusion coefficient (E , E ) and dis-
charge rate (S) is: x "
-------
increase the accuracy of the boundary values
for both grids.
Fine Grid Outer Boundary
-•-•- Coarse Grid Inner Boundary
• Boundary Values of Fine Grid From
Coarse Grid
X Boundary Values of Coarse Grid from
Fine Grid
Figure 2. Interfacial Boundaries Within
Fine and Coarse Grid Regions
for Water Quality Models.
This procedure is repeated for the desired
length of the simulated time, with the
boundary values of the fine and coarse grid
being interchanged at contiguous intervals
of time of length AT .
Since mass transfer occurs at the boundaries
between the coarse and fine grid regions, the
values of the concentrations in the coarse
grid must be allowed to affect the values
of the concentration in the fine grid and
vice versa. This is the primary motivation
for intermeshing the coarse grid and fine
grid in the manner described.
APPLICATION
The techniques described in the preceding
section are now illustrated by the applica-
tion to the dispersion of a water quality
constituent discharged into a coastal region.
Circulation Model
Grid Size The grid size was selected
to give the desired spatial resolution of
currents and realistic representation of
boundary contours commensurate with computer
costs and capacity. A coarse grid with a
length of 1/3 nautical mile (2025 feet)
between points was used to model the entire
survey area. A fine grid with a length of
1/9 nautical mile (675 feet) was used to ob-
tain the necessary detail in the immediate
vicinity of the discharge point (see Figure 3).
Figure 3 . Fine and Coarse Grid Regions for
Open Ocean Example
Time Step The time step for the coarse
grid was chosen to be 60 seconds. Based on
a sensitivity analysis (the fine grid was
originally run with a time step of 20 sec-
onds) the time step for the fine grid was
also selected to be 60 seconds to minimize
computer costs.
Boundary Conditions - Coarse Grid Tide
he ights were specified on all the open
boundaries . The tide heights on the two
boundaries perpendicular to the coast were
determined from tidal measurements and tide
heights from the nearest National Ocean Sur-
vey tide reference station. The tide heights
along the boundary parallel to the coast
were determined by linearly interpolating the
values at the two end boundaries .
Boundary Conditions - Fine Grid The
boundary conditions for the tine grid were
computed by the coarse grid model. As shown
in Figure 3, the outside boundary of the fine
grid corresponds to a set of interior grid
points in the coarse grid. The numbers com-
puted along this interfacial boundary in the
coarse grid were then used as input to the
fine grid model.
Water Quality Model
The grid layout for the water quality model
is the same as that for the circulation
nodel (shown in Figure 3) for the coarse and
fine grids. The ambient tidal currents
(U,V) are obtained from the circulation model.
The time step was selected as 15 minutes and
5 minutes for the coarse grid and fine grid,
respectively.
These values were based on the stability
criterion:
max [ |U| + |V| ]
< 1
RESULTS
Circulation Model
The results of the application of the coarse
grid/ fine grid technqiues to the open ocean
example are best exemplified in Figures 4
and 5. Instantaneous velocities for both
510
-------
grid sizes are displayed in Figure 4 for a
time of left-flowing tidal currents. The use
of the fine grid allows better delineation
of the coastline with the resulting improve-
ment of resolution near the shore where the
currents are somewhat less (lead in phase)
due to frictional effects. The fine grid
displays the slower velocities quite nicely
whereas the coarse grid does not.
1.0 Contour
0.5 Contour
....0.3 Contour
Figure 4.
Instantaneous Coarse Grid (above)
and Fine Grid (below) Currents
for Time of Left Flowing Currents
Water Quality Model
Figure 5 displays the results of the water
quality model. The need for improved reso-
lution near the discharge can be seen by
noting that the contour lines are less than
three grid lines apart (the coarse grid
resolution) over a large portion of the fine
grid study area. Also, as noted from the
left most portion of the 0.3 contour, the
plume has sufficiently dispersed so that
1/9 mile resolution is no longer necessary
beyond the fine grid region.
Figure 5. Far Field Water Quality
Distribution for Time of
Maximum Leftward Plume
REFERENCES
1. Leendertse, J.J., "Aspects of a Compu-
tational Model for Long-Period Water-
Wave Propagation, " Rand Corp.
Report No. RM-5294-PR, May 1967.
2. Leendertse, J.J., "A Water Quality Simu-
lation Model for Well-Mixed Estuaries
and Coastal Seas: Volume I, Principles
of Computation", Rand Corp. Report No.
RM-6230-RC, February 1970.
3. Maach, F.D., N. Narayanan and R.J.
Brandes, U. Texas, Report Hyd. 12-7104,
August 1971.
4. Laevastu, T. and Staff. "A Vertically
Intergrated Hydrodynamical Numerical
Model, Parts 1-4". U.S. Naval Post
Graduate School, January 1974.
5. Chamberlain, S.G., and G.P. Grimsrud,
"Extraction of Water Quality Information
from Field Data using Mathematical
Models", Proceedings Ocean '72 IEEE
International Conference on Engineering
in the Ocean Environment, Page 397-401,
September 1972.
6. Chamberlain, S.G., and G.P. Grimsrud,
"Numerical Modeling of Water Circulation
and Effluent Dispersion," Raytheon
Company Report, December 1971.
511
-------
BLACK RIVER THERMAL ANALYSIS
Donald R. Schregardus
S. Environmental Protection Agency
Region V
Michigan-Ohio District Office
Fai rview Park, Ohio
Gary A. Amende la
I). S. Environmental Protection Agency
Region V
Michigan-Ohio District Office
Fairview Park, Ohio
ABSTRACT
One-dimensional temperature modeling techniques were
employed to determine allowable thermal loads from
United States Steel Corporation Lorain Works for dis-
charge to the Black River. The Black River from river
mile 5.0 to its mouth in Lake Erie at Lorain, Ohio is
a complex system affected by dilution from Lake Erie,
recirculation resulting from the location of U. S.
Steel water intakes and outfalls, and abrupt changes in
the physical dimensions of the river system caused by
maintenance dredging by the U. S. Army Corps of Engi-
neers. Based upon physical and hydrologic characteris-
tics, the Black River below river mile 5.0 was divided
into three segments. A one-dimensional thermal model-
ing technique was developed and applied to each segment
taking into account river flow, lake dilution, meteoro-
logical data, and heat loadings from U. S. Steel. The
equations were verified with measured data at critical
stream flows and used to compute thermal loads which
can be discharged by U. S. Steel and still meet appli-
cable temperature standards. Practical considerations
were employed in arriving at the final recommended
effluent limitations.
BACKGROUND
The Black River is a system of natural drains flowing
23 miles in a generally northerly direction and empty-
ing into Lake Erie at Lorain, Ohio. The State of Ohio
has classified the river as a warm water fishery and
correspondingly sets temperature standards to maintain
this classification. The water quality standards for
temperature applicable to the Black River limit the
temperature increase of the river attributable to human
activity to 5°F (2.8°C) and set maximum monthly water
temperatures not to be exceeded. The above criteria
are to be achieved at the water quality design flow of
the stream which has been defined as the annual mini-
mum seven-day consecutive flow with a recurrence inter-
val of once in ten years. In the lower portion of the
Black River the water quality design flow has been de-
termined to be about 21 cfs.
The temperature regime in the lower portion of the
river from mile 5-0 to its mouth at Lake Erie is af-
fected by discharges from United States Steel Cor-
poration's Lorain Works, a fully integrated steel
plant. On July 23-26, \31k, Region V - Michigan-Ohio
District Office conducted a comprehensive field survey
on the Black River in an effort to determine the
effect of U. S. Steel's discharges on the quality of
water and to obtain data for verification of predic-
tive mathematical models being applied to the river.
Figure 1 is a location map of the survey area showing
the U. S. Steel Lorain Works five river outfalls and
two intakes and 8 of the 13 stream stations where
water quality was monitored. The temperature data
obtained during the survey indicate that thermal dis-
charges from the U. S. Steel Lorain Works result in
violations of the water quality standards presented
above. Stream temperatures were increased by as much
as 15°F by U. S. Steel outfalls with surface tempera-
tures generally 12°F above ambient temperatures (tem-
peratures measured above U. S. Steel). However,
monthly allowable maximum temperatures were not ex-
ceeded.
GENERAL CONDITIONS
As the Black River approaches Lake Erie, stream level
and water quality become affected by backwaters from
the lake. Velocity profiles as well as sodium and
chloride data obtained during the July 197^ survey and
another U. S. EPA survey conducted on May 2, 1974, in-
dicate that a wedge of cool lake water flows upstream
along the bottom of the river beneath the warmer river
and effluent water 'See Figure 2). Further analysis
of the data reveals that the intruding lake water
causes dilution of river concentrations of sodium and
chloride as far upstream as U. S. Steel intake Wl-3
(RM 3.88). This lake water intrusion is a major com-
ponent in the cooling of heated waters discharged to
the lower portions of the stream.
Estimates of lake intrusion flow during the July sur-
vey were made using sodium and chloride data. Twenty-
FIGURE 1
BLACK RIVER LOCATION MAP
OUTFALL 004
OUTFALL 003
SEGMENT 1 RM 5.00 to 3.88
SEGMENT 2 RM 3.88 to 2.85
SEGMENT 3 RM 2.85.to 2.1)0
FIGURE 2 - STREAM VELOCITY PROFILE
fc
o
24
30
RIVER MILE 2.4
Upstream
Downstream^
-.10
0.0
VELOCITY "IN WWTS
.10
512
-------
four hour equal volume composite samples for sodium
and chloride were obtained at top, middle, and bottom
depths at five survey stations located between Outfall
001 and the downstream end of the turning basin (Fig-
ure 1). Because of the conservative nature of these
elements and the large concentration differences be-
tween the river upstream of U. S. Steel and Lake Erie
these data can be used in a mass equation to estimate
the intrusion flow at each survey station. The compu-
tations are based upon the assumption that the instream
quantities of both sodium and chloride are affected
only by French Creek, discharges from U. S. Steel, and
mixing with a known concentration of intrusion water.
This assumption is reasonable in that the July survey
was conducted during dry weather so that the runoff was
negligible. In addition, stream and discharge flows
and concentrations were relatively constant during the
survey allowing the assumption of steady state condi-
tions to be made. The resulting equation used to esti-
mate the intrusion flow is:
(C -C ) (1)
Where:
0_R = river flow assuming no intrusion, cfs
C = expected river concentration assuming no
intrusion flow, mg/1
C = measured concentration of the river, mg/1
m
CT = concentration of the intruding water, mg/1
The daily intrusion flow at Stations 4, 5, 6, and 7 was
determined by averaging the flow values computed using
the sodium data and the chlorine data. This procedure
was completed twice, once assuming the sodium and
chloride concentration of the intruding water to be
equal to the lake concentration and once assuming the
concentration to be equal to the river concentration
measured at the bottom of the next downstream survey
station. The results of the computations are presented
in Table 1. The computed intrusion flow at Station 4
using Station 3 bottom concentrations appears unreason-
ably high when compared with other data. Further re-
view showed that Stations 3 and 4 have nearly the same
concentrations causing the ratio of concentrations in
Equation 1 to become very large. When concentrations
are very close, small variations in the data can sig-
nificantly alter the computed flow.
Based upon physical and hydrologic characteristics, the
Black River below French Creek was divided into three
segments, each with relatively uniform thermal proper-
ties (Figure 1). The upstream segment from Outfall 001
to Intake WI-3 CRM 5.0-3.88) was considered to be a one
dimensional stream not yet affected by the intruding
lake water. Segment 1 averages about 10 feet deep and
160 feet wide. Water withdrawn at Intake WI-3 is dis-
charged at Outfalls 001 and 005. Heated water dis-
charged at Outfall 001 cools as it flows downstream.
The second segment is located between the turning basin
and Intake WI-3 (RM 3.88-2.9). This segment averages
about 15 feet deep and 250 feet wide. Temperatures
were relatively constant along the length of Segment 2
but some horizontal stratification did exist. The tem-
peratures are affected by lake intrusion but not to the
same extent as the turning basin. Outfall 002 dis-
charges to this portion of the river and heated river
water enters from upstream.
The Black River turning basin (RM 2.9-2.4) is the third
segment. The turning basin is dredged periodically by
the U. S. Army Corps of Engineers to a depth of about
30 feet and averages about 600 feet wide. Large quant-
ities of water flow upstream from the lake and mix with
the heated water discharged from Outfalls 003 and 004
and the heated water entering from upstream. Intake
WI-2, located in Segment 3, supplies the water dis-
charged at Outfalls 002, 003, and 004. Temperatures
were relatively uniform across the surface; however,
vertical temperature stratification existed throughout
the basin during the July 1974 survey.
MATHEMATICAL MODEL
Each of the segments described above was analyzed sep-
arately to determine the allowable thermal loads which
can be discharged to the river. Daily steady-state
conditions were assumed throughout the analysis. This
assumption proves reasonable for the Black River be-
cause diurnal variations of the flows, heat loads and
upstream river temperature were not significant. Com-
plete mixing of the heated discharge with the receiving
water was also assumed. The large discharge flow at
Outfall 001 in relation to the upstream river flow re-
sults in complete mixing just below the outfall. Large
discharge flows at Outfalls 002, 003, and 004 resulted
in a relatively constant horizontal temperature distri-
bution a short distance from the respective outfalls.
Complete vertical mixing was also assumed despite ver-
tical temperature stratification that occurred during
the July survey in Segments 2 and 3- This assumption
affects only the surface heat exchange term in the
energy budget. Based upon the July 1974 data, this
assumption introduces an error of less than 1% to the
temperature computations.
The Edinger and Geyer one-dimensional formulation
was applied to Segment 1. The formulation is based
upon the concept that a raised temperature resulting
from a heated discharge will approach the natural
stream temperature by the exchange of heat at the air-
water interface. Assuming the heat added to the water
body to be thoroughly mixed, the rate at which the
temperature changes in the downstream direction is con-
sidered proportional to the product of an exchange co-
efficient and the temperature excess. Under steady-
state conditions the equation used for estimating tem-
perature downstream of d heated discharge is:
T = E + (T -E)e
(2)
Where:
0_ = river flow rate ft /day
R
TABLE 1
Average Computed Intrusion Flow (cfs)
Station
7
6
5
4
River
Mile
3.88
3.35
2.85
2.40
Lake (])
Concentration
45
95
127
510
Bottom . .
Concentration
69
194
192
1342
(1)
(2)
Intrusion flow was computed by setting the concen-
tration of sodium and chloride in the intrusion
flow equal to the measured values in the lake.
Intrusion flow was computed by setting the concen-
tration of sodium and chloride in the intrusion
flow equal to the measured value at the bottom of
the next downstream station.
513
-------
E = equilibrium temperature, °F
2
K = exchange coefficient, BTU/ft -°F-day
A = surface area of the stream to the point
where T is determined, ft
= density of water, 62.4 Ibs/ft
C = heat capacity of water, 1 BTU/lb-°F
T = mixed temperature of the stream and the heat-
m ed effluent at the outfall
The equilibrium temperature (E) used in Equation 2 is
defined as the temperature at which the net exchange of
heat at the air water interface is zero.
A different formulation was employed for Segments 2 and
3. The low stream velocities and the uniform surface
temperature distributions of these two segments indi-
cate that a cooling pond formulation would more accur-
ately represent actual conditions. In this formulation,
a heat budget equation was constructed. Under steady-
state conditions the total heat content of the segment
remains constant and the heat budget equation can be
solved for the cool ing pond temperature.
The heat budget which applies to both segments is:
(3)
Where:
H- = heat added at the outfalls
H = heat removed by the intakes
H.. = heat entering at the upstream end of the
U
reach
H = heat entering from lake intrusion flow
Hn = heat leaving at lower end of the reach
H = heat lost at the water surface
The expression used to estimate the surface heat ex-
change, H- is:
HS KA (TS-E) (4)
with T being the water surface temperature and the
other variables are as defined previously.
All heat terms except H in Equation 3 represent advec-
tive heat transfer resulting from the transport of
water into or out of the segment. The heat contained
in the flowing water is given by the general expression:
H
(5)
In the analysis of Segment 2, H in Equation 3 is the
heat added at Outfall 002. There are no industrial
water intakes in Segment 2 therefore H. is zero. Sub-
stituting Equation k as well as the appropriate advec-
tive heat transfer terms into Equation 3 and solving
for the Segment 2 temperature results in the following:
Vu+0-2T2+0_l Tl
U U L LL
(6)
S2 KA+pCptQ.,+0,^0^1
Subscripts denote where the water came from prior to
complete mixing in Segment 2 (i.e. upstream, U; Outfall
002,2; lake intrusion, L) .
A similar analysis was used to derive the temperature
equation for Segment 3, the turning basin. Process
water at the basin temperature is withdrawn at Intake
WI-2 and discharged at Outfalls 002, 003, and 00^.
Substituting Equation k and the advective heat terms
into Equation 3 and solving for the basin temperature
yields the expression:
T
S3
Where:
0. = lake flow entering the basin at the down-
stream end, cfs
(V = lake water flowing upstream along the bottom
to the mid-section, cfs
The above equation takes into account that not all lake
intrusion water entering the basin is mixed within this
section. A portion, Q. , flows upstream to Segment 2.
VERIFICATION
Before Equations 2, 6, and 7 were used to determine
allowable thermal loads at the water quality design
flow of the river, the models were tested on the Black
River using July data with the resulting computed tem-
peratures compared to measured values. The July data
base provided an excellent test for the thermal models
because the average measured flow upstream of U. S.
Steel (22.6 cfs) was very close to the water quality
design flow for the river (21 cf si , and U. S. Steel was
at maximum production.
For the July verification, the equilibrium temperature
( E) for all segments was set equal to the flow weighted
average of the values measured at French Creek and Sta-
tion 10 because there are no significant thermal dis-
charges upstream of U. S. Steel. In addition, equilib-
rium temperatures computed using procedures outlined in
Reference 2 and average daily meteorological conditions
recorded at Cleveland, Ohio, agreed very well with the
assumed values. The value for the exchange coefficient
(K) was obtained from the report "Effects of Geographi-
cal Location as Cooling Pond Requirements and Perform-
ance"^.
For computing Segment 1 temperatures, Equation 2 was
applied first from Outfall 001 to Outfall 005
(RM 5.0-3.92) and then from Outfall 005 to Intake WI-3
(RM 3.92-3.88). Mixed river temperatures (Tm) at Out-
falls 001 and 005 were calculated from measured efflu-
ent temperature and computed river temperatures imme-
diately upstream of the outfalls. The three-day aver-
age computed temperature along with the maximum minimum
and average measured temperatures are shown in Fig-
ure 3.
Segment 2 temperatures were computed on a daily basis,
the same period for which the lake intrusion flows were
determined. In applying Equation 6 to the Black River
the lake intrusion flow computed at Station 6 using
Station 5 bottom concentration was used. Correspond-
ingly, the temperature measured at the bottom of survey
Station 5 was used as the intrusion water temperature.
Station 6 intrusion flow was chosen instead of that
determined at Station 5 because Station 6 is located
close to the center of Segment 2 and flows there would
more likely represent the average intrusion flow
throughout the segment. Daily average temperatures
514
-------
recorded at Station 7 and for Outfall 002 were also in-
put to Equation 6. The average of the three daily
values is plotted in Figure 3.
Black River turning basin temperatures were computed
daily using Equation 7. Lake intrusion flows calcula-
ted with lake concentrations of sodium and chloride
were used in the computations since flows computed with
bottom concentrations appeared unreasonably high.
Daily average temperatures and flows measured at Out-
falls 003 and 00k were input to Equation 7- The aver-
age of the top, middle, and bottom temperatures meas-
ured at Station 6 was considered representative of the
upstream water temperature entering the basin. The
average computed basin temperature is presented in
Figure 3.
The computed temperatures along the entire river agree
well with the measured values, Figure 3. In Segment 1,
computed temperatures are generally within the range
of measured values recorded at each station located
within the segment. Average computed values at the
lower end of the segment (RM 3.88) agree within 1°F
of average value measured at Intake WI-3. The com-
puted Segment 2 temperature was also within 1°F of the
average temperature measured at Station 6 mid-depth.
Computed Segment 3 temperatures agree well with aver-
age measured temperatures throughout the basin. The
calculated value is about 3 F above the total average
temperature measured throughout the basin and about
2°F below the average temperature recorded in the top
9 feet of the basin where most of the heat is dis-
charged. This result was expected in that a portion
of the cool lake water was not mixing with water in
the basin but instead was flowing upstream and mixing
in Segment 2.
Based upon the ability of the computational procedures
to replicate measured temperatures during low flow
conditions within reasonable limits, the equations de-
veloped in the previous section were employed to com-
pute allowable thermal loads from the U. S. Steel Lor-
ain Works.
PROPOSED THERMAL LOADINGS
In computing allowable thermal loads, the mixed river
temperature in the segments were set equal to the nat-
ural river temperature plus the maximum temperature
increase permitted in the water quality standards, 5° F
The discharge temperatures and the associated heat
loads were then determined using the equations devel-
oped and verified above. The water quality design
flow of the river upstream of U. S. Steel was assumed
in the computations (21 cfs). To simplify the analy-
sis the temperature of the river upstream of U. S.
Steel, the lake temperature and the equilibrium tem-
perature were set equal. This assumption is reason-
able in that there are no significant heat discharges
above U. S. Steel. The natural water temperature used
in the analysis was obtained from Reference 2 and is
based upon average meteorological conditions recorded
at Cleveland, Ohio during September, the month when
low flows generally occur. The exact equilibrium tem-
perature is relatively insignificant in computing the
temperature profile due to the fact that the water
quality standards are based upon increases above nat-
ural temperature and maximum temperatures are currently
not exceeded with existing loads.
To compute the proposed heat loads at Outfall 001, the
allowable temperature increase from Intake WI-3 to
Outfall 001 was determined. This was achieved by
first determining the discharge temperature which
would increase the mixed river temperature at the out-
fall by 5°F and then simulating river temperatures
down to Intake WI-3, using Equation 2. At Outfall 005
the maximum daily heat load discharged to the river
was assumed to be 15 x 10° BTU/hour, slightly greater
than the maximum value recorded during the July survey,
m x 10° BTU/hour. The computed temperature and the
river flow at intake WI-3 were assumed to mix with the
average daily lake intrusion flow at the intake. In-
trusion water temperature was assumed equal to the
lake temperature, therefore allowing the maximum heat
load to be determined. The results indicate that a
FIGURE 3
BLACK RIVER TEMPERATURE VERIFICATION
001
86
Ll-
10 82
in
LLl
CD
£78
LU
ce
£74
LU
^
&
^70
66
6
1
. 10 9
"j MAX 1 MUM
• AVERAGE
-I MINIMUM
.
)
1
i
8
1 . ,,, . I .
.5 " 5.0
U.S. STEEL OUTFALLS 005 002 003 004
1
LTT ,
r^k^l
>t
•1
SAMPLING
8a 8b*- STATION NOS. — *'
, , . 1 i i . . 1 i
4.5 4.0
1 U
; C
/
)
[
t
1 c
!
T
O
1
-
j 1 <
i I i
654 3 i
NT 2 1-SEGMENT 3-1
1
3.5 3.0 2,5 2.0 I.31 0
RIVER MILE
STATION AVERAGES
SURFACE O
MID-DEPTH 4-
BOTTOM A
BASIN AVERAGES
SURFACE El
TOP 9 FEET a
ALL DEPTHS E
BOTTOM H
COMPUTED VALUES
AVERAGE X
515
-------
temperature increase of 3.4°F may be imparted to the
flow discharged at Outfall 001. Using the following
equation the allowable heat load at 001 was determined
to be 58 million BTUs per hour.
H =" p CpQ.,ATj
Where:
Q. flow discharged at Outfall 001, cfs
AT. = allowable discharge temperature increase
above the intake temperature, °F
Equation 6 was used to determine the allowable thermal
loads discharged at Outfall 002. Setting the tempera-
ture of Segment 2 to 5°F above natural temperature,
Equation 6 was solved for the temperature at Outfall
002. The intrusion flow determined assuming lake con-
centration was used in the computation to be consist-
ent with the assumption that the intruding water was
at lake temperature. The results indicate that Out-
fall 002 can discharge at a temperature 16.9°F above
equilibrium temperature. Assuming the water with-
drawn from the basin at Intake WI-2 to be 5°F above
equilibrium, Outfall 002 can discharge at a tempera-
ture 11.9°F above the intake value or using Equation
8, 123 million BTUs per hour.
A similar procedure was used to determine the combined
thermal load discharged from Outfalls 003 and 004 into
the turning basin. The average temperature of the
turning basin was set equal to 5°F above equilibrium
and Equation 7 was solved for the net heat discharged
to Outfalls 003 and 004. Lake intrusion flow was
assumed equal to the average daily value determined
using lake concentrations with the intrusion tempera-
ture at equal to the lake temperature. The flow en-
tering from upstream, which was composed of lake flow,
the flow from Outfall 002, French Creek, and the river
above U. S. Steel was assumed to be 5°F above equili-
brium as set in the previous computation. The com-
bined heat load for Outfalls 003 and 004 was deter-
mined to be 515 BTUs per hour. This corresponds to a
AT of about 16°F for the total flow of Outfalls 003
and 004.
Prior to the July_1974 survey, the Government had est-
imated thermal loadings from U. S. Steel to be accept-
able in terms of achieving the 5°F AT standards. These
loadings were proposed as effluent limitations pursu-
ant to settlement of Civil Action C71-445 (N.D. Ohio)
against U. S. Steel (Table 2).
Equations 6 and 7 were employed to determine the re-
sultant temperature of Segments 2 and 3 using the pro-
posed settlement loadings. All other inputs and flows
were kept the same. Segment 2 temperature, computed
assuming a thermal load of 6? million BTUs per hour at
Outfall 002, was found to be 3.7°F above the ambient
stream temperature. With this computed temperature and
600 million BTUs per hour from Outfall 003 and OO't,
(8) Segment 3 was computed to be 5.3 F above ambient. An
allowable thermal loading of 600 million BTUs per hour
from Outfalls 003 and 004 appears reasonable consider-
ing the sensitivity of the basin temperature to lake
intrusion flow, and the uncertainty involved in estima-
ting intrusion flow. Reduction of thermal loads to 600
million BTUs per hour can be accomplished without sub-
stantial additional capital expenditures whereas reduc-
tion below that value will require costly additional
cool ing towers.
Based upon this analysis, Ohio Water Quality Standards
for temperature can be maintained on the Black River
by reducing U. S. Steel Lorain Works heat loadings to
the values presented herein or those proposed for
settlement of Civil Action C71-445.
REFERENCES
1. Edinger, J.E., and Geyer, J.C., "Heat Exchange
in the Environment", Edfson Electric Institute,
New York, June 1965
2. Thackston, E.L., and Parker, Frank L. , "Effect of
Geographical Location on Cooling Pond Require-
ments and Performance", EPA Pub. No. 16130 FDO_,
03/71, March 1971.
TABLE 2
U. S. STEEL LORAIN WORKS THERMAL LOADINGS
(106BTU/hr)
Outfall
001
005
002
003,004
Total
July 1974
D ischarqe
177
13
303
694
1187
Loadings
from this
Analysis
58
15
123
ill
711
Proposed Settlement
Civil Action C71-445
60
10
67
600
737
516
-------
WATER MODELING IN OHIO EPA
Robert 6. Duffy
Water Quality Surveillance Section Chief
Ohio EPA
Columbus, Ohio
A. Ben Clymer
Consulting Engineer
Columbus, Ohio
Steady-State Stream Modeling in Ohio
Earliest Modeling Efforts
In 1965 the Ohio Department of Health developed
the Garrett-McAnaney computer program for modeling
steady-state stream quality for a river mainstem.
The equations comprising the model were the Streeter-
Phelps equations plus the equations for mixing at a
node point. That is, the only parameters modeled
were dissolved oxygen and BOD.
In 1972-73 the Ohio EPA developed the Clymer-
Duffy computer program which enables a designer to
determine various combinations of allowable loads from
a single sewage treatment plant, such that water
quality standards would not be violated anywhere
downstream.
Features of the Garrett-Clymer-Duffy Models
Two advanced stream water quality models were
developed by Ohio EPA in 1973 to project allowable
loads for non-conservative parameters (i.e. D.O.,
6005, NH3-N). The two models were a "mainstem" model
and a "mini-basin" model. The equations used in both
models were obtained by closed-form integration of the
linear constant-coefficient differential equations for
first order kinetics. Mixing equations were written
at each node point.
A feature unique to the mini-basin model is a
set of equations to calculate the average stream
velocity and depth when cross-section data are un-
available. These equations are based on the Chezy-
Manning formula for channel flow.
In the mainstem model the change in D.O. as water
flows over a dam is taken into account. The re-
aeration equation over a dam is described by Klein (1).
The mainstem model allows for the borrowing of water
from a river for once-through cooling purposes. A
reduction in D.O. concentration is calculated, if the
water is heated beyond saturation. A special canal
subroutine was developed for the Cuyahoga River
whereby a certain volume of water is diverted from the
river to a canal running parallel to the river. Over-
flows from the canal divert water back into the river
at several points. Phenol and cyanide decay, and
hydrolysis of organic nitrogen to ammonia is also
modeled in the mainstem model.
The effect of benthal deposits on D.O. is address-
ed in both models. All suspended solids are assumed
to settle out behind a dam pool or elsewhere only if
the stream velocity is less than 0.6 ft./sec.
Osman-Clymer-Kim Model and Program
The Garrett-Clymer-Duffy programs lacked some
features which became desirable in 1975 in connection
with a multibasin planning project, denoted herein
as the Water Quality Planning Model Project, or
"WQPM Project". These desired features were:
1. Ability to model a branching configuration of
tributaries along with a mainstem, instead of
just one chain of reaches;
2. Inclusion of algebraic formulas for the costs
of waste-treatment and waste-conveying facilities;
3. Provision of an automatic load-allocation
"loop" to insure that dissolved oxygen would
meet water quality standards everywhere;
4. Addition of models for certain nonconservative
parameters, such as the count of bacteria per
unit volume;
5. Consideration of time of travel as a given
value for each reach, from which velocity would
be calculated as reach length divided by time of
travel;
6. Provision for conservative substances as
parameters;
7. Incorporation of a pre-existing in-house
stream temperature program as a subroutine in the
WQPM program;
8. Refinement of the formula for the oxidation
rate "constant" for phenol to incorporate non-
linear dependence upon temperature and concentra-
tion;
9. Inclusion of pH as a known input for each
reach.
In all other respects the WQPM builds upon the
Garrett-Clymer-Duffy mainstem model.
Validation Check of Ohio EPA Model
The Garrett-Clymer-Duffy mainstem model output
was checked against field data collected by the
U.S.E.P.A. Michigan-Ohio District Office on Feb. 12-13,
1975. The comparison for dissolved oxygen (D.O.) is
shown in Fig. 1. Fig. 2_ compares D.O. field data
collected by OTTio EPA in the Scioto River in August
1974. In both cases the difference is of the order
of 1 ppm of D.O..which is typical for water quality
models (2).
517
-------
Past Applications
An early version of the Garrett-Clymer-Duffy
mainstem model was applied to the Little Miami River.
This model was unable to simulate reaeration over a
dam, benthal demand, or thermal withdrawals.
However, the model applied to the Scioto, Mahoning,
and Cuyahoga Rivers did simulate these phenomena.
When modeling the Cuyahoga River, the canal sub-
routine was used. The mini-basin model was applied
to problem areas in the Maumee, Hocking, Rocky Fork,
Licking and Wabash Basins, including Findlay, Lima,
Lancaster, Mansfield, and Newark. All of the forego-
ing studies constitute the modeling work that has
been done to date by this agency to comply with the
requirements of Section 303(e) basin planning
studies.
Present Applications
The WQPM project is scheduled to prepare and
analyze long-range wastewater treatment plans for
major portions of the following basins by September,
1976: Little Miami River, Great Miami River, Mad
River, Stillwater River, Alum Creek, Darby Creek,
Tuscarawas River, Chippewa Creek, Sandy Creek, and
Nimishillen Creek. These ten segments include
representatives of most of the water quality problems
which occur in Ohio.
The studies being performed have been designed
to make maximum use of the Ohio EPA Water Quality
Planning Model. Appropriate regionalization and
economical processes for all new treatment plants
will be found which will meet all present water
quality standards until the year 2000.
Near Future Applications
The "Title X" project will utilize models
developed by Ohio EPA to assess the impact of point
source discharges in the Scioto, Muskingum, and
Little Beaver Creek Basins. Cost-benefit assessment
of different waste treatment schemes, including
regional waste treatment plants, is planned. Plans
are being formulated to model the impact on water
quality of a 1" rainfall following a prolonged dry
period. Modeling of conservative and non-conservative
elements to insure compliance with water quality
standards will be emphasized in the Title X program.
Another application of the models will be made by
the Water Quality Standards Section of the Ohio EPA
for the purpose of revising water quality standards.
Presumably these models will find application
also in future Section 303(e) basin studies and
208 studies.
Limitations of the Stream Water Quality Models
All models mentioned thus far have definite
limitations, which prevent them from being useful for
some purposes of the Ohio EPA:
1. These existing models assume steady flow,
which is an invalid assumption for the study of
urban or rural runoff from a storm, or any other
transient flow problem;
2. The models assume one-dimensional flow, which
is not applicable to a wide and/or stratified
reservoir or estuary;
3. The programs are not designed to be economical
tools for Monte Carlo studies of the stochastic
effects of stream flow, sewage treatment plant
performance, influent flow and composition, etc.,
upon stream water quality;
4. Because instantaneous and perfect mixing are
assumed at each node point throughout the cross-
section, the models cannot evaluate water quality
distribution in a mixing zone;
5. Since models fail to treat the biota
explicitly (except for Coliforms), they cannot be
used to draw conclusions about the ecosystem in
a stream;
6. The programs do not relieve the user of all
tedious tasks in connection with the preparation
of input data; hence, additional labor-saving
features might be desirable;
7. The models do not deal with a thermal plume in
a river or lake.
Accordingly, there is clear need for research and
development of other types of model, as discussed
further below.
Research and Models Needed
Unsteady Stream Flow and Water Quality Model
The appropriate equations for transient (unsteady)
stream velocity, depth, and concentrations of a
pollutant having first-order kinetics are:
_ !U M 8U. 3u U
(1) 3t gtan a + g8x + U3x+'pH2
£ H. 3W
+ 2 W 3x
(2)
3H 1 3Q
3t W 3x
(3) Q WHU
3£ c dW 3Q ^c
(4) 3t W- dH ~3x — U 3x
- K c + F (x,t)
J_
HW
__
3x
3c,
(5) W W (H,x)
where U is section-average velocity, t is time, g is
the acceleration of gravity, tan a is the slope of the
stream bed (+ up), H is section-average depth, x is
the space independent variable along the stream
center!ine, p is equivalent viscosity, p is water
density, W is section width, Q is stream flow rate,
c is pollutant concentration, K is the longitudinal
diffusion coefficient, K-) is the kinetic rate
constant of "decay" of c, and F (x,t) is a varying
and distributed source. The partial differential
equations (1, 2,4) can be converted to ordinary
differential equations by spatial finite differencing
of the dependent variables. They can then be solved
by numerical integration in time.
518
-------
The desired model should have the following
features:
1. Ability to model depositing and resuspending
of at least one size-and-density class of
suspended solids;
2. Inclusion of nitrate and at least one form
of phosphorus from rural runoff as parameters;
3. A lumped model of any sewer system and
treatment plant in the area;
4. Inclusion of urban and/or rural runoff during
and shortly after a storm.
Reservoir and Lake Models
Ohio has numerous reservoirs and lakes in which
water quality is of concern. Ohio also has many
rivers which discharge into Lake Erie. It is desir-
able, therefore, that the Ohio EPA have computer
programs capable of modeling pollution, photo-
synthesis, wind-driven currents, etc., in a lake well
enough for water quality management purposes.
The simplest case of a reservoir is one which
results from a dammed up stream and which is re-
latively narrow. When the water is not stratified, it
can be modeled as a deep stream. When the water is
stratified, it might be dealt with as two streams, one
on top of the other, with a minor amount of mutual
coupling. However, most reservoirs and lakes are so
wide that the mixed-stream assumption would be
invalid, necessitating a treatment in at least two
dimensions (lateral and longitudinal). A wide dam
pool in a stream should be modeled as a lake,
especially if it is used as a source of cooling water.
The parameters of lake models which are most
important include the velocity and temperature fields,
D.O., BOD, benthic demand, and nutrients. Most of
the problems can be considered in seasonal steady-
state, although some are progressive during a season,
as in the case of a lake bottom going anaerobic in
summer as a result of organic matter.
There seem to be available a number of models
meeting most of the foregoing requirements. (3-5)
"Estuary" Models
The rivers in Ohio which flow north have
"estuaries" where they enter Lake Erie. In an
estuary there are changing gradients of temperature
and concentrations of salts. A city with substantial
industrial and municipal discharges to an estuary
might require special water quality standards. An
estuary model is needed for this purpose.
Many phenomena complicate the modeling of such
an estuary (6): a thermocline at some times of year,
currents and circulations due to the wind vector, a
wedge of cold water at the bottom from lake or river,
and sloshing back and forth of water (at much
greater flow rates than the river flow) due to lake
level fluctuations. These problems are at the
frontier of the modeling art. However, simpler
estuary models are available. (7-9)
Stochastic Stream Model
Recognition of the essentially-stochastic nature
of water quality is implied in the practice of ex-
pressing standards in terms of 7-day 10-year low
flow. It would be desirable to push the stochastic
approach to water quality further by development and
use of a stochastic model of stream minimum D.O. re-
sulting from rainfall episodes. Because of the cost
of the large number of long computer runs, it is not
economically feasible to enclose a transient stream
segment, sewer system, and treatment plant model in
a Monte Carlo (repeated trials) loop. Accordingly,
it is necessary to shorten the time for each itera-
tion run. One approach is to replace the transient
model with a nonlinear algebraic stochastic model
containing the principal phenomena, component
frequency distribution-and other building blocks.
One way to get the algebraic model is to do
regression analysis on the results from a transient
model in a variety of cases. A complementary way is
to assemble the stochastic model from theoretical
building blocks, which include empirical parameters
having unknown values to be determined from model-
fitting studies with the transient model.
Mixing Zone Models
Many water quality standards are expressed in
terms of a mixing zone downstream of a discharge.
However, stream models have customarily been based
upon the assumption of instantaneous uniform mixing
across the entire cross-section at the discharge.
Thus there is need for a two-dimensional model capable
of describing the steady-state plan view concentration
field in the mixing zone. The required inputs are
the stream flow, width, average depth, bottom rough-
ness, characteristic height or other determinant of
transverse diffusion (10), and discharge parameters
(flow, concentration, location, and direction of
discharge). Ideal vertical mixing would be assumed in
shallow streams.
Biochemical Kinetics Models
There is much to be learned about the empirical
functions which describe the rate constants of bio-
chemical "decay" of pollutants in a stream. One of us
(A.B.C.) has studied the rate constant for the
oxidation of phenol as a function of temperature and
concentration. The data base used was for the 3-mile
reach on the Mahoning River from Struthers to
Lowellville. At both ends of this reach the Ohio EPA
had determined phenol concentration and temperature
30 times "from 1973 to 1975.
The usual practice of making the logarithm of the
rate constant linear in the temperature was found to
be grossly inadequate by not showing a peak; a
quadratic term is necessary, and a cubic term is
desirable. The logarithm of the rate constant should
contain also a term proportional to the logarithm of
concentration. It is hoped that similar regression
studies of the rate constants of this and other
reactions will be performed in Ohio EPA and elsewhere.
Due to the poor reproducibility of the 8005 test,
an in-house research project was initiated to deter-
mine if more reliable tests such as COD, TOC, or TOD
could be used to model or estimate BODc. The
carbonaceous component of BOD was studied by using a
chemical to inhibit the nitrogenous component.
Analysis of the data is incomplete, but preliminary
results indicate that a strong correlation between
BODs & COD, BOD5 & TOC and BODs & TOD does not exist.
519
-------
Stream Hydrology Models
Conclusion
Ohio water quality standards are expressed in
terms of the 7-day 10-year critical low flow.
However, the stream hydrological data are available
ordinarily only at much higher flow conditions. It
is necessary, therefore, to find a means to ex-
trapolate the hydrologic data to critical low flow
from the flow value which existed. Thus a model of
stream hydrologic parameters as functions of flow is
required.
The most commonly used model for this purpose is
a power function, namely,
W
aQb; H cQf; U - kQ"
where the lower case letters are empirical constants.
The exponents must satisfy the constraint b+f+m=l,
in order that the empirical formulas yield values of
W, H, and U, whose product WHU equals Q. Points
(b, f, m) can be plotted in an equilateral triangle
as shown in Figure 4L. The points representing the
exponents for different cross-sections of a given
stream tend to cluster or form a streak in the tri-
angle. Thus the triangular plot is useful in
studying data for the exponents.
Other Models
Ohio streams and lakes constitute ecosystems which
are important to the Ohio EPA. The importance arises
from, for example, the commercial and sports fish-
eries, on the one hand, and the difficulties associat-
ed with eutrophication and algae, on the other hand.
However, the Ohio EPA has not yet done any aquatic
ecosystem simulations. Nevertheless, as modeling
evolves in the agency, such studies will be done in
the next few years. Good progress in the development
of freshwater ecosystem models has been made by the
Deciduous Forest Biome project in the International
Biological Program.
A benthic community analysis for the Scioto Basin
was undertaken by the aquatic biology staff of Ohio
EPA. Their findings clearly demonstrate that a good
correlation exists between species diversity and D.O.
This is illustrated graphically in Figure J_.
Dr. F.S. Bagi of the Ohio EPA has been applying
least-squares regression to actual cost data from
Ohio waste treatment facilities and interceptor
sewers, in order to build up a cost model for a
complete drainage basin. A preliminary version of
such a cost model is currently being added onto the
WQPM program, in order that alternative treatment
plans for a basin may be compared on a cost basis. It
is expected that the basin cost model will reveal
opportunities for savings through regionalization.
In the near future several alternative treatment
processes will be costed, when a % removal of BOD is
specified.
Many of the foregoing types of models would be
useful for long-range planning of treatment facilities.
In all such applications, a need exists for a pre-
program to generate projections of future flows and
loads from all industrial and municipal plants in the
basin. The user would supply data such as assumed
constant growth rates of familiar parameters like
daily per capita water usage, BOD and ammonia
production, industrial production, and population.
Progress has been made by the Ohio EPA in the
development and utilization of water quality models
and computer programs, as described herein.
However, the problems facing this agency will require
the development and application of various advanced
models.
Acknowledgements
The authors wish to acknowledge generous help from
George Garrett, Paul Flanigan, Ed Armstrona.
Dr. Tom Birch, and Pat Abrams, all of the Ohio EPA,
in providing information and data for this paper. We
are indebted to George also for having conveyed to us
over a period of years much of his deep concern for
and some of his extensive knowledge of water quality
problems.
References
1. Klein, "River Pollution", Butterworths, London,
Vol. 2, 1962.
2. Harper, M.E., "Assessment of Mathematical Models
Used in Analysis of Water Quality in Streams
and Estuaries", Washington State Water Research
Center, Pullman, Wash., June 30, 1971, 81pp.
3. Gordon, John A., and Babb, Malcolm C., "Problems
Associated with the Validation and Use of
Reservoir Water Quality Models", presented at
5th Annual Environmental Engineering and Science
Conference, Louisville, Ky., March 3-4, 1975.
Contains 31-item bibliography.
4. Baca, Robert G., Waddel, William W., Cole,
Charles R., Brandstetter, Albin, and Cearlock,
Dennis B., "Explore I - A River Basin Water
Quality Model", Battelle Memorial Institute
Pacific Northwest Laboratories, Richland, Wash.,
99352, August, 1973.
5. Sheng, Yea-Yi Peter, "The Wind-Driven Currents and
Contaminant Dispersion in the Near-Shore of
Large Lakes'1, Case Western Reserve Univ., Oct.,
1975.
6. Horowitz, J., Adams, J.R., and Bazel, L.A.,
"Water Pollution Investigation: Maumee River and
Toledo Area", U.S.E.P.A. Publication #905/9-74-
018, January, 1975.
7. Thomann, Robert V., "Systems Analysis and Water
Quality Management", Environmental Science Services
Division, Environmental Research and Applications,
Inc., New York, 1972.
8. Eco-Labs Inc., "Water Quality Study of the
Cuyahoga River (Literature Survey and Simulation
Model)", Prepared for U.S.E.P.A., Region V,
pg. 108-157, 1974.
9. Amendola, G.A., Schregardus, D., and Delos, C.,
Technical Support Document for Proposed NPDES
Permit-United States Sfeel Corporation Lorain
Works", U.S.E.P.A., Region V, Michigan-Ohio
District Office, Appendix VI, July, 1975.
10. Yotsukura, N., and Cobb, Ernest D., "Transverse
Diffusion of Solutes in Natural Streams", U.S.
Geological Survey Professional Paper 582-C, U.S.
Government Printing Office, Washington, D.C., 1972.
520
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o
ci
FIGURE I
OEPA MODEL VERIFICATION DATA FOR MAHONING RIVER
13
12
5 10 15 20 25
MILES DOWNSTREAM FROMLEAVITTSBURG GAGE
30
35
+ " OEPA MODEL OUTPUT )
©= MODO USEPA FIELD DATA)
FEBRUARY 12-13,1975
FIGURE 2
ACTUAL vi MODELED D.O. IN SCIOTO RIVER
- PROJECTED D.O.
® MEASURED D.O.
10
20 30 40 50 60
MILES DOWNSTREAM OF OLENTANGY RIVER
70
80
FIGURE 3
V D.O. v« SPECIES DIVERSITY IN SCIOTO RIVER
FOR AUGUST, 1974
CO «W
ee
111
*• —
PROJECTED D.O.
SPECIES DIV. VALUE
10
20 30 40 50
MILES DOWNSTREAM OF OLENTANGY RIVER
60
70
FIGURE 4
WATER MODELING IN OHIO EPA.
-------
THREE-DIMENSIONAL MODEL DEVELOPMENT FOR THERMAL POLLUTION STUDIES
Subrata Sengupta and Samuel Lee
School of Engineering, University of Miami
Coral Gables, Florida
and
Roy A. Bland
National Aeronautics and Space Administration
Kennedy Space Center, Florida
BACKGROUND
Because of the growing importance of thermal pol-
lution and because of the possibility of detecting it by
means of remote sensing, the National Aeronautics
and Space Administration (NASA)-Kennedy Space
Center (KSC) has sponsored a study on this many-
faceted problem. A team of researchers at the
University of Miami has been under KSC contract to
develop a universally applicable three-dimensional
thermal pollution math model. When completed this
model will predict the three-dimensional motion
and temperature of thermal plumes within waters to
which they are discharged.
This mathematical model can include effects of winds,
ocean currents, cyclic tidal flushings in bays and
estuaries, variable winds and realistic bottom topog-
raphy. Remotely sensed data and in situ measure-
ments are used for model calibration and verification.
An airborne scanner system backed up by satellite
infrared remote sensing systems is used to measure
water surface temperatures.
The airborne scanner system used is a Daedalus
DS-1250 multispectral line scanner system and is
installed in a C-45H Tri-Beechcraft (NASA-6). An
Hg:CO:Te detector is used for sensing 8-14 micron
IR radiation. The system is owned and operated by
the NASA Kennedy Space Center. Two kinds of
satellite data are used to supplement the aircraft-
derived IR data. These are the NOAA-2 and NOAA-3
satellites, which operate in the 10.5 and 12.5 micron
region with 0. 5 nautical mile resolution. Also used
in the study are data from the Air Force DMSP
satellite, which operates in the 8-13 micron range
with 0.3 nautical mile resolution.
This mathematical model will serve a dual purpose.
It can be used in surveillance studies and also it
will enable environmental planners to predict the
behavior of hot discharges in a given region and,
therefore, to determine whether such discharges
exceed allowable temperature limits at depth and on
the surface. In other words, this model can be used
in the location of future nuclear power plants in
order to select the most advantageous sites.
MATHEMATICAL MODEL
DEVELOPMENT PLAN
After a feasibility study was completed in January
1974, it was concluded that the mathematical model
development would take four years to complete. As
an end product, the model will be well documented,
readily transferable, and initial and boundary con-
ditions easily altered so that the model can be uni-
versally applicable. This four-year period will be
divided into four phases.
In the first phase, the basic concepts of the model
were established and the optimum numerical scheme
(finite differences) for the solution of the math
model's governing equations was selected. In the
second phase, completed in December 1975, the
model was developed and applied to Biscayne Bay,
Florida, using the Cutler Ridge power plant thermal
discharges as a testing case. Both rigid lid and free
surface models of Biscayne Bay were written during
this phase, but only the rigid lid far field version
has been completely verified to date. Velocity and
temperature fields have been computed for different
atmospheric conditions and for different boundary
currents produced by tidal effects. The computations
have been carried out for different time periods
between one and six hours of real-time. Four air-
craft infrared data runs, roughly one each quarter,
were made over Biscayne Bay during this phase to
supply data for the model.
In the third phase, which began in January 1976, a
twelve-month period will be devoted to three tasks.
The modeling of Biscayne Bay will be completed and
computer results verified against remote sensing
and in situ measurements. In the second task, the
mathematical model will be revised as needed and
applied to the St. Lucie, Florida, nuclear power
plant, which discharges onto the off-shore continental
shelf. This will be an interesting contrast to
Biscayne Bay, which is a shallow lagoonal estuary.
The third major task results from a recommendation
by several EPA and NRC/ERDA officials. Their
recommendation was to initially apply the rigid lid
version of the model to a deep lake reservoir. In
consultation with the progressive Duke Power
Company, it was concluded that the rigid lid model
522
-------
should first be tested on a thoroughly understood lake
where abundant real-time measurements are taken.
The lake selected and approved was Lake Belews,
North Carolina, which serves as a cooling reservoir
for a large fossil fuel plant. Thus, the third task in
this phase of the implementation plan will be to model
Lake Belews, North Carolina, in cooperation with and
under the sponsorship of the Duke Power Company.
In the fourth and final phase of the development plan,
the mathematical model will be further generalized
so that it will be readily applicable to any geograph-
ical discharge area site. The computer program will
be finally documented so as to afford a user comput-
ing facility minimum difficulty in making this program
operational. In cooperation with EPA and NRC/ERDA
officials as well as the electrical power generating
companies, the NASA-KSC will work toward utilizing
this model as an industrial standard. As needed,
further applications of the model will be carried out
in this final stage.
MATHEMATICAL MODEL
A considerable amount of work has been done in
modeling thermal discharges. A three-dimensional
model including the effects of buoyancy, topography,
and other parameters has not been developed yet.
Akers discussed some of the models that are in
existence. Policastro2' ^' 4 in a series of review
papers has compared the existing plume models with
field data. He considered a range of models from
analytical to quasi-three-dimensional numerical
models. Harleman's^' 6, 7 pioneering work led to a
numerical model with Stolzenbach, which has been
widely used in plume analysis. The only existing
complete three-dimensional models are by Waldrop
Q Q
and Farmer and Paul. However, Paul's model
assumes symmetry, thereby eliminating the possi-
bility of including wind or current effects. Both
models are for constant depth basins. The objective
of the present study is to develop a comprehensive
three-dimensional model including the effects men-
tioned above.
Details of formulation, solution, and development
have been discussed in reports by Lee et al.10> -11
The need for remotely sensed data in model develop-
ment and verification has been discussed by Sengupta
1 *?
et al. A general description of the various models
comprising the thermal pollution mathematical model
package will be presented here.
Thermal anomalies caused by a heated discharge
usually affect areas of a few miles in extent. Initially,
the discharge is dominated by a jet-like behavior.
Then, turbulent entrainment and buoyancy influences
the trajectory and spreading. Finally, the flow is
governed by the far field conditions and the ambient
meteorological state. The domain of interest can be
classified into a near field, where effects of the
discharge are significant, and a far field, which
affects the plume but is not appreciably affected by the
plume. The numerical characteristics of these two
domains are quite different. The procedure,
therefore, is to obtain a far field solution with a
coarse finite difference grid and to use this to obtain
the near field (plume) solution using a finer mesh
size.
The governing equations describing the state at a
point in the flow field are a system of coupled, non-
linear, second-order, three-dimensional partial
differential equations which satisfy local conservation
laws for total mass, species mass, momentum and
energy. The constitutive equations complete the
system of equations. In laminar flows the molecular
transport properties for heat and mass transfer may
be used. Most environmental situations are,
however, turbulent. The time averaged transport
equations are therefore used. The turbulent closure
condition is specified by approximating the Reynolds
stress terms by eddy transport coefficients. For
studies where salinity variations are important, a
salt conservation equation similar in form to the
energy equation can be added.
The surface waves can be eliminated by imposing a
rigid lid condition whereby the vertical velocity at
the surface is equated to zero. The transients are
somewhat distorted but the steady-state general
circulation is not significantly affected. The elimi-
nation of surface gravity waves allows larger integra-
tion time steps, thereby reducing computation time.
However, in cases where surface elevation changes
are significant and transients are to be investigated,
a free surface model has to be used. The rigid lid
formulation for a variable depth basin has been
I O
developed by Sengupta and Lick. A free surface
14
model has been used by Freeman et al. to study the
circulation and periods of oscillation of Lake Huron.
The computer program package that is being develop-
ed is to be applied in a wide variety of geophysical
situations, so both the free surface and rigid lid
models are being developed. Both these models are
further sepcialized to be applied to near and far fields.
Therefore, there are four separate programs.
Rigid lid model
(i) Far field version
(ii) Near field version
Free surface model
(i) Far field version
(ii)
Near field version
The rigid lid model has been used to obtain general
circulation and temperature distributions in Biscayne
Bay. The free surface model is in its final stages of
development and application. The rigid lid model
will be described here together with the results and
the verification based on ground truth and remote
sensing data. Figure 1 shows the program package
with applicable geographical locations.
523
-------
Rigid Lid Model
The programming difficulties for a three-
dimensional basin suggest a stretching of the vertical
coordinate with respect to the local depth. This
converts the basin to constant depth. The same num-
ber of grid points in the vertical direction can be used
at the shallow or deep parts of the basin without
using variable grid sizes. The stretching introduces
extra terms in the momentum equations. The details
of the derivation are presented by Sengupta and
T • i, 13
Lick.
The governing equations consist of the continuity
equations, the three momentum equations, the energy
equations, and the equation of state . The vertical
momentum equation is simplified using the hydro-
static approximation. The Boussinesq approximation
is made. Constant though different eddy transport
coefficients are chosen for vertical and horizontal
diffusion. The equation of state is an empirical
relation between density and temperature. The
vertical velocity at the lid is zero. This causes the
surface pressure to be different from atmospheric
pressure. The x and y momentum equations are
integrated over depth and combined after differentia-
tion with respect to x and y, respectively. The
resulting Poisson equation is the predictive equation
for surface pressure. The above set of equations
with appropriate boundary and initial conditions
constitute the mathematical model.
Initial and Boundary Conditions
The nature of the equations requires initial and
boundary conditions to be specified. The velocities,
temperature, and density are given throughout the
domain as initial conditions. Boundary conditions are
specified at the air-water interface, horizontal bound-
aries of the domain, the bottom of the basin and efflux
points. At the air-water interface, wind stress and
heat transfer coefficients are specified. The condi-
tions on the lateral walls allow no slip and no normal
velocity for the momentum equations. These walls
are assumed to be adiabatic. At the floor of the
basin, the conditions of no slip and no normal velocity
are also applicable . The energy equation has a heat
flux boundary condition, considered adiabatic for the
present study. At points of efflux, the velocities are
specified and the graident of temperature normal to
the domain boundary is considered zero. These open
boundary conditions are most difficult to specify.
Method of Solution
An explicit finite difference scheme is used to
integrate the transport equation. The general finite
difference form is:
u -u
n
= (convection) + (pressure) +
n-1, n, n+1
(viscous)
Here u may be replaced by v or T (for the T
equation the pressure term is not used). The spatial
derivatives are centrally differenced using a modified
Dufort-Frankel scheme to avoid time-splitting in
long term integration. Its advantages have been
13
demonstrated by Sengupta and Lick. The pressure
equation is approximated by a five-point scheme and
solved by the Liebmann relaxation procedure. The
algorithm is as follows:
a. Using values at time step n, calculate the
forcing term for the pressure equation
b. Solve the pressure equation iteratively
c. Calculate u and v from the momentum
equations
d. Calculate w from the continuity equation
using u and v at n+1
e. Calculate T from the energy equation
f. Calculate o from the equation of state
The procedure is repeated for each time step.
APPLICATION AND VERIFICATION
Figure 2 shows a map of Biscayne Bay. The bay is
open to the ocean on the eastern side through a shoal
region and some creeks. The northern end is
partially obstructed by a causeway. At the southern
end a shallow region effectively separates the bay
from Barnes Sound. There are two power plants
located on the bay; one at Cutler Ridge and the other
at Turkey Point. The far field conditions affect the
thermal plume from the Cutler Ridge plant. The
Turkey Point plant uses a cooling canal system.
The rigid lid model has been applied to Biscayne Bay.
A wide range of meteorological conditions have been
modeled and detailed results and evaluations present-
ed in a report by Lee et al. In this manner the
program was calibrated and the parameters were
chosen. For verification, the model results were
compared with data gathered from a field experiment
on April 15, 1975. NASA-6 thermal scanner runs
were flown in the north-south direction. Ground
truth data was used to correct for atmospheric effects
and also to record the vertical variation of temper-
ature in the bay. The average wind was from the
southeast at 10 mph and the air temperature was 30 C.
The tide was incoming. Figure 3 shows the interpo-
lated isotherms drawn from the thermal IR data.
There is a hot spot near Featherbed Banks. There
are warm regions wherever the depth is shallow.
Because the near shore regions are warmer, the
central parts of basins of Card Sound are seen to have
closer isotherms. There are warm spots near the
group of islands at Caeser Creek and also near the
island two miles south of Turkey Point. The verifi-
cation for the model involved comparison of this
thermal IR map with computed surface isotherms.
The numerically predicted circulation for the bay in
the case described above is shown in Figure 4. The
incoming tide is primarily diverted to the south. The
effect of the wind is to turn the flow toward the north-
524
-------
west, though the tidal effect predominates. The cur-
rent toward Rickenbacker Causeway is minimal. The
velocities near the shoals are incoming. The mass
flux through the creeks has very localized effects.
The Featherbed Banks reduce the current magnitude,
so the velocity increases in the deeper regions adja-
cent to the banks. The velocities also increase as the
bay narrows to the south.
The measured quantities, namely wind speed (10 mph
southeast), incoming tide, and ambient temperature
(3CPC), were used to obtain the temperature field.
To minimize the effect of initial temperature condi-
tions, the run was executed with as early a starting
time as possible. At 9 AM near Cutler Ridge (1=11,
J=3), the measured temperature was 25.6°C with no
vertical stratification. Since this is a near shore
location, the average temperature in the bay can be
assumed to be lower. Since the detailed temperature
field was not known as an initial condition, it was
assumed that the bay was isothermal with a temper-
ature of 24.5°C at 8 AM. The model predicted the
conditions six hours later, which were compared with
mid-afternoon in situ and remotely sensed data.
Figure 5 shows the surface isotherms predicted by the
model. The surface isotherms show a hot spot over
Featherbed Banks. The warmer near shore regions
are quite clearly seen. The warm area near the is-
lands in the southern part of the bay is also evident.
The comparison with thermal IR data in Figure 3 is
excellent. It should be noted that the IR data are not
synoptic. There is a time lag of almost three hours
between near shore flights and flights over the keys.
Considering this time lag and the approximate speci-
fication of initial conditions, the model may be con-
sidered quite satisfactory for ecological studies.
The ground truth data were obtained only in the morn-
ing of the April 15, 1975, field experiment. Results
for the model after three hours of heating can be
compared with ground truth measurements at location
1-11, J=7 at 11 AM. Figure 6 shows a transect of the
bay along J=7. The predicted isotherms are shown,
with ground truth data at locations marked by aster-
isks. It can be seen that the agreement is within
0.7°C. This is satisfactory for most environmental
applications.
Conclusions
Figure 1. Application Chart for Numerical Models
(University of Miami—NASA-KSC Project)
As part of a generalized model development
program, a three-dimensional rigid lid model has
been developed. Remote sensing and ground truth
data have been used to calibrate and verify the model.
The model has been found satisfactory in predicting
the general circulation and temperature field in
Biscayne Bay.
Acknowlegments
The authors wish to express their gratitude to
Drs. N. Weinberg, H. Hiser, and Mr. James Byrne
for their effort in processing the remote sensing and
ground truth data. The effort of the NASA-KSC data
analysis personnel and flight crews were an integral
part of the investigation.
APPLI CATION
MODEL
RIOID-LID HEM
nr-LO MODEL
FREE 6UWACZ
MODEL
FM FIELD
MODEL
FREE BURFAd
rM FIELD
MODEL
T1IERMA.
LAKE
•
•
L DI6C11ARUE
RIVEA
•
•
BAY
I CHORES
LEVEL
OCEAN
• •
GENERAL CIRCULATION WTO
TEMPERATURE FIELDS
LAKE
•
«
BAY
I CHORE*
CHAMCU
'
OCEAB
IGHORZa
LEVEL
'
COASTAL BOUNDARY
LAYEHfl
LAKE
IGNORES
LEVEL
CHAHCC4
•
•
BAY
LEVEL
•
LEVEL
CHASGES
•
*"*"
•
•
Figure 2. Map Showing the General Area of Biscayne Bay
TURKEY POIHT
NASA-*
IR SCANNER DATA
4/15/75
30.0 Interpretation Aided by
. Ground Truth
Figure 3. Biscayne Bay and Card Sound Florida
525
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•' " / / / / I I \, \ \ i -^ *s •»s ^ ~«
\- ' < < t / I II V \l,'.\^J*^^'1N--\
1 1 ///<;» i\\.\\~-»-^--- ^-»^=r^'
Figure 4. Surface Velocities
1 TEMP:
TIAL TEMP: Zfl.5
10 HPH, Southca
I-cos ing
(10 crVsf
30 C
TIME ELAPSED:
7£0 =TU/Duy'F-rT
6 HP-3.
Figure 5. Surface Isotherms for Biscayne Bay (Rigid-Lid Model)
(Temperature in Degrees Centigrade)
,B ki.lora»t«m horizontal «c»l»
3 ft. v«ttic»l ccnla
(• danotaa locati
WIND: 10 MPU, Southeast
TIDE! 'incoming (10 cm/sac)
AIR TEMP: 30°c
INITIAL TEMP: 24.S°C
HEAT TRANSFER COEFFICIEHTl
750 BIU/Day°F-FT*
TIME ELAPSED: 3 HRS
(TEMPERATURE IN DEGREES CENTIGRADE)
SECTION I J-7
Figure 6. Comparison of Calculated Isotherms for Vertical
Section J-7 With Ground Truth Data
REFERENCES
1. Akers, P., "Modeling of Heated Discharges,
Engineering Aspects of Thermal Pollution, Krenkel
and Parker (Ed), " Vanderbilt University Press, 1969.
2. Policastro, A. J., "Heated Effluent Dispersion in
Large Lakes," Presented at the Topical Conference,
Water Quality Considerations in Siting and Operating
of Nuclear Power Plants, Atomic Industrial Forum
Inc., 1972.
Argonne, Illinois, 1972.
4. Policastro, A. J., and Paddock, R.A., "Analyti-
cal Modeling of Heated Surface Discharges with
Comparisons to Experimental Data," Interim Re-
port No. 1, Presented at the 1972 Annual Meeting
of the A. I. Ch 7.
5. Stolzenbach, K. D., and Harleman, D. R. F., "An
Analytical and Experimental Investigation of Surface
Discharges of Heated Waters," R.M. Parsons
Laboratory for Water Resources and Hydrodynamics,
M. I. T., Cambridge, Massachusetts, Tech. Report
No. 135, 1971.
6. Stolzenbach, K. D., and Harleman, D. R. F.,
"Three Dimensional Heated Surface Jets., " Water
Resources Research, Vol. 9, No. I, 1973.
7. Jirka, G. H. and Harleman, D. R. F., "The
Mechanics of Submerged and MiltLpart Diffusers for
Buoyant Discharges in Shallow Water, " R. M. Par-
sons Laboratory for Water Resources and Hydro-
dynamics, M. I.T., Cambridge, Massachusetts,
Tech. Report No. 169, 1973.
8. Waldrop, W. R., and Farmer, W. J., "Three
Dimensional Computation of Buoyant Plumes,"
J. G. R. Vol 79, No. 9, 1974.
9. Paul, J. F. and Lick, W. J. , "A Numerical Model
for a Three-dimensional, Variable-Density Jet,"
FTAS/TR 7392, School of Engineering, Case West-
ern Reserve University, 1972.
10. Lee, S. S., Veziroglu, T. N., Weinberg, N. L.,
Hiser, H. and Sengupta, S., "Application of Remote
Sensing for Prediction and Detection of Thermal
Pollution," NASA-CR-139182, 1974.
11. Lee, S. S., Veziroglu, T. N., Weinberg, N. L.,
Hiser, H. and Sengupta, S., "Application of Remote
Sensing for Prediction and Detection of Thermal
Pollution," NASA-CR-139188, 1975.
12. Sengupta, S., Lee, S. S., Veziroglu, T. N.,
Bland, R., "Application of Remote Sensing to
Numerical Modeling, " Remote Sensing Energy Re-
lated Studies, T. N. Veziroglu (Ed), John Wiley &
Sons, 1975.
13. Sengupta, S., and Lick, W., "A Numerical
Model for Wind Driven Circulation and Temperature
Fields in Lakes and Ponds," FTAS/TR-74-99.
Case Western Reserve University, 1974.
14. Freeman, N. G., Hale, A.M., Danard, M. B.,
"A Modified Sigma Equations Approach to the
Numerical Modeling of Great Lakes Hydrodynamics,"
J. G. R., Vol 77, No. 6, 1972.
3. Policastro, A. J., and Tokar, J. V., "Heated
Effluent Dispersion in Large Lakes," Report No.
ANL/ES-11, Argonne National Laboratory,
526
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SOME OBSERVATIONS ON MODELLING DISPERSION OF POLLUTANTS
IN NEAR-SHORE WATERS OF LAKE MICHIGAN
Richard H. Snow
Engineering Advisor
IIT Research Institute
Chicago, Illinois 60616
ABSTRACT
Results of an investigation of the effect of effluents
on water quality in the Calumet area of Lake Michigan
are reviewed. The study showed that part of the
effects could be directly traced to the plume of the
largest effluent source, the Indiana Harbor Canal.
Since the number of measurements in the plume was
limited, modelling of the behavior of the plume was
useful to show that the measured conditions were
typical, and could be expected to occur during a large
part of the time.
However, focussing attention on the plume ignored the
more general pollution of near-shore water, which in
one other Great Lakes location was shown to have a
residence time of 40 days. The only existing model of
the long-term dispersion of this pollution does not
take into account the known and suspected behavior of
the near-shore water movement. It is recommended that
measurements of the behavior of the near-shore water
be carried out to form the basis for dispersion
modelling.
INTRODUCTION
It has long been noticed that the near-shore waters of
the Calumet area of Lake Michigan contain higher con-
centrations of pollutants such as NH3-N and phosphorus
than other areas of the Lake which are farther from
large population centers.2 The Calumet region is in
the southwestern portion of the Lake, extending from
Chicago to Burns Harbor, Indiana. Measurements of the
water quality at various water intakes could not be
directly correlated with known effluents, because the
transport and dispersion of the water masses was not
simultaneously measured or predicted.
A first step in understanding the effect of effluents
on water quality is to correlate the measurements with
the motions and dispersion of effluent plumes in the
area. An attempt to do this was reported by Snow.10
The effort met with some success and is briefly re-
viewed below. The purpose of the present paper is to
discuss limitations in the approach based on the study
of plume behavior, and to suggest an approach based on
the movement of near-shore water masses covering a
wider area and a longer time span than is observed in
a plume.
STUDY OF IHC PLUME
The largest source of effluents in the Calumet region
is the Indiana Harbor Canal (IHC). Figure 1 is a
Skylab photo showing the IHC plume. In a recent study
for the EPAiO measurements of the water quality were
correlated with motion and dispersion of the plume
Figure 1
Skylab Photo of Calumet Area
of Lake Michigan, Showing Plume
From IHC, Sept. 13, 1973
from the IHC over a distance of up to 19 km.
The following parameters were measured, and this combi-
nation of measurements provided a fingerprint to iden-
tify and track the effluents from the IHC: NH3-N,
total Fe, temperature, conductivity, chloride, fluo-
ride, coliform bacteria, and others. Other agencies
have measured such parameters as phenols, cyanide, oil,
taste and odor, heavy metals, toxic bacteria and
viruses.I" Other pollutants may be expected, such as
PCB's.
GRAVITY SPREADING AND MIXING
The water of the IHC is almost always warmer and less
dense than the Lake water, and this gives rise to a
typical estuary effect at the mouth of the Canal. The
IHC is dredged to a depth of about 10 m; the warmer
canal water flows out in the top 3-5 m of this depth,
527
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and colder Lake water intrudes in the bottom portion.
This behavior is similar to that observed in a salt-
water estuary, and described by Ippen.^ The rate of
gravity spreading is given by Parker and Krenkel8 in
terms of the wave velocity
(1)
where
p is density of water, consistent units
2
g is acceleration of gravity, 9.80 m/sec
H is depth of heated water, m
Measurements of temperature and depth of heated water
were taken at the mouth of IHC, Station CAL06, on
three boat-sampling days, and are given in Table 1.
Velocities were measured with a current meter, and
density differences were computed from the measured
temperature gradient. From these data and Equation 1
we can calculate the outflow velocity based on the
spreading mechanism. It is compared with the measured
outflow velocity in the last two columns of the table.
The agreement is so good that this confirms the
mechanism of outflow.
The colder Lake water which intrudes under the canal
water mixes with the IHC water in the lower part of the
canal. As a result of this inflow and mixing, the IHC
water is already diluted 20 to 50% at the mouth of the
canal, according to our measurements of inflow in
Table 2 (SnowlO).
Inflow is produced because the warmer canal water
flows out of the harbor faster than it is supplied
from upstream. The Lake water is drawn in to make up
the deficit, and to conserve mass.
A calculation shows that gravity spreading is more
important than inertial jet flow of effluents out of
the IHC mouth. The ratio of these two effects is
measured by the Froude number, F.
where
(2)
Uo is centerline velocity of jet, m/sec
From data given in Table 1 we calculate F = 1.1. A
value of F < 2 means that the gravity effect is more
important than the inertia of the jet (Cederwall3).
Once the plume passes outside the mouth of the IHC, it
continues to spread over the colder Lake water, just
as oil spreads on water, because of the gravity differ-
ence. It seeks to flow out and become thinner,
decreasing its gravitational potential. Such a wave-
front is vertical and sharply defined (Cederwall3).
Although the wave front is moving with respect to the
bulk of the water, it may appear stationary if the
water has the same velocity in the opposite direction.
Parker and Krenkel8 describe the phenomenon in some
detail and review mathematical descriptions of it.
The behavior of the plume just outside the IHC mouth
appears to depend on the interaction of gravity
spreading with Lake currents that usually run parallel
to the shore. This pattern is clearly shown by the
Skylab photo, Figure 1. This photo suggests that
there was a fairly strong general current in the main
Lake water flowing from north to south, dragging the
plume around the landfill. The plume gives the
appearance of gravity-spreading behavior on the north
boundary. The width of the plume is determined by
competition between the spreading rate and the Lake
current speed. The rate of spreading was predicted
by a dimensionless correlation from the literature
(Sharp9). The actual dilution factors were measured
in the plume within a few km of the IHC mouth on 3
days. The model for spreading was used to show that
the measured dilutions were typical, since the spread-
ing depends on the known temperature difference and on
the along-shore lake current speeds. The measurement
Table 1
GRAVITY FLOW AT IHC MOUTH (CAL06)
Depth of
Date, outflowing la
1973 m
November 14
November 19
December 7
3.5
3.5
3.5
5*
Outflow velocity,
.,rr Temperature, °C „ ,„__.,*,,.. m/sec
yor,
Top
15.9
15.0
13.5
Bottom g/m£ Calculated
10.0
11.5
10.5
0.00076 0.15
0.00045 0.12
0.00034 0.10
0.12
Measured
0.15
0.13
0.13
*Depth of outflow was uncertain because a large eddy passed during one of two measurements.
Table 2
MEASURED FLOWS AT MOUTH OF IHC
Date
Total Outflow
November 14, 1973
November 19, 1973
December 7, 1973
m/sec
cfs
Lake Inflow
mVsec cfs
89
102
120
3150
3590
4226
44
(14)
(22)
1546
(495)
(778)
528
-------
of Lake currents is described below.
Temperature data from Storet indicate that the IHC is
usually 5°C warmer than the Lake, and this is due to
the fact that IHC water consists of Lake water that
has been pumped through industrial processes and used
for cooling. The only exception is when the Lake
temperature is close to 0°C. In this case the IHC
water may be near 4°C, the temperature of maximum
density, and the plume will tend to sink. Such a
sinking plume has been observed in January (SnowlO,
p. 135).
After the plume has moved a few km, its subsequent
vertical and lateral mixing is expected to depend on
turbulent diffusivity in the Lake. We made an attempt
to apply the diffusion model of Wnek and Fochtman-'-^
and found that with assumed constant diffusivities the
calculated plume concentrations fell off more rapidly
with distance than the measured concentrations.
Wnekl2 had previously obtained more reasonable results
using a diffusivity that varied with distance to the
4/3 power. Further effort would be needed to resolve
this question.
COMPARISON OF PLUME AND NEAR-SHORE WATER POLLUTION
Based on the measured dilution factors in the plume,
the study (SnowlO) recommended reductions of pollu--
tants such as NH3-N to meet water quality limitations
in the harbor within 1-2 km of the mouth of the IHC.
lll'llpl'I'I'I'I'I'I'I'I'I'I'ITI'I'iri'l'I'I'I'I'I'I'I'l
0 .01 J" """""" ~ ~~ " " " ~" ™
SSHuTY I
ITAMOMO I
Figure 2
Ammonia-Nitrogen
Annual Average &
Maximum, mg/Jl
Chicago Water Dept.
South Shore Lake
Survey
529
At this stage
-------
2 8-
o o
Currant m*t«r »t 08th St. orl
L»k« Michigan Chicago w*t*r lnt*k*
M*t«r 17 ft. b«low «urf*c*
n ° n' O'
Figure 3
A Sample of Current Meter
Data From Calumet Area
Further evidence of motion of near-shore waters is
obtained by observing the turbidity patterns of the
water. Surface waves stir the bottom to a depth of
about half the wavelength, or about 2-22 ft (Verber1-1-) .
Figure 4 is a Landsat photo showing sediment patterns
that indicate the movement of near-shore waters
toward the south.
Figure 4. Landsat Photo of Lake Michigan, Aug. 21, 1973.
Turbidity patterns indicate motion of near-shore waters.
Lake bottom cannot be seen.
530
MODELLING ATTEMPTS
Current action in Lake Michigan is more complex than
in the shallower Great Lakes. For this reason hydro-
dynamic models developed for other Great Lakes appear
not to be applicable. The main current patterns in
deep water of Lake Michigan have been identified and
correlated with physical processes that cause
the currents (FWPCA^, and other references
given by Snow-*-") . Most of the current measure-
ments were done in deep water, because the
early current meters were subject to interfer-
ence by waves in shallow water. It has been
found (Verberll, FWPCA^) that the near-shore
currents may follow a different pattern from
currents in deeper water. Figure 3 represents
some of the few data in near-shore waters, and
these data indicate that the near-shore currents
follow the wind more directly than the deep-
water currents.
Katz and Schwab^ attempted to model dispersion
of pollutants by applying a hydrodynamic model
previously developed by Kizlauskas and Katz^.
They predicted currents near shore that follow
the wind direction; but the predicted currents
in deeper water sometimes go in the wrong
direction, when compared with data from FWPCA .
Katz and Schwab^ combined this hydrodynamic
model with a dispersion model by dividing the
Lake into 10-km square cells. The near-shore
water was given no special treatment. Calcula-
tions for the dispersion of effluents from the
IHC during a period of alternating wind direc-
tions showed that the pollutants tended to
remain in the general area, although they were
not confined to the near-shore region. Whether
the method of calculation would give more de-
tailed results in the near-shore area if the
grid size were finer, has not been determined.
-------
Some general hypotheses concerning the behavior of the
near-shore waters can be gleaned from observations of
the current data, the turbidities, and temperatures,
and the pattern of pollutants. It appears that a
demarcation often occurs as seen in Figure 4 between
the near-shore and deep water at a distance of 5 to 10
km from shore. This corresponds to a depth of 10 to
20 m, the location where the summer thermocline inter-
sects the bottom (FWPCA2. p. 125). The demarcation
can be sharp or diffuse. Water in this region drifts
up and down the shore with a speed of 5 to 10 cm/sec
with a reversal frequency of 12 hrs to 4 days (SnowlO,
pp. 120-125), during which time it can travel a dis-
tance of 2 to 35 km. Mixing can be expected at the
outer boundary of the near-shore water, and this might
be modelled like a boundary layer. However, since the
depth is only 10 to 20 m at the outer boundary, while
the width is 5 to 10 km, it will take a long time for
mixing to penetrate to the shore. A more plausible
mechanism for eventual dispersion of pollutants is the
intermittant flow of near-shore waters to the southern
tip of the Lake, where they may meet a current from
the eastern shore, and hence mix out into the Lake.
This is only a hypothesis, since details of such a
flow pattern have not been established.
Sudden replacement of the near-shore water by cold,
clear, and much purer deep-lake water is occasionally
observed. Such incidents may result from upwelling,
caused by unusually strong off-shore winds. The fact
that this occasionally happens is evidence that during
the rest of the time the near-shore residence time is
long.
RECOMMENDED INVESTIGATION
It is the thesis of this paper that measurements of the
behavior of the near-shore waters are needed to form
the basis for dispersion modelling. The objective
should be to follow the motion of the water masses,
and to determine their residence time and trajectory
in the area.
To obtain data needed to form the basis for dispersion
modelling, the following simultaneous measurements are
needed over a period of a few weeks: 1) Current meters
installed 1 and 3 km .from shore at 3 locations in the
area, plus a few deep-water locations. 2) Analysis of
satellite photos showing turbidity effects. Landsat
passes occur so infrequently that few photos will be
obtained during any measurement period. Earlier
photos can be studied, to correlate evidence of shore
current patterns with wind records. 3) Aerial sur-
veillance can provide photos of the near-shore area
twice daily from an altitude of 20,000 to 30,000 ft,
and motion of plumes and sediment can be observed and
measured. 4) Periodic launching into the IHC plume of
markers that can be tracked from aerial photos and
perhaps by radio. Markers should be designed to float
just below the surface so that they follow the water
mass and not directly affected by winds. 5) Measure-
ment of a few water quality parameters, such as NH3-N,
F6i 02, temperature, and turbidity. Samples can be
taken at 5 water intakes twice daily, and from a boat
at a few additional sites, preferably near the floating
markers, to follow the movement and dispersion of water
masses. 6) Recording of wind conditions at existing
Lake stations.
Expected results of such a study will be measurement
of residence time and dispersion of effluent water
masses in the near-shore area, and measurement of the
mixing with deeper water under measured wind conditions.
These data would make it possible to develop a model
for the dispersion in terms of a boundary layer or
other model.
A field measurement program such as this would require
cooperative efforts of several organizations, to
provide current meters, aerial surveillance, water
quality measurements, and data analysis and modelling.
Several agencies have an interest in such measurements
on Lake Michigan, and a program such as this could
provide a framework for a cooperative investigation.
REFERENCES
1. FWPCA, Lake currents, a technical report. 364 pp.
1967.
2. FWPCA, Physical and chemical quality conditions,
Lake Michigan basin. 81 pp. 1968.
3. Cedarwall, Klas, Dispersion phenomena in coastal
environments, J. Boston Soc. Civil Engrs. 57 (1),
34-70, 1970.
4. Ippen, A. T., Estuary and coastline hydrodynamics,
McGraw-Hill, New York, 1966.
5. Katz, P. L., and Schwab, G. M. , Modelling episodes
in pollutant dispersion in Lake Michigan, Research
report No. UILU-WRC-75-0097, University of Illinois,
Chicago Circle. 69 pp. 1975.
6. Kizlauskas, A. G., and Katz, P. L., A 2-layer
finite-difference model for flows in thermally-
stratified Lake Michigan, Proc. 16th Conf. Great
Lakes Research, pp. 743-753, 1973.
7. Palmer, M. D., Coastal region residence time
estimates from concentration gradients. 17th Great
Lakes Research Conference. 1974.
8. Parker, F. L., and Krenkel, P. A., Thermal pollu-
tion status of the art, Report No. 3 prepared for
FWPCA, Vanderbilt University, Nashville, Tenn.
1969.
9. Sharp, J. J., Spread of buoyant jets at the free
surface, J. Hydraulics Div. ASCE 95_ (HY3)
811-825, 1969.
10. Snow, R. H. , Water pollution investigation,
Calumet area of Lake Michigan, Report EPA-905/9-
74-011-A, Region V EPA, Chicago, Vol. 1, 307 pp.
1974.
11. Verber, James, Currents and dilution factors for
lower Lake Michigan, unpublished report of
Technical Committee, Calumet Area Enforcement
Conference, June 1965.
12. Wnek, W. J., and Fochtman, E. G., Mathematical
model for fate of pollutants in near-shore waters,
Environ. Sci. & Tech. 6 (4), 331-7, 1972.
ACKNOWLEDGEMENT
This work was supported in part by U.S. Environmental
Protection Agency, Region V Enforcement Branch, under
the Great Lakes Initiative Program, Contract No.
68-01-1576. Howard Zar was project officer.
531
-------
A RIVER BASIN PLANNING METHODOLOGY
FOR STREAMS WITH DISSOLVED OXYGEN AND
EUTROPHICATION CONSTRAINTS
by
Thomas M. Walski, Sanitary Engineer
Army Corps of Engineers Environmental Effects Laboratory
and
Vicksburg, MS. 39180
Robert G. Curran, President
Curran Associates, Inc. Engineers and Planners Northampton, MA
01060
Optimal Waste Load Allocation Program 2 (OWLAP2) is a
user-oriented optimization model which selects waste-
water treatment levels to meet water quality con-
straints at least cost. This program solves the pro-
blem faced by river basin planners, who by merely
insuring that each wastewater discharge meets effluent
standards, will still be unable to meet water quality
standards. This program selects the least cost com-
bination of additional treatment in the basin that
will insure that water quality standards will be met.
OWLAP2 first simulates water quality in the reaches of
the river under consideration. It then perturbs the
initial conditions to determine the sensitivity of
water quality to changes in effluent. It uses these
sensitivities as inputs to an algorithm for lineariz-
ing non-linear systems so that they can be optimized
utilizing linear programming.
Scope of Problem
A flowing stream provides many valuable services to
those who live along its shores as it can be utilized
as a source of drinking water, a means of transpor-
tation, a location for recreation and a route for re-
moving waste material from a population center. With
increasing population it had become obvious that if
the stream was utilized excessively for waste removal,
this function would interfere with other uses. This
situation eventually reached the point where govern-
ment intervention was necessary to reduce the waste
load to acceptable levels.
Unfortunately, governmental boundaries were generally
not established along those of the river basins and
it was difficult to efficiently reduce the waste
loads to acceptable levels. Realizing this, various
governmental organizations attempted working together
to effectively manage the nation's rivers, and it was
found that sound planning can decrease waste reduction
costs.
With passage of the 1972 Amendments to the Federal
Water Pollution Control Act (PL 92-500), the United
States became committed to "encouraging and facili-
tating the development and implementation of areawide
waste treatment management plans." With this law,
wastewater treatment is emphasized as the method of
choice for achieving water quality goals. Once one
has established wastewater treatment as the method
for achieving water quality goals in a river basin
system, some tools are required for analysis of the
system to best employ the treatment efficiently. The
systems are so complex that a plan based on experi-
enced guesswork will not be sufficient . Instead, the
tools of operations research appear to supply the most
useful laethod for analyzing such complex systems and
arriving at rational engineering designs for waste-
water treatment facilities. Granted, there are a
multitude of engineering judgements which must be con-
sidered in the basin plan, but the techniques of oper-
ations research should provide a comprehensive frame-
work for making these judgements.
It is fortunate that river basin planning should come
to the fore at the time when digital computer tech-
nology is currently available to solve a broad spectrum
of large problems. This allows the planner to handle
a wider range of problems than could be attempted
without computer assistance.
The most powerful of operations research tools is lin-
ear programming. It allows one to handle a wide vari-
ety of very large problems in a reasonably small
amount of computer time. Linear programming will
therefore be employed in this study to find the "opti-
mal" plan for wastewater treatment plant construction
and improvement for a given river basin.
The word "optimal" in the previous paragraph is of
great importance in this discussion as it is necessary
to translate this concept into a linear mathematical
function which can be optimized. This function is
known as the "objective function." The form of this
objective function is of crucial importance as it is
a mathematical manifestation of the goals of those in
the river basin. The objective function, which econo-
mists refer to as the "social welfare function," can
be best described as:
max (B-C)
where B benefits
C = costs
In the cases when benefits from a public good cannot
be estimated, benefit cost analysis must be abandoned
in favor of cost effectiveness analysis. An example
of this is national defense, where there is very
little hope for evaluating benefits. In such a case
cost effectiveness analysis, which involves minimizing
costs for a given output, must be employed. This
approach is attractive in a linear programming context
in which the water quality goals can be included in
the constraint equations without the need to formu-
late them in terms of cost.
Program Outline
OWLAP2 is a river basin planning program which has as
its objective function minimization of wastewater
treatment costs while maintaining at least a minimum
level of water quality. In addition to considering
BOD-DO which exhibit essentially linear behavior,
OWLAP2 can optimize such parameters as nutrients which
exhibit complex dynamics. OWLAP2 determines the opti-
mal treatment level for BOD, organic nitrogen, ammonia-
nitrogen, nitrate-nitrogen and phosphate-phosphorus.
The program methodology, though, can be applied to
other interactive systems fairly easily.
OWLAP2 uses two criteria for judging water quality
levels dissolved oxygen and algal biomass. While
dissolved oxygen is the water quality parameter of
most interest, eutrophication may be a problem in slow
moving streams. In addition to the well-known aesthe-
tic and taste and odor problems, a large algal popu-
lation may have a serious negative effect on dissolved
oxygen levels. This is due to the fact that OWLAP2 is
a steady state model but large algal populations which
produce oxygen during the day and consume it at night
could cause serious diurnal oxygen fluctuation so that
even though the steady state goals may be reached, the
standards may be frequently violated. Constraining
the size of the algal population can circumvent this
problem.
As noted earlier, OWLAP2 handles the problem of linear-
532
-------
izing and optimizing wastewater treatment costs for a
river system in which not only dissolved oxygen but
also nutrient related water quality goals must be met.
The OWLAP2 package consists of a simulation program
(SIMU) and the optimization routine (OWLAP2).
Since the passage of PL 92-500, effluent standards are
very often so stringent that water quality constraints
are not binding. There is virtually no reason to run
an optimization program in this case since the degree
of treatment is determined. The user can check to see
if this is the case by running SIMU the water qual-
ity model of OWLAP2 to determine if water quality
constraints will be binding. Only then need the user
run OWLAP2.
This two-stage approach to determining an optimal sol-
ution serves another purpose. Since the water quality
model employed in OWLAP2 is quite complex and requires
knowledge of a large number of rate constants, it is
desirable to test the model to see if it fits river
data before attempting to run it. SIMU allows the
user to do this testing at a much lower cost than
OWLAP2.
The stream standards for OWLAP2 are enforced in terms
of meeting a given minimum dissolved oxygen concentra-
tion and a maximum algal biomass concentration (algal
biomass is expressed in terms of chlorophyll-a). The
water quality parameters considered in SIMU and OWLAP2
are BOD, ammonia-N, nitrate-N, phosphate-P, organic
nitrogen, dissolved oxygen and algal biomass. The
water quality goals are met by reducing the amount of
BOD, ammonia, nitrate or phosphate discharged in acc-
ord with the cost minimization objective.
The water quality model employed in SIMU and OWLAP2 is
based on several sources including the work of
O'Connor, Thomann and DiToro,1 and Chen and Orlob.2
The overall model is shown in Figure 1. If the user
finds that the model does not accurately describe
the system under consideration, he is encouraged to
modify the model, during the running of SIMU, so that
it does.
kinetics are non-linear, it was virtually impossible
to directly convert the water quality dynamics into a
linear program form. Griffith and Stewart presented
an algorithm for linearizing problems of this type.
The linearization involves doing a Taylor expansion
about the previous solution (based on the effluent
standards initially). The method also checks to in-
sure that the solution is not greatly different from
the initial solution since the equations may be linear
only over a small range.
The methodology of utilizing the OWLAP2 and SIMU pro-
grams is given in Figure 2. The OWLAP2 program con-
sists of a main calling (OWLAP2) program and three sub-
routines :
BUILD: constructs the water quality con-
straints for the linear programming
problem;
COST: sets up cost vector for optimization;
LP : determines the optimal solution to
the linear programming problem.
Optimization Routine
The optimal solution to the problem is determined
using a linear programming formulation. The general
form of the linear programming problem is:
max Z = c_ x_ (1)
subject to:
b
(2)
Equation (1) is known as the objective function (i.e.
the mathematical expression to be optimized). Equa-
tions (2) are the constraint equations (i.e. the
mathematical expression of the water quality effluent,
or other standards to be met) .
There exist numerous programming packages which solve
the linear programming problem. The most commonly
employed programs are those which utilize the "sim-
plex" or "revised simplex" method. These methods are
reliable but somewhat slow.
Since the differential equations describing the algal Another approach is a primal-dual algorithm which can
LOSS TO SEDIMENT
AND HIGHER LEVELS
OF FOOD WEB
Figure 1• Water Quality Model
533
-------
Figure 2: OWLAP2 Outline
arrive at an optimal solution in a shorter time than a
simplex or revised simplex code can. For OWLAP2, the
MINIT (minimum iterations) algorithm developed by
Salazar and Sen4 and translated from ALGOL to FORTRAN
by this investigator were employed. It combines the
features of being easy to use and not requiring a
great deal of computer time or payment of rental fees.
OWLAP2 does not fit precisely into the form of the
classical linear programming problem. OWLAP2, though,
models the behavior of nutrients which cannot be accu-
rately described using linear equations. Therefore,
the nonlinear nutrient models must be linearized.
If the simulation portion of the program indicates the
necessity to further improve treatment beyond the
effluent limits, the cost minimization for the addi-
tional treatment is performed as follows:
Maximize G c x +c x ...+c x (3)
-L J. Z Z K K
subject to:
gi(x1,x2...xk) < bt i 1,2,...,2m (4)
The x's are the decision variables (amount of pollu-
tant discharged)
The c's are cost constants.
The b.'s are the requirements constants
2m is the number of constraints and m is the num-
ber of possible critical points as there is a dis-
solved oxygen and algal biomass constraint at each
critical point.
k is the number of decision variables.
The superscript ° denotes values of the variables
at the initial solution (i.e. only effluent con-
straints utilized).
The problem may be linearized by using a Taylor expan-
sion around a vector 3c° ' ° °^ r— *"u~ """
linear constraints.
!, x£...x°) for the non-
This gives: Maximize G = I [c x°-c (x°-xr)]
= T T T
(5)
subject to: g.(x°)+£ (x°-x )
r
r=l
i-l,2,...2m
(6)
if one makes the Ax.=(x?-x.) terms small enough,
(7)
ax
The wij are constant. Equations (5) and (6) can now be
rewritten as: ,
Maximize (G-v0)=2 -
r r
(8)
subject to: I w. Ax < (b.-v.) i=l,2,...,2m (9)
=1 ir r - i i ^ '
where
v.=E c x°
r=l
Since the gi's are nonlinear, the w^j terms are con-
stant only for small values of Ax. To guarantee that
these are indeed small, it is necessary to include
constraints of the form:
Ax.
-------
Cost Vector
D.O. Constraints
[Value of Objectiv
• function
Algal Biomass |
Constraints 1
f
Linearity Constraints
I
1 » 4k 1
Figure 3: Form of Linear Programming Input
(k B number of discharges)
(m = number of critical points)
GROWTH RATE X AB (12)
The RATE of algal growth can then be given by the
Monod relation:
RATE K
N°3+NH3,
PO,
SP+P°4
S +AB
\-i
(13)
N03
NH3
P04
Sp
nitrate-nitrogen concentration
ammonia-nitrogen concentration
phosphate-phosphorus concentration
half saturation constant for nitrogen
half saturation constant for phosphorus
constant for algal self-shading
The algal death rate is a linear function of algae
present. This model can easily be altered for systems
in which algal die-off follows different patterns.
Algal loss differs.from death in that loss represents
the algae and nutrients being removed from the system
(usually up the food chain). Death, on the other hand,
implies that the nutrients are fed back into the
system.
Biochemical Oxygen Demand
BOD can be removed from the system by oxidation at
rate KI, or sedimentation at rate K3. Aside from dis-
charges at wastewater treatment plants and the BOD
carried in by tributaries, the only BOD source is
death of algae. The BOD considered is ultimate car-
bonaceous BOD. The following formula is employed:
(BOD contribution (death of algae as chlorophyll-a
from algae)
(DEATH) 78.4 gr BOD
gr dead chlorophyll-a (14)
BOD kinetics can be described by:
a BOD
~dt— -(K]+K3)BOD+78.4(DEATH) (15)
DEATH kDAB
KD rate constant for algal death
.Ammonia Nitrogen
Ammonia nitrogen is formed as organic nitrogen, is
broken down, and can either be oxidized to nitrate
and nitrite or used as a nutrient by algae. This
model does not explicitly consider the oxidation of
ammonia to nitrite but rather considers the overall
reaction as given below:
2NH,+40,
bacteria
2N0+2H
The kinetics of ammonia are given below as:
d(NH3)
~dt =Kc
GROWTH (NH3)7.2
(NH3+N03)
(16)
(17)
ON = organic nitrogen concentration
K
on
rateoconstant for oxidation of organic
Nitrate Nitrogen
Nitrate nitrogen is formed by oxidation of ammonia at
rate Kn and is used as a nutrient for algal growth.
The kinetics of nitrate are given by:
d(N03)
~dt
GROWTH (NO )7.2
(18)
Nitrate reduction to gaseous nitrogen is not considered
to be significant but can be included in the model if
low dissolved oxygen levels are to be expected in a
reach.
Phosphate Phosphorus
Phosphate-phosphorus has as its source wastewater dis-
charges and release of phosphorus from dying algae.
The kinetics of phosphate are given below:
-fa = 1.66 (DEATH GROWTH) (19)
The constant 1.66 is derived from the conversion by
Megard.5
1.66 gr P
gr chlorophyll-a
(20)
If removal of phosphorus by sediments is significant,
it can be easily included in the model.
Organic Nitrogen
Organic nitrogen as referred to in this problem is
organic nitrogen, not as living biomass (e.g. amino
acids and polypeptides released from decaying biomass).
Organic nitrogen decays to ammonia and is formed by
decaying living matter. The kinetics of organic nitro-
gen are given below:
on
(ON) + (DEATH) 7. 2
(21)
The constant 7.2 is a conversion factor, since there
are 7.2 mg organic nitrogen per every mg of chloro-
phyll-a, and DEATH is expressed as mg algae (as chlo-
rophyll-a) that die per day. It is also assumed that
nitrogen fixation is not significant.
Dissolved Oxygen
Dissolved oxygen is consumed in oxidztion of carbon-
aceous BOD, organic nitrogen, and ammonia-nitrogen.
It is replaced through atmospheric reaeration and algal
respiration. The rates are respectively K-^, Kn, K2,
and Kr. The kinetics of dissolved oxygen are given by:
d(
= -K. (BOD) -4.57 Kn(NH) + K(C -DO) +K (GROWTH) -SR
1 i / s r
Cs
K2
Kn
Kr
SR
mg/1 chlorophyll-a
rate constant for oxidation of BOD
rate constant for atmospheric reaeration
rate constant for nitrification
rate constant for algal respiration
other oxygen sources and sinks
The K's have units of I/day except for Kr, which is in
mg 02/mg chlorophyll-a/day. The 4.57 in Equation (22)
represents the gram of ammonia nitrogen to nitrate
stoichiometrically.
Special Note
While OWLAP2 provides the framework for optimally
allocating waste loads, the user must realize that the
results of the model will only be as accurate as the
model, model calibration and cost inputs allow. The
program is constructed so that the model can be easily
adjusted to fit virtually any one-dimensional, steady-
state system. Since the model is so flexible, great
care must be exercised in adjusting the model so that
535.
-------
it will be specific for each system. This requires
considerable data collection. Similarly, while typi-
cal cost data is included in the model, the user must
be aware that coses will be site specific and must in-
clude accurate costs as the model is quite sensitive
to these inputs.
Acknowledgements: This program was developed under
EPA Contract 68-01-2916, William P. Somers, Project
Officer.
REFERENCES:
1. O'Connor, D.J., R.V. Thomann and D.M. DiToro,
Dynamic Water Quality Forecasting and Management,
U.S. EPA, Office of Research and Development,
EPA 660/3-73-009, Aug. 1973.
2. Chen, C.W. and G.T. Orlob, Ecologic Simulation
for Aquatic Environments, NTIS PB-218 828, Dec.'72..
3. Griffith, R.E. and R.A. Stewart, "A Nonlinear
Programming Technique for the Optimization of
Continuous Processing Systems," Management Science,,
Vol. 7, p. 379-392, 1961.
4. Salazar, R.C., and S.K. Sen, "MINIT Algorithm for
Linear Programming", CACM, Vol. 11, No. 6, June'76.
5. Megard, R.O., Rates of Photosynthesis and Phyto-
plankton Growth in Shagawa Lake, Minnesota, EPA-
R3-73-039, July 1973.
536
-------
MODELING POLLUTANT MIGRATION IN SUBSURFACE ENVIRONMENTS
Amir A. Metry, Ph.D., P.E.
Project Manager
Roy F. Weston, Inc.
West Chester, Pennsylvania
SECTION I
ACKNOWLEDGEMENTS
This study is funded by a Research and Development
Grant from Roy F. Weston, Inc. The members of the
research team would like to express their appre-
ciation for the financial support and encourage-
ment of Weston Research and Development Committee
members.
Numerical analysis and computer s-imulation was con-
ducted by Dr. Arun K. Deb, Principal Environmental
Systems Engineer of Roy F. Weston, Inc.
The technical support of Dr. James Davidson,
of the University of Florida, and his co-workers
Dr. P.S.C. Rao and Dr. H.E. Selim is greatly
appreciated.
SECTION 2
INTRODUCTION
Need for Proper Assessment of
Potential Groundwater Pollution
Groundwater is one of the earth's most widely distri-
buted and most important resources. Its quantity is
estimated to be six times that of the fresh water
flowing in all the streams on earth. Groundwater
accounts for 20 percent of the total amount of water
withdrawn from all other sources. Groundwater re-
sources have many advantages over surface water
resources because they are more widely and easily
available than surface water supplies. The physical
and chemical quality of groundwater is fairly uniform
throughout the year. It is rarely, if ever, necessary
to consider removal of sediment from groundwater.
The existing demand for groundwater as a source of
conventional water supply will continue to grow;
furthermore, aquifers will be considered as storage
media for flood water in place of dams and reservoirs
as the cost of these facilities grows progressively
more expensive. With the effort to clean up streams
under water pollution control acts, aquifers will be in
demand as alternative means for direct and indirect
disposal of both liquid and solid wastes from indus-
trial and domestic activities. v
Although not as dramatic and apparent as surface water
pollution, degradation of the quality of subsurface
waters is widespread. Several sources of groundwater
pollution have been identified, including leachate
from sanitary landfills; industrial waste seepage
from storage basins; industrial waste introduced
through groundwater recharge; dome'stic waste from
septic tanks; fertilizer, pesticides, and irrigation
salts leached from soils in agricultural areas, and
leachate from raw materials and waste stockpiles, etc.
The successful location and operation of a waste dis-
posal site require quantitative knowledge of how leach-
ing fluids will migrate through an aquifer. This will
depend on hydrogeologic parameters of the leachate/
aquifer system, type of waste, and climatic conditions
at the site area. Experimental methods are required
to quantify the different parameters involved in the
mass exchange between leachate and the aquifer. Among
the different types of models suitable for dispersion
patterns, mathematical models can be conveniently de-
vi sed.
This mathematical model describes the hydrogeologic
relations within a leachate/aquifer system. It is
usually in the form of a second-order partial differ-
ential equation together with a set of auxiliary con-
ditions describing the system's variables and con-
stants. If such equations are sufficiently simplified,
exact solutions may be possible. On the other hand,
however, these simplifications are often physically un-
realistic. Numerical solutions obtained with the aid
of high-speed digital computers offer a great help for
solving such equations under physically realistic as-
sumptions.
Problem Definition
Rainfall over a waste disposal processing or storage
area causes infiltration, and therefore leachate gener-
ation. Most of the states in the U. S. have net infil-
tration; the potential for leachate generation there-
fore exists in these humid areas.
Leachate containing several polluting substances leaves
the waste material and travels through unsaturated
media. During their travel, many of these pollutants
are subject to assimilation by soils, because of the
adsorption and ion exchange capacity of such materials.
Attenuated leachate then leaves the subsaturated zones
and enters the aquifer, where it is subject to dis-
persion in groundwater and to chemical reaction with
earth materials.
In order to determine the impact of a waste handling or
disposal facility on subsurface waters the following
steps must be taken:
1. Determine quantities and characteristics of
the leachate. This can be accomplished by
laboratory and/or field investigations.
2. Determine the degree of leachate assimilation
as it travels through unsaturated media.
3. Determine the pattern of Leachate dispersion
and its eventual concentrations and chemical
reactions in the aquifer.
Scope and Objectives
Modeling leachate dispersion and assimilation in sub-
saturated and saturated media is an essential step in
determining impact of waste disposal facilities on
subsurface water quality.
The main objective of this study is to develop math-
matical and computer models to predict leachate-pol-
1utant migration and fate in subsurface environments.
Because of the hydraulic discontinuity between sub-
saturated earth layers (soils) and saturated layers
(aquifers), two models were developed: 1) a one-
dimensional model to predict pollutant attenuation
in subsaturated media (soils), and 2) a two-
dimensional model to predict pollutant migration
537
-------
and fate in saturated media (aquifers). Four basic
criteria were considered in developing these
models. The models should be--
• Representative of the physical conditions of
both the saturated and unsaturated media.
•Based on sound mathematical principles.
•Easy to understand and usable by engineers
and scientists.
•Practical, and economical to run, on commonly
used computers.
Summary of Literature Review
The literature is rich in theoretical background for
dispersion of soluble matter in porous media. More
work has been done in the area of dispersion in
saturated media than in unsaturated ones. There is
apparent agreement in the literature on the validity
of partial differential equations to model pollutant
dispersion and fate in porous media (soils and
aquifers); however, there is still a tremendous gap
between the degree of sophistication of research in
this field and the actual technology used in day-to-
day applications. In spite of the great research
effort, almost all solid and liquid waste disposal
sites are located on land without any modeling
activity to determine their impact on subsurface
water quality and to determine the need for, and
degree of environmental controls. One reason
for this great gap is the difficulty that engineers
and scientists working in the field have in under-
standing and applying much of the existing research;
unfortunately, most of the published research work
ended up as research for sake of research, rather than
application. Therefore, the need for easy-to-under-
stand and easy-to-apply models utilizing easy-to-
quantify field conditions (hydrogeologic parameters)
is badly needed to predict pollutant fate and dis-
persion in soils and aquifers.
centration c . The following conceptual model was used
for this investigation:
3t
9z
p 9s
e at
Kc
where:
t
D
2
W
P
9
k
constituent concentration (
in soi1 solution
adsorbed constituent concentration
mg/kg)
time (yr)
Hydrodynamic dispersion coefficient (
distance (m)
average pore-water velocity (m/yr)
bulk density of dry soil (g/cm ,) .
soil water-content fraction (cm /cm )
transformation rate constant (yr )
(3.1)
g/cm or mg/L)
M g/g or
m /yr)
The third term on the right hand side of equation (3.1)
represents adsorption. An equilibrium adsorption state
will be assumed with a linear relationship between
solution and adsorbed solute phases. This is expressed
as:
S= Kdc
(3.2)
where Kj is the distribution coefficient (cm3/g). Dif-
ferentiating (3.2) with respect to time gives:
as
3c
at ~ Kd at
(3.3)
Substituting (2.2)into (3.0 and rearranging gives:
PKd \ 3c = p92c w jlfL Kc
3t
O.'O
SECTION 3
MODELING POLLUTANT MIGRATION
IN SUBSATURATED MEDIA
Large quantities of solid waste and hazardous waste are
being disposed of by placing the material on the soil
surface or by burying it in large landfills. These
practices are often conducted without proper consider-
ation of how the waste material will behave in a given
soil or under specific climatic conditions. Procedures
are needed to assist in site selection and to define
proper management schemes for applying waste onto or
below the soil surface. The procedure needs to be
descriptive of how various constituents in a waste
behave in a soil-water system, but simple enough to
be of practical use.
Mathematical Model
This section presents an approach to these problems
which may be of value. The procedure, because of
insufficient research data, has not been validated
and should not be applied without first comparing it
to field data and experience. The physical system
assumes a constant application of a leachate con-
stituent (e.g., Cd, Pb, Hg, As, and Se) of concen-
tration c (n g/cm or mg/L) to the soil surface or
large sources of waste in a landfill that releases a
given constituent to the soil-water system at a con-
_3c
at
D_
R
a?
_vv 3c
R 3z
Kc
R
(3.5)
where R = (1 + ^-p ), which is frequently referred to
as retardation factor. When no adsorption occurs
(Kj 0), the retardation factor is unity. Note that
as the retardation factor is increased above unity, the
effective values for hydrodynamic dispersion, average
pore-water velocity, and transformation rate are re-
duced. The net effect is to reduce the mobility and
chemical transformation parameters of the constituents
being described.
Equation (3.5) was solved for the following initial
and boundary conditions:
c = 0
c c_
x>0
x =0
t = 0
t > 0
The physical meaning of the boundary conditions corres-
ponds to a situation where a soluble constituent in
leachate (e.g., Cd, Pb, Hg, As, or Se) is continually
supplied to a soil surface which did not contain the
material initially. The chemical transformation pro-
cess represents irreversible adsorption, precipitation,
and/or changes in the chemical state of the constituent
being described.
538
-------
Mathematical Solution
The solution to (3.5), subject to the initial and
boundary conditions, is
(erfc (Z tVw'+4D-K:
I V V4D7!
/erfc ( Z + ' Vw" J-JPJi'
I \ \^DT
(3.6)
where:
W = w/R
D1 = D/R
K' = K/R
erfc (z) is the complementary error function.
Model Parameters
The average pore-water velocities (w) used in this
section to illustrate the general utility of equation
(3.6) are 1.75, 0.876,0.438, and 0.088 m/yr. The
corresponding fluxes or Darcy velocities depend upon
soil-water content (9), since average pore-water
velocity (w) is equal to flux or Darcy velocity divided
by soil-water content by volume (6). Therefore, the
annual groundwater recharge represented by these average
pore-water velocities will also depend upon the average
soil-water content in the water transmission zone. The
dispersion coefficient is a function of average pore-
water velocity and was obtained using the following re-
lationship from Biggar and Nielsen (to appear).
D = 0.022 + 0.17 w
1.14
(3.7)
The transformation rate coefficients selected are
0.00876, 0.0876, and 0.876 yr'1 . These are, in
general, small values, and may or may not be realistic
parameters for leachate containing heavy metals (Cd, Pb,
Hg, As, or Se).
A literature search was conducted using the reference in
Copenhauer and Wilkinson (197*0, but transformation rate
constants (k) and distribution coeefficients (Kj) are
not measured or reported generally. The values used in
this report are thought to represent the range that
might be encountered in a natural soil environment. A
Kd if not available for a given soil and leachate con-
stituent could be measured by shaking leachate contain-
ing a known concentration of the solute with soil (e.g.
at 1:1 ratio) until equalibrium, and then measuring the
constituent concentration in the supernatant solution.
This procedure gives the quantity of the constituent
adsorbed. The ratio of equilibrium adsorbed concen-
tration (S) to solution concentration (c) is equal to
Kd. This procedure assumes that the adsorption isotherm
is linear over the concentration range in question.
SECTION 4
MATHEMATICAL MODELING OF POLLUTANT
MIGRATION IN AQUIFERS
In this section different mathematical models will be
formulated to represent migration of pollutants gener-
ated from a waste-disposal site into saturated porous
earth materials. Three major mass-transport mechanisms
are included separately or simultaneously in each model:
• Molecular diffusion -- the transport of pol-
lutants in their ionic state because of the
difference in concentration levels of a given
species in the aquifer.
• Convective dispersion -- the mixing of pollut-
ants in the aquifer caused by the variation
in the microscopic-pore velocities within each
channel of flow, or from one channel to
another.
• Chemical reaction — the transfer of the pol-
luting substances from their liquid carrier to
the solid matrix of the aquifer. In this study
the transfer of pollutants is considered in the
adsorptive rather than the desorptive sense.
Simultaneous Diffusion, Convective Dispersion and
Chemical Reaction Model
The rate of change of concentration dc/d t can be
mathematically defined for the diffusion convective
dispersion models and a chemical reaction term which
can be defined as the function f(c).
3c
div (D
c)
+ div (D' grad c) -v div c - f(c) (4.1)
Including the coefficients Dm and D' in one term D, the
effective diffusivity, Equation (4.1), can be rewritten
as
_3c_
3t
div (D grad c) v div c
f(c)
(4.2)
f(c) is a function of concentration,
where:
pollutant concentration (ML ) .
is the effective diffusivity (L T
groundwater velocity vector (LT~^)
f(c) = b (c-ms)n
s = concentration of polluting substance
per unit weight of the solid matrix
b and M = constants
n = exponent^ 1
SECTION 5
NUMERICAL SOLUTION OF TWO-DIMENSIONAL MODEL
OF POLLUTANT MIGRATION IN AN AQUIFER
In order to use operational methods for solving math-
ematical models, many oversimplifications have to be
imposed in order to solve the second-degree partial
differential equations describing the system: col-
lapsing the model into a one-dimensional state,
assuming homogeneity of the medium, and considering
only one mechanism or two of the three mechanisms
involved in the mass transport in every solution.
These simplifications and assumptions, which are
necessary but physically unrealistic, reduce the value
and applicability of the operations solutions to real
physical problems. In this section, a numerical tech-
nique is developed to solve the mathematical equation
describing simultaneous diffusion, convective dis-
persion, and chemical reaction of pollutants into an
unconfined aquifer in two dimensions under transient
and steady-state conditions.
539,
-------
Formulation of the Finite Difference Scheme
As shown in Section k, the dispersion equation in the
x-z domain can be rewritten as:
3c 32c 32c
IT Dx ^ + Dz 3?
3c Sc
u "3^ w "37
rDz
ru
F cm, n+1,s ~ 2h cm + 1,n, s 2h cm-1, n, s
rw
rw
2k cm, n
m, n-1, s
, n, s (5.8)
15 -\} Introducing the non-dimensional parameters a , a z and
0 , 0 , and K as:
In Equation (5.11 the different variables and para-
meters are defined as follows:
x and T.: Cartesian coordinates in the direc-
tion of groundwater flow and vertical
direction respectively (units: L)
Dx and Dz: are the effective diffusivities in the
x and z directions respectively
(L2 T-1!
u, w: are the components of pore velocities
in the x and z directions respective-
ly (LT-'I
K : is the coefficient of chemical re-
action of the polluting substance with
the porous medium (T- 1.
rDx
h: , and
ru a rw
~h~ PZ IT
rDz
k:
rK
(5.9)
(5.10)
(5.11)
Substituting Equations 5-9, 5-10 and 5-11 into Equa-
t,on g and rear ;
''in, n, s H 1
<=m-1,n,s K + °-
ix - 2az
cm+1,n,s,
Using the backward difference equation for time,
3c
cm, n, s+ 1 cm, n, s
+ (T)
(5.21
'dt' m, n, s T
'Ising the central difference equation for x and z
lijL-s + 0 (h2) (5.3)
3c °m+1,n,s
>3x' m, n, s
2h
cm.n.-1.s
3z'm, n, s
<3zJ 'm, n, s
and
(^t
I3x: ' m, n, s
where:
-
h-
~m-1, n, s
-2cn
, n, s + cm,n+1,s
+ cm+1,n,s
+ 0(k)
(5.12)
The Computational Molecule for the x-z domain can be
written as:
cm,M,b i 1 - cm,n,sl1 2ax 2az K)
+ Left [ax + 0.50X] + Right |ax 0.50X|
+ Up |az + 0.5j3z] + Down |az 0.5(3Z] /5 ^
Left, ^ig^vt, Up, and Down represent the concentra-
tions of the pollutants with respect to the specific
(5.5) grid point cm n s in the finite difference scheme.
Condi tions for Stability of the Numerical S olut ion
0(h)
The necessary conditions for stability of the numer-
ical scheme can be written as
rDx
h, k, T • numerical increments of x, z and t, re-
sp-ect i'Vely .
m, n, s: nannegative integers corresponding to
x, z and t coordinates respectively.
Substituting Equations '5.2) - (5.61 into Equation
(5.1):
1, Dx
T (cm, n, s +1 cm, n, s' Tr~'cm-1, n, s ~2cm,n,s
rDz
and
rK
(5.l
(5.15)
SECTION 6
cm+1,n,s
~2h 'cm+1,n,s
(cm,n-1,s~2cm,n, s + cm,n+1,s'
w
'c
m, n
DEFINITION OF PARAMETERS
Unsaturated Model
The parameters that appear in the mathematical model
for subsaturated media are those found in the fol-
lowing equation:
- k c
m, n, s
(5.7)
Rearranging Equation 5.7, the explicit form of the dif-
ference equation can be written as follows:
D_ 32c
R 3z:
w ^c
R 3z
.11
cm, n, s+
m,n,s
rDx
h2 cm-1, n, s
2rDx
h2
m,n,s
rDx
rDz
2rDz
c, t, z, D and K are similar to the parameters for the
saturated flow media and are discussed in the follow-
ing section.
R is known as the retardation factor and is equal
cm + 1, n, s
cm, n-1, s k2 cm, n, s
540
-------
p is the bulk density of dry soil or earth mate-
rials fg/m') and can be estimated for each
type earth materials or quantified through
laboratory testing of undisturbed core samples,
or by correlation with the degree of soil
saturation
Kd is the distribution coefficient CcrrvVg) . The
value of Kj is a leachate/soi1 specific and
could be measured in the laboratory by shaking
leachate containing a known concentration of
the solute with soil (e.g. 1:1 or 1:10 ratio)
until equilibrium is reached and then measur-
ing the constituent concentration in the
supernatant. The ratio of equilibrium
adsorbed concentration (s) to solute concen-
tration I c) is equal to K., for linear
adsorption isotherms.
$ water content, by volume (ml of water per cm of
soil)
S concentration of adsorbed phase (mg/g soil)
Saturated Model
The parameters that appear in the mathematical model for
saturated media are those found in the following
equation:
If = Dx
+ Dz
3;z
~W
3c
u 3x~
dc
Kc (6.2)
The concentration, co, of each polluting sub-
stance in the leachate as it enters the aquifer is
determined by applying the mathematical equations
3.1 and 3.6 presented in Section 3. The saturated
media model predicts concentrations (c) at various
locations in the aquifer (identified by x,z coordinates)
for differenct values of time, t.
Time (t): Time is the duration of travel of
polluting substances in the aquifer. Time can be
described as: a) a buildup period, in which the
concentration of a certain contaminant increases;
b) a steady state period, in which the concentration
remains constant; or c) recovery period, in which
the concentration starts to decline with the passage
of time. The representative time for a computer run
will vary, depending on aquifer hydrogeologic
character, from several months to ten years. Time
increments vary from several days to several months.
Space Coordinates (x and z) : These are taken in the
direction of groundwater flow and perpendicular to it,
respectively. In the computer runs, the spatial domain
in the direction of flow extends from a few hundred feet
to a few miles, and in the vertical direction it extends
from a few feet to a few hundred feet, depending on the
characteristics of the aquifer. The increment varies
from 10-1000 feet in the direction of flow, and 1-10
feet perpendicular to it.
_Effective Diffusion Coefficients (Dx and Dz) are a
function of molecular diffusion coefficients and pore
velocities (u and w). Their numerical values vary from
from a fraction to several sq ft/day, depending on type
of aquifer materials and pore velocities.
Chemical Reaction Coefficient (<): This value is
expressed as a linear function of the concentration. In
this study,* is considered in the sense of pollutant
removal from solution into the solid matrix. It is dif-
ficult, however, to develop a single value for this
function since it is dependent on geophysical and geo-
chemical properties of the aquifer and on groundwater/
leachate chemical interaction. The value of * is usually
on the order of a small fraction of Day~1 for most aqui-
fers, and it increases with increases in reactive
materials (e.g., clay or salts) content in the aquifer
materials. Chemical reaction coefficients can be
determined using laboratory columns (lysimeters).
SECTION 7
COMPUTER SIMULATION
General Considerations
Pollutant migration through subsaturated soil and
saturated aquifers has been dealt separately using
Equations (3.1) and (5.1), respectively. Equation
(3.1) has been solved analytically and the solution is
given by Equation (3.6). For saturated media, Equation
(5.0 has been solved numerically using finite
difference technique. The finite difference form of
Equation (5.1) is given by Equation (5.6). The con-
ditions of convergence of solution of finite difference
Equation (5.6) to differential equation (5.1) are given
by Equations (5-1^0 and (5-15). A program has been
developed to solve Equation (5.6) numerically using
a high speed digital computer using proper initial
and boundary conditions.
The differential equation for substaturated soil layers
(Eq. 1.1) will be solved first to find the concentration
of a pollutant as it enters the interface of the sub-
saturated and saturated layers. This would constitute
one of the boundary conditions (at z = 0) for the
solution of the saturated model. The concentration
of the pollutant at other boundary conditions is assumed
to be equal to background condition. The initial con-
dition of pollutant concentration at all the x - z grid
points at time t = 0 has been assumed to be equal to the
background concentration.
The computer simulation is expressed as two-dimensional
concentration profiles which can be oriented in either
the vertical or the horizontal domain, under transient or
steady-state conditions.
Program Logic
When the initial and boundary condition values of pol-
lutant concentration in two saturated aquifers are known,
the concentration of pollutants at all the x - z grid
points at t = 0 are known. The computation of concen-
tration for all x-z grid points for the next time in-
ternal, At, would be done using the finite difference
equation (5.6). In a similar manner, a step-by-step
solution for the pollutant concentration at all x-z
grid points for various time intervals may be obtained.
The procedure of "marching solutions" is repeated for
progressing time intervals up to the required time
period for which the results are desired. The selection
of finite difference grid intervals should be made in
such a way that the stability conditions (Equations
5.1^ and 5.15) are satisfied. The program has been
written in FORTRAN IV and is installed in the Weston
computer system.
Input Requirements
The input data required for computation consist of grid
characteristics, initial and boundary concentrations of
pollutants, program operation and control data, and
aquifier characteristics such as velocities and
diffusion coefficients in the x and z directions and
the coefficient of adsorption. The output of the
program consists of the ratio of concentration of pol-
lutant in the two-dimensional domain for various time
periods.
541
-------
Figure 2 and 3 are plots of concentration profiles for
various depts below ground water and for various
distances downstream of source respectively.
FIGURE 1 POLLUTANT ISOPLETHS (RUN 1)
Typical Run
Figures 1 through 3 are graphical presentations of
computer simulation of a typical run based on the
following parameters:
Number of Finite Space Increments in
X Di rection = 20
Number of Finite Space Increments in
Y Direction
Number of Finite Time Increments
Background Concentration of Pollutant
Grid Space Size in X Direction in Feet
Grid Space Size in Z Direction in Feet
Grid Size in Time Direction in Days
Coeff. of Chemical Reaction of Adsorp.
of Poll. = 0.001
Effective Diffusion Coeff. in
X-Direction, ft2/day = 4.000
Effective Diffusion Coeff. in
Z-Direction, ft /day 0.50
Ground Water Flow Velocity in ft/day = 5.00
Vertical Velocity of the Leachate in ft/day = 0.20
Figure 1 is a plot of pollutant isopleths in the
aquifer. The leachate plume dips in the aquifer, which
is attributed to the vertica1-component velocity vector
(recharge velocity).
20
52
0.0100
200.00
5.00
7.00
FIGURES CONCENTRATION PROFILES FOR VARIOUS DISTANCES DOWNSTREAM
FROM SOURCE (RUN 1)
SECTION 8
CONCLUSIONS AND RECOMMENDATIONS
FOR FUTURE RESEARCH
I *
FIGURE 2 CONCENTRATION PROFILES FOR VARIOUS DEPTHS BELOW GWT (RUN 1)
Cone I us!ons
• The models developed in this study: a) have a
sound mathematical basis; b) account for major mass
transport mechanisms; c) are flexible and prac-
tical; and d) are accurate.
• The models can be used to simulate subsurface
contamination from area sources, such as solid
waste disposal sites, wastewater holding basins,
wastewater or sludge application sites, raw
material stockpiles and recharge of contaminated
waters.
• The models can be used as a tool for water quality
studies, disposal site selection and design, eval-
uation of environmental impact, recovery of ground-
water contaminants, and planning related to sub-
surface water resources.
• The accuracy of predicted contamination by the
models depends on the accuracy of hydrogeologic
parameters used in the simulation. It is rea-
lized that quantifying such parameters is one of
the most difficult tasks in simulating subsurface
water contamination.
Recommendations for Future Research
• The "first generation models" developed in this
study should be further tested, using field data.
• More effort is needed in defining and quantifying
various hydrogeologic parameters used in the models.
• The "second generation" models should be upgraded
to account for: a) multiple sources; b) hetero-
geneity of soils and aquifers; c) non-linearity
of chemical reactions; and d) pumping and recharge
in an aquiefer.
• It would be of great value to engineers and
scientists in the field if the computerized
solution of the models were expressed in a series
of nomographs that related pollutant concentration
to hydrogeologicaI parameters of a disposal site
542
-------
A MODEL OF TIDAL FLUSHING FOR SMALL COASTAL BASINS
Albert Y. Kuo
Virginia Institute of Marine Science
Gloucester Point, Virginia 23062
Abstract
An empirical theory is proposed to model the
flushing of a small coastal basin by tidal exchange.
The theory is adapted from Ketchum's tidal prism con-
cept with modification. The application of the method
requires that a water body be divided into segments
such that complete mixing at high tide within each
segment may be assumed. Starting from the mouth, each
segment is defined such that its volume at low tide
equals the total tidal prism landward from the inner
boundary of the segment. Therefore, each segment has
a length equal to the local tidal excursion.
The flushing capability of a segment is defined
as the fraction of dissolved substance removed per
tidal cycle, i.e. the flushing rate, which was derived
from the principle of mass-balance. The concentration
distribution of an introduced pollutant was expressed
in terms of discharge rate, volume, flushing rate,
and decay rate. A model has been set up for the Cock-
rell Creek of Virginia to study a proposed 0.2 MGD
STP. The model was used to project the distribution
of fecal coliform bacteria and biochemical oxygen
demand.
Introduction
Estuaries and coastal waters are being used more
and more frequently as dumping grounds for pollutants
resulting from human activities. If properly balanced
with the assimilative capacity, this may be a practi-
cal use of these water bodies. However, careful plan-
ning must be executed such that the introduced pollu-
tants will not upset the ecological balance and pre-
clude other usage of the water bodies.
The application of water quality models has proven
to be a powerful technique in water resource manage-
ment. The primary results of the model are the pre-
diction of the distribution and concentration result-
ing from discharge of a new pollutant, or an increase
or decrease of an existing pollutant discharged to a
water body. The fundamental goal of a water quality
model is to represent the complex interaction of the
prototype in a simplified form which not only simulates
the existing conditions with accuracy but also can
predict the likely consequence of a proposed change of
pollutant discharge.
The majority of recent developments in the field
of water quality modeling pertain to numerical mathe-
matical modeling . These models used advanced com-
puter techniques to find solutions to the governing
equations of motion and mass balance. An important
feature of these models is the requirement of substan-
tial data from prototype, either for input data or for
calibration and verification of the model. The appli-
cation of these models to a particular water body often
involves a large investment of time and effort. In
the case of small coastal basins (e.g. a coastal creek
of the order of 10 km long, 100 meters width), it is
usually impractical to use this kind of model to study
a proposed small waste discharge. A simple tidal
flushing model for small coastal basins which requires
only the data of tidal range and basin topography is
described in this paper.
Theoretical Consideration and Basic Assumptions
The tidal prism concept has been used to evaluate
2 3
the ability of an estuary to disperse pollutants ' .
The tidal prism is equal to the difference between
water volumes at high and low tides. In an estuary,
part of this volume is contributed by river flow, part
by water which enters through the seaward boundary on
the flooding tide. In a small coastal basin, the con-
tribution of river water may be so small at times that
the tidal prism consists wholly of the water brought
in by the tide. This inter-tidal volume of water
serves to dilute the introduced pollutants and event-
ually flushes them out of the estuary or coastal basin.
The objective of this model is to calculate the
equilibrium distribution of introduced pollutants.
During each tidal cycle, the pollutant concentration
at any location varies with the stage of the tide, but
on successively similar tidal stages, the pollutant
concentration returns to the same value. For the
equilibrium condition to exist, the pollutant discharge
rates and river flow, if any, must be kept constant for
a period much longer than the flushing time of the
water body.
Ketchum's assumption of the tidal prism concept
is adapted with modification. Ketchum assumed complete
mixing of the water entering on flood tide with all of
the water present throughout the estuary at low tide.
He further assumed that the maximum length of the
estuary over which complete mixing is possible is de-
termined by the average excursion of a water particle
on the flood tide. In the present model, Ketchum's
second assumption is retained and the water body is
divided into segments of length equal to the local
tidal excursion. Instead of complete mixing with all
water present at low tide, the water entering on flood
tide is assumed to mix completely with the water
present in the most seaward segment at low tide. Some
portion of this mixture, in turn, enters the next
landward segment and mixes completely with the water
present there at low tide. This process progresses
landward until the limit of the estuary or coastal
basin. On the ebb tide, the part of water making up
the local inter-tidal volume of each segment escapes
to the adjacent seaward segment. The flushing is thus
accomplished by a series of tidal exchanges with the
pollutants moving progressively seaward.
Segmentation
For the purpose of model construction, a water
body is divided into segments each having a length
equal to the local tidal excursion. In a small coastal
basin, the critical time for water quality is usually
at the period when the freshwater input is at a mini-
mum, or zero. The method of segmentation employed by
Ketchum cannot be applied because it requires the
river flow as a non-zero parameter to start the segmen-
tation process from the head of the estuary. In the
present model, the segmentation process starts from
the mouth of the water body and the length of each
segment is chosen to equal the tidal excursion with
zero freshwater inflow.
Figure 1 shows the plain view of a coastal basin
with its volume V(x) and tidal prism P(x) plotted as
function of distance x from the mouth. V(x) is defined
543
-------
as the accumulated low-tide volume along the iain
stem from the mouth to the transect at x. P(x) is
the inter-tidal volume landward from the transect at
x, including those of branches. The most seaward
segment (segment no. 1) is defined between transects
1 and 2 such that its low-tide volume V^ equals to
the tidal prism landward of transect 2, i.e. P.. In
general,
n+1
n+2
(1)
•
l
n+1
where V is the low-tide volume of the nth segment
n
which is between the nth and (n+l)th transects, P ,
n+1
is the tidal prism landward from the (n+l)th transect
and p +1 is the local tidal prism, or inter-tidal
volume of the (n+l)th segment. Therefore, the low-
tide volume of a segment equals the tidal prism land-
ward from it and also it is equal to the high-tide
volume of its adjacent landward segment.
The low-tide volume of a segment decreases mono-
tonically landward as the tidal prism decreases. If
the basin has a vertical shoreline, then in principle,
V •* 0 as n-*=° and there will be an infinite number of
n
segments. Complete mixing is never achieved at the
landward end of the basin because of the diminishing
tidal excursion. If the basin has a sloping beach,
the volume of the most landward segment may be chosen
as the tidal prism of those areas which are exposed at
low tide and submerged at high tide.
Each of the branches of the basin may be segmented
in the same way as that of the main stem.
Distribution of Conservative Pollutants
If one assumes that a conservative pollutant is
discharged into the mth segment at a rate of Q per
tide, the pollutant concentration in each segment may
be calculated by considering the mass balance.
Segments Seaward of Outfall
Under equilibrium conditions, the net amount of
the pollutant 'flushed' across a transect seaward of
the outfall, i.e. n <_ m, must be equal to Q. A volume
of water P is transported seaward and landward on ebb
and flood tides respectively. Let C be the concentra-
n
tion of the nth segment at high tide, then the total
mass transported seaward during ebb tide is P C .
n n
Since the flooding water is assumed to mix completely
with the water present in the (n-1)th segment at low
tide before it is transported across the nth transect,
that water transported landward will have concentra-
tion C _,, the concentration of the (n-1)th segment
at high tide. Therefore
PC -PC . = Q, or
n n n n-1 x>
Cn ' Cn-l
(2)
Equation (2) requires that CQ be specified before the
concentration distribution may be calculated. This is
equivalent to the boundary condition requirement for
solution of an advection-diffusion equation. Assuming
that a fraction a of the water entering the basin
through transect 1 on flood tide is water that escaped
from the basin during the previous ebb tide, then
C = aC,
and equation (2) becomes
Q
Cl
for n
In general, equation (2) becomes
n o
P,
(3)
(4)
If a flushing rate Y is defined as the portion
of the pollutant removed from the nth segment per
tidal cycle, mass balance requires that
(V + >> = «
where C (V + p ) is the total mass of the pollutant
n n n
in the nth segment at high tide. Then
,, - Q
(5)
Segment Landward of Outfall
If the nth segment is located landward from the
outfall, calculation of the pollutant concentration
may be considered an intrusion problem. Under equilib-
rium conditions, there should be no net transport of
the pollutant across the nth transect, thus
PnCn - PnCn-l = °
Cn ' Cn-l
In general,
C C
n m
if n > m
(6)
Distribution of Nonconservative Pollutants
In addition to flushing by tidal action, a non-
conservative pollutant will undergo a decaying process
which will further reduce the concentration distribu-
tion in a water body. The mechanisms of tidal flush-
ing and decay may be assumed to work independently
and their combined effect may be studied through the
principle of mass-balance in a segment of the basin.
If Wn is the total mass of the pollutant in the
nth segment, then the amount of the pollutant removed
per tidal cycle by tidal flushing is y W , where y
is the flushing rate defined previously. The remaining
mass of the pollutant (1-y )W will undergo decay.
Assuming that the pollutant decays linearly with a
decay rate of k per tide, the amount of the pollutant
—k
decaying in one tidal cycle will be (1-y ) W (1-e ) •
Therefore, the total loss of the pollutant per tidal
cycle is
544
-------
-kx
Under equilibrium conditions, the same amount of
the pollutant has to be supplied by the adjacent seg-
ment closer to the pollutant source, thus,
n+1
W =
-k
(7)
If the pollutant were not decaying during the time it
is transported from the (n+1)th segment to the nth
segment, equation (7) might be reduced to
(w
"•
n+1
(8)
where (W ) is the total mass of the pollutant in the
nth segment with no decay in the segment. By combin-
ing equations (7) and (8), the following is obtained
(W )
no
(9)
Equation (9) states that the factor for pollutant
reduction due to decay within the nth segment is
-k
1- (l-Yn) e
which also has been shown independently by Ketchum,
4
et al. . Equations (4) and (6) give the concentration
distribution due to the flushing by tidal action alone.
After applying the decaying factor, the concentration
distribution of a nonconservative pollutant may be
summarized as follows:
m
ir
i=n
Y-i
and
n
TT
i=m
1- (1-Yj.)
(Cn>o
if n < m
if n>m
(10)
(11)
where (C ) is the concentration of a conservative
pollutant and is given by equation (4) or (6) .
If the decay rate is zero, equations (10) and
(11) reduce to C = (C ) . It is apparent that for
any given flushing rate, any increase in the decay
rate will decrease the concentration. However for a
pollutant with a given decay rate, a larger flushing
rate will result in higher relative concentrations
compared to those of the conservative pollutant, since
the pollutant remains within the segment of the water
body for a shorter time.
Model Application
The model has been applied to the Cockrell Creek,
Virginia , a small coastal basin located near the mouth
of the Great Wicomico River, which itself is a tribu-
tary of the Chesapeake Bay. The creek is about 3.5
miles (5.63 km) long with a width ranging from 300 ft.
(91.5m) to 1300 ft. (396m). The total drainage area is
4.6 mi (11.9 km ). Examination of the salinity dis-
tribution (figure 2) reveals that at times in the
summer the creek is well-mixed and the freshwater in-
flow is almost zero. This condition makes the tidal
prism concept most applicable.
A 0.2 MGD (0.0088 m /S) sewage treatment plant
was proposed for the treatment of the sewage from the
town of Reedville and two nearby fish processing
plants. The primary environmental concern is the
effect of the proposed waste discharge on the shellfish
due to the possible increase of coliform bacteria and
depletion of dissolved oxygen. The Food and Drug Ad-
ministration has a water quality standard of 14 MPN/
100 ml of fecal coliform for shellfish harvesting.
Figure 3 shows the segmentation of Cockrell
Creek according to the tidal prism concept. The tidal
prisms, low-tide volumes and flushing rates are listed
in Table 1. Two sets of flushing rates were calcula-
ted, with a 0 and 0.5 respectively, where a is the
fraction of the water entering the creek at flood tide
which left the creek during the previous ebb tide. It
is preferable that a be determined by a tracer experi-
ment in the prototype. However, the data in the table
show that the dependence of flushing rates on the value
of a diminishes rapidly in the landward direction. For
example, a change of a from 0.0 to 0.5 changes the
flushing rate at segment M5 by only 11%.
The model was used to calculate the fecal coli-
form and BOD (biochemical oxygen demand) concentrations
in the creek. The proposed outfall is located in
segment M5. The effluent is secondary treated sewage
with 24 mg/1 of BOD5 and 200/100 ml of fecal coliform.
Assuming a BOD decay rate of O.I/tide and coliform
die-off rate of 0.5/tide, the following concentrations
for segments adjacent to the outfall were obtained with
the flushing rates corresponding to a = 0.5:
Segment
M4
M5
M6
Bl
Cl
BOD
mg/1
0.048
0.078
0.065
0.070
0.074
Fecal Coliform
MPN/100 ml
0.09
0.25
0.14
0.17
0.21
The above table shows that the increase in the
fecal coliform count at segment M5 will be 0.25/100 ml
if a is assumed to be 0.5. For a more conservative
estimate , a is assumed to be 0.9, then the flushing
rate and fecal coliform count at segment M5 will be
0.113/tide and 0.28/100 ml respectively. The low sensi-
tivity of the coliform concentration in response to the
value of a lies in the fact that the lower flushing rate
allows a longer time for bacteria to die off in any
particular segment.
Discussion
The tidal prism method of Ketchum has been modi-
fied and applied to small coastal basins with negligible
freshwater runoff. Ketchum's method was designed for
use in the estuaries where the freshwater may be treated
as a tracer. In his method, the estuary is segmented
from its head to mouth using both the river flow and
tidal prism as parameters. The segmentation process
fails in the singular case of zero freshwater inflow.
The modified method proposed here uses the tidal prism
as the sole parameter to segment a coastal basin from
its mouth to head. The flushing rate of each segment
545
-------
Table 1. Values of Pn, V
segments in the
Segment or P_ V,,
Transect
Ml
M2
Al
A2
A3
M3
M4
M5
Bl
Bll
B12
B2
B21
B3
B31
B4
Cl
C2
C3
C4
M6
Dl
M7
M8
El
M9
M10
Mil
M12
M13
M14
(104ft.3)
3810
3355
215
170
120
2705
2317
2105
603
136
105
364
60
236
84
96
246
200
155
122
950
62
725
600
93
400
280
200
150
100
60
(104ft.3)
3355
2920
170
120
357
2317
2105
1799
500
105
255
296
156
180
192
359
200
155
122
313
787
138
600
493
196
280
200
150
100
60
60
n' Yn f°r
Cockrell
the
Creek.
(I/tide)
a=0.0 a=0.5
1.00
0.53
0.89
0.53
0.11
0.40
0.32
0.26
0.47
0.68
0.14
0.44
0.25
0.40
0.16
0.11
0.69
0.46
0.37
0.09
0.37
0.26
0.32
0.28
0.21
0.30
0.30
0.29
0.28
0.30
0.17
0.5
0.36
0.85
0.52
0.11
0.31
0.27
0.23
0.44
0.66
0.14
0.42
0.25
0.39
0.16
0.11
0.66
0.45
0.37
0.09
0.33
0.26
0.31
0.27
0.21
0.29
0.29
0.29
0.28
0.30
0.17
was derived from a more rigorous mass-balance principle
instead of intuitively defining it as the ratio of
intertidal volume to segment volume.
The proposed model is most practical for environ-
mental studies for a small project in a small coastal
basin. In the absence of freshwater runoff, the small
coastal basins tend to be well-mixed and the tidal
exchange is the sole mechanism to flush out the pollu-
tant. The method requires a minimum amount of data:
the tidal range and the volume of the basin. The only
parameter which needs to be calibrated is the returning
ratio a, the fraction of water entering the basin at
flood tide which left the basin during the previous
ebb tide. This parameter may be determined by con-
ducting tracer experiments in the prototype. However
the dependence of the flushing rates on the value of
a decreases rapidly as the segments proceed landwards.
The predicted concentration distribution of a noncon-
servative pollutant is rather insensitive to the
change in the value of a.
Acknowledgements
I wish to thank Mr. G. Parker for his help with
the numerical calculation. This model was developed
under the Cooperative State Agencies Program, the
continuing support of the Virginia State Water Control
Board is appreciated.
This is Contribution No. 746 from Virginia
Institute of Marine Science.
1.
2.
References
Tracer, Inc., 1971, Estuarine Modeling: An
Assessment. Water Pollution Control Research
Series, 16070 D2V 02/71, Environmental Protection
Agency, Washington, D. C.
Ketchum, B. H., 1951, "The Exchanges of Fresh and
Salt Waters in Tidal Estuaries." J. of Marine
Res., Vol. 10, No. 1.
3. Ketchum, B. H., 1951, "The Flushing of Tidal
Estuaries." Sewage and Industrial Wastes,
Vol. 23, No. 2.
4. Ketchum, B. H., J. C. Ayers and R. F. Vaccaro,
1952, "Processes Contributing to the Decrease of
Coliform Bacteria in a Tidal Estuary." Ecology,
Vol. 33, No. 2.
546
-------
Segmentation Criterion: Vn » Pn+1 + Pb
Vn = low-tide volume of the nth segment
fn±l = tidal prism landward from the (n+l)th transect
Pj3 = tidal prism of the branch connecting to the segment
Figure 1. Segmentation of a Coastal Basin.
ii
SALINITY SURFACE O
BOTTOM A
DISSOLVED OXYGEN SURFACED
BOTTOM X
LWS-JULY 19
6 • g
TIBITHA
GREAT
WICOMICO
RIVER
CHESAPEAKE
BAY
3| Figure 3. Segmentation of the Cockrell Creek.
DISTANCE UPSTREAM (STATUTE MILES)
(1 «itut« •1-1.609 k»)
Figure 2. Longitudinal Salinity Distribution
in the Cockrell Creek, Virginia.
547
-------
EVALUATION OF MATHEMATICAL MODELS
FOR THE SIMULATION OF TIME-VARYING RUNOFF AND WATER QUALITY
IN STORM AND COMBINED SEWERAGE SYSTEMS
Albin Brandstetter
Research Associate
Water and Land Resources Department
Battelle - Pacific Northwest Laboratories
Richland, Washington
Richard Field
Chief
Storm and Combined Sewer Section
Municipal Environmental Research Laboratory
U. S. Environmental Protection Agency
Edison, New Jersey
Harry C. Torno
Staff Engineer
Media Quality Management Division
Office of Research and Development
U. S. Environmental Protection Agency
Washington, D. C.
ABSTRACT
The use of mathematical models for the assessment,
planning, design, and control of storm and combined
sewerage systems is becoming wide-spread in order to
develop more cost-effective wastewater management
schemes than are possible with conventional steady-
state analysis techniques. The U.S. Environmental
Protection Agency has sponsored an assessment of
simulation models to provide a readily available
reference guide for selecting models best suited for
specific purposes. Most models reviewed include the
computation of the time-varying runoff from rainfall
and flow routing in sewerage networks. Some models
simulate the time-varying wastewater quality, and a
few models include mathematical optimization tech-
niques for the least-cost design of new sewer system
components or for optimal real-time operation of
combined sewer overflow structures. The assessment
summarized the principal features, assumptions and
limitations of each model and compared numerical test
results and computer running costs for seven models.
Additional model features were recommended which would
enhance or extend model simulation capabilities and
use.
INTRODUCTION
Mathematical models are being used more frequently for
the assessment of existing sewerage system performance,
the planning and design of new facilities, and the con-
trol of untreated overflows during rainstorms. For
some purposes, primarily the design of sanitary sewer-
age systems, steady-state models are adequate to
compute the least—cost combinations of sewer pipes and
slopes for specified inflows. Nonsteady-state models
are required, however, to adequately analyse complex
storm and combined sewerage systems under dynamic
runoff conditions.
A considerable number of steady-state and nonsteady-
state models have been developed in the last few years
for the analysis of sewerage systems. It is conse-
quently becoming increasingly confusing for the user
to select the model most suited for a particular
application. A review of the more comprehen-
sive nonsteady-state urban hydrologic models was there-
fore conducted to develop a brief summary of most
available models and to provide a reference of model
features and their strengths and limitations.1
MODEL COMPARISONS
The following models were reviewed (models marked
with * were also tested with computer runs):
*1. Battelle Urban Wastewater Management
Model2'3
2. British Road Research Laboratory Model4'5
*3. Chicago Flow Simulation Program6'7
4. Chicago Hydrograph Method8'9 and Runoff
and Pollution Models10
5. CH2M-H111 Wastewater Collection System
Analysis Model11
6. Colorado State University Urban Runoff
Models12'13'14
7. Corps of Engineers STORM Model15'15
*8. Dorsch Consult Hydrograph-Volume Method17 and
Quantity-Quality Simulation Program18
*9. Environmental Protection Agency Storm Water
Management Model19'20
10. Hydrocomp Simulation Program21'22
11. Illinois State Water Survey Urban Drainage
Simulator23
*12. Massachusetts Institute of Technology
Urban Watershed Model24-25
13. Minneapolis-St. Paul Urban Runoff Model26
14. Norwegian Institute for Water Research
Sewerage System Models27
15. Queen's University Urban Runoff Model28
16. Seattle Computer Augmented Treatment and
Disposal System29
*17. SOGREAH Looped Sewer Model30
18. University of Cincinnati Urban Runoff Model
19. University of Illinois Storm Sewer System
Simulation Model32'33
20. University of Massachusetts Combined Sewer
Control Simulation Model34
21. University of Nebraska Urban Hydrologic
Simulator35
22. Watermation Cleveland Sewer Model1
*23. Water Resources Engineers Storm Water
Management Model36
24. Wilsey and Ham Urban Watershed Model37
In general, the reviewed models combine the runoff
from several catchments and route the wastewaters
within the sewer networks. Most of them consider the
spatial nonuniformity of rainfall; the time-varying
runoff resulting from rainstorms of different inten-
sities and durations; spatial and temporal variations
in dry-weather flows; the attenuation of flows during
overland, gutter, and sewer conduit flow routing; and
31
548
-------
Table 1. COMPARISON OF MAJOR MODEL CATEGORIES
MODEL ORIGIN
1
2
3
4
6
7
8
9
10
11
1!
13
14
15
16
17
1!
19
20
21
22
23
24
BATTELLE
NORTHWEST
BRITISH ROAD
RESEARCH LAB
CHICAGO
SANITARY DISTRICT
CH2M-HILL
CITY
OF CHICAGO
COLORADO STATE
UNIVERSITY
COR PS OF
ENGINEERS
CONSULT
AGENCY
HYDROCOMP
ILLINOIS STATE
MIT-RESOURCE
ANALYSIS
MINNEAPOLIS-
SI. PAUL
NORWEGIAN
WATER RES.
QUEEN'S
UNIVERSITY
SEATTLE METRO
SOGREAH
UNIVERSITY
OF CINCINNATI
UNIVERSITY
Of 1L1NOIS
UNIVERSITY
OF MASSACHUSETTS
UNIVERSITY
OF NEBRASKA
WATERMATION
WATER RESOURCES
ENGINEERS
WILSEY
AND HAM
MODEL
ABBREVIATION
BNW
RRL
FSF>
SAM
CHM-RPM
STORM
HVM-OQS
SWMM
HSP
ILLUDAS
MITCAT
UROM-9
NIVA
OUURM
CATAD
CAREDAS
UCUR
ISS
HYDRA
CSM
STORMSEWER
WH-1
YEAR
1973
1969
1974
1974
1974
1974
1974
1975
1974
1974
1974
1972
1971
1974
1975
1974
1974
1974
1973
1974
1974
1975
'973
1972
CATCHMENT HYDROLOGY
MULTIPLE
CATCHMENT INFLOWS
•
S
•
•
•
•
•
•
•
•
•
DRY-WEATHER FLOW
•
7J
•
•
•
•
•
INPUT OF SEVERAL
HYETOGRAPHS
•
•
|
»
•
RUNOFF FROM
IMPERVIOUS AREAS
•
•
»
•
•
•
•
'•
RUNOFF FROM
PERVIOUS AREAS
»
•
•
•
•
WATER BALANCE
BETWEEN STORMS
•
•
SEWER HYDRAULICS
FLOW ROUTING
IN SEWERS
•
«
•
•
•
•
•
•
•
•
UPSTR AND DOWNSTK
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STORAGE
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WASTEWATER QUALITY
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SEDIMENTATION
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WASTEWATER
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QUALITY BALANCE
BETWEEN STORMS
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RECEIVING WATER
FLOW SIMULATION
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RECEIVING WATER
QUALITY SIMUIATI ON
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SIMULATION
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CAN CHOOSE TIME
INTERVAL
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DESIGN
COMPUTATIONS
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APPLIED TO
REAL PROBLEMS
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COMPUTER
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the operation of flow diversion structures and stor-
age facilities under dynamic wastewater flow condi-
tions. Only a few models exist, however, which also
compute the water quality of the urban runoff and route
the pollutants through the sewerage networks. Some
models include options for dimensioning sewer pipes
and two of them use mathematical optimization schemes
for least-cost design of new sewerage system compon-
ents. Three models have provisions for the real-time
control of overflows during rainstorms.
Table 1 lists the principal features of the models.
Detailed model descriptions and comparison tables,
results of numerical testing for 7 models, and
recommendations for future model improvements are
contained in the project report submitted to the U.S.
Environmental Protection Agency.1
A brief review of these models indicates a tremendous
diversity in scope and purpose, mathematical detail,
system elements and hydrologic phenomena being
modeled, size of the system that can be handled, data
input requirements, and computer output. This
diversity, of course, is a result of the varying
conditions and objectives which govern the design and
evaluation of individual sewerage systems, limitations
in the available computer hardware, and progress in
the state-of-the-art of modeling specific phenomena.
For some applications, models are available with con-
siderable simplifications in their mathematical detail
to reduce input data requirements, computer storage
requirements, and computer running time. Some models
include unnecessary approximations considering the
present state-of-the-art of hydrologic modeling and
computer capability. Some of the simplifications,
however, are needed for applications to real-time
control of overflows which require repeated simulations
within fixed time constraints on a small process
computer.
Usually the simplest model which simulates the desired
phenomena with adequately accurate mathematical formu-
lations should be selected. Input data requirements
and computer running times generally decrease with
decreasing complexity of the model. Some models in-
clude options to suppress portions of the simulation
if only selected phenomena are of interest. Although
this feature is not listed, it should be considered in
the model selection. Some proprietary models have
features which appear superior to the publicly avail-
able models, but a user may prefer to run his own
model that does not exactly meet his requirements.
The simulation of water quality adds considerable
complexity to a model, even if it routes only conser-
vative substances. The complexity increases substan-
tially if both storm and dry-weather water quality is
computed from land use characteristics. Additional
549
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complexities are added if wastewater treatment and
receiving water flow and quality are being modeled.
The testing and review of the models indicated also
that the routing of flow and conservative pollutants,
although complex for looping and converging and
diverging branch systems with special structures, are
the best understood phenomena. The selection of par-
ticular mathematical formulations and numerical solu-
tion techniques is governed only by the preference
and needs of the model developer and user. Research
is required, however, to provide a better understand-
ing of sedimentation and scour, and of reactions and
interactions between various pollutants in the sewers.
Considerable uncertainties exist in the modeling of
catchment phenomena, both the flow and water quality
of storm and dry-weather runoff. The definition of
adequate formulations for soil infiltration, the fill-
ing of depression storage, evapotranspiration, ground-
water seepage and soil moisture are extremely diffi-
cult considering the heterogeneity of catchment land
uses, geometry, vegetation, and soils. The adequacy
of catchment water quality computations from catchment
land use and runoff has not been sufficiently demon-
strated. Although various models have shown good
agreement between measured and computed catchment
runoff water quality, the comparisons have been too
limited to assign confidence limits to predictions
for catchments without measurements. The models are
still useful, however, for the evaluation of relative
merits of alternative wastewater management schemes.
In general, a direct relationship between model
complexity and its cost of implementation and appli-
cation exists with respect to the number of major
phenomena which are modeled. Efficient solution
algorithms, however, may reduce this difference
significantly. This is true particularly for propri-
etary models due to their need to stay competitive.
A model which simulates many special sewerage system
facilities will be more complex in structure and
require more data and computer storage than a model
that computes only runoff from a single catchment
without routing flows or which routes only flow in
a simple converging network without computing run-
off from precipitation and land use.
Model testing with hypothetical data showed that
computer running time of models simulating the same
phenomena is governed more by efficient formulations
of the overall model logic than by the basic equations
used for specific phenomena. For instance, no consis-
tent pattern in computer running time was evident be-
tween the use of the kinematic and dynamic wave
equation. Consequently, since the dynamic wave
equation can be solved to simulate downstream flow
control, backwater, flow reversal, surcharging, and
pressure flow (none of which can be simulated by the
kinematic wave equation) the application of models
using the dynamic wave equation is recommended,
provided the selected model includes an efficient
numerical algorithm for its solution.
Some models require only the input of typical sub-
catchment elements and perform hydrologic computations
only for these typical subcatchments, but then con-
sider the actual locations of all subcatchments for
the overland and sewer flow routing computations.
This can save considerable input preparation and
computer running time.
RECOMMENDATIONS
Various models stand out due to their completeness of
hydrologic and hydraulic formulations, the ease of
input data preparation, the efficiency of computa-
tional algorithms, and the adequacy of the program
output. Other models, although deficient in some of
these respects, merit consideration due to special
features which are not included in the more compre-
hensive models but may be required for specific
applications.
The following models are consequently recommended for
routine applications:
1. Battelle Urban Wastewater Management Model
for real-time control and/or design optimiza-
tion considering hydraulic, water quality and
cost constraints, provided the hydrologic and
hydraulic model assumptions are adequate for
particular applications (lumping of many
small subcatchments into few large catchments,
neglect of downstream flow control, backwater,
flow reversal, surcharging, and pressure
flow).
2. Corps of Engineers STORM Model for preliminary
planning of required storage and treatment
capacity for storm runoff from single major
catchments, considering both the quantity and
quality of the surface runoff and untreated
overflows.
3. Dorsch Consult Hydrograph Volume Method for
single-event flow analysis considering most
important hydraulic phenomena (except flow
reversal). A Quantity-Quality Simulation
Program for continuous wastewater flow and
quality analysis is now available, but the
model was completed too late for evaluation.
4. Environmental Protection Agency Stormwater
Management Model for single-event waste-
water flow and quality analysis provided
the hydraulic limitations of the model
are acceptable (neglect of downstream flow
control and flow reversal, inadequate back-
water, surcharging, and pressure flow
formulation). A new version patterned after
the Corps of Engineers STORM Model is now
available for continuous simulation, but
this version was completed too late for
evaluation,
5. Hydrocomp Simulation Program for single-
event and continuous wastewater flow and
quality analysis provided the hydraulic
limitations of the model are acceptable
(approximate backwater and downstream flow
control formulation, neglect of flow reversal,
surcharging, and pressure flow).
6. Massachusetts Institute of Technology Urban
Watershed Model for single-event flow
analysis provided the hydraulic limitations
of the model (neglect of backwater, down-
stream flow control, backwater, flow rever-
sal, surcharging, and pressure flow), or the
use of a separate model for these phenomena
is acceptable.
7. Seattle Computer Augmented Treatment and
Disposal System as an example of an operat-
ing real-time control system to reduce un-
treated overflows. A more comprehensive
computer model simulating both wastewater
flow and quality and including mathematical
optimization should be considered, however,
for new systems.
550
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8. SOGREAH Looped Sewer Model for single-event
wastewater flow and quality analysis con-
sidering all important hydraulic phenomena.
9. Water Resources Engineers Stormwater Manage-
ment Model for single-event wastewater flow
and quality analysis considering all
important hydraulic phenomena.
The remaining reviewed models do not appear to provide
sufficient special features which are not included in
the models mentioned above. Their use may be advan-
tageous, nevertheless, for certain applications where
model assumptions are adequate, and especially where
assistance from the model developers is easily avail-
able.
SUMMARY
In general, the reviewed models provide useful tools
to the engineer and planner for assessing, designing,
planning and controlling storm and combined sewerage
systems. It is extremely important, however, that
the potential model user study the formulations of the
models, their limitations and approximations, if he
is to use the models in an appropriate manner. In
addition, discussions with both the original model
developers and other model users can provide signifi-
cant information with respect to new model features
and use experience not found in published reports.
ACKNOWLEDGMENTS
The work performed for this study was conducted under
contract No. 68-03-0251 of the U.S. Environmental
Protection Agency. Work was completed in August
1975.
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13. Smith, G. L., N. S. Grigg, L. S. Tucker, and
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Treatment and Overflow Model "STORM". U.S.
Army, Davis, California, Hydrologic Engineering
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16, Roesner, L. A., H. M. Nichandros, R. P.
Shubinski, A. D. Feldman, J. W. Abbott, and
A. 0. Friedland. A Model for Evaluating
Runoff-Quality in Metropolitan Master Planning.
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Resources Research Program, Technical Memorandum
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the National Conference on Urban Engineering
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Geiger, F. W. Urban Runoff Pollution Derived
from Long-Time Simulation. Paper Presented at
the National Symposium on Urban Hydrology and
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28-31, 1975.
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Water Resources Engineers, Inc. Storm Water
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08/71, 11024 DOC 09/71, and 11024 DOC 10/71
(4 Volumes), October 1971.
Huber, W. C., J. P. Heaney, M. A. Medina, W. A.
Peltz, H. Sheikh, and G. F. Smith. Storm Water
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Hydrocomp International, Inc. Hydrocomp
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Terstriep, M. L., and J. B. Stall. The Illinois
Urban Drainage Area Simulator. Illinois State
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for Urban Sewerage Systems, Caredas Program.
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Hydrauliques, Grenoble, France, Partial Draft
Report, April 1973. Translated from French
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Papadakis, C., and H. C. Preul. University of
Cincinnati Urban Runoff Model. Journal of the
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Engineers, 98(HY10):1789-1804, Proc, Paper
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1194-1196, July 1973. Closure: 100(HY4):608-
611, April 1974.
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Hydrodynamic Watershed Model III (IHW Model III).
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Department of Civil Engineering, Hydraulic
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Research Report No, 73, October 1973.
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for Combined Sewer Overflows. University of
Massachusetts, Amherst, Department of Civil
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552
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USE OF MATHEMATICAL MODELS FOR HYDROLOGIC FORECASTING
IN THE NATIONAL WEATHER SERVICE
John C. Schaake, Jr.
Assistant Director
Hydrologic Research Laboratory
National Weather Service
National Oceanic and Atmospheric Administration
Silver Spring, Maryland
ABSTRACT
The National Weather Service is implementing a new
system of mathematical models to aid river fore-
casters throughout the United States. Forecasts
of stages and discharges a few days ahead are pro-
duced routinely on a daily "basis and at six-hour
intervals during floods. Also, extended streamflow
prediction of high, low, and expected discharges for
periods up to several months into the future are made
at routine intervals.
This system of models, known as the "National Weather
Service River Forecast System" (NWSRFS), was
q
initiated in 1971 and is now being improved and
expanded. It includes conceptual hydrologic models
of snow, soil moisture, and streamflow routing; it
includes models of unsteady open channel flow; it
has provisions for reservoir operations models; and
it will include stochastic hydrometeorologic models
to account for uncertainty in streamflow forecasts.
NWSRFS also includes programs and procedures for
model calibration and verification with the histor-
ical data. Studies of the validity and accuracy of
the models are reviewed, and some modeling issues
in need of further study are summarized.
Information generated by these models could con-
tribute to EPA's overall environmental mission.
Hydrologic information is readily available in NWS
forecast data files for use with convection and
dispersion models to forecast the fate of pollutants
suddenly released to the hydrologic environment or to
forecast the day to day variations in pollutant
transport properties of selected streams. Currently
under development is a water temperature forecast
model utilizing hydrological and meteorological data
readily available in real time in NWS data files.
Problems faced by NWS managers in understanding and
utilizing NWSRFS are discussed. NWSRFS is being
installed on an IBM 360/195* in Suitland, Md., and
is being operated from remote terminals by field
offices. NWSRFS is developed and supported by the
Hydrologic Research Laboratory, Hydrologic Services
Division, and the field offices.
HISTORY OF MODEL USE IN NWS
For many years, river forecasts in the U.S. have been
made using an Antecedent Precipitation Index (API)
type of rainfall-runoff relation to convert rainfall
7
into rainfall excess or runoff. Unit hydrographs
or time delay histograms have been widely used to
translate runoff through catchments to forecast
"Trade names are mentioned solely for purposes of
identification. No endorsement by the NWS, NOAA,
or Department of Commerce, either implicitly or
explicitly, is implied.
points. These techniques historically have worked
well and are still in use.
In 1966 a project was initiated in NWS to evaluate
newly developed hydrologic models. Models were com-
pared for a. group of seven carefully selected basins
throughout the country. No single numerical scoring
factor seemed adequately to represent model accuracy
because important differences between models seemed
to be evident only in one or two aspects of the
simulation or only in certain hydrologic situations.
Several statistical measures based on observed and
simulated discharge were used to evaluate model
performance. Two models showed an accuracy advantage
over API. One was essentially the same as the
Stanford Watershed Model IV, the other was the
initial version of the Sacramento River Forecast
2
Center Hydrologic Model.
The most notable accuracy advantage of these con-
ceptual models over the API model is during and after
a long dry spell. The more complete moisture
accounting techniques give the conceptual models
enough "memory" to handle situations where large
amounts of rain give little or no streamflow response.
In 1971 a modified version of the Stanford IV model
was incorporated with other data processing programs
into the NWSRFS. A snow accumulation and ablation
model was added to NWSRFS in 1973. This snow model
accounts in detail for the energy balance of the
snow cover by using air temperature to estimate
energy exchanges.
The Hydrologic Research Laboratory in 197^ compared
an improved Sacramento Model with the NWSRFS Stanford
Watershed Model IV. Data from four catchments were
used to test model performance. This was part of a
WMO project on intercomparison of conceptual models.
In general we concluded: (l) there is no significant
difference in model performance in very humid areas;
(2) there seems to be little difference in ability to
simulate large flood events; (3) the Sacramento Model
does simulate monthly volumes and small runoff events
significantly better in semi-arid and moderately humid
areas; and (U) improvements through research seemed
easier to make to the Sacramento Model because of its
modular structure. Following these model tests ,
components of the soil moisture accounting of the
Sacramento Model replaced the original Stanford IV
components in NWSRFS.
Summary of HWSRFS
NWSRFS includes techniques and programs for developing
operational river forecasts from initial processing of
historical data during procedure development to the
preparation of forecasts in real time. The programs
are generalized for use on any river _system including
headwater catchments and downstream river networks.
553
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Programs and example data sets for the initial
version are available to the public through the
National Technical Information Service (NTIS).
Information to purchase these from HTIS can be ob-
tained from the Hydrologic Research Laboratory (W23),
National Weather Service, Silver Spring, Maryland
20910.
The following techniques and models are included in
NWSRFS :
. Mathematical model of the accumulation and
ablation of Snow [Anderson, 1973]
. A catchment model including "both (a) a soil
moisture model to account for flow through and
above the soil mantle and for evapotranspiration
and (b) time delay models to move runoff from the
soil moisture model through the catchment to the
catchment outlet
. Channel routing models to account for movement of
water in a, channel system
. Techniques for modeling the areal distribution
precipitation
. Techniques for estimating mean areal temperature
. Methods to estimate model parameters using
historical hydrometeorological data
CRITERIA FOR MODEL SELECTION
Some of the criteria we used for model selection are:
. Input Data Sampling Interval Operational rain-
fall data are available from a 6-hour reporting
network and a 2lt-hour reporting network. With
this 6-hour reporting interval there is a lower
limit to the size of catchment that can
adequately be modeled.
. Computational Efficiency - Models are operated
for most of the country. Each day, computations
are made for the next few days using 6 hour time
steps . During flood periods , computations are
repeated every 6 hours .
• Data Availability Historical hydrometeorological
data are available in digital form for model
calibration (i.e., model parameter estimation).
Four types of data are available: (a) hourly
precipitation data from the National Climate
Center (NCC), Asheville, North Carolina (card deck
U88); (b) daily observation data (NCC card deck
1+86); (c) synoptic meteorological data for esti-
mating potential evaporation (NCC card decks ikk ,
3^5, and U80) ; (d) USGS daily streamflow data.
All of these data for the period of digital record
are available to NWSRFS users from a. tape library
of about 500 tapes at the NOAA computer center in
Suitland, Maryland. Each of the tapes except
streamflow is in a special format (0/H format)
developed for the NWS Office of Hydrology (copies
of tapes in this format are available to the
public from NCC). Another main source of data are
USGS topographic maps . (We generally use
1:250,000 scale maps. )
^ Validity - Within constraints imposed by
^
computational efficiency and data availability,
models should have physical basis for their
structure and should simulate observed behavior
reasonably well. Although models are usually
compared by looking at differences between models,
it is of interest to notice many models have some
elements of common structure. This occurs because
(a) water is held in storage as it flows through
the hydrologic cycle and (b) rates of flow depend
upon amounts of water in storage and possible
other factors such as temperature, humidity, etc.
Flow into and out of storage is governed by
(a) a continuity relation and (b) a dynamic
relation. Models differ in terms of spatial and
temporal resolution of these relations and in
terms of the factors accounted for in the dynamic
relations.
. Building Block Structure - Models of individual
processes(precipitation, evaporation, snow cover,
soil moisture, channel routing, etc.) have been
organized as building blocks. This offers flex-
ibility to represent particular situations with
varying degrees of physical detail, and it makes
it possible for research on one phase of the
hydrologic cycle to be evaluated in an environment
that considers other phases.
Benefits Gained from these Criteria
Some of the benefits that accrue from these criteria,
particularly the requirement for a strong physical
base, are:
. Enhanced likelihood of adequately predicting
future events especially during unexperienced
hydrologic situations
. Potential to derive initial parameter values from
streamflow records and from observable basin
characteristics
. Parameters related to basin characteristics may
possibly be adjusted without waiting for a new
data base if basin characteristics change.
. Conceptual hydrologic models offer potential for
application other than for forecasting river stage
and discharge such as movement of pollutants
through the environment, water temperature pre-
diction, and prediction of soil moisture levels
for agricultural purposes.
MODEL APPLICATIONS
Operational River Forecast Preparation
Daily river forecasts are prepared in 12 River Forecast
Centers (HFC's) throughout the U.S. These RFC's
transmit forecast information to Weather Service
.forecast offices (WSFO's) for dissemination to the
public. The WSFO's gather precipitation and other
data and transmit these to the RFC's.
There currently are about 6700 precipitation gages in
our operational network. River stage data are
gathered at least daily at 3100 locations. These data
are used to prepare forecasts of river stage (and
possibly discharge) at 2500 locations. Conceptual
hydrologic models are now used at less than 10 percent
of these forecast points.
Although the actual forecasts are made by profes-
sionals, not by computers, the computer is an essential
tool in generating forecast information. A new
operational forecast computer program currently is
being developed under contract. This will be a disk-
oriented system incorporating all of the NWSRFS
hydrologic models and will be used from remote
terminals by our RFC's. It will reside at the NOAA
computer center in Suitland, Md. NOAA has 3 IBM
360/195 computers and these are used by NWS's National
Meteorological Center (NMC) to operate its atmospheric
554
-------
simulation and forecast models and by the National
Environmental Satellite Service (NESS) to operate two
Geostationary Orbit Environmental Satellites (GOES).
Additional current hydrologic and meteorological data
from NWS and NESS operations are available or
potentially available in various data files to our
RFC's through this new operational forecast program.
The general configuration of our new operational
program appears in Figure 1. Forecasters enter data
as they become available from cards into time series
files through a time series input routine. When a
forecast is to be made, a preprocessing routine checks
available data, estimates missing values, converts
stages to discharges and computes mean areal precip-
itation, temperature, and potential evaporation.
Then, the forecast routine reads the new mean areal
time series data, the carry-over files from the
previous forecast, and the model parameter data file.
The forecast routine produces river forecasts and
updates the carry-over files.
Figure 1. General Configuration of the NWS
Operational Forecast Program
When new forecast points are added, model parameter
values must be entered in the parameter data files
and initial state variables must be entered in the
carry-over files. The main problem, however, is to
estimate the model parameters by analysis of
historical data.
Parameter Estimation
To reduce the manpower costs of extending HWSRFS to
the entire U.S. it would be nice to completely
automate the parameter estimation process. However,
it seems essential in mathematical optimization of
parameters to start with good initial values and to
constrain the domain of variation to avoid unrealistic
estimates. This means some method other than
automatic optimization is needed to analyze available
information to find good initial values.
Our present approach is first to analyze historical
precipitation and streamflow data to make initial
estimates. These are then used to simulate the
system and results are analyzed to find possible
Q
adjustments. Finally, a pattern search automatic
optimization is used to "tune" the parameter
estimates.
The most difficult part of our estimation procedure
is to know how to make manual adjustments. Not
only must one understand physically the dynamics of
the natural process, but one must also understand
mathematically the dynamics of the model of the
process. There seems to be extremely strong ten-
dencies for most professionals to rely only on their
understanding of the physical process. We tend to
assume how parameters should change rather than deduce
this from our knowledge of the mathematics.
Historical Data Processing
Before parameter estimates can be made, historical
data must be organized. We begin with a library of
about 500 data tapes containing h different types of
hydrometeorological data. We hope to add SCS snow
course data in the near future to aid parameter
estimation for our snow model. We also hope to add
some USGS bi-hourly stage or discharge data. Data
tapes are immediately available to our RFC's and we
have programs to inventory individual tapes. We also
have programs to strip selected time series and enter
these into permanently mounted disk data files for
future analysis. These disk files are part of our
NWSRFS data file system. All of our data analysis and
parameter estimation programs read and write time
series using these files.
The initial version of NWSRFS was tape-oriented. All
time series data, both measured and computed, were
processed with magnetic tapes. This was extremely
cumbersome because many intermediate tapes were
required in preparation for model calibration. The
direct access disk files in our current version
greatly simplified our data handling problems.
Figure 2 illustrates the data processing options
available to our RFC's to estimate parameters in our
models. The inventory programs and preliminary
processing programs strip data from tape to disk.
The program MAP is used to convert raw precipitation
data at hourly and daily stations, into 6-hour mean
areal values. Consistency checks are made via double
mass plots of one station vs. any combination of other
stations. Adjustments can be made in inconsistent
data and missing data are estimated. Programs MAT
and MAPE perform similar functions to produce mean
areal temperature and potential evaporation data. Our
manual calibration program, MCP, is used to simulate
historical events using given parameter estimates.
Our automatic optimization program uses direct search
to find better parameter estimates.
Forecast Updating
Updating is needed in river forecasting because
computed river stages up to the present time do not
agree exactly with observed stages. Differences are
due to errors in estimation of mean areal precipitation
(our average precipitation gage density is only one
gage per 1*50 square miles) and to modeling errors.
In general improved forecasts can be made if
555
-------
Figure 2.
Data Processing for Parameter
Estimation in HWSHFS
differences between observed and computed stages are
used to adjust forecast stages.
This can "be done in several ways. One is to "blend"
computed and observed stages directly by adding a
proportion of the latest difference to the forecast.
This proportion would decrease to zero into the future
and the computed forecast would eventually prevail.
A physically more attractive approach would be to
adjust precipitation input data or unit hydrograph
ordinates until observed and computed values agree
within acceptable limits. Such adjustment procedures
are now being studied by our Hydrologic Research
Laboratory.
Mathematically, this updating problem arises whenever
observations can be made of computed state variables.
For example, we can observe snow water equivalent,
extent of snow cover, soil moisture content, and
ground water levels. Each is related in some way to
model state variables. Unfortunately there is no
general and practical way to use these additional
data as input to conventional deterministic models.
Perhaps a theoretical or conceptual framework can be
derived from the Kalman filter in estimation theory.
But this remains a difficult area of hydrologic
research not only in river forecasting but wherever
measurements of some output state variables are to be
used to improve the estimates of other state
variables.
POTENTIAL INTEREST TO EPA
Water is an important vehicle for transporting
pollutants from point and non-point sources in the
environment. Information on the current and forecast
states of motion of water throughout the United States
are continuously available in NWS data files.
Streamflow Routing
Potentially the streamflow routing models in NWSRFS
could be of particular interest to EPA. We use
several types of routing models ranging from unit
hydrographs and time delay histograms to dynamic
routing models based on the St. Venant partial dif-
ferential equations for unsteady flow in open
channels.
Unit hydrographs and time delay histograms are used
currently to route runoff in headwater basins and
local inflows to a downstream forecast point. Most
widely used to route flow in streams and rivers is a
"variable lag and K" method of accounting for the
attenuation and delay of flood waves moving down-
stream. We currently are investigating possible use
of Kinematic Wave and Diffustion Wave models in
addition to these other models.
We have spent the last few years developing a dynamic
routing model that would be computationally efficient
and sufficiently accurate for operational
h 5
forecasting. We have a project underway to apply
this model to the Mississippi and Ohio Rivers,
including their junction.
Pollutant Transport Models
The potential exists for NWS or EPA to operate con-
vection, dispersion, or other water quality models in
conjunction with NWS models for such purposes as to
forecast the fate of pollutants suddenly released
into the environment, to aid in estimating the
quantities of pollutants present (as opposed to
concentrations), to forecast the day to day pollutant
transport properties of selected streams, or to
forecast quality changes in reservoirs.
ACKNOWLEDGMENTS
Many thoughtful suggestions on the organization and
detailed presentation of these ideas from Dr.
Eugene L. Peck, Hydrologic Research Laboratory
Director, are greatfully appreciated.
REFERENCES
1. Anderson, E.A., "National Weather Service River
Forecast System Snow Accumulation and Ablation
Model," NOAA TM NWS HYDRO-17, 1973
2. Burnash, R.J.C., R.L. Ferral and R.A. McGuire,
"A Generalized Streamflow Simulation System:
Conceptual Modeling for Digital Computers," U.S.
Dept. of Commerce, national Weather Service and
State of California Department of Water Resources,
Sacramento, California, 1973
3. Crawford, N.H. and R.K. Linsley, "Digital
Simulation in Hydrology: Stanford Watershed
Model IV," Dept. of Civil Engrg Tech Rept 39,
Stanford Univ., 1966
k. Fread, D.L., "Technique for Implicit Dynamic
Routing in Rivers with Tributaries," Water
Resources Research, 9CO, 1973, pp 918-926
5. Fread, D.L., "Numerical Properties of Implicit
Four-point Finite Difference Equations of Unsteady
Flow," NOAA TM NWS HYDRO-18,
6. Linsley, R.K., M.A. Kohler and J.L.H. Paulhus,
Applied Hydrology, McGraw-Hill,
556
-------
7. Linsley, R.K., M.A. Kohler and J.L.H. Paulhus,
Hydrology for Engineers, McGraw-Hill, 1975
8. Monro, J.C., "Direct Search Optimization in
Mathematical Modeling and a. Watershed Model
Application," HOAA TM NWS HYDRO-12. 1971
9. Monro, J.C. and E.A. Anderson, "National Weather
Service River Forecasting System," Journal of the
Hydraulics Division, ASCE, Vol. 100, Ho. HY5,
May 1971*
10. Peck, E.L., "Catchment Modeling and Initial
Parameter Estimation for the National Weather
Service River Forecast System," NOAA Technical
Memorandum in Press, 1976
11. Staff, Hydrologic Research Laboratory "National
Weather Service River Forecast Procedures,"
HOAA TM NWS HYDRO-lU, 1972
557
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TESTING OF THE STORM WATER MANAGEMENT MODEL OF US EPA
Jiri Marsalek
Research Scientist
Hydraulics Research Division
Canada Centre for Inland Waters
Burlington, Ontario, Canada
SUMMARY
The results of testing the Storm Water Management
Model (SWMM) on a number of urban test catchments are
presented. The runoff quantity subroutine was tested
and good results were obtained on eight catchments.
The SWMM runoff quality subroutine was tested on
three catchments only. The lack of data allowed only
a qualitative discussion of the quality results ob-
tained.
INTRODUCTION
Rapid advances in urban hydrology led to the develop-
ment of a large number of urban runoff models in rec-
ent years, but only in the last three years have sever-
al comparative studies of various urban runoff models
been undertaken to assist model users in model selec-
tion. Among these studies, the most notable were
those sponsored by the Environmental Protection
Agency1 and the Canadian Department of Environment
As a result of these studies, the Canadian Urban
Drainage Subcommittee decided to adopt the SWMM model
of US.EPA for further study, modification and applica-
tion in urban runoff studies in Ontario. Some of the
questions raised during this process were those of
reliability of the SWMM model, the conditions under
which the model could fail, and the accuracy of the
SWMM simulations. All these questions are of utmost
importance in planning and design of urban drainage
systems.
When the SWMM model was developed, very little urban
runoff data was available for model testing and veri-
fication. Consequently, only a limited testing of the
model was carried out on four catchments and the
limited data available allowed only a qualitative
evaluation of the SWMM simulations1 3. Since then,
several more extensive studies have been carried out
on urban test catchments and the results were re-
ported by Keeps and Mein"1, Jewell et al!, Marsalek
et alf, Preul and Papadakis9, and Shubinski and
Roesner . In all these cases, the number of test
catchments was limited.
In this paper, the results of the SWMM model testing
on a number of new test catchments are reported and
a correlation between the accuracy of field observa-
tions and the accuracy of model simulations is demon-
strated for runoff quantity.
METHODOLOGY FOR TESTING RUNOFF MODELS
When testing conceptual runoff models, the model
tested is used to simulate the observed phenomena
and the goodness of fit of the simulations to the
observations is then evaluated. A set of criteria
for evaluating the goodness of fit has to be devised
and applied.
Modelling Errors
There is a number of sources of error causing the
differences between the observations and simulations.
These error sources include the following:
1. Bias in the simulated output (i.e. flows and
their quality) because of incomplete or biased model
structure.
2. Bias in the simulated output because of random
or systematic errors in the input data (e.g. precipita-
tion, catchment characteristics).
3. Random and systematic errors in the observed
output (flows and their quality) used for comparisons
with the simulated output.
4. Bias in the simulated output because of an
incorrect application of the model (e.g. poor catch-
ment discretization, selection of time steps, etc.).
5. Errors in the simulated output caused by an
erroneous model calibration.
When testing conceptual models and their accuracy, it
becomes extremely difficult to separate the effects
of individual sources of error and to determine their
contribution to the overall error. The last two
errors, i.e. those caused by incorrect model applica-
tion and calibration, can be significantly reduced and
are eliminated here from further consideration. The
errors due to uncertain input and output data (observa-
tions) are grouped here together and their effect on
the accuracy of model simulations will be studied by
statistical methods.
Selection of goodness of fit criteria
Runoff quantity. Numerous criteria of goodness
of fit have been proposed for runoff models. For a
review of some of these criteria, a reference is made
to Fleming's work2. Fleming concluded, that no re-
search has been undertaken to compare the various
criteria available, and therefore, one can not define
the best criteria for hydrologic modelling. He also
suggested that the criteria should evaluate the
following three parameters of a runoff hydrograph:
the total runoff volume, the peak flow and the time to
peak. Consequently, the following three rather simple
criteria were selected for use in this study:
a)Runoff volumes - the ratio of volume observed and
volume simulated
b)Runoff peaks - the ratio of peak observed and peak
simulated
c)The time to peak - the ratio of the time-to-peak
observed and time-to-peak simulated.
Runoff quality. The assessment of runoff quality
simulations is even less developed than that of
quantity simulations. From the runoff management
point of view, the criteria can be defined for each
constituent similarly as it was done for the quantity,
i.e. describing the constituent pollutograph by the
following three parameters:
558
-------
a)The total constituent emission
b)The peak constituent concentration
c)The time to peak concentration.
These goodness of fit criteria for runoff quantity
and quality were then used on the test catchments
studied.
URBAN TEST CATCHMENTS
Description of Data Collection Projects
The Urban Drainage Subcommittee has obtained urban
runoff data from a. number of test catchments. These
catchments and their basic characteristics are
listed in Table 1.
Catchment
lame
iannatyne
Brucewood
Calvin Park
East York
lalifax
iiamilton
Malvern
Toronto-West
Toronto-East
Location
Winnipeg, Man.
Toronto, Ont.
Kings ton, Ont.
Toronto, Ont.
Nova Scotia
Ontario
Burlington, Ont .
Ontario
Ontario
Sewer
System
Combined
Separate
Separate
Separate
Combined
Combined
Separate
Combined
Combined
Catchment
name
Bannatyne
Brucewood
Calvin Park
East York
Halifax
Hamilton
tolvern
Toronto-West
Toronto-East
Phenomena monitored
Precip. Runoff Quality
a
X
X
X
X
X
b
X
X
a
X
b
X
a
X
X
X
X
X
b
X
X
a
X
b
X
a
X
X
X
b
X
X
b
X
Area
Size
(acres)
542
48
89
40
168
176
58
2330
338
Refer-
ence
14
14
10
16
15
3
7
14
8
limited number of events
projects started recently, no data available as yet
The test catchments cover a wide range of catchment
sizes (40 acres to 2300 acres) as well as of resid-
ential developments. Brucewood, Calvin Park and
Malvern represent modern residential areas served
by separate sewers. Bannatyne, Halifax, Toronto-
West and Toronto-East are older residential areas
served by combined sewers. East York is an older
area on which the sewers were separated only re-
cently. The storm sewers receive runoff mostly
from roads and side-walks. The roof drains are
connected to the old combined sewer.
On all the areas, precipitation and runoff were
monitored. Quality data were collected with a
various degree of success on all the areas except
for Calvin Park and Toronto-West.
All of the projects are not at the same stage. The
Brucewood and Bannatyne projects have been dis-
continued. The remaining data collection projects
are continuing to a various extent although the
data collected in East York have not yet been fully
analyzedsand the Hamilton and Toronto-East projects
which started only recently have as yet no signifi-
cant data.
Some results from a. previous study10 with the SWMM
model on two additional urban catchments (Oakdale,
Chicago and Gray Haven, Baltimore) were also in-
cluded. Thus for runoff quantity simulations, the
data for the following eight areas were available
for the testing of the SWMM model: Bannatyne,
Brucewood, Calvin Park, Halifax, Malvern, Oakdale,
Gray Haven and Toronto-West.
The runoff quality data are much less plentiful.
In fact, only limited data and quality simulations
were available for the Bannatyne, Brucewood and
Malvern catchments.
Uncertainty in the collected data
A quantitative evaluation of uncertainties in the
collected data was not possible due to the lack of
information. Therefore, only a qualitative evalua-
tion was made here, the uncertainty in the data was
ranked and this ranking was then used in a later
part of this study. The ranking of the data from
the eight areas under consideration is shown in
Table 2, where a low rank number indicates the
better data set.
Table 1.Urban Test Catchments.
AREA
Bannatyne
Brucewood
Calvin Park
Halifax
Gray Haven
Oakdale
Malvern
Toronto-West
Rank
7
5
1-3 (assigned aver.rank=2)
6
1-3(2)
4
1-3(2)
8
Table 2.Ranking of data uncertainties for the studied
urban areas.
559
-------
The Calvin Park, Gray Haven and Malvern data were
given the highest rank. In all these cases, the
catchments were well defined and surveyed, the
precipitation was measured on the catchment, and
checked against another gauge, flows were measured
by calibrated constriction flow meters, a good
synchronization of precipitation and runoff records
was evident. The measured data were checked for
correctness.
The Oakdale and Brucewood data were rated slightly
lower. It would appear that the flow meters were
not calibrated and there is no evidence that the
collected data were checked. It was expected
that the data from the smaller Oakdale catchment
were better defined (more accurate) than those from
the Brucewood catchment.
The next data ranked are the Halifax data collected
on an older area with some uncertainties in the
catchment imperviousness. Otherwise, the instru-
mentation system is fairly good; a raingauge is
located within the catchment and flows are measured
by a critical flow meter.
The lowest rated data were those collected on the
Bannatyne and Toronto-West catchments. There were
no rain data collected directly on the Bannatyne
catchment. Consequently, the data from some
nearby rain gauges had to be used. In the case of
Toronto-West, the flow rates were only inferred
from the depth of flow measurements and the Manning
equation. Only one raingauge was used to measure
the precipitation.
DISCUSSION OF RESULTS
Runoff quantity
The results of runoff quantity simulations with the
SWMM model are given in Table 3. For runoff
volumes, peak flows, and times to peak, the ratios of
observed to simulated, values were computed. The
results were described by the mean value of these
ratios, standard deviation about mean and the
percentage of simulations for which the simulated
values were within ±20% of the observed ones
(see Table 3).
Bannatyne
Brucewood
Calvin Park
Gray Haven
Halifax
Oakdale
Malvern
Toronto-West
Runoff volumes
Ratio Vol. , /Vol. .
obs. sim.
aver-
age
1.40
0.91
1.03
—
1.01
—
1.01
0.87
standard
deviation
0.34
0.19
0.17
—
0.14
—
0.12
0.26
% of simulations
within ± 20% of
observations
24%
66%
75%
~
85%
—
89%
50%
Bannatyne
Brucewood
Calvin Park
Gray Haven
Halifax
Oakdale
Malvern
Toronto-West
Runoff peak flows
**ti0 Qpobs./Qpsim.
aver-
age
1.12
1.22
1.09
0.98
0.78
1.04
1.05
1.12
standard
deviation
0.09
0.26
0.16
0.24
0.22
0.19
0.16
0.14
% of simulations
within ± 20% of
ob servat ions
81%
42%
72%
61%
44%
70%
77%
70%
Bannatyne
Brucewood
Calvin Park
Gray Haven
Halifax
Oakdale
Malvern
Toronto-West
Times to peak
**tio TP0bs./Tpsim
aver-
age
0.98
0.91
0.93
1.02
1.11
0.92
0.96
1.13
standard
deviation
0.12
0.10
.09
0.05
0.21
0.13
0.07
0.22
% of simulations
within ± 20% of
observations
90%
87%
92%
100%
60%
81%
99%
55%
Table 3.SWMM runoff quantity simulations-goodness of
fit.
For runoff volumes, the best goodness of fit was ob-
tained for the Malvern catchment - nearly 90% of all
the simulated volumes were within the ±.20% limits.
For peak flows, the best fit was found for the
Bannatyne catchment, 81% of all simulations were with-
in the above accuracy limits. Finally, for the
times to peak, the best fit was found for the Gray
Haven catchment, practically all the simulations were
within the above accuracy limits. The overall good-
ness of fit was also evaluated. The Malvern catch-
ment ranked the highest, the Toronto-West data
ranked the lowest.
A large variation in the goodness of fit of the SWMM
simulations on the test catchments led to a question
of whether there is a correlation between the un-
certainty in the input data and the goodness of fit.
Since the data on hand did not allow the use of
parametric statistics, this question was studied
using non-parametric statistical methods. The null
hypothesis was defined as follows: There is no
correlation between the uncertainty in the input data
and the goodness of fit of simulated to observed
data. This would imply that the errors in the simula-
tions are caused by a biased model structure.
The above nul'l hypothesis was tested using the Spear-
man rank correlation coefficient. The calculation
is given in Table 4.
I 560
-------
Test catchment
Bannatyne
Brucewood
Calvin Park
Gray Haven
Halifax
Oakdale
Malvern
Toronto-West
Input data
uncertain-
ty rank
7
5
2
2
6
4
2
8
Goodness of
fit rank
(after
Table 3)
5
6
3
2
7
4
1
8
Differ-
ence
2
1
1
0
1
0
1
0
Ex2 +Zv2 -Ed2
xz£z1
73.0
80.9
0.90
Table 4.Ranking of input data uncertainty and the
goodness of fit.
For eight observations, the value of Spearman rank
correlation coefficient of 0.90 is significant at the
0.01 level of confidence12 and the null hypothesis
has to be rejected. Thus there is a correlation
between the uncertainty in the input data and the
goodness of fit of the SWMM runoff quantity simula-
tions. This indicates, that lower simulation
accuracies obtained with the SWMM model on some
areas, e.g. Toronto-West, are not necessarily caused
by the modelling bias, but rather by inaccurate
input data. A rigorous evaluation of the input data
errors could not be done for any of the studied
areas, since this would require much more extensive
data records than those available (e.g. several
precipitation records, etc.). Only on a thoroughly
instrumented area one could directly separate the
modelling bias errors from those caused by the input
data errors.
One condition, under which the SWMM model fails, is
the surcharged flow in sewers. A technique in
which the sewer surcharging was avoided by arbitrarily
increasing the sewer pipe capacity was used by
Waller15 in conjunction with the SWMM model on the
Halifax catchment. As one would expect, it led to
an overestimate of peak flows and a shortening of
times to peak. These results, however, were more
realistic than the truncated hydrographs produced
by the normal SWMM runoff subroutine.
Runoff quality
Only limited runoff quality data have been collected
on the studied areas so far and not all of these
data have been processed to this date. In fact,
quality data were available only for the following
three catchments: Brucewood, Bannatyne, and Malvern.
These data do not allow proper statistical analysis
as was done for the quantity data. Consequently,
only a qualitative discussion of the processed data
follows.
The runoff quality data and the SWMM simulations are
given in Table 5. The ratios of observed to
simulated values were calculated for the total
pollutant emissions and peak concentrations. For
individual catchments, these ratios were character-
ized by the mean values.
(a)
Total BOD obs.
Total BOD sim.
Total SS obs.
Total SS sim.
Total COD obs.
Total COD sim.
Total N obs.
Total N sim.
Total P obs.
Total P sim
(b)
Peak BOD obs.
Peak BOD sim.
Peak SS obs.
Peak SS sim.
Peak COD obs.
Peak COD sim.
Peak N obs.
Peak N sim.
Peak P obs.
Peak P sim.
Reference
Bannatyne
ISS=0 ISS=1
2.90 6-43
14
Brucewood
ISS=0 ISS=1
14
Malvern
ISS=0
7
Table 5.SWMM model runoff quality simulations des-
cribed by mean values of the ratios (a) Total con-
stituent emission observed to that simulated (b) The
peak constituent concentration observed to that
simulated.
The Brucewood and Malvern catchments are relatively
clean areas, served by separate sewers. The observed
Biochemical Oxygen Demands (BOD) for minor storms did
not exceed 25mg/litre, the observed Suspended Solids
(SS) concentrations did not exceed the value of
500 mg/litre. A large scatter in the observed and
simulated data comparisons was evident. No conclusions
can be drawn regarding the use of the options to cal-
culate the suspended solids. The exponential decay
option (code ISS=0) yielded simulated concentrations
that were too high; the other option (an empirical
relationship, code ISS=1) yielded simulated concentra-
tions that were too low. On average, the calculated
BOD concentrations were underestimated. The estimate
of the suspended solids concentrations depended on the
selection of the calculation option.
The concentration of Nitrogen and Phosphates were on
average underestimated in the SWMM simulations. On
the other hand, the Chemical Oxygen Demands (COD)
were consistently overestimated in the simulations.
It is expected that these runoff quality data will be
further analyzed and attempts will be made to explain
the lack of goodness of fit.
The Bannatyne catchment is served by combined sewers.
Unusually high values of BOD and SS concentrations
were observed on this area. As indicated in Table 5,
the SWMM simulations underestimated the total BOD
and SS emissions as well as the peak concentrations
of both BOD and SS.
Uncertainties in the collected runoff quality data
cannot be estimated and in fact, they could be fairly
high. Consequently, one cannot conclude, if the
errors are due to modelling bias or due to errors in
the quality data. It may take another one or two
561
-------
years before a sufficient volume of runoff quality
data is accumulated under the present program and
a full evaluation of the SWUM quality subroutine
is possible. Meantime, the runoff quality data
obtained with the SWMM should be accepted and used
only with great caution.
CONCLUSIONS
The runoff quantity subroutine of the Storm Water
Management Model was tested with a good success
on a number of new urban test catchments. The
goodness of fit of the simulated to the observed
data was found to be dependent on the uncertainty
in the input data. No presently instrumented
catchment allows separation of the errors due to
the modelling bias from those due to the uncertainty
in the input data. On the best instrumented
catchment, fairly accurate results were obtained
with the SWMM model. In fact, up to 90% of runoff
volumes, 77% of runoff peak flows and 100% of times
to peak were simulated with an accuracy better than
±20% of the observed values.
The SWMM model runoff quality simulations were found
to be less satisfactory. Though the insufficient
data prevent drawing any firm conclusions, it
appears that the quality subroutine is not readily
applicable to all urban catchments. The SWMM
quality simulations should be treated with great
caution, particularly if used for a selection of
urban runoff control alternatives, or policy en-
forcement. It may require another one or two years
of data collection before the SWMM quality subroutine
can be fully evaluated for the feasibility of
application on Canadian urban catchments.
REFERENCES
1. Brandstetter, A., "Assessment of Mathematical
Models for Storm and Combined Sewer Management",
Preliminary Report, Battelle Pacific Northwest
Laboratories, RIchland, Washington, Aug. 1975.
2. Fleming, G., "Computer Simulation Techniques in
Hydrology", American Elsevier Publishing Co.
Inc., New York, 1975.
3. Gore & Storrie, Ltd., "Interim Report on the
Hamilton Test Catchment", (Unpublished), sub-
mitted to the Canada Centre for Inland Waters,
Burlington, Ont., March 1975.
4. Heeps, D. P., and Mein, R. G., "An Independent
Evaluation of Three Urban Runoff Models",Civil
Engineering Research Report No. 4, Monash Univer-
sity, Victoria, Australia, 1973.
5. Jewell, T. K., et al., "Application and Testing
of the EPA Storm Water Management Model to
Greenfield, Massachusetts", In: Short Course on
Applications of Storm Water Management Models,
University of Massachusetts, Amherst, Mass.,
Aug. 1974.
6. Marsalek, J., Dick, T. M., Wisner, P. E., and
Clarke, W. G., "Comparative Evaluation of Three
Urban Runoff Models", Water Resources Bulletin,
Vol. 11, No. 2, pp. 306-328, April 1975.
7. Marsalek, J., "Burlington Urban Test Catchment -
Progress Report No. 1", Techn. Report, Hydraulics
Res. Div., Canada Centre for Inland Waters,
Burlington, Ont., March 1976.
8. M. M. Dillon, Ltd., Communication re the Toronto-
East Test Catchment, 1975.
9. Papadakis, C. N., and Preul, H. C., "Testing of
Methods for Determination of Urban Runoff",
Journal of the Hydraulics Div., ASCE, Vol.99,
No.HY9, pp. 1319-1335, Sept. 1973.
10. "Review of Canadian Design Practice and Compari-
son of Urban Hydrologic Models", Research
Report No. 26, Canada-Ontario Agreement Re-
search Program, October 1975. Available from
Training and Technology Transfer Division,
Environment Canada, Ottawa, Ontario, K1A OH3
11. Shubinski, R. P., and Roesner, L.A., "Linked
Process Routing Models", Symposium on Models
in Urban Hydrology, AGU, Washington, D.C.,
April 16-20, 1973.
12. Siegel, S., "Nonparametric Statistics for the
Behavioral Sciences", McGraw-Hill Book Co.,
New York, 1956.
13. "Storm Water Management Model, Volumes 1-IV",
Environmental Protection Agency, Water Quality
Office, Water Pollution Control Research
Series, Washington, D.C., July 1971.
14. "Storm Water Management Study", (Unpublished),
A Draft Report on a Study Commissioned by the
Canadian Urban Drainage Subcommittee to
Proctor & Redfern, Ltd.,and J. F. MacLaren,
Ltd., Jan. 1976.
15. Waller, D. H., Coulter, W. A., Carson, W. M.,
and Bishop, D. G., "A Comparative Evaluation
of Two Urban Runoff Models", A Report submitted
by the Nova Scotia Technical College to En-
vironment Canada, April 1974.
16. Mills, W. G., Personal Communication, 1974.
562
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APPLICATION OF STORM AND SWMM FOR ASSESSMENT
OF URBAN DRAINAGE ALTERNATIVES IN CANADA
Paul E. Wisner
Manager, Water Resources Group
James F. MacLaren Limited
Andrew F. Roake
Environmental Engineer
James F. MacLaren Limited
Adel F. Ashamalla
Senior Water Resources Engineer
James F. MacLaren Limited
Environmental Consultants, 435 McNicoll Avenue
Willowdale, Ontario, M2H 2R8
Abstract
A limited programme of research and several app-
lications of urban runoff models indicate that there
is no unique pattern for model application in drainage
and pollution control studies. Use of the simplest
model compatible with the requirements of planners and
decision makers helps to minimize unnecessary data
collection and avoid communication problems. More
sophisticated models will be required as a study pro-
gresses from screening and initial planning phases to
the final planning and design phases. STORM is con-
sidered as primarily a screening model for comparison
of alternatives, identification of critical events and
problem definition. For predominantly urban areas a
lumped SWMM and a recently developed Generalized Qual-
ity Model are considered as planning models for the
analysis of critical events. A detailed SWMM and the
WREM are considered as tools for final planning and
design work. A computerized unit hydrograph approach
is preferred for planning in areas with low percentage
imperviousness, while the comprehensive analysis of
Stanford-type models is recognized as necessary for
major projects in large watersheds.
Background
At present there is no specific urban runoff con-
trol legislation in Canada. A 1973 inquiry into urban
drainage practice in Canada revealed that at that
time all major municipalities (with the exception of
2
Toronto) employed the Rational Formula exclusively in
urban drainage planning and design. Within the last
few years the Canada/Ontario Urban Drainage Programme
has sponsored several studies related to the calibra-
tion/validation and development of urban runoff models
134
and the advantages of a modelling approach to
drainage problems have been recognized by several large
urban centres which have instigated programmes of model
implementation. The principal models currently used
in drainage studies in Canada are STORM , SWMM , WREM
and computerized unit hydrograph models.
The Water Resources Division of James F. MacLaren
Limited has been extensively involved in the model de-
velopment and verification studies for the Canada/
Ontario Urban Drainage Programme and in a considerable
number of practical model applications for cities and
municipalities in Canada. It is the intent in this
Paper to present our views, as consultants on the rela-
tive priorities for model improvement and the imple-
mentation of modelling in drainage planning and design,
and the role of some existing models in these fields.
Model Application and Improvement
Most urban runoff models encountered in the pro-
' «_ 1 4
grammes of model testing ' have required a significant
effort in "de-bugging" before being rendered fully
operational. Additional de-bugging is often required
upon the release of later versions of an existing model.
The correction of programme errors can be a lengthy and
frustrating process and is apt to deter potential users
and cause mistrust of models in planners and decision
makers. Some operational models have proved to be well
suited to certain applications but inaccurate in others.
Table 1 summarizes the modifications and routines dev-
eloped to enable existing models to be applied in Cana-
dian conditions.
Table 1
4
Some Recent Improvements to SWMM and STORM
1. Snowmelt Quantity and Quality model integrated with
the SWMM RUNOFF block for Canadian conditions
2. Recommendations for lumping SWMM in simplied simu-
lations
3. Modification of STORAGE and TREATMENT blocks reflec-
ting new data
4. Modification of the TRCOST routine for Canadian
Cost estimates
5. Development of a Data Analysis Model for processing
of Canadian Atmospheric Environment Service data
for direct input to STORM.
Models, such as STORM, are readily accepted by
non-modellers because of their simple formulation and
statistical interpretation of the model output. How-
ever, traditional hydrologists appear sceptical of
these 'oversimplified' models. Because of the large
investments involved in major watershed projects, the
use of a much more sophisticated approach such as that
Q
offered by Stanford-type models has been advocated.
The dilemma appears to be that as more models are for-
mulated, the chance of each of these being accepted by
planners or decision makers at a municipal level becomes
more remote. In the interim, outmoded empirical meth-
ods continue to be used for design purposes in some
costly storm sewer projects and modelling is not used
to its full extent in the examination of alternative
solutions to such problems as sewer separation, and
the need for upgraded treatment plants. We consid-
er that at the present status of model implementation
in Canada, further refinement of models and the cons-
truction of new models should be carefully weighed
against the hidden constraints involved, i.e. addit-
ional de-bugging, time required for familiarization
and potential reluctance to implement new and untested
models. If currently applied models can be used in a
creative and problem oriented manner and be demonstrat-
ed to be a means to novel design and economic benefits
then at present these efforts will be more effective in
promoting the widespread acceptance of modelling than
further model refinement.
No Single Model
The designation of STORM as a "planning model" or
SWMM as a "design model" may cause a user to be model
oriented rather than problem oriented. Few models, if
any, are completely universal and, therefore, some cau-
tion should be exercised when an existing model is app-
lied in a new and untested role. The deficiencies of
some well accepted models noted in Table 2 indicate
some of the situations in which these models do not
perform well. For instance, STORM does^pot simulate
peak flows accurately because of its long time step (1
563
-------
hour) and lack of flow routing routines. SWMM does
not accurately simulate hydrographs under surcharged
conditions. Conversely the highly sophisticated WREM
is unsuitable for initial planning applications be-
cause of the extensive data preparation and consider-
able computer time required. While SWMM and WREM have
been widely tested and verified on urban watersheds
9 104
' ' little evidence of their suitability in predom-
inantly rural situations has been published. Conse-
quently we have used a computerized unit hydrograph
approach in predicting rural runoff flows
Table 2
Model
STORM
SWMM
WREM
Some General Model Deficiencies
Comment
- peak flows not accurate due to 1 hour time
step and no flow routing
- simplistic storage and treatment routines
- antecedent conditions have usually to be
assumed
- poor simulation of hydrographs in surchar-
ged systems
- not well validated for predominantly rural
areas
- quality model hard to calibrate, somewhat
oversophisticated for most applications
receiving water model does not account for
pollutant transport by diffusion
- very short time steps required to avoid
unstability
- extensive data requirements
Many models offer significant advantages if used
sensibly within their proven limitations. Table 3
summarizes 12 practical modelling studies in which the
authors participated. The model applications involved
in these studies may be broadly categorized as; screen-
ing (1) - (3) ,- planning (4) (8) ; final planning/des-
ign (9) (12). This work has emphasized the advan-
tages of choosing the model most appropriate to the
task in hand and of using several interfaced models
during a single study.
A Hierarchy of Models
The early planning stages of some urban drainage
projects are typified by limited amounts of relevant
data and several alternative patterns for development
or solution of existing problems. The use of a simple
model, such as STORM, at this stage represents an econ-
omic approach to screening alternative policies at a
level of sophistication compatible with available data
and acceptance by non-technical planners and decision
makers. If the limitations of STORM are recognized it
may also be used to screen long meteorological records
for the identification of conditions antecedent to
critical events. For instance, the relative import-
ance of snowmelt compared with summer storm runoff may
be assessed and important sequences of meteorological
events identified. STORM can be used to determine the
events to be simulated in more detail later in the pro-
ject. This facilitates the selection of a historical
"design" storm with known antecedent conditions, rath-
er than the somewhat hypothetical synthetic design
storm , f°r subsequent modelling with SWMM or WREM
(see Figure 1).
Three recent studies conducted by James F. MacLar-
en incorporated this screening approach.
(1) Screening a Long-Term Meteorological Record
An assessment of frequency of flooding and prob-
lems associated with soil erosion during floods is be-
ing investigated for a watershed of about 9 square
miles in Eastern Ontario. Urban encroachment onto the
lower regions of the flood plain has aggravated flood-
ing problems. The relative significance of spring
snowmelt flows compared with the standard 1:25, 1:50
and 1:100 year design flows is required for the selec-
tion of the appropriate control measures. STORM was
used to simulate all snowmelt events in a meteorologi-
cal record of precipitation and temperature of 100 yrs.
duration. Critical events can be extracted from the
summary output and detailed event hydrographs computed.
The model can then be used for initial estimates of the
effects of storage reservoirs on critical flows.
(2) Screening a Number of Development Alternatives
Twelve alternative development concepts were pro-
posed in the initial planning stage for the new North
Pickering Townsite, east of Toronto. STORM was used
to provide an initial assessment of the probable annual
changes in urban runoff volume and quality associated
with each of the alternatives in the three main water-
sheds affected (West Duffin Creek 58 square miles,
East Duffin Creek - 46 square miles, Petticoat Creek
10 square miles). The proposed land uses were supplied
as input to the model for each case and the annual poll-
utant load (B.O.D., S.S., Settleable Solids, N, P04>
and the total annual runoff was computed. Similar com-
putations were performed for the existing land use patt-
ern, which provided a base case. A simple ranking mod-
el was developed to facilitate comparison and ranking
of the development alternatives on the basis of their
overall water quality impact. It was demonstrated, us-
ing STORM, that for any alternative, a storage-treatment
relationship (i.e. a set of storage-treatment combina-
tions) exists for which the overall water quality imp-
act of that alternative can usually be reduced to a pre-
determined level (existing condition or a pre-defined
'allowable loading1). The effect of low frequency
floods was investigated in the same study. The unit
hydrograph method is generally applied for flood syn-
thesis in Ontario. A computerized version of this
method (FROUT) was developed to predict the effects of
low frequency floods and associated erosion before and
after urbanization. The results of this study formed
part of an overall planning matrix involving considera-
tions other than water quality impacts of urbanization,
with a view to selecting the preferred alternative.
(3) Identification of Critical Areas
Sewer system inadequacies and changing land use patt-
erns often result in a considerably higher number of
combined sewer overflows from some areas in a city than
from other areas in the same city. The most cost-effec-
tive approach to limiting the pollution of receiving
waters due to combined sewer overflows is to limit over-
flows from the critical areas. The first stage in such
an effort is obviously to define the critical areas.
STORM was used for this purpose for the City of Winni-
peg. Five years meteorological records were processed
for the simulation of the quality of runoff and snow-
melt in 35 combined sewer areas. Calibrations to City
records enabled period total emissions of B.O.D. and SS
to be reproduced to within t 10 percent of the measured
totals. A number of critical areas were identified on
564
-------
the basis of average annual pollutant discharge and
mass discharge per overflow event and critical events
were subsequently simulated in more detail with SWMM
in order to evaluate various control alternatives.
It has been shown that fairly sophisticated single
event models, such as SWMM, can be applied in a lumped
5 14
' manner (i.e. the input characteristics describing
the subcatchments and transport system can be aggrega-
ted) for simplified simulation. This implies that in
situations where only basin outlet hydrographs from
design events are required, such as in the initial pla-
nning stages, data preparation time may be minimized.
At this stage, it is considered that the sophisticated
pollutant routing routines of SWMM are not justified.
Consequently, the use of a Generalized Quality model
(Appendix 1) in conjunction with lumped SWMM, or unit-
graph models is advocated.
In the final planning stages of the project, more
detailed information and monitoring results become
available and the number of alternatives is reduced.
At this stage a detailed simulation involving fine dis-
cretization and calibration for accurate water quality
prediction is warranted. At this juncture, the effects
of untreated and treated discharges to the receiving
water would be assessed. A more sophisticated one-
dimensional or two-dimensional receiving water model
than that in SWMM (i.e. RECEIV) might be required in
15
some cases
The WREM model is sometimes employed in final
planning for an analysis of the benefits of surcharged
design. According to our experience in studies con-
ducted in Winnipeg, Port Credit and Edmonton, the in-
tentional use of surcharge in the design of relief sew-
ers ' or in the analysis of interceptor capacity
can lead to considerable reduction in peak stormwater
flows. Consequently, it appears reasonable to employ
only a model with sophisticated routing, such as the
WREM, capable of simulating surcharged flow in the des-
ign of relief sewers or in the final planning phase of
new projects where in-line storage by surcharge is feas-
ible.
During the course of a project from screening to
design, model sophistication, data requirements and
computer costs will all increase. The results of each
model should lead logically to the next, more sophis-
ticated application and good communications with the
decision makers should ensure a shared objective. The
involvement of non-technical planners and decision
makers in regular consultations is essential in this
regard.
Our experience in studies for the City of Winni-
peg indicates that once flow simulation techniques are
understood and the potential benefits appreciated, there
is a natural tendency of planners and decision makers
to become interested in quality simulation as a part of
pollution control policy planning.
Conclusions
One of the primary goals of those involved in
urban runoff modelling in Canada should be the replace-
ment of outmoded empirical design formulae currently
widely used in Canadian urban drainage planning and
design by more accurate and reliable methodologies. At
present this goal will be best served by the implement-
ation in engineering practice of existing well valida-
ted models. The experience in a number of research
and practical urban drainage and pollution control stu-
dies confirms that modelling is a dynamic process. No
single model or unique pattern of application can be
recommended. Best results are likely to be achieved
with a series of interfaced models applied within pro-
ven limitations. This approach may logically result
in the ultimate acceptance of highly sophisticated con-
tinuous simulation models in the final planning phase
of most major watershed studies.
Table 3
Examples of Practical Model Application and Interface
STUDY
SCOPE
MODELS
SIMULATIONS
(1) Effects of Comparison of FROUT
urbanization. low frequency
Screening devel- floods s water
opment alterna- quality impacts
tives for North of 12 develop-
Pickering Commu- ment alterna-
nity (Phase 1) tives STORM
(2) Comparison Relative mag- STORM
of Flood Cont- nitude of
rol Alternatives snowmelt run-
on the partially off compared
urbanized Graham to summer =WMM
Creek watershed storm runoff .
( snow-
melt)
1:10, 1:25,
1:50 years
floods and
associated
solids ero-
sions
Modification
of total ann-
ual runoff &
runoff pollu-
tant loads S
effects of
storage S
treatment (1
year)
Screening of
100 yrs met-
eorological
data
snowmelt ,
urban areas
FROUT
non-urban
area runoff,
flow routing
(3) Evaluation
of combined
overflow poll-
ution in Winni-
peg
Problem iden- STORM
tification.
Critical areas
and major
events. Pre-
liminary anal-
ysis of control
alternatives
SWMM
RECEIV
Comparison of
annual pollu-
tant loads in
overflow over
5 years in 34
districts
Simulation of
critical ev-
ents for diff-
erent control
policies
(4) Master Effects of dev- FROUT
Drainage Plan elopment on
for Thornhill- peak flows.
Vaughan develop- Outline for SWMM
ment, Ontario main drainage (lumped)
lines and sto-
rage facilities
1:25, 1:100
year floods
Sizing of main
trunk storm
sewers and
runoff deten-
tion ponds
(5) P.A.C.E. Simulation of STORM
Study of Runoff overflows
from Oil Distri- Quantity and
bution Terminals Quality of Ter-
minal Runoff
SWMM
GQM
Simulation of
annual over-
flows-reduced
time step em-
ployed for
small areas
Runoff hydro-
graphs
peak concen-
trations and
event total
pollutant load
565
-------
Table 3 (cont'd)
Association Congress in New Orleans
STUDY
(6) Toronto In-
ternational
Airport Run-
off Study
(7) Humber
River Out-
fall,
Toronto
(8) Winnipeg
Drainage
Criteria Man-
ual
(9) Port
Credit Storm
Relief Study
(10) Relief
Sewers in
Jessie,
Winnipeg
(11) Edmonton
Interceptor
Study
(12) Winnipeg
Stormwater
Pumping Sta-
tion Study
SCOPE MODELS
Demonstration STORM
of relation- SWMM
ships between
airport oper-
ations and GQM
runoff pollu-
tion . Com-
parison of
control alt-
ernatives
Planning RECEIV
study for
the optimum
location of
nearshore
landfill de-
velopments
Development SWMM
of drainage
policies and
procedures
involving
small ponds
and roof
storage
Analysis of SWMM
existing storm
sewer system.
Requirements WREM
for upgrading
system per-
formance
Analysis of SWMM
existing com-
bined system
in Jessie WREM
district.
Design of
relief lines
Analysis of SWMM
existing sys-
tem S relief
requirements.
Investigation WREM
of regulators
and overflows
Analysis of WREN
pumping sta-
tion perfor-
mance and
effect of in-
line storage
SIMULATIONS
Snowmelt events
Storm runoff
simulation
Event total
pollutant loads
Simulation of
critical water
quality condi-
tions for diff-
erent landfill
configurations
Examples of
sewer and stor-
age design
methodologies
(<200 acres)
Runoff and non-
surcharged flows
Analysis of sur-
charged condi-
tions, testing
of relief
alternatives
Runoff and non-
surcharged flows
Analysis of sur-
charged condi-
tions, design
with surcharge
Inlet hydrograph
from detailed
areas
Analysis of sur-
charge and over-
flows during
design and his-
torical storms
Simulation of
flows during
critical his-
torical storms,
surcharged con-
ditions.
References
1. James F. MacLaren Ltd., 1974, "Review of Canadian
Storm Sewer Design Practice and Comparison of Urban
Hydrologic Models", a report to the Canadian Depart-
ment of the Environment, Canada Centre for Inland
Waters
3. James F. MacLaren Ltd., 1974, 1975, 1976 "Report on
the Brucewood Monitoring Program" unpublished reports
obtainable via Canada Centre for Inland Waters,
Burlington, Ontario
4. Proctor and Redfern Ltd. and James F. MacLaren Ltd.,
1976, "Storm Water Management Model Study", a draft
report prepared for Environment Canada and the Ont-
ario Ministry of the Environment
5. U.S. Army Corps of Engineers H.E.C., 1975, "Urban
Storm Water Runoff, STORM", A Generalized Computer
Program, Davis, California
6. U.S. Environmental Protection Agency, 1971, "Storm
Water Management Model", Vol. I-IV, Water Pollution
Control Res. Series. No. 11024 DOC09/71, Washington
D.C.
7. "San Francisco Storm Water Model User's Manual and
Program Documentation" prepared by Water Resources
Engineers for the City and County of San Francisco,
Dept. of Public Works, 1975
8. Crawford, N.H., and R. K. Linsley, 1966, "Digital
Simulation in Hydrology; Stanford Watershed Model
IV", Tech. Report No. 39, Dept. Civ. Eng., Stan-
ford University
9. Brandstetter, A.B., 1975, "Assessment of Mathemat-
ical Models for Storm and Combined Sewer Management"
a preliminary report, Battelle Pacific Northwest
Laboratories
10. Keeps, D.P. and R. G. Mein, 1973, "An Independent
Evaluation of Three Urban Storm Water Models", Mon-
ash University Civil Engineering Res. Report No. 4
11. Soil Conservation Service, U.S. Dept. of Agricul-
ture "Hydrology" Section 4, SCS National Engineer-
ing Handbook
12. Wisner, P.E. et al, 1975, "Interfacing Urban Run-
off Models", a paper presented at ASCE Environmental
Eng. Div. Specialty Conference on Environmental Eng.
Research and Design, Gainesville, Florida
13. Kiefer, C.J., and H.H. Chu, 1957, "Synthetic Storm
Pattern for Drainage Design", Journal of Hydraulic
Division ASCE, August 1957
14. Wisner, P.E., and Perks, A., 1975, "Lumping the
SWMM Model", a paper presented at the SWMM User's
Meeting, Gainesville, Florida
15. Barnwell, T.O., Cavinder, T.R., 1975, "Application
of Water Quality Models to Finger Fill Canals", Pro.
2nd Annual Symposium of the Waterways, Harbours &
Coastal Eng. Div., ASCE
16.Clarke, W.G. et al, "Hydrograph Methods in Relief
Sewer Design A Case Study", a paper presented at
the SWMM User's Meeting, Gainesville, Florida
17. James F. MacLaren Ltd., 1975, "Report on Storm Wat-
er Outlets in Port Credit", an unpublished report
prepared for the City of Mississauga, Ontario.
18. James F. MacLaren Ltd., 1976, "Edmonton Master Dra-
inage Study", an unpublished report prepared for the
City of Edmonton, Alberta
2. Koplyay, T.M., 1975 "Urban Drainage Studies in Can-
ada", a paper presented at the American Public Works
566
-------
Append ix 1
Generalized Quality Model (GQM)
The Generalized Quality Model computes surface
runoff quality in basically the same manner as the SWMM.
Some of the important aspects of the new model are
summarized below:
(a) Aggregated single catchment model
(b) Five land uses possible
(c) Separate input hydrograph forms basis for qual-
ity computations. (This may be generated by
any model or originate from measurements. Any
time interval can be used for hydrograph input)
(d) User supplied dust and dirt composition and
loading rates for each land use
(e) No quality routing or pollutant decay computa-
tions
(f) No erosion or deposition of sediments computed
(g) Two methods for Suspended Solids computation
(h) Catchbasin contributions modelled
(i) Quality calculations may be based on either
flow from the total area, or only on flow from
the impervious area
(j) Ten pollutants may be simulated (BOD, COD, Sus-
pended Solids, Settleable Solids, Coliforms, N,
PO , Cl, lead, oil and grease)
(k) No default values supplied
(1) Pollutographs, mass curves and surface load
statistics are available for each pollutant
The principal advantage of the Generalized Quali-
ty Model is the reduced cost of computations and re-
duced data preparation time achieved by aggregating
the properties of the entire study area and modelling
it as a single catchment. The model is extremely flex-
ible and may be used for the study of many aspects of
stormwater pollution.
FIGURE 1
THE ROLE OF MODELS IN DIFFERENT PHASES OF DRAINAGE STUDIES
I
^ STORM
3
D
UNIT
HYDROGRAPH
SWMM
WREM
STORM
GQM
X
3
§, SWMM
Sophisticated
Receiving
Water Model
f
TIME^
^ . PLANNING — >~* DESIGN *-
Critical Annual Effect of
Events Runoff Storage
Changes
Rural and semi-rural
basins
lumped: urban areas detailed: no surcharge
surcharged conduits only
Critical Comparison Estimates
Events of Alter- of Storage
natives s Treatment
capacities
Peak concentrations
Event mass emissions
Effect in Refine Storage Calibrated
Receiving and Treatment for final
water Options analysis
1-D or 2-D for diffusion
567
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ON THE VERIFICATION OF A THREE-DIMENSIONAL PHYTOPLANKTON MODEL OF LAKE ONTARIO
Robert V. Thomann
Environmental Engineering & Science Program
Manhattan College
Bronx, N.Y. 10471
Richard-P. Winfield
Environmental Engineering & Science Program
Manhattan College
Bronx, N.Y. 10471
INTRODUCTION
The purpose of this paper is to highlight
the growing need for detailed and quantita-
tive verification of water quality models
that goes well beyond model computation and
determines measures of model adequacy for the
decision maker. In particular, this paper
is focused on the need for verification of
phytoplankton-nutrient models, the number of
which has increased significantly in recent
years. These models all make use of a simi-
lar underlying deterministic framework of
coupled interactive non-linear differential
equations which are solved numerically in
discrete space and time.
Indeed, the state of the computing art of
such frameworks is advancing rapidly and to-
day it is no longer of great moment if hun-
dreds of sets of non-linear equations are
successfully solved on a large computer. What
is of significance however, is whether the
numerical computations are "reasonable" rep-
resentations of the real world. It is at
this point that considerable confusion re-
sults both in the realm of the model builder
and in the mind of the decision maker. What
is "reasonable"? Is it sufficient to gener-
ate computed values that "look" like what
we are observing? For example, is it suffi-
cient that a phytoplankton model simply
generate a spring pulse which has been ob-
served or is there a certain quantitative
measure that must be introduced to determine
not only that a spring pulse is calculated
but that it's magnitude is correct in some
sense? The question addressed in this paper
therefore is "What criteria might one use to
determine the adequacy of the model?" It is
strongly believed that unless a detailed
examination of the comparison of the model
to observed data is carried out, there is no
way of judging the adequacy of the computa-
tion. There may, of course, be situations
where this is not possible; as for example in
projecting phytoplankton conditions in a res-
ervoir that is not yet in existence. Such a
problem context is not considered here. The
thrust of this paper is aimed at detailed
verification, where possible, so that the
credibility and utility of a modeling frame-
work are established.
THE LAKE ONTARIO MODEL
A three dimensional model of the phytoplank-
ton of Lake Ontario is used as an illustra-
tion of the kind of problem that one faces in
attempting a detailed verification analysis.
The basis of this model, called Lake 3 has
been discussed previously(. The kinetics
of the model include linear and non-linear
interactions between 1) phytoplankton chloro-
phyll, 2) herbivorous zooplankton, 3) car-
nivorous zooplankton, 4) detrital nitrogen,
5) ammonia nitrogen, 6) nitrate nitrogen,
7) detrital phosphorus and 8) orthophosphate
phosphorus. The details of the kinetics are
given in (1) where a lakewide model (using
only vertical definition) was used to verify,
by judgment, open lake behavior.
Fig. 1 shows the spatial configuration of the
computational grid used for Lake 3; 67 seg-
ments are used and for the eight dependent
variables, 536 non-linear equations are inte-
grated in time for a maximum period of 14
months.
*• i i n r.
Fig. 1 Lake 3 Model Grid
A time step of .08 days is used throughout and
solution is accomplished on a CDC 6600 and re-
quires some 63K of storage and about 1 hour
of equivalent main frame computing time. The
model is relatively large and for any one run
generates some 100,000 numbers. The analyst
attempting to absorb the behavior of such a
model faces a formidable, indeed almost im-
possible task since attention can only be
directed towards certain portions of the
model (either in variable or physical space).
Furthermore, since the various portions of
the model are so interactive, "adjustments"
to improve the model in one region may result
in an undersirable change in another of the
model. Therefore, a strategy for determining
the behavior of the model and its verifica-
tion status must be developed. Such a
strategy must of necessity include the utili-
zation of an available data base such as the
results from the International Field Year on
the Great Lakes (IFYGL) for Lake Ontario. Fig.
2 shows the flow diagram adopted for the anal-
ysis of the Lake 3 model.
REDUCTION OF IFYGL DATA BASE
The IFYGL data base is resident in STORET and
contains approximately 200,000 observations,
encompassing 75 water quality parameters.
This data base is the most complete set of
observations obtained to date on Lake Ontario
and contains a wealth of information on the
568
-------
">nrfss
STORET
Data Base
iCDIT
SUMMARY STATISTICS
IFYGLOata
SUMMARY
PLOTS
Iki
PflOCKT
LAKE 3
Model Output
& EDIT
SUMMARY STATISTICS
Model Output
SUMMARY
PLOTS
Lv/
Fig. 2. Flow diagram for model verification analysis
dynamics of the Lake. The task as shown in
Fig. 2 is to utilize the data set to produce
summary statistics of the IFYGL data, which
would be used to analyze the results of the
Lake 3 model. These statistics are generated
for volumes of the Lake corresponding to the
segmentation of the Lake 3 model. Given the
IFYGL cruises, monthly mean and variance stat-
istics are used. After the segment statis-
tics are generated for the various water qual-
ity parameters of interest, a display package
is accessed to generate microfilm or paper
plots of the parameter statistics versus time.
The STORET data base is accessible to the user,
through program packages for standard re-
trievals and manipulations of the data with
fixed output format. Since the data set is
large (2 x 10 observations) a methodology
had to be formulated that would facilitate the
sizable reduction task. Recognizing that the
reduced statistical data set would be used on
an entirely different computer system (CDC
6600) than EPA's 370-155 and the need to ac-
complish the data reduction in the shortest
time possible,such a methodology is a neces-
sity.
The scheme was carried out for each of the 67
segments and a total of over 200 runs were
made. Each segment required three reduction
runs since a maximum of eight parameters per
run could be made and twenty variables were
reduced per s-egment.
The first step was to prepare decks which_des-
cribed the segment volumes. Each volume was
defined using a latitude/longitude polygon
with depth constraints. The STORET program
Mean was used to generate the segment statis-
tics; monthly mean, standard deviation, num-
ber of observations, maximum and minimum.
Since the output from Mean is fixed and the
results were to be transported to the CDC-
6600 via data cards, manipulation of the out-
put file was necessitated. OSI's 370-155
operating system contains an online interac-
tive text editor named Wylbur. Using Wylbur
and its limited macro capability, text edit-
ing module programs were developed that re-
duced the output from 140 to 80 characters
per line and eliminated all extraneous lines
of information. This compressed data set was
then punched and therefore, was in a form
processable by the CDC-6600. A Fortran pro-
gram was written to manipulate this data in-
to the format required by the verification
analysis and graphic display programs. The
result of this effort was an IFYGL data set
of monthly statistics for twenty variables
for 67 segments for the period May, 1972
through June, 1973.
A graphical display program was also written
in Fortran to display the temporal variation
of the parameters. Monthly means plus or
minus one standard deviation are displayed.
The graphical output of this program can be
routed either to paper or microfilm. The
use of microfilm for both graphical and
printed output has proven to be of immense
utility when dealing with large scale prob-
lem such as Lake Ontario and is to be recom-
mended.
VERIFICATION ANALYSIS
In the lower path of Fig. 2, the continuous
Lake 3 model output is also processed to gen-
erate monthly mean values by segment, month
and variable. A merge of data and model out-
put is then accomplished, computer generated
plots of theory and data are prepared for the
analyst and a verification program is then
accessed for testing the behavior of the
model and for preparation of verification
scores and summaries. Fig. 3 shows a typical
plot(redrawn)as generated from one of the
runs for segment #21 and shows the overplot
of the theory and the observed data. The
SEGMENT 21
728
Fig. 3. Typical merge of model output(solid
line) and data
amount of effort to reach the stage of Fig.3
is significant and should not be underesti-
mated.
Several simple tests comparing model output
to observed data have been constructed and in
this paper, emphasis is placed on testing the
difference of means. A standard "t" test is
used.
Thus, let x. ., =observed mean for vari-
1JK
569
-------
able If segment j and month, k and
comparable computed mean. Then d=c - x is
the difference of means assumed to be distri-
buted as a Student's "t" probability density
function. If the variance of the model is
assumed equal to the observed variance, then,
t =
d -
sd
(1)
where 6 is the true difference between the
model and the data and s-; is the standard
deviation of the difference given by the
pooled variance or
2
2s
sd =
N
(2)
d = ±t
c
Sd
and for a 95% confidence range (5% chance of
making a Type I error),
2.83
(4)
The distribution of d and the critical regions
are shown in Fig. 4. As indicated if
(-d < d dc
-i- d for -d>-d
C C
for s as the data variance for specific month,
segment and variable. Under the_null hypothe-
sis: 6=0, there is a "critical" d which de-
lineates the region of rejection of the hy-
pothesis and is given by
(3)
(6)
(7)
Another simple measure that may be used is the
number of segments in a given month that have
a V score equal to zero. Therefore, let
K. ., = 1 for V. = 0.
ijk i]k
A score defined as the S score for variable
i and month k is therefore given by
n
sik
= I
/n
(8)
where n is the total number of segments where
a V score can be computed, either for the
entire lake or for just certain vertical
layers or regions of the lake (as for example,
near shore vs. open lake). The score then
simply represents the fraction (or percent) of
segments that "passed" the verification test
of V=0. Since up to perhaps 10 variables are
analyzed in this verification analysis, an
overall aggregated S score can be also com-
puted. Verification of all variables may not
be of equal concern. For example, one may be
willing to accept a lack of verification of
ammonia nitrogen for the Lake but may be par-
ticularly concerned about say, total phosphor-
us and chlorophyll. Therefore, a series of
weights, w., can be assigned to each variable
i representing the relative importance of each
variable. The aggregated score for month k
is then given by
Sk=| X w.K. .k/(nZw. ) (9)
where r is the number of variables that are
in the aggregated score. S, therefore repre-
sents the weighted fraction of the total num-
ber of segment variables that passed a "t"
test of V=0 for month k. It should be noted
that not all segments and variables can be
tested at each month, so that r and n are
functions of the data availability for month k.
RESULTS FROM LAKE 3 MODEL RUNS
For this paper, three runs of the Lake 3 model
were available for verification analysis with
the IFYGL data. These runs emphasized the
sensitivity of the verification to the initial
conditions for each variable and segment. For
all runs, the average temperature variation,
solar radiation, flow transport ancL horizontal
and vertical dispersion were used . This
is in contrast to using the actual conditions
during the 1972-1973 IFYGL year. The kinetic
structure used for the homogeneous Lake 1
model was also employed. The runs are: l)Run
#1, which used initial conditions equal
throughout the Lake for January 1, such con-
ditions being chosen from Lake 1 runs, 2)Run
#2, which incorporates some spatial changes
in initial conditions for chlorophyll, ortho-
phosphate and nitrate based on IFYGL data,
computation also begins on January 1; 3) Run
570
-------
#3, which begins computation on May 1, 1972
and uses as initial conditions the observed
segment averages for May, 1972 as given by
the IFYGL data. Run #3 presumably then repre-
sents a "better" run in the sense that the
initial conditions are chosen from the ob-
served data. Not all segments had equal
amounts of data and in some cases, signifi-
cant data gaps existed for various months.
Fig. 5 shows some typical results of the veri-
fication analysis for phytoplankton for seg-
ment #16; Run #1. The gaps in the record can
. .
O
DC
g
1
o
i
-2
SEGMENT NO. 16
I
I S Ik s
g-g-s $& §
K K U_ /)>C LL
- - MODEL MEAN- OBSERVED MEAN
£2 195% CONFIDENCE LIMITS/
NO SIGNIFICANT DIFFERENCE
BETWEEN MEANS
I
1 I I I I I I I
MJJASONDJFMAMJ
1972
TIME OF YEAR
1973
Fig. 5. Typical statistical comparison of
model and data, Run #1
be seen as well as the region of no statis-
tically significant difference between model
and observed mean (Eq.(4)) and the monthly
differences between the model mean and the
observed mean. "Insufficient data" indicates
that the variance of the sample mean could
not be computed, implying that only one sam-
ple was available. The range of the no
difference region is significant and as shown
can be as much as - 4yg chlor/1. The appli-
cation of Eqs. (5) to (7) would therefore
lead to V scores of zero for months such as
July to a maximum overestimation of 3.7 yg/1
in June.
Computations such as represented in Fig.6
are carried out for each segment so that the
analyst can also view the V score spatially
by month. A typical result for Run #2 and
June 1972 conditions is shown in Fig. 6.
44°
43°
JUNE 1972 CONDITIONS
Contours: Phytoplankton Chlorophyll Verification Score Ijig/l)
TORONTO
79° 78° 77"
Fig. 6. Distribution of V score, Run #1,
As shown, a significant region of the Lake is
verified for this run although there are cer-
tain sectors where the model overestimated
the mean.
In order to provide further insight into the
behavior of the model compared to the observ-
ed data, lake wide averages of each of the
segment statistics were computed for two
layers. Figs. 7 and 8 show some of these
results for phytoplankton and Run #1.
O +2
-------
across each of the segment V scores for each
month as opposed to Fig. 7 and 8 where the
average was first taken of all of the means
and a single score computed. All three runs
0 to 4-METER LAKE-WIDE AVERAGE
yj
LL ^
O 40
I-
z
LU
U
S 20
Q.
"PERFECT" VERIFICATION
RUN NO. 1
1 1 1 1
J L
MJJASOND|JFMAMJ
1972 TIME OF YEAR 1973
Fig. 10. Overall segment-variable score for
Runs #l-#3
percent of the total number of segment-vari-
ables that had individual V scores of zero.
During the 1972 period of verification approx-
imately 50% of the segment-variables verified
while during the 1973 period only 30-40% veri-
fied. (It should be noted however, that the
data available in 1973 is significantly less
than that in 1972.) Further, Run #3 which was
constructed to further improve model perform-
ance did not really improve the overall veri-
fication; in fact it decreased the S score.
None of the runs provided a substantial change
in the S score. The S score therefore, repre-
sents a measure that incorporates the be-
havior of each of the key variables and pro-
vides a basis for determining whether the
model verification is improving or deterior-
ating under different model input. It does
not however indicate quantitatively the de-
gree to which each segment variable failed
to verify. The quantitative V score provides
such an estimate. Plots such as Figs. 9 and
10 therefore complement each other in terms
of displaying the overall verification of the
model.
CONCLUSIONS
This paper has not addressed directly the
question of whether the present Lake 3 model
of Lake Ontario is a "good" model, but has
rather concentrated on highlighting the need
for development of measures of model verifi-
cation. The analysis of the verification
statistics of Lake Ontario does provide how-
ever an illustration of this very important
need. It is no longer sufficient to simply
develop numerical solutions to the complex
interactive equations of phytoplankton models.
Rather, a substantial effort must be expended
to utilize available data bases together with
statistical measures of verification in order
to determine the overall credibility and
adequacy of the model. The illustrative re-
sults presented here for Lake Ontario indi-
cate how these measures of verification per-
formance behave under different assumptions
on model initial conditions. Overall, phyto-
plankton chlorophyll was verified to about
lyg/1 chlorophyll outside of the limit of no
difference between model mean and observed
mean and approximately 40-50% of the segment-
variables were verified regardless of the
initial conditions.
REFERENCES
1. Thomann, R.V. et al. Mathematical Model-
inging of_ Phytoplankton in. Lake Ontario. 1.
Model Development and Verification, EPA
660/3-75-005, ORD, Corvallis, Oregon,
March, 1975, 177pp.
ACKNOWLEDGEMENTS
The assistance of William Beach, Jan-Tai Kuo
and John Segna of Manhattan College is ac-
knowledged together with the insights of our
colleagues Drs. Donald O'Connor and Dominic
Di Toro. This work was carried out under
EPA Research Grant No. R803680-01.
572
-------
MATHEMATICAL MODEL FOP. THE EXCRETION OF 14C02 DURING
RADIO RESPIROMETRIC STUDIES
Rumult Iltis
U. S. Environmental Protection Agency
Health Effects Research Laboratory
Cincinnati, Ohio
ABSTRACT
"Mathematical model" described in this paper
applies to a biological process that can be expressed
in a well defined analytical form. Specifically,
it pertains to the rate of excretion of 14r (injected
i.v.) from the lungs of rats during the radiorespiro-
metric investigations. In the experiment, the rate
of excretion of l^cc^ from the lungs is changed by a
toxic agent (methyl mercury) ingested 24 hours prior
to the experiment. In this study, the model for '^£$2
excretion is presented in the form of a solution to
four first order differential equations reduced to a
fourth order differential equation. The integral of
the model for the controls and the exposed animals at
a selected time ti is used to measure the severity of
toxicity by taking the difference of the two integrals.
The model has 8 constants, thus it is possible to
take 8 independent measurements, at the early stages
of the experiment, and obtain eight independent
equations to yield a solution (i.e. the distribution
of the excretion with time). In this way a predic-
tion of the effect, if any, can be made. Using
heuristic approach, however, the model can be
simplified to yield a skewed distribution that can be
fitted to data up to the selected time tj . The
heuristic distribution contains only two parameters
(unknowns), thus only two measurements at the beginn-
ing of the study are sufficient to predict the
effects at any other point in time.
INTRODUCTION
Biological investigations including radio-
respirometry require collection of large amounts of
data in order to arrive at a statistically signifi-
cant conclusion. This statement implies that
experiments must be lengthy with large number of
animals a costly exercise that is not always
possible. Mathematical modeling serves to circumvent
this difficulty by predicting effects based upon
small sets of data. As to its validity in an "absolute
sense" it can be only stated that as long as it
represents a simplification of reality its "utility"
i.e. the extent to which it helps the user - is the
only fruitful criterion on which it can be judged.
The modeling of radiorespirometry provides a con-
venient and economic method of screening large number
of toxicants by reducing the time required for each
experiment and the number of experiments required to
make proper assessment.
In the experiment proper, investigators have been
able to successfully explain the effects of metabolic
conversion of ^C-labeled substrates to respiratory
^COo and the influence of various factors on the
metabolism (Wang, 1967; Dost et al., 1973). The
development of this method contributed significantly
towards being able to observe chemical reactions that
take place in experimental subjects without sacri-
ficing the subjects. An animal can be used for both
control and experimental purposes and, furthermore,
the cumulative effect of repeated administration of
an agent or recovery from a certain effect can be
observed.
Materials and Methods
Forty-eight male rats (Charles River Laboratory)
were used in this series of experiments. The radio-
labeled substrate ( '^C-1-glucose) used in this study
was obtained from New England Nuclear Corporation.
The theoretical consideration, design of experi-
ments, detailed methodology, and other background
information have been published by this laboratory
(Lee et al., 1972) and others (Wang, 1967; Tolbert
et al., 1956).
Exhaled ^C02 was monitored continuously using
Gary vibrating reed electrometers in conjunction with
ionization chambers. The analog output of the
electrometers was fed into a data acquisition system
that printed the data in digital form on paper tape
which was then decoded on a PDP8I computer. The
block diagram of the flow system and the instrumenta-
tion are shown in Figure 1. The decoded data was
later used for modeling and curve fitting on an analog
and digital computer. The derivation of the model is
based on biological processes in the course of
excretion of ^C02 from the lungs of experimental
animals. In the experiment, 14c is introduced into
the animal by i.v. injection. The rate of 14co2
excretion from the lungs is then modified by a toxic
agent (methyl mercury in this case) via ingestion, 24
hours prior to i.v. injection of 14c.
In the model it is assumed that there exists a
"two-pool open system" (Shipley et al ., 1972) in which
one pool is the central compartment~Tblood pool) and
the other is the conglomerate of all peripheral pools;
liver, kidney, lung, etc. Any communication between
peripheral pools occurs only through the central
compartment as shown in Fig. 2. On solving the pro-
blem a system of 4 first-order differential equations
is obtained leading to a solution for a skewed
distribution that has eight constant coefficients as
unknown. To predict the excretion rate and the
severity of toxicity at a later time, eight measure-
ments of excreted rate data at the beginning of the
study are made. Eight independent equations are set
yielding the eight constant coefficients. The distri-
bution (hence the solution) for any desired time is
573
-------
then obtained. The integrals of the distribution at
a selected time t for the control and the exposed
animals are compared. The difference, if any,
represents the severity of the effect.
The validity of the model is proven by testing
it on an analog computer and fitting data from four
experiments to the model on a digital computer.
Another advantage of the method is the possibil-
ity of predicting effects for a given concentration
of administered toxic agent, provided the controls
and some intermediate curves for a particular animal
are available. At this point it can be stated that
the model is valid for any agent and for any animal
that has the process behaving the way it is presented
in this paper. Only the rate coefficients could be
different for different animals or agents.
A clinical compartment follows linear kinetics
in which the rate of flow from a compartment is
proportional to the partial pressure of an agent (C02
in this case) within the compartment (Piotrkowski,
1971, Atkins, 1969). The output from each compartment
is a solution to the first order differential equation
of the form:
(1)
where y is the output or the amount of an agent
excreted as a percent of total pollutant and
t is the running time.
The lung is not a single compartment (Riley, R.
L, 1920), but is composed of three classical ones.
The first one consists of the alveoli -- the gas
exchange compartment [blood releases and takes in
gases via the capillaries surrounding the alveoli].
The second one is the anatomical "dead space" in the
alveoli. The third one is the "dead space" in the
respiratory tracts. It is quite reasonable to con-
sider the last two compartments as one, thus
simplifying the analysis via a two compartmental model.
Figure 3 shows graphically the two compartments. It
should be noted that COg from the blood is transferred
to alveoli with a rate coefficient k , but also (not
necessarily at the same time) some of the agent in the
alveoli is fed back into blood. This feedback is an
important process in the analysis. Blood (the rapid
exchange compartment) is a complex one, exchanging
its content with other compartments leading to an
assumption that blood is a vehicle by which the effect
of ingested Ch^HgCl is superimposed on all other
peripherals, thus influencing the I^C excretion
pattern. The excretion from the blood pool is not
linear in nature, thus the solution to the kinetics
is not known (Piotrowski, 1971, pp 9-22), but it is
probable that at some point in time there will be an
equilibrium during which the rate of excretion of 14c
from the blood is proportional to the concentration
of 14c in the blood. Thus, within this span of time
blood can also be represented as a first order process
(R. Aris, 1966). To make it right, however, the
effect of other storage organs (liver, kidney, etc.)
on the blood must be taken into account. If one
considers the effect of all the storage organs
collectively as one compartment, one obtains a fairly
good model as shown in Fig. 4.
From Figure 4 we observe that the total amount of
14c must be accounted for (preservation of matter) at
every instant of time.
Where B, L, A, EO and F are concentrations of
1*C in blood, lung, expired air, storage organs and
excretion via feces and urine, respectively.
A System of differential equations that will
satisfy this condition is as shown:
•jj| = -UT + k4) B + k6L + k8EO
^. k?A + k]B - (k6 + kg) L k]B-(k6+k2)L
since ky = 0
-(3)
dA
dzO
k2L
k4B
k5)
At t = 0, '^C is injected into blood, thus B(0) 100%
constant C.
The four first order differential equations are
reduced to one fourth order of the form:
4n 3 2 HA
+^ + AA ° ------
+L+A+i0+F= Constant
-(2)
The solution to the model is:
A = CT EXP (-^t) + c2 EXP (-A2t) + c3 EXP
(-V) + C4 EXP CV) ----------------------- (5)
were A amount of total injected, 14C excreted
in unit time
u,e,A,A1)A2,A3,Alt, constant coefficients that
depend on the animal and the toxic agent.
The initial conditions for the model require that
at t 0, A(o) = 0 therefore C] + C2 + 03 + 64 0.
The model was tested against data from four
experiments on an analog and digital computer. The
system of data acquisition and curve fitting of model
to the data is shown in Figure 5.
The analog computer program is shown in Fig. 6.
The output of amplifier 10 is the solution to equation
5. The output from integrator 5 is the total cumula-
tive value of '^C-excreted, and its value at time ti
is used to measure the severity of effect by comparing
the values of the integral at t] between the control
and the exposed animals.
In modeling the process on the analog computer,
data mean values are plotted vs. time on a graph paper
and the output from amplifier 10 is plotted (using
x y recorder) on the same graph. Rate coefficients
represented by potentimeters (numbers in circles see
Fig. 6) are varied, until a fit is obtained. Typical
output is shown in Fig. 7.
The total cumulative value of excreted 14C is
obtained from integrator 5 (Fig. 6). The result is an
S shaped curve. By selecting a point in time t]
V^IM f+F *h? Saturat1on region) as a reference, the
rnntrn? H* Inte9»;al at this point is used to compare
control and exposed animals yielding a "yardstick of
severity" of effect. Example is shown in Fig! 8.
The actual computation of effects for the four
experiments has been done on a digital computer
574
-------
The results are tabulated in Table 1 and the closeness
between the actual data and the simulated one is clear.
Typical fit between data and the model is shown in
Fig. 9 (control) and Fig. 10 (exposed), while the
cumulative value computed is shown in Fig. 11.
Simplified Model
Although taking 8 measurements reduces the time
required for the experiment, it still makes the method
of prediction a tedious one. Real simplification is
obtained if some approximation of the model is accepted.
Models having two unknown coefficients can be developed
that will provide same answers at time t-j to that of
the actual model. The simplified model is developed
as follows:
As mentioned before, blood is a central compart-
ment where mixing of a number of effects occurs.
Mathematically this can be expressed as a multiplica-
tion. The proposed model is shown in Figure 12.
The decrease cf 14C in the blood (following
injection) has a distribuion that decreases non-
linearily with time. By trial and error, an empirical
function is suggested that offers a solution to the
problem.
Assume the decrease with time of
blood follows a distribution:
2
14,
C in the
where BJ is a constant and t is the running time.
The output from the blood compartment is then equal to:
11 =
t (l-_
1-Pi t2
• y
-(6)
Where y1 = 1st derivative of 14C02 excretion
11
2nd derivative of C02 excretion
y
Let y1 p
Then
In p 1 Bit2 + In (1 - Bjt2) + ^nal
where a
and p
integration constant
rvp I o + *-/?\
LAr I p i L / L. }
1-Bit2 oj = y1
-(7)
Integrating equation 7 a distribution with time for
is:
the exhaled
y
EXP(-Bjt2/2)
(8)
with 04 and BI being constant coefficients that are
used in prediction of effects. Equation (8) satisfies
all boundary conditions:
t = 0
t = -
t =\T
y = 0
y 0
y max
The model in eqn. 8 has only two unknown co-
efficients alt Bi therefore taking two separate
measurements at the beginning of the study, prediction
can be made as to the effects at a later time. Using
the model of eqn. 8, the four studies have been
analyzed on the digital computer with results shown
in Table 2. The closeness between the model of eqn. 3
and the model in eqn. 8 is self evident.
DISCUSSION
A mathematical model has been described that
simulates the distribution with time of the l^COp
excretion from the lungs during the radiorespiratory
experiment. The model described by eqn. 3 calls for
8 measurements during the early stages of the experi-
ment. To simplify the matter, a simple model with
only two coefficients is described in eqn. 8. To
simulate the models, analog and digital computers have
been used.
Although the analog method is sufficient to
solve the problem and the value of al and B!
coefficients for each animal can be read directly from
the settings of the coefficient potentiometers, a
solution on digital computer has been sought. A
digital computer provides the direct numerical values
needed to answer the effects of a pollutant. The
analog computer, however, permits a quick determination
of the on-going process and also permits an
instantaneous change of coefficients making it a
flexible tool in the hands of a researcher.
In Tables 1 and 2, results from four experiments
compared to the two model are presented. In
particular, it can be seen that, up to time t t],
just before the saturation, the values for total
excretion indicate a substantial decrease in the
excretion in the exposed animals and that the correla-
tion between the calculated values and the models is a
readily acceptable one. These facts suggest that it
is possible to predict biological effects of a
pollutant or toxicant under specific conditions by
simulation and interpolation on a computer.
TABLE I. Comparisi
Croup
A
B
C
D
No. of
Animals
4
4
4
4
Calculated Cu
^ = 145
Control
65.08
61.56
66.17
Exposed
61.64
60.27
mulative
ing Data
a
3.43
5.9
*.fi
5.20
8.92
Cumulative Value in *
Using Model
t! = i4S rain.
Control
66.17
65.21
Exposed
50.56
5S.4
fl
S.61
6.8
U
8.47
8.27
10.5
Group
A
B
C
D
No. of
Animals
4
4
4
4
'Calculated Cumulative
tj = 145 min.
Control
65.08
71.04
61.56
66.17
Exposed 1 A
04.64
48.577
55.97
60.27
3.43
22.46
5.6
5.9
\4
5.20
jl.6
9.01
8.92
Cumulative Value in '*
tj = 145 min.
Control
62.7
71.34
61.64
66.175
Exposed
59.5
47.05
56.145
58.87
A
3.2
24.29
5.50
7.30
%4
5.10
34.00
8.90
11.03
575
-------
REFERENCES
1. Atkins, R. L. Multicompartment Models for
Biological Systems. Methuen and Co., Ltd.
London, Ennland, 1969.
2. Aris, R. "Comnartmental Analysis and the Theory
of Residence Time Distribution in Intracellular
Transport", Ed. K. P. "arren, II.Y. A.P. 1966.
3. Dost, F. M., Johnson, D. E. and Wang, C. H.
Metabolic Effects of Monomethyl Hydrazine.
•"erospace Medical Research Laboratory, Aero-
sr>ace Medical Division Air Force Systems Command,
',!right-Patterson Air Force Base, Ohio. AMRL-TR-
73-33, .lune 1973.
4. Lee, S. D., Butler, K. C., Danner, P.. M.,
McMillan, L., Moore, H. and Stara, J. F.
Radiorespirometry in the Study of Biological
Effects of Environmental Pollutants. Amer.
Laboratory, December, 1972.
5. Piotrkowski, .1. The Application of Metabolic
and Excretion Kinetic to Problems of Industrial
Technology. U.S. DHE'<', 1971.
S. Riley, P.. L. Has Exchange Transportation.
"Physiology and Biophysics", T. C. Ruch and
H. D. Patton, Eds. '!.!<'. Saunders Co. Phil.
and London on 771-77.
7. ^hipley, R. A. and Clark, R. E. Tracer Methods
for i_n vivd Kinetics. Academic Press, 1972.
3. Tolbert, B. " Kirk, M. and Baker, E. M.
Continuous c'^0, and CO Excretion Studies in
Experimental Animals. Amer. J. Phvsiol. 185:
269-274, 1956.
9. l.'ano, C. H. Radiorespirometry. Methods of
P-iochemical Analysis, XV: 312-368, 1967.
FLOW METER
MSHKOID
METABOLISM
CAGES lONIZtTIOH
DRIHITE CH1M8EBS
D
k
k4
L _
K5
1
(
I
I
«
k
k
3
2
KG
0 f 1
" 1
Figure 2. Generalized Kinetic MDdel for Transfer Process
of an Agent from Blood to Other Parts of the Animal's Body
B = Agent in the blood
C = Agent in fast exchange organs
D = Agent in slow exchange organs
I = Agent removed "irreversibly" from lungs
E = Agent excreted by urine and feces
k2, k3' k5' k6 = ^^ coefficients; and
depending on the agent, k4 and ks >_ 0
LUNG
*~AIR
TO & FROM
BLOOD COMPARTMENT
Figure 3. Lung System Represented by Two Cctnparbnents
L = Alveoli compartment
A = "Dead space" compartment
k^, k2, k3, kg, TK.-J = Rate coefficients of
agent excreted to and from compartments
Figure 1. Flow System and Instrumentation Block Diagram
for Radiorespirometry
576
-------
INTO AIR
Figure 4. Model for Blood Lung Interaction
B = Agent level in the blood
L - Agent level in the alveoli
A = Agent level in the "dead space"
ZO = Agent in other organs (liver, kidney, etc.)
kj, k2, k3, k4 = Rate coefficients of excretion from
a compartment
kg, ky, kg Rate coefficients of excretion returned
to a compartment
ky = Coefficient of return rate from "dead space" to
alveoli - 0
ks Rate coefficient of excretion of irreversibily
removed agent by urine and feces
Figure 6. Analog Computer Program for the Msdel of CO.
Excreted from the Lungs
Integrator B = Blood compartment
Integrator L = Alveoli compartrrent
£ 0 = Compartment representing other body organs
A = "Dead space" compartments
6, 7, 8, 10 = Amplifiers
5 = Integrator producing total cumulative value of
excreted 14C
Numbers in circles represent rate coefficients
(2)= Initial condition (I.V. injection)
SIMULATING AND CURVE I
FITTING SYSTEM I
Figure 5. System Flow Diagram for Data Acquisition and
Curve Fitting of Model to Data
577
-------
o MODEL
XDATA
. PERFECT
TIME IN
MINUTES
49.9 97.7 146
TIME SCALE: .25"=10 MIN.
193
TIME IN
"^"'MINUTES
Figure 10. Curve Fitting Between Experimental Data and
the Model of Group B - Exposed
Figure 7. Comparison Between the Curve Generated by the
Analog Computer and the Experimental Data
CONTROL
EXPOSED
= MEASURE OF EFFECT
^SELECTED TIME
FOR COMPARATIVE
MEASUREMENT.
97.7 146 193
TIME SCALE: .25"=10 MIN.
i i
i ,_ ( TIME IN
241 MINUTES
Figure 11. Total Cumulative Recovery for Control and
Exposed Group A
• t TIME IN MINUTES
Figure
Exairple of a Total Cumulative Excretion Curve
for a Control and Exposed Aniiral
X MODEL
° DATA
. PERFECT
49.9
97.7 146
TIME SCALE: .25"=10 KIN.
TIME IN
MINUTES
EFFECT OF
OTHER ORGANS
Figure 12. Simplified Kinetic Model for Transfer Process
of an Agent from Blood to Lungs
= Percent of ^C excreted in unit time
y
y1
wii
= First derivation of y
= Second derivation of y
Figure 9.
Curve Fitting Between Experimental Data and
the l>todel of Group B - Control
578
k, d = Constant rate coefficients that depend
on the process
I.V. 14C = I.V. injection of 14C into blood
B = Blood compartment (multiplier)
L = Alveoli compartment
A = "Dead space1' compartment
-------
ESTIMATION OF THE OPTIMAL SAMPLING INTERVAL IN ASSESSING
WATER QUALITY OF STREAMS
Leo J. Hetling, G.A. Carlson and J.A. Bloomfield
Environmental Quality Research Unit
New York State Department of Environmental Conservation
50 Wolf Road, Albany, New York 12233
The problem of estimating the sampling resources
necessary to characterize water quality is one that
has received little attention. Until recently, the
problem was unimportant because the resources avail-
able for monitoring were limited and the thrust of
most programs was not so much to characterize the
system as to detect specific violations of a set
water quality standard. Recently, however, the
resources available for monitoring of the environ-
ment have been increasing and a determination of
optimum utilization of these resources becomes of
practical significance. Additionally, the progress
made in point source pollution control has led to
greater emphasis on non-point source pollution
problems. Non-point source problems require a more
detailed knowledge of annual and seasonal loadings
rather than measurement of deviation from a standard.
The problem most often encountered is to deve-
lop a sampling strategy for statistical characteri-
zation of the concentration and annual loading of a
pollutant from a watershed. Most existing monitoring
programs are set up such that chemical samples of a
stream are collected at fixed sampling intervals;
i.e., weekly, bi-weekly, monthly, etc. Stream
flow at the point and time of sampling is noted.
Average annual concentrations and loadings are then
calculated from this data base. Although the
limitations of this approach have been recognized,
little analytical or experimental work has been
done to document errors involved with the strategy.
We first attempted to approach the problem ana-
lytically. However, it was found that since neither
stream flows nor concentrations are normally dis-
tributed, attempts at analytical solutions were
frustrating. As a result, the following more ex-
perimental approach was pursued. A continuous
stream flow gage was installed on a small stream
and grab samples for water quality were collected
daily. Using equally-spaced subsets of the resulting
data set, average concentrations and loadings were
calculated and compared to the average obtained by
utilizing the entire data set. This approach was
first suggested by Treunert, e_t al_ (l); however,
his analysis was limited in that concentration
measurements available to him were spaced at three-
day intervals.
Mill Creek, the stream utilized for this study,
is a small stream draining 2,454 ha in Rensselaer
County near Albany, New York (Figure 1). The land
use in the watershed is predominantly forest (54%)
and agriculture (43%). The stream is unregulated
and has no known point sources of pollution. A
complete description of this watershed is available
(2). Stream flow was measured via a standard stage
height recording station installed, rated and main-
tained by the United States Geological Survey.
Chemical samples were collected, preserved and
delivered to the New York State Department of
Health's Division of Laboratories and Research for
analysis. The actual chemical analyses performed
are described in Krishnamurty and Reddy (3).
This paper utilizes 275 daily samples taken from
March 1, 1975 through November 30, 1975.
Twenty water quality constituents were
analyzed including major ions and the various forms
of carbon, nitrogen and phosphorus. This paper will
concentrate on elucidating the effect of sampling
interval on the estimation of the average daily con-
centration and average instantaneous load of total
suspended solids (retained on a 0.45 M filter),
chloride and particulate and dissolved phosphorus.
The average daily concentrations (C) and the
average daily loadings (L) were calculated for sub-
sets of the data taken at fixed intervals ranging
from one to 60 days. Sampling frequencies of longer
than two months were considered to be random rather
than fixed-interval sampling and hence ignored.
Ten sample populations of 265 days length were
withdrawn from the general population by beginning
fixed interval sampling on each of the first ten
days of the sample space (Sample - March 1, 1975)
(Figure 2). The average concentration is defined
as follows:
Cj.n, = I
where:
and
j-i-s-r
E
by m
Ci
r -t- m
(1)
(2)
n = number of samples in each discrete
population
j — the initial sample chosen (March 1=1,
1< J
-------
The equation for average instantaneous daily
loading is:
i+s-r
J
where :
^
by m
Qi = instantaneous flow at the time of colleo-
_ tion of the ith sample (m3/sec)
Lj,m = the arithmetic average daily loading
calculated beginning on the jth day at
an interval of m days (Kg/day)
The results of the calculations are shown in
Figures 3 through 6. The abscissa of these plots is
the imposed sampling frequency; i.e., daily, every
other day, weekly, every third day, etc. On the
ordinate, the average of the ten data sets obtained
for imposed sampling frequency along with the
range of values observed was plotted. As a reference,
the average value obtained utilizing the entire data
set is shown along with lines showing a 25, 50 and
75% deviation from this value.
All of the plots have several characteristics
in common. The range of values spreads rather
rapidly as the sampling interval is increased. This
rapid deviation is to be expected since the number
of samples within a data set decreased rapidly as
the sampling interval is increased. This is il-
lustrated in Figure 7 where the number of samples
from the 275 sample data sets obtained is plotted
against the sampling frequency.
The rate at which the range increases varies
with the parameter being studied. It is least
rapid for the chlorides (a dissolved, conservative
ion) , more rapid for dissolved phosphorus which
takes part in a variety of chemical sorption, and
exchange reaction with the stream bed and surrounding
soils, and most rapid for the particulate-related
parameters of suspended solids and particulate
phosphorus.
A wider band of errors can be noted for load-
ing than for the concentration values.
It is apparent from these plots that unless
one samples very frequently (at least every other
day) , average values calculated from the data can
range considerably from the actual daily average.
Frequent sampling is of even more importance with
the particulate-related material where order of
magnitude errors could be encountered with less than
a three-day sampling frequency.
A tendency for the average value to decrease
as sampling frequency is increased is also noted
for the particulate parameters. Apparently as the
sampling frequency decreases, the likelihood of
sampling the major stream flow events also decreases.
Since extreme events have a profound effect on
averages, a value somewhat less than the average
obtained by utilizing all of the data is obtained.
This indicates that as sampling frequency decreases,
there will be a tendency to underestimate the actual
average concentrations and loadings for particulate
material.
Conclusions
As a result of this analysis, it can be con-
cluded that for small streams similar to Mill Creek,
fixed interval sampling to obtain average concen-
trations is of little value unless the sampling
interval is less than two or three days. Attempts
to obtain annual loads are even less productive
unless daily or every other day samples are taken.
Apparently this occurs because of the im-
portance of a relatively few major hydrological
events on the annual average. Hopefully, a sam-
pling strategy centered around these events can
be devised to obtain reasonable estimates of
average concentrations and yield without the ex-
treme investment needed for daily sampling.
Future plans of this study are to repeat
the above and similar analyses utilizing a full
year's worth of the Mill Creek data. A greater
number of parameters will be studied and the effect
of utilizing the continuous stream flow record with
fixed interval chemical quality sampling will be
investigated. The effectiveness of various event
sampling strategies will also be tested.
References
1. Treunert, E., A Wilhelms and H. Bernhardt,
"Effect of the Sampling Frequency on the
Determination of the Annual Phosphorus Load
of the Average Streams", Hydroohem. hydro-
geol. Mitt., Vol. 1, pp 175-198, March 1974.
2. El-Baroudi, H., D.A. James and K.J. Walter,
"Inventory of Forms of Nutrients Stored in a
Watershed", Rensselaer Polytechnic Institute,
Troy, N.Y., August 1975.
3. Krishnamurty, K.V. and M.M. Reddy, "The
Chemical Analyses of Water and Sediments in
the Genesee River Watershed Study Procedure
Manual", Environmental Health Center, Division
of Labs, and Research, New York State Depart-
ment of Health, Albany, N.Y., September 1975.
580
-------
CHLORIDE LOADS
RENSSELAER COUNTY
STATE OF NEW YORK
SCALE I INCH « 5 MILES
noune I.
DI
WI
1 9 10 19 K
MARCH
10 19 » 25 31
OCT.
AVAILABLE SAMPLE SPACE (S ) • 275 doyt
FIGURE 2.
1000
J>
O
z
0
g
J too
F ., AsA A n /s. A
^^ ^W XA^V . ,\x . \ / V /.. U \.
. - - "VAX ^^-AXY/-
75
25
0
25
90
75
CHLORIDE CONCENTRATIONS
75
SO
29
0
FLOW
SAMPLING INTERVAL
FIGURE 3.
10.000 t-
DISSOLVEO PHOSPHORUS LOADS
O.I
i
K
I
DISSOLVED PHOSPHORUS CONCENTRATIONS
N>>\ A^V/y .
v
_ _J U T
5 S t! 1
2 ^ 5 I
SAMPLING INTERVAL
4 .
61
i
i
581
-------
PARTICULATE PHOSPHORUS LOADS
100,000 r
10.000
1.000 r
100 -
O.I
0.01 -
MRTICULATE PHOSPHORUS CONCENTRATIONS
SAMPLING INTERVAL
FIGURE 5.
1,000,000
100,000
SUSPENDED SOLIDS LOADS
SUSPENDED SOLIDS CONCENTRATIONS
1,000
100
i
t-
I
SAMPLING INTERVAL
FIGURE 6.
0 20 40 60 80 100 120 140 160 180 200
FIGURE 7.
582
-------
FIELD DATA FOR ENVIRONMENTAL MODELING—ADJUNCT OR INTEGRAL?
Philip E. Shelley, PhD
Director, Energy and Environmental Systems
EG&G Washington Analytical Services Center, Inc.
Summary
Two types of field data are required for virtually all
environmental prediction models: calibration data and
verification data. The former type is used within the
model itself to ready it for specific application,
whereas the latter is used to establish the validity/
and probable accuracy of the results obtained from the
model. The paper points out that, historically, too
little attention has been given to the collection of
field data for use with environmental models and
that the quality of the current modeling state-of-the-
art generally far exceeds the quality of the supporting
data base. An incredible lack of good data faces the
model developer, evaluator, and user alike, and this
often unrecognized fact quite seriously impacts on the
activities of each. Using urban hydrology models as
an example, the severity of the problem is demonstra-
ted. The need for determining estimates of data
quality prior to their use in modeling is noted, and
the dangers associated with the "blind" use of existing
data are indicated.
Introduction
adjunct (o/'uwg kt) 1. Aam&tlting added to an.oth.eA th^ing
but not ut,e.ntiaLty a pcuvt o& -it.
tnte.g'iai [tn'ts gAsi) 7. o{>, p&itcu.nj,ng to, on. be.-
tongtng a!> an eJiAe.ntiat pafit of, the. whote..
Environmental modeling is performed in order to obtain
a picture of probabilistic events likely to occur
given a set of input conditions. The "portrait"
obtained will be of the right "person", but even a
charicature can be useful in many instances, despite
its exaggerations, as long as it is recognizable.
Regardless of whether the application arises from the
needs of planning, design, facility operation, alter-
native assessment, or other needs, the simulation
process involved is intended to duplicate the essence
of a system without actually attaining reality itself;
the model is simply a device used to carry out the
simulation. The validity of the results, i.e.,
their agreement with reality, depends upon two primary
factors: how well the model represents the actual
processes involved, and how representative the set
of input conditions are. In general, both of these
factors involve the use of field data and, for any
given model, the better (i.e., more realistic/
representative the field data, the closer the simula-
tion will be to reality. Although the following is
drawn from the field of urban hydrology, most of what
is stated essentially applies to other environmental
modeling areas as well.
Regardless of whether the model of interest is sto-
chastic versus deterministic on the one hand, or ana-
lytic versus synthetic on the other, there are two
uses that are generally made of field data. To em-
phasize the importance of distinguishing between the
two, they will be referred to here as data types.
Because of the complexity of the processes being mod-
eled, most of the models that are popular today re-
quire field data both for estimating empirical
parameters in their structure and for fitting other
application-specific parameters (calibration). For
example, one version of the Sanford Watershed Model
has twenty parameters: two are based on meteorological
data, four are based on hydrograph separation, five
are computed from physical measures, three are estima-
ted from empirical tables, and six are fitted. All
field data that are used within any model structure,
i.e., to ready the model for specific application,
will be referred to here as calibration data.
The chief concern of the model-user is how well the
model outputs (which are its sole reason for being)
compare to reality. This comparison forms a measure
of the predictive capability of the model. Here,
also, input and output field data are required, but
their fundamental use is quite different from that of
calibration data. They will be referred to here as
verification data, since they are used to verify the
results of a particular model exercise.
This distinction between field data types is not made
to suggest that different gathering techniques are re-
quired for calibration versus verification data; in
fact, they are the same. The reason for making the
distinction is simply that calibration data must never
be used for model verification. The importance of this
simple statement cannot be overestimated.
Data in Model Selection
The various stormwater management models that are
available today require data on the catchment, precip-
itation, and runoff quantity and quality. Such data
might include historical and current records plus re-
lated information such as present and projected land
use parameters, demographic projections, remote (sat-
ellite or aerial) imagery, treatment plant records,
and the like.
The purpose of the simulation, i.e., the use to which
the model results are put, must be kept in mind in
selecting the model to be employed, but it is also
very important to carefully review and inventory the
existing data base. As Lager has noted, "Rather than
selecting a model and then seeing if you can fill its
data requirements, it is preferable to analyze your
available data and then choose the model that can use
these data most effectively to achieve study objec-
tives." !
The various models not only have different basic data
requirements; they also vary widely in the detail
of temporal and spatial distribution of data required.
For example, some models require time steps of less
than one minute to satisfy numerical stability condi-
tions, while others can be run with hourly, daily, and
even up to semimonthly data. These considerations,
with their attendant field data gathering cost implica-
tions, bear heavily on model selections.
Considerations other than the model structure are also
involved in determining the cost of a field data gath-
ering program. For example, both the quantity and
quality of stormwater runoff are highly variable and
transient in nature, being dependent upon meteorologi-
cal and climatological factors, topography, hydraulic
characteristics of the surface and subsurface conduits,
the nature of the antecedent period, and the land use
583
-------
activities and housekeeping practices employed. It is
this highly variable and transient nature of storm-
water flows that makes their characterization so dif-
ficult and, hence, expensive. In addition to
tremendous dynamic ranges, the poor quality of storm-
water draining from the urban environment has a signif-
icant effect on the choice of suitable sampling and
flow measurement equipment and methods as well as an
impact in the analytical laboratory.
Data Quality
In addition to assessing the quantity of data on hand
and to be gathered, some assessment of data quality is
required if we are to be sure that our "portrait" is
of the "right person." We are not yet overwhelmed
with existing data on stormwater characteristics. As
stated by Torno, "One of the serious problems that
faces either a new model developer or one who must
evaluate several models is the incredible lack of good
data..."2 To be effectively utilized, we need
more than simple values as data products. We need to
know something about the data quality, i.e., about the
"goodness" or truthfulness of the data. Two terms
that relate to the data-gathering process are conven-
tionally used to describe data quality: accuracy and
precision. Accuracy refers to the agreement between
the measurement and the true value of the measurand,
with the discrepancy normally referred to as error;
precision refers to the reproducibility (repeatability)
of a measurement when repeated on a homogenous time-
stationary measurand, regardless of the displacement of
the observed values from the true value, and thus,
indicates the number of significant digits in the
result. We are, therefore, interested in establishing
the best estimate of a measured quantity and the
degree of precision of this estimate from a series of
repeated measurements. Calibration, whether it be of a
piece of flow measurement equipment, a chemical method
for wastewater analysis, or a stormwater management
model, is simply the process of determining estimates of
accuracy and precision.
Discrepancies between the results of repeated observa-
tions, or errors, are inherent in any measurement
process,since it is recognized that the true value of
an object of measurement can never be exactly estab-
lished. These errors are customarily classified in
two main groups: systematic and random (or accidental)
errors. Systematic errors usually enter into records
with the same sign and frequently with either the same
magnitude (e.g., a zero offset) or with an establish-
able relationship between the magnitude of the measure-
ment and the error. The methods of symmetry and
substitution are frequently used to detect and quantify
systematic errors. In the method of symmetry, the
test is repeated in a symmetrical or reversed manner
with respect to the particular condition that is
suspect. In the method of substitution, the object of
measurement is replaced by one of known magnitude (a
calibration standard), an instrument with a known
calibration curve is substituted for the measuring in-
strument in question, and so on. Thus, systematic
errors bear heavily on the accuracy of the measurement.
Random errors, on the other hand, are due to irregular
causes, too many in number and too complex in nature
to allow their origin to be determined. One of their
chief characteristics is that they are normally as
likely to be positive as negative and, therefore, are
not likely to have a great effect on the mean of a set
of measurements. The chief aim of a data quality as-
surance effort is to account for systematic errors and
thereby reduce errors to the random class, which can
be treated by simple probability theory in order to
determine the most probable value of the object of
observation and a measure of the confidence placed in
this determination.
The statistical measures of location or central ten-
dency (e.g., the various averages, mean, median, mode)
are related to accuracy. The statistical measures of
dispersion or variability (e.g., variance and standard
deviation, coefficient of variation, and other measures
derived from central moments of the probability density
function) are related to precision.
There are also some annotations that the data gatherer
can make to increase the usefulness of the data. For
example, inspection of equipment and records may indi-
cate periods of instrument malfunction or failure
(e.g., power interruptions). These facts are important
and should form a part of the total record. There may
be circumstances discovered during site visits that
would have had an effect on preceding data that cannot
be readily determined, e.g., a partially blocked sampler
intake or a rag caught in the notch of a weir. These
facts should also be noted and, where at all feasible,
some qualitative notation as to expected data quality
(e.g., poor or very good) should be made.
The importance of notations of data quality results
from the ultimate use of the data. For example, at
the risk of seeming ridiculous, ±50-percent data
should not be used to calibrate a model whose outputs
are desired within ±20 percent, nor should strong
model verification judgments be made based upon a very
small sample of data with a high variability. The
levels of data quality desired vary with the intended
use of model outputs. The needs for overall basin
planning, treatment plant design, plant operation, and
research are all quite different, and this must be
kept in mind in designing the data-gathering program
(or system).
Instrumentation
The ability of available instrumentation and techniques
to gather reliable wastewater characterization data
varies widely with design and implementation factors.
Shelley has reviewed the sampling problem3>4 and ,-
has collected comparative data using various samplers.
Shelley and Kirkpatrick have recently provided ;
in-depth monographs on-instrumentation for flow meas-
urement*^ and sampling. A summary of the use of
instrumentation for collecting field data for storm-
water model calibration has been given by Shelley.^;
who has also examined the use of remote sensor data to
measure water quality, especially sediment.9
To summarize the foregoing as it pertains to stormwater
flow measurement, it can be stated that, although ac-
curacies bn the order of ±5 percent can be achieved
with the proper site, instrumentation, and care, in-
strument readings that differ from spot checks by 25 to
50 percent or more are much more typical. There are a
number of factors involved, but the greatest con-
tributor seems to be the use of slope-area methods
such as the Manning formula in uncalibrated reaches or
inappropriate instances.
Reviews of project experience have revealed cases where
individual meters have been in error by over 200 per-
cent, due to lack of proper maintenance, installation
errors, or misapplication.
Insofar as sampling is concerned, the lack of a manual
sampling protocol has resulted in a situation where
differences of as much as 150 percent have been ob-
served between samples taken manually from the same
source at the same time, the differences being attri-
butable to equipment and technique. In a recent
584
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side-by-side test of four different automatic sampler
designs, a controlled synthetic waste stream was em-
ployed.5 The results of laboratory analyses of
samples taken with these equipments ranged from
understatements of pollutant concentrations by 25 per-
cent or more to overstatements by as much as 200 per-
cent and higher. Again, a number of factors are
involved, but equipment design characteristics (espe-
ially intake and sample-gathering subsystems) appear to
account for much of the observed performance variation.
As regards chemical methods for the analysis of water
and wastes, the picture is relatively brighter. Even
here, the lack of well-accepted baseline standards or
alternate techniques results in an inability to speak
of accuracies for a number of tests. Furthermore,
precision expressed as standard deviation is not out-
standing for some tests. As an example, USEPA10
quotes the results of 86 analysts in 58 laboratories
who analyzed natural water samples plus an exact in-
crement of biodegradable organic compounds. At a mean
value of 175 mg/1 BOD, the standard deviation was
±26 mg/1 (±15 percent). For other tests, especially
at low levels, even larger variances may be
encountered.
When the foregoing sources of error are combined, for
instance, as is necessary if mass discharges are to be
computed/predicted, the picture is not very optimistic.
Straightforward calculation shows that results can
vary by over an order of magnitude; hardly a comforting
situation for model calibration or verification.
Along the same line, Harris and Keffer, 11 as a •
result of extensive comparative testing in the field,
have noted that apparent treatment plant efficiencies
can be varied by a factor of 2 or 3 or even higher,
depending upon site selection and equipment used.
Conclusion
Although it was strongly implied earlier that field
data should be viewed as integral to environmental
modeling, the present state of affairs suggests that
such data have been treated as adjunct in terms of the
effort and resources that have been applied to the^
development and refinement of computer models vis-a-
vis that devoted to the collection of good field data.
This observation is not meant to suggest that all work
on model refinement and use should be abandoned for a
massive data-gathering expedition, but rather that we
must bring our application of resources for environ-
mental characterization/prediction into better balance.
Obviously, much remains to be done in terms of refine-
ment of equipment and techniques before our field data
are up to the sophistication of some of our models,
and it is past time that this fact be more widely
recognized.
References
1. Lager, J.A., "Criteria for Selection of Stormwater
Management Models," in Application of Stormwater Man-
agement Models -1975, University of Massachusetts
Short Course Handbook, Amherst, MA, 1975, 47 p.
2. Torno, H.C., "Stormwater Management Models," in
Urban Runoff - Quantity and Quality, W. Whipple, Jr.,
ed., American Society of Civil Engineers, New York, NY,
1975, pp 82-89.
3. Shelley, P.E., "A Review of Automatic Sewer Sam-
plers," in Urban Runoff - Quantity and Quality.
VI. Whipple, Jr., ed., American Society of Civil Engi-
heers, New York, NY, 1975, pp 183-191.
4. Shelley, P.E. and G.A. Kirkpatrick, "An Assess-
ment of Automatic Sewer Flow Samplers," in Water
Pollution Assessment, ASTM Publication STP-58T7 1975,
pp 19-36.
5. Shelley, P.E., Design and Testing of a Prototype
Sewer Sampling System, USEPA Environmental Protection
Technology Series No. EPA-600/2-76-006, 1976 ix and 96p.
6. Shelley, P.E. and G.A. Kirkpatrick, Sewer Flow
Measurement - A State-of-Art Assessment, USEPA
Environmental Protection Technology Series No. EPA-
600/2-75-027, 1975, xi and 424 p.
7. Shelley, P.E. and G.A. Kirkpatrick, An Assess-
ment of Automatic Sewer Flow Samplers - 1975, USEPA
Environmental Protection Technology Series N. EPA-600/
2-75-065, 1975, xiv and 336 p.
8. Shelley, P.E., "Collection of Field Data for
Stormwater Model Calibration," in Application of
Stormwater Management Models - 1975, University of
Massachusetts Short Course Handbook, Amherst, MA,
1975, iii and 179 p.
'9. Shelley, P.E., Sediment Measurement in Estuarine
and Coastal Areas, WASC TR-7115-001 1975, to appear
as a NASA publication, vi and 97 p.
10. United States Environmental Protection Agency,
Methods for Chemical Analysis of Water and Wastes.
Environmental Monitoring Support Laboratory (formerly)
Methods Development and Quality Assurance Research
Laboratory) and Office of Technology Transfer,
Cincinnati, OH, 1974, xvii and 298 p.
11. Harris, D.J. and W.J. Keffer, Wastewater San-
pling Methodologies and Flow Measurement Techniques,
Report No. EPA 907/9-74-005, Surveillance and Analysis
Division, USEPA Region VII, Kansas City, KA, 1974,
ix and 117 p.
585
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DATA DEFICIENCIES IN ACID MINE DRAINAGE MODELING
Vincent T. Ricca, Ph.D.
Professor
Department of Civil Engineering
The Ohio State University
Columbus, Ohio
ABSTRACT
Recently developed digital computer models for Acid
Mine Drainage Quality and Quantity for discharges from
deep mines, strip mines, and refuse piles are currently
being validated by application to field sites. A task
in this current research was to select suitable test
sites with extensive hydrologic and acid mine drainage
data. Experience has shown that data for the some 200
modeling parameters as well as the length and consis-
tency of the records have not been satisfactorily col-
lected in the past on even the most highly investigated
study sites. The object of this paper is not to criti-
cize these prior collection efforts, for some were
quite extensive indeed; but rather, to indicate what
data should be collected if acid mine drainage modeling
is to be advanced.
BACKGROUND
Over the past five years, researchers at The Ohio State
University have been developing computer models to de-
scribe the quantity and quality generation of coal mine
drainage. A two-year, EPA-sponsored research project
titled, "Resource Allocation Model to Optimize Mine
Pollution Abatement Programs"'- was completed in 1974.
A major component of the work in that project was the
development of unit source models. These models pre-
dict the mine drainage flow and its associated acid
load for deep or drift mines, strip mines, and refuse
piles. They were created by combining highly sophisti-
cated hydrologic simulation models and mine acid pro-
duction models developed by the acid mine drainage task
group at The Ohio State University. The outcome of
this initial work on these unit source models is deemed
quite successful and encouraging by the researchers in-
volved. An objective of this original work was to pro-
duce models as detailed and sophisticated as possible,
using the highest level currently available in the
fields of hydrologic simulation and mine acid pro-
duction. This approach was taken with the belief that
it is a more feasible future task to simplify these
highly detailed models than to upgrade simplistic
models as field applications disclose the nature and
availability of data involved in the phenomenon of acid
production and mine discharges. Details of the basic
unit source models are discussed in the final report of
the model development project-'-.
A follow-up EPA project^ is currently nearing comple-
tion. An objective of this latter project is to apply
the previously developed models to field situations to
evaluate their validity. These applications provide
information for another project objective: "Identi-
fying Data Deficiencies and Formulate Data Acquisition
Guidelines". This last objective will be the subject
of this paper.
DISCUSSION OF THE DATA NEEDS OF THE MODELS
The unit source models are considered as highly sophis-
ticated in their structure and performance. They are
capable of producing continuous time outputs of gener-
ated mine site discharges and attendant acid quality
of the flows as well as receiving stream or basin
outlet flows. In order to accomplish this continuous
time trace throughout the modeling period it is neces-
sary to have compatible detail and consistency on the
climatic input data. Also,much detail is needed on the
physical and chemical aspects of the mines and spoils
along with the site watershed. Some 200 parameters in
total may be involved in a modeling endeavor depending
upon degree of detail desired.
The listing below is a category description of the
major information items, or input, required to operate
the models. Explicit details on the input data and
model parameters are given in the technical discussion
of the model found in the project report. 1
Basin Information. Watershed drainage, Land use and
distribution, Flow capacity of main channel, Mean over-
land flow path length, Retardance coefficient for sur-
face flows, Average ground surface slopes, Interflow
and baseflow recession constants, Channel routing para-
meters, and Index parameters reflecting interception,
depression storage, infiltration, soil moisture storage,
interflow movement, groundwater movement, etc.
Climatic Data. Precipitation records, Streamflow
records, Evaporation rates and coefficients, and Mete-
orological information for snowmelt.
Deep Mine Information. Mine area; Coal seam descrip-
tion, materials, thickness; Pyrite oxidation rate para-
meters reflecting diffusion, reaction, and temperature;
Acid transport parameters reflecting gravity diffusion,
inundation, and leaching; Initial acid storages; and
Alkalinity conversion factors.
Refuse Pile-Strip Mine Information. Strip mine and
refuse pile areas; Representative soil profiles of acid
producing areas; Pyrite oxidation rate parameters re-
flecting diffusion, reaction, and temperature; Initial
acid storages; and Acid transport mechanism parameters
reflecting depth leached by direct runoff, leaching
parameters, effective acid solubilities.
Discharge Data. Drainage flow records; and Drainage
quality records.
SELECTION OF TEST SITES
In order to validate the unit source models, field or
"test sites'1 were sought. Those working in the area
of acid mine drainage and related coal mining problems
are aware that many reports on demonstration projects
and mining operations are available in the literature.
Project researchers at OSU were aware of such litera-
ture and expected to find numerous "test sites" upon
which to apply the models. However, once into this
task,a wealth of information was found; but,consistency
or completeness immediately surfaced as a major problem.
To properly assess the possible test sites a systematic
evaluation or selection methodology was developed. A
discussion of this methodology follows.
The Nature of the Literature Review for Site Selection.
Since this project is concerned with testing of the
models, it is important to find the best possible
watersheds, that is to say, the watersheds with the
largest amount of available field data to use in the
models. This requires the best Streamflow records,
stream quality records, meteorological and physical
586
-------
data that can be obtained, thus eliminating as many
sources of error as possible. The researchers re-
viewed 40 separate reports concerning 33 watersheds.
The majority of these reports were prepared by private
consulting firms as a part of "Operation Scarlift"
which was funded by the Department of Mines and Mineral
Industries, Pennsylvania. Other sources of literature
were EPA demonstration projects, U. S. Geological Sur-
vey Professional papers and those from other federal
and state agencies.
A typical Scarlift-type report contains, first, a
description of the watershed, including information
such as area, population, land use, geology, and the
mining history of the region. Next, the definitions of
key terms (i.e., pH, acidity), and the procedures and
the results of the watershed study are given. This
section describes the general quality and quantity of
the water in the basin during the study period.
Finally, sections giving the conclusions drawn from the
study and recommendations for treatment or abatement
measures are included. Most of the reports conclude
with several appendices which include all data from the
study, various maps of the watershed (i.e., topo-
graphic, extent of mining, land use), drawings of
recommended treatment measures, and any other appro-
priate, supporting information.
General Test Site Evaluation. Since there was an ex-
tensive amount of literature to search for appropriate
test sites, which was impossible for one person to ac-
complish in a reasonable amount of time, a joint
effort was-undertaken by five project graduate research
associates. The input data needed for the models was
categorized into general information topics of
physical, climatological, streamflow, deep mine, strip
mine, spoil and refuse pile, pyrite reactivity, acid
solubility, and cost for treatment. Each topic is
further subdivided, but only into general areas. Any
possible watershed was to be first rated along these
general guidelines, using a scale from 0 to 10, with
0 being unacceptable or totally absent (missing) data
and 10 being excellent data available. This is the
initial evaluation of possible watersheds; first,
allowing elimination of totally unsuitable watersheds
due to gross deficiencies of data, and second,indi-
cating a beginning priority of watersheds to study. If
only one watershed is being considered, the first eval-
uation gives an indication of whether to continue with
the watershed or to dismiss it as an unsuitable basin.
Biemel's Master of Science thesis discusses these
evaluations in detail.^
Of the 33 mined basin investigations, the use of the
general evaluation worksheets indicated that only these
eight were worthy of further investigation: Alder Run,
Penna.; Beaver Creek, Kty.; Big Scrub Grass Creek,
Penna.; Cherry Creek and Casselman River, Md.; Elkins
Demonstration Project, W. Va.; Hillman State Park,
Penna.; Moraine State Park, Penna.; and Two Lick Creek,
Penna.
Detailed Evaluation Worksheets. An intensive study was
undertaken next to evaluate the eight chosen watersheds
more closely. After a thorough study of the acid mine
drainage models, detailed evaluation worksheets were
developed which not only account for the nine cate-
gories mentioned above, but also for the availability
of the data and importance of each data set. Follow-
ing is a brief discussion of the detailed worksheets
used in the evaluation. Biemel's thesis^ contains an
expanded version.
The detailed evaluation worksheets list a certain para-
meter or an aid in computing that parameter. For
example, the watershed area was input to the models
and a topographic map aided in determining the area.
All the required model input information was listed by
category on worksheets. Each parameter (or aid) was
assigned an importance factor (IF) ranging from '!',
data unnecessary to '4', most necessary. Some exam-
ples are: average daily dewpoint temperature '!',
total daily solar radiation '2', average ground slope
'3', and precipitation data '4'. Next,as a test site
was evaluated, a rating from '0', worst, to '10', best,
was assigned to each parameter to reflect the goodness
of its data. Guidelines were developed to increase
consistency, among the different researchers evaluating
test sites, for each parameter evaluated. A weighted
adequacy number was formed by multiplying its impor-
tance factor by its goodness value. These individual
weighted parameter values were then tallied as a grade
to be assigned to the data group. For example, cli-
matic data might have a score of 34/40. This score can
then be used to compare test sites by category data
group. This indicates the strength and weakness in
certain areas of the reports and permits fairly easy
comparison among test sites. These evaluation sheets
include reviewer's comments to qualify the data con-
ditions or add other information that might be useful
in assembling the data.
A detailed evaluation of a watershed report requires a
considerable amount of time. While a reviewer reads
the watershed report, he can also complete many
sections of the worksheets. However, the report may
indicate other sources of data for which the reviewer
must search before deciding on the suitability of a
particular watershed for modeling.
The detailed evaluation worksheets, being fourteen
pages long, were found to be unwieldly for comparing
watersheds. The results of these analyses were com-
piled onto summary sheets to allow easier comparison
among several watersheds.
Evaluation of the Data Availability. The previously
described analyses were applied to the reports avail-
able to this research project. Of the original 33
basins under study, eight were found to contain enough
information to merit a. detailed study. All of the
watersheds were given this analysis, but only the
eight indicated earlier were considered for computer
modeling. The remaining 25 basins received analyses
in an effort to evaluate the detailed worksheets and to
provide insight as to data deficiencies. Seven basic
topics were analyzed with respect to availability of
data and suitability of data included in the reports.
The following chart illustrates the frequencies of
occurrence of specific rankings given to several gener-
al data divisions required for operating the models.
These are based upon about 25 site evaluations. The
last column gives a weighted value of the data avail-
ability. Generally, scores less than 5 indicate poor
status. Following the chart is a discussion of the
problems found in the major data categories.
Water Quality Records for the streams are usually avail-
able, frequently being monitored at the mine sources or,
in some instances,by the USGS in the receiving streams.
Groundwater quality records are more frequently not
contained in the reports. If they have been considered,
they are usually satisfactory. Water quality data is
used to check the output from the acid generation
portion of the model. Therefore, a '4' would probably
result in much difficulty in making an accurate check
on the modeling output.
Deep Mine Parameters are determined from mine maps. If
maps are not contained within the report, they can
sometimes be obtained from the mining companies.
Several reports stated that maps were not available for
the watershed. Thus, difficulty would arise in assign-
587
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Chart 1.
Categories
Climatological
Data
Precipita-
tion Data
Evapotran-
spiration
Snow Melt
Parameters
Physical
Data
Watershed
Parameters
Interception
Parameters
Overland
Flow
Soil Moisture
Parameters
Streamflow and
Routing
Parameters
Streamflow
Parameters
Routing
Parameters
Water Quality
Groundwater
Quality
Parameters
Groundwater
Parameters
Deep Mine
Parameters
Physical
Parameters
Complexity of
Deep Mine
System
Acid Removal
Parameters
Acid Pro-
duction & Mine
Conditions
Refuse Pile
Inputs
Combined Refuse &
Pile Strip
Mine Model
Physical
Data
Acid Producing
Parameters
Hanking Values
0
0
0
0
0
0
0
0
0
1
5
5
7
0
0
7
1
1
0
0
0
3
1
0
1
1
0
0
0
0
0
0
0
0
1
3
1
1
1
1
5
0
2
0
2
0
0
0
0
4
2
0
0
0
0
0
0
0
0
7
0
1
1
3
0
0
1
1
1
1
1
2
4
0
2
3
0
0
0
0
0
0
1
0
3
1
I
2
5
1
1
1
1
1
1
0
6
4
5
1
4
0
0
2
0
3
1
4
0
4
1
2
0
3
1
6
3
0
3
2
0
3
2
6
3
b
0
0
4
4
7
3
9
7
1
2
1
7
4
6
2
3
4
0
8
12
2
3
3
7
6
5
1
8
13
4
6
2
I
2
0
0
0
1
4
0
6
2
2
0
7
2
4
4
2
7
10
0
5
5
4
3
1
3
2
5
1
1
3
3
2
3
6
4
3
0
2
2
1
0
8
7
6
2
0
2
6
1
4
0
4
1
2
0
3
0
1
2
3
4
0
0
0
1
0
9
0
9
1
0
0
2
1
4
0
2
5
0
0
1
0
0
0
3
2
1
0
0
0
0
10
0
6
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
Avg.
7.1
8.9
6.2
6.0
5.8
7.1
5.5
7.1
3.4
4.6
5.0
3.2
4.1
5.8
2.4
5.1
5.4
6.9
5.5
5.4
3.5
4.1
4.7
3.5
ing values to the parameters. Soil borings and geo-
logic profiles are needed for a portion of the para-
meters. Most acid production parameters and mine con-
dition parameters ^will have to be found by trial and
adjustment. Since not much information is available
on these parameters, their initial values must be esti-
mated. As more information is found or as problems
occur in acid mine drainage simulation, these para-
meters may be adjusted to improve simulation. Due to
the lack of mine maps, deep mine parameters are some-
times difficult to obtain. This is often a weak part
of the reports. A minimum rank of '5' is acceptable
here.
Refuse Pile Parameters. These are usually found
by trial. Such data as bulk porosity or pyritic con-
tent can be used to determine the acid production rate
and solubility of acid product. This information is
obtained from pile borings which frequently are missing.
A minimum rank of '3' is acceptable because something
must be known about the piles in order to make an
initial estimate of the parameter values.
Climatological Data is usually obtained from the
National Weather Service. When the gaging stations
are not in the watershed, particularly in mountainous
regions, problems with precipitation records can be
substantial. Sometimes watershed precipitation can be
synthesized from nearby, outside the basin records.
Evaporation data has similar problems plus it may be
missing for the winter season at some stations. Of the
three subtopics for climato]_ogical data (precipitation,
evapotranspiration, and snowmelt), precipitation data
is usually the most complete,while availability of
snowmelt parameters is the most uncertain. The hydro-
logic model can be run without snowmelt data, but simu-
lation improves with snowmelt. In order to run the
model, the overall ranking for climatological data
should be at least '5'. This value is frequently
attained without much difficulty.
Physical Data Parameters are partially obtained from
USGS topographic maps, aerial photographs, and land use
maps, which are usually adequately included in the
reports. Soil borings, geologic profiles, and well
logs needed to assess soil moisture parameters are
frequently not included. Watershed parameters and
overland flow parameters are the most complete, while
soil moisture parameters are the least complete. On
the whole, physical data is usually good enough for
the models. A value of '5' is the minimum acceptable
for physical data.
Streamflow and Routing Parameters are obtained from
USGS records and rating curves for the watershed. If
a USGS station is not located on the stream, then
Streamflow data will probably be incomplete. However,
having a USGS station does not necessarily guarantee
that there will be sufficient data. The frequency
chart above shows that in most cases, either Streamflow
data is satisfactory ('5' or more), or it is totally
unacceptable ('0' ranking). Streamflow records are a
high-priority data set for the hydrologic simulation
portion of the models.
Refuse Pile and Strip Mine Parameter information can be
found from borings, topographic maps, and aerial photo-
graphs. From the soil borings the coal type can be
determined which will be used to determine the pyritic
content. This then can be used to find the acid solu-
bility and pyrite reactivity. Some knowledge of the
chemistry involved here is desirable. Discussions by
Clark et al.1 will give a good background in this acid
chemistry. The parameters for refuse pile and strip
mine modeling are often a weak part of the reports.
Since many of the values for refuse pile and strip mine
588
-------
parameters must be found by trial and adjustment, a
ranking of 'A' is required.
Evaluation Conclusions. Many differences occurred in
the evaluating and ranking of the modeling parameters
for the different watersheds. What one evaluator con-
sidered good data on a subject, another considered to
be poor data. Even when the evaluators agreed on the
quality of the data available, often the ranking
values were different. It was therefore necessary to
specify the requirements needed for the ranking by
compiling a list of definitions for the model para-
meters and the means and considerations made in each
evaluation. These definitions are in Biemel's thesis.^
Differences, undoubtedly, will continue to exist due
to personal biases; however, these definitions should
minimize evaluation discrepancies.
The minimum rankings assigned to the various topics are
intended to indicate the lowest level at which infor-
mation pertaining to the particular topic is accept-
able for computer modeling. In most cases the
rankings should and will be higher than these minimums.
Also, if all subtopic rankings are satisfactory ex-
cept for one, then probably enough work can be done on
the unsatisfactory subtopic so that a run can be made.
Throughout the evaluation process,comments concerning
where specific pieces of data can be found are neces-
sary. These comments are based on information in the
report about what agency collected certain data and
where the data is stored. Undoubtedly, all the data
needed for both hydrologic and acid mine drainage
simulation will not be included in the report, thus
these comments serve to remind the researcher where
the data can be found. Experience shows that tele-
phone calls and trips to the data holding agency will
probably be necessary.
As previously mentioned, eight of the 33 watersheds
were deemed worthy of.consideration beyond the initial,
general evaluation. The evaluations were weighted
toward hydrologic and acid mine drainage simulation.
If the report of a studied watershed indicated that a
particular data set required for hydrologic or acid
production simulation was unsuitable or absent, then
that report was immediately rejected as having un-
suitable data. For example, daily recorded average
streamflow is required for hydrologic simulation. In
many cases, streamflow measurements were made once per
month, or even with less frequency and this lack of
acceptable data was cause for immediate rejection of
a given basin.
Another area of interest in the watershed review pro-
cedure was the amount of reclamation, treatment, or
abatement cost information contained in the reports.
This information, used in the Basin Optimization Model
(another model developed in this research to aid in
pollution abatement) for determining optimal acid re-
duction decisions, must be kept up to date as costs of
construction, operation, and maintenance increase.
While cost information was not emphasized throughout
the reviewing, space for comments on the availability
and amount of cost data in each report was provided
on the worksheets. This research group found that
approximately 75% of the reports contained cost infor-
mation which the reviewer felt was detailed enough to
aid in assessing values for acid controlling measures.
Chosen Study Watersheds. From the evaluation de-
scribed above, three of the possible eight watersheds
appeared most suitable for hydrologic and acid mine
drainage simulation. Two of these watersheds are the
Roaring Creek basin and the Grassy Run basin near the
town of Elkins, West Virginia. These basins border
each other and were studied by the U. S. EPA as well as
other governmental agencies. The Roaring Creek basin
is large (75.63 km2, 29.2 mi2) while the Grassy Run
basin is comparatively small (7.41 km2, 2.86 mi2). The
watersheds have the three acid producing mechanisms;
that is, strip mines, deep mines, and refuse piles. A
complication with these two watersheds is an under-
ground mine that transfers about 12,000 m-Vd (3500 ac-
ft/yr)of water from the Roaring Creek basin to the
Grassy Run basin.
The third basin chosen is the Cane Branch sub-basin of
Beaver Creek in south-central Kentucky. This sub-
basin, along with two others on Beaver Creek, were the
subjects of an extensive study from 1956 through 1961
under the United States Geological Survey and other
state and federal agencies. This is a small sub-basin
(1.74 km2, 0.67 mi2) containing mainly strip mines and
refuse piles with two drift mines.
Intensive effort is now underway on applying the unit
source models to these basins. Even those selected as
the most promising of the group have major data de-
ficiencies. However, data synthesis techniques are
being developed in attempt to salvage these sites for
modeling.
SUMMARY, CONCLUSIONS AND RECOMMENDATIONS
Summary. Application of Acid Mine Drainage Unit
Source Models requires large amounts of input data.
This research group developed and tested a method of
systematic watershed evaluation when considering
applying these computer models. Many government
sponsored mined watershed studies were reviewed using
this evaluation procedure and from these reviews an
analysis was made of general data deficiencies in the
reports. Of the 33 watershed reports reviewed, three
were chosen for modeling; Roaring Creek basin and
Grassy Run basin near Elkins, West Virginia, and the
Cane Branch basin of Beaver Creek, Kentucky.
Conclusions. The major conclusion possible from this
study is that the majority of Scarlift-type reports
performed on mined watersheds do not result in suf-
ficient collection and publication of data to permit
straight-forward hydrologic and acid mine drainage
modeling. In general, the reports are strong in water
quality data and weak in streamflow data. The models
need daily average streamflow as input data, but
streamflow measurements were often made no more than
twice monthly, far too infrequent for hydrologic
modeling. Water quality data, because it is only used
for comparing simulated acid loads to recorded acid
loads, need not be collected daily, although daily
quality data would be ideal.
Daily precipitation and evaporation data are crucial
for operating the model. Some of the studies recorded
precipitation in the watershed while others did not.
Evaporation data was not collected on the site in any
case. For accurate simulation using the models, the
precipitation data should be collected on the study
site, and, if possible, the evaporation should be
measured on the site using Class A pans.
A major weakness found in the reports is the lack of
usable data for mining parameters; that is, deep mine
parameters, refuse pile inputs, and combined refuse
pile-strip mine parameters. Information such as void
ratio of the strata, minimum flow rate for acid removal
by flooding, oxygen concentration in the mines, tem-
perature in the mines, gas diffusivity, acid production
rates, solubility of acid products and other parameters
are rarely included in coal mine drainage basin re-
ports. Some of these parameters can be evaluated from
other data (i.e., pyrite reactivity, soil borings);
however, even these ancillary pieces of data are often
589
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absent, forcing the reviewer to either search further
for the data, go to the watershed and directly collect
the data, synthesize or estimate the data, or complete-
ly abandon the watershed for acid production simula-
tion.
Recommendations. Six areas of large data deficiencies
were found to be common to the majority of mined water-
shed reports which were reviewed. The first three
recommendations given below will aid with the applica-
tion of the hydrologic model by supplying required in-
put data for adjusting the model to a particular study
watershed. The final three recommendations, if fol-
lowed, are designed to collect the data necessary to
run the acid production model and to verify its output.
The six recommended steps for data collection are:
(1) Record at least three years of daily streamflow,
(2) Install a recording precipitation gage in the
watershed during the period of streamflow gaging,
(3) Install a Class A pan for evaporation in the
watershed during the streamflow monitoring period,
(4) Make accurately documented soil borings in spoil
piles, and unmined areas within the watershed,
(5) Determine pyrite content of refuse piles and strip
mines, and
(6) Record water quality at the watershed outlet and
at major acid pollution sources.
The hydrologic portion of the model requires a minimum
of three years of daily, average streamflow data in
order to self-adjust to conditions of the watersheds.
This data is essential, first, to compare simulated
streamflow to recorded streamflow for testing the
accuracy of simulated flow, and secondly, to internally
adjust certain parameters to improve streamflow simu-
lation when a comparison of simulated and recorded
streamflow indicates unacceptable differences between
them. Thus, daily streamflow gaging is recommended for
any future watershed monitoring projects.
Due to the dependence of the hydrologic model on large
quantities of input data, and because the accuracy of
this data is of utmost importance, a recording, year-
round precipitation gage in the watershed is of prime
importance. This gage, when properly maintained and
used for the entire stream monitoring period, will pro-
vide an accurate account of all water entering the
basin as precipitation, thereby removing the problems
of heavy localized rainfall at a precipitation gage
outside the watershed while the watershed receives no
precipitation, or vice versa.
Class A pan evaporation data, another essential data
group, should be collected on the watershed throughout
the duration of streamflow gaging. Daily, year-round
evaporation data on the watershed removes the need to
search for suitable nearby evaporation data stations
and it assures that the evaporation data is representa-
tive of that in the watershed.
Accurately documented soil borings are important so as
to assure precise description of certain hydrologic in-
puts as well as to aid in determining acid production
parameters. These borings should record the types of
soil encountered, the depths to and thicknesses of the
different soil types, the level at which groundwater is
reached, and also other data, such as permeability,
porosity, or void ratio, which will assist in esta-
blishing input parameters.
Pyrite content of refuse piles and strip mines provides
the means of determining several acid—production-re-
lated parameters. Actual on-site pyritic content data,
as opposed to estimated values made in the absence of
field data, gives the most accurate acid mine drainage
simulation, thus making collection of pyritic content
data important.
Finally, a record of the quantity and quality of acid
mine discharge from major acid pollution sources into
the receiving stream is of value for comparing the
simulated acid loads with actual field data. The deep
mine discharges, while not subject to the large fluc-
tuations encountered with surface phenomena, do have
long-term variations which the computer simulation
must reflect. The quantity and quality of strip mine
and refuse pile drainage varies much more quickly than
that of deep mines because strip mine and refuse pile
drainage depends largely on surface runoff, a response
occurring during and immediately after precipitation.
The water quantity and quality from major acid pro-
duction sources, as well as the water quality at the
basin outlet, should be monitored at a minimum of once
every second week, more frequently when feasible.
Several times during the period of data collection,
the quantity and quality of runoff from strip mines
and refuse piles should be monitored immediately
following precipitation in order to check the simu-
lated values against the actual data.
In closing, it may be said that any good mine drainage
models (present or future) for acid mine drainage are
going to need the aforementioned types of data to
verify and calibrate them. Therefore, it is highly
recommended that future demonstration projects or
monitoring endeavors have their data collection schemes
consider the parameters discussed herein before the
data collection gets too far along to permit the
proper acquisition of the crucial pieces.
REFERENCES
1. Clark, G. M., Ricca, V. T. , Shumate, K. S., and
Smith, E. E., Resource Allocation to Optimize
Mining Pollution Control, Office of Research and
Monitoring, United States Environmental Pro-
tection Agency, Contract #68-01-0724, final
report, June, 1975.
2. Clark, G. M., Ricca, V. X., and Smith, E. E.,
"Predictive and Pollution Abatement Model for Mine
Drainage", United States Environmental Protection
Agency, Mining Pollution Control Branch, IWTRL,
NERC, Cincinnati, Ohio, Eugene Harris, Project
Officer, Contract #68-03-2008, 1974-76.
3. Ricca, V. T., The Ohio State University Version
of the Stanford Streamflow Simulation Model,
Office of Water Resources Research, U. S. Depart-
ment of the Interior, Project #B-005-OHIO and B-
019-OHIO, 1972.
4. Biemel, G. C., Watershed Evaluation and Data Needs
for Hydrologic and Acid Mine Drainage Modeling,
Master of Science Thesis, Department of Civil
Engineering, The Ohio State University, 1975.
ACKNOWLEDGEMENTS
The author would like to express his appreciation of the
efforts of the many individuals who have assisted in
this project. Acknowledgement is given to Ron Hill and
Gene Harris, project officers, Mining Pollution Control
Branch, IWTRL, NERC, U.S.EPA, Cincinnati, Oh., for their
cooperation in furnishing the numerous reports and con-
sultations needed to accomplish this study. Gratitude
is expressed to the U.S.EPA for their support through
the above two referenced projects. Most of the work
accomplished herein was done by OSU, Dept. of Civil
Engineers Graduate Research Associates George Biemel,
James Bonta, Michael Hemmerich, Gary Lockwood, Ronald
Schultz, and William Wallace. Special thanks is given
to project co-researchers, Professors Gordon Clark and
Edwin Smith. Special thanks are extended to Joan A.
Orosz for her spendid job in typing this manuscript.
590
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A MODELING TECHNIQUE FOR OPEN DUMP BURNING
Marvin Rosenstein
Systems Analysis Branch
U.S. Environmental Protection Agency (EPA)
Region I, Boston, Massachusetts
Valentine J. Descamps
Regional Meteorologist*
U.S. Environmental Protection Agency (EPA)
Region I, Boston, Massachusetts
ABSTRACT
This paper describes a modeling technique for estimat-
ing the impact of open dump burning upon ambient par-
ticulate concentrations. The technique is based upon
two major assumptions. First, the entire area of the
dump is not fired at the same time. Rather, it is
assumed that the dump burns "progressively" with a con-
stant rate at which the fire spreads through the dump.
Second, once a portion of the dump is fired, the total
burn time for that portion consists of an initial "hot
phase" followed by a longer "smolder phase". Plume
rise is based upon Briggs' formulations and diffusion
calculations are performed by the EPA point source
model PTDIS. The technique is crude and no attempt
has been made to validate it with field data. Limita-
tions of the technique and suggestions for improving
it are discussed.
BACKGROUND
Primarily for economic reasons, several New England
states are permitting towns, particularly small rural
communities, to use open dump burning for the disposal
of community solid waste under variance procedures
until more environmentally acceptable dis-
posal methods are implemented. Because of their con-
cern for the maintenance of adequate air quality, the
Department of Environmental Protection of the State of
Maine requested assistance from us in developing a
technique for estimating the impact of open dump burn-
ing upon ambient particulate levels. (Note that EPA
regards open dump burning as hazardous to air quality,
public health, and water quality and opposes it as a
permanent solution to the disposal of solid waste.)
Discussion with other EPA personnel in the fields of
diffusion modeling and solid waste disposal, as well as
a literature search, revealed scant information upon
which we could base the development of a technique.
Also, the press of operational duties, which leave
little time for development activities, dictated that
the technique should utilize existing diffusion and
plume rise formulations that could be rapidly and con^
veniently applied. It was therefore recognized at the
outset that the technique would of necessity be crude
and most likely conservative in nature, such that pre-
dicted concentrations could be regarded as upper bounds.
THE NON-PROGRESSIVE TECHNIQUE
Our first attempt at a modeling technique involved what
we call a "non-progressive" burn. Although we later
discarded this technique, we will describe it in some
detail because many of the features and assumptions of
this technique carry over to our final "progressive"
model. Also, we feel that the idea of a progressive
burn is of paramount importance and can only be fully
appreciated when viewed against the background of a
non-progressive burn.
In the non-progressive approach, we assume that the
entire area of the dump is set on fire at the same
time. Gerstle and Kemnitzl, based on laboratory sim-
ulations of the open burning of municipal refuse,
suggest a total burn time of 12 hours consisting of
an initial "hot phase" of duration 1 to 1^ hours fol-
lowed by a "smolder phase" for the remainder of the
12 hours. (In future sections, subscript A will always
refer to the hot phase and subscript B will always re-
fer to the smolder phase). Approximately 90% of the
refuse burns rapidly during the hot phase, and the re-
mainder burns slowly during the smolder phase. After
consultation with regional personnel in the field of
solid waste disposal (hereafter referred to as regional
personnel) we settled on a (1 hour - 75%) hot phase and
an (11 hour 25%) smolder phase. We assumed that the
refuse burns fairly evenly with respect to time during
each of the two phases. Gerstle and Kemnitz also
suggest an emission factor of 16 pounds of particulates
per ton of refuse burned. The State of Maine sugges-
ted that each person generates 20 pounds of refuse per
week. With these figures one can easily calculate par-
ticulate emission rates for the first hour and for each
of the next eleven hours. Populations of 1000, 2000 and
3000 were considered.
The hourly concentrations for each of the twelve hours
were calculated as follows. First, plume rise was
calculated using Briggs' (2,3,4) formulations. The
buoyancy flux, F, was calculated via the equation
below.
F(m4sec-3)= KQH, K= (3. 7) • (10-5)m4Cal-1sec-2 (1)
The heat emission rate Q,,(cal sec- ) was easily cal-
culated for each of the twelve hours from the computed
pounds of refuse burned per hour and the heat factor
of 4675 Btu per pound of refuse burned. This heat
factor was extracted from LoweS who states that it is
for municipal waste that has had some separation treat-
ment for use in a power boiler. A lower value seems
more appropriate to unsegregated residential/commercial
waste that may be dampened by exposure to a generally
moist climate. After consultation with regional per-
sonnel we decided to run the technique for an addi-
tional case that used a heat factor of 2000 Btu.
Diffusion calculations, using the emission rates and
olume rises as determined above, were performed by the
EPA point source model PTDIS developed by Turner& and
based on the steady-state Gaussian formulations as
detailed in Turner'. This model computes hourly center-
line concentrations at specified (by the user) dis-
tances downwind of an isolated point source in rela-
tively flat and open terrain and for a rural atmos-
phere. Meteorological conditions consisting of sta-
bility class, wind speed and mixing height are input
by the user. We used seven receptor distances from
0.1 to 10.0 km and four meteorological conditons of
stability classes B and F combined with wind speeds of
1.0 and 5.0 m sec • Constraints on vertical disper-
sion via a mixing height were not included. For each
combination of meteorology, population and heat factor
only two diffusion calculations are necessary, i.e.,
one for the hot burn hour that yields an hourly con-
centration of XA and one for the smolder burn type
*0n assignment from ARL/NOAA Department of Commerce
591
-------
of hour that yields an hourly concentration of XB (the
same value for each of the eleven smolder hours). The
24-hour concentration is therefore calculated through
the relationship presented below.
X = XA +
(2)
24
Before presenting some results for the non-progressive
technique, several conservative assumptions should be
pointed out since they will also apply to the progres-
sive model developed in the next section. First, a
given stability-wind speed condition persists for the
entire burn time. Second, only centerline concentra-
tions are calculated. Therefore, a constant wind
direction over the entire burn time is assumed. Third,
the dimensions of the dump are small enough such that
the dump can be considered a point source instead of
an area source. A line source model was considered
for the technique but was discarded after trial calcu-
lations which invoked assumptions concerning the di-
mensions of the dump produced results essentially iden-
tical to those obtained with the point source model.
Tables 1 and 2 present some results for the non-pro-
gressive technique for the wind speed of 1.0 m sec~l.
The effect of reducing the heat factor from 4675 Btu to
2000 Btu is dramatic with maximum concentrations in-
creased by a factor of two or more due to the smaller
plume rises. For the 5.0 m sec case, the overall
maximum concentrations were 47 and 93 ug m~3 for the
4675 and 2000 Btu heat factors respectively. The
large increase in maximum concentration from the 1.0
m sec~^case to the 5.0m sec~^case indicates the dom-
inance of the effect of wind speed on plume rise over
that of the wind speed on dilution. There is some
tendency for maximum concentration to increase with
increasing population (particularly for the 5.0 m sec"*
case which is not shown) although this is not always
the case because of the competing effects of increas-
ing emissions versus increasing plume rises.
Table 1
Final Plume Rise (m) during (hot phase/smolder phase)
for non-progressive technique and wind speed of 1.0
Population
Stability B
4675 Btu
2000 Btu
Stability F
4675 Btu
2000 Btu
1000
896/78
528/41
129/40
97/30
2000
1359/131
799/68
162/50
122/38
3000
1735/178
1020/93
185/58
140/44
Table 2
Maximum 24-Hour Concentrations (ug m~3) for non-
progressive techniques and wind speed of 1.0 m sec~l
Population
Stability B
4675 Btu
2000 Btu
Stability F
4675 Btu
2000 Btu
1000
5
11
9
17
2000
4
13
9
21
3000
10
21
THE PROGRESSIVE TECHNIQUE
Discussion of the non-progressive technique with the
State of Maine and regional personnel indicated several
improvements could be made. Particularly alarming were
some of the very large plume rises as given in Table 1.
Field observations by Maine indicated that such large
plume rises do not occur. These same field observa-
tions also indicated that the total burn time is more
likely to be on the order of twenty-four hours and
that an entire dump is not normally fired at once.
Instead, the fire normally spreads through the dump
at a gradual rate such that it takes hours for the
entire dump to be fired. This consideration lead to
the development of the progressive model.
In the progressive technique, it is assumed that the
dump is fired progressively at a constant rate (which
can be varied from case to case) such that the fire
gradually spreads through the dump. The rate of
spreading should depend on prevailing meteorological
conditions but this effect is ignored in the cases to
follow. Once a portion of the dump has been fired, the
assumption of a hot phase-smolder phase regime applies
in the same way as for the non-progressive technique.
As an example, refer to Table 3. Here we have assumed
a total burn time of twelve hours. In the first hour,
1/6 of the dump is fired and part of this portion of
the dump is consumed in a hot phase burn. The remain-
ing part of this portion of the dump smolders over the
following six hours (hours 2 through 7). In the second
hour, another 1/6 of the dump is fired. The smolder
phase now lasts for hours 3 through 8. And on it
goes. It takes a total of six hours for the entire
dump to be fired. Each block in Table 3 gives the
partial contributions of each 1/6 portion of the dump
to the total hourly concentrations listed at the bot-
tom of the table. As with the non-progressive tech-
nique, only two basic diffusion calculations need to
be done. In contrast to equation (2) for the non-
progressive twelve hour burn, the 24-hour average con-
centration is calculated via the equation below.
X =6XA+(6)(6)Xs= XA+6XB
24 4
(3)
The technique can be generalized (for total burn times
of 24 hours or less) as follows. Let Y equal the num-
ber of hours it takes for the fire to spread through
the entire dump, i.e., 1/Y of the dump is fired in
each of the first Y hours. Let S equal the number of
hours that each 1/Y portion of the dump smolders. Then
the 24-hour average concentration is calculated by the
equation below.
„
xi
24
(Y)XA+(Y) (S)XB
2%
Therefore, for a 24-hour burn with a hot phase d iration
of 12 hours, and a 12 hour smolder duration, we nave
12XA+(12)(12)XB
24
(5)
The progressive technique can also be used for total
burn times of greater than 24 hours, but the general
relationship expressed in equation (4) will not hold.
But equations similar to equations (3) and (5) can
still be derived from tables constructed like Table 3.
592
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Table 3
Twelve Hour Progessive Burn Sequence, Hot Phase Dura-
tion = 6 hours, Smolder Phase Duration = 6 hours. See
discussion in text for explanation.
HOUR
234567
9 10 11 12
HOT BURN
SLOW BURN
DUE TO FIRE
IN HOUR It
1
2
3
4
5
6
TOTAL
HOURLY
CONCENTRATION
Xi, 1=1, 12
XA
-A
3
xj>
Xj
XB
>-B
XB
XB
XB
XB
XB
>XB
XB
XB
XB
XB
XB
iXB
XB
XB
XB
XB
4X
XB
"B
XB
3XB
XB
XB
2XB
XB
XB
The particulate and heat emission rates, Qp and Q$
that are required for the diffusion and plume rise cal-
culations can be calculated from the following equa-
tions :
00 (S)
QHB=-25(
(6)
(7)
= (population) (Ibs refuse) (Ibs particulates) (8)
person pound of refuse
= (population) (Ibs refuse) (_
person
Btu
)
pounds of refuse
The plume rise calculations and diffusion calculations
are performed in the same way that they were for the
non-progressive technique. The same conservative
assumptions that were discussed in the section on the
technique apply here as well. Each portion of the
dump that is fired is considered a point source and
separation distances between the various portions are
ignored. Meteorology is constant for the duration of
the burn.
Three cases using the progressive technique were in-
vestigated. Table 4 lists the assumed values for the
operating parameters for each case. Equation (3)
applies in case 1, while equation (5) applies in cases
2 and 3. Receptor distances of 0.1, 0.25, 0.4.0.7,1.0,
1.5, 2.0, 2.5 and 3.0 km were used. A representative
range of up to 22 stability-wind speed combinations
were investigated.
Table 5 lists some of the calculated plume rises for
the three cases for a wind speed of 1.0 m sec~l. Table
5 is constructed in the same fashion as Table 1 to
enhance comparisons between the non-progressive and
progressive techniques. The plume rises are purposely
listed for the 1.0 m sec"1 case for two reasons. First,
the inverse relationship between plume rise and wind
speed implies that the listed plume rises should be
representative of the maximum rises that can be expec-
ted. Second, high wind speeds are not relevant because
of the danger of spreading fire to areas surrounding
the dump. The progressive cases yield plume rises that
are much less than those of the non-progressive cases.
The most realistic plume rises appear to be those for
progressive case number 2 which yields plume rises
generally less than 200 m.
Table 5
Final Plume Rise (m) during (hot phase/smolder phase)
for progressive techniaue and wind speed of 1.0m see"
Population
Stabilities
Case 1
Case 2
Case 3
Stability E
Case 1
Case 2
Case 3
1000
(A-D)
223/26
87/6
164/11
78/30
51/16
68/21
2000
374/43
146/10
277/19
98/37
64/20
86/26
3000
487/58
198/14
375/26
112/43
74/22
98/30
Table 6 presents a selection of predicted 24-hour con-
centrations under neutral (D) stability and wind
speeds of 1.0 and 5.0 m sec~l for the three progres-
sive cases. Results for these meteorological condi-
tions were chosen for presentation because of the
prevalence of these meteorological conditions in many
sections of New England and because only neutral
stability can persist for 24 hours. Neutral stability
also generally yielded the highest predicted concentra-
tions. As previously discussed, observations in the
field by the State of Maine personnel indicate cases
2 and 3 to have the most realistic operating parameter.
It is for these cases that the technique indicates a
potentially serious threat to the National Ambient Air
Quality Standards of 260 ug m-3 (primary) and 150 ug
m~3 (secondary) for 24-hour average concentrations of
particulates. Case 2 yields the most realistic esti-
mates of plume rise and the highest predicted con-
centrations.
DISCUSSION OF PROGRESSIVE TECHNIQUE
Thus far, we have not been able to obtain sufficient
data with which we could attempt to validate the
technique. However, it is encouraging that the tech-
nique is able to produce plume heights that seem
593
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Table 4
Assumed Operating Parameters for Three Progressive Burns
Total Burn Time Hot Phase Smoulder Phase
(Hours) Duration (hrs) Duration (hrs)
Case 1
Case 2
Case 3
12
24
24
6
12
12
6
12
12
Heating Value
Per Ib waste
(Btu/lb)
3500
2000
4675
Waste Per Person
(Ibs/person/week)
20
20
20
Emission Factor
Ibs of partic-
ulate per ton
of waste(Ibs/T)
16
16
16
Table 6
Predicted 24-Hour Average Concentrations (ug m~3) for progressive techniques, neutral (D) stability, wind
speeds of 1.0 and 5.0 m sec , (X = concentration less than State of Maine Standard of 100 ug m~^) .
Case 1
Case 2
Case 3
1000
Wind
Speed
m/sec 0.1 0.25 0.4 0.7 1.0
Town Size in Population Count
2000
Distance Km
X
192
X
X
786 288 138
366 115 X
X 186 114
313 X X
X
X
X
X
X
X
X
X
0.1 0.25 0.4 0.7 1.0
X X
128 X
X
X
X 132 138 X
504 127 X X
348 426 240 102 X
647 139 X XX
3000
0.1 0.25 0.4 0.7 1.0
X X
X 108
X
X
X X 108
576 180 X
X 432 300 144 X
889 201 100 X X
reasonable on the basis of rural sightings of dump
plumes. As for predicted concentrations, without
sufficient field data to compare them with, about all
we can say is that they do not seem implausible.
The technique has two important advantages. First, it
is relatively easy to use, being based upon familiar
and readily available diffusion and plume rise form-
ulations. Secondly, the technique can be easily tuned
via the values that must be assumed for the following
operating parameters: total burning time, hot phase
duration, smolder phase duration, fraction of refuse
consumed in each phase (values other than 75% for the
hot phase and 25% for the smolder phase may be approp-
riate), pounds of refuse generated per person, pounds
of particulates generated per ton of refuse, and the
heating factor (Btu per pound of refuse).
As previously discussed, the technique as it presently
exists has several limitations that may introduce a
very high degree of conservatism into the predictions.
The very bad assumption of constant meteorology as
well as the lesser evil of using point sources instead
of areas sources could both be remedied through suit-
able computer programming. The virtual point source
concept could be introduced to handle area source
configurations. The technique could also be changed
so as to allow meteorological input (stability, wind
speed and wind direction) that varies from hour to
hour and receptor locations that vary in both horizon-
tal directions. Unfortunately, as discussed in the
background section, we did not, nor are we likely to
ever, have the time to carry out the above suggestions.
In conclusion, we
technique that is
ing the impact of
ticulate levels.
of future efforts
validity.
believe that we have developed a
potentially very useful for estimat-
open dump burning upon ambient par-
Furthermore, we believe it is worthy
to both improve it and establish its
REFERENCES
(1) Gerstle, R.W. and D.A. Kemnitz, 1967; Atmospheric
Emissions from Open Burning, J. Air Pollution Control
Association, 17 P 324
(2) Briggs, G.A., 1969; Plume Rise USAEC Critical
Review Series TID25075, National Tech. Information
Service, Springfield, Virginia 22151
(3) Briggs, G.A., 1971; Some Recent Analyses of Plume
Rise Observation, pp 1029-1032, in Proceedings of the
Second International Clean Air Congress, edited by
H.M. Englund and W.T. Berry, Academic Press, New York
(4) Briggs, G.A., 1972; Discussion on Chimney Plumes
in Neutral and Stable Surroundings, Atmospheric
Environment, 6 P 507
(5) Lowe, R.A., 1973; Energy Reocvery from Waste, EPA
Publication SW-36d.ii, 24 pp, Available from Super-
intendent of Documents, U.S. Government Pringing Office
(6) Turner, D.B. Draft Copy PTDIS User's Manual, EPA
Research Triangle Park, North Carolina
(7) Turner, D.B., 1970: Workbook of Atmospheric
Dispersion Estimates, EPA Publication AP-26, 84 pp.
594
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DEVELOPMENT AND USE OF A FIXED CHARGE PROGRAMMING MODEL
FOR REGIONAL SOLID WASTE PLANNING*
Warren Walker
The New York City-Rand Institute
Michael Aquilina
Champlin Petroleum Company
Dennis Schur
U.S. Environmental Protection Agency
Abstract
The problem of deciding on the number, type, size
and location of the solid waste disposal facilities to
operate in a region, and allocating the region's
wastes to these facilities is formulated as a fixed
charge problem. A system for solving this problem,
developed for the U.S. Environmental Protection Agency
is described. The system includes a heuristic al-
gorithm for the fixed charge problem. A description
is given of a hypothetical application of the system
in the Seattle-King County region of the State of
Washington.
Introduction
Solid waste management is a crucial problem
facing every municipality. The average person gen-
erates over five pounds of material per day for which
he no longer has any use and, therefore, discards.
Among the services supplied by most -municipal gov-
ernments is the collection, transport, and disposal
of such solid wastes.
The collection operation consists of the removal
of solid waste (usually in a truck) from its point of
generation. It is then transported to an intermediate
facility or an ultimate disposal site. At an inter-
mediate facility it may undergo some processing (such
as incineration, resource recovery, biochemical ox-
idation, or compaction) that leaves a residue of
waste that must still be disposed. Most ultimate dis-
posal sites are sanitary landfills.
Prior to their explosive growth, in the 1950's and
1960's, most cities had no problem disposing of all
their solid waste within their own borders. However,
as available land begins to disappear and sites begin
to be used up, cities are beginning to look outside
their own boundaries for disposal sites. In addition
technological processes for waste reduction and re-
cycling are too expensive and inefficient for single
municipalities to consider using. But, by taking ad-
vantage of economies of scale, such facilities can be
built and operated for use by several municipalities
with a net cost saving to the region as a whole.
Therefore, an increasing number of cities, towns,
and villages are joining together to perform solid
waste planning for an entire region. For example, in
New York State, 35 percent of the State's 1500 muni-
cipalities use solid waste disposal facilities op-
erated in cooperation with other units of local gov-
ernment .
Several recent studies have dealt with the mini-
mization of transportation and disposal costs in re-
gional solid waste management systems.
*This paper was prepared for presentation at the 46th
joint meeting of the Operations Research Society of
America and the Institute of Management Sciences held
in San Juan, Puerto Rico, October 16-18, 1974.
Anderson developed an algorithm for determining the
optimum solution to a regional disposal problem, but
his model assumes that all costs are linear. Marks
and Liebman-' treat the more limited problem of deter-
mining the locations of transfer stations and include
the fixed costs of building and operating such facil-
ities in their formulation. The special structure
of the resulting problem (a capacitated transshipment
problem) allows them to obtain optimal solutions using
a. minimum cost—maximum flow network algorithm.
In6, Morse and Roth formulate the problem without
capacity constraints and attempt to solve it by com-
plete enumeration, comparing the costs resulting from
each of the 23-1 solutions for a given set of j pos-
sible disposal facility locations. Kuhner and
Harrington solve a similar problem using the branch-
and-bound algorithm that is part of IBM's MPSX-MIP
program^.
The formulation that Skelly developed provides the
basis for the model described in this paper. To solve
his problem he used an early version of the computer
program we describe.
In this paper we develop an integer programming
model for selecting from potential and existing sites
those that should be developed, at what capacity and
how the wastes should be routed through them so that
the total transport, processing, and disposal costs
for the entire region are minimized. Fixed charge
cost functions are included for all facilities, as is
a consideration of the time-staging of the construction
of facilities.
The output from the model provides information on:
What types of disposal facilities should be
built?
When should they be built?
What should be their capacity?
How much of its solid waste should each
community ship to each of the disposal
facilities?
What will be the cost of the solution (both
fixed cost and cost per tonl?
It is what Marks and Liebman-' refer to as a capaci-
tated transshipment facility location problem, with
fixed and variable costs associated with the use of
each facility and variable haul costs. A heuristic
* Figures in superscript refer to bibliographical
references listed at the end of this paper.
** Transfer stations are intermediate facilities where
collection vehicles transfer their loads to larger
vehicles, more suited for long-haul transportation.
The larger vehicles transport the waste to the disposal
site.
595
-------
algorithm has been developed that produces solutions
that are almost always optimal. This algorithm has
been embedded in a computer program tnat includes a
routine for generating the problem matrix and a. re^
port generator for displaying the results. The pro^
gram has been given the name "SWAM" for Solid Waste
Allocation Model.
In the following sections we describe the math.^
ematical model, the heuristic algorithms -used to
solve it, and the data requirements of the SWAM model.
A sample application of the SWAM -model using data
from the Seattle region where the model was "used in
d regional planning effort during 19J3 will be pre-
sented at the Conference but cannot Be included with.
the text of this paper due to the excessive space re^
quirements.
The Mathematical Model
In order to simplify the problem and make it
computationally feasible to solve, we assume that all
the refuse of a community is generated at d single
point, its center of mass, and, therefore, that all
waste transported from the community- travels from its
center of mass. This permits TIS to separate the
transport and disposal subsystems from the collection
subsystem.
We assume that there are K potential disposal
sites being considered, J intermediate facilities,
K-J final disposal sites, and that there are N com-
munities .
The general problem formulation for the one-
period (say, one week) static model is:
K N K J K
Minimize v v c-,x., + £ Y C.x + y
22 ik ik L •*- jk jk L F $
k=l i=l k=j+l j=l k-1
(k=l,2,
where:
C is the cost of transporting and proces-
1 sing one ton of waste from source i at
disposal facility k ($/ton);
C is the cost of transporting and processing
one ton of waste from intermediate facility
j at final facility k ($/ton);
F is the fixed cost associated with opening
and operating disposal facility K ($/week) ;
W. is the quantity of waste generated at
source i (tons/week);
A. is the capacity of intermediate site j
-1 Ctons/week) ,-
B is the weekly capacity of final disposal
site k (B depends upon the number of
k
trucks the site can handle, and, since
landfill sites get filled up, the length
of time it is desired to operate the site)
and;
P. is the proportion of the weight of the
waste that remains after being processed
at intermediate site j.
The decision variables are:
Subject to
K
2
k=l
Xik
.
x (1=1,2,...,N; k*l,2,...,K): the amount of
community i's waste that is to be sent to
disposal facility k; and
x.k Cj=l,2,...,J; k=J+l,...,K) : the amount of
waste that is to be transported from in-
termediate disposal facility j to final
disposal facility k-
The Constraints
We discuss each of the constraining equations in
turn.
N
2
J
2 x.
Constraint (2.2) requires that all of the solid
waste generated at a source during one week be
transported to some disposal facility during the
same week.
P.
D
N
2
N
2 x..
2 *-v
. , ik
K
2 a
k=J+l
J
+ 2
= ° if yk ' °
1 if y > 0
K.
= 0 (j=l,...,J)
-y, = 0 Cj=l,-..,JJ
Constraint C2.3) recognizes the limited processing
capacities of incinerators and transfer stations.
If this constraint is omitted, the model can be
used to determine a desirable capacity for a pro-
posed facility.
Constraint (2.4) recognizes the limited capacity
of a landfill site. Its weekly capacity depends
on its ultimate capacity (say, T tons) and its
targeted useful life (say, Yk years).k Then Bfc
is given by: B^T-^/52 Yk. The weekly capacity may
also be affected by the capacity of access roads
to handle traffic without congestion, and the un-
loading rate at the landfill site.
Ck=l,2...,K)
596
-------
• Constraint C2.5L is a balance equation for
intermediate sites. It specifies that what-
ever waste is received at an intermediate site
must be shipped from that site to a final dis-
posal site, adjusted for the weight reduction
produced by intermediate processing.
• Constraints C2.6L, C2.7L, and (2.81 insure that
the fixed costs of building and operating a
disposal facility are included in the objective
function if the site is to Be utilized at a
positive level. If site k is utilized, y will
be greater than zero and * will assume the value
"1". Thus, the fixed cost Ffc associated with
facility k would be added to the -value of the
objective function. If site k is not utilized
y^ will be zero, i will be zero, and Fj^ will
not be added to the objective function.
• Constraints C2.&1 and C2.10). are the non-
negativity constraints on the xilc's and y^'s.
The Objective Function
The objective of this model is the -minimization
of the total regional costs of solid waste disposal.
These costs include transport costs (from a community
to an intermediate site, from a community to a land-
fill site, and from an intermediate site to a land-
fill site), and operating and capital costs associated
with a disposal facility.
We assume that each of the individual components
of total cost can be represented by one of the two
types of cost functions shown in Figs. 1 and 2.
Typically, the cost of transporting waste from a
site i to site k can be represented by a linear
function (Fig. 1) of the amount of waste shipped. We
will let H. be the unit transportation cost.
The cost function associated with each disposal
facility, k, is of the form shown in Fig. 2. There is
a fixed initial construction and/or overhead cost, F^,
as well as variable operating costs, V^, which are
dependent on the amount of waste processed.
Each cost factor C^ or Cjk, defined above, is
therefore, the sum of a. unit transportation cost and
a unit operating cost. That is:
cik vk
-jk
, .. . ,N;K=1,2,.. . ,
Hjk
In many cases the operating cost curves for fac-
ilities such as incinerators and transfer stations are
not linear, but exhibit economics of scale. We will
assume that any such curve can be represented by a
piece-wise linear concave cost function such as that
shown in Fig. 3. In this illustration there are three
different operating ranges. If less than h2 tons are
shipped to the facility, the operating cost is c^
dollars per ton; for between h2 and 113 tons, it is c2
dollars per ton; and for above {13 tons, it is C3
dollars per ton. The three segments of the cost curve,
when extended, intercept the y-axis at points f^, f2,
and f3.
Such a function can be easily represented as a
fixed charge cost function and added to the general
objective function derived above. For the example
shown in Fig. 3, define new decision variables A 1,
A2, and A3, corresponding to the three segments of
the cost curve (in general, the curve can have any
number of segments). With each Aj, associate the
variable cost Cj and the fixed cost fj, so that the
cost function for each Aj is of the form shown in
Fig. 2. Then' the general formulation is modified as
follows:
• One constraint is added to the problem:
x y A =0
The following terms are added to the objective
function:
A fixed charge constraint is added for each
variable:
0 if A =o
1 if
> 0.
Note that no upper or lower bound constraints need be
put on theAj's. It is shown in " that, if Aj is
positive in an optimal solution to the problem
(1) all other A associated with that cost function
will be zero, and
(2! hj
-------
Multi-Year Planning Considerations
The mathematical model described above assumes
that every week or year in the planning period looks
the same as every other week or year (in terms of
costs and waste production) and that any site selected
is available at the start of the planning period and
lasts for the entire period. The optimization of this
system is a gross simplification of real-world pro-
blems.
In the Solid Waste Allocation Model,the concept
of "staging," breaking the planning period into sev-
eral smaller periods, is used to provide a more re-
alistic solution. One fixed charge problem is solved
for each period. Although each period is solved sep-
arately and independently from all other periods, re-
maining ultimate capacities of facilities such as
landfills are transferred and updated from stage to
stage. At the end of the planning period the results
for each of the stages are summarized and totaled to
determine the overall cost for the planning period.
The number and duration of the periods are determined
partly by the user and partly by the program. The
closing of a facility, the opening of a new facility,
and the creation of a new waste source will all cause
a new stage to be started (i.e., a new problem to be
solved). The user supplies all opening and closing
dates as well as ultimate capacities. In addition,
if a facility reaches its ultimate capacity during
one of these user-defined stages, the program will
create a new stage, and a fixed charge problem with
this facility eliminated will be solved to determine
where the waste that had been going to that facility
should now be transported.
Although there is no real interdependency be-
tween stages, the concept of "staging" does allow
for a great deal of flexibility in creating a real-
istic solid waste plan.
The Solid Waste Al-Ic-catron Model
The Solid Waste Allocation Model (SWAM) is a
system of FORTRAN programs that has been developed
by the U.S. Environmental Protection Agency's Office
of Solid Waste Management Programs under contract to
Roy F. Weston, Inc.^' to solve the fixed charge in-
teger program (2.1)-(2.10) . It accepts as input some
simple data on the disposal facilities and the com-
munities in the region under consideration, and cal-
culates the coefficients for the integer program. It
then solves the problem for one or more stages, and
prints output reports summarizing the solution.
The following sections briefly discuss the model's
data requirements and the heuristic algorithm used in
the solution of the problem. The output reports are
described as part of the discussion of the application
of the model to be covered in the verbal presentation
of this paper.
Data Requirements
In order to properly model the transportation,
processing, and disposal components of solid waste
planning, some specific and detailed data are re-
quired. These data are divided into three categories:
(1) source data; (2) facility data; and C3) transpor-
tation data.
The "source" in SWAM is a point of waste gener-
ation that represents a reasonably large residential
area, such as a census tract, transportation zone, or
planning district. The quantities of waste generated
at these sources, specified in tons per week, will be
allocated by the model to various processing and dis-
posal facilities. Associated with each waste source,
in addition to the generated waste, is a haul cost
(in dollars per ton-hour]. This cost is used to con-
vert the transportation time from the source to each.
facility into a dollar cost. The haul cost is a func-r
tion of the collection vehicles and crews associated
with the specific source.
The Solid Waste Allocation Model considers Both in-
termediate and ultimate disposal facilities. Th_e
basic data necessary to define an intermediate fac-
ility are the maximum operating capacity in terms of
tons per week, an operating cost curve, the capital
cost of the facility, associated useful life, and the
transfer coefficient indicating the percentage weight
of incoming waste that will remain after processing.
In addition, a unit haul cost (in dollars per ton-
hour) is required in order to convert the transpor-
tation times from intermediate facilities to ultimate
disposal sites into dollar costs. To define an ul-
timate disposal site the following pieces of data are
needed: the maximum operating capacity in tons per
week, the ultimate capacity in tons, the capital cost
of the facility, an operating cost curve, and a use-
ful life. The operating cost curve associated with a
disposal facility can be one of three types: (1) st-
raight line of the form y=ax+b; (2) semi-log of the
form log y=ax+b; and (3) log-log of the form y=a log
x+b. Curve types (2) and (3) are approximated by
piece-wise linear curves using the linear regression
procedure described in Section II.
In order to determine allocations of waste from
sources to facilities, the model must be supplied with
the set of paths along which the waste can be trans-
ported. These paths are defined by pairs of locations
which can indicate paths from sources to intermediate
facilities, from sources to ultimate disposal sites,
or from intermediate facilities to ultimate sites.
The transportation time in minutes plus the turn-
around time at the facility must be supplied for each
pair of locations.
The data described above are all that is necessary
to run the model for one time period. There are other
options in the model, such as multi-year planning and
automatic path generation, each with its own data re-
quirements, which will not be described here.
Solving the Fixed Charge Problem
The problem formulated in Section II is a fixed
charge problem, which is a special type of integer pro-
gramming algorithm. It can be solved exactly by any
mixed integer programming algorithm. Unfortunately,
these algorithms are generally too slow to solve the
large problems constructed for practical applications
in a reasonable amount of time (although Kuhner and
Harrington report some success using IMB's MPSX-MIP
system on large problems^).
The United States Environmental Protection Agency's
Office of Solid Waste Management Programs, therefore,
decided to use a heuristic algorithm developed by
Warren Walker to solve the problem. The algorithm is
described completely in 9, where its speed of execu-
tion and optimality of solutions are compared to other
solution techniques. It was found to be computational-
ly efficient and sucessful in producing the optimum
solution a high percentage of the time.
The algorithm consists of two phases. The first
phase is identical to the standard simplex method of
linear programming, except that the method of choosing
the vector to bring into the basis is modified to
take the fixed charges into account. In the second
phase, vectors are forced into the basis even though
they increase the total cost, in the hope that, by
resuming simplex iterations from a new extreme point,
a better solution can be found.
598
-------
References
1. "A Mathematical Model to Plan and Evaluate Re-
gional Solid Waste Systems," a report prepared
for the New York State Department of Environ-
mental Conservation by Roy F. Weston, Inc.,
West Chester, Pennsylvania, June 1971.
2. Anderson, L.E., "A Mathematical Model for the
Optimization of a Waste Management System,"
University of California Sanitary Engineering
Research Laboratory, Report No. 68-1, February
1968.
3. "Development of a Solid Waste Allocation Model,"
a report prepared for the U.S. Environmental
Protection Agency by Roy F. Weston, Inc., West
Chester, Pennsylvania, July 1973.
4. Kuhner, Jochen and Joseph J. Harrington, "Large-
Scale Mixed Integer Programming for Investigat-
ing Multi-Party Public Investment Decisions:
Application to a Regional Solid Waste Management
Problem," presented at the 45th National ORSA/
TIMS Meeting, April 23, 1974, Boston, Mass.
5. Marks, David H. and Jon C. Liebman, "Mathemati-
cal Analysis of Solid Waste Collection," Public
Health Service Publication No. 2065, U.S. Dep-
artment of Health, Education and Welfare, 1970.
6. Morse, Norman and Edwin W. Roth, "Systems Analy-
sis of Regional Solid Waste Handling," Public
Health Service Publication No. 2065, U.S. De-
partment of Health, Education and Welfare, 1970.
7. Midwest Research Institute, "Resource Recovery-
The State of Technology," February 1973.
8. Skelly, Michael J., "Planning for Regional Re-
fuse Disposal Systems," Ph.D. thesis, Cornell
University, September 1968.
9. Walker, Warren E., "A Heuristic Adjacent Ex-
treme Point Algorithm for the Fixed Charge
Problem," P-5042, The New York City-Rand
Institute, June 1973.
599
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INCENTIVES FOR WASTE COLLECTION BASED ON WORK CONTENT MODELING
Richard L. Shell, P.E.
Professor of Industrial Engineering
Dean S. Shupe, P.E.
Associate Professor of Mechanical Engineering
UNIVERSITY OF CINCINNATI
Cincinnati, Ohio 45221
ABSTRACT
A successful incentive system JOT solid waste
personnel must satisfy both technical and politi-
cal requirements. The technical requirement is
that each route assignment must contain a known
collection work time. This paper describes the
use of computerized modeling to develop waste
collection route areas for either time or wage
incentives. A recommended wage incentive program
for solid waste workers is included with a simple
example to illustrate application. The recommended
program features an "Elective Incentive Contract"
that combines three basic concepts: incentive
teams, time and wage incentives, and elective work
loads, i.e., teams choose their level of incentive
work load.
INTRODUCTION
Service cut-backs, layoffs, reduction in
capital investments, and possible financial
default -- these headlines evidence the
growing economic plight of many cities
across the nation. The typical municipal-
ity is being hard pressed to maintain its
service-oriented, labor intensive functions
in the face of continuing inflation while
on a relatively fixed income base. "Over
the past two decades, state and local
spending, now running at $221.5 billion,
has grown faster than any other sector of
the economy. State and local expenditures,
exclusive of federal aid, rose from 7.4
percent of gross national product in 1954
to 11.6 percent last year"[l].
The revenues of local government have not
kept pace with the spiraling expenditures.
The bottom line result to date has been
deeper budget deficits. Figure 1 illus-
trates the worsening financial condition
since 1973.
PRODUCTIVITY AND SOLID WASTE COLLECTION
In most cities, solid waste collection
ranks third in total cost, behind educa-
tion and roads. Collection has been
traditionally noted for its intensive la-
bor requirements. Typically over 70
percent of collection/disposal costs are
required for collection manpower.
Collection productivity has remained es-
sentially unchanged since the introduction
of the compactor truck nearly four decades
ago. One approach to increasing producti-
vity is the application of worker incen-
tives .
+ 12
w
3
o
H
-12
1970
75
Source: U.S. Commerce Department
FIGURE 1. STATE AND LOCAL GOVERNMENT
BUDGET SURPLUS/DEFICITS
WORKER INCENTIVES
Any compensation offered for improved
performance or behavior is an incentive.
Incentive plans can be divided into three
broad categories: direct monetary, indirect
monetary, and non-monetary [5]. Under a
direct monetary plan, each employee is com-
pensated directly for his or her output or
increased output. Direct plans can be
either individual or group. Under the group
plan, each member of the group is compensated
an equal percent of bonus for the group's in-
creased output.
600
-------
A study of over 400 companies of all sizes
to determine the effect on productivity of
work measurement and wage incentives
indicated that productivity in plants with
wage incentive plans was 42.9 percent
higher than plants with measured day work
alone, and 63.8 percent higher than plants
with no measurement [3,4]. These surveys
indicate that a key to increased producti-
vity is work measurement. "Without mea-
surement, we don't know where we are or
where we're going"[6].
Although monetary incentives have been
utilized in manufacturing industries for
several decades, their application to the
service-oriented sector of the economy
has traditionally been limited. The re-
cent shift in the economy from manufac-
turing to services has been accompanied by
a growing interest in the use of incentive
programs for service-oriented public
employees as recently reported by the
National Commission on Productivity and
Work Quality [2].
SOLID WASTE SYSTEM REQUIREMENTS
A wage incentive program for collection
personnel must satisfy two major require-
ments: teahn-ioal and polit-lcal.
A sound technical base is fundamental to
an incentive program. Each route assign-
ment must contain a known collection work
content, i.e., the work time required to
accomplish a given task at a normal work
pace. In waste collection, work content
is the standard time required for com-
pleting the collection assignment, proper-
ly allowing for variations in tonnage,
haul distance, equipment, crew-size, and
other influencing variables. The work
content must be accurately calculated
utilizing work measurement techniques [10].
The second major requirement is political
in nature. All involved parties -- elected
officials, citizens, public works manage-
ment, and workers/union -- must be amenable
to the concept of time and wage incentives.
On an on-going basis, management must con-
tinue to support the program fairly, e.g.,
defend the program to the citizens and to
municipal employees not included in the
incentive plan, and maintain competitive
base earnings. In addition, all parties
must be willing to share the savings re-
sulting from increased productivity.
TEAM TIME INCENTIVES
Several constraints are inherent in solid
waste collection effect system design and
modeling. These include 1) the daily col-
lection route is fixed, 2) the daily work
content is variable, and 3) the work is
typically accomplished by crews.
If each collection route is to be picked up
consistently on its scheduled day, provi-
sion must be made for handling the fluctu-
ations that inevitably occur in the work
content of a collection area from day to
day. Management has only two alternatives
for dealing with these variations: either
make changes in the resources assigned to
the task, or allow the time required for
the task to vary into overtime or
into 'undertime' (in which case the men
would be idle a portion of the day).
Generally, municipalities tend to avoid
overtime, electing instead to permit the
crews to complete their assignments early.
If the workers are allowed to leave on
completion of their assignment and are paid
for a complete day, the program provides a
time incentive (the 'task system').
Although time incentive programs are fre-
quently used and offer advantages to both
management and workers, they require bal-
anced work assignments for cost effective-
ness and fairness to individual employees
[12]. On a day-to-day basis, balanced
work assignments are difficult to maintain
between individual crews due to uncontrol-
lable factors, especially sudden equipment
failure [11].
An approach used by some municipalities to
reduce the inequities between individual
crews is to group several crews together
into a team under the field supervision of
a foreman [7]. The team approach not only
provides a mechanism for dealing with daily
fluctuations in the work loads of its mem-
ber crews but also tends to average out
inevitable changes in waste generation
patterns occurring in a dynamic city, there-
by requiring somewhat less frequent route
revision [9].
WASTE COLLECTION ROUTE DEVELOPMENT
In the- development of waste collection routes,
it is recommended that each route assignment
be specified by a bounded geographic area.
Detail sequential routing within the
assigned area is best accomplished by public
works management and collection personnel
utilizing their experience and knowledge.
Typically, a collection area consists of
only a few square blocks, thus permitting
heuristic design by collection personnel. In
addition, most motivation and job performance
investigations indicate that workers perform
at higher overall productivity levels if
they have been involved in the design and
planning of their work activities. There-
fore , detail sequential modeling of waste
collection, e.g., the Chinese Postman,
Eulerian Tour, and Traveling Salseman algo-
rithms, has little practical value.
Route area development requires partition-
ing of the city into team and crew col-
lection areas each defined so as to provide
the desired work day. The total work con-
tent for each area must account for all work
time elements: the sum of the pickup times
as computed for each block, disposal time,
refueling time, allowance for unavoidable
delays, and worker rest breaks.
The development of route areas through
modeling requires a knowledge of all work
content time elements. Fundamental to the
determination of pickup times for each
block is detailed block-by-block field data
601
-------
on all variables influencing collection
times and tonnages. This data includes set-
out containerization, street width and
street length, and may be obtained by field
survey teams that accompany crews during
collection.
Utilizing the route area concept based on
work content modeling, new collection routes
were developed and implemented for Coving-
ton, Kentucky. Covington has a population
of over 50,000 and is located in the Great-
er Cincinnati metropolitan area.
Based on the block-by-block data for Coving-
ton, together with work measurement results,
predictive equations were developed for cal-
culating the standard collection time for
every block in the City. Times for the
other work content elements were obtained
by direct field timing and work sampling.
A system of simulation programs incorpor-
ating all of the work time elements was
utilized to design collection route areas
for the City. The programs were user-ori-
ented with remote terminals linked to an
IBM 370/168. Fixed inputs included collec-
tion frequency, crew size, and length of
work day. Variable inputs included individ-
ual block identification numbers and map
distances. Detailed outputs included all
clock times and load tonnages as each truck
progressed through its work day (reference
Appendix A for example printout). Final
output defined the number of truck crews re-
quired for collection of the entire City.
In addition, balanced route area assignments
were determined for individual truck crews,
as shown in Figure 2. This type of route
development provides the technical basis
for a wage incentive program.
A RECOMMENDED WAGE INCENTIVE
PROGRAM FOR SW WORKERS
If the technical and political prerequi-
sites can be satisfied, an effective wage
incentive program may be developed that
offers high probability of long term suc-
cess. A wage incentive program that lends
itself particularly well to solid waste
collection in medium and larger cities
combines three basic concepts: incentive
teams, a time/wage incentive, and elective
work loads. It will be referred to as an
Elective Incentive Contract (EIC) program C8 ].
Incentive Teams
Under EIC, collection is accomplished by
incentive groups or teams consisting of
approximately three to nine trucks and
their assigned crews supervised by a
field foreman. All supportive SW personnel
including maintenance and disposal workers
as well as the superintendent receive an
incentive bonus based on the average of
all teams.
Time Incentive
Each team is assigned a collection route
area consisting of a standard work day
mm,.
FIGURE 2. AREA ROUTE ASSIGNMENTS FOR TEAM II
(TRUCKS 7 THROUGH 12).
(e.g., 6.5 hours average) that is less than
the normal 8-hour day. Team members are
paid for the full day and are permitted to
leave work after their respective team area
has been collected to the satisfaction of
their field foreman. The time incentive
encourages workers to reduce their collec-
tion time by increasing the .work pace,
reducing break time, or through worker
ingenuity.
Elective Participation
In addition to the 6.5-hour standard work
day, individual teams may elect to contract
additional work content in return for a
wage incentive bonus. The bonus is based
on an equal sharing by workers and city
of the resulting savings.
602
-------
EIC EXAMPLE
To illustrate the EIC program, consider a
small solid waste collection/disposal
system with two collection teams, both
teams initially consisting of five rear-
loading packers and drivers , five laborers,
and a field foreman. Team I contracts the
standard 6.5-hour work day and receives
base salaries without a wage incentive
bonus. Team II contracts for a 7.5-hour
work day and receives base salaries plus a
wage incentive calculated by the simple
equation below:
Wage Incentive
(percent)
(Contract - Standard Day)
8 Hours
x 100
For a 7.5-hour contract day, the computa-
tion is :
Wage Incentive = (7.5 - 6.5) 100
(percent) 8 .0
12.5%
In the case of a Team II worker earning a
base salary of $200 weekly, the resulting
wage incentive bonus would be $25 weekly.
A 7.5-hour contract work day for the 10-
worker team reduces the equivalent manpow-
er requirements for the total system by:
Manpower _ (7.5 - 6.5 hours/worker) 10
Reduction 6.5 hours/worker
1.54 workers
Assuming a 30 percent overhead (including
fringe benefits), the manpower reduction
savings resulting from the 7.5-hour con-
tract work day are:
Manpower Reduction
Savings
($200/week)(1.54)
x (1.30) $400/week
Net labor savings to the city is equal to
the manpower reduction savings less bonus
payments to team workers, foreman, and
supportive personnel. Bonus payments to
the workers of Team II would amount to
$250 (10 workers @ $25 each). Assuming
that bonus payments to the foreman and
support personnel amount to $50, the net
labor savings to the city would be:
Net Labor
Savings
$400 - $250 - $50 $100/week
In addition to labor savings, the city
would realize equipment savings associated
with the reduction in manpower. For each
crew reduced (2 workers), there is a reduc-
tion of one truck. Assuming a weekly truck
cost of $200, the equipment savings would
be:
Equipment
Savings
1.54 ($200/week) = $154/week
In this example, total weekly savings to
the city equals $254 while the total weekly
bonus payments to workers (including fore-
man and support personnel) equal $300.
Obviously truck and manpower reductions can
occur only in integer units.
Since under the EIC program, the work
groups contract to complete their elected
collection assignment, overtime pay is
avoided except for scheduled holidays.
Care must be exercised during implementa-
tion of collection improvements to avoid
employee layoffs if at all possible.
Consequently, actual savings may lag
implementation until manpower levels are
adjusted through attrition or reassignment.
CONCLUSION
The findings from this project indicate
that a wage incentive program for municipal
solid waste personnel is feasible and
technically possible, but that political
problems more complex than found in private
industry must be dealt with.
The recommended Elective Incentive Contract
(EIC) program is based on carefully de-
fined truck route areas with work content
determined from computerized modeling based
on detailed field data and work measure-
ment techniques. Incentives are paid to
small groups electing work content levels
above standard. Savings resulting from
increased productivity are shared equally
between worker groups and management, and
the municipality.
ACKNOWLEDGEMENTS
This research was in part supported by Environ-
mental Protection Agency Grant R801617. The
authors wish to extend their appreciation to the
City Manager, the Department of Public Works, and
the City Commissioners in Covington, Kentucky;
and to the officials of District Council No.
51, The American Federation of State, .County, and
Municipal Employees, AFL-CIO, and the men of its
Local No. 237.
REFERENCES
1. Borrowing Too Much To Keep Running",
Business Week, September 22, 1975.
2. Employee Incentives To Improve State
And Local Government Productivity,
National Commission on Productivity
and Work Quality, March 1975.
3. Fein, M., Rational Approaches To
Raising Productivity, Work Measure-
ment and Methods Engineering Division,
Monograph No. 5, American Institute of
Industrial Engineers, 1974.
4. Fein, M., "Work Measurement and Wage
Incentives", Industrial Engineering,
Vol. 5, No. 9, September 1973.
603
-------
5. Niebel, B.W., Motion and Time Study,
Fifth Edition, Irwin, 1972.
6. Rice, R.S., "Work Measurement: An
Upward Trend," Industrial Engineer-
ing, Vol. 7, No. 9, September 1975.
7. Shebanek, R..B., Shell, R.L., and Shupe,
D.S., "Increase Productivity Through
Crew Assignment'1 , Proceedings , Twenty-
Fifth Annual Institute Conference,
American Institute of Industrial
Engineers , 1974.
8. Shell, R.L., Shupe, D.S., and Albrecht,
O.W., "The Use of Incentives in Solid
Waste Collection/Disposal" , News of
Environmental Research in Cincinnati,
U.S.Environmental Protection Agency,
March 1976.
9. Shell, R.L., and Shupe, D.S., "A Study
of The Problems of Predicting Future
Volume of Wastes", Solid Waste Manage-
ment Refuse Removal Journal, Vol. 15,
No. 3, March 1972.
10. Shell, R.L., and Shupe, D.S., "Pre-
dicting Work Content For Residential
Waste Collection", Industrial Engineer-
ing, Vol. 5, No. 2, February 1973.
11. Shell, R.L., and Shupe, D.S., "Work
Standards For Waste Collection",
Proceedings, Annual Systems Engineering
Conference, American Institute of
Industrial Engineers , 1973.
12. Shupe, D.S., and Shell, R.L., "Balanc-
ing Waste Collection Routes", J. En-
viron. Sys., Vol. 1(4), December, 1971.
HOW GO RHERD RHD STRRT PUNCHING THE ID'S
ID #
74^341
ID *
?34£
ID #
?344
ID #
7351
ID *
7353
ID £
7354
ID #
n.4 i0s;
£>:.9 £££0 8:50
33.9 371::
53.3 5835 9s£4
69.7 6888 9:35
C'O . o o
9:49
98.6 96£8 '10; 4
s*:ss THE LORD IS FULL «®®®
PLEHSE ENTER THE DISTRNCE IN MRP-INCHES FROM
THE LRND-FILL
THIS LORD WEIGHS 96£8 POUNDS
TOTfiL WEIGHT IN THE ROUTE = 96£8 Pill INDS
TOTfiL TIME IN COLLECTION = 98.6 MINS.
TIME SPENT IN TRRUELLING = 34,1 MINS.
TOTRL COLLECTION TIME IN THE ROUTE = 98
TIME SPENT RT THE LRND-FILL = 10.0 MINS.
CLOCK TIME IS 10:48
APPENDIX A.
SAMPLE COMPUTER OUTPUT OF ROUTE
DESIGN SIMULATION. TEAM I.
RUN NEWMOIU
NEWNOD1 14:49 0£.-'07.-"76 SRTURIiflY
DO YOU WfiNT RBBREUIRTED OUTPUT?
YES=1
N0=0
71
IS IT R NEW ROUTE?
YES=1
NO=Q
71
ID #
111.9
144. 3
1357
,1.91313
11: 1
11 s 34
G ss;*s WRRNING **«* WRRNING ®*W
ID # 4 WRS ENTERED RS ITEM tt 9 IN THE RC
PLERSE ENTER: OTHER ID# RGRIN
ID #
76
PLEHSE PUNCH THE ESTIMRTED MfiP-IHSTRNCE IN IN I:' s
FROM THE GRRRGE TO THE FIRST STOP ':''7
?£6
TIrlE FIT THE FIRST STOP IS 8:18
RLLOWING 8.0 MINS. FOR FUELLING
CLOCK TIME IS 8: £6
ID ft
•"'9
149.9
156.3
6046
67£0
11: 39
US'
7349
1£:
NOW IT IS TIME FOR THE LUNCH. WE SHRLL
RDURNCE THE CLOCK BY 30 MINUTES.
604
-------
PLANNING FOR VARIATIONS IN SOLID WASTE GENERATION
Donald Grossman, Graduate Student
Civil Engineering Systems Laboratory
Massachusetts Institute of Technology
Cambridge, Massachusetts 02139
A methodology developed for analysis of municipal
solid waste collection explicitly plans for variations
in waste generation. Using the method, a variety of
district size, truck size, and crew size alternatives
can be evaluated in a multiobjective framework, based
upon a probabilistic description of overtime require-
ments. The methodology is applied in a case study for
Warwick, Rhode Island.
Objectives considered in the case study included
economic efficiency and the fraction of days requiring
overtime. The model uses the historical distribution
of district waste generation to forecast variations in
waste generation as a function of district size. Col-
lection productivity for a variety of truck and crew
combinations is also forecast. System alternatives are
evaluated analytically. The output provides a basis
for choice by explicit representation of the tradeoffs
between objectives.
Resource Allocation Decisions
Selection of truck, crew, and district size is a
key element in municipal solid waste management. This
research investigates these resource allocation deci-
sions and develops a model to forecast the tradeoffs
between objectives for alternative planning policies.
The resource allocation decision variables are isolated
at the primary controls on collection available to
local system managers. A variety of other controls are
possible, but these are typically constrained by envir-
onmental factors or decisions taken over a longer time
horizon.
The choice of truck size is one principle resource
decision. Capacity, given district sizes, crew sizes,
and a processing site configuration, determines the
expected frequency and total duration of haul. As capac-
ity increases, there are increased costs due to large
truck sizes, but these trade off in savings in crew
and vehicle costs due to decreased frequency of haul.
Secondary effects from choosing large vehicles are a
limited turning ability and less queuing at processing
sites.
The choice of crew size is the second principle
resource decision. Increased crew size, given truck
size, district size, and a processing site configura-
tion, results in expected decreases in overtime; these
trade off against expected increases in fixed hour
labor costs and in nonproductive haul time. Secondary
considerations are crew safety and crew comfort; also,
labor relations or political considerations may act to
constrain the available crew sizes. Note that recent
practice supports one to three member crews.
The choice of district size, and therefore the
number of trucks and crews required for collection
(assuming one truck and crew per district), is the
third principle resource decision. A priori, the number
of districts, and therefore the number of trucks and
crews, likely has the greatest impact upon system per-
formance. Larger district sizes imply a smaller number
of districts, and therefore fewer trucks and crews to
service a given town. For a fixed truck and crew size,
larger districts result in an expected decrease in cap-
ital costs because fewer resources are required, but
these trade off against increases in truck and crew
operating costs due to longer expected work days.
The above exemplifies some of the cost tradeoffs
in resource allocation. The problem is framed as a
supply problem with trucks and crews as inputs. One
objective to consider is cost. In addition, there is
likely some disutility for excessively long collection
days, and thus suggests that the system manager might
want to consider multiple planning objectives.
Waste generation is not deterministic. Assuming
a constant rate of collection, the length of the collec-
tion day varies, and this induces a variation in the
cost and other objectives. In addition, costs associat-
ed to resources are not well behaved, but are realized
in discrete increments. Resources themselves are also
discrete. For example, crews are typically paid for 8,
9, 10, or 11 hour days, and not for continuous time-
steps. Both the stochastic character of waste genera-
tion and the discontinuities in input cost can be
modeled using the methodology of this research.
Methodology
This section presents a procedure for choosing a
resource allocation alternative, readily adaptable for
use by a local system manager. First, possible collec-
tion system objectives are proposed, including appropri-
ate measures of effectiveness. Second, the set of
alternatives to be considered is identified. Third, a
structure is developed for the evaluation of proposed
resource allocation alternatives. Fourth, a multi-
attributed utility framework is presented as a means of
choosing between alternative collection system config-
urations.
The analysis assumes a single decision maker, and
choice within a maximum utility framework. The most
obvious objective is financial, measured in present
value dollars. The case study has shown that dollar
costs provide insufficient basis for choice. Using only
dollar costs, the manager would always choose to operate
very few small trucks, and prefer to pay large amounts
of overtime. Instead, a second objective is to limit
the expected length of overtime, expected number of days
on which overtime is paid, or the expected number of
days with one, two, three, or more hours of overtime.
Modeling this objective affords the manager control of
distribution and frequency of overtime hours.
The set of alternatives may be characterized as
points in a three dimensional space. Truck size altern-
atives are based upon industry standards (e.g. 13, 16,
18, 20, 25 cubic yards) and limited only by technical
considerations such as highway weight regulations. Crew
sizes generally range from one to three members and may
be constrained by union or similar considerations. Dis-
trict size alternatives depend upon the number of trucks
and a design number of households. Generally, the number
of districts will be a uniform multiple of the number
of trucks (e.g. 1,2,3... trucks imply 5,10,15... daily
collection districts).
605
-------
The framework for evaluation of alternatives is an
accounting scheme. The proposed method will yield ana-
lytic results. District size determines the number of
trucks and crews. This, in conjunction with truck
capacity and crew size, determines the regular costs
paid on a fixed length workday basis, and the capital
costs associated to owning the trucks and ancillary
support facilities. This component of total system
cost is deterministic and easily calculated. The other
important costs are those for truck operation or over-
time. The evaluation of these requires a description
of the demand for collection services including the
time variation of district waste generation. The
evaluation also requires a model of the supply side,
that is a model of the productivity of truck and crew
combinations.
The waste collected from a residential waste col-
lection district will normally vary greatly over time.
The data from Warwick showed the magnitude of these
excursions to be greater than 50 percent of the mean
weekly wasteload measured in pounds. Three sources are
expected to explain these variations. First, even
after correcting for changes in the numbers of house-
holds, the data may exhibit a long range trend in waste
generation rates. This suggests changing consumption/
disposal patterns in the population as a whole. If the
analyst has a sufficiently long record of weights, it
is possible to remove the trend and later reintroduce
it for an appropriate design year. Second, variations
will normally be manifest within a single year due to
seasonal consumption and disposal patterns. These
arise because of sociological factors including vaca-
tions, habits, and economic trends, and because of
natural factors including weather and climate. Again,
if the analyst has a sufficiently long, trend free
record, the seasonal variations could be removed by a
technique such as Fourier analysis. Third, it is
postulated that there is an underlying random component
in household waste generation. The process need not
necessarily be known, but the analyst must test whether,
at the district level of aggregation, an arbitrarily
chosen set of households exhibits the same waste gener-
ation character as any other district containing an
equal number of households.
The following discussion assumes that the decision
maker's purpose is to choose a single resource alloca-
tion. The importance of considering only a single
allocation is that it enables the analyst to model the
distribution of the quantity of waste generated for
collection, without the need to model the relationship
of different waste quantities over time. Specifically,
the preservation of autocorrelation need not be con-
sidered.
The minimum data requirement to model time varia-
tion are weekly wasteloads from sample daily collection
districts for a year, and the members of households for
each observed district. If the wastes aggregated to
the district level can be shown to be normal, it is
possible to model the district wasteload as the sum of
independent, identically distributed waste generation
distributions. The household distribution independence
and form cannot be tested with available data. It is
possible, however, to arbitrarily choose to model indi-
vidual households as normal, and, as long as a reason-
able number are aggregated into districts, the normal
distribution in district level waste, if substantiated
by the data, can be preserved. For the case where ob-
served districts have an average of k households
m = n u
32= k n s2
(1)
(2)
where n is the number of households in the district
size alternative to be forecast, and u and s are the
estimated parameters assumed to characterize the normal
distribution on wastes generated for collection by in-
dividual households. Using the model of equations (1)
and (2), the demand for waste collection services for
a range of district size alternatives may be forecast.
The second concern is to describe the productivity
of various crew and truck size alternatives for the
set of proposed district size alternatives. To relate
these to system objectives, total collection time must
be predicted for forecast wasteloads, and, in turn,
these collection times can be translated into expected
cost and other systems objectives. For a particular
district size, consider the examination of t , t,, t
...t, length workdays (for example 8, 9, 10, and 11
hour days). The discretization should correspond to
cost increments. Corresponding to these times are
maximum collectable wasteloads, call these w., w_, w_,
...w, , for each truck and crew alternatives.
The total workday may be characterized as the sum
of on route collection travel (from garage to and from
route, and from route to processing or disposal site),
and nonproductive time (breaks, breakdowns, and main-
tenance) . Typical values for nonproductive time may
be estimated. The number of hauls and on route col-
lection time depend on wasteload, truck size, and crew
productivity. To complicate this analysis, trucks are
volume constrained. Therefore, an expected density of
waste is required to convert volumetric capacity of
each truck size alternative to a corresponding weight
capacity. The procedure for estimating density is to
use observed data points having more than a single haul
to the processing site, and assuming the first haul
full. Then the analyst can estimate density using
known truck weights and volume. In the Warwick case
study, a point estimate of density was justifiable.
Shuster1* has developed and calibrated, a model to fore-
cast Y, the service time per household, in minutes.
The regression equation, estimated for a curbside, once
weekly, incentive system is
Y = .0088 X:L .0570 x2 - .0010 XB - .0423 + .770
(3)
where x. is the pounds of waste per service per week,
x,, is the crew size, x. is the percent one-way items,
and x, is the collection miles per day. Shuster esti-
mates similar models for other levels of service and
work rules. Therefore, for each resource allocation
alternative, the on route collection time may be fore-
cast for all levels of w, . Under an assumed waste
k
density, the number of hauls and the corresponding
travel times may also be determined. Then, for each
resource allocation alternative, the analyst has de-
termined each w, associated to each workday length t^.
It is important to note that productivity is assumed
to be deterministic, and more research is required to
test the validity of this assumption.
Therefore, for each resource allocation alternative,
the distribution on wasteloads yields a distribution
on the total length of collection day. Given estimates
of cost for varying leneth collection days, the expect-
ed cost of collection and values for other objectives
may be developed. The levels of attainment of objectives
can be represented by points on a transformation curve.
The decision maker's problem is to choose between
alternative operating points along the transformation
curve. The chosen point is the desired level of
606
-------
tradeoff between system objectives. It should repre-
sent the alternative with the greatest utility to the
system manager. Choice can be made subjectively,
from a graphical representation, or can be made in a
multiobjective framework as described by Keeney3, and
others.
Case Study - Warwick, R.I.
The resource allocation methodology was applied
in a case study for Warwick, R.I. First, Warwick and
the available data sources are described. Second, the
key steps and results of the evaluation process are
presented. Third, output under a variety of assump-
tions and system objectives is presented. Finally,
tentative resource allocation policy recommendations
are drawn.
Warwick is a moderately large community with a
1970 census count of 83,694 people. The municipal
Public Works Department provides collection from resi-
dences: there are nearly 24,000 dwelling units ser-
viced in public collection. At the time of data col-
lection, eleven 20-yard loadmaster compactors were
the town's primary collection vehicles. The vehicles
were operated by three member crews paid on a 40-hour
incentive system, with overtime paid at time and one-
half. Data were collected by ACT Systems1 for 20 of
Warwick's collection districts for the entire period
from November, 1972 to November, 1973. Data collected
included total weekly wasteloads, and the respective
numbers of households in each of the districts. Dis-
aggregation to weight per haul enabled estimation of
waste density. The data used for the Warwick case
study represent a minimum set necessary for analysis.
The 20 timestreams of 52 observations in weekly
district waste generation contained only 996 non-zero
observations. These, average weights per household
per week were calculated. A week test suggested that
all producers behaved as if drawn from a single popu-
lation. Using the 996 observations as independent
samples from a distribution on average household
wastes, then the hypothesis that the underlying dis-
tribution is normal may be tested. Independence of
samples was screened by checking correlation statis-
tics across districts, the estimated sample para-
meters for the distribution were a mean of 61.63
pounds and a standard deviation of 18.42 pounds. In
addition, a 'minimum correlation sample of 52 observa-
tions produced essentially the same distribution para-
meters. Using a Chi-squaredgoodness of fit test, the
hypothesis that the samples came from a normal dis-
tribution with the estimated parameters could not be
rejected. Using the sample parameters, distributions
in waste generated were forecast for district size
alternatives ranging from 270 to 600 households per
district.
The modeling of waste collection time used Shuster'
regression equation. In addition three-quarter hours
of official breaks were assumed. The garage and pro-
cessing site are at the same location, and were model-
ed as equidistant from all districts. Only the three
member crew size alternative was tested. ACT Systems
data reported 72 percent one-way items and also re-
ported data which were converted to collection miles
per household. Using the model of equation (3), the
total collected wasteload w , for each level of time,
f>
t, , could be forecast.
Five commercially available truck size alterna-
tives were selected. Capacities ranged from 13 to 25
cubic yards. The mean density of waste used to con-
vert volumetric capacity to weight capacity was 666
pounds per cubic year. The assumed discretization of
costs were those associated with 8, 9, 10, and 11 hour
long days. These were converted to probabilistic
equivalents. Table 1 shows the model output for a 20
cubic yards truck, with a three member crew, operating
in a district of 480 households.
P - Prob (t s 8 hours) .73
P = Prob (8 < t < 9) = .20
P = Prob (9 < t < 10) = .04
P4 = Prob (t > 10 hours) = .03
Table 1: Sample Distribution on Collection
Day Length
The model forecasts that roughly 73 percent of the
days have collection times less than 8 hours. Similar
information may be inferred for all other resource
allocation and day length alternatives.
Two objectives were chosen for the Warwick case
study. One proposed objective is the cost for each
system alternative, measured in dollars; costs include
regular, capital, operating, and overtime components.
In a supply model framework the dollar benefits should
be the same for all supply alternatives. The second
proposed objective, the fraction of days exceeding 8
hours in length, provides some measure of the dis-
utility of overtime incidents not captured by the
dollar costs. Resource allocations having both lower
cost and lower fraction overtime requirements are pre-
ferred.
The expected fraction of workdays exhibiting over-
time is easily developed from information such as that
in Table 1. Standard cost data collected by ACT
Systems were used in the assessment of system costs.
For the Warwick case study, a single year planning
horizon was modeled in order to assure comparibility
with the historical data. Costs were normalized to
dollars per ton. Figure 1 shows the tradeoffs between
the attributes of the system objectives.
18. §
17--
16-..
14..
il2
11
0 .1 .2 .3 .4 .5
Fraction Overtime
Figure 1: Attribute Transformation Array
607
-------
Each point represents a distinct resource allocation
and shows the levels of attributes forecast for that
alternative. A southwest corner rule identifies non-
dominated alternatives. These are the circled points
in the figure.
The actual choice of objective requires prefer-
ences for tradeoffs between objectives. The past War-
wick resource allocation shows implicitly the prefer-
ences between objectives. In 1973, Warwick used eleven
20-yard trucks with three member crews. The model
forecast for Warwick's chosen alternative was collec-
tion costs of $12.75 per ton, and overtime paid on 15
percent of the workdays. The actual Warwick system,
using the historical records from November, 1972 to
November, 1973 exhibited collection costs of $12.82 per
ton. The model forecast falls within one percent of
the actual system cost. No historical data on the act-
ual distribution of overtime were available.
Actual validation of the forecasts is difficult.
A plausible technique is testing the sensitivity of the
chosen alternative to the input assumptions. To illus-
trate, this research tested changes in overtime and
wage rates. The effect of different overtime rates
could provide information for a negotiation process.
For Warwick, double, and even triple normal wage rates
for overtime resulted in only minor cost advantages for
larger trucks. Higher overtime rates had greatest
effect for alternatives with a greater expected function
of overtime, but overall fixed hour wages and base
truck costs dominated total system costs. Similarly,
doubling regular wage rates had little effect on the
least cost system alternative; this suggests that wages
already dominated the total costs.
In general, the Warwick Case Study shows that the
actual 1973 collection system had evolved to represent
a fairly reasonable tradeoff between the investigated
alternatives. Observe that low overtime alternatives
result in significant cost increases. For the total
system, the model forecast approximately a one-quarter
million dollar increase in costs by changing from a 15
percent to a no overtime alternative. Due to the vari-
ability in the district waste generation, planning for
even moderate amounts of overtime is likely advantage-
ous. Whenever possible within the context of overtime
considerations, fewer and larger districts are prefer-
able. Total system costs seem relatively insensitive
to truck costs: labor costs dominate. This suggests
the choice of larger trucks, but, beyond a certain
size, additional capacity affords little cost advantage
because the expected number of hauls do not decrease
further. In any case, the resource allocation method-
ology applied to Warwick provides a wealth of informa-
tion conveniently represented and useful for decision
making.
Conclusions
The resource allocation proposed in this research
incorporates multiobjectives, uncertainty, and non-
linearity. It is not an optimization procedure: there
is no directed search towards most preferred alterna-
tives. Instead all alternatives are simulated, analytic-
ally, and exhaustive search is used to choose the
resource allocation. A more detailed simulation is
possible, but this would require more extensive data
and might be a useful tool for testing the method. Non-
linear vector optimization using mathematical program-
ming is also possible, but the formulation would be
difficult, and integer constraints might make the
solution impossible. In light of the relative ease of
application of the method, and the importance of certain
modeled system characteristics, the resource allocation
procedure of this research seems effective for the
planning of municipal collection services.
Several extensions are possible. The analyst
might model changes in the underlying waste generation
process through trend extrapolation, or alternatively
through causal modeling of the waste generation process.
The latter is currently beyond the state of the art.
Alternatively, seasonal allocations of resources in-
stead of a single level of resource allocation might be
developed. Different seasons appear to have different
waste characteristics. Therefore, seasonal allocation,
facilitate better matching of supply to the demand for
collection services. Tests with Warwick data indicate
that each season can be modeled as described in this
paper, and a dynamic programming formulation used to
coordinate the seasonal allocations to maximize overall
system objectives. Another extension, requiring more
research, is modeling several populations of waste pro-
ducer. One possible approach is to partition the popu-
lations into separate subsystems.
The potential gains due to the use of an analysis
model of the type developed are significant. The method
is easily applied to local collection system planning.
Analysis helps identify and clarify the framework and
assumptions of the decision process, and provides a
basis for testing and comparison of alternative decision
strategies. The method, using easily available data,
tests and can model a variety of important process
characteristics, test a variety of input assumptions,
and lend valuable insight into the tradeoffs between
system objectives under alternative resource allocations.
Acknowledgements
This work was supported by a grant from the Sloan
Research Foundation. Data for the case study were
collected by ACT Systems for the Office of Solid Waste
Management Programs of the Environmental Protection
Agency. The author appreciates the insights and guidance
from Professor David Marks and colleague James Hudson.
References
1. ACT Systems, Inc., Residential Collection Systems -
Final Report, Cincinnati: U.S. Environmental
Protection Agency, 1974.
2. Grossman, Donald, Resource Allocation for Solid
Waste Collection, Cambridge: Unpublished S.M.
Thesis, Massachusetts Institute of Technology,
Department of Civil Engineering, June, 1975,
3. Keeney, R.L. Multidimensional Utility Functions:
Theory, Assessment, and Application. Cambridge:
Massachusetts Institute of Technology, Operations
Research Center, TR 43, October, 1969.
4. Shuster, K.A., Districting and Route Balancing for
Solid Waste Collection, Washington: U.S. Environ-
mental Protection Agency, unpublished mimeograph,
1973.
5. Stone, R., A Study of Solid Waste Collection Systems
Comparing One Man With Multi-man Crews, Washington:
U.S. Department of Health, Education, and Welfare,
1969.
608
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MODEL OF THE MOVEMENT OF HAZARDOUS WASTE CHEMICALS FOR
SANITARY LANDFILL SITES
Eugene Elzy
Department of Chemical Engineering
Oregon State University
Corvallis, Oregon 97331
F. Tom Lindstrom
Departments of Statistics and Mathematics
Oregon State University
Corvallis, Oregon 97331
A simple mathematical model has been developed to
aid in the management of hazardous chemical disposal in
sanitary landfill sites. The model is based upon a chem-
ical mass balance and incorporates the important physi-
cal-chemical parameters: 1) hydrodynamic flow velocity
based upon the porosity and hydrodynamic gradient of
the porous medium; 2) variable water table; 3) variable
rainfall; 4) reversible adsorption-desorption phenomena;
5) first-order irreversible sorption, if any; 6) first-
order chemical reaction; and 7) first-order microbial
degradation kinetics. The chemical, which is deposited
into the landfill in any time pattern desired, is routed
vertically by rainfall infiltration to the water table
where movement in the horizontal direction occurs. The
simplicity of the model and the resulting computer sim-
ulation program permits a ten year run to be computed
and plotted automatically for approximately sixty dol-
lars. The application of the model for a typical sani-
tary landfill is demonstrated.
Introduction
In determining whether a specific material is en-
vironmentally hazardous under a given disposal situa-
tion, a number of factors must be considered. Import-
ant material properties or characteristics include tox-
icity, solubility, biodegradation rate, vapor pressure,
adsorption on soil, amount, concentration, and others.
Other important factors include containment and geologic
or hydrologic conditions of disposal.
In only a few instances can the environmental haz-
ard of disposal of a certain material be defined on
the basis of only one or two of the factors mentioned
above. In most cases it appears necessary to consider
many factors and consequently hazard evaluation may be-
come quite complicated. The major threat to the envir-
onment presented by the disposal of hazardous or toxic
chemicals in sanitary landfill disposal sites is con-
tamination of ground water or surface water. In order
to predict potential ground water or surface water con-
tamination it would be necessary to consider all impor-
tant physical and chemical characteristics and environ-
mental conditions (geologic and hydrologic) at the same
time by a mathematical approach.
A review of the literature reveals numerous papers
dealing with the mathematical aspects of water and chem-
ical movement in both unsaturated and saturated porous
media. Extensive mathematical modeling and computer
simulation studies of regional ground water flow have
been performed by Freeze-*' . He considers the inter-
action between a pollutant source and the soil-moisture
and groundwater flow systems. The Freeze model can pre-
dict both transient and steady state subsurface flow
patterns in two or three dimensions and includes con-
sideration of both saturated and unsaturated zones.
Quantitative interpretation of Freeze's results provides
predictive values of the rate of entry of pollutants
into the flow system, lengths of flow paths, travel
times of pollutants, discharge rates to surface water,
water table movements, and pressure field development.
These results do not consider dispersion or hydrochemi-
cal interactions between pollutants and soils.
Finder and coworkers ' have also developed so-
phisticated two and three dimensional models of ground
water flow systems, including mass transport in flowing
ground water. Schwartz considered the simulation of
hydrochemical patterns in regional ground water flow.
In this sanitary landfill modeling project, con-
straints of time and funds virtually eliminated con-
sideration of modeling using the techniques of the
above workers. For example, Freeze^ reported that
transient two-dimensional hydrodynamic models required
from 10 to 30 minutes of computer time (IBM 360/91) for
100 time step solutions. Since the current project re-
quires a simulation of the landfill behavior over a
time period of years, it is obvious that computer
charges would be prohibitive for routine use of the
model.
For practical reasons, a simple approach was taken
using the vertical moisture routing procedure of Remson
et. al.8, Fungaroli,5 and Bredehoeft et. al.2, coupled
with a simple model of the chemical transport in the
horizontal direction. The hydrodynamics are not com-
puted. Constant horizontal water velocities in the
landfill and soil are estimated from soil or landfill
permeability and porosity and local hydraulic gradients.
The water table variations are entered as input data and
are obtained from measurements taken near the landfill
site.
While this approach of using greatly simplified
hydrodynamics has obvious inadequacies, the simple mod-
el should be useful for management of chemical disposal
in sanitary landfills. The assumptions and simplifica-
tions utilized to construct the simple model result in
higher predicted concentrations than is expected in
actual disposal situations. Thus the model is con-
servative with respect to potential health hazard, a
desirable approach to waste disposal management. Fu-
ture comparisons of model predictions with actual sani-
tary landfill behavior will enable the model accuracy
to be determined.
The SLM-1 Model
The objective of this project is to develop a com-
puter model of a sanitary landfill which is as simple
as possible and yet still include the principal factors
affecting the underground transport of the contaminant:
At a minimum, the model must account for the fol-
lowing factors:
1. both vertical and horizontal movement of the
contaminant (i.e. two dimensional distribution of chem-
ical) ,
2. adsorption of the porous media,
3. biodegradation of the contaminants,
4. variable water table which may rise to any
height in the landfill (possibly even completely flood-
ing the landfill) or drop to a depth below the landfill,
5. permeability, porosity, hydraulic gradient and
moisture bearing characteristics of the soil and landfill.
609
-------
The sanitary landfill model SLM-1f developed in
this study, is based on a vertical routing of contamin-
ant by a method similar to Remsom et al.° and a hori-
zontal routing corresponding nearly to flow through a
series of stirred tanks. The model is greatly simpli-
fied by performing a mass balance on the contaminant
only. No water balance is performed. The horizontal
velocity of the groundwater is assumed constant in the
landfill and soil and is estimated from the permeabili-
ty, porosity, and the hydraulic gradient of each media.
Both the landfill and the soil are assumed to be homo-
geneous with uniform permeability, porosity, hydraulic
gradient, biodegradation, and adsorption characteris-
tics within each porous medium.
Two-Dimensional Structure of SLM-1
The landfill and soil region is divided into a
grid, each compartment having dimensions of length
DELX, depth DELZ = 2 feet, and width WIDTH sufficient
to encompass the contaminated zone of the landfill.
SLM-1 is considered to be a two-dimensional model since
calculations account for distribution of chemical in
two directions only; i.e., vertical and horizontal.
Since dispersion of chemical in a lateral direction
is ignored, the model tends to calculate a higher con-
centration at a point downstream from the landfill than
would exist if the three-dimensional dispersion char-
acter were modeled.
Rainfall
Landfill
Column 1234567 KL=3, KT-7
Figure 1. Two-Dimensional Structure of SLM-1
The elevation of the top of each landfill and soil
column and the elevation of the bottom of each land-
fill column are specified as input data. It is assumed
that columns 1 to KL are landfill columns followed by
KL+1 to KT columns of soil where KL and KT are speci-
fied as input data. KL=0 means that the entire region
is soil.
Water Movement
The horizontal groundwater flow below the water
table is assumed to be unidirectional with a velocity
V(l) ft/day in the landfill and V(2) ft/day in the
soil. Movement of the chemical in the lateral direc-
tion is neglected.
Rainfall at an arbitrary rate R(J) falls on the
landfill and soil region and a fraction XINFL is as-
sumed to infiltrate into the porous media. This water
moves downward in the columns according to the simple
mechanism suggested by Remson et. al.°
Each two foot layer above the water table has an
initial moisture volume fraction of YI(1) for landfill
and YI(2) for soil. Water entering the top layer in a
column is retained until a moisture volume fraction
corresponding to field capacity is reached, i.e.,
YF(1) for landfill and YF(2) for soil. Additional water
entering a layer at field capacity freely drains to the
next layer below and so on. Eventually, all layers
above the water table will reach field capacity. Ad-
ditional water into the top layer will then move down-
ward to the water table carrying the chemical contamin-
ant into the groundwater. Each calculational time per-
iod is two days; thus, it is assumed that the porous
media above the water table can drain from saturation
to field capacity within this time.
Chemical Source
At time zero, the chemical contaminant distribu-
ted in any compartment of the landfill or soil columns
is specified as M(I,K) grams (entered as input data)
where I is the layer number and K is the column number.
An arbitrary source S(I,K) of chemical can be speci-
fied for any layer I,K as a function of time period J.
Groundwater flowing below the water table into column
1 and the precipitation entering the top layer of each
column are assumed to contain no chemical contaminant.
Adsorption Characteristics
Reversible adsorption of the contaminant onto the
soil and/or landfill material is assumed to be describ'-
ed by the Freundlich equation:
MA = K • C • SOLID
(1)
where: MA = chemical adsorbed (grams),
C = concentration of chemical in free solution
(mg chemical/liter or ppm),
SOLID = grams of porous solid material,
K = adsorption constant; may be different for
soil and landfill material (liter/gm solid).
Biodegradation of Contaminant
Biodegradation of the contaminant is assumed to
be first order:
MC = k • C • W • At • 10
-3
(2)
where: MC chemical degraded by reaction (grams),
k = rate constant (hr~l); may be different
for soil and landfill material
W = volume of solution under consideration
(liters),
At = time period (hours).
Chemical Mass Balance
Layer Above the Water Table. Each layer receives
leachate from the layer immediately above and dis-
charges leachate of different concentration to the lay-
er immediately below. The mechanism proposed for mass
balance calculations for a two-day period is as follows:
The volume of leachate from Qin liters, is added
to the volume of liquid in the layer from the previous
time period.
W = WQld + Q with W and Q, measured in liters. (3)
The total grams of contaminant is computed.
M
total
M + Q. • C. • 10 3 + S,
old in in '
(4)
where S is the source function, i.e., grams of contam-
inant added during this two-day period. The total grams
of chemical now is considered to adsorb on the porous
surface, to degrade by reaction or to remain in free
solution.
"
(5)
total ~ lui T M """ ML
where: MA adsorbed chemical (grams),
MF contaminant in the free solution (grams),
MC chemical degraded (grams).
MF
Since C = — (1000), where C is the concentration in
ppm, the equations can be combined to yield:
610
-------
MF =
total
1 + 77 • SOLID • 10 + kAt
(6)
justed accordingly, M = M MC.
Variable Water Table
The total grams of chemical in free solution MF, the
free concentration C, and the grams of chemical de-
graded MC can now be calculated. If the volume of liq-
uid in the layer exceeds that corresponding to field
capacity, VFC liters, the layer is drained to field
capacity, i.e., if W > VFC, Q
Q01
Q,,.
W - VFC, otherwise
0. The loss of contaminant to the layer below
out
10
-3
grams, is computed next. The total
liquid in the layer is now reset to W - Q and the
total grams of chemical adjusted to M = M - MC -
Q . C • 10~3.
out
The layer collects the leachate from above, mixes,
adsorbs, reacts, and then drains to field capacity to
supply leachate to the layer below. Thus, the process
proceeds.
Layer Below the Water Table. A layer below the
water table has a horizontal flow input and output due
to groundwater flow. It is assumed that the layer im-
mediately below the water table receives all the chem-
ical in the leachate which is routed vertically due to
rainfall infiltration. This assumption implies that
the landfill is located in a groundwater discharge area.
Layers further below the water table do not distribute
the chemical vertically.
Rising Water Table. If the water table has risen
since the last time period, it is assumed that the lay-
ers now saturated which were previously at field capa-
city (or lower) are brought to saturation with water
having no contaminant. That is, bringing these layers
to saturation has resulted in no movement of chemical.
Then, calculations are performed to distribute the
chemical vertically by infiltration and horizontally
by groundwater flow as described earlier for the con-
stant water table case.
Falling Water Table. When the water table drops,
the layers at saturation capacity above the new water
table must drain to field capacity which causes a verti-
cal routing of chemical in a manner similar to the us-
ual case for layers above the water table.
For calculational simplicity, the water due to
rainfall infiltration and this excess water (VSAT-VFC)
are routed vertically at the same time.
Validation of the SLM-1 Model
In the SLM-1 model, there are three major calcula-
tional procedures which should be validated.
1. Vertical rSuting of the chemical from the landfill
or soil media to the water table, an unsaturated
flow mechanism,
A layer below the water table is saturated, i.e.,
W VSAT. Horizontal routing is assumed to occur in
the following way. QH liters of liquid flows from a_,
compartment at concentration C ppm, thus QH • C • 10
grams are transferred downstream to the next column in
the same layer. QH = volume of liquid into the layer
in a two-day period.
QH = V • DELZ • WIDTH
28.32 • YS
(7)
where: V = groundwater velocity (ft/day),
28.32 = conversion factor (ft to liters),
YS = saturated volume fraction for porous
media = porosity.
Source chemical (S grams), chemical in the groundwater
from the layer immediately upstream (MTX) and chemical
from the layer above (only for the first layer below
the water table) are added to the layer.
M = M, - QH
last J x
10 3 + MTX + Q. . C.
in in
10
-3
(down- (up- (above)
stream) stream)
+ S.
(source)
(8)
QH litet
MTX grams
Kn. Cin I
Source S grams
QH liters, C
Free Concentra-
tion, C
2. Horizontal distribution of chemical by groundwater
flow beneath the water table, a saturated trans-
port mechanism,
3, And routing of the chemical near the water table
interface as the water table rises or falls.
Vertical Routing of Chemical Above the Water Table
o
The SLM-1 model uses the method of Remson et al.
to route moisture downward in the unsaturated media to
the water table. These investigators have shown that
this simple procedure satisfactorily agrees with exper-
imental results in a laboratory landfill. The SLM-1
model extends the Remson procedure to chemical routing
by assuming that each two foot layer of porous media
acts as a well-mixed vessel in transporting the chemi-
cal downward. Although untested with experimental
data, this procedure is expected to satisfactorily pre-
dict chemical movement above the water table, provided
the soil can drain freely to field capacity in a two
day time period.
Horizontal Distribution of Chemical in Groundwater Flow
To determine the validity of the SLM-1 model pre-
dictions of chemical movement beneath the water table,
two auxiliary models were developed in this study.H A
continuous one-dimensional model with an exponential
source function and a multi-tank approximation of the
continuous model were compared with SLM-1. SLM-1 pre-
dicts essentially the same horizontal distribution as
the multi-tank model. Results from the multi-tank model
approach the continuous model behavior as the tank size
is decreased. It was concluded that the SLM-1 model
agrees reasonably well with the classical model of one-
dimensional species movement in a saturated porous media.
Variable Water Table Effect on Chemical Distribution
The total chemical now mixes, adsorbs, and is partially
degraded. The total grams of chemical Mthis j is ad-
The model calculations for the case of a rising
or falling water table have not been validated due to
611
-------
the lack of a satisfactory standard for comparison.
Future studies should attempt to validate the assumed
distribution mechanism.
Case Study
Brown's Island Landfill, Salem, Oregon
A general description of the Brown's Island area
is included in the report by Balster and Parsons^. A
complete report by Sweet 10 concerning the hydrogeology
of the landfill site is on file with the Oregon State
Engineer and the Department of Environmental Quality.
The Brown's Island landfill is located between the
Willamette River and a meander channel of the river.
It occupies the lowest geomorphic unit in the valley,
the flood plain, and is subject to surface water inun-
dation. Both the soils and the immediate subsurface
deposits at the site have relatively high hydraulic
conductivity.
Infiltrating precipitation and a water table which
regularly saturates the putrescible material deposited
at the site results in the generation of leachate at
the site. The down-gradient flow of the leachate is
sub-parallel to the flow direction of the adjacent sur-
face water bodies. This results in the degradation of
the shallow ground waters in the local system and the
eventual drainage of some contaminants into the local
surface water bodies, i.e. the sloughs,, the ponds in
the borrow pit bottoms, and the Willamette River.
A ground water monitoring system has recently been
installed at the site. In the future it will be pos-
sible to monitor the quality of the groundwater in the
vicinity of the landfill and to compare the observed
leachate concentrations with those predicted by the
model.
SLM-1 Model Calculations - Hypothetical Source
Figure 2 gives all the input data used in this
case study. A typical annual water table elevation,
in feet above mean sea level, of the Brown's Island
area is shown. It was assumed that 45,400 grams of a
chemical were initially distributed in an area 4 ft by
40 ft by 20 ft at the top of the landfill with no
source added thereafter. The simplified rainfall and
soil characteristics correspond to conditions typical
of the Brown's Island area.
Figure 3 shows concentration distributions as a
function of time at 400 feet down the hydraulic grad-
ient from the landfill site. Observe that in all the
cases shown in this figure that it takes at least three
years before any appreciable concentration amplitude is
obtained at the 400 foot distance from the landfill
site. That peaks (pulses) of chemical concentration
are generated and then dispersed while translating
down gradient is a very real physical phenomenon and
reflects among other things, the physical interplay of
a pulse type annual rainfall and the variable elevation
of the water table under both the landfill site eleva-
tion (chemical source) and the soil conduit. The ex-
planation of the peak(s) formation is as follows. A
portion of the rain that falls upon the surface of the
landfill site penetrates the surface creating the po-
tential for moving some of the chemical vertically
downward according to the rules of moisture routing.
Simultaneously, the water table is moving up and down.
When enough water moving downward from the top of the
landfill site (carrying some but not all of the chem-
ical with it) meets the water table, then chemical
moves horizontally and eventually out into the various
soil conduits. Only four layers of soil conduits are
shown in Figure 2. However, this is adequate to demon-
strate the model, Once the chemical pulse reaches one
of the soil conduits, it can continue to be distributed
by convection and dispersion down gradient so long as
the water table covers that conduit. When the water
table drops below the level of that conduit then hori-
zontal motion ceases and vertical motion is allowed to
proceed according to the previously mentioned rules of
the model. The net result, as might be observed in a
monitoring well (impervious casing) bored through the
top three conduit (layers) and into the fourth at the
400 feet down gradient point, is the concentration dis-
tribution curves shown in Figure 3. This figure demon-
strates the effects that reversible linear adsorption
and irreversible microbial degradation and/or first or-
der chemical reaction would have on the concentration
distributions.
Numerous computer simulation runs have been made
for various source functions and for a wide range of
adsorption-degradation conditions. All parameters of
the model have been studied to demonstrate model sensi-
tivity. Adsorption and degradation are the key para-
meters for predictive model calculations.
Each computer run of ten year duration costs ap-
proximately $60 using the Oregon State University CDC
3300 computer, including the plotting of all results.
The model is usually run from a remote location by
timesharing with the results plotted on a graphics ter-
minal for ease of interpretation.
Recommendations
It is believed that this rather general predictive
model for the movement of hazardous waste chemicals in
both the landfill and the surrounding porous medium is
valid enough to be used as a decision-making tool in
the management of hazardous waste disposal. It clearly
sets the upper limits on the expected concentrations
for a real field situation. However, the complete mod-
el should be given a long-term field test. This field
test might be carried out by incorporating a sufficient
number of monitoring wells together with known charges
(geometric position and actual chemical mass known at
the time of introduction) of certain industrially and
agriculturally important chemicals, which may typically
be dumped into a landfill site. While the model is com-
posed of generally field-tested components (vertical
routing techniques worked out at Drexel University by
Remson et. al., and horizontal saturated flow tech-
niques well-known in chemical engineering), this par-
ticular model which combines both the vertical and hor-
izontal techniques has never been field tested.
Acknowledgement
This research work was supported by the National
Institute of Environmental Health Sciences (Grant ES-
00210) and the Oregon Department of Environmental Qual-
ity's grant with the Environmental Protection Agency
(#2-G05-EC-0014-04). Special thanks are also due to
Professor L. Boersma, OSU Department of Soil Science;
Randy Sweet, State of Oregon Engineer's Office; and
Pat Wicks, Oregon Department of Environmental Quality
for their active participation on the OSU Environmental
Sciences Center Task Force on Environmentally Hazardous
Wastes .
References
1. Balster, C.A. and R.B. Parsons (1968), Geomorphol-
ogy and Soils, Willamette Valley, Oregon, Agri-
cultural! Experiment Station, Oregon State Uni-
versity, Special Report 265, 9-15.
2. Bredehoeft, J.D. and G.F. Pinder (1973), Mass Trans-
port in Flowing Groundwater, Water Resour. Res.,
9, 194.
612
-------
3. Freeze, R,A. (1971), Three-Dimensional, Transient,
Saturated-Unsaturated Flow in a Groundwater
Basin, Water Resour. Res., ]_, 346.
It. Freeze, R.A. (1972), Subsurface Hydrology at
Waste Disposal Sites, IBM J. Res, Develop.,
_16, 117.
5. Fungaroli, A.A. (1971), Pollution of Subsurface
Water by Sanitary Landfills, Interim Report
SW-12rg to U.S. Environmental Protection
Agency, Vol. 1.
6. Pinder, G.F. and J.D. Bredehoeft (1968), Applica-
tion of the Digital Computer for Aquifer Eval-
uation, Water Resour. Res,, 4^ 1069.
7. Pinder, G.F. and H.H. Cooper, Jr. (1970), A Num-
erical Technique for Calculating the Transient
Position of the Saltwater Front, Water Resour.
Res. , 6^, 875.
9.
Remson, I., A.A. Fungaroli, and A.W. Lawrence
(1968) , Water Movement in an Unsaturated Sani-
tary Landfill, J. Sanitary Engineering Divi-
sion, ASCE, SA2, April, 307.
Schwartz, F.W. and P.A. Domenico (1973), Simula-
tion of Hydrochemical Patterns in Regional
Groundwater Flow, Water Resour, Res., 9_, 707.
10. Sweet, H.R. (1972), Brown's Island Landfill, Re-
port to Department of Environmental Quality,
September 6, 1972, Oregon State Engineer's
Office, 7.
11. Wang, C.H. et.al. (1974), Disposal of Environ-
mentally Hazardous Wastes, Task Force Report
for the Environmental Health Science Center,
Oregon State University.
OS. STUN Of A SftllTAW UtOTL. SlffllM 10 BKMi'S [SUM AT SAlfA CSEOH
ISO'-
400 ft -
IkwuolS
2 Dw lilt tarn
T-0
HATER T»
3ft - 4020), m, 2025), 3024), 2<]25), ]26, ]24, 2022), ]26, ]24, 122, 3<120), J22,
E8, 126,122, 3020), 124, 3U26), 130,132, 134, 12, '30, 15, 128. 2(126),
4024), 3U2D, 5020), 122,126, 2(128), 124, 122, 4020), 2(126), 3U24),
5020), 3024), ID5U2D)
SOME: <6, 4X owe DISTRIBUTED UIIRRH.V IN TOP 4 FT. v LMFIU. (ncR A HIDIH OF
20 FT. WD A \OKTH CF 4) FT. AT TIIC ZERO. Ib ADDITICNAL SORCZ AF1ER T-0.
SUIF«I EitvATlOH: 6Q«), 44(126)
M OF BOTTOM OF LMFIU.: 4(120)
Figure 2. A Case Study of Brown's Island Sanitary Landfill
Figure 3. Typical Concentration Plots at 400 Feet Fro the Landfill
613
-------
PHYTOPLANKTON BIOMASS MODEL OF LAKE HURON AND SAGINAW BAY
Dominic M. DiToro
Environmental Engineering and Science Program
Manhattan College
Bronx, New York 10471
Walter F. Matystik, Jr.
Environmental Engineering and Science Program
Manhattan College
Bronx, New York 10471
Summary
The basis for this analysis and projection of
Lake Huron and Saginaw Bay phytoplankton bio-
mass is a dynamic mathematical model which
relates the growth and death of phytoplank-
ton biomass to the nutrient concentrations on
the one hand and zooplankton biomass on the
other, as well as the effects of mass trans-
port due to the water motions and the exo-
genous variables, water temperature and inci-
dent solar radiation. The particulars rele-
vant to the application of such a model to a
setting such as this where there exists large
differences in concentrations of biomass and
nutrients between Saginaw Bay and Lake Huron
proper are discussed. The model is shown to
agree reasonably well for both regions
simultaneously which provides strong evidence
that it is a reasonable representation of the
situation in the lake and bay.
Background
Lake Huron, the second largest of the Great
Lakes and fifth largest lake in the world,
has a water surface area of 23,000 square
miles.-'- Saginaw Bay is an inland extension
of the western shore of Lake Huron pro-
jecting southwesterly midway into the south-
ern peninsula of Michigan. It receives
drainage from a basin seven times bigger than
the bay itself, or over 8,000 square miles.2
Major inflows to Lake Huron proper are from
the St. Mary's River draining Lake Superior
and across the Straits of Mackinac from Lake
Michigan. Other tributary flows enter the
lake in Georgian Bay and the North Channel
from the Canadian basin and along the State
of Michigan shoreline on the U.S. side. Out-
flow is via the St. Clair River.
The Saginaw River is the major tributary to
Saginaw Bay and enters the bay at its south-
western end. It receives both municipal and
industrial discharges and its total tribu-
tary system drains an area of approximately
6,200 square miles.1 Significant loading
to Saginaw Bay results from the input of the
Saginaw River. Since the bay is shallow
relative to Lake Huron most of the effect of
Saginaw River input is felt within the bay
itself. The resultant situation, then, is an
essentially oligotrophic Lake Huron with eu-
trophic conditions in Saginaw Bay.
It is this complex problem setting which the
model described herein specifically addresses.
Kinetics of Phytoplan'kton Biomass
Application to other problem settings3'4
and in particular a detailed exposition and
application to Lake Ontario 5'6 provide the
background for the discussion below. The
basic structure, assumptions,and compilation
of relevant coefficients is also available,7
The phytoplankton biomass that develops in a
body of water depends on the interactions of
the transport to which they are subjected and
the kinetics of growth, death, and recycling.
The structure of the model is shown in Figure
1. Phytoplankton biomass growth kinetics are
a function of water temperature, incident-
available solar radiation, and nutrient con-
centrations, specifically inorganic nitrogen
and phosphorus. Phytoplankton also endogen-
ously respire and are predated by herbiverous
zooplankton which grow as a consequence. They,
in turn, are predated by carnivorous zooplank-
ton whose biomass increases as a result. Zoo-
plankton grazing and assimilation rates are a
function of temperature and, for the herbiv-
erous zooplankton, the phytoplankton biomass
as well. Zooplankton respiration is tempera-
ture-dependent. The nutrients, which result
from phytoplankton and zooplankton respira-
tion and excretion, recycle from unavailable
particulate and soluble organic forms to in-
organic forms,ammonia and orthophosphate for
nitrogen and phosphorus respectively. The
recycle kinetics are temperature-dependent.
In addition, they are a linear function
of the phytoplankton biomass present. The
latter assumption is a modification introduced
for the Lake Huron model and is based on the
following reasoning: the recycling is either
being accomplished by the phytoplankton them-
selves; they break down the soluble organic
material prior to assimilation, or by the
bacteria present as a consequence of their
metabolizing the detrital material. For the
former mechanism phytoplankton biomass de-
pendence is expected. For the latter situ-
ation, if the rate is dependent on bacterial
biomass, and if phytoplankton primary pro-
duction is the major source of organic
carbon for the bacteria, it is reasonable to
suppose that bacterial biomass is proportion-
al to phytoplankton biomass, which results
in the same dependence of recycle rate on
phytoplankton biomass.
In addition to the kinetics described above,
the mass balance equations which comprise
the model account for the transport of
material between Lake Huron and Saginaw Bay,
the inputs into Saginaw Bay from the Sag-
inaw River and other sources, and the loss
of phytoplankton and particulate detritus
via sedimentation. The magnitude of the
rate of regeneration of the nutrients
associated with the sedimented material
is an issue yet to be resolved.
614
-------
©AtH-KATE*
IMTEAfACE
DISTRIBUTED &
K)LNT SOURCES
ORGANIC
NITROGEN
"0
f
^-^
-Qy—
AMMONIA
"I
~*
f
* *
Figure 1. Kinetic Interactions
The range of the magnitude of the rate con-
stants for the kinetic terms in the mass
balance equations are obtained in the first
instance from the literature. The ac-
tual values used are obtained by a calibra-
tion of the model using a set of observed
data which includes observations for every
variable computed. For the case of the Sag-
inaw Bay - Lake Huron model, the constants
are chosen so that the model reproduces the
observed behavior of all variables in both
the bay and the lake proper. This is a
stringent test of such a model, since nutri-
ent concentrations, primary production rates,
phytoplankton and zooplankton biomass differ
by an order of magnitude.
Segmentation of the System
The model constructed for Lake Huron is a
large spatial scale seasonal time scale
model comprising five volumes representing
Northern Lake Huron epilimnion and hypo-
limnion, southern lake epilimnion and hypo-
limnion and Saginaw Bay. Figure 2 illus-
trates this model segmentation.
This structure reflects the three character-
istic regions of the lake: Saginaw Bay;
Southern Lake Huron which is influenced to
some degree by the bay due to circulation
patterns; and the open waters of the Northern
Lake which appears to act as a large receiv-
Top Layer
0-15 meters
ing body for the inputs from Lakes Michigan
and Superior.
The top layer ranges from the surface to a
depth of 15 meters which is the depth of
stratification. The second layer extends
from 15 meters to the lake bottom. The verti-
cal layers are necessary for the incorpora-
tion of effects such as biomass sinking with
associated nutrient loss from the epilimnion
as well as the effects of stratification on
nutrient availability.
Data Sources
The verification of a complex eutrophication
model requires a large amount of comprehen-
sive, detailed, physical, chemical, and biol-
ogical data. The credibility of a model is
judged, in large measure, by its agreement
with observations. Thus a detailed review
of available data was made. The historical
data for Lake Huron and Saginaw Bay was inad-
equate in many ways so that a coordinated sur-
vey effort was mounted in 1974. The agencies
involved were: the Canada Centre for Inland
Waters (CCIW), University of Michigan, Great
Lakes Research Division (GLRD), and Cranbrook
Institute of Science (CIS) with both GLRD
and CIS under the direction of the Environ-
mental Protection Agency, Grosse lie Labor-
atory. CCIW concentrated in the Northern
Lake, GLRD in the Southern Lake, and CIS in
Saginaw Bay.
Second Layer
15 meters - bottom
Figure 2. Model Segmentation
615
-------
The verification data base which resulted
from aggregation of these sources is quite
large. Altogether, a total of 35 cruises
and about 225 individual sampling stations
measured data over a range of depths. The
processing of these data for use in model
verification requires that means and stan-
dard deviations for all stations of each
survey within a segment for each cruise be
computed. The values for each survey are
then overplotted and the result is a set of
data for each model segment for all para-
meters to be verified. The utility of this
comprehensive data set cannot be over-empha-
sized since the historical data prior to
these surveys were not adequate for the veri-
fication of a lake model of the type pre-
sented herein.
Transportation Structure and Verification
The major external influences on Saginaw Bay
are the incoming flow of the Saginaw River
and a circulating flow from Lake Huron which
enters along the northwestern shore and exits
along the southeastern shore. The flow has
been characterized by several investiga-
tors 8,9,10 all of Whom have postulated this
west to east circulatory flow in Saginaw Bay
at least under one generalized type of wind
pattern. This Saginaw Bay - main lake flow
exchange is incorporated into the model .
One of the aims of the transport verifica-
tion is to estimate its magnitude, since it
determines the flushing rate of the bay.
Another feature of the model transport struc-
ture is a north to south main lake circula-
tory flow. Values used are consistent
with observed surface velocities, although
no strong gradients exist, making it
difficult to verify.
The other major aim of the transport verifi-
cation exercise is to estimate the magnitude
of vertical mixing between northern and
southern main lake epilimnion and hypolim-
nion. This is vital to a vertically struc-
tured model since it determines the degree
of nutrient availability in the open lake
epilimnion during stratification.
The verification procedure for transport in-
volves calculating the distribution of a
suitable tracer and comparing it to observa-
tions. In Saginaw Bay, the horizontal trans-
port regime was verified using the large
gradients which exist between the bay and
the main lake for temperature, chlorides,
and total phosphorus. In the main lake the
vertical transport was verified using ver-
tical temperature gradients. Figure 3 shows
the observed versus computed profiles for
temperature and total phosphorus in the Sag-
inaw Bay model segment and for temperature
in the main lake epilimnion and hypolimnion
segments. The agreement achieved indicates
that the Saginaw Bay transport and the ver-
tical exchange rates are consistent with
observation.
Estimates of Nutrient Inputs
Having verified a transport regime and incor-
porated this into a phytoplankton modeling
framework, the only remaining exogenous var-
iables to be specified are the waste load
inputs for the parameters to be modelled.
Recently, much new data for Lake Huron waste
loading has been made available. 1/1?
This comprehensive data base includes Sagi-
naw River loading as well as municipal and
industrial inputs for both the Province of
Ontario and the State of Michigan, tributary
inputs for these same sources including esti-
mates of load contributed by ungaged drain-
age basins, atmospheric inputs and inputs
from the St. Mary's River and the Straits of
Mackinac.
Utilizing the best available information,
these loads were structured for input to the
model. Some significant results of this in-
formation are that inputs to Saginaw Bay of
approximately 7,000 Ibs total phosphorus/day
make up about one third of total phosphorus
input to the entire lake, that atmospheric
sources contribute a significant portion of
the total nitrogen (31%), and that most of the
impact of Province of Ontario tributary load-
ings to North Channel and Georgian Bay are
felt within those localized areas and do not
have a great impact on Lake Huron proper.
This formulation is used for model
verifications.
; Phytoplankton Biomass Model Verification
Figure 4 illustrates computed versus observed
profiles for phytoplankton chlorophyll, zoo-
plankton, ammonia and reactive phosphorus,
for the Saginaw Bay and northern and southern
main lake epilimnion model segments. Other
parameters which were equally well verified
were total phosphorus, nitrate, and primary
productivity.
Phytoplankton chlorophyll in the northern
lake epilimnion segment increases during the
spring to an early summer maximum limited by
available phosphorus. Herbivorous zooplank-
ton grazing then lowers the concentration
substantially which then recover as carniv-
orous zooplankton prey on the herbivors.
The secondary recovery utilizes phosphorus
provided by the recycle mechanisms. The
spring increase of phytoplankton chlorophyll
is more pronounced in the southern lake
epilimnion segment. Zooplankton predation
again causes a decrease with a secondary
bloom occurring in the fall. Nutrient pat-
terns are similar to the northern lake epil-
imnion. Total zooplankton biomass is both
calculated and observed to remain substantial
throughout the fall months.
It is important to note the order of magni-
tude difference in concentrations of phyto-
plankton biomass and nutrients for the Sagi-
naw Bay model segment versus the northern
and southern epilimnion model segments.
Agreement between calculations and observa-
tions indicates that the model is capable of
reproducing behavior in both situations. It
should be emphasized that the kinetic con-
stants used are the same for both the main
lake and the bay.
616
-------
TEMP
'0.03
60.00 120.00 180-OO 2W-00
TIME DRYS SEGMENT 1
300.00
3 °D.OJ
eo.oo
ISO. 00
^80.oo
TIME DflYS SEGMENT 4
eso .00
300'00
360.00
'o.CO
eo.00 120.00 leo.Qo aw-oo
TIKE DRY3 SEGMENT 2
300.00
* §
TEMP
360.00
TOT P
C-O) 60.00 1M.M 180.00 SW .00
TIME MIS SEGMENT 3
300.00
60.00 120.00 160.CO 2*3 ,K
TIMF OflVS SEGMENT 3
390.00
Figure 3. Computed Versus Observed Profiles for Temperature (°C) in All Model Segments
and Total Phosphorus in the Saginaw Bay Model Segment
Conclusions
It is common to require as a criterion for
verification of a model that it reproduces
observed phenomena over a range of envir-
onmental conditions. It is especially use-
ful if the conditions cover the region for
which model projections are desired. Al-
though this is seldom possible, the Saginaw
Bay - Lake Huron model does reproduce obser-
vations which vary over a wide range of
nutrient concentrations. Hence it appears-
reasonable to claim that the model is veri-
fied at least to that extent. The signifi-
cance, then,of this verified model is that
it becomes'a useful planning tool to esti-
mate the effects of nutrient reduction
policies. These policies will tend to lower
the concentrations in Saginaw Bay and thereby
bring values closer to Lake Huron values for
which the model is also verified.
References
Great Lakes Basin Framework Study,
Appendix 7, Great Lakes Basin Commission.
Freedman, Paul L. EPA-905/9-74-003, 1974.
Di Toro, D.M.; D.J. O'Connor & R.V.
Thomann; Simulation in Ecology, Vol. Ill,
1975.
4. Thomann, R.V.; D.M. Di Toro & D.J.
O'Connor; Proc. Amer. Soc. Civil Eng.
100 (EE2), June 1974.
5. Thomann, R.V. R.P. Winfield & D.M.
Di Toro; Proc. 17th Conf. Great Lakes
Res. 1974.
6, Thomann, R.V.; D.M. Di Toro; R.P.
Winfield & D.J. O'Connor, EPA-660/3-75-
005, 1975.
7. Di Toro, D.M.; D.J. O'Connor, & R.V.
Thomann; "Nonequilibrium Systems in
Natural Water Chemistry," Advan. Chem Ser.
106, 131-180. Amer. Chem. Soc.'
Washington D.C., 1971.
8. Ayers, J.C.; D.V. Anderson; D.C. Handler;
& G.H. Lauff, University of Michigan
Great Lakes Res. Div. Pub 1, 1956.
9. Beeton, Alfred M. Trans. Amer. Fish.
Soc. 87, 1958.
10. Johnson, James H., Spec. Soc. Rept.
Fish. No. 267, U.S. Dept. Int. Fish
& Wildlife Service, 1958, 1956.
11. Richardson, William L. & Victor J. Bierman,
Jr. to appear in EPA, Ecological Res.Series,
12. International Joint Commission - Vol. II
Ch. 2 Upper Lakes Reference Study Report .
Acknowledgements
The insight of our colleagues, Drs. Robert
V. Thomann and Donald J. O'Connor^is grate-
fully acknowledged as well as the assistance
of Suwan Numprasong and William Beach. This
research was sponsored by the U.S. EPA under
Grant No. R803030.
617
-------
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SEGMENT 3
°bserYe? Profiles for phytoplankton chlorophyll (A); herbivorous
) and total (D) zooplankton; amnonia nitrogen (E); soluble reactive
in northern lake epilimnion (segment 1). southern lake epilimnion (segment 2)
and Saginaw Bay (segment 3) model segments.
618
-------
COMPARISON OF PROCESSES DETERMINING THE FATE
OF MERCURY IN AQUATIC SYSTEMS
Lassiter, R.R., Malanchuk, J.L., Baughman, G.L.
Environmental Research Laboratory
Athens, Georgia
Summary
An analysis of factors affecting the fate
of mercury in aquatic systems is made using a
mathematical model. Three forms of mercury
(mercuric, elemental, and methyl) are
represented. All forms are considered to be
present in both the water and sediment
portions of the system. Processes
influencing the behavior of mercury forms are
assumed to be oxidation, reduction,
methylation, demethylation, sorption,
sediment/water exchange, volatilization, and
longitudinal transport. Environmental
factors of importance are pH, concentration
of suspended particulates, depth of water,
and depth of sediment. Three dimensional
graphs (concentration vs. time and distance)
are used to portray the temporal behavior of
the mercury forms along a stretch of slowly
moving stream. Mercuric mercury flows
through the reach, partitioning into the
sediment as it flows. The spatio-temporal
pattern of methyl and elemental forms in both
water and sediment is controlled largely by
the mercuric mercury sorbed to the sediments.
This effect and the sensitivity of all the
forms to a range of values used for the
sediment/water partition coefficient for
mercuric ion, lead to the conclusion that
sorption is the single most important factor
influencing the behavior of mercury in
aquatic systems. There is a slow loss of
total mercury to the system by
volatilization. Predicting the
concentrations of mercuric mercury species in
a system accounts for most of the total
mercury. However, the model, directed toward
environmental pollution predictions, must
also account for the fate of low-level but
hazardous forms such as methyl mercury.
Introduction
The fate of mercury in environmental
systems results from the concurrent
functioning of many processes. Some of these
processes respond in complex ways to several
environmental factors. For example, one
pathway of oxidation of elemental mercury is
a function of the oxygen concentration and
hydrogen ion concentration; the extent of
sorption of mercuric ion is a function of the
concentration and nature of the particulate
material, the hydrogen ion concentration, and
other factors.
Simultaneous (parallel) processes are
competitive, yet any one of them may operate
in a chain of serial processes, e.g.,
sorption of mercuric ion could act as the
concentrator for microbially mediated
methylation. The web of interconnected
serial and parallel processes forms the
biogeochemical cycle of mercury. A necessary
condition for predicting the fate of mercury
is to have a basic understanding of its
biogeochemistry. That condition, however, is
not sufficient to permit one to predict its
fate, because its biogeochemistry is complex
and resources are finite. Thus predicting
the fate of mercury becomes an exercise in
judicious selection of the chemical forms to
consider, the important processes that link
these forms, and the resources to use for
making the predictions.
Because of the complexities introduced by
environmental variables driving these
processes, and by the multiplicity of these
processes occurring serially and in parallel,
a computer model was the means chosen for
making the prediction. The forms selected
and the processes linking these forms into a
biogeochemical cycle were chosen to
ultimately permit prediction of methyl
mercury and its biological consequences.
Before attempting the detailed predictions
for methyl mercury, the biogeochemistry
linking it and the other two forms, mercuric
and elemental mercury, needs to be
satisfactorily represented in the model. The
biogeochemical cycle linking these forms of
mercury in a water/sediment system is
represented in Figure 1.
Air
l-Oxidation 4-Methylation
2-Reduction 5- Demethylation
3-Volatilization 6- Sediment-Water Exchange
7-Flow
Figure 1. Schematic Representation of the
Components, Transformations, Exchanges and
Transport Pathways Represented in the Model.
619
-------
One process, sorption, is not indicated
explicitly in Figure 1. However, sorption
is represented in the model by partitioning
mercuric and methyl mercury into sorbed and
dissolved fractions.
Model Description
A set of differential equations is used
to describe the dynamics of the forms of
mercury in the system. In Figure 2 a set of
equations for a system without hydrodynamics
is given, using mnemonic abbreviations for
the term descriptions.
d[Hg(+2)]w
dt
= oxid - swx- red - meth
d[CH3HgX]w.
dt
d[Hg°]w
dt
= meth-swx-demeth
= red + demeth -swx-oxid - volat
d[Hg(+2)]s
dt
=oxid + swx- red-meth
d[CH3HgX]s.
dt
d[Hg°]<
dt
= meth+swx-demeth
= red + demeth + swx-oxid
Figure 2. Differential Equations Indicating
Source/Sink Terms.
swx = sed/water exchange
meth = methylation
volat = volatilization
demeth = demethylation
oxid = oxidation
red = reduction
The aquatic system described by the model
consists of a body of moving water in contact
with the atmosphere and underlying sediments.
The hydrodynamics of the moving water is
represented by advection and dispersion terms
in one dimension. Each equation is of the
form
= D 32[Hg] _ V 3 [Hg]
3x2
3x
S([Hg])
in which Hg represents any one of the forms
mentioned above and listed in Figure 2, the
first term on the right represents
dispersion, the second advection, and the
third a set of terms from the appropriate
equation of Figure 2, and which represent
sources and sinks. The source-sink terms, S,
are written as functions of environmental
descriptors, e.g., pH, concentration of
suspended particulate material, or depth of
sediment and water. Although a great deal is
known about the chemistry of mercury, none of
the source or sink terms can be written
without conjecture. Nevertheless, an attempt
was made to structure each term to reflect as
much as is understood about the chemistry of
the process.
An example from the mercury model will
illustrate some of the uncertainties
accompanying the writing of source or sink
terms. Oxidation and reduction of elemental
mercury and mercuric ion, respectively, is
described by the following equilibrium
expression (Parks, G.A., pers. comm.)
[Hg°]
[Hg2+]
However, observations from several types of
experiments show that the reactions do not
proceed rapidly to completion, i.e.,
solutions containing mercuric ion continue to
produce elemental mercury for days (1,2,3).
Because of these observations the reactions
are better represented by rate terms rather
than by algebraic equilibrium expressions.
Equilibrium expressions do not necessarily
reflect mechanisms, and rate expressions
cannot properly be obtained from them. In
spite of this fact, the following reactions,
given by Parks (4), were used to represent
oxidation and reduction pathways:
Hg
2 +
The term for oxidation was taken to be
k [Hg°] [H+]2
and reduction was
For the environment reduction cannot be
as simply represented as this term. It is
complicated in most natural waters by the
presence of suspended particulate material
which is probably encased by a layer of
organic material (5). Mercuric ion complexes
strongly (6) with sulfhydryl-containing
compounds and is expected to bind strongly to
suspended particulates. The question facing
the modeler is whether reduction of mercuric
ion bound to particulates can be represented
by a simple proportion as assumed for the
dissolved fraction. If not, the bound
mercuric ion concentration must be computed.
The following equations are used as an
approximation for computing the bound
mercuric ion, also taking into account
hydrolysis.
620
-------
Hg2+ + H 0
HgOH
Hg2+
+ H o:
2
:Hg
HgOH + H
Hg(OH) + H"1
2H+
Each term in the model was subject to
similar uncertainties. The question of how
to express accepted chemical, biochemical or
other equations in the context of a complex
natural system is the basic difficulty facing
the "environmental modeler".
Results and Discussion
Here, < , is a symbol for suspended particles
treated as though they are a dissolved
constituent. The three equilibria are
[HgOH+]
[Hg2+]
= K
[Hg(OH
Figures 3-8 show a pulse input of
mercuric ion to the system and its fate in
the system, i.e, its transformation to other
forms, its transport to the sediment, and its
loss from the system. The simulated time is
20 days. Mercuric mercury is introduced and
quickly flows through the system (Figure 3}
leaving mercuric mercury bound to the
sediments (Figure 4) and leaving elemental
and methyl mercury transformation products
(Figures 5-8).
[HgOH+]
[Hg]
and the free mercuric ion fraction, <$, is
[K K K + K [P]"]-1
IK*? + [H+]2 J
Depending upon whether reduction of only free
mercuric ion or of both bound and free can be
described by the constant proportion, the
reduction term is either
-------
Figure 5. Concentration of Elemental Mercury
in Water Versus Time (Right Axis, 20 Days) and
Distance (Left Axis, 1 km).
Figure 7. Concentration of Methyl Mercury in
Water Versus Time (Right Axis, 20 Days) and
Distance (Left Axis, 1 km).
Figure 6. Concentration of Elemental Mercury
in Sediment Versus Time (Right Axis, 20 Days)
and Distance (Left Axis, 1 km).
Figure 8. Concentration of Methyl Mercury in
Sediment Versus Time (Right Axis, 20 Days) and
Distance (Left Axis, 1 km).
Sorption holds mercuric mercury in the
sediments so that, unlike the pattern in
water, it remains at a point along the stream
with loss essentially by transformation only.
This gives the graph (Figure 4) its solid
appearance relative to that of Figure 3.
In the sediments there is continual
transformation of mercuric mercury to the
elemental and methyl forms. Graphs of these
forms (Figures 5-7} more or less resemble
that of mercuric mercury (Figure 4). It is
apparent from these figures that sorption is
a major controlling factor of the temporal
behavior of mercury in aquatic systems.
Only two permanent losses are
represented, outflow and volatilization. The
effect of outflow is shown in in Figure 3.
The effect of volatilization can be
visualized by observing that all the slopes
of the concentrations with time are
negative. These negative slopes result from
volatilization of elemental mercury from the
water and from recycling of the forms to
mercuric with subsequent outflow. Another
loss, not explicitly considered, which may be
nearly permanent is conversion to mercuric
sulfide. However, it can be considered to be
implicitly contained in the partition
coefficient.
622
-------
In evaluating the importance of sorption,
the partition coefficient for binding of
mercuric ion to solids, Kp, was varied over
five orders of magnitude, and the behavior of
the forms of mercury was observed. Figures 9
and 10 show the behavior of methyl mercury as
a result of varying degrees of sorption of
mercuric mercury. Methyl mercury
concentration was higher in the sediments
for smaller values of Kp (Figure 9), whereas
the opposite is true of water (Figure 10).
0.27
— 0.26
K>
O 0.25
7 °-24
IT
0.23
x 0.22
UJ 0.21
O
S 0.20
0.19
10
-2
10"'
10°
Kn
10'
10'
10°
Figure 9. CH..HGX IN SEDIMENT AS A FUNCTION
OF Kp
The bulk of total mercury in a system is
undoubtedly some form of mercuric mercury.
The elemental form has rarely, if ever, been
measured in an environmental sample, and
methyl mercury is seldom measured in water
samples (7,8). One could delete both
elemental and methyl mercury from the model
and still account for an overridingly large
portion of the total mercury. But elemental
mercury is important to the ultimate fate of
mercury. It is formed at different rates
under differing conditions, and is the only
loss from total water systems. Methyl
mercury, a minute portion is important
because of its health and ecological
implications. In general, predicting the
fate of a pollutant will consist of
predicting the fate of the bulk, so that the
fate of small but hazardous portions
can be predicted.
Conclusions
Using a skeletal model of the
environmental chemistry of mercury a few
processes emerge as dominant in its fate.
Sorption is the most prominent feature in the
temporal behavior of mercury. It affects the
pattern of loss of mercury from the system by
both outflow and volatilization. Predicting
the fate of mercury involves not only
predicting the fate of the major portion, but
also predicting the fate of minute fractions
whose health and ecological effects make them
important.
0.32
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g
^ 0.24
'(/)
C£ 0.20
UJ
-; 0.16
(f)
UJ
0.12
0.08
0.04-
0.00
IO
'2
IO'1
10
I01
I0
I0
Figure 10. CH3HGX IN WATER AS A FUNCTION OF K
Literature Cited
Bisogni, J.J., Lawrence, A.W., Kinetics
of Microbially Mediated Methylation of
Mercury in Aerobic and Anaerobic Aquatic
Environments. Technical Report 63.
Cornell University Water Resources and
Marine Sciences Center. Ithaca, New
York. 180p. (1973).
Holm, H.W., Cox, M.F., Mercury in Aquatic
Systems: Methylation, Oxidation-
Reduction and Bioaccumulation. Report
NO. EPA-660/3-74-021. U.S.
Environmental Protection Agency.
Corvallis, Oregon. 38p. (1974).
Baier, R.W., Wojnowich, L., Petrie, L.,
Mercury Loss From Culture Media. Anal.
Chem. 44,2464-2467 (1975).
Parks, G.A., Dickson, F.W., Leckie, J.O.,
McCarty, P.L., Trace Elements in Water:
Origin, Fate and Control: I. Mercury.
Report of Progress, Mar. 1, 1972 to Feb.
1, 1973. Submitted to National Science
Foundation. Stanford University.
Stanford, California. 247p. (1973).
Neihof, R.A., Loeb, G.W., The Surface
Charge of Particulate Matter in Seawater.
Limnol. Oceanogr. 17,7-16 (1972).
Baughman, G.L., Gordon, J.A., Wolfe,
N.L., Zepp, R.G., Chemistry of
Organomercurials in Aquatic Systems.
Report No. EPA-660/3-73-012. U.S.
Environmental Protection Agency.
Corvallis, Oregon. 97p. (1973) .
Andren, A., and Harriss, R.C.,
Methylmercury in Estuarine Sediments.
Nature 245,256-257 (1973).
Chau, Y.K., and Saitoh, H., Determination
of Methylmercury in Lake Water. Int. J.
Environ. Anal. Chem. 3, 133-139 (1973).
623
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ASPECTS OF MATHEMATICAL MODELS AND MICROCOSM RESEARCH
James W. Haefner
Department of Wildlife Science
Utah State University
Logan, Utah 84322
James W. Gillett
Environmental Protection Agency
200 SW 35th Street
Corvallis, Oregon 97330
ABSTRACT
Some features of the conceptual structure of
a potential mathematical model are presented to
illustrate the important role mathematical models
can and should play in future microcosm research.
Mathematical models can help microcosms achieve their
goals of screening exogenous substances, understand-
ing the fate and effects of exogenous substances, and
designing suitable management strategies. The con-
ceptual structure reported here emphasizes the role
of biotic components in controlling pesticide flows.
INTRODUCTION
As the experimental manipulation of microcosms
becomes an increasingly important tool for both pure
research and management purposes, it is necessary
that the role of mathematical models be clearly
delineated. It is our position that mathematical
models are extremely useful for research programs
embodying microcosm studies. We hope, in this
paper, to document this position by snowing how the
conceptual structure of a potential mathematical
model can influence the measurements and experiments
of a terrestrial microcosm. The mathematical model
itself is still in early stages of forumulation.
A. The Terrestrial Microcosm
Since 1974 the Corvallis Environmental Research
Laboratory has been developing and testing a terres-
trial laboratory microcosm system for screening the
disposition and effects of pesticides. This system
o p
was derived from the work of Metcalf e_t al_. , and
from a conceptual model of pesticide fate (Gillett
ejt aK, 1974 ). The basic objective of the program
is to develop a tool for screening potentially ad-
verse environmental behavior of pesticides by
assessing the fate of radio-labeled chemicals and
quantifying observable effects associated with the
introduction of the chemical into the system. A
secondary objective is to correlate these disposi-
tions and effects with the physical properties of
the chemicals and environmental components and thus
synthesize an understanding of the relationships of
classes of compounds to ecological effects. It
should be apparent that, whereas pesticides are
discussed in relation to the studies, one could
apply this approach to any potentially hazardous or
toxic substance.
The details of this system have been presented
elsewhere. It is comprised of (a) a Terrestrial
Microcosm Chamber (TMC) and associated biota and
support systems; (b) an operational format or pro-
tocol; and (c) an analytical scheme for determining
the distribution and identification of C-residues.
The TMC is a 101 x 75 cm glass box with plastic lid
enclosing about 40 cm of head space over 20 cm of an
artifical soil containing endemic micro-flora and
fauna. The unit is semi-closed, in that it is open
to energy (heat and radiation supplied by overhead
fluorescent and incandescent lamps), while purified
air and water are circulated through the TMC and
exit to sampling systems (but can be arranged to be
closed or recirculating).
Normal operation includes addition of certain
terrestrial macrofauna (nematodes, earthworms, soil
insect larvae) prior to planting selected crops and
weeds (alfalfa, rye grass, corn, soybean). Sub-
sequently higher organisms are added after plant
growth has reached the desired level (Collembola,
crickets, pi 11 bugs, snails and then gravid vole --
Microtus canicaudus).
Experimentation and sampling in the chambers
14
involves the application and monitoring of C-
labeled pesticides. Variations in these experiments
can be achieved by altering the biotic constituents
(especially the plant species and planting pattern),
the abiotic operating parameters, and the chemical
(nature, formulation, quantities, timing, and mode
of application).
Monitoring during an experiment includes
periodic measurements of the pesticide and its
degradation products in the water, air, at specified
soil depths, and in selected plant species. Soil
moisture and temperature are monitored. The amount
of pesticide adsorbed onto the inside surfaces of
the box can also be measured frequently. At the
end of an experiment (6-8 weeks) the vertebrates are
sacrificed to determine the pesticide levels in their
tissues. Appropriate concomitant controls are
utilized.
B. Model Objectives
The primary objective of the model of the
microcosm is to determine the dynamic behavior of
14
C-isotope residues when the radioactive label is
attached to specified classes of chemicals that
are physically applied to the microcosm in known
amounts and by known methods. The model is to be
constructed so as to permit a mass balance analysis
of the residues as they are distributed between
diverse components and compartments of that ecosystem.
To accomplish this the mathematical model must pro-
vide under the biotic and abiotic conditions pre-
vailing at the time of the experiment a dynamic des-
cription of:
(1) the amounts of pesticide (exemplified by
"dieldrin" and "parathion") and its pro-
ducts that are incorporated into plant
and animal tissues, bound to biotic com-
ponents, or removed from the microcosm via
water and air;
(2) the amounts of pesticide transformed into
major derivative by-products (metabolites,
conjugates, or bound residues);
624
-------
(3) the effects of the pesticide and by-pro-
ducts on the feeding, growth, and repro-
ductive behavior of the organisms in the
microcosm;
(4) the effects of the feeding, defecation,
movement and related behavior of the
organisms in the microcosm on the dispo-
sition and movement of the pesticide;
(5) the amount of CCL and organic carbon pre-
sent in (a) the living tissue of the
organisms, (b) non-living particulates,
and (c) both the atmospheric and water
portions of the microcosm; and
(6) the effects of abiotic conditions (e.g.,
temperature, pH, and soil moisture) on the
processes governing the movement and
transformation of the pesticide.
MODELING APPROACH
The primary concern of this model is the move-
ment of a pesticide among the components of a
terrestrial microcosm. These components include
both biotic and abiotic elements and a model must
incorporate both. This is accomplished in this
modeling approach by explicitly modeling the role
that biota play in regulating pesticide movement.
The concept of biotic control of abiotic
processes can be given a very simple structural
description, illustrated in Figure 1. The Pesticide
Transport Process (PTP) is a system that receives in-
puts from external sources and from the Biotic Control
Processes (BCP). In addition, PTP delivers outputs to
external sinks and to BCP. PTP also possesses internal
pathways and feedbacks that are symbolized by the
curved, self-directed arrow. The BCP component is
structured in much the same way; it has external
sources and sinks, internal feedbacks, and a coupling
with PTP. In later discussion, the coupling of PTP
and BCP will be referred to as the "control system."
PESTICIDE
INPUT
/"
PESTICIDE
TRANSPORT
PROCESSES
(PTP)
PESTICIDE
OUTPUT
^
V
BIOTIC fc
INPUT
BIOTIC
PROCESSES
«s
BIOTIC
OUTPUT
Figure 1. Diagrammatic representation of the control
system. Shown are its two basic components:
pesticide transport and biological control.
The control system approach to modeling pesti-
cide disposition has several advantages that are
important enough to note. First, this approach is
more realistic since it specifically includes the
mutual actions and effects of organisms and pesti-
cides. At the same time, by uncoupling pesticides
and biological flows except for control effects, the
model structure takes cognizance of the minor effect
the biota have on the mass flow of pesticides in
natural or constructed ecosystems. Second, the
control system approach permits simulation experimen-
tation on the counter-intuitive effects that pesti-
cides have on a particular biota (including economi-
cally important crops) through actions on other
pathways or components in the food web. Third, the
uncoupling aspect of the control system is important
because the dimensions of state variables describing
pesticide disposition (molar equivalents of C)
differ from the contents of state variables descri-
bing the biota (grams of C). Models with consistent
equations require state variables with consistent
units.
A. Pesticide Transport Processes
Figure 2 provides more detail of the control
system approach. For the purpose of the PTP the
microcosm is composed of four layers: an above-
ground subsystem, soil layer I, soil layer II, and
soil layer III (the number of layers is not fixed
and can easily be either increased or decreased).
Each layer is composed of a "center" and an "edge".
Within the three soil layers are two different
classes of soil types: Isolated (I) and Contiguous
(C). I'solated soil is soil that has no connection
with the atmosphere by means of its interstitial
connections. Contiguous soil has a direct, if not
straight, connection with the atmosphere. It is
assumed, further, that the vapor phase in contact
with contiguous soil is in equilibrium with the
above-ground atmosphere, although there may be indirect
connections with the atmosphere by means of soil water.
This distinction is important in describing volatili-
zation of pesticides from soil particles. Volatiza-
tion can occur and have an input to the above-ground
atmosphere only if the surface of the soil particle
is connected, in the gaseous phase, to the above-
ground atmosphere. It seems clear, also, that the
fraction of isolated soil will increase with increasing
depth from the surface and increasing percent soil
moisture. This provides a good operation definition
of soil layers. The "surface" (soil layer I) can be
defined as that set of depth intervals for which the
soil possesses, for example, 5% or less isolated soil.
One can also define soil layer III to be that set of
depth intervals for which the soil possesses 5% or
less contiguous soil. Other layers can be defined in
a similar way.
The total volume of soil comprising the surface
will vary in time. This variation will be caused
by the dynamics of such processes as moisture fluc-
tuations, tunneling, and root growth. As a result,
for computational purposes the terrarium will be
divided up into many thin "layers" each of which can
be described by its percent isolation. Since the
total amount of pesticide volatizing in any time
step will be a function of the total volume of
"surface" soil present, it will be necessary to sum
the volumes of all layers meeting the criterion for
soil layer I.
Within each of these compartments (layers; edge,
center; isolated and contiguous) certain processes
of pesticide movement and transformation occur. Those
that will be discussed in this report (after Gillett
et^ aj_., ) are movement by mass flow in water, adsorp-
tion, volatilization, and transformation. Figure 2
shows the basic control system of biota and pesticide
movement plus some detail in the pesticide component.
Most pesticide movement in PTP is associated with
physical transport by water flow. Within the soil,
gravity, diffusion, and capillary action are forces
and processes for transferring pesticides dissolved
in water. A certain fraction of pesticides volatizes
from contiguous soil and may be lost from the system
through the exhaust system or may adsorb onto above-
ground surfaces. Because of water condensation on
625
-------
the walls and roof some atmospheric pesticide may
find its way back to the soil. Within the soil a
portion of the pesticide may adsorb more or less
severely to soil particles. The water moving
through the soil may leach some pesticide to ground-
water.
Besides the direct control effects of the BCP
on these pesticide processes (described below), there
are a number of important abiotic factors that
influence their rates: temperature, moisture, pH,
and ionic content. These not only directly alter
the rates of pesticide movement, but they influence,
and are indirectly influenced by, the BCP as well.
Thus, the biota have both direct and indirect effects
on the PTP.
| ABOVE-GROUND
BELOW-GROUND
r
13
CENTER
(SOIL LAYER I)
EDGE
(SOIL
LAYER II)
EDGE
(1,0)
CENTER
(SOIL LAYER I
I
PESTICIDE TRANSPORT PROCESS (PTP)
Figure 2. The processes of pesticide transport in
the microcosm. Processes are denoted by number.
(1) loss from atmosphere and unrecycled water,
(2) loss to biota plus effects on Biota, (3)
= recycled water, (4) water input, (5) = pest-
icide application, (6) input from Biota plus
control by Biota, (7) = volatization from
contiguous (C) soij_. (8) runoff from walls
and roof, (9) = adsorption and desorption onto
walls and roof, (10) = lateral movement in soil,
(11) - gravity flow of water and pesticide, (12)
= upward diffusion and capillary action, (13)
adsorption onto soil surface, (14) degrada-
tion. Unit of flow within PTP is molar equi-
valents of 14C.
In addition to physical removal from the micro-
cosm by the air and water evacuation systems a mole-
cule of pesticide may also disappear because of de-
gradation or transformation. This PTP process (via
photolysis and hydrolysis) is accelerated by the
BCP (via metabolic transformation).
B. Biotic Control Processes
In this section we illustrate the role of the
BCP in the control system by describing those por-
tions of the BCP that interact with the PTP as shown
in Figure 2. As stated in the model objectives the
substance of flow in the BCP is carbon. The general
pattern of this flow is shown in Figure 3. The below-
ground ecosystem is further elaborated in Figure 4;
the "higher trophic levels" compartment is elaborated
in Figure 5. These relationships permit us to enun-
ciate some of the mechanisms by which the PTP and BCP
interact in this model.
Figure 3. The basic structure of the biotic compon-
ent of the microcosm control system. Unit of
flow is carbon.
Figure 4. Generalized trophic processes of the below-
ground ecosystem. Unit of flow is carbon.
626
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Figure 5. Inter-relations of the higher trophic level
subsystem.
An important effect of the biota on the eco-
system is the alteration of the physical structure
of the soil. By tunneling, compaction, and root
growth the biota alter the effects of gravity, diffu-
sion, and capillary action on patterns of movement of
water and therefore, pesticide. Conversely, a major
effect of pesticidal toxication on the biota is to
alter gross behavior such as "tunneling" (Figure 6).
Vertical grazers influence vertical flows between
layers directly by their tunneling activity (as repre-
sented by the dotted information arrow from "vertical
grazers" to "tunneling factor"). The effects of the
pesticide can alter this behavior without signifi-
cantly affecting the amount of carbon contained within
a state variable (e.g., "vertical grazer"), as repre-
sented by an informational arrow from PTP to the
"tunneling factor".
The biota also influence the physical structure of
the soil by the production of Particulate Organic Car-
bon (POC) that has great adsorptive potential. Such
particles include solid feces, exoskeletons, root
parts from sluffage, and so on. Moreover, organisms
that move horizontally alter mechanically the flow
rates between the Edge and Center compartments (Fig-
ure 6).
Figure 6. Illustrative interactions between BCP and
PTP.
The Dissolved Organic Carbon (DOC) compartment is
important in determining carbon fixation. Bacterial
metabolism is predominantly internal so that organic
material must be in dissolved form to be utilized by
bacteria. Because different organic substances (cellu-
lose, hemi-cellulose, lignins, sugars, etc.) have dif-
ferent decomposition rates (Edwards, e_t al_., ; Dickin-
son and Pugh, ) both the quantity and quality of DOC
must be considered. Mayberry, e_t al_., present experi-
mental data which suggests how this can be done
efficiently. They have shown that pure strains of
bacteria yield 3 gm of cells per equivalent "available
electron" in the substrate. An "available electron"
is one which is "not involved in a molecular orbit
with oxygen" in the structure of the substrate (refer-
ence 7). This interesting approach should be pursued,
since co-metabolism is the driving force permitting
bacterial biotransformation of pesticides.
In these few figures we have indicated some
sections of a model designed to study the complex
interactions between biotic and abiotic components
of microcosms. In what follows we articulate how
such models may guide microcosm research.
RELEVANCE OF MODELING TO MICROCOSM RESEARCH
The conceptual structure of this model and the
processes of elaboration and documentation that will
provide a functional mathematical statement for sim-
ulation experimentation are intimately involved in
the overall achievement of the several objectives
of the microcosm research program, i.e., screening,
understanding of ecosystem processes, and develop-
ment of effective management strategies. Current
studies on pesticides in microcosms rely on empiri-
cal efforts that need a sound, theoretical basis.
Outputs for screening decisions are based on a
relatively small number of observations (in compari-
son to that number which might be used); a success-
ful model would help assuage criticism of those
empirical measurements by revealing the necessary
and sufficient data points most crucial to the
disposition of a given chemical. Further, the inte-
grating process within the model and the requirement
of the mathematical model for explicitness should
reveal features of the disposition or effects not
visible in the empirical approach.
The conceptual model has already enunciated
several aspects of the microcosm system that need
theoretical or pragmatic definition: the distinc-
tion between "edge" and "center", the "isolated" vs
"contiguous" soil, the "tunneling factor" and other
behavioral variables, and the interaction between
pesticides and abiotic factors in their effects on
carbon flow in BCP. Explicit hypotheses have sug-
gested particular experiments, and eventually the
mathematical model should reach a state where mathe-
matical simulations can be performed. Then parameter
sensitivity analysis and other modeling techniques
should lead to further improvements in critical
analysis of microcosm tests.
Mathematical modeling is also directing micro-
cosm research toward better understanding of the
processes of disposition and effect of classes of
chemicals. A dynamic, simulation model places
emphasis on elucidation of rates of flows and their
controls, rather simply on the measurement of state
variables. The interaction between the microcosm
research program and the Benchmark Chemical Program
becomes clearer and more explicit as one considers
the need for high quality physical chemical data to
parameterize the model processes. As the relation-
ships between the benchmarks and the parameters are
better understood, then simplification of process
diagnostic analysis should result, especially with
the aid of computer model simulation.
Finally, a mathematical model based on the pre-
sent conceptual structure can also influence manage-
627
-------
ment strategies based on microcosm research. Simula-
tion experiments can explore the requisite control
characteristics needed to effect a particular pesti-
cide disposition, by indicating the restricted
classes of natural ecosystem to which the pesticide
might be applied without disrupting the ecosystem
or the pesticide disposition goals (i.e., delivery
to target for effective time). Alternatively, the
model might indicate management action required to
counteract adverse disruption of the system or
disposition goals when the target area is not in
one of the above classes.
CONCLUSIONS
In this paper we have reviewed sections of the
conceptual structure of a mathematical model as it
pertains to the improvement of microcosm research.
We have used this discussion to show how models of
microcosms may aid the achievement of the microcosm
objectives of screening, understanding, and manage-
ment strategies. Our emphasis has been complex and
subtle interactions between pesticides and the
biotic component of terrestrial microcosms. This
was formalized by the "control systems" approach
which constitutes the core of the conceptual struc-
ture. Our recommendations for future microcosm
research emphasize investigations of the distinction
between soil sectors and their properties, the be-
havioral effects of pesticides on biotic components
of the microcosm, and the interaction of abiotic
inputs with pesticide effects.
REFERENCES
1. Bailey, 6. W. and J. L. White. 1970. Factors
influencing the adsorption, desorption and
movement of pesticides in soil. Res. Rev.
32:29-92.
2. Cole, L. K., R. L. Metcalf, and J. R. Sandborn.
1975. Environmental Fate of Insecticides in
Terrestrial Model Ecosystems. Presented at
Ecological Society of America meeting, Cor-
vallis, Oregon. August 20, 1975.
3. Dickinson, C. H. and G. J. F. Pugh (eds). 1974.
Biology of plant litter decomposition. Vols. I
and II. NY, Academic Press. 775p.
4. Edwards, C. A., D. E. Reichle, and D. A. Cross-
ley. 1970. The role of soil invertebrates in
turnover of organic matter and nutrients. In:
Analysis of temperate forest ecosystems. D. E.
Reichle (ed) Berlin, Springer-Verlag Publishers.
p. 147-172.
5. Gillett, J. W. and J. D. Gile. 1975. Progress
and Status Report on Terrestrial In-House
System. In: Substitute Chemicals Program The
First Year of Progress. Proceedings of meeting
at Fredericksburg, VA. July 30, 1975.
6. Gillett, J. W., J. Hill, IV, A. W. Jarvinen, and
W. P. Schoor. 1974. A conceptual model for
the movement of pesticides through the environ-
ment. Environmental Protection Agency, Wash-
ington, DC. USEPA Rep. No. EPA-660/3-74-024.
79p.
7. Mayberry, W. R., G. J. Prochazka, and W. J.
Payne. 1967. Growth yields of bacteria on
selected organic compounds. Appl. Microbiol.
15:1332-1338.
Metcalf, R. L., G. K. Sangha, and I. P. Kapoor.
1971. Model ecosystem for the evaluation of
pesticide biodegradability and ecological mag-
nification. Environ. Sci. Techno!. 5:709-713.
Stotzky, G. 1974. Activity, ecology, and
population dynamics of microorganisms in soil.
In: Microbial ecology. Laskin, A. I. and
H. Lechevalier (eds) Cleveland, Ohio, CRC
Press, pp 57-135.
628
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AN ECOLOGICAL MODEL FOR THE GREAT LAKES
by
Donald Scavia, Brian J. Eadie, and Andrew Robertson
National Oceanic and Atmospheric Administration
Great Lakes Environmental Research Laboratory
2300 Washtenaw Avenue
Ann Arbor, Michigan 48104
Summary
A one dimensional ecological model, developed and cali-
brated for Lake Ontario, has been applied to the other
Great Lakes to test its generality. The model, physi-
cally segmented into two layers, simulates concentra-
tions of phytoplankton, zooplankton, detritus, phos-
phorus, nitrogen, and total inorganic carbon. Driving
the ecological model with physical data from the other
Great Lakes results in accurate simulations for the
upper lakes after minor recalibration of the kinetics;
however, the western and central basins of Lake Erie
could not be simulated due primarily to the effects of
physical phenomena which are not considered in the
model (e.g., sedimentary regeneration of nutrients,
resuspension).
The kinetic recalibration involved the adjustment of
two coefficients, one representing algal phosphorus
requirements (the half-saturation constant for growth
on phosphorus) and the other determining the regulation
by food of zooplankton growth. The adjustment of these
coefficients was based on the theory of competitive
succession.
As a result of the verification tests the following
conclusions were reached:
(1) For an ecological model to be able to predict
ecological changes occurring during eutrophication, it
must include at least several compartments in each
level of the food chain to allow natural selection to
be simulated. In this way "recalibration" will take
place automatically as succession and adaptation would
in nature.
(2) Further investigations are needed to gain insight
into the mechanisms that allow phytoplankton and zoo-
plankton to exist in varying environments. The mecha-
nisms governing the succession and adaptation of spe-
cies will have to be studied in order to develop
mathematical relations that describe these mechanisms.
(3) In some lakes, especially shallow ones, the ef-
fects of physical and chemical interactions between
sediment and the water column can greatly influence
the seasonal dynamics of the lake biota. Models
should account for these processes when they are
important.
(4) The seasonal effects of allochthonous loads
should be included in a eutrophication model for lakes
with short residence times.
(5) Once the model discussed in this paper has been
parameterized to include coefficients of the individ-
ual phytoplankton and zooplankton groups, it should be
broad enough for rather general application.
Introduction
There presently exist two broad classes of aquatic
models: (1) general, relatively simple models, based
on large diverse data bases and usually addressing
a single water quality variable1"2'3 and, (2) more
site-spec!fie, complex ecological models, developed
for a particular system or system-type and usually
Contribution No. 64 of the Great Lakes Environmental
Research Laboratory, NOAA, Ann Arbor, Michigan.
4 5
simulating many ecologically significant variables ' '
6>7. Models of the first group are generally designed
to transform simple input into useful output. While
these models provide accurate predictions of their
respective parameters, they do not address many of the
questions pertinent in water resource management. The
second category of models attempts to address more
specific water quality parameters and processes (i.e.,
concentrations of phytoplankton groups; seasonal
dynamics of the model components; and phosphorus,
nitrogen, light, and temperature limitation) but have
been indicted as losing their generality during the
development of complex process formulations and the
evaluation of coefficients-^.
The generality of a model is most critical to its
applicability; that is, if a model is very specific,
its use beyond simulating historical data is disput-
able. Very specific models may be useful for testing
certain hypotheses, but extrapolations into the future
and to other bodies of water are of questionable
validity.
The purpose of this paper is to investigate the poten-
tial generality of the Lake Ontario ecological model
developed by Scavia et al. by applying it to all
five of the Lauentian Great Lakes.
Lake Ontario Calibration
This model was developed parameterized, and calibrated
for Lake Ontario and has undergone extensive testing
for ecological realism^. It includes calculations of
the concentrations of available phosphorus, dissolved
organic nitrogen, ammonia, nitrate, non-living parti-
culate organic carbon, inorganic carbon, four groups
of phytoplankton, six groups of zooplankton, and
benthic macroinvertebrates. Solution of the equations
describing the biological processes is accompanied by
calculation of diffusion and sedimentation between
three vertical segments, as well as of the concentra-
tions of the components of the carbonate equilibrium
system. The ecological model, driven by temperature
and diffusion calculated by a physical model based on
the work of Sundaram and Rehm^ and by solar radiation,
represents the open-water zone of Lake Ontario.
Certain modifications were made to the existing model
to aid in its application to the other lakes. The
physical segmentation of the model was reduced from
three to two segments: the epilimnion and hypolimnion,
and the solar radiation and driving data for the
physical model were obtained from climatological stud-
ies9»10.H>l2. Also, the method of numerical inte-
gration was changed from a fourth order, variable-
step Runge-Kutta-Merson algorithm to a simple, for-
ward step Euler procedure.
None of the alterations seriously affected the results
obtained for Lake Ontario. For a complete list of
coefficient values and initial conditions for Lake
Ontario consult Scavia et al.^
Verification: Application to the other Great Lakes
Data for verification were obtained for all the Great
Lakes from two sources --a broad survey of the
literature and unpublished measurements35 made by
629
-------
GLERL.
trophic status similar to that of Lake Ontario.
With few exceptions, the available phytoplankton data
are reported as chlorophyll or total biomass. For
this reason, the values for concentrations of carbon
obtained for the four phytoplankton groups in the model
have been combined. This total has then been compared
to the actual measurements after these were converted
to carbon by assuming a carbon to chlorophyll ratio of
50:1 or a fresh weight biomass to carbon ratio of 10:1.
Further, the literature values are usually only repre-
sentative of surface (0-5m) conditions, whereas the
model simulates average epilimnetic conditions. This
difference is critical during late summer-early fall
when simulated epilimnion depths reach over 30 m in
most of the Great Lakes. Predictions of average
concentration of the phytoplankton in the epilimnion
segment will usually underestimate the observed sur-
face (0-5 m) concentrations.
The total zooplankton carbon prediction is the summa-
tion of the five epilimnetic zooplankton groups of the
model. These five groups do not necessarily represent
all of the zooplankton present in the lakes, and the
literature generally provides only values for crus-
tacean carbon. Because the predictions and the
observed data do not exactly correspond, we are limit-
ed to comparing the general dynamics and approximate
concentrations of the zooplankton. Data from the 50 m
vertical hauls are used for comparison to the average
epilimnetic concentrations calculated by the model.
The seasonal nutrient values35 from the model are
average epilimnion concentrations based on the predict-
ed segment thickness, while most of the ranges in the
literature are for surface conditions.
The data used for comparisons and to drive the model
are limited at this point, and results from the follow-
ing verification give only an indication of the model's
validity for each lake. While caution is urged in
interpreting the results, one can consider the poten-
tial generality (and limitations) of such a model.
Initial Simulations
The initial verification test consisted of using the
coefficients determined by the Lake Ontario calibra-
tion and the physical driving data and initial condi-
tions for each new lake or basin. The results of each
simulation were then compared to the observed data.
The simulations of phytoplankton for the upper lakes
(Superior, Huron, and Michigan) resulted in generally
lower predictions than corresponding measurements.
Also, in all three lakes the predicted zooplankton
concentration decreased sharply throughout the year.
Lake Erie was considered as three separate lakes: the
shallow western, larger central, and deeper eastern
basins. The simulations of all three basins failed in
a fashion similar to the upper lakes, but additional
constraints were also evident and will be discussed
later.
In an attempt to explain the poor verification of our
model for lakes other than Ontario, we considered the
differences in trophic status among the lakes.
Differences in nutrient levels are most certainly an
important factor in determining the dominant species
in the phytoplankton community of a lake. Taking
this argument one step further, one can also hypothe-
size that differences in types and abundance of phyto-
plankton in lakes will result in shifts in dominance
and in intraspecific adaptations within the zooplankton
community. Since the original model had been calibrat-
ed to the indigenous biota of Lake Ontario, we con-
cluded that, with these coefficient values, accurate
predictions would only be possible for lakes with
The structure of the model, however, is such that the
coefficients describe the state variables on a species-
type level whereas the formulations are based on func-
tional relationships and should be consistent for all
species within the modeled group. With this in mind
one would expect the model could be recalibrated for
each new lake.
There are procedures available for efficient curve
fitting, and the use of trial-and-error could also lead
to recalibrated simulations of the lakes; however, such
simulations would not be very interesting or useful,
for they would not produce any additional information
about the lakes or even the model itself. Instead,
we have varied a minimum number of coefficients in an
ecologically prescribed manner to determine if simple
recalibrations can lead to simulations that agree to a
substantial degree with the available data.
The selection of these coefficients was based on two
assumptions: (1) the Great Lakes phytoplankton are, for
the most part, phosphorus limited, and (2) the relative
dominance of specific phytoplankton and zooplankton
groups has been determined by the specific environments
of the lakes. The model equations involving these two
assumptions are the nutrient-regulated growth equation
for phytoplankton and the food-dependent grazing
equation for zooplankton. The coefficients critical
to these mechanisms are the half saturation constants
of phytoplankton growth on phosphorus (XKP) and of
zooplankton grazing on total food (XKG). A complete
description of these constructs can be found else-
where'*.
Low nutrient levels in Lake Superior probably have
favored the dominance of algal species with the ability
to grow successfully at these concentrations. This is
represented mathematically by a low half-saturation
constant. XKP has generally been reported between 1
and 10 ygP/113'14'1^, so we used 1.0 ygP/1 for oli-
gotrophic Lake Superior. The constants for the other
lakes were selected (Table 1) following the trophic
schemes suggested for the Great Lakes by Vollenweider
et al.16 and Dobson et al.17
Table i. Predicted trophic status variables and recalibration coefficients.
Maximum
Phytoplankton
Sedimentation
Maximum
Production
Available
Phosphorus
Inorganic
Nitrogen
XKP
XKG
«
.05
5.6
.04
110
0.1
1.0
.26
.29
1.0
.02
1
.12
7.8
.13
438
0.2
3.0
.21
.26
2.0
.04
£
.15
8.3
.10
411
0.3
4.0
.24
.32
5.0
.08
u
.28
11.6
.36
775
0.6
8.0
.09
.19
6.0
.16
u
.31
10.3
.43
706
0.7
9.0
.05
.16
8.0
.16
g
.56
21.6
.26
1648
0.6
15.
.06
.27
9.0
.16
^
.83
8.7
1.09
1026
0.5
25.
.23
.64
10.0
.16
3
mgC/1
gC/m2/yr
gC/m%r
mgC/m2/day
minimum
maximum
minimum
maximum
UgP/1
mgC/1
The coefficient relating zooplankton grazing to food
concentration (XKG) has not been as thoroughly studied
as XKP. Data from RichmanlS imply a value of 1.3xl04
cells/ml or, in terms of carbon, 0.16 mgC/1 for this
constant. This value worked rather well in the Lake
Ontario calibration and is therefore considered to be
in the higher end of the range for XKG. The nutrient-
poor waters of Lake Superior support a sparse food
supply for the zooplankters, and species adapted to
such conditions have most likely been favored. Math-
ematically this would be represented by a lower value
for XKG. The lower extreme of the range for XKG was
set at 0.02 mgC/1 based on relative phytoplankton
concentrations in Lake Superior and Ontariol7,19, and
630
-------
the values for the remaining lakes were determined in
the same way as those for XKP (Table 1).
With only these two changes, the model was rerun for
the various lakes. Selected aspects of the results
are compared to reported measurements in Table 2. The
seasonal dynamics of certain model parameters are
presented and compared to actual results in Figure 1.
Table 2. Predicted and observed variables-
Predicted Observed Units Ref. Note
Lake Superior
Max.
Phyto.
Max.
Zoo.
Max.
Prod.
N03+NH3
Avail. P
Lake Huron
Max.
Phyto.
Zoo.
Range
Max.
Prod.
NOj+NHj
Avail. P
Sed.
Rate
0.05
1.0
0.01
110
.26-. 29
0.1-1.0
.12
2.4
.002-. 012
438
.21-. 26
.15-3.0
7.8
0.4-1.8
<1.0
0.018
183
76-507
.22-. 28
0.5
.03-. 18
1.2-2.4
.006-. 058
121-358
.18-. 26
.5
2.0
5.6
15.1
mgC/1
ugChla/1
vgChla/1
mgC/1
mgC/m2/day
mgC/m2/day
mgN/1
ygP/1
mgC/1
pgChla/1
mgC/1
mgC/m2/day
mgN/1
HgP/1
HgP/1
gC/m2/year
gC/m2/year
17
16
21
20
20
17
17
16
17
24
23
17
19
19
22
22
obs. range
obs . max.
from #/m3
obs. max.
obs. range
obs. range
obs. const.
from wet wt .
obs. range
obs. range
from hr
obs. range
obs. mean
obs. max.
north
south
Lake Michigan
Phyto .
Peaks
Max.
Max.
Zoo.
Max.
Prod.
NH3
N03
Avail. P
Sed.
Rate
Lake Erie
Max.
Phyto .
Max.
Zoo.
Max.
Prod.
NOs+NHj
Avail. P
Sed.
Rate
Lake Erie
Max.
Phyto.
Max.
Zoo.
Max.
Prod.
NOs+NHj
Avail. P
Lake Erie
Max.
Phyto.
Max.
Zoo.
Max.
Prod.
N03+NH3
Avail. P
.15, .06
3.0
.012
411
.01-. 028
.22-. 30
0.3-4.0
8.3
- eastern
.28
5.6
.02
775
.09-. 19
0.6-8.0
11.6
centrat
.31
6.2
.03
706
.05-. 16
0.7-9.0
- western
.83
16.6
.07
1026
0.3-.64
0.5-25.
0.2, .04
0.6-3.7
.037
.2
67-1030
.006-. 024
.1-.21
10. -3. 5
11.12
basin
0.1-0.4
1.4-5.4
.06-. 27
140-1440
.02-. 18
1.0-7.0
160
basin
.06-. 60
2. -10.
.06-. 27
120-1590
.02-. 14
1.-8.
basin
.1-1.3
4.9-25.9
.06-. 27
110-1900
.08-. 64
5.0-23.
mgC/1
ligChla/1
mgC/1
mgC/1
mgC/m2/day
mgN/1
mgN/1
(JgP/1
gC/m2/year
mgC/1
ygChla/1
mgC/1
mgC/m2/day
mgN/1
ygP/1
gC/m2/year
mgC/1
ygChla/1
mgC/1
mgC/m2/day
mgN/1
UgP/1
mgC/1
ygChla/1
mgC/1
mgC/m2/day
mgN/1
HgP/1
27
16,26
28
28
16,26
27
27
26
29
16
30
24
16
17
17
22
16
17
24
32
17
17
16
17
24
32
17
17
Gr. Trav. Bay
obs . range
from ml/m3
nearshore
obs. range
Gr. Trav. Bay
Gr. Trav. Bay
assume 4% C
(see ref. 22)
from wet wt.
obs. range
from dry wt.
obs. range
obs . range
obs . range
see text
from wet wt.
obs. range
from dry wt .
obs. range
obs. range
obs. range
obs . range
obs. range
from dry wt.
obs. range
obs. range
obs. range
With a few exceptions the results of these simula-
tions match the measurements quite well. The sedi-
mentation rate for the eastern basin of Lake Erie
(Table 2) is considerably underestimated. Burns
suggests that much of the eastern basin sediment
originates in the western basin. The model prediction
is based solely on material derived from the over-
tying water and does not consider horizontal
transport; therefore, if Burns is correct our under-
estimate is to be expected. The prediction of sedi-
mentation in the central basin is also considerably
lower than that observed and the same mechanism may
be operating. The most obvious failing of the model
is in its inability to predict accurately the seasonal
dynamics of the properties of the central and western
basins of Lake Erie; this problem will be discussed
in more detail below.
Lake Comparisons
In Table 1 the lakes are arranged in order of increas-
ing trophic state according to predicted maximum
phytoplankton concentration, sedimentation, and
primary production. The ordering of the lakes based
on our results agrees with trophic schemes reported
in the literature16'17.
The trend is also observed in predicted available
phosphorus, especially the maximum values. Since
phosphorus is generally accepted as the most common
limiting nutrient in the Great Lakes, the increase in
the maximum values is an accurate portrayal of the
trend in trophic status. All of the lakes seem to
have sufficient nitrogen available to the plankton;
however, the trend in the minimum predicted value
indicates that, as we look toward the more eutrophic
lakes, the minimum inorganic nitrogen value decreases
and the difference between the minimum and maximum
values increases. The indication that the supply of
nitrogen in the lower lakes is approaching levels
critical to phytoplankton growth is also observed in
the data compiled and reviewed by Dobson et al.17 The
effect of this nitrogen depletion is emphasized when
one realizes that the average nitrogen half-saturation
constant for phytoplankton growth is approximately
0.027 mgN/l14-33.
Discussion
The results of the above simulations allow the lakes
to be categorized in two groups: (1) those simulated
quite well after minor recalibration of the Lake
Ontario model and (2) those simulated less well and
requiring further work. The upper lakes and possibly
eastern Lake Erie fall into the first category, while
the western and central basins of Lake Erie are in the
second group. Examination of the lakes that fall in
the two categories provides information on the gener-
ality and limitations of this specific model, as well
as some implication of the requirements for models in
general.
Upper Lakes
Although these lakes do have similarities (e.g., great
size, climate, origin), they differ in trophic status
and in aspects of ecological dynamics. Modeling a
series of lakes of varying trophic status is analogous
to modeling the eutrophication process in one lake.
The ability of the model to predict accurately the
levels of nutrients and biota in the upper Great Lakes
lends credence to its potential generality; however,
the fact that recalibration was necessary to obtain
these predictions suggests that the model would not be
able to predict accurately eutrophication within a
lake without such recalibration. A model that was
parameterized for phytoplankton adapted to the low
nutrient levels in an oligotrophic lake would over-
predict the outcome of enriching the lake. Upon in-
creasing the nutrient levels, the algae as parame-
terized would grow excessively. In nature, algae out-
competed at low nutrient levels would succeed at high-
er levels because of other competitive advantages
(e.g., size selective predation) and replace the
oligotrophic forms. Multispecies models are required
631
-------
Lake Superior
Figure 1. Comparisons of seasonal changes in observed and predicted values for phytoplankton carbon (C) and
available phosphorus (P) for the Great Lakes with separate comparisons for the western, central, and
eastern basin of Lake Erie. The predicted values for both C and P are represented by the lines. The
observed values of C^6'Z5>30 (mgC/l) are represented by dots and the observed P values35 (vgP/l) by
the white areas which include the mean ± one standard deviation. The abscissa represents time from
day 60 to 330.
The need to change the second coefficient, XKG, im-
plies the necessity for multispecies models of zoo-
plankton. It also directs attention to the fact that
very little is known about this coefficient and re-
search should be directed towards its evaluation and
determining what other processes are operating to
affect succession during eutrophication.
to predict this sequence since single-species models
cannot produce such succession.
To test this hypothesis, a simulation was run for Lake
Superior with two of the four phytoplankton groups
given a XKP value of 1 ygP/1 and the other two a value
of 9 ygP/1. This simulation resulted in almost exact-
ly the same prediction for total phytoplankton as be-
fore; however, the algal groups with low nutrient re-
quirements dominated and the ones requiring higher
concentrations (XKP=9) were lost. This recalibrated
model is not necessarily a general model, however,
since it only accounts for one side of the competitive
interactions at various trophic levels. We assume
that in lakes with higher nutrient levels some
counteracting competitive relationship favors the
algal types that have higher nutrient requirements.
The nature of this relation (or relations) is not
clear at present, however, and so it cannot be added
to the model. Even in this incomplete state of the
model, however, our test indicates that multispecies
models can mimic natural selection and, if the model
is detailed enough to allow this succession to occur,
can accurately predict the total phytoplankton bio-
mass, as well as succession.
The development of multispecies models may not be the
only alternative available to simulate eutrophication.
Another method could be to make the important coef-
ficients functions of the environment. Allowing XKP,
for example, to change as a function of phosphorus
concentration is one way to simulate adaptations of
the phytoplankton community. Although this method
may be more easily implemented, we feel multispecies
models will be more realistic.
Lake Erie
The Lake Erie simulations were generally less success-
ful than those for the upper lakes. This limitation
of the model suggests that ecological models will
often fail when applied outside the physical realm
for which they were developed.
632
-------
The failure in the central basin was most attributable
to not accounting for the special processes associated
with anoxic hypolimnetic conditions. Under anaerobic
conditions in Lake Erie, the regeneration of phospho-
rus from the sediment is approximately 11 times great-
er than under aerobic conditions . As a result of
ignoring this process, the seasonal dynamics of the
biota of this basin were not simulated accurately; and
the phytoplankton concentrations were grossly under-
estimated during late summer and early fall, when the
sedimentary regeneration occurs.
The western basin is also greatly influenced by physi-
cal properties not considered in the model. Alloch-
thonous loadings to the large, deep upper lakes
probably do not affect the seasonal dynamics, whereas
the episodic inputs to western Lake Erie, which has a
short residence time, certainly affect the biota.
Also, the shallow basin would be perturbed by any
relatively high intensity winds, resulting in resus-
pension of sediment. This process and anoxic release
of sedimentary phosphorus are not included in this
version of the model, and we feel these omissions have
resulted in the poor predictions for this basin.
Conclusion
We feel that this analysis points out that models
built to describe the ecology of lakes can be general
enough for use in a range of situations; however, they
will have to include multispecies compartments in the
food web in order to simulate natural succession. To
accomplish this end, substantial efforts are needed
to describe and document the processes critical to
the ecological models at the "functional species"
level.
This study also emphasizes the need to analyze criti-
cally a body of water before developing a new model.
In many cases only the physical processes of a model
(depth, stratification, sediment/water exchange) need
to be altered to adapt a preexisting model.
Acknowledgements
The authors are grateful to J. Manor for compiling
the seasonal nutrient data for this study. The
drawing was done by R. James, and the manuscript was
typed by J. Grasso and R. Hill.
References Cited
1. Vollenweider, R. A. 1968. Tech. Rept. DAS/DSI/68,
1-182. Organ. Econ. Coop. Dev., Paris.
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3. Dillon, D. J. and Rigler, F H. 1974. Limnol.
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4. Scavia, D., Eadie, B. J. and Robertson, A. (in
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formulation and preliminary evaluation.
5. Thomann, R. V., DiToro, D. M. , Winfield, R.P., and
O'Connor, D. J. 1975. Ecological Research Series.
Environ. Prot. Agency Rept. No. EPA-660/3-75-005.
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6. Park, R. A., Scavia, D., and Clesceri, N. L. 1975.
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Patton, ed) Systems Analysis and Simulation in
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8. Sundaram, T. R. and Rehm, R. G. 1973. Tellus. 25:
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and Stadelmann,
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Irbe, J. G. 1972. Climatological Studies No
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Great
No. 17,
633
-------
Simulation and Mathematical Modeling
of Water Supply Systems - State-of-the-Art
Rolf A. Deinlnger
School of Public Health
The University of Michigan
Ann Arbor, Mich. 48109
SUMMARY
Mathematical Modeling and Simulation Techniques have
been used extensively in many parts of the overall
water supply system ranging from the actual abstrac-
tion of water from ground and surface water sources,
to the primary collection and conveyance system, the
water treatment plant and the final distribution sys-
tem. The following areas have found attention:
Population projections and forecasts of demand
Design and Operation of Wellfields
Regional Water Supply Networks
Design and Operation of Treatment Plants
Design and Operation of the Distribution System
Population Projections and Forecasts of Demand
This very important aspect of water supply planning
is covered elsewhere at this conference and will not
be treated here.
Design and Operation of Well Fields
In the design and operation of well fields several
aspects are of interest. The first one is the
following: given an areally extensive aquifer, how
many wells of what size should be placed where and
how should they be pumped to obtain the required yield
from the field at minimum total cost? The second
level of the problem is: given an existing well field,
how should it be operated for maximum yield, or given
the required yield, how should it be operated for
minimum cost of production.
The first of the above problems is the more difficult
one, since it involves the process of selecting the
number, type, and location of wells. An approach in
this direction has been shown in a paper by Aguado
involving an optimal plan of dewatering a construction
site. The flow of water in the aquifer is described
by finite-difference approximations of the governing
differential equations. The problem is then for-
mulated as a linear programming problem which deter-
mines the necessary amount of pumpage from the wells
which arranged on a grid line. Both steady state and
transient conditions were investigated.
The second type of problem, namely the operation of a
well field, has been investigated by Deininger^6 and
also Aguado £t al. Linear programming techniques
were used to determine the optimal pumping from a
given set of wells, subject to pump limitations,
boundary drawdown limits, and aquifer characteristics.
Regional Water Supply Networks
the
The major problem addressed in these studies is
development of sources of water supply and the
delivery of the water to the points of consumption.
Typical of these studies is for example the one by
Carey7 who studied the water transfer in the New York
Metropolitan area, the one by Deininger^6 who described
algorithms for the optimization of regional water
supply networks. The basic problem can be stated as
follows: Given a number of surface or ground water
sources, which of these sources should be developed
at what time and to what extent and how should that
water be treated, stored and transported such that
634
the needed quantity and quality of water will be avai-
lable at the demand points and the total costs are re-
duced to a minimum.
The major design variables are the number, size and
location of surface reservoirs, including their ele-
vations; the size, number and location of wells in a
well field; the routing, number and sizes of the
transmissions mains including the pumping stations;
the treatment of the water to make it potable; and
finally the rules of operation of the system.
The formulation of the above problems leads to ty-
pical network problems and a variety of algorithms,
mostly linear and nonlinear programming have been
used to analyze the problem.
Two further studies which are worth mentioning are
those by Young and Pisano^-'- and a study by Weddle .
The study of Young focuses on the James River and
estuary and the water supply to the cities of Richmond
and Hampton Roads. A variety of sources of water is
considered, such as surface water, ground water,
brackish water, sea water, and renovated waste water.
The major decision variables are the surface water
reservoir, the location and number of wells for
tapping the ground water, the location of a possible
electro-dialysis plant and a desalination plant, the
location and type of a. waste water renovation plant,
and the necessary pipe lines for transferring the
waters. The entire quantity and quality problem was
formulated as a nonlinear programming problem, and
was solved under different assumptions for costs and
technology to identify the most promising solutions.
The study by Weddle focuses on an unspecified coastal
situation, and again the elements of supply consider-
ed are conventional surface water, seawater desalina-
tion and wastewater renovation. The demands are
municipal, industrial and agricultural. The resulting
mathematical programming model was a mixed integer
programming model, and several good solutions were
generated.
Design and Operation of Treatment Plants
At the treatment plant level the questions arise as
to what type of treatment is necessary, what combi-
nation of units is required, and how a minimum cost
treatment plant can be designed. There are very few
attempts in the literature to formulate this as an
optimization problem, and the few existing studies
appear to be more on an academic level. On the other
hand the capacity expansion of a plant has found
greater attention, as shown by other papers here at
this conference.
Design and Operation of the Distribution System
This area of a water supply system has attracted by
far the most studies. While the earlier work has
been mostly in trying to balance the flow in the
network, the newer ones attempt to design a least
cost network which satisfies the demand and pressure
requirements. Several good methods and algorithms
exist, although from a strictly mathematical point of
view we still lack a method for designing a least
cost network. The basic questions of network
connectivity and reliability should also warrant
more attention.
For all the above-mentioned areas of modeling the
dynamic and time aspects must be taken into consider-
ation, which means a study of the capacity necessary
at a given time, looking over a finite planning
period. This gives rise to the typical capacity
expansion problems and the sequencing of the construc-
tion of individual parts of the system.
-------
Towards a Drinking Water Quality Index
The Public Health Service Drinking Water Standards
were first adopted about 60 years ago to protect the
health of the traveling public. In 1946, 1956, 1962,
and again in 1975 amendments and revisions were made
to reflect the changing environment and new knowledge
about what substances to expect in water and what
concentrations are thought to be allowable. And thus
the "Safe Drinking Water Act" (PL 93-523) calls for
new standards on the maximum allowable concentrations
of substances in drinking water.
Any water supplies not meeting the new standards will
be subject to the provisions for correcting the
situation, but the interest should be on those water
supplies which meet the standards. Among these,
there must be some which are better than others.
The basic question is how to rank them, and if such
a ranking would be undertaken, whether or not one
would see a difference in the quality of the supplies.
In an attempt to see if a ranking is possible a
printout of the data of the Interstate Carrier
program was obtained which lists values for 24
parameters of water quality. In an attempt
to stratify one city from each of the 52
states was selected only guided by the principle
that as many parameters as possible should be
available.
Each of the parameters has a single numerical
standard. Thus, for example, the concen-
trations for lead and mercury are .05 and
.002 mg/1, respectively. It can be argued
that none of these substances are needed by
the human body, and that the most desirable
value would be zero. In other cases, for
example, sulfates, it was felt that while the
standard was 250 mg/1, a desirable value would
be about 35 mg/1. In other words, for each
parameter there exists a standard and the most
desirable value, the latter being usually zero
or lower in concentration than the standard.
An average index can then be calculated which
measures the degree by which a particular
water is close to the desirable concentration
levels. Such an index formulation was applied
to the data, and a ranking of the supplies
was possible and showed the wide differences
in quality.
Conclusions
Mathematical Modeling and Simulation techniques have
been used in practically every aspect of a water
supply system. The number of studies and applica-
tions in the design of well fields appears to be
rather limited, and some further concentrated
effort appears to be in order. In the area of
regional water supply systems several models exist,
and the practice of carefully evaluating alter-
natives seems to be standard practice. Direct
optimization of the design of treatment plants
and the operation of them is rather limited and seems
to be constrained to academic exercieses.
The design of a distribution system has attracted
many studies, and at the present time good algorithms
exist, although from a strict mathematical point
of view none of .them guarantee the global optimum.
Basically, the use of mathematical models and
simulation techniques such as linear programming,
dynamic programming, etc. , aids in the analysis
of water supply systems in four major ways:
1. It allows the analysis of more alternatives
at every level of decision-making;
2. It allows a better testing of the assump-
tions and estimation of the influence of
economic, political and environmental un-
certainties;
3. It provides a mechanism whereby all assump-
tions and judgements are made explicit
and are clearly laid out, and
4. It serves as a communication tool for alll
the professionals involved in water supply
systems planning.
An extensive literature exists, as shown on the pages
following. It is up to the profession to put it into
practice.
Note: Due to space limitations only a brief summary
of the paper is presented here. A complete
paper is available from the author.
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638
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CAPACITY EXPANSION FOR MUNICIPAL WATER AND WASTEWATER SERVICES:
INCORPORATION OF UNCERTAINTY
Robert G. Curran
President, Curran Associates, Inc.
Northampton, Massachusetts
David H. Marks
Resource Analysis, Inc.
Cambridge, Massachusetts
Donald S. Grossman
Resource Analysis, Inc.
Cambridge, Massachusetts
Methods for management of local water and waste-
water investments are outlined. The strategy is to
choose the least cost supply alternative that services
a forecast but uncertain equilibrium demand. Careful
attention is paid to the overall usability of the
method by local planners.
The research defines water and wastewater ser-
vice demands, and identifies some controls available
to local decisi %n makers for modification of these
demands. The l^vel of future requirements for planning
is uncertain; the form and magnitude of the uncertain-
ty is explicitly included. Supply alternatives and
forecast costs of supply are also presented. Fore-
casts are developed for local relevance and to best
utilize available information.
A detailed analysis of time phasing and scale of
capacity expansion requires forecasts of the impact of
supply shortage. Short term alternatives in shortage
can either act to limit demand or to increase supply..
Recommended cost assessment for these strategies is
empirical. The criterion for expansion planning is to
choose the alternative which minimizes total costs,
where costs include construction, operating, and short-
age penalty fees. The recommended expansions explicit-
ly incorporate forecast uncertainty in the evaluation
of alternative investment patterns.
Problem Description
Municipal water and wastewater investments repre-
sent a large and important segment of the capital ex-
penditures made by local governments. The traditional
response of designers to the problem of sizing incre-
ments of capacity has been to build for arbitrarily
long planning periods, that is, to overbuild in order
to assure safe and adequate supplies. This is due, at
least in part, to the relatively naive approach pre-
sented by traditional engineering textbooks and requir-
ed by Federal funding guidelines. A growing body of
evidence indicates that overbuilding is not the best
response to the uncertainties inherent in future demands
for service. Two basic reasons may be cited. First,
oversized system elements are not economically efficient.
Second, water resource related investments may have
impacts upon whether or not land is used, and for what
purposes.
Public water supply and wastewater disposal is
undertaken for a variety of reasons. Commonly accepted
considerations for municipal provision of water supply
and wastewater disposal include public health, public
safety, resource regulation, land use regulation, and
economic efficiency. Given the basic premise of pro-
viding water related public services, the local de-
cision maker still has a range of options that define
the extent and quality of service. The character of
service depends also upon the sorts of demands, and
the consequences of not meeting those demands.
The immediate decisions available include size and
location of water distribution or sewer collection
mains, the size and location of treatment or supply
facilities, pricing or metering policies, and the
types of users and uses allowed. Some of these, espe-
cially those related to sizing capital facilities, are
generally made in the long term in order to take advan-
tages of the economies of larger developments. Others,
such as changes in pricing or allowable uses, are
easily changed on a short term basis.
Demand has important effects upon the quality of
the services offered. In order to size the supply,
the factors which influence demand for service, and
the magnitude of the influence, must be ascertained.
It is relatively recent that an outstanding of the
elasticity of the demand for water has been establish-
ed. Also, the consequences of not meeting demand must
be thought of in realistic and unemotional terms.
Shortage of supply need not result in unsanitary con-
ditions or shortage of water for drinking. Rather than
restricting the availability to always meeting demand,
planning should exhibit some sensitivity to the costs
of not meeting demands.
The traditional engineering approach may be briefly
characterized as supply oriented. The steps are to
project demand, and then to find the least cost supply
to satisfy demand. There are several shortcomings with
this approach. First, methods for demand projection
including curve fitting or graphical analysis are naive
in that they only preserve past trends in the data.
Second, the method limits the range of study to struct-
ural rather than nonstructural alternatives (e.g pric-
ing). Third, demand is assumed as a given, no matter
how much it costs to satisfy that demand: that is,
planned inadequacies or shortages are ruled out. Fourth.
arbitrary design horizons are often set, which ignore
the tradeoff between economies of scale and the cost of
capital.
More generally, a large number of inputs necessary
for decision making are uncertain. These include
future demands, cost of addition to supply, costs of
shortage, and interest rates. In order to effectively
plan in an environment of uncertainty, the analyst must
understand the sensitivity of system objectives to
variations in policy. If the output does not show
much response to input assumptions or policies, then
despite uncertainties or policy changes, then the un-
certainties are of little concern. If the outputs are
sensitive, then the analyst may collect more data, re-
model the planning process, or try to explicitly model
the uncertainties.
639
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Model Framework
The framework proposed for planning in this
paper is basically a least cost supply model. The
simplest case to plan for is the expansion decisions
for a single facility, for example, a single link in
a pipe network, or a single treatment plant. A key
assumption is that there is an identifiable service
area. The steps proposed for planning in such a case
are to:
(a) Forecast demand
(b) Estimate costs of expansion of supply
(c) Estimate costs of shortages
(d) Decide on the increment of plant
capacity, and the timing of these
increments, based upon forecast
demands, and the costs of meeting
or failing to meet forecast demand.
Rather than ignore the uncertainties that are known to
exist, and are universally agreed upon, an effort is
made to focus upon the forms and degree of uncertain-
ties. The philosophy is that this enables the analyst
to use more of the information available for planning.
Unfortunately, it is difficult to check the
validity of this method, except through in depth
studies of field experience with the planning tool.
These have not been possible within the limited time
horizon of this research. Rather, the proposed
approach is to see how the model results compare with
models using differing input assumptions. For example,
one test would be to compare total system costs and
investment strategies assuming certainty, and then
assuming uncertainty in demand, all other things being
equal. The output from tests such as this should
better enable the analyst to choose a method which
matches his understanding of the problems in planning
water and wastewater investments.
Demand Analysis and Forecasting
The traditional methods of demand forecasting by
naive trend extrapolation are reviewed in several
references (4, 32, 36, 37), but McJunkin's article (32)
is the classic study for civil engineers. More sophis-
ticated models require some understanding of the
causality of demand processes. The view of demand for
service taken in this research is that of a heirarchi-
cal process of development, inhabitation, and consump-
tion.
Models for understanding the development process
are numerous, and readily found in the transportation
or urban planning literature. It is anticipated that
developers look at sites from the same viewpoint as
households or businesses that seek to locate. The
developers seek sites consistent with the preferences
of the groups to whom they are trying to market. A
theoretical basis for understanding residential loca-
tion is well developed. Alonso (3) postulated that
budget constrained households choose a site that maxi-
mizes their utility, where utility is a fraction of
amount of land, commuting costs, and composite measure
of all household goods. A number of models have been
developed for forecasting on this basis (17,23,42).
The theory of location of the firm is less well devel-
oped.
Although this describes the relative attractive-
ness of locations within a region, it in no way pro-
vides a rationale for the driving force behind growth
in population, or differences in growth between
regions. Therefore, the usual approach is to forecast
population and employment on a regional level, and to
allocate the forecast within the region.
As early as 1963, research (39) showed that sewer
service was significant in inducing conversion of
vacant to developed land. Later, it was shown (24)
that an index of utility availability explained inter-
regional differences in growth. More recent studies
(13, 14, 44, 45) have attempted to quantitatively
model the impact of wastewater infrastructure invest-
ments. The state-of-the-art ability to model the
magnitude of development changes is limited. Key draw-
backs of the models include strong data dependence, and
the unavailability of accurate projections for the para-
meters that force or drive the output. Rather, the
importance for the analyst or planner is careful recog-
nition of water or wastewater policy relationships to
development.
Given an equilibrium developed stock of residences,
stores, offices, and industrial sites, consumption
depends directly upon the degree to which the stock is
utilized.. Normal vacancy rates for residences are
approximately 3% (21); in some urban care areas the
vacancy rate can be dramatically above 10%. The
important observation is that even if developed stock
can be accurately inventorized, this need not be a good
indicator for assessing consumption.
Conditioned upon development, and thereupon inhabi-
tation of an area, the total water and wastewater
supply required is determined by both level of service
offered and by individual consumer demand character-
istics. The ensuing discussion emphasizes that water
and sewer services can and should be treated as economic
goods. Level of service changes can cause shifts in
demand, and, similarly, the preferences of consumers
can change over tine.
Different elements of the system must be designed
to satisfy different components of demand. Demand for
water exhibits daily, weekly, and annual cycle varia-
tions. Annual cycles are important for planning basic
source; demands on the maximum day are important for
planning transmission, facilities, treatment facilities,
distribution pumping stations, and major feeder mains;
peak hour demands or maximum fire flow are important
for planning local distribution mains, connections, and
local storage. Wastewater demands typically exhibit a
close relationship to observed water demands. A number
of crude rule-of-thumb multipliers are available for
relating demand components.
Four district classes of user generally cited in
water and wastewater planning are residential, com-
mercial, industrial, and public unaccounted uses, Re-
search on residential water usage has been extensive
(15, 16, 19, 20, 25, 42, 44, 46). The basis for most
of the studies cited is, at least indirectly, a project
to study residential water use conducted at Johns
Hopkins University. A summarization of the project
results is presented in a paper by Howe and Linaweaver
(20). The Howe and Linaweaver study concludes that
residential users respond to price as a quality of
service indicator. The importance of this sort of re-
search is in quantification of the effects that changes
in level of service can have on demand. It provides a
basis for analysis that is readily applicable and easily
reproduced, and helps guide in the formulation of level
of service policy changes.
Unfortunately, due to a lack of transferrable
models and data, the most convenient way to forecast de-
mand for service is to project population, and then to
apply population to use multipliers. Two points must be
640
-------
emphasized. First, the focus need not be on the devel-
opment of better point estimates for future population
levels, but instead on a quantification of the uncer-
tainty in population forecasts. Second, the analyst
should, as much as possible, utilize locally-based con-
sumption data in calibrating use multipliers.
The traditional engineering texts have paid pain-
fully little attention to the subject of demand fore-
casting. A study by James, Matalas, and Bower (22)
shows, for one particular system, the economic develop-
ment projection to be the most important variable in
water resources planning, yet many current texts still
propose graphical extrapolations or simple regressions
as the basis for demand forecasts. A method for dealing
with this dilemma is to make several projections, and
perform an ad hoc sensitivity analysis. If, in fact,
investment planning decisions are shown to be sensitive
to economic development projections, as expected, then
the analyst must in some way combine the information
from several projections in order to formulate an in-
vestment strategy. Rather than choose between projec-
tions in some arbitrary fashion, the analyst might con-
sider trying to model the likelihood of the projections.
Several models of this type for modeling popula-
tion growth as a stochastic process are available and
easily applied (5, 28, 33, 34, 35). Limited evidence
shows that the stochastic model performs better in
capturing the variance of the underlying population
growth (34): Often, this is severely underestimated by
regional planners. A common formulation is to model
birth, death, and migration rates as stochastic pro-
cesses. First, a form for the process is chosen.
Second, process parameters are estimated using histor-
ical data. Third, the observed parameters and chosen
form are used to simulate future population growth.
Fourth, a distribution form is chosen, and statistics
gathered on the uncertainty in future population levels.
This modeling approach uses data available more fre-
quently than census data, so process parameters may be
estimated with greater confidence. Also, the method
has causal structure which allows for improvements
beyond those possible with aggregate population models.
One important area for future research is extension of
the basic model structure to use subjective or regional
information in a Bayesian fashion. Another is the re-
finement of models for use in regions with dependent
subareas. The use of stochastic population models seems
to be a promising area for additional research.
Population is only a surrogate for the desired
metric of demand for water or wastewater services. The
proposed method is to convert stochastic population
forecasts to demand forecasts through the use of con-
sumption multipliers. Standard multipliers are avail-
able in a number of sources (19). These do not account
for consumption habits, pricing effects, climate, and
other factors which can cause variations in water or
wastewater production. Therefore, the analyst should
endeavor to gather local data to estimate consumption
multipliers. Care should be taken to include the com-
ponent of demand due to infiltration, inflow, or leak-
age (4, 19). A preferred method, to model the variation
in observed use, is not possible due to the lack of data
and lack of theoretical framework.
Supply Analysis
The choice of supply alternative depends upon the
type of demands being planned for, and upon the site
characteristics of climate, topology, geology, and
existing or planned development. The choice of supply
will also depend upon the relative costs and upon the
availability of supply alternatives to satisfy demand.
A key assumption taken in this analysis is that the
cost function for the current project is independent
of the number and sizing of projects preceding the cur-
rent decision. In other words, the cost function for
system expansion appears identical at all points in
time.
Within the analysis of water or wastewater facil-
ities, the planner can choose the depth of analysis. The
simplest approach for facility analysis is to determine
a functional form for the costs of expansion, and then
to utilize standard parameters to determine the exact
scaling of the function. A more sophisticated approach
is to use observed or synthetically generated points to
calibrate the cost function parameters. Both of these
methods will be reviewed in this section. It is im-
portant to note that due to the strong dependence on site
characteristics, local calibration of parameters is the
preferred alternative.
In general, over a wide range of sizes, water and
wastewater system elements exhibit economies of scale:
it is possible, however, to get out of the range of
economies. The most commonly used representation for a
cost relationship of this sort is
C = kQ"
(1)
where C is the total cost (usually in dollars, k is the
scale parameter, Q is the total capacity, and m is a
scale parameter. This relationship exhibits economies
of scale for values of m between zero and one. Observe
that the function is continuous, suggesting that the
equipment is available in any sizing. Although in
practice, this is not possible due to standardization
of components or to site irregularities, it seems to be
a reasonable assumption that helps improve analytic
tractability.
The two parameters have been estimated for a number
of system elements. These estimates have been taken,
in general, from two sources of information. One way to
estimate the parameters is to use a broad base of observed
costs and installed capacities, and use regression or
some other curve fitting technique. A second way to
develop a basis for fitting the cost function is to
synthetically cost a number of alternative installation
sizes, and to fit a function to the synthetic data. The
latter method is useful in trying to develop cost func-
tions with local significance. Examples of parameters
in the literature are numerous (1, 2, 4, 5, 7, 8, 9, 10,
18, 27, 36, 40). The variation in reported parameters
reflects a number of differences in data or underlying
assumptions. The comparisons may be misleading due to
site specific differences. Also, units may be incommen-
surate due to misadjustment for exchange level or tech-
nology.
Site specificity is of primary importance. Clearly,
the costs of capacity depend heavily upon the relative
suitability of sites for development. The above model
assumes the only difference between projects to be size*
Variation in cost could also be due to hydrology, top-
ology, geology, existing development, planning develop-
ment, durability of installation, site aquisition, legal,
construction materials, site preparation, and so forth.
Any number of these might be included as explanatory
variables if the data were available and if they could be
forecast for future planning: neither is the case. A
suggested approach, therefore, is to try and qualitatively
control for sources of variation other than size. This
would require definition of categories exhibiting
significantly different cost parameters, and estimation
of those parameters for use in a look-up table. Neither
the data nor the theoretical basis exist to accomplish
this. In the interim, generalized scale factors are the
only alternative to site specific cost assessment.
641
-------
Differences in costing assumptions or accounting
stance may also explain variations in scale factors.
The parameters are based solely on primary construction
costs, and no secondary environmental or socioeconomic
impacts are included. Other accounting issues include
transformations between currencies and intertemporal
comparisons. These require choice of a suitable ex-
change rate and discount rate for transformation to a
common datum. Another accounting issue is the problem
of inflation of water and sewer prices differing from
the general rate of inflation. In the case of water and
sewer plant, the ENR index has been increasing at a rate
of 5.5 percent per year, while the consumer price index
has increased at a rate of 2.8 percent per year. A cor-
rection must be made to reduce the opportunity costs of
capital by the rate of relative price increase.
Thus far, little attention has been paid to the
definition of the quality supplied. Assuming a design
configuration (and operating policy, if applicable), the
level of supply is variable due to climatic variations
or reliability problems, and there is typically some
probability that the source installation chosen will not
satisfy demand. The usual method for treating this is
to consider component reliability for a certain confi-
dence level. If possible, sensitivity analysis should
be employed to test the validity of the reliability level
chosen.
Finally, a simple analytic form was chosen for the
cost function. The capacity expansion model, in its
most general form, does not require an analytic cost
function. The models developed in this research may be
readily generalized for use with any monotonic cost
function. However, this has not been fully implemented
in this version.
Costs of Shortage
Estimation of the costs of shortage is a new and an
important area for research (40). The key concept is
that the costs of shortage are not infinite. Shortage
may merely imply inconvenience or it may mean a much more
serious condition. Adjustments can sometimes be made by
consumers in order to lessen the impact of shortage. This
section discusses the types of adjustments possible, and
considerations for estimation of the costs of these ad-
justments.
Most engineers and utility managers accept the
premise that systems should be designed to accommodate
demand at all times. Shortfalls are not acceptable, and
should, therefore, be avoided with accurate forecasting,
planning, and (over) design of facilities. Implicit in
this approach is the assumption of an infinite cost of
shortfalls in supply capacity or in delivery capacity.
One suspects the true costs to relate to the adjustments
that are possible.
Adjustments in the case of shortage may be categor-
ized as either acting to increase supply or to reduce
demand. For water, measures that increase supply in-
clude emergency storage and interconnections with other
systems. Measures that reduce demand include changes in
pricing, changes in the pricing mechanism (e.g. the
installation of meters), restrictions on uses (e.g. lawn
watering or car washing prohibitions) , and restrictions
requiring reuse (e.g. recirculating air conditioning
equipment). Note that adjustments that reduce water de-
mand affect both distribution and source shortage. For
sewer, measurements that increase supply include inline
storage and flow regulating devices. Measures that re-
duce demand are expected to be similar to those used for
water supply.
The major study of supply shortage is that of
Russell, Avery, and Kates (40), who have documented
productivity losses for several Massachusetts commun-
ities during the Northeast drought from 1961-1966.
Their general methodology defined water-shortage losses
as "gross annual benefits lost by disappointed users
less costs avoided by the supplier." The authors
assumed full employment and assigned costs to the
resources diverted to meet a drought crisis. The cal-
culation of actual losses was corrected in several
ways to reflect different interest rates and accounting
stances. In cases where firms deprived of normal
quantities of water undertook investments in water con-
serving technology, it was counted as a benefit. In a
number of cases, the net result from a national point
of view of the effect of drought on commerce and in-
dustry was that the investment in water saving technology
produced a benefit rather than a cost.
Observed losses were related to the percent
shortage, which was in turn related to the measure of
system inadequacy. Two difficulties arose. First,
system managers' anticipation of shortage caused costs
to be incurred without shortage having actually occurred.
Second, existing safety factors were not known. None
the less, an exponential cost function was esti-
mated.
There is strong reason to believe that the loss
relationships will differ for different geographical
sections of the country and for areas with differering
levels of usage in industrial, commercial, domestic,
and municipal sectors. For example, cost of drought
could be significantly higher in more arid areas.
Overall, the work of Russell, Avery, and Kates is
an excellent effort in quantifying an elusive relation-
ship. More work needs to be done to verify the results,
and their transferability. A significant effort must;
be made to obtain similar results for the costs of waste-
water service shortfalls. Analysis of capacity expan-
sion investments should help quantify the sensitivity of
total system costs to the costs of shortage.
Capacity Expansion Decision Making
Given demand forecasts, costs of expansion, and
costs of shortage, the final planning step is the choice
of timing and sizing of increments for supply expansion.
This problem is closely related to the inventory con-
trol problem, and a number of models have been proposed
in the literature. This section discusses the available
models, including several new applications to water and
wastewater planning. A number of models are presented
to allow the user a considerable degree of flexibility
in the depth of analysis undertaken. This also allows
for the added ability to incorporate uncertainty in
demand, or not.
There have been two classes of research in this
problem. One is the choice of a finite set of projects
with known costs and supply potential, and simple
sequencing of these projects to meet forecast demand at
least cost (11, 30, 31). This approach requires the
solution of a combinatorial problem, and the feasibility
of solution depends heavily upon the number of projects
under consideration. The advantage of this method is
that it takes account of the exclusivity of projects.
The disadvantage, which is overriding, is that the choice
of projects, and their sizes, is made independently of
rather than simultaneously to the sequencing problem.
This hierarchical decision process can be suboptimal.
The second approach (5, 6, 7, 12, 18, 26, 28, 29, 38, 40,
41) is to choose the timing and sizing of capacity
increments to satisfy demand at least cost, where de-
mand may be uncertain, and where the costs may be due
to construction, operation, maintenance, and to short-
age.
642
-------
Eight models are proposed for a planning pack-
age. These include varying assumptions about linearity
or nonlinearity and certainty or uncertainty in demand.
They also include varying assumptions about allowabil-
ity of shortages. Table 1 shows a categorization of
the models.
Linear
Non-
Linear
Certainty
Shortfalls
Shortfalls
Shortfalls
no Shortfalls
Uncertainty
Shortfalls
no Shortfalls
Shortfalls
110 Shortfalls
Table 1: Model Typology
The reason for considering this broad a set is that
the simpler models, for example certain linear demand
with no shortfalls, have closed form or very efficient
solution procedures. The more complex models, for
example nonlinear uncertain demands with shortfalls,
require elaborate solution procedures such as stochastic
dynamic programming. The analyst interested in exten-
sive sensitivity analyses could, therefore, sacrifice
the greater realism of the more complex models for the
efficient soluability of the simpler model.
jects, expansion costs for the form C kQ , shortage
costs quadratic (or greater) in the magnitude of shortage,
no budget constraints, and no operating or maintenance costs.
Two uses were made of the model. It was applied,
ex poste, to judge the quality of water supply investments
for several New England towns. This is somewhat unfair
because it uses information on population not available
at the time the actual decisions were made. The model was
also applied to develop prototype rule of thumb guidelines
for investment planning by local decision makers. Results
were represented in terms of a dimensionless level of in-
adequacy, defined as the ratio of 'current' use to safe
yield. Based upon input assumptions about the discount rate,
shortage costs, and economies of scale, the tabulated re-
sults indicate the level of inadequacy at which to build,
and also the length of planning period for which to build.
Higher discount rate, higher economies of scale, or higher
shortage costs all lead to the recommendation to build for
shorter planning periods, and vice versa. The research does
not, however, provide insight into the value of modeling
nonlinear demand growth as compared to using a linear ap-
proximation to the growth in demand. It does show that if
demands are uncertain then total system cost is sensitive
to the costs of shortage.
The solution procedure was a nonlinear programming
algorithm based on the method of Zoutendijk. A number of
combinations of loss function parameter, scale parameters,
discount rate, population growth rate, and per capita con-
sumption growth rate were studied. Total costs were fairly
insensitive to the loss function parameter, but highly
sensitive to the discount rate. Not only did costs change
All four cases of model assuming linear demand have wlth differin§ discount rates, but capacity increment
sizes also changed. The total costs were sensitive to
economy of scale parameter but the sizing of increments
was less sensitive. Overall, the model provides a basis
for analyzing nonlinear growth in demand with shortage.
been studied extensively by Manne (28, 29), and several
have been applied in planning water or wastewater in-
vestments (5, 6, 26, 38). The assumptions that go into
these models are all similar. The assumptions include
infinite economic lifetimes for projects, an infinite
planning horizon, and no budget constraints. For the
cases of uncertain future demands, a Bachelier-Wiener
diffusion process in continuous time is used as the
model. The form of expansion costs is C = kQm. Opera-
ting and maintenance costs cannot be included in these
models. Costs of shortfalls are linear in the magnitude
of shortage. Although these assumptions result in a
highly simplified model of the capacity expansion plan-
ning process, the advantage is that the models have
closed form solutions or require simple one or two di-
mensional searches.
It can be shown that capacity expansion decisions
for an arbitrary monotonic demand path can be modeled as
a dynamic programming problem. For the cases with shortage,
this simply requires a suboptimization step. The dynamic
programming problem formulation can be readily solved us-
ing any of a number of efficient shortest path algorithms.
To expand the nonlinear demand model to include cases of un-
certainty in demand, a stochastic dynamic programming form-
ulation can be established. This is related to previously
studied stochastic inventory control models. The distribu-
tion on demands is generally discretized. Models of this
type have yet to be applied to planning water or waste-
water investments.
Using these models, the sizing of capacity incre-
ments has been found to be sensitive to discount rates,
economy of scale parameters, demand, and demand uncer-
tainties. The indication in research by Manne is that
lower discount rates, or higher economy of scale para-
For the nonlinear demand models, the additional com-
plexity of a budget constraint may be introduced. Similarly,
restrictions on available plant sizes and maximum allowable
shortages may be included. The form of cost and shortage
meters, leads the analyst to recommend larger investments COSt functlons maY be varied, and operating and maintenance
in capacity installments. The exact nature of the re- <;OSts added' A11 of these are relatively straightforward
lationship between time that the investment should sup- but as yet untrled extensions.
ply, economy of scale, and the discount rate is available
in several published sources, including Manne. When the
penalty cost is assumed to be infinite, that is, no
shortages are allowed, and in the case of demand uncer-
tainty, Manne indicates that one should overbuild, as
compared to the case of certainty. When the shortage
penalty cost is less than infinite, no definite results
have been drawn.
The four cases of model assuming nonlinear growth
in demand have not been dealt with as extensively. The
only related study in the water and wastewater planning
literature is that of Russell, Avery, and Kates (40)
which reviewed costs of shortage for the mid-1960's
New England drought. The model used to optimize invest-
ment strategy for deterministic demands was a nonlinear
programming algorithm. The assumptions included deter-
ministic demands, infinite economic lifetimes for pro-
643
Conclusions
There is no general availability of a set of models for fore-
casting demand, estimating expansion costs, estimating short-
age costs, and planning capacity expansion for water and waste-
water investments. Such models in a usable package would pro-
vide municipal decision makers with the flexibility to model
in a simple sketch planning fashion, or the ability to model
more complex assumptions about the underlying system. Rather
than develop a single plan for capacity expansion, a range of
plans might be developed. Sensitivity to input assumptions,
or the underlying distributions of input variables would aid
in incorporation of the large uncertainties inherent in plan-
ning social systems. Ultimately, these might be abstracted
to provide simple rules of thumb for planning.
-------
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30. Marin, Thomas, "Optimal Sequencing of Capacity Ex-
pansion Projects," Journal of the Hydraulics Division
ASCB, NY: 9972 (HY 9): 1605-
31. Marin, Thomas L., and Roy E. Marsten, A Hybrid
Dynamic Programming/Branch and Bound Approach to a
Class to Sequencing Problems, Evanston, Illinois:
Technological Institute, Northwestern University,
March, 1975.
32. McJunkin, Frederick E., "Population Forecasting by
Sanitary Engineers," JSED, ASCE, N.Y.: 3993
(SAY): 31-58, August, 1964.
33. Meier, Peter, Stochastic Population Dynamics for
Regional Water~Supply and Waste Management Decision
Making, Amherst, Ma.: University of Massachusetts,
Department of Civil Engineering, EVE 25-70-S,
August, 1970.
644
-------
34. Meier, Peter, "Stochastic Population Projection at
Design Level," JSED. ASCE. N.Y.: 9436 (SA6)
883-896, December, 1972.
35. Meier, Peter M., "A Search Algorithm for the Estim-
ation of Interregional Migration in Local Areas,"
Environment and Planning; ( ) 5:45-59, 1973.
36. Metcalf and Eddy, Inc., Wastewater Engineering:
Collection, Treatment, Disposal, New York: McGraw
Hill Book Company, 1972.
37. Morrison, Peter A., Demographic Information for
Cities: A Manual for Estimating and Projecting Local
Population Characteristics, Santa Monica: The Rand
Corporation, R-618-HUD, June, 1971.
38. Rachford, Thomas, Russell Scarato, and George
Tchobanogloss, "Time Capacity Expansion of Waste
Treatment Systems," JESED, ASCE, NY.: 6957 (SA6):
1063-1077, December, 1969.
39. Rogers, A., The Time Lag of Factors Influencing Land
Development. Chapel Hill, North Carolina: University
of North Carolina at Chapel Hill, Center for Urban
and Regional Studies, Institute for Research in
Social Science, 1963.
40. Russell, Clifford S., David G. Avery, and Robert W.
Kates, Drought and Water Supply; Implications of
the Massachusetts Experience for Municipal Planning,
Baltimore; The Johns Hopkins Press, 1970.
41. Russell, Clifford S., "Uncertainty and Choice of
Plant Capacity," NAWWA (Notes), Washington: 63 (6):
390-391, June, 1971.
42. Thompson, Russell G., et al, Forecasting Water
Demands, Arlington, Virginia: National Water Com-
mission, (NTIS PB-206 491), November, 1971.
43. Traffic Research Corporation, Reliability Test
Report; EMPIRIC Land Use Forecasting Model, New
York: Report to Boston Regional Planning Project,
1964.
44. Turnovsky, Steven J., "The Demand for Water: Some
Empirical Evidence on Consumer's Response to a
Commodity Uncertain in Supply," Water Resources
Research. Washington : 5(2): 350-361, April, 1969.
45. Urban Systems Research and Engineering, Interceptor
Sewers and Suburban Sprawl: The Impact of Con-
struction Grants on Residential Land Use, Cambridge:
Volume I, Analysis (NTIS PB-236 477), Volume II,
Case Studies (NTIS PB-236 871), July, 1974.
46. Whitford, Peter William, Forecasting Demand for
Urban Water Supply, Stanford: unpublished Ph.D.
Thesis, Stanford University, Department of Civil
Engineering, 1971 (Also University Microfolms
71-13, DOS). NTIS PB 195 664).
645
-------
ADAPTIVE SHORT-TERM WATER DEMAND FORECASTING
David H. Budenaers
Systems Control, Inc.
Palo Alto, California
A dual set of short-term water demand models is de-
scribed. These models have the feature of adaptability
to changing data. That is to say, given changes in the
data sequence, the models' parameters will self-adjust
to provide a better model. The models also have the
property of being real-time computer-implementable.
The two models are a stochastic (or time-series)
model and weather component of demand model. The
stochastic model is an extension of the Box-Jenkens
type of modeling for time series. The weather model
uses the method of principal components to identify the
effective weather variables.
The results of the application of these models to
data from the San Jose, California, Water Works are
presented.
Background
Demand forecasting is of central importance for the
development and implementation of a methodology for de-
sign and operation of water distribution systems be-
cause it forms the basis for developing operational
policies for [1,2]:
• Storage management
• Scheduling of sources of water production.
The methodologies selected for implementation in
the demand forecasting algorithm are of two types:
• Stochastic models
• Weather model methods .
Stochastic methods make use of the historical
empirical demand time series to predict or extrapolate
the future. Stochastic methods attempt to explain the
demand time series by using the series' internal cor-
relation structure without use of any external or ex-
planatory variables. In order to implement a stochast-
ic model, a detailed statistical analysis of the time
series' correlation structure must be performed.
For example, it must be determined if, as a rule,
today's water demand is highly correlated with yester-
day's demand.
On the other hand, weather models try to explain
the demand time series by use of external variables.
Intuitively, the most predominant external variables
to affect water demand are weather variables. Thus,
in weather models, a detailed study of the relationship
between weather variables and water demand must be
implemented.
Once the relationship between weather variables
and water demand has been identified, then it becomes
possible to forecast water demand based upon weather
predictions.
The Stochastic Model
An examination of typical demand data for water
demand (Fig. 1) suggests that a high-gain stochastic
model could model the demand time series. The term
"high gain" means that the internal correlation, de-
scribed in the previous section, is highly adaptive
to new data. In light of this fact and the fact that
stochastic modeling has proven to be successful in
other similar applications, the following model is
proposed [3] :
D(t) = B(t) + X(t), t 0, 1, 2,...
X(t) = a X(t-l) + u(t), t = 1, 2, 3,.
(1)
(2)
where
D(t) is the demand at time t
B(t) is the base effect at time t
X(t) is the autoregressive term given by (2)
(autoregressive lag one)
u(t) is a sequence of independent random
variables where E[u(t)] = 0, and
Var[u(t)] = a.
2
Both a and O are unknown parameters. In ad-
dition, B(t) is an unknown quantity.
Observe that
E[D(t)]
B(t)
Var[D(t)] =
(3)
(4)
1-a
DATE
Day/Mo
710
719
720
722
7?3
725
726
727
72?
730
73)
t 1
e 2
e 3
8 4
e s
e b
6 7
* a
B 9
e 0
e i
e 2
6 J
6 4
8 5
6 6
6 7
s e
e 9
6 0
8 t
8 2
e 3
6 5
e 6
e 7
e B
e 9
630
ej i
9oi
902
903
JOfl
905
906
907
906
909
91 1
912
DAY INDEX
(1974) 12
564.00
546.00
S(.7.0Q
568.00
569.00
571.00
572.00
573-00
574.00
575.00
576.00
577.00
57B.OQ
579.00
5BQ.OD
581,00
582-00
583.00
584.00
585.00
SBt.OO
567.00
586.00
569.0
590.0
591.0
592.0
593.0
574.0
595-0
596.0
597.0
596.0
599.0
600.0
602.0
603.0
604.0
605.0
606.0
607.0
608.0
604.0
610.0
611.0
612.0
613.0
614.0
615.0
616.0
617.0
618.6
614.0
620>0
DEMAND x 10 GALLONS
0 1
,
i
r
4
t
i
t
i
t
t
t
i
f
4
*
1
*
9
r
1
t
t
*
f
,
t
I
T
»
,
(
I
1
*
t
4
t
*
0
,
f
Figure 1. Example of Water Demand Time Series for To-
tal System Demand for San Jose Water Works
646
-------
It can also be assumed that
2
D(t)
(5)
where
Equation (12) is the key equation for estimating
the base effect. The a is known as the "gain" of
the estimates.
Equation (10) can be used to compute expectation
and the variance of the estimator B(T).
is a normal distribution with mean B(t) and variance
2
E[B(T)] = I a B E[D(T-i)]
1-0
ITT ^
£ a B1 B. = B
1=0 t T
(13)
Estimating and Updating the Base Element
The base effect can be modified by using short-run
averages. This can best be formulated by introducing
the notion of discounted estimation (discounted least
squares). The problem is as follows:
Given D(t), t 0,..., T, it is required to
estimate B(t)
where E[D(t)] = B(t) = B (6)
and
Var(B(T))
(14)
In summary, Equation (12) gives a procedure for
updating the base. This equation is known as an ex-
ponential discount scheme. The gain is a and the
discounting is 1 - a. To compute the effective memory
of Equation (12) , it is required to compare (l-ot)K
with D(T) for various values of K . When (l-a)K D(T)
is relatively small, the effective memory is K time
periods. The procedure is initialized by using
Var[D(t)] = -2—, 0 < B < 1, B is known,
6
t 0, 1.....T (?)
where B is the true short-run average at t.
Equation (6) has replaced the time variability of
the base by a constant and Equation (7) indicates that
the variance on the demand gets larger the further back
in time one goes (T is the present).
Using standard methods of estimating B, the result
B(T) = ^ I D(i) (15)
1=1
over an appropriate time period.
Estimating and Updating the Autoregressive Element
The autoregressive element of the model is esti-
mated by forming
R(t) = D(t) - B(t)
(16)
over an appropriate part of the historical data base.
B =
E BT ± D(i)
1=0
T-i
(8)
i=0
Using the Yule-Walker equations for an auto-
regressive process, the following result is obtained
[4]:
ro = E [ytyt] =
(17)
Since
T
I
1=0
T-i
1 -
_T+1
1 -
(9)
Then Equation (8) can be written in limiting form
(|B| < 1, T large)and putting 1 - 0 = a) as:
(10)
B - Z a B D(T-i)
i=0
Writing S in Equation (10) as a function of t
B(T) = a D(T) + I a B D(T-i) UD
1=1
Equation (11) can be rewritten as
B(T) - a D(T) + B B(T-l) (12)
(1-a2)
(18)
T and T^ can be estimated by using either the
maximum likelihood method or the method of moments
[4,5].
The estimates are:
r ! v
F° = » 1=1
N-l
N
Z
1=2
(19)
(20)
The same analysis that was carried out in the
previous subsection can be implemented for the esti-
mates of F and T .
647
-------
Letting y be the gain, the result is:
r0(N) = Y y N + (i-Y) r0 (N-D
(N-D
(21)
(22)
The remarks in the previous subsection concerning the
gain Y or the discounting factor (1-y) can be made
here.
Before proceeding to a description of the model, a
few remarks on the correlation of other weather vari-
ables with demand are in order. Scatter plots of other
variables and demand are available in "Identification
of Water Demand Models" [6].
An overview of the correlations of demand to
lagged weather variables is presented in Figure 4 for
the test data. From Figure 4, as well as the individ-
ual scatter plots, it becomes a clear that the only seri-
ous candidate for a set of exogenous variables are the
lagged average temperatures.
As in the previous subsection, the values of r and
F are initialized by using Equations (19) and (20) °
over part of the historical data base.
Having estimates of TQ and T , the estimate of a ,
and a2 for the demand model is easily obtained using
Equations (17) and (18) as follows: ;
a(N) j, ,j^ (23)
0
02(N) = rQ(N) (1 - a(N)2) (24)
The Weather Model
An examination of a weather plot relating tempera- !>8
ture to demand indicates that there exists a high de- '.
gree of correlation between demand and incident temp- -6
eratures. Figure 2 illustrates an example of such a
scatter plot. The correlation coefficient for the data
illustrated in Figure 2 is - 0.85. (Water demand .2
increases with temperature.)
Water tenant] x 10 Callona
]!:;: ( ( / ( - " " " -4
Jin ^ [t • _ ' _r _ ,;. -6
;i i ' ! S '
\ I i i is' i
'. ) 2 J V I 1 1
S; 01 3 i s l 1 I 1 l 1
Si 9. i ii i i 1 ^ l (i: • ^1 l
It 1 ' V 'i I * 1111 112IJ 21 HI
° 0 L 1 1 1 1 1221 II Il2i2« 2211 „_
.. ; _ . _. l - - 1 1 -1-- U J l 2221 21 2 Va
.1 t 13 1 1 22 _.
!•; . ,', „',',',?* ,'S .. ' l°i
^ ,; i i i a e i i i u
« 3 •! 1 11 1 1 1 1
i 0 ~ " " 1 11 "l 1 111
S 1 111
/ 7 11 1
i ^ • 1 I
n
!'.<* 4 1
! " ! :"- ; correlation
correlationy- ;
lag
. i-
.6 ^ _!..
-.It • i --
.12 : .
!; . J ;J i.., .;.|ij. :j_- .;..;_•..
• iii '
...._. :. . i !
i M !
-. . ' .-—...; !•• -•-
_..._.-. ... .... ...... j.. . -: ....
: ! ! . :
. : ; 1 | : . 1 ;
• i . !. j '
' ': ' ' 1 i , '
.,: i • 2.j.i |.j« , 5. .6 ; i 8 i 9 ;io .^....'..j .:.. . :. ,.| :: |. ;...
nigure 3. Lagged Days Average Temperature . |
Correlated to Demand, 1973-1974,— i
San Jose Water Works !
,- .
! j ' ! •
•; | :-
1 ,• 1 !
| • .; ••-. • . i •
! L. ' i i '
~~-iT:fTf~~~"
"~~-»- — . — . — . • • • , i • i
; : : ; • \: ,;:-'-!;-:'.-
:
2 i 3 ; 4
: i '
i 1 - 6 •
! ^ \ - - /;- •
• .[ . p ?! 8 ; '
.:|.. .:,...i...
. .^_. .. .. .^. ;_
; 2, day1 :
. i ! • ;
— ^J . .; . . . j. • j._ .... L ; .
^V ' LM; . -
\ : . : . i '.['..
10 \ 11 ; 12 13 14 15 16 AT~I$
'•••• ' ^— — ^_ ' ' ' Y'
9,10' : Il"-'l5 " 17,18
dew' . 6 days average
2 days '• , ; j . ; sPe?d .
Figure 4. Lagged Days Other Weather Correlated ; -j—
to Demand, 1973, San Jose Water Works
In light of these introductory remarks on weather
riables , the weather demand model is defined as f ol-
xrs:
D(t) B(t) + W(t) + X(t) t = 0, 1, 2,... (25)
X(t) b X(t-l) + u(t) t = 1, 2,... (26)
W(t) c fj(t) t 1, 2,... (27)
Figure 2. Temperature vs. Demand
where
Further examination of scatter plots for demand D(t)
vs. temperature on the previous day indicates again
that a strong correlation exists. This lagged correla- B(t)
tion of course makes sense, since water demand is an W(t)
effect that has "memory." Figure 3 illustrates the
lagged temperature vs. demand correlation effect for
the test data.
The fact that the lagged temperature vs. demand X(t)
relationship is so strong, as well as the fact that
when operating with a pure stochastic model the fore-
cast "outliers" are highly weather-correlated, leads to
the consideration of a structured weather model.
is the water demand at time t
is the base effect at time t
is the weather component of demand given
by Equation (27) where c is an unknown
constant and fl(t) is the effective weather
variable at time t (defined later)
is the autoregressive term given by Equa-
tion (26) where b is unknown and u(t) is
a sequence of independent random variables
with
E[u(t)] = 0
and .
Var[u(t)] = a .
648
-------
An examination of Equation (25) yields that the
following parameters are to be estimated from the data
base:
B(t) = the base effect
c = the weather effect loading constant
b = the autoregressive coefficient
O = the model variance .
Observe that
E[D(t)] = B(t) + W(t)
and that
Var D(t)/ [W(t), B(t)]
(28)
(29)
Equations (28) and (29) will be used for generating a
weather demand forecast. Equation (29) means the con-
ditional variance of D(t) with respect to known W(t)
and B(t).
As in the stochastic model, the parameters are
estimated using step-wise regression. The mathematical
details for the estimation of B(t), b and a , are
similar to the details presented in the above section.
The estimation c uses the same principles [6].
Identification of the Effective Weather Variable
The method of principal components (PC) is used to
define an effective temperature [3,4]. The PC method
works as follows:
had been performed on the original untransforaed
variables [7].
For the test data of lagged temperatures (San Jose
Water Works service area weather information 1973-1974),
it turns out that 80% of the variability is explained
by one variable.
The results for the principal component analysis
are presented in Table 1. This table shows that one
component is sufficient to define an effective weather
variable.
Table 1
CORRELATION OF EFFECTIVE TEMPERATURE WITH
DEMAND FOR 1973 AND 1974 SJWW DATA
\^OMPONENT
YEAR ^^-^^
1973
1974
FIRST COMPONENT
Explains 79% of
lagged temperature
variance.
Correlation = 0.87
95% Confidence =
(0.84, 0.89)
Explains 83% of
lagged temperature
variance.
Correlation = 0.86
95% Confidence =
(0.83, 0.88)
SECOND COMPONENT
Explains 8% of
lagged temperature
variance.
Correlation = -0.10
95% Confidence =
(-0.20, 0.00)
Explains 7% of
lagged temperature
variance.
Correlation = -0.14
95% Confidence =
(-0.23, 0.00)
Let
= (t
0.
t ) be a vector of
lagged temperature variables observed at time i (t
_
j tempera-
ture, etc.). Then the sample covariance matrix of the
incident temperature, t. is lagged to day
is defined as follows:
S = - I (T.-T)
n . - i
where
(30)
(31)
Now suppose it is possible for an artibrary T vector
to choose a set of vectors C', C ',..., C^ such that:
Var(C'T) > Var(C!T) > , ..
1 — Z —
.. > (Var(C'T) (32)
— K.
and
and
for i ^ j (orthogonal)
1 (unit length)
(33)
Then the quantities in (32) are called the princi-
pal components and the C , i = I,..-, k are called the
principal component transformations. If it turns out
that a small number of Var(C^T) explains most of the
variance of S then these small number of scalar
quantities can be used as effective (or substitute) in-
dependent variables in a regression problem. Further,
it can be demonstrated that regression problems per-
formed using principal components have smaller variance
of the estimated coefficients than if the regression
Performance of Models for San Jose Data
A summary of the data analysis is as follows:
1. The weather model and the stochastic model are
completely correlated for one-step-ahead
forecasting.
2. The best stochastic model performance is given
in Table 2 for a data base of 682 days through
all seasons of a year.
Table 2
OVERVIEW OF PERFORMANCE OF STOCHASTIC MODEL
FOR APPROXIMATELY TWO YEARS OF FORECASTING
R « Relative Error
in 2
3.5
7.0
10.5
Z of Days With Error
Less Than R
40
62
78
Details on the performance will be provided in Figures
5-8. Complete details are available in [6].
Figure 5 illustrates the distribution of the rela-
tive errors for the choice of a. priori parameters
a = 0.8 and y = 0-8. From this figure it is clear that
most of the relative errors are less than 7%.
Figure 6 presents a histogram of the forecast
standard deviations for a = 0.8 and Y = 0.8. Figure 7
illustrates the number of estimated standard deviations
that the actual value of demand differs from the fore-
cast demand.
The utility of Figures 6 and 7 becomes apparent
when probabilistic forecasts are made using the
649
-------
forecasted standard deviation. For example, suppose
the forecasted demand is D and that the forecasted
standard deviation is 5. Then Figure 7 is used to con-
struct the probability associated with the confidence
interval for the true demand, D, as follows:
and
D + 2.27 0 = 55% confidence for true demand
D + 6.80 a = 78% confidence for true demand
That is to say, D + 2.27 S contains the true demand
with 55% probability.
From Figure 5 it can be observed that a value of
a 1 x 10^ is "typical." Therefore, in a "typical"
case, demand can be forecasted to roughly 2.3 x 10^
gallons.
x - 7
S - 7
682 Events
.7 4.9 8.4 11.9 15.4 18.9
X Relative Error
Figure 5. Distribution of Stochastic Residuals
(a = .8, y = -8)
X - 1.53
S - 1.34
682 Events
.26 .77 1.28 1.79 2.30 2.81 3.32 3.83 4.43
0 106 Gallons
Figure 6. Distribution of 3 for Stochastic Model
(a .8, y = .8)
X • 6.81
S - 9.08
632 Events
2.27 6.80 11.33 15.86 20.39 24.92
Number of a Units
It is important to note that the 75% confidence
interval can be used to "flag" outliers or anomalies in
the forecast.
Figure^S shows the distribution of the estimated
parameter a for the stochastic model. Recall that a
is the autoregressive loading for the model. Values of
a > 1 imply that the model is becoming unstable.
.1
.09
.08
.07
.06
>>
s -05
3.
£ -04
.03
.02
.01
X - .61
S - .40
662 Events
0 .67 i.43
Value of o
Figure 8. Distribution of the Estimated Parameter a
Acknowledgement
The author wishes to express his thanks to W. Wink-
ler for programming support for this project. Also the
author wishes to thank T. G. Roefs, who was the contract
monitor for the project which supported this research.
The research for this project was conducted while work-
ing on Contract 14-B1-0001-5221 for the Office of Water
Research and Technology, U.S. Department of Interior.
References
[1] R. DeMoyer, "A Statistical Approach to Dynamic
Modeling and Control," Ph.D. Thesis 1973, Poly-
technic Institute of Brooklyn, ESS.
[2] H. S. Rao, et al., "Studies on Operations Planning
and Control of Water Distribution Systems," SCI
Final Report, Contract Number 14-31-0001-4242, pre-
pared for Office of Water Research and Technology.
[3] D. H. Budenaers, "Sequential Short-Term Electric
Power Demand Forecasting," Proceedings ASA Business
and Econometrics, Atlanta Meeting, August 1975.
[4] T. W. Anderson, "The Statistical Analysis of Time
Series," John Wiley & Sons, Inc., New York, 1971.
[5] M. G. Kendall and A. Stuart, "Advanced Theory of
Statistics," Vol. 2, Hafner Publishing Co., New
York, 1960.
[6] D. H. Budenaers, "Water Demand Forecasting," SCI
Final Report, March 1976.
[7] H. Theil, "Principles of Econometrics," John Wiley
and Sons, Inc., New York, 1971.
Figure 7. Number of a Units Forecast Deviates from
Actual (a = .8, y = -8)
650
-------
HYDROLOGIC IMPACT STUDIES OF ALTERNATIVES TO MEET
WATER NEEDS IN SOUTH -(CENTRAL PENNSYLVANIA
David H. Marks, Guillermo J. Vicens, Brendan M. Harley, and John C. Schaake, Jr.
Resource Analysis, Inc., 1050 Massachusetts Avenue, Cambridge, Massachusetts 02138
ABSTRACT
This paper presents the use of several interrelated
models to investigate the potential hydrologic impacts
of several proposed water supply alternatives for the
South Central Pennsylvania area. The area contains
major demand centers in Harrisburg.York, Lancaster,
Lebanon, Manheim, Elizabethtown, Ephrata, New Holland,
Lititz, Carlisle, and Mechanicsburg, which for the
most part depend on local surface waters for their
water supply with supplemental withdrawals from the
Susquehanna River and from groundwater. Withdrawals
from all of these sources could have an impact on the
flows in the Susquehanna itself. Since this river is
the main source of freshwater to Chesapeake Bay, it
was important to assess the relative impact of each of
the proposed alternatives on the outflow distribution
to the Bay. The scope of the study was limited to the
hydrologic aspects of the problem. The models used to
evaluate the impacts of the alternatives were:
1. A synthetic streamflow augmentation and generation
model to first augment the existing records up to
a full 80-years, and second generate a set of 200-
year synthetic records which resembled the histor-
ical records in their statistics.
2. A linear regression model relating monthly rain-
fall and evapotranspiration to streamflow in the
tributaries used to evaluate the impact of
groundwater withdrawals on surface water flows.
3. A simulation model used as an accounting device
to show the impact of the alternatives on the
monthly flows at several locations in the area
including the outflow of the Susquehanna to
Chesapeake Bay.
INTRODUCTION
The objective of this paper is to describe the
methodology used in hydrologic investigations
carried out on a series of water supply alternatives
for the South Central Pennsylvania area (Resource
Analysis. Inc.. 1974b). The area contains major demand
centers in Harrisburg, York, Lancaster, Lebanon, Man-
heim, Elizabethtown, Ephrata, New Holland, Lititz,
Carlisle and Mechanicsburg, Pennsylvania as shown in
Figure 1. In general, these communities depend on
local surface water for their water supplies, with
additional supplies coming from the Susquehanna River
and from groundwater. With continuing increases in
population in the area, major capital investment in
new facilities and water sources will be necessary.
Withdrawals from groundwater or local surface water
storage may have a different impact on flows in the
Susquehanna and its tributaries than withdrawals from
the Susquehanna itself. While the area is itself
relatively water rich, different withdrawal patterns
will lead to changes in the flow characteristics of
the local tributaries and to different distributions
of outflows from the Susquehanna to Chesapeake Bay.
Since a change in the outflow distribution for the
main freshwater input to the Bay could have major
1 Now at Hydrologic Research Laboratory, National
Weather Service, Silver Spring, Maryland 20910
ecological impacts, this outflow is of significant
interest.
Objectives of Study
The primary objective of the study was to assess the
relative impact of the proposed alternatives for water
supply development on the distribution of monthly
outflows from the study area. In addition, estimates
of the impacts on low flows in local tributaries were
made. Other parts of the study conducted by other
contractors dealt with institutional, ecologic, and
engineering feasibility considerations. Our study
dealt only with hydrologic considerations, i.e., the
distribution of outflows from the system and on the
tributaries as they are affected by the different
alternatives.
Study Area
The study area is shown in Figure 1 and contains all
or parts of Cumberland, Adams, York, Dauphin, Lebanon,
and Lancaster Counties in the south central part of
the Commonwealth of Pennsylvania. Major tributaries
to the Susquehanna River in the study area are Swatara,
East Conewago, Chickies, and Conestoga Creeks on the
east side; and Conodoquinet, Yellow Breeches, West
Conewago, and Codorus Creeks on the west side. Present
water supply usage and future water demand (year 2020)
are shown for each major municipal area in Table 1.
The major demand areas include surrounding water com-
panies as well as the new municipalities. In general,
Harrisburg (East) presently depends on Clark, Stony,
and Swatara Creek sources; Harrisburg (West) on
Yellow Breeches, and Conodoquinet Creeks; Mechanics-
burg on Yellow Breeches; Elizabethtown and Manheim on
Chickies Creek; Lebanon on the Swatara; Lititz and New
Holland on groundwater; Ephrata on Conestoga Creek;
and York on the Codorus. Only Lancaster presently
draws major supplies from the Susquehanna.
Alternatives for Mater Supply
A variety of different water supply options exists for
the area ranging from all ground and local surface
water to all Susquehanna water, as well as combinations
of the two. As there is a relatively large amount of
water available in the area, the question of importance
is which sources should be developed rather than
whether it is possible to find the water. For example,
Harrisburg (East and West), Mechanicsburg, Lebanon,
Elizabethtown, York, Lancaster, and New Holland could
go directly to the Susquehanna for additional sources.
Alternatively, new or improved impoundments on the
Conodoquinet, Swatara, E. Conewago, and W. Conewago
Creeks; and the South Branch of Codorus Creek could
also be used to supply future water needs. Ground-
water in areas like York, Lebanon, Elizabethtown,
Ephrata and New Holland could serve their new water
needs. To consider the options available a series of
alternatives were conceived by the U.S. Army Corps of
Engineers and the Commonwealth of Pennsylvania, and
developed by the Anderson-Nichols Co. to consider
651
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combinations of these possibilities. A brief discus-
sion of the alternatives is shown in Appendix A.
Hater Supply Service Areas and Demands for 1970 and 2020
Major Demand Areas
Carlisle
Mechanicsburg
Harrisburg (West)
Harrisburg (East)
Lebanon
York
Elizabethtown
Manheim
Lancaster
Lititz
Ephrata
New Holland
Total
Municipalities Demand (MGD)
Included 1970 2020
Carlisle Boro and 3.7
Suburban
Millsburg, Grantham,1.8
Mechanicsburg W.C.
Riverton W.C.
7.7
Harrisburg W.C., 22.4
Dauphin, Hershey,
Middletown,
Steel town
Lebanon-City, 8.2
Keystone, Cornwall,
Meyerstown,
Heidelburg
Red Lion, Dover 21.0
Boro, Dover Twp.,
West Manchester,
York W.C.
Rheems, Elizabeth- 0.8
town, Mount Jay
Manheim
Columbia, Mount-
ville, E. Hemp-
stead, E. Peters-
burg, Lancaster,
Millers
Lititz
Akron, W. Earl-
ham, Ephrata
Leola, New
Holland, Blue
Bell
0.5
17.4
1.0
1.1
0.7
6.9
6.2
19.8
32.7
16.8
40.2
3.6
0.7
40.1
3.0
2.2
2.7
86.3 174.9
Outline of Methodology
The information available for this study was the
following:
1. Estimates of future demands from municipal and
industrial (M&I), agricultural, and consumptive
powers cooling users.
2. Monthly gauging records for several locations in
the area including the Susquehanna River, Codorus,
Conodoquinet, Swatara, W. Conewego, and Conestoga
Creeks.
3. Monthly precipitation records at York, Harrisburg,
Lancaster, and Lebanon.
4. Configurations for each water supply alternative
including reservoir capacities and allocation of
demands to sources.
Given this data base, the objective was to assess the
hydrologic impacts of each alternative through a simu-
lation study. The following tasks were carried out to
evaluate the alternatives:
1. Process the rainfall and streamflow data into the
RAI Hydrologic Data Management System (Resource
Analysis. Inc., 1974a).
2. Augment the streamflow records to produce a "full"
set of records of consistent length to be used for
parameter estimation purposes.
3. Estimate the statistical parameters of these
records, and generate a set of 200-year synthetic
records,
4. Develop a linear regression model relating the
effect of groundwater withdrawal on future stream-
flows. This relation was to be used to. assess
impacts of groundwater development on local
surface water flows.
5. Simulate the operation of the system under both
the historical and synthetic streamflow records
for each alternative plan in order to assess its
reliability and the resulting hydrologic impacts.
The following sections briefly describe each of the
above steps. A full discussion of the methodology
and results is contained in the final project report,
Resource Analysis, Inc. (1974b).
GENERATION OF SYNTHETIC STREAMFLOW RECORDS
Available Streamflow Data
Historical records at eleven gauging sites in or
near the study area were available. The length of
these records is shown on Figure 2. All stations
had at least 40 years of observations except for
Station 5755 which had 32 years, and Stations 5745
and 5765 which had some small gaps.
An improvement in the parameter estimates was obtained
by extending or "filling-in" the shorter records by
correlation with nearby stations. Regression analysis
has been frequently used to carry out the augmentation
of records. The theory on which these procedures are
based has been discussed by Fie ring (1962), Matalas
and Jacobs (1964), and Gjlroy (1970), and will only be
briefly summarized here.
The streamflow data at the gauging stations with the
shorter record yt»are related to the data at other
sites x^, Xg^.,..., Xpt, through a linear regression
model given by:
= a
blxlt + b2x2t
bpV
(1)
where et is a standardized normal random deviate.
The parameters of this model: a, bj, b2 and bp
are computed from the available data through standard
least square procedures for regression analysis.
These values are then used in the model to estimate
the streamflow at station y where these values are
missing. Similarly, in the case of shorter records,
the record at station y is extended by this same
procedure from the longer observed nearby or related
records.
652
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Three data augmentation runs were carried out. These
are described in Table 2. The objective of the first
run was to obtain a full forty years. Run No. 2
extended the 8 stations to 73 years. Finally in,
Run No. 3, the nine shorter records were extended an
additional seven years by regression from the longest
record. The final output was a set of 80-year records
at all eleven stations.
Table 2
Data Augmentation
Run Stations Other Period Period of
No. Augmented Stations Augmented Estimation
5145
5755
5765
5730 5705
5700 5750
5740
10/1932
to 9/1972
*10/1932
to 9/1972
where Q represents streamflow in month t, Pt and Et
denote the rainfall and evapotranspiration in month t,
and the values of aQ, a^ bQ, ... , bm are to be eval-
uated for each sub-basin. The precipitation variables
Pt should be basin average values which can only be
estimated from point values. Likewise, the evapotrans-
piration variable, Et, should be the basin average
value. The disturbance term \T accounts for the
errors introduced by using point measurements instead
of the "true" basin average values.
The effects of groundwater withdrawals on surface
flows was then assumed to be similar in response to
the rainfall-runoff relations derived above. Thus the
streamflow depletion in month t denoted as Dt was
related to the groundwater withdrawals for the six
previous months, W
through W , by:
L-O
5700 5730
5745 5750
5760 5765
5740 5755
5670 5700
5745 5750
5760 5765
5730 5255
5670 5705
5705
10/1899
to 9/1972
10/1891
to 9/1972
10/1932
to 9/1968
10/1932
to 9/1968
Dt= £
i=0
ciWt-i
*Includes only extension of record length, not
monthly gaps.
Synthetic Streamflow Generation
A 200-year synthetic streamflow record was generated
based on the procedures described in Valencia and
Schaake (1972, 1973). Briefly, the procedure is first
to generate a series of annual flows at the selected
stations. These annual flows are then disaggregated
into seasonal flows. Finally, a similar procedure
disaggregates seasonal flows into monthly flows.
This scheme preserves the means and variances of the
seasonal and monthly flows, the correlation between
monthly flows at the s.ariie.>s.ite or different sites, and
the correlation between any monthly flow and any
seasonal flow, and between the seasonal flow and the
annual flow. The generated monthly values at any site
will add up to the corresponding annual value, which
guarantees the preservation of annual statistics.
GROUNDVJATER MODEL
A simple model of the impacts of groundwater with-
drawals or surface water flows was developed. This
model was based on a theoretical analysis of the
range of potential impacts to be expected, as well as
a statistical analysis of rainfall and streamflow data
to evaluate the dynamic properties of the aquifers in
the study region.
The historical rainfall and streamflow records avail-
able for this region were used to determine the time
delay characteristics of the natural groundwater
system. A mathematical description of this system
was created, based on the following assumptions.
First, the average streamflow in each month consists of
groundwater and direct runoff components. Second, the
amount of direct runoff is assumed to depend upon the
current month's precipitation. Finally, the amount of
groundwater is assumed to depend upon the current and
previous months' precipitation in excess of evapotrans-
pi ration. An equation representing this is:
where the coefficients C- are computed from:
b.
(3)
(4)
i=0
A similar formulation was used by Nieswand and
Granstrom (1971) to model the Mullica River Basin in
New Jersey.
The coefficients obtained from the analysis of the
Susquehanna data are shown in Table 3.
Table 3
Groundwater Withdrawal Impacts on
Local Streamflows
BASIN Streamflow responses in various months due
to a unit groundwater withdrawal in month t
t t+1 t+2 t+3 t+4 t+5 t+6
Codorus .147 .188 .237 .212 .151 .051 .014
Creek
Conodo- .178 .171 .225 .201 .153 .018 .054
quinet
Creek
Swatara .456 .207 .105 .087 .115 .030 0.00
Creek
Conestoga .165 .139 .175 .206 .165 .102 .048
Creek
SIMULATION MODEL
To assess the impacts of each of the alternatives on
the distribution of flows in the Susquehanna and the
low flows in the tributaries, and to evaluate the
reliability of the proposed alternatives, a simulation
study of the operation of the system was carried out.
A modified version of the MIT River Basin SIMulation
653
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Model (MITSIM) was used for this purpose (Schaake, et.
al_, 1974).
MITSIM was designed to generate and display both eco-
nomic and physical information to aid in evaluating
system response. The model is an accounting procedure
that takes the synthetic or historical data developed,
seasonal water demands and consumptive use, the ground-
water response functions, the operating rules for the
various reservoirs, pipelines, and groundwater
systems, and operates them to find the monthly system
flows at specified locations. The structure of the
model is of nodes connected by branches with all water
entering or leaving the system at the nodes. Typical
nodes are:
1. Start nodes nodes at which historic or synthetic
streamflow data is input to the system. For the
case study, a start node was used for all streams
including non-gauged streams, and major overland
flow areas to the Susquehanna. A special program
was written to disaggregate data available at
gauging stations (both historic and synthetic
records) to input data for the start nodes.
2. Confluence nodes the joining of two branches of
the system used to show the connectivity of the
activities.
3. Reservoir nodes for each reservoir node, a capac-
ity, seasonal target, and seasonal release sche-
dule is given. Water may be removed from a reser-
voir node to meet demands provided enough water is
in storage and release requirements are met.
4. Groundwater Nodes represents the pumping of
groundwater to meet a specified demand. A ground-
water function relates seasonal withdrawal to
impacts on local surface water in present and
future seasonal withdrawal to impacts on local
surface water in present and future seasons.
A seasonal consumptive use coefficient shows how
much of the groundwater is released to the surface
water after use.
5. Irrigation Node for each irrigation area, seasonal
demands and consumptive use coefficients are com-
bined to compute the portion of the specified
demand in season that is returned to local surface
waters in the present and future seasons.
6. M&I Node a municipal and industrial demand and
consumptive use coefficient is specified for each
surface water demand in each season to calculate
withdrawals and returns to streams.
A typical schematic for a system is shown in
Figure 3 and Appendix B describes the function of
each of the nodes shown.
RESULTS
All of the alternatives described in Appendix A were
simulated with the 200-year synthetic record. In
addition, Alternatives 1,2 and 3 were simulated with
the 80-year augmented historical record as inputs.
The first question to be investigated was which of the
records was more stringent or conservative. Compari-
son of the simulation results of Alternatives 1 through
3 for both the historic and synthetic records, showed
that the 200-year synthetic record produced, on the
average, lower monthly outflows from the study area
even though two extensive drought periods were obser-
ved in the historic record. Since the relative
impact of the alternatives on the distribution of the
outflows from the system was of utmost importance in
this study, the synthetic record was selected for
detailed comparison of alternatives.
Monthly outflows were calculated at the lower boun-
dary of the study area which was the intersection of
the boundary of Lancaster County, Pennsylvania with
the Susquehanna River. This line is slightly above
the Conowingo pool,and thus our calculation of system
outflow represents runoff from a slightly smaller
drainage area than that supporting inflows to the
Conowingo Pool, which other studies have focused on.
Table 4 presents a summary of the results obtained
from the simulation runs. This table shows estimates
of the annual and monthly 30-day low flow which occurs,
on the average, once every twenty years (Q30-20) at
the outflow of the study area. The results for each
alternative plan with Year 2020 demands are shown, as
well as a "Present" case for comparison purposes.
Table 4
Estimates of Q30-20 at the System Outflow 200-Year
Synthetic Streamflow Trace and 2020 Demands.
(Present Run Uses 200-Year Synthetic Trace and
1970 Data)~
Al tern .
Present
1
2
3
4
5A
SB
5C
6A
6B
6C
7A
7B
7C
Aug.
3622
3412
3410
3405
3411
3411
3411
3405
3415
3425
3411
3422
3427
3407
Q3Q-20
Sept.
3266
3051
3050
3048
3052
3052
3052
3048
3056
3044
3052
3062
3065
3050
(cfs)
Oct.
3055
2943
2945
2944
2944
2944
2944
2944
2944
2944
2944
2946
2945
2945
Annual
3075
2840
2820
2818
2840
2840
2840
2818
2853
2873
2840
2858
2879
2821
The overall results of the study were:
1. There is very little difference between alterna-
tives in terms of Q30-20 or monthly average flows
at the outflow of the study area. The values of
annual Q30-20 for the alternatives range from
2818 cfs to 2879 cfs. The present case produces
a value of 3075 cfs. Estimates of Q30-20 for
August, September and October show similar results
Most of this decrease is due to a consumptive use
increase in power cooling through 2020, which peaks
at 345 cfs. The lower values are also due to
increased groundwater and Susquehanna water usage,
while the higher values are a result of reservoir
storage in the tributaries.
2. From the viewpoint of flows in the tributaries, the
alternatives with large groundwater usage decrease
tributary flows slightly. However, all other alter
natives tend to substantially increase tributary
flows due either to diversions of Susquehanna
water or larger reservoir impoundments.
3. Any reliability problems for M&I water availabil-
ity are due to over estimates of present source
capabilities and can be easily improved by
increasing reliance on new sources. All alterna-
tives are equally reliable.
654
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SUMMARY
The use of several interrelated models to investigate
the potential hydrologic impacts of several proposed
water supply alternatives for South Central Pennsyl-
vania has been presented. The objective of the study
was to assess the relative impacts of the alternatives
on the distrubution of the outflows to Chesapeake Bay.
The methodology developed for this study consisted of
several hydrologic models which processed the availa-
ble hydrologic and water demand data to evaluate the
impacts of the alternatives.
ACKNOWLEDGEMENTS
This study was performed by Resource Analysis, Incor-
porated under contract to the U.S. Army Corps of
Engineers (North Atlantic Division, Special Studies
Group) for their Northeastern United States Water
Supply (NEWS) Study.
REFERENCES
Fiering, M.B., "On the Use of Correlation to Augment
Data," Journal of the American Statistician Associa-
tion, 57 (297), pp. 20-32, 1962.
Gilroy, E.J., "Reliability of a Variance Estimate
Obtained fron a Sample Augmented by Multivariate
Regression," Water Resources Research, 6 (6),
pp. 1595-1600, 1970.
Matalas, N.C., and B. Jacobs, "A Correlation Proce-
dure for Augmenting Hydrologic Data," U.S. Geologi-
cal Survey Professional Paper 434-E, 1964.
Nieswand, G.H., and M.L. Granstrom, "A Chance-Con-
strained Approach to the Conjunctive Use of Surface
Waters and Groundwaters," Water Resources Research,
7 (6), pp. 1425-1436, December, 1971.
Resource Analysis, Incorporated, Hydrologic Data
Storage System: Users' Manual, Report to the Depart-
ment of Natural Resources, Commonwealth of Puerto
Rico, January, 1974a.
Resource Analysis, Incorporated, Hydrologic Impact
Studies of Alternatives to Meet Water Needs in South
Central Pennsylvania, Report to North Atlantic Divi-
sion of U.S. Army Corps of tngineers, September,
1974b.
Schaa.ke, J.C., et.al., "Systematic Approach to Water
Resources Plan Formulation," M.I.T. Ralph M. Parsons
Laboratory for Water Resources and Hydrodynamics
Report No. 187, July, 1974.
Valencia, Dario and J.C. Schaake, Jr., " A Disaggre-
gation Model for Time Series Analysis and Synthesis,"
M.I.T. Ralph M. Parsons Laboratory for Water Resources
and Hydrodynamics Report No. 149, June 1972.
Valencia, D., and J.C. Schaake, Jr., "Disaggregation
Processes in Stochastic Hydrology," Water Resources
Research. 9 (3), pp. 580-585, June, 1973.
Appendix A
DESCRIPTION OF ALTERNATIVES
Alterna-
tive #
Developments
5A
draw from present sources with some additional
groundwater development.
Lebanon would develop new storage and improve
existing storage on the Swatara, with some new
groundwater development.
York would go to the Susquehanna as a source
and develop groundwater.
Elizabethtown, Ephrata, New Holland, and Lititz
would develop additional groundwater sources.
Lancaster and Manheim would continue with pres-
ent sources.
Considers major use of groundwater in the
future, especially for York and Lebanon. No
new impoundments or Susquehanna sources.
Considers Susquehanna as the major source of
new water demands for Lebanon, York, and Eliz-
abethtown,with no new impoundments built.
Considers new impoundment on Swatara Creek for
Lebanon, and York water supply
from Susquehanna.
Considers impoundment on Swatara Creek for
Lebanon and Elizabethtown, and York supply
from Susquehanna.
1 Considers development each municipality
would undertake without outside assistance.
Harrisburg, Mechanicsburg.and Carlisle would
5B Same as 5A except reservoir development on
E. Conewago Creek is considered for Eliza-
bethtown.
5C Susquehanna is used for Lebanon, Harrisburg,
(East and West), York and for some additional
needs in Carlisle and Mechanicsburg. Reser-
voir on E. Conewago Creek is used for Eliza-
bethtown .
6A Considers a new reservoir on the Swatara and
groundwater for Lebanon. New reservoir on
S. Branch of the Codorus for York.
6B Lebanon impoundment retained, but Elizabeth-
town switched to Susquehanna and York to a
W. Conewago reservoir.
6C York, Lancaster, New Holland and Elizabethtown
use Susquehanna, and new impoundments are dev-
eloped on Conodoquinet Creek and Swatara Creek.
7A Large groundwater development, Lebanon uses
Susquehanna and York uses impoundment on W.
Conewago Creek.
7B Same as 7A except Lebanon uses a reservoir on
the Swatara.
7C Combines 5C and 6C and includes a reservoir on
the Conodoquinet.
Appendix B Node Descriptions
Reservoir CODRRES
M&I - CARLILMI, HARRWCDQ, MECHBGMI, HARRWYBC, YORKCODR,
YORKCBC, YORKSUSQ, LANCSTSQ, EPHRTAMI, ELIZCHK,
MANHMMI, LEBSWT, HARRESWT, HESUSQ, HARRESCL,
SUSQMI
Groundwater CARLILGW, MECHBGGW, YORKGW, LEBANGW,
ELIZGW, LITITZGW, NEWHOLGW, LANCSTGW,
EPHRTAGW
Irrigation - CDQIRR, WCONIRR, CODRIRR, CSTIRR, CONWIRR,
SWTIRR
All others are start or confluence nodes.
655
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Figure 1; Study Area
PERIOD OF RECOf
5700 Conodoqulnet Cr.
5705 Susq. K. at Kirrlsburg '
5750 i. Br. Codorui Cr. near York
5765 Corwstoga Cr.
5730 SirtUra Cr.
5745 H. Br. Codorus Cr. at Spring Grove
5740 U. Conewgo Cr.
5755 Codorus Cr. near Tort
56fl5 Clark Cr.
S760 Susquehannfl R. »t Harriett!
5670 Juniata R. ,_
1900 1910 1920 1930 1940 1950 I960
Figure 2: Available StreMf
C E E « L
S P P E A
T H H H N
I R R H C
R T T 0 S
R A A L T
H G G G
I H H U
Figure 3: Typical Schematic
656
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Ashok N. Shahane
Environmental Systems Engineer
THE OPERATIONAL WATER QUANTITY MODEL
Paul Berger
Scientific Programmer
Robert L. Hamrick
Division Director
Water Planning Division, Resource Planning Department
Central and Southern Florida Flood Control District
West Palm Beach, Florida 33402
SUMMARY
A recently completed operational water quantity model
based on hydrologic-hydraulic simulations is presented
in this paper. Using the rainfall input, initial state
conditions and basin parameters, the model estimates,
among many hydrologic entities, the streamflows contri-
buted by the watersheds. An iterative type routing
model is then developed to distribute the simulated
streamflows through the primary conveyance systems of
lakes, canals, and channelized river controlled by the
gate operations at the controlling structures. The
designed methodology is demonstrated for the Kissimmee
River basin of Florida for the year 1970 by considering
21 canals, 14 lakes and 14 controlling structures. The
outcome of the model relates to simulated lake stages,
water levels at tailwater and headwater sides of the
controlling structures and simulated discharges through
controlling structures every 3 hours for the full year
of 1970. The comparison of simulated values with the
corresponding historical data indicates clearly the
"working" of all the individual pieces of the opera-
tional water quantity model, although a few critical
links are currently being refined to obtain better simu-
lated lake stages.
INTRODUCTION
Although the conventional watershed models are devel-
oped with different purposes, methodologies, tools and
settings, they are usually valid for natural hydrologic
drainage systems. Therefore, it seems that these
models have to be modified in some fashion to analyze
the typical water system with a chain of lakes and
channels managed by several controlling structures.
Thus, a basic characteristic of the operational water
quantity model is related to its capability of including
operational functions of the water system with adequate
theoretical and experimental data for formulating basic
hydrologic processes. Secondly, based on the analytical
principles, simulation and optimization techniques with
stochastic and deterministic inputs are currently being
used in planning and design of water systems. Con-
sidering the necessary assumptions and speculated condi-
tions required for reaching a mathematical solution,
these design models give general answers to the over-
all problem and do not generate the most desired prod-
uct for the operational needs4: As further pointed out
by Lindahl and Hamrick4, operationally oriented models
should give specific answers to very specific questions
and circumstances. Thirdly, the operational models are
usually designed to function as a short-term and long-
term decision making aide within an operational set-up
and within existing peripherial monitoring capabilities
for a typical system. In other words, using hydrologic
and hydraulic characteristics of the river basin, the
operational models can provide valuable assistance in
operating the gates manually or automatically to main-
tain water levels or adequate flow of water in normal
as well as unusual circumstances.
The specific water system for which the presented
operational water quantity model was developed is the
Kissimmee River system as depicted in Figure 1. As
shown in Figure 1, the Kissimmee water system consists
of 14 lakes, 25 canals and 14 controlling structures.
As shown in Figure 2, the Kissimmee basin is further
divided into 19 drainage basins (also called planning
units) that drain into the primary conveyance system
of lakes, canals and controlling structures of Figure 1.
It is to be emphasized that the procedure of the oper-
ational water quantity model and the related computer
programs are developed for specific configuration of
the water system as shown in Figures 1 and 2.
COMPONENTS OF THE OPERATIONAL WATER QUANTITY MODEL
Since past attempts have been made in three distinct
stages to bring the model to its current form, its
developmental procedure is broken down into three
component parts: 1. Sub-basin model, 2. Routing pro-
cedure, and 3. Routing methodology to combine the
routing technique with the sub-basin model. Basic
computational steps of the model are outlined in
Figure 3.
Description of the sub-basin model:
The basic foundation on which the sub-basin model was
developed and modified is essentially a parametric
approach for formulating the physical system of the
Kissimmee basin in terms of hydrologic
simulation.4>5,8,9,10 it can be seen from Figure 4
that the major computational steps are related to:
(a) processing of input rainfall values, (b) Formu-
lations of infiltration phenomenon, (c) surface storage
and overland flow equations, (d) estimation of water
losses, and (e) quantification and routing of sub-
surface flow through a multi-layer soil system.
Since the detailed descriptions and discussions of
rationale behind these formulations were previously
reported by Hoi tan, Lopez, Lindaljl. Sinha. Hamrick,
Khanal, and Shahane, et. al,] ,2,4,5,8,9,10 tnese
formulations are briefly discussed in the following
section.
Processing of input rainfall values: Using the
available network of raingaging stations over the
entire Kissimmee River basin, daily rainfall values
are obtained for each of the 19 planning units from
the daily rainfall values of surrounding representative
raingaging stations. These recorded daily rainfall
values are further synthesized to generate hourly
values using a linear stochastic model for the consecu-
tive hourly rainfall record as reported in reference 10.
657
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Formulations for infiltration phenomenon: Among
various formulations and concepts proposed by many soil
scientists, a modified form of the empirical equations
originally developed by Hoi tan is used in quantifying
the infiltration phenomenon.1'2 Such equations are:
f = A(SA)1'4 for SA >_ G
and
f = A(SA)1'4 + FC for SA < 6
(1)
- - (2)
where
f = capacity rate of filtration, A surface
penetration index, SA storage currently available
in the soil reservoir, FC constant rate of infil-
tration between consecutive layers, G total
amount of free or gravitational water in a soil
profile of selected depth.!»2,8,9
Surface storage and overland flow: Besides
infiltration, a part of precipitation is contributed to
the storage in surface depressions. Such surface
storage is computed as
VD
f-DT
(3)
After a part of precipitation input percolated
into the ground and after a part filled the maximum
volume of surface depressions, precipitation excess is
contributed to overland flow. Mathematically, it is
computed from simple subtraction as
Overland flow P-f when VD=VDM and P > f (4)
where
P precipitation input, f infiltration rate,
VD = amount of water currently stored in surface
depressions, VDM maximum volume of surface
storage.8,9
Estimation of water losses: In the sub-basin
model, water losses are considered as the part of preci-
pitation input that reaches the around surface but never
appears at the watershed outlet.'.8,9,10 with this
definition, water loss can occur in different categories;
i.e., water loss due to direct soil evaporation, evapo-
transpiration by existing vegetation and water loss due
to deep percolation. These losses are in turn functions
of various factors as shown in the following-formula-
tions :
1. Water loss due to indirect soil evaporation,
Loss 1 Ci(l nm-M^—on ](PT)- (5)
2. Portion of water that is lost due primarily to
the existing vegetation
Loss 2 = C^GJC^^^I DT (6)
3. Water loss due to deep percolation,
Loss 3 (FC)(DT) (7)
where
C-] ratio of maximum evapotranspi ration to maximum
pan evaporation value,
DWT water table depth = (SA)(D)/G; - (8)
D total depth of'soil profile; G = total amount'of
free gravity water that could exist in a soil
profile, DWTM maximum depth to water table at
which DWT will have a negligible contribution toward
Loss 1, EP pan evaporation, NW = number of weeks,
DT = time increment, C2 constant = 0.78, Gi = an
overall growth index for the existing vegetation,
FC constant rate of infiltration between consec-
utive layers, SA = storage currently available in
reservoir.
Adding these three losses together gives the total loss
of water from a given soil profile. This value of
total water loss is accounted for in estimating the
recovery of water from the soil reservoir to the main
channel.
Quantification and routing of sub-surface flow:
The basic purpose of this computational step is to
estimate the spatial and time contribution of the sub-
basin flow from different soil reservoirs to the main
channel. Thus, the first task is to determine the
number of reservoirs. This is done by reverse integra-
tion of the runoff hydrograph by establishing storage-
flow relationships for a simple recession curve. Using
this technique it is established that for our 19 plan-
ning units, soil profile can be represented by not
more than three soil reservoirs. After determining
the number of soil reservoirs, the basic continuity
equation and a storage outflow curve is combined to
provide contributions of each soil reservoir to the
stream channel and also the total storage available
in these reservoirs at the end of each time step.
These computations reported by Lindahl^ take into
account (l)the volume of water that is infiltrated
during time DT, (2)initial available storage in a soil
reservoir, (3)sum of water losses, (4)volume of sub-
surface drainable water, (5)time interval for the vol-
ume of the subsurface drainable water, and (6)the up-
dated available storage. At the end of these compu-
tations, the discharges contributed by each soil layer
and overland flow are obtained for each time interval.
In the next step, these discharges are multiplied by
the routing coefficients (which are estimated from
Nash's routing equation) and resulting values are
added together to obtain time distribution of stream-
flows at the watershed outlet.8,9
Input Data Requirements:
To carry out these computational steps for the 19 plan-
ning units of the Kissimmee basin, the parameters of
the formulations should be known. Since these param-
eters represent the agricultural-related water charac-
teristics of the basin, they are estimated based on
the available research publications of the ARS and
many reports delineating the regional character-
istics. 4,5,8,9,10
To compute infiltration characteristics, the appropri-
ate basin parameters are: (a) total available storage
in three soil reservoirs, i.e., TAS(l), TAS(2) and
TAS(3); (b) constant rates of infiltration in three
layered soil systems from one layer to another desig-
nated as F(l), F(2) and F(3); (c) total ammount of
gravitational water in these three layers, i.e., G(l),
G(2), and 6(3); (d) portion of G that can be drawn
into surface water i.e., GD(1), GD(2), and GD(3),and
(e) total depth of the soil profile (D) in inches.
In addition, for estimating three types of water
losses, overland flow, and sub-surface flow, the fol-
lowing parameters are required: (a) depth of water
table at which evaporative water loss is considered
significant, (b) maximum volume of surface storage
(VDM), (c) ratio of evapotranspiration and maximum pan
evaporation value (PPAN), (d) sub-surface discharges
through three soil layers Q(l), Q(2), and Q(3), and
(e) corresponding storages in these three soil reser-
voirs SG(1), SG(2), and S6(3).
658
-------
Finally, routing coefficients to combine flows from
three sub-surface layers with the overland flow i.e.,
TK(1), TK(2), TK(3), TK(4) for representative loca-
tions in the Kissimmee basin are also necessary along
with the assumed number of cascades in layer i (CNR
ROUTING MODEL
In our specific investigations, the basic purposes of
developing routing methodology are: (1) to distribute
sub-basin model output through the system of the lakes,
channels and controlling structures,(2) to combine
stage-storage fluctuations of the lake with the stage-
discharge characteristics of the channel sections for
developing a simple joint methodology of reservoir and
channel routing, (3) to include operational character-
istics of the controlling gates coupled with the
routed simulated stages for estimating discharges
through various controlling structures, (4) to improve
sub-basin model output by including the key process
(if any) of the lake or channel which might be excluded
from the assumed conceptual physical system, and (5) to
provide the basis for examining the effects of changing
operational parameters on the hydrologic characteristics
o}". the Kissimmee water system with complete independ-
ence from the analysis of the historical data.
Input Information and Essential Formulations:
Input information: While trying to demonstrate
the routing model for a one year period of 1970, it is
essential to obtain hydrologic base line information
just before this period for all the lakes, channels,
and controlling structures. Such information (also
known as initial conditions) includes: (1) the re-
corded stages at 14 lakes of the upper and lower
Kissimmee, (2) recorded tailwater and headwater eleva-
tions at 14 controlling structures, (3) proportioning
factors for distributing sub-basin model output in
corresponding lakes of a particular planning unit,
(4)various constants to convert monthly pan evapora-
tions to 3 hour lake evaporation values.
Essential Formulations:
As an essential part of the simulation procedure, our
methodology also depends heavily on the formulations of
various water systems. Basic forms of the equations
which are used in our analysis are summarized in Table
1. As shown in this table, formulations are classified
according to the type of system (i.e., lake, channel
or controlling structures). They are described below.
Formulations for lake system: Essentially, the
parameters which are useful in the simulation are
stages, storages, inflows and outflows for various
lakes. The first two equations of the lake system given
in Table 1 tie together, change in storage (AS) and
changes in stage to the characteristics of inflow, out-
flow and initial stages. These equations are simple
forms of mass-balance equations. In addition, it is
also necessary to know the stage-storage relationships
for all the lakes of the upper Kissimmee. These rela-
tionships can be in either tabular form or in math-
ematical form.
Formulations for controlling structures: Opera-
tional characteristics of the Kissimmee water systems
are reflected in the formulations of the controlling
structures. Variables considered in these formulations
are gate openings (60), headwater elevation (HWE), and
tailwater elevation (TWE) with discharge as a depend-
ent variable as shown by Equation 1 for structure oper-
ations in Table 1. In the routing methodology these
equations are used to compute the discharge through the
structure knowing the simulated tailwater and headwater
stages for a given set of gate openings.
Channel formulations: The development of the
channel formulations and using them in a convenient
fashion in routing methodology are some of the steps
that make our procedure different than previously
attempted techniques. Essentially, the hydraulic
formulations given in Table 1 for the channel system
relate to: (1) a differential equation representing
gradual varied flow with- slope of energy line, channel
bottom slope, discharges, cross-sectional area, top
width of the channel and velocity head coefficients as
variables and rate of change of depth (with distance)
as a dependent variable (Equation 1 of Table 3),
(2) Manning's equation combining hydraulic character-
istics of the flow (i..e., velocity, Manning's coeffi-
cients, slope of energy line) with the physical charact-
eristics of the channel cross-sections such as cross-
sectional area (A) and perimeter (P). (Equation 2 of
Table 1 of channel system.), (3) an interative equation
based on a numerical integration technique of trape-
zoidal rule applied by Prasad6 to estimate the water
depth (and then water surface elevation) at the end of
the channel section (Equation 3 of Table 1 of the
channel system). Using these formulations, the exist-
ing FCD backwater program is run to perform backwater
computations for all the 25 channel sections of the
Kissimmee with the available channel cross-sectional
data. For a given channel section, the program gener-
ates a set of upstream, downstream stages along with
discharges and storages. Using this data set, empirical
relationships based on statistical principles are de-
rived for these variables. These established mathe-
matical relationships (also known as backwater func-
tions) are then used in the program to replace directly
the backwater computational steps. Among many develop-
ed equations, the selected formulations are given in
Tables 2, 3, and 4. For better accuracy, these
formulations are used in conjunction with corresponding
correction factors. The rationale and different points
for developing these equations are discussed in detail
by Shahane, et al.'
COMPUTATIONAL METHODOLOGY
After developing various pieces presented earlier, the
next important step is to link them together to distri-
bute the sub-basin flows through the lake, channel, and
controlling structures of the Kissimmee basin. Among
other possible procedures, the selected method is de-
scribed briefly in the following section.
At the outset, the three lakes system is considered
with emphasis on the middle lake and the associated
two channel sections (i.e., one on each side of the
middle lake). Using the recorded initial stage of the
659
-------
middle lake, its initial storage is computed from a
stage-storage values. From the initial recorded stages
of the three lakes, the initial discharges are esti-
mated by channel formulations given in Table 5. If a
controlling structure is located in one or both chan-
nel sections, the initial discharges are computed
from the discharge rating curves for controlling
structures knowing the recorded tailwater, headwater
elevations (TWE and HWE) and the 3 hour gate opening
data. Using these initial estimates of discharges
flowing into or away from the middle lake and the
local inflow generated by the subbasin model, the
change in storage (AS) in the middle lake is esti-
mated from the simple mass-balance equation. Know-
ing the initial storage and the computed change
in storage, a new storage and new stage is obtained
for a prescribed time step. If the new discharges
corresponding to the new stage make the change in
storage (AS) in the middle lake significantly dif-
ferent than the previously estimated S, then S is
again computed using the average values of the new and
previous discharges through two channel sections.
This iterative procedure is continued until ;the dif-
ference between previous and new estimates of AS is
within the prescribed limit. At the end of the itera-
tion, final estimates of discharges through the chan-
nels, and the lake stage of the middle lake are ob-
tained. These steps are repeated for the next three
lake systems and continued for each lake system start-
ing from Alligator Lake to Kissimmee Lake and for five
channel systems of the lower Kissimmee basin using all
the formulations shown in Tables 2, 3, and 4.
Other details of the computational methodology are
discussed by Shahane, et al.7
RESULTS AND VERIFICATIONS
Results:
After putting together the pieces of the water quan-
tity model as shown in Figure 9, the output is essen-
tially the net result of the interactions of various
sub-components of such hydraulic simulation procedure.
The primary output from such methodology consists of
(1) simulated hydrologic parameters such as sub-surface
flow, total losses, deep seepage, available storage in
the soil, storage in depression and mean streamflows
for 19 planning units on a 3 hour basis, (2} 3 hours
simulated discharges through all the channel sections
of the upper and lower Kissimmee for the year 1970,
(3) 3 hours simulated mean discharges through all the
control structures for the full year of 1970, C4) 3
hours simulated stages for 14 lakes of the upper
Kissimmee basin, (5) 3 hours simulated tailwater and
headwater stages at all the control structures of the
upper and lower Kissimmee basins, (6) storages in all
the major lakes and storages for five sections of the
lower Kissimmee at the end of every 3 hours for the
entire year of 1970.
Verifications:
The methodology of the sub-basin model was first
applied by previous investigators to the Taylor Creek
drainage basin of 100 square miles located on the
north side of Lake Okeechobee in Florida. Since the
hydraulic, hydrologic and agricultural characteristics
of the Taylor Creek watershed are well monitored by
the ARS of the U. S. Department of Agriculture, and
since this drainage area was in its natural form with
no control structures to change its natural drainage
characteristics during the test period, it was an
ideal place to verify and test the FCD sub-basin model.
The typical result of such an effort is depicted in
Figure 5 which indicates clearly the adequacy of the
sub-basin model and suggests the appropriate choice of
coefficients covering the key hydrologic processes.8»9
When the same sub-basin model is applied to the 19
drainage basins (also known as planning units) of the
Kissimmee, the streamflows at the mouth of these drain-
age areas are generated. These values are compared
with the available yearly historical data (with wet
and dry period values) compiled by the Hydrology Divi-
sion of the FCD. The typical graphical comparison
is shown in Figure 6. Based on this comparison, it
appears that the sub-basin model simulates hydrologic
components which are in general agreement with the
recorded values.
The success of the routing methodology can be viewed
in terms of the various comparisons of simulated
stages and discharges with the corresponding recorded
values. The results of our routing methodology for
the upper Kissimmee basin were compared with the histor-
ical values using a particular set of state conditions,
basin parameters of sub-basin models coupled with a
specific set of proportioning factors, tabular values
and mathematical formulations of the routing model.
A typical comparison is shown in Figure 7. Although
the correlations depicted in Figure 7 for discharges
are excellent, the comparative graphs of simulated
and recorded stages of some of the lakes of the
upper Kissimmeeshow significant differences. To
illustrate this point, typical results in the form of
graphical comparison for Lake Tohopekaliga are
depicted in Figure 8. These comparisons indicate
clearly, (1) the capability of our overall framework
of operational watershed model to comvine the sub-basin
model with the routing methodology and to generate
the wanted simulated information, (2) the relative
importance of gate openings as against the head
difference across the structure in the discharge
rating formulations for the control structures,
and (3) the adequacy of the developed operational water
quantity model for considering the interactions of
stage-storage and discharge characteristics of lakes,
canals and controlling structures, making it possible
to further examine the effects of changed conditions
on the different parameters under investigation.
CONCLUSIONS
1. After designing, formulating, modifying and re-
fining various component parts of the operational water
quantity model as shown in Figure 3, it is demonstrat-
ed that the hydrologic and hydraulic performance of the
controlled water system for a given set of rainfall
distribution and gate operations can be adequately
simulated.
2. With a realistic framework of assumptions, simpli-
fications and approximations the developed computer
program (which takes about 5 hours of computer time for
one year of simulation on the CDC 3100 computer) is
shown to be successful in performing the following
operations: (a) simulating hydrologic parameters (such
as sub-surface flow, surface flow, evaporation losses,
deep seepage loss, available soil storage, storage in
depression and finally streamflows) on a 3 hour basis
for 19 planning units using rainfall, state conditions
and basin parameters as input data for the year of
1970, (b) routing these generated streamflows of 19
planning units through the controlled system of lakes>
channels and operating structures, (c) simulating 3
hour lake stages, headwater and tailwater-elevations
at structures and discharges through the structures of
the upper and lower Kissimmee, (d) comparing the simu-
lated values with recorded values in terms of plotted
graphs and tables, and (e) performing parametric sensi-
tivity analysis by changing the key parameters of the
660
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sub-basin model and the routing model.
3. It appears that the developed model can be di-
rectly or indirectly useful in (a) examining the
effects of certain physical parameters on the final
outcome of discharges and stages, (b) providing opera-
tional information regarding the required set of gate
openings to maintain water levels and discharges at a
particular level at specific locations, and (c) uti-
lizing the generated hydrologic information in the
other practical aspects of water management.
ACKNOWLEDGEMENTS
The authors wish to acknowledge Mr. W. V. Storch,
Director of the Resource Planning Department, Central
and Southern Florida Flood Control District, for en-
couraging the authors to present their modeling method-
ology in this national conference on Environmental
Modeling and Simulation.
REFERENCES
1. Holtan, H. N., Stiltner, G. J., Henson, W. H.,
Lopez, N. C., "USDAHL-74 Revised Model of Water-
shed Hydrology", Technical Bulletin No. 1518, ARS,
United States Department of Agriculture, Dec. 1975.
2. Holtan, H. N., "A Concept for Infiltration Esti-
mates in Watershed Engineering", ARS 41-51, Oct.
1961, p. 25.
3. "Hydrology and Hydraulics Section", Soil Conserva-
tion Service, National Engineering Handbook, Aug.
1972.
4. Lindahl, L. E., "Review of Techniques Pertaining
to Basin Models: a Memorandum Report to W. V.
Storch, Director of Engineering, Central and
Southern Florida Flood Control District, Dec. 1967.
5. Lindahl, L. E. and Hamrick, R. L., "The Potential
and Practicality of Watershed Models in Operation-
al Water Management", a paper presented at ASCE
National Water Resources Engineering meeting at
Memphis, Tenn., Jan. 26-30, 1970.
6. Prasad, R., "Numerical Method of Computing Flow
Profiles", ASCE Hydraulic Division, Vol. 96, No.
HY1, Jan. 1970.
7. Shahane, A. N., Berger, P. and Hamrick, R. L., "A
Framework for the Operational Water Quantity Model"
an interim report of FCD submitted to the Florida
State Department of Administration, July 1975,
p. 71.
8. Sinha, L. K., "An Operational Model: Step 1-b,
Regulation of Water Levels in the Kissimmee River
Basin", American Water Resources Association Con-
ference, Oct. 27-30, 1969.
9. Sinha, L. K. and Lindahl, L. E., "An Operational
Watershed Model: General Considerations, Purposes
and Progress", Transactions of ASAE, Vol. 14, No.
4, 1971, pp. 688-691.
10. "Water Yield of Kissimmee River Basin by the Use
of the FCD Model" an in-house report of Central
and Southern Florida Flood Control District, 1973.
NOTATIONS
AS change in storage,
WSE water surface elevation,
S storage,
SO bottom bed slope,
SE slope of the energy line,
n Manning's coefficient,
V velocity,
HR hydraulic radius,
Q discharge,
A cross sectional area,
Y depth,
GO gate opening,
EH headwater elevation (HWE) - tailwater ele-
vation (TWE),
DX distance between reaches i+1 and i,
a velocity head coefficient,
T top width of the channel,
g gravitational acceleration,
a,b,p,r,s constants
UPPER
KISSIMMEE BASIN
LOWER KISSIMMEE BASIN
SCHEMATIC REPRESENTATION OF THE
CHAIN OF UPPER KISSIMMEE LAKES AND LOWER KISSIMMEE FIVE POOLS
NOT TO SCALE
FIGURE 1
661
-------
MAP SHOWING THE LOCATIONS
OF THE 19 PLANNING UNITS OF THE KISSIMMEE BASIN
DEPRESSION
3TORAOE
SOIL MOISTURE
LAYER H
SOIL MOISTURE
LAYER HI
Figure 4 FT C. D. SUB-BASIN MODEL
Figure 2
Figure 5 COMPARISON OF SIMULATED AND RECORDED DISCHARGE
FOR TAYLOR CREEK (8,9)
Figures FLOW CHART OF MAJOR
COMPUTATIONAL STEPS INVOLVED
IN FC.D. WATER QUANTITY MODEL
COMPARISONS OF ANNUAL VALUES OF RAINFALL
RUNOFF ESTIMATES OF SUB-BASIN MODEL WITH HISTORICAL
' DATA FOR THE PERIOD 1960-70 FOR THE ENTIRE KISSIMMEE BASIN
RUNOFF-INCHES
Figure 6
662
-------
Figure 7
50 100 150 200 250 30O 35C
1970-EAST LAKE TOHOPEKALIGA
Figure s COMPARISON OF SIMULATED AND
RECORDED STAGES FOR EAST LAKE
TOHOPEKALIGA FOR THE YEAR 1970
Table 1. Basic forms of equations useful in the model.*
System
Lake System
Channel System
Structures
Operations
Formulations
1. (stage)t+1 (stage)t + (4S)t+1
2. US)t+, - lt+, - Ot+,
3. USE • a (S)b
4. polynomial equations
, d^ _ SO - SE = »
'"J?
" "C 2.22 (H.R)V3
n2Q2p4/3
2.2 A l0/3
1. Q(H) - P(GO)r (EH)S
(A)
(B)
(C)
)* (o)
(E)
(F)
(G)
(H)
'Notations are explained at the end of the paper.
Table 2. Nonlinear formulations of discharges for the
typical seven channel sections of the upper
Kissimmee basin.
Channel
Section
C-32G
C-32B
C-32D
C-32F
C-29
C-37
C-36
Nonlinear Relationship
Q = (US-DS)* (DS)B
A
0.19562817
0.12933563
0.11312801
0.02812316
0.23189354
0.44362025
0.40565648
B
1.37327452
1.31192007
1.28232715
1.14778715
1.53817995
2.25302023
2.17679705
r2
0.99036109
0.99028838
0.98835559
0.98488793
0.99206125
0.99901088
0.99862609
r •= correlation coefficient,
Q = mean discharge,
US = upstream stage,
OS • downstream stage
Table 3. Stage-storage-discharge relationships for the
lower Kissimmee basin.
Channel
Section
C-38A
C-38B
C-38C
C-38D
C-38E
Nonlinear Relationship
US = (DS)fl(logt))B
A
0.93525909
0.80300638
0.72539726
0.72979747
0.84436366
B
0.12357836
0.34915258
0.45337676
0.42254163
0.22342889
r2
0.99999427
0.99997801
0.99993335
0.99995117
0.99995183
r a correlation coefficient,
US c upstream stage,
DS = downstream stage,
Q = mean discharge,
Q > 0
* C-38A = channel section of C-38 between structures S-65 and S-65A
C-38B " " " " " " S-F5A and S-65B
C-3BC = " " " " " " S-65B and S-65C
C-38D = " " " " " " S-65C and S-65D
C-38E » " " " " S-66D and S-65E
Table 4. Stage-storage-discharge relationships for the
lower Kissimme basin.
Channel
Section
C-38A
C-38B
C-38C
C-38D
C-38E
Nonlinear Relationship
DS = (logQ)A(logST)B
A
0.46661167
0.06123664
-0.11387716
-0.32464046
-0.31844141
B
1.29225620
1.59817418
1.70097296
1.79672855
1.68094907
r2
0.9974083
0.99994493
0.99985066
0.99987939
0.99921370
r = correlation coefficient,
DS - downstream stage,
Q = discharge,
ST = storage in acre ft.,
Q > 0
663
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HOW TO MAKE SIMULATIONS MORE EFFECTIVE
George S. Fishman
University of North Carolina
Chapel Hill
Discrete event simulation on a digital computer
has been with us as a tool of analysis for over two
decades. Among the attractions it offers are the
ability to model detail (where analytical methods
fear to tread) and the ability to control variation
(which real world experimentation cannot). The first
of these abilities, modeling detail, seems to have
been oversold, and the second, control of variation,
has been undersold. The presentation concentrates on
these two topics, offering examples and guidance as
to how thoughtful reflection on these two areas, be-
fore simulation modeling and programming begin, can
lead to more effective use of the simulation method.
1. Introduction
In today's presentation my remarks are intended
to put the problems that arise in a simulation on a
digital computer in perspective and to offer direc-
tion in solving some of the statistical ones. Hope-
fully, this perspective and direction will facilitate
our discussion here on just what can be done to
increase user satisfaction with the building blocks
of simulation.
2. Features of the Simulation Method
As a tool for studying complex systems, simula-
tion offers many attractions. These include:
1. compression of time
2. expansion of time
3. model detail
4. selection of outputs
5. control of measurement errors
6. control of variation.
A properly constructed simulation model can
compress time so that several years of system activ-
ity can be simulated in minutes or, in some cases,
seconds. This ability enables one to run through a
variety of operational designs of interest in a frac-
tion of the time required to try each on the real
system.
The ability to expand time also has its bene-
fits. By arranging for statistics of interest to be
produced over small intervals of simulated time, one
can study the detailed structure of system change
that cannot be observed in real time. This figura-
tive time dilation is especially helpful when little
data exist on change in the real system.
Model detail is often cited as the most notable
feature of computer simulation. Although all model-
ing involves some abstraction from reality, the
ostensible reason for using simulation in the minds
of many analysts is that it allows them to model de-
tail that other methods would have to omit in order
to admit a solution. This ability to include detail
has occasionally led to a euphoria about what simula-
tion can do. Unfortunately the dark side of the pic-
ture is seldom mentioned in advance and inevitably a
user who exploits this ability to include detail
learns that all is not well at a later stage in his
use of simulation. Section 3 discusses the subject
of detail with regard to its dark side in depth.
The ability to select output and reports of
varying degrees of detail also contribute to the ap-
peal of simulation. However, it should be remembered
that the computation of output statistics take time.
Therefore, a judicious simulation user devotes prior
thought to what the relative importance of different
outputs is and to the ways in which he can manipulate
a small internal data base to produce many outputs of
interest. For example, in a queueing system the iden-
tity L AW where L denotes mean queue length; A,
the arrival rate; and W, the mean waiting time holds
under fairly general conditions. Therefore, one need
collect data to estimate either L or W since the
other can be obtained by either division or multipli-
cation by the known arrival rate \.
Control of measurement errors offers a great com-
fort to simulation users. Presumably the automatic
fashion in which data are collected in a computer
simulation together with the fact that machine errors
are virtually absent has, until recently, led to
complacency about the possibility of error. With the
advent of the simulation of computer systems in which
the time between events is of the order of micro-
seconds but run lengths are of the order of hours, it
has become clear that the accumulated simulation time
which is generally computed by adding the times be-
tween events is subject to substantial error. Whether
or not this is a serious issue for a simulation
study depends on the nature of interevent times
relative to run length times.
Control of variation is the least appreciated
feature of computer simulation. This may be a result
of the fact that some knowledge of statistics is
necessary to exploit this feature. In particular,
application of this control of variation enables one
to obtain results with a specified accuracy at lower
cost than if one ignored the potential for control.
Section 4 offers a number of examples to illustrate
how easily this exploitation can be made to work.
3. Detail
There exists a general presumption among analysts
that if they were just able to make their models con-
form more closely to the observed behavior, then they
would increase chances of having a successful study.
Simulation, being a descriptive tool, allows one in
theory to make a model as close to resembling reality
figuratively as one likes. However, in order to
close the gap between model and reality, one has to
have a definitive picture of the behavior to be
modeled.
To study detail we use a simulation of a fire sup-
port system as an example. Fire support involves a
host of microphenomena; they include:
A. target acquisition
1. detection
2. identification
3. location
B. target engagement
1. priority rules
2. weapons availability
3. weapons selection rules
C. fire support performance
1. target characteristics
2. weapons characteristics
3. measures of effectiveness.
Each calls for detail which hopefully would arise
from actual battlefield experience. If the knowledge
needed to derive a more adequate representation of
target detection, location and identification exists,
then one has to decide whether its inclusion in the
simulation will improve representational accuracy to
an extent that makes the extra modeling effort worth-
while. However, this improvement can only be mea-
sured after the fact. In particular, inclusion of
known detail in a comprehensive fire support descrip-
tion would have to be preceded by extensive testing of
alternative mathematical and logical representations.
664
-------
To do this one needs data.
Every extension of a simulation's detail intro-
duces new parameters. These require estimation which
relies on data, whether it be sample observations or
expert judgment. Naturally the more detail that is
desired, the more data that are required. This poses
a dilemma for the analyst. While he may be able to
describe a phenomenon conceptually, he may not have
the data needed to fit the parameters of the corres-
ponding mathematical representation. If he does have
the data, he must then face the issue as to how rep-
resentative the parameter estimates are when this
particular micromodel is used in a variety of alter-
native settings. That is, parameter values may be a
function of the setting in which the model is used
and, therefore, an analyst may need several sets of
data to estimate the values that parameters assume in
different settings.
The third dark issue that more detail induces is
increased bookkeeping and computation in a simulation
computer program. More detail implies more events or
state changes per unit time in the model. From a
programming viewpoint this requires additional data
structures and logical structures. This requirement
adds to the cost of putting the program together.
Although it is true that languages such as GPSS and
SIMSCRIPT II make these supplements relatively easy
to introduce representationally, an analyst is still
faced with the problem of fitting his program into
the computer on which he plans to do his work.
If FORTRAN is used for modeling then a serious
additional problem arises. Fire support simulation
involves relatively intricate time sequencing of many
diverse events. Whereas specialized simulation pro-
gramming languages all contain timing routines that
perform this time sequencing automatically, the user
of FORTRAN must build his own timing routine. This
effort alone can be so cost consuming as to defeat
the purpose of using FORTRAN for its computational
efficiency. In particular, FORTRAN lacks a list pro-
cessing capability, a principal feature of all simu-
lation programming languages. For this reason alone
one has to question the flexibility and versatility
of a fire support model programmed in a language
other than a simulation programming language.
The effect of detail on program development rep-
resents only one issue in this area. Detail seriously
affects program execution also. In addition to
creating more data and logical structures, more de-
tail causes more events to occur per unit time in a
simulation. This implies that the list of scheduled
events on which the timing routine relies for direc-
tion is longer. This means that when a new event is
to be scheduled the timing routine takes more CPU
time to find the correct position for the correspond-
ing event notice in the list of schedule of events.
Unfortunately the current state of development of
most simulation languages have contributed to the
seriousness of this problem in practice. In order to
retain a simplicity in list structures and processing
for general simulation, these languages search, add
and delete from these lists using algorithms that in
no way exploit the nature of the event list for par-
ticular problem settings. Moreover, many simulation
users do not recognize that alternative ways exist to
process the list of scheduled events as well as other
lists that materialize during the course of a simula-
tion.
By now, many people recognize that the generality
of simulation programming languages may represent an
impediment to computational efficiency in the fire
support area. This recognition has led to a proposal
there for more tailoring to the needs of this kind of
simulation. This idea deserves encouragement. How-
ever, one hopes the tailoring will not be restrictive
of the resulting simulation programs' use for alter-
native fire support studies. Using a simulation
language to formalize concepts and structures would
help to insure this generality.
Few, if any, tailored simulations have been re-
ported in the literature. What has been reported are
ways to speed up list processing in general. One
suggestion which most experienced simulation users
follow, regardless of the problem, is to create a
single event notice for two diverse events that
always occur simultaneously. Then a subroutine call
within the executable code of one of the events en-
ables the other event to be executed. A second sug-
gestion concerns conditionality. Occasionally one
event occurs only after another type of event has
occurred. However, the second event does not always
occur. In this case an event notice for the neces-
sary event is generated in the simulation and within
the executable code for this event a test is made to
see if execution of the other type of event has to
occur. The effect of these two suggestions is to re-
duce the number of event notices in the list of
scheduled events, thereby reducing the processing
time for this list. Unfortunately the very emphasis
on events in a language such as SIMSCRIPT encourages
a user to overlook the fact that simple suggestions
such as these two can considerably shorten execution
time.
Recently, other suggestions have appeared in the
literature. The papers by Vaucher and Duval [9] and
Wyman [10] in the Communications of the ACM relate
experience with alternative search procedures aimed
at reducing list search time. In GPSS the judicious
user of a user chain to shorten the length of the
current events chain offers dramatic savings, when
properly used
Improved processing of other lists can also induce
efficiencies in large scale simulation. For example,
suppose that available resources in a fire support
simulation are all kept on a single available resource
list. Presumably the type of resource is distin-
guished by a value assigned to its attribute that
designates type. Every time a resource is required,
a search of the resource list occurs. If there are
many available resources of many different types the
search is time consuming. Alternatively, if one ju-
diciously constructs several lists based on type then
the simulation needs only to search the selected
shorter list. The price paid for search efficiency is
the increased number of list structures defined in the
simulation. The exact balance between the cost of
having more lists and the saving in search time de-
pends on the particular system under study.
4. Control of Variation
Although control of variation seldom receives seri-
ous attention in large scale simulation, it is in
this writer's mind one of the most attractive fea-
tures of the simulation method. Control of variation
includes the ability to control the pattern of varia-
tion in the streams of random numbers that serve as
input to an ongoing simulation. Thoughtful use of
this ability enables a user to attain a desired sta-
tistical accuracy with less computer time than ne-
glect of the option would require. This benefit can
accrue when running replications of an experiment in
which all input parameters are the same. It can also
occur when comparing runs of an experiment in which
at least one of the input parameters assumes different
values. An example illustrates the point.
Consider an airline reservation office with m
reservationists. If at least one reservation!'st is
idle when a call occurs the call immediately receives
service. If all reservationists are busy the caller
listens to a 9 second recorded message excusing the
delay. At the end of the message the caller receives
665
-------
service, if a reservationist is available. Otherwise,
he is put into a queue with first-come-first-served
discipline. Intercall times follow an exponential
distribution with mean 1/X. Each caller makes a one-
way reservation with probability 1-p and a round trip
reservation with probability p. Service times for one
way trips are exponential with mean 1/ui. Round trip
service times are Erlang with shape parameter 2 and
mean 2/u. Times are in minutes.
Consider the case in which x = 1, w = 0.5,
m 6, and p = 0.75. Suppose one wishes to estimate
mean waiting time to within +0.025 minutes or, equiya-
lently, +J.5 seconds. Let Y. denote sample mean wait-
ing time on replication i. Let
(1) Y. = k'1 l Y, s2 (Y) (k-1)'1 I (Y, - Yk)2.
k i=1 1 K i=1 1 K
Suppose we adopt the following design for our experi-
ment: Continue to collect independent replications
until [1] , oo
s , (Y) < k(0.025r/tf i
K — K-1
where tk -, is the .975 significance point of the t dis-
tribution with k-1 degrees of freedom. Then if
Y,,...,Y, are normally distributed the probability
that Yk is within +0.025 of the true waiting time is
approximately'1' 0.95. Table 1 shows the results using
independent replications.
This particular simulation was run in SIMSCRIPT
II.5 with intercall times generated on stream 1, ser-
vice times on stream 2 and type of call (one way or
two way) on stream 3. In a simulation of a single
server queueing system Page [7] has shown that revers-
ing the streams of random numbers for interarrival and
service times on a second replication can induce siza-
ble variance reductions. Presumably, low interarrival
times and high service times produce high congestion
on the first«run whereas reversal of streams produces
high interarrival times and low service times and,
therefore, low activity on a second run. Therefore,
average sample output over the two runs should have a
smaller variance than in the case of independent rep-
lications.
Table 2 presents the results of reversing seeds
on streams 1 and 2 on pairs of replications. In order
to allow comparison with Table 1, the experiment here
was designed to have about half as many completions
per run as in Table 1. The results in Table 2 indi-
cate that only 12354 completions were required to
obtain the same statistical accuracy as in Table 1,
which required 25543. In terms of variance one has
(2) S25(X) = 7.55 x 10'4 S25(Z) = 23.34 x 10~4.
Then one way to measure variance reduction is to ex-
amine the simple ratio
(3) [s25(X) + s25(Z)]/4s25(Y) = 2.03
which indicates that seed switching has cut the vari-
ance by about one half.
Other methods of controlling variation are also
available. Let X and Y have means y and y , respec-
tively. Suppose that y is known but y is to be
x y
estimated. One estimate is Y, another is Z=Y+c(X-y )
X
for which var(Z) <_ var(Y) if
(4)
c <_ - 2 cov(X,Y)/var(X)
Consider the airline reservation problem again
and let X denote the sample intercall time, y = 1/x
and c 1. The choice of c is based on the observa-
tion that if X yx is positive the intercall times in
a replication are above average and, therefore, con-
gestion and waiting time are below average.
Table 3 presents the results of using intercall
time as a control variate. The extent of variance is
evident.
When comparing results on experiments with dif-
ferent inputs, variance reduction is again possible.
These range from using common seeds for corresponding
streams to varying the number of observations col-
lected on each run [3]. For example, suppose that one
wants to measure the reduction in mean waiting time
that accrues when the number of reservationists in-
creases from 6 to 7. Moreover, the accuracy required
is d 1/60 minutes or 1 second.
Table 4 shows the results when common seeds are
used for corresponding streams on corresponding runs.
Since - . ~ ,,
(5) s 3(X) 4.4 x 10'4 s 3(Z) 2.10 * 10'4
variance reduction is estimated to be
(6) [s23(X) + s23(Z)]/s23(Y) = 15.5,
impressive by most standards.
In some simulation settings it is not possible
to match seeds or to induce the necessary correlation
between runs to effect a variance reduction. This is
especially true when comparing the results or radi-
cally different experiments. Here one may have to
settle for independent replications, however, variance
reduction can still occur. Consider two experiments
with outputs X and Z and sample sizes per replication
2 2
of n and n . Let var(X) = a /n and var(Z) a /n
under the assumption that one is able to create inde-
pendent observations within each replication[(2, 4].
Let c and c denote the unit costs of collecting and
processing observations in each replication. If one
2 2
wants to achieve a specified variance V= a /n + a /n
XX Z Z
for Y = X - Z on each replication then n and n
should be selected so that
(7)
r = nx/nz =
2 2,2
rl = Vaz
- cx/cz
Using (7) with n + n = n instead of n n/2 leads
X Z X o
to a saving in computing cost of (r, r~) /
(1 + r2)(l + r2,) x 100 percent.
In preliminary runs of the simulation for m 6
-2 2
and 7 we estimated a /a 5.5 and c /c = 0.95 so
X Z X Z
that r = 2.41. Ten replications of each experiment
were run with n 600 and n =250. Upon computation
X Z
of the appropriate terms the estimated saving in com-
puter^ tinie needed to achieve the resulting variance
for Y, = X, - Z, was about one third. From this one
has to deduct the cost of the two preliminary runs;
but that cost was incidental.
The methods of variance reduction discussed here
represent a few among many techniques. All exploit
the structure of the individual problems to a marginal
extent only. However, methods do exist that exploit
the properties of individual problems in such a way
that substantial variance reductions are possible.
These are discussed in [3, Sections 11.2 11.3].
fSee [8] for details.
666
-------
5. References
1. Chow, Y.S. and H. Robbins, "On the Asymptotic
Theory of Fixed Width Sequential Confidence Inter-
vals for the Mean," Ann. Math. Stat.. Vol. 36,
1965, pp. 457-462.
2. Crane, M.A. and D.L. Iglehart, "Simulating Stable
Stochastic Systems I: General Multiserver Queues,"
J. ACM, Vol, 21, No. 1, January 1974, pp. 103-113.
3. Fishman, G.S., Concepts and Methods in Discrete
Event Digital Simulation, Wiley, 1973.
4. Fishman, G.S., "Statistical Analyses of Queueing
Simulations," Man. Sci., Vol. 20, No. 3, November
1973, pp. 363-369.
5. Fishman, G.S., "Achieving Specified Accuracy in
Simulation Output Analysis," Technical Report
No. 74-4, Curriculum in Operations Research and
Systems Analysis, University of North Carolina at
Chapel Hill, 1974.
6. I.B.M., General Purpose Simulation System V User's
Manual, 5734-XS2(OS), 5736-X53(DOS), White Plains,
New York, 1971.
7. Page, E.S., "On Monte Carlo Methods in Congestion
Problems II: Simulation of Queueing Systems,"
Oper. Res.. Vol. 13, No. 2, 1965, pp. 300-305.
8. Starr, N., "The Performance of a Sequential Pro-
cedure for the Fixed width Interval Estimation of
the Mean," Ann. Math. Stat., Vol. 37, 1966,
pp. 36-50.
9. Vaucher, J.G. and P. Duval, "A Comparison of Simu-
lation Event List Algorithms," Comm. ACM, Vol. 18,
No. 4, April 1975, pp. 223-230.
10. Wyman, F.P., "Improved Event-Scanning Mechanisms
for Discrete Event Simulations," Comm. ACM. Vol.18,
No. 6, June 1975, pp. 350-353.
Table 2
Sequential Estimation of Mean Waiting Time
Using Seed Switching
d 0.025 minutes, significance level 0.05
k
1
2
3
4
5
Xk
0.1649
.2240
.2250
.1755
.2618
Zk
.1699
.2338
.1679
.2483
.1373
V
(Xk+Zk)/2
0.1674
.1739
.1965
.2119
.1695
\
0.1674
.1707
.1893
.1874
.1838
SVY)
dS-4)
2.11
2.33
4.22
3.81
kd2/t2k ,
do'4) '
0.08
1.01
2.47
4.06
No. of
Completions
1262 + 1335
1255 + 1113
1165 + 1220
1352 + 1251
1178 + 1223
12354
Table 3
Sequential Estimation of Mean Waiting Time
Using a Control Variate
d = 0.025, significance level = 0.05
k
1
2
3
4
5
6
7
Zk
0.2100
.1648
.1760
.1528
.1624
.2079
.2134
\
0.2100
.1874
.1836
.1759
.1732
.1790
.1839
Sk (Z)
HO'4)
10.22
5.54
6.07
4.91
5.94
6.64
"X-l
do'4)
0.08
1.01
2.47
4.06
5.64
7.31
No. of
Completions
2651
2497
2781
2500
2629
2550
2595
18203
Table 1
Sequential Estimation of Mean Waiting Time
d 0.025 minutes, significance level 0.05
k
1
2
3
4
5
6
7
8
9
0
Yk
0.2243
.1705
.1721
.1619
.1583
.2275
.2222
.1576
.2362
.2138
Yk
0.2243
.1974
.1890
.1822
.1774
.1858
.1910
.1868
.1923
.1944
no-4)
14.47
9.37
8.08
7.20
9.94
10.18
10.12
11.56
10.74
(ip-4)"
0.08
1.01
2.47
4.06
5.67
7.31
8.94
10.58
12.22
No. of
Completions
2651
2497
2781
2500
2629
2550
2595
2422
2440
2478
25543
Table 4
Sequential Estimation of Mean Waiting Time Difference
d = 1/60 minutes, significance level = 0.05
k
1
2
3
Xk
m=6
0.1884
.1575
.1976
Zk
m=7
0.0628
.0411
.0687
Yk
Xk Zk
0.1256
.1164
.1289
Yk
0.1256
.1210
.1236
Sk
io-4
0.42
0.42
kd'/tjl-l
ID'4
0.03
.45
667
-------
THE FACTUAL BACKGROUND OF ECOLOGICAL MODELS:
TAPPING SOME UNUSED RESOURCES
E. C. Pielou
Biology Department, Dalhousie University,
Halifax, Nova Scotia, Canada
Successful ecosystem modeling on a large scale re-
quires knowledge of the relative performance of many
species in response to changes in numerous environmen-
tal variables. Without such knowledge it is impossible
to estimate the relative magnitudes, or even the signs,
of the numerical constants in prediction equations.
Acquiring this knowledge is difficult, expensive, and
time-consuming. If the information now stored in the
ecological literature and data banks can contribute,
it should be used.
Much information exists on biogeographic and eco-
logical zonation patterns, and it constitutes a partic-
ularly rich source for deriving new ecological insights
from old data. This paper describes two new ways of
analyzing such data. One entails determining the
overlap score of a group of species in order to judge
whether the species are competing. The other (incom-
pletely developed) method entails comparing coeffi-
cients of concordance in order to judge the relative
importance of different environmental factors in con-
trolling community composition.
Introduction
Most theoretical ecologists, and hence the applied
ecologists who consult them, are aware of a growing
split in their subject. It has two separate, diverging
areas. One is "mathematical" ecology and the other
"statistical" ecology. However, ecology per se is
still one subject and the unfortunate divergence of its
parts is merely because of the styles of mathematical
argument employed and the kinds of theoreticians who
practice them.
For the most part, theoretical modeling in ecology
has been the work of mathematical, as opposed to sta-
tistical, ecologists. Models of many kinds all have
two indispensable ingredients, or sets of ingredients:
processes and parameters. The processes are the changes
in size and age structure of interacting living popula-
tions, and the accompanying flows of energy and mate-
rials, as modeled by equations. Whether these are sim-
ple linear regression equations or esoteric non-linear
integro-differential equations, they are still "forms"
with (temporarily, at least) no numerical content. The
parameters are the numerical coefficients (or, for
studies of qualitative system stability, the signs of
the coefficients) that must be entered in the process
equations before any concrete predictions can emerge.
Now consider from where the numbers are to come.
There are various possibilities. Educated guesses are
one source, to see how the model (i.e., the process)
will behave in a wide range of conditions.
A second source is experiment. For example, if
processes in such microcosms as Paramecium species in
vials of water or Tribolium species in vials of flour
are to be modeled, the birth and death rates and the
growth and feeding rates of the animals, and the way
these rates vary in response to changing abiotic con-
ditions can, with persistence and patience, be discov-
ered by experiment.
A third source of numerical parameters is observa-
tion of the system to be modeled, itself. This is the
customary procedure when a "statistical model" a
hypothesized statistical distribution - is to be fitted
to an empirical frequency distribution. The data are
first made to yield the desired parameters, with the
familiar loss of degrees of freedom and, of course,
generality.
A fourth source of numbers is the vast accumula-
tion of miscellaneous ecological data, reposing in the
literature and in various data banks, gathered for pur-
poses of every conceivable kind. A body of data gath-
ered for one purpose is available, if it has been suit-
ably stored, for another purpose; not to use hard-won
data in as many ways as possible is wasteful in the
extreme. Admittedly, to expect data collected for one
purpose to yield the precise coefficients required for
an unrelated ecological model to be "run" is probably
to expect too much. However, some kinds of data can
certainly yield useful information. For example, the
data on the zonation patterns of plant and animal spe-
cies, both ''regional" (along short environmental gra-
dients a few kilometers long) and "geographical" (along
long gradients, typically latitudinal gradients, of
perhaps thousands of kilometers) could yield useful in-
formation.
Much published data exist on regional (or ecolog-
ical) and geographical (or biogeographical) zonation.
They obviously tell something about the tolerance
ranges of different species in response to different
abiotic environmental factors, and about the relative
importance of the various factors. They also tell
something about the way species interact, and the ways
'in which their interactions vary from place to place.
Thus, perhaps, one can learn whether groups of related
species do in fact compete, instead of postulating they
compete and inferring a result that is merely con-.
ditional on the correctness of the postulate. It is
obviously worthwhile to devise ways of ransacking exist-
ing data on zonation for useful information that can be
fed into, or at any rate can inspire, models. This
paper describes two rather tentative approaches to the
task.
Competing Species and Overlapping Zones
Everyone knows that related species may occupy
somewhat different zones on an environmental gradient.
The gradient performs a natural sorting experiment (a
laboratory analog is paper chromatography) and each
species comes to occupy its characteristic zone. This
raises the following question: Do related species, for
example, congeneric species, tend to occupy zones whose
amount of overlap is slight because of competitive ex-
clusion, either over the short term, or evolving over
the long term? Or, alternatively, do their zones tend
to coincide because, owing to their common ancestry,
their tolerance ranges for the chief factor and its
associated factors that vary along the gradient are all
fairly similar? To discriminate between these con-
trasted possibilities, one must set up a null hypothesis:
What would be observed if the spatial extents and ar-
rangements of a set of zones were mutually independent?
Consider two species, A and B,of sessile organisms
living on a gradient. Suppose their zones are discern-
ible. Label the species' upgradient boundaries Al and
Bl and their downgradient boundaries A2 and B2. Assume
that (in the diagram below) the gradient descends from
left to right. Then we must have Al to the left of A2
and Bl to the left of B2 but, under the null hypothesis
of zone independence, all permutations of Al, A2, Bl, and B2
668
-------
consistent with these constraints are equiprobable.
There are only three such permutations, namely:
In symbols
Al A2 Bl B2
Al Bl A2 B2
Al Bl B2 A2
Graphically -
Overlap score
0
In the graphic representation the zones are ass-
umed to stretch up and down the page and the lines
(solid for A, broken for B) show the widths of the
zones. Scores to be assigned for the three degrees
of overlap are shown on the right.
Now suppose there are several, say k, species.
We shall assign to their zone pattern a total overlap
score, L , which is the sum of the k(k-l)/2 pair-
wise scores reached by taking the species two at a
time. For example, for the pattern below in which
k = 4, the total score is easily found to be L = 7.
Hence it will be found that
f3(L) 1 for L = 0 and 6 ;
f (L) 2 for L = 1 and 5 ;
f3(L) =3 for L = 2, 3 and 4 ;
and £f3(L) = 15 .
Similar arguments lead straightforwardly to the
following recurrence relation for ^v^) •
L
fk(D =
fk-l(j) f°r L 0.!»••-.k(k-D
j=L-2k+2
with fk_1(J) = 0 for j < 0 and j > (k-1)(k-2).
The maximum value of L, which is k(k-l), occurs
when all (k-1)1/2 scores of the zones taken in pairs
are equal to 2. From symmetry, it is seen that the
mean of L must fall halfway between its extremes.
Therefore E(LJk) = k(k-l)/2 .
kfk-1)
xxxxxxxx
Also put
2" k:
Observe that the lengths of the lines (representing
the widths of the species' zones) are immaterial; it
is only the relative arrangement of their boundaries
that concerns us.
Now derive the probability distribution, and
the mean and variance, of L given the null hypothe-
sis.
Let rk(L) be the number of ways in which k
zones can give a score of L. As shown above, when
k 2, fk(L) = 1 for L = 0,1,2. Now suppose that
to A and B a third species, C, is added. Its upper
boundary, Cl, is assumed to be to the left of Al and
Bl; this assumption does not reduce the number of pos-
sible zone arrangements since the species can always
be labeled so that their upgradient boundaries are in
the order Cl, Al, Bl. Then, whatever the pattern
(and hence the score) of the pair of zones A + B, there
are five possible positions for C2 relative to the four
existing boundaries Al, A2, Bl and B2. Thus, if the
pair A + B has the pattern shown by the solid and
broken lines in the diagram below, addition of species
C, whose possible zones are the dotted lines, can lead
to five distinguishably different patterns labeled
Zl,..., Z5. Then, depending on the position of C2
relative to Al, A2, Bl and B2, the total score for all
three species together is the sum of the score L 1
that pertains to the A + B pair already, and the
"added score" (from C + A and C + B) shown on the
right. Moreover, these five equiprobable values for
the added score are the same regardless of the score
already possessed by the A + B pair.
Cl
Al
Bl
A2
B2
zi
Z2
Z3
Z4
Z5
Added score
Then the probability of obtaining a specified score,
L, for given k, is
Pk(L) - fk(L)/Tk .
The variance of L for given k, namely Var(LJk) is
found as follows.
First, put V (LJk)
Pk(D .
That is, V (L|k) is the second moment of L about
an arbitrary constant x given that the number of
species is k. Then, since
£)LPk(L) = E(L|k) = k(k-l)/2 ,
V (LJk) = V (L|k) - xk(k-l) + x2
Now, from the way in which
is seen that
V (L|k+l) = ^ j* x
k+1 x=-2k
is constructed, it
V (L|k)
(2k+l)V0(L|k) k(k-l)
,x +
= V (L|k) + k (k-1) + k(4k+l)/3
Therefore Var(L|k+l) = Var(LJk) + k(k+l)/3 .
Repeated use of this recurrence relation now shows
that Var(L|k) Var(L|k-l) + (k-l)k/3
Var(L|k-2) + (k-2) (k-1)/3 + (k-l)k/3
then Var(L|k) k(k-l)(k+1)/9 .
669
-------
The distribution tends to normality with increas-
ing k and for k > 20 the discrepancy between the
true cumulative distribution of L and that of a nor-
mal distribution with the same mean and variance no-
where exceeds 17.. For low values of k, the distrib-
ution of L is platykurtic. To test the null hypo-
thesis (that the boundaries of the zones of k spec-
ies occurring on a gradient are independent of one
another) when k < 20, the critical values C, tab-
ulated below may be used. These values are for a 5%
two-tailed test. That is, if Ck < L < k(k-l)-C,
the null hypothesis should be accepted; (note that C,
itself, and k(k-l)-C, , are included in the accept-
ance region).
Table 1. Critical Values of L for k
19
k
2
. 3
4
5
6
7
Ck
0
0
2
4
7
11
k
8
9
10
11
12
13
Ck
16
21
28
35
43
52
k
14
15
16
17
18
19
Ck
62
73
85
98
111
126
impracticable. In particular, measurements of species
quantities seldom inspire confidence, and tests using
ranks are therefore often more appropriate than those
depending on absolute measurements. A "natural" way
to perform the comparison described above (natural in
that it would occur to anyone with a taste for non-
parametric statistics) would therefore be to use as
data the ranks of the species in each of the samples.
Suppose a total of nd regularly arrayed stations
have been sampled, at n latitudes and d depths,
and the quantities of the same k species are ranked
for each sample. Then the data can be displayed as
an n*d table in which each cell contains a list of
the ranks of the k species. For instance, if k=3,
the table would appear thus:
Depth
1
Latitude
1 2 3
3 2
3 2
2 1
3l W
I n-
An example of the use of the test is given in the
section, Examples.
Concordances Among Different Groups of Samples
In this section, an entirely different way is
described of extracting, from data on species zona-
tion, information that may be useful to ecosystem
modelers. The method is "work in progress" which
means work incomplete; a lot remains to be done both
to the theory and the practice.
Every species of organism has tolerance limits
with respect to numerous environmental factors. For
the sake of concreteness, think of several related
species of the marine benthos. Each species has its
own specific tolerance limits for temperature and
light intensity, to name only two of the (presumably)
many environmental factors that control its survival.
Considering the effect of a gradient of one of these
factors on a mixed community of these species, the
relative proportions of the species in a sample would
be expected to depend on the level of the gradient at
which the sample was taken. And if a batch of samples
were taken from various levels, the within-level vari-
ation in species composition would be less than the
between-level variation.
Next suppose that we wish to compare the relative
importance of two environmental factors. As before,
let these factors be temperature and light intensity,
and imagine an idealized north-south coastline where
the following conditions obtain: there is a strong
latitudinal gradient in temperature and, at right ,
angles to it, a steep east-west depth gradient and,
hence, a strong gradient in light intensity at the
bottom. We can now ask which of the two factors,
temperature or light intensity, dominates in control-
ling community composition (this is a conceptual ex-
periment and we choose to disregard all the other vary-
ing factors). By sampling at an array of sampling
stations so that we have samples from a sequence of
depths in each latitude and from a sequence of lati-
tudes at each depth, the necessary data for a straight-
forward multivariate analysis of variance could (in
theory) be obtained.
However, ecological sampling rarely is straight-
forward, and ambitious plans often turn out to be
The coefficients of concordance of the rankings
within each of the rows, say W1. ,..., W , are now
computed; likewise, the concordances of the rankings in
, W ,. (For computa-
each of the columns, W
tional details see, for example, References 1 and 5).
We do not enquire whether any of these concordances
differ significantly from zero. Almost certainly all
of them will. But we do enquire whether the within-
latitude concordances tend to differ from the within-
depth concordances. If, for example, the within-depth
concordances tended to be the greater, we should infer
that light intensity influenced community composition
(and hence the success of the component species) more
strongly than temperature.
The test one is tempted to use to compare the two
sets of concordances is the Mann-Whitney test. But,
strictly, it is a test for two independent samples and
obviously the values of W.
(i = 1,..., n) and W.
(j - 1,..., d) are not independent since each set is
based on all nd rankings in the table. I do not
know whether the Mann-Whiney test is robust enough for
this not to matter. The desired comparison is, in-
deed, difficult to make. It is difficult enough to
compare two coefficients of concordance, that is, two
individual values of W, let alone two interdependent
sets of W's. Li and Schucany2 (and see Schucany and
Frawley, ) described a test to compare two independent
values of W, Their test statistic, W , takes values
in the range [-1, +1]. If concordance is perfect
within each set and also the two sets concord exactly
with each other, then W = +1; if concordance^is per-
fect within each set and the two sets discord totally
with each other (so that the ranking in one set of
lists is the exact opposite of the ranking in the
other) then W = -1. However, values of W close to
zero are ambiguous; they imply either that one (or
both) of the sets has poor internal concordance; or
else that, though concordance is good within each set,
the two sets are somewhat (not totally) discordant.
This latter state of affairs is the one most likely to
crop up in the ecological context we are considering.
And, as the foregoing discussion suggests, it may
prove difficult to diagnose.
Another, and perhaps more important, difficulty
that arises is that when a community occupying a
670
-------
gradient is examined it is usually found that as one
goes down the gradient, "upslope" species successively
disappear and at the same time a succession of "down-
slope" species are encountered for the first time. If
the abundance of the same k species have to be ranked
at each station to enable a test to be done, then only
a short segment of the gradient can be studied. The
same set of k species will not be found in distant
samples.
This raises in acute form a conundrum often faced
by ecologists concerned with presences and absences of
species. Present species can be ranked but not absent
ones, though one is often justified in feeling that
some are more absent than others. At any point on a
gradient a species whose zone starts nearby is "less
absent" than one whose zone starts farther away. And
besides having magnitude, an absent species' degree of
absence from a point should have a sign that depends
on whether its presence (its zone) is upslope or down-
slope from the point.
At this stage, speculation must (temporarily) stop.
The analysis of ecological data from environmental
gradients obviously has much to offer, both to statis-
ticians devising methods and to ecological modelers
searching for information on how species in nature do,
in fact, react to environmental factors and to one
another.
Examples
To exemplify the methods described in the two pre-
vious sections, data from Phleger are used. He gives
lists of the percentages of different foraminifera
species (living and dead) in bottom samples collected
at stations at different depths along 12 traverses
across the continental shelf in the Gulf of Mexico.
The number of stations per traverse ranged from 25 to
55.
Overlap Scores Within Genera
For benthic organisms, zones are not visible, of
course. Therefore the zone of any one species was es-
timated to begin at the shallowest station where it was
found and end at the deepest station. It was hoped
that because of the large number of traverses errors of
estimation in individual traverses would have negligi-
ble effect. Small overlaps might chance to go unde-
tected but such errors would tend to be offset by "ac-
cidental" specimens occurring outside their zones. Since
observations were necessarily discrete, "ties" were
possible and were scored thus:
Score 0.5
Score 1.5
Score 1.5
(The method of portrayal corresponds with that in the
section, Competing Species and Overlapping Zones.)
All genera with three or more species in at least
ten of the traverses were tested to ascertain whether
there was any reason to reject the null hypothesis that
their zone boundaries were randomly and independently
located. The two alternatives were that the zones
might show excessively low, or excessively high, over-
lap. Results for three genera are tabulated below.
The two columns for each genus show k, the number of
species of the genus in the traverse named (by a Roman
numeral) on the left, and the standardized overlap
score L* (L-E(L|k)}//Var(L|k). With data from 12
traverses available, values of L need not be tested
individually. It is clear that the species in the
genera Cassidulina and Elphidium show too much over-
lap for the null hypothesis to be acceptable, whereas
for Cibicides it is acceptable. It should be noticed
that (disregarding type II errors) the null hypothesis
may be found acceptable either because departures
from it are insignificant, or because they are inde-
terminate. The latter will happen if the traverses
are too short to go beyond the shallowest and deepest
zone boundaries of many of the species; their apparent
boundaries will then be randomly ordered.
Table 2.
Values of k and L* for Three Genera
in Twelve Traverses
Traverse
I
II
III
IV
V
VI
VII
VIII
IX
X
XI
XII
Cassidulina
k
4
5
5
5
5
2
5
5
5
5
5
4
L*
0.61
1.92
1.92
2.05
1.64
1.23
2.33
1.92
2.60
1.23
0.68
-0.41
Elphidium
k L*
3
3
3
4
4
4
4
4
4
4
2
2
0.92
0.92
0.61
1.74
1.36
1.55
1.36
0.97
1.16
1.36
0.61
0.61
Cibicides
k
6
5
8
8
9
6
9
8
8
8
8
6
L*
0
0.41
0.53
-0.47
-0.06
-0.21
-0.78
0
-0.73
0.07
-0.60
-1.04
Concordances of Ranked Species Abundance Lists
The relative abundances of eight common speciest
(chosen to serve as "community indicators") in samples
from three traverses at four depths were listed. The
table below shows the traverse numbers (roman) as row
labels, the depth ranges as column labels, and values
of W. and W . to the right of and below the re-
levant rows and columns. The three entries in each
cell of the table are, from top to bottom, the station
number where the sample was collected, the depth at
that station in meters, and the number of foram tests
in the sample. As may be seen from the values of W.
and W ., there is no reason to suppose that community
composition varied more with depth than with the hori-
zontal distance between traverses. The traverses did
not sample different latitudes; they extended roughly
southwards from the Gulf coast of Louisiana and Texas.
Even so, the concordances among species rankings from
the same depth did not, so far as this small sample
shows, tend to exceed the concordances among rankings
from different depths on one traverse. With only four
traverses and three depths (and these covering only a
small depth range) a significant difference would be
unlikely to appear in any case; the example is given
here merely for illustration. Consideration of only a
small range of depths was necessary to ensure that
never fewer than six of the eight species chosen as
"community indicators" were present in a sample. For
the method to be applied over a larger range of depths,
a means of scoring absent species objectively must be
devised. This is the direction that the work will take
next.
tThe species: Bolivina lowmani, B.simplex, Cibicides
concentricus, Elphidium discoidale, E.gunteri var gal-
vestonense, Proteonina comprima, P.difflugiformis,
Rotalia beccarii var parkinsoniana, Virgulina pontoni.
The names given here are those in Phleger's^ memoir.
Name changes resulting from taxonomic revisions have
been ignored to facilitate consultation of the original
data.
671
-------
Table 3. Concordances of Species' Ranks Among Samples
Grouped by Depths and by Traverses
Depths
22-27m
28-32m
33-37m
38-42m
VI
VIII
X
#97
22m
350
#380
27m
2000
#411
26m
1300
W , =
•1
0.887
#101
29m
300
#378
31m
400
#418
29m
3200
W -
•2
0.425
#105
33m
4300
#375
35m
2300
#420
35m
5400
W - =
•3
0.860
#111
38m
1550
#373
40m
4800
#424
42m
250
W , =
.4
0.590
Wl
0.
2
0.
0.
0.665
Acknowledgements
I thank Eric Robinson, University of Sydney,
Australia, for help with computer programming, and
Anita Williams, Halifax, for help with data collation.
The work was funded by a grant from the National
Research Council of Canada.
Added Note: Dr. F. B. Phleger of the Scripps Institu-
tion of Oceanography revised names of the foram spe-
cies listed in the footnote in the last section. A
complete list of names is, in the same order as in the
footnote: Bolivina lowmani, B_. ordinaria, Hanzawaia
strattani, Cellanthus discoidale, Elphidium gunteri,
Nouria polymorphinoides. Reophax difflugiformis,
Ammonia beccarii var parkinsoniana, Fursenkoina
pontoni.
References
1. Conover, W. J., Practical Nonparametric Statistics,
Wiley, New York, 1971.
2. Li, L. and W. R. Schucany, "Some Properties of a
Test for Concordance of Two Groups of Rankings,"
Biometrika 62:417-423, 1975.
3. Phleger, F. B., "Ecology of Foraminifera, North-
west Gulf of Mexico. I Foraminifera Distribution,"
Geol. Soc. Amer. Mem. 46, 1951.
4. Schucany, W. R. and W. H. Frawley, "A Rank Test for
Two Group Concordance," Psychometrika 38:249-258,
1973.
5. Siegel, S., Nonparametric Statistics for the
Behavioral Sciences, McGraw Hill, New York, 1956.
672
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TIME SERIES ANALYSIS AND FORECASTING FOR AIR POLLUTION
CONCENTRATIONS WITH SEASONAL VARIATIONS
Der-Ann Hsu and J. Stuart Hunter
Department of Civil Engineering
School of Engineering and Applied Science
Princeton University
Princeton, New Jersey
ABSTRACT
Annual time series records of daily averages of hourly
sulfur dioxide concentrations recorded over several
major cities exhibit strong seasonal patterns in both
level and variation. To construct models useful for
prediction and analysis, a Box-Cox transformation is
first employed to stabilize the data variability. The
transformed data provides a dramatic improvement in the
data plots. Further, the transformed data are readily
modeled using simple seasonal plus stochastic com-
ponents following Box-Jenkins time series methods. The
fitted models, forecasts and confidence limits are then
constructed.
New statistical comparison techniques to compare the
stochastic structure of the time series in periods be-
fore and after changes in pollution regulations are
briefly discussed. These procedures should prove use-
ful in the evaluation of environmental policies.
INTRODUCTION
In this paper, as an illustration of some useful
statistical techniques, we analyze twelve annual
series of air pollution SO. concentrations, collected
over four cities: Chicago, Philadelphia, St. Louis and
Washington, D.C. All of the series exhibit strong
seasonal patterns in both the level and variance. A
Box-Cox transformation [1] is first used to stabilize
the variances. The transformed data are then fitted
by a cosine curve to model the seasonal influences and,
following the techniques suggested by Box and Jenkins
[2], a stochastic model fitted to account for the day
to day time dependent character of the data. Parameter
estimates for each of the twelve annual series are
provided.
An illustration of forecasting for Chicago S02 con-
centrations using the fitted model is further demon-
strated.
In the later part of this paper some techniques useful
for comparison of time series are briefly sketched.
Potential applications of these methods in the eval-
uation of environment policies are suggested, and
further references furnished.
THE DATA AND THEIR SEASONAL STRUCTURE
Data on SO- concentrations were collected from four
major cities in the U.S. during the three year period
1969-71. The data consist of hourly readings of the
SO. concentration for each of the twenty-four hours of
a day, measured in units of 0.01 ppm. Although instru-
ment breakdowns, failures of the measuring process, and
the negligible levels of concentration during the
summer months caused approximately 15% of the readings
to be missing, daily averages were computed based upon
the available readings within days. A time series plot
of the daily averages of SO- concentrations in Chicago
during 1969, typical of all the series obtained, is
displayed in Figure 1.
As can be seen from Figure 1, both the level and the
variation are large during the winter and small during
the summer. Reasons for these changes are the vast
amounts of SO released from household heating
systems in the winter, and the different diffusion
characteristics due to seasonal temperatures. Over
short periods of time, the data also demonstrate
skewness towards high SO values.
The failure of the observations to possess a Normal
distribution, and/or a homogeneous variance,
seriously impedes the ability of the engineer and
statistician to postulate models, and to estimate the
parameters In these models. For this reason, the Box-
Cox transformation[l] was applied to the S0_ data to
enhance Normality, to stabilize the variance, and thus
improve the modelling and estimation procedures.
For a variable y,
z where
the transformation is expressed as
(X)
(y+x2)
- i
X1[gm(y+X2)]
gm(y+X9) log (y+X9)
0)
o)
(1)
and
gm(y+X2)
rn
11
L±-l
(yi+x2)
l/n
where n is the number of observations of the vari-
able y and gm is the geometric mean. It has been
shown by Box and Cox that the estimates of X and X-,
the parameters required in the transformation, can be
obtained by minimizing the sum of squares of the
residuals after fitting a model. In the present case,
the model is a cosine curve, illustrative of seasonal
changes in the response level and given by
c = 8 + 8, cos(2irt/365+a), t=l,2,... ,365, (2)
where t is the ordinal number of the days within the
year and a is the phase angle indicating the starting
location of the cosine curve. The model can thus be
expressed as
(X)
(X)
(3)
where z ^" , is the Normal variance-stabilized series
of the observed SO concentrations. The series of
residuals ^etK maY De serially correlated, as dis-
cussed in a later section.
The estimation of the various parameters in Equations
(1) and (2), i.e. Xj, X2, a, 8 , 81, requires a set of
365 2
values which minimize £ e . Many published
t=l
computer programs are useful for determining this
minimum point (e.g. the subroutine ZXPOWL in the
673
-------
E
PL
PL
iH
O
C
C
O
O
It)
>
Y*
• •
..*
*• V
0 50 100 150 200 250 300 350 400
Time (in days)
FIGURE I. OBSERVED DAILY SO CONCENTRATIONS IN CHICAGO FOR THE YEAR 1969.
• : Transformed observed data
- : Fitted cosine curve
50 100 150 200 250 300
Time (in days)
350
400
FIGURE 2. THE TRANSFORMED DAILY S02 CONCENTRATIONS IN CHICAGO FOR
THE YEAR 1969 AND A FITTED COSINE CURVE.
IBM's IMSL package). Again, as an illustration, the
estimated parameters for the 1969 Chicago data are as
follows:
= 0.29, \ = 0.00, a = -.29,
= 4.43, B ,=5.63.
Using this set of estimates, the transformed observed
data and fitted cosine curve are displayed in Figure 2.
The remarkable performance of the transformation in
both stabilizing the variance and in elucidating the
model is readily seen from the plot.
Similar parameter estimates were obtained for the re-
maining annual series for the other cities and years.
The results are reported in Table 1. Some features of
the results are worth commentary. First, all but one
estimate of a (the phase angle) falls within the range
-.64 to .33 indicating the association between the
winter and the high level of SO concentration. Second,
all but one of the estimates of the transformation
parameter \^ are negligible, revealing that a trans-
formation with A = 0 is adequate in general. Third,
the estimates of X fall between 0.00, (the logarithm
transform) and 0.33, (a cube root transform).
THE MODEL FOR THE RESIDUALS
No modelling is complete without an investigation of
the residuals. As part of this investigation the
sample lagged autocorrelation coefficients, r, for each
of the twelve series were computed using the residuals
from the fitted model, where
365
(e -e) (e -e) /m
-
t=k+l
365
/ n
and where m and n are the number o_f available residuals
involved in the calculations, and e is the average of
the series {e }. Here e equals zero. The first ten
values of r^, i.e. r ,..., r1Q for the 1969 Chicago
data are: (.26, -.03, -.02, .08, .07, .04, .11, .10,
674
-------
TABLE 1. ESTIMATES OF THE PARAMETERS IN THE MODEL FOR DAILY SO CONCENTRATIONS
City Year f Obe. a \i X2 6 BI gm(y+X2) SSR Pi 8 "£
Chicago 1969 272 -0.2911 0.2857 0.0000 4.4295 5.6257 3.883 2304.4158 0.2605 -0.2811 7.8518
1970 273 -0.5791 0.0882 0.0000 1.6039 3.8816 2.263 815.7686 0.2641 -0.2856 2.7627
1971 196 -0.5703 0.1952 0.0000 1.3642 3.9261 2.783 1000.3269 0.4626 -0.6707 3.5202
Phila- 1969 226 0.1902 0.0208 0.0000 2.4258 1.0056 2.627 865.5786 0.1651 -0.1699 3.7226
delphia
1970 313 -0.6367 0.1928 0.0021 3.8179 1.4788 3.340 1998.3765 0.3030 -0.3375 5.7317
1971 284 -0.1887 0.2587 0.0000 1.9199 0.1773 2.303 869.4617 0.3749 -0.4512 2.5436
St.Louis 1969 289 -0.3646 0.3168 0.0000 2.8203 0.2137 2.822 1521.6904 0.4375 -0.5896 3.9072
1970 236 0.3229 0.2571 0.0000 1.7968 0.2833 2.281 779.0459 0.2797 -0.3059 3.0186
1971 314 -2.0339 0.0563 0.0000 0.7458 0.4240 1.616 477.5051 0.3528 -0.4130 1.2992
Washington
D.C. 1969
1970
1971
283 -0.3215 0.2764 0.0000 1.0519 1.6009 1.609 183.3711 0.3038 -0.3386 0.5813
270 -0.3170 0.2597 0.0000 0.4850 1.0057 1.320 232.9175 0.3790 -0.4588 0.7127
326 -0.3914 0.1106 0.7438 3.2043 1.5680 3.019 255.6146 0.2721 -0.2959 0.7210
The number of observations used in estimation.
**The sum of squares of residuals £
-------
transformations were applied to each series.
FORECASTING OF THE CONCENTRATIONS
Forecasting is important in all time series modeling,
both as a check on the adequacy of the model as a
description of a system, and for the purpose of control
of the system. From the models fitted in previous
sections, forecasts of the S02 concentrations for a
moderate length of time ahead can be obtained. The
first stage of determining forecasts is to predict the
values of e at time T+l, T+2, ..., assuming that we
stand at time T, the time origin of prediction. Again,
as suggested by Box and Jenkins, the best forecasts of
ST+k' k=1'2'"' are
and
T+l
T+k
- 6
for k > 2
(7)
where a can be obtained by fitting the model ex-
pressed by Equation (4) to the observed series of e .
The value of e in this case is equal to zero. The
upper and lower bounds, at the .95 confidence level,
of the forecasts can be computed following the
equations displayed below:
o
p
B
HI
O
e
o
CJ
» : Observed concentrations
— : Forecasts
— : 95% confidence limits
of forecasts
0
20
40
60
80
100
Time (in days)
FIGURE 3.
CHICAGO FOR THE FIRST HUNDRED DAYS OF 1970.
FORECASTING SO CONCENTRATIONS IN
COMPARISON OF TIME SERIES
± 1-96
T+k
T+k
for k
where e's indicate half the length of the confidence
intervals.
To express the forecasts in the original form and
scale, a seasonalization and reverse variance-
stabilizing transformation is made where
Besides forecasting, the comparison of time series is
an important problem in applied statistics.
(8) Situations which require comparison of time series may
} arise when the effects of, say, changes of pollution
regulations are to be assessed. The time series of
pollution concentrations before and after the regu-
lation changes, for instance, may be investigated and
compared with respect to such essential features as
their overall level, autocorrelation structure,
variation and the probability of exceeding some regula-
tory standard (or the frequency of occurrence and
duration of excedences of a regulatory standard).
T+k
T+k
a]
+1} +
(9)
(10)
The confidence limits of yT+, are secured by adding or
subtracting from Equation (9) an ET+, already defined
and then going through the procedure expressed in
Equation (10). Using the Chicago example the daily
averages of SO- concentrations for the first hundred
days of 1970 are displayed in Figure 3. The forecast
which is the expected median of future realizations of
SO^ concentration at time T+k and its associated upper
and lower 2.5% probability limits are also displayed in
Figure 3. The observed concentrations fall within the
forecast confidence band in a fashion very consistent
with theoretical expectation.
In viewing Figure 3, it is important to remember that
the probability density in the original metric of the
observations appears skewed to the upper side and
further, that the variance is not independent of level.
In addition, it is interesting to note the tendency of
the observations to gradually drift below the forecast
line near the end of the 100 day series. We have here
an indication of the possible inadequacy of the fore-
cast function and are led naturally to the question
of comparing the 1969 and 1970 models.
Comparison through the use of forecasts. A simple
method to test whether two time series have identical
structure is to perform forecasting for one series
(series B), using the model constructed from the other
(series A). The differences between the forecasted and
observed values for series B can be tested for
potential model discrepancy. Tiao, Box and Hamming[5]
proposed that the errors of one-step-ahead-forecasts,
i.e. a , k=l,2,3,..., be squared and summed and then
checked against the significance point of a x distri-
bution, given that Normality may be assumed for the
errors.
SO- concentrations, the fitted model
In the case of
L
including the estimates of \-\ , Xj, a, B Si and 0, for
o
the A series can be used to obtain forecasts for B
series. If the parameters are different between the
two series the corresponding forecast errors will ex-
hibit a systematic bias, or a structured stochastic
pattern. An illustration of this comparison technique
is not shown in this paper, but is under current study.
Comparison using a test statistic for Normal stationary
models. A test statistic for comparing two autore-
gressive time series has been developed by Hsu[3] and
illustrated in a practical example by Hsu and Hunter[4].
This technique is useful for comparing two series of
residuals with respect to parameters 6 and a .
Comparison using a complete test. Ideally, a test
676
-------
statistic or scheme can be developed to examine all the
parameters of two series. Such a test, which promises
to be complicated and to require much computation is
left for future research.
CONCLUDING REMARKS
Series of daily averages of S02 concentrations have
been analyzed to demonstrate a profitable use of some
statistical techniques. Data which originally appeared
to be lacking a simple structure were variance-stabil-
ized, deseasonalized and fitted by a simple stochastic
model. Forecasts of future levels of pollution con-
centrations were easily obtained using the fitted
model. Further, series observed from different
locales could be compared based on the information
gathered from their analyses and models. Activities
such as evaluation of environmental policies,
selection of alternative regulations, etc., may thus
benefit from such studies. Further, analyses of
hourly data within a day are also possible and may be
expected to provide valuable information. Geographi-
cal comparison, combinations of statistical and
physical models, schemes adaptive to pollution control,
etc., are all subjects for further investigation. The
authors hope the statistical techniques described here
may prove useful in these future research activities.
REFERENCES
[1] Box, G.E.P., and Cox, D.R. (1964), "An Analysis
of Transformations," Journal of the Royal
Statistical Society, Series B26, 211-252.
[2] Box, G.E.P., and Jenkins, G.M. (1970), "Time
Series Analysis, Forecasting and Control, Holden-
Day, San Francisco.
[3] Hsu, D.-A. (1973), Stochastic Instability and the
Behavior of Stock Prices. Ph.D. Dissertation,
Dept. of Statistics, University of Wisconsin-
Madison.
[4] Hsu, D.-A. and Hunter, J.S. (1975), "Analysis of
Simulation-Generated Dynamic Responses," Civil
Engineering Research Report #75-TR-2, Civil
Engineering Department, Princeton University,
March 1975.
[5] Tiao, O.C., Box, G.E.P. and Hamming, W.J. (1975),
"Analysis of Los Angeles Photochemical Smog Data:
A Statistical Overview," Journal of Air Pollution
Control Association, 25 . March 1975.
677
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METEOROLOGICAL ADJUSTMENT OF YEARLY MEAN VALUES FOR
Am POLLUTANT CONCENTRATION COMPARISONS
Steven M. Sidik
NASA-Lewis Research Center
Cleveland, Ohio
Harold E. Neustadter
NASA-Lewis Research Center
Cleveland, Ohio
Summary
The results of some linear regression analyses relating
pollutant concentrations to certain specified meteorologic
and economic variables are presented. The resulting models
provide about a 20 percent improvement in predicting con-
centrations. An outline of the use of the predictive equations
in adjusting for meteorological effects is then presented.
Introduction
This paper presents an approach to interpretation of 24-
hour averaged air pollutant measurements taken in compli-
ance with U. S. Environmental Protection Agency guidelines
when analyzed in conjunction with such meteorological data
as may be readily obtained from the National Weather Ser-
vice. The specific example considered is Total Suspended
Particulates in Cleveland, Ohio, for which some monitoring
has been performed by the municipality since 1967; initially
every 6th day and currently every 3rd day. The meteoro-
logical data are also for the same 24-hour periods and was
obtained from National Oceanic and Atmospheric Agency as
decks of punched cards. The information is ground level in-
formation and devoid of such things as inversion heights.
We fit linear regression models to pollutant concentra-
tions using the following combinations of meteorologic vari-
ables as predictors: daily delta temperature (defined as the
maximum temperature minus the minimum) and its first dif-
ference; daily minimum temperature and its first and second
differences; daily average barometric pressure; daily total
precipitation (water equivalent in inches); and daily resultant
wind velocity. We included two rough indicators of economic
activity and allowed for the existence of both a linear '' drift''
in time and a seasonal component with a period of 1 year.
The overall results are that the mean TSP concentration
(1) increases as delta temperature increases and as its first
difference decreases; (2) increases as mini mum tempera-
ture increases and as the first and second differences in-
crease; (3) increases as pressure increases; (4) generally
decreases initially with increasing wind velocity except when
there is a source upwind; and (5) signifjp.ant.1y decreased
over the period of the study with a clear indication of sea-
sonal fluctuation.
The goodness of fit of the estimated models to the data
is partially reflected by the squared coefficient of multiple
correlation, indicating that at the various sampling stations
the models accounted for about 23 to 47 percent of the total
variance of observed TSP concentrations. However, there
is still a large variability unaccounted for so that predic-
tions of individual values are not very helpful.
About a 20 percent improvement when using these equa-
tions in place of simple mean observed values is obtained
when (1) predicting mean concentrations for specified meteo-
rological conditions or (2) comparing yearly averages after
being adjusted so as to remove meteorological effects.
Pollutant Concentration Data
The Cleveland Division of Air Pollution Control has
taken 24-hour averaged air quality samplings of TSP since
January 1967. There are currently 21 sampling stations
around the city which sample TSP. A more complete analy-
sis of all these stations (including analysis of SO2 and NO2
data) is presented elsewhere. Only a summary of the re-
sults for TSP is included herein and illustrated by the re-
sults from a typical station.
Summaries of the air pollution data used for this study,
including tabulations of means, standard deviations and
goodness of fit to lognormality on an annual basis have been
o
reported earlier.
The sampling method for TSP is high volume air sam-
pling using Glass fiber filters. A previously published study
showed that, for such HiVol air sampling of TSP in Cleve-
land, approximate 95 percent confidence limits on the errors
introduced by filters and samplers were about 12 percent
o
high to 11 percent low.
Regression Analysis
Models and Method
The method chosen for data analysis was multiple linear
regression analysis which is explained in such texts as
Searle, Draper and Smith, and Daniel and Wood.
We assume models of the general form
(1)
where
vi
the i observed pollutant concentration, or some
transformed value of that concentration. In this
paper we use y = log(TSP)
the observed value of the j predictor variable (i. e.,
meteorologic economic) for the i observation.
The particular predictor variables (such as baro-
metric pressure) used are presented in Table 1
the unknown intercept values
678
-------
0. unknown coefficients (slopes) which are to be estimated.
Multiple linear regression as used here estimates
these unknown coefficients by the method of least
squares. (Estimated values are denoted by J3.)
ej an unobserved random error component. This random
error is assumed to follow a normal distribution with
mean of zero and a standard deviation of a which is
unknown. We further assume that the e- are uncor-
related with each other
The random error ^ will include, among other things,
errors of measurement of the concentrations, inherent vari-
ability of concentration because of varying emission rates
and/or atmospheric instability, inadequacies in the model,
and to some extent the errors of measurement of the predic-
tor variables. Our data base consists primarily of 24-hour
averaged concentrations at 3 day intervals. A previous
study found that concentrations observed every 3 days have
a very low correlation. Thus the assumption that the ej
are uncorrelated is reasonable.
Derived Variables and Estimated Coefficients
Pollutant concentrations at a given time and location are
the result of emissions from various sources which have
undergone transport and dispersion processes in the atmo-
sphere. In general, for a fixed rate of emission from all
sources, pollutant concentrations are inversely proportional
to atmospheric mixing. The factors generally considered to
control the degree of mixing are the effective mixing height,
Q
wind velocity, and wind stability. In most locations, how-
ever, the NWS does not routinely monitor mixing heights.
Thus, this information has not been incorporated even
though such measurements were made locally by the NWS
for a period of 1 year.
To construct model equations which can predict pollu-
tant concentrations for known meteorological conditions, we
defined new predictor variables derived from those basic
variables known or suspected to be related to atmospheric
mixing. In constructing derived variables we were guided
primarily by Holzworth' s qualitative account of large scale
weather influences on air pollution concentrations.
Table 1 presents the 29 derived variables used in the
predictive models. These variables, the rationale for their
inclusion and the results are discussed in depth in Ref. 1.
This model was fitted separately at each station. Due to
space limitations, we present the results of the regression
analysis at only one of the sampling stations. Full analysis
is presented in Ref. 1. The chosen station is typical in the
sense that it falls approximately in the middle of the range
of how well the equations fit the data.
Table 2 presents (1) the estimated coefficients for each
predictor variable, (2) the value of square of multiple cor-
o
relation coefficient (R ), (3) the number of observations
available for fitting, (4) the estimate of the error variance
(a ) and error standard deviation (cr), and (5) the mean of
the observed concentrations (y). The meaning and use of
each of these quantities are discussed in the following sec-
tions.
Goodness of Fit and Error Estimate
Table 2 of Ref. 1 shows that for TSP the R values
range from a low of 0. 23 to a high of 0. 47 with most of the
values near 0. 40. In other words, the models account for
from 23 to 47 percent of the total variance of the log(TSP)
values.
Table 2 of Ref. 1 also shows that, for log(TSP), a
ranges from 0. 140 to 0. 233 with most values being around
0.160. The importance of a to the problem of using the
models to predict concentrations will be covered in the
following section.
Applications
Predictions from Fitted Models
The primary motivation of this work was to develop a
method for making predictions. Actually, two different pre-
dictions are of interest. The first is the prediction (or esti-
mate) of the mean pollutant concentration as a function of the
predictor variables and the second is the prediction of a
single further pollutant concentration. Both predictions re-
sults from inserting the specified values of the predictor
variables (i. e. , the x.) into the estimating equation yielding
However, the uncertainties (standard deviations) associated
with each application are different.
The uncertainty in the prediction of the mean of the y1 s
for specified x.
r of tiie
uncertainty i
is a function only of the actual x. and the
tie estimates J3.. (See Draper and Smith
and Hahn for details. We consider predictions only at the
means of the x= for notational and conceptual simplicity. )
The estimated standard deviation of y when the x. are all
equal to the means of the x. is 3yvN. For the TSP data
of station 1 we obtain a standard deviation of 0. 176/\/364 =
0. 0092. Thus an approximate 95 percent confidence limit
on y is
y - (1. 96)(0. 0092) ^ log(TSP) s y + (i. 96)(0. 0092)
In terms of TSP directly this results in proportional limits
of
or roughly =t4 percent. Thus the regression equation itself
is pretty well estimated. These confidence limits change as
the x. change.
The uncertainty in a further predicted value includes not
only the uncertainty in the regression equation but also the
uncertainty involved in a single observation. The standard
deviation of a further predicted value at the mean of the
679
-------
predictor variables is thus
At station 1 for log(TSP) we thus obtain 0. 1762.
Approximate 95 percent confidence limits (in terms of
proportional limits) thus becomes
That is we can predict single values with a 95 percent con-
fidence of being within 55 percent low to 122 percent high.
Thus although the regression function is well estimated, it
is obvious that it is practically useless for prediction of spe-
cific single day concentrations because of the large residual
error. We will now consider a situation where the regres-
sion equation can be used to advantage.
Use in Meteorological Adjustment
The previous section showed that the large residual
variability precluded meaningful individual predictions of
concentrations. Nevertheless, if many concentrations are
predicted and then averaged, the average concentration can
be estimated with dramatically improved reliability.
Suppose we use the current predictive models for a pe-
riod of say 1 year and that during this year we accumulate
N = 100 further observations. Among other differences be-
tween this year and previous years are the differences in
meteorological conditions on the days for which data was ob-
tained. If we assume that measured concentrations are re-
lated to emission rates and we want to compare the emission
rates of this year with those of previous years based on the
changes in measured concentrations, then it is necessary to
first remove (adjust for) these meteorological differences.
This is accomplished by computing the estimated deviations
of the predicted concentrations (yp from the observed (y^
values. If there have been no changes in the processes gen-
erating the pollutants then the predicted and the observed
concentrations should be the same on the average. That is,
the ej would ideally have a distribution with a mean of zero
and we expect the computed mean, ~i, to be near zero.
(Note that the e^ will not have the same variance. See
Ref. 5 for details. )
If there has been an increase in emissions, "e would
tend to be greater than zero, while the opposite would be
true if there were a decrease in emissions. Thus a statis-
tical test of the hypothesis of unchanged conditions is equiv-
alent to a test of the significance of the difference of ~e
from zero. The standard deviation of ~i is related to the
standard deviation of 6j by the factor of l/>/N. Thus,
using the log(TSP) data of Table 2 and assuming N = 100
observations we obtain an estimated standard deviation of
0.01762 for "e which translates to approximately ±8 percent
for a 95 percent confidence interval on ~e.
Obviously, as more data became available (e. g., each
year) updating of the data base should be done and the models
refitted. At these times the models could also be improved
by the inclusion of other variables found to be of significance.
Degree of Improvement
We have discussed how well the models fit the data and
the use of the models for prediction purposes. We now
consider the question of how much improvement we have
achieved by using the estimated regressions as opposed to
using the mean of the observed concentrations without any
adjustment. The quantity D = 1 - fl - R , where R2 is
as defined previously (i. e., the square of the multiple cor-
relation coefficient) expresses the proportional decrease in
the standard deviation of a predicted concentration when the
regression equation is used as opposed to simply using the
mean of the observed values. (Duncan, pp. 696-699.)
From the
values of Table 2 of Ref. 1 we find that
D=l- yi-R^ ranges from a low of 0. 123 to a high of
0.272. Most of the R2 values are near R2 = 0.40 which
gives a value of D = 0. 225. We thus find a percent im-
provement of from 12. 3 to 27. 2 percent with most values
near 20 percent.
References
1. Sidik, S. M.; and Neustadter, H. N. - Meteorological
Adjustment of Yearly Mean Values for Air Pollution
Concentration Comparisons. NASA TN in process.
2. Neustadter, Harold E.; et al.; Air Quality Aerometric
Data for the City of Cleveland from 1967-1970 for
Sulfur Dioxide, Suspended Particulates, and Nitrogen
Dioxide. NASA TM X-2496, 1972.
3. Neustadter, H. E.; et al.: The Use of Whatman-41
Filters for High Volume Air Sampling. Atmos.
Environ., vol. 9, no. 1, Jan. 1975, pp. 101-109.
4. Searle, Shayle R.: Linear Models. John Wiley & Sons,
Inc., 1971.
5. Draper, Norman R.; and Smith, H.: Applied Regression
Analysis. John Wiley & Sons, Inc. , 1966.
6. Daniel, Cuthbert; Wood, Fred S.: Fitting Equations to
Data. Wiley-Interscience, 1971.
7. Neustadter, Harold N.; and Sidik, Steven M.. On Evalu-
ating Compliance with Air Pollution Levels "Not to be
Exceeded more than once a Year. " Air Pollution Con-
trol Assoc. J., vol. 24, no. 6, June 1974, pp. 559-563.
8. Stern, Arthur C.; ed.. Proceeding of Symposium on
Multiple-Source Urban Diffusion Models. AP-86,
Environmental Protection Agency (PB-198400), 1970.
680
-------
9. Holzworth, G. C.; Large-Scale Weather Influences on
Community Air PoUution Potential in the United States.
Air Pollution Control Assoc. J., vol. 19, no. 4, Apr.
1969, pp. 248-254.
10. Hahn, Gerald J.; Simultaneous Prediction Intervals for
a Regression Model. Technometrics, vol. 14, no. 1,
Feb. 1972, pp. 203-214.
11. Duncan, Acheson J.: Quality Control and Industrial
Statistics. 3rd ed., Richard D. Irwin, Inc., 1965.
TABLE 1. - DERIVED PREDICTOR VARIABLES USED IN THE REGRESSION MODELS
Vari-
able
Xl
*2
X3
X4
X5
X6
x7
X8
Y
X10
x
11
X12
Symbol
AT
AT'
min
min'
min"
B. P.
Pr
(Pr)2
Work
Steel
VN
VN
Definition
Tmax T . • maximum temperature
minus temperature, °F
+3 AT, 4 AT. .. + AT. Q; related to
1 1~ J. 1~ £i
noncentral first difference of AT on
day i
Tmin; minimum temperature, °F
+3 min^ 4 min. ^ + min. 2; related to
noncentral first difference of min
on day i
-2 min. + 5 min. , 4 min. „ + min. „;
related to noncentral second difference
of min at day i
Daily average barometric pressure in
inches of mercury
Total water equivalent of precipitation
in inches
The square of X^
Indicator of workdays vs nonworkdays
Co Saturday, Sunday, Federal
Work = J holidays
[l Otherwise
Weekly regional steel tonnage index
f Resultant velocity; when wind is
J out of the North octant
1
[0.0; Otherwise
*?1
Vari-
able
X13
X14
x15
X16
x17
X18
X19
X20
X21
X22
•y
X23
Xgg
X26
-27
X28
X29
Symbol
VNE
V2
VNE
VE
VE
VSE
2
VSE
VS
• vl
VSW
o
vsw
vw
V2
W
VNW
^W
t
sin(0)
cos(0)
Definition
Similar to X. .., X_2 when wind is from NE
Similar to X, , , X, „ when wind is from E
11' T.2
Similar to X, , , X, „ when wind is from SE
11 L&
Similar to X. , , X, „ when wind is from S
Similar to X11? X12 when wind is from SW
Similar to X^, X^2 when wind is from W
Similar to XI]L, X^ when wind is from NW
Number of days from Jan. 1, 1967
divided by 100 (Jan. 1, 1967 is
nominal beginning of sampling
program)
sin(2Trt/3. 6525)
cos(27rt/3. 6525)
681
-------
TABLE 2. RESULTS OF REGRESSION ANALYSIS AT A TYPICAL STATION FOR
TOTAL SUSPENDED PARTICULATES
Coeffi-
cient
00
*1
02
03
04
05
06
07
08
09
Variable
Intercept
AT
AT
min
mln'
min"
B. P.
Pr
(Pr)2
Work
Estimate
-2.91
a. 0080
-.00034
a. 0033
a. 0022
a. 0013
a.17
a-.30
a.16
.016
Coeffi-
cient
010
011
012
013
^14
%5
016
017
018
019
Variable
Steel
VN
VN
VNE
VNE
VE
vE
VSE
vL
VS
Estimate
-0.00040
a-.040
.0019
a-.045
a.0021
a-.070
a. 0044
-.027
.00065
a-.020
Coeffi-
cient
020
021
022
023
024
025
026
027
028
029
Variable
^1
VSW
^W
vw
vW
VNW
VNW
t
sin 9
cos 6
Estimate
0. 00042
-.011
.00008
a-.024
.00099
a-.044
a. 0027
a-.0081
all
a. 090
Denotes the coefficient is significantly different than zero at approximately the 10 percent
significance level.
N
Y
R2
364
2.09
0.38
a2
CT
D
0.0310
0.176
0.21
682
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THE APPLICATION OF CLUSTER ANALYSIS TO
STREAM WATER QUALITY DATA
Jay A. Bloomfield
Environmental Quality Research Unit
New York State Department of Environmental Conservation
50 Wolf Road, Albany, New York 12233
Abstract
Cluster analysis, a multivariate classification
technique was used to examine spatial and temporal
heterogeneity in stream water quality data. To
examine spatial patterns, stream water quality data
from 44 watersheds in the Genesee River basin in
western New York State were analyzed. Nine groups
of watersheds and seven groups of water quality vari-
ables were identified. To examine temporal trends,
data collected daily at a small rural watershed,
Mill Creek, were examined. Three clusters of state
variables were produced, based upon the stability
of each variable during runoff events. Cluster
analysis by sample yielded subsets representing
runoff events, recessional periods and base flows.
Introduction
One of the more challenging problems in the en-
vironmental sciences today is the interpretation
of data collected from field studies. These data
often consist of many state variables measured at
several locations over a period of time. The sheer
volume of data obtained in this manner often over-
whelms even the most thorough observer, intent upon
discerning meaningful patterns in the data. Several
roultivariate techniques have been used to find
patterns in environmental data, primarily in the
fields of geology, taxonomy, and terrestrial ecology.
These techniques include multiple components analysis
(McCammon, 1968), ordination (Bray and Curtis, 1957)
and cluster analysis (Fortier and Solomon, 1966).
This paper will be concerned solely with the latter,
a hierarchical classification technique used to
determine subsets of samples or state variables.
Two data sets will be analyzed using cluster analy-
sis: one to examine spatial heterogeneity, and the
other to examine temporal variability in stream water
quality.
Sources of Heterogeneity in Stream Hater Quality
Data
Heterogeneity in stream quality is due to two fac-
tors, time and location. Temporal variability in
water quality is induced by seasonal and short-term
changes in climatic factors, primarily precipitation,
but to a lesser extent, solar radiation and the
movement of air masses. Spatial variability is
often explained by differences in soil or bedrock
type, topography, vegetation or the influence of
the activities of man.
Stream quality surveillance networks are rarely
designed to evaluate both spatial and temporal
variations in water quality, either because of
limited resources ox lack of insight. Little effort
is made in determining l) the proper sampling
interval, 2) the placement of stations, or 3)
redundancy in the state variables (primarily
chemical constitutents) measured. Cluster analysis
can be used to examine each of these three problem
areas.
Cluster Analysis
Cluster analysis is simply a classification technique
which graphically describes a similarity matrix with a
dendrogram (Sokal and Sneath, 1963). The similarity.
matrix can be constructed by comparing samplesft-mode)
or state variables (R-mode). For each pair of samples
or variables, a similarity coefficient is calculated.
Although the correlation coefficient is often used,
it has the disadvantage of marked sensitivity to the
nature of the frequency distribution of the state
populations (variable or sample) considered (Park,
1968; Gevirtz, Park and Friedman, 1971).
A distance coefficient proposed by Sorensen (1948)
tends to be less sensitive to the form of the fre-
quency distribution of the data (Park, 1968) and
therefore, has been used in this paper.
Sorensen' s coefficient (s) for multistate data is
defined as»
n
Sjk = 2*
(minimum (X^, Xifc))
For Q-mode analysis, n is the number of samples, X^j
the value of the jth state variable in the ith sample,
and X^k the value of the kth state variable in the ith
sample. For R-mode analysis, the logic is transposed.
It can be seen that the coefficient represents the
relative amount a pair of samples or variables has in
common.
The generation of the dendrogram is accomplished by
pair-wise calculation of elements of the similarity
matrix. From this matrix, the pair of states with
the maximum value of S are temporarily deleted from
683
-------
the analysis, and the program recalculates the simi-
larity matrix with an additional state obtained from
a combination of the pair of states deleted. Thus,
n-1 iterations are required to produce the dendrogram.
This step-wise procedure allows one to examine the
hierarchy among subsets (King, 1967).
An example of a dendrogram is shown in Figure 2. The
horizontal scale represents percent similarity
(100. * S). The states are listed vertically and are
connected with parallel lines. If states A and B are
similar at a 90% level, parallel lines are drawn hori-
zontally to this level and connected. If state C is
similar to this subset at a 75% level, parallel lines
are extended from the A-B subset (90%) to 75% and are
connected to a horizontal line from state C. The
simplest procedure for defining a cluster is to com-
pare the relative similarity within a group to the
similarity of the group to the remainder of the states.
Gevirtz et al (1971) sites a disadvantage with clus-
ter analysis: the technique produces subsets of
states, and hence obscures gradients among states.
Additionally, McCammon (1968) has warned to ignore
low level clusters (S < .2) and Park (1974) has sug-
gested scaling each state variable (either by the .
maximum value of each variable or the range). Both
of these suggestions have been followed in this
paper. Also, the author believes the results ob-
tained from cluster analysis should be used judi-
ciously, taking into account the limitations of the
data and should function as one facet of a rigorous
analytical strategy.
Cluster analysis has been used in geology (Harbaugh
and Merriam, 1968), marine biology (Gevirtz et al,
1971), paleoecology (Del Prete, 1972; Bloomfield,
1972) and limnology (Cairns, Kaesler and Patrick,
1970). The technique has application to a wide range
of multistate environmental data where grouping of
similar states is desired.
Results
Two sets of multivariate stream water quality data
were examined using a cluster analysis program written
in FORTRAN and described by Gevirtz et al (1971).
Each data set was chosen so as to examine the problems
of spatial and temporal heterogeneity.
The Genesee River Watershed, 1972
During June 1972, the United States Geological Survey
sampled 44 streams in the Genesee River Basin in
western New York (Figure l). Twenty-one water quality
parameters including water temperature and stream dis-
charge were determined for each stream (United States
Department of the Interior, 1973). On June 23, 1972,
Hurricane Agnes, one of the most severe storms ever to
affect New York State, caused vastly increased stream
discharges. Of the 48 total sampling sites, six were
sampled after the storm. Five of these post-storm
sites were on the main stem of the Genesee River and
one on a major tributary. Cluster analysis was used
to group both sampling sites (Q-mode) and state vari-
ables (R-mode). The Q-mode dendrogram is shown in
Figure 2 and the R-mode dendrogram in Figure 3.
The Q-mode analysis generated nine distinct clusters,
four intermediate samples, and one sample (Vfolf Creek)
that was unique from the other 44 samples. Four
samples were not included in the analysis because of
missing values for one or more state variables. Two
of the clusters (C and D) and two intermediate sta-
tions (Genesee River at Wellsville and Avon) account
for the six post-storm sampling sites. The remaining
cluster (AI, A2> AS, A4, B, E and F-) represent pre-
storm sites. The geographical distribution of these
clusters is shown in Figure 4. It is apparent that
the pre-storm clusters are areally compact, repre-
senting regions with similar environmental conditions.
Table 1 displays land use, soil quality and bedrock
geology for the seven pre-storm clusters.
The A clusters represent a forested region (Hardy and
Shelton, 1970) in slightly-coarse textured, moderate
to somewhat poorly-drained acidic soils (Cline, 1961)
underlain by Upper Devonian shales and siltstones
(New York State Education Department, 1970). Cluster
B has bedrock geology and soils similar to the A
clusters but there are some agricultural areas in the
watersheds of this cluster. Clusters E and F repre-
sent agricultural watersheds in lime-rich well-
drained soils. The watersheds of cluster E are un-
derlain by Devonian shales and limestones while the
watersheds of the F cluster are underlain by Upper
Silurian shales, dolostones and evaporites.
Examination of the geographic distribution of the
Q-mode clusters (Figure 4) would dictate that the
unique Wolf Creek sample be a member of cluster B.
Inspection of the data from Wolf Creek shows rela-
tively high sodium (600 mg/l) and chloride (1200
mg/l). The apparent reason for the uniqueness of
this site is the existence of a large salt mining
operation in the Wolf Creek watershed (New York
State Department of Health, 1961).
Table 2 summarizes the average value and range of
three water quality parameters, chloride, nitrate-
nitrogen and alkalinity by Q-mode cluster. Alka-
linity, chloride and nitrate are decidedly higher in
the agricultural clusters (E and F). Figures 5
through 8 show the geographic distribution of chlo-
ride, nitrate-nitrogen alkalinity and electrical
conductivity. What causes these trends is most
probably a combination of land use, soil type and
bedrock geology. An ongoing study (New York State
Department of Environmental Conservation, 1974) is
attempting to determine which of these three factors
is most directly responsible for trends in stream
water quality in the Genesee River Basin.
The R-mode analysis resulted in seven groups of water
quality variables (Figure 3):
l) Ca++, hardness
2) 504, non-carbonate hardness
3) Dissolved solids, electrical conductivity
4) pH, water temperature, SiO~3
5) HCOjj, alkalinity
6) Stream discharge, total Fe, total Mn
7) Na+, Cl~
The composition of several of the R-mode clusters are
readily explainable, showing redundancy between state
variables. For example, cluster 5 contains alka-
linity and HCO;j, which is the major component of
alkalinity encountered at neutral pH. Cluster 3 con-
tains electrical conductivity and dissolved solids,
the concentration of the latter being the major
factor in determining the electrical conductivity of
an aqueous solution.
Cluster 1 contains hardness and its major constituent
calcium. Cluster 6 relates stream discharge, iron
and manganese. This cluster results from high iron
and manganese in post-storm samples only, possibly
related to increased levels of suspended sediment.
Cluster 7 probably results from the influence of
salt deposits (NaCl) in the watershed. Cluster 2
684
-------
relates sulfate ion and non-carbonate hardness
(polyvalent dissolved cations such as strontium and
zinc). Cluster 4 consists of pH, stream temperature
and silicate. The author can offer no simple ex-
planation for clusters 2 and 4.
Thus, cluster analysis can be used to examine spatial
variation in stream water quality data from the
Genesee watershed and has allowed classificiation of
seven groups of water quality parameters.
The Mill Creek Watershed. 1975
Eighteen water quality parameters were measured at
Mill Creek, New York, for one year beginning March 1,
1975 (Hetling, Carlson and Bloomfield, 1976). The
watershed has an area of about 25 km2 and land use
is evenly divided between agriculture and forest
(El-Baroudi, James and Walter, 1975). Stream dis-
charge was gaged continuously and one water sample
was collected each morning. Additional samples were
collected during major runoff events.
Cluster analysis was performed on a data set con-
sisting of the morning samples collected between
April 1, 1975 and October 31, 1975 (214 samples).
The Q-mode dendrogram is summarized in Figure 9. In
general, the samples representing the three major
runoff events (April 4, August 8 and October 18)
form one cluster (j). Each of these events repre-
sent a prolonged stream discharge of over 2.0m3/sec.
Other clusters represent smaller runoff events
D, H), recessional periods immediately following
events (A, B, C, E, G, I) or prolonged periods of
drought (F). These twelve unique Q-mode clusters
account for slightly over one-third of the total
number of samples. The remaining samples form a
very diffuse cluster of similarity greater than 95%.
These samples represent base flow conditions and
yield water quality information that is extremely
redundant.
The results of the Q-mode analysis suggest more
frequent sampling during runoff events with fewer
samples during base flow. Anomalous extended dry
periods should be sampled more frequently when
possible.
The R-rnode dendrogram (Figure 10) shows three major
clusters of water quality variables:
1) Dissolved organic carbon, dissolved kjeldahl
nitrogen, chloride, dissolved orthophosphate
phosphorus, total dissolved phosphorus, ammonia
nitrogen and nitrate nitrogen.
2) Alkalinity, electrical conductivity, sulfate,
pH, dissolved oxygen and nitrate nitrogen.
3) Particulate organic carbon, particulate phosphorus,
suspended solids, particulate kjeldahl nitrogen
and stream discharge.
Cluster 1 represents dissolved constituents which
exhibit changes in concentration during runoff events.
Cluster 2 also represents dissolved constituents.
However, these variables tend not to be as influenced
by runoff events. The constituents in cluster 3 are
extremely influenced by runoff events. Cluster 3 in-
cludes stream discharge and four particulate (retained
on a 0.45 pm membrane filter) variables. In summary,
the R-mode analysis indicates that three subsets of
water quality variables can be defined based upon
their relationship to runoff events.
Conclusions
Cluster analysis can be used to examine spatial and
temporal heterogeneity in stream water quality data.
It can also be used to check for redundancy among
water quality variables.
Analysis of water quality data from the Genesee River
Basin indicates that land use and geology tend to be
the most significant factors in determining the
actual grouping of subwatersheds within the basin.
The use of cluster analysis on time-course data from
Mill Creek, New York, reveals three subsets of vari-
ables; stable dissolved, variable dissolved and ex-
tremely variable particulate constituents. Q-mode
analysis of the Mill Creek data resulted in grouping
samples into runoff event, hydrograph recession and
low flow groups. This result tends to agree with the
results of Bouldin, Johnson and Lauer (1975) and
Hetling, Carlson and Bloomfield (1976) that runoff
event-oriented and not fixed-interval sampling yields
more reliable data on stream water quality.
Acknowledgements
The author wishes to acknowledge Dr. L.J. Hetling,
Mr. G.A. Carlson, and personnel from the New York
State Department of Environmental Conservation, who
helped in review and preparation of this manuscript.
Dr. R.A. Park of Rensselaer Polytechnic Institute
supplied the computer programs used in this paper.
This work was in part supported by the Environmental
Protection .Agency Grant No. R005144-01 in cooperation
with the International Joint Commission.
Bibliography
Bloomfield, J.A., 1972, Diatom Death Assemblages as
Indicators of Environmental Quality in Lake George,
New York. Unpublished Masters Thesis, Rensselaer
Polytechnic Institute, Troy, N.Y., 86 pp.
Bouldin, D.R., A.H. Johnson and D.A. Lauer, 1975, The
Influence of Human Activity on the Export of Phos-
phorus and Nitrate from Fall Creek. In "Nitrogen
and Phosphorus, Food Production, Waste and the
Environment", K.S. Porter (Editor), Ann Arbor
Science Publishers, Inc., Ann Arbor, Mich.,
pp 61-120.
Bray, J.R. and J.T. Curtis, 1957, An Ordination of
the Upland Forest Communities of Northern Wisconsin,
Ecol. Mon., (27), No. 4, pp 3250349.
Cairns, J., R.L. Kaesler and R. Patrick, 1970,
Occurrence and Distribution of Diatoms and Other
Algae in the Upper Potomac River, Notulae Naturae,
(436), pp 1-12.
Cline, M.G., 1961, Soil Association Map of New York
State, Cornell University, Ithaca, N.Y.
Del Prete, A., 1972, Postglacial Diatom Changes in
Lake George, N.Y.,Unpublished Doctoral Dissertation,.
Rensselaer Polytechnic Institute, Troy, N.Y.,110 pp.
El-Baroudi, H., D.A. James and K.J. Walter, 1975,
Inventory of Forms of Nutrients Stored in a Water-
shed, Rensselaer Polytechnic Institute, Troy, N.Y.,
209 pp.
Fortier, J.J. and H. Solomon, 1966, Clustering
Procedures in Multivariate Analysis, Academic Press,
New York, N.Y., pp 493-506.
685
-------
Gevirtz, J.L., R.A. Park and G.H. Friedman, 1971,
Paraecology of Benthonic Forminifera and Associated
Microorganisms of the Continental Shelf off Long
Island, New York. Jour. Paleontology, (45), No. 2,
pp 153-177.
Harbaugh, J.W. and D.F. Merriam, 1968, Computer
Applications in Stratigraphic Analysis, John Wiley
and Sons, New York, N.Y., 282 pp.
Hardy, E.E. and R.L. Shelton, 1970, Inventorying
New York's Land Use and Natural Resources, New York
Food and Life Sciences, (3), October-December,
Cornell University, Ithaca, N.Y.
Hetling, L.J., G.A. Carlson and J.A. Bloomfield,
1976, Estimation of the Optimal Sampling Interval
in Assessing Water Quality of Streams, in prepa-
ration.
King, B., 1967, Stepwise Clustering Procedures, Jour.
Am. Stat. Assoc., (62), pp 79-85.
McCammon, R.B., 1968, Multiple Component Analysis
and its Application in Classification of Environ-
ments, Am. Assoc. Petroleum Geologists Bull., (52)
No. 11, pp 2178-2196.
New York State Department of Environmental Conserva-
tion, 1974, Genesee River Watershed Study, Des-
cription and Detailed Work Plan, 36 pp.
New York State Department of Health, 1961, Upper
Genesee Drainage Basin, Genesee River Drainage
Basin Survey Series, Report Number 2, 219 pp.
New York State Education Department, 1970, Geologic
Map of New York State, four sheets.
Park, R.A., 1968, Paleoecology of Venericardia sensu
lato (Pelecypoda) in the Atlantic and Gulf Coastal
Provinces: An Application of Paleosynecological
Methods, Jour. Paleontology, (42), No. 4,
pp 955-986.
Park, R.A., 1974, A Multivariate Analytical Strategy
for Classifying Paleoenvironments, Int. Assoc. for
Math. Geo. Jour., (6), No. 4
Sokal, R.R. and P.M.A. Snealth, 1963, Principles of
Numerical Taxonomy, W.H. Freemand and Co.,
San Francisco, Ca., 359 pp.
Sorensen, T., 1948, A Method of Establishing Groups
of Equal Amplitude in Plant Sociology Based on
Similarity of Species Content and its Application
to Analyses of the Vegetation on Danish Commons,
Biol. Skr. (5), No. 4, pp 1-34.
United States Department of the Interior, 1973, Water
Resources Data for New York for 1972, Part 2, Water
Quality Records, 262 pp.
Key to Figure 1
Watersheds sampled prior to Hurricane Agnes
1) Spring Creek (Pumpkin Hill)
2) Black Creek (Churchville)
3) Hotel Creek
4) Mill Creek (West Chili)
5) Spring Creek (Mumfbrd)
6) Pearl Creek
7) Stony Creek
8) Warner Creek
9) Trout Brook
10) Wolf Creek
11) Beards Creek
12) Jaycox Creek
13) Christie Creek
14) White Creek (Canawaugus)
15) Dugan Creek
16) Honeoye Creek
17) Spring Brook
18) Mill Creek (Honeoye Park)
19) Bradner Creek
20) Stony Brook
21) Sugar Creek
22) Ewart Creek
23) Cold Creek
24) Rush Creek
25) Crawford Creek
26) Wigwam Creek
27) White Creek (Belfast)
28) Baker Creek
29) Black Creek (Benetts)
30) Phillips Creek
31) Knight Creek
32) Vandermark Creek
33) Brimmer Brook
34) Elm Valley Creek
35) Railroad Brook
36) East Valley Creek
37) Dyke Creek
38) Quig Hollow Brook
39) Ford Creek
40) Marsh Creek
41) Chenunda Creek
42) Cryder Creek
Streams sampled after Hurricane Agnes
43) Genesee River (Rochester)
44) Genesee River (Avon)
45) Genesee River (Mount Morris)
46) Canaseraga Creek (Dansville)
47) Genesee River (Portageville)
48) Genesee River (Wellsville)
686
-------
TABLE 1
DESCRIPTION OF LAND USE, SOILS DATA AND BEDROCK GEOLOGY FOR THE
SEVEN PRE-STORM Q-MODE CLUSTERS
Q-mode Number of Dominant
Cluster Watersheds Land Use
A^ 6 Forest - 6
A2 5 Forest - 4
Agriculture). ^
and forest )
A3 3 Forest 3
A^ 5 Forest 5
B 4 Agriculture 2
Agriculture)
with some )- 2
forest )
E 8 Agriculture - 8
F 4 Agriculture - 4
Q-mode Number of
Cluster Watersheds
A^ 6
A2 5
A3 3
A4 5
B 4
E 8
F 4
Soils Data
Texture p'H
Slightly Acidic
coarse
Coarse Acidic
Slightly Slightly
coarse acidic
Slightly Acidic
coarse
Slightly Acidic
coarse
Fine Basic
No trend Slightly
basic
TABLE 2
AVERAGE CHEMISTRY
Drainaqe
Somewhat poor
Moderate
Somewhat poor
Moderate
No trend
Well-drained
Well-drained
Nitrate-Nitrogen
Chloride (mq/l) (mq/l)
Avq Range
21.1 1.9-81
9.9 3-26
3.4 2.2-5
4.8 1.7-9.8
11.7 5.7-20
44.5 27-72
48.8 36-69
Avg Range
0.03 .01-. 07
0.16 .01-. 30
0.01 .01-. 20
0.18 .04-. 30
1.23 .07-1.80
0.84 .02-2.70
0.98 .70-1.30
Bedrock Geoloqy
Upper Devonian shale and
siltstone
Upper Devonian shale and
siltstone with some sand-
stone
Upper Devonian shale and
siltstone
Upper Devonian shale and
siltstone
Upper Devonian shale and
sandstone with some silt-
stone
Middle Devonian shale and
limestone with some upper
Devonian shale and lime-
stone
Upper Silurian shale, dolo-
stone, salt and gypsum
Alkalinity
(mq/l)
Avg Ranqe
64 54-80
58 34-74
93 83-99
26 16-32
119 97-128
204 128-245
234 194-291
687
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Figure 1. Location of Sub-Watersheds Sampled
During June, 1972
% SIMILARITY
80 70
BRIMMER BR.
PHILLIPS CR.
BAKER CR
WIGWAM CR.
CHENUNOA CR.
KNIGHT CR.
EWART CR.
SUGAR CR
RAILROAD BR.
STONY BR.
FORD CR
CRYDER CR.
WHITE CR. (BELFAST)
CRAWFORD CR.
RUSH CR.
DYKE CR.
QUIG HOLLOW BR.
EAST VALLEY Cfl.
ELM VALLEY CR.
VANDERMARK CR.
MARSH CR.
TROUT CR.
BRADNER CR.
WARNER CR.
STONY CR.
MILL CR. (HONEOYE PARK )
GENESEE R. ( PORTAGEVILLE }
CANASERAGA CR.
GENESEE R. ( WELLSVILLE )
GENESEE R. (AVON, 6/23)
GENESEE R. ( MT MORRIS }
GENESEE R. (AVON. 6/30)
BEARDS CR
SPRING BR.
JAYCOX CR.
WHITE CR. { CANAWAUGUS )
PEARL CR.
HONEOYE CR.
MILL CR. (MUMFORO }
CHRISTIE CR.
DUGAN CR.
SPRING CR (PUMPKIN HILL)
MILL CR. (WEST CHILI )
HOTEL CR.
WOLF CR.
•A I
STREAM
MKHMSt
SODIUM
CHLORIDE
CAMONATE
FIGURE 3 R-MOOE DENDROGRAM OF GENESEE DATA.
A3
A4
B
C
POST STORM SITES
WOLF CREEK
FIGURE 2. 0-MODE DENDROGRAM OF GENESEE DATA.
Figure h. Geographic Distribution of
Q-Mode Clusters
688
-------
Figure 5. Geographic Distribution of Chloride
(mg/l)
Figure T. Geographic Distribution of
Alkalinity (mg/l)
Figure 6. Geographic Distribution of
Disolved HOj-N
Figure 8. Geographic Distribution of
Electrical Conductivity
(M mhos/cm)
689
-------
FIGURE 9. Q-MOOE DENDROGRAM OF MILL CREEK DATA
B
C
G
H
FIGURE 10. R-MODE DENDROGRAM OF MILL CREEK DATA
% SIMILARITY
100 tO (0 70 «O 50 40 SO 10
DISSOLVED
ORGANIC CARBON
DISSOLVED
KJELDAHL NITROGEN
CHLORIDE
ORTHOPHOSPHATE
PHOSPHORUS
DISSOLVED
PHOSPHORUS
AMMONIA
NITROGEN
NITRITE
NITROGEN
ALKALI NITY
ELECTRICAL
CONDUCTIVITY
SULFATE
pH
DISSOLVED
OXYGEN
NITRATE
NITROGEN
PARTICIPATE
ORGANIC CARBON
PARTICIPATE
PHOSPHORUS
SUSPENDED
SOLIDS
KJELDAHL NITROGEN
STREAM DISCHARGt
I A
IB
690
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APPLICATION OF PATH ANALYSIS TO DELINEATE THE
SECONDARY GROWTH EFFECTS OF MAJOR LAND USE PROJECTS
Tom McCurdy, Environmental Planner
Strategies and Air Standards Division, EPA, Durham, North Carolina
Frank Benesh, Environmental Planner Peter Goldberg, Senior Scientist
Walden Research, Cambridge, Massachusetts
Dr. Ralph D'Agostino
Professor of Mathematics, Boston University
Abstract
This paper presents a path analytic modeling pro-
cess used to test various factor theories of induced
urban development. The original and final "trimmed"
path models are discussed, as well as statistical
problems associated with using path analysis to des-
cribe a non-recursive system.
Introduction
This path analysis effort is a part of an Envi-
ronmental Protection Agency (EPA) project entitled
"Growth Effects of Major Land Use Projects", or
GEMLUP for short.
The main purpose of GEMLUP is to formulate a non-
proprietary statistical methodology to predict air
pollution emissions from (1) two major land use devel-
opment types—large places of employment and large
residential projects,* (2) secondary development that
is induced** by the major project, and (3) motor ve-
hicular traffic associated with both kinds of urban
development. Subsidiary purposes are to formulate and
test a factory theory of induced development using
path analysis and to generate and apply land use
oriented emission factors based on current energy con-
sumption dataJ
GEMLUP relates to a number of EPA programs, in-
cluding air quality maintenance areas (AQMA) planning2,
environmental impact statement (EIS) review', the
indefinitely suspended portions of indirect source re-
view , and the prevention of significant air quality
deterioration, or non-degradation.5 Explicit or im-
plicit in these programs is an evaluation of air qual-
ity impacts of land use plans or project developments,
but the Agency does not provide, specify, or recommend
a method for evaluation in any of the programs. GEM-
LUP is designed to formulate and test a method of
evaluating land use impacts at the project level.
Theory and Approach
Of the many t\
in the literature
pes of scientific theory discussed
, the most rigorous type of theory
*Definitions of the project types investigated in
GEMLUP are:
1. Place of employment: an office building or complex,
an industrial building or complex, or a research and
development building or complex constructed between
1954 and 1964 and having a minimum employment of
2,250 persons within five years of initial operation.
2. Residential project: an apartment structure or
complex, residential subdivision, planned unit devel-
opment, or new town constructed between 1954 and 1964
and having a minimum population of 4,500 persons with-
in five years of initial occupancy.
**Induced development is land use development
caused by, or constructed because of, the major land
use project.
***See references 6-10.
that we could ascribe to is "factor theory," which is
characterized by narrow and non-overlapping generali-
zations, a selective, explicit enumeration of (all)
factors thought to influence a given phenomenon, and
the utilization of empirically defined variables to
represent the factors involved. While almost every
effort at causal explanation involves factor theory, it
is limited theory because it does not readily suggest
other generalizations, due to its relatively narrow fo-
cus6. Consequently, we had to operationalize the fac-
tor theory by using a model. The next step was then
clear: formulate a theory of induced development and
choose a model to test it.
A Theory of Induced Development
Taking the industrial/offices major land use pro-
ject type as the more general case of the two types
investigated, we devised the following theory of in-
duced development.*
Constructing a large source of employment like an
industrial/office complex generates jobs which result
in the nearby construction of dwelling units; these in-
duce retail development to locate near them and gener-
ate demand for community, cultural, and religious faci-
lities (schools, recreation areas, libraries, churches,
theaters, fire and police stations, etc.). All of this
requires the construction of streets and highways that
then improve accessibility to the area. Better access
fosters continued urban development, particularly high-
way-oriented commercial and office land uses. Addition-
al sources of employment come into the area as secondary
(and tertiary) industry or services located near the
original major project, spurring on another round of
residential development, and so forth. This can be
summarized as:
induced land use
f (size of major project,
other endogenous variables,
other exogenous variables) (1)
where the other endogenous variables are the other in-
duced land uses in the model and the other exogenous
variables are vacancy rates, accessibility measures,
etc. which affect the influence of the major project on
induced development.
That is what was hypothesized to happen. As can
be noted, feedback in the system was explicitly hypo-
thesized. Our theory also specified that within a
10,000 acre circular "area of influence" centered on
the original major land use project, all of the above
development would occur within ten years after the
employment source opened. Our rationale for the where
and when will have to be discussed elsewhere.11 The
structural equations and path analytic diagrams dis-
cussed below rigorously depict the model used to test
the theory; however, we still must explain why we chose
path analysis as the modeling methodology in the first
place.
*The theory is not entirely new. Most of the urban
development models referenced in the next section are
based upon the same general relationships posited in our
theory,though they are usually less explicit than ours.
691
-------
Analytic Approach^
Part of the reason for using path analysis to _
te<-t our theory was programmatic: we did not have time
or money to do more. For instance, the highly detailed
deterministic approaches patterned after Lowry^ or
ForresterlS Or others working in the same vein were
simply infeasible. They were also inappropriate be-
cause of their concern with highly aggregated regional
development and/or long planning horizons. Because of
this and the problems associated with deterministically
modeling a social system, it was decided to utilize a
statistical or probabilistic approach.
It was also obvious that a dynamic modeling ap-
proach was infeasible because of the effort involved in
obtaining longitudinal data to incorporate time into
the system and in solving the simultaneous differential
equations "involved. For similar reasons, a difference
equation approach (i.e. predicting the change in land
use over the ten year period) was also infeasible.
The static approach to testing our inherently change-
oriented theory is justified by three factors: (1) our
theoretical assumption that induced development follows
a single basis causal structure for all cases or obser-
vations, (2) the use of a cross-sectional method of ob-
taining data for variables observed in a static state
and the assumption that input variables were initial-
ized at time 0 and held constant long enough so that
all the causal consequences in the system were re-
alized, and (3) the use of certain time-lagged exoge-
nous variables in the system. The conceptual useful-
ness of these factors in testing causal theory is well
described in HeiselS and Blalock.20
Conceptually, the total land use in the 10,000
acre area of influence at the end of the ten year time
period can be defined as three components:
total land u
(2)
(prior land uset)+(project induced land
uset^.+10)+(non project induced land
usVt+io'
The prior land use in time t is the amount of land use
existing in the year of the initial occupancy of the
major project. Non project induced land use in the
period t to t+10 is the amount of land use growth,
t to t+10, that occurred in the area of influence but
was not induced by the major project. The non project
induced land use includes growth due to regional ex-
pansion and random effects.
The selection of a cross sectional approach limi-
ted our model to the prediction of the total land use
in the year t+10. Consequently, the basic structure of
our model is a series of simultaneous equations of the
following form:
total land use
t+10
f(Type I variables,
Type II variables) (3)
where Type I variables are predictors of the induced
portion of the total land use (see Equation 1) and Type
II variables are predictors of the prior land use in
year t and non project induced land use in the period
t to t+10.
Finally, there was not enough existing information
on project-level induced development to be able to de-
fine the form of the relationships in the system. The
form, therefore, was assumed to be linear. This is not
Hill [14], Seidman [15], and Center for Real Es-
tate and Urban Economics [16]. In addition to these
general or comprehensive models, there are many single
sector models that have been developed since the early
1960's. See references 17 and 18 for a review of ur-
ban development models.
a bad a priori approximation in most social science
applications, and it allows the use of well developed
statistical techniques. There is accumulating evi-
dence that many social systems can be approximated by
a linear function as long as operating conditions re-
main fairly stable. 19 Even complex non-linear rela-
tionships can often be approximated by a constant re-
lation in discrete subregions of the relationship.21
Also, if a relationship is thought to be nonlinear on
theoretical grounds (e.g., multiplicative, exponential),
the data can be transformed prior to entering it in
the linear analysis.22
For all of these reasons, the path analytic tech-
nique based on multiple regression analysis seemed
appropriate to test our theory of induced development.
Path analysis was developed by biologist Sewall Wright
in the 1920's as a technique for examining observed
interrelated variables that are assumed to be comple-
tely determined by exogenous variables.
It is not capable of deducing causal rela-
tions from available quantitative information
(viz., correlation coefficients), but rather
it is intended to combine this quantitative
information with qualitative information that
is available on the causal relations to give
a quantitative interpretation. It is a
technique useful in testing theories rather
than in generating them and it can be used
to study the logical consequences of various
hypotheses involving causal relations. In
order to implement the technique, the re-
searcher must make explicit a theoretical
framework or model.22
Use of the technique requires two assumptions
about causality in the system: (1) a weak causal order
exists among the variables and it is known, and (2)
relationships among variables are causally closed.
Weak causal ordering exists in a two variable set, Xj
and Xj, it it is known on logical, empirical, or
theoretical grounds that X-j may (or may not) affect Xj
and that Xj cannot affect Xn-. Causal closure is simply
the concept that given a bivariant covariation between
X-j and Xj and weak causal ordering (X-j->Xj), the ob-
served covariation between the two variables must be
due to the causal dependence of Xj on X-j, their mutual
dependence on some outside variable(s), or a combina-
tion of these two factors.23
Path diagrams (see below) depict the hypothesized
causal relations among variables. Causality is shown
by a single-headed arrow (or path) and interaction
(correlation) between two variables is shown by a cur-
ving double headed arrow. A,coefficient P-H is asso-
ciated with each path and can be interpreted as a re-
gression coefficient; that is, the amount of change in
the dependent variable caused by a one unit change in
the independent variable with all other independent
variables held constant. The coefficient on the inter-
action arrows is the correlation coefficient R-JJ. All
of the statistical assumptions of regression analysis
(e.g., independence of observations, uncorrelated re-
siduals, a normal distribution of means of sample data)
apply to path analysis as well.
Path analysis has been used at least once before
in environmental modeling. Researchers at Argonne Na-
tional Laboratories chose the technique to causally re-
late four independent variables (land area, number of
employees, process weight rate, and energy use) to a
dependent variable, regulated point source emissions of
particulate air pollution.24 While the authors were
unhappy because land area and number of employees did
not relate well to the dependent variable, the rela-
tionships depicted in the system are logical and cer-
tain of the path coefficients are significant.
692
-------
Model Specification
The theory of induced development was translated
into two models, a residential project model and an
industrial/office project model. Due to the limited
length of this paper, only the industrial/office model
will be discussed. The specification and testing of
the residential model was undertaken in a similar
manner.
The industrial/office project model was specified
as 13 equations, 5 of which are simultaneous and the
remaining 7 are recursive. The path diagram of the
model is shown in Figure 1. The definition of each
variable is shown in Table 1. The theoretical basis
of each path is discussed elsewhere.25
Methodological Issues
Based on certain criteria, the most important
criterion being the minimum size of major project
(see page 1), a sample of twenty case studies of each
major project type was selected. The size of the
sample was limited by available resources (over 7% man-
months was required to collect data for the present
sample). This small sample size created two important
methodological problems.
Degrees of Freedom in First Stage of Two Stage Least
Squares
While one would prefer as large a sample as pos-
sible, the use of a sample of twenty in an ordinary
least squares regression with four or five independent
variables, such as in the seven recursive equations of
our model, is not uncommon. However, in the specifica-
tion of our model there is a simultaneous block of five
equations. In this situation it would be inappropriate
to use ordinary least squares (OLSQ), as such a tech-
nique would produce biased and inconsistent estimates.
Accordingly, we made use of the two stage least squares
(2SLS) technique to estimate the structural coeffi-
cients in the five simultaneous equations. As the
first stage of 2SLS estimates the right hand side endo-
genous variables with all the exogenous variables in
the simultaneous block, the degrees of freedom in the
first stage of the 2SLS in our analysis is zero.
(There are twenty exogenous variables).
Our approach to solving this problem was to use
stepwise OLSQ to delete those instrumental variables
that were insignificant in the first stage of the 2SLS.
First, one instrumental variable for each endogenous
variable was identified as having the strongest a_
priori causal influence. These five variables, in ad-
dition to the major project size, were entered in the
first step of a stepwise OLSQ predicting each endoge-
nous variable. (This was done to insure identifica-
tion). Then the others were allowed to enter in the
order of their significance of their added partial con-
tributions. The seven instrumental that overall were
of least significance were deleted. This left 6 de-
grees of freedom (20-1-13=6) for the first stage of the
2SLS.
Stability of Estimated Coefficients
In order for path analysis to be of use the re-
sulting estimates should be stable. They will be of
little use if they change radically depending on sample
observations. In most applications of path analysis,
this is achieved by using large samples and reliable
measuring instruments. In our application, with a sam-
ple of twenty, the stability of the estimates must be
explicitly addressed.
Our approach to this problem involved the use of
the statistical techniques of "Jack-Knife" Instead of
running one regression using twenty observations, 20
(MINCRJ
Figure 1. ORIGINAL SPECIFICATION OF MODEL
693
-------
Table 1
MODEL VARIABLES AND DEFINITIONS
1ES = number of housing units in area of influence in
1970 (excluding major project).
COMM = commercial land use in area of influence in 1970
in 1,000 square feet.
OFFICE office land use in area of influence (exclu-
ding major project) in 1970 in 1,000 sq. feet.
>1ANF manufacturing land use in area of influence (ex-
cluding major project) in 1970 in 1,000 square
feet.
WHOLE wholesale/warehouse land use in area of in-
fluence in 1970 in 1,000 square feet.
HOTEL Hotel and motel land use in area of influence
in 1970 in 1,000 square feet.
HOSPTL hospital, etc. land use in area of influence
in 1970 in 1,000 square feet.
CULTUR cultural land use in area of influence in 1970
in 1,000 square feet.
CHURCH religious land use in area of influence in
1970 in 1,000 square feet.
ED = public educational land use in area of influence
in 1970 in 1,000 square feet.
REC = active outdoor recreational land use in area of
influence.
HWLM highway lane miles in area of influence in 1970.
DU-ACRE dwelling units per acre in area of influence
in 1960.
VACACR = percent vacant developable acreage in area of
influence in year (t + 0)
VACHSG percent vacant housing in area of influence
in 1960.
HWYINT highway interchanges in area of influence in
year (t + 5)
MINCC median income of families and individuals in
area of influence relative to U.S. median
income in 1960.
INCMP variable indicating the median income level of
major project compared to surrounding community
in year (t + 2}
OFFVAC percent office buildings vacant in metropoli-
tan area in year (t + 0)
OFFACR office employment per acre in area of influenc
in year (t + o)
DISCED -> distance from center of major project to CBD
in year (t + 0)
ENERGY cost factor for electricity ($/1500 KWH) for
commercial users in the metropolitan area in
year (t + 0) divided by the average U.S.
commercial rate in 1960.
RRMI railroad mileage in area of influence in year
(t + 0)
WWEA warehouse and wholesale employment per acre in
area of influence in year (t + 0)
EMPACR total employment per acre in area of influ-
ence in year (t + 0)
NONHSE nonhousehold population per acre in area of
influence in 1960.
MPKIDS school-age children per dwelling unit in major
project in year (t + 2)
ENRACR public school enrollment per acre in area of
influence in 1960.
MANACR manufacturing employment per acre in area of
influence in year (t + 0)
DELPOP growth factor for total regional population
between 1960 and 1970 (county data)
DELEMP growth factor for total regional employment
between 1960 and 1970 (county data)
MINCR = median income of the region in year (t + 0)
relative to the median U.S. income in 1960.
MAJOR PROJECT = number of employees in major project
in 1970, 1968, t + 2.
AUTO = automobile drivers per acre in country in 1960.
regressions are run each containing nineteen observa-
tions. The path coefficients are then examined for
stability. In our analysis, after trimming the model
to a final set of path coefficients, each equation was
subjected to a jack-knife. The brevity of this paper
does not permit the presentation of this analysis. It
is discussed elsewhere."
Path Analysis of Model
Our approach to path analysis was to develop the
most elaborate system possible, given the sample size,
and then after estimating the involved path coeffi-
cients, refine or trim the system by dropping those
paths that have coefficients that are "close to zero".
The original model was thus refined or trimmed and
thereby made more parsimonious.
Specifically, vie retained a specific path if
its t value exceeded unity in absolute value. This
guaranteed that the adjusted R2 is larger with its in-
clusion that without its inclusion for OLSQ.)
- its beta weight exceeded .1 in absolute value. This
was judged to reflect a substantially meaningful rela-
tion, and
- it was deemed a priori to be of substantive impor-
tance and its sign (i.e., the sign of the coefficient
b) was of the expected direction.
It is important to note that our trimming procedure was
an interactive process; at each step the remaining path
coefficients were examined to see how the deletion of
one path coefficient affected our ability to reproduce
the original observed correlations. This is particular-
ly critical in 2SLS, where' the deletion of one exoge-
nous variable in one equation can effect another equa-
tion because of its deletion as an instrumental variable.
Following the above procedure, the original path
diagram was trimmed to model shown in Figure 2. The
number on each path is the path coefficient; the number
inside the box of an endogenous variable is the R? of
the equation predicting that variable.
Summary of Results
In general, the trimmed path model is a success-
ful test of our theory of induced developments. The
size of the major project in time t+10 was specified as
an exogenous variable in the residential.commercial,
office, manufacturing, highway facilities, hotel/motel,
and hospital equations. Though it was trimmed from the
hospital and highway facilities equations, its causal
influence in the remaining equations was substantial.
Additionally, the causal analysis of the model
leads us to be optomistic about the model's subsequent
calibration. Pending the calibration and a possible
validation study, our preliminary assessment is that
the static cross-sectional modeling approach can be
used to predict the induced land uses from the construc-
tion and operation of a major land use development.
References
1. Thomas McCurdy,"Request for Proposal: Growth Effects
of Major Land Use Projects"(RFP #DU-75-C181,Dec.23,1974).
2. 40 Federal Register 49048 (October 20, 1975),
40 Federal Register 41941 (September 9, 1975),
40 federal Register 25814 (June 19, 1975),
40 rederal Register 23746 (June 2, 1975),
40 Federal Register 18726 (April 29, 1975),
39 Federal Register 16343 (May 8, 1974),
•38 Federal Register 15834 (June 18, 1973),
38 Federal Register 9599 (April 18, 1973), and
38 Federal Register 6279 (March 8, 1973).
3. U.S. Environmental Protection Agency. Review of Fed-
eral Actions Impacting the Environment. Washington oTC:
LPA, 1975 (Manual TN2/3-1-75).
694
-------
Office of Federal Activities, U.S. Environmental Pro-
tection Agency. Guidelines for Review of Environmental
Impact Statement's; Volume I; Highway Projects. Washing-
tbn.D.C.: EPA, 1973. (Volume II on Airports and Volume
III on Steam Channelization will be published shortly.)
39 Federal Register 16186 (May 7, 1974).
Office of Air Quality Planning andStandards, U.S.
EPA. Guidelines for Preparing Environmental Impact
Statements. Research Triangle Park, N.C.: OAQPS.May 1975.
$. 40 Federal Register 28064 (July 3, 1975),
39 Federal Register450T4 (December 30, 1974),
39 Federal RegTster 25292 (July 9, 1974),
39 Federal Register 7270 (February 25, 1974), and
38 Federal Register 15834 (June 18, 1973).
40 Federal Register 25004
39 Federal Register 42510
39 Federal Register 31000
June 12, 1975),
December 5, 1974),
August 27, 1974),
38 Federal Register 18986 (July 16, 1973), and
37 Federal Register 23836 (November 9, 1972).
6. Eugene J. Meenan. The Theory and Method of Political
Analysis. Homewood, 111.: The Dorsey Press, 1965.
7. Ernest Greenwood, "The Relationship of Science to
the Practice Professions," Journal of the American In-
stitute of Planners (1958) 28: 223-232.
8. May Brodbeck. Readings in the Philosophy of the So-
cial Sciences. New York: The Macmillan Company, 1968.
9. Abraham Kaplan. The Conduct of Inquiry. San Fran-
cisco: Chandler Publishing Company, 1964.
10. Karl Popper. The Logic of Scientific Discovery.
New York: Harper and Row Publishers, 1959.
11. Thomas McCurdy and Frank Benesh, "A Causal Analysis
of Induced Development" (in preparation).
12. Ira Lowry. A Model of Metropolis. Santa Monica,
Calif.: The RAND Corporation, 1964 (RM-4035-R6).
13. Jay Forrester. Urban Dynamics. Cambridge, Mass.:
The MIT Press, 1969.
14. Donald Hill,"A Growth Allocation Model for the Bos-
ton Region" Journal of the American Institute of Plan-
ners (1965) 31: This is the EMPIRIC model.
15. D.R. Seidman. The Construction of an Urban Growth
Model. Philadelphia: Delaware Valley Regional Planning
Commission, 1969. This is the Penn-Jersey model.
16. Center for Real Estate and Urban Economics. Jobs,
People, and Land:Bay Area Simulation Study.Berkeley:
U. of CA.,1968(Special Rpt. #6).This is the BASS model.
17. James C. Ohls & Peter Hutchinson,"Models in Urban
Developmenf'pp.165-200 in: Saul I. Gass & Roger L. Sis-
son (ed s.). A_GjjJKJe_Jx^1odjl_s_jjT_G^)y^
Operations. Potomac,Md.: Sauger Books, 1975.
18. Office of Air Quality Planning & Standards.Guide-
lines for Air Quality Maintenance Planning & Analysis;
Vol. 4: Land Use & Transportation Considerations. Re-
search Triangle Park, N.C.: U.S. EPA,1974 (EPA-450'4-74-004).
1.9. David R. Heise.Casual Analysis. Chapel Hill.N.C.:
Unpublished manuscript, 1974.
20. Hubert M. Blalock.Jr. Theory Construction. Engle-
wood Cliffs, N.J.: Prentice-Hall, 1969.
21. William S. Meisel & David C. Coll ins,"Repro-Model-
ing:An Approach to Efficient Model Utilization & Inter-
pretation ','^EEE_Jrj[nj>aj:1nj)£s_p^
netics (1973) 3:349-358.
22. Ralph D'Agostino,"Path Analysis,"Boston :Unpub'd, 1975.
23. Norman Nie et al. Statistical Package for the So-
cial Sciences, McGraw Hill, 2nd ed., 1975.
24. Thomas E. Baldwin and Allen S. Kennedy. "The Fea-
sibility of Predicting Point Source Emissions Using In-
dustrial Land Use Variables: A Path Analysis;" 67th An-
nual Meeting of the Air Pollution Control Association,
Denver, Colorado: June 1974 (Paper 74-145).
25. Frank Benesh, Dr. Ralph D'Agostino, Peter Guldberg.
"Growth Effects of Major Land Use Projects. Volume I:
Specification and Causal Analysis of Model." Prepared
by Wai den Research for Strategies and Air Standards
Division, EPA, Durham, North Carolina, April 1976.
Figure 2. TRIMMED MODEL WITH PATH COEFFICIENTS
v_y
695
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PREDICTION OF PHYTOPLANKTON PRODUCTIVITY IN LAKES
V. W. Lambou, L. R. Williams, S. C. Hern, R. W. Thomas, J. D. Bliss
Water and Land Quality Branch, Monitoring Operations Division
Environmental Monitoring and Support Laboratory
U.S. Environmental Protection Agency
Las Vegas, Nevada
SUMMARY
This study presents relationships between phyto-
plankton productivity as measured by yearly mean
chlorophyll a levels, and ambient water quality and
hydrologic measurements. Among the nutrients examined,
phosphorus forms were most highly correlated with
chlorophyll a levels. The effects of such factors as
retention time, primary nutrient limitation, strati-
fication, and macrophyte dominance upon productivity
responses are evaluated. Additional parameters re-
lated to productivity include turbidity, Secchi disc,
nitrogen to phosphorus ratio, pH, total alkalinity,
and forms of inorganic nitrogen. Discussions of the
factors affecting phytoplankton productivity and the
application of the limiting nutrient concept are in-
cluded.
INTRODUCTION
The National Eutrophication Survey was initiated
in 1972 in response to an Administration commitment
to investigate the nationwide threat of accelerated
eutrophication to freshwater lakes and reservoirs.
Consistent with the Survey objectives to develop
information on nutrient sources and impact on fresh-
water lakes, we are examining relationships between
ambient nutrient concentrations and existing lake
conditions.
The purpose of this report is to help to establish
lake classes and elucidate the relationships between
ambient nutrients and lake water quality by lake type.
The data were collected in 1972 from the New England
States, New York, Michigan, Wisconsin, and Minnesota.
Only lakes sampled during three seasonal sampling
rounds are included.
MATERIALS AND METHODS
Lake Selection: Selection of lakes and reservoirs in-
cluded in the Survey in 1972 was limited to lakes 40
hectares or more in surface area, with mean hydraulic
retention times of at least 30 days, and impacted by
municipal sewage treatment plant (MSTP) effluent either
directly or by discharge to an inlet tributary within
40 kilometers (km) of the lake. Specific selection cri-
teria were waived for lakes of special State interest.
Lake Sampling: Sampling was accomplished by two teams,
each consisting of a limnologist, pilot, and sampling
technician, operating from pontoon-equipped helicopters.
With few exceptions, each lake was sampled under spring,
summer, and fall conditions. Sampling site locations
were chosen to define the character of the lake water
as a whole and to investigate visible or known problem
areas, e.g., algal blooms, sediment or effluent plumes.
The number of sites was limited by the survey nature of
the program and varied in accordance with lake size,
morphological and hydrological complexity, and practi-
cal considerations of time, flight range, and weather.
At each sampling depth, water samples were collected for
nutrient, alkalinity, pH, conductivity, and dissolved
oxygen determinations. Contact sensor packages were used
to measure depth, conductivity, turbidity, pH, dissolved
oxygen, and temperature. Fluorometric chlorophyll a
(chla) analyses were performed at the end of each day in
the mobile laboratory. Nutrients and alkalinity were
determined by automated adaptations of procedures
described in "Methods for Chemical Analysis of Water
and Wastes' at the Las Vegas laboratory. Details
of Survey methods are presented elsewhere. >^
Data Management: Data collected were stored in STORE!
and manipulated, as prescribed by Bliss, Friedland, and
Hodsen.^ Basic calculations for parameters measured in
sampled lakes were performed in such a way to give
equal weight to: each depth sampled at a station;
each sampling station sampled on an individual lake
during a sampling round; and each sampling round
on an individual lake during a sampling year.
Mean parameter values for each sampling station
were calculated as follows:
D
_
Parj = I Par^/D,
(1)
_
where Parj = mean value for a parameter at the j^h sam-
pling station during a sampling round, Par£ = value for
the £*" depth, and D = the number of depths for which a
parameter was measured at the j*™ sampling station dur-
ing a sampling round. Mean parameter values for each
sampling round were calculated as follows :
== S _
Parfe = I, Par-/S, (2)
= th
where Par^- = mean value for the k sampling round on a
given lake, and S = number of sampling sites. Mean lake
parameter values for a given sampling year were calcu-
lated as follows:
_s 3 ===
Par = I Par7,/3, (3)
k=l ^
where Par = mean parameter value for a given sampling
year. Lake parameter values were calculated only when
values were available for the first, second, and third
sampling rounds during a given sampling year from a
lake. Formulas 1, 2, and 3 were used to determine
parameter values for total phosphorus (TP) , dissolved
phosphorus (DP) , ammonia-N (NH) , nitrite-nitrate-N (NO) ,
ammonia-nitrite-nitrate-N (IN), and total alkalinity
(AL) , all expressed in milligrams per liter (mg/liter) ,
temperature in degrees Celsius (°C) (T) , turbidity in
percent transmission (TB) , pH (PH) , Secchi disc in
inches (SD) , and hydraulic retention time in days (RT) .
The ratio of IN/DP (N/P) for each sampling station
was calculated as follows :
= IN/DP,
(4)
however, at the formula 1 level a dissolved phosphorus
value was deleted if either nitrogen complement was
missing. Round and yearly values were calculated using
formulas 2 and 3.
Unlike the above parameters where measurements
were made at various depths, only one chla measurement
was made at any individual sampling station during
a sampling round. Therefore,
chla.,- = chla
u
(5)
where chlaj = the mean chla concentration in micrograms
per liter (pg/liter) for the jth sampling station
during a sampling round, and chla = the chla concentra-
696
-------
tion in yg/liter for an integrated water sample from
the surface to 4.6 meters (m) or to a point just off
the bottom when the depth was less than 4.6m.
DATA LIMITATIONS
The primary selection criterion for the 1972 Sur-
vey lakes was direct or indirect receipt of MSTP efflu-
ent (151 out of 191 lakes), resulting in a list of
obvious bias. Fortunately, special interest lakes,
representing a broad range of water quality, were also
included which provided some trophic balance to the
list. Although lakes selected were not necessarily rep-
resentative of average conditions existing in the study
area, the relationships observed between ambient nutri-
ents and lake water quality should not be biased.
A number of factors required for a complete nutri-
ent budget analysis have not been evaluated thus far.
Among these factors are the following: 1) groundwater
contributions were not considered; 2) macrophytes were
not measured quantitatively; 3) nitrogen-fixation was
not estimated; 4) coincidence of sampling with "turn-
over" or macrophyte nutrient release periods was not
sufficiently precise to make accurate estimates of
nutrient maxima; 5) no estimates of sediment load,
sediment-water nutrient exchange or sediment binding
capacity were made; and 6) sampling frequency was
generally inadequate to determine dynamic changes in
nutrient limitation, where present; however, seasonal
shifts could be determined.
LIMITING NUTRIENTS
Nitrogen and phosphorus are frequently mentioned as
the nutrients most likely to limit growth of plants. The
concept of a limiting nutrient, as related to Leibig's
Law of the Minimum, is that some nutrient, least avail-
able relative to the growth requirements of a given
organism, imposes primary limitation on the growth of
that organism.
The Algal Assay Procedure Bottle Test5 utilizes the
response of the green alga Selenastrvm oapvioovnutum to
nutrient spikes, usually nitrogen and phosphorus, alone
and in concert, to determine the growth-limiting nutri-
ent. The assumption is that if indeed a specific nutri-
ent is limiting the growth of the algal culture,
addition of that nutrient will result in a positive
growth response. If the addition of the "limiting nu-
trient" Is large enough, growth will proceed until
another takes over the controlling role, now being the
least available relative to the growth needs of the
culture. Various estimates have been proposed as to
what constitutes that ratio of nitrogen to phosphorus at
which the addition of either results in the limitation
by the other. Such estimates have been reported as low
as 5/1 and as high as 30/1 or more, by weight, generally
centering about 12/1 to 14/1. These are in reasonable
agreement with theoretical needs based upon stoichio-
metric equations of algal constituents.
Frequency distributions of the ratios of inorganic
to orthophosphorus (N/OP) were determined from chemis-
tries taken on fall samples just prior to algal ass-
say. 2>3 Among the nitrogen-limited (N-limited) lakes
(by algal assay) the N/OP values were distributed as
follows: <10 = 60 lakes; 10 to 14 = 10; and >14 = 1.
For the phosphorus-limited (P-limited) lake group the
values were: <10 = 3 lakes; 10 to 14 = 7; and >14 59.
Note the overlap of P- and N-limited lakes in the zone
extending from N/OP = 9 to 15. Within this range fell
several additional lakes which evidenced "co-limitation"
on assay and were included in neither distribution. In
these samples no growth response was noted with the ad-
dition of either nitrogen or phosphorus, but response
was dramatic to the simultaneous addition of both.
We divided the lakes sampled into P-limited
(N/P>14), transition (KKN/PXL4), and N-limited (N/P<10)
groups based upon the yearly mean N/P observed in the
lake. The frequency distribution of N/P values was:
<10 79 lakes; 10 to 14 = 44; and >14 = 69. While
admittedly arbitrary, the suggested division represents
a convenient means of comparing groups of lakes presum-
ably representing "largely nitrogen-limited" and
"largely phosphorus-limited" populations, and a third
group, representing a buffer between the first two
groups. This group contains a number of lakes whose
N/P ratios, by sampling round, suggest seasonal shifts
from one dominant limiting nutrient to the other across
a transition zone in which pronounced interaction is
likely.
The ranges selected are not suggested to possess
sharp cutoffs at which shifts in limiting nutrient oc-
cur. Preliminary analyses of Survey algal assay data
suggest that any such sharp cutoff is unlikely with
laboratory monocultures, much less with mixed natural
populations. Rather the N- and P-limited groups rep-
resent "tails" toward which the influence of the
secondary interactant is progressively reduced. Also,
as N/P ratios progressively deviate from the buffer
zone in either direction, the influence of the secondary
interactant is continually reduced. Chiaudani and Vighi'
present data which suggest a range of N/P ratios about
four to five units wide within which neither nitrogen
nor phosphorus effects are independent. However, they
found no response to phosphorus addition below N/P = 10
with Selenastman.
While the limiting nutrient concept has some
utility in allowing prediction of the potential growth
limits of laboratory monocultures, its extrapolation
into natural system studies should be approached warily.
A number of enrichment studies have found the effects of
phosphorus and nitrogen to be interdependent, >''•'-'
modified by the presence of trace organic materials in
the waters, and dependent upon previous algal culture
exposure, i.e., prior luxury uptake of nitrogen or
phosphorus.
It is not unlikely that a mixed natural phytoplank-
ton population would contain elements with a range of
optimal growth requirements and predisposing nutritional
status. Addition of either nitrogen or phosphorus could
potentially evoke a net increase in phytoplankton growth,
especially in those cases in which the ambient N/P ratio
is intermediate between the optimal growth requirements
of the various phytoplankton elements. The presence of
organic materials may increase nutrient assimilation
in some members of the community^,12 or Inhibit it in
others.13 Conditions may exist, over a range of N/P
values, favoring response to the addition of either
phosphorus or nitrogen and representing essentially
"net co-limitation." Different species within a
community may be limited by different nutrients
simultaneously.*-^ A theoretical basis for simultane-
ous co-regulation of the specific growth rate of a
single population by multiple nutrient is presented by
Sykes.l5 Verduin^ proposes the use of the Baule-
Mitscherlich equation, with slight modification, to
predict yield as a product of the levels of interacting
nutrients. The goodness-of-fit of the "Verduin model"
is presently being tested with the Survey data base;
the results will be reported in the near future.
Although phosphorus and nitrogen-are considered the
most important limiting nutrients in freshwaters^ and
the supply of Inorganic carbon and total carbonate is in
excess in most natural waters'-'^' the possibility of at
least transient carbon limitation, under highly en-
riched conditions, should not be ignored.1° It should
be noted that the Algal Assay Procedure Bottle Test,
without modification, does not detect carbon limitation.
697
-------
Table 1. Product moment coefficients of correlation (r) of parameters affecting productivity with yearly
mean lake chla concentrations. All data were converted to base 10 logarithmic expressions.
All lakes with:
Lakes with RT£l4 days and are:
Par
No. of
Lakes
TP
DP
TP-DP
NH
NO
IN
AL
PH
TP(AL)
T
RT
N/P
SDl
TB1
All
Lakes
191
0.74*
0.66*
0.81*
0.48*
0.26*
0.42*
0.37*
0.49*
0.71*
0.30*
0.04
-0.51*
-0.74*
(178)
-0.51*
(186)
RT
<14 Days
60
0.35*
0.28§
0.50*
0.11
0.24t
0.20
0.21
0.285
0.40*
0.27§
0.40*
-0.21
-0.40*
(54)
-0.12
(59)
RT
>14 Days
131
0.84*
0.77*
0.89*
0.59*
0.33*
0.53*
0.44*
0.58*
0.78*
0.33*
-0.02
-0.18§
-0.84*
(124)
-0.56*
(127)
P-
Limited
54
0.91*
0.85*
0.92*
0.76*
0.51*
0.71*
0.42*
0.48*
0.80*
0.325
-0.15
-0.33t
-0.87*
(52)
-0.51*
(53)
Transition
24
0.84*
0.64*
0.86*
0.62*
0.49§
0.62*
0.27
0.21
0.70*
0.51*
-0.09
0.04
-0.73*
(23)
-0.485
(24)
N-
Limited
53
0.72*
0.65*
0.79*
0.23t
0.25t
0.25t
0.345
0.65*
0.66*
0.30§
0.21
-0.67*
-0.75*
(49)
-0.63*
(50)
Stratified
80
0.80*
0.72*
0.87*
0.65*
0.17
0.51*
0.48*
0.53*
0.73*
0.23t
-0.18t
-0.55*
-0.81*
(80)
-0.15
(80)
Non-
Stratified
51
0.80*
0.72*
0.85*
0.48*
0.45*
0.51*
0.43*
0.54*
0.77*
0.23t
0.24t
-0.41*
-0.77*
(44)
-0.67*
(47)
Phyto-
plankton
Dominated
66
0.88*
0.82*
0.90*
0.68*
0.38*
0.62*
0.58*
0.68*
0.84*
0.24§
0.08
-0.64*
-0.86*
(63)
-0.55*
(64)
Macro-
phyte
Dominated
65
0.78*
0.67*
0.87*
0.41*
0.28§
0.35*
0.16
0.38*
0.65*
0.48*
-0.17
-0.42*
-0.76*
(61)
-0.60*
(63)
iNumber of lakes given in parentheses.
*r significant at 0.01 level.
FACTORS AFFECTING PRODUCTIVITY
Chlorophyll a concentration (a measure of phtyo-
plankton biomass) was used as an index of productivity
of the lakes sampled. Dillon and Rieler, " Jones and
Bachmann,20 and Bachmann and Jones,2^ and others have
presented the strong relationship which exists between
summer chla levels and ambient TP concentrations meas-
ured at spring turnover, under summer conditions, or
estimated from total inputs. The Dillon and Rigler19
study lakes are Canadian shield lakes which undergo
summer thermal stratification. Jones and Bachmann's^O
study lakes are mostly wind-driven systems in Iowa in
which summer stratification, if any, is transitory.
Regression equations for the two studies are quite
similar, and each has a high coefficient of correlation.
The summer chla/TP relationship (r = 0.95) presented
by Jones and Bachmann is derived from a composite of
their data and literature-cited data from 143 lakes
covering a broad range of trophic states. The regression
equation for the composite data is:
log chla = -1.09 + 1.46 log TP (mg/m3). (6)
If the phosphorus units are changed to mg/liter (our
units), the comparable regression equation is:
log chla = 3.29 + 1.46 log TP. (7)
The regression equation for all 191 Survey lakes is:
log chla = 1.78 + 0.57 log TP (r = 0.74) (8)
Our equation yields lower chla values per unit TP than
the Jones and Bachmann equation given. The most likely
explanation for this discrepancy is that the averaged
seasonal chla values used in generating our response
equations underestimate the summer chla maxima. To
clarify the relationships of factors affecting produc-
tivity in the lakes sampled, a series of regressions was
computed. The effects of phosphorus, nitrogen, total
alkalinity, pH, light penetration, hydraulic retention
time, nitrogen to phosphorus ratio, stratification, and
phytoplankton versus macrophyte lake-domination were
considered.
§r significant at 0.05 level.
tr significant at 0.10 level.
Retention times of the lakes were calculated using
flow data provided by the U.S. Geological Survey (USGS)
and known or estimated lake volumes. Where USGS flow
data were not available, estimates of retention time
were obtained from local or State agents familiar with
the lake. Stratification was established using depth/
temperature relationships from the Survey data and was
verified or supplemented, where possible, by State per-
sonnel. An attempt was made to restrict "stratified
lakes" to those which maintained a thermocline (minimum
of 1° C change/meter depth) throughout most of the sum-
mer. Lakes exhibiting brief temporary stratification
within the spring or summer periods were included as
non-stratified. Information on phytoplankton- versus
macrophyte-dominance was obtained from field observa-
tions, historical information, and contact with State
and local personnel. Lakes which exhibited extensive
reaches of submerged or floating higher aquatic plants,
with histories of recurrent weed problems, and/or re-
ported to be problem lakes in this regard were consid-
ered "macrophyte-dominated." Otherwise the lakes were
included in the "phytoplankton-dominated" category.
The product moment coefficients of correlation (r)
for the regressions are given in the table. The r values
for all variables in the subpopulation of lakes with
RT<14 are much lower than the corresponding r for lakes
with RT>14, with the exception of RT itself. As the RT
falls below 14, the relationship between chla and
variables weakens as RT is insufficient to reach poten-
tial biomass development. In studies by Payne22 asymp-
totic levels for Selenastrwn, Anabaena, and M-ioroayetis
were generally reached within 14 days after nutrient
enrichment. The correlation of chla with RT is better
in short RT lakes; chla development increases with
time until it plateaus at about 14 days. The predic-
tion of chla for all lakes with RT>14 is:
log chLa = 1.95 + 0.68 log TP (9)
with 71% of the variation in chla being explained by
changes in TP levels (r = 0.84; r2 = 0.71).
698
-------
Chlorophyll a correlations with DP mimic TP correl-
ations but are lower in all subpopulations. Total phos-
phorus is highly correlated (r = 0.98) with DP and the
regression equation is:
TP = 0.03 + 1.17 DP.
(10)
It is not surprising that the highest chla correlations
were with particulate phosphorus (TP-DP), as both are
components of phytoplankton. The prediction equation
for chla for all lakes with RT>14 is:
log chla = 2.36 + 0.75 log (TP-DP).
(11)
The ratio of TP-DP/chla for 184 Survey lakes was
2.0, while Antia et al.,^3 working with marine phyto-
plankton, reported an average ratio of 1.8. The close
agreement between the ratios indicates that TP-DP/chla
ratios are consistent between freshwater and marine com-
munities. High mobility and short turnover times of
phosphorus2^ through and between compartments within
the general "phosphorus pool" make TP a good approxi-
mation of bioavailable phosphorus.
Of the forms of nitrogen examined, NH was found to
be most strongly correlated with mean chla. This posi-
tive correlation is strongest in the P-limited (r =
0.76), declines in the transition (r = 0.62), and is
very weak in the N-limited lakes studied (r = 0.23).
This pattern of decline is also noted with NO and IN.
That the relationships between the dissolved nitro-
gen forms tested and mean chla decline dramatically as
we move from P- to N-limited lakes is somewhat of a
paradox. It is not unreasonable to expect higher cor-
relations between a nutrient and biological response as
that nutrient exerts a greater degree of limitation on
the biological response, e.g., the phosphorus relation-
ship. A possible explanation for this apparent contra-
dication is increased fixation of atmospheric nitrogen
by blue-green algae. The N-limited lakes studied were
generally nutrient rich. An increase in the frequency
of Andbaena or Aphani-zomenon blooms (both nitrogen-
fixers) in association with nutrient enrichment is con-
sistent with general observations in the aquatic litera-
ture. Short RT lakes show very weak relationships
between the nitrogen forms examined and chla. The
relationship with respect to NO does not appreciably
improve in longer RT lakes, but improves substantially
for NH. It should be noted that similar processes often
produce parallel increases in phosphorus and NH within
the hypolimnion.
The relationship of PH to chla was found to be
much stronger in phytoplankton- than in macrophyte-
dominated lakes (r = 0.68 versus r = 0.38). The weak
relationship in the latter group is not unexpected, as
no attempt was made to quantitatively sample macrophytes
or their associated chla. The PH increases with the re-
moval of carbon dioxide ((X>2) by photosynthetic activity.
It should be noted that phytoplankton utilization of C0£
per unit volume (and hence the corresponding PH change)
has been reported to be 10 times as high as macro-
phytes.25 The differences noted in short and long RT
lakes (r = 0.28 versus r = 0.58) suggest that diurnal
C02 changes alone do not explain the PH/chla relation-
ship.
The relationship between AL and chla is, once
again, much stronger in phytoplankton- than macrophyte-
dominated lakes. In general, increased AL and nutrient
enrichment go hand in hand. However, the degree and
nature of macrophyte "dominance" and its effects upon
nutrient reduction (competition with phytoplankton),
shading (submerged versus floating macrophytes), etc.,
result in a broad scatter of chla values and generally
weak relationship.
The two-factor parameter TP(AL) is used to assess
to what degree the "unit response" (chla per unit TP)
is a function of AL levels. Addition of AL did not im-
prove the basic chla/TP relationship; the correlations
were slightly lower throughout the lake groups examined.
Chlorophyll a response as a function of N/P ratio
was found to be much stronger in N- than P-limited or
transition lake groups (r = 0.67 vs. r = 0.33 or r =
0.04). As phosphorus levels increase, the N/P ratio
generally decreases and chl levels increase. This is
consistent with our observation that the N-limited lakes
examined were generally high in phosphorus.
Edmondson26 found a negative hyperbolic relation-
ship between SD and chla concentrations in Lake
Washington. We found SD and TB to be negatively cor-
related with chla. The largest difference between SD
and TB correlations (r -0.81, r = -0.15, respectively)
occurred in the stratified lakes. A likely explanation
is that TB values were averaged through the entire water
column and include a greater percentage of "clear"
waters from below the euphotic or epilimnetic zones in
stratified lakes. The strongest correlation was noted
in non-stratified lakes where TB values represent meas-
urements taken within the effective mixing zone. These
relationships suggest that the bulk of photic zone
turbidity in the stratified lakes sampled was of phyto-
plankton origin.
The correlations for various chemical and physical
parameters, with the exception of NH and NO, are quite
similar in stratified and non-stratified lakes. The NH
correlation with chla is higher in stratified lakes
than in non-stratified lakes; the reverse is true for
NO. A possible explanation for this is that under
reducing conditions, such as hypolimnetic deoxygen-
ation, NH and phosphorus are concomitantly released.
In non-stratified lakes the prevalent inorganic nitro-
gen component is nitrate-N.
Most correlations of chla with chemical and
physical parameters are higher in the phytoplankton-
dominated subpopulation than in the macrophyte-
dominated subpopulation. The contribution of
macrophyte chla was not measured, and no informa-
tion on the relative quantities of submerged versus
floating weeds is available for Survey lakes. Many
submerged aquatics, with little reliance on ambient
nutrient levels in the water, can survive on nutri-
ents absorbed through their root systems. However,
free-floating macrophytes and phytoplankton have
similar ambient nutrient requirements. The predic-
tion equations for all phytoplankton-dominated lakes
with RT>14 are:
log chla = 1.91 + 0.68 log TP, and (12)
log chla = 2.31 + 0.73 log (TP-DP). (13)
STUDIES IN PROGRESS
Other aspects being investigated include the ef-
fects of additional parameters on productivity, the
intercorrelation of parameters affecting productivity,
effects of lake use upon water quality "suitability,"
effects of manifestations of nutrient enrichment on
water use, and prediction of lake condition from
ambient and loading conditions.
LITERATURE CITED
1. U.S. Environmental Protection Agency. 1971.
Methods for chemical analysis of water and wastes.
Analytical Quality Control Laboratory, Cincinnati,
Ohio. 312 p. EPA-625/6-74-003.
699
-------
2. . 1974. National Eutrophication Survey
methods for lakes sampled in 1972. National
Eutrophication Survey Working Paper No. 1.
National Environmental Research Centers, Las
Vegas, Nevada, and Corvallis, Oregon. 40 p.
3. . 1975. National Eutrophication Survey
methods 1973-1976. National Eutrophication
Survey Working Paper No. 175. National Environ-
mental Research Centers, Las Vegas, Nevada, and
Corvallis, Oregon. 91 p.
4. Bliss, J. D., M. J. Friedland, and J. Hodsen.
1975. Statistical manipulation of National
Eutrophication Survey data in STORET. National
Eutrophication Survey Working Paper No. 472.
National Environmental Research Center, Las
Vegas, Nevada. 15 p.
5. U.S. Environmental Protection Agency. 1971.
Algal assay procedure: bottle test. U.S.
Govt. Printing Off.: 1972-795-146/1. Region X.
82 p.
6. Vollenweider, R. A. 1968. Scientific
fundamentals of the eutrophication of lakes
and flowing waters, with particular reference
to nitrogen and phosphorus as factors in
eutrophication. Technical Report to OECD,
Committee for Research Cooperation. 159 p.
7. Chiaudani, G., and M. Vighi. 1974. The N:P
ratio and tests with Selenastmm to predict
eutrophication in lakes. Water Res. 8:1063-1069.
8. Hutchinson, G. E. 1941. Limnological studies
in Connecticut, IV. The mechanisms of inter-
mediary metabolism in stratified lakes. Ecol.
Monogr. 11:21-60.
9. Goldman, C. R., and R. Armstrong. 1969. Primary
productivity studies in Lake Tahoe, California.
Verh. Int. Verein. Theor. Angew. Limnol. 17:49-71.
10. Ketchum, B. H. 1939. The absorption of phos-
phate and nitrate by illuminated cultures of
Nitzsahia alosterium. Amer. J. Bot. 26:399-407.
11. Powers, C. F., D. W. Schults, K. W. Malueg, R. M.
Brice, and M. D. Schuldt. 1972. Algal responses
to nutrient additions in natural waters, II.
Field experiments. In: G. E. Likens (ed.).
Nutrients and eutrophication: the limiting
nutrient controversy. Amer. Soc. Limnol.
Oceanogr., Publ. 1:141-154.
12. Rodhe, W. 1958. The primary production in lakes:
some methods and restrictions of the -^C method.
In: Measurements of primary production in the
sea, rapp. P-V Reun. Cons. Perm. Int. Explor.
Her. 144:122-128.
13. Williams, L. R. 1975. The role of heteroin-
hibition in the development of Anabaena
flos-aquae waterblooms. In: Proc. of the Bio-
stimulation Nutrient Assessment Workshop. 1973.
Corvallis, Oregon.
14. Fitzgerald, B. P. 1964. Detection of limiting
or surplus nutrients in algae. Progress report
to NIH, 1961-1964 project. Working Paper
No. 297. 48 p.
15. Sykes, R. M. 1974. Theory of multiple limiting
nutrients. J. Water Pollut. Control Fed. 46(10):
2387-2392.
16.
17.
18.
Verduin, J. 1964. Principles of primary pro-
ductivity: phothosynthesis under completely
natural conditions. In: D. F. Jackson (ed.).
Algae and man. Plenum Press, New York.
p. 221-237.
Ketchum, B. H.
phytoplankton.
5:55-74.
1954. Mineral nutrition of
Amer. Rev. Plant Physiol.
Maloney, T. F., W. E. Miller, and T. Shiroyama.
1972. Algal response to nutrient additions in
natural waters. In: G. E. Likens (ed.).
Nutrients and eutrophication: the limiting
nutrient controversy. Amer. Soc. Limnol.
Oceanogr. 1:134-140.
19. Dillon, D. J., and F. H. Rigler. 1974. The
phosphorus-chlorophyll relationship in lakes.
Limnol. and Oceanogr. 19:767-773.
20. Jones, J. R., and R. W. Bachmann. In press.
Prediction of phosphorus and chlorophyll levels
in lakes. J. Water Pollut. Control Fed.
21. Bachmann, R. W., and J. R. Jones. 1974.
Phosphorus inputs and algal blooms in lakes.
Iowa State J. Res. No. 49(2):155-160.
22. Payne, A. G. 1973. Response of the three test
algae of the algal assay procedure bottle test.
Presented at the 36th Annual Meeting of the
American Society of Limnology and Oceanography.
23. Antia, N. J., C. D. McAllister, T. R. Parsons,
K. Stephens, and J. D. H. Strickland. 1963.
Further measurements of primary production using
a large-volume plastic sphere. Limnol. Oceanogr.
8(2):166.
24. Lean, D. R. S. 1973. Movements of phosphorus
between its biologically important forms in lake
water. J. Fish. Res. Bd. Canada 30(10):1525-
1536.
25. Verduin, J. 1953. A table of photosynthetic
rates under optimal, near natural conditions.
Amer. J. Bot. 40(9):675-679.
26. Edmondson, W. T. 1970. Phosphorus, nitrogen
and algae In Lake Washington after diversion of
sewage. Science 169:690-691.
700
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APPLICATIONS OF THE SINGLE SOURCE (CRSTER) MODEL TO POWER PLANTS: A SUMMARY
Joseph A. Tikvart*
Connally E. Mears
Source Receptor Analysis Branch
Office of Air Quality Planning and Standards
U.S. Environmental Protection Agency
Research Triangle Park, N.C.
*0n Assignment from the National Oceanic
and Atmospheric Administration (NOAA)
For the last three years the Environmental Pro-
tection Agency has conducted a series of atmospheric
dispersion model studies of power plants. These
studies have considered the impact of approximately
700 utility power plants whose generating capacity is
25 megawatts or greater. Included in these studies
are (1) dispersion model estimates of S0? concentra-
tions downwind from each power plant, (2) validation
of the Single Source Model with data for several typi-
cal power plants and (3) a sensitivity analysis of
this model. The results of these studies have been
used effectively in a number of energy/environmental
policy considerations. This paper summarizes the
findings of the various studies.
Introduction
Shortages in the availability of low-sulfur fossil
fuels have been given national prominence. These
shortages are particularly significant to utility
power plants for two reasons: (1) power plants typi-
cally use large quantities of fossil fuels and (2)
many of the State Implementation Plans (SIPs) require
severe reductions in sulfur dioxide emissions from
power plants which burn fossil fuels. The shortage of
low-sulfur fuel necessitates the elimination of unduly
stringent SIP control regulations, where this can be
done without endangering air quality standards. The
fuel shortage has also led to legislation which em-
powers the Federal Energy Administration to require
that specific power plants switch from oil or gas to
coal. This switch to coal, however, cannot be allowed
to result in a threat to air quality standards. Fur-
thermore, to meet the Clean Air Act requirement for
.attainment and maintenance of acceptable air quality,
it may be necessary to revise the SIPs for selected
source categories, including power plants. The power
plant studies summarized in this paper support actions
like those noted above.
Estimates of the air quality impact caused by
power plants are major components of these studies. A
dispersion model is a commonly used technique for re-
lating pollutant emissions to ambient air quality. It
is a mathematical description of pollutant transport,
dispersion,and transformation processes that occur in
the atmosphere. The Single Source (CRSTER) Model is
the primary dispersion model applied in all the power
plant studies discussed in this summary paper.
Due to severe time constraints and the fact that
models like the Single Source Model are widely applied
and considered state-of-the-art, the accuracy of this
model was not analyzed in the initial phase of the
power plant studies. However, some analyses of the
Single Source Model have been recently completed and
others are continuing. These include validation
studies, sensitivity analysis and model improvement.
Following sections of this paper discuss (1) the
Single Source Model, (2) power plant studies in which
it is applied, (3) evaluation of the model through
validation and a sensitivity analysis, and (4) appli-
cations to energy/environmental policy considerations.
Single Source (CRSTER) MODEL
The Single Source (CRSTER) Model is a Gaussian
plume model. It is based on the dispersion coeffi-
cients and equations described by Turner and on the
2
plume rise equations described by Briggs . The model
is essentially the same as that discussed by Hrenko
et al . It is designed to estimate concentrations
for averaging times of 1 hour, 24 hours, and 1 year
due to sources at a single location. The concentra-
tions are estimated for a circular array of receptor
sites which are located so as to approximate the
downwind distances at which the highest concentra-
tions are likely to occur.
The model estimates concentrations for each hour
of a year, based on wind direction (in increments of
10 degrees), wind speed, Pasquill stability class,
and mixing height. Meteorological surface data for
1964 are frequently used in the power plant studies,
although, with the proper data, any year could be
used. The reasons for the routine use of 1964 mete-
orological data are (1) data from earlier years do not
have an adequate resolution of wind direction, and
(2) data from subsequent years are not readily avail-
able on an hourly basis. Mixing height data are from
the upper air observations made at selected National
Weather Service stations. Hourly mixing heights are
estimated within the model by use of an objective
interpolation scheme. Decay of the pollutant between
source and receptor is ignored.
To simulate the effect of elevated terrain in
the vicinity of plant sites, a terrain adjustment
procedure is used. This procedure decreases the
effective plume height by an amount equal to the
difference in elevation between the plant site and
the specific receptor site. The model then uses the
adjusted plume height in estimating concentrations at
that receptor. In those cases where terrain features
are found to be greater than the effective plume
height of the plant, the Single Source Model is not
apolied.
701
-------
Power Plant Studies
Purpose and Limitations
The power plant studies have considered the
impact of approximately 700 utility power plants whose
generating capacity is 25 megawatts or greater. The
studies may be divided into three parts. These are
analyses for (1) the feasibility of compliance exten-
sions in 51 selected Air Quality Control Regions
(AQCRs), (2) the feasibility of oil-to-coal conversions
at selected power plants and (3) the general impact of
power plants on ambient S02 concentrations in 128
AQCRs. In all cases the studies are primarily con-
cerned with estimates of the maximum 24-hour concen-
trations of S0?. This averaging time and this
pollutant are the critical ones for which power plants
must meet primary National Ambient Air Quality
Standards (NAAQS). The second study is the only one
which considers particulate concentrations. Also, in
those cases where it is estimated that neighboring
power plants could contribute concentrations which add
to those caused by the plant under consideration, an
interaction analysis is performed.
All source data used in the power plant studies
are taken from the Federal Power Commission (FPC Form
67) for base years of 1971 or 1972. In those cases
where emissions are projected to 1975, appropriate
A
data are taken from "Steam Electric Plant Factors" .
Emissions data are based on average monthly oper-
ations for each month of the year; such monthly data
are the limit of detail routinely available from the
FPC. A power plant could quite possibly operate at
near-maximum rated capacity for 24 hours, which
would not be apparent from the monthly data. If
these operations were coincident with days of poor
dispersion conditions, the estimated maximum concen-
trations could be significantly low. Thus, two sets
of emission conditions are routinely considered. One
is the nominal load case in which average hourly
emission rates are used; they are assumed to be con-
stant, except for variations by month. The other is
the maximum load case where emissions and plume rise
are based on the plant continuously operating at 95
percent of rated capacity. Both sets of emissions
data are considered and the one which results in the
highest estimated concentrations is used.
It should be noted that any use of these studies
must recognize the inherent limitations resulting from
the data and procedures used in the modeling effort.
Before final judgment on the control of specific
plants is made, other factors, not addressed in these
studies, should be considered. These include: the
impact of other sources in the area, projected growth
in the area, measured air quality data, known or sus-
pected downdraft or fumigation problems, unique nearby
terrain features, nearby land use patterns and popu-
lation distributions, more specific operational data
for the plant, impact of new units, specific meteoro-
logical studies for the area, and additional studies
or findings by other investigators.
Compliance Extension Studies
In 1972 a study by EPA on the aggregate demand
created by the SIPs for low-sulfur coal was conducted.
This study indicated a nationwide potential deficit of
about 100 million tons/year of such coal by 1975.
The deficit was considered most acute in 12 states
with high coal consumption rates. One means to alle-
viate the deficit would be to selectively reduce the
requirements for low-sulfur coal in those cases where
a higher sulfur coal could be used without endangering
the NMQS.
An initial modeling study of S0_ emissions in
several AQCRs had been conducted. This study showed
that some of the large power plants could be temporar-
ily allowed to burn coal at 1970 sulfur levels with-
out threatening the 24-hour NAAQS. Based on the
results of this study, it was decided to consider
selected power plants in 12 states which are heavily
dependent on coal. This involved a total of approxi-
mately 200 power plants in 51 AQCRs.
The study ' finds that at approximately 55 per-
cent of the plants considered, some relaxation of
emission limitations is possible. Relaxation could
result in increasing the average allowable percent
sulfur content of fuel from approximately 1 percent
sulfur content to 2 percent sulfur content at the
plants considered. Thus, the projected deficit in
low-sulfur coal could be eliminated.
Fuel Conversion Studies
The compliance extension studies discussed in
the preceding section had been conducted prior to the
overall oil shortage and energy crisis which became
apparent in late 1973. The oil shortage initiated a
second study of selected power plants on the U.S.
7 R
East Coast. In this second study ', fuel conversion
from oil to coal for selected boilers within specific
plants is analyzed to evaluate the impact on S0~ and
particulate concentrations. Increased SOp emissions
due to fuel conversions at 16 of 43 plants considered
are estimated to result in concentrations from the
plants alone which exceed the 24-hour NAAQS. Seven
of the plant conversions are estimated to result in
concentrations from the plants alone which exceed the
24-hour particulate NAAQS. The analysis indicates
that in some cases partial conversion from oil to
coal at selected power plants appears to be a viable
option for alleviating the East Coast oil shortage.
Studies of Power Plants in 128 AQCRs
Further studies ' of about 400 power plants dis-
tributed throughout the U.S. have been conducted in 1974
and 1975. The purpose is twofold: (1) to complete,
on a national basis, analyses of the threat of large
emitters of S02 to the NAAQS and (2) to add to the
overall analysis of the power plant industry being
conducted by governmental agencies and industry
itself. Thus, a base for further analyses is devel-
oped and is available if additional decisions must be
made concerning general EPA policy on compliance
extensions or fuel use options for power plants. Of
these 400 additional plants it is found that nearly
20 percent currently may exceed, by themselves, the
24-hour S02 air quality standards.
Evaluation of Model
Validation Studies
To determine the validity and overall accuracy
of the Single Source Model, validation studies have
been performed for the Canal, Paradise, Philo, Stuart
and Muskingum River power plants. The Canal Plant
is located in Massachusetts along Cape Cod Bay. The
12 13
Paradise Plant ' is located in Western Kentucky.
The other three plants are located in Southern
702
-------
1415
Ohio ' • In all cases, hourly variations in SO-
emissions are determined for each plant. These
emissions are then used with hourly meteorological
data which are representative of transport and dis-
persion in the vicinity of the plant. These data are
input to the model and 1-hour, 3-hour, 24-hour, and
annual concentration estimates are made for the sites
at which air quality monitors are located. The esti-
mated and the observed concentrations are then sub-
jected to several statistical comparisons. These in-
clude comparisons of highest and of second-highest con-
centrations and comparisons of observed and estimated
concentration frequency distributions.
As shown in Table 1, the model generally tends to
underestimate the highest and the second-highest 24-
hour average concentrations. This is also true for
3-hour average concentrations. However, 1-hour
averages are equally divided between overestimates and
underestimates. In cases where surrounding terrain is
nearly as high as the stack top (see the Philo Plant
in Table 1), the model overestimates concentrations
for all averaging times. It should be noted that most
dispersion models comparable to the Single Source Model
are not truly applicable in the vicinity of such sig-
nificant terrain features.
Table 1. Comparison of Observed and Estimated
Concentrations
1-Hour Average Concentrations 24-Hour Average Concentrations
2nd Highest Highest 2nd Highest Highest
Sampling b
Plant Station 0 E 0 E 0 E 0 E
Canal
Stuart
Musklngum
River
PMlo
1
2
3
4
1
2C
3
4
5
6
7C
1
2
3
4
1
2
3
4
5
6
435
553
446
575
685
685
1022
750
495
980
325
857
786
996
735
525
735
745
665
575
565
253
174
446
427
1372
814
565
515
823
595
976
980
1304
873
465
1295
945
4049
1945
1279
2369
438
618
732
638
857
1014
1153
883
565
1053
435
• 925
786
1179
786
893
891
917
695
675
595
283
179
509
479
1393
948
1022
541
1219
693
1000
1083
1310
933
645
1639
1059
4593
1981
1344
2482
66
36
77
63
259
63
181
79
63
147
69
133
131
165
109
132
67
127
62
87
121
16
9
38
4
149
75
91
45
57
69
73
81
82
73
45
133
86
471
165
222
282
75
46
83
75
277
159
225
83
77
195
77
170
137
227
115
133
110
132
158
94
138
29
11
39
16
161
98
102
49
75
83
120
97
91
74
47
147
104
541
220
226
356
Observed concentrations with subtracted background.
Estimated concentration.
Samplers were In operation for less than half the year.
In the comparison of observed and estimated fre-
quency distributions, disparate results are found.
There is considerable variation in comparisons from
site-to-site and plant-to-plant. However, agreement
improves for frequency distributions which include all
monitoring sites around a particular plant. As shown
in Figure 1, all but the few highest and lowest con-
centration percent!les are accurately estimated for
the distributions which include all sites.
Until further studies become available, it may
be concluded from these validation studies that the
Single Source Model Is generally accurate within a
factor of two. This is not surprising since this
accuracy is widely accepted for such point source
models. However, an important element is identifica-
tion of the tendency to underestimate, rather than
overestimate, concentrations for averaging times
associated with NAAQS. This tendency undercuts the
position of those who contend that such models are
overly conservative when used in determining emission
control requirements. It also places an added burden
on pollution control officials to ensure that an envi-
ronmental threat is not understated.
PERCENTAGE OF CONCENTRATIONS
GREATER THAN INDICATED VALUE
PERCENTAGE OF CONCENTRATIONS
LESS THAN INDICATED VALUE
Figure 1.
Stuart Plant Cumulative Frequency Distr-
Stations.
bution for 24-Hour SOp Concentrations at All
Sensitivity Analysis
To further understanding of the behavior of the
Single Source Model, a sensitivity analysis has
been conducted. Specifically, this analysis examines
the impact of variations or errors in the input data
on the concentration estimates produced by the model.
Thus, it identifies the model parameters which have
the greatest influence on concentration estimates.
In the analysis the incremental change in pre-
dicted concentration is determined for an incremental
change in input. A case study approach is used with
the three Ohio power plants noted above. The analysis
is limited to the maximum estimated 24-hour concentra-
tion, since this is generally considered to be the
most important averaging time for power plants with
regard to primary air quality standards.
Both source parameters and meteorological param-
eters are considered. The source parameters are (1)
stack height, diameter, gas exit velocity, and gas
exit temperature, (2) emission rate and its monthly
variation and (3) terrain adjustment. The meteorolog-
ical parameters considered are mixing height, wind
speed, ambient temperature and stability class. With
the exception of stability class, each parameter is
varied by a factor of +_ 5, +_ 10, and + 25 percent
while all other parameters are held constant.
From the analysis summarized in Tables 2 and 3,
it is found that for sources with relatively short
stacks, for example the Philo Plant which has stacks
about 300 feet high, a percent change in any stack
parameter results in at least that percent change in
the maximum 24-hour concentration. For sources with
relatively tall stacks, for example the Stuart Plant
which has stacks about 800 feet high, a lack of such
sensitivity is found. Stability class, a meteorolog-
ical parameter, is found to be a highly sensitive
703
-------
factor for all plants, since this parameter can take
on only six discrete values. The importance of
parameters such as wind speed and mixing height varies
depending on the meteorological conditions that result
in highest concentrations for a plant. In all cases,
the percent change in the maximum 24-hour concentra-
tion is less than the percent change in these meteoro-
logical parameters. Tables 2 and 3 indicate percent
changes in maximum 24-hour concentrations for positive
variations in source and meteorological parameters.
Comparable changes in concentration can also be shown
for negative variations in these parameters.
Table 2. Percentage Change From Base Case—Maximum
24-Hour Concentrations Due to Variations in Source
Related Parameters.
^\4.n Parameter
Paraneter ^v
Stack height (m)
Stack temp (°C)
Exit ve1ocity{m/s)
Stock diameter(m}
Terrain ADO (m)
Emissions{gm/sec)
Musk in gun
River
+ 5
-2
-4
-5
-11
1
5
+10
-5
-8
-9
-17
3
10
+25
-11
-17
-19
-30
12
25
Philo
+ 5
-6
-4
-6
-11
5
5
+ 10
-12
- 8
-10
-20
9
10
+25
-27
-18
-23
-43
24
25
Stuart
+ 5
-2
-2
-2
-3
1
5
+ 10
-5
-4
-3
-6
1
10
+ 25
-11
- 7
-7
-15
3
25
Table 3. Percentage Change From Base Case—Maximum
24-Hour Concentrations Due to Variations in Meteoro-
logical Parameters.
Mixing height (m)
Hind speed (m/s)
Ambient temp ("C)
Stabi1ity class*
IHiskiricjuin
River
*Uiased by +1 Stability Class
The sensitivity of the maximum estimated concen-
trations to changes in meteorological data sets is
also determined. Three data sets are used with each
set of source data. Changes in maximum concentration
from the base case which are shown in Table 4, range
from an increase of nearly 50 percent to a decrease of
almost 30 percent. Inherent in the change of maximum
concentration are the effects of the wind direction
and the variability of wind direction. These are not
considered individually in the sensitivity analysis.
However, wind direction and its variability, which are
a function of the meteorological conditions peculiar
to each data set, play a major role in the percent con-
centration changes shown in Table 4. This illustrates
the importance of a meteorological data set which is
as representative of transport and dispersion in the
vicinity of the plant as possible.
As a result of this analysis it can be concluded
that: (1) the sensitivity of model estimates to accu-
racy in the input parameters varies from source to
source; (2) accuracy in the source parameters
becomes more critical as the stack becomes shorter;
(3) errors in individual meteorological parameters,
with the exception of stability class, result in some-
what smaller errors in estimated concentrations; (4)
the cumulative errors in meteorological parameters,
which result from the use of data from an unrepresent-
ative site, can cause substantial errors in estimated
concentrations.
Table 4. Percentage Change From Base Case—Maximum
24-Hour Concentrations Due to Variations in the
Meteorological Data Sets.
Surface/Upper Air
Data Set
Hunt ington/.lunting ton
Col umbtis/Cay ton
Cincinnati /Day ton
Muskingum
River
17.8
11.6
Philo
-28.4
-5.8
Stuart
-19.4
36.0
Model Improvement
As a result of the model validation and the sen-
sitivity analysis, studies to improve the Single
Source Model are being undertaken. Two specific areas
under investigation are (1) the use of other stability
classification and dispersion parameters which may
allow better estimates of plume dilution and (2) the
use of more precise information on the stack param-
eters which affect plume rise. Also, additional
analyses are being undertaken to evaluate the accu-
racy of hourly concentration estimates for various
meteorological regimes. The goal is to assess the
need for better data inputs or more precise algorithms
in the model. Based on these studies, improvements
in the model will be considered.
Applications of Power Plant Studies
Limitations on the model and its application in
the power plant studies have been noted. Even with
these 1 imitations, the power plant studies are of
value for use in generalized analyses which assess
the overall effect of some plan of action for the
utility industry. These studies have been used effec-
tively in a number of energy/environmental policy con-
siderations.
The Clean Fuels Policy is an EPA program to
encourage some states to eliminate unnecessarily
stringent control regulations in their SIPs and there-
by alleviate the shortage of low sulfur coal. The
power plant studies demonstrated the potential use-
fulness of such a policy and helped to indicate those
SIPs where unnecessarily stringent regulations might
exist.
The power plant studies were used in early analy-
ses of proposed oil-to-coal conversions. They were
useful in indicating the types of sources which were
good candidates for conversion and specifically indi-
cated several plants that were poor candidates.
These studies have been used for roughly assessing
the allowable percent sulfur coal which could be used
in oil-to-coal conversions required under the Energy
Supply and Environmental Coordination Act. They will
serve as a basis for more detailed subsequent analy-
ses.
In the development of EPA policy on tall stacks
and meteorological control systems, the power plant
studies were used frequently. They were used to
analyze alternatives for limitations on stack height
704
-------
increases. They allowed the frequency and amount of
emission reductions that would be required by meteoro-
logical control systems to be compared, for various
categories of power plants, to permanent control re-
quirements.
The power plant studies have been the basis for
analyses in support of a viable S02 control strategy
for Ohio. They were used as justification for exist-
ing regulations in the 1974 Ohio S02 hearings. They
were used as an initial base in developing EPA Region
V's current proposed regulations for Ohio . They
have also been used by Region IV in the development
and revision of SIPs applicable to power plants lo-
cated in the Southeastern United States.
Industry has used the power plant studies in
•I Q
statements to the U.S. Congress on options for con-
trol of SOg. These studies have also been used in
evaluating the impact of proposed legislation to pre-
vent significant deterioration of air quality.
Based on the demand for the reports resulting
from such power plant studies, it is logical to con-
clude that other regulatory agencies and industrial
groups are using these studies. In most cases, they
are being extended by more detailed analyses. It
appears that these studies will continue to play an
important role in the development of regional and
national environmental policies which affect utility
power plants.
Acknowledgments
The authors wish to recognize the major contri-
butions of their co-workers to these power plant
studies. Major contributions were made by D. Barrett,
W. Freas and R. Lee under the overall direction of
H. Slater. Special recognition is also due to those
individuals who performed the bulk of the work under
contract to EPA. These include: P. Morgenstern and
L. Morgenstern of Walden Research Division of Abcor,
Inc.; R. Koch of GEOMET, Inc.; and M. Mills and
R. Stern of GCA Corporation. Thanks are also due to
Mrs. B. Stroud who diligently prepared this manu-
script.
References
1. Turner, 0,B., "Workbook of Atmospheric Dispersion
Estimates." Office of Air Programs Publication
No. AP-26. Superintendent of Documents, Govern-
ment Printing Office, Washington, D.C., 1970.
2. Briggs, G.A., Plume Rise, U.S. Atomic Energy
Commission, Division of Technical Information,
Oak Ridge, Tennessee, 1969.
3. Hrenko, J., D.B. Turner, and J. Zimmerman,
"Interim User's Guide to a Computation Technique
to Estimate Maximum 24-Hour Concentrations from
Single Sources," Meteorology Laboratory, Environ-
mental Protection Agency, Research Triangle Park,
N.C., 1972 (Unpublished Manuscript).
4. National Coal Association, "Steam Electric
Factors," Washington, D.C., 1973.
5. Morgenstern, P., "Summary Report on Modeling
Analysis of Power Plants for Compliance Exten-
sions in 51 Air Quality Control Regions." Publi-
cation No. EPA-450/3-75-060. Prepared by Walden
Research Division of Abcor, Inc., under Contract
No. 68-02-0049. Environmental Protection Agency,
Research Triangle Park, N.C., 1973.
6. Morgenstern, P., et al, "Modeling Analysis of
Power Plants for Compliance Extensions in 51 Air
Quality Control Regions," J. Air Poll. Control
Assn., Vol. 25, No. 3, 1975.
7. Morgenstern, L., "Summary Report on Modeling
Analysis of Power Plants for Fuel Conversion."
Publication No. EPA-450/3-75-064. Prepared by
Walden Research Division of Abcor, Inc. under
Contract No. 68-02-1377. Environmental Protection
Agency, Research Triangle Park, N.C., 1975.
8. Morgenstern, L., et al, "Air Quality Modeling
Analysis of Power Plants for Fuel Conversion."
APCA Paper No. 75-33.6, Boston, Mass., 1975.
9. Morgenstern, L., "Summary Report on Modeling
Analysis of Selected Power Plants in 128 AQCRs
for Evaluation of Impact on Ambient SO. Concen-
trations, Volume I". Publication No. EPA-450/3-
75-062. Prepared by Walden Research Division of
Abcor, Inc., under Contract No. 68-02-1484.
Environmental Protection Agency, Research
Triangle Park, N.C., 1975.
10. Koch, R., "Summary Report on Modeling Analysis of
Selected Power Plants in 128 AQCRs for Evaluation
of Impact on Ambient SO,, Concentrations, Volume
II." Publication No. EPA-450/3-75-063. Prepared
by GEOMET, Inc., under Contract No. 68-02-1483.
Environmental Protection Agency, Research Triangle
Park, N.C., 1975.
11. Mills, M., "Comprehensive Analysis of Time--
Concentration Relationships and the Validation of
a Single Source Dispersion Model." Publication
No. EPA-450/3-75-083. Prepared by GCA Corporation
under Contract No. 68-02-1376. Environmental
Protection Agency, Research Triangle Park, N.C.,
1975.
12. Klug, W., "Dispersion from Tall Stacks."
Publication No. EPA-600/4-75-006. Environmental
Protection Agency, Washington, D.C., 1975.
13. Enviroplan, Inc., "A Comparison of Predicted
and Measured Sulfur Dioxide Concentrations at
the Paradise Power Plant in 1969." Draft Report
No. 1, prepared under Contract No. 68-01-1913.
Environmental Protection Agency, Washington,
D.C., 1975.
14. Mills, M., and R. Stern, "Model Validation and
Time—Concentration Analysis of Three Power
Plants." Final Report prepared by GCA Cor-
' poration under Contract No. 68-02-1376, Environ-
mental Protection Agency, Research Triangle
Park, N.C., 1975.
15. Lee, R., M. Mills, and R. Stern, "Validation
of a Single Source Model." Paper presented at
the 6th NATO/CCMS International Technical
Meeting on Air Pollution Modeling, Frankfurt/
Main, Germany, FR, September, 1975.
16. Freas, W., "Sensitivity Analysis of the Single
Source Model." Office of Air Quality Planning
and Standards, Environmental Protection Agency,
Research Triangle Park, N.C., 1976 (Unpublished
Manuscript).
17. Environmental Protection Agency, "Technical
Support Document: Development of a Sulfur
Dioxide Control Strategy for the State of Ohio,
Volume 1'" Chicago, Illinois, September, 1975.
18. Environmental Research and Technology, "An
Evaluation of Sulfur Dioxide Control Require-
ments for Electric Power Plants." Report pre-
pared for Edison Electric Institute, New York,
N.Y., April, 1975.
705
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MODIFIED DISPERSION MODELING PROCEDURES
FOR INDIANA POWER PLANTS
S. K. Mukherji, Chief
Program Support Branch
Indiana Air Pollution Control Division
Indianapolis, Indiana
C. R. Hansen
Program Support Branch
Indiana Air Pollution Control Division
Indianapolis, Indiana
M. W. Bobb
Program Support Branch
Indiana Air Pollution Control Division
Indianapolis, Indiana
H. D. Williams
Director
Indiana Air Pollution Control Division
Indianapolis, Indiana
David R. Maxwell
Standards § Planning Branch
Indiana Air Pollution Control Division
Indianapolis, Indiana
A modified procedure for short-term dispersion
modeling of Indiana power plants located along river
valleys is presented in this study. Rough terrains
and occasional high winds persistent for hours produce
high surface turbulence in this particular region.
Based on empirical observations, the meteorological
stability input to the PTMTP modeling program of the
UNAMAP package was appropriately decreased. The
artificial stability change simulated the augmented
atmospheric turbulence due to surface friction.
Generation of more accurate sulfur dioxide level
estimates indicated the feasibility of using conven-
tional short-term models with suitable changes in
particular cases.
Introduction
A modified procedure for short-term sulfur dioxide
dispersion modeling of four Indiana power plants
located in the Ohio River § Wabash River valleys is
presented in this study. These river valley regions
are characterized by undulating hills and bluffs at
some distance from the river and occasionally
persistent strong winds blowing across the river towards
the rough terrain. The basic assumptions incorporated
in the available simulation models for atmospheric
transport of S02 do not account for this type of
situation. As a result, the conventional short-term
dispersion models, viz., the programs included in
United States Environmental Protection Agency's
modeling package consistently underpredicted maximum
S02 levels around the power plant. A simple change
involving meteorological parameter inputs to the
computer model was, therefore, initiated to simulate
the actual atmospheric conditions more closely and gen-
erate more accurate estimates, using conventional
modeling programs.
The particular UNAMAP package model targeted for
modification was the Multiple Point Source routine
PTMTP1 (also identified as DBT51). In this program the
usual simplifying assumptions are made; namely, steady
and uniform meteorological conditions with no wind
direction shear, Gaussian Plume behavior, flat or
gently rolling terrains, no aerodynamic downwash
conditions, etc. One important and desirable feature
of PTMTP is that an hourly stability condition can be
assessed by a meteorologist from the available ambient
data before being input to the model. Since the local
topography and wind data suggested the possibility of
considerable mechanical turbulence generation, the
stability class evaluation was isolated as the program
area suitable for prediction improvements. The
analytical considerations that led to hourly stability
postulations are now described.
Analytical Background
A theoretical treatment of the effects of an
extensive area of given roughness on the short-range
vertical spread from a source, using gradient-
transfer methodologies, has been available for some
time. 2 Influences of terrain roughness changes on
pollutant dispersions have also been detailed by
Pasquill, et al . ' ' Expectedly, moderately
rough terrains, i.e. , ridges and valleys seem to
cause strong mixing. > ' > This mixing pattern is
usually prominent during late morning hours under
slightly unstable conditions of the atmosphere and
compares favorably with thermally induced stability
alterations. It is true that low-level (less than
100m) sources within a confined narrow valley some-
times do not reflect any mechanical mixing. 9 However,
it is generally acceptable that local atmospheric
turbulence can be greatly increased, at least, within
the lower 500 to 1000 meters of the atmosphere through
surface friction effects. 3
Counihan1^ studied average strong wind or neutral
boundry layers and concluded their appropriate depth
to be about 600 meters. He proposed an expression for
surface friction velocity u^ as follows
•, /?
(Ug/20)( 1 H 0.24 log (z0/0.38)) _ (1)
In this equation, Ug denotes the geostrophic wind
speed and zo represents the characteristic surface
roughness. For wooded rural terrain, Counihan cites a
value of z0 = .38m. Rougher terrains encountered in
the Ohio River or Wabash River Valley regions of
Indiana can be presumed to possess surface roughness
eqivalent to approximately 0.58m. In other words,
the friction velocity for the Indiana study ranges
from O.OSOUg to 0.051 Ug. A theoretical analysis by
Wippermanll suggests that the boundary layer depth is
about 0.8 kug/f falling to 0.2 kuj/f under very stable
conditions (where f, the Coriolis parameter approxi-
mately equals 10/4s and k is the dimensionless
Von Karman's constant 0.4). Thus the mesoscale
boundary layer depths h in the vicinity of the power
plants vary from 160Ug to 163Ug for so-called neutral
706
-------
stabilities. The value of h decreases to about 40U in
very stable conditions. Translated in terms of numEers,
the boundary layer can extend to about 800m for
sustained windspeeds greater than 5 m/s typically en-
countered in the area.
Dispersion in a mechanically stirred boundary
layer has been discussed by Moore.12 According to the
analysis, maximum diffusivity within a boundary layer
is expected to occur at around h/4 corresponding to
200m height on windy days. Indiana power plant stacks
under study are well below the depth of 200m.
Therefore, any plume behavior on these days is expected
to be significantly affected by the mechanically
induced turbulence in the atmosphere. The effects of
higher turbulence on the S02 plume were simulated in
the PTMTP model by reducing the atmospheric stability
by one class from the conventional one when the
situation dictated so. The algorithms for the
stability reduction are described below.
Modeling Modification
To begin with, preliminary topography and wind
direction surveys were carried out for the individual
power plant to be modeled. The purpose was to
ascertain the magnitude of terrain roughness changes
within 5 km of the plant and its likely effects on the
plume rise and spread. Next, a set of guidelines was
laid down to establish the likelihood of strong
friction-generated turbulence interacting with the
plume. This consisted of scanning (a) the elevation
changes around the plant and (b) the hourly
meteorological data, namely, time of day, season, cloud
cover, wind speeds, etc. Upon the set of pre-estab-
lished criteria being met, the conventional stability
class (based on Pasquill-Gifford-Turner suggestions)
was decreased by one. Thus, if during summer daytime
the windspeed was greater than 4 m/s with the sky
being at least partly clear, the stability class was
lowered by one provided the wind was blowing the plume
over the rough terrain. The flow chart leading to the
synthetic decrease of the stability parameter as input
to the PTMTP model is indicated in Figure 1.
2. It plinl locaud wjtMn 2 km of L«k« Mlcnioan
3.0ir««tion> Injm which wind will produc* • topographical •tt*cl
Figure 1. Flow Chart to Assess Stability Alterations
It is noted that no change of stability was allowed for
classes 1 and 2. Turbulence generated by thermal
instability associated with these two classes was
assumed to be much more dominant compared to dynamic
turbulence production.
Results
Typical elevation changes around two of the power
plants are presented in Figures 2(a) and 2(b). Fig-
ure 2(a) depicts a sudden 110m jump in elevation at a
distance of 6 to 12 stack heights from the source,
i.e., a step change in the floor level of the flow.
A more modest elevation increase is seen in Fig-
ure 2(b), where the elevation changes may be construed
as rough elements embedded at the lower boundary of
the surface layer flow.
CLIFTY CREEK
9 10 11 12 13 14
Distance (thousands of feet )
Figure 2(a). Elevation Changes at Clifty Creek Plant
ALCOA
(hundred*
•of ltd)
Oistanc* (thousands ol fe«t)
Figure 2(b). Terrain Roughness Around
Warrick-Culley Units
In both cases, an artificial change of stability for
any flow over the elevated terrain generated more
accurate estimates.
Comparisons of the actually monitored sulfur
dioxide readings with the levels projected by the
lowered stability input to the PTMTP model are
compiled in Table 1 on the following page.
707
-------
TABLE 1. Comparison of Actual Reading Versus
24-Hour Predictions (ug/m-5)
Conventional Altered Actually
Stability Stability Monitored SC>2
Point Source Assumptions Assumptions Reading
Karrick-Culley
Clifty Creek
Wabash River
3/3/74
226
17
126
97
0.002
0.3
435
368 •
532
336
126
49.6
479
479
506
275
29
20
23
31
31
Assessments of the SC>2 levels using conventional
stability assumptions are shown side by side. The
results reflect the days when persistent strong winds
were measured flowing over the rough terrains. In
both sets of computations, the actual elevation of the
receptors was taken into account. It should be noted
that the Warrick-Culley monitors/receptors were
generally very close to the plume centerline during the
days of study. On the other hand, the monitors for the
Clifty Creek and Wabash River plants were located
kilometers away from the estimated maximum SCU impact
sites. For the low-level ranges of SC^ indicated by
the monitors, the accuracy of the equipment was within
10 percent of the observed readings at best. Finally,
the background S02 levels over the river valley basins ,
are estimated to be around 10-25 ug/m^ on the basis of
acquired data and wind persistence studies.
Typical alterations in SC>2 isopleths when the
stability classes were decreased are portrayed in Fig-
ures 3(a) and 3(b) for two power plants.
CLIPnT CREEK STATION
Conceatratiooa at
High Stability
km from Source
Figure 3(a). Isopleths for Projected Levels
Around Clifty Creek Plant
km from Source
.Figure 3(b). Estimated S02 Impacts of Warrick-Culley
Stations
Displacements of the maximum impact locations caused
by the meteorological changes are clearly discerned.
It is also evident from these figures that the effects
of stability changes drop off sharply from the
maximum impact location. At a distance of 3-5 kilo-
meters away from the maximum S02 level region, the
difference between the two estimates becomes
negligible. The minor differences between the
numerical S02 estimates for Clifty Creek and Wabash
River monitor/receptors are attributable to this
effect. In view of these considerations, it is
reasonable to propose that the actual stability
parameters estimate the pollution levels somewhat
better than the conventional stability inputs.
To substantiate this statement further, a
detailed review of resuls obtained from the Warrick-
Culley Power Plant complex is presented in Table 2.
TABLE 2. Comparison of Estimated S02 Levels Near
Warrick-Culley Plants
Monitor Monitor Location Obs. 24-hr 24-hr S07 Level Estimates (ug/m3)
SO? Leve~ (includes background levels)
Lower Stability Higher Stability
Ml
CMobile Site) 0.95 km.
472
472
83
131
104
52
20
52
208
314
421
365
222
99
120
26
30
26
151
126
30
26
162
60
69
' 134
31
133
26
26
708
-------
These results represent days on which high levels of
S02 were projected to occur at or near one of the
operating samplers due to direct impact. Such a choice
of days tended to provide a more valid comparison
between the two estimates (based on different hourly
stability parameters), since the uncertainty effects
for off-axis plume concentration predictions were less
significant. It is seen from the results that the
lower stability assumptions generated more accurate
projections for nine out of ten days. Within this
duration the total number of hours for which stability
levels were artificially decreased by one class
exceeded one hundred. An hourly correlation analysis
between the actual readings and the two estimates
yielded low values for the coefficient 'r', i.e. 'r'
was less than 0.40. However, the analysis spanning
this period indicated better regression results for
the lower stability cases. The lesser S02 estimates
for the nearby monitor Ml probably resulted from
inaccurate wind direction assessment for the two days.
In the overall analysis, forced lowering of
stability to represent a more turbulent flow field
provided a more accurate assessment of the samplers.
On the basis of results presented it is suggested that
similar procedures be routinely incorporated in any
dispersion modeling scheme where dominant mechanical
turbulence effects are anticipated.
Summary of Conclusions
1) A modification was surmised for conventional short-
term dispersion models, such as the UNAMAP packaged
PTMTP, to assess S02 levels around some Indiana power
plants located in a rough terrain.
2) The alteration consisted simply of an artificial
lowering of the hourly stability class by one when an
appropriate combination of topography effects and
meteorological patterns occurred. A suitable
algorithm could be easily incorporated within the
PTMTP model.
3) Projections based on decreased hourly stability
were much closer to actually sampled S02 levels than
conventional stability predictions.
4) Incorporation of similar procedures is suggested
for any modeling scheme where strong mechanical
turbulence due to surface friction is likely to occur.
REFERENCES
1. Turner, D.B. and A.D. Busse, PTMTP "Users' Net- •
work for Applied Modeling of Air Pollution," Nat.
Env. Res. Ctr., U.S. Environmental Protection
Agency, Research Triangle Park, N.C., 1973.
2. Kalder, K.L., "Eddy Diffusion and Evaporation in
Flow Over Aerodynamically Smooth and Rough
Surfaces," Quart. J. Mech. Applied Math., 2,
p. 153, 1949.
3. Pasquill, F., Atmospheric Diffusion, Halsted-
Wiley (2nd Edition), New York, N.Y., 1947.
4. Csanady, G.T., Turbulent Diffusion in the Environ-
ment, Reidel Publishing Co., Boston, Mass., 1973.
5. Lumley, J.L. and H.A. Panofsky, The Structure of
Atmospheric Turbulence, Wiley Inter Science, New
York, N.Y., 1964.
10.
11.
12.
Holland, J.A., "A Meteorological Survey of the
Oak Ridge Area," USAEC Report ORO-99, Technical
Information Center, Oak Ridge, Tenn., 1953.
Hewson, E.W., "The Meteorological Control of At-
mospheric Pollution by Heavy Industry," Quart.
J. Royal Met. Soc., 71, p. 266, 1945.
Cermak, J.E., "Fluid Mechanics Applications to
Problems of Wind Forces on Structure and Air
Pollution," Development in Mechanics, 7_, Univ.
of Pittsburgh Press, Pittsburgh, Pa., 1973.
Panofsky, H.A., and B. Prasad, "The Effect of
Meteorological Factors on Air Pollution in a
Narrow Valley," J. Appl. Met., 6_, p. 493, 1967.
Counihan, J., "Adiabatic Atmospheric Boundary
Layers," to be published in Atmospheric Environ-
ment, 1976.
Wipperman, F., "The Planetary Boundary Layer of
the Atmosphere," Deutsch. Wetterdienst, p. 106,
1973.
Moore, D.J., "Application of CEGB Plume Rise
and Dispersion Results to Prediction Models for
Ground Level Concentrations," Proc. Inter. Clean
Air Conf., Rotorua, New Zealand, 1975.
709
-------
SEVERITY OF STATIONARY AIR POLLUTION SOURCES -
A SIMULATION APPROACH
E. C. Eimutis, B. J. Holmes, L. B. Mote
Monsanto Research Corporation
Dayton, Ohio 45'407
Abstract
A measure of specific point source air
pollution severity has been defined as the
ratio of its ground level concentration con-
tribution of a given species relative to some
potentially hazardous concentration of that
species. For well-documented source types,
e.g. coal-fired steam electric utilities, it
is possible to analyze the severity on a
plant-by-plant basis and to examine the sever-
ity frequency distribution deterministically.
For many other source types, e.g. industrial/
commercial boilers, cotton gins, asphalt batch
plants, solvent evaporation, etc., the points
of emission number in the thousands and in
some cases in the hundred thousands. These
source types require a statistical approach.
We present a Monte Carlo simulation technique
together with efficient algorithms for fitting
the inverse Weibull, Gamma, normal, and log-
normal cumulative density functions. Using
coal-fired steam electric utilities as an ex-
ample, we show a significant correlation be-
tween deterministic and simulated severity
results.
Source Severity
The air pollution severity, S, of a
given source should in some way be proportion-
al to the degree of potential hazard it im-
poses upon individuals in its environment.
The relative hazard, H, from a specific emis-
sion can be defined as being directly propor-
tional to the delivered dose, the probability
of dose delivery, and number of people who
would receive it, and inversely proportional
to the toxicity of the material as follows:
H
NPV
LD
50
(1)
where
of the peo-
S = source severity
H = relative hazard
N = number of persons
LD50 = lethal dose for
pie exposed
P = probability of dose delivery
f = delivered dose = B-R'-/x(t)dt
B = average breathing rate
R' = lung retention factor
x(t) = concentration time history
The source severity is herein, defined as
the ratio of the dose of a pollutant delivered
to a population, relative to some potentially
hazardous dose. Since LD50 data are not
available for human beings, another measure of
potentially hazardous dosage was used.
The potentially hazardous dose for a
given pollutant from a specific point source
in a given region is defined as follows:
= NBR'
TLV(t) K dt
(2)
where
V_, = potentially hazardous dose, g
N = population exposed to a specif-
ic source, persons
B = average breathing rate, m3/s-
person
R' = lung retention factor for the
pollutant of interest (dimen-
sionless factor, 0
-------
Simulation Methodology
In many statistical analyses of data, it
is frequently desired to consider a random
variable which is a function of other random
variables. An example pertinent tq air pollu-
tion studies is given by the severity equa-
tions for ground-level concentrations of air
pollutants.1 For example, the severity equa-
tion for S02 emissions from the stacks of
coal-fired electric utility plants is given
by:
o _ 50Q
3 "
where Q = emission rate, g/s
h = emission height, m
The emission rate can be calculated from:
(10)
sulfur)(Kj)
(ID
where
or
CC = coal consumed, g/yr
E = emission factor =
0.01'9 g S02(l$ sulfur coal)
g of coal consumed
sulfur = percent of sulfur in the
coal _8
Kj = 3.171 x 10 (to convert
g/yr to g/s)
(K2)(CC)(5? sulfur)
S —
(12)
where K2 = 3
10
-9
Next, consider a general setting where
the random variable z is a function of the
random variables xls ..., xn given by z =
f(xls ..., xn) for some function f. Suppose
the actual distributions of the input random
variables x1? ..., x are known including
their probability density functions (p.d.f.)
and the corresponding cumulative distribution
functions (c.d.f.). Then it seems reasonable
to assume that the distribution of the random
z can be obtained. In a sense this is true in
that integral formulae have been developed
which give the probability density function
and the cumulative distribution function for z
as a function of the same functions for the
x,.2 These formulae, however, are complex
even for the case of the simple sum, differ-
ence, product, or quotient of two random vari-
ables. Also, even if the integrals are suc-
cessfully evaluated, the resulting probability
density function for z will in general not be
exactly one of the standard distributions and
as a result may be difficult to handle. There
are certain special cases in which the result-
ing p.d.f. will be known. In these instances,
the analytical approach to finding z explicit-
ly is by far the best approach. In other in-
stances certain simplifying assumptions about
the distribution of z can be made provided
certain things are true about the coefficient
of variability or equivalently the coefficient
of skewness of the input variables. However,
in cases where there are more than two input
variables or there is considerable skewness
exhibited by the variables or the function f
becomes complicated, then the strict analyti-
cal approach to finding the distribution of z
explicitly will in general not be applicable.
Sometimes it is desired to find informa-
tion on the distribution of z when some things
are known about the distribution of the input
variables
Since the general ap-
proach of finding the explicit distribution
function for z is not possible, "many" values
of z may be calculated for explicit values of
the input variables xi, ..., x and these val-
ues may be used to estimate (rather closely if
enough values of z are known) such things as
the mean, standard deviation, etc., for z.
This approach is called the deterministic ap-
proach because in this technique it is possi-
ble to determine explicit values for z from
.explicit values of the input variables xls
Consider the situation when either no ex-
plicit values of the input variable are avail-
able from which values of z can be calculated
or the number of such values is too small to
permit calculation of enough values of z to
determine useful information regarding Its
distribution. In this situation we use a com-
puter simulation to obtain values for z. For
example, instead of knowing many values for
the input variables xla ..., xn, only limited
information may be available, such as an esti-
mate of the mean and possibly the range and
symmetry or skewness properties. In this
case, the input variables are fitted to some
theoretical distribution and the small amount
of available information about the variables
Is used to determine the parameters of the
distributions. A computer is then used to
sample from each input variable's distribution
function and to subsequently use these data to
calculate values of z from which the mean,
standard deviation, etc., can be estimated and
frequency histograms and cumulative distribu-
tion plots for z can be prepared. Some of the
techniques and procedures used In such a com-
puter simulation are described below.
The equation for the severity (equation
12) of ground-level concentrations of S02
emissions from the stacks of coal-fired elec-
tric utilities will be used to illustrate the
methodology utilized in the simulation ap-
proach.
When all of the input random variables
are independent random variables, the method-
ology is relatively simple. A large sample
(e.g., of size n) is drawn from the distribu-
tion of each of the input variables. These
data are then used one by one to calculate n
values of S. From these n values of S, the
mean, standard deviation, etc., can be calcu-
lated and a frequency histogram and cumulative
distribution can be plotted.
Some comments are in order regarding the
method by which samples are drawn from the
distribution of the input variables. First,
it should be noted that the input variables
are restricted to one of four types of contin-
uous distributions: the Weibull, Normal, Gam-
ma, or Log-normal distribution. The type of
each input variable and the corresponding par-
ameters for its distribution function must
711
-------
thus be specified. The method of obtaining
the "best11 type for each variable and the cor-
responding parameters is described in another
publication.1 It is necessary to have a ran-
dom sample of data points for the input vari-
able in order to be able to fit it to the
proper distribution. However, certain situa-
tions may arise when that much information
about the input variable is not available.
For example, two extreme points on the distri-
bution and either the mean or mode may be
known, or some information may be available to
determine whether the distribution is symmet-
ric or skewed. In such situations where the
goodness-of-fit program is inoperable, it may
still be possible to fit the variable to one
of the four distributions above and to obtain
its parameters.
As a demonstration of the above proce-
dure, consider the following example. Suppose
that for an input variable, x, it is known
with 95% confidence that the values of x will
be between e and e5 (where e = 2.1..). Sup-
pose also that the mode of the distribution Is
known to between e and e2 and that the mean is
approximately equal to e3. These points then
indicate that x is a rather heavily skewed
right distribution. The graph for the p.d^f,
of x may resemble the one shown below:
Since it is known that the 0.025 point on
the cumulative graph is approximately equal to
e and the 0.975 point is approximately equal
to e5, this information can be used alone to
calculate A and B in a Weibull fit. Thus, one
finds that A = 1.25 and B = 7.29 x 10~3.
These values of A and B yield a theoretical
mean y = 47-7 which is larger than the esti-
mated e3 value for the mean. The theoretical
mode is 1*1.2 which again is larger than the
estimated mode. Thus, the Weibull fit could
be used as an approximation to the "true" dis-
tribution of x.
Another way of obtaining a distribution
for x is to assume that it is log-normally
distributed since the Log-normal distribution
is a right-skewed distribution. If x is as-
sumed to be a Log-normal distribution, then
log x must be Normal. Hence, by taking the
logarithm of the 0.025 point and 0.975 point
of x, the same points on the cumulative graph
of log x are obtained which were assumed to be
Normal. These points are 1 and 5, respective-
ly. Thus, the mean y of log x should be taken
to be 3 and, since 1 and 5 are the 0.025 and
0.975 points, respectively, it is found that
a = 1.2. The values u = 3 and o = 1.2 can
thus be used as parameters to sample from the
Normal for values of log x. By taking anti-
logarithms of the sample, a sample for x can
be obtained.
In view of the above discussion, it is
evident that several avenues are available
for obtaining a distribution to fit the given
data or information about each input varia-
ble. The simulation program (for the case of
independent input variables) simply takes the
parameters for the given type of distribution
for an input variable and samples from this
distribution to obtain a random sample for
that input variable.
Example of Use of Simulation Approach
with Coal-Fired Electric Utilities
In order to obtain an indication of how
well the simulation procedure approximates
the "true" population, S02 emissions from the
stacks of coal-fired electric utilities were
examined. Data were available on % sulfur,
CC, and h for 224 power plants in the United
States. This was considered to be the total
population which was to be simulated by using
only a small number (24) of plants in order
to obtain information about the distributions
of % sulfur, CC, and h.
To obtain a ''random" sample, the first
24 plants on the list were selected. % sul-
fur, CC, and h for these 24 plants was then
fitted to the four distributions considered
in the simulation program. The distributions
were then selected which appeared to fit the
data better on an overall basis considering
the SE, x2-value, actual class interval com-
parisons, and coefficient of skewness and
measure of kurtosis calculations. For % sul-
fur, the Weibull Maximum Likelihood Fit was
selected and clipped at the 5% and 99% points.
Also, h was found not to be independent of CC.
Hence, It was decided to treat h as a depend-
ent variable correlated with the independent
variable CC by using the raw data on the 24
plants to obtain R. The coefficient of skew-
ness indicated that h was not normal but
skewed to the right. Furthermore, the coef-
ficient of skewness and measure of kurtosis
for log h indicated "near-normality." Hence,
it was decided to use the Log-normal distri-
bution for h.
Using equation 12 for S, the data, as
indicated above, are entered into the simula-
tion program and 5000 values were calculated
for S. Subsequently, the mean, standard de-
viation, maximum value, and minimum value
were calculated. A deterministic calculation
of these values was performed for all 224
plants in the population and the results are
compiled in the table below:
Table 2. RESULTS OF DETERMINISTIC
CALCULATIONS
Parameter
Mean
Standard devi-
ation
Maximum value
Minimum value
Simulated
value
9-25
12.5
154.5
0.08
Deterministic
value
8.9
12.4
136.0
0.36
Frequency histograms and cumulative fre-
quency plots were also drawn for both the sim-
ulated values and the deterministic values of
S and these are shown in Figures 1 through 4.
712
-------
The large-sample t-test was performed to
determine whether there was a significant
difference in the simulated and deterministic
mean values obtained above. The test, as
might be expected, showed no significance in
the difference at the 0.01 or 0.05 levels.
Furthermore, the F test for significant dif-
ference in the variances was also negative,
indicating no significant difference.
SflHPLE SIZE = 5000
MIN. VHLUE = 0.08
MflX. VflLUE = 154.45
HERN = 9.25
STD. DEV. 12.48
SRMPLE SIZE = 224
HIM. VflLUE - 0.36
flflX. VflLUE = 135.SB
KERN = e.ee
STO. DEV. 12.31
SRHPLE SIZE = 224
HIM. VflLUE = 0.36
MHX . VRLUE = 135.96
HERN = 8.88
STD. DEV. = 12.37
Acknowledgment s
This work was conducted under EPA con-
tract No. 68-02-1874 with Dr. Dale Denny as
EPA contract project officer and Dr. R. C.
Binning as the MRC project manager.
References
1. E. C. Eimutis, B. J. Holmes, L. B. Mote,
"Severity of Stationary Air Pollution
Sources - a Simulation Approach", EPA
Contract No. 68-02-l8?4, Final report in
print.
2. E. Parzen, "Modern Probability Theory and
It's Applications", John Wiley & Sons,
New York, Wiley Publication in Statistics,
I960.
SfltlPLE SIZE = 5000
. MIN. VflLUE = 0
(MX. VRLUE = 154.45
MEHN = 9.2S
STO. OEV. = 12.49
"•JWSV3 BPflrafWfc. rtffits,
Figure 3. Cumulative frequency for the Severity of SO2 emissions froi
713
-------
ATMOSPHERIC POLLUTANT DISPERSION USING SECOND-ORDER
CLOSURE MODELING OF THE TURBULENCE*
W. S. Lewellen and M. Teske
Aeronautical Research Associates of Princeton, Inc.
Princeton, New Jersey
Abstract
A method is described for calculating
turbulent diffusion of plumes in the planetary
boundary layer based on Donaldson's second-
order closure approach to turbulent flows.
The method calls for solving dynamic, partial
differential equations for the species flux,
variance, and its mean concentration, as well
as the second-order turbulent velocity and
temperature correlations to determine the
turbulence in the ambient atmospheric boundary
layer in which the plume is embedded. The
parameters governing dispersion in the plane-
tary boundary layer are identified and dis-
cussed. Results from a sample calculation of
dispersion in a free convection layer are com-
pared with laboratory observations.
1. Introduction
This exact equation introduces variables other
than second-order correlations and thus leaves
the system of equations undetermined. The
task of second-order closure is to model these
terms as functions of the second-order corre-
lations and mean flow variables.
Our philosophy has been to choose the
simplest models that have proper tensor
symmetry, dimensionalization, and the desired
physical properties. The modeled form of the
species flux equation may be written for high
Reynolds numbers as
9t
+ 0.3
(2)
A valid estimate of turbulent diffusion
in the atmospheric boundary layer is required
to determine the impact of a pollutant release
on the air quality at some distance from the
point of release. Our purpose here is to re-
view and present some results from a model
based on solving a specific dynamic differ-
ential equation for the turbulent flux of
species. This approach, based on second-order
closure of the ensemble-averaged moments of
the fluctuating variables, is currently being
studied by a number of investigators for com-
puting turbulence in the atmosphere.1"11 We
review the essence of the model in the next
section. The parameters identified by this
model as governing the dispersion of a
neutrally buoyant, nonreactive species in the
planetary boundary layer are presented in
Section 3. A sample calculation is compared
with results from a laboratory simulation of
dispersion in a free convection layer in
Section 4.
2. Model Equations
We take as our starting point the en-
semble-averaged, Eulerian equation of mass
continuity for the species concentration C
3C
3(UJC
= S + D ±± (i)
This equation is exact but undetermined even
if the velocity U^_ is known because of the
presence of the additional variable FT . By
taking moments of the instantaneous variables
and averaging, we can generate an exact
equation for the species flux uTc" . 2
t
This research has been partially funded with
Federal funds from the Environmental Pro-
tection Agency under Contract No. EPA 68-02-
1310, and from National Aeronautics and Space
Administration under Contract No. NAS8-31380
We do not expect that the last two
modeled terms in Eq. (2) used to replace the
complex terms of the exact equation will
faithfully represent all of the information
present. However, for most problems, we are
interested in only a small part of the infor-
mation contained in the complete turbulent
spectrum. We believe that the two modeled
terms provide at least the minimum amount of
desired information needed to close the
system at the second order. The first modeled
term introduces diffusion to prevent excessive
gradients in the species flux. The other
modeled term, a tendency-towards-isotropy
term, introduces the required feedback which
permits the flux to reach an equilibrium level
even in the presence of large production con-
tributed by the first three exact terms on the
right-hand side of Eq. (2).
The effect of stability on diffusion
comes into Eq. (2) in two ways: through the
influence of stability on the velocity
fluctuations2 and through the buoyant term
appearing directly in Eq. (2). This term is
not a result of our closure modeling but
arises directly from the buoyant term in the
momentum equation. However, modeled terms
must appear in the equation derived for 06 .
If these are treated in a similar fashion to
those in Eq. (2), the equation for c9 may be
written as
3e6
3t
+ U.
3c6
3Xj
- U.5
J
3C
-u.c
30
3x.
0.3
(3)
With the velocity and temperature fields
specified, Eqs. (1), (2) and (3) form a com-
plete set for the determination of C . The
velocity and length scales, q and A ,
appearing in Eqs. (2) and (3), are appropri-
ately related to the companion scales q
714
-------
and A of the ambient turbulent field. The
mean velocity, temperature, and second-order
velocity and temperature fluctuations may be
obtained from field observations or calculated
from similarly modeled equations?'9'10 As
long as we are dealing with a nonreactive,
neutrally buoyant species, the two sets need
not be coupled together.
3- Governing Parameters
A solution to the dispersion equations,
Eqs. (1-3), for a neutrally buoyant, non-
reactive species requires specification of the
U,
velocity
stress, u.u. ;
scale, A ; and
temperature, 0 ; Reynolds
heat flux, u.0 ; turbulent
source S , as functions of
time and space. Although one may argue with
the details of our modeling, it appears un-
likely that a more accurate model would re-
quire less information. Thus, very detailed
measurements of turbulence are required if
one attempts to predict dispersion on the
basis of measured wind and turbulence fields
alone. Measurement of the average wind speed
and direction plus an estimate of the
stability class of the turbulence are unlikely
to provide sufficiently accurate data.
It is naturally desirable to parameterize
this dependence with as few a number of para-
meters as possible. The critical parameters
may be deduced by examining the equations
governing the ambient turbulence in the
planetary boundary layer.10
A. Surface Layer Parameterization
Within the surface layer, when the equi-
libration time A/q of the turbulence is
small in comparison to flow times over changes
in surface features, a few direct parameters
will suffice. Estimates of the surface shear
stress, Ujf , surface heat flux, 8S , and the
effective surface roughness, z , are adequate
to specify the wind, temperature, and turbu-
lence fields completely through the Monin-
Obukhov similarity functions. These empiri-
cally correlated functions may in fact be pre-
dicted from our modeled turbulence equations
in the limit of stationary, unidirectional
flow with us and 6S held fixed, while the
other variables are allowed to be functions of
the vertical coordinate alone. "* For this to
be true, it is necessary to have
(U1A /q ( ))g( )/3x1«l . This same re-
striction may be applied to the species flux
equation, Eq. (2). If we also neglect the
diffusion terms, which should be small in the
lower portions of the surface layer where
A = A = 0.65z 5 and q = q , then Eq. (3)
may be used to eliminat^ c6 , and an alge-
braic expression for we" obtained. Thus,
we
/4wwA
V 3q
1 +
!£
3z
The bracketed quantity in Eq. (4) defines an
effective eddy viscosity K which is a
function only of us , z and L
face-layer K is plotted in Fig.
by-its neutral value of
strong function of z/L
3.2r
2.8
2.4
0 .
This sur-
normalized
It is a
2.0
.8
Z/L
Fig. 1. Effective turbulent diffusion co-
efficient K as a function of height and
Monin-Obukhov length L in the surface
layer as .predicted by the superequilibrium
limit of our turbulent model.
The downstream vertical dispersion of a
plume from its source depends on the wind
distribution as well as K . This observation
introduces a dependence on z in addition to
and L
Under neutral conditions, the
surface layer extends to approximately 100m;
under very stable conditions its extent may be
reduced to only 20m. Under unstable con-
ditions the height of the surface layer de-
pends upon the height of the inversion layer
at the top of the planetary boundary layer.
Surface layer approximations are valid in this
case for z/z. <_ 0.1 . In no case, however,
is the surface layer approximation valid above
an altitude of a few hundred meters.
The only difficulty with dispersion in
the surface layer is the prediction of the
horizontal dispersion. The conditions
necessary for the horizontal wind variance to
obey Monin-Obukhov similarity are much more
strenuous than those for the vertical vari-
ance. This fact is reflected in the large
scatter observed in the reported measured
values of the horizontal wind variance in the
surface layer.
Theoretically, the cause
appears to be the low frequency lateral ve-
locity fluctuations forced by inhomogeneities
in terrain or mesoscale meteorological phe-
nomena. These low frequency flucuations have
a much larger time constant associated with
their decay. Thus, the flow conditions must
be steady and spatially homogeneous on a much
larger scale for the horizontal wind variance
to satisfy in detail the surface layer
approximation necessary for Monin-Obukhov
similarity to hold.
715
-------
B. Parameterization in the Ideal Planetary
Boundary Layer
Above the surface layer region the para-
meterization of dispersion becomes much more
complicated. Not only are several additional
parameters introduced, but the time required
for the flow to reach an equilibrium state is
greatly increased. The characteristic time
for the neutral planetary boundary layer is
the reciprocal of the Coriolis parameter f
(approximately 3 hours at mid-latitudes). In
practice neutral conditions rarely exist long
enough for the steady state, neutral layer to
be achieved. Rather, the surface heat flux
forces a continuing evolution of the boundary
layer above it. This evolution as a function
of time for a typical summer day in the Mid-
west , as computed by our model, has been
given previously.7'10 Similar calculations
using different versions of the closure model
have been made by Mellor and Yamada.6'11
At sunrise an unstable surface layer be-
gins to grow, developing into a deep mixing
layer with high turbulence by afternoon. The
height of the unstable mixed layer then con-
tinues to increase slowly until sunset.
Shortly after sunset a stable layer with a
temperature inversion develops at the surface.
This surface inversion layer increases in
depth during the nocturnal hours while the
upper level inversion slowly decreases in
altitude. This development leaves a mixed
layer of decaying turbulence trapped between
the two inversion layers until the unstable
surface layer breaks through the low-level in-
version the next morning to re-energize this
region. The turbulence distribution across
the entire boundary layer at any particular
time of day may only be crudely represented
by a single stability parameter.
3.2r
Because of the slow growth of the noc-
turnal, low-level inversion during the early
morning hours, it is possible to parameterize
approximately the distribution below this
altitude as a function of a single stability
parameter (such as a Richardson number) and a
Rossby number parameter to indicate the rela-
tive importance of rotation. We may also
approximate the strongly unstable distri-
butions in terms of the characteristic ve-
locity Wjf appropriate for free convection.
Our model prediction for the vertical variance
in this limiting similarity form compares
quite well with laboratory simulations.9 Away
from this limiting case, two parameters, one
measuring the stability and one measuring the
height of the inversion layer, are required to
specify the distributions even under quasi-
steady conditions. These two parameters may
be taken as a Richardson number Ri and as
the ratio of the inversion height to the
Monin-Obukov length z./L . The relative in-
fluence of Rossby number and Richardson number
on the profiles of the quasi-steady wind and
vertical velocity variance are shown in
Pig. 2. Several observations are: (1) for
equal Ro the neutral or stable boundary
layer becomes thicker as the distance from the
equator and/or the geostrophic wind increases;
(2) the dimensionless height of the boundary
layer is reduced as Ro increases; (3) the
crosswind, perpendicular to the geostrophic
wind, increases as Ro increases; (4) in-
creasing Ri also increases the crosswind
component and decreases the boundary layer
thickness; (5) the only significant shift in
the direction of the wind with altitude for
the unstable profiles is in the vicinity of
the upper level inversion.
.3
V/U0
.04 .08 .12 .16 .2
(w"w)
U0
Fig. 2. Profiles for (a) mean wind in the direction of the geostrophic wind, (b) mean wind in
the direction normal to the geostrophic wind, (c) vertical velocity variance, for various
values of Ro = Ug/zQf and Ri , the bulk Richardson number based on the velocity and
temperature differences between the surface and 10m height. The height may be read directly
in Km for U = lOm/sec and f = 10"^ sec"1 .
716
-------
These limiting parameterizable cases
probably occur more often than the neutral,
steady-state profiles, but still represent
the exception rather than the rule. Even in
an ideal diurnal variation case, the para-
meterization would represent somewhat less
than half of the altitude-time domain, since
it does not account for the mixed layer be-
tween the two inversion layers between sunset
and noon the next day. When the diurnal sur-
face heat flux variation is significantly re-
duced in the presence of a relatively strong
stable lapse rate, the altitude of the top
inversion layer is drastically reduced and
the domain over which this parameterization
is valid correspondingly decreases.13
At least two other physical mechanisms
reduce the domain over which the previously
presented parameterization is valid: baro-
clinicity and radiation flux divergence. Both
of these influences are frequently present in
the planetary boundary layer. Not only do
they serve to increase the number of para-
meters governing the flow, but they introduce
additional dynamics and reduce the time over
which the quasi-steady parameterization is
valid. Results for some assumed time vari-
ations of these two influences as calculated
by our model have been presented in ref. 13.
Even when influences of nonhomogeneous terrain
are eliminated, the characterization of the
wind and turbulence distributions in the
planetary boundary layer in terms of two or
three parameters is necessarily rough and at
time highly erroneous. We believe 'much
better results for a valid prediction of
the distributions at any given time may be
•found by tracking the time variation of the
forcing boundary conditions for at least
twelve hours prior to the desired observation
time.
C. Additional Dynamics Introduced by
Diffusion Equations
When the wind and turbulence fields are
known, the additional parameters necessary to
determine the dispersal of a neutrally
buoyant, nonreactlve species are those neces-
sary to characterize the source S . Whenever
the characteristic time scale of the turbulent
mixing is much less than any time scale t
S
associated with S , the left-hand side of
Eq. (2) may be neglected and a superequilibri-
um (or K) theory should be approximately
valid. In the surface layer this reduction
would lead to Eq. (4) for K . Although this
approximation will not be valid for pollutant
sources with sufficient spatial inhomogenei-
tieSj it should be useful in many cases and,
in fact, probably forms the basis of the
limited success of Gaussian plume models para-
meterized for different stability classes.
It is easy to think of many cases where
A/q is no longer much smaller than t . Two
S
common examples are when A « A , or when
the plume scale divided by the crosswind ve-
locity is less than or of the same order.as
A/q . In such cases K theory may lead to
considerable error. In general, reliable dif-
fusion models must be able to compute u.c
accurately whether or not the time rate of
change of u1
significant. We believe Eq. (2) has this
capability. Results of sample calculations
for both line and point source releases have
been presented elsewhere . 1 ° ' 1 "* Space limits
us to one example here.
4. Sample Calculation for Free Convection
Figure 3 presents the results of a
sample model calculation for dispersion in a
free convection mixed layer. Deardorff and
Willis15)16 simulated dispersion in the atmos-
pheric mixed layer by releasing a large number
of small, neutrally buoyant particles as an
instantaneous line source into the bottom of a
water convection tank. They interpret their
results in terms of a continuous point source
release into a uniform wind. Initial compari-
sons of our predictions with their obser-
vations for both the species dispersal and
turbulence field have been made . » l '* Here we
will take advantage of their most recent
published results to update this comparison.
3.0
Fig. 3- Isopleths of the crosswind integrated
concentration, Cr , as a function of down-
stream distance and height when a continuous
point source is released into an unstable
mixed layer. (a) Model predictions; (b)
Laboratory observations of Deardorff and
Willis.16
We begin our calculations with a
Gaussian plume distribution with a = a =
y z
0.006z. , since our model can not actually
start with a point release. A uniform wind is
applied and the calculation marches in x ,
the direction of the wind, to follow the plume
development. We plot the variation of the
normalized crosswind integral of the con-
centration
(or the advection of u^c) is
717
-------
+ 00
cy =
CUz,
(5)
In the completely mixed layer, approached as
x _,. oo , c~y = 1 for all z . In the early
development of the plume, both the obser-
vations and the predictions show the local
maximum in concentration rising above the
level of initial source,* z = 0.067z. .
o J-
Willis and Deardorff show that this effect
would correspond to a negative K over much
of the spatial domain if one attempted to
predict this by K theory alone. In our
model it is a direct result of the buoyant
forcing term in Eq. (2).
The greatest discrepancy between the pre-
dictions and the observations occurs in the
upper portions of the plume during the early
development and at the surface near X = 1 .
The discrepancy at the upper edge of the
plume may be partially due to the low
Reynolds number of the experiment (~ 1730
when based on q and z.) while our model
7
run was made for much higher Re (= 10 ) to
more nearly simulate atmospheric conditions,
but probably reflects some error in our
turbulent scale as the inversion layer is
approached. The higher rise of the plume as
well as a stronger horizontal dispersion of
the plume at altitude allows the observed
surface concentration to be lower than that
predicted. The general character of the dis-
persion is quite favorably predicted, es-
pecially considering the fact that no em-
pirical information from this particular
experiment has been used in determining the
model.
5. Concluding Remarks
Our model is currently capable of making
calculations for individual, neutrally
buoyant, nonreactive plumes. A three-
dimensional source release may be followed if
the wind and turbulent fields are assumed
stationary over the characteristic time re-
quired for the development of the plume. For
a two-dimensional source release this station-
arity requirement may be relaxed, but the wind
field must be independent of the third di-
mension. Steps are now underway to incorpo-
rate the capability to compute a buoyant plume
with internally generated turbulence. Some
refinements in the modeled terms and coef-
ficients should be expected as more compari-
sons with reliable measurements are made and
as fundamental theoretical work proceeds.
However, comparison of the results of the
current model with experimental observations
demonstrates that it is a valid tool for
studying the sensitivity of dispersion to
different time and space variations of the
boundary conditions on the planetary boundary
layer.
The model shows that quasi-steady para-
meterization is valid within the surface
layer, and in some limited regions of the
physically realizable time-altitude domain of
the planetary boundary layer; but, solution
of the species flux equation appears to be the
way to deal more accurately with the dispersal
problem in general.
References
"""Donaldson, C. duP. , Sullivan, R.D., and
Rosenbaum, H.: "A Theoretical Study of the
Generation of Atmospheric Clear-Air Turbu-
lence," AIAA J. 10_, 2, 1972, pp. 162-170.
2
Donaldson, C. duP.: "Construction of a
Dynamic Model of the Production of Atmos-
pheric Turbulence and the Dispersal of
Atmospheric Pollutants," Workshop on Micro-
meteorology, AMS, Boston, 1973, PP. 313-392.
^Lewellen, W.S. and Teske, M.: "Prediction of
the Monin-Obukhov Similarity Functions from
an Invariant Model of Turbulence," J. Atmos.
Sci., 30, 7, 1973, PP. 1340-1345.
Lumley, J.L. and Khajeh-Nouri, B.: "Compu-
tational Modeling of Turbulent Transport,"
Advances in Geophysics, 18A, Academic Press,
New York, 1974, pp. 169-192.
^Wyngaard, J.C., Cote, O.R., and Rao, K.S.:
"Modeling the Atmospheric Layer," Advances
in Geophysics, ISA, Academic Press, New
York, 1974, pp. 193-212.
6Mellor, G.L. and Yamada, T.: "A Hierarchy of
Turbulence Closure Models for Planetary
Boundary Layers," J..Atmos. Sci., 31, 1974,
pp. 1791-1806.
7
'Lewellen, W.S., Teske, M., and Donaldson, C.
duP.: "Turbulence Model of Diurnal Vari-
ations in the Planetary Boundary Layer,"
Proc. 1974 Heat Transfer and Fluid Mechanics
Inst., Stanford U. Press, 1974, pp. 301-319.
8Lewellen, W.S., Teske, M., et al.: "In-
variant Modeling of Turbulent Diffusion in
the Planetary Boundary Layer," EPA Rept. No.
EPA-650/4-74-035, 1974b.
^Lewellen, W.S., Teske, M., and Donaldson, C.
duP.: "Examples of Variable Density Flows
Computed by a Second-Order Closure De-
scription of Turbulence," AIAA Paper No.
75-871, 1975.
10
11
12
13
14
15
16
Lewellen, W.S. and Teske, M.: "Turbulence
Modeling and its Application to Atmospheric
Diffusion," EPA Rept. No. EPA-600/4-75-016,
Dec. 1975.
Yamada, T. and Mellor, G.L.: "A Simulation of
the Wangara Atmospheric Boundary Layer Data,"
J. of Atmos. Sci., 32_, 1975, PP. 2309-2329.
Panofsky, H.A.: "The Atmospheric Boundary
Layer Below 150 Meters," Annual Review of
Fluid Mechanics, Annual Reviews, Inc., Palo
Alto, Calif., 1974, pp. 147-177.
Lewellen, W.S. and Williamson, G.G.: "Wind
Shear and Turbulence Around Airports," Parts
1 & 2, A.R.A.P. Rept. No. 267, Jan. 1976.
Lewellen, W.S. and Teske, M.E.: "Second-Order
Closure Modeling of Diffusion in the Atmos-
pheric Boundary Layer" (to be published in
Boundary-Layer Meteorology).
Deardorff, J.W. and Willis, G.E.: "Physical
Modeling of Diffusion in the Mixed Layer,"
Proc. Symp. on Atmospheric Diffusion and Air
Pollution, Santa Barbara, Calif., Sept. 1974,
AMS, Boston, pp. 387-391.
Deardorff, J.W. and Willis, G.E.: "A Para-
meterization of Diffusion in the Mixed
Layer," J. of Appl. Meteorology, 14, Dec.
1975, PP. 1451-1458.
718
-------
POINT SOURCE TRANSPORT MODEL WITH A SIMPLE
DIFFUSION CALCULATION FOR ST. LOUIS
Terry L. Clark*
Robert Eskridge*
Meteorology and Assessment Division
Environmental Sciences and Research Laboratory
Environmental Research Center
Research Triangle Park, N.C. 27711
Abstract
The transport of an inert gaseous contaminant in
St. Louis is modelled by a numerical method. The nu-
merical model calculates, from a wind field, a two-
dimensional field of streamfunction values character-
izing the air flow. The wind field is objectively
analyzed from 15-minute averaged RAPS (Regional Air
Pollution Study) data using orthogonal functions.
The streamfunction values are calculated from an el-
liptic equation solved by successive over-relaxation.
After assuming a non-divergent, two-Himensional
flow, streamlines are analyzed from the streamfunction
field. Trajectories are then computed by displacing
puffs of a contaminant along a specified streamline.
A simple diffusion calculation is included in the
model to demonstrate one of its possible uses.
Measurements obtained from a SF, tracer study
provide data with which the results of the transport
model are compared. Six of the nine sets of measure-
ments obtained along 3 highways in St. Louis during
August 12-13, 1975 are considered.
Introduction
Accurate simulation of air pollution concentra-
tions has been of interest,for many years beginning
with the works of Roberts. He developed the basic
plume formulas, which have been used for point source
releases and other applications. Mathematical models
based upon these and other formulations have been de-
veloped to simulate air pollution concentrations. In
the last several years, urban-scale grid point models
have been developed by Systems Applications Incorpo-
rated and IBM 2,3. m addition, an urban-scale trajec-
tory grid point model has been developed by Eschen-
roeder.4
The grid point models include variable winds,
but because of limited resolution, are unable to be
applied to single point-source cases. Gaussian plume
models, on the other hand, are capable of calculating
concentrations for single point sources, but do not
account for variable wind velocities. A model with a
high spatial resolution that employs wind fields vary-
ing over short periods of time would be useful on an
urban-scale. Some practical uses of this type of
model would include identifying areas affected by in-
stantaneous releases from one or more point sources
and supplying the transport mechanism for deposition
studies.
The transport model described in this paper was
developed to apply to instantaneous point-source
emissions in the form of puffs. Wind and streamfunc-
tion fields, from which trajectories were calculated,
were generated from 15-minute averaged data. The cal-
culation of trajectories ensured a spatial resolution
much better than the grid point models. Moreover, the
selected averaging period reflected small-scale changes
of the wind velocity, which, theoretically, would en-
hance the Quality of the trajectory calculations.
In this paper, the development of the transport
model and results of six puff releases are described.
The results were compared to an Atmospheric Tracer
Study which involved continuous SF, releases. In or-
der to demonstrate the usefulness of the transport
model, a simple diffusion calculation was added. A
more complex diffusion calculation can be substituted
easily.
Data
A. Meteorological
The wind fields employed in this application of
the transport model were analyzed from wind data meas-
ured from the Regional Air Pollution Study (RAPS) in
St. Louis, Missouri during August of 1975. The Re-
gional Air Monitoring Stations (RAMS) network consists
of 25 sites, 21 of which are located within 26 km of
downtown St. Louis (Fig. 1). Data from these 21 sites
were considered for the wind analyses. The grid lo-
cations of two of these sites, namely 116 and 121, were
relocated slightly so that they were located on the
wind analysis grid. One-minute averages of wind speed
and direction were obtained from continuous measure-
ments atop a 10-meter tower at sites 108,110,114-118,
and 121 and a 30-meter tower at the remaining sites.
The height differences of the levels of measurements
accounted for local obstructions to the air flow.
After the data were validated, 15-minute averages were
computed for each, site for selected time periods.
B. Tracer Measurements
* On assignment from the National Oceanic and Atmos-
pheric Administration, U.S. Department of Commerce
Measurements from the Atmospheric Tracer Study
taken by the California Institute of Technology in Aur
gust of 1975 were employed to compare the results of
the trajectory and concentration computations. In
this study, continuous releases of SFg tracer were
completed from one of three sites in St. Louis during
five periods in August of 1975. The results of the
model corresponding to the tracer study case for Au-
gust 12-13 are discussed in this paper.
The SFg tracer was released, in this case, from a
point 20 feet above the ground at Webster College
(just to the southwest of St. Louis) from 8:40 P.M. un-
til 3:00 A.M. at a rate of 6.2 gm sec .
719.
-------
During this period, the sky was clear, the surface
temperatures were in the lower 70's, and the winds
were strong from the south-southwest.
Between 10:25 P.M. on August 12 and 2:26 A.M. on
August 13, 9 automobile traverses were conducted
along segments of 3 highways in St. Louis where the
SF, plume was expected to pass. Throughout each tra-
verse, a passenger in the automobiles took a grab
sample in a 30 cm3 plastic syringe every 0.1, 0.2 ,•
0.3, 0.4, or 0.5 miles along the route. The interval
depended upon both the distance from the point source
and the steadiness of the wind.
116
r
Fig. 1. The 40 x 40 km analysis grid and location
of 21 of the 25 RAMS sites in St. Louis, Missouri.
Every tenth grid point on the interior and every
tenth grid point on the boundary are indicated.
The "*" indicates the location of Webster College.
Hind Field Analysis
Meridional, zonal, and resultant wind fields were
objectively analyzed on a 40 x 40 grid (Fig. 1 ) by a
technique based upon a generalized orthogonal function
approach developed by Jalickee and Rasmusson.P The
technique prescribes a relationship between a set of
M observations,
, i 1-.2, ..... M
with space-time coordinates,
* i (x^y^z^t.) , i = 1,2,..
and a set of N base functions,
f Ic 1 9 M
Tk , K l,^,....,N
multiplied by a set of coefficients,
bk , k 1,2, M
according to Eq. 1.
>l f !.(*-• ) + Z.
M
The term, z. represents a random variable signifying
noise in the observations.
The particular set of 15 base functions employed
in the model were
I,x.xy,y,x2,x2y,x2y2,xy2,»2.x3,x3y.xy3,y3,x4,y4.
The optimal set of coefficients was determined by
minimizing the quantity
(1)
15
Tfie resulting equation
-------
were more agreeable with the data when determined from
a smaller grid. The values obtained at each grid
point were dependent upon the total wind field, due to
the iterative process employed. Isolines of the re-
sulting streamfunction values represented streamlines
for the case of two-dimensional, non-divergent flow.
Assuming this type of flow, the equation of con-
tinuity can be written as
(2)
3U.
o.
_
ay
The streamfunction,
-------
After the grid point values of the streamfunction
were calculated, the value of the streamfunction at ' i
the specified location of the parcel or puff was de-
termined. This was accomplished by the use of a 16-
point interpolation scheme developed by Gandin and
Boltenkov.9 This value identified the isoline or
streamline the puff would follow during the ensuing
15-minute period.
Next, the equation of the particular streamline
was determined. First, the points where the stream-
line intersected the borders of the 16 grid squares
nearest the puff were identified. The identification
was made possible by the use of an interpolation
scheme employing finite differences CEq- 9).
P(x) = f[xQJ + f[x-|,x0](x-x0) + f[x2,x1,x0](x-x0)(x-x1)
(9)
where x ,x,, and x? are x- coordinates on the grid.
The y- Boordinates of the points of intersection ar
y- Coordlnates~ot the points
calculated in a similar fashion.
are
The x- coordinate of the initial location of the
puff (x ) and the x- coordinates of the two nearest
points of intersection downwind from the puff
(x-i,Xp) were fitted by a quadratic polynomial, gCx),
using finite differences (Eq. 9.). The puff was then
displaced along the curve described by gfx) at a rate
equal to an interpolated value of the wind speed for a
period of 100 seconds. The final displacement posi-
tion relative to the starting point was determined by
using the arc length. Eq. 10 is the arc length for-
mula used to calculate the puff displacement in the x
direction. The formula to calculate the puff displace-
ment in the y direction is similar.
where
1/2
g(x) = ax + bx + c.
dx
(10)
The values of x and D were known and x.- was de-
termined by Newton's method. The value of xf, which
represented the displacement along the x- axis, was
added to or subtracted from the position along the
axis at the end of the 100-second period.
This process was repeated 8 more times using the
same wind field. At the termination of 900 seconds
(15 minutes), a new wind field was calculated based
upon up-dated, 15-minute averaged winds. The puff
was transported for an additional 15 minutes starting
from the termination point of the previous period.
This process ended when the position of the puff was
beyond the area where the plume from the tracer study
was sampled.
Concentration Calculation
The concentration of each puff was calculated at
the end of each 100-second period. This was performed
using a diffusion calculation based upon Eq. 11, which
was derived by Roberts.1
c(x,y,z) =
-3/2
-r
(n;
where Q is the initial generation of contaminant (gm);
K is the diffusion coefficient (m2 sec-1); t represents
the time after the release of the puff from the source
(sec); and r is the distance from the center of the
puff (m). From the tracer study, the emission rate of
SF6 was known. The value assigned to Q in Eq. 11 was
the mass of SF6 emitted during a one-minute period.
It was assumed that the diffusion coefficients
along the x-,y-, and z- axes were equal to a constant
coefficient, K. However, the method of determining
the values of the coefficient was beyond the scope of
this research. The treatment of the K- theory in ex-
isting models was examined instead. The pollution
model constructed by IBM assumed a value of 500 m
sec'1. 7 The planetary boundary layer model developed
by Gerrity used values of K between 1 and 100 nr
sec-1. 1° In the transport model, a value of 10 was
chosen for generally stable conditions and 100 nr
sec-1 for generally unstable conditions.
Results and Conclusions
The results of the transport model for 6 of the 9
instrumented automobile traverses of the St. Louis
tracer study during August 12 and 13, 1975 are pre-
sented in Figs. 3A-F. The puff positions are shown
on the 40 x 40 km grid at the termination of every 15-
n'nute period. In every case, the source point was
located at Webster College (denoted by "WC") near the
southwest corner of the grid. The shaded numbers in-
dicate RAMS sites where data was omitted intentionally
(#103 and #104 on the east side of St. Louis), or ei-
ther missing or highly questionable. It is important
to note that data were missing from several key sites
throughout the periods.
The small bars along portions of highways #40,
#70, and #270 represent segments of the roads where
SFs tracer was -measured via the traversing automo-
biles. The maximum measured concentrations of the SFg
plumes are listed adjacent to each figure. This value
might not equal the actual maximum concentration, !
since grab samples were taken at prescribed intervals
along the routes.
Fig. 3A indicates that the model transported the
puff released at 12:30 A.M. across highway #40 at a
point 1.5 km east of the area where the plume was de-
tected. At this point, the puff was 5 km downwind
from Webster College. The calculated concentration at
the surface directly beneath the center of the puff
was 841 ppt (parts per trillion). This is 30% of
the maximum concentration measured at this time.
Fig. 3B shows that the puff released at midnight
traversed highway #70 at approximately 1:00 A.M. The
point of intersection agrees with the measurements.
At this time, the puff was 14 km from the source. The
calculated concentration was 220 ppt or 91% of the
maximum concentration measured there.
Fig. 3C indicates that the puff released at 11:45
P.M. on August 12 traversed highway #270 at approxi-
mately 1:15 A.M. on August 13. The point of inter-
section also agrees with the tracer study data. The
puff at this time was approximately 20 km from the
source point. The concentration calculated as the
puff crossed the highway was 122 ppt, which is 67% of
the maximum concentration measured.
Fig. 3D indicates that the puff released at 1:45
A.M. crossed highway #40 at a point less than 1 km
from the section of the highway where the tracer plume
was detected. At this point, the puff was 5 km from
the source point. The calculated concentration at
this time was 841 ppt or 43% of the maximum concentra-
tion measured.
Fig. 3E shows that the puff released at 1:00 A.M.
crossed highway #70 at a point where the tracer plume
was detected. The puff at this time was approximately
14 km from the source. The concentration calculated
was 286 ppt or 47% of the maximum concentration mea-
sured.
722
-------
•©—
•
-------
The puff released at 12:30 A.M. was transported
across highway #270 near the intersection of highway
#67, as shown in Fig. 3F. This was in agreement with
the tracer study data. The puff was more than 20 km
from the source point at this time. The calculated
concentration was 125 ppt or 55% of the maximum con-
centration measured.
Four of the six puff trajectories presented here
indicate that the model was spatially accurate in
transporting the puffs across three highways in St.
Louis. However, the temporal accuracy cannot be de-
termined from the data used here, since the SFg tracer
was emitted continuously. It should be noted, how-
ever, that both the tracer study and the transport
model indicated that at approximately 2:00 A.M., the
contaminant traversed a segment of highway #270 4-5
km to the east of the segment where the contaminant
traversed the highway at approximately 1:15 A.M. (see
Figs. 3C and 3F).
The remaining trajectories were approximately 1
km from the section of the highways where the tracer
plume was detected by the instrumented automobile
traverses. In these two cases, the puffs were trans-
ported across the grid in an area where data were
missing from key RAMS sites #111 and #119. No data
were available in the southwest corner of the grid,
so the assumption was made that the 15-minute aver-
aged wind velocity at RAPS sites #106 was representa-
tive of the averaged wind velocity at site #119.
Therefore, the objective analyses of the wind was
biased towards the wind velocity at site #106. This
could have been the cause of the slight eastward dis-
placement errors illustrated in Figs. 3A and 3D.
The concentrations calculated by the simple dif-
fusion equation at the surface directly beneath the
puffs were either comparable with or 2-3 times small-
er than the maximum concentrations observed from the
tracer study. The value of the diffusion coefficient
in the diffusion equation was not calculated in this
model. It was assigned a value thought to represent
the atmospheric conditions at the time of the tracer
study. Moreover, the amount of contaminant in the
puff at its time of generation was arbitrarily de-
fined by the amount of contaminant released during a
one-minute time period. This diffusion calculation
was a simple one and was used only to demonstrate an
application of the transport model.
References
1. Roberts, O.F.T.; Pro. Roy. Soc. London, Series
A, 104, 640-654, 1923.
2. Reynolds, S.D., P.M. Roth and J.H. Seinfeld;
Atmos. Env. , ]_, 1033-1061, 1973.
3. Shir, C.C. and L.J. Shieh; J_. App. Met., }3_> 185-
204, 1974.
4. Eschenroeder, A.Q. and J.R. Martinez; G.R.C.,
Santa Barbara, Calif., IMR1210, 1969.
5. Shair, F.H., B.K. Lamb, and J.D. Bruchie; EPA
Grant No. R 802160-03-2, 206 pp., 1975
6. Jalickee, J.B. and E.M. Rasmusson; Proceedings
of the Third Conference on Probability and
Statistics in Atmospheric Science, June 19-22,
1973.
7. Heffter, J.L., 6.J. Ferber, andA.D. Taylor;
NOAA Tech Mem ERL ARL-50, 28 pp., 1975.
8. Frankel, S.P.; Math. Tables Aids Comput., 4_,
65-75, 1959.
9. Gandin, L.S.; Israel Program for Scientific
Translations, IPST Cat. No. 1373, Jerusalem,
1965.
10. Gerrity, Jr., J.P.; Mon. Wea. Rev., 95, 261-282,
1967.
724
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THE CHANGE IN OZONE LEVELS
CAUSED BY PRECURSOR POLLUTANTS:
AN EMPIRICAL ANALYSIS*
Leo Breiman
Technology Service Corporation
Santa Monica, CA. 90403
William S. Meisel
Technology Service Corporation
Santa Monica, CA. 90403
Abstract
An empi-r-ical analysis of ambient air data is used to
relate the one-and two-hour change in oxidant levels
in the urban environment to the preceding level of
precursor pollutants and to meteorological variables.
The intent was to demonstrate the feasibility of de-
veloping a set of empirical difference equations for
the production of oxidant over time. The main vari-
ables determining one-and two-hour oxidant changes
were extracted using nonparametric regression tech-
niques. A model for two-hour oxidant changes was
developed using nonlinear regression techniques.
The implications of the model are discussed.
Introduction
Typical objectives of a modeling effort are (1)
qualitative understanding and (2) quantitative impacts.
In air quality modeling, these objectives are aimed at
the ultimate objectives of determining the effects of
alternative control policies and understanding which
policies will be most productive. Ozone air quality
modeling efforts have been largely concentrated at
extremes of the spectrum of approaches to modeling:
(1) simple statistical models with limited application,
or (2) complex models based on the underlying physics
and chemistry of the process. The former class of
models provides easy-to-use, but rough, guidelines,
the latter class of model is capable of detailed tem-
poral and spatial impact analysis, but costly and dif-
ficult to use.
This paper illustrates the feasibility of an inter-
mediate class of model which is relatively inexpensive
and easy-to-use, but which is capable of providing
reasonably detailed temporal and spatial estimates of
oxidant concentration. Further, the form of the model
makes it possible to understand (with careful inspec-
tion) the qualitative implications of the model as a
guide to the design of control strategies.
We hasten to emphasize, however, that a full model in
this class is not a result of this paper; rather, we
present an analysis which we believe indicates the
feasibility of the development of such a model. In
particular, we develop an empirical difference equa-
tion for the production of oxidant from chemical
precursors, as effected by meteorological variables.
A full model would involve difference equations for
the precursor pollutants as well. Further, data
easily available did not include all meteorological
variables of possible interest or emission data.
(Since ozone is a secondary pollutant, emissions of
primary pollutants over a brief interval, e.g., one
hour, will not effect the change in ozone levels over
that interval to the degree they effect the change in
primary pollutant levels. Since we did not derive
difference equations for the primary pollutants in
^
This work was supported in part by Contract No.
68-02-1704 with the Environmental Protection Agency.
this study, not including emissions did not prove
serious.) The context in which the reader should
then interpret the results is as the degree to which
the change in ozone can be explained despite these
limitations. Whatever degree of explanation of the
variance in one- or two-hour changes in ozone we can
achieve within these limitations can be improved when
more of the omitted factors are taken into account.
This analysis will thus provide a pessimistic estimate
of the degree of success that can be expected in a
full-scale implementation of the approach. This paper
summarizes work reported more fully elsewhere [1].
Form of Model
We consider a "parcel" of air, and define 03(1) as the
oxidant concentration averaged over the hour preceed-
ing time t. We further define A03(t) as the change in
the hourly average oxidant concentration (in pphm) in
the time interval At following t; explicitly,
A03(t)
03(t + At)
03(t)
(I!
(We will consider At 1 hour and At 2 hours.)
We seek an equation predicting the change in hourly
average concentration after time t from measurements
of pollutants and meteorology available at time t.
Pollutant measurements other than ozone we will con-
sider as possible precursors include the following,
all of them in terms of concentration averaged over
the hour preceding time t:
N0(t)
N02(t)
HC(t)
CMt)
NO concentration (pphm)
NO- concentration (pphm)
Non-methane hydrocarbon concentration
(ppm)
Methane (ppm).
Meteorological variables considered explicitly include
the following, again averaged over the hour preceding
time t:
o
SR(t) solar radiation (gm-cal/cm /hrs)
T(t) temperature (°F).
Mixing height was not used in the present study.
We thus seek a relationship of the form
A03(t) F[03(t), N0(t), N02(t), HC(t),
CH4(t), SR(t), T(t)]
(2)
which accurately reflects observed data. Referring to
(1), equation (2) can be alternatively written as
725
-------
03(t + At) 03(t) + F [03(t), N0(t), N02(t),
HC(t), CH(t), SR(t),
This form indicates explicitly how such a relationship,
if derived, can be used to compute a sequence of hourly
or bi-hourly oxidant concentrations. (Similar equa-
tions would be derived for the primary pollutants to
provide a complete model.)
We must incorporate transport effects. We have adopted
a rather simple model. The model estimates the tra-
jectory of a "parcel" of air from ground-level measure-
ments of the wind field. A parcel arriving at a given
location at a given time (e.g., Pasadena at 1600 hours)
is estimated, from the current wind direction, to have
been at another location upwind one hour earlier. The
distance traveled from that direction is given by the
current wind speed. The trajectory is tracked back-
wards to give a sequence of hourly locations. The
"actual" values of pollutant levels at these points at
the given times are obtained by an interpolation pro-
cedure from measured data at fixed monitoring stations.
The motivation for tracking parcels backwards rather
than forwards is to allow choice of parcels which end
up at monitoring stations; in part so that the last
(and often highest) pollutant concentration need not
be interpolated. The air parcel trajectory approach
is obviously a simplification of the true physics of
the system; this approach is similar to assumptions
employed in some physically based air quality models
[2]. In the present empirical modeling context, the
trajectory approach is a statistical approximation
rather than an assumption; that is, the inaccuracy of
the approximation will be reflected in the overall
error of the final empirical model.
The Data
Data collected by the Los Angeles Air Pollution Control
District was employed. Air quality data from the
seven monitoring stations indicated in Figure 1 was
utilized.
We interpolated the wind field in a region of the Los
Angeles basin so that we were able to track parcels
of air as they moved through the basin. The pollutant
readings at seven APCD stations were also interpolated
so that we could keep hourly records of the pollutants
discussed. We also had the hourly solar radiation
readings at the Los Angeles Civic Center location of
the APCD, and hourly temperature readings at three
representative locations in the basin.
Our study was carried out using data from the five
summer months, June through October 1973. About 7000
trajectories were formed and placed in the primary
data base.
From the bank of 7000 trajectories, we extracted a
sample of about 1900 data vectors of the form
(A03, 03, NO, N02, HC, CH4, SR, T) ,
where A03 was a one-hour change and about 1800 vectors
where A03 was a two-hour change.
The Analysis
Since time is only implicit in (2), we search for a
fixed relationship
A03 F(03, NO, N02> HC, CH4> SR, T) . (4)
Equally important, we want to determine which of the
variables were most significantly related to the
change in ozone. Therefore, we really had two objec-
tives in this study:
(1) To find those subgroups of the variables
most significantly related to the ozone
change.
(2) To find the form of the function F providing
the best fit to the data.
Variable Selection
For the variable selection and exploratory phase, we
used INVAR, a general nonparametric method for esti-
mating efficiently how much of the variability in the
dependent variable can be explained by a subgroup of
the independent variables [3]. This technique esti-
mates the limiting value of percent of variance ex-
plained (PVE) by a "smooth" nonlinear model.* We first
tested all independent variables as individual pre-
dictors, then pairs of variables, and then added vari-
ables to find the best three, etc. Some results for
single variables are tabulated in Table 1. The most
significant individual variables (in approximate order
of importance) are SR, NO^, T, and 0.,.
Exploring pairs of variables, we found the results
shown in Table 2. Other pairs were run that resulted
in lower percent of variance explained than those in
the table.
Triplets of variables were then explored with one
really significant improvement showing. Some results
are shown in Table 3.
The final significant increase occurred when we added
temperature to 03, NO?, SR. But, somewhat strangely,
the increase was significant only for the data base of
one hour AO,. Here we obtained
Variables
03, N02, SR, T
One-Hour PVE
65.9
In all of the INVAR runs using HC and CH4, neither of
them significantly increased the PVE. For instance,
when HC and CH^ were individually added to the vari-
ables NOo, NO, Oo, and SR, the maximum increase in PVE
was 2.1%. J
These results are encouraging; the three variables
03, N02, SR predict about 71% of the variance in two-
hour ozone changes, that is, with a correlation be-
tween predicted and actual values of 0.84 over 1800
samples.
Specific Functional Relationship
The exploratory analysis provided nonparametric esti-
mates of the degree of predictability of two-hour
A03 as a function of 03, N02, SR. In this section,
Percent of variance explained equals
,QO -I variance of error in prediction
variance of dependent variable
726
-------
BURSANK PASADENA
i\ 7*\ AZUSA
' * «-
~~--^POMONA
N
SCALE IN MILES
TON BEACH
Figure 1. We Study Region.
Table 1. Percent of Variance Explained
(Single Variables)
Table 3. Percent of Variance Explained
(Triplets of Variables)
Variable
°3
NO
N02
HC
,CH4
SR
T
Table 2.
One-hour
15.8
13.4
25.7
19.2
16.6
30.3
17.1
A03 Two-hour A03
24.1
12.9
41.7
15.6
19.3
36.7
35.8
Percent of Variance Explained
(Pairs of Variables)
Variable
N02> 03
N02, SR
N02> T
N02> NO
03, SR
SR, T
0,, T
One-hour
40.8
42.3
38.7
34.8
53.0
43.6
33.2
A03 Two- hour A03
55.0
49.6
52.9
50.1
58.8
52.1
46.7
Variables
0,, NO,, SR
«J L.
N02, NO, SR
0,, NO,, T
3 2
One-hour A03
60.2
46.7
46.7
Two- hour
71.1
53.8
64.9
A03
we discuss the derivation of a specific simple func-
tional form to make explicit this relationship.
To get a continuous functional form for the relation-
ship of A03 to 03, N02, and SR, we used continuous
piecewise linear regression [4,5]. Since the function
generated by this method is smoother and less general
than that used in INVAR estimates, we did not achieve
the level of PVE obtained by INVAR. The continuous
piecewise linear function which minimizes the mean-
square error in the fit to the 1800 sample points is
given by*
A03 = 5.125 • max {A,B,C}
1.167 • max {D,E,F} + 10.48
(5)
where:
A 0.2146
0,
.0701 • NO,
.002268
.02114- 0,
.1638 • 0,
-.1013
- .09855- NO
N02 - .01075
SR + .9376
SR + 2.275
.005938 • SR .2263
The notation max {A,B,C} means the largest of the
three values computed by equations A, B, and C.
727
-------
0 = .02709 • C
E = -.009565 •
F = -.0144 • 0,
.3015 • N02 + .001298 • SR + 2.304
+.0005252 • N02 .001079 • SR+.2306
.2066 • N00 .003171 • SR 2.943
(The unusual form of the equation has no physical
interpretation, but is simply a consequence of the
particular methodology employed.) This equation ex-
plained 60.7% of the variance, a correlation between
predicted and actual values of 0.78.
This equation can be used to calculate a sequence of
oxidant concentrations in a parcel of air by using
known values of the other pollutant concentrations
(since difference equations for these pollutants have
not been derived). Figures 3, 4, and 5 illustrate the
result for three air parcel trajectories.
INTERPRETATION OF MODEL IMPLICATIONS
Let us attempt to interpret the functional form in (5).
The final fited surface is fairly simple, consisting of
a continuous patching together of eight hyperplane
segments. A three-dimensional slice of this surface
is graphed in Figure 2. Of the eight regions, there
are three small regions that together contain only
1.0% of the total number of points. We will ignore
these and restrict our analysis to the information
contained in the functional fit to
other regions.
AO, in the five
As a quick preliminary summary, in Table 4 we give the
means of all variables corresponding to the points in
each region.
Table 4. Means of Variables by Region
three regions, with a total of 20% of the sample
points, represent more extreme conditions.
The linear equations in each region are given in
Table 6; these are derived from equation (5).
Table 6. Linear Equations for AO, by Subregion
Region
1
2
3
4
5
Equations
-.14 (03)
-.097(03)
-.87 (03)
-.092(03)
-.82 (03)
+ .87
+ .52
+ .86
+ .28
+ .26
(NO
(NO
(NO
(NO
(NO
2>
2>
2>
2)
2>
+ .054
+ .056
+ .029
+ .059
+ .034
(SR)
(SR)
(SR)
(SR)
(SR)
-3
-1
+9
+2
+15
.9
.4
.0
.3
.1
Before discussing these results, since the size of the
above coefficients depend on the scaling of the vari-
ables, we introduce normalized variables by dividing
the original variables by their overall standard de-
viations, i.e., denoting normalized variables by primes:
0,
03/6.2, N02 N02/5.2, SR = SR/52.8. (6)
The equations are given in terms of the normalized
variables, in Table 7.
Table 7. Normalized Equations for AO,
(AO, not normalized)
Region
Overall
Region 1
Region 2
Region 3
Region 4
Region 5
Percent of
Points
100
46
33
8
7
5
A03
7.1
3.7
11.0
1.2
14.7
8.7
°3
6.1
3.6
4.6
20.4
5.4
16.7
N02
9.0
4.9
11.9
7.3
20.3
12.8
SR
100
73
118
139
119
149
In Table 5 the mean values are characterized by region.
Table 5. Mean Value Characteristics
Region
1
2
3
4
5
A03
very low
high
very low
high
above avg.
°3
very low
low
high
below avg.
high
N02
very low
above avg.
below avg.
high
above avg.
SR
very low
above avg.
high
above avg.
high
This layout of mean values is itself interesting.
Region 1, containing almost half of the sample points,
is representative of low pollution levels, low 03
production, and low solar radiation. Region 2, with
33% of the points, contains data with above average
mean M02 and solar radiation levels, below average
03 levels, and high positive changes in 03. The other
Region
1
2
3
4
5
Equations
-0.
-0.
-5.
-0.
-5.
9
6
4
(o3)
(o3)
(0,)
57(03)
1
(o3)
+4.
+2.
+4.
+1.
+1.
5
6
4
4
4
(N02)
(N02)
(N02)
(N02)
(N02)
+2.8
+2.9
+1.5
+3.1
+1.8
(SR)
(SR)
(SR)
(SR)
(SR)
-3.
-1.
+9.
+2.
+15.
9
4
0
3
1
The major qualitative conclusions that can be inferred
from these tables (see [1] for fuller discussion) are
the following:
o:
(2)
At below average 03 levels, the 03 change
is determined largely by the SR and NOg
levels, with larger values of these latter
two related to larger values of the 03 change.
The largest positive changes in 03 occur in
this regime.
At above average 03 levels, the Og has a
strong negative association with 03 change,
and moderate to high levels of N02 and SR are
associated with low to only moderately above-
average changes in 03.
Conclusion
We were able to derive surprisingly accurate equations
predicting the short-term change in oxidant concentra-
tion (considering the limitations of the data and the
difficulty of the problem). These results are encour-
aging in terms of the practicality of a full model
involving emission variables and all the major reactive
pollutants.
728
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References
1. Breiman, Leo, and William S. Meisel, "Short-term
Changes in Ground-Level Ozone Concentrations:
An Empirical Analysis," Final Report for EPA
Contract No. 68-02-1704, October 1975.
2. Wayne, Kokin, and Weisburd, "Controlled Evaluation
of Reactive Environmental Simulation Model (REM),"
Vols. I & II, NTIS PB 220 456/8 and PB 220 457/6,
February 1973.
3. Breiman, L., and W. S. Meisel, "General Estimates
of the intrinsic Variability of the Data in Non-
linear Regression Models," March 19, 1975, to be
published in Journal American Statistical Asso.
4. Horowitz, Alan, W. S. Meisel, and D. C. Collins,
"The Application of Repro-Modeling to the Analysis
of a Photochemical Air Pollution Model," Final
Report for EPA Contract No. 68-02-1207,
December 31, 1973.
5. Meisel, W. S., and D. C. Collins, "Repro-Modeling:
An Approach to Efficient Model Utilization and
Interpretation," IEEE Trans, on Systems, Man, and
Cybernetics. July 1973.
Figure 2. Graph of Regression Surface,
with SR = 100.
O Actual value
• Predicted value
(pphm)
7 AM
1 PM 3PM
(pphra)
O Actual value
• Predicted value
9 AH
1 PM
O Actual value
• Predicted value
(pphm)
7 AM 9 AM
11 AM 1 PM
3 PH 5 PM
Figures 3, 4, & 5. Wind Parcels Arriving at the
Pomona Station at 3, 4, & 5
PM, respectively.
729
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QUALITY ASSURANCE AND DATA VALIDATION FOR THE
REGIONAL AIR MONITORING SYSTEM OF THE
ST. LOUIS REGIONAL AIR POLLUTION STUDY
Robert B. Jurgens*
Environmental Sciences Research Laboratory
Research Triangle Park, North Carolina 27711
And
Raymond C. Rhodes
Environmental Monitoring and Support Laboratory
Research Triangle Park, North Carolina 27711
The success of model development and evaluation
from a body of monitoring data depends heavily upon
the quality of that data. The quality of the
monitoring data in turn is dependent upon the various
quality assurance (QA) activities which have been
implemented for the entire system, commencing with
the design, procurement, and installation of the
system and ending with validation of monitoring data
prior to archiving. Of the many sources of aeromet-
tric and emissions data that exist, the St. Louis
Regional Air Pollution Study (RAPS) is the only known
study specifically designed for model development and
1 2
evaluation on an urban/rural scale. '
The prime objective of RAPS is to develop and
evaluate mathematical models which will be useful in
predicting air pollution concentrations from informa-
tion of source emissions and meteorology. In addition
to detailed emissions and meteorological data, an
extensive base of high quality pollutant monitoring
data is required to verify and to refine the models.
The Regional Air Monitoring System (RAMS) is the
ground-based aerometric measurement system of RAPS and
consists of 25 automated data acquisition sites
situated in and about the St. Louis metropolitan area.
Data from these 25 stations are transmitted over
telephone lines to a central computer facility for
processing and then sent to Research Triangle Park for
archival. Details of RAMS have been described by
Meyers and Reagan. The complex air pollution,
meteorological, and solar radiation measurements that
are made at RAMS sites are shown in Table 1. Also
shown are the recording intervals and the number of
recording stations for each instrument.
Two main challenges exist for an effort of the
magnitude of the St. Louis study:
1. To efficiently and effectively handle the
large quantity of monitoring data; and
2. To obtain high quality monitoring data.
In general, data validity results from: (1) A
quality assurance system aimed at acquiring acceptable
data, and (2) A screening process to detect spurious
values which exist in spite of the quality control
process.
Table 1. RAMS NETWORK MEASUREMENTS
AIR QUALITY:
METEOROLOGICAL:
SOLAR RADIATION:
SULFUR DIOXIDE
TOTAL SULFUR
HYDROGEN SULFIDE
OZONE
NITRIC OXIDE
OXIDES OF NITROGEN
NITROGEN DIOXIDE
CARBON MONOXIDE
METHANE
TOTAL HYDROCARBONS
WIND SPEED
WIND DIRECTION
TEMPERATURE
TEMPERATURE GRADIENT
PRESSURE
DEW POINT
AEROSOL SCATTER
PYRANOMETER
PYRHELIOMETER
PYRGEOMETER
MEASUREMENT
INTERVAL (min)
5
t
5
i
\
1
1
1
5
5
5
13
12
13
13
25
25
25
25
25
25
25
25
25
25
7
7
25
25
E
4
4
QUALITY ASSURANCE SYSTEM
The following list includes the elements of a
total quality assurance system for aerometric
monitoring:
Quality policy
*Quality objectives
*Quality organization
and responsibility
QA manual
*QA plans
Training
*Procurement control
Ordering
Receiving
Feedback and
corrective action
*Calibration
Standards
Procedures
Internal QC checks
Operations
Sampling
Sample handling
Analysis
Data
Transmission
Computation
Recording
* Validation
*Preventive maintenance
*Rellability records and
analysis
*Document control
Configuration control
*Audits
On-site system
Performance
Corrective action
Statistical analysis
Quality reporting
Quality investigation
Inter!ab testing
Quality costs
*0n assignment from the National Oceanic and Atmos-
pheric Administration, U.S. Department of Commerce.
Detailed definition and discussion of the
elements of quality assurance for air pollution „
measurement systems have recently been published.
The elements of particular concern to RAMS
fall into three general categories:
1. Procurement and management, those activities
which need to be established or accomplished early
in the program;
2. Operation and maintenance, those activities
which need to be performed routinely to assure
continued operation of the system; and
*These particular elements, of major concern to data
screening, are discussed herein.
730
-------
3. Specific data quality control activities,
those activities which involve the calibration and
data output from the meteorological and pollutant
measurement instruments and are explicitly involved
in acquiring quality data.
Procurement and Management
Data Quality Objectives. A requirement of the
initial contract stated that 90% valid data were to
be achieved. Valid data for pollutant measurements
were defined as the data obtained during periods
when the daily zero and span drifts were less than
2 per cent, with an allowance for the time required
to perform daily zero/span checks and periodic
multi-point calibrations.
Procurement. In planning to achieve the
objectives very stringent requirements were placed
on the suppliers of the various instruments of the
system and extensive performance tests (with numerous
rejections) were conducted prior to final acceptance.
First Article Configuration Inspection (FACI).
The first remote station was installed and performance
tested by the contractor under EPA review. Various
indicated corrections were made before proceeding
with the installation of the entire network.
System Acceptance Test (SAT). After installation
of the entire network, a one-month system performance
demonstration was required to assure satisfactory
operation with respect to obtaining data of adequate
quantity and quality. The SAT was completed in
December 1974.
Incentive Contract. The current contract has
introduced award fee performance incentives for manage-
ment, schedule, and for quality. The quality portion
of the award fee provides a continual motivation for
obtaining and improving data quality.
Quality Assurance Plans. An extensive QA plan has
been developed by the contractor. A point of emphasis
is that the QA plan (and its implementation) is dynamic
—continually being revised and improved based upon
experience with the system. The QA plan outlines in
detail the activities of the various QA elements
previously mentioned.
Organization. To implement the QA plan, one
full-time employee is assigned to overall QA
responsibilities reporting directly to the Program
Manager. In addition, two persons are assigned for QA
on a half-time basis, one for the remote monitoring
stations, and the other for the central computer
facility.
Operation and Maintenance
Document Control. Detailed operation and
maintenance manuals have been prepared for the remote
stations and for the central computer facility. These
manuals are issued in a loose-leaf revisable and
document-control format so that needed additions
and/or revisions can be made. Also, a complete history
of changes are kept so that traceability to the
procedures in effect for any past period of time can
be made. A document control system also exists for
the computer programs.
Preventive Maintenance. Record-keeping and
appropriate analysis of the equipment failure records
by instrument type and mode of failure have enabled
more ef.ficj.ent and effective scheduling of maintenance
and optimum spare parts inventory with resultant
improvement in instrument performance. RAMS station
preventive maintenance is completed twice each week.
Normally, the remote stations are unattended except
for the weekly checks, for other scheduled maintenance,
or for special corrective maintenance.
Central Computer Monitors. Central computer
personnel, using a CRT display, periodically monitor
the output from all stations to detect problems as
soon as possible. To maximize the satisfactory opera-
tion of the network equipment, the assigned QA
personnel review the following activities associated
with preventive maintenance:
1. remote station logbook entries,
2. remote station corrective maintenance reports,
3. laboratory corrective maintenance reports,
and
4. central computer operator log.
Additionally, the QA individuals are in frequent
verbal communication with field and laboratory
supervisors to discuss quality aspects of the
operations.
Reliability Records and Analysis
Telecommunications Status Summaries. Each
day, a summary of telecommunications operations is
prepared to determine which stations and/or telephone
lines are experiencing significant problems that
might require corrective action.
Daily Analog/Status Check Summaries. Each
day, the central computer prepares a summary of analog/
status checks by station so that major problems can be
corrected as soon as possible by available field
technicians. These analog/status checks are explained
in the section on data validation.
Configuration Control. Histories are kept
of the station assignment of specific instruments,
by serial number, so that possible future problems
with specific instruments can be traced back to the
stations. A logbook for each instrument is maintained
for recording in a systematic manner the nature and
date of any changes or modifications to the hardware
design of the instruments.
Specific Data Quality Control Activities
Calibration
Calibration References for Gaseous Pollutants.
NBS standard reference materials are used for calibra-
tion standards if available. Otherwise, commercial
gases are procured and certified at NBS for use as
standards.
Multipoint Calibrations. As a check on the
linearity of instrument response, an on-site, 5-point
calibration is scheduled at each station at 8-week
intervals. Originally, acceptability was determined
by visual evaluation of the calibration data plots;
more recently, quantitative criteria are being
established for linearity.
Measurement Audits. Independent measurement
audits for pollutant instruments are performed by the
contractor using a portable calibration unit and
independent calibration sources at each station once
each calendar quarter. Similar audits are performed
on the same frequency for temperature, radiation, and
731
-------
mass flowmeters; and independent checks are made on
relative humidity, windspeed, and wind direction
instruments. In addition to the internal audits per-
formed by the contractor on his own operation, a
number of external audits have been performed by EPA
and other contractors to check the entire measurement
system.
Qn-Site System Audit. A thorough, on-site quality
system audit of RAMS was performed for EPA by an
independent contractor. The results of this audit
pointed out several areas of weakness for which
corrective actions have been implemented.
Data Validation. As a part of the overall QA
system, a number of data validation steps are
implemented. Several data validation criteria and
actions are built into the computer data acquisition
system:
Status Checks. About 35 electrical checks
are made to sense the condition of certain critical
portions of the monitoring system and record an
on-off status. For example, checks are made on power
on/off, valve open/shut, instrument flame-out, air
flow. When these checks are unacceptable, the
corresponding monitoring data are automatically
invalidated.
Analog Checks. Several conditions including
reference voltage, permeation tube bath temperature,
and calibration dilution gas flow are sensed and
recorded as analog values. Acceptable limits for
these checks have been determined, and, if exceeded,
the corresponding affected monitoring are invalidated.
Zero/Span Checks. Each day, between 8-12 pm,
each of the gaseous pollutant instruments in each
station are zeroed and spanned by automatic, sequenced
commands from the central computer. The results of
the zero/span checks provide the basis for a two-point
calibration equation, which is automatically computed
by the central computer and is used for converting
voltage outputs to pollutant concentrations for the
following calendar day's data. In addition, the
instrument drift at zero and span conditions between
successive daily checks are computed by the central
computer and used as a basis for validating the
previous day's monitoring data. Originally, zero and
span drifts were considered as acceptable if less than
2 per cent, but the span drift criterion has recently
been increased to 5 per cent, a more realistic level.
If the criteria are not met, the minute data for the
previous day are flagged. Hourly averages are
computed during routine data processing only with data
which have not been flagged as invalid.
DATA SCREENING IN RAMS
The tests which are used to screen RAMS data are
summarized in Table 2. Specific tests and associated
data base flags are listed. The types of screens that
have been employed or tested will be detailed, the
mechanisms for flagging will be reviewed, and then
the implementation of screening within RAMS will be
discussed.
Table 2. SCREENING CATEGORIES AND ASSOCIATED FLAGS FOR RAMS DATA
Category FU^
I Modus Operand!
Ho Instrument '0
Hissing measurement 1037
Status Value « 1
CalIbratlon 10
II. Continuity and Relational
A. Intrastation
Gaseous analyzer drift Value
Gross limits lO3^
Aggregate frequency distributions
Relationships
Temporal contlnulty
Constant output
Being Implemented
u= iHA rt in"
23
H. Interstation
Meteorological network uniformity
Statistical outliers
Dixon Ratio
III. A Posteriori
Review of station log
Unusual events or conditions
Visual inspection of data
Value * 10'
Being implemented
Value * lO1*1
-20
Value * 10
ValIdate - Remove
flag
For descriptive purposes, the tests are divided
into three categories. The first category, "Modus
Operandi," contains checks which document the network
instrument configuration and operating mode of the
recording system. Included are checks for station
instrumentation, missing data, system analog and
status sense bits, and instrument calibration mode.
These checks, which have been described above, are
part of the quality control program incorporated in
the data acquisition system and central facility data
processing, and are an important data management
function used to document system performance.
The second category, "Continuity and Relational,"
contains temporal and spatial continuity checks and
relational checks between parameters which are based
on physical and instrumental considerations or on
statistical patterns of the data. A natural sub-
division can be made between intrastation checks,
those checks which apply only to data from one station,
and interstation checks, which test the measured
parameters for uniformity across the RAMS network.
Intrastation checks include tests for gaseous
analyzer drift, gross limits, aggregate frequency
distributions, relationships, and temporal continuity.
The drift calculations, which are part of the quality
control program, have been discussed above.
Gross limits, which are used to screen impossible
values, are based on the ranges of the recording
instruments. These, together with the parametric
relationships which check for internal consistency
between values, are listed in Table 3. Setting limits
for relationship tests requires a working knowledge of
noise levels of the individual instruments. The
relationships used are based on meteorology, atmos-
pheric chemistry, or on the principle of chemical mass
balance. For example, at a station for any given
minute, TS cannot be less than SO, + H2S with allow-
ances for noise limits of the instruments.
732
-------
Table 3. GROSS LIMITS AND RELATIONAL CHECKS
PARAMETER
Ozone
Nitric Oxide
Oxides of
Nitrogen
Carbon Monoxide
Methane
Total Hydro-
carbons
Sulfur Dioxide
Total Sulfur
Hydrogen Sulfide
Aerosol Scatter
Wind Speed
H1nd Direction
Temperature
Dew Point
Temperature
INSTRUMENTAL OR
NATURAL LIMITS
LOWER
0 ppm
0 ppm
0 ppm
0 ppm
0 ppm
0 ppm
0 ppm
0 ppm
0 ppm
0.000001m"1
0 m/s
0"
-20°C
-30° C
- 5°C
UPPER
5 ppm
5 ppm
5 ppm
50 ppm
50 ppm
50 ppm
1 ppm
1 ppm
1 ppm
0.00099m"1
22.2 m/s
360°
45°C
45°C
5°C
Gradient
Barometric
Pressure
Pyranometers
Pyrgeometers
Pyrhellometers
950 mb
- 0.50
0.30
-0.50
INTERPARAMETER
CONDITION
N0*03 .10.04
CH4 - THC ^Noise (CH4)
CH THC < Noise (THC)
4 ~
S02 - T5 < Noise (S02)
1050 mb
2.50 Langleys/min
0.75 Langleys/min
2.50 Langleys/min
tested since it can remain constant (to the number of
digits recorded) for periods much longer than 10
minutes. The test was modified for other parameters
which reach a low constant background level during
night-time hours.
A) SINGLE OUTLIER
\
C) SPIKE
••*•.•
El MISSING
G) DRIFT
B) STEP FUNCTION
• *• ••*••••••••
D) STUCK
.••„
F) CALIBRATION
Figure 1. Irregular instrument response.
A refinement of the gross limit checks can be
nade using aggregate frequency distributions. With a
cnowledge of the underlying distribution, statistical
limits can be found which have narrower bounds than
the gross limits and which represent measurement
levels that are rarely exceeded. A method for fitting
a parametric probability model to the underlying
distribution has been developed by Dr. Wayne Ott of
EPA's Office of Research and Development.7. B.E.
Q
Suta and G.V. Lucha have extended Dr. Ott's program
to estimate parameters, perform goodness-of-fit tests,
and calculate quality control limits for the normal
distribution, 2- and 3-parameter lognormal distribu-
tion, the gamma distribution, and the Weibull
distribution. These programs have been implemented
on the OSI computer in Washington and tested on
water quality data from STORE!. This technique is
being studied for possible use in RAMS as a test for
potential recording irregularities as well as a
refinement of the gross limit check currently
employed.
Under intrastation checks are specific tests
which examine the temporal continuity of the data as
output from each sensor. It is useful to consider,
in general, the types of atypical or erratic responses
that can occur from sensors and data acquisition
systems. Figure 1 illustrates graphically examples
of such behavior, all of which have occurred to some
extent within RAMS. Physical causes for these
reactions include sudden discrete changes in component
operating characterisitcs, component failure, noise,
telecommunication errors and outages, and errors in
software associated with the data acquisition system
or data processing. For example, it was recognized
early in the RAMS program that a constant voltage
output from a sensor indicated mechanical or electri-
cal failures in the sensor instrumentation. One of
the first screens that was implemented was to check
for 10 minutes of constant output from each sensor.
Barometric pressure is not among the parameters
A technique which can detect any sudden jump in
the response of an instrument, whether it is from an
individual outlier, step function or spike, is the
comparison of minute successive differences with
predetermined control limits. These limits are
determined for each parameter from the distribution
of successive differences for that parameter. These
differences will be approximately normally distributed
with mean zero (and computed variance) when taken over
a sufficiently long time series of measurements.
Exploratory application of successive differences,
using 4 standard deviation limits which will flag 6
values in 100,000 if the differences are truly
normally distributed, indicate that there are abnormal
occurrences of "jumps" within certain parameters.
Successive difference screening will be implemented
after further testing to examine the sensitivity of
successive difference distributions to varying
computational time-periods and to station location.
The type of "jump" can easily be identified. A
single outlier will have a large successive difference
followed by another about the same magnitude but of
opposite sign. A step function will not have a return,
and a spike will have a succession of large successive
differences of one sign followed by those of opposite
sign.
The interstation or network uniformity screening
tests that have been implemented in RAMS will now be
described. Meteorological network tests are performed
on hourly average data and are based on the principle
that meteorological parameters should show limited
differences between stations under certain definable
conditions typically found in winds of at least
moderate speeds (>4 m/sec). Each station value is
compared with the network mean. The network mean is
defined as the average value for a given parameter
from all stations having reported valid data. (If
more than 50% are missing, a network mean is not
733
-------
computed and the test is not made.) Values exceeding
prescribed limits are flagged. The limits have been
set on the advice of experienced meteorologists. The
tested parameters and flagging limits are listed
below.
Maximum allowable deviations from network mean
under moderate winds (network mean > 4 m/sec)
Wind speed
Wind direction
Temperature
Temperature difference
Dew point
Adjusted pressure
2 m/sec or MEAN/3
(whichever is larger)
30°
3°C
.5°C
3°C
5.0 millibars
In addition to network screening techniques
which are based on knowledge of underlying physical
processes, methods from statistical outlier
n in
theory were also examined. Specifically, the
Dixon ratio test was implemented to determine
extreme observations of a parameter across the RAMS
network. The Dixon ratio test is based entirely on
ratios of differences between observations from an
assumed normal distribution and is easy to calculate.
The Dixon criteria for testing a low suspect value
from a sample size of n, n <_ 25, are shown in
Figure 2. Though the entire sample is shown as
ranked, only the extreme 2 or 3 values need to be
ordered. Associated with each value of n are
tabulated ratios for statistical significance at
various probability levels. For example, if n=25,
X, would be considered as an outlier at the 1% level
of significance when r-p L .489. Since the under-
lying distribution may not be normal, the calculated
probabilities may not be exact, but are used as
indicators of heterogeneity of the network observations
at a given time.
ORDERED SAMPLE: *i
-------
SENSOR
IWTRUMEKTS
ACQUISITION
SYSTEM
PROCESSING
AND
ANALYSIS
SCREENING
DATA
BASE
ARCHIVAL
Figure 3. Generalized data flow for environmental measurement systems.
Data screening should take place as near to
data acquisition as possible either in data processing
which is traditionally concerned with laboratory
analysis, conversion to engineering units, transcribing
intermediate results, etc., or in a separate module,
as illustrated, designed specifically for the screening
process. Screening data soon after data acquisition
permits system feedback in the form of corrective
maintenance, changes to control processes, and even
to changes in system design. This feedback is
essential to minimize the amount of lost or marginally
acceptable data.
The RAMS screening tests, which have been
developed at Research Triangle Park (RTP), are now
part of the data processing carried out at the RAPS
central facility in St. Louis. Slow computation
speeds of the St. Louis POP 11/40 computer required
restricting the intrastation screening tests to hourly
average data. RAMS data is still passed through the
RTP screening module before archiving.
SUMMARY
The experiences gained in RAMS and applicable to
other monitoring systems are:
1. Data validity is a function of quality
assurance and data screening.
2. A QA plan and data screening rules should
be established initially and maintained throughout
the program.
3. The QA plan and screening rules are dynamic,
being improved as additional knowledge and experience
is gained.
4. Applied during data acquisition or shortly
thereafter, quality control and screening checks
constitute an important feedback mechanism, indicating
a requirement for corrective action.
REFERENCES
1. Burton, C.S. and G.M. Hidy. Regional Air
Pollution Study Program Objectives and Plans,
EPA 630/3-75-009, Dec. 1974.
2. Thompson, J.E. and S.L. Kopczynski. The Role of
Aerial Platforms in RAPS, Presented at an EPA
meeting on Monitoring from Las Vegas, Nevada,
March 1975 (unpublished).
3. Meyers, R.L. and J.A. Reagan. Regional Air
Monitoring System at St. Louis, Missouri,
International Conference on Environmental Sensing
and Assessment, Sept. 1975 (unpublished).
4. Quality Assurance Handbook for Air Pollution
Measurement Systems, Volume I, Principles,
EPA 600/9-76-005, March 1976.
5. von Lehmden, D.J., R.C. Rhodes and S. Hochheiser.
Applications of Quality Assurance in Major Air
Pollution Monitoring Studies-CHAMP and RAMS,
International Conference on Environmental Sensing
and Assessment, Las Vegas, Nevada, Sept. 1975.
6. Audit and Study of the RAMS/RAPS Programs and
Preparation of a Quality Assurance Plan for RAPS,
Research Triangle Institute, Research Triangle
Park, N.C. 27707, EPA Contract No. 68-02-1772.
7. Ott, W.R. Selection of Probability Models for
Determining Quality Control Data Screening
Range Limits, Presented at 88th Meeting of the
Association of Official Analytical Chemists,
Washington, D.C., Oct. 1974.
8. Suta, B.E. and G.V. Lucha. A Statistical
Approach for Quality Assurance of STORET-Stored
Parameters, SRI, EPA Control No. 68-01-2940,
Jan. 1975.
9. Grubbs, F.E. Procedures for Detecting
Outlying Observations in Samples, Technometrics
11 (1), 1-21, 1969.
10. Anscombe, F.J. Rejection of Outliers,
Technometrics 2 (2), 123-147, 1960.
11. Dixon, W.J. Processing Data for Outliers,
Biometrics 9 (1), 74-89, 1953.
735
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QUANTITATIVE RISK ASSESSMENT FOR
COMMUNITY EXPOSURE TO VINYL CHLORIDE
Arnold M. Kuzmack
Office of Planning and Evaluation
U.S. Environmental Protection Agency
Washington, D.C. 20460
Robert E. McGaughy
Office of Health and Ecological Effects
U.S. Environmental Protection Agency
Washington, D.C. 20460
Summary
Vinyl chloride is a known human carcino-
gen; it has produced liver angiosarcoma, a
very rare form of cancer, as well as other
cancers and non-cancer effects in occupation-
ally exposed populations. It is also known to
be emitted into the atmosphere from plants
which produce vinyl chloride monomer (VCM
plants) and plants which polymerize the mono-
mer to polyvinyl chloride (PVC plants). Al-
though concentrations of vinyl chloride in the
ambient air are much less than those which
caused cancer in workers, it is generally con-
sidered prudent to assume that there is no
threshold for chemical carcinogens, so that
any exposure involves some risk. In conjunc-
tion with EPA consideration of rulemaking ac-
tion to regulate emissions of vinyl chloride
from VCM and PVC plants, the Administrator of
EPA requested that an analysis be performed
which would estimate quantitatively the risk
resulting from VC emissions and assess the re-
liability of the estimates. This paper re-
ports the results of that analysis. The de-
tails are presented in Appendices A through E,
which are available from the authors on re-
quest .
Method of Analysis
The analysis involves three steps which
are discussed below. They are an estimate of
size of the exposed population, concentrations
of vinyl chloride to which it is exposed, and
number of liver angiosarcomas and other health
effects which would result from this exposure.
Of these, the last estimate is by far the most
difficult to make. In addition, an investi-
gation was made of the places of residence of
all people known to have died of liver angio-
sarcoma in the last 10 years in an attempt to
detect clustering around PVC and VC plants.
Although excess birth defects have been
reported in communities near some plants, the
current data is too fragmentary for conclu-
sions to be drawn; thus, these effects have
not been considered in this paper.
Size of Exposed Population
A study by the American Public Health
Association (APHA), performed under contract
to EPA's Office of Toxic Substances, deter-
mined the number of people living within
various distances, up to S miles, from each of
9 VCM plants and 33 PVC plants. The study was
based primarily on census tract information.
The validity of the methodology used was con-
firmed by a more detailed analysis of the
population living around a few plants, per-
formed by EPA's Office of Planning and Evalua-
tion.
The total population living within 5 miles
of all PVC and VCM plants is shown in the
following table:
Distance (mi)
0 - 1/2
1/2 1
1 3
3 5
TOTAL
Population
47,000
203,000
1,491,000
2,838,000
4,579,000
Thus, a total of 4.6 million people live
in the vicinity of these plants. The use of
residence data involves some error, of course,
since people spend part of their time away
from their homes and are exposed to varying
levels of vinyl chloride. There does not
seem to be any practical way around this
problem, short of a detailed study of travel
patterns of 4 million people in over 40 sepa-
rate communities.
Ambient Vinyl Chloride Concentrations
Annual average ambient concentrations of
vinyl chloride were calculated by standard
diffusion modeling techniques. Two independ-
ent studies were made, one by EPA's Office of
Air Quality Planning and Standards (OAQPS)
and one by Teknekron, Inc.2 The agreement
among the two studies was good, with differ-
ences generally less than 25%. It was
decided to use the Teknekron results in the
actual calculations since they included data
on variations in meteorological conditions
from location to location.
For an average uncontrolled PVC or VCM
plant in an area with average meteorological
conditions, the annual average concentration
of vinyl chloride in each annulus around the
plant is shown in the following table:
Distance (mi)
0 1/2
1/2 1
1 3
3 5
Vinyl Chloride Concentration
Tppb]
PVC Plant
323
57
15
5.7
VCM Plant
113
20
5.2
2.0
It can be seen that concentrations around VCM
plants are significantly smaller than around
PVC plants. This fact combined with the much
smaller population living near VCM plants
implies that by far the greatest part of the
public health risK is from emissions of PVC
plants.
736
-------
In calculating the average population
exposure, it is necessary to consider,for
each population affected, the type of plant
(VCM or PVC), the size of plant, the multi-
plicity of plants nearby, and the meterologi-
cal conditions at the plant site. Informa-
tion from OAQPS and from the APHA study was
used to determine areas where more than one
plant was located, and OAQPS characterized
the size of each plant as "average" or
"large." The Teknekron study was used to
categorize the meteorological and topographic
conditions at each location.
The net result of these calculations is
that the average exposure faced by a person
chosen at random from the 4.6 million people
living within 5 miles of plants is 17 ppb.
Unfortunately, it has not been possible
to make a systematic comparison of the
diffusion modeling results with data obtained
from actual monitoring, although they appear
generally consistent. It is therefore diffi-
cult to estimate the uncertainty of these
estimates. Lacking anything better, we can
take the difference between the two diffusion
modeling efforts of up to 25% as an estimate
of that uncertainty.
Health Effects Resulting From Exposure
What are the results of exposing 4.6
million people to an average of 17 ppb of
vinyl chloride? The first major decision to
face in answering this question is to arrive
at some combination of two basic approaches.
One approach is to rely largely on human
data (which exists for vinyl chloride but not
for many other chemicals of concern to EPA);
the second is to make projections from
animal experiments. Both involve difficul-
ties. Use of human data eliminates the un-
certainties that result because we do not
know the differences in response between the
test animals and humans. On the other hand,
with the data on human (occupational) expo-
sure, it is necessary to guess at exposure
levels over the past 30 years and approximate
the total number of workers involved and the
number of cancers caused by past exposures
for which symptoms may not appear until many
years in the future. By using animal data we
can avoid these problems, but only at the
price of uncertainty in the relevance of
animal experiments to human exposures. The
approach taken in this analysis is to use
animal data to predict the probability of
human liver angiosarcoma, and then use the
human data to the greatest extent possible
to interpret those predictions.
A second major decision that must be
made is how to project the results observed
at high doses in animal experiments and in
the occupational exposures to the much lower
doses encountered in the environment. Two
alternative assumptions are frequently made
in the scientific literature. The first is
a straight-line projection to zero dose,
assuming no threshold (the "linear model").
This is also referred to as the "one hit"
model, since it would follow logically from
the assumption that each minute increment of
exposure to a carcinogen has the same inde-
pendent probability of causing a cancer,
regardless of the dose level. This assumption
is generally accepted as prudent in radiation
carcinogenesis. For chemical carcinogenesis,
the model is usually considered to provide an
upper limit to the level of effects likely at
extremely low doses, because the existence of
detoxification mechanisms would render small
doses less effective in causing cancer and
would therefore result in a threshold, or at
least fewer effects.
The second commonly used projection method
is based on the assumption that the observed
changes in response with dose are the result
of variations of susceptibility in the popula-
tion, which is assumed to be log-normally
distributed with dose. For convenience, we
refer to this as the "log-probit" model
because it forms a straight line when the
logarithm of the dose is plotted against the
proportion of responses expressed in probabi-
lity units (probits). The log-probit model
is used in the Mantel-Bryan procedure.
In this analysis, both models are used.
For technical reasons, the log-probit model
is difficult to apply to this case. There-
fore, the basic calculations were done using
the linear model, but a sensitivity analysis
was done to show how the results would change
under the log-probit assumption. Thus, the
log-probit model results are shown below as a
range, not a definite number.
A third decision that must be made is how
to predict human incidence rates from animal
data. Again, there is little hard data to
provide guidance. The assumption used here
is that a lifetime exposure of humans to a
given concentration of vinyl chloride would
produce effects in the same proportion of
individuals as a lifetime exposure of rats.
Thus, the one-year exposure in the animal
experiments would be equivalent to about 30
years of exposure for humans.
A fourth decision to make is how to use
the available human data on liver angiosar-
coma cases among highly-exposed workers to
calculate the probability per year of expo-
sure that cases will eventually develop in
people. This calculation is needed for com-
parisons with the animal model. There are
three aspects to this problem: 1) to find in
the literature a realistic estimate for the
fraction of highly-exposed workers who have
contracted liver angiosarcoma at some time in
their lives, 2) to account for the fact that
the currently-observed rates underestimate
the actual incidence because they do not
include workers who have been exposed more
recently than IS to 20 years ago, and 3) to
account for the fact that people can die from
other causes before a latent case of liver
angiosarcoma becomes manifest.
These issues were treated as follows: Of
the four occupational epidemiology studies
from which it is possible to estimate an
incidence rate, 3-6 the two with the smallest
number of subjects and the best separation of
highly-exposed workers from the group of all
workers^'^ had the largest incidence of
angiosarcoma. This incidence was assumed to
be valid for all highly-exposed workers. The
737
-------
latency time distribution for liver angiosar-
coma and the growth in the number of person-
years of exposure since 1940 are two factors
which affect the number of cases we have ob-
served through 1974. These factors are ana-
lyzed in Appendix D. The result of the analy-
sis is an estimate of the probability per year
of exposure that a person will get angiosar-
coma some time in his life. The remaining
problem of multiple risks competing for mor-
tality was not treated because of its complex-
ity.
A fifth decision that must be made is how
to quantatively describe the other effects of
vinyl chloride exposure besides liver angio-
sarcoma. This problem was handled by estimat-
ing from the literature3,7-9 ratios of the
number of people with other cancers and the
number of people with liver damage compared to
the number with angiosarcoma. As an index of
liver damage, the bromsulphalein (BSP) test is
used because it, among all liver function
tests that have been used, correlates best
with vinyl chloride exposure and because an
abnormal BSP test indicates that severe damage
has occurred in the liver, either because the
liver cells are not able to assimilate the in-
travenously injected BSP dye from the blood
and excrete it into the bile passages, or that
the bile passages are no longer structurally
intact enough to carry the dye out of the
liver.
Results of Analysis
The results of these five aspects of the
problem are presented below in reverse order.
The approximate ratio of severe liver damage
cases to liver angiosarcoma cases is about 30,
the result being consistent for two indepen-
dent occupational studies. It was also found
that about twice as many cases of cancer of
all sites are caused by vinyl chloride as
cases of liver angiosarcoma alone. The animal
experiments have shown approximately the same •
ratio of all cancers to liver angiosarcoma,
after background incidence is taken into
account.
In calculating the probability per year
of exposure that a highly-exposed worker will
get angiosarcoma some time in his life, we
found that the fraction of highly-exposed
workers who have been currently diagnosed is
0.02. They have been exposed for an average
of 17 years before diagnosis. The analysis,
which was based on the available data on the
time distribution of person-years of exposure
and the distribution of latency times from
first exposure to diagnosis, showed that only
about 401 of the highly-exposed workers who
are expected to get angiosarcoma some time in
their lives have been diagnosed already.
Since the data was incomplete, several assump-
tions had to be made in order to complete the
analysis. Therefore, the probability that one
of these people will get angiosarcoma some
time in their lives is 0.02/(17 x 0.40)
0.003 per year of exposure. In Appendix D,
the calculation is explained in greater detail.
The 17-year average concentration to
which these workers were exposed was estimated
to be 350 ppm on the basis of one study. Only
one company has reported measurements of
vinyl chloride for the jobs in their plant.
These measurements, started in 1950, show
the highest exposure jobs ranged from 120 to
385 ppm before 1960, when the exposures were
reduced because of suspected toxicological
problems with vinyl chloride. In estimating
the average, it was assumed that the other
factories, most of which probably did not
monitor the concentration of vinyl chloride,
were less concerned about industrial hygiene
and, therefore, took fewer precautions to keep
the levels low.
In predicting the human angiosarcoma rate
from the animal dose-response data, it was
projected, from the linear model, that expo-
sure to vinyl chloride would cause 0.071
cases of liver angiosarcoma and 0.15 cases of
all types of cancer per million people per
year per ppb of continuous exposure. Details
of these calculations are given in Appendix
B. Converting to a 7-hour per day, 5-day
per week work schedule of exposure to 350 ppm,
the model predicts an angiosarcoma incidence
rate of 0.0052 per person-year exposure. It
is shown in Appendix D that this rate is
numerically indistinguishable from the rate
of 0.003 calculated from the human data,
considering the known quantifiable errors of
estimating the parameters of the animal and
human data. It can be concluded that the
slope of the linear animal dose-response
relationship for angiosarcomas is consistent
with the human data.
The extrapolation of the animal dose-
response relationship to a concentration of
17 ppb (the average concentration around the
uncontrolled plants) yields the following
predicted number of cases in the 4.6 million
people living within 5 miles of the plants.
For details, see Appendix B.
Cases Per Year of Exposure
Log-Probit
Type of Effect Linear Model Model
All cancer 11 0.1 - 1.0
Liver angiosarcoma 5.5 0.05 0.5
This is the expected number of cases pro-
jected to be caused per year at current
levels of emissions; the people exposed now
will not be diagnosed for another 15-20 years.
Similarly, any cases observed now would have
been caused by exposure 15-20 years ago (if
in fact caused by vinyl chloride) when pro-
duction was about 10% of current levels.
In order to arrive at a final estimate of
the number of people adversely affected by
vinyl chloride emissions, the important re-
sults of this analysis to consider are as
follows: 1) the number of cancers at all
sites caused by vinyl chloride is twice the
number of liver angiosarcomas; 2) the number
of people with severe liver damage is 30
times the number of liver angiosarcomas; 3)
the animal model predicts that the number of
liver angiosarcomas in the population around
plants is 5.5 cases per year of exposure;
4) the number of cases calculated from the
human data is 60% of the number predicted from
the animal model; 5) the use of a log-probit
model for extrapolation to low doses gives
predictions of 0.1 to 0.01 times the number
738
-------
predicted by the linear model; 6) the error in
the estimate of 5.5 cases per year ranges from
+55% to -10%. This error includes statistical
uncertainty in estimating the dose-response,
uncertainty in ambient concentration estimates,
and errors resulting from not considering ex-
posures beyond 5 miles or decomposition of
vinyl chloride in the atmosphere. It is not
symmetrical because it includes possible ef-
fects beyond 5 miles from the plants, which
were not explicitly considered in the analysis.
It does not account for our uncertainty about
the appropriateness of using a linear model
extrapolated to zero dose or of extrapolation
from animal data; 7) the quantifiable error in
the rate calculated from the human data is
about ± 67%. This includes uncertainties in
the 17-year average dose received by the
workers, uncertainty in the number of hours
per day of actual high exposure, and uncer-
tainty in the fraction of highly-exposed
workers who have been diagnosed with liver
angiosarcoma. Other errors cannot be quanti-
fied, and are discussed in Appendix D.
Conclusions
When all these uncertainties are consid-
ered, our judgment is that the number of liver
angiosarcoma cases produced per year of expo-
sure in people residing near vinyl chloride
plants is somewhere between less than 1 and 10
cases. The cases produced by this year's ex-
posure will not be diagnosed until 15 to 20
years from now. If the EPA regulations are
implemented, the number of cases is expected
to be reduced in proportion to the reduction
in the ambient annual average concentration,
which is expected to be 5% of the uncontrolled
level.
The vinyl chloride exposure around plants
is also producing somewhere between less than
1 and 10 cases of primary cancer at other
sites, mainly lung, brain, and bone. Assuming
no threshold for liver damage, somewhere be-
tween less than 1 and 300 cases of serious
liver damage would be predicted. The number
of liver damage cases is likely to be less
than this because a liver damage threshold at
low dose probably exists.
In order to find out whether people liv-
ing near VC-PVC plants have, as of 1974, had
higher rates of liver angiosarcoma diagnosis
than the overall U.S. population, a search of
the residence records of all known liver angio-
sarcoma cases in the last 10 years was per-
formed using data collected by the Center for
Disease Control. Out of 176 cases where resi-
dence at time of death was known, 3 people
lived within 5 miles of a plant. Unfortun-
ately, the diagnosis of these cases has not
yet been confirmed by the National Cancer In-
stitute. In addition one infant whose parents
lived within 1 mile of a plant died of a rela-
tively common liver tumor. It was shown in
Appendix E that this rate of occurrence is not
higher than the national average. However,the
survey is too incomplete to draw any conclu-
sions at the current time.
Considering the results of the foregoing
analysis, one would only now expect to be see-
ing some evidence of vinyl chloride exposure.
If the highest rate in our range were actually
occurring, 10 cases of liver angiosarcoma per
year of exposure would be developing; 15-20
years ago when the vinyl chloride production
was about 10% of current levels, one case
would be expected per year of exposure (with
constant population). This is to be compared
to a background rate of 0.6 cases per year ex-
pected in the population around the plant.
The survey of liver angiosarcoma cases
would probably detect the existence of 10 cases
over the 10-year period. Since this was not
observed we can conclude that the real in-
cidence is not significantly greater than the
predicted upper limit of 10 cases initiated per
year of exposure unless migration of people in
and out of the regions around plants has been
excessive. If the lower rates in the range of
the above analysis were to be true, increased
incidence of angiosarcoma would not be ob-
servable .
References
1. Landau, E., "Population Residing Near
Plants Producing Polyvinyl Chloride,"
American Public Health Association,
Contract Report. EPA, August 1975.
Teknekron, Inc. unpublished report, 1975.
Tabershaw, I.R. and Gaffey, W.R., "Mortal-
ity Studies of Workers in the Manufac-
tory of Vinyl Chloride and Its Poly-
mers," J. Occupational Medicine 16 509-
518, 1974.
Wagoner, J.K., Testimony in Vinyl Chlor-
ide , Hearings before the Subcommittee
on Commerce, 93rd Cong., 2nd Sess.
(Serial No. 93-110), August 21, 1974,
p. 59.
Nicholson, W.J.; Hammond, E.G.-, Seidman,
H.-, Selikoff, I . J . ; "Mortality Experi-
ence of a Cohort of Vinyl Chloride-
Polyvinyl Chloride Workers," Ann. N.Y.
Acad. Sciences,24^, 225-230, 1975.
Heath, C.W. and Falk, H., "Characteristics
of Cases of Angiosarcoma of the Liver
Among Vinyl Chloride Workers in the
United States," Ann. N.Y. Acad.
Sciences,246, 231-236, 1975.
Marsteller, H.J.-, Lelback, W.K.; Muller,
R.; Gedigk, P.; "Unusual Splenomegalic
Liver Disease as Evidenced by Perito-
neoscopy and Guided Liver Biopsy Among
Polyvinyl Chloride Production Workers,"
Ann. N.Y. Acad. Sciences, 246, 95-134,
1975.
Veltman, G. -, Lange, E.E.; Juhe, S.; Stein,
G.; and Bachner, U.; "Clinical Manifes-
stations and Course of Vinyl Chloride
Disease," Ann. N.Y. Acad. Sciences,
246, 6-17, 1975.
Creech, J.L. and Makk, L., "Liver Disease
Among Polyvinyl Chloride Workers," Ann.
N.Y. Acad. Sciences, 246, 88-94, 1975.
739
-------
NEW M3DELS FOR OPTIMAL SEWER SYSTEM DESIGN
Ben Chie Yen
Harry G. Wenzel, Jr.
Larry W. Mays
Wilson H. Tang
Department of Civil Engineering
University of Illinois at Urbana-Champaign
Urbana, Illinois 61801
SUMMARY
Three new models have been developed for the least-cost
design of storm sewers. All three models consider the
sewers as a system. The basic model designs the crown
elevations, slopes, and diameters of the sewers. The
sewer system layout is predetermined. Routing is
accomplished by lagging the hydrographs by a travel
time. Optimization is achieved through a discrete dif-
ferential dynamic programming technique to produce the
least-cost design of the system based on specified cost
functions for installation of the sewers and manholes.
The second model is an expansion of the basic model
incorporating risk-based damage costs in the design
procedure, and the risks for each sewer associated with
the least-cost design are also given as part of the
design results. The third model is similar to the
basic model except that the least-cost sewer layout is
also a part of the design result instead of being
predetermined.
INTRODUCTION
Urban storm sewer simulation models can be classified
into two basic categories. The majority are flow
simulation models for existing systems. They are
useful for urban storm runoff management, operation and
pollution control purposes by providing information
useful for flow regulation. Many of these models have
been mislabeled as "design" models whereas in fact they
produce nothing more than runoff hydrographs that may
be used for design. Evaluations of the important flow
simulation models have been reported by Chow and
Yen , Brandstetter
others.
James F. MacLaren, Ltd. , and
The second category are design models for determination
of the size, and perhaps also slopes and layout of the
sewers. There are only a few design models in
existence. A comparative study of hydraulic design
models was reported by Yen and Sevuk . These models
determine the sewer sizes with predetermined sewer
slopes and layout. Recently a number of optimization
models for the least-cost design of sewer systems have
been proposed and a review has been reported by the
12
authors . Most of these models offer a limited de-
gree of optimization in determining the sizes and
slopes of sewers using linear programming or dynamic
programming.
In this paper three new sewer design models are re-
ported. An optimization procedure is incorporated into
each of the models to determine the least-cost design
for the entire sewer system. The first model employs
a simple hydrograph shift routing scheme and determines
the crown elevations, slopes, and diameters of the
sewers. The second model is based on the first,how-
ever the uncertainties and risks are considered in the
design procedure. The third model is similar to the
first in its scope and extent except that it also
determines the layout of the sewer system. In the
following the constraints, assumptions and basic opti-
mization techniques adopted in all the three models are
first discussed. The three design models developed and
listed in Table 1 are then described briefly. Finally
an example is presented to illustrate the advantages of
the new design models over the traditional design
methods.
CONSTRAINTS AND ASSUMPTIONS
The following constaints commonly used in sewer designs
are adopted in this study:
(a) Free-surface flow exists for the design dis-
charges or hydrographs, i.e., the sewer system
is "gravity flow" so that pumping stations and
pressurized sewers are not considered.
The sewers are commercially available circular
sizes no smaller than 8 in. in diameter. The
pipe sizes in inches are 8, 10, 12, from 15 to
30 with a 3 in. increment and from 36 to 120
with an increment of 6 in.
The design diameter is the smallest commercial-
ly available pipe that has flow capacity equal
to or greater than the design discharge and
satisfies all the appropriate constraints.
Storm sewers must be placed at a depth that
will not be susceptible to frost, drain base-
ments, and allow sufficient cushioning to
prevent breakage due to ground surface loading.
Therefore, minimum cover depths must be
specified.
The sewers are joined at junctions such that
the crown elevation of the upstream sewer is no
lower than that of the downstream sewer.
To prevent or reduce permanant deposition in
the sewers, a minimum permissible flow velocity
at design discharge or at barely full-pipe
gravity flow is specified. A minimum full-
conduit flow velocity of 2 fps is required or
recommended by most health departments and is
adopted in this study.
To prevent occurrence of scour and other un-
desirable effects of high velocity flow, a
maximum permissible flow velocity is also
specified. The most commonly used value is 10
fps and is adopted here.
At any junction or manhole downstream sewer
cannot be smaller than any of the upstream
sewers at that junction.
(b)
(c)
(d)
(e)
(f)
(g)
(h)
Furthermore, the following additional assumptions are
made:
(a) The sewer system is a dendritic network con-
verging towards downstream without closed
loops.
(b) The sewer system consist of junctions or man-
holes (nodes) joined by sewers (links). For
the sake of simplicity and to demonstrate the
models, other facilities such as weirs, regu-
lators, interceptors, etc. are not considered.
740
-------
TABLE 1. Illinois Least-Cost Sewer System Design Models
Model
ILSD-1
ILSD-2
ILSD-3
Design
Sewer diam, crown
elevations, man-
hole depths
Sewer diam, crown
elevations, man-
hole depths
Sewer layout,
sewer diam, crown
elevations, man-
hole depths
Optimization
Technique
DDDP
DDDP
DDDP and
set par-
titioning
Considering
Hydraulics Risks
Hydrograph time lag No
and Manning's formula
Hydrograph time lag Yes
and Manning's formula
Hydrograph time lag No
and Manning's formula
Input
Sewer layout, ground eleva-
tions, min soil cover,
acceptable max and min
velocities, cost functions,
time and space increments
for routing computations ,
optimization parameters
Same as above, in addition,
design service life, risk-
safety factor relationship
Manhole locations , ground
elevations, min soil cover,
acceptable max and min
velocities, cost functions,
time and space increments
for routing computations,
optimization parameters
(c)
(d)
(e)
(f)
No negative slope is allowed for any sewers in
the dendritic network.
The direction of the flow in a. sewer is
uniquely determined from topographic consider-
ations .
The design inflows into the sewer system are
the inlet hydrographs.
A set of simple cost functions proposed by Alan
1,8
M. Voorhees & Assoc."
lustrative purposes.
are adopted for 11-
OPTIMIZATION TECHNIQUES
Isonodal Line Representation of Manholes
For all the three design models discussed in this
paper, the locations of the manholes must be predeter-
mined and is input data for the design. Imaginary
lines called isonodal lines (INL) are used to divide
the dendritic sewer system into stages. An INL of a
given stage passes through all the nodes (manholes)
which are separated from the sewer system outlet by the
same number of links (sewers). For the purpose of
optimization a stage n includes all the sewers
connecting upstream manholes on INL n and downstream
manhole on INL n+1. As an example, the INL's for an
2
example system used in ASCE Manual 37 is shown in Fig.
1. When the sewer layout is specified, the links be-
tween the manholes for different stages are known. If
the layout is also to be designed, all the feasible
manhole connections should be considered.
Discrete Differential Dynamic Programming (DDDP)
For each possible connection of manholes there are
many possible sewer slopes and corresponding diameters
which could carry the design discharge, although only
one of these gives the least-cost system. However,
the slope is equal to the difference of crown eleva-
tions between the ends of the sewer divided by its
length, and the diameter can be determined from the
slope and discharge. Hence, the crown elevation at
each end of the sewer is chosen as the optimization
variable. The objective is to select the set of up-
stream and downstream crown elevations, among the many
possible crown elevations (states) as shown in Fig. 2,
that gives the least-cost sewer system. Although
standard dynamic programming could be used as the
Q
search technique, DDDP has been found far superior for
such optimization problems and therefore is adopted.
DDDP is an iterative technique for which a trial set of
crown elevations for the entire system (called the
initial trial trajectory) is first selected together
with a range of crown elevations (called corridors)
within the state-stage domain (feasible crown eleva-
tions) . The recursive equation of DP is then used
within a corridor to search for an improved trajectory
within the corridor. Subsequently, the improved tra-
jectory is used to set up the new corridor for the next
iteration. This procedure is repeated until a least-
cost design is obtained within an acceptable cost
error. Details of DDDP applied to sewer design have
6,7,8,12
been presented elsewhere
here.
and hence not repeated
MODEL ILSD-1
The Illinois Least-Cost Sewer System Design Model 1
(Model ILSD-1) is the simplest among the three models
Introduced in this paper. In this model the design
Involves the determination of the crown elevations, and
consequently the slope, diameter of the sewers, and the
depth of the manholes. The sewer system layout is pre-
determined and serves as input into the model. Risks
are not considered in the design. DDDP is applied to
select the least-cost sewer system. The sewer dia-
meter, d In ft, is computed by using Manning's formula
assuming just-full gravity flow
2 , 3/4
in which n is Manning's roughness factor; S is the
sewer slope; and Q is the peak discharge in cfs of the
sewer inflow hydrograph. The sewer outflow hydrograph
is obtained through lagging the inflow hydrograph by a
travel time, t , computed as
L/V
(2)
in which L is the sewer length and V is a velocity com-
puted by
V =
•n d'
The manhole junction condition is described by the
principle of mass conservation
(3)
741
-------
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manhole, and Q is the outflow from the manhole into
°Ut 10
the downstream sewer. Yen and Sevuk have shown that
this simple routing method produces hydraulic sewer de-
signs very similar to those obtained by using more
sophisticated routing methods. Therefore, this hydro-
graph time lag method is adopted for all three models
because of its simplicity and relatively small computer
requirements. The flow charts and computer program
listing for Model ILSD-1 can be found in Yen et al.12
M3DEL ILSD-2
Model ILSD-2 is the Illinois Least-Cost Sewer System
Design Model with risk considerations. Risks are
considered in the design through the use of a set of
risk-safety factor curves for the drainage basin con-
sidered. The development of the risk-safety factor
9 11 12
curves for a basin has been described elsewhere. ' '
In the least-cost design considering risks, the cost
consists of the sum of the installation cost of sewers
and manholes and the expected damage cost during the
service period of the sewer. The latter cost is
evaluated as the product of the assessed damage value
in the event of a flood exceeding the sewer capacity,
Q , and the risk, i.e., the probability of occurrence
of this event during the service period of the sewer.
To evaluate the risk, the safety factor is first com-
puted by SF = Q /Q where
(a) Street System Layout"*
= 0,463 d8/3 1/2
en o
(5)
Isonodal Lines
Fig. 1. Example sewer System
I Q
in
(4)
in which Q. is the discharge of the inflowing sewers
into the manhole; Q. is the surface inflow at the
With the value of SF known, the corresponding risk can
be obtained from the risk-safety factor curve cor-
responding to the service life of the sewer.
Model ILSD-2 is essentially Model ILSD-1 with the
addition of risk considerations. The same hydraulic
method is used and the sewer system layout is pre-
determined. Details and flow charts for Model ILSD-2
12
can be found in Yen et al. ,
MODEL ILSD-3
Model ILSD-3 is the Illinois Model for Least-Cost
Sewer System Design including Layout. This is a
screening model based upon DDDP. In addition, the
model consists of a scheme (using set-partitioning) to
select the least-cost connection of manholes. The
sewer system input includes the locations of the man-
holes and ground elevations and the design gives the
sewer layout in addition to the crown elevations,
slope, and diameter of the sewers and depth of manholes
as for the previous two models. The same hydraulic
method is used as in the previous two models. Risks
are not considered in the design. Details on the opti-
mization technique have been presented by Mays.
DESIGN EXAMPLE
Many sewer engineers are familiar with the example
2
sewer system used in ASCE Manual 37 demonstrating the
design of sewer diameters for a given network layout
and slopes using the traditional rational method.
Hence this sewer system (Fig. la) is adopted here as an
example to illustrate the advantages of the proposed
least-cost design models over the traditional hydraulic
design methods.
In ASCE Manual 37 the inflow data were given only as
peak flows obtained by using the rational formula.
These peak flow data are converted into manhole inflow
742
-------
TABLE 3. Designs of Example Sewer System
Stage
Crown
Elevatio
Fig. 2. Drops in Crown Elevations Between Manholes
hydrographs. The inflow hydrographs are assumed to be
symmetric and triangular in shape with a base time of
40 min starting at the same initial rise time and with
a constant base flow of 0.10 cfs. The peak discharges
are listed in Table 2. The minimum sewer size used is
12 in. and Manning's n is 0.013 for all the sewers.
The minimum soil cover depth is 3.5 ft.
TABLE 2. Design Example Input Data
Isonodal
Line
1
2
3
4
5
6
7
Manhole
Number
1
1
2
1
2
3
1
2
1
2
1
1
Ground
Elev.
ft
98.4
94.9
96.2
91.8
92.3
94.6
89.7
92.7
89.5
91.6
88.5
88.0
Down-
stream
Manhole
Number
1
1
2
1
1
2
1
1
1
1
1
Sewer
Length
ft
400
400
400
400
400
400
400
400
400
400
125
Peak
Inflow
QD
cfS
2.0
3.1
4.7
6.6
1.2
1.5
10.1
1.0
5.0
2.0
7.1
Models ILSD-1 and ILSD-2 are applied to the example
system and the resulting sewer diameters, slopes, and
crown elevations of the least-cost designs are
summarized in Table 3. In applying Model ILSD-2, a
5-yr risk-safety factor curve developed for Urbana,
Illinois is assumed applicable and the assessed damage
value is assumed to be $10,000 for each of the sewers.
The traditional rational method design given in ASCE
Manual 37 is also summarized in Table 3 for comparison.
The risks associated with these designs over a 5-yr
period are listed in Table 3 and the costs are given in
Table 4 for comparison. For the ILSD-1 and ASCE de-
signs, the risks are evaluated by using the same 5-yr
risk-safety factor curve employed in Model ILSD-2.
The safety factor for a sewer is computed by
SF = Q /Q with Q given by Eq. 5. Accordingly the
risk for the sewer associated with the design can be
determined. The expected damage cost for each sewer is
Upstream
Isonodal
Line
6
5
4
3
2
1
6
5
4
3
2
1
6
5
4
3
2
1
Up-
stre
Crown
Elevations
am Up-
Manhole stream
1
1
2
1
2
1
2
3
1
2
1
1
1
2
1
2
1
2
3
1
2
1
1
1
2
1
2
1
2
3
1
2
1
ft
Design Using
83.75
84.69
88.10
86.20
89.20
88.30
88.80
91.10
91.40
92.70
94.90
Design Using
84.13
85.44
88.10
86.20
89.20
88.30
88.80
91.10
91.40
92.70
94.90
Design Given in
83.55
85.15
85.15
86.25
86.75
87.90
88.05
89.55
91.00
91.80
94.35
Down-
Sewer
stream Slope
ft
Model
83.00
83.75
85.00
84.69
86.00
86.20
86.20
89.20
-88.30
88.80
91.40
Model
83.00
84.19
84.13
85.44
85.44
86.20
86.20
89.20
88.30
88.80
91.40
ASCE
83.05
83.55
81.55
85.05
83.15
90.30
86.55
86.75
87.40
87.80
90.75
ILSD-1
0.00600
0.00234
0.00775
0.00378
0.00800
0.00525
0.00650
0.00475
0.00775
0.00975
0.00875
ILSD-2
0.00900
0.00312
0.00994
0.00191
0.00941
0.00525
0.00650
0.00475
0.00775
0.00975
0.00875
Manual 37
0.0040
0.0040
0.0090
0.0040
0.0090
0.0060
0.0070
0.0070
0.0090
0.0100
0.0090
Sewer
Dia-
meter
in.
36
36
12
30
12
21
18
12
15
15
12
average
42
42
12
42
12
24
18
12
18
18
12
average
36
36
12
30
12
21
18
12
15
15
12
average
Risk
0.283
0.592
0.077
0.610
0.142
0.554
0.125
0.051
0.416
0.217
0.051
0.283
0.002
0.036
0.032
0.046
0.086
0.113
0.115
0.051
0.020
0.007
0.050
0.051
0.670
0.453
0.066
0.685
0.249
0.572
0.145
0.020
0.451
0.228
0.066
0.328
evaluated as the product of the risk and the assessed
damage value. The expected damage cost computed for
the entire system as well as the installation and total
costs for the ILSD-1, ILSD-2, and ASCE designs are
given in Table 4.
As seen from Table 4, applying optimization indeed pro-
duces designs with lower costs, and Table 3 further
shows that the risk of failure is also reduces, e.g.,
from 0.328 for ASCE design to 0.283 for Model ILSD-1.
The installation cost of the ILSD-1 design is n lower
than the ASCE design. In fact, by merely adding the
peak discharges successively in the network gives the
same design discharges as for the ASCE design and a
DDDP optimization design for these discharges
the installation cost from $70,087 to $69,062.
12
reduces
The superiority of Model ILSD-2 is clearly demonstrated
in Table 4. The total cost of this design is 25% lower
than that of the ASCE design for a 5-yr service period,
and the savings will be considerably more for a longer
service period. In order to offset the expected damage
costs due to flooding, the sewer sizes are larger than
those for the ILSD-1 and ASCE designs (Table 3), pro-
viding a better trade-off between installation and
damage costs to give a minimum total cost. With larger
sewer sizes for the ILSD-2 design, the associated risks
are reduced considerably as shown in Table 3.
743
-------
Model
Cost in Dollars
ASCE
ILSD-1
ILSD-2
TABLE 4. Cost Comparison for Example Designs 10- Yen> B- c> ' and A- s- Sevuk, "Design of Storm
Sewer Networks," Jour. Env. Eng. Div., ASCE, Vol. 101,
No. EE4, pp. 535-553, Aug. 1975.
11. Yen, B. C., and W. H. Tang, "Risk-Safety Factor
Relation for Storm Sewer Design," Jour. Env. Eng. Div.,
ASCE, Vol. 102, No. EE2,April 1976.
Installation Damage Total
70,087 (36,037) (106,124)
67,001 (31,183) (98,184)
76,155 5,602 81,757
CONCLUSIONS
12. Yen, B. C., H. G. Wenzel, Jr., L. W. Mays, and W.
Considerable savings in sewer designs can be achieved H" Tan§> "Advanced Methodologies for Design of Storm
by considering the sewers as a system and searching for Sewer Systems," Research Report No. 112, Water
the least-cost design using optimization techniques. Resources Center, University of Illinois, Urbana, 111.,
Considering the uncertainties and risks in the design March 1976.
through evaluation of risk-based expected damage costs
provides further improvement. In this paper three
such least-cost design models are briefly described.
Crown elevations and slopes of sewers in addition to
their diameters are all determined in the design
procedure. In addition, the least-cost sewer layout
can also be determined if desirable by using the
appropriate model.
ACKNOWLEDGMENT
This paper is a product of the research project,
"Advanced Methodologies for Design of Storm Sewer
Systems," sponsored by the Office of Water Research and
Technology, USDI, under Agreement No. 14-31-0001-9023,
Project No. C-4123.
REFERENCES
1. Alan M. Voorhees & Associates, Inc., "Sewer System
Cost Estimation Model," Report to the Baltimore, Md.
Regional Planning Council, McLean, Va., (available as
PB 183981, from NTIS, Dept. of Comm., Springfield, Va.)
Apr. 1969.
2. American Society of Civil Engineers, and Water
Pollution Control Federation, "Design and Construction
of Sanitary and Storm Sewers," ASCE Manual No. 37,
New York, 1969.
3. Brandstetter, A., "Comparative Analysis of Urban
Stormwater Models," Battelle Pacific Northwest Lab-
oratories, Richland, Wash., Aug. 1974.
4. Chow, V. T., and B. C. Yen, "Urban Stormwater Run-
off-Determination of Volumes and Flowrates," Environ-
mental Protection Technology Series. National Environ-
mental Research Center, US EPA, 1975.
5. James F. MacLaren, Ltd., "Review of Canadian Storm
Sewer Design Practice and Comparison of Urban Hydro-
logic Models," Unpublished Report to Canadian Center
for Inland Waters, Burlington, Ont., 1973.
6. Mays, L. W., "Optimal Layout and Design of Storm
Sewer Systems," Ph.D. Thesis, Dept. of Civil Eng.,
Univ. of Illinois at Urbana-Champaign, 111., 1976.
7. Mays, L. W., and H. G. Wenzel, "A Serial DDDP
Approach for Optimal Design of Multi-level Branching
Storm Sewer Systems," to be published in Water
Resources Research, April 1977.
8. Mays, L. W., and B. C. Yen, "Optimal Cost Design of
Branched Sewer Systems," Water Resources Research.
Vol. 11, No. 1, pp. 37-47, February 1975.
9. Tang, W. H., and B. C. Yen, "Hydrologic and
Hydraulic Design Under Uncertainties," Proceedings.
International Symposium on Uncertainties in Hydrologic
and Water Resource Systems, Vol. 2, pp. 868-882, Tucson
Ariz., December 1972.
744
-------
THE USE OF LITHIUM CHLORIDE
FOR AERATION TANK PERFORMANCE ANALYSIS
^Robert C. Ahlert
Professor, Chemical &
Biochemical Engineering
Rutgers University
Abstract
Thomas J. Olenik
Assistant Professor
Civil and Environmental Engineering
New Jersey Institute of Technology
Robert Gesumaria
Graduate Student
Rutgers University
Lithium Chloride (LiCl) was used as a tracer to
analyze the flow-through performance of a mechanical
and diffused aeration process at two different act-?
ivated sludge plants. A slug of aqueous LiCl was
dumped at the entrance of each tank and effluent
samples were anlayzed using an atomic absorption spec-
trophotometer. These results and the corresponding
mathematical models showed how the existing facilities
were operating in an inefficient manner. It is reason-T-
able to assume that this technqiue can be applied to
all aeration tanks with the hope of eliminating dead
space and shortcircuiting.
Introduction
The design of aeration tanks for the activated
sludge process revolves around several basic design
parameters. These parameters are: biochemical oxygen
demand (BOD) loading, detention time in the tank,
mixed liquor suspended solids (MLSS) , sludge age etc..
All of these design values are supposed to guarantee
sufficient destruction of waste products in order for
the sewage treatment plant (STP) to achieve its design
removals of BOD and suspended solids. After construct-
ion of the facilities, there is seldom any checking of
aeration tank performance unless removals are not being
met or operational problems appear. However, it is
entirely possible that an adequately designed aeration
tank may be operting at very Inefficient levels with
regard to the flow of the mixed liquor through the
tank's volume. That is, short-circuiting, existence
of dead space or a combination of the two may be
occuring that result in less than ideal tank perform-
ance.
A check of the flow-through conditions by use of
a tracer will indicate the existing conditions. Based
on this analysis, which is described below, it may be
possible that an existing aeration tank can accept a
higher loading in the form of flow and/or waste.
Therefore, by performing this analysis a municipality
may be able to avoid unnecessary expansion of its
aeration tank system or the plant may be able to accept
additional flow.
Lithium Chloride Tracer Analysis
lithium Chloride as a Tracer
One of the previous drawbacks of tracer analysis
of aeration tanks was the poor performance of the
tracer used. That is, organic dyes are subjected to
biological breakdown along with incorporation of the
dye into the sludge particle resulting in inaccurate
test results. In the studies described below, it was
decided to use lithium chloride (LiCl) as the tracer
for the following reasons:
1. LIC1 is highly soluble in small amounts of
water.
2. The LiCl will not be incorporated into the
sludge particles.
3. The concentration of the Li can be detected
accurately to 0.01 milligrams per liter (mg/1)
by an atomic adsorption spectrophotometer (AAS).
4. LiCl is fairly inexpensive (approx. $l;20/lb.)_-
Analysls of Tracer Testing
As outlined in Himmelblau and Bischoff's (2) work
on Population-rBalance Models, a vessel whether it is
for a chemical or biological reaction, can be describ-
ed through the use of age distribution functions.
Most chemical and biological reactors have been studied
under the assumption that their flow patterns are
either plug flow or perfectly mixed. Plug flow can be
defined as that flow in which the fluid velocity is
uniform over the entire cross—section of the vessel
(fluid particles do not intermingle with other fluid
elements). Perfect mixing assumes that the tank's
contents are completely homogeneous (effluent proper-
ties are Identical to the tank's properties). In
actual reactor performance, the flow patterns lie be-
tween these two extremes. In order to describe what
Is occuring within the tank and, in turn, achieve a
description of the effluent's characteristic, an age
distribution function Is developed through use of a
tracer or other tracking mechanism. Therefore, a
graph of lithium concentration versus time is developed
by sampling the effluent end of an aeration tank.
This graph can then be compared to the one shown as
Figure 1. The bell-shaped curve in this figure is
what is expected for actual reactors. The other curve
exhibits dead space (long tail) and some short-circuit-
ing (peak to the left of t or average detention time).
Mathematical modeling of biological reactors such
as aeration tanks and receiving waters has been
studied with great intensity over the last decade.
These models often attempt to describe the ability of
the reactor to remove BOD, etc., by obtaining a large
amount of field data and applying it to the model.
Recently, a method based on the "black-box" approach
developed by Wilson and Norman (3) has been attempted.
Very simply this method uses a network of ideal well-
stirred tank and plug flow reactors, to fit residence
time distribution data from either laboratory scale
models or field tracer studies. Thus, this input-out-
put method allows all of the complex internal process-
es (turbulence, etc.) to be reflected directly in the
network without monitoring all of the interior and
often quite complex processes. The network model will
not of necessity take the same physical appearance as
the natural system. But the great advantage of in-
cluding micro—mixing processes and stochastic varia-
tions greatly affect the lack of direct physical
correspondence to the actual reactor. This method of
using combined plug flow and well-stirred reactors can
be of great value when describing the partially mixed
reactors that occur in treatment plant or in the en-
vironment. The model can be used to predict the eff-
ect changes in a system, such as loadings, may have on
the reactor unit process or a receiving water.
The modeling techniques that were used are those
based on Wilson's work (3) and a recent paper by
Ahlert and Hsueh (1) of the Department of Chemical and
Biochemical Engineering at Rutgers University. Mr.
Hsueh was especially helpful in setting up the program
and analyzing the data.
Wilson utilized the "black-box1' approach and the
basic concepts of the Fourier Transform Function. That
745
-------
is, by ignoring the complex internal mechanics of a
unit process, the problem of data collection involved
in a deterministic type model is avoided. The Fourier
Transform Function or Laplace Transform allows trans-
fer of time domain data collected at the effluent end
of a tank into the frequency of or domain. This action
yields a description of the system by algebraic re^
lationships in the frequency domain instead of com-
plicated linear differential equations in time domain.
This change allows the use of block diagrams to des^
cribe the process with a model that can predict what
will happen to the system when loaded differently.
The transfer function is defined by the equation:
where
Z(s)
X(s)
CD
where Z(s) is the transfer function, Y(s) and X(.s)
are the Laplace Transform of the output and input
data respectively. Therefore, once Z(s) is known for
a system, any other applied loading in terms of X(s)
can be converted to output in the frequency domain and
the characteristic equation of the output In the time
domain (y(t)) by performing the inverse transform
operations.
The transfer function and the inverse computat-
ions are relatively easy to perform. This fact is
applied in using Wilson's approach, as the lithium
chloride was inputed as a Dirac-delta function. The
equations and assumptions involved in Wilsonrs method
are described below:
The frequency content S(o)) of an aperiodic
function is described by its Fourier Transform
S(ui) = F(f(t))
f(t)
-jut ,
e J dt
cos (cot) dt
B / y y(t) sin(uit) dt
o
C =
x x(t) cos(ut) dt
x(t) sin(u)t) dt
(8)
(9)
(10)
(11)
(2)
The model block diagram construction can start
based on two ideal chemical reactors. The two re-
actors are the plug-flow tubular reactor (PFTR) which
acts as a pure time delay mechanism, and the continu-
ous stirred tank reactor (CSTR) which is an instant-
aneously mixed system where dispersion reaches a max-
imum. The PFTR and CSTR are linear in the time domain
and are transferred into the complex (s)-domain to
obtain the system Transfer Functions. Linearity all-
ows the construction of complex networks based on
these components.
Taking the field data, Equation 5 through 11 are
used to derive the real and imaginary parts of the
transfer function. A Bode plot is used in defining
poles and zeros; from these a first estimate of the
number of CSTR components needed can be made for a
trial network configuration. The network configura-
tions are evaluated by a least—squares procedure by
using the sum of the squared vectorial deviations in
the frequency domain as shown below in Equation 12.
where
(Re(oo)o -
For convenience purposes, S(uj) is normalized by
dividing it by the value at zero frequency.
S(ui)
Area under f(t)
(3)
then the Fourier Transfer Function is given by
7< , fj y(0 e ->* dt
Z^> - . . (4)
x(t) e
dt
where T and T are the upper limits of the integra-
tion for the output and input function, respectively,
and x(t) and y(t) are the time domain functions of
the input and output signals respectively. By apply-
ing the identity
-jut
cos u) t -j sinojt
(5)
the real, Re(m), and imagining, Im(u>) , parts of the
Transfer Function are given as:
AC + BD
(6)
Re (co)
C2+D2
AD - BC
(7)
(12)
where the o and p refer to observed data and predicted
values using the model, respectively.
Tests Performed and Results
The techniques described were used at two activa-
ted sludge plants, the Madison-Chatham and Hanover
Park sewage treatment plants.
Madison-Chatham Plant
The aeration system at the Madison-Chatham plant
is divided into two physically distinct tanks. The
first and largest tank is a diffused air system. The
other tank, containing mechanical aerators, was the
one chosen to be traced using lithium chloride
(Figure 2). The equipment employed was the following:
1. 50 Ibs. of LiCl.
2. 2 Sigmamotor automatic samplers.
3. Garbage can.
4. 10 feet of 6-inch smoke pipe to dispense the
solution of LiCl.
The test procedure was to dump instantly a slug
of aqueous LiCl solution, by use of the garbage can,
into the influent pipe of the mechanical aeration
system. An instantaneous slug was necessary to approx-
imate a Dirac-delta function to make the mathematical
746
-------
model of the system easier to produce. Automatic
samplers CSigmamptor Co.X were needed to obtain samples
on a continuous basis after the LiCl had been dumped.
These samplers can be set at time intervals ranging
from 1 to 60 minutes. At the end of each sample period
the machine resets itself to another bottle, so
discrete, not combined samples are taken. Through
use of an automatic purping device, the sample pump
and tubing are evacuated. Two samplers were needed
because of recycling of secondary settling tank sludge
that could contain some lithium and return it to the
system. Two samplers were located as shown in Figure
2, and were in operation for about 72 hours. Samples
were analyzed using an atomic adsorption spectophoto-
meter (Perkins-Elmer Model No. 403).
The data are plotted using concentration versus
time as the scales in Figure 3. A computation of the
mass balance for lithium showed that 88 percent of the
lithium was accounted for. Since this first run
operated at sample time intervals of 30, 40 and 60
minutes, and since it was felt that a great deal of
short-circuiting occurred in the first 30 minutes, the
first 3 hours of the experiment was repeated using 35
pounds of LiCl. The time interval of the sampling
for the second run was 1 minute for the first half
hour and 5 minutes to the end of the experiment
(4 hours total). A mass balance showed that 20 per-
cent of the lithium was accounted for in this time
period (Figure 4) .
The curve of concentration versus time for the
first run as shown in Figure 3 can be compared to
Figure 1. This curve shows that appreciable amounts
of tracer still exist in the aeration tank well past
the average detention time of about 5.3 hours (design
detention time is 4.5 hours). Also, during the first
run (50 pounds of LiCl) periodic samples of the dead
spots (see Figure 5) showed higher concentration of
lithium when compared to the effluent suggesting these
dead spots were isolated areas where detention
time of the mixed liquor is higher. It should be
noted that the return sludge, did not contribute
appreciable amounts of lithium because the sludge had
been diluted considerably by flow from the much larger
diffused aeration tanks.
From the above experimental results it can be
seen that the hydraulic flow through characteristics
of this aeration tank causes a severe short-circuit-
ing and a limited amount of dead space. It is obvious
that this tank is not being used in an efficent
manner. This fact is brought out further by an ex-
amination of the mathematical models produced for the
two runs described above. An examination of Figures
6 and 7 that were developed through the use of a
computer program allows the following additional
conclusions:
1. The optimum models obtained for each run and
their transfer functions can now be used to predict
the performance of the aeration tank for various
loadings.
2. The second run is an improvement over the
first, because of the fact that the second run's data
were taken at a smaller time interval. From Figure 7,
the small effect short-circuiting (segment f2"fl')
has on the overall model can be seen. The bottom
half of the model (segment f2') is where 95 percent
of the flow passes through, which results in a large
increase in the residence time. Thus, the summation
of the residence times (.Tj, T4, and Tj) adds up to
approximately 380 minutes (6.3 hours) which exceeds
the average design detention time of 4.5 hours. It
is felt that the poor hydraulics of the system causes
this effect.
Florham Park Plant
This plant was chosen to be tested in a similar
fashion because of the fact that its method of aeration
was by diffusers. A flow diagram is shown below
(Figure 8).
The same procedure used at the Madison-Chatham
Plant was applied at this plant. The actual results
are shown in Figures 9 and 10 with the following obser-
vations made:
1. An actual average detention time of 8.56 hours
was observed (Figure 9) as compared to the design
detention time of 4 to 6 hours.
2. On a mass basis, 89.5 percent of the Li was
recovered in 30 hours of sampling.
3. Branch f^ (0.76Q) shows a large amount of dead
space in the system. The detention time in this
branch (Tj^ + T3) is 12.37 hours (742.42 minutes). This
value greatly exceeds the design detention time of
4 to 6 hours which is computed by the ratio of tank
volume to flowrate. Branch f2 (0.24Q) shows a
significant amount of short-circuiting in the system.
The detention time in this branch (T2 + T2 + TS) is
2.05 hours (123.12 minutes) which is considerably less
than the design detention time of 4 to 6 hours cited
above.
Conclusions and Recommendations
It appears obvious from the two studies performed
concerning aeration tanks used in the activated sludge
process, that poor flow^through conditions cause a
gross inefficiency in the treatment plant system.
While this technique can produce a very involved and
costly analysis if the modeling is performed, a simple
concentration of Li versus time can give an engineer
an adequate picture of what is occurring in the
aeration tank that is the key unit process in the
treatment plant. This is not limited to the analysis
of aeration tanks. It is hoped that this technique
will be applied to receiving water analysis along with
expanded uses in analyzing existing sewage treatment
processes.
Bibliography
1. Ahlert, R.G., and Hsueh, S.F., "A Reactor Network
Model of the Passaic River," Rutgers, The State
University, 1973.
2. Himmelblau, D.M., and Bischoff, K.B., "Process
Analysis and Simulation: Deterministic Systems," New
York: John Wiley and Sons, 1968.
3. Wilson, A.W., "Mathematical Modeling of Partially
Mixed Reactors," Doctoral Dissertation, McMaster
University, Hamilton, Canada, 1971.
747
-------
Time, hours
FIGURE 1 IDENTIFICATION OF INEFFICIENT AERATION
TANK OPERATION
Return Sludge
Sampling Point
To 2nd
Settling Tank
30'
30'
Surface
Aerator
0
©
©
.uent'
Effli
Sampling
Point
f ' ' 14"g f ^ influent
Flow
Splitter
Box
.«.._.., Inflow
To diffused
Aeration
Tanks
Tank
Numbers feet
Depth Volu^e Volume
Gallons
feetj
10
10
14
9,000
9,000
12,600
67,320
67,320
94,248
FIGURE 2 MECHANICAL AERATION SYSTEM,
MADISON-CHATHAM PLANT
100 150
FIGURE 4 LITHIUM TRACER STUDY, SECOND RIM, MADISON-CHATHAM PLAHT
MECHANICAL AERATION SYSTEM
210 240
Dead Spot
7
To Secondary
Settling Tank
FIGURE 5 PLAN VIEW OF MECHANICAL AERATION TANK SHOWING
LOCATION OF DEAD SPOTS
FIGDRE 3 LITHHH TRACER STUDY . FIRST RUN, MADISON-CHATHAM PLAHT
MECHANICAL AERATION SYSTEM
748
-------
Q - 1.2 ngd
f. - 0.43877
f, - 0.56123
q • 40.53 mln.
t • 246.32 mln.
T^ - 6.63 mln.
• (*) - 0.12602
Transfer Function
FIGURE 6 MIXING MODEL FOR RUN NO. 1, MADISON-CHATHAM PLANT
MECHANICAL AERATION SYSTEM
1 VERSUS TIKE
FLOBHAH PARK SEWAGE TREATMENT PLANT
FLORHAH PABX. NEW JERSEY
-1.2 ragd
• 0,05
- 0.95
- 0,30925
• 0.69075
- 1.6184 mln
- 14.22 mln.
- 140.0 nln.
• 75.058 mln
• 164.75 mln
- 0.05628
- 0.0035
- 0.034
Q - 0.7 MCD
f^ - 0.76051
:2 - 0.23949
i, - 645.76 mln.
T2 - 13.277 mln.
T3 - 96.657 rain.
i'Q - 6.0000 nln.
» - .023182
FIGURE_1_Q REACTOR NETWORK Cffi)FIGURATION, DIFFUSED AERATION SYSTEM
FLORHAM PARK SEWAGE TREATMENT PLANT
FLORHAM PARK. NEW JERSEY
PICURE_7 MIXING MODEL FOR RUN NO. I, MADISON-CHATHAM PLANT MECHANICAL AERATION TANK
Exceaa Activated Sludge
yiCURE_B FLOW DIAGRAM OF THE FLORHAM PARK SEWAGE TREATMENT
PLJWT, FLORHAM PARK, NEW JERSEY
749
-------
SWAN
A SEWER ANALYSIS AND MODELING SYSTEM
Elias C. Tom'as, P.E.
Director of Computing Center and Associate
Philip C. King, P.E.
Project Engineer
ERDMAN, ANTHONY, ASSOCIATES, CONSULTING ENGINEERS, ROCHESTER, NEW YORK
ABSTRACT
The need for a thorough understanding of the sewage
collection systems for many municipalities has
resulted in the development of a system of computer
programs to analyze an existing network. This
computer system, called SWAN (an acronym for Sewer-
Analysis), can be employed to examine the collection
network as a whole or in part(s), thus enabling the
investigators to see the total character of the net-
work at a glance and to make coordinated decisions
concerning expansion and improvement.
SWAN can store an entire sewage collection network
on a data base which can be easily modified and
employs a mathematical model to simulate the network
flows under various sanitary and storm conditions
and combinations thereof. SWAN was originally based
on the Rational Method. Recent modifications have
incorporated the Surface Hydrograph Method commonly
referred to as the Chicago Method.
Although SWAN's primary purpose is to analyze exist-
ing sewer systems, it may be utilized as a design
tool. The principle of design by iterative analysis
is facilitated immensely by SWAN's built-in feature
of recommending appropriate pipe sizes for upgrading
inadequate sewer reaches. Graphic documents produced
automatically by the computer system may be utilized
as final report or contract documents.
SWAN is ideally suited for a small (IBM-1130) compu-
ter readily available to many consulting engineering
offices and small governmental agencies and municipal-
ities. Although SWAN is intended for batch proces-
sing, it may easily be revamped for an inter-active
environment.
The authors wish to acknowledge the efforts of ,
Mssrs. Charles S. Hodge and Alfred J. DeYoung during
the development of the original system.
INTRODUCTION
The original sewer system in many older communities
was a storm sewer, as this was the bigger and more
visible problem, which evolved into a combined sani-
tary and storm sewer. In many other communities, it
was economics that dictated that the sewers be built
as combined sewers. As time went on, community-
wide treatment facilities were built. The excessive
storm flows necessitated the construction of over-
flows into any convenient water body. It has become
necessary therefore for municipalities to take a
very close look at their wastewater collection
systems, especially where the collection systems are
combined facilities.
The result is a growing need for information about
existing sewer networks and the character of the
storm flows that are carried in these networks. Too
often, a municipality's wastewater collection system
is not known and is not inspected unless a problem
exists. Existing sewer systems are usually the
result of a series of expansions and improvements to
the original, and often no longer adequate set of
conduits. Urban growth has placed a burden on the
older conduits and in many situations the systems
have not been improved to handle these additional
flows.
This need to understand the sewage collection and
transport systems has necessitated the development
of numerical techniques for analysis and flow simu-
lation of complex sewer networks. There are present-
ly several computer software packages designed to
accomplish this.
When creating a sewer modeling program, the following
parameters must be considered:
1. Methodology of load generation
2. Methodology of load transport
3. Special features to be analyzed such as pumps,
overflows, weirs, etc.
4. Extent of network to be analyzed (how many
pipes, manholes, overflows, or other special
features).
5. Ease of use by the practicioner with respect
not only to input generation but also to output
interpretation.
6. Availability of and selection of hardware
SWAN is an entirely analytic system. It does not
employ statistical methods other than those necessary
to reduce field observed statistics. SWAN employs
common hydraulic principles that are used by hydrau-
lic engineers in normal design and analysis such as
Manning's Equation, Hazen-Williams Equation, the
Rational Method, the Surface Hydrograph Method
(Chicago Method), hydrograph and backwater techniques.
SWAN's use is enhanced by its ability to apply them
to a large network, thereby relieving the engineer
from tedious calculations and allowing him to concen-
trate on the major questions.
OPERATIONAL CONCEPTS
SWAN receives data and performs operations through a
series of commands. These commands are one word
signals which transfer control to the various oper-
ations which may in turn receive data. Commands may
be streamed together. Each command has some terminal
device which will cause the system to seek a new
command. All of the commands are tied together in
that they all use the various files which are devel-
oped in a specific order. Therefore, some commands
may be prerequisite for others.
Most of the commands employ extensive error diagnos-
tics. There are five basic groups of commands in
SWAN:
750
-------
1. The CONTROL, GEOMETRY and EDIT cornnands are
used to build the data base from which all
other operations take their cue.
2. The VELOCITY, GAUGING and FLOWS commands are
used to reduce field observations and generate
reports for system verification.
3. The PROFILE, CONDITIONS and PLOT commands
generate profile plots with a table of conduit
descriptions.
4. The LOAD, CURVE, HYDROGRAPH and BACKWATER
commands are used to analyze and simulate the
flows.
5. There are three other commands: END, STOP and
EXIT, which are used to terminate commands or
the entire system run.
The prerequisites of SWAN are basic in concept:
1. There must be a problem definition something
to analyze.
2. The system to be analyzed must be described
accurately.
3. The user has to be familiar with the actual
network and should have an in-the-field aware-
ness of actual conditions.
4. The user must have a knowledge of hydraulics
and hydrology.
PROBLEM DEFINITION
The use of SWAN must be pointed towards a specific
situation. The user must know what he is attempting
to show with his sewer analysis. SWAN is not a
mysterious miracle worker. It is a tool to be
employed to effectively analyze a problem. In turn,
it may be used to assist in designing a correction
for the problem.
In order to utilize SWAN, data must be collected and
entered into the data base. Sewer networks have to
be described by their geometries. This description
of the sewer geometry requires the following infor-
mation:
1. Length of each conduit between manholes.
2. Shape of conduit and dimensions.
3. Invert elevations at each manhole.
4. Manning's n for each conduit.
5. Continuity of flow.
6. Manhole rim elevation if profile plots are
desired.
The geometry is usually available to municipalities
in the form of design or as-built plans or previous
sewer studies. The definition of the sewer geome-
tries is fundamental to proper SWAN operation.
Should data about existing sewers be questionable,
field measurements should be made to resolve these
questions. SWAN can analyze systems containing a
multiplicity of different basic conduit cross-
sections. There are presently 33 shapes on line.
The hard geometric data which defines a sewer must
be supplemented by a geometric logic describing the
layout of each sewer component. This logic is des-
cribed by nodes (manhole numbers) and incidences
(downstream manhole to upstream manhole). The sewer
network has three basic elements: the "reach", the
strip", and the "drainage area". The reach, the
smallest and most descriptive element, consists of
two manholes and their connecting conduit. Manholes
may be real or "pseudo": a real manhole actually
exists in the network; the "pseudo" or imaginary
manhole is a nodal point at which some feature in
the conduit changes. The pseudo manhole provides
the system with the flexibility to describe changes
in the conduit between manholes. Thus the conduit
in each reach is uniform in shape, material and
slope.
Many reaches linked end to end would constitute a
"strip". A strip begins at some downstream manhole
(real or pseudo) and proceeds manhole by manhole to
some upstream manhole. This upstream point may be a
dead end manhole or it may be the limit of investiga-
tion.
Many strips tied together by common manholes would
constitute a "drainage area". The drainage area can
have only one outlet.
FIELD OBSERVATIONS AND VERIFICATION
The mathematical model of flows in a sewer network
built by SWAN is only as good as the data base on
which it is founded. Therefore, it is advisable
that field observations be made in order to validate
the base and subsequent modeling.
Field observations should include determination of
Manning's n where necessary, storm flow gauging, dry
weather flow gauging, condition of sewer conduits
and manholes and resolution of ambiguous geometric
data.
The character of drainage areas serviced by a network
may change with time, especially in districts close
to central business areas. Urbanization results in
a general increase in the imperviousness of a water-
shed, rendering storm or combined sewers in these
districts inadequate. Observations of these condi-
tions are extremely important in order to validate
the computer model.
Verification of the SWAN modeling may be made by
placing flow meters capable of recording the water
surface with respect to time at control manholes.
By appropriate reduction of recorded data, actual
hydrographs for recorded storms may be obtained at
each of these test manholes. Theoretical hydrographs
for the same points and recorded storms may be
generated by SWAN and superimposed upon the actual
hydrographs for verification.
HYDROLOGIC CONSIDERATIONS
There are presently several methods available to
determine the amount of rainfall entering a sewer
network ranging from oversimplified approximations
to highly mathematical modeling approximations. All
of the available methodologies, regardless of their
sophistication, do depend upon empirical data whether
they are runoff coefficients, imperviousness factors.
or impoundment constants. Of these, two have gained
widespread use in present practice, the Rational
Method and the Surface Hydrograph or Chicago Method.
SWAN was originally designed to determine runoff by
the Rational Method. Verification of its results
was made for 25 year design storms. Recently the
Chicago Method was incorporated into the system to
allow the user this option.
SWAN's application of the Rational Method is based
on rainfall-intensity curves promulgated by local
weather offices utilizing contributing areas of city
block size or smaller and composite imperviousness
factors. The program uses the inputed time of
concentration and the computed elapsed time of flow
in the sewer as a storm duration abscissa to find
the rainfall intensity from the rainfall/intensity
curve. Times of concentration, much like the Manning
751
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n factors, require judgment and evaluation. Pub-
lished tables are available to assist in their
selection.
In addition to direct time of concentration entry,
SWAN offers the ability to compute such time by the
equation:
0.50 0.333
TINLT 1.8(1.1-BCOF)(BLEN) /(BSLOP)
Where: TINLT is the inlet time in minutes
BCOF is the basin coefficient of runoff
BLEN is the basin length in feet
BSLOP is the basin slope in percent
The Rational Method is based on a uniform rainfall
on the entire drainage area under investigation.
Violent summer storms of infrequent occurrence do
not fit this pattern as they are not uniform in
rainfall intensity nor uniform on the entire area.
Users therefore should be aware of these limitations
because they tend to yield conservative results and
generally indicate too many conduits as being under-
sized when such a storm is applied.
SWAN's application of the Chicago Method utilizes a
model hyetograph and generates time dependent surface
hydrographs for every manhole. These hydrographs
take into consideration surface imperviousness and
impoundments as well as evaporation.
SYSTEM LOADS
SWAN offers the ability to load the sewer system
with domestic and industrial loads, storm flows and
infiltration. The storm load determination has been
described under the hydrologic considerations of
this report. Domestic loads may be defined by
acres, population density and per capita usage,
census population and per capita usage or direct
point load. Infiltration and industrial loads are
entered as direct point source loads or as a per
capita allowance.
The loading feature (called the LOAD operation) is
employed to analyze nearly all situations. It
applies the normally accepted design methods in an
analysis mode. It indicates those conduits which
are undercapacity for the specified condition.
The LOAD operation can be applied directly to analyze
proposed sewers. The effect of urbanization of a
network's watershed can also be analyzed to indicate
the deficiencies or unused capacity of the network.
The effect of proposed sewers on an existing network
is still another powerful application which can
provide insights into land use management under
existing conditions.
With sanitary accumulations, combined sewer overflows
to receiving waters can have their pollutant quantity
predicted for specific storm conditions. Increases
in dry weather sanitary flows caused by dramatic
changes in the area served by a network may require
readjustment of a combined sewer's overflow regulator.
The LOAD command, having received the loads of the
manholes, proceeds to accumulate them upstream to
downstream keeping track of time of concentration
(Rational Method) and elapsed travel time of flow in
the sewer.
Having determined the flow, the program institutes a
half interval search based upon the continuity of
flow and Manning's equations to find the depth of
flow. The search starts at one-half the full depth
and continues until one of the following acceptance
criteria is met:
1. Change in depth from previous trial to present
trial less than 0.001 inches.
2. Load flow previously computed differs from flow
at trial depth by less than 0.01 cfs.
Once the depth is found, the velocity is easily
calculated and the elapsed time of flow is incre-
mented by the time-of-flow in the present reach.
If the flow developed previously 1s greater than the
capacity of the conduit, the search operation is
omitted and the time is computed based on full depth
of flow. Any reach which had a computed flow greater
than capacity is flagged and its description is
stored for future tabulation. The command can
institute a "design" which will give the size of a
circular conduit which will carry the load using a
Manning's n of 0.013 and at the slope of the existing
sewer.
HYDROGRAPH DEVELOPMENT
Hydrographs of flow from a watershed are useful
tools for analysis of any facility carrying or
treating storm flow runoffs. While the Rational
Method is weak for analysis of runoff, the hydrograph
development techniques incorporated into SWAN can be
utilized for analysis of any size uniform intensity
storm passing in any direction across the watershed
area. Hydrographs can be developed for any reach in
the drainage area for any given storm. In this
application, the physical wave front of the storm
flow can be developed and time-flow relationships
can be derived and applied to a backwater analysis.
Storm flow hydrographs are powerful devices for
analyzing quantity of overflow to receiving waters.
SWAN's hydrograph module also provides mass flow
diagrams. The developed hydrographs and mass dia-
grams in the form of coordinates of flow or mass
versus time may be printed or plotted.
Sewage treatment of storm water is gaining in popu-
larity. Although it is not new, the treatment of
storm water is far from being a well established
science. Design criteria are presently being formu-
lated by regulatory agencies. The basic design
parameters for storm water treatment are rate and
quantity of storm runoff. These parameters are
developed by the hydrograph feature of SWAN.
The actual hydrograph development is based on an
accumulation of simple trapezoidal hydrographs of
each runoff area. For the Rational Method, time of
concentration is an important factor- A new element
has been added: "start time". For even the most
intense storms, rainfall must saturate the ground
before runoff begins. Asphalt and concrete pavements
have cracks and voids that trap water before runoff
begins. This period before water eventually reaches
the sewer is called "start time". It can be a
matter of seconds or minutes and is a judgment
factor as is time of concentration. For the Chicago
Method, the above are taken into account in the
surface hydrograph generation.
The HYDROGRAPH command accumulates the local water-
shed hydrographs. It takes its ordinate (either
flow or watershed area) and adds to it all the other
local hydrographs, displacing each by its travel
time down to the reach being investigated. Each of
the local watersheds should not exceed an area of
752
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about 2 acres. If the areas are larger, the assump-
tion of a trapezoidal local hydrograph becomes
questionable.
The hydrograph method can be used to give a reasonable
approximation of the effect of a uniform storm on
the drainage area but should not be substituted for
the actual field observed flows.
The application of a uniform storm to a drainage
area is a problem with the hydrograph as it is with
the Rational Method in the LOAD command. The differ-
ence is that with the HYDROGRAPH command, the input
may be selected to conform to an actual storm.
Accepted unit hydrograph techniques can be employed
by using an intensity of 1.0 to create the unit
hydrograph.
BACKWATER
Backwater techniques have long been recognized for
the analysis of open channel flow (creeks, rivers,
ditches, etc). In a closed conduit the backwater
principles are the same except when the sewer is
surcharged, i.e. flowing full under a head. Sur-
charged sewers can be analyzed using pressure flow
principles.
The availability of a backwater technique analysis
to flow in sewers allows a multitude of applications.
The most frequent application is the analysis of a
series of reaches having a constriction caused by a
singular undercapacity conduit.
The backwater analysis in SWAN can perform two func-
tions:
1. Calculate the required piezometric head to
sustain a given flow.
2. Calculate the flow sustained by a predetermined
piezometric head.
The first function can be applied to analyze the
surcharge capacity of a sewer. This capacity may be
significantly larger than the gravity flow capacity.
The surcharge capacity of a sewer is important when
sewers are analyzed for short-term high-intensity
storms. This type of storm has been historically
ignored because of the complex nature of any manual
analysis. Runoff flows through the sewer in a time-
related manner, i.e. the peak flow, need be sustained
for only a short period of time (say 3 to 5 minutes).
This peak may be 25% to 50% greater than the gravity
flow capacity. The sewer can in many cases carry
this flow. It has been shown that a storm sewer
that was designed for a 10 year recurrence-period-
rational-method storm can sustain a 25 year high-
intensity short-term storm. The analysis of these
storms is a difficult process and requires the
development of hydrographs for specific storms.
The ability to calculate a flow sustained by a given
head is useful in determining surcharged flows for
specific upstream conditions in a sewer. Flow
splitting caused by overflow regulators or relief
sewers is a good example. Overflow regulators are
usually designed in a gravity flow environment.
However, in actual practice, these regulators may be
surcharged during peak flows, especially if they are
regulating flows from dense urban areas.
The operation must start at a known elevation at the
downstream end of the investigation. In a sewer
this could be one of two conditions.
1. The water surface elevation of a receiving
water if the outfall conduit is submerged.
2. The known starting elevation as a function of
the conduit hydraulic properties if the sewer
flow falls free such as in a drop manhole
device or in an overflow outfall.
Using the starting elevation, the operation applies
"gradually varying flow" theory to find the water
surface within a reach up to its upstream manhole.
Using the conservation of energy principle, the
starting elevation for the next reach can be calcu-
lated. This procedure is repeated until the limit
of investigation is reached.
Gradually varying flow theory considers that the
water surface can be predicted by a profile curve.
This profile is a function of the quantity of flow
and the geometries of the channel.
The flows utilized by the BACKWATER command may be
defined in one of three manners.
1. Direct Q (flows in cfs) at each manhole.
2. Flows in terms A*C with a request for a half
interval iteration search to determine the flow
and subsequent water surface elevation (piezo-
metric head).
3. A modification of 1 above, where Q's are read
from the surface runoff hydrographs (Chicago
Method) computed earlier in the system and
stored in a file.
The third type of loading above may be explained by
Figures 1A and IB which depict a dendritic network
and corresponding manhole loading hydrographs respec-
tively. .
O2
0 at
MH5
Q at
MH4
Oat
MH3
Qot
MK2
Oot
MH 1
/~
/
/
y
031
J?
Oil
051
\
\
041
~N
/"
t
022
/T
012
X
052
.042
\
032
~\
\
013
053
043
033
Q23
~>v
\
FIGURE i
DENDRITIC
NETWORK
TIME
FIGURE IB:
LOADING
HYDROGRAPHS
753
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Water profiles by backwater means are determined at
various time intervals t], t2, tj and so on with t=0
being the start of the storm. In this manner, the
worst profile for any sewer reach may be determined.
For time interval \-i, for example, the loading at
Manhole 1 is Q12 obtained from the surface hydrograph
contributing to Manhole 1. Similarly Q22 is obtained.
At Manhole 3, the hydrograph includes the accumula-
tion of the hydrographs at Manholes 3, 7, 8 and 9,
taking into account the respective times of travel
to Manhole 3. This methodology is continued to
Manhole 5 at the upstream end of the system.
Within each manhole the following losses may be
taken into account by SWAN:
1. Bend losses varying with the upstream velocity
head.
2. Change in velocity losses - due to the change
in velocity heads and always positive.
3. Change in flow losses - due to an increase in
flow caused by flow entering from a side strip.
If the sewer is surcharged because the flow is
greater than the capacity, the piezometric head is
defined by the energy gradient from the Hazen-
Williams equation. If the surcharge is caused by
downstream conditions and the conduit would normally
carry the flow, the piezometric head is defined by
the friction slope from the Manning equation.
The BACKWATER command is* a very useful tool. Sur-
charged storm sewers can be shown to have larger
capacities than that found by the Manning equation.
A deep sewer can sustain a very large surcharge and
perform with flows 100% higher than normal flow
capacity. However, a constriction in a sewer can
cause the capacity to be reduced for all upstream
reaches. This may not be evident from analysis by
other means.
Backwater techniques can be employed to analyze
relief sewer capacity by simulating a surcharged
system up to the piezometric head that equals the
relieved sewer's overflow wiers. Overflow structures
can be analyzed using this same approach.
These techniques should not be used when the sur-
charged piezometric head is in excess of three or
four times the conduit diameter above the sewer
crown. The assumptions are questionable under these
conditions.
CONCLUSION
The use of SWAN on various projects since its incep-
tion in 1971 by Erdman, Anthony, Associates has
shown it to be a valuable and accurate tool for the
simulation of sewer flows. Its use, however, must
be tempered with good engineering judgment, for it
was not intended to circumvent the Engineer.
The implementation of SWAN can be a very useful and
inexpensive method of keeping accurate records of a
municipality's sewer networks. As the community
grows, the data base can be expanded to include
additions and improvements. Additions and improve-
ments can be analyzed in the planning stages or
checked in the design stage and thus reduce the
chance of inadequate service. The municipal agency
responsible for wastewater collection and disposal
would have its network records and the procedures
for analysis in one easily accessible source.
As the environmental movement picks up momentum and
as more monies are made available for water pollution
abatement, SWAN will be even more valuable to engi-
neers and planners. Municipalities which do not
have long-term statistical data available may employ
SWAN to develop reasonably accurate models of criti-
cal events, and reduce the time from investigation
to design.
It is the intent of the authors, depending of course
on the availability of time and funds, to utilize
the options of SWAN to compare the Rational Method
with the Chicago Method and to determine their
effects upon analysis and design. Several theore-
tical comparisons have been made, but to the know-
ledge of the authors, none have been made on actual
complex and extensive sewer systems.
SWAN is a simple to use computer system which re-
quires neither monstrous hardware nor tedious or
complicated input form preparation. The output is
neatly presented for ease of interpretation and the
plotter features reduce the efforts of transferring
computer output to hard copy. SWAN is upward compa-
tible with respect to hardware within a FORTRAN
environment. Lack of space prohibits a detailed
description of SWAN and Its related output. Those
interested may feel free to contact the authors for
further details.
BIBLIOGRAPHY
1. "OPEN CHANNEL HYDRAULICS" by Ven Te Chow,
McGraw-Hill, 1959.
2. "HANDBOOK OF APPLIED HYDROLOGY" by Ven Te Chow,
McGraw-Hill, 1964.
3. "HANDBOOK OF APPLIED HYDRAULICS" by C.V. Davis,
2nd Edition, McGraw-Hill, 1952.
4. "DESIGN AND CONSTRUCTION OF SANITARY AND STORM
SEWERS" by the American Society of Civil Engi-
neers and the Water Pollution Control Federation •
A.S.C.E. M&R No. 37.
5. "HYDROLOGY OF URBAN RUNOFF" by A.L. Tholin and
C.J. Keifer, ASCE Transactions Paper 3061,
March 1959.
6. "CHICAGO HYDROGRAPH METHOD NETWORK ANALYSIS
OF RUNOFF COMPUTATIONS (N.E.R.O.)" by C.J.
Keifer, J.P. Harrison and T.O. Hixson, City of
Chicago D.P.W., 1970.
7. "SYNTHETIC STORM PATTERN FOR DRAINAGE DESIGN"
by C.J. Keifer and Henry Hsien Chu, Proceedings
ASCE, Hydraulics Division Paper 1332, August
1957.
8. "WATER SUPPLY AND POLLUTION CONTROL: by Viessman
and Clark, International Textbook Company,
1966.
9. "WATER SUPPLY AND WASTE DISPOSAL" by W.A.
Hardenburgh and E.B. Rodie, International
Textbook Company, 1963.
10. "WATER SUPPLY AND WASTE WATER DISPOSAL" by G.M.
Fair and J.C. Geyer, John Wiley and Sons, 1966.
11. "HYDRAULICS" by H.W. King and C.O. Wisler and
J.G. Woodburn, John Wiley and Sons, 1963.
754
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ON-LINE MODELS FOR COMPUTERIZED CONTROL
OF COMBINED SEWER SYSTEMS
J.W. Labadie and N.S. Grigg
Department of Civil Engineering
Colorado State University
Fort Collins, Colorado
P.O. Trotta
Department of Civil Engineering
University of Colorado
Denver, Colorado
Automatic computer control is a cost-effective
approach to controlling polluting discharges from com-
bined sewer systems. Perhaps the greatest challenge
is development of programmable models and control
logic that can find the best positioning of field con-
trol elements within the restrictions of the on-line,
real-time environment. Control strategies can be
developed off-line or on-line, and may be reactive or
adaptive. It appears that simple reactive control,
or rule curves, can adequately control total overflows,
but may produce high overflow rates. Stochastic adap-
tive policies produce a smoother distribution of over-
flows, but are highly dependent on the accuracy of the
storm inflow forecasting model. Autoregressive moving-
average transfer function models are proposed as an
efficient approach to forecasting. Initial indications
are that total city-wide automatic control is feasible,
both technically and economically.
Introduction
Increasing political and economic pressures are
causing today's urban water manager to place a greater
emphasis on cost-effectiveness of urban services and
efficient spending of the public dollar. Accordingly,
he has a great interest in searching for innovative
solutions. It has been conclusively demonstrated that
storm and combined sewer discharges are significant
contributors to the total pollution reaching our re-
ceiving waters and the price tag to clean up these
discharges has been estimated to be in the $200 billion
range. Since neither this country as a whole nor
individual cities can afford expenditures of this
magnitude for the problem, better ways to manage
existing systems and affordable new systems must be
found.
Automatic computer control has been applied with
success in industry for more than 15 years. It is
only recently, however, that a few U.S. cities have
implemented limited scale computer systems for con-
trolling combined sewer overflows from portions of
their urban complexes, with a number of other cities
in various stages of planning for such systems.
It makes sense to consider automatic control of
storage and flow in a combined sewer system by digital
computer, especially in light of the tremendous ad-
vances made in recent years in industrial computer
control. The availability of attractive computer
hardware, however, does not by itself guarantee success
in automating a system. The cost of such hardware may
be the least of the costs involved.
The normal computer control project should pro-
ceed cautiously through phases, beginning with the
simple to the more complex. The four basic levels of
computer control can be listed as follows:
1. Data logging and processing
2. Conventional remote supervisory control
3. Automation of parts of systems and computer
assisted control
4. Closed loop automatic computer control.
Once a commitment to the eventual implementation
of automatic control is made, the greatest challenge
is the development of programmable models and control
logic that can ensure the most effective utilization
of storage and treatment in the system. It is the
control strategy development problem that is addressed
herein.
Control Objectives
Application of automatic control to combined
sewer systems requires that strategies be developed
and implemented for remotely controlling adjustable
valves, orifices, gates, and pumps within the system,
during a real-time storm event, in such a way that
certain control objectives are met as closely as
possible, such as:
1. minimize the total volume of overflows
reaching receiving waters during a storm event.
2. minimize the maximum rate of overflow dis-
charge.
3. minimize the total mass of pollutants.
4. minimize the maximum rate of pollutant dis-
charge .
5. minimize the detrimental impact of untreated
overflows on the receiving water.
6. maximize the effective utilization of treat-
ment plant, interceptor sewer, trunk sewer, and stor-
age capacities.
7. minimize localized flooding from surcharged
sewers.
Objective 5, though highly desirable, is depend-
ent on the availability of accurate models for pre-
dicting wastewater quality and its impacts on re-
ceiving waters. Such models may not be available,
since water quality prediction is much more difficult
than quantity modeling and prediction. Objectives 3
and 4 are also dependent upon wastewater quality pre-
diction models. The City of Cleveland has reported
using Objective 3 for their control system. Utili-
zation of Objective 4 might be an indirect means of
satisfying 5, since it appears that the pollutant
loading rate from discharges is more critical for
receiving waters than the total mass of pollutants.
In the absence of adequate quality prediction
models, one must settle for Objectives 1 or 2, used
in conjunction with Objective 7. This latter objec-
tive is usually given a higher priority, due to the
high nuisance level and sanitation problems associated
with localized flooding and the fact that it bsitb
people ulh&ie. tk&y Li\)i. Sewer discharges leading to
overflows, on the other hand, tend to pass oat oft
Ai.gkt, out 0(j mind. It is obvious that any computer
control system must be designed to control the system
with regard to a proper tradeoff between overflow
minimization objectives and localized flooding mini-
mization objectives. Satisfaction of these objectives
will indirectly satisfy Objective 6.
Figure 1 presents a simple example as a means of
comparing Objectives 1 and 2. Suppose that application
755
-------
5
4
«
*
— 3
Q>
> n
O 2
I
0
Totol Overflows
= 0+5 + 1 =6
Total Squared Overflows
t-l t f+l
Discrete Time Periods
a) Results of Objective I
5
4
tn
I 3
Total Overflows
=2+3+2 = 7
Total Squared Overflows
!= 17
t-l t t+l
Discrete Time Periods
b) Results of Objective 2
Figure 1. Comparison of Objectives 1 and 2
of Objective 1 for optimal control of stormwater re-
sults in the overflow distribution shown in Figure
1(a), for some hypothetical real-time storm event.
For Objective 2, an indirect means of minimizing the
maximum overflow rate, or the total overflows during
any discrete time period, is to minimize the sum of
the ^nuojiid overflows. This might result in an over-
flow distribution as shown in Figure 1 (b), for the
same storm event. Even though total overflows resul-
ting from Objective 2 may be greater than those from
Objective 1, the pollution shock on receiving waters
may be less in the former case, where the maximum
overflow rate is less.
Notice that in the case of Objective 2 (Figure
l(b)) overflows are taken during period t-l, even
though there might be available storage capacity to
store these flows. This is allowed in the interest of
Smoothing out the distribution of overflows so that
impacts on the receiving waters are lessened.
Furthermore, multiplying overflows (or squared
overflows) at particular points in time and space by
We-igktotg (,0£.toti!> is an indirect way of considering
pollution impacts. For example, bypass points with
a history of overflows with higher pollutant concen-
trations could be assigned a higher weight than those
for other bypass points. In this way, overflows are
more heavily penalized at this location and therefore
given a greater priority for control. Likewise, due
to initial ^tu&ki.nQ effects, overflows occurring
early in the storm event could be weighted more
heavily than those occurring later. In addition, tidal
or river level fluctuations might necessitate the
adjustment of weighting factors. The utilization of
weighting factors is a way of expressing subjective
information in a quantitative manner, in the absence
of accurate quality prediction models. It essentially
is a means of setting up a priority scheme for
allowing overflows when there is no choice but to
allow them.
Objective 2, in a real-time context, could be
indirectly expressed as:
minimize
N
V
M
£
i=l t=m
where 0 (t) are the total predicted overflows, as a
result of some control policy, at bypass point i ,
during a discrete interval t ; u . are the weighting
factors on overflow; N is the total number of bypass
points; m is the current real-time interval since
the storm began at t=l; M is some future time inter-
val to which storm inflows are forecasted (m < M);
Q (t) are the predicted throughflows to treatment
and c is a positive coefficient which oted-cts through-
flows and discourages unnecessary storage.
Control Constraints
Having specified the control system objectives,
which must in some way be placed in quantitative
terms, it is then necessary to specify the constraints
under which the control system is to operate. These
can be listed as follows:
1. The interceptor, trunk sewers, and detention
storage devices have a limited capacity which, if ex-
ceeded, will result in localized flooding and un-
treated overflows.
2. The treatment plant(s) has (have) a maximum
capacity for treating wet weather flow.
3. The transfer of rainfall to runoff to sewer
flow operates under certain dynamic physical laws
that can be approximated by mathematical models. In
effect, these laws act as constraints on the control
system.
4. The remote data acquisition system will have
a limited capacity for retrieving and transferring
information, both in time and space.
5. The hardware and software associated with
the computer control system will have a limited capa-
bility.
6. The computer control system will have a re-
stricted amount of time, to render decisions in real-
time and properly respond to a rapidly progressing
storm event.
7. The system must operate under constraints of
possible human error and equipment malfunction and
breakdown.
The goal of the computer control system, then,
is to meet the specified objectives as closely as
possible, while operating under the above constraints.
The design of the computer control system is there-
fore based on analysis of tradeoffs between cost of
the system and its effectiveness in meeting the ob-
jectives under these constraints.
Off-Line vs. On-Line Control Development
The question that now arises is: how should
computer control logic be developed in order to meet
the above control objectives, subject to the con-
straints? There are two basic approaches to control
logic development: off-line and on-line. By off-line
development, we mean that the control policies are
synthesized independently of the real-time control
situation. That is, instead of programming the
756
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necessary mathematical models onto the real-time
computing machinery, they are programmed onto batch-
mode computing systems not interfaced with the actual
control system. Many optimizations are then performed
for an assumed range of probable storm events that
could occur, based on historical or synthetically
generated events. The resulting optimal strategies
are then stored as rule curves in the on-line computer
system for real-time control.
The advantage, of off-line optimization is that
sophisticated models of the sewer system and accurate
analysis techniques can be used in an off-line manner,
whereas it would be difficult to use them in an on-
line computing system with limited hardware and time
for making control decisions. The major disadvantage.
of off-line optimization is that its effectiveness is
based on how well the range of predetermined storm
events corresponds to what actually can occur in real-
time. Obviously, there is an infinite number of
possible events that can take place.
On-line development implies that the control
optimization is actually carried out in real-time on
the on-line computing system as a storm is passing
over the urban area. The obvious advantage is that
optimal controls can be developed that uniquely respond
to the event at hand, as well as the current state of
the sewer system in terms of flows and storage levels.
The disadvantage is that simplified models and analy-
sis techniques may be required because of hardware
and software limitations of the on-line computing
system (which might be a minicomputer, for example)
and the limited time available to render control
decisions.
Reactive vs. Adaptive Control Policies
Control policies resulting from off-line develop-
ment tend to be /ie.acJu.vQ. in nature. Other terms would
be toaaJL, bit point, or myopi-C control. That is,
these kinds of control policies are £&54 dependent on
anticipation or forecasting of storm inflows. They
simply react to the current flow situation. Some
forecasting may be necessary if there are several rule
curves programmed onto the computing system, and it
is desired to select the best one for the current
event, as well as modify it so some extent as the
storm progresses.
On-line optimization implies a gx.e.ateA dependence
on storm forecasting, as well as more extensive fore-
casting. The extreme would be an attempt to forecast
future storm inflow rates over short time increments.
Control policies based on on-line optimization might
be termed adaptive.. • Though it is possible to have
on-line optimization which is reactive (Brandstetter,
et.al.2) and off-line control development which results
in adaptive policies,^ there is generally less emphasis
on comprehensive forecasting in off-line development.
It may be limited to forecasting only total depth and
duration of the storm.
Adaptive control is based on the sequential and
systematic updating of storm inflow forecasts as new
information on the ensuing storm is gathered from an
automated data acquisition system. Control policies
can then be appropriately modified, based on the up-
dated forecasts. In effect, then, a forecasting
model is designed to be a te.aAnln.g mode/ that can
efficiently incorporate new information into its
structure as it becomes available, so that succeeding
forecasts ideally become better as real-time infor-
mation on the storm event in progress is obtained.
The ultimate goal is what might be termed i>to-
adaptive. c.on&wl. That is, instead of totally
basing the evaluation of control policies on a fore-
casted storm event, it is recognized that there is con-
siderable u.nc.eAta>wty (although a more appropriate
term is itlbk} associated with that forecast, and this
uncertainty tends to increase as we attempt to fore-
cast further into the future. This approach is more
realistic since if an optimal control policy is based
on the certain occurrence of a sequence of future in-
flows, and it turns out that the actual inflows
deviated considerably from the forecast, then the
optimality of the control is in question. It would
be better if a band oft an.c.eJvtaAntij (Figure 2) was
associated with the forecast and a .A-tocAoi^c control
policy development carried out which considered cer-
tain assumed probabilities of deviation from the most
likely or expected levels of the forecast.
Bond of Uncertainty
Inflows
Figure 2.
Future Time
Inflow Forecasting Under
Uncertainty (or Risk)
Under stochastic adaptive control in real-time,
Equation 1 might be written as:
minimize E
[N M
E E K
i=l t=m 1
[o1^]2
(2)
where E denotes e.x.pe.cte.d \iaLuZ.
On-Line Modeling Requirements
Rainfall-Runoff and Routing Models
Off-line control development can be based on
either the simplest and most intuitive of analyses,
or sophisticated studies involving mathematical models
of system response. Given a set of historical or syn-
thetic storm events, these rainfall data are passed
through a tLOA-n^oJUL-tiuno^ model, which predicts direct
inflows to the sewer transport system. A 4eweA Muting
modeJt, is then required for predicting overflows.
Rainfall-runoff models range in sophistication
from simple unit hydrographs to kinematic wave approa-
ches (as in SWMM). Likewise, sewer routing models
range from simple time-lag approaches to solution of
the full unsteady flow equations (as in the San Fran-
cisco Stormwater Model (SFSM)9).
Again, off-line control development offers greater
latitude in the degree of model sophistication, but
results in more reactive type control. On-line control
development, on the other hand, requires more simpli-
fied models, but can more uniquely respond to a
current event in an adaptive mode.
757
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The major limitation for on-line control is in the
area of sewer transport routing. It is not yet feasi-
ble to solve the St. Venant equations on-line in real-
time. Seattle^ nas found that the kinematic wave model
developed for SWMM, modified to include backwater
effects using simple continuity relationships, per-
formed satisfactorily in real-time.
Forecasting Model
In addition to rainfall -runoff and sewer routing
models, some kind of forecasting model is required for
on-line control development. The more advanced models
currently available attempt to describe the activity
of storm >wJiyi dUJLLk , which can be defined as local
areas of convective circulation resulting in more in-
tensive rain. Rain cells in turn operate within larger
areas of less intense rain called band&. A large
collection of investigators have contributed to an
understanding of the life cycle of cells within bands.
An extensive bibliography on this subject can be found
in TrottalO. The overall result of this rain
cell research is that there appear to be definable
statistical properties associated with rain cell acti-
vity. Since these models were primarily developed for
simulation studies, there is some question as to their
adaptability to real-time forecasting. The models
tend to be large and time-consuming.
As an alternative to these comprehensive simula-
tion models, certain techniques originating from elec-
trical engineering may be applicable to rainfall fore-
casting. The two most important general forecasting
approaches are (i) the extended Kalman filter, and
(ii) the so-called autoregressive moving-average
transfer function models. Graupe^ has concluded that
the latter models are preferable in terms of compu-
tational speed and simplicity, especially when certain
aspects of the persistence or degree of autocorrelation
of the inputs are not well understood, as is the case
with stormwater forecasting.
Figure 3 gives a simple illustration of this
approach. The regression relations are of the form
(with the moving average terms deleted) :
a R(t-p)
J'J(i)
[bn.Rj(t)
(3)
where t is the current real-time interval; R1(t+l)
is the forecasted inflow; J(i) is the set of all
pertinent locations j adjacent to i ; a_ and b_
are parameters determined from historical data and the
current storm event. These parameters can be easily
updated in real-time, as shown by Trotta^1-1. Though
stationarity is assumed for the above model, nonsta-
tionarity can be considered by using a cU.^{,eAe.nc^Lng
operator. Equation 3 can be used sequentially to
generate forecasts for any lead time.
In some cases it may be advantageous to forecast
direct storm runoff rather than rainfall input. This
is because the rainfall-runoff process tends to per-
form a smoothing and integrating action on rainfall
input. These integrated data might be more conducive
to analysis for forecasting purposes than rainfall
data.
Correlated
Noise
(Random
Model
Error)
Historical Inflows
At Location x
Historical Inflows
At Adjacent
Locations
Information from
Other Sources
(e.g., Meteorologic
and Radar Data)
Linear
Regression
Relations
Correlating
Input and Output
(Parameters
Updatable in
Reol-Time)
Forecasted Inflows
At Location x
INPUT
Figure 3.
MODEL
OUTPUT
Illustration of Autoregressive
Moving-Average Transfer Function
Model
Optimizing Model
A quantified control objective and mathematical
specification of all pertinent constraints on system
response (including specification of some kind of
sewer routing model), in conjunction with a syste-
matic optimization algorithm for finding the best or
near-best controls, is called an opt-Lm-iz-Lng model..
The on-line control environment places restric-
tions on the degree of sophistication of the opti-
mization algorithm, which in turn restricts the level
of the mathematical models used (particularly the
sewer routing model). The most popular optimization
algorithm is the simplex method of lA.ne.afL ptiogna.mming,
which has been applied by Bradford1 to combined sewer
control. Obviously, the use of linear programming
constrains all sewer routing to be linear or piece-
wise linear. Nonlinear routing can be used with dy-
namLc. pftognamming, but other computational difficul-
ties arise. 1 Application of the ma.)wnm psu.nc.-i.pte.
and Sia.gu£.eutoSi tke.osiy3 is also a possibility, but
routing also is a problem here.
Introducing stochastics further complicates the
optimizing model. In addition, the city-wide control
problem is large-scale and unwieldy, with many control
variables. Labadie, et.al.6 have proposed a hierar-
chical or multilevel optimization approach which can
effectively deal with the large-scale problem.
Development of efficient, yet sufficiently accur-
ate optimizing models for on-line use, remains a
challenging area for future research.
Research Results and Conclusions
Intensive research on automatic control of com-
bined sewer systems has been carried out at Colorado
State University for the past five years. Work has
primarily concentrated on the San Francisco Master
Plan for Wastewater Management as a case study.
The most recent research results are described
in Trotta^. The hierarchical approach to the control
optimization is applied to the San Francisco system,
where the urban area is divided into a number of
758
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subbasins which are essentially independent except for
their contributions of storm runoff to a common inter-
ceptor and treatment facility. The controls for each
subbasin are derived separately by the use of a sto-
chastic dynamic programming formulation. Each subbasin
problem, however, is constrained by an upper limit on
its releases to the interceptor, which is determined
by a master control problem. This master control pro-
blem, which ties together the separate subbasin pro-
blems, decides how interceptor and treatment capacity
should be allocated to the subbasins. It uses a modi-
fied cyclic coordinate search algorithm. The inflows
are forecasted using an autoregressive transfer func-
tion model which can be updated in real-time to respond
to new information on the storm event.
The control algorithm was tested for selected
design storms which were based upon the historic
record. The tests were conducted on a batch-mode com-
puter, but a hierarchy of minicomputers appears to be
a more efficient approach to effecting the multilevel
optimizations in real-time.
The results of this work indicate that the large-
scale algorithm can converge within the time frame
anticipated for real-time control. Controls based
upon the stochastic models were superior to those
based upon forecasts which were assumed deterministic.
The adaptive aspects of the model appear to be justi-
fied by the superior distribution of the overflows
which resulted when overflows were unavoidable. That
is, the maximum rate of overflow was lowest for this
model. This result is notable in that the forecasting
model was deliberately designed to be relatively in-
accurate. Total overflows were, however, minimized
to a higher degree by a reactive model which was also
tested, though the maximum overflow rate was higher.
The overall conclusion appears to be that even though
the adaptive model with risk is highly dependent on
the accuracy of the forecasting model, at least some
stormflow anticipation will reduce maximum overflow
rates. Thus, reactive policies better meet Objective
1, as long as weighting factors are not used, and sto-
chastic adaptive policies are superior for Objective 2.
As illustrated in Figure 4, if a storm event is
definitely considered to be non-overflow producing,
then simple rule curves or reactive policies are ade-
quate. If a storm is definitely overflow producing,
rule curves tend to produce higher rates of overflow
than stochastic adaptive policies. There is, of
course, a gray area in between, the size of which
depends on the accuracy of the forecasting model. The
safest procedure in these gray areas is to use reactive
policies, since if the forecasting model is relatively
inaccurate, unnecessary overflows may be taken.
Initial cost estimates presented in Grigg, et.al.5
show that computer hardware would cost around $200,000
for implementing the proposed city-wide hierarchical
control strategy for San Francisco. Software, develop-
ment costs would be about the same, for a total of
$400,000. This is a relatively insignificant amount,
in comparison with total project costs that could
approach $1 billion.
Acknowledgments
The financial support of the National Science
Foundation (Research Applied to National Needs) and
the Office of Water Research and Technology, Department
of Interior, are gratefully acknowledged. Much of the
data which made the research possible were furnished
by the Department of Public Works, City and County of
San Francisco. In addition, the technical advice and
Definitely on
Overflow — Producing Storm
Use Stochastic Adoptive
Control Policies
Poor
Forecasting
Model
Definitely Not an
Overflow — Producing Storm
Use Reactive Control Policies
Figure 4. Effect of Forecasting Model Accuracy
on Control Policy Selection
assistance provided by Mr. Murray B. McPherson, Direc-
tor, ASCE Urban Water Resources Research Program, was
instrumental in stimulating the research.
References
1. Bradford, B.H., "Real-Time Control of a Large-Scale
Combined Sewer System," Ph.D. Dissertation, Depart-
ment of Civil Engineering, Colorado State Univer-
sity, August 1974.
2. Brandstetter, A., R.L. Engel, and D.B. Cearlock,
"A Mathematical Model for Optimum Design and Con-
trol of Metropolitan Wastewater Management Sys-
tems," Water Resources Bulletin, Vol. 9, No. 6,
pp. 1188-1200, 1973.
3. Chan, M.L., "Optimal Real-Time Control of Urban
Stormwater Drainage," TR 87, Water Resources and
Marine Sciences Center, Cornell University, 1974.
4. Graupe, D., Identification of Systems, Van Nos-
trand Reinhold Company, New York, 1972.
5. Grigg, N.S., J.W. Labadie, G.R. Trimble, Jr., and
D.A. Wismer, "Computerized City-Wide Control of
Urban Stormwater," to appear as Tech. Memorandum
of the ASCE Urban Water Resources Research Program.
6. Labadie, J.W., N.S. Grigg, and B.H. Bradford,
"Automatic Control of Large-Scale Combined Sewer
Systems," Jour, of the Environmental Engineering
Division, ASCE, Vol. 101, No. EE1, pp. 27-39,
February 1975.
7. Labadie, J.W., N.S, Grigg and P.O. Trotta, "Mini-
mization of Combined Sewer Overflows by Large-
Scale Mathematical Programming," Computers and
Operations Research, Vol. 1, pp. 421-435, 1974.
8. Leiser, C.P., "Computer Management of a Combined
Sewer System," USEPA Report, July 1974.
9. San Francisco Department of Public Works, San Fran-
cisco Stormwater Model: User's Manual and Program
Documentation, prepared by D.F. Kibler, et.al.,
Water Resources Engineers, Inc., Walnut Creek, CA.
10. Trotta, P.O., "Adaptive On-Line Control of Com-
bined Sewer Systems," Ph.D. Dissertation, Dept. of
Civil Engineering, Colorado State University,
December 1975.
759
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MATHEMATICAL MODELS FOR CALCULATING
PERFORMANCE AND COST OF WASTEWATER TREATMENT SYSTEMS
Richard G. Eilers
Systems and Economic Analysis Section
Wastewater Research Division
Municipal Environmental Research Laboratory
U.S. Environmental Protection Agency
Cincinnati, Ohio
ABSTRACT
The Systems and Economic Analysis Section of the
Wastewater Research Division of EPA in Cincinnati,
Ohio is concerned with finding quantitative expres-
sions for calculating the performance and cost of
wastewater treatment processes as a function of the
nature of the wastewater to be treated and the design
variables associated with the individual unit pro-
cesses. These models are intended primarily to
characterize the treatment of municipal sewage.
Since the procedure for solving all of the quantita-
tive equations is usually too laborious or complex
to be accomplished by hand calculation, various
FORTRAN computer programs have been developed to
perform the task.
BACKGROUND
Mathematical models for wastewater treatment processes
are required to express the performance of the pro-
cesses over the full range of operational modes and
design criteria. These models can be steady state,
quasi-steady state, or time-dependent. By quasi-
steady state it is meant that a steady state model is
used to simulate a process that is, in reality, not
necessarily steady state. Most sewage treatment
systems are not steady state. The time-dependent or
dynamic models are of interest when the quality of the
effluent stream from a process is important as a func-
tion of time, or when the effectiveness of various
kinds of control schemes on a process is being studied.
For a model to be fully effective for design and plan-
ning purposes, it must be based on valid scientific
principles, flexible enough to simulate experimental
data from a full-scale process (not merely pilot-scale
data), and represent the performance and cost of the
process with adequate precision.
The collection of valid, complete experimental data
followed by adjustment of the model parameters to
make the computed results agree with experimental
results within an acceptable tolerance is also an
important phase of model development.
Packaging mathematical models as computer programs
not only provides ease and accuracy of calculation,
but also has the additional advantage of convenience
of distribution to interested individuals, such as
consulting engineers and urban planners, in a
readily usable form.
MODELS DEVELOPED
Over the past eight years, a number of computer models
have been developed in-house by the Systems and
Economic Analysis Section and through contracting
activity with outside sources. Each program deals
in some way with the cost and/or performance of waste-
water treatment systems. All of the computer pro-
grams were written in FORTRAN and designed to run on
a 16K IBM 1130 machine, and supporting documentation
has been prepared for each. Table 1 gives a listing
of the models which were produced in-house, and
Table 2 shows the models which resulted from extra-
mural sources. A brief description of the most
significant of these computer programs will follow.
Table 1. Computer programs produced by the Systems
and Economic Analysis Section.
1. Preliminary Design and Simulation of Conventional
Wastewater Renovation Using the Digital Computer
(1968).
2. Executive Digital Computer Program for Preliminary
Design of Wastewater Treatment Systems (1968).
3. A Mathematical Model for a Trickling Filter (1969).
4. Preliminary Design of Surface Filtration Units-
Microscreening (1969) .
5. A Generalized Computer Model for Steady State
Performance of the Activated Sludge Process (1969).
6. Fill and Draw Activated Sludge Model (1969).
7. Mathematical Simulation of Ammonia Stripping
Towers for Wastewater Treatment (1970).
8. Mathematical Simulation of Waste Stabilization
Ponds (1970).
9. Simulation of the Time-Dependent Performance of
the Activated Sludge Process Using the Digital
Computer (1970).
10. Economics of Consolidating Sewage Treatment
Plants by Means of Interceptor Sewers and
Force Mains (1971) .
11. Per Capita Cost Estimating Program for Waste-
water Treatment (1971) .
12. Wastewater Treatment Plant Cost Estimating Pro-
gram (1971).
13. Design of Concrete and Steel Storage Tanks for
Wastewater Treatment (1971).
14. Water Supply Cost Estimating Program (1972).
15. Cost of Phosphorus Removal in Conventional
Wastewater Treatment Plants by Means of
Chemical Addition (1972).
16. A Mathematical Model for Aerobic Digestion (1973).
17 Design and Simulation of Equalization Basins
(1973).
18. Mathematical Model for Post Aeration (1973).
19. Optimum Treatment Plant Cost Estimating Program
(1974) .
20. Waste Stabilization Ponds Cost Estimating Program
(1974).
760
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21. Granular Carbon Adsorption Cost Estimating Program
(1974).
22. Control Schemes for the Activated Sludge Process
(1974) .
23. Cost Estimating Program for Disinfection by Ozona-
tion (1974) .
24. Nitrification/Denitrification Cost Estimating Pro-
gram (1975) .
25. Cost Estimating Program for Alternate Oxygen
Supply Systems (1975) .
26. Cost Estimating Program for Land Application
Systems (1975).
27. Combustion Model for Energy Recovery from Sludge
Incineration (1975) .
28. Energy Consumption by Wastewater Treatment Plants
(1975).
29. Stream Model for Calculating BOD and DO Profiles
(1976).
Table 2. Computer programs produced as a result of
contract activity.
1. Ammonia Stripping Mathematical Model for Waste-
water Treatment (1968).
2. Mathematical Model for Wastewater Treatment by
Ion Exchange (1969).
3. Mathematical Model of the Electrodialysis
Process (1969).
4. Mathematical Model of Tertiary Treatment by Lime
Addition (1969).
5. Mathematical Model of Sewage Fluidized Bed Incine-
rator Capabilities and Costs (1969).
6. Reverse Osmosis Renovation of Municipal Waste-
water (1969) .
7. Methodology for Economic Evaluation of Municipal
Water Supply/Wastewater Disposal Including Con-
siderations of Seawater Distillation and Waste-
water Renovation (1970).
8. Mathematical Model of Recalcination of Lime
Sludge with Fluidized Bed Reactors (1970).
9. Computerized Design and Cost Estimation for
Multiple Hearth Incinerators (1971).
10. Cost program for Desalination Process (1971).
EXECUTIVE PROGRAM
The major product of all this effort has been the
"Executive Digital Computer Program for Preliminary
Design of Wastewater Treatment Systems." It was
realized that a tool was needed which would allow
the process designer to select a group of unit pro-
cesses, arrange them into a desired configuration,
and then calculate the performance and cost of the
system as a whole. The Executive Program meets
this need by simulating groups of conventional
and advanced wastewater treatment unit processes
arranged in any logical manner. Each unit pro-
cess is handled as a separate subroutine which
makes it possible to add additional process models
to the program as they are developed. There are
presently 24 process subroutines in the program, and
these are listed in Table 3. Additional subroutines
are planned to be included in the future, and a
tentative list is shown in Table 4.
The first step in using the Executive Program is to
draw the desired system diagram showing the unit pro-
cesses to be used and the connecting and recycle
streams. All streams and processes are then numbered
by the program user. Figure 1 depicts a typical,
conventional activated sludge treatment system with
incineration for sludge disposal. Volume and char-
acteristics of the influent stream to the system and
design variables for each process used must be
supplied as program input. By an iterative technique,
each process subroutine is called in the proper
sequence and all stream values are recomputed until
the mass balances within the treatment system are
satisfied. Performance, cost, and energy requirements
for each unit process and the system as a whole are
included in the final printout.
Table 3. Unit process models contained in the
Executive Program.
1. Preliminary Treatment
2. Primary Sedimentation
3. Activated Sludge-Final Settler
4. Stream Mixer
5. Stream Splitter
6. Single Stage Anaerobic Digestion
7. Vacuum Filtration
8. Gravity Thickening
9. Elutriation
10. Sand Drying Beds
11. Trickling Filter-Final Settler
12. Chlorination-Dechlorination
13. Flotation Thickening
14. Multiple Hearth Incineration
15. Raw Wastewater Pumping
16. Sludge Holding Tanks
17. Centrifugation
18. Aerobic Digestion
19. Post Aeration
20. Equalization
21. Second Stage Anaerobic Digestion
22. Land Disposal of Liquid Sludge
23. Lime Addition to Sludge
24. Rotating Biological Contactor Final Settler
Table 4. Unit process models to be added to the
Executive Program
1. Ammonia Stripping of Secondary Effluent
2. Granular Carbon Adsorption
3. Ion Exchange
4. Electrodialysis
5. Reverse Osmosis
6. Bar Screening
7. Comminution
8. Grit Removal
9. Flow Measurement
10. Waste Stabilization Ponds
11. Microscreening
12. Rough Filtration
13. Multi-Media Filtration
14. Ozonation
15. Nitrification
16. Denitrification
Detailed cost data applicable for preliminary design
estimates are generated by the Executive Program. Con-
struction cost (in dollars), amortization cost, opera-
tion and maintenance cost, and total treatment cost
(all in cents per 1,000 gallons of wastewater treated)
are calculated individually for every unit process,
and a sum total of each cost is given for the entire
system. Capital cost is also computed by adding onto
construction expenses the costs of yardwork, land,
engineering, administration, and interest during con-
struction. All of the cost information can be updated
or backdated with respect to time by means of cost
indices that are supplied as input to the program.
761
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The Executive Program cannot be used for extremely
detailed design purposes. However, it can be a
valuible preliminary design tool for the consulting
engineer or planner. The performance of existing
or proposed wastewater treatment plants can be
simulated along with providing cost estimates for
building and operating these plants. It is also
possible to optimize a particular treatment system
by varying design parameters and noting the effect
on performance and cost. Cost-effectiveness studies
can be made by comparing alternate treatment systems.
Initial studies along these lines are becoming of
increasing importance because of the soaring costs
of plant construction that are now being experienced.
A recent application of the Executive Program was
an investigation of the potential economic advant-
ages associated with 261 different methods for
treating and disposing of sewage sludge. Sludge
production and the costs of constructing and operating
the various systems were computed. Each system was
either primary or activated sludge treatment followed
by some combination of the following 12 sludge hand-
ling processes--lime stabilization, gravity thicken-
ing, air flotation thickening, single-stage anaerobic
digestion, two-stage anaerobic digestion, aerobic
digestion, elutriation, vacuum filtration, centri-
fugation, sludge drying beds, multiple hearth incine-
ration, and land disposal of liquid sludge. The
outcome of the study showed that the cost (in January
1974 dollars per ton of dry solids processed) for
treating and disposing of sewage sludge ranges from
about $30 per ton for anaerobic digestion followed
by dewatering on sand drying beds to over $100 per
ton when the sludge is dewatered by vacuum filtra-
tion or centrifugation and then incinerated. Treat-
ment and disposal of sludges produced in municipal
wastewater treatment plants were shown to account
for as much as 60% or as little as 20% of the total
cost of treatment. Therefore, careful consideration
should be given to selecting the sludge handling
method which meets the site-specific constraints at
a minimum cost. The Executive Program, which is
capable of examining the cost and performance of a
wide variety of alternative sludge handling schemes,
can be used as a management tool to narrow the range
of options when design conditions are known.
The Executive Program has been around for several
years now, beginning with its original development
in 1968. The model has been expanded, modified,
and corrected many times since then, and it will
continue to change in the future. The goal will
remain the same: to provide the best possible
characterization of the cost and performance of
municipal wastewater treatment systems.
MODELS FOR THE ACTIVATED SLUDGE PROCESS
Considerable effort has been expended in develop-
ing more accurate models for the activated sludge-
final settling process. Previous models that were
produced by various researchers covered a wide
range of forms corresponding to differing sets of
assumptions about the hydraulic and biological
relationships believed to be significant in the
process. Because of the problems of measurement
and the difficulty of fitting data to complex
models, simplified models were often used which
either omit or make some plausible assumption
concerning the role cf various factors in the
process.
In all, four different digital computer models for
the activated sludge process have been developed.
The first, CSSAS (Continuous Steady State Activated
Sludge), is a steady state model which is flexible
enough to simulate the performance of any configura-
tion proposed (complete mix, plug flow, multiple
aeration tanks, step aeration, step return flow,
contact stabilization, extended aeration, etc).
Two classes of microorganisms are considered:
heterotrophs which use 5-day BOD as substrate and
Nitrosomonas which use ammonia nitrogen as sub-
strate to produce new cells. The model allows the
maximum rate constant for synthesis to vary with
process loading. The second program, FADAS (Fill
and Draw Activated Sludge), attempts to simulate
the biological activity in a fill and draw bench
experiment where activated sludge is mixed with
substrate in any proportion. The third program,
TDAS (Time-Dependent Activated Sludge), simulates
the dynamic behavior of the biological aspects of
the activated sludge process. The model numerically
integrates the mass balance and biological rate
equations which are assumed to represent the
process. Three classes of microorganisms are
considered: heterotrophs, Nitrosomonas, and
Nitrobacter. This model can also be used to
investigate the potential advantages associated
with the following control schemes: dissolved
oxygen control, sludge wasting control, and
sludge inventory control. The fourth program,
CMA.S (Completely Mixed Activated Sludge), is used
to simulate the performance of conventional and
modified activated sludge, separate nitrification,
or separate denitrification. With an adjustment
of the process parameters, it can also be used
to characterize the pure oxygen activated sludge
system.
SPECIALIZED COST ESTIMATING PROGRAMS
When making preliminary cost estimates for building
and operating certain wastewater treatment systems,
it is often necessary to have more detailed cost
data. For this reason, special economic models were
developed for several particular applications.
A waste stabilization pond cost estimating program
computes the costs of stabilization ponds and aerated
lagoons along with influent pumping, surface mechani-
cal aerators, embankment protection, and chlorination
facilities. The granular carbon adsorption cost
estimating program calculates the costs of influent
pumping, carbon contactors, regeneration facilities,
and initial carbon required. The nitrification/
denitrification cost estimating program predicts
the costs of dispersed floe systems for the removal
of nitrogen from wastewater. A cost estimating pro-
gram for wastewater treatment by direct land appli-
cation computes the costs of preapplication treatment,
transmission, storage, field preparation, distribution,
renovated water recovery, and monitoring facilities.
All of these economic models factor in the costs of
yarkwork, contingencies, engineering, land, adminis-
tration, and interest during construction.
CONCLUSION
The primary goal of this modeling effort is to
improve the rule-of-thumb or hand calculation
method of process design which is still commonly
used today. The principal deterrents to better
process design are usually the manual effort
required in computing the cost and performance
of alternative designs and the labor required to
accumulate and correlate the large amount of
experimental process design performance data
which is often available. The mathematical com-
puter model can minimize the computational work
required for examining alternative designs, and,
762
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if the model has been correctly developed, it
will reflect the best experimental and scientific
information obtainable. Thus, the process designer
has within his grasp the tools for quantitatively
selecting the most cost-effective system of processes
to achieve any desired wastewater treatment goal. The
Systems and Economic Analysis Section within EPA is
very much interested in promoting the use of compute-
rized design techniques in order to achieve better
treatment at a minimum cost.
RWP raw wastewater pumping
PREL - preliminary treatment
MIX stream mixer
PRSET primary sedimentation
AERFS activated sludge/final settler
SPLIT stream splitter
CHLOR chlorination/dechlorination
THICK gravity thickening
DIG single stage anaerobic digestion
DIG2 second stage anaerobic digestion
SHT sludge holding tanks
VACF vacuum filtration
MHINC multiple hearth incineration
Figure 1. System diagram for a conventional activated sludge treatment plant.
763
-------
THE ECOLOGICAL.MODEL AS APPLIED TO LAKE WASHINGTON
Carl W. Chen
Tetra Tech, Inc.
Lafayette, California
Donald J. Smith
Tetra Tech, Inc.
Lafayette, California
INTRODUCTION
A lake is a giant reactor where many physical, chemi-
cal and biological processes take place. Heating and
cooling at the water surface due to solar insolation,
conductance, back radiation and evaporation generate
the thermal stratification and seasonal overturn
phenomenon. Thermal stratification separates the lake
water into layers with different physical, chemical,
and biological characteristics. It influences where
the tributary inflows are deposited and where outflows
are withdrawn.
Tributary inflows bring in plant nutrients (carbon,
nitrogen and phosphorus) either in the dissolved form
or as particulate organic matter. Bacteria or fungi
decompose organic matter to liberate nutrients and
consume oxygen in the process. With the help of solar
energy, phytoplankton reuse the nutrients to synthe-
size new organic materials and produce oxygen. Under
stratified conditions, phytoplankton activity predomi-
nates in the epilimnion (above the thermocline) and
bacterial activity predominates in the hypolimnion,
creating an imbalance for oxygen resources. At the
surface, the water may be saturated with oxygen, but
the hypolimnion water may become anerobic, killing
fish and other organisms residing near the bottom.
Biomass generated by bacteria and phytoplankton serve
as food for zooplankton, benthic animal and fish.
Carbon, nitrogen and phosphorus contained in the bio-
mass are conserved in each succession of organisms.
Upon death, they become organic materials to be worked
at by bacteria.
This paper describes an ecological model that simu-
lates the physical, chemical and biological processes
of the complex lake ecosystem. The model represents
the state of ecosystem by a set of water quality para-
meters including biomass of various organisms. The
model calculates throughout the annual cycle the
vertical profiles of temperature, dissolved oxygen,
biochemical oxygen demand (BOD), pH, plant nutrients
(C02, NH , N02, NO , PO,), particulate organic matter,
organic sediment, algae, zooplankton, benthic animals,
and fishes.
The model provides a. scientific tool for engineers to
evaluate effectiveness of various management alterna-
tives . It also serves for the multidisciplinary in-
tegration of bits and pieces of information that has
been accumulated in various branches of sciences, i.e.,
meteorology, hydrology, hydrodynamics, limnology, eco-
logy, chemistry, biology, and sanitary engineering.
Lake Washington data, collected by Dr. Edmondson of
the University of Washington, were used for the model
calibration and sensitivity analyses.
LAKE WASINGTON
f\ 9
Lake Washington has a surface area of 110 x 10 m and
Figure 1 shows the location of Lake Washington and itSi
tributaries including waste water discharges and storm
water overflows. As shown, the Sammamish River enters
the lake in the north and the Cedar River in the south.
Numerous small creeks empty into the lake for the local
drainage. The outflow is regulated by the ship canal
connecting the lake and Puget Sound. Table 1 sum-
marizes the inflow and outflow hydrology of Lake
Washington.
9 3
a volume of 3.6 x 10 m .
65 m.
It has a maximum depth of
Figure 1. Lake Washington and Its Tributaries
Table 2 presents the mean monthly weather conditions
for the years 1966 and 1967 as observed at the Tacoma
Airport. The weather conditions are assumed the same
as those experienced by the lake.
In 1941, the lake received one discharge of secondary
effluent. By 1963, the sewage discharge reached about
0.53-0.75 CMS (cubic meter per second) or 12-17 MGD
(million gallons per day), exclusive of combined storm
water overflows. In 1963, sewage diversion began and
by February, 1968 all sewage was exported.
764
-------
Table 1. Inflow and Outflow Hydrology
SirumuTmh Ccdir Local Lil
Month Rivet River dninage Ciij
crurjrtc include Sh
inuary 20
•rch V 1
pril 1
»y
une
uly
ugust
September
October
November 1
3eccmber 1
6
[
)
S
S
S
0
3.6 85 0
3.0 7.0 0.
S 2 5.6 0.
».0 3 4 0.
0 0 2.3 0.
0.0 1 S 0.
0.0 1.3 0
8.S 1 S 0.
5.0 20 0.
S.O 4.5 0.
S.S 70 0
5
S
2
0
0 C
•
5
S C
11 0.08 0.01
11 0 OS 0.01
10 0 08 0.01
C9 0 08 0.01
07 007 001
.09 O.OS 0.01
09 010 0.01
.10 010 001
.11 010 OOt
.1 0.11 O.Ot
rogd.
2,0
rt.O
S.O
S.O
0.0
70
5.0
7.0
S.O
0.0
0.0
charge* include San Point
and Kirkland. the Dcllevue dii-
INFLOWS
rwotK, and Eul Mercer, and the Bryn Mawr discharge* include Boeing
Table 2. Weather Conditions at Tacoma Airport
Cloud Sharlv,nve'
ingwnve* Dry bulb Wet bulk
January
February
Mirch
April
May
June
July
Auguit
September
October
November
December
1015
1017
1016
1020
1018
1017
1016
1018
1018
1019
1015
1014
92
HO
77
67
60
76
60
52
61
77
86
9+
0.009
0.020
0.034
0.045
O.OS2
0.055
0065
0.055
0042
0.020
O.OU
0.008
0.06S
0.06S
0.065
0.068
0070
0.075
ooao
0.078
0.075
0.070
0.068
0.065
48
6.3
7.5
9.5
1.0
5 0
80
8.0
5.0
2.0
8.5
54
2
2
2.6
S.O
6,6
9.2
11. 4
11.8
12.2
7.8
52
4.6
.6
.5
.5
0
0
8
.S
.4
.3
.8
.0
• Computed from longitude 47.36N, latitude 122 2W, sun angle!, and cloud coven for 1966-67.
The secondary effluent contained 4-12 mg/1 of phos-
phorus, 8-20 mg/1 of nitrogen, and 5-25 mg/1 of BOD.
In 1963, sewage contributed about 84% of the total
phosphorus and 40% of the total nitrogen input to the
lake. The total annual phosphorus and nitrogen inputs
were estimated at 120,000 kg and 220,000 kg respec-
tively.
According to Edmondson's data, the lake water is well
mixed horizontally. A set of historical water quality
data have been furnished by Edmondson for this study.
ECOLOGICAL MODEL
The concepts of the ecological model have been pre-
sented previously by Chen (1). A detailed description
of modeling approaches, mathematical formulation and
solution techniques can be found elsewhere (2).
Basically, the physical geometry of the lake is repre-
sented by stacked layers of water. Layers are added
or deleted with the rise or fall of the water surface.
The cross sectional area, volume, width and side slope
of each layer are input items.
Water quality parameters are defined for each layer,
and are expressed in the appropriate unit. The object
of the model is to calculate the parameter values for
each layer as a function of time.
To facilitate the computation, differential equations
are developed to describe the changing rate of mass
concentration or heat content as a function of such
physical processes as 1) deposition of tributary in-
flow; 2) withdrawal of outflow; 3) advection between
layers; 4) diffusion between layers; 5) sedimentation,
if any, from the upper layer to the lower layer; 6)
reaeration of the surface (CO and 0.); and 7) solar
insolation near the surface.
Deposition of tributaries and the concomitant advection
are idealized by Figure 2 which shows the sinking of
the inflow to an appropriate layer with approximately
the same density.
C
*i
^
i \
" \
OUTKLDWV.
NX
s,, x
1
•^
/
/
/
/
Figure 2. Inflows, Outflows, and Concomitant Advection
In addition, the mass concentration of quality consti-
tuents can be modified by the biological processes of
1) the oxidation of ammonia, nitrite, BOD, and detri-
tus; 2) photosynthetic oxygenation, nutrient uptake
and release of algae; and 3) the growth, mortality,
and respiration of zooplankton, fish and benthic ani-
mals. The biological processes are usually represen-
ted by the product function of a temperature dependent
coefficient and the mass concentration of the reacting
constituents. For the biological parameters, the
growth rate is expressed by a hyperbolic function of
the substrate concentration.
Resulting differential equations are typically of the
form
dz '
dt
where: V
C
t
Q
water volume
mass concentration or water
time
advective flows
temperature
-:— = diffusion between layers
dz
S
various quality constituents, sources,
sinks, and chemical, physical and biologi-
cal reactions within each layer
There are as many equations as there are quality con-
stituents and physical layers modeled. Numerical solu-
tions are provided by the computer program which calcu-
lates C's from an initial time (t ) to a short incre-
(t = At),
(t )
in a recursive manner. Time
ment of time
step of computation can be as long as a day.
The output contains the vertical distribution of
temperature, dissolved oxygen, BOD, alkalinity, pH,
CO , NH , NO , PO, , coliform, algae (2 groups), zoo-
765
-------
plankton, detritus, IDS, organic sediment and benthic
animals. Fish productivity, evaporation loss, and
formation are calculated for the surface on a per unit
area basis.
SIMULATION RESULTS
The model was applied to simulate 1) the pre-diversion
condition of sewage from Lake Washington; 2) the recov-
ery of the lake after sewage diversion; 3) the sensi-
tivity analyses.
Pre-diversion Case
Figure 3 shows the observed and computed temperature
profiles throughout the annual cycle. The comparison
is good considering that the mean weather conditions
have been used as the model input.
TEMPERATURE, °C
y 9 10 2
10-
20-
30-
40-
50-
»
0 0 1
i
Computed
JAN
-
-
-
_
)
>
,
0 2
00 10 20 0 10 20
FEB
_ ,
- (
- c
IV 1
0
MAR
-
:
-
_
i i
APR
V
ir 10--
UJ
ti 20--
l" 30--
t
u 40-]- c
5CM- d
I
MAY
JUN
JUL
AUG
V
10-
20-
30^
40-
50^
— <
- <
/
'
SEP
-
-
- c
- a
- 0
/'
OCT
-
-
-
-
_
1
NOV
-
-
-
-
1
DEC
Figure 3. Calculated and Observed Temperature Prof iles
Figure 4 plots the concentration profiles of dissolved
phosphorus as observed in the field and computed by
the model. Upon the onset of thermal stratification,
the dissolved phosphorus at the surface is seen to be
consumed by algae, creating a reversed concentration
profile.
Other quality profiles that have been plotted to illu-
strate the reasonableness of the model include dissol-
ved oxygen (DO), nitrate, and ammonia.
Lake Recovery
The model was set up to simulate the lake recovery
after sewage diversion. It was run for a time period
of three years. Sewage input was imposed during the
first year and excluded for the last two years. All
other boundary conditions remained the same.
DISSOLVED, P04-Plxug/l
r? 0 20 40 60 0 20 40 60 0 20 40 60
V I J_ ^ -J I t —i ~i '— ' — I t _
to
tr
10--
20--
•= 30--
t 40-
LU
Q 50--
60
Computed
i-L FEB
o
o
o
o
_ APR
_ JUN
V _ - -
co 10-
CL
UJ
LtJ
^30-
zf
t 4°-
UJ
Q 50-
60-
~ i y \ \ \ \
*> (
-« ^"^-— .^
o ^^v
0
o
o
_ AUG o
I
'
1
•
1 HI 1 - 1 1 1 I
•1 o
- •^o*,^^
^^^
0 Ik
o
o
o
_ OCT o
.
i
i
i t i i i
t
— i
- i
_ DEC
i I
i
•
,
Figure 4. Calculated and Observed Concentation Pro-
files of Phosphorous
Figure 5 shows the model responses for P, N, DO, algae
and pH at the surface and hypolimnion. Representative
data observed during the pre-diversion years are plot-
ted with the first year results and those observed
during the post-diversion years are plotted with the
third year results
The rapid recovery of the lake is predicted adequately
by the model. The end of year phosphorus concentra-
tion is seen to reduce from 59 yg/1 to 45 yg/1 in one
year and to 37 yg/1 in two years after diversion.
Nitrogen levels were reduced from 440 yg/1 to 420 yg/1
to 415 yg/1.
The minimum hypolimnion DO improves from 1.9 mg/1 to
3.5 mg/1. The algal density is shown to reduce from
3.0 mg/1 to 2.2 mg/1. The observed chlorophyl £ level,
converted to biomass by an approximate factor of 1:20,
was shown to have a dramatic reduction in 1967 as pre-
dicted.
Sensitivity Analyses
During the early phase of model development, the half
saturation constant of C02 was estimated at 0.6 mg/1
carbon. The CO exchange rate at the air-water inter-
face was assumed to be 90% of the oxygen reaeration
rate.
As a result, the model never predicted a pH higher than
8.4 during the summer. To maintain a pH of 9.2 in the
summer as observed by Edmondson, the sensitivity
analysis indicated that the C02 exchange rate should
be 10% of the oxygen reaeration rate. The half satu-
ration constant for CO should be 0.025 mg/1 carbon.
The latter value has been confirmed by laboratory
study (3).
To assess the relative importance of oxygen sinks in
the hypolimnion, model simulations were performed with
1) the doubled decay rates of detritus and organic
sediment; 2) algal respiration rate reduced to zero;
766
-------
and 3) eliminating the waste input without modifi-
cation of the initial conditions.
pH 7.1
ALK 30
Figure 5. Recovery of Lake After Sewage Diversion
Model responses of DO profiles are presented in
Figure 6. The most important sinks of hypolimnion DO
are the respiration of algae and the decay of organic
materials accumulated in the bottom.
The waste inputs appear to contribute very little to
the direct oxygen consumption. They stimulate the
growth of algae which settles and respires in the
hypolimnion.
SUMMARY AND CONCLUSIONS
A general purpose water quality ecological model was
developed and applied to Lake Washington. The model
represents the Lake as stacked layers of hydraulic
elements. Hydraulic routing, heat budget and mass
balance computations are performed with a daily time
step throughout the annual cycle. The output contains
the vertical distribution of temperature, dissolved
oxygen, BOD, alkalinity, pH, C02, NH3, N03, P04>
Coliform, algae (2 groups), zooplankton, detritus,
TDS, organic sediment, and benthic animal. The evap-
oration loss, ice formation, surface algal produc-
tivity, and fish productivity for cold, warm and
benthic fishes are also calculated.
Application of the model to pre and post diversion
cases of sewage from Lake Washington indicates the
validity of the results as -compared to Edmondson's
data. Sensitivity analyses indicate that half satu-
ration constant for C02 should be 0.025 mg/1. The
sinks of hypolimnion oxygen are equally divided be-
tween the decay of organic materials accumulated near
sediment and the respiration of settling algae. The
model predicts the rapid recovery of the lake due to
the flushing effects of tributary inflows.
i-DEPTH, METERS
<^^L/IOOWI_V I_L/ wAiUL_iM,my/i w
yo 24689246892468
10-
20-
30-
1
\
•
Sensitivity^^ •
Base
_ Case-
^m
.•' s
.• /
• — -"•
*ii
f
^
B-
•** ^
1
)
.j>
.••'"''
-
_
i
' a
Jf
• •
fj
.**'?
t.-' s
• .
• /
• *
— • 1
JUN AUG OCT
a. Increased Decay Rates of NH,, NOp, BOD, Detritus
V
10-
20-
30-
1 1 1
„'
if
\ i
-
-
i
s
f
j
s \
i
•
•
'*
i i i i i
t
/;
/;
~ s •'
S /
* •
j •
I •
j :
JUN AUG
b. Reduced Algal Respiration
OCT
V
10-
20-
II 1 IV
4
^
':
t
\
I
1
I:
1:
1-
i i iii
j
X
c
\
i
i
|
i i i i i
/
/
~
[ /
JUN
AUG
OCT
c. Reduced Waste Load Input
Figure 6. Model Responses to Sensitivity Analyses
REFERENCES
1. Chen, C.W. , "Concepts and Utilities of Ecological
Model", J. Sanitary Engineering Division, ASCE 96,
No. SA5, 1970.
2. Chen, C.W. , and G.T. Or lob, "Ecologic Simulation
for Aquatic Environments," in Systems Analyis and
Simulation in Ecology, Vol. Ill, Academic Press,
N.Y., 1975.
3. Goldman, J.C., W.J. Oswald, and D. Jenkins, "The
Kinetic of Inorganic Carbon Limited Algal Growth,"
Journal WPCF, Vol 46, No. 3, March 1974.
767
-------
A LIMNOLOGICAL MODEL FOR EUTROPHIC
LAKES AND IMPOUNDMENTS
Robert G. Baca
Water and Land Resources Department
Battelle-Northwest Laboratories
Richland, Washington
Ronald C. Arnett
Research Department
Atlantic Richfield Hanford Company
Richland, Washington
ABSTRACT
A general limnological model is formulated in terms of
key environmental variables including dissolved oxygen,
biochemical oxygen demand, temperature, phytoplankton,
zooplankton and the principal nutrients. The major
controlling factors such as light, temperature, nutri-
ent loading rates, sediment interactions, and flow
patterns are integrated into the model formulation to
provide a detailed portrayal of the important limnetic
processes. The model formulation is generalized to
apply to well-mixed and stratified systems. The
capabilities of the limnological model are demon-
strated with applications to three lakes: Lake Wash-
ington near Seattle, Lake Mendota and Lake Wingra at
Madison, Wisconsin.
INTRODUCTION
The problems associated with the eutrophication of
lakes and impoundments are becoming of increased con-
cern. One preliminary *survey of problem lakes and
reservoirs in the U.S. identified numerous cases
where the water quality has deteriorated to the extent
that restoration measures are needed. Considerable
research has been devoted to understanding the role
of principal nutrients2'3'1* in controlling the rate of
eutrophication. Particular emphasis has been placed
on applying this new knowledge to the development of
effective control and restoration measures5. Although
a wide variety of techniques^ have been developed, no
general guidelines are currently available with which
to assess the technical and economic feasibility of
alternate techniques. Considering the high costs
generally associated with the implementation of lake
rehabilitation techniques, there is a great need for
reliable predictive tools with which to assess and
evaluate the effectiveness of rehabilitation techniques
and to estimate the rates of lake recovery. The
logical tool which can be used to develop such a
predictive capability is mathematical modeling.
In a recent research project7 for EPA, a general
methodology based on the application of modeling tech-
niques was developed for use in assessing the rates of
eutrophication in lakes and impoundments. The
methodology uses three specific modeling techniques
for: (1) estimating nutrient loading rates from land
use patterns and historical data8, (2) predicting the
long term changes in key eutrophication indicators as
functions of nutrient loading rates , and (3) predict-
ing short term changes in several water quality param-
eters as functions of nutrient loading, climatic con-
ditions, lake morphometry, hydrologic features,
thermal and ecologic regimes . In this paper, we
present the generalized limnological model developed
for short term predictions (less than 10 years) with
results from recent applications.
MODELING APPROACH
The conceptual framework of the generalized model is
based on a description of the fundamental limnetic
processes such as heat transport, constituent transport,
hydromechanics, chemical and biological cycles. A quasi-
two-dimensional approach is used based on a segment-
layer representation shown in Figure 1.
768
Segments
River
Inflow
Tributary
Inflow
Layers
Figure 1. Segment-Layer Representation
This approach reduces the multi-dimensional problem
into a series of one-dimensional ones. The fundamental
conservation laws for mass and energy are used to
derive principal model equations. Chemical and
biological cycling are modeled by first order kinetic
equations.
TRANSPORT
The heat and mass balance equations for the segment-
layer representation are
Q.,
3_T
3 t
?F = D
4 3 z z
- Qv, JO + H
(D
and
3C
3 t
(k)
3_C
3z
(k)
= D
32C(k)
+ S
(k)
-Mo c (k)
AAz^h.i i
- Q.
;h,o^
(2)
where
(k)
T,T
C. '
Qh,o
Q
^ ' =
A,Az
= lake and inflow temperatures, °C
= lake and inflow concentrations, mg/1
= horizontal inflow and outflow.m /day
= vertical flow rate, m /day
settling velocity, m/day
source or sink terms, °C/day, mg/l-day
2
element surface area and thickness, m ,
The source terms H account for the atmospheric ^s
heat exchanges across the air-water interface and S
describes the biogeochemical cycling in the aqua'tic
-------
system. The specific formulations for S are given in
the following sections.
DISPERSION AND MIXING
G = Min
np
(6)
Wind shear on the water surface plays a major role in
generating epilimnetic mixing. The following empiri-
cal formula is used to calculate vertical dispersion:
a. + a.v e
1 2 w
thermocline, m; and
where v^ is wind speed, m/sec; d is the depth of the
and a. are empirical constants,
m^/sec, m. When well-mixed conditions exist, i.e., no
thermocline, the depth parameter, d, is set to 6
meters; this represents a minimum stirred depth. Con-
vective mixing produced by density induced instabil-
ities is modeled as a mechanical mixing process. The
procedure consists of checking the density profile
obtained from the predicted temperatures, locating
any region of instability and then mixing the adjacent
layers until a stable condition is reached. The out-
come of this process is a mixed mean temperature and
concentration over the region of instability.
PHYTOPLANKTON
The phytoplankton submodel is based on a carbon bal-
ance. A single species formulation is used given by
f - (G - D )P (4)
dt p p v '
where P is the phytoplankton concentration, mg-C/1;
G is gross specific growth rate, I/day; and D is
the death rate, I/day. The equation for G relates
the growth rate to the limiting nutrient concentration,
light intensity and temperature:
G G.G
m £ np
(5)
The term, G , is the maximum specific growth rate and
is corrected for temperature according to a Q10 formula.
The light limiting term G., is calculated using the
equation:
(5)
where A is a light constant, I/lux; I is light inten-
sity, lux; and a is a photoinhibition factor, I/lux.
Light intensity is distributed vertically through the
water column according to
where C, and C, are ammonia and nitrate nitrogen,
mg-N/1; D. is inorganic phosphorus, mg-P/1; and Kn and
K are Michaelis constants.
P
The decrease in phytoplankton concentration occurs
through endogenous respiration, decomposition, sinking,
and zooplankton grazing. The formulation for D is
D =
P
R + C Z, z d
P 8 e
(9)
where R is endogenous respiration, I/day; F is
decomposition rate, I/day; C is zooplankton grazing,
1/mg-C-day; and d is euphotic depth, m. All algal
cells within the euphotic zone are treated as active
cells which photosynthesize in a lighted environment
and respire in a dark one; below the euphotic depth,
all algal cell, are inactive cells in the death
phase and thus decomposing.
ZOOPLANKTON
The formulation of the zooplankton submodel is given
by
8
(10)
where G and D are the growth and death rates, I/day.
The zooplankton growth and death rates are calculated
from
G — A. C T, i TI
z zp g K + P
mp
D = R + F
z z z
(11)
(12)
where A is the conversion efficiency, decimal; C
zp g
is grazing rate, I/day; K is Michaelis constant,
mp
mg-C/1; and R respiration rate, I/day; F is a
z z
predation rate, I/day. Growth and death rates a
corrected for temperature.
PHOSPHORUS
(7)
where I is surface light intensity, lux; u is extinc-
tion coefficient of water, m ; g is self-shading
factor, m /mg-C/1; and P~ is average phytoplankton con-
centration above depth, z, mg-C/1. The diurnal pattern
of light is calculated from standard light day equation:
1=1 %(1 + cos 4^ t)
o max X
(8)
The phosphorus submodel considers algal uptake and
release, zooplankton release, degradation of organic
phosphorus (D~) with consequent release of inorganic
phosphorus (DI), loss of both organic and inorganic
phosphorus to the sediments (D ), and anaerobic
release from the sediments. The organic phosphorus
pool is assumed to be in a particulate form. Settling
of particulate P is accounted for in the transport
equation. The submodel equations are
where I is calculated from net short wave radiation;
max
t is time, hours; and A is the day length factor hours.
The factor, G , relates the growth rate to the concen-
np
tration of the principal nutrients:
dt
(13)
769
-------
+ R PA + D ZA
P PP z pz
d4V - i2D2
dt
(I4D2- [I3D3])
(14)
(15)
DISSOLVED OXYGEN
The dissolved oxygen submodel considers the effects of
(1) temperature, (2) oxidation of suspended and dis-
solved organic matter, (3) benthic uptake, (4)
reaeration, (5) algal photosynthesis, respiration and
decomposition:
where A and A are the yield coefficients; I, is
PP Pz -1
sediment uptake rate, I/day; I2 is organic phosphorus
decay, I/day; I, is sediment release, I/day; and 1^
is sediment trapping, I/day. The terms in parenthesis
apply for the hypolimnion; brackets designate
processes dependent on anaerobic conditions. The rate
coefficient I., !„, I, and I, are corrected for tem-
perature.
NITROGEN
The nitrogen submodel considers algal uptake and
release, zooplankton release, decay of organic (C.)
and sediment (C,-) nitrogen, and the oxidation of
ammonia (C.) and nitrite (C2) to nitrate (C,). During
anaerobiosis, nitrification is inhibited and denitrifi-
cation occurs with the loss of nitrate. Sediment
interactions include nitrate uptake and release of
ammonia. The organic nitrogen pool is assumed to be
in particulate form; settling of particulate N is
accounted for in the transport equation. The submodel
equations are
Jl
c1+c3
dCj
dt
dt J1C1 J2C2
dC C
IT ' J2C2 - PGPV ^TcT - J3C3
J4C4 + (J5C5)
(16)
(17)
(18)
dDO
dt
a-(G -D )P
3 p p
a,J,,C, - T5- + K (DO -DO)
222 Az r s
(21)
where DO is dissolved oxygen saturation, mg/1; L, is
benthic oxygen uptake rate, g/m -day; a , a and a.
are stoichiometric constants; and K is reaeration
coefficient I/day. All other variables are as
previously defined.
A simple linear relationship is used to model
reaeration rate as functions temperature and wind
speed:
a.v )0
2 w
(T-20)
(22)
where v is wind speed, m/day; a. and a_ are empiricial
w 12
coefficient; and T is temperature in °C. 6 is 1.075.
MODEL APPLICATIONS
The chemical and biological submodels described above
have been implemented into a generalized computer model.
The simulation procedure for a general application con-
sists of two steps. First, the heat transport, mixing
and fluid flow are simulated for the entire period of
interest using 1 day time steps. Next, these results
are input to the limnological model for solution of the
equations for constituent transport, which are solved,
using 4 to 12 hour time steps, for each of 11 constitu-
ents. A finite difference technique is used to obtain
approximate solutions for the transport equations.
LAKE WASHINGTON
dt
= J,C,
zZANZ
, is organic nitrogen decay,
J,.
is sediment nitrogen decay, I/day; ,.
is
are the
where J. is the ammonium oxidation rate, I/day; J0 is
nitrite oxidation rate, I/day; J is denitrification
rate constant, I/day; J
I/day; J
sediment uptake rate, I/day; and A and A,
NP NZ
nitrogen to carbon ratios for algae and zooplankton,
mg-N/mg-C. Denitrification is inhibited during aerobic
conditions. The rate coefficients J , J , . . ., J
are adjusted for temperature.
BIOCHEMICAL OXYGEN DEMAND
The behavior of BOD is modeled by
dL
c
dt
K,L +
1 c
a (F P + R Z)
op z
where L is the BOD5 concentration, mg/Jl, K is the
decay rate, I/day, and
mg-02/mg-C.
is a stoichiometric constant,
(19) Lake Washington is a large, relatively deep, mesotrophic
lake located at Seattle, Washington. The pollution
history and recovery of the lake has become a classic
example of how a eutrophic lake can show a positive
response to nutrient diversion. Because of the lake's
depth and aerobic environment, the lake lacks signifi-
cant sediment-water interactions. Consequently, Lake
Washington is a good case for testing a model's ability
to describe the transport of dissolved and particulate
matter, nutrient cycling and algal growth patterns as
they are influenced by the annual stratification cycle.
The limnological model was applied for the time period
April 1 through December 31, 1962. This period was
selected because it represented that portion of the
year over which the chemical and biological changes
were most dynamic. A single segment with 20 elements
was used to represent the lake geometry. The inflow
quality data for the lake were adapted from estimates
developed by Chen11 in a previous modeling effort. The
model results are compared with observed data in
(20) Figure 2. The good-to-excellent agreement of these
results indicate the model has a strong capability to
describe the direct and reciprocal relationships be-
tween algae dynamics and nutrient cycling. Calibration
of the temperature model required about 10 minutes
computer time, on a POP 11/45, and 30 minutes of staff
770
-------
time. The limnological model required about 1 hour of
computer and staff time to calibrate.
TEMPERATURE, °C
D
0 20 »
'
10 20 w o in ?n M o 10 20 10 o 10 » *
•
•
i
•/
,
<
t
1
) 10 20 30
•
] 10 a) » jo so o ?o 40 60 so
CHLOROPHYLL a, yg'l
0 20 JO 60JjO 0 20 dp 60 SO 0 20 JO 60 30 0 20 JO 60 SO
0 10
H 20
g 30
1 «
-I
A 50
I
15 0 5 10 15
0 M Q.08
I
INORGANIC P mo/1
0 OM O.OS 0 O.M O.QE Q O.OJ 0.09 0 O.OJ O.OS
FIGURE 2. Lake Washington Application
LAKE MENDOTA
Lake Mendota is a large, moderately deep, eutrophic
lake located at Madison, Wisconsin. The largest of the
Madison lakes, it enjoys the notable distinction of
being one of the most studied and well characterized
lakes in the world. The limnological patterns in the
lake are very diverse and complex. The phytoplankton
cycle is characterized by a species succession typical
of eutrophic lakes. The nutrient cycles are very
dynamic and strongly related to the phytoplankton and
dissolved oxygen cycles. Thus, Lake Mendota represents
a considerable challenge for any limnological model.
The model was applied to Lake Mendota for the period
from May 8 through October 18, 1972. The major chem-
ical and biological transformations occur within this
period. Considerable, in-lake data.12-are available for
the lake. The inflow quality was estimated from data
compiled by Sonzogni and Lee.
13
The lake was repre-
sented by a single segment with 16 layers. The model
results are compared with the observed data in Fig-
ure 3. These results clearly show that the model has
a strong capability to track the algal growth and
nutrient cycling patterns in stratified lakes with
sediment interactions and anoxic regimes. These
results further demonstrate that the model can realis-
tically relate the biological, chemical and physical
response of the lake to major controlling factors. The
model produced excellent results for temperature,
chlorophyll a., inorganic phosphorus, and ammonia nitro-
gen. Good-to-excellent results for dissolved oxygen
were obtained. The results for nitrate nitrogen indi-
cate that additional development work is needed to
improve the nitrogen submodel.
0 10 20 30
TEMPERATURE. C
10 20 30 0 10 20 30 0 10 20 30
CHLOROPHYLL a, uq/l
0 20 40 60 0 20 40 60 0 20 40 ffl 0 20 40 60
7
DISSOLVED OXYGEN, mg'l
0 10 ?0 0 10 _ 20 0 10 20 0 10 20
INORGANIC P, mg'l
Q O.d OS
AMMONIA N, mg/l
0123 0123 0123 0123
FIGURE 3. Lake Mendota Application
0 10 20 30
0 20 40 60
0 10 20
0123
771
-------
LAKE WINGRA
Lake Wingra is a small shallow lake located near the
university of Wisconsin at Madison. The lake is pre-
sently in an advanced eutrophic state. Because the
lake receives its nutrients from intermittent sources
(precipitation, dry fallout, urban and rural runoff)
the net loading rate history resembles a high frequency
random signal. The instantaneous flushing rate also
varies from a few weeks to several months. The net
result is that the chemical and biological state of the
lake are very sensitive to the boundary conditions dur-
ing certain parts of the year.
The limnological model was applied for the time period
April 1 through October 31, 1970. Inflow quality data
were developed from measurements reported by
Kluesener14 and estimates of diffuse inputs (dry
fallout, rainfall). The in-lake data collected
Kluesener1*4 and Koonce15 were used for initial condi-
tions and the model comparison. A single segment
representation composed of six layers was used.
The comparisons between the in-lake data and the model
results show good agreement for most water quality
parameters. Temperature and dissolved oxygen were
modeled exceptionally well. Since the biomass data
were calculated from cell counts and volumes there are
some questions about the comparability of the phyto-
plankton biomass results. Nevertheless, the model
results are quite reasonable and show the proper rela-
tionship between parameters.
CALENDAR YEAR
J F M A M J____J A S 0 N D
DATA
oT
• DO
15 1
1.6
~O
Oi
E
g
DATA
• BIOMASS
o P04-P
2.0 | 1 1 \ 1 1 1 1 1 1 1 1 F 10.10
0.08
0.06
0.8 - - 0.04
!A • • N. /V*
0.41- ^JT. !A «>)Liv . -J0.02
0
0 50 100 150 200 250 300 350 400
JULIAN DAYS
FIGURE 4. Lake Wingra Application
CONCLUSIONS
The general capability of the models developed in
this work has been demonstrated with applications to
three lakes: Lake Washington at Seattle, Lakes
Mendota and Wingra at Madison, Wisconsin. These
three lakes represent a class of eutrophic lakes with
different morphometric, meteorologic, hydrologic,
thermal, and ecologic regimes. The comparisons
between observed data and model results demonstrate
that the models have a general capability to track
the seasonal water quality patterns in limnetic
systems.
The generalized limnological model presented in this
paper can provide a convenient interpretative tool
and can be used to develop an understanding of the
limnetic system as a whole. By providing information
on the cause and effect relationships, these models
can help expand our insight and improve our abilities
to predict the ecological consequences of altering
various controlling factors.
REFERENCES
1. Ketelle, M. J. and P. D. Uttormark. "Problem Lakes
in the United States," University of Wisconsin,
Madison, WI, December 1971.
2, Likens, G. E. (Editor). Nutrients and Eutrophica-
tion: The Limiting-Nutrient Controversy, American
Society of Limnology and Oceanography, Inc.,
Lawrence, KS, 1972.
3. Allen, H. E. and J. R. Kramer (Editors). Nutrients
in Natural Waters, Wiley-Interscience, New York,
NY, 1972.
4. Eutrophication: Causes, Consequences, Correctives,
Proceedings of a Symposium, National Academy of
Sciences, Washington, D. C., 1969.
5. Anon. "Measures for the Restoration and Enhance-
ment of Freshwater Lakes," EPA-430/9-73-005, U.S.
Environmental Protection Agency, Washington, D. C.,
1973.
6. Dunst, R. C., et. al. "Survey of Lake Rehabili-
tation Techniques and Experiences," Technical
Bulletin No. 75, Department of Natural Resources,
Madison, WI, 1974.
7. Baca, R.G., R. C. Arnett, W. C. Weimer, L. V. Kimmel,
H. E. McGuire, A. F. Gasperino and A. Brandstetter.
"A Methodology for Assessing Eutrophication of Lakes
and Impoundments," Battelle, Pacific Northwest
Laboratories, Richland, WA, January 1976.
8. Weimer, W. C., H. E.\McGuire and A. F. Gasperino.
"A Review of Land Use Nutrient Loading Rate Rela-
tionships," Battelle, Pacific Northwest Labora-
tories, Richland, WA, January 1976.
9. Baca, R. G., L. V. Kimmel and W. C. Weimer. "A
Phosphorus Balance Model For Long.Term Prediction
of Eutrophication in Lakes and Impoundments,"
Battelle, Pacific Northwest Laboratories, Richland,
WA, January 1976.
10. Baca, R. G. and R. C. Arnett. "A Limnological
Model for Eutrophic Lakes and Impoundments,"
Battelle, Pacific Northwest Laboratories, Richland,
WA, January 1976.
11. Chen, C. W. and G. T. Orlob. "Ecologic Simulation
for Aquatic Environments," Water Resources Engin-
eers, Inc., Walnut Creek, CA, December 1972.
12. Sonzogni, W. C. "Effects of Nutrient Input Reduc-
tion on Eutrophication of the Madison Lakes," Ph.D.
Thesis, University of Wisconsin, 1974.
13. Sonzogni, W. C. and G. F. Lee. "Diversion of Waste-
Waters from Madison Lakes," Environmental Engineer-
ing, ASCE, 100, EG1, pp. 153-170, February 1974.
14. Kluesener, J, W. "Nutrient Transport and Transforma-
tions in Lake Wingra," Ph.D. Thesis, University of
Wisconsin, 1972.
15. Koonce, J. F. "Seasonal Succession of Phytoplankton
and a Model of the Dynamics of Phytoplankton Growth
and Nutrient Uptake," Ph.D. Thesis, University of
Wisconsin, 1972.
772
-------
MATHEMATICAL MODELING OF PHYTOPLANKTON DYNAMICS IN
SAGINAW BAY, LAKE HURON
V. J. Biennan, Jr.
U.S. Environmental Protection Agency
Large Lakes Research Station
Environmental Research Laboratory-Duluth
Grosse lie, Michigan
D. M. DoIan
U.'S. Environmental Protection Agency
Large Lakes Research Station
Environmental Research Laboratory-Duluth
Grosse lie, Michigan
A mathematical model of phytoplankton production
has been applied to a set of physical, chemical, and
biological data from Saginaw Bay, Lake Huron. The
model includes five phytoplankton types, two zooplank-
ton types, and three nutrients: phosphorus, nitrogen,
and silicon. The phytoplankton types include diatoms,
greens, both nitrogen-fixing and non-nitrogen fixing
blue-greens and "others".
The purpose of the paper is to illustrate the
use of the model in both research and management ap-
plications. A major research use to be discussed is
the interpretation of experimental data. An example
is the calibration of model output for total phos-
phorus concentration to actual field data. This cali-
bration indicated the possibility of a previously
unconsidered phosphorus source influencing the bay
in the fall of 1974.
An important management application of the model
is its use as a tool for comparing the effects of var-
ious wastewater management strategies. An example is
the simulation of differences in response among the
various phytoplankton types as a function of nutrient
load reduction in Saginaw Bay. These examples and
others are discussed in this paper.
Introduction
Mathematical modeling techniques can provide a
quantitative basis for the comparison of various
management strategies designed to reduce waste load-
ings to receiving bodies of water. Different manage-
ment strategies for the Great Lakes have been analyz-
ed in this manner. Thomann, et al. have used these
techniques to investigate the effects of phosphorus
and nitrogen reduction on chlorophyll levels in Lake
Ontario.1 Bierman, et al. have investigated the ef-
fects of changes in phosphorus, nitrogen, and silicon
loadings on phytoplankton biomass in Saginaw Bay,
Lake Huron.2
Exhaustive research must be conducted with math-
ematical models prior to their use as management
tools, to ensure that they accurately describe the
particular physical, chemical and biological process-
es that they were designed to simulate. Canale and
Middlebrooks, et al. have reported on various re-
search oriented whole-system and component models
which were designed to obtain greater insight with re-
gard to chemical and biological processes in aquatic
ecosystems. > "*
The present work is part of the International
Joint Commission's Upper Lakes Reference Study invol-
ving Saginaw Bay, Lake Huron. The ultimate goal of
this work is to develop a mathematical model which
can be used both to describe the physical, chemical
and biological processes that occur in Saginaw Bay
and to predict the effects of reduced waste-loadings.
Model development is proceeding along two par-
allel pathways. The first of these involves the
development of research-oriented process models which
include biological and chemical detail but which,
for simplicity, do not include any spatial detail.
The second pathway involves the development of an
engineering-oriented water quality model which des-
cribes, as closely as possible, the actual physical
system, including spatial detail. At any point in
time, the water quality model will simulate those
chemical and biological processes which have been
successfully investigated and developed using the
spatially-simplified model. There is constant feed-
back between the above two pathways and constant
interaction between the entire modeling effort and
an ongoing sampling program on Saginaw Bay.
The purpose of the present paper is to de-
scribe the basic concepts of the Saginaw Bay model
and to present sample output from the model which
illustrates its use both as a research tool and as
a management tool. All reported results were ob-
tained using a spatially-simplified model applied
to the inner portion of Saginaw Bay (Figure 1),
which has been assumed to be a completely-mixed
reactor.
Model Concepts
The basic model equations and preliminary simu-
lations appear elsewhere.5'6 The compartments in
the model are five phytoplankton, two zooplankton,
higher predators, and three nutrients: phosphorus,
nitrogen, and silicon (Figure 2). The phytoplankton
types are diatoms, greens, both nitrogen-fixing and
non-nitrogen-fixing blue-greens, and "others", mostly
dinoflagellates and cryptomonads in Saginaw Bay.
The motivation for a multi-class modeling ap-
proach is that different classes of algae have very
different nuprient requirements; for example, dia-
toms have an absolute requirement for silicon and
certain types of blue-greens can fix atmospheric
nitrogen. In addition, not all of these classes
have the same nuisance characteristics. Diatoms
and green algae are grazed by zooplankton, but
blue-green algae are not significantly grazed and
can form objectionable floating scums.
A unique feature of the model is that cell growth
is considered to be a two-step process involving sepa-
rate nutrient uptake and cell synthesis mechanisms.
The motivation for this variable stoichiometry ap-
proach is that an increasingly large body of experi-
mental evidence indicates that the mechanisms of nu-
trient uptake and cell growth are quite distinct.7»8»9
10,11 The mo
-------
of a cell's immediate metabolic needs. Specific cell
growth rates are assumed to be dependent on the intra-
cellular levels of these nutrients, in contrast to the
use of Michaelis-Menten equation for relating growth
rates directly to extracellular nutrient concentra-
tions.
Model Implementation
A major problem in attempting to implement a com-
plex chemical-biological process model is the lack of
sufficient experimental data. It is often possible
that more than one set of model coefficients could
produce acceptable agreement between the model output
and a given data set. In the transition from single-
class to multi-class models, this problem becomes
particularly acute because it is no longer sufficient
to ascertain a range of literature values for a given
coefficient. Multi-class models necessitate the de-
finition of class distinctions within this range.
Given the present state of the art of ecosystems mod-
eling and associated experimental work, many of the
coefficients in such models must simply be estimated.
The primary operational differences among the
phytoplankton types in the model are summarized in
Table 1. The working equations of the model and sen-
sitivity analyses of some of the more important co-
efficients have been presented elsewhere.
One of the implicit assumptions of the model is
that cell biomass concentration is a more accurate in-
dicator of phytoplankton standing crop than is chloro-
phyll a_ concentration. Furthermore, chlorophyll &_ is
a lumped parameter and cannot be used to distinguish
between different functional groups of phytoplankton.
For these reasons, chlorophyll a_ concentration does
not appear in any of the kinetic equations of the
model.
The computer program which actually solves the
model equations is written in FORTRAN IV and is
structured in a form such that any number of phyto-
plankton and zooplankton types can be simulated,
along with any set of food web interactions for these
groups. The version of the model in Figure 2 con-
sists of 23 simultaneous differential equations.
The solutions were obtained using a fourth-order
Runge-Kutta method with a time step of 30 minutes
for the nutrient kinetics equations and a time step
of 3 hours for the growth equations. For a 365-day
simulation, approximately 5 minutes of CPU time are
required on an IBM 370/158 computer. For the same
simulation, approximately 60 minutes of CPU time is
required on the Grosse lie Laboratory's PDP-8/e mini-
computer with floating point hardware.
Experimental Data
Chemistry and chlorophyll data were collected
for Saginaw Bay by Cranbrook Institute of Science.12
During 1974, 12 cruises were conducted and samples
were collected from 59 stations. Samples were taken
at 1 meter and at all depths from 5 meters to the
bottom in 5-meter intervals. A total of 111 sta-
tion-depth combinations were sampled on most of the
cruises. Analyses were conducted for 21 chemical
parameters, including phytoplankton chlorophyll.
Since the present modeling study is restricted only
to the inner portion of Saginaw Bay (Figure 1), only
data from the 33 field stations in this region were
used.
The phytoplankton data used were collected on
the above cruises by the University of Michigan at
1 meter depths.1^ Species counts were conducted on
all samples. In order to transform these data for
comparison with model output, the species counts
were first integrated to the genus level. At this
level, cell volumes were assigned and these volumes
were then integrated to the level of the five func-
tional groups in the model. The cell volume con-
centrations at this level were converted to dry
weight (biomass) concentrations.
The zooplankton data used were collected on
the above cruises by the University of Michigan at
the same station-depth combinations as the chemical
data. Individual species counts were converted
directly to dry weight concentrations and then inte-
grated to the level of the two functional groups in
the model.
All phytoplankton and zooplankton mean concen-
trations are reported as the geometric mean + 34% of
the area under the frequency distribution curve.
This is analogous to the arithmetic mean + one full
standard deviation. Analyses of the biological data
indicated that a log-normal distribution was a more
accurate representation than a normal distribution.
All other data are reported as the arithmetic mean
+ one-half standard deviation.
Nutrient loadings to Saginaw Bay from the Sagi-
naw River, the primary source, were determined on
the basis of a field sampling program. For the
first half of the year, samples were taken at two to
three-day intervals at the Dow Chemical Company
water intake at the mouth of the Saginaw River.
From July to December, samples were taken from the
Midland Street Bridge in Bay City every two weeks.
During this period, the Dow intake was too strongly
influenced by the bay itself because of the intru-
sion of bay water up the river. The Midland Street
Bridge is approximately 5 miles upstream from the
river mouth and is not influenced by the bay during
this period. Concentrations were obtained for chlo-
ride and total and dissolved forms of phosphorus,
nitrogen, and silicon. Daily flow rates were ob-
tained from the U.S. Geological Survey.
Boundary Conditions and Forcing Functions
Since the physical system under consideration
is only part of a larger physical system, Lake
Huron proper, the interaction between Saginaw Bay
and Lake Huron is extremely important. The predomi-
nant flow pattern in the bay is counterclockwise
with Lake Huron water flowing in along the north
shore and a mixture of Lake Huron water and Saginaw
River water flowing out of the bay along the south
shore (Figure 1) . The concentrations of nutrients
and biota in the water which flows across the indi-
cated inner bay-outer bay boundary are examples of
boundary conditions which must be specified. These
concentrations were determined using the cruise data
from the two sampling stations nearest to the area
of water inflow from the outer bay. Daily concen-
tration values were calculated by linearly interpola-
ting between the cruise averages for these stations.
External nutrient loads are the most important
forcing functions in the present study. Total daily
flow from the Saginaw River was calculated by summing
the primary tributary gauges and the estimated flow
from the ungauged tributary area. Daily nutrient
loading rates were calculated using the measured
nutrient concentrations on that day. These daily
loading rates were then plotted and time-series of
loading rates were generated by linearly interpolat-
774
-------
ing between all of the significant peaks and troughs.
For example, for total phosphorus, a series of 28
loading rates/time-breaks was generated. For ortho-
phosphorus, a series of 46 loading rates/time-breaks
was generated.
Model Calibration
The spatially-simplified Saginaw Bay model has
been calibrated to 12 simultaneous and independent
parameters: chloride, biomass concentrations for
five functional groups of phytoplankton, total zoo-
plankton, total phosphorus, total nitrogen, and dis-
solved forms of phosphorus, nitrogen, and silicon.
For simplicity, only selected results are presented
here (Figures 3-5).
Water circulation rates between the inner and
outer bay were determined by modeling chloride concen-
trations in the bay and chloride loadings from the
Saginaw River in a manner similar to that of Richard-
son.15 Advective flows and turbulent dispersions in
the model were adjusted until the chloride output cor-
responded to the field measurements (Figure 3). Time-
variable flows were used which corresponded to hydrau-
lic detention times ranging from 45 to 120 days for
the inner bay.
Model output for total phosphorus (Figure 4) is
consistent with the actual data with the exception
of the late-fall period. Since the only external
nutrient sources considered were the Saginaw River
and Lake Huron, the present results must be considered
preliminary in nature. The possible roles of sedi-
ments and atmospheric sources must be considered be-
fore a complete picture of the nutrient dynamics in
Saginaw Bay can be obtained.
One of the recent advances in the area of phy-
toplankton modeling has been the resolution of total
phytoplankton biomass into functional groups. There
are important differences in biology and nutrient
chemistry among different types of algae, as well as
differences in water quality implications. In Sagi-
naw Bay, the principal concern is with the differ-
ences between diatoms and blue-green algae. The
total biomass curve (Figure 5) was therefore resolved
into its diatom and blue-green components (Figure 6)
by plotting the computed biomass concentrations of
these phytoplankton types. Comparison of the curves
indicates that the diatoms (Figure 6a) comprise 99%
of the first biomass peak, while the sum of non-
heterocystous blue-greens (Figure 6b) and heter-
cystous blue-greens (Figure 6c) comprises 80% of the
second biomass peak. The results agree reasonably
well with biomass data for individual phytoplankton
types.
Research Applications
The present model can be applied to a variety of
research problems. It can be an extremely useful re-
search tool when used in numerical experimentation
or sensitivity analyses. Those system parameters
which are sensitive over the range of interest can be
identified. Given a limited research budget, the in-
formation can be useful in optimally directing spend-
ing. The model provides an alternate framework for
data analysis which can supplement traditional methods
such as statistical summaries or empirical models.
Use of the model can lead to new interpretations of
existing data or make clear new data requirements.
The total phosphorus calibration (Figure 4) pro-
vides a good example of the model providing a frame-
work within which to interpret data. The calculated
phosphorus concentration in the 4th quarter is con-
sistently low when compared to the actual data. This
indicates that an additional total phosphorus source
is probably influencing the system in the fall and
that this source is not included among the model in-
puts. In support of this hypothesis, the calculated
phosphorus concentrations agree quite well with ob-
served data in the other parts of the year and the
calculated chloride concentrations and hence, water
circulation rates agree with the observed data over
the entire year. Phosphorus sources thought to be
insignificant on an annual basis have been recon-
sidered for possible seasonal inputs. Such sources
include contributions from the atmosphere, resuspen-
sion of sediments and possible leaching from dredge
spoils. This apparent discrepancy could not have
been discovered by looking at total phosphorus load-
ings and open-water concentrations alone. The model
provides a link between the two that allows such a
conclusion to be made.
Additional research insight can be gained by the
resolution of total phytoplankton biomass into var-
ious functional groups. With this increased resolu-
tion, the full range of phytoplankton-nutrient inter-
actions can be investigated including:
1. nutrient recycling among different
functional groups,
2. differences in nutrient stoichlometries
and kinetics among the functional groups,
3. effect of silicon and nitrogen on species
composition and succession,
4. supply of nitrogen to the system by
nitrogen fixing blue-green algae.
Research with a sophisticated mathematical model
requires the investigator to consider new data and to
reconsider existing data. Explanation of previously
undiscovered phenomena now becomes necessary. Also,
as the model attains more realism, empirical coeffi-
cients and constants are eliminated and experimental-
ly determined parameters take their place. Some ex-
amples follow.
Chlorophyll a_ concentrations in water are rela-
tively easy to determine. In conventional chlorophyll
models, the chlorophyll a_ to biomass ratio for phyto-
plankton is assumed to be constant. Chlorophyll a_
concentrations are therefore taken to be adequate
measures of phytoplankton abundance. However, when ac-
tual biomass data were collected for calibration of the
multi-class model in Saginaw Bay, the chlorophyll a_
to biomass ratio was found to vary over the year by
as much as a factor of 16. Furthermore, these data
indicated that the chlorophyll a_ to biomass ratio
changed as phytoplankton species succession occurred
throughout the year. This observation suggested that
each functional group in the model should have a dis-
tinct chlorophyll a_ to biomass ratio, and that the
overall ratio at any given time depends on the rela-
tive abundance of each of the functional groups. As-
signing chlorophyll a_ to biomass ratios by phyto-
plankton group reduced significantly the yearly var-
iation in the overall chlorophyll a_ to biomass ratio.
Field data alone cannot provide information need-
ed to replace empirical coefficients in simpler mod-
els. The development of the model has necessitated
comprehensive process-rate studies to determine phy-
toplankton-nutrient uptake kinetics, as well as phy-
toplankton-zooplankton interactions. These types of
process studies have value independent of their mod-
775
-------
eling utility, but the modeling process can assure
that they are conducted in an orderly fashion.
Management Applications
A model that has been rigorously calibrated and
verified can be used for planning and management pur-
poses. The achievement of significant reductions in
algal biomass, especially nuisance blue-greens, is a
problem that the multi-class phytoplankton model is
uniquely qualified to address. The problem can be
quantified by introducing the possibility of reduc-
tions in the key nutrients: phosphorus, nitrogen
and silicon in the case of Saginaw Bay. The model
is capable of predicting reductions in each class of
algae given a percent reduction in the loadings of
these three nutrients. It should be emphasized that,
in practice, such reductions would have to be accom-
plished by consideration of the controllable portion
of each of the nutrient loads, the timing of the
loadings and the availability of each nutrient to
the algae.
Although, in the strict sense, the present model
is not verified, hypothetical simulations were con-
ducted in which the external loads of phosphorus, nit-
rogen and silicon, respectively, were reduced by 50%.
The effect of a 50% reduction in nitrogen loadings
was found to have a negligible effect on algal bio-
mass. This is not surprising because nitrogen is a-
bundant in Saginaw Bay at the time of the spring dia-
tom bloom and nitrogen-fixing blue-greens can make up
any deficit in. the supply of dissolved nitrogen later
in the season. A 50% reduction in silicon loading
was found to cause a minor reduction in the diatom
crop. Silicon reductions were less effective than
expected because zooplankton grazing is apparently
as important as silicon depletion in the termination
of the spring diatom bloom. In addition, a large
amount of silicon enters the bay from Lake Huron.
Two sets of boundary conditions were considered
for the simulation of 50% reduction in phosphorus
loadings. In the worst case situation, it is assumed
that the outer bay phosphorus concentration remains
the same despite the phosphorus load reduction. In
the best case situation, it is assumed that the outer
bay phosphorus concentration becomes similar to the
Lake Huron phosphorus concentration in response to
the phosphorus load reduction. The actual "state of
nature" will lie within these two extremes. Such an
approach is necessitated by the lack of spatial re-
solution in the present model. With spatial resolu-
tion, the outer bay could be modeled also. Thus the
ambiguity in boundary conditions would be removed
since the system boundary would be Lake Huron which
has well defined concentrations for the parameters
of interest.
The reduction in algal biomass for the 50% phos-
phorus load reduction occurs primarily in the latter
half of the year. Therefore, it is essentially a re-
duction in blue-greens, since 80% of the second bio-
mass peak is blue-green biomass. Actual percent re-
duction in total blue-green biomass depends on the
specification of the boundary conditions (Figure 7).
The best case blue-green reduction (Figure 7b) is
73% of the peak biomass, while the worst case reduc-
tion (Figure 7a) is 26% of the peak biomass. Im-
proved estimates of blue-green responses to waste
load reductions in Saginaw Bay can only be obtained
with a spatially segmented version of the model.
Nutrient reduction simulations can be used by
managers and planners to decide which nutrient or
nutrients to focus on in reduction programs and how
much reduction in the nutrient is required for signi-
ficant improvements in water quality.
Future Research
Near term research with the model has two im-
portant goals: calibration of a spatially refined
model to 1974 data and verification of this model
with 1975 data.
A 5-segment version of the model has been devel-
oped and is awaiting calibration. The additional
spatial resolution will allow examination of effects
in different areas of the bay and will reduce the
dependence of future projections of water quality on
boundary conditions.
Additional spatial resolution depends on ade-
quate representation of the water movement between
spatial segments of the model. Work is underway on a
hydrodynamic model that will be compatible with the
phytoplankton model and will specify the transport on
a time varying basis when given wind speed and direc-
tions as input.
Longer term goals for Saginaw Bay include the
monitoring of water quality trends in the bay as
nutrient loadings decrease. During the next several
years nutrient reductions are expected to occur due
to ongoing abatement programs. Actual projections
made with the model indicate that significant improve-
ments in water quality will occur as these reductions
are attained. The Saginaw Bay sampling program should
detect these trends and thus provide an opportunity
for model verification.
This modeling effort has, in addition, some
broader, user oriented goals. The phytoplankton mod-
el will be tested on other physical systems to deter-
mine its generality and to obviate any unforeseen
difficulties which might be experienced. An ultimate
goal is to transfer a documented version of the model
to interested users for research, planning, and
management purposes.
References
1. Thomann, R.V., DiToro, D.M., Winfield, R.P. and
O'Connor, D.J. 1976. Mathematical Modeling
of Phytoplankton in Lake Ontario. II. Simula-
tions Using Lake 1 Model. U.S. Environmental
Protection Agency. In press.
2. Bierman, V.J., Jr., Richardson, W.L., and Dolan,
D.M. 1975. Responses of Phytoplankton Biomass
in Saginaw Bay to Changes in Nutrient Loadings.
Saginaw Bay Report. A report to the Internation-
al Reference Group on Upper Lakes Pollution, In-
ternational Joint Commission, Windsor, Ontario.
3. Canale, R.P., ed. 1976. Mathematical Modeling
of Biochemical Processes in Aquatic Ecosystems.
Ann Arbor Science Press. In press.
4. Middlebrooks, E.J., Falkenburg, D.H. and Maloney,
T.E., eds. 1973. Modeling the Eutrophication
Process. Proceedings of a Workshop, September
5-7, 1973. Utah Water Research Laboratory and
Division of Environmental Engineers, Utah State
University, Logan. National Eutrophication
Research Program, U.S. Environmental Protection
Agency, Corvallis, Oregon.
5. Bierman, V.J., Jr. 1976. Mathematical Model
of the Selective Enhancement of Blue-Green Al-
gae by Nutrient Enrichment. In press in
776
-------
"Mathematical Modeling of Biochemical Processes
in Aquatic Ecosystems", R.P. Canale, ed., Ann
Arbor Science Press.
6. DePinto, J.V., Bierman, V.J., Jr. and Verhoff,
F.H. 1976. Seasonal Phytoplankton Succession
as a Function of Phosphorus and Nitrogen Levels.
In press in "Mathematical Modeling of Biochemi-
cal Processes in Aquatic Ecosystems", R.P.
Canale, ed., Ann Arbor Science Press.
7. Fuhs, G.W. 1969. Phosphorus Content and Rate
of Growth in the Diatoms Cyclotella nana and
Thalassiosira fluviatilis. Journal of Phycology
5: 312-321.
8. Fuhs, G.W., Demmerle, S.D., Canelli, E. and
Chen, M. 1971. Characterization of Phosphorus-
Limited Planktonic Algae. Nutrients and Eutro-
phication: The Limiting Nutrient Controversy.
Proceedings of a Symposium, February 11-12, 1971.
American Society of Limnology and Oceanography
and Michigan State University, East Lansing,
Michigan pp. 113-132.
9. Droop, M.R. 1973. Some Thoughts on Nutrient
Limitation in Algae. Journal of Phycology 9:
264-272.
10. Caperon, J. and Meyer, J. 1972a. Nitrogen-
Limited Growth of Marine Phytoplankton-I.
Changes in Population Characteristics with
Steady-State Growth Rate. Deep Sea Research 19:
601-618.
11. Caperon, J. and Meyer, J. 1972b. Nitrogen-
Limited Growth of Marine Phytoplankton-II.
Uptake Kinetics and Their Role in Nutrient
Limited Growth of Phytoplankton. Deep Sea
Research 19: 619-632.
12. Smith, V.E. 1975. Saginaw Bay (Lake Huron):
Survey of Physical and Chemical Parameters.
Saginaw Bay Report. A report to the Inter-
national Reference Group on Upper Lakes Pollu-
tion, International Joint Commission, Windsor,
Ontario.
13. Stoermer, E.F. 1975. Saginaw Bay Phytoplank-
ton. Saginaw Bay Report. A report to the Inter-
national Reference Group on Upper Lakes Pollution,
International Joint Commission, Windsor, Ontario.
14. Gannon, J.J. 1975. Crustacean Zooplankton in
Saginaw Bay, Lake Huron. Saginaw Bay Report. A
report to the International Reference Group on
Upper Lakes Pollution, International Joint Com-
mission, Windsor, Ontario.
15. Richardson, W.L. 1976. An Evaluation of the
Transport Characteristics of Saginaw Bay Using
a Mathematical Model of Chloride. In press in
"Mathematical Modeling of Biochemical Processes
in Aquatic Ecosystems", R.P. Canale, ed., Ann
Arbor Science Press.
TABLE 1
Operational Differences Among
Phytoplankton Types
Characteristic
Property
Diatoms
Greens
Others
Blue-Greens
(non n-fixing)
Blue-Greens
(n-fixing)
Nutrient
Requirements
Phosphorus
Nitrogen
Silicon
Phosphorus
Nitrogen
Phosphorus
Nitrogen
Phosphorus
Nitrogen
Phosphorus
Relative Growth
Rates Under
Optimal Conditions High
Saturation Light
Intensity High
Sinking Rate High
Grazing Pressure High
High
High
High
High
Low
High
High
None
Low
Low
Low
None
Low
Low
Low
None
777
-------
10 0 10 20 30 M|
10 0 10 20 30 40 50 ....
i i i I i i i KM
Scale, 1:1,000,000
Figure 1. Saginaw Bay watershed indicating dis-
tinctions between inner and outer
portions of the bay.
HIGHER PREDATORS
MS
ABLE
LABLE
ON
> y
X
/ \
ZOOPLANKTER
2
.. i
|
1
GREEN ALGAE
"i
I
T
PHOSPHORUS
i
NON AVAILABLE
PHOSPHORUS
OTHERS BLUE-GREENS BLUE-GREENS ', j _„
• t
AVAILABLE ATMOSPHERIC
NITROGEN NITROGEN
{
]
NONN,Tro£r |
Figure 2. Principal compartments of the Saginaw
Bay, inner portion, as compared to
model ouput.
50
Ol
^ 40
z
0
H
cc 30
H
z
LU
0
I 20
UJ
D
CC
g 10
I
0
0
1 1 1 —
_
x^1
-
1 1 F 1 M ' >
1
t
* 1
1 1 1
Vi
J- J
vl 1 J ' J ' t-
— 1
1
x 1 s
— r
_^ .'
i
— i — >
~
-
_^
H"
.
0 ' N ' D
1974
Figure 3. Chloride distribution for 1974 in '
Saginaw Bay, inner portion, as com-
pared to model output.
\ IUU
01
3.
C/5
§ 8°-
i
Q-
OD
O
S 60
_]
<
H
O
1—
40
Z
g
i-
<
K 20
z
LU
(J
§ 0
<— > U
1 1 1 1 1 1 1 1 1 1 1
-
/X-"~\T ITT
^J \ • T
/ 'N T IT
/ 4 T
J I1 V\ fl
T----J
1
J'F'M A M jljlAls'o'N'D
1974
Figure 4. Total phosphorus distribtution for
1974 in Saginaw Bay, inner portion,
as compared to model output .
1 go —
en
a.
§ 10.0
TOPLANKT
Q_
I
0
00
^ 0.10
^
O
CO
n ni
U.U 1
5 =
~ T "~
" T ~
! T'/\ T T 1
L K HTIHLH
h — "•• ilY l 1
- ' -
= 1 =
— ^
- -
J I F I M | A M J | J | A I S | 0 | N D!
1974
Figure 5. Total biomass distribution for 1974
in Saginaw Bay, inner portion, as
compared to model output.
778
-------
JFMAMJ|J|A|SONO
Figure 6(a). Diatom biomass distribution for 1974
in Saginaw Bay, inner portion, as com-
pared to model output.
E (bl NON-HETEROCYSTOUS BLUE-GREENS E
BJ 1 F 1 M | A
/
I o
Figure 6(b). Biomass distribution of non-hetero-
cystous blue-green algae for 1974 in
Saginaw Bay, inner portion, as com-
pared to model output.
E (c) HETEROCYSTOUS BLUE-GREENS
J|F|M|A|M|J|J|A|S|O|N|D
1974
2.0 -
< 1.0
2-0
1.0
00
CALIBRATION RUN INO P LOAD
REDUCTION! / \
/ \
OUTER BAY BOUNDARY CONDITIONS /
150% P LOAD REDUCTIONI / i
-CALI BRA TION RUN INO P LOAD
REDUCTIONI
-LAKE HURON BOUNDARY CONDITIONS /
150% P LOAD REDUCTIONI /
I
J ' A ' S ' 0 ' N ' D
1974
Figure 7(a). Comparison between calibration run and
50% P load reduction simulation for
blue-green biomass in Saginaw Bay with
outer bay boundary conditions.
Figure 6(c). Biomass distribution of heterocystous
blue-green algae for 1974 in Saginaw
Bay, inner portion, as compared to mod-
el output.
779
-------
THE APPLICATION OF A STEADY-STATE WATER QUALITY MODEL
TO THE PERMIT WRITING PROCESS, LAKE MILNER, IDAHO
John R. Yearsley
EPA Region X
Seattle, Washington 98101
SUMMARY
The Milner Reach of the Snake River, between
Minidoka Dam and Milner Dam (see Figure 1), is
classified as being water quality limited. One of
the important limiting water quality parameters is
dissolved oxygen. Data collected by the Federal
Water Quality Administration (FWQA) and the
Environmental Protection Agency (EPA) at Milner
Dam show extended periods of low dissolved oxygen.
Conditions have been particularly critical during
periods of low flow when the discharges from
municipal and industrial waste sources were at
their peak. For example, during November, 1969
the minimum dissolved oxygen was less than 6.0
mg/1 on twenty-three days. The effects of low
dissolved oxygen upon aquatic life have reached
serious proportions. Major fish kills occurred in
the Milner Reach during the 1960, 1961, and 1966
food processing seasons. In addition to the
discharge of organic wastes from industrial and
municipal sources, the oxygen demand associated
with return flow from irrigation wasteways, decay
of algae in impoundments and oxygen demand from
bottom sediments contribute to the observed dis-
solved oxygen problems.
Reductions in waste discharge since 1971,
coupled with above-average flows in the Snake
River, have resulted in substantial improvement in
the dissolved oxygen of the Milner Reach. No
dissolved oxygen levels below 6.0 mg/1 have been
observed since 1971. However, dissolved oxygen
levels below 90% saturation were measured during
the food processing seasons of 1973 and 1974.
In October, 1974, the Idaho Operations Office
of the EPA Region X drafted National Pollutant
Discharge Elimination System (NPDES) permits for
the industrial waste sources, J. R. Simplot and
Ore-Ida, in the Burley-Heyburn area. A steady-
state dissolved oxygen model was used to support
the permit writing process. At the same time, a
comprehensive field study program was designed to
verify the model results in the Milner Reach.
Cg " the saturation dissolved oxygen, mg/1,
K-£ " the deoxygenation rate, I/days,
L - the carbonaceous biological oxygen
demand (BOD), mg/1,
c - the dissolved oxygen sources, mg/1/second
r_ • the dissolved oxygen sinks, mg/1/second.
Similarly, the BOD budget is:
u dL - -K,L + * - T (2)
-7—• J. L L
dx
where,
L " the BOD sources, mg/1/second,
r^ = the BOD sinks, mg/1/second,
In the initial permit analysis, the only
dissolved oxygen sources considered were those
associated with surface and groundwater return
flow. The only dissolved oxygen sink was the
demand associated with bottom sediments.
Sources of BOD were associated with surface
and groundwater return flows, and municipal and
industrial discharges. No BOD sinks were
included.
The solutions to Equations (1) and (2) are,
respectively:
-K2x
c = cs - (cs - c0)
.
(K2 -
(3)
and,
METHOD OF ANALYSIS
The steady state dissolved oxygen budget for
a vertically and laterally well mixed stream, in
which diffusion and dispersion processes are
neglected, can be written:
u dC - -K2(C - CS) - KjL
dx
(l)
where,
the stream velocity, feet/second,
the dissolved oxygen, mg/1,
the distance along the axis of the river,
positive downstream, feet,
the reaeration rate, I/days,
L0
<*L -
(4)
For the special case when there is no
reaeration (K2 = 0.0), which is of interest
during the winter ice cover condition, Equation
(1) has the following solution:
C = GO + L0(e
APPLICATION OF THE MODEL
Estimates of the dissolved oxygen and BOD
concentrations were made for that portion of the
Milner Reach between Snake River Miles 654.0 and
780
-------
640.0. These estimates were obtained from
Equations (3), (4), and (5) using various organic
loading levels for the NPDES permits. The effect
of these loadings upon water quality was estimated
for January with no ice cover, January with
complete ice cover, March, August, and October.
These months were chosen as critical seasons from
the standpoint of river flow and in-stream water
quality.
The water quality characteristics, river
hydrology, and cross-sectional characteristics for
each of the months analyzed are described below.
Water Quality Characteristics
The water quality characteristics for the
Snake River at River Mile 654.0 were estimated
from the results of surveys made by EPA Region X
in 1971, 1972, and 1973. The data from these
surveys are stored in the EPA's STORET system.
The concentrations of temperature, dissolved
oxygen, and BOD used in the analysis are shown in
Table 1.
Table 1. Water quality characteristics of
the Snake River at River mile 654.0
Hydrology
Discharge of the Snake River at River Mile
654.0 was varied over a range of flows. The
quantity of surface and groundwater return flows
was kept constant, as shown in Table 3. These
return flows correspond to one-half (50%) of the
total return flow in the Milner Reach, as given
in the U. S. Bureau of Reclamation's 1971 base
flow study. The average monthly and l-in-10 seven
day low flow for the Snake River below Minidoka
Dam are also shown in Table 3.
Table 3.
Month
January
March
August
October
Hydrologic characteristics of the
Snake River below Minidoka Dam for
selected months.
Average l-in-10 Return
Flow Flow Flow
(cfs) (cfs) (cfs/tnile)
2167
3189
8750
2488
276
488
5528
1593
4.0
0.0
16.0
15.0
Temp.
(C)
0.0
0.0
5.0
22.0
10.0
D.O.
(mg/1)
11.3
11.3
9.9
6.4
10.0
B.O.D.
(mg/1)
1.5
1.5
1.5
1.5
1.5
Month
January
(no ice cover)
January
(100% ice cover)
March
August
October
Water quality for the surface and ground
water return flow, assumed to be the same for both
sources, is shown in Table 2. Data of this nature
for the Milner Reach are limited. It was,
therefore, necessary to use estimates made from
available data. In this case, water quality
studies from the Boise River basin were used as a
means for estimating quality of the return flows.
Table 2.
Month
January
(no ice cover)
January
(100% ice cover)
March
August
October
Water quality characteristics of
surface and groundwater return flow
flow in the Milner Reach, as
estimated from Boise River data.
Temp.
(C)
0.0
0.0
22.0
10.0
D.O.
(mg/1)
8.0
8.0
6.0
8.0
B.O.D.
(mg/1)
0.0
0.0
1.0
1.0
River Cross-sectional Characteristics
The Milner Reach below River Mile 654.0 was
divided into five segments. River widths and
depths were assumed to be constant throughout each
of the five segments. River miles included in
each segment and corresponding width and depth are
given in Table 4.
Cross-sectional characteristics
of segments in the Milner Reach
of the Snake River.
Table 4.
Segment
No.
Rate Constants
The deoxygenation rate, Kj, was assumed to
be 0.15 I/days (base e), at 20 C, for the entire
reach. This rate was obtained from long term BOD
measurements of the J. R. Simplot effluent in
-March 1972. The rate was adjusted for temperature
according to the relationship:
River
Mile
654-653
653-649
649-645
645-643
643-640
Width
(feet)
1200
1200
1200
1200
1200
Depth
(feet)
4.5
4.8
8.7
4.9
18.0
20
(T - 20)
1.047
(6)
781
-------
where,
Field Studies and Model Verification
KI ~ the deoxygenation rate at temperature,
2Q T, I/days (base e),
K^ - the deoxygenation rate at temperature,
T = 20 C, I/days (base e).
The reaeration rate, K2 , was estimated from
the method given by O'Connor and Dobbins^ :
,20
0.5
12.9 u
(7)
1.5
H
and adjusted for temperature, T, according to:
20 (T ' 20)
K2 - K|u 1.024
(8)
The sediment oxygen demand rates, FC, were
obtained from field studies made by Kreizenbeck2 .
Observations were made at four stations, and the
results are given in Table 5. It was assumed
that the values remained constant throughout each
segment. Furthermore, it was assumed that the
sediment demand varied with temperature according
to the relationship:
0.07(T - 22)
fcTc e <9>
Table 5. Observed sediment oxygen demand
and corresponding D.O. sink
strength in the Milner Reach of the
Snake River (after Kreizenbeck2 ).
River Oxygen Strength of
Mile Demand D.O, Sink
(gm/m2/day) (mg/l/sec)
654-653 0.89 7.54x10-6
653-649 1.04 8.21x10-6
649-645 1.85 8.03x10-6
645-643 1.85 14.28x10-6
643-640 5.33 11.22x10-6
Loading Levels
Best practicable control technology (BPT)
currently available for the Ore-Ida and J. R.
Simplot waste discharges was used as a starting
point for the analysis. These loadings, terms of
BOD (5 day) are given in Table 6.
Table 6. Organic waste loadings for Ore-Ida
and J. R. Simplot in the Milner
Reach, as determined by BPT.
Source
Ore-Ida
J. R. Simplot
BOD (5 day) Load
(Ibs/day)
4100
6300
During October 1974, a comprehensive field
study program was conducted in the Milner Reach of
the Snake River for the purpose of verifying the
mathematical model. In-stream water quality,
industrial and municipal discharges, irrigation
return flow and river hydrologic characteristics
were measured by EPA Region X, EPA'S National
Field Investigation Center (Denver), and the State
of Idaho's Department of Health and Welfare.
Survey results indicated that irrigation
return flow was not significant between Snake
River Mile 654.0 and River Mile 640.0. In
addition, algal photosynthesis and respiration
were found to be important sources and sinks,
respectively, of dissolved oxygen. Detailed
results of this study are reported by Yearsley^ .
Comparison of predicted and observed
dissolved oxygen levels, using data from the
October 1974 field study, are shown in Figure 2.
Sensitivity of the mathematical model to random
errors in sediment oxygen demand, net algal oxygen
production, deoygenation rate, reaeration rate and
river velocity are reflected by the one standard
deviation (CT) band in Figure 2.
The success of the model in simulating field
measurements, coupled with its relative
lack of sensitivity to errors in parameter choice,
indicated that the model would be useful for the
purposes of permit writing. The model, as
described previously was applied to the permit
writing process. Algal productivity was not
included in the permit analysis, since it was
felt that this was not a reliable source of
oxygen. Simulation results also showed that when
algal oxygen production was not included in the
model, simulated dissolved oxygen levels were very
nearly the same as minimum dissolved oxygen levels
measured during the field studies.
PERMIT ANALYSIS
The State of Idaho water quality criterion
for dissolved oxygen in the Milner Reach of the
Snake River requires that the dissolved oxygen be
greater than 6.0 mg/1, or 90% saturation, which-
ever is greater. For the initial conditions
given in Table 1 and loading levels given in Table
6, model simulations indicated that these
standards would be violated whenever the flow was
less than the monthly average (Table 3). The
permits for the two discharges were, therefore,
designed such that the treatment levels varied
with the river flow. It was assumed that a ten
(10) per cent variation in dissolved oxygen at any
flow was not significant. The BOD loading from
Ore-Ida and J. R. Simplot, only, which caused this
much variation was computed, as a function of
flow. For those flows resulting in loadings
equal to, or greater, than 100 per cent of those
values given in Table 6, BPT was acceptable. For
river flows resulting in a loading between fifty
(50) and 100 per cent of the values in Table 6,
advanced waste treatment was required. When the
computed loading was less than fifty (50) per cent
of the values in Table 6, no discharge to the
river was permitted. The resulting flow
restrictions, as estimated from the mathematical
782
-------
model, are given In Table 7.
Table 7.
Month
Treatment requirements, as a
function of flow in the Snake
River, for Ore-Ida and J. R.
Simplot, in the Mllner Reach of
the Snake River.
January
(no ice cover)
January
(100 % ice cover)
March
August
October
Zero Discharge
Below
')
450 cfs
690 cfs
800 cfs
1450 cfs
700 cfs
BPT
Above
750 cfs
1030 cfs
1190 cfs
2600 cfs
1300 cfs
REFERENCES
1. O'Connor, D.J., and Dobbins, W.E., "The
Mechanism of Reaeration in Natural
Streams," ASCE Trans., Vol. 123, 1958,
pp. 641-666.
2. Kreizenbeck, R.A., "Milner Reservoir
Benthic Oxygen Demand Study," EPA Region
X, 1974.
3. Yearsley, J.R., "Evaluation of Lake Milner
Water Quality Model," EPA Region X,
Working Paper No. EPA-910-8-75-092, 1975,
81 pp.
-i-MAX - OBSERVED
646 648
SNAKE RIVER MILE
PREDICTED AND OBSERVED DISSOLVED OXYGEN
IN THE LAKE MILNER REACH OF THE SNAKE RIVER.
SURVEY ON 10/22/74 10/24/74.
LOCATION OF MAJOR INDUSTRIAL AND MUNICIPAL
DISCHARGES IN THE LAKE MILNER REACH OF
THE SNAKE RIVER, IDAHO (OCTOBER 1974)
MAIN DRAIN
tOCATION MA
FIGURE 1
783
1 AMALGAMATED SUGAR
2 RUPERT STP
3 J.R. SIMPLOT
4 HEYBURN STP
5 BURLEY STP
6 BRYANTS MEATS
7 ORE-IDA
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BUOYANT SURFACE JET
Mostafa A. Shirazi
Research Mechanical Engineer
Corvallis Environmental Research Laboratory
U.S. Environmental Protection Agency
Con/all is, Oregon 97330
Lorin R. Davis
Associate Professor
Department of Mechanical Engineering
Oregon State University
Corvallis, Oregon 97330
ABSTRACT
In order to obtain improved prediction of heated plume
characteristics from a surface jet, a comprehensive
set of field and laboratory data was correlated and
used for modification of an existing analysis due to
Prych. The correlated data was conveniently subgrouped
and used for comparisons with related predictions from
the model. This way, all the coefficients such as
entrainment, turbulent exchange, drag and shear values
were estimated based on the mean of each subgroup of
data. Modifications were made to the model to best
obtain an overall agreement with the data.
INTRODUCTION
Various mathematical models of heated surface jets are
available for the prediction of two and three dimen-
sional plume configurations. Two widely accepted
methods are used for solving the equations in these
models, namely one based on the integral analysis
approach and the other based on the differential numer-
ical analysis methods. The latter approach, while
capable of greater generality, is considerably more
costly and due to limited funds and resources was ex-
cluded from further consideration for this work. How-
ever, a certain degree of generality of results is re-
tained by considering only three dimensional plume
models herein.
A comprehensive review of thermal plume models is pre-
sented in Reference 4. Among the three dimensional
surface jet models seriously considered is one by
Stolzenbach and Harleman (MIT Model) , another by
Prych and the third model by Stefan, et al. It is
outside the scope of this paper to discuss in detail
results of all experiments on the three models during
our attempt to provide a working program. The MIT
model, despite its many fine features, runs into con-
siderable computational difficulties. Prych's model
is the result of reasonably successful attempt to re-
move from MIT's model some of these difficulties.
Stefan's model was written for the developed zone alone
and thus can't be compared with others directly. Even
though it includes wind effects absent in the other
two, it ignores the hydrostatic pressure in the longi-
tudinal direction.
In general,^the MIT and Prych models yield comparable
predictions . The greatest deviation between the pre-
dictions of both models and data is in plume width.
Both models overestimate the plume width.
An effort is made here to introduce modifications in
Prych's model to make it better agree with existing
data. These modifications as well as certain other
additions, are discussed below.
BUOYANT SPREADING
Stolzenbach and Harleman present an order of magnitude
analysis of the momentum equations as applied to the
jet. They show that the lateral acceleration of fluid
particles within the plume is neglible only when the
jet is nonbuoyant. Otherwise, the fluid particles
accelerate (spread laterally) due to the influence of
two interacting forces, namely, the inertia and buoy-
ant forces. Since the full nonlinear equations of
motion describing a buoyant plume are too difficult to
solve, the lateral spreading due to buoyant forces in
the MIT, and Prych models are calculated independently
of spreading due to nonbuoyant forces. The two
spreading rates are assumed to make additive contribu-
tions, thereby ignoring the nonlinear interaction be-
tween the two forces. As a consequence of the assump-
tions in this linearization their analyses overesti-
mate the plume width when the inertia and buoyant
forces are the same order of magnitude (i.e., when the
densimetric Froude number is not too large). When the
plume inertia forces are dominant such as with strong
ambient current or large densimetric Froude numbers,
reasonable width predictions can be obtained.
The buoyant spreading function used by Prych is based
on the analysis of an immiscible film, such as oil
spreading over water that ignores the shear interaction
between the fluid systems and the variation in density
of the lighter fluid from the edge to the center of the
plume. In this analysis, the fluid particles are
assumed to move with a velocity equal to the velocity
caused by abrupt density waves alone.
In a separate analysis of a buoyant spreading of a pool
of warm water, Koh and Fan accounted for the inter-
facial shear interaction but ignored the actual en-
trainment of the cool water. They found that near the
source the spreading velocity and the fluid velocity
used by Prych are the same, i.e.,
g'H
Where H is the local depth of the buoyant pool. How-
ever, far away from the source where the shear forces
become very important, the fluid front velocity is
V
Where g'H is proportional to c , (e/Hp) is proportional
to the shear velocity and H/B is the ratio of the local
pool depth to its width. If interpreted in terms of
plume spread, this finding implies that spreading vel-
ocity is inversely proportional to the local aspect
ratio of the plume.
The appearance of the local aspect ratio in the expres-
sion for the plume velocity offers an intuitively
appealing ground for assuming,
2 ~
(g'H)(H/B)
This can also be explained as follows. The lower den-
sity of the plume causes it to rise slightly about the
free surface of the surrounding water. The height of
rise at any point is proportional to the local verti-
cal density difference between the plume and the
ambient and the depth of the plume at this point.
Since both the density difference and depth of the
plume decrease from the center to the edge, this
height varies from a maximum at the center to zero
at the edge causing the plume to spread in that dir-
ection. The spreading rate due to buoyancy is re-
lated to the slope of this free surface. Since the
784
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height of rise at the center is proportional to
gAp H/p, the slope of the free surface and thus the
spreading rate is a function of gAp H/pB.
This slight modification to Prych's analysis was intro-
duced in the model. As a result, a satisfactory fit
with data became possible.
DEVELOPMENT LENGTH
Analysis of the jet development zone is complicated
because of the need to examine simultaneously the
characteristics of a core region as well as a tur-
bulent outer jet region. Stolzenbach and Harleman
developed a three dimensional program for this re-
gion, but in his modification of the program, Prych
adopted a one dimensional approach in which he em-
ployed celerity relations for the spreading of the
buoyant unmixed core region. He then used the appro-
priate conservation equations to relate the fluid pro-
perties at four jet diameters away from the outlet to
the fluid properties at the outlet. The fixed develop-
ment length of four diameters is based on the assump-
tion of a semicircle with an area 2 B H . Prych's
development length S. can be written as
j|i = 6.38A1/2
where A is the channel aspect ratio.
Note that the above development length does not change
with the initial densimetric Froude number. However,
calculations with the MIT model show that the develop-
ment length does change with initial densimetric
Froude number as well as the jet aspect ratio.
Since a better agreement of model predictions with
the data is expected if this aspect of the model is
also appropriately adjusted, resort was made to labora-
tory experiments to obtain this information. Experi-
ments were conducted in a still water tank with a
heated jet at the EPA Corvallis Environmental
Research Laboratory. Several jet aspect ratios and jet
densimetric Froude numbers were tested. A hot film
anemometer probe was used to traverse the jet develop-
ment zone laterally at several stations downstream
from the outlet. The presence of the core was detected
from subdued turbulent temperature fluctuations as well
as the temperature level. The coincidence of the
increased turbulence fluctuations, the beginning of the
temperature drop, and the disappearance of a uniform
core at a point downstream of the outlet signaled the
end of development zone. The data for this length was
correlated to give
!l _ 5 4 /A^l/3
Ho ' V
This tentative result is subject to refinement (parti-
cularly with respect to the effect of the ambient cur-
rent) when better experimental investigations currently
underway become available. Meanwhile, the use of this
correlation was found very helpful to fit the model
with available plume data.
FITTING THE MODEL WITH DATA
Reference 2 provides a comprehensive set of data that
is a good representation of available experiments
both in the field and laboratory. The data provide a
wide range of plume conditions with which one can test
and accordingly adjust numerous analytical functions of
the plume model. The plume model contains a number of
free variables such as entrainment coefficient E , tur-
bulent exchange coefficients E, , E , drag coefficient
CD and shear coefficient Cp. The magnitudes of these
coefficients must be prespecified so that the model
produces the best fit with the measured plume charac-
teristics.
In order to accomplish this task, the following pro-
cedure is adopted: (a) Data for plume character-
istics are subgrouped with a narrow range of certain
experimental parameters such as the current ratio, R,
the densimetric Froude number, F , the jet aspect
ratio, A, and the angle of discharge, 0 . Each sub-
group consists of several experiments and several
sources, thus providing considerable degree of realism
with respect to possible experimental scatter and var-
iations in experimental parameter scales. The choice
of a narrow range in certain experimental parameters
was dictated by the desire to obtain as strong a cor-
relation of the data within a given subgroup as pos-
sible, (b) For each subgroup, the range and the mean
of all experimental parameters are determined, (c) The
data are correlated using dimensional analysis and
multiple regression methods separately for each sub-
group following the procedure outlined in Reference 2.
(d) The measured plume characteristics are plotted
against dimensionless axial distance using the cor-
relation results, (e) A representative smooth curve
is drawn through the mean data and local standard
deviations are displayed on both sides of the mean
curve to show the scatter. This mean curve is a fair
representation of the subgroup, and is represented by
the mean parameters obtained in item b above, (f)
Finally, the program is used to calculate the plume
characteristics in each subgroup for the mean of the
experimental parameters R, F, A, and 0 . Agreement
between the calculated characteristics and the data
mean is sought by adjusting one or more of the model
coefficients E , E. , E , DD and Cp. This process is
repeated for several subgroups, adjusting in each
trial one or more coefficients until best fits are
obtained to plume characteristics for all subgroups.
It should be pointed out that correlations of each
data subgroup are useful mainly for the mean data in
that subgroup. They are not universal correlations
and cannot be used outside the data range they re-
present.
The data set most suitable for determining the effects
of ambient turbulence on plume behavior is provided
by Weil ' . In his experiments, Weil injected heated
water at the surface in a turbulent channel from a
semi-circular jet at a relatively large densimetric
jet Froude number. The discharge was in the direction
of the channel current (0 0). The jet velocity in
all his experiments was held equal to the local chan-
nel flow velocity. Since the relative velocity be-
tween the plume and ambient water is zero and since
buoyancy effects are small due to a high Froude num-
ber, dilution is largely due to turbulence effects.
For the conditions of this experiment, the following
simplifications can be introduced in the mathematical
model: (a) there is no relative velocity between the
jet and the ambient water. Therefore the contribution
of the terms containing the entrainment coefficient,
E , can be set equal to zero, (b) For the same reason,
contribution of terms containing the shear coefficient,
Cp, is also zero, (c) The drag coefficient CQ, is
zero because the jet is parallel to the ambient cur-
rent and the pressure distributions on the left and
right hand sides of the plume are identical, (d) For
the dimensionless surface heat exchange coefficient,
one can choose a typical value of K 10" without
affecting the calculated plume characteristics greatly
one way or another, because we are dealing with small
areas and small temperature differences, (e) Since
the jet densimetric Froude number is high, the
785
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influence of the buoyant forces on the plume, spread is
not substantial. The plume width grows predominantly
due to turbulent entrainment of the ambient water, a
mechanism which the model accounts for through Eh and
v'
Figure 1 is the plot of correlated temperature data
showing the local mean and standard deviations. Figure
2 is the replot of the mean temperature data together
with several computer calculations based on the model
for F 16, A 2, 0 0, and K = 10" . Calculations
are made for several°values of E, and E /E, as well as
the free factor of the spreading function, XK1. The
plots for the calculated and measured plume width data
L EGEND
LABORATORY DATA
RER2),WEIL(I9T2)
• LOCAL ME AN OF DATA
• LOCAL STANDARD DEVIATION
10
100
Fig. 1 Correlated Temperature Data for Coflow
Discharge, R=l
io'r
Fig. 2 Comparison of Calculated Temperatures with
Measured Plume Temperature Data of Fig. 1
Fig. 3 Comparison of Calculated and Mean Measured
Widths for Coflow Discharge, R=l
are shown in Figure 3. The measured width data were
closely spaced with excellent correlation. For this
reason individual data points were not plotted.
Instead, a narrow band showing the spread of all exper-
mental data are presented.
A visual inspection of Weil's data of Figures 2 and 3
shows that the best fit is obtained with E, = .02, E /
Eh .2 and XK1 = 1.4.
The next group of data consists of information from
several sets of laboratory and some field experiments
for a surface discharge in zero or negligibly small
cross current. The correlation of temperature data are
plotted in Figure 4 and the width data in Figure 6.
Fig. 4 Correlated Temperature Data for Discharge into
Zero or Negligible Ambient Current
OMPUTED FOR Eh •-02. E •-2 . '
8 f * " E0 c, ;
O 8.3 Z.O
~t V 2.0 20
'A 30 23
' 0 Zfl
' f 2.
It) ^
I.O
-------
~ 10' ~^
t- ; -|furT7/7f'''r \fr L"E«
Fig. 6 Correlated Width Data for Discharge into
Zero or Negligible Ambient Current
itf
10°
10
Fig. 7 Comparison of Calculated Widths with Mean
Measured Surface Plume Width Data of Fig. 6
For given values of discharge angle, Froude number,
aspect ratio, and ambient current, the plume trajec-
tory is mainly influenced by the entrainment of am-
bient fluid with a minor influence due to pressure
drag. Since the entrainment coefficient is prescribed
from the above, only the drag coefficient can be used
to further adjust the trajectory. Consequently, we
need to regroup the trajectory data for a reasonably
wide range of all plume parameters mentioned above.
Such data are plotted in Figure 8 showing the-data
sources, the local mean and standard deviations. Fig-
ure 9 is a replot of the mean trajectory showing the
comparison with computed values. It is found that the
best fit is with C = 1.0.
Fig. 9 Comparison of Calculated and Mean Measured
Trajectory Data of Fig. 8
In order to complete the adjustment of the model to fit
the data, we need to check the model against measured
plume width and temperature for a wide range of para-
meters. If agreement is obtained with such data with-
out the need to readjust the previously specified co-
efficients E , E, , E , CF and CD, then the fitting of
the model with data is considered complete.
The raw data and calculated values based on previous
coefficients are compared in Figure 10 for plume width
and Figure 11 for plume temperature. The agreement
obtained from the comparison of calculated and measured
plume width is excellent and the agreement for plume
temperature is reasonably good.
X/Hn
Fig.
10 Comparison of Calculated and Measured Width
Data for Discharge into a Cross Current
Fig. 8 Correlated Trajectory Data for Discharge
into an Ambient Current
Fig. 11 Comparison of Calculated and Measured Temp-
erature Data for Discharge into a Current
787
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DISCUSSION
Entrainment coefficient
A notable degree of data scatter could not be avoided
when attempting to correlate information on plume
characteristics from several sources. Physical factors
not included in the data analysis, but which are be-
lieved to have contributed to the data scatter are:
a) the lack of a universal simple exponential correla-
tion such as used in this report; b) the influence of
diverse turbulence scales, c) the influence of surface
heat transfer, d) time dependency and boundary effects,
and 3) instrumentation and experimental errors.
The exponential correlations employed are intended for
data presentation in a compact form within each data
grouping. They are not used to explain the physics of
the problem exclusive of the mathematical model. They
do, however, provide a statistical presentation of the
level of data scatter one can expect when dealing with
data from numerous sources.
There are at least two reasons why data from more than
one source should be used. These are: (1) there
exists no single set of data that covers a sufficiently
wide range of parameters relating to initial jet condi-
tions and ambient current; (2) data obtained for a wide
range of ambient turbulence levels are reported in the
literature. While the ambient turbulence level and
turbulence scale affect the plume characteristics, in-
formation on these parameters is lacking in nearly all
the data reported. It is felt, therefore, that a plume
analysis based on several sources carries a greater
degree of realism than one based on a single source.
It should be noted that the turbulence exchange coef-
ficient in the model is back-calculated based on the
best fit with the data. The coefficient is entered
in a form of a turbulent Reynolds number (H U0/e)~
where e is the turbulent eddy diffusivity and H and
U are the jet depth and velocity respectively. In
tnis manner, even though diffusivities are not
directly measured in each experiment the use of the
model does provide an indirectly calculated value for
the correlation parameter e/H U that best represents
the available data. If in a given application one has
a better knowledge of this or any other coefficients
entering the model then, of course, those should be
used in the model instead.
Calculations based on the foregoing modified sur-
face jet model are presented in great detail in Ref-
erence 11. That workbook provides a compilation of
numerous nomograms suitable for use in practical pro-
lems. Even though the computer program and sample
examples are also given, the use of the workbook
directly might be preferrable to the majority of the
users.
LIST OF SYMBOLS
B Local characteristic width of jet /20
BQ Half width of outlet
B^g Plume half width 177 an
Cp Form drag coefficient
Cp Interfacial shear drag coefficients
c Celerity of a density front
D Local plume depth = 2a
E, Dimensionless horizontal eddy diffusion coeffi-
cent eh/UoHo
EV Ratio of vertical to horizontal eddy diffusion
coefficients E /E,
Densimetric Froude number at outlet, U //g'H
Acceleration due to gravity
Reduced gravitational acceleration g Ap/p
Local characteristic thickness of jet
Depth of outlet
K Dimensionless heat transfer coefficient lO/pc U
1C Atmospheric heat transfer coefficient
s Curvilinear coordinate along jet centerline
S. Distance from outlet to end of initial zone.
AT Local excess water surface temperature on center-
c line
AT Difference between outlet and ambient water temp-
peratures
TH Angle between positive S- and X- directions (0)
U Local excess jet velocity on jet centerline
U Discharge velocity from outlet
X Rectilinear coordinate parallel to ambient current
Y Rectilinear coordinate, horizontal and perpendi-
cular to X
Z Coordinate in vertical direction
V Ambient current velocity
a Angle used in data analysis of Ref. (2) a = Tr-00
Ap Difference between outlets and ambient water
densities
E, ,EV Ambient turbulent diffusion coefficient for
horizontal and vertical directions
0 Angle between X axis and outlet velocity direc-
tion
v Kinematic viscosity
p Fluid density
SUBSCRIPTS
a Ambient conditions
c Centerline value at surface
i Refers to variables at end of development zone
o Discharge conditions
788
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REFERENCES
1. Prych, Edmund A. "A Warm Water Effluent Analysis
as a Buoyant Surface Jet" Swedish Meteorological
and Hydrological Institute, Series Hydroli, Nr 21,
1972.
2. Shirazi, Mostafa A., "Some Results from Experi-
mental Data on Surface Jet Discharge of Heated
Water" Proceeding of the International Water
Resources Association, Chicago, 1973 (see also
Reference 12).
3. Stolzenbach, K. D. Harlemann, D. R. F. "An Analy-
tical and Experimental Investigation of Surface
Discharges of Heated Water." Water Pollution
Control Series 16130 DJV 02/71, February, 1971.
4. Policastro, A. J. and Tokar, J. V. "Heated
Effluent Dispension in large Lakes: State-of-the
art of Analytical Modeling Part I, Critique of
Model Formulations? Argonne National Laboratory
ANL/ES-11 January 1972 (see also Reference 12).
5. Stolzenbach, K. D., Adams, E. E. and Harleman, D.
F. "A User's Manual for Three-Dimensional Heated
Surface Discharge Computations" Environmental
Protection Technology Series EPA-R2-73-133, Jan.
1973.
6. Koh, R. C. Y., Fan, L. N. "Mathematical Model for
the prediction of Temperature Distributions Resul-
ting from the Discharge of Heated Water into Large
Bodies of Water" Water Pollution Control Series
16130 DWO 10/70, October 1970.
7. Stefan, Heinz. Personal Communication (see also
Reference 13).
8. Weil, J. "Mixing of a Heated Surface Jet in Tur-
bulent Channel Flow" Report No. WHM-1, Department
of Civil Engineering, University of California,
Berkeley, June 1972.
9. Ellison, T. H., and Turner, J. S., "Turbulent En-
trainment in Stratified Flows." Jour, of Fluid
Mechanics, Vol. 6, Part 3 p. 423-448.
10. Stefan, Heinz, Hayakawa N., and Schiebe, F. R.
x "Surface Discharge of Heated Water" Water Pollu-
tion Control Research Series 16130 FSU 12171,
December 1971.
11. Shirazi, Mostafa A., and Davis, Lorin R. "Work-
book of Thermal Plume Prediction." Vol. 2,
Surface Discharge, Environmental Protection Tech-
nology Series, EPA-R2-72-005b, May 1974.
12. Dunn, W., Policastro, A. J. and Paddock, R.
"Surface Thermal Plumes: Evaluation of Mathe-
matical Models for the Near and Complete
Field" Argonne National Laboratory ANL/WR-75-3,
Part One May 1975, Part Two August 1975.
13. Stefan, Heinz, Bergstedt, Loren and Mrosla,
Edward, "Flow Establishment and Initial En-
trainment of Heated Water Surface Jets" Envir-
onmental Protection Agency, Ecological Research
Series EPA-660/3-75-014.
789
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AGROECOSYSTEM A LABORATORY MODEL ECOSYSTEM
TO SIMULATE AGRICULTURAL FIELD CONDITIONS
FOR MONITORING PESTICIDES
M. Leroy Beall, Jr, Ralph G. Nash § Philip C. Kearney
USDA.ARS, Agricultural Environmental Quality Institute,
Pesticide Degradation Laboratory,
Beltsville Agricultural Research Center,
Beltsville, Maryland 20705
ABSTRACT
Quantitative measurements of rates and modes of disap-
pearance of pesticides under field conditions are dif-
ficult to obtain because environmental parameters can-
not be satisfactorily controlled and monitored. A
laboratory model agroecosystem was constructed to
simulate field conditions which permitted simultane-
ous measurement of pesticide residues in soil, plants,
water and air. The design and construction of five
agroecosystems are described in detail. The first
phase of research in the agroecosystem was devoted
to measuring pesticide residues in air.
Our agroecosystem has a number of advantages, i.e. it
is inexpensive, easy to operate, monitor, and sample;
versatile in the number of plants and soils that can be
studied; adjustable to rainfall and potentially adjust-
able to wind velocity, light intensity and duration;
and conducive to balance studies where pesticide mobil-
ity can be compared under similar conditions. It has
an advantage over previous systems because the large
volume of air exchanged provides cooling, prevents
moisture condensation, and permits sufficient air sam-
ple volumes for measurement of very low residue concen-
tration. The aerial residues in the exhaust air are
trapped on polyurethane foam plugs, which are sampled
periodically. Initial results demonstrated that toxa-
phene and DDT volatilized off of fiber-glass cloths
and cotton leaf surfaces, but the rate of volatiliza-
tion decreased very rapidly with time. Efficiency of
trapping by the polyurethane plugs was very high with
recoveries
Our initial objectives are to test the utility of the
agroecosystem for comparing the mobility of different
classes of pesticides and thereby identifying potential
environmental problems. Our long-term objectives are
to explore the possibilities of determining bioaccumu-
lation of pesticides in terrestial organisms and in-
terfacing our system with other model ecosystems,
particularily the aquatic ecosystem. Our ultimate
objective is to devise methods of reducing pesti-
cide mobility.
BACKGROUND
Monitoring the behavior and disappearance of pesticides
under field conditions is often difficult for a variety
of reasons. Among these is an uneven pesticide distri-
bution on plant or soil surfaces, drift, and volatili-
zation during and after application. Accurate air sam-
pling is difficult because of changes in wind currents.
In an attempt to somewhat control field variability,
glass chambers (agroecosystems) were designed and built
for monitoring pesticides in the air, soil, water, and
on plants. The chambers are large enough to grow many
crop species to maturity. Although the concept of
model ecosystems for air sampling is not new (Hill et
al. 1971), our system was designed to incorporate a
new method of sampling air for pesticides. Further,
our system is inexpensive compared to elaborate growth
chambers. The method consists of drawing air through
flexible porous polyurethane foam filters, then extract-
ing the filters with an organic solvent to remove the
pesticide for analysis.
In 1970, Bowen reported the absorptive properties of
polyurethane foam and used this material to concentrate
metallic ions from dilute aqueous solutions. In 1971,
Gesser et al. successfully used polyurethane foam to
absorb polychlorinated biphenyls (PCB) from water and
mentioned that the foam was not specific for PCB, but
could absorb organochlorinated pesticides as well. In
1974, Bidleman and Onley found the foam to be highly
efficient in trapping PCB from air. We were introduced
to the possible use of polyurethane foam for trapping
pesticides in air by Taylor, Glotfelty and Turner
(1975).
MODEL AGROECOSYSTEM DESCRIPTION
Chamber Construction
Five retangular chambers were constructed (Renwar
Scientific Co., Gaithersburg, Md. 20760) and placed
in the greenhouse (Fig. 1 and 2). The chambers were
constructed from 3/8" (1-cm) plate glass and held to-
gether with clear silicone aquarium cement. All
sides, top, and bottom were made of glass to assure
a minimum of pesticide adsorption and ease of clean-
ing between experiments. Inside dimensions are 150
cm long, 115 cm high and 50 cm wide. After allowing
for a 15-cm soil layer, the remaining volume is
0.75 m3. To add rigidity and to protect the bottom
of the chamber, each chamber was assembled directly
and remained permanently in a 3/4" (1.9-cm) plywood
tray lined with 1/4" (0.6 cm)-thick felt padding
to absorb shock. Walls of the tray are 15 cm high.
The chambers were set at a 1% slope back to front.
For servicing, one side of each chamber is equipped
with two sliding access panels (72.4 cm high) which
ride in felt-lined aluminum channels. Each panel
contains two 2.5-cm finger holes for sliding or lift-
ing. When closed, the panels butt against each other,
cushioned and sealed by a strip of polyurethane foam
weather stripping attached to the end of one panel.
Centered in the front-end of each chamber are two 2.5-
cm holes; 5 and 15 cm from the bottom. The lower hole
is used to siphon off soil-leachate water and the up-
per hole is used to collect run-off water. Both ends
of each chamber contain 12 5-cm holes for air intake
and exhaust. They are centered 20 cm apart vertically
and 16.7 cm horizontally, beginning 35 cm from the
bottom of the chamber.
Sprinkler Construction
To simulate rain, each chamber is equipped with a
790
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Fig. 1 - Front angle closeup of a model agroeco-
system. Note the 12 polyurethane foam
plugs in the glass thimbles protruding
into the manifold box.
sprinkler system, centered and running the length of
the chamber 2 1/2" (6 cm) from the top (Figs. \, 2,
and 3). Each system was fashioned from standard 1/8"
brass pipe (ca. 0.6 cm i.d.)> threaded fittings, and
four spray nozzles spaced 37.5 cm apart. The noz-
zles (Model 1/8TTG0.3 from Spraying Systems Co., Whea-
ton, 111.) each deliver 0.042 gal (159 ml) of water
per min at 20 p.s.i. and give a solid cone spray
pattern. When "rain" is desired, tap water is suppli-
ed to a sprinkler system through a small rubber hose
fitted with a quick release coupler. Water supply is
controlled by an adjustable pressure regulator and
timeclock-controlled solenoid valve. At 20 p.s.i., 1"
(2.5 cm) of "rain" is delivered in ca 29 min.
Manifold Construction
An equal amount of suction to each of the 12 exhaust
holes is provided by a rectangular manifold box (Fig.l)
constructed from 1/4" (6.4 mm) clear acrylic plastic
sheet and reinforced inside with six pieces of extruded
acrylic tubing 3/4" (19 mm) o.d., 1/2" (12.7 mm) i.d.
One end of the manifold contains 12 2 1/4" (5.7-cm)
diameter holes to line-up with the 12 exhaust holes in
the front of the agroecosystem chamber. Centered on
the other end of the manifold is a 5" (12.7-cm) exhaust
hole into which was cemented a piece of 12" (30.5-cm)
acrylic tubing, 4 1/2" (11.4 cm) i.d. which extends
from the manifold box and is reinforced with a 5/8"
(1.6-cra) thick x 7" (17.8-cm) square acrylic collar
cemented to both the manifold box and the exhaust tube.
A 1/2" (1.3-cm) hole, 1 7/8" (4.8 cm) from the blower
end, allows entrance for a hot-wire anemometer probe
for measuring air speed in the tube. A 1" (2.5 cm)
hole is located on one side of each manifold for a man-
ometer connection.
Final connection of the manifold exhaust tube to a suc-
tion fan was made with a 9" (22.8-cm) length of 5"
(12.7 cm) i.d. flexible-spring-steel-reinforced nylon
and vinyl covered hose. This provides an overall dis-
tance of 50 cm between the manifold and suction fans.
Fig. 2 - Overall view and spatial arrangement in
the greenhouse.
Wooden benches support the suction fans and manifold
boxes. Latex caulking provides an air-tight seal be-
tween the manifold box and agroecosystem chamber.
Air System
Air is pulled through the chamber using a 115 V, 1/3 HP
high-pressure direct-drive blower (suction fan) for
each chamber. These suction fans provide ca 3 m3/min
air at ca 13-cm water pressure under our conditions.
The high-pressure suction fans were necessary to pull
air through filters that were positioned in each of
the 12 air-exhaust holes of the chamber.
Air movement through a chamber, provided by suction
fans, serves three purposes; 1) to collect volatilized
pesticides, 2) to provide cooling, and 3) to prevent
moisture condensation inside the chamber. Air volumes
are calculated by measuring air velocity with a hot-
wire anemometer in the tubing which separates the suc-
tion fan and manifold box. A mean velocity for each
set of 12 plugs is determined by taking 11 measure-
ments (10 equal annular areas and a central circle) at
the intersections of a diameter and the set of circles
which bisect the annuli and the central circle. Mea-
surements are taken on each side of the cross section
at V(2n-l)/10 (n=l,2,3 to 10/2) of the tube radius
from the center (Perry et al., 1963). In our case, we
could only obtain 9 velocity measurements because the
physical size of the anemometer prevented measuring of
the outer cross-sectional areas. Therefore, the lowest
measurement obtained on each side was doubled to approx-
imate measurements 10 and 11. The outer velocity mea-
surements were very low compared to the central circle
and the adjacent cross-sectional areas. Typical mea-
surements ranged from 600 to 2000 ft/min (183 to 610
m/min), with the two outer measurements slightly higher
than their adjacent inner measurement. The unorthodox
velocities near the edge apparently results from turbu-
lance in the short 50-cm length of the tube plus flex-
ible hose between the manifold and suction fan.
Although there was some variation among chambers and
among sets of plugs in a given chamber, airflow aver-
aged 2.9 +_ 0.3 m3/min (mean of five chambers and stan-
dard deviation). This flow rate translates to an
average air speed of 0.22 mph (0.35 km/hr) through the
chambers. Our system, therefore simulates calm wind
conditions.
Trapping Filters
Pesticide trapping filters were made by cutting 2"
791
-------
(5-cm) circular plugs from 2" (S-cm) thick polyure-
thane foam. Cutting was done with a twisting motion
of a length of brass pipe sharpened on one end like
a cork borer. Ti.e foam used was a dark gray, ester
base, open cell type with a density of 2 Ib +_ 10% per
ft (ca. 0.032 g/cc) manufactured by the William T.
Burnette Co. of Baltimore, Md. Prior to use, the
plugs were extracted for 12 hr with hexane:acetone
(1:1 v/v) in a Model 11EX/H1 Jobling extractor rigged
for Soxhlet extraction. Approximately 46 plugs can be
extracted at one time if carefully stacked in the
extractor. After extraction, the plugs were squeezed
fairly dry and stored in a large rectangular chroma-
tography jar. The remaining solvent is allowed to
evaporate before use.
Plugs are held in place (in each of the 12 exhaust
holes of an agroecosystem chamber) by thimbles (Fig.
1) fashioned from 45 mm i.d. borosilicate glass tube
with 2-mm walls (Renwar Scientific Co.). Total
length of the thimble is 68 mm. The intake end of
the thimble is expanded to 46 mm i.d. for 30 mm of
its length to allow easier insertion of a plug. The
rim of the intake-end has a 3-mm rounded lip to re-
tain a rubber 0-ring for sealing and to prevent the
thimble from going all the way through an exhaust
hole. The exhaust end of the thimble contains a glass
rod grill to retain the foam plug. The thimbles are
installed from inside the agroecosystem chamber and
protrude out into the manifold box.
Fig. 3 - Rear angle closeup showing some of the air
intake filters and part of the sprinkler
system.
Each of the 12 air intake holes on the back of the
agroecosystem chamber is fitted with a 2 5/8" (6.7-cm)
diameter disk of 1/8" (0.3 cm) thick polyurethane foam
air filter to prevent the entrance of insects and dust
(Fig. 3). Filter holders were fashioned from clear
acrylic tubing. The holder body consists of a 1 7/16"
(3.7-cm) length of tube 2" (5 cm) o.d.^ 1 3/4" (4.5 cm)
i.d. with a 3/8" (0.9S-cm)-wide ring collar [made from
2 1/2" (6.4 cm) o.d., 2" (5.0 cm) i.d. tube] concen-
trically positioned and cemented 9/16" (1.4 cm) from
one end. The collar limits the distance that the hold-
er can enter the air intake hole. The filter disk is
installed by placing it over the outside end of the
holder body then pressing a removable ring (same size
as the ring collar above) over the disk and holder
body. This mechanism provides a quick and simple meth-
od for changing the filter disks. Each filter holder
is removable but held firmly in its hole in the agro-
ecosystem chamber when pressed through a 2" (5 cm) i.d.
rubber 0-ring which is cemented around the periphery
of the chamber hole. These filters result in slight
(0.2 to 0.5 cm water) negative pressure inside the
chambers.
Temperature and Lighting
The chambers are subjected to normal greenhouse tem-
perature fluctuations, however, air flow through the
systems prevents excessive heat buildup and moisture
condensation. On hot sunny days, chamber tempera-
tures may occasionally reach 3°C above ambient green-
house temperatures. Some moisture condensation was
observed on very cool but bright days after the plants
filled the chambers.
Recently, a 180 W low pressure sodium vapor light was
installed (not shown in Figs.) 5 cm above each of the
agroecosystem chambers. The 42" (107 cm)-long tubu-
lar lights (from Norelco-North American Phillips
Lighting Corp., Highstown, N. J.) are time-clock con-
trolled and can be used to supplement and/or extend
daylight periods.
PRELIMINARY TESTS WITH FOAM PLUGS
Extraction Efficiency
Since DDT (1,l,l-trichloro-2,2-bis[£-chlorophenyl]-
ethane) and toxaphene (chlorinated camphene,67-69%
chlorine) were selected to be used in our first agro-
ecosystem experiment, it was necessary to develop a
method of extracting these pesticides from the plugs.
A group of randomly selected plugs (pre-extracted with
hexane:acetone[1:1 v/v]) were treated with ^C-labeled
DDT or toxaphene. Treatment consisted of making five
100 yl injections of a benzene solution randomly into
each plug. Each plug received a total of 141pg of DDT
or 675 us of toxaphene. Solvent was allowed to evapor-
ate prior to extraction trials. Soxhlet extraction
with 150 ml of petroleum ether (30-60°C b.p.) proved
to be quite effective. Scintillation counting of ali-
quots of the concentrated extracts showed that quanti-
tative recovery (based on four replications) of both
DDT and toxaphene was obtained in four hours (one plug/
Soxhlet). Even with two plugs/Soxhlet, 97.2% of the
DDT and 96.8% of the toxaphene was recovered in only
two hours.
Pesticide Trapping Efficiency
To test the pesticide trapping efficiency of the foam
plugs under conditions similar to the agroecosystems,
a plug testing system was built. The system consists
of a manifold box connected to a high-pressure suction
fan and a set of 12 special plug-holding thimbles. The
manifold box and suction fan are essentially identical
to those used with agroecosystems, except that the box
lays horizontally with the exhaust tube in one end and
the 12 intake holes facing upward. The glass test
thimbles were made identical to those used in the agro-
ecosystems except that a 5-cm-long widened (5.9 cm i.d.
6.4 cm o.d.) extension tube was added at their rims.
The thimbles fit down into the 5-cm diameter holes in
the manifold box with the extension tube remaining out-
792
-------
side. A rubber 0-ring around the thimble (just below
the widened extension tube) provides a seal. Polyure-
thane foam plugs are placed down into the thimbles,
then a 10-cm-square piece of loosely woven fiberglass
cloth is placed over the end of the thimble extension.
The cloth is held in place by pressing a snug fitting
plastic ring around the cloth and the rim of the ex-
tension. The cloth provides a surface on which a pes-
ticide can be applied. Pesticide molecules volatiliz-
ing from the cloth are trapped by the plug as air flows
through the testing system. With the suction-fan run-
ning, organic solvents evaporate quickly from the
cloth, thus, repeated applications of ca. 100 yl of
pesticide solution can be made if necessary. Suction
created by the fan assures that the volatilizing pesti-
cide is drawn toward the plug.
At the end of a run, the cloths and plugs are removed
from their thimbles and analyzed for pesticide content.
Pesticide trapping efficiency is determined by summing
the amounts in the plugs and on the cloths. If the to-
tal is less than the amount applied, the difference is
assumed to be the amount not trapped by the plugs.
DDT and toxaphene were tested on the system at room
temperature and were both found to be effectively trap-
ped by the plugs. Hexane solutions of 11(C-labeied DDT
or toxaphene (500 yg pesticide/thimble) were applied
and the suction fans allowed to run continuously for 72
hr. At the end of the run the plugs and fiberglass
cloths were Soxhlet extracted for 4 hr with 150 ml pet-
roleum ether. Aliquots of the concentrated extracts
were counted by liquid scintillation. Of the amounts
originally applied to the cloths, 97.45% of the DDT and
99.02% of the toxaphene were accounted for, based on
four replications. Of the DDT applied, 30.42% remained
on the cloths, while 67.03% was found in the plugs. Of
the toxaphene applied only 8.99% remained on the cloths
while 90.03% was found in the plugs. Of the amounts of
the pesticides that actually volatilized, the plugs
trapped 96.33% of the DDT and 98.92% of the toxaphene.
During the 72 hr run, approximately 922 m3 of air pass-
ed through each plug.
Efficiency of trapping by the plugs was further tested
by applying toxaphene and DDT to fiber-glass cloths as
above and harvesting the plugs at 0.5, 2.5, 24, 72, 144
and 168 hr. Fresh plugs were installed at each time
period, but the original treated cloths were reinstal-
led. The plugs were extracted for 4 hr. After 168 hr
97.24% of the toxaphene could be accounted for and
99.90% of the DDT. The fiber-glass cloths contained
6.13% of the applied toxaphene and 56.78% of the DDT,
while the accumulative sets of plugs contained 91.11%
of the toxaphene and 43.12% of the DDT. These two ex-
periments demonstrated that the polyurethane plugs were
very efficient absorbers of volatilized toxaphene and
DDT whether the time period was short (0.5 hr) or long
(72 hr).
Test Run
For the first experiment, cotton (Gossypium hirsutum
L., var. 4-42-77 glanded) was treated weekly for 6
weeks with commercial emulsifiable toxaphene and DDT.
DDT was sprayed at the rate of 1.33 kg/ha the first 2-
weeks, then 1 kg/ha thereafter. Toxaphene rates were
double that of DDT. Two chambers were used for DDT
and two for toxaphene, leaving one for a control.
The polyurethane foam plugs were harvested and
replaced with clean plugs at 0.5, 2.5, 24, 72 and 144
hr after each application. The plugs were extracted
and the extract analyzed by gas-liquid chromatography.
The highest insecticide residue concentration in the
air occurred the first 30 min (Table 1), then decreas-
ed very rapidly with time. After 6 days, residue con-
centration was only about 5% of that found initially.
Toxaphene was more volatile than DDT. The amount of
toxaphene volatilized was consistently more than double
that of DDT, though the treatment rate was just twice
as much. Repeated insecticide applications had little
effect on the magnitude of the values obtained after
an additional application. The magnitude of the values
appeared to be affected more by ambient temperatures
than by repeated applications. Even though there was
considerable variation in aerial residue concentrations
among treatments, the shapes of the curves were almost
identical when aerial concentration was plotted against
time. A more detailed presentation of the results is
under preparation for a following publication.
Table 1. Toxaphene and DDT volatilization from
an agroecosystema
Hours
Compound
after Toxaphene
treatment
0
2
.5
.5
24
72
144
15.
9.
2.
1.
0.
,108
,046
.414
,425
,815
p_,p_ -DDE
Wg/
0.
0.
0.
0.
0.
097
065
017
008
005
o,p_ -DDT £,
1.
0.
0.
0.
0.
,033
,746
,231
,087
.032
1.
1.
0.
0.
0.
p_ -DDT
720
292
445
175
112
amean of six weekly treatments
Mention of proprietary products does not imply endorse-
ment or approval by the U.S. Department of Agriculture
to the exclusion of other suitable products.
REFERENCES
1. Bidleman, T. F. and C. E. Olney. 1974. High-volume
collection of atmospheric polychlorinated biphenyls.
Bull, of Environ. Contam. and Toxicology. 11:442-450.
2. Bowen, H. J. M. 1970. Absorption by polyurethane
foams; new method of separation. J. Chem Soc.
(Sec. A) 1082-1085.
3. Gesser, H. D., A. Chow, F. C. Davis, J. F. Uthe and
J. Reinke. 1971. The extraction and recovery of
polychlorinated biphenyls (PCB) using porous poly-
ethylene foam. Analytical Letters. 4:883-886.
4. Hill, A. C. 1967. A special purpose plant environ-
mental chamber for air pollution studies. J. Air
Poll. Control Ass. 17:743-748.
5. Perry, R. H., C. H. Chilton and S. D. Kirkpatrick,
Editors. 1963. Chemical Engineers Handbook, 4th ed.
McGraw-Hill Book Co., New York, N.Y.
6. Taylor, A. W., D. E. Glotfelty and B. C. Turner.
1975. Personal Communication. USDA,ARS,AEQI, Agri-
cultural Chemicals Management Laboratory, Belts-
ville, Md,
793
-------
A CONCEPTUAL MODEL FOR ECOLOGICAL EVALUATION OF
POWER PLANT COOLING SYSTEM OPERATION
Marc W. Lorenzen
Senior Research Engineer
Tetra Tech, Inc.
Lafayette, California
Summary
Mathematical models can be useful tools to
systematically analyze the impact and signi-
ficance of cooling system operation. Such
models, to have predictive value, must con-
sider the important physical, chemical, and
biological processes associated with the cool-
ing system. The first and perhaps the most
important stage of this model conceptuali-
zation was to select a suitable physical
representation of the system. The selected
representation provides realistic approxima-
tion of entrainment probability, residence
times, and material transport in the aquatic
ecosystem, the power plant, and the interface,
which includes intake and discharge zones.
For a given location, there are physical and
chemical properties and biological components
including phytoplankton, zooplankton,
benthic animals (eggs and larvae), and fishes
(eggs, larvae, young, and adult). Inter-
actions among these components are approxi-
mated by kinetic expressions for biological
and physical processes with particular
emphasis on the effect of temperature. The
population dynamics of organisms can be
influenced by entrainment and the imposed
temperature regime. Both direct and second-
ary impacts of cooling system operation can
thus be calculated for interpretation.
Introduction
Installation and operation of large cooling
systems may produce many environmental effects.
Planktonic organisms(phytoplankton, zoo-
plankton, fish eggs, fish larvae, and benthic
animal larvae) may be entrained and suffer
direct biological damage: thermal shock,
thermal death, mechanical stress and other
disruption. At the point of discharge, more
organisms may be subject to plume entrain-
ment, thermal shock and turbulence. Dis-
location of organisms between intake and dis-
charge points may also be significant. The
heated physical environment in the discharge
area may influence the distribution of
fishes. It may change the temperature regime
influencing rooted aquatic plants, which
in turn can produce an impact on animal
habitat. Nutrient-rich and oxygen-poor water,
which may also be saturated with nitrogen gas,
may be heated and transported from bottom to
surface water.
The direct damage resulting from plant and
plume entrainment can induce further ecolog-
ical effects. Under certain circumstances
the loss of eggs and larvae could mean a
reduction in subsequent adult populations.
Large losses of phytoplankton and zooplankton
could alter the patterns of production and
predator prey relationships in the receiving
water.
Carl W. Chen
Director, Environmental
Systems Engineering
Tetra Tech, Inc.
Lafayette, California
The Water Pollution Control Act Amendments of
1972 (PL 92-500) classify heat as a pollutant
and provide for regulation of thermal dis-
charges. However, the Act recognizes that not
all discharges are necessarily detrimental and
provides a mechanism for exemptions to efflu-
ent limitations if it can be shown that no
appreciable harm would be inflicted on the bal-
anced indigenous community of the receiving water.
Large expenditures may be required to conduct
field and laboratory studies to quantify cool-
ing system effects. The collected data must
then be analyzed and interpreted to ascertain
if a cooling system operation has or will
inflict appreciable harm on the balanced
indigenous community of the receiving water.
Both the direct effects of entrainment and the
subsequent manifestations in the receiving
water must be determined as quantitatively as
possible. A model which can integrate the
chemical, physical, and biological character-
istics of a cooling system including the
receiving water environment would be a useful
tool in providing such an analysis. In addi-
tion to providing integration of data,
environmental or ecological models can and
should influence the design and operation of
plants. To provide an overall picture, and
more importantly, to predict impacts in quanti-
tative terms, a model must consider the
important physical, chemical, and biological
processes associated with the cooling
system.
The general approach to developing such a
model has been first to examine specific
problems and develop sub-models. These sub-
models are then integrated into larger system
models. Sub-models include 1) thermal plume
simulations to define the area, volume, and
residence time of water at various tempera-
tures with in the plume; 2) receiving water
transport models to compute entrainment ratios;
3) temperature dose-biological effect models
for passage through the cooling system and
4) water quality-ecological models that
simulate water quality behavior and population
dynamics of the biota.
Prototype Representation
In order to model a complex ecological system
it is necessary to carefully select the meth-
ods of idealizing or representing the physi-
cal conditions and biological processes
occuring withing the system. For evaluation
of cooling system effects, a physical and a
biological representation are necessary.
Appropriate units for quantification of
environmental characteristics must be selected
so that changes can be evaluated.
Physical
Figure 1 shows a general physical representa-
794
-------
tion of a power plant cooling system. The major
components of the physical environment which
are important to impact assessment are: the
boundaries, intake zone, condensers, discharge
conduit, and mixing zones defined by water
volumes at various temperatures. Each physi-
cal segment represents a point or volume for
which physical, chemical, and biological
characteristics can be defined.
BOUNDARY CONDITION
QIO
CONDEN-
SER
+Q2
OUTLET
CONDUIT
I S
02
Y
PLUME AND MIXING ZONES
Figure 1. Physical Representation of Power
Plant Cooling System
The representation shown in Figure 1 allows
for a variable boundary location and recircu-
lation between discharge and intake. The
establishment of boundary conditions is ex-
tremely important because small-scale models
can be completely dominated by the imposed
conditions at the boundaries. Ideally, the
water and constituents entering the model
boundary are not influenced at all by pro-
cesses occurring within the modeled area. It
may be desirable to run several models with
different boundaries in order to establish the
significance of boundary location. The in-
take zone must also be carefully defined. A
great deal of attention has been given to dis-
charge plumes and circulation. However, it
is equally important to know the source of
the intake water. The concentration of
planktonic oranisms may be very dependent on
the origin of cooling water.
The characteristics of the condensers are
considered to include temperature changes,
pressure gradients, and time of passage.
Operational characteristics may be somewhat
different than originally designed. For
operational plants, measurements should be
made to determine actual temperature increases
as a function of unit load. Time of passage
and pressure changes should also be measured.
The discharge conduit must be considered an
integral part of the system. This portion
of the cooling system may inflict the greatest
damage to plankton because it normally repre-
sents the greatest time of exposure to
elevated temperatures.
The discharge zone must be considered due to
its effects on both plant- and plume-entrained
organisms as well as a potential impact on
benthos, rooted plants, and fish. The time
of exposure to various temperatures within the
plume should be known in order to compute
thermal doses to entrained organisms.
Biological
Figure 2 shows a biological representation
designed for evaluation of cooling system
impacts. For each physical segment represent-
ing the study area, a system consisting of
chemicals, algae, zooplankton, fish, benthos,
detritus, and rooted plants can be simulated.
The system shown in Figure 2 has only one
compartment for each group. However, any
number of species or taxonomic groups could
be included. The system shown allows for two
types of direct impact: plant entrainment and
plume entrainment. Mortality is computed
directly according to exposure-mortality
relationships.
PLANT ENTRAINMENT
PLUME ENTRAPMENT
PREVIOUSLY ENTRAINED
Figure 2. Biological Representation of Power
Plant Cooling System
The ecological consequences of the direct im-
pacts are computed indirectly by modeling the
larger system. Sub-lethal effects are
computed by distinguishing between organisms
which have and have not passed through the
plant. The pool of organisms which have
passed through the plant may have altered
survival or reproductive characteristics.
"Offspring"of organisms which have been en-
trained are returned to the "normal" pool.
Mathematical Formulation
The mathematical formulation of the model(s)
consists primarily of a set of differential
equations describing the rates of change in
concentration of each parameter in each
compartment modeled.
For example, for constituent i, in compartment
795
-------
k, connected to compartment n:
dCi,k _
dt
ZQ C . - Q, C .
n i,n k i
+ G - £L
where: Q = advective flow from compartment n
Q, = advective flow from compartment k
jc
C. , = concentration of constituent i
lf in compartment k
C. = concentration of constituent i
/n in compartment n
V, = volume of compartment k
K.
t = time '
G = growth
L = loss
The present conceptualization assumes that
advective flows will be input from either
hydrodynamic models or an analysis of circula-
tion patterns and plant operation.
The gross growth rate of all organisms is
considered to be temperature-dependent.
Figure 3 shows a typical relationship between
growth rate and temperature. This approach
allows an increasing growth rate up to some
optimum temperature (range) followed by a
declining growth rate at higher temperatures.
Gross growth rates are also considered to be
"substrate"-dependent as shown in Figure 4.
The "substrate" may be nutrients, prey, or
light. All growth is considered to be first
order with respect to the organism modeled.
1.5
TEMPERATURE
Figure 3. Temperature Modulation of Gross
Growth Rates
Loss rates include respiration, sinking,
natural mortality, predation, and effects of
the plant. Respiration is considered to be
a simple first order reaction which increases
exponentially with temperature. Sinking rates
for phytoplankton are input parameters that
can be modified as a result of sudden pressure
changes. Predation is considered to be first
order with respect both to the predator and
the prey. Susceptibility to predation can be
modified as a result of thermal or mechanical
stress. The direct effects of the plant must
be input as specific functions for each group
of organisms. For example, plant-induced
mortality can be input as a function of
temperature, temperature increase, and time
of exposure.
1.0
LJ
tro
0
Z.O
0.5 1.0 1.5
SUBSTRATE CONCENTRATION
Figure 4 . Food Density Modulation of Growth
Rate Coefficient
It must be noted that the detailed formulation
of growth and loss terms may include the mass
concentration of other constituents and coup-
ling effects of the various quality constitu-
ents are therefore included in the model.
There are as many differential equations as
quality constituents and physical compartments
modeled. The equations are solved simultane-
ously to yield the concentrations of each
constituent as a function of time. The re-
sults can then be assessed to determine en-
vironmental impacts of a cooling system.
Modeling Framework
The general framework for model development
and application consists of four interacting
stages. During stage I, data are compiled for
the pertinent biological, physical, and cool-
ing system characteristics. These data rela-
tions, temperature-pressure mortality rela-
tionships , substrate and temperature growth
rate relationships, physical boundaries,
bathymetry, circulation patterns, and a defi-
nition of conditions to which entrained or-
ganisms will be exposed.
During stage II, data are input to a storage
and retrieval system. Summaries and statis-
tical analysis can be provide. Regressions
and correlations can be determined for pos-
sible use in defining relationships needed in
the models.
Stage III is the actual model formulation and
includes definition of equations and program-
ming modifications necessary for site-specific
conditions .
The final stage is the execution of the model.
The program can be used for baseline simula-
tions, computation of direct impacts, and
ultimate effects in the ecosystem.
Biological Data
The first step in defining the biological
system is to determine the major and impor-
tant components of the ecosystem which may be
affected. Importance may be a reflection of
food web relationships, aesthetics, economics,
or recreational resources. For example, the
major ecosystem components of the
San Francisco Bay-Delta are the striped bass;
king salmon; and the oppossum shrimp, Neo-
796
-------
mysis mercedis. The phytoplankton, zooplank-
ton, and benthos as general groups are impor-
tant but are less likely to be affected by
cooling system operation.
Analysis of the major species or groups must
then be conducted to determine life histories
and thermal tolerance data. Life histories
should be complete enough to determine which
life stages are susceptible to adverse
effects and when they occur in relation to
cooling system operation. Thermal tolerance
data should define the effects of short- and
long-term exposure to elevated temperatures.
For some groups, the effects of exposure to
heat are dependent on both temperature in-
crease and time of exposure. An example of
this type of relationship is shown in Figure 5.
Other organisms, such as Neomysis,experience
mortality as a funciton of maximum temperature,
as shown in Figure 6.
Ld
to
<
Ld
cc
o
LU
cr
h- - -
cc
UJ
0.
INCREASING
SEVERITY
OF EFFECT
EXPOSURE TIME
Figure 5. Time-Temperature-Effect Plot
Following identification of susceptible life
stages and thermal tolerance data, general
relationships between temperature and growth
or reproduction rates, mortality rates and
spawning activities should be determined. It
is important to key these relationships to
time as well as temperature in order to inte-
grate the results with plant operational data.
Physical Data
One of the most important and often neglected
aspects of cooling system evaluations is
analysis of the physical transport of organ-
isms which are subject to entrainment. There
are three basic types of physical systems
which must be treated differently. Unidirec-
tional river flow is the simplest and normally
would require only a hydrologic analysis to
relate frequency of river flow to seasons and
abundance of organisms of interest. The per-
cent of river flow, or organisms entrained,
which is a function of time is then a simple
ratio of cooling water flow to river flow. It
is necessary to determine the level of lateral
mixing and distribution of organisms (side,
mid-channel, surface, bottom).
uu-
80-
60-
40-
20-
7
0—0-^
~~ ^
V
6 Minute Heat Exposure \
Mortal/ties in the Laboratory \
fl'l'r l1^ ~*l ' ^ 9
— (nOtr, Ij/U /T
Through the Plant Mortal/ties
at Pittsburg Power Plant, 1969
(Kelly /5*7/1
"
| |
0 75 80 85
\
X
»!
\
I
\
\
N,V
'
1 \
\ \
L >
\ \
\ \
\ \
\ X
\ X
\ X
N^ X
90 9
MAXIMUM TEMPERATURE (°F)
Figure 6. Effects of Elevated Temperature on
Neomysis Survival
Tidal estuaries are somewhat more complicated
due to the oscillatory nature of the flow.
However, an "entrainment ratio" can be calcu-
lated with the use of a number of simulation
models. Figure 7 shows computed entrainment
ratios for a power plant with cooling water
flow of 1000 cubic feet per second located
mear the confluence of the Sacramento and San
Joaquin Rivers on the San Francisco Bay-Delta.
The figure shows the fraction of water at each
location that would have passed through the
power plant if steady-state conditions were
reached. The computations were carried out
for summer conditions with a net fresh water
flow of 4000 cubic feet per second and a
typical semi-diurnal tidal cycle.
Open coast locations are the most difficult
to quantify due to the uncertain boundary
conditions. Coastal currents and circulation
patterns can be input as boundary conditions
to the study area. However, the definition of
the study area is extremely subjective. One
approach to this difficulty is to provide an
analysis with several different study area
boundaries and attempt to assess the effects
as a function of study area size. For example,
2% of the zooplankton within three miles of a
plant may be killed each day. Whereas only
0.5% may be killed each day within six miles
of the plant.
797
-------
0.3- -
0.2--
01- -
o
<
cr
MILES ABOVE GOLDEN GATE
Figure 7. Fraction of Water Which Has Passed
Through the Plant Under Steady-State Condi-
tions of 4000 cfs Delta Outflow and 1000 cfs
Cooling Water Flow
In general, physical data should include bath-
ymetry, flow regimes, currents, circulation
patterns, and entrainment ratios. Thermal
plumes should be determined in sufficient de-
tail to describe location, area, volume, res-
idence time, and whether or not the plume
affects rooted plants or animals.
Cooling System Data
Cooling system data must be sufficient to
evaluate the impacts on both the organisms
entrained in the plant and the plume. For
power plants it is necessary to define the
temperature and time of exposure for plant
passage. Most cooling systems consist of a
number of units which may have different
characteristics. It may be important to ob-
tain operational data describing these condi-
tions through each unit as a function of
travel time. Sheer stress, pressure changes,
and chemical additions may affect survival of
organisms and should be ascertained.
Model Use
Although this model is only in the conceptual-
ization stage, previous work has shown the
utility of certain sub-models and confirmed
the need for an integrated approach. For
example, the design of units 2 and 3 at the
San Onofre Nuclear Generating Station calls
for extended diffusers on the once-through
cooling water system discharge. The design
will expose plant-entrained organisms to
temperature increases of approximately 20°F
for 7 to 12 minutes longer than the existing
system for unit 1. The model which has been
described would be a valuable tool to analyze
the significance of extended exposure to ele-
vated temperatures compared to slightly more
rapid dissipation of heat in the discharge
plume. The significance of alternative ef-
fluent locations could also be analyzed.
In another application of a limited modeling
approach, hourly power generation data for
each of seven units of a power plant were
used to compute temperature increases through
the condensers. The temperatures experienced
passing through each unit were then related to
survival of young striped bass using survival
functions reported in the literature.3'4
The percent of young bass which would be ex-
pected to have survived plant passage were
averaged on a weekly basis. The results are
shown in Figure 8. Based on estimates of
striped bass abundance in the intake area, the
number of fish passing through the plant were
estimated and the cumulative number killed
were computed.
UNITS 1-6
Kerr Mortality Function
1970
I
I
1972
I
UNITS 1-6
Kelly & Chadwick Mortality Data
1971 I 1972 I 1973
WEEKLY AVERAGES
1974
Figure 8. Computed Percent Survival of Young
Bass Passing Through a Power Plant Cooling System
Unfortunately, time and funds have not per-
mitted the analysis to go the next step in
determining the significance of these com-
puted mortalities to the overall bass popu-
lation. Furthermore, the computations are
based on a number of assumptions (survival
data, power generation-temperature increase
relationships intake concentrations). How-
ever, the approach is quantitative and pro-
vides a systematic appraisal of data needs
as well as a methodology for evaluation.
Conclusions
Comprehensive models can be used to provide
a rational and quantitative interpretation
of data as well as guidance in monitoring
program design. Modeling results can be used
to evaluate the impact of alternative designs.
Although direct effects can be computed and
verified with field data, consequences often
cannot be verified. The most valuable benefit
of modeling is therefore, the capability to
project ecological consequences resulting from
a variety of assumptions and hypotheses.
References
(1):
1. Hair, R.J., California Fish & Game 57
17-27, 1971.
2. Kelly, R., California Fish & Game, Anad.
Fish. Br. Admin. Kept. 71-3, 6 pp. (mimeo),
1971.
3. Kelly, R., and H.K. Chadwick, California
Fish & Game, Anad. Fish. Br. Admin. Rept.
71-9, 11 pp. (mimeo), 1971.
4. Kerr, J.E., Fish Bull. No. 93, California
Fish & Game, 66 pp., 1953.
798
-------
REVIEW OF THE STATUS OF MODELING
ENVIRONMENTAL NOISE
William J. Galloway
Bolt Beranek and Newman Inc.
Canoga Park, California
ABSTRACT
Models for predicting the noise produced
around airports and highways have been devel-
oped over a period of years, have reached a
reasonably high degree of accuracy, and are
in widespread use. These models provide
site-specific information. More recent
models have been developed to predict
general urban noise and noise produced by
construction equipment and other major noise
sources. Differentiation is made between
models for a specific site, as required in
environmental impact reports for specific
projects, and models predicting the total
population exposed to noise, as used in
assessing proposed noise source regulatory
actions. The effect of noise source data
requirements, sound propagation modeling
problems, and operating condition specifi-
cations on modeling precision and accuracy
are discussed using specific examples
relevant to current EPA activities.
BACKGROUND
Acoustical modeling uses both scale model
analogs of a real environment and simulation
through mathematical models. Physical scale
models are used primarily to study sound
propagation phenomena in the presence of
complicated geometric configurations, e.g.,
inside a building, between buildings in an
urban area, the effect of barriers along a
highway. As such, these models consider a
restricted geographic area, use artificial
sound sources that usually do not scale in
magnitude to their real counterparts, and
do not generate sound levels representative
of a real environment.
Mathematical models of noise environments,
on the other hand, are used to predict noise
environments at a point, over a local area,
or even to estimate national noise exposure.
Existing models vary widely in detail,
scope, and purpose. The purpose of this
paper is to review the general characteris-
tics of simulation models for predicting
noise environments and provide a current
status report on existing models.
GENERAL CHARACTERISTICS
An acoustical model can vary widely in terms
of its sophistication. For example, the
noise produced at a point 20 m to the side
of a level road by an automobile traveling
at a constant speed is a simple algebraic
expression involving only a constant with
speed and distance as variables. On the
other hand, modeling the noise produced in
a community from a complex stretch of
highway, complete with multiple lanes of
traffic moving at different speeds with
different vehicle mixes, curving roadways at
varying grade levels, including the effect
of noise barriers, requires a sophisticated
program operating on a high speed scientific
computer. Each model, however, has certain
attributes in common:
1) Information on the magnitude, frequency
distribution of sound level, and time
variation of the source must be provided.
2) A propagation model from source to
receiver needs to be defined.
3) A measure of noise suitable for use in
describing human response is required.
The complexity of the modeling process
relates directly to which of these points
receives the most emphasis. For example,
the designer of a jet transport aircraft
attempting to predict whether a new aircraft
will comply with FAA noise regulations will
put essentially all his sophistication into
describing the noise sources in detail so
that he can predict the time pattern of
sound pressure levels in one-third octave
frequency bands at a point on the ground
during a flyover of the aircraft. The air-
port planner, on the other hand, wants to
compute the cumulative noise exposure, at
points in the entire community surrounding
the airport, produced by the total complex
of different aircraft and flight paths used
at the airport. For this purpose the noise
source descriptor is chosen to be as simple
as possible, with the emphasis in the model
being placed on summing the contributions,
at many points in the surrounding area,
from the variety of sources involved.
Finally, again using aircraft as an example,
it is often of use to have a model in which
all the operational factors, propagation
characteristics, and exposed population
distributions have been aggregated in such
a way that changes solely in source strength
can be related directly to national impact.
Evaluating the impact on the national noise
exposure of retrofit noise control measures
for the air transport fleet is an application
of such a model.
In the following discussion examples of
these three levels of modeling will be con-
sidered, the "micro," "macro," and "global"
approaches'. The examples are primarily
aircraft and surface transportation noise
sources, since, by far, these are the per-
vasive sources of environmental noise and
thus have the most well developed noise
models. Models for factories, construction
sites, refineries, and other sources of
799
-------
community noise have been developed to a
much lower state of sophistication only
because of their lesser importance as
major noise contributors to the national
noise environment.
Before describing environmental noise model
building history, it is worth noting that
one of the primary psychoacoustical contro-
versies in community noise evaluation, the
selection of a community noise descriptor,
has been only a minor factor in the phy-
sical and mathematical evolution of noise
model development. Whether loudness level,
perceived noise level, A-weighted sound
level, or any other of a myriad of noise
descriptors is chosen, the physics of the
model building process is basically un-
changed. The only circumstance where choice
of noise measure has influenced the model
development process is in the desire in
some models to predict measures of the time
distribution function of noise level, for
example the median level, denoted LCQ' or
the level exceeded 10 percent of the time,
L-.Q. It is usually fairly simple to
estimate such measures for a single class
of noise sources assumed to produce normal
distributions of level with time. Where
multiple sources having different time
distributions are involved, estimating the
combined distribution function is almost
hopeless.
Fortunately, the relatively recently evolved
international consensus that community
response is most directly related to the
mean square value of sound pressure, aver-
aged over a specified time period, greatly
simplifies the modeling process. With this
assumption, the contributions of individual
sources to the cumulative noise exposure at
a point is a simple mathematical process.
A major step forward in developing a unified
presentation of model results was the EPA
publication of its "Levels" document1 in
which it prescribes that all environmental
noise, irrespective of source, should be
specified in terms of average (sometimes
called equivalent) A-weighted sound level
over a specified time interval. This
quantity is simply ten times the logarithm
of the time integral of A-weighted, squared
sound pressure, divided by a specified
reference time (one hour, twenty-four hours,
etc.) and reference sound pressure. A
number of simplified expressions for cal-
culating this measure for typical time
distributions of noise signals are provided
in Appendix A of Ref. 1.
SURFACE TRANSPORTATION MODELS
Noise from motor vehicles is the most exten-
sive source of noise in most communities2.
Most early attempts to model noise from
traffic have considered the "freely flowing"
case of a freeway on flat, open terrain.
One of the first models used a Monte Carlo
simulation of a Poisson flow of vehicles to
predict the noise level distribution at a
point as a function of vehicle speed and
mean traffic flow volume3. Later models
generally assumed a uniform distribution
of vehicles along a roadway, and for high
volumes obtained the same answers as the
Monte Carlo simulation "*.
One of the first attempts to simulate a com-
plex flow of traffic, expanding on the Monte
Carlo simulation was completed in 19675.
Although the simulation was performed with
a computer, the model was really not suited
for routine analysis of highway problems,
in that highway configuration, grade differ-
ences, and other real highway configuration
effects were not considered. The first
design guide provided by the Highway Research
Board to account for these factors was
completed in 19696. The attempt here was to
reduce the simulation results to a series
of nomograms suitable for use in hand cal-
culations. The procedure was still cumber-
some, and was first programmed for computer
use by the Michigan Highway Department. An
alternate model, similar in nature, was
developed by the Transportation System
Center in 19727.
An impetus to use these models routinely was
provided by the requirement of the Federal
Highway Administration8 that noise pre-
dictions for highway planning and improve-
ment projects be performed in all federal-
aid highway programs. Meanwhile, with more
highway departments using the models a
number of noise measurement programs were
conducted to determine the accuracy of the
models. It was also found that hand imple-
mented versions of the models were not
sufficiently detailed to satisfy many
highway designers. An improved program
incorporating many detailed refinements and
reflecting the measurement program results
was developed in 197^9 and is now available
in Fortran versions for CDC and IBM com-
puters. Another model developed by the
Ontario Ministry of Transportation also
appeared in 19751°.
The present state of highway noise simulation
is represented by the HRB, TSC, and Ontario
models. Each has detailed differences and
varying ease of application, but is capable
of predicting environmental noise to accur-
acies of the order of a few decibels of the
real values obtained from validation
measurements11.
AIRCRAFT NOISE MODELS
Simulation of the noise produced by aircraft
operations has had a history similar to that
of highway noise. Early airport noise models
were designed to provide a means for com-
puting the noise produced at a point by a
number of different aircraft, generally
clustering operations by general aircraft
types, e.g., transport aircraft, fighters,
propeller-driven, using nomograms and manual
computation12. Means were provided to
develop families of contours of equal noise
exposure that could be used to define the
total noise environment around an airport if
one knew the number and kind of aircraft
involved and the flight tracks flown. An
improved version was implemented as a Fortran
program in 1 **, but still did not provide for
detailed consideration of individual aircraft
800
-------
performance, and required summation of
individual contours by a hand drafting
procedure.
Implementation of the Environmental Policy
Act by the Department of Defense and the
Federal Aviation Administration gave impetus
to the development of substantially more
refined airport noise models in the past
few years. Using somewhat different mathe-
matical approaches to achieve the same
goals, two major computer programs have
been developed by FAA and the Air Force15'16.
•These programs now allow input of the
detailed performance characteristics of
individual aircraft, variation in power
management schedules during a flight oper-
ation, dispersion in flight paths, variations
in atmospheric conditions, and a host of
other improvements. Output is now available
in completed contour form through the use
of highly sophisticated plotting routines.
The accuracy of airport noise model pre-
dictions is very much a function of the
accuracy of the input operational data.
Noise source characteristics of aircraft
are quite well known, but the ability to
describe flight paths accurately is diffi-
cult. Further, the accuracy of noise
prediction decreases as the distance from
the aircraft increases. The daily average
noise level of a complex of operations can
be predicted to within one to three decibels
for distances of up to 10,000 feet from a
flight path. At farther distances the
accuracy decreases due to variation in both
knowledge of where the flight paths really
are and variation in sound propagation in
a real as compared to ideal atmosphere.
Two additional approaches to aircraft noise
modeling are of interest. One very
ambitious effort at NASA Langley Research
Center is a long term project to permit
noise prediction as a function of detailed
aircraft design characteristics17. This
program consists of a series of individual
modules related to state-of-the-art pre-
diction of individual noise sources such
as jet noise, compressor noise, etc., and
an executive program to combine the
individual component effects into a
composite of the noise produced by the
whole aircraft. The goal here is to upgrade
individual models as the knowledge of
detailed source predictions improves. This
is in contrast to the usual airport noise
models that treat the overall noise of an
aircraft directly.
The second approach is a "global" model of
airport noise that predicts total population
exposed to a specified noise value in terms
solely of current aircraft fleet noise
characteristics and numbers of operations—
either for a single airport or for all air
carrier airports . Use of this model
allows a simple calculation of changes in
population affected by a source noise change,
or change in numbers of operations. This
model is currently used by the Civil
Aeronautics Board as a screening tool in
airport/route changes to determine whether
a change is minor or major, and thus
requiring more detailed analysis19.
URBAN NOISE MODELS
No suitable models exist for predicting
general urban noise from a collection of
discrete sources. A first cut estimate,
based on a statistical sample of urban
noise, allows a general space average noise
exposure estimate to be made on the basis
of population density alone20. For any
specific location the level may vary as
much as + 8 decibels from this average,
depending upon local street structure and
traffic volumes. Development of a general
purpose urban noise model that accurately
accounts for discrete noise sources, local
topography, and urban design is the next
major challenge in environmental noise
model development.
CONCLUSION
Sophisticated models exist for predicting
the environmental noise produced by freeway
and airport operations. Accuracies of
prediction are of the order of a few
decibels—comparable to the discriminability
of people to assess noise. Generalized
urban noise models are not yet available,
although some work is in progress.
REFERENCES
1) Anon., "Information on Levels of
Environmental Noise Requisite to Protect
Public Health and Welfare With an
Adequate Margin of Safety," 550/9-74-004,
EPA, March 1974.
2) W. J. Galloway, G. Jones, "Motor Vehicle
Noise: Identification and Analysis of
Situations Contributing to Annoyance,"
Trans. Soc. Auto. Eng., 1060-1074, 1972.
3) W. J. Galloway, W. E. Clark, "Prediction
of Noise From Motor Vehicles in Freely
Flowing Traffic," Proc. IV International
Congress on Acoustics, August 1962.
4) D. R. Johnson, E. G. Saunders, "The
Evaluation of Noise From Freely Flowing
Road Traffic," J. Sound and Vib. 7_,
No. 2, 287-309, 1968.
5) W. J. Galloway, W. E. Clark, J. S.
Kerrick, "Highway Noise—Measurement,
Simulation, and Mixed Reactions, NCHRP
Report 78, 1969.
6) C. G. Gordon, W. J. Galloway, B. A.
Kugler, D. L. Nelson, "Highway Noise -
A Design Guide for Highway Engineers,"
NCHRP Report 117, 1971.
7) J. E. Wesler, "Manual for Highway Noise
Prediction," Report DOT-TSC-FHWA-72-1,
1972.
8) "Noise Standards," PPM 90-2, Fed. Hwy.
Adm.., June, 1972.
9) B. A. Kugler, D. E. Commins, W. J.
Galloway, in publication as NCHRP Report.
801
-------
10) J. J. Hajek, "Ontario Highway Noise
Prediction Method," Research Report 197,
Ministry of Transportation and Communi-
cations, Ontario, Canada, 1975-
11) "Highway Traffic Noise Prediction
Methods," Transportation Research
Circular Number 175, January 1976.
12) K. N. Stevens, A. C. Pietrasanta,
Procedures for Estimating Noise Exposure
and Resulting Community Reactions Prom
Air Force Operations," WADC TN-57-10,
Wright-Patterson Air Force Base, Ohio,
1957-
13) W. J. Galloway, A. C. Pietrasanta, "Land
Use Planning Relating to Aircraft Noise,"
BBN Report 821, published by PAA in 1964.
14) D. E. Bishop, R. D. Horonjeff, "Proce-
dures for Developing Noise Exposure
Forecast Areas for Aircraft Flight
Operations," FAA Report DS-67-10,
August 1967.
15) C. Bartel, L. C. Sutherland, "Airport
Noise Reduction Forecast," Report DOT-
TST-74, August 1974.
16) R. D. Horonjeff, R. R. Kandakuri,
N. R. Reddingius, "Community Noise
Exposure Resulting From Aircraft
Operations: Computer Program
Description," AMRL TR-73-109, Aerospace
Medical Research Laboratory, Wright-
Patterson Air Force Base, Ohio,
October 1974.
17) J. P. Raney, "Development of a New
Computer System for Aircraft Noise
Prediction," 2nd AIAA Aeroacoustics
Specialists Conference, NASA Langley
Research Center, March 1975.
18) W. J. Galloway, "Predicting the
Reduction in Noise Exposure Around
Airports," Proc. Inter-Noise 72,
356-361, October 1972.
19) Part 312, Economic Regulations, Civil
Aeronautics Board, 24 September 1975.
20) W. J. Galloway, K. M. Eldred, M. A.
Simpson, "Population Distribution of
the United States as a Function of
Outdoor Noise Level," EPA Report
550/9-74-009, June 1974.
802
-------
COMMUNITY NOISE MODELING
by
Basil Manns
U.S. Environmental Protection Agency
Washington, D.C. 20460
SUMMARY: This paper discusses the use and need for
mathematical models for planning, developing, and
managing regulatory programs for community noise
control. Both sources and propagation noise emission
models are essential to determine the beneficial im-
pacts in the community for each new source regula-
tion. Very elementary and statistical models have
been used thus far in dealing with the major noise
sources. However, as additional noise sources are
identified for regulation, the continued use of these
elementary models will not show the real benefits of
a particular regulation to the community. This paper
will focus on the description of models used for urban
traffic and freeway noise. Other models used for
construction sites or airports will not be discussed
in this paper.
NOISE DESCRIPTORS: It must be clearly understood
that one role of the Environmental Protection
Agency's Office of Noise Abatement and Control
(EPA/ONAC) is to reduce and control community noise
by developing regulations for noise emission of newly
manufactured products, interstate railroad and inter-
state motor carrier. The 3PA/ONAC does not establish
ambient standards. It does establish operating
standards for interstate rail and motor carriers, and
certain newly manufactured products at the time of
manufacture. The products identified for regulation
are generally based on those that have greatest impact
on the cortmunity. The Table I shows that urban traffic
category is the highest regarding community noise.
Home appliance is ranked as high as it is because the
impact level goes down to 45 dB.
Community noise requires the inclusion of all the
noise in the outdoor acoustical environment. The out-
door community noise environment varies in both mag-
nitude and character at various locations. The
community noise environment also varies as time of
day. Thus in describing descriptors for community
noise it is necessary to determine the time and loca-
tion of variations in the outdoor noise environment
throughout the community in such a manner that the
descriptors are relevant to its effects on people
located in various land use categories, either
indoors or outdoors.
In describing sound and its effects on people the
factors to consider are the frequency spectrum, the
overall Sound Pressure Level (SPL), and the temporal
variations of both spectrum and SPL. To simplify the
approach the frequency spectrum has been weighted to
the human hearing sensitivity and summed to obtain a
single SPL number. This is the A-weighted SPL in
decibels, written as dB(A).
Although the A-weighted SPL is weighted with the
human hearing sensitivity it is not a perfect method
for accounting for a persons perception of the fre-
quency characteristics of a sound. Many other scales
have been developed to better quantify loudness and
noisiness. The tone corrected perceived noise level
better accounts for the human hearing response by dif-
ferentiating betweeen broadbands and pure tones.
Perceived noise levels exceed the A-weighted noise
levels typically by 11 to 17 decibels. Because the
perceived noise level scale is somewhat more exact
than the A-weighted in relating to physical charac-
teristics of a sound to perceived noisiness, particu-
larly for aircraft, it has become a major element in
certifying aircraft.
Tone corrected perceived noise level measurement
methodologies require complex instrumentation and
data analysis to define a sound. Therefore, they
have found little application in the measurement of
outdoor community noise. The simple A-weighted sound
level meter so far appears to serve the purpose
adequately. Therefore most analytical and computer
models dealing with surface transportation noise
impact analysis are based on the A-weighted sound
pressure level in decibels.
The temporal variations of the noise level in terms
of the dynamic range variations, discrete single event
occurences, and the time and length of these occur-
ences can easily be observed on a graphic recorder. In
order to cope with these variations statistical des-
criptors are used. These descriptors give the percen-
tage of total time that the value of the noise is
above a given level. Frequently used levels are L10,
L50 and L90 corresponding to the sound level that is
exceeded 10%, 50% and 90% of the time respectively.
Other descriptors used particularly by the EPA/ONAC
are Leq and Ldn shown in equations 1 and 2.
• 10 los>.
P2(t)
dt
(1)
dn
15 10
Ld/10
(2)
10
(Ln+10)/10
The Leq is the energy equivalent noise level or the
average SPL over a given time period, usually 8 hours
or 24 hours. The Ldn is the day-night energy equiva-
Table 1. Summary of Noise Impact in the United States by Category
Cumulative Number of People Whose Exposure Exceeds Indicated Idn (Millions)
45dB 5CWB 55dB 60dB 65dB 70dB 75dB 80dB 85dB
Urban Traffic
Home Appliances
Aircraft Operations
Industrial
Construction
Freeway Traff ic
Operators/Passengers
Ran Line Operations
79.7
44.2
93.4
17.1
24.5
—
26.2
13.7
—
2.0
59.0
4.4
16.0
—
8.7
8.1
—
0.9
24.3
0.6
7.5
—
2.4
4.5
—
0.3
69.9
0
3.4
16.7
0.5
2.3
11.5
0
1.3
0
1.5
12.2
0
1.0
11.5
0
0.1
0
0.2
8.6
0
0.3
1.6
0
0
0
0
3.8
0
0
1.6
0
1975 1992
Noise No ise
trpact Impact
(Millions of units)
Total Impact
34.6
26.5
10.2
8.2
6.2
5.3
5.1
0.55
T77T"
5.9
3.9
2.5
2.3
0.5
1.7
0.7
0.04
ITTT
803
-------
lent noise level where a 10 dB penalty is given to the
9 night hours (10 p.m. to 7 a.m.). The Leq and Ldn
levels have been used by the EPA/ONAC to characterize
the health and welfare impacts associated with noise.
Impulse or single event noise has been shown to cause
interference with communication, disruption of sleep,
annoyance, and other physiological effects in addition
in some cases hearing loss. However, it is not treated
separately but averaged into the Leq or Ldn level to
describe the health and welfare impacts.
MODEL DESCRIPTORS: The models used to describe the
noise levels produced by various vehicles can be used
both for highway planning and design projects and for
developing strategies and assessing regulatory alter-
natives of noise emission source regulations. The
basis of all models for highway is the description
of the noise produced by a single vehicle observed at
a fixed point as the vehicle passes along a straight
highway. Three basic approaches to the modeling of
highway noise have been used, (1) compute the instan-
taneous noise levels expected for a randomly occurring
flow of vehicles along a single lane equivalent
roadway, (2) superimpose the individual sources to
constitute a flow, assuming vehicles to be uniformly
distributed and spaced along a single lane equivalent
roadway, and (3) compute the total acoustic power that
is distributed along a single lane equivalent roadway.
Using these approaches mathematical expressions have
been derived that will describe the observed noise
level at a given distance as a function of the vehicle
speed, the vehicle flow rate, and the vehicle noise
reference level. Using propagation theory and empher-
ical correction factors additional parameters such as
vehicle noise frequency spectrum, barriers, ground
absorption, atmospheric absorption, reflection, and
road geometry are incorporated into the model.
A number of equations have been developed to predict
the propagated noise level to a given distance. An
early equation, equation (3), developed by Johnson
and Saunders shows L50 or the median noise level at
sufficient distances from the highway and/or at higher
traffic densities. The noise source is shown to smear
L50=20+101ogV-101ogD+201ogS
(3)
out into a line source whose levels decrease by 3 dB
per double distance. The variable V is the vehicle
per hour, D is the distance from the highway and S is
the vehicle speed. Galloway was the first to develop
a simulation model that accounts for the statistical
LlO-Leq, Decibles
/
/
/
/
^—
~\L10-Leq=1.28s-0.115s2
\
\
\
\
\
0246 B 10 12 !-J
Standard Deviation, Decibles
Figure I. Difference between L10 and Leq for
a Normal Distribution.
distribution of the noise level as a function of time.
The basic equation is shown in equation (4). This
L50=29+101ogV-151ogD+301ogS+ (4)
101og(tanh(1.19xlO~3VD/S))
equation is for automobiles, and a similar equation is
used for trucks. The variables V, D, and S are the
same as above. To convert L50 to L10, equation (5) is
L10=101og
cosh(1.19xlO~3pD)
cosh(1.19x10-3PD)-0.95
+L50
(5)
used where PO is the traffic density. In this simula-
tion empherical expression the traffic represents
something between a line source and a point source.
Figure I is then used to convert L10 to Leq, since Leq
is used by EPA/ONAC as a primary descriptor to assess
impact on residential and land use categories, A
normal distribution is assumed which is often not a
valid assumption for traffic or freeway noise.
Another expression developed by the Department of
Transportation shown in equation (6), calculates the
average intensity for a vehicle group knowing the mean
SPL of the vehicle group. The variable r is the ref-
erence distance, d the perpendicular distance from
1=
d
road
segment
10ioe.s.35)2!
,-D/lO,-L/io 0.5(s/4.
vehicle
group
(6)
roadway, Aa the enclosed angle at the receiver at two
ends of the road segment, D the attenuation of sound,
L the mean SPL, is the standard deviation of the
normal distribution of the reference SPL.
The Leq is the calculated as 10 Log I.
A similar approach developed by Plotkin caluculates
the equivalent energy by using equation (7) for each
(7)
single lane "j" of traffic. I is the vehicle inten-
sity level, P is the fraction of the vehicle that
produces a sound level I, S the vehicle passby per
unit time, V the vehicle speed, d the passby distance
and dj the lane distance. Again the assumption of a
line source is used and Leq is found from 10 Log I.
It is really not the purpose of this paper to discuss
the details of these simulation expressions or others
that have been developed. However, the basic features
of these expressions need to be understood to apply
mathematical predictive methodologies to assess urban
or community noise impact. The important feature in
assessing impacts on the community is that a specific
site or scenario needs to be defined, including the
source since the propagation characteristics of
sources do vary.
ASSESSMENT METHODOLOGIES: As part of the requirement
of the Noise Control Act of 1972, the EPA identified
community noise levels that are "requisite to protect
the public health and welfare with an adequate margin
of safety." Various land use areas include residential,
commercial, industrial, educational, recreational
areas, and inside transportation. Generally, Leq
levels of 70 decibels are identified to protect
against activity interference. Other levels are shown
on Table II.
804
-------
Table II. Noise Levels Protective of Health and Welfare
dB(A) and the population model is in Ldn, any change
in Ls would produce an equal displacement in Ldn. To
Human Response Leg Idn
Hearing Loss-' (8 hours per day)** 75 —
Hearing Loss* (24 hours pec day) 70 —
Outdoor Annoyance — 55
Indoor Annoyance, Speech Interference — 45
*6ased on exposure over 40 years at eat level.
**As long as the exposure over the remaining 16 hours per day
is low enough to result in a negligible contribution to the
24 hour average.
The procedures used to assess impact due to environmen-
tal noise follows the same fundamental analysis used
for any environmental assessment. First, the initial
acoustical environment must be defined. Second, the
final acoustic environment must be defined. Third,
the relationship between specific acoustic environments
and the expected human impact must be analyzed. These
three steps are used in planning and developing highway
construction projects and also in assessing the impact
of planned or developed regulations of specific noise
emission sources. When planning and developing a par-
ticular road, one uses this assessment approach on a
single or group of houses. When assessing the impact
of a noise emission source regulation, all houses near
the entire national and local highway system are
considered.
To simulate various traffic conditions in the United
States, the EPA/ONAC has considered both an urban
traffic situation and a urban freeway situation.
For both scenarios, the models are designed to
assess the total United States population affected by
particular noise source emission regulations.
URBAN TRAFFIC MODEL: The urban traffic model is a
statistical model used for estimating the national
urban population benef itted from a regulation. The
model uses the following assumptions.
(1) In an urban environment the average speed is
27 mph.
2) The vehicle mixture is 1% heavy trucks, 6% medium
trucks; 91.5% automobiles, 0.5% buses and 1.0%
motorcycles.
(3) The base line noise levels for each vehicle is
heavy truck 85 dBA, medium truck 77 dBA, automo-
bile 65 dBA, buses 79 dBA and motorcycle 83 dBA.
(4) The population density as a function of outdoor
noise level is based on empherical data shown on
Figure II.
The results shown on Figure II are taken on a sample
of 100 sites chosen to represent a wide range of popu-
lation densities throughout the United States. The
sites were chosen away from freeways, construction
sites, airports and aircraft noise in order to
represent urban traffic noise. The cumulative U.S.
population exposed to levels in excess of specific
values are shown on Figure III. These data are also
taken from the 100 site study and takes into account
other noise sources.
The effect of a noise emission regulation on a vehicle
category in an urban environment can be assessed by
analyzing the change in the equivalent source level
produced by changes in the particular noise emission
source. Although the equivalent source level Ls, is in
50
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- 10 l»9 P
* 22 dB
4 26 dB
50 ° 55 40 S5 70 75
Day Night Average Sound Level, Ldn(dB)
Figure II. Population Density as a function of Day Night
Average Sound Level.
Day Night Average Sound Level, Ldn(dB)
Figure III. Cumulative Population Exposed to Levels in
Excess of Day Night Average Sound Levels.
805
-------
calculate the effect of a noise emission regulation,
compute Ls for all noise source categories involved,
heavy trucks, medium trucks, automobiles, buses and
motorcycles. Knowing the distribution an dthe noise
levels of each vehicle, Ls is just the logrithmic
summation, expressed in equation (8), where i is the
vehicle, Li is the noise level of the i vehicle and
Di10Li/10
(8)
Di is the fractional distribution of the i vehicle.
Ls is calculated before regulatory levels are imposed
and after, to determine the before and after conditions
for a particular source regulation. The "before" and
"after" Ls is equated to equal values of Ldn.
Figure II and III are then used to show relative bene-
fits of a regulation. Figure II shows a lowering of
the overall urban noise or din at a given population
density. The plot on Figure II will be shifted or
displaced left as a result of a source regulation.
Additional regulations would also incrementally shift
the plot left so that at a given population density the
overall urban din can be shown to be less. Figure III,
however, shows the cumulative population exposed to
levels in excess of specified values. Again since any
change in Ls calculated by equation (8) is equal to
a change in Ldn, a change in population can be deter-
mined that is exposed to levels in excess of the
specified values. Thus the number of people actually
benefitted by the reduction of the urban noise level
is found.
FREEWAY NOISE MODEL: The Freeway Noise Model used by
the EPA/ONAC estimates the number of people benefitted,
or impacted by a particular regulation that live
along the miles of urban freeway. As mentioned pre-
viously, the analysis to determine the impact due to
noise is site specific. For national impact analysis
a number of very general assumptions has been used to
simulate a site to represent the average urban freeway.
The scenario consists of a freeway passing through an
urban residential area having the following properties:
(1) Freeway consists of six traffic lanes
(2) Freeway has no grade relative to surrounding
property
(3) Population density adjacent to the freeway is 5000
people per square mile
4) EWellings are single-family, one story high located
on one hundred foot lots, two lots deep
(5) Traffic volume is 7200 vehicles per hour with an
average speed of 55 miles per hour
(6) Traffic distribution is 10% heavy diesel trucks and
90% automobiles
(7) There are 8000 miles of urban freeway
These assumptions are then used to compute the hourly
equivalent levels at various distances from the
freeway. The level is computed for both trucks and
automobiles and their combinations. The same equation
used for the urban traffic model, equation (8), is
used for comparing the equivalent source level, usually
at 50 feet for a particular combination of sources.
The individual source levels used are the levels im-
posed by the standards being considered. It is
assumed that any change in the equivalent source level
would produce an equal change in the day night average
sound level, Ldn.
The Figure IV represents the noise level adjacent to
urban freeways using a 1974 base case of 7200 vehi-
cles per hour, 10% trucks and 90% automobiles, at an
average speed of 55 mph. Using equation (8) and
calculating the "before" and "after" conditions the
change in Ls will produce an equal change of Ldn.
Thus an increase in distance from the freeway for
the "after" condition is found. The Ldn levels in
5 dB increments from the freeway are computed, and
the population in these contours are estimated knowing
the population density of 5000 people per square mile
and 8000 miles of urban freeway.
It is important to realize that Figure IV illustrates
a base case using empherical data representing a
situation resembling an average urban freeway. The
attenuation is considerably greater than the 3 or 4.5
dB per double distance as described in equations 3
thru 7. The attenuation of 9 dB per double distance
is used since this represents the average attenuation
of the particular source spectrum expressed in terms
of day night average sound level taking into account
atmospheric attenuation, ground absorption, building
reflection and refraction, and other physical losses.
As other sources are analyzed in this model the par-
ticular attenuation rate will need to be determined.
PROBLEM AREAS: There are a number of questions that
often arise in dealing with the noise descriptors or
the models. The descriptors Leq and Ldn have the
basic advantage in that they are easy to measure.
However, the objection to the use of Leq or Ldn might
be that the long term average is not appropriate to
describe harmful or annoying effects of short dura-
tion, high level noise. This is true where short
duration levels may result in permanent hearing dam-
age. However the nature of the decibel is such that
an impulse of 110 dB for one second will raise a 24
hour 55 dB average level, to a 24 hour-Leq of 62 dB.
The average descriptors show an effect to impulse
noise and therefore in most cases it is sufficient
to use these average descriptors.
Another area which is requiring further study is the
use of nationally averaged scenarios to represent envi-
ronmental impact of various noise emission sources. In
using an averaged scenario, the high impact areas are
lost in the average. There is a need for a national
indicator for assessing the relative impact of various
regulations. However, the national indicator would be
more meaningful if the average were arrived through
a system of scenario sampling. Often more eirmision
sources are used in certain geographic areas
V >
•as
0.01
, —
Lan= 30-30 log i
0.03 0.07 0.10 0.80
Distance from Right of Way, Miles
Figure IV. Day Night Average Sound Levels Adjacent
to Urban Freeways.
806
-------
than in others. Many situations exist where commun-
11Tles ^re severely impacted by highway noise. Other
situations exist where expensive noise abatement pro-
grams are underway. Obviously all worst case scenarios
cannot be found, but a statistical sample of both urban
and freeway scenarios can be developed. Techniques are
available to accurately predict the levels of exposure
in each scenario and determine the number of people
impacted.
Currently efforts are underway to look at a number of
urban sites and identify characteristic features that
could lead to a sampling model. In each scenario
site features include acceleration/deceleration areas,
lane miles, traffic characteristics (volume, speed,
and distribution), topography (vegetation and barrier
types) , roadway characteristics (configuration and
grade), types of housing (single dwelling, or multi-
family) and general land use areas such as school,
recreation, industrial and commercial areas. These
sites could then be used to illustrate a range of scen-
arios and the impacts and benefits of each regulation
could be expressed in terms of specific sites. The
next step would be to indicate how these sites repre-
sent subgroups within the national population distri-
bution impacted by noise sources.
CONCLUSION: The question that arises when using any
model is the accuracy. The data gathered from the
100 sites shown in Figure II indicate that the stan-
dard error of estimate of the Log of the population
density on Ldn is about 4dB. This is considered
analogous to a standard deviation of 4dB. The stan-
dard deviation gives the measure of the dispersion of
the distribution. However, no data are available as
to the variability of traffic mixes used in the Urban
Traffic Model. The assumptions used need to be under-
stood in interpreting the results.
Propagation noise model variations are another area
where accuracy and understanding of variations are
critical. Consider a model which predicts a 70 dB
contour at 500 feet from a freeway. If the model over
predicted by 5 dB, the 70 dB contour would be 1075
feet from the freeway. An over prediction of 10 dB
would move the 70 dB contour out to 2320 feet. Errors
of overprediction may cause needless noise abatement
programs, either regulations or actual highway bar-
riers, soundproofing buildings or acquisition of
public land. Errors of underprediction would cause
excessive noise impact on the public.
Finally it should be realized that there is enough
known about the characteristics of noise and that
technology is available to develop complex models.
However, the amount of information required to include
all sources of environmental noise, all factors
affecting propagation, and the wide range of human
responses would be overwhelming. Therefore a number
of assumptions has been made to reduce the complexity
of the models, primarily because of lack of data.
As more data become available the models will include
additional parameters to more accurately describe and
assess impacts at specific sites and project site im-
pacts to the nation as a whole.
SELECTIVE REFERENCES:
1. "Community Noise: U.S. EPA, NTID 300.3,
December 1971.
2. Galloway, W. J. et. al., "Population Distribution
of the United States as a Function of Outdoor
Noise Level," U. S. EPA, 550/9-74-009, June 1974.
Hajek, J. J. "Ontario Highway Noise Prediction
Method," Ministry of Transportation and Communica-
tions, RR 197, January 1975.
"Highway Noise, .a Design Guide for Highway
Engineers Cooperative Highway Research Program
Report 117, 1971.
"Information on Levels of Environmental Noise
Requisite to Protection Public Health and Welfare
with an Adequate Margin of Safety," U. S. EPA,
550/9-74-004, March 1974.
Kugler, B.A. et. al., "Design Guide for Highway
Noise Prediction and Control," Transportation
Research Board Report 3-7/3, November 1974.
Plotkin, Kenneth J., "A Model for the Prediction
of Highway Noise and Assessment of strategies for
its Abatement through Vehicle Noise Control,"
Wyle Research Report, September 1974.
Sharp, B. H., Research on Highway Noise Measure-
ment Sites." California Highway Patrol, March 1972.
Wesler, J. E., "Manual for Highway Noise Predic-
tion," DOT-TSC-FHWA-72-1, March 1972.
807
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THE COST OF WATER SUPPLY UTILITY MANAGEMENT
Robert M. Clark
Systems Analyst
Water Supply Research Division
U. S. Environmental Protection Agency
Cincinnati, Ohio 45268
James I. Gillean
President
Act Systems, Inc.
Orlando, Florida
ABSTRACT
Passage of the Safe Drinking Water Act has
intensified a growing awareness of problems
related to the supply of safe drinking water
to the American public. Of major concern is
the economic impact which might result from
promulgation of regulations under the "Act".
In an attempt to understand these impacts,
EPA's Water Supply Research Division is
conducting a study in which one or more water
utilities are being investigated in each of
EPA's ten regions. In this paper
representative cost data which have been
collected from these case studies are
presented. These data will be useful in
evaluating the economic impact of the Safe
Drinking Water Act. They should also lead to
a greater understanding of the economic
factors which affect the costs of the various
components making up a water supply system.
INTRODUCTION
Problems related to water supply have become
increasingly important in recent years. In
the past, supplying water to the consumer was
considered to be a routine matter, and water
itself seemed to be available in almost
unlimited quantities. But this is no longer
the case in most parts of the United States.
Perhaps water itself is not a scarce
resource, but supplying water of acceptable
quality to an increasingly urban population
is no longer a simple matter.2 Spreading
urban boundaries force many potential water
supply customers to locate farther and
farther away from available water sources.
Some areas which are inherently water limited
have attracted significant population growth,
thereby straining the available water
resource. A scarcity of the land, labor, and
capital resources needed to convey water to
places of useful application have contributed
to these problems.
Passage of the Safe Drinking Act with its
primary and secondary regulations has
intensified a growing interest in problems
related to water supply and water supply
utility management.5 The primary regulations
which are health related and the secondary,
non-enforceable, aesthetics related
regulations cannot help but have some
economic impact. For this reason one of the
primary concerns expressed in the Act relates
to the magnitude and form of this economic
impact upon the American public.
In an attempt to obtain data which can be
utilized to assess the Act's economic impact
and to understand the factors which influence
the cost of water supply the EPA's Water
Supply Research Division has been conducting
a series of case studies. One or more
utilities have been investigated in each of
EPA's ten regions. Data from one of these
case study areas (Cincinnati Water Works) are
presented in this paper. These data are
typical of those being collected in the other
case studies, and reflect the costs as they
affect the functional categories and physical
supply problems associated with water supply
utility management.
DATA GATHERING PROCEDURES
Water supply systems are generally composed
of (1) collection works, (2) purification
systems, where needed, and (3) transportation
and distribution systems. The collection
works either tap a source of water that can
satisfy present and reasonable future demand
on a continuous basis, or they convert an
intermittent source into a continuous supply
by storing surplus water for use during
periods of low flows. If the water is not of
satisfactory quality at the point of
collection, it is treated to make it
esthetically attractive and palatable.
Water containing iron or manganese is
subjected to deferrization or
demanganization; corrosive water is
stabilized chemically; and excessively hard
water is softened. The transportation and
distribution works convey the collected and
treated water to the community, where it is
distributed to the consumers.
Because large operating and capital
investments are involved, it is important to
be able to compare costs between utilities to
understand the components which make up the
operation.^ To make these kinds of
comparisons it is necessary to collect the
data in a standardized manner. One approach,
and the one which will be utilized in this
report, is to define the utility's operations
in such a manner that they can be categorized
into functional areas. Figure 1 illustrates
a typical utility in which the operations
have been defined as being composed of the
functions of acquisition, treatment, and
distribution. This is an oversimplified
categorization but serves as a useful
beginning point. One important area not
included is the management function. By
collecting data that describe these
808
-------
functional categories it is (in theory)
possible to compare the costs of one water
supply with those of another. This is the
principle that has been used to gather data
on the Cincinnati Water Works, although the
functional categorizations are much more
detailed than presented in the example.
The Cincinnati Water Works operations have
been defined as follows: acquisition,
purification, transmission and distribution,
power and pumping, and support services.
These functional categories are common to all
water utility operations although the
specific costs assigned to each functional
category may vary depending on the utility.
All of the costs, with the exception of the
support services category, are those which
make that specific activity operational.
Support services includes management,
customer services, and all of those costs
which do not relate to specific operating
activities, for example, laboratory personnel
costs are included in the purification
activity, but the mangement costs of the
purification treatment division are included
in the support services category.
Maintenance and repair costs are allocated to
each category where appropriate.
In addition to the Operating Costs, one must
also include Capital Costs in the analysis in
order to be complete. For the purposes of
this analysis, Capital Costs are defined as
the depreciation on the utility's existing
plant in service, and the interest on any
types of borrowing mechanisms which the
utility may use to raise money for capital
investment. Depreciation as reported here is
based on the actual cost of the facility
divided by its useful life, and not on
reproduction cost. The data as reported for
depreciation, therefore, will reflect lower
costs for older utilities. This is true in
the case of the Cincinnati Water Works, since
most of its facilities were built from 1930
to 1940. In order to understand the
magnitude of the bias which such an
assumption introduces, an analysis of the
replacement cost for the utilities facilities
has been made. Using a standardized
construction cost index, the original cost of
each facility currently in use has been
inflated to a 1974 cost base.4 The analysis
is contained in a section which will follow.
The interest costs are those which the
utility has historically paid for money.
Table 1 summarizes the cost categories utilized
in this analysis.
TABLE 1
Operating Costs
Overhead
Acquisition
Purification
Transmission and Distribution
Power and Pumping
Capital Costs
Depreciation
Interest
All of the cost analysis which will be
discussed in this paper is based on revenue-
producing water. The unit costs presented
will be calculated using , the revenue-
producing water pumped by each utility during
the water year from 1964 through 1973.
SERVICE AREA
The present service area lies almost entirely
within Hamilton County with fringe extensions
into three adjoinging counties. Although for
the most part they are surrounded by the
Cincinnati Water Works service area, a number
of communities maintain their own systems.
Emergency service is provided to most of
them, but, as long as their source of supply
can be maintained, most of the communities
will not change their present status.
The current source of supply is the Ohio
River, from which water is pumped to the
treatment plant. It has a capacity of 235
million gallons per day (mgd), in 1973 it
treated an average of 136 mgd. Water is
distributed to the east through a series of
pumping stations and tanks. To the north and
west, water passes through two gravity
tunnels and through two pump stations into a
large reservoir and is then repumped into
outlying service areas.
COST ANALYSIS
Figure 2 shows the total water pumped by the
utility during calendar years 1964 through
1973 as well as metered (revenue-producing)
water and water which was accounted for but
did not produce revenue. All cost data are
based on revenue-producing water, for
example, purification costs in dollars per
million gallons ($/mil gal) are based on
revenue-producing water and not on the total
number of gallons of water pumped by the
utility. As can be seen from Figure 2, the
total water pumped exceeds revenue-producing
water by nearly 13,000 million gallons in
1973.
809
-------
Table 2 contains the total operating cost for
each of the previously mentioned categories.
The Support Services category includes all of
those operating costs that support but are
not directly chargeable to the production of
water. It includes such items as general
administration, accounting and collection,
and meter reading. The Purification category
includes those costs related to the cost of
operating the laboratory, labor involved in
the treatment function, chemicals for
purifying the water, and maintenance of the
treatment plant. Power and Pumping includes
those costs related to operating labor,
maintenance, and power for pumping water
throughout the service area. The
Transmission and Distribution category
includes the operating labor and maintenance
costs associated with supplying water to the
consumer.
It can be seen from the table that the
Support Services costs have more than doubled
between 1964 and 1973. Although all of the
other cost categories increased during this
period, their rate of increase was less than
that of this category. Total operating costs
increased by about 65 percent.
Table 2 also contains the total average unit
operating costs for each major category based
on the number of revenue-producing gallons
pumped in a given year. As can be seen, all
the cost categories increased by a factor of
less than two, and the total operating cost
increased by about 40 percent. Each cost
category is presented as a percent of total
operating cost. It is obvious that Support
Services accounted for a significant and
increasing portion of the utility's budget,
from approximately 26 percent in 1964 to 31.5
percent in 1973. The other cost categories
either decreased or remained constant.
Depreciation and Interest Expense are defined
as the capital expenses for the waterworks
system. These capital expenses remained
essentially constant but operating expenses
increased by approximately 65 percent. As
can be seen from Table 2, the percent of
expenditures allocated to capital decreased
from approximately 27 percent to 22 percent
during the period. Operating expenditures
are always reported in inflated or current
dollars, while capital expenditures are
depreciated in historical dollars over a long
period of time. The problems related to the
depreciation of capital will be discussed
later. Since the Support Services category,
which is labor intensive, played an
increasingly important role in the cost of
water supply, labor and manpower costs will
be analyzed in the following section.
Labor Cost Analysis
To evaluate the impact of labor costs on
operating costs for water supply, it is
necessary to examine the payroll of the water
utility (Table 3). It can be seen that labor
costs accounted for 64 percent of the
utility's operating costs in 1964 and for 62
percent in 1973. The average cost per man-
hour increased 71 percent, while the number
of man-hours/mil gal of metered consumption
decreased by 23 percent. The bottom line in
the table shows a decreasing capital/labor
cost ratio. Although economies of scale were
achieved with respect to the number of man-
hours used to produce water, the effect on
cost was nullified by wage increases. The
table, therefore, illustrates the importance
of labor in what is typically presumed to be
a capital intensive industry.
Depreciation Analysis
As mentioned earlier, capital expenditures
comprise a large portion of the cost of water
supply. Depreciation reflects historical
costs and not the cost of replacing a capital
facility based on current costs. Historical
costs refer to the original construction cost
of a capital facility, while reproduction
costs reflect the capital expenditures
necessary to build an identical plant today.
Historical cost is exact, but reproduction
cost is based on the original investment
modified by an appropriate index.
The records of the Cincinnati Water Works
show the historical value of the plant-in-
service to be $111,700,315. The value of
pipelines, plant, or equipment previously
replaced or fully depreciated is excluded.
Using the historical costs, a reproduction
cost was calculated using the ENR Building
Cost Index (1913 = 100) for buildings and
equipment and the ENR Construction Cost Index
(1903 = 100) for pipes and valves. (A
skilled labor cost factor is used to compute
the Building Cost Index, and a common labor
cost factor is used to compute the
Construction Cost Index). Having weighted
these capital expenditures with the proper
indices, a reproduction cost of $458,990,287
was found for the current plant-in-service,
which represents a 311 percent increase over
the historical value. These capital
expenditures do not include the capital
investment in a new treatment plant (Great
Miami) which is expected to be operational
soon. Derivation of a reproduction value
facilitates examining the impact of inflation
on capital cost and the current worth of
capitals contribution to output. The
computations discussed in this section are
summarized in Table 4.
SYSTEM EVALUATION
Using the cost data for the various
functional areas discussed earlier, costs
were allocated to specific treatment,
transmission, storage, and pumping facilities
in the system. A general cost was determined
for distribution, interest, and overhead.
Using costs based on 1973 $/mil gal and
assuming a linear allocation of costs for a
given area against capacity required to serve
it, the facility costs associated with each
service area, such as pumping and storage,
were established as shown in parentheses in
Figure 3.
The codes in the schematic diagram (Figure 3)
can be related to cost values. For example,
the acquisition cost for water from the Ohio
810
-------
River, including depreciation of the facility
and operating costs, is $16.70/mil gal. As a
unit of water (mil gal) moves through each
facility to another service area, the unit
cost of moving water through that area is
added to the cost of getting water to that
area, thereby creating incremental costs.
The facility and transmission costs are added
to the costs of distribution, interest, and
overhead to yield an average unit cost to
serve that area. A service zone represents a
customer service area and a demand point for
water. For purposes of this analysis an
attempt was made to discriminate between the
water demanded in a given distribution area
and the water transmitted through the area
into the next service zone.
To illustrate the way in which cost changes
from one service area to another, we can
examine the Bl and B2 cost areas (Figure 4).
The cost per million gallons for area Bl is
composed of acquisition cost ($16.70),
treatment cost ($60.26), distribution cost
($50.52), interest cost ($17.57), and
overhead cost ($85.22). This yields a total
cost of $336.86/mil gal. For the B2 area,
the pumpin'g and storage costs ($80.45) and
the transmission costs ($60.26) must be added
to the Bl, and this yields a cost of
$477.60/mil gal. These values are plotted in
Figure 4. The costs in each zone are
described by a. step function. As water is
pumped from the treatment plant through the
Bl zone, the average cost per million gallons
(using this analysis) remains constant,
however, as water is repumped into the B2
zone, the costs take a definable jump to a
higher level.
The step function suggests the possibility
that as additional service zones are added to
the periphery of the utility service area the
cost functions will continually increase. It
is revealing to compare this costing analysis
to the prices actually charged in the utility
service area.
PRICING ANALYSIS
Figure 5 is a map of all of the cost zones
which make up the Cincinnati Water Works
service area. Table 5 contains a comparison
between the revenues received from the ten
largest users in the service area and the
cost of service. It can be seen that many of
the major users are not meeting the costs of
supplying water to them.
NATIONAL EVALUATION
Cost data for the other water supplies
studied have been developed in the same format
as presented in this paper. Table 6 contains
the costs for these utilities using the cost
categorizations discussed. The following
approximate breakdown of the percentage of
cost which makes up each category is
interesting: Acquisition 15%; Treatment
12%; Distribution 29%; Support Services
24%; and Interest - 20%.
SUMMARY AND CONCLUSIONS
This report documents the application of a
functional approach to the analysis of water
supply utility management costs.
Functionally, these costs have been defined
in the following manner: Support Services;
Acquisition; Purification; Transmission; and,
Power and Pumping. Having defined these
costs in a functional manner, they can be
reaggregated into capital and operating costs
for the various physical components which
make up the water delivery system. It is
apparent from the first analysis that
manpower costs are a significant part of
water supply operating costs and that this
factor is playing an increasingly important
role in the total cost of water as delivered
to the consumer. As water is pumped from
treatment plant to consumer, costs are added,
and they increase with respect to distance
from the central supply. By using a specific
utility as an example, this kind of analysis
can be related to "real world" costs.
However, it is obvious that the basic
principles discussed apply to all water
supplies and that they must be considered in
planning and design of water systems. The
functional analysis is extremely important
for regional considerations. Perhaps the
major choice facing most small to medium
water supplies will be to join a larger water
system or to develop and improve their own
water supply systems (4). The approach taken
in this analysis should materially assist
planners and policy makers in making these
types of decisions.
REFERENCES
1. Cincinnati Water Works, Annual Report
1973.
2. Clark, Robert M., Cost and Pricing for
Water Supply Management, accepted for
publication in the Journal of the
Environmental Engineering Division of the
American Society of Civil Engineers.
3. Clark, Robert M., and Goddard, Haynes C.,
Pricing for Water Supply: Its Impact on
Systems Management, EPA-670/1-74-001,
April 1974, National Environmental
Research Center, Office of Research and
Development, U. S. Environmental Pro-
tection Agency, Cincinnati, Ohio 45268.
4. Engineering News Record, McGraw Hill
Publishing Co., March 20, 1973, p. 63.
5. S.433, Public Law 93-523, Safe Drinking
Water Act, 93rd Congress, Washington, D.C
(Dec. 16, 1974).
811
-------
STORAGE TRANSPORT TREATMENT STORAGE DISTRIBUTE
ACQUISITION TREATMENT DISTRIBUTION
FIG 1 -SCHEMATIC DIAGRAM OF ACQUISITION, TREATMENT AND
DISTRIBUTION FUNCTIONS FOR A TYPICAL WATER
SUPPLY SYSTEM
i «-!
S
.T
FIGURE 2. Pumped and metered water for Cincinnati Water Works (1964-1973).
(J3143)
C3b
(136 86)
($37.50}
(S46.881
C2
JSO 311
Gravity
A
($5537) (180.481
isnojo)
t
(13605)
9 Kro9*, Compony
10. E. Kohn't and Son'i
FIGURE 5. Major facilities in Cincinnati Water Works i
Supp
Acqu
Furl
Tran
Disc
Iota
Dcpr
Inta
Iota
Iota
Capl
ten
ill
oE
111
/ml
lea
of
/ml
111
/ml
Did
ibu
111
of
/ml
Op
111
ela
111
111
Co
ill
Op
Bl
111
/ml
64 65
OCVlCBB
on S 1.360 1.331
total 25.6 25.2
EBl 42.41 40.24
on S 0.395 0.369
gal 12.25 11.15
Ion
total 17.2 17.2
gal 28.48 27.42
Pimping
on S 1.086 1.115
total 20.5 21.1
gal 33.88 33.74
on S 1.558 1.554
total 29.3 29.5
gal 48.60 47.00
rating Costs
on S 5.310 5.275
on S 1-177 1.230
on S 0.826 0.947
on $ 2.003 2.177
rating and
on S 7.314 7.452
gal 228.10 225.41
" 67 68
1.413 1.499 1.616
25.2 24.9 26.1
41.90 43.87 46.55
0.374 0.372 0.380
6.7 6.2 6.1
11.10 10.90 10.94
16.6 16.7 16.4
27.69 29.41 29.14
1.1B2 1.256 1.247
21.0 20.9 20.2
35.07 36.77 35.92
1.711 1.885 1.928
30.5 31,3 31.2
50.74 55.19 55.52
5.615 6.017 6.183
1.422 1.550 1.605
0.927 0,877 0.887
2.349 2.427 2.492
7.964 8.444 8.665
236.14 247.19 249.56
KQ
2.109
29.9
58.25
0.405
5.8
11.19
14.8
28.76
1.412
20.0
39.01
2.084
29.5
57.57
7.051
1.634
0.8fl7
2.521
9.571
264.41
in
2.081
28.6
56.06
0.427
5.9
11.50
14 '.6
2B.69
19.0
37 , 23
2.323
31.9
62.58
7.277
1.632
0.793
2.425
9.702
261.39
71
2.371
29.1
62.20
0.496
6.1
13.02
14 ', 3
30.54
1.638
20.0
42.97
2.4B7
30.5
65.23
8.158
1.657
0.802
2.459
10.617
27B.45
72
2.633
30.7
69.43
.480
.6
1 .66
1 .4
32.70
1.635
19.0
43.10
2.606
30.3
68.72
8.595
1.699
0.711
2.410
11.005
290.14
7?
2.766
31.5
72.60
0.485
5.5
12.73
13. B
31.75
1.667
19. D
43.75
2.654
30.2
69.65
8.7B2
1.771
0.669
2.440
11.223
294.54
FIGURE 3. Schematic diagram of facility costs in Cincinnati Water Works system.
(To convert S/mil. gal. to S/1000 cum, multiply by 0.26.)
o
J
S336.86*
COST CURVE
B1
SERVICE AREA
B2
SERVICE AREA
FIGURE 4. Step function cost curve for B1 and B2 service areas.
(To convert $/mil. gal. to S/1000 cum, multiply by 0.26.)
-^965 1966 L96T
32.063 33,061 33,725 34,160 34,722 36,199 37,117 3B.128 17,MB 38,104
105.840 102 812 108.660 115.540 117.676 122,84S 120.358 130.604 13B.711 143.675
34.62 33.76 32.70 32.Bl 33.08 31.53 30.06 28.70 28.25 27.47
3.06 3.04 3.32 3.52 3.56 3.B9 4.00 4.55 4.91 5."
Mecertd"
Total Rour»/HC»'*
Avetago Coat For
Kan Hour
Capital/Labor Co«
812
-------
TABLE 5
Actual Charge Versus Cost Comparisons for Ten "ajor Users
in Cincinnati Water Works
Historical and
TABLE 4
Reproduction Costs of Plant-In-Service
for Cincinnati Water Works (Dollars)
Capital
Facility
Plant
Pipe
Misc. Plant*
Total
*Capital expenditures
Historical Reproduction
Cost Cost (1973-74 Dollars)
42,649,160 146,981,272
54,848,943 296,771,626
13,202,213 15,237,389
110,700,315 458,990,286
which are not specifically identified.
User
Norwood
Hilton Davis
Sun Chemical
Procter & Gamble
Davison Chemical
Metropolitan Sewer
Cincinnati Milacron
Kroger Company
(Suburb)
Kroger Company
(City)
E. Kahn's Sons
Revenue
($/MG)
294.12
168.83
174.67
169.87
175.44
308.70
321.12
87.54
180.26
175.19
185.44
175.07
187.95
313.54
328.26
181.90
197.73
181.67
195.17
Cost*
($/mg)
272.80
262.99
275.54
275.54
272.80
264.56
272.80
262.99
264.56
264.56
*The value for $/MG (dollars per million gallons) can be converted
to dollars per 10 cubic meters by multiplying by 0.26.
TABLE 6. - Summary of Costs for Utilities Studied
(1973-74)
1973-74
Billed Acquisition Treatment Distribution Support Interest Private Total Dividends
Utility Consump- Services Utility Cost
tion Taxes
(bil gal/yr) ($/mil/gal) ($/mil/gal)($/mil/gal) ($/mil/gal)($/mil/ ($/mil/ ($/mil/ ($/mil/
gal) gal) gal) gal)
Kansas City, Mo.
Dallas, Texas
San Diego, Calif.
New Haven, Conn.*
Fairfax Co. Virginia
Kenton Co. Kentucky
Orlando, Fla.
Elizabeth Water Co.*
New Jersey
Cincinnati, Ohio
26.9
63.0
47.2
17.7
19.2
2.2
12.5
38.2
38.1
15
25
279
28
34
12
39
59
16
.28
.17
.61
.97
.79
.41
.65
.52
.70
81
51
27
15
61
102
25
42
60
.98
.70
.47
.38
.54
.60
.51
.07
.26
138.
119.
105.
107.
128.
124.
132.
111.
127.
64
91
86
34
33
41
82
45
41
144.52
83.46
95.64
118.19
88.27
81.63
110.31
89.80
72.60
50.32
57.71
6.73
116.70
208.57
73.26
85.12
113.16
17.57
430
337
515
196.44 583
521
394
393
96.71 512
294
.70
.95
.31
.02 87.86
.50
.31
.41
.71 45.63
.54
*Privately Owned
813
-------
MATHEMATICAL MODELING OF
DUAL WATER SUPPLY SYSTEMS
Arun K. Deb
Roy F. Weston, Inc.
West Chester, Pennsylvania
Kenneth J. Ives
University College London
London, England
ABSTRACT
A small percent of total domestic water usage is
usually required to be of potable water quality; the
rest of domestic need may not warrant excellent
quality. Dividing water supply into two portions,
potable and nonpotable, a mathematical model of con-
ventional and dual supplies has been developed to
evaluate the technical and economical feasibility of
dual supplies under various conditions. The sensi-
tivity of the model has been evaluated for various
parameters.
INTRODUCTION
Technological advances coupled with increases in popu-
lation during the past decades have caused the demand
for fresh water and the discharges of effluents and
wastewater to rivers, lakes and coastal waters to
increase. A fundamental need of any community is an
adequate supply of biologically and chemically safe,
palatable water of good mineral quality. If the
present rate of growth of population and industry
continues, the quality of natural water will deteri-
orate and it will be difficult to guarantee the high
quality of bulk water supply for domestic uses. With
the development of new chemical compounds day by day
for an ever-increasing demand of the consumer market,
and with the increasing use of chemicals in agri-
culture and industry, new micro-pollutants are finding
their way into natural water courses.
Although it is possible that by treatment the mineral
quality and palatability of water can be improved,
additional treatment cost to remove trace chemicals
and high TDS will be high. tt would be difftcult and
costly to produce very high quality bulk water for
all domestic purposes from such sources.
It has been reportedl that of the water used in
households in England only about 3.2 percent is used
for drinking and cooking and about 9.6 percent is
used for dishwashing and cleaning. About 35 percent
is used for personal hygiene; another 35 percent is
used for toilet flushing, and 10 percent is used for
laundering. The remainder is used for gardening and
car washing. This analysis of various household uses
indicates that about 87 percent of household water
does not require water of very good quality with re-
spect to TDS and trace chemical contaminants which
would cause objection if ingested for a long time.
However, if it is assumed that only a small fraction
(about 13 percent) of household water must be of the
quality of drinking water, the volume of water to be
treated by expensive sophisticated treatment pro-
cesses would be small enough to allow economy in
treatment. The remaining nonpotable portion of the
domestic water would be biologically safe and
supplied through a separate distribution system.
Haney and Hamann^ made a rational comparative study
of conventional and dual water systems. The objective
of the present study is to develop a mathematical
model to evaluate the technical and economical feasi-
bility of dual supply systems for two hypothetical
British towns using twelve alternative schemes of
treatment and supply.
PROJECTED WATER DEMAND
In this study the planning period was taken as 1971
to 2001. The demands on public water supply for do-
mestic and industrial uses are assessed separately.
Instead of projecting the total demands of past
years, in this study the contributing factors are
separated into per capita domestic demand, per capita
industrial demand, and population growth.
By regression analysis of past domestic water con-
sumption data of nine British towns, the best-fit
equation for the per capita domestic demand index
percent is given by:
100 IDt = 67.24 + 1.23 t
(1)
in which 100 IDt = per capita domestic demand index
(percent) in the year t; t = number of years after
the year 1950. Similarly, the best-fit equation for
the per capita industrial demand index (percent) has
been developed as:
100 ITt = 63.85 + 1.314 t1'0888 (2)
in which 100 ITt = per capita industrial demand
index percent in the year t after 1950.
Combining Equations (1) and (2) and giving proper
weighting for domesttc and industrial demand, per
capita total demand index percent can be approxi-
mated as:
100 lt = 65.95 + 1.26 t1'08" . (3)
The value of lt for the year 1971 is 1.00.
By regression analysis of past population data of
various towns, the best-fit equation for population
index percent is obtained as:
100 I Pt = 82.65 + 0.826 t (4)
After assessing separately the growths of population
and per capita water demand, the total water demand
projection for a town can be obtained by combining
per capita water demand with population:
= POP71 (187.10 + 3.57 t " ) (0.827 + 0.00827 t) , (5)
in which 0_t = total water demand in t-th year after
1950, in million liters; POPyi = population in the
year 1971 in thousands.
814
-------
COST FUNCTIONS
To develop mathematical models for conventional and
corresponding dual suppltes, the capital costs and
0 & M costs of various units of treatment and dis-
tribution as functfons of flow are required. Cost
data for various units of treatment and distribution
which are valid for England have been taken from the
1 iteratureS.'t and updated and formulated in mathe-
matical functions valid for 1971, the base year in
this study. All the various components considered in
this study are divided into two groups as treatment
and distribution and are listed with useful life
periods in Table 1.
Unit No.
Unit Component
Useful
Life
years
1
2
3
A
5
6
7
8
9
10
11
12
River Intakes
Impounding Reservoir
Conventional Treatment
Chiorination Equipment
Contact Tank
Wells
Activated Carbon
Elect rod i a lys is
Pumping Mains
Pumping Stations
Service Reservoirs
Distribution Mains
30
60
30
15
1*0
15
15
15
30
15
1(0
30
Table 1, Useful Life Periods of Components.
Capital cost (y) and 0 S M cost (Y) functions of
various treatment units valid for 1971 are given in
Tables 2 and 3, respectively. Costs are expressed in
British Pounds (i 1 = $2.07) and flows (Q) are ex-
pressed in mi 11 Ton liters per day.
Wells
Activated Cai'bon
• 65,000 + (3,500 H
d - dosage (mg/L)
yn • (7.78 IDS + 5.070) 0. + 11,275;
0 IDS •> TDS In raw water (rag/L)
• In pounds ( C 1 • S2.07). Q • plai
Table 2. Capital Cost Functions.
Table 3. 0 & M Cost Functions of Treatment Units.
Distribution System
From available literature^, the total installed
Unit No.
I
2
3
*
5
6
7
8
Treatment Unit
River Intakes
Impounding Reservoir
Conventional Treatment
Chiorination Equipment
Contact Tank
Wells
Activated Carbon
Electrodialysls
•Costs are In pounds/year HI - 52
million liters.
'1
V2
Y3
\
Y,.
¥6
Y7
V8
07).
0 S H Cost Functions for 1971*
- 651 q
- 27-5 q1'35
- 1,635 q
= 36.5 q
" 0.42 q
- 930.75 q + 173.9 q *
= l,785q/(q 8.5)°-'07
. 8,888 q°'9
q ™ production per day In
capital cost of a pipeline can be expressed as a
function of diameter:
C = KDm (6)
in which C = cost of pipeline per meter length and
D = diameter of pipe in millimeters. For England
(1971) in open areas the values of K = 0.0067 and
m = 1.272; for built-up areas K = 0.0134 and
m = 1.272. The 0 S M cost of water distribution
mains of a town in England has been found to be £76
per kilometer per year.
Pumping station capital cost has been expressed in
the 1 iterature't.S as a function of installed power:
Vio = k,0 (kW)m'<> (7)
in which yig = capital cost of pumping station,
kW = installed power in kilowatts, and k^Q and
m-\Q are parameters of the cost function. For England
(1971) the value of kio = 523.0 and of mio =
0.785 when yig is expressed in pounds.
Operating costs of a pumping station including the
costs of labor, electricity and maintenance for
England (1971) are a function of operating head as:
Y|0 (13.61 H + 379.0) q (8)
in which Y = pumping station 0 6 M cost in
£ /year; q = average daily pumping rate in million
liters per day, H = operating head, in meters.
From a regression analysis of the cost data from
England and considering a 24-hour storage in the
service reservoir, the capital cost function for a
service reservoir can be expressed in terms of
design flow:
yn kii Qm" (9)
in which yn = capital cost in pounds; Q = design
flow in million liters/day; kji = 19,169 and
m-| i = 0.723. Operating costs of the service
reservoir in pounds can be expressed as a function
of design flow in million liters/day as:
Yn = 20 Q . (10)
DISTRIBUTION SYSTEM ANALYSIS
Considering the total cost of a pumping system con-
sisting of capital costs of pumps and pipelines and
their 0 S M costs, a mathematical model of a pumping
system has been developed in order to optimize the
total cost in seeking the least cost diameter for the
pipelineS. The cost functions for pumps and water
mains valid for England (Equations 6, 7, and 8) have
been used to obtain the most economical diameter as a
function of flow:
D
opt
(11)
where kg and mg are functions of cost function param-
eters, flow equation parameters and interest rate.
For this study, it has been found that
D
opt
(12)
combining with the cost function of capital cost of
the pipeline (Equation 6):
Capital Cost of Optimum Main, y ex Q
0.59
(13)
815
-------
Pumping Ha ins
To compare the optimum capital costs of a convention-
al (single) system and a dual system of supplies,
consider a total flow of 0_, potable flow of rO_, and
nonpotable flow of (1 - r) 0_. For the same lengths
of mains, the cost of mains in a single system
Yr is proportional to 0_°-59; in the dual system
0.59 0.59 0.59 ,
Yn is proportional to Q lr + (1 — n J.
The ratio of cost of mains in a dual system and a
single system can be given as:
0.59 .0.59
YD/YS = r +d-r)
Gravity Mains
(14)
The costs of single and dual mains under the same
hydraulic gradient have been compared. Using the
Hazen-Wi11iams Equation for ptpe flow and pipeline
cost function (Equation 6), the cost of a gravity
main with constant hydraulic gradient can be expressed
as proportional to 0.0.483. The ratio of cost of
gravity mains in a dual system and a single system
can be expressed as:
YD/YS = r °-483 + (1 -r)0-483 (15)
Distribution mains from the service reservoir to the
consumers have been assumed to be under a constant
hydraulic gradient.
MODEL FORMULATION
Mathematical models of dual and conventional water
supplies considering 12 different treatment systems
(Table 4) have been developed. Two typical hypo-
thetical British towns with 1971 populations of
100,000 (Town A) and 500,000 (Town B) have been con-
sidered to develop treatment system and distribution
system models of dual supply. Total treatment and
distribution costs of conventional supply and of dual
supply for all 12 treatment systems have been formu-
lated, and the difference of treatment and distri-
bution costs between single and dual supplies for all
the 12 systems have been calculated. In formulating
the mathematical models, the parameters such as
potable-to-total-flow ratio, r; interest rate, i;
annual capital cost increase rate, cc; and annual
0 £ M cost increase rate, co, are considered as
variables.
ils:^ ??"••';•..
Table k. Various Treatment Systems Considered for
Dual Supply.
Basis of Formulation
The econo-mathematical models for all the systems have
been developed on the following basis: 1) The models
represent hypothetical new British towns and there-
fore are general theoretical models rather than
specific ones. 2) Cost functions are derived from
the literature and provide only approximate costs;
they are indicative, not definitive. They are
certainly not applicable, without adjustments, to
specific cases. 3) The quality of water from the
single-supply source is assumed to be the same as
the potable supply in a dual-supply system. 4) Quanti-
ties of water required are obtained by projecting
per-capita domestic and industrial demand; however,
the rate of growth has been kept as a variable so
that other rates of growth can also be incorporated
in the model. 5) A leakage loss of 15 percent has
been assumed. 6) Administrative costs have been in-
cluded in all cost functions.
In comparing the costs of single supply and corre-
sponding dual supply, all the costs incurred during
the planning period (1971-2001) have been converted
to the present value of the base year (1971). If
some of the treatment or distribution units have
residual design life remaining at the end of the
planning period, the residual values of the units
have also been considered as assets in the calcu-
lation of the system cost.
Treatment Systems
The present values of all capita] and 0 & M costs incur-
red during the planning period of all treatment units
have been calculated using corresponding cost functions
for design flow, 0_; potable flow rQ; and nonpotable
flow (l-r)0_. As the design period for chlortnatton
equipment, activated carbon treatment, electrodialysis
and pumps has been assumed to be 15 years, the design
flow for these units has been taken as the water
demand in the year 15 years after installation. The
design period for all other units has been assumed to
be the same as that of the water demand at the end of
the planning period.
The operational cost functions for various units have
been related to the variable water demand, Q,t, during
the planning period. The present value of the total
operation cost of a unit throughout the planning
period has been obtained by summation of the present
values of all yearly operational costs, which may be
expressed as 30
Ypv
-------
capital cost per year. Equation 17 can be rewritten
for potable and nonpotable flow in order to incor-
porate the cost of a dual supply system.
The present value formulations of capital and 0 & M
costs of treatment of single and dual supply of 12
treatment systems of Table k have been made. A sche-
matic diagram of Treatment System No. 1 is shown in
Figure 1 and a corresponding investment diagram during
the planning period is shown in Figure 2.
Figure 1. Schematic Diagram of Treatment System No.1.
1986
TREATMENT COST SCHEMATIC DIAGRAM
DISTRIBUTION COST SCHEMATIC DIAGRAM
Figure 2. Treatment System No. 1.
The total present value formulations of capital and
0 6 M costs of Treatment System No. 1 for single and
dual systems are given as follows:
(i) Single Supply
ypv(S1S) = y0(TN3)Qi30 + y0(TN4)Qils +V0(TN5)Q(30
+ PVy,s(TN4)Q:30 + RVy30(TN5)Q/30
t = , • T + i • LYtQ,t + YtQ,t
+ Yt(TN5)Q|t f (18)
in which ypv(S1S) = present value of total treatment
costs of System No. 1 in single supply.
Ypv =
Dual Supply
rQ,3o + Yo'TN4>rQ,ls + Vo'TN5'rQ,3o
Y0 t + Yt (TN5)(1 _ r)Q;t] (
in which ypvCSID) = present value of total treatment
costs of system No. 1 for dual supply.
In Equations 18 and 19 the treatment costs of treat-
ment units 1 and 2 have not been included, since the
costs of these units in both the systems are equal.
In a similar way the treatment cost formulation of
all the 12 treatment systems has been developed and
incorporated in the model.
Distribution System Formulation
The distribution system formulation of all the 12
treatment systems will be the same. The total costs
of a distribution system consist of capital costs and
operation and maintenance costs of pumping mains,
pumping stations, service reservoirs, gravity mains
and yearly addition of gravity mains in the distribu-
tion system. All the costs involved during the plan-
ning period have been converted to present value and
formulated as follows:
Single supply
ypv (DSS) = Present value (1971) of total distribution cost in a
single supply system.
= Yoam,3o + YoQ,3o-RVV3o'TU11>Q,3o
30
v I" i + c *
^ Yt(TU13)Qt (—IS) - -L (^-1±
1 = 1 ' 1 + i 30 1 +i
,5 a,
(TV
30
, Yt(TU11)Q(,
1 + i
t= 1
(20)
Dual Supply
Vpv
yov (DSD) Present value (1971) of total distribution cost in a
dual supply system.
= YorQm,3o + Y0(TU9)(1_r)Qm/30
+ y (TU10)Q + y (TU10)(1 ,
rrv Q~,, is
+ PVy15 (TU10)rQ _30 + PVy15 (TU10)(1 _ r)Q
+ Y0(TU11>rQ,3o + YorQ,3o + Yo
-------
Vt(TU13)(1_r)Qit)
[Yt(TU12)rQt
t = 1 1 -
+ Yt (TU12)(1 _ r)Qit + Yt (TU10)rQ/t + Yt (TU10)(1 _ r)Q/t
f YtrQ,3o + Yt'TU11>(1-r)Q,3o] . (21)
Equations 20 and 21 represent the total present value
in pounds of all capital and operation costs of distri-
bution systems during the planning period (1971~2001)
in single supply and dual supply systems, respectively.
RESULTS AND DISCUSSION
The econo-mathematlcal models for single and dual sup-
ply for 12 treatment systems of total present costs of
treatment and distribution of water were solved using
a high-speed computer for various potable/total flow
ratios (r values), interest rates (i values), capital
cost increase rates (cc values), operational cost in-
crease rates (co values) for A-type (base population
100,000) and B-type (base population 500,000) towns.
The computer output comprises total treatment costs,
both capital costs and 0 S M costs, and total distri-
bution costs for all the 12 systems. The cost
advantage of dual supply over single supply, DEL,
is expressed by the difference of total present
value costs of single and dual systems in pounds
sterling.
POPULATION -100,000
RATE OF INTEREST = 0.07
RATE OF INCREASE OF CAPITAL COST = 0.04
RATE OF INCREASE OF OPERATION COST - 0.06
0.1 0.2 0.3 0.4
POTABLE TO TOTAL FLOW RATIO, r
Figure 3. Cost Ratio of Dual to Single System versus
Flow Ratio.
The cost ratio of a dual system to a single system has
been plotted with potable to total flow ratio, r, for
12 treatment systems In Figure 3. The cost advantage
of dual supply over single supply (DEL values) has
also been plotted with interest rate, i, and operation
cost increase rate, co, in Figures 4 and 5, to show
the sensitivities of i and co to DEL values.
Figure k. DEL versus i. Figure 5. DEL 'versus CQ
For Treatment System No. 1, where the potable supply
requires complete conventional treatment and the non-
potable supply requires only chlorination, and dual
system is found to be more economical than a conven-
tional system if the potable requirement is less than
29 percent of the total.
Where the raw water source contains high TDS and
demineralization is required (Treatment Systems
3,' k, 6, 1, 9, 10 and 11), a dual system is more
economical than demineralizatton of the entire supply.
Where a limited supply of high quality ground water
is available, a dual system is more economical than a
conventional system.
REFERENCES
1. Working Party on Sewage Disposal, "Taken For
Granted," Report of Jeger Committee, H.M.S.O.,
England, 1970.
2. Haney, P.O. and Hamann, C.L., "Dual Water Systems,1
JAWWA, Volume 57, No. 5, September 1965.
3. Burley, M.J. and Mawer, P.A., "Desalination as a
Supplement to Conventional Water Supply," Tech-
nical Paper 60, Water Research Association,
England, 1967.
k. Miller, D.G., Burley, M.J. and Mawer, P.A., "A
Survey of Water Supply Costs," Chem. and Ind.
No. 21, 23 May 1970.
5. Deb, A.K., "Pipe Size Optimization in a Pumping
System," J. Inst. of Engrs. (India), Volume
53 PH, October 1972.
818
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DATA COLLECTION FOR WATER QUALITY MODELING IN THE
OCCOQUAN WATERSHED OF VIRGINIA
T.J. Grizzard, C.W. Randall, and R.C. Hoehn
Department of Civil Engineering
Virginia Polytechnic Institute and State University
Blacksburg, Virginia
ABSTRACT
A large-scale water quality monitoring program has
been instituted to provide runoff water quality data
in sufficient detail to facilitate calibration of a
predictive model using pollutant washoff theory. The
sampling program involves the installation of automa-
tic sampling stations, automated chemical analysis of
collected samples, and use of the EPA STORET system as
a data management tool.
BACKGROUND
The Occoquan Reservoir lies on the southern periphery
of the Washington, B.C. Metropolitan area. The con-
tributing drainage basin comprises portions of six po-
litical jurisdictions as shown in Figure 1. Impounded
in 1957, the reservoir today provides a useful storage
of 9.8 X 109 gallons (3.7 X 1010 liters), and serves
as the raw water supply for an estimated 600,000 cus-
tomers in suburban Virginia. In the late 1960's,
rapid development began to occur immediately above the
headwaters of the reservoir, creating the unusual sit-
uation of having an urbanizing area directly upstream
of a water supply impoundment. Currently, eleven se-
condary waste treatment plants in the Manassas-Western
Fairfax County area discharge about 8 MGD (3 X 107
LPD) of treated wastewater to the surface waters of
the basin.
Observations of the reservoir in the period 1968-1970
showed advancing signs of cultural eutrophication,
characterized by periodic blooms of nuisance algae and
accompanying low raw water quality at the Fairfax
County Water Authority Treatment Works (1). Unusual
steps, including the application of massive quantities
of copper sulfate to the reservoir body, hypolimnetic
aeration of the intake area and the addition of acti-
vated carbon slurry to the treatment flow, have been
taken to date to assure the continued use of the im-
poundment as a raw water supply.
In an effort to solve the above problem, the Virginia
State Water Control Board, in July 1971, issued a
"Policy for Waste Treatment and Water Quality Manage-
ment in the Occoquan Watershed" (2). Two major arti-
cles of that document required that existing waste
discharges be consolidated and treated by a "state-of-
the-art" advanced wastewater treatment (AWT) plant in
the Manassas area, and that a continuous, basin-wide
water quality surveillance program be instituted to
evaluate the effectiveness of the AWT processes in re-
ducing pollution problems in the reservoir. As a
corollary to this, it was necessary for the monitoring
program to initiate efforts to quantify and project
the sources of diffuse pollutant yields in the storm-
water runoff from urban and agricultural lands in the
basin.
POLLUTANT WASHOFF
At present, most stormwater quality models (3, 4, 5)
assume first order kinetics in simulating the washoff
of pollutants from the land surface during runoff
events. That is to say, the amount of any pollutant
removed from the ground surface during a given time
interval is proportional to the quantity present at
the beginning of the time interval, as in the follow-
ing equation:
dx
— = -kx
.[1]
where,
x = Pollutant Load (mass)
t = Time
k = Decay Coefficient (time ~x)
This relationship has been used widely as a predictive
tool in modeling the washoff of pollutants that accum-
ulate on the land surface. It does not account for
pollutant runoff yields associated with soil erosion
and, therefore, has its best pure application in the
simulation of washoff from urban (impervious) land
uses. It has, however, been shown to be a reasonable
tool to use in the simulation of applied materials
washoff from agricultural lands (4, 5). The inclusion
of such items as fertilizers, crop residues, and
animal wastes in this category greatly enhances the
suitability of the relationship for use in agricul-
tural areas.
Upon integration and applying appropriate boundary con-
ditions equation [1] becomes:
X0-X = X0 (1 - e-k
.[2]
where,
XQ = Initial pollutant load on ground surface
(mass)
X = Pollutant load remaining at time, t
X-Xg = Pollutant load washed off at time, t
Empirical evaluation of the constant, k, is essential
to the application of equation [2] to the simulation
of pollutant runoff loads. One approach is to assume
that k varies in direct proportion to the rate of
stormwater runoff according to:
k = br
[3]
where,
r = runoff rate for watershed (depth/time)
In order to evaluate b, it is necessary to make an as-
sumption about the quantity of pollutant removed from
the ground surface by a given runoff event. One ap-
proach has been to assign a 90 percent removal to a
uniform runoff of 0.5 inch/hour on an impervious sur-
face and 50 percent on pervious surfaces (4). This
results in the following relationships:
X0-X - x0 (1 - e-A.6rt).
for impervious surfaces (4) and:
.[4]
819
-------
.[5]
X0-X = X0
for pervious surfaces (A).
The runoff rate, r, may be satisfactorily predicted
using a number of hydrologic models currently availa-
ble (6, 7).
MODEL CALIBRATION
The previous equations allow the investigator to com-
pute the quantity of a given pollutant washed off the
ground surface during a runoff event, and allow,
therefore, the determination of runoff-borne pollutant
loads and assessment of their impacts on receiving wa-
ters downstream.
Such a tool, however, can be only as good as its cal-
ibration from real-time observation of water quality
data during runoff events. The key factor in the mo-
del is the successful estimation of XQ, the quantity
of pollutant on the ground surface at the initiation
of runoff. The determination of XQ is based upon the
assumption of a constant rate of accumulation of a
given constituent on the ground surface during the dry
days preceding a runoff event. Figure 2 is a dimen-
sionless representation of the assumed relationship
between storm runoff, pollutant loading, and pollu-
tant-loading graph are approximately the same. This
observation has been reported numerous times in the
literature (8, 9, 10) and is descriptive of most types
of surface runoff except where the so-called "first-
flush" phenomenon is observed in heavily storm-sew-
ered areas (9). The bottom portion of the figure is a
representation of the washoff function described by
equation [2] rearranged to read:
X X0EXP(-kt)
.[6]
The discontinuities in the function occur at those
times when runoff ends and begins anew, respectively.
The linear portions between those times are represen-
tative of the assumed-to-be-constant "pollutant ac-
cumulation rate" used to arrive at XQ for the next
storm to occur. The length of the time axis between
the beginning and end of an accumulation period is in-
terpreted as the number of dry days between storms, as
the length during decay periods is interpreted as the
duration of a runoff event.
It may also be inferred from Figure 2 that:
X0i
Ax [t± -
At
[7]
That is, that XQ^ for any storm is determined by sum-
ming the quantity of pollutant remaining after the
last storm and the product of the number of ensuing
dry days and the accumulation rate, AX.
~Kt
The calibration procedure is as follows:
1. A data base consisting of pollutant loading
graphs and hydrographs for a sequence of
storm events in the watershed of interest is
selected.
2. A pollutant loading curve for the initial
storm event is plotted. Xg-X is taken to be
the area lying under the curve. This value
is substituted into the washoff equation [4]
[5] along with observed values of "r" and "t"
and a solution for XQ is obtained.
3. A trial accumulation rate, — , is chosen.
4. The model is executed for a series of storms,
the hydrologic and water quality data for
which already exist. The simulated pollutant
washoff loads are then compared to the ob-
served loads.
5. Sequential adjustments are made in the assumed
accumulation rate until the simulated runoff
loads match the observed ones.
6. The above procedure is repeated for each con-
stituent to be simulated.
SAMPLING METHODOLOGIES
Data to be used for runoff water quality model cali-
bration must necessarily be more detailed than that
generated for periodic ambient water quality assess-
ments. It is necessary to have sufficient information
to calculate a total pollutant load for each runoff
event used in the calibration. Such information ne-
cessarily must consist of flow and concentration data
of varying detail. A discussion of the methods of
sampling commonly used and commentary on their suita-
bility follows. The assumption is made that flow and
concentration measurements are made at the same fre-
quency .
Grab Sampling
Historically, most stream water quality surveys have
been made using grab sampling. The unmodified proce-
dure has little use in runoff model calibration, how-
ever, because it generates a pollutant load descrip-
tive of only one instantaneous condition and takes no
cognizance of the variation in load along the pollu-
tant loading graph. A load calculated from the pro-
duct of a single flow and concentration and extended
to include the entire period of runoff could differ
tremendously from the actual load (10).
Simple Composite Sampling
In this method, sample aliquots of equal volume are
withdrawn at intervals during a runoff event and are
composited into one volume for analysis. The flow
used to estimate total load is the mean of the instan-
taneous flows at the times of sample collection. This
method assigns equal weight to each aliquot of the
composite; consequently, those portions taken during
periods of relatively high flow affect the final con-
centration less than they should. Depending on the
relationship between concentration and flow, the true
load may be either over—estimated or under—estimated.
Flow-Weighted Composite Sampling
In this method, variable size aliquots of sample are
composited,with the volume of each being directly pro-
portional to the flow occuring at the time of sam-
pling. The total load then is computed from the mean
flow and the flow-weighted mean concentration of the
composite sample. The technique gives an excellent
estimate of Total Pollutant Load during a runoff event
if sampling time intervals are small (3). Even so,
the next method of sampling to be discussed offers a
better means of characterizing pollutant variation in
runoff.
Sequential Discrete Sampling
While this method is the most expensive option for
sample collection, because it requires the most analy-
tical work, it also provides the greatest flexibility
for checking the calibration of the washoff equation
[2]. In this method, discrete samples are withdrawn
at numerous points on the storm hydrograph. The sam-
820
-------
pies are separately analyzed and the results coupled
with flow data taken at the time of collection in
order to produce a number of instantaneous pollutant
loads during the period of runoff. Plotting these
loads on a time axis produces an approximation of the
general pollutant loading graph illustrated in Figure
2. As the interval between samples decreases, the ad-
herence to the actual loading curve increases (as do
analytical costs). The quality of the total load es-
timate made by computing the area under the plotted
pollutant loading curve is matched only by that from
the flow weighted composite method. The latter, how-
ever, does not allow the investigator to determine the
shape of the loading curve, and, therefore, prevents
him from making any observations regarding the rela-
tionship between pollutant concentration and hydro-
graph shape. Additionally, knowledge of the pollutant
loading curve makes it possible to consider making
more refined estimates of the coefficient b in equa-
tion [3].
Table I shows a set of runoff data collected by the
Occoquan Watershed Monitoring Laboratory (OWML) from a
tributary to Bull Run near Manassas, Virginia. The
summary loadings (a through e) contrast the total load
estimates that would have been made on the set of data
using each of the sampling methods discussed against
the total load calculated by computing the area under
a "smooth-curve" of pollutant load vs. time. As may
be seen, the single grab sample method gives the worst
estimate, errors ranging from -88 to +79 percent. The
use of the simple composite method produced errors
from -5 to +15 percent, depending upon the size of the
composite. The flow weighted composite method pro-
duced an error of -7 percent using the smaller number
of samples and an error of less than one percent using
the full number of samples. The sequential discrete
sampling method also produces the same total load es-
timate as the all sample flow weighted composite. As
stated above, however, it also allows the investiga-
tor to determine the morphology of the loading curve.
FIELD APPLICATION OF SAMPLING PROCEDURES
OWML currently operates automatic sampling stations at
seven locations in the Occoquan Watershed as shown on
Figure 1. The drainage areas of the stations and the
general land use types are given in Table II. All
the streams on which sampling stations are located are
perennial and, therefore, base loading measurements
are necessary to enable the definition of runoff
loads. Base loads are determined by sampling at all
stations on a weekly basis during dry weather flow.
Experience has shown that is not feasible to rely on
individuals to occupy sampling sites during runoff
events because such events are so unpredictable.
During high intensity, short duration rainfall, runoff
may commence immediately, and if sampling is not ini-
tiated concurrently, a significant portion of the pol-
lutant load may be missed entirely. This happens in
heavily sewered areas in particular, due to the likli-
hood of observing the so-called "first-flush" effect.
It appears, then, that satisfactory sampling of runoff
events necessitates the use of automatic equipment for
sample collection, storage, and measurement of flow.
Many automatic sampling devices are now available com-
mercially, but most were initially developed for
wastewater sampling; therefore, careful evaluation of
proposed units should be made prior to purchase to as-
sure that adequate performance may be expected in re-
trieving runoff samples. In particular, attention
should be given to the recovery of suspended solids
because of the propensity of stormwater runoff to
carry some materials of higher specific gravity than
those normally carried in wastewater discharges. Con-
sideration should be given to heating the installation
if normal operation during winter months is desired.
Remote sampling equipment has decreased in size and in-
creased in performance in recent years, and units are
now available that may be easily carried by one person,
and yet perform as well as the earlier, more bulky mo-
dels. Recent studies (11, 12) have evaluated commer-
cially available equipment and given guidelines for
sampler selection. In general, an acceptable remote
sampler will meet the following criteria:
1. Be weathertight and battery powered.
2. Be capable of collecting a minimum of 24 dis-
crete samples of not less than 500 ml each and
storing them in an insulated container.
3. Be capable of actuation from an external sig-
nal or from an internal clock at varying in-
tervals.
A. Be capable of lifting a sample against a suc-
tion head of 10 feet at a minimum transport
velocity of 3 feet per second (.91 m/s).
5. Have the capacity to distribute a single sam-
ple among several containers as it may be ne-
cessary to add differing preservatives for
subsequent analytical work to be performed.
6. Be capable of conducting a pre- and post-sam-
ple purge of the intake hose to prevent clog-
ging and cross-contamination of samples.
7. Have an intake that can be placed sufficiently
high above the channel bottom to avoid sam-
pling suspended bed load.
In performing runoff studies, equally important as ob-
taining representative samples is the measurement of
flow, because no loading calculations may be made with-
out reasonably accurate discharge measurements. In
perennial streams with adequate natural control, flow
measurements may be readily obtained by calculations
involving velocity (obtained with a current meter) and
cross-section measurements (13). In small watersheds
that drain only during storm events, and lack an ade-
quate natural constriction, the installation of some
artificial control structure may be necessary. Seve-
ral types of weirs and flumes have been used with suc-
cess in studies of the hydrology of small watersheds
(1A). In urban storm sewer systems, the use of the
Manning formula to compute flow as a function of stage
provides the simplest method of obtaining flow data.
However, selection of the value of the roughness coef-
ficient, n, in all but the most recently installed con-
duits, poses a difficult problem. As the sewer ages,
growths and other depositions cause changes in the sur-
face roughness which can only be approximated when se-
lecting a value for n. If the Manning formula is to be
used with success, an indirect measurement of n for the
reach of sewer in question should be made. "Calibra-
tion" of a sewer may be readily accomplished by using
chemical gaging techniques to develop a reliable set of
discharge-depth of flow relationships. The values of
flow thus obtained may be used to compute a valid n for
use in the Manning formula. Lithium chloride has re-
cently been shown to be a satisfactory tracer for use
in chemical gaging studies (16). In any case, adequate
flow measurements are essential and obtaining them
should be given high priority.
Figure 3 is a schematic of a permanent sampling instal-
lation operated by OWML. Flow measurements are ob-
tained by making a continuous record of stream stage
and comparing it against a stage-discharge curve pre-
pared previously. The water-stage recorder wheel holds
821
-------
bar magnets spaced at 0.25 foot (.076M) intervals
along its circumference. As the stream stage rises or
falls, the magnets passing over a stationary reed
switch provide a inomentary contact closure that ac-
tuates the sampler in the adjacent building causing
samples to be taken at known stage increments. Sam-
ples are stored in separate containers until retrieved
and transported to the laboratory for analysis.
ANALYTICAL TECHNIQUES
As stated earlier, the sequential discrete sampling
method is both the most reliable and the most expen-
sive for generating accurate estimates of total load
and loading rates. The greatly increased analytical
workload is the major reason for higher costs. Be-
cause the number of samples to be analyzed may be an
order of magnitude higher than that required in a pro-
gram where samples are composited, consideration
should be given to adopting automated analysis proce-
dures where possible. Runoff samples from stations
are retrieved as soon as possible following a storm.
Table III shows the analytical schedule considered to
be necessary to adequately describe the impact of nu-
trient and organic material runoff loads on receiving
waters.
Nitrogen and Phosphorus
Nitrogen determinations are performed on both whole
samples and aliquots filtered through 0.45 micron mem-
brane filters (with the exception of nitrite and ni-
trate, because these forms are anionic and do not
readily adsorb on suspended soil particles). For all
other forms of nitrogen and phosphorus, the two types
of analysis are necessary to determine the distribu-
tion between particulate and dissolved phases. This
distribution is critical when considering the ultimate
water quality impact of nutrient loadings.
Organic Matter
Two measures of organic loading are utilized: Biochem-
ical Oxygen Demand (BOD) and Total Organic Carbon
(TOC). The BOD determinations are made either in sta-
tic bottles or with a manometric apparatus. TOC mea-
surements are made in parallel with BOD analyses and
correlations established with a view to using TOC as a
"real-time" parameter for the measurement of organic
matter.
Data Storage
All data are currently stored in the EPA STORET data
management system. Data are reduced in the labora-
tory, coded, and stored on a biweekly basis. The sys-
tem software greatly simplifies the computations re-
quired to develop pollutant loading information. By
using the "MEAN" or "PLOT" routines (16), the investi-
gator is able to obtain instantaneous load vs. time
information in 'either tabular or graphical form. Upon
integrating the loading curve by numerical or plani-
metric procedures, and using the proper scale conver-
sions, "it is possible to obtain the total storm load
from the area lying beneath the curve.
SUMMARY
The Occoquan Watershed Monitoring Lab has established
a network of automatic water samplers at locations on
tributaries to the Occoquan Reservoir. Samplers are
programmed to collect and store sequential discrete
samples at increments of rising and falling stream
stage during runoff. When combined with concurrent
flow data, analysis of such samples allows the genera-
tion of pollutant loading graphs. Such loading data
are invaluable in the precise calibration of most math-
ematical models used to simulate pollutant quantities
in surface runoff. For calibration, the measured
rates of constituent accumulation will be sequentially
varied to achieve agreement in loadings between ob-
served and simulated storms.
ACKNOWLEDGEMENTS
The authors gratefully acknowledge the contributions
of the political jurisdictions participating in the
Occoquan Watershed Monitoring Program. Additionally,
the authors wish to acknowledge the tireless efforts
of the OWML staff members without whom operation of the
monitoring program would be impossible.
REFERENCES
1. Sawyer, C.N. 1969 Occoquan Reservoir Study. Met-
calf & Eddy, Inc. April 1970.
2. Virginia State Water Control Board. A Policy For
Waste Treatment'and Water Quality Management in the
Occoquan Watershed, 1971.
3. Marsalek, J., "Sampling Techniques in Urban Runoff
Quality Studies, Water Quality Parameters, ASTM
STP 573, 1975, (526-542).
4. Hydrocomp, Inc. "Hydrocomp Simulation Programming,"
Palo Alto, Cal., 1973.
5. Metcalf & Eddy, Inc. et al. "Stormwater Management
Model," Environmental Protection Agency, EPA-
11024 Doc07/71, July 1971.
6. James, L.D. "Using a Digital Computer to Estimate
the Effects of Urban Development on Flood Peaks,"
Water Resources Research. 1 (2), 1965, (223-244).
7. Linsley, R.K. "A Critical Review of Currently
Available Hydrologic Models for Analysis of Urban
Storm Water Runoff." Hydrocomp International, Inc.
Palo Alto, California (1971).
8. Colston, N.V. "Characterization of Urban Land Run-
off," presented at National Meeting on Water Re-
sources Engineering, ASCE, Los Angeles, Calif.,
1974.
9. Randall, C.W., J.A. Garland, T.J. Grizzard, and
R.C. Hoehn, "Characterization of Urban Runoff in
the Occoquan Watershed of Virginia," Proceedings,
American Water Resources Association Symposium on
Urbanization and Water Quality Control, Rutgers
University, 1975.
10. Harms, L.L. and E.V. Southerland, "A Case Study
of non-point source pollution in Virginia," Bulle-
tin 88, VA. Water Resources Research Center,
Blacksburg, VA (1975).
11. Parr, J.F., G.H. Willis,'L.L. McDowell, C.E. Mur-
phree, and S. Smith, "An Automatic Sampler for
Evaluating the Transport of Pesticides in Suspen-
ded Sediment," Journal of Environmental Quality,
3(3), 1974, (292-294).
12. Shelley, P.E. and Kirkpatrick, C.A., "An Assess-
ment of Automatic Sewer Flow Samplers," Water
Pollution Assessment: Automatic Sampling and
Measurement, ASTM STP 582, 1975, (19-36).
13. Geological Survey, USKI, "Stream-Gaging Procedure",
Water-Supply Paper No. 888, 1943.
14. Agricultural Research Service, USDA, "Field Manual
822
-------
for Research in Agricultural Hydrology", Handbook
No. 224, June 1962.
15. Grizzard, T.J. and L.L. Harms. "Flow Measurement
by Chemical Gaging." Water and Sewer Works. 121
(11), 1974, (82-83).
16. Storet Users Assistance Section, USEPA, "Storet
Handbook" (Interim Version)", 1976.
/ \
/ A SEWAGE TREATMENT PLANTS
/ S SAMPLING STATIONS
/ COUNTY BOUNDARY
/, WATERSHED BOUNDARY
SCALE ^-m • I MILE
ngle jjq-
*
*
*
8
9
0*
1
2
3*
4
5
6*
Date/Tira
07-13 1315
1320
1330
1350
1400
1410
1445
1620
1630
1730
1900
07-14 0600
0740
0945
1200
1545
Flow Tot
_fa_ _sa
48
68
90
15
41
69
41
41
69
30
10
05
77 0
80 0
33 0
33 0
al P
/I Sample Mo. Dace/Tim?
17 07-14 1730
IB 1830
19* 1915
20 1950
2 2030
2 2110
2 * 2150
2 2220
1 2310
2 2350
2 * 07-15 0100
2 0230
2 0445
30 0800
31* 1100
b. f. Flow Weighted Corap
. Flou Weighted Composite (All Samples) - 1766
Figure 1. Occoquan Watershed
HIGH INTENSITY
'SHORT DURATION
OOLLUTWIT ACOMJLATION
RATE (WSS/TIlt)
STATION
Hooes Run Near Occoquan
Bull Run Near Clifton
Occoquan Creek Near Manassa!
Broad Run Near Brlstow
Cedar Run Near Aden
Cub Run Near Bull Run
Bull Run Near CaCharpin
MAJOR LAMP USE
Medium-high Density Residential
Mixed Urban
Mixed Rural (Sum of 4 & 3)
Rural-Agricultural (Pasture)
Mixed Urban
511-
FIGURE 2. REPRESENTATION Or RELATIONSHIPS 1ETWEEN STOPWATER RUNOFF,POLLUTANT LOADING RATES AND
POLLUTAfn" WASHOFF
TABLE III
Analytical Schedule For
Non-Point Studies
PLANT NUTRIENTS
Total Phosphorus
Ortho Phosphorus
Total Soluble Phosphorus
Total Kjeldahl Nitrogen
Soluble Kjeldahl Nitrogen
Total Organic Nitrogen
Soluble Organic Nitrogen
Nitrite + Nitrate
ORGANICS
BOD
TOG
SOLIDS
Total Suspended
-I-.JRE Z. *CT1AT1C 0= FLO- tASURI ^ KG A TOWT1C ^PLIT, INSTALLATFr
823
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WATER SUPPLY SYSTEMS PLANNING,
MANAGEMENT AND COMMUNICATION THROUGH
AN INTERACTIVE RIVER BASIN SIMULATION MODEL
Robert A. Hahn
Civil Engineer, Systems Analyst
U.S. Army Corps of Engineers, Ohio River Division
Cincinnati, Ohio
The Washington Metropolitan Area Water Supply Study
initiated the development of a unique river basin
simulation model designed to be incorporated into an
open planning process. The model is a flexible, user
oriented tool suitable for a number of different
purposes. It has been used to educate Corps person-
nel in the intricacies of the Washington Area water
supply system and to evaluate a number of water
supply device alternatives. Potential uses include
public demonstration of the complexity of the existing
water supply system, evaluation of social, economic,
or environmental impacts of water supply alternatives,
the modeling of operational rules and as a "real-time"
decision tool to show the effects of operational man-
agement decisions on all parts of the system.
Introduction
The water supply simulation model described in this
paper was developed as part of the Northeastern United
States Water Supply (NEWS) Study.-*• This study was
authorized by Congress^ in response to the mid-60's
drought throughout most of the Northeastern United
States, for the purpose of preparing plans to meet
long-range water supply needs of that area. The
Washington, D.C. Metropolitan Area (WMA) was identi-
fied as one of several critical areas of the northeast
urgently requiring additional water supply capacity.
Detailed planning began in the WMA in the fall of 1972
with an extensive "open planning program" designed to
find out as much as possible about the alternative
water supply solutions available and the preferences
of the local public and private agencies and indivi-
duals.
It became obvious by the spring of 1973 that the
problem was too complex for hand analysis of the
various planning alternatives. Meta Systems Inc.^ was
asked to develop a tool which would allow the study
team to examine a large range of alternative solutions
without the time-consuming and error-prone drudgery of
analyzing each variation by hand. Many aspects of the
study could not be modeled, but those amenable to an
analytic approach and within the limits of modeling
technology were included. This paper will limit
itself to those aspects of the study incorporated in
the model. The complexity of the problem is due to
the combined effect of three separate factors: the
unusually complicated nature of the existing water
supply system; the social, economic, and environmental
issues discovered during the open planning process
which broadened the way in which the problem must be
solved; and the range of alternative engineering
solutions proposed.
Existing Water Supply System
The study area was defined as the portion of Maryland,
Virginia, and Washington, D.C. within the Washington
Area SMSA which includes seven counties, several
incorporated cities, 3,000 square miles, 2.9 million
people using 390 million gallons of water per day, and
the nation's capital. The area's water is supplied by
two river basins, the Patuxent, which is small (930
square miles), well regulated, and located entirely in
Maryland, and the Potomac, which is large (14,700
square miles), unregulated, and located in four states
and the District of Columbia. The major supply
source is the Potomac River, which has large seasonal
variations, highly random daily variations, and drought
stages of less than six percent of the average. Since
maximum daily withdrawals have already exceeded mini-
mum flow in the Potomac, and since most, if not all,
future source development will be in this basin,
supply analysis becomes a problem in time and fre-
quency. The question asked is not only how large are
the deficits, but also how long, how often, and at what
probability.
Two of the three major water suppliers in the study
area presently use this source to supply 65 percent of
the region's needs, and the third expects to use the
river in the immediate future. Two other sources,
reservoirs on the Patuxent and Occoquan Rivers, are
also used to provide portions of the region's needs.
These independent sources are only minimally inter-
connected, which raises the question of deficit loca-
tions. These questions, deficit location, probabil-
ity, frequency, and magnitude are very important to
the analysis of the existing system and evaluating the
proposed improvements. They are also very difficult
to answer as they require statistical processing of a
large amount of data.
Social, Economic, and Environmental Issues
During the early "open planning" stage of the study,
several issues were developed which had to be con-
sidered in any water supply solution. Many of these
issues, though relatively complex socially, polit-
ically, and institutionally, were simple from an
analytic point of view. An example is the interrela-
tion of water and wastewater management. Other issues,
such as the environmental impact of reservoirs, are
also complex analytically and can only be analyzed
quantitatively to the extent that functions can be
derived which relate environmental parameters to water
quantity. Finally, a large group of questions per-
taining to overdesign and efficient resource use
condense quantitatively to questions of planning not
for the worst conceivable drought but for some lesser
drought defined in terms of magnitude, duration,
location, and frequency of shortage. Not only had
this question never been seriously considered by water
planners before, but existing literature and analytic
techniques are not capable of answering the question
to everyone's satisfaction.
Range of Alternative Solutions
The broad range of water supply technologies being
considered in the study added further analytical
complications. These included a range of water con-
servation measures, interbasin transfers, the use of
treated estuary and wastewater, groundwater, and local
and remote reservoirs.
Model Conception and Design
The concept of the model was simple—answer as many of
the above questions as possible. Furthermore, answer
the questions in a manner that is believable, with a
model that can be operated by any technically competent
person; that has flexible input, operation, and output;
and that can be operated in an open planning session
involving the public, other agencies, or the study team.
The difficulty in structuring, coding, calibrating,
824
-------
and finally documenting such a model should be obvious
to any experienced model builders, but at the time of
its proposal, no lesser model would satisfy the needs
of the study team. The model design can be examined
in six main categories: model structure, interactive
features, nodal definition, hydrologic simulation,
model output, and. social, economic, and environmental
parameters.
Model Structure
The model is structured around a collection of 200
different nodes representing one of eighteen (18) node
types at which water can be added, subtracted, or
stored and a number of statistics can be collected.
Figure 1 is a schematic illustrating the nodal chain
and node types used. If, for example, the node were
defined as a reservoir, (node type 1) natural and/or
pumped inflow and outflow can occur, which will vary
the storage within the reservoir accordingly. Statis-
tics can be maintained of these variables, inflow,
storage, etc., which are then outputs of the model.
These nodes are strung together in a network which
represents the region's water supply system. The
model begins at the first node at time t = 0 and adds
or subtracts waters from that node according to in-
structions coded for that node type and the values of
user-supplied parameters such as reservoir capacity.
The transaction is recorded, statistical counters are
updated, and the model proceeds to the next node to be
considered. This process is repeated until all 200
nodes have been processed at which time the model's
clock is incremented by one and the program starts
over again. The clock increments are either monthly
or daily depending on the output desired. Decision
switches automatically compare the flow or storage at
a particular node with user-supplied maximum or mini-
mum values, and adjusts the process sequence. For
example, if the flow in the Potomac is less than a
given minimum, and interbasin transfers are being
modeled, the model will route through the Patuxent
nodes before the Potomac nodes. At each node and time
increment, the program will print out any parameter
values desired for the nodes chosen. Finally at the
end of the session, the user can choose to see statis-
tics on any node and parameter of interest. A wide
SHENANDOA
SYMBOL
KEY
NODE TYPE
Flow Point
Reservoir
Flood Skimming
Estuary Treatment
Wastewater Treatment
Water Treatment
Groundwater Withdrawal
Groundwater Recharge
Interbasin Transfer
Demand Center
Supply Point
Conduit
Stream-Gaging Station
Demand Reduction
Land Treatment
Storm Runoff
Upstream Reservoir
OCCOQUAN
FIGURE 1. Schematic Illustrating Nodal Chain
825
-------
variety of alternative events can be simulated by
varying the nodal chain, the values of nodal para-
meters, and the switches used. This movement from
node to node is controlled by the main program which
calls subprograms to do the nodal transactions, to
remember the transaction, to accumulate transaction
statistics, and to control communication with the
operator.
Interactive Features
A unique feature of the model is the way in which it
communicates with the operator. This feature allows a
technically trained person with some understanding of
the system being modeled to learn to use the model in
several hours. It also gives interested non-
technical observers confidence that no trick is being
performed and that they can interpret the results. It
was incorporated into the model for the express pur-
pose of planning in real time so that questions or
alternative suggestions could be answered, or sets of
results obtained, without time-consuming delays
and difficult data manipulation problems associated
with batch process programs. This feature required
well over half of the coding (which consists of
more than 3,000 Fortran lines) to be devoted to
the interactive aspects of the program. It also
consumes a large amount of computer resources
during model operation, but its contribution
in ease and flexibility of operation and in
data handling and believability of results does
add significantly to the value of the model as a
planning tool.
Nodal Definition
Each of the eighteen node types shown in Figure 1
serve to represent a different type of water account-
ing. Many of the nodal types do not simulate the
indicated function but merely act as a source or sink
for water supply. The model does not simulate ground-
water movements, for example, but merely supplies
water on demand to a demand center up to a specified
rate. Simulating the groundwater movement itself
would have been difficult, impossible to calibrate,
and unnecessary. Eliminating it greatly simplified
the model without causing significant planning inac-
curacies. The model is equipped with a data base
called "BASE" which includes values for all the para-
meters necessary to simulate the existing situation.
At the beginning of each session, the user has the
opportunity to change the values of the parameters at
the nodes to simulate the construction of a project.
Impoundment A, for instance, does not presently exist
and is represented in the data base as a. reservoir
with zero storage and pumping capacities. These
capacities can be changed at the beginning of the run
should the user wish to implement that reservoir and
if the results are satisfactory, the revised data base
can be saved for later use.
Hydrologic Simulation
Most of the model consists merely of accounting rou-
tines to subtract water from one node location, add it
to another, and record the transaction. The one major
exception, the driving force of the model, is the
simulation of hydrologic events. Each of the rivers
and tributaries modeled consist of a number of "dummy"
and "routing" reaches connecting the river nodes
together. Most of the reaches are "dummy" reaches, in
which no routing or storage occurs and outflow of the
upstream node becomes inflow to the node below it.
The hydrology of the basin is simulated within the
"routing" reaches. The flows recorded at eighteen
D.S. stream-gaging stations are used to load the model
with one of two historical water years (1930 or 1966)
which were serious drought periods. Each of the
"routing" reaches is related to one of the stream-
gaging stations through drainage ratios, and the net
water inflow in the region is allocated to the routing
reaches as stream runoff or as stream inflow. Rivers
act as natural reservoirs, with varying storage ca-
pacity which is also simulated in the routing reaches
using Muskingum routing coefficients. The routing
reach number, location, and routing coefficients were
adjusted during calibration to accurately capture the
response of the prototype.
Model Output
One of the major advantages of the model is the flex-
ibility of output. At the beginning of each run the
user can chose to observe the dynamic change in one or
more parameters at one or more of the nodes, and these
values will be printed at the terminal for each time
period in the simulation. The feature is useful for
observing changes in parameter values as they occur,
and the relationship between values at a given time
increment. This enables decisions on improvements for
the next run and choices as to the final statistics
desired. At the end of each run, a programmer can
choose to see the statistics of any parameter, for any
node. The statistics available are mean and standard
deviation, a histogram of all events, and a trace of
the events as they occur. The user may choose to see
the output at the terminal or on a high-speed line
printer. Normally, the user would choose to see a
small portion of the output at the terminal, certain
key parameters, for instance, and if the run were
successful, he would ask to see all statistics printed
on the high-speed printer for a permanent record and
for later detailed study. The user may also write a
message at the beginning of the printed output such as
the date of the run, the users name, solutions used,
and preliminary interpretation so that the output can
be more readily used at a later date.
Social, Economic, and Environmental Parameters
The incorporation of social, economic, and environ-
mental parameters "is a feature built into the model
that has not yet been used. At the present time,
all output is limited to water quantity values
measured as a rate (mgd) or a volume (bg). Many
social, economic, and environmental factors related to
water supply solutions can be described as functions
of water quantities. For example, the region's eco-
nomic growth is in part related to deficit probabil-
ities , the cost of pumping water is directly related
to the volume pumped, and certain environmental para-
meters in the estuary can be described in terms of the
volume of fresh water flowing into the estuary. The
model is designed to incorporate relationships such as
these and is capable of generating these values and
related statistics so that social, environmental, and
economic impacts of any water supply decision can be
at least partially simulated. To utilize this capa-
bility, the appropriate functions relating these
impacts to water quantity must be provided.
Model Calibration
The value of any model depends on the confidence one
has in the accuracy of its output, which can only be
obtained by calibrating the model relative to the
prototype for a range of conditions. Establishing the
model's performance is particularly important when new
modeling concepts are being used. It is seldom
convenient to calibrate an entire model satisfactorily
826
-------
and in our case it was impossible because no complete,
consistent system-wide data base exists. It is un-
likely that such a set will ever be collected because
the model imitates extreme events (droughts) for which
one must wait on nature for the appropriate sampling
conditions and because it predicts water supply system
failures, which presumably will never be allowed to
happen. It was, however, possible to calibrate four
critical areas of the model independently to obtain an
estimate of the accuracy of the entire model. These
are streamflow routing, generation of streamflow gage
records, generation of daily demand records, and the
accounting procedure which moves water from one part
of the system to the other. In each of these areas,
excellent results were obtained giving an overall
estimate of model accuracy at better than 90 percent,
which far exceeds the requirements for a region-wide
water planning model.
Streamflow Routing
Accurate imitation of drought conditions in a free-
flowing stream requires an adequate procedure for
computing instream storage with respect to time. The
Muskingum three-coefficient equation
CoZi
(1)
was used to perform the routing where Co, C]_, and C2
are routing coefficients and are a function of travel
time, routing period, and inflow-outflow weighting
factors. These coefficients are difficult to obtain,
particularly for drought conditons, since they are
sensitive to stream bank conditions and river stage.
Obtaining these coefficients (and in the process,
calibrating this part of the model) could only be done
by comparing computer-generated and observed stream-
flow during low flow conditions. The stream gage
records and water production records of the water
supply utilities were obtained for October 1970. The
consultant then varied the number of river reaches and
the storage coefficients to optimize the reproduction
of the observed record by the generated record. The
resultant streamflow simulation satisfactorily imi-
tates the prototype with the critical flow parameters,
low flow, mean flow, and temporal response within 10
percent, 4 percent, and 7 percent respectively, of the
observed values.
Streamflow Generation
The primary input parameter of the model is stream
gage records from eighteen locations in the region.
The flow in each river reach is a function of inflow
and outflow (change of storage) and runoff which are
natural occurrences, and withdrawals and discharges
which are man-made. The natural occurrences are
determined through drainage area relationships from
the stream-gaging records. Most of the gaging sta-
tions did not have records for the 1930 drought period,
though fortunately the most significant gages did, and
all records had one or more data gaps. Because the
model simulated daily events, it was necessary to have
a complete daily record for each gage for any his-
torical or synthetic drought year modeled. Several
established generating techniques were tried to com-
plete incomplete records and for synthetic generation.
These were found unacceptable because they could not
adquately describe daily phenomena (which is highly
skewed) or else they could not capture drought statis-
tics satisfactorily. A procedure was found using the
log normal distribution with skew unspecified for
filling gaps in the record. The algorithm for filling
the gaps used serial correlation for the longer records
and cross-correlation for the shorter records based
upon correlation coefficients for the portions of the
records which overlap. This procedure was considered
adequate to complete the records, but was not con-
sidered appropriate for use in a stochastic generator
as it tended to distort serial correlation. Con-
fidence in the completed historical records was gained
in the process of completing the records.
Synthetic Demand Generation
The purpose of all planning simulation models is to
predict the future behavior of existing or proposed
systems. In this case the future is represented by
the projected annual water demands, which must be
supplied to the model. In order to use these demands
in a daily flow model, it is necessary to modify the
demands to reflect cyclic seasonal and random daily
phenomena before they can be used to generate mean-
ingful daily storage statistics. This requires a
demand generator that takes annual demand for nineteen
demand nodes and develops daily values for those nodes
without distorting any of the meaningful demand sta-
tistics. Conceptually, this is a much simpler task
than streamflow generation, as significant historical
demand records are maintained at all the water supply
utilities and satisfactory results were obtained
relatively quickly using well established analytic
techniques. However, few of the records were readily
available and none in machine-readable form,which
greatly increased the labor required to perform the
task. We are confident that the demand generator will
accurately generate daily demands in the model because
of the accuracy with which it can duplicate historical
demand patterns.
Accounting Procedure
Calibrating the accounting procedure which moves water
from one part of the system to another is simple
though time consuming and consists merely of evalu-
ating the printed output of all parameters at all
nodes for each time period under a number of given
situations. The model was found to faithfully account
for water movement about the system, neither losing or
creating water, and moving it from location to loca-
tion in the amount and the time expected. A funda-
mental constraint to the model was that its clock in-
crement was daily which required that all water trans-
fers be in multiple units of days. The time of travel
(pumping distances) of pressurized water supply mains
are small, significantly less than one day, so it was
assumed that water transfer could occur from one part
of the system to another instantaneously. Wastewater
flows, however, which travel by gravity over greater
distances, have varying travel times from location to
location within the system. This was simulated by
delaying wastewater return to the system by one day.
Neither of the assumptions, that pressurized flow
takes zero days to travel and that unpressurized flow
takes one day, should cause significant errors.
Model Use
The purpose for which a model is developed and the way
in which it is used when finished do not always
correspond. This model has not yet been used in an
"open planning" session to illustrate the intricacies
of the water supply system or to experiment with al-
ternative solutions. Nor has it been used to develop
statistics about the location, duration, magnitude,
frequency, and probability of deficients. It has also
not been used to evaluate the proposed final alterna-
tive solutions. Time and money constraints, informa-
tion delays, changing roles and approach of the team
towards the study, and other unforeseen and uncontrolled
827
-------
events led to the completion of the model just shortly
before the completion of the study. The credibility
of both the model and the water supply study would
have been enhanced had there been more time available.
Actual Model Use
The model was, however, extremely useful to the study,
for in the process of developing the model much was
learned about the proposed solutions, and the region
itself, which would not have been learned otherwise.
This is primarily because the model was not developed
in one stage but was changed during the study as more
was learned about the prototype, the model, and the
solutions to be analyzed. At each stage of develop-
ment, the model was operated for a range of system
variations in order to learn as much as possible about
the prototype, the model, and the solutions. Also,
the difficulties encountered and overcome while
obtaining a consistent correlated model required
thorough analysis of data which revealed much about
the system's hydrologic and demand patterns. For
example, information gathered in the process of demand
generation revealed that an analytic approach to
system shortages is not possible with present mathe-
matical techniques so that the location, magnitude,
frequency, duration, and probability of the shortages
must be obtained using sampling technique. This would
consist of running the model hundreds of times with
the same configuration to obtain statistical repre-
sentation of the computed shortages. Resources did
not permit this type of analysis but evaluation of the
data revealed that some simplifying approaches would
be appropriate. Another suprising result of the data
analysis was that the demand patterns were highly
predictable; indicating the possibility that con-
servation techniques may be more reliable than other-
wise thought.
At each stage of the model, experiments were run to
analyze the proposed solutions to determine their
potential value and, if possible, obtain some para-
meter values that appeared promising. This analysis
was done on a device-independent basis which does not
indicate the interactions between devices in a system.
This is not a concern with the final set of alter-
native solutions, however, since they would be imple-
mented and operated with minimal device interaction.
One of the preliminary experiments was to vary the
regulation roles of the existing and proposed reser-
voirs. This led to the conclusion that these reser-
voirs could be used more efficiently, from a water
supply standpoint than indicated by previous analysis.
Although this model was not used directly in plan
formulation, information learned about the system
and the alternative solutions led to the development
of a simpler and more efficient, but also more limited,
model which was used in plan formulation. Smong other
things, the simpler model considered the demand supply
network in two nodes, Pototmac supply and demand and
non-Potomac supply and demand. It was found in the
early experiments on the water simulation model that
satisfying these two demand supply nodes would be a
satisfactory simplification of the prototype for the
level of detail documented in the study report.
Potential Model Use
There are several potential uses for this model which
have not been attempted and had not been considered
when the model was developed. These became apparent
as the alternative water supply solutions were formu-
lated and as experience with the model was obtained.
The model will be extremely useful as a public commu-
nications vehicle to educate the public on the existing
water supply system and on the potentials for water
supply development. Its use should decrease the
problems of complicated and massive data bases neces-
sary to document" proposed projects and should increase
the confidence that the public has in water supply
plans. It can also be used by planning agencies as it
was intended, as a planning tool to compare alternatives
and.determine the most appropriate solution to the
water supply problem. Once the environmental, eco-
nomical, and social parameter functions are included
in the model, it will be valuable in determining the
impacts of water supply solutions and can be used to
keep the decision makers aware of the impacts of their
decisions. It will assist in economic and environ-
mental impact assessments, and could be used in cost-
sharing and in the billing of utilities for the cost
of regional water supply development and operation.
Before the region can decide whether or not it will
accept shortages, it must have a thorough understand-
ing of the deficits that will occur. The model can
be used to obtain these statistics. In its present
form it would be extremely inefficient for this task
but it can be converted into a batch process model
relatively quickly and cheaply. Finally, many of the
proposed solutions would be dynamically operated and
the model could be used to establish the most effi-
cient operating policies. Alternatively, it could be
used to make operational decisions in "real time"
predicting the consequences of any operational deci-
sion before that decision is made, greatly increasing
the efficiency and decreasing the risk of operating
those solutions.
References
1. Publication:
"Washington Metropolitan Area Water Supply
Study Report" (Draft, 1975), Part of
"Northeastern United States Water Supply
(NEWS) Study," New York, N.Y., U.S. Army
Corps of Engineers, North Atlantic Division,
2. Authority:
Public Law 89-298, "Northeastern United
States Water Supply" enacted October 27,
1965.
3. Consultant:
Meta Systems Inc., Cambridge, Mass.
Principal Investigator—Russell deLucia,
Model Coding—Lewis Koppel, Hydrologic
Simulation—Gerald Tierney, Water Demand
Analysis—Myron Fiering.
828
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FUTURE DIRECTIONS IN URBAN WATER MODELING
Michael B. Sonnen, Prin. Engr.
Larry A. Roesner, Prin. Engr.
Water Resources Engineers, Inc.
Walnut Creek, California
Robert P. Shubinski, Vice Pres.
Water Resources Engineers, Inc.
Springfield, Virginia
A review was made for the Storm and Combined Sewer
Section of the U.S. Environmental Protection Agency
(EPA) concerning existing urban water mathematical
modeling capability. From this review, gaps in needed
modeling technology were identified, and a philosoph-
ical approach to filling those gaps was developed.
Finally, a phased implementation program for developing
the needed models was suggested.
Introduction
In 1974-75, a review was performed by Water
Resources Engineers (WRE) for EPA's Storm and Combined
Sewer Section concerning the state-of-the-art of urban
water modeling. Moreover, WRE was then to recommend
what model development work could be undertaken most
feasibly in the next five years. The scope of the
review was to include all the urban water subsystems,
such as watersheds, water supplies, treatment, or water
use, but the emphasis for obvious reasons was placed on
storm and combined sewer problems and their modeling.
In this paper we outline our findings with
respect to most of the urban water subsystems
reviewed and suggest that inadequacies that continue
to exist in problem-solving capability are more
philosophical and scientific than numerical.
Subsystem Modeling Needs
Urban Watershed Hydrology
Urban hydrology received considerable attention
from modelers as soon as computers became routinely
available to them. This resulted in part because
urban flooding and drainage problems were acute;
damages were high and frequent. Moreover, analysts
knew intuitively that the rational method for
designing runoff facilities was theoretically weak
and yet tedious in complex applications. So hydro-
graphs, unit hydrographs, instantaneous unit hydro-
graphs, systems of linear reservoirs, infiltration
equations, Markov chains, and numerous other pieces
of these and other puzzles were fed into the computer.
Urban watershed models of quantity and quality have
been the latest result. The recent attention to
"nonpoint" sources of pollution has raised the
importance of the urban runoff problem, while the
ability to model the phenomena occurring, partic-
ularly the quality phenomena, has culminated for the
moment with "dirt and dust" linkages that are theo-
retically weak, if empirically capable of calibration.
Hater Distribution Systems
Water distribution systems have been analyzed
with computer methods for years. Numerous utilities
and private consultants have more than adequate
versions of programs that balance heads and flows in
these closed systems. Some, if not most, of the
programs deal with numerically complicating system
paraphernelia such as pressure reducing valves,
variable speed pumps, and the like. The quality
of water in these systems has not been included,
however, and recent discussions of lead poisoning
and carcinogenic substances in water supplies may
draw more analysis attention to this important piece
of the urban water system. Computerized, automatic
operation is on the drawing boards as well, awaiting
realization.
Water Use
To the writers' knowledge, the urban water use
subsystem has never been rigorously simulated, in a
cause-and-effect sense. The most elaborate model
constructed appears to be MAIN-II, developed by
Hittman Associates.1 This model either accepts
projections or makes its own for "independent"
variables such as population density, values of
dwelling units, and numbers of dwelling units in
each value range. Among residential, commercial -
institutional, industrial, and public-unaccounted
sectors of the community, 150 separate water use
categories can be projected. Other models include
those of Schaake and Major,2 and the "Data Management
Systems" of WRE3 and Montgomery-WRE.4 All of these
approaches to water use projection, however, depend
on prior projections of independent variables, for
example, population, per capita income, or water
pricing policy. As such, they are all computeri-
zations of effects and their trends, rather than
models of water demand causes that simulate resultant
effects.
TihanskyS and Sonnen^ have each developed some
quality-use-consumer-cost programs that calculate the
added costs to homeowners or industries of excessive
hardness or TDS in their supplies, but these accept
demands as given and do not account for any diminution
in projected unit demands if quality deteriorates,or
increases in use if quality is improved. In short,
much more work could be done in simulation and economic
modeling analysis of urban water use.
The water use subsystem is the most critical of
all because it sets the quantity and quality demands
for all upstream subsystems, plus it is the source of
the quantity and quality loads imposed on all subsystems
downstream.
Sewer Systems
Sewer design problems have been approached with
models that adopt the steady-state "design flow"
concept which obviously makes them more applicable to
sanitary sewers than to storm sewers. Mathematical
programming techniques have been used to discover
optimal sizes, slopes, and—in rare cases—configu-
rations of drainage networks. Fisher, et al_.7
presented an integer programming formulation for the
diameter-slope problem. In spite of finding a 10
percent cost savings over a traditional design method,
the authors concluded that uncertainties in excavation
costs, the dynamic nature of actual flows, and the
arbitrary nature of velocity constraints detract
829
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considerably from the significance of the indicated
saving. Argaman, et £[•, have also considered optimal
network configuration as well as pipe sizes and slopes.
They found their dynamic programming approach to
require amounts of computer time that severely limit
the size of the sewer network that can be considered.
The development of programming techniques for sewer
design is relatively recent, and their application to
real problems has not been documented.
Analysis models describe the performance of a
given collection and conveyance system under given
inflow conditions. Model output is usually in terms
of flow rates, and possibly in terms of impurity con-
centrations over time at various points including at
the system outfall. Brandstetter9 has conducted a
comprehensive review of the more sophisticated of
these models. The initially developed hydraulic
transport routine for EPA's SWMM model'0 is typical.
Depending on the level of resolution needed to repre-
sent temporal variables and the pipe network,
relatively coarse to highly sophisticated analytical
models are available. SWMM is one of the more sophis-
ticated (and expensive) of these models.
Water Resources Engineers has developed11 and the
Corps of Engineers has documented^ a planning level
model (STORM) in which continuous computer simulation
(at hourly intervals) with historical rainfall records
is used to predict the effects of various treatment
and storage capacities on overflow quantities and
quality. No consideration is given to the collection
and conveyance system, however, and no cost relation-
ships or optimizing algorithms have been included. A
significant outcome of using this model, however, has
been the emergence of the concept of the "design
event" including a dry period for accumulation of
pollutants on the watershed, as opposed to the purely
hydrologic concept of a "design storm."
Waste Treatment
This subsystem received a flurry of modeling
attention from early systems analysts. Most of this
work was directed at optimizing the amount of waste
treatment at various points along a stream, given a
dissolved oxygen standard and the Streeter-Phelps
equation. A later tack was taken to simulate waste
treatment processes themselves. The majority of this
work to date has been an exercise in programming the
rules of thumb of sanitary engineering design, but
some elucidation of process variables has resulted.
A recent article by Christensen and McCarty'3 gives
a hopeful signal that causes can be modeled funda-
mentally to predict effects rather than having to
"predict" the answer from statistical analyses of
the measured answers at 20 other plants.
Receiving Waters
Many, many programs to solve the Streeter-Phelps
equation along streams were developed in the early
1960's. Link-node models for estuaries with dynamic
hydraulic solutions were developed by 1965 for the
Delaware estuary and for San Francisco Bay. Lake and
reservoir temperature models and groundwater models
followed by 1967-1969. In 1969-1971 the receiving
water model called RECEIV was incorporated in the EPA
SWMM model. During this period, the feasibility of
modeling several aquatic trophic levels and their inter-
related responses to ambient water quality was shown.
This philosophy was eventually demonstrated for San
Francisco Bay and Lake Washington. Since then many
stream, estuary, and lake models have been developed
and updated to include the "ecologic model" inter-
relationships.
Throughout the roughly 15-year history of modeling
of receiving waters, the capabilities of the developed
models have lagged behind the scope of the problems
being faced by urban water management decision makers.
Current problems specified for attention by the Water
Pollution Control Act Amendments of 1972 include deri-
vation of "wasteload allocations" for waters designated
as "water quality class segments." Current ecologic
models applied to this problem have proved helpful but
less than completely satisfactory. The Safe Drinking
Water Act of 1974 implies a need for a model to treat
as many as 150 substances and their interactions.
Recommended Future Water Models
From its review of the state-of-the-art and its
view of what is 1) most likely of early success,
2) most required in terms of pressing needs, and
3) most feasible in terms of EPA's research posture
and wherewithal, WRE recommended'4 the following
models receive development attention in the next 5
years:
Planning Models
1. A new and better watershed quality model.
2. A transport simulation capability in a planning
model for storage/treatment/overflow evaluations
(STORM-II).
3. Capability to simulate quality control or treatment
processes in STORM-II.
4. A long-term (10-30 year) receiving water ecologic
model.
5. An economics model for assessing users' water
supply benefits and costs.
6. An economics model for assessing receiving water
users' benefits and costs.
Design/Analysis Models
1. A solids deposition and scour capability in a
hydraulically sound sewer transport model.
2. Dry-weather waste treatment simulation capability
in a SWMM-type model.
3. Reclamation or reuse routing capability in a
transport/treatment model.
4. Nonstructural runoff control simulation capability
in a SWMM-type runoff module.
Operation/Control Models
1. Real-time control software for sewer systems.
2. Real-time spatially varied runoff prediction
capability.
Modeling Philosophy
There are two points about modeling that our
project has suggested may be more important to getting
problems solved than the mere statement of a subsystem's
set of unresolved technical circumstances. These are:
1) What are the consequences of poor communication
between the developer of a model and its subsequent
user? 2) What are the consequences of claiming to
model a process when in reality we are managing somehow
to reproduce the expected value of its output?
830
-------
These problems are related to one another, and
they may each be restatements of a more general riddle
which could be stated, Why are we building all these
models anyway? The quick, obvious answer is, We need
them, just to perform all the computations for us,
just to do the arithmetic involved in analyzing a
basin-wide pollution problem over a 30-year period.
Fine, that's answer enough. But such an answer implies
1) that the model developer and the user of the model's
output each understand perfectly what arithmetic needs
to be done, 2) that they are each confident that the
computer is being told to do the correct arithmetic
via the program, and, of course, 3) that the machine
will do correctly what it is told to do. It seems to
us that the last of these three assumptions is the
only one worth betting on.
We conducted an informal survey of ten people,
roughly half of which were model developers, acade-
micians, researchers; the other half were model users,
front-line water and waste managers, city officials,
Federal data collectors, utility managers. With few
exceptions we heard that communication between the
developer of a model (computer program, really) and the
subsequent user has been garbled at best. Invariably,
a delivered program contains bugs, solves a slightly
different and usually much simpler problem than the
one(s) advertised, or simply will not function or
execute with a different set of data.
There are many variations of the same communi-
cations problem. Often the delivered card deck and
documentation reports do not clearly annotate the
options available or assumptions implicit in the
programs. Sometimes the mathematical statement of
the general problem is far more precise than the data
used to "verify" the model, and hence the program
takes inordinate amounts of time and money to generate
its highly approximated and questionable results.
Saddest of all are the cases where the model developer
and the ultimate user of the model's results, often
the fellow who paid for the development, never
communicated from the start; and the model developed
addresses a problem the user never had, while his real
problem is still unsolved.
Every developer of a model who has given his pro-
gram to someone to use has heard these complaints.
Ironically, he knew he would, and he let the program
out of his hands anyway. Usually, he lets it go
because the user bought it from him. But he knows,
and the user cannot believe, that there will be
problems with the very next application. Sometimes
there is no excuse for this phenomenon, just as there
is no excuse for somebody else's meatloaf not tasting
like your mom's. They just are not the same; they
were made differently even though they were called the
same thing. Another reason it occurs is because the
modeler knows from the start that he is setting out
to approximate a solution to a theoretical problem
with both an approximation of the theory and an
approximation to the prototype water body. The model
user or the user of the model's results views his
problem, and the theoretical statement, as precise
and infinitesimal. Almost invariably, the first
application of a handed-over program is made to a
problem that either 1) lies outside the range of
applicability of the equations simplified in the
program, or 2) requires a time step shorter than the
model or its "theory" can accept. Highly qualified
and experienced programmers make these mistakes just
as neophytes do. The nondeveloper-user almost always
expects a new program to be both more exact and more
flexible than it is or was ever intended to be.
Lastly, it occurs because modelers make mistakes.
Without question, improvements in model documen-
tation and preparation of user's manuals can be made.
The communications problems between modelers and
subsequent users of their products are too numerous
and well documented for simple sloppiness of expla-
nation to continue. Responsibilities lie with both
parties, however, and the tedious method of constant
re-explanation between the developer and the subsequent
user is the only failsafe procedure. A nondeveloper-
user who picks up a program deck cold certainly is go-
ing to have problems with it, period.
So much for crossed wires and simple not hearing
what the other fellow said. The more insidious prob-
lem is the "model" that both the parties accept but
that is not a model at all. One of the respondents to
our survey said, "... analysis of the results of the
model run are the real key to application of any model."
Right on. It is worth amplifying that computer print-
outs rarely if ever contain a singular answer to a real
problem. The significant analysis leading to solution
of a real problem starts when a successful run or set
of runs ends. A model user has to be a qualified
results analyst, or he is not a user at all. Getting
a program to execute with data given in the format
described in a user's manual is one problem, but
interpreting the results is quite another and more
important problem. To interpret the results correctly,
of course, means that the user can correctly interpret
the model's inputs and its general workings as well;
and perhaps most importantly he must know and understand
the particular water body, land surface, or treatment
process being modeled. In other words, there is an
onus on the user of the model or of its results to sort
through the mass of modeled evidence to satisfy himself
that either the model or the data are not quite correct
or that the prototype could indeed behave in such a
strange or unexpected way. If the results are just
what he would have expected, he must still be able to
determine whether the model and he were both right or
he must be willing to accept the consequences.
For example, a computer program that predicts the
suspended solids concentration in the effluent of a
primary clarifier, from a relationship between overflow
rate and the removal efficiency measured at 60 existing
plants, is not a model of the behavior of a primary
sedimentation tank. In a given situation, such a
program may be adequate. It may even prove to have
been right, once the 61st, "modeled" tank has been
built. But the program was never written to simulate
what would happen in the 61st tank, and the model
developer could hardly be blamed if the 61st tank and
its contents behaved quite differently. Unless, of
course, he had claimed that he had modeled the sedimen-
tation process, which he clearly had not. We might
add, since currently there are so many people clamoring
to use runoff quality models that exist today, that many
of them have been built to "predict" qualities not on
the basis of what happens on a watershed surface but on
the basis of what has been measured to have resulted in
the waters that ran off many other surfaces. There may
be a big difference, and while some modelers may not
even be aware that they're doing that, a user of the
model must know it. In other words, many simulation
models around today are designed to predict effects
based on measured effects elsewhere; they are not
designed to simulate causes which operate on input data
to produce expectable effects. Future urban water
models should be, but they are not now so designed be-
cause so much is still unknown about causative factors.
Future users, remember that despite the best inten-
tions or dreams of the developer, a model is always im-
perfect. What you cannot forget is that a less than
perfect representation of prototype systems is the goal
of the process from the beginning.
831
-------
Developers, remember that while adding more and more
padding to a mannekin might make a better and better
approximation of Requel Welch, it would be a delusion
to expect Raquel to finally appear in the flesh. Both
of you remember, it is fallacious to believe that an
extra large bikini is a model of Raquel merely because,
for at least part of the prototype, "it seems to fit."
Acknowledgments
This paper is based on a contract (68-03-0499)
sponsored by the Storm and Combined Sewer Section of
the U.S. Environmental Protection Agency. The Project
Officer for EPA was Chi-Yuan Fan. Richard Field also
contributed product review for EPA. The guidance and
support from these gentlemen and EPA is acknowledged
with gratitude.
References
1. Hittman Associates, Inc., Forecasting Municipal
Water Requirements, Report HIT-413, Hittman
Associates, Inc., Columbia, Maryland, September
1969; Vol. I, "The MAIN II System," 208 p.;
Vol. II, "The MAIN II System Users Manual," 425 p.
2. Schaake, J.C., Jr., and D.C. Major, "Model for
Estimating Regional Water Needs," Water Resources
Research AGU, Vol. 8, No. 3, June 1972,
pp. 755-759.
3. Water Resources Engineers, An Investigation of Salt
Balance in the Upper Santa Ana River BasfrTj
presented to the State Water Resources Control
Board and the Santa Ana River Basin Regional Water
Quality Control Board, March 1969, 198 p.
4. Montgomery-Water Resources Engineers, Water, Waste-
water, and Flood Control Facilities Planning Model,
Submitted to the San Diego Comprehensive Planning
Organization, January 1974, 189 p.
5. Tihansky, D.P., "Damage Assessment of Household
Water Quality," Journal of the Environmental
Engineering Division, ASCE, Vol. 100, No. EE4,
August 1974, pp. 905-918.
6. Sonnen, M.B., "Quality Related Costs of Regional
Water Users," Journal of the Hydraulics Division,
ASCE, Vol. 99, No. HY10, October 1973, pp. 1849-
1864.
7. Fisher, J.M., 6.M. Karadi, and W.W. McVinnie,
"Design of Sewer Systems," Water Resources Bulletin,
AWRA, Vol. 7, No. 2, April 1971, pp. 294-302.
8. Argaman, Y., U. Shamir, and E. Spivak, "Design of
Optimal Sewerage Systems," Journal of the Environ-
mental Engineering Division, ASCE, Vol. 99,
No. EE5, October 1973, pp. 703-716.
9. Brandstetter, A., Comparative Analysis of Urban
Stormwater Models, BN-SA-320, Pacific Northwest
Laboratories, Battelle Memorial Institute,
Richland, Washington, August 1974, 88 p.
10. Environmental Protection Agency, Storm Water
Management Model, 4 Volumes, Washington D.C.,
1971, "Volume I-Final Report," "Volume II-
Verification and Testing," "Volume Ill-User's
Manual," and "Volume IV-Program Listing."
11. Roesner, L.A., H.M. Nichandros, R.P. Shubinski,
A.D. Feldman, J.W. Abbott, and A.O. Friedland,
A Model for Evaluating Runoff-Quality in Metro-
832
poll tan Master Planning, ASCE Urban Water Resources
Kes.earch. Program lechmcal Memorandum No. 23,
American Society of Civil Engineers, New York,
April 1974, 73 p.
12. U.S. Army Corps of Engineers, Urban Runoff:
Storage, Treatment and Overflow Model "STQKM",
Draft Generalized Computer Program 723-58-2250,
Hydrologic Engineering Center, Davis, California,
September 1973, 62 p.
13. Christensen, D.R. and P.L. McCarty, "Multi-Process
Biological Treatment Model," Journal of the Water
Pollution Control Federation, Vol. 47, No. II,
November 1975, pp. 2652-2664.
14. Sonnen, M.B., L.A. Roesner and R.P. Shubinski,
Future Direction of Urban Water Models, Prepared
for the Office of Research and Development, EPA,
by Water Resources Engineers, Inc., Walnut Creek,
California, Printed by NTIS as PB-249 049,
February 1976, 90p.
-------
TRANSPORT MODELING IN THE ENVIRONMENT
USING THE DISCRETE-PARCEL-RANDOM-WALK APPROACH
S. W. Ahlstrom
Water and Land Resources Department
Battelle Pacific Northwest Laboratories
Richland, Washington
H. P. Foote
Water and Land Resources Department
Battelle Pacific Northwest Laboratories
Richland, Washington
Abstract
When formulating a mathematical model for simulating
transport processes in the environment, the system of
interest can be viewed as a continuum of matter and
energy or as a large set of small discrete parcels of
mass and energy. The latter approach is used in the
formulation of the Discrete-Parcel-Random-Walk (DPRW)
Transport Model. Each parcel has associated with it
a set of spatial coordinates as well as a set of dis-
crete quantities of mass and energy. A parcel's move-
ment is assumed to be independent of any other parcel
in the system. A Lagrangian scheme is used for com-
puting the parcel advection and a Markov random walk
concept is used for simulating the parcel diffusion
and dispersion. The DPRW.technique is not subject to
numerical dispersion and it can be applied to three-
dimensional cases with only a linear increase in
computation time. A wide variety of complex source/
sink terms can be included in the model with relative
ease. Examples of the model's application in the
areas of oil spill drift forecasting, coastal power
plant effluent analysis, and solute transport in
groundwater systems are presented.
Introduction
The fundamental principle upon which the Battelle
Generalized Transport Model and all other mass trans-
port models are based is the law of conservation of
mass. This law can be expressed as:
The rate of change of
mass concentration of
chemical species k within
a given control volume
the net advective flux
= of the species k into
the control volume
the net diffusive flux
+ of species k into the
control volume
the net rate of produc-
+ tion of species k with-
in the control volume
(1)
A mathematical statement of Equation 1 is usually re-
ferred to as an equation of continuity. A general form
of the continuity equation for a non-isothermal multi-
component fluid consisting of K chemical species can
be written as :
(2)
where:
fe = 1.2.3...K
F = the mass concentration of species fe
v = the mass average velocity of the fluid
j the mass flux of k relative to v (diffusive
flux)
$ the net rate of production of species fe
within the control volume.
The addition of K equations of this kind gives the
equation of continuity for a mixture. Each term of
Equation 2 corresponds directly with the terms of
Equation 1.
The term on the left-hand side of Equation 2 is re-
ferred to as the transient term. It may be inter-
preted as the total rate of change of mass concentra-
tion of species k at a point in space at a given
instant in time. The mass concentration of any
species is in general assumed to be a function of
temperature, of time, and of spatial coordinates, as
well as the concentration of all the other species
present. The primary function of a transport model
is to predict and quantify these changes in concentra-
tion as a function of time and location.
The first term on the right-hand side of Equation 2 is
referred to as the advective term. This term repre-
sents a change in concentration of the system result-
ing from the gross movement of fluid in which species
fe is transported. The mass average velocity vector
of the fluid mixture, v", is a function of time, space,
temperature, and the chemical composition of the
mixture. If v is constant with respect to time, the
flow field is said to be steady. For most applica-
tions to large scale environmental systems the
assumption of a steady flow field is usually adequate
only for short-term simulations. For most long-term
simulations, the velocity field cannot reasonably be
assumed to be constant.
The second term on the right-hand side of the equation
of continuity Is called the diffusive term. This term
represents the change in concentration of the system
resulting from the random molecular motion of each
species in the mixture. The driving force of the
-fe
relative mass flux, j , can be concentration,
pressure, temperature or other gradients. In many
large scale environmental transport analyses the
contribution of molecular diffusion is often very
minor, but when eddy diffusion is coupled with
molecular diffusion, this term may become much more
significant. The rationale for the inclusion of eddy
diffusion in this term is discussed below.
The last term in Equation 2 represents all internal
mechanisms that tend to change the net amount of
species fe present in a control volume. The reactivity
of a chemical system may be a function of temperature
and any or all of the fe mass concentrations in the
mixture. Ideally this term should consist of a series
of rate expressions which represent all known
mechanisms by which species fe can react with its
833
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immediate environment. Species for which $ is zero
are referred to as conservative substances because they
are neither created nor destroyed within a control
volume.
Equation 2, as written, is a very general expression.
It applies to both liquid and gaseous mixtures contain-
ing an arbitrary number of components in any ratio,
reacting over a wide range of temperatures and pres-
sures. Workable models are, by necessity, much more
limited.
Simplifying Assumptions
Equation 2 serves as the starting point for the expla-
nation of the assumptions that are present in the
existing DPRW code. Simplifying assumptions were made
for one or more of the following reasons :
1. A portion of the general equation, based on
an analysis of the best available informa-
tion, appeared to be relatively insignifi-
cant for the anticipated applications of
the model.
2. The quality of existing data or additional
data that can be reasonably obtained does
not justify considering anything above a
certain level of complexity.
3. To allow a numerical solution within
reasonable economical constraints.
Each simplifying assumption will be denoted by se-
quential numbers enclosed in square brackets preceding
the assumption as it appears in the text; i.e., the
fifth assumption will be preceded by [5].
When advective fields are calculated or measured it is
not practical to resolve the micro-advection patterns
that are known to exist in nearly all large scale
environmental flow systems. These turbulent flow
patterns, often the primary mixing mechanism, achieve
essentially the same result as diffusive processes
only much more rapidly. In some respects, micro-
advection phenomena, commonly called eddy or turbulent
diffusion can be thought of as a random process,
occurring on a larger scale, but having many character-
istics in common with molecular scale diffusion. Be-
cause of these similarities, it has been the practice
historically to [1] approximate this phenomena by
including it with the molecular diffusion in the rela-
tive mass flux term, j .
If it is assumed that [2] the relative mass flux can
be adequately described by expressions having the form
of Pick's First Law, then j" can be expressed as:
components of the tensor are considered to be signifi-
cant then Equation 3 can be reduced to:
3 =
?w - r v
(3)
where :
r = total mass density of the solution
D = molecular diffusivity tensor
m J
D = eddy or turbulent diffusivity tensor
w = the mass fraction of species fe (r /r)
The diffusivity tensors are in general functions of
both space and time. If the molecular diffusivity
is assumed [3] to be negligible with respect to the
turbulent diffusivity and if [4] only the longitudinal
-v-fe
- rpvw
(4)
where
V = longitudinal components of the eddy
diffusivity tensor
The velocity distributions required for a transport
simulation can be derived from a hydrodynamic numer-
ical or physical model study, and/or a field measure-
ment program conducted prior to running the simulation.
The assumption inherent in this practice is that [5]
the advection patterns are not dependent on the
chemical composition or temperature of the solution,
or in other words, the momentum, mass and energy
transport processes are decoupled. This assumption
is valid for systems that are not highly non-isothermal
and which contain relatively low concentrations of
contaminants.
Another assumption [6] considers the transporting
medium (water) to be incompressible. This assumption
is considered valid for most water mixtures that are
not near the boiling point. The restriction to
incompressible fluids causes the convenction term of
Equation 2 to be simplified as follows:
= r
= 0 for incompressible fluids
"(v-v) + (v-vrfe) = v-vrfe (5)
If all of the above assumptions are incorporated into
Equation 2, and also assuming that [7] the total mass
density, T, of the mixture remains relatively con-
stant. The result is:
nk. / / I
ar
3t
- (v-vr)
(6)
Although this equation was developed from a mass
balance point of view, it can also describe the
transport of heat under appropriate circumstances.
Starting with the law of conservation of energy, and
making assumptions identical or analogous to those
made above, one can derive an energy balance with
the same functional form as Equation 6. Consequently,
the transport of mass or heat can be calculated by
the same numerical computation code.
Boundary Conditions
Boundary conditions for transport analyses can be
specified quite simply. Four boundary types are
defined:
1. Free Flow Boundary - any matter or energy
transported across this type of boundary
is assumed to have exited from the system.
2, Reflecting or No Flow Boundary - any com-
ponent encountering this type- of boundary
is reflected back into the system.
3. Dnconditional Sticking Boundary - any sub-
stance that comes in contact with this
type of boundary will adhere to it.
4. Conditional Sticking Boundary when matter
comes in contact with this type of boundary
it may adhere to the boundary or be reflect-
ed from it. The percentage of the coincident
834
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matter that is allowed to stick is calculated
from a predefined probability distribution
function.
The Numerical Solution Algorithm
A system of matter can be viewed from two alternative
frames of reference. The classical approach is to
view the advection-diffusion processes from an Eulerian
point of view, establishing the transport equation from
a consideration of concentrations and flux of a con-
tinuum at fixed points in space. A quantity of matter
can also be thought of as being comprised of a large
number of discrete particles. Keeping this in mind,
it is also possible to approach the transport problem
from a Lagrangian viewpoint, focusing on the history
of particle motions. To arrive at useful results,
statistical properties of the motions have to be con-
sidered, so that this second approach may be labeled
as "statistical", in contrast to the "phenomenological"
method mentioned above.
Both of these approaches, if pursued, will yield Equa-
tion 2. However, the viewpoint that is chosen to
derive the transport equation has some very definite
implications relating to possible numerical solution
techniques. The phenomenological approach which views
matter as a continuum suggests the application of
finite difference or finite element numerical techni-
ques. The statistical viewpoint suggests a different
type of approach using a discrete particle, Lagrangian
algorithm. This type of numerical scheme is used in
the most recent version of Battelle Generalized Trans-
port Model and is referred to as the Discrete-Parcel-
Random-Walk method.
The basic device or tool employed by this technique
is a hypothetical entity called the computational
parcel. A quantity of matter or energy is represented
as consisting of a finite ensemble of these parcels.
Each parcel has associated with it a set of Cartesian
and a set of discrete
n, where:
n
n
spatial coordinates (x , y
quantities of matter or heat £
n.
O
P
p = the parcel index (p = 1,2,3...P) where P is
the total number of parcels used to represent
a given quantity of matter.
k = the transported species index (fe. = 1,2,3...K)
where K is the total number of constituents
present in the system.
n = the time level index (W = 1,2,3...N) where N
is the number of time increments to be computed.
* n , n n
yp=yp+ At vp
* n , , n n
z - z + At w
P P
(7b)
(7c)
where At is the time increment, and * denotes an inter-
mediate or temporary value.
If a smooth continuous solution is desired the maximum
value of At should be limited by the requirement that
the maximum distance any parcel is transported must
be less than or equal to the distance between data
points in the velocity matrix.
The dispersive component for each parcel is then cal-
culated by assuming that the parcels are subject to
Brownian-like random motion resulting from turbulence
present in the transporting medium. From statistical
considerations it can then be shown that the root-
mean-squared (rms) distance moved by a given parcel
during the time, At, in three-dimensional isotropic
space is
v/6t?At
(8)
where V is the eddy diffusivity which is proportional:
to the square of the "typical" eddy size.
The dispersive step size for an individual parcel is
generated by:
rrf = [R]' (9)
[R] represents a random number in the range 0 •+• z
where z must be chosen so that the rms value of all of
the r j generated is equal to the value specified by
Equation 8. The random number generators available on
most computer systems will return values in the range
0.0 -»• 1.0 . The rms value of the set of all numbers
output by a number generator of this type is given by
Equation 10 if, in fact, the generator is truly
random.
l/2
VJ
(10)
Assuming that an adequate random number generator of
this type is available, dispersive step lengths with
the appropriate rms distance can be generated by
[R]
(ID
For example, the location of parcel 3 after 5 time
steps is (x5- y5- z5). If the problem is concerned
3' 3' 3
with 5 distinct constituents, this parcel would have
associated with it 5 separate heat or mass quantities
-5>5
r2>5
r3>5
'3 - 53'D' 53>D' S3 ' ?3
The DPRW transport code requires a velocity matrix
describing the flow patterns of the transporting media
as input data. The flow field is allowed to be a
function of both time and space. The two spacial
velocity components at the location of parcel "p",
(uH, vrt, wn), can be interpolated from the surrounding
p' p' pj'
matrix of values. The advective transport component
is then computed by:
p
. n n
At Up
(7a)
The new Cartesian coordinates of each parcel are then
calculated by
) (12a)
) (12b)
(12c)
2w and * is a random
n+1
Xn
p
yp+1
n+1
ZP
*
= x + r ,cos
p 0.
= y* + rdsin
*
~ zp rdcos
(6) sin
(0) sin
(*)
where 0 is a random angle from 0
angle from 0 -*- TT .
Parcel "p" has thereby been transported by advection
and diffusion mechanisms from (x
n+1 n+1
n n. . n+1
V V to (xp '
) during time step "n.". The trace of a parcel
during this time step is illustrated in Figure 1.
835
-------
n+1 n+1
'P ' yP '
Figure 1. Vector Diagram of Transport Components
When this computation has been completed for every
parcel in the system, a grid network can be super-
imposed upon the spatially distributed ensemble of
parcels. The nodal points of the grid are labeled
with -t,y,£ indices where:
-i. = 1,2,3.... 1 = number of nodal points in
x-direction
y = 1,2,3.... J = number of nodal points in
y-direction
L 1,2,3.... L = number of nodal points in
z-direction.
The nodal points form the vertices for (1-1) x (J-l)
•x. (i-1) rectangular solids which are referred to as
cells. Parcel "p" is said to lie within cell (-i,j,l)
if
n+1
X . < X < X . ,
-c — p -c+1
y . < y
- y
n+1
(13a)
(13b)
(13c)
The total amount of matter or energy within cell (-L,
j',£) is computed by summing the E, ' values for all
parcels that lie within the cell for each species:
fe *
"JLjt
I
m=l
(14)
(sfe>n)
V ' iljL
n,-;« = number of parcels within cell (ltjt£)
The volume of the cell, V- •/,, is a known quantity.
Consequently, an average intensive quality variable,
usually a concentration or temperature, can be com-
puted for each constituent in each cell by:
(15)
where Z = an appropriate conversion factor to convert
F to the units desired by the user (e.g.,
the factor for converting from cal/cm
to °F).
To complete the numerical scheme the contributions of
the source/sink term must now be accounted for. The
method used to model these contributions varies de- ,
pending upon the type of mechanisms represented by .
If the source/sink mechanism is simply a discharge of
material into the system or a removal of material
from it, parcels are either added to or removed from
appropriate areas of the solution maxtrix.
Many source/sink mechanisms are of a. more complicated
type that describe interactions between the various
constituents that may be present and between the
constituents and the environment. These types of
interactions may be specified by reaction rate or
heat exchange expressions, or by equilibrium constraints.
A reaction-rate type of mechanism, r , is a set of pre-
defined functions that describe the rate of change of
r as a function of all the species present in the
system.
fe
The change of r in cell (-L,j,t)- during a given time
step can be calculated explicitly by:
k,n+l _ k,* k( m,*\
Tlj£ ~ Tljl + r ^y£JAt
m = 1,2,3...K
which can be evaluated directly or implicitly by
k,n+l = fe,* fc
lit lit
(16)
(17)
which can be solved using standard iterative matrix
inversion methods.
If the source/sink mechanism is specified by constrain-
ing the system to be at equilibria at the end of each
time step, the solution of a set of simultaneous non-
linear equations of the form shown in Equation 18 is
required.
r
lit
•\fel)
m = 1,2,3. ..K
(18)
where E|j represents a set of algebraic functions that
specify the necessary conditions for equilibria to
exist. These functions usually represent mass and
charge balances and either mass-action expressions or
relationships that specify the minimization of the
Gibbs free energy. Systems of equations of this type
are usually solved by a Newton-Raphson iteration or
some other type of iterative procedure. The concen-
tration values immediately following the advection-
dispersion computations are used to provide starting
values for the iterative procedure.
Once the concentration at the next time level, r.V
*-i
has been determined the mass associated with each
parcel is adjusted by the ratio of the change.
fe,n+l
,fe,w+l
(19)
The conversion of 5 to T does not necessarily have to
be made prior to computing some types of source/sink
term contributions, but F is usually a much more con-
venient quantity to work with than the extensive
variable, 5- For some simple rate expressions, such
836
-------
as an Irreversible first order decay, the extensive
variables can be modified directly:
£M+1=CM e-AAt
where \ is the decay constant.
The solution can then proceed to the next time level.
Examples of Model Application
The Battelle Generalized Transport Model functions in
three operational modes:
• Oil spill drift forecasting,
• Powerplant outfall analysis, and
• Groundwater contaminant plume prediction.
The operational modes differ primarily in the type of
source/sink terms that have been coupled to them.
The model is currently is use in each operational mode
by various governmental land state agencies. Samples
of the output generated by each mode are shown in
Figures 2-4. A document describing the details of
the oil spill operational mode is available3. Documen-
tation of the other two modes is currently under
preparation.
Figure 2. Oil Spill Operational Mode
Maximum Temperature 7.784
Figure 3. Powerplant Outfall Operational Mode
TRITIUM, 1 YEflRS
Figure 4. Groundwater Solute Operational Mode
References
1. Bird, R. B., W. E. Stewart and E. N. Lightfoot,
Transport Phenomena, John Wiley and Sons, Inc.,
1960.
2. Csanady, G. T., Turbulent Diffusion in the
Environment, D. Reidel Publishing Company,
Boston, 1973.
3. Ahlstrom, S. W., A Mathematical Model for Pre-
dicting the Transport of Oil Slicks in Marine
Waters, Battelle, Pacific Northwest Laboratories,
BN-SA-558, 1975.
837
-------
AN INTERACTIVE SYSTEM FOR TIME SERIES
ANALYSIS AND DISPLAY
OF
WATER QUALITY DATA
S. Buda
Michigan Department of Natural Resources
Lansing, Michigan
R. L. Phillips
G. N. Cederquist
D. E. Geister
Unidata, Incorporated, Ann Arbor, Michigan
ADROIT is an interactive computer graphics system
which is capable of rapid retrieval, statistical pro-
cessing and graphical display of water quality data.
It is used here to analyze trends in Soluble Ortho
Phosphorus data collected on Michigan's Grand River,
by the Michigan Department of Natural Resources be-
tween 1963 and 1974. Soluble Ortho Phosphorus concen-
trations are declining, and the decline is not due
solely to increasing stream flows. Relationships be-
tween concentration, stream flow and loading rates for
Soluble Ortho Phosphorus are examined. Further analy-
sis, using ADROIT as an analytical tool, to define the
impact of phosphorus abatement programs in Michigan is
recommended.
ADROIT
ADROIT" (Automated Data Retrieval and Operations In-
volving Timeseries) is an interactive system which is
capable of rapid retrieval, statistical processing and
graphical display of water quality data. The system
is basically an interpreter for a special-purpose
problem-oriented programming language. It has been
designed to produce retrospective statistical time
series analyses of water quality data and, without
further user intervention, to produce report-ready
graphs of selected results. ADROIT comprises two ma-
jor subsystems, the computational subsystem and the
display subsystem. In addition, the system includes a
stand-alone program called COMPOSE which is capable of
additional graphical operations.
At the heart of the ADROIT Computational Subsystem
(ACS) is a special purpose interpretive programming
language. The language has been designed to properly
handle timeseries data types, specifically those per-
taining to water quality observations. Being an in-
terpretive language, like BASIC, the computational
task specified by the user is carried out immediately;
there is no compilation step as in FORTRAN. The fa-
miliar data types of logical, string and numeric are
present in ACS as well as novel data types such as obs
and timeint. Each variable of type obs is actually a
four-tuple of values, comprising the mean, sample
variance, sample weight, and time of observation asso^-
ciated with water quality data. The introduction of
this data type insures rigorous and proper handling of
data observations in all arithmetic and statistical
operations. The timeint data type has been introduced
to permit arbitrary time period restriction and aggre-
gation of data. Using variables of this type in con~
junction with those of type obs enables the user to
perform a wide range of water quality analyses.
In order to facilitate operations with timeseries data
types, ADROIT provides a complete range of special
* ADROIT, A System for Water Quality Data Analysis and
Display, Unidata, Incorporated, P. 0, Box 2227, Ann
Arbor, Mi., June 1975,
built T-in functions, as well as the standard numeric
data type functions found in most programming lan-
guages , There are functions for extracting the com-
ponents of an obs, for restricting data to a specified
time interval, and for aggregating observations by
specific intervals. In addition, there are statisti-
cal functions that compute the inverse normal, chi-
squared, Fisher's F and Student's t distributions.
These provide the building blocks for arbitrary com-
plex statistical analyses that can be developed by the
user,
A unique feature of ADROIT is the capability of build-
ing up a library of user-defined procedures. Thus,
when the user finds there are functions that he fre-
quently performs and finds useful, he can catalog them
in a special procedure file by giving them a unique
name. When the function is to be invoked, the user
simply types its name (and any appropriate arguments)
and the ACS executes the function immediately. For
example, a procedure that computes both a water quali-
ty index and phosphate loading at a selected station
is invoked by
WQIPHOS.('700026' ,P665,TIME 70 THRU 74)
where the arguments are the station number, EPA param-
eter number, and the time interval for which the com-
putations are to be performed.
The ADROIT Display Subsystem (ADS) is so flexible and
provides such a wide range of capabilities that a user
can, on the one hand, specify every aspect of the
graph to be displayed or allow the system to produce
all of its features automatically.
Just as the special data types in ACS are essential to
the operation of the computational subsystem, a rigor-
ous , canonical definition of a graph and its elements
is a fundamental aspect of ADS. This graph descrip-
tion is maintained by the system in a form called a
structure which the user can interact with to modify
all or part of a graph. The structure is an ordered
list of graph elements each of which requires one or
more parameters to describe it. Typical graph elements
would be the axes_. tick marks, grid lines, labels,
titles, etc. Independent x and y parameter (horizontal
and vertical) specifications of each of these elements
is under control of the user. Thus, he may elect to
produce y-grid lines only and omit those for the
x-axis. Among the display options available to the
user are
.choice of linear or logarithmic axes
.point, line, or bar graph plotting of data
.curve smoothing or least squares data fitting
.absolute, relative or cumulative histograms
.general textual annotation
.three color Calcomp plots
838
-------
Figures 1 through 15 are examples of finished graphs
produced by ADROIT, using the facilities of both the
computational and display subsystems.
Through ADROIT, large amounts of data extracted from
the U.S. Environmental Protection Agency STORET system
are available for rapid access and manipulation.
Thus, the system is expected to be a valuable tool for
research on the effectiveness of water quality control
procedures.
Statistical Procedures Applied to Grand River Data
A number of ADROIT Procedures were used to process
stream flow and soluble ortho phosphorus data for the
Grand River at Grand Haven, Michigan.
The phosphorus data (mg/1) collected between 1963
through 1974- is plotted in Figure 1. During this pe-
riod most of the data was collected monthly. Occa-
sionally 2 samples per month were collected. There
are numerous occasions when samples were not collect-
ed, particularly during winter months.
Figure 2 depicts this phosphorus data (mg/1) aggre-
gated by year. The mean of the observations made
during each year is plotted. An interval of +1 stan-
dard deviation is also plotted with each mean.
The ADROIT Procedure INDICES, was used to compute the
monthly seasonal indices.1 These twelve indices
(Table 1) indicate the fraction of each year's aver-
age phosphorus level (mg/1) that occured in each
month, respectively. For January, 1.43 indicates that
all January phosphorus levels (mg/1) averaged 43%
higher than corresponding yearly averages over the 11
year period. If there were no seasonal influence,
each month's level would be the same as every other
month and the seasonal indices would all be close to
1.0. The seasonal indices for the phosphorus data
(mg/1) are shown in Table 1.
The ADROIT Procedure DESEASON. was used to deseasona-
lize the phosphorus data (mg/1) by dividing each ob-
servation by the appropriate monthly index. The de-
seasonalized phosphorus data (mg/1) is shown in Figure
3. The principle effect of this process is to reduce
the variability of the original data by removing that
portion of the total variability due to non-random
seasonal effects. Figure 4 shows that the standard
deviations have been reduced, while the annual sample
means have remained the same as Figure 2. (NOTE: the
standard deviations for 1973 and 1974 increased after
deseasonalization due to partial yearly data.)
Figure 5 is a plot of the sample means of the phospho-
rus data (mg/1) with associated 90% confidence inter-
vals. In this case the sample means and sample vari-
ances are used to estimate the interval within which
the true population mean is likely to be 90% of the
time. We are therefore inferring the value of the
population means by using the sample statistics.
Three ADROIT Procedures were used to compute Figure 5.
Figure 5 is the best estimate of the mean phosphorus
concentration for each year, with seasonal and serial
correlation effects accounted for. Procedure SERIAL.
was used to compute the 1st order serial correlation
coefficient, R, for the deseasonzlized phosphorus
data.3 For this period of record, R 0.43. To de-
termine if this value of R was significant for the
number of observations used, the 1st order serial cor-
relation coefficient and 95% confidence limits were
computed for an artificial, normal, random time
series.* This was done with Procedure TESTR. Since_
R = 0.43 for our data is greater than the upper confi-
dence limit of the random time series of 0.16, R is
significant at the
level.
Procedure VARADJ. is used to adjust the variances of
the deseasonalized phosphorus data to account for the
serial correlation. In effect the variances were in-
creased by 15-53% depending on the number of observa-
tions each year. These adjustment factors were com-
puted on the basis of an artificial time series (first
order Markov process) with the same degree of serial
correlation. Applying these factors to our data is an
approximation, but it allows us to adjust for serial
correlation and arrive at a better estimate of the
confidence intervals. As the sample size decreases,
the factors increase.
In a similar manner, the flow data is processed and
the results are shown in Table 2 and Figures 6 through
10.
Figures 11 and 12 (previously presented as Figures 5
and 10) are plots of the mean soluble phosphorus con-
centration (mg/1) and stream flow (cfs) respectively,
with 90% confidence intervals. All data has been de-
seasonalized. Since stream flow affects concentration
data, the phosphorus loading rate has been computed as
a way to consider changes in concentration and flow
together.
Procedure LOAD, was used to compute these loadings.
The instantaneous loading rate is the product of the
concentration and stream flow at that time. (in addi-
tion to a unit constant) Because there are occasions
when more than one concentration sample or flow mea-
surement per month were made, procedure LOAD, aggre-
gates by month first, to assign a single flow and con-
centration observation for each month. Then for those
months with corresponding concentration and flow ob-
servations the product is taken to yield a monthly
loading observation.
Procedure LOAD, operated on deseasonalized concentra-
tion and flow data and therefore the loading data is
deseasonalized. Procedures SERIAL, and TESTR. were
used to yield a serial correlation coefficient of 0.30
which is significant at the 95% level when compared to
the highest expected value of 0.18.
Procedure VARADJ. was used to adjust the variances for
this serial correlation and Figure 13 is a plot of the
sample means of the phosphorus loading (Ibs/day) rate
with associated 90% confidence intervals.
Figure 14 is a plot of stream flow versus soluble
phosphorus concentration (mg/1) for the period 1963
through 1974. It was produced using procedure VERSUS.
which aggregates all data by month, and assigns plot-
ting pairs for each month. The regression line is
also plotted. Procedure LINCOR. was used to compute
the linear correlation coefficient which was 0.297.
Similarly, Figure 15 is a plot of stream flow versus
soluble phosphorus loading (Ibs/day) for the same
data. The linear correlation coefficient is +0.783.
Discussion of Results
Soluble Phosphorus Concentrations Over Time
A major objective of this analysis is to determine if
water quality is improving or not. Soluble ortho
phosphorus., an important nutrient for aquatic organ-
isms , is examined with these statistical techniques
as one of a number of parameters which can be analyzed
similarly. Water Quality is improving if the phos-
phorus concentration is decreasing over time in a
statistically significant way.
839
-------
SOLUBLE ORTHO PHOSPHORUS AS P, MG/L
0.4T
D
IT)
FIG. 2 *W.
RAW DATA
STANDARD DEVIATIONS
700026
S3 64 85 68 87 SB 83 70 7i 72 73 74 75
TIME OF OBSERVATION
83 84 85 88 87 88 63 70 71 72 73 74 75
TIME OF OBSERVATION
O.*i
V)
0.*
0.1
a
in
FIG. 3
DESEASONALIZED DATA
STN • 700028
0.4-1
0.0
83
040508070809 70 71 7273 74 75
TIME OF OBSERVATION
O.tH
FIG. 4
STN - 700028
DESEASONALIZED DATA
STANDARD DEVIATIONS
84 83 « 87 « M 70 71 72 73 74 75
TIME OF OBSERVATION
TABLE 1
SOLUBLE ORTHO PHOSPHORUS
SEASONAL INDICES
JAN 1.43
FEB 1.28
MAR
APR
MAY
JUN
1.09
0.70
0.57
0.80
JUL 0.85
AUG 0.85
SEP 0.38
OCT 0.96
NOV 1.06
DEC 1.34
i
to
v>
o
o
o.a-
0.1
0.0
FIG. 5
STN " 700020
DESEASONALIZED DATA
90 PER CENT
CONFIDENCE INTERVALS
83040308878809 70 71 7273 74 75
TIME OF OBSERVATION
840
-------
STREAM FLOWr CUBIC FT/SEC
20000.T
«n 15000.
t
u
I0000. •
sooo. •
0.
FIG. 6
RAW DATA
20000.
FIG. 7 ""
RAW DATA
STANDARD DEVIATIONS
- 70002*
TIME OF OBSERVATION
TIME OF OBSERVATION
20000.
13000.
u
t-t
§
g 10000.
3000.
0.
FIG. 8 *TN-™««
DESEASONALI2ED DATA
20000.
1SOOO.
O
cf
5000.
FIG. 9
DESEASONALIZED DATA
STANDARD DEVIATIONS
STN - 70002*
84 OS M «7 «6 « 70 71 72 73 74 75
TIHE OF OBSERVATION
OT *7 M « 70 71 72 73 74 75
TIME OF OBSERVATION
TABLE 2
STREAM FLOW
SEASONAL INDICES
JAN
FEB
MAR
APR
MAY
JUN
0.32
1.15
1.86
1.85
1.14
0.89
JUL
AU6
SEP
OCT
NOV
DEC
0.63
0.55
0.62
0.66
0.83
0.91
t
20000.
15000.
toooo.
sooo.
0.
FIG. 10
DESEASONALIZED DATA
90 PER CENT
CONFIDENCE INTERVALS
am • 700020
TIME OF OBSERVATION
841
-------
ID
ol
in
en
S
o
o.*i
0.3-
0.2
o.i
o.o
FIG. 14
- 700028
SOLUBLE PHOSPHORUS
CONCENTRATION VS
STREAM FLOW
5000. 10000. 1SOOO. 20000. 25000. 30000.
STREAM FLOW»CUBIC FT/SEC
20000.
> 13000.
)10000.
3
u.
3000.
0.
FIG. 12
DESEASONALIZED DATA
90 PER CENT
CONFIDENCE INTERVALS
3TH • 700028
>- sooo.
a
a.
4000-
3000.
a- 2000.
S
O 1000.-
O
in
04 83 W «7 00 W 70 71 72 73 74 73
TIttE OF OBSERVATION
o.
FIG. 15
STN » 70002B
SOLUBLE PHOSPHORUS
LOADING VS
STREAM FLOW
0. 5000. 10000. 19000, 20000. 25000. 30000.
STREAM FLOW.CUBIC FT/SEC
>-
I
MOO.T
5000.
4000.
3000.
2000.
1000.
OT 0.
FIG. 13
DESEASONALIZED DATA
90 PER CENT
CONFIDENCE INTERVALS
SIN • 70002B
83 »4 83 88 87 S» 83 70 71 72 73 74 75
TIME OF OBSERVATION
842
-------
Figure 5 indicates that the phosphorus concentration
has declined. The confidence intervals for any two
years may be compared. If there is no overlap of the
intervals (i.e. 1963 compared to 1972) the difference
in the means may be considered significant.* We con-
clude therefore that the phosphorus concentrations in
the early 1970's are significantly lower than levels
in the early 1960's. Indeed the data could be aggre-
gated over 5 year periods to demonstrate this. The
confidence intervals were computed using the t distri-
bution, well suited for small samples (less than 30
observations), the data was deseasonalized to remove
an important non-random component of the sample vari-
ance and the variance was adjusted to account for the
serial correlation of the data. This analysis se-
quence can be applied to other parameters to produce
interval estimates of the population mean.
Stream Flow Levels Over Time
We now must consider some possible cause and effect
relationships. It must be emphasized that this data
base of monthly observations may not be sufficient to
answer all questions we will now raise. However,
these statistical techniques will give us some in-
sight.
Figure 10 is the stream flow analogy of Figure 5. It
indicates that stream flow has increased significant-
ly, since 1963. The large confidence intervals for
1973 and 1974 are due in part to reduced sample size.
Concentration - Stream Flow Relationships
Is concentration decreasing because flow is increas-
ing? This question is addressed in Figures 11 and 12.
Between 1963 and 1971 concentration declines while
flow increases. However from 1972 through 1974 con-
centration remains at about the same level (the over-
lap of the confidence intervals implies the apparent
increase is not significant) while flow continues to
increase. This latter period seems to contradict the
original relationship. The relationship is unclear.
Figure 13 is the phosphorus loading rate resulting
from the concentration and flow data of Figures 11 and
12. The loading rate appears to be influenced most by
the stream flow, with concentration acting as a rela-
tive constant in the loading product. The best way to
discern the relationships between concentration, flow
and loading is shown in Figures It and 15.
Figure 14- plots concentration versus associated
streamflow. The relationship is poor, as demonstrated
by a wide range of concentration observations asso-
ciated with flows of 5000 cfs and less. A regression
line is shown. The linear correlation coefficient of
0.297 indicates a poor linear relationship. Figure 14
does not mean that concentration is not a function of
flow, but rather, flow is not the only factor influ-
encing soluble phosphorus concentration. It is likely
that storm intensity and duration along with other
hydrographic factors are significant. We must con-
clude however that the apparent decline of phosphorus-
concentrations of Fi'gure 11 cannot be attributed to
flow, Since phosphorus removal facilities for munici-
pal treatment plants were constructed during this
period, it is possible that Figure 11 reflects this^
change. Further analysis is necessary to define this
relationship.
As expected, Figure 15 demonstrates that there is a
strong relationship between streamflow and soluble^
* The t test may be applied as a rigorous test, but
this graphical method is a good approximation.
phosphorus loading rates, The linear correlation co-
efficient is +0,783 indicating a good linear correla-
tion. In light of Figure 14, we must conclude that
soluble ortho phosphorus loading rates reflect the
strong influence of flow in the loading rate product,
and that loading rates as a parameter for measuring
trend provide little new information in this case.
References
1 Spiegel, M.R., "Theory and Problems of Statistics",
(Schaum's Outline Series, McGraw-Hill Book Co.,
1961), p. 293,
2 Spiegel, p. 299.
3 Yevdjevich, M.V., "Statistical and Probability
Analysis of Hydrologic Data", (Handbook of Applied
Hydrology, McGraw-Hill Book Co., 1964), p. 8-79.
11 Yevdjevich. p. 8-83.
5 Yevdjevich, p. 8-86.
843
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CONFERENCE COMMITTEES
CONFERENCE COORDINATOR
Vernon J. Laurie
LOGISTICS COMMITTEE
Joseph Castelli
Delores J. Platt
STEERING COMMITTEE
John B. Moran
Willis Greenstreet
PROGRAM COMMITTEE
Wayne R. Ott, Co-Chairman
Elijah L. Poole, Co-Chairman
Oscar Albrecht
Robert Clark
Robert Kinnison
Albert Klee
Harry Torno
Bruce Turner
Ronald Venezia
ADVISORY COMMITTEE
Aubrey Altshuller Peter House
Dwight Ballinger John Knelson
Delbert Earth Victor Lambou
William Benoit John P. Lehman
Kenneth Biglane William McCarthy
Matthew Bills George Morgan
Andrew W. Breidenbach Thomas Murphy
Ken Byram MeMn Myers
Peter L. Cashman Edward Nime
Daniel Cirelli Edmund Notzon
William Cox Robert Papetti
John Dekany James J. Reisa
Richard T. Dewling William Rosenkranz
David W. Duttweiler William Sayers
Ronald Engel S. David Shearer
R. J. Garner Thomas Stanley
Carl Gerber D. F. Swink
Donald Goodwin Christopher Timm
James Hammerle A. C. Trakowski
Steve Heller Frode Ulvedal
John W. Hollis Morris Yaguda
CONFERENCE SPONSORS
OFFICE OF RESEARCH AND DEVELOPMENT
Wilson K. Talley
Albert C. Trakowski
OFFICE OF PLANNING AND MANAGEMENT
Alvin L. Aim
Edward Rhodes
844
-------
AUTHOR INDEX
Adrian, D.D.-419
Ahlert, R.C. - 745
Alhstrom, S.W. - 833
Allen, M. - 236
Amendola, G.A. - 512
Anderson, J.A. - 308, 353
Anthes, R.A. - 313
Aquilina, M. 595
Arnett, R.C. - 768
Ashamalla, A.F. - 563
Atherton, R.W. - 429
Ayers, R.U. - 288
Baca, R.G. - 768
Baker, D.A. - 204
Ball, R.H.-218
Bansal, M.K. - 335
Barrington, J. - 446
Baughman, G.L.-619
Beal, J.J. - 326
Beall, M.L. - 90
Becker, C.P. - 466
Beckers, C.V., Jr. - 45, 344
Bedient, P.B. - 362
Benesh, F.-691
Berger, P. - 657
Berman, E.B. - 377
Bierman, V.J. - 773
Binkowski, F.S. - 473
Bland, R.A. - 522
Bliss, J.D. - 696
Bloomfield, J.A. - 579, 683
Bobb, M.W. - 706
Brandstetter, A. - 548
Breidenbach, A.W. - 3
Breiman, L. - 725
Broadway, J.A. - 264
Buda, S. - 838
Budenaers, D.H. - 646
Burr, J.C. - 82, 322
Colder, K.L. - 483
Callahan, J.D. - 508
Carbone, R. - 478
Carlson, G.A. - 579
Casey, D.J.- 176
Cederquist, G.N. - 838
Chamberlain, S.G. - 45, 344, 508
Chang, G. - 252
Chang, T.P.- 129
Characklis, W.G. - 367
Chen, C.W. - 764, 794
Cho, B. - 308
Christiansen, J.H. - 77, 97
Clark, L.J. - 133
Clark, P.A.A. - 176
Clark, R.M. - 808
Clark, T.L.-719
Cleary, R.W. - 434
Clymer, A.B. - 82, 517
Cohen, S. - 223
Cooper, A.S. - 414
Covar, A.P. - 326, 340
Crawford, N.H. 151
Cukor, P.M.-218, 223
Curran, R.G. - 532, 639
D'Agostino, R.-691
D'Arge, R.C. - 446
Davis, L.R. - 784
Deb, A.K.-814
Deininger, R.A. - 634
Delos, C- 115
deLucia, R.J. - 453
Demenkow, J.W. - 508
Descamps, V.J. - 591
Diniz, E.V. - 367
DiToro, D.M.-614
Dolan, D.M. - 773
Donigian, A.S., Jr. - 151
Doyle, J.R. - 139
Duffy, R.G.-322, 517
Duttweiler, D.W. 10
Eadie, B.J. - 629
Ehler, C.N. - 407
Eilers, R.G. - 760
Eimutis, B.C.-710
Ellett, W.H. - 161
Elzy, E. - 609
Eskridge, R.E.-719
Eubanks, L. - 446
Fabos, J. Gy. - 396
Falco, J.W. - 156
Falkenburg, D.R. - 57
Field, R. 548
Finnemore, E.J. - 14, 391, 429
Fishman, G.S. - 664
Fitch, W.N. - 69
Foote, H.P. - 833
Gage, S.J. - 223
Galloway, W.J. - 799
Geister, D.E. - 838
Geller, E.W. - 503
Gesumaria, R. - 745
Gillett, J.W. - 624
Gillian, J.I. - 808
Goldberg, S.M. 199
Gorr, W.L. - 478
Greenberg, A. - 308
Gregor, J.J.- 209
Gribik, P.R. - 86
Griffin, A.M., Jr. - 466
Grigg, N.S. - 755
Grimsrud, G.P. 14, 391
Grizzard, T.J.-819
Grossman, D. - 605, 639
Guldberg, P.H.-298, 691
Outer, G.A. - 424
Haefner, J.W. - 624
Hahn, R.A. - 824
Hameed, S.-318
Hamrick, R.L. - 657
Hansen, C.R. - 706
Harley, B.M.-651
Harlow, C. - 353
Hasan, S.M.-139, 358
Hasselblad, V. - 191
Heaney, J.P. - 139, 358, 362
Heilberg, E. - 40
Hern, S.C. - 696
Hertz, M. - 196
Hess, R.C. - 247
Hetling, L.J. - 579
Hill, D.-401
Hines, W.G. - 62
Hoehn, R.C.-819
Hoenes, G.R. - 204
Holloway, D.E. - 367
Holmes, B.J.-710
Hossain, A. 129
Howe, C.W. - 247
Hsu, Der-Ann - 673
Huber, W.C. - 139, 358, 362, 493
845
-------
Hung, J.Y.- 129
Hunter, J.S. - 673
Hwang, P.H. - 92
Iltis, R. - 573
Ives, K.J.-814
Johanson, P.A. 111
Johnston, T.L. 223
Joyner, S.A., Jr. - 396
Jurgens, R. - 730
Katzper, M.-214
Kaufman, H.L. - 144
Kearney, P.C. - 790
Kendall, G.R. - 223, 230
Keyser, D.-313
King, P.C. - 750
King, T.G.-414
Kingscott, J. - 120
Kneese, A.V. - 274
Knelson, J.H. - 191
Koch, R.C. - 92
Kortanek, K.O. - 86
Krabbe,D.M.-381
Kreider, J.F. - 247
Kuhner, J. - 453
Kuo, A.Y. - 543
Kuzmack, A.M. - 736
Labadie, J.W. - 755
La, FuHsiung - 1444
Lambie, F. - 236
Lambou, V.W. - 696
Lassiter, R.R. - 619
Lawson, R.E., Jr. - 493
Lebedeff, S.A.-318
Lee, S. - 522
Lewellen, W.S.-714
Lienesch, W.C. - 453
Lindstrom, F.T. - 609
Liu, Hsien-Ta - 503
Livingston, R.A. - 230
Lo, Kuang-Mei- 414, 419
Logan, S.E. - 199
Lorenzen, M.W. 111,794
Lovelace, N.L. - 133
Lown, C.S. - 466
Luken, R.A. - 106
Malanchuk, J.L.-619
Manns, B. - 803
Marks, D.H.-372, 639, 651
Marsalek, J. - 558
Marshall, R.N. - 45, 344
Matystik, W.F., Jr.-614
Maxwell, D.R. - 706
Mays, L.W. - 740
McAllister, A.R. - 298
McCurdy, T.-691
McGaughy, R.E. - 736
McKenzie, S.W. - 62
Mears, C.E.-701
Meenaghan, G.F. - 386
Meier, P.M. - 293
Meisel, W.S. - 483, 725
Menchen, R.W. - 230, 241
Mendis, M.S.,-241
Metry, A.A. - 537
Mote, L.B.-710
Mukherji, S.K. - 706
Mulkey, L.A. - 156
Murphy, M.P. - 358
Nagel, L.L. - 458
Nash, R.G. - 790
Nelson, W.C. 191
Neustader, H.E. - 678
Norwood, D.L. - 264
'Nossa, G.A. - 166
Olenik, T.J. - 745
Orr, D.V. - 247
Parker, P.E. - 344
Paul, J.F. 171
Pechan, E.H. - 106
Pelton, D.J. - 92
Petri, P.A. - 282
Pheiffer, T.H. - 133
Phillips, R.L. - 838
Pielou, B.C. - 668
Plotkin, S. -218
Poole, E.L. 1
Porter, R.A. - 97
Prasad, C. - 303
Princiotta, F. -218
Pritsker, A.A.B. -259
Ramm, A.E. - 101
Randall, C.W.-819
Rao, S.T. - 499
Rhodes, R.C. - 730
Ricca, V.T. - 586
Richardson, W.L. - 20
Rickert, D.A. - 62
Riggan,W.B.-196
Riley, J.J. - 503
Roake, A.F. - 563
Robertson, A. - 629
Roesner, L.A. - 829
Rosenstein, M. - 591
Ross, N.P.-214
Ryan, T.C. - 424
Samson, P.J. - 499
Sanders, W.M., III-10
Sandwick, J.P. - 176
Santiago, H.P. - 230
Sargent, D.H. 126
Sauter, G.D. - 30
Scavia, D. - 629
Schaake, J.C., Jr.-553, 651
Schregardus, D.R.-512
Schultz, H.L.,111-241
Schur, D.A. - 595
Selak, M. - 353
Sengupta, S. - 522
Shahane, A.N. - 657
Shapiro, M. - 453
Shirazi, M.A. - 784
Shell, R.L. - 600
Shelley, P.E. - 583
Shubinski, R.P. - 69, 829
Shupe, D.E. - 600
Sidik, S.M. - 678
Skretner, R.G. - 353
Smith, D.J. - 764
Smith, E.T. - 439
Smith, L. - 218, 223
Snow, R.H. - 627
Snyder, W.H. - 488, 493
Soldat, J.K. - 204
Solpietro, A. - 176
Sonnen, M.B. - 829
Spofford, W.O., Jr. - 407
Sullivan, R.E. - 161
Svendsgaard, D.J. - 269
Sweigart, J.R. - 86
Tang, W.H. - 740
846
-------
Tapp, J.S. - 50, 350
Teske, M. -714
Thomann, R.V. - 568
Fhomas, N.A. - 20
Thomas, R.W. - 696
Thompson, R.S. - 488, 493
Thuillier, R.H. - 35
Tikvart, J.A.-701
Tonias, B.C. - 750
Toino, H.C. - 548
Trakowski, A.C. - 2
Trotta, P.O. - 755
True, H.A. - 74
Truppi, L. - 196
Udis, B. - 247
Upholt, W.M.-182
Van Bruggen, J.B. - 196
Vicens, G.J.-651
Waddel, W.W. - 111
Walker, W. - 595
Walski, T.M. - 532
Walton, JJ. - 26
Wang, C.L. - 252
Weatherbe, D.G. - 330
Weil, CM. - 186
Wenzel, H.G., Jr. - 740
Westermeier, J.F. - 424
Whang, D.S. - 386
White, D.W. - 326
Whitman, I.L. - 7
Wickramaratne, P.J. - 508
Williams, H.D. - 706
Williams, L.R. - 696
Winfield, R.P. - 568
Wisner, P.E. - 563
Wright, T.E. - 298
Yearsley, J.R. - 780
Yen, B.C. - 740
Young, J.T. - 247
847
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TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1. REPORT NO.
EPA-600/9-76-Q16
2.
3. RECIPIENT'S ACCESSION NO.
4. TITLE AND SUBTITLE
Proceedings of The EPA Conference on Environmental
Modeling and Simulation
5. REPORT DATE
June, 1976
6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S)
Wayne R. Ott, editor
(over 300 authors)
8. PERFORMING ORGANIZATION REPORT NO.
9. PERFORMING ORGANIZATION NAME AND ADDRESS
N/A
10. PROGRAM ELEMENT NO.
1HD621
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U. S. Environmental Protection Agency
401 M Street S.W.
Washington, D.C. 20460
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EPA/ORD
15. SUPPLEMENTARY NOTES
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16. ABSTRACT
This document contains the Proceedings of the EPA Conference on Environmental
Modeling and Simulation held in Cincinnati, Ohio, on April 19-22, 1976. This
national Conference was the first of its kind to cover the state-of-the-art of
mathematical and statistical models in the air, water, and land environments.
This document contains 164 technical papers on environmental modeling
efforts in air quality management, air and water pollutant transport processes,
water runoff, water supply, solid waste, environmental management and planning,
environmental economics, environmental statistics, ecology, noise, radiation, and
health. The Conference was directed toward the technical and administrative
communities faced with the need to make environmental decisions and predict future
environmental phenomena. The Proceedings are believed to be the most complete
summary of environmental modeling efforts currently available.
17.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.IDENTIFIERS/OPEN ENDED TERMS
Mathematical models, -Computer simulation,
Econometrics, Systems analysis, Statistica
analysis, Pollution - Water pollution,
Air pollution", Sanitary engineering, Water
supply, Environmental engineering, Civil
engineering
Environmental modeling
Environmental statistics
Environmental engineer-
ing
Computer simulation
Systems analysis
Operations research
i r.al modeling
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04B
05C
06F
12A
12B
13B
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861
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