United States
Environmental Protection
Agency
Office of Health and
Environmental Assessment
Washington DC 20460
EPA/600/8-87/042
July 1987
Research and Development
vvEPA
Selection Criteria for
Mathematical Models
Used in Exposure
Assessments
Surface Water Models
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EPA/600/8-87/042
July 1987
SELECTION CRITERIA FOR MATHEMATICAL
MODELS USED IN EXPOSURE ASSESSMENTS:
SURFACE WATER MODELS
Exposure Assessment Group
Office of Health and Environmental Assessment
U.S. Environmental Protection Agency
Washington, D.C.
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DISCLAIMER
This document has been reviewed in accordance with U.S. Environmental
Protection Agency policy and approved for publication. Mention of trade names
or commercial products does not constitute endorsement or recommendation for
use.
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CONTENTS
Tables v
Figures. . vi
Foreword vii
Preface. viii
Abstract ix
Authors, Contributors, and Reviewers .... ........ x
1. INTRODUCTION 1-1
1.1. ESTIMATING EXPOSURE AREAS 1-1
1.2. MODEL SELECTION PROCESS 1-3
1.3. DOCUMENT OBJECTIVES. 1-3
2. BACKGROUND INFORMATION 2-1
2.1. DEFINITION OF TERMS 2-2
2.2. BASIC MATHEMATICAL MODEL EQUATIONS 2-6
2.3. HYDROLOGIC TRANSPORT PROCESSES 2-9
2.4. ATTENUATION MECHANISMS 2-11
2.4.1. Hydrolysis 2-13
2.4.2. Oxidation-reduction 2-13
2.4.3. Photolysis 2-14
2.4.4. Volatilization 2-14
2.4.5. Sorption 2-15
2.4.6. Biodegradation 2-15
2.4.7. lonization 2-16
3. MODEL STRUCTURE 3-1
3.1. RIVERS . . 3-2
3.2. LAKES AND RESERVOIRS 3-7
3.3. ESTUARIES 3-9
3.4. TEMPORAL SCALE 3-16
3.5. DIMENSIONALITY 3-21
3.6. DEGRADATION PROCESSES 3-23
3.7. SEDIMENT TRANSPORT AND SORPTION PROCESSES 3-25
3.8. NONPOINT SOURCE RUNOFF 3-27
3.8.1. Simple Pollutant Yield Models 3-28
3.8.2. Empirical Loading Functions 3-29
3.8.3. Nonpoint Source Simulation Models . . 3-30
4. IDENTIFICATION OF MODEL PROCESSES 4-1
4.1. TRANSPORT PROCESSES 4-3
4.2. DEGRADATION PROCESSES 4-6
m
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CONTENTS '(continued)
MODEL SELECTION CRITERIA.
5.1. STRUCTURE OF THE MODEL SELECTION-CRITERIA.
5.2. MODEL SELECTION PROCESS
5.3. DIFFERENT APPLICATIONS ." .........
5.4. MODEL SUMMARY TABLES
USE OF THE SELECTION CRITERIA
6.1. DESCRIPTION OF EXPOSURE ANALYSIS PROBLEM
6.2. PRELIMINARY EXPOSURE ASSESSMENT
6.2.1.
6.2.2.
6.2.3.
6.2.4.
Initial Analysis
Selection of a Nonpoint Source Runoff Model
Surface Water Flow
Surface Water Contaminant Transport . . . .
6.3. DETAILED SITE-SPECIFIC ANALYSIS.
6.3.1. Selection of a Nonpoint Source Runoff Model . .
6.3.2. Surface Water Flow .
6.3.3. Surface Water Contaminant Transport
7. REFERENCES
8. REVIEW OF EXAMPLE SURFACE WATER MODELS.
8.1. NONPOINT SOURCE RUNOFF MODELS.
8.2. SURFACE WATER FLOW MODELS. . .
8.3. SURFACE WATER TRANSPORT MODELS
APPENDIX A: DEFINITION OF SYMBOLS ....
5-1
5-4
5-7
5-26
5-28
6-1
6-1
6-2
6-2
6-3
6-4
6-4
6-8
6-9
6-9
6-10
7-1
8-1
8-1
8-13
8-31
A-l
iv
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TABLES
3-1
5-1
5-2
5-3
5-4
Factors affecting temporal scale
Outline of the model selection process
Summary matrix of nonpoint source runoff models
Summary matrix of surface water flow models . .
Summary matrix of surface water contaminant transport
models, . . . . .
3-16
5-8
5-13
5-19
5-25
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FIGURES
2-1
3-1
3-2
3-1
Block diagram for a water quality system.
Vertical representation of a lake and longitudinal
representation of a river
Ratio of boundary concentration to centerline
concentration as a function of dimensionless downstream
distance
Classification of estuarine stratification
2-1
3-2
3-5
3-11
VI
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FOREWORD
When performing exposure assessments using predictive methods, assessors
frequently ask the following questions: "How do I select'the best fate model
to use in my assessment," "How can I tell if the model someone else used in
their assessment is appropriate," and "What are the strengths and weaknesses of
these models?" This document is a first step in addressing these questions.
One of the functions of the Exposure Assessment Group is to develop guide-
lines for exposure assessments. On September 24, 1986, the U.S. Environmental
Protection Agency published Guidelines for Estimating Exposures. During the
development of the guidelines and subsequent review and comment, four areas
were identified that required further research. One of these areas was selec-
tion criteria for mathematical models. This first selection criteria document
deals with surface water models. Similar documents will follow dealing with
ground-water models and air models, and in the future, other types of models.
This document is designed to help the exposure assessor evaluate the
appropriateness of models for various situations. The report defines the terms
and discusses the general approaches that modelers take to a problem so that
exposure assessors may more readily evaluate the appropriateness of both new
and existing models. In addition, step-by-step criteria are provided to enable
the assessor to answer the questions posed above. These criteria will eventu-
ally be made available as an interactive program for a personal computer (PC).
Michael A. Callahan
Di rector
Exposure Assessment Group
vii
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PREFACE
The Exposure Assessment Group (EAG) of the Office of Health and Environ-
mental Assessment (OHEA) is preparing several documents addressing selection
criteria for mathematical models used in exposure assessments. These documents
will serve as technical support documents for the Guidelines for Estimating
Exposures, one of five risk assessment guidelines published by the U.S. Envi-
ronmental Protection Agency in 1986.
The purpose of this document is to present criteria which provide a means
for selecting the most appropriate mathematical model(s) for conducting an
exposure assessment related to surface water contamination.
The literature search to support the models discussed in this report is
current to January 1987.
vm
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ABSTRACT
Prior to the issuance of the Guidelines for Estimating Exposures in 1986,
the U.S. Environmental Protection Agency (EPA) published proposed guidelines in
the Federal Register for public review and comment. The purpose of the guide-
lines is to provide a general approach and framework for carrying out human and
nonhuman exposure assessments for specific pollutants. As a result of the re-
view process, four areas were identified that required further research. One
of these was the area of selection criteria for mathematical models used in
exposure assessment.
The purpose of this document is to present criteria.which provide a means
for selecting the most appropriate mathematical model(s) for conducting an
exposure assessment related to surface water contamination.
A concerted effort was made to provide general background information
regarding surface water flow and contaminant transport and to characterize the
important assumptions and limitations of existing models. These include a
detailed summary matrix and model writeups for ten runoff models, twelve sur-
face water flow models, and twelve contaminant transport models that have
been used previously by EPA to study surface water quality problems. General
guidelines and principles for model selection are presented, such as the over-
view of the modeling process and important issues related to model selection
(e.g., familiarity, model reliability, model selection vs. model application).
Following the general guidelines is a step-by-step approach for identifying the
appropriate model(s) to use in a specific application.
IX
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AUTHORS, CONTRIBUTORS, AND REVIEWERS
The Exposure Assessment Group within EPA's Office of Health and Environ-
mental Assessment was responsible for the preparation of this document and
provided overall direction and coordination during the production effort.
The first draft of this document was prepared by ICF Technology, Inc. under a
contract with Camp, Dresser and McKee, Inc. (EPA contract no. 68-01-6939; John
Segna, Project Manager). In subsequent drafts, Chapters 1 and 2 were exten-
sively revised. .
AUTHORS
Tom J. McKeon
ICF Northwest ,
Rich!and, WA
John J. Segna
Exposure Assessment Group
Office of Health and Environmental Assessment
U.S. Environmental Protection Agency
Washington, DC
CONTRIBUTORS
Robert B. Ambrose
Environmental Research Laboratory
U.S. Environmental Protection Agency
Athens, GA
Charles Delos
Office of Water Regulations and Standards
U.S. Environmental Protection Agency
Washington, DC
Patrick Kennedy
Office of Toxic Substances
U.S. Environmental Protection Agency
Washington, DC
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Carolyn K. Offutt
Office of Toxic Substances
U.S. Environmental Protection Agency
Washington, DC
Elizabeth Southerland
Office of Solid Waste and Emergency Response
U.S. Environmental Protection Agency
Washington, DC
REVIEWERS
Vincent James Cogliano
Carcinogen Assessment Group
Office of Health and Environmental Assessment
U.S. Environmental Protection Agency
Washington, DC
Robert W. Eli as
Environmental Criteria and Assessment Office
Office of Health and Environmental Assessment
U.S. Environmental Protection Agency
Research Triangle Park, NC
Thomas T. Evans
Exposure Assessment Group
Office of Health and Environmental Assessment
U.S. Environmental Protection Agency
Washington, DC
Richard C. Hertzberg
Environmental Criteria and Assessment Office
Office of Health and Environmental Assessment
U.S. Environmental Protection Agency
Cincinnati, OH
David P. Kyllonen
U.S. Environmental Protection Agency, Region 9
San Francisco, CA
Richard Moraski
Exposure Assessment Group
Office of Health and Environmental Assessment
U.S: Environmental Protection Agency
Washington, DC
John Years!ey
U.S. Environmental Protection Agency, Region 10
Seattle, WA
XI
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1. INTRODUCTION
In the last three decades there has been a dramatic increase in the pro-
duction and use of chemicals in our society. The chemicals have been developed
and applied to a variety of beneficial uses in domestic, 'industrial, and agri-
cultural applications. In some cases the chemicals have had unexpected adverse
effects. As a result, concern has grown over the impacts of some chemicals,
both at the point of use or application and in distant areas to which the
chemicals may be transported via various environmental pathways.
As the process of regulating and controlling the release of these potenti-
ally hazardous chemicals into the environment becomes a more complex task, the
U.S. Environmental Protection Agency (EPA) has focused its energy towards a
risk assessment/risk reduction framework for making regulatory decisions. Part
of this risk assessment process has been the development and publication of the
Guidelines for Estimating Exposures (U.S. EPA, 1986). These guidelines "provide
the Agency with a general approach and framework for carrying out hunan or
nonhuman exposure assessments for specified pollutants."
1.1. ESTIMATING EXPOSURE AREAS
The five major areas to be evaluated when estimating exposures to environ-
mental contaminants are (U.S. EPA, 1986):
1. Source Assessment -- A characterization of a source of contamination;
2. Pathways and Fate Analysis -- Description of how a contaminant may be
transported from the source to the potentially exposed population;
3. Estimation of Environmental Concentration -- An estimate using
monitoring data and/or modeling of contaminant levels away from
one source where the potentially exposed population is located;
4. Population Analysis A description of the size, location, and
habits of potentially exposed human and environmental receptors;
and
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5. Integrated Exposure Analysis -- The calculation of exposure levels
and the evaluation of uncertainty.
The process of estimating the environmental concentration of a contaminant
plays a significant role in exposure assessment. Often the most critical ele-
ment is the estimation of a pollutant concentration at an exposure point. This
estimation is usually carried out by means of a combination of field data and
mathematical modeling results. In the absence of field sampling data, this
process relies primarily on the results of mathematical models.
An ideal exposure assessment model would account for multiple emission
sources, estimate contaminant concentrations in all media (air, water, food,
and soil) resulting from emissions, define multiple,pathways of exposure, and
estimate exposure to humans, plants, and animals. An ideal model would also
contain methods for estimating the simultaneous exposure of humans, plants,
and animals to a number of contaminants so that synergistic or antagonistic
effects could be estimated as part of a risk assessment. Although the ideal
model is not available, component models that address various aspects of expo-
sure assessment are available. Therefore, decisions based on a modeling
analysis may require the use of multiple models to account for pollutant trans-
port through different media.
This potential need for multiple model usage in exposure assessments was ,
a major issue during the development of the exposure assessment guidelines.
Prior to the issuance of the Guidelines for Estimating Exposures in 1986,
the U.S. Environmental Protection Agency (EPA) published proposed guidelines in
the Federal Register for public review and comment. The purpose of the guide-
lines is to provide a general approach and framework for carrying out human and
nonhuman exposure assessments for specific pollutants. As a result of the re-
view process, four areas were identified that required further research. One
1-2
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of these was the area of selection criteria for mathematical models used in
exposure assessment.
1.2. MODEL SELECTION PROCESS
In general, the selection guidelines for mathematical models are written
for the exposure assessor, whose goal is to understand the implications that
the use of a mathematical model has for exposure assessment. Once this goal is
achieved, the assessor can then determine which model(s) best describe the
problem that needs to resolved.
Estimating environmental concentrations requires not only the appropriate
mathematical model and the necessary data (model input parameter data and field
data to compare against the model results), but also the expertise of the expo-
sure assessor. To the extent that the assessment is weak in any of these three
areas, the uncertainty in the model results will increase.
1.3. DOCUMENT OBJECTIVES
The purpose of this document is to describe a set of criteria that will
assist in the selection of appropriate surface water models suitable for vari-
ous situations. It is intended primarily to assist potential model users who
are not experts in water quality modeling; specifically, to make the reader
aware of the complex nature of mathematical modeling, the process involved in
choosing a model, and the principles behind the selection.
This document deals with surface water models used to predict pollutant
concentrations in water bodies or sediments for nonpoint source runoff, lakes,
reservoirs, rivers, and estuaries. The results of these models may be used as
input to other models which calculate the dose and associated risk of chemicals
to a specific target organism or population.
All of the surface water models presented herein are designed for situa-
tions in which the contaminant is at trace concentration levels. A number of
1-3
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assumptions are implicit in this restriction, including the formulation of the
kinetic reactions and the implication that the properties of the contaminant do
not affect the properties of the environmental system. The models are not
designed to be used in an emergency response framework, such as an accidental
spill, because in those situations the contaminant is not likely to be at trace
concentrations initially, and the time required to set up the model, run the
model, and evaluate results is generally greater than the emergency response
times. There are models available to deal with these types of problems; how-
ever, they are outside the scope of this report.
Characterizations of the important assumptions and limitations of the
existing models are presented in this document, as are definitions of relevant
terms. The existing models are generally the best available technology, and
are useful tools when applied properly. However, model accuracy is very sen-
sitive to input, parameters, and calibration with field data is essential. In
any modeling study, the assumptions and limitations of a particular model,
along with the means by which it is applied, should be clearly understood by
the model user as well as by persons making decisions based, in part, on the
modeling results.
The organization of this document is as follows:
Chapter 2. Background Information; definition of terms and descriptions of
equations and processes
Chapter 3. Model Structure; descriptions of different water bodies, associated
processes, and model formulation
Chapter 4. Identification of Important Processes; simplified analytical means
for comparing the relative importance of processes
Chapter 5. Model Selection Criteria; step-by-step process for identifying
suitable models
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Chapter 6. Use of Selection Criteria
Chapter 7. References
Chapter 8. Review of Example Surface Water Models
1-5
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2. BACKGROUND INFORMATION
In the exposure assessment field, many of the assessors involved in either
the development or review of documents containing modeling results do not
necessarily understand the mathematical equations that influence model values.
The purpose of this chapter is not- to make the reader an "instant" expert in
surface water models (modelers themselves have a difficult problem gaining that
title), but instead to give the reader a basic understanding of the theory that
underlines the modeling process.
£
Before discussing the basic mathematical equations that make up the model,
it is first important to understand the fundamental processes involved in
formulating a water quality problem in terms of equations. Thomann (1972)
discusses this water quality problem in terms of a system component that iden-
tifies those phenomena that are "causation," those that are "responsive," and
those that act as links between cause and effect. Figure 2-1 aids in under-
standing these components for a particular problem.
CHEMICAL
DISCHARGE
INPUT
STREAM FLOW,
AREA,
REACTION COEFFICIENTS
SYSTEM
WATER
QUALITY
OUTPUT
Figure 2-1. Block diagram for a water quality system.
2-1
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2.1. DEFINITION OF TERMS
Throughout this report, a number of terms or phrases are used which may
be interpreted as having somewhat different meanings by readers with varying
backgrounds and experience. In an attempt to avoid misinterpretations, this
section provides definitions of the following terms: calibration, validation,
analytical model, numerical model, mathematical model, screening-level and
detail-level assessment, and near-field and far-field analysis.
Calibration In this document we will use the term calibration to de-
scribe the initial phase of a modeling study, in which the input coefficients
of a model are adjusted in an attempt to match measured field data (e.g.,
velocity, concentration). Model coefficients will differ depending on the
types of models being used (nonpoint source, surface water flow, and trans-
port). For example, the types of coefficients that are commonly adjusted in
transport models include dispersion coefficients, rate constants, and possibly
source and sink terms.
Validation This term will be used to describe a separate step of a
modeling study where the calibrated model (i.e., fixed coefficients, no further
adjustments) is applied to a different set of field data. The validation phase
is an attempt to see if the model can reproduce field data under conditions dif-
ferent from those used in the calibration phase. In actual applications, it
may be impossible to obtain a separate data set. The calibration phase may also
indicate poor model performance and may require that data normally used in the
validation phase be used instead to correct the calibrated model. If these
circumstances were to occur, the uncertainty in the model results would need to
be considered in the decision-making process.
Analytical Models -- Analytical models can usually be represented as
models with (1) one or several algebraic equations, (2) one ordinary differen-
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tial equation, or (3) one partial differential equation. If a model contains
equations which do not fit one of the three classifications given above, the
model will usually be difficult to solve by analytical methods (Rich, 1973).
An example of an analytical model is the Water Quality Analysis Model (WQAM) by
Mills et al. (1982). The WQAM was developed as a computer program to analy-
tically compute surface water concentrations of a chemical in large basins.
Solutions of analytical models are exact.
Numerical Models Numerical models are usually classified as models with
complex mathematical equations that are essentially impossible to solve by
analytical methods. Numerical models are written as computer programs because
of the complexity of the mathematical equations involved. For example, the
WASTOX model (Connolly and Winfield, 1984) is a numerical model for simulating
the transport and degradation of toxic chemicals in water bodies, and uses a
large number of differential equations to describe the physical system.
The relationship between the analytical and numerical model may be thought
of as follows: An analytical solution solves a very simple water quality equa-
tion exactly by means of hand calculations. An analytical model solves a
more complex, but still relatively simple, set of equations exactly by means
of a computer program. A numerical model solves a simple or complex set of
equations approximately by means of a computer program.
The terms "analytical code" or "numerical code" typically refer to the
computer program (the set of computer instructions written in a programming
language and run on a computer), whereas an analytical or numerical model is
the implementation of the code with a specific data set (either site-specific
or generic) to test the simulated representation of the system against observed
or measured behavior.
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Mathematical Model This term will be used to describe the mathematical
representation of the physical system. The model may represent an analytical
solution to these equations, or may be an approximate numerical representation
of the equations. In some cases, models based on analytical solutions are
simple enough that the calculations can be performed using a hand calculator.
In other cases the analytical models are more complex, and often are imple-
mented as programs to be run on a computer. In most cases, numerical models
are written in a computer language as a program to be run on a computer.
Models run on a computer are usually referred to as codes, or computer codes.
This document uses the term "model," as opposed to "code" wherever
appropriate.
Screening-Level and Detailed-Level Assessment -- The types of modeling
analysis that are described in this document may be very broadly categorized as
screening-level or site-specific exposure assessment studies. We have chosen
to use the term "screening-level" to represent studies where limited calibra-
tion and validation data are available and the uncertainty associated with the
predicted results is comparatively large, somewhere in the nature of an order
of magnitude. The terms "detailed-level" or "site-specific" with regard to
analysis are used to predict results on the order of a factor of two to ten.
Calibration and validation data are necessary in order to reduce the uncertain-
ty inherent in the results, and also in order to attempt to quantify the bounds
of uncertainty associated with the model results in the validation step and
with the model results when various model parameters are tested (the latter is
called sensitivity analysis).
The models used in a screening-level analysis are generally easier to
set up because the analysis requires only a general estimate of the contamina-
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tion problem. Models that are used in screening-level analysis make certain
restrictive assumptions (loading, stream flow, and time changes are assumed
to be constant), so that the results the model generates should reflect these
assumptions.
In a more complex site-specific-level analysis, the models used need to
account for more random changes in the study area, and are therefore more dif-
ficult to use, since the assumptions in the model are not restrictive. In
site-specific cases, the input data requirements for the model, i.e., the col-
lection of additional parameter values, are usually substantially greater than
in screening-level cases.
'Near Field and Far Field -- The mixing of a contaminant in a water body
is often separated into two zones, referred to as the near field and the far
field. The near field refers to the mixing zone where the properties of the
discharged fluid have a significant impact on the mixing and resulting dilution
of the discharged fluid by the ambient water body. The important properties
of the discharged fluid include the density relative to the ambient water body,
and the initial momentum of the discharge. Other characteristics of a dis-
charge pipe, such as a sewage outfall, may be important, and in many cases are
designed to maximize the dilution that occurs in the near field. The near-
field zone considers the mixing of the initial jet and resulting plume as the
discharge is diluted.
The second mixing zone, the far field, refers to the area where the mixing
processes are no longer a function of the type of discharge and initial proper-
ties of the discharged fluid. In the far field, the mixing processes are dom-
inated by turbulence within the ambient water body and variability of the
advective velocity field. All of the models described in this report are
intended for the analysis of far-field mixing processes. Detailed descriptions
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of the near-field mixing processes, along with descriptions of modeling tech-
niques suitable in this zone, are given by Fischer et al. (1979).
2.2. BASIC MATHEMATICAL MODEL EQUATIONS
Fundamental to the analysis of any water quality problem is the basic
equation of continuity, which attempts to describe the relationship of mass
transport through a volume of water and the sources and sinks of mass within
it. This equation is developed by constructing a material balance about a
volume and introducing the principle of the conservation of mass: the time
rate of change of mass within the volume plus the net rate of mass flow in
and out of the volume must equal that produced by the sources and reduced
by the sinks. The continuity equation is a mathematical statement of the
principle of mass balance*
All water quality models are based on the conservation of mass. The
conservation of mass for the transport of a dissolved contaminant in a water
body may be written in differential form as:
^P_ + v(Cq) = DV2C + ZT + zr ± s
where
C is the concentration of dissolved contaminant (M/L^),
t is time (T),
V is the Del operator (vC = 3C/3X + 3C/3y + 3C/3z) (1/L),
q is a vector of the x,y,z velocity components (L/T),
D is a dispersion coefficient (L^/T),
2T represents any phase transfer mechanisms (M/L^/T),
Zr represents any reactions (M/L-^/T), and
s represents any source or sink terms (M/L^/T).
2-6
(Eq. 2-1)
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The statement of the conservation of mass shown in Equation 2-1, also
known as the advective dispersion equation, is the fundamental equation in many
water quality models. This equation states that the time ratio (t) of change
of the substance (c) is equal to the amount of input less both the amount dis-
charged and the amount lost by the decay of the substance in the water body.
Generally the advective and dispersive terms, v(Cq) and DV2C, are considered
to be the hydrologic or hydrodynamic transport terms, whereas the transfer,
reaction, and source/sink terms, ET, zr, and s, are used to represent trans-
formation and degradation processes along with source/sink terms. The source/
sink term is usually composed of several components including: (1) point
sources, such as a pipe discharge; (2) distributed nonpoint sources, such as
runoff along the length of a river; and (3) a distributed source or sink along
boundaries of the water body resulting from some previous impact, as in benthal
deposits.
One distinguishing characteristic of many toxic substances is their affinity
for contaminant adsorption to particulates. As a result, the mass of contami-
nants is partitioned between the dissolved and the particulate adsorbed forms.
In order to develop a descriptive model, two relationships or equations in
addition to Equation 2-1 are necessary. The first equation defines the concen-
tration of particulates in the water body, while the second defines a relation-
ship between dissolved contaminants and the contaminants adsorbed to the par-
ticulates. The particulate concentration in the water column, is generally
represented by some form of an advection dispersion equation with the addition
of one or more terms, such as a settling velocity acting in the vertical direc-
tion. For example:
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iH + 7(Mq) - wp jM = D V2M ± s
3t s 8z m
(Eq. 2-2)
where
M is the concentration of participate matter (M/L3),
ws represents the settling velocity of the particulate (L/T), and
sm represents any source or sink terms for the particulate (M/L3/T).
The settling velocity used in Equation 2-2 is dependent on the size of the
particulate matter, and is usually estimated from basic fluid mechanics princi-
ples relating the settling velocity to the diameter and density of the particu-
late. Under steady-state conditions (when input data such as loading, water
flow, velocity, and reaction coefficients are constant over time), Equation 2-2
may be simplified to yield analytical descriptions of the vertical distribution
of suspended particulate matter (for examples see Vanoni, 1975). The boundary
conditions for the general form of Equation 2-2 are complex relationships
relating the erosion and deposition of sediments to the suspended particulate
concentration and characteristics of the flow regime in the vicinity of the
boundary.
The relationship between dissolved and adsorbed forms of a contaminant is
usually represented in the form of an equilibrium partition coefficient. The
partition coefficient is defined as the ratio of the mass of the substance
adsorbed to the particulates (per unit mass of particulates) over the dissolved
concentration of the solute. The particulate adsorbed contaminant is repre-
sented as:
P = Rp M
(Eq. 2-3)
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where
P is the concentration of adsorbed contaminant (M/L^), and
Rp is the mass of chemical per unit mass of particulate (M/M).
The partition coefficient may be represented as:
Kp = Rp/C
(Eq. 2-4)
where
o
Kp is the partition coefficient (L /M).
This relationship assumes instantaneous partitioning between the dissolved and
adsorbed forms of a contaminant. It is only valid for very low concentrations
of the solute so that a linear approximation to the adsorption isotherm may be
made.
2.3. HYDROL06IC TRANSPORT PROCESSES
A wide variety of physical processes occur in natural water bodies which
are important, to varying degrees, in the analysis of pollutant fate and trans-
port. A more detailed description of these processes is given by Fischer et
al. (1979) and Schnoor (1985). Some of the important hydrologic transport
processes include:
Advection Transport of water flowing in a particular direction (more or
less horizontal), such as water flowing due to the current in a stream or river.
Convection Vertical transport of water due to density gradients. This
is a form of transport where the driving forces of the currents are density
gradients resulting from temperature differences in deep lakes, and temperature
and salinity differences in estuaries.
Molecular Diffusion Scattering of particles by random molecular motion,
commonly characterized by Pick's law of diffusion.
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Turbulent Diffusion Scattering of particles by random turbulent motion
(advective transport via turbulent motion in the form of eddies).
Shear Mixing due to variations in the fluid velocity at different posi-
tions in the water body. One example of this could occur in a lake where a
significant decrease in temperature occurs with depth, thereby causing a ther-
mal resistance (resistance of colder and, therefore, denser and lower-lying
water to be displaced by warmer, lighter and higher-lying water). A shear
plane divides the surface currents that follow the wind from the return cur-
rents that run counter to the wind (Fair et a!., 1968).
Dispersion The scattering of particles due to the combined effect of
shear and diffusion (molecular and turbulent). Usually the combined effect
of shear and transverse diffusion, represented as an effective dispersion, is
orders of magnitude greater than other diffusive mechanisms acting in the
direction of flow in rivers and estuaries.
Particle Settling The sinking of particles having densities greater than
the fluid of the water body, such as sediments or suspended solids.
Particle Deposition The settling of particles from the water body to
the underlying bed.
Particle Entrainment The picking up or lifting of particles from the
underlying bed of a water body by turbulent motion over the bed.
In most water quality models, the processes of molecular and turbulent
diffusion and shear are combined as a dispersion coefficient. This assumes
that the mixing from all of these processes may be combined and represented by
an equation similar to Pick's law of diffusion (i.e., the flux is proportional
to the concentration gradient). The dispersion coefficient is the coefficient
of proportionality used to relate the flux to the concentration gradient. In
addition to these processes, estuary models that are formulated as tidally
2-10
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averaged (averaged over a tidal cycle) also combine any intra-tidal advective
transport into the dispersion coefficient. In contrast to true Fickian diffu-
sion, where the diffusion coefficient is only a function of the diffusing
material, the resulting dispersion coefficient is a specific characteristic of
the water body, i.e., strongly dependent on the flow patterns, and must be
determined in the calibration process or via experimental measurements on the
specific water body of interest.
2.4. ATTENUATION MECHANISMS
The primary physical, biological, and chemical processes included in
various water quality models are hydrolysis, oxidation-reduction, photolysis,
ionization, volatilization, sorption, and biodegradation, and ionization.
The kinetic formulation and rate constants used to describe these processes are
based on laboratory measurements. The results of the laboratory measurements
are incorporated in the water quality models as source or sink terms in the
general advection-dispersion equation.
The transfer of controlled experimental results to natural aquatic systems
is not always straightforward. Uncertainties arise in the definition of driv-
ing forces such as the available light for photolysis, sensitivity to tempera-
ture and pH of the natural system, availability of additional ions which may
catalyze or retard various reactions, and atmospheric conditions. In spite
of the uncertainties, these processes are incorporated in many water quality
models, and some models have been calibrated to field conditions. Models that
are carefully calibrated have been shown to be useful for representing the
transport and transformation of various chemicals.
Most of the available models use some form of first-order reaction
kinetics to represent the different processes that will degrade or trans-
form a specific chemical. For a simple first-order reaction, ignoring all
2-11
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other mechanisms, the concentration can be represented as a first-order
differential equation:
dc = _kc
dt
(Eq. 2-5)
where k is the rate constant (1/T). While in the simpler models the rate con-
stant does not change, in the more complex models the rate constant(s) may be
variable due to changing environmental conditions. The analytical solution to
Equation 2-5 when k is a constant is:
C(t) = C0 e
-kt
(Eq. 2-6)
where
C(t) is the time-dependent concentration (M/L3), and
C0 is the initial concentration (M/L3).
From this equation an estimate of the time, t, required for the process to
reduce the contaminant concentration below a fixed "action level" can be deter-
mined as follows:
t = Ln {[C(t)/C0]/(-k)}
(Eq. 2-7)
Often the reaction rates of various chemicals subject to different kinetic
processes are characterized in terms of their half-life, ti/2. This is a mea-
sure of the time required for some kinetic process to degrade or transform the
specific chemical to one-half of the initial concentration. The half-life is
calculated from Equation 2-7 with C(t)/C0 set to 1/2.
2-12
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A brief description of several important transformation processes is
included for potential users unfamiliar with the terminology. Much more
detailed descriptions including assumptions, limitations, kinetic formulations,
and methods for estimating rate constants are given by Delos et al. (1984) and
Neely and Blau (1985).
2.4.1. Hydrolysis . ,
Hydrolysis is the breaking of bonds in a molecule due to reaction with
water. Typically a compound is altered in a hydrolytic reaction by the re-
placement of some chemical group of the compound with a hydroxyl group. The
hydrolysis reactions are commonly catalyzed by the presence of hydrogen or
hydroxide ions, and hence the reaction rate is strongly dependent on the pH of
the system. Hydrolytic reactions alter the structure of the reacting compound
and may change its properties. Depending on the specific reaction, the new
compound is usually less'toxic than the original compound. Neely (1985) lists
several functional groups that are susceptible to hydrolytic reactions, includ-
ing alkyl halides, amides, carbamates, carboxylic acid esters, epoxides, lac-
tones, phosphoric acid esters, and sulfonic acid esters. For many functional
groups, and therefore a considerable number of compounds, hydrolysis will not
occur.
2.4.2. Oxi dati on-Reducti on
Oxidation-reduction reactions involve the transfer of electrons from the
reduced species to the oxidized species. The oxidation-reduction potential is
an important process in that it can control the oxidation number of the metals
present in solution and may also change the oxidation state and structure of
organics. Oxidation-reduction reactions are used in models in the form of mass
action equations with resulting equilibrium constants related to stability.
The primary difficulty in applying these reactions to environmental models is
2-13
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that many redox reactions are very slow, and the concentrations of some species
may be far from those predicted via thermodynamic equilibrium. In addition,
some redox reactions are catalyzed by metal ions. Some compounds in which
redox reactions have been observed to be important include mercury, toxaphene,
and DDT (Tinsley, 1979).
2.4.3. Photolysis
Photolysis is the degradation process whereby radiant energy in the form
of photons breaks the chemical bonds of a molecule. Direct photolysis involves
direct absorption of photons by the molecule. Indirect photolysis involves the
absorption of energy by a molecule from another molecule that has absorbed the
photons. In indirect photolysis, the two steps are usually combined and the
photochemical reaction is characterized by first-order kinetics. The reaction
rate is dependent on the energy required to break the chemical bonds, available
light intensity, and the presence of intermediate compounds making indirect
photolysis possible. Characterization of light intensity as a function of
depth, time of day, time of year, and dissolved particulate matter in the water
column is difficult. These problems add uncertainty to the use of laboratory-
derived photolysis rates in field conditions. Mill and Mabey (1985) describe
the types of photolysis reactions affecting a variety of compounds including
chloroaromatics, ketones, and aldehydes.
2.4.4. Volatilization
Volatilization is a physical transfer process where a chemical is trans-
ferred between the water body and the atmosphere at the water-air interface.
For volatile materials, such as benzene, volatilization is an important pro-
cess in understanding environmental fate in water. The two-film or two-resis-
tance model of Whitman (1923) is a commonly used method for estimating a rate
constant, and first-order kinetics are used to represent the transfer process.
2-14
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Mass transfer rates are easily measured experimentally. Uncertainty in scal-
ing the laboratory rates to natural systems is complicated by'variations in
velocity, depth, stratification, salinity, wind speed, and diurnal atmospheric
conditions.
2.4.5. Sorption
Sorption is a transfer process whereby dissolved chemicals in the water
become attached to sedimentary materials. The process is commonly described
using a partition coefficient. The definition of the partition coefficient is
the ratio at equilibrium of the amount of chemical sorbed on the solid phase
divided by the amount of chemical left in solution, as shown in Equation 2-4.
The important assumptions in using this formulation are: (1) the chemical is
at trace concentrations, and hence the sorption isotherm may be assumed to be
linear, and (2) the system is at equilibrium.
Some problems associated with field application of this concept include:
(1) rapid movement of water and sediments in rivers and estuaries may not sat-
isfy the assumption of system equilibrium; (2) some chemicals may exhibit non-
reversible sorption characteristics; hence, desorption from sediments to the
water column may not be correctly represented; (3) different particle sizes
(sand, clay, and silts) exhibit different properties and should be accounted
for separately; and (4) salinity in estuarine systems may affect the sorption
process. Some of the compounds that may be strongly affected by sorption
include heavy metals and many hydrophobic nonpolar compounds.
2.4.6. Biodegradation
Biological transformations are reactions due to the metabolic activity of
aquatic microbes, primarily bacteria. Depending on the specific chemical, the
transformations may be very fast due to the presence of enzymes; for other com-
pounds the process may be very slow. For chemicals where the transformation is
2-15
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fast, biodegradation is often the most important transformation process in the
aquatic environment. Various kinetic formulations have been proposed, includ-
ing first- and second-order forms. The rate coefficients are known to be a
function of temperature, pH, and available nutrients. The second-order
kinetic formulations describe the degradation rate as a function of the con-
centration of the compound and the size of the bacteria population, which is
changing as the compound is degraded. A variety of organic compounds may be
subject to biodegradation; a discussion is provided by Klecka (1985).
2.4.7. lonization
The fate of toxic organics that are either acids or bases can be strongly
affected by the concentration of hydrogen ions in a water body. To the same
extent, organic chemicals that partition among the gaseous, solid, and solution
compartments could be determined from acid-base interactions between chemical
and the aqueous or soil/sediment components of the environment. Since many
toxic organics seem to exist in very low concentrations and are at best only
weak acids or weak bases, they will have little influence, if any, on the pH
values of the water. The hydrogen ion concentration of the water will, however,
determine whether acids or bases exist in neutral or ionic forms (Mills et al.,
1985).
An organic acid or base that is extensively ionized could be markedly dif-
ferent from the corresponding neutral molecule in solubility, adsorption, bio-
centration, and toxic characteristics. For example, the ionized species of an
organic acid is generally absorbed by sediments to a much lesser degree than is
the neutral form. The solubility of an ionic form of an organic chemical will
likely be greater than for the neutral species. Therefore, as a chemical is
ionized under environmental conditions, the change in physical properties as
well as the chemical reactivity will change with pH. The pH values found in
2-16
-------
most aquatic systems range from approximately pH 4 to 9, with extreme values
down to pH 2 and up to pH 11.
2-17
-------
-------
3. MODEL STRUCTURE
The choice of model structure is dependent on a variety of physical para-
meters related to the water body, the source terms, and the biochemical proper-
ties of the pollutant of interest. There are a variety of surface water models
applicable to the types of water bodies the reader will need to analyze, which
include streams, rivers, lakes, estuaries, and oceans. However, the methods by
which these models are applied for each type of water body could be distinctly
different. Water bodies, depending upon which type one is analyzing, may be
dominated by different mixing and transport processes. For example, rivers are
dominated by advective transport because water flow is in one direction and may
move quite rapidly. For lakes, the dispersion process dominates because lake
water is usually slow-moving, allowing the contaminant to spread and mix within
the volume of water.
A simple example of the difference between a lake and a river is shown in
Figure 3-1. The mixing and transport processes that control a lake usually re-
quire a model that can simulate concentration changes by depth. In this case,
the lake has two vertical compartments representing the water column, and a
third compartment representing the bed. Longitudinal compartments may not be
necessary for a lake, since water movement out of the lake can be very slow.
For a river, the mixing and transport processes are controlled by advection,
and the model used requires concentration changes by distance downstream.
Longitudinal compartments are more important, while understanding concentration
changes by depth may not be as important.
This chapter describes the mixing and transport processes that are most
important for each type of water body. In addition, some relatively simple
equations are presented which may be used to provide an initial estimate
3-1
-------
of dispersion coefficients and mixing distances appropriate for water bodies.
The representations of dispersion coefficients and mixing'distances are based
on theoretical and empirical considerations, along with analytical solutions to
Equation 2-1. The available models generally require a user-defined dispersion
coefficient as an input parameter. This may be a single or spatially variable
value, depending on model requirements. The equations given in this chapter
are meant to provide an initial estimate for dispersion coefficients. The
estimated values will most likely need to be refined in the calibration phase
of a modeling study.
\ *
\ -
1 /
* /
V *" 3 J
Figure 3-1. Vertical representation of a lake and
longitudinal representation of a river.
3.1. RIVERS
The dominant transport process in most rivers is advection. Mixing over
the vertical water column usually occurs rapidly as a result of shear flow and
turbulent diffusion. An initial estimate of a vertical mixing coefficient is
* ..'-.".* j ,
given by Fischer et al. (1979) as
Ev = 0.067 du
3-2
(Eq. 3-1)
-------
where
o
Ev is the vertical mixing coefficient (L/T),
d is the depth (L), and
u* is the shear velocity (L/T).
The shear velocity is defined as
*
u =
gdS
(Eq. 3-2)
where
g is the acceleration of gravity (L/T^), and
Sis the channel slope (L/L).
Transverse mixing in natural rivers and channels is dependent on a wide
variety of factors which may generate transverse motion within the stream.
These factors include curves in the channel, groins, and variations in geome-
try. A useful estimate of the transverse mixing coefficient is given by Fischer
et al. (1979) as
= a du
*.
(Eq. 3-3)
where
i
Et is the transverse mixing coefficient (L/T), and
a is a coefficient that varies from approximately 0.4 to 0.8.
Using this transverse mixing coefficient, and assuming that vertical mix-
ing is very rapid, estimates of the downstream distance for approximately
uniform lateral mixing are given by Fischer et al. (1979) as
X = 0.1 U W /£.(. (for centerline discharge)
(Eq. 3-4)
3-3
-------
and
X = 0.4 U W2/Et (for side discharge)
(Eq. 3-5)
where
X is the distance downstream of the point source where the distribution
across the stream is nearly uniform (L),
W is the stream width (L), and
U is the mean cross-sectional velocity (L/T).
These formulas are useful in the absence of field data for identifying
the point at which a one-dimensional analysis is adequate. The uniform lateral
mixing formulas are based on an analytical solution to the advection dispersion
equation. The definition of approximately uniform lateral mixing used in these
equations is that the concentration is within 5% of its mean value everywhere
on the cross section. If a one-dimensional analysis is used in a situation
where uniform lateral and vertical mixing has not occurred, the model results
will be likely to underestimate the peak concentrations. In effect, the mass
of contaminants will be spread uniformly over the cross-section rather than
being limited to some smaller portion of the channel.
If a different definition of uniform lateral mixing is deemed appropriate
for a specific application other than that stated above, Figure 3-2 may be used
to estimate the numerical coefficients used ,in Equations 3-4 and 3-5; Figure
3-2 is based on an analytical solution to Equation 2-1 'With a constant point
source term at X = 0, a stream with a uniform depth and velocity, where the
effects of dispersion in the longitudinal direction are considered minimal.
The boundaries are represented by the superposition of image sources. The y
/
axis represents the ratio of the concentration at the stream boundary, at a
specific cross-section, to the peak concentration, and the x axis represents a
dimension!ess distance downstream.
3-4
-------
SIDE DISCHARGE
CENTER DISCHARGE
I~~T 1 T I I I
O.3O 0.4O 0.5O O.6O
O.OO O.1O
X1 = (X/U)(ET/W2)
Figure 3-2. ' Ratio of boundary concentration to centerline
concentration as a function of dimensionless downstream
distance.
3-5
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Probably the most difficult part of contaminant transport studies in riv-
ers is related to the interactions with suspended and bed sediments. Various
water quality models treat the sediment transport process with varying degrees
of sophistication, and may be separated into three very broad classifications.
The most sophisticated models in terms of sediment transport (SERATRA, CHNTRN,
HSPF), examine the processes in a mechanistic fashion, describing scouring,
settling, resuspension, and finite sources of bed sediments. The next level of
models (WASTOX, TOXIWASP) requires that the user specify the .sediment trans-
port terms, including fluxes and dispersive terms, and the models calculate the
resulting concentration of both suspended sediments and the sediment in the
bed. The simpler models (EXAMS, SLSA, WQAM) require that the user specify the
concentration of suspended sediments and any flux terms.
In all of these models, some of the terms describing the sediment trans-
port processes must be treated as calibration parameters. The calibration
parameters are adjusted to fit field data. For the most sophisticated models,
the important parameters, such as credibility coefficients, critical shear
stress coefficients, and grain size distributions may sometimes be determined
from laboratory experiments. However, it may often be necessary to treat some
of these parameters as calibration coefficients. It should be stated that one
estimate of a model parameter does not necessarily fix the validity of the
model. However, the more information that is available and specific to a
particular modeling analysis, the greater the understanding of the uncertainty
associated with the computed results. If a situation arises in which a model
is used and the available field data are limited, caution should be used in
interpreting the model results, since under conditions of limited field data,
the model results may be open to technical criticism even though the choice of
the model was justified.
3-6
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The incorporation of sediment contaminant interactions is important for
situations where the contaminant of interest has a high affinity for adsorp-
tion. If the sediment contaminant interactions are not incorporated, the
predicted concentration of dissolved contaminant's ;in the water column would be
higher than actually exists. If the contaminated bed sediments are ignored,
the potential for a long-term source of pollution through, resuspension and de-
sbrption cannot be fully evaluated.
3.2. , LAKES AND RESERVOIRS
A variety of different transport mechanisms are active over different time
frames in lakes and reservoirs. The one relatively constant transport mech-
anism is diffusion. This is because, even without mechanical mixing, the
concentration of substance in solution will eventually become uniform (Fair et
al., 1968).; Other important mechanisms are advection due to wind stresses and
convective transport, as a result of surface cooling and the resulting unstable
density structure. The time frame of advective mixing due to wind stresses is
commonly short (hours to days), and complete mixing of the water body may not
result. Convective overturn on an annual or biannual basis may completely mix
the water body. -
: :: .Historically, water quality models for lakes have basically followed two
lines of development: (1) From an engineering point of view, model developers
have tried to characterize circulation and exchange processes while simplifying
the aquatic ecosystem;- and (2) from the point of view of aquatic biology, model
developers have tried to represent biological interactions and kinetics of
different- life stages, while simplifying transport processes and often repre-
senting the water .body as a continuously stirred reactor (CSTR). The type of
model appropriate for the exposure assessment of toxic chemicals must lie
between these two extremes.
3-7
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A common characteristic of many lakes and reservoirs is stratification on
a seasonal basis. When a lake is stratified it is roughly separated into two
layers: the upper layer of warmer water, referred to as the epilimnion; and
the lower, more dense layer of colder water referred to as the hypolimnion.
The boundary between the two layers is the thermocline, where a rapid change
in temperature profile occurs. The vertical transport across the thermocline
is often dominated by unpredictable events, such as wind-induced eddies, storm
surges, and internal seiches. Generally these processes are not represented
with a mechanistic formulation, but rather as diffusion processes.
An understanding of the reader's modeling objectives will help define the
appropriate type of model structure in terms of necessary spatial dimensions
and temporal characteristics. If the objective of the study is to identify
the long-term accumulation of some conservative material over many years, the
appropriate time step may be on the order of seasons or a year. The mixing
processes within a reservoir over the time frame of a year may be relatively
predominant; hence, a zero-dimensional single-compartment analysis may be the
best choice of model structure. This type of analysis will provide a spatially
averaged concentration that is appropriate for problems such,as.longrterm ;
accumulation.
In contrast, any analysis attempting to identify peak.concentrations or
the extent of a contaminant plume from some specific source will require the
analysis of some spatial dimensions. The dimensionality of a model used for
water quality in a lake will depend on several factors. If the lake is stra-
tified, the vertical compartments will need to be analyzed. At a minimum, the
vertical compartments of the lake should include the epilimnion and the hypo-
limnion. The necessity of analyzing longitudinal compartments will,, depend on
the source terms and the degree of lateral mixing. Point source termsfor
3-8
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example, a pipe dischargemay indicate that the lateral dimensions need to be
evaluated, whereas nonpoint source termsfor example, soil runoffmay justify
the use of a laterally averaged model.
The residence time of a lake is another important parameter in defining
appropriate model structure. The residence time is defined as the theoretical
length of time it take for a liquid to pass through the lake, assuming that all
of the liquid moves through the lake at the same uniform velocity. Residence
time can be determined by taking the volume of a lake and dividing by the
incoming river inflow. For large deep lakes or reservoirs, the residence time
may' be on the order of several years and, in many cases (some exceptions exist),
vertical one-dimensional models may be appropriate. This is because the lake's
"flushing" time is very long and chemical reactions by depth are more likely to
occur. For smaller reservoirs, such as run-of-river reservoirs, the residence
time may be on the order of a week, and significant longitudinal concentration
gradients may exist. In these cases, the longitudinal dimension should also be
analyzed. When the "flushing" time of the lake is short (weeks), the type of
chemical reaction that occurs by depth may not be as likely, and therefore one
may wish to analyze only surface or near-surface problems.
Sediment contaminant interactions are important in lakes for any contami-
nant that has a high affinity for particulate matter. The actual sedimentation
processes are usually much simpler than those encountered in rivers in that the
primary process is the settling and deposition of particulates, with a smaller
amount of resuspension due to diffusion and physical mixing at the bed. Over a
long time period (on the order of 10 years), this interaction in deep lakes is
important and must be evaluated.
3.3. ESTUARIES
Estuaries are probably the most complex water bodies in terms of hydro-
3-9
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dynamic flow and the resultant mixing processes. In addition, formulating
various physical, chemical, and biological transformation processes in estu-
aries is complicated by variations in salinity, both spatially and temporally.
An estuary is defined as a semi-closed coastal body of water that is subject to
tidal action and in which the sea water is measurably diluted by fresh water
(Rich, 1973). In real time and three-dimensional space, the dominant transport
mechanism is advection. However, water movement in an estuary varies signifi-
cantly from that in a stream. In those reaches of a river that are subjected
to tides, the motion of the water is caused not only by flow due to gravity but
also by the rise and fall of tides, density currents (due to salt and fresh-
water movement), and wind effects. Toxic compounds released into such an
estuary are mixed with water and are gradually diminished in concentration as
they are transported back and forth over many tidal cycles. If a model is
formulated to account for tidally averaged values, all of the advective trans-
port due to tidal excursions is combined into one tidal mixing term, which is
referred to as an effective dispersion coefficient.
Various classifications of estuary types have been suggested by different
authors based on hydrodynamic conditions, geomorphological characteristics,
time scales, and geometry. For the purposes of this report, the most useful
classification is based on the following three major hydrodynamic or strati-
fication categories, which were suggested by Pritchard (1967) and are shown in
Figure 3-3:
(1) Sharply stratified estuaries, such as fjords and salt-wedge types,
where the fresh water inflow flows over the top of the heavier salt
water; examples include Puget Sound, Washington, and the Mississippi
River estuary in Louisiana.
3-10
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O
Ul
oe
H
0)
O
IU
X
IU
o
Ul
X
cc
<
o.
c
o
td
O
rO
S-
to
01
s-
ca
3
4->
CO
O)
^-
o
o
-------
(2) Partially stratified estuaries where significant vertical density
gradients exist; examples include the James River estuary, Virginia,
and the Chesapeake Bay.
(3) Well-mixed estuaries where the salinity profile is nearly uniform
over the vertical column; examples include San Francisco Bay, Cal-
ifornia, and San Diego Bay, California.
This type of classification is useful for defining the necessity of
modeling the vertical dimension within the estuary. Complications with these
categories often arise as a result of large storm events, which may change the
stratification characteristics, and in cases where different portions of a
given estuary fit different general classifications.
Other estuarine classifications are discussed in varying degrees of detail
by Fischer et al. (1979), Walton et al. (1984), and Mills et al. (1985). '
Additionally, the last two references describe some of the characteristics of
many estuaries in the United States, and list how specific estuaries fit the
different classification schemes. In order to determine how a specific site
fits the hydrodynamic or stratification categories, several simplified analysis
techniques are available, the first is referred to as an "Estuarine Richardson
Number" by Fischer et al. (1979), and is discussed in more detail in Chapter 4.
The second means is the use of a stratification circulation diagram (Hansen and
Rattray, 1966). This methodology is discussed by Fischer et al. (1979), Walton
et al. (1984), and Mills- et al. (1985), and the reader is referred to those
sources. These simplified analysis techniques are useful tools. However,
there is no substitute for direct field observations of the different charao
teristics of a water body.
3-12
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Different estuaries may exhibit significant longitudinal and/or lateral
variations, and site-specific analyses must include measurements in the study
area to capture these variations. Some of the important parameters to measure
include salinity, temperature, velocities, and dispersive characteristics.
The primary driving forces causing circulation are usually tidal wave
action and fresh water inflows. Secondary forces are usually the wind stresses
and internal density variations as a result of fresh water and salt water in-
flows. In some wide estuaries the Coriolis effect, due to the earth's rota-
tion, may also affect circulation. For example, the Coriolis effect may cause
a water flow to drift to one side as it moves down from a channel (Mills et
al., 1985). The circulation within an estuary causes the advective transport
of contaminants and several other dispersive mechanisms. The first dispersive
mechanism is the result of shear and turbulent diffusion, as in rivers, except
that flow direction ,and magnitude are continually changing. In stratified
estuaries, this dispersive mechanism is complicated by the fact that the sur-
face layer of less dense fresh water must exhibit a net tidally averaged sea-
ward velocity. The lower layer of more dense salt water may, in contrast,
exhibit a tidally averaged landward velocity. This phenomenon is referred to
as a current reversal, where the tidally averaged currents in the stratified
layers flow in opposite directions. If a contaminant is discharged in a region
of an estuary where a current reversal exists, the contaminant plume may split
into two clouds, with the cloud in the upper layer traveling seaward and the
cloud in the lower layer traveling some distance landward. Obviously, a one-
dimensional, longitudinal model cannot represent this phenomenon, and a longi-
tudinal and vertical analysis, at a minimum, is necessary.
The second dispersive mechanism is referred to as "tidal pumping" or
residual circulation. A detailed description of this mechanism is given by
3-13
-------
Fischer et al. (1979). A simplistic description of the process is that the
incoming flood tide may flow through some constriction forming a sort of jet,
whereas the outgoing ebb tide flows from throughout the estuary towards the
constriction. The end result is large circulation patterns or gyres on the
landward side of the constriction.
The third dispersive mechanism is referred to as "tidal trapping" by
Fischer et al. (1979). A brief description of tidal trapping is that differ-
ent regions or zones of an estuary will have velocities less than that of the
main channel due to greater fractional forces. In these regions the tidal wave
will not propagate as far upstream. On the outgoing ebb tide, the particles or
contaminants that have not traveled as far upstream will reach the main channel
ahead of those that traveled farther upstream, and an effective mixing or dis-
persive mechanism will occur.
The estimation of empirical forms for vertical, transverse, and longitud-
inal mixing coefficients applicable to estuaries is a difficult process. For
very wide estuaries with irregular cross-sections, no simple equations are
available, and experimental measurements are the only suitable estimation
techniques. For other estuaries that are relatively long, narrow, and uniform,
similar to rivers, some empirical relationships are suggested 'by Fischer et al.
(1979). These empirical relationships are of the same form as those suggested
for rivers. The general form of the relationship for transverse mixing coeffi-
cients is the same as in Equation 3-3, but with different coefficients.
where
Et = odu
E.J. is the transverse mixing coefficient (L^/T), and
-------
The results of several experiments by various scientists are described by
Fischer et al. (1979) indicating that a very approximate range for the para-
meter a is between 0.4 and 1.6. The slope term, S, used in Eq. 3-2 is not
defined in an estuary, an alternative estimate of the shear velocity, u*, is
u* = 0.1 U
(Eq. 3-7)
An approximate estimate of the vertical mixing coefficient is
Ev = 0.0024 d VA
(Eq. 3-8)
where
\
Ev is the vertical mixing coefficient (1//T), and
VA is the depth mean amplitude of the current (L/T).
This .coefficient is suggested for uniformly mixed estuaries at mid-depth.
Several other more complex relationships are suggested for stratified systems.
The reader is referred to Fischer et al . (1979), pp. 249-251, for more details.
In addition, a number of assumptions, limitations, and caveats for the simpli-
fied expressions are also described. It is advised that the reader consult
this specific reference before using these equations to estimate mixing coef-
ficients.- , '; '
The sediment transport processes occurring in estuaries are similarly
complex when compared to those occurring in rivers, and include scouring, re-
suspension, settling, and finite sources of bed sediments. In terms of sedi-
ment, contaminant interactions, the processes are more complex due to the time
scale and spatially-variable salinity occurring in estuaries. The salinity may
affect various sorption processes along with other kinetic reactions. For this
reason, the kinetic rate constants.used in estuarine modeling should be spatial-
3-15
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ly variable and, in some cases, temporally variable. If a single or constant
coefficient is used, greater uncertainty is introduced into the modeling re-
suits.
3.4. TEMPORAL SCALE . , ,f,
The temporal variation used in a water quality model may be classified as,
dynamic (time-varying) or steady-state. Types of temporal variation are dis-.
cussed in Thomann (1972) and are shown in Table 3-1. In a steady-state model,..
all variables are considered to be constant over time. The constant variables-,,
include source terms, flow rates, any boundary conditions, and the resulting t
spatial concentration distributions. In a transient model, some variables are
considered to be changing in time. However, not all transient models consider
all variables to be time-dependent. For example, some models may allow tran-
sient source terms under steady flow conditions. At the very least, they-must
consider source terms and resulting concentration distributions as time-vari- ,,
able. Additional categories are sometimes referred to as quasi-dynamic or
quasi-steady-state. These terms are usually applied toimodels where a source, ,
term is assumed to be constant for a long period of time until steady-state ,-.,,.
concentrations are reached, at which point the source term is removed; and ttie -.
time required for the system to "cleanse" itself is calculated. ., ,f/,-
TABLE 3-1. FACTORS AFFECTING TEMPORAL SCALE ... ,.
Waste load input
Water flow velocity,
reaction coefficient
Water quality output
Constant
Time-variable
Constant
Time-variable
Constant
Constant
Time-variable
Time-variable
Constant
Time-variable
Time-variable
Time-variable
3-16
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The basic difference between a transient model and a steady-state model is
that the transient model has a "memory" of the initial state or previous condi-
tion of the system, which may correspond to a different source strength or flow
rate. In a steady-state model, the previous or initial conditions do hot affect
the results. When applied to identical flow conditions and source terms (i.e.,
both constant) the steady-state model will predict a single spatially variable
concentration distribution with a peak value. In contrast, a transient model
starting from specified initial conditions will predict a series of time- and
spatially variable concentration distributions that will initially have peak
concentrations less than that predicted by the steady-state model. At some
point in time, the transient results will asymptotically approach the steady-
state results.
The time required for the transient results to approach steady-state con-
ditions is highly dependent on the system being analyzed. For example, the
water column at a specific point in a river has a very short "memory" of pre-
vious conditions due to the strong influence of advection, and will approach a
steady-state condition relatively quickly. In contrast, the bed sediments in
a river respond much more slowly to changes in source terms, and will only very
slowly approach a steady-state condition. In reality, because of changes in
flow rates and other factors, bed sediments may never actually reach a true
steady-state condition.
In most applications in which a steady state model is used, the model may
"ft
be applied to a variety of different conditions in a Monte Carlo analysis.
From this, type of simulation a probability density function of the concentration
*Monte Carlo refers to a statistical simulation which allows the prediction of
the expected probability distribution of the model results based on the dis-
tribution of model inputs. This technique allows estimation of the predicted
uncertainty of the model results. - -
3-17
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may be developed which may be used to estimate the probability Of'exceeding
some exposure level. A comparison between the frequency distributions devel-
oped from a steady-state arid a transient model is described by Mulkey et al.
(1982). The conclusions are applicable to concentrations in the water column1
in rivers where the loading terms are constant,but the flow rate is variable. .
The conclusions cannot be generalized to bed sediments,' lakes:, or estuaries
where different processes are important (i.e. dispersion, detention time). The
frequency distribution derived -from the Monte Carlo simulations with a steady-e-
state model were nearly the same as the frequency. Distributions derived using a
continuous-simulation model. .,:-. . :: \ - ::.' ; ; , . ,
A variety of factors will influence the choice between a dynamic or a
steady-state model.. Important factors include source-terms, hydrblbgic condi-
tions, atmospheric conditfons, biological effects, farid attenuation processes.
If the source terms ip the water: quality analysis are, strongly time-varying,
a transient analysis is necessary. Examples of time-varying source terms
include accidental spi 11s,"' 'seasonal appTication: of- pesticides and fertilizers,
and, perhaps, intermittent dischargeSi from in-dustrial sources where some pro-.
cess is only performed on an; pccasiona;! :or irregular basis. Some'steady (or
nearly steady) source terms may include ;sewage;treatment1 plant'discharges'tfnch
industrial wastes. Some source terms may Wave a> daily variation: ft hat can ,iin.
some cases, be treated, as a steady, continuous'source. ' : v-.;?v .-;, .-,:.-,
A hydrologic condition of importance.swhen choosing between^ a steady-state
and transient model is the flow rate:. For lakes and rivers, >if?the flow rate
is known to be relatively constant,«-the'hydrologic. conditi-ons would'indicate >
the use of a steady-state model.;'A common methodology is to use-historic; ,; ,.
records of 1 ow f.1 ows and to assume that the 1 owef' vol um'es' of- 'water and' 1 onger
residence times will give- conservative^ estimatesnof':eoncen-tration;;(overpredict).'
3-18:
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The dynamic, nature of flow: in estuarine systems indicates that a transient
analysis should, be used. .Steady-state ana1ysis,;of highly/variable systems such,
as estuaries' should be used with extreme care, and only as. a general screening
tool. -Hinwood and Wall is (1975) state that a steady-state model is inappro-
priate for short estuaries .where the tidal excursion distance is a significant
portion, of the. total:-length.*? Additionally,, they, State that a steady-state
mode;! will be unsatisfactory if .the wa^te load, river inflow, or tidal range
vary appreciably with a, period 'close to the flushing time of the area of inter-
est. An additional, subclass if i cation: within the dynamic category is a tidally,
averaged analysis, which only applies to estuarine systems. A t.idally averaged
analysis will use a time step greater :than^a e
available --in the.1 selected model:. If a pollutant is acutely toxic and exposure .
for very -short time frames:.must be exam.ined,, a, model capable of analyzing short
time frames is necessary. If. a: pollutant is only to.xic when exposures occur
for very long, periods, this particular, icriteri on may indicate the use of a.
steady-state model. The importance of different atten.uation mechani sms must.:
-------
also be considered along with tthe. temporal characteristics of the model.
An important physical characteristic, unrelated to time variability, is
the ratio of the volume of.the estuary to the river inflow. In a steady-state
analysis, the only advective transport is the result of river inflows. All of
the tidally induced phenomena are represented by a dispersion coefficient.
Walton et al. (1984) offer one example, as an extreme, of a closed-end canal
system where there is little or no inflow and, hence, no advection towards the
outlet. The analysis will depend entirely on the calibration of a dispersion
coefficient. For any estuarine system where the freshwater inflows are small,
this type of analysis is likely to be subject to large errors if applied to any
conditions different than those used for calibration.
If a dynamic analysis (time-varying) is necessary, the selection of the
proper time step (hours, days, months, or years) becomes very important. The
factors influencing the choice of a time step will include stability criteria
for numerical integration, and time variability of source terms and other
driving functions. The stability criterion is a model-dependent parameter that
should be described in a user's manual. Generally, the criterion is a relation-
ship between the spatial resolution and the time step; the use of a coarser-grid
resolution will usually enable the use of larger time steps at the expense of
spatial accuracy. Limiting stability criteria may also arise from the rate
constants associated with .degradation processes; a simple example is provided
by Walton et al. (1984). Explicit integration techniques commonly require
smaller time steps for stable solutions than those required for implicit
integration techniques, which are also subject,to stability constraints for
nonlinear problems. The time variability of source terms and other driving
functions are problem-dependent parameters that must be identified by the user.
3-20
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If a steady-state model is used in a problem where the source terms are
time-variable, the steady-state results will probably underpredict the peak
concentrations. The reason for this is that the transient nature of the source
term will be averaged over the on and off periods; hence, the average source
strength will' be lower than the transient peaks. If a different source-term
averaging procedure is used, such as a constant source at the peak transient
rate of discharge, the model results may overpredict the'peak concentrations.
The use of this type of source-term averaging is likely to complicate the cal-
ibration process because the mass of contaminant input to the system will be
too large. Attempting to match some observed concentrations with the model
results will overestimate dispersive or degradation mechanisms.
3.5. DIMENSIONALITY
" the choice of the number of spatial dimensions to be incorporated in a
given analysis should depend primarily on whether or not a contaminant is
completely or uniformly mixed over a given spatial dimension. The best means
of resolving this issue is through field measurements of the contaminant of
interest or some other conservative or nonconservative substance with known
degradation rate, discharged at the same location.
For any estuary or reservoir, one should first determine whether or not
the water body is stratified. If the water body is stratified, the vertical
dimension should be analyzed. With a few exceptions, the analysis of large
reservoirs with long residence times has traditionally been simplified to a
one-dimensional vertical problem. This approach is probably adequate for con-
taminant problems resulting from nonpoint source terms. However, it should
be used cautiously for problems with point source terms where mixing over
horizontal directions may take a significant amount of time. If this type of
analysis is used where uniform horizontal mixing has not occurred, the peak
3-21
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concentrations in the vicinity of the source terms will be underpredicted by
the model.
The flow patterns, mixing processes, and resulting transport in estuaries
are very complex and are difficult to describe with one, two, or three-dimen-
sional models. Specific situations where a one-dimensional '"(longitudinal)'' '
model may be appropriate include unstratified water bodies that are relatively
long and relatively narrow. Three tests or criteria are suggested by Fischer
et al. (1979) to determine the usefulness of a one-dimensional approach:
(1) The time scale for transverse mixing across the estuary is signifi-
cantly less than the time required for the effluent to pass out of
the estuary or for the substance to degrade. An estimate of the
time scale for transverse mixing is given as 0.4W^/Et, Where W is
the width of the estuary and Et is the transverse mixing1 coefficient.
(2) The estuary is not significantly stratified, so that the contaminant
may be assumed to be completely mixed over depth.
(3) Allowance is made in the analysis for higher concentrations near the
source before cross-sectional mixing is complete.
As a final comment, the authors note that for practical reasons, a one-dimen-
sional analysis is used in many cases even if criteria (1) and (2) are not 'met,
but the results may be subject to larger errors. ' '' ' ' ''"
For estuaries which are not relatively long, narrow, and uniform, :the mech-
anisms of tidal pumping and tidal trapping may become important. These mecha-
nisms are the result of variations in the geometry of the system, including r
both the bathymetry and constrictions. The complex geometry must, as "a" mini-
mum, be represented using a two-dimensional (longitudinal, lateral) analysis.
The vertically averaged models are only applicable to well-mixed (unstratified)
estuaries, and currents are constrained to be entirely in the horizontal direc-;
3-22
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tions. Some estuaries which are stratified may be represented as a two-dimen-
sional (longitudinal, vertical) system if the estuary is relatively long,
narrow, and uniform. If the stratification is very distinct, as in salt-wedge
estuaries, the vertical dimension may sometimes be represented by two layers.
The final case is estuaries where stratification, tidal pumping, and tidal
trapping are all important. .Under these circumstances, a three-dimensional
analysis may be necessary. Considerable expertise, along with extensive
computational resources and funds, are necessary for the three-dimensional
analysis of estuarine, systems or any other water body.
For, the analysis of contaminant transport in rivers, one-dimensional
models are commonly used and are appropriate. The mixing length concepts pre-
sented by Fischer et al. (1979) and outlined earlier in this chapter are use-
ful for determining where a .one-dimensional analysis is appropriate. The
limitation of a one-dimensional analysis in rivers would be to study the con-
centration levels near the discharge source or when the analysis involves a
very wide river, on the order of 2,000 feet, where transverse mixing may not
be complete for 10 to 100 miles downstream.
As a general rule of thumb for any water body, reducing the number of
spatial dimensions .analyzed may cause the model to underpredict the peak con-
centrations. If the water body is uniformly mixed over the particular spatial
dimension, t.hen dropping that dimension from the analysis is justified. If the
contaminant is not uniformly mixed, such as near point sources, the model
results should be interpreted with the full knowledge that peak concentrations
will be underpredicted by the model.
3.6.. DEGRADATION PROCESSES
A wide variety ,of degradation and transformation processes are known to
affect the migration and fate of chemicals in the environment. Any process
3-23
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that has been shown to affect a specific chemical should be incorporated into
the analysis if possible. Most complex models incorporate the group of atten-
uation processes that were discussed in Chapter 2. Some models are formulated
in such a manner that the user may easily specify additional processes as
subroutines to the main program.
The determination of specific rate constants used in the kinetic formula-
tions may be subject to substantial uncertainty. As a result, sensitivity
studies must be performed to indicate which parameters contribute most to un-
certainties. Through the use of sensitivity studies, some degree of confidence
in the model results, or lack thereof, may be established. Additionally, the
dominant processes may be identified and quantified better or formulated dif-
ferently if possible.
If an important degradation process is not incorporated in the analysis,
the predicted concentration of the affected chemical will be high. This
problem may be complicated in the calibration process by the inappropriate
adjustment of some other parameter, such as another rate constant or dispersion
coefficient. This type of problem may have an important impact when the cali-
brated model is then applied to different conditions in a validation phase or a
planning exercise. As a result, it is essential to incorporate all processes
known to have a significant impact on the degradation of a particular chemical.
It is also preferable to represent the processes individually rather than with
a combined first-order decay term, so that the different environmental condi-
tions affecting the different processes may be evaluated.
Another important problem that may arise if certain transformation pro-
cesses are not incorporated is that some secondary or daughter substance's will
not be identified. If the secondary substances are not harmful, this is not a
problem. If they are toxic, this is important because they,may react differ-'
3-24
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ently (faster or slower, depending on the substances) than the original form of
the chemical. '
3.7. SEDIMENT TRANSPORT AND SORPTION PROCESSES
Many toxic substances ape adsorbed onto particulates and may settle into
bed sediments. As a result, the characteristics of the sediment transport
process and resulting bed movement and accumulation are important factors in
the identification of appropriate models. A useful classification structure is
described by O'Connor and St. John (1982) and is included here. The three
categories described are related to the mixing processes associated with the
bed. the bed categories are: stationary, exchanging, and moving. These clas-
sifications are based primarily on the flow of water above the bed and the
resulting turbulence and mixing processes. Another important mechanism is the
role of sediment organisms in mixing the upper layer of sediments. This is
most important in lakes where the other mixing processes are relatively small.
The stationary bed is characterized by very small or negligible horizon-
tal motion. The primary water bodies where this condition is present would be
very deep lakes and reservoirs that are not subject to strong mixing by winds.
Under this rather idealized condition, the primary process is the accumulation
of material on the bed. This process is described by a sedimentation velocity.
An exchanging bed is characterized by some amount of mixing in the upper
layer of the bed, in addition to the sedimentation velocity. The mixing in the
upper layer may be the result of biological action or shear resulting from
fluid motion over the bed. The different types of water bodies where this
condition may exist include rivers with low to moderate flows, lakes or regions
within lakes where the wind effects extend-to the bottom, and some estuaries
or regions of estuaries where the velocities and tidal mixing effects are not
dominant.
3-25
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A moving bed is characterized by both mixing and advective transport of
the bed sediments. The velocity over the bed is strong enough to cause erosion
and resuspension of the sediments and to horizontally transport the suspended
and bed materials. This type of bed condition may require a detailed or mech-
anistic description of the sediment transport process. The types of water
bodies where this condition may be found include streams and rivers, under
moderate to high flow rates; and estuaries or regions of estuaries ^where the
velocities and tidal mixing effects are strong. Mechanistic descriptions of
sediment transport have been studied for many years by hydraulic engineers pri-
marily interested in the sedimentation of rivers and some reservoirs. These
studies have concentrated primarily on coarse-grained materials, such as sands
and gravel. In contrast, the sedimentary materials to which most contaminants
are adsorbed are finer materials, such as clays and organic matter. Limited
data are available regarding the characteristics of the finer-grained materials.
The models using a mechanistic description of sediment transport include
SERATRA, CHNTRN, and HSPF for rivers, and FETRA for estuaries. The basic ad-
vantage of these models is that when calibrated and used in an analysis where
a sediment transport characteristic is substantially different than calibration
conditions, such as flow rate, results can be interpreted with more confidence.
In most cases, the disadvantage of these mechanistic models is the lack of
required input data (e.g., critical shear stress coefficients, erodibility
coefficients, grain size distributions).
The sorption process whereby dissolved contaminants become adsorbed to
particulates in the water column and bed sediments is represented in two"dif-
ferent ways among the existing models. The majority of the models use a par-
tition coefficient. The use of a partition coefficient assumes that the con-
taminant is at trace concentrations, .so that the sorption isotherm.is approx-
3-26
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imately linear. Additionally, it assumes instantaneous equilbrium. A few
models (SERATRA, FETRA, and HSPF) incorporate sorption as a first-order rate
process which approaches an equilibrium condition defined by the partition
coefficient.
The importance of incorporating sediment-contaminant interactions depends
primarily on the sorptive characteristics of the pollutant of interest. The
sorption process is a mechanism whereby a contaminant is removed from the water
column. The relative importance of this mechanism is dependent on the parti-
tion coefficient of a particular contaminant and particulate concentration. If
this process is not incorporated, the model results should overpredict the con-
centration of.dissolved contaminants, and ignore the contaminant concentration
in the bed sediments. For any transient problem, the contaminated bed sedi-
ments may also act as a relatively long-term contaminant source to the water
column after the original source has ended. -
3.8. NONPOINT SOURCE RUNOFF
Nonpoint sources of pollution, both from agricultural and urban areas, may
constitute a significant portion of the pollutant loading rates to surface
water bodies. The recognition of this problem is relatively new (the last 10
to 20 years), and, therefore, the analytical tools for evaluation of the problem
are less developed and validated, relative to models developed for water bodies.
The physical processes and spatial variability involved in surface runoff,
sediment transport, and dissolved contaminant transport are very complex and
are difficult to characterize from a fundamental, conservation-of-mass point of
view. Accordingly, the available models all use varying degrees of empirical
equations to represent the physical processes.
The physical processes are based on the hydrologic cycle. The important
mechanisms incorporated, to varying degrees, in different runoff models include
3-27
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precipitation, evapotranspiration, overland flow, and groundwater recharge/
discharge. The various mechanisms important to the evapotranspiration process
include: interception, depression storage, and transpiration by plants. Sur-
face runoff or overland flow is the primary means for the transport of sedi-
ments and dissolved contaminants from the land surface to a water body.
Groundwater discharge is another pathway for dissolved contaminants to reach
the water body.
Within the overland flow, various sediment transport processes are impor-
tant. They include bed load, contact load, saltation load, and suspended load.
The primary kinetic process included in most runoff models is adsorption and
desorption. Other processes may be present, but in many models it is assumed
that the time scale of the runoff process, on the order of hours, allows one
to ignore the other transformation processes until the pollutant has reached a
water body. A few models also evaluate the transport of dissolved contaminants.
The available models for the analysis of nonpoint source pollutants can be
generally placed in three categories, based on their purposes and formulations
(Homer et al., 1986):
(1) Simple pollutant yield models,
(2) Empirical loading functions, and
(3) Nonpoint source simulation models.
Other categories are suggested by Huber and Heaney (1982) and Reckhow et al.
(1985).
3.8.1. Simple Pollutant Yield Models
The pollutant yield models generally specify pollutant loading rates, due
to runoff, as a function of the product of a concentration and a runoff rate.
3-28
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The pollutant concentration must be measured or estimated from available
literature. Some methods incorporate an exponential decay to the source term
as a means of representing a first-flush effect after a deposition period.
The pollutant yield models are commonly applied to a design storm of
selected frequency and magnitude. No routing of the pollutant from source
areas to the water body is included, and no adsorption or desorption phenom-
ena are explicitly analyzed. The methods are useful for a screening-level
analysis, and are somewhat more suitable for urban areas with larger amounts of
impervious.area than for agricultural areas.
3.8.2. Empirical Loading Functions
The most common empirical loading function is the Universal Soil Loss
Equation (USLE) by Wischmeier and Smith (1965). The original form of the equa-
tion was developed to predict-erosion losses, from croplands in the midwestern
United States. The USLE is intended to generate mean annual results, not
specific event results or annual results for a specific year. The form of the
equation is:
Y(s) = Rf . Kf Lf - Sgf Cf Pf
(Eq. 3-9)
where
Y(s) is the sediment yield (mass/unit area-year),
Rf is the rainfall factor, expressing the erosion potential of average
annual rainfall (product of the kinetic energy of rainfall, in
units of length-mass/area, times average annual maximum 30-minute
rainfall intensity of all significant storms, in units of depth/
hour),
Kf is the soil credibility factor (mass/unit area-unit R),
Lf is the slope length factor (dimensionless ratio),
3-29
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Sgf is the slope gradient factor (dimensionless ratio), ' , .
Cf is the cover factor, accounting for land surface;features (dimension-
less ratio), and
Pf is the erosion control practice factor (dimensionless ratio).
This equation was developed to estimate sediment loss from an agricultural
plot. Additional work by other researchers has resulted in modifications of .
this equation to account for sediment delivery from the plot to the water body
(McElroy et al., 1976). A variety of modifications to the general form of the
!
USLE have been utilized by various authors, and a review is included in-Horner
et al. (1986). ,
3.8.3. Nonpoint Source Simulation Models ,
Simulation models attempt to represent the major important processes of
the hydrologic cycle. Generally, the hydrologic -portion of these models is;
based on the conservation of mass (volume of water). The watershed is repre-
sented as one area or a series of subareas. Within specific areas, the water-
shed is separated into, a group of storage zones. The transfer of water between
the storage zones is represented by empirical transfer functions. The size of
the storage zones and the coefficients of the transfer functions are problem-
dependent parameters that need to be defined in the conceptualization-and .
calibration phases of the modeling study., , , ;
One of the earliest nonpoint source simulation models'was the Stanford,/,
Watershed Model (SWM) (Crawford and Linsley,-1962). The model simulates the
runoff of water from a-watershed. .Many.of the existing transport models use
the framework of the Stanford Watershed .Model as the basis of the hydrologic
portion of modeling analysis. - - , ,
The nonpoint source simulation, models are the most complex class of runoff
models. It is important to note that they still rely on some empirical rela-
3-30
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tionships, as do the pollutant yield models and empirical loading functions,
and hence, are quite sensitive to the calibration process. When properly
calibrated, they have been shown to be capable of reproducing measured data.
When calibrating the simulation models, two issues must be addressed. The
first is based on the volume of runoff, and the second is based on the concen-
tration of contaminants in the runoff. In general, these models are better
able to reproduce the volume of runoff than the contaminant concentration in
the runoff. This is due to a variety of factors, including the complexity of
the different processes, the availability of reliable calibration data, and the
dependence of concentration estimates on runoff volumes. Without sufficient
field data to calibrate the model, the results may not be accurate.
The selection of a nonpoint source runoff model should depend upon the ob-
jective of the exposure analysis and the desired accuracy of the model results.
For example, a simple objective, would be to evaluate the effects of runoff into
a lake on an annual basis. If'the purpose is to identify the contaminant in-
puts into a specific water body, such as a lake, on an annual basis, the sim- .
plest choice is a modified form of the USLE. If the objective is to evaluate
the effects of runoff on a time-varying scale, a continuous simulation model
is a better choice. A continuous simulation model would provide much more de-
tailed and somewhat more accurate time-dependent information, but at a much
higher cost. The continuous simulation model should be able to give the user
more accurate results by incorporating specific; characteristics of the water-
shed and regional weather patterns; If all of the detailed time-dependent
pollutant loading data are to be averaged into an annual loading rate, the
justification for using a continuous simulation model is small, and the user
should consider a model that incorporates annual time scales.
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4. IDENTIFICATION OF MODEL PROCESSES
In order to select a model appropriate for a specific situation., the model-
er must first identify those transport and degradation processes which are the
most important or dominant factors. However, before a model is selected, the
analyst should attempt to determine whether or not a potential contamination
problem exists. If an existing site is being considered, this determination
should be accomplished via direct field measurements. If the analysis is de-
signed to evaluate, the potential effects where an actual contaminant discharge
has not occurred, a screening-level or preliminary exposure assessment analysis
is necessary. Probably the best name for this step of the modeling study would
be an order-of-magnitude analysis.
A variety of screening procedures for different types of water bodies are
described by Mills et al. (1985). These screening procedures start from simple
dilution calculations and proceed to slightly more complex analytical solutions,
including some forms of transport and first-order degradation. These types of
analysis can usually be performed with a hand calculator. In virtually every
situation, the screening procedures of analysis should be performed before the
process of model selection for a more detailed analysis is started.
The first level of a screening procedure, when evaluating potential con-
taminant concentrations in a water body, is to estimate the dilution based on
the contaminant discharge divided by the river flow rate. This approach is
called mass balance, and is shown in Equation 4-1.
where
C = JL
Q
4-1
(Eq. 4-1)
-------
C is the concentration in the river (M/L3,)
m is the mass discharge rate to the river (M/T), and
Q is the flow rate of the river (L3/T).
Mass balance makes the assumption that the mass of the contaminant is uniformly
mixed across the water body. For exposure purposes, the assumption is that the
receptor is exposed to the average concentration given by m/Q. If uniform mix-
ing occurs, this assumption is obviously true. Even if uniform mixing does not
occur, the average or "expectation" value for the concentration may be the best
number to use if the actual concentration to which the receptor is exposed is
unknown. In the vicinity of the discharge, the mass balance approach may under-
estimate peak concentrations.
The next level of complexity in the screening procedure is to apply
analytical solutions to the advection-dispersion equation in the vicinity of
the discharge source. A variety of-analytical solutions are available (Fischer
et al., 1979; Mills et al., 1985). If the results of this screening procedure
indicate that a predicted concentration is several orders of magnitude less
than some regulatory standard or "safe" exposure level, then a more detailed
analysis is probably not necessary. If the results of this approach indicate
that a predicted concentration is within an order of magnitude, or greater than
some regulatory standard or "safe" exposure level, then a more detailed model-
ing analysis may be necessary.
The value of the screening-level analysis is that it is simple to perform
and may indicate that no significant contamination problem exists. It will
also aid the user in conceptualization of the physical system, identification
of important processes, and location and determination of available data. The
assumptions used in the preliminary analysis should represent a reasonable
worst-case condition (conservative), such that the predicted results over-
4-2
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estimate potential conditions, limiting "false negatives."
If the field measurements and/or screen-ing analysis indicate that a con-
tamination problem exists, then a modeling study may be useful. The analyst
must first identify the important processes to be incorporated in the modeling
study. The remainder of this chapter describes some simple analytical means
for comparing the importance of different^processes that may be incorporated.
4.1. TRANSPORT PROCESSES
. In order to assess the relative importance of different mixing, degrada-
tion, and transport processes, several techniques are suggested by Schnoor
(1985), Eschenroeder (1983),,and Fischer et al. ..(1979). The techniques include
the use of dimensionless parameters and characteristic mixing times. Three
characteristic mixing times are suggested by Eschenroeder (1983): advection
time, t/^; diffusion time, t^; and transformation time, tj. The advection time
is proportional to the principal length scale of the domain, 1, divided by the
mean velocity, u: ' ,
tA ~ 1/u (Eq. 4-2)
The diffusion time is proportional to the square of the transverse direction,
W,. divided by the dispersion coefficient, D:
tD ~ VT/2D
(Eq. 4-3)
The transformation time is proportional to the reciprocal of the rate coeffici-
ent, k: , ,
tT
(Eq. 4-4)
4-3
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These three parameters are very simple but quite useful in the model selec-
tion process. The basic concept is that if one specific characteristic mixing
time is much smaller than the others, that process may transport or degrade the
chemical before the other processes have a significant effect. If the transfor-
mation time is much smaller than the advection and diffusion time (tj << t^ and
ty « t0) then there should be a rapid chemical change before significant move-
ment occurs. In this case a far-field model may not be necessary because the
chemical degrades in the near field. If the diffusion time is much smaller
than the advection time and the transformation time (tp « t^ and tp « tj),
then the process is dispersion-dominated, and contaminant may be spread nearly
uniformly throughout the water body. In this case a box model, potentially
a zero-dimensional (CSTR) analysis, may be appropriate. The last example
described by Eschenroeder (1983) is the situation in which all three mixing
times are of the same order of magnitude (t^ ~ tg ~ tj). In this situation,
all three processes act simultaneously, and an appropriate model should include
advection, dispersion, and chemical reactions.
The use of appropriate dimensionless parameters in the screening phase of
an analysis is suggested by Fischer et al. (1979) and Schnoor (1985). The
basic idea behind dimensional analysis is to define useful dimensionless groups
of variables that describe physical and chemical processes and may provide the
basis for comparisons between models and prototypes. Many dimensionless para-
meters have been derived, and it is not necessary for a modeler to rederive
them. Rather, the existing parameters may be used as a means of estimating the
importance of different processes.
The first dimensionless parameter to examine is the Peclet number, defined
as
4-4
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PE = ul/D
(Eq. 4-5)
where
u is the mean velocity (L/T),
1 is the segment length (L), and
D is a dispersion coefficient (L2/T).
This dimensionless parameter is a ratio of the advective transport process to
the dispersive transport process. If the Peclet number is significantly great-
er than 1.0, the system is advection-dominated; if it is much less than 1.0,
dispersion dominates the transport of dissolved conservative substances.
Another useful dimensionless parameter is referred to as a Reaction number,
defined as
Rvw = kD/u2
(Eq. 4-6)
where k is a first-order reaction rate constant representing a transformation
process or combination of processes (1/T). This dimensionless parameter is the
ratio of the combined effect of reactions and dispersion to that of advection.
Schnoor (1985) suggests that if the Reaction number is greater than 10, the
system may be approximated as completely mixed (under steady conditions). If
the Reaction number is less than 0.1, advection dominates and a plug flow model
(advection only, no dispersion) may be adequate. If the Reaction number is
greater than 0.1 and less than 10, the analyst must consider both advection
and dispersion as important processes. This same dimensionless parameter is
referred to as an estuarine number by references cited in Souther!and et al.
(1984).
4-5
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A third dimensionless parameter useful in identifying important processes
in estuarine systems is called an "Estuarine Richardson Number" by Fischer
(1972), and is defined as
R = C(AP/p)g Qf]/W Ut:
(Eq. 4-7)
where
R is the Estuarine Richardson Number,
Ap is the difference in density between the river and ocean water (M/L^),
p is the density of the ocean water (M/L^),
g is the acceleration of gravity (L/T2),
Qf is the freshwater inflow (L3/T),
W is the channel width (L), and
Ut is the root mean square tidal velocity (L/T).
< . ...-,... ,.»
This parameter is a ratio of the input of buoyancy from the river, to the mix-
ing power available from the tide. Estuaries with very large R may be expected
to be strongly stratified, and those with very small R values are likely to be
well mixed. A very approximate range suggested by Fischer et al. (1979) is
that the transition from a 'well-mixed to a strongly stratified estuary occurs
for (0.08 < R < 0.8).
4.2. DEGRADATION PROCESSES
The choice of important or necessary degradation processes to be incor-
porated into a model depends primarily on the chemical and physical properties
of the contaminant of interest. Secondary in the choice of degradation pro-
cesses are various properties of the water body which may have some effect on
the transformation process. A simple example is related to the adsorption of a
contaminant by particulate matter. If a contaminant has a high affinity for
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adsorption, as do many hydrophobia compounds, the adsorption process will be
an important part of the analysis. For compounds that have a relatively low
affinity for adsorption, the process may not be as important; however, the
characteristics of the water body need to be considered. If the sediment load
in the water body is low, then ignoring adsorption should not have a signifi-
cant impact on the results unless benthic concentrations are important. If
the sediment load in the water body is very high, a significant amount of the
contaminant may be removed from the water column even though the contaminant
has a low affinity for adsorption.
In order to estimate the relative importance of the different degrada-
tion processes influencing the fate of pollutants in the aquatic environment,
the reader is referred to several useful references: Callahan et al. (1979),
Tinsley (1979), and Mills et al. (1985). Another good reference for estimating
the importance of various degradation processes, along with methods for esti-
mating specific rate coefficients, is Neely and Blau (1985). If some degrada-
tion or transformation process is identified as being important for a particular
contaminant, then rate constants used in the description of the kinetic process
must be estimated from a review of available literature or experimental measure-
ments.
When examining different processes affecting a particular chemical, the
half-life or some other representative decay time is a good indicator of which
processes to incorporate and which to ignore. For example, if the different
processes we wish to examine have time scales that differ by orders of magni-
tude (minutes versus days), then it is usually appropriate to focus on the
process that has the much shorter decay time.
4-7
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5. MODEL SELECTION CRITERIA
The purpose of this section is (1) to describe a specific series of
steps, the selection criteria, that may be used in the process of evaluating
the important physical and chemical characteristics of the study area, and (2)
to match those characteristics with the capabilities of available models when
used in exposure assessments. In the first part of this chapter, we discuss
the formulation and structure of the selection criteria. In the second part,
we discuss the specific selection criteria and how they apply to different
types of water bodies. The final section includes a summary of some of the
available models.
The selection of models for the analysis of exposure to contaminants
involves factors addressing a number of issues, not all of which are amenable
to expression in specific criteria. Certain judgmental factors are better
suited to statement in the form of general guidelines and principles. Many of
these guidelines and principles arise from the nature of the overall modeling
process, of which model selection is but a single step. Five general steps may
be identified in the modeling process. Although model selection is meant to be
the primary emphasis of this report, the different steps influence each other
and need to be described. The five general steps are:
(1) Problem Characterization The analyst clearly identifies the expo-
sure assessment study objectives and constraints.
(2) Site Characterization The analyst reviews available data on the
site, develops a conceptual model identifying processes of interest,
and performs a preliminary exposure assessment. If a model study is
necessary, the next step is to identify and obtain necessary data.
The results of the site characterization will determine technical
5-1
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specifications for model selection by identifying the significant
processes at the site.
(3) Model Selection Criteria The analyst matches the objective, tech-
nical , and implementation criteria to available models and selects
the most appropriate model(s).
(4) Code Installation If the model selected is a computer code, the
code is installed on the computer system and tested to document pro-
per installation and ability to reproduce accepted solutions to
standard problems.
(5) Model Application The verified model uses site characterization
data as input for the exposure assessment simulation.
These five general steps are not the model selection criteria, but rather
the overall process by which a problem is identified and a model selected.to
perform an exposure assessment study. Model Selection Criteria is listed as
the third step in this process. The two previous steps, Problem Characteriza-
tion and Site Characterization, are crucial in the selection of appropriate
model(s). While the steps can be considered sequential in nature, it is
important to recognize interactions and feedback mechanisms between them. For
instance, knowledge of the Model Selection Criteria is important to assure that
Site Characterization is adequate and properly formatted. An understanding of
Code Installation procedures is required for proper scheduling and resource
allocation. Familiarity of candidate models is needed to assure that Site
Characterization provides necessary input data.
The first step of the process, Problem Characterization, is important
because a wide variety of models and modeling approaches are available. Dif-
ferent modeling techniques are suitable for different objectives and physical
problems. The exposure assessment objectives must define what the goals of the
5-2
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analysis should be and also must be defined in a manner consistent with known
project constraints, such as schedule, budget, and other resources.
The second step of the process, Site Characterization, is an important
step because the conceptualization of the physical system, whether it is a
specific site or a generic problem, will obviously influence any additional
steps. If the objectives of the exposure assessment are to evaluate,an exist-
ing known contamination problem, then this step should include field measure-.
ments and/or review of available data pertinent to the specific study area.
Depending on the specific type of water body, the field measurements may in-
clude: pollutant concentration, depth and channel characteristics, flow rate,
velocity profiles, salinity profiles, temperature profiles, sediment charac-
teristics, and overall dispersive characteristics. Field measurements may
identify the extent of the contamination problem and whether or not the con-
centration levels are above some regulatory or dangerous level. In addition,
if these initial studies identify a contamination problem and a modeling study
is to be performed, then the field measurements will be used in the selection
of appropriate model(s) and for model calibration.
If the objectives of the analysis are to evaluate a potential problem
where an actual contaminant discharge has not occurred, then field measurements
of pollutant concentration are obviously not possible. Under these circum-
stances a screening level or preliminary exposure assessment approach is neces-
sary. The simplest screening analysis is described in Chapter 4. The results
of a preliminary exposure assessment should indicate whether or not a more
detailed analysis is necessary.
The third step in the process, Model Selection Criteria (the primary goal
of this report), is entirely dependent on the first two steps. This step is
covered in more detail in the rest of this chapter.
5-3
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The fourth step, Code Installation, only applies when the model chosen in
the third step is a computer code. When a code is first obtained and installed
on a specific computer system, it is essential that the model be tested to veri-
fy that it is working correctly and can reproduce suitable example problems.
Various computer systems and the necessary model software may have a variety of
differences, some distinct and others more subtle. These differences may re- '
quire some modification to an acquired code (e.g., changing output formats) on
different computer systems. Verification assures that modifications have not
changed model results significantly. This step should be performed by the
individual doing the model analysis.
The fifth step of the process, Model Application, relates to the use of a
model in an attempt to answer the questions defined in the objectives. Depend-
ing on the objectives of the analysis, this step may consist of several parts,
including calibration, validation, and application of a model for different
conditions or scenarios.
5.1. STRUCTURE OF THE MODEL SELECTION CRITERIA
The proper selection of a model is essential to the successful simulation
of an exposure assessment for surface water systems. This section defines in
detail Step 3 of the general modeling process, Model Selection Criteria. *
The structure of the Model Selection Criteria is as follows:
(1) Objectives criteria specify the nature and intent of the analysis to
be performed. ,
(2) Technical criteria specify the site-specific processes to be simulated
by the model.
(3) Implementation criteria specify the quality assurance (QA) and documen-
tation requirements. ;
5-4
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The objectives criteria may be roughly classified as preliminary exposure
assessment or site-specific (detailed) exposure-assessment analysis. The study
context and objectives determine the amount of uncertainty permitted, which in
turn, together with the system characteristics, determine the degree of tech-
nical complexity required in the modeling process. The simplest exposure
assessment models require restrictive assumptions regarding the dimensionality
and time variability of the system, along with the formulation of kinetic pro-
cesses. The more complex exposure assessment models may relax some of the re-
strictive assumptions; however, more extensive input data are usually required.
The selection of simplified exposure assessment techniques can only be justi-
fied if the project objectives are defined as a preliminary exposure assessment
and/or the technical specifications for model selection are satisfied (see next
section). Implicit in the objectives criteria must be a realization of the
available resources, including staff and money. When available resources are a
limiting factor, the objectives of the study must be defined within, the appro-
priate context.
The technical criteria for model selection are based primarily on: (1)
physical mixing and transport processes; (2) biological, .chemical, and physical
degradation and transformation processes; and (3) geometry and/or dimensional-
ity and time variability of the system. In Chapter 3 of this report, the im-
portant processes relative to different water bodies are described; In Chapter
4, simplified means are presented for assessing the relative importance of the
different processes. ,
The implementation criteria are related to the degree of quality assurance
(QA) and documentation to which a model has been subjected. It is .preferable
to obtain exposure assessment codes from federal agencies and departments where
stringent QA procedures are in effect. Whenever possible, public domain codes
5-5
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should be selected.
Documentation requirements refer to selecting models for which user's man-
uals and test verification documentation exist. Test problems for comparison
should be available in the user's manual or from the source where the model was
obtained. This requirement is necessary for step 4 of the general modeling
process, Code Installationi It is not mandatory that such documentation exist
for the selected model; however, it is strongly recommended that the analyst
select standard, well-documented models', particularly if the model selected is
a computer code. If possible, models should be selected for which site-spe-
cific simulations are documented in the open literature and for which the model
results were compared with field data.
Other general aspects of Model Selection Criteria which should never over-
ride the objective, technical, or implementation criteria include schedule,
budget, and staff and equipment resources. Time and cost constraints, as im-
posed by mandatory schedules and budgets, must be incorporated into the defini-
tion of project objectives and may dictate both the type of model selected and
the general modeling approach. In cases where both the simpler and more com-
plex models meet the selection criteria, one should then consider time to run
the modeling analysis and projects costs as deciding factors. Time require-
ments will be important if staff .are not familiar with any of the appropriate
models. These constraints may require the use of a different modeling team
that is experienced with the selected models. ,
Staff resources are also a major consideration in modeling. Regardless of
the quality of the model selected, the expertise of the analyst has a major
impact on model results. Staffing can also affect model selection when the
analyst is familiar with one or more of the appropriate models. , In the sim-
plest case, if the analyst has direct experience with an acceptable model, then
5-6
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tYiat model is preferred. Similarly, if the analyst has experience with a par-
ticular type of model (e.g., finite element versus finite difference), one of
that type should be selected. In certain cases, familiarity with a model more
complex than required may dictate the use of that model, since there will be no
loss of resolution and the added staff experience would compensate for time and
cost differences. In no case, however, should familiarity with a model dictate
its selection when it does not satisfy the objective, technical, and implemen-
tation criteria.
Hardware requirements and availability are also major considerations in
modeling. The more complex mathematical codes require more powerful computers
with larger mass storage devices and extra peripheral equipment. If both ana-
lytical models and those based on computer codes meet the selection criteria,
available hardware may dictate the use of the simpler analytical model. If a
sophisticated code is required and adequate equipment is not 'available, alter-
nate means of conducting the modeling must be found. Equipment constraints
should not be used to justify the use of a model'that does not meet the selec-
tion criteria.
5.2. MODEL SELECTION PROCESS
This section describes the model selection process in detail. It is
assumed at this point that a preliminary exposure assessment has been performed
and the results indicate that a more detailed analysis is necessary. It is
also assumed that data from the study area and contaminants of interest have
been sampled and collected. Table 5-1 illustrates the selection process in the
form of an outline. The remainder of this section describes in more detail im-
portant considerations related to each step of the outline. Wherever possible,
we have provided some guidance with regard to potential errors (under-predicted
versus over-predicted concentration levels) that may result from an inappropriate
model choice.
5-7.
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TABLE 5-1. OUTLINE OF THE MODEL SELECTION PROCESS
I. INITIAL ANALYSIS
A. Identify project objectives
B. Identify contaminant sources
C. Identify chemical and physical properties of the contaminant
II. SELECTION OF A NONPOINT SOURCE RUNOFF MODEL
A. Identify the type and use of the land area
B. What time characteristics are necessary?
C. What are the spatial characteristics of the area?
D. Identify the important physical, chemical, and biological
processes
E. Select a nonpoint source runoff model ,
III. SURFACE WATER FLOW
A. Identify the water body as a river, lake, or estuary
B. Is the water body stratified or well mixed?
C. Steady-state or transient analysis necessary?
D. One-, two-, or three-dimensional analysis?
E. Select appropriate model for surface water flow
IV. SURFACE WATER CONTAMINANT TRANSPORT
A. Point or nonpoint sources?
B. Steady-state or transient analysis necessary?
C. One-, two-, or three-dimensional analysis necessary?
D. What are the dominant mixing and transport processes?
E. Are sediment contaminant interactions important?
F. What biological, chemical, and physical reactions need to be
incorporated?
6. Select appropriate model for surface water contaminant
transport analysis
5-8
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I. INITIAL ANALYSIS . :
I.A. Identify Project Objectives
The first step in the selection of a model or models is a clear definition
of the purpose of the modeling study. What is the particular contaminant(s) of
interest? Exposure assessment models are commonly, used as, predictive tools for
the evaluation of chemical hazards and various pollution control scenarios. In
defining the study objectives, some characterization of the acceptable uncer-
tainty is necessary. The objectives and associated acceptable uncertainty must
be defined in the context of the available budget, time and staff constraints.
If available resources pose a limiting constraint, the study objectives may
necessarily be defined as a preliminary exposure assessment analysis.
The types of methods or models used will depend upon the project objec-
tives. For example, a three-dimensional, transient analysis may be required
to identify maximum point concentrations resulting from a hypothetical spill
of toxic materials. In contrast, a one-dimensional, or possibly a zero-dimen-
sional, steady-state model may be appropriate for the analysis of nonpoint
discharges into a lake. If an analysis is being performed to determine if a
water quality standard is exceeded, the specific constraints of the standard
may define several aspects of the appropriate model. Walton et al. (1984) re-
fer to these constraints as regulatory scales. Examples of these constraints
are allowable mixing zones near discharges and short time frames where some
standard may be temporarily exceeded. A model that can resolve these charac-
teristics spatially and temporally must be chosen.
I.B. Identify Contaminant Sources
The sources of the contaminants entering the water body need to be identi-
fied. The different types of sources may include instantaneous point sources
due to spills, continuous point sources such as discharge from a pipe, and non-
5-9
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point sources due to surface runoff. Along with the location and type of the
contaminant sources, the specific contaminants of interest must be identified.
The identification of contaminant sources is a very important step that
will help define the sequence of choices related to model dimensionality, time
frame, and degradation processes. However, not all models may incorporate
the types of source terms existing in the physical system. The obvious exam-
ples are point sources, such as a pipe discharge, versus distributed nonpoint
sources, such as surface runoff, and transient source terms, such as a cyclic
discharge or a spill, versus a continuous discharge.
I.C. Identify the Chemical and Physical Properties of the Contaminant
Once the specific contaminant of interest has been defined, the next step
is to identify the chemical and physical properties of the contaminant. Many
toxic chemicals are subject to a variety of degradation and transformation pro-
*
cesses. Depending upon the chemical, only specific processes may be important.
These processes may include hydrolysis, oxidation and reduction, photolysis,
volatilization, ionization, and degradation due to biological activity.
Another important process, sorption to sedimentary materials, may affect the
fate of heavy metals and many hydrophobic compounds. To determine "the chemical
and physical properties of the contaminant may involve laboratory experiments
and/or a review of the available literature. Sources of data available in the
literature include Callahan et al. (1979), Mills et al. (1985), and Neely and
Blau (1985).
II. SELECTION OF A NONPOINT SOURCE RUNOFF MODEL '
Several approaches for the selection of specific pollutant runoff models
are described by Reckhow et al. (1985) and Huber and Heaney (1982). The ap-
proach outlined in this section is from Huber and Heaney (1982). <
5-10
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II.A. Identify the Type and Use of Land Area
Land areas may be roughly classified as urban or nonurban, with a variety
of subclassifications within each general category. Urban areas may be further
subclassifie as residential, commercial, industrial, and open-space. The non-
urban areas can be classified as agriculture, silviculture, and mining. Within
the agricultural subclassification, important categories may include irrigated
versus nonirrigated, different crop types, and tilled fields versus range land.
II.B. What Time Characteristics are Necessary?
The choice of particular time-dependent properties of different pollutant
runoff models should depend on the modeling objectives. Three categories of
time-dependence are incorporated in available models: (1) seasonal or annual
average; (2) continuous simulation; and (3) single-event simulation. The con-
tinuous-simulation models use a time step on the order of 15 minutes to 1 day,
and can be used to simulate study area conditions over one season or for sev-
eral years. The single-event simulation models use a time step on the order of
a minute, and are used to estimate runoff from a single rainstorm.
For a preliminary exposure assessment analysis, a long-term accumulation
such as a seasonal or annual average model is probably the best choice. If
project objectives include identifying peak time-dependent concentrations, a
continuous-simulation model will be necessary. If a very detailed analysis of
runoff is required, Huber and Heaney (1982) suggest that all three types of
models be used in sequence 1, 2, 3. The annual average analysis is used as an
initial approach, the continuous-simulation model is used to evaluate the
dynamic nature of different and multiple storm events, and the single-event
simulation is used to evaluate specific storm events determined to be the most
crucial.
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II.C. What are the Spatial Characteristics of the Area?
The physical size of the study area and whether multiple catchments or
zones need to be defined in the model are important spatial characteristics' of
an area. The catchment size is important in determining whether or not flow
routing is necessary. A "very crude rule of thumb" offered by Huber and Heaney
(1982) is that routing effects should be considered whenever the catchment size
is greater than 50 acres.
If the area of interest contains separate catchments with distinctly
different land use practices, such as an agricultural area versus a forest, a'
model capable of simulating multiple catchments is necessary.1 Some models are
designed to evaluate one specific area, such as an agricultural field, while
others have multiple catchment capabilities. ,
II.D. Identify the Important Physical, Chemical, and Biological Processes
A significant physical characteristic is catchment size. In small catch-
ments, flow routing may not be as important when compared to larger catchments.
Snowmelt runoff is another physical process that affects nohpoint source runoff
conditions. A physical process to consider in urban areas is runoff storage in
engineered facilities. The. interactions and degradation of different chemicals
in the soil system and root zone may also be very important processes for
determining the proper model for specific applications in agricultural areas.
Models that treat these interactions are available, and may be the best choices
to satisfy certain project objectives.
II.E. Select Nonpoint Source Runoff Model
After completing steps I.A, B, C, and II.A, B, C, D of the Model Selection
Process, the user should proceed to Table 5-2, which is the summary matrix of
nonpoint source runoff models. Using Table 5-2, the user should compare the
capabilities and characteristics of the available models with the needs of the
5-12
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specific study, and select a model, or group of models, that best satisfies
those needs.
III. SURFACE WATER FLOW /
In the analysis of many water quality problems, the dominant mechanism for
the transport of contaminants is the advection of dissolved and particulate
contaminants by the flowing water. For this reason, it is necessary to charac-
terize the flow patterns within the water body. Characterizing the flow within
a water body could result in choosing one of several different strategies.
These include extensive field measurements, limited measurements coupled with
a numerical hydrodynamic model, and examination of historical records of flow
rates. The rest of this section will deal with the selection of numerical
hydrodynamic models. Under some conditions, such as a preliminary exposure
assessment using a simple steady-state model, this surface water flow section
can be bypassed if the user assumes only low-flow conditions.
III.A. Identify Water Body as a River, Lake, or Estuary
To choose a hydrodynamic flow model, one must first classify the water
body as a stream or river, lake or reservoir, or estuary. Although these
classifications seem fairly distinct, some cases may arise in which the classi-
fication is not clear and engineering judgment must be exercised. An example
of such a classification problem could be the difference between a run-of-river
reservoir and some upstream reaches of river estuary systems. Within these
general categories, there are several subclassifications. Estuaries may be
classified as well-mixed, partially mixed, or salt-wedge types. Lakes may be
classified as shallow run-of-river impoundments with relatively short residence
times (weeks), or as very deep impoundments with long residence times (years).
The proper classification of a water body will help determine the dominant
transport and mixing process. In addition, the water body classification could
5-14
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also help determine the correct choice of model dimensionality. Well-mixed
estuaries may, in some cases, be adequately represented using a one-dimension-
al, longitudinal model. In contrast, a salt wedge or sharply stratified estu-
ary will require, at a minimum, a two-dimensional, longitudinal, and vertical
model to adequately represent the important transport and mixing processes.
For the intermediate, partially mixed estuary, the selection of the model and
the model dimensionality may not be obvious and will require additional judg-
ment by the user. The model selection should depend on various factors, but
should stay within the project objectives of the study (e.g., necessary accu-
racy).
III.B. Is the Hater Body Stratified or Hell Mixed?
The next step is to identify whether the water body is stratified or well-
mixed over the vertical water column. This step does not usually apply to
rivers. Stratification results from density variations due to temperature
differences in lakes, and salinity and temperature differences in estuaries.
Stratification is commonly a seasonal phenomenon in many lakes and in deep,
fjord-type estuaries such as the Puget Sound. If stratification is significant
within a particular water body, it is necessary to analyze the vertical dimen-
sion along with other spatial dimensions.
The best way to determine whether or not stratification exists is by
examining measurements of salinity and/or temperature over the vertical water
column. Approaches for estimating the density of water as a function of tem-
perature and salinity are included in Fischer et al. (1979). If such measure-
ments cannot be made or are not available, predictions of the degree of thermal
stratification should be made as specified by Mills et al. (1985) for reser-
voirs. The same authors state that stratification may be the single most
important phenomenon influencing water quality in many impoundments. The
5-15
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Estuarine Richardson Number described in Chapter 4 can be used for determining
the stratification for estuaries.
III.C. Steady-State or Transient Analysis
Once the water body is classified, the next step is to determine whether a
steady-state or transient analysis is necessary. Several factors must be con-
sidered in this decision, including project objectives, contaminant sources,
chemical and physical properties of the contaminants, and characteristics of
the water body. A steady-state analysis would be appropriate for problems
where the project objective is to identify waste load allocation procedures,
the source terms are known or assumed to be constant, and the flow field is
based on some minimum flow rate in a river. For any problems dealing with in-
stantaneous sources, such as spills, a transient contaminant transport analysis
is required, but a steady-flow analysis may be adequate if the flow field does
not change significantly over the time frame of the analysis. Rivers and lakes
could have flow fields that do not change significantly over the time require-
ments of the analysis.
For estuaries the flow system is dynamic, with approximately a twice-daily
cycle. For contamination problems that occur at a single time (instantaneous
sources), a dynamic flow field is necessary in order to understand the effect
of the contaminants as they are carried away from the source. For contamina-
tion problems that occur over a long time period (continuous sources), a
tidally averaged flow field could be appropriate. If a tidally averaged flow
field is used, the model will require field measurements of salinity to deter-
mine the dispersion coefficients. The salinity measurements will help to
characterize the intra-tidal advective transport that is not represented in the
tidaily-averaged analysis.
5-16
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Where a transient analysis is used, two factors are important in defining
the time step. The first factor relates to the time scale determined by pro-
ject objectives, regulatory standards, and the rate of biological and chemical
degradation. The second factor relates to stability criteria resulting from
the implicit or explicit integration of the time-derivative terms in the gov-
erning equation. Individual models will have different stability criteria.
The documentation and user's manual identify the time step and spatial resolu-
tion relationship necessary for stability.
III.D. Is a One-, Two-, or Three-Dimensional Analysis Necessary?
The dimensionality of the flow field analysis is also dependent on various
factors including project objectives, source terms, and characteristics of the
water body. When studying water quality problems due to nonpoint sources in
lakes or rivers, a one-dimensional or, in some cases, for lakes, a zero-dimen-
sional analysis (for example, a continuously stirred reactor) is adequate
because of the uncertainty in measuring the actual nonpoint source. Almost all
other water quality problems are initially three-dimensional in nature. Mixing
processes, however, may distribute a contaminant uniformly or nearly uniformly
over one or more spatial dimensions. In rivers, one-dimensional, longitudinal
analysis is usually appropriate because mixing over the vertical water column
occurs relatively quickly due to dispersion as a result of shear flow. Mixing
in the lateral directions may also occur quickly. Situations where one-dimen-
sional analysis in rivers is not appropriate are: (1) determining the contam-
inant problem near the actual point sources because vertical and lateral mixing
may not be complete, and (2) when analyzing water quality problems in very wide
rivers (2,000 feet wide) because lateral mixing may take 10 to 100 miles before
it is completed. Analytical means for estimating the,distance of uniform
lateral mixing are described in Chapter 3. These methods are only approximate
5-17
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and should be interpreted as such.
The use of one-dimensional, longitudinal analysis in well-mixed estuaries
may be justified subject to the constraints discussed in Chapter 3. Other
estuarine systems will generally require a two- or three-dimensional analysis,
depending on project objectives. The existing two- and three-dimensional
estuarine hydrodynamic models are quite complex and expensive to use in terms
of both manpower requirements and computer costs. For the more complex models,
considerable experience is necessary in order to apply and calibrate these
models properly.
In most analyses of lakes with large residence times, a one-dimensional
vertical analysis is used. This type of analysis necessarily ignores the
horizontal circulation patterns resulting from wind stresses. Two- and three-
dimensional circulation models for lakes exist, but they are more in the
nature of research tools than the models considered herein. For run-of-river
reservoirs with short residence times, on the order of weeks to months, the
longitudinal variation of water quality may need to be examined in addition to
the vertical water column.
III.E. Select Appropriate Model for Surface Hater Flow
Incorporating all of the information in Sections I.A, B, C and 111.A, B,
and C, the next step is to choose a flow model with the necessary capabilities.
Table 5-3 lists the capabilities of various flow models. The choice of models
should be based on the listed criteria;, if more than one model satisfies all
the criteria, the simplest model;should be chosen. A somewhat more complex
model may be chosen based on availability and user familiarity. Another
important factor in the choice may be that a particular contaminant transport
model was developed to be used with a specific flow model such as CHNTRN (Yeh,
1982a) and CHNHYD (Yeh, 1982b). When a situation arises in which two particular
5-18
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models are coupled together and they satisfy all the criteria, the logical
choice would be a flow model because incorporating the results of a flow into a
transport model is the .least time-consuming procedure.
IV. SURFACE WATER CONTAMINANT TRANSPORT
After the flow field has been defined via field measurements and/or numer-
ical models, the next step is to choose a water quality model to evaluate the
transport and degradation of contaminants. A variety of available models are
applicable to most water bodies where the flow field has previously been de-
fined, including lakes, rivers, and estuaries.
IV.A. Point or Nonpoint Sources?
It is important to evaluate whether the model incorporates the types of
sources necessary. If the model does not incorporate point and/or nonpoint
sources, it may not be useful for the particular analysis. In some cases,
nonpoint sources may be simulated as a series of point sources located along
the boundary of the water body where the nonpoint runoff enters the system.
This method should be adequate as long as the point sources mix together rela-
tively quickly in relation to the length scale of interest.
IV.B. Steady-State or Transient Analysis?
The choice between a steady-state and a transient model is dependent on
project objectives, source terms, and characteristics of the water body. Pro-
ject objectives, such as waste load allocation and design of effluent stand-
ards, may allow for the use of a steady-state model. When project objectives
are defined as a preliminary exposure assessment, where limited calibration
data are available, a steady-state analysis may be the best approach.
Transient models may be necessary when the effects take place within shor1
time frames and the concentration is rapidly varying. Steady-state models may
be appropriate when the source terms are known to be steady in time, and also
5-20
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in some cases where the cyclic variation in the source strength may be averaged
over time. , . .
The characteristics of a water body that pertain to the choice of a steady-
state or a transient model include the following: For rivers, the flow rate
and corresponding sediment transport; for lakes, the inflow/outflow rates and
residence time; and for estuaries, tidal excursion distances, flushing time,
tidal range, and river inflow rate. If the flow.rate of a river is highly
variable during the time frame of interest, a transient analysis is necessary.
9
Very high flow rates will also significantly change the sediment transport
characteristics that must be analyzed. For large and/or deep lakes with long
residence times, a steady-state or annual analysis may be indicated by the
flow conditions. For smaller lakes, a transient analysis may be necessary to
account for variability in inflow and outflow rates and the corresponding
residence times. In estuaries, if the tidal excursion distances are a sig-
nificant portion of the total length, a transient analysis is necessary. If
the tidal range or the river inflow rate varies significantly, a transient
* '
analysis is necessary.
If a steady-state model is used in a problem where the source terms are
time-variable, the steady state results will underpredict the peak concentra-
tions if the variable source term is averaged over time. If a different source
term is used, such as a constant source at the peak transient rate of discharge,
then the model results may overpredict the peak concentrations.
IV.C. One-, Two-, or Three-Pimensional Analysis?
The choice of dimensionality for the analysis of contaminant transport is
similar to the choice of dimensionality for the flow model. The choice of the
number of spatial dimensions to be incorporated in a given analysis should
depend primarily on whether or not the contaminant is completely or uniformly
5-21 -''
-------
mixed over a given spatial dimension. If field measurements are available,
the user should review the data to determine the contaminant mixing. If field
measurements are not available, the user should review Chapter 3 (Equations 3-4
and 3-5) to best determine the choice of dimensionality.
For any estuary or reservoir that is stratified, the vertical dimension
and the horizontal dimension should be analyzed. The analysis of large reser-
voirs with long residence times has traditionally been simplified to a one-
dimensional vertical problem. For rivers, one-dimensional analysis is usually
appropriate, except near point sources and for very wide rivers., The use of
one-dimensional, longitudinal analysis in well mixed estuaries is justified
subject to certain constraints described in Chapter 3. Other estuarine systems
will generally require a two- or three-dimensional analysis, depending on pro-
ject objectives.
In general, reducing the number of spatial dimensions analyzed may cause
the model to underpredict peak concentrations. If a water body is uniformly
mixed over a particular spatial dimension, dropping that dimension from the
analysis is justified. If a contaminant is not uniformly mixed, such as occurs
near point sources, the model results will underpredict the peak concentrations
in that vicinity.
IV.D. What are the Dominant Mixing and Transport Processes?
The significant mixing and transport processes within the water body must
be identified. These may include advection, convection, dispersion, molecular
diffusion, turbulent diffusion, shear, mixing by plumes and buoyant jets,
particle settling, and entrainment. The mixing and transport processes that
are predominant depends upon the water body the user is analyzing. Several
approximate means for determining the relative importance of different mixing
and transport processes are described in Chapter 4.
5-22
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As a general rule, advection in the longitudinal direction is necessary for
analysis of rivers, while in some cases (steady-state analysis, high velocities)
longitudinal dispersion may be, ignored without .significantly affecting results.
In the analysis of estuaries, both advective,and dispersive transport must be
considered. In. some seasonally stratified systems, convective transport due to
unstable stratification must also be, considered. , In lakes with long residence
times, dispersive and vertical convective transport are often the most signifi-
cant processes. In lakes with short residence times, advective longitudinal
transport is,the most significant process. .
IV.E. Are Sediment Contaminant Interactions Important?
Interactions between dissolved contaminants and particles should be exam-
ined for contaminants with jiigh affinity for particulate matter. Another sig-
nificant criterion is whether or not the water body has a significant sediment
load. The different, types of sediment may also be very important because ex-
periments have shown that some contaminants may have a high affinity to adsorb
to clays or organic material, and may have a lower affinity to adsorb to other,
more coarsely-grained sediments. ,.-..-
The degree of complexity used in the. analysis of sediment transport and
contaminant interactions with the sediment depends upon the objectives of the
analysis, the availability of data, and the type of. water body under consi-
deration. In, the analysis of lakes and reservoirs, the sediment, transport
processes are much simpler than those occurring in rivers and estuaries, and
the use of models in which the user specifies sediment fluxes is adequate. In
rivers and estuaries under, high flow rates, a .mechanistic sediment transport
model may be necessary to define sediment fluxes if the original objectives
include any sort of 'extrapolation beyond existing or measured conditions.
5-23
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IV.F. What Biological, Chemical and Physical Interactions Need to be
Incorporated?
The final criterion for the selection of a water quality transport model
is to identify the important biological, chemical, and physical interactions
between the aquatic environment and the particular contaminant. Some models
have been formulated such that other specific kinetic reactions may be easily
incorporated by a user as subroutines. Other important characteristics of the
contaminant include the degradation of original compounds into new compounds or
into daughters of the original contaminant. Several technical documents are
available which characterize the importance of different kinetic processes
affecting a variety of chemicals. These include Callahan et al. (1979), Mills
et al. (1985), and Neely and Blau (1985).
The majority of the water quality models addressed in this document incor-
porate all of the above physical and biochemical degradation processes. How-
ever, among the transport models there are some differences in the formulation
of reaction kinetics. Just two of the twelve models, EXAMS and HSPF, incor-
porate reactions of the daughters of the primary compound within the original
simulation. Some of the other ten models may be used to evaluate the degrada-
tion of the secondary substances using the results of previous model runs on
the primary compound.
IV.6. Select Appropriate Model for Contaminant Transport Analysis
Using all of the previous information, the next step is to select a trans-
port model. Combining the problem-specific information pertinent to each
selection criterion with the .model capabilities listed in Table 5-4, the user
should select a model or group of models appropriate for the specific problem.
The simplest model satisfying all of the previous criteria should be chosen.
Somewhat more complex models may be used based on availability and user famili-
5-24
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arity.
5.3. DIFFERENT APPLICATIONS
The selection criteria are written primarily from the point of view of an
analyst performing an exposure assessment study. The basic process begins with
defining project objectives, assessing a physical situation, and then selecting
a model to represent the important processes relevant to the project objectives ''
and physical conditions. Another use of the selection criteria is from the
point of view of a regulatory agency that is reviewing an exposure assessment
study. Under these circumstances, the reviewer needs to evaluate the choice
of the model used in performing the study. The selection criteria must be
fundamentally the same for both applications; one to select a model, the other
to determine if the model used is appropriate. This section is included to
describe the differences in both applications.
The first step in .reviewing the exposure assessment study is to identify
the characteristics and capabilities of the specific model. Examples of model
characteristics and capabilities are listed in the tables in section 5.4. The
models shown in section 5.4 do not represent all available models; other models
exist that may be appropriate for specific applications., A users's manual and
description of the model is necessary in order to review the choice of a spe-
cific model (see implementation criteria, section 5.1). From a user's manual,
the data relative to the different categories listed in Tables 5-2, 5-3, and v
5-4 must be identified.
The single most important step in choosing a model is to define project
objectives. Similarly for reviewing a model selection, the most important step
must be to identify what the objectives of the study are. The objectives of
the analysis should clearly state whether it is performed as a preliminary
exposure assessment, or if a more detailed site-specific analysis, with
5-26
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priate data for calibration and validation, is intended. In cases where the
objectives are not clearly defined, the only option is to interpret how the
results and conclusions of the study are presented (e.g., associated uncer-
tainty, potential impacts, and importance of decisions based on the results).
This could be difficult and may require a subjective decision. After this
initial step, the rest of the selection criteria are essentially the same for
both the selection of a model and review of a model selection by another per-
son.
It is important that the reviewer examine the presentation of results and
conclusions to see whether they are consistent with the,study objectives, model
choice, and model application. A preliminary exposure assessment should incor-
porate uncertainty in the nature of an order of magnitude at least. For more
detailed site-specific analysis, the validation phase of a modeling study may
provide, some guidance in defining the uncertainty associated with the model
predictions.
A simple example illustrating the relationship between the project objec-
tives, model choice, and results is as follows: Consider a preliminary expo-
sure assessment of some hydrophobic compound where sorption is important. For
a preliminary analysis, it is probably adequate to include all attenuation
mechanisms, including sorption, as a combined first-order decay term, and some
form of an analytical solution may be an appropriate model choice. The results
should be presented as a screening-level (orders of magnitude estimate) of con-
centrations in the water column. This type of estimate is consistent with the
project objectives and model choice. The analysis may not examine the accumu-
lation of contaminants in the bed sediments (depending on the specific analy-
tical solution) and, hence, no conclusions in relation to the importance of the
bed sediments can be made. Another modeling approach must be used to evaluate
5-27
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the accumulation of contaminants in the beds.
5.4. MODEL SUMMARY TABLES
Tables 5-2, 5-3, and 5-4 describe the capabilities and characteristics of
a variety of different models that may be used in an exposure assessment study.
The models included in the summary tables do not constitute an all-inclusive -
list of every available model. The user can choose from a number of other mod-
els that are available from a variety of sources. All of the models included
r
in Tables 5-2, 5-3, and 5-4 have some form of documentation and/or user's
manual. The properties of the models included in the tables were obtained by
reviewing user's manuals, literature sources describing specific model applica-
tions, and literature sources reviewing available models.
The tables are to be used by first proceeding through the appropriate part
of the selection criteria and noting the problem-specific characteristics rela-
tive to each selection criterion. This information will describe the needs of
the specific analysis. The problem-specific needs may then be compared with
the capabilities of available models and a model, or group of models, may be
chosen which best satisfy the needs of the specific problem.
Table 5-2 lists the capabilities of nonpoint source runoff models. Table
5-3 lists the capabilities of surface water flow models. Table 5-4 lists the
capabilities of surface water contaminant transport models. In terms of the
degradation and transformation processes associated with the transport models,
all of the models have a first-order decay term as a minimum. The first-order
decay coefficient may be defined to incorporate all of the different attenu-
ation processes. A single combined first-order decay coefficient will not
allow the user to understand the variability of process as a-function of chang-
ing environmental conditions. The models that incorporate a single combined
first-order decay term are: WQAM, SLSA, MICHRIV, CTAP> and FETRA.
5-28
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6. USE OF THE SELECTION CRITERIA
The purpose of this chapter is to show, by means of examples, h.ow the
selection criteria may be used. Two examples are included. The first relates
to a preliminary exposure assessement, and the second is a site-specific eval-
uation of a complex real problem. The same physical problem is used in both
examples, with different objectives defined for the two cases. The two exam-
ples are intended to illustrate that different project objectives will have a
distinct impact on the modeling process and selection of .appropriate models.
As this document is used and applied to actual exposure assessment studies,
future updates of this document will incorporate these studies.
6.1. DESCRIPTION OF EXPOSURE ANALYSIS PROBLEM
An exposure assessment group has been requested to perform an exposure
assessment on a former chemical recycling plant in the western end of the State
of Kentucky. .Land disposal of solvents at the facility resulted in the contam-
ination of the soils with heavy metals and organic and inorganic chemicals.
The site is about 20 acres in size, and is bounded by a stream that leads to
a larger river, which is used for drinking water supplies and aquaculture.
Vegetation on the site consists of tall weeds, trees, and shrubs on approx-
imately 2/3 of the site, with the remaining 1/3 barren.due.to roads, parking
lots, and disposal areas.
A variety of contaminants have been measured in the adjoining creek, in-
cluding benzene, toluene, trichloroethylene, and phenol. Samples of tissue
from fish in the adjoining creek and further downstream;in the river have in-
dicated bioaccumulation of heavy metals. .Much cleanup work has been performed
at the site, and.it is suggested that further work be done. The additional
work will cost several millions of dollars* and the parties responsible for the
6-1
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site question the amount of cleanup that is necessary. The decision will be
based in part on the expected risk to the public and on potential impacts to
the aquaculture facilities downstream.
The two levels of analysis, preliminary exposure assessment and detailed
site-specific assessment, have substantially different data requirements. The
preliminary exposure assessment will be based on a limited amount of field
data. The field data may include: an estimate of the mass of contaminants
disposed of at the site, a limited number of soil and surface water samples,
an estimated low-flow condition for a stream or river, and estimates of the
biochemical properties of the contaminants. The more detailed site-specific
analysis will require additional data on the amount of surface runoff, the
contaminant and sediment concentration in the runoff, precipitation and flow
rate records, stream sediment transport characteristics and contaminant con-
centration in the stream sediments, and downstream samples of contaminant
concentrations. As the study progresses, additional data,may be necessary.
6.2. PRELIMINARY EXPOSURE ASSESSMENT
6.2.1. Initial Analysis
The objectives of the analysis are to provide a reasonable order of magni-
tude estimate of the concentration of contaminants in the water column. The
first approach can be a relatively simple hand calculation. Using an estimated
loading term from some modified form of the USLE, and a recorded or assumed
low-flow condition, a simple dilution calculation could be generated. The
uncertainty in this calculation could be large, with as much as several orders
of magnitude difference from the actual contaminant concentration found in the
water.
The preliminary analysis consists of two components. The first is to
determine if a more detailed analysis is necessary. The second is to provide
6-2
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estimated ranges in terms of flow rates and downstream distances at which
sampling may provide useful calibration data. The primary concerns are the
potential contamination of drinking water supplies and the bioaccumulation of
the chemical in fish.
The constraints of the analysis are that it must be performed in a short
time frame, with limited resources, and that little field data are available.
With the limited amount of field data, the analysis is necessarily reduced to
a preliminary exposure assessment. The only source of the specific chemicals
entering the stream is from the land area surrounding the closed recycling
plant. The specific contaminants to be analyzed are heavy metals, such as
chromium, lead, mercury; and organics, such as trichloroethylene, phenol,
benzene, and toluene. Based on data presented in Callahan et al. (1979), the
following processes are important for the constituents of interest: sorption,
volatilization, hydrolysis, and biodegradation. These processes should be
incorporated into the model that is selected.
6.2.2. Selection of a Nonpoint Source Runoff Model
The land area is identified as an urban area that is relatively open and
is adjoined by commercial and residential areas. Based on the defined project
objectives of a preliminary exposure assessment and the limited field data with
which to calibrate the model, an annual time scale is appropriate. The spatial
characteristics of the area are that it is 20 acres in size and bounded on one
side by a stream. It is assumed that the dominant mechanism for transporting
the contaminants from the land area to the stream is particulate sorbed ero-
sion. Based on this information, the project objectives, and the assumptions,
the MRI nonpoint source loading functions would likely be the best approach.
The project objective of a preliminary analysis, in terms of required accuracy
and lack of calibration data, are the primary factors involved in this choice.
6-3
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The timing of the nonpoint source loading, which the MRI analysis cannot
provide, will be important, and the assumptions regarding streamflow rates and
loading terms must be made in a conservative manner. If a more detailed analy-
sis is necessary after the preliminary exposure assessment, further data will
be collected and a more complex model will be selected.
6.2.3. Surface Water Flow
The water body of interest is a river system. In a preliminary exposure
assessment, the project objectives indicate the use of a steady-state analysis
of the flow system because the data are limited. A one-dimensional approach is
appropriate for the system. Several different options may be considered at
this point. The most conservative option would use the estimated or recorded
low-flow rates (a reasonable worst-case condition); a somewhat less conserva-
tive analysis may use a yearly average flow rate. The annual variablity in the
flow rate, along with some sensitivity studies, should provide some judgment on
the choice of model. The surface water flow analysis may include an analytical
estimate of velocity (i.e., Manning's equation); a computer-based model; or
field measurements of velocity and travel time information between reaches. If
a computer model is used, the HEC-2 model would be an appropriate choice for
the river system.
6.2.4. Surface Mater Contaminant Transport
Although the contaminant is a nonpoint source, the site is relatively small
and could be represented as a point source, since the user is more interested
in the impact of contaminant concentrations a considerable distance downstream.
The contaminant from the surface runoff will be highly variable, only occurring
during rainfall periods. If a continuous nonpoint source is used at the annual
average rate estimated from the MRI loading function, the concentration esti-
mates will underpredict the peak concentrations.
6-4
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A conservative analysis could be performed by using a model with transient
source terms and apportioning the MRI annual loading term between a few events.
The first option to consider would be the most conservative analysis; that is,
to use the entire annual contaminant loading in a single event. If the results
indicate a potential exposure problem, the next step would be to represent the
surface runoff contaminant loadings as a series of separate events. -An analy-
sis of rainfall and streamflow records may provide some guidance in the appor-
tioning of annual loading terms into individual events. , , ,
Since the project objectives are to perform a preliminary exposure assess-
ment, a one-dimensional contaminant transport, model is the most appropriate.
The model selected should consider advection, and particle settling and trans-
port, as dominant processes in the analysis. The contaminants, such as the
heavy metals, tend to adsorb to the sediments, and the sorption process should
be considered. The most relevant degradation and transformation processes in
the study are hydrolysis, volatilization, and biodegradation. For a conserva-
tive analysis, the rate constants associated with these attenuation mechanisms
should be conservative (longer half-life), so that the results overpredict
concentration levels. . ,
The models that fit the selection criteria process include WASTOX, TOXI-
WASP, CHNTRN, HSPF, and SERATRA. These models incorporate the transient nature
of the contaminant. All of these models are fairly complex, and the number of
input parameters and detailed description are more than may be necessary for
the preliminary exposure assessment. Successful application of the models in a
short time frame may not be possible.
Another option is to use an analytical solution to the transient advection
dispersion equation with a first-order decay rate* A first-order decay rate ;
must include all of the degradation and transformation processes, :along with
6-5
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the sorption mechanism for removing dissolved pollutants from the water column.
Multiple sources may be superimposed in time if necessary. This approach is
probably the most consistent with the.defined project objectives, and may also
be the only approach that may be completed within the time constraints. The
concentration of dissolved and adsorbed fractions in the water column may be
calculated based on the partition coefficient and suspended sediment concentra-
tion. Details of the formdlation, along with particle settling as an effective
decay term, are described by Delos et al. (1984). An appropriate analytical
solution for one-dimensional advection, dispersion, and decay was provided in
Fischer et al. (1979):
CT(x,t) =
M!
exp -
KTt
/4Dt
(Eq. 6-1)
where
Cj is the total concentration (dissolved :and adsorbed forms) i'n the water
column (M/L3), , , ....,-,
X is the downstream distance (L),
t is time (T),
MI is the mass input of contaminant (M),
A is the cross-sectional area of the, river (L2),
D is the longitudinal dispersion coefficient (L2/T)
U is the average velocity (L/T),
Ky is the total first-order decay coefficient for the dissolved and
adsorbed fractions, and particulate adsorbed settling is represented
as an effective decay term (1/T).
6-6
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The following is a flow chart of the model selection process just de-
scribed. This material is included to show how the selection process shown in
Table 5-1 may be used as a form of a worksheet.
I. INITIAL ANALYSIS
A. Objectives: Preliminary exposure assessment of contaminant concen-
tration in water column; dilution calculation indicates potential
problem. Limited resources are presently available, and a screening
analysis is necessary.
B. Contaminant Source: Runoff from recycling plant: chromium, lead,
mercury, trichloroethylene, phenol, benzene, toluene.
C. Important Processes: Sorption, volatilization, hydrolysis, biodegra-
dation.
II. NONPOINT SOURCE RUNOFF
A. Land Use: Open urban area.
B. Time Characteristics: Annual (based on screening level objectives).
C. Space Characteristics: One area 20 acres in size.
D. Processes: Sorption and erosion.
E. Model Selection: MRI nonpoint source loading functions.
III. SURFACE WATER FLOW
A. Type of Water Body: Stream river system.
B. Stratification: Not applicable,'
C. Time: Steady state, use low-flow condition for conservative analy-
sis. . - . .
D. Dimensionality: One-dimensional for stream and river.
E. Model Choice: Analytical, Manning formula.
6-7
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IV. SURFACE WATER CONTAMINANT TRANSPORT
A. Source Type: Distributed runoff, but point source will be adequate.
B. Time; Source term is strongly variable; transient analysis is
needed.
C. Dimensionality: One-dimensional mixing should be nearly uniform at
the downs.tream distances of concern.
D. Mixing and Transport: Advection primarily; longitudinal dispersion
secondarily.
E. Sediment Contaminant Interactions: Sorption.
F. Processes: Volatilization, hydrolysis, and biodegradation.
G. Model Selection: The transient models in Table 5-3 (WASTOX,
TOXIWASP, HSPF, CHNTRN, SERATRA) are more complex than required for
the preliminary analysis. Instead, a one-dimensional analytical
solution, Equation 6-1, is chosen, representing transient source
terms (through superposition), advection, dispersion, and combined
first-order decay rate to represent all attenuation mechanisms.
6.3. DETAILED SITE-SPECIFIC ANALYSIS
The objectives of the study are to estimate the long-term accumulation and
fate of heavy metals and organic contaminants in the bed sediments and to
predict the concentration in the water column. The results of the modeling
study will have some impact on the decision to perform or require more cleanup
work at the site. In addition, the modeling study could indicate potential
risk to the general public via the contaminants found at theVi,te. Therefore,
the detailed site-specific analysis may impact the decision to spend'several
millions of dollars for Additional cleanup work. The detailed site-specific
analysis should have lower uncertainties in the modeling results.
6-8
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As with the preliminary analysis, the primary interests are the potential
threat to drinking water supplies and accumulation in fish. The source of con-
taminants is surface runoff from the closed recycling facility. The specific
contaminants to be analyzed are heavy metals such as chromium, lead, and mer-
cury; and organics such as trichloroethylene, phenol, benzene, and toluene.
Reviewing data presented in Callahan et al. (1979), the following processes
are considered to be important for the constituents of interest: sorption,
volatilization, hydrolysis, and biodegradation.
6.3.1. Selection of a Nonpoint Source Runoff Model
The land area is identified as an urban area that is relatively open and
is adjoined by commercial and residential areas. Based on' the defined objec-
tives of a detailed analysis, a short time scale on the order of minutes to
days is necessary. The spatial characteristics of the area are that it is 20
acres in size and bounded on one side by a stream. It is assumed that the
dominant mechanism for transporting the contaminants from the land area to the
stream is particulate sorbed erosion. The contaminants may also be entering
the stream through the discharge of contaminated groundwater. Measurements of
contaminant concentrations in the groundwater and the stream during low-flow
periods may be necessary. The highly transient nature of the surface runoff
can only be described with a continuous simulation model, and the timing of
loading terms to the stream will be important in relation to various sedimen-
tation processes. The appropriate group of models satisfying the above cri-
teria include: HSPF, ARM-II, ACTMO, and CREAMS.
6.3.2. Surface Water Flow
The water body of interest is a stream-river system. The defined objec-
tives of the study, and the relationship between the timing of the source term.
flow rate, and sedimentation processes, indicate that a transient analysis of
6-9
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the flow system is necessary. A one-dimensional approach is appropriate for
the river. The group of models which satisfy the above criteria include CHNHYD,
HEC-6, SEDONE, HSPF, and DWOPER. The sedimentation capabilities of SEDONE and
HSPF, in addition to the nonpoint source runoff capabilities of HSPF, should be
considered in this choice.
6.3.3. Surface Hater Contaminant Transport
The small area of nonpoint source runoff may be represented as a point
source, since we are interested in concentrations a considerable distance
downstream. A transient analysis is necessary to describe the source terms and
flow conditions. A one-dimensional analysis is appropriate, and the important
processes to consider are advection and particle settling and transport. The
scouring, deposition, and burial of sediments may also be very important,
depending on the sediment load of the stream and river. The contaminants do
adsorb to sediments, and the sorption process is considered to be important.
The important degradation and transformation processes are identified as hy-
drolysis, volatilization, and biodegradation.
The initial group of models which fit the general criteria include:
WASTOX, TOXIWASP, CHNTRN, HSPF, and SERATRA. The MEXAMS model is the only
model with the capability for analyzing the complex interactions of metals,
but it does not handle the1transient source terms and flow conditions. The
HSPF model may be the best choice because of the combined ability to simulate
nonpoint source runoff, flow characteristics, and the resulting transport and
fate of contaminants. The MEXAMS model may also be useful as an additional
tool, under a steady-state simplification, to assess the relative importance of
the different interactions.associated with the fate of metals. A steady-state
simplification appropriate for the MEXAMS model might be identified through
examination of the transient results from another model. A time frame may be
6-10
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selected on the basis of a critical period where the potential risk is 'highest
and the source terms and flow conditions assumed to be constant at those con-
ditions. The model selection process just described is summarized in the
following flowchart.
I. INITIAL ANALYSIS
A. Objectives: Detailed analysis of contaminant concentration in
water column, and accumulation in bed sediments. Dilution calcu-
lation, preliminary exposure assessment, and field measurements
indicate contamination problem. Available resources do not pose a
limiting constraint, and uncertainty in model predictions should be
minimized.
B. Contaminant Source: Runoff from recycling plant: chromium, lead,
mercury, trichloroethylene, phenol, benzene, toluene.
C. Processes: Sorption, volatilization, hydrolysis, biodegradation.
II. NONPOINT SOURCE RUNOFF
A. Land Use: Open urban area.
B. Time Characteristics: Continuous simulation necessary; event simu-
lation may also be useful.
C. Space Characteristics: One area, 20 acres in size.
D. Processes: Sorption and erosion.
E. Model Selection: HSPF. ARM-II, ACTMO, CREAMS.
III. SURFACE WATER FLOW
A. Type of Water Body: Stream river system.
B. Stratification: Not applicable.
6-11
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C. Time: Timing between the source term, flow rate and sedimentation
processes will be important. A transient flow analysis may be
necessary.
D. Dimensionality: One-dimensional for stream and river.
E. Model Choice: CHNHYD, HEC-6, SEDONE, HSPF, DWOPER.
IV. SURFACE WATER CONTAMINANT TRANSPORT
A. Source Type: Distributed runoff, but point source will be adequate,
B. Time: Source term is strongly variable; transient analysis is
needed.
C. Dimensionality: One-dimensional mixing should be nearly uniform at
the downstream,distances of concern.
D. Mixing and Transport: Advection primarily, longitudinal disper-
sion secondarily.
E. Sediment Contaminant Interactions; Sorption, sediment transport.
F. Processes: Volatilization, hydrolysis, and biodegradation.
G. Model Selection: WASTOX, TOXIWASP, HSPF, CHNTRN, SERATRA.
The MEXAMS model may also be useful for examining the complex
interaction of metals.
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7. REFERENCES
Callahan, M.A.; Slimak, N.W.; Gabel, N.W.; May, I.P.; Fowler, C.F.; Freed,
J.R.; Jennings, P.; Durfee, R.L.; Whitmore, F.C.; Maestri, B.; Mabey,
W.R., Holt, B.R.; Gould, C. (1979) Water-related environmental fate
of 129 priority pollutants, Vols. I and II. U.S. Environmental Protec-
tion Agency, Washington, DC.
Connally, J.P.; Winfield, R.P. (1984, Aug.) A user's guide for WASTOX, a
framework for modeling the fate of toxic chemicals in aquatic environ-
ments. Part 1: Exposure concentration. EPA-600/3/84-077. Washington,
DC.
Crawford, N.H.; Linsley, R.K. (1962) The synthesis of continuous streamflow
hydrographs on a digital computer. Technical Report No. 39. Stanford
University, Department of Civil Engineering.
Delos, C.G.; Richardson, W.L.; DePinto, J.V.; Ambrose, R.B.; Rodgers, P.W.;
Rygwelski, K.; St. John, J.P.; Shaughnessy, W.J.; Faha, T.H.; Christie,
W.N. (1984) Technical guidance manual for performing wasteload allo-
cations. Book II: Streams and rivers; Chapter 3: Toxic substances.
EPA-440/4-84-022. U.S. Environmental Protection Agency, Washington, DC.
Eschenroeder, A. (1983) The role of multimedia fate models in chemical risk
analysis. In: Swann, R.L.; Eschenroeder, A., eds. Fate of chemicals in
the environment. ACS Symposium Series 225. Washington, D.C.: American
Chemical Society.
Fair, G.M.; Geyer-, J.C.; Okun, D.A. (1968) Water and wastewater engineering,
Vol. 2. Water purification and wastewater treatment and disposal. New
York, NY: John Wiley & Sons. ISBN 0-471-25131-3.
Fischer, H.B. (1972) Mass transport mechanisms in partially stratified estu-
aries. J. Fluid Mechanics 53:671-687.
Fischer, H.B.; List, E.J.; Koh, R.C.Y.; Imberger, J.; Brooks, N.H. (1979)
Mixing in inland and coastal waters. New York, NY: Academic Press.
Hansen, D.V.; Rattray, M. (1966) New dimensions in estuary classification.
Limnology and Oceanography 11(3):319-325.
Hinwood, J.B.; Wallis J.G. (1975, Oct.) Classification of models of tidal
waters. J. Hyd. Div., Proc. of the American Society of Civil Engineers
101(HY10):1315-1331.
Horner, R.R.; Mar, B.W.; Reinelt, L.; Richey, J.S.; Lee, J.M. (1986) Design
of monitoring programs for detecting biological change resulting from
nonpoint sources of water pollution in Washingtion State. Report to
Washington State Department of Ecology, Olympia, WA.
7-1
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Huber, W.C.; Heaney, J.P. (1982) Analyzing residuals generation and dis-
charge from urban and nonurban land surfaces. In: Basta, D.J.; Bower,
B.T., eds. Analyzing natural systems: analysis for regional residuals-
environmental quality management. Washington, DC: Resources for the
Future.
Klecka, G.M. (1985) Biodegradation. In: Neely, W.B.; Blau, G.E., eds.
Environmental exposure from chemicals, Vol. 1. Boca Raton, FL: CRC Press.
McElroy, A.D.; Chin, S.Y.; Nebgen, J.W.; Aleti, A.; Bennett, F.W. (1976)
Loading functions for assessment of water pollution from nonpoint
sources. EPA-600/2-76-151. U.S. Environmental Protection Agency, Office
of Research and Development, Washington, DC.
Mill,!,; Mabey, W. (1985) Photochemical transformations. In: Neely, W.B.;
Blau, G.E., eds. Environmental exposure from chemicals, Vol. 1. Boca
Raton, FL: CRC Press.
Mills, W.B.; Dean, J.D.; Porcella, D.B.; Gherini, S.A.; Hudson, R.J.M.; Frick,
W.E.; Rupp, G.L.; Bowie, G.L. (1982, Sept.) Water quality assessment: a
sreening methodology for toxic and conventional pollutants. Parts 1, 2,
and 3. EPA-600/6-82-004a,b,c. U.S. Environmental Protection Agency,
Washington, DC.
Mills, W.B.; Porcella, D.B.; Ungs, M.J. ; Gherini, S.A.; Summers, K.V. ; Mok, L.;
Rupp, G.L.; Bowie, G.L.; Haith, D.H. (1985) Water quality assessment: a
screening procedure:for toxic and conventional pollutants in surface and
groundwater, Parts I and II. EPA-60U/6-85/002a,b. U.S. Environmental
Protection Agency, Washington, DC.
Mulkey, L.A.; Ambrose, R.B.; Barnwell, T.O. (1982) Aquatic fate and trans-
port modeling techniques for predicting environmental exposure to organic
pesticides and other toxicants: a comparative study. International Work-
shop on the Comparison of Applications of Mathematical Models, held by
UNESCO in LaCoruna,: Spain.
Neely, W.B. (1985) Hydrolysis. In: Neely, W.B.; Blau, G.E., eds. Environ-
mental exposure from chemicals, Vol. 1. Boca Raton, FL: CRC Press.
Neely, W.B.; Blau, G.E.,'eds. (1985) Environmental exposure from chemicals,
Vols. 1 and 2. Boca Raton, FL: CRC Press.
O'Connor, D.J.; St. John, J.P. (1982) Assessment of modeling the fate of
chemicals in the aquatic environment. In: Dickson, K.L.; Maki, A.W.;
Cairns, J., eds. Modeling the fate of chemicals in the aquatic environ-
ment. Ann Arbor, MI: Ann Arbor Science Publishers.
Pritchard, D.W. (1967) Observations of circulation in coastal plain estu-
aries. In: Lauff, G., ed. Estuaries. Pub! ication'No. 83. Washington,
D.C.: American Association for the Advancement of Science.
Reckhow, K.H.; Butcher, J.B.; Marin, C.M. (1985) Pollutant runoff models:
selection and use in decision making. Water Resources Bull. 21(2):185-
195.
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Rich, L.G. (1973) Environmental systems engineering. McGraw-Hill Series .
in Water Resources and Environmental Engineering. New York, NY: McGraw-
Hill. ISBN 0-07-052250-2.
Schnoor, J.L. (1985) Modeling chemical transport in lakes, rivers, and
estuarine systems. In: Neely, W.B. ; Blau, G.E., eds. Environmental
exposure from chemicals, Vol. 2. Boca Raton, FL: CRC Press.
Southerland, E. ; Wagner, R.; Metcalfe, J. (1984) Technical guidance manual
for performing wasteload allocation. Book III: Estuaries. U.S. Environ-
mental Protection Agency, Washington, DC. (Draft)
Thomann, R.V. (1972) Systems analysis and water qua!ity management. New
York, NY: McGraw-Hill. ISBN 0-07-064214-1.
Tinsley, I.J. (1979) Chemical concepts in pollutant behavior. New York, NY:
Wiley Interscience.
Vanoni, V.A., ed. (1975) Sedimentation engineering. Manuals and Reports
on Engineering Practice No. 54. New York: American Society of Civil
Engineers.
Walton, R.; George, T.S.; Roesner, L.A. (1984) Selecting estuarine models.
Contract No. 68-01-6403. U.S. Environmental Protection Agency, Washing-
ton, DC. (Draft) :
Whitman, W.G. (1923) A prel imi.nary experimental configuration of the two-film
theory of gas adsorption. Chem. Metal. Engr. 29:146-148.
Wischmeier, W.H.: Smith, D.D. (1965) Predicting rainfall-erosion losses from
cropland east of the Rocky Mountains. Agricultural Research Series Hand-
book No., 282. U.S. Department of Agriculture, Washington, D.C.
U.S. Environmental Protection Agency. (1984) Proposed guidelines for exposure
assessments. Federal Register 49:46304-46312.
U.S. Environmental Protection Agency. (1986) Guidelines for estimating expo-
sures. Federal Register 51:34042-34054.
Yeh, G.T. (1982a) CHNTRN: a channel transport model for simulating sediment
and chemical distribution in a stream/river network. ORNL-5882. Oak
Ridge National Laboratory, Oak Ridge, TN.
Yeh, G.T. (1982b) CHNHYD: a channel hydrodynamic model for simulating flows
and water surface elevations in a stream/river network. ORNL-5701. Oak
Ridge National Laboratory, Oak Ridge, TN.
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8. REVIEW OF EXAMPLE SURFACE WATER MODELS
8.1. NONPOINT SOURCE RUNOFF MODELS
8-1
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METHOD NAME: Midwest Research Institute (MRI) Nonpoint Source Loading Function
PURPOSE: The method is designed to be used for preliminary estimation of
nonpoint source loading rates for urban and nonurban areas.
SOLUTION TECHNIQUE: The method is empirical and uses the Universal Soil Loss
Equation to predict sediment erosion.
DESCRIPTION: The loading .functions are useful as a "first cut" estimate of
nonpoint source loading rates. Only the transport of sediment-attached consti-
tuents is considered (e.g., no dissolved contaminants). Various constituents
are considered, including pesticides and heavy metals. The method is applicable
to a single, small to large, catchment. Loading rates are estimated as annual
averages. All processes throughout the study area are lumped together so that
no spatial resolution is available.
INPUT: Catchment characteristics: location, size, and land use categories.
USLE parameters: source area, rainfall, soil credibility, slope length and
gradient, land use practices, ground cover, and sediment delivery ratio.
OUTPUT: The results of the method include the average daily contaminant load-
ing rates from each land use category, and 30-day maximum and 30-day minimum
loading rates.
COMPILATION REQUIREMENTS:
Source Language: Not applicable
Hardware Requirements: Calculator
Mass Storage Requirements: Unknown
EXPERIENCE REQUIREMENTS: Moderate.
TIME REQUIREMENTS: Low.
SOURCE; See documentation.
DOCUMENTATION/REFERENCES:
McElroy, A. D.; Chiu, S. Y.; Nebgen, J. W.; Aleti, A.; Bennett, F.W. (1976)
Loading functions for assessment of water pollution from nonpoint sources.
EPA-600/9-76-151. NTIS No. PB-253-325. U.S. Environmental Protection
Agency, Washington, DC.
8-2
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METHOD NAME: NPS
PURPOSE: The NPS model was developed to estimate nonpoint source pollutant
loads in urban and rural areas.
SOLUTION TECHNIQUE: Empirical.
DESCRIPTION: The NPS model is a continuous simulation model that can be used
to simulate nonpoint source pollutant loads., The hydro!ogic runoff portion of
the model is based on the Stanford Watershed Model. The model does not incor-
porate decay or degradation of pollutants and is not applicable to nonconserva-
tive substances. The model does not include a channel routing routine and
should not be used for land areas greater than about 2 square miles (although
it could be coupled with a channel routing model).
A variety of watershed-dependent parameters are required, including various
soil moisture capacity parameters (defined as storage zones). During a storm
event, rainfall is partitioned between the storage zones. After the rainfall,
water is transferred between the storage zones. The sediment processes are
modeled as the detachment of fines and subsequent transport of fines.
\ , ' '
INPUT: Hydrologic parameters: rainfall records, soil moisture capacity para-
meters (defined as various storage zones), snow pack characteristics, sediment
loading parameters, land-use characteristics, and sediment accumulation and
removal rates (for dry periods) for impervious areas.
OUTPUT: The output of the model includes hydrographs for storm events, sedi-
ment and pollutant loads and concentrations as a function of time, and dis-
solved oxygen concentrations and temperature.
COMPILATION REQUIREMENTS:
Source Language: IBM FORTRAN IV
Hardware Requirements: IBM 360
Mass Storage Requirements: Unknown
EXPERIENCE REQUIREMENTS: Extensive.
TIME REQUIREMENTS: Medium, weeks.
SOURCE:
Lee A. Mulkey
U.S. Environmental Protection Agency
Environmental Research Laboratory
College Station Road
Athens, GA 30605
DOCUMENTATION/REFERENCES:
Donigian, A.S., Jr.; Crawford, N.H. (1976a) Modeling pesticides and nutrients
on agricultural lands. EPA-600/2-76-043. U.S. Environmental Protection
Agency, Environmental Research Laboratory, Athens, GA.
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Donigian, A.S., Jr.; Crawford, N.H. (1976b) Modeling nonpoint pollution from
the land surface. EPA-600/3-76-083. U.S. Environmental Protection Agency,
Environmental Research Laboratory, Athens, GA.
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METHOD NAME: Agricultural Runoff Model (ARM II)
PURPOSE: The Agricultural Runoff Model is a nonpoint source model that can be
used to estimate pollutant loadings in agricultural areas.
SOLUTION TECHNIQUE: Empirical.
DESCRIPTION: ARM II is a continuous simulation model applicable to agricultural
areas. The original basis of the model is the Stanford Watershed Model. The
model can be used to simulate the transport of various pollutants from agricul-
tural lands to streams. The model simulates runoff of water, sediments, nutri-
ents, and pesticides for intervals of 5 or 15 minutes. The kinetics used to
characterize degradation and transformation of pollutants are described by
first-order rate equations. The model does not incorporate a channel routing
routine and hence should not be used for land areas larger than 2 square miles
(although it could be coupled with a channel routing model). A variety of
watershed-dependent parameters are required, including soil moisture capacity
parameters and snowmelt parameters.
INPUT: Hydrologic parameters: rainfall records; streamflow records (for
calibration); soil moisture capacity parameters; snowmelt rates; snowpack
characteristics; sediment loading parameters; and topography of land, surface,
and soil type. Chemical parameters: pesticide degradation rates, adsorption/
desorption coefficients; and nutrient reaction rates and storage parameters.
OUTPUT: The output of the model includes: Volume of water stored in watershed
in various zones, volume of runoff, concentration of dissplved nutrients and
pesticides in runoff, concentration of adsorbed nutrients and pesticides in
runoff, amount of nutrients stored in soil and plant materials.
COMPILATION REQUIREMENTS:
Source Language: FORTRAN
Hardware Requirements: Implemented on an IBM 370/160
and also on a Hewlett Packard 3000 Series II
Mass Storage Requirements: Unknown
EXPERIENCE REQUIREMENTS: Extensive.
TIME REQUIREMENTS: Medium, weeks.
SOURCE:
Lee A. Mulkey
U.S. Environmental Protection Agency
Environmental Research Laboratory
College Station Road
Athens, GA 30605
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DOCUMENTATION/REFERENCES:
Crawford, N.H.; Donigian, A.S., Jr. (1973) Pesticide transport and runoff
model for agricultural lands. EPA-660/2-74-013. U.S. Environmental Pro-
tection Agency, Office of Research and Development, Washington, DC.
Donigian, A.S., Jr.; Crawford, N.H. (1976) Modeling pesticides and nutrients
on agricultural lands. EPA-600/2-76-043. U.S. Environmental Protection
Agency, Environmental Research Laboratory, Athens, GA.
Donigian, A.S., Jr.; Davis, H.H., Jr. (1978) Agricultural Runoff Management
(ARM) Model User's Manual: Versions I and II. EPA-600/3-78-080. U.S.
Environmental Protection Agency, Environmental Research Laboratory, Athens,
GA.
Donigian, A.S, Jr.; Beyerlein, D.C.; Davis, H.H., Jr.; Crawford, N.H. (1977)
Agricultural Runoff Management (ARM) Model: Version II, Refinement and
Testing. EPA-600/3-77-098. U.S. Environmental Protection Agency,
Environmental Research Laboratory, Athens, GA.
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METHOD NAME: AGRUN
PURPOSE: The AGRUN model is a nonpoint source model applicable to agricultural
watersheds.
SOLUTION TECHNIQUE: Soil loss is estimated using the USLE, infiltration is
based on Morton's equation, and streamflow is simulated using a finite-differ-
ence procedure.
DESCRIPTION: The AGRUN model consists of several compatible programs designed
to simulate agricultural runoff, transport, and movement in the receiving
stream. The USLE is used to.compute the suspended solids in the runoff, and no
decay of pollutants is incorporated. The model is designed as a single-event
simulation model. The physical processes simulated by the model are overland
flow, erosion, and channel flow. The model can simulate multiple catchments
and dendritic channel systems. The model is a modification of the SWMM model.
INPUT: Precipitation data; geometry of catchments; soil parameters (depth of
layers, permeability, field capacity, and saturation); channel geometry (cross-
section data, length, slope, and Manning's n).
OUTPUT: The output of the model is the concentration of constituents in a
river as a function of space and time.
COMPILATION REQUIREMENTS:
Source Language: FORTRAN
Hardware Requirements: UNIVAC 1108
Mass Storage Requirements: 512K bytes of core
EXPERIENCE REQUIREMENTS: Extensive.
TIME REQUIREMENTS: Medium, weeks.
SOURCE:
Dr. Larry Roesner
Camp, Dresser and McKee Inc.
7620 Little River Turnpike
Annandale, VA 22003
DOCUMENTATION/REFERENCES:
Roesner, L.A.; Zison, S.W.; Monser, J.R.; Lyons, T.C. (1975) Agricultural
Watershed Runoff Model for the Iowa-Cedar River Basins. Prepared by Water
Resources Engineers Inc., under contract no. 68-01-0742, for the U.S.
Environmental Protection Agency, Systems Development Branch, Washington,
DC.
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METHOD NAME: ACTMO
PURPOSE: The ACTMO model is a nonpoint source model applicable to agricultural
areas.
SOLUTION TECHNIQUE: Empirical.
DESCRIPTION: The model is a continuous simulation model. The hydrologic
of the model is coupled with the USDA watershed model, USDAHL-74
1975). The model is applicable to agricultural areas with one or more'
The physical processes included in the model are downs!ope surface
stream channel, subsurface infiltration, groundwater interflow,
snow accumulation and melt, and erosion based on the Uni-
analysis
(Holton,
catchments.
flow towards
evapotranspi rati on,
versa! Soil Loss Equation. A variety of chemical processes are incorporated,
including adsorption, degradation, mineralization, and plant uptake of agricul-
tural chemicals. The model is designed primarily for the analysis of agricul-
tural chemicals, fertilizers, and pesticides.
INPUT: Watershed characteristics: slope, length, width, soil credibility,
ground cover, management practices, soil layers, and subsurface characteristics.
Chemical data: date of application, application rate, absorption coefficients,
breakdown coefficient, mixing depth, and preference for size fractions. Soil
characteristics: field capacity, porosity, texture, and dispersion factor.
Hydrologic data: rainfall, runoff, infiltration, and soil moisture. Erosion
data: erosion rates, sediment deposition, and sediment texture fraction ,of
area in rills and rill depth.
OUTPUT: The output of the:model includes streamfTow hydrograph, watershed
erosion, quantity of chemicals in runoff, and quantity of chemicals in each
model zone.
COMPILATION REQUIREMENTS:
Source Language: FORTRAN
Hardware Requirements: The model is operational on an
IBM 360 or 365 and UNIVAC 1108 computers
Mass Storage Requirements: Unknown
EXPERIENCE REQUIREMENTS; Extensive.
TIME REQUIREMENTS: Medium, weeks.
SOURCE;
Agricultural Research Service
U.S. Department of Agriculture
Hyattsville, MD
DOCUMENTATION/REFERENCES:
Frere, M.H.; Onstad, C.A.; ;Holtan, H.W. (1975) ACTMO: an agricultural chem-
ical transport model. Publication No. ARS-H-3. U.S. Department of Agri-
culture, Agricultural Research Service, Hyattsville, MD.
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Holtan, H.W.; Stiltner, G.W.; Henson, W.H.; Lopez, H C
revised model of watershed hydrology. Technical Bulletin No. 1518._ 1Kb.
Department of Agriculture, Agricultural Research Service, Hyattsville, MD<
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METHOD NAME: CREAMS
PURPOSE: The CREAMS model is a nonpoint source model that may be used to
estimate pollutant loadings! from agricultural areas.
SOLUTION TECHNIQUE: Empirical.
DESCRIPTION: The CREAMS model structure consists of three major components-
nydroiogy, erosion/sedimentation, and chemistry. The hydrology component
estimates the volume and rate of runoff, evapotranspiration, soil moisture
content, and percolation. Two options are included for the estimation of
runoff: 1) Soil Conservation Service curve number method, and 2) infiltration
capacity based on the Green and Ampt equation. The first method is useful when
only daily precipitation data are available, and the second is used when more
detailed (hourly) data are available.
The erosion/sedimentation portion of the model considers the processes of soil
detachment, transport, and deposition. The detachment of soil is modeled by a
modified form of the USLE. The sediment transport is dependent upon the small-
er of: 1) transport capacity or 2) detached sediments available for transport.
. It the transport capacity is exceeded, deposition occurs. A critical shear
stress is used to define erosion within channels. Deposition of coarse-grained
particles occurs as a result of reduced flow velocity in ponded areas.
The chemistry portion of the model considers nutrients and pesticides The
transport of soluble and sediment-attached chemicals is evaluated. Interaction
between plants and chemicals within the root zone.is also considered.
The model is designed to require a bare minimum of calibration parameters and
is intended to be used for comparison of different management and land use
strategies. The spatial scale of the model is intended to be the size of an
agricultural field.
INPUT: Precipitation records, SCS curve number of infiltration parameters
USLE parameters, partition coefficients (for different chemicals), and decay
coefficients. /» j
OUTPUT; The output of the model includes surface runoff, erosion, sediment
delivery to water body, and chemical concentration in the sediments and in the
soil system.
COMPILATION REQUIREMENTS:
Source Language: Fortran
Hardware Requirements: Unknown
Mass Storage Requirements: Unknown
EXPERIENCE REQUIREMENTS: Moderate.
TIME REQUIREMENTS; Medium, weeks.
8-10
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SOURCE:
Walter G. Knisel
U.S. Department of Agriculture
Southeast Watershed Research Laboratory
Tifton, Georgia 31793
DOCUMENTATION/REFERENCES:
Knisel, W.G., ed. (1980) CREAMS: a field scale model for chemicals, runoff,
and erosion from agricultural management systems. Conservation Report No.
26. U.S. Department of Agriculture, Science and Education Administration,
Washington DC.
Svetlosanov, V.; Knisel, W.G., eds. (1982) European and United States Case
studies in application of the CREAMS Model. Report No. CP-82-S11.
International Institute for Applied Systems Analysis.
8-11
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METHOD NAME; SWMM
PURPOSE: The SWMM model is designed to simulate nonpoint source runoff, pri-
marily from urban areas.
SOLUTION TECHNIQUE; Some processes in the model are represented empirically,
while others are represented by finite difference formulations.
DESCRIPTION; The SWMM model is an extensive program that models the rainfall/
runoff cycle in urban areas in a comprehensive manner. The model is a contin-
uous simulation model. Some methods for calculating infiltration rates are
incorporated. The model is capable of simulating multiple catchments and
dry-weather accumulation of particulate matter. Flow routing is calculated
including storage and backwater effects. Conventional pollutants are simula-
ted, as are arbitrary conservative substances. Erosion is simulated with the
USLE.
INPUT; Precipitation data and other meteorological data; channel/pipe geometry
and characteristics; properties of catchments (geometry, slope, roughness,
infiltration parameters, impervious areas, and storage); USLE parameters; and
parameters defining deposition ratio and washoff functions.
OUTPUT; The output of the model includes hydrographs and pollutographs at
different points within the system.
COMPILATION REQUIREMENTS:
Source Language: FORTRAN
Hardware Requirements: Applied on variety of mainframe computers
Mass Storage Requirements: 350K bytes of core
EXPERIENCE REQUIREMENTS; Extensive.
TIME REQUIREMENTS; Long, months.
SOURCE:
Tom Barnwell
U.S. Environmental Protection Agency
Environmental Research Laboratory
College Station Road
Athens, 6A 30613
DOCUMENTATION/REFERENCES;
Jtober, W.C.; Heaney, J.P.; Nix, S.J.; Dickinson, R.E.; Polmann, D. (1982, June)
Storm Water Management user's manual: Version III. EPA-600/2-84-109A.
U.S. Environmental Protection Agency, Cincinnati, OH.
Torno, H.C. (1980) Proceedings, Stormwater Management Model (SWMM) user's
group meeting, January 10-11, 1980. EPA 600/9-80-017. U.S. Environmental
Protection Agency, Washington, DC.
8-12
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8.2. SURFACE WATER FLOW MODELS
8-13
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CODE NAME: HEC-2
PURPOSE: The HEC-2 program Is designed to calculate the water surface profile
in rivers for a steady flow discharge.
DIMENSIONALITY: One-dimensional.
SOLUTION TECHNIQUE: The model is a numerical model based on a finite difference
formulation of the governing differential equation.
DESCRIPTION: The model is a one-dimensional representation of the continuity
equation coupled with the conservation of energy equation. Friction losses are
calculated with the Manning equation. Various energy loss terms are included
to account for expansion and contraction of the flow area, and obstruction by
bridge piers. The solution algorithm starts at the bottom reach and solves the
nonlinear energy equation iteratively, one reach at a time, moving upstream.
The roughness parameter, Manning's n, may vary at each cross-section and may
also be calculated directly for each reach if discharge and water surface
elevation are available at each reach.
INPUT: Geometric data (channel areas, reach lengths); roughness coefficient,
Manning s n; flow rate; tributary inflows; and downstream water surface eleva-
tion.
OUTPUT: The output of the model includes the water surface profile and velocity
at each cross-section.
COMPILATION REQUIREMENTS:
Source Language: FORTRAN
Hardware Requirements: The program has been implemented on various systems
including CDC 7600, UNIVAC 11087, IBM 360, and Honeywell 635
Mass Storage Requirements: Unknown
EXPERIENCE REQUIREMENTS; Moderate.
TIME REQUIREMENTS: Medium, week(s).
SOURCE:
Hydro!ogic Engineering Center
U.S. Army Corps of Engineers
Davis, CA
DOCUMENTATION/REFERENCES:
U.S. Army Corps of Engineers. (1973, Oct.) HEC-2: water surface profiles:
user s manual. Hydrologic Engineering Center, Davis, CA.
8-14
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CODE NAME: CHNHYD
PURPOSE: A hydrodynamic model for simulating flows and water surface elevation
in stream/river networks.
DIMENSIONALITY: One-dimensional.
SOLUTION TECHNIQUE: The model is a numerical model based on an integrated com-
partment formulation. Time integration may be performed explicitly or implicit-
1^'
DESCRIPTION: The CHNHYD model is based on the conservation of mass and momen-
tum equations. The conservation equations are represented using the integrated
compartment method (ICM) (Yeh, 1981). The method combines the advantages of
finite difference, finite element, and compartment analysis techniques. Fric-
tion losses are represented using a Manning formulation. Wind stresses at the
water surface are also incorporated. Very general forms of boundary conditions
are incorporated so that the model may be applied to a wide variety of situa-
tions. Networks or branching of channel systems can be analyzed.
INPUT: Geometry and grid definition; roughness coefficient, Manning's n; wind
stress parameters; initial conditions: flow rates and water surface profile;
boundary conditions: flow rate, water surface.
OUTPUT: The output of the model includes the velocity and water surface eleva-
tion at each reach of river-system at each time step.
COMPILATION REQUIREMENTS:
Source Language: FORTRAN
Hardware Requirements: IBM 3033
Mass Storage Requirements: Unknown
EXPERIENCE REQUIREMENTS: Extensive.
TIME REQUIREMENTS: Moderate, weeks.
SOURCE;
G. T. Yeh
Environmental Sciences Division
Oak Ridge National Laboratory
P. 0. Box X
Oak Ridge, TN 33830
DOCUMENTATION/REFERENCES:
Yeh, G.T. (1981) ICM: an integrated compartment method for numerically solving
partial differential equations. ORNL-5684. Oak Ridge National Laboratory,
Oak Ridge, TN.
8-15
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Yeh, G.T. (1982) CHNHYD: a channel hydrodynamic model for simulating flows
and water surface elevations in a stream/river network. ORNL-5701. Oak
Ridge National Laboratory, Oak Ridge, TN.
8-16
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COPE NJWE: HEC-6
PURPOSE: The HEC-6 program is designed to calculate the water surface profile
and the stream bed profile. Sediment load, water velocity, and water depth are
calculated.
DIMENSIONALITY: One-dimensional.
SOLUTION TECHNIQUE: The model is a transient numerical model based on a finite
difference formulation.
DESCRIPTION: The model is a one dimensional representation of the continuity
equation coupled with the conservation of energy equation. Friction losses are
calculated with the Manning equation. The time integration is performed using
an explicit integration scheme. The sediment transport is modeled by the
continuity equation coupled with empirical equations for transport capacity and
credibility. The model is only applicable to subcritical flows. No mathe-
matically rigorous stability criteria are developed; however, rule-of-thumb
criteria are suggested. The flow rate is constant, but changes in stream bed
may change velocities.
INPUT: Geometric data (channel areas, reach lengths); roughness coefficient,
Manning's n; flow rate; tributary inflows; concentration of suspended and bed
sediments; unit weight of sediments; and water temperature.
OUTPUT: The output of the model includes the water surface profile, the stream
bed profile, and the concentration of suspended sediments in each reach of the
system.
COMPILATION REQUIREMENTS:
Source Language: FORTRAN
Hardware Requirements: CDC 7600 and UNIVAC 1108
Mass Storage Requirements: 65K words of central memory and 500K words of
extended memory
EXPERIENCE REQUIREMENTS: Extensive.
TIME REQUIREMENTS: Extensive, months.
SOURCE:
Hydrologic Engineering Center
U.S. Army Corps of Engineers
Davis, CA
DOCUMENTATION/REFERENCES:
U.S. Army Corps of Engineers. (1977, Mar.) HEC-6: scour and deposition in
rivers and reservoirs; user's manual. Hydrologic Engineering Center,
Davis, CA.
8-17
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CODE NAME: SEDONE
PURPOSE: The SEDONE model is a transient model for simulating hydrodynamic
flow and sediment transport in rivers and estuaries.
DIMENSIONALITY: One-dimensional.
SOLUTION TECHNIQUE: The model is a numerical model based on a discrete element
formulation of the conservation of mass.
DESCRIPTION: The primary emphasis of the SEDONE model is the simulation of
sediment transport processes. The model also simulates the momentum and con-
tinuity equations for water. Three sediment layers are considered for each
reach of a stream or estuary: 1) a stationary resident bed layer, 2) a bed
slurry layer, and 3) a suspended sediment layer. Longitudinal transport is
considered only in the upper two layers, and the bottom resident layer serves
as a finite reservoir with vertical transport to the slurry bed layer. Differ-
ent size classes of sediments with different physical properties are incorpora-
ted. The spatial discretization of the domain results in a system of coupled
ordinary differential equations for the water surface elevation, flow rate, and
sediment size concentration in the three layers. The ordinary differential
equations are numerically integrated in time, using a Runge-Kutta-Gill integra-
tion scheme. ;
INPUT; Geometry and grid definition, stream flow, lateral inflows, physical
properties of each sediment size class, precipitation, and tidal boundary.
OUTPUT: The output of the model includes the water surface profile, flow
rates, and sediment concentrations for each size class in the three layers for
each reach of the system.
COMPILATION REQUIREMENTS:
Source Language: FORTRAN
Hardware Requirements: The model has been implemented on an IBM 360/91
Mass Storage Requirements: Unknown
EXPERIENCE REQUIREMENTS; Extensive.
TIME REQUIREMENTS: Extensive, months.
SOURCE:
DOCUMENTATION/REFERENCES:
Hetrick, D.M.; Eraslan, A.H.; Patterson, M.R. (1979) SEDONE: a computer code
for simulating tidal transient, one-dimensional, hydrodynamic conditions
and three-layer, variable sediment concentrations in controlled rivers and
estuaries. NUREG 6/CR-0430; ORNL/NUREG/TM-256. Oak Ridge National Labor-
atory, Oak Ridge, TN.
8-18
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COPE NMAE; DViOPER
PHYSICAL PROCESSES: A hydrodynamic model for simulating flow in rivers.
DIMENSIONALITY: Transient, one-dimensional.
SOLUTION TECHNIQUE: Numerical solution using an irregular finite difference
grid.Time integration is performed implicitly.
DESCRIPTION: DWOPER is based on a one-dimensional form of the conservation of
mass and momentum equations (St. Venant equations). The model can be used to
simulate transient one-dimensional flow in river systems. The model is quite
general in that it incorporates spatially variable physical parameters such as
channel geometry, roughness parameters, lateral inflows, flow diversions,
off-channel storage, local head losses, lock and dam operations, and wind
stresses. The implicit time integration technique allows for the use of large
time steps when appropriate. Additional features of the model include an
automatic calibration procedure, internal to the model, whereby the roughness
parameters in the friction slope term are automatically adjusted to minimize
the difference between computed and observed stages. Data management routines
are included to assist in the development of input parameters and the interpre-
tation and display of output parameters.
CODE INPUT: River system configuration: channel configuration; cross-section
geometry, initial roughness coefficients (Manning n), off-channel storage
areas, and lateral inflows. ,
Initial conditions: estimated stage and discharge at each cross-section.
Boundary conditions: known stage or discharge at the upstream boundary as a
function of time and stage or discharge hydrograph at downstream boundary.
CODE OUTPUT: Stage and discharge at each cross-section as a function of time.
COMPILATION REQUIREMENTS:
Source Language: FORTRAN
Hardware Requirements: Small, Medium, and Large Storage sizes are avail-
able requiring 170, 235, 300K words (8 byte) of memory storage
EXPERIENCE REQUIREMENTS: Moderate, short courses are offered by the National
Weather Service.
TIME REQUIREMENTS: Weeks.
SOURCE:
D. L. Fread
Hydrologic Research Laboratory
National Weather Service, NOAA
Silver Spring, MD 20910
8-19
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DOCUMENTATION/REFERENCES:
"" - """ " t
Chen, Y.H.; Simons, D.B. (1975, Sept.) Mathematical modeling of alluvial
channels. In: Modeling 75: symposium of modeling techniques. Vol. 1.
American Society of Civil Engineers, pp. 466-483.
Fread, D.L. (1973a) Effect of time step size in implicit dynamic routing.
Water Resources Bull. 9(2):338-351.
Fread, D.L. (1973b) Technique for implicit dynamic routing in rivers with
major tributaries. Water Resources Bull. 9(4):918-926.
Fread, D.L. (1974, Mar.) Numerical properties of implicit four-point finite
difference equations of unsteady flow. Technical Memorandum NWS HYDRO
18. National Oceanic and Atmospheric Administration, Washington, DC.
Fread, D.L. (1976) Flood routing in meandering rivers with flood plains.
In: Rivers '76, Vol. I: symposium on inland waterways for navigation,
flood control, and water diversions, held August 10-12, 1976, at
Colorado State University. American Society of Civil Engineers, pp.
16-35.
Fread, D.L. (1978, Apr.) National Weather Service Operational Dynamic Wave
Model. National Oceanic and Atmospheric Administration, Washington, DC.
Fread, D.L.; Price, R.K. (1975) Discussion of comparison of four numerical
methods for flood routing. J. Hydraulics Div..ASCE 101(HY3):565-567.
Fread, D.L.; Smith, 6.F. (1978) Calibration technique for one-dimensional
unsteady flow models. J. Hydraulics Div. ASCE 104(July).
Fread, D.L.; Amein, M.; Fang, C.S. (1971) Discussion of implicit flood rout-
ing in natural channels. J. Hydraulics Div. ASCE 99(HY7):1156-1159.
8-20
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CODE NAME: Dynamic Estuary Model (DYNHYD3)
PURPOSE: DYNHYD3 was developed to simulate hydrodynamic flow and contaminant
transport and degradation in rivers and estuaries. The hydrodynamics program
DYNHYD4 has been updated and linked to WASPS.
DIMENSIONALITY: One-dimensional (link-node two-dimensional)
SOLUTION TECHNIQUE: The model is a numerical model using the finite differ-
ence method to approximate the governing differential equations. The model is
a one-dimensional model formulated in a "link node" manner so that some two-
dimensional geometry may be represented by a series of channels and junctions.
DESCRIPTION: The model is a transient model based on conservation of momentum
and continuity. The physical processes included in the model are tidal dynam-
ics, river flow, and the advection and dispersion of contaminants. Various
chemical processes are incorporated in the water quality portion of the model,
including coupled and uncoupled reactions and first-order decay. A variety of
chemical constituents are considered, including pesticides and heavy metals.
The time integration is performed explicitly; hence, an appropriate time step/
grid size relationship must be chosen to avoid instabilities. Only constant
sources of contaminants can be considered.
The hydrodynamic flow portion of the model can be run until a "dynamic steady
state" condition is reached using the same tidal driving forces. Alternative-
ly, the hydrodynamics can be run with variable inflows, wind, and tidal ranges,
The tidally fluctuating velocities and water surface elevations are then used
in the water quality simulation.
INPUT: Junction and channel geometry; friction coefficient (Manning's n);
head water and tributary,inflows; dispersion coefficients; rate constants for
kinetic reactions; initial conditions (velocity, water surface elevation, con-
centrations)- and boundary conditions (seaward tidal condition, source terms).
OUTPUT: The output of the model includes the velocity, water surface eleva-
tion, and contaminant concentrations as a function of space and time over the
tidal cycle.
COMPILATION REQUIREMENTS:
Source Language: FORTRAN
Hardware Requirements: IBM 370/168; DYNHYD3 is available on PC-compatible
microcomputers
Mass Storage Requirements: Some disk storage, amount unknown
EXPERIENCE REQUIREMENTS: Extensive.
TIME REQUIREMENTS: Extensive, months.
8-21
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SOURCE:
R. B. Ambrose
U.S. Environmental Protection Agency
College Station Road :
Athens, 6A 30605 '
DOCUMENTATION/REFERENCES;
Ambrose, R.B.: Roesch, S.E. (1982, Feb.) Dynamic estuary model performance.
Paper No. 16847. J. Environmental Engineering Div. ASCE 108(EE1):51-71.
Feigner, K.D.; Harris, H.S. (1970) Documentation report, FWQA Dynamic Estuary
Model. U.S. Department of the Interior, Federal Water Quality Administra-
tion, Washington, DC.
Water Resources Engineers, Inc. (1974) Computer program documentation for the
dynamic estuary model. U.S. Environmental Protection Agency, Systems
Development Branch, Washington, DC.
8-22
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CODE NAME: EXPLORE-I
PURPOSE: The EXPLORE-I model was developed to simulate hydrodynamics and water
quality processes in water bodies (rivers, lakes, and estuaries).
DIMENSIONALITY: One-dimensional (link-node two-dimensional)
SOLUTION TECHNIQUE: The model is a numerical model using the finite difference
technique.The model is a one-dimensional model formulated in a "link node"
manner so that some two-dimensional geometry may be represented by a series of
channels and junctions.
DESCRIPTION: The EXPLORE-I model consists of four separate computer codes: a
hydraulic code for rivers and estuaries, a water quality code for rivers and
estuaries, a hydrothermal code for thermally stratified reservoirs, and a water
quality code for thermally stratified reservoirs. The hydraulic model is based
on the conservation of momentum and mass (St.. Venant equations). The river
water quality model examines only the advection and degradation of contaminants;
no dispersion term is included.
INPUT; Junction and channel geometry, friction coefficient (Manning's n),
inflow and outflow, rate constants for kinetic reactions, initial conditions
(contaminant concentrations), and boundary conditions (stage, discharge, con-
taminant concentration, and source term).
OUTPUT; The output of the model includes stage, discharge, and contaminant
concentration at each node for each time step.
COMPILATION REQUIREMENTS:
Source Language: FORTRAN
Hardware Requirements: The model is implemented on IBM
370 and Univac 1100 computers
Mass Storage Capacity: Disk storage 44K words
EXPERIENCE REQUIREMENTS: Extensive.
TIME REQUIREMENTS: High, month(s).
SOURCE:
R. B. Ambrose
U.S. Environmental Protection Agency
Athens Environmental Research Center
College Station Road
Athens, GA 30613
DOCUMENTATION/REFERENCES:
Baca, R.G.; Waddel, W.W.; Cole, C.R.; Brandstetter, A.; Cearlock, D.B. (1973a)
EXPLORE-I: a river basin water quality model. Prepared by Battelle Pacific
Northwest Laboratories, Richland, WA, for the U.S. Environmental Protection
Agency.
8-23
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Onishi, Y. (1982) User's manual for EXPLORE-I: a river basin water quality
module (hydraulic module only). EPA-600/3-82-054. U.S. Environmental
Protection Agency.
8-24
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CODE NAME: CAFE
PURPOSE: Two-dimensional hydrodynamics simulation in estuaries.
DIMENSIONALITY: Two-dimensional horizontal plane.
SOLUTION TECHNIQUE: The model is a numerical model that uses a finite element
approximation to the governing partial differential equations.
DESCRIPTION: The two-dimensional, depth averaged model is based on the conser-
vation of momentum and mass. The partial differential equations are incorpora-
ted in finite element form with triangular elements. The use of triangular
elements are convenient for the description of irregular boundaries. The model
assumes that the fluid density is independent of the velocity field. Friction
is represented as an effective shear stress. The model incorporates wind
stresses at the water surface.
INPUT: Geometry and grid definition; initial conditions for velocities and
water surface elevation; boundary conditions, water surface elevations, and/or
velocities; bottom friction coefficients; eddy viscosity coefficients; and wind
magnitude and direction.
OUTPUT: Fluid velocities and water surface elevation as a function of space
and time.
COMPILATION REQUIREMENTS:
Source Language: FORTRAN
Hardware Requirements: CDC 7600
Mass Storage Requirements: Unknown
EXPERIENCE REQUIREMENTS; Extensive.
TIME REQUIREMENTS: High, months.
SOURCE: See user's manual.
DOCUMENTATION/REFERENCES:
Pagenkopf, J.R.: Christodonlou, G.C.; Pearce, B.R.; Connor, J.J. (1976)
A user's manual for Case I, a two-dimensional finite element circulation
model. Report No. 217. Cambridge, MA: Massachusetts Institute of Tech-
nology, Department of Civil Engineering.
Wang, J.D.; Connor, J.J. (1975) Mathematical modeling of near coastal circu-
lation. Report No. 200. Cambridge, MA: Massachusetts Institute of Tech-
nology, Department of Civil Engineering.
8-25
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CODE NAME; WATFLO
PURPOSE; A hydrodynamic model for simulating flow in rivers and estuaries.
DIMENSIONALITY; Two-dimensional, horizontal plane.
SOLUTION TECHNIQUE: The model is a numerical model using the finite difference
technique to approximate the governing differential equations.
DESCRIPTION; The model is a two-dimensional depth averaged model based on the
couple equations describing conservation of momentum and mass. Time integration
is performed using a multi-operational finite difference scheme. The domain of
the system is represented on a staggered finite difference grid. The model is
a modification of Leendertse's 2-D model; adaptations were performed by the
Delft Hydraulics Laboratory* One important modification is a curvilinear coor-
dinate transformation particularly well suited for the simulation of rivers.
The model does not include density effects, and friction is represented as an
effective shear stress.
INPUT: Geometry and grid definition; bathymetry; friction coefficient (Chezy's
C); initial conditions (water elevation and 2-D velocity field); and boundary
conditions (inflows, water surface elevation, and or velocity).
OUTPUT; The output of the model includes the water surface elevation and the
depth averaged X-Y velocity components.
COMPILATION REQUIREMENTS:
Source Language: FORTRAN
Hardware Requirements: Unknown
Mass Storage Requirements: Unknown
EXPERIENCE REQUIREMENTS: Extensive.
TIME REQUIREMENTS: High, months.
SOURCE: Available on contractual basis from
Charles E. Sweeney
Engineering Hydraulics Inc.
P. 0. Box 3099 :
Redmond, WA 98052 :
(206) 881-7700
DOCUMENTATION/REFERENCES: Available from Engineering Hydraulics Inc., and
Leendertse, J.J. (1967) Aspects of a computational model for long-period
water-wave propagation. RM-5294-PR. Santa Monica, CA: The Rand Cor-
poration.
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CODE NAME: Water Quality Simulation Model for Well-Mixed Estuaries and Coastal
Seas (Leendertse-2D).
PURPOSE: A hydrodynamic and water quality model for simulating flow and con-
taminant transport.
DIMENSIONALITY: Two-dimensional.
SOLUTION TECHNIQUE: The model is a numerical model using the finite difference
technique to approximate the governing differential equations.
DESCRIPTION: The model is a two-dimensional, depth-averaged model based on the
coupled equations describing the conservation momentum and mass (both fluid and
contaminant). The time integration is performed using a multi-operational
finite difference scheme. The domain of the system is represented by a stag-
gered finite difference grid. The model is capable of simulating water flow
and the advection and dispersion of contaminants in coastal seas and well-mixed
estuaries.
The model does not include density effects or wind stress effects.
velocity fluctuations are aggregated into the shear stress terms.
Small scale
INPUT: Geometry and grid definition; bathymetry; friction coefficient (Chezy's
C); dispersion coefficients; initial conditions (water surface elevation, X and
Y velocity components, and contaminant concentrations); and boundary conditions
(contaminant sources, inflows water surface and/or velocity, and tidal eleva-
tion).
OUTPUT: The output of the model includes the water surface elevation, depth
averaged X and Y velocity components, and contaminant concentration as a func-
tion of space and time.
COMPILATION REQUIREMENTS:
Source Language: FORTRAN
Hardware Requirements: Unknown
Mass Storage Requirements: Unknown
EXPERIENCE REQUIREMENTS: Extensive.
TIME REQUIREMENTS: High, month(s).
SOURCE:
David Liu
Rand Corporation
Santa Monica, CA
DOCUMENTATION/REFERENCES:
Leendertse, J.J. (1967) Aspects of a computational model for long-period
water-wave propagation. RM-5294-PR. Santa Monica, CA: The Rand Corpora-
tion.
8-27
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Leendertse, J.J. (1970) A water quality model for well mixed estuaries and
coastal seas. In: Principles of computation, Vol. I. RM-6230-RC. Santa
Monica, CA: The Rand Corporation.
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CODE NAME: A Three-Dimensional Model for Estuaries and Coastal Seas
(Leehdertse-3D).
PURPOSE: A model for simulating hydrodynamic flow and transport in estuaries
and coastal seas.
DIMENSIONALITY: Three-dimensional.
SOLUTION TECHNIQUE: The model is a numerical model using the finite difference
technique to approximate the governing differential equations.
DESCRIPTION: The model is a three-dimensional model based on the coupled
equations describing the conservation momentum and mass. The momentum equation
is only represented in the X and Y directions, based on the assumption that the
vertical accelerations (Z direction momentum equation) are much smaller than
the acceleration due to gravity and may be neglected. The time integration is
performed using an explicit finite difference scheme with the variables at
each X-Y point over the vertical water column (Z direction) solved for impli-
citly to enhance stability. The domain of the system is represented by a
staggered finite difference grid. The model is capable of simulating water
flow and contaminant transport in coastal seas and well-mixed estuaries.
The model includes density effects and wind stress effects. The density vari-
ations are represented with an equation of state incorporating temperature
and salinity changes. Wind stress at the water surface is represented, as a"
quadratic function of the wind speed. Shear stress at the bottom is represented
as quadratic function of the X and Y fluid velocity components.
INPUT: Geometry and grid definition; bathymetry; friction coefficient (Chezy's
C); dispersion coefficients; initial conditions (water surface elevation, X, Y
and Z velocity components, and contaminant concentrations); and boundary condi-
tions (contaminant sources, inflows water surface and/or velocity, and tidal
elevation).
OUTPUT: The output of the model includes the water surface elevation, X, Y and
Z velocity components, and contaminant concentration as a function of space and
time.
COMPILATION REQUIREMENTS:
Source Language: FORTRAN
Hardware Requirements: IBM 360-91
Mass Storage Requirements: Unknown
EXPERIENCE REQUIREMENTS: Extensive.
TIME REQUIREMENTS: High, months.
SOURCE:
David Liu
Rand Corporation
Santa Monica, CA
8-29
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DOCUMENTATION/REFERENCES:
Leendertse, J.J.; Liu, S.-K. (1975) A three-dimensional model for estuaries
and coastal seas. Vol. II: Aspects of computation. R-1764-OWRT.
Santa Monica, CA: The Rand Corporation.
Leendertse, J.J.; Liu, S.-K. (1977) A three-dimensional model for estuaries
and coastal seas. Vol. IV: Turbulent energy computation. R-2187-OWRT.
Santa Monica, CA: The Rand Corporation.
Leendertse, J.J.; Alexander, R.C.; Liu, S.-K. (1973) A three-dimensional
model for estuaries and coastal seas. Vol. I: Principles of computation.
R-1417-OWRR. Santa Monica, CA: The Rand Corporation.
Leendertse, J. J., Liu, S.-K.; Nelson, A.B. (1975) A three-dimensional model
for estuaries and coastal seas. Vol. Ill: The interim program, R-1884-
OWRT. Santa Monica, CA: The Rand Corporation.
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8.3. SURFACE WATER TRANSPORT MODELS
8-31
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METHOD NAME: Hater Quality Assessment Methodology (WQAM)
PURPOSE: The methodology was developed as a screening tool for the assessment
of surface water quality in large basins.
DIMENSIONALITY: Zero-, one-, and two-dimensional.
SOLUTION TECHNIQUE: Analytical/empirical. '.'.-
DESCRIPTION: The methodology is a collection of formulas, tables, and graphs
for the preliminary assessment of water quality in large basins. Subject
categories include: point and nonpoint waste load estimation, temperature,
DO/BOD, nutrients, toxic chemicals, priority pollutants, and conservative and
nonconservative constituents. Nonpoint source loading is based on the modified
Universal Soil Loss Equatibn. Stream water quality is based on steady-state
conservation of mass assuming plug flow. Water quality in lakes is based on
a mass balance and empirical stratification relationship. The estuary water
quality section is based on a tidal prism and/or fraction of freshwater analy-
ses.
INPUT; Land use patterns, stream lengths, flow rates, reservoir volumes and
depths, estuary salinity distributions, and point source loads.
OUTPUT: The output of the analyses is a steady-state concentration of the
various constituents and pollutants subject to the loading rates defined.
COMPILATION REQUIREMENTS:
Hardware Required: Calculator
EXPERIENCE REQUIREMENTS: Low.
TIME REQUIREMENTS: Low, days.
SOURCE:
T. 0. Barnwell
U.S. Environmental Protection Agency
Environmental Research Laboratory
Center for Water Quality Modeling
College Station Road
Athens, GA
DOCUMENTATION/REFERENCES:
Mills, W.B.; Dean, J.D.; Porcella, D.B.; Gherini, S.A.; Hudson, R.J.M.; Frick,
W.E.; Rupp, G.L.; Bowie, G.L. (1982, Sept.) Water quality assessment:
a screening methodology for toxic and conventional pollutants. Parts 1,
2, and 3. EPA-600/6-82-004a,b,c. U.S. Environmental Protection Agency,
Washington, DC.
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METHOD NAME: Simplified Lake/Stream Analyses (SLSA)
PURPOSE: SLSA is a screening model for the analysis of dissolved and sorbed
steady-state concentration distributions in the water column and bed sediments
of rivers and lakes.
DIMENSIONALITY: Zero- and one-dimensional.
SOLUTION TECHNIQUE: Analytical solution.
DESCRIPTION: SLSA can be used to analyze the steady-state advective transport
of a pollutant; no 'dispersion term is incorporated. Degradation processes are
represented by first-order rate constants, which are summed to yield an aggre-
gate decay rate. Sediment suspension and exchange between the water column and
the bed sediments are incorporated in this simplified modeling analysis. The
sediment concentration suspended in the water column is a constant user-speci-
fied value. Only one reach of the river system is analyzed, assuming uniform
flow and geometry characteristics. The model is a steady-state model with some
"quasi-time varying" capabilities.
When applied to the analysis of rivers, the method is a one-dimensional analy-
sis. When applied to the analysis of lakes, the method is a zero-dimensional
(CSTR) analysis.
ASSUMPTIONS/LIMITATIONS: All decay kinetics are first-order. Dispersion is
not considered. Bed sediment is assumed to be stationary, and completely mixed.
Only one particle size is considered. One single point source is considered.
Only one river reach is considered, with no lateral inflows.
INPUT: Pollutant loading; flow rates, water and sediment depths, and length
of reach; suspended solids in water column, sedimentation", and resuspension
velocities; rate constants for kinetic reactions in water column and sediment
distribution coefficients.
OUTPUT: The output of the model is the pollutant concentrations in the water
column and in the bed sediments.
COMPILATION REQUIREMENTS:
Source Language: FORTRAN, calculations are also simple enough for a calcu-
lator
Hardware Requirements: Suitable for microcomputer
Mass Storage Requirements: None
EXPERIENCE REQUIREMENTS: Low.
TIME REQUIREMENTS: Low/ days.
8-33
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SOURCE:
William Gullege
Chemical Manufacturers Association
2581 M Street, N.W.
Washington, DC 20037
DOCUMENTATION/REFERENCES:
HydroQual Inc. (1981) Analysis of fate of chemicals in receiving waters.
Phase I. Prepared for Chemical Manufacturers Association, Washington, DC,
HydroQual Inc. (1982) Application guide for CMA-HydroQual chemical fate
models. Prepared for Chemical Manufacturers Association, Washington, DC.
8-34
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CODE NAME: MICHRIV
PURPOSE: MICHRIV is a steady-state model for simulating the transport of con-
taminants in the water column and bed sediments in streams and nontidal rivers.
DIMENSIONALITY: One-dimensional.
SOLUTION TECHNIQUE: Analytical computer model.
DESCRIPTION: MICHRIV:can be used to analyze the steady-state advective trans-
port of a pollutant; no dispersive term is incorporated. 'Degradation processes
are represented as an aggregate first-order decay rate. The river can be seg-
mented into successive reaches where characteristics are reasonably constant.
The sediment concentration within the water column is a solution variable which
is a function of the flow characteristics and sources. Since the model is
based on an analytical solution, it is comparatively easy to set up and use.
ASSUMPTIONS/LIMITATIONS: All decay coefficients are first-order. Dispersion
is not considered. Only one particle size is considered. This modeling analy-
sis is only applicable to steady-state flow and loading conditions.
INPUT: System geometry, flow rates, loading rates of pollutants and particu-
lates, partition coefficients, first-order decay coefficients, and sediment/
water exchange parameters.
OUTPUT: The output of the model includes the pollutant concentration, in
dissolved and particulate forms, as a function of distance from the source.
The suspended sediment concentration is also predicted.
COMPILATION REQUIREMENTS:
Source Language: FORTRAN
Hardware Requirements: Suitable for microcomputer
Nass Storage Requirements: None
EXPERIENCE REQUIREMENTS: Low.
TIME REQUIREMENTS: Moderate, weeks.
SOURCE:
Bill L. Richardson
U.S. Environmental Protection Agency
Environmental Research Station - Duluth
Large Lakes Research Station
Grosse He, MI 48138
DOCUMENTATION/REFERENCES:
DePinto, J.V.; Richardson, W.L.; Rygwelski, K. (1984) Technical guidance
manual for performing waste load allocation. EPA-440/4-84-022. U.S.
Environmental Protection Agency, Washington, DC.
8-35
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CODE NAME: Chemical Transport and Analysis Program (CTAP)
PURPOSE: CTAP is a multi-dimensional, steady-state model for the analysis of
dissolved and sorbed concentration distributions in the water column and bed
sediments of rivers, lakes, and estuaries.
DIMENSIONALITY: One-, two-, or three-dimensional.
SOLUTION TECHNIQUE: The model is a numerical model in finite difference form.
The numerical approximation is formulated in compartments so that it may be
applied to one-, two-, or three-dimensional problems.
DESCRIPTION: The CTAP model simulates the hydrologic transport and degradation
of contaminants in water systems. The hydrologic transport processes included
are advection and dispersion. Degradation is represented by first-order reac-
tion kinetics for photolysis, oxidation, hydrolysis, and biodegradation. Decay
rate coefficients are supplied by the user and summed to form an aggregate
decay rate. Sorption of dissolved contaminants to sediments is incorporated
as an equilibrium process. Sedimentation processes included in the model are
bed movement, settling, suspension, burial, and diffusive exchange between bed
sediments and dissolved contaminants. Five different particle sizes are
accounted for, and multiple source terms are allowed.
ASSUMPTIONS/LIMITATIONS: Degradation is limited to first-order kinetics. The
flow field must be defined externally via direct measurements or a hydrodynamic
simulation model. Nonpoint sources are not incorporated. Steady-state analy-
sis is limited to continuous sources.
INPUT: Geometry and grid definition, fluxes between compartments and disper-
sion coefficients, pollutant loadings, sediment fluxes between compartments and
dispersion coefficients, sediment loadings, equilibrium distribution coeffici-
ents for each sediment category, kinetic reaction coefficients.
OUTPUT; The output of the model is the spatial distribution of chemical con-
centrations in dissolved and particulate forms. Concentrations are described
for both the water column and the bed sediments.
COMPILATION REQUIREMENTS:
Source Language: FORTRAN
Hardware Requirements: The model has been implemented on various computers
including IBM 360/370, Univac 1108, CDC 6600, POP 11/70, VAX 11-750,
11-780, IBM 1130. '
Mass Storage Requirements: Some subroutine overlay with disk scratch files
may be necessary to implement the model on minicomputers (without
virtual memory). ;
EXPERIENCE REQUIREMENTS: Moderate.
TIME REQUIREMENTS: Moderate, weeks.
8-36
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SOURCE:
William Gull edge
Chemical Manufacturers Association
2581 M Street, N.W.
Washington, DC 20037
(202) 887-1183 ;
DOCUMENTATION/REFERENCES:
Games, L. (1981) Practical applications and comparisons of environmental
exposure assessment models. Presented at the American Society for Test-
ing and Materials Sixth Symposium of Aquatic Toxicology, St. Louis, MO.
HydroQual Inc. (1981) CTAP Documentation: Chemical Transport Analysis Pro-
gram. Prepared for the Chemical Manufacturers Association, Washington,
DC.
HydroQual Inc. (1982) Application guide for CMA-HydroQual chemical fate
models. Prepared for the Chemical Manufacturers Association, Washing-
ton, DC.
8-37
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CODE NAME: EXAMS . . . .
PURPOSE: Designed to evaluate the fate, exposure, and persistence of toxic
chemicals in water systems vjfhere the concentrations of pollutants are at trace
levels and the pollutant loading rates can be assumed to be steady state.
DIMENSIONALITY: One-, two-, or three-dimensional.
SOLUTION TECHNIQUE: The model is a numerical model in finite difference form.
The numerical approximation is formulated in compartments so that it may be
applied to one-, two-, or three-dimensional problems.
DESCRIPTION: EXAMS can be used to simulate the hydrologic transport and bio-
chemical transformation of toxic chemicals in the water environment. The
hydrologic transport processes that are included are advection and dispersion.
The transformation processes' that are included in the model are photolysis,
hydrolysis, biotransformation, oxidation reaction, and sorption with sediments
and biota. In addition, volatilization at the water-air interface is also
incorporated. Secondary daughter products and subsequent degradation of those
products are considered.
The model is not designed to evaluate the contaminant concentration from pollu-
tant problems such as spills of toxic chemicals. This limitation is the result
of two assumptions incorporated in the model: 1) the steady flow field may not
adequately describe the hydrologic transport processes associated with a large
spill; and 2) the transformation processes included in the model assume that a
toxic contaminant does not change th.e environments! factors that govern its
transformation; in other words, the contaminants are present at trace levels.
ASSUMPTIONS/LIMITATIONS: The important assumptions/limitations are: steady-
state or monthly-varying loading and flow field; the hydrodynamic flow field is
determined externally from the model and input as vectors of flux and disper-
sion between compartments; chemicals in the water system are at trace levels
and hence do not change the characteristics of the water system responsible for
the transformation of the chemicals; sorption/desorption processes are assumed
to be at equilibrium within each compartment; and the chemicals within any
compartment are assumed to be uniformly mixed and homogeneous throughout the
given compartment.
INPUT: System geometry (volumes, areas, and transport pathways between zones);
hydrologic parameters (fluxes between zones, rainfall, evaporation rates,
entering stream flows, nonpoint source loads, sediment loads, and groundwater
flows); transformation parameters (sediment and biota sorption, volatilization,
photolysis, oxidation, hydrolysis, and biotransformation); and environmental
parameters (temperature, wind speed, pH, solar insulation, and scattering).
OUTPUT: The output of the model is the concentration of the pollutant of
interest in the water, sediment, and biota for each zone. In addition, the
concentrations of any daughter products due to transformations are included.
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COMPILATION REQUIREMENTS:
Source Language: FORTRAN .
Hardware Requirements: The model has been implemented on various computer
systems including IBM 370, CDC Cyber, POP 11, HP 3000, and PC-compati-
ble microcomputers.
Mass Storage Requirements: 2.5K words
EXPERIENCE REQUIREMENTS: Moderate.
TIME REQUIREMENTS: Moderate, weeks.
SOURCE:
Lawrence A. Burns
U.S. Environmental Protection Agency
Athens Environmental Research Laboratory
College Station Road
Athens, GA 30613
DOCUMENTATION/REFERENCES:
Burns, L.A.; Cline, D.M.; Lassiter, R.R. (1982) Exposure Analysis Modeling
System (EXAMS): user manual and system documentation. EPA-600/3-82-023.
U.S. Environmental Protection Agency, Athens, GA.
Burns, L.A.; Cline, D.M. (1985) EXAMS-II: Exposure Analysis Modeling System,
Reference Manual for EXAMS-II. EPA-600/3-85-038. U.'S. Environmental
Protection Agency, Athens, GA.
8-39
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CODE NAME: MEXAMS
PURPOSE; MEXAMS is a steady-state model designed to evaluate the fate and
transport of metals in aquatic systems. The model is a linking of a geochem-
ical model, MINTEQ, and EXAMS.
DIMENSIONALITY: One-, two-, or three-dimensional.
SOLUTION TECHNIQUE: The model is a numerical model in finite difference form.
The numerical approximation' is formulated in compartments so that it may be
applied to one-, two-, or three-dimensional problems.
DESCRIPTION:
MEXAMS can be used to evaluate the hydrologic transport, biochem-
transformation, and speciation of dissolved adsorbed and precipitated
in the water environment. The chemical interactions are based on ther-
ical
metals
modynamic equilibrium relationships between the different species of the metal
and pertinent water quality parameters. Several different adsorption algo-
rithms are incorporated in the model. A thermodynamic data base for the fol-
lowing metals is incorporated in the model: arsenic, cadmium, copper, lead,
nickel, silver, and zinc. The primary advantage of the MEXAMS model lies in
its ability to represent the complex chemistry of metals in water bodies,
particularly the effect of chemical speciation on adsorption and precipitation.
ASSUMPTIONS/LIMITATIONS: Steady-state loading and flow field; hydrodynamic
flow field is determined externally; all chemical processes are considered to
be equilibrium processes; the thermodynamic data base is limited to specific
metals; and the chemicals within any given compartment are assumed to be uni-
formly mixed and homogeneous throughout.
INPUT: The first part of the input data is related to the EXAMS portion of the
model and is described in the previous code description. The second part of
the input data is related to the MINTEQ portion and is contained in a data base
that goes with the model (but it is limited to the specific metals in the data
base). !
OUTPUT: The output of the model includes the concentration of the different
metal species in different forms (dissolved, adsorbed, and precipitated) in
each compartment of system.
COMPILATION REQUIREMENTS;
Source Language: FORTRAN
Hardware Requirements: POP 11/70 or HP 3000; MINTEQA1 available on
PC-compatible microcomputers.
Mass Storage Requirements: Unknown
EXPERIENCE REQUIREMENTS: Extensive.
TIME REQUIREMENTS: High, month(s).
8-40
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SOURCE:
David Brown
U.S. Environmental Protection Agency
Athens Environmental Research Laboratory
Athens, GA 30613
DOCUMENTATION/REFERENCES:
Burns, L.A.; Cline, D.M.; Lassiter, R.R. (1982) Exposure Analysis Modeling
System (EXAMS): user manual and system documentation. EPA-600/3-82-023.
U.S. Environmental Protection Agency, Athens, GA.
Felmy, A.R.; Brown, S.M.; Onishi, Y.; Argo, R.S.; Yabusaki, S.B. (1982)
MEXAMS: the Metals Exposure Analysis Modeling System. Contract No.
68-03-3089. Battelle Pacific Northwest Laboratories, Richland, WA.
Brown, D.S. (1987) MINTEQA1, an Equilibrium Metal Speciation Model: users
manual. Final draft. U.S. Environmental Protection Agency, Athens, GA.
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CODE NAME; TOXIWASP
PURPOSE: TOXIWASP is a transient model for simulating the transport and fate
of toxic chemicals in water bodies. The model is basically a combination of
the EXAMS and WASP models with additional sediment transport capabilities.
DIMENSIONALITY: One-, two-, or three-dimensional.
SOLUTION TECHNIQUE; The model is a numerical model in finite difference form.
The numerical approximation is formulated in compartments so that it may be
applied to one-, two-, or three-dimensional problems.
DESCRIPTION; TOXIWASP can be used to simulate the hydrologic transport and
biochemical transformation of toxic chemicals in the water environment. The
hydrologic transport phenomena included are advection and dispersion. Various
biochemical transformation processes are incorporated, ' - --
biolysis, photolysis, oxidation, and volatilization.
onto biota and sediments are included. The transport
advection, diffusion, and settling.
including hydrolysis,
In addition, sorption
of sediment includes
ASSUMPTIONS/LIMITATIONS: The important assumptions of the model are: the con-
centration in any compartment is completely mixed; sorption is treated as an
equilibrium process; and the degradation rates for the different processes can
be combined linearly to form a single degradation rate for particular chemicals
in each segment. The explicit integration scheme is only conditionally stable,
so that the time step must be chosen carefully. The hydrodynamic flow field
must be determined externally.
INPUT: Geometry and grid definition; fluxes between zones; dispersion coeffi-
cients; initial conditions; boundary conditions; input loads; sediment proper-
ties (density, organic content, settling velocities, dispersion rates)- chem-
ical properties and rates (partition coefficients, hydrolysis, photolysis, and
oxidation); and temperature, pH, light intensity, wind speed, and extinction
coefficients.
OUTPUT: The output of the model is the contrations); and chemicals in the
water and in the sediments as a function of space and time. Also output are
some summary statistics and spatial plots of concentration.
COMPILATION REQUIREMENTS:
Source Language: FORTRAN77
Hardware Requirements: the model has been implemented on POP 11-70,
IBM 370, and PC-compatible microcomputers.
Mass Storage Requirements: Disk storage 32K words; 512K and math
coprocessor.
EXPERIENCE REQUIREMENTS: Extensive.
TIME REQUIREMENTS: High, month(s).
8-42
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SOURCE:
Robert B. Ambrose, Jr.
U.S. Environmental Protection Agency
Athens Environmental Research Laboratory
Athens, 6A 30613
DOCUMENTATION/REFERENCES:
Ambrose, R.B., Jr.; Hill, S.I.-; Mulkey, L.A. (1983, Mar.) User's manual for
the Chemical Transport and Fate Model (TOXIWASP), Version 1. EPA-6.00/3-
83-005. U.S. Environmental Protection Agency, Environmental Research
Laboratory, Athens, GA.
Abrose, R.B. (1986, Mar.) WASPS, A Hydrodynamic and Water Quality Model
(DYNHYD3), Model Theory, User's Manual and Programmer's Guide. EPA-
600/3-86-034. U.S. Environmental Protection Agency, Environmental
Research Laboratory, Athens, GA.
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CODE NAME: WASTOX
PURPOSE: WASTOX is a transient model for simulating the transport and degrada-
tion of toxic chemicals in water bodies.
DIMENSIONALITY: One-, two-, or three-dimensional.
SOLUTION TECHNIQUE: The model is a numerical model in finite difference form.
The numerical approximation,is formulated in compartments so that it may be
applied to one-, two-, or three-dimensional problems.
DESCRIPTION: WASTOX can be'used to simulate the hydrologic transport and bio-
chemical degradation of toxic chemicals in the aquatic environment. The hydro-
logic processes included are advection and dispersion. The model considers
chemicals both in dissolved form and adsorbed to particulates. Kinetic pro-
cesses are specified through subroutines that may be modified by the user. The
model is similar to the TOXIWASP model, with some differences in the mechanisms
for transport between bed sediments and the water column.
ASSUMPTIONS/LIMITATIONS: The important assumptions of the model are the con-
centration of contaminant in any compartment is completely mixed; and the
degradation rates for the different processes can be combined to form a single
degradation rate for the particular chemical in each compartment. The explicit
integration scheme is only conditionally stable, so the time step and spatial
resolution must be chosen carefully. The hydrodynamic flow field must be
determined externally.
INPUT; Geometry and grid definition; fluxes between zones; dispersion coeffi-
cients; initial conditions; boundary conditions; rate constants for reaction
kinetics; sediment characteristics; and temperature, pH, wind speed, and ex-
tinction coefficients.
OUTPUT: The output of the model is the pollutant concentration as a function
of space and time. The contaminant concentration is given for both dissolved
and particulate forms, along with the concentration with depth in the sediment.
COMPILATION REQUIREMENTS: :
Source Language: FORTRAN
Hardware Requirements: The model is implemented on a POP 11-70
Mass Storage Requirements: Disk storage 25K words
EXPERIENCE REQUIREMENTS; Extensive.
TIME REQUIREMENTS: High, mohth(s).
SOURCE:
John P. Connolly
Manhattan College
Bronx, NY 10471
8-44
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DOCUMENTATION/REFERENCES:
Connolly, J.P.; Winfield, R.P. (1984, Aug.)
framework for modeling the fate of toxic
ments. Part 1: Exposure concentration.
mental Protection Agency, Washington, DC.
A user's guide for WASTOX, a
chemicals in aquatic environ-
EPA-600/3-84-077. U.S. Environ-
8-45
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CODE NAME: Channel Transport Model (CHNTRN)
PURPOSE; The CHNTRN model is a transient model for simulating the transport of
sediments and contaminants in rivers and well-mixed estuaries.
DIMENSIONALITY; One-dimensional (possibly more with modifications).
SOLUTION TECHNIQUE; The model is a numerical model based on an integrated com-
partment formulation. A system of ordinary differential equations is formulated
based on the conservation of mass for each compartment. Time integration may
be performed explicitly or implicitly.
DESCRIPTION; The CHNTRN model is based on the conservation of mass and incor-
porates a variety of chemical kinetics, sediment transport, deposition, and
scouring for sand, silt, and clay. The hydrologic transport processes included
in the model are advection and dispersion. The model incorporates second-order
kinetics using the EXAMS framework to account for hydrolysis, oxidation, pho-
tolysis, volatilization, biodegradation, and adsorption by biota. Sediment
transport is represented in a mechanistic fashion, where the concentration and
flux of sediments are unknown solution variables. The model is capable of
simulating channel networks so that branching river and tributary systems may
be analyzed. The integrated compartment formulation of the model may make
modifications to the model, such as two- or three-dimensional simulations for
lakes or estuaries, somewhat easier.
ASSUMPTIONS/LIMITATIONS: The important assumptions and limitations of the
m?del ar^:the one-dimensional formulation limits the application to situa-
tions where parameters are well mixed vertically and laterally; hydrodynamic
data must be specified externally (a companion code CHNHYD is available for
hydrodynamic simulation); and extensive input data is required characterizing
sediment sizes and chemical properties of the different sizes.
INPUT: Geometry and grid definition; hydrodynamic data, fluxes between com-
partments, dispersive coefficients; rate coefficients for photolysis, hydroly-
sis, oxidation, and biodegradation; pollutant sources and loads; sediment types
and distributions; and temperature, wind speed, vapor pressure, and extinction
coefficients.
OUTPUT; The output of the model includes: dissolved chemical concentration as
a function of space and time, particulate concentration suspended in the water
column and in bed sediments, and suspended sediment concentration and amount of
sediment remaining in the bed.
COMPILATION REQUIREMENTS:
Source Language: FORTRAN IV
Hardware Requirements: The model has been implemented on an IBM 3033
Mass Storage Requirements: Unknown
EXPERIENCE REQUIREMENTS: Extensive.
TIME REQUIREMENTS: Moderate, weeks.
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SOURCE:
G. T. Yeh
Environmental Sciences Division
Oak Ridge National Laboratory
P. 0. Box X
Oak Ridge, TN 33830
DOCUMENTATION/REFERENCES:
Yeh, G.T. (1981) ICM: an integrated compartment method for numerically
solving partial differential equations. ORNL-5684. Oak Ridge National
Laboratory, Oak Ridge, TN.
Yeh, G.T. (1982) CHNTRN: a channel transport model for simulating sediment
and chemical distribution in a stream/river network. ORNL-5882. Oak
Ridge National Laboratory, Oak Ridge, TN.
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CODE NAME; HSPF
PURPOSE: HSPF is a series of coupled computer codes designed to simulate:
1) watershed hydrology; 2) land surface runoff; and 3) the fate and transport
of pollutants in receiving water bodies. The model is a transient model appli-
cable to rivers and well-mixed (unstratified) reservoirs.
DIMENSIONALITY: The analysis of rivers is one-dimensional and the analysis of
reservoirs is zero-dimensional.
SOLUTION TECHNIQUE: The model is a numerical model in finite difference form
with some empirical components.
DESCRIPTION: The HSPF model is a comprehensive model designed to simulate a
wide variety of hydrologic and environmental phenomena affecting the fate and
transport of pollutants. The hydrologic portions of the model include: 1) a
watershed hydrology model similar to the Stanford Watershed Model; 2) a runoff
model using algorithms similar to the Non-Point Source (NPS) model; and 3) a
stream routing component using a kinematic wave approximation.
The analysis of sediment transport in the model is formulated in a mechanistic
fashion. The sediment transport mechanisms incorporated in the model include
settling, deposition, and scouring. Three particle sizes are incorporated in
the model, generally corresponding to sand, silt, and clay. The adsorption/
desorption processes are calculated separately for each particle size, suspen-
ded in the water column and in the bed sediment.
The degradation/transformation processes included in the model are: hydroly-
sis, photolysis, oxidation, volatilization, and biodegradation. The kinetic
reactions are formulated as second-order processes. Secondary or "daughter"
chemicals are also simulated; up to two daughter chemicals can be analyzed in
a single simulation.
The model was initially formulated as the integration of several existing
models, including: SWM, NPS, ARM, EXAMS, SERATRA, and HSP. Rather than iden-
tify the existing models as subroutines, the entire modeling framework was
rewritten to make understanding and modifications to the program easier for
users.
ASSUMPTIONS/LIMITATIONS: The important assumptions and limitations of the
model are the one-dimensional formulation limits application of the model
to river systems where pollutants are uniformly mixed both laterally and ver-
tically; the kinematic wave formulation of flow in rivers is not applicable
to rivers where the gradient is very small or where backwater effects are
present; data requirements for the model may be quite extensive depending on
the particular application; and the zero-dimensional representation of lakes
assumes that pollutants are uniformly mixed throughout and that the lake is not
stratified.
INPUT: The amount and types of input data are dependent on the particular
options used in a given simulation. These data may include:
8-48
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Time series inputs, including air temperature, precipitation, evapo-
transpiration, channel inflow, surface water and groundwater inflow,
and wind movement;
Constant parameter inputs, including channel geometry, vegetative cover
indexi surface detention storage, groundwater storage volume, soil
moisture content, overland flow slope, snow-pack data, infiltration
index, and interflow index;
Land sediment factors: soil detachment coefficients, sediment influx,
surface cover, and sediment washoff coefficient;
Soil temperature data: air temperature time series, slope, and inter-
cept of land temperature to air temperature equation;
Dissolved gas in land water: ground elevation, interflow, and ground-
water DO and C02 concentrations;
Quality constituents associated with sediment: washoff potency factor
and scour potency factor;
.Quality constituents concentrations in interflow and groundwater;
Agrichemical quality constituent: solute leaching factors; soil layer
depths; soil densities; and pesticide and nutrient sorption parameters,
solubility factors, and degradation rates;
Impervious land quality factors: surface runoff removal rates, solids
washoff coefficient, rate of solids placement and removal on surface,
and overland flow-borne pollutant accumulation and storage rates; and
Reach and reservoir water quality characteristics, coefficients, and
rates.
OUTPUT: HSPF output consists of multiple printouts, including system state
variables, pollutant concentrations at a point versus time, and yearly sum-
maries describing pollutant duration and flux. The model also includes a
frequency analysis which provides a statistical summary of time-varying con-
taminant concentrations and provides the link between simulated instream tox-
icant concentrations and risk assessment.
COMPILATION REQUIREMENTS:
Source Language: FORTRAN??
Hardware Requirements: Originally developed on a HP 3000 system, the model
has been installed on a wide variety of mainframe and virtual memory
systems, and PC-compatible microcomputers.
Mass Storage Requirements: Twelve internal files are required and 128K
bytes of instruction and data storage.
EXPERIENCE REQUIREMENTS: Extensive.
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TIME REQUIREMENTS; Moderateito high, weeks to months (depending on applica-
tion]^
SOURCE:
T. 0. Barnwell
U.S. Environmental Protection Agency
Environmental Research Laboratory
College Station Road
Athens, GA 30613
DOCUMENTATION/REFERENCES:
Donigian, A.S.; Imhoff, J.C.; Bicknell, B.R.; Kittle, J.L. (1984, June)
Guide to the application of the Hydrological Simulation Program: FORTRAN
(HSPF). EPA-600/3-84-065. U.S. Environmental Protection Agency, Environ-
mental Research Laboratory, Athens, GA.
Imhoff, J.C.; Kittle, J.L.; Donigian, A.S.; Johanson, R.C. (1984, June)
Hydrological Simulation ProgramFORTRAN (HSPF): User's manual for
Release 8.0. EPA-600/3-84-006. U.S. Environmental Protection Agency,
Environmental Research Laboratory, Athens, GA.
Johanson, R.C.; Kittle, J.L. (1983) Design, programming, and maintenance of
HSPF. J. Technical Topics in Civil Engineering 109(1):41-57.
Johanson, R.C.; Imhoff, G.C.; Davis, H.H. (1980) User's manual for Hydro-
logical Simulation Program: FORTRAN (HSPF). EPA 600/9-9-80-015. U.S.
Environmental Protection Agency, Environmental Research Laboratory, Athens,
GA. , ,
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CODE NAME: FETRA
PURPOSE: The FETRA model is a two-dimensional, depth averaged, transport
modelThe model simulates the transport of dissolved contaminants, sediments,
and contaminants adsorbed by the sediments. The model is applicable to well-.
mixed estuaries, coastal seas, and some shallow lakes.
DIMENSIONALITY: Two-dimensional, horizontal plane.
SOLUTION TECHNIQUE: The model is a numerical model that uses a-finite'element
approximation to the governing partial differential equations.
DESCRIPTION: The model is based on the general advection-diffusion equation
with decay, source/sink terms, and appropriate boundary conditions. Three
coupled submodels are included incorporating sediment transport, dissolved
contaminant transport, and particulate contaminant transport. Sediment trans-
port processes incorporated in the model include advection, and dispersion,
settling, deposition and erosion, and mixing from point and nonpoint sediment
sources. Contaminant transport processes included in the model are advection,
dispersion, adsorption/desorption by sediments, decay and biochemical degrada-
tion, and mixing of point and nonpoint contaminant sources.
INPUT: Geometry and grid definition; velocity field from a compatible flow
simulation model; verticaldispersion coefficient; distribution coefficients
(Kd) for each sediment-; deposition and erosion rates for sediments; decay rate
coefficients; particle settling velocity; particle density and diameter; cri-
tical shear stresses for bed scouring and sediment deposition; degradation and
decay rates; initial conditions (dissolved contaminant concentrations, sedi-
ments, adsorbed contaminant concentrations, and bed conditions); and boundary
. conditions (sediment, dissolved and particulate contaminant concentrations at
boundaries, and contribution from point and nonpoint sources).
OUTPUT: Concentration of contaminants as a function of space and time in dis-
solved and adsorbed form and location of sediment movement in bed and suspended
in the water column.
COMPILATION REQUIREMENTS:
Source Language: FETRA is written in the FORTRAN preprocessor language
FLECS. A standard FORTRAN IV version is available; however, it is
difficult to interpret and the FLECS version is much easier to follow
Hardware Requirements: IBM, VAX, CDC-7600
Mass Storage Requirements: Unknown
EXPERIENCE REQUIREMENTS: Extensive.
TIME REQUIREMENTS; Months.
SOURCE
Y. Onishi
Battelle,
Richland,
Pacific Northwest
WA 99352
Laboratories
8-51
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DOCUMENTATION/REFERENCES;
Onishi, Y.; Thompson, F.L. (1984) Mathematical simulation of sediment and
radionuclide transport in coastal seas. Vol. 1: Testing of the sediment/
radionuclide, transport model, FETRA. Vol. 2: User's manual and computer
listing for FETRA. NUREG/CR-2424; PNL-5088-1. Battelle Pacific Northwest
Laboratory, Richland, WA.
8-52
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CODE NAME: SERATRA
PHYSICAL PROCESSES: The SERATRA model can be used to simulate the transport of
contaminants and sediments in rivers over a two-dimensional vertical plane.
DIMENSIONALITY: Two-dimensional.
SOLUTION TECHNIQUE: The model is a numerical model using the finite element
method to approximate the governing differential equations.
DESCRIPTION: The model is based on the general advection-diffusion,equation
with decay, source/sink terms, and appropriate boundary conditions. Three
coupled submodels are included which incorporate sediment transport, dissolved
contaminant transport, and particulate contaminant transport. The sediment
transport processes incorporated in the model include advection, dispersion,
settling, deposition and erosion, and contributions from tributaries. The
contaminant transport processes incorporated in the model include advection,
dispersion, adsorption/desorptiqn by sediments, decay and biochemical degrada-
tion, and mixing of point and nonpoint contaminant sources. Degradation pro-
cesses included in the model are photolysis, oxidation, hydrolysis, biological
decay, and volatilization at the water-air interface.
<*
The model does not include a longitudinal diffusion term. A "downstream march-
ing solution" is employed in the model; hence it is not applicable to tidal
rivers, where the directions of flow may reverse.
ASSUMPTIONS/LIMITATIONS: The model represents a two-dimensional vertical plane,
so that lateral variations across the stream are ignored (lateral variations
may be important near point source and also in wide rivers); extensive input
data is required characterizing sediment sizes and chemical properties of the
various sizes; longitudinal dispersion is not considered, but variations in the
longitudinal velocity over the vertical column can be incorporated; the flow
field must be determined externally in a hydrodynamic simulation model or
direct measurements.
CODE INPUT: The input to the model includes: geometry and grid definitions;
discharge and depth of river; inflows from tributaries, overland runoff, and
point and nonpoint sources; vertical dispersion coefficient; sediment sizes and
densities; settling velocities; critical shear stress for erosion and deposi-
tion; erodibility coefficients; distribution coefficients for each sediment
size; degradation and decay rates; initial conditions for sediments, dissolved,
and particulate contaminants; and boundary conditions for sediments, dissolved,
and particulate contaminants.
CODE OUTPUT: The output of the model includes the concentration of sediments,
and dissolved and particulate contaminants as a function of space and time.
In addition, changes in bed elevation and contaminant concentration in the bed
sediments are provided.
8-53
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COMPILATION REQUIREMENTS:
Source Language: SERATRA is written in the FORTRAN preprocessor language
FLECS. A standard FORTRAN version is available; however, it is diffi-
cult to read (due to the FLECS translation), and the FLECS version is
much easier to interpret.
Hardware Requirements: CDC and VAX
Mass Storage Requirements: Unknown
EXPERIENCE REQUIREMENTS: Extensive.
TIME REQUIREMENTS: Months.,
SOURCE:
Y. Onishi
Battelle,
Rich!and,
Pacific Northwest
WA 99352
Laboratory
DOCUMENTATION/REFERENCES:
Onishi, Y.; Wise, S.E. (1982) User's manual for the Instream Sediment-
Contaminant Transport Model SERATRA. EPA-600/3-82-055. U.S. Environ-
mental Protection Agency, Washington, DC.
Onishi, Y.; Wise, S.E. (1982) Mathematical model, SERATRA, "for sediment-
contaminant transport in rivers and its applications to pesticide
transport in Four Mile and Wolf Creeks in Iowa. EPA-600/3-82-045.
U.S. Environmental Protection Agency, Washington, DC.
8-54
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APPENDIX A
DEFINITION OF SYMBOLS
Symbol
A
C
Cf
d
D
Ev
Et
g
k
KT
Kf
Kp
1
m
M
Mj
p
PF
PE
q
Definition
Average cross sectional area of river
Concentration of dissolved contaminants
Cover Factor
Initial concentration
Total concentration, dissolved and adsorbed
Depth
Dispersion coefficient
Vertical mixing coefficient
Transverse mixing coefficient
Acceleration-of gravity
Rate coefficient
Total first order rate coefficient
Soil credibility factor
Partition coefficient
Segment length
Slope gradient factor
Mass discharge rate
Concentration of particulate matter
Initial mass of contaminant
Concentration of adsorbed contaminants
Erosion control practice factor
Peclet number
Vector of x,y,z velocity components
Units
L2 .
M/L3
M/L3
M/L3
L
L2/T
L2/T
L2/T
L/T2
1/T
1/T
T/L2
M/M
L
M/T
M/L3
M
M/L3
L/T
A-l
-------
Symbol
Q
Of
sr
R
Rf
Rp
Rxn
s
sm
S
Sgf
t
ZT
*
u
U
Va
Vt
W
«s
x
X
Definition
Flowrate
Freshwater inflow rate
Summation of reactions terms
Estuary Richardson number
Rainfall factor
Mass of chemical per unit mass of
particulate
Reaction number
Source/sink terms for dissolved
contaminants
Source/sink terms for particulate
matter
Channel slope
Slope gradient factor
Time
Advection time
Diffusion time
Transformation time
Summation phase transfer mechanisms
Shear velocity
Mean cross sectional velocity
Depth mean amplitude of current
Root mean square tidal velocity
Width
Settling velocity
Cartesian coordinate
Downstream distance
Units
L3/T
L3/T
M/L3/T
M/T
M/M
M/L3/T
M/L3/T
L/L
T
T
T
T
M/L3/T
L/T
L/T
L/T
L/T
L
L/T
L
L
A-2
-------
Symbol
y
Y(s)
z
v
a
P
Ap
Definition
Cartesian coordinate
Annual sediment yield
Cartesian coordinate
Del operator
Dimensionless empirical coefficient
Density
Difference in density
Units
L
M/L2
L
1/L
M/L3
M/L3
A-3
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