vvEPA
United States
Environmental Protection
Agency
Office of Research and
Development
Washington, DC 20460
EPA/600/3-87K139
January 1988
WASP4, A
Hydrodynamic and
Water Quality Model
Model Theory, User's
Manual, and
Programmer's Guide
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EPA/600/3-87/039
January 1988
WASP4, A HYDRODYNAMIC AND WATER QUALITY MODEL--
MODEL THEORY, USER'S MANUAL, AND PROGRAMMER'S GUIDE
by
Robert B. Ambrose, Jr., P.E.
Tim A. Wool1
John P. Connolly, Ph.D.2
Robert W. Schanz3
Environmental Research Laboratory
Athens, Georgia 30613
Computer Sciences Corporation
Athens, Georgia 30613
^Manhattan College
Bronx, NY 10471
o
^Woodward-Clyde Consultants
Walnut Creek, CA 94596-3564
ENVIRONMENTAL RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
ATHENS, GEORGIA 30613
Printed on Recycled Paper
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DISCLAIMER
The information in this document has been funded wholly or in part by
the United States Environmental Protection Agency. It has been subject to
the Agency's peer and administrative review, and it has been approved for.
publication as an EPA document. Mention of trade names or commercial
products,does not constitute endorsement or recommendation for use by,the
U.S. Environmental Protection Agency.
ii
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FOREWORD
As environmental controls become more costly to implement and the penal-
ties of judgment errors become more severe, environmental quality management
requires more efficient management tools based on greater knowledge of the
environmental phenomena to be managed. As part of this Laboratory's research
on-the occurrence, movement, transformation, impact, and cdntrol': of*1 environ-
mental contaminants, the Assessment Branch develops state-of-the-art mathema-
tical models for use in water quality evaluation and management.
The Water Quality Analysis Program (WASP) was developed in 1981 by
Dominic Di Toro, James Fitzpatrick, and Robert Thomann of Hydroscience, Inc.
(presently Hydroqual, Inc.). Because of its unique flexibility, the model
has been widely used throughout the United States to predict water quality
responses to natural and man-made pollution. As part of the mandate of the
USEPA Center for Exposure Assessment Modeling in Athens, GA to develop, main-
tain and distribute water quality models, WASP version 4 (WASP4) has been
developed. WASP version 4 is a variable complexity modeling system for simu-
lating the movement of water and the movement and interaction of both conven-
tional and toxic pollutants within the water. Appropriate application of the
model will provide valuable information on which to base various pollution
management decisions.
This framework is designed to supercede WASTOX and TOXIWASP by incorpo-
rating and expanding components of each. The transport structure and steady-
state solution scheme of WASTOX have been incorporated in version 4 and a
toxic chemical kinetic package has been developed that contains elements of
WASTOX, TOXIWASP and EXAMS II. The scope of our work included the develop-
ment of the toxic chemical kinetic package and the incorporation of the
WASTOX steady-state solution into WASP4.
Rosemarie C. Russo, Ph.D.
Director
Environmental Research Laboratory
Athens, Georgia
111
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ABSTRACT
The Water Quality Analysis Simulation Program Version 4 (WASP4) is a
dynamic compartment modeling system that can be used to analyze a variety of
water quality problems in a diverse set of water bodies. WASP4 simulates
the transport and transformation of conventional and toxic pollutants in
the water column and benthos of ponds, streams, lakes, reservoirs, rivers,
estuaries, and coastal waters. The ¥ASP4 modeling system covers four major
subjects: hydrodynamics, conservative mass transport, eutrophication-
dissolved oxygen kinetics, and toxic chemical-sediment dynamics. This
manual contains three main parts: Model Theory, User's Manual, and Pro-
grammer's Guide.
The WASP4 modeling system consists of two stand-alone computer
programs, DYNHYD4 and WASP4, that can be run in conjunction or separately.
The hydrodynamic program, DYNHYD4, simulates the movement of water and
the water quality program simulates the movement and interaction of
pollutants within the water. The latter program is supplied with two
kinetic sub-models to simulate two of the major classes of water quality
problems: conventional pollution (dissolved oxygen, biochemical oxygen
demand, nutrients and eutrophication) and toxic pollution (organic
chemicals, heavy metals, and sediment). The substitution of either sub-
model constitutes the models EUTR04 and TOXI4, respectively.
This report covers the period January 1, 1985 to September 30, 1987,
and work was completed as of September 30, 1987.
iv
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CONTENTS
Disclaimer ii
Foreword . . iii
Abstract iv
Figures viii
Tables xi
Acknowledgments , xv
Preface xvi
1. WASP4 Model Theory. . . 1
1.1 Overview of the WASP4 Modeling System . ... 1
1.2 The HydrodjTiamics Model 2
Overview of DYNHYD4. . . . 2
The Hydrodynamic Equations 2
The Model Network 13
Implementation of the Equations . . 16
The Model Parameters 18
Application of the Model 25
1. 3 The Basic Water Quality Model 26
Overview of WASP4 26
The General Mass Balance Equation 27
The Model Network 29
Transport 33
Summary of Model Equations 48
The Model Parameters 50
Application of the Model 56
1.4 The Eutrophication Model 57
Overview of EUTR04 57
Phytoplankton Kinetics 59
Stoichiometry and Uptake Kinetics 72
The Phosphorus Cycle 73
The Nitrogen Cycle 78
The Dissolved Oxygen Balance 82
Sediment-Water Interactions 86
Variable Complexity Levels 95
v
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CONTENTS (Continued)
1.5 The Toxic Chemical Model 100
Overview of TOXI4 100
lonization 103
Equilibrium Sorption 105
Kinetic Transformation 109
Hydrolysis Ill
Photolysis 114
Oxidation 120
Bacterial Degradation 121
Volatilization 125
Extra Reaction 130
Heavy Metals 132
Variable Complexity Levels 134
Summary of Data Requirements 141
2. WASP4 User's Manual 146
2.1 Overview 146
2.2 The Hydrodynamics Model 147
Introdouction 147
DYNHYD4 Data Group Tables 157
DYNHYD4 Output 166
2.3 The Basic Water Quality Model 167
Introduction 167
WASP4 Data Group Descriptions 168
WASP4 Data Group Tables 188
WASP4 Output 197
2.4 The Eutrophication Model 198
Introduction 198
EUTR04 Data Group Descriptions 198
EUTR04 Output 211
2.5 The Toxic Chemical Model 213
Introduction 213
TOXI4 Data Group Descriptions 214
TOXI4 Output 237
3. WASP4 Programmer' s Guide 238
3.1 Overview 238
3.2 The Hydrodynamic Model 238
vi
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CONTENTS (Continued)
Hardware and Software Requirements. 238
Installation and Implementation.. . 239
Description of Computer Program 239
DYNHYD4 Input/Output Units .,,. 240
3.3 The Basic Water Quality Model 245
Hardware and Software Requirements 245
Installation and Implementation 246
Description of Computer Program. 246
References 265
Appendices
Appendix A - Symbols for Section 1.2.... 272
Appendix B - Symbols for Section 1.3 274
Appendix C - Symbols for Section 1.4 278
Appendix D - Symbols for Section 1.5 285
Appendix E - Derivation of Finite Difference Equations 293
vii
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FIGURES
Number ' . , Page
1.1.1 The Basic WASP4 System •. 3
1.2.1 Gravitational Acceleration. . 5
1.2.2 Frictional Acceleration 6
1.2.3 Wind Acceleration (Magnitude) 7
1.2.4 Wind Stress (Direction) 9
1.2.5 Wind Stress 10
1.2.6 Wind Stress Vector Analysis 11
1.2.7 Wind Stress Effects 12
1.2.8 Equation of Continuity 13
1.2.9 Model Network 14
1.2.10 Representation of the Model Network 15
1.2.11 Definition Sketch for Junctions 19
1.2.12 Definition Sketch for Channels 21
1.2.13 Inflow Time Function , 23
1.2.14 Definition Sketch of Downstream Boundary 24
1.3.1 Coordinate System for Mass Balance Equation 28
1.3.2 Model Segmentation 29
1.3.3 Spatial Scales Used in Lake Ontario Analysis 30
1.3.4 Frequency Distribution of Observed and Calculated Values
of a Quality Variable 31
Vlll
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FIGURES (Continued)
Number
1.3.5 Sediment Transport Regimes (Graft, 1971) 42
',,,.: , . ' • .- ',:. . iW '.i/triKo •!.' - ,
1.3.6 WASP4 Sediment Burial (Variable Volume Option) , 45
1.3.7 WASP4 Sediment Erosion (Variable Volume Option) 47
1.4.1 EUTR04 State Variable Interactions 58
1.4.2 Phytoplankton Kinetics 60
1.4.3 Effects of Nutrient Limitation on Growth Rate. . f 68
1.4.4 Phosphorus Cycle 74
: . '. • '.•.}-' \ • vt * " •
1.4.5 Nitrogen Cycle 79
1.4.6 Ammonia Preference Structure. t , 81
1.4.7 Oxygen Balance . 83
1.4.8 Sediment-Water Exchange , 88
1.5.1 Speciation, Transport, and Transformation Processes in
the Aquatic Environment . ..*... 100
1.5.2 Equilibium Speciation 101'
1.5.3 . Hydrolysis Reactions. , .;......... i. " 112
1.5.4 pH Dependence of Hydrolysis Rate. Constants ..........<.... 113
1.5.5 Photolysis Reactions. . . '.v 115
1.5.6 Microbial Transformations of Toxic Chemicals....;.....,....... 122
1.5.7 Volatilization Reaction. 126
1.5.8 Processes Influencing the Fate of Metals in Rivers .....; 133
1.5.9 Speciation of Metals in Aquatic Environment. 134
ix
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FIGURES (Continued)
Number Page
1.5.10 Potential Reaction Products in TOXI4 ,.....,.......<.:. 141
2.4.1 Constants for Level 1 205
2.4.2 Constants for Level 2 205
2.4.3 Constants for Level 3 , 206
2.4.4 Constants for Level 4 206
2.4.5 Constants for Level 5 207
2.4.6 Additional Constants for Level 6 207
3.2.1 DYNHYD4 Flow Chart 240
3.2.2 Summary File Description 244
3.3.2 Eutrophication Subroutine Structure 256
3.3.3 Toxic Chemical Subroutine Structure 260
El Definition Sketch for Finite Difference Equation 294
x
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. TABLES
Number
1.3.1
1.3.2
1.3.3
1.4.1
1.4.2
1.4.3
1.4.4
1.4.5
1.4.6
1.4.7
1.4.8
1.4.9
1.4.10
1.5.1
1.5.2
1.5.3
1.5.4
1.5.5
1.5.6
Comparison of Hydraulic Exponents
Stoke 's Settling Velocities at 20 °G , .
rt
Values of Numerical Dispersion in m /sec
Calculated Solar Radiant Energy Flux to a Horizontal
Surface Under a Clear Sky
Carbon to Chlorophyll a Ratio
Phytoplankton Net Growth Equation
Phosphorus -to -Carbon and Nitrogen- to -Carbon Ratios
Phosphorus Reaction Terms
Nitrogen Reaction Terms
CBOD and DO Reaction Rates
Sediment Layer Nitrogen Reaction Terms
Benthic Layer BOD and DO Reaction Rates
Benthic Layer Phosphorus Reaction Terms
Concentration Related Symbols Used in Mathematical
Equations
TOXI4 lonization Date
TOXI4 Sorption Data
TOXI4 General Kinetic Data
TOXI4 Hydrolysis Data
Wavelength Intervals and Specific Light Extinction
Coefficients Used in the Photolysis Calculation
Page
35
41
53
64
66
70
73
75
80
87
91
93
94
103
105
109
111
114
117
xi
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TABLES (Continued)
Number Page
1.5.7 TOXI4 Photolysis Data 119
1.5.8 TOXI4 Oxidation Data 121
1.5.10 TOXI4 Bacterial Degradation Data 123
1.5.11 Size of Typical Bacterial Populations in Natural Waters 125
1.5.12 TOXI4 Volatilization Data 131
1.5.13 Speciation of Priority Metals Between Dissolved and
Adsorbed Phases as a Function of Suspended Solids
Concentrations in Streams 135
1.5.14 Environmental Properties Affecting Interphase Transport
and Transformation Processes 143
1.5.15 Chemical Properties Affecting Interphase Transport and
Transformation Processes 144
1.5.16 Time Variable Environmental Forcing Functions 145
2.2.1 Cross Reference for DYNHYD4 Input Variables 157
2.2.2 DYNHYD4 Display Variables 166
2.2.3 Cross References for WASP4 Input Variables 197
2.4.1 EUTR04 Systems and Complexity Levels 199
2.4.2 Cross References for EUTR04 Input Variables 210
2.4.3 EUTR04 Kinetic Display Variables 211
2.5.1 Summary of TOXI4 System 213
2.5.2 TOXI4 Parameters 215
2.5.3 Constants for Simple TOXI4 Reactions 218
2.5.4 General Chemical Constants 219
xii
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TABLES (Continued)
Number
2.5.
2.5,
2.5.
2.5.
2.5,
6 lonization Constants
6 Sorption Constants for Total or Neutral Chemical.
7 Location of Ionic Sorption Constants
8 Volatilization Constants
9 Second Order Biodegradation Constants for Total or Neutral
Chemical
2.5.10 Location of Ionic biodegradation Constants.
2.5.11 Second Order Alkaline Hydrolysis Constants for Total
or Neutral Chemical . .
2.5.12 Location of Ionic Alkaline Hydrolysis Constants.....
2.5.13 Second Order Neutral Hydrolysis Constants for Total
or Neutral Chemical
2.5.14 Location of Ionic Neutral Hydrolysis Constants
2.5.15 Second Order Acid Hydrolysis Constants for Total or
Neutral Chemical
2.5.16 Location of Ionic Acid Hydrolysis Constants
2.5
17 Second Order Oxidation Constants for Total or
Neutral Chemical
2.5,
2.5,
2.5,
2.5.
18 Location of Ionic Oxidation Constants
19 TOXI4 Photolysis Constants
20 Global Constants for TOXI4 Photolysis Option 1.
21 Location of Ionic Photolysis Constants
219
220
221
222
222
223
223
224
224
225
225
226
226
227
228
229
230
xiii
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TABLES (Continued)
Number Page
2.5.22 Extra Second Order Reaction Constants for Total or
Neutral Chemical 231
2.5.23 Location of Ionic Extra Reaction Constants 231
2.5.24 Yield Constants for Chemical 1 Reactions 232
2.5.25 Yield Constants for Chemical 2 Reactions 233
2.5.26 Yield Constants for Chemical 3 Reactions 234
2.5.27 TOXI4 Kinetic Display Variables 237
3.3.1 Contents of "NFS.DAT" 250
xiv
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, ACKNOWLEDGMENTS
The WASP4 project was initiated with funding from the EPA Large Lakes
Research Station and the Great Lakes Program. Supplemental funding was pro-
vided through EPA's Ecological Risk Assessment research program. We grate-
fully acknowledge these programs and those individuals who helped initiate
the project, particularly Chieh Wu and William Richardson.
A manual of this type necessarily draws heavily upon the work of others.
Part 1--Theory--incorporates much material from WASPS (Robert Ambrose, •
Scarlett Vandergrift, and Timothy Wool), WASTOX (John Connolly and Richard P.
Winfield), and EXAMS-II (Lawrence Burns). WASPS incorporated much material
from DYNHYD2 (Steven Roesch and Leo Clark), WASP (Dominic DiToro, James
Fitzpatrick, and Robert Thomann), the Potomac Eutrophication Model (Robert
Thomann and James Fitzpatrick), and TOXIWASP (Robert Ambrose, Sam Hill, and
Lee Mulkey). In particular, text for Chapter 1.4 on the eutrophication model
was taken with some modification from the PEM documentation report. We grate-
fully acknowledge Dr. Thomann and Mr. Fitzpatrick for this work. Text for
the discharge coefficients in Chapter 1.3 was taken from the QUAL2E report.
We acknowledge Dr. Brown and Mr. Barnwell for this section.
Those who have written manuals know the burdens placed upon the secre-
taries and other support staff. Once again, Ms. Annie Smith has gracefully
and efficiently done the job. Help was also provided by Ms. Tawnya Robinson,
Ms. Jessica Edwards, and Mr. William Chung, who drafted the figures.
Finally, we'd like to thank the many users who participated in the
courses, shared professional experiences, and offered useful suggestions.
Stuart Stein and Roger Kilgore of GKY, Inc., contributed useful enhancements
to the DYNHYD4 code. The peer reviewers of this manual were thorough and
incisive.
xv
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PREFACE
The application of mathematical modeling techniques to water quality
problems has proved to be a powerful tool in water resource management. As
a diagnostic tool, it permits the abstraction of a highly complex real world.
Realizing that no one can ever detail all the physical phenomena that com-
prise our natural world, the modeler attempts to identify and include only
the phenomena, be they natural or man-made, that are relevant to the water
quality problem under consideration. As a predictive tool, mathematical
modeling permits the .forecasting and evaluation of the effects of changes in
the surrounding environment on water quality. Although engineering insight
and political and socioeconomic concerns play important roles in water re-
source management, some water quality problems are of such a complex nature
that the predictive capability of mathematical models provides the only real
means for screening the myriad number of management alternatives.
It is important for a computer program to be very general in nature if
it is to serve as the basis for the mathematical modeler. The program should
be flexible enough to provide the modeler with the mechanisms to describe and
provide input data for the geophysical morphology, the transport processes,
and the transformation processes that go into the framework of the model.
Transport processes, basically hydrodynamic in nature, include advection,
turbulent diffusion, and, when spatial averaging is included, dispersion.
Transformation (or reactive) processes, which are the sources and sinks that
act upon a particular water quality parameter, may be physical, chemical or
biological. Examples of these processes are the sedimentation and floccula-
tion of organics, the assimilative capacity of a water body to receive an
acid waste discharge, and the predator-prey relationship of zooplankton-
phytoplankton.
Numerous frameworks are available for modeling toxic chemicals in surface
waters, ranging from simple steady-state analytical solutions that consider
only a single first-order decay rate to complex time-variable numerical
solutions that describe, in detail, the physical, chemical and biological
transfer and transformation processes affecting a chemical. Two frameworks
may be included in the later type; TOXIWASP (Ambrose et al., 1983) and WASTOX
(Connolly and Winfield, 1984). Both frameworks were developed from the
general water quality model, WASP (Di Toro et al., 1981). TOXIWASP was
developed within WASP and is part of WASP version 3 (Ambrose et al., 1986).
WASTOX is separate from the WASP framework and is essentially a revision of
the transport (flow and dispersion) structure of WASP to permit convenient
application to toxic chemicals. The descriptions of the transfer and
transformation processes included in both frameworks are modifications of
those included in EXAMS (Burns et al., 1982).
xvi
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The WASP4 modeling system was designed to provide the generality and
flexibility necessary for analyzing a variety of water quality problems
in a diverse set of water bodies. The particular components described in
this manual can be used for the hydrodynamics of large branching rivers,
reservoirs, and estuaries; the mass transport in ponds, streams, lakes,
reservoirs, rivers, estuaries, and coastal waters; and the kinetic inter-
actions of eutrophication-dissolved oxygen and sediment-toxic chemicals.
This manual contains three main sections that can be used independent-
ly by various members of a modeling team. The first section, WASP4 Model
Theory, documents the equations and assumptions underlying the WASP4 model
components. Some guidance on the use of these models is offered, along
with sample input data values, when appropriate. More general summaries,of
equations and data are provided in the "Rates Manual" (Bowie et al., 1985)
the "Screening Manual" (Mills et al., 1985), and the "Toxicant Rates Manual"
(Schnoor et al., 1987).
The second section, WASP4 User's Manual, documents the input data speci-
fications necessary to run the WASP4 models. Each data group is.described,
with input variable names, formats, and definitions. Convenient tabular
summaries of each data group are provided, followed by an alphabetical listing
of variables for quick reference.
The third section, WASP4 Programmer's Manual, documents, the computer
requirements necessary to support the WASP4 models. Hardware and software
specifications are given, followed by installation and implementation instruc-
tions and a description of command files. A description of the computer
programs themselves includes an overview of the system, the computer files,
COMMON blocks, subroutines, and overlay structures.
xvii
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SECTION 1
WASP4 MODEL THEORY
The ¥ater Quality Analysis Simulation Program--4 (WASP4), an enhancement
of the original WASP (Di Toro et al., 1983), helps users interpret and predict
water quality responses to natural phenomena and man-made pollution for var-
ious pollution management decisions. WASP4 is a,dynamic compartment modeling
program for aquatic systems, including both the water column and the underly-
ing benthos. The time-varying processes of advection, dispersion, point and
diffuse mass loading, and boundary exchange are represented in the basic
program.
Water quality processes are represented in special kinetic subroutines
that are either chosen from a library or written by the user. WASP is struc-
tured to permit easy substitution of kinetic subroutines into the overall
package to form problem-specific models. Versions of WASP have been used to
examine eutrophication and PCB pollution of the Great Lakes (Thomann, 1975;
Thomann et al., 1976; Thomann et al., 1979; Di Toro and Connolly, 1980),
eutrophication of the Potomac Estuary (Thomann and Fitzpatrick, 1982), kepone
pollution of the James River Estuary (O'Connor et al., 1983), volatile organ-
ic pollution of the Delaware Estuary (Ambrose, 1987), and heavy metal pollu-
tion of the Deep River, North Carolina (JRB, 1984). In addition to these,
numerous applications are listed in Di Toro et al., 1983.
The flexibility afforded by the Water Quality Analysis Simulation Pro-
gram is unique. WASP4 permits the modeler to structure one, two, and three-
dimensional models; allows the specification of time-variable exchange coeffi-
cients , advective flows, waste loads and water quality boundary conditions;
and permits tailored structuring of the kinetic processes, all within the
larger modeling framework without having to write or rewrite large sections
of computer code. Although WASP's multidimensionality and time-variable
input capabilities are strong points, it is probably the ease with which one
may develop new kinetic or reactive structures that is WASP's main strength.
WASP's generality, however, requires an additional measure of judgment and
insight on the part of the modeler. The kinetic and transport structures are
not "hard wired" in WASP (i.e., the equations are not "fixed" and "buried" in
the code). Therefore, the burden is on the modeler (perhaps together with a
programmer) to write the applicable kinetic equations (or use those already
implemented) for a given problem context.
1.1 OVERVIEW OF THE WASP4 MODELING SYSTEM
The WASP4 system consists of two stand-alone computer programs, DYNHYD4
and WASP4, that can be run in conjunction or separately (Figure 1.1.1). The
hydrodynamics program, DYNHYD4, simulates the movement of water while the
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water quality program, WASP4, simulates the movement and interaction of
pollutants within the water. The latter program is supplied with two kinetic
sub-models to simulate two of the major classes of water quality problems:
conventional pollution (involving dissolved oxygen, biochemical oxygen demand,
nutrients and eutrophication) and toxic pollution (involving organic chemi-
cals, metals, and sediment). The linkage of either sub-model with the WASP4
program gives the models EUTR04 and TOXI4, respectively. This is illustrated
in Figure 1.1.1 with blocks to be substituted into the incomplete WASP4 model.
The tracer block is a dummy sub-model for substances with no kinetic interac-
tions .
The basic principle of both the hydrodynamics and water-quality program
is the conservation of mass. The water volume and water-quality constituent
masses being studied are tracked and accounted for over time and space using
a. series of mass balancing equations. The hydrodynamics program also con-
serves momentum, or energy, throughout time and space.
In conjunction with TOXI4, which calculates toxicant concentrations in
space and time, the user may predict accumulation in the food chain with the
associated Food Chain Model (Connolly and Thomann, 1985). This computer pro-
gram has been modified to read the appropriate concentrations from disk
files created by TOXI4, and can be considered a part of the WASP4 system.
The theory and operational considerations may be found in Connolly and
Thomann (1985). Linkage with the pharmacokinetics-based FGETS model (Barber
et al., 1987; Suarez et al., 1986), which calculates food and gill exchange
of toxic substances, is also being planned.
1.2 THE HYDRODYNAMICS MODEL
Overview of DYNHYD4
The WASP4 hydrodynamics model DYNHYD4 is an enhancement of the Potomac
Estuary hydrodynamic model DYNHYD2 (Roesch et al., 1979), which was a com-
ponent of the Dynamic Estuary Model (Feigner and Harris, 1970). DYNHYD4
solves the one-dimensional equations of continuity and momentum for a
branching or channel-junction (link-node), computational network. Driven
by variable upstream flows and downstream heads, simulations typically
proceed at 1- to 5-minute intervals. The resulting unsteady hydro-
dynamics are averaged over larger time intervals and stored for later use
by the water-quality program.
The Hydrodynamic Equations
The hydrodynamic model solves one-dimensional equations describing the
propagation of a long wave through a shallow water system while conserving
both momentum (energy) and volume (mass). The equation of motion, based on
the conservation of momentum, predicts water velocities and flows. The
equation of continuity, based on the conservation of volume, predicts water
heights (heads) and volumes. This approach assumes that flow is predominant-
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INPUT
DATA
MODEL
OUTPUT
DATA
TOXIC ORGANICS
EUTROPHICATION
Figure 1.1.1. The basic WASP4 system.
ly one-dimensional, that Coriolis and other accelerations normal to the
direction of flow are negligible, that channels can be adequately represented
by a constant top width with a variable hydraulic depth (i.e., "rectangular"),
that the wave length is significantly greater than the depth, and that bottom
slopes are moderate. Although no strict criteria are available for the latter
two assumptions, most natural flow conditions in large rivers and estuaries
would be acceptable. Dam-break situations could not be simulated with DYNHYD4,
nor could small mountain streams.
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Equation of Motion
The equation of motion is given by:
au au
+ a + a +
1.2.1
where:
at
au
at
ax
au
U
3x
_
x
t
U
A
the local inertia term, or the velocity rate of change
with respect to time, m/sec
the Bernoulli acceleration, or the rate of momentum
change by mass transfer; also defined as the convective
inertia term from Newton's second law, m/sec
gravitational acceleration, m/sec
o
frictional acceleration, m/sec
r
wind stress acceleration along axis of channel, m/sec''
distance along axis of channel, m
time, sec
velocity along the axis of channel, m/sec
longitudinal axis
Gravitational acceleration is driven by the slope of the water surface.
Referring to Figure 1.2.1, the acceleration along the longitudinal axis is
where:
ax - - g sin S 1.2.2
o
g - acceleration of gravity -=9.81 m/sec
S - water surface slope, m/m.
Because the value of S is small, sin S can be replaced by S. Expressing S
as the change of water surface elevation with longitudinal distance gives:
3H
- g
1.2.3
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where:
H = water surface elevation, or head (height above an arbitrary
datum) , m
GRAVITY
Acceleration of Gravity = g
a oi **
g
Figure 1.2.1. Gravitational acceleration.
The frictional acceleration term can be expressed using the Manning
equation for steady uniform flow:
u
R2/3 aR 1/2
n 3x
1.2.4
where:
R
hydraulic radius (approximately equal to the depth for
wide channels), m
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n — Manning roughness coefficient (usually between
0.01 and 0.10), sec/m1/3
£H — the energy gradient, m/m
Referring to Figure 1.2.2, gravitational acceleration balances frictional
resistance for steady flow conditions, such that:
3H
g
ax
1.2.5
FRICTIONAL RESISTANCE
For Steady Uniform Flow
Manning .
Equation '
2/3
n
Figure 1.2.2. Frictional acceleration.
Unfortunately, tidally influenced estuaries rarely experience truly steady
flow. Over short time intervals, however, flow may be considered steady and
uniform. .Consequently, the energy gradient from equation 1.2.4 can be substi-
tuted into 1.2.5 to give:
-------
g
U
1.2.6
where U2 has been replaced by U times the absolute value of U so friction
will always oppose the direction of flow.
Referring to Figure 1.2.3, one sees that the magnitude of the wind acce-
leration term can be derived from the shear stress equation at the air-water
boundary:
'w
WIND STRESS
A. Magnitude
1.2.7
/ Wind \
•*• W vSpeed'
10 Meters
• w
pa W
' "s
aw=Fw/(Vw.yow)
w ~ w* "s
°W = -R-
Cd =0.0026 '
p /p =1.165 X10'3
ra/rw
Figure 1.2.3. Wind acceleration magnitude.
7
-------
where:
rw — the boundary shear stress, kg/m-sec
Cjj — the drag coefficient (assumed to retain constant value of
0.0026), unitless
o
pa - the density of air, kg/m
W — the wind speed (relative to the moving water surface) measured
at a height of 10 meters, m/sec
The force exerted on the water surface, A. , is:
w
rw As
Substituting equation 1.2.7 gives:
w
1.2.8
1.2.9
This force causes a volume of water Vw to accelerate in the wind direction:
1.2.10
V,
w
The hydraulic radius, R, is the channel cross sectional area divided by the
wetted perimeter. In natural channels where the width is much larger than
the depth, the wetted perimeter is almost equal to the width. Over a channel
length, then, the average hydraulic radius is approximately equal to the
volume of water divided by the surface area:
R
Vw/As
1.2.11
o
where: Ag — surface area, m
V,
w
o
water volume, m
Substituting equations 1.2.9 and 1.2.11 into 1.2.10 gives the following
equation for the wind acceleration term:
1.2.12
where: pw - density of water, kg/nr
1.165 x 10'3
-------
Referring to Figure 1.2.4, the component of acceleration along the chan-
nel axis is:
Cd
—
R
cos
1.2.13
where f = the angle between the channel direction and the wind direction
(relative to the moving water surface)
B. Direction
W
Magnitude = W
Direction = a
N
Channel
Channel Direction = Q
Wind Direction =• a
Relative Angle
cos
Figure 1.2.4. Wind stress direction.
Both the water and wind have velocity components that contain both magnitude
and direction. If the water is moving with a velocity U, then the wind
vector W experienced at the water surface is given by the following (see
Figure 1.2.5):
-------
- u
1.2.14
WOBS
Wind
Magnitude = WOBS
Direction = <
Channel
Magnitude2 u
Direction = 8
N
where:
W =
Effective
Wind
Vector
Magnitude = W
Direction = a
-6
OBS
W'
Figure 1.2.5. Wind stress.
the wind vector observed at a stationary location, 10 meters
above the water surface (magnitude = W, direction
obs
U — the current vector (magnitude •=» U, direction = 0) , m/sec
Therefore, W is the relative wind vector with magnitude W, and the
effective wind angle relative to the channel axis is
* - a - 6
1.2.15
10
-------
Given observations of Wobs, U, , and 6, the magnitude and direction of W
can be calculated using vector analysis (Figure 1.2.6):
W2 - U2 + Wobs2 - 2 U Wobs cos(6 -
a
tan
|Wobs sin * - U sin 6|
'1 | _ |
lwobs cos 0 - U cos 6|
1.2.16
1.2.17
WIND STRESS
From Vector Analysis
Vector
U
X-dir
Usin 6
Y - dlr
Ucos 6
WOBS WOBS sin <*> WOBSCOS 4>
W WOBS sin - cos*
Figure 1.2.6. Wind stress vector analysis.
Wind 'acceleration can either enhance or oppose stream flow, depending
on the relative direction of the wind $. For wind blowing normal to the
channel axis, cos * = 0, and there is no acceleration along the axis. For
wind blowing along the axis in a positive direction, cos
-------
Wind Stress Effect
Wind and Stream
Directions
cos^/
Figure 1.2.7. Wind stress effects.
Effect
vMul
w—
u—
W-*
*-u
— w
u-»
*-w
~-u
90°
0°
180°
180°
0°
0
1
-1
-1
1
None
Enhanced
Acceleration
Opposed
Opposed
Enhanced
Equation of Continuity
The equation of continuity is given by:
dA 3Q
at dx
where:
A - cross-sectional area, m^ •
O
Q - flow, m /sec
For rectangular channels of constant width B (refer to Figure 1.2.8):
3H 1 aq
3t B 3x
12
1.2.18
1.2.19
-------
RECTANGULAR CHANNELS
(Q +80)
8H 1 3Q
dt ="B dX
Rate of
Water Surface
Elevation Change
Rate of
Volume
Change
Figure 1.2.8. Equation of continuity.
where:
B = width, m
H - water surface elevation (head), m
9H = rate of water surface elevational change with respect to
9t time, m/sec
1 8Q = rate of water volume change with respect to distance
B dx per unit width, m/sec
The Model Network
Equations 1.2.1 and 1.2.19 form the basis of the hydrodynamic model
DYNHYD4. Their solution gives velocities (U) and heads (H) throughout the
water body over the duration of the simulation. Because closed-form analyti-
cal solutions are unavailable, the solution of equations 1.2.1 and 1.2.19
requires numerical integration on a computational network, where values of U
and H are calculated at discrete points in space and time.
13
-------
A flexible, computationally efficient type of network has been developed
for these equations (Feigner and Harris, 1970). The "link-node" network
solves the equations of motion and continuity at alternating grid points.
At each time step, the equation of motion is solved at the links, giving
velocities for mass transport calculations, and the equation of continuity is
solved at the nodes, giving heads for pollutant concentration calculations
(Figure 1.2.9).
MODEL NETWORK
LINKS (CHANNELS) - CONVEY WATER
NODES (JUNCTIONS) - STORE WATER
AT EACH TIME STEP:
EQUATION
OF
MOTION
EQUATION
OF
CONTINUITY
LINKS
NODES
w
w
VELOCITY
FLOWS
HEADS
VOLUMES
fc
h
MASS
TRANSPORT
POLLUTANT
CONCENTRATION
Figure 1.2.9. Model network.
A physical interpretation of this computational network can be developed
by picturing the links as channels conveying water and the nodes as junctions
storing water (Figure 1.2.10). Each junction is a volumetric unit that acts
as a receptacle for the water transported through its connecting channels.
Taken together, the junctions account for all the water volume in the river
or estuary. Parameters influencing the storage of water are defined within
this junction network. Each channel is an idealized rectangular conveyor
that transports water between two junctions, whose midpoints are at each end.
Taken together, the channels account for all the water movement in the river
or estuary. Parameters influencing the motion of water are defined within
this channel network. The link-node computational network, then, can be
viewed as the overlapping of two closely related physical networks of chan-
nels and junctions.
Junctions are equivalent to segments in the water quality model, whereas
channels correspond to segment interfaces. Channel flows are used to calcu-
late mass transport between segments in the water quality model. Junction.
volumes are used to calculate pollutant concentrations within water quality
segments.
14
-------
c
o
(1.
HI
o
I
Z
^•x
t>
o
I)
o
JC
l_
o
O
o
£
o
'f;
c:
S
O
S
g
•H
§
CO
0)
M
ft
OJ
o
.,—I
•
-------
Link-node networks can treat fairly complex branching flow patterns and
irregular shorelines with acceptable accuracy for many studies. They cannot
handle stratified water bodies, small streams, or rivers with a large bottom
slope. Link-node networks can be set up for wide, shallow water bodies if
primary flow directions are well defined. Results of these simulations
should be considered descriptive only.
Implementation of the Equations
To apply differential equations 1.2.1 and 1.2.19 to a link-node computa-
tional network, they must first be written in a finite difference form. The
equation of motion becomes:
u - u
At
All,-
- - U4
- §
Ax,
R<
3d Pi
cos
1-2.20
R
where: U? — the velocity in channel i at time t, m/sec
Ax^— the channel length, m
At — the time step, sec
i — channel or link number
AUj= velocity gradient in channel i with respect to
Ax? distance, sec"
AH,- water surface gradient in channel i with respect to
Ax£ distance, m/m
All values on the right hand side of equation 1.2.20 are referenced to the
previous time step (t-At).
The water surface gradient, AH^/Ax^, can be computed from the junction
heads at either end of the channel. The velocity gradient, however, cannot
be computed directly from upstream and downstream channel velocities because
of possible branching in the network. If branching does occur, there would
be several upstream and downstream channels, and any computed velocity gra-
dient would be ambiguous. An expression for the velocity gradient within a
channel can be derived by applying the continuity equation 1.2.18 to the
channel and substituting U A for Q:
3A
at
3Q
3A
- U
- A
au
a~x
16
1.2.21
-------
Rearranging terms:
3U 1 3A U 8 A
ax A at A ax
1.2.22
Writing this in finite difference form and substituting B R for A and
B AH for 3A gives the following expression for the velocity gradient:
ATI,-
AH,-
At
1.2.23
Ri
The term AH^/At is computed as the average water surface elevational
change between the junctions at each end of channel i during time step t.
Substituting equation 1.2.23 into 1.2.20 and rearranging gives the explicit
finite difference equation of motion applied to each channel i:
Uf =
+ At [
\ AHi
- g) _
/ AX:L
COS
R
1.2.24
i A
Writing the equation of continuity (1.2.19) in finite difference form
gives:
HJ -
At
BJ AXJ
1.2.25
where: j = junction or node number
The numerator AQj is given by the summation of all flows entering and
leaving the junction. The denominator B^ Ax^ can be expressed directly
as the surface area AJ of the junction. Substituting these identities
into equation 1.2.25 and rearranging gives the explicit finite difference
equation of continuity applied to each junction j:
Qij
Ht
Hi
- At
^
J
1.2:26
At this point, one equation for each channel and each junction in the,
computational network exists. Given input parameters describing the network
configuration and geometry, initial values for channel velocities and junc-
tion heads, boundary conditions for downstream heads, and forcing functions
17
-------
for freshwater inflow and wind stress, equations 1.2.24 and 1.2.26 are solved
using a modified Runge-Kutta procedure. The solution proceeds in eight
steps, which are repeated throughout the simulation:
1) For the middle of the next time interval (i.e., for time t + At/2),
the mean velocity for each channel is predicted using the channel
velocities and cross-sectional areas and the junction heads at the
beginning of the current time interval.
2) For t + At/2, the flow in each channel is computed using the
velocity obtained in step (1) and the cross-sectional area at the
beginning of the current interval.
3) At t 4- At/2, the head at each junction is computed using the
flows derived in step (2).
4) At t + At/2, the cross-sectional area of each channel is computed
using the heads computed in step (3) .
5) The mean velocity for each channel is predicted for the full time
step (t + At) using the velocities, cross-sectional areas, and
junction heads computed for t + At/2 in steps (1), (3), and (4).
6) The flow in each channel for t + At is computed using the
velocity for the full time step (computed in step 5) and the
cross-sectional area computed for t + At/2 in step (4).
7) The head at each junction after t + At is computed using the full
step flow computed in step (6).
8) The cross-sectional area of each channel after a full time step is
computed using the full step heads from step (7).
9) Steps (1) through (8) are repeated for the specified number of time
intervals.
The Model Parameters
This section summarizes the input parameters that must be specified in
order to solve the equations of motion and continuity. Other parameters
calculated by the model also are discussed.
Junction Parameters
The input parameters associated with junctions are initial surface
elevation (head), surface area, and bottom elevation. Volumes and mean
depths are calculated internally. A definition sketch is given in Figure
1.2.11.
18
-------
JUNCTION
SURFACE AREA
HEAD
BOTTOM
ELEVATION
(AVERAGE)
Figure 1.2.11. Definition sketch for junctions.
Surface elevation or head, m--Junction heads represent the mean eleva-
tion of the water surface above or below an arbitrary horizontal datum. The
datum is usually the mean local sea level. If initial surface elevations
are not input, they will be calculated from bottom elevation and depth.
19
-------
Surface area, m^-- Except when branching or looping occurs (i.e., when
more than two channels enter a junction), the surface area of a junction is
equated to one-half of the sura of the surface areas of the two channels
entering the junction. When branching or looping does occur, the junction
surface areas can be determined by laying out a polygon network using the
Thiessen Polygon method, as in Figure 1.2.11. Since the polygons are normally
irregular, a planimeter must be used to obtain the surface areas.
Bottom elevation. m--The mean elevation of the junction bottom above
or below the datum is defined as the bottom elevation. If initial surface
elevations are specified, bottom elevations will be calculated internally
by subtracting the mean depth from the mean head.
Volume, m^-- Initial junction volumes are computed internally by multi-
plying the junction surface area by the mean depth of the channels (weighted
by their cross -sectional area) entering the junction. Junction volumes are
updated throughout the simulation by adding the product of the surface area
and the change in surface elevation to the initial volume.
Channel Parameters
The input parameters associated with channels are length, width, hydrau-
lic radius or depth, channel orientation, initial velocity, and Manning's
roughness coefficient. A definition sketch is given in Figure 1.2.12.
Length. m--The channel length is the distance between the midpoints
of the two junctions it connects. Channels must be rectangular and should
be oriented so as to minimize the depth variation as well as reflect the
location and position of the actual prototype channels. The channel length
is generally dependent on a computational stability criteria given by:
±Ui) At 1.2.27
where :
L£ — length of channel i, m
y. = mean depth of channel i, m
Uj — velocity in channel i, m/sec
At = computational time step
g •= acceleration of gravity
Width, m- -There is no apparent limit on the width of a channel. If a
channel, is too wide in relation to its length, however, the mean velocity
predicted may mask important velocity patterns occurring on a more local
scale. For well defined channels, the network channel widths are equated to
the average bank to bank width.
20
-------
VELOCITY
PROFILE
^K t
j ) WIDTH
LX i
^c i
TOP
VIEW
1
1
~ ^ AVERAGE
1 j VELOCITY
1 1
VELOCITY
PROFILE
1 T7
! ) AVERAGE
y DEPTH
^^ I '
HYDRAULIC
RADIUS
r
SIDE
VIEW
CROSS ,
SECTIONAL '
AREA i
•WIDTH---
AVERAGE
DEPTH
I PLAN
I VIEW
N
~®yD
&•
CHANNEL
ORIENTATION
Figure 1.2.12. Definition sketch for channels.
21
-------
o
Cross-sectional area, m --The cross-sectional area of a channel is
equal to the product of the channel width and depth. Depth, however, is a
channel parameter that must be defined with respect to junction head or water
surface elevation (since both vary similarly with time). Initial values of •
width and depth based on the initial junction heads and the initial cross-
sectional areas are computed internally. As the junction heads vary, the
channel cross-sectional areas are adjusted accordingly.
Roughness coefficients, sec/m / --Channels are assigned "typical" Manning
Roughness coefficients. The value of this coefficient should usually lie
between 0.01 and 0.08. Because this parameter cannot be measured, it serves
as a. "knob" for the' calibration of the model.
Velocity. m/sec--An initial estimate of the mean channel velocity is
required. Although any value may be assigned, the computational time re-
quired for convergence to an accurate solution will depend on how close the
initial estimate is to the true value. Convergence is usually rather quick.
Hydraulic radius, m--Previous applications of DYNHYD have used channels
whose widths are greater- than ten times the channel depth. Consequently, the
hydraulic radius is usually assumed to be equal to the mean channel depth.
Channel orientation, degrees--The channel orientation is the direction
of the channel axis measured from true north.. The axis is assumed to point
from lower junction number to higher junction number, which by convention, is
the direction of positive flow.
Inflow/Outflow Parameters
Inflows and outflows can be specified as constant or time variable.
Inflows are represented by negative flows; outflows are represented by posi-
tive flows. For each time-variable inflow, a piecewise linear function of
flow versus time is specified, as in Figure 1.2.13. If the simulation ex-
tends beyond the last specified flow, the flow assumes a constant inflow
equal to the last specified flow.
Downstream Boundary Parameters
The downstream boundaries can be defined by either specifying outflows
or surface elevations (tidal function). Outflows are handled as negative
inflows, as discussed above. Surface elevations at each downstream boundary
can be specified by an average tidal function or by a variable tidal func-
tion. A definition sketch is provided in Figure 1.2.14.
22
-------
Flow
Time
Piecewise Linear Function
Day
1
2
3
4
5
6
7
Time
HourrMin
09 30
10 00
13 00
12 30
12 00
18 30
09 30
Flow 1
o , '
m /sec j
30. |
40. |
•80. |
70. |
75. |
20. , |
30 I
Figure 1.2.13. Inflow time function.
For some simulations, the average tidal variability will produce accurate
predictions of tidal transport. Tidal heights (referenced to the model datum)
are specified at equally spaced intervals throughout the average tidal cycle.
Normally, 30-minute intervals will suffice. These data can be obtained from
tidal stage recorders located at or near the model boundary. If no recorders
are available, the predictions presented in the U.S. Coast and Geodetic
Survey Tide Tables can be used. , '
DYNHYD4 reduces the height versus time data to the following function
using the subroutine REGAN.
where:
A± + A2sin(wt)4A3sin(2tot)+A4sin(3wt)
+ A5cos(wt)+Agcos(2wt)+Aycos(3wt)
tidal elevation above or below the model datum, m
regression coefficients, m
23
1.2.28
-------
u
o
tr
LU
CO
CO
o
-C
uT
co
C\J
CJ — O V
H- •*•
O
,&
h-UJ.
CVJ
i
0
3
O
o
13
CJ
4-1
0)
A5
CD
O
•H
4-)
•H
-S
2
O
H
c
'E
•H
En
O
e y
H UJ
^ ro o
24
-------
w
27r/tidal period, hr"1
t = time, hr
If the regression coefficients
of the height versus time data.
specified in the above order.
throughout the simulation.
A^ are known, they can be specified instead
All seven of the coefficients must be
The average tidal function is repeated
If data are available, variable tidal patterns may be simulated by
specifying the high and low tidal heights versus time for multiple tidal cy-
cles. In this case, the subroutine RUNKUT will interpolate with a sinusoidal
curve between the data points. If simulation extends beyond the specified
tidal cycles, the sequence will repeat. To insure proper repetition, an odd
number of data points must be specified with the last data point equal to the
first.
¥ind Parameters
The input parameters associated with wind acceleration are wind speed,
wind direction, channel orientation, and channel hydraulic radius. The last
two were discussed as channel parameters. A definition sketch was provided
in Figure 1.2.11.
Wind speed (m/sec) and direction (degrees from true north) are measured
at a point 10 meters above the water surface. This wind is to be representa-
tive for the entire water body. Values of wind speed and direction can vary
with time. Piecewise linear functions of wind speed and direction versus
time are specified (similar to Figure 1.2.13 for flow). If the simulation ex-
tends beyond the last specified wind, the piecewise linear functions are
repeated. '
Application of the Model
A great deal of flexibility is allowed in laying out the network of
interconnected channels and junctions that represent a system, but there are
several guidelines for making the best representation. First, both hydraulic
and quality factors should be considered when selecting boundary conditions.
Ideally, the downstream boundary should extend to a flow gage, a dam, or the
ocean. The upstream boundary should extend to or beyond the limits of any
backwater or tidal effects on the inflowing streams. Such a network elimi-
nates problems associated with dynamic boundary conditions, such as changing
salinity or other quality conditions, which could be present if an inland
point were chosen for the seaward boundary. Other considerations influencing
boundary locations and the size of network elements include the location of
specific points where quality predictions are required, the location of
existing or planned sampling stations (and the availability of data for
verification), the degree of network detail desired, and the computer time
available for solution.
25
-------
In most applications of DYNHYD4, Manning's, roughness coefficient (n)
will be the primary calibration parameter. The value of n can be highly
variable, depending on such factors as bed roughness, vegetation, channel
irregularities in cross-section or shape, obstructions, and depth. Values
of n can potentially vary from less than 0.01 to greater than 0.08. For the
larger rivers, reservoirs, and estuaries to which DYNHYD4 can be applied,
however, values will usually fall between 0,01 and 0.04. Deeper, straighter
reaches have lower roughness coefficients. In general, the value of n in-
creases upstream as channels become more constricted and shallow.
When calibrating DYNHYD4, changing the! value of n in one channel affects
both upstream and downstream channels. Increasing n causes more energy to be
dissipated in that channel. As a result, the height of a tidal or flood wave
will decrease and the time of travel through the channel will increase.
Lowering n decreases the resistance to flow, resulting in a higher tidal or
flood wave and a shorter time of travel.
If the hydrodynamic results generated by a DYNHYD4 simulation are to be
stored for use by WASP4, then both the networks and the time steps must be
compatible (though not identical). Every DYNHYD4 junction must coincide
exactly with a WASP4 segment. WASP4 may have additional segments not repre-
sented by junctions. For example, WASP4 benthic segments will have no cor-
responding junctions. Junction numbering need not correspond to segment
numbering. Junction to segment mapping is specified in the WASP4 input data
set. The WASP4 time step must be an even multiple of the DYNHYD4 time step.
The ratio of time steps must be specified in the DYNHYD4 input data set as
parameter NODYN. Typical ratios are between 6 and 30. Segmentation and time
steps for WASP4 are discussed in the next section. DYNHYD4 averages each
channel flow over NODYN hydrodynamic time steps, and stores this average
value for use at the corresponding WASP4 segment interface. DYNHYD4 stores
each junction volume at the end of NODYN time steps for use at the correspond-
ing WASP4 segment. This averaging and storage process continues for the
entire hydrodynamic simulation. WASP4 will use these flows and volumes,
repeating the sequence if the water quality simulation is longer than the
hydrodynamic simulation.
1.3 THE BASIC WATER QUALITY MODEL
WASP4 is a dynamic compartment model that can be used to analyze a
variety of water quality problems in such diverse water bodies as ponds,
streams, lakes, reservoirs, rivers, estuaries, and coastal waters. This
section presents the basic water quality model used to simulate dissolved,
conservative chemicals, such as chlorides or dye tracer.
Overview of WASP4
The equations solved by WASP4 are based on the key principle of the
conservation of mass. This principle requires that the mass of each water
quality constituent being investigated must be accounted for in one way or
26
-------
another. WASP4 traces each water quality constituent from the point of
spatial and temporal input to its final point of export, conserving mass in
space and time.
To perform these mass balance computations, the user must supply WASP4
with input data defining seven important characteristics:
simulation and output control
model segmentation
advective and dispersive transport
boundary concentrations
point and diffuse source waste loads
kinetic parameters, constants, and time functions
initial concentrations
These input data, together with the general WASP4 mass balance equations and
the specific chemical kinetics equations, uniquely define a special set of
water quality equations. These are numerically integrated by WASP4 as the
simulation proceeds in time. At user-specified print intervals, WASP4 saves
the values of all display variables for subsequent retrieval by the post-
processor W4DSPLY. This program interactively produces tables of variables
specified by the user. The variables available are discussed in,the eutro-
fication and toxics section of the user manual.
The General Mass Balance Equation
A mass balance equation for dissolved constituents in a body of water
must account for all the material entering and leaving through direct and
diffuse loading; advective and dispersive transport; and physical, chemical,
and biological transformation. Consider the coordinate system shown in
Figure 1.3.1, where the x- and y-coordinates are in the horizontal plane, and
the z-coordinate is in the vertical plane. The mass balance equation around
an infinitesimally small fluid volume is:
ac a a
_ = - _ (ux o - _
at ax ay
K
1.3.1
27
-------
WATER QUALITY EQUATION
Figure 1.3.1. Coordinate system for mass balance equation.
where :
G
t
ux,uy,uz
B
K
concentration of the water quality constituent, mg/L (g/m )
time, days
longitudinal, lateral, and vertical advective velocities, m/day
longitudinal, lateral, and vertical diffusion coefficients,
m/day
o
direct and diffuse loading rate, g/m -day
boundary loading rate (including upstream, downstream, benthic,
and atmospheric), g/m -day
total kinetic transformation rate; positive is source, negative
is sink, g/m -day
By expanding the infinitesimally small control volumes into larger ad-
joining "segments," and by specifying proper transport, loading, and trans-
formation parameters, WASP implements a finite-difference form of equation
1.3.1.. For brevity and clarity, however, the derivation of the finite-
difference form of the mass balance equation will be for a one-dimensional
reach. Assuming vertical and lateral homogeneity, we can integrate equation
1.3.1 over y and z to obtain
28
-------
a a ac
(A C) = (-Ux A C + Ex A __) + A (SL + Sfi) + A SK
at ax ax
1.3.2
where:
cross-sectional area,
This equation represents the three major classes of water quality processes--
transport (term 1) , loading (term 2)., and transformation (term 3). The
finite-difference form is derived in Appendix E. The model network and the
major processes are discussed in the following sections.
The Model Network
The model network is a set of expanded control volumes, or "segments,"
that together represent the physical configuration of the water body. As
Figure 1.3.2 illustrates, the network may subdivide the water body laterally
and vertically as well as longitudinally. Benthic segments can be included
along with water column segments. If the water quality model is being linked
to the hydrodynaniic model, then water column segments must correspond to the
hydrodynamic junctions. Concentrations of water quality constituents are
calculated within each segment. Transport rates of water quality constituents
are calculated across the interface of adjoining segments.
A*. ,ft...., I^_^ "C "v• >..-^-^-sfVllI^F"""""~—"*%
Segment Types
1. Surface water
2. Subsurface water
3. Surface bed
4. Subsurface bed- BsisfB
Figure 1.3.2. Model segmentation.
29
-------
Segments in WASP may be one of four types, as specified by the input
variable ITYPE. A value of 1 indicates the epilimnion, 2 indicates hypo-
limnion layers, 3 indicates an upper benthic layer, and 4 indicates lower
benthic layers. The segment type plays an important role in bed sedimenta-
tion and in certain transformation processes. The user should be careful to
align segments properly. The segment immediately below each segment is spe-
cified by the input variable IBOTSG.
Segment volumes and the simulation time step are directly related. As
one increases or decreases, the other must do the same to insure stability
and numerical accuracy. Segment size can vary dramatically, as illustrated
in Figure 1.3.3. Characteristic sizes are dictated more by the spatial and
temporal scale of the problem being analyzed than by the characteristics of
the water body or the pollutant per se. For example, analyzing a problem
involving the upstream tidal migration of a pollutant into a water supply
might require a time .step of minutes to an hour. By contrast, analyzing a
problem involving the total residence time of that pollutant in the same
water body could allow a time step of hours to a day. In Figure 1.3.3, the
first network was used to study the general eutrophic status of Lake Ontario.
The second network was used to investigate the lake-wide spatial and seasonal
variations in eutrophication. The third network was used to predict changes
in near-shore eutrophication of Rochester Embayment resulting from specific
pollution control plans.
SPATIAL SCALES USED IN
LAKE ONTARIO ANALYSIS
MODEL
DESIGNATION
HORIZONTAL
NUMBER OF SCALE (Km*)
SEGMENTS EPILIMNION
SCUM ° SEGMENTS
LAKE 1
LAKE 3
13,OOO
67
200-1000
ROCHESTER ^
EMBAYMENT :%£
72
10-100
Figure 1.3.3.
analysis.
Spatial scales used in Lake Ontario
30
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As part of the problem definition, the user must determine how much of
the water quality frequency distribution must be predicted. For example, a
daily-average dissolved oxygen concentration of 5 mg/L would not sufficiently
protect fish if fluctuations result in concentrations less than 2 mg/L for
10% of the time. Predicting extreme concentration values is generally more
difficult than predicting average values. Figure 1.3.4 illustrates typical
frequency distributions predicted by three model time scales and a typical
distribution observed by rather thorough sampling as they would be plotted on
probability paper. The straight lines imply normal distributions. Reducing
the model time step (and consequently segment size) allows better simulation
of the frequency distribution. This increase in predictive ability, however,
also entails an increase in the resolution of the input data.
FREQUENCY DISTRIBUTION OF OBSERVED AND
CALCULATED VALUES OF A QUALITY VARIABLE
m
O
1
OBSERVED
TIME SCALE 2
TIME SCALE 1
STEADY-STATE
50 95
CUMULATIVE PROBABILITY
Figure 1.3.4. Frequency distribution of observed and calculated
values of a quality variable.
Once the nature of the problem has been determined, then the temporal
variability of the water body and input loadings must be considered. Gen-
erally, the model time step must be somewhat less than the period of varia-
tion of the important driving variables. In some cases, this restriction can
be relaxed by averaging the input over its period of variation. For example,
phytoplankton growth is driven by sunlight, which varies diurnally.- Most
eutrophication models, however, average the light input over a day, allowing
time steps on the order of a day.
31
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Care must be taken so that important non-linear interactions do not get
averaged out. When two or more important driving variables have a similar
period of variation, then averaging may not be possible. One example is the
seasonal variability of light, temperature, nutrient input, and transport in
lakes subject to eutrophication. Another example involves discontinuous
batch discharges. Such an input into a large lake might safely be averaged
over a. day or week, because large scale transport variations are relatively
infrequent. The same batch input into a tidal estuary cannot safely be
averaged, however, because of the semi-diurnal or diurnal tidal variations.
A third example is salinity intrusion in estuaries. Tidal variations in
flow, volume, and dispersion can interact so that accurate long-term predic-
tions require explicit simulation at time steps on the order of hours.
Once the temporal variability has been determined, then the spatial
variability of the water body must be considered. Generally, the important
spatial characteristics must be homogeneous within a segment. In some cases,
this restriction can be relaxed by judicious averaging over width, depth,
and/or length. For example, depth governs the impact of reaeration and sedi-
ment oxygen demand in a column of water. Nevertheless, averaging the depth
across a river would generally be acceptable in a conventional waste load
allocation, whereas averaging the depth across a lake would not generally be
acceptable. Other important spatial characteristics to consider (depending
upon the problem being analyzed) include temperature, light penetration,
velocity, pH, benthic characteristics or fluxes, and sediment concentrations.
The expected spatial variability of the water quality concentrations
also affects the segment sizes. The user must determine how much averaging
of the concentration gradients is acceptable. Because water quality condi-
tions change rapidly near a loading point and stabilize downstream,' studying
the effects on a beach a quarter-mile downstream of a discharge requires
smaller segments than studying the effects on a beach several miles away.
A final, general guideline may be helpful in obtaining accurate simula-
tions: water column volumes should be roughly the same. If flows vary signi-
ficantly downstream, then segment volumes should increase proportionately.
The user should first choose the proper segment volume and time step in the
critical reaches of the water body (Vc, Atc), then scale upstream and down-
stream segments accordingly:
Qi/Q
1.3.3
Of course, actual volumes specified must be adjusted to best represent the
actual spatial variability, as discussed above. This guideline will allow
larger time steps and result in greater numerical accuracy over the entire
model network, as explained in the section on "Simulation Parameters."
32
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Transport
Transport includes advection and dispersion of water quality constituents.
Advection and dispersion in WASP are each divided into six distinct types, or
"fields." The first transport field involves advective flow and dispersive
mixing in the water column. Advective flow carries water quality constituents
"downstream" with the water and accounts for instream dilution. Dispersion
causes further mixing and dilution between regions of high concentrations and
regions of low concentrations. The second transport field specifies the move-
ment of pore water in the sediment bed. Dissolved water quality constituents
are carried through the bed by pore water flow and are exchanged between the
bed and the water column by pore water diffusion. The third, fourth, and
fifth transport fields specify the transport of particulate pollutants by the
settling, resuspension, and sedimentation of solids. Water quality consti-
tuents sorbed onto solid particles are transported between the water column
and the sediment bed. The three solids fields can be defined by the user as
size fractions, such as sand, silt, and clay, or as inorganic, phytoplankton,
and organic solids. The sixth transport field represents evaporation or
precipitation from or to surface water segments.
Water Column Advection
Advective water column flows directly control the transport of dissolved
and particulate pollutants in many water bodies. In addition, changes in
velocity and depth resulting from variable flows can affect such kinetic
processes as reaeration, volatilization, and photolysis. An important early
step in any modeling study is to describe or simulate water column advection
properly. In WASP4, water column flow is input via transport field one in
Data Group D. Circulation patterns may be described (flow option 1) or
simulated by DYNHYD4 (flow options 2 or 3).
For flow option 1, WASP4 tracks each separate inflow specified by the
user from its point of origin through the model network. For each inflow,
the user must supply a continuity or unit flow response function and a time
function. The time function describes the inflow as it varies in time. The
continuity function describes the unit flow response as it varies throughout
the network. The actual flow between segments that results from the inflow
is the product of the time function and the continuity function.
If several inflow functions are specified, then the total flow between
segments is the sum of the individual flow functions. Segment volumes are
adjusted to maintain continuity. In this manner, the effect of several
tributaries, density currents, and wind-induced gyres can be described in a
simple manner. For unsteady flow in long networks, however, lag times may
become significant, and hydrodynamic simulations may be necessary to obtain
sufficient accuracy.
For flow options 2 or 3, WASP4 reads unsteady water column flows, ve-
locities , volumes, and depths from a formatted or unformatted file generated
by a previous DYNHYD4 simulation. The user must supply the mapping of DYNHYD4
junctions and WASP4 segments. There must be a WASP4 surface water segment
33
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equivalent to each DYNHYD4 junction. The numbers designating the WASP4
segments may be in a different order from the DYNHYD4 junctions. There may
be additional WASP4 segments (usually benthic) that are not represented by a
DYNHYD4 junction. If this flow option is chosen, the simulation time step
will be reset by the hydrodynamic file. The time steps read in Data Group A
will be ignored. Similarly, water column segment volumes will be read from
the hydrodynamic file. The user must nevertheless enter a time step and
volumes for each segment in the usual location.
A good description of segment geometry as a function of flow conditions
can be important in properly using WASP4 to simulate rivers. For flow options
2 and 3, velocity and depth are computed within BYHHYD4 (assuming rectangular
channels), and are read by WASP4. For flow option 1, a set of user-specified
hydraulic discharge coefficients from Data Group C defines the relationship
between velocity, depth, and stream flow. This method, described below,
follows the implementation in QUAL2E (Brown and Barnwell, 1987).
Discharge coefficients giving depth and velocity from stream flow are
based on empirical observations of the velocity-depth-stream flow relation-
ship (Leopold and Maddox, 1953). The equations relate velocity, channel
width, and depth to streamflow through power functions:
V - a Q
D - c Q
B - e Q
1.3.4
1.3.5
1.3.6
where: D is average depth, m
B is average width, m
a, b, c, d, e, and f are empirical coefficients or exponents
Given that area is a function of average width (B) and average depth (D),
A - D B 1.3.7
it is clear from continuity that:
Q - V A
- V D B
- (aQb) (cQd) (eQf)
-(ace)Qb+d+f
and, therefore, the following relationships hold:
ace-1 1.3.8
34
-------
b + d + f = 1
1.3.9
WASP4 only requires specification of the relationships for velocity
(Equation 1.3.4) and depth (Equation 1.3.5); the coefficients for Equation
1.3.6 are implicitly specified by Equations 1.3.8 and. 1.3.9.
These options can be put into perspective by noting that, for a given
specific channel cross-section, the coefficients (a, c, e) and exponents (b,
d, f) can be derived from Mannings equation. For example, if a channel of
rectangular cross-section is assumed, then width (B) is not a function of
streamflow (Q), the exponent (f) is zero (0.00) and the coefficient (e) is
the width of the rectangular channel (B). By noting that hydraulic radius
(R) is approximately equal to depth (D) for wide streams and that A = D B,
the discharge coefficients for rectangular cross sections can be shown to ,be
0.4 for velocity and 0.6 for width.
Leopold et al. (1964) have noted that stream channels in humid regions
tend towards a rectangular cross-section because cohesive soils promote steep
side slopes whereas noncohesive soils encourage shallow sloped, almost
undefined banks.
Table 1.3.1 compares hydraulic exponents for a rectangular channel with
data reported by Leopold et al. (1964). Note that the average velocity
exponent is relatively constant for all channel cross sections. The major
variation occurs as a decrease in the depth exponent and concomitant increase
in the width, exponent as channel cross-sections change from the steep side
slopes characteristic of cohesive soils to the shallow slopes of arid regions
with noncohesive soils.
TABLE 1.3.1. COMPARISON OF HYDRAULIC EXPONENTS
Channel
Cross-Section
Exponent for
Velocity (b)
Exponent for
Depth (d)
Exponent for
Width (f)
Rectangular
Average of 158
US Gaging Stations
Average of 10 Gaging
Stations on Rhine River
Ephemeral Streams in
Semiarid US
0.40
0.43
0.43
0.34
0.60
0.45
0.41
0.36
0.00
0.12
0.13
0.29
35
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For bodies of water such as ponds, lakes, and reservoirs, velocity and
depth may not be a function of flow. For these cases, both the velocity and
depth exponents (b and d) can be chosen to be zero (0.00). Because Q to the
zero power is equal to one (1.0), the coefficients a and c must be the velocity
and depth, i.e.,
IF b - 0.0 THEN a - V, and
IF d - 0.0 THEN c = D.
When the depth exponent is zero, WASP4 will adjust segment depths with segment
volumes assuming rectangular sides.
For site-specific river or stream simulations, hydraulic coefficients
and exponents must be estimated. Brown and Barnwell (1987) recommended
estimating the exponents (b and d) and then calibrating the coefficients (a
and c) to observed velocity and depth. The exponents may be chosen based on
observations of channel shape noted in a reconnaissance survey. If cross
Sections are largely rectangular with vertical banks, the first set of expo-
nents shown in Figure 1.3.5 should be useful. If channels have steep banks
typical of areas with cohesive soils, then the second set of exponents is
appropriate. If the stream is in an arid region with typically noncohesive
soils and shallow sloping banks, then the last set of exponents is recom-
mended.
The key property of the channel that should be noted in a reconnaissance
survey is the condition of the bank slopes or the extent to which width would
increase with increasing streamflow. Clearly the bank slopes and material in
contact with the streamflow at the flow rate(s) of interest are the main
characteristics to note in a reconnaissance. Table 1.3.1 gives general
guidance but it should be noted that values are derived for bankful flows.
Even in streams with vertical banks, the low flows may be in contact with a
sand bed having shallow sloped, almost nonexistent banks more representative
of ephemeral streams in semiarid areas.
Water Column Dispersion
Dispersive water column exchanges significantly influence the transport
of dissolved and particulate pollutants in such water bodies as lakes,
reservoirs, and estuaries. Even in rivers, longitudinal dispersion can be
the most important process diluting peak concentrations that may result from
unsteady loads or spills. Natural or artificial tracers such as dye, salin-
ity, or even heat are often used to calibrate dispersion coefficients for a
model network.
In WASP4, water column dispersion is input via transport field one
in Data Group B. Several groups of exchanges may be defined by the user.
For each group, the user must supply a time function giving dispersion
coefficient values (in m /sec) as they vary in time. For each exchange in
the group, the user must supply an interfacial area, a characteristic mixing
length, and the segments between which the exchange takes place. The
36
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characteristic mixing length is typically the distance between segment mid-
points. The interfacial area is the area normal to the characteristic mixing
length shared by the exchanging segments (cross-sectional area for horizontal
exchanges, or surface area for vertical exchanges). The actual dispersive
exchange between segments i and j at time t is given by:
A,-.
- C±)
where:
1.3.10
Mi
mass of chemical in segment i, g
total chemical concentration, mg/L
dispersion coefficient time function for exchange
"ij", m2/day
interfacial area shared by segments i and j , m^
characteristic mixing length between segments i and
j , m
Pore Water Advection
Pore water flows into or out of the bed can significantly influence
benthic pollutant concentrations. Depending on the direction of these flows
and the source of the pollutants, pore water advection may be a source or
sink of pollutants for the overlying water column.
If benthic segments are included in the- model network, the user may
specify advective transport of dissolved chemicals in the pore water. In
WASP4, pore water flows are input via transport field two. Pore water advec-
tion transports water and dissolved chemical; sediment and particulate chemi-
cal are not transported. The mass derivative of chemical due to pore water
flow from segment j to segment i is given by:
— " QlJ fDj Cj/
ot
f C/ni
1.3.11
where:
mass of chemical in segment i, g -
total chemical concentration in segment j, mg/L (g/m3)
37
-------
n.5 — porosity of segment j ,
fj)4 — dissolved fraction of chemical in segments i and j
Q£.= — pore water flow rate from j to i, m /day
Dissolved fractions fp may be input by the user in Data Group J or computed
from sorption kinetics.
WASP4 tracks each separate pore water inflow through the benthic network.
For each inflow (or outflow), the user must supply a continuity function and
a time function. The actual flow through benthic segments that results from
each inflow is a product of the time function and the continuity function.
If a flow originates in or empties into a surface water segment, then a
corresponding surface, water flow function must be described in flow field 1
that matches the pore water function.
Pore Water Diffusion
Diffusive pore water exchanges can significantly influence benthic
pollutant concentrations, particularly for relatively soluble chemicals and
water bodies with little sediment loading. Depending on the dissolved
concentration gradient, pore water diffusion may be a source or sink of
pollutants for the overlying water column.
If benthic segments are included in the model network, the user may
specify diffusive transport of dissolved chemicals in the pore water. In
WASP4, pore water diffusion is input via transport field two in Data Group B.
Several groups of exchanges may be defined by the user. For each group, the"
user must supply a time function giving dispersion coefficient values (in
m /sec) as they vary in time. For each exchange in the group, the user must
supply an interfacial area, a characteristic mixing length, and the segments
between which exchange takes place. The characteristic mixing length is
typically the distance between two benthic segment midpoints (multiplied
internally by the tortuosity, which is roughly the inverse of porosity). For
pore water exchange with a surface water segment, the characteristic mixing
length is usually taken to be the depth of the surficial benthic segment.
The interfacial area is the surficial area of the benthic segment (multiplied
internally by porosity). There may be several surficial benthic segments
underlying a water column segment, representing discrete benthic deposits (or
habitats). The concentration of chemical diffusing Is' the dissolved fraction
per unit pore water volume. The actual diffusive exchange between benthic
segments i and j at time t is given by:
an.
at
n,-
(fDj Cj/nj - fDi
1.3.12
38
-------
where:
Di'fDj
dissolved fraction of chemical in i and j
average porosity at interface "ij",
diffusion coefficient time function for exchange
»ij», m2/day
interfacial area shared by segments i and j , m^
characteristic mixing length between segments i
and j , m
Sediment Transport
Sediment transport is potentially a very important process influencing
chemical transport and fate. Many chemicals sorb strongly to sediment and
thus undergo settling, scour, and sedimentation. Sorption also affects a
chemical's transfer and transformation rates. Volatilization and base-
catalyzed hydrolysis, for example, are slowed by sorption. Both sediment
transport rates and concentrations must be estimated in most toxic chemical
studies.
In general, the stream transport capacity for suspended sediment is in
excess of its actual load, and the problem is one of estimating sediment
source loading--namely, watershed erosion. In areas of backwater behind dams
or in sluggish reaches, the stream transport capacity may drop enough to
allow net deposition. Strongly sorbed pollutants may build up significantly.
Because sediment transport can be complex, site-specific calibration of the
settling, scour, and sedimentation rates is usually necessary.
In WASP4, solids transport rates in the water column and the bed are
input via transport fields 3, 4, and 5 in Data Group D. These fields describe
the settling, deposition, scour, and sedimentation flows of three kinds of
solids. The transport of particulate chemicals follows the solids flows.
The user must specify the particulate fraction for each chemical and the
solids field that it follows.
Initial dissolved fractions and the solids field may be entered in Data
Group J. The toxic chemical model provides special constants to describe
sorption of chemical to all three solids.
Water Column Transport--Sediment and particulate chemicals in the water
column may settle to lower water segments and deposit to surficial bed seg-
ments. Settling, deposition, and scour rates in WASP4 are described by ve-
locities and surface areas in transport fields 3, 4, and 5. Particulate
transport velocities may vary both in time and in space, and are multiplied
by cross-sectional areas to obtain flow rates for solids and the particu-
late fractions of chemicals.
39
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Settling velocities should be set within the range of Stoke's velocities
corresponding to the suspended particle size distribution:
8.64 g
18
1.3.13
where:
V
&
s
Stokes velocity for particle with diameter dp and
density pp, m/day
2
acceleration of gravity — 981 cm/sec
o
p - absolute viscosity of water = 0.01 poise (g/cm -sec) at
20 °C
dp — particle diameter, mm
Values of Vs for a range of particle sizes and densities are provided in
Table 1.3.2.
Benthic Exchange--Benthic exchange of sediment and particulate chemicals
is driven by the net scour and deposition velocities:
WBs -
Si - WD
1.3.14
where:
W
'Bs
i
j
net sediment flux rate, g/day
o
sediment concentration, g/m
deposition velocity, m/day
scour velocity, m/day
9
benthic surface area, m
benthic segment
water segment
The deposition velocity can be calculated as the product of the Stokes
settling velocity and the probability of deposition:
wD-Vs«D 1.3.15
where :
O>T\ — probability of deposition upon contact with the bed.
40
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TABLE 1.3.2. STORE'S SETTLING VELOCITIES (IN M/DAY) AT 20 °C
Particle
Diameter, mm
1.8
Particle Density, g/cm3
2.0 2.5
2.7
Fine Sand
0.3
0.05
Silt
0.05
0.02
0.01
0.005
0.002
Clav
0.002
0.001
300 400
94 120
94 120
15 19
3.8 4.7
0.94 1.2
0.15 0.19
0.15 0.19
0.04 0.05
710
180
180
28
7.1
1.8
0.28
0.28
0.07
800
200
200
32
8.0
2.0
0.32
0.32
0.08
The probability of deposition depends upon the shear stress on the ben-
thic surface and the suspended sediment size and cohesiveness. Likewise, the
scour velocity depends upon the shear stress, the bed sediment size and cohe-
siveness, and the state of consolidation of surficial benthic deposits. Fig-
ure 1.3.5 is offered as initial guidance in specifying initial deposition and
scour velocities. For example, course silt of 0.05 mm diameter may settle at
100 to 200m/day, but should not deposit where mean stream velocity is above
0.5 cm/sec. Where mean velocity rises above 30 cm/sec, erosion is expected,
and nonzero scour velocities should be specified. For fine silt of 0.005 mm
diameter settling at 1 to 2 m/day, deposition is not expected, even under
quiescent conditions. Nonzero scour velocities should be specified where
mean velocity is above 2 m/sec. Site specific calibration is necessary to
refine the initial estimates.
41
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Relationship Between Stream Velocity,
Particle Size, and the Regimes of
Sediment, Erosion, Transport, and
Deposition
1000
CLAY
SILT
SAND
PARTICLE SIZE DIAMETER, mm
Figure 1.3.5. Sediment transport regimes (Graft, 1971)
Sediment Loading
Sediment loading derives primarily from watershed erosion and bank
erosion. These can be measured or estimated by several techniques, and in-
put into each segment as a point source load. For some problems, long term
average sediment loads can be calculated using the Universal Soil Loss Equa-
tion (Wischmeier and Smith, 1978). A useful treatment of this process is
given by Mill et al. (1985). This technique works poorly for short term or
inherently dynamic problems because much of the sediment loading occurs
during a few extreme storm or snow melt events. If available, suspended
sediment data at local gaging stations can be extrapolated to provide area-
wide loading estimates. Alternatively, daily runoff loads can be simulated
with a watershed model and read in directly from an appropriately formatted
nonpoint source loading file.
The Sediment Bed
The bed sediment plays an important role in the transport and fate of
water quality constituents. Sediment-sorbed pollutants may be buried in the
42
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bed by deposition and sedimentation, or they may be released to the water
column by scour. In WASP4, the movement of sediment in the bed is governed
by one of two options. In the first option, bed segment volumes remain
constant and sediment concentrations vary in response to deposition and
scour. No compaction or erosion of the segment volume is allowed to occur.
In the second option, the bed segment volume is compacted or eroded as sedi-
ment is deposited or scoured. Sediment concentration in the bed remains
constant. In both options chemical may be transported through the bed by
pore water flow and dispersion.
The Constant Bed Volume Option--The first bed option, referred to as the
constant volume option, allows the sediment concentration of the bed to change
according to the net flux of sediment. Bed segments are located in reference
to the rising or falling bed surface. The rate at which the bed rises or
falls is represented by a sedimentation velocity, input in flow fields 3, 4,
and 5 for each sediment size fraction. Sediment in the bed is added through .
deposition and lost through scour and sedimentation.
Assuming the depth of the bed remains constant and neglecting dispersive
mixing, the mass balance of sediment in a stationary upper bed is given by:
as.
di
at
WD Sj - (WR + ws)
1.3.16
where:
w.
Si
sedimentation velocity of the upper bed, m/day
sediment concentration in the upper bed, g/m
sediment concentration in the water, g/m^
depth of the upper, bed, m
For a lower bed layer,
O S T
1
at
ws si - wsl sl
1.3.17
where:
sediment concentration in the lower bed, g/nr
wsl = sedimentation velocity of the lower bed, m/day
d^ = depth of the lower bed, m
43
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In most applications the sediment concentration of the bed will be nearly
constant over time. In this case the mass derivative 8S/dt will be zero. The
resulting mass balance in the upper bed is:
wDSj - (WR + ws)
In the lower bed,
wssi - wsl sl
1.3.18
1.3.19
It should be noted that under the constant volume option WASP4 does not
require a balance of sediment fluxes into and out of a bed segment. The user
should, therefore, take care that deposition, scour, and sedimentation veloc-
ities reflect the intended mass flux of sediment in the bed.
The constant volume option also has a provision for a movable upper bed
layer. This layer is modeled by specifying a total advective flow rate (flow
field one) between upper bed segments. Thus, when a flow rate Q^j is speci-
fied from upper bed segment j to upper bed segment i, all of the sediment,
pore water, and chemical in j is transported to i. To maintain a mass balance
in segment i, a similar flow rate should be specified out of i. This option
allows for the lateral transport of sediment across the upper bed, and can be
used to represent bed load transport.
The Variable Bed Volume Option--The second bed volume option,, referred
to as the variable bed volume option, allows bed volumes to change in response
to deposition and scour. Two types of bed layers are assumed: an upper
uncompacted layer, and one or more lower compacted layers. When deposition
exceeds scour, the upper layer increases in volume as the surface of the bed
rises. After a period of time, the added volume of upper bed compresses and
becomes part of the lower bed. When scour exceeds deposition, the volume of
the upper layer decreases as the surface of the bed drops. When the upper
layer erodes completely, the next layer of bed is exposed to scour.
In locations where sediment deposition exceeds scour (Figure 1.3.6), bed
compaction is triggered by a sedimentation time step. This sedimentation
time step is input by the user and will generally be much larger than the
simulation time step. As sediment and sorbed chemical settle from the water
column, the top bed segment increases in volume, sediment mass, and chemical
mass. Sediment concentrations remain constant. The volume of the upper bed
continues to increase until the end of the sedimentation time step. At this
time, the volume of the upper bed that has been added by net deposition is
compressed to the density of the lower bed. Since the porosity of the uncom-
pressed bed is greater than the porosity of the compressed bed, pore water
and dissolved chemical are squeezed into the water column.
During compression, the lower bed segments rise to include the com-
pressed portion of the upper bed. The volumes and sediment concentrations of
these lower bed segments remain constant. A portion of the bottom bed segment
is buried out of the network, however, as bed segments rise in response to
sedimentation. Thus, chemical mass in the lower bed is added through com-
pression of the upper bed, and lost through sediment burial.
44
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to
V
i
tl
V
J
t2
V
*
t2+At
V
i
Segment
1
2
3
4
Time = 1 0
Depth Density Cone.
d, 1.0 C^O)
d2 Pz 0.0
d3 P3 0.0
d4 P4 C4 (0)
Time = 1 2
Depth Density Cone.
d,-d2(2) 1.0 ci<2>
p
dzCO+ds^ ^2 C2(2)
d3 f3 0.0
d4 (°4 C4(0)
Time = 1 2 + A t
Depth Density Cone.
dn-d3 1.0 ci(2)
da (°2 C2(2)
P
rt 10 i-* r*t\ 3
a3 r3 C2(2)p4
d4 (°4 ,,0.0
Figure 1.3.6. WASP4 sediment burial (variable volume option).
45
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After compression, the top bed segment returns to its original pre-
deposition volume. Sediment and chemical concentrations in the upper bed are
not changed by compaction. In the lower beds, segment volumes and sediment
concentrations are unchanged. Chemical mass from the compacted portion of
the bed Is added to the lower bed, and chemical mass in the bottom bed seg-
ment is buried out of the model network.
For locations where sediment scour exceeds deposition, ¥ASP responds as
in Figure 1.3.7. As sediment and sorbed chemical erode from the bed, the top
bed segment decreases in volume, depth, chemical mass, and sediment mass.
Its density remains constant. When the sediment mass in the top bed layer
equals zero, then segment renumbering is triggered. All the properties of
the remaining bed segments, including chemical concentration, remain un-
affected by renumbering. The new top bed segment, for example, has the same
depth, volume, sediment and chemical concentration as the old second bed
segment. A new bottom bed segment is created with the same physical proper-
ties as the other bed segments. Its chemical concentration, however, Is zero.
Renumbering and creation of a new bottom segment completes the WASP erosion
cycle (or time step).
As a consequence of the way the variable bed volume option treats
sedimentation, certain constraints are imposed on the bed segment properties
defined in the input data set. The density (or sediment concentration) of a
top bed segment must be less than or equal to the density of the lower bed
segments within a vertical stack. The volumes, depths, and densities of
lower bed segments should be significantly smaller than the top bed layer.
Since the compaction routine implicitly handles sedimentation, no sedimenta-
tion velocities to lower beds may be specified in the sediment transport
fields. Finally, the user must simulate sediment as a state variable in
order to use this option. Sediment is a state variable in the toxics pro-
gram, but not the eutrophication program.
Evaporation and Precipitation
For some water bodies, evaporation and precipitation play a significant
role in the overall water balance. Precipitation may be a low level source of
some pollutants. Evaporation concentrates pollutants in the body of water.
In WASP4, evaporation and precipitation are input via transport field six in
Data Group D. Different groups of segments having the same evaporation or
precipitation rates may be defined by the user. For each group, the user
must supply a time function giving evaporation or precipitation velocities
(in m/sec) as they vary in time. For each segment in the group, the user
must supply the surface area (in m^) and a segment number pair. For evapora-
tion, the pair is from "ISEG" to "0". For precipitation, the pair is from
"0" to "ISEG." ISEG must be the number of a surface water segment. The
actual precipitation input to segment i at time t is given by:
3M-!
Ai
1.3.20
46
-------
to
1
V
I
v
i
t2+At
V
I
Segment
1
2
3
4
Time = 1 0
Depth Density Cone.
d! 1.0 0.0
d2 l°2 C2 (0)
d3 |°3 C3(0)
d4 <°4 C4 (0)
Time = 1 2
Depth Density Cone.
d^d^O) 1.0 C,(2)
0 /°2 C2(0)
d3 P3 C3(0)
d4 f>4 C4(0)
Time = 1 2 + ^ t
Depth Density Cone.
d! +d2(0) 1.0 C/2)
d2 /°3 C3(2)
da P3 C4(2)
d4 ,o4 0.0
Figure 1.3.7. WASP s'ediment erosion (variable volume option)
47
-------
where:
Pi(t)
precipitation velocity time function for segment i,
m/day
A£ — surface area of segment i, m
Coi(*-) " concentration of pollutant in precipitation, mg/L
In addition, segment volumes are adjusted:
O V S
at
where:
1.3.21
evaporation velocity time function for segment i, m/day
Summary of Model Equations
The equations implemented by WASP4 account for the transport of dissolved
and particulate matter in the water column and benthos as summarized below:
At
L - S (-Qy) +
flow, precipitation, and evaporation
1.3.22
At
ij GIJ £Dj)
S (-Qij Cij) +S (
water column and pore water advection
+ S S (-w
i s
sij
fsj)
solids transport
+ S (Rjj A Cjj) + S
i i
water column and pore water dispersion
+ SWLj + 2 WNj +2 (QjQ CBj)
L J N J B J J
point, nonpoint, and boundary loads
+ SS (Vj Skcj)
k c,
kinetic transformations
1.3.23
48
-------
where:
J
i
s
L
N
B
k
c
V,
E«
AJ
Wsij
sj
segment index
adjacent segment index
solids transport field index
point source index
nonpoint source index
boundary source index
kinetic transformation index
chemical index
o ' v
volume of segment j , m
concentration of the water quality constituent in segment
j > g/m
time, day . /
evaporation rate from segment j, m/day
precipitation rate into segment j, m/day
surface area of segment j, m^
advective flow between segments i and j, defined as positive
when leaving segment j, and negative when entering, m3/day
pore water flow between segments i and j, defined as positive
when leaving segment j, and negative when entering j, m^/day
constituent concentration advected between i and j, g/m3
i/ Gj + (1 - i/) G£ when entering j
i/ Cj_ + (1 - i/) C.j when leaving j
numerical weighting factor (advection factor), 0-0.5
solids transport velocity between segments i and j, defined as
positive when leaving segment j, and negative when entering,
m/day
dissolved fraction of chemical in segment j
fraction of chemical sorbed to solid type "s" in segment j
49
-------
R-i
dispersive flow between segments i and j, m /day
Eij
Lcij
Lcij ^ .;; - -,
o
dispersion coefficient between segments i and j, m /day
p
cross-sectional area between segments i and j, m
characteristic mixing length between segments i and j, m
o • ;v..-
pore water diffusive exchange flow, m /day
QJO
CBj
skcj
Lcij tij
average tortuosity of segments i and j, mwater/m
o o
average porosity of segments i and j, m^ater/m
point source loads into segment j, g/day
nonpoint loads into segment j, g/day
Q
boundary inflows to segment j, m /day
o
boundary concentrations for segment j, g/m
kinetic transformation k for chemical c within segment j,
g/m3-day
Water column advection and dispersion parameters are specified for water
column segments, whereas pore water advection and diffusion parameters are
specified for benthic segments. Adjacent water column and benthic segments
may be joined by pore water advection and diffusion parameters, and by solids
transport parameters representing scour and deposition.
The Model Parameters ' •
This section summarizes the input parameters that must be specified in
order to solve the mass balance equation. '
Model Identification and Control Parameters
These parameters give the basic model identity. They include the number
of water quality constituents being simulated and the number of segments in
the network. Also included are titles describing the water body and the
simulation.
50
-------
This group of parameters controls the simulation and checks the stabi-
lity of the solution. Simulation parameters include the initial and final
times, integration time steps, the advection factor, maximum concentrations,
and a negative solution option.
Initial time, days--The time at the beginning of the simulation must be
specified in order to synchronize all the time functions. The day, hour, and
minute can be input.
Final time, days--The time at the end of the simulation must be speci-
fied in days (including decimal fraction).
Integration time step, days--A sequence of integration time steps (At)
must be specified, along with the time interval over which they apply. Given
specific network and transport parameters, time steps are constrained within
a specific range to maintain stability and minimize numerical dispersion, or
solution inaccuracies. To maintain stability at a segment, the advected,
dispersed, and transformed mass must be less than the resident mass:
(S Q Cj+ S R Cj+ S S
At <
1.3.24
Solving for At and applying the criterion over the entire network gives
the maximum stable step size:
V
At
max
- Min (.
j
1.3.25
SRi1 + S (S1k V
ik J
If reactions are linear, then the last term in the denominator reduces to
Kj Vj. Usually At is controlled by advective or dispersive flows.
Numerical dispersion is artificial mixing caused by the finite difference
approximation used for the derivatives. If the advection factor v «= 0, the
backward difference approximation of dc/dx is used in the advection term,;and
U L
num
1.3.26
where:
L
length of the segment
For the Euler scheme, the forward difference approximation of 5c/ 3t is used,
and
U2 At
E.
num
1.3.27
The total numerical dispersion, then, is
51'
-------
u
num
1.3.28
Note that increasing the time step up to Ax/U (or V/Q) decreases numerical
dispersion to 0. The conditions for stability discussed above require a
time step somewhat less than V/Q for most segments. So to maintain stability
and minimize numerical dispersion in a water body subject to unsteady flow,
the sequence of time steps must be as large as possible, but always less
than Atmax given in 1.3.25.
Advection factor. dimensionless--The advection factor v can be specified
to modify the finite difference approximation of 3c/dx used in the advection
term by WASP. For v =0, the backward difference approximation is used. This
is most stable, and is recommended for most applications. For v =0.5, the
central difference approximation is used. This is unstable in WASP, and is
not recommended.
A nonzero advection factor is helpful in situations where the network
size and time step produce large numerical dispersion. A nonzero advection
factor reduces the numerical dispersion produced by a particular velocity,
length, and time step combination. According to Bella and Grenney (1970):
U
-
2
Enum- - EC1-2 "> L - U At]
1.3.29
Note that a v of 0 reduces this to equation 1.3.28. Values of Enum for a
length of 2000 meters and various combinations of velocity and time step are
provided in Table 1.3.3. For a particular velocity, say 0.4 m/sec, numerical
dispersion can be reduced by increasing the time step. For v =0, increasing
the time step from 1000 to 4000 seconds decreases Enum from 320 to 80 m2/sec.
If the time step must be 1000 seconds, however, numerical dispersion can
still be reduced by increasing v. In this case, increasing v from 0 to 0.4
decreases Enum from 320 to 0 m/sec.
Negative solution option--Normally, concentrations are not allowed to
become negative. If a predicted concentration at t+ At is negative, WASP
maintains its positive value by instead halving the concentration at time t.
The negative solution option lets the user bypass this procedure, allowing
negative concentrations. This may be desirable for simulating dissolved
oxygen deficit in the benthos, for example.
Transport Parameters
This broad group of parameters describes the network of segments repre-
senting the water body along with the advective and dispersive flow fields
connecting the segments. Input parameters include segment volumes, advective
flows, sediment transport velocities, dispersion coefficients, cross-sectional
areas, and characteristic lengths. Although the nominal units expected by the
52
-------
TABLE 1.3.3. VALUES OF NUMERICAL DISPERSION (m2/sec)
v
0.1
U (m/sec)
0.2 0.4
0.6
0.8
1.0
0.0
0.1
0.2
0.3
0.4
0.0
0.1
0.2
0.3
0.4
0.0
0.1
0.2
0.3
0.4
0.0
0.1
0.2
0.3
0.4
95
75
55
35
15
90
70
50
30
10
80
60
40
20
0
60
40
20
0
•
180
140
100
60
20
160
120
80
40
0
120
80
40
0
--
40
0
_ _
--
--
At = 1000 sec
320 420 480 500
240 300 320 300
160 180 160 100
80 60 0 --
0
At = 2000 sec
240 240 160 0
160 120 0
80 0 -- --
0 -- --
.--' .'--
At - 4000 sec
80
o
• _ .
• - - •
--
At = 8000 sec
.. - --. • -- --
..
- - _ _ __ »_
--
--
model are SI, English or other units can be used along with proper specifica-
tion of conversion factors.
o
Segment volume, m--Initial volumes for each segment can be calculated
from, navigation charts or a series of transects measuring depth versus width
along the river. Sometimes, volumes can be estimated from travel time of a
well-mixed cloud of dye through a reach. Initial segment volumes can be
53
-------
automatically adjusted for continuity during a simulation by specifying IVOPT
- 2. For simulations using hydrodynamic results from DYNHYD4, volumes from
the SUMRY2 file are used and continuity is maintained.
•3
Advective flow, m/sec--Steady or unsteady flows can be specified between
adjoining segments, as well as entering or leaving the network as inflow or
outflow. The user must be careful to check for continuity errors, as the
model does not necessarily require that flow continuity be maintained. For
example, the user may specify that more flow enters a segment than leaves.
If IVOPT - 2, continuity will be maintained and that segment will grow in
volume indefinitely. If IVOPT = 1, however, the volume will remain constant
and pollutant mass will build up in the segment indefinitely. For simulations
using hydrodynamic results from DYNHYD4, flows from the SUMRY2 file are used
and flow continuity is automatically maintained.
Sediment transport velocities, m/sec--Settling, deposition, scour, and
sedimentation velocities can be specified for each type of solid. These
velocities are multiplied by cross-sectional areas and treated as flows that
carry sediment and sorbed chemical between segments. Settling velocities are
important components of suspended sediment transport in the water column.
Scour and deposition velocities determine the transfer of sediment and
pollutants between the water column and the sediment bed. Sedimentation
velocities represent the rate at which the bed is rising in response to net
deposition.
Dispersion coefficient, m/sec--Dispersive mixing coefficients can be
specified between adjoining segments, or across open water boundaries.
These coefficients can model pore water diffusion in benthic segments, verti-
cal diffusion in lakes, and lateral and longitudinal dispersion in large
water bodies. Values can range from 10"10 m2/sec for molecular diffusion to
5x10 m/sec for longitudinal mixing in some estuaries.
Gross-sectional area, m --Cross-sectional areas are specified for each
dispersion coefficient, reflecting the area through which mixing occurs.
These can be surface areas for vertical exchange, such as in lakes or in the
benthos. Areas are not modified during the simulation to reflect flow changes.
Characteristic mixing length, m--Mixing lengths are specified for each
dispersion coefficient, reflecting the characteristic length over which
mixing occurs. These are typically the lengths between the center points of
adjoining segments. A single segment may have three or more mixing lengths
for segments adjoining longitudinally, laterally, and vertically. For surfi-
cial benthic segments connecting water column segments, the depth of the
benthic layer is a more realistic mixing length than half the water depth.
Boundary Parameters
This group of parameters includes boundary concentrations and waste
loads.
54
-------
Boundary concentration. mg/L--Steady or time-variable concentrations
must be specified for each water quality constituent at each boundary. A
boundary is either a tributary inflow, a downstream outflow, or an open
water end of the model network across which dispersive mixing can occur.
Advective and dispersive flows across boundaries are specified by the
transport parameters.
Waste load, kg/day--Steady or time-variable loads may be specified for
each water quality constituent at several segments. These loads represent
municipal and industrial wastewater discharges, urban and agricultural runoff,
precipitation, and atmospheric deposition of pollutants.
Transformation Parameters
This group of parameters includes spatially variable parameters, con-
stants, and kinetic time functions for the water quality constituents being
simulated. None are necessary for dissolved, conservative chemicals.
Initial Conditions
This category includes initial concentrations, dissolved fractions, and
densities.
Initial concentration. mg/L--Concentrations of each constituent in each
segment must be specified for the time at which the simulation begins. For
those water bodies with low transport rates, the initial concentrations of
conservative substances may persist for a long period of time. Accurate
simulation, then, would require accurate specification of initial concentra-
tions. If initial concentrations cannot be determined accurately, then
longer simulations should be run, and early predictions discounted.
Dissolved fractions--The initial fraction of chemical dissolved in the
water portion of a segment is input as a fraction of total chemical concen-
tration. The dissolved fraction is important in determining the amount of
chemical transported by pore water flow and dispersion, and by solids trans-
port. Dissolved fractions may be computed from sorption kinetics in the
transformation subroutines.
Solid densities. g/cm^--The density of each type of solid is needed to
compute the porosity of bed segments. Porosity will be a function of sedi-
ment concentration and the density of each solid type.
Maximum concentrations. mg/L--Maximum concentrations must be specified
for each water quality constituent. The simulation is automatically aborted
if a calculated concentration falls outside these limits. This usually indi-
cates computational instability, and the time step must usually be reduced.
55
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Application of the Model
The first step in applying the model is analyzing the problem to be
solved. What questions are being asked? How can a simulation model be used
to address these questions? A water quality model can do three basic tasks--
describe present water quality conditions, provide generic predictions, and
provide site-specific predictions. The first, descriptive task is to extend
in some way a limited site-specific data base. Because monitoring is expen-
sive, data seldom give the spatial and temporal resolution needed to fully
characterize a water body. A simulation model can be used to interpolate
between observed data, locating, for example, the dissolved oxygen sag point
in a. river or the maximum salinity intrusion in an estuary. Of course such a
model can be used to guide future monitoring efforts. Descriptive models
also can be used to infer the important processes controlling present water
quality. This information can be used to guide not only monitoring efforts,
but also model development efforts.
Providing generic predictions is a second type of modeling task. Site-
specific data may not be needed if the goal is to predict the types of water
bodies at risk from a new chemical. A crude set of data may be adequate to
screen a list of chemicals for potential risk to a particular water body.
Generic predictions may sufficiently address the management problem to be
solved, or they may be a preliminary step in detailed site-specific analyses.
Providing site-specific predictions is the most stringent modeling task.
Calibration to a good set of monitoring data is definitely needed to provide
credible predictions. Because predictions often attempt to extrapolate
beyond the present data base, however, the model also must have sufficient
process integrity. Examples of this type of application include waste load
allocation to protect water quality standards and feasibility analysis for
remedial actions, such as tertiary treatment, phosphate bans, or agricultural
best-management practices.
Analysis of the problem should dictate the spatial and temporal scales
for the modeling analysis. Division of the water body into appropriately
sized segments was discussed in Section "Model Network." The user must try to
extend the network upstream and downstream beyond the influence of the waste
loads being studied. If this is not possible, the user should extend the
network far enough so that errors in specifying future boundary concentra-
tions do not propogate into the reaches being studied.
The user also should consider aligning the network so that sampling
stations and points of interest (such as water withdrawals) fall near the
center of a segment. Point source waste loads in streams and rivers with
unidirectional flow should be located near the upper end of a segment. In
estuaries and other water bodies with oscillating flow, waste loads are best
centered within segments. If flows are to be input from DYNHYD4, then a
WASP4 segment must coincide with each hydrodynamic junction. Benthic seg-
ments, .which are not present in the hydrodynamic network, may nevertheless
be included in the WASP4 network. Furthermore, WASP4 segment numbering does
not have to be the same as DYNHYD4 junction numbering. Segments stacked
56
-------
vertically do not have to be numbered consecutively from surface water seg-
ments down, as required in WASP3.
Once the network is set up, the model study will proceed through four
general steps involving, in some manner, hydrodynamics, mass transport, water
quality transformations, and environmental toxicology. The first step ad-
dresses the question of where the water goes. This can be answered by a
combination of gaging, special studies, and hydrodyhamic modeling. Flow data
can be interpolated or extrapolated using the principle of continuity. Very
simple flow routing models can be used; very complicated multi-dimensional
hydrodynamic models can also be used with proper averaging over time and
space. At present, the most compatible hydrodynamic model is DYNHYD4.
The second step answers the question of where the material in the water
is transported. This can be answered by a combination of tracer studies and
model calibration. Dye and salinity are often used as tracers.
The third step answers the question of how the material in the water and
sediment is transformed and what its fate is. This is the main focus of many
studies. Answers depend on a combination of laboratory studies, field moni-
toring, parameter estimation, calibration, and testing. The net result is
sometimes called model validation or verification, which are elusive concepts.
The success of this step depends on the skill of the user, who must combine
specialized knowledge with common sense and skepticism into a methodical
process.
The final step answers the question of how this material is likely to
affect anything of interest, such as people, fish, or the ecological balance.
Often, predicted concentrations are simply compared with water quality cri-
teria adopted to protect the general aquatic community. Cafe must be taken
to insure that the temporal and spatial scales assumed in developing the
criteria are compatible with those predicted by the model. Sometimes princi-
ples of physical chemistry or pharmacokinetics are used to predict chemical
body burdens and resulting biological effects. This field holds promise, but
is still in its infancy.
1.4 EUTROPHICATION
The eutrophication model, EUTR04, is a simplified version of the
Potomac Eutrophication Model, PEM (Thomann and Fitzpatrick, 1982). The
following text is taken from the PEM documentation report, with some
modification.
Overview of EUTR04
Several physical-chemical processes can affect the transport and inter-
action among the nutrients, phytoplankton, carbonaceous material, and dis-
solved oxygen in the aquatic environment. Figure 1.4.1 presents the princi-
pal kinetic interactions for the nutrient cycles and dissolved oxygen.
57
-------
OPO4
3
4
^
OP
8
r i
S.dlm.nt
Figure 1.4.1. EUTR04 state variable interactions.
EUTR04 can be operated by the user at various levels of complexity to simu-
late some or all of these variables and interactions. To simulate only BOD
and DO, for example, the user may bypass calculations for the nitrogen,
phosphorus, and phytoplankton variables (the bypass option is documented in
the User Manual). Six levels of complexity are identified and documented at
the end of this section: (1) Streeter-Phelps, (2) Modified Streeter-Phelps,
(3) Full linear DO balance, (4) Simple eutrophication kinetics, (5) Inter-
mediate eutrophication kinetics, and (6) Intermediate eutrophication kinetics
with benthos. The user should become familiar with the full capabilities of
EUTR04 even if simpler simulations are planned.
Consider phosphorus: dissolved or available phosphorus is utilized by
phytoplankton for growth and interacts with particulate inorganic phosphorus
via a sorption-desorption mechanism. Phosphorus is returned from the
phytoplankton biomass pool to dissolved and particulate organic phosphorus
and to dissolved inorganic phosphorus through endogenous respiration and non-
predatory mortality. Organic phosphorus is converted to dissolved inorganic
phosphorus at a temperature-dependent rate.
58
-------
The kinetics of the nitrogen species are fundamentally the same as the
phosphorus system. Ammonia and nitrate are used by phytoplankton for growth.
The rate at which each is taken up is proportional to its concentration rela-
tive to the total inorganic nitrogen (ammonia plus nitrate) available. Nitro-
gen is returned from the algal biomass and follows pathways that are similar
to phosphorus. Organic nitrogen is converted to ammonia at a temperature de-
pendent rate , and ammonia is then converted to nitrate (nitrification) at a
temperature- and oxygen -dependent rate. Nitrate may be converted to nitrogen
gas (denitrification) in the absence of oxygen and at a temperature -dependent
rate.
Dissolved oxygen is coupled to the other state variables. The sources
of oxygen considered are reaeration and evolution by phytoplankton during
growth. The sinks of oxygen are algal respiration, oxidation of detrital
carbon and carbonaceous material from waste effluents and nonpoint discharges,
and nitrification.
EUTR04 simulates the transport and transformation reactions of up to
eight state variables, illustrated in Figure 1.4.1. They can be considered
as four interacting systems: phytoplankton kinetics, the phosphorus cycle,
the nitrogen cycle and the dissolved oxygen balance. The general WASP4 mass
balance equation is solved for each state variable. To this general equation,
the EUTR04 subroutines add specific transformation processes to customize
equation 1.3.23 for the eight state variables in the water column and benthos.
The rest of Section 1.4 covers the specific details for the several transfor-
mation sources and sinks
Phytoplankton Kinetics
Phytoplankton kinetics assume a central role in eutrophication, affecting
all other systems. An overview of this system is given in Figure 1.4.2.
It is convenient to express the reaction term of phytoplankton, S^^, as
a difference between the growth rate of phytoplankton and their death ana •"
settling rates in the volume V^ . That is:
Sk4j - (Gplj " DP1J * ks4j> Pj 1-4'1
where :
= reaction term, cells/L-day (or mg carbon/L-day)
P.J = phytoplankton population, cells/L (or mg carbon/L)
Gpli = growth rate constant, day"
Dpli = death plus respiration rate constant, day"
kg^-s = settling rate constant, day"
j -= segment number, unitless
59
-------
C:N:P
C4 : Phytoplankton Carbon
/ I \
growth death settling
Figure 1.4.2. Phytoplankton kinetics.
The subscript 1 identifies the quantities as referring to phytoplankton type
1, (only one type is considered in this particular model); the subscript j
refers to the volume element being considered. The balance between the
magnitude of the growth rate and death rate (together with the transport,
settling, and mixing) determines the rate at which phytoplankton mass is
created in the volume element V±. In subsequent text and in figures, sub-
scripts i and j will be omitted unless needed for clarity.
Growth—As pointed out by Di Toro and Matystik (1980), the growth rate
of a population of phytoplankton in a natural environment is a complicated
function of the species of phytoplankton present and their differing reac-
tions to solar radiation, temperature, and the balance between nutrient avail-
ability and phytoplankton requirements. The complex and often conflicting
data pertinent to this problem have been reviewed by several researchers
(Rhee, 1973; Hutchinson, 1967; Strickland, 1965; Lund, 1965; and Raymont,
1963). The available information is not sufficiently detailed to specify the
growth kinetics for individual algal species in a natural environment.
Hence, in order to accomplish the task of constructing a growth function, a
simplified approach is followed. Rather than considering the problem of
different species and their associated environmental and nutrient require-
ments, this model characterizes the population as a whole by the total bio-
mass of the phytoplankton present.
60
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For single species, the direct measure of the population size is the
number of cells per unit of volume. For studies of a single species in a
well-controlled laboratory environment these cell counts may be obtained
fairly readily. In naturally occurring populations, however, this measure
may be somewhat ambiguous: it is difficult to discern viable and non-viable
cells, and species that tend to colonize pose a problem because the count
usually does not distinguish individual cells and because the sizes of the
colonies are quite variable.
The sum of the numbers of each species, the total count, is a possibi-
lity but because cell size varies substantially the nanoplankton would domi-
nate such an aggregation. To account for this, the total bio-volume or wet
weight of phytoplankton, assuming unit density, can be calculated using
characteristic volumes for each identified species. Unfortunately, volumes
can vary appreciably as a function of nutrient status. Conversion to phyto-
plankton dry weight and carbon involves further species-dependent constants
that are also nutrient dependent and, therefore, are subject to variation and
uncertainty. Thus, although the use of phytoplankton dry weight or carbon
concentration is an appealing solution to the issue of aggregation, it suf-
fers from some practical difficulties.
An alternate solution is to measure a parameter that is characteristic
of all phytoplankton, namely, chlorophyll a, and to use this as the aggre-
gated variable. The principal advantages are that the measurement is direct;
it integrates cell types and ages, and it accounts for cell viability. The
principal disadvantage is that it is a community measurement with no differ-
entiation of functional groups (e.g., diatoms, blue-greens); also, it is not
necessarily a good measurement of standing crop in dry weight or carbon units
because the chlorophyll-to-dry-weight and carbon ratios are variable and
non-active chlorophyll (phaeopigments) must be measured to determine viable
chlorophyll concentrations.
As can be seen from the above discussion, no simple aggregate measure-
ment is entirely satisfactory. From a practical point of view, the availabi-
lity of extensive chlorophyll data essentially dictates its use as the
aggregate measure of the phytoplankton population or biomass for calibration
and verification purposes. For internal computational purposes, however,
EUTR04 uses phytoplankton carbon as a measure of algal biomass. The reason
for choosing phytoplankton carbon as the internal state variable reflects
the decision to include a mechanism in. the modeling framework that attempts
to recognize the variable carbon to chlorophyll stoichiometry that occurs
in the water body for a given temperature and light condition. If one had
decided to use a fixed carbon-to-chlorophyll ratio and to use chlorophyll-a
as a biomass measure, it would be relatively simple to determine the equiv-
alent algal carbon deposited in the sediment due to settling and to deter-
mine its equivalent sediment oxygen demand (SOD). The same could not be
done if chlorophyll a were still to be used as a biomass measure and if the
carbon-to-chlorophyll ratio in the overlying water column were permitted to
vary. .One would not be able to determine the equivalent detrital carbon con-
tent of the sediment (and therefore the equivalent SOD) because the variable
carbon-to-chlorophyll ratio determined for the overlying water column would
not be valid for the sediment layer. Instead a dual approach is taken: (1)
61
-------
as stated previously, phytoplankton carbon is used as the internal state
variable, which facilitates the computation of the sediment carbon and sedi-
ment oxygen demand; (2) using the variable carbon to chlorophyll mechanism
(discussed subsequently), phytoplankton chlorophyll a may be computed and
used as the calibration and verification variable to be compared against
observed chlorophyll-a field data.
With a choice of biomass units established, a growth rate that
expresses the rate of production of biomass as a function of the important
environmental variables (temperature, light, and nutrients) may be developed.
The specific growth rate, Gp^^, in segment j is related to G^max(20), the
maximum 20 °C growth rate at optimum light and nutrients, via the following
equation.
plj
GRTj GRIj GRNj
1.4.2
where:
JRTj
the temperature adjustment factor for the direct effects of
temperature on growth, dimensionless
the light attenuation factor as a function of T, I, f, D, and Ke,
dimensionless:
1.4.3
GRIj - g(T,I,f,D,Ke)
the nutrient limit.
inorganic phosphorus and nitrogen (DIP and DIN), dimensionless:
GRN1 ~ cke nutrient limitation factor as a function of dissolved
JRNj
- g(DIP.DIN)
1.4.4
where:
T — ambient water temperature, °C
I — incident solar radiation, Ly/day
f — fraction of daylight, unitless
D — depth of the water column, m
Ke - extinction or light attenuation coefficient, m
-1
DIP,DIN - available nutrients for growth, dissolved inorganic phosphorus
(orthophosphate) and dissolved inorganic nitrogen (ammonia
plus nitrate), mg/L
Note that temperature has both direct effects on the phytoplankton growth
rate and indirect effects through its ability to adjust to changing light
conditions. The net effect of temperature, then, can be complicated and
difficult to establish.
62
-------
An initial estimate of Gj_max can be made based upon previous studies of
phytoplankton dynamics and upon reported literature values (such as Zison
et al., 1978) and subsequently refined during the calibration and verifica-
tion process. The selected maximum growth rate is then temperature-corrected
using temporally- and spatially-variable water column temperatures as reported
in field studies. The temperature-corrected growth rate is computed using:
Glmax = Glmax(20
1.4.5
where:
temperature coefficient, unitless
Di Toro and Matystik (1980) report a value of 1.068 for Q±. This temperature-
corrected growth rate is then adjusted to reflect attenuation due to ambient
light and nutrient levels .
In the natural environment, the light intensity to which the phytoplankton
are exposed is not uniformly at the optimum value. At the surface and near-
surface of the air-water interface, photoinhibition can occur at high light
intensities , whereas at depths below the euphotic zone light is not available
for photosynthesis due to natural and algal- related turbidity. A modeling
framework developed by Smith (1980), extending upon a light curve analysis
formulated by Steele (1962), accounts for both the effects of supersaturating
light intensities and light attenuation through the water column. The in-
stantaneous depth- averaged growth rate reduction developed by Smith is pre-
sented in Equation 1.4.6 and is obtained by integrating the specific growth
rate over depth:
Ke D
[ exp <- exp ( -K,
- exp(-
1.4.6
where:
max c u
where:
D
*,
max
K,,
the average segment depth, m
the quantum yield, mg carbon fixed per mole of light quanta
absorbed
the total extinction coefficient, computed from the sum of the
non-algal light attenuation, Ke, and the self-shading
attenuation due to ambient phytoplankton population, m"1
the extinction coefficient per unit of chlorophyll, m^/mg
chlorophyll a
63
-------
fu - units conversion factor (0.083, assuming 43% inciden light
is visible and 1 mole photons is equivalent to 52,000 cal),
mole photons/m -ly •
Io — the incident light intensity just below the surface, assusmed
to average 0.9 I, ly/day
Is — the saturating light intensity of phytoplankton, ly/day
0C — the ratio of carbon to chlorophyll in the phytoplankton, (mg
carbon/mg chlorophyll~a)
e - the base of natural logarithms (2.71828), unitless
Typical clear sky values of surface light intensity for different latitudes
and months are provided in Table 1.4.1.
TABLE 1.4.1. CALCULATED SOLAR RADIANT ENERGY FLUX TO A HORIZONTAL
SURFACE UNDER A CLEAR SKY (langleys/day)
Latitude
30°N
40 °N
50°N
Time
Of Dav
Mean1
Mid-Day2
Mean
Mid-Day
Mean
Mid-Day
Season
Spring
680
2100
650
1900
590
1700
Summer
750
2200
740
2100
710
1900
Fall
530
1700
440
1400
330
1000
Winter
440
1400
320
1000
190
650
Annual
Mean
600
1900
540
1600
460
1300
Mean values represent calculated seasonal means under a clear sky.
These should represent upper limits for solar radiant energy at sea
level. Reference: Weast and Astle (1980).
o
Mid-Day values represent mid-day flux extended over a 24-hour period.
These assume an atmospheric turbidity of 0, precipitable water content
of 2 cm, and an atmospheric ozone content of .34 cm NTP. Reference:
Robinson (1966).
As Smith (1980) points out, since the early experiments of Warburg and
Negelein (1923), maximum photosynthetic quantum yield ($max) has been
measured for a wide range of conditions (reviewed by Kok, 1960), and a
nearly temperature-independent value of 0.08 to 0.1 mole 02 per mole of
photons absorbed is now widely accepted for photosynthesizing plants in
64
-------
general in the laboratory. Bannister (1974a) gives good arguments for
adopting 0,06 mole carbon (0.07 mole 02) per mole of photons as the maximum
yield for plankton in nature. Reported values for KC generally fall in the
range 0.01 to 0.02 nrmg , and 0.016 m?mg~^ has been suggested as the
approximate average (Bannister, 1974b)'. • •
Equation 1.4.6 is an instantaneous rate and is numerically integrated
over the day within the computer . program to obtain'daily growth, i.e.,
G(I,t)dt
1.4.8
where: t varies from 0 to 1 day.
Equation 1.4.6 is quite similar to that formulated by Di Toro et al.
(1971), which is also available as an option in this model:
f [exp{- _
D ( I
exp(-K
.
- exp(- _)
1.4.9
where: f = fraction of daylight during day. The term Is, the temperature-
dependent light saturation parameter, which-is unknown and must be determined
via the calibration-verification process, is replaced with a term involving
the ratio of $max and G^max. The advantage of doing this is that both
parameters, $max and Glmax, are particularly well documented in the
literature.
A second feature incorporated in the modeling framework derived from
Smith's work is the calculation of a variable carbon to chlorophyll ratio
based on the assumption that adaptive changes in carbon to chlorophyll occur
so as to maximize the specific growth rate for ambient conditions of light
and temperature. Smith found that phytoplankton adjusts chlorophyll composi-
tion so that Is roughly equals 30% of the average available light. The ex-
pression used to calculate the carbon to chlorophyll ratio is presented in
Equation 1.4.10:
IaV e)
1.4.10
where:
Ia = the average daily solar radiation just below the surface,
assuming 10% reflectance loss, ly/day.
A review of reported carbon/chlorophyll ratios in nature (Eppley-and Sloane,
1966) suggests that physiological factors (in part the energy cost of syn-
thesizing chlorophyll as compared with other cellular compounds) come into
play to prevent 6 from going much below 20, even in very low light. This
lower limit of 20 has been included when determining a value for 8. Pre-
viously reported values of 6 from algal composition studies conducted by EPA
65
-------
Region Ill's Central Regional Laboratory (CRL) are compared in Table 1.4.2
to calculated values of 6 using Equation 1.4.10. There is general agreement
between the measured and calculated values. Unfortunately, no winter algae
composition studies were available for comparison purposes.
TABLE 1.4.2. CARBON TO CHLOROPHYLL-A RATIO
Carbon/Chlorophyll a
fig C//ig Chlorophyll a
Sampling
Period
July 20-Oct.
August 1-29,
Sept. 7-28,
Sept. 7-28,
•
6, 19701
19772
19782
19783
Observed
Mean
45
28
21
i
Observed
Range
25-68
12-37
15-27
26-30
Predicted
Range
24-28
23-26
26-30
1. Elemental analysis of blue-green algae
2. Laboratory elemental analysis of overall phytoplankton population
3. Estimates of cell composition based upon field data
The effects of various nutrient concentrations on the growth of phyto-
plankton have been investigated and the results are quite complex. As a
first approximation to the effect of nutrient concentration on the growth
rate, it is assumed that the phytoplankton population in question follows
Monod growth kinetics with respect to the important nutrients. That is, at
an adequate level of substrate concentration, the growth rate proceeds at
the saturated rate for the ambient temperature and light conditions present.
At low substrate concentration, however, the growth rate becomes linearly
proportional to substrate concentration. Thus, for a nutrient with concen-
tration N^ in the jth segment, the factor by which the saturated growth rate
is reduced in the jth segment is: Nj/C*^ + Nj). The constant, K^ (called
the Michaelis or half-saturation constant) is the nutrient concentration at
which the growth rate is half the saturated growth rate. Because there are
two nutrients, nitrogen and phosphorus, considered in this framework, the
Michaelis-Menten expression is evaluated for the dissolved inorganic forms
of both nutrients and the minimum value is chosen to reduce the saturated
growth rate,
DIN
DIP
G(N) - Min (.
1.4.11
+ DIN
+ DIP
66
-------
At the user's discretion, the multiplicative formulation for nutrient limita-
tion may be selected. This formulation multiplies the two terms in 1.4.11.
It is not generally recommended.
Figure 1.4.3 presents plots of G(N) versus DIN and DIP with K,,^ -
25 /tg-N/L and I^p - 1 jug-P/L, respectively. The upper plot shows the
standard Michaelis-Menten response curve to various concentrations of the
inorganic nutrients. As can be seen, no significant reduction in growth rate
is achieved until,DIN is less than 200 ftg/L (0.2 mg/1) or until DIP is less
than 8 /ig/L (0.008 mg/L). . ...
The lower plot on Figure 1.4.3 uses an expanded .nutrient scale and shows
the Michaelis-Menten formulation in a slightly different format. Here the
impact of the function may be evaluated quite readily. For example, a
particular reach of the water body may have .concentrations of DIN equal to
100 MS/L- This corresponds to a 20% reduction in the growth rate (G(N) =
0.8). In order for phosphorus to become the limiting nutrient in the same .
reach, dissolved inorganic phosphorus must reach a level of 4 //g/L or less.
It should also be noted that if upstream nitrogen controls were instituted
such that DIN was reduced to,60 /ig/L for that same reach, then a further
reduction in DIP to 2.5 /zg/L would be required to keep phosphorus as the
limiting nutrient. In other words, as water column concentrations of DIP
begin to approach growth limiting levels due to continued reduction in point
source phosphorus effluents, any nitrogen control strategies that might be
instituted would require additional levels of phosphorus removal in order to
keep phosphorus as the limiting nutrient.
Death'-Numerous mechanisms have been proposed that contribute to the
biomass reduction rate of phytoplankton: endogenous respiration, grazing by
herbivorous zooplankton, and parasitization. The first two mechanisms have
been included in previous models for phytoplankton dynamics, and they have
been shown to be of general importance.
The endogenous respiration rate of phytoplankton is the rate at which
the phytoplankton oxidize their organic carbon to carbon dioxide.per unit
weight of phytoplankton organic carbon. Respiration is.the reverse of the
photosynthesis process and, as such, contributes to the reduction in the
biomass of the phytoplankton population. If the respiration rate of the
phytoplankton as a whole is greater than the groxtfth rate, there is a net loss
of phytoplankton carbon or biomass. The endogenous respiration rate is
temperature dependent (Riley', 1949). and is determined via Equation 1.4.12:
, k1R(T).. = ,k1R(20
1.4.12
where:
k1R(20 °C) = the endogenous respiration rate at 20 °C, day"1
1
IR'^' = t*ie temperature corrected rate, day"
elR '• • , = temperature .coefficient, dimensionless
67
-------
DIN-
DIP
0
O
200 400 600
8 16 24
NUTRIENT CONCENTRATION (fj.q/\)
800
32
10.0
CL
H
O
NITROGEN
LIMITATION
PHOSPHORUS
LIMITATION
240
Figure 1.4.3.
Effects of nutrient limitation on growth rate,
assuming K^ = 25 /ig-N/L, K^ - 1 ju
68
-------
Reported values of endogenous respiration at 20° vary from 0.02 day"-*- to
0.60 day"1, with most values falling between 0.05 day"1 and 0.20 day"1
(Bowie et al., 1985). Di Toro and Matystik (1980) report a value of 1.045
for 9
1R-
The total biomass reduction rate for the phytoplankton in the jth seg-
ment is expressed via Equation 1.4.13:
klR + klD + klG
1.4.13
where:
lD
klG
Z(t)
,= biomass reduction rate, day"1
= death rate, representing the effect of parasitization, i.e., the
infection of algal cells by other microorganisms, and toxic
materials, such as chlorine residual, day"1
= grazing rate on phytoplankton per unit zooplankton population,
L/mgC-day
herbivorous zooplankton population grazing on phytoplankton,
mgC/L
Note that the zooplankton population dynamics are described by the user, not
simulated. If population fluctuations are important in controlling phyto-
plankton levels in a particular body of water, the user may want to simulate
zooplankton and their grazing. On the other hand, many studies heed only a
constant first order grazing irate constant, where grazing rates are assumed
proportional to phytoplankton levels. In that case, k1G can be set to the
first order constant with Z(t) omitted (default value = 1). Reported grazing
rates vary from 0.1 to 1.5 L/mgC-day (Bowie et al., 1985).
Settling--The settling of phytoplankton is an important contribution to
the overall mortality of the phytoplankton population, particularly in lakes
and coastal oceanic waters. Published values of the settling velocity of
phytoplankton, mostly under quiescent laboratory conditions, range from
0.07-18 m/day. In some instances, however, the settling velocity is zero or
negative. Actual settling in natural waters is a complex phenomenon, affected
by vertical turbulence, density gradients, and the physiological state of the
different species of phytoplankton. Although the effective settling rate of
phytoplankton is greatly reduced in a relatively shallow, well mixed river or
estuary due to vertical turbulence, it still can contribute to the overall
mortality of the algal population. In addition, the settling phytoplankton
can be a significant source of nutrients to the sediments and can play an
important role in the sediment oxygen demand. In EUTR04, phytoplankton are
equated to solid type 2 (introduced under solids transport in 1.3). Time and
segment-variable phytoplankton settling velocities can be input by the user,
then, using transport field 4, so that:
69
-------
k£
where:
Vs4ij
1.4.14
- the effective algal settling or loss rate, day
-1
Vs4ij ~ ttie net settlinS velocity of phytoplankton from segment j to
segment i, m/day
D.J — depth of segment j , equal to volume/surface area, m
Summary- -This completes the specification of the growth and death rates
of the phytoplankton population in terms of the physical variables: light,
temperature, and the nutrient concentrations present. (Table 1.4.3 summa-
rizes these equations,) With these variables known as a function of time, it
is possible to calculate the phytoplankton chlorophyll throughout the yean:.
TABLE 1.4.3. PHYTOPLANKTON NET GROWTH EQUATION
S14j " Glmax " Glmaxel
Light Reduction
I0(t) - 0.9
e 1
- ke
lRlR
on
Vs4
' klD ' K1GZ
T-20
(e'"1 - e"a°)dt, where o^ = aQexp(KeD), aQ
Ke D o
Glmax
*max c
8 - Carbon/Chlorophyll Ratio =0.3
•
Nutrient Limitation
[DIN] [DIP]
G(N) - Min ( ,
K
Glmax
-------
TABLE 1.4.3. PHYTOPLANKTON NET GROWTH EQUATION (Continued)
Exogenous Variables
Description Notation Values
Extinction Coefficient K. .1-5
C
Segment Depth D .1-30
Instantaneous Surface Solar Radiation Io^c^ 0-2200
Average Daily Surface Solar Radiation Ia 200-750
Temperature T 0-35
Time t
Rate Constants
Value Used in
the Potomac
Description Notation River Studv
Maximum Specific Growth Rate @ Glmax 2-°
20 °C
Temperature Coefficient 9-^ 1.068
Maximum Photosynthetic Quantum ^max 720.0
Yield
Phytoplankton Self -Light KC 0.017
Attenuation
Half -Saturation Constant for K^ 25.0
Nitrogen
Half -Saturation Constant for i^p 1.0
Phosphorus
Algal Endogenous Respiration k-^R 0.125
Temperature Coefficient . 9^R 1.045
Algal Settling Velocity vg4 0.1
Algal Death k1D 0.02
Zooplankton Grazing Rate kig 0
Zooplankton Population Z 0
Units
m'1
m
langleys/day
langleys/day
°C
day
Units
day"1
none
mg C
mole photon
o
m /mg Chi a
Mg N/L
* P/L
day"1
none
m/day
day"1
L/mgC - day
mgC/L
71
-------
The nutrients are not known a priori, however, because they depend upon the
phytoplankton population that develops. That is, these systems are inter-
dependent and cannot be analyzed separately. It is necessary to formulate a
mass balance for the nutrients as well as the phytoplankton in order to cal-
culate the chlorophyll that would develop for a given set of environmental
conditions.
Stoichiometry and Uptake Kinetics
A principal component in the mass-balance equations written for the
nutrient systems included in the eutrophication framework is the nutrient
uptake kinetics associated with algal growth. To specify the nutrient uptake
kinetics associated with this growth, however, it is necessary to specify the
population Stoichiometry in units of nutrient uptake/mass of population syn-
thesized. For carbon as the unit of population biomass, the relevant ratios
are the mass of nitrogen and phosphorus per unit mass of carbon. A selection
of these ratios presented by Di Toro et al. (1971) indicates that their vari-
ability is quite large. The use of constant ratios in the analysis, then, is
questionable.
Upon further investigation, however, it is clear that the reason these
ratios vary is the varying cellular content of nutrients, which is, in turn,
a. function of the external nutrient concentrations and the past history of
the algal population. Large ratios of carbon to nitrogen or phosphorus corre-
spond to that nutrient limiting growth; small ratios reflect excess nutrients.
Thus, the choice of the relevant ratios can be made with the specific situa-
tion in mind.
The operational consequence of this choice is that the population Stoi-
chiometry under non-limiting conditions may be underestimated, but under
limiting conditions should be estimated correctly. Hence the tradeoff is a
probable lack of realism during a portion of the year versus a correct esti-
mate of algal biomass during periods of possible nutrient limitations.
Because this is usually the critical period and because most questions to be
answered are usually sensitive to maximum summer populations, this choice is
a practical expedient. A comparison of carbon-to-nitrogen and carbon-to-
phosphorus ratios measured in the Potomac Estuary is provided in Table 1.4.4.
Once the stoichiometric ratios have been determined, the mass balance
equations may be written for the nutrients in much the same way as is done,
for the phytoplankton biomass. The primary interaction between the nutrient
systems and the phytoplankton system is the reduction or sink of nutrients
associated with phytoplankton growth. A secondary interaction occurs
wherein the phytoplankton system acts as a source of nutrients due to
release of stored cellular nitrogen and phosphorus during algal respiration
and death.
72
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TABLE 1.4.4. PHOSPHORUS-TO-CARBON AND NITROGEN-TO-CARBON RATIOS
Phosphorus/Carbon
mg P/mg C
Nitrogen/Carbon
mg N/mg C
Sampling
Period
July 20-Oct
August 1-29
Sept. 7-28,
Sept. 7-28,
Model
. 6, 19701
, 19772
19782
19783
Observed
Mean
0.023
0.024
0.030
0.031
0.025
0
0
0
Observed
Ranee
.010-0.046
.012-0.028
.017-0.047
Observed
Mean
0.26
0.24
0.26
0.26
0.25
Observed
Range
0.10-0.48
0.15-0.36
0.18-0.35
1. Elemental analysis of blue-green algae
2. Laboratory elemental analysis of overall phytoplankton population
3. Estimates of cell composition based upon field data
The Phosphorus Cycle
Three phosphorus variables are modeled: phytoplankton phosphorus,
organic phosphorus, and inorganic (orthophosphate) phosphorus. A summary is
illustrated in Figure 1.4.4. Organic phosphorus is divided into particulate
and dissolved concentrations by spatially-variable dissolved fractions.
Inorganic phosphorus also is divided into particulate and dissolved concen-
trations by spatially variable fractions, reflecting sorption. Table 1.4.5
presents the reaction rate terms used in the Potomac study. A fraction of
the phosphorus released during phytoplankton respiration and death is in
the inorganic form and readily available for uptake by other viable algal
cells. In work on the Great Lakes, this fraction was assigned at 50% (Di
Toro and Matystik, 1980).
The remaining fraction released is in the organic form and must undergo
a mineralization or bacterial decomposition into inorganic phosphorus before
utilization by phytoplankton. In their work on Lake Huron and Saginaw Bay,
Di Toro and Matystik (1980) proposed a nutrient recycle formulation that was
a function of the localized phytoplankton population. This proposal was
based on both an analysis of available field data and the work of others
(Hendry, 1977; Lowe, 1976; Henrici, 1938; Menon, 1972; and Rao, 1976) that
indicated bacterial biomass increased as phytoplankton biomass increased.
The mechanism chosen, saturating recycle, was a compromise between the
conventional first-order, temperature-corrected mechanism, and a second
order recycle mechanism wherein the recycle rate is directly proportional
to the phytoplankton biomass present, as had been indicated in pure culture,
bacteria-seeded, laboratory studies (Jewell and McCarty, 1971). The various
relationships may be written:
73
-------
T-20
First order recycle: kg3(T) - kg3(20 °C) 983
Second order recycle: kg3(T) = k83(20 °C) eg3T~20 C4
T-20
1.4.15
1.4.16
1.4.17
Saturating recycle: kg3(T) - kg3(20 °C) 9g3
where terms are as defined in Table 1.4.5.
Saturating recycle permits second order dependency at low phytoplankton
concentrations, when Pc « I^pj,, where K^pc is the half-saturation constant
for recycle, and permits first order recycle when the phytoplankton greatly
exceed the half-saturation constant. Basically this mechanism slows the
recycle rate if the algal population is small but does not permit the rate
to increase continuously as phytoplankton increase. The assumption is that
at higher population levels other factors are rate limiting the recycle
kinetics so that it proceeds at its maximum first order rate.
4. PHYTOPLANKTON PHOSPHORUS
3(C4apc)
D
C4a
4pc
growth death settling
8. ORGANIC PHOSPHORUS
'8 T-20 V S3 '
— -* Dp, C4a pe - k83883 XPRCC8
death mineralization
3. ORHTOPHOSPHATE PHOSPHORUS
settling
mineralization
growth
settling
X
C4
PRO '
K
mPC'1
Phytoplankton affects mineralization
Figure 1.4.4. Phosphorus cycle
74
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TABLE 1.4.5. PHOSPHORUS REACTION TERMS
Description
Notation
Value
Units
Phytoplankton biomass as carbon
Specific phytoplankton growth rate
Phytoplankton loss rate
Phosphorus to carbon ratio
Dissolved organic phosphorus mineralization
at 20 °C
Temperature coefficient
Half saturation constant for phytoplankton
limitation of phosphorus recycle
Fraction of dead and respired phytoplankton
recycled to the organic phosphorus pool
to the phosphate phosphorus pool
Fraction dissolved inorganic phosphorus
in the water column
DPU
aPC
k83
mg C/L
(cf 1.4.2) day"1
(cf 1.4.13) day"1
0.025 mg P/mg C
6
83
0.22
1.08
1.0
0.5
a-fop> °-5
fD3 0.85,
0.70
day'1
none
mg C/L
none
npne
none
Fraction dissolved organic phosphorus
Organic matter settling velocity
Inorganic sediment settling velocity
fD8
Vs3
Vs5
none
m/day
m/day
There is an adsorption-desorption interaction between dissolved in-
organic phosphorus, and suspended particulate matter in the water column.
The subsequent settling of the suspended solids together with the sorbed
inorganic phosphorus can act as a significant loss mechanism in the water
column and is a source of phosphorus to the sediment. Because sufficient
suspended solids data were not available to provide for a calibration and
verification analysis of suspended solids as a state variable, an alternate
formulation to the adsorption-desorption kinetics was required. This alter-
nate formulation takes advantage of the fact that the rates of reaction for
adsorption-desorption are ,in the order of minutes versus reaction rates in
the order of days for the algal and biological kinetics, and so permits an
"instantaneous equilibrium" assumption to be made. Instantaneous equili-
brium implies that the dissolved and particulate phosphorus phases "instan-
taneously" react to any discharge sources of phosphorus or runoff or shore-
75
-------
line erosion of solids so as to redistribute the phosphorus to its "equili-
brium" dissolved and solids phase concentrations.
Consider Cpjp to be the concentration of dissolved inorganic phosphorus
in the water column. It interacts with the particulate concentration, Cpjp.
The interaction may be an adsorption-desorption process with the solids or an
assimilation-depuration process with the phytoplankton. If the total sus-
pended solids is considered, the particulate concentration can be defined as:
Cplp - Cplp M
1.4.18
where:
'PIP
M
— concentration of phosphorus sorbed to solids, mgP/kg M
— concentration of solids, kg/L
The total inorganic phosphorus is then the sum of dissolved inorganic and the
particulate inorganic phosphorus
CTIP ~ CDIP
JPIP
1.4.19
The underlying assumption that is made, as mentioned previously, is
"instantaneous equilibrium" between the adsorption-desorption processes. The
equilibrium between the dissolved inorganic phosphorus in the water column
and the mass concentration of inorganic phosphorus of the solids is usually
expressed in terms of a partition coefficient:
K-
PIP
•TIP
JDIP
1.4.20
where:
- partition coefficient for particulate phosphorus, mgP/kg M
per (mg P/L) or (L/kg M)
•TIP
KPIP M CDIP
1.4.21
Equation 1.4.21 is the linear portion of the Langmuir isotherm. Although
not always representative of actual conditions, it is a reasonable approxima-
tion when (mgPsorbe^/kgM) per (mgPdissolved/L) or (L/kgM) is much less than
the ultimate adsorbing capacity of the solids. Combining Equations 1.4.19
and 1.4.21, the total concentration may be expressed as
CTIp - CDIp
Kplp S CDIp
1.4.22
The dissolved and particulate fractions may be expressed, respectively, as
CD3
JDIP
CTIP
1 + Kplp M
1.4.23
76
-------
CP3
JPIP
JTIP
KPIP M
1 -f K
1.4.24
PIP
M
A wide range of partition coefficients is found in the literature.
Thomann and Fitzpatrick (1982) report values between 1,000 and 16,000. Using
a range in partition coefficients from 1,000 - 16,000 and a range of inorganic
solids of from 10 to 30 mg/L in the water column leads to a range in the
fraction particulate inorganic phosphorus of from 0.01 to 0.33.
The mechanism incorporated in the model framework for computing dis-
solved and sorbed phosphorus sacrifices some degree of realism for computa-
tional simplicity. Essentially the dissolved and particulate phosphorus
phases are assigned as fixed fractions of the total inorganic, phosphorus.
Internally the computation is performed as follows: at the beginning of each
computational step in the integration procedure for each segment in the
model, the total inorganic phosphorus is computed as the sum of the dissolved
and sorbed inorganic phosphorus in that segment, and then redistributed to
the dissolved phase, for algal uptake, and the particulate phase, for set-
tling, using an assigned fraction for each phase. The computational steps
may be written:
TIP
DIP
PIP
where:
= DIP+
- f,
D3
(1 -
TIP
TIP
1.4.25
1.4.26
1.4.27
TIP
DIPt-l
the total inorganic phosphorus, mg/L
the dissolved inorganic phosphorus resulting from the
previous integration step, mg/L
PIP
t-1
DIP
PIP
sorbed inorganic phosphorus resulting from the pre-
vious integration step, mg/L
the fraction of the total inorganic phosphorus assigned to
the dissolved phase, unitless
the new "equilibrium" dissolved inorganic phosphorus,
available for algal uptake, mg/L
the new "equilibrium" sorbed inorganic phosphorus, which
may then settle to the sediment layer from the water column,
mg/L.
Particulate organic and inorganic phosphorus settle according to user-
specified velocities and particulate fractions. Particulate organic phos-
77
-------
phorus is equated to solid type 1, which represents organic matter. Time and
segment-variable organic phosphorus settling velocities can be input by the
user using transport field 3, so that
v
s3ij
1.4.28
where:
^s81 ~ organic phosphorus settling rate, day"
- settling velocity of organic matter from segment j to
i, m/day
- dissolved fraction of organic phosphorus in segment j
Particulate inorganic phosphorus is equated to solid type 3, which represents
inorganic sediment. Time and segment variable inorganic phosphorus settling
velocities can be input by the user using transport field 5, so that
k^-j^
where:
V
s5j
D3j
D
- fD3j>
1.4.29
"
inorganic phosphorus settling rate in segment j , day
settling velocity of inorganic sediment from segment
j to i, m/day
dissolved fraction of inorganic phosphorus in segment j
The Nitrogen Cycle
Four nitrogen variables are modeled: phytoplankton nitrogen, organic
nitrogen, ammonia, and nitrate. A summary is illustrated in Figure 1.4.5.
Table 1.4.6 summarizes the terms used in the nitrogen system kinetics.
During algal respiration and death, a fraction of the cellular nitrogen is
returned to the inorganic pool in the form of ammonia nitrogen. The fraction
recycled to the inorganic pool for Great Lakes models has been assigned at
50% (DiToro and Matystik, 1980). The remaining fraction is recycled to the
organic nitrogen pool. The particulate fraction of organic nitrogen (l-fpy-j)
may settle out at the same velocity as organic matter (vs3^j), leading to the
loss term shown in Figure 1.4.6. Organic nitrogen undergoes a bacterial de-
composition whose end-product is ammonia nitrogen. Ammonia nitrogen, in the
presence of nitrifying bacteria and oxygen, is converted to nitrate nitrogen
(nitrification). Both ammonia and nitrate are available for uptake and use
in cell growth by phytoplankton; however, for physiological reasons, the pre-
ferred form is ammonia nitrogen. The ammonia preference term takes the
following form:
78
-------
NH3
ON
1. AMMONIA NITROGEN
ctC, T-20
mineralization
T-20 / CB
growth
nitrification
death
2. NITRATE NITROGEN
'NC
nitrification
growth
-k fl7'20
K12"12 1
rwu " C<
NHl
denltrification
C2
ammonia preference factor
4. PHYTOPLANKTON NITROGEN
et(C4aNC) VS4
dt "PI PI~ D ' C4'
growth death settling
-
death mineralization settling
Figure 1.4.5. Nitrogen cycle.
79
-------
TABLE 1.4.6. NITROGEN REACTION TERMS
Description
Nitrogen to carbon ratio
Organic nitrogen mineralization
rate @ 20 °C
Temperature coefficient
Nitrification rate @ 20 °C
Temperature coefficient
Half saturation constant for
oxygen limitation of
nitrification
Denitrification rate @ 20 °C
Temperature coefficient
Michaelis constant for denitri-
fication
Fraction of dead and respired
phytoplankton recycled. . .
to the organic nitrogen pool
to the ammonia nitrogen pool
Preference for ammonia uptake term
Value
from Potomac
Notation Estuary Model Units
aNC
k71
e71
k12
912
KNIT
k2D
92D
KN03
fON
d-fON)
PNH3
0.25 mg N/mg C
0.075 day'1
1 . 08 none
0.09 day"1
0.13
1.08 none
2.0 mg 02/L
0.09 day'1
1 . 045 none
0.1 mg 02/L
0 . 5 none
0 . 5 none
cf. Eq. none
1.4.30
Fraction dissolved organic nitrogen f
Organic matter settling velocity
D7
Vs3
1.0
none
m/day
80
-------
NO.
PNHo = NH-3
+ NHc
(NH3+N03)(KmN+N03)
1.4.30
The behavior of this equation, for a Michaelis value, K^, of 25 jug N/L,
is shown in Figure 1.4.6. The behavior of Equation 1.4.30 is most sensitive
at low values of ammonia or nitrate. For a given concentration of ammonia,
as the available nitrate increases above approximately the Michaelis limita-
tion, the preference for ammonia reaches an asymptote. Also as the concen-
tration of available ammonia increases, the plateau levels off at values
closer to unity, i.e., total preference for ammonia.
Ammonia Preference Structure
1.0.
z
o
2
cc
o
o
cc
LJ
U-
LU
CC
o.
NH,= 200 fj.q / I
100
50 tig/I
10/ig/l
40
8O
N0
120
160
200
Figure 1.4.6. Ammonia preference structure (Thomann and Fitzpatrick,, 1982)
The process of nitrification in natural waters is carried out by aerobic
autotrophs; Nitrosomonas and Nitrobacter predominate in fresh waters. It is
a two-step process with Nitrosomonas bacteria responsible for the conversion
of ammonia to nitrite and Nitrobacter responsible for the conversion of
nitrite to nitrate. Essential to this reaction process are aerobic condi-
tions. Also this process appears to be affected by high or low values of pH
that inhibit Nitrosomonas growth, particularly for pH below 7 and greater
than 9. Anthonisen et al. (1976) postulate that the existence of free
ammonia and nitrous acid inhibits nitrifying organisms by causing differences
between intercellular and extracellular pH.
81
-------
As with phytoplankton, the nitrifying bacterial populations are sensitive
to flow. During periods of high flow or storm runoff, upstream bacteria may
be advected downstream, with some lag time after a flow transient before they
can build up to significant levels again.
Therefore, the process of nitrification in natural waters is a complex
phenomenon depending on dissolved oxygen, pH, and flow conditions, which
in turn leads to spatially and temporally varying rates of nitrification.
To properly account for this complex phenomenon in the modeling framework
would require an additional five state variables: nitrite, Nitrosomonas
and Nitrobacter bacteria, and total inorganic carbon and alkalinity from
which to calculate pH. Unfortunately, the data base to support the cali-
bration/verification of these additional state variables is usually unavail-
able. Therefore, the process of nitrification is of necessity reduced to a
simple spatially invariant, but temperature-corrected, first-order reaction
rate.
Denitrification refers to the reduction of NO^ (or NC^) to N2 and other
gaseous products such as ^0 and NO. This process is carried out by a large
number of heterotrophic, facultative anaerobes. Under normal aerobic condi-
tions found in the water column, these organisms use oxygen to oxidize organic
material. Under the anaerobic conditions found in the sediment bed or during
extremely low oxygen conditions in the water column, however, these organisms
are able to use NOg as the electron acceptor.
The process of denitrification is included in the modeling framework
simply as a sink of nitrate. This process is assumed to always occur in
the sediment layer where anaerobic conditions always exist. In the water
column, however, denitrification should occur only under extremely low dis-
solved oxygen conditions. This is accomplished computationally by modifying
the linear first-order denitrification rate by the expression KjjQ3/(K^Q3 +
DO). This expression is similar to the Michaelis - Menten expression, and
for concentrations of DO greater than 1 mg/L, this expression reduces deni-
trification to near zero, whereas for DO levels less than 0.1 mg/L this
expression permits denitrification to occur.
The Dissolved Oxygen Balance
Five state variables participate in the DO balance: phytoplankton
carbon, ammonia, nitrate, carbonaceous biochemical oxygen demand, and dis-
solved oxygen. A summary is illustrated in Figure 1.4.7. The reduction of
dissolved oxygen is a consequence of the aerobic respiratory processes in the
water column and the anaerobic processes in the underlying sediments. Both
these processes contribute significantly and, therefore, it is necessary to
formulate their kinetics explicitly.
The methodology for the analysis of dissolved oxygen dynamics in natural
waters, particularly in streams, rivers, and estuaries is reasonably well-
developed (O'Connor and Thomann, 1972). The long history of applications have
focused primarily on the use of biochemical oyxgen demand (BOD) as the mea-
sure of the quantity of oxygen-demanding material and its rate of oxidation
82
-------
Atmosphere
5. CARBONACEOUS BOD
olCc
clt
D C4 a
death
T-20
:-kD0D C5
oxidation
D
settling
- — — k 6T"2°(
denitrification
6. DISSOLVED OXYGEN
K
>VN03 .
reaeration
64 . nr-20
T-20
oxidation
\ _ 32
.,
cs(-
BOD * Ve
SOD
nitrification
respiration sediment
+ G C ( 32 * 483NC f 1 p \]
GP'C4Vt4 M— PNH3)J
growth using CO2, NH3, NO3 (photosynthesis)
Figure 1.4.7. Oxygen balance.
as the controlling kinetic reaction. This has proven to be appropriate for
waters receiving a heterogeneous combination of organic wastes of municipal
and industrial origin since an aggregate measure of their potential effect is
a great simplification that reduces a complex problem to one of tractable
dimensions. , •
A byproduct of photosynthetic carbon fixation is the production of
dissolved oxygen. The rate of oxygen production (and nutrient uptake) is
proportional to the growth rate of the phytoplankton since its stoichiometry
is fixed. An additional source of oxygen from algal growth occurs when the
available ammonia nutrient source is exhausted and the phytoplankton begin
83
-------
to utilize the available nitrate. For nitrate uptake the initial step is a
reduction to ammonia which produces oxygen as shown in equation 1.4.31:
2NOc
2NH
30
1.4.31
Thus, for each mg of phytoplankton carbon produced by growth using nitrate,
aNC mS °^ phytoplankton nitrogen are reduced, and (48/14) a^Q mg of 02 are
produced. Oxygen deficient, i.e., below saturation, waters are replenished
via atmospheric reaeration. The reaeration coefficient is a function of the
average water velocity, depth, wind, and temperature. EUTR04 calculates
flow-induced reaeration based on the Covar method (Covar, 1976). This method
calculates reaeration as a function of velocity and depth by one of three
formulas, Owens, Churchill, or O'Connor-Dobbins, respectively:
k_,(20 °C) - 21.7 V
aj x
kaj(20 °C) - 11.7
or kaj(20 °C) - 12.9
tj
°'67
1.4.32
1.4.33
1.4.34
where:
-1
ka.s — reaeration rate coefficient at 20 °C, day
Vj-.s — average water velocity in segment j , m/sec
.
_ average segment depth,
m
The Owens formula is automatically selected for segments with depth less than
2 feet. For segments deeper than 2 feet, the O'Connor-Dobbins or Churchill
formula is selected based on a consideration of depth and velocity, beeper,
slowly moving rivers require O'Connor -Dobbins; moderately shallow, faster
moving streams require Churchill.
Wind-induced reaeration is determined by
k_.(20 °C) - 0.46 W + 0.136 W2
1.4.35
where:
W
time-varying windspeed at 10 cm above surface, m/sec
,-1 i.
A minimum value of 1.6/D.s day"1 is imposed on kaj(20 °C) . Windspeed affects
reaeration, then, above o meters/sec. The reaeration velocity used to com-
pute volatilization is either the flow-induced reaeration or the wind-induced
reaeration, whichever is larger. Segment temperatures are used to adjust
kaj(20 °C) by the standard formula:
kaj(T) - kaj(20
1.4.36
84
-------
where:
T
kaj(T)
temperature, °C
reaeration rate coefficient at ambient segment
temperature, day
-1
9a = temperature coefficient, unitless
Dissolved oxygen saturation is determined as a function of temperature and
salinity S (APHA, 1985):
- -139.34 + (1.5757 x 105/"T) - (6.6423 x 107-)/T2
+(1.2438 x 1010/T3) - (8.6219 x lO11^4) - 0.5535
S[3.1929 x 10'2) - (1.5428 x 10/T) + (3.8673 x 103/T2)]
1.4.37
Oxygen is diminished in the water column as a result of algal respira-
tion, which is basically the reverse process of photosynthesis:
12
_
32
COr
1.4.38
where :
oc
phytoplankton carbon, mg/L
oxygen to carbon ratio for phytoplankton respiration,
Additional losses of oxygen occur as a result of nitrification:
202 -* N03 + H20 + H+ , •
1.4.39
and of oxidation of carbonaceous material (including detrital phytoplankton) .
These three reactions together with sediment oxygen demand (to be detailed
below) account for the loss of oxygen in the water column.
The oxidation of carbonaceous material is the classical BOD reaction.
Internally the model uses ultimate carbonaceous biochemical oxygen demand
CBOD as the indicator of equivalent oxygen demand for the carbonaceous
material. The principal source of CBOD, other than man-made sources and
natural runoff, is detrital phytoplankton carbon, produced as a result of
algal death. The loss mechanisms associated with CBOD are oxidation
C0
H0
CxHyOz -* 2 2
and denitrif ication
4NOo
5CH20
5H20
4H+ -* 5CO^
2N
12H20
1.4.40
1.4.41
although the latter is not a significant loss in the water column.
85
-------
Direct comparisons between observed BODcj data and model output cannot be
made using the internal CBODg computed by EUTR04, since field measurements
may be tainted by algal respiration and the decay of algal carbon. Therefore
a correction must be made to the internally computed model 0600$ so that a
valid comparison to the field measurement may be made. This results in a new
variable, known as the bottle 6005, which is computed via equation 1.4.42.
Bottle BOD5 - CBOD5 +
aocPc(l-e5klR)
1.4.42
where:
CBODc
oc
the internally computed 5-day CBOD, mg/L
the oxygen to carbon ratio, mg C>2/mg C
the phytoplankton biomass in carbon units, mg/L
the algal respiration rate at 20 °C, the temperature
at which the field samples were incubated, day
-1
Note that Equation 1.4.42 is a conservative estimate of the observed
bottle BOD because it does not include a correction for the decay of detrital
algal carbon, which in turn depends upon the number of non-viable phytoplank-
ton. Also, Equation 1.4.42 may tend to underestimate observed bottle BODs if
a nitrifying inhibitor is not used before setting the BODs. Therefore,
depending upon environmental conditions in the water body from which the
samples were taken, some oxygen utilization may be occurring in the bottle due
to nitrification, which is not included in the internal computation of bottle
BOD by EUTR04. Therefore, it is reasonable to expect that the model will
underestimate bottle BOD.
Table 1.4.7 summarizes the water column CBOD and DO reaction parameters.
The formulation for the sediment reactions require a more detailed explana-
tion of the sediment mass transport and kinetics and these are presented
subsequently.
Sediment - Water Interactions
The decomposition of organic material in benthic sediment can have
profound effects on the concentrations of oxygen and nutrients in the over-
lying waters. The decomposition of organic material releases nutrients
to the sediment interstitial waters and also results in the exertion of an
oxygen demand at the sediment-water interface. As a result, the areal fluxes
from the sediment can be substantial nutrient sources or oxygen sinks, on a
volumetric basis, to the overlying water column. Additionally, the occur-
rence of anoxia, due in part to the sediment oxygen demand, may dramatically
increase certain nutrient fluxes. The details of the mechanisms responsible
for this increase are as yet unclear but they are related to a set of complex
redox reactions that change the state and concentrations of various nutrients
and metals thereby releasing bound nutrients. The relative importance of the
sediment oxygen demand and nutrient fluxes vis-a-vis future nutrient control
86
-------
TABLE 1.4.7. CBOD AND DO REACTION TERMS
Description
Value from Potomac
Notation Estuary Model Units
Oxygen to carbon ratio
32/12
mg 02/mg C
Ratio of the ultimate to 5-day
carbonaceous biochemical
oxygen demand
1.85
none
Deoxygenation rate @ 20 °C
Temperature coefficient
0.21
0.16
1.047
-1
day
none
Half saturation constant for
oxygen limitation
K
•BOD
0.5
mg 02/L
Oxygen to nitrogen ratio
aON
32/14
mg 02/mg N
Oxygen to carbon ratio for
nitrate uptake
aN03C (48/14)aNC mg 02/mg C
Reaeration rate @ 20 °C
Temperature coefficient
cf Eq. 1.4.32- day
1.4.34
1.028
-1
none
Dissolved oxygen saturation
D0sat cf Eq. 1.4.37 mg 02/L
Fraction dissolved CBOD
CD5
0.5
none
Organic matter settling velocity
m/day
87
-------
strategies requires the incorporation of a dynamic sediment layer and its
associated interactions with the overlying water column in a framework that
is consistent with that discussed in the previous sections.
This model provides two options for nutrient and oxygen fluxes: descrip-
tive input and predictive calculations (Fig. 1.4.8). The first option is
used for networks composed of water column segments only. Observed fluxes
and surface areas must be specified for ammonia, phosphate, and dissolved
oxygen (i.e., sediment oxygen demand). Time functions may be specified for
ammonia and phosphate, reflecting seasonal changes.
The calculational framework incorporated for benthic-water column
exchange draws principally from a study of Lake Erie, which incorporated
sediment-water column interactions, performed by Di Toro and Connolly (1980).
The mass-balance equations for dissolved and particulate materials are pre-
sented first, principally to show mass transport, followed by the descrip-
tions of the kinetics for nitrogen, oxygen, and phosphorus as were incor-
porated in the modeling framework.
1. OBSERVED FLUXES
^-""^ ^-^As ^ — jS^\ Water Column
Segments
Ail
jit..
ill Surface
1 * * Flux Area
1. AMMONIA LOAD
= + FNH., • As •
2. PHOSPHATE LOAD = *F?0ll • As •
Time '
Function
TFNH4
TFPO4
3. DISS OXYGEN LOAD =• -SOD • As
2. CALCULATED FLUXES
Water Column Segment
Benthic Segment
^
1,2,3,6,7.8 Constituent Numbers
Figure 1.4.8. Sediment-water exchange.
For a one-layer benthic layer with thickness,
dissolved mass balance equations are, respectively:
3C.
'PJ
at
D.
'sd
"Pi
V
R
PJ
(m) , the particulate and
1.4.43
and
Cwj
1.4.44
-------
where:
j, i = indicates benthic layer and water column, respectively
Cp.= , Cp^ = the particulate material concentrations in the benthic layer
and water column respectively, mg/L
— the dissolved concentrations in the benthic interstitial waters
and overlying water column respectively, mg/L
Vp = the deposition velocity of particulates across the water
column-benthic interface, m/day
vs(j = the sedimentation velocity induced by sedimentation, relative
to a coordinate system fixed with respect to the benthic
surface, m/day
V£ = the resuspension velocity of particulates, m/day
the diffusive exchange rate between dissolved concentrations in
the interstitial water and the overlying water column, m/day
kp, k^j. = first order reaction rates associated with the particulate and
dissolved phases, respectively, day .
¥ASP4 allows a A more detailed parameterization of settling into the benthos
that includes not only a downward settling velocity but an upward resuspension
velocity as well. In this context, then, the net particulate flux to the
sediment is due to the difference between the downward settling flux and the
upward resuspension flux.
One of the first decisions to be made regarding the benthic layer is to
determine its depth. Two factors influence this decision. The first is to
adequately reflect the thickness of the active layer, the depth to which the
sediment is influenced by exchange with the overlying water column. Secondly
one wishes the model to reflect a reasonable time history or "memory" in the
sediment layer. Too thin a layer and the benthos will "remember" or be
influenced by deposition of material that would have occurred only within the
last year or two of the period being analyzed; too thick a layer and the
model will "average" too long a history, not reflecting, as in the case of
phosphorus, substantial reductions in sedimentary phosphorus resulting from
reduced phosphorus discharges from sewage treatment plants. The choice of
sediment thickness is further complicated by spatially variable sedimentation
rates. The benthic layer depths, together with the assigned sedimentation
velocities, provide for a multi-year detention time or "memory', providing a
reasonable approximation of the active layer in light of the observed pore
water gradients.
The next consideration is the application of these mass balance equa-
tions to the nitrogen species in a reducing sediment (Berner, 1974). Parti-
culate organip nitrogen is hydrolyzed to ammonia by bacterial action within
the benthos. In addition to the ammonia produced by the hydrolysis of parti-
89
-------
culate organic nitrogen in the benthos, ammonia is generated by the anaerobic
decomposition of algae. In a study of this reaction, Foree and McCarty
(1970) showed that the anaerobic rate of decay of algae is substantial
(0.007-0.022 day"1). However, the end product initially is not exclusively
ammonia. Rather, a fraction of the algal, nitrogen becomes particulate or-
ganic nitrogen, which must undergo hydrolysis before becoming ammonia.
Ammonia produced by the hydrolysis of non-algal organic nitrogen and.
the decomposition of detrital algal nitrogen may then be exchanged with the
overlying water column via diffusion. No nitrification occurs in the sedi-
ment due to the anaerobic conditions present in the sediment. Denitrifica-
tion, the conversion of nitrate to nitrogen gas, may occur, however. Nitrate
is present in the benthos due to diffusive exchange with the overlying water
column.
The analysis of the benthic nitrogen concentrations and the resulting
flux of ammonia is relatively straightforward because of the simplicity of
the kinetics: hydrolysis and anaerobic algal decay produce a stable end
product, ammonia, which does not undergo further reactions in the anaerobic
sediment. The equations resulting from the above framework are presented in
Table 1.4.8.
The reactions that convert algal and refractory carbon to their end
products are more complex. The initial step in which the algal and refrac-
tory carbon are converted to reactive intermediates appears to be similar to
the refractory organic and algal nitrogen degradation, and in the subsequent
calculations, the rates for carbon and nitrogen decomposition are assumed to
be equal. The reactive intermediates, however, participate in further reac-
tions: for example, volatile acids react to become methane, and the mecha-
nisms that control these reactions are somewhat uncertain. In addition, few
measurements of these intermediate species are available and a calculation
that incorporates their concentrations explicitly would of necessity be
speculative. Thus, one uses a simplified, yet realistic, formulation of
these reactions.
The method proposed by Di Toro and Connolly (1980), and highlighted here,
is based upon separating the initial reactions that convert sedimentary organ-
ic material into reactive intermediates and the remaining redox reactions that
occur. Then using a transformation variable and an orthogonality relation-
ship, Di Toro and Connolly derive mass balance equations that are independent
of the details of the redox equations. Rather they are only functions of
the component concentration, and it suffices to compute only the component
concentrations, which can be treated in exactly the same way as any other
variable in the mass transport calculation.
90
-------
TABLE 1.4.8. SEDIMENT LAYER NITROGEN REACTION AND FLUX TERMS
Total Organic Nitrogen (TON)
rp Ort rT* rt/v
Sk7j ~ aNCfONtC4l '
Ammonia Nitrogen
q a f fir a~ T-20xrr i i, a T-20
bklj aNCtNH3^kPZD0PZD MwJ ' ^OND^ND
Nitrate Nitrogen
Sk2j = - k2D92DT"2° C2
o
Sediment Ammonia Flux Rate (g/m -day)
Er
NH-3
}flux
3j
(positive rate ->• flux from sediment to water column)
O ' ' : >
Sediment Nitrate Flux Rate (g/m -day) ......
Er
NO
3flux
Jj
(negative rate -»• flux from water column into sediment)
Value
from Potomac
Description
Anaerobic algal decomposition rate
Temperature coefficient
Organic nitrogen decomposition rate
Temperature coefficient
Diffusive exchange coefficient
Benthic layer depth
Benthic layer
Water column
Notation
kPZD
9PZD
kOND
9OND
EDIF
°j
j
i
Estuarv Study
0.02
1.08
0.0004
1.08
2-2.5
x lO'4
0.2-0.7
Units :
day'1
none
day"1
none
0
m /day.
ft
91
-------
The convenient choice of components for the calculation are those that
parallel the aqueous variables: carbonaceous BOD and dissolved oxygen.
Restricting the calculation to these components, however, eliminates the
possibility of explicitly including the effects of other reduced species
such as iron, manganese, and sulfide, which play a role in overall redox
reactions and may be involved in the generation of sediment oxygen demand.
This sirapllcation appears reasonable in light of the preliminary nature of
the benthic calculation.
The decomposition reactions that drive the component mass balance equa-
tions are the anaerobic decomposition of the algal carbon, and the anaerobic
breakdown of the benthic organic carbon. Both reactions are sinks of the
oxygen and rapidly drive its concentration negative, indicating that the
sediment is reduced rather than oxidized. The negative concentrations com-
puted can be considered the oxygen equivalents of the reduced end products
produced by the chains of redox reactions occurring in the sediment.
Because the calculated concentration of oxygen is positive in the over-
lying water, it is assumed that the reduced carbon species (negative oxygen
equivalents) that are transported across the benthic water interface combine
with the available oxygen and are oxidized to CC>2 and 1^0 with a consequent
reduction of oxygen in the overlying water column. The sediment mass balance
equations for carbonaceous BOD and DO, together with the equation for sedi-
ment oxygen demand, are presented in Table 1.4.9.
A complete analysis of the phosphorus fluxes from sediments would require
a rather complex and elaborate computation of solute-precipitate chemistry
and its interaction with the mass transport of the dissolved species. The
reasons for this are twofold: first, it is well known (Nriagu, 1972) that
for phosphorus the formation of precipitates affects the interstitial water
concentrations, thereby affecting the interstitial water transport of the
various phsophorus forms or species; second, the dissolved concentrations are
affected by the redox reactions, which in turn, affect the phosphorus fluxes
that occur during aerobic and anaerobic conditions. (Phosphorus fluxes are
enhanced under anaerobic conditions.)
A computation of solute-precipitate chemistry was judged to be outside
the scope of this study. Instead, a simplified approach was taken, which
to a. large degree relies on empiricism. Anaerobic decomposition of refrac-
tory organic phosphorus and detrital algal phosphorus is assumed to occur
using the same rate expressions and rate constants as those for organic
nitrogen. The fraction of the end product, dissolved inorganic phosphorus,
that remains in the interstitial water, however, is not involved in the
formation of precipitates and is not sorbed onto the benthic solids, rather
it varies spatially. This spatial variation reflects the ionic chemical
makeup of the benthos in various regions of the water body.
92
-------
TABLE 1.4.9. BENTHIC LAYER BOD AND DO REACTION RATES
Carbonaceous 5 -day Biochemical Oxygen Demand
k5j
- 5 32 k
4 14
2D
Dissolved Oxygen
T-20
ak6j = -KDSWDS
Sediment Oxygen Demand (g/m -day)
SOD =
aDIF
ID
-------
TABLE 1.4.10. BENTHIC LAYER PHOSPHORUS REACTION TERMS
- kOPD9OPDT"2°[DOp]
Dissolved Organic Phosphorus (DOP)
m Ort
Sk8j " aPCfDOP[C4l
Dissolved Inorganic Phosphorus (DIP)
Sk3j - aPCfDIP
-------
Variable Complexity Levels
EUTR04 kinetics can be implemented at six levels of complexity to
analyze dissolved oxygen and eutrophication problems: (1) Streeter-Phelps,
(2) Modified Streeter-Phelps, (3) Full linear DO balance, (4) Simple eutrophi-
cation kinetics, (5) Intermediate eutrophication kinetics, and (6) Inter-
mediate eutrophication kinetics with benthos. These are described briefly
below. The input data set-up for each is described in Section 2.4.
Streeter-Phelps
The simplest dissolved oxygen balance solves the Streeter-Phelps BOD-DO
equations in a slightly modified form:
Vs3
Sk5 " -kd C5 - <1 - fD5> C5 1.4-45
D
SOD
Sk6 = +k2 - kd C5 - 1.4.46
D
where:
C5 = total biochemical oxygen demand, (BOD), mg/L (use
System 5)
Cg = dissolved oxygen, mg/L (System 6)
Cg = dissolved oxygen saturation, mg/L
SOD = sediment oxygen demand, g/m^-day
k
-------
Vs3
- fD5> C5
1.4.47
skl
Vs3
1.4.48
Sk6
where:
SOD -
Vs3 "
D5
Dl
D
(Cg - C6) - kd C5 -
SOD
D
1.4.49
carbonaceous biochemical oxygen demand (CBOD), mg/L
(System 5)
nitrogenous biochemical oxygen demand (NBOD), mg/L
(use System 1)
dissolved oxygen, mg/L (System 6)
dissolved oxygen saturation, mg/L
t\
sediment oxygen demand, g/m -day
carbonaceous deoxygenation rate constant, day
organic matter settling velocity, m/day
nitrogenous deoxygenation rate constant, day
reaeration rate constant, day"
CBOD dissolved fraction
NBOD dissolved fraction
depth, m
-1
-1
Systems 2-4, 7, and 8 are bypassed; System 1 is considered NBOD, which can be
estimated as 4.5 TKN (TKN is organic nitrogen + ammonia nitrogen). The
particulate fractions of Systems 1 and 5 are associated with transport field
3, organic matter settling.
Full Linear DO Balance
The full DO balance equations divide the NBOD process into mineralization
and nitrification, and add the effects of photosynthesis and respiration from
given phytoplankton levels:
96
-------
Sk7
skl
Vs3
+k71 c7 - k12
+k!2 Cl
"kd C5
v,
s3
- fD7)
1.4.50
1.4.51
1.4.52
1.4.53
Sk6 - +k2 - kd C5 - 4.5 k12
32
— C4
12
SOD
D
1:4.55
where:
Jl.
s
SOD
k71
k12
kd
Vs3
k2
klC
klR
organic nitrogen, mg/L (System 7)
ammonia nitrogen, mg/L (System 1)
nitrate nitrogen, mg/L (System 2)
carbonaceous biochemical oxygen demand, mg/L (System 5)
dissolved oxygen, mg/L (System 6)
dissolved oxygen saturation, mg/L
sediment oxygen demand, g/m^-day
mineralization rate constant, day"1
nitrification rate constant, day"1
carbonaceous deoxygenation rate constant, day"
organic matter settling velocity, m/day
reaeration rate constant, day"
average phytoplankton growth rate constant, day"1
(user must input light and nutrient limited value)
average phytoplankton respiration rate constant, day"1
97
-------
C4
fD5
fD7
phytoplankton carbon, mg/L (System 4)
CBOD dissolved fraction
organic nitrogen dissolved fraction
depth, m
Systems 3, 4, and 8 are bypassed. The phytoplankton concentrations to be
used in the DO balance are input under initial conditions as ug/L chlorophyll
a. If the carbon to chlorophyll ratio is not input, then a default value of
30 is used. The particulate fractions of Systems 5 and 7 are associated with
transport field 3, organic matter settling.
Simple Eutrophication. Kinetics
The simple eutrophication kinetics simulate the growth and death of
phytoplankton, with its effects on the nutrient cycles and DO balance. Growth
can be limited by the availability of inorganic nitrogen, inorganic phosphorus,
and light. Light limitation is described by the Di Toro formulation.
Sk7
Vs4
(Gpl - Dpl - _ ) C4
D
+Dpl (
Vs3
pc
- k 9
83 8
D
+k 92° C - G C a
83 83
Vs5
P1 4 aPC
D
+Dpl C4 aNC - kn
Vs3
1.4.55
1.4.56
1.4.57
1.4.58
3kl
C71 971 C7 ' GP1 C4 PNH3 aNC
-k
12
+k12 9122° Cl - GP1 C4
aNC
1.4.59
98
-------
4k5
+klD C4 aoc - kD 6D~2°
Vs3
- fD5> C5
1.4.61
64 k12
14
- k
lR
+Gpl C4 (32 + 48 aNG (1 -
12 14
oc
- SOD
D
1.4.62
Terms and variables are as described in Figures 1.4.3, 1.4.5, 1.4.6, and
1.4.8 and Tables 1.4.2, 1.4.4, 1.4.5, and 1.4.6. Growth is calculated using
equations 1.4.2, 1.4.9, and 1.4.11. Death is calculated using equations
1.4.12 and 1.4.13. The particulate fractions of Systems 5, 7, and 8 are
associated with transport field 3, organic matter settling. System 4 is
associated with transport field 4, phytoplankton settling, the particulate
fraction of System 3 is associated with transport field 5, suspended sediment
settling.
Intermediate Eutrophication Kinetics
The intermediate eutrophication kinetics add certain nonlinear terms and
functions to the simple eutrophication kinetics described above. The equa-
tions are those presented in the Figures and Tables throughout Section 1.4.
Light limitation is described by .the Smith formulation, equations 1.4.6,
1.4.7, 1.4.8, and 1.4.10. The latter equation predicts the carbon to chloro-
phyll ratio based on the availability of light, then predicts the saturating
light intensity based on the carbon to chlorophyll ratio. Other terms in-
cluded in intermediate kinetics are the phytoplankton effect on mineraliza-
tion of organic phosphorus and nitrogen.(equation 1.4.17); dissolved oxygen
limitation on nitrification; and denitrification.
Intermediate Eutrophication Kinetics with Benthos
Simulating benthic interactions requires the addition of benthic seg-
ments to the model network. All state variables are simulated in the ben-
thic segments. Dissolved fractions of NHg, NOg, PO^, CBOD, DO, ON, and OP
may exchange with the water column by diffusion. Particulate fractions of
PO^, CBOD, ON, and OP may deposit to or be scoured from the'benthic segments.
Benthic layer decomposition rates for organic phosphorus, organic nitrogen,
phytoplankton, and CBOD must be specified. The equations used are those in
Tables 1.4.7, 1.4.8, and 1.4.9.
99
-------
1.5 THE TOXIC CHEMICAL MODEL
TOXI4 is a dynamic compartment model of the transport and fate of
organic chemicals and metals in all types of aquatic systems.. It combines
the hydrodynamic capabilities discussed in Section-1.2 and the transport
capabilities discussed in Section 1.3 with the sediment balance and chemical
transformation capabilities discussed here. The chemical transformations
were adopted from EXAMS (Burns et al., 1982; Burns et al., 1985), which
remains a good reference manual.
Overview of TOXI4
Several physical-chemical processes can affect the transport and fate of
toxic chemicals in the aquatic environment. The most important are pictured
in Figure 1.5.1, taken from the chapter on aquatic chemistry in Mills et al.
(1985). TOXI4 explicitly handles most of these, excluding only reduction and
precipitation-dissolution. If the kinetics of these reactions are described
by the user, they also can be included as an extra reaction.
PHYSICAL-CHEMICAL PROCESSES
NOOW
i"1* . ///
I Deposition / //
_T {•Wet OeposHi
SPECUTIOH, TRANSPORT AND TRANSFORMATION PROCESSES IN THE AQUATIC
ENVIRONMENT
Figure 1.5.1. Speciation, transport and transformation processes in the
aquatic environment (Mill et al., 1985).
TOXI4 simulates the transport and transformation of one to three chemi-
cals and one to three types of particulate material (solids classes). The
100
-------
three chemicals may be independent, such as congeners of PCB, or they may be
linked with reaction yields, such as a parent compound-daughter product
sequence. Each chemical exists as a neutral compound and up to four ionic
species. The neutral and ionic species can exist in five phases: dissolved,
sorbed to dissolved organic carbon (DOC), and sorbed to each of the up to
three types of solids (Figure 1.5.2). Local equilibrium is assumed so that
the distribution of the chemical between each of the species and phases is
defined by distribution or partition coefficients. In this fashion, the
concentration of any specie in any phase can be calculated from the total
chemical concentration. Therefore, only a single state variable (WASP system)
representing total concentration is required for each chemical. The model,
then, is composed of up to six systems, three chemical and three solids, for
which the general WASP4 mass balance equation 1.3.29 is solved.
WASP4 (Toxics) EQUILIBRIUM REACTIONS
Chemical Constants
KOW . K oc
Environmental Parameters
DOC
S-t , S2 , S3
•oc1 j *oc2 j *oc3
PH
R"
OR"
S,R"
S2R"
S3R"
RH~
o RH"
S,RH~
S2RH"
S3RH~
RH2
0 RH2
S,RH2
S2RH,
S3RH2
RH^ RH4++
O RHl O RH4++
SOU O DLJ
,""3 ^,""4
SZRH; s2RHr
SDU* O DLJ ++
3"n3 ^>3"r14
ionic
Species Anionic
Phase
Aqueous
DOC
s,
Neutral
Cationic
Figure 1.5.2. Equilibrium speciation.
101
-------
In an aquatic environment, a toxic chemical may be transferred between
phases and may be degraded by any of a number of chemical and biological
processes. Transfer processes defined in the model include sorption, ioniza-
tion and volatilization. Defined Transformation processes include biodegra-
dation, hydrolysis, photolysis, and chemical oxidation. Sorption and ioniza-
tion are treated as equilibrium reactions. All other processes are described
by rate equations. Rate equations may be quantified by first-order constants
or by second-order chemical specific constants and environment-specific
parameters that may vary in space and time.
TOXI4 uses equation 1.3.29 to calculate sediment and chemical mass and
concentrations for every segment in a specialized network that may include
surface water, underlying water, surface bed, and underlying bed. In a simu-
lation, sediment is treated as a conservative constituent that is advecte.d
and dispersed among water segments, that settles to and erodes from benthic
segments, and that moves between benthic segments through net sedimentation,
erosion, or bed load.
In a simulation, the chemical can undergo several physical or chemical
transformations. It is convenient to group these into fast and slow reac-
tions. Fast reactions have characteristic reaction times on the same order
as the model time step and are handled with the assumption of local equili-
brium. Slow reactions have characteristic reaction times much longer than
the model time step. These are handled with the assumption of local first
order kinetics using a lumped rate constant specified by the user, or calcu-
lated internally, based on summation of several process rates, some of which
are second-order. Thus, the effective first order decay rate can vary with
time, and space, and is recalculated as often as necessary throughout a
simulation. The chemical is advected and dispersed among water segments, and
exchanged with surficial benthic segments by dispersive mixing. Sorbed
chemical settles through water column segments and deposits to or erodes from
surficial benthic segments. Within the bed, dissolved chemical migrates
downward or upward through percolation and pore water diffusion. Sorbed
chemical migrates downward or upward through net sedimentation or erosion.
Both rate constants and equilibrium coefficients must be estimated in most
toxic chemical studies. Although these can be calculated internally from
chemical properties and local environmental characteristics, site-specific
calibration or testing is desirable.
Some limitations should be kept in mind when applying TOXI4. First,
chemical concentrations should be near trace levels, i.e., below half the
solubility or 10"5 molar. At higher concentrations, the assumptions of
linear partitioning and transformation begin to break down. Chemical density
may become important, particularly near the source, such as in a spill.
Large concentrations can affect key environmental characteristics, such as pH
or bacterial populations, thus altering transformation rates. TOXI4 does not
include such feedback phenomena.
In the following development it is convenient to define concentration
related symbols as in Table 1.5.1.
102
-------
TABLE 1.5.1. CONCENTRATION RELATED SYMBOLS USED IN MATHEMATICAL EQUATIONS
Symbol
Definition
Units
Bj
m
sj
BJ
Concentration of total chemical in segment j.
Concentration of dissolved chemical in segment j.
Concentrationfof dissolved chemical in water in
segment j. CwJ = GWJ,
Concentration of sorbed chemical on sediment type
"s" in segment j.
Concentration of sorbed chemical on sediment type
"s" in segment j . C^ - CSJ/MSJ.
Concentration of DOC-sorbed chemical in segment j.
Concentration^ DOC-sorbed chemical in biota in
segment j. Cfij = CBJ/Bj
Concentration of sediment type "s" in segment j.
Concentration of sediment type "s" in segment j.
M». i n " 6
-? s= m^ . iu
Concentration of sediment type "s" in water in
in segment j. MJ - Mj/nj
Concentration of DOC in segment j.
Concentration of DOC in water in segment j
Bj - Bj/nj
Porosity or volume water per volume segment j.
Partition coefficient of chemical on sediment type
"s" in segment j.
Partition coefficient of chemical on DOC.
mgc/L
mgc/L
mgc/L
mgc/kgs
mgc/L
mgc/kgb
mgs/L
kgs/L
kgb/L
lonization
A chemical being modeled by TOXI4 is presumed to exist as a neutral or
unionized molecule that may, or may not, react with a water molecule to form
103
-------
singly and, possibly, doubly charged cations and anions. Such reactions may
be written as:
AH2 + H20 <--> AH^ + OH'
AH$ + H20 <--> Al^4"1" + OH"
AH2 + H20 <--> AH" + H30+
AH" + H20 <--> A" + H30+
1.5.1
1.5.2
1.5.3
1.5.4
The chemical may then exist in from one to a maximum of five forms simul-
taneously. Transformation and transfer reactions are separately specified
for each of the forms. The existance of any ionic species is specified by
a set of constants stored in vector SPFLG, as described in the users manual.
The ionization reactions are defined by equilibrium constants:
[AH$][OH-]
[AH2]
[AHJ+HOH-]
[AH|]
1.5.5
1.5.6
1.5.7
[AH2]
K
a2
1.5.8
[AH'
The functional dependence of these constants on temperature may be des-
cribed by the Van't Hoff equation:
-Ej/RT
or in logarithmic form:
log Kj. =
where:
2.3 RT
equilibrium constant
frequency factor
104
1.5.9
Ei
1.5.10
2.3 RT
-------
R
activation energy, kcal/mol
gas constant, kcal/°K-mol
temperature, °K
To describe the ionization reaction the user must specify-log(Ai) and E-. If
zero is specified for E±, -log^) is the pKaj^ of the reaction. The ionic
speciation data required by TOXI4 are summarized in Table 1.5.2.
TABLE 1.5.2. TOXI4 IONIZATION DATA
Description
Notation
Common S.I.
Range Units
Negative log of hydrogen ion activity [H+]
Negative log of ionization constants for acid
Negative log of ionization constants for base
Activation energy for ionization reactions
Water temperature
PH
PKai
PKbi
Ei
T
5-9
-
•
4-8 kcal/mole
4-30 °C
Equilibrium Sorption
Dissolved chemical in water column and benthic segments interacts with
sediment particles and dissolved organic carbon to form five phases--
dissolved, DOC-sorbed, and sediment-sorbed (three sediment types "s"). The
reactions can be written with respect to unit volume of water:
M.
w
Cs/n
CB/n
1.5.11
1.5.12
The forward reaction is sorption and the backward reaction is desorp-
tion. These reactions are usually fast in comparison with the model time
step, and can be considered in local equilibrium. The phase concentrations
Cw, Cs, and Cfi are governed by the equilibrium partition coefficients K^-ci
and KB (L/kg): Tsu
105
-------
Cs/n
MB
s
GW"
1.5.13
CB/n Cj
'*~ C?
1.5.14
cw
These equations give the linear form of the Freundlich isotherm,
applicable when sorption sites on sediment and DOC are plentiful:
Cs
CB "
Cw
cw
1.5.15
1.5.16
The partition coefficients depend upon characteristics of the chemical and
the sediments or DOC onto which sorption has occurred. Many organic pollu-
tants of current interest are non-polar, hydrophobic compounds whose parti-
tion coefficients correlate quite well with the organic fraction of the
sediment. Rao and Davidson (1980) and Karickhoff et al. (1979) have deve-
loped empirical expressions relating equilibrium coefficients to laboratory
measurements leading to fairly reliable means of estimating appropriate
values. The correlations used in TOXI4 are
" focs Koc
SB
- 1.0 K,
oc
1.5.17
1.5.18
where:
K
oc
organic carbon partition coefficient,
f — organic carbon fraction of sediment
1.0 — organic carbon fraction of DOC
If no log Koc values are available, one is generated internally using the
following correlation with the octanal-water partition coefficient KQW
K
oc
al
^ow
1.5.19
If a0 and a-i are not specified, default values of log 0.6 and 1.0 are
assumed.
The value of the partition coefficient is dependent on numerous factors
in addition to the fraction organic carbon of the sorbing particles. Of
these, perhaps the most potentially significant and the most controversial is
the effect of particle concentration, which was first presented by O'Connor
and Connolly (1980). Based on empirical evidence, O'Connor and Connolly
concluded that the partition coefficient was inversely related to the particle
106
-------
coricentration. Much research has been conducted to prove or disprove this
finding. At present, the issue remains contentious. A particle interaction
model has been proposed (Di Toro, 1985) which describes the effects of parti-
cle concentration. This model was shown to be in conformity with observa-
tions for a large set of adsorption-desorption data. At present, this should
be considered an empirical relationship. The equation defining partition
coefficient is:
1.5.20
1 +
X
where:
limiting partition coefficient with no particle
interaction (focs KQC for neutral organic chemicals)
solids concentration, kg/L
'x
ratio of adsorption to particle-induced desorption rate
Di Toro found that i/x was of order 1 over a broad range of chemical and solids
types. This formulation has been included in TOXI4. The user may include
the effect of particle concentration on adsorption by using a value of i/x of
order 1 (see Di Toro, 1985 for more detail); the effect may be eliminated by
specifying a large value.for i/x (a default value of 1012 is provided). If
i/x is specified to be 1.0, the model will predict a maximum particulate
fraction in the water column of 0.5 for all hydrophobic chemicals (K^s0Ms > 10)
For each chemical modeled, up to 20 partition coefficients are defined
representing the five species of chemical (neutral plus four ionic) and the
four sorbants (DOG and three types of solids). Normally, only a subset of
these would be used, as defined by those species and solids being modeled.
Sorption of the neutral chemical to DOC and the solids is defined by the fQC
of the sorbant (assumed to be 1 for DOC), the octanol-water partition
coefficient of the chemical (KQW), the user defined relationship between Row
and Koc, and the particle interaction parameter i/x values for .each species.
The input ionic species partition coefficients are used as the limiting
partition coefficients in equation 1.5.20.
The total chemical concentration is the sum of the five phase concen-
trations
C = c n + S CB Ms + Cg B
1.5.21
Substituting in equations 1.5.15 and 1.5.16, factoring, and rearranging terms
gives the dissolved fraction fD:
w
1 +
1.5.22
B'
+ S
s
107
-------
Similarly, the sediment-sorbed and DOC-sorbed fractions are
t i
/•» w V Kf
cs Ms Kps Ms
1 +KpB
JX-nT2 •
jj£)
1 + K^r>
s
B'
B' + S K,,.,
s • Ms
• Ma
1.5.23
1.5.24
These fractions are determined in time and space throughout a simulation
from the partition coefficients, internally calculated porosities, simulated
sediment concentrations, and specified DOC concentrations.
Given the total concentration and the five phase fractions, the dis-
solved, sorbed, and biosorbed concentrations are uniquely determined:
- C f
D
Cs - C fs
CB ~ C fB
1.5.25
1.5.26
1.5.27
These five concentrations have units of mg/L, and can be expressed as concen-
trations within each phase:
cw - Cw/n
B
CB/B
These concentrations have units of
1.5.28
1.5.29
1.5.30
, mg/kgs, and mg/kgfi, respectively.
In some cases, such as near discharges, the user may have to alter input
partition coefficients to describe the effect of incomplete sorption. As
guidance, Karickhoff and Morris (1985) found that typical sorption reaction
times are related to the partition coefficient:
- 0.03
1.5.31
where :
desorption rate constant, hr
Thus, compounds with high, medium, and low KQW's of 105, 103 , and 10 sorbing
onto 2% organic sediment should have reaction times of a day, a half hour,
and seconds. Given that time to equilibrium is roughly three times the
reaction time, the three compounds should reach equilibrium within 3 days, 1
hour, and 30 minutes.
108
-------
TOXI4 data specifications for sorption are summarized in Table 1.5.3,
TABLE 1.5.3. TOXI4 SORPTION DATA
Description
Suspended sediment concentration
Benthic sediment concentration
Dissolved organic carbon
Partition coefficient, phase i
Lumped metal distribution coefficient
Octanol -water partition coefficient
Organic carbon fraction, phase i
Particle interaction parameter
Common
Notation Range
ms 10-100
Mfi 0.5-2
DOC, B 0-10
Kpi lO-LlO5
KD 10° -105
Kow 10°-106
foci 0.005-0.5
i/x 1-1012
S.I.
Units
mg/L
kg/L
mg/L
L/kg
L/Kg
-
-
-
Kinetic Transformation
The various ionic species and phases of a chemical in water column and
benthic segments are subject to several transformation processes. Several
variables may be influencing each process, leading to a multi-term and often
non-linear lumped transformation rate. If a single process is dominant in a
homogeneous aquatic system, then a single rate constant may be sufficient to
describe the kinetic reaction:
Skc = "Kkc c
1.5.32
where;
Sfcc = total kinetic transformation rate for chemical c, g/m^-day
Kjy, = first order rate constant for process k, day"-*-
C = total concentration of chemical, mg/L (g/m )
If a half-life is entered, then it will be converted to a rate constant:
Kkc - 0.693/tHkc 1.5.33
109
-------
If multiple rate constants are entered, they will be added together:
'kc
Kkc G
1.5.34
For nonhomogeneous aquatic systems where rates vary in space, the user may
supply a spatially variable, lumped first-order rate constant K^c(x), so
that:
kc
1.5.35
For nonhomogeneous aquatic systems where rates may vary in space and time,
or for cases where rate constants are unknown or cannot be calibrated, TOXI4
uses the strategy implemented in the original Exposure Analysis Modeling
System (Burns et al., 1982). Each process is considered separately using
mixed second order kinetics:
C + [E]k ----> Pkc 1.5.36
where:
[E]k — the intensity of environmental property affecting process "k,"
such as light intensity or bacterial population
Pkc — transformation product for process k acting on chemical c
The reaction rate Skc in mg/L-day for process k acting on chemical c is:
£>kc *" *^kc t ^ J ic ^kc ^ 1.5.37
where:
kkc - second-order rate constant for process k on chemical c
Ykc — yield coefficient for production of chemical from process k acting
on chemical c; assumed to be -1 for production of chemical c by
itself
Given a local value for [E]k, a pseudo-first order rate coefficient Kkc in
day" can be specified:
Kkc - k
kc
1.5.38
For a compound undergoing several reactions, the lumped transformation reac-
tion is
ESS
k c
kc
1.5.39
The local first order assumption is generally accepted to be accurate
for most chemicals at environmental concentrations. The assumption is
invalid at concentrations near the solubility limit, however. If the user
110
-------
does not specify a maximum concentration CMAX(l), TOXI4 sets this limit at
half the solubility or 10"5 molar, whichever is less, and aborts the simula-
tion if concentrations exceed this value.
The individual transformation processes considered by TOXI4 are hydro-
lysis, photolysis, oxidation, and microbial degradation. In addition, vola-
tilization is calculated and added to the transformation rate. Good dis-
cussions of these processes have been published, for example Smith et al.
(1977), Burns et al. (1982), Mill et al. (1982), Mabey et al. (1982), and
Mills et al. (1985). The following sections summarize how TOXI4 calculates
the local rate constant for each of these processes. Input data requirements
are given for each process. The general kinetic data required by TOXI4 are
.summarized in Table 1.5.4.
TABLE 1.5.4. TOXI4
Description
First order rate constant for process
Half life for process "k"
Lumped first order rate constant
Chemical solubility
Water temperature
GENERAL KINETIC
Notation
•k" Kk
fcHk
}\rn
Sol
T
DATA
Range
0-10
0.07-00
0-10
10'6-106
4-30
Units
day'1
days
day'1
mg/L
°C
Hydrolysis
Hydrolysis, or reaction of the chemical with water, is known to be a
major pathway for degradation of many toxic organics. An example reaction is
shown in Figure 1.5.3. The reaction can be catalyzed by hydrogen ions or
proceed by consuming hydroxide ions. Figure 1.5.4 illustrates the effects of
base hydrolysis on carbaryl, neutral hydrolysis on chloromethane, and acid
and base hydrolysis on 2,4-D.
In TOXI4, hydrolysis by specific-acid-catalyzed, neutral, or base path-
ways is considered for the various species and phases of each chemical:
^HN
1.5.40
Hffl
K,
•HOH
2 S k
I j
aij
S S kbij [OH'] fj
1.5.41
1.5.42
111
-------
where:
K
•HN
— net neutral hydrolysis rate constant, day
-1
- net acid catalyzed hydrolysis rate constant, day
-1
KHOH
fc
-1
"1
net base catalyzed hydrolysis rate constant, day
:bii ~ specific acid catalyzed and base rate constants for ionic
specie i-in phase j, respectively, molar" day"
kjjji - neutral rate constant for ionic specie i in phase j , day
fji — fraction of chemical as ionic specie i in phase j
TOXI4 hydrolysis data specifications are summarized in Table 1.5.5. The
reaction coefficients can be specified as constants, with activation energy
constants left as 0. If the user wants TOXI4 to determine rates based on the
temperature-based Arrhenius function, then non-zero activation energies
specified as constants will invoke the following calculation for each rate
constant k.
HYDROLYSIS
NEUTRAL
ACID-
CATALYSIS
BASE-
CATALYSIS
H
H2O
OH"
P5
> P + P'
EXAMPLE
+H2NCH3 + C02
oarbaryl + water—^ naphthanol + methylamine + carbon dioxide
Figure 1.5.3. Hydrolysis reactions.
112
-------
-1
-5
-6
CH,
CH,
_c, Ta A
2 *0-CH2-CHj-0-CH/
Carbaryl
O Chloromethane
A 2.4-D (2-butoxyethyl
ester)
PH
Figure 1.5.4. pH dependence of hydrolysis rate constants.
k(Tk) -
where:
Tk =
TR -
EaH -
R
1000 -
k(TR) exp[1000 E^CTk,- TR)/(RTkTR)]
1.5.43
water temperature, °K
reference temperature for which reaction rate is reported, °K
Arrhenius activation energy for hydrolysis reaction, kcal/mole
1.99 cal/mole °K
cal/kcal
113
-------
TABLE 1.5.5. TOXI4 HYDROLYSIS DATA
Description
Negative log of hydrogen ion activity [H+]
Acid hydrolysis rate constant for specie i,
phase j
Neutral hydrolysis rate constant for specie
phase j
Base hydrolysis rate constant for specie i,
phase j
Water temperature
Activation energy for hydrolysis reaction
for specie i
Notation
pH
kHAij
*•> kHNij
kHBij
T
EaHi
Range
5-9
0-107
0-102
0-107
4-30
15-25
Units
-
L
mole[H+]
day"1
L
mole [ OH";
°C
kcal
mole °C
day
1 day
Activation energies may be specified for each ionic specie and each hydroly-
sis reaction (acid, neutral, base) simulated. If no activation energies are
given, then rates constants will not be adjusted to ambient water tempera-
tures. . >
Photolysis
Photolysis is the transformation of a chemical due to absorption of
light energy. An example of several photochemical pathways is given in
Figure 1.5.5. The first order rate coefficient for photolysis can be calcu-
lated from the absorption rate and the quantum yield for each ionic specie
and phase:
S S kaij
1.5.44
where:
first order photolysis rate coefficient at reference light
intensIty, day
specific sunlight absorption rate for specie i, E/mole-day or
(E/L)/(mole/L)/day
114
-------
PHOTOLYSIS
Photochemical pathways of an excited molecule
A,4httt
Ch*mic*t n*ctfon
Chemical mction
A0 - ground state of reactant molecule
A*— excited state
Qo — ground state, of, quenching molecule
Q* — excited state
PHOTOCHEMICAL PATHWAYS OF AN EXCITED MOLECULE.
EXCITED MOLECULES DO NOT ALV/AYS CHEMICALLY REACT.
Figure 1.5,5. Photolysis reactions,
115
-------
^i — reaction quantum yield for specie i in phase j , mole/E
f.j* — fraction of chemical as specie i in phase j
The specific sunlight absorption rate is the integral or summation over
all bandwidths of the average light multiplied by the molar absorptivity
and the optical path:
kai
IGk ekid (2303) (86400)/(6.022 x 10
23
1.5.45
where :
•"-Gk
£ki -
d
2303 -
' o
average light intensity of wavelength k, photons/cm -sec
decadic molar absorptivity of wavelength k by specie i,
L/mole-cm-ln 10
optical path, cm/cm
,,3
cm
In 10
In e
86400 - sec/day
6.022 x 1023 - Avagadro's number, photons/E
The user may specify that the model calculate the first order photolysis
rate constant using equations 1.5.44 and 1.5.45 or the user may provide a
near water surface rate (for presumed cloudless conditions). If the user
supplied rate constant is representative of conditions at a location other'
than the water body being modeled, the model corrects the rate for the
difference in latitude between the two and any difference in cloud cover.
To calculate the rate constant, the model divides the wavelength spectrum
between 280 and 800 nm into 46 intervals. For each interval the user must
specify a molar absorptivity. The light intensity at each of the 46 wave-
lengths is internally calculated from the location of the water body (i.e.,
latitude), the time of year, and the atmospheric conditions (air mass type,
relative humidity, atmospheric turbidity and ozone content, cloudiness). The
location and time of year are used to define the light intensity at the outer
edge of the atmosphere. The atmospheric conditions are used to define the
light decay through the atmosphere. The light intensities and the molar
absorptivities are used with a user defined optical path (d) to calculate the
specific sunlight absorption rate (see equation 1.5.46). The first order rate
constant is then calculated using equation 1.5.45. This calculation was
taken directly from EXAMS II (Burns and Cline, 1985) and is based on formula-
tions published by Green, Cross and Smith (1980).
The photolysis rate constants for each water column segment are deter-
mined from the calculated or input near-surface rate constant and the
116
-------
rate of light decay in the water column (Ke). Ke may be specified by the
user as a segment parameter or internally calculated. If the near-surface
photolysis rate constant has been calculated, Ke values are also calculated
by the model. The formulation used was taken from EXAMS II:
where:
K
ew
CHL
DOC
m
1.5.46
Kew = pure water extinction coefficient, 1/m
CHL = phytoplankton chlorophyll concentration, mg/L
DOC = dissolved organic carbon concentration, mg/L
m = solids concentration, mg/L
*?1> *?2' *?3 = specific extinction coefficients, L/mg-m
Values of Kew, y^, »/2> *?3 f°r each of the 46 wavelengths are supplied in
the program as data statements in subroutine BEER and are shown in Table
1.5.6. Segment average photolysis rate constants are computed for each wave-
length and then summed to yield an overall rate.
For a user supplied near surface photolysis rate constant, a user supplied
Ke value is used. If a zero value is specified for Kg then a value is computed
from equation 1.5.46 using coefficient values at the user specified wavelength
of maximum light absorption.
TABLE 1.5.6.
WAVELENGTH INTERVALS AND SPECIFIC LIGHT EXTINCTION
COEFFICIENTS USED IN THE PHOTOLYSIS CALCULATION.
VALUES TAKEN FROM EXAMS II (BURNS AND CLINE, 1985)
Number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Wavelength
nm
280.0
282.5
285.0
287.5
290.0
292.5
295.0
297.5
300.0
302.5
305.0
307.5
310.0
312 . 5
315.0
317.5
Specific Light Extinction Coefficients
Pure Water Chlorophyll DOC Solids
1/m L/mE-m L/mE-m L/me-m
0.288
0.268
0.249
0.231
0.215
0.194
0.174
0.157
0.141
0.133
0.126
0.119
0.105
0.0994
0.0952
0.0903
145.
138.
132.
126.
120.
115.
109.
106.
101.
95.
90.
85.
80.
78.
75.
72.
7.90 0.34
7.65
7.41
7 . 18
6.95
6 . 73
6.52
6 . 30
6 . 12
5.94
5.76
5.57
5.39
5.22
5.06 »
4.90
117
-------
TABLE 1.5.6.
WAVELENGTH INTERVALS AND SPECIFIC LIGHT EXTINCTION
COEFFICIENTS USED IN THE PHOTOLYSIS CALCULATION.
VALUES TAKEN FROM EXAMS II (BURNS AND CLINE, 1985)
(Continued)
Number
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
Wavelength
nm
320.0
323.1
330.0
340.0
350.0
360.0
370.0
380.0
390.0
400.0
410.0
420.0
430.0
440.0
450.0
460.0
470.0
480.0
490.0
503.75
525.0
550.0
575.0
600.0
625.0
650.0
675.0
706.25
750.0
800.0
Specific Light Extinction Coefficients
Pure Water Chlorophyll DOC Solids
1/m L/mg-m L/mg-m L/mg-m
0.0844
0.0793
0.0678
0.0561
0.0463
0.0379
0.0300
0.022C
0.0191
0.0171
0.0162
0.0153
0 . 0144
0.0145
0.0145
0.0156
0.0156
0.0176
0.0196
0.0295
0.0492
0.0638
0.0940
0.244
0.314
0.349
0.440
0.768
2.47
2.07
70.
68.
64.
59.
55.
55.
51.
46.
42.
41.
39.
38.
35.
32.
31.
28.
26.
24.
22.
19.
14.
10.
8.
6.
5.
8.
13.
3.
2.
0.
4.74 0.34
4.56
4.17
3 . 64
3 . 15
2 . 74
2 . 34
2 . 00
1 . 64
1.39
1.19
1.02
0.870
0.753
0.654
0.573
0 . 504
0.444
0.396
0.357
0.282
0.228
0.188
0.158
0.0
0.0
0.0
0.0 "
0.0
0.0
Light extinction is calculated with the integrated Beer-Lambert formulation:
m
- exp(-d Ke D)
. 1.5.47
d Ke D
118
-------
where:
K,
D
spatially variable light extinction coefficient, m"
depth of water segment, m
The time variable surface light relative to the reference light is input as
time function PHTON. This can be used to represent diurnal or seasonal
changes. TOXI4 photolysis data specifications are summarized in Table 1.5.7.
TABLE 1.5.7. TOXI4 PHOTOLYSIS DATA
Description
Observed rate constant for a chemical
under reference light intensity IQ
Fraction of reference light averaged
through water column
Reference light intensity causing
photolysis rate KpG
Surface light intensity
Cloud cover, fraction of sky
Cloud cover reduction factor
Light extinction coefficient in
water column
Chlorophyll a concentration
Dissolved organic carbon
Depth of water column segment
Reaction quantum yield fraction
for specie i in phase j
Molar absorptivity by wavelength
k by specie i
Notation Range
KpG 0-10
[L] 0-1
IG 10-7-2xlO'6
I0 10"7-2xlO'6
CG 0-1
CR 0.3-0.7
Ke 0.1-5
CHL lO^-lO'1
DOC 0-10
D 0.1-10
^y 0-0.5
eki 0-
Units
day'1
-
f\
E/cm -sec
0
E/cm -sec
m'1
mg/L
mg/L
m
moles/E
L/mole-
cm-ln 10
119
-------
Oxidation
Chemical oxidation of organic toxicants in aquatic systems can be a
consequence of interactions between free radicals and the pollutants. Free
radicals can be formed as a result of photochemical reactions. Free radicals
that have received some attention in the literature include alkylperoxy
radicals, RC^.; OH radicals; and singlet oxygen.
In TOXI4, oxidation is modeled as a general second-order process for
the various species and phases of each chemical:
K0 - [R02] S S koij
where:
1.5.48
K.
o
[R02] -
koij -
net oxidation rate constant, day"
molar concentration of oxidant, moles/L
second order oxidation rate constant for chemical as specie
i in phase j, L/mole-day
The reaction coefficients may be specified as constants, with activation
energy constants left as 0. If the user wants TOXI4 to determine rates based
on the temperature based Arrhenius funtion, then non-zero activation energies
specified as constants will invoke the following calculation for each rate
constant k:
k(Tk) - k(TR) exp[1000 Eao(Tk - TR)/(RTk TR)
1.5.49
where:
Arrhenius activation energy for oxidation reaction, kcal/mole
Activation energies may be specified for each ionic specie simulated. If no
activation energies are given, then rate constants will not be adjusted to
ambient water temperatures.
Because of the large number of alkylperoxy radicals that potentially
exist in the environment, it would be impossible to obtain estimates of kQX
for each species. Mill et al. (1982) propose estimation of a rate coeffi-
cient using t-butyl hydroperoxide as a model oxidizing agent. They argue
that other alkylperoxides exhibit similar reactivities to within an order of
magnitude. The second-order rate coefficients are input to TOXI4 as con-
stants.
In addition to estimating a rate coefficient, an estimate of free radi-
cal concentrations must be made to completely define the expression for free
radical oxidation. Mill et al. (1982) report R02 concentrations on the order
of 10"y M and OH concentrations on the order of 10"^ M for a limited number
of water bodies. Zepp et al. (1977) report an average value on the order of
M for singlet oxygen in water bodies sampled. The source of free radi-
10
120
-------
cals in natural waters is photolysis of naturally occurring organic molecules.
If a water body is turbid or very deep, free radicals are likely to be gene-
rated only near the air-water interface, and consequently, chemical oxidation
will be relatively less important. In such cases, the concentrations cited
above are appropriate in only the near-surface zones cif water bodies. The
molar oxidant concentrations are input to TOXI4 using parameter OXRADG (ISEG).
TOXI4 oxidation data specifications are summarized in Table 1.5.8.
TABLE 1.5.8. TOXI4 OXIDATION DATA
Description
Notation Range
Units
Oxidation rate constant for specie i,
phase j
Activation energy fo-r oxidation of
specie i
Water temperature
Concentration of oxidants
Koi
Eaoi
T
[R02]
15-25
L/mole-day
kcal/mole
4-30 ' °C
10"17-10'8 moles/L
Bacterial Degradation
Bacterial degradation, sometimes referred to as microbial transformation,
biodegradation or biolysis, is the breakdown of a compound by the enzyme
systems in bacteria. Examples are given in Figure 1.5.6. Although these
transformations can detoxify and mineralize toxins and defuse potential
toxins, they can also activate potential toxins.
Two general types of biodegradation are recognized--growth metabolism
and cometabolism. Growth metobolism occurs when the organic compound serves
as a food source for the bacteria. Adaptation times from 2 to 20 days were
suggested in Mills et al., 1985. Adaptation may not be required for some
chemicals or in chronically exposed environments. Adaptation times may be
lengthy in environments with a low initial density of degraders (Mills et
al., 1985). For cases where biodegradation is limited by the degrader popu-
lation size, adaptation is faster for high initial microbial populations and
slower for low initial populations. Following adaptation, biodegradation
proceeds at fast first-order rates. Cometabolism occurs when the organic
compound is not a food source for, the bacteria. Adaptation is seldom neces-
sary, and the transformation rates are slow compared with growth metabolism.
121
-------
(Pote-tial Toxin)
o(c:n2)3cooH
— Cl
(Less Toxic 5ubstan.es)
OH
CI
OCH2CH,OSO3H
-C!
C!
(Potential Toxin)
cr, * :-:,3 f ci"
Figure 1.5.6. Microbial transformations of toxic chemicals
(Alexander 1980).
In TOXI4, first order biodegradation rate constants or half lives for
the water column and the benthos may be specified. If these rate constants
have been measured under similar conditions, this first order approach is
likely to be as accurate as more complicated approaches. If first order
rates are unavailable, or if they must be extrapolated to different bacterial
conditions, then the second-order approach may be used. It is assumed that
bacterial populations are unaffected by the presence of the compound at low
concentrations. Second-order kinetics for chemical in the water column and
the bed are considered:
^Bw
Bwij
1.5.50
122
-------
K
•Bs
Pbac
net biodegradation rate constant in water segment, day
-1
= net biodegradation rate constant in benthic segment, day
— second order biodegradation rate constant for specie i,
phase j in water segments, ml/cell-day
= second order biodegradation rate constant for specie i,
phase j in benthic segments, ml/cell-day
= active bacterial population density in segment, cell/ml
= fraction of chemical as specie i in phase j
-1
TOXI4 biodegradation data specifications are summarized in Table 1.5.10.
The second order rate constants for water and for bed segments can be speci-
fied as constants. Temperature correction factors can be left at 0. If the
user wants TOXI4 to correct the rate constants for ambient segment tempera-
tures , then nonzero temperature correction factors specified as constants
will invoke the following modification for each rate constant kg.
TABLE 1.5.10. TOXI4 BACTERIAL DEGRADATION DATA
Description
Notation Range
Units
Observed first order degradation rate in
water column
Observed first order degradation rate in
benthos
Bacterial activity or concentration of
bacterial agent
Observed second-order rate coefficients for
specie i, phase j in water and benthos
Biodegradation temperature coefficients
for specie i, phase j in water and benthos
Water temperature
K
Bw
K
Bs
bac
Bsij
QTwij
QTsij
0-0.5
0-0.5
>-6
1.-5-2.5
4-30
day
-1
day
-1
102-107 cells/mL
mL/cell-day
123
-------
(T)
1.5.52
(T)
where:
1.5.53
- "Q-10" temperature correction factor for blodegradation of
specie i, phase j in water
Qlsij ™ "Q-10" temperature correction factor for biodegradation of
specie i, phase j in benthic segments
T - ambient temperature in segment, °C
The temperature correction factors represent the increase in the biodegra-
dation rate constants resulting from a 10°C temperature increase. Values
in the range of 1.5 to 2 are common.
Total bacterial populations for water and benthic segments are input
using parameter BACTOG(ISEG). Typical population size ranges are given in
Table 1.5.11. Time functions that multiply the water and benthic segment
populations are input using functions BACNW and BACNS. The product of para-
meter BACTOG and these time functions gives a description of the time- and
space-variation of bacterial populations. If the time functions are omitted,
populations remain constant in time.
Environmental factors other than temperature and population size can
limit bacterial rates. Potential reduction factors must be considered
externally by the user. Nutrient limitation can be important in oligotrophic
environments. The following reduction factor was used by Ward and Brock
(1976) to describe phosphate limitation of hydrocarbon degradation:
EP04
where:
0.0277 Cpo4
1.5.54
1 + 0.0277 C
P04
JP04
dissolved inorganic phosphorus concentration, ug/L
This adjustment must be made to the input rate constants by the user for
situations of nutrient limitation. Low concentrations of dissolved oxygen
can cause reductions in biodegradation rates. Below DO concentrations of
about 1 rag/L, the rates start to decrease. When anoxic conditions prevail,
most organic substances are biodegraded more slowly. Because biodegradation
reactions are generally more difficult to predict than physical and chemical
reactions, site-specific calibration becomes more important. TOXI4 allows
several methods to correct rates to reflect field data.
124
-------
TABLE 1.5.11. SIZE OF TYPICAL BACTERIAL POPULATIONS IN NATURAL WATERS
Water Body Type
Bacterial Numbers (cells/ml)
Ref.
Oligotrophic Lake
Mesotrophic Lake
Eutrophic Lake
Eutrophic Reservoir
Dystrophic Lake
Lake Surficial Sediments
40 Surface Waters
Stream Sediments
Rur River (winter)
50 - 300
450 - 1,400
2000 - 12,000
1000 - 58,000
400 - 2,300
8xl09 - 5xl010 cells/100 g dry wt
500 - IxlO6
107 - 108 cells/100 g
3xl04
References:
aWetzel (1975). Enumeration techniques unclear.
Paris et.al. (1981). Bacterial enumeration using plate counts.
cHerbes & Schwall (1978). Bacterial enumeration using plate counts.
Larson et al. (1981). Bacterial enumeration using plate counts.
Volatilization
Volatilization is the movement of chemical across the air-water inter-
face. The dissolved neutral concentration attempts to equilibrate with the
gas phase partial pressure, as illustrated in Figure 1.5.7. The equation in
this figure shows that equilibrium occurs when the dissolved concentration
equals the partial pressure divided by Henry's Law Constant. In most cases,
organic toxicants in the atmosphere are at much lower.levels than partial
pressures equilibrated with water concentrations. Consequently, volatiliza-
tion reduces to a first-order process with a rate proportional to the con-
ductivity and surface area divided by volume:
125
-------
where :
V
w
at
kv
D
(cw-
H/RT
Cw = DISSOLVED CONCENTRATION IN WATER, /ig/L
Ca = CONCENTRATION IN AIR, /
-------
D
average depth of the segment, m
D
dissolved fraction of the chemical
The value of ky., the conductivity, depends on the intensity of turbu-
lence in a water body and in the overlying atmosphere. Mackay and Leinonen
(1975) have discussed conditions under which the value of k^. is primarily
determined by the intensity of turbulence in the water. As the Henry's Law
coefficient increases, the conductivity tends to be increasingly influenced
by the intensity of turbulence in water. As the Henry's Law coefficient
decreases, the value of the conductivity tends to be increasingly influenced
by the intensity of atmospheric turbulence.
Because Henry's Law coefficient generally increases with increasing
vapor pressure of a compound and generally decreases with increasing solubi-
lity of a compound, highly volatile low solubility compounds are most likely
to exhibit mass transfer limitations in water and relatively nonvolatile high
solubility compounds are more likely to exhibit mass transfer limitations in
the air. Volatilization is usually of relatively less magnitude in lakes and
reservoirs than in rivers and streams.
In cases where it is likely that the volatilization rate is regulated
by turbulence level in the water phase, estimates of volatilization can
be obtained from results of laboratory experiments . As discussed by Mill
et al. (1982), small flasks containing a solution of a pesticide dissolved
in water that have been stripped of oxygen can be shaken for specified
periods of time. The amount of pollutant lost and oxygen gained through
volatilization can be measured and the ratio of conductivities (KVOG) for
pollutants and oxygen can be calculated. As shown by Tsivoglou and Wallace
(1972) , this ratio should be constant irrespective of the turbulence in a
water body. Thus, if the reaeration coefficient for a receiving water body
is known or can be estimated and the ratio of the conductivity for the pollu-
tant to reaeration coefficient has been measured, the pollutant conductivity
can be estimated.
In TOXI4, the dissolved concentration of a compound in a surface water
column segment can volatilize at a rate determined by the two -layer resis-
tance model (Whitman, 1923) , where the conductivity is the reciprocal of the
total resistance:
1.5.56
where :
R
K
RG
KG
liquid phase resistance, day/m
liquid phase transfer coefficient, m/day
gas phase resistance, day/m
gas phase transfer coefficient, m/day
127
-------
The two-resistance method assumes that two "stagnant films" are bounded
on either side by well mixed compartments. Concentration differences serve
as the driving force for the water layer diffusion. Pressure differences
drive the diffusion for the air layer. From mass balance considerations, it
is obvious that the same mass must pass through both films, thus the two
resistances combine in series. There is actually yet another resistance
involved, the transport resistance between the two interfaces, but it is
assumed to be negligible. This may not be true in two cases: very turbulent
conditions and in the presence of surface active contaminants. Although this
two-resistance method, the Whitman model, is rather simplied in its assump-
tion of uniform layers, it has been shown to be as accurate as more complex
models. Laboratory studies of volatilization of organic chemicals confirm
the validity of the method as an accurate predictive tool (Burns et al.,
1982).
The model allows the user maximum flexibility in specification of the
volatilization rate. The volatilization rate may be input directly or it may
be calculated using one of two semi-theoretical formulations. If the
volatilization rate is calculated, the liquid transfer resistance may be
computed from an input oxygen reaeration rate or it may be calculated from
characteristics of the chemical and the water body.
If a reaeration rate is provided, the liquid phase transfer coefficient
KL (1/R^) Is calculated as
KL ~ KLQ
K-
L0
732/MW
1.5.57
where:
KT
— reaeration velocity, m/d
MW
— ratio of volatilization rate to reaeration rate
— molecular weight of the chemical, g/mole
If a reaeration rate is not provided, the calculation of K^ depends on
the water body type (constant 2) and the velocity and depth of the segment.
For a flowing system (type 0) the transfer coefficients are controlled by
flow induced turbulence. K^ is computed by one of three equations, based on
the Covar method (Covar, 1976). For segments with depths less than 0.61 m
the Owens formula is used to calculate the reaeration rate:
u
0.67
K
= 5.349
1.5.58
128
-------
where:
u = velocity of the water, m/s
D = segment depth, m
KL is then calculated from equation 1.5.57. For segments with a velocity
less than 0.518 m/s or a depth (m) greater than 13.584 u2'9135, the O'Connor-
Dobbins formula is used:
(w \
t)
8.64 x 104
1.5.59
where:
Dw = diffusivity of the chemical in water (internally calculated) (m/s)
In all other cases, the Churchill formula is used to calculate reaeration
rate: ' '
u
0.969
5.049
D0.673
1.5.60
The gas transfer coefficient (KG) is assumed constant at 100 m/day for flowing
systems.
For lake and reservoir systems (type 1), the transfer coefficients are
controlled by the wind velocity. Formulations presented by O'Connor (1983)
and Mackay (1985) have been incorporated in the model. The user chooses
which will be used. The O'Connor equations are:
0.5 ,,0.33
Scw
-0.67
1.5.61
,0.33
KG
1.5.62
where:
u*
W
10
shear velocity (m/s) = cd ~* W10
drag coefficient = 0.0011
wind velocity 10m above water surface, m/s
129
-------
Pa'
K
Sca, Scw -
Q
density of air and water, kg/m
von Karmen's constant =0.74
dimensionless viscous sublayer thickness
air and water Schmidt Numbers = u
pD
viscosity, kg/m-sec
= 4
The Mackay equations are:
KT
10'6 + 0.00341 u* Scw'°-5 u* > .3 m/s
1.5.63
KL - 10'6 + 0.0144 u|'2 Scw-°-5 u* < .3 m/s
1.5.64
Kg - 10'3 + 0.0462 u* Scw-0-67
1.5.65
The input or computed volatilization rate constant is for a temperature
of 20 degrees C. It is adjusted for segment temperature using the equation:
3T-20
1.5.67
where:
9 — user input temperature correction factor
T — temperature °C
Although there are many calculations involved in determining volatili-
zation, most are performed internally using a small set of data. TOXI4
volatilization data specifications are summarized in Table 1.5.12. Not all
of the constants are required. If Henry's Law constant is unknown, it will
be calculated internally from vapor pressure and solubility. If k^ is not
measured, it will be calculated internally from molecular weight.
Extra Reaction
TOXI4 allows the user to specify an additional second order reaction for
the various species and phases of each chemical:
130
-------
TABLE 1.5.12. TOXI4 VOLATILIZATION DATA
Description
Measured or calibrated conductance
Henry's Law Constant
Partial pressure of chemical in
atmosphere
Molecular weight
Reaeration coefficient (conductance
of oxygen)
Experimentally measured ratio of
volatilization to reaeration
Current velocity
Water depth
Water temperature
Wind speed 10 m above surface
Notation Range
ky. 0.6-25
H lO'^-lO'^
P 0-0.1
Mtf 10-103
kLQ2 0.6-25
^vo O'1
Ux 0-2
D 0.1-10
T 4-30
W1Q 0-20
tnits
m/day
atm
(mole/m )
atm
g/mole
m/day
m/sec
. m
°C
m/sec
where:
*E
[E]
keij
K
[E] E E k
i j
eij
net extra reaction rate constant, day
-1
1.5.67
intensity of environmental property driving this, reaction
second order rate constant for chemical as specie i in
phase j, in [E] day"
fjj = fraction of chemical as specie i in phase j
An example of a kinetic process that may be modeled as this extra reaction is
reduction. If reduction is- modeled, [E] may be interpreted as the concentra-
tion of environmental reducing agents RH2, so that -^
131
-------
C + RHr
1.5.68
and
[E] — concentration of RH2, moles/L
ke — second order rate constant, L/molerday
P — reduced product
The identity of the reducing agent and the second order rate constant must be
identified and quantified by laboratory kinetics studies. If both the
environmental oxidizing and reducing agents are in excess, then two chemicals
may be simulated as a redox pair:
where:
C-L + R02 <* C2 + RH2 1.5.69
reduced chemical
oxidized chemical
oxidizing agent
reducing agent
Laboratory kinetics studies can control the concentrations of RC>2 and RH2 to
determine rate constants for both oxidation and reduction. These may be
specified as constants kox and kg. Yield coefficients YQ12 and YE21 must
also be specified as constants. The spatially variable concentrations
and [RHo] must ^e specified as parameters.
R02 -
Heavy Metals
Although TOXI4 was .designed explicitly for organic chemicals, it can be
used to simulate metals with judicious specification of certain key para-
meters. Because of the inherent complexity of metals behavior, site-specific
calibration is required. Physical processes affecting the fate of metals in
rivers are illustrated in Figure 1.5.8.
Heavy metals in the aquatic environment can form soluble complexes with
organic and inorganic ligands, sorb onto organic and inorganic particulates,
and precipitate or dissolve (Figure 1.5.9). Geochemical models such as
MINTEQAl (Brown et al., 1987) can be used to predict metal speciation for a
set of chemical conditions. These calculations can then be used to para-
meterize and interpret TOXI4 data. TOXI4 lumps all soluble complexes with the
free ion to give the dissolved metal concentration. Precipitated metal is
lumped with all sorbed species to give particulate "sorbed" metal concentra-
tion. A spatially variable lumped partition coefficient K_ describes the two
phases. There is no general consistency in reported Kp values for particular
metals in the natural environment, so site-specific values should be used when
possible. Partition coefficients should depend upon the sorbent character,
132
-------
including mineralogy, chemical structure, composition and electrical proper-
ties, presence of coatings, and the age and origin of humic substances pre-
sent. Table 1.5.13 summarizes K^ values reported in Delos et al. (1984) for
eight metals. These values are generally high, and are provided as a starting
point for the user. Spatially-variable 1C values can be input to TOXI4 using
parameter FOC(ISEG,'I) omitting all other partitioning parameters.
SORPTION
-DESORPTION
WITH SEDIMENTS
DISSOLVED
ik .."*•'
PAHTICULATE
Figure 1.5.8. Processes influencing the fate of metals in rivers
(Mills et al., 1985).
133
-------
SOLUBLE COMPLEXES
WITH ORGANIC LIGANDS
SOLUBLE COMPLEXES
WITH INORGANIC
LIGANDS
ADSORBED SPECIES
« ADSORPTION/COPRECIPITATION ON
HYDROUS IRON/MANGANESE OXIDES
• ION EXCHANGE
• ADSORPTION TO CLAYS, SILICATES.
OTHER MINERALS
• ADSORPTION TO ORGANIC SOLIDS
Figure 1.5.9. Speciation of metals in aquatic
environment (Felmy et al., 1984).
Variable Complexity Levels
TOXI4 can be implemented at various levels of complexity to analyze toxi-
cant transport and fate problems. These different levels involve increasing
sophistication in solids behavior, equilibrium reactions, and kinetic reac-
tions. Solids behavior may be modeled at four levels of complexity: 1.
descriptive solids concentration field, 2. descriptive solids concentration
field with specified solids transport rates, 3. simulated total solids, and
4. three simulated solids types. Equilibrium reactions may be modeled at
five levels of complexity: 1. constant partition coefficient, 2. spatially
variable partition coefficients, 3. hydrophobic sorption, 4. solids-dependent
partitioning, and 5. sorption plus ionic speciation. Kinetic reactions may
be modeled at four levels of complexity: 1. constant half lives or rate
constants, 2. spatially variable rate constants, 3. second order rates, and
4. second order rates with transformation products. Each of these levels is
discussed in detail in the following section.
134
-------
TABLE 1.5.13. SPECIATION OF PRIORITY METALS BETWEEN DISSOLVED AND ADSORBED
PHASES AS A FUNCTION OF SUSPENDED SOLIDS CONCENTRATIONS IN STREAMS
Metal
Arsenic
Cadmium
Chromium
Copper
Lead
Mercury
Nickel
Zinc
SS(mg/L)
1
10
100
1000
1
10
100
1000
1
10
100
1000
1
10
100
1000
1
10
100
1000
1
10
100
1000
1
10
100
1000
1
10
100
1000
Kp(L/kg)
5xl05
9xl04
2xl04
3xl03
4xl06
3xl05
2xl04
2xl03
3xl06
4xl05
5xl04
5xl03
IxlO6
2xl05
3xl04
UAi.,
3xl05
2xl05
IxlO5
9xl04
3xl06
2xl05
2xl04
IxlO3
5xl05
IxlO5
4xl04
9xl03
IxlO6
2xl05
5xl04
IxlO4
%Dissolved
70
50
30
24
20
25
30
40
25
20
17
15
50
30
25
14
75
30
10
1
25
30
30
45
70
50
20
10
40
30
17
10
%Adsorbed
30
SO
•J \S
70
76
80
75
70
60
75
80
U V
83
\J ^J
85
50
70
/ V/
75
86
25
70
90
99
75
70
70
55
30
50
80
90
60
70
83
90
135
-------
The increasing complexity levels allow better description and extrapola-
tion of the solids, equilibrium, and kinetic reactions. The increased model
capability requires specification of more input data. Although it is quicker
and easier to simulate at the lower levels of complexity, the decreased model
capability requires more judgment on the part of the user. Consider analyz-
ing a problem where a dissolved ionic specie of a transformation product is
extremely toxic. Useful simulations of this problem using a low complexity
level would be very difficult. For best results, the user must match the
complexity of the model with the requirements of the problem.
In the following subsections, specific model input variable names and
options are mentioned. The user should refer to the user manual section for
their explanations.
Solids behavior--
Level 1--The simplest level for solids is to specify an average concen-
tration field. This is done by setting the initial conditions for system 2
to the average observed concentrations and setting SYSBY(2) to 1. Solids
concentrations will,then influence chemical partitioning and, indirectly,
transport and transformation.
Level 2--The next level for solids is to specify an average concentra-
tion field along with settling, deposition, scour, and sedimentation veloci-
ties. As before, initial conditions for system 2 are set to average sediment
concentrations and SYSBY(2) is set to 1. Solids transport velocities are
specified in transport field 3. Solids concentrations will directly influence
chemical partitioning; solids transport velocities will directly influence
particulate chemical transport.
Level 3--The third level for solids is to simulate total solids. Loads,
boundary concentrations, and initial conditions are specified for system 2.
Solids settling, deposition, scour, and sedimentation velocities are speci-
fied in transport field 3. Solids concentrations can be calibrated to ob-
served data, leading to more accurate calculations of particulate chemical
transport.
Level 4--The fourth level for solids is to simulate three sediment types.
Loads, boundary concentrations, and initial conditions are specified for
systems 2, 3, and 4. Solids settling, deposition, scour, and sedimentation
velocities are specified in transport fields 3, 4, and 5. Solids concentra-
tions by type can be calibrated to observed data, leading to more accurate
calculations of chemical partitioning and transport.
Equilibrium reactions--
Level l--The simplest equilibrium reaction is described by a single
constant partition coefficient. This is done by specifying a value for
PIXG(l.l) and omitting all other partitioning information--LKOW, LKOC, and
136
-------
FOC(ISEG,1). Although the partition coefficient is constant, the dissolved and
sorbed chemical fractions vary with sediment concentrations:
%
fs
(1 +
Mj/n)'
1.5.70
1.5.71
where:
n
partition coefficient, L/kg
solids concentration, kg/L
porosity
Porosity is calculated by TOXI4 using input sediment density DSED(2) and
sediment concentration:
n = 1 - (M-L/DSEDC2))
1.5.72
where:
DSED(2) - sediment density, specified under initial conditions, kg/L
Level 2--The next level for equilibrium reactions is to specify spa-
tially-variable partition coefficients. This is done by. supplying K^ values
to parameter FOC(ISEG, 1) and omitting all other partitioning information--
LKOW, LKOC, and PIXC(1, 1). The equations used by TOXI4 are as described in
the paragraph above. This option allows more precise site-specific calibra-
tion of partition coefficients to observed dissolved to particulate chemical
ratios.
Level 3--The third level of complexity for equilibrium reactions pre-
dicts spatially-variable K^ values for hydrophobic sorption. This is done by
specifying values for FOC(1,ISEG) and LKOC or LKOW. If values for DOC(ISEG)
are specified, then TOXI4 will also calculate sorption to dissolved organic
carbon. If concentrations for sediment types 2 and 3 are given or simulated
along with corresponding FOC(2, ISEG) and FOC(3, ISEG) values, then TOXI4
will calculate the fraction of chemical in five phases:
Koc focj(x>. J -'
(1 + S Kp1 M./n + KQC DOC/n)'1
' j. .
D
n, j - 1, 3, 3
EDOC
fD Koc DOC/n
1.5.73
1.5.74
1.5.75
1.5.76
This level allows more precise description of chemical partitioning and
transport and better extrapolation of hydrophobic sorption to different
sediment regimes.
137
-------
Level 4--The next level of complexity adds solids-dependent partitioning
to hydrophobic sorption. This is done by specifying values for NUX(l), the
solids-dependent partitioning constant. TOXI4 calculates the partition
coefficient as
1.5.77
where:
i/ -
the solids independent partition coefficient, L/kg
the solids dependent partition constant, kg/L
If no values are specified for NUX(l) (i.e., i/x) , then TOXI4 assigns a large
default value. A value of 1 describes this effect in many surface waters.
This relationnship is not applied to bed segments.
Level 5 --The fifth level of complexity for equilibrium reactions adds
ionic speciation to sorption. For each ionic specie "I" , SPFLG(I) must be
set to 1 and values for PKA(I) must be specified. To include temperature
dependence, values for EPKA(I) must be specified. In addition, sorption
coefficients for each ionic specie must be specified, including PIXC(1,I) and
perhaps PIXC (2,1), PIXC(3,I), PIDOC(I), and NUX(I) . If ionic species undergo
kinetic transformation, then appropriate second order rate constants must be
supplied for each specie (unless overall first order constants are specified
for the chemical as a whole) . TOXI4 calculates f ^ , the fraction of chemical
as species "i" in phase " j . " This level allows for more precise description
of chemical transport and transformation if sorption coefficients and rate
constants have been measured for the neutral and ionic specie. In addition,
this level allows better comparison of chemical exposure to biological effects
if toxicity studies have been done for the neutral and ionic specie.
Kinetic reactions--
Level l--The simplest kinetic reaction is described by a constant half
life or rate constant. If the user supplies first order decay constants KV,
KBW, KBS, KHN, KHH, KHOH, KO, KF, or KE for the transformation reactions,
then they will be used directly:
where:
5kl
-s
1.5.78
— chemical concentration, mg/L
- first order decay constants, day"1, including:
KHN> KHH> KHOH = neutral> acid, and base-catalyzed hydrolysis
constants,day"
138
-------
KBw» KBs = water column and benthic biodegradation
constants, day"-'-
Kp = photolysis constant, day"
KQ = oxidation constant, day"
K
= volatilization constant, day'
extra constant,
If half lives are provided for the transformation reactions--THV, THBW, THBS,
THHN, THHH, THHOH, THO, THF, THE--they will be converted internally to first
order rate constants and used as above:
= 0.693/TRi
1.5.79
where:
THi = half-lives, days, including:
THHNJ THHH' THOH "* neutral, acid, and base-catalyzed half lives,
days
THBW' THBS
water column and benthic biodegradation
half lives, days
THF = photolysis half life, days
TJJQ = oxidation half life, days
Tjjy = volatilization half life, days
TJJE = extra half life, days
Level 2--Because environmental conditions may change throughout a water
body, decay rates are expected to vary. The second kinetic level allows
spatially variable decay rate constants TOTKG(ICHM, ISEG) to be specified by
the user so that
SkC = -KTc Cl 1.5.80
where:
KTc(x) = spatially variable lumped first order decay rate
constant for chemical "c," days"-'-
For those segments where a nonzero KT is supplied, TOXI4 will bypass further
kinetic calculations. For those segments where Km is zero or not specified,
TOXI4 will apply any given process rate constants.
139
-------
Level 3--Because environmental 'conditions may change significantly in
time, the empirically-determined lumped decay rate constants may be somewhat
inaccurate upon extrapolation. This third level of kinetic complexity calcu-
lates decay rates based on second order kinetics as described in detail in
this chapter, so that, effectively:
where:
KTc
kijkc
KTc - S S S k£jkc [E]k fijc
i j fc
1.5.81
-1
- overall first-order rate constant for chemical "c," day
- second order rate coefficient for specie "i," phase "j,"
process "k" of chemical "c"
[E]k - intensity of environmental property affecting process "k"
fj4C - fraction of chemical "c" as specie "i" in phase "j"
The user may implement any given reaction by specifying values for the rate
constants (by ionic* specie and phase) and the relevant environmental para-
meters and time functions.
Level 4--The fourth level of kinetic complexity allows simulation of
transformation products. This level is implemented by simulating two or
three chemicals (NOSYS = 5 or 6) and by specifying appropriate yield coeffi-
cients for each process:
bkcl ~
Skc2 =
Skc3 -
S S Kkc Cc Ykcl> c = 2, 3
c k
c k
Cc Ykc2'
1, 3
c k
Kkc Cc Ykc3- c - 1, 2
1.5.82
1.5.83
1.5.84
where :
Skcl' Skc2» Skc3 = production of chemicals 1, 2, and 3 from chemical
"c" undergoing reaction "k," mg/L-day
Kkc
Ykcl> Ykc2> Ykc3
effective rate coefficient for chemical "c,"
process "k," day"
yield coefficients for production of chemicals 1,
2, and 3 from chemical "c" undergoing reaction "k"
The input yield constants that may be specified are YHOHxy, YHNsy, YHHxy,
YBWxy, YBSxy, YFxy, YOXxy, and YExy where x is the chemical reactant (1, 2,
or 3) and y is the chemical product (1, 2, or 3). Figure 1.5.10 illustrates
some of the reactions that can be simulated by specifying appropriate yield
coefficients.
140
-------
WASP4 (Toxics) REACTION PRODUCTS
r
GENERAL
CASE 1 C,
independentreactions
CASE 2
sequential reactions
CASES
parallel reactions
CASE 4
back reactions
Figure 1.5.10. Potential reaction products in TOXI4.
Summary of Data Requirements
TOXI4 adds several specific transfer and transformation processes to the
basic WASP mass transport equations. These additional processes require the
specification of several environmental parameters, chemical constants, and
environmental time functions, which were discussed in the preceding sections.
This section provides a summary.
141
-------
The environmental data required for a chemical simulation depend upon
which transformation processes are important. Table 1.5.14 gives the environ-
mental properties influencing each process in TOXI4, and a range of expected.
values. For a series of simulations involving many compounds, approximate
values for all environmental properties should be specified. For those pro-
cesses found to be most important, better estimates of the relevant environ-
mental properties can be provided in a second round of simulations.
The chemical properties of each compound control what transformation
processes are important in a particular environment. Table 1.5.15 summarizes
chemical properties influencing each process in TOXI4. Although the model
allows specification of different rates for the dissolved, sorbed, and DOC-
sorbed chemical phases, such data are not generally available. Measured rate
constants are often assigned to the dissolved chemical phase. The model also
allows specification of temperature correction parameters for each process.
Such data are often difficult to find without special studies, and need not
be input except for very hot or cold conditions, or where seasonal variability
is being studied.
Time variable functions can be used to study diurnal or seasonal effects
on pollutant behavior. The 17 time-variable environmental forcing functions
are summarized in Table 1.5.16. As shown, some of these time functions are
multiplied by spatially variable parameters within TOXI4 to produce time-
and spatially-variable environmental conditions. If no time variability is
required, the time functions may be omitted. Their values default to 1.0.
Although the amount and variety of data potentially used by TOXI4 is
large, data requirements for any particular simulation can be quite small.
Usually only sorption and one or two transformation processes will signifi-
cantly affect a particular chemical. To simulate the transport of many
soluble compounds in the water column, even sorption can often be disregarded.
Indeed, for empirical studies, all chemical constants, time functions, and
environmental parameters can be ignored except the user-specified transforma-
tion rate constant TOTKG(ICHM,ISEG) and, if desired, the partition coeffi-
cientorganic fraction pair of LKOC and FOC(ISEG,J). Thus, TOXI4 can be used
as a first-order water pollutant model to conduct standard simulations of dye
tracers, salinity intrusion, or coliform die-off. What is gained by the
second-order process functions and resulting input data burden is the ability
to extrapolate more confidently to future conditions. The user must determine
the optimum amount of empirical calibration and process specification for
each application.
142
-------
TABLE 1.5.14. ENVIRONMENTAL PROPERTIES AFFECTING INTERPHASE TRANSPORT
AND TRANSFORMATION PROCESSES
Environmental Property
.01
Environmental Process
Input Value Kp Kj KV KR KQ Kp Kfi
Sediment Concentrations :
Suspended, in mg/L
Benthic, in kg/L
Organic Carbon Fraction:
Suspended Sediment
Benthic Sediment
Dissolved Organic Carbon, mg/L
Water Column Depth, in m
Water Column Temperature, in °C
Average Water Velocity, in m/soc
Wind Speed at 10 cm, in m/sec
pH, Standard Units
5-500 X
1.2-1.7 X
.01-. 10 X
.01-. 10 X
0-10 X
0.5-100 X X
4-30 X XX X X
0-2 X
0-20 X
5-9 X X
Concentration of Oxidants, in
moles/L
Surface Light Intensity, in
Langleys/day
Cloud Cover, tenths of sky
Light Extinction Coefficient,
in per meter
Active Bacterial Populations:
Suspended, in cells/ml
Benthic, in cells/lOOg
io-9-io-12
300-700
0-10
.1-5
103-106
103-106
X
X
X
X
X
X
(3) Sorption; (4) lonization; (5) Volatilization; (6) Hydrolysis;
(7) Oxidation; (8) Photolysis; (9) Bacterial Degradation
143
-------
TABLE 1.5.15.
CHEMICAL PROPERTIES AFFECTING INTERPHASE TRANSPORT
AND TRANSFORMATION PROCESSES
Chemical Property
Environmental Process
Input Units Kp KZ KV KR KQ KF KB
(2) (3) (4") (5) (6) (7) (8) (9)
Molecular Weight
Solubility
Vapor Presure
Octanol-Water Partition
Coefficient
g/mole
mg/L
torr
VLo
Dissociation Constant
Activation Energy for Dissociation kcal/mole
Organic Carbon Partition
Coefficient
Partition Coefficient for Ionic
Species
Henry's Law Constant
Liquid Phase Volatilization/
Reaeration Ratio
Alkaline Hydrolysis Rate Constant
Neutral Hydrolysis Rate Constant
Acid-Hydrolysis Rate Constant
Activation Energy for Alkaline,
Neutral, and Acid Hydrolysis
Oxidation Rate Constant
Activation Energy for Oxidation
Measured Surface Rate Constant '
Wavelength of Maximum Light
Absorption
Absorption by Wavelength
Quantum Yield
Measured Rate Constant
Water Column Rate Constant
Benthic Rate Constant
Temperature Dependence
Multiplier (for 10°C change)
X
X
X
X
X
X
x
X
o
m -atm/mole
L/mole-day
day'1
L/mole-day
kcal/mole
L/mole-day
kcal/mole
X
X
X
X
X
X
X
X
-1
day
L/mole-cm In 10
mole/E
day"1
ml/cell-day
ml/cell-day
X
X
X
X
X
X
X
(3) Sorption; (4) lonization; (5) Volatilization; (6) H>5rolysis;
(7) Oxidation; (8) Photolysis; (9) Bacterial Degradation
144
-------
.TABLE 1.5.16. TIME VARIABLE ENVIRONMENTAL FORCING FUNCTIONS
Time Function
Constant or
Parameter
Environmental Property
TEMPN(TMPFN) x TEMP(ISEG)
VELN(VELFN) x VELOCG(ISEG)
WINDN x WVEL(ISEG)
PHNW
PHNS
REARN
AIRTMPN
CHLN
PHTON
BACNW
BACNS
x PH(ISEG)
x PH(ISEG)
x REAER(ISEG)
x AIRTMP
x CHPHL(ISEG)
x BAC(ISEG)
x BAC(ISEG)
Water temperature (x,t), °C
Water velocity (x,t), m/sec
Wind speed at 10 m above
surface (x,t), m/sec
Water Column pH.(x.t),
. log activity
Benthic pH (x,t), log activity
Reaeration or volatilization
rate (x,t), m/day
Air temperature (t), °C
Chlorophyll concentration,
mg/L
Average normalized light
intensity at water surface
(t), used for photolysis
option 2 only,; (unitless)
Water column bacteria popula-
tion (x,t), cells/mL ,
Benthic bacteria population
(x,t), cells/mL
145
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SECTION 2
WASP4 USER'S MANUAL
2.1 OVERVIEW
To simulate water quality in a. body of water with the WASP4 modeling
system, the user must first decide what variables to simulate and at what
level of complexity. Three general models are provided: DYNHYD4, EUTR04,
and TOXI4. If unsteady flow in large rivers or estuaries is to be simulated,
then DYNHYD4 must be run first. Summary files of the calculated flows and
volumes are created and stored for later input into the water quality
simulations. If dissolved oxygen, nutrient, or eutrophication kinetics are
to be simulated, then EUTR04 must be run. If sediment or toxicants are to be
simulated, then TOXI4 must be run.
To run DYNHYD4, EUTR04, or TOXI4 on a VAX computer, the user must first
type in the command "RUN DYNHYD4 (or EUTR04 or TOXI4)." On a PC-compatible
microcomputer, the user simply types in "DYNHYD4 (or EUTR04 or TOXI4)." 'The
model will then ask the user for the name of an appropriate input data set.
The user must type in the full name of a valid input data set (e.g.,
"POND1.INP") and hit carriage return. The model will then proceed through
the simulation, giving screen messages and producing output files.
At the conclusion of a simulation, the user may interactively create and
examine tables of display variables in time and space by typing in the VAX
command "RUN W4DSPLY." On the PC, the user simply types in "W4DSPLY." The
output program will first ask the user for the name of the output file from
the simulation. This output file will have the name of the input data set
with the extension "PMP" (i.e., "POND1.DMP"). Next, the output program will
ask the user what kind of tables to create and which variables to display.
Three kinds of tables may be created: segment versus time for a Variable,
variable versus time for a segment, and variable versus segment for a time.
Tables may be saved and printed, if desired.
To run the WASP4 or DYNHYD4 models, an input data set describing a speci-
fic water body must be constructed. These data sets are divided into input
data groups and are read into the programs in batch mode. For convenience,
the data groups are separated according to subject matter.
Each data group contains several "records" or lines. Records are usually
one 80-space line, but in a few instances a record will constitute as many
lines as needed to complete the data group. Records are always input sequen-
tially and each record begins on a new line. Do not skip lines between
records unless a "blank" record is specifically instructed. Likewise, do not
146
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enter blank lines between data groups; the models simply read from one line
to the next.
The introduction in each section gives an overview for each of the data
group's subject matter. The data group descriptions give detailed informa-
tion of all records and detailed definitions for all "ariables in that group.
The data group tables provide quick reference to record structure, variable
format, and definition. The variable definition section supplies an alphabe-
tical listing with definitions for all input variables for that particular
model.
This manual consists of a section for each of four models--the hydro-
dynamic model, the basic water quality model, the eutrophication model, and
the toxics model. Within each section, there is an introduction, description
of data groups, data group tables, and variable definitions. Within the
eutrophication and toxics sections, only those data group descriptions speci-
fically pertaining to EUTR04 or TOXI4 are provided.
2.2 THE HYDRODYNAMIC MODEL ,
Introduction .
This section describes the input required to run the DYNHYD4 hydro-
dynamics program. To arrange the input into a logical format, the data are
divided into eight groups: . •-,-.•••,•< -
A
B
C
D
E
F
G
H
Simulation Control
Printout Control
Hydraulic Summary
Junction Data
Channel Data
Inflow Data
Seaward Boundary Data
Wind Data
The following is a brief explanation of each data group.
Data Group A consists of preliminary data, such as network parameters
(number of channels, number of junctions), simulation time step, and the
beginning and ending day of simulation. .
Data Group B allows the user to specify printing options.
147
-------
Data Group C is responsible for the storage of flows and volumes. The
stored file created by this data group can be used as an input data set for
the water quality model.
Data Group D describes the model network and initial conditions at each
junction.
Data Group E describes the model network and initial conditions at each
channel.
Data Group F lists all inflows into the model system. Flows may be
constant or variable. Inflows are considered to be negative, and outflows
are positive.
Data Group G describes the seaward boundaries. The maximum number of
seaward boundaries has been set to five, but can be respecified by the user.
There are two types of tidal inputs: average tide, and variable tide. The
average tide is a smooth, repetitive curve that fits the equation:
Head -
sin(ut) A3 sin(2wt) A^ sin(3wt)
cos(wt) Ag cos(2wt) Ay cos(3wt)
2.2.1
The variable tide is a half sine wave that has highs and lows as specified by
the data set.
Data Group G has three options for defining the tidal cycle. Option 1,
the user specifies the coefficients in equation 2.2.1 for an average tide.
Option 2, the user specifies data and the model calculates the coefficients
in equation 2.2.1 which define the average tide. Option 3, the user specifies
the highs and lows of a variable tide and the model fits a half sine curve
through the points.
Data Group H lists wind speeds and directions.
DYNHYD4 Data Group Descriptions
DATA GROUP A: Simulation Control--
VARIABLES
Records 1. 2--Model Identification (20A40)
ALPHA(J) =
alphanumeric characters to identify the system,
date and run number. (20A4)
Record 3--Data Group Identification (20A4)
HEADER
alphanumeric characters to identify the data
group, "PROGRAM CONTROL DATA." (20A4)
148
-------
Record 4--Simulation Control Data (315. F5.0. 15. F5.0. F3.0. F2.0.
F5.0. F3.0. F2.0)
NJ
NC
NCYC
DELT
ICRD
ZDAY
ZHR
ZMIN
EDAY
EHR
EMIN
number of junctions in the model network. (15)
number of channels in the model network. (15)
total number of time steps for execution (number
of cycles). If equal to zero, the model will
compute NCYC internally (cycles). (15)
time interval used in execution (sec). (F5.0)
file containing the initial conditions for
junctions and channels: If equal to 0 or 5, data
set is read. If equal to 8, a file 8, previously
created by subroutine RESTART, is read. (15)
beginning day of simulation (day). (F5.0)
beginning hour of simulation (hr). (F3.0)
beginning minute of simulation (min). (F2.0)
ending day of simulation (day). (F5.0)
ending hour of simulation (hr). (F3.0)
ending minute of simulation (min). (F2.0)
ALPHA(l), ALPHA(2), and HEADER assist the user in maintaining a iog of
computer simulations, but are not actually used by the DYNHYD4 program.
ORGANIZATION OF RECORDS
Each record in Data Group A is input once; therefore, Data Group A
consists of 4 lines of data. Data Group B starts on the 5th line (no blank
line).
DATA GROUP B: Printout Control--
VARIABLES
Record l--Data Group Identification (20A4)
HEADER
alphanumeric characters to identify the data
group, "PRINTOUT CONTROL DATA." (20A4)
149
-------
Record 2--Output Control Information (2F10.0. 15)
FPRINT = time for printout to begin (hr). (F10.0)
PINTVL - time interval between printouts (hr). (F10.0)
NOPRT
number of junctions for which printouts (results)
are desired, can be 1 through NJ. (15)
Record 3--List of Junctions (1615)
JPRT(I) = junction number for results to be printed. (15)
There will be NOPRT entries in Record 3 (I = 1 to NOPRT).
ORGANIZATION OF RECORDS
Records 1 and 2 are entered once. Record 3 may contain several lines
depending upon NOPRT. One line may contain up to 16 entries. Therefore,
if NOPRT is equal to 1-16, then Record 3 will consist of 1 line. If NOPRT
is equal to 17-32, then Record 3 will consist of 2 lines, etc. The total
number of lines for Data Group B equals 2 + (1 + INT((NOPRT-1)/16))).
DATA GROUP C: Hydraulic Summary--
VARIABLES
Record l--Data Group Identification (20A4)
HEADER
alphanumeric characters to identify the data group
"Summary Control Data." (A4)
Record 2--Summary Control Data (15. F5.0. F3.0. F2.0. 2F5.0)
SUMRY
TDAY
THR
option number that controls how the hydrodynamic
scratch file (file 2) is processed to create a
permanent summary file (file 4) for the water
quality model to read. If equal to zero, then no
summary file .will be created. If equal to 1, an
unformatted file will be created, which is unlegi-
ble, but quicker and saves space. If equal to 2, a
formatted file will be created which is legible.
(15)
day to begin storing parameters to file (day).
(5.0)
hour to begin storing parameters to file (hr).
(F3.0)
150
-------
TMIN
DTDUMP
NODYN
minute to begin storing parameters to file (rain).
(F2.0)
time interval for storing intermediate results in
scratch file; usually 12.5, 24.0, or 25.0 hours
(hr). (F5.0)
number of hydraulic time steps per quality time
steps desired. (F5.0)
ORGANIZATION OF RECORDS
Records 1 and 2 are entered once. Therefore, Data Group C consists of
two lines.
DATA GROUP D: Junction Data--
VARIABLES
Record l--Data Group Identification (20A4)
HEADER
alphanumeric characters to identify the data group,
"JUNCTION DATA." (20A4)
Record 2--Junction Parameters (15. 3F10.0. 615)
JJ
Y(J)
SURF(J)
BELEV(J) -
NCHAN(J,I)=
junction number. (15)
initial head (or surface elevation) in reference to
a horizontal model datum, at junction JJ (m).
(F10.0)
o
surface area at junction JJ (m ) . (F10.0)
bottom elevation above (or below) the horizontal da-
tum plane (usually taken to be mean sea level) (m).
(F10.0)
channel number entering junction JJ. Maximum number
of channels entering any one junction is six (I =
1 - 6) . Start list with lowest channel number.
(15)
ORGANIZATION OF RECORDS
Record 1 is entered once in Data Group D. Record 2 is entered NJ times
(NJ = number of junctions). One line is used for each junction. Therefore,
Data Group D consists of 1 + NJ lines.
151
-------
DATA GROUP E: Channel Data--
VARIABLES
Record l--Data Group Identification (20A4)
HEADER
alphanumeric characters to identify the data group,
"CHANNEL DATA." (20A4)
Record 2--Channel Parameters (15. 6F10.0. 215)
NN
CLEN(N)
B(N)
R(N)
CDIR(N)
CN(N)
V(N)
NJUNC(N,1) =
NJUNC(N,2>
channel number. (15)
length of channel NN (m). (F10.0)
width of channel NN (m). (F10.0)
hydraulic radius or depth of channel NN (m).
(F10.0)
channel direction, or angle in degrees measured from
true north. The channel direction points in the
direction of positive flow, from the higher junction
number to the lower junction number (degrees).
(F10.0)
Manning roughness coefficient for channel NN (sec
. m'1/3). Ranges from 0.01 to 0.08. (F10.0)
the initial mean velocity in channel NN, m/sec.
(F10.0)
the connecting junction at the lower end of channel
NN. (15)
the connecting junction at the higher end of
channel NN. (15)
A channel may only connect two junctions. Therefore, only NJUNC(N,1)
and NJUNC(N,2) exists.
ORGANIZATION OF RECORDS
Record 1 is entered only once in Data Group E. Record 2 is entered NC
times (NC — number of channels). One line is used for each channel.
Therefore, Data Group E consists of 1 + NC lines.
152
-------
DATA GROUP F: Inflow Data--
VARIABLES
Record l-^ata Group Identification (20A41
HEADER
alphanumeric characters to identify the data
group and type of inflows, "CONSTANT INFLOW DATA "
(20A4)
Record 2--Constant Inflow Number (151
NCFLOW = the number of constant inflows that will be read
(15)
Record 3--Constant Inflow Data (IIP. F10.0)
JRCF(I)
junction that will be receiving the following
inflow. (110)
CFLOW(I) = the value of the constant inflow into junction
JRCF(I) (m3/sec). Value will be negative for
inflow, positive for outflow. (F10.0)
Record 4--Data Group Identification (20A41
HEADER = alphanumeric characters to identify the type of
inflows, "VARIABLE INFLOW DATA." (20A4)
Record 5--Variable Inflow Number (15)
NVFLOW = the number of variable Inflows that will be read
(15)
Record 6--Variable Inflow Breaks (21101
JRVF(I)
NINCR(I)
junction that will be receiving the following
variable inflows. (110)
number of data points (breaks) for variable
inflow into junction JRVF(I). (110)
Record 7--Variable Inflow Data (4(F5.0. F3.0. F2.0. FlO.Cm
• DAY(K) = day of VFLOW(I.K) (day). (F5.0)
HR(K) = hour of VFLOW(I.K) (hr). (F3.0)
MIN(K) = minute of VFLOW(I.K) (min). (F2.0)
153
-------
VFLOW(I,K)= value of the variable flow corresponding to DAY(K),
HR(K), and MIN(K) (m3/sec). Value will be negative
for inflow, positive for outflow. (F10.0)
ORGANIZATION OF RECORDS
Records 1 and 2 are entered once in Data Group F. Record 3 is entered
NCFLOW times with one junction number and one flow per line. Records 4 and
5 are entered once in Data Group F. Record 6 is entered NVFLOW times, but
not consecutively. Record 6 should be entered (one junction, one number of
breaks), then Record 7 with 4 flows per line until NINCR(I) flows have been
entered. Then Record 6 entered again followed by Record 7. The number of
lines for Data Group F is equal to
4 + NCFLOW + NVFLOW (1 + INT((NOPRT-1)/16))
DATA GROUP G: Seaward Boundary Data--
VARIABLES
Record l--Data Group Identification (20A4)
HEADER
alphanumeric characters to identify the data
group, "SEAWARD BOUNDARY DATA." (20A4)
Record 2--Seaward Boundary Number (15)
NSEA
number of seaward boundaries on model network.
(15)
If NSEA >0, proceed to Record 3. If NSEA =0, go to Data
Group H.
Record 3--Seaward Boundary Parameters (515. 3F5.0)
SEAOPT
JJ
NDATA
Seaward boundary input option (115):
1: input regression coefficients for single tidal
cycle
2: input height versus time for single tidal cycle
3: enter high and low tidal heights versus time
for multiple tidal cycles
junction number receiving the tidal input. (15)
number of data points (or breaks) used to describe
the seaward tide (15). If SEAOPT = 2, height versus
time data for a single tidal cycle will be fit to
the following regression:
154
-------
MAXIT
MAXRES
TSHIFT
PSHIFT
YSCALE
Head = A1(J,1) + A2(J,2) sin(wt)
+ A3(J,3) sin(2wt)
+ A4(J,4) sin(3wt)
+ A5(J,5) cos(wt)
+ A6(J,6) cos(2wt)
+ A7(J,7) cos(3wt)
If SEOPT = 3, tidal highs and lows will be fat to
half sine curves.
maximum number of iterations allowed to calculate
average tide. (15)
maximum error allowed in calculation of average
tide (calculates coefficients to describe tidal
cycle). (15)
allows tidal cycle to be shifted on the time
scale. Therefore, if all data have been entered '••
and error of 6.5 hours has been made in time scale,
one can enter 6.5 for TSHIFT (hr). Usually equal
to zero. (F5.0)
allows tidal cycle to be shifted on the phase
angle scale (radians). Usually equal to zero.
(F5.0)
scale factor for observed heads, B(HEAD) = B(HEAD)
* YSCALE, (F5.0) .
If SEAOPT = 1, use Records 4 and 6 => coefficients for average tide
are given.
If SEAOPT = 2, use Records 4 and 5 => calculates coefficients for
average tide.
If SEAOPT = 3, use Record 5 => variable tide is calculated.
Record 4--Tidal Parameters (2F10.0)
PERIOD(J) = tidal period (hr). (F10.0)
TSTART(J) - starting time for tidal input (hr). (F10.0)
Record 5--Tidal Data (4(F5.0. 1XF20. F2.0. FlO.O)")
DAY(I) - day corresponding to BHEAD(I) (day). (F5.0)
HR(I) = hour corresponding to BHEAD(I) (hr). (F2.0)
MIN(I)
minute corresponding to BHEAD(I) (min). (F2.0)
155
-------
BHEAD(I)
tidal elevation (head) at time DAY(I), HR(I),
and MIN(I) (m). (F10.0)
Record 6--Coefficients (7FW.Q)
1st Coefficient.
2nd Coefficient.
3rd Coefficient.
4th Coefficient.
5th Coefficient.
6th Coefficient.
A1(J,2)
A1(J,3)
A1(J,4)
A1(J,5)
A1(J,6)
A1(J,7)
7th Coefficient.
(F10.0)
(F10.0)
(F10.0)
(F10.0)
(F10.0)
(F10.0)
(F10.0)
These coefficients describe the curve with the following equation:
Head - A1(J,1) + A2(J,2) sin(wt)
+ A3(J,3) sin(2wt)
+ A4(J,4) sin(3wt)
+ A5(J,5) cos(ut)
+ A6(J,6) cos(2ut)
+ A7(J,7) cos(3wt)
ORGANIZATION OF RECORDS
As discussed in Section 2.2.1, three options for describing the tidal
cycle exists: 1) give coefficients for average tide, 2) calculate coeffi-
cients for average tide, or 3) give highs and lows for variable tide. For
all three options, records 1, 2, and 3 are entered once. For Option 1,
Record 4 and Record 6 are entered once. For Option 2, Record 4 is entered
once, and Record 5 is entered as many times as needed with 4 tidal elevations
on each line. For Option 3, Record 5 is entered as many times as needed with
4 tidal elevations on each line.
DATA GROUP H: Wind Data--
VARIABLES
Record l--Data Group Identification (20A4)
HEADER
alphanumeric characters to identify the data group,
"WIND DATA." (20A4)
156
-------
Record 2--Wind Data Number (15)
NOBSW » number of wind data points (or breaks).
Record 3--Wind Data (4(F5.0. IX. F2.0. F2.0. 2F5.0))
DAY(K) = day corresponding to the following wind speed
and wind direction (day). (F5.0)
HR(K) = hour corresponding to the following wind speed
and wind direction (hr). (F2.0)
MIN(K) = minute corresponding to the following wind
speed and wind direction (min). (F2.0)
WINDS(K) = wind speed measured at a distance of 10 meters
above the water system (m/sec). (F5.0)
WDIR(K) = wind direction measured at a distance of 10 meters
above the'water system. Must be measured from
True North (degrees). (F5.0)
ORGANIZATION OF RECORDS
Records 1 and 2 are entered once for Data Group H. Record 3 is entered
as many times as needed with 4 wind speeds on each line. The total number of
lines in Data Group H is equal to 2 + (1 + INT((NOBSW-l)/4).
DYNHYD4 Data Group Tables
TABLE 2.2.1. CROSS REFERENCES FOR DYNHYD4 INPUT VARIABLES
Name
Data
Record
Name
Data
Record
Name
Data
Record
Name
Data
Redord
ALPHA
BHEAD
CN
DTDUMP
EHR
HR
JRCF
MIN
NCYC
NJUNC
NOPRT
PINTVL
SUMRY
TMIN
VFLOW
YSCALE
Al, A2
G5
E2
C2
A4
F7, G5, H3
F3
F7, G5, H3
A4
E2
B2
B2
C2
C2
F7
G3
Al
CDIR
DAY
EMIN
ICRD
JRVF
NC
NDATA
NN
NSEA
PSHIFT
SURF
TSHIFT
WDIR
ZDAY
G6
E2
F7, G5, H3
A4
A4
F6
A4
G3
E2
G2
G3
D2
G3
H3
A4
B
CFLOW
DELT
FPRINT
JJ
MAXIT
NCFLOW
NINCR
NOBSW
VNFLOW
R
TDAY
TSTART
WINDS
ZHR
E2
F3
A4
B2
D2, G3
G3
F2
F6
H2
F5
E2
C2
G4
H3
A4
BELEV
GLEN
EDAY
HEADER
JPRT
MAXRES
NCHAN
NJ
NODYN
PERIOD
SEAOPT
THR
V
Y
ZMIN
D2
E2
A4
A3, (B-H)l
B3
G3
D2
A4
C2
G4
G3
C2
E2
D2
A4
157
-------
A I
A 2
A 3
A 4
T^an3"CroLip A: Simulation CpnTroT"
Variable
AI A AUPHA(I)
A2 B AU>HA(2)
A3 Header
M C NJ
D NC
E KCYC
F DELT
G ICRD
II ZDAY
I ZHR
J 2MIN
K EOAY
L EUR
M EMIN
Definition
Identification of simulation
Identification of simulation
Title of card group
Number of junctions In noiwork
Number of channel! in network
Total number of time steps
Tlmo Interval used In the solullon
File number which contains Initial conditions
Beginning day jf simulation
Beginning hour of slmullion
Beginning minute of simulation
Ending da/ of simulation
Ending hour of simulation
Ending minute of simulation
Units
day
hr
mln
day
hr
mln
B 2
I J
Coi'd Group B; Printout'sonlroP
— ''
Dofinillon
ni HEADER Tlllo of card group B
B2 A FPRINT Time used for first printout
B PINTVL Time Interval belweon printouts
C NOPRT Number of Junctions to be prlntod
B3 D JPRT(I) First (unction to hove values prlnlod for
E JPRT(2) Second (unction to have vaues printed for
Q JPRT(NOPRf) Last junction to have values prints for
hr
hr
• Note •
LJnn 05 should be repealed until HOf'Rf junctions hcive
been listed
158
-------
Variable
Definition
Units
Cl HEADER Tltla of cord group
C2 A SUMRY Controls the creation of the permanent hydrodynamle fll« for u«e
by the water quality model V/ASP; 0 = no file; 1 = unformatted
file; 2 = formatted file
B TDAY Day to begin storing parameters
C THR Hour to begin storing parameters
D TMIN Minute to begin storing parameters
E DTDUMP Time Interval for storing Intermediate results on scratch file;
usually J2.5, 24.0, or 25.0 hours
r HODYN Number of time steps per water quality time steps
day
hr
mln
hr
Card Group D: Junction Data
'*itos'
m
SBffiffl
D1
D2
Vorioble
HEADER
A JJ
B Y(J)
SURF(J)
BELEV(J)
NCHAN(J.t)
NCHAN(J,2)
NCHAN(J,3)
H NC!IAN(J,4)
1 NCHAN(J.S)
Title of Card Group
Junction number
Initial head at |unctlon J
Initial surface area at junction J
Bottom elevation at junction J
First channel entering junction J
Second channel entering junction J
Third channel if It exists
Fourth channel
Fifth channel
m"-
m
• No.'e •
Line A4 should b» repeated IIJ (number of junctions) times
159
-------
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NN
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B
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H NJUHC(N.l)
B(N)
R(N)
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m
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R«p«at lln* EZ NC (numbw of channel*) times.
160
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DYNHYD4 Output
DYNHYD4 simulations produce several files that may be examined by the
user. These files use the file name of the input data set with a unique
extension - *.DMP, *.OUT, *.HYD, and *.RST (where * is the name of the input
data set).
The DMP file contains 6 display variables for each junction at each
print interval throughout the simulation. These variables are defined in
Table 2.2.2. To examine these variables in tabular form, the user may run
W4DSPLY as explained in Section 2.1.
TABLE 2.2.2. DYNHYD4 DISPLAY VARIABLES
Number
Variable
Definition
1
2
3
4
5
6
7-18
Y
DEP
FLOWG
QDIR
VELOCG
ITYPE
Blank
Segment head, m
Segment depth, m
o
Segment flow, m /sec
Segment flow direction, degrees
Segment velocity, m/sec
Segment type, (1)
The OUT file contains a record of the input data along with any simula-
tion error messages that may have been generated. A printed record of user-
selected junction and channel volumes and flows at print intervals throughout
the simulation is provided.
The HYD file contains averaged hydrodynamic variables for use in future
WASP4 simulations. These include basic network and inflow information;
junction volumes (m3), inflows (nr/sec), flows (nr/sec), depths (m) , and
velocities (m/sec); and channel flows (m/sec). This file may be in ASCII or
binary format, depending on whether the user specified 2 or 1 for SUMRY.
The RST file contains a snapshot of junction volumes and channel flows
at the conclusion of the simulation. This file may be read by DYNHYD4 to
continue a series of simulations.
166
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2.3. THE BASIC WATER QUALITY MODEL
Introduction
This section describes the input required to run the WASP water quality
program. To arrange the input into a logical format, the data are divided
into 10 groups, A through J.
A - Model Identification and Simulation Control
B - Exchange Coefficients
C - Volumes
D - Flows
E - Boundary Concentrations
F - Waste Loads
G - Environmental Parameters
H - Chemical Constants
I - Time Functions
J - Initial Conditions
The following is a brief explanation of each data group:
DATA_GROUP A is generally for model identification and contains simula-
tion control options. The user must specify the number of segments and the
number of systems. The user must also specify time steps and print intervals
here.
DATA GROUP B contains dispersive exchange information. Dispersion
occurs between segments and along a characteristic length.
DATA GROUP C supplies initial segment volume information.
DATA GROUP D supplies flow and sediment transport information between
segments. Flows may be constant or variable.
DATA GROUP E supplies concentrations for each system at the boundaries.
All system concentrations must be supplied for each boundary.
DATA GROUP F defines the waste loads and segments that receive the waste
loads for both point and diffuse sources.
DATA GROUP G contains appropriate environmental characteristics of the
water body. These parameters are spatially variable.
167
-------
DATA GROUP H contains appropriate chemical characteristics or constants.
DATA GROUP I contains appropriate environmental or kinetic time
functions.
DATA GROUP J contains initial concentrations for each segment and each
system.
WASP4 Data Group Descriptions
DATA GROUP A: Model Identification and Simulation Control
TITLE1
VARIABLES
Record 1--Title of Simulation (A80)
descriptive title of simulation (A80).
TITLE2
Record 2--Description of Simulation (A80)
description of simulation (A80).
HEADER
Record 3--Record 4 Names (A80)
names of Record 4 variables, positioned properly; for
user convenience only (A80).
Record 4--Simulation Control Parameters (815. 2Fb.O. F3.0. F2.0. 315. F10.0)
KSIM
NOSEG
NOSYS
ICFL
MFLAG
simulation type: 0 - dynamic, 1 - steady state. (15)
number of segments in model network. (15)
number of model systems (state variables). (15)
flag controlling use of restart file; 0 = neither read from
nor write to restart file (initial conditions located in
input file); 1 - write final simulation results to restart
file (initial conditions located in input file); 2 = read
initial conditions from restart file created by earlier
simulation, and write final simulation results to new
restart file. (15)
flag controlling messages printed on screen during
simulation; 0 — all messages printed; 1 =
simulation time only printed; 2 = all messages are
suppressed. (15)
168
-------
JMASS
NEGSLN
INTYP
ADFAC
ZDAY
ZHR
MIN
IDSY
IDSG1,
IDSG2
TADJ
system number for which mass balance analysis will be
performed, (15)
negative solution option; 0 «= prevents negative solutions;
1 = allows negative solutions. (15)
time step option; 0 - user inputs time step history;
1 = model calculates time step. (15)
advection factor; 0 - backward difference; 0.5-= central
difference; 0-0.4 recommended. (F5.0)
day at beginning of simulation; 1 is first day. (F5.0)
hour at the beginning of simulation. (F3.0)
minute at the beginning of simulation. (F2.0)
system for which concentrations will be displayed on
screen throughout the simulation. (15)
segments for which system "IDSY" concentrations will be
displayed on screen throughout the simulation. (215)
factor by which input kinetic rates will be adjusted; 0
or 1.0 will cause no adjustment; 24.0 will adjust input
rates in hours'- to days"-1-; 86400. will adjust input
rates . in seconds'-*- to days'-*-. (F10.0)
NOBRK
Record 5--Number of Time Steps (15)
number of different model time steps (15)
DTS(I)
Record 6--Time Steps (4CF10.0. F10.0))
time step to be used until time T(I), days. (F10.0)
time up to when time step DTS(I) will be used days
(F10.0)
NPRINT
Record 7--Number of Print Intervals CI51
number of print intervals. NOTE: The maximum number
of printouts must be equal to or less than the FORTRAN
parameter MP that was used when compiling the program
(15)
169
-------
Record 8--Prlnt Intervals (4(F10.0. F10.0))
PRINT(I) - print interval to be used until time TPRINT(I), days.
(F10.0)
TPRINT(I) - time up to when print interval PRINT(I) will be used,
days. (F10.0)
Record 9--System Bypass Options (1615)
SYSBY(ISYS) - bypass option for system ISYS; 0 = system will be
simulated; 1 = system will be bypassed. (15)
DATA GROUP B: Exchange Coefficients
Exchange coefficients are computed from input dispersion coefficients,
cross-sectional areas, and characteristic lengths. Dispersion coefficients
may vary in time according to piecewise-linear time functions, with groups
of segment pairs having the same dispersion time function. Exchange data
are read for each exchange field. Field one contains dispersion coeffi-
cients for water column exchanges. Field two contains exchange data for
pore water exchange. Fields three, four and five contain sediment ex-
change data, with a separate field available for each solid type.
VARIABLES
Record 1--Number of Exchange Fields (15. 75X)
NRFLD - number of exchange fields. NRFLD will generally equal
2 for water column and pore water exchanges. (15)
TITLE
— -name of data group. (75X)
If no exchange rates are to be read, set NRFLD to zero and continue with
Data Group C.
Record 2--Exchange Time Functions for Each Field (15. 2F10.0)
NTEX(NF) - number of exchange time functions for field NF. (15)
SCALR - scale factor for exchange coefficients. All exchange
coefficients for field NF will be multiplied by this
factor. (F10.0)
CONVR - conversion factor for exchanges in field NF. (FlO.O)
NF - 1, NRFLD
170
-------
To skip exchange field NF, set NTEX(NF) to zero and continue with the
next exchange field.
NORS(NF.NT)
NT = 1, NTEX(NF)
Record 3--Exchange Data (15)
number of exchanges for field NF, time function NT.
(15)
Record 4--Areas. Characteristic Lengths (2F10.0. 215)
A(K) = area in square meters for exchange pair K. (F10.0)
EL(K) = characteristic length in meters for exchange pair
K. (F10.0)
IR(K),JR(K)
K = 1, NORS(NF,NT)
segments between which exchange occurs.
of the segments is unimportant. (215)
The order
Record 5--Number of Breaks in Time Function (15)
NBRKR(NF,NT)
number of values and times used to describe
dispersion coefficient piecewise-linear time
function. (15)
Record 6--Piecewise Linear Dispersion Time Function (4CF10.0. F10.0))
RT(K)
TR(K)
K = 1, NBRKR(NF.NT)
value of dispersion coefficient in m /sec at time
TR(K). (F10.0)
time in days. (F10.0)
RBY(K)
K = 1, NOSYS
Record 7--Exchange Bypass Options (1615)
= 0, exchange occurs in system K. (15)
1, bypass exchange for system K.
ORGANIZATION OF RECORDS
Record 1 is entered once for Data Group B. Records 2 through 6 are
repeated for each exchange field, and Records 3, 4, 5, and 6 are repeated for
171
-------
each time function in a given exchange field. Record 4 uses as many lines as
necessary to input NORS sets of A(K), EL(K), IR(K), and JR(K), with 1 set on
each line. Record 6 uses as many lines as needed to input NBRKR pairs of
RT(K) and TR(K), with 4 pairs occupying each line. After data for all ex-
change fields are entered, Record 7 is input on the following line with NOSYS
entries.
DATA GROUP C: Volumes
Record 1--Preliminary Data (215. F10.0. 60X)
IVOPT = 1, constant water column volumes. (15)
— 2, 3, volumes adjusted to maintain flow continuity.
(15)
IBEDV = 0, constant bed volumes. (15)
— 1, bed volumes change in response to sediment
transport. (15)
TDINTS = time step in days for porosity computations,
IBEDV = 0. (F10.0)
= time step in days for sediment bed compaction,
IBEDV - 1. (F10.0)
TITLE — name of data group. (60X)
SCALV
CONW
Record 2--Scale Factors (2F10.0)
scale factor for volumes. All volumes will be
multiplied by this factor. (F10.0)
conversion factor for volumes. (F10.0)
Record 3--Segment Types arid Volumes (3110. 5F10.0)
ISEG
IBOTSG
ITYPE(ISEG)
segment number.
segment immediately below ISEG. (110)
segment types;
1 = surface water segment,
2 — subsurface water segment,
3 — upper bed segment,
172
-------
BVOL(ISEG)
VMULT(ISEG)
VEXP(ISEG)
DMULT(ISEG)
DXP(ISEG)
ISEG = 1, NOSEG
4 = lower bed segment. (110)
volume of segment ISEG in cubic meters. (F10.0)
hydraulic coefficient "a" for velocity in ISEG as
a function of flow:
v = a Qb
If b = 0, VMULT is a constant velocity in m/sec.
(F10.0)
hydraulic exponent "b" for velocity in ISEG as a
function of flow (0-1). A value of 0.4 represents
rectangular channels. (F10.0)
hydraulic coefficient "c" for depth of ISEG as a
function of flow:
d = c Qd
If d =0, DMULT is a constant depth in m. (F10.0)
hydraulic exponent "d" for depth of ISEG as a func-
tion of flow (0-1)-. A value of 0.6 represents
rectangular channels. (F10.0)
ORGANIZATION OF RECORDS
Records 1 and 2 are entered once for Data Group C. Record 3 is repeated
NOSEG times. If ICFL =. 2 in Data Group A, volumes are read from the restart
file (*.RST, where * is the input data set name), and Records 2 and 3 should
not be included in the input data set.
DATA GROUP D: Flows
Data Group D consists of the flows 'that are used in the model. Flows
may be input for several fields. Field one consists of advective flows in
the water column, and may be input by one of three options. . Field two consists
of pore water flows, while Fields three, four, and five consist of sediment
transport velocities and cross-sectional areas. A separate sediment transport
field is specified for each solid type. Field six is for evaporation and
precipitation velocities and cross-sectional areas. All flows may vary in
time according to piecewise linear time functions.
Record 1 is read first. If IQOPT «= 1, Data Block Dl is read next; if
IQOPT =• 2 or 3, Data Block D2 is read. Data Blocks D3, D4, D4, D4, and D5
follow in order for NFIELD =2, 3, 4, 5, and 6, respectively. Following all
specified Data Blocks, Record 7 is read.
173
-------
VARIABLES
Record l--Data Input Options: Number of Flow Fields (215)
IQOPT — 1, Field one (advective) flows are specified
directly by user.
= 2, Field one flows are read from an unformatted
file (SUMRY2.0UT) created by DYNHYD4.
- 3, flows are read from a formatted file created by
DYNHYD4. (15)
NFIELD
number of flow fields. The first two fields are
advective and pore water flows. An additional field
(3, 4, or 5) is used for each type of solid modeled.
Field 6 is used for evaporation and precipitation.
If no flows are used, set NFIELD to zero and continue
with Data Group E. (15)
DATA BLOCK D.I: Direct Input of Field One Flows (IQOPT = 1)
VARIABLES
Record 2--Number of Flow Time Functions (15. 2F10.0)
NINQ(l) - number of time functions for Field One. If no flows
are used in field one, set NINQ to zero and skip to
next field. (15)
SCALQ = scaling factor. All flows in Field one are multi-
plied by SCALQ. (FlO.O)
CONVQ = units conversion factor. (FlO.O)
NOQS(1,NI)
Record 3--Number of Flows (15)
number of unit flow responses in field one, time
function NI; each unit flow is defined for a single
segment pair. (15)
Record 4--Flow Routing for Field One (4(F10.0. 215))
BQd.NI.K)
JQ(1,NI,K)
portion of flow for field one, time function NI that
flows between segment pair K. (FlO.O)
upstream segment. (15)
174
-------
IQ(1,NI,K) = downstream segment. (15)
K - 1, NOQS(l.NI)
Record 5--Number of Breaks in Advective Time Functions (15)
NBRKQ(1,NI)
the number of flows and times used to describe
piecewise linear time function NI. (15)
Record 6--Piecewise Linear Advective Time Function (4(2F10.0))
QT(1,NI,K) = advective flow in m3/s. (F10.0)
TQ(1,NI,K) = time in days. (F10.0)
K - 1, NBRKQ(1,NI)
ORGANIZATION OF RECORDS
Records 1 and 2 are input once for Data Block D.I. Records 3, 4, 5, and
6 are input once for each flow time function. Record 4 uses as many lines as
needed to input NOQS sets of BQ, JQ, and IQ, with four sets per line. Record
6 uses as many lines as necessary to input NBRKQ sets of QT and TQ, with four
sets on each line.
DATA BLOCK D.2: DYNHYD4 Field One Flows (IQOPT=2 or 3)
VARIABLES
Record 2--Scale and Conversion Factors (2F10.0)
SCALQ = scaling factor for flows. All DYNHYD3 flows will be
multiplied by SCALQ. (F10.0)
CONVQ = units conversion factor. (F10.0)
NSEA
JSEA(I)
1=1, NSEA
Record 3--Seaward Boundaries (15)
number of downstream (seaward) boundary segments
(same as in hydrodynamic simulation). (15)
segment numbers for downstream boundary segments.
(15)
175
-------
JUNSEG(I)
I - 1, NJ
Record 4--Junction-Segment Map (1615)
— segment number corresponding to hydrodynamic
junction I. (15)
ORGANIZATION OF RECORDS
Records 2 and 3 are read in once for Data Block D.2.
repeated until NJ entries have been input.
Record 4 will be
DATA BLOCK D.3: Field Two (Pore Water) Flows
VARIABLES
Record 2--Number of Pore Water Time Functions (15. 2F10.0)
NINQ(2)
SCALQ
CONVQ
number of pore water time functions. If no flows
are used in Field Two, set NINQ to zero and skip to
sediment transport fields. (15)
scaling factor for pore water flows. (F10.0)
units conversion factor. (F10.0)
NOQS(2,NI)
NI - 1, NINQ(2)
Record 3--Number of Flows (15)
number of segment pair flows in Field 2, time
function NI. (15)
Record 4--Flow Routing for Field Two (4(F10.0. 215))
BQ(2,NI,K)
JQ(2,NI,K)
IQ(2,NI,K)
portion of pore water flow for time function NI that
flows between segment pair K. (F10.0)
upstream segment. (15)
downstream segment. (15)
Record 5--Number of Breaks in Pore Water Time Function (15)
NBRKQ(2,NI) = number of pore water flows and times used to describe
piecewise linear fime function NI. (15)
176
-------
Record 6--Piecewise Linear Pore Water Time Function (4C2F10.0))
QT(2,NI,K) = pore water flow in m3/s, (F10.0)
TQ(2,NI,K) = time in days. (F10.0)
K = 1, NBRKQ(2,NI)
ORGANIZATION OF RECORDS
Record 2 is input once for Data Group D.3. Records 3, 4, 5 and 6 are
input once for each pore water time function. Record 4 uses as many lines as
necessary to input NOQS sets of BQ, JQ, and IQ, with four sets on each line.
Record 6 uses as many lines as necessary to input NBRKQ sets of QT and TQ,'
with four sets on each line.
DATA BLOCK D.4: Sediment Transport Fields
Sediment transport flow data are input as velocities and areas. Veloci-
ties may vary in time, and represent settling, sedimentation, deposition, and
scour. Only solids and sorbed chemical are transported by these fields. A
separate field is specified for each sediment size fraction. If no solids
are modeled, skip directly to Record 7 (Flow Bypass Options).
VARIABLES
Record 2--Number of Velocity Time Functions (15. 2F10.0')
NINQ(NF)
SCALQ
CONVQ
NF = 3, 5
number of velocity time functions for Field NF.
(15) •:..-.
scaling factor for velocities. (F10.0)
units conversion factor. (F10.0)
NOQS(NF,NI)
NI = 1,NINQ(NF)
Record 3--Number of Segment Pairs (15)
= number of segment pairs involved in sediment
transport. (15)
177
-------
Record 4--Areas for Sediment Transport (4(F10.0. 215))
BQ(NF,NI,K) — area In square meters between segment pair K.
(F10.0)
JQ(NF,NI,K) = segment sediment is transported from. (15)
IQ(NF,NI,K) - segment sediment is transported to. (15)
K - 1, NOQS(NF.NI)
Record 5--Number of Breaks in Velocity Time Function (15)
NBRKQ(NF.NI) - number of velocities and times used to describe
piecewise linear time function NI. (15)
Record 6--Piecewise Linear Velocity Time Function (4(2F10.0))
QT(NF,NI,K) - sediment transport velocity in m/s. (F10.0)
TQ(NF,NI,K) = time in days. (F10.0)
K - 1, NBRKQ(NF.NI)
ORGANIZATION OF RECORDS
Records 2 through 6 are read for each solid transport field. Records 3,
4, 5 and 6 are input for each time function in each field. Record 4 uses as
many lines as needed to input NOQS sets of BQ, JQ, and IQ, with four sets on
one line. Record 6 uses as many lines as needed to input NBRKQ sets of QT
and TQ, with four sets per line.
DATA BLOCK D.5: Evaporation and Precipitation Field
Evaporation and precipitation flow data are input as velocities and
areas. Velocities may vary in time to represent rainfall events or seasonal
evaporation. No chemical is transported with evaporation, but volumes are
adjusted to maintain continuity. If this field is not modeled, skip directly
to Record 7 (Flow Bypass Options). After all transport field data is entered,
Record 7 is input with NOSYS entries. If no evaporation or precipitation
fields are specified, Record 7 follows Data Group D.4 (solids transport).
VARIABLES
Record 2--Number of Velocity Time Functions (15. 2F10.0)
NINQ(NF)
number of velocity time functions for Field 6. (15)
178
-------
SCALQ
CONVQ
NF = 6
scaling factor for velocities. (F10.0)
units conversion factor. (F10.0)
Record 3--Number of Segment Pairs (15)
NOQS(NF,,NI) - number of segment pairs involved in sediment
transport. (15)
Record 4--Areas for Sediment Transport (4(FJO.O. 215))
BQ(NF,NI,K)
area in square meters between segment pair K.
(F10.0)
JQ(NF,NI,K) = segment water is transported from; if = 0, this
is precipitation. (15)
IQ(NF,NI,K) = segment water is transported to; if = 0, this is
evaporation. (15)
K = 1, NOQS(NF.NI)
Record 5--Number of Breaks in Velocity Time Function (15)
NBRKQ(NF,NI) = number of velocities and times used to describe
piecewise linear time function NI. (15)
Record 6--Piecewise Linear Velocity Time Function (4(2F10.0))
QT(NF,NI,K)
water transport velocity in m/s; if more traditional
units of cm/day or cm/year are desired, ;then
specity CONVQ = 1.1574E-7 or 3.169E-10, respectively.
(F10.0)
TQ(NF,NI,K) = time in days. (F10.0)
K - 1, NBRKQ(NF.NI)
-END OF DATA BLOCKS FOR D-
QBY(ISYS)
Card 7--Flow Bypass Options (1615)
0, flow transport occurs in system ISYS.
179
-------
1, bypass flow transport for system K. (15)
K - 1, NOSYS
The flow bypass option allows flow transport to be set to zero in one or
more systems. The bypass option applies to all transport fields.
DATA GROUP E: Boundary Concentrations
Data Group E is repeated, in its entirety, NOSYS times.
VARIABLES
Record l--Data Input Option--Number of Boundary Conditions (IIP. 70X)
NOBC(K) = number of boundary conditions used for system K. (110)
TITLE - name of data group. (70X)
K - 1, NOSYS
If no boundary conditions are to be input, set NOBC(K) equal to zero
and either continue with the next system or go to the next card group.
Record 2--Scale Factor for Boundary Conditions (2F10.0).
SCALB — scale factor for boundary conditions. All boundary
conditions will be multiplied by this factor. (F10.0)
CONVB = unit conversion factor for boundary conditions.
Boundary conditions are expected to be in milligrams
per liter (mg/L). If boundary conditions are given in
SI units (grams per cubic meter), CONVB will be 1.0.
(F10.0)
IBC(K)
NOBRK(K) -
K - 1, NOBC
Record 3--Boundary Conditions (215)
boundary segment number. (15)
number of values and times used to describe the broken
line approximation. The number of breaks must be equal
for all boundary conditions within a system. (15)
180
-------
Record 4--Boundary Concentrations (4(2F10.0))
BCT(K) = value of the boundary concentration at time T(K) in mg/L.
(F10.0)
T(K) = time in days. If the length of the simulation exceeds
T(NOBRK), the broken line approximation is repeated,
starting at T(l), i.e., the approximation is assumed
to be periodic, with period equation to T(NOBRK). All
break times must agree for all segments, i.e., T(l) must
be the same for all boundaries, T(2) must be the same for
all boundaries, etc. (F10.0)
K = 1, NOBRK
, ORGANIZATION OF RECORDS
Records 1 and 2 are entered once. Records 3 and 4 are a set and are
repeated NOBC times. Within each NOBC set, Record 3 is entered once and
Record 4 is repeated until NOBRK entries are input. Four entries (four
BCT(K)-T(K) pairs) will fit on each 80-space line. The whole group is
repeated NOSYS times, once for each model system.
DATA GROUP F.I: Waste Loads
Data Group F.I contains the point source waste loads used in the model.
Data Group F.I is repeated NOSYS times for point source loads. Following
complete specification of point source loads, nonpoint source loads will be
read from Data Group F.2.
VARIABLES
Record l--Data Input Option: No. of Forcing Functions (IIP. 70X)
NOWK(ISYS) =
TITLE
number of forcing functions used for system ISYS. Forc-
ing functions may also be considered as sources (loads)
or sinks of a water quality constituent. If no forcing
functions are to be input, set NOWK(ISYS) to zero, and
continue with next system or go to next data group.
(HO)
name of data group. (70X)
Record 2--Scale Factor for Forcing Functions (2F10.0')
SCALW = scale factor for forcing functions. All forcing
functions will be multiplied by this factor. (F10.0)
181
-------
CONVW
unit conversion factor for forcing functions.
Forcing functions are expected to be in kilograms per
day. If forcing functions are given in English units
(pounds per day), this factor will be 0.4535. (F10.0)
IWK(K)
NOBRK(K) =
K - 1, NOWK
Record 3--Number of Point Sources C2I5)
segment number that has forcing function BWK(K).
(15)
number of breaks used to describe the forcing function
approximation. The number of breaks must be equal for
all forcing functions within a system. (15)
Record 4--Point Source Time Function (4C2F10.0))
WKT(K) - value of the forcing function at time T(K), in kg/day.
(F10.0)
T(K) — time in days. If the length of the simulation exceeds
T(NOBRK), the approximation is repeated, starting at
T(l), i.e., the approximation is assumed to be periodic
with period equal to T(NOBRK). All break times must
agree for all segments; i.e., T(l) must be the same for
all loads, T(2) must be the same for all loads, etc.
(F10.0)
K - 1, NOBRK
ORGANIZATION OF RECORDS
Records 1 and 2 are input once. Records 3 and 4 are a set and are
repeated (as a set) NOWK times. Within each set, Record 3 is entered once
and Record 4 is repeated until all NOBRK entries are entered. Four entries
(WKT(K)-T(K) pairs) will fit on each 80-space line. The entire group is
repeated NOSYS times, once for each system.
DATA GROUP F.2, Nonpoint Source Waste Loads
VARIABLES
Record 1--Number of Runoff Loads. Initial Day (215)
NOWKS = number of segments receiving runoff loads. (15)
182
-------
NPSDAY
the time in the runoff file corresponding to the initial
simulation time, in days. (15)
If NOWKS - 0, skip to Data Group G. If NOWKS >0, read records 2, 3, and 4.
Record 2--Scale Factor for Runoff Loads (2F10.0)
SCALN = scale factor for runoff loads. All runoff loads will be
multiplied by this factor. (F10.0)
CONVN = unit conversion factor for runoff loads. Runoff loads
are expected in kilograms per day. If runoff loads are
given in English units (pounds per day), this factor will
be 0.4535. (F10.0)
Record 3--Runoff Segments (1615)
INPS(J) = segment number to which runoff load J is applied. (15)
J = l.NOWKS
KT1
KT2
KPRT(I)
I = 1,NOSYS
Record 4--Print Specifications (1615)
initial day for which nonzero runoff loads from file
NFS.DAT will be printed. (15)
final day for which nonzero runoff loads from file
NFS.DAT will be printed. (15)
indicator specifying whether nonzero runoff loads will be
printed for each system. If KPRT(I) is greater than
zero, then runoff loads will be printed for system I.
(15)
ORGANIZATION OF RECORDS
Records 1 and 2 are entered once in Data Group F2. Record 3 has NOWKS
entries and uses as many 80-space lines as needed to enter all NOWKS segment
numbers. Sixteen entries will fit on one line. Record 4 is entered once.
DATA GROUP G: Parameters
The definition of the parameters will vary, depending upon the structure
and kinetics of the systems comprising each model. The input format, however,
is constant.
183
-------
NOPAM
TITLE
VARIABLES
Record 1--Number of Parameters (IIP. 70X)
— number of parameters required, by the model. If no
parameters are to be input, set NOPAM to zero and go
to Data Group H. (110)
= name of data group. (70X)
Record 2--Scale Factors for Parameters (4(A5. 15. F10.0))
ANAME(ISC) - descriptive name for parameter ISC. (A5)
ISC = parameter number identifying parameter. (15)
PSCAL(ISC) - scale factor for parameter ISC. (F10.0)
K - 1, NOPAM
ISG
Record 3--Segment Number (IIP)
segment number for the following parameter values.
(110)
Record. 4--Segment Parameters (4(A5. 15. F10.0')')
PNAME(ISC) — an optional one to five alphanumeric character
descriptive name for parameter PARAM(ISG,ISC).
(A5)
ISC
PARAM(ISEG.K) =
K - 1, NOPAM
ISEG - 1, NOSEG
parameter number identifying parameter. (15)
the value of parameter ISC in segment ISG. (F10.0)
ORGANIZATION OF RECORDS
Record 1 is input once in Data Group G, occupying one line. Record 2
has NOPAM entries. Four entries will fit on one line; thus, Record 2 uses
as many 80-space lines as needed to enter all NOPAM entries. Records 3 and
4 are entered NOSEG times, once for each segment. For each segment, Record
4 uses as many lines as needed to enter all NOPAM entries.
184
-------
DATA GROUP H: Constants--
The definition of the constants will vary,, depending upon the structure
and kinetics of the systems comprising each model. This data group is sub-
divided into global constants and constants for each system (thus NOSYS+1
groups are read). Each of these groups can be subdivided into any number of
fields containing similar kinds of data.
TITLE
VARIABLES
Record 1--Header (8PX)
name of data group. (SOX)
Record 2--Data Fields in Group K (AlO. IIP)
CHNAME(K) = a ten-character descriptive name for System (K).
(AlO)
NFLD = number of fields of constants for this group;
0 =• no constants for this group; the user may
subdivide the constants into any number of arbi-
trary fields. (110)
If no constants are to be input for this group, set NFLD equal to
zero and continue with next group.
Record 3--Number of Constants in Field (AlO. IIP)
FLDNAME = ten-character name identifying field of constants.
(AlO)
NCONS = number of constants to be entered in this field;
0 = no constants for this field (skip to next
field). (110)
Record 4--Constants (2(AlO. IIP. F10.0)) ;
TNAME(ISC) = name identifying constant ISC. (AlO)
ISC = number identifying constant; these numbers are
set by model developer. (110.)
CONST(ISC) = value of constant ISC. (F10.0)
185
-------
ORGANIZATION OF RECORDS
Record 1 is entered once in Data Group H. Records 2 through 4 are
entered as NOSYS +1 groups. For each group, Records 3 and 4 are entered NFLD
times. For each field, Record 4 uses as many lines as needed for NCQNS
entries (2 per line).
DATA GROUP I: Kinetic Time Functions--
The definition of the kinetic time function will vary depending upon the
structure and the kinetics of the systems comprising each model. The input
format, however, is constant.
VARIABLES
Record 1--Number of Time Functions (IIP. 70X)
NFUNC = number of time functions required by the model.
If no time functions are to be input, set NFUNC
equal to zero and go to Card Group J. (110)
TITLE - name of data group. (70X)
Record 2--Time Function Descriptions (A5. 215)
ANAME(ISC) — an optional one to five alphanumeric character
descriptive name for the time function K. (A5)
NOBRK(ISC) = number of breaks used to describe the time
function K. (15)
ISC = number identifying the time function; these
numbers are set by the model developer. (15)
I - 1, NFUNC
Record 3--Time Functions (4(2F10.0))
VALT(K) - value of time function ISC at time T(K). (F10.0)
T(K) = time in days. If the length of the simulation
exceeds T(NOBRK), the time function will repeat
itself, starting at T(l), i.e., the approximation
is assumed to be periodic, with period equal to
T(NOBRK). (F10.0)
K - 1, NOBRK
186
-------
ORGANIZATION OF RECORDS
Record 1 in entered once in Data Group I. Records 2 and 3, as a set,
are repeated NFUNC times. Within each NFUNC set, Record .2 is input once and
Record 3 uses as many 80-space lines as needed to input NOBRK entries. Four
entries (four VALK(K)-T(K) pairs) will fit on each 80-space line.
4
DATA GROUP J: Initial Concentrations--
The initial conditions are the segment concentrations and densities for
the state variables at time zero (or the start of the simulation).
VARIABLES
Record 1--System Information (A40. 15. F5.0. F10.0. 20X)
CHEML — chemical or system name (A40).
IFIELD = solids field (3, 4, or 5) that transports this
system in its pure or sorbed form (15).
DSED = density of system; 0.0 for chemical, 0.5-2.5 for
solids, kg/L. (F5.0).
CMAX = maximum concentration, mg/L. (F10.0)
TITLE = name of data group. (20X)
Record 2--Initial Conditions (3CA5. 2F10.0')')
ANAME(K) = an optional one to five alphanumeric character
descriptive name or number identifying segment K. (A5)
C(ISYS,K) •= initial concentration in segment K of system ISYS
in the appropriate units, mg/L. (F10.0)
DISSF
K = 1, NOSEG
ISYS = 1, NOSYS
dissolved fraction of chemical in segment K. (F10.0)
ORGANIZATION OF RECORDS
Records 1 and 2 are a set and will be repeated NOSYS times. Within each
NOSYS set Record 2 will use as many 80-space lines as needed to input NOSEG
entries. Three entries (ANAME-C-DISSF) will fit on one line. After NOSEG
entries have been entered in a NOSYS set, begin the next NOSYS set on the
following line. If ICFL = 2 in Data Group" A, initial conditions are read
from the restart file (*.RST, where * is the input data set name), and Data
Group J should not be included in the input data set.
187
-------
WASP4 Data Group Tables
Card Group A: Sltnu
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Definition
Title of simulation
Description of ilmulotton
Ham«* of Record M vcriab!o«. positioned properly
Simulation type: 0 - Dynamic, 1 - Steady State
Number of segment* In model network
Number of model «ystem» (State Variables)
Flag controlling u»» of restart files; 0 = do not use restart
flit*; t s wrtre final conditions to restart flies; 2 = read
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Flag controlling messages printed on screen during simulation
0 = all messages printed; 1 = simulation time only printed;
2 = ail messages are suppressed
System Ho. for which mass balance analysis wiil be performed
Negative solution opKon; 0 = prwento negative solutions;
1 & allows negative solutions
Time step cpflon; 0 = usor Inputs time step history; 1 = model
calculates time atep
Adveetion facton 0 = backward difference; 0.5 = central
difference; 0-0.4 recommended
Day at beginning of simulation; 1 Is first day
Hour at the beginning of simulation
Minute at the beginning of simulation
System for which coneetrstions will be displayed en screen
throughout the simulation.
Segments fo which systemlDSYconc«atratkins will be
displayed on s«rten throughout the simulation.
Segments fo which systemiDSYconcentraHons will be
displayed on screen throughout the simulation
Factor by which Input kinetic rates will be adjusted
0. or 1. =» no adjustments; 24. = adjust Input hours to
days; 86400. = adjust Input seconds to days.
Number of different model tim* steps
Time step to be used until time T(l)
Time up to when time step DTS(I) will be used
Number of different print Intervals
Print Interval to be used until time TPRINT(I)
Time up to when print interval PRINTQ) will be used
Bypass option for system ISYS; 0 = system will
be simulated; 1 = system will be bypassed
Unfa
day
hr
mln
days
days
days
days
188
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Variable
E1-A-NOBC(ISYS)
E2'& SCALB(ISYS)
C-CONVB
E*- D- 1BC(ISYS)
E-NOBRK
E4-F-BCT(J)
F-T(J)
Number of boundary conditions
Scale factor for adjusting system 'ISYS1 boundary concentration
Units conversion factor for adjusting sytrtem 'ISYS' boundary
concentrations
Segment number that boundary 'I' is connected with
Number of data points defining boundary 'I' time function
Boundary concentration at time 'T(J)'
Time at which boundary concentration 'BCT(J)' applies
NOTE: Repeat block E1-E4 NOSYS times, once for'each system.
Repeat block E3-E4 NDBC times, once for each boundary condition.
Units
mg/l
' days
r i
r 2
F 3
f 4-
Variable
Fl A NOWK(ISYS)
F2 B SCALW(ISYS)
C CONVW
F3 D IWK(ISYS)
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F4 F WKT(J)
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:T
t 3 4 3 « 7 S 9,0
*
S
t
.ski
2343470IO
J 3 4 3 • 7 S 1,0
- -j-
I'fe
Units
Number of loads ' •-..'•
Scale factor for adjusting system 'ISYS' loads
Units conversion factor for adjusting system 'ISYS' loads
Segment number that load T enters
Number of data points defining load 'I* time function
Load at time T(J)'
Time at which load 'WKr(J)' applies
NOTE: Repeat block F1-F4 NOSYS times, once for each system.
Repeat block F3-F4 NOWK times, onco for each load.
kg/day
days
193
-------
F i
r s
r 3
r 4
1
1
!A
r
A|A
t|e
0£
H
EEE
Care
5T
II
f
H
E
II
~0
t
II
5
E
H
b
F
H
J Group F2:
e
ii
F
H
E
H
Waste Lo<
--
ids
'Won PC
iir»t Source
Loads)
5
Variable Definition
FI A NOWKS Number of segments receiving nonpoint source loads. If NOWKS Is
greater than 0, NFS file is read.
B NPSDAY The time in the runoff file 'NFS.DAT' corresponding day to the
initial simulation time
F2 C SCALH Scale factor to adjust runoff loads. All runoff loads will
bo multiplied by this factor
D CONVN Unit? conversion factor to adjust runoff loads. Runoff loads are
expected in Kg/Day. If runoff loads are give in S.A.E. units
(Lbs./Doy), this factor will be 0.454
F3 E INPS(J) Segment number ia which runoff load 'J' is applied; J = 1. NOWKS
F4 F KT1 Initial day for which nonzero runoff loads from file 'NFS.DAT'
will bo printed
G KT2 Final day for which nonzero loads from file NFS.DAT will
bo printed
H KPRT(I) Indicator specifying whether nonzero runoff loads will be .printed
for system 'I*. 0 = runoff loads will not be printed; 1 = runoff
loads will be printed; 1 = 1, NOSYS.
C I
0 2
C J
C 4
Units
days
days
Tnrrl Group G: Environmentali Parameters!
Variable Definition
Gt A NOPAM Number of parameters for the WASP model; TOXI4 has up
to 18; EUTR04 has up to 9. If no parameters are to be
input, set NOPAM to zero and skip to Data Group H.
G2 B ANAME(I) Descriptive name for parameter 'ISC(l)1
c |SC(|) Parameter number identifying parameter; these numbers
are set by model developer.
D PSCAL(I) Scale factor for Parameter 'I'; the values of para neter
'I1 in each segment will be multiplied by this factor
G3 E 1SG Segment number for the following parameter values
G4 F PHAME Descriptive name for parameter T; usually same as ANAME
G |s~ Parameter number identifying parameter
H PA"?AM The value of parameter 'I1 in segment 'ISG
NOTE: Repeat block G3-G4 NOSEG times, once for each segment.
Units
194
-------
H 1
H 2
H 3
H 4
Card Group H: Constants :
8
0
F
B
D
F
8
D
F
-
-
c
E
0
c
E
G
l
C
E
G
-
-
-
-
hi
H
.1
H
F
F
4
F
G
0
&
G
H
H
«
H
t
,1
Variable Definition
H1 A HEADER Title for data group 'H: Constant'
H2 B CHNAME Name of system for which constants are supplied; there will be
NOSYS +'l groups of constants - one global and, one for each
system
C NI'U) Number of fields of constants for this group; 0 = no constants for
this group; the user may subdivide the constants into any number
of arbitrary fields
H3 D FLDNAME Name identifying .field of constants
E, NCNS Number of constants to be entered in this field; 0 = no constants
for this field
H4 F TNAME(I) Name identifying constant 'ISC(I)'
G ISC(I) Number identifying constant; these numbors are set by model
developer
H CONST(I) Value of constant 'ISC(I)'
NOTE: Repeat block H2-H4 NOSYS + 1 times, once for global data
and once for each system data. Repeat block G3—G4 NFLD times,
once for each constant's field.
Units
195
-------
t I
t J
1 J
-|f ""
Card Group 1: Time Functions
r „ , «| _ . . . 2! 31 . ^TI si si n
cclc
' Ett
frri.rrj:n:
J-lTP-4--
1 11 I IT|F|F|F
f I IT rt t j I
1 1 tTn IEIEIE
1
1
F[? F
E
E
E
F
F
F
E
E
E
~~~TI~
"""1±"
+• -
' F F
Variable Definition
11 A NFUNC Number of time functions for this WASP model; TOXI4 has up to 8
Units
time functions; EUTR04 has up to 14 time functions. If no time
functions are to be input, set NFUNC equal to zero and skip to
Data Group J.
12 B ANAME(I) Descriptive name for time function 'I'
C NOBRK(I) Number of data points defining time function '!'
D ISC(I) Number identifying the time function; these numbers are set by
the model developer.
13 E VALT(J) Value of the time function at time 'T(J)'
F T(J) Time at which time function assumes value 'VALT(J)'
If the simulation exceeds T(NOBRK), the time function
will repeat itself, starting at T(1); thus the time
function is periodic, with period equal to T(NOBRK)
NOTE: Repeat block 12-13 NFUNC times, once for each time
function.
days
J I
J 2
Jl
A CHEML
B (FIELD
C DSED
D CMAX
J2 L AHAME
F C
G DISSF
Card Group J: Initial Conditions
t
E£E
Definition
Chemical or System name
Solids field (3,4, or 5) that transports this system In Its
pure form or in sorbed form.
Density of system; 0.0 for chemical, 0.5 — 2.5 for solids
Maximum possible concentration for this system
Name or number Identifying segment
Concentration of system in segment
Dissolved fraction of chemical In segment
NOTE: Repeat block J1-J2 NOSYS limes, once for each system.
..Kg/I
mg/l
mg/l
196
-------
TABLE 2.2.3. CROSS REFERENCES FOR WASP4 INPUT VARIABLES
Name
A
BQ
CHKNAME
CONVN
CONVW
DTS
IBEDV
IDMP
IQ
ISEG
IWK
JMASS
JUNSEG
KT2
NCONS
NFUNC
NOPAM
NOSYS
NPSDAY
PARAM
QBY
SCALB
SCALV
TADJ
TDINTS
TR
WKT
Data
Record
B 4
D 4
H 2
F2 2
Fl 1
A 6
C 1
A 4
D 4
C 3
Fl 1
A4
D2 4
F2 4
H 3
I 1
G 1
A 4
F2 1
G 4
D 7
E 2
C 2
A4
C 1
B 6
Fl 4
Name
ADFAC
BVOL
CMAX
CONVR
DISSF
DXP
IBC
IFIELD
IQOPT
ISG
JQ
IDSY
KPRT
MELAG
NEGSLN
NINQ
NOQS
NOWK
NRFLD
PNAME
QT
SCALN
SCALW
TNAME
VALT
ZDAY
Data
Record
A 4
C 3
I 1
B 2
J 2
C 3
E 3
J 1
D 1
G 3
D 4
A4
F2 4
A 4
A 4
D 2
D 3
Fl 1
B 1
G 4
D 6
F2 2
Fl 1
H 4
I 3
A 4
Name
ANAME
C
CONST
CONVQ
DMULT
EL
IBOTSG
INPS
IR
ITYPE
JR
IDSG1
KSIM
NBRKQ
NFIELD
NOBC
NORS
NOWKS
NSEA
PRINT
RBY
SCALQ
SYSBY
TPRINT
VEXP
ZHR
Data
Record
G 2, I 2, J 2
J 2
H 4
C 2
C 3
B 4
C 3
F2 3
B 4
C 3
B 4
A4
A 4 '
D 5
D 1
El
B 3
F2 1
D2 3
A 8
B 7
D 2
A 9
A 8
C 3
A 4
Name
BCT
CHEML
CONVB
CONW
DSED
FLDNAME
ICFL
INTYP
ISC
IVOPT
JSEA
IDSG2
KT1
NBRKR
NFLD
NOBRK
NOSEG
NPRINT
NTEX
PSCAL
RT
SCALR
T
TQ
VMULT
ZMIN
Data
Record
E 4
J 1
E 2
C 2
I 1
H 3
A 4
A 4
G 2, G 4,
H 4, I 2
C 1
D2 3
A4
F2 4
B 5
H 2
A 5, E 3,
Fl 3, 12
A 4
A 7
B 2
G 2
B 6
B 2
A 6, I 3,
E 4, Fl 4
D 6
C 3
A 4
WASP4 Output
WASP4 simulations produce several files that may be examined by the
user. These files use the file name of the input data set with a unique
extension. The most important of these is the DMP file, which contains all
kinetic display variables for each segment at each print interval throughout
the simulation. These display variables include concentrations, certain
calculated variables, and some rates. Available display variables for EUTR04
and TOXI4 are summarized in the eutrophication and toxics user manual sections.
The W4DSPLY program is provided to help the user interactively examine
the display variables contained in the DMP file. To use this program, simply
type in the VAX (VMS) command "RUN W4DSPLY" or the PC (DOS) command "W4DSPLY."
197
-------
The program will prompt the user for information, as explained in Section 2.1.
Other files created by a WASP simulation include *.OUT, *.TRN, *.MSB,
and *.RST (where * is the name of the input data set). The OUT file contains
a record of the input data plus any simulation error messages that may have
been generated. The TEN file contains a set of transport associated variables
for each segment at each print interval throughout the simulation. These
variables include the time step (day), calculated maximum time steps (day),
segment volumes (m ) , segment flows (m /sec), flow changes (m /sec), time
constants for segment flow (day ), segment exchange flows (m /sec), the time
constant for segment exchanges (day ), the segment dispersion coefficient
(m /sec), and the numerical dispersion coefficient (m /sec). The MSB file
contains a mass balance record for one designated system in the model network
as a whole (in kg). For each print interval, this file records the accumu-
lated mass in from advection, dispersion, and loading; the accumulated mass
out through advection, dispersion, burial (or volatilization, and kinetic
transformation; the total resident mass; and the residual (unaccounted for)
mass.
The RST file contains a snapshot of volumes and concentrations of each
system in each segment at the conclusion of the simulation. This file can be
read by WASP4 to continue a series of simulations.
2.4 THE EUTROPHICATION MODEL
Introduction
EUTR04 requires the same input format as the basic WASP4 model. This
format is explained in detail in Section 2.3. This section describes vari-
ables needed specifically for EUTR04. Elaborations on WASP4 occur only in
Data Groups G, H, and I. Records or variables within a record that are not
mentioned here remain the same as described in Section 2.3.
As described in Section 1.4, the 8 systems for eutrophication modeling
are: ammonia nitrogen, nitrate nitrogen, ortho-phosphate phosphorus, phyto-
plankton carbon, carbonaceous BOD, dissolved oxygen, organic nitrogen, and
organic phosphorus. Table 2.4.1 summarizes these systems and their use in
six discrete levels of complexity.
EUTR04 Data Descriptions
DATA GROUP A: Model Identification and System Bypass Option--
NOSYS
SYSBY(K)
Record 4--Model Identification
8
0 for those variables checked in the relevant
complexity level in Table 2.4.1.
198
-------
1 for those variables not checked in the relevant
complexity level in Table 2.4.1.
TABLE 2.4.1. EUTR04 SYSTEMS AND COMPLEXITY LEVELS
System
Number
Symbol Name
Use in Complexity Level
123456
1
2
3
4
5
6
7
8
NH3 Ammonia nitrogen
N03 Nitrate nitrogen
P04 Inorganic phosphorus
CHL Phytoplankton carbon
CBOD Carbonaceous BOD
DO Dissolved oxygen
ON Organic nitrogen
OP Organic phosphorus
X X X X X
X X X X
XXX
XXX
X X X X X X
X X X X X X
X X X X
XXX
Complexity
Level
Explanation
1
2
3
4
5
6
"Streeter-Phelps" BOD-DO with SOD
"Modified Streeter-Phelps" with NBOD
Linear DO balance with nitrification
Simple eutrophication
Intermediate eutrophication
Intermediate eutrophication with benthos
199
-------
DATA GROUP B: Exchange Coefficients--
No changes.
DATA GROUP C: Volumes--
No changes.
DATA GROUP D: Flows--
No changes.
DATA GROUP E: Boundary Concentrations--
No changes. Input is repeated 8 times, once for each system. No
boundary concentrations need be specified for those systems being bypassed.
DATA GROUP F: Waste Loads--
No changes. Input is repeated 8 times, once for each system.
need be specified for those systems being bypassed.
No loads
DATA GROUP G: Environmental Parameters--
Listed below are the 9 parameters required for eutrophication. For
Level 1 and 2 analyses, only TMPSG, TMPFN, and SOD1D (3, 4, and 9) need be
specified. For Level 3 analysis, VELSG and FNH4 (2 and 7) may be added
(DEPTH and VELSG are used to compute reaeration; if rate constant K2 is
specified (Constant 82), then VELSG can be omitted). For analyses at Level 4
and above, all parameters should be specified.
ISC PARAM (ISEG.ISC)
Definition and Units
1 VELFN(ISEG)
SAL(ISEG)
TMPSG (ISEG)
Pointer to the time-variable velocity function tp be
used for ISEG. The four velocity functions are de-
fined by the user in data group I.
Average salinity of ISEG, in g/L; used in calcu-
lation of DO saturation.
Segment temperature multiplier (°C). TMPSG varies
over space and can be either actual temperature or a
normalized function, depending on the definition of
TEMP. TMPSG(ISEG) * TEMP(TMPFN(ISEG)) = STP, the
temperature of segment ISEG.
200
-------
4 TMPFN (ISEG)
5 KESG (ISEG)
KEFN (ISEG)
FNH4 (ISEG)
FP04 (ISEG)
SOD1D (ISEG)
Flag designating the time-variable temperature
function to be used for ISEG. The four temperature
functions are defined by the user in data group I.
Segment extinction coefficient multiplier (m ).
KESG varies over space and can be either an actual
extinction coefficient or a normalized function,
depending on the definition of KE. KESG(ISEG) *
KE(KEFN(ISEG)) = Ke, the extinction coefficient for
segment ISEG.
Pointer designating the time variable extinction
coefficient (KE) to be used for segment ISEG. The
five extinction coefficients available are defined
in data group I.
Average ammonium flux multiplier for segment
(mg/mz-day).
Average phosphate flux multiplier for segment
(mg/mZ-day).
0
Sediment oxygen demand for segment (g/m -day).
DATA GROUP H: Constants--
Listed below are the 42 constants available for a full eutrophication
simulation. Figures 2.4.1 through 2.4.6 list the constants required for each
level of complexity.
ISC
11
12
13
21
22
23
CONST (ISC)
K1320C
K1320T
KNIT
K140C
K140T
KN03
ANAME(ISC)
K12C .
K12T
KNIT
K20C
K20T
KN03
Definition and Units
Nitrification rate at 20°C, per day.
temperature coefficient for K1320C.
Half -saturation constant for nitrification-
oxygen limitation, mg 02/L.
Denitrification rate at 20 °C, per day.
Temperature coefficient for K140C .
Half -saturation constant for denitrifica-
41 K1C
42 KIT
K1C
KIT
tion oxygen limitation, mg02/L.
Saturated growth rate of phytoplankton
(day"1).
Temperature coefficient.
201
-------
ISC CONSTdSC) ANAMECISCn
43 LGHTSW LGHTS
44 PHIMX
45 XKC
46 CCHL
47 IS1
48 KMNGl
49 KMPG1
50 K1RC
51 K1RT
52 KID
53 K1G
54 NUTLIM
55 KPZDC
PHIMX
XKC
CCHL
IS1
KMNG1
KMPG1
K1RC
K1RT
KID
K1G
NUTLIM
KPZDC
Definition and Units
Light formulation switch:
= 1, use Dick Smith's (USGS) formulation
= 2, use DiToro et al. (1971) formulation
Maximum quantum yield constant. Used only
when LIGHTSW - 1, mg C/mole photons.
Chlorophyll extinction coefficient. Used
only when LGHTSW
1, (mg chla/m3 ) '
Carbon- to -chlorophyll ratio. Used only
when LGHTSW = 2 (mg carbon/mg chla) .
Default - 30.
Saturation light intensity for phytoplank-
ton. Used only when LGHTSW = 2 (Ly/day) .
Nitrogen half -saturation constant for nitro-
gen for phytoplankton growth, which also
affects ammonia preference, mg-N/L. NOTE:
This affects ammonia preference:
= 0, PNH3G1 -1.0
= Large, PNH3G1 = NH3/(NH3 + N03)
NOTE: For standard model application,
use a large KMNG1.
Phosphorous half -saturation constant for
phytoplankton growth, mg PO^-P/L.
Endogenous respiration rate of phyto-
plankton at 20° C, day"1.
Temperature coefficient for phytoplankton
respiration.
Non-predatory phytoplankton death rate,
day'1.
Grazing rate on phytoplankton per unit
zooplankton population, L/cell-day.
Nutrient limitation option (default
0 — minimum
1 = multiplicative
0).
Decomposition rate constant for phytoplankton
in the sediment at 20°C, per day.
202
-------
isc coNSTdscn
56 KPZDT
57 PCRB
58 NCRB
59 KMPHYT
71
72
75
KDC
KDT
73 KDSC
74 KDST
KBOD
81 OCRB
82 K2
91 K1013C
92 K1013T
ANAMEdSC)
KPZDT
PCRB
NCRB
KMPHY
KDC
KDT
KDSC
KDST
KBOD
OCRB
K2
K71C
K71T
Definition and Units
Temperature coefficient for decomposition of
phytoplankton in sediment.
Phosphorus-to-carbon ratio in phytoplankton,
mg P04-P/mg C.
Nitrogen-to-carbon ratio in phytoplankton,
mg N/mg C.
Half-saturation constant for phytoplankton,
mg carbon/L. NOTE: As phytoplankton
increases, mineralization of organic
nitrogen and organic phosphorus increases.
KMPHYT = small; little phytoplankton
effect on mineralization
= large; large concentration of
phytoplankton needed to drive
mineralization
For standard model application, use
KMPHYT =0.
BOD deoxygenation rate at 20°C, per day.
Temperature coefficient for carbonaceous
deoxygenation in water column.
Decomposition rate of carbonaceous BOD in
the sediment at 20 "C, per day.
Temperature coefficient for carbonaceous
deoxygenation in the sediment.
Half saturation constant for carbonaceous
deoxygenation oxygen limitation.
Oxygen to carbon ratio in phytoplankton,
mg 02/mg C.
Reaeration rate constant at 20°C for entire
water body, day"1. NOTE: If K2 is not
entered, the reaeration rate will be calcu-
lated from water velocity, depth, and wind
velocity.
Mineralization rate of dissolved organic
nitrogen, per day.
Temperature coefficient for K1013C.
203
-------
ISC CONST(ISC)
93 KONDC
94 KONDT
95 FON
100 K58C
101 K58T
102 KOPDC
103 KOPDT
104 FOP
ANAME(ISC) Definition and Units
KONDC Decomposition rate constant for organic
nitrogen in the sediment at 20°C, per
day.
KONDT Temperature coefficient for decomposition of
organic nitrogen in the sediment.
FON Fraction of dead and respired phytoplankton
nitrogen recycled to organic nitrogen.
Default =1.0.
K83C Mineralization rate of dissolved organic
phosphorus, per day.
K83T Temperature coefficient for K58C.
KOPDC Decomposition rate of organic phosphorus
in the sediment at 20°C, per day.
KOPDT Temperature coefficient for decomposition of
organic phosphorus in the sediment.
FOP Fraction of dead and respired photoplankton
phosphorus recycled to organic phosphorus.
Default =1.0.
204
-------
L2
C L
ft ti
N 0
P 6
P H
B 0
d •
00
ox
UN
0 C
3
O
J
4
Y
5
o
X
i
U
I
X
9
5
A
I
—
1
L
9
n
7
S
e
a
a
n
t
-
?
a
K
e
K
y
t
0
2
L
1
SL
-
1
.3
C
-
b
V-
N'S
-
-
-
9
1
7
B
0
A
0
0
0
0
0
T
1
1
1
1
2
0
0
1
ti
2
I
t
4
F
3
0
-
6
K
-
1
0
0
n
9
-
2
5
J
0
I
J
0
1
-
t
E
-
3
1
I
-
3
r
R
-
7
n
i
o
F
-
-
t
r
2
^
s
4
t
«
2
1
Q
v]
i
0
F
L
-
-
i
3 4 5 e 7 f
1
-
i
V
>
Y^^oJ
-
1251
9 « 7 •
-
"I
V
Figure 2.4.1. Constants for Level 1.
LZ
5 L
H ti
n I
NO
PO
PH
C O
DO
O X
0 N
OP
J
O
j
I
3
4
Y
r
1.
_4
D
r
T
b
J
J
A
•
e
L
d
d
n
7
S
e
•
0
B
O
O
K
I
JL
X
K
X
U
•
K
q
y
N
y
2
2
1
O
•t
N
2
S
5,
T
5
A
e
N
z
T
0
?
F
1
7
8
0
b
0
1
2
1
0
6
6
2
i
i
i
2
0
b
l
R
,?
7
3
M
1
O
;|l
n
«
i
7_,
F
6
0
0
R
i
0
r
1
2
3
J
0
n
5
j
0
L
3
3
S
1
T
?
R
8
F
-
3L
•
T
K
K
8
F
N
D
4
0
H
T
T
L
1.
p
3
H]
1
s.
i
s
P
^
s
B
-
?
T
7
1
2
2
1^
z.
p
i
V
t
a.
L
f
7
2
1
1
f
f
0
0
!
9
a
s
j_
-
?
-
j
j
J
"~
i
Figure 2.4.2. Constants for Level 2.
205
-------
. r
c o N ; i •
•in a .. .
n : ' . . .5 S $ - ,
K 1 2 C
SO 3
PCM
P H fT
ghoto, (••»[;_
K 1 C
K 1 RC
corb"d«oxy
K DC
ON
r 1 n • r o 1 1 I •
K7 1 C
or
o x U» i 5 o J B o o LZ^ri,? * 2 " ? 9 Lt-iLi.? n 7 ** ^ ° 1 5L5J ? f 7 P
" F O!R LINEAR DO o A L A N]C E . LEVEL 3
•H-"-- :±
-. ::±: :::::::::::::
1.5 I : !
0 _ _ -
] . _ _
1
4
*i o.-»o < i i __i\ Li
50 6.25
-------
i fl r, ^
i'i
X 3JJ f JLIJL9
J 8 f 1LS I 5
*r , -r A
Figure 2.4.5. Constants for Level 5.
LA
D E
El'
C 0
d «
d •
1
N
t
r
c
c
1
A
T
i
b
o
o
I
D
H
o
71
T
«
D
0
P
K
d
-
K
P
K
7
1
S
1
\>
•
K
n
0
-
0
a
T
a
Z
o
D
1
N
P
P
«,
1
n
D
X
S
t
D
h
I)
1
0
0
k
C
I
C
r
C
o
C
a
N
-
2
A
3
L
^L
Z
C
f
6
z,
N
-
a
S
1
9
T
5
7
S
*
A
4
2
5
2
J
2
J
2
02
1 2
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a,
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0
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0
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0
0
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0
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D
-
0
0
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0
J
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-
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4
4
4
1
N
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K
K
K
R
P
K
0
0
E
-
Z
n
H
p
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s
D
D
2
T
r
T
T
12343«7S«0
r
1
0
N
S
L
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7
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-------
DATA GROUP I: Miscellaneous Time Functions--
Listed below are the 18 time functions available for eutrophication.
Only TEMP(l) is required for Level 1 and 2 analyses. For Level 3 analyses,
TFNH4, VELN(l), and WIND may be added (WIND is needed only for calculating
reaeration in non-flowing water bodies such as lakes). For analyses at Level
4 and above, ITOT, F, KE, and TFP04 should be used. For resolution of spatial
variability in temperature, light extinction, and water velocity the four
TEMP functions, the five KE functions, and the four VELN functions may be
used.
NOTE: Functions 1-4 are the four temperature-function options available
for TMPFN in Data Group G. Functions 8-12 are the five extinc-'
tlon coefficient options for KEFN in Data Group G. Functions
15-18 are the four water velocity options for VELFN in Data Group
G.
ISC ANAMEaSG)
1 TEMP(l)
2
3
4
TEMP(2)
TEMP(3)
TEMP (4)
VALT(ISC)
Time-variable temperature function 1. TEMP(K) can
be either a normalized function or an actual
temperature in °C, depending upon the definition
of the parameter multiplier TMPSG(ISEG) .
Time-variable temperature function 2, unitless or
Time-variable temperature function 3, unitless or
Time -variable temperature function 4, unitless or
5
6
7
8
ITOT
F
WIND
KE(1)
9 KE(2)
10 KE(3)
Total daily solar radiation, langleys .
Fraction of daylight, days.
Wind velocity, m/sec.
Time-variable extinction coefficient function 1.
This can be either a normalized function or an
actual extinction coefficient in m , depending
upon the definition of the parameter multiplier
KESG(ISEG) .
Time-variable extinction coefficient function 2,
-1
unitless or m
Time-variable extinction coefficient function 3,
unitless or m
-1
208
-------
11 KE(4)
12 KE(5)
13
14
15
16
17
18
19
TFNH4
TFP04,
VELN(l)
VELN(2)
VELN(3)
VELN(4)
ZOO
Time-variable extinction coefficient function 4,
unitless or m .
Time-variable extinction coefficient function 5,
unitless or m. .
Normalized ammonium flux from bed, unitless.
, Normalized phosphate flux-from bed, unitless.
Time variable velocity function 1, m/sec. This
.velocity is added to the net velocity VELOCG(ISEG)
computed from the segment flow and the hydraulic
parameters read in Data Gro.up G.
Time variable velocity function 2, m/sec.
Time variable velocity function 3, m/sec.
Time variable velocity function 4, m/sec.
Herbivorous zooplankton population, mgC/L.
DATA GROUP J: Initial Concentrations--
No changes. Input is repeated 8 times, once for each system. Solids
transport fields must be specified for the particulate fraction of each system
(Solids Field 3 here is particulate organic matter; Solids Field 4 is phyto-
plankton; Solids Field 5 is inorganic sediment). The dissolved fraction of
each system in each segment must also be specified.
IFIELD(l)
IFIELD(2)
IFIELD(3)
IFIELD(4)
IFIELD(5)
IFIELD(6)
IFIELD(7)
IFIELD(8)
Record 1--Solids Transport Fields
= 3
= 5 . . -
5 , - .
= . 4 (make sure DISSF =0.0)
'3
= 5 (make sure DISSF =1.0)
= 3
= 3
209
-------
TABLE 2.4.2. CROSS REFERENCES FOR EUTR04 INPUT VARIABLES
Name
CCHL
FP04
FON
K12T
K1RC
K20C
K83C
KDST
KE(4)
KMPHYT
KMPG1
KONDT
KPZDT
OCRB
TEMP(3)
TFNH4
VELN(2)
XKC
Data
Number
H 46
G 8
H 95
H 12
H 50
H 21
H 100
H 74
I 11
H 59
H 49
H 94
H 56
H 81
I 3
I 13
I 16
H 45
Name
DEPTH
1S1
K1C
FOP
K1RT
K20T
K83T
KE(1)
KE(5)
KESG
KNIT
KOPDC
LGHTSW
PCRB
TEMP (4)
TFP04
VELN(3)
ZOO
Data
Number
G 1
H 47
H 41
H 104
H 51
H 22
H 101
I 8
I 12
G 5
H 13 •
H 102
H 43
H 57
I 4
I 14
I 17
I 19
Name
F
ITOT
KID
KIT
K71C
KBOD
KDT
KE(2)
KEFN
KN03
KOPDT
KCRB
PHIMX
TEMP(l)
TMPFN
VELFN
VELN(4)
Data
Number
I 6
I 5
H ,52
H 42
H 91
H 75
H 72
I 9
G 6
H 23
H 103
H 58
H 44
I 1
G 4
G 1
I 18
Name
FNH4
K12C
K1G
K2
K71T
KDC
KDSC
KE(3)
KMNG1
KONDG
KPZDC '
NUTLIM
SOD1D
TEMP(2)
TMPSG
VELN(l)
WIND
Data
Number
G 7
H 11
H 53
H 82
H 92
H 71
H 73
I 10
H 48
H 93
H 55
H 54
G 9
I 2
G 3
I 15
I 7
210
-------
EUTRgfr Output
The standard WASP4 output files were summarized in Section 2.3,. EUTR04
stores in the DMP file 36 kinetic display variables. These variables are
defined in Table 2.5.2. To, examine these variables in tabular, form, the user
may run W4DSPLY as explained in Section 2.3.
TABLE 2.5.2. EUTR04 KINETIC DISPLAY VAKJABLES
Number
I
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
Variable
SEG. DEPTH
WATER VEL.
ITOT
SEG. TEMP
SEG. TYPE
PHYT
RESP
DEATH
LIMIT
TCHLAX
XEMP1
XEMP2
GP1
RLIGHT
RNUTR
PNH3G1
NH3
Definition .:. ;
Depth in segment (m) .
Water velocity within segment (m/sec) .
Incoming solar radiation (Langleys/day) .
Temperature within segment (°C).
Segment type (1, 2, 3 or 4)
Phytoplankton biomass as carbon (mg/L) .
Phytoplankton respiration rate consant (day ) .
. .. • . • '.: • .'. : :
Phytoplankton death rate constant (day ) .
Nutrient limitation indicator ("+" = nitrogen,
'"-" = phosphorus). ' ••;'.'.
Phytoplankton chlorophyll a concentration (//g/L) .
Nitrogen limitation factor for phytoplankton. "''•'<':'.'
Phosphorus limitation factor for phy toplankton. '
Light and nutrient limited phytoplankton growth 'irate
. .constant (day .
Light limitation factor for phytoplankton growth.
Nutrient limitation factor for phytoplankton.
Preference factor for ammonia over nitrate.
Segment ammonia concentration (mg/L) .
211
-------
TABLE 2.5.2. EUTR04 KINETIC DISPLAY VARIABLES (Continued)
Number
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
Variable
N03
ON
TIN
TOT. N
TON
CN
OP
OP04
TIP
TOP
RATIO
DO
CBOD
BOD5
UBOD
DOMIN
DOMAX
CS
KDC
DEL02
Definition
Segment nitrate plus nitrite concentration (mg/L) .
Segment organic nitrogen concentration (mg/L) .
Total inorganic nitrogen concentration (mg/L) .
Total nitrogen concentration (mg/L) .
Total organic nitrogen concentration (mg/L) .
Total inorganic nitrogen (mg/L) .
Segment organic phosphorus concentration (mg/L) .
Segment orthophosphate concentration (mg/L) .
Total inorganic phosphorus concentration (mg/L) .
Total organic phosphorus concentration (mg/L) .
Inorganic nitrogen to phosphorus ratio (mg/mg) .
Dissolved oxygen concentration (mg/L) .
Carbonaceous biochemical oxygen demand (mg/L) .
5 -Day biochemical oxygen demand (mg/L) .
Ultimate 30 -day BOD (mg/L) .
Minimum diurnal dissolved oxygen (mg/L) .
Maximum diurnal dissolved oxygen (mg/L) .
Dissolved oxygen saturation concentration (mg/L) .
Specific carbonaceous BOD deoxygenation rate at 20 °C
(day'1).
Diurnal dissolved oxygen variation (mg/L) .
212
-------
2.5 THE TOXICS MODEL
Introduction
TOXI4 requires the same input format as the basic WASP4 model, which
is explained in detail in Section 2.3. This section describes variables
needed specifically for TOXI4. Elaborations on WASP4 occur only in Data
Groups G, H, and I. Records or variables within a record that are not
mentioned here remain the same as described in Section 2.3.
The two systems for toxics modeling are chemical and solids as outlined
in Table 2.5.1. TOXI4 can be run at different levels of complexity for solids
behavior, equilibrium reactions, and kinetic reactions. The amount of input
data that must be specified depends upon which levels are chosen.
TABLE 2.5.1. SUMMARY OF TOXI4 SYSTEMS
Levels of Complexity
System
Number
1
2
3
4
5
6
Solids
Symbol Name 1, 2 3
GI Chemical 1 XX
S-L Solid 1 X
S2 Solid 2
S3 Solid 3
C2 Chemical 2
C3 Chemical 3
Kinetics
4 1-3 4
XXX
X
X
X
X
X
Complexity
Level Explanation
Solids 1
Solids 2
Solids 3
Solids 4
Equil 1
Equil 2
Equil 3
Equil 4
Equil 5
Kinetic 1
Kinetic 2
Kinetic 3
Kinetic 4
Descriptive solids concentration field
Descriptive solids concentration field with
transport rates
Simulated total solids
Three simulated solids types
Constant partition coefficient
Spatially-variable partition coefficients
Hydrophobic sorption
Solids -dependent partitioning
Sorption plus ionic speciation
Constant half lives or rate constants
Spatially-variable rate constants •
Second order rates
Transformation products
specified solids
213
-------
TOXI4 Data Group Descriptions
DATA GROUP A: Model Identification and System Bypass Option--
NOSYS
Record 1--Model Identification
1-6, depending on solids and kinetic complexity levels
chosen.
SYSBY(K)
Record 9--Bypass Optins
0 for those variables checked in the relevant
complexity level in Table 2.5.1.
1 for those variables not checked in the relevant
complexity level in Table 2.5.1.
DATA GROUP B: Exchange Coefficients--
No changes.
DATA GROUP C: Volumes--
No changes.
DATA GROUP D: Flows--
No changes.
DATA GROUP E: Boundary Concentrations--
No changes. Input is repeated for each system.
DATA GROUP F: Waste Loads--
No changes. Input is repeated for each system.
DATA GROUP G: Environmental Parameters--
Table 2.5.2 gives the 18 parameters that may be used by TOXI4. The user
need input only those required to model the particular reactions being
considered. For solids, equilibrium, and kinetics Level 1, no parameters are
necessary.
214
-------
TABLE 2.5.2. TOXI4 PARAMETERS
ISC PARAM (ISEG,ISC)
Definition. Units. Reactions Affected
1 VELFN (ISEG)
2 TMPFN (ISEG)
3 TEMP (ISEG)
4 WVEL (ISEG)
5 REAR (ISEG)
6 DOC (ISEG)
7 FOG (ISEG.1)
8 FOC (ISEG,2)
9 FOC (ISEG,3)
10 CHPHL (ISEG)
11 PH (ISEG)
12 XKE2 (ISEG)
13 OXRAD (ISEG)
14 BAG (ISEG)
15 EXENV (ISEG)
16 TOTKG (ISEG.l)
17 TOTKG (ISEG,2)
18 TOTKG (ISEG,3)
Pointer to water velocity time function (1-4); V.
Pointer to normalized temperature time function
(1-4); ALL.
Multiplier for water temperature time function
(°C); ALL.
Multiplier for wind velocity (10 meters above seg-
ment surface) time function (meters/sec); V
Multiplier of time function 5, whose definition
depends on volatilization option XV (constants
236,736,1336): XV = 1 volatilization rate constant
XV = 2,3 oxygen reaeration rate constant
XV = 4,5 REAER not used; enter 0. (meters/day); V.
Dissolved organic carbon concentrations (mg/L); S, P
Fraction organic carbon of solids class 1; S
Fraction organic carbon of solids class 2; S
Fraction organic carbon of solids class 3; S
Multiplier for phytoplankton chlorophyll concen-
tration time function (mg/L); P.
Multiplier for pH time function; H, I.
Light extinction coefficient for photochemically
active light (I/meter); this value is used only
for photolysis option XPHOTO = 2 (constants 286,
886,1486). For photolysis option 1 or 2 when
XKE2 =0.0 the extinction coefficient is calculated
from solids, DOC, and chlorophyll concentrations; P.
Concentration of oxidants, such as Og or #2^2
(moles/L); 0.
Density of active bacteria (cells/100 cc) the units
for bacterial density must be consistent with those
used for the second order biodegradatiori rate con-
stants KBI020 (constants 146-160, 746-760, 1346-
1360); the product of BAG and KBI020 must be units
of day'1; B.
Property of aquatic environment that affects the
user-defined "extra reaction." The units for
EXENV must be consistent with those used for
second order rate constants KE20 (constant 576-
590, 1176-1190, 1776-1790); the product of EXENV
and KE20 must yield units of day"1; E.
Total lumped first-order decay rate constant for
chemical 1 in segment (day ).
Total lumped first-order decay rate constant for
chemical 2 in segment (day ).
Total lumped first-order decay rate constant for
chemical 3 in segment (day ) '
I = ionization, S
H — hydrolysis, 0
sorption, V = volatilization, B = biodegradation,
oxidation, P = photolysis, E = extra reaction
215
-------
For equilibrium level 2, FOC(ISEG,1) is used to enter partition coeffi-
cients. For equilibrium levels 3 and above, FOC(ISEG,1) is fraction organic
carbon of solids class 1. DOC(ISEG) may be entered. If two or three solids
classes are being simulated (solids level 4), then FOC(ISEG,2) and FOC(ISEG,3)
must be entered. For equilibrium level 5, PH(ISEG) values are necessary.
At kinetics level 2, TOTKG(ISEG,1) is specified. If two or three chemi-
cals are being simulated at this level, then TOTKG(ISEG,2) and TOTKG (ISEG,3)
must be specified. Kinetics level 3 may require the remaining parameters,
depending on the kinetic processes of importance. If water temperatures
differ significantly from 20°C, then TEMP(ISEG) may be necessary for all
processes (depending on the accuracy required of the simulation). Volatili-
zation requires REAR(ISEG) for options 1, 2, and 3, but not for 4 and 5. If
reareation values are not available for volatilization options 2 and 3, then
rates can be calculated internally if parameters DEPTH(ISEG) and VELOC (ISEG)
are given. Volatilization options 4 and 5 require parameter WVEL (ISEG).
Photolysis requires DEPTH(ISEG) values. In addition photolysis option 1
requires DOC(ISEG) and CHPHL(ISEG). Photolysis option 2 may use either DOC
(ISEG) and CHPHL(ISEG) values or XKE2(ISEG) values. The remaining processes
of hydrolysis, oxidation, biodegradation, and extra reaction require one
parameter each: PH(ISEG), OXRAD(ISEG), BAG(ISEG), and EXENV(ISEG), respec-
tively.
DATA GROUP H: Chemical Constants--
A large number of constants are available to characterize the various
chemical reactions at different levels of complexity. Very few need be
specified for any one simulation. Table 2.5.3 summaries the constants that
may be used for equilibrium and kinetics level 1. Only two of these need be
specifled--PIXC(1,1) and either a half life or, a first order rate constant.
For equilibrium and kinetics level 2, no constants need be specified--parti-
tion coefficients and rate constants are entered via parameters.
For kinetics level 3, some general chemical constants are usually
available, as summarized in Table 2.5.4. MOLWT, SOLG, and VAPRG are sometimes
used In volatilization computations, while LKOW can be used in sorption
calculations.
If a chemical is ionic, then constants from Table 2.5.5 may be specified.
For each ionic specie I, SPFLG(I) and PKA(I) must be specified. EPKA(I) may
also be given. Ionic speciation is considered to be equilibrium level 5.
The presence of ionic species requires significantly more data specifications
for the remaining processes.
Hydrophobic sorption is equilibrium level 3, with constants from Table
2.5.6. If LKOC is unknown, then LKOW, AO, and Al should be specified (if AO
and Al are unknown, they default to log 0.6 and 1, respectively). NUX(l) and
PIXC(I.l) should be left out. Solids-dependent partitioning constitutes
equilibrium level 4. NUX(l) should be given a value of around 1. For
216
-------
equilibrium level 5, ionic sorption constants must also be specified.
locations are given in Table 2.5.7.
Their
For kinetics level 3, constants must be specified for each relevant
process. Constants for volatilization, biodegradation, alkaline hydrolysis,
neutral hydrolysis, acid hydrolysis, oxidation, and Iphotolysis are given in
Tables 2.5.8, 2.5.9, 2.5.11, 2.5.13, 2.5.15, 2.5.17, 2.5.19, and 2.5.20;
respectively. Constants for a user-specified extra reaction are givenin
Table 2.5.22. If ionic speciation is being considered, then,ionic rate
constants must also be specified for each existing ionic specie. Locations
of these constants are given in Tables 2.5.10, 2.5.12, 2.5.14, 2.5.16, 2i5.18,
2.5.21, and 2.5.23.
For kinetics level 4, reaction products are simulated. Four cases are
illustrated in Figure 1.5.10. Yield coefficients for each relevant process
must be specified. Yield coefficients for chemical 1, 2, and 3 reactions are
listed in Tables 2.5.24, 2.5.25, and 2.5.26. The reactions themselves need
not be second order to simulate reaction products.
DATA GROUP I: Kinetic Time Functions
Listed below are the 17 time functions available in TOXI4. Their
interaction with spatially-variable parameters is summarized in Table 1.5.17.
ISC ANAME(ISC')
1 TEMPN(l)
2 TEMPN(2)
VALTCISC)
Time-variable temperature function 1." TEMPN(K)
can be either a normalized function or. an actual
temperature in °C, depending upon' the definition
of the parameter multiplier TEMP(ISEG).
Time variable temperature function 2, unitless or
TEMPN(3)
Time variable temperature function 3 , unitless or
4 TEMPN(4)
5 VELN(l)
6 VELN(2)
Time variable temperature function. 4, unitless or
Time variable velocity function 1, m/sec.' This
velocity is added to the net velocity VELOCG(ISEG)
computed from the segment flow and the hydraulic
parameters read in Data Group C.
Time variable velocity function 2, m/sec. This
velocity is added to the net velocity VELOCG(ISEG)
computed from the segment flow and the hydraulic
parameters read in Data Group C.
217
-------
TABLE 2.5.3. CONSTANTS FOR SIMPLE TOXI4 REACTIONS
Constant Number
Cl GO Co
111
711
1311
Variable
Definition
PIXC(1,1) Constant partition coefficient for
sorption to solids (class 1) , L^/kgs
1
K^: First order loss rate constants, day"
140
141
142
181
182
183
256
287
571
143
144
252
253
254
257
289
572
740
741
742
781
782
783
856
887
1171
743
744
852
853
854
857
889
1172
1340
1341
1342
1381
1382
1383
1456
1487
1771
1343
1344
1452
1453
1454
1457
1489
1772
KV
KBW
KBS
KHOH
KHN
KHH
KO
KF
KE
THi
THBW
THBS
THHOH
THHN
THH
THO
THF
THE
Volatilization
Water column biodegradation
Benthic biodegradation
Alkaline hydrolysis
Neutral hydrolysis
Acid hydrolysis
Oxidation
Photolysis
Extra reaction
Half lives for reactions ,
day
Water column biodegradation
Benthic biodegradation
Alkaline hydrolysis
Neutral hydrolysis
Acid hydrolysis
Oxidation
Photolysis
Extra reaction
218
-------
TABLE 2.5.4. GENERAL CHEMICAL CONSTANTS
Constant Number
cl
9
81
82
83
84
C2
609
681
682
683
684
C3
1209
1281
1282
1283
1284
Variable
TDINT
MOLWT
SOLG
VAPRG
LKOW
TABLE 2.5.5.
Definition
Time interval at which rate constants
are recomputed, days
Molecular weight, g/mole
Solubility, mg/L
Vapor pressure, torr
Log octanol-water partition
coefficient, LQ/!^
IONIZATION CONSTANTS
Constant Number
Cl
85
86
87
,88
91
92
93
94
95
96
97
98
C2
685
686
687
688
691
692
693
694
695
696
697
698
C3
1285
1286
1287
1288
1291
1292
1293
1294
1295
1296
1297
1298
Variable
SPFLG(l)
SPFLG(2)
SPFLG(3)
SPFLG(4)
PKA(l)
PKA(2)
PKA(3)
PKA(4)
EPKA(l)
EPKA(2)
EPKA(3)
EPKA(4)
Definition
Flags indicating existence of ionic
species +, ++, -, and --; if SPFLG(I) =
1, ionic species I exists
For ionic species I, the constant in
the Arrhenius equation describing
temperature dependence of the equili-
brium constant for dissociation:
log K(I) = -PKA(I) -. EPKA(I)/2.303 RT
For ionic species I , the activation
energy of the dissociation reaction,
kcal/mole ,
219
-------
TABLE 2.5.6. SORPTION CONSTANTS FOR TOTAL OR NEUTRAL CHEMICAL
Constant Number
Variable
Definition
84 684 1284 LKOW
101 701 1301 LKOC
102 702 1302 AO
103 703 1303 Al
106 706 1306 NUX(l)
Log 10 of the octanol- water partition
coefficient, log
Log 10 of the organic carbon partition
coefficient, log (Lw/kgoc)
Intercept in the KQW - KQC correlation:
log KQC = AO + Al . log Kow; default =
log 0.6
Slope in the KQW - KQC correlation;
default =1.0
Solids-dependent partitioning parameter
(tO of the chemical onto solids;
TO
default = 10 makes KL, independent of
solids concentration
111 711 1311
116 716 1316
121 721 1321
PIXC(1,1)
PIXC(2,1)
PIXC(3,1)
Solids -independent (limiting) partition
coefficient KpO for sorption to solid
Solids -independent (limiting) partition
coefficient KpO for sorption to solid
2, IvAis
Solids -independent (limiting) partition
coefficient K_,0 for sorption to solid
3,
If = 0, Kp0 for neutral chemical will
be calculated from LKOC and parameter
FOG
PIDOC
Partition coefficient to DOC; for
neutral chemical, KOC is used; L/kg
220
-------
TABLE 2.5.7. LOCATION OF IONIC SORPTION CONSTANTS
Constant Number
cl C2 C3
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
1306
1307
1308
1309
1310
1311
1312
1313
1314
1315
1316
1317
1318
1319
1320
1321
1322
1323
1324
1325
1326
1327
1328
1329
Variable Ionic Specie
NUX(l) 0
NUX(2) +
NUX(3) -H-
NUX(4)
NUX(5)
PIXC(l.l) 0
PIXC(1,2) +
PIXC(1,3) ++
PIXC(1,4)
PIXC(1,5)
PIXC(2,1) 0
PIXC(2,2) 4-
PIXC(2,3) ++
PIXC(2,4)
PIXC(2,5)
PIXC(3,1) 0
PIXC(3,2) +
PIXC(3,3) -H-
PIXC(3,4)
PIXC(3,5)
PIDOC(l) +
PIDOC(2) ++
PIDOC(3)
PIDOC(4)
Sorptive Phase
S
S
S
S
S
sl
sl
sl
sl
sl
S2
s2
S2
S2
S2
S3
S3
S3
S3
S3
B
B
B
B
221
-------
TABLE 2.5.8. VOLATILIZATION CONSTANTS
Constant Number
Variable
Definition,
136 736 1336 XV
137 737 1337 HENRY
138 738 1338 KLT
139 739 1339 KVOG
2 602 1202 WTYPE
5 605 1205 AIRTMP
8 608 1208 ATMOS
Volatilization option:
0 = no volatilization
1 = measured volatilization
2 = meaured reaeration + O'Connor for
gas transfer
3 — measured reaeration + MacKay for
gas transfer
4 = calculated using O'Connor
5 - calculated using MacKay
O
Henry's constant, atm-m /mole
Volatilization temperature correction
factor, dimensionless
Measured ratio of volatilization to
reaeration rates
Water body type (0 = flowing stream, river,
or estuary; 1 = stagnant pond or lake)
Multiplier for air temperature time function
Atmospheric concentration of chemical, /tg/L
TABLE 2.5.9,
SECOND ORDER BIODEGRADATION CONSTANTS FOR
TOTAL OR NEUTRAL CHEMICAL
Constant Number
cl
146
151
156
161
166
171
C2
746
751
756
761
766
771
C3
1346
1351
1356
1361
1366
1371
Variable
KBI020(1,1)
KBI020(2,1)
KBI020(3,1)
QlODIS(l)
QlODOC(l)
QlOPAR(l)
Definition
Second- order 20 °C biodegradation rate
constant for aqueous, DOC-sorbed, and
sediment-sorbed phases, mL/cells-day
Temperature correction factor for bio-
degradation of aqueous, DOC-sorbed, and
sediment-sorbed phases; multiplication
factor for 10 °C temperature increase
222
-------
TABLE 2.5.10. LOCATION OF IONIC BIODEGRADATION CONSTANTS
Constant Number
cl
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
C2
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
TABLE
C3
1346
1347
1348
1349
1350
1351
1352
1353
1354
1355
1356
1357
1358
1359
1360
1361
1362
1363
1364 .
1365
1366
1367
1368
1369
1370
1371
1372
1373
1374
1375
2.5.11.
Variable
KBI020(1,1)
KBI020(1,2)
KBI020(1,3)
KBI020(1,4)
KBI020(1,5)
KBI020(2,1)
KBI020(2,2)
KBI020(2,3)
KBI020(2,4)
KBI020(2,5)
KBI020(3,1)
KBI020(3,2)
KBI020(3,3)
KBI020(3,4)
KBI020(3,5)
QlODIS(l)
Q10DIS(2)
Q10DIS(3)
Q10DIS(4)
Q10DIS(5)
QlODOC(l)
Q10DOC(2)
Q10DOC(3)
Q10DOC(4)
Q10DOC(5)
QlOPAR(l)
Q10PAR(2)
Q10PAR(3)
Q10PAR(4)
010PARC5")
SECOND ORDER
Ionic Specie Sorptive Phase
0 W
+ W
++ W
W
W
0 B
4- B
++ B
B
B
0 S
+ S
o-o. Q
i i • \j
S
S
0 W
+ W
++ W
W
W
0 B
+ B
++ B
B
B
0 S
+ S
i i C
1 1 O
S
-- S
ALKALINE HYDROLYSIS CONSTANTS FOR
' TOTAL OR NEUTRAL CHEMICAL
Constant Number .
Cl
184
186
191
196
231
C2
784
786
791
796
831
C3
1384
1386
1391
1396
1431
Variable
TREFH
KH20(1,1,1)
KH20)1,2,1)
KH20 (1,3,1)
EHOH(l)
Definition
Reference temperature at which hydroly-
sis rates were measured, °C
Second order, 20 °C alkaline hydrolysis
rate constants for aqueous, DOC-sorbed,
and sediment- sorbed phases, L/mole-day
Activation energy for alkaline hydroly-
sis . kcal/mole
223
-------
TABLE 2.5.12. LOCATION OF IONIC ALKALINE HYDROLYSIS CONSTANTS
Constant Number
Ci Co Co
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
231
232
233
234
235
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
831
832
833
834
835
1386
1387
1388
1389
1390
1391
1392
1393
1394
1395
1396
1397
1398,
1399
1400
1431
1432
1433
1434
1435
Variable Ionic Specie
KH20(1,1,1) 0
KH20(1,1,2) +
KH20(1,1,3) ++
KH20(1,1,4)
KH20(1,1,5)
KH20(1,2,1) 0
KH20(1,2,2) +
KH20(1,2,3) ++
KH20(1,2,4)
KH20(1,2,5)
KH20(1,3,1) 0
KH20(1,3,2) +
KH20(1,3,3) ++
KH20(1,3,4)
KH20(1,3,5)
EHOH(l) 0
EHOH(2) +
EHOH(3) ++
EHOH(4)
EHOH(5)
Sorptive Phase
W
W
W
,W
W
B
B
B
B
B
S
' S
S
S
S
' A
A
A
A
A
TABLE 2.5.13. SECOND ORDER NEUTRAL HYDROLYSIS CONSTANTS FOR
TOTAL OR NEUTRAL CHEMICAL
Constant Number
Variable
Definition
184
201
206
211
236
784
801
806
811
836
1384
1401
1406
1411
1436
TREFH
KH20(2,1,
KH20(2,2,
KH20(2,3,
EHN(l)
1)
1)
1)
Reference temperature at which hydroly-
sis rates were measured, °C
20 °C neutral hydrolysis rate constant
for aqueous, DOC-sorbed, and sediment-
sorbed phases, day"
Activation energy for neutral hydroly-
sis, kcal/mole
224
-------
TABLE 2.5.14. LOCATION OF IONIC NEUTRAL HYDROLYSIS CONSTANTS
Constant Number
Ci Co Co
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
236
237
238
239
240
801
802
802
804
805
806
807
808
809
810
811
812
813
814
815
836
837
838
839
840
1401
1402
1403
1404
1405
1406
1407
1408
1409
1410
1411
1412
1413
1414
1415
1436
1437
1438
1439
1440
Variable Ionic Specie
KH20(2,1,1) 0
KH20(2,1,2) +
KH20(2,1,3) -H-
KH20(2,1,4)
KH20(2,1,5)
KH20(2,2,1) 0
KH20(2,2,2) +
KH20(2,2,3) -H-
KH20(2,2,4)
KH20(2,2,5)
KH20(2,3,1) 0
KH20(2,3,2) +
KH20(2,3,3) ++
KH20(2,3,4)
KH20(2,3,5)
EHN(l) 0
EHN(2) +
EHN(3) ++
EHN(4)
EHN(5)
Sorptive Phase
W
W
W
W
W
B
B
B ;
B
B
S
s
S
S
S
A
A
A
A
A
TABLE 2.5.15. SECOND ORDER ACID HYDROLYSIS CONSTANTS FOR
'-.. TOTAL OR NEUTRAL CHEMICAL
Constant Number
Variable
Definition
184
216
221
226
241
784
816
821
826
841
1384
1416
1421
1426
1441
TREFH Reference temperature at which hydroly-
sis rates were measured, °C
KH20(3,1,1) Second order, 20°C acid hydrolysis rate
constant for aqueous, DOC-sorbed, and
KH20(3,2,1) sediment-sorbed phases, L/mole-day
KH20(3,3,1)
EHH(l)
Activation energy for acid hydrolysis,
kcal/mole
225
-------
TABLE 2.5.16. LOCATION OF IONIC ACID HYDROLYSIS CONSTANTS
Constant Number
cl C2 C3
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
241
242
243
244
245
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
841
842
843
844
845
1416
1417
1418
1419
1420
1421
1422
1423
1424
1425
1426
1427
1428
1429
1430
1441
1442
1443
1444
1445
Variable Ionic Specie
KH20(3,1,1) 0
KH20(3,1,2) +
KH20(3,1,3) -H-
KH20(3,1,4)
KH20(3,1,5)
KH20(3,2,1) 0
KH20(3,2,2) +
KH20(3,2,3) ++
KH20(3,2,4)
KH20(3,2,5)
KH20(3,3,1) 0
KH20(3,3,2) +
KH20(3,3,3) ++
KH20(3,3,4)
KH20(3,3,5)
EHH(l) 0
EHH(2) +
EHH(3) ++
EHH(4)
EHH(5)
Sorptive Phase
W
W
W
W
W
B
B
B
B
B
S
S
S
S
S
A
A
A
A
A
TABLE 2.5.17. SECOND ORDER OXIDATION CONSTANTS FOR
TOTAL OR NEUTRAL CHEMICAL
Constant Number
Variable
Definition
258
261
266
271
276
858
861
866
871
876
1458
1461
1466
1471
1476
TREFO
KOX20(1,1)
KOX20(2,1)
KOX20(3,1)
EOX(l)
Reference temperature at which oxida-
tion rates were measured, °C
Second- order, 20 °C oxidation rate
constant for aqueous-, DOC-sorbed, and
sediment -sorbed phases, L/mole-day
Activation energy for oxidation,
kcal/mole
226
-------
TABLE 2.5.18. LOCATION OF IONIC OXIDATION CONSTANTS
Constant Number
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
1461
1462
1463
1464
1465
1466
1467
1468
1469
1470
1471
1472
1473
1474
1475
1476
1477
1478
1479
1480
Variable Ionic Specie
KOX20(1,D 0
KOX20(1,2) +
KOX20(1,3) -H-
KOX20(1,4)
KOX20(1,5)
KOX20(2,1) 0
KOX20(2,2) +
KOX20(2,3) ++
KOX20(2,4)
KOX20(2,5)
KOX20(3,1) 0
KOX20(3,2) . ;+,
KOX20(3,3) -H-
KOX20(3,4) - . '•'
KOX20(3,5)
EOX(l) 0
EOX(2) +
EOX(3) * .... ++
EOX(4) - '
EOX(5)
Sorptive Phase
. w
w :'.'
W;
•*. -V:
. W; ,' ,
, B ;
;B ^:
•• B- .,;:;•
'" t '.
B
B _ ;__'
S
;;;.. S
,s
• .,.-:- -.8, ,,
S
, All
All
All
All
All
227
-------
TABLE 2.5.19. TOXI4 PHOTOLYSIS CONSTANTS
Constant Number
Ci Co Co
Variable
Definition
286 886 1486 XPHOTO Photolysis option: 0 = no photolysis;
1 — computed from absorptivity;
2 — measured surface rate
288 888 1488 RFLATG Latitude at which surface photolysis
rate was measured, degree and tenths
(option 2)
291 891 1491 KDPG(l) Measured surface photolysis rate for
neutral specie, day" (option 2)
296 896 1496 LAMAX(l) Wavelength of maximum light absorption
for neutral specie, nm (option 2)
301- 901- 1501- ABS(K,1,L) Molar absorptivity of neutral specie
346 946 1546 of chemical K at wavelength number L,
L/mole-cm-lnlO (option 1)
551 1151 1751
QUANTG(1,1) Quantum yield of dissolved neutral
chemical
556 1156 1756
QUANTG(2,1) Quantum yield of DOC-sorbed neutral
chemical
561 1161 1761
QUANTG(3,1) Quantum yield of sediment-sorbed
neutral chemical
L - Wavelength 1-46 (see Table 1.5.6).
228
-------
TABLE 2.5.20. GLOBAL CONSTANTS FOR TOXI4 PHOTOLYSIS OPTION 1
Constant Number
Ci Co Co
1
3
4
6
7
11-
23
24-
36
37-
49
50-
62
601
603
604
606
607
611-
623
624-
636
637-
649
650-
662
1201
1203
1204
1206
1207
1211-
1223
1224-
1236
1237-
1249
1250-
1262
Variable Definition
TO Julian date at beginning of run
ELEVG Average ground surface elevation, m
1ATG Latitude of water body, degrees
XLITE Water surface light intensity option;
0 = do not compute light; 1 = annual
average; 2 = average for month indicated
by TO; 3 = monthly step function
DFACG Ratio of optical path length to vertical
depth; 1.17
CLOUDG(I) Mean monthly cloudiness, in tenths of
full sky coverage (0-10)
AIRTYG(I) Mean monthly air mass type; 1 = rural,
2 •= urban, 3 — maritime, 4 •= tropospheric
RHUMG(I) Mean monthly daylight relative humidity,
percent
ATURBG(I) Mean monthly atmospheric turbidity,
in equivalent aerosol layer thickness
km
63- 663- 1263-
75 675 1275
OZONEG(I) Mean monthly ozone content of atmosphere,
in cm NTP (0.2 - 0.3)
229
-------
TABLE 2.5.21. LOCATION OF IONIC PHOTOLYSIS CONSTANTS
Constant Number
Variable
Ionic Specie
Sorptive Phase
291
292
293
294
295
296
297
298
299
300
301-
346
351-
396
401-
446
451-
496
501-
546
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
891
892
893
894
895
896
897
898
899
900
901-
946
951-
996
1001-
1046
1051-
1096
1101-
1146
1151
1152
1153
1154
1155
1156
1157
1158
1159
1160
1161
1162
1163
1164
1165
1491
1492
1493
1494
1495
1496
1497
1498
1499
1500
1501-
1546
1551-
1596
1601-
1646
1561-
1696
1701-
1746
1751
1752
1753
1754
1755
1756
1757
1758
1759
1760
1761
1762
1763
1764
1765
KDPG(l) 0
KDPG(2) 4
KDPG(3) 44-
KDPG(4)
KDPG(5)
LAMAX(l) 0
LAMAX(2) 4
IAMAX(3) 44
LAMAX(4)
LAMAX(5)
ABS(K,1,L) 0
ABS(K,2,L) 4
ABS(K,3,L) 44
ABS(K,4,L)
ABS(K,5,L)
QUANTG(1,1) 0
QUANTG(1,2) 4
QUANTG(1,3) 44
QUANTG(1,4)
QUANTG(1,5)
QUANTG(2,1) 0
QUANTG(2,2) 4
QTJANTG(2,3) 44
QUANTG(2,4)
QUANTG(2,5)
QUANTG(3,1) 0
QUANTG(3,2) 4
QUANTG(3,3) 44-
QUANTG(3,4)
QUANTG(3,5)
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
W
W
W
W
W
B
B
B
B
B
S
S
S
S
S
230
-------
TABLE 2.5.22.
EXTRA SECOND ORDER REACTION CONSTANTS FOR
TOTAL OR NEUTRAL CHEMICAL
Constant Number
Variable
Definition
573 1173 1773
576
581
586
591
1176
1181
1186
1191
1776
1781
1786
1791
TREFE
KE20(1,1)
KE20(2,1)
KE20(3,1)
EEX(l)
Reference temperature at which extra
reaction rates were measured, °C.
Second-order, 20°C extra reaction rate
constant for aqueous, DOC-sorbed, and
sediment-sorbed phases, l/[E]-day
Activation energy for extra reaction,
kcal/mole
TABLE 2.5.23. LOCATION OF IONIC EXTRA REACTION CONSTANTS
Constant Number
Ci_ CQ Co
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
1176
1177
1178
1179
1180
1181
1182
1183
1184
1185
1186
1187
1188
1189
1190
1191
1192
1193
1194
1195
1776
1777 -
1778
1779
1780
1781
1782
1783
1784
1785
1786
1787
1788
1789
1790
1791
1792
1793
1794
1795
Variable Ionic Specie
KE20(1,1) 0
KE20(1,2) +
KE20(1,3) ++
KE20(1,4)
KE20(1,5)
KE20(2,1) 0
KE20(2,2) +
KE20(2,3) ++
KE20(2,4)
KE20(2,5)
KE20(3,1) 0
KE20(3,2) +
KE20(3,3) ++
KE20(3,4)
KE20(3,5)
EEX(l) 0
EEX(2) +
EEX(3) -H-
EEX(4)
EEX(5)
Sorptive Phase
W
W
W
W
W
B
B
B
B
B
S
S
S
S
S
All
All
All
All
All
231
-------
TABLE 2.5.24. YIELD CONSTANTS FOR CHEMICAL 1 REACTIONS
Constant Number
1 2 3
176
177
246
248
250
281
566
596
178
179
247
249
251
282
567
597
Variable
Y( )12:
YBW12
YBS12
YHOH12
YHN12
YHH12
YOX12
YF12
YE12
Y( )13:
YBW13
YBS13
YHOH13
YHN13
YHH13
YOX13
YF13
YE13
Definition
Yield coefficient for production of G£
from Ci , mgCo/mgCi
Water column biodegradation
Benthic biodegradation
Alkaline hydrolysis
Neutral hydrolysis
Acid hydrolysis
Oxidation
Photolysis
Extra reaction
Yield coefficient for production of
Co from Ci , mgCo/nigCi
Water column biodegradation
Benthic biodegradation
Alkaline hydrolysis
Neutral hydrolysis
Acid hydrolysis
Oxidation
Photolysis
Extra reaction
232
-------
TABLE 2.5.25.. YIELD CONSTANTS FOR CHEMICAL 2 REACTIONS
Constant Number
Ci Co Co
776
111
846
848
850
881
1166
1196
778
779
847
849
851
882
1167
1197
Variable
Y( )21:
YBW21
YBS21
YHOH21
YHN21
YHH21
YOX21
YF21
YE21
Y( )23:
YBW23
YBS23
YHOH23
YHN23
YHH23
YOX23
YF23
YE23
Definition
Yield coefficient for production of C-^
from C2 , mgC2/mgC^
Water column biodegradation
Benthic biodegradation
Alkaline hydrolysis
Neutral hydrolysis
Acid hydrolysis
Oxidation
Photolysis
Extra reaction
Yield coefficient for production of
Cq from C2 , mgCo/mgC2
Water column biodegradation
Benthic biodegradation
Alkaline hydrolysis
Neutral hydrolysis
Acid hydrolysis
Oxidation
Photolysis
Extra reaction
233
-------
r
TABLE 2.5.26. YIELD CONSTANTS FOR CHEMICAL 3 REACTIONS
Constant Number
cl C2 C3
1376
1377
1446
1448
1450
1481
1766
1796
1378
1379
1447
1449
1451
1482
1767
1797
Variable
Y( )31:
YBW31
YBS31
YHOH31
YHN31
YHH31
YOX31
YF31
YE31
Y( )32:
YBW32
YBS32
YHOH32
YHN32
YHH32
YOX32
YF32
YE32
Definition
Yield coefficient for production of C^
from Co , mgCi/mgCo
Water column biodegradation
Benthic biodegradation
Alkaline hydrolysis
Neutral hydrolysis
Acid hydrolysis
Oxidation
Photolysis
Extra reaction
Yield coefficient for production of
Co from Co i mgCo/mgCo
Water column biodegradation
Benthic biodegradation
Alkaline hydrolysis
Neutral hydrolysis
Acid hydrolysis
Oxidation
Photolysis
Extra reaction
234
-------
ISC
7
10
11
12
13
14
15
ANAME(ISG')
VELN(3)
VELN(4)
WINDN
.PHNW
PHNS
REARN
AIRTMPN
CHLN
PHTON
16
BACNW
17
BACNS
VALT(ISC)
Time variable velocity function 3, m/sec. This
velocity is added to the net velo.city VELOCG(ISEG)
computed from the segment flow and the hydraulic
parameters read in Data Group C.
Time variable velocity function 4, m/sec. This
velocity is added to the net velocity VELOCG(ISEG)
computed from the segment flow and the hydraulic
parameters read in Data Group C.
Normalized wind speed function, dimensionless.
This is multiplied by the segment wind speed
multiplier WVEL(ISEG).
Normalized water column pH function, dimensionless,
This is multiplied by the segment pH multiplier
PH(ISEG) for water column segments.
Normalized benthic pH function, dimensionless.
This is multiplied by the segment pH multiplier
PH(ISEG) for benthic segments.
Normalized reaeration or volatilization rate
function, dimensionless. This is multiplied by
the segment reaeration or volatilization multi-
plier REAR(ISEG).
Normalized air temperature function, dimensionless.
This is multiplied by the air temperature constant
AIRTMP.
Normalized chlorophyll a concentration, dimen-
sionless. This is multiplied by the segment
chlorophyll a multiplier CHPHL(ISEG).
Normalized light intensity, dimensionless. This
is used for photolysis option 2 to adjust the
measured rate constant under controlled light
intensity to a predicted rate constant .under
ambient light intensity.
Normalized water column bacteria function,
dimensionless. This is multiplied by the
segment bacteria multiplier BAC(ISEG) for water
column segments.
Normalized benthic bacteria function, dimen-
sionless. This is multiplied by the segment
bacteria multiplier BAC(ISEG) for benthic
segments.
235
-------
For kinetics levels 1 and 2, no time functions need be specified. For
kinetics level 3, time functions for each relevant process may be specified.
TEMPN can affect all reactions. Volatilization option 1 uses REARN. Volati-
lization options 4 and 5 use WINDN and AIRTMPN. Volatilization options 2 and
3 use either VELN or REARN. Photolysis option 1 uses CHLN; photolysis option
2 requires PHTON. Hydrolysis and ionization use PHNW and PHNS. Biodegrada-
tion uses BACNW and BACNS. Functions not specified default to 1.0.
DATA GROUP J: Initial Conditions--
No changes. Input is repeated for each system.
TOXI4 Output
The standard WASP4 output files were summarized in Section 2.3. TOXI4
stores in the DMP file 18, 30, or 42 kinetic display variables, depending on
whether 1, 2, or 3 chemicals were simulated. These variables are defined in
Table 2.5.27. To examine these variables in tabular form, the user may run
W4DSPLY as explained in Section 2.3.
236
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TABLE 2.5.27. TOXI4 KINETIC DISPLAY VARIABLES
Variable Number,
Ci j Co . Co
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
;
19 31
20 32
21 33
22 34
23 35
24 36
25 37
26 38
27 39
28 40
29 41
30 42
Variable
TOTSOL
SOLID 1
SOLID 2
SOLID 3
STEMP
ITYPE
TOTCHEM
TOTDIS
TOTDOC
TOTPAR
TOTPAR1
TOTION
KB10
KHYD
KFOT
KVOL
KOX
KEXT
Definition ', :, , : ,
Total solids concentration, mg/L
Solids type 1 concentration, mg/L
Solids type 2 concentration, mg/L
Solids type 3 concentration, mg/L .• .
Segment temperature, °C •
Segment type (1, 2, 3, or 4)
Total chemical concentration (1, 2", or 3) , pg/L
Dissolved chemical concentration, Mg/L
DOC-sorbed chemical concentration, /zg/L
Total sorbed chemical concentration, /jg/L
Total sorbed chemical concentration, ng/kg
Total ionic chemical concentration, /zg/L
Biodegradation rate constant, day'
Total hydrolysis rate constant, day"
Photolysis rate constant, day"
Volatilization rate constant, day"^
Oxidation rate constant, day"
Extra rate constant, day"
237
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SECTION 3
WASP4 PROGRAMMER'S GUIDE
3.1 OVERVIEW
This section is designed to supply information to familiarize the user
with the programming aspects of the models. This section should facili-
tate making any desired modifications to the model and linking user defined
kinetic subroutines.
3.2 THE HYDRODYNAMIC MODEL
Hardware and Software Requirements
Minimum Operational System--
PC Requirements--The execution of DYNHYD4 on a personal computer
requires the following environment:
Storage Requirements:
Random Access Memory - 256K bytes
Diskette Drive - Required for installation only
Hard Disk Drive - 1.5 megabyte or larger
Installation Size - Approximately 440K bytes
DOS Version - 2.12 or higher
Numerical Coprocessor - 8087 or 80287 optional
Dot Matrix Printer - 132 column capability.
Although the program is small enough to run on a single floppy drive,
DYNHYD4 uses a scratch file that requires more space than afforded by a
floppy disk. While the executable task image was linked with a mathematical
library which emulates the 8087 math chip, it is recommended that if you are
going to make several runs, the 8087 or 80287 math chip will decrease your
run time substantially.
238
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VAX requirements--Since the development and improvement of DYNHYD4 have
been processed on a Digital Computer, the program requirements will be dis-
cussed for a VAX 11/785 only. In addition, DYNHYD4 requires the use of
approximately 800 blocks of hard storage, which increases proportionally
with the length of simulation and number of time steps.
Development System--
The DYNHYD4 program was ported to the personal computer environment
using the following software development tools.
Language: FORTRAN 77
Operating System: PC DOS 3.2
Compiler: Ryan McFarland FORTRAN (RMFORT) V2.0
Linkage Editor: Phoenix Software Associates (PLINK 86) V2.12
The selection of Ryan McFarland's FORTRAN compile was due to its close ad-
herence to the ANSI FORTRAN Standards. These standards allow for a pure
transportable code for other machines and compilers.
Installation and Implementation
Personal Computer--
A README.2ST document is supplied with each model request, which ex-
plains in a step by step fashion how to install the program.
The executable task image DYNHYD4.EXE for the IBM PC and compatible
systems has been included on distribution diskettes. The Ryan McFarland
FORTRAN compiler and linkage editor (RMFORT and PLINK86) are not required
to run the DYNHYD4 program. If any modification of the FORTRAN source
code is desired, however, then both of these software development tools
will be required.
Description of Computer Program
Overview of Systems--
Figure 3.2.1 is a flow chart of DYNHYD4 illustrating the functional
relationships among the subroutines. The main program opens files, calls
DYNHYD, closes files, and calls the post-processor subroutines that create
the saved output files. Subroutine DYNHYD accomplishes the data input, simu-
lation, and printed output, with assistance from SEAWRD, REGAN, WIND, and
RUNKUT.
239
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I I
j DHYDMAIN j DHYD.COM
I I
DYNHYD
I
| INPUT |
I I
I
j-SEAWRD
I I
I REGAN
|-WIND
I
SIMULATION |
I
I
j-RUNKUT
I
-WIND
I
j OUTPUT
I.
I I
j OUTPUT FILES |
I -I
-RESTRT
-SUMRY1
I
MEAN
-SUMRY2
I
MEAN
Figure 3.2.1. DYNHYD4 flow chart.
DYNHYD4 Input/Output Units
All the input/output units used in DYNHYD4 are controlled by definable
variables. These variables are in the global common block DHYD.COM and can
easily be reassigned. The individual units are listed below with their
default integer values. A brief description is provided to illustrate how
the units are used within the program.
ICRD: 5 or 8, depending on the input switch ICFL. File 5 refers to the
input data set DYNHYD4.INP. An 8 denotes the input data stream is in File 8.
File 8 is created from File 9 and contains a snapshot of the final conditions
from the previous run (created by the subroutine RSTRT). Files 5 and 8 are
formatted sequential files. Example: READ(ICRD).
IN: Default value is 5. The value 5 denotes the input data stream is
in DYNHYD4.INP. The input data stream is a formatted sequential file.
Example: READ(IN).
240
-------
MESS: Default value is 6. Mess is used to display messages to the
standard output device. It has been implemented to provide the user with
runtime status messages so that at any point the user will know where the
model is executing.
OUT: The default value is 1. File 1 is the output file called
DYNHYD4.0UT. File 1 is a formatted sequential file. Example: WRITE(OUT).
RSTR: The default value is 9. File 9 contains a snapshot (flows and
volumes) of the final conditions of a run. File 9 will be converted to File
8, an input stream for the next run. File 9 is a formatted sequential file.
Example: WRITE(RSTR).
SCB: The default value is 2. File 2 is the scratch file processed by
the subroutine SUMRY1 (or 2). File 2 is an unformatted sequential file.
Example: READ and WRITE(SCR).
SUMY: The default value is 4. File 4 is the SUMRY file containing
flows and volumes used by the water quality model. File 4 is a formatted
or unformatted sequential file. Example: WRITE(SUMY).
Common Block--
DYNHYD4 has a common block transferred between subroutines. This common
block consists of nine sections that are grouped according to subject matter.
The following is a listing of the common block, plus the variables associated
with each section:
COMMON /CHAN/ AK(CH), AREA(CH), AREAT(CH), B(CH), CLEN(CH),
* CN(CH), NJUNC(CH,2), Q(CH), R(CH), V(CH),
* VT(CH),CDIR(CH)
COMMON /JUNG/ JPRT(JU), NCHAN(JU,5), SURF(JU), VOL(JU),
* Y(JU), YT(JU), QIN(JU),BELEV(JU)
COMMON /VFLO/JRVF(VF), NINCR(MQ), NQ(MQ), NVFLOW, QCYC(VF,MQ), v
VFLOW(VF,MQ), VQIN(JU), VQ(VF.JU)
COMMON /CFLO/ CQIN(JU), , NCFLOW, JRCF(CF), CFLOW(CF)
COMMON /SEA/ A1(SB,7), PERIOD(SB), NS, NK, NSEA, NINL, RANGE(SB),
- *.. , BTIME(SB,TC2), BREAD(SB,TC2), NTV(SB), NHCYC(SB),
.. * DTIME(SB),TREP(SB),TSTART(SB) ', •
COMMON /TIME/ DELT, DT, DT2, T, T2, TEND, TZERO, TTIME(SB)
COMMON /MISC/ ALPHA(SO), G, ICYC, NJ, NC, NCYC, W(SB), MOM(CH),
* FRIC.CCH), GRAV(CH), WIN(CH>
.COMMON /FILE/ SUMRY,ITAPE,LTAPE,ICRD.NODYN . ' ;
COMMON /WIND/ WINDS(MQ), WDIR(MQ), NOBSW, IW, WTIM(MQ), FW(CH),
, * IREADW, WSLOPS, WSLOPA, TREPW, DTIMW ,
The COMMON "CHAN" refers to all variables associated with channels.
The COMMON "JUNG" refers to all variables associated with junctions,. The
COMMON "VFLO" refers to, all variables associated with variable inflows. The
COMMON "CFLO" refers to all variables associated with constant inflows. The
COMMON "SEA" refers to all variables associated with seaward boundaries. The
241
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COMMON "TIME" refers to all variables associated with the time step. The
COMMON "MISC" is a collection of miscellaneous variables. The COMMON "FILE"
refers to input/output fields. The COMMON "WIND" refers to all variables
associated with the wind.
In each common, the dimensions of a variable are defined by parameters.
The value of these parameters are also defined in a common block called
"DHYD.COM." The separation of these parameters allows easy alterations.
The following is a list of parameter definitions.
JU
CH
VF
CF
ND
MQ
NR
SB
TC
number of junctions
number of channels
number of variable inflows
,: .'; !
number of constant inflows
number of time steps per quality time steps
maximum number of flow or wind values in time function
ND + 1
number of seaward boundaries
maximum number of tidal cycles.
Subroutine Descriptions--
The following is a brief explanation of each subroutine function
contained in DYNHYD4:
DHYDMAIN
The DHYDMAIN subroutine is the control module. It assigns input and
output unit numbers, and operates the calling sequence for the input,
simulation, and output subroutines.
DYNHYD .
DYNHYD reads most of the input data: program description and control
data (A), output control data (B), hydraulic summary data (C), junction data
(D), channel data (E), and inflow data (F). Subroutines WIND and SEAWRD are
called to read the observed wind conditions and seaward boundary data, res-
pectively. DYNHYD calls the simulation (processing) subroutines: WIND and
RUNKUT for each time step. Information is printed and the following values
are initialized: constants, junction volumes, the scratch file, counters, and
variables.
242
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SEAWRD
SEAWRD has three options for reading the observed seaward boundary data.
The first option reads the regression coefficients directly for the average
tide. The second, option calls REGAN to compute the average tide regression
coefficients from average observed tidal heights versus time,. The, third
option reads variable (highs and lows) observed tidal heights versus time and
fits a repetitive one-half sine wave to the data points.
WIND .'....
WIND has two sections. The first section, executed only once at the
beginning of the simulation, reads in wind speed and direction versus time
and sets up two piecewise linear functions of time. The second section
updates the wind speed and direction by linear interpolation and calculates
the wind accelerational force.
REGAN
REGAN, called by SEAWRD, performs a least squares fit to the observed
seaward boundary data to describe an equation of the form:
Y(T) = Al + A2 sin(wt) + A3 sin(2wt) + A4 sin(3tot) -f
A5 cos(tot) + A6 cos(2wt) + A7 pos(3«t)
by solving normal equations.
RUNKUT
RUNKUT solves the equations of continuity and momentum using a modified
Runge-Kutta technique. Channel velocity, channel flow, junction heads,
junction volumes, and channel cross-section are computed for every half time
step and every full time step. RUNKUT also checks stability of the system
and exits program if the channel velocity exceeds 7 m/sec.
RESTRT
As a start-up for the next run, RESTRT produces a snapshot of the cur-
rent run's final conditions. At the end of the simulation, the title, vari-
able TRSTRT, variable NRSTRT, junction information (number, head, surface
area, flow, and connecting channels), and channel information (number, length,
width, surface area, Manning roughness coefficient, velocity, and hydraulic
radius) are written to file RSTR.
SUMRY1 and SUMRY2
SUMRY1 and SUMRY2 summarize and save a record of the hydraulic condi-
tions . Hydraulic parameters are saved with a frequency dependent on the
lengths of the hydraulic time step and the time step used in the water quality
model accessing the stored hydraulic data. The parameters stored for use by
the quality model (see Figure 3.2.2 for sequence and definitions) are junction
243
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I A I B I
I
ITAPE
I
ITAPE + NODYN
I
LTAPE
A) ALPHA(1-40), NJ, NC, DELT, ITAPE, LTAPE, SUMRY, NODYN
(CLEN(N), B(N), CN(N)(NJUNC(N,I) 1=1,2) N=i,NC)
Title, Network Size, Time Interval, Beginning Cycle, End Cycle,
Tape Format, Number Hydraulic Time Steps per Quality Time Step,
Length of Channel, Width of Channel, Lower or Higher Junction
Designator
B) ((SURF(J), NCHAN(J.K) K=l,5) J-l.NJ)
Surface Area of Junction, Channel Number Entering Junction
C) NCFLOW (FRCF(I), CFLOW(I) I-l.NCFLOW)
Number of Constant Flow Inputs, Junction Receiving Constant Flow,
Constant Inflow + or -
D) NVFLOW (JRVF(I), NINCR(I) 1=1,NVFLOW)
Number of Variable Flows, Number of Increments in Variable Flow
E) (QCYC(I,K) (VFLOW(I.K) K=1,NI) 1=1,NVFLOW)
Hydrodynamic Cycle (Time Step), Flow value for Variable Flow
F) CYCLE, (VOL(J), QINSAV(J), J=1,NJ) Hydrodynamic Cycle, Volume of
Junction, Inflow into Junction, Average Junction Flow, Average
Junction Velocity, Average Junction Depth
G) (QSAVE(N), VSAVE(N), RSAVE(N) N-l.NC)
Average Flow, Average Velocity, Average Hydraulic Radius
Figure 3.2.2. Summary file description.
244
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volumes and inflows, channel flows, velocities, and depths. SUMRY1 creates
an unformatted file and SUMRY2 creates a formatted file. For averaging
flows, velocities and depths SUMRY calls MEAN.
MEAN • • .
MEAN computes the average junction volumes and inflows, channel flows,
velocities, and depths over a time step (DELTQ) equal to the hydraulic time
step (DELT) times the water quality time step (NODYN) divided by 3600 seconds:
DELTQ = DELT * NODYN/3600. MEAN is capable of three averaging options:
Simpson's transformation, trapezoidal transformation, and straight transfor-
mations. At the present, MEAN is hardwired to use the trapezoidal transfor-
mation.
3.3 THE BASIC WATER QUALITY MODEL
Hardware and Software Requirements
Minimum Operational System--
Personal Computer Requirements
The size and structure of the WASP program require the following
personal computer environment:
- 512 kilobyte Random Access Memory (RAM)
-.. 360 kilobyte diskette drive
- 5/10/20 megabyte hard disk drive
- 8087 math coprocessor (optional)
- DOS version 2.12 or higher
- dot matrix printer with 132 column capability
These requirements refer to the distribution versions. Depending upon the
user's specific simulation, the variables may need redimensioning, thus
increasing the Random Access Memory (RAM) requirements. The executable was
linked with a mathematical library which emulates the 8087/80287 math
coprocessor chip, it is recommended that if you are going to make several
runs, the 8087 or 80287 math chip will decrese your run time substantially.
Development System for the Personal Computer--
The WASP system of programs were ported to the personal computer
environment using the following software development tools:
Language:
Operating System:
FORTRAN 77
PC DOS 3.2
245
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Compiler:
Linkage Editor:
Ryan McFarland's FORTRAN (RMFORT) V2.0
Phoenix Software Associates, Ltd
(PLINK86) V2.12
The selection of Ryan McFarland's FORTRAN (RMFORT) was due to its adherence
to the ANSI Fortran Standards. The PC version of WASP is an exact implemen-
tation of the VAX mainframe version. Phoenix Software's PLINK86 was chosen
because of its ability to overlay both code and data.
Installation and Implementation
Personal Computers: A READINE.2ST document is supplied with each
model request, which explains in a step by step fashion how to install the
program.
Description of Computer Program
Overview of System--
Input/Output Files
All the input/output units can be reassigned an integer value in the
WASP MAIN subroutine. It is suggested that the new user not change these
units until he becomes more familiar with the structure and function of the
program. The following is a brief description of each integer and their
default integer values.
AUX: Default value is 4. AUX refers to the use of an auxiliary flow
file. This file has been created outside the WASP programs and is used to
input flows and volumes. Example: READ(AUX).
HYDRO: Default value is 7. HYDRO is the input data set created by
DYNHYD4 (SUMRY1.0UT or SUMRY2.0UT). This file contains flows and volumes
calculated by DYNHYD3. HYDRO is a sequential formatted (SUMRY1.0UT) or
unformatted (SUMRY2.0UT) file. Example: READ(HYDRO).
IN; Default value is 2. The value 2 refers to the input data set.
Input data set is a sequential formatted file. May also be used to
represent the integer 2. Example: READ(IN).
OUT: Default value is 5. OUT refers to the output file "WASP.OUT."
OUT may also represent the integer 5. WASP.OUT is a sequential formatted
file. Example: WRITE(OUT).
RBSRT: Default value is 9. RESTRT refers to the file containing a
snapshot of final conditions. This file may then be used as initial
conditions in the next run. RESTRT is a sequential formatted file.
Example: WRITE(RESTRT).
246
-------
MESS: DEfault value is 6. MESS is used to write inquiry messages to
the screen and display run time status messages. For more information see
MFLAG variable in card group A.
ITRNS: Default value is 16. ITKNS is used to write out transport
parameters that are calculated throughout the simulation.
IMASS: Default value is 20. IMASS is used to write the mass balance
table for the desired system, that was stipulated in the input data set.
IDMP: Default value is 15. IDMP is used to write all the simulation
calculations that can be latter recalled and printed out using the W4DSPLY
program.
Figure 3.3.1 is a flow chart of WASP4 illustrating the functional rela-
tionships among the subroutines. The main program opens files, calls the
input, simulation, and output subroutines, and closes files. The input sub-
routines are called sequentially, as shown. Subroutine EULER controls the
actual simulation, calling DERIV each time step to recalculate mass deriva-
tives . The output subroutines are called sequentially as shown after the
simulation is completed. The utility subroutines can be called by the other
subroutines as needed.
Common block
****** WASP C0..4MON BLOCK ******
Depending upon which version of the WASP program you plan to recompile,
certain common blocks must be available for a successful compilation of the
programs. These common blocks are the WASP DRIVER common block (WASP.CMN)
and the associated KINETIC subroutine common blocks. A list and description
of each included common block is given below.
TOXIWASP.CMN
EUTRWASP.CMN
The common block used by the WASP DRIVER program
to build the TOXI4 executable.
The common block used by the WASP DRIVER program to
build the EUTR04 executable.
Both these common blocks contain the "PARAMETER" statements, which
control the dimensions of the simulation constraint parameters, such as
number of segments and number of systems.
NOTE: If you recompile the program without using
the supplied batch command file, you must rename the
TOXIWASP.CMN or EUTRWASP.CMN common block to WASP.CMN
depending on which WASP program is desired.
KNETIC.CMN
Common block used by the TOXIC kinetical routine
to store degradation rates and constants.
247
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ENVIRON.CMN
PHYSCHM.CMN
OPTION.CMN
PHOTOL.CMN
CONG.CMN
SSCOM.CMN
CHMLOC.CMN
PARAM.EQU
GLOBAL.EQU
CHEM1.EQU
CHEM2.EQU
CHEM3.EQU
SOLID.EQU
EUTRO.CMN
Common block used by the TOXIC kinetical routine to
store environmental information.
Common block used by the TOXIC kinetical routine to
store information related to the physical-chemical
calculations.
Common block used by TOXIC kinetical routine to hold
values for options selected by the user.
Common block used by the TOXIC kinetical routine to
store information related to the photolysis reaction
pathway.
Common block used by the TOXIC kinetical routine to
store chemical concentrations from simulation
calculations.
Common block used by both the WASP DRIVER and TOXIC
Kinetical routine to hold simulation type (time
variable or steady state) and intermediate steady
state calculations.
Include block to declare all locally used chentical
variables in TOXIC kinetical routine.
Include equivalence statements for the environmental
parameters in TOXIC kinetical routine.
Include equivalence statements for the global
constants in TOXIC kinetical routine.
Include equivalence statements for the chemical 1
constants in TOXIC kinetical routine.
Include equivalence statements for the chemical
2 constants in TOXIC kinetical routine.
Include equivalence statements for the chemical
3 constants in TOXIC kinetical routine.
Include equivalence statements for the solid '
constants in TOXIC kinetical routine.
Include common block for EUTRO kinetical routine
contains the equivalences and variable declarations.
Subroutine Descriptions--
WASP4 is a modular program. Its many subroutines can be grouped into
the functional categories of "input," "process," "output," and "utility," as
248
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in Figure 3.3.1.
WASP COMMON.
Data are shared among the subroutines primarily through the
WASP4V
The WASP4 main program is the control module. It assigns input and
output unit numbers, and operates the calling sequence for the input,
simulation, and output subroutines.
Input Subroutines
WASP1
WASP1 opens the input and output units, then reads Data Group A for
model identification and system bypass options. Information is printed and
values and arrays are initialized.
WASP2
WASP2 reads Data Group B for sets of dispersion coefficients, cross-
sectional areas, and characteristic lengths. These are converted to.bulk
exchanges, and information is stored in memory and printed.
WASP3
WASP3 reads Data Group C for volumes. If indicated, volumes'are read
from restart file "ICRD." Information is stored in memory and printed.
WASP4
WASP4 reads Data Group D for advective flows, which are converted to
internal units of cubic meters per day. Information is stored in memory
and printed. If indicated, WAS4A is called to read flows from a hydro-
dynamic file created by DYNHYD4.
WAS4A
If indicated, WAS4A opens the hydrodynamic file "SUMRY2.OUT" created by
DYNHYD4, and reads some basic hydrodynamic network information in either a
formatted or unformatted mode. WAS4A then reads the junction to segment
correspondence, sets the WASP time step, and prints information.
249
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WASPS
WASPS reads Data Group E for boundary concentrations for each model
system. Information is stored in memory and printed.
WASP6
WASP6 reads Data Group F for waste loads for each model system.
nation is stored in memory and printed.
Infor-
WAS6A
If indicated, WAS6A opens the unformatted loading file "NPS.DAT" created
by a runoff model and stored in the sequence illustrated in Table 3.3.1. The
runoff day corresponding with the initial WASP simulation day is read. Input
segment numbers corresponding to each runoff load are read. Actual runoff
loads from the file are printed as specified. Finally, the file is posi-
tioned properly to begin the WASP simulation.
TABLE 3.3.1. CONTENTS OF "NPS.DAT"
Record
Number
Contents of Record
1
2
3
NWKS, MDUM, MDUM, MDUM
((NPSWK(I,J),1=1,NOSYS),J-l.NWKS)
((NPSWK(I,J),I=1,NOSYS),J=1,NWKS)
N+l
Variable
NWKS
MDUM
NPSWK
NOSYS
I
J
N
( (NPSWK( I, J ),!-!, NOSYS ),J-1, NWKS)
Tvpe Definition
1*4 The number of runoff loads
1*4 Dummy variable, not used
R*4 Runoff loads, averaged over day,
1*4 Number of water quality variables
1*4 Water quality variable counter
1*4 Runoff load counter
in ka/day
(or systems)
1*4 Number of days for which loads are available
250
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WASP7
WASP7 reads Data Group G for parameters for each segment. It then reads
Data Group H for constants. Finally, it reads a specified number of kinetic
time functions. Information is stored in memory and printed.
WASP9
WASP9 reads Data Group J for bulk densities, initial concentrations, and
dissolved fractions in all segments for each model system. If indicated,
initial concentrations are read from restart file "ICRD." Information is
stored in memory and printed. WASP9 finally reads Data Group K for maximum
and minimum concentrations for each model system.
Process Subroutines
Once input data groups A-J are read, control is passed to EULER to
perform the simulation.
EULER
EULER is the heart of the simulation, stepping through time performing
a first-order EULER integration. First, counters and time functions are
initialized to TZERO with help from subroutine TINIT. Initial printouts are
set up with a call to WAS13, then initial mass derivatives are computed with
a call to DERIV. A fatal input error condition is checked for, then the
integration proceeds, time step by time step.
For each time step, EULER loops through each system and segment, com-
puting the new mass as follows:
new mass = old mass + mass derivative
time step
Each new concentration is set to the new mass divided by the new volume, and
the mass derivative is reset to zero. If the negative solution option is
"0," any negative concentrations are replaced by one-half of the old mass
divided by the new volume. Next, EULER increments the time and adjusts the
new day counter if necessary. If it is the proper time, EULER calls WAS13 to
produce intermediate printouts and trigger storage of all display variables
(by returning IDISK - 1). New mass derivatives are obtained with a call to
DERIV. Volumes are stored if IDISK = 1. The final task for each time step
is to check for a new time step and for the end of the simulation. New time
steps are periodically set by calling WAS14.
When the final time for the simulation is detected, EULER triggers a
final storage of display variables, then stores final volumes and concentra-
tions in file "RESTRT." Control is then passed back to MAIN.
251
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DERIV
DERIV Is called by EULER to calculate mass derivatives. It first checks
and obtains new flows and volumes from a hydrodynamic file by calling DHYD1
or DHYD2. It then obtains the kinetic derivative by calling WASPB. Finally,
it obtains the transport and loading derivatives by calling WAS12.
DHYD1 and DHYD2
One of these subroutines may be called by DERIV to obtain new hydro -
dynamic information from the hydrodynamic file "SUMRY2.0UT, " created by
DYNHYD3. These subroutines are equivalent, except that DHYD1 reads an
unformatted file while DHYD2 reads a formatted file.
For the first time step, DHYDx reads the basic hydrogeometry and ini-
tializes its arrays. Hydrodynamic junction to water quality segment corre-
spondence is established, and flow directions are fixed. Upstream and sea-
ward boundaries are set up, and boundary concentrations are located for each.
The hydrodynamic file is positioned properly in time, and flows for the first
time step are printed.
For each time step throughout the simulation, DHYDx is called and reads
new flows and volumes from SUMRY2.0UT. These are scaled and converted to
internal WASPS units. New boundary flows are set up. If the end of the
hydrodynamic file is properly detected, it is reset to its beginning point,
and the simulation proceeds. If the file end is improperly detected in the
middle of a read, the simulation is aborted.
WAS12
WAS12 is called by DERIV to obtain the transport and loading derivatives .
Upon entry to WAS12, only the kinetic portion of the mass balance derivative
has been evaluated by WASPB. WAS12 calculates the mass derivatives due to
advective flow, dispersive exchange, point source waste loading, and runoff
loading, and adds them to the kinetic derivative. WAS12 goes through the
following steps :
a. Using the IQ and JQ vectors as drivers, WAS12 computes advective
transport. Variable flows are updated by calling WAS8B, and volumes are
adjusted for continuity. For each system, variable boundary concentrations
are updated by calling WAS8A if necessary. For each flow, Q, proper upstream
and downstream concentrations are assigned by calling WA12A. The advected
concentration CSTAR is determined, and mass derivatives for the downstream
and upstream segments are adjusted by + Q. CSTAR.
b. Using the IR and JR vectors as drivers, WAS12 computes dispersive
transport. Variable exchanges are updated by calling WAS8B. For each system
and each exchange flow, R, proper upstream and downstream concentrations €2
and C^ are assigned by calling WA12A. Mass derivatives for the downstream and
upstream segments are adjusted by + R .
252
-------
c. Using the IWK vector as a driver, WAS12 computes point source
loading. For each system, variable loadings are updated by calling WAS8A
if necessary. For each load L (in kg/day), the mass derivative for the
affected segment is adjusted by + L.
d. Using the INPS vector as a driver, WAS12 computes diffuse source
loading if appropriate. New loads are read from file NFS. DAT at the beginn-
ing of each new day. For each load L' (in kg/day), the mass derivative for
the affected segment is adjusted by + L' .
WA12A
WA12A is called by WAS12 to determine the proper upstream and downstream
concentrations Co and C^ for advective flow from segment JQ to segment IQ or
dispersive exchange between segments JR and IR. For flows or exchanges with
a downstream boundary, the proper boundary concentration is located for C^.
For flows or exchanges with an upstream boundary, the proper boundary concen-
tration is located for V-
WASPB
WASPB is the user- specified water quality subroutine that calculates the
kinetic mass derivative and stores the proper display variables for later
printout. WASPLB may call several other subroutines. These are discussed
below for eutrophication and toxic chemical subroutines.
WASPS
WASPS is called by WAS12 to update the piecewise linear functions of
time, if any, kinetic time functions. This means computing new slopes and
intercepts, and setting a variable to indicate the next simulation time that
the functions are to be updated. The following convention is used for the
ith update.
slope
intercept
next update time
WAS8A
WAS8A is used to update the piecewise linear functions of time, if any,
for boundary conditions and forcing functions . This means computing new
slopes and intercepts for any system or state variable that requires an
update, and setting a variable to indicate the next simulation time that the
253
-------
piecewise linear functions are to be updated. The same conventions used in
WASPS are used in WAS8A for computing slopes and intercepts.
WAS8B
WAS8B is called by WAS12 to update piecewise linear functions of time
for dispersion coefficients and flows. Updated dispersion coefficients for
each exchange field and time function are stored in the array BRINT(NF,NT).
Updated flows for each field and time function are stored in the array
QINT(NF.NT).
BEDSED
BEDSED, called in WAS12, computes changes in volumes and porosities for
sediment bed segments, depending upon the sediment bed option used. For
constant bed volumes, porosity is calculated every sedimentation time step.
For variable bed volumes, volumes change in response to sediment transport,
erosion and compaction.
WAS13
WAS13 is called every print interval by EULER to print intermediate
concentrations or mass checks on a designated constituent. At this time, the
solution stability is checked by comparing the maximum concentrations speci-
fied by the user with calculated concentrations. If any concentrations
exceed the maximum, the simulation is aborted.
WAS 14
WAS14 is called by EULER to adjust the integration step size (time step)
as specified by the user in Data Group M.
TINIT
TINIT is called by EULER at the beginning of the simulation to adjust
time functions to the initial time TZERO. TINIT checks and adjusts time
functions for exchanges, flows, kinetic time functions, boundary concentra-
tions, and loads.
TOPT
TOPT can be called by the user WASPB subroutine to maximize the time
step subject to the flow and dispersion stability constraints. This should
reduce numerical dispersion, but is not unconditionally stable. The time
step calculated by TOPT is 0.5 days will fall between 0.01 and 0.5 days.
254
-------
Utility Subroutines
Several utility subroutines can be called to help perform routine tasks.
BRKERR
BRKERR prints an error message to output file and screen concerning
the number of data points in a time function; the simulation is aborted.
FMTER
FMTER prints an error message to output file and screen concerning input
data formats; the simulation is aborted.
SCALP
SCALP multiplies a real vector by a scale factor.
SETCA
SETCA sets a character array to a specified character value.
SETIA
SETIA .sets an integer array to a specified integer value.
SETRA
SETRA sets a real array to a specified real value.
SETRB
SETRB sets a real three-dimensional array to a specified real value.
SCAL3D
SCAL3D multiplies a real three-dimensional array by a scale factor.
SETXA
SETXA sets a double precision array to a specified double precision
value.
255
-------
WERR
WERR writes error messages for improper segment designation's and missing
boundary conditions; the simulation is aborted.
WMESS . ,
WMESS prints a message when stability criteria are violated; the simula-
tion is aborted.
Eutrophication Kinetic Subroutines
The WASP4 eutrophication kinetics are calculated through a special
WASPB subroutine structure, illustrated in Figure 3.3.2. These subroutines
combine biological and chemical constants with environmental parameters to
determine transformation rates among the eight eutrophication systems (state
variables). From these rates and the concentrations passed by WASP, kinetic
mass derivatives are calculated and passed back to WASP where they are inte-
grated along with ,the transport and loading derivatives every time step.
I
EUTRWASPB j EU03CMN
I
EU03IN I
I
-|EU03S4|
-|EU03S8[
-|EU03S3|
- IEU03S71
-|EU03S1|
-EU03S2
-|EU03S5|
-|EU03S6|
EU03DU
-|EU03K2|
-|EU03SX|
Figure 3.3.2. Eutrophication subroutine structure.
256
-------
WASPB (EUTRWASPB)
EUTRWASPB serves as the main program for the kinetic portion of
EUTRWASP, calling other subroutines when appropriate. Initialization is
performed during the first time step by calling EU03IN. Kinetic time
functions are updated throughout the simulation. For each segment, ambient
concentrations and environmental conditions are determined, then mass
derivatives are obtained with successive calls to EU03S4, EU03S8, EU03S3,
EU03S7,; EU03S1, EU03S2, EU03S5, andEU03S6. At print intervals, state
variable and display variable concentrations are stored by calling EU03DU.
EU03IN • . " ' •
EU03IN is called during the first time step only to initialize para-
meters , counters , and functions for the simulation. For the phytoplankton
system, initial and boundary concentrations are converted from the input
units of ug-Chla/L to the internal units of mg-CRB/L.
EU03S4 :
EU03S4 calculates the phytoplankton kinetics, and is called first be-
cause it affects all the other systems. For water column segments, the
growth rate is first calculated. The maximum growth rate is adjusted for
temperature, then reduced according to ambient light conditions using either
the Dick Smith or DiToro formulation. Ammonia preference is calculated, then
the growth rate is further reduced if nitrogen or phosphorus is in limited
supply. Respiration, death, and settling rates are calculated, and, finally,
the mass derivative.
EU03S8
EU03S8 calculates the sources and sinks of organic phosphorus and
computes the mass derivative.
EU03S3
EU03S3 calculates the sources and sinks of inorganic phosphorus and
computes the mass derivative.
EU03S7
EU03S7 calculates the sources and sinks of organic nitrogen and computes
the mass derivative.
257
-------
EU03S1
EU03S1 calculates the sources and sinks of ammonia nitrogen and
computes the mass derivative.
EU03S2
EU03S2 calculates the sources and sinks of nitrite plus nitrate nitrogen
and computes the mass derivative.
EU03S5
EU03S5 calculates the sources and sinks of carbonaceous biochemical
oxygen demand and computes the mass derivative,
EU03S6
EU03S6 calculates the sources and sinks of dissolved oxygen and computes
the mass derivative. The reaeration rate is obtained for surface water
segments by calling EU03K2.
EU03K2
EU03K2 calculates the ambient reaeration rate based on temperature,
wind speed, water velocity, and water depth. The current-driven portion
of this rate is calculated using the Covar method, which chooses among
three formulas based upon velocity and depth. The oxygen saturation
level is finally calculated as a function of water temperature.
EU03DU
EU03DU is called every print interval to store state variable and dis-
play variable concentrations. First the display variables are calculated,
then the simulation time is stored in memory. Address counters for the
storage arrays are calculated, and four variables are stored in memory for
each system.
EU03SX .
EU03SX calculates the dispersive exchange of dissolved phases between
water column and benthic segments, and adjusts the mass derivatives accord-
ingly. If no benthic segments are present, this calculation is skipped.
Finally, additional ammonium and phosphate fluxes as specified by the user
are added, and derivatives are adjusted.
258
-------
Toxic Chemical Kinetic Subroutines
The WASP4 toxic chemical kinetics are written in a modular structure
that includes numerous subroutines, as shown in Figure 3.3.3. Each transfor-
mation and transfer process is separated into one or several subroutines.
This structure allows for convenient addition or modification of the
kinetic descriptions.
WASPB
WASPB serves as the main program for the kinetic portion of the toxic
chemical model. It is called each time step by subroutine EULER. Several
tasks are performed:
1) The current.values for the piecewise-linear functions of time are
calculated. WASPS is called if a time break has been reached for any
of the functions.
2) At time zero the input needed to calculate solar intensity at
the water surface is read from the input file and SOLAR is called
to perform the calculation.
3) For each segment of the model the following tasks are performed:
a) the current values of environmental characteristics are
computed.
b) CHEM1 is called to evaluate the kinetic portion of the deri-
vative describing chemical 1. If a print interval has been
reached, the concentrations of the components of the chemical
are stored in memory.
c) The locations in the F array that define application of the
.transport fields to the transport of solids are set.
d) If NOSYS is equal to or greater than 5, CHEM2 is called to
evaluate the kinetic portion of the derivative describing
chemical 2. If a print interval has been reached, the con-
centrations of the components of the chemical are stored in
memory.
e) If NOSYS equals 6, CHEM3 is called to evaluate the kinetic
portion of the derivative describing chemical 3. If a print
interval has been reached, the concentrations of the compo-
nents of the chemical are stored in memory.
CHEMl(I)
CHEM1 determines the kinetic portion of the derivative describing chemical
1 in segment I. Tasks executed are:
259
-------
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260
-------
1) At time zero, if the user has chosen photolysis option 1, the molar
absorptivitities of the chemical are read from the input file.
2) The following preperties of the chemical are computed:
a) molecular diffusivity in air and in water
b) octanol-water partition coefficient
c) organic carbon partition coefficient (Kow)
d) solids-water partition coefficient (from subroutine PRTITION)
e) air-water partition coefficient
f) distribution coefficients (ratio of ionic to molecular con-
centration) for each ionic form
3) FRCTION is called to determine the fraction of total chemical for
each of the 15 components defined by the 3 phases (dissolved, sorbed to DOC
and sorbed to solids) and 5 species (neutral and 4 ionic).
4) Subroutines BIODEG, HYDROL, LMDAMAX, BEER, PHOTO, VOLAT and OXID are
called to determine the transfer and transformation rates that make up the
kinetic portion of the derivative. . - '
5) The individual rates returned by the subroutines called are summed
to yield the total kinetic portion of the derivative.
6) The derivative is multiplied by the segment volume to be consis-
tent with the transport derivative calculation.
CHEM2
CHEM2 determines the kinetic portion of the derivative describing chemi-
cal 2 in segment I. The tasks executed are identical to those described for
CHEM1 with one addition. The rate of production of chemical 2 is computed
and added to the derivative if chemical 2 has been specified as a transforma-
tion product of chemical 1.
CHEM3 ,
CHEM3 determines the kinetic portion of the derivative describing chemi-
cal 3 in segment I. The tasks executed are identical to those described for
CHEM1 with one addition. The rate of production of chemical 3 is computed
and added to the derivative if chemical 3 has been specified as a transforma-
tion product of chemical 1 or chemical 2.
261
-------
surface intensity is computed for each specie of the chemical at its wavelength
of maximum light absorption.
LMDAMAX(LAMAXG)
LMDAMAX determines the wavelength index for the user specified wavelength
of maximum light absorption for each species of the chemical (LAMAXG). This
index corresponds to one of the 46 wavelengths considered by the model.
SOLAR(ILITE,ELEVG,LATG)
SOLAR computes the solar irradiance just below the water surface for
each of the 46 wavelengths considered by the model. This routine and those
called by it (SOLFCT, DINTRP, DINTPT, DIVDIF, DSPLY) were taken from the
EXAMS II modeling framework. Minor changes were made to SOLAR to provide
compatability with the WASP4 kinetic package. Otherwise, these routines are
identical to their EXAMS II versions. The user is referred to EXAMS II
documentation for a more complete explanation of these routines.
SSTATE - called by MAIN this subroutine controls the steady state option.
Subroutine TINIT is first called to initialize counters and the time functions
to TZERO. If hydrodynamic flow fields are specified either DHYD1, DHYD2 or
SWFLOW is called. Subroutine WSS12 which computes the transport elements of
the [A] matrix is then called. This is followed by calls to WSS02 and WSS03
which cumulate the elements and then solve the [A] matrix, respectively. The
suspended solids systems (systems 2, 3, and 4) are first solved followed by
the chemical systems. Subroutine WSS04 then writes the summary of the results
to the output file.
WSS12 - is essentially a modification of WAS12 utilized when the steady
state option is selected. The transport elements of the [A] matrix are
computed and written to scratch file 81 and the components of the load vector
(w) are written to scratch file 81.
BDSDSS - this routine reminds the user that when the steady state option
is selected the defined suspended solids transport must yield no net buildup
or erosion of solids in the bed. If variable bed option (IBEDV = 1) is
selected the run terminates with a message to the user.
TOXIDUMP
At specified intervals, TOXIWASPB calls TOXIDUMP to prepare or print
output from the simulation.
264
-------
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271
-------
A
af
ag,A
B
cd
g
H
i
j
e
Q
R
S
t
APPENDJX A
Symbols for Section 1.2
wind direction, degrees.
cross-sectional area, m .
f\
frictional acceleration, m/sec .
gravitational acceleration, m/sec .
regression coefficients for tidal heights, m.
surface area, m .
wind stress acceleration along axis of channel, m/sec .
width, m.
drag coefficient (= 0.0026), unitless.
acceleration of gravity =9.81 m/sec .
water surface elevation, head, or (height above an arbitrary
datum) m.
channel or link number, unitless.
junction or node number, unitless.
length of channel i, m.
Manning roughness coefficient (usually between 0.01 and 0.10),
sec-m"1/3.
channel direction.
flow, nr/sec.
hydraulic radius (approximately equal to the depth), m.
water surface slope, m/m.
time, hr or sec.
272
-------
'w
U
U
U3
US
V,
w
"obs
At
Pa. -
'w -
w =
the boundary shear stress, kgm/m-sec^.
velocity along the axis of channel, m/sec.
the current vector (magnitude = U, direction = Q), m/sec.
velocity in channel i, m/sec.
the velocity in channel i at time t, m/sec.
water volume, m .
the wind speed (relative to the moving water surface) measured
at a height of 10 meters above water surface, m/sec.
the observed wind velocity at a stationary location, m/sec.
distance along axis of channel, m. .
tidal elevation above or below the model datum, m.
mean depth of channel i, m. . ,
the angle between the channel direction and the wind direction
(relative angle) .
the computational time step, sec.
the channel length, m.
the density of air,
density of water, kg/m .
tidal frequency, 2?r/tidal period, hr"^.
velocity gradient in channel i with respect to distance, sec .
_ — water surface gradient in channel i with respect to distance, m/m.
logitudinal axis .
273
-------
B
B
C
Bj
Et(t)
E (t)
APPENDIX B
Symbols for Section 1.3
t\
cross-sectional area, m .
o
surface area of segment i, m .
9
interfacial area shared by segments i and j , m .
benthic surface area, m.
o
surface area of segment j, m .
probability of deposition upon contact with the bed.
boundary source index.
average width, m.
o
concentration of the water quality constituent, g/m .
o
boundary concentrations for segment j, g/m .
constituent concentration advected between i and j, g/m .
concentration of the water quality constituent in segment j,
mg/L (g/m3).
depth of segment, m.
depth of the upper bed, m.
depthof the lower bed, m.
solid particle diameter, mm.
longitudinal, lateral, and vertical diffusion coefficients,
m /day.
evaporation velocity time function for segment i, m/day.
o
dispersion coefficient between segments i and j, m/day.
evaporation rate from segment j, m/day.
274
-------
• fDj
i
j
K
L
A
N
ni
dissolved fraction of chemical in segments i and j.
fraction of chemical sorbed to solid type "s" in segment j.
o
acceleration of gravity, 981 cm/sec .
benthic segment or adjacent segment index.
water segment index.
kinetic transformation index.
point source index.
length of the segment, m.
characteristic mixing length between segments i and j, m.
mass of chemical in segment i, g.
nonpoint source index.
porosity of segment j, 1^/L.
average porosity at interface i and j,, ly/L.
precipitation velocity time function for segment i, m/day.
precipitation rate into segment j ,.m/day.
volumetric flow — A . Ux, m /sec.
advective flow between segments i and j, positive when
leaving segment, j, negative when entering j, m /day.
o • . • •:
boundary inflows to segment j, m/day.
pore water flow between segments i and j, defined as posi-
tive when leaving segment j, and negative when entering j,
vr/day.
o • '
dispersive flow = EA. m /sec.
A
3 EiJ A
dispersive flow between segments i and j , m /sec =
Kpij
O
pore water diffusive exchange flow, nr/sec ^
cij
275
-------
s
s
SB
5kcj
u
"
solids transport field index.
sediment concentration.
sediment concentration inlower bed, g/m .
boundary loading rate (including upstream, downstream, benthic,
and atmospheric), g/m -day.
•j
sediment concentration in the upper bed, g/nr*.
sediment concentration in the water, g/m .
total kinetic transformation rate; positive is source, negative
is sink, g/m -day.
kinetic transformation k for chemical c within segment j,
g/m3-day.
o
direct and diffuse loading rate, g/m-day.
total source/sink rate = SL + Sg + SK, g/m3-day.
time, days.
average tortuosity of segments i and j, mwater/m.
longitudinal, lateral, and vertical advective velocities,
m/day.
o
absolute viscosity of water =0.01 poise (g/cm -sec) at
20°C.
volume of segment j, m .
Stokes velocity for a solid particle with diameter dp, and
density pp, m/day.
net sediment flux rate, g/day.
deposition velocity, m/day.
point source loads into segment j, g/day.
nonpoint loads into segment j, g/day.
scour velocity, m/day.
sedimentation velocity of upper bed, m/day.
276
-------
Wc
W
si
-At
solids transport velocity between segments i and j, defined as
positive when leaving segment j, and negative when entering,
m/day. ; - , ;
sedimentation velocity of lower bed, m/da;y.
the time step, typical between 15 minutes, and a half day,
day. •-.,•-••
numerical weighting factor between 0 and 1, unitless.
277
-------
aNC
aN03C
aoc
aON
aPC
BODU5
CBOD5
Cj
Cpi'CPJ
°PIP
cwi«cwj
CTIP
TIP
G4
C5
APPENDIX C
Symbols for Section 1.4
nitrogen to carbon ratio, mg N/mg G.
oxygen to carbon ratio for nitrate up.take, mg C^/mg C.
the oxygen to carbon ratio, mg C>2/mg C.
oxygen to nitrogen ratio, mg 02/mg N.
phosphorus to carbon ratio, mg P/mg C.
ratio of the ultimate to 5-day carbonaceous biochemical
oxygen demand, unitless.
the internally computed 5-day CBOD, mg/L.
concentration of total chemical in segment j, mg/L.
the particulate material concentrations in the benthic
layer and water column respectively, mg/L.
concentration of phosphorus sorbed to suspended solids,
mgP/Kg m.
K
•PIP
. M . C
DIP-
the dissolved concentrations in the benthic interstitial
waters and overlying water column respectively, mg/L.
CDIP + CPIP-
JDIP
+ KPIP . S . C
DIP-
nitrogenous biochemical oxygen demand (NBOD), mg/L
(System 1).
nitrate nitrogen, mg/L (System 2).
phytoplankton carbon, mg/L.
total biochemical oxygen demand (BOD), mg/L (use System 5)
278
-------
D
D
DIP, DIN
DIP'
DIP
DIP
t-1
DO
sat
D.
f
fu
carbonaceous biochemical oxygen demand, mg/L (System 5).
dissolved oxygen, mg/L (System 6).
concentration of sorbed chemical on sediment type "s" in
segment j, mgc/L.
dissolved oxygen saturation, mg/L.
depth of water column segment, m.
benthic layer depth, m.
available nutrients for growth, dissolved inorganic
phosphorus (orthophosphate) and dissolved inorganic
nitrogen (ammonia plus nitrate), mg/L.
the new dissolved inorganic phosphorus resulting from the
previous integration step, mg/L.
the new "equilibrium" dissolved inorganic phosphorous,
available for algal uptake, mg/L.
the dissolved inorganic phosphorus resulting from the previous
integration step, mg/L.
dept'bi of segment j , equal to volume/surface area, m.
dissolved oxygen saturation, mg C^/L.
biomass reduction rate, day .
death rate, day"1.
death plus respiration rate constant, day"1.
the natural logarithm = 2.71828, unitless.
the diffusive exchange rate between dissolved concentrations
in the interstitial water and the overlying water column,
m /day.
o
diffusive exchange coefficient, jsr/day.
2
dispersion coefficient between segments i and j, m /day.
fraction of daylight, unitless.
units conversion factor (0.083) mole photons/m2-ly.
NBOD dissolved fraction.
279
-------
D8j
H
D3
D5
D8
ON
Glmax
GRTj
GRIj
GRNj
Kt)
i.j
the fraction of the total inorganic phosphorous assined to
the dissolved phase, unitless.
dissolved fraction of organic phosphorus in segment j.
the ammonia nitrogen pool, unitless.
dissolved fraction of inorganic phosphorous in segment j.
BOD dissolved fraction.
CBOD dissolved fraction.
organic nitrogen dissolved fraction.
fraction dissolved organic phosphorus.
the organic nitrogen pool, unitless.
fraction of dead and respired phytoplankton recycled to the
organic phosphorus pool, unitless.
the particulate organic phosphorus pool, unitless.
growth rate constant, day"-'-.
specific phytoplankton growth rate, day"-*-.
maximum Specific Growth Rate @ 20'C, day"-'-.
the temperature adjustment factor for the direct effects of
temperature on growth, dimensionless.
the light attenuation factor as a functin of T, I, f, D,
and Ke, dimensionless.
the nutrient limitation factor as a function of dissolved
inorganic phosphorous and nitrogen (DIP and DIN),
dimensionless.
incident solar radiation, ly/day.
the average daily solar radiation just below the surface,
ly/day.
the incident light intensity just below the surface,
assumed to average 0.9 I, ly/day.
instantaneous surfae solar radiation, ly/day.
indicates benthic layer and t^O column, respectively.
280
-------
Kaj
Kaj(T)
K,
•BOD
c
DS
K
K
Kv
kOND
KOPD
K
PIP
CPZD
segment number, unitless.
reaeration rate (§ 20°C, day"1.
reaeration rate coefficient at 20°C, day"1.
reaeration rate coefficient at ambient segment temperature,
day"1.
half saturation constant for oxygen limitation, mg C>2/L.
phytoplankton self-light attenuation; the extinction
coefficient per unit of chlorophyll, m /mg chlorophyll-a.
..-1
deoxygenation rate constant, day .
carboaceous deoxygenation rate constant, day
organic carbon (as CBOD) decomposition rate, day" .
extinction or light attenuation coefficient, m" .
the total extinction coefficient, computed from the sum
of the non-algal light attenuation, Ke, and the self-
shading attenuation due to ambient phytoplankton population,
m.
half saturation constant for nitrogen, /*g N/L.
half saturation constant for phosphorus, ^tg P/L.
half saturation constant for phytoplankton limitation,
mg C/L.
nitrogenous deoxygenation rate constant, day" .
half saturation constant for oxygen limitation, mg
Michaelis constant for denitrification, mg 02/L.
organic nitrogen decomposition rate, day
-1
organic phosphorus decomposition rate, day
-1
first order reaction rates associated with the particulate
and dissolved phases respectively, day
-1
partition coefficient for particulate phosphorus, mgP/Kg M,
per (mg P/L) or (L/kg M).
anaerobic algal decomposition rate, day"1.
281
-------
Klc
ks8j
klD
ks3j
ks4j
klG
k!2
klR
klR
klR
k1R(T)
k1R(20°C)
k2
k20
k58
k68
k71
C83
fc
140
C1013
C1314
Lc
m
P.
average phytoplankton growth rate constant, day"-'-.
organic phosphorous settling rate, day"1.
a non-predatory death rate, representing the effect of
parasitization, day"1.
inorganic phosphorus settling rate in segment j, day"1.
settling rate constant, day"1.
grazing rate on phytoplankton per unit zooplankton populating
L/mg c-day.
nitrification rate constant, day .
the algal respiration rate at 20°C, the temperature at
which the field samples were incubated, day .
algal endogenous respiration, day" .
average plhytoplankton respiration rate constant, day" .
temperature corrected rate, day" 1.
the endogenous respiration rate at 20'C, day"1.
reaeration rate constant, day"1.
denitrification rate at 20°C, day"1.
dissolved organic phosphorus mineralization at 20°C, day"1.
particulate organic phosphorus mineralization rate at
20°C, day"1.
mineralization rate constant, day"1.
dissolved organic phosphorus mineralization at 20°C, day"1.
denitrification rate @ 20°C, day"1.
organic nitrogen mineralization rate @ 20°C, day .
nitrification rate @ 20°C, day"1.
characteristic mixing length between segments i and j, m.
concentration of solids, kg/L.
the phytoplankton biomass in carbon units, mg/L.
282
-------
PIP'
PIP
PIP
t-1
the sorbed inorganic phosphorus resulting from the previous
integration step, mg/m.
the new "equilibrium" sorbed inorganic which may then settle
to the sediment layer from the water column, mg/L.
the sorbed inorganic phosphorous resulting from the previous
integration step, mg/L.
preference for ammonia uptake term, unities?-.
J
Sk4j
SOD
t
T
T
TIP
vo
Vn
Vs3
Vs3ij
vsd
vsl
Vs4
Vs4i,j
Vs5
phytoplanktori population, cells/A.
reaction term.
p
sediment oxygen demand, g/m -day.
time, day.
ambient water temperature, °C.
temperature, °T.
the total inorganic phosphorus, mg/L.
the deposition velocity of particulates across the water
column-benthic interface, m/day.
the resuspension velocity of particulates, m/day.
the net settling velocity of particulates across the
water column-benthic interface, m/day.
organic matter settling velocity, m/day.
settling velocity of organic matter from segment j to i, m/day.
the sedimentation velocity induced by sedimentation, m/day.
the net settling velocity of phytoplankton from the water
column to the sediment, m/day.
algal settling velocity, m/day.
the net settling velocity of phytoplankton from segment j
to i, m/day.
inorganic sediment settling velocity.
settling velocity of inorganic sediment from segment j to i
m/day.
283
-------
'tj
W
W
Bj
0
20
9
9
'DS
*OND
'OPD
PZD
e58
968
0
71
0
'83
9140
91013
91314
*max
*max
average water velocity in segment j, m/sec.
time-varying windspeed at 10 cm above surface, m/sec.
boundary loads into segment j, g/day.
the ratio of carbon to chlorophyll in the phytoplankton,
(mg carbon/mg chlorophyll-a).
temperature coefficient, unitless.
temperature coefficient, unitlss.
temperature coefficient, unitless.
temperature coefficient, unitless.
temperature coefficient, unitless.
temperature coefficient, unitless.
temperature coefficient, unitless.
temperature coefficient, unitless.
temperature coefficient, dimensionless.
temperature coefficient, unitless.
temperature coefficient, unitless.
temperature coefficient, unitless.
temperature coefficient, unitless.
temperature coefficient, unitless.
temperature coefficient, unitless.
temperature coefficient, unitless.
maximum photosynthetic quantum yield, mg C .
mole photon
the quantum yield, mg carbon fixed per mole of light
quanta absorbed.
numerical weighting factor (0-0.5), unitless.
284
-------
APPENDIX D
Symbols for Section 1.5
C2
C
Bj
JP04
CHL
frequency factor.
o
surface area of water segment, m .
concentration of DOC in segment j, kg-biomass/L.
concentration of DOC in water in segment j.
Bj = Bj/nj, kgb/V
o
chemical concentration, mg/L (g/m ).
reduced chemical.
oxidized chemical.
concentration of DOC-sorbed chemical in segment j, mgc/L.
concentration of DOC-sorbed chemical in biota in segment j
GBj = CBj/Bj> mSc/kSb-
drag coefficient = 0.0011.
cloud cover, tenths of sky (1-10).
o
constituent concentration advected between i and j, g/m .
concentration of total chemical in segment j, mgc/L.
dissolved inorganic phosphorus concentration, /Jg/L.
cloud cover reduction factor.
sorbed chemical concentration, rog/kgsediment•
phytoplankton chlorophyll concentration, mg/L.
concentration of sorbed chemical on sediment type "s"
in segment j, mgc/m.
concentration of sorbed chemical on sediment type "s"
on sediment in segment j. Csi = Csj/^j
285
-------
ft
cw
D
DOC.B
DSHD(2)
d
d
EaH
Eao
Eaoi
EDIF
Ei
[E]
D
oci
H
i
Gk
dissolved chemical concentration, g/m- .
concentration of dissolved chemical in segment j, mgc/L.
concentration of dissolved chemical in water in segment j.
cwj ~ Cwj/nj. mgc/I^.
average depth of the water segment, m.
dissolved organic carbon, mg/L.
sediment density, specified under initial conditions, kg/L.
optical path, cm/cm.
benthic layer depth, m.
Arrhenius activation energy, kcal/mole.
Arrhenius activation energy for oxidation reaction, kcal/mole.
activation energy for oxidation of specie i, kcal/mole.
diffusive exchange coefficient, m2/sec.
activation energy (kcal/mole).
concentration of RH^, moles/L.
the intensity of environmental property affecting process
"k", such as light intensity or bacterial population.
dissolved fraction of the chemical.
fraction of chemical as ionic specie i in phase j.
fraction of chemical "c" as specie "i" in phase "j".
organic carbon fraction, phase i.
organic carbon fraction of sediment, unitless.
Henry's law constant, atm-m^/mole.
benthic segment, unitless.
reference light intensity causing photolysis rate KpG,
E/cm -sec.
average light intensity of wavelength k, photons/cm2-sec.
286
-------
j
kai
kaij >kbij
K
•Bs
K
•Bsi
K
•Bsij
K
•Bw
K,
•Bwi
K
Bwij
T)
Keij
Kew
KF
KHAij
KHBij
K,
•HH
surface light intensity, E/cm -sec.
water segment, unitless.
specific sunlight absorption rate for phase i, E/mole-day
or (E/L)/(mole/L)/day.
specific acid and base catalyzed rate constants for ionic
specie i in phase j, respectively, molar"1 . day" .
net biodegradation rate constant in benthic segment, day" .
second order biodegradation rate constant for phase i
in benthic segments, ml/cell-day.
second order biodegradation rate constant for phase i in
benthic segments, ml/cell-day.
net biodegradation rate constant in water segment, day" .
second order biodegradation rate constant for phase i
in water segments, ml/cell-day.
second order biodegradation rate constant for phase i in water
segments, ml/cell-day.
desorption rate constant, hr .
lumped metal distribution coeficient, L/Kg.
spatially variable light extinction coefficient, m
second order rate constanc, L/mole-day.
-1
second order extra rate constant for chemical as specie
i in phase j, in [E]"1,- day"1.
pure water extinction coefficient, 1/m.
net extra rate constant, day
-1
-1
photolysis rate constant, day"
gas phase transfer coefficient, m/day.
acid hydrolysis rate constant for specie i, phase j.
base hydrolysis rate constant for specie i, phase j
mole[OH"]day
net acid catalyzed hydrolysis rate constant, day
287
-1
-------
K
•HOH
^HN
K
•HNIj
H
Ki
k
Ijkc
kc
K
K
L02
"nij
K
oij
K
ow
K
net base catalyzed hydrolysis rate constant, dayrl.
net neutral hydrolysis rate constant, day"1.
neutral hydrolysis rate constant for specie i, phase j,
day
first-order decay constants, day
equilibrium constant.
-1
"1
second order rate coefficient for specie "i", phase "j",
process "k" of chemical "c".
first orde rate constant for process "k".
second order rate constant for process k on chemical G.
first order rate constant for process k, day"1.
liquid phase transfer coefficient, m/day.
reaeration velocity, m/day.
neutral rate constant, day"1.
neutral rate constant for ionic specie i in phase j, day
net oxidation rate constant, day"1.
oxidation constant, day"1.
organic carbon partition coefficient,
oxidation rate constant for specie i, L/mole-day.
net oxidation rate constant, day"1.
octanol-water partition coefficient.
temperature corrected reaeration velocity, m/day.
partition coefficient of chemical on DOC, 1^/kgb.
partition coefficient, L/kg.
first order photolysis rate coefficient at reference light
intens ity, day " •*•.
observed rate constant for a chemical under reference light
intensity IQ, day"1.
288
-------
T
KV
[L]
m
M
M
B
M
si
partition coefficient, phase 1, L/kg,
the solids independent partition coefficient, L/kg.
partition coefficient of chemical on sediment type "s"
in segment j, m L^/kgs.
limiting partition coefficient with.no particle interaction.
lumped first order rate constant, day' .
overall first-order rate constant for chemical "c", day
-1
spatially-variable lumped first order decay rate constant for
chemical "c",, days
-1
-1
net volatilization rate constant, day
conductivity of the chemical through the water segment,
m/hr.
measured or calibrated conductance, m/day.
ratio of volatilization rate to reaeration rate.
experimentally measured ratio of volatilizaion to reaeration.
volatilization constant, day" .
fraction of reference light IG in segment (Im/IG), unitless. m
solids concentration, mg/L.
molecular weight of the chemical.
benthic sediment concentration, kg/L.
concentration of sediment in segment j, kgs/L.
concentration of sediment in segment j, mgs/L.
concentration of sediment in water in segment j,
suspended sediment concentration, mg/L.
solids concentration, kg/L.
concentration of sediment type "s" in segment j, kgs/L
mj - mj 10"6. , ,
289
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MW
Ml
n
nj
P
P
PH
R
%
RH2
RL
[R02]
R02
S01
Scai'scw '
Skc
Skcl'skc2'
Skc3
molecular weight of the chemical, g/mqle.
solids concentration, kg/L.
porosity.
average porosity of segments i and j, I^/L.
porosity or volume water per volume segment j,
reduced product.
sediment wet weight to dry weight ratio, kg (sediment +
water), kg (sediment).
active bacterial population density in segment, cell/mL.
negative log of hydrogen ion activity [H+].
transformation product for process k acting on chemical c.
"Q-10" temperature correction factor for biodegradation
of specie i, phase j in benthic segments.
"Q-10" temperature correction factor for biodegradation
of specie i, phase j in water.
ideal gas constant =1.99 cal/mole °K.
gas phase resistance, day/m.
reducing agent.
liquid phase resistance, day/m.
molar concentration of oxidant, moles/L.
oxidizing agent.
chemical solubility, mg/L
air and water Schmidt numbers
pD
total kinetic transformation rate for chemical c, g/m^-day.
production of chemicals 1, 2, and 3 from chemical "c" under-
going reaction "k", mg/L-day.
290
-------
T
T
T
t
rHBW'THBS
••HE
1HF
THHN'THHH'
THOH
LHK
LHv
u*
u
Ux
V
V
W
W
W10
WD
ambient temperature in segment, °C.
temperature, °K. '
water temperature, °C.
time, day.
water column and benthic biodegradation half lives, days.
extra half life, days.
photolysis half life, days.
neutral, acid, and base-catalyzed half lives, days.
half-lives, days.
half life for process "k"/days. ,
oxidation half life, days.
volatilization half life, days.
water temperature, °K.
reference temperature for which reaction rate is reported,
°C. .
shear velocity (m/s) = C^ 0.5 W^Q.
velocity of the water, m/sec.
current velocity, m/sec.
o
volume of the water segment, m .
average segment velocity, m/sec.
wind speed at 10 cm above surface, m/sec.
time-varying windspeed at 10 cm above surface, m/sec.
wind velocity 10 m above water surface, m/s.
deposition velocity, m/sec.
yield coefficient for production of chemical from process k
acting on chemical c; assumed to be -1 for production of
chemical c by itself.
291
-------
Ykc2»
Ykc2
£kl
K
V
X
e
yield coefficients for production of chemicals 1, 2, and 3
from chemical "c" undergoing reaction "k".
decadic molar absorptivity of wavelength k by specie i,
L/mole-cm-ln 10.
von Karmen's constant =0.74.
absolute viscosity of water = 0.01 poise (g/cm2-sec)
at 20 °G.
numerical weighting factor, 0-0.5, unitless^
the solids dependent partition constant (ratio of
adsorption to particle-induced desorption rate).
density of air and water (kg/m3).
reaction quantum yield for specie i in phase j, mole/E.
dimensionless viscous sublayer thickness =• 4.
user input temp, correction factor for volatilization.
292
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APPENDIX E
Imlementation of the Mass Balance Equation
WASP solves a finite difference approximation of equation 1.3.1 for a
model network that represents the important characteristics of the real
water body. This section explains the derivation of WASP's finite differ-
ence mass balance equation using the one -dimensional, form for convenience.
Regrouping the terms in 1.3.2 for mathematical convenience gives:
a a a
— (A c) - - — (Q c) + —
at ax ax
ac
A — ) + A S
ax ....
where:
ST =
total source/sink rate - SL + Sfi + SR, g/nr'-day
'• • • ,• ' i' •' '
volumetric flow = A Ux, nr/day
Assuming that derivatives of C are single-valued, finite, continuous func-
tions of x, as in Figure El, then the Taylor's series expansion gives:
+ Ax = Cx0 + Ax
ac
3x
x0 + - Ax-
33C
3x-
. . . 2
- Ax
ac
- Ax —
3x ix°
a2c
a3c
...3
Assuming that terms containing the third and higher powers of Ax are negli-
gible in comparison with the lower powers of Ax, then equations 2 and 3 can
be subtracted to give:
3c
CxQ+Ax - Gx0-Ax
2Ax
293
-------
with an error term of order Ax2. Referring to Figure El, this equation
states that the slope of the line AB is equal to the slope of the tangent
centered at P. This is known as the central-difference approximation. The
slope at P may also be approximated by the slope of the line PB, giving the
forward-difference formula:
xa-2Ax XO-AX x
X0-2AX Xe-AX X0 X0tAX X0+2AX
J-l
I
j +1
I I~"~H I
r-'i-Ti "I" 'i'i*i~H
Figure El. Definition sketch for finite difference equation.'
3c | CxQ+Ax - Cx0
3x | ° Ax
Similarly, the slope at P may be approximated by the slope of the line AP,
giving the backward-difference formula:
3c |
^K
Cx0 - Cx0-Ax
Ax
294
-------
Equations 4 and 6 can be obtained from 2 and 4, respectively, by assuming the
second and higher order powers of Ax are negligible. The error term for
both the forward- difference and the backward difference approximation is of
order Ax.
Substituting the central difference approximation into the advection
term of 1 gives:
9x
(Q C)
x0+Ax -
x xQ-A x
2 Ax
Similarly, the dispersion term becomes:
3c | 3c |
a ac (E A)XO+AX . ax |XO+AX -
3x
(E A)xQ- Ax
2 Ax
2 Ax
2 Ax
When applying the difference approximations to segment "j" in a network
as in Figure El, XQ corresponds to the center of j, xo + Ax to the inter-
face j, j+1, XQ - Ax to the interface j-1, j, XQ + 2 Ax to the center of
j+1, and XQ - 2 Ax to the center of j-1. The mass balance equation for
segment j can be written:
-
-------
Multiplying through by A^ gives:
a
(V. CO Q.J
a7 J J J
+ Rj
11
where:
R
volume of segment j
*
m
o
dispersive flow = E A/LC, m /day
characteristic length, m
and C.j i ^ must be expressed in terms of the
Interface concentrations C
segment concentrations:
- " cj+l +
-------
c>t + —
15
where:
At
the time step, typically between 15 minutes and a half
day, day
Given new masses at time t + At, WASP4 finds the new concentrations by
dividing by the new volumes:
Cj,t+At =
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