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TITLE: Technical Guidance Manual for Performing Wasteload Allocations, 

Book III: Estuaries – 

Part 1: Estuaries and Wasteload Allocation Models 

EPA DOCUMENT NUMBER: DATE: May 1990 

ABSTRACT 

As part of ongoing efforts to keep EPA’s technical guidance readily accessible to 

water quality practitioners, selected publications on Water Quality Modeling and 

TMDL Guidance available at http://www.epa.gov/waterscience/pc/watqual.html 

have been enhanced for easier access. 

This document is part of a series of manuals that provides technical information 

related to the preparation of technically sound wasteload allocations (WLAs) that 

ensure that acceptable water quality conditions are achieved to support 

designated beneficial uses. The document provides technical information and 

policy guidance for performing WLAs in estuaries, which, because of their 

complex transport processes, cannot be treated as simple advective systems like 

many rivers. 

Book III Part 1 contains an overview of estuary characteristics, water quality 

problems, and the processes affecting those problems. It also provides 

specialized modeling guidance for the WLA, discusses the steps involved in 

modeling, and presents background information on 19 different models that are 

classified according to the spatial and temporal complexity of the models’ 

hydrodynamic component. The companion volume “Part 2: Application of 

Estuarine Waste Load Allocation Models” is a guide to monitoring, and to model 

calibration and testing. 

KEYWORDS: Wasteload Allocations, Estuaries, Modeling, Water Quality Criteria 

EPA 823/R-92-002
United States

Environmental Protection

Agency

Office of Water

Washington, DC 20460

EPA-823-R-92-002

May 1990

Technical Guidance

Manual for Performing

Waste Load Allocations

Book III

Estuaries

Part 1

Estuaries and Waste Load

Allocation Models
TECHNICAL GUIDANCE MANUAL

FOR PERFORMING WASTE LOAD ALLOCATIONS

BOOK III: ESTUARIES

PART 1: Estuaries and Waste Load Allocation Models

Project Officer

Hiranmay Biswas, Ph.D.

Edited by

Robert B. Ambrose, Jr. P.E.1

James L. Martin, Ph.D.,P.E.2

Sections written by

Robert B. Ambrose, Jr., P.E.1

James L. Martin, Ph.D., P.E.2

John F. Paul, Ph.D.3

1. Center for Exposure Assessment Modeling,

Environmental Research Laboratory, U.S. EPA, Athens, GA

2. AScI Corp., at the

Environmental Research Laboratory, U.S. EPA, Athens, GA

3. Environmental Research Laboratory,

U.S. EPA, Narragansett, RI

Prepared for

U.S. ENVIRONMENTAL PROTECTION AGENCY

401 M Street, S.W.

Washington, DC 20460

Table of Contents

Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .ix

Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv

Executive Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii

PART I: Estuaries and Waste Load Allocation Models . . . . . . . . . . . . . . . xvii

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii

Overview of Processes Affecting Estuarine Water Quality . . . . . . . . . . . . . xvii

Model Identification and Selection . . . . . . . . . . . . . . . . . . . . . . . . . xviii

PART II: Application of Estuarine Waste Load Allocation Models . . . . . . . . . xix

Monitoring Protocols for Calibration and Validation of Estuarine WLA Models . . . xix

Model Calibration, Validation, and Use . . . . . . . . . . . . . . . . . . . . . . . . xx

Simplified Illustrative Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxi

Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxiii

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-1

1.1. Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-1

1.2. Introduction to Estuaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-2

1.3. Potential Problems to Address . . . . . . . . . . . . . . . . . . . . . . . . 1-3

1.4. Overview of the Waste Load Allocation . . . . . . . . . . . . . . . . . . . 1-3

1.5. Steps in the Modeling Process . . . . . . . . . . . . . . . . . . . . . . . . 1-5

1.6. Organization and Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-5

1.7. References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-5

2. Overview of Processes Affecting Estuarine Water Quality . . . . . . . . . . . . . . 2-1

2.1. Organization Of This Section . . . . . . . . . . . . . . . . . . . . . . . . . 2-1

2.2. Estuarine Morphology and Classification . . . . . . . . . . . . . . . . . . . 2-1

2.3. Factors Affecting Circulation And Mixing . . . . . . . . . . . . . . . . . . . 2-2

2.4. Sediment Transport and Sediment/Water Quality Interactions . . . . . . . . 2-4

2.5. Organic Wastes, Dissolved Oxygen And Nutrients . . . . . . . . . . . . . . 2-5

2.6. Synthetic Organic Chemicals . . . . . . . . . . . . . . . . . . . . . . . . . 2-8

2.7. Metals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-9

2.8. Model Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-10

iii
SUPPLEMENT I: Factors Affecting Circulation and Mixing

Model Equations . . . . . . . . . . . . . . . . . . . . . . 2-10

SUPPLEMENT II: Sediment Transport and Sediment/Water Quality

Interactions . . . . . . . . . . . . . . . . . . . . . . . . 2-18

SUPPLEMENT III: Organic Wastes, Dissolved Oxygen and Nutrients . . . . 2-20

SUPPLEMENT IV: Synthetic Organics . . . . . . . . . . . . . . . . . . . . . 2-26

SUPPLEMENT V: Metals . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-30

2.9. References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-32

3. Model Identification and Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-1

3.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-1

3.2. Model Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-1

3.3. Model Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-11

3.4. References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-22

 

 

 iv
List of Figures

Figure 2-1. Factors affecting changes in momentum. . . . . . . . . . . . . . . . . 2-12

Figure 2-2. Relationship between water density, salinity, and temperature. . . . . . 2-13

Figure 2-3. Factors affecting change in constituent mass. . . . . . . . . . . . . . . 2-15

Figure 2-4. Model dimensions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-16

Figure 2-5. Sediment variables and processes. . . . . . . . . . . . . . . . . . . . . 2-18

Figure 2-6. Basic variables and processes for dissolved oxygen. . . . . . . . . . . 2-21

Figure 2-7. Standard variables for eutrophication and DO. . . . . . . . . . . . . . . 2-21

Figure 2-8. Additional variables and processes for trophic interactions. . . . . . . . 2-23

Figure 2-9. Additional variables and processes for nutrient interaction. . . . . . . . 2-24

Figure 2-10. Benthic interactions for nutrients and DO. . . . . . . . . . . . . . . . . 2-25

Figure 2-11. Basic variables and processes for reactive organic chemicals. . . . . . 2-27

Figure 3-1. Stratification circulation diagram and examples. . . . . . . . . . . . . . . 3-4

Figure 3-2. Vertical velocity profiles. . . . . . . . . . . . . . . . . . . . . . . . . . . 3-6

Figure 3-3. Vertical dye concentration profiles. . . . . . . . . . . . . . . . . . . . . . 3-6

v

List of Tables

Table 1-1. Organization of Guidance Manual for Performance of Wasteload

Allocations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-1

Table 1-2. Major Constituents and Macronutrients in Seawater [Smith (1974)] . . . . 1-2

Table 2-1. Fundamental Model Equations . . . . . . . . . . . . . . . . . . . . . . 2-11

Table 3-1. General Scales of Interest . . . . . . . . . . . . . . . . . . . . . . . . . 3-2

Table 3-2. Topographic Estuarine Classification . . . . . . . . . . . . . . . . . . . . 3-7

Table 3-3. Stratification Classification . . . . . . . . . . . . . . . . . . . . . . . . . 3-7

Table 3-4. Summary of Methodology for Estuarine Water Quality Assessment . . . 3-14

Table 3-5. Basic Model Features . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-22

Table 3-6. Water Quality Problems Addressed . . . . . . . . . . . . . . . . . . . 3-22

vii

Glossary

Acute Toxicity1 - Any toxic effect that is produced

within a short period of time, usually 24-96 hours.

Although the effect most frequently considered is

mortality, the end result of acute toxicity is not necessarily death. Any harmful biological effect may be the

result.

Aerobic1 - Refers to life or processes occurring only

in the presence of free oxygen; refers to a condition

characterized by an excess of free oxygen in the

aquatic environment.

Algae (Alga)1 - Simple plants, many microscopic,

containing chlorophyll. Algae form the base of the

food chain in aquatic environments. Some species

may create a nuisance when environmental conditions are suitable for prolific growth.

Allochthonous1- Pertaining to those substances, materials or organisms in a waterway which originate

outside and are brought into the waterway.

Anaerobic2 - Refers to life or processes occurring in

the absence of free oxygen; refers to conditions characterized by the absence of free oxygen.

Autochthonous1 - Pertaining to those substances,

materials, or organisms originating within a particular

waterway and remaining in that waterway.

Autotrophic1 - Self nourishing; denoting those organisms that do not require an external source of organic

material but can utilize light energy and manufacture

their own food from inorganic materials; e.g., green

plants, pigmented flagellates.

Bacteria1- Microscopic, single-celled or noncellular

plants, usually saprophytic or parasitic.

Benthal Deposit2 - Accumulation on the bed of a

watercourse of deposits containing organic matter

arising from natural erosion or discharges of wastewaters.

Benthic Region1 - The bottom of a waterway; the

substratum that supports the benthos.

Benthal Demand2 - The demand on dissolved oxygen

of water overlying benthal deposits that results from

the upward diffusion of decomposition products of the

deposits.

Benthos1 - Organisms growing on or associated principally with the bottom of waterways. These include:

(1) sessile animals such as sponges, barnacles, mussels, oysters, worms, and attached algae; (2) creeping forms such as snails, worms, and insects; (3)

burrowing forms, which include clams, worms, and

some insects; and (4) fish whose habits are more

closely associated with the benthic region than other

zones; e.g., flounders.

Biochemical Oxygen Demand2 - A measure of the

quantity of oxygen utilized in the biochemical oxidation

of organic matter in a specified time and at a specific

temperature. It is not related to the oxygen requirements in chemical combustion, being determined entirely by the availability of the material as a biological

food and by the amount of oxygen utilized by the

microorganisms during oxidation. Abbreviated BOD.

Biological Magnification1 - The ability of certain organisms to remove from the environment and store in

their tissues substances present at nontoxic levels in

the surrounding water. The concentration of these substances becomes greater each higher step in the food

chain.

Bloom1 - A readily visible concentrated growth or aggregation of minute organisms, usually algae, in bodies

of water.

Brackish Waters1 - Those areas where there is a

mixture of fresh and salt water; or, the salt content is

greater than fresh water but less than sea water; or, the

salt content is greater than in sea water.

Channel Roughness2 - That roughness of a channel,

including the extra roughness due to local expansion

or contraction and obstacles, as well as the roughness

of the stream bed proper; that is, friction offered to the

flow by the surface of the bed of the channel in contact

with the water. It is expressed as roughness coefficient

in the velocity formulas.

Chlorophyll1 - Green photosynthetic pigment present

in many plant and some bacterial cells. There are

seven known types of chlorophyll; their presence and

abundance vary from one group of photosynthetic organisms to another.

Chronic Toxicity1 - Toxicity, marked by a long duration,

that produces an adverse effect on organisms. The end

result of chronic toxicity can be death although the

usual effects are sublethal; e.g., inhibits reproduction,

reduces growth, etc. These effects are reflected by

changes in the productivity and population structure of

the community.

ix
Coastal Waters1

 - Those waters surrounding the continent which exert a measurable influence on uses of

the land and on its ecology. The Great Lakes and the

waters to the edge of the continental shelf.

Component Tide2 - Each of the simple tides into

which the tide of nature is resolved. There are five

principal components; principal lunar, principal solar,

N2, K, and O. There are between 20 and 30 components which are used in accurate predictions of tides.

Coriolis Effect2- The deflection force of the earth’s

rotation. Moving bodies are deflected to the right in

the northern hemisphere and to the left in the southern

hemisphere.

Datum2 - An agreed standard point or plane of state

elevation, noted by permanent bench marks on some

solid immovable structure, from which elevations are

measured or to which they are referred.

Density Current2 - A flow of water through a larger

body of water, retaining its unmixed identity because

of a difference in density.

Deoxygenation2 - The depletion of the dissolved oxygen in a liquid either under natural conditions associated with the biochemical oxidation of organic matter

present or by addition of chemical reducing agents.

Diagenetic Reaction - Chemical and physical

changes that alter the characteristics of bottom sediments. Examples of chemical reactions include oxidation of organic materials while compaction is an

example of a physical change.

Dispersion2 - (1) Scattering and mixing. (2) The mixing of polluted fluids with a large volume of water in a

stream or other body of water.

Dissolved Oxygen2 - The oxygen dissolved in water,

wastewater, or other liquid, usually expressed in milligrams per liter, or percent of saturation. Abbreviated

DO.

Diurnal2 - (1) Occurring during a 24-hr period; diurnal

variation. (2) Occurring during the day time (as opposed to night time). (3) In tidal hydraulics, having a

period or cycle of approximately one tidal day.

Drought2 - In general, an extended period of dry

weather, or a period of deficient rainfall that may

extend over an indefinite number of days, without any

quantitative standard by which to determine the degree of deficiency needed to constitute a drought.

Qualitatively, it may be defined by its effects as a dry

period sufficient in length and severity to cause at

least partial crop failure or impair the ability to meet a

normal water demand.

Ebb Tide1- That period of tide between a high water and

the succeeding low water; falling tide.

Enrichment1 - An increase in the quantity of nutrients

available to aquatic organisms for their growth.

Epilimnion1 - The water mass extending from the surface to the thermocline in a stratified body of water; the

epilimnion is less dense that the lower waters and is

wind-circulated and essentially homothermous.

Estuary1 - That portion of a coastal stream influenced

by the tide of the body of water into which it flows; a

bay, at the mouth of a river, where the tide meets the

river current; an area where fresh and marine water

mix.

Euphotic Zone1 - The lighted region of a body of water

that extends vertically from the water surface to the

depth at which photosynthesis fails to occur because

of insufficient light penetration.

Eutrophication1 - The natural process of the maturing

(aging) of a lake; the process of enrichment with nutrients, especially nitrogen and phosphorus, leading to

increased production of organic matter.

Firth1 - A narrow arm of the sea; also the opening of a

river into the sea.

Fjord (Fiord)1 - A narrow arm of the sea between

highlands.

Food Chain1 - Dependence of a series of organisms,

one upon the other, for food. The chain begins with

plants and ends with the largest carnivores.

Flood Tide2 - A term indiscriminately used for rising tide

or landward current. Technically, flood refers to current.

The use of the terms “ebb” and “flood” to include the

vertical movement (tide) leads to uncertainty. The

terms should be applied only to the horizontal movement (current).

Froude’s Number2 - A numerical quantity used as an

index to characterize the type of flow in a hydraulic

structure that has the force of gravity (as the only force

producing motion) acting in conjunction with the resisting force of inertia. It is equal to the square of characteristic velocity (the mean, surface, or maximum

velocity) of the system, divided by the product of a

characteristic linear dimension, such as diameter or

expressed in consistent units so that the combinations

will be dimensionaless. The number is used in

x
open-channel flow studies or in cases in which the free

surface plays an essential role in influencing motion.

Heavy Metals2 - Metals that can be precipitated by

hydrogen sulfide in acid solution, for example, lead,

silver, gold, mercury, bismuth, copper.

Heterotrophic1 - Pertaining to organisms that are

dependent on organic material for food.

Hydraulic Radius2 - The right cross-sectional area of

a stream of water divided by the length of that part of

its periphery in contact with its containing conduit; the

ratio of area to wetted perimeter. Also called hydraulic

mean depth.

Hydrodynamics2 - The study of the motion of, and the

forces acting on, fluids.

Hydrographic Survey2 - An instrumental survey

made to measure and record physical characteristics

of streams and other bodies of water within an area,

including such things as location, areal extent and

depth, positions and locations of high-water marks,

and locations and depths of wells.

Inlet1 - A short, narrow waterway connecting a bay,

lagoon, or similar body of water with a large parent

body of water; an arm of the sea, or other body of

water, that is long compared to its width, and that may

extend a considerable distance inland.

Inorganic Matter2- Mineral-type compounds that are

generally non-volatile, not combustible, and not biodegradable. Most inorganic-type compounds, or reactions, are ionic in nature, and therefore, rapid

reactions are characteristic.

Lagoon1 - A shallow sound, pond, or channel near or

communicating with a larger body of water.

Limiting Factor1

 - A factor whose absence, or excessive concentration, exerts some restraining influence

upon a population through incompatibility with species requirements or tolerance.

Manning Formula2 - A formula for open-channel flow,

published by Manning in 1890, which gives the value

of c in the Chezy formula.

Manning Roughness Coefficient2 - The roughness

coefficient in the Manning formula for determination

of the discharge coefficient in the Chezy formula.

Marsh1 - Periodically wet or continually flooded area

with the surface not deeply submerged. Covered

dominantly with emersed aquatic plants; e.g., sedges,

cattails, rushes.

Mean Sea Level2 - The mean plane about which the

tide oscillates; the average height of the sea for all

stages of the tide.

Michaelis-Menton Equation2 - A mathematical expression to describe an enzyme-catalyzed biological

reaction in which the products of a reaction are described as a function of the reactants.

Mineralization2 - The process by which elements combined in organic form in living or dead organisms are

eventually reconverted into inorganic forms to be made

available for a fresh cycle of plant growth. The mineralization of organic compounds occurs through combustion and through metabolism by living animals.

Microorganisms are ubiquitous, possess extremely

high growth rates and have the ability to degrade all

naturally occurring organic compounds.

Modeling2 - The simulation of some physical or abstract

phenomenon or system with another system believed

to obey the same physical laws or abstract rules of

logic, in order to predict the behavior of the former

(main system) by experimenting with latter (analogous

system).

Monitoring2 - Routine observation, sampling and testing of designated locations or parameters to determine

efficiency of treatment or compliance with standards or

requirements.

Mouth2 - The exit or point of discharge of a stream into

another stream or a lake, or the sea.

Nautical Mile2 - A unit of distance used in ocean

navigation. The United States nautical mile is defined

as equal to one-sixteenth of a degree of a great circle

on a sphere with a surface equal to the surface of the

earth. Its value, computed for the Clarke spheroid of

1866, is 1,853.248 m (6,080.20ft). The International

nautical mile is 1,852 m (6,070.10 ft).

Nanoplankton2 - Very minute plankton not retained in

a plankton net equipped with no. 25 silk bolting cloth

(mesh, 0.03 to 0.04 mm.).

Neap Tides1 - Exceptionally low tides which occur twice

each month when the earth, sun and moon are at right

angles to each other; these usually occur during the

moon’s first and third quarters.

Neuston2 - Organisms associated with, or dependent

upon, the surface film (air-water) interface of bodies of

water.

Nitrogenous Oxygen Demand (NOD)2 - A quantitative

measure of the amount of oxygen required for the

biological oxidation of nitrogenous material, such as

xi
ammonia nitrogen and organic nitrogen, in wastewater; usually measured after the carbonaceous oxygen

demand has been satisfied.

Nutrients1 - Elements, or compounds, essential as

raw materials for organism growth and development;

e.g., carbon, oxygen, nitrogen, phosphorus, etc.

Organic1 - Refers to volatile, combustible, and sometimes biodegradable chemical compounds containing

carbon atoms (carbonaceous) bonded together and

with other elements. The principal groups of organic

substances found in wastewater are proteins, carbohydrates, and fats and oils.

Oxygen Deficit1 - The difference between observed

oxygen concentration and the amount that would

theoretically be present at 100% saturation for existing conditions of temperature and pressure.

Pathogen1 - An organism or virus that causes a disease.

Periphyton (Aufwuchs)1 - Attached microscopic organisms growing on the bottom, or other submersed

substrates, in a waterway.

Photosynthesis1 - The metabolic process by which

simple sugars are manufactured from carbon dioxide

and water by plant cells using light as an energy

source.

Phytoplankton1 - Plankton consisting of plant life.

Unattached microscopic plants subject to movement

by wave or current action.

Plankton1 - Suspended microorganisms that have

relatively low powers of locomotion, or that drift in the

water subject to the action of waves and currents.

Quality2 - A term to describe the composite chemical,

physical, and biological characteristics of a water with

respect to it’s suitability for a particular use.

Reaeration2 - The absorption of oxygen into water

under conditions of oxygen deficiency.

Respiration1 - The complex series of chemical and

physical reactions in all living organisms by which the

energy and nutrients in foods is made available for

use. Oxygen is used and carbon dioxide released

during this process.

Roughness Coefficient2 - A factor, in the Chezy,

Darcy-Weisbach, Hazen-Williams, Kutter, Manning,

and other formulas for computing the average velocity

of flow of water in a conduit or channel, which represents the effect of roughness of the confining material

on the energy losses in the flowing water.

Seiche1 - Periodic oscillations in the water level of a lake

or other landlocked body of water due to unequal

atmospheric pressure, wind, or other cause, which sets

the surface in motion. These oscillations take place

when a temporary local depression or elevation of the

water level occurs.

Semidiurnal2 - Having a period or cycle of approximately one half of a tidal day. The predominating type

of tide throughout the world is semidiurnal, with two

high waters and two low waters each tidal day.

Slack Water2 - In tidal waters, the state of a tidal current

when its velocity is at a minimum, especially the moment when a reversing current changes direction and

its velocity is zero. Also, the entire period of low velocity

near the time of the turning of the current when it is too

weak to be of any practical importance in navigation.

The relation of the time of slack water to the tidal

phases varies in different localities. In some cases

slack water occurs near the times of high and low water,

while in other localities the slack water may occur

midway between high and low water.

Spring Tide1 - Exceptionally high tide which occurs

twice per lunar month when there is a new or full moon,

and the earth, sun, and moon are in a straight line.

Stratification (Density Stratification)1 -Arrangement

of water masses into separate, distinct, horizontal layers as a result of differences in density; may be caused

by differences in temperature, dissolved or suspended

solids.

Tidal Flat1 - The sea bottom, usually wide, flat, muddy

and nonproductive, which is exposed at low tide. A

marshy or muddy area that is covered and uncovered

by the rise and fall of the tide.

Tidal Prism2 - (1) The volume of water contained in a

tidal basin between the elevations of high and low

water. (2) The total amount of water that flows into a

tidal basin or estuary and out again with movement of

the tide, excluding any fresh-water flows.

Tidal Range2 - The difference in elevation between high

and low tide at any point or locality.

Tidal Zone (Eulittoral Zone, Intertidal Zone)1 - The

area of shore between the limits of water level fluctuation; the area between the levels of high and low tides.

Tide1 - The alternate rising and falling of water levels,

twice in each lunar day, due to gravitational attraction

xii
of the moon and sun in conjunction with the earth’s

rotational force.

Tide Gage2 - (1) A staff gage that indicates the height

of the tide. (2) An instrument that automatically registers the rise and fall of the tide. In some instruments,

the registration is accomplished by printing the heights

at regular intervals; in others by a continuous graph in

which the height of the tide is represented by ordinates

of the curve and the corresponding time by the abscissae.

Toxicant1 - A substance that through its chemical or

physical action kills, injures, or impairs an organism;

any environmental factor which, when altered, produces a harmful biological effect.

Water Pollution1 - Alteration of the aquatic environment in such a way as to interfere with a designated

beneficial use.

Water Quality Criteria1 - A scientific requirement on

which a decision or judgement may be based concerning the suitability of water quality to support a designated use.

Water Quality Standard1 - A plan that is established

by governmental authority as a program for water

pollution prevention and abatement.

Zooplankton2 - Plankton consisting of animal life.

Unattached microscopic animals having minimal capability for locomotion.

1Rogers, B.G., Ingram, W.T., Pearl, E.H., Welter, L.W.

(Editors). 1981, Glossary, Water and Wastewater

Control Engineering, Third Edition, American Public

Health Association, American Society of Civil Engineers, American Water Works Association, Water

Pollution Control Federation.

2Matthews, J.E., 1972, Glossary of Aquatic Ecological

Terms, Manpower Development Branch, Air and

Water Programs Division, EPA, Oklahoma.

xiii

Acknowledgements

The contents of this section have been removed to

comply with current EPA practice.

xv

Executive Summary

The Technical Guidance Manual for Performing Waste

Load Allocations, Book III: Estuaries is the third in a

series of manuals providing technical information and

policy guidance for the preparation of waste load allocations (WLAs) that are as technically sound as current

state of the art permits. The objective of such load

allocations is to ensure that water quality conditions

that protect designated beneficial uses are achieved.

This book provides technical guidance for performing

waste load allocations in estuaries.

PART I: ESTUARIES AND WASTE LOAD

ALLOCATION MODELS

Introduction

Estuaries are coastal bodies of water where fresh

water meets the sea. Most rivers and their associated

pollutant loads eventually flow into estuaries. The complex loading, circulation, and sedimentation processes

make water quality assessment and waste load allocation in estuaries difficult. Transport and circulation

processes in estuaries are driven primarily by river flow

and tidal action. As a consequence of its complex

transport processes, estuaries cannot be treated as

simple advective systems such as many rivers.

Wastewater discharges into estuaries can affect water

quality in several ways, both directly and indirectly. In

setting limits on wastewater quantity and quality, the

following potential problems should be assessed: salinity, sediment, pathogenic bacteria, dissolved oxygen

depletion, nutrient enrichment and overproduction,

aquatic toxicity, toxic pollutants and bioaccumulation

and human exposure.

A WLA provides a quantitative relationship between

the waste load and the instream concentrations or

effects of concern as represented by water quality

standards. During the development of a WLA, the user

combines data and model first to describe present

conditions and then to extrapolate to possible future

conditions. The WLA process sequentially addresses

the topics of hydrodynamics, mass transport, water

quality kinetics, and for some problems, bioaccumulation and toxicity.

For each of the topics addressed in a modeling study,

several steps are applied in an iterative process: problem identification, model identification, initial model

calibration, sensitivity analysis, model testing, refinement, and validation.

After the WLAs have been put into effect, continued

monitoring, post-audit modeling and refinement should

lead to more informed future WLAs.

Overview of Processes Affecting Estuarine

Water Quality

The estuarine waste load allocation process requires a

fundamental understanding of the factors affecting

water quality and the representation of those processes in whatever type of model is applied (conceptual

or mathematical) in order to determine the appropriate

allocation of load. Insight into processes affecting water

quality may be obtained through examination of the

schemes available for their classification. Estuaries

have typically been classified based on their geomorphology and patterns of stratification and mixing. However, each estuary is to some degree unique and it is

often necessary to consider the fundamental processes impacting water quality.

To determine the fate and affects of water quality

constituents it is necessary first to determine processes

impacting their transport. That transport is affected by

tides, fresh water inflow, friction at the fluid boundaries

and its resulting turbulence, wind and atmospheric

pressure, and to a lesser degree (for some estuaries)

the effects of the earth’s rotation (Coriolis force). The

resulting transportation patterns may be described (determined from field studies) in waste load allocation

studies, or, as is becoming more frequently the case,

estimated using hydrodynamic models. Hydrodynamic

models are based on descriptions of the processes

affecting circulation and mixing using equations based

on laws of conservation of mass and momentum. The

fundamental equations generally include: (A) the conservation of water mass (continuity), (B) conservation

of momentum, and (C) conservation of constituent

mass.

An important aspect of estuarine WLA modeling often

is the capability to simulate sediment transport and

sediment/water interactions. Sediments not only affect

water transparency, but can carry chemicals such as

nutrients and toxic substances into receiving waters.

Unlike rivers, which have reasonably constant water

quality conditions, the large changes in salinity and pH

in an estuary directly affect the transport behavior of

many suspended solids. Many colloidal particles agglomerate and settle in areas of significant salinity

gradients. Processes impacting sediment transport include settling, resuspension, scour and erosion, coagulation and flocculation.

xvii
The water quality parameters of interest vary with the

objectives of the waste load allocation study, from

“conventional pollutants” (e.g. organic waste, dissolved oxygen and nutrients) to toxic organics and

trace metals.

The focus of WLA models of conventional pollutants is

often DO and biochemical oxygen demand (BOD) as

a general measure of the health of the system, or the

focus can be primary productivity when eutrophication

is the major concern. Conventional WLA models usually include temperature, major nutrients, chemical

characteristics, detritus, bacteria, and primary producers. WLA models may include higher trophic levels (i.e.

zooplankton and fish) because of higher trophic level

effects on other more important variables, such as

phytoplankton, BOD and DO. Synthetic organic chemicals include a wide variety of toxic materials whose

waste loads are allocated based upon threshold concentrations as well as tolerable durations and frequencies of exposure. These pollutants may ionize and

different forms may have differing toxicological effects.

The transport of the materials also may be affected by

sorption and they can degrade through such processes as volatilization, biodegradation, hydrolysis, and

photolysis.

Trace metals may be of concern in many estuaries due

to their toxicological effects. The toxicity of trace metals

and their transport is affected by their form. Upon entry

to a surface water body, metal speciation may change

due to complexation, precipitation, sorption, and redox

reactions. Metals concentrations are diluted further by

additional stream flow and mixing. Physical loss can

be caused by settling and sedimentation, whereas a

physical gain may be caused by resuspension.

Model Identification and Selection

The first steps in the modeling process are model

identification and selection. The goals are to identify

the simplest conceptual model that includes all the

important estuarine phenomena affecting the water

quality problems, and to select the most useful analytical formula or computer model for calculating waste

load allocations. During model identification, available

information is gathered and organized to construct a

coherent picture of the water quality problem. There

are four basic steps in model identification: establish

study objectives and constraints, determine water

quality pollutant interactions, determine spatial extent

and resolution, and determine temporal extent and

resolution. Following model identification, another important step is advised: perform rapid, simple screening calculations to gain a better understanding of

expected pollutant levels and the spatial extent of

water quality problems.

The first step in identifying an appropriate WLA model

for a particular site is to review the applicable water

quality standards and the beneficial uses of the estuary

to be protected. Local, state, and federal regulations

may contribute to a set of objectives and constraints.

The final result of this step should be a clear understanding of the pollutants and water quality indicators,

the areas, and the time scales of interest.

After the pollutants and water quality indicators are

identified, the significant water quality reactions must

be determined. These reactions must directly or indirectly link the pollutants to be controlled with the primary water quality indicators. All other interacting water

quality constituents thought to be significant should be

included at this point. This can best be done in a

diagram or flow chart representing the mass transport

and transformations of water quality constituents in a

defined segment of water. The final result of this step

should be the assimilation of all the available knowledge of a system in a way that major water quality

processes and ecological relationships can be evaluated for inclusion in the numerical model description.

The next step is to specify the spatial extent, dimensionality, and scale (or computational resolution) of the

WLA model. This may be accomplished by determining

the effective dimensionality of the estuary as a whole,

defining the boundaries of the study area, then specifying the required dimensionality and spatial resolution

within the study area. The effective dimensionality of

an estuary includes only those dimensions over which

hydrodynamic and water quality gradients significantly

affect the WLA analysis. Classification and analysis

techniques are available. Specific boundaries of the

study area must be established, in general, beyond the

influence of the discharge(s) being evaluated. Data

describing the spatial gradients of important water

quality constituents within the study area should be

examined. Dye studies can give important information

on the speed and extent of lateral and vertical mixing.

It is clear that choice of spatial scale and layout of the

model network requires considerable judgment.

The final step in model identification is to specify the

duration and temporal resolution of the WLA model.

The duration of WLA simulations can range from days

to years, depending upon the size and transport characteristics of the study area, the reaction kinetics and

forcing functions of the water quality constituents, and

the strategy for relating simulation results to the regulatory requirements. One basic guideline applies in all

cases - the simulations should be long enough to

eliminate the effect of initial conditions on important

water quality constituents at critical locations.

xviii
The temporal resolution of WLA simulations falls into

one of three categories - dynamic, quasi-dynamic, and

steady state. Dynamic simulations predict hour to hour

variations caused by tidal transport. Quasidynamic

simulations predict variations on the order of days to

months. The effects of tidal transport are time-averaged. Other forcing functions such as freshwater inflow, pollutant loading, temperature, and sunlight may

vary from daily to monthly. Steady state simulations

predict monthly to seasonal averages. All inputs are

time-averaged. Two schools of thought have persisted

regarding the utility of dynamic versus quasidynamic

and steady state simulations. For some problems the

choice is reasonably clear.

In general, if the regulatory need or kinetic response is

on the order of hours, then dynamic simulations are

required; if regulatory needs are long term averages

and the kinetic response is on the order of seasons to

years, then quasidynamic or steady simulations are

indicated.

The goal of model selection is to obtain a simulation

model that effectively implements the conceptual

model identified for the WLA. Models selected for

discussion here are general purpose, in the public

domain, and available from or supported by public

agencies. The selection of an estuarine WLA model

need not be limited to the models discussed in this

document. Other models that are available to a project

or organization should also be considered. The models

summarized in this report represent the typical range

of capabilities currently available. Estuarine WLA models can be classified as Level I to Level IV according

to the temporal and spatial complexity of the hydrodynamic component of the model. Level I includes desktop screening methodologies that calculate seasonal

or annual mean pollutant concentrations based on

steady state conditions and simplified flushing time

estimates. These models are designed to examine an

estuary rapidly to isolate trouble spots for more detailed analyses.

Level II includes computerized steady state or tidally

averaged quasidynamic simulation models, which

generally use a box or compartment-type network to

solve finite difference approximations to the basic partial differential equations. Level II models can predict

slowly changing seasonal water quality with an effective time resolution of 2 weeks to 1 month. Level III

includes computerized one-dimensional (1-d) and

quasi two-dimensional (2-d), dynamic simulation models. These real time models simulate variations in tidal

heights and velocities throughout each tidal cycle.

Their effective time resolution is usually limited to

average variability over one week because tidal input

parameters generally consist of only average or slowly

varying values. The effective time resolution could be

reduced to under 1 day given good representation of

diurnal water quality kinetics and precise tidal input

parameters. The required data and modeling effort are

usually not mobilized in standard WLAs.

Level IV consists of computerized 2-d and 3-d dynamic

simulation models. Dispersive mixing and seaward

boundary exchanges are treated more realistically than

in the Level III 1-d models. These models are almost

never used for routine WLAs. The effective time resolution of the Level IV models can be less than 1 day

with a good representation of diurnal water quality and

intratidal variations.

The advantages of Level I and II models lie in their

comparatively low cost and ease of application. The

disadvantages lie in their steady state or tidally averaged temporal scale. When hydrodynamics and pollutant inputs are rapidly varying, steady state models are

difficult to properly calibrate.

The dynamic models (Levels III and IV) have advantages over steady state and tidally averaged models in

representing mixing in partially mixed estuaries because advection is so much better represented. The

success with which these models can predict transient

violations depends upon both the accuracy and resolution of the loading and environmental data, and the

model’s treatment of short time scale kinetics such as

desorption or diurnal fluctuations in temperature, pH,

or sunlight. While dynamic models are capable of predicting diurnal and transient fluctuations in water quality

parameters, the input data requirements are much

greater.

PART II: APPLICATION OF ESTUARINE

WASTE LOAD ALLOCATION MODELS

Monitoring Protocols for Calibration and

Validation of Estuarine Waste Load

Allocation Models

The monitoring data collected in support of a modeling

study is used to: (1) determine the type of model

application required (e.g. dimensionality, state variables); (2) perturb the model (e.g. loadings, flows); (3)

provide a basis for assigning rate coefficients and

model input parameters (model calibration); and (4)

determine if the model adequately describes the system (model evaluation).

The specific types of data and quantity required will

vary with the objectives of the WLA modeling study and

the characteristics of the estuary. Data are always

required to determine model morphometry, such as

depths and volumes (e.g. available from sounding data

xix
or navigation charts). Data are also required for transport. Transport within the modeled system may either

be specified (measured, e.g. current meters) or computed from hydrodynamic models. Flows into the system must be measured, or in the case of the open

boundary, water surface elevations must be determined.

The water quality data required, beyond that needed

to quantify transport, will vary depending on how the

variables will be used and their anticipated impact on

the system. Data requirements will differ if the WLA

modeling study is intended for dissolved oxygen, eutrophication or toxics. Concentrations for all pertinent

water quality variables should be provided at the model

boundaries, providing the perturbation for model predictions, as well as at points within the waterbody to

provide a basis for estimating model parameters and

evaluating model predictions. Data should be available

to determine variations in water quality parameters

over space and time.

Planning monitoring studies should be a collaborative

effort of participants involved in budgeting, field collection, analysis and processing of data, quality assurance, data management and modeling activities.

Collaboration insures that fundamental design questions are properly stated so that the available resources are used in the most efficient manner possible

and that all critical data for modeling are collected. The

use of monitoring and modeling in an iterative fashion,

wherever possible, is often the most efficient means of

insuring that critical data are identified and collected.

A rigorous, well documented, quality assurance, quality control (QA/QC) plan should be an integral part of

any waste load allocation program.

Model Calibration, Validation, and Use

While models can be run with minimal data, their

predictions are subject to large uncertainty. Models are

best operated to interpolate between existing conditions or to extrapolate from existing to future conditions, such as in the projection of conditions under

anticipated waste loads. The confidence that can be

placed on those projections is dependent upon the

integrity of the model, and how well the model is

calibrated to that particular estuary, and how well the

model compares when evaluated against an independent data set (to that used for calibration).

Model calibration is necessary because of the semiempirical nature of present day (1990) water quality

models. Although the waste load allocation models

used in estuary studies are formulated from the mass

balance and, in many cases, from conservation of

momentum principles, most of the kinetic descriptions

in the models that describe the change in water quality

are empirically derived. These empirical derivations

contain a number of coefficients and parameters that

are usually determined by calibration using data collected in the estuary of interest.

Calibration alone is not adequate to determine the

predictive capability of a model for a particular estuary.

To map out the range of conditions over which the

model can be used to determine cause and effect

relationships, one or more additional independent sets

of data are required to determine whether the model is

predictively valid. This testing exercise, which also is

referred to as confirmation testing, defines the limits of

usefulness of the calibrated model. Without validation

testing, the calibrated model remains a description of

the conditions defined by the calibration data set. The

uncertainty of any projection or extrapolation of a calibrated model would be unknown unless this is estimated during the validation procedure.

In addition, the final validation is limited to the range of

conditions defined by the calibration and validation

data sets. The uncertainty of any projection or extrapolation outside this range also remains unknown. The

validation of a calibrated model, therefore, should not

be taken to infer that the model is predictively valid over

the full range of conditions that can occur in an estuary.

For example, a model validated over the range of

typical tides and low freshwater inflow may not describe

conditions that occur when large inflows and atypical

tides occur.

This is especially true when processes such as sediment transport and benthic exchange occur during

atypical events but not during the normal, river flow and

tidal events typically used to calibrate and validate the

model.

Following model calibration and validation, several

types of analyses of model performance are of importance. First, a sensitivity analysis provides a method to

determine which parameters and coefficients have the

greatest impact on model predictions. Second, there

are a number of statistical tests that are useful for

defining when adequate agreement has been obtained

between model simulations and measured conditions

in order to estimate the confidence that may be assigned to model predictions. Finally, a components

analysis indicates the relative contribution of processes

to variations in predicted concentrations. For example,

the cause of violations of a dissolved oxygen standard

can be determined from the relative contribution of

various loads and the effect of sediment oxygen demand, BOD decay, nitrification, photosynthesis, and

reaeration.

xx
Once the model is calibrated and validated, it is then

used to investigate causes of existing problems or to

simulate future conditions to determine effects of

changes in waste loads as part of the waste load

allocation procedure. Once critical water quality conditions are defined for the estuary, harbor or coastal

area of concern, determining the waste assimilative

capacity is relatively straightforward. Models are available to relate critical water quality responses to the

loads for most problems. However, the definition of

critical conditions for estuaries is not straightforward.

For streams receiving organic loads, this is a straightforward matter of determining the low flow and high

temperature conditions. In estuaries, fresh water,

tides, wind, complex sediment transport, and other

factors can be important to determining the critical

conditions. As of yet, there are no clear methods of

establishing critical conditions, especially in terms of

the probability of occurrence. The analyst must use

considerable judgement in selecting critical conditions

for the particular system. Once loads and either critical

conditions or estimated future conditions are specified,

the calibrated model can be used to predict the water

quality response. The investigation may involve study

of extreme hydrological, meteorological, or hydrographic events that affect mixing; waste loadings from

point and non-point sources; and changes in benthic

demands.

Simplified Illustrative Examples

This section presents illustrative examples of estuarine

modeling using both simple screening procedures and

the water quality model WASP4. The screening procedures are based upon simple analytical equations and

the more detailed guidance provided in “Water Quality

Assessment: A Screening Procedure for Toxic and

Conventional Pollutants - Part 2.” WASP4 examples

demonstrate model based estuarine WLA application.

WASP4 is a general multi-dimensional compartment

model supported and available through the U.S. EPA

Center for Exposure Assessment Modeling.

The examples provided consider eight water quality

concerns in three basic types of estuaries. A one

dimensional estuary is analyzed by screening methods

for conservative and nonconservative toxicants and

chlorine residual. Bacteria and DO depletion are simulated. Nutrient enrichment, phytoplankton production,

and DO depletion in a vertically stratified estuary are

simulated. Finally, ammonia toxicity and a toxicant in a

wide, laterally variant estuary are simulated.

The screening procedures can be applied using calculator or spreadsheet. While they may not be suitable as

the sole justification for a WLA, they can be valuable

for initial problem assessment. Three screening methods are presented for estimating estuarine water quality impacts: analytical equations for an idealized

estuary, the fraction of freshwater method, and the

modified tidal prism method. These example procedures are only applicable to steady state, one-dimensional estuary problems.

Deterministic water quality modeling of estuarine systems can be divided into two separate tasks: description of hydrodynamics, and description of water quality.

The WASP4 model was designed to simulate water

quality processes, but requires hydrodynamic information as input. Hydrodynamic data may be directly specified in an input dataset, or may be read from the output

of a separate hydrodynamic model. The examples here

illustrate tidal-averaged modeling with user-specified

hydrodynamics. Both the eutrophication and toxicant

programs are described and used.

For the six examples using WASP4, background information is provided, the required input data are summarized, selected model results are shown, and certain

WLA issues are briefly described.

xxi

Preface

The document is the third of a series of manuals

providing information and guidance for the preparation

of waste load allocations. The first documents provided

general guidance for performing waste load allocation

(Book I), as well as guidance specifically directed

toward streams and rivers (Book II). This document

provides technical information and guidance for the

preparation of waste load allocations in estuaries. The

document is divided into four parts:

Part 1 of this document provides technical information

and policy guidance for the preparation of estuarine

waste load allocations. It summaries the important

water quality problems, estuarine characterisitics and

processes affecting those problems, and the simulation

models available for addressing these problems. Part

two provides a guide to monitoring and model calibration and testing, and a case study tutorial on simulation

of waste load allocation problems in simplified estuarine systems. The third part summarizes initial dilution

and mixing zone processes, available models, and

their application in waste load allocation.

This part, “Part 4: Critical Review of Estuarine Waste

Load Allocation Modeling,” summarizes several historical case studies, with critical review by noted experts.

Organization: “Technical Guidance Manual for Performing Waste Load Allocations. Book III:

Estuaries”

Part Title

1 Estuaries and Waste Load Allocation Models

2 Application of Estuarine Waste Load Allocation Models

3 Use of Mixing Zone Models in Estuarine Waste Load Allocation Modeling

4 Critical Review of Estuarine Waste Load Allocation Modeling

xxiii

1. Introduction

Robert B. Ambrose, Jr., P.E.

Center for Exposure Assessment Modeling

 Environmental Research Laboratory, U.S. EPA, Athens, GA

1.1. Background

This document is the third in a series of manuals

providing technical information and policy guidance for

the preparation of waste load allocations (WLAs) that

are as technically sound as current state of the art

permits. The objective of such load allocations is to

ensure that water quality conditions that protect designated beneficial uses are achieved. An additional

benefit of a technically sound WLA is that excessive

degrees of treatment, that do not produce corresponding improvements in water quality, can be avoided.

This can result in more effective use of available funds.

This guidance document contains seven elements: 1)

an overview of water quality problems and estuarine

characteristics, 2) descriptions of estuarine simulation

models, 3) descriptions of the monitoring and data

collection necessary for model application, 4) guidance

on the model calibration and validation, 5) simplified

example case studies, 6) review and discussion of past

WLA studies, and 7) guidance on use of mixing zone

models.

Table 1-1 lists the various “books” and “chapters” that

make up the set of technical guidance manuals.

303(d)/TMDL program guidance is currently under development. This guidance will address programs and

procedural issues related to total maximum daily loads,

wasteload allocations, and load allocations

(TMDLs/WLAs/LAs).

Users of this manual also should be aware that other

information may affect the wasteload allocation process. For instance, criteria and standards for DO, ammonia, and other parameters are in a continuous

process of change. Therefore, any standards used in

examples contained in this chapter should not be applied to real-life situations without first consulting the

latest applicable criteria and standards.

BOOK I 303 (d)/TMDL PROGRAM GUIDANCE

 Under development

BOOK II STREAMS AND RIVERS

 Chapter 1 - BOD/Dissolved Oygen Impacts and Ammonia Toxicity

 Chapter 2 - Nutrient/Eutrophication Impacts

 Chapter 3 - Toxic Substance Impacts

BOOK III ESTUARIES

BOOK IV LAKES, RESERVOIRS AND IMPOUNDMENTS

 Chapter 1 - BOD/Dissolved Oxygen Impacts and Ammonia Toxicity

 Chapter 2 - Nutrient/Eutrophication Impacts

 Chapter 3 - Toxic Substance Impacts

Table 1-1. Organization of Guidance Manuals for Performance of Wasteload Allocations

1-1
1.2. Introduction to Estuaries

Estuaries are coastal bodies of water where fresh

water meets the sea. They are traditionally defined as

semi-enclosed bodies of water having a free connection with the open sea and within which sea water is

measurably diluted with fresh water derived from land

drainage (Pritchard, 1967). These classical estuaries

are the lower reaches of rivers where saline and fresh

water mix due to tidal action. The term has been

extended to include coastal waters such as bays and

sounds that receive riverine discharge. The backwater

river reaches draining into the Great Lakes have also

been included as estuaries.

Estuaries are biologically productive bodies of water.

They are the spawning and nursury grounds for many

important coastal fish and invertebrates. Thus they

support commercial and recreational fishing and shellfishing. Many are valuable for recreational boating and

bathing, and prized for their aesthetics. At the same

time, many estuaries house important harbors, ports,

and navigation channels. Many have been used to

dilute and flush municipal and industrial wastewater.

These various uses of an estuary may cause conflicting demands and burdens on its water quality.

1.2.1. Factors Affecting Estuarine Water Quality

Estuaries are the crossroads of river, sea, atmosphere,

and sediment. Most rivers and their associated pollutant loads eventually flow into estuaries. Many major

cities and ports are located on estuaries, affecting their

quality through domestic and industrial wastewater

and dredging. Estuarine circulation can trap nutrients

and other pollutants from these waste discharges, the

upstream river drainage basin, subsurface waters of

the coastal ocean, and atmospheric deposition. Underlying sediments can store and transform these pollutants, either releasing them to the water or burying

them. Sedimentation processes are filling or altering all

estuaries in response to sea level changes, sediment

influx, and intra-estuarine circulation patterns (Shubel,

1971). The complex loading, circulation, and sedimentation processes make water quality assessment and

waste load allocation in estuaries difficult.

As estuaries mix fresh water with sea water, their

chemistry varies dramatically in space as well as with

time. Average values of the major constituents of

seawater, and average concentrations and ranges for

macronutrients are reported in Table 1-2 . As a general

rule, in sea water nitrogen limits phytoplankton productivity, whereas in fresh water, phosphorus is the primary limiting nutrient. In estuaries, either nutrient may

limit growth.

The importance of atmospheric nitrogen deposition to

estuaries has recently received attention with estimates that up to 39% of nitrogen reaching Chesapeake

Bay originated in atmospheric deposition (Fisher, et al,

1988). Nitrogen may deposit to watersheds or directly

to estuaries in rainfall and dryfall, which includes the

deposition of particles greater than 3 microns, aerosol

impaction, and gas absorption. A significant amount of

nitrogen input to a watershed is removed through denitrification. Estimates range from 20 - 75% (Waddell,

1989). Annual nitrogen inputs of inorganic nitrogen in

bulk precipitation across the United States range from

0.1 g/m2/year in some western locations to as high as

0.8 g/m2/year in the east. Organic nitrogen inputs range

from 0.1 to 0.4 g/m2/year (Waddell, 1989). Dry deposition may account for about the same input, doubling

the total nitrogen inputs.

1.2.2 . Estuarine Transport

Transport and circulation processes in estuaries are

driven primarily by river flow and tidal action. In shallow

estuaries, wind stress can dominate transport. Longitudinal salinity gradients lead to a net upstream drift of

heavier sea water. Strong river flow or weak tidal mixing

can lead to vertical stratification, where relatively fresh

water flows over saline bottom water. Entrainment of

bottom water may dilute pollutants in the surface, but

upstream transport of salt and pollutants can occur

along the bottom. Coriolis acceleration, deflecting currents to the right in the northern hemisphere, may be

significant in large estuaries.

As a consequence of these complex transport processes, estuaries cannot be treated as simple advective

systems such as many rivers. In rivers, flushing of

pollutants is driven primarily by advection. In estuaries,

however, both advection and dispersion must be conConstituent Average Conc.

(mg/L)

Conc. Range

(mg/L)

chloride 19350.0

sodium 10760.0

magnesium 1300.0

sulfate 2700.0

calcium 400.0

potassium 400.0

bicarbonate 145.0

bromine 67.3

silicon 2.0 0.0 - 4.9

nitrogen 0.28 0.0 - 0.56

phosphorus 0.03 0.0 - 0.09

Table 1-2. Major Constituents and Macronutrients in

Seawater [Smith (1974)]

1-2
sidered. Equations and models used for riverine waste

load allocation must be carefully considered before

application to estuaries.

1.3. Potential Problems to Address

Wastewater discharges into estuaries can affect water

quality in several ways, both directly and indirectly. In

setting limits on wastewater quantity and quality, all

potential problems should be assessed. Wastewater

limits should be set to assure attainment of water

quality standards.

1.3.1. Salinity

Salinity is important in determining available habitat for

estuarine organisms. Large wastewater discharges

into relatively small estuaries or embayments can alter

the local salinity regime through dilution. Large saline

discharges could introduce excess salinity into freshwater embayments of the Great Lakes. Even when the

salinity is not affected by the discharge, it is measured

and modeled in order to quantify advection and dispersion. These processes help determine how wastewater is assimilated into the estuary.

1.3.2. Sediment

Sediment enters estuaries from many sources, and

can alter the habitat of benthic organisms. Sediment is

also an important carrier of such pollutants as hydrophobic organic chemicals, metals, and nutrients. Sediment transport can move pollutants upstream, or

between the water column and the underlying bed.

Even when wastewater does not introduce excess

sediment into an estuary, it is often measured and

modeled in order to quantify the transport of sedimentbound pollutants.

1.3.3. Bacteria and Viruses

Bacteria and viruses may enter estuaries in runoff from

farms and feedlots and in effluent from marinas as well

as from municipal or industrial wastewater discharges.

These pathogens may be transported to bathing

beaches and recreational areas, causing direct human

exposure and possibly disease. Pathogens also may

be transported to shellfish habitat; there they may

accumulate in oysters, clams, and mussels and, subsequently, cause disease when eaten by humans.

1.3.4. Dissolved Oxygen Depletion

Adequate, sustained DO concentrations are a requirement for most aquatic organisms. Seasonal or diurnal

depletion of DO, then, disrupts or displaces estuarine

communities. Ambient DO levels are affected by many

natural processes, such as oxidation of organic material, nitrification, diagenesis of benthic sediments, photosynthesis and respiration by phytoplankton and

submerged aquatic vegetation, and reaeration. The

natural balance can be disrupted by excessive wastewater loads of organic material, ammonia, and nutrients. Other sources of nutrients, such as runoff from

agricultural, residential, and urban lands and atmospheric deposition, also can disrupt the DO balance.

Excessive heat input from power plants can aggravate

existing problems. Because of its intrinsic importance,

and because it is affected by so many natural and

man-influenced processes, DO is perhaps the best

conventional indicator of water quality problems.

1.3.5. Nutrient Enrichment and Overproduction

Adequate concentrations of nitrogen and phosphorus

are important in maintaining the natural productivity of

estuaries. Excessive nutrient loading, however, can

stimulate overproduction of some species of phytoplankton, disrupting the natural communities. Periodic

phytoplankton “blooms” can cause widely fluctuating

DO concentrations, and DO depletion in benthic and

downstream areas. Nutrient loads can be introduced in

wastewater and runoff and through atmospheric deposition.

1.3.6. Aquatic Toxicity

Ammonia, many organic chemicals, and metals, at

often very low concentrations, can disable or kill

aquatic organisms. Acute toxicity is caused by high

exposure to pollutants for short periods of time (less

than 4 days). Chronic toxicity is caused by lower exposures for long periods of time (greater than four days).

The toxicity of a chemical can be affected by such

environmental factors as pH, temperature, and sediment concentrations. Overall toxicity results from the

combined exposure to all chemicals in the effluent and

the ambient waters.

1.3.7. Bioaccumulation and Exposure to Humans

Lower concentrations of organic chemicals and metals

that do not cause aquatic toxicity can be taken up and

concentrated in the tissues of estuarine organisms. As

fish predators consume contaminated prey, bioaccumulation of these chemicals can occur. This food chain

contamination can persist long after the original chemical source is eliminated. Humans that regularly consume tainted fish and shellfish can receive harmful

doses of the chemical.

Human exposure to harmful levels of organic chemicals and metals can also occur through drinking water

withdrawals from fresh water tidal rivers.

1.4. Overview of the Waste Load Allocation

Book I, 303 (d)/TMDL Guidance discusses the overall

TMDL process, procedures, and considerations. The

1-3
reader is referred to this book for procedural guidance.

This book gives specialized modeling guidance.

A WLA provides a quantitative relationship between

the waste load and the instream concentrations or

effects of concern as represented by water quality

standards. The reliability of this relationship depends

upon the accuracy and completeness of the data,

certain characteristics of the model, and the skill and

judgment of the modeler. During the development of a

WLA, the user combines data and model first to describe present conditions and then to extrapolate to

possible future conditions. The process is iterative:

observed data are used to refine model input (or even

model equations) and modeling results are used to

guide monitoring efforts.

The WLA process sequentially addresses the topics of

hydrodynamics, mass transport, water quality kinetics,

and for some problems, bioaccumulation and toxicity.

1.4.1. Hydrodynamics

The topic of hydrodynamics addresses where the

water goes. Both primary and secondary water circulation patterns can significantly affect water quality. In

some estuaries, monitoring programs can adequately

quantify the primary circulation patterns associated

with tidal excursions and tributary inflow. Hydrodynamic models may be needed, however, to investigate

secondary currents associated with the net residual

tidal action, wind, density differences, or Coriolis acceleration. Hydrodynamic models also may be used to

interpolate data between monitoring stations or to extrapolate data to future conditions. The final result of

the hydrodynamics study is a record of water flow and

volume (or velocity and elevation) throughout the water

body over an appropriate period of time.

1.4.2. Mass Transport

Mass transport addresses the fate of dissolved, nonreactive substances. These tracers are subject to advection with the water currents and to turbulent

diffusion. If only the primary circulation is resolved in

the hydrodynamics step, then secondary circulation,

such as density currents and lateral shear, are parameterized into dispersion coefficients. The values of

these coefficients are determined by calibrating the

model to salinity or dye tracer data. This calibration

process also can be used to refine the advective flows

estimated in the hydrodynamics step. Recalibration of

advective flows based on tracer data can be particularly important in cases where net tributary inflow to the

estuary is uncertain. The final result of the mass transport step is a record of advective and dispersive fluxes

(or the appropriate model coefficients) for dissolved,

nonreactive substances throughout the water body

over the period of study.

1.4.3. Water Quality Kinetics

Water quality kinetics describe what happens to a set

of physical, chemical, and biological constituents as

they are transported throughout the water body. The

set of constituents modeled depends upon the water

quality problem of concern. General models are available describing the primary constituents and reactions

for the water quality problems outlined in this manual.

For most WLA studies, the user must provide appropriate site-specific values for the reaction coefficients and

the environmental conditions (such as temperature,

sunlight, and pH). In some complex studies, the user

may have to modify model equations describing the

reactions or add more simulated constituents. Although

literature values are available to guide initial model

parameterization, local monitoring data are required to

refine these values and construct a site-specific model.

The user arrives at appropriate parameter values

through an iterative model calibration and testing process. The final result of the water quality kinetics step is

a record of constituent concentrations throughout the

water body for the period of study and for hypothetical

future periods under various waste load management

strategies.

1.4.4. Bioaccumulation and Toxicity

Often, water quality constituent concentrations (or toxicity units) are directly compared with appropriate

standards to infer potential risk to humans or the

aquatic community. Waste loads may be adjusted so

that concentrations do not exceed (or fall below) these

standards under design conditions. Alternatively,

waste loads may be adjusted so that concentrations

exceed standards for less than a specified frequency

and duration over a realistic range of future conditions.

Recent advances in environmental toxicology allow the

direct calculation or simulation of bioaccumulation and

toxicity for some classes of chemicals. To simulate

bioaccumulation by individual fish (or a local species of

fish), the user must specify an exposure scenario plus

a few physiological parameters. Although literature

values for the parameters are available, monitoring

data should be used for site-specific calibration. Direct

toxicity due to the narcotic effects of neutral hydrophobic organic chemicals can be predicted. To simulate

food chain bioaccumulation, the user must define the

main components of the local food web (who eats

whom), and calibrate the physiological parameters for

each. This task requires considerable judgment and a

good data base.

1-4
1.5. Steps in the Modeling Process

For each of the topics addressed in a modeling study,

several steps are applied in an iterative process. The

first step is problem identification. The modeler reviews

existing data related to all potential problems, which

were discussed in Section 1.2. The second step is

model identification. Starting with knowledge of the site

and the water quality problems of concern, the modeler

reviews existing data and identifies an appropriate

simulation model or data base. Additional monitoring

is planned to gain further knowledge about existing

conditions and important processes.

The third step is initial calibration of the model to

existing data. Where site-specific data are lacking,

literature values and user judgment are employed.

Sensitivity analysis is used to estimate the uncertainty

in model predictions due to each uncertain input. This

information can be used to guide ongoing monitoring

efforts.

As more data sets become available, the calibrated

model is tested and refined. Recalibration should address all previous data sets. Throughout this step, the

user should be guided by the principle of parsimony -

calibration and validation of the model should be accomplished with the fewest possible parameters. A

single longitudinal dispersion coefficient that adequately represents an entire estuary is preferable to a

series of coefficients that allow a slightly better fit to

data. Model parameter values should be consistent

across the range of tested data. If values must vary,

they should follow some rational function. This functional relationship becomes an external part of the

model that should be documented and tested.

After some effort at recalibration and testing, the

modeler decides either that the model is sufficiently

reliable to produce a sound waste load allocation, or

that available time and resources do not permit continued refinement. At this point, the degree of model

validation must be assessed. Traditional practice dictates that an independent data set be used for a final

validation test of the model. Sometimes such a data

set is unavailable, or has already been used in the

recalibration process. In any case, a final uncertainty

analysis should document the model’s expected reliability over the range of conditions tested. Validation is

contingent upon the waste load options to be considered. A model may be considered valid to study some

options, but invalid to study others.

After the WLAs have been put into effect, some degree

of monitoring should be pursued to track the effectiveness of the actual waste load reductions in meeting

water quality goals. When sufficient data are available,

a post-audit should test model predictions under the

new conditions. Refinements in the model at this point

may guide refinements in the waste load allocation and

contribute to more informed judgment in future studies

involving similar pollutants and estuaries.

1.6. Organization and Scope

The basic estuarine guidance document is comprised

of four parts. Part 1, “Estuaries and Waste Load Allocation Models,” summarizes the important water quality problems, estuarine characteristics and processes

affecting these problems, and the simulation models

that are available for addressing these problems. Part

2, “Application of Estuarine Waste Load Allocation

Models,” provides a guide to monitoring and model

calibration and testing, and a case study tutorial on

simulation of waste load allocation problems in simplified estuarine systems.

Part 3, “Use of Mixing Zone Models in Estuarine Waste

Load Allocations,” summarizes initial dilution and mixing zone processes, available models, and their application in waste load allocation. Part 4,"Critical Review

of Estuarine Waste Load Allocation Modeling," summarizes several historical case studies, with critical reviews by noted experts.

1.7. References

Fisher, D., Ceraso, J., Mathew, T., and Oppenheimer,

M. 1988. Polluted Coastal Waters: The Role of Acid

Rain. Environmental Defense Fund, New York.

Pritchard, D.W. 1967. What is an Estuary: Physical

Viewpoint. Estuaries. ed: Lauff, G.H., American Association for the Advancement of Science, Publication

No. 83, Washington, D.C.

Shubel, J.R. 1971. The Origin and Development of

Estuaries. The Estuarine Environment-Estuaries and

Estuarine Sedimentation. American Geological Institute.

Smith, F.G.W., ed. 1974. CRC Handbook of Marine

Science, Vol. I. CRC Press, Cleveland, OH.

Waddell, T.E. 1989. Draft Report: State of the Science

Assessment: Watershed and Estuarine Nitrogen

Transport and Effects. U.S. Environmental Protection

Agency, Athens, GA.

1-5

2. Overview of Processes Affecting Estuarine Water Quality

James L. Martin, Ph.D., P.E.

AScI Corp., at the

Center for Exposure Assessment Modeling

 Environmental Research Laboratory, U.S. EPA, Athens, GA

Robert B. Ambrose, Jr., P.E.

Center for Exposure Assessment Modeling

 Environmental Research Laboratory, U.S. EPA, Athens, GA

John F. Paul, Ph.D., P.E.

Environmental Research Laboratory, U.S. EPA,

Narragansett, RI

2.1. Organization Of This Section

This section is organized into six major parts. Section

2.2 contains an overview of estuarine morphology and

classification. A more detailed description of physical

processes impacting estuarine circulation and mixing

is provided in Section 2.3. Subsequent parts of Section

2 deal with major processes affecting water quality,

including sediment transport and sediment water quality interactions (Section 2.4), organic wastes, dissolved

oxygen (DO) and nutrients (Section 2.5), synthetic

organic chemicals (Section 2.6), and metals (Section

2.7). Sections 2.2 to 2.7 provide an overview of processes followed by supplemental text describing in

greater detail how each of these basic processes are

described in estuarine waste load allocation (WLA)

models.

2.2. Estuarine Morphology and Classification

The geomorphology of estuaries strongly affects the

transport of pollutants and ultimately their water quality

characteristics. Estuarine depth controls propagation

of the tidal wave. Shallow channels and sills increase

vertical mixing; deep channels are more likely to be

stratified and to have greater upstream salinity intrusion. Shallow sills near the mouth of an estuary may

limit circulation and flushing of bottom waters. The

length of the estuary and conditions at the upstream

boundary determine the type of tidal wave, the phase

between current velocities, and the tidal heights. The

width affects velocities (narrow constrictions increase

vertical mixing and narrow inlets restrict tidal action).

Wind-induced circulation is transient and interacts with

channel geometry to produce various circulation patterns. Estuaries have typically been classified based

on their geomorphology and patterns of stratification

and mixing.

Based on their hydrodynamics, estuaries have been

classified as sharply stratified, partially stratified and

well mixed (Bowden 1967, Pritchard 1967). Sharply

stratified estuaries exhibit little mixing between the salt

wedge and fresh water flow. Examples include fjords

and salt-wedge estuaries, such as the Mississippi River

estuary. In sharply stratified estuaries tidal action is not

sufficient to mix the separate layers. Completely mixed

estuaries do not exhibit significant vertical density variations and tidal flow is normally greater than fresh water

inflow. Examples of this include the Delaware and

Raritan River estuaries which are normally well mixed.

Partially stratified estuaries are intermediate between

sharply stratified and completely mixed estuaries. Partially stratified estuaries exhibit significant vertical density gradients but the gradients are less sharp than in

sharply stratified estuaries. Examples include the

James River Estuary (Mills et al. 1985).

Hannsen and Rattray (1966) proposed a classification

scheme based on vertical variations in salinity and the

strength of the internal density-driven circulation. A

stratification parameter is computed from the vertical

salinity gradient which is then compared to a circulation

parameter computed from net surface and fresh water

flow velocities. These parameters are calculated at

various points along the estuarine channel and may be

used to estimate degree of stratification of the system.

Further description of the method is provided by Mills

et al. (1985).

Based on their geomorphology, typical classifications

(Fischer et al. 1978) are: (1) drowned river valleys or

coastal plain estuaries (e.g., Chesapeake Bay, Delaware Estuary), (2) bar-built estuaries (e.g., Galveston

Bay, Pamlico Sound), (3) fjords (e.g., Puget Sound),

and (4) other diverse formations (e.g., San Francisco

Bay).

2-1
Coastal plain estuaries are generally broad and relatively shallow (rarely over 30 m in depth) with gently

sloping bottoms and depths increasing uniformly towards the mouth and with extensive areas of deposited

sediment. Such estuaries usually have been cut by

erosion and are drowned river valleys, often displaying

a dendritic pattern fed by several streams. Coastal

plain estuaries are usually moderately stratified and

can be highly influenced by wind. The majority of

estuaries in the contiguous United States are of the

drowned river or coastal plain type.

Bar-built estuaries are bodies enclosed by the deposition of a sand bar off the coast through which one or

more channels provide exchange with the open sea.

These are usually unstable estuaries, subject to gradual seasonal and catastrophic variations in configuration. Many estuaries along the Gulf Coast and Lower

Atlantic regions are of this type. They are generally

shallow (e.g. a few meters deep or less), often vertically

well mixed, and highly influenced by wind.

Fjords are generally long and narrow with steep sides

and relatively deep waters. They typically are strongly

stratified and have shallow sills at the estuarine mouth

that often limit mixing of deep waters. They usually are

formed by glaciation and are typically found in Alaska.

The fresh water streams that feed a fjord generally

pass through rocky terrain. Little sediment is carried to

the estuary and the bottom is likely to be a rocky

surface.

Estuaries not covered by the above classifications

usually are produced by tectonic activity, faulting, landslides or volcanic eruptions. An example is San Francisco Bay which was formed by movement of the San

Andreas Fault system (Mills et al. 1985).

2.3. Factors Affecting Circulation And Mixing

Estuaries and coastal seas have circulation patterns

that are highly variable in time and space. Awareness

of characteristic time and space scales of flows generated by the tides, winds, density gradients resulting

from the interaction of fresh and ocean water, and the

effects of the earth’s rotation (the Coriolis force) will

help to define the mixing regime of the water body.

Estuaries generally are large water bodies that have

more vigorous circulations than occur in rivers and

most lakes. Like rivers and lakes, however, internal

factors such as friction and vertical mixing play similar

physical roles in the marine environment to those in

fresh water systems in the redistribution of pollutants.

The existence of stratification (vertical density gradients) in estuaries, as well as the more complex external

forcings (such as tidal fluctuations), modify the effects

of vertical mixing and friction to the extent that parameterizations used to evaluate mixing in fresh water must

be used with caution if at all. This section briefly

discusses the physical forces affecting estuaries. More

extensive discussions can be found in standard texts

on estuaries such as that by Fischer et al. (1978).

2.3.1. Tides

The ocean tides are produced principally by interaction

of the gravitational fields of the earth, moon, sun and,

to a lesser degree, other solar system bodies. The

principal effects are caused by the moon and occur on

a roughly 12.4-hour period. Solar effects occur at 1-day

periods. Because all the bodies in the solar system are

in motion relative to one another, the effects of their

gravitational fields vary in time. One result is the familiar

spring-neap cycle of tides. Astronomical tidal motion is

highly predictable. Such information is published annually in the National Ocean Service Tide Tables and

Tidal Current Tables. Tide tables provide predictions of

times and heights of high and low water. Tidal current

tables provide predicted times, magnitudes and directions of maximum ebb and flood and high and low water

slacks for principal coastal stations referenced to the

standard locations.

Tides are expressed in terms of amplitude (the variation of water level about some datum level) and tidal

current (the ebb and flood velocity fields). Tidal amplitudes in North America vary from tenths of meters in

the Gulf of Mexico to more than 10 meters in parts of

Alaska and the Canadian Maritime Provinces. Tidal

current magnitudes are also highly variable, with the

highest values being recorded in topographically constrained straits. Tidal amplitude and tidal current are

usually out of phase so the time of high water is not the

same as the time of high water slack. Such differences

in phase and interaction between main and side channels can lead to tidal trapping of parcels of water in side

channels or embayments.

The effect of the tides is to cause: (1) time-variable

mixing through frictional interaction with the bottom and

(2) spatially asymmetric flow patterns on ebb and flood

through interaction with the bottom topography. The

interactions of the tides with other driving forces and

with topography also may result in residual circulation

patterns of small magnitude but great persistence,

which could play a significant role in the transport of

pollutants.

2.3.2. Earth’s Rotation Effects -Coriolis Force

The effect of the earth’s rotation on the motion of fluids

is to deflect the flow to the right (left) in the northern

(southern) hemisphere. In estuaries wide enough to be

affected by this force, the effect is to move less dense

water to the right (left) side, looking seaward, of the

estuary. A further effect is that the interface between

2-2
waters of different densities tends to be sloped as the

pressure gradient forces and the Coriolis force balance

each other to achieve geostrophic balance. The effect

can be enhanced in estuaries by the action of the tides

and can result in regions of persistent inflow of sea

water on the left and outflow of fresher water on the

right. The Coriolis effect is considered important for low

Rossby numbers (NR<0.1, where NR is the Rossby

number, the ratio of the inertial force to the Coriolis

force).

The time scale for rotational effects is the local inertial

period, which increases north to south. Inertial periods

for the contiguous states range from about 15 hours in

Washington state to 30 hours in southern Florida. The

appropriate length scale in estuaries is the internal

Rossby radius, which is the ratio of the internal wave

speed to the local inertial frequency. This length scale

accounts for both local density structure (degree of

stratification) and water depth.

2.3.3. Fresh Water Inflow

Fresh water inflow volume to an estuary can vary from

short-term response to local storms or the passage of

hurricanes to seasonal wet and dry cycles. In some

estuaries, the volume of fresh water is sufficient to

maintain a density difference over large distances before being completely mixed into sea water. Such

density differences result in flow patterns that tend to

maintain the density differences. Areas with high gradients, the pycnocline and fronts, tend to resist the

localized processes of mixing and may result in “pools”

of fresher water confined along one section of the

coast. Examples include the Chesapeake Bay Plume

and a band of fresher water confined within about 15

km of the shore along the South Atlantic Bight (Georgia

and the Carolinas). Pollutants introduced into these

waters may be confined there for relatively long periods.

Increased fresh water inflow can change the character

of an estuary from well-mixed to partially mixed or

possibly stratified. Decreased inflow could have the

opposite effect with concomitant increased upstream

intrusion of sea water. Such changes in the vicinity of

an outfall can change the degree of mixing of the

effluent. Fresh water inflow varies primarily on seasonal scales but large amounts of fresh water can be

introduced to estuarine systems by severe storms,

especially tropical cyclones along the East and Gulf

Coasts during late summer and fall. The response of

estuarine circulation to changes in fresh water flow will

vary according to the type of estuary. The time scale

of the response is roughly the flushing time of the water

body, which can vary from a few days for an estuary

with large fresh water flows and strong tides (the

Columbia River estuary) or for numerous shallow estuaries along the Gulf Coast (the Brazos River and

Colorado River Estuaries) to several months for an

estuary that is shallow and has weak tides such as

Pamlico Sound.

2.3.4. Friction and Vertical Mixing

Friction is the term in the equations of fluid motion that

accounts for the dissipation of energy by small scale

turbulent motions. Similarly, turbulence generated by

vertical shear in the fluid tends to mix dissolved constituents and acts to reduce sharp vertical gradients.

Friction forces retard or change the direction of fluid

flow. The friction term is used here to parameterize the

turbulent transfer of momentum and mass within a fluid

or between the fluid and the boundaries, such as

between the atmosphere and the water (wind stress)

or between the water and the bottom. Frictional effects

are seen in the formation of turbulent boundary layers

in fluids and in the turbulent mixing of properties in

those layers. Frictional effects have rather short time

scales for small scale turbulence but several hours may

be required for the frictional spin-down of a fluid flow

after its driving force is removed. Bottom boundary

layers may have vertical scales up to 10 meters,

whereas horizontal boundary layers can be several

kilometers wide. In general, the effects of horizontal

boundary layers are ignored and efforts concentrate on

the vertical layers caused by wind stress and bottom

interactions. Because the scale of the vertical layers is

small, shallow water is more easily affected by friction

than deep ocean waters. Generally, the stronger the

flows, either due to tides or wind effects, the more

turbulent the water column with a tendency for rapid

vertical mixing.

2.3.5. Meteorological Effects

Meteorological effects considered here are the result

of both local and remote wind forcing and other atmospheric pressure forcing separate from the wind. Rainfall

as an input of fresh water is considered separately.

Wind effects include generation of persistent circulation patterns caused by seasonal weather changes in

a particular area, modification of circulation patterns by

localized weather, and generation of waves and storm

surges. Water responds to an applied wind stress

within a few hours and to the cessation of the wind in

about the same time frame. The winds vary on a variety

of time scales, such as diel variations (sea breeze), the

time scale of frontal passages and the seasonal

changes in prevailing winds. Variability of wind speed

and direction over periods shorter than the frontal

passage scale will be evidenced primarily in the production of turbulent mixing within a few meters of the

surface.

Atmospheric pressure affects sea level through the

“inverse barometer” effect where low atmospheric

pressures cause the sea level to be higher than normal

2-3
(about 1 cm per millibar) and high atmospheric pressure lowers the sea level. This effect and those associated with strong winds (wind setup and setdown)

modify the astronomical tides and are called meteorological tides.

In estuaries with relatively small input of fresh water

and small tide range, such as Mobile Bay, Alabama,

wind is the dominant force in driving the overall circulation and in generating turbulent mixing. The wind

driven circulation has time scales of a few days at the

period of local frontal passages. On open coastlines

the winds are also the dominant forcing mechanism

through the generation of long-period waves(length

scales of order 100 to 1000 km, time scales 2 to 10

days). Sea level fluctuations due to strong storms (i.e.

winter or extratropical cyclones) are called storm

surges which can have devastating effects on low lying

coastal regions. In this way, both local and remote

winds can play a large role in the dynamics of an open

coast.

2.4. Sediment Transport and Sediment/Water

Quality Interactions

2.4.1. Concepts

Sediment typically is associated with agricultural and

urban runoff. Sediment not only affects water transparency, but can carry chemicals such as nutrients and

toxic substances into receiving waters. Therefore, an

important aspect of water quality modeling is the capability to simulate sediment transport and sediment/water interactions.

Unlike rivers, which have reasonably constant water

quality conditions, the large changes in salinity and pH

in an estuary directly affect the transport behavior of

many suspended solids. Many colloidal particles agglomerate and settle in areas of significant salinity

gradients.

Sediments are also in a constant state of flux due to

the time varying currents in estuaries, and movement

of sediments along the bottom often does not occur in

a net downstream direction as in stream reaches.

Consequently estuaries tend to trap sediments (Mills

et al. 1985).

Estuarine sediment transport has two main components — bed load and suspended load — both of which

may be important.

Even when no sediment is transported by the flow,

deposited sediments can have a strong influence on

water quality in the overlying water. Through adsorption, biofilm assimilation and other chemical/biochemical transformations, sediments can become sinks or

sources of materials such as oxygen, toxic chemicals,

or nutrients.

For water quality assessment purposes, the finer fractions of materials (silts, clays, organic detritus and live

plankton materials) are often of most importance. Particles are characterized by size, shape, density, surface

area, and surface physical and chemical properties

including electric charge. A review of particle regime

composition, behavior and interaction with water density was given by Lal (1977).

2.4.2. Processes

2.4.2.1. Fall Velocities, Settling, Deposition

For water quality modeling, the fall velocity of particles

and their resistance to resuspension under shear

stress, once they are deposited, are most significant.

Fall velocities are functions of size, shape (drag coefficient) and density ( of both the water and particle) and

can be reasonably well predicted for larger mineral

particles (Dietrich 1982; Gibbs et al. 1971). For micrometer-size particles and particularly for organic particles, the large diversity in sizes, shapes, and density

(Lal 1977; Ives 1973) often require indirect determinations of fall velocities from settling traps or mass balances. Settling velocities are used to calculate the

movement of sorbed chemical downward through the

water column. The settling characteristics of particles

may vary as they respond to water quality conditions in

an estuary (See 2.4.2.4.).

2.4.2.2. Resuspension, Scouring, Erosion

The resuspension or entrainment of sediments is a

function of the sediment properties, and flow-induced

shear stress at the sediment-water interface. For noncohesive sediments, this relationship is “explosive” in

nature. Very low or no resuspension occurs until a

threshold shear stress is reached. Then resuspension

rates increase in proportion to some power of the

excess shear stress.

For cohesive sediments, which are of primary interest

in water quality studies, entrainment is affected by

salinity, sediment type, microfauna, organic content,

and the time-history of the bottom sediments (Sheng

1983). Bed compaction may result in there being a finite

See Supplement I for greater detail on how

processes affecting circulation and mixing are

described in estuarine models. This Supplement is found on page 2.10 at the end of this

chapter.

2-4
amount of sediment that can be entrained at a given

shear stress (Lick et al. 1987), where the amount

depends upon the time-history of the bottom sediment,

rather than entrainment depending solely on particle

density and shear velocity. The lack of well established

descriptions of entrainment for cohesive particles requires site-specific calibration to refine initial estimates.

2.4.2.3. Cohesion

Cohesion of particles in the deposited bed increases

the resistance to resuspension and is a function of

consolidation history (Stefan, Ambrose and Dortch

1988). Investigations of this behavior have been reviewed by Mehta (1986). In addition to bedshear,

stresses due to wind driven flows and perturbations by

boat movement or organisms (bioturbation) can greatly

increase rates of resuspension of cohesive sediments.

Resuspension effects of wind have been conceptualized by Rodney and Stefan (1987).

2.4.2.4. Coagulation and Flocculation

Extremely fine particles often destabilize (coagulate) in

regions of significant salinity gradients and agglomerate to form larger particles (flocculate). The resulting

floc may then settle at a much different rate, due to the

greater agglomerated mass, than the individual particles. Coagulation occurs when electrolytes, such as

sodium chloride, neutralize the repulsive forces between clay particles allowing them to adhere upon

collision (flocculate). Flocculation rates are dependent

upon the size distribution and relative composition of

the clays and electrolytes and upon local boundary

shear stresses (Mills et al. 1985; Stefan, Ambrose and

Dortch 1988).

2.4.2.5. Sorption

Suspended sediment, besides being a very important

water quality parameter in its own right, also can have

a very strong relationship with chemical species dissolved in the water through adsorption/desorption, for

example, of nutrients or synthetic organics (often toxic

materials). This is an area of very active research (e.g.

Golterman et al. 1983; Stumm and Morgan 1981;

Karickhoff 1984) and will be addressed in a later section in more detail.

2.4.2.6. Bottom Boundary Layer

The interaction between particles and water chemistry

becomes particularly complex near the bed because

of: (a) strong vertical velocity gradients associated with

shear forces; (b) activities of organisms such as

biofilms, invertebrates, crustaceans andfish; and (c)

pore water movement, which leaches into and out of

the outlying waters.

Microcosm models or measurements of these systems

are necessary to provide the input or withdrawal rates

of dissolved substances. Examples include sedimentary oxygen demand (Chen et al. 1984, Gantzer et al.

1988), phosphorus release and polychlorinated

biphenyl (PCB) resuspension.

2.5. Organic Wastes, Dissolved Oxygen And

Nutrients

2.5.1. Concepts

This section is a brief overview of the common processes used to model organic wastes, DO and nutrients

(referred to as conventional pollutants) and their interactions. For more detailed information, the reader

should refer to other resources (Bowie et al. 1985;

Orlob 1983; Chapra and Reckhow 1983; Thomann and

Mueller 1987). The focus of WLA models of conventional pollutants is often DO and biochemical oxygen

demand (BOD) as a general measure of the health of

the system, or the focus can be primary productivity

when eutrophication is the major concern. Conventional WLA models usually include temperature, major

nutrients, chemical characteristics, detritus, bacteria,

and primary producers. WLA models may include

higher trophic levels (i.e. zooplankton and fish) because of their effects on other more important variables, such as phytoplankton, BOD and DO.

Zooplankton and fish also provide a means of controlling lower trophic levels, which can affect nutrients and

DO (bio-manipulation). Additional information on modeling these processes is provided in Section 3.

2.5.2. Fate Processes

Upon entry to the estuary, settling of particulate organic

matter and particulate nutrients generally occurs. High

flow events may scour previously deposited material.

Organic matter is oxidized, drawing upon the DO supply, which is replenished by reaeration.

Organic nitrogen is mineralized to ammonia, which

reaches equilibrium with its ammonium form. Nitrification further draws upon the DO supply converting ammonia to nitrite and then nitrate. Nitrate may be

converted back to ammonia or to nitrogen gas through

See Supplement II for greater detail on sediment transport and sediment/ water quality

interactions. This Supplement is found on

page 2-18 at the end of this chapter.

2-5
denitrification in low DO regions of the estuary. Ammonia and nitrate may be taken up by phytoplankton and

aquatic plants and incorporated into the food chain,

eventually returning to the water as organic nitrogen.

Organic phosphorus is mineralized to orthophosphate,

which reaches sorptive equilibrium with suspended or

benthic sediment. Particulate sorbed phosphate settles; dissolved phosphate is rapidly taken up by phytoplankton and aquatic plants and incorporated into the

food chain, eventually returning to the water as organic

phosphorus.

Organic material deposited to benthic sediment is oxidized in the upper aerobic layer, and reduced in the

lower anaerobic layers. Upward fluxes of ammonia and

reduced organic species are produced, the latter contributing to sediment oxygen demand.

The transfer, or flux of phosphorus, across the sediment water interface is enhanced by anaerobic conditions as particulate phosphorus may be resolubilized

and reenter the water. In some aquatic environments,

net sedimentation buries a substantial fraction of the

nutrients and organic matter deposited to the bed.

Although many of these interacting fate pathways are

well known and included in most recent conventional

water quality models, accurate simulations remain difficult. Extensive site-specific data collection is required

to characterize both the sources and the process rates

over the range of expected conditions. Many of the

rates are biologically mediated, with descriptive constants and parameters that vary both with environmental conditions and predominant species. The major

pathways and cycles will be briefly discussed in the

following sections and the supplement from the model

developer’s perspective. Additional information is provided in Section 3.

2.5.2.1. Phytoplankton Kinetics

Phytoplankton kinetics assume a central role in eutrophication affecting both the nitrogen and phosphorus

cycles, the DO balance, and food chain response.

The reaction term for phytoplankton is expressed as

the difference between the growth rate and the death

and settling rates in each volume element. The growth

rate of phytoplankton is a complicated function of the

species present and their differing reactions to solar

radiation, temperature, and the balance between nutrient availability and phytoplankton requirements. Phytoplankton “death” rates are conventionally expressed

as the sum of the endogenous respiration rate, the

death rate, and the grazing rate. Available information

does not allow simulation of individual species in a

natural environment. Hence, models either simulate

the phytoplankton community as a whole, or as classes

such as greens, diatoms, blue-greens, and dinoflagellates.

Phytoplankton kinetics affect the oxygen, nitrogen,

phosphorus, and carbon cycles primarily through uptake and secondarily through death. Proper specification of average stoichiometry is necessary to

accurately model these interactions. The ratios of phytoplankton carbon to phytoplankton nitrogen, phosphorus, and chlorophyll-a vary among species and in time.

Few applied modeling frameworks account for the dynamics of stoichiometry. The user is forced to specify

average values or those characteristic of stressed systems.

2.5.2.2. The Phosphorus Cycle

Organic phosphorus in the water is present in various

particulate and dissolved forms that mineralize and

settle at different rates. Some models lump all organic

phosphorus into a single state variable; others divide

organic phosphorus into two, three, or four state variables that differ in settling and mineralization rates.

Mineralization or bacterial decomposition is generally

modeled as a first order temperature-corrected reaction, although second order and saturating rates based

upon phytoplankton biomass have been employed.

Dissolved inorganic phosphorus sorbs to suspended

particulate matter in the water column. Subsequent

settling of the solids and sorbed phosphorus can provide a significant loss mechanism of phosphorus from

the water column to the benthos. Process based functions that accurately calculate the phosphorus partition

coefficient would improve prediction of this important

variable significantly. Phosphorus may resolubilize under anaerobic conditions and the flux of phosphorus to

the water column may be enhanced under anaerobic

conditions at the sediment-water interface as well as

by high pH conditions.

Dissolved inorganic phosphorus is taken up by phytoplankton at the stoichiometrically modified growth rate.

Although there is evidence for “luxury storage” of inorganic phosphorus in phytoplankton, most models assume the internal pool of phosphorus is biomass.

Grazing causes transfer of phytoplankton phosphorus

up the food chain. Upon respiration and death, biomass

phosphorus is recycled to the various forms of organic

and inorganic phosphorus at user-specified ratios.

2-6
2.5.2.3. The Nitrogen Cycle

Nitrogen may be characterized as organic and inorganic forms, where inorganic forms may include ammonia-nitrogen, nitrate-nitrogen and nitrite-nitrogen.

As for organic phosphorus, some models lump all

organic nitrogen into a single state variable, whereas

others divide organic nitrogen into two, three, or four

state variables. Some modeling approaches use nitrogenous biochemical oxygen demand (NBOD) as a

state variable. Mineralization to ammonia can be represented as first-order, or second order or saturating

dependence on bacterial biomass.

Ammonia-nitrogen in the presence of nitrifying bacteria

and oxygen is converted to nitrite then nitrate-nitrogen.

The process of nitrification in natural water is complex,

depending upon DO, pH, total inorganic carbon, alkalinity, Nitrosomonas and Nitrobacter bacteria, and flow

conditions.

Most models represent the reaction with a first-order,

temperature-corrected rate constant.

Some models treat nitrate and nitrite-nitrogen as a

single lumped variable. Some models allow spatial

variations calibrated by the user or empirical DO limitation terms. Obviously, a process-based predictive

function for this rate would be quite valuable.

Denitrification is the reduction of nitrate to ammonia

and nitrogen gas. Primarily a benthic reaction, it is

included in some models as a loss rate of nitrate. It is

modeled as a first order reaction, sometimes multiplied

by a modified Michaelis-Menten term to suppress the

reaction in the presence of a small amount of oxygen.

Un-ionized ammonia may also be degassed and is of

additional importance due to its toxicity.

Both ammonia and nitrate are taken up by phytoplankton at the stoichiometrically modified growth rate.

Some models include a preference function for ammonia uptake when its concentration is high enough.

Grazing causes transfer of phytoplankton nitrogen up

the food chain. Upon respiration and death, biomass

nitrogen is recycled to the various forms of organic

nitrogen and ammonia at user-specified ratios.

2.5.2.4. The Carbon-Dissolved Oxygen Balance

Organic carbon is composed of a variety of materials

in estuaries, both dissolved and particulate. Some

models lump all organic carbon into a single state

variable expressed in units of oxygen—carbonaceous

biochemical oxygen demand (CBOD). Other models

represent various fractions of organic carbon, with their

separate oxidation and settling rates. Oxidation is generally modeled as a first order temperature-corrected

rate. Some models allow spatial variations calibrated

by the user.

Traditional models of organic waste do not compute

inorganic carbon and the associated variables of pH

and alkalinity. This carbonate system could be important for simulating the effects of acidic wastes on unionized ammonia concentrations or potential carbon

dioxide limitation in low alkalinity, high nutrient waters.

Models that include the carbonate system calculate

total inorganic carbon as the sum of bicarbonate, carbonate, and carbon dioxide. These species are in

equilibrium controlled by the equilibrium constants of

the dissociation reactions and the pH of the water.

Carbon dioxide (and thus total inorganic carbon) is

produced by respiration, consumed by algal growth,

and replenished by atmospheric exchange.

Carbonate alkalinity is the sum of bicarbonate concentration plus twice the carbonate concentration plus the

hydroxide concentration minus the hydrogen ion concentration. Addition of acids and nitrification lowers the

pH and reduces alkalinity. Nitrate uptake by phytoplankton produces hydroxide and increases alkalinity.

DO is depleted by oxidation of organic carbon, nitrification, and respiration. Benthic reactions depleting oxygen are usually modeled as a spatially variable flux of

sediment oxygen demand. Respiration effects may be

combined for simplicity or separated into components

such as respiration by bacteria, plankton, macrophytes, fish, etc. The respiration of decomposers that

utilize organic matter is referred to as decomposition.

Oxygen is used during some chemical transformations,

such as nitrification and the oxidation of reduced substances (e.g. sulfide, methane, reduced iron, and reduced manganese).

Biochemical oxygen demand (BOD) is a measure of

the materials present in a sample which may be oxidized by biochemical processes. The BOD exerted is

determined by the change in oxygen concentrations of

a sample over time under specific analytical conditions.

The modeling problem with BOD is that it combines the

effects of several oxygen consuming processes into

one variable; this approach may be too simple for

modeling some systems.

The more realistic approach is to separate oxygen

demands into various components, such as biodegradable organic (carbonaceous) demands, nitrogenous

demands, and oxidation of other substances (e.g.,

reduced metals, sulfide, etc.). Biodegradable organic

demands may be due to dissolved and particulate

matter in the water column and bottom sediments.

2-7
Some models separate water column organic matter

into particulate and dissolved forms, referred to as

POM and DOM. Because some forms of organic matter decay at faster rates than others, organic matter

may be further divided into those that decay at a fast

rate (labile) and those that decay at a slower rate

(refractory). As labile organic matter decomposes, a

portion is transferred to the refractory state. A similar

approach can be used for organic sediments. Sources

of organic matter include external waste loads and

excretions and mortality of living substances.

DO is replenished by phytoplankton growth (photosynthesis) and by reaeration. Many reaeration formulas

exist as well as in-situ measurement techniques.

Reaeration formulas based solely on velocity and

depth applicable to tidal rivers and estuaries include

O’Connor-Dobbins (1958, for slower, deeper rivers),

Churchill (1962, for moderately deep, faster streams)

and Owens et al. (1964, for shallow streams) (see

Thomann and Mueller 1987).

The Tsivoglou and Wallace method (1972) calculates

reaeration in rivers and streams from the slope and

travel time. Relationships that include the effects of bed

roughness, secondary flow and wind are under development. Numerous relationships exist for wind-induced reaeration. Wind induced reaeration may be

dominant in many estuaries due to the presence of

off-sea breezes and the large fetch near the ocean

outlet. However, a comprehensive approach to estuarine reaeration has not been developed. There remains a need for critical review and assimilation of all

the formulas.

2.5.2.5. Benthic-Water Interactions

The decomposition of organic material in benthic sediment can significantly affect the concentrations of oxygen and nutrients in the overlying waters. Areal fluxes

from the sediment due to diagenetic reactions can be

substantial nutrient sources or oxygen sinks. The occurrence of anoxia may dramatically increase nutrient

fluxes.

Most traditional models described these benthic fluxes

as spatially variable source and sink terms. Some

recent models have included benthic compartments in

which state variables are simulated. Particulate nitrogen, phosphorus, and carbon are added to the bed by

settling and lost by scour or sedimentation (burial).

Dissolved species of nitrogen, phosphorus, carbon,

and oxygen exchange with overlying water by pore

water diffusion. Benthic oxidation rates are generally

assumed first-order, with low rate constants producing

ammonia and consuming organic carbon and oxygen

equivalents (functionally, reduced organic species that

are oxidized at the water interface). Recently, efforts

have been made to simulate the diagenetic reactions

and resulting fluxes more realistically (DiToro 1986).

These efforts hold great promise for more accurate and

predictive modeling of organic and nutrient wastes.

Discussions of the processes impacting benthic fluxes

as well as modeling and measurement techniques may

be found in Hatcher (1986).

2.6. Synthetic Organic Chemicals

2.6.1. Concepts

Synthetic organic chemicals include a wide variety of

toxic materials whose waste loads are allocated based

upon threshold concentrations as well as tolerable

durations and frequencies of exposure. These pollutants may ionize and different forms may have differing

toxicological affects. The transport of the materials also

may be affected by sorption and they can degrade

through such processes as volatilization, biodegradation, hydrolysis, and photolysis.

2.6.2. Fate Processes

2.6.2.1. Ionization

Ionization is the dissociation of a chemical into multiple

charged species. Ionization can be important because

of the different toxicological and chemical properties of

the unionized and ionized species.

2.6.2.2. Sorption

Sorption is the bonding of dissolved chemicals onto

solid phases such as benthic and suspended sediment,

biological material, and sometimes dissolved or colloidal organic material. Sorption can be important in controlling both the environmental fate and the toxicity of

chemicals. Sorption may cause the chemical to accumulate in bed sediment or bioconcentrate in fish. Sorption may retard such processes as volatilization and

base hydrolysis, or enhance other reactions including

photolysis and acid-catalyzed hydrolysis.

A common assumption is that equilibrium sorption is

linear with dissolved chemical concentrations, and the

distribution is controlled by a partition coefficient and

the amount of solids present. For organic chemicals,

See Supplement III for greater detail on

organic wastes, dissolved oxygen and nutrients. This Supplement is found on page

2-20 at the end of this chapter.

2-8
lab studies have shown that the partition coefficient is

related to the hydrophobicity of the chemical and the

organic matter content of the sediment.

2.6.2.3. Settling, Deposition, and Scour

Suspended particles carrying sorbed chemicals can

settle through the water column and deposit on the

underlying bed.

Benthic particles carrying sorbed chemicals can scour

and become suspended in the water column. Mass

fluxes for settling, deposition, and resuspension are

controlled by the settling, deposition, and scour velocities, and the concentrations of suspended and benthic

sediment (See Section 2.4).

2.6.2.4. Loss Kinetics

Chemical concentrations and resulting observed toxic

effects often decline over time due to physical and

chemical processes. The loss processes considered

in most chemical fate models include volatilization,

hydrolysis, photolysis, and bacterial degradation.

Chemical oxidation and reduction are sometimes included as well.

Volatilization is the flux of a chemical across the airwater interface. The volatilization rate is proportional to

the gradient between the dissolved concentration in

the water and the concentration in the overlying atmosphere. For most chemicals, the partial pressure in the

atmosphere is negligible and the equation describing

volatilization reduces to a first-order form with the

removal rate coefficient.

The conductivity, or rate of transfer between the atmosphere and water column, is influenced by both

chemical properties (molecular weight, Henry’s Law

constant) and environmental conditions at the airwater interface (turbulence-controlled by wind speed,

current velocity, and water depth). Toxic chemical

models either require the user to input a value for the

transfer rate (kv) or internally compute a value using

the two-film theory first proposed by Lewis and Whitman (1924). This theory assumes that the rate of

transfer is controlled by diffusion through laminar layers in the air and water at the interface in which the

concentration gradients driving transfer are localized.

Hydrolysis is a reaction in which cleavage of a molecular bond occurs in the chemical and there is formation

of a new bond with either the hydrogen or the hydroxyl

component of a water molecule. Hydrolytic reactions

are usually catalyzed by acid and/or base and the

overriding factor affecting hydrolysis rates at a given

temperature is generally hydrogen or hydroxide concentration (Wolfe 1980).

Photodegradation (photolysis) is the transformation or

degradation of a compound that results directly from

the adsorption of light energy. Its rate is a function of

the quantity and wavelength distribution of incident

light, the light adsorption characteristics of the compound, and the efficiency at which absorbed light produces a chemical reaction.

Photolysis is classified into two types that are defined

by the mechanism of energy absorption. Direct photolysis is the result of direct absorption of photons by

the toxic chemical molecule. Indirect or sensitized photolysis is the result of energy transfer to the toxic

chemical from some other molecule that has absorbed

the radiation.

Biodegradation encompasses the broad and complex

processes of enzymatic attack by organisms on organic chemicals. Bacteria, and to a lesser extent fungi,

are the mediators of biological degradation in surface

water systems. Dehalogenation, dealkylation, hydrolysis, oxidation, reduction, ring cleavage, and condensation reactions are all known to occur either

metabolically or via organisms that are not capable of

utilizing the chemical as a substrate for growth.

2.7. Metals

2.7.1. Concepts

Metals are found naturally in the earth’s crust. As a

result of irrigation in some regions, metals may be

solubilized and transported to surface waters. Metals

are also present in municipal treatment plants and

industrial effluents, in landfill leachates and in nonpoint

source runoff from urban areas.

2.7.2. Fate Processes

Upon entry to a surface water body, metal speciation

may change due to complexation, precipitation, sorption, and redox reactions. Metals concentrations are

diluted further by additional stream flow and mixing.

Physical loss can be caused by settling and sedimentation, whereas a physical gain may be caused by

resuspension.

2.7.2.1. Metal Complexation, Precipitation

Heavy metals can form complexes with organic and

inorganic ligands and precipitate or dissolve. At equiSee Supplement IV for more detail on synthetic organic chemicals. This Supplement is

found on page 2-27 at the end of this chapter.

2-9
librium, the distribution of metals among the possible

complexes is controlled by the amount of metals and

ligands present, the reaction coefficients and solubility

products. In natural waters, sorption also affects the

distribution by reducing the amount of metal available

for complexation and precipitation.

Complexation reactions can affect transport by either

increasing or decreasing the soluble fraction. Sometimes one chemical species is known to be much more

toxic than another for a given heavy metal. This is

especially important because some states and EPA

have been moving towards “site-specific water quality

standards,” in which chemical speciation will be considered on a site-by-site basis. For example, a site that

is known to have a great deal of naturally occurring

dissolved organics may not require as stringent a water

quality standard because the dissolved organic material may complex the heavy metal and render it nontoxic to biota.

2.7.2.2. Sorption

Heavy metals frequently adsorb or “bind” to solid surfaces. The mechanism of sorption or attachment is via:

1) physical adsorption to solid surfaces, 2) chemical

sorption or binding by ligands at the solid-water interface, or 3) ion exchange with an ion at the solid water

interface. In addition, if the heavy metal is complexed

in solution by an organic ligand, it could sorb into the

organic solid phase much like an organic pollutant. The

mathematical formulation for describing the partitioning of a heavy metal between the solid phase and the

aqueous phase is the same as for organic chemicals

except the Kpi is usually called the “distribution coefficient” for heavy metal (although it may be referred to

as the partition coefficient or the binding constant in

some cases). In most measurements and simulation

models, all soluble complexes are lumped with the free

ion to give the dissolved metal concentration. Precipitated metal is lumped with all sorbed species to give

the total particulate metal concentration. A spatially

variable, lumped distribution coefficient KD describes

the distribution between the two phases. There is no

general consistency in reported KD values for particular

methods in the natural environment, so site-specific

values should be used when possible.

2.7.2.3. Redox Reactions

Metals can change oxidation states through various

oxidation and reduction reactions. Under some conditions, the kinetics of oxidation or reduction may be

important to simulate.

2.8. Model Structure

Mathematical models vary widely in their ability to

simulate the circulation and mixing processes as well

as the processes impacting DO variations, eutrophication, synthetic organic chemicals, and metals as described in this Section. Some of the models that are

presently available for use in estuarine waste load

allocation studies and criteria for their selection are

discussed in the following section (Section 3.0).

See Supplement V for greater detail on metals

as they relate to estuarine models. This Supplement is found on page 2.31 at the end of

this chapter.

SUPPLEMENT I: FACTORS AFFECTING CIRCULATION AND MIXING MODEL

EQUATIONS

I. Model Equations

The processes affecting circulation and mixing discussed in Section 2.2 may be described using equations based on laws of conservation of mass and

momentum. The fundamental equations generally include: (A) the conservation of water mass (continuity),

(B) conservation of momentum, and (C) conservation

of constituent mass. The equations for the mean components are provided in Table 2-1.

A. Continuity Equation

The continuity equation expresses the fundamental

principal that the sum of all volume transfers must

equal zero. For example, for a given control volume

the inflow minus outflow must equal the change in

storage over time. This expression alone, when used

in conjunction with measured data such as outflows,

surface elevation changes, and constituent concentrations, has formed the basis for estimating flows used

to transport water quality constituents (using Equation

2.5) in many water quality studies. This type of solution

is of greatest utility for describing flows in very simple

systems and is often of limited use in estuarine studies

with the possible exception of one-dimensional tidally

averaged analyses. To predict flows, the continuity

equation is usually coupled with momentum equations

to form the basis of hydrodynamic models.

2-10
A. Conservation of Water Mass (Continuity)

∂u

∂x

+

∂v

∂y

+

∂w

∂z

= 0 (2.1)

(1) (2) (3)

B. Conservation of Momentum

x - direction:

∂u

∂t

+

∂(uu)

∂x

+

∂(uv)

∂y

+

∂(uw)

∂z

= −

1

ρ

∂P

∂x

+ fu + g +

∂

∂x







Ex ∂u

∂x







+

∂

∂y







Ey ∂u

∂y







+

∂

∂z







Ez ∂u

∂z







(2.2)

(4) (5) (6) (7) (8) (9) (10) (11) (12) (13)

y - direction:

∂v

∂t

+

∂(vu)

∂x

+

∂(v v)

∂y

+

∂(vw)

∂z

= −

1

ρ

∂P

∂y

+ fv + g +

∂

∂x







Ex ∂v

∂x







+

∂

∂y







Ey ∂v

∂y







+

∂

∂z







Ez ∂v

∂z







(2.3)

(4) (5) (6) (7) (8) (9) (10) (11) (12) (13)

z - direction:

∂w

∂t

+

∂(wu)

∂x

+

∂(wv)

∂y

+

∂(ww)

∂z

= −

1

ρ

∂P

∂z

+ fw +g +

∂

∂x







Ex ∂w

∂x







+

∂

∂y







Ey ∂w

∂y







+

∂

∂z







Ez ∂w

∂z







(2.4)

(4) (5) (6) (7) (8) (9) (10) (11) (12) (13)

C. Conservation of Constituent Mass (Transport)

∂C

∂t

+

∂ (uC )

∂x

+

∂(vC )

∂y

+

∂ (wC )

∂z

=

∂

∂x







Kx ∂C

∂x







+

∂

∂y







Ky ∂C

∂y







+

∂

∂z







Kz ∂C

∂z







+ Σ S (2.5)

(14) (15) (16) (17) (18) (19) (20) (21)

where the numbered equation terms are:

(1 to 3) = the velocity gradients in the x ,y and z direction

(4) = local acceleration

(5 to 7) = are convective acceleration terms in the x,y and z direction

(8) = pressure gradient

(9) = the Coriolis force

(10) = gravitational acceleration

(11 to 13) = parameterization of the Reynold’s stresses in the x, y and z direction

(14) = rate of change in concentration

(15 to 17) = advective terms

(18 to 20) = turbulent diffusion

(21) = constituent source/sink term (e.g. kinetics and transfers, boundary loadings)

Equation variables are defined as:

t = time

P = pressure

g = gravitational acceleration

ρ = density

f = Coriolis frequency

Ex, Ey, Ez = turbulent diffusion coefficient for momentum in the x, y and z direction

u, v, w = mean velocity components in the x, y and z direction

x, y, z = rectangular coordinates, where x and y are horizontal coordinates and z is vertical

Kx, Ky, Kz = turbulent diffusion coefficient for mass in the x, y and z direction

C = concentration of water quality constituent

S = Constituent source/sink term

Table 2-1. Fundamental Model Equations

2-11
B. Conservation of Momentum

The conservation of momentum equation is derived

from Newtons’s second law of motion, which states

that the sum of all forces acting on a system is equal

to the time rate of change of linear momentum of the

system, where momentum is mass times velocity. The

factors affecting changes in momentum are illustrated

by Figure 2- 1 for a given control volume. The terms in

the conservation of momentum equation are expressions of: (4) local acceleration, (5-7) convective acceleration, (8) pressure forces, (9) coriolis force, (10)

body force, and (11-13) turbulent stress terms. The

equations as written in Table 2-1 assume that the fluid

is incompressible, that the velocities are Reynold’s

averages, that turbulent diffusion is much greater than

molecular diffusion, and that turbulent transfer of mass

and momentum is directly related to concentration and

velocity gradients (Boussinesq assumption). The

equations may be found in the literature in a number

of equivalent forms, differing due to mathematical manipulations or assumptions with regard to the system’s

geometry or boundary conditions. Unknowns in the

equation include the velocities (u,v and w), the pressure (P), and the eddy viscosity coefficients

(Ex,Ey,Ez).

The local acceleration (4) terms refer to the rate of

change of velocity with respect to time. They are also

referred to as the local inertia terms.

The convective acceleration (5-7) or convective inertia

terms express the effects on the momentum balance

of spatially varying velocities.

The pressure force (8) describes the effect of pressure

gradients on the velocity field. For a homogeneous

water body, i.e. one with no density differences, the

pressure gradients are proportional to the slope of the

water surface and the equal pressure surfaces are

parallel to the water surface throughout. Flows induced

by the water surface slope are referred to as barotrophic flow. Changes in density in nonhomogeneous

water bodies establish pressure gradients inducing

flows which are referred to as baroclinic.

An empirical relationship is generally used to establish

the relationship between water density, temperature,

and salinity and the relationship is generally referred

to as the “equation of state.” The equation of state

provides a means of linking water quality and hydrodynamic models. The relationship is given by

Figure 2-1. Factors affecting changes in momentum.

2-12
ρ = ρT + ∆ρS + ∆ρSS (2.6)

 where ρ is the water density (kg m-3), ρT is the density

as a function of temperature, and ∆ρS and ∆ρSS are

the changes in density due to dissolved and suspended solids, respectively.

An empirical relationship between density and temperature is given by (Gill 1982)

ρT = 999.8452594 + 6.793952 x 10−2T

− 9.095290 x 10−3T

2

+ 1.001685 x 10−4T

3

− 1.120083 x 10−6T

4

+ 6.536332 x 10−9T

5

 (2.7)

where T is the temperature (oC) and the change in

density due to salinity is (Gill 1982)

∆ρs = CSL (0.824493 − 4.0899 x 10−3T

+ 7.6438 x 10−5T

2

− 8.2467 x 10−7T

3

+ 5.3875 x 10−9T

4

) + C SL

1.5 (− 5.72466

x 10−3+ 1.0227 x 10−4T − 1.6546 x 10−6T

2

)

+ 4.8314 x 10−4 C SL

2

 (2.8)

where CSL is salinity (kg m-3). The relative affect of

temperature and salinity on water density is illustrated

in Figure 2-2. The effect of suspended solids may also

be considered using (Gill 1982)

∆ρSS = CSS (1 − 1 ⁄ SG ) x 10−3 (2.9)

where ∆ρSS is the change in density due to suspended

solids, CSS the suspended solids concentration (g

m

-3), and SG the specific gravity of the solid. Some

models include terms for the effects of spatial variations in the atmospheric pressure on the velocity

fields.

Some estuary models with vertical resolution, such as

the laterally averaged model CE-QUAL-W2 (Environmental and Hydraulics Laboratory 1986) and

CELC3D, assume that the vertical acceleration is negligible compared to the vertical pressure gradient and

gravitational acceleration (the hydrostatic approximation; i.e. the magnitude of terms 4-7, 9 and 11-13 of the

vertical momentum equation, Equation 2.4, are negligible compared to terms 8 and 10). The hydrostatic

assumption reduces the vertical momentum equation

to

1

ρ

∂P

∂z

 = g (2.10)

Figure 2-2. Relationship between water density, salinity, and temperature.

2-13
The formulation for the mean pressure, P, is performed

in one of two ways, either as a free surface calculation

or a rigid lid computation (i.e. the water surface elevation does not vary). For the more complex estuarine

application, the free surface formulation is required

due to the importance of tidal oscillations as a system

forcing function. Free surface versions of estuary models often exploit the hydrostatic pressure equation to

make an implicit relation between free surface elevation and the pressure field (Bedford 1985). Models

which solve for the free surface implicitly are attractive

due to less restrictive time step formulations (Paul and

Nocito, 1983).

The Coriolis force (6) describes the effect of the earth’s

rotation which acts to deflect the motion of fluids to the

right (left) in the northern (southern) hemisphere. The

Coriolis force is an apparent force to allow a frame of

reference to be used that is relative to the rotating

earth. The force is usually described as a function of

the angular velocity of the earth (Ω) and the latitude of

the estuary. The Coriolis frequency ( f ) is estimated

from

f= 2 Ω sin (Φ) (2.11)

where Ω is the angular velocity of the earth, Φ is the

latitude, and the time scale for rotational effects is

approximately of the order 1/f and ranges from about

15 hours in Washington State to 30 hours in southern

Florida.

The eddy viscosity terms (11-13) arise from time-averaging the turbulent fluctuations of velocity components. The velocity components may be written as

U = u + u ' ; V = v + v ' ; W = w + w ' (2.12)

where u,v,w are the mean velocity components and

u’,v’, and w’ are the fluctuations relative to the mean

velocities. The time-averaging of the velocities gives

rise to turbulent correlation terms of the form:

u'u'

___

u'v'

___

u'w'

___

 (2.13)

The Boussinesq analogy assumes that the turbulent

stresses are proportional to the mean velocity and the

turbulent stresses are often rewritten in the form shown

in Equations 2.2-2.4 (terms 11-13)

u'u'

___

= Ex

∂u

∂x

 ; u'v'

___

= Ey

∂u

∂y

 ; (2.14)

u'w'

___

= Ez

∂u

∂z

referred to as the eddy viscosity formulation. This

formulation is generally applicable where large scale

turbulence is of importance. These terms are unknown

quantities and represent what is referred to as the

closure problem in hydrodynamic modeling. Rewriting

the quantities in terms of eddy viscosity does not

eliminate the problem but has put the terms in a form

that has proved useful in practical calculations. A

variety of procedures have been developed for turbulence closure, described as zero-equation, one-equation, two-equation, and higher order methods and have

been reviewed by Rodi (1980), Bedford (1985) and

others.

The horizontal eddy viscosity is often held constant in

models (Ex = Ey). Procedures for estimating the magnitude of the eddy viscosity are described in Section 5

(Supplement III).

The vertical eddy viscosity at the interfaces of water

segments for models with vertical resolution is often

described as a constant or a function of the decay of

surface shear. The shear at the surface boundary is

generally described as a function of wind shear such

as

ρo Ez (

∂u

∂z

 ,

∂v

∂z

 )=ρa Cda (uw

2

+vw

2

)

0.5 (uw , vw )

(2.15)

in the x and y directions, respectively,where ρo is the

surface water density, ρa the air density, Cda the drag

coefficient, and uw and vw are the wind velocities in the

x and y directions at some height above the water

surface. This computation requires that representative

data be available for both wind speed and direction.

The vertical stress at the bottom boundary is usually

described as a function of bottom friction, such as in

the quadratic stress formulation

ρ Ez (

∂u

∂z

 ,

∂v

∂z

)=ρ Cd (u

2

+ v

2

)

0.5 (ub , vb) (2.16)

where Cd is a drag coefficient and ub and vb are the

horizontal velocities at some point above the bottom.

A constant drag coefficient has been used in modeling

studies.

The drag coefficient has also been related to the Chezy

coefficient (Cz) as

Cd = g ⁄ Cz

2

 (2.17)

or the Manning’s roughness coefficient, n,

Cd =

g n

2

R

4

⁄3

 (2.18)

where R is the hydraulic radius (m). Guidance on the

selection of bottom roughness coefficients is provided

in Section 5 (Supplement I).

The vertical eddy viscosity is reduced significantly by

stable stratification. Some formulations to account for

2-14
this effect contain empirical relationships between vertical eddy viscosity and the Richardson number (Ri),

an index of stratification stability given by

Ri = −

g

ρ

∂ρ⁄∂z

(∂u⁄∂z)

2

 (2.19)

The most widespread of these formulations was developed by Munk and Anderson (1948) where

Ez = Ez,o (1 + 10 Ri)

−0.5 (2.20)

where Ez,o is the value of Ez for neutral stratification

(i.e. the estuary is unstratified).

Boundary conditions, such as water surface elevations

and flows, provide the forcings which are propagated

through the model solutions as computed variations in

velocities and surface elevations.

C. Conservation of Constituent Mass

The conservation of constituent mass or transport

equation forms the basis for estimating variations in

water quality over space and time. The equation is a

statement that the time rate of change of concentrations, or material accumulation, (14) is equal to the

material entering or leaving the system due to advective transport (15-17) or turbulent diffusion (18-20) plus

the change due to physical, chemical, or biological

transformations (21) as illustrated by Figure 2-3. The

advection of constituents can be estimated from field

measurements, computations using tracers and continuity, or hydrodynamic models. The diffusion coefficients are related to turbulence. For three-dimensional

mass transport models using small time steps (on the

order of a few minutes) the governing equations contain only turbulent diffusion terms. However, if the

equations are temporally or spatially averaged then

dispersion will result, and the magnitude of the dispersion term will depend upon how the averaging is done

(Harleman, R.F., in his review of this document).

The eddy viscosity and mass dispersion coefficient are

related by the turbulent Prandtl/Schmidt number (i.e.

the ratio of transfer of momentum and mass). A complete review of dispersion relationships is found in

Fischer et al. (1978). Guidance on the selection of the

dispersion coefficient is provided in Section 5 (Supplements III and V).

II. Model Complexity

 The solution of the equations for circulation and mixing

(Equations 2.1-2.4) is generally based upon simplifications and assumptions regarding the spatial and temporal complexity of the system and its boundary

conditions. These basic assumptions make it less

difficult to solve the governing equations. Generally,

simplifying assumptions may be made regarding the

Figure 2-3. Factors affecting change in constituent mass.

2-15
hydrodynamic complexity of the system, its dimensionality, temporal resolution, and kinetic resolution.

A. Spatial and Temporal Resolution

With regard to spatial resolution, models may be one,

two or three dimensional. Most practical hydrodynamic

models are either one, two (vertically or laterally averaged) or quasi-three dimensional, as illustrated by

Figure 2-4. This often prevents their application to

near-field problems where a high degree of turbulence

occurs. For example, a model which does not include

vertical momentum could not resolve momentum

transfer due to a submerged jet. Nihoul and Jamarf

(1987) describe available three-dimensional models.

Similarly, mass transport models may be one, two or

three dimensional. Tidally varying one-dimensional

models are useful for tidal flow in narrow, relatively

uniform channels, such as the long braided network of

sloughs sometimes found in deltas or tidal rivers (Fischer et al. 1978). In wide and irregular channels, two

or three dimensional models may be required.

With regard to temporal resolution, estuarine mass

transport problems are usually characterized as intertidal or intra-tidal. Intra-tidal computations, which consider variations within a tidal cycle, generally require

application of coupled hydrodynamic and water quality

models in order to obtain real time predictions.

For inter-tidal computations, a variety of simplified

methods are available to estimate circulation and mass

transport. Simplified modeling approaches are often

based on using either measured flows or flows estimated using continuity (Equation 2.1) for use with

models based on constituent mass balance equations.

The most simple models solve only the transport equation (Equation 2.5), usually assuming steady-state

(∂C ⁄ ∂t = 0) to obtain average conditions. Models of

intermediate complexity estimate flows based on field

data or use simplified methods to describe circulation,

generally tidally averaged.

Mills et al. (1985) describes some simplified methods

for calculating estuarine circulation, including fraction

of freshwater methods, modified tidal prism method

and Pritchard’s Box model for a two-dimensional estuary.

Figure 2-4. Model dimensions.

2-16
The freshwater and tidal prism method are described

further in Section 6 of Part 2 of this manual. Officer

(1976, 1977) described analytical solutions to decoupled hydrodynamic and mass transport equations.

Lung and O’Conner (1984) developed a tidally averaged method for two-dimensional (longitudinal-vertical) estuaries that allows analytical computation of

horizontal and vertical velocities and vertical eddy

viscosity terms.

Hydrodynamic models, based on the solution of the

equations for circulation and mixing (Equations 2.1-

2.4), are linked with water quality models, based on the

constituent mass balance equation (Equation 2.5),

when time varying predictions are required of both

flows and water quality, such as for intratidal variations.

Some models directly link solutions for the hydrodynamic and constituent transport equations with equations of state allowing variations in water quality to be

considered in flow predictions. In other cases the

hydrodynamic predictions are separate from water

quality and may be averaged over space and time to

allow use of coarser time or space scales in water

quality modeling. This time and space averaging is

often difficult to accomplish since important advective

and diffusive information is lost in direct proportion to

the length of the spatial and temporal averaging period

and there are no quantitative guidelines for multidimensional models to indicate the extent of the information lost (Harleman, D., in review). Thus,

empiricisms are often introduced as a result of the

averaging. Studies on the interfacing problem have

been conducted by Ford and Thornton (1979), Walters

(1980), Imboden et al. (1983), Wang and Harleman

(1984), Shanahan and Harleman (1984) and others

which are applicable to estuarine conditions as well as

studies conducted on Chesapeake Bay.

B. Kinetics

Descriptions or predictions of estuarine circulation may

be coupled with detailed descriptions of constituent

transformations. For a “conservative material” (one not

subject to transformations, i.e. salinity and some tracers) the last term (S) in Equation 2.5 is equal to zero.

However, the constituents of interest in estuarine WLA

studies rarely behave conservatively. For most materials of interest, such as DO, nutrients, synthetic organics and metals, their physical, biological, and

chemical transformations must be estimated. The factors influencing those transformations is the subject of

the remainder of this section (Sections 2.3-2.6).

C. Additional Considerations

A tendency may be to select the resolution (spatial,

temporal and kinetic) for a particular waste load allocation study on the scale of interest for the model

output rather than the physics, biology and chemistry

of the system. An additional tendency may be to base

model selection on those techniques which are perceived to be the simplest to use. However, the relationship between model simplicity and simplicity of

application is not straightforward.

For example, inappropriate spatial and temporal averaging for hydrodynamic computations can result in a

model that is far removed from the physics of the

system. Inappropriate averaging may necessitate the

introduction of empiricisms which must then be calibrated to data, and may result in increased rather than

decreased data requirements to support the modeling

studies. For example, averaging may introduce dispersion terms whose magnitude depends on how the

averaging is done. Harleman (D.R.F., in his review)

suggests that the data required to support a two-dimensional laterally averaged model is often more than

that for a three-dimensional model, while the amount

of synoptic data required to support a one-dimensional

model (averages over a cross section) may be enormous. Therefore, if the physics of the system is not

adequately considered, the data required to support a

modeling study may increase with increasing “simplicity”.

Similarly, the clumping of kinetics terms for “simpler”

models may, if not carefully done, introduce empiricisms which have little relationship to the chemistry

and biology of the system. Thus, the empirical coefficients may often be determined only through calibration, often to inadequate data, and the coefficients

must often be varied over space and time to get the

“best” calibration. Alternatively, the uncertainty of

model predictions increases nonlinearly with the addition of uncertain parameters. Therefore, the Principle

of Parsimony should apply: that is that it should be

attempted to obtain a model calibration and validation

with the fewest possible parameters (R.V. Thomann,

in review of this document).

2-17
SUPPLEMENT II: SEDIMENT TRANSPORT AND SEDIMENT/WATER QUALITY

INTERACTIONS

I. Source and Sink Term Processes

The processes affecting sediments are illustrated in

Figure 2-5. Using the segmentation scheme illustrated,

constituent mass balance equations (Equation 2.5)

would be written for each vertical water segment. The

advective and diffusive transport terms were described

previously. The remainder of the processes would be

described in the source/sink term (S). The source/sink

term would typically be represented as

S =

A

V

β C (2.21)

where A is area, V volume, C solids concentration and

β is a coefficient with units of velocity (e.g. settling or

resuspension velocity).

II. Settling

For settling the coefficient β is dependent upon

Brownian motion, turbulent diffusion, and fall velocities. Brownian motion is negligible for most particles of

interest in water quality modeling. The fall velocities

(ws) can be estimated from Stokes law, which is

ws =

g d

2

18 μ

(ρp − ρf) (2.22)

where g is gravitational acceleration, d is particle diameter, ρp the particle density, ρf the fluid density and

μ the dynamic viscosity of the fluid. Stokes settling or

fall velocities for a range of materials are tabulated in

Section 5 (Supplement VIII). The silts and clays carrying pollutants typically range in diameter from 0.002 to

0.02 mm, with densities of 2 to 2.7 g/cm3.

Figure 2-5. Sediment variables and processes.

2-18
Stokes law is valid for Reynolds numbers

(Re = ρf ws d ⁄ μ) less than about 0.1.

Collisions between small cohesive particles tend to

lead to coagulation and the formation of flocs. Flocculation rates are dependent upon the size distribution

and relative composition of the clays and electrolytes

and upon local boundary shear stresses (Mills et al.

1985) as well as salinity. Turbulence increases the

collisions while salinity increases the cohesion between particles (Sheng 1983). The effective density of

the floc may vary considerably from that of the individual particles, making prediction of settling velocities

difficult and requiring site-specific model calibration

(Stefan, Ambrose and Dortch 1988).

III. Deposition

The deposition of sediments onto the surface sediment

layer is a process by which suspended sediments

leave the water column, either temporarily or permanently, and become part of the bottom sediments

(Sheng 1983). In order to be deposited the particles

must overcome resistances due to turbulent transport

in the water column, resistances due to the thin viscous

layer at the interface, and resistances due to chemical

or biological activity after they reach the bottom. The

deposition velocity depends on the extent to which

settling is affected by turbulence. Sheng (1983) indicated particles of diameters less than approximately

100 μm will completely follow the eddy motions. The

deposition velocity can be estimated as the product of

the settling velocity and the probability of deposition on

contact with the bed, which can vary from 0 for very

turbulent systems to 1 for stagnant pools, and deposition velocities will generally vary from 0 to 5 m/day

(Ambrose et al. 1988; Stefan, Ambrose and Dortch

1988).

IV. Entrainment

Entrainment or resuspension occurs when the flow

induced shear stress at the sediment-water interface

exceeds the cohesive forces of the surficial sediments

(Sheng 1983). For granular non-cohesive materials

the relationship between bed shear and entrainment is

“explosive” in nature. Very low or no resuspension

occurs until a threshold shear stress is reached. Then

resuspension rates increase in proportion to some

power of the excess shear stress. Powers of one have

been found in estuarine studies, but powers of four and

five have been found for granular river material according to a review by Akiyama and Fukushima (Wang et

al. 1986). The rate of resuspension can be balanced

by the rate of deposition. At that point, vertical concentration profiles above the bed show a balance of downward fluxes of sediment by settling and upward fluxes

by turbulence as summarized by Vanoni (1975).

According to Rouse (see Vanoni 1975), the dimensionless parameter Vs(Ku*

)

-1 (where Vs = particle fall velocity, K = 0.4 and u*

 = bed shear velocity = √τb ⁄ ρ with

τb = shear and ρ = water density) determines for flow

over flat bottoms the degree for which vertical sediment distribution will be uniform. It will be uniform

within ± 10 percent when Vs(Ku*)

-1 is less than about

0.02.

Rates of entrainment of non-cohesive materials have

been specified in numerous alternative forms by

Ariathurai (1982), Ariathurai and Krone (1976), and

others (see Wang et al. 1986; Mehta 1986). Akiyama

and Fukushima (in Wang et al. 1986) specified a

dimensionless resuspension rate parameter Es as:

Es = 3 x 10−12 Z

10 (1 − 5 ⁄Z )

for 5 <Z < 13.4

Es = 0.3 for Z > 13.4 (2.23)

where

Z =

u

∗

Vs

Rp

Rp =( g ' D )

1

⁄2 D ⁄ ν

g ' = g (ρs ⁄ ρ − 1)

reduced acceleration of gravity of submerged particles; D = particle diameter; and ν = kinematic viscosity.

The entrainment (or resuspension, scour or erosion)

rate depends not only upon the shear stress on the

benthic surface, and the sediment size but also on the

state of consolidation of the surficial benthic deposits.

Site-specific calibration is necessary to refine initial

estimates of scour (Stefan, Ambrose and Dortch

1998).

Entrainment of cohesive sediments is less well understood. Unfortunately, cohesive sediments are of primary interest in water quality studies. For cohesive

sediments, the resuspension rate is affected by bottom

shear stress, salinity, sediment type, and the time

history of bottom sediments (Sheng 1983). Lick et al.

(1987) indicated that, as a result of cohesion and the

resulting compaction, only a finite amount of cohesive

sediment may be resuspended at a given shear stress

as opposed to non-cohesive sediments which have a

uniform rate of resuspension. Lick suggested that the

amount of cohesive sediment that can be entrained is

a function of the time after deposition, the shear stress,

and an effective critical stress which needs to be

determined experimentally for particular sediments.

2-19
V. Burial

Burial refers to the net sedimentation velocity, or the

velocity by which deposited sediments are buried by

additional deposits. Burial, compaction, and the cohesive forces between sediment particles result in varying sediment properties (e.g. density and porosity) with

depth below the upper mixed sediment zone.

SUPPLEMENT III: ORGANIC WASTES, DISSOLVED OXYGEN AND NUTRIENTS

I. Important Processes and Variables

The basic variables and processes used in the prediction of DO and nutrient concentrations are illustrated

in Figures 2-6 and 2-7, where separate constituent

mass balance equations are generally written for each

variable indicated by the boxes (constituents, C in

Equation 2.5). The processes affecting those variables

and the interactions between variables are indicated

by arrows, and comprise the source/sink terms in the

constituent mass balance equation (S, Equation 2.5).

These processes are often modeled as zeroth-order,

S = K 0th (2.24)

where K is a constant with units of concentration/time;

first-order,

S =K 1st C (2.25)

where C is concentration and K is a rate term with units

of 1/time; or higher-order (nonlinear) processes where

the rate term is dependent upon variations of other

variables or constituents. The variables are also affected by advective and dispersive transport, as described by Equation 2.5. Transport and reaction rates

are affected by temperature as described below.

II. Temperature

Temperature affects transport through density terms

(as described by the equation of state, Equation 2.5)

as well as reaction kinetics. Temperature effects on

reaction processes are usually computed as the product of a temperature adjustment factor and the rate

term measured at some reference temperature, where

the temperature adjustment factor (XT) is estimated

from

XT = θ

T − Tr (2.26)

where θ is a coefficient, T is temperature, and Tr is a

reference temperature.

Temperature variations may either be modeled or

specified in water quality models (see Thomann and

Mueller 1987). The temperature (thermal energy)

equation can be obtained from the conservation of

mass equation (Equation 2.5) by replacing concentration (mass/volume) by the heat/volume ( i.e. ρ Cp T).

Dividing through replaces C (concentration) with T

(temperature) and the source/sink term (S, Equation

2.5) may be given as

S =

H A

V Cp ρo

 (2.27)

where A is area (m2), V volume, H the total heat flux

(Watts/m2), Cp is the specific heat of water

(Joule/KgoC), and ρo the density of water at the given

temperature (Kg/m3).

The total heat flux includes fluxes due to conduction or

sensible heat transfer, evaporation, long wave back

radiation from the atmosphere, back radiation from the

water surface, and absorption of short wave radiation.

All predictive approaches to temperature modeling are

based on one or more empirical functions that must be

specified, such as the wind speed function. Guidance

on the selection of the wind speed function is provided

in Section 5 (Supplement VI).

III. Indicator Bacteria

The bacteria of interest in WLA studies dealing with

organic wastes of human origin include total or fecal

coliforms, where the coliforms may be pathogenic in

some cases or are used as indicators of the presence

of pathogenic bacteria. Coliform bacteria generally can

not reproduce in aerobic natural waters and are modeled using first-order kinetics, where the rate term

represents a die-off rate. However, coliforms can reproduce in sediments and be resuspended in the water

column. Guidance on the selection of die-off rates and

their reference temperature (Tr) for temperature adjustments of the rate (Equation 2.26) is provided in

Section 5 (Supplement VII). Coliform die-off may also

vary with light and salinity as well as temperature.

Thomann and Mueller (1987) provide additional discussion of modeling considerations for indicator or

pathogenic bacteria.

2-20
Figure 2-6. Basic variables and processes for dissolved oxygen.

Figure 2-7. Standard variables for eutrophication and DO.

2-21
IV. Organic Material and Dissolved Oxygen.

DO is depleted by oxidation of organic carbon, nitrification, and respiration and is replenished by surface

exchange and primary production (Figure 2-6). More

complex interactions considering the effects of eutrophication have been considered (Figure 2-7).

Historically, deoxygenation by decomposition of organic material has been modeled using coupled equations for DO and Biochemical Oxygen Demand (BOD),

where BOD is a measure of the oxidizable matter due

to biochemical processes expressed in oxygen units.

BOD has typically been divided into two components,

Carbonaceous BOD (CBOD) and Nitrogenous BOD

(NBOD) due to the difficulty of predicting variations in

total BOD (CBOD + NBOD). CBOD removal processes usually included in model formulations include

decomposition or oxidation by organisms, and settling.

In addition, CBOD can be entrained or resuspended.

The source/sink term for CBOD can be written as

S = (Kd + Ks) L + La (2.28)

where Kd is the water column deoxygenation rate

coefficient, Ks is the settling rate, L the ultimate CBOD

and La a zero order CBOD resuspension rate. For

DO, the loss rate due to deoxygenation is KdL. Further

information and guidance on the selection of rate terms

is provided in Section 5 (Supplement XI).

The utility of CBOD is limited since it lumps the effects

of a number of processes into one variable. Some

modeling approaches will separate oxygen consuming

reactions into various components. CBOD is essentially the only variable presently written into most WLA

permits for the control of DO.

DO may also be depleted due to benthic demand.

Discussions of the processes impacting sediment oxygen demand as well as modeling and measurement

techniques may be found in Hatcher (1986).

V. Phytoplankton

Primary productivity by phytoplankton produces oxygen while respiration consumes oxygen. In addition,

phytoplankton are often of primary interest in assessing eutrophication and in predicting nutrient interactions.

For simplistic DO models, as illustrated by Figure 2-6,

it may be sufficient to describe the effects of phytoplankton using simple zeroth order terms for primary

productivity and community respiration. These terms

may often be estimated from field studies using measurements of variations in carbon isotopes, oxygen or

carbon dioxide. This approach is often of limited utility

where changes in productivity are expected to occur

in response to waste loadings. Most estimates of primary productivity in common mathematical models

involve coupling algal growth equations with

stoichiometric equations for photosynthesis in order to

relate primary productivity to oxygen and nutrient production/consumption.

Modeling of specific algal species is usually not attempted. Instead major groups, such as diatoms,

greens, blue-greens and dino-flagellates are simulated. Algal losses due to settling and grazing are also

often simulated. Some of the more complex models

include equations for zooplankton groups in order to

predict variations in grazing losses (Figure 2-8).

The growth rate of phytoplankton (G) is usually formulated as the product of the maximum 20 o

 C species or

group specific growth rate (under optimum light and

nutrient conditions) with a temperature adjustment

factor (XT), a light adjustment factor (XL), and a nutrient

limitation factor (XN).

G = G max XT XL XN (2.29)

The temperature adjustment factor (XT) is normally

computed using an expression similar to Equation

2.26. Light attenuation functions (XL ) generally follow

the analysis by Steele (1962), accounting for the effects of supersaturating light intensities and light attenuation through the water column, and lead to

XL =

2.718 f

η d

 [exp (− Io

Is

 exp (− η d )) − exp (− Io

Is

)]

(2.30)

where d is the depth (m), η is the light extinction

coefficient including self shading (m), f is the photoperiod correction, Io is the incident light intensity just

below the surface (langley day-1), and Is is the algal

saturation light intensity at the maximum photosynthetic rate. The above formulation is for a surface layer

and a more general formulation is given by Chapra and

Reckhow (1983).

Smith (1980) developed a framework for calculating Is

based upon the maximum growth rate, the quantum

yield of chlorophyll, the extinction coefficient per unit

of chlorophyll, and the ratio of carbon to chlorophyll in

the phytoplankton. This framework allows for adaptation by changing the carbon to chlorophyll ratio. Recent

developments in phytoplankton kinetics models use

photosynthetically active radiation (PAR) (μEm-2day1

) instead of total energy Is (langley day-1). They also

apply Haldane kinetics in place of Steele’s equation

(Megard et al. 1984).

2-22
The nutrient limitation factor is based on the assumption that phytoplankton follow Monod kinetics with

respect to the important nutrients. Generally, the minimum function for inorganic nitrogen and phosphorus

is used:

XN = Min [ CIN

KMN + CIN

 ,

CIP

KMP + CIP

 ] (2.31)

where CIN is inorganic nitrogen (μg/l), CIP is inorganic

phosphorus (μg/l), KMN is the Michaelis half-saturation

constant for nitrogen (μg/l), and KMP is the Michaelis

half saturation constant for phosphorus (μg/l). Occasionally, XN is expressed as the product of the nitrogen

and phosphorus terms. Additional terms may include

separation of nitrogen into ammonia-nitrogen and nitrate-nitrogen. Dissolved available silica is included

where simulation of diatoms is required.

Phytoplankton “death” rates are conventionally expressed as the sum of the endogenous respiration

rate, the death rate, and the grazing rate. The first two

are generally modeled as the first order temperature

corrected rates. Grazing may be expressed as first

order, or second order if the herbivorous zooplankton

population is specified or simulated. To capture the

phytoplankton population dynamics properly,

zooplankton may have to be simulated. If average

phytoplankton levels are adequate, then the first order

approach is acceptable.

The relationship between phytoplankton kinetics and

variations in DO and nutrients is expressed using

stoichiometric relationships. Proper specification of average stoichiometry is necessary to accurately model

these interactions. The ratios of phytoplankton carbon

to phytoplankton nitrogen, phosphorus, and chlorophyll-a vary among species and in time. Few applied

modeling framework account for the dynamics of

stoichiometry. The user is forced to specify average

values or those characteristic of stressed systems.

Guidance on the selection of parameters and coefficients for modeling phytoplankton nutrients and settling is provided in Section 5.

VI. Nutrients

Simulation of nutrients is critical to eutrophication models and to some DO models which include mechanistic

descriptions of phytoplankton kinetics. Simulation of

ammonia-nitrogen is also necessary in studies involving ammonia-toxicity. Sources of nutrients include bottom sediments, point source loadFigure 2-8. Additional variables and processes for trophic interactions.

2-23
ings, non-point loadings from the watershed, and atmospheric deposition.

Atmospheric deposition has been implicated as a major source of nutrients in some large estuaries.

For the simplified DO-BOD modeling, as illustrated by

Figure 2-6, it may be sufficient to consider only nitrogenous oxygen demand (NBOD). Similarly to CBOD,

NBOD is modeled as a first-order process, where

NBOD is expressed in oxygen units. Guidance on

first-order nitrification rate constants is provided in

Section 5 (Supplement X).

Models which include nutrient cycles vary in their

complexity, as illustrated by the nutrients considered

in the eutrophication model illustrated in Figure 2-7 as

compared to that illustrated in Figure 2-9. The primary

nutrients considered to impact eutrophication are nitrogen, phosphorus, and silica.

Nitrogen is present in particulate and dissolved, organic and inorganic forms (Figure 2-9). Nitrogen is

consumed by algae during growth, where the nitrogen

loss rate is stoichiometrically related to the algal growth

rate (Equation 2.29). During algal respiration and

death, some nitrogen is returned directly to the inorganic nitrogen pool, while particulate organic nitrogen

may be lost due to settling. Organic nitrogen undergoes bacterial decomposition whose end product is

ammonia-nitrogen. Nitrification may then result in the

oxidation of ammonia-nitrogen to nitrate-nitrogen and

finally to nitrate-nitrogen. Denitrification by bottom

sediments may be a major loss mechanism in some

systems. Guidance on selection of rate terms for the

various processes impacting nitrogen concentrations

is provided in Section 5 (Supplement XI).

Simulation of nitrogen is also of importance due to the

toxicity of unionized ammonia (NH3). Direct simulation

of ammonia speciation requires the simulation of pH.

However, if pH is not expected to vary it may often be

sufficient to simulate the nitrogen cycle in order to

predict total ammonia concentrations. Knowing the

equilibrium relationship between the two forms

Figure 2-9. Additional variables and processes for nutrient interaction.

2-24
and that the total ammonia-nitrogen present or predicted (NHT) is the unionized ammonia plus the ionized

ammonia (NH4+), (NHT = NH3 + NH4+ ) the portion

occurring as NH3 can then be estimated from

NH3 = 1

1 + [H+

] ⁄ Kh

NHT (2.33)

Some caution needs to be exercised concerning the

reporting of units of nitrogen (i.e. as nitrogen or as

ammonia). Speciation is also effected by temperature

and the distribution of cations and anions. The aqueous ammonia calculations are discussed in detail by

Thurston et al. (1974) and Emerson et al. (1975), as

well as the effects of temperature and pH on calculations assuming zero salinity. These calculations are

also summarized by Bowie et al (1985). Whitfield

(1974) provided guidance on the effects of seawater

on ammonia speciation. The speciation of ammonia

may also be estimated using equilibrium speciation

models such as MINTEQA1 (Brown and Allison 1987).

Phosphorus may also occur in the water column in

organic or inorganic, particulate or dissolved forms

(Figure 2-9). Phosphorus is released during phytoplankton respiration and death in either organic or

inorganic form. Phosphorus is utilized in algal growth

as indicated in Equation 2.29. Dissolved inorganic

phosphorus sorbs to suspended particulate matter in

the water column, coming to an equilibrium expressed

either with a partition coefficient or as a calibrated

fraction dissolved:

f DIP = 1

1 + K PIP SS (2.34)

where fDIP is the fraction inorganic phosphorus dissolved, SS is the suspended sediment concentration

(kg/L), and KPIP is the partition coefficient in (L/kg).

Subsequent settling of the solids and sorbed phosphorus can provide a significant loss mechanism of

phosphorus from the water column to the benthos.

Process based functions that accurately calculate

the phosphorus partition coefficient would improve

prediction of this important variable significantly.

Phosphorus loss mechanisms are generally described using firstFigure 2-10. Benthic interactions for nutrients and DO.

2-25
order kinetics, and guidance on rates is provided in

Section 5 (Supplement XII).

VII. Sediment Interactions

Sediment processes may have profound affects on DO

and nutrients in some systems. The decomposition of

deposited organic material releases nutrients and results in an oxygen demand. Denitrification by sediments is often a major loss mechanism for nitrogen

(Figure 2-10). Sediments may continue to have impacts on water quality long after sources of organic

materials and nutrients have been eliminated.

Although often of critical importance, the predictive

capability of most presently available models of sediment interactions is limited. Description of these impacts is often reduced to field measurements followed

by use of zeroth order rate terms based on those

measurements in models to describe their effects on

other variables and processes. Guidance on selection

of rate terms is provided in Section 5 (Supplement XV).

VIII. Surface Exchange

The surface exchange of dissolved oxygen, is typically

modeled based on Whitman’s two-film model (Lewis

and Whitman 1924) assuming resistance in the liquid

controls. This reduces the source/sink (S, Equation

2.5) term for surface exchange to

S = K2 (C − Cs) (2.35)

where K2 is a reaeration rate, C is the water concentration, and Cs the saturation concentration. The saturation concentration for dissolved oxygen is typically

computed using empirical expressions including the

effects of temperature and dissolved solids. The

reaeration rate has been computed using a variety of

formulations. Guidance on the selection of reaeration

coefficients for dissolved oxygen is provided in Section

5 (Supplements XIII and XIV).

For other gases, such as unionized ammonia and

many toxic materials, the gas film rather than the liquid

film may control gas transfer, which must be reflected

in the formulation of the rate term.

Additionally, the method for computing saturation concentrations will vary (see Supplement IV, Volatilization).

SUPPLEMENT IV: SYNTHETIC ORGANICS

I. Loss Rates

Synthetic organic concentrations are described using

the constituent mass balance equation (Equation 2.5)

similarly to other materials. The processes impacting

their physical, chemical and biological transformations

differ, as illustrated by Figure 2-11. Physical losses

occur through mechanisms such as volatilization, settling, and sedimentation, while physical gains can occur through resuspension. Chemical transformations

may result from hydrolysis, photolysis, oxidation and

reduction and ionization. Biological transformation and

loss can result from bacterial degradation and accumulation in biota. Additional differences result where

materials do not mix, or only partially mix, with the

mean flow, such as some oils. The mathematical treatment of immiscible or only partially miscible oils often

requires specialized modeling techniques, such as

those used in oil-spill modeling.

For constant environmental conditions, the overall

chemical loss rate of synthetic organics is often approximated as a first-order reaction:

S = − KT C (2.36)

where KT is the observed loss coefficient (day-1), C is

the total chemical concentration (g/m3) and, and S is

the source/sink term of the constituent mass balance

equation (Equation 2.5). The value KT represents a

single set of environmental conditions only.Changes

in temperature, velocity, depth, sunlight, wind, sediment concentrations, or pH can affect the total loss rate

in ways that can not be considered using this approach. Alternatively, each of the processes impacting

the transformations may be simulated.

An overview of methods used to describe these transformation processes is provided below. Additional

information is provided by Chapra and Reckhow

(1983), Thomann and Mueller (1987) and elsewhere.

A method to complement field survey data is the

chemical process approach. This approach combines

laboratory-measured chemical constants with fieldmeasured environmental properties to estimate sitespecific rate coefficients, Ki (x,t), for several loss

processes “i”;

Ki (x , t ) = Ki Ei (x , t ) (2.37)

where Ki is a laboratory measured second order rate

constant and Ei (x,t) is the intensity of the relevant

2-26
 PARAMETERS

Tair= air temperature

Vwind= wind speed

Vwater= water velocity

Ddepth= water depth

Cair= atmospheric concentration

S=Solids concentration

foc= fraction organic carbon

Tw= water temperature

Ro= concentration of oxidant

CEC= cation exchange capacity

Rr= concentration of reductant

Bs= bacterial concentration in sediment

Bw= bacterial concentration in water

I= incident light

Ke= extinction coefficient

Figure 2-11. Basic variables and processes for reactive organic chemicals.

2-27
environmental parameter. If more than one loss process is active for a chemical in an environment, the

overall loss coefficient can be estimated by summing

the individual rate constants. Combining the chemical

process approach with the field survey approach

should increase the reliability of modeling estimates,

allowing extrapolation to a much wider range of environmental conditions.

II. Physical Loss Mechanisms

A. Volatilization

Volatilization in most models is treated similarly to

surface oxygen exchange (Equation 2.35) where the

loss due to volatilization (Sv) is equal to the difference

in chemical concentrations multiplied by a transfer

coefficient, as

Sv = kv (Cw − Ca) (2.38)

where kv is the transfer rate, Cw the dissolved concentration of the chemical in water, and Ca the saturation

dissolved concentration, dependent upon the atmospheric partial pressure and Henry’s Law constant for

the material.

A common assumption is that the atmospheric concentration is much less than the water concentration,

allowing simulation of the transfer as a pseudo-first

order rate. Where the toxicant mass balance expression (Equation 2.5) is written for the total concentration

(dissolved plus particulate), the concentration must

also be adjusted for the fraction dissolved (fd) as

Sv = kv fd Ctw (2.39)

where Ctw is the total concentration in water.

The transfer rate is usually computed as the reciprocal

of the resistances in the two films (gas and liquid), as

kv = (RL + RG)

−1

 (2.40)

where RL is the liquid phase resistance and RG the gas

phase resistance.

The liquid and gas transfer coefficients are dependent

on turbulence at the interface, on temperature, and on

properties of the chemical such as diffusivity. Empirical

correlations have been developed relating transfer

coefficients either directly to physical parameters such

as wind velocity and the density and viscosity of the

water (MacKay et al. 1983; Southworth et al. 1979a),

plus the molecular weight and diffusivity of the chemical or to the field-measured transfer coefficients of

oxygen and water vapor (Liss and Slater 1974).

O’Connor (1983) has presented a theoretical development for the liquid transfer coefficient applicable to a

wide range of hydrodynamic conditions, but application requires estimates of several coefficients that are

not easily obtained.

B. Sorption

Many toxic materials sorb strongly onto particulates.

Estimates of sorption are required in modeling toxic

materials since processes impacting dissolved and

particulate fractions differ. Sorption is the bonding of

dissolved chemicals, C, onto solid phases, Si, such as

benthic and suspended sediment, biological material,

and sometimes dissolved or colloidal organic material

resulting in the formation of the chemical-sediment

bond, C-Si.

Si + C = C − Si (2.41)

Sorption reactions are usually fast relative to other

environmental processes, and equilibrium may be assumed. For environmentally relevant concentrations

(less than 10-5 M or one-half water solubility), equilibrium sorption is linear with dissolved chemical concentration (Karickhoff 1984) or:

Ci = Kpi Cd (2.42)

where Ci is chemical concentration in the solid phase

i (mg/kg), Cd is dissolved chemical concentration

(mg/L), and Kpi is the sorption partition coefficient

between the two phases (L/kg). At equilibrium, then,

the distribution among the phases is controlled by the

partition coefficient, Kpi. The total mass of chemical in

each phase is controlled by Kpi and the amount of solid

phase present.

Values for the partition coefficients can be obtained

from laboratory experiments. For organic chemicals,

lab studies have shown that the partition coefficient is

related to the hydrophobicity of the chemical and the

organic matter content of the sediment. Normalization

of the partition coefficient by the organic-carbon content of the sediment has been shown to yield a coefficient, KOC, that is relatively independent of other

sediment characteristics or geographic origin (Karickoff 1981). Correlation of KOC with the water solubility

of the chemical or the octanol/water partition coefficient of the chemical has yielded successful predictive

tools for incorporating the hydrophobicity of the chemical in an estimate of its partitioning. These correlations

do poorly for chemicals with very low or very high

hydrophobicity, however, because of deviations from

hydrophobic adsorption.

Chemicals containing polar functional groups and low

octanol/water partition coefficients tend to exhibit hydrophilic contributions to adsorption. Large nonpolar

molecules with high octanol/water partition coefficients

generally require long time periods to reach

2-28
equilibrium resulting in low estimates of KOC when

sorption is measured over short time frames (Karickoff

1984). The latter effect is particularly significant because it suggests that the assumption of instantaneous equilibrium used by the toxic chemical models may

not be valid for those chemicals for which adsorption

is the most important process (Ambrose et al. 1988).

In addition to the assumption of instantaneous equilibrium, implicit in the use of Equation 2.42 is the assumption of reversibility. Laboratory data for very

hydrophobic chemicals suggest, however, that a hysteresis exists, with desorption being a much slower

process than adsorption. Karickhoff (1984) suggests

that this effect may be the result of intraparticle kinetics

in which the chemical is slowly incorporated into components of the sorbant. This phenomenon is not well

understood and no quantitative modeling framework is

available to characterize it (Ambrose et al. 1988).

Empirical evidence has suggested that the partition

coefficient is inversely related to the particle concentration. A particle interaction model has been proposed

by Di Toro (1985) which describes this relationship.

III. Chemical Loss Mechanisms

A. Hydrolysis

The overall hydrolysis rate constant in most toxic

chemical models is calculated by:

KH = Σ(kHAi ⋅ [H

+

] + kHNi + kHBi ⋅ [OH−]) (2.43)

where kHAi is the acid hydrolysis rate constant for

phase i (L mole-1sec-1), kHNi is the neutral hydrolysis

rate constant for phase i (sec-1), kHBi is the alkaline

hydrolysis rate constant for phase i (mole-1sec-1), [H+]

is the hydrogen ion concentration (moles L-1), and

[OH-] is the hydroxide ion concentration in (moles/L).

The models do not compute hydrogen or hydroxide ion

concentrations. Instead these are input to the models

assuming that their concentrations are unaffected by

the hydrolysis reaction because of the low concentration of the toxic chemical present and reacting.

B. Photolysis

A quantitative framework that permits the prediction of

direct photolysis from the incident light and the characteristics of the chemical (Zepp and Cline 1978) has

been incorporated into several of the toxic chemical

modeling frameworks. Use of this framework in natural

water systems is complicated by the lack of a satisfactory model of UV-light penetration that incorporates the

effects of both dissolved organics and particulate material in the water column. A comprehensive framework for photolysis also must include sensitized

photolysis. Unfortunately, the spectrum of compounds, particularly dissolved organics, involved in

photochemical reactions is not known (Miller 1983). In

addition, valid frameworks to predict free radical reactions have not been developed and the importance of

these reactions remain undetermined (Zepp 1980).

A less rigorous method for predicting the photolysis

rate coefficient Kp involves extrapolations of observed

rates from one environmental condition to another:

Kp = KPG [L] Σ φ Pi fi (2.44)

where KPG is the observed rate coefficient (s-1) for a

reference light intensity, [L] is the fraction of the reference light intensity averaged through the water column, φ Pi is the relative yield for the chemical in phase

i, and fi is the fraction of the total chemical concentration in phase i. The reference light fraction [L] accounts

for depth, light extinction, cloud cover, latitude

changes, and surface light variability.

C. Oxidation/Reduction

Chemical oxidation of organic materials can be a consequence of interactions between free radicals and the

pollutants. Free radicals can be formed as a result of

photochemical reactions. Free radicals that have received some attention in the literature include alkylperoxy radicals, RO2; OH radicals, and singlet oxygen.

Oxidation is often modeled as a second order process

dependent upon concentration of the oxidant and

chemical.

D. Ionization

Consider a weak acid AH3 or base BH3 which may or

may not react with water modules to form charged

anions and cations (ionize):

AH3 = AH 2−+ H

+

 , Ka1 (2.45)

BH3 = BH +4

+ OH − , Kb1 (2.46)

where Ka and Kb are the equilibrium first ionization

constants for the reactions. These reactions are rapid.

At equilibrium, the distribution of chemicals between

the un-ionized and the ionized species is controlled by

the pH of the water and the ionization constants (Ambrose et al. 1988). Stronger acids and bases may

undergo further ionization, controlled by ionization

constants Ka2, Ka3, Kb2, Kb3, the second and third

ionization constants for the acid and base respectively.

However, toxic organics are generally weak acids or

bases. Examples of weak acids are the phenols (chlorophenol, dichlorophenol, trichlorophenol and pentachlorophenol), and a base is benzidine (Mills et al.

1985).

2-29
SUPPLEMENT V: METALS

I. Modeling Techniques

The simulation of metals in aquatic systems has been

approached from several levels of complexity. Presently, only approximate methods are available for estimating the dynamic mass transport of metals in

complicated natural environments. The sorptive interactions of metals with particulate matter is the major

process affecting the fate of toxic metals in the natural

environment (Medine and McCutcheon 1989).

Modeling studies have been conducted using field

derived or estimated, constant or varying, partition

coefficients to describe the association of metals with

solids, with associated transport due to settling and

resuspension. For example, the riverine model

MICHRIV (Large Lakes Research Station 1987) utilizes this approach and was used to analyze metal

contamination in the Flint River, Michigan as described

by Delos et al. (1984) and Mills et al. (1985). Thomann

and Meuller (1987) described the simulation of sediment cadmium concentrations in the Sajo River, Hungary, using a partition coefficient which varied with

suspended solids concentrations. Mills et al. (1985)

describes several screening level approaches considering sorption. These methods may also be appropriate for some estuarine waste load allocations for metals. However, care should be exercised in using data

to estimate sorption that does not reflect similar water

chemistry and sediment characteristics to the system

being modeled (Medine and McCutcheon 1989).

An alternative approach to using descriptive methods

for partitioning may be required where sufficient field

data are not available for estimating partition relationships, where chemical conditions are expected to

change or where it is necessary to identify the form of

the metal present in order to estimate its hazard.

Equilibrium speciation models, such as MINTEQA1

(Brown and Allison 1987) may provide estimates of

equilibrium aqueous speciation, adsorption, gas phase

partitioning, solid phase saturation states, and precipitation-dissolution for multimetal, multiligand systems.

For waste load allocation purposes, equilibrium speciation models must then be run in conjunction with

transport and transformation models, such as WASP4

(Ambrose et al. 1988).

The ability to simulate ionization, the disassociation of

a chemical into charged species, may be critical for

chemicals that exhibit different chemical characteristics in different ionic states. For some chemicals,

such as ammonia or hydrogen cyanide, it may be

necessary to predict ionization in order to predict variations in toxic effects. Increases in observed toxicity of

hydrogen cyanide (HCN) above pH 9 correlate well

with the fraction in the anionic form (CN), (Burns 1985).

Ionization was described previously for ammonia

(Supplement III, part V).

IV. Biological Loss Mechanisms

A. Biodegradation

Biodegradation is generally assumed to follow

Michaelis-Menten enzyme kinetics. Values for the half

saturation constant Km and the maximum rate of degradation are not easily measured. Toxic chemical models generally assume the chemical concentration is

much less than the half saturation constant and simplify the Michaelis-Menten equation to:

KB = − B max Km

−1

B = − kB B (2.47)

where KB is the second order rate coefficient (mL

cells-1 day-1). The bacterial activity, B (cells mL-1), is

equal to the reactant enzyme concentration (Ambrose

et al. 1988). However, enzyme concentration cannot

be measured in the field and the environmental and

ecological effects on enzyme activity are difficult to

estimate (Lewis et al. 1984). Consequently, other biological parameters are substituted, such as the concentration of bacterial cells.

The growth kinetics of the bacterial population degrading a toxic chemical are not well understood. The

presence of competing substrates and of other bacteria, the toxicity of the chemical to the degrading bacteria, and the possibilities of adaptation to the chemical

or co-metabolism make quantification of changes in

the population difficult as well as the extrapolation of

laboratory to field conditions questionable. As a result,

toxic chemical models generally assume a constant

biological activity rather than modeling the bacteria

directly. Often, measured first order biodegradation

rate constants obtained from experiments under field

conditions as used rather than second order rates

obtained from laboratory experiments that then require

the additional estimation of field bacterial concentrations (Thomann and Mueller 1987).

2-30
II. Process Descriptions

The form of the metal will be determined by the net

result of interactions between complexation, chemical

precipitation, adsorption, and oxidation-reduction. The

combined effects of these interactions are computed

using computer programs such as MINEQL (Westhall

et al. 1986), MINTEQA1 (Brown and Allison 1987) and

others which compute equilibrium composition in a

multimetal, multiligand system, using mass balance

and mass action equations and considering the effects

of chemical precipitation, redox, and sorption.

A. Complexation.

Complexation refers to the reaction of a metal (e.g. Ag,

Cd, Cu, Pb, Zn, etc.) with organic and inorganic ligands

(e.g. OH-, CO32-, SO42-, Cl-, F-, NH3, S2-, amino acids,

humates, fulvates, etc.) in water, to form a third species

(the metal-ligand complex).

To compute the form of a particular metal is likely to be

in, it is usually necessary to consider all of the dominant

sets of reacting ligands and competing metals. This

involves the simultaneous solution of a series of nonlinear equations. To develop these equations in a

general form, we may first represent the components

of a dissolved complex (metals and ligands) as X(j),

where X(j) is the activity for the component j of the

complex (or molar concentration if ionic strength is

zero). For example, if “a” moles of component X(1)

reacts with “b” moles of component X(2) to form a

complex, the reaction may be written as

a X (1) + b X (2) = X (1)a X (2)b (2.48)

Assuming equilibrium, the reaction may be written as

K (i ) =

C(i )

X (1)

a

X (2)

b

and then

C (i ) = K (i ) X (1)

a

X (2)

b

 (2.49)

where C(i) is the activity of the complex (X(1)aX(2)b)

and K is a stability constant. If we further let the

stoichiometric coefficients be represented as a(i,j) for

the complex i and component j (for example above a

= a(i,1) and b= a(i,2)) then the reaction may be written

in more general form as

C (i ) = k (i ) ∏

j = 1

N

X (j )

a(i,j)

 (2.50)

where N is the total number of components (metals

and ligands) in complex i (2 in the above example), and

a(i,j) is the stoichiometric coefficient for the jth component of the ith complex.

A mass balance may be written for any given component distributed among all of the complexes. For example the amount of a component X(j) in a complex

C(i) is a(i,j)C(i). The total amount of the component

among all complexes may be written as

XT(j ) = ∑

i=1

M

a (i,j ) C (i ) (2.51)

where M is the total number of complexes. Substituting

from Equation 2.50, Equation 2.51 may be rewritten as

XT (j ) = ∑

i=1

M

a (i,j ) k (i ) ∏

j=1

N

X (j )

a (i,j )

 (2.52)

The solution procedure, used in such models as MINEQL (Westall et al. 1986) and MINTEQA1 (Brown and

Allison 1987), is to make an initial guess as to the

activity (or concentration) of each of the j components.

The concentration of the individual species is then

computed, using Equation 2.50, and the total of each

component calculated (Equation 2.52, XT(j)). This total

is then compared to the known total (T(j)), as

D (j ) = XT (j ) − T (j )

for all components and if the difference (D(j)) is greater

than some criteria, a second guess estimate of the

activities is made. The solution procedure is iterated

until the known totals for each of the components and

computed totals converge to within some specified

difference. The procedure is accomplished numerically using techniques such as the Newton-Raphson

method for solving simultaneous non-linear equations.

B. Precipitation and Dissolution.

In some cases, the transport and fate of metals is

affected by chemical precipitation and dissolution,

either through direct precipitation of metal solids ( e.g.

CdS, CuSO4) or through coprecipitation where a major

ion precipitate is formed which binds metals in the

process (Medine and McCutcheon 1989). The possible concentrations of metal ligand complexes are constrained by their solubility, as expressed by the

solubility product for the ith complex, Ksp(i). However,

determination of the solubility requires consideration

of all possible reactions and equilibria (Stumm and

Morgan 1981). Chemical equilibrium models such as

MINTEQA1 can examine the process of precipitation

of pure metals forms in aqueous systems, assuming

equilibrium conditions.

C. Redox Reactions.

Metals can change oxidation states through various

oxidation and reduction reactions, expressed as

M

++ + e−

= M

+

 , Kri (2.53)

2-31
2.9. References

Akiyama, J. and Stefan, H.G. 1985. Turbidity Current

with Erosion and Deposition, ASCE, Jour. of Hydraulic

Engineering, 111(HY12).

Ambrose, R.B. Jr., Connoly, J.P., Southerland, E.,

Barnwell, T.O. Jr., and Schnoor, J.L. 1988. Waste

Allocation Simulation Models. J. Water Poll. Cntrl. Fed.

60(9), pp. 1646-1656.

Ariathurai, R. 1982. Two and Three-Dimensional Models for Sediment Transport, RMA 1980, Resources

Management Associates, Lafayette, CA.

Ariathurai, R. and Krone, R.B. 1976. Finite Element

Model for Cohesive Sediment Transport. J. Hydraulic

Division, ASCE, 102(HY3), pp. 323-338.

Bedford, K.W. 1985. Selection of Turbulence and Mixing Parameterizations for Estuary Water Quality Models, Miscellaneous Paper EL-85-2, USAE Waterways

Experiment Station, Vicksburg, MS.

Bowden, K.F. 1967. Circulation and Diffusion, in Estuaries (G.H. Lauft, ed.) AAAS Publ. No. 85, Washington, DC. pp 15-36.

Bowie, G.L. et al. 1985. Rates, Constants, and Kinetics

Formulations in Surface Water Quality Modeling (second ed.), U.S. Environmental Protection Agency, Athens, GA. EPA/600/3-85/040.

Brown, D.S. and Allison, J.D. 1987. MINTEQA1, An

Equilibrium Metal Speciation Model: User’s Manual,

U.S. Environmental Protection Agency, Athens, GA.

EPA/600/3-87/012.

Chapra, S.C. and Reckhow, K.H. 1983. Engineering

Approaches for Lake Management, Vol. 2: Mechanistic Modeling, Butterworth Publishers, Woburn, MA.

Chen, R.L., Brannon, J.M., and Gunnison, D. 1984.

Anaerobic and Aerobic Rate Coefficients for Use in

CE-QUAL-R1, Waterways Experiment Station, Miscellaneous Paper E-84-5, July 1984.

Churchhill, M.A., Smith, D.J., and Lee, S. 1962. The

Prediction of Stream Reaction Rates, ASCE, J. Sanitary Engr. Div. 88(SA4), pp 1-46.

Delos, C.G., Richardson, W.L., DePinto, J.V., Ambrose, R.B., Rogers, P.W., Rygwelski, K., and St.

John, J.P. 1984. Technical Guidance Manual for Performing Waste Load Allocations: Book II Streams and

Rivers, Office of Water Regulations and Standards,

U.S. Environmental Protection Agency, Washington,

D.C.

Dietrich, W.E. 1982. Settling Velocities Of Natural

Particles, Water Resources Research, 18(6), p. 1615-

1626.

Di Toro, D.M. 1985. A Particle Interaction Model of

Reversible Organic Chemical Sorption, Chemosphere

14(10), pp. 1503-1538.

Di Toro, D.M. 1986. A Diagenetic Oxygen Equivalents

Model of Sediment Oxygen Demand, in Sediment

Oxygen Demand: Processes, Modeling, and Measurement, editor K.J. Hatcher, Univ. of Georgia, Athens,

GA., pp. 171-208.

where M++ is oxidized metal, M+ is reduced metal, eis an electron, and Kri is the equilibrium coefficient for

reaction i. Oxidation-reduction reactions exert significant controls on the chemistry of major ions and trace

metals and their mobility, particularly between suspended and bed solids forms (Medine and McCutcheon 1989). Reduction reactions, such as in the

formation of sulfides in sediments, may strongly affect

the dissolved concentrations and ecotoxicity of trace

metals. Redox reactions are generally included in

chemical equilibrium models, such as MINTEQA1.

D. Sorption.

The modeling of metal adsorption to metals is receiving

considerable interest due to its importance in regulating metal movement in aquatic systems (Medine and

McCutcheon 1989). However, sorption is strongly affected by the interactions between metals forms. Sorption is strongly affected by pH, often varying from 0 to

100 percent adsorption over a narrow range of pH

(often less than 2 units).

A standard relationship for metals sorption may be

written as

M + Sm = MSm (2.54)

and

KAM =

(M Sm )

[M ] (Sm)

(2.55)

where KAM is a standard adsorption constant and Sm

an adsorbing surface of type m and M is the free metal

ion concentration. Other models proposed to describe

adsorption and included in the MINTEQA1 code are

activity Langmuir sorption, activity Freundlich, ion exchange sorption, constant capacitance and triple-layer

surface complexation models (Medine and McCutcheon 1989, Brown and Allison 1987).

2-32
Emerson, K., Russo, R.C., Lund, R.E., and Thurston,

R.V. 1975. Aqueous Ammonia Equilibrium Calculations: Effect of pH and Temperature, J. Fish. Res.

Board Canada, 32(12): 2379-2383.

Environmental and Hydraulics Laboratories. 1986.

CE-QUAL-W2, A Numerical Two-Dimensional Model

of Hydrodynamics and Water Quality, User’s Manual,

Instruction Report E-86-5, USAE Waterways Experiment Station, Vicksburg, MS.

Fischer, H.B. et al. 1978. Mixing in Inland and Coastal

Waters. Academic Press, N.Y. 483 pp.

Ford, D. and Thornton, K.W. 1989. Time and Length

Scales for One-dimensional Assumptions and its Relationship to Ecological Models, Water Resources Research 15(1).

Gantzer, C.J., Kolig, H.P., Rittmann, B.R., and Lewis,

D.L. 1988. Predicting the Rate of Trace-organic Compound Removal by Natural Biofilms, Water Research,

22(2), pp. 191-200.

Gibbs, R.J., Matthews, M.D., and Link, D.A. 1971. The

Relationship Between sphere Size and Settling Velocity, Jour. Sedimentary Petrology, 41(1).

Gill, A.E. 1982. Appendix 3, Properties of Seawater, in

Atmospheric-Ocean Dynamics, Academic Press, New

York, pp. 599-600.

Golterman, H.L., Sly, P.G., and Thomas, R.C. 1983.

Study of the Relationship Between Water Quality and

Sediment Transport, WNESCO, Tech. Papers in Hydrology No. 26.

Hansen, D.V. and Rattray, M. 1966. New Dimension

in Estuary Classification. Limno and Oceanography

11, 319-325.

Hatcher, K.J. (ed.) 1986. Sediment Oxygen Demand;

Processes, Modeling, and Measurement, Univ. of

Georgia, Athens, GA.

Imboden, D.M. et. al. 1983. Mixing Processes in

Lakes: Mechanisms and Ecological Relevance,

Scherz. Z. Hydrol. 45(1).

Ives, K.J. 1973. The Scientific Basis of Filtration, Nato

Advanced study Inst., Cambridge, UK, D. Reidel Publishing Co., 1973.

Karickhoff, S.W. 1981. Semi-Emperical Estimation of

Sorption of Hydrophobic Pollutants on Natural Sediments and Soils, Chemosphere 10, pp 833-846.

Karickhoff, S.W. 1984. Organic Pollutant Sorption in

Aquatic Systems, Jour. Hydraulic Engineering, ASCE,

110(6), pp. 707-735.

Lal, D. 1977. The Oceanic Microcosm of Particles,

Science, 198(4321), pp. 997-1009.

Large Lakes Research Station. 1987. Users’s Manual

for the Transport and Fate Model MICHRIV, USEPA

Large Lakes Research Station, Grosse Ile, MI.

Lewis, W.K. and Whitman, W.C. 1924. Principles of

Gas Adsorption, Industrial & Engineering Chemistry,

16.

Lewis, D.L. et al. 1984. Application of Single and

Multiphase Michaelis-Menten Kinetics to Predictive

Modeling for Aquatic Ecosystems, Environ. Tox.

Chem., 3(4), pp. 563-574.

Lick, W., Ziegler, K., and Tsai, C. 1987. Resuspension,

Deposition and Transport of Fine-grained Sediments

in Rivers and Near-shore Areas, Prepared for the

USEPA Large Lakes Research Station, Grosse Ile, MI.

Liss, P.S. and Slater, P.G. 1974. Flux of Gases Across

the Air-Sea Interface, Nature, 247, pp. 181-184.

Lung, W.S. 1987. Advective Acceleration and Mass

Transport in Estuaries, ASCE J. Hydraulic Engr.

112(9), 874-878.

Lung, W.S. and O’Connor, D.J. 1984. Two-Dimensional Mass Transport in Estuaries, ASCE J. Hydraulic

Engr. 110(10), 1340-1357.

Lung, W.S. and Testerman, N. 1989. Modeling Fate

and Transport of Nutrients in the James Estuary,

ASCE J. Environ. Engr. Div. (In Print).

Lung, W., Mackay, D., and Yeun, A.T.K. 1983. Mass

Transfer Coefficient Correlations for Volatilization of

Organic Solutes from Water, Environ. Sci. Technol.,

17(4), pp. 211-217.

Medine, A.J. and McCutcheon, S.C. 1989. Fate and

Transport of Sediment-Associated Contaminants, in

Hazard Assessment of Chemicals (ed. J. Saxena),

Hemisphere Publ. Corp., New York, pp. 225-291.

Megard, R.O., Tonkyn, D.W., and Senft, W.H. II. 1984.

Kinetics of Oxygen Photosynthesis in Planktonic Algae, Jour. of Plankton Research, 6(4), pp. 325-337.

Mehta, A., ed. 1986. Estuarine Cohesive Sediment

Dynamics, Springer Verlag, 486 pp.

Miller, S. 1983. Photochemistry of Natural Water Systems, Environ. Sci. Technol., 19(12), pp. 568-570A.

2-33
Mills, W., et al. 1985. Water Quality Assessment: A

Screening Procedure for Toxic and Conventional Pollutants, Parts 1 and 2. US EPA Athens, Ga,

EPA/600/6-85/002.

Morel, F.M.M. 1983. Principles of Aquatic Chemistry.

Wiley, New York.

Munk, W. and Anderson, E.R. 1948. Notes on a Theory

of the Thermocline. J. Marine Res. 7, 276-295.

Nihoul and Jamarf. 1987. Three-Dimensional Models

of Marine and Estuarine Dynamics. Elsevier Scientific,

Amsterdam.

O’Connor, D.J. and Dobbins, W.E. 1958. Mechanisims

of Reaeration in Natural Streams, ASCE Transactions,

pp 641-684, paper 2934.

O’Connor, D.J. 1983. Wind Effects on Gas-liquid

Transfer Coefficients, Jour. Environmental Eng.,

ASCE, 109(3), pp. 731-752.

Officer, C.B. 1976. Physical Oceanography of Estuaries, John Wiley and Sons, New York.

Officer, C.B. 1977. Longitudinal Circulation and Mixing

Relations in Estuaries, Estuaries Geophysics and The

Environment (Ed. C.B. Officer), National Academy of

Sciences, Washington, DC, pp 13-21

Orlob, G.T. and Selna, L.G. 1970. Temperature Variations in Deep Reservoirs, ASCE, Jour. Hydraulic Div.,

96(HY2), pp 391-410.

Orlob, G.T. 1983. Mathematical Modeling of Water

Quality in Streams, Lakes and Reservoirs. Wiley and

Sons, 518 pp.

Owens, M., Edwards, R.W., and Gibbs, J.W., 1984.

Some Reaeration Studies in Streams, International

Jour. of Air and Water Pollution, 8, pp. 469-486

Paul, J.F. and Nocito, J.A., 1983. Numerical Model for

3-D Variable-Density Hydrodynamic Flows: Documentation of the Computer Program. U.S. EPA Environmental Research Lab, Duluth, Minnesota.

Pritchard, D.W. 1967. Observations on Circulation in

Coastal Plain Estuaries, in Estuaries (G.H. Lauft, ed.)

AAAS Publ. No. 85, Washington, DC, pp 15-36

Rodi, W. 1980. Computation of Turbulent Flow, Ann.

Review of Fluid Mechanics, 8, pp. 183-208.

Rodney, M. and Stefan, H. 1987. Conceptual Model

for Wind-generated Sediment Resuspension in Shallow Ponds, Proceedings, 1987 National Symposium

on Mining, Hydrology, Sedimentology and Reclamation, Univ. of Kentucky, Lexington.

Shanahan, P. and Harleman, D.R.F. 1984. Transport

in Lake Water Quality Modeling, ASCE J. Environ.

Engr. 110(1).

Sheng, Y.P. 1983. Mathematical Modeling of Three-dimensional Coastal Currents and Sediment Dispersion:

Model Development and Application, Technical Report

CERC-83-2, USAE Waterways Experiment Station,

Vicksburg, MS.

Southworth, G.R. et al. 1979a. The Role of Volatilization in Removing Polycyclic Aromatic Hydrocarbons

from Aquatic Environments, Bull. Environ. Contam.

Toxicol., 21, pp. 507-514.

Southworth, G.R. et al. 1979b. Transport and Transformation of Anthracene in Natural Waters, in Aquatic

Toxicology, L.L. Marking and R.A. Kimerle (eds.),

American Society for Testing and Materials, Philadelphia, PA, ASTM STP 667, pp. 359-380.

Steele, J.H. 1962. Notes on Some Theoretical Problems in Production Ecology, in Primary Production In

Aquatic Environments, Goldman, C.R. ed., pp. 383-

398, Univ. of California Press, Berkeley.

Stefan, H., Ambrose, R., and Dortch, M. 1988. Surface

Water Quality Models: Modeler’s Perspective. Proceedings of the June 19-23 International Symposium

on Water Quality Modeling of Agricultural Non-Point

Sources, Utah State University, Logan, Utah.

Stumm, W. and Morgan, J. 1981. Aquatic Chemistry,

An Introduction Emphasizing Equilibrium in Natural

Waters, John Wiley and Sons, 780 pp.

Thomann, R.V. and Mueller, J.A. 1987. Principles of

Surface Water Quality Modeling and Control, Harper

and Row, 608 pp.

Thurston, R.V., Russ, R.C., and Emerson, K. 1974.

Aqueous Ammonia Equilibrium Calculations, Technical Report 74-1. Fisheries Bioassay Laboratory, Montana State University, Boseman, Montana.

Tsivoglou, E.E. and Wallace, J.R. 1972. Characterization of Stream Reaeration Capacity. U.S. Environment Protection Agency, Washington, DC,

EPA-R3-72-012.

Vanoni V., ed. 1975. Sedimentation Engineering, Manual No. 54, ASCE 745 pp.

Wang, S.Y., Shen, H.W., Ding, L.Z. 1986. River Sedimentation, Estuarine and Coastal Sedimentation,

2-34
School of Engineering, The University of Mississippi,

University, MI, 1822 pp.

Wang, M. and Harleman, D.R.F. 1984. Modeling Phytoplankton Concentrations in a Stratified Lake, Proceedings of the Ecology Modeling Conference,

Colorado State University.

Westhall, J.C., Zachary, J.L., and Morel, F.M.M. 1986.

MINEQL, A Computer Program for the Calculation of

the Chemical Equilibrium Composition of Aqueous

Systems, Report 86-01, Department of Chemistry,

Oregon State Univ., Corvallis, OR.

Whitfield, M. 1974. The Hydrolysis of Ammonium Ion

in Seawater-A Theoretical Study, J. Marine Bio. Assoc.

United Kingdom, 54, pp. 565-580.

Wolfe, N.L. 1980. Determining the Role of Hydrolysis

in a Fate of Organics in Natural Waters, in R. Haque

(ed.), Dynamics, Exposure, and Hazard Assessment

of Toxic Chemicals, Ann Arbor Science, Ann Arbor, MI,

pp. 163-17.

Zepp, R.G. and Cline, D.M. 1978. Rate of Direct Photolysis in Aquatic Environments, Environ. Sci. Technol., 11(4), pp. 359-366.

Zepp, R.G. 1980. Assessing the Photochemistry of

Organic Pollutants in Aquatic Environments, in R.

Haque (ed.), Dynamics, Exposure, and Hazard Assessment of Toxic Chemicals. Ann Arbor Science, Ann

Arbor, MI, pp. 69-110.

2-35

3. Model Identification and Selection

Robert B. Ambrose, Jr., P.E.

Center for Exposure Assessment Modeling

Environmental Research Laboratory, U.S. EPA, Athens, GA

3.1. Introduction

The first steps in the modeling process are model

identification and selection. Specific water quality problems are identified and study objectives are set. The

goals are to identify the simplest conceptual model that

includes all the important estuarine phenomena affecting the water quality problems, and to select the most

useful analytical formula or computer model for calculating waste load allocations. Selection of too simple a

model can result in inaccurate predictions of future

water quality under hypothetical load reductions. This

can happen even if the model calibration “fits” existing

data. Inaccurate projection from present to future can

be caused by a changing balance among important

processes, such as carbonaceous, nitrogenous, and

sediment oxygen demand. The result is a waste load

allocation that is either too expensive or underprotective of water quality.

On the other hand, selection of too complex a model

will most likely result in misdirected study resources,

delays in the study, and increased cost. Predictive

uncertainty may increase because of extra “free”

model parameters that cannot be estimated with available data. Study costs will increase because of the

additional data requirements and the expanded computer and manpower time needed for model runs,

analysis, and sensitivity studies.

This chapter provides general guidance and some

specific procedures for identifying an appropriate

model. The term “model” in Section 3.2 is used in a

general sense to identify the variables and equations

solved, the dimensionality, and the space and time

resolution. Specific analytical formulas and computer

models are discussed in Section 3.3.

3.2. Model Identification

During model identification, available information is

gathered and organized to construct a coherent picture

of the water quality problem. The goals are to develop

the most effective monitoring strategy and to select the

most appropriate computer model.

There are four basic steps in model identification:

— Establish study objectives and constraints

— Determine water quality pollutant interactions

— Determine spatial extent and resolution

— Determine temporal extent and resolution

These steps are generally considered sequentially.

They are related, however, and later steps may require

refinement of earlier decisions. Indeed, after the study

has been initiated, new data or model results may

suggest changes in the conceptual model initially identified.

Following model identification, another important step

is advised:

— Perform rapid, simple screening calculations

These calculations should help the modeler gain a

better understanding of expected pollutant levels and

the spatial extent of water quality problems. Analytical

solutions are often used along with available data

throughout the model identification stage. These techniques are discussed in Section 3.3.2.

3.2.1. Study Objectives and Constraints

The first step in identifying an appropriate WLA model

for a particular site is to review the applicable water

quality standards and the beneficial uses of the estuary

to be protected. Local, state, and federal regulations

may contribute to a set of objectives and constraints.

Each may specify particular pollutants or classes of

pollutants, and imply time and space scales that must

be resolved by the model. For example, proscription of

“toxic pollutants in toxic amounts” implies simulation of

whole effluent toxicity dilution. Ammonia or metals

standards imply simulation of those specific chemicals.

Regulations may specify an “allowable mixing zone” in

the vicinity of the outfall. This requires that a model

have sufficient spatial resolution to resolve near-field

dilution and mixing processes. For example, the regulation for a thermal outfall may require that waters

return to within 2 °C of the ambient temperature within

100 m of the outfall. This requires a model with an

analytical solution, or a numerical model segmented on

the order of 10 meters. By contrast, standards for

minimum daily average dissolved oxygen require an

3-1
estuarine-wide, or far-field model that extends beyond

the range of influence of the discharge.

The next step in identifying an appropriate WLA model

for a site specific application is to review the existing

data on waste loads, stream flows, and ambient water

quality with respect to the beneficial uses of the estuary

and the applicable water quality standards. These data

should indicate whether standards violations or water

quality problems are associated with diurnal fluctuations, storm events, flow variation, and/or season of the

year. The modeler can use this information to determine the temporal resolution (steady-state, tidally averaged, real time) and the important pollution sources

(point source, nonpoint source) that must be included

in the selected model. The ambient water quality data

should also indicate where violations or problems are

occurring and whether significant spatial gradients in

concentration exist. The combined information collected on the water quality problems will help determine which driving forces (freshwater inflow, tides,

wind, etc.) must be represented in the model. In order

to further define required model capabilities, future

developments planned for the watershed should be

identified. Projected new point source discharges or

land use changes may require the WLA model to have

different capabilities than the existing situation merits.

The final result of this step should be a clear understanding of the pollutants and water quality indicators,

the areas, and the time scales of interest. The spatial

and temporal scales for a range of standard water

quality problems are suggested in Table 3-1. These are

for general guidance, and must be interpreted more

precisely for each specific waste load allocation.

3.2.2. Water Quality - Pollutant Interactions

After the pollutants and water quality indicators are

identified, the significant water quality reactions must

be determined. These reactions must directly or indirectly link the pollutants to be controlled with the primary water quality indicators. All other interacting

water quality constituents thought to be significant

should be included at this point. This can best be done

in a diagram or flow chart representing the mass

transport and transformations of water quality constituents in a defined segment of water. Figures 2-4 through

2-10 (Section 2) illustrated variables and processes

important to the major water quality problems. Not all

of these have to be included in the actual WLA model

selected for use. Those excluded from a model, however, should be considered externally and parameterized in the coefficients. Figure 2-4 covered sediment

transport. Figures 2-5 through 2-9 illustrated conventional pollutant interactions affecting dissolved oxygen,

nutrient enrichment, and eutrophication. Figure 2-10

dealt with toxicants, such as organic chemicals.

Each water quality constituent must be examined to

determine the important forcing functions and boundaries, such as the air-water or water-benthic sediment

interfaces. For example, dissolved oxygen is influenced strongly by reaeration across the air-water

boundary. The nature of the reaeration function, then,

should receive particular attention in the monitoring

and modeling process. Constant or spatially-variable

rate constants might be specified as calibration parameters. For estuaries dominated by flow or

wind,reaeration rates might better be specified as function of velocity, depth, and wind speed. At the benthic

boundary, sediment oxygen demand is usually specified as a spatially-variable flux, to be measured or

calibrated. This flux, however, can be expected to

change with future reductions in waste loads. There

have been recent attempts to include benthic organic

material as a model variable, with the flux computed

internally. While satisfying conceptually, the benthic

components of these models are difficult to calibrate

because of the long time frames controlling benthic

reactions. Good practice at present may be to include

these reactions in the conceptual model, but calculate

or estimate their effects external to the waste load

allocation model. An example calculational framework

was proposed by Di Toro (1986).

The final result of this step should be the assimilation

of all the available knowledge of a system in a way that

major water quality processes and ecological relationships can be evaluated for inclusion in the numerical

model description. The conceptual model is the starting

point from which systematic reductions in complexity

can be identified that will provide an adequate representation of the system, while meeting the objectives

of the study.

Problem Context Spatial Scale Temporal Scale

Salinity Estuarine-wide Seasons

Sediment Estuarine-wide Days to Seasons

Bacteria Mid/Far-field Hours/Days

Heat Near-field Hours

D.O. Depletion Far-field Days to Seasons

Nutrient Enrichment Far-field Seasons to Year

Toxicity Near-field Hours to Days

Human Exposure

-metals Far-field Weeks to Years

-volatile organics Far-field Days to Weeks

-hydrophobic organics Far-field Seasons to Years

Table 3-1. General Scales of Interest

3-2
3.2.3. Spatial Extent and Scale

The general area affected by the waste load allocation

and the significant water quality reactions were identified in steps 1 and 2. The purpose of this step is to

specify the spatial extent, dimensionality, and scale (or

computational resolution) of the WLA model. This may

be accomplished by determining the effective dimensionality of the estuary as a whole, defining the

boundaries of the study area, then specifying the required dimensionality and spatial resolution within the

study area.

3.2.3.1. Effective Dimensionality

Real estuaries are, of course, three dimensional. There

are gradients in hydrodynamic and water quality constituents over length, width, and depth. The effective

dimensionality of an estuary includes only those dimensions over which these gradients significantly affect the WLA analysis. Justifiable reductions in

dimensionality result in savings in model development,

simulation, and analysis costs. Usually the vertical

and/or lateral dimension is neglected. Eliminating a

dimension from the WLA analysis implies acceptable

uniformity of water quality constituents in that spatial

dimension. For example, use of one dimensional longitudinal models implies acceptably small concentration deviations from the cross-sectional mean, both

vertically and laterally. This judgment requires understanding both the transport behavior of estuaries and

the specific goals of the WLA study.

For estuarine WLA modeling, the longitudinal (x) dimension can almost never be neglected. The analyst

must decide whether the lateral (y) or vertical (z)

dimensions must also be retained. The most frequent

cause of variation in the vertical direction is density

stratification. Lateral variations may be caused by large

widths and slow lateral mixing. Vertical and lateral

variations can be observed by plotting water quality

concentration variations with width and depth. If such

data are not available, vertical and lateral variations

can be predicted in one of several ways:

— density, salinity, or temperature gradients,

— tidal or residual velocity reversals over width or

depth,

— dye cloud splitting and differential advection,

— geomorphological classification.

A. Degree of Stratification.

Fisher et al. (1972) suggested a method to predict the

degree of stratification in an estuary as a whole. Freshwater is lighter than saltwater. This produces a buoyancy of amount:

Buoyancy = ∆ ρ g QR (3-1)

where

∆ ρ= the difference in density between sea and river

water, (about 0.025 kg/m3),

g = acceleration of gravity, (about 9.81 m/sec2), and

QR = freshwater river flow, m3/sec

The tide on the other hand is a source of kinetic energy,

equal to:

Kinetic energy = ρ W Ut

3

 (3-2)

where

ρ = the seawater density, about 1.025 kg/m3,

W = the estuary width, m, and

Ut = the square root of the averaged squared velocities,

m/sec.

Width and velocities should be taken at a representative cross section of the estuary. The ratio of the

above two quantities, called the “Estuarine Richardson

Number,” is an estuary characterization parameter

which is indicative of the vertical mixing potential of the

estuary:

R = ∆ ρ g QR ⁄ ρ W Ut

3

(3-3)

If R is very large (above 0.8), the estuary is typically

considered to be strongly stratified and the flow dominated by density currents. If R is very small, the estuary

is typically considered to be well-mixed and the vertical

density effects to be negligible.

Another desktop approach to characterizing the degree

of stratification in the estuary is to use a stratificationcirculation diagram (Hansen and Rattray, 1966). The

diagram (shown in Figure 3-1) is based on measurements from a number of estuaries with known degrees

of stratification. Its use requires the calculation of the

Stratification Parameter = ∆ S ⁄ So (3-4)

and the

Circulation Parameter = Us ⁄ Uf (3-5)

where

∆S = time averaged difference between salinity levels

at the surface and bottom of the estuary,

So = cross-sectional mean salinity,

3-3
Figure 3-1. Stratification circulation diagram and examples.

3-4
Us = net non-tidal surface velocity, and

Uf = mean freshwater velocity through the section.

For best results, mean salinity and velocity should

represent averages over several tidal cycles. The

stratification parameter is much less sensitive to tidal

variations than the circulation parameter. To apply the

stratification-circulation diagram, calculate the parameters of Equations 3-4 and 3-5, and plot the resulting point on the diagram. Type 1 estuaries have

seaward flows at all depths, and the upestuary salt

intrusion is due to tidal diffusion. Type 1a represents

slight stratification as in a laterally homogeneous, wellmixed estuary. In Type 1b, there is strong stratification.

Type 2 is partially well-mixed and shows flow reversals

with depth. In Type 3a the transfer is primarily advective, and in Type 3b the lower layer is so deep, as in a

fjord, that circulation does not extend to the bottom.

Finally, Type 4 represents the salt-wedge type with

intense stratification (Dyer, 1973). The purpose of the

stratification-circulation analysis is to determine the

degree of vertical resolution needed for a modeling

study. If the estuary is well-mixed, the vertical dimension may be neglected, and all constituents in the

water column are assumed to be dispersed evenly

throughout. If the estuary is highly stratified, it is appropriate to model at least two layers. The approach for a

partially-mixed system is not so clear and judgment

must be exercised. For a recent toxics study (O’Connor et al., 1983), the James River, which is partially

stratified, was treated as a 2-layer system.

A final desktop method for characterizing the degree

of stratification is the calculation of the estuary number

proposed by Thatcher and Harleman (1972):

Ed = Pt Uo

2

⁄ Ud

2

T (3-6)

where

Ed = estuary number,

Pt = tidal prism volume, m3,

Ud = densimetric velocity, m/sec,

 = (g D ∆ ρ ⁄ ρ)

1

⁄2

∆ ρ= the density difference between river water and

sea water (about 0.025 kg/m3),

ρ = density of sea water (about 1.025 kg/m3),

Uo = maximum velocity at mouth of estuary, m/sec

D = depth, m,

g = acceleration due to gravity (9.81 m/sec2

), and

T = tidal period, (about 44,700 sec).

Again, by comparing the calculated value with the

values from known systems, one can infer the degree

of stratification present.

The degree of stratification determined by one of the

above methods may be translated into the following

criteria for model selection:

— strongly stratified - include the vertical dimension in

at least a 2 layer model

— moderately stratified - may include the vertical

dimension in a multi-layered model, or

— vertically well-mixed - neglect vertical dimension,

unless water quality processes dictate vertical resolution

B. Tidal or Residual Velocity Reversals.

Beyond the use of a stratification diagram, the analysis

of vertical dimension reduction becomes more difficult

and intuitive. However, the following criteria seem

reasonable (Figure 3-2):

— tidal velocity reversals - should include vertical

dimension in at least a 2-layer model,

— residual velocity reversals - may include the vertical

dimension in a multi-layered model or may neglect

vertical dimension if vertical variability is small,

— no observable reversals - may neglect vertical

dimension.

C. Dye Studies.

Dye studies simply replace the Eulerean observations

of current meters with the Lagrangian movement of a

dye cloud study. Again, quantitative analyses are difficult, but the following criteria seem reasonable (Figure 3-3):

— Dye cloud separates and moves -cloud is responding to a vertical flow reversal and moves as 2 or more

distinct units, indicating the vertical dimension should

be included in at least a 2-layer model,

— Dye cloud spreads in non-Gaussian manner - some

differential shearing is present and the system may be

studied using a multi-layer model, or,

— Dye cloud moves downstream and diffuses in a

Gaussian manner - little differential shearing is present

and the system may be modeled neglecting the vertical

dimension.

3-5
D. Geomorphological Classification.

Over the years, a systematic geomorphological classification of estuaries has evolved. If little or no data

are available, one can try to categorize the estuary

within the basic morphological definitions of Dyer

(1973). Dyer (1973) and Fischer et al. (1979) identify

four groups:

Drowned river valleys (coastal plain estuaries)

Fjords

Bar-built estuaries

Other estuaries that do not fit the first three classifications

Typical examples of North American estuaries are

presented in Tables 3-2 and 3-3. The characteristics

of each geomorphological classification were discussed in Section 2-1. Using these classifications, the

approach is to estimate the degree of stratification from

known conditions in a geomorphologically similar estuary and use the criteria given below under “degree

of stratification”.

3.2.3.2. Study Area Boundaries

After the effective dimensionality of the estuary has

been determined, specific boundaries of the study area

must be established. In general, the boundaries should

be located beyond the influence of the discharge(s)

being evaluated. Otherwise, proper specification of

boundary concentrations for model projections is very

difficult. Sometimes this guideline is not possible. One

rule strictly applies -boundaries influenced by a discharge should be located far enough from the discharge

so that errors in the boundary concentrations do not

significantly affect predicted maxima or minima upon

which the WLA is being based.

Beyond these rules, several common sense guidelines

can help locate proper model boundaries. Boundaries

should be located where flow or stage and water quality

are well monitored. Upstream boundaries should be

located at a fall line, or at a gaging station in free-flowing,

riverine reaches. Downstream boundaries are best located at the mouth of an estuary, or even nearby in

Figure 3-2. Vertical velocity profiles.

Figure 3-3. Vertical dye concentration profiles.

3-6
the ocean. For large estuaries with relatively unaffected seaward reaches, the downstream boundary

can be located within the estuary near a tidal gage and

water quality monitoring station.

If these guidelines are not possible because of excessive computational elements, consideration should be

given to nested grids. A crude grid could span the

estuary and predict tidal flows and concentrations.

Two or more internal elements in the coarse grid could

serve as boundaries to a fine grid. This strategy may

be particularly useful for assessing near-field effects in

a strongly tidal estuary.

3.2.3.3. Study Area Resolution

If the study area constitutes all or most of the estuary,

the model dimensionality should equal the effective

estuarine dimensionality. If, however, the study area is

a discrete segment of the estuary, then further simplifications in dimensionality may be possible. Data describing the spatial gradients of important water quality

constituents within the study area should be examined.

Dye studies can give important information on the speed

and extent of lateral and vertical mixing. The rate of

mixing must be compared with water quality reaction

rates to determine if lateral or vertical gradients are to

be expected for particular constituents. For example, an

estuarine reach that mixes laterally in 1 day can be

laterally averaged for pollutants with characteristic reaction times of days (such as BOD). This same reach,

however, should not be laterally averaged for pollutants

with reaction times of hours (such as coliform bacteria

or some organic chemicals).

Lateral mixing can be described by the convective

length, Lc, over which the discharge plume is mixed

laterally (Fischer et al., 1978, Holley and Jirka, 1986).

Complete mixing is defined when the concentration is

within 5 percent of its mean value everywhere in the

cross section. For centerline and side discharges, respectively, the mixing length Lc is given by

Lc = 0.1 u W

2

⁄ E y (3-7)

Lc = 0.4 u W

2

⁄ E y (3-8)

where

u = mean downstream velocity, m/day

W = channel width, m

Ey = lateral diffusion coefficient, m2/day

These formulas strictly apply to steady, unidirectional

flow. Complete mixing is not achieved during ebb or

flood tide if the lateral mixing time Lc/u is greater than 6

hours. Steady discharges can become laterally well

mixed within the mixing length even if the lateral mixing

time exceeds 6 hours due to tidal reversals. Lateral

diffusion coefficients are best estimated by dye studies

or other site specific data. Several general formulas are

Type Lateral Type River Discharge Example

Highly Stratified Laterally

Homogeneous

Large Mississippi

River

Mobile River

Partially Mixed Partially Mixed Medium Chesapeake

Bay

James Estuary

Potomac River

Vertically Moderate to Small Delaware River

Homogeneous High Raritan River

Variability Tampa Bay

San Francisco

Bay

San Diego Bay

Table 3-3. Stratification Classification

Type / Dominant Long

Term Process

Vertical Degree

of Stratification

Lateral

Variability

Example

Coastal Plain /

River

Moderate Moderate Chesapeake

Bay

Flow James River

Potomac River

Delaware

Estuary

New York Bight

Bar Built / Wind Vertically Well

Mixed

High Little Sarasota

Bay

Apalachicola

Bay

Galveston Bay

Albemarle

Sound

Palmico Sound

Pugent Sound

Fjords / Tide High Small Alberni Inlet

Silver Bay

Other Various Various San Francisco

Estuaries/ Columbia

Various River

Table 3-2. Topographic Estuarine Classification

3-7
given in Bowie et al., (1985). The time required for

complete lateral mixing (Lc/u) can be usefully compared to reaction half lives (∆ t 1

⁄2 ) to predict the degree

of lateral mixing for various pollutants and water quality

constituents. Half lives can be estimated from the first

order reaction rate constant K:

∆ t

1

⁄2 = 0.693 ⁄ K (3-9)

The convective mixing length should be compared to

the study area dimensions to determine the relative

importance of lateral mixing on the study area as a

whole. If the effects are significant, or if regulations

enforce water quality standards at the edge of the

mixing zone, then a near-field model is required. Numerical models should be composed of computational

elements with short length ∆ x and width ∆ y:

∆ x ≤ 0.2 Lc (3-10)

∆ y ≤ 0.2 W (3-11)

Smaller dimensions will give better precision, but at

greater computational cost.

If near field effects are judged unimportant, then spatial

resolution for the entire study area must be determined. Dye studies can give important information

about the advective velocities and flushing times

through the study area. The rate of downstream transport must be compared with water quality reaction

rates to determine if longitudinal gradients are to be

expected for particular constituents. Steeper water

quality gradients require more detailed spatial resolution. The length of model computational elements

should be significantly less than that required for concentrations to halve:

∆ x < u ∆ t

1

⁄2 (3-12)

The characteristic velocity can be either tidal or tidalaveraged, depending upon the type of simulation chosen. This decision is discussed in the next section.

Other considerations may affect the choice of spatial

scale and the actual layout of the model network. One

is the desired spatial resolution in critical areas to be

protected, as along a public beach or around a water

intake. Computational elements should be centered on

these features, so that predicted concentrations can

be related directly to appropriate standards or goals

set to protect these resources. Likewise, computational elements should be centered on monitoring stations and important discharges. The model network

may also have to account for unique features of the

study area, such as embayments, marshes and tidal

flats, channels, and islands. If the required spatial

resolution is much larger than these features, they may

be ignored. They should be accounted for when the

required spatial resolution is of a similar size or less.

Another set of considerations affecting spatial scale is

the required time resolution and the dynamics of the

loading, transport, and kinetic processes. The need for

monthly or seasonal average concentrations may allow

quite large computational elements. If high or low tidal

concentrations are needed, however, computational

elements must be a fraction (say 20% or less) of the

length of a tidal excursion. Predicting the effects of a

steady discharge may allow large computational elements, while tracking the direct effects of batch discharges or storm runoff with characteristic times (∆tE)

constrains the computational lengths:

∆ x ≤ u ∆t E (3-13)

Direct effects include such problems as acute toxicity

and bacterial exposure. Indirect effects from unsteady

discharges, such as the impact of nutrients on eutrophication and dissolved oxygen, generally don’t constrain

the computational lengths. An exception is when load is

correlated with tidal transport, such as batch discharges

into ebb tide only.

It is clear that choice of spatial scale and layout of the

model network requires considerable judgment. Knowledge of the regulatory problem must be combined with

knowledge of the loading, transport, and transformation

processes and an understanding of the WLA model

chosen to perform the simulations. Competing factors

must often be balanced, such as precision and cost, or

better fitting one section of the network versus another.

For best results, the modeler should retain the flexibility

to refine the model network during the calibration phase

of the WLA study. Examples of 6 different model networks applied in actual case studies are given in Part 4

of this manual.

3.2.4. Temporal Extent and Scale

The WLA problem context and its general time scale

were identified in step 1. The purpose of this step is to

specify the duration and temporal resolution of the WLA

model.

3.2.4.1. Duration of WLA Simulations

The duration of WLA simulations can range from days

to years, depending upon the size and transport characteristics of the study area, the reaction kinetics and

forcing functions of the water quality constituents, and

the strategy for relating simulation results to the regulatory requirements. One basic guideline applies in all

cases - the simulations should be long enough to eliminate the effect of initial conditions on important water

quality constituents at critical locations. This will ensure

that errors in the initial conditions do not significantly

affect predicted concentrations upon which the WLA is

being based.

3-8
The size and transport characteristics of the study area

determine its flushing time. This is the time required to

remove a parcel of water (along with associated dissolved non-reactive pollutants) from an upstream location in an estuary. Factors that control flushing

include tidal action, freshwater inflow, and wind stress.

All of these forcing functions are time variable. Flushing time calculations are usually based on average

tidal range and average or low freshwater inflow, with

wind effects neglected. Because estuarine flushing is

inherently dispersive in nature, there is no unambiguous point at which the original water and pollutants are

completely replaced. Flushing times can be defined for

90%, 95% or even 99% removal. Typical flushing times

range from days in small estuaries or those dominated

by tributary flow to months in large estuaries during low

tributary flow conditions.

Several formulas have been used to estimate flushing

times. The Fraction of Fresh Water Method, the Tidal

Prism Method, and the Modified Tidal Prism Method

are described in Mills, et al., (1985). These are screening calculations only and should not be considered

accurate. Better estimates can be obtained directly

from dye studies or simple box models calibrated to

salinity or dye data.

Flushing times give the minimum duration for simulations of dissolved, non-reactive pollutants. Reaction

kinetics affect the required duration for those pollutants

and water quality constituents controlled by various

physical, chemical, and biological transformations and

removal processes. Pollutants controlled by rapid loss

rates, such as fecal bacteria or some volatile organic

chemicals, can generally be characterized by simulations that are shorter than the flushing time. For water

quality constituents affected by transformation rates,

the time required to complete the entire reaction chain

or cycle must be considered. Some chemicals that

interact extensively with benthic sediments may require simulations greatly exceeding flushing times because their removal is controlled by desorption and

benthic diffusion kinetics. Examples include nutrients

and hydrophobic organic chemicals. Sediment diagenesis models should be helpful in analyzing chemical dynamics and fate in such situations.

The dynamics of major loading and kinetic forcing

functions may dictate longer simulations than flushing

times and kinetic reactions suggest. Nonpoint sources

may provide significant “background” loads that must

be considered in a WLA study. These are highly intermittent, but seasonal in nature and may extend sediment, dissolved oxygen, and nutrient enrichment

simulations from weeks to seasons. The annual sunlight and temperature cycles almost require that eutrophication simulations range from seasons to years.

The final factor affecting the duration of simulations is

the strategy for relating simulation results to the regulatory requirements. Sometimes a set of “design conditions” can be defined, allowing for shorter simulations.

Care must be taken to ensure that a particular combination of design conditions, such as flow, temperature, and

nonpoint source loads, does not reflect an unreasonably

low probability of occurrence and thus an overly restrictive WLA.

Another strategy is to extend a simulation for many

years, defining the variability of the major forcing functions as realistically as possible. Often, historical records

of tide, flow, temperature, and rainfall are used to ensure

the proper interaction among processes. Predicted concentrations are expressed as a frequency or probability

of exceedance of water quality goals or standards.

Critical combinations of factors leading to violations may

be isolated and examined in more detail.

3.2.4.2. Temporal Resolution

The temporal resolution of WLA simulations falls into

one of three categories - dynamic, quasidynamic, and

steady state. Dynamic simulations predict hour to hour

variations caused by tidal transport. Diurnal forcing may

also be included, although not necessarily if output is to

be time-averaged. Quasidynamic simulations predict

variations on the order of days to months. The effects of

tidal transport are time-averaged, and net or residual

flows are used to drive advection. Other forcing functions such as freshwater inflow, pollutant loading, temperature, and sunlight may vary from daily to monthly.

Steady state simulations predict monthly to seasonal

averages. All inputs are time-averaged.

Two schools of thought have persisted regarding the

utility of dynamic versus quasidynamic and steady state

simulations. For some problems the choice is reasonably clear. Dynamic models are necessary for analysis

of control options for complex situations in estuaries.

Predicting the upstream migration of pollutants from an

outfall to a beach or water supply intake requires a

dynamic simulation. Predicting water quality effects

from batch discharges into ebbing tide requires a dynamic simulation.

On the other hand, quasidynamic and steady state

models are currently more practical for long term analysis of water quality response. Predicting the year to year

eutrophication response or the accumulation of hydrophobic organic chemicals in the benthic sediments of

large estuaries is best accomplished by quasidynamic

simulations. In general, if the regulatory

3-9
need or kinetic response is on the order of hours, then

dynamic simulations are required; if regulatory needs

are long term averages and the kinetic response is on

the order of seasons to years, then quasidynamic or

steady simulations are indicated.

Between these two extremes lie many WLA problems

that might be addressed by either dynamic or quasidynamic simulation. Some experts assert that even for

long term analyses where only average predictions are

needed, dynamic simulations are practical and more

desirable. Dynamic simulations can be expected to

more accurately account for interactions among the

important tidal and diurnal forcing functions controlling

average water quality conditions. Calculated maxima

and minima at a location can account for the major tidal

and diurnal processes; calculated concentrations,

then, can be compared directly to water quality criteria

expressed in terms of daily or hourly maxima and

minima, or in terms of frequency or return intervals.

Quasidynamic and steady state simulations require

statistical calculations outside the model to relate predicted average concentrations with maxima or minima

criteria. Further, quasidynamic and steady simulations

require careful calibration to long term average salinity

data rather than shorter slack water data. It is argued

that data needs for calibrating dynamic models are

actually less because extensive averaging over cross

sections and time is not necessary.

Others prefer quasidynamic simulations when the

choice is ambiguous. Some experts assert that for

standard WLA analyses, dynamic models are often not

necessary and are too formidable for two and three

dimensional situations. Dynamic simulation requires

fully calibrated hydrodynamic models to drive the water

quality computations. It is argued that an extensive

data base is necessary to calibrate the dynamic calculations. Quasidynamic simulations cost less because

of their longer time steps and less use of hydrodynamic

simulation. The lower costs allow for longer simulations than dynamic models, and thus greater ability to

explore seasonal and yearly trends. The lower costs

also allow for more water quality variables and processes to be simulated.

The computational time step used by the WLA model

will depend upon the temporal resolution chosen as

well as the spatial network, the transport characteristics of the estuary, and the numerical solution

technique of the model. Most computer waste load

allocation models use explicit schemes—that is, variables at the new time step are calculated using known

values at previous time steps. This leads to several

common conditions that must be satisfied to ensure

model stability (i.e., solutions remain within bounds and

do not “blow up”). Furthermore, satisfying these conditions will often result in smaller time steps that would

generally be needed from solution resolution conditions

alone.

The conditions, or criteria, for one-dimensional models

using explicit solution schemes are usually:

— a hydrodynamic criterion (Courant condition)

∆ t ≤ ∆ x ⁄ √ gh ± u (3-14)

— mass transport, dispersion, and kinetic conditions

∆ t ≤

∆ x ( 2α − 1)

u

+

∆ x

2

2 E L

+

1

K

(3-15)

where

u = maximum tidal velocity, m/sec

g = gravitational acceleration, 9.81 m/sec2

h = hydraulic radius, or depth, m

EL = longitudinal dispersion coefficient, m2/sec

K = first order decay rate, 1/sec

α = finite difference weight, (1 for backward differences, 1⁄2 for central differences)

Similar conditions exist for 2 and 3-dimensional models,

and other conditions, such as a friction term criterion,

may also be required. Chemical and biological components of the WLA model may cause restrictions in the

time step if reaction kinetics are rapid. In that case, the

reaction is often written as an equilibrium relationship,

which does not affect the time step. The most stringent

condition is usually the Courant condition (unless vertical diffusion and/or momentum transfer is explicitly

treated, in which case a criterion like Equation 3-15 is

required with ∆z replacing ∆x). Many models solve for

the mass transport equations in a separate model, or at

a different time step than the hydrodynamic solution. In

these cases, all the above criteria should be checked.

Dynamic models are governed by equations 3-14 and

3-15 where u is the maximum tidal velocity. Time steps

are on the order of seconds to minutes for the hydrodynamic component or model, and minutes to an hour for

the mass transport (and water quality) model. Quasidynamic models are governed by equation 3-15 where u

and EL are tidal-averaged values (u being smaller and

EL being larger than nonaveraged values). Time steps

are on the order of one to several hours.

Some models, particularly current hydrodynamic programs, use an implicit technique to approximate the

3-10
governing equations. In these cases, the model may

be unconditionally stable, which means that the choice

of the time step is not limited by stability considerations. Here, the time step should be chosen to provide

adequate resolution of temporal processes. Care

should still be taken because even implicit schemes

may have certain limiting time or space conditions.

3.3. Model Selection

The goal of model selection is to obtain a simulation

model that effectively implements the conceptual

model identified for the WLA. The available set of

general purpose models may not always fully implement a specific conceptual model. In this case, calculations or assumptions may be made outside the

model’s computational framework, or model code may

be refined. Models that are known to the user and that

are easily modified provide valuable flexibility to the

WLA study. In the final analysis, how a model is used

is more important to the success of a WLA than exactly

which model is used. Nevertheless, while selection of

an appropriate model will not guarantee success, it will

help. Selection of an inappropriate model will not guarantee failure, but will render a successful outcome

more difficult.

Models may be classified in different and somewhat

arbitrary ways. Some models may not quite fit in any

category, or may fit well in several. In addition, models

tend to evolve with use. The exact capabilities of the

individual models described here may change. In particular, kinetic reactions may be modified and new

variables inserted. Dispersion functions may be updated. Usually the computational framework and the

basic transport scheme remain stable over time. For

this reason, transport characteristics will provide the

basis for the model classification scheme used here.

Models selected for discussion here are general purpose, in the public domain, and available from or

supported by public agencies.

The selection of an estuarine WLA model need not be

limited to the models discussed in this document.

Other models that are available to a project or organization should also be considered. The models summarized in this report represent the typical range of

capabilities currently available. Other available computer programs can generally be grouped into one of

the following categories:

— Variants of the models discussed here;

— Proprietary models held by consulting firms;

— Models developed for research purposes.

It is recommended that where project staffs do not have

access to or familiarity with a wide range of computer

programs, effort should be focused on those discussed

in this document.

One important word of caution: it is highly likely that all

computerized models discussed here contain a few

undiscovered software and documentation errors. The

user must be careful to verify that the models are

implemented properly and are providing reasonable

calculations. With support from EPA’s Office of Water,

the EPA Center for Exposure Assessment Modeling

(CEAM), Athens, Georgia, maintains some of these

models, providing their users with an information and

error clearinghouse. These models may be obtained

over the CEAM electronic bulletin board system, or by

mailing in the appropriate number of diskettes.

3.3.1. Classification of Models by Transport

Complexity

Estuarine WLA models consist of two components—hydrodynamic and water quality. In the simplest case,

hydrodynamics may be represented in a model by usersupplied velocity and flow data. In a more complex

model, hydrodynamics may be represented by numerical solution of the equations of motion and continuity. In

either case, water quality conservation-of-mass equations are executed using the hydrodynamic output of

water volumes and flows. The water quality component

of the model calculates pollutant dispersion and transformation or decay, giving resultant concentrations over

time. All the estuarine WLA models discussed in this

report include as a minimum the first order decay of BOD

and the prediction of DO concentrations. The more

comprehensive models include nutrient-algal relationships and benthic source/sink terms. A few estuarine

models that include reaction rate coefficients and transformation processes for toxic materials also are available.

Although the hydrodynamic submodel is independent of

the water quality submodel, water quality depends on

the advection, dilution, and dispersion controlled by

hydrodynamics. As a result, estuarine WLA models can

be classified as Level I to Level IV according to the

temporal and spatial complexity of the hydrodynamic

component of the model. The model classification

scheme followed in this report was recommended by

Ambrose et al. (1981).

Level I includes desktop screening methodologies that

calculate seasonal or annual mean pollutant concentrations based on steady state conditions and simplified

flushing time estimates. These models are designed to

examine an estuary rapidly to isolate trouble spots for

more detailed analyses. They should

3-11
be used to highlight major water quality issues and

important data gaps in the early, model identification

stage of a study.

Level II includes computerized steady state or tidally

averaged quasidynamic simulation models, which

generally use a box or compartment-type network to

solve finite difference approximations to the basic partial differential equations. Steady state models use an

unvarying flow condition that neglects the temporal

variability of tidal heights and currents. Tidally averaged models simulate the net flow over a tidal cycle.

These models cannot predict the variability and range

of DO and pollutants throughout each tidal cycle, but

they are capable of simulating variations in tidally

averaged concentrations over time. Level II models

can predict slowly changing seasonal water quality

with an effective time resolution of 2 weeks to 1 month.

Level III includes computerized one-dimensional (1-d)

and quasi two-dimensional (2-d), dynamic simulation

models. These real time models simulate variations in

tidal heights and velocities throughout each tidal cycle.

One-dimensional models treat the estuary as wellmixed vertically and laterally. Quasi 2-d models employ a link-node approach that describes water quality

in two dimensions (longitudinal and lateral) through a

network of 1-d nodes and channels. The 1-d equation

of motion is applied to the channels while the continuity

equation is applied at nodes between channels. Tidal

movement is simulated with a separate hydrodynamic

package in these models. Although the Level III models will calculate hour-to-hour changes in water quality

variables, their effective time resolution is usually limited to average variability over one week because tidal

input parameters generally consist of only average or

slowly varying values. In this case, model results

should be averaged to obtain mean diurnal variability

over a minimum of 1 week intervals within the simulated time period (Ambrose and Roesch 1982). The

effective time resolution could be reduced to under 1

day given good representation of diurnal water quality

kinetics and precise tidal input parameters. The required data and modeling effort are usually not mobilized in standard WLAs.

Level IV consists of computerized 2-d and 3-d dynamic

simulation models. Dispersive mixing and seaward

boundary exchanges are treated more realistically

than in the Level III 1-d models. These models are

almost never used for routine WLAs. While 2-d models

are beginning to find regular use for some engineering

applications, at the present time practical 3-d models

and modeling techniques are still developing. The only

3-d models currently reported in the literature are

hydrodynamic models that include simple first order

decay rates for uncoupled nonconservative pollutants

(Swanson and Spaulding 1983) and box type models

configured in three dimensions (HydroQual 1987). The

effective time resolution of the Level IV models can be

less than 1 day with a good representation of diurnal

water quality and intratidal variations. The required data

and modeling effort are usually not mobilized in standard

WLAs.

The advantages of Level I and II models lie in their

comparatively low cost and ease of application. The

disadvantages lie in their steady state or tidally averaged temporal scale. When hydrodynamics and pollutant inputs are rapidly varying, steady state models are

difficult to properly calibrate. Consequently, these models are less satisfactory in short estuaries or when waste

load, river inflow, or tidal range vary appreciably with a

period close to the flushing time of the water body.

Steady state and tidally averaged models require calibration of a dispersion coefficient using field data. The

calibrated value is applicable to the condition monitored

and cannot be extrapolated to proposed modifications

in estuary shape, tidal volume, or river discharge.

As Hinwood and Wallis (1975) explain, dispersion is

caused by the combined action of turbulence and a

nonuniform velocity profile. Nonuniform velocities elongate a wastewater slug, whereas turbulence, acting

normal to the mean velocity, mixes the waste. Velocities

at any section of the estuary vary due to shear at the

bed and sides of the channel. In addition, irregularities

in channel shape, salinity and temperature induced

density currents, and wind-induced currents, cause

nonuniform velocities. In a wide estuary, the Coriolis

force and streams entering on one side of the channel

also may produce nonuniform velocities.

Dispersion coefficients in the Level I through IV models

represent different transport phenomena. The flux of

matter through an estuary can be represented with the

following simplified notation:

Flux = Net advection from freshwater flow (1)

+ Tidal dispersion (2)

+ Net transverse gravitational circulation (3)

+ Net vertical gravitational circulation (4)

+ Transverse oscillatory shear (5)

+ Vertical oscillatory shear (6)

+ Turbulent or eddy diffusion (7)

One-dimensional, tidally averaged or steady state models calculate term 1 directly but represent terms 2

3-12
through 7 with a tidal average or steady state longitudinal dispersion coefficient. In contrast, the Level III

1-d, real time models calculate terms 1 and 2 directly

and use the cross-sectional averaged longitudinal diffusion coefficient to represent terms 3 through 7. The

Level IV 2-d, depth-averaged models represent even

more terms directly. These models calculate terms

1,2,3 and 5 directly, using the depth-averaged longitudinal and lateral diffusion coefficients only to represent

terms 4, 6 and 7.

As a model is simplified from Level IV to Level II, the

dispersion coefficients become larger and more

unique to each flow situation. The steady state or

tidally averaged Level II models require the dispersion

coefficient to include the effects of tidal mixing. As a

result, the coefficient must be calibrated using salinity

measurements, and it cannot be used to predict the

water quality effects of projected changes in estuarine

topography or river inflows. Due to shorter time scales,

the Level III and IV dispersion coefficients do not have

to include the effects of tidal mixing and can be more

closely based on the physical properties of the channel

(hydraulic radius and roughness coefficient). Changes

in these properties can then be made in the model to

predict the effect of proposed changes in channel

geometry or freshwater inflows.

The dynamic models (Levels III and IV) have advantages over steady state and tidally averaged models

in representing mixing in partially mixed estuaries because advection is so much better represented. Although shear effects and the effects of spatial

averaging must still be accounted for, the effects of

time averaging can be avoided.

The short time step of dynamic models allows them to

be more sensitive predictors of the duration of violations of water quality standards. Dynamic models can

provide a more accurate response to nonpoint source

loads and pollutant spills, short term events that can

produce water quality standard violations with a duration less than one tidal cycle in length. The success

with which these models can predict transient violations depends upon both the accuracy and resolution

of the loading and environmental data, and the model’s

treatment of short time scale kinetics such as desorption or diurnal fluctuations in temperature, pH, or sunlight. While dynamic models are capable of predicting

diurnal and transient fluctuations in water quality parameters, the input data requirements are much

greater. Lack of detailed data or process descriptions

often render their real predictive resolution significantly

longer than their computational time step.

The Level III, 1-d models can produce good estimates

of tide heights, mean velocities, and pollutant concentrations for estuaries with fairly regular channels that are

much longer than they are wide. Near points of waste

injection, however, model predictions can be significantly in error due to lateral variations in concentrations.

The quasi 2-d approach can solve this problem, but the

difficulty in estimating effective dispersion coefficients

still remains. The Level IV longitudinal and lateral 2-d

models have the advantage of representing the lateral

variations in velocity and waste concentrations that arise

in all estuaries and bays because of the nonuniformity

of cross-sections, embayments, branching channels,

and bends (Hinwood and Wallis 1975). In addition, these

models can include the effects of Coriolis and wind

circulations. The remaining flaw is that the lateral-longitudinal models assume an estuary is vertically wellmixed. This assumption can lead to significant errors in

predictions for stratified estuaries.

3.3.2. Level I Models

The purpose of modeling at Level I is to screen trouble

spots for more detailed analysis. Level I desktop methodologies may be done with a hand held calculator and

are based on steady state conditions, first order decay

coefficients, simplified estimates of flushing time, and

seasonal pollutant concentrations.

Level I screening of a given waterbody may entail selected analyses to answer individual questions (e.g., is

the estuary stratified in a particular location; what is the

flushing time of the estuary; what is the annual phosphorus loading), or it may entail a comprehensive examination of the estuary. A comprehensive analysis may be

accomplished with models such as the Simplified Estuary Model (SEM) or the Water Quality Assessment

Methodology (WQAM). SEM and WQAM both require

only hand calculations and are used chiefly for preliminary assessments of estuarine water quality. Documentation on WQAM is available from CEAM.

3.3.2.1. Water Quality Assessment Methodology

WQAM is a steady state desktop model that includes

both one-dimensional and two-dimensional box model

calculations (Mills et al. 1985). Use of WQAM procedures requires classification of an estuary into one of

three possible types: stratified, well-mixed, or partially

mixed. Two methods are presented to determine the

appropriate classification. The Hansen and Rattray

method utilizes vertical salinity gradients, freshwater

inflow velocities, and surface tidal current velocities

averaged over a tidal cycle to characterize the system.

The flow ratio calculation method classifies the estuary

using a comparison of freshwater flow volume and tidal

flood volumes (tidal prism) over a tidal cycle. Values

3-13
calculated from these input data are compared to

ranges set for each estuarine classification.

WQAM includes calculations to estimate the transport

of BOD, DO, pH, arbitrary conservative substances,

thermal pollution, turbidity, sediment, and organic

chemicals in an estuary. Pollutant distribution can be

estimated using either a far field or a near field method

of analysis. The near field technique predicts initial

dilution of submerged discharges through the use of

tabulated data from MERGE, a computerized plume

model. For well-mixed estuaries, far field pollutant

distributions can be predicted using the fraction of

freshwater method, modified tidal prism method, or

one-dimensional advection-dispersion equations. For

partially mixed and stratified estuaries, WQAM far field

analysis uses Pritchard’s two-dimensional box model

approach, which represents the estuary as a series of

longitudinal segments with a surface and a bottom

layer. The analysis is performed by solving a system of

simultaneous linear equations for pollutant concentrations in each layer. WQAM consists of a number of

individual analyses, listed in Table 3-4 (Mills et al. 1985).

The document is available from the Center for Exposure

Assessment Modeling in Athens, Georgia.

3.3.2.2. Simplified Estuarine Model

SEM is a one-dimensional steady state desktop model

capable of simulating water quality in tidal rivers and

non-stratified estuaries (Hydroscience 1971). Coupled

BOD-DO reactions, arbitrary conservative substances,

and uncoupled nonconservatives with first order decay

(nutrients and coliforms) are represented in SEM. The

model is based on user-specified hydraulics that consider only longitudinal variations and handle only point

source inputs. Advection is represented in the form of

freshwater flow velocity and dispersion in the form of a

Calculations Methods Type of Estuary

Estuarine Classification * Hansen & Rattray 1 D/ 2 D

* Flow ratio 1 D/ 2 D

Flushing Time * Fraction of freshwater 1 D/ 2 D

* Modified tidal prism 1 D

Pollutant Distribution * Fraction of freshwater (conservative pollutants+) 1 D

* Modified tidal prism (conservative or first-order decay

pollutants)

1 D

* Dispersion-advection equations (conservative, first-order

decay pollutants+ and dissolved oxygen)

1 D

* Pritchard’s Box Model (conservative pollutants+) 2 D

* Initial dilution 1 D/ 2 D

* Pollutant concentration at completion of initial dilution

(conservative pollutants+, pH, dissolved oxygen)

1 D/ 2 D

* Farfield distribution (conservative and first-order pollutants+,

and dissolved oxygen)

2 D

Thermal Pollution * ∆ T of water passing through condenser N/A

* Maximum discharge temperature N/A

* Thermal block criterion 1 D/ 2 D

* Surface area criterion 1 D/ 2 D

* Surface temperature criterion 1 D/ 2 D

Turbidity * Turbidity at completion of initial dilution 1 D/2 D

* Suspended solids at the completion of iniitial dilution 1 D/ 2 D

* Light attenuation and turbidity relationship 1 D/ 2 D

* Secchi disk and turbidity relationship 1 D/ 2 D

Sedimentation * Description of sediment movement 1 D/ 2 D

* Settling velocity determination 1 D/ 2 D

* Null zone calculations 2 D

* One dimensional (1D) means a vertically well-mixed system.

A two dimensional (2 D) estuary is vertically stratified.

+ These methods apply to either conventional or toxic pollutants

Table 3-4. Summary of Methodology for Estuarine Water Quality Assessment

3-14
dispersion coefficient that accounts for the mixing and

translation of the tides.

SEM uses a synthetic parameter called the estuary

number (O’Connor, 1960) to determine the relative

magnitude of advection and dispersion at a given

location and to characterize the reach as either tidal

river or estuarine segment. The estuarine number (N)

is calculated from the values of the dispersion coefficient (E), the freshwater flow velocity (V) and the

deoxygenation coefficient (Kd). If the estuarine number

(N=KdE/V2) is less than 10, the reach is considered a

tidal river and initial dilution is calculated using freshwater inflow and the effects of tidal dispersion. Above

the breakpoint of 10, the reach is considered to behave

in a purely estuarine fashion, and the initial dilution

neglects freshwater inflow.

3.3.3. Level II Models

Level II includes computerized steady state and tidally

averaged simulation models that generally use a box

or compartment-type network. Steady state models

are difficult to calibrate in situations where hydrodynamics and pollutant releases are rapidly varying.

Consequently, these models are less appropriate

when waste load, river inflow, or tidal range vary

appreciably with a period close to the flushing time of

the waterbody.

Both tidally averaged and steady state models use a

dispersion coefficient calibrated from survey data. The

network and time step used by these models add

“numerical dispersion” to the calculations, which tends

to spread out concentration profiles in a similar manner

as dispersive mixing processes. Consequently, calibrated dispersion coefficients apply to the specific

network and situation monitored; they cannot be extrapolated to major modifications in estuary shape,

tidal volume, or river discharge.

A recent modeling strategy is to drive a Level II compartment model that has been configured in two or

three dimensions with tidal-averaged or steady flows

and volumes from a 2-d or 3-d hydrodynamic model.

This strategy is briefly discussed under Level IV models. A variation of this strategy is to use compartment

models with net advective flows calculated from measured vertical and longitudinal salinity distributions. An

iterative calculation has been published by Lung and

O’Connor (1984) and Lung (1986) for two-dimensional

estuaries characterized by a horizontal seaward velocity in the upper layer and a net landward velocity in the

lower layer. This analysis gives analytical solutions to

the horizontal and vertical tidally-averaged velocities,

as well as values of vertical eddy viscosity. This analysis has been applied to the Sacramento-San Joaquin

Delta, the James River Estuary, the Patuxent River

Estuary, and the Hudson River Estuary.

The Level II models supported by CEAM are QUAL2E

and the Water Quality Analysis Simulation Program

(WASP4), with its associated toxic chemical and eutrophication programs TOXI4 and EUTRO4. Other models

described here include HAR03, FEDBAK03, and AUTOQUAL.

3.3.3.1. QUAL2E

QUAL2E is a steady state one-dimensional model designed for simulating conventional pollutants in streams

and well-mixed lakes. It has been applied to tidal rivers

with minor adaptations to the hydraulic geometry and

dispersion functions. Water quality variables simulated

include conservative substances, temperature, bacteria, BOD, DO, ammonia, nitrite, nitrate, and organic

nitrogen, phosphate and organic phosphorus, and algae. QUAL2E is widely used for stream waste load

allocations and discharge permit determinations in the

United States and other countries. It has a 15-year

history of application and is a proven, effective analysis

tool. QUAL2E Version 3 incorporates several uncertainty analysis techniques useful in risk assessment.

This model can be obtained from the Center for Exposure Assessment Modeling, Athens, Georgia (requires

4 diskettes).

3.3.3.2. WASP4

WASP4 is a general, multi-dimensional model that utilizes compartment modeling techniques (DiToro et al.

1981; Ambrose et al. 1987). Operated in either the

quasidynamic or steady state mode, the user must

supply initial segment volumes, network flow fields, and

inflow time functions. The user also must calibrate dispersion coefficients between compartments. Depending

on the process model with which it is linked, WASP4 has

the capability of simulating a range of conventional and

toxic pollutants. Problems that have been studied using

WASP4 include BOD, DO dynamics, nutrients and eutrophication, bacterial contamination, and toxic chemical

movement (DiToro, 1981). WASP4, along with the associated programs TOXI4, EUTRO4, and DYNHYD4,

can be obtained from the Center for Exposure Assessment Modeling, Athens, Georgia (requires 3 diskettes).

A. TOXI4

TOXI4 is a version of WASP4 that is designed to simulate organic chemicals and heavy metals (Ambrose et

al. 1987). TOXI4 was created by adapting the kinetic

structure of EXAMS-II to the transport framework of

WASP4 and adding sediment balance algorithms. It can

simulate up to three chemicals and three sediment

3-15
classes. In addition to segment volumes, flows, and

dispersive exchanges, the user must supply sediment

deposition and scour rates, bed sediment velocity,

water column/sediment exchange coefficients, and

sediment/pore water exchange coefficients.

In TOXI4 the total transformation rate of an organic

chemical is based on the simple addition of the rate

constants for individual photolysis, hydrolysis, biolysis,

and oxidation reactions. These rate constants may

either be specified by the user or calculated internally

from second order rate constants and such environmental conditions as light intensity, pH, bacteria, oxidants, depth, velocity, and wind speed. Internal

transport and export of organic chemicals occur via

advective and dispersive movement of dissolved, sediment-sorbed, and biosorbed materials, and by volatilization losses at the air-water interface. Internal

transport and export of heavy metals occur via advective and dispersive movement of dissolved, sedimentsorbed, and biosorbed materials. Sorption of both

organic chemicals and heavy metals on sediments and

biomass is calculated assuming local equilibrium using

a constant partition coefficient and spatially varying

environmental organic carbon fractions. TOXI4 has

the capability of simulating up to two daughter products

of organic chemical transformations. Exchange between the water column and the bed can occur by

settling or resuspension of particulates, diffusion of

dissolved pollutants between the water column and

pore water, direct adsorption/ desorption between the

water column and bed, and percolation or infiltration.

Within the bed, a pollutant can move vertically by

diffusion, turnover, percolation and burial, and horizontally with bed load transport.

B. EUTRO4

EUTRO4 is a version of WASP4 that is designed to

simulate conventional pollutants. EUTRO4 combines

a kinetic structure adapted from the Potomac Eutrophication Model with the WASP transport structure. EUTRO4 predicts DO, carbonaceous BOD,

phytoplankton carbon and chlorophyll a, ammonia,

nitrate, organic nitrogen, organic phosphorus, and orthophosphate in the water column and, if specified, the

underlying bed. In addition to segment volumes, flows,

and dispersive exchanges, the user must supply deposition and resuspension velocities for organic solids,

inorganic solids, and phytoplankton. The fraction of

each water quality variable associated with these solids also must be given. Rate constants and half-saturation coefficients for the various biochemical

transformation reactions must be specified by the user.

Finally, the time and/or space variable environmental

forcing functions, such as light intensity, light extinction, wind speed, cloud cover, temperature, and benthic

fluxes must be input.

3.3.3.3. HAR03

HAR03 is a steady state, multi-dimensional model that

utilizes compartment modeling techniques (Chapra and

Nossa 1974). An orthogonal system of segmentation is

used with each segment having up to six interfaces. The

model includes the effect of net advection and dispersive tidal exchange. HARO3 models the BOD-DO deficit

system as a coupled reaction with first order decay of

BOD. With minor modifications, the program may also

be used to model variables analogous to the BOD-DO

system such as ammonia-nitrate. Zero order net photosynthetic and benthic oxygen demands can be usersupplied to the model and used in the DO balance.

3.3.3.4. FEDBAK03

FEDBAK03 is a steady state, multi-dimensional model

that utilizes compartment modeling techniques (Nossa

1978). Each estuarine segment may have up to six

interfaces. The model simulates net advection and dispersive tidal exchange. FEDBAK03 is written in general

form so that it is applicable for any substances that

undergo consecutive first order reactions with feedback.

The model is thus capable of simulating nitrification and

associated DO deficits as well as BOD-DO reactions.

The program can be modified to allow for the input of net

photosynthetic and benthic oxygen demands.

3.3.3.5. AUTOQUAL

AUTOQUAL and a later update AUTOQD are steady

state and quasidynamic models for simulating conventional pollutants in streams and estuaries (Crim and

Lovelace 1973, Lovelace 1975). Transport is calculated

from user-specified flow and dispersion. Water quality

variables simulated include carbonaceous BOD, nitrogenous oxygen demand, DO, total phosphorus, and

total nitrogen.

3.3.4. Level III Models

Level III includes computerized 1-d and quasi 2-d models that simulate variations in tidal height and velocity

throughout each tidal cycle. Level III models are generally composed of separate but compatible hydrodynamic and water quality models. These two models are

run sequentially, and the output of the hydrodynamic

model becomes part of the input to the water quality

model. Level III models enable the characterization of

phenomena rapidly varying within each tidal cycle, such

as pollutant spills, stormwater runoff, and batch discharges. Level III models also are

3-16
deemed appropriate for systems where the tidal

boundary impact, as a function of the hydrodynamics

and water quality, is important to the modeled system

within a tidal period.

The application of tidally varying (intratidal) models has

found most use in the analysis of short-term events, in

which the model simulates a period of time from one

tidal cycle to a month. Some seasonal simulations

have also been run. In most cases, the hydrodynamic

model must be run for several tidal cycles before an

actual event can be simulated. This will dampen out

any errors in the initial conditions and achieve stability

in the hydrodynamic simulation. Following this initial

period, the model will simulate a cyclical steady-state

in which the tidal characteristics are repeated for subsequent tidal periods. This approach can be applied

when a particular design tide is used to simulate water

quality. In this case, the hydrodynamic model is run

and the cyclical steady state output saved as input to

the water quality model. By running the two models in

this fashion, multiple cases can be examined with the

water quality model without the need to rerun the

hydrodynamic model.

For simulating storm events where both loads and

flows are rapidly varying, the hydrodynamic model is

run for the entire simulation period. The first step is to

run the hydrodynamic model to steady-state for the

nonstorm period to obtain initial conditions for the

storm simulation. The storm flows are specified as

input to the hydrodynamic model, which must be run

for a sufficient number of tidal cycles after the storm

event to simulate the water quality response throughout the estuary. The water quality model, using the

pollutant loads from an input file and the flows from the

hydrodynamic model, simulates the same period

(number of tidal cycles) as the hydrodynamic model.

Although the storm may only last a few hours, the

actual simulation time may be considerably longer

(days or weeks) in order to characterize the full response of the system to the event.

In using Level III models, one must decide whether a

simple 1-d link-node longitudinal system is sufficient,

or whether a quasi 2-d model with branching networks

or triangular/rectangular configuration is required to

model the longitudinal and lateral variations in the

estuary. For estuaries with channels longer than their

width and which are reasonably well mixed across their

width, a 1-d model may be chosen. If large differences

exist in water quality from one side of an estuary to the

other, then a quasi 2-d model would be appropriate.

The length of model segments or links will depend on

the resolution required in the study, as discussed in

Section 2.3.3. The length and position of segments

depends on the physical properties of the estuary. Homogeneity of physical characteristics should be the

basis for defining segments. Where bends, constrictions, or other changes occur, smaller segments are

generally defined to improve resolution.

In their treatment of conventional pollutants, Level III

models deal mainly with biochemical processes. All

Level III models considered here can simulate simple

BOD-DO interactions. Most of these models also are

formulated to simulate the reactions and interactions of

organic phosphorus and orthophosphorus; organic nitrogen, ammonia, nitrite and nitrate; algal growth and

respiration; and DO. These models also include settling

rates and benthic flux rates for several different constituents such as phosphorus, nitrogen and sediment oxygen demand. Only one model is designed to simulate

the physiochemical processes affecting organic chemicals and metals.

The Level III model supported by CEAM is the Water

Quality Analysis Simulation Program (WASP4), with its

associated hydrodynamic program DYNHYD4 and its

toxic chemical and eutrophication programs TOXI4 and

EUTRO4. Other models described here include the

Dynamic Estuary Model, EXPLORE-1, and the MIT

Dynamic Network Model.

3.3.4.1. WASP4

The Water Quality Analysis Simulation program,

WASP4, is a general multi-dimensional model that uses

compartment modeling techniques (DiToro et al. 1981,

Ambrose et al. 1987). Version 4 may be operated in the

tidal dynamic mode through linkage with the associated

hydrodynamic model DYNHYD4. DYNHYD4 is a linknode model that may be driven by either constantly

repetitive or variable tides. Unsteady inflows may be

specified, as well as wind that varies in speed and

direction. DYNHYD4 produces an output file of flows

and volumes that can be read by WASP4 during the

water quality simulation.

Two water quality programs accompany WASP4.

TOXI4 simulates organic chemicals, metals, and sediment in the water column and underlying bed. EUTRO4

simulates DO, carbonaceous BOD, phytoplankton carbon, chlorophyll a, ammonia, nitrate, organic nitrogen,

organic phosphorus, and orthophosphate in the water

column and, if specified, the underlying bed. These

programs are described more fully in Section 3.3.3.3.

WASP4, along with the associated programs TOXI4,

EUTRO4, and DYNHYD4 can be obtained from the

Center for Exposure Assessment Modeling, Athens,

Georgia (requires 3 diskettes).

3.3.4.2. Dynamic Estuary Model, DEM

3-17
DEM is a quasi 2-d model that represents tidal flow in

the lateral and longitudinal directions with a branching

link-node network (Feigner and Harris 1970). Two

versions of the hydrodynamic component of DEM exist. One version is limited to steady inflows and constantly repetitive tide. The steady inflow version cannot

explicitly handle short-term stochastic transients such

as wind stress or large storm flushing and has difficulty

in predicting long-term patterns such as the 2-week

spring-neap-tide cycle or the seasonal freshwater inflow pattern. Consequently, this version is most reliable when predicting high and low values for diurnal or

tidal cycles, or both, averaged over a relatively steady

2-week period (Ambrose and Roesch, 1982). Real

time simulations of water quality are possible with the

steady inflow version of DEM, but with some inaccuracies. Newer hydrodynamic versions of the model can

handle variable inflows and can thus generate a more

accurate real time prediction of water quality.

Several water quality submodels also have been used

with DEM. All versions include nutrient modeling and

algal growth, photosynthesis, and respiration. The following is a brief description of the versions of DEM

currently available:

— DEM, Chen-Orlob version, is the most comprehensive version of the model currently available (Chen and

Orlob 1972). The model has the capability of representing 22 coupled biotic and abiotic constituents including: temperature, pesticides, heavy metals,

CBOD, DO, phosphate, ammonia, nitrite, nitrate, total

dissolved solids, alkalinity, pH, carbon dioxide, phytoplankton, zooplankton, fish, benthic animals, suspended detritus, and sediment detritus.

— DEM, Pearl Harbor version, is limited to steady

inflows and constantly repetitive tide (Genet et al.

1974). It incorporates the heat budget terms of the

Tidal Temperature Model and simulates temperature,

DO, CBOD, ammonia, nitrite, nitrate, total nitrogen,

phosphate, chlorophyll-a, and total dissolved solids.

— DEM, Potomac version, is documented as handling

only steady inflows and constantly repetitive tide, but

a newer version is available that is capable of handling

variable inflows (Roesch et al. 1979). The model simulates CBOD, DO, ammonia, nitrate, phosphate, and

chlorophyll-a.

3.3.4.3. MIT Dynamic Network Model, MIT-DNM

MIT-DNM is a one-dimensional model that uses a finite

element, branching network to simulate the flow regime of an estuary with unsteady tidal elevation and

upstream flow (Harleman et al. 1977). The model was

originally developed for aerobic, nitrogen limited systems and includes detailed simulation of the nitrogen

cycle as well as temperature, CBOD, DO, and fecal

coliforms. Two versions of the model are currently available, and are described below.

— MIT-DNM, Potomac version, includes nutrient modeling and algal growth, photosynthesis, and respiration

and represents bacterially mediated reactions for ammonia, nitrite, nitrate, phytoplankton-N, zooplankton-N,

particulate organic N, and dissolved organic N (Najarian

and Harleman 1975).

— MIT-DNM, St. Lawrence version, includes nutrient

modeling and algal growth, photosynthesis, and respiration, and represents CBOD, DO, inorganic phosphorus, organic phosphorus, inorganic nitrogen, organic

nitrogen, phytoplankton, and zooplankton (Thatcher et

al. 1975).

3.3.4.4. EXPLORE-I

EXPLORE-I is a quasi 2-d model that represents tidal

flow in the lateral and longitudinal directions with a

branching link-node network (Chen and Orlob 1972).

The full 1-d hydrodynamic equations are solved, but the

water quality model excludes dispersive transport. EXPLORE-I has the capability of simulating DO, conservatives, toxic pollutants, coliforms, sedimentary

phosphorus, soluble phosphorus, organic phosphorus,

organic nitrogen, ammonia, nitrite, nitrate, total organic

carbon, refractory organic carbon, phytoplankton,

zooplankton, CBOD, and benthic BOD. Sedimentation

and scour of organic matter is represented in the model

as well as algal growth, photosynthesis, and respiration.

3.3.5. Level IV Models

Level IV includes a variety of computerized 2-d and 3-d

intratidal models. These may be divided into three broad

categories: 2-d vertically averaged (x-y), 2-d laterally

averaged (x-z), and 3-d. While they are not routinely

used in most WLAs, they are now finding use by experts

in special studies.

Although many 2-d vertically averaged, finite-difference

or finite-element hydrodynamic programs exist, relatively few contain a water quality program that simulates

constituents other than salinity and/or temperature.

Likewise, a number of 2-d, laterally averaged models

(longitudinal and vertical transport simulations) treat

mass transport of salt and temperature but very few

include nonconservative constituents or water quality

routines. Models in this category simu3-18
late vertical stratification but neglect lateral effects,

including Coriolis effects. Last is the category of 3-d,

finite-difference and finite-element models. These

models allow all physical processes to be included,

although many were developed for systems of constant salinity (lakes or oceans). A summary of 3-d

marine and estuarine models is provided in Nihoul and

Jamarf (1987).

A Level IV model would be used when finer spatial

definition is required than is provided by a Level III

model and when finer temporal definition is required

than is provided by a Level II model that has been

configured in two or three dimensions and driven by

the averaged hydrodynamic output of a Level IV hydrodynamic model. In particular, these models will be

selected for investigations where diurnal and tidal fluctuations are of prime importance to the study.

The quasi 2-d Level III model is applicable where there

is a need to project lateral differences in water quality

for wide estuaries. The quasi 2-d model, however,

which uses 1-d equations of motion applied to the

channels, cannot estimate longitudinal and lateral dispersion as effectively as the true 2-d model of Level

IV. Although the quasi 2-d and the true 2-d model both

assume that the estuary is vertically mixed, the true

2-d model can effectively represent lateral variation in

velocity and constituent concentration for estuaries

with nonuniform cross sections, branching channels,

and embayments. The 2-d model also can account for

the effect of Coriolis forces and wind circulation.

For a wide, stratified estuary the application of a 3-d

model would be appropriate for intratidal simulations.

There are no well documented intratidal 3-d models

with coupled constituent interactions applicable to tidally driven estuaries. Fully 3-d models that can predict

longitudinal, lateral, and vertical transport are the most

complex and expensive to set up and run. Due to their

cost and complexity, these models have not been

widely used. For experts with access to supercomputers, these models are feasible for special applications.

A recent modeling strategy is to drive a Level II compartment model that has been configured in two or

three dimensions with either averaged or tidally varying flows and volumes from a 2-d or 3-d hydrodynamic

model. This strategy attempts to combine the transport

rigor of Level IV models with the convenience, flexibility, and cost efficiency of compartment models. A

recent and currently ongoing example is a study of the

Chesapeake Bay. There, the averaged output of a

finite difference stretch coordinate hydrodynamic

model was linked to a specially adapted compartment

model, AESOP and run to steady state (HydroQual,

1987). When running the water quality model at different time steps or on a coarser grid, the user must still

calibrate horizontal and vertical dispersion coefficients

to observed salinity or tracer data.

The criteria for the specification of time and space scales

for Level IV models are similar to those discussed for

Level III with the additional need to consider a vertical

scale for a 3-d model application. For 2-d and 3-d

models, the time step would be calculated as a function

not only of the longitudinal space steps and longitudinal

dispersion coefficient (as described by Equations 3-14

and 3-15), but also as a function of the lateral and

vertical space steps and dispersion coefficients.

At present, no Level IV model is supported by CEAM. A

variety of these models currently being used is described below.

3.3.5.1. H.S. Chen Model

The H.S. Chen model is a real time 2-d (x-y) model that

simulates conventional pollutants (Chen, 1978). The

hydrodynamic submodel considers inertial forces, convective forces, hydrostatic pressure, wind forces, Coriolis forces, bottom friction, and internal water column

forces due to eddies. The parameters simulated by the

model include the following: conservatives, coliforms,

chlorophyll-a, organic nitrogen, ammonia, nitrite, nitrate,

organic phosphorus, inorganic phosphorus, CBOD, and

DO. Algal growth, photosynthesis, and respiration are

represented in the model as well as benthic oxygen

demand and bottom releases of ammonia and inorganic

phosphorus. Equations are solved by a finite element

technique.

3.3.5.2. FETRA

FETRA is a real time, 2-d (x-y) water quality model that

utilizes a finite element solution technique to simulate

toxic pollutants (Onishi 1981). Hydrodynamic data must

be supplied by a separate model such as EXPLORE-I.

FETRA consists of three submodels linked to simulate

the transport and transformation of sediments and contaminants by the processes of advection, diffusion/ dispersion, adsorption/ desorption, and degradation/

decay. The sediment transport submodel simulates advection and dispersion of sediments, fall velocity and

cohesiveness, and deposition or erosion for the bed.

Three sediment sizes are modeled, and calculations are

made of bed elevation changes and the distribution of

sediment sizes within the bed. The dissolved contaminant transport submodel predicts advection and diffusion/dispersion of dissolved pollutants, adsorption by

both moving and stationary sediments, desorption from

sediments, and degradation or radionuclide decay. The

particulate contaminant

3-19
transport submodel includes advection and dispersion

of sediment-attached contaminants, adsorption/desorption with sediment, degradation or radionuclide decay; and settling/resuspension.

3.3.5.3. TABS-2

TABS-2 is a generalized numerical modeling system

for open-channel flows, sedimentation, and constituent transport developed and supported by the U.S.

Army Engineers Waterways Experiment Station, Hydraulics Laboratory (Thomas and McAnally, 1985). It

consists of more than 40 computer programs to perform modeling and related tasks. The major modeling

components—RMA-2V, STUDH, and RMA-4—calculate two-dimensional, depth-averaged (x-y) flows,

sedimentation, and dispersive transport, respectively.

The other programs in the system perform digitizing,

mesh generation, data management, graphical display, output analysis, and model interfacing tasks.

Utilities include file management and automatic generation of computer job control instructions.

TABS-2 has been applied to a variety of waterways,

including rivers, estuaries, bays, and marshes. It is

designed for use by engineers and scientists who may

not have a rigorous computer background.

3.3.5.4. WIFM-SAL

WIFM-SAL is a two dimensional depth-averaged (x-y)

finite difference model that generates time-varying

water surface evaluations, velocities, and constituent

fields over a space staggered grid (Schmalz, 1985).

This model was developed by the U.S. Army Engineers, Waterways Experiment Station. Units of measure are expressed in the English system

(slug-ft-second). Results computed on a global grid

may be employed as boundary conditions on more

spatially limited refined grid concentrated around the

area of interest. In addition, the user may select either

of two distinct transport schemes. Scheme 1 is a

flux-corrected transport scheme capable of resolving

sharp front without oscillation. Scheme 2 is a full, three

time level scheme directly compatible with the three

time level hydrodynamics. The telescoping grid capability in conjunction with the user selectable constituent

transport scheme is a powerful concept in practical

transport problem solving.

3.3.5.5. FCSTM-H

FCSTM-H, by Earl Hayter at Clemson University, is a

finite element modeling system for simulating two-dimensional depth-averaged (x-y) surface water flow

and cohesive sediment transport consisting of three

separate computer programs (Hayter, 1987). FEGRD

is a two-dimensional finite element grid generation/modification program. FLWM-H is a hydrodynamic

model that solves the depth-averaged equations of motion and continuity for model horizontal velocity components and flow depths. The effects of bottom, internal

and surface shear stresses and the Coriolis force are

represented in the equations of motion. CSTM-H is a

cohesive sediment transport model that solves the advection-dispersion equation for nodal depth-averaged

concentrations of suspended sediment and bed surface

elevations. The processes of erosion, dispersion, aggregation, deposition and consolidation are simulated. A

layered bed model is used in simulating bed formation,

subsequent consolidation and erosion. An example

problem, including input and output data, is included.

FLWM-H and CSTM-H are semi-coupled in the following

manner. First, the flow field is calculated for the current

time step using FLWM-H. Second, the predicted flow

field is used in CSTM-H to calculate the transport of

cohesive sediments during the same time step. The flow

field may be updated due to erosion or deposition and/or

unsteady boundary conditions.

The following sediment related properties are calculated

for each element: sediment bed structure (bed density

and shear strength profiles, bed thickness and elevation), net change in bed elevation over a given interval

of time (e.g. over a certain number of tidal cycles), net

vertical mass flux of sediment over an interval of time,

average amount of time sediment particles are in suspension, and the downward flux of sediment onto the

bed. These parameters are essential in estimating the

bed-water exchange of chemicals adsorbed onto cohesive sediments.

The FCSTM-H modeling system may be used to predict

both short term (less than one year) and long term (one

year and longer) scour and/or sedimentation rates in

vertically well mixed bodies of water. Because of the

iterative routine used in the hydrodynamic model, long

term simulations will require large (order of magnitude

of one or more hours) CPU times, even on mainframe

computers. Limited computer resources and budgetary

constraints will often require extrapolation of short term

simulations.

3.3.5.6. CE-QUAL-W2

CE-QUAL-W2 is a dynamic 2-d (x-z) model developed

for stratified waterbodies (Env. and Hyd. Laboratories

1986). This is a Corps of Engineers modification of the

Laterally Averaged Reservoir Model (Edinger and

Buchak 1983, Buchak and Edinger, 1984a, 1984b).

CE-QUAL-W2 consists of directly coupled hydrodynamic and water quality transport models. Hydrodynamic computations are influenced by vari3-20
able water density caused by temperature, salinity,

and dissolved and suspended solids. Developed for

reservoirs and narrow, stratified estuaries, CE-QUALW2 can handle a branched and/or looped system with

flow and/or head boundary conditions. With two dimensions depicted, point and non-point loadings can

be spatially distributed. Relative to other 2-d models,

CE-QUAL-W2 is efficient and cost effective to use.

In addition to temperature, CE-QUAL-W2 simulates as

many as 20 other water quality variables. Primary

physical processes included are surface heat transfer,

shortwave and longwave radiation and penetration,

convective mixing, wind and flow induced mixing, entrainment of ambient water by pumped-storage inflows, inflow density current placement, selective

withdrawal, and density stratification as impacted by

temperature and dissolved and suspended solids. Major chemical and biological processes in CE-QUAL-W2

include: the effects on DO of atmospheric exchange,

photosynthesis, respiration, organic matter decomposition, nitrification, and chemical oxidation of reduced

substances; uptake, excretion, and regeneration of

phosphorus and nitrogen and nitrification-denitrification under aerobic and anaerobic conditions; carbon

cycling and alkalinity-pH-CO2 interactions; trophic relationships for total phytoplankton; accumulation and

decomposition of detritus and organic sediment; and

coliform bacteria mortality.

3.3.5.7. EHSM3D

The EHSM3D model was developed by Y. P. Sheng

at University of Florida calculates three-dimensional

unsteady currents and sediment dispersion in estuaries and lakes (Sheng, et al., 1987, Sheng, 1989).

Given proper boundary and initial conditions, the code

can calculate the three-dimensional time-dependent

distributions of flow, velocity, temperature, salinity,

suspended sediment concentration, density, and dissolved species concentration. The status of the sediment dispersion model is preliminary since research is

continuing with the development and validation of this

portion of the model.

3.3.5.8. John Paul Hydrodynamic Model

This numerical model, developed by John Paul and

colleagues at the U.S. EPA, is capable of realistically

describing the hydrodynamics in lakes, embayments,

nearshore marine coastal areas, and river and thermal

outfall plumes (Paul and Nocito, 1989). The model is

time-dependent, three dimensional, and variable density. Both rigid-lid and free-surface flows can be determined. The main assumptions used in the

development of the model include hydrostatic pressure variation, Boussinesq approximation, and eddy

coefficients to account for turbulence. A new solution

procedure, which is a modification of the simplified

marker and cell method, is used. The procedure permits

selected terms in the equations to be treated implicitly

in time. A compatible 3-D, time dependent numerical

physical transport model is available for use with this

model.

3.3.6. Summary of Model Capabilities

The important features of the models selected for discussion in this manual are summarized in Tables 3-5

and 3-6. The information provided in these tables is

primarily qualitative and sufficient to determine whether

a model may be suitable for a particular application. For

complete information, the potential user must consult

the appropriate user’s manuals, the supporting agency,

and other experienced users.

Table 3-5 summarizes the basic features of the models.

The time scales are dynamic (D), quasidynamic (Q), and

steady (SS). Spatial dimensions are 1 (x), 2 (xy, xz, or

xx for link-node networks), or 3 (xyz or B, for box

models). Hydrodynamics are either input by the user (I)

or simulated (S). Solution techniques are analytical (A),

finite difference (FD) or finite element (FE). Finally,

models are implemented on mainframes (M) or personal

computers (PC).

Table 3-6 summarizes the water quality problems that

may be directly addressed by the models. All models

address salinity and bacteria either explicitly or by specifying appropriate boundaries, loads, and first order decay constants for another state variable. Sediment may

be modeled using calibrated deposition and scour velocities (1), or by using functional relationships with

shear stress and shear strength to predict these velocities (2). Dissolved oxygen may be modeled along with

total BOD (1), with CBOD, NBOD, and prescribed sediment oxygen demand (SOD) and net photosynthetic

production (2), or with CBOD nitrification, SOD, and

simulated nutrients and phytoplankton (3). Nutrient enrichment and eutrophication may be simulated using

total phytoplankton biomass (1), multiple phytoplankton

classes (2), or multiple phytoplankton and zooplankton

classes (3). Organic chemicals may be modeled with

calibrated decay rates and partition coefficients (1), with

predicted transformation rates and partition coefficients

(2), or with predicted rates and coefficients for the original chemical plus reaction products (3). Metals may be

modeled as dissolved and particulate fractions with

calibrated partition coefficients (1), or as multiple species predicted with a thermodynamic data base and

process models (2).

3-21
3.4. References

Ambrose, R.B., Najarian, T.O., Bourne, G., Thatcher,

M.L. 1981. Models for Analyzing Eutrophication in

Chesapeake Bay Watersheds: A Selection Methodology. USEPA, Office of Research and Development,

Chesapeake Bay Program, Annapolis, MD.

Ambrose, R.B. and Roesch, S.E. 1982. Dynamic

Estuary Model Performance. Journal of the Environmental Engineering Division, American Society of

Civil Engineers, 108(EE1).

Ambrose, R.B. Jr. et. al. 1987. WASP4, A General

Water Quality Model for Toxic and Conventional Pollutants, U.S. Environmental Protection Agency, Athens, Georgia.

Blumberg, A.F. 1975. A Numerical Investigation into

the Dynamics of Estuarine Circulation. Chesapeake

Bay Institute, Johns Hopkins University, Baltimore

MD. NTIS PB-248 435/OCP.

Bowie, G.L. et. al. 1985. Rates, Constants, and Kinetics Formulations in Surface Water Quality Modeling

D-dynamic x-1 dimensional I-hydrodynamics input A-analytical solution M-mainframe computers

Q-quasidynamic (tidal-averaged)xy-2 dimensional, longitudinallateralS-hydrodynamics

simulated

FD-finite difference

solution

PC-personal computers

SS-steady state xz-2 dimensional, longitudinalverticalB-compartment or bos 3D

xx-link node branching 2D

FE-finite element solution

xyz-3 dimensional

Model Time Scale Spatial Dimension Hydrodynamics Solution Tech. Computer

SEM SS x I A—

WQAM SS x I A—

HARO3 SS B I FD M

FEDBAKO3 SS B I FD M

QUAL2 SS x I FD M, PC

AUTOQUAL/QD Q x I FD M, PC

WASP4:

stand alone Q B I FD M, PC

with DYNHYD4 D xx S FD M, PC

DEM D xx S FD M

EXPLORE-I D xx S FD M

MIT-DNM D x S FD M

Chen D xy S FE M

FETRA D xy I FE M

CE-QUAL-W2 D xz S FD M

TABS-2 D xy S FE M

WIFM-SAL D xy S FE M

FCSTM-H D xy S FE M

EHSM3D D xyz S FD M

J. PAUL D xyz S FD M

Table 3-5. Basic Model Features

Model Salinity

Bacteria

SedimentDO EutrophicationOrg.

Chem.

Metals

SEM X 2

WQAM X 1 2 1

HARO3 X 2

FEDBAKO3 X 2

QUAL2 X 3 1

AUTOQUAL X 2

WASP4:

EUTRO4 X 3 1

TOXI4 X 1 1,2,3 1

DEM X 3 1

EXPLORE-I X 3 3

MIT-DNM X 3 1

Chen X 3 1

FETRA X 2 1

CE-QUAL-W2 X 1 3 1

TABS-2 X 2

WIFM-SAL X

FCSTM-H X 2

EHSM3D X 2

J.PAUL X

Table 3-6. Water Quality Problems Addressed

3-22
(second ed.), U.S. Environmental Protection Agency,

Athens, Ga. EPA/600/3-85/040.

Buchak, E.M. and Edinger, J.E. 1984a. Generalized,

Longitudinal-vertical Hydrodynamics and Transport:

Development, Programming And Applications, Document No. 84-18-R, U.S. Army Corps of Engineers,

WES, Vicksburg, Mississippi.

Buchak, E. M. and Edinger, J.E. 1984b. Simulation of

a Density Underflow into Wellington Reservoir using

Longitudinal-vertical Numerical Hydrodynamics,

Document No. 84-18-R, U.S. Army Corps of Engineers, WES, Vicksburg, Miss., March.

Chapra, S. and Nossa, G.A. October, 1974. Documentation for HARO3, 2nd Edition. USEPA Region II, New

York, NY.

Chen, H.S., August 1978. A Mathematical Model for

Water Quality Analysis. Proceedings of ASCE Hydraulics Division Specialty Conference on Verification of

Mathematical and Physical Models in Hydraulic Engineering, American Society of Civil Engineers, New

York, NY.

Chen, C.W. and Orlob, G.T. December, 1972. Ecological Simulation for Aquatic Environments. NTIS Doc.

PB 218828, Water Resources Engineers, Inc., Walnut

Creek, California, for Office of Water Resources Research, U.S. Department of the Interior, Washington,

D.C.

Crim, R. and Lovelace, N.L. 1973. AUTO_QUAL Modeling System. U.S. Environmental Protection Agency,

Washington, D.C. EPA-440/9-73-004.

Di Toro, D.M., 1986. A Diagenetic Oxygen Equivalents

Model of Sediment Oxygen Demand, in Sediment

Oxygen Demand; Processes, Modeling, and Measurement, editor K. J. Hatcher, Univ. of Georgia, Athens,

GA, pp 171-208.

Di Toro, D.M., Fitzpatrick, J.J., and Thomann, R.V.

1981. Water Quality Analysis Simulation Program

(WASP) and Model Verification Program (MVP)-Documentation. Hydroscience, Inc., Westwood, New Jersey, for U.S. Environmental Protection Agency,

Duluth, MI.

Dyer, K.R. 1973. Estuaries: A Physical Introduction.

John Wiley and Sons, New York.

Edinger, J.E. and Buchak, E.M.1983. Developments

in LARM2: A Longitudinal-vertical, Time-varying Hydrodynamic Reservoir Model, Technical Report E-83-

1, USAE Waterways Experiment Station, Vicksburg,

MS.

Elliott, A.J. 1976. A Numerical Model of the Internal

Circulation in a Branching Tidal Estuary. Chesapeake

Bay Institute, Johns Hopkins University, Baltimore, MD,

Special Report 54.

Environmental and Hydraulics Laboratories. 1986. CEQUAL-W2, A Numerical Two-Dimensional Model of Hydrodynamics and Water Quality, User’s Manual.

Instruction Report E-86-5, USACE Waterways Experiment Station, Vicksburg, MS.

Feigner, K.D. and Harris, H.S. July, 1970. Documentation Report -FWQA Dynamic Estuary Model. Prepared

for USEPA, Water Quality Office, Washington, D.C.

NTIS No. PB 197 103.

Fisher, J.S., Ditmars, J.D., and Ippen, A.T. 1972. Mathematical Simulation of Tidal Time-Averages of Salinity

and Velocity Profiles in Estuaries. Ralph M. Parsons

Laboratory, Massachusetts Institute of Technology,

Cambridge, MA, MITSG-772-11, NOAA-72110204.

Fischer, H.B. et al. 1978. Mixing in Inland and Coastal

Waters. Academic Press, N.Y. 483 pp.

Genet, L.A., Smith, D.J. and Sonnen, M.B. 1974. Computer Program Documentation for the Dynamic Estuary

Model. Water Resources Engineers, Inc., Walnut Creek,

California for U.S. Environmental Protection Agency,

Systems Development Branch, Washington, D.C.

Hamilton, P. 1975. A Numerical Model of the Vertical

Circulation of Tidal Estuaries and its Application to the

Rotterdam Waterway. Geophys. J. R. Astr. Soc., 40:1-

21.

Hansen, D.V. and Rattray, M. 1966. New Dimensions in

Estuarine Classification. Limnology and Oceanography

11(3):319-316.

Harleman, D.R., Daily, J.E., Thatcher, M.L., Najarian,

T.O., Brocard, D.N., and Ferrara, R.A. January, 1977.

User’s Manual for the M.I.T. Transient Water Quality

Network Model. EPA-600/3-77-010. USEPA Environmental Research Lab, Corvallis, Oregon.

Hayter, E.J. 1987. Finite Element Hydrodynamic and

Cohesive Sediment Transport Modeling System. Dept.

of Civil Engineering, Clemson University, Clemson, SC.

Hinwood, J.B. and Wallis, I.G. October 1975. Classification of Models of Tidal Waters, Journal of the Hydraulics

Division, Proceedings of the American Society of Civil

Engineers, 101(HY10).

3-23
Holley, E. and Jirka, G. 1986. Mixing in Rivers. U.S.

Army Corps of Engineers, Vicksburg, MS. COE TR-E86-11.

HydroQual, Inc. August, 1987. Steady State Coupled

Hydrodynamic/Water Quality Model of Eutrophication

and Anoxia Process in Chesapeake Bay. HydroQual,

Inc. under contract to Battelle Ocean Sciences, Duxbury, MA for U.S. Environmental Protection Agency,

Chesapeake Bay Program, Annapolis MD.

Hydroscience, Inc. March, 1971. Simplified Mathematical Modeling of Water Quality. US Government

Printing Office: 1971-44-367/392. Water Programs,

U.S. Environmental Protection Agency, Washington,

D.C.

Lovelace, N.L. 1975. AUTO-QUAL Modelling System:

Supplement I. Modification for Non-Point Source

Loadings. U.S. Environmental Protection Agency,

Washington, D.C. EPA-440/9-73-004.

Lung, W.S. 1987. Advective Acceleration and Mass

Transport in Estuaries, ASCE J. Hydraulic Engr.

112(9), 874-878.

Lung, W.S. and O’Connor, D.J. 1984. Two-Dimensional Mass Transport in Estuaries, ASCE J. Hydraulic

Engr. 110(10), 1340-1357.

Mills, W.B., Dean, J.P., Porcella, D.B., Gherini, S.A.,

Hudson, R.J.M., Frick, W.E., Rupp, G.L. and Bowel,

G.L. September, 1982. Water Quality Assessment: A

Screening Procedure for Toxic and Conventional Pollutants. EPA-600/6-82-004. USEPA Environmental

Research Lab, Athens, Georgia.

Mills, W.B., Porcella, D.B., Ungs, M.J., Gherini, S.A.,

Summers, K.V., Lingfung, M., Rupp, G.L., Bowie, G.L.,

and Haith, D.A. 1985. Water Quality Assessment: A

Screening Procedure for Toxic and Conventional Pollutants. U.S. Environmental Protection Agency, Athens, GA, EPA/600/6-85/002a,b.

Najarian, T.O. and Harleman, D.R. July, 1975. A RealTime Model of Nitrogen Cycle Dynamics in an Estuarine System. R.M. Parsons Laboratory for Water

Resources and Hydrodynamics, Massachusetts Institute of Technology.

Nihoul, J. and Jamarf, Ed. 1987. Three-Dimensional

Models of Marine and Estuarine Dynamics. Elsevier

Scientific, Amsterdam.

Nossa, G.A. November, 1978. FEDBAKO3 - Program

Documentation and Users Guide, USEPA Region II,

New York, NY.

O’Connor, D.J. and Lung, W. 1983. Suspended Solids

Analysis of Estuarine Systems. Journal of the Environmental Engineering Division, Proceedings of the American Society of Civil Engineers. 107(EE1).

Onishi, Y.1981. Sediment-Contaminant Transport

Model. Journal of the Hydraulics Division, American

Society of Civil Engineers, 107(HY9).

Paul, J.P. and Nocito, J.A. 1989. Numerical Model for

Three-Dimensional, Variable-Density Hydrodynamic

Flows: Documentation of the Computer Program. U.S.

Environmental Protection Agency, Duluth MN (in press).

Roesch, S.E., Clark, L.J., and Bray, M.M. 1979. User’s

Manual for the Dynamic (Potomac) Estuary Model.

EPA-903/9-79-001. Technical Report 63. U.S. Environmental Protection Agency, Annapolis, MD.

Schmalz, R.A. 1985. User Guide for WIFM-SAL: A

Two-Dimensional Vertically Integrated, Time-Varying

Estuarine Transport Model. U.S. Department of the

Army, Waterways Experiment Station, Corps of Engineers, Vicksburg, MS.

Sheng, Y.P. 1989. A Three-Dimensional Numerical

Model of Hydrodynamics and Sediment Dispersion. University of Florida, Gainesville, FL for U.S. Environmental

Protection Agency, Athens, GA (in press).

Sheng, Y.P., Parker, S.F., and Henn, D.S. 1987. A

Three-Dimensional Estuarine Hydrodynamic Software

Model (EHSM3D). Aeronautical Research Associates of

Princeton, Inc., Princeton, NJ, for U.S. Geological Survey, Contract 14-08-0001-21730.

Swanson, C. and Spaulding, M. March, 1983. User’s

Manual for Three Dimensional Time Dependent Numerical Dispersion Model of Upper Narragansett Bay.

Prepared for USEPA Region I, Boston, MA.

Thatcher, M.L., Pearson, H.W. and Mayor-Mora, R.E.

September, 1975. Application of a Dynamic Network

Model to Hydraulic and Water Quality Studies of the St.

Lawrence River. Presented at the Second Annual Symposium of the Waterways, Harbors and Coastal Engineering, ASCE, San Francisco, CA.

Thatcher, M.L. and Harleman, D.R.F. 1972. Prediction

of Unsteady Salinity Intrusion in Estuaries: Mathematical Model and Users Manual. Ralph M. Parsons Laboratory, Massachusetts Institute of Technology,

Cambridge, MA, Technical Report 159.

Thomas, W.A. and McAnally, W.H. Jr. 1985. User’s

Manual for the Generalized Computer Program System

- Open Channel Flow and Sedimentation TABS-2. U.S.

3-24
Department of the Army, Waterways Experiment Station, Corps of Engineers, Vicksburg, MS.

Wang, J.D. and Connor, J.J. 1975. Mathematical Modeling of Near Coastal Circulation. MIT Sea Grant Program, Massachusetts Institute of Technology,

Cambridge, MA, Report MIT-SG-75-13.

3-25

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