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

-------

-------
                                         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

-------
                               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

-------
                                   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

-------
                                   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

-------
                                   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

-------
                             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

-------
                             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

-------
                                   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

-------
                             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

-------
                             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

-------
.  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

-------
                              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

-------
                              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

-------
                              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

-------
                              , 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

-------
                                    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

-------
     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

-------

-------
                                  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

-------
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-

-------
                    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.

-------
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

-------
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

-------
          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

-------
     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

-------
     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

-------
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

-------
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

-------
     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

-------
 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

-------
     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

-------
        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

-------
                        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

-------
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

-------
     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

-------
 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

-------
     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

-------
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

-------
     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

-------
       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

-------
                   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

-------
                                  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

-------
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

-------
E  1
£  z

•}•]*
,11*

•
A

*t*l*l*
*lll

*

1
J
a


• •


«
-1

.1.
B'I

.1.1.
II







HJA
1

N
C

N
C

EJt.
q




saDaiDnnnnnnnnnnnnDnnnnnnannDannrjnnnnnnniMMliiiHiM
fill ISHWOI I t I 1 1 I f QE1EI ! 1 1 1 1 I |FlF| f\ 1 I 1 1 1 i IfilGlQl ! [HfHM 1 Illlfl! t 1 I I 1
      El
      E2
Veriobl*

HEADER
NN
A
B
C
0
E
F CN(N)
H NJUHC(N.l)
           B(N)
           R(N)
Ttd* of card group
Chann*) numb«r
Ungth of chonn*! N
WMKi  of chanm! N
Hydraulic rodtu* of charm*! N (or depth)
Channal direction from fru« north
Manning's roughnms co*fftd*nit for channol N
Lower {uncHon numbw «ni*ring channtl N
HJflhw juncttsn numbw entaring channel N
                                                                                           UnH»
                                                                                 m
                                                                                 m
                                                                                 m
           *Hot»*
               R«p«at lln* EZ NC (numbw of channel*) times.
                                              160

-------
I  I
I  I
         I   I  I
         III


























o
J>-
c
a

^
o
»




.**
"
Q


?


n
fc.
n
->





























no
t»
«D
l-«
•>
A

p
M

-•0
<*
n
K
«
A
»«-
»*>
N

OO
(»
•>
K
«•
A
•*•
f>
eji
••
no
<&•
e
f»
•>
m
•^
to
N
*-
*O
»
«0
h-
«0
A
it-
n
^
*-
^oo
»
c
1^
to
1ft
•«*•
IO
«
—
tt
«
h.
»
A
•*•
IO
w
•-
— o
e»
c
h-
—
(/>
z
o





























































































<
<
<






























































o
u







n
a
CO




















0
»
»
ft
ft
*
*
ft
*
ft
•
ft
ft
ft
ft
ft
ft
ft
ft
6
*
*
ft
•
ft
ft
ft

<
h-
<
a

5:
O
_i
u.
z
—

Ul
-J
tn
<
—
ce
<

•
*
*
•
»
•
»
•
*
B
•
•
•
•
•
•
B
•










































































a
o
a






























































"uT
u.







UJ
«J
UJ








>
>







—

h-


V,
if,
V


a:
a:
a-







o

a.


o
a
o


z
z
z







a

_i


i£
^:
^


__
-9







«.

I


O
o
o


               o
       J3


    	 3'
       O


  3l +

  g-r >
  -co

  * 5 ?
  o « ,~
a.t:
=- t      ^

o 2. °> * .5
\_ « C O H-
    > 5S
   •"  -^ "•" 5)

1-p!

"II
o o
«- >. c
o » o
  •if t3 c
o £ g o> o
••- 3 -i D •>-
                                                          •5  C
                                                          0) .C





                                                        2^9
     s^s
         « fe 4;
                                                        "SIS


                                                       •8 8-S
                                                        Q- Q. -o
                                                        o o —
                                                        1-1-3
                                                        •o -o
                                                        "5 "5

                                                        .81
                                                        o a o
                                                        ceo
                                                        n 3 5
                                                        o
                       -»b
                 161

-------














€)
U

0
n


9
>
<.
*^


o
r^

>
l_
a
•o
c
-t
o
Tl

TI
l_
O
>





**
t—

12

a
3
i>

t3

2



















•0
*
•
t*
»
w>
«*
r>
t4
•»
f*O
*
•
r*
<•
»
w
N
V*
•O
a
•
t*
•
to
*
n
w
«•
DO
•»
•
r*
•»
n
<*
n
94
••
*o
•b
a»
r*
•
•»
«
»o
M
•»
no
*
•
r*
•§
«
•*
«
«
••
C4O
•1
*
r»
•
*>
••
10
«4
^
••o
•
«
N
«
K>
^
«
N
-







































^
h"
<
O

>-
PC
*
a


O
ea

a
se
•<
#=
<
Ul
irt





























































































<
<
<









































•«
—
«.


=:




a
CJ
c*


U.
U.
U.


Ul
Ul
Ul


a
0
a


u
o
o


CD
CO
m





























































1C
•x.
sc







"3
">
•3

















a:
QZ
tr






A
a
o







a.
a.
a.









0







z
z
X

















_1
_I
_1







          o
                                                    !»
                                                    .C O

                                                    r:
                                                    S n
                                                    |fc
                                                    £ <2
                                                    »1
                                                    •5 &
                   5 a
              " « « _
              A *} Q -F-

           EEl5|^
           3 3 3= O- £

           JJia^.b^-o

           s sill's! s
           a2
-------













^
ft)
u
— m

9
n
n
u
«
>.
<
^•^

n-
o
fi



o
o
e
T
O
B

TF
£
O
>





» *
M

t-j


3
P

o

5

if ^

















»o
«
•
N
0
*>
f
n
«l
~
»O
O
«
1^
V
n
*
n
M
^
ae
a
«o
. ^
•
n
»
n
«4
v>
no
01
•
i»
•
n
**
n
M
^
»0
a
«
h>
«
M
<#
n
M
*•
00
«
a
IS
O
A
*>
10
M
••
NO
a
«
^
•
n
•»
n
C4
M
-O
a
•0
^
•
«>
*
n
M
•-








































<
t-
<
o

>•
n-
<
o
z
3
0
CD

0
cc.
<
y
<
Ul
v>






























































































<
<
<










































—
-"
"-•


X
2C
3:


<9
O
O


U.
Ik
U.


Ill
u
Ul


a
o
o


u
u
o


m
m
o






























































1C
1C
X







•»
•o
->







<
<
<







N

>-


X
X
X


jh
f
5







>

=>


i—
i—
»-


V)
tn
U)







ae

o


a.
a.
a.


6
o
o







i

=*


_£
_J
«


                                                                                                                   «
                                                                                                                   fcj
•-«>«!•>*«


O O O <9 <9
                                                   163

-------

            5-E















13
•»

t>
ft


1.
u
>
«*"

P
n
Q

>
i-
O
TJ
f~
-5
o
QQ

TI
£
n




/)

• •
"O
*
c/

Q
J
P

CD

p


U
















IK>
4k
•
t*
9
n
<*
W
t4
*-
X*
ffl
•
(N.
•
A

w
»»
vo
•»
*»
h-
•
o
<*
w
w
*•
no
«
•»
s
•
n
^
r>
tN
*•
TO
•
•
t*»
*
n
•*•
•o
n
V
noJ
»
•
t%
w
ir>
*
n
M
*-

•
•
t*
*
n
<*
n
N
«-
**O
*
•
K
•
to
If
n
^
—








































•<
»-
•c
0

^M
ee
^
a
5C
2>
6
n

o
cr
•<
^
^
Ul
en






























































































<
4(
X










































— »
«•
«>


X
X
3=


O
O
o


u.
u.
u.


Ill
UJ
UJ


a
a
a


(3
o
a


ca
m
tn



>•
>•







X

%


^
>
>


±7
t3
3







H

V)


(C
cc
QC


O









a.

o


z
2
X


91
ial
ai







_j

it


-^
->
^


  i
  Jl
  a
      •o
 3
 1
 T3

 i

&1
^

H
•si

ii
o
>
u
£
1
~»
tl
c
a
&
o»
3|

*
o
«
"5
TJ
^
0

Ol
z
5
n
g
•
3
1
3
U

s
£
It
!






n
c
^
•1
u
8
JC
^lllll
P ^ z a 2 w
                                o *•

                                Is
                                it

                                jjj
                                J?t
                                •0 o S
                                   8
E
31


sif

ill
m 6 ee
                                  *
             164

-------
I  I
I  I
         o •>
         e S
                           e o
                              £•*-.£,
                                     o



























u
o
o




>


*•
jL

O
^1
0

^>

u


u






























«o
a
B
1-
0
*)
^
f
CM
•-
v«
»
•0
r»
e
A
*
o
N

•oo
et
B
N.
«
*)
•t
n
N

no
w
«
K
«
n
T
X)
«l
*»l
*0
B>
tt
f-J
10
K>
•*
r
!S
*-
TO
«








«4O






n
N
•-
-e
a
f>
r-.
to
*>
*
n
M
-




















































<
h-
<
a

a
X
—
£






























































































<
<
<



3
~


V-
t-
t-


tr

a:


o
o
o


a.
a.
a.


o
o
o


z

a


_j
_i
-j


ic
^c
^


-a
*T>
-3


—

X


o
0
o


A.
il_
i.


1J
1J
Ul


0

0


m
03
CD


           o




       O   -fe
                   o

     • w 9
     Q S
  = S.
S
£ £

-I1
-f. "O
a c


71
  s

  o
  o
ponding

ondin
      E
      e
      »»~

      •o
      £
      3

      O
      e
  S   S
£i 6 7^
b S S £
u *

IA*
123:
sp

dir
3 t> T»

C _C C
     W&lf   I
     "crTa z   j;
     g s > '  !;
     5 S     ^
     S   £   £
       O     3
     O • •*• D>   M

     .»?!•  1
     £ =5 <=   E
     ^ = S   ^
     c o 2- •  c

     S-S-i-o^

     lisll
     o o 0 n  "a
      • i: "3 "O  ~o
                     • (O
                      a
                      Z
                             JC,


                             o
                            3



                            E
                            o
        O v_x (/)
        u (/i J--i
            a z
I?!1
— ^

i §

8.8-
» o
£ t
E O
O O
0 ,.
>s 3
O O
&

O
•t-

o
_c

TO
c
o
a.
n



ll
       — Q
       -a z
       4) 5»
11
  "O


II
s.g
=5 o
  o
c >••
^ o
> o
  o

IP
* o
o "*"
•*• o>
o>.£
£ T


!!
? c
I S
O m
                                     -C


                                     O
          £


          -a

          £
          3

          0
          0)
        II
       3C 2
  C
  Q


"I
e g

8-=5

•a -o
c c
                                              S
                                             m
                                             o
                                              a
                                              o>
                                              o.
                                             JQ


                                             2
                                             3
                                             o
                                             u
                                             o
     r ~ -~f ~ >. v_^ ^~
O"*t of — — Q Zrce —
eo = 2*3:QX2
   KJ
   JC
                        •K)
                           Q n:
                                  •&s
                                  . Q '£'
                                             o
                                             z
                165

-------
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

-------
 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
                                                   OTion Control Parqm*
                                                                       t 1 3 4 • * 7 8 • Alt 11 4 I • 7 • I Ml 11 4 * • 7 • I
                      3 4it 7 i
                                               13 •CBt 7 SCO
                                                            H348 «71»i
A  1
A  2
A  3
A  4
A  a
A  •
A  7
A  •
A  *
K3 I
       NSCS
        <>DO
             KSYS
              EEE
                     CUD
                     FFF
                          UFLC
                           see
                                  DtJP
                                  HHH
                                       HSL H
                                               NT Y
                                                            ILL
        TTT
                                  TTT
                                               UUU
                                                            TTT
 vvv
                     XXX
                                               XXX
            Variable

      A1 A T1TLE1
      A2B TTTLE2
      A3    HEADER
      A4 C KSIU
         D NOSEG
         £ HOSTS
         F SCO.
          Q MFLAC


          H ItWP
          i  NESSLN

          J INTYP

          K ADFAC

          L ZOAY
          yZHR
          N U1N
          0 IDSY

          P IDS®

          Q 1DSG2

          R TADJ
       ASS NOBRK
       A6 T DTS(0
          UT(l)
       A7 V NPRINT
       AS W PRiMT(i)
          X TPRJNT(I)
       A9Y SYSBY(ISYS)
                                      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
                    InJtkU conditions from restart file and write final condit-
                    ions to new restart file.
                    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

-------






















*~
c
a


•*-



^j




u
.c
u
X
JLJ


T)

n

o

r*\

r

c
^

























o
o
•0
f-k
<0
*)
«4-
n
C4
V
o
0
•3
|>s
«
VI
«*
n
M
v>
10 O
9
«
r-
«
ft
•*
n
(4
»-
no
»
00


n
*t
r>
C4
-.
•va
o»
n
i



m


-»o




V) O
•* Q
n o
M O
— Q
NO



V C
n o
*«• O
K» O
o

fQ




ft < CD
•* < tn
n •*• J£


-i
-j
_i
— j






. • i<:
iC =
s iC
^






_J
_l
_J
_J






^
ic
ii
ic






_J
_J
_J
_t






— ic
— iC
— ac
it

x
X
:


O —I 3
O -13
o — j :
O -J

;
3
2


u. ic 3
u. ic a
u. it: 2
u. ^

LJ -3 3

UJ -3 3


                                                                                     n
                                                                                     M
                                                                                     o
                               P     *~ 2
                               ffl      II  ^

                               £     U. -
          _o
          t*^
           u

           D
                              _—      .   »^.  "U  03

                              =|     £ jo  1 J


                              3      c |  £
                                         £  8
                                   »  =
                                •  2  -H
    o   c
    °   D
           _».

           '5
                      c
                      o
                                                         O- D)

                                                         m  C
                                                                       o
                                                                       o
                                                                       Q.


                                                                      '•o
                   u
                   u
                                        0)
               •3
               U
               O)

               0) 00
                                                          a

                                                          o
                                                                                                u
                                                                                                o
                                                                                                0)
u
c
                                                                                                to
                                                                                                m
                                      ~  g   u
                                                                               o
                                                                               u
                                                                  o


                                                                  X
o
o
                                                                  o
                                                                  o
                                                                  c
                                                                  o
                                                       .£


                                                       B
                                                                                      o   E
                                                                           Q)   O

                                                                           O   3
                                                    o
                                                   .c
                              2:  OZMO2Z<0
                                                                   tO  Z  D. >  S- Ul  Q)
                                                                                                 O      CQ

                                                                                                —       I


                                                                                                —      m
                                                        o
                                                        o
                                                        Q.

                                                       or
                              Q


                              ce



                              <



                              m
  '5 >  OT*
    < 2  Di
    ooo
    01 o  2:
m  u o


oa
           ui  E£ -3

           O  X _
                                     CQ

                                     0£
Kl
ca
to
ca
^- M »o -r to to r^



CO CD 00 CQ 03 O3 QQ
                                                    189

-------
r
                                         If
              I  !  I
              I  I  !
                   n
                   a)
                   o
                   >
                   O
                   3

                   2
                   S
                   o

                         2
                         o
                             I
i   i
                                     m
                                 5

          octuiu-ox  _ ->


            S   3
I
                                     o

                                     3!
                      r- CM IO



                      U O U
                                                 190

-------























^™

c
o
'J-"
a


i




?•
o



••
u

u
3
O
w
O

JJ

o
o


























BO









*.









»c









r









•re









r









MO









*•








*•






































































a
a
CD


^
^
^

























































u
u
u







a
a
o







o
0
o













































































u.
u.
u.



~
—


X
X
x


o
o
o







—
—•
«


x

X


o
o
o







.
—
—


X
X
X


o
€9
O







«.
«.
«.


X
X
X


«9
C9
€9


















































































•T*
^
•^



«^
_1







^
^£
V







J
™i
_j







)£
>c
b£







_!
-I
«!







^C
X
X







•J
»
»







^
ac
x








































































a
a
a


§i

a


a
a



§
i
^
O    r*
I    i
<    m
                         z
                         o
o O  o or
vt o  z m
Q Ul  U. O

      22
                                                              z z
-»    b«: _j 2
s    s •   •&
                        191

-------
o
M
   « i
       1
       1
       i
                                M   I     III
                                                          (•*•>. i  "^"^

                                                                H
                                                                it
                                   i bl  U.
                                  S3
O X _
222
                                                                zoo.
SS5   SSS
   a  o o o o o o a a
                                   192

-------
E-t-
E-2.
E-3-
E-4-

l-23-4«-87






U



D



U









A
A
U
E
F
8
A
B
E
F
0
A
B
E
F

1




?34












A




87»»





CC

SO
„•

C

<•
Card
,




2




.1




4




387890















F



F



F
Group E: Boundary Conditions
1234387890































tt



a



S
1234387890































F



F



F
1234387890































R



R



C
1234387890































F



F



F
123438789$































r.



RR
            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)
         E NOBRK
      F4 F WKT(J)
         G T(J)






U

U

U


A
B
AA
SB
m
J234587880


*

r







c.

c

c

3t a «Jiu
234387







-•


iU
t

?
Bfi
J3 3 438789
-f- r
f










S



M-
• 7» » 0




: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
Sfl


















a,
s









.1









s
F






O

0
e
0
-


0




?-,
R


0



0

0
n




0

0

0
?
D
-
0

0

0

0
J
0
E
-
2

4

4

4
1
N









i
T









i
H









A








4
S « 7 » » 0









-
K



K

K
R


P

K

0

0
E
-
Z

n

H

p
A

0

s

D

D
2

T

r

T
T
12343«7S«0
r









1









0









N









S




























L







T
E


5

7

9

0
V


6

4

4
3
1Z345D78SO
E









L



















B
































1

1

t

1



,

i



.



0

0

0

0



8

B

8

n
1J34;5*7»»9










H









j



















C









0









N









S









T









A









JL 2 5 4 S 9 7_
-------
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

-------
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

-------
                                  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

-------
     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

-------
                            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

-------
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

-------
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

-------
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

-------
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

-------
          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

-------
     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

-------
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

-------
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

-------
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

-------
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

-------



1
i
*

<
1






(
t
1
I
II
•
II









J
•

<
1











D
Q
MMB
V?
D
__






£
1.
n
3
5;










••••
z
X,
->
































































































H
Z

2
UJ
T
o



1—
z
CM
s
UJ
X
o

1-
z
T-

s
UJ
X























t




















































Q
0

Q.
X



C9
2
III
X
o

CM
S
LU
X
O

T-
2
LU
J_
O


Q

_l
O
(O

oc
<
1

to




z
UJ









































































X
<
2
o
2
_J

o
H

u:
Q.


O
X
o
H
<
_l
O
>
1
_J
o
IV*

Q
>-
X,

0
UJ
Q

CO


Z
O
h-
o
DC
U.

Z
o
h-
i_
i
U.
Q.




CC
UJ

CO






























                                                                 4-)
                                                                 O
                                                                 0)
                                                                 c
                                                                 •H
                                                                 4-1
                                                                 3
                                                                 O
                                                                 VJ

                                                                 •§
                                                                 CO
                                                                  nJ
                                                                  u
                                                                 •H
                                                                  o

                                                                  o
                                                                 •H
                                                                  X
                                                                  O
                                                                  Q)
                                                                  (-1
                                                                  d
                                                                  (30
                                                                 •H
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

-------
                                   REFERENCES

Alexander, M.  1980. Biodegradation of Toxic Chemicals in Water and Soil.
     In: Dynamics, Exposure, and Hazard Assessment of Toxic Chemicals, R.
     Haque, editor.  Ann Arbor Science, Ann Arbor, MI.

Ambrose, R.B. et al.  1983.  User's Manual for the Chemical Transport and
     Fate Model (TOXIWASP), Version 1. U.S. Environmental Protection
     Agency, Athens, GA.  EPA-600/3-83-005.

Ambrose, R.B. et al.  1986.  WASP3, A Hydrodynamic and Water Quality Model--
     Model Theory, User's Manual, and Programmer's Guide.  U.S. Environ-
     mental Protection Agency, Athens, GA.  EPA/600/3-86-034.

Ambrose, R.B.  1987.  Modeling Volatile Organics in the Delaware Estuary.
     American Society of Civil Engineers.   Journal of Environmental
     Engineering, V. 113, No. 4, pp 703-721.

Anthonisen, A.C., et al.. 1976.  Inhibition of Nitrification by Ammonia and
     Nitrous Acid.  Journal Water Pollution Control Federation, Vol. 48.
     No. 5.  pp. 835-852,

APHA (American Public Health Association).  1985.  Standard Methods for
     the Examination of Water and Wastewater, 15th Edition.  APHA.
     Washington, DC.

Banks, R.B. and F.F. Herrera.  1977.  Effect of Wind and Rain on Surface
     Reaeration.  Journal of the Envir. Engr. Div.,  ASCE, Vol. 103, No. EE3,
     Proc. Paper 13013, pp. 489-504.

Bannister, T.T. 1974a.  Production Equations in Terms of Chlorophyll Concen-
     tration, Quantum Yield, and Upper Limit to Production.  Limnol. Oceanogr.
     19:1-12.

Bannister, T.T. 1974b.  A General Theory of Steady State Phytoplankton Growth
     in a Nutrient Saturated Mixed Layer.   Limnol. Oceanogr. 19:13-30.

Barber, M.C., L.A. Suarez, and R.R. Lassiter.  1987.  A Model for Kinetic
     Exchange of Nonpolar Organic Pollutants by Fish.  Environ. Tox. Chem.
     (submitted).

Bella, D.A. and W.J. Grenney.  1970.  Finite-Difference Convection Errors.
     Journal of the Sanitary Engineering Division, ASCE, Vol. 96, No. SA6,
     pp. 1361-1375.

Berner, R.A.  1974.  Kinetic Models for the Early Digenesis of Nitrogen
     Sulfur, Phosphorus, and Silicon in Anoxic Marine Sediments.  In:  The
     Sea, Vol. 5, ed. E.D. Goldberg.  J. Wiley and Sons.  New York.
                                    265

-------
Bowie, G.L. , W.B. Mills, D.B. Porcella, C.L. Campbell, J.R. Pagenkopf,  G.L.
     Rupp, K.M. Johnson, P.W.H. Chan, S.A. Gherini and C.E. Chamberlin.  1985.
     Rates, Constants, and Kinetics Formulations in Surface Water Quality
     Modeling.  Second Edition.  U.S. Environmental Protection Agency
     Athens, GA.  EPA-600/3-85-040.

Brown, L.C. and T.O. Barnwell.  1987.  The Enhanced Stream Water Quality
     Models QUAL2E and QUAL2E-UNCAS:  Documentation and User Manual.   U.S.
     Environmental Protection Agency, Athens, GA.  EPA/600/3-87-007.

Brown, D.S., et al.  1987.  MINTEQAl, An Equilibrium Metal Speciation Model:
     Users Manual.  U.S. Environmental Protection Agency, Athens, GA.
     (In Preparation.)

Burns, L.A. , D.M. Cline, and R.R. Lassiter.  1982.  Exposure Analysis Model-
     ing System (EXAMS): User Manual and System Documentation, U.S.
     Environmetal Protection Agency, Athens, GA.  EPA-600/3-82-023.

Burns, L.A. and D.M. Cline.  1985.  Exposure Analysis Modeling Sysltem,
     Reference Manual for EXAMS II.  U.S. Environmental Protection Agency,
     Athens, GA.  EPA-600/3-85-038.

Connolly, J.P. and R. Winfield.  1984.  A User's Guide for WASTOX, a Frame-
     work for Modeling the Fate of Toxic Chemicals in Aquatic Environments.
     Part 1:  Exposure Concentration.  U.S. Envionmental Protection Agency,
     Gulf Breeze, FL.  EPA-600/3-84-077.

Connolly, J.P. and R.V. Thomann.  1985.  WASTOX, A Framework for Modeling the
     Fate of Toxic Chemicals in Aquatic Environments.  Part 2:  Food Chain.
     U.S. Environmental Protection Agency, Gulf Breeze, FL and Duluth,  MN.

Covar, A.P.  1976.  Selecting the Proper Reaeration Coefficient for Use in
     Water Quality Models.  Presented at the U.S. EPA Conference on Env.
     Simulation and Modelling.

Delos, C.G., W.L. Richardson, J.V. DePinto, R.B. Ambrose, P.W. Rodgers, K.
     Rygwelski, J.P. St. John, W.L. Shaughnessy, T.A. Faha, and W.N.  Christie.
     1984.  Technical Guidance Manual for Performing Waste Load Allocations,
     Book II.  Streams and Rivers, Chapter 3, Toxic Substances.  U.S. EPA,
     Washington, DC.  EPA-440/4-84-022.

Di Toro, D.M., D.J. O'Connor, and R.V. Thomann.  1971.  A Dynamic Model of the
     Phytoplankton Population in the Sacramento San Joaquin Delta.  Adv. Chem.
     Ser. 106, Am. Chem. Soc., Washington, DC., pp. 131-180.

Di Toro, D.M. and J.P. Connolly.  1980.  Mathematical Models of Water Quality
     in Large Lakes, Part 2:  Lake Erie.  EPA-600/3-80-065. pp. 90-101.

Di Toro, D.M. and W.F. Matystik.  1980.  Mathematical Models of Water Quality
     in Large Lakes, Part 1:  Lake Huron and Saginaw Bay. EPA-600/3-80-056.
     pp. 28-30.
                                    266

-------
Di Toro, D.M., J.J.  Fitzpatrick, and R.V. Thomann.  1981, rev. 1983.  Water
     Quality Analysis  Simulation Program  (WASP) and Model Verification Program
     (MVP)  - Documentation.  Hydroscience, Inc., Westwood, NY, for U.S. EPA,
     Duluth, MN, Contract No.  68-01-3872.

Di Toro, D.M.  1985.   A Particle Interaction Model of Reversible Organic
     Chemical Sorption, Chemosphere 14(10):1503-1538.

Eppley, R.W. and P.R.  Sloane.  1966.  Growth Rates of Marine Phytoplankton:
     Correlation with  Light Absorption by Cell Chlorophyll-a.  Physiol. Plant.
     19:47-59.

Feigner and Harris.  1970.  Documentation Report -- FWQA Dynamic Estuary
     Model.  U.S. Department of the Interior, Federal Water Quality Adminis-
     tration.

Felmy, A.R., D.C. Girvin, and  E.A. Jenne.  1984.  Minteq - A Computer Program
     for Calculating Aqueous Geochemical Equilibria.  For U.S. Environmental
     Protection Agency, Athens, GA.  EPA/600/3-84-032.

Force, E.G. and P.L. McCarty.  1970.  Anaerobic Decomposition of Algae.
     Environ. Sci. & Technol.  4(10), pp. 842-849.

Green, A.E.S., K.R. Cross, and L.A. Smith.  1980.  Improved Analytical Charac-
     terization of Ultraviolet Skylight, Photochem. and Photobio.  31:59-65.

Hendry, G.S.  1977.  Relationships Between Bacterial Levels and Other Charac-
     teristics of Recreational Lakes in the District of Muskoka.   Interim
     Microbiology Report, Laboratory Services Branch, Ontario Ministry of the
     Environment.

Henrici, Arthur T.,  1938.  Seasonal Fluctuation of Lake Bacteria in Relation
     to Plankton Production.  J. Bacteriol.,  35:129-139.

Herbes, S.E. and L.R.  Schwall.  1978.  Microbial Transformation of Polycyclic
     Aromatic Hydrocarbons in  Pristine and Petroleum-Contaminated Sediments.
     Appl.  and Environ. Microbiology, Volume 35, No. 2.   pp.  306-316.

Hutchinson, G.E.   1967.  A Treatise on Limnology.  Vol.  II.   Introduction to
     Lake Biology and  Limnoplankton.  Wiley.   New York.   pp.  306-354.

Hyer, P.V., C.S.  Fang,  E.P.  Ruzecki, andW.J. Hargis.  1971.   Hydrography
     and Hydrodynamics of Virginia Estuaries, Studies of the Distribution of
     Salinity and Dissolved Oxygen in the Upper York System.   Virginia
     Institute of Marine Science.

Jewell, W.J. And P.L. McCarty.  1971.  Aerobic Decomposition of Algae.
     Environ.  Sci. Technol.  1971.  5(10).   p.  1023.

JRB,  Inc.   1984.   Development of Heavy Metal  Waste Load Allocations for the
     Deep River,  North Carolina.   JRB Associates,  McLean,  VA,  for U.S.  EPA
     Office of Water Enforcement and Permits, Washington,  DC.

                                    267

-------
Karickhoff, S.W., D.S. Brown, and T.A. Scott.  1979.  Sorption of Hydrophobia
     Pollutants on Natural Sediments.  Water Res. 13:241-248.

Karickhoff, S.W. and K.R. Morris.  1985.  Sorption Dynamics of Hydrophobic
     Pollutants in Sediment Suspensions.  Environ. Toxicology and Chem.
     4:469-479.

Kok, B.  1960.  Efficiency of Photosynthesis.  In:  W. Ruhland (Edison),
     Hanbuch der Pfanzenphysiologie.  Vol 5, Part 1.  Springer, Berlin,  pp.
     563-633.

Larson, R.J.  G.G. Clinckemaillie, and L. VanBelle.  1981.  Effect of Temper-
     •ature and Dissolved Oxygen on Biodegradation of Nitrilotriacetate.
     Water Research, Volume 15.  pp. 615-620.

Leopold, L.B. and T. Maddox.  1953.  The Hydraulic Geometry of Stream
     Channels and Some Physiographic Implications, Professional Paper
     252, U.S. Geological Survey, Washington, DC.

Leopold, L.B., M.B. Wolman and J.P. Miller.  1964.  Fluvial Processes
     in Geomorphology, W. H. Freeman and Co., San Francisco, CA.

Liss, P.S.  1973. Deep-Sea Research.  Volume 20.  pp. 221-238.

Lowe, W.E.  1976.  Canada Centre for Inland Waters 867 Lakeshore Road, Bur-
     lington, Canada  L7R 4A6.  Personal communication.

Lund, J.W.G.  1965.  The Ecology of the Freswhater Phytoplankton.  Biol. Rev.
     40. 231-293.

Mabey, W.R., J.H. Smith, R.T. Podell, H.L. Johnson, T. Mill, T.-W. Chou,
     J. Gates, I.W. Partridge, H. Jaber, and D. Vandenberg.  1982.  Aquatic
     Fate  Process Data for Organic Priority Pollutants.  U.S.  Environmental
     Protection Agency Agency, Washington, DC.   EPA 440/4-81-014.

Mackay, D.  and P.J. Leinonen.  1975.  Rate of Evaporation  of Low-Solubility
     Contaminants from Water Bodies  to Atmospheres.   Environ.  Sci. Technology.
     7:611-614.

Manhattan  College Course.  Notes  for  Summer  Institute in Water Pollution.
     1977.

Menon, A.S., W.A. Gloschenko,  and N.M.  Burns.   1972.  Bacteria-Phytoplankton
     Relationships  in Lake Erie.  Proc.  15th Conf.  Great  Lakes Res.   1972:
     94:101.   Inter.  Assoc.  Great Lakes  Res.

Mill,  T.,  W.R. Mabey, P.C. Bomberger, T.W.  Chou,  D.G. Herdry,  and  J.H.  Smith.
     1982.   Laboratory Protocols for Evaluating the Fate  of Organic  Chemicals
     in Air and Water.   U.S.  Environmental Protection Agency,  Athens,  GA.
     EPA-600/3-82-0220.
                                     268

-------
Miller, G.C. and R.G. Zepp.  1979.  Effects of Suspended Sediments on Photolysis
     Rates of Dissolved Pollutants.  Water Research 13:453-459.     '

Mills, W.B., D.B. Porcella, M.J. Ungs, S.A. Gherini, K.V. Sununers, Lingfung,
     Mok, G.L. Rupp,,G.L. Bowie, and D.A. Haith.  1985.  Water Quality Assess-
     ment: A Screening Procedure for Toxic and Conventional Pollutants, Parts
     1 and 2.  U.S. Environmental Protection Agency, Athens, GA.
     EPA- 600/6- 85 -002a and b.
Nriagu, J.O.
     System
1972.
                     Stability of Vivianite and Ion-Pair Formation in the
                     -H3P04H20.  Geochim. Cosmochim Acta. 36. p. 459.
O'Connor, D.J. and R.V. Thomann.  1972.  Water Quality Models :   Chemical,
     Physical and Biological Constituents.  In:  Estuarine Modeling:  An
     Assessment.  EPA Water Pollution Control Research Series 16070 DZV,
     Section 702/71.  pp. 102-169.

O'Connor, D.J., J.A. Mueller, and K.J. Farley.  1983.  Distribution of Kepone
     in the James River Estuary.  Journal of the Environmental Engineering
     Division, ASCE. 109(EE2): 396-413.                      ,

Paris, D.F., W.C. Steen, G.L. Baughman and J . T . Barnett, Jr.  1981.  Second-
     Order Model to Predict Microbial Degradation of Organic Compounds in
     Natural Waters.  Applied and Environmental Microbiology. 4(3) : 603-609 .

Rao, S. S.  1976.  Observations on Bacteriological Conditions in the Upper
     Great Lakes.  1968-1974.  Scientific Series.  No. 64.  Inland Waters
     Directorate CCIW Branch, Burlington, Ontario.

Rao, P.S.C. and J.M. Davidson.  1980.  Estimation of Pesticide Retention and
     Transformation Parameters Required in Nonpoint Source Pollution Models.
     Environmental Impact of Nonpoint Source Pollution.  Ann Arbor Science,
     Ann Arbor, MI.  pp. 23-67.                                 .

Raymont, J.E.G.  1963.  Plankton and Productivity in the Oceans,  pp. 93-466.
     Pergamon.  New York.                                    •---...

Rhee, G.Y.  1973.  A Continuous Culture Study of Phosphate Uptake, Growth
     Rate, and Polyphosphates in Scenedemus sp.  Journal Phycol. 9:495-506.

Riley, G.A. , H. Stommel and D.F. Bumpus.  1949.  Quantitative Ecology of the
     Plankton of the Western North Atlantic.  Bull. Bingham Oceanog. Coll.
Robinson, N. , ed.  1966.  Solar Radiation.  Elsevier Publishing, Amsterdam,
     London, and New York.  347 pp.

Roesch, S.E,,' L.J. Clark, and M.M. Bray.  1979.  User's Manual for the
     Dynamic (Potomac) Estuary Model. U.S. Environmental Protection Agency,
     Annapolis, MD. EPA- 903/9 -79 -001.
                                    269

-------
Schnoor, et al.  1987.  Processes, Coefficients, and Models for Simulating
     Toxic Organics and Heavy Metals in Surface Waters.  U.S. Environmental
     Pro'tection Agency, Athens, GA.  EPA/600/3-87/015.

Smith, J.H., W.R. Mabey, N. Bohonos, B.R. Hoh, S.S. Lee, T.W. Chou, D.C.
     Bomberger and T. Mill. 1977.  Environmental Pathways of Selected Chemi-
     cals in Freshwater Systems.  Part I: Background and Experimental Proce-
     dures.  U.S. Environmental Protection Agency, Athens, GA.  EPA-600/7-77-
     113.

Smith, R.A.  1980a.  The Theoretical Basis for Estimating Phytoplankton
     Production and Specific Growth Rate from Chlorophyll, Light and Tempera-
     ture Data.  Ecological Modeling.  10.  pp. 243-264.

Smith, R.A.  1980b.  Private Communication of correlation functions for
     nitrite + nitrate and inorganic sediment in letter to S. Freudberg,
     Metropolitan Washington Council of Governments, December 30, 1980.

Steele, J.H.  1962.  Environmental Control of Photosynthesis in the Sea.
     Limnol. Oceanogr. 7:137-150.

Strickland, J.D.H.  1965.  Chemical Oceanography, Production of Organic
     Matter in the Primary Stages of the Marine Food Chain. Vol. 1.  p. 503.
     J.P. Riley and G. Skivow, eds.  Academic, New York.

Suarez, L.A., et al.  1986.  GETS, a Simulation Model for Dynamic Bioaccumu-
     lation of Nonpolar Organics by Gill Exchange:  A User's Guide.  U.S.
     Environmntal Protection Agency, Athens, GA.  EPA/600/S3-86/057.

Thomann, R.V.  1975.  Mathematical Modeling of Phytoplankton in Lake Ontario,
     1. Model Development and Verification.  U.S. Environmental Protection Agency,
     Corvallis, OR.  EPA-600/3-75-005.

Thomann, R.V., R.P. Winfield, D.M. DiToro, and D.J. O'Connor.  1976.  Mathe-
     matical Modeling of Phytoplankton in Lake Ontario, 2. Simulations Using
     LAKE 1 Model.  U.S. Environmental Protection Agency, Grosse lie, MI,
     EPA-600/3-76-065.

Thomann, R.V., R.P. Winfield, and J.J. Segna.  1979.  Verification Analysis
     of Lake Ontario and Rochester Embayment Three Dimentional Eutrophication
     Models.  U.S. Environmental Protection Agency, Grosse lie, MI, EPA-600/3-
     79-094.

Thomann, R.V. and J.J. Fitzpatrick.  1982.  Calibration and Verification of a
     Mathematical Model of the Eutrophication of the Potomac Estuary.  Pre-
     pared for Department of Environmental Services, Government of the Dis-
     trict of Columbia, Washington, D.C.

Tsivoglou, E.E. and J.R. Wallace.  1972.  Characterization of Stream Reaera-
     tion Capacity.  U.S. Environmental Protection Agency, Washington, DC
     EPA-R3-72-012.
                                    270

-------
Warburg, 0. and E. Negelein.  1923.  Uber den einfluss der Wellenlange auf
     den Energieumsatz bei der Kohlensaureassimilation.  A. Phys. Chem.
     106:191-218.

Ward, D.M. and T.D. Brock.  1976.  Environmental Factors Influencing the
     Rate of Hydrocarbon Oxidation in Temperate Lakes, Applied and Environ-
     mental Microbiology 31(5) :764-772.

Weast, R.C., and M.J. Astle, ed.  1980.  CRC Handbook of Chemistry and
     Physics.  CRC Press, Boca Raton, FL.

Wetzel, R.G.  1975.  Limnology.   W.B. Saunders Co.  Philadelphia.  743 pp.

Whitman, R.G.  1923.  A Preliminary Experimental Confirmation of the Two-
     Film Theory of Gas Absorption.  Chem. Metallurg. Eng. 29:146-148.

Wischmeier, W.H. and D.D. Smith.  1965.  Predicting Rainfall--Erosion Losses
     from Cropland East of the Rocky Mountains.  Agriculture Handbook 282.
     U.S.  Department of Agriculture.  Agriculture Research Service.

Wischmeier, W.H. and D.D. Smith.  1978.  Predicting Rainfall Erosion Losses -
     A Guide to Conservation Planning.  Agriculture Handbook No. 537.  U.S.
     Dept. of Agriculture, Washington, DC.

Zepp, R.G. And D.M. Cline.  1977.  Rates of Direct Photolysis in Aquatic
     Environment.  Environ. Sci. Technol. 11:359-366.

Zison, S.W. , W.B. Mills, D. Demer, and C.W. Chen.  1978.  Rates. Constants,
     and Kinetic Formulations in Surface Water Quality Modeling.  U.S.
     Environmental Protection Agency, Athens, GA.  EPA-600/3-78-105.
                                    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

-------
 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

-------
                                  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 = 
-------

-------