United States
Environmental Protection
Agency
Environmental Research
Laboratory
Athens GA 30613
EPA-600/9-85-003
January 1985 •
Research and Development
Proceedings of
Stormwater and
Water Quality
Model Users
Group Meeting
April 12-13, 1984

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                                   EPA-600/9-85-003
                                   January 1985
           PROCEEDINGS
                OF
STORMWATER AND WATER QUALITY MODEL
       USERS GROUP MEETING
        April  12-13, 1984
           Edited by

      Thomas 0.  Barnwell,  Jr.
 Center for Water Quality  Modeling
 Environmental  Research Laboratory
         Athens, GA 30613
 ENVIRONMENTAL RESEARCH LABORATORY
 OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
         ATHENS, GA 30613

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                                 DISCLAIMER

      The work described in these papers was not funded by the U.S. Environ-
mental Protection Agency.  The contents do not necessarily reflect the views
of the Agency and no official endorsement should be inferred.

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                                   FOREWORD

     A major function of research  and  development  programs  is to effectively
and expeditiously transfer technology  developed  by  those  programs  to  the
user community.  A corollary function  is  to  provide  for the continuing ex-
change of information and ideas between  researchers  and users,  and  among  the
users themselves.  The Stormwater  and  Water  Quality  Model Users Group,
sponsored jointly by the U.S. Environmental  Protection Agency and  Environment
Canada/Ontario Ministry of the Environment,  was  established to  provide such
a forum.  The group has recently widened  its  interest to  include models other
than the Stormwater Management Model and  other aspects of modeling  water
quality in urban and natural waters.   This report, a compendium of  papers
presented at the April  1984 Users  Group meeting  in Detroit MI,  is  published
in the interest of disseminating to a  wide audience  the work of group members.
                                      Rosemarie C.  Russo, Ph.D.
                                      Director
                                      Environmental Research Laboratory
                                      Athens, Georgia
                                     ni

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                                  ABSTRACT

      This proceedings includes 17 papers on topics related to the develop-
ment and application of computer based mathematical models for water quantity
and quality management.  The papers were presented at the semi-annual meeting
of the Joint U.S.-Canadian Stormwater and Water Quality Model Users Group
held on April 12-13, 1984, in Detroit, Michigan.

     Two papers  discuss the application of microcomputers to real-time control
of combined  sewer overflows and to the estimation of nutrient and pollutant
loadings.  In separate papers, the SWMM program is applied to hydraulic
modeling in  an unsteady pressure flow regime and to sensitivity analysis of
water quality predictions.  Other model applications include HSPF to simulate
stormwater arid water quality aspects of ponds and WASP to simulate acidifica-
tion of lakes.   A combined hydrologic time series and topographic database
manager (CHGTSM) is presented, and revisions to the QUAL-2 water quality
model are discussed.

      Aspects of rainfall modeling are examined in a program for analyzing
rainfall inputs  in computing storm dynamics and in a system for acquiring
and processing rain data using Apple  II work-alikes.  Estuary studies in-
clude developing flow and loading inputs for steady state models and modeling
negatively buoyant thermal discharge.

      Milwaukee's modeling approach to water quality and sewer system analysis
is described, and Ohio's method for determining the reaeration coefficient
for streams  is presented.  Additional papers examine kinematic distribution
of detention storage, discuss the need for hydrologic model validation, and
provide water temperature modeling guidance.
                                     IV

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                                  CONTENTS

                                                                       Page

FOREWORD	in
ABSTRACT	   1v
ACKNOWLEDGMENT 	  vii

MILWAUKEE'S INTEGRATED MODELING APPROACH TO WATER QUALITY AND SEWER
   SYSTEM ANALYSIS 	     1
   N.U. Schultz,  CH2M HILL, and G.A.  Gagnon, Milwaukee Metropolitan
      Sewerage District

USING A TIMEX-SINCLAIR 1000 MICROCOMPUTER FOR REAL-TIME CONTROL
   OF COMBINED SEWER OVERFLOWS 	    16
   M. Stirrup and W. James, McMaster University

HYDRAULIC MODELING WITH SWMM IN AN UNSTEADY PRESSURE FLOW REGIME ...    31
   J.D. Perry and T.P. Finn, CE Maguire

A LAKE ACIDIFICATION MODEL USING WASP  	    47
   W.-S. Lung, University of Virginia

SENSITIVITY ANALYSIS OF SWMM PREDICTIONS ON WATER QUALITY IN THE
   DETROIT RIVER   	    67
   A. El-Sharkawy and R.H. Kummler, Wayne State University

RAINPAK—A PROGRAM PACKAGE FOR ANALYSIS OF STORM DYNAMICS IN
   COMPUTING RAINFALL INPUTS 	    81
   W. James and R. Scheckenberger, McMaster University

DEVELOPMENT OF FLOWS AND LOADS FOR STEADY-STATE ESTUARY MODELS:
   TAMPA BAY CASE STUDY  .	   101
   S.A. Hanson and J.P. Hartigan, Camp Dresser & McKee Inc.

WATER SCREEN—A MICROCOMPUTER PROGRAM FOR ESTIMATING NUTRIENT
   AND POLLUTANT LOADINGS  	   121
   B.L. Bird, Anne Arundel Community College, and K.M. Conaway,
      Anne Arundel County

SIMULATION OF THE STORMWATER AND WATER QUALITY ATTRIBUTES OF PONDS
   WITH HSPF	   147
   M.P. "Sullivan and T.R. Schueler, Metropolitan Washington Council
      of Governments

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                              CONTENTS (cont'd)


KINEMATIC ANALYSIS OF DETENTION STORAGE 	   163
   D. Stephenson, McMaster University

THE NEED TO VALIDATE HYDROLOGIC MODELS	175
   S. Udhiri, Maryland-National Capital Park and Planning Commission

MODELING OF A NEGATIVELY BUOYANT THERMAL DISCHARGE IN AN ESTUARINE
   ENVIRONMENT	189
   A.K. Deb and J.K. Snyder, Roy F. Weston, Inc.

RAINFALL DATA ACQUISITION AND PROCESSING USING APPLE II WORKALIKES  .  .   205
   M. Robinson and W. James, McMaster University

CHGTSM—A COMBINED HYDROLOGIC TIME SERIES AND TOPOGRAPHIC DATA BASE
   MANAGER	217
   W. James and A. Una!, McMaster University

MODIFICATIONS TO THE QUAL-2 (SEMCOG) WATER QUALITY MODEL  	  233
   R.C. Whittemore, National Council of the Paper Industry for Air
      and Stream Improvement, Inc., and L.C. Brown, Tufts University

PREDICTING THE REAERATION COEFFICIENT FOR OHIO STREAMS   	  249
   D.S. Skalsky, L.D. Fischer, and S. Arnragy, The Ohio Environmental
      Protection Agency

WATER TEMPERATURE MODELING:  A PRACTICAL GUIDE   	  273
   P. Shanahan,  Environmental Research and Technology

LIST OF ATTENDEES   	296
                                    VI

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                               ACKNOWLEDGMENT

      The Stormwater and Water Quality Model  Users Group relies on local
hosts to make arrangements for meeting rooms  and participant housing.   The
hosts for the meeting reported in this proceedings were Dr.  Ralph H.  Kummler
of the Department of Chemical  and Metallurgical  Engineering, Wayne State
University; Dr. Thomas Heidtke of the Department of Civil  Engineering,  Wayne
State University; and James A. Anderson of Urban Science Applications,  Inc.
                                    vii

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          MILWAUKEE'S INTEGRATED MODELING APPROACH
          TO WATER QUALITY AND SEWER SYSTEM ANALYSIS

                             by

           Nancy U. Schultz, CH2M HILL, Milwaukee
                             and
  Gary A. Gagnon, Milwaukee Metropolitan Sewerage District

ABSTRACT

Milwaukee's Water Pollution Abatement Program is a multi-year,
multi-agency program geared to plan, design, and construct
sewage collection and treatment facilities required for the
area's surface waters to meet water quality criteria.   The
efforts are coordinated through a program management office
which conducts systemwide studies and coordinates site speci-
fic projects.  Over the past years the program management
office has developed and/or applied numerous computer models
to aid in this analysis and in coordination of the project.
This paper describes how the several models and their
respective data bases have been integrated into a modeling
approach which emphasizes strengths of the various
individual models and acknowledges the weaknesses by
supplementing with other models.

The surface water models used in the program to date include
STORM, SWMM, SAM, CAM, HSP, several data base and statistical
packages, and some single purpose models written specifically
for the Milwaukee program.  The paper presents a chronology
of the use of these models, discussing why a specific model
was chosen for a given application, how it was used, key
results and limitations of its application.  Uses discussed
in the paper include:

     o    Water quality impact analysis
     o    Sewer system relief needs evaluation
     o    Infiltration/inflow prediction
     o    Storage volume calculation
     o    Combined sewer design flow calculation
     o    Hydraulic analyses
     o    Instrumentation and control needs definition

The paper concludes with a description of anticipated future
uses of the integrated modeling approach of the Milwaukee
Pollution Abatement Program.

                               1

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INTRODUCTION

The Milwaukee Water Pollution Abatement Program is a joint
effort of the Milwaukee Metropolitan Sewer District  (MMSD),
CH2M HILL and numerous other consultants to plan, design, and
construct all sewerage facilities necessary to meet federal,
state, and court ordered pollution control regulations.  The
program planning area covers 424 square miles, drained by over
12 million linear teet of sewers and interceptors.  Twenty
seven square miles are drained t>y combined sewers.  Milwaukee's
combined sewer area connects to the separate sewer system only
at the regulators controlling flow to the interceptors.  Unlike
most combined systems, upstream separate sewers do not tlow
into combined sewers.

Originally, all sewers flowed toward the center city Jones
Island wastewater treatment plant which is shown in Figure 1.
Since the late 1960's, many sewer diversions have been
installed to allow discretional routing of about two-thirds of
the separate sewer system towards the new South Shore
wastewater treatment plant.

When the program started, separate sewers bypassed to the
rivers several times per year, and combined sewers overflowed
during most rainstorms.  Regulations require that essentially
all, separate sewer bypasses be eliminated by 1986.  The
regulatory agencies have required that even the storm of
record cannot cause separate sewer bypasses from the future,
upgraded system.  In addition, combined sewer overflows must
be controlled.  Current estimates require a half year level of
protection for the combined sewers, but ongoing studies will
determine the final requirements.

Several years ot facility planning have concluded the control
objectives can be realized through:

     o    Infiltration/inflow reduction

     o    Sewer relief construction

     o    Treatment plant rehabilitation

     o    Construction ot a tunneled interceptor to be used
          for conveyance and storage ot both separate sewage
          and combined sewer overflows

     o    construction ot connecting sewers and control works
          to enable joint, but selective, use of the
          conveyance/storage system

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Planning facilities for such a large area in a short time
required extensive data handling and computation.  Computers
have been used extensively to facilitate the computations and
enable detailed analysis of alternative pollution control
facilities and operational plans.  This paper discusses
computerized water resources models used for:

     o    Combined Sewer Overflow analysis
     o    Infiltration/Inflow Study
     o    System Wide Analysis
     o    Environmental Assessment
     o    Sewer System Evaluation Survey
     o    Predesign of Combined Sewer Collectors
     o    Operational Control Analysis
     o    Hydraulic Design

This paper summarizes the applications and uses of the water
resources models.  The bibliography contains several
references for more thorough discussion of the models and
their individual applications.

COMBINED SEWER OVERFLOW ANALYSIS

An analysis of combined sewer overflows and their control
requirements was undertaken in the late 1970's.  Three water
resources models were used in these studies:

     o    Stormwater Management Model  (SWMM)
     o    Storage, Treatment, Overflow, and Runoff Model
           (STORM)
     o    Harper/Owes Receiving Water Quality Model

SWMM

The SWMM model was developed in the late 1960Ts by Water
Resources Engineers and is currently distributed and supported
by the EPA Center for Water Quality Modeling in Athens,
Georgia.  Three modules of the SWMM package were used for the
combined sewer study in Milwaukee:

     o    The RUNOFF block was used to calculate stormwater
          runoff from design storms.

     o    The QUALITY block was used to calculate quality
          characteristics of the combined stormwater and
          sanitary sewage.

     o    The TRANSPORT block was used to route flows and
          pollutants through the combined sewer network to the
          ox:tfalls.

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The primary outputs of the SWMM application were calculated
pollutographs used as input to the receiving water quality
analysis and peak flows used for preliminary sizing of
collector sewers proposed to carry flows from existing outfall
locations to future storage locations.

This early SWMM application was limited by sparse data
availability, hence sewer networks were only roughly
approximated and the hydrology portion of the analysis was not
calibrated.  Furthermore, the SWMM TRANSPORT assumption that
flows exceeding sewer capacity store at upstream locations
significantly altered the shape of outflow hydrographs and
underestimated peak flows.  Peak flows calculated by SWMM were
increased 20 percent in surcharged systems to compensate for
the assumed storage.

STORM

The STORM is distributed and supported by U.S. Army Corps of
Engineers Hydrologic Engineering Center in Davis, California.
The continuous hydrology portion of the model was used to
calculate total combined sewer overflow in the Milwaukee area
for summer periods from 1941 through 1974.  The resultant
flows were analyzed to evaluate storage volumes required to
achieve target levels of protection against combined sewer
overflow.

Like the SWMM analysis, the STORM analysis was not calibrated
due to a lack of available hydrologic data.  Furthermore, the
analysis failed to consider the early spring snowmelt periods
which significantly impact runoff volumes in the upper
midwest.

HARPER/OWES RECEIVING WATER QUALITY MODEL

Messrs. Harper and Owes developed a water quality model
specifically adapted for evaluating the water quality impact
of combined sewer overflows into the lower Milwaukee River.
The model, coupled with overflow pollutographs from SWMM, was
used to evaluate receiving water quality response to several
storms and several control alternatives.

Calibration of the Harper/Owes model was limited by:  the need
to represent upstream loads by averages since storm specific
data were lacking; a lack of data for hydrologic calibration;
and an inability to simulate the observed immediate response
to combined sewer overflow events.  The model was adjusted to
simulate bottom sediment disturbance as an immediate dissolved
oxygen sink when subsurface discharge of combined sewage
occurred.  This modification improved calibration and
indicated a need for further research regarding the oxygen
demand of disturbed sediments.

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COMBINED SEWER OVERFLOW ANALYSIS RESULTS

The model analysis were coupled with economic, engineering,
and environmental evaluations to conclude:

     1.   A half year level of protection would meet receiving
          water quality goals.

     2.   Partial separation of sewers  (providing storm sewers
          but not disturbing private property to disconnect
          building drains) represented the most cost effective
          method of achieving water quality goals,
          particularly in view of the then pending court case
          which would have required elimination of all
          combined sewer overflows. Later developments in the
          court case resxilted in the partial separation
          recommendation being dropped from the pollution
          abatement program.

INFILTRATION/INFLOW STUDY

An infiltration/inflow  (I/I) study of the separate sewer
system was conducted coincident with, but independent of, the
Milwaukee combined sewer overflow study.  Two water resources
models were used in the I/I analysis:

     o    Milwaukee I/I flow model
     o    System Analysis Model  (SAM)

MILWAUKEE I/I FLOW MODEL

The Milwaukee I/I flow model was developed from pre-existing
separate sewer flow data.  Flow data were available for
several locations throughout the system for a short period
(two to three years) and for a longer period  (about 10 years)
at the South Shore treatment plant.  The short records were
used to develop characteristic hydrograph shapes for various
regions of the service area.  The hydrographs were scaled to
represent a storm of record throughout the system on the basis
of the peak to peak ratio comparing local, short term records
with the system, long term record at the treatment plant.
Attempts to relate I/I peak flows to rainfall and sewer basin
characteristics were unsuccessful since no significant
correlation could be demonstrated between the rainfall and
sewer flow data.


SAM

SAM was developed by CH2M HILL in the late 1960's to aid
municipalities in evaluating storm and sanitary sewer systems.
The I/I studies used the kinematic wave sewer hydraulics

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approach to route the I/I hydrographs discussed previously
through the Milwaukee Metropolitan Intercepting System (MIS).
The analysis calculated routed peak flows in all sections of
the MIS and identified sewer reaches requiring relief to
accommodate existing and future flows.  SAM also calculated
hydraulic gradeline elevations required to pass peak flows
through surcharged sewers.  Relief was deemed necessary only
where the hydraulic gradeline exceeded flag elevations above
which property damage could be expected.

I/I STUDY RESULTS

The I/I analyses concluded that a 48 percent reduction of the
infiltration/inflow could be cost effectively achieved in the
Milwaukee separate sewer system.  Even with that I/I reduction,
relief sewers would be necessary in several locations.  The
most significant relief needs required large diameter inter-
ceptors paralleling the Milwaukee and Menomonee Rivers.
Analysis indicated the most cost effective alternative would
involve deep rock oversized tunneled sewers with capacity for
inline storage and conveyance of excess peak flows with
eventual pumpout to treatment.  Later studies reduced the
percentage of I/I which could be cost effectively removed from
the system/ necessitating additional relief sewer projects.

SYSTEM WIDE ANALYSIS

A system wide analysis was undertaken to evaluate the
potential for joint use of the tunneled inline storage/
conveyance system for both separate sewer and combined sewer
overflow relief.  Two water resources models were developed
for this analysis:

     o    Regression Flow Model
     o    Storage Analysis Model

REGRESSION FLOW MODEL

A sewer flow model which consistently projected both separate
sewer flows and combined sewer flows for a wide variety of
events was needed to evaluate the joint use of one storage/
conveyance facility for both systems.  Hydrologic theory
indicated both I/I and combined sewer flow should respond
(albeit to differing degrees) to the hydrologic processes
governed by land use, precipitation, soil moisture, snow melt,
evapotranspiration, etc.

The Southeastern Wisconsin Regional Planning Commission
(SEWRPC) had recently completed a thorough analysis of
available hydrologic data through the calibration of  the
Hydrocomp Simulation Program  (HSP) version of the Stanford
Watershed Model.  That analysis output a 39.6 year record

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(January 1940 through July 1979) of hourly calculations of
subsurface flows, impervious surface runoff and pervious
surface runoff in units of inches per unit area.

Available sanitary sewer flow data, sewer basin data, and the
continuous hydrologic output from HSP were tested in a variety
of linear and psuedo linear regression models.  The following
relationships were found to adequately predict separate sewer
infiltration and inflow:

     Infiltration = D + E*  (SUBRO)
     Inflow = B* (SUBRO) + C*  (IMPRO + OLFRO)
                                     2
     where:
          SUBRO = subsurface flow per unit area
          IMPRO = impervious area runoff per unit area
          OLFRO = pervious area runoff per unit area
          B     = 0.486* number of buildings
          C     = [0.398* number of buildings +_18.12 * number
                  of commercial buildings] * 10
          D     = 0.845* feet of sewer + 1062* number of
                  industrial and commercial buildings
          E     = 1.001* feet of laterals *10

Combined sewer flow could be similarly predicted from the same
hydrologic data base using the relationship:

     Stormwater flow = infiltration + IMP* IMPRO +  (1-IMP)
                       *OLFRO] *area drained

     where
               infiltration, IMPRO and OLFRO are as
               defined above
               IMP = impervious area fraction

STORAGE ANALYSIS MODEL

A simplified storage analysis model was developed to route
separate and combined sewer flows through the system to either
treatment, storage or river overflows under a variety of
system configurations.  The model employed linear storage
routing concepts to route the entire 39.6 year record of flows
developed with the regression flow model.  A daily time step
was used to speed evaluation of the more than 50 alternative
configurations studied.  Variables addressed in the
alternatives included:
     o    Inline storage volume
     o    Offline storage volume
     o    Available treatment capacity
     o    Pumpout rate
                                8

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SEWER SYSTEM EVALUATION SURVEY

The several models developed in the I/I analysis and the
System Wide Analysis (SAM, Regression, Storage) were used
jointly in the sewer system evaluation survey to determine
conveyance and storage facility requirements to offset
uncontrolled infiltration and inflow.  These models, along
with computerized sewer inspection records, were used to
conclude that approximately 13 percent of existing I/I could
be cost effectively removed from the system and to define
sewer relief needs.

ENVIRONMENTAL ASSESSMENT

Water resources computer models were used to evaluate
receiving water impacts of the Milwaukee Water Pollution
Abatement Program.  Three models were used in early phases of
the study:

     o    Hydrocomp Simulation Program (HSP)
     o    Milwaukee Harbor Circulation Model
     o    Plume dispersion model

HSP

HSP was used to calculate nonpoint loads and receiving water
response to the combined impact of point and nonpoint source
loadings under a variety of decentralization and
regionalization alternatives.   Application of HSP was greatly
simplified since extensive hydrometeorologic data base
development and model calibration had previously been
completed on a regional scale by the Southeastern Wisconsin
Regional Planning Commission.

HSP was used to evaluate receiving water response only in
riverine reaches unaffected by Lake Michigan backwater
impacts.

MILWAUKEE HARBOR CIRCULATION MODEL

The Milwaukee Harbor Circulation Model was developed by
University of Wisconsin-Milwaukee researchers.   It is a
hydrodynamic model which represents the wind and seiche driven
currents characteristic of the Milwaukee outer harbor.  It was
used to characterize dominant circulation, pollutant
transport, and dispersion of discharges from the Milwaukee
River and the Jones Island wastewater treatment plant into the
Milwaukee Harbor.

PLUME DISPERSION MODEL

A plume dispersion model was used to calculate pollutant
dispersion from both the Jones Island and South Shore

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discharges under a variety of dominant current and nearshore
wind conditions.  The analyses were used to project treated
discharge impacts on nearshore waters, beaches/ and water
intakes with alternative discharge locations  (nearshore and
deep water).

COMBINED SEWER PREDESIGN

Predesign analysis of the combined sewer collector system used
the System Analysis Model for three purposes:

     o    Calculation of storm runoff hydrographs
     o    Routing and calculation of peak design flows
     o    Evaluation of hydraulic interactions between
          combined sewers and interceptors

Milwaukee combined sewers greater than 36 inches in diameter
and numerous diversions in the existing system were included
in the hydraulic routing model  (Figure 2).  The area drained
was divided into subbasins of 1 to 20 acres from which runoff
hydrographs were calculated for the design storm and routed
through the sewer systems tributary to each of the 114 outfall
locations.  Collector sewer models routed the outfall
hydrographs to the proposed dropshafts connecting combined
sewer overflows to the tunnel conveyance/storage system.  The
collector sewer models were used for initial pipe sizing and
hydraulic profile calculations.

SAM was also used in an iterative mode to balance flows from
the combined sewers through the intercepting structures to the
intercepting sewers.  Since the intercepting sewers surcharge
during storms, few intercepting structures have free outfalls.
Flows through the intercepting structures are governed by
hydraulic heads both in the interceptor and in the combined
sewers.  SAM was used to calculate interceptor hydraulic
gradelines under a variety of intercepting structure flow
assumptions.

SAM was chosen for the combined sewer collector predesign even
though SWMM had previously been used in the combined sewer
area for three reasons:

     1.   SWMM had been applied at a large scale, planning
          level.  Considerable detail had to be added to the
          SWMM representation if it was to be used.

     2.   SWMM had no simple means for addressing surcharged
          sewers.  Many of the combined sewers surcharge under
          the design storm and SAM directly addresses the
          surcharge flow.

     3.   The analysis had to be completed in six to eight
          months using eight people from five different firms,

                              10

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       (CALX IN
FIGURE 2
COMBINED  SEWER AND
MIS SYSTEMS  MODELED
CSO • AFP
                                                           11
LEOCND

	COMBINED SEWER
	SIPHON
 |IJ!g MIS BYPASS
   •   DIVERSION
   °m INTERCEPTING STRUCTURE
  lg£_ OUTFALL
  ^_ HUMBOLOT AVE
      DETENTION TANK
   •  PUMP STATION

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          only one of whom had previous computer modeling
          experience.  SAM's data management package
          simplified the user interface.

OPERATIONAL CONTROL ANALYSIS

The operation control analysis involved detailed definition of
system diversion and control facilities for the separate
sewers, combined sewers, and joint use tunnel conveyance/
storage system.  The analysis developed design hydrographs,
system hydraulic profiles, control algorithms, process and
instrumentation diagrams, and preliminary control setpoints.
The operation control analysis utilized four computerized
water resources models:

     o    MACRO storage routing model
     o    Prediction model
     o    TUNNEL control model
     o    Control Analysis Model  (CAM)

MACRO STORAGE ROUTING MODEL

MACRO uses a storage routing concept similar to that used in
the earlier System Wide Analysis to evaluate long-term storage
and routing of both combined sewage and separate sewage.  It
uses hourly flow projections derived from the regression flow
model and routes them through capacity limited conveyance
facilities to the conveyance/storage tunnel.  The model was
used to evaluate storage needs under a variety of control
algorithms.

PREDICTION MODEL

A separate sewer I/I storage prediction model was developed to
enable early identification and reservation of storage volumes
required to prevent separate sewer overflows.  Both separate
sewers and combined sewers respond to  snowmelt and rainfall.
Combined sewers respond rapidly to many events and will
frequently overflow in the absence of  available storage.
Separate sewers respond more slowly to larger events, and
require available storage capacity only during major snowmelt
and/or precipitation.  Milwaukee will  use one storage facility
for both separate and combined sewage  storage.  The dynamics
of sewer response dictate combined sewage could fill storage
before separate sewers begin to require relief.  Consequently,
storage space for separate sewage must be predicted and
reserved prior to a storm event and control must be exercised
to prevent combined sewage from filling that volume reserved
for separate sewage.  The prediction model uses historic
precipitation and snowmelt data and projected 24 hour
precipitation to estimate the storage  volume which must be
reserved for separate sewage.


                              12

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The prediction model and MACRO were used jointly to develop
and test a control strategy which allows combined sewage to
fill only that storage volume not required for separate
sewage, then allows combined sewage spills to the rivers while
reserving the remaining storage volume for separate sewage.
Using a 1.5 safety factor, it is predicted that this control
strategy will result in no separate sewage spills to the river
and about two combined sewage overflows per year.  Without the
prediction model, storage volumes would have to be nearly
doubled to achieve the same levels of protection.

TUNNEL CONTROL MODEL

The TUNNEL control model performs detailed calculations of how
the control strategy for controlling inflows to the storage/
conveyance tunnel will alter the hydrograph entering the
tunnel.  It was used to generate critical hydrographs to be
used for tunnel hydraulic design.

CONTROL ANALYSIS MODEL

The System Analysis Model was specially adapted to accommodate
systemwide solution of the full St. Venant equations to enable
detailed calculation of pipe filling, backwater, and pipe
dewatering for evaluation of inline storage alternatives.  In
addition, control gates, wiers, orifices, and pump stations
were coded which allowed for variation in operation based upon
flows or water levels sensed either near or remote from the
control structure.  The model uses the regression flow model
to calculate separate and combined sewer flows, then routes
the flows through the complex sewer network and controls
indicated in Figure 3.  The model was used to calculate
required control locations, gate and wier sizes and
elevations, initial set points and system operation
strategies.

HYDRAULIC DESIGN

Transient hydraulic pressures anticipated in the tunnel system
have been addressed through the use of:

     o    CAM
     o    SURGE
     o    Transient model
     o    Physical models of dropshafts

CAM

The previously used CAM model was used to evaluate filling
characteristics of the tunnel system — how fast it fills,
which reaches fill first, etc.  Results of these analyses were
used to calculate air relief needs and evaluate transition
hydraulics.

                             13

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FIGURE
MMSD
COLLECTION
SYSTEM

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SURGE

SURGE is a water hammer program which was used to calculate
pressures generated by sudden changes in flow rate in the
surcharged portions of the inline tunnel conveyance/storage
system.   SURGE was also used for water hammer analyses in
pressure lines elsewhere in the Milwaukee Metropolitan Sewer
System.

TRANSIENT MODEL

A transient flow model developed at the University of
Minnesota St. Anthony Falls hydraulic laboratory was utilized
to evaluate the magnitude of transient pressures which might
be expected during the transition from open channel to closed
conduit flow in the conveyance/storage system.

PHYSICAL MODELS

Physical models of proposed vortex dropshafts were developed
and evaluated at the University of Iowa hydraulic laboratory.
These were used to evaluate alternative dropshafts
configurations, establish scale factors, and estimate
dropshaft design dimensions and pressures.

FUTURE MODEL USES

As indicated in the previous section, numerous water resources
models have been required, developed, and used in the planning
and design of the Milwaukee Water Pollution Abatement Program.
The MMSD believes that it will have two types of uses for the
computer models in the future.  The first will be to use three
of the models to assist in the operation and control of the
District's proposed inline storage system.  The second will be
to use the Systems Analysis Model (SAM) for a variety of
applications.  These will include applications of the SAM
model for analyses similar to those previously described and
for data management.  It has not been definitely determined
that all the computer models will actually be used in the
manner described.  However, it is the intent of this paper to
identify the various ways that the models could be used in the
future.   As the Milwaukee Water Pollution Abatement Program
continues to develop, the extent of the continued use of the
models will be determined.

OPERATION AND CONTROL

Three of the computer models have application to the control
and operation of the inline storage system by using the models
in a real time operation mode.  These three models are the
prediction model, CAM, and TUNNEL.
                              15

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The prediction model can be used to aid in the prediction of
separate sewer events that will require the use of storage.
As discussed in the operation control analysis, the prediction
model will use historic and predicted meteorologic data to
determine the volume to be reserved for separate sewage.

Once the storage system is receiving flows from either the
separate or combined sewer areas, the CAM model becomes useful
for evaluating the filling of the system and responding to any
changing conditions.  For example, as the inline storage
system is filling the tunnel volume occupied by wastewater and
the influent flow rates at various points would be known.
Given this information as inputs, the CAM model can be used to
predict the effects on various parts of the tunnel system when
the gates which allow combined or separated sewage into the
system are modulated.

The third model, TUNNEL, becomes useful as the system is
approaching full.  Because gates cannot be closed
instantaneously and because of the need to avoid surcharging
of the tunnel system to avoid the possibility of exfiltration
and resulting groundwater contamination, the system must be
controlled such that it approaches its full capacity
asymptotically.  The TUNNEL model uses the volume of
wastewater in the tunnel and the rate of flow approaching the
gates as inputs to calculate which of the gates should begin
closing first and how fast the gates should be closed to avoid
surcharging of the tunnel system.  TUNNEL algorithms will also
assist in closing combined sewer inflow gates to reserve space
for separate sewage.

SYSTEM ANALYSIS MODEL USES

As noted previously, the other potential future uses of the
computer models developed for the Milwaukee Water Pollution
Abatement Program center around the use of the system analysis
model (SAM).  The multiple uses of SAM stem from its ability
to route a flow hydrograph through a sewer system to determine
its effects on the downstream system.  When some physical
change is made to the system itself or to its service area,
SAM provides a valuable tool for evaluation of the effects so
that any resultant problems can be addressed and solved and
not merely moved to a different location in the system.  The
future uses of the SAM model include:

     o    continuing SSES evaluations
     o    evaluation of future system expansion
     o    analysis of combined sewer rehabilitation
     o    data management

The MMSD has conducted an extensive sewer system evaluation
survey on its tributary sewer systems which resulted in


                             16

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various recommendations for sewer rehabilitation and relief
which are now being implemented.  However, it is recognized
that such efforts will undoubtedly be needed on a continuing
basis, though at a smaller scale.  The SAM model could be used
for continuing evaluation.

Additionally, land use and population changes will continue to
occur in the service area.  Even though the current program
was planned to meet the needs of the planning area to the year
2005, there obviously are no guarantees that growth will occur
at the same time or in the same patterns as predicted.
Accordingly, new or different sized interceptor sewers may be
required even before the year 2005 and almost certainly will
be needed after that year.  The SAM model will be used to
evaluate the effects of such changes on the downstream sewer
system.  Such changes could potentially affect the diversion
structures and operational control strategies for the inline
storage system.

In addition to the uses by the Milwaukee Metropolitan Sewerage
District, the model has application to the continuing combined
sewer rehabilitation effort which has been ongoing within the
City of Milwaukee for many years.  Many parts of the combined
sewer system approach and even exceed 100 years in age and
have been sized using criteria far different from those used
today.  Because of this, the City of Milwaukee has had a long
standing program of replacing portions of its combined sewer
system each year and upgrading the sizes of combined sewers to
meet the present day storm water conveyance criteria.  Since
the combined sewer area is approximately 27 square miles in
size, there is potential in replacing selected sections of
combined sewers to merely relocate a problem to a different
area unless one has the ability to fully analyze the effects
of such a change.  Although such analyses can and have been
done manually, the use of the model provides a faster and more
definitive evaluation.  This in turn permits a more optimally
designed solution to any downstream problems created by the
rehabilitation.

Finally, the model is useful for data management since it can
serve as a library of information on the sewer system.  Such
data as diameter, slope, invert elevations, materials of
construction, and general condition of a sewerline can be
stored in the model's data base.  Despite the fact that the
District has a better than average set of system records, such
data are more accessible and more easily retrievable if they
are in computer files rather than only in plan files.  Past
experience has shown that retrieval of such information from a
plan file can easily take 30 or more minutes of a technician
or engineer's time while such data can be retrieved and
displayed on a cathode ray tube  (CRT) within a minute or two.
                              17

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In summary, we believe that the District's Water Pollution
Abatement Program has used state of the art storm water, water
quality, and hydraulic computer modeling to a greater extent
than probably any such municipal program in the country.
Because much of the modeling .effort conducted was specific to
the Milwaukee Water Pollution Abatement Program, the models
are expected to have continued uses to the District in the
future and, with minor modifications and fine tuning may prove
to be useful for as long as many of the physical facilities
which will be constructed.
                               18

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        USING A TIMEX-SINCLAIR 1000 MICROCOMPUTER FOR REAL-TIME
                  CONTROL OF COMBINED SEWER OVERFLOWS

                                       by
                          Mark Stirrup and William James
                         Computational Hydraulics Group
                               McMaster University
                        Hamilton, Ontario, Canada L8S 4L7
                            Telephone:  (416)257-6944
                                   ABSTRACT
      Large quantities of combined sewage  are diverted to Hamilton's receiving waters
during storm events, significantly degrading the water quality. The pollution  load can
be lessened through more efficient flow control at the mechanized diversion structures
in the city.  The paper describes how a $30  micromputer may be  used as a data  logger
and real-time  controller.   The computer communicates  with on-site raingauges and
flowgauges through a specially developed input/output interface.  Software written  in
BASIC for the microcomputer processes incoming rainfall and predicts runoff  at the
diversion structure one step ahead  in time  using  a  simple discrete  linear  transfer
function time-series model based on past rainfall and runoff.   This rainfall-runoff model
is developed from the output from a calibrated Stormwater Management Model, Version
3.2 (SWMM3),  run in a continuous mode with a  five-minute time-step.   The micro-
computer automatically controls the  diversion structure so as to minimize the volume
of combined sewer overflow,  based  on the forecast  runoff.  Flow forecast can be
improved with  the addition of an on-site flowgauge.  Actual  measurements can be used
to correct any  inaccurate forecasts, thereby  ensuring  that  small  errors do not
accumulate. The microcomputer can handle hardware and software additions, increas-
ing the  level of control.  The computer  can be  used to coordinate the operation  of
several  diversion  structures and gauges and/or nearby storage  tanks simultaneously.
Thus,  city-wide control of diversion structures can be attained by implementing more
complex rainfall-runoff time-series models using data from a network of several gauges
to track a storm across the sewershed.
                                      19

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                                INTRODUCTION
      Many major cities in North Eastern America are at least partly served by com-
bined sewer networks which handle both storm and sanitary flows.  During dry weather,
all sanitary sewage travels to a sewage treatment plant (STP).  During rainfall events,
when stormwater runoff far exceeds the STP capacity, diversion structures in the com-
bined sewer system  divert excess  flow, often directly to the receiving waters.   The
diverted  flow  includes sanitary  wastewater.   The paper discusses  a  methodology to
reduce the impact of these combined sewer overflows (CSO).  In particular, the feasibi-
lity of using a Timex-Sinclair 1000 microcomputer (TS1000) to control CSO diversion
structures in real-time is investigated.
                                                              Hamilton
                                                                    CBD
       Royal  Avenue
           CSO
                                        Figure 1,
                                        20

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       Hamilton's sewer system  presently contains mechanized diversion structures
which  might be controlled in real-time. We have chosen the combined sewer overflow
structure located at  Royal Avenue in West Hamilton (Figure 1).  The contributing area
measures  approximately 20  sq.  km. and  is mainly comprised of single and multiple
family dwellings, and open parkland.
       Inside  the  regulator chamber at Royal Avenue, a motorized gate controls the
entry of sewage into the mainline sanitary sewer which travels across  the city.  The
gate is currently activated  by a float recorder  in the chamber but its operation is
usually remotely  overridden  by  staff at the Hamilton  Wentworth Sewage  Treatment
Plant.

                             SCOPE OF THE STUDY
       Real-time control (RTC) of diversion structures should be designed to:
       (a)   make more efficient use of in-line storage,
       (b)   prevent unnecessary or premature diversion of combined sewage,
       (c)   divert unavoidable overflows to less  sensitive receiving areas using a  RTC
           system including several CSO structures,
       (d)   control  off-line  storage  facilities   to store  CSO until  the  sanitary
           interceptor  can accommodate additional flow.
These strategies all allow more sewage to be treated at the STP.
       Several North American cities have either implemented or recommended  RTC
systems. A computer augmented treatment and disposal (CATAD) system was proposed
by Gibbs and  Alexander  (1969) for the Seattle Metropolitan area.  Morrow and Labadie
(1980)  discussed an automated real-time control  system for the city of San Francisco.
McPherson (1980) investigated the "integral control of combined sewer regulators using
weather radar", using Montreal as the study  area.  Henry  and James (1981)  proposed
microcomputer control of combined sewer overflows in the Hamilton downtown area.
       Until  recently, RTC of hydrologic systems was  effected  by a  large,  expensive
mainframe computer, usually centrally located  with data telemetered from remote
gauging stations.  The stormwater models used were generally relatively complex.  This
scale of RTC system is still typical of river flood forecast warning systems which  work
on a one-hour (or larger) time-step.  The time-step or lead time is  necessarily much
smaller for RTC of CSO, due to the rapid response time of urban catchments. A time-
step of one to five minutes is more suitable.

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                               SYSTEM HARDWARE
       The system we have investigated includes the following components:
       1.    TS1000 microcomputer, manufactured in North America by Timex-Sinclair,
            and costing less than $30 U.S.,
       2.    16K RAMPACK for memory expansion,
       3.    Input/output interface for TS1000, produced in-house,
       4.    Drop counter precipitation sensor, produced in-house,
       5.    Pressure sensitive flow/depth gauge.
       These components  are all suitable  for  on-site  installation  at  the  diversion
structure but in our study have so far only been tested in the laboratory. The TS1000
acts as the controller for the system, processing incoming observed rainfall and runoff
data, and implementing the desired diversion strategy.
       The TS1000 utilizes a Z80  microprocessor and is supplied with Sinclair BASIC in
an 8K ROM. The basic TS1000 is supplied with only 2K  RAM but is expandable to 64K.
Sinclair produces a 16K expansion pack,  but 32K and 64K extensions are available from
many other hardware suppliers.
       The srnaJl keyboard is covered by a plastic membrane. Rapid entry of coding on
this  keyboard is  difficult but this problem is alleviated to some  extent by Sinclair
BASIC, whereby all BASIC keywords are entered by a single keystroke.  The  membrane
keyboard  is better protected from the  damp environment of manholes  than full-size
standard, electro-mechanical keyboards.
       Low-resolution  graphics  (44 x 64) is  included.   Graphics capabilities can  be
improved with hardware or software additions.
       A cassette tape interface is included for easy loading and saving of programs but
the transfer speed is relatively  slow.  Floppy disk interfaces are also available, and
provide faster loads and saves.
       The computer bus is accessible through the exposed  edge connector at the back
of the machine.  This feature makes it easy  to use the TS1000 as a data-logger and
controller.
       We have designed and built our own input/output  interface which simply fits over
the edge  connector.  The interface handles all  incoming rainfall data  and  drives the
relay for the motorized gate in  the diversion structure.  Three four-bit  counters are
cascaded  for each gauge  to log up to 4095 drops in each five-minute time-step.  This
translates to a maximum rainfall intensity of 6.00 in/hr.  The counters are driven by the
drop  counter precipitation sensor (DCPS) developed at McMaster University (Haro,

                                         22

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Kitai and James, 1983).
       Each set of counters is accompanied by a set of tristate buffers.  These buffers
control the input and output of information along the eight data lines.  When enabled, a
set of  Instates allows the data on the corresponding  counters to be retrieved by the
TS1000.  Sets of counters  and buffers are  enabled in sequence by  the computer to
collect the data from each DCPS.
      The data lines are available for output when all the tristate buffers are disabled.
The TS1000 uses the output portion of the interface to control a mechanized gate in the
diversion structure.
      A Timex 2040 thermal printer is used to plot hyetographs and tabulate the data
for recorded storm events.  The printer plugs  onto the exposed  edge connector in the
same way as the I/O interface.
      The  16K RAM  pack, necessary to run our  RTC system software, plugs onto a
similar edge connector provided at the  back of  the printer  or  the I/O  interface,
depending on which is being used.

                       REAL-TIME CONTROL SOFTWARE
      Programs may be written in Sinclair BASIC or 280  machine code.  Our software
was written in Sinclair BASIC for simplicity. Machine  code routines may be preferable
in cases where computational speed is of great importance.
      Our  software has been titled "RTCONTROL".  It  was designed to control the
automatic gate in the diversion structure at  Royal  Avenue in real-time. In order to
effect this control, RTCONTROL must perform several tasks at once.
      RTCONTROL  handles  all hydrological  data  input to the TS1000 through the
specially  designed I/O interface.  Drop counts for each time-step  are brought to the
computer by polling the data lines every  five minutes. The BASIC command  to  input
the data  from the interface is PEEK.  A  POKE outputs information  to  the interface.
PEEK  and  POKE  refer  to  the address  in memory   with  which  the  interface
communicates.  In our case,  this address  is 8192.  As an example, in  order to  retrieve
the data,  the following BASIC instructions are executed:
            100 POKE 8192,1
            110 LET N1=PEEK 8192
            120 POKE 8192,2
            130 LET N2=PEEK 8192
            140 LET N=N1+256*N2

                                       23

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Because the interface uses a twelve-bit counter, and the TS1000  is only an eight-bit
machine, data must be input in  two steps. The first POKE enables the tristate buffers
for the eight least significant bits of the drop count.  These eight bits are then PEEKed
into the TS1000.  This procedure is then repeated for the four most significant bits of
the drop count.   The total number of drops  is then calculated and converted to rain
intensities (in/h.) for each five  minute period. The final POKE clears all the counters
to begin the next time step.
      The  TS1000 does not have a real-time clock built in but there is a facility for
keeping track of elapsed time.  The bytes in memory from  16384 to 16508 are set aside
for specific uses by the system.  They can be PEEKed to query the status  of the system,
and some can be POKEd to control the system. These system variables have names, but
are referred to by their address only.  FRAMES  is a system variable which  counts the
number of frames displayed  on  the  television  monitor.   The  TS1000 works  at  a
frequency of 60 Hz, thus displaying 60 frames per second. Bit 15 of FRAMES is 1.  Bits
0 to 14 are decremented for each frame displayed.  If 65535 is POKEd into FRAMES at
the start of the simulation, it can then be PEEKed frequently to check elapsed  time.
FRAMES will  return  to 65535  approximately every 546 seconds, or 9  minutes.   The
timing routine in RTCONTROL  recycles FRAMES and  runs continuously  until the
program is terminated. The time-step used by RTCONTROL can be varied by the user.
      Drop counts are POKED  into memory  locations which are represented by a REM
statement at the beginning of the program. Each drop count uses two bytes.  The REM
statement begins at location 16509, just above the system variables. Collected data
thus becomes  part of RTCONTROL and can  be  saved with the program.  In order to
save memory only non-zero drop counts and the number of dry  time steps  between  these
are stored.
      After POKEing some data into the REM statement
           5 REM  XXXXXXXXXXXXXXXXXXXXXX
it might appear as:
           5 REM $  =  M + : /  /   0+   E XX  =
      The drop  counts which are POKEd into memory are represented by the printed
character which has the character code equal to the drop  count.  Codes from 0  to 64
are used to store the  rainfall data.  Codes 156 to 186 are used to store  the  number of
timesteps  between  non-zero drop counts. These appear as inverse characters  in the
REM statement.  The  last two characters in the REM statement identify the  location in
memory where the final measured drop count is stored.
                                       24

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      The runoff hydrograph at the diversion structure,  measured and/or forecasted,
can be stored in memory in a similar manner.

                          TRANSFER FUNCTION MODEL
      The computed rainfall intensities form  one input time-series to the rainfall-
runoff forecast  model.   As described  later,  an  observed flow time-series may also be
used as input to the model.
      The rainfall-runoff process is represented by a discrete  linear transfer function
(TF) model of the following form:
where o>(b)    =  u - uil*B - oj2*B2 - ... - wS*Bs
      1*B - <|>2*B2 - ... - $r*Br
      B      =  difference operator
      b      =  lag time between rainfall input and runoff response
      X(t-b)  =  rainfall I(t-b)
      Y(t)    -  runoff Q(t)
      R,S    =  order of the w, 6 terms
      Identification of the  model  follows  the  methods  outlined  in  "Time Series
Analysis:  Forecasting  and Control", by  Box and  Jenkins (1976).   Continuous rainfall
records  at five minute intervals form the input to  the model with corresponding runoff
time-series comprising the output.
      Data  is  analyzed using the  auto- and cross-correlation functions between the
input  and output.  The process is assumed to be  stationary if  the  auto- and cross-
correlation functions of the (X(t), Y(t)) series damp out quickly. The series may need to
be differenced to induce stationarity.
            y(t) = (l-B)d Y(t),  x(t) = (l-B)d X(t)
      The degree of differencing, d is usually  0,  1, or 2.   The orders of the model
(r,s,b,) are identified from the impulse and step response  functions for the process.
      Model residuals  are calculated by substituting least squares estimates for the
w(B) and d(B)  parameters. If the auto- or cross-correlation functions of the residuals
show marked correlation patterns the model is likely inadequate.  These patterns may
suggest  the  type of modification needed to fit an adequate TF model.  An  ARIMA type
noise model  may also be fitted to the residuals.

                                        25

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       For identification  purposes  we chose to use as output the runoff time-series
obtained from SWMM3 RUNOFF simulations using a five minute timestep.
       Much work has  been done on continuous runoff modelling in Hamilton (Robinson
and James, 1981).  Total pollutant loadings to Hamilton  Harbour over the summer
months from 1971 to 1978 were estimated  by  continuous SWMM2 and, more recently,
SWMM3 using a one hour timestep. At  present Robinson and James are  investigating
the introduction of variable time-step continuous  modelling in SWMM3.  Such a model
would  incorporate a five minute step during storm events and a one hour  time-step
during intervening dry periods.
       Our current SWMM3  continuous model has been calibrated on a discrete event
basis due  to insufficient  continuous quantity and quality records.  However, calibration
was completed using a five minute time step as required by RTCONTROL.
       The model  includes the entire west Hamilton area, draining to Cootes Paradise.
Contained within this area is the Royal Avenue  drainage basin.
       The reasons for using  computed rather than observed flows for the runoff time
series are threefold:
1.     Long-term  continuous observed flow records at five minute intervals were not
       available due to occasional equipment malfunctions and breakdowns.
2.     Using computed results reduces the need for field equipment; expensive gauging
       equipment is needed only  for shorter calibration and validation data sets.
3.     The operation of the RTC system may  be checked by simulating the  TF model
       and various diversion strategies  using  continuous SWMM3.   In this way the
       performance of the RTC system can be  evaluated  from both  a quantity and
       quality  standpont.   Important  quality parameters  used  include  PO4,  NIT,
       settleable solids, and BODS.
       Initial identification of a rainfall-runoff TF model for the larger  basin proved
quite successful.   This identification used actual  flows and was done on several of the
more significant discrete events:

                _ 9.55 + 13.43*8 „   ,    .
            Y(t) -   1 - 0.93*B      X(t 4)

or:
            Y(t) = 0.93 *  Y(t-l) + 9.55 * X(t-4) + 13.43 * X(t-5)
       The TF  model was validated for  the  storm  of July 22,  1982 using the  rainfall
record from the  gauge at McMaster University  and the hydrograph  measured at the

                                        26

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Hydro Substation site.  Results are given in figure 2.
                 vi IMJ
                 S>
                 ~ ID:.
                 u.
                 | e:
                   ha.
                   «.
                   70,
                            puvo?r mtwnwj'ro i>i HI wo
                                                 jtf. i ??. isr.
                                              oesERVCfl 	
                                              f ottcnsi	
                                              iFomeo  	
                                              roREOCT
                            3iW      (,109
                               aw* lift (tfts
                                                     17i00
                                   Figure 2.
      The TF forecast model performs  fairly well when compared to recorded  flows.
The timing and magnitude of the peaks are quite accurate. However the receding limbs
of the  hydrograph  are  not adequately  represented.    This  presents  a problem  in
determining the proper time to reopen the gate.  If the flows on the falling limb  of the
inflow hydrograph are overestimated overflow  to the  receiving waters  will likely be
above desirable levels.
      Additional  parameters  were  included  in the  TF  model  but  proved  to  be
insignificant.  The addition of  real-time  flow readings to the  RTC system  can  vastly
improve the TF  model's forecasting capabilities. Real-time flow  measurement can be
substituted for Y(t-l) in the TF model, correcting the previous forecast.  Figure 2 shows
a marked improvement in the  receding  portion  of the  hydrograph.   Predicted  runoff
volumes are much more accurate.

                              DIVERSION STRATEGY
      Based upon the forecast  of runoff at  the diversion  structure  RTCONTROL
effects operation of  the automatic gate controlling the  flow of  combined sewage  to the
local treatment  plant and receiving waters. The exact  level at which the gate is to be
opened and closed is decided using SWMM3  continuous models which incorporate the
rainfall-runoff TF model  and diversion strategies.   Various diversion schemes can be
evaluated in terms of receiving water quality.
      The chosen diversion strategy is programmed into the TS1000 which controls the
                                        27

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gate through the I/O interface.
                               DATA PROCESSING
       RTCONTROL is completely interactive, prompting the user for  input regarding
the TF model and diversion strategy and displaying all hydrological information in real-
time.  Used in  the control  mode the program collects data,  stores  it in the REM
statement, and operates the diversion structure in real-time.
       Used in  the  data  processing mode,  RTCONTROL retrieves the data from the
REM statement and produces listings and hyetographs of the events on the Timex 2040
printer (figure 3).
                            L-5 LC'CH-
                           ••-~ TIME
                                                      I' < H =
                                    HUGU5"
350   0050   (2:150
           TIME
                                                 025Q   0350
                                       Figure 3 .

      The full version  of RTCONTROL currently  logs  approximately three days of
continual rainfall at five minute intervals using a 16 K  RAM pack.  The field version of
RTCONTRO1 requires much less  memory  than the  full  version because  it  is not
interactive nor does it print to the monitor. This allows at least one month of continual
rain to be logged for one gauge.

                                 CONCLUSIONS
      A system  for  controlling combined sewer  overflows  in  real-time  has been
                                       28

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designed and tested using a Timex/Sinclair 1000 microcomputer.   Rain gauges collect
data  in real-time  and  communicate with the  TS1000 through a  specially developed
intput/output interface, all installed on-site at the diversion structure.
       The software which runs the RTC system is written in BASIC.  The program is
named RTCONTROL and accomplishes the following tasks:
1}     counts drops in programmable time intervals using a special sensor,
2)     computes rain intensity from drops counted,
3)     logs rain data,
4)     forecasts flows using a transfer function model to represent the rainfall/runoff
       process,
5)     outputs a signal to drive the relay for a mechanized gate,
6)     plots hyetographs on TS2040 printer and lists data.
       The full,  interactive, version of the program currently logs  about three to four
days of continual data at five minute time steps.  The stripped down  field version of
RTCONTROL allows at least one month of continual rain to be logged for one gauge.
       The system performs well in the lab and we foresee no problems with  its field
installation  in the  near future.  The rainfall-runoff transfer function  forecast  model
provides fairly accurate predictions of runoff one step-ahead in  time.  Its performance
is further improved with the addition of real-time flow measurements to the basic
system configuration.  Recorded flows can be used to correct for inaccurate TF  model
forecasts.
       Ongoing work includes:
1)     modification  of input/output interface  to  include  an analogue  to  digital
       converter to log streamflow data,
2)     use of more sophisticated time-series models to  represent the  rainfall-runoff
       process; including multivariate models  and/or kinematic storm modelling,
3)    development of a variable time-step option for SWMM3 continuous model,
4)    definition of measures of effectiveness for the system  using SWMM3 continuous
       models  incorporating the  rainfall-runoff  transfer function  model and diversion
      strategies.
      The TS1000  microcomputer provides an  efficient means  of  collecting data and
controlling combined sewer overflow structures in  real-time.  This system  is  easily
implemented and very inexpensive.
                                       29

-------
                                  REFERENCES
Box, G.E.P. and Jenkins, G.M. (1976).  Time Series Analysis:  Forecasting and Control.
575 pp.

Gibbs,  C.V. and  Alexander, S.M. (1969).  CATAD System Controls for Regulation of
Combined Sewage Flow. Water and Wastes Engineering, Vol. 6, No. 8, pp. 46-49.

Haro, H., Kitai,  R.  and James,  W. (1982).  Precipitation  Instrumentation Package for
Sampling of Rainfall.  Institute of Electrical and Electronics Engineers (Transactions on
Instrumentation and Measurement). Vol. IM32, No. 3, pp. 423-429.

Henry,  D. and James, W. (1981).   Investigation of  Management Alternatives  for
Combined Sewer Overflows for  the City of  Hamilton.  Proceedings of  the Conference
on Water Quality and Stormwater Management Modelling.  Niagara Falls, Ontario.  U.S.
EPA, p. 493-512.

Robinson, M.A. and James, W. (1981). Continuous SWMM Quality Modelling for the City
of  Hamilton  using Atmospheric  Environment  Service  Data.   Proceedings  of the
Conference on Water Quality and  Stormwater Management  Modelling, Niagara  Falls,
Ontario, U.S.  EPA, pp. 469-492.

McPherson, M.B.  and Ammon,  D.C. (1980).  Integrated  Control of Combined Sewer
Regulators using Weather Radar.   Municipal  Environmental Research  Laboratory.
Office of Research and Development, U.S. EPA, 87 pp.

Morrow,  D.M. and  Labadie,  J.W.  (1980).   Urban Stormwater Control Package  for
Automated Real-Time  Systems.  Proceedings of the  Canadian Hydrology Symposium:
80 - Hydrology of Developed Areas.  NRC of Canada, pp. 28-39.

Vickers, Steven (1982). Timex User Manual - Timex Sinclair 1000. Timex Corporation
and Sinclair Research Limited, 154 pp.
                                      30

-------
                   HYDRAULIC MODELING WITH SWMM IN AN
                      UNSTEADY PRESSURE FLOW REGIME

                      by:  James D.  Parry,  PE  and
                           Thomas P.  Finn, EIT

                               APRIL, 1984
INTRODUCTION:



     The  Nonticello  Drainage  Basin  (MDB)  comprises  approximately  480

acres of  the  City  of  Norfolk,  Virginia.   Located on the Elizabeth River,

a tributary of the Chesapeake Bay (Figure 1), this highly urbanized basin

is  subject  to tidal tailwater  influences in  addition  to  limited  topo-

graphical variations.   In the last  several  years, major  commercial  and

residential  redevelopment has taken place  under  the  direction  of  the

Norfolk  Redevelopment  and Housing  Authority  (NRHA).   As  is  typical  of

many cities,  the urbanization  of the Monticello  area of  Norfolk has led

to a high degree of impervious land cover which, in turn,  has resulted in

a much increased quantity of stormwater runoff.



     Installed prior to  the  redevelopment, the MDB storm sewer system is

presently  incapable  of  accommodating the  increased  runoff  from  storm
 Water Resources Project Manager, CE Maguire, Providence, RI
2
 Civil and Marine Project Engineer, CE Maguire, Providence, RI
                                   31

-------
N
               1 O
               oZ
                            NORFOLK, VIRIGINIA

                               VICINITY MAP


                                       FIGURE 1

-------
events which approximate  a  one-year frequency.   Many parts  of  the  Basin




are subject to  flooding  several  times per year, due  to  the inadequacies




of  the  drainage  network.   Hence,  the  Monticello   Drainage  Study  was




conceived to develop  phased  stormwater system improvements such as  would




handle a more acceptable storm event.








     In the summer of 1983,  the Department of Public  Works of the City of




Norfolk  authorized  CE  Maguire,  Inc.   to study  the MDB and  recommend




improvements  to  the  existing  drainage   system  which  would  alleviate




street-flooding during  the  coincidence of  a two-year storm event  and a




mean high tide  (elevation  102.3  Norfolk City Datum)  as  the  tailwater at




the outfalls.   The  MDB was  addressed in  this  study as  a  high  priority




region,  requiring  major  improvements to  reduce  or  eliminate  flooding,




which  has  been the  cause  of private property damage and  severe traffic




congestion.








     In order to evaluate  the  total urban rainfall-runoff process for an




area  as  large as  the  MDB,  it  was  recognized  that  a  comprehensive




mathematical computer simulation model would  be  required.  The  model must




have been able  to assimilate an accurate  depiction of the typical system




and also provide an  opportunity  to  evaluate alternate  flood  abatement




procedures.  Due  to  the nature  of  the  existing  conduit  network and the




constant tailwater influence,  it  was  imperative  that the model of choice




be capable of simulating parallel pipes, looped  systems  and, perhaps most




importantly,  surcharge within  the  system.   The  Stormwater  Management




Model  (SWMM)   Version  III,   August,  1983  release   was  selected.    The






                                   33

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Extended  Transport Module  (EXTRAN),   considered  to be  one of  the  most




sophisticated  computer  programs  available  in  the  public  domain  for




detailed  hydraulic  analysis  of  storm  water  systems,  permitted  the




flexibility required for this analysis.








THE MONTICELLQ DRAINAGE BASIN (MDB):








     The  480  acre  MDB (Figure 2) drains  generally  to  the south with the




basin  outfall discharging  into  The Hague  on  the eastern  branch  of the




Elizabeth River.   During  periods of high tide, the outfall conduits are




completely submerged and a  large percentage of the available pipe storage




is occupied by  tidal  waters.  The  existing  stormwater  system  in the MDB




consists  of a series  of circular conduits ranging in size from 6" to 66"




in diameter  and box  culverts as  large  as 48" x 72".    This  network is




comprised of  three major  trunk  lines  identified as the Northern, Central




and  Southern  Trunks,  all  three of which  are  confluent at the outfall




system.








     As was stated earlier, much of the basin's land cover is impervious.




Major  commercial  and residential redevelopment has increased  the degree




of imperviousness  to  approximately 40  percent  of  the  entire  MDB  land




area.  The resulting increased quantity of storm runoff, coupled with the




generally low-lying nature  of this coastal drainage basin,  has  made the




antiquated stormwater network obsolete.
                                   34

-------

MONTICELLO DRAINAGE BASIN
                               tco
                                   ewe
                     MONTICELLO DRAINAGE BASIN



                         LOCATION PLAN
                          SCALE = 1 : 20,000  FIGURE 2
                     35

-------
     For  the  analysis of  the  MDB,  the RUNOFF and  EXTRAN  Blocks  of SWMM




were  adopted  as  the  computer program  arrangement necessary  for total




runoff system simulation.   The latter was the transport method of choice




due  to  its ability to  accurately  simulate  backwater,  flow  reversal,




surcharging  and   pressure  flow.   Thus,  overland  flow  derived  from




precipitation was  routed in RUNOFF by non-linear reservoir approximation




using Manning's  equation and the continuity equation.   Inlet flow hydro-




graphs were developed in  RUNOFF and used by  EXTRAN  to simulate closed-




conduit flow via a dynamic  flow routing model.








     Use  of the  RUNOFF block  required the  input of rainfall intensities




versus time for the period of  simulation.   The hyetograph  used in the




model was  a two-year six-hour duration storm event.  Initially, rainfall




intensity  values  were  input  for five-minute intervals (THISTO).  Sub-




sequently,  in an effort  to  "smooth out"  hydrograph peaks, this interval




was  reduced to  one minute    These revisions effectively reduced inlet




hydrograph  peaks by  five to  twenty percent.








     Discretization  of the MDB included  the subdivision of the catchment




into  sixty  (60)  subcatchment areas.  These ranged  in size from three (3)




to  nearly  seventeen (17)  acres.  The  mathematical  abstraction  of the




physical  drainage  system required that each of  the subcatchment areas be




characterized by various parameters such  as slope, percent imperviousness




and width.  "Width"  is a  fairly  subjective approximation  of the distance




which overland flow travels to reach the main conduit  or  channel passing
                                   36

-------
through a  subcatchment.   Table  1 enumerates the range of values assigned

to the above-mentioned parameters.

                                  TABLE 1

                     Variable Subcatchment Parameters

     Parameter                     Low                      High

     Slope (Ft/Ft)                 0.003                    0.02

     Imperviousness (%)                5                      80

     Width (Ft)                      100                    1,600

In addition to  the  above, several parameters were  assumed  constant over

the  entire  sixty-catchment  area.    These  constants  are  presented  in

Table 2.

                                  TABLE 2

                     Constant Subcatchment Parameters

          Parameter                                    Value

          Manning's "N":

               Impervious Area                         0.013

               Pervious Area                           0.27

          Depression Storage (in):

               Impervious Area                         0.30

               Pervious Area                           0.35

          Green-Ampt Infiltration Parameters:

               Capillary Suction (in)                 10.00

               Hydraulic Conductivity of Soil
                    (In/Hr)                            0.1

               Initial Moisture Deficit

                    (Vol. Air/Vol. Voids)              0.32
                                   37

-------
     The conduit  network  was  defined in EXTRAN  as  a  series of links and



nodes.   Inlet  structures  were identified as  nodes  to accommodate inflow



from RUNOFF.   In  addition,  junction and outfall structures were utilized



to define conduit termini.  For each structure, rim and invert elevations



were established.  The rim  (ground) elevation at each structure served as



an  upper  boundary  to  the  hydraulic  gradient,   exceeding  this  limit



resulted in "street flooding".  The EXTRAN model is very sensitive to the



time-step  integration period  (DELT).   If  this  increment  is  too large,



flows  in the  conduit  system  cannot balance  and an  oscillating  network



results.   To  avoid  this  situation, the  time-step must  approximate  the



wave  celerity  in  the system,  and is estimated by the following equation:







 At  =    L         where At  =    time  for  a  surface  wave  to  travel
   c   	              c


       \J gD                        from  one  end  of  a  conduit  to  the



                                   other (seconds)







                           I =     Conduit Length (feet)



                           g = 32.2 (ft./sec2)



                           D  =  Channel depth  or  pipe  diameter (feet)







     For simulation of the MDB, discretization resulted in  the lengths of



modeled  conduit  ranging beuween one hundred  (100) and five hundred (500)



feet.   Early attempts to utilize  a 15 second time-step  (At£  ) produced



erroneous  results.   It  was  necessary to set  the time-step at 10 seconds



in order to accommodate the shortest conduits in the  system.

-------
     The  terminus  of the  schematized  existing system consisted  of  four




(A)  free  outfalls  at  The  Hague.    Tidal  backwater  conditions  were




simulated  assuming  a  constant  stillwater  level  (SWL)  of  102.3  feet




Norfolk City Datum  (NCD),  which  is approximately mean high water (MHW).




This tidal  elevation was  projected  into the conduit  system  by  initial-




izing water depths at junctions which experienced tidal inflow.








APPLICATION OF THE MODEL








     As stated previously,  the  two SWMM blocks utilized  in  this  analysis




were RUNOFF  and  EXTRAN.   The  TRANSPORT block  could  not be  effectively




used due to the significant degree of surcharging in the  existing system.




The overall objectives of this modeling process were as follow:








     1.   To model  the existing  hydrologic  and hydraulic  conditions  in




          the  basin and  to calibrate the  model  with historic  flooding




          information.








     2.   To evaluate alternate flood abatement measures.








     Due  to  the  many  conduits  and branches  in the  system,  the initial




development  of  the  link  and  node pattern  was a critical  aspect of the




overall  process.   Since  the  EXTRAN  improvement  runs  would  consider




looping  and  cross-connecting  the  northern,  central and  southern trunks,




the entire basin had to be modeled simultaneously rather than modularly.




The total  number of links and nodes  in  the system became a very serious







                                   39

-------
concern,  since  EXTRAN limits  the  user to a maximum of  187  conduits and




187 junctions.









     For  the  existing conditions,  the storm  sewer  network was described




with 140  links  and approximately  110 nodes.  This network went through a




very rigorous process of verification and calibration.  As is typical of




computer  simulation,  the  initial  runs  displayed  a  high  degree  of




balancing  instability  and  oscillating  flow  rates.   Typically,  these




problems were solved by reducing the computational time-step (DELT) to 10




seconds and adjusting the lengths  of the shorter links in the system with




the  equivalent  pipe  method.   Both of  the  methods are  discussed in the




User's Manual for  EXTRAN (Roesner et al, 1982) and are clearly presented




and well documented.








     Through  further  review  of  the   output,   a  dramatic  hydraulic




continuity imbalance was discovered in each of the conduits classified as




a  rectangular section.   Due to the large quantity of reinforced concrete




box  sections  in the model, this problem  had  very serious ramifications.




The  continuity  imbalance was  detected in the  output  table  described as




"Summary Statistics for Conduits".   Typical information and data shown on




this table  include the  conduit numbers and  vertical  depth,  the maximum




computed  flow  and velocity,   and the  maximum water  depths  above  the




inverts.  During  a period  of  time when a conduit  is  surcharged,  a very




simple  continuity   check  (i.e., Q = V  x A)  can  be performed  with the




information on  the summary table  and with the known cross-sectional area




of  the  full-flowing  conduit.   The maximum computed flow  was  divided by






                                   40

-------
the cross-sectional area in order to establish an estimate of the maximum




computed  velocity.   For  circular  and  arch  pipes  the  estimates  were




consistently within 5  percent of the expected values  and were generally




within  1  percent.   On  the  other hand, the  velocity estimates  for the




rectangular  sections  were between  10  and  255  percent  greater  than the




maximum computed  velocities  from the program.  Table 3 presents a sample




of the  continuity imbalances encountered.   All of the conduits listed on




the table are in a surcharged condition.  Conduit type number 2 refers to




a rectangular section and type 5 refers to a basket-handle cross-section.
                                  TABLE 3
                 Rectangular Section Continuity Imbalance
(1)
CONDUIT
NUMBER
(2)
CONDUIT
TYPE



H

(3)
SIZE
X W

(FT)
(A)
AREA
(FTZ)
(5)

MAXIMUM
COMPUTED
FLOW (CFS)

13821

13398

13665

13366

13369


2
5
2
5
2
5
2
5
2
5

3
3
3
3
3
3
1
1
3
3

.5
.5
.5
.5
.0
.0
.5
.5
.5
.5

X
X
X
X
X
X
X
X
X
X

5.
5.
5.
5.
4.
4.
5.
5.
5.
5.

0
0
0
0
0
0
0
0
0
0

17.5
17.5
17.5
17.5
12.0
12.0
7.5
7.5
17.5
17.5

156.
68.
89.
73.
36.
29.
125.
69.
128.
80.

9
9
3
8
9
9
1
3
3
7
(6)
MAXIMUM
COMPUTED
VELOCITY
(FPS)
5.1
3.9
4.2
4.2
2.8
2.5
4.7
9.7
4.9
4.6
(7)
VELOCITY
5/4
(FPS)

9.0
3.9
5.1
4.2
3.1
2.5
16.7
9.2
7.3
4.6
     In an  attempt to identify  the  cause of the problem  the  input data




was  scrutinized  but no  errors  were found.  Following  the input review,

-------
all of  the  rectangular sections were  replaced  by basket-handle sections




in an  effort to  rectify the  imbalance  problem.   Results  from the sub-




sequent  EXTRAN  run  show  that the  continuity  imbalance  was  rectified.




Table 3 also shows  the comparative  results  for the  rectangular versus




basket-handle sections  for  selected  conduits.   At  this  point  in time




(April, 1984), it  is  not known if  the problem  with rectangular conduits




lies with the compiled version of  SWMM  used  by the authors, or if it is




universal to the source tape.








     With  the existing  condition  model being debugged  and functioning




properly,  the  process  of  calibration  could  then  begin.   Calibration




involved both the  RUNOFF and EXTRAN blocks simultaneously.  In this way,




the  effects of  the  runoff  calibration  parameters were  observed right




through  the storm drainage network.   This  was  advantageous  since  the




calibration was being geared towards matching areas which are known to be




historically prone to flooding.








     Parameters used  to  calibrate the model are listed below in descend-




ing order of sensitivity:








     a)   Percent  Impervious;  As shown on Figure 3,the sensitivity index




          (SI) for a  change  in percent  impervious ness  is  about 0.8 over




          the range  of  values tested.   Peak  discharge   in RUNOFF was,




          therefore,  found  to be  very  sensitive  to  revisions  in  the




          percent  of impervious area.
                                   42

-------
 1.00
P.80
CO
X
111
Q
  .60-
r .40 -
z
UJ
*
  .20 H
                                 SI=
                                  AQ
                           r^
                  50
                              100
  150
          200%
                      CHANGE IN WIDTH (AW)
                 CHANGE IN IMPERVIOUSNESS
     * "SENSITIVITY INDEX' (SI) IS A MEASUREMENT OF THE RELATIVE
        CHANGE IN PEAK FLOW (*Q) WITH RESPECT TO EITHER THE
        CHANGE IN SUBCATCHMENT "WIDTH" (*W) OR THE CHANGE
        IN "IMPERVIOUSNESS'
                                 „_
                                 ol-
                                    AQ
                                    AW
OR
    AQ
SI=——
    AI
                                         SENSITIVITY INDEX
                                                     FIGURE 3
                             43

-------
     b)   Subcatchment Width:     Figure  3   also   shows   the   relative




          sensitivity of  changes  in the width of the  subcatchment  area.




          The SI  ranged between  0.15  and  0.41 indicating that  the peak




          discharge is moderately sensitive to changes  in width.








     c)   Ground Slope:    Slope  changes created only minor variations  in




          the peak discharge.   Even 10-fold increases -did not result in a




          significant flow rate change.








     d)   Roughness Factor, Depression Storage & Infiltration Rates:  The




          peak  discharge  was  found  to be  insensitive  to each  of  these




          parameters.








     After the  model was  calibrated to assimilate the  physical realities




of  the  basin,   alternate improvements  were  investigated  in  order  to




determine  the  most  cost-effective  solution.   Abatement methods  included




the following options:








          a)   Tide gates at each outfall;




          b)   Tide gates in conjunction with pumping;




          c)   Expanding  the  hydraulic capacity of  the system by adding




               new conduits.








     The  application of  tide  gates   to the model,  along  with various




assumed  initial  water elevations within the  system  was not  as simple as




indicated  in the  User's Manual  (Roesner  et  al,  1982).  For  the  basin







                                    44

-------
being  modeled,  many  of the  150  junctions  had  inverts  below the  tide




level.  Since  at this  point  in time  there  is no way  of simultaneously




initializing  the  starting  water  surface   elevation  at  all  of  the




junctions, the procedure must involve a review of each junction elevation




and adjustment of the initial depths.








     When  the  existing  system  was  expanded  to  include  all  of  the




modifications and improvements  for the 2-year rainfall event,  the limits




of  EXTRAN's  capacity  were nearly  attained.   The  network  included  182




links and 150 nodes  with 187 being the maximum for each.








CONCLUSIONS AND RECOMMENDATIONS








     The SWMM Version  III  model was successfully utilized to  simulate a




large, highly  developed drainage system.   The entire conduit  system  was




modeled with EXTRAN  due to  the  surcharging environment.









     Several shortcomings  in  the  EXTRAN  block,  which  caused  difficulty




from the user's point of view,  are shown below.








     1.   Conduits could  not  be  classified  as   rectangular.   Erroneous




          results occurred  with rectangular sections.








     2.   Starting junction water  depths  could not be  determined by  the




          program  even  if  the  system  were to start  at  a  constant




          elevation.






                                   45

-------
     Recommendations  include  a  review of  the SWMM Version  III,  August

1983  program to  determine if a  problem  exists with rectangular conduit

shapes  in EXTRAN.  As the  SWMM program is updated, it would be desirable

to  include  the  capability of  determining  starting depths  at junctions

when  a  constant  elevation  is desired.  When  a constant elevation is not

appropriate,  the  program  could  then default  to the present method or

vice-versa.
                           LIST OF REFERENCES
Aldrich,   J.A. ,   and  Roesner,   L.A.   (1982),   "An  Improved  Surcharge
Computation   in   EXTRAN",  Proceedings of Stormwater and Water Quality
Management Modeling Users  Group Meeting,  Washington,  B.C.,   March,  1983
(EPA-600/9-81-015, August,  1982).

CE   Maguire,   Inc.    (1984),   Monticello Storm Drainage Improvements:
Computer Analysis and Draj-naje Study  (Preliminary Draft), Virginia Beach,
Virginia.

Huber,   Wayne  C.  (1983),  "The   EPA   Storm  Water  Management  Model:
Documentation    and    Maintenance11,    Proceedings of the Conference on
Frontiers in Hydraulic Engineering,   Cambridge,   Massachusetts,  August,
1983.

Huber, Wayne C.; Heaney, James P.; Nix, Stephan J.; Dickinson, Robert E.;
and   Polmann,  Donald   J.   Storm Water Management Model User's Manual-
Version III, Gainesville, Florida, Fifth Printing:  January, 1983.

Parker,  W.M.,  III  (1980),  "The  Use  of  SWMM  to  Economically  Model
Surcharged  Combined  Sewer  Systems",  Proceedings Stormwater Management
Model Users Group Meeting,   Gainesville,   Florida,   January,   1980  (EPA
600/9-80-017, March, 1980).

Roesner,  Larry   A.,   Shubinski,   Robert   P.,   and   Aldrich,   John  A.
Stormwater Management Model User's Manual Version III;  Addendum I EXTRAN,
Annandale, Virginia, Fourth Printing:  October, 1982.
                                   46

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                     A Lake Acidification Model  Using WASP

                                 Wu-Seng  Lung
                        Department of Civil  Engineering
                            University of Virginia
                          Charlottesville, VA 22901
Introduction
     The purpose  of  this modeling  study  is to  develop  a lake  acidification
model which is capable of predicting  pH and alkalinity levels in a lake  on a
seasonal basis.   In  general,  two different  modeling  approaches can be  found
among  existing  models.  Simplified,  empirical  methods  or models  have  been
developed  using  historical  lake chemistry data  from lakes  receiving  acid
inputs.  These  simplified  models are based  on the  equilibrium of  chemical
constituents in the lake  water.   They  are  often used  to identify lake  acidifi-
cation and  to estimate the degree  of acidification.  The  models or  methods
fall into this category include  the  excess sulfate  method  (16),  pre-acidifica-
tion alkalinity method (17),  alkalinity vs. calcium and magnesium plot  (22),
pH vs. calcium model  (16),  and  calcium and magnesium vs. sulfate model  (17).
These simplified models or plots, while interesting in describing the  general
trends  in  lakes,  are  too  crude to  permit a quantitative  analysis  of  the
effects of acid input on  lake  water  quality in terms  of pH and alkalinity.  As
a  result,  their  predictive  capability is highly  limited  because  inferring
acidification or  the  reverse  of acidification are not accounted  for in the
models.

     Another approach utilizes a more  complicated representation of  the entire
watershed  system  and  lake basin than the  simplified modeling  approach.   It
incorporates  interactions  between  the watershed  and  lake water.   Such  an
approach  requires a  significant  amount  of  data to  characterize  numerous
watershed hydrology and neutralization factors as  well as physical,  chemical,
and biological processes  in the .lake.   This approach,  with sufficient data, is
designed to quantify a cause-and-effect relationship  between  the acid deposi- .
tion rate  and the lake's response  in terms of explicit calculations  of  alka-
linity,  pH,  and major cations  and anions in  the lake water.   This is the
approach adopted in this  study to develop  a lake acidification model.

Proposed Model and Major Mechanisms

     While  many  integrated watershed-lake acidification  models address the
terrestrial  and  aquatic systems,  the model  developed focuses  on the  water
column  in  a  lake  or  impoundment.   Such  a simplification is not intended to
discount the  importance  of  the  land system.  Instead, input  from the  land or
watershed is  incorporated as input data for the lake acidification model.


                                      47

-------
     Model Variables — The primary acidification indicators addressed in this
model  are  alkalinity  and  carbon dioxide  acidity.   Understanding  the  carbon
dioxide-bicarbonate-carbonate equilibria  in natural water systems  (30)  indi-
cates  that  alkalinity,  carbon  dioxide  acidity, and  pH are  the  three  most
important water  quality indicators in  the lake acidification  process.   Usu-
ally,  the pH  of a natural water  system  can be determined once alkalinity and
carbon dioxide acidity  levels are known.   Thus,  alkalinity, C02 acidity and pH
are  considered the primary water  quality variables  in the model.

     Lake Hydrology and Transport — Lake  conditions vary seasonally during an
annual cycle.   One  of the important seasonal phenomena is temperature strati-
fication.  For example, during  the  summer  months, limited exchange  of mass and
heat energy occurs  in the vertical direction because of stratification.  As a
result,  significant  concentration gradients   (alkalinity,  for  example)  may
result.  The degree of  vertical resolution needed to address the  concentration
gradients is primarily determined by  the extent of data available  to quantify
the  vertical exchange  of mass.  A two-layer resolution is adopted in the model
to  approximate  the  vertical concentration  gradient  in  the water column.  The
surface  layer  is referred  to   as the  epilimnion and the bottom  layer  as the
hypolimnion  of  the  lake.   In  addition  to internal  transport,  interactions
between  the lake and  its watershed are also included.  For example, tributary
flows  to the lake  and lake outflows  via outlets  are  included.   The general
quantification  of the mass  flux associated with these flows is in  the form of
mass loading  rate which equals the product of  concentration  and flow  in the
tributary.  Ground water flow into  the hypolimnion  is also incorporated.

     Air-Water  Interface  Exchange —  Carbon-dioxide can be transported across
the  air-water  interface  and therefore  affects  the pH  levels  in the water
column.  The  direction of this transport  depends  upon whether the epilimnion
of  the lake  is undersaturated  or oversaturated with respect  to C02.   Thus, a
gain or  loss of  C02 due to this process  is quantified as a gain or  loss of C02
acidity  in the  epilimnion.   A  similar mechanism for alkalinity does not exist
at  the air-water interface.  Thus,  alkalinity,  as defined in standard chemical
terms,  does  not  change in value with a  gain  or  loss of  dissolved  COZ-   In
other words, C02 variations do  not  alter  the charge balance of  the  system that
is,  in turn, reflected  in the alkalinity value.

     Biochemically Mediated Processes  — The carbonate system is not the only
buffering  system operative  in  lakes  or  impoundments  against acidification.
For  example, photosynthesis  can be looked  upon as  a net consumer of hydrogen
ions.  Hypolinmetic sulfate reduction  during   period of  anoxia will increase
the  buffering capacity by  decreasing  the total  charge on nonprotolytic anions
(i.e.SOit).  On  the other hand,  the  nitrification reaction, in which ammonia is
oxidized  to  nitrate,  decreases alkalinity  (i.e.  H is produced).  Weber  and
Stumm  (31)  summarized a number of  biochemically mediated processes affecting
the  pH and alkalinity  levels  in natural  waters (see Table 1).   The net result
of  these processes may be significant  in neutralizing acidic  input  to some
lakes.   Schindler (25)  reported that in Lake 223 of Experimental Acidification
in  Canada,  over 60% of  the  acid  neutralization was  accounted for by sulfate
reduction  and  denitrification.  Thus,  it  is  important  to  incorporate  the
buffering mechanism .offered by some  of  the  biologically  mediated processes
into the modeling framework.

                                      48

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           Table  1.  Biologically Mediated Processes  (affecting pH
                           and Alkalinity) in Lakes
Processes
   (1)
                            Reaction
                               (2)
                                                             Effect on
                                                        pH        Alkalinity
                                                        (3)         (4)
  In Epilimnion:
    Photosynthesis     6 C02 + 6 FLO •»• C6H12°6 + 6°2 increase   no change


    Nitrification      NH, + 20. •*• N0~ + H20 + 2H    decrease    decrease
                                 2-    +
Sulfide Oxidation  HS  + 202 * SO,  + H
                                                     decrease    decrease
  In Hypolimnion:
Respiration
                                                     decrease   no change
Denitrification    5 C,H._0, + 2ANO~ + 24H
                      D 1 f. 0       J
                     30 C02
                                         42
                                                     increase    increase
                                 2-     +
Sulfate Reduction  C,H100, + 3 SO,   + 3H  ->
                    o Iz b       q

                     6 C02 + 3 HS~  + 6 H00
                                                     increase    increase
     Model Structure  — Based  on  the description  of the major  model mecha-
nisms,  the  lake  acidification  model  developed  is  schematically  shown  in
Fig. 1.  Mathematical  formulation of  the model  processes and  mechanisms  is
described in next section.

Model Formulation

      C02  Exchange Across  Air-Water Interface  — The  formulation of  C02  ex-
change at  the  air-water interface  is,
    C02 Mass Rate  =
                                       -  [C02]g)  A
                                                                            (1)
                                      49

-------
I
1
Nitrification
(Negative Alkalinity)

Alkalinity
Sulfide Oxidation
L
ll
" ~ g.
>s
\
Denitrification

\
\
1

Alkalinity
Sulfate Reduction
t
g
n 2
a o
fsss//tig??^/W/£$s$w/S% <-> £
.2
•= . vy/osnN27 n °
y a> .2
2 o o
OL
r
L
AIR
Photosynthesis
EPIUMNION
HYPOLIMNION
Respiration

SEDIMENT
GOVERNING EQUATIONS.
           at
3 [C02 Acy]

    3t
                            A   3y
                                            [C02 Acy]
                                   Physical Transport
pH - ALKAUNITY - CO2 ACIDITY EQUIUBRIA:
                         [C02AcyJ
                           Alk  +
and
        SCT  "  SAlk
      Biological, Chemical &
      Physical Processes
                              if Alk  < 0
Figure 1     Kinetics and  Equilibria of lake  Acidification Model
                                   50

-------
where 1C is  the  C02  transfer  coefficient across the lake surface, [C02, x] is
the saturation concentration of dissolved C02 in natural waters,  [C02]  Is the
average concentration of dissolved but  unionized  C02 in the epilimnion, and A
is  the  air-water interface  area.   In  Eq. 1,  [C02]   can be  replaced  by
[C02 Acy] , the concentration of C02 acidity in the epilimnion without signif-
icant error (9,26).  However, a more accurate approximation can be achieved by
replacing [C02]  by [C02 Acy]  less [H ] for the pH range normally encountered
in acidified waters.

     In lakes  and impoundment where water  movement and  turbulence  are rela-
tively small compared to those encountered  in  streams  and rivers, wind action
is  the  predominant factor  in  determining  the  rate of transfer  of  dissolved
oxygen or carbon  dioxide.   Experimental  investigations and  analytical studies
of this phenomenon can be found in various studies (12,19,33).  In this study,
the empirical  formulae for  dissolved oxygen transfer coefficient developed by
Banks and Herrera (3) is adopted:

               1^  =  0.728W*5  -  0.317W  +  0.0371W2                      (2)

in which VL   =  dissolved oxygen transfer coefficient in m/day at 20°C
         W   =  windspeed over the lake surface in m/sec

The C02 transfer  coefficient  is  derived from the following  equation based on
the molecular weights of C02 and 02 (28):

                          a)  (44/32)" j   =  O.SlKOa)                   (3)
The temperature correction for the transfer coefficient is expressed as
                                     T— ?n
               1^ (T)  =  KL (20°C) 9   U                                  (4)

in which T  is  temperature in °C and  6  is an empirical constant  ranging from
1.005 to. 1.030 with 6 =  1.024 being commonly used (19).

     The  C02  saturation  concentration,  [C02, .]  is  determined  from  the
following equation (21):                       (s)

          rrn    ,  _    [2385. 73/T - 17,5184  + 0.0151641T]               ,_.
              (s)   ~                                                      ^ '

in which [C02, .] is in mole/1 at temperature T (in K) .

     Vertical Diffusion -  Fluxes  of alkalinity  and C02  acidity  across  the
epilimnion-hypolimnion interface due  to  turbulent diffusion and concentration
gradients between the two layers are  characterized as:
                                            1    -   I  U A
     Vertical Diffusion Mass Rate  =         e _ h                  ,,,
                                      - (Le  +   V/2
                                      51

-------
in which E  =  vertical diffusion coefficient
     [  ]   =  concentration of alkalinity or C02 acidity in the epilimnion
     [  ]^  =  concentration of alkalinity or C02 acidity in the hypollmnion
      L     =  average thickness of the epilimnion
      L^    = average thickness of the hypolimnion

The vertical diffusion coefficient is calculated by the flux-gradient method
(23) using temperature gradient  in  the  vertical direction on a time variable
basis.
     Reaction  Kinetics —  Most  of  the  biologically  mediated  processes  in
Table 1 depend on  the  kinetics  of their reactions.   At present, knowledge of
the  reaction  kinetics is  not complete,  although  their  chemical equilibrium
may be understood.   For  example,  reduction of sulfate by microbial processes
produces  alkalinity  (31).  One  equivalent of  HCC>3  being produced  for each
equivalent of SOi* reduced according to  the following equation:
  5380^   -»•  106  HC03  +   53H2S  +   16 NH3
                                                                          (7)
This process may  occur  in anaerobic hypolimnetic waters, interstitial waters
and  in  anaerobic  conditions that  occur  in winter under  ice  cover.   At what
rate,  the  reaction in  Eq.  7  can  proceed in  a lake requires  a significant
amount of data to quantify.  For most lake, data of this nature do not exist.
Therefore, it is  extremely  difficult  to  include these processes in the model
on  an  individual basis.   A more  simplified  approach  to  characterize these
processes  is required.   Thus, in the  modeling  framework developed,  these
biologically mediated processes are  being grouped collectively  in  terms of
sources and sinks for alkalinity and  C02 acidity in the epiliranion and hypo-
llmnion.   For  example,  in  the   epilimnion,   photosynthesis  decreases  C02
acidity (but causes no  change  in alkalinity) and is considered as a sink for
C02  acidity.   On  the other hand,  respiration which generates  C02 in   the
hypolimnion  is  considered a source for  C02  acidity.    As  a  first approxima-
tion,  photosynthesis   is  considered  in  the  epilimnion  and  not  in  the
hypolimnion.  Likewise, respiration is introduced  in  the hypolimnion and not
in the epilimnion in  the present modeling  framework.  Similarly, the sink for
alkalinity in  the epilimnion  is characterized  collectively  by nitrification
and sulflde oxidation.  These  two  oxidation processes do not cause any change
in  C02  acidity  (see  Table  1)  and therefore  not included  in the  sinks or
sources for  C02 acidity  in  the epilimnion.   In  the  hypolimnion, denitrlfi-
cation and sulfate  reduction are grouped together to characterize the source
for  alkalinity.   Based on  the above discussion,  the  following conceptual
expressions  are used in  the  modeling  framework  to  quantify  the  reaction
kinetics in the lake:
Nitrification and  sulfide  oxidation  in  the  epilimnion
     Decrease of     Kinetic             Alkalinity  in
     alkalinity    =  coefficient  (ji  ) * epilimnion
      (mass/time)
(/time)
(mass/volume)
   Epilimnetic
*    volume

    (volume)
                                     52

-------
Photosynthesis  in the epilimnion
     Reduction  of    Kinetic               C02 acidity
     C02 acidity  =  coefficient  (u2) *   ^n epilimnion
                                                                   Epilimnetic
                                                                *     volume
Denitrif ication and sulfate reduction in  the hypolimnion
      Increase  of     Kinetic                Alkalinity         Hypolimnetic
      alkalinity   =  coefficient  (y3> *    in hypolimnion  *     volume
Respiration in  the hypolimnion
     Increase of      Kinetic
     C02  acidity   =  coefficient
                                          *    C02 acidity     *   Hypolimnetic
                                               in hypolimnion       volume
The above empirical approach which approximates  the reaction kinetics using a
first-order  kinetics  has   been  reported  in  lake  eutrophication  modeling
studies (23,29).   The  kinetic  coefficients uj  to y^  defined in this formula-
tion will be estimated  in the next section.

     Model Equations - The  governing  equations in  the modeling framework  are
presented as follows:
         a.  Total alkalinity In the epilimnion

                           ([Alk]2 -  (Alk),)   -  Ml[Alk],V, *

                        >
                      eddy diffusion      reaction     loading
                          Q,^ (a (Alk),  +  B[Alk]2)

             outflow            vertical advection
                    -QoutfAlk]i
                                                                   (8)
v>
  b.   CO 2 acidity  in Che epilimnion


d[C02Acyh  = €Ai>Z ([co2Acy]2 - [C02Acyh)
  dt        I., 2
              i
                   eddy diffusion
                                                K A <{C02
                                                L
                                                           - (C02ACy)1 + |H
         reaction        loading    outflow

         c.   Total Alkalinity in  the hypolimnion
                                                C02 exchange of air-water exchange

                                              i2(
-------
The notations  in  Eqs.  8  to  10  are  listed  in Appendix  II.

     The  developed working equations compute  the  alkalinity and C02' acidity
concentrations in the  epilimnion and  hypolimnion on a time-variable basis.  In
these  calculations, alkalinity  and  C02  acidity  can be either  negative or
positive,  depending  on  the   relative  concentrations of  the  various  ions.
Negative values of alkalinity  are  numerically  equivalent to  "mineral acidity"
in standard  chemical definitions.

     Once  the  alkalinity and C02 acidity  levels in each layer are calculated,
the  hydrogen  ion  concentration  is  then  determined   from  the  C02/HCO~/CO^~
equilibria in  the following fashion:                                   3   3
      +     K,  ([C02Acy] - K2- K  /K^
 1.   [H ] =  	[Alk]  + K	   if  [Alk] > 2 x  10~5 mole/1



 2.   [H+] =  3.2  x  10~5 - [Alk]           if  -2 x  10~5 <  [Alk] < 2 x 10~5 mole/1


 3.   [H*] =  -  [Alk]                      if  [Alk] < - 2  x 10~5 mole/1

 where [H ]      - hydrogen ion concentration in mole/1

      [Alk]     = total alkalinity  concentration in mole/1

      [C02  Acy] = COz acidity concentration in mole/1

      K-        = first dissociation constant of carbonate equilibrium
                     (temperature  dependent)

      K-        = second dissociation constant of carbonate equilibrium
                     (temperature  dependent)

      K         = dissociation constant of water (temperature dependent)



Use of the WASP to Implement Proposed Modeling Framework

     In many  of the  water  quality modeling programs currently available, the
basic variables and  interactions  are specified, and  it is generally not easy
 to change the number of variables, or more importantly, the complexity of the
interactions.  As a  result, effort  has  also  been  expended to select computer
software packages that are more general,  open-ended,   and  depend on  user
specified  interactions  for specific  problems.  The  most suitable  computer
program for this  study  is the Water Quality Analysis Simulation Program (WASP)
originally  developed by Hydroscience,  Inc. and recently  documented  for U.S.
EPA (10).
                                     54

-------
     Designed to  serve  as a  general  purpose code, WASP  is very  general in
nature.   The program is  flexible  enough to  provide the  modeler with  the
freedom to describe the kinetic processes and  the  inputs  to these processes,
as well as the  transport  processes  and  the  geophysical morphology or setting
that go into the framework of the model.  The kinetic  and/or transport struc-
tures are not "hard wired" in WASP (i.e., the equations are not fixed and thus
imbedded in  the code).  While the lake  hydrological transport  processes such
as inflow, outflow, advective and diffusion flows can  be readily incorporated
into WASP, a kinetic subroutine is  required  to  implement  the source and sink
terms of alkalinity and  C02 acidity  in the model.

Model Application

     The  developed  Lake Acidification  Model (LAM) has been  applied  to  the
Bickford  Reservoir in  central  Massachusetts  to  test  the validity   of  the
general modeling framework.  A limited  amount  of data collected from July to
December 1981 (13) was used in deriving the model coefficients.

     Bickford Reservoir —  The  Bickford  Reservoir  (Fig.  2),   located  in  the
towns  of  Hubbardston and Princeton,  was  formed by  expanding  the  original
Bickford Pond following  the construction of a dam and  auxiliary dike.   Hydro-
logically, the Bickford  watershed includes an upstream reservoir, Mare Meadow
Reservoir, and its drainage area.  However,  the Bickford Reservoir serves as a
backup for  the  Mare Meadow  Reservoir which  overflows through  an  emergency
spillway into the Bickford only  a few times a year.   In addition to the Mare
Meadow spillway, two other streams  drain the watershed.   One  of  them  is  the
West Wachusetts Brook which contributes over 50% of the inflow  to the Bickford
Reservoir on an annual basis.

     Hydrology and Mass Transport —  The first  step  in model  application to
the Bickford Reservoir is  to determine the lake hydrology  and mass transport.
That is,  the modeling analysis requires  the input of various time-variable
inflows,  outflows,  and  exchange  flows between  the  two  layers.  Thus,  the
monthly average  flows  in  the West  Wachusetts Brook,  Mare  Meadows  Reservoir
outflow (only once in July 1981),  an unnamed brook, ground water inflow to the
hypolimnion,  and reservoir outflow at the Bickford spillway were incorporated
into the  model  (Fig.  3).   Direct precipitation and  evaporation,  although a
minor portion of  the  total flow,  were also  included  in the hydraulic budget
but are not  shown in Fig.  3.  The seasonally  variable flows  reached their
minimum levels during the  months of  August and September,  and  rose sharply in
October 1981.

     Mass transport between  the epilimnion  and hypolimnion in the Bickford
Reservoir was characterized by the advective flow from the hypolimnion to the
epilimnion as well  as by  the diffusion flow.  Figure 3b  shows the advective
flow and vertical diffusion  coefficient.  The vertical diffusion coefficient
which is calculated using  temperature data ranges from below 1  cm2/sec during
the summer stratification  months to  9.5 cm2/sec in November and December.
                                      55

-------
                                    BicWord
                                    Re»»rvoir
                                    MA
figure 2    Bickford Reservoir and Watershed

                      56

-------
                               Mare Meadow

                                  Outflow

                                  1.83cfs
                                                                      m

                                                                      _o


                                                                      o
                                                                               10
=•   8


I


E   6
•


V)
c

•   4
;o

_o

O
         Mare Meadow

         O Spillway
                                Ground Waier
                            West Washusett Brook
                                                                                                           Unnamed Brook
                                                                                     I    I   I    i   I   i
171
                  —  10
                  •
                  x
                 CM

                  o
                II
                SI
                O ft

                If
                Is
                !§
                Q-I
                c E
                • tu
                > c
                  m
                                                                               10
ffi
c
                Legend:

               — Calculated (in Epilimnion)
                                                                                     ^^^ Calculated (in Hypolimnion)

                                                                                        o    Observed (Depth-Avg)
                                                                                     I	I
                                                                                                                 N
                                  Figure 3     Hydrologic Characteristics of  the Bickford  Reservoir,

                                                Massachusetts, 1981

-------
     The above  independent  derivation  of  the  hydraulic budget and mass trans-
port  can  be confirmed by  applying the derived values  to model the chloride
concentration  (a  conservative  substance  usually  used  as  a tracer)  in the
impoundment.   As such, the  chloride  concentrations in the reservoir inflows
were  also  incorporated  into the  model  (Fig.  3c).   As  shown,  the chloride
concentrations  in these inflows were  relatively  constant and  low during the
study  period,  with the highest  level  in the ground water  at  4.2 mg/1.   The
calculated  chloride concentrations  are shown  in  Fig.  3d.  Also  shown, for
comparison  purpose, in  Figure  3d  are the measured  chloride  concentrations
(depth averaged) in the Bickford  Reservoir.   The  results  indicate that the
chloride  level  in  the  reservoir is  relatively constant at 3-4  mg/1.   This
relatively  low chloride level is  associated  with limited influence by man's
activities.   Being located  in  an  isolated  area, the  reservoir  has limited
access, which  appears to be  the  logical explanation of low chloride levels.
The  calculated values show that the  chloride  level  is very  uniform  in the
lake,  such  that the  concentrations  in  the  epilimnion and hypolimnion are
almost identical.   The  reason for  such a steady chloride level is due to the
steady concentration of chloride  in the  reservoir inflows.   Also  note that
the  calculated  chloride  level in  the epilimnion  is  close to  the chloride
concentration  in the West  Wachusetts  Brook which  is  the predominant inflow
(see Fig. 3a)  to the epilimnion.

     Seasonal Variations of Alkalinity and pH in  the Bickford Reservoir — In
addition  to  the hydraulic  budget and transport  pattern  for  the Bickford
Reservoir,  direct  precipitation  in terms  of alkalinity  (negative)  and C02
acidity concentrations in  the tributary flows and ground water flows were also
incorporated  to analyze the  seasonal  variations  in alkalinity and  pH in the
epilimnion  and  hypolimnion.   These  input  data  were   derived  from  field
measurements  (13)  and are  summarized in Table 2.

     The  model  application  also required  assigning  values to  four kinetic
coefficients  p.,  ju,  y_,  and  u,   which characterized  the  generation  and
consumption of  alkalinity  and C02  acidity in the epilimnion and hypolimnion,
respectively.   Under this  situation, the  best means to determine their values
was by model calibration.   Due to  the  significant uncertainty associated with
these  kinetic coefficients, a number of model runs were  conducted to match the
calculated  alkalinity  levels  with  the measured  alkalinity levels in both the
epilimnion  and  hypolimnion, while  the previously determined hydraulic budget
and transport pattern were  held constant  throughout *:he calibration.

     The modeling results   are shown  in Fig.  4 and  the kinetic coefficients
calibrated  are  presented  in Table  3.   Examination  of Fig.  4  and Table  3
suggests that  the calibrated kinetic  coefficients  produce  the results which
reasonably match the measured alkalinity  levels in terms of the magnitude and
seasonal trend  of alkalinity  levels.   Also shown in Fig. 4 is  the comparison
between the calculated and measured pH  levels in the Bickford Reservoir.   The
pH values measured  in the Bickford spillway (outlet of the Reservoir) are used
for  comparison   since  they approximate  the  pH in  the epilimnion  under the
completely .mixed assumption for  the surface layer.   No data on the pH in the
hypolimnion are  available and, therefore, only the calculated pH values in the
hypolimnion are  shown in Fig. 4.
                                      58

-------
       Table 2.  Model Input for Alkalinity and C02 Acidity Analysis
                        of Bickford Reservoir, 1981
      Input Variables          July   Aug.   Sept.   Oct.    Nov.    Dec.
Direct Disposition (Ib/day)
  Alkalinity as CaCO          -24.04  -6.45 -19.74  -24.83  -13.10  -24.83

Watershed Contribution of
  Alkalinity (Ib/day as
  CaCO )                       21.94   5.84   8.45   14.88  -21.66  -15.86

Temperature (°C)

  Epilimnion                   24.0   23.2   19.0    11.6     8.0     6.0
  Hypolimnion                  15.0   17.5   15.5    11.5     8.0     6.0

Windspeed (m/sec)               6.0    6.0    7.0    10.2    10.2     8.0
          Table 3.  Seasonal Variable Biological Kinetic Coefficients
                         for Bickford Reservoir, 1981
Kinetic Coefficient (day  )    July   Aug.   Sept.   Oct.    Nov.    Dec.
Alkalinity Consumption in
  Epilimnion, j^               -0.05  -0.24  -0.88   -0.42   -0.28   -0.25

C02 Acidity Consumption in
  Epilimnion, u2               -0.10  -0.15  -0.05   -0.03   -0.05   -0.05

Alkalinity Generation in
  Hypolimnion, u3               0.13   0.38   1.18    1.00    0.25    0.15

C02 Acidity Generation in
  Epilimnion, u                 0.22   0.42   0.72    0.50    0.10    0.05
                                    59

-------
en
o
I
                 80
                 60
                 40
                 20
                •20
                     Epllimnlon
   Legend:
 o   Observed
—  Calculated   —
                       I    I   I    I   I    I   I   I    I   I    I
                                                   3   =•

                                                       I
                                                       m
                                                                   4
                                                   -1
             I
                 80
                 60
                 40
                 20
                -20
                      Hypolimnlon
                                    Legend:
                                 O   Observed
                                 —  Calculated
                                               J    I   i   J
                                                   3  s
                                                       a

                                                       n
                                                   2  °
                                                       •
                                                      O
                                                       S

                                                   1  I
                                                                      Epitimnton
                                     Hypolimnlon
                                                                                                           o Monthly Avg.
                                                                              i    I   I   I    I   I
                                                                                                                N
                                                                                  1   J    I   I   I    I   1    1
                                                   N
                                  Figure 4     Alkalinity and pH  in the Bickford  Reservoir,
                                                Massachusetts, 1981

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     C02  acidity  (or  inorganic carbon)  was  not  measured  in  the  Bickford
Reservoir  (13).   Thus,  no attempt was  made to  check the model  results  for
calculated C02 acidity.  However, since pH is dependent on lake alkalinity and
C02 acidity  in natural waters,  favorable comparison between  calculated  and
measured  pH  levels (Fig. 4)  has provided  some  degree of confidence  in  C02
acidity calculations for the Bickford Reservoir.   In addition, the calculated
C02 acidity levels are all within the reasonable ranges which are reported in
the literature.

Discussions of Results

     The results in Fig. 4 also provide a good understanding of the alkalinity
in the Bickford  Reservoir.  Beginning in  July  1981,  alkalinity levels in the
epilimnion and the hypolimnion were relatively equal.  As the summer stratifi-
cation progressed  through August and September, alkalinity  concentration in
the hypolimnion increased sharply due to biologically mediated reactions (see
Fig. 4 and \i  in Table 3).   Eshleman (13)  reported significant denitrification
in the Bickford Reservoir.   At the same time, alkalinity concentrations in the
epilimnion remained stable and were much lower than those in the hypolimnion.
That  is  because  stratification is  limited supply  of  alkalinity from  the
hypolimnion to  the epilimnion.   As the lake stratification  became less pro-
nounced in October, possibly  due  to wind-induced mixing in  the reservoir,
alkalinity levels  in the epilimnion  increased  slightly  and alkalinity levels
in  the  hypolimnion decreased.   As stream  flows increased  (see Fig.  3)  to
further dilute  the alkalinity levels in the reservoir,  alkalinity levels in
the epilimnion and hypolimnion became more  uniform and  reduced to much lower
values.

     Examination of  the kinetic coefficients  in Table 3  indicates  that  the
maximum values  of  u. ,  pu,  and  v,  occurred  in September when  the biological
activities were most significant during the  year.  However, there is no clear
trend in the temporal behavior of vu from this modeling calibration exercise.
In addition, the magnitudes of u_  are small, much smaller than  those of  p1,
U-, and u,,  It appears that the E02 consumption rate (possibly due to photo-
synthesis; in  the  eplimnion was low (i.e.,  very insignificant algal produc-
tion).  Thus, the \i  values shown in Table 3 are nothing more than the system
fluctuations about a relatively small mean value.

Summary and Conclusions

     A modeling  framework for lake acidification assessment is  developed by
incorporating two model variables — alkalinity and C02 acidity in a two-layer
(epilimnion and hypolimnion)  fashion.  Biologically mediated processes in the
epilimnion and  hypolimnion  are incorporated with physical processes  such as
C02 exchange at air-water interface and vertical diffusion between the epilim-
nion  and   hypolimnion.  The C02/HCO~/CO ~  equilibria  are also  included  to
determine pH levels based on the calculated  alkalinity and C02 acidity concen-
trations.   In  addition,  external inputs  from  the  atmosphere  and the ground
water system are also included.
                                      61

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     The Water Quality Analysis  and  Simulation  Program (WASP)  is used as the
general computer  code  to implement the above modeling framework.   A kinetic
subroutine has been  specifically written to  formulate the  kinetic processes
for alkalinity and  C02 acidity.   The formulation of  the individual biologi-
cally mediated processes is not explicit in the model at the present time due
to the limited understanding  of  the  processes.   Instead, these processes are
grouped together  as the sources  and sinks of  alkalinity and  carbon dioxide
acidity via  parameterization.   Designed  to  be general  in nature,  WASP  is
flexible enough  to  provide the freedom to  incorporate the  kinetic processes
and the inputs to these processes, as well as the transport processes and the
geophysical morphology or  setting that go into the  framework  of  the model.
This model has been found  running very efficiently  on both main  frame and
mini-computer systems.

     The  developed  modeling  framework  has  been  applied   to   the  Bickford
Reservoir in Massachusetts.   The modeling  results indicate  that the seasonal
variations of  alkalinity in  the  epilimnion and hypolimnion of the Bickford
Reservoir are  reproduced for the 1981 conditions.   The model results explain
the generation of alkalinity  in the hypolimnion of the reservoir.  The general
applicability of  the modeling framework to acidified  lakes can be expanded by
applying the framework to other lakes.
                                      62

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Appendix I - References

 1.  Aimer,  B.W.,  Dickson,  W.,  Ekstrom,  C.,  and  Hornstrom,   E.,  "Sulfur
          Pollution and  the  Aquatic  Ecosystem,"  Sulfur  in  the  Environment,
          Part II;   Ecological Impacts, J.O. Nriagn,  ed., Wiley-Interscience,
          New York, NY, 1979,  pp.  271-311.

 2.  Altwicker,   E.R.   and  Johannes,   A.H.,  "Wet   and   Dry  Deposition  into
          Adirondack  Watersheds,"  The Integrated Lake-Watershed Acidification
          Study;   Proceedings  of  the ILWAS Annual Review  Conference, Electric
          Power Research Institute EA-2827,  1983.

 3.  Banks,  R.B.  and  Herrera,  F.F.,  "Effect  of  Wind  and  Rain  on Surface
          Reaeration,"  ASCE  Journal  of  Environmental  Engineering Division,
          Vol. 103, No. EE3, June  1977,  pp.  489-504.

 4.  Brosset, C.,  "Factors Influencing  pH in Lake  Water,"  Swedish Water and
          Air Pollution Research Institute Report B443,  1978, 9p.

 5.  Brosset, C., "The Acid-Base Balance in Lake Water,"  Swedish Water and Air
          Pollution Research Institute Report B540,  1980,  21p.

 6.  Brown, W.E.,  "Technique  to  Assess  the  Impacts of  Acid Rain on Surface
          Water Supplies, Proceedings of  American  Society of Civil Engineers
          1982 National Conference on Environmental Engineering,  Minneapolis,
          Minnesota.

 7.  Chadderton,  R.A.  and  Shane,  R.M.,  "A Model of  the Behavior  of  pH
          Determining Parameters  in Impoundments,"  Water Resources Bulletin,
          Vol. 14,  No.  6,  1978, pp.  1357-1373.

 8.  Chen,  C.W.,  Gherini,  S.,  and   Goldstein,   R.,   "Modeling  the  Lake
          Acidification Process,"  Paper presented   at  the Lake Acidification
          Workshop, Sept.  4-7,  1978,  Central  Electricity  Generating  Board,
          England.

 9.  Di Toro, D.M., "Combining Chemical  Equilibrium  and Phytoplankton Models—
          A  General  Methodology,"  Modeling  Biochemical  Processes in  Eco-
          systems,  R.P. Canale, ed., Ann Arbor  Science Publishers,  Inc.,  1976,
          pp. 233-255.

10.  Di Toro,  D.M.,   J.J.  Fitzpatrick,  and   R.V.  Thomann,  "Water  Quality
          Analysis  Simulation Program  (WASP)  and Model  Verification Program
          (MVP)  Documentation/' EPA  Report 1980.

11.  Edzwald, J.K.  and De Pinto,  J.V.,  "Recovery of Adirondack Lakes with Fly
          Ash Treatment," Final Report  No.  RC-A-76-4, Engineering  Foundation
          Grant,  1978.

12.  Eloubaidy,  A.F.  and Plate, E.J.,  "Wind Shear-Turbulence  Diffusion and the
          Reaeration  Coefficient," ASCE Journal  of Hydraulics Division, Vol.
          98, No. HY1,  Jan.  1972,  pp.  153-170.


                                     63

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13.  Eshleman,  K.,  "A  Biogeochemical  Mass  Balance  Approach  to  Reservoir
          Acidification by Atmospheric Deposition,"  MS  Thesis,  MIT Department
          of Civil Engineering, 1982, 117p.

14.  Hendrey, G.R., Galloway, J.N., and Schofield, C.L., "Temporal and Spatial
          Trends  in  the  Chemistry  of   Acidified   Lakes  under  Ice  Cover,"
          Electric Power  Research  Institute  Research  Project  1109-5  Interim
          Report, May 1981, pp.7-1  to 7-5.

15.  Hendrey, G.R. and Kaplan, E.,  "Identification  of  Freshwaters Susceptible
          to  Acidification,"  Brookhaven  National  Laboratory,   Upton,   NY,
          BNL-31000, CONF-820240-1, 7p.

16.  Henriksen,  A.,  "Acidification of  Freshwaters:  A  Simple Approach  for
          Identification   and  Quantification,"  Nature,   Vol.   278,   1979,
          pp.542-545.

17.  Henriksen,  A.,  "Acidification  of Freshwaters—A Large  Scale Titration,"
          Ecological   Impact   of   Acid   Precipitation,  Proceedings  of   An
          International  Conference,  Sandefjord,  Norway, March  11-18,  1980,
          pp.68-74.

18,  Henriksen, A. and Wright, R.F.,  "Effect of  Acid Precipitation on a  Small
          Acid  Lake in  Southern  Norway,"  Nordic  Hydrology,  Vol.  8,  1977,
          pp.1-10.

19.  Holley, E.R., "Oxygen Transfer at the Air-Water Interface," In Transport
          Processes in Lakes  and  Oceans, Gibbs, R.J.,  ed.,  Plenum Press,  New
          York,  1977.

20.  Jassby, A.  and  Powell, T-,  "Vertical Patterns of  Eddy Diffusion During
          Stratification   in   Castle   Lake,    California,"  Limnology   and
          Oceanography, Vol. 20, No. 3, pp.530-543.

21.  Kelly,  M.G., Church,  M.R.,  and  Hornberger,  G.M.,  "A Solution of  the
          Inorganic Carbon Mass Balance  Equation and  its   Relation  to  Algal
          Growth  Rates," Water Resources  Research, Vol.  10,  No.  3, June  1974,
          pp. 493-497.

22.  Kramer,  J.  and  Tessier,  A.,  "Acidification  of  Aquatic  Systems:    A
          Critique   of   Chemical  Approaches,"   Environmental   Science   &
          Technology," Vol. 16, No.  11, 1981, pp.606A-615A.

23.  Lung, W.S.  and  Canale,  R.P., "Projections of Phosphorus Levels  in  White
          Lake, ASCE Journal  of Environmental Engineering Division,  Vol.  103,
          No. EE4, pp.663-670.

24.  Lung, W.S.,  "Development of  a  Lake  Acidification Model," Paper presented
          at  the  Technical  Symposium  on  Acid  Precipitation  Transport  and
          Transformation  Phenomena, University  of  Vermont, Burlington,  VT.
          September 22, 1983.
                                      64

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25.  Schindler,  D.W.,  Wagemaun,   R. ,   Cook,  R.B.,  Ruszczynski,   I.,   and
          Prokopowich,   J.,    "Experimental   Acidification   of   Lake   223,
          Experimental Lake  Area:   Background Data  and  First Three  Years  of
          Acidification," Canadian  Journal Fishery  and Aquatic  Science,  Vol.
          37, No. 3, 1980, pp.342-354.

26.  Schnoor,  J.L.,  Carmichael,  G.R. and  Van Schepen,  F.W., "An  Integrated
          Approach  to Acid  Rainfall Assessments,"  Energy and  Environmental
          Chemistry, Vol  2,  Acid Rain,  L.  H. Keith,  ed., Ann  Arbor Science
          Publishers, Inc.,  1982, pp.225-243.

27.  Schofield, C.L., "Effects of  Acid  Rain  on Lakes," Acid  Rain,  Gunnerson,
          C.G. and Willard,  B.E., eds.,  ASCE,  New York, NY, 1979, pp.55-69.

28.  Shen,  T.T.,  "Hazardous  Air Emissions  from Industrial  Waste  Treatment
          Facilities,"  Proceedings  of   14th Mid-Atlantic  Industrial  Waste
          Conference, College Park, Maryland,  June 27-29,  1982.

29.  Stumm, W. and Leckie, J.O., "Phosphate Exchange with  Sediments;  its Role
          in the Productivity  of Surface Waters," Paper presented at  the 5th
          International Water Pollution  Research  Conference,  July-August 1970.

30.  Stumm, W. and Morgan, J.J., Aquatic Chemistry,  John Wiley  and  Sons,  New
          York, NY,  1981.

31.  Weber, W. J.,  Jr. and Stumm, W., "Mechanisms of  Hydrogen Ion Buffering in
          Natural Waters," Journal  American Water Works Association,  Vol.  55,
          No. 12, pp.1553-1578.

32.  Yeasted,  J.C.   and  Shane,  R., "pH Profiles  in  a   River  Systems  with
          Multiple  Acid Loads,"  Journal Water Pollution  Control  Federation,
          Vol. 48,  No. 1,  1976, pp.91-106.

33.  Yu,  S.L.,  "Atmospheric  Reaeration  in a Lake." Department  of Civil  and
          Environmental Engineering Report, Rutgers University,  New Brunswick,
          NJ, August 1977, 50p.
Appendix II - Notation

     The following symbols are used in this paper:

                     A  =  lake surface area;

                  A1>2  =  interfacial area between epilimnion and
                           hypolimnion;

              , [Alk]2  =  alkalinity concentrations in the epilimnion and
                           hypolimnion, respectively:
                                      65

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[C02Acyh, [C02Acy]2  =  C02 acidity concentrations in the epilimnion and
                         hypolimnion, respectively;

            [C02, \]  =  saturated concentration of C02;
                \Sy
              [C02]   =  C02 concentration in the epilimnion;

          D ., ,  D     =  loading rates of alkalinity and C02 acidity from
                   2     direct deposition and tributary input to the
                         epilimnion;

                [H ]  =  concentration of hydronium ion;

              KI, K2  =  first and second dissociation constants of
                         carbonate equilibria;

                  K   =  dissociation constant of water;
                   w
            K-  (C02)  =  reaeration coefficient for C02;

             K,  (02)  =  reaeration coefficient for 02;

                  L   =  average depth of the epilimnion;

                  L,  =  average depth of the hypolimnion;
                   n
                LI 2  ~  average of the epilimnion depth and
                   '      hypoliranion depth;

                Ql 2  =  advective flow between the epilimnion and
                   '      hypolimnion;

                0     =  outflow from the epilimnion;
                 out
                   T  =  temperature;
              Vi, V2  =  volumes of the epilimnion and hypolimnion
                         respectively;

                   W  =  windspeed;
          W   '  W n   =  ground water input of alkalinity and C02 acidity
           Alk   C02     respectively;

                   8  =  temperature correction constant for reaeration
                         coefficient;

      Ul» U2> VB> W»  =  first-order kinetic coefficients for alkalinity
                         and C02 acidity in the epilimnion and hypolimnion,
                         respectively;

                a, 6  =  weighting factors to determine the concentrations
                         at the epilimnion-hypolimnion interface; and

                   £  =  vertical diffusion coefficient in the water column.
                                    66

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                  SENSITIVITY ANALYSIS OF SWMM PREDICTIONS

                    ON WATER QUALITY IN THE DETROIT RIVER


                                    by
                   Alaa El-Sharkawy and Ralph H. Kummler
                     Department of Chemical Engineering
                           Wayne State University
Abstract
     The Fourier Amplitude Sensitivity  Test  (FAST)  has been applied  to  the
Detroit  River  Plume  Model  employed  in the  Detroit  201  study.  The  plume
model  superimposes  all SWMM CSO  sources,  the Detroit  Wastewater  Treatment
Plant Plume and  the confluence of the Rouge River  to obtain composite pre-
dictions of concentrations in the Detroit River.   First order error analysis
could not be applied to a highly nonlinear case  such as  this.   The partial
variances for dissolved oxygen, fecal colifonn,  and  total  phosphorus concen-
trations are  calculated as  a  function  of the model  input  parameters:   the
turbulent  diffusivity,  the  river  velocity  and  depth and the  background
concentrations and the SWMM model output waste loadings.

     The  resulting   sensitivity  coefficients  as a  function of  position in
the River are  displayed and  the significance of  the  results are discussed.

Introduction

     The Detroit Water and Sewerage  Department provides  wastewater collec-
tion and treatment  services  over an  area encompassing  650  square miles and
including 3,200,000 people  and over  1500 industrial  dischargers.   About 62
percent  of  the service area  is served by separated storm and sewage sewers;
the rest is served by  combined sewers.

     Once wastewater reaches the city,  flow is generally towards the Detroit
or Rouge Rivers  where major interceptors divert  dry  weather flow to a  sin-
gle, large  treatment plant  near the  confluence of the two rivers.  Signifi-
cant  rainfall  creates  runoff  in excess of  interceptor  capacity  which, by
design,  overflows to the Detroit and Rouge Rivers at approximately 80 loca-
tions, called  combined sewer overflows  (CSO's).

     In  September 1977  a  Consent Judgement mandated that  the quantity and
quality  of  combined sewer overflows  from the City of Detroit be determined.

                                     67

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     The objectives of the Section 201 Study that followed were:

     1.    To determine the  quantity  and quality of combined sewer overflows
          to the Detroit and Rouge Rivers.

     2.    To quantify the  impacts  of combined sewer overflows on the  Rouge
          River, Detroit Waste  Water Treatment Plant,  and Detroit River for
          the purposes of facilities planning.

     3.    To provide  a  tool for evaluating the  impacts  of  various CSO con-
          trol alternatives on the Detroit and Rouge Rivers.

     The  area  modeled included  the  entire City of Detroit  along with some
small portions of  a  few  suburban  communities which  totaled  approximately
88,000 acres.   The  evaluation of potential alternatives was conducted  using
the USEPA Storm Water Management Model (SWMM) , RUNOFF and TRANSPORT blocks,
supplemented by QUAL  II,  RECEIVE II, and  models  developed  in the 201  study
to predict  the dynamic  behavior of the 800MGD treatment facilities and one,
two and  three  dimensional dynamic impacts on  receiving streams.   The model-
ing package consisted of  five coupled models,  including  1) the collection
system model,  2)  the  Rouge River model, 3) the Detroit Wastewater Treatment
Plant  (DWWTP)  model  STPSIM2,  4)  a Plume  model  (Detroit River near shore),
and 5) the  overall Detroit River model  (USSMPX).

     The  details  of the overall 201 study and the models employed have been
given by Kummler  [1982]  and references  therein,  and will  not  be repeated
here.  An uncertainty analysis of the  modeling  package  (1) through (4) was
conducted by Kummler,  et al.  [1981] using Monte Carlo techniques.  In this
work we  describe  a more formal procedure  for  uncertainty analysis using the
Fourier Amplitude Sensitivity Technique.   We focus herein on the Plume  Model
using SWMM  as  input.

The Gaussian Plume Model

     The basic equation governing the conservation of mass in flowing fluids
is the  equation of continuity for the  time averaged concentration, assuming
stationary, homogeneous  turbulence,  which should be an excellent assumption
for extensive  reaches of  the Detroit  River.   The continuity equation for
species  i,  then becomes,  for flow  aligned in  the  x  direction, neglecting
dispersion  in  the  axial direction  and assuming complete  vertical mixing:

                    32c.
If K ,  the lateral  diffusion coefficient,  is a constant,  then  there is an
exac^ solution for  a  continuous  point source located at  (x  ,y  )  in an un-
bounded river
as presented  by Seinfeld  (1975),  where c. = concentration  of  species  i at


                                     68

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location  (x,y)  due  to a source of strength Q. located at (x ,y ); u = river
velocity;  h  = average river depth; x  = distance from the  source;  y = dis-
tance from the  shore line; p = effective  lateral  penetration; and k = rate
constant for a first order kinetic decay.

     The model  employed  for  the Detroit 201 study was a superposition solu-
tion  allowing  for 48  sources,  an arbitrary  x,y grid pattern,  and coupled
first  order   reactions.   The  model  has  been presented  by  Liang, et  al.
(1981).  The  experimental  verification of the model was  conducted by Liang
(1981).

The FAST Method

     The method to be  briefly described  in  this  section  was developed by
Shuler  and coworkers  (see,  for example, Cukier, et al.  (1973)  and (1975))
and  reduced  to  computer code  by McRae,  et al.  (1982)  and by Koda,  et  al.
(1979).   The version  employed by  our  group  was  obtained through Norbeck
(1983).

     In general, modeling requires the solution of  either

     1.   a set of n coupled differential equations

     2.   a system of algebraic equations

               F(x;t;k) = 0
          where x is an n dimensional state vector,  and
                k is an m dimensional parameter vector.

The problem we are addressing herein is to understand what effect variations
in the  input  k's  will have on the  output x's  at various values of t.   Tay-
lor's theorem  is  often used (neglecting higher order  terms)  to measure the
sensitivity of x to k in accordance with
                                         m  3x.
     Axi(t,k) = x..(t, k+Ak) - xi(t,k) =  Z  ^ Ak.  + f(Ak?) + ...
                                        j_l   j   J        J


where

     9x.
     jrr— is called the sensitivity coefficient.
       J
     The Taylor Series  truncation  provides a local  sensitivity analysis be-
cause  it  is  only applicable to small  variations of  Ak about  its  nominal
value.  It  does  not  assess the  effect of  simultaneous  large variations in
all parameters.   On  the other hand, what  is actually  desired for most com-
plex modelling, is  a global sensitivity analysis which  measures the sensi-


                                     69

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tivity of the model's output to the total range of uncertainty of the model.
It is usually  totally impractical, costly, and misleading to attempt a Tay-
lor Series analysis for a complex numerical model.  The FAST method provides
a global analysis with reasonable cost.

Definitions

     If the  probability  density function for  a  given x.  at specific values
of the  parameters k  is given  by p(k- ,  k? ...  k  ),  then the  ensemble mean
for x. is given by: m                            m

      = /  .. / x.(t; kn, k.  ... k ) pCk,, k   ... k ) dkt ... dk
       i               ilzml/ml       m

and the variance by:
                       -  2

      The  m dimensional  integral  for  the  ensemble  mean  can be  con-
verted  into a  one  dimensional form  by  the  transformation

      k£ = G£[sin (w£s)j   A = 1,2  ... m,

where the Gp functions  are  chosen  such that the arc  length,  ds,  is propor-
tional  to pOk. ,  k. . . .  k ) for all  &.
              12.      m

      It has been  shown that the G ' s  can be chosen (Weyl, 1938) such  that
                                   Jv
      Xi  =    ~ LiD1 2T -T  Xi [ki(s)'  k2(s)  ••
                            -T
The  use  of integer frequencies causes  the k-'s to be periodic functions  in s
and  the s-space  search curve  is closed.   jThen,  the Fourier  Coefficients:
         £      -71


       f •}      n

         i      -71                ~~

                                         p = l,2...m

are a measure  of the sensitivity of x.  to the k^ variation.

     The ensemble average, ,  can  therefore be expressed in terms  of  the
Oth Fourier  coefficients
2 = ._
  1      O       O       O
                   + B«2  = A(t)2
                                     70

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The frequency variance is

     a^)2 = 2  I  [A<;>2 + B^2]
               p=l

Both the frequency variance, a  (i)2, and the total variance,  cr(i)2 be cal-

culated.  The partial variance is defined as the ratio:


                " n      o        f * \     f * \
     s  (i) =
      V     (o(l))*   ffi  j=l  JWA     JW2


The ability to  determine  which is the most  important  uncertainty in a com-
plex calculation is unique to the FAST method.

Results and Discussion

     The FAST method has  been applied to  the  case of CSO input  to  the De-
troit River  in  our  previous  work  (El-Sharkawy,  et al.  (1983)).   Therein,
we considered single  plume  discharges and an analysis of the full model al-
lowing for variation in the diffusion coefficient, the  river  velocity, the
river depth,  the  background concentration and the  temperature.   Herein,  we
extend that work to include variations in the SWMM input flux to the Detroit
River.

     In  Figure  1, we  illustrate the  locations  of the  CSO  stations on the
Detroit  River.  The  major stations include three  (401,  402,  and 403) which
enter Conner's  Creek before joining the Detroit River and Leib (410).  Leib
is approximately 16,773 ft downstream from Conner's Creek.  We use the plume
model to examine concentrations on the USA side of the Detroit River.  There
are no CSO  stations  on the Canadian  side  and  Belle Isle effectively separ-
ates the River into two portions at this point.  Hence only US contributions
need be  considered.   The  SWMM model provides  the  input pollutant fluxes to
the plume model.  The SWMM results for Detroit have been described previous-
ly (Kummler, 1982) and will not be repeated herein.

     We  will  focus  in  this paper  on variations in the  SWMM  output to the
Detroit  River and will use the FAST method to examine the relative contribu-
tion  of  various upstream stations  to  downstream concentrations at  selected
locations.  We  will  also  examine the  relative magnitude of the  flux uncer-
tainty as  compared with the uncertainty caused  by turbulent diffusion, ve-
locity  and  depth.   Lastly,  we will evaluate the  total  error  and the  rela-
tive standard deviation in  the overall calculation.

     We  begin by  considering outflow  from the three CSO  stations  located at
Conner's Creek.   In  this vicinity,  the Detroit River may  be described by the
nominal  variables  in Table  1.
                                     71

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PO
                           City of Detroit
           ROUGE
          -PI VSR
           12
                                          PLUME  MODEL GRID SYSTEM
                                                                                          LEGEND

                                                                                        '2/0 REACH NUMBER (TYP)
                                                                                        >«-7
                                                                                     	3 TRANSECT AND NUMBER
                                                                                            (TYPJ
                                                                                            MODELED PORTION OP
                                                                                            DETROIT RIVER
                                                   FIGURE  1.

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                                    Table 1
                     Nominal  Values  for  the  Detroit  River
      Turbulent Diffusivity,  K ,  ft2/hr:                 2180

      Velocity, u,  ft/hr:                                7250

      Depth,  h, ft:                                        26
     The characteristics of  the  outfalls  at the CSO  stations  considered in
these calculations are given in Table 2.

                                   Table  2
                   Outflow Concentrations  at Each Station
                                                                   Waste
Station  BOD   DO*    SS    VSS     DS       P    CAD      COLI    Flow
  No.    mg/£  mg/Ji  mg/£   rog/£   mg/S,    mg/A   tag/SL   #/100 IE£  (CFS)

  401    20.69  5.97  80.70  52.70  228.00  0.791  6.712  6.70xl05  2101.7

  402    19.59  5.63  76.40  49.90  201.20  0.724 10.71   1.7xl06    412.6

  403    16.70  5.62  71.50  46.60  200.70  0.590  0.25   5.l4xl05  1033.0
                                          •

  408    53.06  5.88 237.4  154.8   674.7   0.664  0.0048 5-96xl05    79.6

  410    38.36  5.54 139.5   91.0   373.9   1.057  1.1830 2.71xl06  1454.0

Background Concentration

   C .      l.O   9.42   1.00  18.00   95.00  0.01   0.00033   19.0
    01

*The outflow concentration of DO is given as the DO deficit.   The background
 concentration represents the actual concentration.

     The  relative location of  the CSO  stations along  the  US side  of the
river  beginning arbitiarily  at  the  inactive  Fox Creek  CSO are  given in
Table 3.


     Procedurally, we varied the waste volumetric flow rate which has the
effect of varying the mass flux for all of the species simultaneously.

Hence, a single parameter can be used to analyze the uncertainty contribu-
tion of the source function for all eight parameters considered in the De-
troit 201 study.  Herein, we will illustrate results using TP and .Coli-
form.

                                    73

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                                   Table 3
                 Relative Location of Detroit River CSO Sites
                              Along the US  Side
 L    XQ(FT)
 1  0.0
 2  6.80000E+03
 3  6.80000E+03
 4  6.BOOOOE+03
 5  1.39240E+04
 6  1.40180E+04
 7  1.59900E+04
 8  1.66530E+04
 9  2.07370E+04
10  2.30470E+04
11  2.35730E+04
12  2.43730E+04
13  2.60970E+04
14  2.70190E+04
15  2.76220E+04
16  2.80610E+04
17  2.91000E+04
18  2.91000E+04
19  2.95400E+04
20  3.06260E+04
YQ(FT)
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
1
1
1
1
1
1
1
1
1
1,
4,
1,
1,
1.
1,
1,
1,
1,
1,
PQ(FT)
 OOOE+02
 OOOE+02
 OOOE+02
 OOOE+02
 OOOE+00
 OOOE+00
 OOOE+00
 OOOE+00
 OOOE+00
 OOOE+00
 OOOE+01
 OOOE+02
 OOOE+00
 OOOE+00
 OOOE+00
 OOOE+00
 OOOE+00
 OOOB+00
 OOOE+00
1.OOOE+00
 STATION NAME              STAT.  NO,
FOX  CREEK                  480
CONNER CK BKWATER GATE    401
CONNER PUMP  STATION       402
FREUD PUMP STATION        403
FAIRVIEW PUMP  STATION     404
MC CLELLAN                 405
FISCHER                    406
IROQUOIS                   407
HELEN                      408
MT.  ELLIOTT                409
LEIB                       410
ADAIR                      411
JOS.  CAMPAU                412
CHENE                      413
DUBOIS                     414
ST.  AUBIN                  415
ORLEANS                    416
ORLEANS RELIEF             417
RIOPELLE                   418
RIVARD                     419
       In Figure 2, we present the station by station partial sensitivity of
  the total  phosphorus (TP)  concentrations in the Detroit River at a point 70
  ft offshore as a function  of downstream distance.  This figure shows that
  the partial sensitivity is a strong function of the mass flux associated
  with each  station.  Station 401 has the highest flow  rate and the highest
  TP concentration and therefore resulting concentrations in the river are
  most sensitive to uncertainties in the mass flux from station 401.  In
  Figure 3,  the similar analysis for coliform is presented.  Because the fecal
  coliform concentration from station 403 is only a  third of the concentration
  from station 402, we see that the relative importance of stations 402 and
  403 is reversed from that  displayed in Figure 2.  In  both cases illustrated
  in Figures 1 and 2, only the input flux, Q., is varied; hence, the partial
  sensitivities are independent of longitudinal, or  downstream, distance.  Ex-
  amination  of equation II and a first order error analysis would lead to the
  same conclusion.  The relative standard deviation, defined as the total
  standard deviation divided by the nominal calculated  concentration is dis-
  played in  Figure 4 as a function of longitudinal distance.  Again, the rela-
  tive standard deviation is insensitive to distance, but only because the
  background concentration of TP in the Detroit River is low.  There is a
  small trend toward lower relative standard deviation  downstream as expected.
       Next  we consider variations in stations 401,  408, and 410.
  tance between these stations are given in Table 3.
                                              The dis-
                                     74

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            FIGURE  2.
JWmAL WBfTMTY M. UONOnUDMAL MWO POU TF *
050
                                   -o
  0?
                                        Legend
                                         STATION 1401
                                         S TfflON 1402
                                         STW10N #403
    6000   9000   10000   11000   12000
     Longitudinal Distance in ft,
             FIGURE 3.
mmvM. MMTMrr vi. UManvtMM. MWNOI KM ccuK>m*y*nj3Fr.
0.754,
0.35-
                   o
                                       Legend
                                      0  STATION 1401
                                         STATION 1402
                                         STATION f 403
    6000   9000   10000   UOOO   12000
     Longitudinal Distance in ft,
                     75

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     In Figure 5, the relative standard deviation is presented as a function
of downstream distance.  There, we see that the total deviation is high
where station 401 contributes  (up to 14,000 ft), is zero where the flow has
not yet reached during the time selected and increases past 23,000 ft due to
the contribution of station 410.  The contribution of station 408 is very
small and is barely discernable.

     Next, we consider a case  in which the effect of mass flux is examined
together with the effects of K , u, and h.  The source strength of station
401 is varied while others are^held constant.  The results are given in
Figure 6.  At short distances  downstream from station 401 velocity is a
major factor in the partial sensitivity, but far downstream, river depth is
the most important variable.   The effect of source strength as measured by
the partial sensitivity due to flow accounts for about 15% of the total
error.  For the same  case, the relative standard deviation is portrayed in
Figure 7.  The magnitude of the uncertainties has caused roughly a  factor
of two overall uncertainty in  the final result.  As the concentration drops
downstream so does the relative  deviation.  As expected when more parame-
ters are allowed to be uncertain, we get a bigger error.

      Finally,  we consider variations in three stations,  401,  402,  and 403,
 all at Conner's Creek for a 90% input uncertainty in the effluent source
 strength of fecal coliform.    In Figure 8,  we display the Relative Standard
 Deviation vs.  downstream distance.   The output uncertainty is independent
 of distance downstream and is considerably less than 90% over the range
 studied.

 Summary

      The FAST method has been used to evaluate the relative contributions of
 uncertainties in the input parameters to the overall uncertainty in water
 quality predictions on the Detroit River.   The FAST method allows an ana-
 lysis of station by station contributions as well as insight into the river
 parameters which cause model predictions to deviate from measured data.

 References

 Cukier, R.I.,  C.M. Fortuin,  K.E.  Shuler, A.G. Petschek and J.H.  Schaibly, J.
 Chem.  Phys.  59, 3873 (1973).

 Cukier, R.I.,  J.H. Schaibly and K.E. Shuler, J. Chem. Phys. 63,  1140 (1975).

 El-Sharkawy,  A., R.H. Kummler and C-S Liang, Proceedings of the Engineering
 Foundation Conference, Niagara-on-the-Lake, Ontario, Canada,  November 1983.

 Giffels,  Black and Veatch, a  CS-806 Report on Quantity and Quality of Com-
 bined Sewer Overflows, Vol.  II, September 1980.

 Koda,  M.,  G.J.  McRae and J.H. Seinfeld, Int. J. Chem. Kin. 11_, 427 (1979).
                                      76

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                     FIGURE 4.
         RELATIVE SAMMfiD DEVIATON % VS. OBWNCE POM TP AT Y^TO.OFT
         100
      8
      '£   75-
      Q)
      Q
      •E
      -3   50-
      g

          25-
            6000   9000   10000   11000   12000
             Longitudinal Distance in ft,

                       FIGURE 5.
RELATIVE STANDARD DEVIATION % VS. DISTANCE FOR COUFORM AT Y-TO.OFT
    50
1
   37.51
    25-
   12.5-
      8000  11000   14000   17000  20000  23000  26000  29000
                 Longitudinal Distance in ft.
         Station 401      Station 408    Station 410
                               77

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                      FIGURE 6.

           MRT1AL B8OTTVTTY V& UWOFTUDMAL OBWCE FOB Tf a Y-«XOFT.
                                              Legend
                                             O FLOW
                                               DlF.COEf.
                                             • VELOCITY
                                             D DEPTH
              8000   9000   10000   11000   13000
               Longitudinal Distance in ft.
                        station 401
                       FIGURE 7.
RELATIVE STANDARD DEVIATION % VS. DISTANCE FOR TP AT Y-70.0FT
1
    100 •*
    75-
    50-
I
      6000
9000        10000        11000
Longitudinal Distance in ft.

        Station 401
12000
                              76

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Kumraler,  R.H. ,. J.G. Frith, L-S. Liang and J.A. Anderson, "Uncertainty Analy-
sis in Stormwater  and Water Quality Modelling,"  Proceedings of the SWMM
Users Group Meeting, USEPA and McMaster University, Hamilton, Ontario,
Canada, September  1981.

Kummler,  R.H.,  "SWMM Modelling for the Detroit 201 Final Facilities Plan:
Final Results," Proceedings of the USEPA SWMM Meeting, Ottawa, Ontario,
October 1982.

Liang, Cheiri-Sung, "Use of Multispectral Remote  Sensing Data to Predict the
Turbulent Diffusion Coefficient in the Detroit River," Master's Thesis under
R.H. Kummler,  Department of Chemical Engineering, Wayne State University,
Detroit,  Michigan  (1981).

Liang, Chein-Sung, S. Winkler and R.H. Kummler,  "A Gaussian Plume Model of a
Two Dimensional River," Symposium on Section 201 Planning; Modeling for Com-
bined Sewer Overflow Abatement, Paper 8d, 91st National AIChE Meeting, De-
troit, Michigan, August 1981.

McRae, G.J., J.W.  Tilden and J.H. Seinfeld,  Computers and Chemical Engineer-
ing 6, 15 (1982).
                            FIGURE 8.

                     STANDARD DEVIATION % V& DBWCE FOR OJUFOM* AT
               100
           1
           '>   75 H
            0)
           Q
                50-
                25-
                   O
-o
o
                   8000   9000    10000   11000    12000
                    Longitudinal Distance in ft.
                                    79

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Norbeck, J., Ford Motor Company Technical Report (1983).

Roginski, Gregory T., "A Finite Difference Model of Pollutant Concentrations
in the Detroit River from Combined Sewer Overflows," Ph.D. Dissertation
under R.H. Kumraler, Department of Chemical Engineering, Wayne State Univer-
sity, Detroit, Michigan, 1981.

Seinfeld, J.H., Air Pollution Physical and Chemical Fundamentals, McGraw
Hill Book Company, New York  (1975).

Weyl, H., Amer. J. Math. 60, 889  (1938).
                                    80

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                  RAINPAK - A PROGRAM PACKAGE  FOR  ANALYSIS OF
                  STORM DYNAMICS IN COMPUTING  RAINFALL INPUTS

                                       by
                        Wm. James and R,  Scheckenberger
              Computational  Hydraulics Group,  McMaster University
                       Hamilton,  Ontario,  Canada,  L8S 4L7
                             PHONE:  (416)   527-6944
                                    ABSTRACT

     A software package entitled 'RAINPAK' comprising four separate programs has
been developed to process rainfall  observations in order to estimate storm cell
characteristics such as speed and direction of motion, spatial dimensions and
growth/decay functions.  These estimated properties are then used to model
rainfall produced by one or more storm cells.  The discretized hyetographs
produced by the rainfall model thus incorporate dynamic storm characteristics.
     Application of RAINPAK to rainfall events will be covered in another
publication.

                                  INTRODUCTON
     Drainage network design procedures typically require a da :aset describing
the 'as-is* hydrological characteristics of the problem catchment. Certain
parameters, such as conduit length, conduit slope, conduit roughness and
subcatchment area are easily determined; others such as percent  imperviousness,
                                      01

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infiltration and subcatchment width, require calibration. Calibration procedures
in turn require historical runoff and  rainfall time series; the physical
drainage network or environmental dataset  is used  in conjunction with the
observed rainfall and  runoff time series dataset.  By varying the most sensitive
environmental parameters,  an optimal match  between the computed and observed
hydrographs  is obtained. This procedure  is  repeated for  several observed events
until an overall  'best1  set of  calibration  parameters has been determined.
Normally, the next step  in the  design  requires the use of a design storm with a
prescribed  return period as input to the calibrated hydrological model. The
output hydrograph is then  used  to design the drainage system, e.g. sewers,
retention ponds, overflow  structures,  etc.  Using this approach, the design
hydrographs  are  assumed  to have the  same return period originally assigned to
the design  rainfall hyetographs.
     There  are several difficulties  associated with this procedure, the most
important relating to  the  use of rainfall  time series.  In most catchment areas
there are very few rain-intensity gauges (often there will be none at all). The
engineer may adopt a hyetograph from a single  gauge,  assuming that this temporal
rainfall distribution  is  representative of the entire catchment  area. Except  for
small, relatively impervious  catchments, and  long, soaking rainfalls, this  is
not a reasonable assumption.  For summer storms and most  catchments, the  result
is erroneous calibration.
      Other  shortcomings exist  in the  implementation of  the design storm. Design
 storms are  usually derived from long  historical  records consisting of several
 types of storms. The synthetic  design storm is then applied uniformly over the
 entire catchment area - an unrepresentative condition in many cases. Finally,
 the  computed runoff hydrograph  (usually the peak  flow)  produced by this design
                                      82

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storm is assumed to have the same return period as the rain hyetograph {usually
the total rainfall). This does not take into account the antecedent conditions
present in the catchment area, nor the new response time of the problem
catchment, altered by virtue of the design or proposed drainage changes. Current
methodology obviously makes no provision for storm dynamics or multicellular
features apparent in rainstorms. The accuracy of present runoff models has
outstripped the accuracy of available input time series. This paper focuses on
better ways of determining the input time series.
     A program package, RAINPAK, has been written to develop rainfall input and
a new design methodology incorporating dynamic storm modelling is introduced.
The descriptions of physical processes behind the temporal and spatial distri-
bution of storm rainfall, specifically thunderstorms, derived from raingauge,
radar and satellite observations form the basis for most of the concepts used in
RAINPAK.
     A network of intensity measuring raingauges is used to estimate  storm
characteristics such as speed, direction and cell growth/decay mechanisms. A
new procedure, storm calibration (fitting computed hyetographs to observed
hyetographs), is described and applied to observed data. A methodology to
develop a numerical storm model from simple hyetographs is presented. This storm
model is used to compute rainfall in space over a catchment area. It  is
suggested that hydrological models can be more accurately calibrated  using such
improved rainfall representation. The importance of better calibration is
obvious. The design of overflow structures, super-sewers, interceptor sewers,
etc. is more reliable.
     A series of numerical experiments were conducted to determine how well  an
estimated storm cell shape will reproduce observed hyetographs.  Results will  be
presented elsewhere.
                                      83

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                   RUNOFF SENSITIVITY TO RAINFALL VARIABILITY

     Several hydrologists have studied the effect of storm dynamics on  runoff.
These studies have included numerical rainfall models, numerical experiments
applying synthetic rainfall to a hypothetical catchment, and the application of
various rainfall distributions to a dataset describing an actual catchment.
     If variable storm patterns are not accurately  accounted for,  the  resulting
errors are  considered particularly important  to  computational modelling
(Troutman,  1981).  Because of these errors, Troutman recommends that model
calibration be  performed  using input  data  subject to the same kind of  errors.
By incorporating areally-distributed  inputs  into a  model, taking account  of
spatial variability.   Improved computed hydrographs will result.   This  is due
primarily to the significant effect of distributed  rainfall  volumes (Seven and
Hornberger, 1982).
     Idealized  numerical  rainfall models  have been  applied to data sets of real
and  hypothetical catchments, and  the  subsequent  computed  runoff  analysed  (Wilson
et al, 1979; Amorocho,  1981; James and Scheckenberger,  1982).  Wilson  compared
computed runoff hydrographs  produced  by  a  network  of twenty  gauges to  those
produced by one randomly  chosen  gauge.  A  moving rainfall model  was used  to
produce  'storms' with an  areal  mean  depth in excess of two inches  and moving at
twelve mph. The storms ranged  from highly random to highly organized spatial
distributions  and  were applied  to a  26.5 sq.ml. catchment  area  1n  Puerto Rico.
The  results are tabulated below.

   % DIFFERENCE BETWEEN THE  USE  OF  TWENTY GAUGES AND ONE GAUGE
     STORM  DEPTH         RUNOFF  VOLUME          PEAK DISCHARGE
     Mean    Max         Mean       Max          Mean    Max
     8        22          13         35            13     52

                                      84

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     It may be concluded that when the spatial  variability of rainfall is
ignored (e.g. by using only one input rainfall  time series), computed runoff
incurs unacceptably high errors.
     Others have examined runoff sensitivity to rainfall variability by applying
a temporal  rainfall distribution in a static or kinematic fashion (Aron et al,
1982; James and Scheckenberger, 1982).  Aron et al  examined the sensitivity of
computed peak discharge for an actual and hypothetical catchment to temporal  and
spatial rainfall .variations. They concluded that, as drainage areas decrease  in
size, the sensitivity of peak discharge to time distribution and maximum short
duration rainfall intensity increases. It thus becomes increasingly more
difficult to estimate peak discharge. A 'late'  peaking rainstorm produced
computed runoff peaks up to 30% higher than 'early1 peaking storms. Travelling
storms (i.e. rainfall distributions lagged spatially in time) moving in the
general direction and speed of the runoff down the drainage network, produced
computed peak discharges 30-35% higher than equivalent stationary storms. These
results concur with those obtained by James and Scheckenberger; both sets of
authors recommend the use of storm dynamics in the design of drainage systems.
Robinson and James  (1982) optimized  the design of  storage units  by  varying  the
speed  and  direction  of  storms  across  an urban  centre.
      In  a  study  conducted in  Stevenage, England, Colyer  (1981)  analysed  21
observed storm  events.  The  peak discharge was  computed  by the  Wallingford
Hydrograph  Method  using hyetographs  recorded at  two  gauging  sites  individually
and  in combination.  These gauges  were 1390  m apart and  had  a 23 m  difference in
elevation.  Using a dimensionless  parameter  to  represent  the degree of fit
between  observed and computed  peak discharge,  Colyer found  dramatic variations.
For  example, when  comparing computed peak  discharge using  the 'lower'  gauge
against  the 'upper1  gauge the ratio  between computed peak  and observed peak
                                      85

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varied between 0.354 and 1.479. Thus Colyer concluded that using  a  single
raingauge as input could lead to  very unrealistic  representations of  Individual
storms over an urban catchment.
     It seems quite clear  from these numerical  and  laboratory  experiments that
the temporal and spatial distribution of  rainfall  has a  marked Influence on  the
computed runoff hydrograph.  Moreover, when  rainfall  is convectlve,  characterized
by short duration, high  intensities and  localised  1n space,  any rainfall-runoff
model without an appropriate description  of the spatial  and  temporal  character
of the rain input may  produce unacceptable  errors   (Wilson  et  al, 1979).

                                  STORM DYNAMICS
     Some storm motion characteristics are  obtainable from  radar  measurements
(Huff et al, 1981). Usually  storm motion  1s estimated by tracking the centre of
gravity of  the  rain area  (BelIon  and Austin,  1977). Difficulties  arise because
the process is  computer-intensive. Radar data are  not as available  as raingauge
data and the available record is  relatively short. Thus  hydrologists  ftave
developed methods to  determine cell  motion  and characteristics from raingauge
networks.
     Possibly the simplest method of estimating storm movement 1s to sequent-
ially multiply  a  rainfall  total  on a network  grid by its distance from the V
and  'y'  axes. By  summing this quantity  for all ralngauges Involved and dividing
by the total  rainfall, the coordinates  of the centre-of-grav1ty are determined".
This method will  usually provide a good  estimate of general storm motion,  but 1f
more than one cell  is present, the estimate of speed may be In error. Moreover,
this methodology  requires that the storm centre passes through the gauging
network  (Shearman,  1977).
                                      86

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     In another technique, an identifiable feature in the hyetograph, such as
the start of rainfall, is tracked. Unfortunately, a long time is required to
preprocess the hyetographs (Shearman, 1977).
     A third technique involves lag correlation analysis (Marshall, 1980). This
technique requires a gauging network sufficiently dense that gauges within the
same raincell will produce a high correlation coefficient at zero time lag
(Niemczynowicz and Jonson, 1981). If the lag time is known or estimated,
correlations between pairs of gauges will be improved in the direction of the
storm movement. This technique assumes rainfall to be isotropic (i.e. rainfall
at any distance from the storm centre is independent of direction). The
'optimum' lag time can be obtained between hyetographs from a correlogram. By
repeating this procedure for all pairs of raingauges in the network a set of
'optimum' lag times is obtained. A least squares method is used to determine a
single best  lag time from the set. A confidence estimate is made by determining
total variance due to regression and residual variance.
     Shearman (1977) performed  several  numerical  experiments  using  Marshall's
correlation  technique.   Irregular  gauge  networks,  including  outliers,  produced
significant  errors  using idealized  data.  By  applying  random timing  errors  of 0,
+/-5,  +/-10, +/-15  minutes  to  the  lag  time at  the  15  gauges,  the  sensitivity  to
timing  errors  was determined.  For  three  idealized  test  storms,  the largest  error
for  a  25 sq.km storm  cell moving  at  0.4  m/s and  225 degrees,  was  +2.5  m/s.and
+13/6  degrees.

                                     RAINPAK
     RAINPAK comprises  four programs:  STOVEL,  THOR4DPT, THOR4D and THOR3D.
STOVEL,  THOR40PT  and  THOR4D, while having stand-alone capabilities,  are usually
executed consecutively.  THOR3D is  a simplified version of the procedures
                                      87

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addressed by the other three programs. RAINPAK uses hyetograph data as input and
models storm dynamics. For details on input formats, limitations and sample I/O,
refer to the RAINPAK USERS MANUAL (Scheckenberger and James, 1984).
     The basic analyses performed by the various programs in RAINPAK can be
summarized as follows:

     1.  Storm Dynamics Analysis (STOVEL)
     2.  Cell Calibration  (THOR4DPT)
     3.  Hyetograph Synthesis  (THOR4D, THOR3D)

                                     STOVEL
     STOVEL  (STOrm VELocity) is  logically  the  first program used in a hydrologic
analysis. Using  at least three hyetographs, STOVEL provides an estimate of the
speed and direction of a storm cell. In  addition, STOVEL examines  patterns of
growth  and  decay associated  with the  storm lifetimes.  As  cells move across  a
study area,  optimum  relationships  are  determined which define characteristic
cell development.
     Thunderstorms display intense,  short  duration  rainfall,  rapidly  varied
spatially.  Due  to variabilities  in  wind, terrain (natural  and man-made),
moisture availability etc.,  each hyetograph displays  variability,  but certain
features,  such  as peak intensity and  duration, may  be  identified,  even  for  the
more common  complex  multicell  thunderstorm (Huff, 1967).
     The drawback to  tracking  an identifiable feature  of  a storm is the
subjectivity involved, as  well as  the  lengthy processing  time (Shearman,  1977).
     Thunderstorm cells  generally preserve their shape (especially over short
distances).  Persistence  of speed and  direction has  been observed over several
hours  (Moses, 1981).  STOVEL  estimates  the speed and direction of a cell by
tracking an  identifiable feature between gauging stations, noting the relative
                                      88

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timing. In STOVEL the peak intensity was chosen rather than the start or end  of
rainfall for two reasons: firstly the start and especially the end of rainfall
are highly influenced by environmental conditions, much more than the peak
intensity; secondly because of the isotropic nature of thunderstorm  rainfall,
the observed peak intensity is closely correlated with the observed  volume of
event rainfall at any gauging site.
     The Cartesian coordinates of at least three raingauges and the  relative
time of peak at each gauge are required by STOVEL to estimate the direction and
speed of a storm cell. Every combination of three raingauges produces a cell
speed vector. When more than three gauges are used, an arithmetic and weighted
average of storm cell velocity vectors is determined. The weighted average is
based on the  inverse of the distance between gauges, i.e., the perimeter  of the
triad of gauges. The idea  is based on the tendency for uniform structure  to be
strong  on short paths but  subsequently decrease with increasing path length
(Orufuca, 1978). This weighting  approach is  similar to that used  by  Kelway  and
Herbert  (1969). When the difference between  arithmetic and weighted  vectors  is
large,  the  inverse  perimeter weighted vector  is preferred.
      In addition to speed  and direction, STOVEL determines the locus of the
storm  cell.  The most  intense  rainfall typically occurs  near or at the centre  of
the  cell  area. A locus will  invariably  be  produced within the  gauging network
area using  this  technique. This  will  only  be a  disadvantage when  the area
defined by  the  network  is  considerably  smaller  than  the  catchment under
analysis.  Nguyen et al  (1978) proposed  a  similar  approach based  on hourly
timesteps.
      When  more  than three  gauges exist, it is unlikely that  the  average velocity
vector determined  by STOVEL will produce  peak times  identical  to those observed.
Therefore,  the  time-to-peak at  each rain  gauge is recalculated using a least-
                                       89

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squares fit, adjusting computed times closer to those observed. The relative
temporal position of the computed  peak times is maintained. In order to model a
thunderstorm's rainfall intensity variation in time, STOVEL analyzes the peak
intensity at each gauge. A non-linear curve is fitted to the peak intensities
and their time of occurrence.  The curve allows the  computed thunderstorm cell to
grow and/or decay while moving across a study area.
     The output, which can be  used directly by one  or more of  the other programs
in RAINPAK without  any additional user  intervention,  is:
      1)  date of storm event
     ii)  listing of all  possible triad combinations,
          their computed directions, speeds and perimeters
    ill)  arithmetic and perimeter-weighted average storm velocity
          vector and its standard deviation.
 The following are output for  both the arithmetic and inverse  perimeter weighted
 average storm velocity vectors:
    (iv)  hyetograph start time
     (v)  time for storm cell  to reach first gauge
    (vi)  equation of storm track, x, y, intercepts
   (vii)  parabolic growth and decay function constants
  (viii)  indicator of possible problematical raingauge
    (ix)  timing sensitivity analysis

      The standard deviation of the average velocity vector, meaningful for two
 or more triad combimations, is provided in units of degrees and km/h. It is
 extremely useful for assessing the reliability of  the determination.
      All gauges in a triad combination producing a storm velocity vector, whose
 direction is more than one standard deviation from the mean,  are flagged as
 possible sources of timing error. This can also result in several 'accurate1
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gauges being flagged. However, gauges with 'significant' timing errors will be
flagged in several erroneous vector determinations. A table 'Indicator of
Possible Problematical Raingauge' is provided showing all such occurrences. By
removing the 'most' erroneous gauge from the analysis, the standard deviation
will be reduced, thereby improving the reliability of the determination.
     In addition, a timing sensitivity analysis is carried out. The time-to-peak
at each raingauge is automatically altered plus and minus one user-specified
time increment (this increment is usually the minimum resolution of the
hyetograph). This is repeated for every raingauge and the resultant velocity
vector and its standard deviation are determined.
THOR40PT
     THOR4DPT is the next program to follow a STOVEL analysis.  Using the  output
from STOVEL, THOR4DPT is used to compute hyetographs at the raingauge locations
used in the STOVEL analysis.  In  the THOR40PT  'storm calibration1 procedure,
cellular shape and dimensions are systematically varied to optimize the  degree-
of-fit between observed and computed hyeto- graphs. The key objective functions
used to assess goodness of fit are:
     a)  total precipitation
     b)  peak rainfall intensity
     c)  shape (timing of peak)
     d)  duration
     The theoretical  storm cell  shape incorporated in the methodology compares
closely with those described  by  many earlier  works. THOR4DPT  incorporates  the
following  assumptions:
     1.  Storm cells  are  generally  oblong, may  be  approximated  by  an  ellipse
         with circular being  a special  case,  and  remain so throughout their
         lifetime.
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     2.  Peak rainfall  intensity is located at the centre of the specified
         shape.
     3.  Rainfall  intensity away from the centre varies exponentially,
         decreasing to  a user specified level at the cell boundary (i.e. a
         circular  cell  would have an isotropic distribution).
     4.  Storms can be  multicellular, where cells are free to merge and overlap
         (Kelway and Herber, 1969).
     5.  Rainfall  cells are oriented with their own axes parallel to  its motion
         (NOTE: in a study of over 542 cells  in the Montreal area, over 60%
         conformed to this  (BelIon and Austin, 1977).
     The location of the thunderstorm cell is computationally controlled by
moving the geometric storm centre by an incremental distance. The computational
time increment  in THOR4DPT is one minute. The STOVEL determined  cell  speed and
direction are  used to define the incremental  distance.
     During  the life cycle of a typical thunderstorm cell,  several cell
properties constantly change. THOR40PT has also been provided with four time
varying functions:
     1)  peak  cell  rainfall intensity
     2)  cell  areal coverage
     3)  cell  speed
     4)  cell  direction
     The growth/decay of peak rainfall  intensity  is accounted for by  the
parabolic relation  determined by STOVEL.  In  THOR4DPT exponential  functions can
be used to vary both peak  rainfall  intensity and  areal  coverage. The  other two
cell properties addressed  are speed  and direction;  a starting speed  and/or
direction is specified  and  then  a  time  rate  of  change  estimated  (i.e.
acceleration or deceleration  and counter-clockwise  or  clockwise  rotation).
     Two types of  data  are  required, meteorologic and  geographic.  Meteorologic
input  consists of:
     1.      peak cell  intensity
     2.      cell shape  and  dimensions
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     3.     boundary rainfall  intensity
     4.     area, speed and direction as time dependant functions
     5.     eel 1  speed
     6.     cell  direction
     7.  Cartesian coordinates at start time of cell centre
     8.  peak growth/decay modulating function.
The first three parameters are revised by the storm calibration procedure.
Parameter 4 is .optional.  STOVEL provides parameters 5 through 8.
     Starting values for the first three parameters may be estimated from
hyetographs  prior to  calibration.
     For a given cell, the hyetograph observed at any number of raingauges will
have approximately the same duration (exceptions include gauges located on the
periphery of a storm cell). Also the peak intensities of the raingauges located
nearest to the determined cell track can be used for an initial estimate of  the
peak rainfall intensity of the cell.
     The two remaining input parameters, the transverse cell dimension  (only
applicable to ellipses) and the cell boundary  rainfall intensities, can be
considered to be calibration parameters. Initial values of these  parameters  can
be estimated by  using: transverse dimension =  longitudinal dimension and cell
boundary rainfall  intensity equal to one-twentieth  of  peak intensity.  Although
arbitrary, these parameters converge reasonably quickly to  'acceptable*  values.
A comprehensive  chart  has  been prepared which  describes the  use  and effect  of
these  calibration  parameters  (the chart appears in  the RAINPAK -  Users Manual).
     The only geographic  data  required  by THOR4DPT  are the  raingauge Cartesian
coordinates,  identical to that required by  STOVEL.
     The output  from  THOR4DPT  consists  of computed  hyetographs and rainfall
totals at  the  specified  raingauge  locations.  If the computed and observed
                                     93

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hyetographs do not compare favourably, appropriate changes should be made to the
calibration parameters. Of course, discrepancies will always exist between
observed and simulated hyetographs, especially  in densely gauged areas. Some of
the possible reasons  are:
     1.  the idealized cell  rainfall  distribution
     2.  turbulence caused  by wind  eddies  around  geographic
         features, both  natural  and man-made
     3.  incomplete,  irregular merging  of  cells
     4.  data  timing  and  recording  errors
     5.  cells missing gauges entirely

                                      THOR4D
     THOR4D is identical  to  THOR4DPT  but  rather than computing point  rainfall
intensities, THOR40 produces time and areally-averaged  hyetographs  for  sub-
areas.  Thus THOR4D determines the average  rainfall  hyetograph  falling over every
subcatchment within a larger watershed  for use  as  input for  a  hydrologlcal
program such as  the SWMM.  The higher  the  level  of  discretization  of the water-
shed, the  higher the  level  of discretization  of the storm. By  utilizing the
meteorologic data determined by STOVEL  and THOR4DPT, in addition  to geographic
input,  THOR4D  develops sub-basin wide averaged  rainfall input  incorporating  all
of the  characteristics of kinematic  storms.
     Subcatchments are laid  out on  the  same Cartesian plane  as the  raingauges  in
the STOVEL analysis.  Subcatchments  can  take on  an  infinite number of  irregular
shapes,  however  these shapes can become increasingly regular,  especially  in
urban centres, where  drainage pipe  networks rather than physical  terrain  usually
dictate  subcatchment  delineation. Often,  for  the usual  North-American grid-
style urban centres,  Subcatchments  are  approximately rectangular.
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     Rectangular subcatchments have been adopted as the most practical areal
representation in THOR4D thereby reducing the data abstraction effort
substantially.
     In THOR4D, point rainfall intensity is averaged areally by double numerical
integration. Trapezoidal integration is used when integrating the theoretical
exponential  'raincone'  because the more complex numerical integration routines
investigated showed no significant improvement in accuracy despite their higher
computing costs.
     Numerical experiments were carried out on the number of points representing
a rectangular subcatchment. This is the most computationally intensive sub-
routine in TMOR4D. Sensitivity analysis showed a small increase in accuracy when
the number of divisions along a subcatchment dimension increases beyond 5.
     The meteorological data  required by THOR4D is identical to that  required by
THOR4DPT and provided by STOVEL. The geographic data describing the subcatch-
ments must be acquired  from maps. Five data items are required to represent
subcatchment orientation and  configuration in a Cartesian plane.
     The first of the items are the co-ordinates of the  subcatchment  centroid.
The centroid of  a rectangle is simple to obtain, however  highly irregular  shapes
present difficulty. Subjective estimates should generally be adequate
(Scheckenberger  and James, 1984). Nonetheless,  a sensitivity analysis on the
location of the  areal centroids to  determine their  influence on runoff  charact-
eristics is recommended.
     The other  four data  items  required  are weighted  widths in  the  N-S,  E-W and
NW-SE,  NE-SW  directions.  Since  very few  subcatchments  will  be  aligned in  a
purely  N-S  or  NW-SE orientation,  it proved  convenient  to adopt  two  co-ordinate
systems  in  THOR40. The  assumption  is that  when  several  subcatchments  exist in a
                                      95

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watershed, their orientation will best be approximated by a mixture of both
co-ordinate systems. Practice has shown that usually more than two-thirds of the
subcatchments are common to both co-ordinate systems (Scheckenberger and James,
1984).
     THOR4D output comprises SWMM formatted hyetographs at a user specified
timestep, one hyetograph for every  subcatchment.  It was necessary to change the
SWMM code to accept more than six hyetographs.

                                     THOR3D
     Unlike the other  programs  in RAINPAK, THOR3D does not necessarily require
observed  rainfall for  input.  THOR3D develops design storms. Typical use of
THOR3D would be to develop  kinematic ranfall input  for a  rainfall/runoff model.
Critical  storm speeds,  directions and  distributions of rainfall can be deter-
mined which would significantly aid in the design of safer, more efficient
drainage  networks. Another  possible use of a slightly revamped THOR3D is for
flood warning; real-time analysis of rainfall from  remote raingauges could
produce  rainfall  input  for  a flood  model.
     In  THOR3D the dimension transverse to storm  motion is infinite. This shape
is more  conservative from a flood design  standpoint*
     Unlike THOR4D, the peak intensity may be located anywhere within the cell,
e.g. as  in the quartile rainfall distributions  (Huff, 1967). Huff showed that
the location of peak rainfall  intensity within  a  rain period can be a regional
characteristic. The location of the peak  can be critical  for drainage network
design.  Since the dynamics  of  flow  in  drainage  networks,  particularly large
urban centres, is unique to the system, various networks  can be more or  less
affected  by the same temporal  and spatial distribution. THOR30 affords the
                                     96

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engineer the flexibility to vary the location of the peak intensity to determine
the most severe design case unique to the particular drainage network under
analysis. The position of the peak intensity is specified by the ratio of the
time of hyetograph recession to the time of hyetograph rise.
     THOR3D is not used to simulate observed events: no provision has been made
to synchronize the timing of computed and observed rainfall  movement over a
catchment area. In THOR30 the leading edge of the line-storm is assumed to be
located at the outermost cardinal boundary of the catchment area at computation
time zero. THOR3D internally determines eight outermost catchment boundaries in
the N, NEf E, SE, S, SW, W and NW directions respectively.
     Similar to THOR4D, THOR3D requires a minimum 'cutoff rainfall intensity at
the leading and trailing edges of the line storm. This parameter is used in con-
junction with the time of hyetograph rise to determine the exponential rising
constant.
     In THOR30 the minimum rainfall intensity is used in a pseudo-calibration
manner. For a given total precipitation during a rainfall event, a range of peak
intensities within the same storm duration can be obtained by varying the
minimum rainfall intensity (i.e. the higher the minimum rainfall intensity, the
lower the peak rainfall intensity and vice-versa). This is accomplished intern-
ally in THOR3D, through the use of continuity equations which preserve total
precipitation as well as the  ratio of time of recession to time of rise. In
THOR3D, the user specifies:
       1)  Total precipitation (TOPR)
       2)  Time of recession/Time of rise  (RCSNFR)
       3)  Minimum rainfall intensity as a fraction of the peak  intensity
           (PKFRI)
                                      97

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       and either
       4)  Peak one-minute rainfall intensity (PEAK)
       or
       4)  Time of hyetograph rise (TMRISE)
     Provision has been made in THOR3D to simulate more than one line storm
during a single event, analogous to the multi-cellular capability of THOR4D.  In
THOR3D each line storm must be completely parameterized and a lagtime is
required to separate cell occurrences. Again, as  in THOR4D, line storms are
allowed to merge and overlap with  one another. This is a feature in THOR3D which
can be used to pre-wet a watershed to various degrees of saturation prior to  the
application of a design storm, similar to continuous hydrologic modelling. With
slight modifications, THOR3D, could produce  a continuous dynamic rainfall record
for every subcatchment, thereby replacing synthetic design storm methodology.
     The spatial orientation and configuration of subcatchments are represented
numerically in exactly the same manner as in THOR4D. The exponential growth-
decay of the peak intensity of the line storm is  also provided  in THOR30.
     The output format and usage of THOR30 is identical to that of THOR4D. The
engineer can examine the effects of storm dynamics on urban drainage system
response. Runoff characteristics such as peak flov», volume of runoff, hydrograph
shape and system storage are highly influenced by storm characteristics such  as
speed, direction and time distribution. Design engineers can use THOR3D to
perform a comprehensive sensitivity analysis determining which  storm
characteristics are most critical  to the runoff characteristics for  the
drainage  network  under  analysis.
                                      98

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                                ACKNOWLEDGEMENTS

     Funding for this research was supplied by research grants to Dr. James by

the Natural Science and Engineering Research Council,  Inland Waters Directorate,

Employment and Irmiigration Canada, the Ministry of the Environment and Hamilton-

Wentworth Regional  Engineering Department.  The contributions from these

agencies is most gratefully appreciated.


                                  BIBLIOGRAPHY


1.  Amorocho, J., "Stochastic Modelling of Precipitation in Space and Time",
presented at the International Symposium on Rainfall-Runoff Modelling,
Mississippi State University, 20 pp. May 1981.

2.  Aron, G., Riley, K.A. and Kibler, D.F., "Sensitivity of Urban Flood Peaks to
Rainfall Intensity Patterns", 15 pp., 1982.

3.  Bel Ion, A., and Austin, G., "The Real-Time Test and Evaluation of 'SHARP'. A
Short Term Precipitation Forecasting Procedure", Quebec, 19 pp. March 1977.

4.  Beven, K.J. and Hornberger, G.M., "Assessing the Effect of Spatial Pattern
of Precipitation in Modelling Stream Flow Hydrographs", Water Resources
Bulletin, Vol. 18, No. 5, October, 1982.

5.  Colyer, P.J., "The Variation of Rainfall Over an Urban Catchment", presented
at the Second International Conference on Urban Storm Drainage, Illinois, June,
1981, Wallingford, England, Report No. IT211, pp. 19-26, January 1981.

6.  Drufuca, G., and Rogers, R.R., "Statistics of Rainfall over Paths From 1 to
50 km", Atmospheric Environment, Great Britain: Vol. 12, pp. 2333-2342, 1978,

7.  Huff, F.A., "Time Distribution of Rainfall in Heavy Storms", Water Resources
Research, Vol. 3, No. 4, pp. 1007-1019, 1967.

8.  Huff, F.A., Vogel, J.L. and Changnon, Jr. S.A., "Real-Time Rainfall
Monitoring - Prediction System and Urban Hydrologic Operations", Journal of the
Water Resources Planning and Management, ASCE, Vol. 107, No. WR2, pp. 419-435,
October 1981.

9.  James, W., and Scheckenberger, R.B.,  "Application of a Kinematic  Storm Model
to Runoff Modelling", EOS, Vol. 63, No. 13, pp. 323, May 1982.

10.  Kelway, P.S. and Herbert, S.I.,  "Short-Term Rainfall Analysis",  Weather,
Vol. 24, pp. 342-353, 1969.
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11.  Marshall, J.K., "Local  Considerations Affecting the Choice  of  Design  Storm
Frequency", Storm Input, p.  19-30, 1980. (uncredited manuscript).

12.   Moses, F.,  "Convective Cloud-Tracking Techniques for Estimating
Precipitation from Geostationary Imagery", Preprint Fourth Conference on
Hydrometeorology, Reno, Nevada, pp. 151-158, October 7-9, 1981.
13.  Niemczynowicz, J. and Jonsson, 0., "Extreme Rainfall Events in Lund
1979-1980", Nordic Hydrology, Vol. 12, pp. 127-142, 1981.

14.  Nguyen, V., McPherson, M.B., and Rousselle, J., "Feasability of Storm
Tracking for Automatic Control of Combined Sewer Systems", ASCE, New York,
Technical Memorandum No. 35, 29 pp. November 1978.

15.  Robinson, M.A. and James, W., "Continuous SWMM Modelling of Hamilton  Summer
Stormwater  Including Certain Quality  Indicators - Preliminary Output Time  Series
Using Discrete-Event Calibration  for  Non-Industrial Areas", McMaster University,
Hamilton, Ontario, Canada, January 1982.

16.  Scheckenberger, R.B. and James,  W.,  "RAINPAK - User's Manual", to  be
published by CHI Publications, 1984.

17.  Shearman, R.J., "The Speed and Direction of Movement of Storm Rainfall
Patterns",  Meteorological Office, Brachnell, Berkshire, England, March  1977.

18.  Troutman, B.M.,  'The Effect  of Input Errors in Using Precipitation Runoff
Models for  Runoff  Prediction", International Symposium on Rainfall-Runoff
Modelling,  sponsored by the WRR,  12 pp. May 1981.

19.  Wilson, C.B., Valdes, J.B. and Rodrigues,  Iturbe,  I., "On the Influence of
the Spatial Distribution of Rainfall  in Storm Runoff", Water Resources  Research,
Vol. 15, No. 2 pp.  321-328, April  1979.
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                     DEVELOPMENT OF FLOWS AND LOADS FOR
                        STEADY-STATE ESTUARY MODELS:
                            TAMPA BAY CASE STUDY

                                     By      i
                          Sue A. Hanson, P.E.  and
                          John P.  Hartigan,  P.E.
INTRODUCTION
An Intensive waste!oad allocation study of the Tampa Bay region is cur-
rently being undertaken by the Florida Department of Environmental  Regula-
tion.  Previous effluent standards were typically set at "zero discharge"
for both Industry and sanitary sewage treatment plants.   This wasteload
allocation study being undertaken by the DER is the first comprehensive
analysis of the eutrophication problem of Tampa Bay and  is the first of its
kind within the State of Florida.

The study is using the University of South Florida's (USF)  Tampa Bay Model
(1).  It is an intratidal estuary model which simulates  hydrodynamics and
mass transport over relatively short time intervals within the 12.4-hour
tidal cycle.  Because of the prohibitive computer costs  associated with
running such a model  with long-term, time-variable nonpoint source inputs,
the model is being used instead for steady-state analyses.   It is the
purpose of this paper to describe the methodology used to calculate the
flows and loads required as input to the steady-state model  (2).

This methodology can be applied to other estuary drainage areas which have
adequate databases to determine flows and loading factors.   It is important
to note that the types of data used in this study are available to the
general public for other areas all over the United States.

STUDY AREA DESCRIPTION

The Tampa Bay study area presented in Figure 1 consists  of three distinct
bays: Old Tampa Bay, Hillsborough Bay and the main portion of Tampa Bay.
More than 50 percent of the 1,785 square mile (sq mi) drainage area drains
into Hillsborough Bay.  Most of the flow from this area  is regulated by the
Hillsborough Reservoir, a water supply impoundment which is located at the
1  Water Resources Engineer, Camp Dresser & McKee Inc., Annandale, VA 22003
2  Senior Engineer, Camp Dresser & McKee Inc., Annandale, VA  22003
                                   101

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11 isborough
i.. River Ji
     •JlHinsboroughKy-
           Bay
  TAMPA BAY STUDY AREA
         FIGURE  1
           102

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mouth of Hillsborough River.  Tampa Bay also has  an  unusual  characteristic.
Due to the natural  phosphate deposits in the area which  is  inherent in  the
runoff, algal  growth throughout the Bay is  limited not by phosphorus but
instead by nitrogen.

The flows and  loads for input to the estuary model were  calculated  for  the
38 points shown in  Figure 2.  These points  represent not only  river con-
fluences but also points of stormwater inflow.  The  flows and  loads were
then used as input  to the grid system of the USF  Model shown in  Figure  3.

DESCRIPTION OF METHODOLOGY

Introduction.   Point source waste!oad allocation  studies for estuaries  are
typically based upon low streamflows (7Q10  values) and the  assumption of
continuous, constant wastewater loadings for a  duration  that allows the
system to reach steady-state.   One of the major advantages  of  steady-state
estuary modeling studies is that the modeler does not have  to  be concerned
about accurately defining the  initial  water quality  conditions at the start
of the simulation period.  This is because  the  assumed initial conditions
do not affect  the final  steady-state concentration calculated  by the
estuary, model.

Nonpoint source studies of estuaries have generally  applied one  of  two
types of loading characteristics:  average annual  loads or loads  produced by
design storms.  The average annual  loads cannot accurately  predict  "worst
case" impacts.  On  the other hand, design storms  may not be appropriate for
areas requiring a longer time  period to reach steady-state.

In this study, we chose to determine a range of flow and load  values that
would encompass all possible study alternatives.   We set up different
recurrence intervals and the different duration periods  to  reach steady-
state conditions.  Several  assumptions had  to be  addressed  concerning these
parameters.

Flow-Frequency Analysis.  In this study, flows  were  calculated based on the
pervious and impervious percentage in each  land use.  USGS  streamflow
gaging statistics (inches of runoff) were applied to the pervious sections
of the Tampa Bay drainage area, and rainfall records were used to develop
runoff from the impervious fraction, typically  for portions of urban land
uses only.

Because of the positive relationship between flow and nonpoint pollution
load (3), the resulting receiving water quality calculated  by  the estuary
model can be assumed to have the same frequency of occurrence  as the flow
condition.  The flow event and the resulting water quality  condition in the
estuary are assumed to be completely dependent  events, meaning that the
probability of their joint occurrence is equal  to the probability of either
event occurring.  These assumptions are critical  to  the  assessment  of the
recurrence Interval associated with estuary model projections  of water
quality impacts from nonpoint pollution loadings.
                                     T03

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NODES REPRESENTING INFLOW POINTS FOR BASIN FLOWS AND LOADINGS
                          FIGURE 2
                             104

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The frequency of occurrence is also important on a bay-wide scale.  If the
entire area did not produce synoptic streamflows of the same frequency of
occurrence, then individual basin flows developed from the statistical
analysis could not be used to produce the same frequency of occurrence for
the bay-wide water quality projections.  However, an analysis of streamflow
records in the Tampa Bay region indicated that the major tributary basins
have exhibited synoptic flows approximating each flow statistic (i.e.,
2-year, 10-year, 25-year recurrence intervals).  Therefore, statistically
generated flows can be applied to the USF Model.

Ideally, the frequency of occurrence of the design flow period for estu-
aries should reflect the spatial and temporal characteristics of the bene-
ficial use(s) to be protected or achieved.  The protection of certain
beneficial uses (e.g., fisheries) may require that a minimum dissolved
oxygen concentration of 5 mg/1 be maintained in every segment of the es-
tuary for the entire year.  This would indicate the use of a relatively
infrequent design low flow condition to minimize risks of significant use
impairment.  By comparison, the protection of other beneficial  uses may not
require the maintenance of the 5 mg/1 dissolved oxygen level  at all  times
and locations.  Instead, only a survival-type of environment need be main-
tained at all times.  The latter situation lends itself to the use of a
design low flow with a shorter recurrence interval  than the first.  The
recurrence Intervals chosen for this study were the 2-, 5-, 10-, 20- and
25-year intervals.

Design Flow Durations.  For the Tampa Bay waste!oad allocation study, the
most important factor in the selection of the duration of the design flow
conditions is the time required for different sections of the estuary to
reach an equilibrium concentration under steady-state conditions.   USF has
found that the simulation period required for concentrations in the estuary
to reach equilibrium under steady-state flow and loading conditions is on
the order of 3 to 4 weeks based on previous baywide studies.   Time to
equilibrium conditions is typically shorter for portions of the upper
estuary (e.g., upper Hillsborough Bay)  due to the smaller storage volumes
and shorter transport times, and even shorter for studies of nearfield
water quality in sections of the estuary which adjoin major discharge
points.

Since the duration of the flow and loading input should correspond to the
required time to reach steady-state, this study developed streamflow esti-
mates for three different durations which will  permit both nearfield and
farfield assessments: 7-day, 15-day, and 30-day.   The 7-day flow condition
permits nearfield assessments, while the 30-day flow condition  1s  used for
baywide assessments.  The 15-day value  is appropriate for Intermediate
scale assessments 1n cases where a 30-day response  time is excessive.

Thunderstorm Scenario.   Nearfield areas which adjoin the urban  areas drain-
ing into Tampa Bay are likely to experience the greatest water quality
impact from urban runoff slug loads.  Due to the stabilizing influence of
impervious cover,  urban runoff volumes  tend to be relatively similar
throughout the wet season whereas nonurban runoff volumes tend to  be higher

                                    106

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In August and September due to the increase in soil  moisture and saturated
pervious areas that occur as the wet season progresses.

Therefore, the most critical  portion of the wet season  for  urban runoff
impacts is the month of June when nonurban flows are relatively  low and
rainfall is relatively high.   In order to  assess the potential impacts  from
urban runoff early in the wet season, an isolated thunderstorm flow sce-
nario (3-hr/6-month design storm) was developed for  testing with the
estuary model.

The thunderstorm scenario assumes that urban runoff  will  be produced by a
short duration/high intensity rainstorm in subbasins adjoining the  estuary.
The actual USF Model  simulation of the thunderstorm  impacts is dynamic  in
nature.  The storm loads are applied to boundary conditions representing
average June flow conditions.  Once the storm event  has ended, the  average
June flows will again be simulated, using  as initial  conditions  the slug
concentrations derived from the storm.  This will  allow the simulation  to
track the impact of the thunderstorm loads after the conclusion  of  the
storm event.

DEVELOPMENT OF FLOWS AND LOADS FOR ESTUARY MODEL INPUT

Land Use Character}sties.  The calculations of the flows  and loads  were
based upon individual  land uses within each river basin.  The land  use
delineation was chosen for two reasons.  First, the  water quality data
available for the rivers in this area are  highly biased by  land  use char-
acteristics of the basin (e.g., phosphate  mines in the  Alafia River basin).
The application of these data to other ungaged basins would require similar
land uses, soil and streamflow characteristics within the two basins.
Second, the calculation of the flows and loads by land  uses permits a more
accurate projection of future land use impacts and the  reductions in
loadings due to the implementation of best management practices.  The
existing land uses within the Tampa Bay drainage area are presented in
Table 1.  More than 75 percent of the basin is covered  by undeveloped land.

Flow Calculations.  The flow calculations  were based on the pervious and
impervious areas of each land use.  Rainfall statistics were used to cal-
culate the runoff from the impervious areas (typically  in urban  areas only)
and streamflow gaging statistics were used to calculate the runoff  from the
pervious areas.  Rainfall records were analyzed to coincide with the
duration/frequency scenarios set for the streamflow  statistics.

The streamflow statistics were based upon  the data available for the eight
US6S stations presented in Table 2 and Figure 4.  Drainage  areas ranged
from 35 to 650 square miles.  Land uses in each basin were  typically rural/
agricultural.  The soil characteristics presented in Figure 4 were  one  of
the criteria.used to assign the gaged basins to ungaged basins.

The statistical analysis package was accessed throught  the  STORET database
at the EPA Computer Facility in Research Triangle Park, NC.  The high and
                                    107

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                                  TABLE 1

                          EXISTING LAND USE WITHIN
                   TAMPA BAY DRAINAGE AEA (1,785 sq. mi.)
              Land Use                         % of Total Area
         Forest                                16.6
         Cropland                              17.6
                                                            76.8%
         Pasture                               38.9
         Other Rural                            3.7
         Urban Residential                     14.2
         (Single & Multi-Family)
         Urban Commercial                       5.5
                                                            23.2%
         Urban Industrial                       1.5
         Urban Other                            2.0
         (Recreational and Open Space)
                                       TOTAL:              100.OX
Note:  This table does not include water surface area for Tampa Bay,
                                    108

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            82°45
                                                                 82° 00'
28«I5' -
28*00* -
27-45' -
                                             HILLS80ROUGH .,,£* /COUNTY
                         (S^-r   i
                     ST. PETERSBURG
         EXPLANATION
    _SOIL- INFILTRATION  INDEX
      SUBAREA BOUNDARY

1.90 S01L"|NF|LTRATION
                                   MANATEE COUNTY
        • B  USGS Gage Station
              TAMPA BAY  REGION MAP SHOWING USGS STREAMGAGES AND
                     SOIL INFILTRATION  INDEX


                                FIGURE 4

              SOURCE:  LOPEZ AND WOODHAM,  1983
                                   109

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                                  TABLE 2

    USGS GAGES USED IN RIVER BASIN STREAMFLOW AND WATER QUALITY ANALYSIS
Map                                                         Drainage
Key*     	USGS Gage	        Area
 A       02304500:  Hlllsborough River near Tampa, FT.      650 sq.  ml.
 B       02303000:  Hlllsborough River near                 220 sq.  ml.
                    Zephyrhllls, Fl.**
 C       02302500:  Blackwater Creek near Knights, Fl.      110 sq.  ml.
 D       02301500:  Alafla River at Llthia, Fl. **          335 sq.  ml.
 E       02301000:  North Prong Alafla River                135 sq.  ml.
                    at Keysvllle, Fl .**
 F       02300500:  Little Manatee River                    149 sq.  ml.
                    near Wlmauma, Fl.**
 G       02307000:  Rocky Creek                             35 sq. ml.
                    near Sulphur Springs, Fl .**
 H       02301300:  South Prong Alafla River                107 sq.  ml.
                    near L1th1a, Fl.**
*  See Figure 4
** Used for loading factor calculations
                                     no

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low flow statistics were developed based upon a Log-Pearson  Type III  dis-
tribution.  It should be noted that the STORE! flow data and statistical
package are available to the general  public and can be accessed with
relative ease.

The flows generated by the statistical  package were converted to inches  of
runoff.  This allowed us to use the Individual  land use acreage, the  dura-
tion of the flow and loading averaging  period, and  the inches of runoff  to
calculate the flow for each particular  input point  to  the model.  The total
flow for any of the six land uses was the weighted  average of the pervious
and Impervious flows of the land use.  The total  flow  for the Input points
was then the summation of the flows from the Individual  land uses.

Load Calculations.  Loading factors were developed  for each  of the  land
uses for each of the following constituents: total  phosphorus, ortho-
phosphorus, organic phosphorus, total nitrogen, ammonia,  TKN, organic
nitrogen, nitrate-nitrite, BODg and dissolved oxygen.   The USEPA Nationwide
Urban Runoff Program (NURP) database for the Tampa  Bay area  was used  to
develop the loading factors for the urban land uses.(4,  5).   The USGS
NASQAN  database was used to develop the loading factors for the rural/
agricultural runoff.  Once the factors  were developed, they  were verified
by applying them to the USGS Urban Watershed study  area (6,  7, 8) and
comparing our final calculations with the observed  data.

The NURP data were acquired from 5 single land use  watersheds varying 1n
size from 9 to 194 acres.  The USGS NASQAN data were from the six stations
specified In Table 2.  The measured concentration datasets were checked  for
a normal or log-normal  distribution based upon the  one-sided Kolmogorov-
Smirnov (K-S) statistical test.  Once the distribution was established,
mean concentrations for each constituent were calculated based upon the
distribution.

The loading factors developed for the rural/agricultural  land use at  each
of the six USGS stations are presented  in Tables 3  and 4 for the wet  season
and dry season, respectively.  The factors for the  wet season were  applied
to the high flow conditions and the dry season factors were  applied to the
low flow conditions.  The factors were  then assigned to the  ungaged basins
dependent upon similar hydrologlc characteristics and  other  basin
characteristics (7, 8, 9).  These assignments are present in Table  5.

The final urban land use loading factors are presented in Table 6.  The
test basins listed in the table are the NURP watersheds which we used to
develop these factors.  These factors were applied  to  the runoff from both
the previous and impervious areas of each land use.

The validity of the urban land use loading factors  was verified with  the
data from a USGS Urban Watershed study  1n the Tampa Bay region.  The  9 USGS
test watersheds consisted of mixed land uses and ranged In size from  0.45
to 3.45 sq ml.  Three statistical tests were used to determine the
goodness-of-fit of the calculated loadings values with the observed values:
                                     111

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                                                                      TABLE  3
                                             MEAN  CONCENTRATION  FOR USGS  RIVER  8ASIN  DATABASE:  WET SEASON
ro
CONSTITUENT
Ortho-P (mg/L as P)
Total P (mg/L as H)
Ammonia N (mg/ L as N)
TKN (mg/L as N)
Nitrite + Nitrate-H (mg/ L as N)
Total N (mg/L as N)
B005 (mg/L)
Dissolved Oxygen (ng/L)
Flow (cfs)
NOTES:
1. KEY: Mean Concentration/Type
LITTLE
MANATEE R.
0.50/LN*
(27)
0.53/LN
(27)
0.06/N
(21)
0.85/N
(21)
0.1 8/N
(32)
1.05/N
(21)
1.78/LN
(4)
6.3 /N
(23)
147.2 /LN
(35)
of Distribution
N. PRONG
ALAFIA R.
6.66/N
(10)
6.84/N
(10)
0,59/LN
(10)
1.26/LN
(10)
2.76/LN
(10)
3.90/LN
(10)
-
5.1 /N
(9)
221.9 /LN
(ID
where N = Normal
S. PRONG
ALAFIA (J.
2.0P/N
(9)
2.19/N
(9)
0.06/LN
(9)
0.82/LM*
(9)
0.18/LN
(9)
1.00/L"*
(9)
-
6.9 /N
(9)
143.3 /LN
(9)
Distribution
ALAFIA R.
AT LITHIA
4.56/N
(16)
4.74/N
(16)
0.12/LN
(15)
0.9B/LN
(14)
1.41/LN
(15)
2.25/LN
(14)
-
6.6 /N
(15)
446. 0 /LN*
OR).
and LN = LognormaT
HILLS. R. AT
ZEPHYRHTLLS
0.80/LN
(29)
O.R4/LN
(34)
0.29/LN
(36)
1.16/LN
(34)
1.18/LN
(39)
2.27/LN
(34)
1.52/LN*
(3)
5.7 /N
(32)
241.2 /LN
(41)
Distribution
ROCKY
CREEK
0.18/LN
(23)
0.21/LN
(23)
0.18/LN
(21)
1.02/LN
(18)
0.18/N
(27)
1.21/LN
(18)
1.40/N*
(3)
3.9 /LN
(23)
50.7 /LN
(34)

                          (Number of Observations)
           2.   Means  are  based upon the period 1976 - 1981 for Alafia River gages and the  period HY 1969 -  WY 1981 for all  other gages.
           3.   Distribution which did not pass the one-sided K-S test for 95* confidence interval  is indicated by * {e.g., N*)

-------
                                                           TABLE  4
                                  MEAN CONCENTRATION FOR US6S RIVER BASIN DATABASE:   DRY  SEASON
CONSTITUENT
Ortho-P (mg/L as P)
Total P (mg/L as P)
Ammonia-N (mg/L as N)
TKN {mg/L as N)
Nitrite + Nitrate-N (mg/L as N)
Total ri (rog/L as N)
BOD5 (mg/L)
Dissolved Oxygen (mg/L)
Flow (cfs)
NOTES :
1. KEY: Mean Concentration/Type
LITTLE
MANATEE R.
0.32/N
(62)
0.36/LN*
(62)
0.05/LN
(46)
0.59/LN
(42)
0.26/LH*
(74)
0.84/LN
(42)
0.77/N
(7)
7.4 /N
(50)
78.1 /LH
(83)
of Distribution
N. PRONG
ALAFIA R.
6.83/N*
(24)
7.35/N*
(24)
1.40/N*
(24)
1.85/LN
(24)
3.45/LM
(24)
5.35/LN
(24)
0.9 /N*
(2)
6.7 /N
(22)
93.1 /LM
(26)
where N = Normal
S. PRONG
ALAFIA R.
1.92/N
(19)
2.01/N
(19)
0.07/LN
(18)
0.65/LN
(18)
0.24/N
(19)
0.90/LN
(18)
-
ft. 4 /N
(18)
69.9 /LN
(20)
Distribution
ALAFIA R.
AT LITHIA
4.34/N
(37)
4.49/N
(37)
0.2S/LN*
07}
0.96/LN
(36)
2.10/LN
(37)
3.0S/LN
(36)
1.50/N*
(3)
8.2 /N
(32)
240.0 /LN
(38)
and LN = Lognormal
HILLS. R. AT
ZEPHYRHILLS
0.60/LN
(59)
0.60/LN
(67)
0.59/LN*
(78)
1.21/LN*
(75)
1.47/LN*
(82)
2.71/LN*
(75)
0.50/LN'
(8)
7.0 /N
(68)
119.0 /LN
(38)
Distribution
ROCKY
CREEK
0.09/LN
(55)
0.12/LH
(55)
0.20/LN
(46)
0.91/LN*
(38)
0.22/N*
(63)
1.11/LN
(36)
1.55/N
(11)
4.0 /LN
(43)
20.2/LN
(76)

               (Number of Observations)
2.   Means are based upon the  period  1976  -  1981 for Alafia River gages and the period WY 1969 - MY  19fil  for  all other gages.
3.   Distribution which did not  pass  the one-sided K-S test for 95X confidence interval is  indicated  by  *  (e.g., H*)

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                                  TABLE 5
                 ASSIGNMENT OF USGS WATER QUALITY GAGES TO
           RURAL-AGRICULTURAL SECTIONS OF TAMPA BAY RIVER BASINS
Inflow
Point*
1 & 2
3
3
4 & 5
6
7
8
8
12
9-11,13-16
17-33
34
35
36
37 & 38
River Basin
Interbay E & W
Hillsborough River Upstream of Reservoir
Hillsborough River Downstream of Reservoir
Seddon Channel & Ybor City
Palm River
Delaney Creek
Alafia River Upstream of Lithia Gage
Alafia River Downstream of Lithia Gage
Little Manatee River
Other Eastern Shore Tributaries
Western Shore Tributaries
Lake Tarpon Canal
Double Branch Creek
Rocky Creek
Sweetwater W & E
USGS Gage
Rocky Creek
Zephyrhills
Rocky Creek
Rocky Creek
Rocky Creek
Rocky Creek
Lithia
Little Manatee
Little Manatee
Little Manatee
Rocky Creek
Rocky Creek
Rocky Creek
Rocky Creek
Rocky Creek
*See Figure 2
                                     114

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                                            TABLE 6
                            LOADING FACTORS USED FOR URBAN LANDUSES
                                          Mean Concentration (mg/l)
Land Use
(Test Basin) Total P Ortho-P Total N TKN
Single Family
Res 1 dent I a 1
(CH Only) 0.39 0.19 2.36 t.70
(CH + WD) 0.29 0.11 1.87 1.34
Multi-Family
Residential 0.33 0.16 1.65 t .34
(J.L. Young)
Commercial 0.15 0.08 LIB 0.83
(Nome Park)
Industrial 0.15 0.08 1.18 0.83
(Norma Park)
Institutional 0.20 0.07 1.77 1.39
(N. Jesuit)
Recreational and
Open Space 0.21 0.18 1.21 1.02
(Rocky Creek)
Nltrate-N Ammonla-N BOO

0.66 0.17 T1.7
0.53 0.20 14.3
0-31 0.23 14.8
0.35 0.32 10.9
0.35 0.32 10.9
0.3B 0.27 14.5
0.18 0.18 1.4
1   Nltrate-N represents the sum of Nitrite and Nitrate
2  Mean concentrations based on only the Charter and Harding dataset
3  Mean concentrations based on the pooled Charter and Harding and Wilder Ditch datasets
                                             115

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1) one-sided K-S test (comparing the distributions of the two data sets);
2) F-test (comparing the variances of the data sets); and 3)  t-test
(comparing the means of the data sets).

Load Projections.  In order to highlight some of the Implications of the
selected approach to developing flow and loading inputs,  load calculations
for total nitrogen, total phosphorus and BOD,- are presented in Tables 7
through 9, respectively.  In addition to low flow and high flow inputs for
three different duration-frequency combinations and a thunderstorm
scenario, the Tables also show average annual loading inputs  based upon the
total annual load for a year of average streamflow conditions.  Three input
points were chosen to represent the impacts due to different land use
characteristics.  The Hillsborough River (point 3 in Figure 2) 1s a 650 sq.
ml. basin with a large rural/agricultural area in its upper basin and a
main stem reservoir in the lower portion of the basin.  The Little Manatee
River (point 12) is a 149 sq. ml. basin that is almost entirely rural/
agricultural.  St. Petersburg Airport (point 26) is highly urbanized 17 sq.
mi. basin.

The most important result to note is the difference between the 7Q2 sce-
narios (which represent average conditions associated with 50 percent
probability of occurrence) and the thunderstorm scenario.  No impact is
seen at all from the Little Manatee River as 1t has no urban areas adjoin-
ing the Bay.  Thunderstorm loads from the highly urbanized St. Petersburg
Airport basin are more than double the 7Q2 loads.  The Hillsborough River
thunderstorm loads are much less than the 7Q2 loads because the reservoir
holds back any upstream influence; therefore, urban storm runoff 1s
generated from below the reservoir only.

Another point to note is the difference between the average annual loads
and the high flow loads.  All high flow loads are much greater than the
average annual loads, emphasizing the importance of specifying a design
duration of steady-state conditions for waste!oad allocation studies. A
wasteload allocation study using average annual loads could significantly
underestimate the impact from nonpoint source loads.

The constituent loads from different land uses can also be analyzed in
these tables.  Consider the ratios of the 7Q2 loads to the thunderstorm
loads for the Hillsborough River.  Recalling that the reservoir collects
the upstream flow (which is primarily rural/agricultural) during the
thunderstorm, the thunderstorm loads are only from the highly urbanized
area downstream of the reservoir.  The 7Q2 loads consist of a high pro-
portion of the rural/agricultural loadings.  The ratios of these loads give
an Indication of how much load is attributable to the urban land uses
versus the rural/agricultural land uses.  The nitrogen ratio is 17.7, the
phosphorus ratio is 35.0, and the BOD,- ratio Is 4.2.  The phosphorus ratio
reflects the high natural phosphorus content in the nonpoint source runoff.
The BOD5 load, on the other hand, 1s significantly influenced by the urban
areas.
                                    116

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                                  TABLE 7
                              CALCULATED LOADS
                               TOTAL NITROGEN
                                 (Ibs/day)
    Scenario
Low Flows*
      7Q10
     14Q10
     30Q10
HUlsborough
   River
      146
      146
      152
Little Manatee
    River
        19
        28
        37
St. Petersburg
    Airport
      0.73
       6.3
       7.0
High Flows*
       7Q2
      15Q2
      30Q2
   35,170
   27,160
   19,970
    10,140
     6,800
     4,860
     1,020
       710
       497
Thunderstorm
Average Annual
    1,990

    5,180
         0
     1,140
     2,680

       213
* Inputs for "n-day/1-year"  conditions (I.e.,  7Q10 refers  to 7-day/10-year
  streamflow).
 DISCUSSION
 The actual  flow and  load  calculations presented here are  simple and
 straight-forward.  Similar  data  bases are  available for areas  all over  the
 U.S.  The  general  public  has  easy  access to  this  data.  These  calculations,
 therefore, can be  used  for  any wasteload allocation study.
 However,  the assumptions  we made to  allow  us to make these  simple calcula-
 tions required a thorough Investigation of the basin characteristics, both
                                    117

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                                  TABLE 8
                              CALCULATED LOADS
                              TOTAL PHOSPHORUS
                                  fibs/day)
    Scenario
Low Flows*
      7Q10
     14Q10
     30Q10
HUlsborough
   River
       13
       13
       15
Little Manatee
    River
       8.0
        11
        15
St. Petersburg
    A1 rport
      0.12
       1.0
       1.2
High Flows*
       7Q2
      15Q2
      30Q2
   11,980
    9,260
    6,810
     4,970
     3,340
     2,380
       177
       124
        87
Thunderstorm
Average Annual
      342

    1,490
         0
       520
       447

       *36
* Inputs for "n-day/1-year" conditions (I.e., 7Q10 refers to 7-day/10-year
  streamflow).
 1n terms of flows and loading factors.   It Is here that the engineer would
 have to exercise considerable Judgment In carrying out the analysis.
 Nearfleld and farfleld assessments are critical  In determining the  proper
 steady-state condition to use for estuary modeling.  The examples presented
 here show the Impact of the selected design condition on the loads  genera-
 ted within the Tampa Bay area.  This approach can be used 1n other  waste-
 load allocation studies which depend upon steady-state models.
                                    118

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                                  TABLE 9

                              CALCULATED LOADS
                                    BODK
                                 (Ibs/day)
    Scenario
Hillsborough
   River
Little Manatee
    River
St. Petersburg
    Ai rport
Low Flows*
7Q10
14Q10
30Q10
High Flows*
7Q2
15Q2
30Q2
Thunderstorm
Average Annual

82
83
94

63,190
45,530
33,470
15,170
8,360

36
53
70

19,990
13,410
9,580
0
2,320

1.3
11
13

6,740
4,710
3,300
19,980
1,010
* Inputs for "n-day/i-year" conditions (i.e., 7Q10 refers to 7-day/10-

  streamflow).
                                              •year
                                     119

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                                 REFERENCES

(1)   Ross, B.E.  and P.O.  Jenkins, "Computer Simulation of Nutrients  in
     Tampa Bay,  Florida,"  Structures,  Materials,  and Fluids  Department,
     College of  Engineering, University of South  Florida, Tampa,  FL,  August
     1978.

(2)   Hartigan, J.P. and S.A Hanson-Walton, "Tributary Streamflows and
     Pollutants  Loadings  Delivered to  Tampa Bay," Camp Dresser &  McKee
     Inc., Annandale, VA,  January 1984.

(3)   Hartigan, J.P., et al., "Calibration of Urban Nonpoint  Pollution
     Loadings Models," Proceedings of  ASCE Hydraulics Division Specialty
     Conference  on Verification of Mathematical and Physical  Models  in
     Hydraulic Engineering, American Society of Civil Engineers,  New York,
     NY, August  1978, pp.  363-372.

(4)   Priede-Sedgwick, Inc., "Runoff Characterization:  Water Quality and
     Flow," prepared for  Tampa Nationwide Urban Runoff Program Study-Phase
     II, March 1983.

(5)   Metcalf and Eddy, Inc., "Tampa Nationwide Urban Runoff  Program  (Phase
     II):  Tasks II.6, II.9, and 11.10," prepared for City of Tampa,  FL,
     July 1983 (Draft).

(6)   U.S. Geological Survey, "Tampa Bay Region Urban Watershed Study Data-
     base:  1972-1980."

(7)   Lopez, M.A. and D.M.  Michael is, "Hydrologic  Data from Urban  Watersheds
     in the Tampa Bay Area, Florida,"  Water Resources Investigations Open-
     File Report 78-125,  U.S. Geological Survey,  Tallahassee, FL, 1979.

(8)   Giovanelli, R.F. and J.B. Murdoch, "Urban Stormwater Runoff  in  the
     Tampa Bay Area," prepared for Bay Area Scientific Information
     Symposium (BASIS), Tampa, FL, 1982.

(9)   Lopez, M.A. and W.M.  Woodham, "Magnitude and Frequency  of Flooding on
     Small Urban Watersheds in the Tampa Bay Area, West-Central  Florida,"
     Water Resources Investigations Open-File Report 82-42,  U.S.  Geological
     Survey, Tallahasee,  FL, 1983.
                                     120

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           WATER SCREEN - A MICROCOMPUTER PROGRAM FOR ESTIMATING
                      NUTRIENT AND POLLUTANT LOADINGS

                                     by
                               +                       [ |
                  Bruce L. Bird  and K. Marlene Conaway
INTRODUCTION

        Because of the high cost of carrying out significant spatial and
temporal sampling to adequately characterize even a small watershed, other
alternatives have been sought.  A great deal of effort has been devoted to
the development of detailed computer models that can be used to simulate the
water, nutrient, and pollutant transport within a watershed.  These detailed
models include processes with short time scales so that the hydrology can
follow effects of a single storm event or follow variations in daily rainfall.
The models then relate sediment,'nutrient, and pollutant transport to the
hydrologic simulation. ^-"^

         Because many local agencies do not have the resources required for
proper application of the detailed models, a further simplification has been
made.  Watersheds with sufficient data to calibrate and verify a model are
used to generate average loading factors for nutrients and pollutants and for
different land uses. ~°  A loading factor gives the average amount of pollu-
tant produced by a given land use in terms of pounds per acre per year.  If
the watershed from which the loading factors are derived is similar to the
watershed of local interest, then an estimate of nutrient and pollutant
loadings can be made once the land use patterns of the local watershed are
determined.  This is one of the approaches used in the microcomputer program
WATER SCREEN.

         An alternative method for estimating nutrient and pollutant loadings
is based on the Modified Universal Soil Loss Equation (MUSLE).  The USLE was
developed by soil scientists to estimate soil loss from agricultural fields.
It was later modified by the addition of a sediment delivery factor so that
the amount of soil that reaches a natural water body can be estimated.
Nutrient and pollutant loadings can be related to the amount of delivered
sediment. 9"1-1  This approach is also used in WATER SCREEN to allow comparison
with the loading factor method for forest and agricultural land use.
 + Environmental Center, Anne Arundel Community College, Arnold, Maryland
-H- Office of Planning and Zoning, Anne Arundel County, Annapolis, Maryland

                                     121

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                                 WATER SCREEN

         A computer  program,  WATER SCREEN,  has  been written  for  the Apple II
microcomputer.12 This  program can be used by  land use  planners to estimate
the amounts  of  sediment,  nitrogen, phosphorous,  BOD, lead,  and zinc that are
produced by  various land  use patterns within a watershed.   Both a modified
universal soil  loss equation and a loading factor method are used in the pro-
gram  to  estimate nutrient and pollutant  loadings.

         The  computer program WATER SCREEN  uses input parameters provided by
the operator to calculate nutrient and pollutant  loadings from  a watershed.
In the first part of this report,  personnel requirements, computer hardware,
program  logic,  and  loading equations  for this  program are described.  Appli-
cation of WATER SCREEN  to a  small  watershed is described in the second part
of this  report.

Personnel Requirements

         A person with minimum computer experience can run WATER SCREEN.  A
knowledge of BASIC  is not required; however, some acquaintance  with BASIC on
the level of Apple  II User's Guide, by Poole,  would allow the operator to take
full  advantage  of the logical structure  and data  file generating capabilities
of the program.   The user need not be an expert in hydrology or ecology, but
he/she should become familiar with the material covered In  references 6 and 9.

Machine  Requirements

         WATER SCREEN has  been written and  run  on  an Apple II microcomputer
system with  48K of  memory.   The system consists of a single  disk drive and a
NEC PC-8023A printer connected to  the Apple II using the Orange Micro (Srappler
interface.   As  written, for  seven  subwatersheds,  the program without REMARK
statements occupies 29K of memory.  It is  estimated that a watershed with up
to 20 subwatersheds could be run before  one would run out of memory on a 48K
machine.   If more subwatersheds were  needed, the  watershed could be separated
into  smaller sections and then each section evaluated using  the  program.
While the program is written in Applesoft  BASIC,  it could readily be modified
for use  on other machines using the appropriate translations.   The printer
commands  are listed in  separate subroutines and can be  easily modified for
other printers  if needed.  Modifications of the file commands used to store
input data on disk  would  require the  most  effort.

Program Logic

        WATER SCREEN can  easily be modified to  accommodate changes that may
be proposed  to  the  algorithms  now  used or  to incorporate new algorithms.  The
program consists  of three major sections:   (1) create, read,  and  edit input
data file; (2) calculation of  pollutant  and nutrient loading using the modi-
fied universal  soil loss  equation  (MUSLE)  and  algorithms described by Zison
et al^ for nitrogen,  phosphorous and  organic matter;. (3) calculation of
nutrient  and  pollutant  loading using  loading factors developed  by the Northern
Virginia  Planning District Commission  (NVPDC)  in  their  extensive study of the
Occoquan  River Basin.6

                                     122

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        The data file part of the program asks the user to input factors for
the MUSLE and for soil and rainfall information needed to calculate nitrogen,
phosphorous, and organic loadings.  Loading factors for various categories
of land use must also be input to the program.  Much of this information is
requested by subwatershed so that variations within the watershed can be
accommodated.

        The application of WATER SCREEN to the Church Creek watershed will be
discussed in later sections.  For this watershed with six subwatersheds it
takes about twenty minutes to input all the required data.  The program stores
this data in a disk file where it can later be recalled and edited if desired.
The run time of the program depends upon the number of subwatersheds selected
and the speed of the printer.  The printout of the results from the Church
Creek watershed takes about twenty minutes using an eighty  characters per
second printer.  Subtotals and totals are printed by subwatershed, land use,
and pollutant type.

        The file editing features makes it possible to quickly see the sensi-
tivity of the calculation to changes in the value of a parameter, such as
slope or loading factor, by running the program, using the editing feature to
change the desired parameter, and then rerunning the program.

        A flow diagram for the major subsections of WATER SCREEN is shown in
Figure la and lb.  Because of the logic used in the program it is  quite easy
to add or delete subroutines that use different methods of calculating nutrient
and pollutant loadings and to add or delete the corresponding records that
contain the parameters used in the calculation.  Commercially available
utility programs, such as Apple Doc, are very helpful in this process,

Algorithms Used in WATER SCREEN

A.  Modified Universal Soil Loss Equation

    Agricultural and soil scientists have been concerned for decades with the
problem of controlling soil loss from farm land.  The universal soil loss
equation was developed to estimate soil loss from a field and to predict the
effects of crop rotation, management practices, etc.  The USLE  has the form:

        Y(S)E = A R K L S C P
where
        Y(S)p = soil loss due to surface erosion (tons/year)

        A     = area of field (acres)

        R     = rainfall factor, indicates the erosion potential of average
                  annual rainfall (R unit)

        K     = soil-erodibility factor (tons/acre/R unit)
        L     = slope-length factor (dimensionless ratio)

        S     = slope-steepness factor (dimensionless ratio)

        C     = cover factor (dimensionless ratio)

        P     = erosion control practices factor (dimensionless ratio)

                                     123

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   T~  •  L
      ©
END
              A% =  1  Run  Program
              A% =  2  Inspect  File Parameters
Load Records from file stored on disk.

Subroutine:  SOIL
  Calculates soil loss using USLE.
  Calculates delivered soil using MUSLE.

Subroutine:  NITROGEN
  Calculates nitrogen loading from  erosion  and rain.

Subroutine: • PHOSPHOROUS
  Calculates phosphorous loading

Subroutine:  ORGANIC MATTER
  Calculates organic matter loading.

Subroutine:  LOADING FACTOR
  Calculates loadings using loading factor  method.

   FIGURE la   FLOW DIAGRAM FOR WATER SCREEN
            Subroutine:  FILE
                            Choose
                            1.  Create and read file,
                            2.  Read file.
                            3.  Edit file.
             Subroutine:  RECORDS  (CH% = 1)
              Asks keyboard input for file and calculation parameters<

             Subroutine:  RECORDS  
-------
        The U.S. Department of Agriculture has carried out extensive
experimental studies on fields located throughout the United States.  From
these studies accepted values for the factors in the USLE have been tabulated.
Local values are obtainable from handbooks published by the Soil Conservation
Service.1^  As has been pointed out by various authors, the USLE only predicts
the soil lost from a field.  It does not estimate the actual amount of soil
that is delivered to a stream channel.  In order to estimate this, an addi-
tional factor, the sediment delivery ratio, is needed. 15

        To estimate the amount of soil delivered to a stream the modified
universal soil loss equation (MUSLE) is used.  The MUSLE has the form:
where
          Y(S)D -

          Y(S)  = soil delivered to stream channel (tons/year)

          Y(S)_, = soil lost from field (tons/year)
              E
          S     = sediment delivery ratio (dlmensionless ratio)

The sediment delivery ratio is probably the most difficult factor in the
MUSLE to estimate with any degree of reliability.15  Its value in different
watersheds has been obtained by observing the silting rate of dams.  Obtained
this way it accounts not only for field losses but also all other erosion
processes, such as stream channel erosion, which are not accounted for by
the USLE.

        It is generally accepted that the soil lost from an individual field
can be reliably estimated using appropriate local values for the factors in
the USLE.  However, it is quite another matter to reliably estimate the sedi-
ment loading from a watershed composed of many fields with varying slopes,
ground cover, distance from stream channel, etc.  For example, it is not
clear how to handle fields with concave slopes.  Soil lost from one part of
a field may redeposit in another part of the same field or in another part
of the watershed.1"

        The MUSLE has been applied primarily to agricultural and forest land
although some work has been done to extend it to residential land use.  In
this report the MUSLE will only be applied to forest and agricultural land
use.

B.  Nitrogen Loading Function

    Zison et al^ point out that the movement of nitrogen compounds within an
ecosystem is complex and still not thoroughly understood.  For an estimate
of the amount of total nitrogen produced by runoff and erosion, excluding
leaching losses, they suggest the following expression:
        Y(NA) = fNY(NT)E + Y(N)pr
where
        Y(NA) = total available nitrogen (Ibs/year)

        f     = ratio of available to total nitrogen in sediment
                (dimensionless)

                                    125

-------
        Y(NT)E = total nitrogen loading from erosion (Ibs/year)
              r = stream nitrogen loading from precipitation (Ibs/year)
Y(NT)E  is  found  from the expression:

        Y(NT)£ = 20  Y(S)D CS(NT)  rN

where
        Y(S)   = soil delivered to  stream channel  (tons /year)
                =  total  nitrogen concentration in  soil  (g/lOOg)

         r       =  nitrogen enrichment ratio

The  factor  of  20  takes  into account  the  units used  in  this  equation.

Y(N)    is found from the  expression:

         VfWS    =
         Y(N)Pr
where

         A       =  area (acres)

         Q(OR)   =  overland flow from  precipitation (in/year)
         Q(Pr)   =  total  amount  of precipitation (in/year)

         N       =  nitrogen loading in precipitation  (Ib/acre/year)
         b       =  attenuation factor

Zison et al* discuss  the  methods of  evaluation of the  parameters in the
nitrogen loading  function.

C.  Phosphorous Loading Function

    A great deal  of  confusion  still  exists about  the proper  terms for
describing  the various  physical and  chemical  states of phosphorous*  There
is also  some disagreement about the  effectiveness of chemical extraction
procedures  to  selectively remove a particular phosphate from the soil.l'
Because  of  these  uncertainties  the values of  the  parameters  used in the
loading  function  for  phosphorous are only rough approximations.  Zison et
suggest  that based on the soil  erosion transport  mechanism the loading
function for phosphorous  should have the form:

        Y(PA)  = 20 fp Y(S)D  Cg(PT) rp

where
        Y(PA)  = loading of available phosphorous  (Ibs/year)
         f      = ratio of  available phosphorous  to total phophorous
                (dimensionless)

        Y(S)   = soil  delivered  to stream channel  (tons/year)


                                     126

-------
        C (PT) = total phosphorous concentration in soil (g/lOOg)
         O

        r      = phophorous enrichment ratio
Zison et al  discuss the methods for determining the parameters in the
phophorous loading function.

D.  Organic Matter Loading Function

    Zison et.al^ also suggest a loading function for organic matter of the
form:
        Y(OM)E = 20 CS(OM) Y(S)D rQM

where   ytOM),, = organic loading (Ibs/year)
             E
        C (OM) = organic matter concentration in soil (g/lOOg)
         u
        Y(S>   = soil delivered to stream channel (tons /year)
        r.     = enrichment ratio for organic matter in eroded soil

Procedures for determining the values of the parameters in the organic
loading function are given by Zison et al.9

E.  Loading Factors

    During the last seven years field and detailed modeling studies of non-
point pollution from small watersheds with one predominant land use have
been funded by the Water Resources Planning Board, Washington Council of
Governments, and by the Environmental Protection Agency Chesapeake Bay
Program.  The modeling studies were carried out by the Northern Virginia
Planning District Commission (NVPDC) ,  The earlier watershed studies on the
Occoquan River Basin were done by personnel from the Civil Engineering De-
partment, Virginia Polytechnic Institute,  Later watershed measurements
were done in the Ware River Basin (southeastern Virginia) , Pequea Creek
Basin (Lancaster, Pennsylvania) ,Patuxent River Basin (western shore of
Chesapeake Bay), and Chester River Basin (eastern shore of Chesapeake Bay).
These measurements were done by groups from Virginia Institute of Marine
Science, U.S. Geological Survey, and State of Maryland, respectively. 18-22

    As a result of this work non-point pollution loading factors have been
generated which can be used to estimate loadings produced in a watershed by
using the equation:

        Y(X) = T   F (X) A
              i = 1  !     1

where   y(x)  = ioading of pollutant X (Ibs/year)

        F. (X) = loading factor for pollutant X and land use i (Ibs/acre/year)

        A.    = area of land use i  (acres)

In this report we have used the loading factors given in reference 6,  A
recalibration of these factors has recently been reported, °

                                     127

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         APPLICATION OF WATER SCREEN TO THE CHURCH CREEK WATERSHED

Introduction

        A small watershed was selected to demonstrate the application of
the WATER SCREEN program.  In this section we describe the Church Creek
watershed land use patterns of this watershed in 1974, 1981, and a hypo-
thetical development pattern based on the General Development Plan (GDP),
and the choice of input parameters for WATER SCREEN.  We then compare the
results of the modified universal soil loss equation  (MUSLE) method with the
loading factor approach for forest and agricultural land use, and discuss
the estimated loadings for all forest, 1974, 1981, and GDP land use patterns.

Description

        Church Creek is located just south of Annapolis, Maryland.  It is
a mile-long tidal tributary of South River, which is a subestuary of
Chesapeake Bay.  The watershed has an area of 1200 acres.  The soil type
within the watershed is predominantly Monmouth loamy sand with some Colling-
ton fine  sandy loam.    Typical land slopes are in the 0 to 10% range with
higher slopes on land close to the shores of the Creek.

        For purposes of analysis the watershed was divided into six sub-
watersheds based on water drainage patterns.  The sub-watershed boundaries
are indicated by dashed lines in Figures 2, 3 and 4, and are identified by
SW1, SW2, etc.  The land use patterns that existed in 1974 and 1981 are
shown in Figures 2 and 3, using the code shown in Table 1.  A hypothetical
land use pattern based  upon the present General Development Plan is shown
in Figure 4.  It should be emphasized that this projected land use is not
possible because of existing development patterns and regulatory controls.
It is presented as an extreme to which present land use can be compared.
The relative percentage of land use for 1974 , 1981 and the GDP is shown in
Figure 5.  The land use classifications used in this report are forest,
pasture, hayfield, conventional tillage crop, minimum tillage crop, idle,
low density residential (h- 1 dwelling unit IDU] per acre), low/medium
density (2-5 DU/acre), medium density (5-10 DU/acre), high density
(greater than 10 DU/acre). and commercial.


                         TABLE 1  LAND USE CODES

      1  Forest                    7  Low Density Residential

      2  Pasture                   8  Low/Medium Density Residential

      3  Hayfield                  9  Medium Density Residential

      4  Conventional Crop        10  High Density Residential

      5  Minimum Tillage          11  Commercial

      6  Idle
                                    128

-------
FOREST
         LOW/MEDIUM
           DENSITY
         2-5  DU/ACRE
PASTURE
         MEDIUM DENSITY
         5-10 DU/ACRE
HAYFIELD

         HIGH DENSITY
         10 OR MORE
           DU/ACRE
CROPLAND
         COMMERCIAL-
           GENERAL
MINIMUM
TILLAGE
         COMMERCIAL
            UNDER
        CONSTRUCTION
IDLE
        INDUSTRIAL
           PARK
LOW DENSITY
1/2-1 DU/ACRE
Table 1 (continued)
 Land Use Code
            129

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                                                  SW 5
                                               .50
                                    Figure  2
                                    1974 Land Use
South River
               130

-------
                                              .50
                               Figure  3
                               1981 Land Use
South River
                 131

-------
                                                 .50
South River
Figure 4
General Development
Plan Land Use
                132

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      Forest
    Pasture
    Hayfield
Conventional
       Crop

    Minimum
     Tillage
        Idle
        Low
    Density

Low/Medium
    Density
     Medium
     Density
       High
    Density
 Commercial
                  10     20   '   30     40
                  PERCENT LAND USE
50
             Figure 6    Percentage of Land Use
                        in Church Creek Watershed
                           133

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          Commercial areas are located primarily in subwatershsds 3 and 4.
  These are shopping centers or office buildings.  There is no heavy industrial
  land use within the watershed.  Agricultural land lies primarily in subwater-
  sheds 1, 2 and 6.  Comparison of 1974 with 1981 land use indicates an increase
  of commercial land by 25% and a decrease in conventional tillage land by 78%
  largely due to changes in farming practice, from conventional to minimum
  tillage.

  Input Parameters for WATER SCREEN

          Input parameters for the Church Creek watershed used in WATER SCREEN
  are listed in Table 2.

          Soil maps indicate most of the watershed is composed of loamy sand,
  but in subwatershed 4 there is some fine sandy loam; the soil erodibility
  factor K was adjusted to account for this.

          The length-slope factor (LS) was obtained from the 1:4800 contour
  maps by "eyeball" estimates of average lengths to a stream channel and
  typical changes in elevation.  LS values were in the range from 0.2 to 3.0.

            TABLE 2  PARAMETER VALUES FOR CHURCH CREEK WATERSHED
Function

  MUSLE
Parameter
R
K





LS
Sub-
Watershed
All
1
2
3
4
5
6
All
Land
Use
All
All
11
11
11
11
ii

Parameter
Value
200
.43
.43
.43
.35
.43
.43

Source
Reference 9
IT 11
«




1/4800 seal
                            All        Forest         .003
                                       Pasture        .013
                                       Hayfield       .009
                                         Idle         .012
                                     Conventional
                                         Crop         .319
                                       Minimum
                                     Tillage Crop     .185
                            All      Non-cropland     1.0
                                       Cropland       .75
Reference 9
Reference 14
Reference 14
                                      134

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         TABLE 2   PARAMETER VALUES FOR CHURCH CREEK WATERSHED (CONT'D)
Function
MUSLE




NITROGEN






'HOPHOROUS


ORGANIC
MATTER
Parameter
SD




fN
Cg (NT)
rN
Q(OR)
Q(PR)
NPr
b
fp
CS(PT)
rP
Cg (OM)
*"
Sub-
Watershed
1
2
3
4
5
6
All
ti
ti
ii
ii
"
ti
All
ii
ii
All
ti
Land
Use
All
ti
"
"
ii
Forest &
Agriculture
it
Tl
tl
tl
" 1
tl
Forest &
Agriculture
•'
Forest &
Agriculture
Parameter
Value
Source
.5 1/4800 scale maps
.54 Reference 9
.48
.54
.54
.56
.02
.07 g/lOOg
2.1
28.8 in/year
48 in/year
.78 Ib/acre/yr
.75
.048
,07 g/lOOg
1.5
1.4 g/100g
i ^




Local Value
Reference 9
Local Value
Reference 9
Local Value
Reference 9
Reference 9
Local Value
Reference 9
Reference 9
Reference 9
"D« £j-k>»«T1 J-» tt O
                 'OM
Some of the loading factors listed in Table 3 have been revised based on
recent recalibration measurements.

Comparison^of MUSLE method with Loading Factor Approach

         Loading estimates from both the MUSLE and loading factor methods are
shown for sediment, total nitrogen, and total phosphorous in Figures 6, 7 and
8 respectively.  These results are only for forest and agricultural land use
within the watershed.  As can be seen, the MUSLE method estimates a much
larger amount of sediment, by a factor of 10 to 20, than that estimated from
the loading factor method.  However, estimates for total nitrogen and total
                                     135

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 TABLE 3   LOADING FACTORS (LBS/ACRE/YEAR) SELECTED FOR CHURCH CREEK WATERSHED
                                          Land Use
Pollutant
Sediment
Nitrogen
Phophorous
BOD
Lead
Zinc
Forest
20
2.4
.1
6
.01
.01
Pasture
20
4.3
.3
13
.01
.01
Hay field
20
2.6
.1
6
.01
.01
Conventional
Crop
1580
12.5
2.3
29
.02
.1
Minimum
Tillage
900
8.7
1.1
19
.02
.1
Idle
20
2.6
.1
6
.01
.01
                                       Land Use
 Pollutant

 Sediment

 Nitrogen

 Phosphorous

 BOD

 Lead

 Zinc
Low
Density
120
5.1
.5
13
.12
.11
Low/Medium
Density
240
7.1
.8
18
.29
.23
Medium
Density
420
9.7
1.1
25
.59
.38
High
Density
560
12.5
1.7
36
.97
.55
Commercial
480
13.2
1.6
163
2.58
2.06
phosphorous are just the opposite; the MUSLE estimates are a factor of 4 to 15
times lower than those given by the loading factor approach.  Only in the case
of minimum tillage crop are the estimates of comparable size.  Both the nitro-
gen and phosphorous loading functions used with the MUSLE approach relate the
amount of nutrient to the amount of sediment; therefore one would expect the
sediment, nitrogen, and phosphorous estimates to all be high or low, but they
are not.

         Possible reasons for the discrepancy between the two methods are:
         1.  Nitrogen and phophorous loading functions that were used are
             not correct or not appropriate for this watershed.

         2.  The loading factors used are not appropriate for this watershed.

         The transport of nitrogen and phosphorous have been intensively
studied because of their importance in the eutrophication of natural waters'-/»  ^»  5

                                      136

-------
They are part of  an extremely complex process with  some of the details still
not well understood.   It is therefore not unlikely  that the simplified method
of estimating nitrogen and phosphorous loadings by  means of loading functions
is not correct.

         Recent work in the Chesapeake Bay Program  found that the loading
factors developed for the Occoquan River basin in Northern Virginia were
comparable to values  found in small watersheds located in the Pequea Creek
region near Lancaster, Pennsylvania.22  Work with other watersheds within
the Chesapeake Bay watershed also indicated comparable loading factors.  This
suggests that these loading factors are appropriate for use with the Church
Creek watershed provided there are no unique characteristics of the Church  Crfeek
watershed which distinguish it from the watersheds  on which the loading factors
are based.
                     i  i   i
                                                             I	I
             Forest
            Pasture
            Haylleld
          Convention
              Crop
            Minimum
         Tillage Crop
           Idle Land
                    10  20 30 40  SO 60 70 80  90 100
                                                                      1974
                                                                     1981
                                                            400
                                                                  SOO   600
                                     SEDIMENT (tons/year)
                                                 Figure 6
                                                 Comparison of MUSLE and
                                                 loading factor estimates-sediment
                                       137

-------
         While  writing this report we received the recently revised loading
factors from NVPDC based on additional measurements.**  There were no changes
in the nitrogen,  phophorous, and BOD loading factors.  A 33% reduction in the
zinc loading factor for single family residential (0.5-6.0 DU/acre) and town-
house garden apratments (6.0-20.0 DU/acre)  was recommended.  For lead a 50%
reduction was recommended for single family residential and a 33% reduction
for townhouse garden apartments.  Based  on  a better sampling technique for
suspended solids  they recommend a 33% reduction in the sediment loading
factor for  all  residential land use categories.

         Part of  the reduction in the lead  loading factor may be due to the
increased use of  no-lead gasoline so that the original lead loading factor
may be more appropriate for the 1974 and 1981 land use patterns.  In any case,
the revised loading factors do not significantly affect the total nutrient
and pollutant loading estimates in this  report which are based on the earlier
loading factors from NVPDC.
           Forest
           Pasture
          Hayfleld
        Conventional
             Crop
          Minimum
        Tillage Crop
          idle Land
                  0  20  40 90 80 100 120 140 1«0 180 200   400    600   800   1000  1200

                              TOTAL NITROGEN (Ibs./year)
                      Figure 7
                      Comparison of MUSLE and loading factor estimates -Total nitrogen
                                       138

-------
    Forest
   Pasture
   Hayflald
Conventional
      Crop
   Minimum
    Tillage
      Crop
      Idle
MU3LE

Loading Factor
                                                               1974
              10  20  30 40 50 60 70  60 90 100 '   1SO    200   250

                            TOTAL PHOSPHORUS (Ibs./year)
                                    Figure  8
                                    Comparison of MUSLE and loading
                                    factor  estimates-Total phosphorus
                                   139

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Nutrient and Pollutant Discharge  to Church Creek

         The loading factor method was used to estimate nutrient and pollutant
loadings for four different land  use patterns:

         1.  The  appropriate  loading  factor  for  forest land  use was multiplied
             by the  total land area  (1200 acres)  to  give  an estimate for  each
             pollutant  of the  total loadings  if the  whole watershed were  com-
             pletely forested.  This is  called the "all forest" land use
             pattern and  serves as an  index of minimum loadings from the
             watershed.

         2.  1974 land  use.

         3.  1981 land  use.

         4.  Hypothesized development  based on the current General Development
             Plan (GDP).   This serves  as an index of the  maximum loading  from
             the watershed.

         The loadings for sediment, total nitrogen,  total phosphorous, bio-
logical oxygen  demand (BOD), lead, and zinc for each of the eleven categories
of land use were estimated.  Figures 9 and 10 summarize the estimated total
pollutant  loading by pollutant type for  the four  different development patterns
considered.  In general,  no significant  change in loadings between 1974 and
1981 was noted  except in  two categories.  The change from conventional to
minimum tillage practices on some of the farmland reduced the sediment, total
nitrogen,  and total  phosphorous from this land use by a significant amount.
On the other hand, increase in commercial land use increased  BOD, lead, and
zinc loadings by 25%.   If one  uses the "all forest"  values for normalization,
then by 1981 yearly  sediment loading had increased by a factor of 10, total
nitrogen by 2,  total phosphorous  by 7, BOD by 4.5, lead by 60, and zinc by 40.
If the hypothetical  land  use patterns  based on the GDP were to occur, then
sediment would  increase by a factor of 18, total  nitrogen by  4, total phos-
phorous by 12,  BOD by 9,  lead  by  100,  and zinc by 75,

         Comparing the loadings for all  four  land use  patterns indicates  that
high density residential  and commercial  land  use  can contribute significant
loadings for all the pollutants studied.  For example, in 1981, sediment  from
commercial land was  almost as  much as  from cropland.   One of  the more sur-
prising results is the large amount of BOD loading produced by commercial
land.  In  1981  the BOD loading from commercial land  use in the watershed  was
a factor of three larger  than  would have been produced if all the land were
still forested, even though commercial land in 1981  made  up only 12% of the
entire watershed.  Loadings of  zinc and  lead  are  also  disproportionally
higher for commercial land as  compared to other land uses within the watershed.

         A process that is not  accounted for  in these  calculations is the
disturbance and exposure  of soil  at construction  sites or new road constrution.
At present, there are no  good  procedures for  estimating the nutrient and
pollutant  discharges from construction sites.  The reason for this is the
uniqueness of each construction site in  terms of  land  disturbance, sedi-
ment control practices,  intensity and  duration of storms  that occurred while

                                     140

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                           MM All Forest
                           •I 1974
                           I—I 1981
                           S3 GDP
       1           2
     SEDIMENT (102tons/year)
 2     46     8    10    12
  TOTAL NITROGEN (103lbs./year)
 2     46     8    10    12    14
TOTAL PHOSPHORUS (102lbs./year)
 Figure 9
 Total Pollutant Loading from Church Creek
 Watershed (Sediment, Nitrogen, Phosphorous)
                HI

-------
12345
       BOO (104lbs./year)
      4     6     8    10
      LEAD (102lbs./year)
12
                                     All Forest
                                     1974
                                     1981
                                     GDP
      4     6     8     10    12
        ZlNC<102lbs./year)

     Figure 10
     Total Pollutant Loading from
     Church Creek Watershed (BOD.Lead, Zinc)
                  142

-------
bare soil was exposed, etc.  Because construction activity has been neglected
in our model the estimated loadings are probably conservative.

Discussion

         In the previous section we have obtained estimates of yearly nutrient
and pollutant loadings from the Church Creek watershed.  In this section we
discuss the following questions:

         1.  What happens to these nutrients and pollutants once they enter
             Church Creek?

         2.  What impact do these nutrients and pollutants have on the water
             quality of Church Creek?

         The first question cannot be answered without a thorough physical,
chemical, and biological study of Church Creek.  Even if this were available,
many of the chemical and biological interactions that control the transport
of nutrients and pollutants within an estuary are still not completely under-
stood.  This is particularly true of the water-sediment interface at the
bottom of the creek.

         The second question is not answerable at the present time.  There is
insufficient scientific knowledge to predict the amount of a particular
nutrient or pollutant that will cause a decline in the water quality of an
        77 ")H
estuary.1"'-'0  There is not even a consensus among scientists as to the proper
choice of variables required to define the water quality of an estuary.29-31

         The impact of nutrient enrichment on an estuary and corresponding
management implications are discussed in an excellent collection of review
articles edited by Neilson and Cronin.^2  The overall sense of these reviews
is that while a great deal has been learned about nutrient cycling within an
estuary, much still remains to be discovered.

         With the present state of knowledge of estuarine ecology, what
method can planners use to establish reasonable patterns of land use within
a watershed?  We suggest that the ratios R , where

         R  = total loading of pollutant i from watershed (Ibs/year)	
              total loading of pollutant i for completely forested watershed
                                                                   (Ibs/year)
be used as the index of tne state of the watershed.   If there is a correlation
between the "health" of an estuary and these pollutant ratios, there maximum
ratio values could be assigned based on comparison of several watersheds
within a county.  For this purpose the "health" of an estuary could be based
on fairly broad criteria, such as water clarity, odor production, dissolved
oxygen history, etc.  Adjustments to the maximum ratios may be needed to
account for factors such as flushing time and quality of benthic material.

         These maximum ratio values could be used as guidelines in the
establishment of general development plans for a watershed.  Admittedly,


                                     143

-------
the establishment of maximum loading ratios is not a trivial task and is well
beyond the scope of work reported here.  We offer it as a suggestion that we
believe is reasonable and within the resources of local government agencies.
Planning guidelines based on watershed characteristics will focus the atten-
tion of both planners and citizens on the ecological unit that often deter-
mines the health of an estuary—its watershed.

Acknowledgement

         This study was partially funded through a grant from the Maryland
Coastal Zone Management Program.


References

1.  Swank, R.R., "U.S. Environmental Protection Agency Program On Nonpoint
    Source Modeling," in Environmental Impact of Nonpoint Source Pollution,
    M.R. Overcash and J.M. Davidson, eds., (Ann Arbor Science, 1980), p. 1.

2.  Simons, D.B. and R. Li, "Modeling of Sediment Nonpoint Source Pollution
    from Watersheds," in Environmental Impact of Nonpoint Source Pollution,
    M.R. Overcash and J.M. Davidson, eds., (Ann Arbor Science, 1980), p. 341.

3.  Donigan, A. and N. Crawford, "Modeling - Nonpoint Pollution from the
    Land Surface," EPA 600/3-76-083, EPA, Athens, GA., July 1976.

4.  Johanson, R.C., J.C. Imhoff, and H. Davis, "Users Manual for Hydrological
    Simulation Program - FORTRAN (HSPF)," EPA 600/9-80-015, EPA, Athens, GA.,
    April 1980.

5.  Haith, D.A., "Models for Analyzing Agricultural Nonpoint Source Pollution,"
    Research Report 82-17, International Institute for Applied Systems
    Analysis, April 1982.

6.  Northern Virginia Planning District Commission, "Guidebook for Screening
    Urban Nonpoint Pollution Management Strategies," prepared for Metropolitan
    Washington Council of Governments, Washington, DC, November 1979.

7.  Northern Virginia Planning District Commission and Virginia Polytechnic
    Institute and State University, "Occoquan/Four Mile Run Nonpoint Source
    Correlation Study," Final Report prepared for Metropolitan Washington
    Council of Governments, Washington, DC, July 1978.

8.  Northern Virginia Planning District Commission, "Washington Metropolitan
    Area Urban Runoff Demonstration Project," Final Report prepared for
    Metropolitan Washington Council of Governments, Washington, DC, April 1983.

9.  Zison, S.W., K.F. Haven, and W.B. Mills, "Water Quality Assessment - A
    Screening Method for Nondesignated 208 Areas," EPA 600/9-77-023, EPA
    600/9=77-023, EPA, Athens, GA., 1977
                                     144

-------
10.  Davis, M.J., M.K. S-yder, and J.W. Nebgen, "River Basin Validation of
     the Water Quality Assessment Methodology for Screening Nondesignated 208
     Areas.  Volume I:  Nonpoint Source Load Estimation," EPA 600/3-82-057a,
     EPA, Athens, GA., 1982.

11.  Dean, J.D., B. Hudson, and W.B. Mills, "River Basin Validation of the
     Water Quality Assessment Methodology for Screening Non-designated 208
     Areas, Volume II:  Chesapeake-Sandusky Nonaesignated 208," EPA 600/3-82-
     057b, EPA, Athens, GA, 1982.

12.  Bird, Bruce L. and K.M. Conaway, "Church Creek Watershed - An Illustration
     of the Application of Microcomputers For Estimating the Effects of Land
     Use Changes on Nutrient and Pollutant Loading," Environmental Center,
     Anne Arundel Community College, June 1983.

13.  Wischmeier, W.H., "A rainfall erosion index for a universal soil-loss
     equation,"  Soil Sci. Soc.  Amer. Proc. 23:  246-249 (1959).

14.  Stephens, H., "Guide for Predicting Rainfall-Erosion Losses from Agri-
     cultural Land in Maryland and Delaware," Technical Note Conservation
     Planning 1-78, Soil Conservation Service,  USDA, College Park, Maryland,
     July 1978.

15.  Walling, D.E., "The Sediment Delivery Problem,"  J. of Hydrology, 65,
     (1983) 209.

16.  Foster,  G.R., "Soil Erosion Modeling:  Special Considerations for Non-
     point Pollution Evaluation of Field Sized Areas," in Environmental Impact
     of Nonpoint Source Pollution, M.R. Overcash and J.M. Davidson, eds.,
     (Ann Arbor Science, 1980),  p. 213.

17.  Logan, T.J., "The Role of Soil and Sediment Chemistry in Modeling
     Nonpoint Sources of Phosphorous," in Environmental Impact of Nonpoint
     Source Pollution, M.R. Overcash and J.M. Davidson, eds., (Ann Arbor
     Science, 1980), p. 189.

18.  USEPA Chesapeake Bay Program, "Monitoring Studies of Nonpoint Pollution
     in Chesapeake Bay Test Watersheds:  Final Completion Report," U.S.
     Environmental Protection Agency, Annapolis, Maryland,  (In Press) .

19.  Bosco, C., G.F. Anderson, and B. Neilson,  "Ware River Intensive Watershed
     Study.  2.  Estuarine Receiving Water Quality," final report to Virginia
     State Water Control Board,  (Virginia Institute of Marine Science,
     Gloucester Point, Virginia), July 1982.

20.  Weand, B., and T. Grizzard, "Evaluation of Management Tools in the
     Occoquan Watershed," final report to Virginia Water Control Board,
     (Occoquan Watershed Monitoring Laboratory, Virginia Polytechnic Institute
     and State University, Manassas, Virginia), 1982.

21.  Bostater, C.,'D. McCraney,  S. Berlett, and D. Puskar,  "Intensive Watershed
     Study -  The Patuxent River Basin," final report to EPA Chesapeake Bay Pro-
     gram, (Maryland Depart of Natural Resources, Annapolis, MD), 1983.

                                     145

-------
22.  Hartigan, J.P., T.F. Quasebarth, and E. Southerland, "Use of Continuous
     Simulation Model Calibration Techniques to Develop Nonpoint Pollution
     Loading Factors," Proceedings of Stormwater and Water Quality Management
     Modeling Uaers Group Meeting;  March 25-26. 1982. EPA 600/9-82-015, U.S.
     Environmental Protection Agency, Athens, GA., 1982, p. 101.

23.  Kirby, R. and E.D. Matthews, "Soil Survey of Anne Arundel County,
     Maryland," Soil Conservation Service, U.S. Department of Agriculture, 1973,

24.  Nielsen, D.R. and J.G. MacDonald, eds., Nitrogen in the Environment,
     Vol. 1.  Nitrogen Behavior in Field Soil, (Academic Press, 1978).

25.  Tanji, Kenneth, "Problems in Modeling Nonpoint Sources of Nitrogen in
     Agricultural Systems," in Environmental Impact of Nonpoint Source Pollu-
     tion, M.R. Overcash and J.M. Davidson, eds.,(Ann Arbor Science, 1980),
     p. 165.

26.  Baker, R.A., ed., Contaminants and Sediments, Vol. 1 and 2,  (Ann Arbor
     Science, 1980).

27.  Biggs, R.B., and L.E. Cronin, "Special Characteristics of an Estuary,"
     in Estuaries and Nutrients, B.J. Neilson and L.E. Cronin, eds,, (Humana
     Press, 1981), p. 3.

28.  Hegemann, D., A.H. Johnson, and J.D. Keenan, "Determination of Algal-
     available Phosphorous on Soil and Sediment:  A Review and Analysis,"
     J. Environ. Qual., Vol. 12, No. 1, (1983), p. 12.

29.  Ott, W.R., Environmental Indices, Theory and Practice, (Ann Arbor
     Science, 1978).

30.  McErlean, A.J., and G. Reed, "Indicators and Indices of Estuarine Enrich-
     ment," in Estuaries and Nutrients. B.J. Neilson and L.E. Cronin, eds.,
     (Humana Press, 1981), p. 165.

31.  Jaworski, N.A., and 0. Villa, Jr., "A Suggested Approach for Developing
     Water Quality Criteria for Management of Eutrophication," in Estuaries
     and Nutrients, E.J. Neilson and L.E. Cronin, eds.,  (Humana Press, 198L),
     p. 499.

32.  Neilson, B.J., and L.E. Cronin, eds., Estuaries and Nutrients,  (Humana
     Press, 1981).
                                      146

-------
          SIMULATION  OF THE STORMWATER AND  WATER QUALITY
                    ATTRIBUTES OF PONDS WITH HSPF
                                     by
                 Michael  P.  Sullivan and Thomas  R. Schueler
                       Dept.  of Environmental  Programs
               Metropolitan Washington Council of Governments
                          Washington,  D.C.  20006

                               INTRODUCTION
     Stormwater management policies and  regulations  have  been implemented in
most Washington Metropolitan Area jurisdictions over the past ten years.  The
objective of these programs has chiefly  been localized flood control and pro-
tection  against  stream bank  erosion.   The use of  Best  Management Practices
(BMP's) that achieve  additional nonpoint  pollution control has been encouraged
in a few area jurisdictions, but the use  of these practices has not been wide-
spread.  Mos*t of the  3,100 structures that have been constructed  along with new
development  since  the early  1970's  are "dry" detention  ponds  (MWCOG,  Aug.,
1983).   These ponds typically to not incorporate multipurpose design features
that would permit them to achieve significant nonpoint pollutant removal.

     A major element  of the research in urban runoff conducted in Washington un-
der the  auspices of  EPA's Nationwide Urban  Runoff  Program (NURP)  project in-
volved  extensive  field investigations  of the  comparative pollutant  removal
efficiencies of best management practices (BMP's) that included a variety of
stormwater ponds  (MWCOG, Dec., 1983).  Information on the costs of constructing,
operating  and maintaining  different  types  of  stormwater  ponds  was  also
developed.  Findings  from these investigations can be applied in the planning of
individual sites,  or in assessing  the effectiveness of large scale stormwater
management programs for an entire watershed or planning area.

     The purpose of  this paper is  to  evaluate  the relative pollutant removal
performance of wet  and dry ponds using data developed from BMP site monitoring
and watershed simulation models.  The stormwater and pollutant removal capabili-
ties of several types of ponds are  presented and contrasted.  The capability of
widespread employment of stormwater ponds to achieve  stream bank  erosion and
flood control objectives  within  a  20 mi2  watershed  is  examined.  This examina-
tion was  conducted with a previously calibrated  and verified watershed model
(MWCOG, Sept., 1983)  that  represented an  application of the HSPF model (Hydro-
comp, 1980).  It was  necessary to explicitly model ponds within HSPF in order to
include  and contrast the behavior of ponds with  different attributes in the
analysis.  Considerable attention is therefore given in the paper to describing
the manner in which ponds were modeled since this may  be of interest  to the water
quality modeling user community.
                                    147

-------
            COMPARATIVE  EVALUATION  OF STORMWATER PONDS

     Three  types  of  ponds  were evaluated  in the NURP  field  investigations.
These were  a dry stormwater pond, an extended detention  dry  pond,  and two wet
ponds.  Schematic  diagrams  of  the principal  components  of the ponds  are  pre-
sented in Figure 1.  All of these ponds were  situated in  stable suburban neigh-
borhoods and were comparable to structures commonly in use in the area.

Pond Design and Function

     "Dry11  stormwater  detention ponds are designed for the temporary storage of
runoff to attenuate or "shave" increases  in  peak flow associated with land de-
velopment and  increases in  impervious area.  These structures  have been the sin-
gle  most  commonly  applied stormwater   control  within  the  Washington  area.
Normally  empty  during dry  weather , they fill up rapidly during  large  storm
events.  Storage is therefore  limited to  the volume required to accomodate the
design storm (typically 2 years) and release it at pre-development flow rates.
The release rate of water  is controlled by the size of the  outlet pipe or control
device that drains the pond.   Within the Washington Metropolitan  Area,  these
structures are typically designed to detain stormwater for one to two hours.

     An extended detention  dry pond  is a modified version of a regular  dry pond.
A major question evaluated  under the NURP study was the extent  to which the de-
tention time in  conventional dry stormwater  ponds could be increased to enhance
pollutant  removal. Based upon previous  local investigations  (NVPDC,  1980), it
was thought  that modifications to design  that extended detention would provide
time for increased settling and removal  of pollutants  entrained  in urban runoff.

                    FIGURE 1.  DIAGRAM OF POND TYPES

                        CONVENTIONAL DRY POND
                                                          • Water Lev* I During Sean
            !->•• -fe^MiigiisiusHLi ;:;£•. .-aii.Ss.S
                    EXTENDED DETENTION DRY POND

                           	  F«rfor«t«d
Shavin? Stor«g«

Exc«nd«d

                                                                        Stor*
-------
To test this hypothesis, a conventional dry pond was improved to achieve greater
detention times.  As shown in Figure 1, the outlet is a perforated riser.   The
extended detention storage is controlled by the flow of water through the perfo-
rations.

     Stormwater retention or "wet" ponds represent a small but growing segment
of local stormwater structures.  In addition to providing temporary storage for
peak runoff voumes, wet ponds also have additional storage and an outlet device
that maintains  a  permanent  pool of water  throughout the year.   The permanent
pool is controlled by the outlet at the  top of the unperforated riser.  An impor-
tant  hypothesis  investigated  under  the  Washington  NURP project was  that  wet
ponds had the potential to be very effective in removing pollutants borne in ur-
ban runoff.  Several different  pollutant  removal  mechanisms were believed to be
operative in these ^»onds including physical settling, chemical flocculation and
transformation, and biological  uptake.   These  structures can also serve as  a
multipurpose landscape feature  in some settings as they  provide aesthetic, rec-
reational and wildlife  attraction benefits to the  neighborhood.

Pond Performance

     Monitoring stations including flow meters and automated samplers were  in-
stalled at the  inlet and outlet of each pond.  This sampling arrangement made it
possible to collect  flow-composited storm samples. Field sampling was conducted
over a 12 to 18-month period, and between 33 to 45 individual  storm events were
monitored at each site.  Long term pollutant removal  efficiencies for each pond
for  total suspended- solids,  pl-ant nutrients, oxygen demanding  materials  and
trace metals were  calculated.  This information is summarized in Figure 2.

Dry stormwater  pond.   Overall,  the dry pond did  not perform effectively as a
best management practice.   Removal rates  varied considerably during most storms
(e.g.  sediment removal  ranged from positive 98 percent to negative 300 percent).
           FIGURE  2.  COMPARATIVE  LONG  TERM POLLUTANT  REMOVAL
                     PERFORMANCE -  METRG DC  NUSP STUDY
      100-
       35-

   h
   U
   Q£.
   HI
   Q.
        !0-
0-
      .
   n^
   rv
   i \v\
                                                              IIRY PONE
                          i •«=
                          !••<£•
              f::
              ,-t:.
              r.
                                                 g
                                        n
                                                                 3ET
                                                                   'DND !
                       U
                                             U
 i       i       i      i       i       r      i
rss    COT    Ft>     zn     TP     OP     TN
              WATER QUALITY  PARAMETERS
                                                            TKN
                                                          N83
                                     149

-------
The general trend, however, was towards negligible or even negative efficiency
for most parameters of interest.  This is readily apparent in Figure 2 in which
the removal rates for the 'three different types of ponds are compared.

     The poor to mediocre performance observed at the dry pond site is probably
related to several factors.  First,  the brief residence time of stormwater with-
in the structure (usually less than 2 hours) severely limits the degree to which
physical and  chemical  pollutant  removal  can take place.  Secondly,  the lack of
permanent  water  storage precludes  removal by biological means.  Thirdly, the
substantial number of storms with negative efficiencies suggests that the poorly
vegetated  pond  bed was prone to  scour and erosion.  Resuspension of previously
deposited materials was thought  to  be an important factor related  to poor per-
formance of the  pond.  The performance of this pond may have been better if the
bed had been more stabile.

Extended detention  dry pond.  During the course of  the  field investigations,
stormwater detention times of 6  to  8 hours were achieved.  As shown in Figure 2,
this extended detention appeared to be promising as a method for improving pol-
lutant removal  efficiency.  Removal of particulate forms of urban pollutants in
the  extended  detention pond  was  typically high.  For example,  sediment removal
was  approximately 64 percent, organic nitrogen removal was 30  percent, and the
reduction  in COD was 30 percent.  Removal rates for trace metals were also very
high.  Fifty-seven percent of the zinc and 84  percent of the  lead  entering the
pond was retained.  However, removal of soluble nutrient forms was minimal, with
long term  removal of  only  1 percent  of the ortho-phosphorus  and  10 percent of
the  nitrate-nitrogen.   Removal  of  total nitrogen  (24%)  and  total phosphorus
(10%) was also quite low.

     Much  of the explanation  for the  improved  pollutant removal performance of
these modified  dry  ponds can be directly attributed to the extended detention
achieved.  The  6 to 8 hours of  detention was  sufficient for  the effective re-
moval of particulates.  Settling column studies conducted by VPl's Occoquan Wat-
ershed  Monitoring  Laboratory (OWML,  1983)  supported this conclusion.  Other
design  features that contributed to  the high  removal of particulates were the
paved channel along the pond's bottom between  the principal inflow point and the
riser,  and the  established  vegetation within  the pond bed.  These  features re-
duce the likelihood of scour  or resuspension.

Wet ponds.  The field monitoring  data and calculated pollutant removal efficien-
cies (Figure 2)  clearly showed that wet ponds  were the most effective for non-
point source  pollution control.  In addition  to particulates,  these ponds were
observed to  remove  a  significant portion of  soluble nutrients as  well.  This
high removal rates for soluble nutrients such as ortho-phosphate and nitrate was
in sharp contrast to the minimal removals noted at the dry pond and extended de-
tention pond  sites.  These data  suggest the importance of biological uptake in
wet  ponds  as  an  effective removal  mechanism  for biologically-available nutri-
ents.  Long term removal rates for particulate pollutants in wet ponds were also
high and suprisingly comparable to the rates demonstrated for extended detention
ponds.  For example, the removal rate for suspended sediment was 54 percent, COD
removal was approximately 30 percent, and total phosphorus reduction was 64 per-
cent.  Observed  removal rates for trace metals  were also consistently high, with
long term removals for zinc and lead at 51 and  65 percent, respectively..


                                     150

-------
     Operative mechanisms  for achieving pollutant removal in wet ponds are mani-
fold.  It appears that  biological  uptake  is the predominant  removal mechanism
for nitrate.  Deposition,  rather than oxidation, seems to be the primary removal
mechanism for organic nitrogen.  Depositional  processes  also  appear to be fully
capable of  accounting  for the  organic phosphorus removal  observed.  Uptake by
algae or  rooted  aquatic plants  seems to be the dominant removal mechanism for
ortho-phosphorus.  The similarity  in removal rates for particulates observed in
wet and extended detention ponds  implies  that  depositinal processes,  such as
settling and flocculation, are more than sufficient to explain the observed pat-
terns of removal  for sediments,  COD,and trace metals  in wet ponds.

     In summary,  the three types of ponds exhibited  markedly different behavior
in their ability to  remove dissolved and particulate pollutants.  Wet ponds dis-
played the best overall  performance.  Encouraging results were also obtained for
the extended  detention  dry pond.   Although not examined in  the  field,  it was
thought that an extended detention wet pond combining the best features of both
(i.e., permanent pool and  longer drawdown)  would further maximize the potential
for pollutant removal.

     A more complete discussion of the pollutant removal capabilities of these
and other urban  BMP's  can be found in the  NURP final report  (MWCOG, December,
1983).


                  CONFIGURATION  OF PONDS WITHIN HSPF

     Results from the field investigation of ponds were  used  extensively in the
Little Seneca Creek Watershed Management Study (MWCOG, September, 1983; Schuel-
er and Sullivan,  1983).  The Little  Seneca Creek Study relied  heavily on a cali-
brated and verified HSPF model application.   Simulation of the behavior of ponds
within HSPF was  an important aspect of this work.  Processes  that occur within
open or closed channels  or completely mixed lakes are typically simulated in the
RCHRES module of HSPF.  In this application, pond hydraulics, sediment deposi-
tion and  water quality  processes  were directly or indirectly simulated in the
RCHRES module. The use of  HSPF  for the modeling of pond performance proved to be
a valuable and innovative  way in which to evaluate load  reductions and physical
impacts upon watershed streams.


Pond Characteristics

     Simulation  of  the  dry pond was intended  to  represent the  single purpose
stormwater  control  practices currently required  by most local  jurisdictions.
These ponds provide volume control to the  extent that the 2-year peak discharge
from  a  given area is not   increased following development.  Functional 1-y, they
are peak shaving devices that act to prevent added downstream flooding and ero-
sion  during  storms  of two years or greater frequency.  Separate ponds were
simulated to  represent both low  and high density development.  The principal lo-
cational and storage requirments for these dry ponds were set to be consistent
with local practices and are shown in Table  1.

     Wet ponds were simulated to replicate the types of retention ponds that are
becoming more widely used  in the Washington area.  Separate  ponds were again si-

                                    151

-------
raulated  for  low and high  density  development,  with the associated description
and  requirments  of each outlined  in Table 1.   The common denominator for both
was  a permanent pool with a storage capacity equivalent  to one-half inch of run-
off  over the entire drainage  area.   Beyond this the low density wet pond had
additional storage  for runoff  in order  to  maintain the  two-year peak discharge
rate at  predevelopm&nt levels.  In the  case  of  high density development, an ex-
tended detention wet pond  was  simulated in order to maximize the water quality
benefits of both wet ponds  and extended detention.  Although extended detention
wet  ponds  were  not evaluated  in  the field  investigation,  it  was assumed that
pollutant, removal was equivalent to the regular wet ponds, and that the extended
detention would be  governed by storage  volume  and the outflow device.  The key
features of this pond were a larger drainage area,  extra storage volume to acco-
modate extended detention,  and a drawdown time of approxminately 30 hours.

     All of the ponds were considered to be on-site facilities.  Stormwater sto-
rage volumes  and predevelopment discharges  for the 2-year' storm were obtained
from accepted local storrawater engineering and planning guidelines  (CH2 MHill,
1983; DeTullio and Thomas,  1972).
       TABLE 1.  CHARACTERISTICS OF DRY AND WET PONDS
   DRY PONDS

    LOW DENSITY :

    HIGH DENSITY:

   WET PONDS

    LOW DENSITY :

    HIGH DENSITY:
                  DRAINAGE
                    AREA
                   (ACRES)
25

10


25

50
        IMPERVI-    STORAGE
         OUSNESS     VOLUME
          {%)      (CU. FT.)
20%

50%


20%

50%
 30,000

 33,000


 75,000

250,000
REMARKS



NO PERMANENT POOL

NO PERMANENT POOL
PERMANENT POOL = 45,000 CU. FT.
& NORMAL DETENTION
PERMANENT POOL = 90,000 CU. FT.
& EXTENDED DETENTION TO 30 HRS
 Hydrology

      Ponds were  modeled in the HYDR section of  the  RCHRES Module, which  simu-
 lates the hydraulic  processes within a  free, flowing reach or mixed  reservoir.
 The ponds were considered to be completely mixed closed  channels with  well  de-
 fined  volume/outflow relationships.  Pond volume,  inflow and outflow are  the
 chief state variables of interest.  Flow  through  the simulated pond ts unidirec-
 tional.  The geometric (depth,  surface area, volume) and hydraulic properties of
 a pond are placed in an HSPF function table  (FTABLE)  that defines the pond dis-
 charge for  different  depths or volumes  of water in storage.  An  example  of an
 FTABLE describing the geometric and hydraulic properties of a dry  pond for  low
 density development is presented in  Table 2.
                                      152

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         TABLE 3.   EXAMPLE OF FTABLE FOR DRY POND
                     FTABLE     1
                   ROWS COLS ***
                     13    4
                       DEPTH
                        (FT)
                        .000
                        . 1
                       0.5
                       1.0
                       1.5
                       2.0
                       2.5
                       3.0
                       3.1
                       3.2
                       3.5
                       U.O
                       5.0
                    END FTABLE
SFAREA
lACRES)
.000
.23
.23
.23
.23
.23
.23
.23
.23
.23
.23
.23
.23
VOLUME
(AC- FT)
.000
.023
.115
.230
.3<»5
.1*60
.575
.690
.713
.736
.781
.920
1. 150
DISCH
(CFS)
.000
1.698
3.796
5.369
6.575
7.592
8.1(69
9.299
18.9
36. M
116.0
312.000
86*4.000
**»»*»
*******













     The outflow relationship contained in the FTABLE was calculated as follows.
Pond volume for the 25 acre unit of low density development was determined to be
30,000 ft3.  The predevelopment peak  flow for the 2-year storm was calculated to
be 9.3 cfs.  The  pond was assumed to be 100 ft long,  100 ft wide, and 3 ft in
height.  Further calculations  to  determine  outflow rates  were based on the gen-
eral orifice equation  (APWA, 1981)

        Q = CA (2-H)0'5                                          (1)

Where:  Q = discharge in cubic feet per second
        C = a dimensionless discharge coefficient of 0.75
        A = area of orifice in square feet
        G = gravitational constant of 32.2 feet per second
        H = head of water above orifice in feet


     With peak discharge limited to 9.3 cfs and H equal to 3 ft, equation 1 can
be rearranged to solve for A, the  area of the orifice, as
               A =  	                                     (2)

                    C (2gH) °'S

     Calculation of the orifice diameter is then easily  accomplished.  Knowing
the orifice area A it is possible  to calculate the outflow discharge Q for heads
of  less  that  3 ft.  For stages greater than 3 ft it was assumed that the pond
would overflow, and that one end of,the pond would function as a broad crested
                                      153

-------
 weir.  Pond overflow is calculated with a general weir equation*(APWA, 1981)

                Q = CLH l'5                                       (3)

      Where: C = a dimensionless discharge coefficient of 3.0
             L = length of weir (spillway) in feet
             H = head above crest in feet

 Discharges calculated  in  equations  1  and 3 are summed for such overflow situ-
 ations.  The FTABLE is prepared by calculating the appropriate volume  and dis-
 charge for a  full range of depth within the pond and for overflow situations.

      Hydrologically, the  ponds  performed  as intended by storing water and re-
 leasing it at a controlled rate.  The type of stormwater attenuation achieved is
 given in the hydrographs of Figure 3 which depicts a case of uncontrolled runoff
 and  a  case of outflow from the dry pond for the low density development situ-
 ation.  These contrasting hydrographs  were produced from a storm of 2.0 inches
 of rainfall.
      FIGURE  3.   COMPARISON  OF  CONTROLLED  CDRV POND)
                  VS UNCONTROLLED  HfOROGRftPHS
                                    b      ?
                                 HOURS
Sediment and Water Quality

     Average  removal  efficiencies  derived from the Washington NURP work  were
used to estimate water quality effects of different BMP strategies.  In the case
of sediment,  settling within the ponds was intended to reproduce losses that had
been observed in  the  field.  Settling rate studies and other laboratory exper-
iments with  clay,  silt and sand particles provided additional guidance (OWML,
1983).  Based upon this work, different percentages of sand and silt in runoff
were made available for settling in the dry and wet ponds.  The sediment load in
the pond outflow thus reflected a net loss of material that had been deposited
in the pond.   Removal efficiencies for other water quality  constituents  were
treated similarly.  Since  the  physical,  chemical and biological  processes af-
                                      154

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fecting these  constituents were  not modeled per SB, removal efficiencies were
imbedded in the HSPF NETWORK block as a  fixed rate related to pond outflow.  The
NETWORK  block  is the section of  HSPF input where  linkages  among  land areas,
channels, constituents and other  processes  are described.  The multiplication
factors typically used in these blocks to account for land area or unit conver-
sions were adjusted to include removal efficiencies as a percent.  The removal
efficiencies that were used (Table 3) were on the conservative side of efficien-
cies observed in the field.
 TABLE 3.   POLLUTANT REMOVAL RATES USED IN MODEL SIMULATIONS
                              BOD
TP
TN
                                                       TSS
           REGULAR DRY POND:      0%      0%      0%

           REGULAR WET POND:     50%     50%     30%

 EXTENDED DETENTION WET POND:     75%     50%     50%
              100% SAND

              100% SAND; 60% SILT

              100% SAND; 80% SILT
Intrawatershed Links

     The individual ponds described in Table 1 and their appropriate drainage,
including impervious land, were modeled separately.  PERLND  (pervious area) and
IMPLND (impervious area) inputs of runoff, sediment and constituent loads were
routed in the  NETWORK block to the appropriate  RCHRES  segment representing a
specific pond.   Outflow from these ponds was in turn routed directly to a RCHRES
segment representing  e  tributary  or mainstem stream.  NETWORK block multipli-
cation  factors were  used  to  account  for  the amount of area  within  a given
subwatershed or drainage area that was governed by the individual pond controls.

     The diagram in Figure 4 describes the general way in which the  runoff, sed-
iment and water quality constituent products generated within the pervious and
impervious land segments were modeled in a subwatershed.  Arrows are used to re-
present connections between HSPF modules where multiplication factors are uti-
lized.  The extensive use of multiplication factors in determining distributions
within this configuration is very important.
                                     155

-------
               FIGURE 4. DIAGRAM OF CONNECTIONS WITHIN HSPF
                            RCHRE3 11   HMN CMM4NEL SlKtAn StfrHEVH
                                                                I	,
              APPLICATIONS OF  HSPF TO EVALUATE  IMPACTS
           PROJECTED FOR MASTER PLAN DEVELOPMENT OPTIONS
     The Little Seneca Creek watershed presented  an opportunity to use the re-
sults from the field investigations of ponds and the calibrated watershed model
(HSPF)  in the development of a Master Plan.  The  Little Seneca Creek watershed
(Figure 5) l^es approximately 25 miles to the  northwest of Washington, D.C.  in
an  area  of  suburban  Montgomery  County,  MD   that  'is  experiencing  rapid
development.  The 20 mi2 area drains to a 600 acre water supply and recreational
lake that is currently under construction. Because of the lake, an interstate
highway that bisects the watershed, and associated pressure for development,  a
revised Master Plan is being formulated for the area.  Several  land use planning
alternatives ranging from agricultural preservation to a rather dense level  of
commercial and residential development are under  consideration.  Concern about
the environmental consequences  of these alternatives upon watershed tributaries
and  the proposed  lake prompted  the evaluation  of alternatives  and remedial
storrawater management practices.

     The use of different types of ponds for the control of stormwater runoff in
new development was  simulated  in order to contrast control effectiveness on a
basin-wide level.   Model calculations were made for a full  year that represented
average climatological conditions.  The projected effectiveness of implementing
dry ponds vs. wet  ponds  for the "ultimate" land use alternative, the alternative
under consideration with the densest  development, is presented in Table 4.  The

                                      156

-------
               FIGURE 5.  LITTLE SENECA CREEK WATERSHED
                          Ten
                          Mil*
                        Cr**kf Cabin
                             Branch
dry pond scenario was intended to represent the effects of stormwater management
as required by existing regulations and practices.  Consequently, dry ponds were
earmarked to control 70 percent of new development.  This  approximation reflects
the level of new development actually receiving controls under the existing con-
trol  regulations which  frequently permit waivers  of stormwater requirements
under certain conditions.  In contrast,  100 percent coverage of  new development
was assumed  in  the wet pond scenario.  The uncontrolled or  "no pond" situation
for the ultimate development land use alternative, a projection representing the

        TABLE  4.  SUMMARY OF  PROJECTIONS FOR CONTROL OPTIONS
                       IMPACTS TO TRIBUTARIES            IMPACTS TO  THE LAKE

PREDEVELOPMENT:
(100% FOREST)
EXISTING:
(1980 LAND USE)
ULTIMATE:
(NO CONTROLS)
ULTIMATE:
(DRY PONDS)
ULTIMATE:
t \ tr~T- nxxfttrt** i
PEAK
(CFS
1295
1400
1947
1632
1348
Q LOW Q
5.8
5.5
4.4
4.5
4.9
STRMBNK
EROSION
80
115
248
241
188
CHAN
DEPO
(T/MI
13
122
83
41
16
                                                  TP   TN   BOD   SED    AVG
                                        	    LOAD  LOAD  LOAD  LOAD  CHLrf-A
                                       (T/MI/YR)  (1000'S LBS/YR)   (T/YR)  (UG/L)

                                                 3.0   74    336   4.5    6


                                                14.5   221    810  20.5   26


                                                14.6   243   1083  16.5   26


                                                14.6   242   1083  14.6   26


                                                 7.0   168    526  10.5   12
                                       157

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existing  land use, and one representing a predevelopment (100% forest) condition
are provided in Table 4 as an additional basis for comparison.  Individual meas-
ures  of projected impact upon  tributary  streams  and upon the proposed Little
Seneca  Creek Lake were  identified and calculated so  that  stormwater management
options could be evaluated in a meaningful  manner.   Impacts  to tributaries and
the lake are discussed separately below.

Impacts to Tributaries

      The  effect of  land use  change on peak  storm discharge and potential flood-
ing  is  one of  the  major  concerns of a stormwater management program as it can
have  a  direct  impact upon human safety and  property  damage.  It has been demon-
strated that the implementation of detention basins,  especially  in downstream
subareas,  can  have  the  unintended effect  of increasing peak flows  at downstream
points  (Travers,  R.G. and Chadderton, R.A., 1983).   An evaluation of whether or
not the ponds  were actually shaving peak  flow rates was very important.  Several
physical  processes  such as  low  flow, streambank erosion and  sedimentation also
play  an important role in determining the  quality of  the aquatic  and riparian
environment  along streams.

      As shown,  the  use  of wet ponds was projected to  keep the peak  discharge be-
low the existing or predevelopment rate.   Flood control objectives  were thus re-
alized.   In  contrast,  the  dry pond option  showed some reduction  from the
uncontrolled postdevelopment situation, but a net increase of 17% over the pre-
development  rate was  still  projected.   The better results associated with the
wet pond  strategy are in  large  part due to  the simulation of  extended detention
wet ponds for high density  development.  The extended drawdown of these ponds
provides  a great deal of  attenuation that has a very positive effect in dampen-
ing downstream peak flow rates.  The possibility of stormwater ponds providing a
net contribution to downstream  flooding is  greatly reduced with the use of ex-
tended  detention wet ponds.  The inability of the dry pond strategy to maintain
predevelopment  peak flow  levels  was in part due to the 70 percent coverage as-
sumption  that  was mentioned above.  Beyond this the one  to  two hour detention
periods are  often not  long  enough  to have  much of  a positive effect on down-
stream  flooding.

      The  effect of  the ponds on low discharge during the driest month was not
pronounced,  but  slightly  more  favorable with wet ponds.  Wet ponds would play a
role, albeit a  minor one in the case simulated, in contributing to higher levels
of baseflow during dry periods.

      The wet ponds do provide a  large measure of protection  against streambank
erosion.  However, an increase in streambank erosion  is still  projected for this
level  of  urbanization  notwithstanding  the widespread  application of  these
ponds.  The  projected  increase in streambank erosion occurs because the total
amount  of stormwater generated from the new development is increased.  This vol-
ume of water is  sufficient,  even as it is attenuated in the  ponds, to generate
extensive streambank erosion because of the increased frequency and longer dura-
tion  of high velocity "scouring" flow.   The deposition of sediments in stream
channels  was  projected  to be sharply reduced under' both of the pond options.
Wet ponds would appear to  be  capable of bringing sedimentation rates down nearly
to the  predevelopment  level.  The large  amount of agricultural land, with high


                                      158

-------
sediment yield provides some explanation for the high sedementation rate associ-
ated  with  the existing  land  use  situation.   Since the tributary str.eams  are
swift flowing and well aerated,  there were no discernable changes in dissolved
oxygen concentrations.

Impacts to  Little Seneca Creek Lake

     Water  quality in the  proposed  Little Seneca Creek Lake  was an important
consideration in the  master plan process.  Several measures that were thought to
either directly or indirectly affect the lake and lake water quality were iden-
tified  and included  in  the  evaluation of control options.  The total  annual
loads  of sediment,  BOD,  nitrogen and phosphorus are shown  in Table 4  to be
greatly  reduced with  the  wet  ponds.  Projected  reductions  associated with the
dry ponds,  however, were negligible.  Taking these projections one step further,
several preliminary conclusions  can be drawn.  The wet ponds would act to limit
the delivery of oxygen demanding material to the lake,  thereby benefiting dis-
solved  oxygen  levels.   Similarly,  sediment  loads  would  be   less  and  the
consequences of this  would be better water clarity  (less  turbidity) and a re-
duced amount of  sedimentation on  the lake bottom.  Projected total  phosphorus
loads were  used to estimate mean annual chlorophyll-a.levels  for  the lake.  The
estimation  of chlorophyll-a served as a substitute measure for algae production.
Estimates were based  upon  applying  the biologically  available fraqtion of the
total phosphorus load and the relevant geometric and  hydraulic data to the Vol-
lenweider  Eutrophication  Model  (USEPA,  1977).   The   resulting   levels  of
chlorophyll-a were associated with trophic conditions as  shown in Table 4.  Be-
sides the predevelopment condition,  the wet pond option was the only projection
that provided for a non-eutrophic condition.  This reflected the higher phospho-
rus removal rates  simulated  for  wet pond structures  vis  a  vis dry  or extended
dry ponds.

Comparative Costs of Dry and Wet  Stormwater Ponds

     A major focus of the Washington area NURP  study was  directed  towards the
development of a reliable method for estimating the costs involved in construct-
ing, operating and maintaining  stormwater ponds  (MVCOG,  June, 1983).  From a
management  viewpoint, this information is important  since the full  cost of im-
plementing  and operating a stormwater control is  usually the controlling factor
in the development of an effective and feasible stormwater management strategy.
The full cost of  a stormwater pond was defined  as the initial capital cost of
construction plus the subsequent O&M payments. Estimates assumed a twenty-year
project life,  and 8 percent discount rate,  and  a 1980 price base.

     The comparative  costs of stormwater ponds  in the Washington metropolitan
area are illustrated  in Figure 6.   In panel A, the total annual payment for indi-
vidual  dry,  wet.  and extended detention  ponds  are shown in  relation  to  land
use/storage requirements.  Panel B displays the  same information, but in terms
of annual payment per dwelling unit.  Land use densities included  on this figure
include  large lot  single  family (LLSF), medium  density single  family (MDSF),
townhouse/gatden apartment (THGA), and high rise/high density (HI RISE).  Dif-
ferences  in  pond  costs  are  largely  attributable  to  the  extra  storage
requirements of the wet and extended detention wet ponds.  As can be  seen, a wet
pond of  similar  size costs from 26 to 46 percent more than single-purpose dry


                                      159

-------
                 FIGURE 6.  COMPARISON OF POND COSTS
 .
 LL
 -1
 U. b^
 rrt
 6
T  a
K
                                                        MICH »ISE
                                               PANEL A
        10
                    3«
                           I      f
                          40    =a
                        VOLUME  :
 i      r     i     r
 bfl    ?»    a a   ea
ffl'M  C'F CUBIC FEETb
                                                          ± a a
                                                                 I
                                                                ± in
                                                         HlfrH  RISE
                                                              :j •• ,v •  ary pond  •
            I
           13
                      30
 f
dffl
                                 i      I
                                 S3    eta    7 a    a a
                                 ; I23B' a OF CUE 1C
 I
3. a a
                               I
                              no
ponds.  Similarly,  extended  detention ponds typically entail 10 to 12 percent
more cost than single purpose dry ponds.  In general, the cost differential be-
tween wet ponds or extended detention ponds and the single-purpose dry pond nar-
rowed as  land use  density  increased.  Figure 6 also suggests that economies of
scale can be achieved in stormwater  pond construction.  As an example, larger,
centralized  off-site wet  ponds were found  to be  as  economical  as  smaller,
de-centralized dry ponds in the  Little Seneca Lake Study (Schueler and Sullivan,
1983).  Finally,  the greater cost of wet and extended detention wet ponds may be
offset to some degree by the realization of aesthetic amenities including recre-
ation,  landscape,   and  wildlife benefits  attributed  to  these  multi-purpose
ponds.
                                      160

-------
                                 CONCLUSION
Field investigations revealed a marked difference in the pollutant  removal abil-
ities of  dry ponds  and wet ponds.  Removal efficiencies were enhanced in ponds
where settling and biological processes were active.  The  simulation of pond be-
havior  in  HSPF  proved  to  be  a  valuable  addition  to  watershed management
planning.  The cumulative effect of a widespread application of BMP's was sys-
tematically  evaluated within individual tributaries  and  at  the downstream
terminus  of  the watershed.  The simulation of dry and wet  ponds allowed relative
differences  in  peak discharge rates,  streambank erosion, pollutant transport,
and  potential  levels  of  algal production to be calculated.  The superior per-
formance  of  wet  ponds   over dry  ponds  in   the   basin-wide   assessment  was
demonstrated for  nearly all of the measures of interest.  The  cost of implement-
ing  a wet pond management strategy was shown to be greater than costs associated
with implementing the more conventional  dry ponds.  However, cost differences
are  minimized with  increasing density, and there also appear to be other bene-
fits associated with wet ponds.

     This approach to  watershed modeling and the simultaneous  evaluation of con-
trol options and  land use planning alternatives was very well  suited for the en-
vironmental  and planning issues addressed in the Little Seneca Creek Watershed
Study.  Several other questions  or  issues  that could potentially be addressed
with HSPF include:  1) the placement and sizing of ponds  to minimize peak dis-
charge  rates at  -all  places within a watershed; 2) the explicit modeling of
sediment  and water quality processes within ponds;  and 3) the evaluation of de-
sign features to enhance pond performance.
                                REFERENCES

American Public Works Association.  "Urban Stormwater Management:   Special  Re-
port No.  49", Chicago, IL, 1981.

CH2MHILL.   "Seneca  Phase  II   Watershed   Study",   report   prepared   for   the
Maryland-National  Capital  Park and  Planning  Commission,   Silver  Spring,  MD,
1983.

DeTullio, D. and Thomas,  R.  "Stormwater Management  Cost Study",  USDA  Soil Con-
servation Service, report prepared for the Maryland-National  Capital Park  and
Planning Commission, Silver Spring, MD,  1977.

Hydrocomp,   Inc.,  "User  Manual  for  Hydrologic Simulation  Program  -  Fortran
(HSPF)",  U.S.  Environmental  Protection  Agency, Environmental Research  Laborato-
ry, Athens,  GA,  1980.

Metropolitan Washington Council  of Governments, "An Evaluation of  the Costs of
Stonnwatar  Management  Pond Construction  and  Maintenance", Washington, D.C.,
June, 1983.
                                     161

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Metropolitan Washington Council of Governments, "Potomac River Water Quality -
1982:  Conditions and Trends in Metropolitan Washington", Washington, D.C.,  Au-
gust 1933.

Metropolitan  Washington Council  of Governments, "The  Seneca  Creek  Watershed
Management Study: Final Report", Washington, D.C., September  1983.

Metropolitan Washington Council of Governments, "Urban Runoff in the Washington
Metropolitan Area",  Final NURP Report, Washington, D.C., December 1983.

Occoquan Watershed Monitoring Laboratory (OWML), "Final Contract Report on Met-
ropolitan Washington  Urban Runoff Demonstration Project", report prepared for
Metropolitan Washington Council of Governments by VPI & SU, OWML, 1983.

Schueler, T.R. and Sullivan, M.P., "Management of Stormwater and Water Quality
in an Urbanizing Watershed", Proceedings of 1983 International  Symposium on Ur-
ban Hydrology, Hydraulics  and Sediment Control, University of Kentucky, Lexing-
ton, KY, 1983.

U.S. EPA,  "Water Quality  Assessment: A screening Method for Nondesignated 208
Areas", EPA-600/9-77-623,  Environmental Research  Laboratory, Athens, GA,  1977.

Travers, R.G. and Chadderton, R.A.,  "The Downstream Effects of Storm Water De-
tention Basins", Proceedings of International Symposium on Urban Hydrology, Hy-
draulics and Sediment Control,  University of Kentucky, Lexington, KY,  1983.
                                      162

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                   KINEMATIC ANALYSIS OF DETENTION STORAGE




                                     by D. Stephenson




                         Visiting Professor, McMaster University and




         Professor of Hydraulic Engineering, University of Witwatersrand, Johannesburg









                                       ABSTRACT




       The role of detention storage in attenuating peak floods is investigated in a general manner




using the kinematic flow equations. A diinensionless form of the equations is used to provide guides




to the design of channels and ponds in order to  optimize surface or channel detention or pond sizes.




Resulting hydrograph shapes for different types of control are presented.




       The paper looks at channel storage as well as pond storage.  Channel storage and catchment




(on site) storage are achieved by retarding the runoff such as by lengthening the flow path, reducing




slope or increasing roughness.  These effects are  achieved  with numerical models based on the




kinematic equations.




       A kinematic model for simulating conduit flow between detention storage ponds is presented.




The model accounts for fluctuating storage volumes and inflows and outflows.









INTRODUCTION




       Many research  projects have been based on the use of mathematical models to study the




runoff off urban and rural catchments. In fact the number of such reports could approach the number




of catchments or candidates, whichever is lesser, multiplied by the number of models available. Much




of the research is published but even more is  in a form of little value to the practicing engineer.




Sensitivity studies and model calibration have to be performed from scratch for new drainage designs.





                                           163

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       It has been the objective of the Water Systems Research Programme at the University of


Witwatersrand to condense as much of the information from catchment models as possible into simple


relationships for use by practicing engineers (Stephenson, 1982). Such design aids have included


peak flow rates and identification of critical storm durations for any catchment. Hydrographs for


simple and complex catchments have been generated  (Constantinides and Stephenson, 1982)  and the


effects of storm dynamics and movement have been identified.  All these studies have been performed


in a generalized way and the results plotted in the form of dimensionless charts.


       The kinematic equations have been used in analytical and numerical form for  many of the


studies. The following study attempts to generalize the effects of channel and pond detention storage


on runoff rate and evaluates the relative effects on storage volume  and channel capacity.





STORAGE FUNCTIONS


       Starting with the St. Venant equations it is easy to see the components of storage:


                                      dA -    £                                       m
                                         — —                                           i-ij
                                      at       ax
The first equation is the continuity equation and the second the so-called dynamic equation, in fact


the first equation is not a storage equation, it represents the rate of change in cross sectional area of


flow as a function of inflow and outflow. The second equation contains more about the distribution of


storage.  The last  two terms represent the wedge component of storage, which are absent in the


kinematic equations. The kinematic equations therefore treat storage as a prism, with storage in


blocks and no allowance for difference in slope between bed and water surface is made.


       Since the second equation is replaced by a  friction equation and SQ =  Sf in the kinematic


equations, only the first equation can be used to calculate storage changes.
                                            164

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Comparison with Muskin^um Equations

       The continuity equation may be written as

                                 2=1 + A2"A* = o                                     (3)
                                  Ax       At


where O is outflow. I is inflow over a reach of length Ax, and Aj and A2 are the cross sectional areas

before and after At respectively. If O = (Oj  + O2)/2 and I = (It + I2)/2 and AAx is replaced by S, the

storage which is a function of Aj and AQ, which in turn are functions of flowrate, eg. S = xl 4- (l-x)O,

then the above equation becomes the one frequently used for open channel routing,

                                 °2 = C1J1 + C2 *2 + C3 °1                                (4)

where Cj, c2 and c3 are functions of x. The latter equation is referred to as Muskingum's equation. If

x = 0 the routing equation corresponds to level pool or reservoir routing.  The more general equation

with x = 1/2 represents a 4-point numerical solution of the continuity equation as employed in

kinematic models (Brakensiek,  1967).



CHANNEL RESISTANCE AND STORAGE

       Channel storage performs a similar function to pond storage, and there are many analogies to

be drawn between the two. Channel storage is a function of friction resistance and channel shape.

       The form of friction equation, as well as the friction factor,  affect the  reaction  speed of a

catchment and the volume stored on  the catchment.  The excess rain stored  on the catchment,

whether in channels or on planes, is a form of detention storage, and as such, affects the concentration

time and consequently the peak rate of runoff.

       Both the exponent of y in the equation q — zym and the roughness coefficient i affect the flow

depth - discharge relationship.  Some friction formulae used in stormwater drainage practice are

listed below (SI units)

       Darcy                 Q = (8/f)1/2 A(RSg)1/2                                        (5)

       Chezy                 Q = 0.55CA(RS)1/2                                         (6)


                                          165

-------
       Manning              Q = A R2'3 S1/2/n                                            (7)




       Strickler              Q = 7.7 A(R/k)U6 {RSg)l/2                                    (8)




R is the hydraulic radius AJP where A is the area of flow and P the wetted perimeter. S is the energy




gradient, f is the friction factor and k is a measure of roughness.




       If it is assumed that the friction factors are constant then Q is proportional to S1/2 in all cases.




This is true for high Reynolds numbers but for shallow flow the friction factors should be increased.




       By comparing the Manning and Strickler equations it may be deduced that n = 0.13 k1/6/g1/2




and by comparing with the Darcy equation, n = (f/8g)1/2 R1/6. The latter will be found to hold




reasonably well for high Reynolds numbers but for lower Reynolds numbers f is known to increase




and n should increase too.  The following table indicates increasing values of n for a wide channel




with an initial n of 0.02 at 1 m depth, a slope of 1/100 and decreasing depths. The n is calculated from




f which in turn is calculated from the Colebrook-White equation.
Water depth, m
1.0
0.1
0.01
0.001
Reynolds No.
1 000 000
40000
1000
20
Manning n
0.02
0.023
0.040
0.062
Darcy f
0.03
0.09
0.6
3.0
       The Manning roughness coefficient does not vary as much as the Darcy coefficient with




reducing Reynolds number.  On the other hand, the square root of Darcy's coefficient is employed to




calculate flow rates which compensates to a small degree, but generally it would appear the Manning




coefficient is a more reliable number to use for channels (at high Reynolds numbers) and overland




flow (at low Reynolds numbers), as a more reliable estimate of n is  possible than f, since n does not




vary as much.
                                            166

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       The variation  in peak flow from catchments depends on the roughness coefficient and the



exponent m of R or y. This is largely due to the attenuating effect of friction resulting in a larger time



to equilibrium.  The rain excess intensity-duration relationship is therefore required to evaluate the



effect of each coefficient on peak runoff rate and maximum catchment storage.  The following



expression for excess rainfall intensity is assumed:



                                      i =    a                                            (9)
                                      €          f

                                               Q,


 In this equation it is customary  to express  i and a in mm/h and b and td in hours, t^ is the storm



 duration, assumed equal to time of concentration tc for maximum peak runoff off a simple catchment.



 Starting with the kinematic equation for continuity


                                      3y    da                                            ,,...
                                      — + — = i                                         (10)
                                      dt    ax   e


 and a general resistance equation



                                 q=zym       (m-s units)                              (11)



 then it may be shown that t = (L/z  i m'1)1/m (seconds) where q is the runoff rate per unit width of



 catchment and y is flow depth.



        The rising limb of the hydrograph is given by the equation



                                     q = z(ie t)m (m3/s/m^                                 (12)



 and another  expression may be  derived for the falling limb.   In Fig. 1 are plotted dimensionless



 hydrographs to illustrate the effect of m on the shape of the hydrograph. The graphs are rendered



 dimensionless by plotting Q = q/ieL against T = t/tc.  m is used as a parameter.  Thus m =  1/2



 represents closed conduit  or orifice flow, m =  1 represents a deep vertical sided  channel, m =  3/2



 represents a wide rectangular channel according to Darcy, or a rectangular weir, m  =5/3 represents a



 wide rectangular channel according to Manning and m = 5/2 represents a triangular weir.



        The graphs immediately indicate the effect of m on catchment detention storage. The smaller



 m, the greater the storage. Thus provided storage is economical, throttled outflows increase storage



 and reduce discharge  rate (which is not immediately apparent from these graphs as they are plotted





                                            167

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relative to excess rainfall intensity).  In practice the concentration time increases the greater the




storage so that lower intensity storms became the design storms.  This has a compound effect in




reducing flow rates since losses increase and  it is possible that the entire catchment will not



contribute at the peak flow time.




       A general solution for peak flow and storage in terms of rainfall  intensity-duration




relationships is derived below. Solving (9) with td  = tc for maximum rate of runoff per unit area,



generalized by dividing by a,
                           q /aL= i /a =
                            m       c
                                                 3600
                                         [L/z(a/3600000)m~1]1An\c
                                                                                         (13)
The term L/zam~l is referred to as the lag factor.  The constants are introduced since a is in mm/h,




and time of concentration is in seconds while (9) requires hour units. The maximum peak flow factor




ic/a is plotted against lag factor in Pig. 2, since it is not easy to solve (13) directly for i /a.
                 0
              Fig.l
                                           1
Hydrograph shapes for different values of m in q = zym




               168

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           ie/a and  s/a
              1 -
                                                      F3/2  ,  z=(8gS/f)1/2
            Fig. 2
                                                    L/za1
                          Peak flow and storage versus lag factor
                                                                    ZOO
       An expression for the corresponding catchment storage is derived below.  At equilibrium the
flow per unit width at a distance x down the catchment is
                = zym
therefore      y = (iex/z)1/m.
Integrating y with respect to x yields the total volume down the catchment
                                  V.=
                                       Lm
                                            (ieL/z)
or in terms of the average depth of storage s = V/L,
                                   ,l*n
                                                 l/m
                    s/a =
                           m

                                                                                        (14)
                          m+l\a/    vz(a/3600000)m~l/    360°
where s is in mm, and ifi and a are in mm/h,  s/a is also plotted against lag factor in Fig. 2. It will be
observed that average storage depth does not increase in proportion to L/za"1"1, in fact  the rate  of
increase reduces beyond L/za111"1, =  50-100, and the rate of reduction in peak flow ie/a also decreases

                                           169

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beyond this figure indicating reducing advantage  in increasing channel length or roughness



(z = S  /n).  Since total channel cost is a direct function of storage capacity it would appear to be an



optimum at some intermediate value of L/za"1'1 if there is a cost associated with peak discharge e.g.



culverts or flooding downstream.




       Note that infiltration after the rainfall stops, is neglected in the above analysis. Inclusion of



that effect would lower the ie/a and s/a lines to the right, implying a larger L/za™"1 is best.



       The model provides an indication of total storage in the system. The location (and volume) of



storage could be further optimized using dynamic programming methods or by detailed modelling. It



should be found generally that it is most economical to provide pond storage (m = 1/2) at the outlet,



whereas channel or catchment storage (m = 5/3) is most economic at the head of the system.







KINEMATIC EQUATIONS APPLIED TO CLOSED CONDUITS



INTERCONNECTING RESERVOIRS



       If the open channel kinematic equations are applied to closed conduit flow the  problem



becomes a steady state flow one since flow rates become independent of cross section. This is provided



the conduits remain full and there are no storage ponds at nodes joining conduits.  If one permits



storage variation at nodes one has the reservoir-pipe situation encountered in water supply which is



often analyzed employing pseudo-steady flow equations.



       The continuity equation becomes (see Fig. 3)





                             «  -Q,-q + A^=0                               «5>
                              ^i+1    i.   qi    i dt


where the reservoir surface area A. replaces B dx in the open channel continuity equation where B is



the catchment width,  q is the reservoir inflow here. The dynamic equation is replaced by



                                         Q^zA™                                    (16a)



where A  is the (constant) conduit cross sectional area.  Since the kinematic equations omit  the



dependency of Q on head difference Ah, the latter equation assumes the head gradient along the pipe
                                           170

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                            Fig. 3
Input-output node storage
equals the pipe gradient, i.e. free-surface just full flow. Since A is a constant it is relatively easy to




replace the last equation by one of the form




                                        QJ = zA h."1                                    (I6b)




       This equation is applicable  to free discharge  from an orifice or over a weir. One  more




applicable to conduit flow would be



                                     Q = zA (hj., - hj)m                                  (I6c)




Any one of the above three equations could be applicable in storrnwater drainage. For channel or




overland flow (I6a) applies, for complete storage control (16b) applies and for closed conduit control




(16c) is applicable. The latter form of equation has in fact been employed in water reticulation pipe




network analysis.  It can be applied in storm drainage to  closed systems (not of great interest in




stormwater management practice) or to pipe-reservoir problems.  Surface detention and artificial




detention storage ponds can be handled in  an overall flow balance employing the closed conduit




kinematic method.  It should be noted that the numerical instability problems associated with




solution of the open channel kinematic equations are absent. Time steps can be much larger than for




open channel kinematic modelling.




       Storage fluctuations may be computed in steps and the affect of changes in pond water levels




on flows in conduits can be accounted for.




       One  possible application of such a program  is to an interconnected pond system with




reversible flows  in conduits.  Overload from one  pond can be forced back to another pond.  Such




situations can readily arise from spatially variable storms and possible from travelling storms.




                                            171

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             Off-channel storage can also be accounted for.  Such ponds have the advantage that water

      level variations are not as marked as the head variations in the drain pipes (which may in fact be

      surcharged). This is due to the reversable head loss between the main conduit and the pond.

             The simplified layout  in  Fig. 4 was analyzed employing the kinematic closed  conduit

      continuous simulation program 'KING'. Input and output are appended to illustrate the simplicity in

      this type of analysis. Flow reversal, pond level variations and the large attenuation in peak flow will

      be observed due to the ponds (from 5.6 m3/s down to 1.5 m /s). By adjusting individual pond areas and

      conduit sizes an optimum design could be achieved for any design storm input. A sensitivity analysis

      for alternative storms (e.g. larger deviation or spatially variable) would then be performed.
                                                                1.4m  /s/15nrin
1.4m3/s
                                                                           10000m'
                                                         1.0m
       Fig. 4
Conduit-and storage storm drain network.
     REFERENCES

     Brakensiek, D.L., 1967. Kinematic flood routing. Trans. Am. Soc. Agric. Engrs., 10 (3), p. 340-343.

     Constantinides, C.A. and Stephenson, D., 1982. Dimensionless Hydrographs using Kinematic
     Theory.  Water Systems Research Programme, University of the Witwatersrand, Johannesburg,
     Report 5/1982.

     Stephenson, D., 1982. Peak Flows From Small Catchments Using Kinematic Theory. Water Systems
     Research Programme, University of Witwatersrand, Johannesburg, Report 4/1984.
                                                172

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KING program
10

20

25

30
40
41
          !  KING KIHEMflTIC COHTIH SIMU
          LN OF NETWORKS WITH STORflGE
          DIM C<50>>Q<50),H<50>,Q2<50>
          ,S2<50>,S4<50>,F<50>
          DIM J1CS0), J2<50>,D<50>-X<50
          DISP "NfittE OF NETWORK";
          INPUT N*
          DISP "DRflWOFF DURN , win, SIM  D
          URN,min,OT,min,DRflWOFl
 42
 45
 46
 47
 50

 €0
 62

 64
 65
 67
 63
 69
 70
 75

 80
 85
 90

130
lie
120
125
127
130

140
142
143
144
145
146
147
148
149
150
158
160
165
178
130
190
192
 INPUT T3,T4,T5,Q2<1>
 T3=T3*69
 T.4=T4*60
 T5=T5*60
 OISP "NPIPES,NODES,NRES/DRRC
 Y4";
'INPUT P,J,J3»F1
 DISP "INITL UfiTER  LEV£Ln>,SUR
 FFtCE flREfl  m2";
 FOR L=l TO J3
 OISP L;
 INPUT H,FKL>
 NEXT L
 G=9.8

 DISP MTOPN,BOTN,Lm,Dn»,OUTFLO
 8m3s";.
 FOR K=l TO P  ! PIPE DHTfl
 DISP K;
 INPUT JKK>, J2,X,D(K>,
 Ql
 Q2=F1
 QCK^^S  I4159^cD^fOA2/4
 C=S*D-5/F > =H< Jl >-1/C*GKK

 NEXT K
 FOR L=l TO J
 HKL)=e
 FOR M=l TO P
 IF JKM>=L THEN  147
 IF J2L THEN  149
 ni=MKL> + l
202
204
266
263
209
210
220
230
240
250
NEXT M
NEXT L
W=l .3
T0=.0001
Tl=.01
N0=SQR+5
Nl=SQR(J)-«-10
N2=0
N3=0
PRINT "PIPENET-.N*
FOR T6=T5 TO T4 STEP T5
IF T6<=T3 THEN 210
FOR L=l TO J

Q2=0
NEXT K
                                     260 FOR K=l  TO  P
                                     270 S2xflBS
                                 290
                                 360
                                 310
                                 320
                                 330
                                 335
                                 340
                                 350
                                 360
                                 365
                                 370
                                 380

                                 390
                                 400
                                            410  NEXT  113
                                            420  D2=H
                                            430  HJ THEN  489
                                         FOR L=J3*1  TO J
                                         S4
                                         IF JKM)OL THEN 390
                                         S4CJ1>
                                         IF J2OL THEN 416
                                            440  C2=C2+flBS-D2>
                                            456  S3=S3+l
                                            460  NEXT L
                                            470  IF  C2xS3<=Tl  THEN 538
                                            480  NEXT K
                                            500  FOR K-l  TO P  !  NEW FLOWS
                                            510  S4=GKK>
                                            520  Q
                                            530  IF 1=1  THEN 550
                                            540  GKK>=.5*«a
                                            550  NEXT K
                                            560  C3=0 !  TOLERflNCE CHECK
                                            570  FOR K=l TO P
                                            580  C3=C3*flBS=H-Q2(L>*T5/fUl_>
                                                FOR M3=l TO MKL)
                                                M=M2
                                                IF JKtOOL THEN 626
                                                H=H-Q
                                                IF J2(M)OL THEN 628
                                                H=H-M5*T5/fUL>
                                                NEXT M3
                                                NEXT L
                                                PRINT USING "K, OOOOD, X , K , DOD
                                                DD.DO" > "TS=".T6,»H1=",H<1>
                                                PRINT "TOPN BOT  Xm   Om  Qm
                                                3/s HBOTm"
                                                FOR K=t  TO P
                                                PRINT USING 670 ; J1O;>,J2
-------
      OF NETWORK?
 STORMDRfllN
 DRRMOFF DURN/min/SIM DURN/min,DT
 , min, DRftMOFl mS/s?
 20> 60/5/-1 .4
 NPIPES, NODES, NRES/DRRCYf?
 4/5/4. .014
 INITL WfiTER LEVELm/ SURFflCE RREfl
 M2 1 ?
  2 '?
 106, '4 130
  3 ?
 163/403
  4 ?
 lew, 136 wee
 TOPN/eOTN,Lm,Om,OUTFLOBm3s
 1/3, see/ .8/-i .4
  2 ?
 3,2/ 1280, .7,-! .4
  3 ?
 3/5, see, i/-i .4
  4 ?
 5/4/ 1283,1/0
P1PENET
Ts=  300 Hl=  101
TOPN BOT  Xm   Om
  i  3  900   .see
  3  2 1209   .760
  3  s  see i.000
  5  4 1200 1.000
Ts=  600 Hl=  102
TOPN BOT  Xm   Dm
  1  3  908   .880
  3  2 1206   .708
  3  5  308 1.860
  5  4 1203 1.000
Ts=  960 Hl=  103
TOPN BOT  Xm   Dm
  1  3  900   .800
  3  2 1206   .780
  3  5  880 1.000
  5  4 1200 1.0Q0
Ts= 1209 Hl=  104
TOPN BOT  Xm   Dm
  1  3  900   .800
  3  2 1200   .766
  3  5  300 1.000
  5  4 1200.1.800
Ts= 1500 Hl=  104
TOPN BOT  Xm   Dm
  1  3  900   .800
  3  2 1200   .706
  3  5  806 1.000
  5  4 1200 1.000
Ts= 1800 Hl =  183
TOPN BOT  Xm   Dm
  1  3  900   .800
  3  2 1200   .706
  3  5  303 1.000
  5  4 1200 1.006
    STORMDRRIN
.61
  Qm3/s  HBOTm
   .056   161.6
   .035   101.1
  -.763   108.5
   .634   106.0
.39
  Qm3xs  HBOTM
  -.442   182.3
   .263   162.3
  -.253   101.7
  1.111   100.3
.35
  Qm3/s  HBOTm
   .125   103.4
   .066   183.4
   .093   162.4
  1.303   100.0
.45  '
  Qm3xs  HBOTw
  -.077   104.3
  -.068   104.4
   .261   103.3
  1.552   100.8
.27
  QmSx-s  HBOTm
   .249   103.5
  -.132   104.3
  1.360   102.6
  1.357   100.8
.90
  Qm3/s  HBOTm
   .484   103.2
  -.307   104.1
  1.237   102.1
  1.234   100.8
Ts= 2100 Hl=  103.55
TOPN BOT  Xia   Om  Qm3/s HBOTm
  1  3  900  .800   .475  102 9
  3  2 1200  .760  -.327  103 8
  3  5  800 1.000  1.177  101.9
  5  4 1200 1.000  1.174  100 0
Ts= 2400 Hl=  103.21
TOPN BOT  XM   On  Qm3xs HBOTm
  1  3  900  .806   .449  182 7
 -3  2 1200  .700  -.334  103 6
  3  5  380 1.000  1.123  101 8
  5  4 1200 1.800  1.120  108 6
Ts= 2700 Hl=  102.96
TOPN BOT  Xm   Dm  Qm3^s HBOTm
  1  3  980  .800   .420  162 4
  3  2 1206  .706  -.335  103 3
  3  5  390 1.000  1.072  161.6
  5  4 1200 1.060  1.069  100 e
Ts= 3880 Hl=  102.60
TOPN BOT  Xm   Orn  Qm3/s HBOTm
  1  3  900  .800   .390  102 2
  3  2 1200  .780  -.332  103 1
  3  S  880 1.000  1.022  101 5
  5  4 1280 1.000  1.619  166.8
Ts= 3308 Hl=  182.33
TOPN BOT  Xm   Dm  Qm3's HBOTw
  1  3  900  .806   .362  162 0
  3  2 1208  .706  -.328  102 9
  3  5  800 1.808   .973  101 3
  5  4 1200 1.008   .969  100.e
Ts= 3680 Hl=  162.08
TOPN BOT  Xtn   Dm  Qm3's HBOTm
  1  3  960  .806   .335  101.8
  3  2 1206  .700* -.322  102.6
  3  5  860 1.000   .924  101.2
  5  4 1200 1.000   .926  166.B
                               174

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                 THE NEED TO VALIDATE HYDROLOGIC MODELS

                                   by

                              Stan  Udhiri
         Maryland-National  Capital  Park  and  Planning  Commission
                     Upper  Marlboro,  Maryland  20772



                               ABSTRACT
     Hydrologic models can yield vastly different results depending on
the model used  and  the experience of  the  user.   Several  models  were
utilized  in  estimating   discharge  values  for  storms  of  different
frequencies  in several watersheds in Prince George's County, Maryland.
The estimates were produced independently by unrelated study groups.

     The studies reveal the differences  that  can  exist  between values
derived for  the same  stream segment using  different models, and point
out the critical need to assess the reasonableness of estimates from a
hydrologic  model  before  the employment  of  an estimate  for design or
regulatory purposes.
1.0  INTRODUCTION
     A  hydrologic model  is  a  tool  that  can  be  used  to  assess  a
watershed event, such as a flood or drought.  During or after a flood,
such   a   model  could   be  utilized   in  tracking   the  behavioral
characteristics of the flood wave as it travels along the stream.  How
and where the flood waters  overflow the banks  could be noted, so also
could  the height  of  the flood  waves.   Such information  is extremely
important  to  a  community  as   a   first   step  in  understanding  Its
susceptibility to flooding  and  the  magnitude  and  aerial extent of the
problem.   This  initial  step  of  understanding  or  appreciating  the
problem  is   necessary  prior  to undertaking  a meaningful  corrective
action.  It  is  also  possible with  flow records  of sufficient length,
for a  community to gain some insight into  future flooding problems and
therefore  take  some  preventive  measures  or  actions  to  minimize
prospective  damages.    A  model could  also be  used  to monitor  the
limited  flow in a watershed  during a  drought.    The  fluctuations  1n
flow  along  the stream  and  its  tributaries between  flood and drought

                                  175

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periods would  provide  invaluable information to the  community  on the
stream's ability to meet its water resources needs at all times.

     This paper  presents  case studies of  flood  estimates  obtained by
using  different  hydrologic  models  and  reveals  the  vast  differences
that can exist between  the  estimates.   The studies were all performed
for watersheds  located in  Prince George's County, Maryland  and were
part of a county-wide assessment of flooding and drainage issues.
 2.0  HYDROLOGIC MODELS
     Hydrologic  models  are  used  to  simulate  hydrologic  events  that can
be  considered  as  systems  or processes  {Reference  1).    The models
considered  in the  paper are mathematical  formulations used  to  describe
a watershed's hydrologic and hydraulic  phenomena.   These models can  be
used  to estimate  or  chart  the  runoff  contributions  of subareas, the
aggregation  of  these  contributions  at  various   points   within  the
watershed  and  the effect of  obstructions,  depressions  and other flow
features.   Typical results  from  these models include  discharge values,
runoff  volumes,  hydrographs, hydrograph peaks  and  their times   of
occurrence.   Some of the widely used  hydrologic models are discussed
here.   Technical Release (TR) 20,  developed by the Soil Conservation
Service  (Reference  2),  is  a  single  event  computer program  that
computes   runoff  directly   from  natural   or  synthetic   rainfall   by
applying  runoff curve  numbers to  rainfall  amounts.    A runoff curve
number  (RCN) is  a  number which represents the watershed's  potential  to
transform  rainfall  into runoff  by  considering the  soil  types  and
groups  and the  soil  cover  complexes in  the watershed.    Soil  cover
complexes  are descriptions  of the  combinational  effect  of  land use and
land  use  treatment  such as  rural   agricultural  with  vegetative cover
and conservation practices, and  the soil  groups  refer to the four soil
group classifications  (A, B,  C,  0)  as defined by the  Soil Conservation
Service  {Reference  3).    Soil  group  A  describes  soils  consisting
chiefly  of  sands  and  gravels with low  runoff potential  while soil
group  D describes soils  with high  runoff  potential.   B  and  C group
soils represent  soils with  moderate runoff  potential.

      Runoff curve numbers  can range from a low of 6 for a pasture  or
range in good condition with contoured  treatment to a high of 98 with
the  lower  numbers  representing  low  runoff  yield   and   the higher
numbers,  high   runoff  yield.   TR-20 uses   the  CN  method  to  compute
runoff  and develop  flood  hydrographs  by  using the  unit hydrograph
addition   procedure.     The  unit   hydrograph  in   the   program  is   a
dimensionless   curvilinear   unit  hydrograph  that   has  a  point   of
inflection  approximately  1170 times  the time-to-peak  (Tp) and  the time
to peak 0.2 of  the time-of-base  (Tb).

     "HYTAIN"  (Reference 4)  is  also a  single  event  computer  program
for  computing   runoff   from natural or  synthetic  rainfall.    It  was
developed  by  the  engineering firm  of  Clark, Finefrock  and  Sackett.

                                  176

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              Dimensionless  Curvilinear Unit Hydrograph
     "Log-Pearson Type III" (Reference 5) is a statistical model  that
is  used  to  estimate  peak  flows   by   fitting   a   Pearson-Type   III
distribution to a  logarithm transformation  of  annual peak discharges
at a gauge site.   The  mechanics  involved in this method  requires  the
computation of  three  parameters:   the  mean  (x),  standard  deviation
(s), and coefficient of skew (g)  of  the  lagarithms of the  values.   The
mean (x), standard deviations  (s), and the  coefficient of  skew  (g)  are
derived using  the following equations:
         x =
                                 (3)
         s =
Px-7)2    1 0.'
^TJ—  J
(4)
in which:
         x = logarithm mean
                                 177

-------
         x = logarithm  of  annual  peak  flow

         n = number  of  peak  flows in data set

         s = standard deviation  of lagarithms

         g = skew  coefficient  of logarithms
•These  parameters  are  then  used  to  calculate  the  logarithms  of  the  peak
values   corresponding  to   the   required   recurrence   interval.     The
equation  used  in  the  computation is:

          Log Q   =  x" + KS
where         Q   = discharge  value for the required  recurrence
                    i nterval

               "x  - logarithm  mean

               S  = standard deviation  of  logarithms

               K   = a  Pearson Type III coordinate  corresponding  to
                     the required interval  and  the  computed
                     coefficient  of skew (g)  (Reference  5)
     Regression  models  are  mathematical formulations  used  to  derive
flood   discharges  from   variables   such  as  meteorology,   geology,
topography  or  a  combination  of  these.    The  combination  of these
variables,  termed the  independent  variables and how  they  affect  the
flow  discharge (the  dependent  variable) is  usually  established by  a
technique  called  multiple regression analysis (Reference 6).   Some  of
the  more popular regression  models  are:   (a) the Maryland  geological
Survery  regression model  (Reference  7).   This model  is  of the  form:


                  Q  = A1  BJ  zCk yD1  Em Fn

where              Q  = peak flow discharge in cfs  (the  dependent
                       (variable)

   A, B, C, D, E,  F  = the independent variables  representing the
                       meteorologic,  geologic, topographic
                       characteristics of the drainage  area.

   i, j, k, 1, m, n  = the regression exponents

               z, y  = regression constants
                                  178

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Through  a  stepwise  procedure,  those   independent  variables,   their
constants  and exponents which  best estimate  the dependent  variable are
established.

     A summary of the regression relations is  shown in Table  1.
                                    TABLE  1

                     MARYLAND GEOLOGIC SURVEY REGRESSION MODEL

                            (Model:  Pn = KA8SbFcGd)
Recurrence
interval (n) , in
years, for
flood peaks (P)

2


5


10


25


50

100 *
Regression
constant
K
54.2
fiO.7
17.1
88.9
100
30.8
112
41.5
42.0
141
57.5
58.3
46.0
42.8
84.9
87.1
Regression exponents for
indicated basin characteristics
a
Area (A)
0.947
.945
.913
.921
.920
.890
.908
.883
.878
.894
.871
.865
.915
.911
.874
.858
b
Slope(S)
0.331
.339
.274
.329
.338
.270
.336
.284
.288
.350
.303
.308
.377
.410
.350
.358
c
Forest(F)
-0.394
- .428
0
- .362
- .398
0
- .337
0
0
- .302
0
0
0
0
0
0
d
Geography (G)
0.809
0
0
.856
0
0
.956
1.05
0
1.11
1.20
0
.909
0
1.25
0
Standard
error
± *
31.7
36.2
42.9
30.5
35.1
41.3
32.4
37.0
43.2
37.4
40.3
48.2
36.7
41.3
38.4
46,2
 * Relations not valid for Coastal Plain drainage basins.
(b) The  Udhiri  and Motayed  regression model  is  of the form:
               Qn
                D =   drainage area of the watershed in  square miles,
                S =   main  channel slope  in ft/mile and
                                    179

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              S^ =   surface storage in percent.
         i» j> k =   regression exponents

A summary of the regression relations is presented in Table 2.


                                  TABLE 2


                   UDHIRI AND MOTAYED REGRESSION MODEL


     Q2    =  23.0 D-873 $.291 sst-.205  ..(1)

     Q10   =  75.7 D-814 $.266 sst-.419  ..(2)

     Q50   =  188.4 D-765 S-243 Sst-.514 ..(3)

     QlOO  =  27&.4 D-742 S-229 Sst-.588 ..(4)


where Q£   =  peak discharge in cfs for a 2-year recurrence flood

      D    =  drainage area of the watershed in square miles

      Sst  =  surface storage in percent.



3.0  PISCATAWAY CREEK FLOOD ESTIMATES
     Some  of  the various hydrologic models  discussed  previously were
used to estimate flood flows for different recurrence intervals at the
same  point on  Pi scat away Creek.   The  Creek is  a tributary  of the
Potomac  River- and  is  located  in the  southwest  portion  of  Prince
George's  County,  within  the   Atlantic  Coastal  Plain  physiographic
province  in  Maryland (Figure  1).   The  Creek  flows  in  a  southwest
direction  for approximately  20 miles  and  empties  into  the  Potomac
River,  some seven miles  south  of Washington, D.C.   Piscataway Creek
rises within  the Andrews  Air Force Base  just north of South Perimeter
Road at elevation  260 feet  mean sea level  and drains  a  total  area of
62.8 square miles.

       The  soils  in  this  area consist  of silty,  sandy  and gravelly
Pleistocene  outwash  from  unconsolidated  materials  of   the  Coastal
Plain.  The predominant soils in the area  belong to soil group C which
defines  soils with  slow  infiltration  rates  when thoroughly  wetted
(Reference  3).    Most  of  the  watershed   is  undeveloped  although
extensive  development  has  taken place in  the northernmost portion of
the watershed.   Overall,  the   watershed  is   approximately  17  percent
developed.
                                  180

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     The  results  of  the  flood  estimates  using  some  of  the  various
models discussed in this paper are displayed in Table 3.
                        Figure 1
                                                         WATERSHED  MAP
                                                          RSCATAWAY CREEK
                                181

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                                    TABLE 3

                  COMPARISON OF PEAK FLOWS BY VARIOUS MODELS

                    PISCATAWAY CREEK TO PISCATAWAY ROAD, MD
                       DRAINAGE AREA - 39.5 square miles
                          100 YEAR PEAK FLOWS IN CFS
                                                             Statistical Model
              TR-20   Regression Model by    Regression     (Log-Pearson
Frequency     Model   Maryland Geological  Model by Udhiri   Type III Distri-
in years     (Ref. 2)  Survey (Ref. 7)    &Motayed (Ref. 8)  bution (Ref. 5))
 100          8980          5228               7647               17746
   4.0  ANACOSTIA RIVER FLOOD ESTIMATES
        Estimates for  floods  for various recurrence  intervals  were made
   at a point  (drainage  area, 72.8 square miles)  on  the Anacostia River
   (Figure  2)   which  flows   through  two  physiographic  provinces  (the
   Piedmont Plateau  and the  Atlantic Coastal  Plain)  in Montgomery  and
   Prince George's  Counties.   The  Piedmont  Plateau is  characterized  by
   rocky channels with  steep-sided valleys  and is  well-drained.   On  the
   other hand,  the Coastal Plain has broad open valleys with streams that
   have flat slopes and shallow channels.  On the Anacostia River, at  the
   computational point, the U.S. Geological  Survey has operated a stream
   gauge continously  since  1939.    The  flood  estimates  on the  Coastal
   Plain portion  of the Anacostia  River at  the  computational  point  for
   various  recurrence  intervals   using some  of  the  various   models
   discussed previously are shown in Table 4.

   5.0  WESTERN BRANCH FLOOD  ESTIMATES


        Western Branch  is  located  in  the  central  portion   of  Prince
   George's County  in  Maryland  (Figure  3).   The stream is situated in the
   Atlantic Coastal  Plain physiographic province, characterized   by wide
   flood plains and shallow  channels.  Western Branch  is formed  by three
   tributaries, Bald  Hill,   Folly  and  Lottsford  Branches,    Folly  and
   Lottsford Branches  converge and  shortly  afterwards form a  confluence
   with Bald Hill Branch.  From  this  confluence,  Western Branch follows  a
   widening  course along  a  flat stream gradient  for approximately 16.5
                                    182

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miles  before emptying  its flow  and those  of  several tributaries that
drain  into  it,  into the  Patuxent River.    With  a total watershed area
of 110 square  miles, Western Branch drains approximately  22 percent  of
the County.

     The  predominant  soil  group in  the  area  is"  soil  group  B which
defines  soils  with  moderate  infiltration  rates when thoroughly wet.


                        Figure  2
                        ANACOST1A RIVER WATERSHED
  UPPER NORTHWEST 3RANCH
                                 LITTLE PAINT
                                  BRANCH
                                                     BEAVEROAM CREEK .<
            LOWER NORTHWEST BRANCH
                                     LOWER INDIAN CREEK AND
                                       NORTHEAST BRANCH
                                  T83

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                                TABLE 4

       PEAK DISCHARGE VALUES OBTAINED BY USING DIFFERENT MODELS
Station
Northeast Branch Anacostia at Riverdale Road, Maryland
{D.A. = 72.8 square miles)
Recurrence
Intervals
in years
2
5
10
25
50
100
Log-
Pearson
Type III
Model
2600
4357
5929
8486
10880
13764

TR-20
Model
8342
11450
14258
15286
18195
20751

'HYTAIN1
Model
9213
12389
14979
16712
18726
21315

uses
Model
2418
3640
4758
6240
7410
8500 *
MD. G.S.
Regression
Model
1714
2770
3756
5184
6000
8530
Udhiri &
Motayed
Model
2027
3200 +
4854
7200 +
9559
12263
+ Values obtained by interpolation
* Values obtained by extrapolation


Development  in  the  watershed  is  presently   patchy  with  extensive
development  occurring  inside  the Capital  Beltway  (1-95)  and sparse
growth  areas outside.

     Estimates  of  flood peaks for  various  recurrence  intervals using
some of the models  discussed  previously  are shown  in Table 5.


6.0  DISCUSSION
     Significant  differences  between  flood  peak  estimates  derived
using different models  become clearly evident in Tables  3,  4,  and 5.
At the  same  point on the  Piscataway  Creek  (See Table 3), there  is a
2419  cfs difference  between  the  regression  models  and  a  3752  cfs
difference  exists between the  TR-20 value  and the  value  from  the
Maryland Geological Survey regression model.   However,  the difference
is  only 1333  cfs between the  TR-20 estimate  and  the  "Udhiri  and


                                 184

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                Figure 3
-N-
                           WATERSHED MAP
                           WESTERN BRANCH
                  185

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Motayed"  regression  model.   The Log-Pearson Type III model yielded  an
estiamte  of  17746  cfs  whereas 8980 cfs was obtained using TR-20.  The
Log-Pearson  Type  II  and  TR-20  models  are  very widely   used  for
hydro!ogic determinations.   The Hydrologic  Committee of the U.S. Water
Resources Council  in  December  1967 and adopted  the  Log-Pearson Type
III  technique  for use  in  all  Federal  planning  involving  water and
related  land  resources.    The  Council  also  recommended  use of this
technique by state,  local government and private engineers.  TR-20  is
being  used with increasing  frequency by state  and local governments
for watershed  planning.   It  is also  receiving wide spread recognition
as  an  effective  planning  tool  by the  private  sector.    Given  the
widespread use of  both of these models, it is interesting to note the
difference in  peak flow estimates derived  from them.  The Log-Pearson
Type  III  model  yielded  an  estimate  which is  approximately  twice  as
large as  the TR-20 estimate.

     In Table  4,  there are  significant  differences between  the TR-20
and the Log-Pearson  Type  III  peak  flow  estimates  for the  more frequent
flood events (2, 5,  and  10).   Using the  10-year  event, for an example,
the  TR-20 value  is  2.4  times  larger than the  Log-Pearson  estimate.
For  the  2  and  5,  the  TR-20  values are  3.2  and 2.6  times   larger
respectively.   The  differences between "HYTAIN"  and  the Log-Pearson
Type  III  estimates  are  approximately  the  same  as  those with  TR-20.
There  is  some  close agreement  between  the  regression  model   estimates
and  the Log-Pearson  Type III  values  especially  for the  more frequent
flood  events,  although  wide differences still  exist.    For  the less
frequent  flood  events (25,  50,  and 100) the   Log-Pearson  Type III


                              TABLE  5

                   COMPARISON OF  PEAK FLOWS BY VARIOUS METHODS

                        WESTERN BRANCH TO LARGO  ROAD, MD
                        DRAINAGE AREA -  30.2  square miles
                            100  YEAR PEAK FLOWS IN CFS
                      Log-Pearson         Drainage-Area       Regression
Frequency     TR-20   Type  III  Distri-  Discharge-Frequency   Model by
in years      Model   bution Model          Method            Anderson
	(Ref. 9)

 100          7240          2411*             7977                7100
*Gauge was discontinued in  1972 because of debris problems
 which constantly affected  gauge readings.

                                 186

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estimates  are  8486,  10880  and  13764  cfs  respectively.    The TR-20
values for the  same frequencies  (25, 50, and 100) are 15286, 18195 and
20751 cfs, yielding differences.

     The Western Branch  100-year peak  estimates derived by the models
in  Table 5  show a  surprising  closeness.   The  TR-20  value  for  the
100-year flood  at the Largo  Road point  (Drainage area of 30.2  square
miles) is 7240  cfs.   The regression model  by "Anderson" (Reference 9)
estimated the flow  as 7100  cfs, and a  7977  cfs estimate was obtained
from a  Drainage Area-Discharge-Frequency  model  (Reference  10).   The
Log-Pearson  Type III  model   estimate  is 2411 cfs  —  a   value  that is
approximately one-third the  size of the other estimates.


7.0  SUMMARY
     The case studies presented herein have shown the differences that
can exist between values derived using several hydrologic models.  The
differences  in  some  instances are  on  the  order  of  two  to  three.
Hydrologic models can yield  vastly  different  results  depending on the
model used and the experience  of the  user.   These values determine to
a large  extent  the  size and  configuration  of measures  to  correct or
prevent watershed problems.   If the values obtained  from a model are
unreasonably large, their employment  would  result  in  uneconomical and
wasteful facilities and their use for regulatory purposes would create
undue burden and hardship on the community.  If on the other hand, the
values are unreasonably  low,  their  employment  in  design would lead to
undersized facilities  with  consequential  results,  and  their  use for
regulatory purposes could have disastrous consequences.

     On the basis of these  case studies, there is  a  need,  a  critical
need, to  assess the  reasonableness  of  flow  estimates  by  hydrologic
models.   Such an  assessment  of estimates from  a  hydrologic model for
reasonableness is oftentimes called validation.
     REFERENCES AND BIBLIOGRAPHY
1.   Chow, V.T., Handbook of Applied Hydrology, 1964.

2.   Soil Conservation Service, Computer Program for Project
     Formulation, Hydrology, Technical Release No. 20, USDA, May  1965

3.   Soil Conservation Service, National Engineering Handbook, Section
     4. Hydrology, USOA, 1971.

4.   Clark, Finefrock and Sackett, HYTAIN. Hydrology Model,  1976.

5.   U.S. Water Resources Council, Guidelines for Determining Flood
     Flow Frequency, Bulletin 17B, September  1981.


                                 187

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6.   Richmond, S.B., Statistical Analysis, 1964.

7.   Maryland Geological Survey, Flow Characteristics of Maryland
     Streams, Report No. 16, 1971.

8.   Udhiri, S., and Motayed, A., Magnitude.

9.   Anderson, D.G., Effects of Urban Development on Floods in
     Northern Virginia, U.S. Geological Survey, Water Supply Paper
     2001-C.

10.  Udhiri, S., Review and Analysis of Storm Discharge Rates,
     Anacostia River Watershed, Technical Report Publication No.
     0764791560, Maryland-National Capital Park and Planning
     Commission, September 1978.
                                  188

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       MODELING OF A NEGATIVELY BUOYANT THERMAL DISCHARGE
                   IN AN ESTUARINE ENVIRONMENT

                 Arun K. Deb and Jerry K. Snyder
              Roy F. Western, Inc., West Chester, PA

INTRODUCTION

Interest in thermal modeling stems from section 316(a) of the
Water Pollution Control Act Ammendments of 1972 (PL92-500)
which required that limits be put on the thermal component of
any discharge to "...assure the protection and propogation of a
balanced, indigenous population of shellfish, fish, and wild-
life in and on the body of water into which the discharge is to
be made,..."

Several mathematical models have been developed over the last
decade for predicting the behavior of thermal plumes.  Since
most cooling water discharges involved addition of heat to the
circulating water, which results in the discharge of a buoyant
or floating plume, most of the mathematical models available
are applicable to floating plume conditions.  There are some
situations however, which result in the formation of negatively
buoyant or sinking plumes.  These include the discharge of rel-
atively dense process waters, blowdown from cooling towers, and
brine discharges.

Some experimental studies have been performed to characterize
the behavior of negatively buoyant plumes but mathematical mod-
els are not readily available.

The structure of any discharge plume can be divided into near
field and far field regions.  In the near field inertial forces
dominate gravitational forces, while in the far field gravita-
tional forces dominate inertial forces.  Mixing of a heated dis-
charge with the ambient water in the near field is primarily
due to inertia induced entrainment, while the natural transport
processes of advection by ambient current and turbulent diffu-
sion control mixing in the far field.

The densiometric Froude number being the ratio of inertial
forces to gravitational forces, provides a convenient defini-
tion of the transition between the near and far fields.  This
transition is generally accepted as the location in the plume
where the densiometric Froude number is unity.

-------
Near Field Conceptual Model

Figures la and Ib  illustrate the behavior of a surface dis-
charge of a  floating plume in  the  near  field.  Figure Ic
illustrates  the  near field region  of  a  sinking plume discharged
at the bottom of the receiving water  body.  A desk  top methodol-
ogy has been developed  by Jirka et al.  (1981) which describes
the near field behavior of a buoyant  surface jet discharged  in-
to shallow water,  as a  function of densiometric Froude number
(Figure Ib).

The primary  variables of interest  are the discharge length
scale, 1 , and the densiometric Froude  number, F  .  The
discharge length,  1 , is defined as the square r8ot of one
half of the  discharge cross-sectional area.  In terms of a cir-
cular pipe  1   is:
                           Do ' T                        (eq. 1)
                        M    8
where D  =the pipe diameter  (ft).   The  densiometric Froude
number is:                 U
                Fo " |g PQ - Pa   0                      (eq. 2)

                           pa
where U  = the discharge velocity  (ft/s),  g = gravitational
acceleration  (ft/sec  "  sec),   p  = discharge density
(gm/ml), P_ = density of ambient receiving water  (gm/ml).
          31

Densities can be  calculated as a function  of salinity and tem-
perature from the following expression:

     P = 0.9997 - 0.0000063(T-4)2+0.0007615(3)         (eq. 3)

where T = temperature (°C) and S = salinity  (PPT).

Jirka et al.  (1981) compared laboratory and field data against
simulations using the surface  jet model of Stolzenbach and
Harleman (1971) to develop a number  of correlations between
bujk near field properties of  a surface jet and the variables
F   and 1 .  These properties  are described briefly below
a8d illustrated by Figure 2b.

Transition distance, lt is the extent of the near field
(Figure Ib) and can be calculated as:

     lfc = 10 FO'  1Q                             (eq. 4)


Maximum plume thickness, h     (Figure Ib)  is the maximum ver-
tical penetration of the pxflme in the near field and can be cal-
culated as:
                               190

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A) PLAN VIEW
         Ik To
B) SURFACE DISCHARGE OF BLOATING  PLUM!
C) BOTTOM DISCHARGE OF SINKING PLUME
                                                      H
   FIGURE  1   NEAR FIELD PROFILES OF BUOYANT SURFACE AND
              NEGATIVELY BUOYANT BOTTOM DISCHARGES
                           191

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     hmax = °'42 Fo' lo                          (e<*- 5)

The distance to the maximum plume thickness, 1     is calculat-
ed as:                                        max


     Xmax = 5-5 Fo' Xo                           (ec*- 6)

Transition thickness, h. is the plume  thickness  at the transi-
tion distance, 1..  The transition  thickness, h  is nearly
constant and equal to about one-half of h    .  Thus:
      ht = °-21 Fo' 1o                           (e(*' 7)

Stable bulk dilution, S.  is the ratio  of plume volumetric
flow at the transition distance, Q.  to volumetric  flow rate
at the discharge, Q .  Sfc also denotes the  ratio of the  jet-
average excess temperature  (or concentration) at the transition
distance to the excess temperature  (or concentration) of the
discharge.  This dilution is given,  by:
                 '
     St = 1.4 FQ                                   (eq.  8)

Stable centerline dilution, S.   is  the ratio  of the  center-
line temperature  (or concentration)  excess at the  transition
distance to the temperature (or  concentration) excess at the
discharge and is given by:

     Stc = 1.0 Pol                                 (eq.  9)

The properties defined by equations  4 through 9 above are for
surface discharges into stagnent, deep receiving waters.  In
shallow water a buoyant surface  discharge will "touch the
bottom" and a negatively buoyant bottom discharge  will  "touch
the surface."  In either case vertical entrainment and  mixing
will be reduced.  Jirka et al.  (1981) studied the  effect of
shallow depths on dilution in the near field  and concluded that
dilution is reduced when maximum plume thickness is  greater
than seventy-five percent of total  water depth.  The ratio,
r , of dilution at shallow water to dilution  at deep water in
t^e near field is given by:
                        for "H > °-75
and  r  =1.0 for hm  /H < 0.75                   (eq. 11)
      S            1113. X   """"

Negatively Buoyant Discharge

While similar to an "inverted surface discharge," a negatively
buoyant bottom discharge will experience additional friction
                               192

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which will reduce the size of the near field and the resulting
dilution.  A few experiments have been performed with negative-
ly buoyant bottom discharges.  The results of one such exper-
iment by Baddour and Chu (1978) were analyzed by Jirka et al.
(1981) using the same dimensional analysis discussed above.  In
comparison with surface discharges the transition distance was
observed to be reduced by about 50 percent while the bulk dilu-
tion was reduced by about 65 percent.  Thus, for a negatively
buoyant bottom discharge in deep water:
and
     lt = 5 FQ  1Q                             (eg. 12)
     St = 0mS Fo                                 (eq' 13)
In the case of shallow water the dilution given by equation 13
may be modified by equation 10.

FAR FIELD MODEL

There are many numerically solved models available to simulate
far field transport behavior.  The transient plume model,  (TPM)
developed by Adams et al., 1980 is an analytically solved far
field model which was formulated for steady-state surface dis-
charges of floating plumes.  It is a three dimensional model
which can simulate tidal variations in the receiving water.
Conservative and non-conservative constituents with first order
decay can be modeled.  Dilution of the plume occurs by turbu-
lent diffusion and advection by the ambient current is taken in-
to account by the model.  The TPM model assumes that receiving
water depth is constant and velocity is considered to be spa-
tially invarient, although temporal variations such as tidal cy-
cles may be specified as a Fourier series function.  Both
along-shore and onshore-offshore components of velocity can be
considered.  The shoreline boundary is assumed to be straight.

Boundary conditions for the mode are obtained from the near
field analysis, and consist of location, volume flux of the
plume, and temperature and plume thickness at the end of the
near field.

Transient heat distribution is computed as a series of discrete
overlapping "puffs" (Figure 2a).  Heat balance is conserved
within each puff while dispersion increases the size of each
puff with time.  Temperatures within each puff are distributed
normally with maximum temperatures at the center of each puff.
Figure 2b is the far field region of a conceptualized plume in
terms of temperature excess isotherms.
                               193

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 a)
        Y

        t
                              V
       -x = x
                            b)
FIGURE 2  PLAN VIEWS OF A PAR FIELD PLUME
As with the  near  field analysis,  the similarity between a float-
ing surface  plume and  a sinking bottom plume makes it possible
to apply this model  to negatively buoyant plumes.  This is ac-
complished by "inverting the  Z  axis" of the coordinate system.
For a floating  surface plume  the  depth coordinate, is normally
considered to be  zero  at the  surface and increases with depth,
however by using  Z = 0 to be  the  bottom, and Z = H to be the
surface, a dense  submerged plume  can be simulated.  This is il-
lustrated in Figure  3.   Specific  input requirements for the TPM
may be found in the  user's manual (Adams et al., 1980).
                    H
                                     //A n /\
                  T^
                   Beginning of Far Field
           FIGURE 3  PROFILE  OF A DENSE SUBMERGED PLUME
                               194

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CASE STUDY

A thermal modeling study was performed to determine the season-
al mixing zone characteristics and temperature increase result-
ing from the interaction of the Proposed Hope Creek Generating
Station (HCGS) heat dissipation system and the Delaware River,
(Deb and Snyder, 1982).

The HCGS is located adjacent to the Salem Nuclear Generating
Station (SNGS) on Artifical Island, a three-mile long strip of
land on the east bank of the Delaware River in Lower Alloways
Creek Township, Salem County, New Jersey.

HCGS construction began in March 1976 and Unit 1 operation, pro-
ducing approximately 1.067 megawatts of electric power, is sche-
duled for 1986.

Cooling tower blowdown will be discharged to the Delaware river
through a 48-inch diameter pipe, extending approximately 10
feet offshore at mean tide and approximately 1,500 feet upriver
of the station intake.  The center line of the opening will be
about 6 feet below low mean water.  The discharge will be at a
velocity of approximately 4.08 feet per second.   The layout of
the Proposed cooling tower blowdown discharge is illustrated in
Figure 4.
                                   Mean Low Water
                                              t
                                              I
    4' Diameter Pipe
                              FIGURE 4

                 LAYOUT OF COOLING WATER DISCHARGE
                              195

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Temperature standards for  Zone 5 of the Delaware River have
been established by the Delaware River Basin Commission, DRBC
(1978).  These regulations require that:

   "The induced increase above ambient temperature shall not
   excegd 4 F (2.2 C) from September to May and 1.5 F
   (0.8 g) from June to August, or a maximum of 86 F
   (30.0 C), whichever is  less, which temperatures shall
   be measured outside of designated heat dissipation
   areas."

   "As a guideline, heat dissipation areas shall not be long-
   er than 3,500 feet, measured from the point where the
   waste discharge enters  the stream."

The objective of the study was to determine whether these tem-
perature standards will be met after the proposed cooling tower
blowdown discharge is put  into operation.

Salinity concentration factors for the cooling tower are esti-
mated to range from 1.42 to 1.68 under normal operating condi-
tions.  Under "worst case" conditions, which are expected to
occur less than 5 percent of the time, the salinity concentra-
tion factor is 1.80.

The months of February, May, August and November were modeled
to simulate the range of seasonal conditions using appropriate
ambient temperature and salinity data.  Each of these 4 months
was modeled under "typical" and "worst case" operating condi-
tions using the operating parameters which are presented in
Table 1.  The near field analysis indicated that the proposed
HCGS discharge would be negatively buoyant under all seasonal
and operating conditions except during May under "worst case"
operating conditions when the discharge will be positively
buoyant.

Eight computer runs were made with the TPM using the results
from the near field analysis for the seasonal and operating con-
ditions described above.  Each computer run simulated condi-
tions at the four tidal phases (i.e., low slack, flood, high
slack, and ebb tides).

In order to visualize the three dimensional nature of the dis-
charge plume, temperature profiles were printed out at the sur-
face, mid-depth, and the bottom of the estuary for each
seasonal, operating, and tidal condition.  Excess temperature
isotherms have been plotted for all runs.  Figures 5 to 9 show
plots of some of the excess temperature isotherms.
                              196

-------
RESULTS AND DISCUSSIOM

The results of this analysis indicated that the DRBC tempera-
ture regulations of 4°F (2.2°C) from September to May and
1.5°F (0.8°C) from June to August or a maximum of 86 F
(30°C) outside of a 3500 feet mixing zone will be met even
under worst case conditions.

The largest mixing zone distance required for conformance with
standards is 2230 feet at the estuary bottom {Figure 5) during
the February worst case condition at high slack tide, well with-
in the DRBC 3500 feet distance.  A temperature increase of
4°F (2.2°C) at the water surface during these same condi-
tions occurs within 600 feet of the HCGS discharge (Figure 6).
The predicted temperature excess profiles for the month of
February at high slack tide under worst case operating condi-
tions at the bottom of the estuary and at the water surface are
shown in Figures 5 and 6 respectively.  The predicted tempera-
ture excess profile at the estuary bottom for the month of
February during the same worst case operating conditions at
ebb, low slack and flood tides are shown in Figures 7, 8, and 9
respectively.

The least critical month was the May typical condition, where
standards are met 500 feet from the discharge.

Maximum temperature in the month of August at the end of the
3500 feet mixing zone will be 80.4°F (26.9°C) which is with-
in the limit of the 86°F (30°C) DRBC standard.

This study clearly indicated that HCGS discharge will meet all
DRBC temperature standards, even under "worst case" conditions.

Summary and Conclusions

A generalized near field and far field analysis applicable to
negatively buoyant discharges was discussed.  The analysis of a
surface discharge of a floating plume was modified to account
for bottom friction and surface interference for application to
a bottom discharge of a sinking plume.
                              197

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                                                           TABLE 1

                                               AMBIENT AND DISCHARGE CONDITIONS
                          AMBIENT RIVER CONDITIONS
DISCHARGE CONDITIONS
00
OPERATING
CONDITIONS
TYPICAL CASE
February
May
August
November
WORST CASE
February
May
August
November
TEMP.
CO
. 1.4
18.9
26.7
9.5
1.4
18.9
26.7
9.5
SALINITY
(PPT)
4.25
3.15
7.85
6.10
4.25
3.15
7.85
6.10
DENSITY
(Pa)
1.00289
1.00070
1.00243
1.00415
1.00289
1.00070
1.00243
1.00415
TEMP. CONC.
( °C) FACTOR
17.5
25.0
29.0
20. S
**
21.0
**
27.0
**
31.0
25.5
1.42
1.61
1.68
1.49
1.80
1.80
1.80
1.80
SALINITY
(PPT)
6.04
5.07
13.19
9.09
7.65
5.67
14.13
10.98
1
1
1
1
1
1
1
1
DENSITY
.00315
.00078
.00581
.00491
.00370
.00069
.00587
.00515
DENSIMETRIC
PO~ "a FROUDE NO.
0.
0.
0.
0.
0.
0.
0.
0.
Pa
00026 (n*
OOOOB (n)
00337 (n)
00075 (n)
00081 (n)
000015 (P)
00343 (n)
00099 (n)

28.1
50.7
7.8
16.6
15.9
116.8
7.7
14.4
             *(n) = negatively buoyant
              (P) D positively buoyant
             **   «» Worst case, exceeded less than 5% of normal operation time

-------
                                               FIGURE 5
                              TEMPERATURE  CAT)  ISOTHERMSC°C)

                           FEBRUARY -  MAXIMUM DISCHARGE  TEMPERATURE
     -800
    -100      -JIM)
 T
1100
                                       •M       MO       It CM

                                           HIGH SLACK TIDE

                                              BOTTOM


» EXPECTED TO BE EXCEEDED LESS THAN SX OF THE TIME DURING NORMAL PLANT OPERATION
         IMa       ZIOQ

-------
                                                  FIGURE 6
                                    TEMPERATURE (AT)  ISOTHERMSC*C)

                                FEBRUARY  - MAXIMUM  DISCHARGE TEMPERATURE
TO
O
o
                  -Ma
                            a
                                                              1200
                                                                I
icoa
1100
                                                                                         2100
                  -UO
                                                              ItU
IMO
                  zioa
                                                                                                    g
                                                                                                    -g
                                                                                                 1100
                                                HIGH SLACK TIDE

                                                   SURFACE
       EXPECTED TO BE EXCEEDED LESS THAN SX OF THE TIME DURING NORMAL PLANT OPERATION

-------
                                                          FIGURE  7

                                            TEMPERATURE (AT)  ISOTHERMSCC)

                                         FEBRUARY  - MAXIMUM  DISCHARGE TEMPERATURE
                                -itoo  -lew
                               i
-MOO
tv>
o
                                                  -1200
             MOM
                                                              -no
                                                                     -too
                               -100
                                                                                 -200
2UB.,
                                                                                               -8
                                -UOD  -1600   -1(00   -1200   -1000    -UO    -800    -tOO    -200


                                                            EBB TIDE

                                                             BOTTOM
                                                  200
              EXPECTED  TO BE EXCEEDED LESS THAN 5X OF THE TIME DURING NORMAL PLANT OPERATION

-------
                                                 FIGURE 8
                                    TEMPERATURE (AT)  ISOTHERMSC 'O
                                FEBRUARY -  MAXIMUM DISCHARGE  TEMPERATURE
          -HBO
                                                                                         MO       MO.
ro
O
  -MOO     -MOO      -lioo      -iioo      -iJoo      ^MU
                                         LOU SLACK TIDE
                                            BOTTOM

EXPECTED TO BE EXCEEDED LESS THAN 5X OF THE TIME DURING NORMAL PLANT OPERATION
                                                                                         MO      too

-------
                                                           FIGURE 9
                                            TEMPERATURE (AT) ISOTHERMSC-C)
                                       FEBRUARY  - MAXIMUM  DISCHARGE  TEMPERATURE
ro
o
                               >2QO
tOQ    «04    MO    100    1DOA   1204    liOO    IUO
                                                                                             1
                                oo   a     too    «oa    coo    MO    1000   ino    uoo    IMW    IMO
                                                         FLOOD TIDE
                                                           BOTTOM
              EXPECTED TO BE EXCEEDED LESS THAN 5X OF THE TIME DURING NORMAL PLANT OPERATION

-------
The methodology  was  applied  to  an  actual  case  study  involving
the proposed  discharge  of  blowdown water  from  a  cooling tower
into an estuarine  receiving  water.   Predicted  temperature  in-
creases in  the receiving water  were presented  and  it was con-
cluded that applicable  temperature regulations in  the receiving
water would not  be violated  under  any  seasonal and operating
conditions.

The near  field and far  field models used  in  the  case study are
generalized tools  which can  be  applied to a  variety  of dis-
charge and  receiving water conditions.

Acknowledgements

The authors wish to  express  their  thanks  to  Hank Innerfeld,
Mark D. London,  and  Robert P. Douglas  of  Public  Services
Electric  and  Gas of  Newark,  New Jersey for their assistance.
The authors also wish to acknowledge Dr.  Eric  Adams  of the
Masachusetts  Institute  of Technology for  his help  and guidance
in conducting this study.
                            REFERENCES
1.  Delaware River Basin Commission, "Administrative Manual-
    Part III, Basin Regulations - Water Quality," Trenton, New
    Jersey, May 24, 1978.

2.  Adams, E., Gaboury, D., and Stolzenbach, K., "Transient
    Plume Model Computer Code and User's Manual, Report, R.
    M. Parsons Laboratory for Water Resources and
    Hydro-dynamics, MIT, Cambridge, MA, September 1980.

3.  Baddour, R., and Chu, V., "Turbulent Gravity - Stratified
    Shear Flows," Report No. 78-3, Fluid Mechanics Lab.,
    Dept. of Civil Engineering and Applied Mathematics, McGill
    University, Montreal, Quebec, Canada, September 1978.

4.  Jirka, G., Adams, E., and Stolzenbach, K., "Buoyant Surface
    Jets," Journal of Hydro. Division, ASCE, Volume 107, No.
    HY11, Nov. 1981, pp. 1467-1487.

5.  Deb, A.K., and Snyder, J. K., "Thermal Modeling Study of
    Hope Creek Generating Station Discharge," Report Submitted
    to Public Services Electric and Gas Co., Newark, New
    Jersey, Roy F. Weston, Inc., West Chester, PA, October,
    1982.
                              204

-------
                    RAINFALL DATA ACPUISlTIflfl AMO PROCESSING

                           USING APPLE II IMRKALP'.ES

                                       hy

                        Mark Robinson and William Janes

                         Computational Hydraulics Group
                              McMaster ilnivfrsity
                           Hamilton, Ontario, Canada
                         IPS 4L7  Phone:  (4)6) B
                                    ABSTRACT

     Because of the spatial and temporal variability of thunderstorm typp

events, rainfall data from a network on a ? km grid is pssential to propprly

model urban stormwater systems.  Conventional  rainfall recording stations

employing tippiny bucket gauyes with strip chart recorders suffer from

inaccuracies in timing, mechanical failure, significant initial capital  outlay

and potentially larye on-yoing data processing costs.

     This paper describes a microcomputer-based data acquisition system,  in

successful operation in Hamilton since  19R1, based on an  inexpensive APPLF  U

workalike functioning as the main data  processing facility for  the  system.


INTRODUCTION

     It has been shown that correct representation of the spatial  and  temporal

resolution of  rainfall is  essential for proper urban  stormwater modelling

(James and Scheckenberger,  19R3).  The  density of the netvmrk  of  raingauges



                                     205

-------
monitoring an urban area will directly  affect  the quality nf f>p Hata obtained.
The larger the number of gauges the  greater  the  potential for accurately
describing storm speed, direction  and cell size  and  hence for obtaining a  proper
estinate of rainfall  intensity during a storm  event.   A  network with a maximum
spacing of about 2 km is essential  if summer thunderstnrn cells are to hp
detected.
     Traditionally, rainfall  nonitoring stations have  employed * tipping huckot
raingauge for collecting the  rainfall and  a  mechanical  strip chart.  rocorHpp
using either ink or pressure  sensitive  paper as  the  recording nHiun.
     It has been our  experience that tipping bucket  gauges  function reliably  hut.
are reldtively expensive to  purchase (approximately  5500 per  instrument).  at
this price a large dense network  is  usually  not  feasihlp.   Mechanical  recorders
have been found to he prone  to  frequent and  significant  errors in  f.ining and
synchroniztion due to gear malfunctions and  basically  insensitive  equipment.
Data is often lost due  to paper jamming on drive sprockets  and interruptions  in
ink flow to the recot  ,ler pens,  for example due to  air  bubbles  in the  ink well.
In Canada, tipping bucket recorders  typically  cost  from  ^00-^00.  Additionally,
if pressure sensitive paper  is  required, the cost  of continuously  recording A to
5 months of data can  exceed  5150/gauge.  These costs add up to a fairly
substantial initial investment  per gauging location.
     Moreover, the hidden cost  in  processing data  from strip charts is high.
The data must be abstracted,  aggregated or disaggregated and subsequently
entered into some  storage facility,  typically  a  computerized  hydrolngic  data
base, often manually, for each  station.  Our experience has shown  this  annual
cost to be several times that of  the initial capital cost.
                                      206

-------
     Our solution to this problem WHS to desiyn and build our own inexpensive



datd acquisition system and to interface it, directly with a central



inicrocoinputpr.






RAINFALL DATA ACQUISITION SYSTEM.



     The Computational  Hydraulics Group at, McMaster University has spent the



past three years developing and implementing a microcomputer based data



acquisition system (Haro et al , 1^83; James et al, l°ft?).  The data acquisition



system has three principal components:



    1.  The rainfall sensor which collects precipitation and converts  it into



        water drops of almost constant size to he counted hy the data  logger.



        This sensor can also be a conventional tipping bucket raingauge.



    2.  The data loyger which senses the drops and counts them for a fixed  time



        interval, typically one minute.  The time is monitored hy the  system



        on a cycle from one to 2^0 minutes using its internal clock.   The tine



        and data are output by the logyer to standard audio cassette tapes.



    3.  The data stored on cassette is in hexadecimal code.  It  is converted to



        ASCII code using a decoder.  This data is output at a speed of 1?nn baud



        through an RS232 serial communications port.






     A rainfall monitoring network comprising nine stations has  been operated



successfully in the city of Hamilton since 19H]  {see Figure 1).  The data



acquired during this period has been used to calibrate storm models  (James  and



ScMeckenberger, 1984)  and models  of the urban drainage system  (Robinson and



James, June  1984). With  proper maintenance, the  system has  been  found  to be nore



reliable,  efficient, accurate  and less  expensive than  conventional  data



acquisition  systems employed  previously.
                                      207

-------
                                                                              HAMILTON-
                                                                              WENTWORTH
                •IAMI9OID
FIGURE 1

-------
     The data acquirer! by the system was initially processed and archived on a
POP 11/23 minicomputer with two lO-megabyte hard disks operating RSX-lT1.
However, as the system demand in terms of available terminals, memory and disk
storage space increased, it was decided to move simpler tasks anH word
processing to peripheral computers such as Apple IT workalikes, for exanple, thp
FRANKLIN ACE 10(1(1.
     The advantages of peripheral  computing include the use of floppy diskettes
as an archive media, an improvement over our current method of backup frnm tho
11/23 to magnetic tape at low speeds (300 baud).  It was subsequently also
decided to implement the data processing utilities on the FRANKLIN ACF and use
it for data capture in the hours when word processing was not hping done.

DATA CAPTURE USING APPLE II WORKALIKES.
     Personal microcomputers such as the Apple II and workalikes are WP! 1 suited
to data acquisition functions for the following reasons:
     1.  They are inexpensive and can he totally dedicated to a task.
     2. Since data acquisition does not require large data arrays or high
        precision calculations, H-bit word size with 4K-fi4 Khyt.es of memory will
        suffice.
    3.  Organization and archiving of files by station can he readily
        accomplished with floppy diskettes.  This storage media is cost
        effective.
    4.  Built-in medium  resolution graphics are  available  for data display.
    5.  Communication between the microcomputer  and  a  larger  computer
        containing  say  the  central data  base,  is easily  achieved.
    6.  The  microcomputer  can  run some  simulation  packages  using  thp
        processed data  directly.
                                      209

-------
     7.  The microcomputers  can  be  interfaced  with  peripheral  devices  such  as
         printers  inexpensively  hy  purchasing  an  interface  card,  usually  at.  a
         cost  of about  S100.
     In our system v/e  have  utilized  the  following hardware  configuration:
     1.  FRANKLIN  ACE  10(10  microcomputer (APPLE  II  compatible)
     2.  4H Kbytes RAM
     3.  DOS 3.3
     4.  One floppy  disk  drive
     b.  Grapplor* Printer  Interface Card
     6.  30 column text card
     7.  PDA232C Serial I/O Card
     b.  EPSON FX-100  printer
     A tool kit of utilities  has been developed,  in APPLESOFT RASIC,  for
processing trie rainfall data  acquired by the system (Robinson anH James,  January
1984). Many of these utilities  v;ere originally written in FORTRAN for t.hp PHP
11/73 and have been  translated  to APPLESOFT BASIC.   The utilities have three
pririary component  functions:
     1.  Decoding  data
     2.  Translating data
     3.  Displaying  (plotting)  data
     The programs  are  controlled by  executive  files which configure memory  and
load relevant  programs  into memory.   A brief outline of the function  of each
component follows.

1. Decoding Data.
     As described  previously, the decoder outputs the data  as a  string of ASCII
numbers to an  RS232  port.   This  port  is  connected directly  to the PDA?3?C Serial

                                      210

-------
I/O card.  Data is transmitted from the decoder to a scratch file on the
FRANKLIN ACE in blocks of 120 characters.  The utility then disables input to
the serial  card.  The utility further converts this data into 80 character
records and stores it on diskette as a permanent file.

2. Translating Data.
     Tne translation utilities process the file of decoded data into a series of
chronological  tines ond rainfall  intensities.  The processed data is displayed
on the system monitor and optionally on the printer as well.  Results nay h<=
calculated  in either system of units.  Volume and intensity on a per minute
basis are output.  Event volume and duration are displayed.  The processed data
is stored on diskette and may be structured so that it is in a form suitable for
input directly to other packages such as a data base management system, a
hyaroloyic  model or graphics routines.  A sample data processing session  is
presented in Figure 2.

3. Displaying Data.
     The file of translated data containing one or more events may he processed
at any time by the graphics utility.  The user selects the event to he displayed
either by start time or by its sequence in the file of events.  The user  selects
whether or  not the scaling of the vertical axis will depend  on the  peak
intensity.   Use of medium resolution graphics  in conjunction with specially
designed shape tables produce hyetographs, such as that  of  Figure 3.   Thp
Dialogue has been designed carefully {James and Robinson,  19R?)  and  the  next
step will e to  integrate the software into our evolving  distributed  data
processing  system (James and Una!,  1984).
                                     211

-------
                FIGURE  2:  SAMPLE DAS INTERPRETER SESSION
         fr t * >
DAb I N t L-.KPRL
             I ER UTILITY WR I Tl EN Bft
                               MAW-  RUL-fiNSUN, OCTOBER  19U3
                               *#**^
ENTER NrtMF. OF FILE IU BE  TRANSLATED
EN1ER NAMfl OF FILE TO CONTAIN IRANSLAIEO DATA
ENTER tiAUBb IDENTIFICATION
EN1ER GAUtfE UNIT NUMBER
ENTER UNITS TO BE USED  (METRIC/IMPERIAL)
ENTER DATA SOURCE (CHARTROLL  UK CASSETTE/
ENTER S1AR1 INti UME < YEAR,MO,DY ,HR,MIN)
ENTER OBSERVED TOTALIZER VOLUME (MM/IN)
ENTER TYPE UF GAUGE (D=DROP COUNTER, T*I IfPING  BUCKED
ENTER TYPE OF DROP COUNTER  (B*BLACK, W=WHITE>
ENTER INTER-EVENT PERIOD  (MINUTES)
ENTER TIME-STEP FOR PLOTTING  HYETOGRAPH (MINUTESJ
                                                        I r.-. sir.: ASF; .
                                                        MCIRIU
                                                        CASSETTE
                                                           0
PROCESSED RAINFALL DATA FUR  1982 FOR 1EST3 UNIT
                                   RAINFALL
                               VOLUME INTENSITY
                                      
-------
                              FIGURE 2  (Continued)
     V    .•:.-'    ' i : .>« '               >.)     i.1
                •? r '"               I . J 4     "d. '1
                                                           j . J 4    I
     V    ,',:    .*. : 1 i-               . K'J..-:     ':. 12
     •V    ;,-.-    ,-: IS               .228     I  J.. 68
WARN! Mi? - MUM  /l-KU  RAINFALL  HAS  BEEN DEI EC TED  f-UI<  ,' EF-'U  I  J Nl.-
          - Dnl.4  LNIRY  ERROR
             ! li-11- /K-ATN  PAIRS GUI  OF  PHMSE
            HfiRDWARt:  ERROR  DURING  PROCESSING  Uh  CuSSE 1  IE
       I     DA IA  IGNORED PLEASE  CHEVCK  RESULTS
          .•J-2    6:2^               . .(t5,i     V. 12
     9    .^'    <>:^u               -J52     9.J2
     V    22    6: '15               . 's'.2&     13.68
WARNING  - /tRU  RAINFALL  DEltCltlJ  Wl'IH NON-ZERO  TIME
ACTION    - DnlA  WILL  BE  IGNORED
            CHtCr  SOURCE DATA  FILE
     9    ,:':/    fe: 5"i               .152     9.12
                                                           1 . 292  •• 46
9
V
9
9
9
9
9
9
9
9
9
9
22 3:
22 8:
22 8:
22 e:
22 B:
22 8:
22 F3:
22 8:
22 0:
22 H:
22 B:
22 H:
3'J
TV^_
34
35
36
_'. /
3'8
.'.v
«10
4i
42
/} 3
O 0
. 1444
. 2123
. 3496
. 1596
. 152
. 1596
. 3268
. 1 292
. 0988
. 228
. 4408

8. 664
12.768
20.976
9.576
V. 12
9. 576
19. 6O8
7 . 752
5.928
1 3 . 68
26. 448
                                                           2.40J6     U.

OBSERVED KM INI- ALL VOLUME FROM  I 0 I Al. I 2 H.R                »3u (MM .»
CALCULAltD RA1NI-ALL  VOLUME FROM CASBEH I ti              -8. G6l6i.«Ovt J vl'IM
DIFFERENCE RE I Wff.LN OBSERVED  AND CALCULATED  VOLUMES ™70. 46 1 3 3 3 3 *.'/. <
 CONCLUSIONS

      Monitoring  rainfall in the conventional  manner using  tipping bucket

 raingauyes and  strip chart recorders  can  be*an imprecise,  time consuming end

 expensive procedure.  The use of  a  microcomputer-based  data  acquisition system

                                        213

-------
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                                           NEKT EUENT V2 I IS-K«

-------
improves the accuracy and reliability of the data collected and reduces the cost

per station.  This in turn opens the way to increased coverage and/or increased

network density.

     Execution of simpler tasks such as data capture are ideally suited to

peripheral  personal  microcomputers such as the APPLE II  series and workalikes,

for example the FRANKLIN ACE 1000.  The low cost and simpler graoM'cs results in

cost effective data  acquisition.  The wide range of communication packages

available permit data to be exchanged with a mainframe computer containing the

central data base while still keeping data acquisition independent;

     By transferring data capture tasks to a peripheral  computer such as the

FRANKLIN ACE from the larger multi-user POP 11/23, thus freeing resources on the

11/23, the same quality and level of productivity can be maintained.


ACKNOWLEDGEMENTS

     The authors wish to acknowledge the work of Hector Haro, Mike Heaven and

Andrew Ukrainec in designing and  implementing the rainfall data acquisition

system and for  hardware modifications to  interface the decoder to the FRANKLIN

ACE.


REFERENCES


1.   Haro,  H.,  Kitai , R.,  and James,  II., "Precipitation  Instrumentation  Package
for Sampling  of Rainfall",  Institute of Electrical  and  Electronics Engineers
(Transactions  on  Instrumentation  and Measurement) Vol.  IM3?,  No.  3,  pp.  d?3-4?Q,
September  1983.


2.   James,  W.,  Haro, H.,  Robinson,  M.A.,  and  Kitai,  R.,  "Hydrometeorologic  Data
Acquisition:  innovative,  High  Resolution,  Programmable  Instrumentation for
Stonnwater Management",  Proceedings of the Conference  on  Stormwater  and Hater
Quality  Management  Modelling.   U.S. EPA,  Washington, D.C.,  EPA 6an/9-R?-P,15 pp.
128-151, August 1982.
                                      215

-------
3.  Janes, I)., and Robinson, M.A., "Interactive Processors for Design USP of
Larye Program Packages", Canadian Journal  of Civil Engineering, Vol.  Q,  No.  3,
pp. 449-4b>7. September 198?.

4.  James, U. and Scheckenberger , R., "Storm Dynamics Model  for Urban Runoff",
International Symposium on Urban Hydrology, Hydraulics and Sediment Control,
Lexington, Kentucky, pp. 11-18, July 25-?8,
b.  James, U. and Scheckenberger, R., "RAINPAC - A Program Package for Analysis
of Rainfall  Inputs in Computing Storn Dynamics", Proceedings of the Stornwater
and Water Quality Modelling Meeting, U.S. EPA, Detroit, Michigan, April  1?-13,
1984.

6.  Janes, W. and Unal , A., "Evolving Data Processing Environment for
Computational Hydraulics Systems", Canadian Journal of Civ.il Engineering, Vol.
11, No. 2 pp. June 1984.

7.  Robinson, M.A. and James, W., "Rainfall Data Processing Manual for the Apple
HE Computer", CHI Publication No. R114,  (about 70 pp.), January 19W.

8.  Robinson, M.A. and James, U., "Continuous Variable Resolution Stormwater
Modelling on a Microcomputer Using a Central Hydrologic Data Rase Manager".
Proceedings  of the Canadian Hydrology Symposiun, Quebec City, Quebec, June
10-12,  1984.
                                     216

-------
     CHGTSM - A COMBINED HYDROLOGIC TIME SERIES AND TOPOGRAPHIC
                             DATA BASE MANAGER
                                       by
                            William James and Ali Unal
               Computational Hydraulics Group, McMaster University
              Civil Engineering Department, Hamilton, Canada, L8S 4L7
                               Phone (416)527-5944

                                   ABSTRACT
     The paper describes a boss microcomputer with  hard disk connected to satellite
microcomputers.  Satellites support the independent  portions  of a very large water
resources package while the boss system hosts the data base  management system.  The
DBMS manages and distributes the time series data from the  hard disk to the satellites
via the boss whenever a request is made.  The whole system is cost efficient since desk-
top microcomputers are used.
     The  paper  describes the attributes  and  capabilities  of the  Computational
Hydraulics  Group Time Series Manager (CHGTSM).   CHGTSM  prepares, manages and
distributes  the CHG-Time Series  Store.   A  communications, synchronization  and
security protocol to connect the satellites and the boss computer so that the time series
store can be  distributed for hydraulic  applications will allow independent blocks  of  a
large water resources package  to  work concurrently in independent but connected
microcomputer systems.

                                INTRODUCTION
     Hardware and  software systems  are evolving rapidly, but apart  from program
systems, little or no overall system building (including for example data acquisition and
control) is evident in urban drainage applications.  Continuous modelling requires use of
climatological archive magnetic tapes for input and  streamflow tapes  as well as for
calibration  and validation  purposes  (Robinson  and  James,  1981).  Large  continuous
modelling packages e.g. HSP-F and SWMM (Johanson  et al., 1981; Huber et al., 1981)
also  include  statistical  processing  and graphics output.  The transition from event
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 modelling  (the  traditional  design  storm  philosophy where startup values must  be
 estimated) to continuous modelling now foreshadows problems of input and output data
 management (James, 1982).  Special software is essential for I/O time series manage-
 ment,  especially for local  area  networks.   The network  indicated comprises micro-
 computers radiating from a central disk operating system functioning on a boss CPU
 dedicated primarily to data base  management (DBM), most of which is devoted to time
 series  management (TSM).   Each peripheral CPU is  dedicated to separable blocks of
 logical routines, associated  with, for example, precipitation analysis, runoff modelling,
 transport or drainage system networks, water quality modelling, cost-benefit analysis,
 or  statistical post-processing.   This  can  now  be achieved  at  a  fraction of  single
 mainframe costs, and probably just as fast in terms of overall turnaround time (James
 and Robinson, 1981).
     The background to our local  area network was presented elsewhere (James and
 Unal,  1984). This paper describes in more detail the attributes and capabilities of the
 Computational Hydraulics Group  Time Series Manager (CHGTSM).  CHGTSM prepares,
 manages and distributes the CHG-Time Series Store (CHGTSS). In CHGTSM a group of
 users share a TS data base system in which the first input TS segment is processed for
 precipitation by one user and, when complete, the output TS  is made available for that
 segment to the rainfall/runoff block of programs, perhaps under control of another user.
 A simple example is: precipitation TS is processed for year  1979 while rainfall/runoff
 TS is  processed up to year 1978, the  transport network is processed up  to 1977, the
 sewage treatment plant processing up  to year 1976, and the dispersion of  the resulting
 pollutants  in  the  receiving  waters  up to year 1975:  all of this processing occurs
 concurrently.
     CHGTSM  was written to  satisfy  a  portion of our  group's   requirements.   It
 constitutes the TSM part of an  overall  DBMS which will be held in the boss computer of
 our group's computing  system.  Although derived from HSP-F,  it will be seen that
 CHGTSM is basically a custom made, application oriented Time Series Manager with
 certain query attributes. It has yet to be expanded to include management routines for
 catchment-environment data, through geographic data banks.
     In addition to the CHG-DBMS the  boss computer will  hold the communications,
 synchronization  and a security protocol to avoid inconsistencies (i.e. to avoid concur-
 rent access to the same piece of  TS data by more than one satellite). The software to
queue  the incoming requests is called the Computational Hydraulics Group Distributed
Processing Software (CHGDPS).

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EVOLVING COMPUTER TECHNOLOGY
     The growing number of independent computer systems used for scientific comput-
ing has created a need for local computer networks which should meet the  following
requirements:  1) relatively high data rates, 2) geographic distances spanning about one
kilometer,  3) ability  to  support  a  suffficient  number  of independent   devices,
4) simplicity, or the ability to provide the  simplest possible mechanisms that have the
required functionality  and  performance, 5) good  error characteristics,  good reliability
and minimal dependence upon any centralized components or control, 6) efficient use of
shared resources, particularly the communications network itself, 7) stability under high
load, 8) fair access to the system by all devices, 9) easy installation of a small system,
with graceful growth as  the system evolves, 10) ease of reconfiguration  and  mainten-
ance, and 11) low  cost.  In  its simplest form, a network  is a software mechanism for
point to point transfer of files.  First, though, the  processors  must be  connected by a
wire cable.   This can be  done  by purchasing a null  modem  cable and  swapping the
transmit and receive lines of  the two processors or by linking  the processors  with
modems. The next step is to write the software  for file transfer.  This program turns
the terminal of one processor into a virtual terminal for the other processor,  and tests
for a valid connection between processors (Birkenmeyer and Hopp, 1985).
     An example of a  current sophisticated  local area network is Ethernet.  The
structure of which follows the  ISO (International  Standards Organization) OSI (open
system interconnect) model, which divides a network functionally into seven layers.
     Ethernet  is a bus  configuration where contention  between multiple stations  is
resolved by  a  technique  called  carrier-sense multiple-access and  collision detect
(CSMA/CD).  The transceiver provides the driver  electronics for the cable, and the
Ethernet interface unit provides address recognition, arbitrarion,  and error detection.
The Ethernet specification supports 10 M-bit/s performance for up to  100 nodes  on a
500-meter segment of Ethernet  coaxial cable,  and  each branch cable can be up to 50
meters long (Baha et al.,  1984).
     Local area networks give the user more power:  the addition of  a  station expands
not only accessibility but also speed and storage capacity (which  is just opposite for
mainframes).   In a  tightly coupled  computer  system,  the  processing units share
memories and peripherals such as  printers  and disks.   In a loosely coupled system, the
processing units usually have their own memory and peripherals and communicate with
each other over a communications network.  A tightly coupled system  is often called
multi-processing, while a loosely  coupled  system is called distributed processing.   In

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both  cases, different processing units perform different tasks and communicate with
each  other to coordinate their actions in a larger overall  task.   Each component
operational  module  is  written to  coordinate  its  activities  with  other  modules.
Coordination of the segments of the program must recognize all possible conflicts, e.g.
when two programs require to change the same data record at the same instant.
      To prepare the distributed computing system  of the 5th generation computers,
users must develop valid procedural solutions  for handling text and data.   The system
starts with the choice of database architecture; the priorities to be set  in database
integration, segmentation, distribution  and maintenance; and the adoption of proper
protocols.   Substantial  benefits  are to  be  derived from  a  properly designed  and
implemented data  base.  "New standards and guidelines promulgated by professional
groups must be observed in the design of computer based information systems.  Unless
our data assets are properly planned, in a few years it will be impossible to exercise
effective control over them" (Chorafas, 1982).

                        DATA BASE MANAGEMENT SYSTEMS
      As soon  as several users require access  to operational data which is being
changed, and which is sufficiently large that personal copies of the data for each user
would represent  a significant load on the computer system, it is  desirable to provide
centralized control of  the  data  bases.   In  this way,  redundancy  can  be reduced,
inconsistency can be  avoided, data can  be shared, standards can be enforced,  security
restrictions can be applied, integrity can  be maintained, and conflicting requirements
can be balanced (Date, 1982).  A DBMS  is a set of procedures  and  data structures that
isolate the application from mundane details of storage  retrieval, creation, modifica-
tion and security of the data base - the user does not refer to physical storage locations
but deals instead with the  conceptual  data structure.  An individual DBMS user will
generally be  interested only in some portions of  the total database and the user's view
of that portion will generally  be  somewhat abstract when compared with the way  in
which data is physically stored.  The external view is the content of the database as
seen  by  some  particular user.   The  conceptual  view,  on  the other  hand,  is  a
representation  of the entire information content  of the database,  again in a  form
somewhat abstract, in comparison with the way  in which the data  is physically stored.
The component of the DBMS responsible for the external/physical  conversion is called
an access method.
      Until recently microcomputer DBMS  software could not replicate mainframe data
structures.  Mainframe  DBMS's are  increasingly adapting  relational architectures  in
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which data structures are defined by a series of tables rather than by individual records,
which  now allows micro  versions of sophisticated  mainframe  packages.  Emerging
integrated  software  links  recently  introduced  by several software  vendors  permit
microcomputers to tap directly into  mainframe databases.  Integrated  software  and
local database  approaches  have merged providing  microcomputer  users  with personal
databases that are as easy to manipulate as spreadsheets.
     These databases will be  tied into intelligent  networks that will  transparently
honor requests for data residing locally, on the mainframe, on another  microcomputer,
or on a database across the  country (Freedman, 1984).

                               SCOPE OF CHG-TSM
     Conventional, general purpose DBMS's, designed  to  organize information into  a
collection  of  different attributes with  a  common relationship,  could  be  used  for
computational hydraulics applications.  For example, the basic element of information
in conventional DBMS used  to maintain water resource data could consist of a data item
such as stage, flow,  or water temperature measurement for a particular station at  a
particular time.  Construction  of a time history of  any of  these variables under this
scheme requires searching through several basic data items.  An alternative is to use  a
block of sequential TS data  as the basic element of  information.  This concept results in
much  more efficient  access of TS data.  The basic concept underlying  CHGTSM is the
organization  of data  into  records  of continuous, applications-related  elements, as
opposed to  individually addressable data items. This general approach is more efficient
for computational hydraulics applications than that of a general purpose DBMS because
it avoids the processing and storage overhead required to assemble an equivalent record
from a general purpose DBMS.
     CHGTSM comprises nine independent programs:
     1) NEWTSS           4) OPELBL           7) RETRIV
     2) CHG-LAB         5) QUERY           8) UPDATE
     3) OPENFL           6) INSERT           9) PATCH

1.   NEWTSS
     NEWTSS is part of HSP-F; it opens the TSS files and determines their dimension,
by writing the TSS-description in the first record of each file. The TSS descriptor holds
the number of records of the file and the number of words in each record.  Its purpose  is
explained as follows:   "NEWTSS is a stand-alone  program  which creates a Time Series

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Store (TSS).  It must, therefore, be  run  before a  user can  perform any runs which
require data to be stored in, or retrieved  from, the TSS.  When running NEWTSS, the
user specifies the size of the TSS, the record length, etc. NEWTSS can also be used to
copy the contents of one TSS to another.  This option is used  if the existing TSS is too
large or too small; the user creates a new TSS of the desired size and  copies everything
to it" (Johanson et al., 1980).

2.   CHGLAB
     CHGLAB  is basically the Time Series Store Manager of  HSP-F,  but was  modified
to work in an 8~bit addressing mode  and  independent of the  rest of the program.  It
writes  into the dataset  directory whenever a dataset  is opened in a  TSS file.  It also
writes  the primary dataset  label for each dataset which  is  opened.   The  general
description of module  TSSMGR is given in the HSP-F manual:  "This module maintains a
user's Time Series Store  (TSS) and performs some housekeeping chores associated with
the datasets in  it.  From the point of view of the computer's operating system, the TSS
is a single file (which may be very large).  However, many distinct time series can be
stored  in this file. This  permits a user easily to keep track of the various time series
with which he is dealing.  Furthermore, he need only refer to a single disc file for all his
time series input and output needs, no matter how many time  series are involved. This
simplifies communication with the computer system".   (Johanson et al., 1980). HSP-F
was originally developed on a HP-3000. We have made the necssary changes to work in
an 8-bit  mode.  CHGTSM  is presently also  running on a PDP-11/23  under RXS-11M.
This operating system  provides an addressable memory of 32 K  bytes to each of 8 users,
but the compiler does not support formatted direct access, which is crucial for HSP-F.
For the PDP-11/23 to  function as the Boss processor of our local area network,  two new
programs were written, equivalent to NEWTSS and TSSMGR or CHGLAB, but using less
memory space and unformatted direct access.  The  new programs are called OPENFL
and OPELBL,  and these  take  over portions of the responsibilities  of NEWTSS and
TSSMGR respectively.
3.   OPENFL
     OPENFL,  written to replace NEWTSS of HSP-F, opens the TSS  files required for
the new TS information and is the first program to be run when preparing  a database
using CHGTSM  software.  OPENFL allows  the user to open files with  a minimum of 65
and a maximum of 185 real words. The user has to assign a file number for the TSS file
to be opened. The dimensions (number of records and the number of words in a record)
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can be assigned by the user or the program can be used to optimize these dimensions.
All information is input through the terminal interactively.  (Note that HSP-F reads a
sequential disk file as input).

4.   OPELBL
     OPELBL was  written  to open  dataset  labels in a TSS  file already opened  by
CHGTSM-OPENFL.  The user assigns the  dataset number to be opened in  a TSS file,
specifying the TSS file by calling its number.

5.   QUERY
     QUERY was  written to access a database (TSS) originally prepared  by  HSP-F.
(Note that HSP-F does not have a variable time step option.) QUERY retrieves the TS
information  from the  TSS and prints into a user-requested external file using HSP-F
access techniques.  Addressing in the dataset  is described as follows in HSP-F  manual:
"The  REAL  words  in  the  dataset are  logically  treated  as if they were numbered
sequentially  from unity starting with the first word of  the first  TSS record of the data-
set.  The label of the  dataset always begins at the first word of the dataset.  The key
area of the  label contains  the address of the REAL  word for the beginning  of each
calendar year stored   in the dataset.  The calendar  years  need not  be stored  in
chronological order but the  data within each calendar year is stored in  chronological
sequence.  Access to TS information  then  takes place  in two steps:  the direct step to
the TSS record containing the first word of the calendar year in question and the search
to find the time interval within the year" (Johanson et al., 1980). Currently HSP-F can
only move TS information from TSS to the  core of the  machine,  to be processes by only
HSP-F application routines.  The  TS information cannot be transferred to a disk file or
printer. Thus HSP-F cannot at present be used as a DBMS for external applications.

6.   INSERT
     INSERT  was written  to prepare  CHGTSM  from  scratch and  comprises two
subroutine groups which give the  user two  different options in preparing CHGTSS. The
DCTSS group processes the TS information initially prepared with variable time steps
whereas the UCTSS group processes  the TS  information with  constant  time  step but
allows  the user to  alter it while  inserting data  into CHGTSS.   Both subroutine groups
prompt  the  user for the TSS  file number,  dataset number and the year of  the TS
information  to be activated.  If the user is preparing  the data  files for the first time

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and has collected data with variable time steps, he may use subroutine DCTSS.  For this
he has to prepare the data file with variable  time steps. Certain control variables to
structure the data base can either  be supplied interactively or with the data file  prior
to execution.
      If the data file is already prepared with constant time steps, the user will likely
use subroutine  group UCTSS.  It provides  an  option  to  store the existing information
with variable time steps through a process called compression. Subroutine group UCTSS
analyzes the given constant time step TS data and informs the user of time spans where
all the TS values are either zero or undefined. In a 185  real-word record size TSS file,
the span could  be three hours for one minute time step data, 6 hours  for five minute
time step data or 1  day for timesteps greater than five minutes.' The  user is  asked if
this span is to be stored in variable  time steps, and the user supplies the new time  step.
Note  that  compression is  possible only if a predetermined span of time has all values
zero.

7.    RETRIV
      RETRIV was written to retrieve information from CHGTSS. Any span of time in a
year may be retrieved (maximum 1 year,  minimum 1 day).  For each request,  RETRIV
asks if a new span is to be retrieved.  Before writing the requested piece of TS to an
external file, RETRIV will ask if aggregation/disaggregation is necessary.  If the answer
is NO, the TSS information will be  retrieved the  way it  was stored in the database.  If
the answer is YES and the output file is to  be prepared with a constant time  step,
RETRIV will aggregate/disaggregate all the  data  to the user supplied constant  time
step.  If the output  file incorporates variable time steps then RETRIV  will inform the
user about the  contents of each  logical record in the database (i.e.  for time steps
greater than five minutes it will give month of the year, the  day and the time step of
the day; for time steps smaller than or equal to five minutes, it will give the month, the
day and the time span of the day - 3rd 1 hour time span, 5th 3 hour time  span etc. -  and
the time step).   In addition RETRIV will warn the user if the content of  a logical record
is all zeros (or undefined) and request the new time  step required in the output data-
file.  RETRIV will decide to aggregate or disaggregate by comparing the timestep given
by the user and that  of the stored TS information.  Any logically existing records can be
aggregated/disaggregated  by the user.  Note that certain logical records may not  exist
in the physical  sense.  If a physically  non-existing record  is to be retrieved  with  no
aggregation/disaggregation specified, 60 minute time intervals are used as default.

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8.    UPDATE
      UPDATE updates the information in CHGTSS, such as the contents of a dataset of
previously inserted TS information. The user can access any span of time within each
year for existing information.  The minimum accessible time span is one day.  UPDATE
informs the user about the status of the information in each record.  Either the control
variables or the TS information can be subject to an update in each logical record.  Any
logical record which does not correspnd to a physical record cannot be updated.

9.    PATCH
      PATCH was written to save portions of TS data which do not necessarily start at
the beginning of a year and end at the end of the year.  Since this condition can occur
during a distributed data processing application, this software is  designed  to work with
minimum user intervention. PATCH will process TS information  initially prepared with
variable time steps.  The control variables to structure the dataset and TS information
are read from a sequential disk file.   On the other hand, the TSS file, dataset number
and the year of the requested TSS  information  are input interactively.   When an
application routine supplies the input file to CHGTSM, for a time space shorter than a
year,  PATCh ensures  that  the periods  before and after that time span  are filled with
zeroes or undefined values.  Note that an output file from an application package acts
as an  input file for CHGTSM and vice-versa.

                             STRUCTURE OF CHGTSS
      CHGTSS comprises  several TSS  files, each  identified by  a unique name, (e.g.
CHGTSS1, CHGTSS2,  etc.)  Files are  composed of a variable number of records, each
file having a record size in words assigned by the user.
      Although  all the records in a file have  the same  physical size the user sees
variable size  records.  The  maximum possible number of words in a record  is a function
of the system in use.  CHGTSM optimizes the usage of disk space when the record size
assigned is 65 real words.   When TSS files are prepared the user has an option to assign
higher record sizes.  These options are 125 real words and 185 real  words. Any record
sizes  greater than 185 real words will function as 185 real words. Since CHGTSM can
work  with 8~bit machines care must be taken if record sizes are to be increased.  The
first record of each TSS file is called the TSS descriptor, defining the characteristics of
the TSS.  Certain of these characteristics will  vary  from  one TSS to another and  it is
therefore necessary that the TSS be self descriptive.

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      As in HSP-F, the first record of each TSS file, called the TSS Descriptor, defines
the characteristics of the TSS.  The TSS Descriptor is followed by the TSS Directory,
which describes itself and the time series datasets in the TSS.
      The number of TSS records to allocate to the directory is set by the user when the
file for the TSS is first created. This first estimate may need to be changed as the TSS
is used.  Thus,  for the  purposes of  dataset  manipulation,  the  TSS  directory is  not
distinguished from a time series dataset. (Johanson et al., 1980).
      TSS directory is followed by  the first dataset label in the file. This label occupies
2  records.  The first  is  called the primary dataset  label.   The  second  is called  the
secondary dataset  label.   PDSL contains  information  describing the  contents of  the
dataset.  SDSL serves as an index to  the first day of each month of each year in the
dataset.  Thus CHGTSM has direct access to the first day of each month of any year.
Between the first day of each month the search is done sequentially.
      The TSS dataset labels are followed by the actual time series information.  Each
dataset may contain several years of time series information all belonging to a unique
source. TS information can be  stored with variable time steps for each day of the year.
As an example, in  a  TSS file with 185  real-words records, if the dominant  time step
exceeds 5 mins. for a particular day, that day occupies  one record.  If the dominant
time step is equal to 5 MINS each 6 HR span occupies one record (.-. 4 logical records to
cover the day).  If the dominant time step is equal to 1  min each 3 hr span occupies one
record (.-. 8 logical records to cover the day).
      The first 5 words in each record are  called control variables.  Control variables
are DAY (day  of the  month),  DOMDEL (dominant time step), COMFLG  (compression
flag), COMDEL  (compression time  step),  NTFRAM (number of time  frames  in  that
record).  COMDEL is  always  equal  to DOMDEL if   DOMDEL  exceeds 5  mins.   If
DOMDEL is equal to 5 mins. (or 1 min), COMDEL can be greater than or equal to 5 mins
(or 1  min).  If  DOMDEL is not equal to  COMDEL at any time  span  of a  given day
COMFLG is equal  to 1  which  means compression exists.   In this case NTFRAM is
determined by COMDEL.
      In each record the control variables are followed by the actual time series data.
The number of TS values in any record is determined by NTFRAM.
      It is clear from foregoing discussion  that CGH-TSM not only stores the  TS with
variable time  steps with respect  to days  but also in  certain cases within  the days.
Those cases  are when the dominant time step is 5 min  or  1 min.  1 min and 5 min time
steps  are very important for  rainfall  data  acquisition  since our raingages supply  the
non-zero rainfall data with these time steps.  When this data is to be inserted  into the
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database, the database administrator (DBA) has to choose his strategy. For example if
the rainfall is not intense  and the data spans  relatively short intervals the DBA  may
decide to structure  the TSS  file with 65 real-word records.   This will  give  a finer
resolution and save  significant amounts of disk space.  If the rainfall is intense and
continuous for relatively long periods  of  time, the DBA should structure  the TSS file
with longer record sizes because shorter record size will not make any difference to the
physical amount of disk space used.  On the other hand both the insertion and retrieval
procedures will be much faster for TSS files with longer record sizes.
     It is important to understand why fewer resolutions (i.e. 65  real-words) saves a
significant amount of disk-space compared to a coarser resolution (i.e. 185 real-words).
If  the data base is structured with 65 real-words, a 1 min dominant time step day will
be composed of 24 logical records, each 1  hr length. But the number of physical records
to represent that day may be less than 24.   Because CHG-TSM  does not store the
compressed time series records with COMDEL equal to 60 min.  The DBA has an  option
to assign 60 to  COMDEL whenever he finds a 1 hour time span with all  zero  values.
Infact this is done by default when using PATCH to structure the data base. Although
this record is not stored (physically) in the data base its existance is acknowledged by
the access method.  The user retrieving information from the  TSS  finds the physically
non-existing record displayed in his logical view.
     If the record size is 185 real words in a given TSS file the DBA has to find a  3 hr
time span with all zero values so that he can compress with  COMDEL equal to 60 mins.
This will  be more difficult to find compared to a 1 hr time span  with all zero values.
     Once a TS record is compressed with COMPEL = 60  mins the  user can retrieve it
just like physically existing records. For example a user  can aggregate or disaggregate
a physically non  existing record to any time step.
                            GEOGRAPHIC DATA BASES
     A geographic data base, a stored computer file of map data, can be created in two
ways:  using grid cell or x, y coordinate is divided into a grid  cell  method. In the grid
cell method the study area is uniform grid and all data encountered  within averaged.
The x,y  coordinate  methods use  point  coordinates to define  the points, lines and
polygons describing geographic variation.
     Grid cell data banks have the following advantages (HEC, 1978):
1.   The grid cell provides an easy way to collect data.  In the simplest method, one
     lays a plastic overlay of grid cells  on top of maps or aerial  phots and interprets
     information directly.
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2.    Computer  storage  and the subsequent access and  processing of this matrix of
     information is extremely straightforward.
3.    Editing of stored data is also straightforward.
4.    Due to its consistent  nature, the grid cell  can  be used for both discrete  and
     continuous types of data analysis. Simple computer programs allow  the user to
     aggregate  many basic data items into the grid cell for different types of display.
5.    Data encoded  by x,y coordinate methods can be directly  translated to a grid
     system by available programs.
6.    Point  data of  a continuous surface nature  (e.g.  air  pollution  records) can  be
     counted to a grid cell scheme by interpolation.
     The major  disadvantage is the loss of resolution.  Resolution  and cost increases as
the size of grid cells decreases,   choice  of the grid cell size and shape  is critical,
different data banks can be prepared using different cell sizes, but any given data bank
will contain only one grid cell size and shape.
     Recently  the US Army Corps of Engineers  Hydrologic  Engineering  Center  has
been developing computer programs in the area of catchment-environmental  DBM as
well as TSM (called  HEC-SAM,  HEC-DSS,  based on Grid  Cell Data Banks).  The HEC-
SAM system is   more than a general purpose  spatial data  procedure.   It  has  the
capability  to assess hydrologic,  flood damage,  and  environmental consequences of
development, perform wildlife habitat  evaluations such as the U.S. Fish and  Wildlife
Habitat Evaluation  Procedure,  perform boolean and overlay analysis, and produce a
variety of computer graphics.   "The  general analytical strategy that comprises HEC-
SAM is to:  a) assemble  and catalog basic geographic and resource information into a
computer data bank,  b) forecast  and  place into the data  bank  selected  alternative
future   development  patterns,   formulate  an   array  of  management  alternatives,
c) perform comprehensive assessments of  the development  scenarios of interest,  and
d) recycle  for additional alternatives" (Davis, 1981).  The following analyses may be
carried out (HEC, 1978):

1.    Hydrologic Analysis
     -  determination of subbasin area statistics
     -  determination of runoff coefficients
        computation of  subbasin precipitation
     -  spatial  display of erosion, sediment deposition and dredge  material sinks
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2.   Economic Analysis
     -  determination of land use statistics
        computation of damage to development in flood plain
        formulation of nonstructural plans
        display of assessed values
     -  determination of proximity to transportation corridor
3.   Environmental Analysis
     -  determination of vegetative cover
        determination of wildlife habitat zones
     -  computation of land surface erosion parameters
     -  computation of urban storm runoff quality parameters
     -  determination of locational attractiveness indexes
     -  assessment of general geographic impact
        coincidents  tabulation of habitat reduction  for use  in scenarios of potential
        impacts
4.   Social Analysis
     -  display spatial distribution of income level
     -  display ethnic zones
     -  assess age variations
     -  compute census statistics

               DISTRIBUTED PROCESSING OF CENTRALIZED DATA
     Where a user group  requires a variety  of computer  hardware and/or operating
systems software,  it  becomes desirable to develop a distributed data processing system
(i.e. local  area networks).  Large hydraulic engineering  application programs that enjoy
a wide distribution or utilization, are the first to be adapted to a distributed processing
system, because these systems offer reduced computational costs as well as maximum
utilization of manpower.  Many problems in computational hydrology are equally if not
more demanding of file access  than of  CPU  time.   This is especially  true when TSS
manipulations are involved. In this case a smaller, less  expensive computer system (i.e.
smaller word sizes,  slower CPU  cycles,  and  less sophisticated  instructions)  with
adequate file use is often just as effective a solution but at a significantly lower cost.
Thus an intelligent disk storage system configured as  a  stand alone DBMS accessible by
several microcomputers may represent a more sophisticated solution.  The intelligent,
expandable, disk  controller  handles all data  access   Including indexing,  searching,

                                       229

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buffering, deblocking and storage management functions.  Such a system makes more
efficient use of each processing unit, so that the user obtains better response times.
      The computing system we propose is a boss computer connected to a hard disk at
one  end and to  a satellite computer system  at the other end.  Satellites support  the
independent portions of  a  very large water resources package  while the boss system
hosts the DBMS.  The DBMS manages and distributes the TS data from the hard disk to
the satellites via the boss whenever a request is made.  A typical  request will occur
when an application  module (satellite) finishes processing TS data and attempts to save
the TS in CHGTSS {Disk)  or needs more data to process from CHGTSS.
      Basically given a  computer  system,  a program has two resources:   time and
memory space.  The  space requirement is the  amount of memory and peripheral storage
used  by  a program.  That  means  the space requirement can  be broken  down into the
amount of primary and secondary storage that is needed.
      Program space refers to the  actual space in  memory that contains the program.
It is  very dependent  upon the hardware/software configuration of each  computing
system.  Instruction set, addressing methods,  operating system  conventions all  play a
role in  the  size of  a program. There  are  very few principals that can be developed
regarding the measurement of the space requirements of a program.
      As far as data space is concerned,  there are some general observations that can
be made about the amount of data space required by a program and how the size of the
data space depends upon the  algorithms used and program input.  Techniques that are
used to estimate data storage  requirements are similar to the techniques that are used
to measure time requirements.
      Estimating the amount of time used by the program can be approached in several
different ways (i.e.,  CPU time, WALL time, I/O time).  The amount  of time and space
required by  a program directly depends on:  1) the actual hardware,  2) the algorithmic
structure of the  program, and 3) the data processed by the pogram.
      During a distributed data processing application it is important  to synchronize the
processing in each individual node of the local  area network. It will never be possible to
optimize the computing such that each node is actively computing all the time instead
of waiting for data to arrive.  On the other hand of the nodes end up waiting for data
for an  unreasonable  span  of time a  single  processor can  do the whole  job with
comparable efficienty.
      Consequently its important to know how much  time a  node will take to finish
computing  once the  data  is  downloaded  from the  DBMS.   Program  measurement
techniques make it possible to  obtain timing as a function of basic execution time of a
                                       230'

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sequence of instructions  and the amount of constraint data.  By  constraint data we
mean the data which controls the number of executions of any loop in the algorithm.
     Timing  functions of routines are used to  inform  the user about the expected
execution time in a given processor for a specified amount of data (or vice versa) prior
to or during execution.

                                 CONCLUSIONS
     The  adoption of 16-bit and 32-bit  personal computers,  with  their  improved
computational power, and reduced costs, inevitably leads to continuous  modelling.  This
turns up  problems of management of large time series.   As software  costs  become a
significant  part  of the total computer costs, data base  management systems  will
ultimately be required  by every group of engineers sharing a computational  hydrology
data base.  Data base software significantly reduces the cost of software development
in several ways:  programmers are not required to maintain their own copy of the data
base and data file, an internal directory describing the relationship among the data is
automatically  maintained and is available to all  users, and  programmers are not
required to  write special purpose programs to fit the data (Gagle and Koehler,  1981).
     The novelty in our approach lies in getting away from a single processing unit with
a single huge  memory, performing in  a sequential step-by-step path.   This  system  is
replaced  by a number of simple processing elements, each endowed with its own small
memory. The processors themselves are arranged  in a hierarchy.   At the top  of the
hierarchy, lies the boss processor which holds CHGTSM  and  CHGDPS, to access the
database. Satellites hold the application packages and their share of the CHG-DPS.
     We are developing  integrated computational hydraulics systems by interfacing
distributed  data  processing  utility modules  with the regular operational or application
modules reuqired and/or developed by other  members of our group.

                             ACKNOWLEDGEMENTS
     Support from the Computational  Hydraulics Group at McMaster University, the
Natural Science  and Engineering Research  Council, the Inland  Waters  Directorate of
Canada, and the  Ontario Ministry of the Environment is gratefully acknowledged.

                                 REFERENCES
Baha, J.J.,  Weurel, H.M., Willits, J.L.  A Local Area Network for  the HP  1000 Series
500 Computers.  HP Journal, March 1984, Volume 35, Number 3, pp.  22-28.

                                      231

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Birkenmeyer, D,R., Hopp, R.J., (1984) The RSX Multi-Tasker, Decus, February, Section
1, pp. 48 to 50.

Chorafas, D.N.  (1982). Databases for Networks and Minicomputers.  Petrocelle Books,
Inc. 281 pp.

Date, C.J. (1981).   An Introduction to Database Systems.  3rd Ed.,  Addison-Wesley
Publishing Co.,  Massachusetts, 574 pp.

Davis,  D.W.  (1981).   Data  Management Systems  for Water  Resources  Planning.
Technical Paper No.  81.   Hydrologic  Engineering Center.   U.S.  Army  Corps  of
Engineers, 11 pp.

Freedman, H.D. (1984). Tapping the Corporate Database.  High Technology, April, 1984
pp. 26 to 28.

Gagle,  M.  and  Koehler,  G.J.  (1981).   Data-base  Management Systems:   Powerful
Newcomers to Microcomputers. Byte. p. 97-122.

HEC (1978).  Guide Manual for the Creation of Grid Cell Data Banks.  HEC, U.S. Army
Corps of Engineers, September, 1978, 74 pp.

Huber,  W.C.,  Heaney, J.P., Nix,  S.J.,  Dickingson,  R.E. and Polmann,  D.J.  (1981).
Stormwater Management  Model, Users  Manual, Version III.  Municipal Environmental
Research Center, U.S. Environmental Protection Agency, Cincinnati, 300 pp.

James,  W. (1982).   Continuous Models Essential for  Detention  Design.   Conference  on
Stormwater Detention Facilities Planning Design  Operation  and  Maintenance, Co-
Sponsored by the  Engineering Foundation and the Urban Water Resources  Research
Council of the A.S.C.E. Henniker, New Hampshire, pp. 163-175.

James,  W.  and  Robinson,  M.A. (1981).  Coordinated Multi-Processing  for Large Scale
Data  Acquisition  and Simulation  of Urban  Drainage for the Hamilton Wentworth
Region.  5th Canadian Hydrotechnical  Conference.   University  of  New Brunswick,
Fredericton, N.B., pp. 801-815.

James,  W. and  Unal, A. (1984).  Evolving Data Processing Environment for Computa-
tional Hydraulics Systems. Canadian Journal of Civil Engineering, Vol. 11, No. 2.

Johanson, R.C., Imhoff,  J.C., Davis, H.H. (1981K   Users  Manual for  Hydrological
Simulation Program - FORTRAN (HSP-F) Release 7.  U-S. EPA, Athens Georgia.

Robinson, M.A.  and  James, W. (1981).  Continuous SWMM Quality Modelling for the City
of Hamilton  using  Atmospheric Environment Service  Data.   Proceedings  of the
Conference on  Water Quality and  Stormwater Management  Modelling, Niagara Falls,
Ontario, US EPA, pp. 469-492.
                                       232

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           MODIFICATIONS TO THE QUAL-2 (SEMCOG)
                    WATER QUALITY  MODEL

            By:  Raymond C. Whittemore,  Ph.D.1
                 Linfield C. Brown, Ph.D.2
                     I.  Introduction
    This paper will outline and briefly discuss recent
changes made by NCASI to the water quality model QUAL-2
{SEMCOG version).  These code changes resulted from the
fact that QUAL-2 has seen extensive use in recent years as
a tool in water resource planning and waste load allo-
cation studies.  Furthermore, many modifications (both ma-
jor and minor) have been made to the original code to re-
flect differing assumptions of algal growth, nutrient/ and
light interactions.  In addition, a number of computer
code errors were uncovered following extensive model test-
ing (1).  Consequently, the "QUAL-2" acronym no longer de-
notes the same model to all users, because substantial
differences exist in the several versions reported in the
public domain.  A need, therefore, existed to: (a) combine
significant state-of-the-art advances in algal kinetics
into one centrally available model, (b) provide a thorough
documentation and testing of the synthesized code, and (c)
provide guidance for its use.  This paper will address the
first of these needs.  The new model will have the acronym
"QUAL-2E" to represent the enhanced model capability.
Partial financial support for the work is acknowledged
from the EPA Center for Water Quality Modeling (CWQM),
Athens, Georgia,
   Research Engineer, National Council of the Paper
       Industry for Air and Stream Improvement, Inc.,
       Northeast Regional Center, Tufts University,
       Medford, Mass.  02155

   Professor, Chairman of Civil Engineering Department,
       Tufts University, Medford, Mass.  02155

                            233

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    The paper will first discuss the historical develop-
ment of the QUAL-2 model and summarize some of the differ-
ences between those versions which exist in the public do-
main.  Specific computer code changes implemented by NCASI
will then be schematically presented and briefly dis-
cussed.

                  II  Historical Development
                         of QUAL-2 Models
      As discussed in NCASI Technical Bulletin No.  391 (1),
  the version of the model QUAL-2 documented and tested by
  NCASI was that obtained from the Southeast Michigan
  Council of Governments (SEMCOG) with assistance from EPA
  Region V.  The model was originally developed by  Water Re-
  sources Engineers, Inc. (now Camp,  Dresser,  McKee,  Inc.)
  and is fully described in two reports (2,3).  This  version
  was orginally selected by NCASI because of the availabil-
  ity of quality documentation and user manuals.

      This version of QUAL-2 has seen extensive use and ap-
  plication by both consultant and regulatory personnel in
  recent years.  More importantly, the model is one of sev-
  eral maintained and supported by the EPA Center for Water
  Quality Modeling in Athens, Georgia.  The EPA has spon-
  sored several workshops throughout  the U.S.  to provide
  training and guidance for the use of QUAL-2.  NCASI has
  participated in these workshops and has provided  EPA with
  copies of Technical Bulletin No. 391 (!)  which presents
  the updated computer code and documentation manual.  In
  addition, NCASI staff has assisted  numerous member  compan-
  ies and their consultants in implementing the QUAL-2 model
  code on differing computer systems.

      Several other versions of the QUAL-2  model have been
  uncovered in NCASI reviews of model applications.  The
  general input/output,  hydraulic and water quality capabil-
  ities,  and other special features are compared in Table 1.
  The five separate models compared are QUAL-2 versions
  attributed to SEMCOG,  the Texas Water Development Board
  (TWDB)  (4),  Meta Systems,  Inc.  (5), Upper Mississippi
  River  208 (6),  and the Wisconsin Department of Natural
  Resources (7).   Major  differences between models  are noted
  under the nitrogen and algae simulation routines.

      NCASI's  application of the  SEMCOG version of  QUAL-2 on
  the Ouachita River Basin provided the justification for
  the current  re-examination of the QUAL-2  model code (8).
  In  this study,  water quality simulations  were examined for
  portions of  a deep,  low velocity river system where algal
  dynamics were dominant.  In this application algal  cells

                            234

-------
were productive in a small zone near the surface where
they could expect to grow at their optimum rate.  The rou-
tine in QUAL-2 requires that the algae be productive over
the entire water column under some artificially low light
level.  The light level calculated is that single average
value necessary to achieve the same algal productivity
that actually occurs over a 24 hour diurnal cycle.  As the
river became deeper near the impoundment, the model dis-
tributes the available light over a larger volume and pro-
duces both lower growth rates and D.O. levels.  The field
data, however, showed that more algal productivity was re-
quired in these areas to simulate high observed D.O.
levels.

    An additional problem in the Ouachita River study was
that of high sensitivity of simulated D.O. to the algal
parameters.  Calibration/verification  was difficult -to
achieve in some cases for the variables ammonia, nitrate,
algal biomass concentration, and D.O.  For example, D.O.
and algal biomass concentrations could toe calibrated with
reasonable parameter values (i.e., within range of pub-
lished values), but simulated nitrogen species concentra-
tions would then be significantly different than measured
values.  The subsequent investigation study of algal cycle
modeling state-of-the-art served as the basis for the
QUAL-2 update reported in this summary.
             Ill  NCASI Modifications to the
                      QUAL-2  (SEMCOG)  Code
    The following tentative list summarizes the modifica-
tions made to the QUAL-2 (SEMCOG) code by NCASI.

    (1)  Algal, Nitrogen, Phosphorus, Dissolved Oxygen
         Interactions(Figure 2)

         - organic nitrogen
         - organic phosphorus

    (2)  Algal Growth Rate  (Figures 3, 4, 5, and 6) .

         - growth rate dependent upon both NH3 and
           NO3 concentrations

         - preference factor input for NH3
         - algal self-shading
         - three light functions for growth rate attenu-
           ation
         - three growth rate attenuation options
         - four diurnal averaging options for light

                          235

-------
    (3)   Temperature  (Figure 7)

         - link to algal growth via solar radiation
         - default temperature correction (6)  faqtors

    (4)  Dissolved Oxygen  (Figure 8)

         - new standard methods D.O. saturation function
         - traditional SOD units (gm/m2 day)
         - dam reaeration option

    (5)  Arbitrary Non-Conservative

         - first order decay
         - removal  (settling) term

    (6)  Hydraulics

         - input factor for longitudinal dispersion
         - test for negative  flow  (i.e. withdrawal greater
           than flow)

    (7)  Input/Output Modifications  (Figure 9)

         - new coding forms
         - local climatological data echo printed
         - enhanced steady state convergence summary
         - five part final summary including plot of
           D.O. and BOD
    These algal, nitrogen, phosphorus and dissolved oxygen
interactions in this listing are shown schematically in
Figure 1.  For the sake of comparison, the SEMCOG inter-
actions for these same constituents are also displayed.
                        IV  Summary
    The computer code for this program will be completed
during the spring of 1984 and submitted to the EPA CWQM.
Subsequent updating of the documentation manual (NCASI
Technical Bulletin No. 391) will follow in late 1984.  It
is important to note that the resulting program will re-
quire thorough and detailed documentation to minimize mis-
use by inexperienced users.  Several input parameter val-
ues have multiple meaning, depending upon the algal, nut-
rient, and light options chosen.  The enhanced output for-
mat, on the other hand, will provide greater detail than
other versions of QUAL-2.  This detail includes several
diagnostics expected to be helpful in simulating and dis-

                            236

-------
solved oxygen concentrations in river systems dominated by
algal productivity.


                 V  Literature References
(1) "A Review of the Mathematical Water Quality Model
    Qual-2 and Guidance for its Use", NCASI Technical
    Bulletin No. 338, October 1980 (Revised No. 391,
    December, 1982).

(2) "Computer Program Documentation for the Stream Quality
    Model Qual-II", prepared for Southeast Michigan Coun-
    cil of Governments, Detroit, Michigan (July, 1977).

(3) "Users Manual for the Stream Quality Model Qual-II",
    prepared for Southeast Michigan Council of Governments,
    Detroit, Michigan (July, 1977).

(4) "Qual-TX User's Manual (Draft)",  Texas Water Develop-
    ment Board, Austin, Texas (June,  1981).

(5) "Calibration and Application of Qual-2 to the Lower
    Winooski River:  Preliminary Studies", prepared for
    state of Vermont by Meta Systems, Inc. (July, 1979).

(6) Norton, W.R., et al, "Computer Program Documentation
    for the Stream Quality Model-Qual-II", for EPA Contract
    68-01-1869 (August, 1974).

(7) Patterson, D., et al, "Water Pollution Investigation
    Lower Green Bay and Lower Pox River", Wisconsin DNR,
    (EPA 68-01-1572), (June, 1975).

(8) "A Study of the Selection,  Calibration, and Verifica-
    cation of Mathematical Water Quality Models", NCASI
    Technical Bulletin No. 367, (March 1982).
                           237

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                                                            TABLE   1   COMPARISON  OF  QUAL  -  2  MODELS
ro
OJ
oo
Hodel Cepabllitlea

Temporal
Simulation

CBOD

800

Maeratlon


Nlthrogen


SEKCOC
Steady State,
Ouaol -dynamic

Mr»t order.
eoo-s, BOD-U
Settling
tero order

8 option*


NH),H02,N03,elgee,
benthic aource/*ink

THD8
Steady state

Sane a* S EH COG

lero order
(revised unltil
9 opt lone,
k2 >2ft/D

Org*nlc-H,NFIl
IH02+M03), algae.
benthic aource/Blnk,
Hodel Veralon
Keta Syat***
Steady etate,
Revlaed Ouaat-dynnelc,
Dlel curve
sn*e aa SEKCOO
Bottle rate to etreeai
Sea* ee BEHCOO

7 opt lone.
k2 > 2tt/D,
da* reaaratlon
Organlc-H.NlfJ, KO2,
N03, a lg«e, benthic
•ourc*/alnk

Hod. Upper HI... 209
Sa*a ai SEHCOQ

S**e mm SEHCOO

Bmmm mm BEMCOO

1 option*.
da* reeeratlon

Organic-*, KH3.B02,
NO), alga*, benthic
•ourc*/* Ink

Hlaconeln DHH
BaM* a* SEHCOO

Dual drat order.
Bottle rate to etraai
rate converalon
Sue ea SEHCOO

B option*


Organ lc-B.NHJ,IIO2,
H03.N gaa, algae
benthic aource/aink
                            Phoiphorui
                            Collfora



                            Non-eonaervitlve.

                            Coniervatlve

                            Teaperature




                            tlydraulice




                            Load*



                            Input/output



                            special
Dla-p,aIqae,benthic
aource/alnk
                                                Growth cycle ,P,1,
benthlc alnk,Delf~
•hading,photolnhlb.,
growth cycle <««cro-
phyte):  »» above

San a a SBKCOC
                                                                                               Dla-P.Total-p.alga*,    8a*a  a*  BEMCOO
                                                                                               benthic aource/alnk
                                               Orowth cycle (chla)i
                                               HH3,N03,P,I.benthic
                                               alnk,*el( *he,d 1 ng,
                                               P-R.dlel curve
                                               Seeie •* BEHCOO
Mrat ordar, aettllng  Save ee BEHCOO

Two                    Been aa BEMCOO
Steady state heat
balance,iieer
apecifled rate
correctlona

Rectangular channel*,
tidal downatreaei
boundary,flow
augnentatIon

Hulti-polnt at one
element,distributed,
headwater,tr ibutary

Reorganized,
atreamllned,llne
printer plot

Senuitlvlty analyala
Steady atate heat
balance, (dynaalc
heat balance?),(I«ed
rat* correct lone

Rectangular channele,
tl*e 0< travel
output,tlow
aug*entatIon

Ba*e ae SEHCOO
                                               Standard OUM, I/O
                                               (line printer plot?)
                                                                                                                      flam* *•  BEMCOa
                                              Be** *a sencoo



                                              aa** •• SEHCOO

                                              S**JC •• BEMCOO

                                              San* *a BEMCOO
Rectangular chann*li
llOM sugBentation
                                                                      SaM •• BCMCOO
Standard OUM, I/O
line printer plot
                                                                                                                                             denit., OI dependent
                                                                                                                                             ratal
                        Growth cycle (chla)i
                        HH).H03.P,I,benthic
                        elnk.aelf (hading,
                        photolnhib.
                        Single conatltuent.
                        eoneervatlve 01  tlrat
                        order

                        See above

                        see above

                        Bee above,  tltmA
                        rate correction*
                                                                      Rectangular channel*.
                                                                      {low augmentation
                                                                      •Dynoaie*  point,
                                                                      "dyna*ic*  headwater,
                                                                      dletrlbuted,tributary

                                                                      ReorganiEed.TTY output
                                                                      option,  line printer
                                                                      plot.  Calcoap plot

                                                                      Guapended  aolida >lmu-
                                                                      latlon

-------
         ORG-N
         N H
         N O
          N O
                       Atmospheric
                       Reaeration
                  6M2
D
I
S
S
0
L
V
E
D

O
X
Y
G
E
N
K4
                                     SOD
                                 TTT
          ORG-P
          DIS-P
                         Chla
                         ALGAE
     a2P
QUAL-2(NCASI/EP
                 FIGURE 1
                    239

-------
      Atmospheric
      Reaeration
            K.
QUAL-2  (SEMCOG)
FIGURE  1  (CONTINUED)

          240

-------
                            FIGURE 2

        ALGAL,  NITROGEN,  PHOSPHORUS, OXYGEN INTERACTIONS



Nitrification Inhibition at Low DO

         * Correction Factor (QUAL-TEXAS)

                    CORDO =  1-2 *  DO
                             1.56 + DO


         * Applied to ammonia and nitrite oxidation rates

           Ammonia:     (0f)inhib.  = (^i^input * CORDO


           Nitrite:     (^inhib.  = (^ input *


         * Magnitude of correction  factor.


                     DO (mgl)             CORDO

                        0                  0.00
                        1                  0.47
                        .2                  0.67
                        3                  0.79
                        4                  0.86
                        5                  0.91
                        6                  0.95
                        7                  0.98
                        8                  1.00
                             241

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                              FIGURE 3

                          ALGAL  GROWTH  RATE



Nutrient Attenuation  Factors

         * Nitrogen:     NE  =  NH3  +  NO3

                         FN  =  NE/{KN +  NE)

                    where:
                         FN  = Nitrogen attenuation  factor
                         KN  = Nitrogen half  saturation
                             coeffienct
         * Phosphorus:

                        FP = P04/(KP + P04)

                    where:
                        FP = Phosphorus attenuation factor
                        KP = Phosphorus half saturation
                             coefficient
Algal Preference for Ammonia
         f =    _ (PT)  (NH3) _
                  (Pi) (NH3) +  (1-P!)N03

         where:

         P! = Algal preference for ammonia nitrogen (0-1.0)
                0 = NO3   1.0 = NH3

         f = Fraction of algal nitrogen uptake from
              ammonia pool.
                             242

-------
                         FIGURE 4
                     ALGAL  GROWTH RATE

Algal Self-shading
         * General Equation
                 X-  X0+  X,»  + X
         where:
                 \ =  light extinction coefficient
                 \ =  non-algal extinction
                 X=  linear algal extinction coefficient
                 X =  non-linear algal extinction coefficient
                 A =  algal concentration  (/ig Chla/1)
         * Special Cases
           - No Self-shading  (SEMCOG)
                 X = X2=o
           - Linear  Self-shading  (META)
                 \*°   X2=o
           -Non-linear Self-shading (TetraTech)
             -9-   X=  X  0.0088A + 0.054A2/3  (Riley Eq. )
                            243

-------
                          FIGURE 5

                      ALGAL GROWTH RATE



Light Functions    (LFNOPT)

         * Option  1:  Half  saturation
                    FL = (I/ X D) In
|~ KL + I

LKL + ie-XD.
                    KL = light  intensity at which growth rate
                         is 50% of the maximum growth rate.

         * Option 2:  Smith's Function



                        "l/KL +  (1 +  (I/KL)2)
        FL =  (I/X D)  In
                         I/KLe~ XD  +  (1  +  (I/KLe  XD)2)1/2
                    KL = light  intensity at which growth rate
                         is 71% of the maximum growth rate.
         * Option 3:  Steele's Equation
                    „   2.718  r-(e-XD(I/KL))    -Z/M.1
                    FL - —£-5- [e                       J
                    KL = light intensity at which growth rate
                         is equal to the maximum growth rate.
         * Notation
         FL = light attention factor
          X = extinction coefficient
          D = depth
          I = surface light intensity
                               244

-------
                         FIGURE 6


                    ALGAL  GROWTH  RATE




Growth Rate Attenuation Options   (LGROPT)


         *Option li  Multiplicative


         G = Gmax * FL * FN * FP



         *0ption 2:  Alternative Nutrient


         G = Gmax * FL * MIN(FN, FP)



         *Option 3:  Inverse Additive


                  * FL * [.   2  .  ]
                          1/FN + 1/FP
                        245

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                              FIGURE  7
Index








  1




  2




  3




  4




  5




  6




  7




  8




  9




 10




 11




 12




 13




 14




 15




 16




 17




 18




 19
DEFAULT THETA VALUES FOR
EPA/NCASI VERSION
Rate Coefficient Default
SEMCOG
BOD Decay 1.047
BOD Settling
Reaeration 1.0159
SOD Uptake
Organic N Decay -
Organic N Settling
Ammonia Decay 1.047
Ammonia Source -
Nitrite Decay 1.047
Organic P Decay -
Organic P Settling
Dissolved P Source -
Algae Growth 1.047
Algae Respiration 1.047
Algae Settling
Coliform Decay 1.047
Non-cons Decay 1.047
Non-cons Settling
Non-cons Source
QUAL-2E
Values
QUAL-2E
1.047
1.024
1.024
1.060
1.047
1.024
1.083
1.074
1.047
1.047
1.024
1.074
1.047
1.047
1.024
1.047
1.000
1.024
1.000
Code
BOD DECA
BOD SETT
OXY TRAN
SOD RATE
ORGN DEC
ORGN SET
NH3 DECA
NH3 SRCE
N02 DECA
PORG DEC
PORG SET
DISP SRC
ALG GROW
ALG RESP
ALG SETT
COLI DEC
ANC DECA
ANC SETT
ANC SRCE
                                 246

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                         FIGURE 8

                     DISSOLVED OXYGEN



Sediment Oxygen Demand Units   (SOD)

         * Mass per bottom area per time

                               or   gm-02/f t^-
         * Bottom Area

              Bottom Width * Length

         * Normal Channels

              Bottom Width = Equivalent Width + 2 * Depth

              Equivalent Width = Area/Depth
                               = Flow/ (Velocity * Depth)


         *Trapezoidal Channels

              Bottom Width = Wetted Perimeter
                            247

-------
                          FIGURE  9

                 INPUT/OUTPUT  MODIFICATIONS



New Coding Forms

          * Forthcoming


Local Climatology Data

          * Echo-printed  in  Steady  State  {Dynamic Optional)


Descriptive Output  for Steady State Convergence

          * Convergence Summary
              Algae Growth  Rate, Nitrification Inhibition,
                 Dam Reaeration

          * Temperature Summary - Solar Values

          * Algae Summary  -  Averaging, Growth and Light
              Function Options, TFACT, AFACT, Solar Values
Five Part Final Summary
         * Hydraulics/Geometry
         * Water Quality Coefficients
         * Water Quality Variables
         * Algae Data
         * Dissolved Oxygen Data
Optional Plot of DO and BOD

         * Line Printer Plot
                         248

-------
          PREDICTING THE REAERATION  COEFFICIENT  FOR  OHIO  STREAMS

   by Daniel S. Skalsky, Lester D.  Fischer,  P.E.,  and  Seif Amragy,  P,E.
                 The Ohio Environmental  Protection Agency
Introduction

The determination of the reaeration coefficient  (Kg)  is  of critical
importance in determining the waste assimilative capacity of  streams.
This information is essential for effective  and  efficient planning and
implementation of pollution control programs.   Comprehensive  basin
planning, waste load allocation,  and the establishment of priorities  for
construction grants are among the activities which  depend upon  accurate
assessment of a stream's ability  to assimilate  wastes.

This report was prepared to support the water quality modeling  activities
of the Ohio Environmental Protection Agency  (OEPA).   The objectives of
this report are to:

    1.  assess the value of eighteen predictive  equations for estimating
        the reaeration coefficient;

    2.  examine the relationship  between the reaeration  coefficient and
        streamflow; and,

    3.  make recommendations regarding  the determination and  use  of the
        reaeration coefficient for waste load allocations.

To achieve the above objectives,  an analysis was performed  using
reaeration data collected during  the period  from January, 1980  through
May, 1983.  Data were collected by the  U.S.  Geological Survey during  1980
- 1982 in cooperation with OEPA.   Field studies  were  continued  by OEPA
beginning in 1983.  Twenty-eight  different  streams  and rivers were studied
across the state of Ohio, including a total  of  61 distinct reaches.   The
majority of the study reaches were downstream of wastewater treatment
plant discharges.

Methodology

The following sections describe the measurement  and calculation techniques
used in the preparation and analysis of the  data.  Additional details of
the field techniques and data reduction methods  currently employed  in
reaeration studies are documented in a  Reaeration Manual which  is being
prepared by OEPA.  In addition to the reaeration coefficient, streamflow,
stream velocity, depth, slope, and cross-section width were also  measured
for most of the study reaches.
                                    249

-------
Measurement of  Kp.   Reaeration coefficients were measured using the
modified tracer technique  with ethylene and/or propane as the tracer gas
(Rathbun et al_. ,  1975)  for all  but four determinations of K2.  These
four values were  determined using the radioactive tracer technique developed
by Tsivoglou  et .a],.  (1968).   All  measured l<2 values were converted to
values  at 20°C  using a  temperature correction coefficient of 1.024 (Elmore
and West, 1961):
         where  T  is  the  measured stream temperature in degrees C.


Most of the  rivers  in  the  data set  have field l<2 values available  for one
or two reaches, although a few,  such  as the Great Miami and Scioto rivers,
have measurements for  additional reaches.   When both ethylene and  propane
l<2 values were  available,  the  average of the two values was used in the
analysis.  A comparison  of ethylene and propane results is presented in
Figure 1.  It is  clear that the  results obtained using the two hydrocarbon
gases are not always in  complete agreement with one another.

The data were edited and in a  few studies  were judged unreliable because of
unusual field conditions,  data inconsistencies, or questions  regarding the
validity of  the assumptions involved  in the measurement procedure.  All
negative l<2  values which were  obtained were associated with unreliable
data and were thus deleted from  the analysis.  Inadequate mixing of dye and
gas tracers  in  the cross-section was  noted as a possible cause of  unreliable
field data.   Poor mixing was suspected when an irregular dye  concentration
versus time  curve was  observed at the first sampling site or  when  an extreme
loss or apparent  gain  of dye mass was observed between sites.

Fifty-four valid  determinations  of  f<2 were included in the final data set,
upon completion of the above editing  procedures.   Reaeration  coefficient
values ranged from 1.05  to 48.0  per day at 20 degrees C (base e).   Two
studies had  l<2  values  greater  than  14.0,  both of which involved rapid
changes in elevation (i.e.,  a  cascade or low head dam).

Velocity Measurement.  Velocity  was calculated by dividing the length of a
given reach  by the time  of travel of  the dye peak through the reach.  Reach
length was determined  from topographic maps.  A comparison of velocities
calculated using peak  and  mean times  of passage for 10 studies showed that
the two methods differed by approximately  11 percent.

The velocities measured  in the study  reaches ranged from .054 to 2.33 feet
per second.   Eighty-five percent of the reaches studied had velocities less
than one foot per second.

Depth Calculation.  Average velocity  and flow measurements were used in
conjunction with one to  four stream top width measurements, obtained within
a given reach to calculate the average depth using the equation:
                                   250

-------
    15-1
o
   A
 -5
i
5
10
                                                    -1,
K2 Determined  Using Propane (days''@ 20°C)
15
             Figure  1:   Comparison of K2 Values Obtained Using
                         Ethylene and Propane  Tracer Gases,
                                  251

-------
[•
                      n
                             -
         where
           H   =  average depth  of flow  (ft);
           Q   =  discharge (cfs);
           V   =  time of travel  velocity (peak  to  peak,  ft/s);
           L   =  length  of reach (ft);
           Wi  =  width of subreach i  (ft);
           Li  =  length  of subreach  i  (ft); and,
           n   =  number  of homogeneous  subreaches.

 In  Equation  2,  the  term in  brackets may be  viewed  as a  local depth,
 indicating the  calculated depth at a  particular  location along the reach
 where  a  width measurement was  taken.   Local depths  are  then weight
 averaged within a  given reach  according to  the length  of their respective
 subreaches,  yielding the average depth for  the reach.

 A comparison  of average depths calculated in  the above  manner to those
 calculated using a  single average width value in conjunction with velocity
 and  flow was  performed.  The  results  yielded  by  the two methods were
 essentially  identical  for the  data examined,  with  less  than 2 percent
 difference between  methods.  The reason for the  close  agreement between
 the  two  calculation procedures may be due in  part  to the limited
 resolution of the width, velocity, and flow data.   In  the case where only
 1 width  measurement was  available, the two  calculation  procedures yielded
 identical  results.   Calculated average depths ranged from 0.2 to 7.3 feet,
 and  only two  reaches had average depths which exceeded  4.0 feet.

 Slope  Measurement.   Water surface slope was surveyed directly in over 90
 percent  of the  reaches  studied and was estimated from  topographic maps in
 the  remaining reaches.   Slopes in the study reaches ranged from 0.63 to
 72.18  feet per  mile, less than 25 percent of  the measured slopes exceeded
 10.0 feet  per mile.

 Streamflow Measurement.  Standard U.S.  Geological Survey procedures were
 used to  measure  Streamflow with  Price AA or Pygmy current meters (refer to
 Buchanon and Somers, 1969 for  details  of this technique).  Flow ranged
 from 0.1  to 1470 cfs among reaches.   Approximately 80 percent of the study
 reaches  had flows between 1 and  300 cfs.

 Analysis of Predictive Equation  Performance.  A comparison was made
 between observed reaeration rates and  those predicted using the equations
 shown  in Table 1.   The data base used  in the  derivation and/or validation
 of each equation is  also noted  in Table 1.  Table 2 summarizes a select
 group  of these data  sets in terms of  the range of several common hydraulic
 variables.

 No attempt was made  to segregate the  available data according to the range
of the original  data used in the derivation and/or validation of the
equations examined.  Segregation of the data  in this manner makes a direct
comparison of performance difficult,  since the data set used for the

                                    252

-------
               Table 1.  Equations  for Predicting K2.
 1. Bansal (1973).  Data from: Churchill et _al_., Langbein -  Durum,
     and O'Connor - Boddins.
          K2 =   4.666  V-6  H'1-4

 2.  Bennett - Rathbun I (1972).  Data from: Churchill _et ^l_.,
     Krenkel-Orlob, Negeleacu-Rojanski, O'Connor-Dobbins, Owens  et
     al. , Thackston-Krenkel, Tsi voglou-Neal (pre-1968 data only).
          K2 = 106.1  V0.413  S0.273  H-l.408

 3.  Bennett - Rathbun II (1972).
          K2 =  20.17  vO-607  H-l.689

 4.  Cadwallader - McDonnell (1969).  Data from: Churchill ^t &]_.,
     Owens et al.,
          K2 = 336.8  (VS)0-5  H-"1-0

 5.  Churchill et al. I (1962).  Authors' data.
          K2 = 0.0944  V2.361  H-2.753  s-0.669

 6.  Churchill et_ aj_. II (1962).  Authors'  data.
          K2 = 11.57  V°-969  H-l.673

 7.  Covar (1976) - combined the equations of O'Connor and Dobbins
     (1958), Churchill et al- n (1962), and Owens et aj_. (1964).
          K2 = 12.81  V0-5    H-1-5    V< 2-3  ft/si   H > 2  ft
             = 11.6   V0-969  H-!-673  V > 2-3  ft/s;   H => 2  ft
             = 21.7   V0-67   H-85                   H< 2  ft

 8.  Dobbins (1965).  Data from: Churchill  ,e_t al>, Krenkel-Orlob, and
     O'Connor-Dobbins.
2 = 127.7
"(1 + F2) (VS}0'375
(0.9 + F)1-5 H
». -
coth
5.11 (VS)0'125
(0.9 + F)°-5
 9.  Foree (1979).  Author's data.

          K2 = (0.56 + 6786  S1 J5)  q°'25

              if q => 1.0  use q - 1.0
                 q * 0.05 use q = 0.05

10.  Isaacs - Gaudy (1968).  Authors'  data.

          K2 = 8.61  V  H'1-5
                                253

-------
         Table 1.  Equations  for  Predicting  K2.  (Continued)
11.  Krenkel - Orlob (1963).  Authors' data.
          K2 = 234.  (VS)°-408  H-°-66
12.  Langbein - Durum (1967).  Data from: Churchill et al_.,
     Krenkel-Orlob, and O'Connor-Dobbins.
          K2 = 7.60  V  H'1-33
13.  Negulescu - Rojanski (1969).  Authors'  data.
          K2 = 10.92  (V/H)0-85
H.  O'Connor - Dobbins (1958).  Authors' data.
          K2 = 12.81  V0-5  H'1-5
15.  Padden - Gloyna (1971).  Authors' data.
          K2 = 6.87  vO-703  H'l-054
16.  Parkhurst - Pomeroy (1972).  Authors' data.
          K2 = 48.39 (1 + 0.17 F2) (vs)Q.37S  ^ .0
17.  Thackston - Krenkel (1969).  Authors' data.
          K2 = 24.94 (1 + F°-5) U*   H'1-0
18.  Tsivoglou - Neal (1976).  Authors' data.
          K2 = C V S
              if  1* Q<10  cfs,  C = 9500
              if 10* Q< 25 cfs,  C = 6860
              if 25< Q,           C = 4650
     where
          K  = reaeration rate coefficient at 20°C (base e,
                 day"1);
          V  = average velocity (ft/s);
          H  = average hydraulic depth (ft);
          S  = slope of the energy gradient  (ft/ft);
          F  =• Froude number = V (32.2 H)"0'5;
                                             2
          q  = specific discharge  (cfs)  / mi   ; and,
          U* = average shear velocity (ft/s) = (32.2  H S)
                                254

-------
           Table 2.  Summary of Selected Reaeration Data Bases (adopted from Bennett and Rathbun, 1972).
ro
REFERENCE
O'Connor-Dobbins, 1958
Churchill et al_., 1962
Krenkel-Orlob, 1963
Owens et a^. , 1964
Isaacs-Gaudy, 1968
Thackston-Krenkel, 1969
Negelescu-Rojanski , 1969
Parkhurst-Pomeroy, 1972
Tsivoglou-Neal , 1976
Foree, 1979
NUMBER
OF DATA
POINTS
38
30
58
32
52
40
8
74
605
42
FLOW K2
(cfs) (days'1)
MIN MAX RIVER FLUME MIN MAX
X 0.04
952 17,300 X 0.53
X 24.5
2.70 2.16 X 0.71
X 0.51
X 17.64
X 19.90
0.4 8.8 Sewers
0.2 3,000 X 0.08
0.3 410 X 0.34
13.36
12.80
266.0
11.32
12.80
149.0
43.07
-
360.0
37.75
DEPTH
(ft)
MIN MAX
0
2
0
0
2
0
0
0


.90
.10
.08
.39
.12
.04
.16
.26
-
-
37.00
11.40
0.20
2.44
11.41
0.23
0.49
1.59
-
-
VELOCITY
(ft)
MIN MAX
0.19
1.80
0.13
0.13
1.85
0.37
0.66
1.88
-
0.06
4
5
2
1
5
2
1
7
2
0
.20
.00
.14
.83
.00
.32
.90
.88
.20
.94
SLOPE
(ft/ft)
MIN MAX
.000027
.000126
.000750
.000156
-
.000650
-
.000160
.000095
0.0
.003600
.002351
.024000
.010600
-
.020400
-
.009800
.056818
.010890

-------
evaluation would be different for each equation.  The current analysis  is
a simple assessment of the performance of several  published equations  for
predicting «2 using the available data on Ohio streams.

The first step in comparing predicted and observed K£ values was the
examination of scatterplots of observed versus predicted values.  The
relationship between predicted and observed values included a great deal
of scatter, as shown in Figure 2.

The data set was then subdivided into groups based on the slope of the
energy gradient and streamflow.  The four classes are defined in Table  3.
Slope and flow were used to classify streams because they reflect
hydraulic regimes concisely.  Both variables are normally measured or
estimated as part of a modeling project.


Table 3.  Description of Data Classes.
Data
Class
1
2
3
4
Number of
Data Points
11
15
13
14
Slope
(ft. /mi.)
-= 3
3 - 10
3-10
=>10
Flow
(cfs)
.
< 30
=> 30
"*
The above classification scheme resulted in 11-15 measured fy values in
each class.  An examination of the percentage errors of each equation was
conducted to determine the best equations in each class, based on four
criteria:

    1.   the percentage of relative errors with absolute values less than
         50 percent;

    2.   the percentage of relative errors less than -80 percent;

    3.   the percentage of relative errors greater than 100 percent; and,

    4.   the percentage of overpredictions and underpredictions.

Although the numerical values used in the above criteria are somewhat
arbitrary, the performance criteria provide a great deal of information
about the error distribution associated with each predictive equation.
The first criterion reflects the percentage of reasonably accurate
predictions and was weighted most heavily in the analysis.  The second and
third criteria indicate extreme negative and positive errors (i.e.,
underestimates and overestimates, respectively).  The final criterion
indicates whether or not the error distribution is centered about zero.
                                    256

-------
    16-
    14-
•o  «H
CNJ
                                   Line  of Perfect Agreement
    10-
 03

T3





 CM
-a
 at

 $-
 
-------
Percent relative error was calculated using the following equation
          E =     - K;>) 100                            (3)
                   K2

     where
         E   = percent relative error;
         K2   = measured K2 at 20°C (base e,  day'1);  and,
         K2'  = predicted K2 at 20°C (base e, day'1).


 Percent  relative  error (E) was selected as  the  basic  measure of agreement
 between  observed  and  predicted reaeration coefficients for  two reasons.
 First,  this  approach  maintains case  by  case detail which  is useful in
 guiding  the  examination of outliers.  Second, percent relative error
 provides a measure of predictive  ability in terms which are similar to
 these used to  define  the  range of K2  values used in wasteload allocation
 sensitivity  studies.

 Results

 Variation of K? With  Streamflow.   The variation of K2 with  streamflow
 is  important,  since reaeration studies  are  rarely conducted under exactly
 the same hydrologic conditions which  are assumed in water quality models
 for waste load allocation purposes.   However, there is a  general lack of
 information  available  on  the  variation  of reaeration  with streamflow in
 Ohio.  The data which  are available are presented in  Table 4 and in each
 case, K2 increased with increasing flow.

 Table 4.  Variation of  Reaeration  Rate with  Varying Flow Conditions.
Velocity Depth
Stream
Pawpaw Cr.

N. F. Licking R.



Reach
1
1
1
1
2
2
(ft/s)
.210
.387
.10
.22
.15
.28
(ft)
1.0
1.1
0.6
0.9
0.6
0.9
Flow
(cfs)
4.55
9.62
8.67
19.20
8.86
19.80
iK2
(day1, 20°C)
3.73
4.94
2.04
3.09
2.23
3.32
To estimate the behavior of K2 with flow variations in the absence of
field measurements velocity versus flow and depth versus flow
relationships may be used in conjunction with a predictive equation for
K2 (Zogorski and Faust, 1973).
                                     258

-------
Comparison of Predictive Equations.   The performance of each equation with
respect to the four performance criteria in each data class (1-4)  is
displayed graphically in Appendix A, Figures A-l through A-4.   The
predictive equations which yielded the best results in each data class are
shown in Table 5.
Table 5. Preferred Predictive Equations.
           Data Class                  Preferred Predictive Equation(s)
             1                         Krenkel-Orlob; Negelescu-Rojanski
             2                         Parkhurst-Pomeroy
             3                         Thackston-Krenkel
             4                         Tsivoglou-Neal
The reaeration coefficients predicted by the Krenkel-Orlob (1963) and
Negelescu-Rojanski equations were closest to the observed values in Class
1 (slopes less than 3 ft/mi).  Over 70 percent of the data in this class
yielded relative errors (E) less than 50 percent in absolute value for
these equations.  Less than 10 percent of the data fell  into either of the
extreme value categories (i.e., E -S.-BQ; E ^ 100).  A complete summary of
the relative errors for all predictive equations when water surface slope
was less than 3 ft./mi. is shown in Appendix A, Figure A-l.  Scatterplots
of observed versus predicted l<2 values for these two equations are shown
in Appendix B, Figures B-l  and B-2.

It is interesting that the Krenkel-Orlob equation performed well in Data
Class 1.  Previous reviewers have noted the unusually high values of l<2
which were obtained in the laboratory experiments upon which this equation
is based (Thackston and Krenkel, 1969; Wilson and Macleod, 1974).  One
possible explanation for this result is that low-slope streams in Ohio are
generally sluggish and may include large pooled reaches.  In such streams
it is conceivable that factors which are not represented adequately by
velocity and depth are more significant in determining the rate of
reaeration (e.g., wind).

A second possible reason for the seemingly high l<2 values in low-slope
streams is that the modified tracer technique may overestimate reaeration
for sluggish reaches.  The data used in this analysis indicate that field
problems and measurement errors are more common on such streams.  However.
a tendency to overestimate the reaeration coefficient cannot be determined
from the available data.  Other researchers have demonstrated that the
modified tracer technique may yield larger l<2 values than the
radioactive tracer method in some cases (Grant and Skavroneck, 1980;
Whittemore, 1982).
                                    259

-------
The best agreement with the experimental data in Class 2 (slope of 3-10
ft./mi. and flow less than or equal to 30 cfs) was observed for the
Parkhurst - Pomeroy equation (1972), followed by the equations of Bansal
(1973), Langbein - Durum (1967), and Padden - Gloyna (1971).  These
equations produced absolute relative errors less than 50 percent for
approximately 70 percent of the Class 2 data.  None of these equations
produced any extreme errors, as shown in Appendix A, Figure A-2.
Scatterplots for observed versus predicted l<2 values for these equations
are shown in Appendix B, Figures B-3 through B-6.

Only the Thackston - Krenkel equation (1969) performed well in Class 3
(slope of 3-10  ft./mi. and flow larger than 30 cfs), as shown in Appendix
A, Figure A-3.  Sixty-nine percent of the relative errors yielded by this
equation in Class 3 data were less than 50 percent in absolute value while
15 percent of relative errors fell in the extreme categories.  A
scatterplot and associated linear  regression statistics for observed
versus predicted l<2 values for the Thackston - Krenkel equation are
shown  in Appendix B, Figure B-7.

In Class 4 (slopes greater than 10 ft./mi.) the equations of Force (1979),
Negelescu-Rojanski, O'Connor-Dobbins, Parkhurst-Poweroy (1972), and
Tsivoglou-Neal  (1976) performed well in terms of relative errors as shown
in Appendix A,  Figure A-4.  Each yielded errors less than 50 percent in
absolute value  for more than 60 percent of the data.  The Tsivoglou-Neal
(1976) equation is clearly preferable because it had the most predictions
within 50 percent relative error, yielded no extreme errors, and the error
distribution was centered about zero (i.e., the equation showed no
tendency to over or underpredict Kg in this data class).  Scatterplots
for the Tsivoglou-Neal (1976) and Parkhurst-Pomeroy (1972) equations are
shown  in Appendix B, Figures B-8 and B-9.  It appears that the
Parkhurst-Pomeroy equation could be improved by refining the leading
coefficient in  the equation to better fit the observed data.

In general, the analysis showed that the performance of predictive
equations varied considerably depending on the type of streams to which
they are applied.  Figure 3 shows a scatterplot of observed versus K2
values predicted using each of the preferred predictive equations in their
respective class (the Krenkel-Orlob equation was arbitrarily selected for
use in Data Class 1).  It is surprising that four of the five preferred
equations were  not developed using extensive stream data, but were based
primarily on flume data (Negelescu and Rojanski, 1969; Krenkel and Orlob,
1963; and, Thackston and Krenkel, 1969) and sewer data, in the case of
Parkhurst and Pomeroy (1972).  This finding supports the use of these
equations, which have not gained wide acceptance because of concern
regarding possible-differences between the hydraulic characteristics of
flumes and natural  streams.

Conclusions

The following conclusions are made based on the proceeding analysis of
reaeration in Ohio streams:
                                    260

-------
°0
   16-
   14-




   12-




^  10-



X
tU   Q_•
-0   8-
IM*



0)   6-
J.
<3J



^   1


    2-
                LEGEND

         * Class 1:  Krenkel-Orlob
         • Class 2:  Parkhurst-Pomeroy
         A Class 3:  Thackston-Krenkel
         o Class 4:  Tsivoglou-Neal
                                           Line of Perfect Agreement
                                      a
             *        »       P       •        *       »        i       i
             2      4       6       8      10      12      14      16

                        Predicted  K2  (day'1  @ 20°C)

           Figure 3:  Comparison  of  Observed Versus Predicted  K2
                      Values  Using a Preferred Equation  in  Each
                      Data  Class.
                                   261

-------
    1.


    2.


    3.
    4.
     Field determinations of &2 are preferable to predictive
     equations when the stream analysis is sensitive to fy.

     Relative errors in predicting l<2 may be reduced by using
     selected equations in specific slope and flow c.1 asses.

     Model sensitivity studies should consider larger ranges of Kg
     than currently used, especially when K£ is below 2.  Absolute
     ranges should also be considered (e.g., 0.1  - 3.0) in sensitivity
     analyses for low reaeration streams.

     Additional  data are needed to define the variation of l<2 with
     streamflow in a given river reach.
References
Bansal, M.  K., 1973.
    Research V. 7, No 5,
Bennett, J. P., and R. E
    US Geological Survey
Buchanon, T. J. and W. P
                  "Atmospheric Reaeration in Natural  Streams" Water
                     pp. 769-82.
                      Rathbun, 1972.        	
                     Professional Paper 737.
                      Somers, 1969.  Discharge Measurements
                                          Reaeration in Open Channel  Flow,
                                                                at Gaging
                                                              the US
    Stations, Techniques of Water Resources Investigations of
    Geological Survey, Book 3, Chapter A8.
Cadwallader, T. E., and A. J. McDonnell, 1969.  "A Multivariate Analysis of
    Reaeration Data," Water Research V. 3, pp. 731-742.
Churchill, M. A.,  H. L. Elmore, and R. A. Buckingham, 1962.  "The
    Prediction of Stream Reaeration Rates,"  Journal of the Sanitary
                                 , No. SA4, pp. 1-46.
                                 the Proper Reaeration Coefficient
Engineering _Div_vt_AS_C_E V.
                                                                  Use
Covar, A. P., 1976.  "Selecting the Proper Reaeration Coefficient for
    in Water Quality Models,"  Proceedings of USEPA Conference on
    Environmental Modeling and Simulation, pp
                                                                  Journal
Dobbins, W. E., 1965.  lfBOD and
    of the Sanitary Engineering
                            Oxygen
                            Div., ASCE
                        West, 1961.
                        Journal of
_      340-343.
Relationships in Streams," 	
    V. 91, No. SA5, pp.  49-55.
       of Water Temperature on
         Engineering Division,
                                 "Effects
                               the Sanitary
Elmore, H. L. and W. F.
    Stream Reaeration," 	    _ 	
    ASCE, Vol. 85, No. SA4, pp. 59-71.
Foree, E.G., 1979.  "Low-Flow Reaeration and Velocity Characteristics of
    Small Streams," Symposium on Reaeration Research, Proceedings
    Hydraulics Division Specialty Conference ASCE, October 28,  1975.   pp.
    185-209.
Grant, R. S. and S. Skavroneck, 1980.  Comparison of Tracer Methods  and
    Predictive Equations for Determination of Stream-Reaeratipn
    Coefficients on Three Small Streams in Wi scons in"!  US Geological
    Survey Water Resources Investigation 80-19.
Isaacs, W. P. and A. F. Gaudy, 1968.  "Atmospheric Oxygenation  in  a
    Simulated Stream," Journal of the Sanitary Engineering Division,
    Vol.  94, No. SA2,
                                                                     ASCE,
Krenkel, P. A.
    Reaeration
    Transactions
                  pp.  319-344.
           and G.  T.  Orlob,  1963.
           Coefficient,"  American
             V.  128,  pp.  293-334.
                                       "Turbulent Diffusion  and  the
                                      Society of Civil  Engineers
                                     262

-------
Langbein, W. B. and Will Durum, 1967.  The Aeration Capacity of Streams,
    US Geological Survey Circular 542.
Negelescu, M. and V. Rojanski, 1969. "Recent Research to Determine
    Reaeration Coefficient," Water Research  V.  3,  No.  3,  pp.  189-202.
O'Connor, D.J. and W. E. Dobbins: 1958, "Mechanism  of Reaeration in Natural
    Streams," American Society of Civil Engineers Transactions V.  123,  pp.
    641-684.
Owens, M., R. W. Edwards, and J.  W.  Gibbs, 1964.  "Some  Reaeration  Studies
    of Streams,"  Int. Journal of Air and  Water  Pollution   V.  8, pp.
    469-486.
Padden, T. J. and E. F. Gloyna, 1971.  Simulation of Stream Processes  in  a
    Model River,  University of Texas, Austin, Report No E11E-70-23,
    CRWR-72.
Parkhurst, J. D. and R. D. Pomeroy,  1972.   "Oxygen  Absorption  in Streams,"
    Journal  of the Sanitary Engineering Division, ASCE  V.  98,  No.  SA1,
    pp. 101-124.
Rathbun, R.  E., D. 0. Shultz, and D.W. Stephens,  1975.  Preliminary
    Experiments with a Modified Tracer Technique  jfor Measuring Stream
    Reaeration Coefficients, US Geological  Survey Open  File Report 75-256.
Thackston, E. L. and P. A. Krenkel,  1969,  "Reaeration Prediction in Natural
    Streams," Journal of the Sanitary Engineering Division, ASCE V. 95,
    No. SA1,  pp. 65-94.
Tsivoglou, E. C., J. B. Cohen, S.D.  Sheaver, and  P.  J.  Godsil, 1968
    "Tracer  Measurement of Stream Reaeration II:  Field  Studies," Journal
    of the Uater Pollution Control  Federation V.  40, No. 2, pp.  285-305.
Tsivoglou, E. C. and L. A. Neal,  1976  "Tracer Measurement of  Reaeration:
    III.  Predicting the Reaeration  Capacity of  Inland  Streams,"  Journal
    of the Hater Pollution Control  Federation V.  48, No. 12, pp. 2669-88.
Whittemore,  R.C., 1982.  A Comparison of Reaeration  Estimation Techniques
    for the  Quachita River Basin, NCASI Technical Bulletin No. 375.
Wilson, G. T. and N. Macleod, 1974.   "A Critical  Appraisal  of  Empirical
    Equations and Models for the  Prediction of the  Coefficient of
    Reaeration of Deoxygenated Water,"  Water Research  V.  8, No. 6, pp.
    341-366.
Zogorski, J. S. and S. D. Faust,  1973.  "Atmospheric  Reaeration Capacity of
    Streams, Part I: Critical  Review of Methods Available  to Measure and
    Calculate the Atmospheric Reaeration Rate Constant," Environmental
    Letters  V. 4, No. 1, pp. 35-59.
                                   263

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                               Appendix A: Summary of Predictive Equation Performance
ro
CTi
                Bansal
                Bennett-Rathbun  I
                Bennett-Rathbun  II
                Cadwallader-McDonnel
Churchill et. al.
Churchil1 et. al.
Covar
Dobbins
Foree
Isaacs-Goudy
Krenkel-Orlob
Langbein-Durum
Negelescu-Rojanski
O'Connor-Dobbins
Padden-Gloyna
Parkhurst-Pomeroy
Thackston-Krenkel
Tsivoglou-Neal
                                   I
                                   II
                                       10        TOOK)10010
                                         Within 5Q%     Above 100%
                                                          10010         10010        100
                                                   Below-80r5    Over Estimates Under Estimates
                   Figure A-l:
                 Summary of Percent Relative  Error of Predictive Equations  For
                 Slope Less Than 3 (ft./mi.).

-------
ro
CT>
CD
                Bansal
                Bennett-Rathbun  I
                Bennett-Rathbun  II
                Cadwal1ader-McDonnel
Churchill et.  al.
Churchill et.  al.
Covar
Dobbins
Foree
Isaacs-Goudy
Krenkel-Orlob
Langbein-Durum
Negelescu-Rojanski
O'Connor-Dobbins
Padden-Gloyna
Parkhurst-Pomeroy
Thackston-Krenkel
Tsivoglou-Neal
                                   I
                                   II
                                        0        10010         10010         10010         10010        100
                                         Within 50%     Above 100%     Below-80%   Over Estimates Under Estimates
             Figure A-2:   Summary of Percent Relative  Error of Predictive  Equations For
                           Slope  From 3 Through 10  (ft./mi.); Flow Less Than  or Equal  to 30  (cfs).

-------
ro
CTl
Bansal
Bennett-Rathbun  I
Bennett-Rathbun  II
Cadwallader-McDonnel
Churchill et.  al.  I
Churchill et.  al.  II
Covar
Dobbins
Foree
Isaacs-Goudy
Krenkel-Orlob
Langbein-Durum
Negelescu-Rojanski
0'Connor-Dobbins
Padden-Gloyna
Parkhurst-Pomeroy
Thackston-Krenkel
Tsivoglou-Neal
                                                   10010
                                             1001
       100
100
                                           Within 50%
                                     Above 100%
Below-80%   Over Estimates Under Estimates
                      Figure A-3:
                Summary  of Percent Relative Error of  Predictive Equations For
                Slope  From 3 Through 10 (ft./mi.);  Flow Greater Than 30  (cfs).

-------
ro
01
                  Bansal
                  Bennett-Rathbun I
                  Bennett-Rathbun II
                  Cadwallader-McDonnel
Churchill et. al.
Churchill et. al.
Covar
Dobbins
Foree
Isaacs-Goudy
Krenkel-Orlob
Langbein-Durum
Negelescu-Rojanski
O'Connor-Dobbins
Padden-Gloyna
Parkhurst-Pomeroy
Thackston-Krenkel
Tsivoglou-Neal
                                    I
                                    II
                                         Within 50%
                                     Above 100%
       10010         10010        100
Below-80%   Over Estimates Under Estimates
                    Figure A-4:   Summary of Percent Relative Error  of Predictive Equations  For
                                  Slope  Greater Than or Equal to  10  (ft./mi.)-

-------
                            Appendix  B:  Plots of Observed  Versus  Predicted Reaeration Coefficients
ro
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          16-
          14-
       o
       oo
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vo
            16-
            14 J
            12-
         S  10-1
         ^o

          (M
         •o   6-
         01   D
             4-
             2-
                                           Line of Perfect  Agreement
                             4       6       8       10      12

                               Predicted  K2 (day1 0 20'C)
                                                                   14
                                                                           16
             Figure  B-3:  Observed  K2  Versus Parkhurst-Pomeroy (1972)
                          Predictions  for Slope From  3-10 (ft./mi.);  Flow
                          Less Than  or Equal to 30  (cfs)
                                                                                 18-
                                                                                  16-
                                                                                  12-
                                                                               >-  10H
                                                                              •a
t.
ai
                                                                              S
                                Line of Perfect Agreement
            2      4      6      a      10      12      14      16     ie

                       Predicted K2  (day'1 9 20°C)


        Figure B-4:  Observed K2 Versus Bansal  (1973)
                    Predictions for Slope From 3-10 (ft./mi.);  Flow
                    Less Than or Equal to 30 (cfs)

-------
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       o

       •o
          16-
          14-
          12-
          10-
       X
       10
        L.
        V
        V)

       3
           6-
           4-
           2-
                                         Line  of  Perfect Agreement
                           4       6      8      TO      12


                             Predicted K2  (day'1  9 20'C)
                                                                14
16
                                                                                   161
                                                                                   14-1
                                                                                   10-
        ^

        •o
        01

        
-------
O
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10
TJ
T)
01
   16-
   14-
   12-
   10-
    B-
                                  Line of Perfect  Agreement
                    4      6       8       10      12      14

                       Predicted  K2  (day'1  0 20"C)
16
    Figure B-7:  Observed K2 Versus  Thackston-Krenkel (1969)
                Predictions for Slope  From 3-10 (ft./mi.); Flow
                Greater Than 30 (cfs)
                                  271

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           16-
           14-
           12-
           10-
            9-
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S-

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                WATER TEMPERATURE MODELING:  A PRACTICAL GUIDE

                                      By

               Peter Shanahan, Senior Water Resources Engineer
                 Environmental Research and Technology, Inc.
                            Concord, Massachusetts
ABSTRACT
     This paper is a review of techniques for the computation of water
temperature in surface water bodies.  Emphasis is placed on the practical
aspects of applying water temperature models.  The discussion focuses
particularly upon the problems of obtaining and adapting the meteorological
data required as input for surface heat transfer calculations.

INTRODUCTION

     Computations of water temperature are employed to determine the
environmental impacts of thermal discharges, to evaluate the performance of
cooling ponds used to dispose of waste heat from power plants, or to
evaluate the hydrothermal characteristics of water bodies in general.  They
are an essential part of the design of waste heat disposal structures and
systems, and in the assessment of environmental effects of waste heat
disposal.

     The calculation of the water temperature of a surface-water body is
based upon a heat balance similar to the water or mass balances employed in
water quality modeling.  The heat balance determines the change in the heat
stored as equal to the influx of heat less the outflux of heat.  The heat
stored in a quantity of water is manifested by its temperature according to
the following proportionality:

     H = V p cp T                                                         (i)

where     H   is the total heat content of the volume of water (Btu),
          V   is the volume of water (ft3),
          p   is the density of water
          Cp  is the specific heat of water (Btu/lb/°F), and
          T   is the water temperature (*F).
                                     273

-------
     The fluxes of heat to or from a water body may be classified as follows:

     1.   Inflowing and outflowing water.  These represent heat fluxes by
          virtue of their temperature.  The calculation of these fluxes is a
          straightforward extension of Equation 1.

     2.   Heat conduction to or from the earth through the bottom of the
          water body.  This is a minor component of the heat balance that is
          usually neglected.

     3.   Heat transfer through the water surface.  This is a major
          component of the heat balance and the primary topic of this paper.

The calculation of water temperature by a computer model is based upon
bookkeeping these fluxes and determining the consequent change in
temperature.

     As with water quality modeling, one may employ various assumptions
concerning the internal distribution of heat or temperature within a water
body.  The simplest assumption is that the water body is isothermal
(fully-mixed).  This is often inaccurate for deep lakes or embayments, which
are vertically thermally stratified, and for flowing streams, which exhibit
longitudinally varying temperature.  One-dimensional models are typically
used for these situations.  An example is the one-dimensional temperature
model in the QUAL-II stream water quality program (Roesner, Giguere and
Evenson, 1977a and 1977b).

     This paper focuses on one important aspect of water temperature
modeling—the computation of surface heat transfer.  Emphasis is placed upon
this particular topic because it is fairly complicated and thus prone to
errors in application.  Further, the surface heat flux calculation has
extensive and complex data requirements.  The means to fill these
requirements are not well documented in the literature, although there are
many helpful "tricks of the trade" that can be used to assemble the needed
data.  The purpose of this paper is to describe various techniques to
develop input data.

Measurement Units

     The measurement units in surface heat transfer calculations have long
been a problem.  In this paper, I will use English system units since those
remain the most used.  For heat flux, the English system units are
Btu/ft2/day.  In the metric system, the preferred units are watt/m2
(1 watt = 1 joule/sec).  Nevertheless, the Langley (abbreviated Ly), equal
to 1 cal/cm2, persists in usage.  The following conversions are useful:

     1 Btu/ft2/day  =  0.131 watt/m2    = 0.271 Ly/day
     1 watt/m2      =  7.61 Btu/ft2/day = 2.07 Ly/day
     1 Ly/day       =  0.484 watt/m2    = 3.69 Btu/ft2/day
                                     274

-------
SURFACE HEAT TRANSFER COMPUTATION

     The techniques and algorithms to model the transfer of heat through the
surface of a water body are well established.  Probably the most
comprehensive reference on surface heat transfer is a 1972 report by
Walter 0. Wunderlich of the Tennessee Valley Authority (TVA, 1972).  Other
excellent references are Ryan and Harleman (1973) and Edinger, Brady and
Geyer (1974).  The QUAL-II computer program documentation (Roesner, Giguere
and Evenson, 197 7a and 1977b) is also a good source of information, although
it references few original sources.

     Surface heat flux consists of five components as illustrated in
Figure 1.  The water is heated by incoming solar (short-wave) radiation and
by incoming atmospheric (long-wave) radiation.  Solar radiation is the
radiation of the sun, less those portions absorbed by clouds, dust, water
vapor and other material in the atmosphere, and less the portion reflected
by the water surface.  Atmospheric radiation is the radiation emitted by
clouds and other material in the atmosphere, less reflection at the water
surface.  The water body cools by emitting long-wave back radiation and by
evaporation and heat conduction.  Back, radiation emission depends upon the
temperature of the water body.  Evaporation is basically a diffusion
process, driven by the gradient of water vapor pressure from the water
surface to the overlying air.  Conduction is similar, but driven by the
gradient in temperature.  Typical magnitudes of the five heat flux
components are shown in Table 1.

     The sum of the five radiation and heat flux terms is the net heat
transfer across the water surface.  This is a function of the temperature of
the water surface and thus it enters into the equation for water
temperature.  There are two basic methods to compute the net heat transfer:
the complete heat budget and the linearized heat exchange method.  Each is
discussed in turn in the following,

Heat Budget Method

     The complete heat budget requires the separate calculation of the
individual heat flux components to arrive at the net surface heat flux.  The
net heat flux is given as:
where     4>n   is the net heat flux into the water surface,
          4>sn  is the net solar (short-wave) radiation into the water
               surface,
          <|>an  is the net atmospheric (long-wave) radiation into the
               water surface,
               is the back (long-wave) radiation from the water surface,
               is the evaporative heat flux from the water surface, and
               is the conductive heat flux from the water surface.
                                     275

-------
All heat  flux components  have the English system units of  Btu/ft2/day.
The formulae for the heat flux components are fairly  involved and thus
tedious for hand calculations.  Nevertheless, they are straightforwardly  and
quickly computed in digital computer programs.

     There is a general  consensus within  the literature  on the appropriate
formulae  to be employed  in computing the  individual heat budget terms.  The
following is a brief presentation of the  commonly used formulae drawn
largely from Ryan and  Harleman (1973).
     Clear-sky solar (short-wave) radiation
     Solar radiation at water surface
     Reflected solar radiation
     Net solar radiation

     Atmospheric (long-wave)  radiation
     Reflected atmospheric radiation
     Net atmospheric radiation

     Back (long-wave) radiation from the water surface

     Evaporative heat flux

     Conductive  heat flux
                    Figure 1    Components of Surface Heat Transfer
                                       276

-------
     Solar Radiation

     The net solar radiation into the water surface is the incoming
radiation from the sun, less that absorbed or scattered in the atmosphere,
blocked by clouds and reflected at the water surface.   The best solar
radiation information is from measurements at the site, however these are
usually unavailable.  Lacking measurements, calculations can be made of the
solar radiation and its various attenuation mechanisms, thus computing the
radiation at the water surface.  The report by Wunderlich (TVA, 1972) gives
a detailed explanation of the calculation procedures.   Unfortunately these
procedures are very complex, even for use in computer programs.

     A less complicated alternative is recommended by Ryan and Harleman
(1973).  They suggest that the clear sky solar radiation be determined from
empirical information.  The clear sky solar radiation is that reaching the
water surface during cloudless conditions.  It includes the attenuating
effects of atmospheric scattering and absorption, but does not include the
effects of cloud cover.  The net solar radiation is then computed by
accounting for reflectance and cloud cover:

          *sn = °-94 *sc d-0-65 C2)                                      (3)

where     <(>sc is the clear sky solar radiation (Btu/ft^/day), and
          C   is the fraction of the sky covered by clouds.

The factor 0.94 accounts for average reflectance at the water surface
following the recommendation of Ryan and Harleman (1973).  Determination of
4>sc is discussed subsequently in this paper.

     Equation 3 is an approximation in that is assumes average reflectance
and employs clear sky solar radiation.  The latter is  usually an estimate
based on average atmospheric attenuation.  Equation 3 works well in nearly
all circumstances.  However, in certain circumstances attenuating mechanisms
are much greater than normal.  For example, Locher (1981) reported studies
in the Pacific Northwest showing significant atmospheric attenuation due to
haze during apparently cloudless conditions.  For situations such as these,
the more complicated formulae described by Wunderlich (TVA, 1972) are
required.

     Atmospheric  Radiation

     Water vapor, carbon dioxide, ozone  and other atmospheric  constituents
cause  the atmosphere  to radiate  as  an  imperfect  black  body, or gray  body.
A  perfect black body  absorbs  all incoming  radiation and  reemits  a  radiative
flux proportional to  the fourth  power  of its  absolute  temperature.   The
constant of proportionality is the  Stefan-Boltzmann constant.  Gray  bodies
radiate  a fraction  of the black  body  radiation,  with  the  fraction  being  the
emissivity.  The  emissivity of the  atmosphere varies with the  air
temperature, moisture content and other  atmospheric variables.   Several
formulae  for atmospheric radiation  were  recently evaluated against field
data by  Hatfield  et al.  (1983).   Although  past researchers have  tended to
recommend the  formula by Swinbank (1963),  Hatfield's  study found the


                                      277

-------
Swinbank relation to perform poorly.  Based on Hatfield's findings, the
formula by Brunt (1932) is adequate:


     .  = 4 x 10~8  (T  + 460)4
       or              s
                                                                           (5)
where Ts  is the water  surface  temperature  (*F).

     Evaporation

     Of the various  components of  the  heat budget,  evaporation  is the most
uncertain.  Evaporative  heat flux  is directly  proportional  to the rate of
evaporative water  loss:
6
where
           L  E
            v
          E  is the evaporation  rate  (ft/day),
          Ly is the latent heat  of evaporation  (Btu/lb),  and
          P  is the density of water  (lb/ft3).
                                                                           (6)
                                      TABLE 1

                 TYPICAL MAGNITUDES OF SURFACE HEAT FLUX COMPONENTS
                                            Btu/ft/dav
                                                               tfatt/m
  Solar radiation,  

  Atmospheric radiation,  4>
  Back radiation,  
                   .
  Evaporation,  $

  Conduction, 
-------
The latent heat of evaporation in Btu/lb is given as a function of
temperature as


     L  = 1087 - 0.54 T                                                    (7)
      V                8
Some researchers take Lv as a constant corresponding to T8 - 212*F, the
boiling point of water.  This is incorrect since Ts will be much less in
environmental situations.

     There is an extensive literature addressing the calculation of
evaporation for both natural and artificially heated water bodies.  The
general form of the equation for evaporation, E, is:

     E = F(W)                                                    (8)

where     E    is the evaporation rate (ft/day),
          es   is the saturation vapor pressure of the air at the
               temperature of the water surface (mm Hg),
          ea   is the vapor pressure at 2 meters above the water surface
               (mm Hg),
          F(W) is the wind speed function (ft/day/mm hg), and
          W    is the wind speed 2 meters above the water surface  (miles/hr).

Usually, Equations 6 and 8 are combined and a constant value of Ly assumed
to define 4>e as

     e = f(W) (es - ea)

where f(W) is the heat flux wind speed function (Btu/ft2/day/mn Hg):

     f(W) = p LV F(W)

A value of Ly corresponding to a surface temperature of approximately SO
to 70 'F is typically assumed.  I will follow that procedure in this paper
and assume Ly = 1060 Btu/lb as do Ryan and Harleman (1973) and Helfrlch
et al. (1982).  In this way, the values of coefficients in f(U) shown in
this paper will be consistent with the literature.  Nevertheless,  there is
little computational effort in computing Lv as a function of Ts.   Thus,
I recommend a correction factor for computing 4>e:

          1087 - 0.54 T

     *e = 	1060	~  f(W> (6s -  V
or
      >  = (1.03 - 5.1 x 10 4 T ) f(W) (e  - e )                           (11)
      e                       s         s    a
                                     279

-------
     Many different expressions have been advanced for the wind speed
function f (W) .   Helfrich et al. (1982) give a systematic review and
evaluation of the major formulae.  Most expressions adhere to the general
form

     f = 17.7
                    1/3
                        + 11.1
                                                                         (14)
where
          A9V  is the difference between the virtual temperature at the
               water surface and in the air
               surface (°F).
                                             2 meters above the water
The virtual temperature is used in Equation 14 to account for the buoyancy
of the moist air above the heated water surface.  The virtual temperature is
the temperature of dry air with the same density as the moist.  It is
defined by Ryan and Harleman  (1973) as:
      v
            T + 460
          1 + .378 e/p
                       _
                                                                         (15)
                                     200

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CO
   Reference

Lake Hefner equation
Harbeck (1952)

Meyer (1942)

USGS/Chattahoochee River
Barnwell (1982)

QUAL-II
Roesner et al. (1977)

Brady, Graves and Geyer (1969)

Ryan and Harleman (1973)

Rimsha and Donchenko (1957)

Throne (1951)
               TABLE 2

        EVAPORATION EQUATIONS


Equation for f(W)

17 W2


80 + 10 W2


60 + 10.2 W2


42.5 + 16.9 W2

70 + W2 2

22.4 (fi6v)1/3 + 14 W2

61 + 1.47 (Ts-Ta) + 13.3 W2

67 + 71 W2
   Conditions

Natural Lakes


Natural Lakes and Ponds


Natural River


Rivers

Cooling Ponds

Cooling Ponds

Heated Streams in Winter

Cooling Pond
        Note:   these equations  do not include recalibration factors computed by Helfrich et al. (1982).

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     250
     200
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                                                                   LEGEND

                                                                     Throne

                                                                   — Himsha-Donchenko(AT=10)

                                                                  —. Mayer

                                                                     Roesner

                                                                     Ryan

                                                                   — USGS (Chatiahoochee R.)

                                                                   •• Brady

                                                                   •— Lake Hefner
     100
                                                                           10     11    12
                                    Wind Speed (miles/hr at 2m)
          Figure  2   Various Evaporation Wind Speed Functions vs  Wind Speed
                                            282

-------
where     6V  is the virtual temperature (*F),
          T   is the air temperature (°F),
          e   is the air vapor pressure (nun Hg), and
          p   is atmospheric pressure (mm Hg).

Many computer programs will not accomodate Equation 14 without modification
of the program code.  For these, the Meyer equation as recalibrated by
Helfrich et al. is recommended for artifically heated waters:

     f(W) =68-1- 8.5 W2                                                  (16)

Alternatively, the wind speed function could be determined by calibration to
site data in those applications where sufficient data exist.  The formulae
of Table 2 should guide such a calibration effort.

     In summary, the evaporative heat flux is given as:

     4»e = (1.03 - 5.1 x 10-* Ts) f(W) (es - ea)                          (17)

where f(W) is selected according to whether the water body is natural or
artificially heated.

     Conduction

     Conduction occurs by a heat diffusion process similar to the moisture
diffusion that drives evaporation.  Thus, the equation for conductive heat
flux is similar in form to that for evaporative heat flux:

     4>c = 0.255 f(W) (Tg - Ta)                                           (18)

     Net Heat Flux

     As stated previously, the net heat flux is the sum of the five
component fluxes outlined above.  English and metric system equations for
the components are summarized in Table 3.  The net heat flux is a function
of the surface water temperature, the overlying air temperature, moisture
content and wind speed, the incoming solar radiation, and the cloud cover
and condition of the atmosphere.

Linearized Heat Exchange Method

     The linearized heat exchange concept was popularized by John Edinger
and others from The Johns Hopkins University.  In this approach, the net
heat flux is assumed to be a linear function of the surface water
temperature:

     4>n =-K (Ts - TE>                                                    (19)

where     K   is the surface heat exchange coefficient
              (Btu/ft2/day/*F), and
          TE  is the equilibrium temperature (°F).
                                     283

-------
                                                                                    TABLE  3

                                                  SUMMARY  OF  EQUATIONS  FOR  SURFACE  HEAT  FLUX  COMPONENTS
                       Component
                                                          Ennliah SYatea
                                                                                                                   Metric  System (S.I.)
                 Heat Flux Components:

                 Net Solar Radiation


                 Net Atmospheric Radiation


                 Back Radiation


                 Evaporation


                 Conduction
                                                     in Bttt/ft /day
                                       0.94 <.   (1-0. 65 C*>
                                  *    = 2.05 z 1(T8 (1 + 0.149 Se  ) (T^+460)4 (1+0.17  C?)
=4.0 x 10


(1.03 - 5.1


0.255 f
                                                                                                                      f(W)
ro
oo
Wind Soeod Punctlona;

Natural Condition!

Artificially heated conditions
(Ryan and Harlenan* 1973)

Artificially heated condition!
(Meyer* 1942)
                                                    f(H> in atu/ft2/day/OH Hit

                                                    f(W) = 17 W2
                                                    ftW) = 17.7 flO
                                                                  1/3
                                                                      + 11.1
                                                    f(H) = 68 + 8.5
                                                                                           f(W) In
f(W) => 3.84  W2


f(W) =2.18  4flv1/3 +2.51


f(W) = 6.87  + 1.92 Wj
                  Paraii»t6r»i

                  C,  cloud cover

                  e4,  air vapor pressure
                    at 2 m above water

                  efl,  aaturatlon vapor pressure
                    at temperature T8

                  Ta,  air tenperature

                  T,,  water surface temperature

                  W^,  wind speed at 2 m
                    above water

                  A6V, virtual teaperctare
                    difference between water
                    surface and 2 a (see text)
                                  fraction  of sky

                                  mm nercury (ma Hj)


                                  mm mercury


                                  degreee F

                                  degrees P

                                  miles/hour


                                  degrees F
fraction of iky

nlllibar Crab)


millibar


degrees C

degrees C

n/>


degrees C
                  * Wind speed  functions recalibrated by  Helfrich et »1.  (1982)

-------
Equation 19 entails two parameters that are artificial,  but nevertheless
useful and intuitive,   The equilibrium temperature is the water surface
temperature that is in equilibrium with the environment:  the net surface
heat transfer is zero.  Water bodies continually seek their equilibrium
temperature, losing or gaining heat as required.  But since environmental
conditions change continuously, the equilibrium temperature also changes and
a water body is seldom at its equilibrium temperature,

     The surface heat exchange coefficient is the incremental change in the
rate of net heat transfer per unit change in surface water temperature.  It
varies with the surface temperature and thus should be recalculated as the
water temperature changes.

     The linearized heat exchange method is attractive since it permits
analytical solutions for a variety of water temperature problems.  However,
it is less accurate than the heat budget method and not suitable for
detailed design or analysis studies.  A general recommendation is that the
linearized method not be used in computer modeling since there is no
difficulty or additional data required to use the more accurate heat budget
method.

     Despite the recommendation that the linearized method not be used, the
equilibrium temperature concept is very useful and attractive.  It is
particularly helpful in screening data—for example in reviewing historical
records to select a critical period for design.  Extended periods of
extremely high equilibrium temperature are those in which thermal aquatic
impacts will be greatest.  These same periods are when cooling ponds and
similar heat rejection systems perform their worst.  Thus, the equilibrium
temperature is a useful variable in selecting simulation periods from  long
data records.  It is also valuable to understanding water temperature  trends
in transient computer simulations.  Table 4 is a BASIC-language computer
program for calculation of the equilibrium temperature.

METEOROLOGICAL DATA REQUIREMENTS

     Probably the greatest burden in water temperature modeling  is the
extensive  input data requirement.  The calculation of the heat budget
requires meteorological data characterizing the air temperature, humidity,
wind speed, cloudiness, and solar radiation at the study site.   It is  rare
that a complete set of data is available from measurements at a  site,  and
thus other  sources must be sought.

     The most comprehensive source of meteorological  data  is  the published
observations of the National Climatic Center in Asheville, NC.   The  center
publishes  data for many locations throughout the country in  a number of
formats.  Monthly  summaries are published  for each state in  the  publication
Climatological Data and daily  and 3-hourly data  are  published each month  for
selected weather stations  in Local Climatological Data.  Data are  also
available  on magnetic  tape for computer modeling of  long periods.
                                      285

-------
                                                                    TABLE  4

                                         BASIC-LANGUAGE COMPUTER PROGRAM  FOR  CALCULATION

                                                        OF  EQUILIBRIUM  TEMPERATURE
ro
CO
100 REM ••
110 REM     CALCULATION OF
120 REM EQUILIBRIUM TEMPERATURE
13O KEM =======================
140 DIM U<3>.HC3)
J50 DISP 'INPUT T» Ur R. S.  521 Cr  F'
160 H1SP '  ENTER STOP TO END RUN'
170 niSP '     f  IS THE AIR  TEMPERATURE.  PEG f
180 DISP '     U IS THE U1NP SPEED. MILES PER HOUR AT  2 M*
190 DISP '     R IS THE RELATIVE HUMIDITY.  PERCENT'
200 DISP '     S  IS THE CLEAR SKY SOLAR RADIATION.  BTU/SO FT/DAY1
210 DISF '    S3 IS THE OBSERVED SOLAR RADIATION.  6TU/SG FT/DAY'
220 DISP '       (EITHER S OR 52 SHOULD BE  SPECIFIED)'
230 DISP '     C IS THE CLOUD COVER. FRACTION'
1MO DISP '     F IS THE WIND SPEED FUNCTION."
250 DISP '        F=l FOR LAKE HEFNER'
J60 DISF '        F=2 FOR MODIFIED RYAN'
270 DISP '        F=3 FOR MODIFIED MEYER'
280 DISP '        F=4 FOR USER SPECIFIED1
290 DISP ' ' (? HISP 'INPUT Tr UN RF S. 52.  C.  F*
.500 INPUT T.U.R.S.S2.C.F
310 IF F»l OR F=2 OR F = 3 THEN 340
320 DISP "ENTER Ar& FOR UINK FUNCTION  F0 THEN 390
370 REM 	COMPUTE SOLAR RADIATION FROM CLEAR SKY  RADIATION	
330 S2=S»(1-.6S*C*C)
390 H3=,94*S2
400 ftEM 	COMPUTE AIR UAPOR PRES AND  VIRTUAL TEMP	
410 El=FNE-460
430 REM 	COMPUTE LONG WAVE RADIATION (ATMOSPHERIC)	
440 H2=.O00000021*U+.149*SDR*T4"4»(1+.J7*C»C>
450 ftEM USE PISECTION METHOD TO COMPUTE EQUILIBRIUM TEMP
460 REM 	
470 11=1
480 12=3
I9u U=T-5
5OO U<2)=T
510 UC3>=^T+S
520 Zl=0
530 FOR 1=11 TO 12
540 Z1=Z1+1
550 Ul=Ul D+460
560 ftEM 	COMPUTE LONG WAVE BACK RADIATION	
57O H1=.00000004*U1~4
580 E2=FN£ IF Ft3 THEN 750
720 REM MEYER UIND FUNCTION
730 Fl=68+e.5*U
MO GOTO 770
750 REM SPECIFY A-fbU UIND FUNCTION
760 Fl=Atfi*U
770 REM 	COMPUTE EVAP HEAT FLUX	
700 H4=F1*(E2-E1>
790 REM 	COMPUTE CONDUCTION	
HOO H5=H4*.255*(U(I)-T)/=H3+H2-H1-H4-H5
630 REM DETERMINE  IS H HAS CONVERGED TO 1  BTU/SO FT/DAY OR LESS
 64O REM 	
650 IF ABS(H(I))-, 1 THEN 1030
860 NEXT  I
 870 11=2
HBO 12=2
 B90 IF H(1> 0 THEN 990
 900 IF H<3):0 THEN 940
 910 Jl=l
 920 IF H(1>*H<2> 0 THEN Jl=3
 93O U(J1)=U(2)
 940 H(J1)=HC2)
 950 GOTO  1010
 960 U<3>=U<3>+10
 970 12=3
 900 GOTO  1010
 990 U< 1 >=UU )-10
 1000  11=1
 1010  U(2]i = 
-------
     Some other, less comprehensive sources of data are useful for rough
calculations.  These are the "Climatic Atlas of the United States",
published by the National Oceanic and Atmospheric Administration (1977) and
an EPA report, "Effect of Geographical Variation on the Performance of
Recirculating Cooling Ponds" (Thackston, 1974).  The EPA publication also
includes extreme monthly conditions which are useful to evaluate surface
heat transfer when it is at its least.

     The representativeness of off-site data is rarely addressed.
Nevertheless, it is an important matter.  The weather bureau station nearest
the site need not be the most representative.  It may fall in a different
geographic or climatic province, and thus be inappropriate.  A rigorous
attempt to synthesize on-site data was made by Jirka et al . (1977) for the
site of the North Anna Power Station in Virginia.  They used statistical
techniques to correlate a single year of on-site meteorological data with
coincident records at three surrounding weather stations.  Then, they
employed their computed statistical correlations to generate a long-term
synthetic record for the site from the records of the weather stations.  A
similar procedure is recommended for detailed design studies where the
representativeness of off-site data is uncertain.  In any study, the modeler
should consider the local climatology to determine the most representative
station for off-site meteorological data.

     Having obtained data, it is often necessary to convert it to a format
compatible with the heat budget formulae.  Air temperature presents no
problem, but humidity, wind speed, cloudiness and solar radiation often need
adjustments or conversions.

Humidity Data

     The humidity of air may be expressed directly as relative humidity, and
indirectly through the dew point or wet bulb temperature.  The wet bulb or
dew point, together with the air (or dry bulb) temperature, may be used to
compute relative humidity using a psychometric chart.  The chart, with
instructions, is given in the Handbook of the American Society of Heating,
Refrigerating and Air-Conditioning Engineers (ASHRAE, 1981) and numerous
other publications.  Another possible conversion method from wet bulb to
relative humidity is available by inverting an empirical equation given by
Thackston (1974):
     Twb = <0-655 + 0.36 RH) Ta                                         (20a>

or

               T

     RH = 2'78 T   ~ 1<82                                               (20b>
                a
                                     287

-------
where   Twb    is the wet bulb temperature  (°F), and
        RH     is the relative humidity  (expressed as a fraction).

This equation  is valid for relative humidity less than about 95%.  TVA
(1972) gives the following conversion  from  dew point temperature to air
vapor pressure over water:

                       7.5 T.-236.9
     e  = exp  (2.3026 (          — +  0.6609)]                           (21)
                          d

where Tj   is the dew point temperature of the air  (*F).

     The humidity conditions  of  the  air must be expressed as the water vapor
pressure in the equations for calculation of evaporative and conductive heat
flux.  The vapor pressure of  the air is computed as:

     ea = RH esat

where  esat  is the  saturation vapor pressure  (turn Hg).

     Calculation of  surface heat transfer requires  that the saturation vapor
pressure be determined  as a function of temperature.  Extremely accurate and
precise tables of this  function  are  found in the Smithsonian Meteorological
Tables (List, 1971).  Several different empirical formulae have been
proposed to compute  the  saturation vapor pressure as a function of
temperature.  For environmental  temperatures,  the empirical equation by
Thackston (1974) is  virtually indistinguishable from the tabulated function:
          = 25. 4 exp  (17.62 -        >                                    <22)
      T is the temperature  ("F).

     In computing evaporative heat flux, the vapor pressure at the water
surface is computed by assuming  it is saturated  (R^ = 1.0) and at the
temperature of the water.   The vapor pressure at a height above the surface
is based upon ambient temperature and relative humidity of the air.

Wind Speed

     The height above the water  or ground surface at which the wind is
measured is an important consideration in the use of wind speed data.
Often, the measuring height is unknown.  But if  it is available, the speed
may be adjusted to the height presumed by the heat transfer formulae
(usually 2 meters).  Based  upon  an assumed logarithmic wind speed profile,
Ryan and Harleman (1973) give the following adjustment relation:
                                     288

-------
                                                                         (23)
where Wz     is the (desired) wind speed at height z,
      W      is the (known) wind speed at height z
       z                                          1
      z      is the height above the water surface presumed by the surface
             heat transfer formula (m) ,
      ZIL     is the height above the water at which the wind speed is known
             (m) , and
      zo     is the wind roughness height (m).

Helfrich et al. (1982) discuss the selection of z0.  A value of
zo = 0.001 meter is a good approximation for most wind conditions.  At
high wind speeds, waves form on the water surface and increase zo.

Cloudiness

     The cloud cover of the sky is usually recorded as the percent (or
number of tenths) of the sky that is covered by clouds.  Occasionally, the
quantity percent possible sunshine will  be given.  The conversion from
percent possible sunshine to cloud cover can be made using an equation
derived from relations given by TVA (1972):
                       1/9
     C m [1.2 (1-P   >]                                                  (24)


where     C is the cloud cover (expressed as a fraction) and
          P is the possible sunshine (expressed as a fraction).

Solar Radiation

     Direct measurements of solar radiation are rare, and consequently these
data must be determined by other means.  Neglecting the influence of the
clouds, the clear sky solar radiation may be determined as a function of the
geographical latitude, the time of year, and the hour of the day.  TVA
(1972), Brock (1981) and any of a variety of references from the
meteorological and heating and air conditioning engineering literature give
formulae to calculate the clear sky solar radiation.  Unfortunately, these
formulae are complex and cumbersome, even for computer calculations.  The
complexity derives from the need for esoteric parameter values and the fact
that clock time cannot be used in the calculations, only solar time (i.e.,
relative to true solar noon) can be used.

     If the modeler desires only daily average values of solar radiation,
there are simple alternatives.  For example, Thackston (1974) employs
curve-fit equations that are reasonably accurate and amenable to both hand
and computer calculations.  Table 5 is a BASIC-language computer program
                                     289

-------
                                                                 TABLE  5

                                      BASIC-LANGUAGE COMPUTER PROGRAM FOR CALCULATION

                                          OF DAILY AVERAGE CLEAR  SKY SOLAR RADIATION
ro
in
o
100 KEM .-••••••...••..•<••«»=.....
110 REM CALCULATION OF CLEAR SKY
12O REM SOLAR KAIHAriON AT WAFER
130 REM  IN UNI TO III LI/311 FT/DAY
140 REh .=--..-....».»..-•.-. = -.«»
130 REM BASED ON fHACKSTON. 1771
140 REM  REPORT EPA-660/2-74-085
170 REH
1BO REH INITIALIZE DATA
190 REM 	
20O REM HAY OF YEAR ARRAY
21O DIM l'9< 12)
220 FOR 1"! 10 12
230 READ 09(I)
240 NEXT I
23O DAIA O,31.S9.90.120,131.181.212.243.273,304.334
240 REM COEFFICIENTS FOR CURVE FII EQUATIONS
270 DIM CK21) .C2<21 ) .C3(2l)
280 FOR 1-1 TO 21
290 READ Cl < I ).CIM I),C3< I >
300 NEXT I
310 REH INPUT LATITUDE AND DATE
320 REM 	
330 DISP 'ENTER  SITE  LATITUDE  '
340 IiISP '   (24  ID  44  DEGREES)'
330 UlSf *   (0  TO  END  RUN)*
360 INPUT  L
370 IF L"0 THEN  STOP
380 L1-INT
390 L3-L1-23
400 L2"CEIL44 THEN 330
430 IF L2<26  OR  L2 44 THEN 33O
440 DI9P  'ENTER  DATE  AS  MONTH.DAY*
450 INPUT  07.D6
440 D-D9+D8
470 REM COMPUTE  CLEAR SKY SOLAR
480 REM 	
490 04>-2*3.14139*0/346
300 S-CKL3)-C2*SIN+D4>
510  IF L1-L2 THCN 340
320
330
MO
330
540
:LXO
380
•j'fO
AOO
610
6:?0
630
640
6 SO
660
6X0
/*'Hf>
'•''<>
AX)
>\U
'JO
/.<0
/40
/SO
/60
//O
/IIO
/'/O
HOO
Ulo
li'.'O
feMO
U40
HSO
640
070
OUO
ti'/O
900
910
920
S2-Cl(L4)-C2(L4)*eiN(C307. J .679
                                                                           HAIA 79.371 .30.236.1.713
                                                                           hrtlA /IJ.S/66.31 ,
                                                                           Ifrtlrt 77.404.31'.
                                                                           DATA 76.6S'J.33. 156. 1 .728
                                                                           liAIA 76.04] .34. 133. 1 .694
                                                                           DA I /\ 7-,. 06 .3H. 194.1.737
                                                                           UAIA 74. 046. 3S. 938.1 .734
                                                                           HAIA 73,161.36.834.1.727
                                                                           DA I A /:;.248.37.69V.l .738
                                                                           IrAlA 71.39.36.599.1.721
                                                                           DrtlA 7O. 394. 39.'* 13. 1 .73
                                                                           DATA 49, 3^.40, 188. 1 .741
                                                                           DATA 60,362.40,982.1.739
                                                                           DATA 67.261.41.706.1.742
                                                                           DATA 66,24.42.442.1 .736
                                                                           DATA 65.197.43.128.1.74
                                                                           DATA 64.113.43.788.1.739
                                                                           DATA 63.01,44.471.1.739
                                                                           DATA 61.911.45.02.1.74
                                                                           DATA 60. 782. 4i. 639,1 .735
                                                                           ENH

-------
utilizing his equations.  Another very workable alternative for hand
calculation is a graphical look-up, as presented by Hamon, Weiss and Wilson
(1954).  Figure 3 is a graph of clear sky solar radiation based on their
empirical results.

     As stated above, distribution of solar radiation throughout the day can
be difficult.  If one only desires to construct a representative daily
variation in solar radiation, then the formulae of TVA (1972) or Brock
(1981) are quite useful.  However, if one wishes to construct a diurnal
variation to be used with measured data,  then the differences between clock
time and solar time require careful attention.  For example, I have
attempted in the past to back-calculate cloud cover from the differences
between measured solar radiation at a site ($s in Figure 1) and a
computed value of clear sky solar radiation ($cs).   The procedure worked
fairly well for daily averages (Wells et al., 1982).  But it worked very
poorly for hourly values due to inexact coordination of clock time and solar
time,

     For some problems, a hand calculation procedure for diurnal variation
of solar radiation is desirable.  For these,  it is possible to distribute
daily solar radiation throughout the day using data given in Chapter 27 of
the ASHRAE Handbook, 1981 Fundamentals.  In the handbook, tables of solar
position and intensity for various latitudes  give the direct normal
irradiation distribution by hours during the  day.  The normalization of the
hourly values by the sum for the day supplies a set of distribution
constants.  These distribution constants may  be applied to the daily average
clear sky solar radiation to construct the diurnal variation of solar
radiation.

     One final, but very important footnote applies to both the solar
radiation and atmospheric radiation components.  These radiation fluxes can
be measured directly to supply far more accurate data than the calculation
procedures above.

SUMMARY

     This paper is a review of the surface heat transfer calculations
necessary to model water temperature in surface water bodies.  The paper
recommends the use of the heat budget technique as more accurate than the
linearized method.  The linearized method is  based on the equilibrium
temperature and surface heat exchange coefficient.   Within the heat budget
technique, there are the following heat flux  components and recommended
procedures:

Solar Radiation -        It is best to measure this directly.  If
                         measurements are not available, clear sky solar
                         radiation may be estimated from Figure 3 or Table 5
                         and then modified for cloud cover and reflectance
                         (Equation 3).  A more exact procedure is
                         recommended for areas with prevalent haze, dust or
                         high water vapor.
                                     291

-------
                3000
ro
                 2SOO
            
-------
Atmospheric Radiation -  It is best to measure this directly.   If
                         measurements are not available,  Brunt's equation
                         (Equation 4) is recommended.

Back Radiation -         This flux is accurately determined by Equation 5.

Evaporation -            Evaporative heat flux is computed as  the product of
                         the latent heat of evaporation,  the gradient in
                         vapor pressure from the water surface to the
                         overlying air, and an empirical  wind  speed
                         function.  The Lake Hefner wind  speed function is
                         recommended for natural water bodies, the
                         Ryan-Harleman for artificially heated.   In computer
                         programs that will not accomodate the Ryan-Harleman
                         equation, the Meyer equation  is  a good substitute.
                         Both the Ryan-Harleman and Meyer equations should
                         include the recalibration factors by  Helfrich et
                         al. (1982).

Conduction -             Conductive heat flux is the product of a constant
                         of proportionality the gradient  in temperature from
                         the water surface to the overlying air, and the
                         wind speed function.

Table 3 is a complete summary of the recommended equations for the heat
budget.  Equations in both English and metric units are included in Table 3.

     The input data required for water temperature modeling are extensive.
Five types of data are required:  the air temperature, the wind speed, the
relative humidity, the cloud cover, and the solar radiation or an estimate
of clear sky solar radiation.  This paper includes descriptions of
procedures to manipulate data as follows:

Humidity -               conversion from wet bulb to relative  humidity

                         conversion from dew point to relative humidity

                         calculation of saturation vapor  pressure

                         calculation of vapor pressure

Wind Speed -             adjustment for measurement height

Cloudiness -             conversion from percent possible sunshine to cloud
                         cover

Solar Radiation -        graphical estimation of clear sky solar radiation

                         computer program to calculate estimated clear sky
                         solar radiation

                         diurnal distribution of clear sky solar radiation

                                     293

-------
The paper also includes a computer program to compute the equilibrium
temperature as a function of the meteorological variables above.

ACKNOWLEDGEMENTS

     Although I hope this paper is a useful collection of information, I
freely confess that few of the ideas presented are mine originally.  I
gratefully acknowledge the instructions and ideas of my former colleagues
Patrick J. Ryan, Martin S. Leonard, Fred H. Wend and Frederick A. Locher at
Bechtel and Donald R.F. Harleman, E. Eric Adams and Keith D. Stolzenbach at
MIT.  My thanks to Margaret Barnett, Linda Blacksmith, Rose Rondeau,
Michelle King and Janet Mahoney for preparing the text, tables and figures.

                                  REFERENCES

ASHRAE (American Society of Heating, Refrigerating and Air Conditioning
     Engineers) 1981.  ASHRAE Handbook: 1981 Fundamentals.  ASHRAE, Atlanta,
     6A.

Barnwell, T. 1982.  Personal communication.  U.S. Environmental Protection
     Agency, Center for Water Quality Modeling, Athens, GA.

Brock, T.D. 1981.  Calculating Solar Radiation for Ecological Studies.
     Ecological Modelling. 14:1/2, pp. 1-19.  November 1981.

Brunt, D. 1932.  Notes on Radiation in the Atmosphere.  Quarterly Journal
     of The Roval Meteorological Society. 58. pp. 389-418.

Edinger, J.E., D.K. Brady and J.C. Geyer 1974.  Heat Exchange and Transport
     in the Environment.  Report No. 14, Research Project RP-49.  Electric
     Power Research Institute, Palo Alto, CA.

Hamon, R.W., L.L. Weiss and W.T. Wilson 1954.  Insolation as an Empirical
     Function of Daily Sunshine Duration.  Monthly Weather Review. 82.:6, pp.
     141-146.  June 1954.

Harbeck, G.E. 1952.  The Lake Hefner Water Loss Investigation.  Circular 229,
     U.S. Geological Survey.

Hatfield, J.L., R.J. Reginato and S.B. Idso 1983.  Comparison of Long-Wave
     Radiation Calculation Methods Over the United States.  Water Resources
     Research. 19.: 1, pp. 285-288.  February 1983.

Helfrich, K.R., E.E. Adams, A.L. Godbey and D.R.F. Harleman 1982.
     Evaluation of Models for Predicting Evaporative Water Loss in Cooling
     Impoundments.  Report CS-2325, Research Project 1260-17.  Electric
     Power Research Institute, Palo Alto, CA.  March 1982.

Jirka, G.H., D.N. Brocard, K.A. Hurley Octavio, M. Watanabe and D.R.F.
     Harleman 1977.  Analysis of Cooling Effectiveness and Transient
     Long-Term Simulations of a Cooling Lake with application to the North
     Anna Power Station.  Report No. 232.  Ralph M. Parsons Laboratory,
     Department of Civil Engineering, Massachusetts Institute of Technology,
     Cambridge, MA.  December 1977.
                                   294

-------
List, R.J. 1971.  Smithsonian Meteorological Tables.  Sixth Revised Edition.
     Smithsonian Institution Press, Washington, D.C.

Locher, F.A. 1981.  Personal Communication.  Bechtel Civil and Minerals
     Corporation, San Francisco, CA.

Meyer, A.F. 1942.  Evaporation from Lakes and Reservoirs.  Minnesota
     Resources Commission, St. Paul, MN.  June 1942.

National Oceanic and Atmospheric Administration 1977.  Climatic Atlas of
     the United States.  National Climatic Center, Asheville, NC.

Rimsha, V.A. and R.V. Donchenko 1957.  The Investigation of Heat Loss from
     Free Water Surfaces in Wintertime (in Russian).  Leningrad
     Gosudarstvennyi CidroloKicheskii. 64.

Rosener, L.A., P.R. Giguere and D.E. Evenson 1977a.  User's Manual for
     the Stream Quality Model QUAL-II.  United States Environmental
     Protection Agency, Center for Water Quality Modeling, Athens, GA.

Rosener, L.A., P.R. Giguere and D.E. Evenson 1977b.  Computer Program
     Documentation for the Stream Quality Model QUAL-II.  United States
     Environmental Protection Agency, Center for Water Quality Modeling,
     Athens, GA.

Ryan, P.J. and D.R.F. Harleman 1973.  An Analytical and Experimental Study
     of Transient Cooling Pond Behavior.  Report No. 161.  Ralph M. Parsons
     Laboratory, Department of Civil Engineering, Massachusetts Institute of
     Technology, Cambridge, MA.  January 1973.

Swinbank, W.C. 1963.  Long-wave Radiation from Clear Skies.  Quarterly
     Journal of the Royal Meteorological Society. 89. pp. 339-348.

Thackston, E.L. 1974.  Effect of Geographical Location on Performance of
     Recirculating Cooling Ponds.  Report No. 660/2-74-085.  U.S.
     Environmental Protection Agency.  November 1974.

Throne, R.F. 1951.  How to Predict Cooling Lake Action.  Power. 95.
     pp. 86-89.  September 1951.

TVA (Tennessee Valley Authority) 1972.  Heat and Mass Transfer Between a
     Water Surface and the Atmosphere.  Water Resources Research Laboratory
     Report No. 14.  Tennessee Valley Authority, Division of Water Control
     Planning, Engineering Laboratory, Norris, TN.  April 1972.

Wells, S.A., E.E. Adams and D.R.F. Harleman 1982.  Calibration and
     Verification of the Cooling Lake Model for North Anna Power Station
     during the period July 1978-September 1981.  Report No. 272.  Ralph M.
     Parsons Laboratory, Department of Civil Engineering, Massachusetts
     Institute of Technology, Cambridge, MA.  March 1982.
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                                 ATTENDEES
Mr. Glen Adams
Room 302
City Hall
P. 0. Box 1607
Windsor, Ontario
N9A 6S1
Mr. Robert B. Ambrose
USEPA Athens Environ. Res. Lab,
Athens, GA   30613

Mr. Ahmed Amragy
City of Ohio
EPA
Columbus, OH   43221

Mr. Thomas Barnwell
USEPA Athens Environ. Res. Lab.
Athens, GA   30613

Mr. Bruce L. Bird
1546 Ellsworth Ave.
Crofton, MD   21113

Mr. Nick Brogge
Dept, of Chemical Engineering
Wayne State University
Detroit, MI   48202

Dr. Linfield C. Brown
NCASI
Tufts University
Medford, MA   02155

Mr. Shin Y. Chang, Ph.D.
Gibbs & Hill, Inc.
11 Penn Plaza
New York, NY   10001

Mr. Arun Deb
Roy F. Weston, Inc.
Weston Way
West Chester, PA   19380

Mr. Alaa El-Sharkawy
Dept. of Chemical Engineering
Wayne State University
Detroit, MI   48202
Mr. Thomas P. Finn
CE Maguire, inc.
1 Davol Square
Providence, RI   02903

Mr. Ward 0. Freeman
U.S. Department of the Interior
Champaign County Bank Plaza
102 E. Main Street
Urbana, IL   61801•

Mr. Gary A. Gagnon,  P.E.
Milwaukee Metropolitan Sewerage Dist,
735 North Water Street.
Milwaukee, WI   53202

Mr. Donald S. Graham
The University of Western Ontario
London, Canada   N6A 5C2

Mr. Ross Hall
USAEWES
P. 0. Box 631
Vicksburg, MS   39180

Ms. Sue Hanson-Walton
Camp Dresser & McKee, Inc.
7630 Little River Turnpike
Annandale, VA   22003

Professor Thomas Heidtke
Department of Civil Engineering
Wayne State University
Detroit, MI   48202

Mr. Richard M. Hobrla
Environmental Engineer
MI Dept. of Natural Resources
Box 30028
Lansing, MI   48909

Mr. Abdul Houssari
Dept. of Civil Engineering
Wayne State University
Detroit, MI   48202
                                   296

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Professor William James
Department of Civil Engineering
McMaster University
Hamilton, Ontario

Dr. Edward J. Kent, Ph.D.
Whitman & Howard, Inc.
45 William St.
Wellesley, MA   02181

Prof. Ralph H. Kummler, Chairman
Dept. of Chemical Engineering
Wayne State University
Detroit, MI  48202

Mr. Wu-Seng Lung
University of Virginia

Mr. D.B. Maunder, P,E.
Paul Thiel Associates Ltd.
700 Balmoral Drive
Bramalea, Ontario   L6T 1X2

Mr. Robert McCarthy
Dallas Water Utilities
1500 Marilla Room 5AS
Dallas, TX   75201

Ms. Lauren Meloche
Room 302
City Hall
P. O. Box 1607
Windsor, Ontario   N9A 6S1

Ms. Julie Osiecki
Dept. of Civil Engineering
Wayne State University
Detroit, MI   48202

Mr. James D. Parry, P.E.
CE Maguire, Inc.
1 Davol Square
Providence, RI   02903

Mr. Arthur R. Schmidt
U.S. Dept. of the Interior
Champaign County Bank Plaza
102 E. Main Street
Urbana, IL   61801
Mr. P. Shanahan
Environ. Res. and Technology
696 Virginia Rd.
Concord, VA   01742

Mr. Lalit K. Sinha
IL Environ. Protection Agency
2200 Churchill Road
Springfield, IL   62706

Mr. Daniel Skalsky
Ohio EPA
361 E. Broad St.
Columbus, OH   43221

Mr. Jerry Snyder
Roy F. weston. Inc.
Weston Way
West Chester, PA   19380

Prof. David Stevenson, Visiting Prof,
Department of Civil Engineering
McMaster University
Hamilton, Ontario
          and
Department of Civil Engineering
University of Witwaterstrand
1 Jan Smuts Avenue
Johannesburg, 2001 South Africa

Mr. Michael p. Sullivan
Dept. of Environmental Programs
Metropolitan Washington Council
   of Governments
1875 Eye Street, NW
Washington, DC   20006

Mr. Anis Uddin
Department of Civil Engineering
Wayne State University
Detroit, Ml   48202

Mr. Stan Udhiri, Chief
Natural Resources Division
The Maryland-National Capital Park
   and Planning Commission
14741 Governor Oden Bowie Drive
Upper Marlboro, MD    20772
                                  297

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Ms. Nancy U. Schultz, p.E.
CH2M Hill, Inc.
P. O. Box 2090
Milwaukee, WI   53201

Mr. Ray Whittemore
NCASI
Tufts University
Anderson Hall
Medford, MA   02155

Mr. Paul Yau
Room 302
City Hall
P. 0. Box 1607
Windsor, Ontario   N9A 6S1

Mr. Novak Zdenek
Ministry of theEnvironment,  Ontario
135 St. Clair West
Toronto, Canada   M4V 1P5

Mr. G. Zukovs
Canviro Consultants Ltd.
178 Louisa Street
Kitenner, Ontario   N2H 5M5
                                  298

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