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.
-------
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
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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
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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
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N
1 O
oZ
NORFOLK, VIRIGINIA
VICINITY MAP
FIGURE 1
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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
-------
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
-------
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
-------
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
-------
[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.
-------
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
-------
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
-------
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
-------
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
-------
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
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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-
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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
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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
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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
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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)
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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.
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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
-------
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
-------
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
-------
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
-------
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*)
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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
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Source Modeling," in Environmental Impact of Nonpoint Source Pollution,
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from Watersheds," in Environmental Impact of Nonpoint Source Pollution,
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600/9=77-023, EPA, Athens, GA., 1977
144
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10. Davis, M.J., M.K. S-yder, and J.W. Nebgen, "River Basin Validation of
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057b, EPA, Athens, GA, 1982.
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16. Foster, G.R., "Soil Erosion Modeling: Special Considerations for Non-
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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
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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
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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
-------
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
-------
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
-------
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
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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
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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
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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
-------
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
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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
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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
-------
Figure 3
-N-
WATERSHED MAP
WESTERN BRANCH
185
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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
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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
-------
ro
rt
X
\
z
I
3-
h-
H
VI
Z
UJ
h-
2
H
IS
IHh
12
II
10
^
3
7
6
5
.
•
3
2
1
d
TEST3 (Dt) l«l§2/^/2l
5 MIN HYETOGRHPH
TOTflL RfllNFflLL (MM) = 2-H-OI
•
!
1
I
1
P
b
>
•
b
tt
M
•
1
.
Z
Ul
u
1 ifc
O
a
Z
UJ
1 i
17
TIME (HOURS)
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
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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
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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,
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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'
-------
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
-------
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
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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
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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
-------
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
-------
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
-------
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
-------
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
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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
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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
-------
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
or>
00
16-
14-
o
oo
•a
ai
-------
ro
cr\
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)
-------
ro
-j
o
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
CVJ
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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ro
o
CM
16-
14-
12-
10-
9-
0)
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
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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
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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
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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
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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
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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
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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).
-------
250
200
a
X
£
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X
CM
i
e
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«
9
a.
w
•o
150
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
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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
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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
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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
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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
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(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
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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
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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
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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.
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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
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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
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295
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