United States Office of Water (4305) EPA-823-R-04-002

Environmental Protection January 2004

Agency

AQUATOX (RELEASE 2)

MODELING ENVIRONMENTAL FATE

AND ECOLOGICAL EFFECTS IN

AQUATIC ECOSYSTEMS

VOLUME 2: TECHNICAL DOCUMENTATION

AQUATOX (RELEASE 2)

MODELING ENVIRONMENTAL FATE

 AND ECOLOGICAL EFFECTS

 IN AQUATIC ECOSYSTEMS

VOLUME 2: TECHNICAL DOCUMENTATION

Richard A. Park

and

Jonathan S. Clough

JANUARY 2004

U.S. ENVIRONMENTAL PROTECTION AGENCY

OFFICE OF WATER

OFFICE OF SCIENCE AND TECHNOLOGY (MAIL CODE 4305T)

WASHINGTON DC 20460
ii

DISCLAIMER

 This document has been approved for publication by the Office of Science and Technology, Office

of Water, U.S. Environmental Protection Agency. Mention of trade names, commercial products

or organizations does not imply endorsement or recommendation for use.

This document describes an aquatic ecosystem simulation model. It is not intended to serve as

guidance or regulation, nor is the use of this model in any way required. This document cannot

impose legally binding requirements on EPA, States, Tribes, or the regulated community.

ACKNOWLEDGMENTS

This model has been developed and documented by Dr. Richard A. Park of Eco Modeling

and Jonathan S. Clough of Warren Pinnacle Consulting, Inc. under subcontract to Eco Modeling.

It was funded originally with Federal funds from the U.S. Environmental Protection Agency, Office

of Science and Technology under contract number 68-C4-0051 to The Cadmus Group, Inc. 

Significant enhancements to the model and revision of the documentation has been performed under

subcontract to AQUA TERRA Consultants, Anthony Donigian, Work Assignment Manager, under

EPA Contracts 68-C-98-010 and 

68-C-01-0037.

Additional Federal funding for program development has come from the U.S. Environmental

Protection Agency, Office of Pollution Prevention and Toxics, through Purchase Orders 7W-0227-

NASA and 7W-4330-NALX to Eco Modeling and a Work Assignment to AQUA TERRA

Consultants. 

The assistance, advice, and comments of the EPA work assignment manager, Marjorie

Coombs Wellman of the Health Protection and Modeling Branch, Office of Science and Technology

have been of great value in developing this model and preparing this report. Further technical and

financial support from Donald Rodier of the Office of Pollution Prevention and Toxics and David

A. Mauriello, and Rufus Morison formerly of that Office, is gratefully acknowledged. Marietta

Echeverría, Office of Pesticide Program, contributed to the integrity of the model through her careful

analysis and comparison with EXAMS. The model underwent independent peer review by Donald

DeAngelis, Robert Pastorok, and Frieda Taub, whose diligence is greatly appreciated. 
iii

TABLE OF CONTENTS

TABLE OF CONTENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii

PREFACE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii

1 INTRODUCTION ........................................................ 1 - 1

1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 - 1

1.2 Background ...................................................... 1 - 4

1.3 What’s New . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 - 5

Enhanced Scientific Capabilities ................................... 1 - 5

Additional User Interfaces ........................................ 1 - 6

Corrected Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 - 6

2 SIMULATION MODELING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 - 1

2.1 Temporal and Spatial Resolution and Numerical Stability .................. 2 - 1

2.2 Uncertainty Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 - 3

3 PHYSICAL CHARACTERISTICS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 - 1

3.1 Morphometry .................................................... 3 - 1

Volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 - 1

Bathymetric Approximations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 - 4

Habitat Disaggregation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 - 6

3.2 Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 - 7

3.3 Washout ......................................................... 3 - 9

3.4 Stratification and Mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 - 9

3.5 Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 - 14

3.6 Light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 - 15

3.7 Wind . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 - 16

4 BIOTA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 - 1

4.1 Algae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 - 2

Light Limitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 - 5

Nutrient Limitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 - 9

Current Limitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 - 12

Adjustment for Suboptimal Temperature ........................... 4 - 12

Algal Respiration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 - 14

Photorespiration and Excretion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 - 16

Algal Mortality ............................................... 4 - 17

Sinking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 - 18

Washout and Sloughing ......................................... 4 - 19

Detrital Accumulation in Periphyton ............................... 4 - 23

Chlorophyll a ................................................. 4 - 23

4.2 Macrophytes .................................................... 4 - 24

4.3 Animals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 - 28
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Consumption, Defecation, and Predation . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 - 30

Respiration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 - 34

Excretion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 - 38

Nonpredatory Mortality ......................................... 4 - 38

Gamete Loss and Recruitment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 - 40

Washout, Drift, and Entrainment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 - 41

Vertical Migration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 - 43

Promotion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 - 44

5 REMINERALIZATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 - 1

5.1 Detritus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 - 1

Detrital Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 - 4

Colonization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 - 5

Decomposition ................................................. 5 - 7

Sedimentation and Resuspension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 - 10

5.2 Nitrogen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 - 11

Assimilation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 - 13

Nitrification and Denitrification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 - 14

5.3 Phosphorus ..................................................... 5 - 16

5.4 Dissolved Oxygen ................................................ 5 - 17

5.5 Inorganic Carbon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 - 22

6 INORGANIC SEDIMENTS ................................................. 6 - 1

6.1 Deposition and Scour of Silt and Clay ................................. 6 - 3

6.2 Scour, Deposition and Transport of Sand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 - 6

6.3 Suspended Inorganic Sediments in Standing Water . . . . . . . . . . . . . . . . . . . . . . . 6 - 8

7 TOXIC ORGANIC CHEMICALS ............................................ 7 - 1

7.1 Ionization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 - 7

7.2 Hydrolysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 - 8

7.3 Photolysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 - 10

7.4 Microbial Degradation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 - 13

7.5 Volatilization .................................................... 7 - 13

7.6 Partition Coefficients .............................................. 7 - 16

Detritus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 - 16

Algae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 - 20

Macrophytes .................................................. 7 - 21

Invertebrates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 - 21

Fish . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 - 22

7.7 Nonequilibrium Kinetics ........................................... 7 - 23

Sorption and Desorption to Detritus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 - 23

Bioaccumulation in Macrophytes and Algae ......................... 7 - 25

Macrophytes ............................................ 7 - 25

Algae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 - 27

Bioaccumulation in Animals ..................................... 7 - 28
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Gill Sorption ........................................... 7 - 29

Dietary Uptake . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 - 31

Elimination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 - 32

Biotransformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 - 33

Linkages to Detrital Compartments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 - 35

8 ECOTOXICOLOGY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 - 1

8.1 Acute Toxicity of Compounds ........................................ 8 - 1

8.2 Chronic Toxicity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 - 7

REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . R - 1

APPENDIX A. GLOSSARY OF TERMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A - 1

APPENDIX B. USER-SUPPLIED PARAMETERS AND DATA ..................... B - 1
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PREFACE

The Clean Water Act— formally the Federal Water Pollution Control Act Amendments of

1972 (Public Law 92-50), and subsequent amendments in 1977, 1979, 1980, 1981, 1983, and 1987—

calls for the identification, control, and prevention of pollution of the nation's waters. In the

National Water Quality Inventory: 2000 Report (US EPA, 2002), 40 percent of assessed river

lengths and 45 percent of assessed lake areas were impaired for one or more of their designated uses.

The most commonly reported causes of impairment in rivers and streams were pathogens, siltation,

habitat alterations, oxygen-depleting substances, nutrients, thermal modifications, metals (primarily

mercury), and flow alterations; in lakes and reservoirs the primary causes included nutrients,

metals, siltation, total dissolved solids, oxygen-depleting substances, excess algal growth and

pesticides. The most commonly reported sources of impairment were agriculture, hydrologic

modifications, habitat modification, urban runoff/storm sewers, forestry, nonpoint sources,

municipal point sources, atmospheric deposition, resource extraction and land disposal. There were

2838 fish consumption advisories, which may include outright bans, in 48 States, the District of

Columbia and American Samoa. Of these 2838 advisories, 2242 were due to mercury, with the

rest due to PCBs, chlordane, dioxin, and DDT (US EPA, 2002). States are not required to report fish

kills for the National Inventory; however, available information for 1992 indicated 1620 incidents

in 43 States, of which 930 were attributed to pollution, particularly oxygen-depleting substances,

pesticides, manure, oil and gas, chlorine, and ammonia.

New approaches and tools, including appropriate technical guidance documents, are needed

to facilitate ecosystem analyses of watersheds as required by the Clean Water Act. In particular,

there is a pressing need for refinement and release of an ecological risk methodology that addresses

the direct, indirect, and synergistic effects of nutrients, metals, toxic organic chemicals, and nonchemical stressors on aquatic ecosystems, including streams, rivers, lakes, and estuaries. 

The ecosystem model AQUATOX is one of the few general ecological risk models that

represents the combined environmental fate and effects of toxic organic chemicals. The model also

represents conventional pollutants, such as nutrients and sediments, and considers several trophic

levels, including attached and planktonic algae, submerged aquatic vegetation, several types of

invertebrates, and several types of fish. It has been implemented for streams, small rivers, ponds,

lakes, and reservoirs. 

AQUATOX Release 2 is described in these documents. Volume 1: User’s Manual

describes the usage of the model. Because the model is menu-driven and runs under Microsoft

Windows on microcomputers, it is user-friendly and little guidance is required. Volume 2:

Technical Documentation provides detailed documentation of the concepts and constructs of the

model so that its suitability for given applications can be determined. Volume 3: BASINS

AQUATOX Extension Documentation describes how AQUATOX can be run with site

characteristics and loadings input directly from the BASINS data layers or from the HSPF and

SWAT watershed models. 
viii
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 1

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1 INTRODUCTION

1.1 Overview

The AQUATOX model is a general ecological risk assessment model that represents the

combined environmental fate and effects of conventional pollutants, such as nutrients and sediments,

and toxic chemicals in aquatic ecosystems. It considers several trophic levels, including attached and

planktonic algae and submerged aquatic vegetation, invertebrates, and forage, bottom-feeding, and

game fish; it also represents associated organic toxicants. It can be implemented as a simple model

(indeed, it has been used to simulate an abiotic flask) or as a truly complex food-web model. Often

it is desirable to model a food web rather than a food chain, for example to examine the possibility

of less tolerant organisms being replaced by more tolerant organisms as environmental perturbations

occur. “Food web models provide a means for validation because they mechanistically describe the

bioaccumulation process and ascribe causality to observed relationships between biota and sediment

or water” (Connolly and Glaser 1998). The best way to accurately assess bioaccumulation is to use

more complex models, but only if the data needs of the models can be met and there is sufficient

time (Pelka 1998). 

The model has been implemented for streams, small rivers, ponds, lakes, and reservoirs. The

model is intended to be used to evaluate the likelihood of past, present, and future adverse effects

from various stressors including potentially toxic organic chemicals, nutrients, organic wastes,

sediments, and temperature. The stressors may be considered individually or together.

The fate portion of the model, which is applicable especially to organic toxicants, includes:

partitioning among organisms, suspended and sedimented detritus, suspended and sedimented

inorganic sediments, and water; volatilization; hydrolysis; photolysis; ionization; and microbial

degradation. The effects portion of the model includes: chronic and acute toxicity to the various

organisms modeled; and indirect effects such as release of grazing and predation pressure, increase

in detritus and recycling of nutrients from killed organisms, dissolved oxygen sag due to increased

decomposition, and loss of food base for animals.

AQUATOX represents the aquatic ecosystem by simulating the changing concentrations (in

mg/L or g/m3

) of organisms, nutrients, chemicals, and sediments in a unit volume of water (Figure

1). As such, it differs from population models, which represent the changes in numbers of

individuals. As O'Neill et al. (1986) stated, ecosystem models and population models are

complementary; one cannot take the place of the other. Population models excel at modeling

individual species at risk and modeling fishing pressure and other age/size-specific aspects; but

recycling of nutrients, the combined fate and effects of toxic chemicals, and other interdependencies

in the aquatic ecosystem are important aspects that AQUATOX represents and that cannot be

addressed by a population model. 
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 1

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Nutrients

Loadings

Light

Atmos. Dep.

Temperature

Wind

Inflow Outflow

Inorganic Sediment

Organic

toxicant

Organic

matter

Oxygen

D

e

ca

y

Death, sinking

Death, defecation

Plants

Phytoplankton

Periphyton

Macrophytes

Uptake

Invertebrates

Animals

Fish

Suspended sediment

Ingestion

In

g

e

stio

n

Figure 1. Conceptual model of ecosystem represented by AQUATOX

Any ecosystem model consists of multiple components requiring input data. These are the

abiotic and biotic state variables or compartments being simulated (Figure 2). In AQUATOX the

biotic state variables may represent trophic levels, guilds, and/or species. The model can represent

a food web with both detrital- and algal-based trophic linkages. Closely related are driving

variables, such as temperature, light, and nutrient loadings, which force the system to behave in

certain ways. In AQUATOX state variables and driving variables are treated similarly in the code.

This provides flexibility because external loadings of state variables, such as phytoplankton carried

into a reach from upstream, may function as driving variables; and driving variables, such as pH and

temperature, could be treated as dynamic state variables in a future implementation. Constant,

dynamic, and multiplicative loadings can be specified for atmospheric, point- and nonpoint sources.

Loadings of pollutants can be turned off at the click of a button to obtain a control simulation for

comparison with the perturbed simulation.
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 1

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Figure 2. State Variables in AQUATOX as implemented for Coralville Reservoir, Iowa.

The model is written in object-oriented Pascal using the Delphi programming system for

Windows. An object is a unit of computer code that can be duplicated; its characteristics and

methods also can be inherited by higher-level objects. For example, the organism object, including

variables such as the LC50 (lethal concentration of a toxicant) and process functions such as

respiration, is inherited by the plant object; that is enhanced by plant-specific variables and functions

and is duplicated for three kinds of algae; and the plant object is inherited and modified slightly for

macrophytes. This modularity forms the basis for the remarkable flexibility of the model, including

the ability to add and delete given state variables interactively.

AQUATOX utilizes differential equations to represent changing values of state variables,

normally with a reporting time step of one day. These equations require starting values or initial

conditions for the beginning of the simulation. If the first day of a simulation is changed, then the

initial conditions may need to be changed. A simulation can begin with any date and may be for any
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 1

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length of time from a few days, corresponding to a microcosm experiment, to several years,

corresponding to an extreme event followed by long-term recovery.

The process equations contain another class of input variables: the parameters or

coefficients that allow the user to specify key process characteristics. For example, the maximum

consumption rate is a critical parameter characterizing various consumers. AQUATOX is a

mechanistic model with many parameters; however, default values are available so that the analyst

only has to be concerned with those parameters necessary for a specific risk analysis, such as

characterization of a new chemical. In the pages that follow, differential equations for the state

variables will be followed by process equations and parameter definitions.

Finally, the system being modeled is characterized by site constants, such as mean and

maximum depths. At present one can model small lakes, reservoirs, streams, small rivers, and

ponds—and even enclosures and tanks. The generalized parameter screen is used for all these site

types, although the hypolimnion entries obviously are not applicable to all. The temperature and

light constants are used for simple forcing functions, blurring the distinctions between site constants

and driving variables.

1.2 Background

AQUATOX is the latest in a long series of models, starting with the aquatic ecosystem model

CLEAN (Park et al., 1974) and subsequently improved in consultation with numerous researchers

at various European hydrobiological laboratories, resulting in the CLEANER series (Park et al.,

1975, 1979, 1980; Park, 1978; Scavia and Park, 1976) and LAKETRACE (Collins and Park, 1989).

The MACROPHYTE model, developed for the U.S. Army Corps of Engineers (Collins et al., 1985),

provided additional capability for representing submersed aquatic vegetation. Another series started

with the toxic fate model PEST, developed to complement CLEANER (Park et al., 1980, 1982), and

continued with the TOXTRACE model (Park, 1984) and the spreadsheet equilibrium fugacity PART

model. AQUATOX combined algorithms from these models with ecotoxicological constructs; and

additional code was written as required for a truly integrative fate and effects model (Park, 1990,

1993). The model was then restructured and linked to Microsoft Windows interfaces to provide

greater flexibility, capacity for additional compartments, and user friendliness (Park et al., 1995).

Release 1 from the U.S. Environmental Protection Agency (US EPA) was improved with the

addition of constructs for chronic effects and uncertainty analysis, making it a powerful tool for

probabilistic risk assessment (US EPA, 2000a, b, c). Release 1.1 (US EPA 2001a, b) provided a

much enhanced periphyton submodel and minor enhancements for macrophytes, fish, and dissolved

oxygen. This technical documentation describes Release 2, which has a number of major

enhancements (see 1.3 What’s New).

This document is intended to provide verification of individual constructs or mathematical

and formulations programming algorithms used in AQUATOX. The scientific basis of the

constructs reflects empirical and theoretical support; and precedence in the open literature and in
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 1

1 - 5

widely used models is noted. Units are given to confirm the dimensional analysis. The mathematical

formulations have been programmed and graphed in spreadsheets and the results have been

evaluated in terms of behavior consistent with our understanding of ecosystem response; many of

those graphs are given in the following documentation. The variable names in the documentation

correspond to those used in the program so that the mathematical formulations and code can be

compared, and the computer code has been checked for consistency with those formulations. Much

of this has been done as part of the continuing process of internal review. The model and

documentation also have undergone successful peer review by an external panel convened by the

U.S. Environmental Protection Agency.

1.3 What’s New

AQUATOX Release 2 has numerous enhancements and a few corrections from Release 1.

Some of these appeared in Release 1.1 and were documented in an Addendum, and some have

occurred since the Release 2 Beta Test version was posted on the developers’ Web site. The

changes fall in three categories.

Enhanced Scientific Capabilities

The model is much more powerful and can better represent a variety of environments,

especially streams and rivers compared to Release 1. Specific enhancements include:

! a large increase in the number of biotic state variables, with two representatives for each

taxonomic group or ecologic guild; 

! the addition of bryophytes as a special type of macrophyte;

! a multi-age fish category with up to fifteen age classes for age-dependent bioaccumulation

and limited population modeling;

! an increase in the number of toxicants from one to a maximum of twenty, with the capability

for modeling daughter products due to biotransformations;

! disaggregation of stream habitats into riffle, run, and pool;

! mechanistic current- and stress-induced sloughing, light extinction, and accumulation of

detritus in periphyton;

! macrophyte breakage due to currents;

! computation of chlorophyll a for periphyton and bryophytes, as well as for phytoplankton;

! fish biomass is entered and tracked in g/m2;

! entrainment and washout of animals, including fish, can occur during high flow;

! the options of computing respiration and maximum consumption in fish as functions of mean

individual weight using allometric parameters from the Wisconsin Bioenergetics Model;

! respiration in fish is density-dependent;

! fish spawning can occur on user-specified dates as an alternative to temperature-cued

spawning;

! elimination of toxicants is more robust;

! settling and erosional velocities for inorganic sediments are user-supplied parameters;
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 1

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! uncertainty analysis now covers all parameters and loadings;

! biotic risk graphs are provided as an alternative means of portraying probabilistic results;

! limitation factors for photosynthesis are output along with the biotic rates; and

! AQUATOX is now an extension to BASINS, providing linkages to geographic information

system data, and HSPF and SWAT simulations.

Additional User Interfaces

The model is even more user-friendly, taking full advantage of current Windows capabilities

on modern high-speed personal computers. Capabilities include:

! a Wizard to guide the user through the setup for a new study;

! context-sensitive Help screens;

! multiple windows for simultaneous simulations and input and output screens;

! a task bar that can be customized by the user;

! enhanced graphics, including secondary Y axes; and

! a hierarchical tree structure for choosing variables for uncertainty analysis.

Corrected Errors

Several errors were discovered and corrected during the course of continuing model

evaluation. Some of these may require recalibration of studies. The example studies provided with

the software have been recalibrated, but users may wish to check their own calibrations in upgrading

from various versions. The corrections include:

! a change in the bathymetric computations affecting the areas of the thermocline and littoral

zone (Release 1);

! removal of an unnecessary conversion from phosphate and nitrate, assuming that all nutrient

input is in terms of N and P; this could affect nutrient limitations (all versions);

! inclusion of an oxygen to organic matter conversion factor (a factor of 1.5) and inclusion of

specific dynamic action in the allometric computation of fish respiration (Release 2 Beta

Test only);

! adding a second-to-day conversion factor for inorganic sediment deposition; previously,

deposition of suspended sediments was much slower than expected (all versions);

! adding a conversion factor for wind measured at 10 m height to wind occurring at 10 cm

above the water surface in the volatilization computations; for some compounds this could

result in a two-fold reduction in volatilization (all versions);

! nitrification is formulated to occur only at the sediment-water interface (Release 1); and

! bioaccumulation, and hence toxicity, are constrained by the life span of an animal (all

versions).
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 2

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2 SIMULATION MODELING

2.1 Temporal and Spatial Resolution and Numerical Stability

AQUATOX Release 2 is designed to be a general, realistic model of the fate and effects of

pollutants in aquatic ecosystems. In order to be fast, easy to use, and verifiable, it has been designed

with the simplest spatial and temporal resolutions consistent with this objective. It is designed to

represent average daily conditions for a well-mixed aquatic system (in other words, a nondimensional point model). It also can represent one-dimensional vertical epilimnetic and

hypolimnetic conditions for those systems that exhibit stratification on a seasonal basis.

Furthermore, the effects of run, riffle, and pool environments can be represented for streams.

According to Ford and Thornton (1979), a one-dimensional model is appropriate for

reservoirs that are between 0.5 and 10 km in length; if larger, then a two-dimensional model

disaggregated along the long axis is indicated. The one-dimensional assumption is also appropriate

for many lakes (Stefan and Fang, 1994). Similarly, one can consider a single reach or stretch of

river at a time. A spatially-distributed version of the model (Version 3.00) that is able to simulate

linked segments also has been developed, but has not been released. 

Usually the reporting time step is one day, but numerical instability is avoided by allowing

the step size of the integration to vary to achieve a predetermined accuracy in the solution. This is

a numerical approach, and the step size is not directly related to the temporal scale of the ecosystem

simulation. AQUATOX uses a very efficient fourth- and fifth-order Runge-Kutta integration routine

with adaptive step size to solve the differential equations (Press et al., 1986, 1992). The routine uses

the fifth-order solution to determine the error associated with the fourth-order solution; it decreases

the step size (often to 15 minutes or less) when rapid changes occur and increases the step size when

there are slow changes, such as in winter. However, the step size is constrained to a maximum of

one day so that daily pollutant loadings are always detected. The reporting step, on the other hand,

can be as long as 99 days or as short as 0.1 day; the results are integrated to obtain the desired

reporting time period.

The temporal and spatial resolution is in keeping with the generality and realism of the model

(see Park and Collins, 1982). Careful consideration has been given to the hierarchical nature of the

system. Hierarchy theory tells us that models should have resolutions appropriate to the objectives;

phenomena with temporal and spatial scales that are significantly longer than those of interest should

be treated as constants, and phenomena with much smaller temporal and spatial scales should be

treated as steady-state properties or parameters (Figure 3, O'Neill et al., 1986). The model uses a

longer time step than dynamic hydrologic models that are concerned with representing short-term

phenomena such as storm hydrographs (and, indeed, it is not intended to capture fully the dynamics

of short-term pulses less than once per day), and it uses a shorter time step than fate models that may

be concerned only with long-term patterns such as bioaccumulation in large fish.
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 2

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Figure 3. Position of ecosystem models such as

AQUATOX in the spatial-temporal hierarchy of

models.

Changing the permissible relative error (the difference between the fourth- and fifth-order

solutions) of the simulation can affect the results. The model allows the user to set the relative error,

usually between 0.005 and 0.01. Comparison of output shows that up to a point a smaller error can

yield a marked improvement in the simulation—although execution time is slightly longer. For

example, simulations of two pulsed doses of chlorpyrifos in a pond exhibit a spread in the first pulse

of about 0.6 :g/L dissolved toxicant between the simulation with 0.001 relative error and the

simulation with 0.05 relative error (Figure 4); this is probably due in part to differences in the

timing of the reporting step. However, if we examine the dissolved oxygen levels, which combine

the effects of photosynthesis, decomposition, and reaeration, we find that there are pronounced

differences over the entire simulation period. The simulations with 0.001 and 0.01 relative error

give almost exactly the same results, suggesting that the more efficient 0.001 relative error should

be used; the simulation with 0.05 relative error exhibits instability in the oxygen simulation; and the

simulation with 0.1 error gives quite different values for dissolved oxygen (Figure 5). The observed

mean daily maximum dissolved oxygen for that period was 9.2 mg/L (US EPA 1988), which

corresponds most closely with the results of simulation with 0.001 and 0.01 relative error.
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 2

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Figure 4. Pond with Chlorpyrifos in Dissolved

Phase.

Figure 5. Same as Figure 4 with Dissolved

Oxygen.

2.2 Uncertainty Analysis

There are numerous sources of uncertainty and variation in natural systems. These include:

site characteristics such as water depth, which may vary seasonally and from site to site;

environmental loadings such as water flow, temperature, and light, which may have a stochastic

component; and critical biotic parameters such as maximum photosynthetic and consumption rates,

which vary among experiments and representative organisms.

In addition, there are sources of uncertainty and variation with regard to pollutants,

including:

pollutant loadings from runoff, point sources, and atmospheric deposition, which may vary

stochastically from day to day and year to year; physico-chemical characteristics such as octanolwater partition coefficients and Henry Law constants that cannot be measured easily;

chemodynamic parameters such as microbial degradation, photolysis, and hydrolysis rates, which

may be subject to both measurement errors and indeterminate environmental controls. 

Increasingly, environmental analysts and decision makers are requiring probabilistic

modeling approaches so that they can consider the implications of uncertainty in the analyses.

AQUATOX provides this capability by allowing the user to specify the types of distributions and

key statistics for any and all input variables. Depending on the specific variable and the amount of

available information, any one of several distributions may be most appropriate. A lognormal

distribution is the default for environmental and pollutant loadings. In the uncertainty analysis, the

distributions for constant loadings are sampled daily, providing day-to-day variation within the
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 2

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Figure 6. Distribution Screen for Point-Source Loading of Toxicant in Water.

limits of the distribution, reflecting the stochastic nature of such loadings. A useful tool in testing

scenarios is the multiplicative loading factor, which can be applied to all loads. Distributions for

dynamic loadings may employ multiplicative factors that are sampled once each iteration (Figure

6). Normally the multiplicative factor for a loading is set to 1, but, as seen in the example, under

extreme conditions the loading may be ten times as great. In this way the user could represent

unexpected conditions such as pesticides being applied inadvertently just before each large storm

of the season. Loadings usually exhibit a lognormal distribution, and that is suggested in these

applications, unless there is information to the contrary. Figure 7 exhibits the result of such a

loading distribution.

A sequence of increasingly informative distributions should be considered for most

parameters (see Volume 1: User’s Manual.) If only two values are known and nothing more can

be assumed, the two values may be used as minimum and maximum values for a uniform

distribution (Figure 8); this is often used for parameters where only two values are known. If

minimal information is available but there is reason to accept a particular value as most likely,

perhaps based on calibration, then a triangular distribution may be most suitable (Figure 9). Note
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 2

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Mean

Minimum

Maximum

Mean - StDev

Mean + StDev

Deterministic

Largemouth Ba2 (g/sq.

6/13/2003 2:02:03 PM

5/9/1969 7/8/1969 9/6/1969 11/5/1969 1/4/1970 3/5/1970 5/4/1970

0.8

0.75

0.7

0.65

0.6

0.55

0.5

0.45

0.4

0.35

0.3

0.25

0.2

Figure 7. Sensitivity of bass (g/m2) to variations in loadings of dieldrin in Coralville Lake,

Iowa.

that the minimum and maximum values for the distribution are constraints that have zero probability

of occurrence. If additional data are available indicating both a central tendency and spread of

response, such as parameters for well-studied processes, then a normal distribution may be most

appropriate (Figure 10). The result of applying such a distribution in a simulation of Onondaga

Lake, New York, is shown in Figure 11, where simulated benthic feeding affects decomposition and

subsequently the predicted hypolimnetic anoxia. All distributions are truncated at zero because

negative values would have no meaning. 
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 2

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Figure 8. Uniform Distribution for Henry’s

Law Constant for Esfenvalerate.

Figure 9. Triangular Distribution for

Maximum Consumption Rate for Bass.

Figure 10. Normal Distribution for Maximum Consumption Rate

for the Detritivorous Invertebrate Tubifex.
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Figure 11. Sensitivity of Hypolimnetic Oxygen in Lake

Onondaga to Variations in Maximum Consumption Rates of

Detritivores.

Efficient sampling from the distributions is obtained with the Latin hypercube method

(McKay et al., 1979; Palisade Corporation, 1991), using algorithms originally written in FORTRAN

((Iman and Shortencarier 1984)Anonymous, 1988). Depending on how many iterations are chosen

for the analysis, each cumulative distribution is subdivided into that many equal segments. Then

a uniform random value is chosen within each segment and used in one of the subsequent simulation

runs. For example, the distribution shown in Figure 10 can be sampled as shown in Figure 12. 

This method is particularly advantageous because all regions of the distribution, including the tails,

are sampled. A non-random seed can be used for the random number generator, causing the same

sequence of numbers to be picked in successive applications; this is useful if you want to be able to

duplicate the results exactly. The default is twenty iterations, meaning that twenty simulations will

be performed with sampled input values; this should be considered the minimum number to provide

any reliability. The optimal number can be determined experimentally by noting the number

required to obtain convergence of mean response values for key state variables; in other words, at

what point do additional iterations not result in significant changes in the results? As many variables

may be represented by distributions as desired, but the method assumes that they are independently

distributed. By varying one parameter at a time the sensitivity of the model to individual parameters

can be determined. This is done for key parameters in the following documentation.
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 2

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Figure 12. Latin Hypercube Sampling of a

Cumulative Distribution with a Mean of 25 and

Standard Deviation of 8 Divided into 5 Intervals.

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An alternate way of presenting uncertainty is by means of a biomass risk graph, which plots

the probability that biomass will be reduced by a given percentage by the end of the simulation

(Mauriello and Park 2002). In practice, AQUATOX compares the end value with the initial

condition for each state variable, expressing the result as a percent decline:

where:

Decline = percent decline in biomass for a given state variable (%);

EndVal = value at the end of the simulation for a given state variable (units

depend on state variable);

StartVal = initial condition for given state variable.

The results from each iteration are sorted and plotted in a cumulative distribution so that the

probability that a particular percent decline will be exceeded can be evaluated (Figure 13). Note

that there are ten points in this example, one for each iteration as the consecutive segments of the

distribution are sampled. 
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 2

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Largemouth Ba2

Biomass Risk Graph

6/13/2003 2:03:53 PM

Percent Decline at Simulation End

45 50 55 60 65 70 75

Percent Probability

100.0

90.0

80.0

70.0

60.0

50.0

40.0

30.0

20.0

10.0

Figure 13. Risk to bass from dieldrin in Coralville Reservoir, Iowa.
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 2

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3 PHYSICAL CHARACTERISTICS

3.1 Morphometry

Volume

Volume is a state variable and can be computed in several ways depending on availability

of data and the site dynamics. It is important for computing the dilution or concentration of

pollutants, nutrients, and organisms; it may be constant, but usually it is time varying. In the model,

ponds, lakes, and reservoirs are treated differently than streams, especially with respect to computing

volumes. The change in volume of ponds, lakes, and reservoirs is computed as:

where:

dVolume/dt = derivative for volume of water (m3

/d),

Inflow = inflow of water into waterbody (m3

/d),

Discharge = discharge of water from waterbody (m3/d), and

Evap = evaporation (m3/d), see (3).

Evaporation is converted from an annual value for the site to a daily value using the simple

relationship:

where:

MeanEvap = mean annual evaporation (in/yr),

365 = days per year (d/yr),

0.0254 = conversion from inches to meters (m/in), and

Area = area of the waterbody (m2

).

The user is given several options for computing volume including keeping the volume

constant; making the volume a dynamic function of inflow, discharge, and evaporation; using a time

series of known values; and, for flowing waters, computing volume as a function of the Manning’s

equation. Depending on the method, inflow and discharge are varied, as indicated in Table 1. As

shown in equation (2), an evaporation term is present in each of these volume calculation options.

In order to keep the volume constant, given a known inflow loading, evaporation must be subtracted

from discharge. This will reduce the quantity of state variables that wash out of the system. In the

dynamic formulation, evaporation is part of the differential equation, but neither inflow nor

discharge is a function of evaporation as they are both entered by the user. When setting the volume

of a water body to a known value, evaporation must again be subtracted from discharge for the

volume solution to be correct. Finally, when using the Manning's volume equation, given a known
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 3

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discharge loading, the effects of evaporation must be added to the inflow loading so that the proper

Manning's volume is achieved. (This could increase the amount of inflow loadings of toxicants and

sediments to the system, although not significantly.)

Table 1. Computation of Volume, Inflow, and Discharge

Method Inflow Discharge

Constant InflowLoad InflowLoad - Evap

Dynamic InflowLoad DischargeLoad

Known values InflowLoad InflowLoad - Evap + (State - KnownVals)/dt

Manning ManningVol - State/dt + DischargeLoad + Evap DischargeLoad

The variables are defined as:

InflowLoad = user-supplied inflow loading (m3

/d);

DischargeLoad = user-supplied discharge loading (m3/d);

State = computed state variable value for volume (m3);

KnownVals = time series of known values of volume (m3

); 

dt = incremental time in simulation (d); and

ManningVol = volume of stream reach (m3

), see (4).

Figure 14 illustrates time-varying volumes and inflow loadings specified by the user and

discharge computed by the model for a run-of-the-river reservoir. Note that significant drops in

volume occur with operational releases, usually in the spring, for flood control purposes.

The time-varying volume of water in a stream channel is computed as:

where:

Y = dynamic mean depth (m), see (5);

CLength = length of reach (m); and

Width = width of channel (m).
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 3

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Figure 14. Volume, Inflow, and Discharge for a 4-year Period

in Coralville Reservoir, Iowa.

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In streams the depth of water and flow rate are key variables in computing the transport,

scour, and deposition of sediments. Time-varying water depth is a function of the flow rate, channel

roughness, slope, and channel width using Manning’s equation ((Gregory and Walling 1973)), which

is rearranged to yield:

where:

Q = flow rate (m3/s);

Manning = Manning’s roughness coefficient (s/m1/3);

Slope = slope of channel (m/m); and

Width = channel width (m).

The Manning’s roughness coefficient is an important parameter representing frictional loss,

but it is not subject to direct measurement. The user can enter a value or can choose among the

following stream types:

! concrete channel (with a default Manning’s coefficient of 0.020);

! dredged channel, such as ditches and channelized streams (default coefficient of 0.030); and

! natural channel (default coefficient of 0.040).

These generalities are based on Chow’s (1959) tabulated values as given by Hoggan (1989).
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 3

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In the absence of inflow data, the flow rate is computed from the initial mean water depth,

assuming a rectangular channel and using a rearrangement of Manning’s equation:

where:

QBase = base flow (m3

/s); and

Idepth = mean depth as given in site record (m).

The dynamic flow rate is calculated from the inflow loading by converting from m3/d to m3/s:

where:

Q = flow rate (m3

/s); and

Inflow = water discharged into channel from upstream (m3/d).

Bathymetric Approximations

The depth distribution of a water body is important because it determines the areas and

volumes subject to mixing and light penetration. The shapes of ponds, lakes, reservoirs, and streams

are represented in the model by idealized geometrical approximations, following the topological

treatment of Junge (1966; see also Straškraba and Gnauck, 1985). The shape parameter P (Junge,

1966) characterizes the site, with a shape that is indicated by the ratio of mean to maximum depth:

Where:

ZMean = mean depth (m);

ZMax = maximum depth (m); and

P = characterizing parameter for shape (unitless); P is constrained

between -1.0 and 1.0.

Shallow constructed ponds and ditches may be approximated by an ellipsoid where Z/ZMax

= 0.6 and P = 0.6. Reservoirs and rivers generally are extreme elliptic sinusoids with values of P

constrained to -1.0. Lakes may be either elliptic sinusoids, with P between 0.0 and -1.0, or elliptic

hyperboloids with P between 0.0 and 1.0. The model requires mean and maximum depth, but if only

the maximum depth is known, then the mean depth can be estimated by multiplying ZMax by the

representative ratio. Not all water bodies fit the elliptic shapes, but the model generally is not

sensitive to the deviations. 
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Figure 16

Volume as a Function of Depth

Figure 15

Area as a Function of Depth

Based on these relationships, fractions of volumes and areas can be determined for any given

depth (Figure 15, Figure 16; Junge, 1966). The AreaFrac function returns the fraction of surface

area that is at depth Z given Zmax and P, which defines the morphometry of the water body. For

example, if the water body were an inverted cone, when horizontal slices were made through the

cone looking down from the top one could see both the surface area and the water/sediment

boundary where the slice was made. This would look like a circle within a circle, or a donut (Figure

17). AreaFrac calculates the fraction that is the donut (not the donut hole). To get the donut hole,

1 - AreaFrac is used.

where:

AreaFrac = fraction of area of site above given depth (unitless);

VolFrac = fraction of volume of site above given depth (unitless); and

Z = depth of interest (m).

For example, the fraction of the volume that is epilimnion can be computed by setting depth

Z to the mixing depth. Furthermore, by setting Z to the depth of the euphotic zone, the fraction of

the area available for colonization by macrophytes and periphyton can be computed:
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 3

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Figure 17

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A relatively deep, flat-bottomed basin would have a small littoral area and a large sublittoral

area (Figure 17).

If the site is a limnocorral (an artificial enclosure) then the available area is increased accordingly:

where:

FracLittoral = fraction of site area that is within the euphotic zone (unitless);

ZEuphotic = depth of the euphotic zone, where primary production

exceeds respiration, usually calculated as a function of

extinction (m); 

Area = site area (m2

); and

LimnoWallArea = area of limnocorral walls (m2

).

Habitat Disaggregation

Riverine environments are seldom homogeneous. Organisms often exhibit definite

preferences for habitats. Therefore, when modeling streams or rivers, animal and plant habitats are

broken down into three categories: “riffle,” “run,” and “pool.” The combination of these three

habitat categories make up 100% of the available habitat within a riverine simulation. The preferred

percentage of each organism that resides within these three habitat types can be set within the animal
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 3

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or plant data. Within the site data, the percentage of the river that is composed of each of these

three habitat categories also can be set. It should be noted that the habitat percentages are

considered constant over time, and thus would not capture significant changes in channel

morphology and habitat distribution due to major flooding events. 

These habitats affect the simulations in two ways: as limitations on photosynthesis and

consumption and as weighting factors for water velocity (see 3.2 Velocity). Each animal and plant

is exposed to a weighted average water velocity depending on its location within the three habitats.

This weighted velocity affects all velocity-mediated processes including entrainment of invertebrates

and fish, breakage of macrophytes and scour of periphyton. The reaeration of the system also is

affected by the habitat-weighted velocities.

Limitations on photosynthesis and consumption are calculated depending on a species’

preferences for habitats and the available habitats within the water body. If the species preference

for a particular habitat is equal to zero then the portion of the water body that contains that particular

habitat limits the amount of consumption or photosynthesis accordingly.

where:

HabitatLimitSpecies = fraction of site available to organism (unitless), used to limit

ingestion, see (78), and photosynthesis, see (31), (73); 

Preferencehabitat = preference of animal or plant for the habitat in question

(percentage); and

Percenthabitat = percentage of site composed of the habitat in question

(percentage). 

It is important to note that the initial condition for an animal that is entered in g/m2 is an

indication of the total mass of the animal over the total surface area of the river. Because of this,

density data for various benthic organisms cannot be used as input to AQUATOX until these values

have been converted to represent the entire surface area. This is especially true in modeling habitats;

for example, an animal could have a high density within riffles, but riffles might only constitute a

small portion of the entire system. 

3.2 Velocity

Velocity is calculated as a simple function of flow and cross-sectional area:
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where

Velocity = velocity (cm/s),

AvgFlow = flow (m3/d),

XSecArea = cross sectional area (m2

),

86400 = s/d, and

100 = cm/m.

where:

Inflow = flow into the reach (m3

/d);

Discharge = flow out of the reach (m3/d).

It is assumed that this is the velocity for the run of the stream. No distinction is made in

terms of vertical differences in velocity in the stream. Following the approach and values used in

the DSAMMt model (Caupp et al. 1995), the riffle velocity is obtained by using a conversion factor

that is dependent on the discharge. Unlike the DSAMMt model, pools also are modeled, so a

conversion factor is used to obtain the pool velocity as well (Table 2). The consequence of these

habitat controls on velocity is shown in Figure 18.

Table 2. Factors relating velocities to those of the average reach.

 Flows (Q = discharge)

Run

Velocity

Riffle

Velocity

Pool

Velocity

 Q < 2.59e5 m3

/d 1.0 1.6 0.36

 2.59e5 m3

/d # Q < 5.18e5 m3/d 1.0 1.3 0.46

 5.18e5 m3

/d # Q < 7.77e5 m3/d 1.0 1.1 0.56

 Q $ 7.77e5 m3

/d 1.0 1.0 0.66
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 3

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0

50

100

150

200

250

300

350

400

1/1/19972/1/19973/1/19974/1/19975/1/19976/1/19977/1/19978/1/19979/1/1997

10/1/199711/1/199712/1/1997

Velocity (cm/s)

Run Riffle Pool 

Figure 18

Predicted velocities in an Ohio stream according to habitat

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3.3 Washout

Transport out of the system, or washout, is an important loss term for nutrients, floating

organisms, dissolved toxicants, and suspended detritus and sediments in reservoirs and streams. 

Although it is considered separately for several state variables, the process is a general function

of discharge:

where:

Washout = loss due to being carried downstream (g/m3 "d); 

Discharge = flow out of the reach (m3

/d), see Table 1;

Volume = volume of stream reach (m3

), see (2); and

State = concentration of dissolved or floating state variable (g/m3

).

3.4 Stratification and Mixing

Thermal stratification is handled in the simplest form consistent with the goals of

forecasting the effects of nutrients and toxicants. Lakes and reservoirs are considered in the

model to have two vertical zones: epilimnion and hypolimnion (Figure 19); the metalimnion

zone that separates these is ignored. Instead, the thermocline, or plane of maximum temperature
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 3

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Figure 19

Thermal Stratification in a Lake; Terms Defined in Text

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change, is taken as the separator; this is also known as the mixing depth (Hanna, 1990). 

Dividing the lake into two vertical zones follows the treatment of Imboden (1973), Park et al.

(1974), and Straškraba and Gnauck (1983). The onset of stratification is considered to occur

when the mean water temperature exceeds 4° and the difference in temperature between the

epilimnion and hypolimnion exceeds 3°. Overturn occurs when the temperature of the

epilimnion is less than 3°, usually in the fall. Winter stratification is not modeled. For simplicity,

the thermocline is assumed to occur at a constant depth. 

There are numerous empirical models relating thermocline depth to lake characteristics. 

AQUATOX uses an equation by Hanna (1990), based on the maximum effective length (or

fetch). The dataset includes 167 mostly temperate lakes with maximum effective lengths of 172

to 108,000 m and ranging in altitude from 10 to 1897 m. The equation has a coefficient of

determination r2

 = 0.850, meaning that 85 percent of the sum of squares is explained by the

regression. Its curvilinear nature is shown in ?, and it is computed as (Hanna, 1990):

where:

MaxZMix = maximum mixing depth for lake (m); and

Length = maximum effective length for wave setup (m, converted from usersupplied km).

Wind action is implicit in this formulation. Wind has been modeled explicitly by Baca

and Arnett (1976, quoted by Bowie et al., 1985), but their approach requires calibration to

individual sites, and it is not used here.

Vertical dispersion for bulk mixing is modeled as a function of the time-varying

hypolimnetic and epilimnetic temperatures, following the treatment of Thomann and Mueller

(1987, p. 203; see also Chapra and Reckhow, 1983, p. 152; Figure 21):
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0

5

10

15

20

25DEPTH (m)

100

5800

11500

17200

22900

28600

34300

40000

LENGTH (m)

MAXIMUM MIXING DEPTH

Figure 20

 Mixing depth as a function of fetch

where:

VertDispersion = vertical dispersion coefficient (m2/d);

Thick = distance between the centroid of the epilimnion and the centroid of

the hypolimnion, effectively the mean depth (m);

HypVolume = volume of the hypolimnion (m3);

ThermoclArea = area of the thermocline (m2

);

Deltat = time step (d);

Thypo

t-1, Thypot+1 = temperature of hypolimnion one time step before and one time step

after present time (°C); and

Tepi

t

, Thypo

t = temperature of epilimnion and hypolimnion at present time (°C).

Stratification can break down temporarily as a result of high throughflow. This is

represented in the model by making the vertical dispersion coefficient between the layers a

function of discharge for sites with retention times of less than or equal to 180 days (Figure 22),

rather than temperature differences as in equation 11, based on observations by Straškraba

(1973) for a Czech reservoir:
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Figure 21

Vertical dispersion as a function of temperature differences

and:

where:

Retention = retention time (d);

Volume = volume of site (m3); and

TotDischarge = combined discharge of epilimnion and hypolimnion (m3

/d); see

Table 1.
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Figure 22

Vertical Dispersion as a Function of Retention Time

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(22)

(23)

The bulk vertical mixing coefficient is computed using site characteristics and the timevarying vertical dispersion (Thomann and Mueller, 1987):

where:

BulkMixCoeff = bulk vertical mixing coefficient (m3/d),

ThermoclArea = area of thermocline (m2

).

Turbulent diffusion of biota and other material between epilimnion and hypolimnion is

computed separately for each segment for each time step while there is stratification:
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Figure 23

Stratification and mixing in Lake Nockamixon,

Pennsylvania as shown by hypolimnetic dissolved oxygen

(24)

where:

TurbDiff = turbulent diffusion for a given zone (g/m3"d) see (22) and (23);

Volume = volume of given segment (m3

); and

Conc = concentration of given compartment in given zone (g/m3).

The effects of stratification, mixing due to high throughflow, and overturn are well

illustrated by the pattern of dissolved oxygen levels in the hypolimnion of Lake Nockamixon, a

eutrophic reservoir in Pennsylvania (Figure 23). 

3.5 Temperature

Temperature is an important controlling factor in the model. Virtually all processes are

temperature-dependent. These include stratification; biotic processes such as decomposition,

photosynthesis, consumption, respiration, reproduction, and mortality; and chemical fate

processes such as microbial degradation, volatilization, hydrolysis, and bioaccumulation. On the

other hand, temperature rarely fluctuates rapidly in aquatic systems. Default water temperature

loadings for the epilimnion and hypolimnion are represented through a simple sine

approximation for seasonal variations (Ward, 1963) based on user-supplied observed means and

ranges (Figure 24):
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where:

Temperature = average daily water temperature (°C);

TempMean = mean annual temperature (°C);

TempRange = annual temperature range (°C),

Day = Julian date (d); and

PhaseShift = time lag in heating (= 90 d).

Observed temperature loadings should be entered if responses to short-term variations are

of interest. This is especially important if the timing of the onset of stratification is critical,

because stratification is a function of the difference in hypolimnetic and epilimnetic temperatures

(see Figure 22). It also is important in streams subject to releases from reservoirs and other

point-source temperature impacts.

3.6 Light

Light is important as the controlling factor for photosynthesis and photolysis. The

default incident light function was formulated for AQUATOX and is a variation on the

temperature equation, but without the lag term:

where:

Solar = average daily incident light intensity (ly/d);

LightMean = mean annual light intensity (ly/d);

LightRange = annual range in light intensity (ly/d); and

Day = Julian date (d, adjusted for hemisphere).

The derived values are given as average light intensity in Langleys per day (Ly/d = 10

kcal/m2

"d). An observed time-series of light also can be supplied by the user; this is especially

important if the effects of daily climatic conditions are of interest. If the average water

temperature drops below 3°C, the model assumes the presence of ice cover and decreases light to

33% of incident radiation. This reduction, due to the reflectivity and transmissivity of ice and

snow, is an average of widely varying values summarized by Wetzel (1975; also see LeCren and

Lowe-McConnell, 1980). The model does not automatically adjust for shading by riparian

vegetation, so a times-series should probably be supplied if modeling a narrow stream. 

Photoperiod is an integral part of the photosynthesis formulation. It is approximated

using the Julian date following the approach of (Stewart 1975) (Figure 25):
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Figure 24 

Annual Temperature

Figure 25

Photoperiod as a Function of Date

where:

Photoperiod = fraction of the day with daylight (unitless); converted from hours

by dividing by 24;

A = hours of daylight minus 12 (hr); and

Day = Julian date (d, converted to radians).

A is the difference between the number of hours of daylight at the summer solstice at a given

latitude and the vernal equinox, and is given by a linear regression developed by Groden (1977):

where:

Latitude = latitude (°, decimal), negative in southern hemisphere; and

Sign = 1.0 in northern hemisphere, -1.0 in southern hemisphere.

3.7 Wind

Wind is an important driving variable because it determines the stability of blue-green

algal blooms, affects reaeration or oxygen exchange, and controls volatilization of some organic

chemicals. Wind is usually measured at meteorological stations at a height of 10 m and is
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 3

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expressed as m/s. If site data are not available, default variable wind speeds are represented

through a Fourier series of sine and cosine terms; the mean and first ten harmonics seem to

capture the variation adequately (Figure 26):

where:

Wind = wind speed; amplitude of the Fourier series (m/s);

CosCoeff0 = cosine coefficient for the 0-order harmonic, which is the mean

wind speed (default = 3 m/s);

CosCoeffn = cosine coefficient for the nth-order harmonic;

Day = Julian date (d);

WaveLength = wave length (= 5); and

SinCoeffn = sine coefficient for the nth-order harmonic.

This default loading is based on an unpublished 140-day record (May 20 to October 12)

from Columbia, Missouri; therefore, it has a 140-day repeat, representative of the Midwest

during the growing season. This approach is quite useful because the mean can be specified by

the user and the variability will be imposed by the function. If ice cover is predicted, wind is set

to 0. A user also may input a site-specific time series, which may be important where the timing

of a blue-green algal bloom or reaeration is of interest.
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Figure 26

Default Wind Loadings for Missouri Pond with Mean = 3 m/s
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4 BIOTA

The biota consists of two main groups, plants and animals; each is represented by a set of

process-level equations. In turn, plants are differentiated into algae and macrophytes,

represented by slight variations in the differential equations. Algae may be either phytoplankton

or periphyton. Phytoplankton are subject to sinking and washout, while periphyton are subject to

substrate limitation and scour by currents. Bryophytes are modeled as a special class of

macrophytes, limited by nutrients in the water column. These differences are treated at the

process level in the equations (Table 3). All are subject to habitat availability, but to differing

degrees. Plants also are characterized by taxonomic group, which is primarily a way of

organizing preferences for grazing and to identify blue-green phytoplankton as floating.

Table 3. Significant Differentiating Processes for Plants

Plant Type Nutrient

Lim.

Current

Lim.

Sinking Washout Sloughing Breakage Habitat

Phytoplankton [ [[ [

Periphyton [[ [ [

Macrophytes [ [

Bryophytes [ [[

Animals are subdivided into invertebrates and fish; the invertebrates may be pelagic

invertebrates, benthic insects or other benthic invertebrates. These groups are represented by

different parameter values and by variations in the equations. Insects are subject to emergence

and therefore are lost from the system, but benthic invertebrates are not. Any fish may be

represented by both juveniles and adults, which are connected by promotion. One fish species

can be designated as multi-year with up to 15 age classes connected by promotion. Differences

are shown in Table 4. Feeding preferences are very flexible and can accommodate combinations

of grazing on plants, detritus feeding, and predation (“predation” is used in the following pages

to refer to any type of feeding by animals). Animals also are characterized by taxonomic type or

guild, primarily as a way of organizing feeding preferences; these types can be overridden. 

Table 4. Significant Differentiating Processes for Animals

Animal Type Washout Drift Entrainment Emergence Promotion Multi-year

Pelagic Invert. [

Benthic Invert. [ [

Benthic Insect [[[

Fish [ [[
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4.1 Algae

The change in algal biomass—expressed as ash-free dry weight in g/m3

 for

phytoplankton, but as g/m2 for periphyton—is a function of the loading (especially

phytoplankton from upstream), photosynthesis, respiration, excretion or photorespiration,

nonpredatory mortality, grazing or predatory mortality, sloughing, and washout; as noted above,

phytoplankton also are subject to sinking. If the system is stratified, turbulent diffusion from one

layer to the other also affects the biomass of phytoplankton:

where:

dBiomass/dt = change in biomass of phytoplankton and periphyton with respect to

time (g/m3

"d and g/m2"d);

Loading = loading of algal group (g/m3"d and g/m2"d);

Photosynthesis = rate of photosynthesis (g/m3"d and g/m2"d), see (31);

Respiration = respiratory loss (g/m3

"d and g/m2"d), see (55);

Excretion = excretion or photorespiration (g/m3"d and g/m2"d), see (56);

Mortality = nonpredatory mortality (g/m3

"d and g/m2"d), see (58);

Predation = herbivory (g/m3

"d and g/m2"d), see (85);

Washout = loss due to being carried downstream (g/m3"d), see (63);

Sinking = loss or gain due to sinking between layers and sedimentation to

bottom (g/m3

"d), see (61);

TurbDiff = turbulent diffusion (g/m3"d), see (22) and (23); and

Slough = loss due to sloughing (g/m2

"d), see (67).

Figure 27 and Figure 28 are examples of the predicted changes in biomass and the

processes that contribute to these changes in a eutrophic lake. In this and following examples,

rates are plotted as a percentage of biomass in an area graph (Figure 28). The thickness of the

band at any particular date is an indication of the magnitude of a given rate. Because both

positive and negative rates are plotted as positive areas, the percentage on a particular date may

exceed 100%. Discontinuities in rates may indicate stratification, turnover, anoxia, or high

turbidity and washout due to storms.
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0

1

2

3

4

5

6

7

8

9

1/1/19892/1/19893/1/19894/1/19895/1/19896/1/19897/1/19898/1/19899/1/1989

10/1/198911/1/198912/1/1989

1/1/19902/1/19903/1/19904/1/19905/1/19906/1/19907/1/19908/1/19909/1/1990

10/1/199011/1/199012/1/1990

Biomass (g/cu m)

Diatoms (mg/L)

Greens (mg/L)

Blue-greens (mg/L)

Cryptomonad (mg/L)

Figure 27. Predicted Algal Biomass in Lake Onondaga, New York

0.00%

20.00%

40.00%

60.00%

80.00%

100.00%

120.00%

140.00%

1/2/892/2/893/2/894/2/895/2/896/2/897/2/898/2/899/2/89

10/2/8911/2/8912/2/89

1/2/902/2/903/2/904/2/905/2/906/2/907/2/908/2/909/2/90

10/2/9011/2/9012/2/90

Percent of biomass/d

Load Photosynthesis Respiration Excretion Mortality Predation Washout Sinking Turb. Diffusion

Figure 28. Predicted Process Rates for Cryptomonads in Lake Onondaga, New York
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Photosynthesis is modeled as a maximum observed rate multiplied by reduction factors

for the effects of toxicants, habitat, and suboptimal light, temperature, current, and nutrients:

The limitation of primary production in phytoplankton is: 

Periphyton have an additional limitation based on available substrate, which includes the

littoral bottom and the available surfaces of macrophytes. The macrophyte conversion is based

on the observation of 24 m2 periphyton/m2 bottom (Wetzel, 1996) and assumes that the

observation was made with 200 g/m2

 macrophytes.

where:

Pmax = maximum photosynthetic rate (1/d);

PProdLimit = limitation on productivity (unitless);

LtLimit = light limitation (unitless), see (34);

NutrLimit = nutrient limitation (unitless), see (47);

Vlimit = current limitation for periphyton (unitless), see (48);

TCorr = limitation due to suboptimal temperature (unitless), see (51); 

HabitatLimit = in streams, habitat limitation based on plant habitat preferences

(unitless), see (13).

FracPhoto = reduction factor for effect of toxicant on photosynthesis (unitless),

see (294);

FracLittoral = fraction of area that is within euphotic zone (unitless) see (11); 

SurfAreaConv = surface area conversion (0.12 m2

/g);

BiomassMacro = total biomass of macrophytes in system (g/m2

); and

Biomass = biomass of algae (g/m2

).

Under optimal conditions, a reduction factor has a value of 1; otherwise, it has a

fractional value. Use of a multiplicative construct implies that the factors are independent. 

Several authors (for example, Collins, 1980; Straškraba and Gnauck, 1983) have shown that

there are interactions among the factors. However, we feel the data are insufficient to generalize

to all algae; therefore, the simpler multiplicative construct is used, as in many other models

(Chen and Orlob, 1975; Lehman et al., 1975; Jørgensen, 1976; DiToro et al., 1977; Kremer and

Nixon, 1978; Park et al., 1985; Ambrose et al., 1991). Default parameter values for the various

processes are taken primarily from compilations (for example, Jørgensen, 1979; Collins and

Wlosinski, 1983; Bowie et al., 1985); they may be modified as needed.
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Light Limitation 

Because it is required for photosynthesis, light is a very important limiting variable. It is

especially important in controlling competition among plants with differing light requirements.

Similar to many other models (for example, Di Toro et al., 1971; Park et al., 1974, 1975, 1979,

1980; Lehman et al., 1975; Canale et al., 1975, 1976; Thomann et al., 1975, 1979; Scavia et al.,

1976; Bierman et al., 1980; O'Connor et al., 1981), AQUATOX uses the Steele (1962)

formulation for light limitation. Light is specified as average daily radiation. The average

radiation is multiplied by the photoperiod, or the fraction of the day with sunlight, based on a

simplification of Steele's (1962) equation proposed by Di Toro et al. (1971):

where:

LtLimit = light limitation (unitless);

e = the base of natural logarithms (2.71828, unitless);

Photoperiod = fraction of day with daylight (unitless), see (26);

Extinct = total light extinction (1/m), see (35);

DepthBottom = maximum depth or depth of bottom of layer if stratified (m); if

periphyton or macrophyte then limited to euphotic depth;

DepthTop = depth of top of layer (m);

LtAtDepth = intermediate variable for photosynthetic light integral at the bottom

of a layer, see (38);

LtAtTop = intermediate variable for photosynthetic light integral at the top of

a layer, see (39), (40); and

PeriphytExt = extinction due to periphyton; only affects periphyton and

macrophytes (unitless).

Because the equation overestimates by 15 percent the cumulative effect of light limitation

over a 24-hour day, a correction factor of 0.85 is applied (Kremer and Nixon, 1978).

Extinction of light is based on several additive terms: the baseline extinction coefficient

for water (which may include suspended sediment if it is not modeled explicitly), the so-called

"self-shading" of plants, attenuation due to dissolved organic matter (DOM), and attenuation due

to suspended particulate organic matter (POM) and inorganic sediment:

where:

WaterExtinction = user-supplied extinction due to water (1/m);
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(38)

(39)

PhytoExtinction = user-supplied extinction due to phytoplankton and macrophytes

(1/m), see (35), (36);

EcoeffDOM = attenuation coefficient for dissolved detritus (0.03/m-g/m3

);

DOM = concentration of labile and refractory dissolved organic matter

(g/m3), see (114) and (115);

EcoeffPOM = attenuation coefficient for particulate detritus (0.12/m-g/m3);

PartDetr = concentration of labile and refractory particulate detritus (g/m3),

see (112) and (113);

EcoeffSed = attenuation coefficient for suspended inorganic sediment (0.17/mg/m3

); and

InorgSed = concentration of total suspended inorganic sediment (g/m3

), see

(198).

For computational reasons, the value of Extinct is constrained between 5-19 and 25. Light

extinction by phytoplankton, periphyton, and macrophytes is a function of the biomass and

attenuation coefficient for each group. Not only does this place a constraint in the form of selfshading, but it represents a mechanism for competition and succession among plant taxa. For

example, in the model as in nature, an early phytoplankton bloom can restrict growth in

macrophytes. Extinction by periphyton is computed differently because it is not depthdependent but rather pertains to the growing surface:

where:

ECoeffPhytoplant = attenuation coefficient for given phytoplankton or

macrophyte (1/m-g/m3

), 

ECoeffPhytoperi = attenuation coefficient for given periphyton (1/m-g/m2

),

Biomass = concentration of given plant (g/m3

 or g/m2), and

The light effect at depth is computed by:

Light effect at the surface of the water body is computed by:

and light effect at the top of the hypolimnion is computed by:
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where:

Light = photosynthetically active radiation (ly/d); and

LightSat = light saturation level for photosynthesis (ly/d).

Phytoplankton other than blue-greens are assumed to be mixed throughout the well

mixed layer, although subject to sinking. However, healthy blue-green algae tend to float.

Therefore, if the nutrient limitation for blue-greens is greater than 0.25 (47) and the wind is less

than 3 m/s then DepthBottom for blue-greens is set to 0.25 m to account for buoyancy due to gas

vacuoles. Otherwise it is set to 3 m to represent downward transport by Langmuir circulation. 

Under the ice, all phytoplankton are represented as occurring in the top 2 m (cf. LeCren and

Lowe-McConnell, 1980). As discussed in Section 3.5, light is decreased to 33% of incident

radiation if ice cover is predicted. 

Approximately half the incident solar radiation is photosynthetically active (Edmondson,

1956):

where:

Solar = average daily light intensity (ly/d), see (25).

The light-limitation function represents both limitation for suboptimal light intensity and

photoinhibition at high light intensities (Figure 29). However, when the photoperiod for all but

the highest latitudes is factored in, photoinhibition disappears (Figure 30). When considered

over the course of the year, photoinhibition can occur in very clear, shallow systems during

summer mid-day hours (Figure 31), but it usually is not a factor when considered over 24 hours

(Figure 32). 

The extinction coefficient for pure water varies considerably in the photosyntheticallyactive 400-700 nm range (Wetzel, 1975, p. 55); a value of 0.016 (1/m) correspond to the

extinction of green light. In many models dissolved organic matter and suspended sediment are

not considered separately, so a much larger extinction coefficient is used for "water" than in

AQUATOX. The attenuation coefficients have units of 1/m-(g/m3

) because they represent the

amount of extinction caused by a given concentration (Table 5). 
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 4

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Figure 29

Instantaneous Light Response Function

Figure 30

Daily Light Response Function

Figure 31

Mid-day Light Limitation

Figure 32

Daily Light Limitation

Table 5. Light Extinction and Attenuation Coefficients

WaterExtinction* 0.016 1/m Wetzel, 1975

ECoeffPhytodiatom

* 0.014 1/m-(g/m3

) Collins and Wlosinski, 1980

ECoeffPhytoblue-green * 0.099 1/m-(g/m3

) Megard et al., 1979 (calc.) 

ECoeffDOM 0.03 1/m-(g/m3

) Effler et al., 1985 (calc.)

ECoeffPOM 0.12 1/m-(g/m3

) Verduin, 1982

ECoeffSed 0.03 1/m-(g/m3

) McIntire and Colby, 1978

* user-supplied
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Figure 33

Contributions to Light Extinction in Lake George, NY

The Secchi depth, the depth at which a Secchi disk disappears from view, is a commonly

used indication of turbidity. It is computed as (Straškraba and Gnauck, 1985):

where:

Secchi = Secchi depth (m).

This relationship also could be used to back-calculate an overall Extinction coefficient if only

the Secchi depth is known for a site.

As a verification of the extinction computations, the calculated and observed Secchi

depths were compared for Lake George, New York. The Secchi depth is estimated to be 8.3 m

in Lake George, based on site data for the various components (Figure 33). This compares

favorably with observed values of 7.5 to 11 (Clifford, 1982). 

Nutrient Limitation 

There are several ways that nutrient limitation has been represented in models. Algae are

capable of taking up and storing sufficient nutrients to carry them through several generations,

and models have been developed to represent this. However, if the timing of algal blooms is not

critical, intracellular storage of nutrients can be ignored, constant stoichiometry can be assumed,

and the model is much simpler. Therefore, based on the efficacy of this simplifying assumption,
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nutrient limitation by external nutrient concentrations is used in AQUATOX, as in many other

models (for example, Chen, 1970; Parker, 1972; Lassen and Nielsen, 1972; Larsen et al., 1974;

Park et al., 1974; Chen and Orlob, 1975; Patten et al., 1975; Environmental Laboratory, 1982;

Ambrose et al., 1991). 

For an individual nutrient, saturation kinetics is assumed, using the Michaelis-Menten or

Monod equation (Figure 34); this approach is founded on numerous studies (cf. Hutchinson,

1967): 

where:

PLimit = limitation due to phosphorus (unitless);

Phosphorus = available soluble phosphorus (gP/m3

);

KP = half-saturation constant for phosphorus (gP/m3);

NLimit = limitation due to nitrogen (unitless);

Nitrogen = available soluble nitrogen (gN/m3);

KN = half-saturation constant for nitrogen (gN/m3);

CLimit = limitation due to inorganic carbon (unitless);

Carbon = available dissolved inorganic carbon (gC/m3

); and

KCO2 = half-saturation constant for carbon (gC/m3

).
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Figure 34 

Nutrient Limitation

(46)

(47)

Nitrogen fixation in blue-green algae is handled by setting NLimit to 1.0 if Nitrogen is

less than half the KN value. Otherwise, it is assumed that nitrogen fixation is not operable, and

NLimit is computed as for the other algae.

Concentrations must be expressed in terms of the chemical element. Because carbon

dioxide is computed internally, the concentration of carbon is corrected for the molar weight of

the element:

where:

C2CO2 = ratio of carbon to carbon dioxide (0.27); and

CO2 = inorganic carbon (g/m3

).

Like many models (for example, Larsen et al., 1973; Baca and Arnett, 1976; Scavia et

al., 1976; Smith, 1978; Bierman et al., 1980; Park et al., 1980; Johanson et al., 1980; Grenney

and Kraszewski, 1981; Ambrose et al., 1991), AQUATOX uses the minimum limiting nutrient,

whereby the Monod equation is evaluated for each nutrient, and the factor for the nutrient that is

most limiting at a particular time is used:

where:
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NutrLimit = reduction due to limiting nutrient (unitless).

Alternative formulations used in other models include multiplicative and harmonic-mean

constructs, but the minimum limiting nutrient construct is well-founded in laboratory studies

with individual species. 

Current Limitation 

Because they are fixed in space, periphyton also are limited by slow currents that do not

replenish nutrients and carry away senescent biomass. Based on the work of McIntire (1973)

and Colby and McIntire (1978), a factor relating photosynthesis to current velocity is used for

periphyton:

where:

VLimit = limitation or enhancement due to current velocity (unitless);

RedStillWater = reduction in photosynthesis in absence of current (unitless);

VelCoeff = empirical proportionality coefficient for velocity (0.057, unitless);

and

Velocity = flow rate (converted to m/s), see (14).

VLimit has a minimum value for photosynthesis in the absence of currents and increases

asymptotically to a maximum value for optimal current velocity (?). In high currents scour can

limit periphyton; see (67). The value of RedStillWater depends on the circumstances under

which the maximum photosynthesis rate was measured; if PMax was measured in still water then

RedStillWater = 1, otherwise a value of 0.2 is appropriate (Colby and McIntire, 1978).

Adjustment for Suboptimal Temperature

AQUATOX uses a general but complex formulation to represent the effects of

temperature. All organisms exhibit a nonlinear, adaptive response to temperature changes (the

so-called Stroganov function). Process rates other than algal respiration increase as the ambient

temperature increases until the optimal temperature for the organism is reached; beyond that

optimum, process rates decrease until the lethal temperature is reached. This effect is

represented by a complex algorithm developed by O'Neill et al. (1972) and modified slightly for

application to aquatic systems (Park et al., 1974). An intermediate variable VT is computed first;

it is the ratio of the difference between the maximum temperature at which a process will occur

and the ambient temperature over the difference between the maximum temperature and the

optimal temperature for the process:
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where:

Temperature = ambient water temperature (°C); 

TMax = maximum temperature at which process will occur (°C);

TOpt = optimal temperature for process to occur (°C); and

Acclimation = temperature acclimation (°C), as described below.

Acclimation to both increasing and decreasing temperature is accounted for with a

modification developed by Kitchell et al. (1972):

 where:

XM = maximum acclimation allowed (°C);

KT = coefficient for decreasing acclimation as temperature approaches Tref

(unitless);

ABS = function to obtain absolute value; and

TRef = “adaptation” temperature below which there is no acclimation (°C).

The mathematical sign of the variable Acclimation is negative if the ambient temperature

is below the temperature at which there is no acclimation; otherwise, it is positive.

If the variable VT is less than zero, in other words, if the ambient temperature exceeds

(TMax + Acclimation), then the suboptimal factor for temperature is set equal to zero and the

process stops. Otherwise, the suboptimal factor for temperature is calculated as (Park et al.,

1974):

where:

TCorr = limitation due to suboptimal temperature (unitless); and

where:
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Figure 35

Temperature Response of Blue-Greens

Figure 36

Temperature Response of Diatoms

(55)

and

where:

Q10 = slope or rate of change per 10/C temperature change (unitless).

This well-founded, robust algorithm for TCorr is used in AQUATOX to obtain reduction

factors for suboptimal temperatures for all biologic processes in animals and plants, with the

exception of algal respiration. By varying the parameters, organisms with both narrow and

broad temperature tolerances can be represented (Figure 35, Figure 36). 

Algal Respiration 

Endogenous or dark respiration is the metabolic process whereby oxygen is taken up by

plants for the production of energy for maintenance and carbon dioxide is released (Collins and

Wlosinski, 1983). Although it is normally a small loss rate for the organisms, it has been shown

to be exponential with temperature (Aruga, 1965). Riley (1963, see also Groden, 1977) derived

an equation representing this relationship. Based on data presented by Collins (1980), maximum

respiration is constrained to 60% of photosynthesis. Laboratory experiments in support of the

CLEANER model confirmed the empirical relationship and provided additional evidence of the

correct parameter values (Collins, 1980), as demonstrated by Figure 37:
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Figure 37

Respiration (Data From Collins, 1980)

where:

Respiration = dark respiration (g/m3

"d);

Resp0 = respiration rate at 0/C (g/g"d);

TResp = exponential temperature coefficient (0.065//C);

Temperature = ambient water temperature (/C); and

Biomass = plant biomass (g/m3).

This construct also applies to macrophytes. The values for Resp0 are given in Table 6.

Table 6. Values for respiration rate at 0/C.

Plant group Resp0 Reference

Diatoms 0.022 LeCren & Lowe-McConnell, 1980, p. 189

Greens 0.006 LeCren & Lowe-McConnell, 1980, p. 189

Blue-greens 0.072 Collins, 1980

Other algae 0.006 arbitrarily set to the same as greens

Macrophytes 0.015 LeCren & Lowe-McConnell, 1980, p. 195
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(57)

Figure 38

Photorespiration

Photorespiration and Excretion

Photorespiration, with the release of carbon dioxide and the concomitant excretion of

dissolved organic material, occurs in the presence of light. Environmental conditions that inhibit

cell division but still allow photoassimilation result in release of organic compounds. This is

especially true for both low and high levels of light (Fogg et al., 1965; Watt, 1966; Nalewajko,

1966; Collins, 1980). AQUATOX uses an equation modified from one by Desormeau (1978)

that is the inverse of the light limitation:

where:

Excretion = release of photosynthate (g/m3

"d);

KResp = coefficient of proportionality between excretion and

photosynthesis at optimal light levels (unitless); and

Photosynthesis = photosynthesis (g/m3"d), see (31),

and where:

where:

LtLimit= light limitation for a given plant (unitless), see (34).

It is a continuous function (Figure 38) and has a tendency to overestimate excretion

slightly at light levels close to light saturation where experimental evidence suggests a constant

relationship (Collins, 1980). The construct for photorespiration also applies to macrophytes.
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(59)

(60)

Algal Mortality 

Nonpredatory algal mortality can occur as a response to toxic chemicals (discussed in

Chapter 8) and as a response to unfavorable environmental conditions. Phytoplankton under

stress may suffer greatly increased mortality due to autolysis and parasitism (Harris, 1986). 

Therefore, most phytoplankton decay occurs in the water column rather than in the sediments

(DePinto, 1979). The rapid remineralization of nutrients in the water column may result in a

succession of blooms (Harris, 1986). Sudden changes in the abiotic environment may cause the

algal population to crash; stressful changes include nutrient depletion, unfavorable temperature,

and damage by light (LeCren and Lowe-McConnell, 1980). These are represented by a mortality

term in AQUATOX that includes toxicity, high temperature (Scavia and Park, 1976), and

combined nutrient and light limitation (Collins and Park, 1989):

where:

Mortality = nonpredatory mortality (g/m3

"d);

Poisoned = mortality rate due to toxicant (g/m3

"d), see ((287));

KMort = intrinsic mortality rate (g/g"d); and

Biomass = plant biomass (g/m3),

and where:

and:

where:

ExcessT = factor for high temperatures (g/g"d);

TMax = maximum temperature tolerated (/ C);

Stress = factor for suboptimal light and nutrients (g/g"d), 

Emort = approximate maximum fraction killed per day with total limitation

(g/g"d);

NutrLimit = reduction due to limiting nutrient (unitless), see (47)

LtLimit = light limitation (unitless), see (34).

Exponential functions are used so that increasing stress leads to rapid increases in

mortality, especially with high temperature where mortality is 50% per day at the TMax (Figure

39), and, to a much lesser degree, with suboptimal nutrients and light (Figure 40). This
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 4

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Figure 39

Mortality Due To High Temperatures

Figure 40

Mortality Due To Light Limitation

(61)

simulated process is responsible in part for maintaining realistically high levels of detritus in the

simulated water body. Low temperatures are assumed not to affect algal mortality. 

Sinking 

Sinking of phytoplankton, either between layers or to the bottom sediments, is modeled

as a function of physiological state, similar to mortality. Phytoplankton that are not stressed are

considered to sink at given rates, which are based on field observations and implicitly account

for the effects of averaged water movements (cf. Scavia, 1980). Sinking also is represented as

being impeded by turbulence associated with higher discharge (but only when discharge exceeds

mean discharge):

where:

Sink = phytoplankton loss due to settling (g/m3

"d);

KSed = intrinsic settling rate (m/d);

Depth = depth of water or, if stratified, thickness of layer (m);

MeanDischarge = mean annual discharge (m3/d);

Discharge = daily discharge (m3

/d), see Table 1; and

Biomass = phytoplankton biomass (g/m3).

The model is able to mimic high sedimentation loss associated with the crashes of

phytoplankton blooms, as discussed by Harris (1986). As the phytoplankton are stressed by

toxicants and suboptimal light, nutrients, and temperature, the model computes an exponential
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Figure 41

Sinking as a Function of Nutrient Stress

 (63)

increase in sinking (Figure 41), as observed by Smayda (1974), and formulated by Collins and

Park (1989):

where:

SedAccel = increase in sinking due to physiological stress (unitless);

ESed = exponential settling coefficient (unitless);

LtLimit = light limitation (unitless), see (33);

NutrLimit = nutrient limitation (unitless), see (47); and

FracPhoto = reduction factor for effect of toxicant on photosynthesis (unitless),

see (294);

TCorr = temperature limitation (unitless), see (51).

Washout and Sloughing 

Phytoplankton are subject to downstream drift. In streams and in lakes and reservoirs

with low retention times this may be a significant factor in reducing or even precluding

phytoplankton populations (LeCren and Lowe-McConnell, 1980). The process is modeled as a

simple function of discharge:

where:
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0

1

2

3

4

5

6

7

3/15/19893/17/19893/19/19893/21/19893/23/19893/25/19893/27/19893/29/19893/31/1989

4/2/19894/4/19894/6/19894/8/1989

4/10/19894/12/19894/14/19894/16/19894/18/19894/20/19894/22/19894/24/19894/26/19894/28/19894/30/1989

5/2/1989

Biomass (mg/cm2

)

Diatoms(g/m2) Oth alg(g/m2) Periphyton Observed

Figure 42. Comparison of predicted biomass of periphyton, constituent

algae, and observed biomass of periphyton (Rosemond, 1993) in Walker

Branch, Tennessee, with addition of both N and P and removal of grazers

in Spring, 1989.

WashoutPhytoplankton = loss due to downstream drift (g/m3"d);

Discharge = daily discharge (m3

/d);

Volume = volume of site (m3

); and

Biomass = biomass of phytoplankton (g/m3).

Periphyton often exhibit a pattern of buildup and then a sharp decline in biomass due to

sloughing. Based on extensive experimental data from Walker Branch, Tennessee (Rosemond,

1993), a complex sloughing formulation, extending the approach of Asaeda and Son (2000), was

implemented. This function was able to represent a wide range of conditions (Figure 42 and

Figure 43): 

where:

WashoutPeriphyton = loss due to sloughing (g/m3

"d);

Slough = loss due to natural causes (g/m3"d), see (67); and

Dislodgeperi, Tox = loss due to toxicant-induced sloughing (g/m3

"d), see (300).
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 4

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0

2

4

6

8

10

12

14

16

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48

Rates (g/m2 d)

Photosynthesis Respiration Excretion Mortality Predation Sloughing

Figure 43. Predicted rates for diatoms in Walker Branch, Tennessee, with

addition of both N and P and removal of grazers in Spring, 1989. Note the

importance of periodic sloughing. Rates expressed as g/m2 d.

 (65)

 (66)

Natural sloughing is a function of senescence due to suboptimal conditions and the drag

force of currents acting on exposed biomass. Drag increases as both biomass and velocity

increase:

where:

DragForce = drag force (kg m/s2

);

Rho = density (kg/m3);

DragCoeff = drag coefficient (2.53E-4, unitless);

Vel = velocity (converted to m/s) see (14);

BioVol = biovolume of algae (mm3

/mm2);

UnitArea = unit area (mm2);

1E-6 = conversion factor (m2

/mm2).

Biovolume is not modeled directly by AQUATOX, so a simplifying assumption is that

the empirical relationship between biomass and biovolume is constant for a given growth form,

based on observed data from Rosemond (1993):
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 (68)

where:

BiovolDia = biovolume of diatoms (mm3

/mm2);

BiovolFil = biovolume of filamentous algae (mm3

/mm2);

Biomass = biomass of given algal group (g/m2).

Suboptimal light, nutrients, and temperature cause senescence of cells that bind the

periphyton and keep them attached to the substrate. This effect is represented by a factor,

Suboptimal, which is computed in modeling the effects of environmental conditions on

photosynthesis. Suboptimal decreases the critical force necessary to cause sloughing. If the drag

force exceeds the critical force for a given algal group modified by the Suboptimal factor and an

adaptation factor, then sloughing occurs:

where:

SuboptimalOrg = factor for suboptimal nutrient, light, and temperature effect on

senescence of given periphyton group (unitless);

FCritOrg = critical force necessary to dislodge given periphyton group (kg

m/s2);

Adaptation = factor to adjust for mean discharge of site compared to reference

site (unitless);

Slough = biomass lost by sloughing (g/m3);

FracSloughed = fraction of biomass lost at one time (97%, unitless).

where:

NutrLimit = nutrient limitation for given algal group (unitless) computed by

AQUATOX; see (47);

LtLimitOrg = light limitation for given algal group (unitless) computed by

AQUATOX; see (33); and

TCorr = temperature limitation for a given algal group (unitless) computed by

AQUATOX; see (51).

The sloughing construct was tested and calibrated (U.S. E.P.A., 2001) with data from

experiments with artificial and woodland streams in Tennessee (Rosemond, 1993, Figure 42).

However, in modeling periphyton at several sites, it was observed that sloughing appears to be

triggered at greatly differing mean velocities. The working hypothesis is that periphyton adapt to

the ambient conditions of a particular channel. Therefore, a factor is included to adjust for the mean

discharge of a given site compared to the reference site in Tennessee. It is still necessary to calibrate
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(70)

FCrit for each site to account for intangible differences in channel and flow conditions, analogous

to the calibration of shear stress by sediment modelers, but the range of calibration needed is reduced

by the Adaptation factor:

where:

MeanDischarge = mean discharge for given site, computed over the period of

the simulation (m3/d);

RefDischarge = mean discharge for reference experimental stream (3.5 m3/d).

Detrital Accumulation in Periphyton

In phytoplankton, mortality results in immediate production of detritus, and that transfer is

modeled. However, for purposes of modeling, periphyton are defined as including associated

detritus. The accumulation of non-living biomass is modeled implicitly by not simulating mortality

due to suboptimal conditions. Rather, in the simulation biomass builds up, causing increased selfshading, which in turn makes the periphyton more vulnerable to sudden loss due to sloughing. The

fact that part of the biomass is non-living is ignored as a simplification of the model.

Chlorophyll a

Chlorophyll a is not simulated directly. However, because chlorophyll a is commonly

measured in aquatic systems and because water quality managers are accustomed to thinking of it

as an index of water quality, the model converts phytoplankton biomass estimates into approximate

values for chlorophyll a. The ratio of carbon to chlorophyll a exhibits a wide range of values

depending on the nutrient status of the algae (Harris, 1986); blue-green algae often have higher

values (cf. Megard et al., 1979). AQUATOX uses a value of 45 :gC/:g chlorophyll a for bluegreens and a value of 28 for other phytoplankton as reported in the documentation for WASP

(Ambrose et al., 1991). The values are more representative for blooms than for static conditions,

but managers are usually most interested in the maxima. The results are presented as total

chlorophyll a in :g/L; therefore, the computation is:

where:

ChlA = biomass as chlorophyll a (:g/L);

BiomassBlGr = biomass of blue-green algae (mg/L);
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Biomassothers = biomass of algae other than blue-greens (mg/L);

CToOrg = ratio of carbon to biomass (0.526, unitless); and

1000 = conversion factor for mg to :g (unitless).

Periphytic chlorophyll a is computed as a linear conversion from the ash-free dry weight

(AFDW) of periphyton; because periphyton can collect inorganic sediments, it is important to

measure and model it as AFDW. All biomass computations in AQUATOX are as AFDW. The

conversion factor is based on the observed average ratio of chlorophyll a to AFDW for the Cahaba

River near Birmingham, Alabama (unpub. data).

where:

PeriChlor = periphytic chlorophyll a (mg/m2

);

PeriConv = conversion from periphyton AFDW to chlorophyll a (6.1 mg/m2

:

g/m2);

BiomassPeri = biomass of given periphyton (AFDW in g/m2).

4.2 Macrophytes

Submersed aquatic vegetation or macrophytes can be an important component of shallow

aquatic ecosystems. It is not unusual for the majority of the biomass in an ecosystem to be in the

form of macrophytes during the growing season. Seasonal macrophyte growth, death, and

decomposition can affect nutrient cycling, and detritus and oxygen concentrations. By forming

dense cover, they can modify habitat and provide protection from predation for invertebrates and

smaller fish (Howick et al., 1993); this function is represented in AQUATOX (see Figure 49).

Macrophytes also provide direct and indirect food sources for many species of waterfowl, including

swans, ducks, and coots (Jupp and Spence, 1977b).

AQUATOX represents macrophytes as occupying the littoral zone, that area of the bottom

surface that occurs within the euphotic zone (see (11) for computation). Similar to periphyton, the

compartment has units of g/m2

. In nature, macrophytes can be greatly reduced if phytoplankton

blooms or higher levels of detritus increase the turbidity of the water (cf. Jupp and Spence, 1977a).

Because the depth of the euphotic zone is computed as a function of the extinction coefficient (11),

the area predicted to be occupied by macrophytes can increase or decrease depending on the clarity

of the water.

The macrophyte equations are based on submodels developed for the International Biological

Program (Titus et al., 1972; Park et al., 1974) and CLEANER models (Park et al., 1980) and for the

Corps of Engineers' CE-QUAL-R1 model (Collins et al., 1985):
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(73)

and:

where:

dBiomass/dt = change in biomass with respect to time (g/m2"d);

Loading = loading of macrophyte, usually used as a “seed” in the simulation;

may be a moderate value if there is rapid regrowth from rhizomes

following breakage or die-back (g/m2"d);

Photosynthesis = rate of photosynthesis (g/m2"d);

Respiration = respiratory loss (g/m2"d), see (55);

Excretion = excretion or photorespiration(g/m2

"d), see (56);

Mortality = nonpredatory mortality (g/m2"d), see (74);

Predation = herbivory (g/m2"d), see (86);

Breakage = loss due to breakage (g/m2"d), see (75);

PMax = maximum photosynthetic rate (1/d);

LtLimit = light limitation (unitless), see (34);

TCorr = correction for suboptimal temperature (unitless), see (51);

HabitatLimit = in streams, habitat limitation based on plant habitat preferences

(unitless), see (13);

FracLittoral = fraction of bottom that is in the euphotic zone (unitless) see (11); and

NutrLimit = nutrient limitation for bryophytes only (unitless), see (47);

FracPhoto = reduction factor for effect of toxicant on photosynthesis (unitless),

see (294).

They share many of the constructs with the algal submodel described above. Temperature

limitation is modeled similarly, but with different parameter values. Light limitation also is handled

similarly, using the Steele (1962) formulation; the application of this equation has been verified with

laboratory data (Collins et al., 1985). Periphyton are epiphytic in the presence of macrophytes; by

growing on the leaves they contribute to the light extinction for the macrophytes (Sand-Jensen,

1977). Extinction due to periphyton biomass is computed in AQUATOX, by inclusion in LtLimit.

Nutrient limitation is not modeled at this time except for bryophytes because most macrophytes can

obtain their nutrients from bottom sediments (Bristow and Whitcombe, 1971; Nichols and Keeney,

1976; Barko and Smart, 1980). 

Simulation of respiration and excretion utilize the same equations as algae; excretion results

in "nutrient pumping" because the nutrients are assumed to come from the sediments but are
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Figure 44

Mortality as a Function of Temperature

(75)

excreted to the water column. (Because nutrients are not explicitly modeled in bottom sediments,

this can result in loss of mass balance, particularly in shallow ponds. This will be addressed in a

future version.) Non-predatory mortality is modeled similarly to algae as a function of suboptimal

temperature (but not light). However, mortality is a function of low as well as high temperatures,

and winter die-back is represented as a result of this control; the response is the inverse of the

temperature limitation (Figure 44):

where:

KMort = intrinsic mortality rate (g/g"d);

Poisoned = mortality rate due to toxicant (g/g"d) (287), and

EMort = maximum mortality due to suboptimal temperature (g/g"d).

Sloughing of dead leaves can be a significant loss (LeCren and Lowe-McConnell, 1980); it

is simulated as an implicit result of mortality (Figure 44).

Macrophytes are subject to breakage due to higher water velocities; this breakage of live

material is different from the sloughing of dead leaves. Although breakage is a function of shoot

length and growth form as well as currents (Bartell et al., 2000; Hudon et al., 2000), a simpler

construct was developed for AQUATOX (Figure 45):

where:

Breakage = macrophyte breakage (g/m2 "d);
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0

0.2

0.4

0.6

0.8

1

1.2

1

21

41

61

81

101

121

141

161

181

201

221

241

261

281

300

Velocity (cm/s)

Breakage (g/m2 ·d)

Figure 45. Breakage of macrophytes as a function of current

velocity; VelMax set to 300 cm/s.

(76)

Velocity = current velocity (cm/s) see (14);

VelMax = velocity at which total breakage occurs (cm/s);

Gradual = velocity scaling factor (20 cm/s);

UnitTime = unit time for simulation (1 d);

Biomass = macrophyte biomass (g/m2

).

At this time there is no provision for computing velocity due to wave action, so that

macrophyte biomass may be overestimated in water bodies where there is significant wave action.

Bryophytes (mosses and liverworts) are a special class of macrophytes that attach to hard

substrates, are stimulated by and take up nutrients directly from the water, are resistant to breakage,

and decompose very slowly (Stream Bryophyte Group, 1999). Nutrient limitation is enabled when

the “Bryophytes” plant type is selected, just as it is for algae. The model assumes that when a

bryophyte breaks or dies the result is 75% particulate and 25% dissolved refractory detritus; in

contrast, other macrophytes are assumed to yield 38% particulate and 24% dissolved labile detritus

and the rest (38%) as refractory detritus. All other differences between bryophytes and other

macrophytes in AQUATOX are based on differences in parameter values. These include low

saturating light levels, low optimum temperature, very low mortality rates, moderate resistance to

breakage, and resistance to herbivory (Arscott et al., 1998; Stream Bryophyte Group, 1999).

Because in the field it is difficult to separate bryophyte chlorophyll from that of periphyton, it is

computed so that the two can be combined and related to field values:

where:

MossChlor = bryophytic chlorophyll a (mg/m2

);
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BryoConv = conversion from bryophyte AFDW to chlorophyll a (8.9 mg/m2:

g/m2

);

BiomassBryo = biomass of given bryophyte (AFDW in g/m2

).

Currents and wave agitation can both stimulate and retard macrophyte growth. These effects

will be modeled in a future version. Similar to the effect on periphyton, water movement can

stimulate photosynthesis in macrophytes (Westlake, 1967); the same function could be used for

macrophytes as for periphyton, although with different parameter values. Jupp and Spence (1977b)

have shown that wave agitation can severely limit macrophytes; time-varying breakage eventually

will be modeled when wave action is simulated. 

4.3 Animals

Zooplankton, benthic invertebrates, benthic insects, and fish are modeled, with only slight

differences in formulations, with a generalized animal submodel that is parameterized to represent

different groups:

where:

dBiomass/dt = change in biomass of animal with respect to time (g/m3"d);

Load = biomass loading, usually from upstream (g/m3"d);

Consumption = consumption of food (g/m3"d), see (85);

Defecation = defecation of unassimilated food (g/m3

"d), see (84);

Respiration = respiration (g/m3

"d), see (87);

Excretion = excretion (g/m3

"d), see (97);

Mortality = nonpredatory mortality (g/m3

"d), see (98);

Predation = predatory mortality (g/m3

"d), see (86);

GameteLoss = loss of gametes during spawning (g/m3

"d), see (102);

Washout = loss due to being carried downstream by washout and drift (g/m3"d),

see (105) and (106);

Migration = loss (or gain) due to vertical migration (g/m3

"d), see (109);

Promotion = promotion to next size class or emergence (g/m3"d), see (110); and

Recruit = recruitment from previous size class or through reproduction

(g/m3"d), see (110);

Entrainment = entrainment and downstream transport with flood waters (g/m3"d), see

(108).
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0

2

4

6

8

10

12

1/1/20002/1/20003/1/20004/1/20005/1/20006/1/20007/1/20008/1/20009/1/2000

10/1/200011/1/200012/1/2000

1/1/20012/1/20013/1/20014/1/20015/1/20016/1/20017/1/20018/1/20019/1/2001

10/1/200111/1/200112/1/2001

1/1/20022/1/20023/1/20024/1/20025/1/20026/1/20027/1/20028/1/20029/1/2002

10/1/2002

Biomass (g/ sq m)

Corbicula (g/sq.m) Gastropod g_m2 (g/sq.m) Shiner (g/sq.m) Bluegill (g/sq.m)

Figure 46. Predicted Changes in Biomass in a Stream

The change in biomass (Figure 46) is a function of a number of processes (Figure 47) that

are subject to environmental factors, including biotic interactions. Similar to the way algae are

treated, parameters for different species of invertebrates and fish are loaded and available for editing

by means of the entry screens. Biomass of zoobenthos and fish is expressed as g/m2

 instead of g/m3.
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 4

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0.00%

20.00%

40.00%

60.00%

80.00%

100.00%

120.00%

140.00%

160.00%

180.00%

1/2/20002/2/20003/2/20004/2/20005/2/20006/2/20007/2/20008/2/20009/2/2000

10/2/200011/2/200012/2/2000

1/2/20012/2/20013/2/20014/2/20015/2/20016/2/20017/2/20018/2/20019/2/2001

10/2/200111/2/200112/2/2001

1/2/20022/2/20023/2/20024/2/20025/2/20026/2/20027/2/20028/2/20029/2/2002

10/2/2002

Consumption Defecation Respiration Excretion Predation Mortality Gamete Loss Entrainment

Figure 47. Predicted Process Rates for the Invasive Clam Corbicula, Expressed as

Percent of Biomass; Spikes are Entrainment During Storm Events

(78)

Consumption, Defecation, and Predation 

Several formulations have been used in various models to represent consumption of prey,

reflecting the fact that there are different modes of feeding and that experimental evidence can be

fit by any one of several equations (Mullin et al., 1975; Scavia, 1979; Straškraba and Gnauck, 1985).

Ingestion is represented in AQUATOX by a maximum consumption rate, adjusted for

ambient food and temperature conditions, and reduced for sublethal toxicant effects and limitations

due to habitat preferences of a given predator or herbivore:

where:

Ingestionprey, pred = ingestion of given prey by given predator or herbivore (g/m3

"d);

Biomasspred = concentration of predator or herbivore (g/m3"d);

CMax = maximum feeding rate for predator or herbivore (g/g"d);

SatFeeding = saturation-feeding kinetic factor, see (80);

TCorr = reduction factor for suboptimal temperature (unitless), see (51);

ToxReduction = reduction due to effects of toxicant (see Eq. (297), unitless); and
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(80)

(81)

HabitatLimit = in streams, habitat limitation based on predator habitat preferences

(unitless), see (13).

The maximum consumption rate is sensitive to body size, so an alternative to specifying

CMax for fish is to compute it using an allometric equation and parameters from the Wisconsin

Bioenergetics Model (Hewett and Johnson, 1992; Hanson et al., 1997):

where:

CA = maximum consumption for a 1-g fish at optimal temperature (g/g"d);

MeanWeight = mean weight for a given fish species (g);

CB = slope of the allometric function for a given fish species. 

Many animals adjust their search or filtration in accordance with the concentration of prey;

therefore, a saturation-kinetic term is used (Park et al., 1974, 1980; Scavia and Park, 1976):

where:

Preference = preference of predator for prey (unitless);

Food = available biomass of given prey (g/m3);

FHalfSat = half-saturation constant for feeding by a predator (g/m3

).

The food actually available to a predator may be reduced in two ways:

where:

BMin = minimum prey biomass needed to begin feeding (g/m3

); and

Refuge = reduction factor for prey hiding in macrophytes (unitless).

Search or filtration may virtually cease below a minimum prey biomass (BMin) to conserve

energy (Figure 48), so that a minimum food level is incorporated (Parsons et al., 1969; Steele, 1974;

Park et al., 1974; Scavia and Park, 1976; Scavia et al., 1976; Steele and Mullin, 1977). However,

cladocerans (for example, Daphnia) must constantly filter because the filtratory appendages also

serve for respiration; therefore, in these animals there is no minimum feeding level and BMin is set

to 0.
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 4

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Figure 48 

Saturation-kinetic Consumption

(82)

Macrophytes can provide refuge from predation; this is represented by a factor related to the

macrophyte biomass that is original with AQUATOX (Figure 49): 

where:

HalfSat = half-saturation constant (20, g/m3

), and

BiomassMacro = biomass of macrophyte (g/m3

).
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 4

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Figure 49 

Refuge From Predation

(83)

AQUATOX is a food-web model with multiple potential food sources. Passive size-selective

filtering (Mullin, 1963; Lam and Frost, 1976) and active raptorial selection (Burns, 1969; Berman

and Richman, 1974; Bogdan and McNaught, 1975; Brandl and Fernando, 1975) occur among

aquatic organisms. Relative preferences are represented in AQUATOX by a matrix of preference

parameters first proposed by O'Neill (1969) and used in several aquatic models (Bloomfield et al.,

1973; Park et al., 1974; Canale et al., 1976; Scavia et al., 1976). Higher values indicate increased

preference by a given predator for a particular prey compared to the preferences for all possible prey.

In other words, the availability of the prey is weighted by the preference factor. 

The preference factors are normalized so that if a potential food source is not modeled or is

below the BMin value, the other preference factors are modified accordingly, representing adaptive

preferences:

where:

Preferenceprey,pred = normalized preference of given predator for given prey

(unitless);

Prefprey, pred = initial preference value from the animal parameter screen

(unitless); and
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 4

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(84)

(85)

(86)

SumPref = sum of preference values for all food sources that are present

above the minimum biomass level for feeding during a

particular time step (unitless).

Similarly, different prey types have different potentials for assimilation by different

predators. The fraction of ingested prey that is egested as feces or discarded (and which is treated

as a source of detritus by the model, see (124)), is indicated by a matrix of egestion coefficients with

the same structure as the preference matrix, so that defecation is computed as (Park et al., 1974): 

where:

Defecationpred = total defecation for given predator (g/m3

"d);

EgestCoeffprey, pred = fraction of ingested prey that is egested (unitless); and

IncrEgest = increased egestion due to toxicant (see Eq. (298), unitless).

Consumption of prey for a predator is also considered predation or grazing for the prey.

Therefore, AQUATOX represents consumption as a source term for the predator and as a loss term

for the prey:

where

Consumptionpred = total consumption rate by predator (g/m3

"d); and

Predationprey = total predation or grazing on given prey (g/m3"d).

Respiration 

Respiration can be considered as having three components. Standard respiration is a rate at

resting in which the organism is expending energy without consumption. Active respiration is

modeled only in fish and only when allometric (weight-dependent) equations are used, so standard

respiration can be considered as a composite “routine” respiration for invertebrates and in the

simpler implementation for fish. The so-called specific dynamic action is the metabolic cost of

digesting and assimilating prey. In the model active respiration is combined with standard

respiration by means of an activity factor, and specific dynamic action is an additive term (Kitchell

et al., 1974):
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 4

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(87)

(88)

(89)

where:

Respirationpred = respiratory loss of given predator (g/m3"d);

StdResppred = basal respiratory loss modified by temperature (g/m3

"d); see

(88) and (89);

Activitypred = a factor for respiratory loss associated with swimming

(unitless), see (92) and (94); and

SpecDynActionpred = metabolic cost of processing food (g/m3"d), see (96).

AQUATOX simulates standard respiration as an optimal observed rate modified by a

temperature dependence and, in fish, a density dependence (see Kitchell et al., 1974):

where:

RoutineResppred = routine respiration rate at optimal temperature for given predator

(g/g"d); parameter input by user as “Respiration Rate” or computed

as a function of the weight of the animal (see below);

TCorrpred = Stroganov temperature function (unitless), see (51);

Biomasspred = concentration of predator (g/m3); and

DensityDep = density-dependent respiration factor used in computing standard

respiration, applicable only to fish (unitless). See (95)

As an alternative formulation, standard respiration in fish can be modeled as a function of

the weight of the fish using an allometric equation (Hewett and Johnson, 1992; Hanson et al., 1997):

where:

BasalResppred = basal respiration rate for given predator (g/g"d); computed as

a function of the weight of the animal, see (90);

MeanWeightpred = mean weight for a given fish (g);

RBpred = slope of the allometric function for a given fish (1/g); 

TFnpred = temperature function (unitless), see (91), (92).

The allometric functions are based on the well known Wisconsin Bioenergetics Model and,

for convenience, use the published parameter values for that model (Hewett and Johnson, 1992;
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 4

4 - 36

(90)

(91)

(92)

(93)

Hanson et al., 1997). However, the basal respiration rate in that model is expressed as g of oxygen

per g organic matter of fish per day, and this has to be converted to organic matter respired:

where:

RApred = basal respiration rate, characterized as the “intercept of the allometric

mass function” in the Wisconsin Bioenergetics Model documentation

(g O2/g organic matter "d);

1.5 = conversion factor (g organic matter/g O2).

Swimming activity may be large and variable (Hanson et al., 1997) and is subject to

calibration for a particular site, considering currents and other factors. Activity can be a complex

function of temperature. The Wisconsin Bioenergetics Model (Hewett and Johnson, 1992; Hanson

et al., 1997) provides two alternatives. Equation Set 1 uses an exponential temperature function:

where:

RQ = the Q10 or rate of change per 10° C for respiration (1/° C);

Temp = ambient temperature (° C).

TFn is then factored into the calculation of StdResppred , which is in turn modified by an

Activity factor as part of the calculation of Respiration (87). Activity is a complex function for

swimming speed as an allometric function of temperature (Hewett and Johnson, 1992; Hanson et

al., 1997):

where:

RTO = coefficient for swimming speed dependence on metabolism (s/cm);

RTL = temperature below which swimming activity is an exponential function of

temperature (° C);

Vel = swimming velocity (cm/s);

RK1 = intercept for swimming speed above the threshold temperature (cm/s);

RK4 = weight-dependent coefficient for swimming speed;

ACT = intercept for swimming speed for a 1 g fish at ° C (cm/s); and

BACT = coefficient for swimming at low temperatures (1/° C),

Equation Set 2 uses the Stroganov function used elsewhere in AQUATOX, see (51):

and activity is a constant:
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 4

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(94)

(95)

1

1.05

1.1

1.15

1.2

1.25

1.3

0.5

1.5

2.5

3.5

4.55.5

6.5

7.5

8.5

9.5

Biomass (g/m2)

DensityDep (unitless)

Figure 50. Density-dependent factor for increase in respiration as fish

biomass approaches the carrying capacity (10.0 in this example).

where:

ACT = activity factor, which is not the same as ACT in Equation Set 1 (g/g).

Standard respiration in fish increases with crowding due to competition for spawning sites,

interference in feeding, and other factors. This adverse intraspecific interaction helps to constrain

the population to the carrying capacity; as the biomass approaches the carrying capacity for a given

species the respiration is increased proportionately (Kitchell et al., 1974):

where:

IncrResp = increase in respiration at carrying capacity (0.25);

KCap = carrying capacity (g/m3).

With the IncrResp value of 0.25, which is a conservative estimate, respiration is increased

by 25% at carrying capacity (Kitchell et al., 1974), as shown in Figure 50. This densitydependence is used only for fish, and not for invertebrates.

As a simplification, specific dynamic action is represented as proportional to food assimilated

(Hewett and Johnson, 1992; see also Kitchell et al., 1974; Park et al., 1974):
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 4

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(96)

(97)

(98)

where:

KResppred = proportion of assimilated energy lost to specific dynamic

action (unitless); parameter input by user as “Specific

Dynamic Action;”

Consumptionpred = ingestion (g/m3"d); and

Defecationpred = egestion of unassimilated food (g/m3"d).

Excretion 

As respiration occurs, biomass is lost and nitrogen and phosphorus are excreted directly to

the water (Horne and Goldman 1994); see (139) and (147). Ganf and Blažka (1974) have reported

that this process is important to the dynamics of the Lake George, Uganda, ecosystem. Their data

were converted by Scavia and Park (1976) to obtain a proportionality constant relating excretion to

respiration: 

where:

Excretionpred = excretion rate (g/m3"d);

KExcrpred = proportionality constant for excretion:respiration (unitless);

and

Respirationpred = respiration rate (g/m3

"d).

Excretion is approximately 17 percent of respiration, which is not an important biomass loss

term for animals, but it is important in nutrient recycling.

Nonpredatory Mortality 

Nonpredatory mortality is a result of both environmental conditions and the toxicity of

pollutants:

where:

Mortalitypred = nonpredatory mortality (g/m3

"d);
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 4

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(99)

(100)

Figure 51

Mortality as a Function of Temperature

Dpred = environmental mortality rate; the maximum value of three

computations, (99), (100), and (101), is used (1/d);

Biomasspred = biomass of given animal (g/m3

); and

Poisoned = mortality due to toxic effects (g/m3"d), see (287).

Under normal conditions a baseline mortality rate is used: 

where:

KMortpred = normal nonpredatory mortality rate (1/d).

An exponential function is used for temperatures above the maximum (Figure 51):

where:

Temperature = ambient water temperature (/C); and

TMaxpred = maximum temperature tolerated (/C).

The lower lethal temperature is often 0/C (Leidy and Jenkins, 1976), so it is ignored at this

time. Total mortality is assumed when dissolved oxygen drops below 0.25 g/m3

, recognizing that

the predicted level is an average for the entire water column or epilimnetic or hypolimnetic segment:
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 4

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(101)

(102)

Gamete Loss and Recruitment 

Eggs and sperm can be a significant fraction of adult biomass; in bluegills these can be 13

percent and 5 percent, respectively (Toetz, 1967), giving an average of 9 percent if the proportion

of sexes is equal. Because only a small fraction of these gametes results in viable young when shed

at the time of spawning, the remaining fraction is lost to detritus in the model. 

There are two options for determining the date or dates on which spawning will take place.

A user can specify up to three dates on which spawning will take place. Alternatively, one may use

a construct that was modified from a formulation by Kitchell et al. (1974). As a simplification,

rather than requiring species-specific spawning temperatures, it assumes that spawning occurs when

the temperature first enters the range from six tenths of the optimum temperature to 1/ less than the

optimal temperature. This is based on a comparison of the optimal temperatures with the speciesspecific spawning temperatures reported by Kitchell et al. (1974). Depending on the range of

temperatures, this simplifying assumption usually will result in one or two spawnings per year in

a temperate ecosystem when a simple sinusoidal temperature function is used. However, the user

also can specify a maximum number of spawnings.

where:

Temperature = ambient water temperature (/C);

TOpt = optimum temperature (/C);

GameteLoss = loss rate for gametes (g/m3

"d);

GMort = gamete mortality (1/d);

IncrMort = increased gamete and embryo mortality due to toxicant (1/d); see

(299);

Biomass = biomass of predator (g/m3

);

PctGamete = fraction of adult predator biomass that is in gametes (unitless); and

FracAdults = fraction of biomass that is adult (unitless).

As the biomass of a population reaches its carrying capacity, reproduction is usually reduced

due to stress; this results in a population that is primarily adults. Therefore, the proportion of adults

and the fraction of biomass in gametes are assumed to be at a maximum when the biomass is at the

carrying capacity (Figure 52):
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 4

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(103)

Figure 52

Correction for Population-Age Structure

(104)

where:

KCap = carrying capacity (g/m3

).

Spawning in large fish results in an increase in the biomass of small fish if both small and

large size classes are of the same species. Gametes are lost from the large fish, and the small fish

gain the viable biomass through recruitment:

 where:

Recruit = biomass gained from successful spawning (g/m3

"d).

Washout, Drift, and Entrainment 

Downstream transport is an important loss term for invertebrates. Zooplankton are subject

to transport downstream similar to phytoplankton: 
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 4

4 - 42

(105)

(106)

(107)

(108)

where:

Washout = loss of zooplankton due to downstream transport (g/m3

"d);

Discharge = discharge (m3

/d), see Table 1;

Volume = volume of site (m3), see (2); and

Biomass = biomass of invertebrate (g/m3).

Likewise, zoobenthos exhibit drift, which is detachment followed by washout, and it is

represented by a construct that is original with AQUATOX:

where:

Drift = loss of zoobenthos due to downstream drift (g/m3

"d);

Dislodge = fraction of biomass subject to drift per day (fraction/d), see (107); and

DislodgeTox = fraction of biomass subject to drift per day because of toxicant stress

(fraction/d), see (301).

Nocturnal drift is a natural phenomenon:

where:

AveDrift = fraction of biomass subject to normal drift per day (fraction/d).

Animals also are subject to entrainment and downstream transport in flood waters. In fact,

annual variations in fish populations in streams are due largely to variations in flow, with almost

100% loss during large floods in Shenandoah National Park (NPS, 1997). A simple exponential loss

function was developed for AQUATOX:

where:

Entrainment = entrainment and downstream transport (g/m3

"d);

Biomass = biomass of given animal (g/m3

);

MaxRate = maximum loss per day (1/d);

Vel = velocity of water (cm/s), (14);

VelMax = velocity at which there is total loss of biomass (cm/s); and
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 4

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0

0.2

0.4

0.6

0.8

1

1.2

0 100 200 300 400 500

Velocity (cm/s)

Fraction Entrained 

Figure 53

Entrainment of animals as a function of stream velocity

with VelMax of 400 cm/s

(109)

Gradual = slope of exponential, set to 25 (cm/s).

Vertical Migration

When presented with unfavorable conditions, most animals will attempt to migrate to an

adjacent area with more favorable conditions. The current version of AQUATOX, following the

example of CLEANER (Park et al., 1980), assumes that zooplankton and fish will exhibit avoidance

behavior by migrating vertically from an anoxic hypolimnion to the epilimnion. Anoxic conditions

are taken to occur when dissolved oxygen levels are less than 0.25 mg/L. The assumption is that

anoxic conditions will persist until overturn. The construct calculates the absolute mass of the given

group of organisms in the hypolimnion, then divides by the volume of the epilimnion to obtain the

biomass being added to the epilimnion:

where:

VSeg = vertical segment;

Hypo = hypolimnion;

Anoxic = boolean variable for anoxic conditions when O2 < 0.25 mg/L;

Migration = rate of migration (g/m3

"d);

HypVolume = volume of hypolimnion (m3), see Figure 19;
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 4

4 - 44

(110)

EpiVolume = volume of epilimnion (m3), see Figure 19; and

Biomasspred,hypo = biomass of given predator in hypolimnion (g/m3).

This does not include horizontal migration or avoidance of toxicants and stressful temperatures.

Promotion

Although AQUATOX is an ecosystem model, promotion to the next size class is important

in representing the emergence of aquatic insects, and therefore loss of biomass from the system, and

in predicting bioaccumulation of hydrophobic organic compounds in larger fish. The model

assumes that promotion is determined by the rate of growth. Growth is considered to be the sum of

consumption and the loss terms other than mortality and migration; a fraction of the growth goes

into promotion to the next size class (cf. Park et al., 1980):

where:

Promotion = rate of promotion (g/m3

"d); 

KPro = fraction of growth that goes to promotion or emergence (0.5, unitless);

Consumption = rate of consumption (g/m3"d), see (85);

Defecation = rate of defecation (g/m3"d), see (84);

Respiration = rate of respiration (g/m3"d), see (87);

Excretion = rate of excretion (g/m3"d), see (97); and

GameteLoss = loss rate for gametes (g/m3"d), see (102).

This is a simplification of a complex response that depends on the mean weight of the

individuals. However, simulation of mean weight would require modeling both biomass and

numbers of individuals (Park et al., 1979, 1980), and that is beyond the scope of this model at

present. 

Promotion of multi-age fish is straightforward; each age class is promoted to the next age

class on the first spawning date each year. The oldest age class merely increments biomass from

the previous age class to any remaining biomass in the class. Of course, any associated toxicant is

transferred to the next class as well. Recruitment to the youngest age class is the fraction of gametes

that are not subject to mortality at spawning. Note that the user specifies the age at which spawning

begins on the multi-age fish screen. 

Insect emergence can be an important factor in the dynamics of an aquatic ecosystem. Often

there is synchrony in the emergence; in AQUATOX this is assumed to be cued to temperature with

additional forcing as twice the promotion that would ordinarily be computed, and is represented by:
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 4

4 - 45

(111)

where:

EmergeInsect = insect emergence (mg/L"d);

Temperature = ambient water temperature (/C); and

TOpt = optimum temperature (/C);
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 4

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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 5

5 - 1

Figure 54

Detritus Compartments in AQUATOX

5 REMINERALIZATION

5.1 Detritus

For the purposes of AQUATOX, the term "detritus" is used to include all non-living organic

material and associated decomposers (bacteria and fungi). As such, it includes both particulate and

dissolved material in the sense of Wetzel (1975), but it also includes the microflora and is analogous

to “biodetritus” of Odum and de la Cruz (1963) . Detritus is modeled as eight compartments:

refractory (resistant) dissolved, suspended, sedimented, and buried detritus; and labile (readily

decomposed) dissolved, suspended, sedimented, and buried detritus (Figure 54). This degree of

disaggregation is considered necessary to provide more realistic simulations of the detrital food web;

the bioavailability of toxicants, with orders-of-magnitude differences in partitioning; and biological

oxygen demand, which depends largely on the decomposition rates. Buried detritus is considered

to be taken out of active participation in the functioning of the ecosystem. In general, dissolved

organic material is about ten times that of suspended particulate matter in lakes and streams

(Saunders, 1980), and refractory compounds usually predominate; however, the proportions are

modeled dynamically.

The concentrations of detritus in these eight compartments are the result of several

competing processes:
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 5

5 - 2

(112)

(113)

(114)

(115)

(116)

(117)

(118)
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 5

5 - 3

(119)

where:

dSuspRefrDetr/dt = change in concentration of suspended refractory detritus with

respect to time (g/m3

"d);

dSuspLabileDetr/dt = change in concentration of suspended labile detritus with

respect to time (g/m3"d);

dDissRefrDetr/dt = change in concentration of dissolved refractory detritus with

respect to time (g/m3

"d);

dDissLabDetr/dt = change in concentration of dissolved labile detritus with

respect to time (g/m3"d);

dSedRefrDetr/dt = change in concentration of sedimented refractory detritus

with respect to time (g/m3

"d);

dSedLabileDetr/dt = change in concentration of sedimented labile detritus with

respect to time (g/m3"d);

dBuriedRefrDetr/dt = change in concentration of buried refractory detritus with

respect to time (g/m3"d);

dBuriedLabileDetr/dt = change in concentration of buried labile detritus with respect

to time (g/m3"d);

Loading = loading of given detritus from nonpoint and point sources, or

from upstream (g/m3"d);

DetrFm = detrital formation (g/m3"d);

Colonization = colonization of refractory detritus by decomposers (g/m3"d),

see (126);

Decomposition = loss due to microbial decomposition (g/m3

"d), see (130);

Sedimentation = transfer from suspended detritus to sedimented detritus by

sinking (g/m3

"d); in streams with the inorganic sediment

model attached see (189), for all other systems see (135);

Scour = resuspension from sedimented detritus (g/m3"d); in streams

with the inorganic sediment model attached see (187), for all

other systems see (135) (resuspension);

Exposure = transfer from buried to sedimented by scour of overlying

sediments (g/m3

"d);

Burial = transfer from sedimented to buried due to deposition of

sediments (g/m3

"d), see (184);

Washout = loss due to being carried downstream (g/m3

"d), see (16);

Ingestion = loss due to ingestion by detritivores and filter feeders

(g/m3"d), see (78); 
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 5

5 - 4

(120)

(121)

(122)

(123)

(124)

Sinking = detrital sinking from epilimnion and to hypolimnion under

stratified conditions, see (135); and

TurbDiff = transfer between epilimnion and hypolimnion due to turbulent

diffusion (g/m3"d), see (22) and (23).

As a simplification, refractory detritus is considered not to decompose directly, but rather

to be converted to labile detritus through microbial colonization, especially through ingestion then

egestion by detritivores (organisms that feed on detritus). Labile detritus is then available for both

decomposition and assimilation by detritivores. Because detritivores digest microbes and defecate

the remaining organic material, detritus has to be conditioned through microbial colonization before

it is suitable food. Therefore, the assimilation efficiency of detritivores for refractory material is

usually set to 0.0, and the assimilation efficiency for labile material is increased accordingly. 

Sedimentation and scour, or resuspension, are opposite processes. In shallow systems there may be

no long-term sedimentation (Wetzel et al., 1972), while in deep systems there may be little

resuspension. In this version sedimentation is a function of flow, ice cover and, in very shallow

water, wind based on simplifying assumptions. Burial, scour and exposure are applicable only in

streams where they are keyed to the behavior of clay and silt. Scour as an explicit function of wave

and current action is not implemented. 

Detrital Formation 

Detritus is formed in several ways: through mortality, gamete loss, sinking of phytoplankton,

excretion and defecation: 
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 5

5 - 5

(125)

(126)

where:

DetrFm = formation of detritus (g/m3

"d);

Mort2detr, biota = fraction of given dead organism that goes to given detritus (unitless);

Excr2detr, biota = fraction of excretion that goes to given detritus (unitless);

Mortalitybiota = death rate for organism (g/m3

"d), see (58), (74) and (98);

Excretion = excretion rate for organism (g/m3

"d), see (56) and (97) for plants and

animals, respectively;

GameteLoss = loss rate for gametes (g/m3"d), see (102);

Def2detr, biota = fraction of defecation that goes to given detritus (unitless); 

Defecationpred = defecation rate for organism (g/m3

"d), see (84);

Sedimentation = loss of phytoplankton to bottom sediments (g/m3"d), see (61); and

PlantSinkToDetr = labile and refractory portions of phytoplankton (unitless, 0.92 and

0.08 respectively).

A fraction of mortality, including sloughing of leaves from macrophytes, is assumed to go

to refractory detritus; a much larger fraction goes to labile detritus. Excreted material goes to both

refractory and labile detritus, while gametes are considered to be labile. Half the defecated material

is assumed to be labile because of the conditioning due to ingestion and subsequent inoculation with

bacteria in the gut (LeCren and Lowe-McConnell, 1980); fecal pellets sink rapidly (Smayda, 1971),

so defecation is treated as if it were directly to sediments. Phytoplankton that sink to the bottom are

considered to become detritus; most are consumed quickly by zoobenthos (LeCren and LoweMcConnell, 1980) and are not available to be resuspended.

Colonization 

Refractory detritus is converted to labile detritus through microbial colonization. When

bacteria and fungi colonize dissolved refractory organic matter, they are in effect turning it into

particulate matter. Detritus is often refractory because it has a deficiency of nitrogen compared to

microbial biomass. In order for microbes to colonize refractory detritus, they have to take up

additional nitrogen from the water (Saunders et al., 1980). Thus, colonization is nitrogen-limited,

as well as being limited by suboptimal temperature, pH, and dissolved oxygen: 

where:
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5 - 6

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

EFFECT

0 10 20 30 40 50 60 70

TEMPERATURE (C)

Figure 55. Colonization and Decomposition as

an Effect of Temperature

(127)

Colonization = rate of conversion of refractory to labile detritus (g/m3

"d);

ColonizeMax = maximum colonization rate under ideal conditions (g/g"d);

Nlimit = limitation due to suboptimal nitrogen levels (unitless), see (128);

DecTCorr = the effect of temperature (unitless), see (127);

pHCorr = limitation due to suboptimal pH level (unitless), see (133); 

DOCorrection = limitation due to suboptimal oxygen level (unitless), see (131); and

RefrDetr = concentration of refractory detritus in suspension, sedimented, or

dissolved (g/m3

).

Because microbial colonization and decomposition involves microflora with a wide range

of temperature tolerances, the effect of temperature is modeled in the traditional way (Thomann and

Mueller, 1987), taking the rate at an observed temperature and correcting it for the ambient

temperature up to a user-defined, high maximum temperature, at which point it drops to 0:

The resulting curve has a shoulder similar to the Stroganov curve, but the effect increases

up to the maximum rate (Figure 55).
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 5

5 - 7

(128)

(129)

(130)

The nitrogen limitation construct, which is original with AQUATOX, is parameterized using

an analysis of data presented by Egglishaw (1972) for Scottish streams. It is computed by:

where:

N = total available nitrogen (g/m3);

MinN = minimum level of nitrogen for colonization (= 0.1 g/m3);

HalfSatN = half-saturation constant for nitrogen stimulation (= 0.15 g/m3

);

Ammonia = concentration of ammonia (g/m3); and

Nitrate = concentration of nitrite and nitrate (g/m3).

 Although it can be changed by the user, a default maximum colonization rate of 0.007

(g/g"d) per day is provided, based on McIntire and Colby (1978, after Sedell et al., 1975).

The rates of decomposition (or colonization) of refractory dissolved organic matter are

comparable to those for particulate matter. Saunders (1980) reported values of 0.007 (g/g"d) for a

eutrophic lake and 0.008 (g/g"d) for a tundra pond. Anaerobic rates were reported by Gunnison et

al. (1985). 

Decomposition 

Decomposition is the process by which detritus is broken down by bacteria and fungi,

yielding constituent nutrients, including nitrogen, phosphorus, and inorganic carbon. Therefore, it

is a critical process in modeling nutrient recycling. In AQUATOX, following a concept first

advanced by Park et al. (1974), the process is modeled as a first-order equation with multiplicative

limitations for suboptimal environmental conditions (see section 4.1 for a discussion of similar

construct for photosynthesis): 

where:

Decomposition = loss due to microbial decomposition (g/m3"d);

DecayMax = maximum decomposition rate under aerobic conditions (g/g"d);

DOCorrection = correction for anaerobic conditions (unitless), see (131);

DecTCorr = the effect of temperature (unitless), see (127);

pHCorr = correction for suboptimal pH (unitless), see (133), (134); and

Detritus = concentration of detritus, including dissolved but not buried (g/m3

).
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Note that biomass of bacteria is not explicitly modeled in AQUATOX, rather it is considered

part of the detritus. In some models (for example, EXAMS, Burns et al., 1982) decomposition is

represented by a second-order equation using an empirical estimate of bacteria biomass. However,

using bacterial biomass as a site constant constrains the model, potentially forcing the rate.

Decomposers were modeled explicitly as a part of the CLEAN model (Clesceri et al., 1977).

However, if conditions are favorable, decomposers can double in 20 minutes; this can result in stiff

equations, adding significantly to the computational time. Ordinarily, decomposers will grow

rapidly as long as conditions are favorable. The only time the biomass of decomposers might need

to be considered explicitly is when a new organic chemical is introduced and the microbial

assemblage requires time to become adapted to using it as a substrate.

 The effect of temperature on biodegradation is represented by Equation (127), which also

is used for colonization. The function for dissolved oxygen, formulated for AQUATOX, is:

where the predicted DO concentrations are entered into a Michaelis-Menten formulation to

determine the extent to which degradation rates are affected by ambient DO concentrations

(Clesceri, 1980; Park et al., 1982):

and:

Factor = Michaelis-Menten factor (unitless);

KAnaerobic = decomposition rate at 0 g/m3 oxygen (g/g"d);

Oxygen = dissolved oxygen concentration (g/m3

); and

HalfSatO = half-saturation constant for oxygen (g/m3).

DOCorrection accounts for both decreased and increased (Figure 56) degradation rates

under anaerobic conditions, with KAnaerobic/DecayMax having values less than one and greater

than one, respectively. Detritus will always decompose more slowly under anaerobic conditions;

but some organic chemicals, such as some halogenated compounds (Hill and McCarty, 1967), will

degrade more rapidly. Half-saturation constants of 0.1 to 1.4 g/m3

 have been reported (Bowie et al.,

1985); a value of 0.1 g/m3

 is used. 
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0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 1 2 3 4 5 6 7 8 9 10

Dissolved Oxygen

DOCorrection (unitless)

KAnaerobic = 1.3 KAnaerobic = 0.3 KAnaerobic = 0

Figure 56. Correction for Dissolved Oxygen

(133)

(134)

Another important environmental control on the rate of microbial degradation is pH. Most

fungi grow optimally between pH 5 and 6 (Lyman et al., 1990), and most bacteria grow between pH

6 to about 9 (Alexander, 1977). Microbial oxidation is most rapid between pH 6 and 8 (Lyman et

al., 1990). Within the pH range of 5 and 8.5, therefore, pH is assumed to not affect the rate of

microbial degradation, and the suboptimal factor for pH is set to 1.0. In the absence of good data

on the rates of biodegradation under extreme pH conditions, biodegradation is represented as

decreasing exponentially beyond the optimal range (Park et al., 1980a; Park et al., 1982). If the pH

is below the lower end of the optimal range, the following equation is used:

where:

pH = ambient pH, and

pHMin = minimum pH below which limitation on biodegradation rate occurs.

If the pH is above the upper end of the optimal range for microbial degradation, the

following equation is used:

where:

pHMax = maximum pH above which limitation on biodegradation rate

occurs.
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Figure 57

Limitation Due To pH

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These responses are shown in Figure 57.

Sedimentation and Resuspension

When the inorganic sediment model is not included in a simulation, the sedimentation of

suspended particulate detritus to bottom sediments and the resuspension of bottom sediments to

suspended detritus are modeled using simplifying assumptions. The constructs are intended to

provide general responses to environmental factors, but they should not be considered as anything

more than place holders for more realistic hydrodynamic functions to be incorporated in later

versions. When the inorganic sediment model is included, the sedimentation and deposition of

detritus is assumed to mimic the sedimentation and resuspension of silt (see (187) and (189)).

Otherwise:

where:

Sedimentation = transfer from suspended to sedimented by sinking (g/m3

"d), see (135);

KSed = sedimentation rate (m/d);

Thick = depth of water or thickness of layer if stratified (m);

Decel = deceleration factor (unitless), see (136); and

State = concentration of particulate detrital compartment (g/m3

).
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Figure 58. Relationship of Decel to Discharge with

a Mean Discharge of 5 m3

/s.

If the discharge exceeds the mean discharge then sedimentation is slowed proportionately

(Figure 58):

where:

TotDischarge = total epilimnetic and hypolimnetic discharge (m3/d); and

MeanDischarge = mean discharge over the course of the simulation (m3

/d).

If the depth of water is less than or equal to 1.0 m and wind speed is greater than or equal

to 5.5 m/s then the sedimentation rate is negative, effectively becoming the rate of resuspension.

If there is ice cover, then the sedimentation rate is doubled to represent the lack of turbulence.

5.2 Nitrogen 

Two nitrogen compartments, ammonia and nitrate, are modeled (Figure 59). Nitrite occurs

in very low concentrations and is rapidly transformed through nitrification and denitrification

(Wetzel, 1975); therefore, it is modeled with nitrate. Likewise, un-ionized ammonia (NH3) is not

modeled as a separate state variable. Ammonia is assimilated by algae and macrophytes and is

converted to nitrate as a result of nitrification:
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(138)

(139)

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where:

dAmmonia/dt = change in concentration of ammonia with time (g/m3

"d);

Loading = loading of nutrient from inflow (g/m3"d);

Excrete = ammonia derived from excretion by animals (g/m3

"d), see (139);

Decompose = ammonia derived from decomposition of detritus (g/m3

"d), see (138);

Nitrify = nitrification (g/m3"d), see (144);

Assimilation = assimilation of nutrient by plants (g/m3"d), see (141) and (142); 

Washout = loss of nutrient due to being carried downstream (g/m3"d), see (16)

and;

TurbDiff = depth-averaged turbulent diffusion between epilimnion and

hypolimnion if stratified (g/m3

"d), see (22) and (23).

Ammonia is a product of decomposition:

It also is excreted directly by animals:

where:

Org2Ammonia = ratio of ammonia to organic matter (unitless);

Decomposition = decomposition rate of given type of detritus, (g/m3

"d), see

(130); and

Excretion = excretion rate of given animal (g/m3

"d), see (97).

Nitrate is assimilated by plants and is converted to free nitrogen (and lost) through

denitrification:

where:
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Detritus

Ammonia

Decomposition

Animals

Excretion

Assimilation

Nitrate

& Nitrite

Assimilation

Nitrification

Denitrification

Plants Plants

Figure 59. Components of Nitrogen Remineralization

(141)

dNitrate/dt = change in concentration of nitrate with time (g/m3

"d);

Loading = user entered loading of nitrate, including atmospheric deposition; and

Denitrify = denitrification (g/m3

"d); see (145).

Free nitrogen can be fixed by blue-green algae. Both nitrogen fixation and denitrification

are subject to environmental controls and are difficult to model with any accuracy; therefore, the

nitrogen cycle is represented with considerable uncertainty.

Assimilation

Nitrogen compounds are assimilated by plants as a function of photosynthesis in the

respective groups (Ambrose et al., 1991):
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where:

Assimilation = assimilation rate for given nutrient (g/m3"d);

Photosynthesis = rate of photosynthesis (g/m3

"d), see (31);

UptakeNitrogen = fraction of photosynthate that is nitrogen (unitless, 0.01975 if

nitrogen-fixing, otherwise 0.079);

NH4Pref = ammonia preference factor (unitless).

Only 23 percent of nitrate is nitrogen, but 78 percent of ammonia is nitrogen. This results

in an apparent preference for ammonia. The preference factor is calculated with an equation

developed by Thomann and Fitzpatrick (1982) and cited and used in WASP (Ambrose et al., 1991):

where:

N2NH4 = ratio of nitrogen to ammonia (0.78);

N2NO3 = ratio of nitrogen to nitrate (0.23);

KN = half-saturation constant for nitrogen uptake (g N/m3

);

Ammonia = concentration of ammonia (g/m3

); and

Nitrate = concentration of nitrate (g/m3

).

For algae other than blue-greens, Uptake is the Redfield (1958) ratio; although other ratios

(cf. Harris, 1986) may be used by editing the parameter screen. At this time nitrogen fixation by

blue-greens is represented by using a smaller uptake ratio, thus "creating" nitrogen.

Nitrification and Denitrification 

Nitrification is the conversion of ammonia to nitrite and then to nitrate by nitrifying bacteria;

it occurs primarily at the sediment-water interface (Effler et al., 1996). The maximum rate of

nitrification, corrected for the area to volume ratio, is reduced by limitation factors for suboptimal
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Figure 60

Response to pH, Nitrification

Figure 61

Response to Temperature, Nitrification

(145)

dissolved oxygen and pH, similar to the way that decomposition is modeled, but using the more

restrictive correction for suboptimal temperature used for plants and animals:

where:

Nitrify = nitrification rate (g/m3"d);

KNitri = maximum rate of nitrification (0.135 m/d, according to Effler et al.,

1996);

Area = area of site or segment (m2);

Volume = volume of site or segment (m3

); see (2);

DOCorrection = correction for anaerobic conditions (unitless) see (131);

TCorr = correction for suboptimal temperature (unitless); see (51);

pHCorr = correction for suboptimal pH (unitless), see (133); and

Ammonia = concentration of ammonia (g/m3).

The nitrifying bacteria have narrow environmental optima; according to Bowie et al.

(1985) they require aerobic conditions with a pH between 7 and 9.8, an optimal temperature of 30°,

and minimum and maximum temperatures of 10° and 60° respectively (Figure 60, Figure 61). 

In contrast, denitrification (the conversion of nitrate and nitrite to free nitrogen) is an

anaerobic process, so that DOCorrection enhances the process (Ambrose et al., 1991):
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Figure 62

Response to pH, Denitrification

Figure 63

Response to Temperature, Denitrification

(146)

(147)

where:

Denitrify = denitrification rate (g/m3

"d);

KDenitri = maximum rate of denitrification (0.1 m/d, according to Di Toro,

2001); and

Nitrate = concentration of nitrate (g/m3).

Furthermore, it is accomplished by a large number of reducing bacteria under anaerobic conditions

and with broad environmental tolerances (Bowie et al., 1985; Figure 62,Figure 63).

5.3 Phosphorus 

The phosphorus cycle is much simpler than the nitrogen cycle. Decomposition, excretion,

and assimilation are important processes that are similar to those described above: 
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(149)

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where:

dPhosphate/dt = change in concentration of phosphate with time (g/m3

"d);

Loading = loading of nutrient from inflow and atmospheric deposition (g/m3

"d);

FracAvail = fraction of phosphate loading that is available (unitless);

Excrete = phosphate derived from excretion by biota (g/m3

"d); see (56) and (97)

for plants and animals, respectively;

Decompose = phosphate derived from decomposition of detritus (g/m3

"d);

Assimilation = assimilation by plants (g/m3"d);

Washout = loss due to being carried downstream (g/m3"d), see (16);

Area = area of site (m2);

Volume = volume of water at site (m3); see (2);

Org2Phosphate = ratio of phosphate to organic matter (unitless);

Excretion = excretion rate for given organism (g/m3

"d), see (56) and (97) for

plants and animals, respectively;

Decomposition = decomposition rate for given detrital compartment (g/m3

"d), see

(130);

Photosynthesis = rate of photosynthesis (g/m3"d), see (31), and

Uptake = fraction of photosynthate that is phosphate (unitless, 0.018).

At this time AQUATOX models only phosphate available for plants; a correction factor in

the loading screen allows the user to scale total phosphate loadings to available phosphate. A future

enhancement could be to consider phosphate precipitated with calcium carbonate, which would

better represent the dynamics of marl lakes; however, that process is ignored in the current version.

A default value is provided for average atmospheric deposition, but this should be adjusted for site

conditions. In particular, entrainment of dust from tilled fields and new highway construction can

cause significant increases in phosphate loadings. As with nitrogen, the uptake parameter is the

Redfield (1958) ratio; it may be edited if a different ratio is desired (cf. Harris, 1986).

5.4 Dissolved Oxygen 
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Oxygen is an important regulatory endpoint; very low levels can result in mass mortality for

fish and other organisms, mobilization of nutrients and metals, and decreased degradation of toxic

organic materials. Dissolved oxygen is simulated as a daily average and does not account for diurnal

fluctuations. It is a function of reaeration, photosynthesis, respiration, decomposition, and

nitrification:

where:

dOxygen/dt = change in concentration of dissolved oxygen (g/m3

"d);

Loading = loading from inflow (g/m3"d);

Reaeration = atmospheric exchange of oxygen (g/m3

"d);

Photosynthesized = oxygen produced by photosynthesis (g/m3"d);

O2Photo = ratio of oxygen to photosynthesis (1.6, unitless);

BOD = instantaneous biological oxygen demand (g/m3"d);

NitroDemand = oxygen taken up by nitrification (g/m3

"d);

Washout = loss due to being carried downstream (g/m3"d), see (16);

O2Biomass = ratio of oxygen to organic matter (mg oxygen/mg biomass;

0.575, but user can change in remineralization screen);

Photosynthesis = rate of photosynthesis (g/m3

"d), see (31), (73);

Decomposition = rate of decomposition (g/m3

"d), see (130);

Respiration = rate of respiration (g/m3"d), see (55) and (87);

O2N = ratio of oxygen to nitrogen (unitless; 4.57, but user can

change in remineralization screen); and

Nitrify = rate of nitrification (g N/m3

"d).

Reaeration is a function of the depth-averaged mass transfer coefficient KReaer, corrected

for ambient temperature, multiplied by the difference between the dissolved oxygen level and the

saturation level (cf. Bowie et al., 1985):
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(155)

(156)

(157)

where:

Reaeration = mass transfer of oxygen (g/m3

"d);

KReaer = depth-averaged reaeration coefficient (1/d);

O2Sat = saturation concentration of oxygen (g/m3

), see (163); and

Oxygen = concentration of oxygen (g/m3).

In standing water KReaer is computed as a minimum transfer velocity plus the effect of wind

on the transfer velocity (Schwarzenbach et al., 1993) divided by the thickness of the mixed layer to

obtain a depth-averaged coefficient (Figure 64):

where:

Wind = wind velocity 10 m above the water (m/sec); 

864 = conversion factor (cm/sec to m/d); and

Thick = thickness of mixed layer (m).

Algal blooms can generate dissolved oxygen levels that are as much as 400% of saturation

(Wetzel, 2001). However, near-surface blue-green algal blooms, which are modeled as being in the

top 0.33 m, produce high levels of oxygen that do not extend significantly into deeper water. An

adjustment is made in the code so that if the blue-green algal biomass exceeds 1 mg/L and is greater

than other phytoplankton biomass, the thickness subject to oxygen reaeration is set to 0.33 m. This

does not affect the KReaer that is used in computing volatilization.

In streams, reaeration is a function of current velocity and water depth (Figure 65) following

the approach of Covar (1978, see Bowie et al., 1985) and used in WASP (Ambrose et al., 1991).

The decision rules for which equation to use are taken from the WASP5 code (Ambrose et al., 1991).

If Vel < 0.518 m/sec:

else:

where:

Vel = velocity of stream (converted to m/sec) see (14); and

TransitionDepth = intermediate variable (m).

If Depth < 0.61 m, the equation of Owens et al. (1964, cited in Ambrose et al., 1991) is used:
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where:

Depth = mean depth of stream (m).

Otherwise, if Depth is > TransitionDepth, the equation of O'Connor and Dobbins (1958, cited in

Ambrose et al., 1991) is used:

Else, if Depth # TransitionDepth, the equation of Churchill et al. (1962, cited in Ambrose et al.,

1991) is used:

In extremely shallow streams, especially experimental streams where depth is < 0.06 m, an

equation developed by Krenkel and Orlob (1962, cited in Bowie et al. 1985) from flume data is used:

where:

U = velocity (converted to fps);

Slope = longitudinal channel slope (m/m); and

H = water depth (converted to ft).

If reaeration due to wind exceeds that due to current velocity, the equation for standing water

is used. Reaeration is set to 0 if ice cover is expected (i.e., when the depth-averaged temperature

< 3°C).
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Figure 64

Reaeration as a Function of Wind

Figure 65

Reaeration in Streams

(162)

(163)

Reaeration is assumed to be representative of 20°C, so it is adjusted for ambient water

temperature using (Thomann and Mueller 1987):

where:

KReaerT = Reaeration coefficient at ambient temperature (1/d);

Kreaer20 = Reaeration coefficient for 20°C (1/d);

Theta = temperature coefficient (1.024); and

Temperature = ambient water temperature (°C).

Oxygen saturation, as a function of both temperature (Figure 66) and salinity (Figure 67),

is based on Weiss (1970, cited in Bowie et al., 1985):

where:

TKelvin = Kelvin temperature, and

S = salinity (ppt).
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Figure 66

Saturation as a Function of Temperature

Figure 67

Saturation as a Function of Salinity

(164)

(165)

(166)

(167)

According to Bowie et al. (1985), it gives results that are not significantly different from

those computed by the more complex APHA (1985) equations that are used in WASP (Ambrose et

al., 1993). At the present time salinity is set to 0; although, it has little effect on reaeration.

5.5 Inorganic Carbon 

Many models ignore carbon dioxide as an ecosystem component (Bowie et al., 1985).

However, it can be an important limiting nutrient. Similar to other nutrients, it is produced by

decomposition and is assimilated by plants; it also is respired by organisms: 

where:
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and where:

dCO2/dt = change in concentration of carbon dioxide (g/m3

"d);

Loading = loading of carbon dioxide from inflow (g/m3"d);

Respired = carbon dioxide produced by respiration (g/m3

"d);

Decompose = carbon dioxide derived from decomposition (g/m3"d);

Assimilation = assimilation of carbon dioxide by plants (g/m3

"d);

Washout = loss due to being carried downstream (g/m3

"d), see (16);

CO2AtmosExch = interchange of carbon dioxide with atmosphere (g/m3

"d);

TurbDiff = depth-averaged turbulent diffusion between epilimnion and

hypolimnion if stratified (g/m3

"d), see (22) and (23);

CO2Biomass = ratio of carbon dioxide to organic matter (unitless; 0.526,

according to Winberg, 1971);

Respiration = rate of respiration (g/m3

"d), see (55) and (87);

Decomposition = rate of decomposition (g/m3"d), see (130);

Photosynthesis = rate of photosynthesis (g/m3"d), see (31); and

UptakeCO2 = ratio of carbon dioxide to photosynthate (= 0.53).

Carbon dioxide also is exchanged with the atmosphere; this process is important, but is not

instantaneous: significant undersaturation and oversaturation are possible (Stumm and Morgan,

1996). The treatment of atmospheric exchange is similar to that for oxygen:

In fact, the mass transfer coefficient is based on the well-established reaeration coefficient

for oxygen, corrected for the difference in diffusivity of carbon dioxide as recommended by

Schwarzenbach et al. (1993): 

where:

CO2AtmosExch = interchange of carbon dioxide with atmosphere (g/m3

"d);

KLiqCO2 = depth-averaged liquid-phase mass transfer coefficient (1/d);

CO2 = concentration of carbon dioxide (g/m3

);

CO2Sat = saturation concentration of carbon dioxide (g/m3), see (170);

KReaer = depth-averaged reaeration coefficient for oxygen (1/d), see (155)-

(162);

MolWtO2 = molecular weight of oxygen (=32); and

MolWtCO2 = molecular weight of carbon dioxide (= 44).
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Figure 68

Carbon Dioxide Mass Transfer

(170)

(171)

(172)

Keying the mass-transfer coefficient for carbon dioxide to the reaeration coefficient for

oxygen is very powerful in that the effects of wind (Figure 68) and the velocity and depth of streams

can be represented, using the oxygen equations (Equations (155)- (160)).

Based on this approach, the predicted mass transfer under still conditions is 0.92, compared

to the observed value of 0.89 ± 0.03 (Lyman et al., 1982). This same approach is used, with minor

modifications, to predict the volatilization of other chemicals (see Section 7.5). Computation of

saturation of carbon dioxide is based on the method in Bowie et al. (1985; see also Chapra and

Reckhow, 1983) using Henry's law constant, with its temperature dependency (Figure 69), and the

partial pressure of carbon dioxide:

where:

and where:

CO2Sat = saturation concentration of carbon dioxide (g/m3

);

CO2Henry = Henry's law constant for carbon dioxide (g/m3

-atm)

pCO2 = atmospheric partial pressure of carbon dioxide (= 0.00035);

MCO2 = mg carbon dioxide per mole (= 44000);

TKelvin = temperature in °K, and

Temperature = ambient water temperature (°C).
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Figure 69

Saturation of Carbon Dioxide
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6 INORGANIC SEDIMENTS1

The sediment transport component of AQUATOX simulates scour, deposition and transport

of sediments and calculates the concentration of sediments in the water column and sediment bed

within a river reach. For running waters, the sediment is divided into three categories according to

the particle size: 1) sand, with particle sizes between 0.062 to 2.0 millimeters (mm), 2) silt (0.004

to 0.062 mm), and 3) clay (0.00024 to 0.004 mm). Wash load (primarily clay and silt) is deposited

or eroded within the channel reach depending on the daily flow regime. Sand transport is also

computed within the channel reach. At present, inorganic sediments in standing water are computed

based on total suspended solids loadings, described in section 6.3.

The river reach is assumed to be short and well mixed so that concentration does not vary

longitudinally. Flow routing is not performed within the river reach. The daily average flow regime

determines the amount of scour, deposition and transport of sediment. Scour, deposition and

transport quantities are also limited by the amount of solids available in the bed sediments and the

water column. 

Inorganic sediments are important to the functioning of natural and perturbed ecosystems

for several reasons. When suspended, they increase light extinction and decrease photosynthesis.

When sedimented, they can temporarily or permanently remove toxicants from the active ecosystem

through deep burial. Scour can adversely affect periphyton and zoobenthos. All these processes are

represented to a certain degree in AQUATOX. In addition, rapid sedimentation also can adversely

affect periphyton and some zoobenthos; and the ratio of inorganic to organic sediments can be used

as an indicator of aerobic or anaerobic conditions in the bottom sediments. These are not simulated

in the model at this time.

The mass of sediment in each of the three sediment size classes is a function of the previous

mass, and the mass of sediment in the overlying water column lost through deposition, and gained

through scour: 

where:

MassBedSed = mass of sediment in channel bed (kg);

MassBedSed, t = -1 = mass of sediment in channel bed on previous day (kg);

DepositSed = amount of suspended sediment deposited (kg/m3); see (184);

ScourSed = amount of silt or clay resuspended (kg/m3

); see (181); and

VolumeWater = volume of stream reach (m3

); see page 3-1.
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The volumes of the respective sediment size classes are calculated as:

where:

VolumeSed = volume of given sediment size class (m3

);

MassBedSed = mass of the given sediment size class (kg); see (173);

RhoSed = density of given sediment size class (kg/m3

);

RhoSand = 2600 (kg/m3

); and

RhoSilt, Clay = 2400 (kg/m3).

The porosity of the bed is calculated as the volume weighted average of the porosity of its

components:

where:

BedPorosity = porosity of the bed (fraction);

FracSed = fraction of the bed that is composed of given sediment class; and

PorositySed = porosity of given sediment class.

The total volume of the bed is calculated as:

where:

BedVolume = volume of the bed (m3

).

The depth of the bed is calculated as

where:

BedDepth = depth of the sediment bed (m);

ChannelLength = length of the channel (m); and 

ChannelWidth = width of the channel (m).
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The concentrations of silt and clay in the water column are computed similarly to the mass

of those sediments in the bed, with the addition of loadings from upstream and losses downstream:

where:

ConcSed = concentration of silt or clay in water column (kg/m3

);

LoadSed = loading of clay or silt (kg/m3 d); 

ScourSed = amount of silt or clay resuspended (kg/m3

 d); see (181);

DepositSed = amount of suspended sediment deposited (kg/m3 d); see (184); and

WashSed = amount of sediment lost through downstream transport (kg/m3 d); see

(185).

The concentration of sand is computed using a totally different approach, which is described

in Section 6.2.

6.1 Deposition and Scour of Silt and Clay

Relationships for scour and deposition of cohesive sediments (silts and clays) used in

AQUATOX are the same as the ones used by the Hydrologic Simulation Program in Fortran (HSPF,

US EPA 1991). Deposition and scour of silts and clay are modeled using the relationships for

deposition (Krone, 1962) and scour (Partheniades, 1965) as summarized by Partheniades (1971).

Shear stress is computed as (Bicknell et al., 1992):

where:

Tau = shear stress (kg/m2);

H2ODensity = density of water (1000 kg/m3

);

Slope = slope of channel (m/m);

and hydraulic radius (HRadius) is (Colby and McIntire, 1978):

where:

HRadius = hydraulic radius (m);

Y = average depth over reach (m); and

Width = channel width (m).
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(182)

(183)

(184)

Resuspension or scour of bed sediments is predicted to occur when the computed shear stress

is greater than the critical shear stress for scour:

where:

ScourSed = resuspension of silt or clay (kg/m3

); see also (183);

ErodibilitySed = erodibility coefficient, (0.244 kg/m2

); and

TauScourSed = critical shear stress for scour of silt or clay (kg/m2); default values are

given in stream data screen, but may be changed by the user.

The amount of sediment that is resuspended is constrained by the mass of sediments stored

in the bed. An intermediate variable representing the maximum potential mass that can be scoured

is calculated; if the mass available is less than the potential, then scour is set to the lower amount:

where:

CheckSed = maximum potential mass (kg); and

MassSed = mass of silt or clay in bed (kg); see (173).

Deposition occurs when the computed shear stress is less than the critical depositional shear

stress:

where:

DepositSed = amount of sediment deposited (kg/m3 day);

TauDepSed = critical depositional shear stress (kg/m2

); default values are given in

stream data screen, but may be changed by the user;
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(186)

(187)

ConcSed = concentration of suspended silt or clay (kg/m3); see (178);

VTSed = terminal fall velocity of given sediment type (m/s); default values are

given in stream data screen, but may be changed by the user; and

SecPerDay = 86400 (seconds / day).

Downstream transport is an important mechanism for loss of suspended sediment from a

given stream reach:

where:

WashSed = amount of given sediment lost to downstream transport (kg/m3

 day);

Disch = discharge of water from the segment (m3

/day);

ConcSed = concentration of suspended sediment (kg/m3

);

SegVolume = volume of segment (m3); see page 3-1.

When the inorganic sediment model is included in an AQUATOX stream simulation, the

deposition and erosion of detritus mimics the deposition and erosion of silt. The fraction of detritus

that is being scoured or deposited is assumed to equal the fraction of silt that is being scoured or

deposited. The following equations are used to calculate the scour and deposition of detritus:

where:

FracScour = fraction of scour per day (fraction/day);

ScourSilt = amount of silt scoured (kg/m3

 day) see (181);

VolumeSilt = volume of silt in the bed (m3); see (174);

MassSilt = mass of silt in the bed (kg); see (173);

ConcAllSedDetritus = all sedimented detritus (labile and refractory) in the stream

bed (kg/m3

);

ScourDetritus = amount of detritus scoured (g/m3 day); and

1000 = conversion of kg to g.

The equations for deposition of detritus are similar:
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(189)

(190)

(191)

where:

DepositionSilt = amount of silt deposited (kg/m3

 day) see (184);

Conc Silt = amount of silt initially in the water (g/m3);

 FracDeposition = fraction of deposition per day (frac / day); and

Conc SuspDetritus = amount of suspended detritus initially in the water (g/m3

); and

DepositionDetritus = amount of detritus deposited (g/m3 day).

6.2 Scour, Deposition and Transport of Sand

Scour, deposition and transport of sand are simulated using the Engelund and Hansen (1967)

sediment transport relationships as presented by Brownlie (1981). This relationship was selected

because of its simplicity and accuracy. Brownlie (1981) shows that this relationship gives good

results when compared to 13 others using a field and laboratory data set of about 7,000 records. 

where:

PotConcSand = potential concentration of suspended sand (kg/m3

);

Rho = density of water (1000 kg/m3)

RhoSand = density of sand (2650 kg/m3

);

Velocity = flow velocity (converted to m/s);

Slope = slope of stream (m/m);

DSand = mean diameter of sand particle (0.30 mm converted to m); and

TauStar = dimensionless shear stress.

The dimensionless shear stress is calculated by:
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(193)

(194)

(195)

(196)

where:

HRadius = hydraulic radius (m).

Once the potential concentration has been determined for the given flow rate and channel

characteristics, it is compared with the present concentration. If the potential concentration is

greater, the difference is considered to be made available through scour, up to the limit of the bed.

If the potential concentration is less than what is in suspension, the difference is considered to be

deposited:
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(198)

where:

CheckSand = maximum potential mass (kg);

MassBedSand = mass of sand in bed (kg);

MassSuspSand = mass of sand in water column (kg);

ConcSand = concentration of sand in water column (kg/m3);

ScourSand = amount of sand resuspended (kg/m3 d);

DepositSand = amount of suspended sand deposited (kg/m3

 d);

PotConcSand = potential concentration of suspended sand (kg/m3

); see (190);

Volume = volume of reach (m3

); see page 3-1.

6.3 Suspended Inorganic Sediments in Standing Water

At present, AQUATOX does not compute settling of inorganic sediments in standing water

or scour as a function of wave action. However, suspended sediments are important in creating

turbidity and limiting light, especially in reservoirs and shallow lakes. Therefore, the user can

provide loadings of total suspended solids (TSS), and the model will back-calculate suspended

inorganic sediment concentrations by subtracting the simulated phytoplankton and suspended

detritus concentrations:

where:

InorgSed = concentration of suspended inorganic sediments (g/m3

);

TSS = observed concentration of total suspended solids (g/m3

);

Phyto = predicted phytoplankton concentrations (g/m3

), see (29), (30); and

PartDetr = predicted suspended detritus concentrations (g/m3

), see (112), (113).

The concentration of suspended inorganic sediments is used solely to calculate their

contribution to the extinction coefficient, which affects the depth of the euphotic zone and the Secchi

depth (see (35), (36)).
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Depuration

Detrital Sorption

Decomposition

Plant Sorption

0.00%

50.00%

100.00%

150.00%

200.00%

250.00%

6/17/1986

6/24/1986

7/1/1986

7/8/1986

7/15/1986

7/22/1986

7/29/1986

8/5/1986

8/12/1986

8/19/1986

8/26/1986

9/2/1986

9/9/1986

9/16/1986

Percent of Chlorpyrifos

Gill Sorption Depuration Detrital Sorption Decomposition Detrital Desorption Plant Sorption

Figure 70. In-situ Uptake and Release of Chlorpyrifos in a Pond

7 TOXIC ORGANIC CHEMICALS

The chemical fate module of AQUATOX predicts the partitioning of a compound between

water, sediment, and biota (Figure 70), and estimates the rate of degradation of the compound

(Figure 71). Microbial degradation, biotransformation, photolysis, hydrolysis, and volatilization

are modeled in AQUATOX. Each of these processes is described generally, and again in more detail

below.

Nonequilibrium concentrations, as represented by kinetic equations, depend on sorption,

desorption, and elimination as functions of the chemical and exposure through water and food as a

function of bioenergetics of the organism. Equilibrium partitioning is computed as a constraint on

sorption and for purposes of computing critical body residues for ecotoxicity, but it is no longer an

output from AQUATOX. Partitioning to inorganic sediments is not modeled at this time.

Microbial degradation is modeled by entering a maximum biodegradation rate for a

particular organic toxicant, which is subsequently reduced to account for suboptimal temperature,

pH, and dissolved oxygen. Biotransformation is represented by user-supplied first-order rate

constants with the option of also modeling multiple daughter products. Photolysis is modeled by

using a light screening factor (Schwarzenbach et al., 1993) and the near-surface, direct photolysis

first-order rate constant for each pollutant. The light screening factor is a function of both the

diffuse attenuation coefficient near the surface and the average diffuse attenuation coefficient for

the whole water column. For those organic chemicals that undergo hydrolysis, neutral, acid-, and

base-catalyzed reaction rates are entered into AQUATOX as applicable. Volatilization is modeled

using a stagnant two-film model, with the air and water transfer velocities approximated by

empirical equations based on reaeration of oxygen (Schwarzenbach et al., 1993).
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Hydrolysis

Photolysis

Microbial Metabolism

Volatilization

Discharge

0.00%

1.00%

2.00%

3.00%

4.00%

5.00%

6.00%

7.00%

8.00%

9.00%

6/17/1986

6/24/1986

7/1/1986

7/8/1986

7/15/1986

7/22/1986

7/29/1986

8/5/1986

8/12/1986

8/19/1986

8/26/1986

9/2/1986

9/9/1986

9/16/1986

Percent Chlorpyrifos Lost

Hydrolysis Photolysis Microbial Metabolism Volatilization Discharge

Figure 71. In-situ Degradation Rates for Chlorpyrifos in Pond

(199)

The mass balance equations follow. For computational ease, the concentrations of all

toxicants are converted to :g/L of water (they also are computed as ppb in each carrier). The change

in mass of toxicant in the water includes explicit representations of mobilization of the toxicant from

sediment to water as a result of decomposition of the labile sediment detritus compartment, sorption

to and desorption from the detrital sediment compartments, uptake by algae and macrophytes, uptake

across the gills of animals, depuration by organisms, and turbulent diffusion between epilimnion and

hypolimnion:

The equations for the toxicant associated with the two sediment detritus compartments are

rather involved, involving direct processes such as sorption and indirect conversions such as

defecation. However, photolysis is not included based on the assumption that it is not a significant

process for detrital sediments. Either scour or resuspension is simulated, depending on whether or

not inorganic sediments are modeled (scour of detritus is linked to scour of silt).
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(201)

(202)

The equations are similar for the toxicant associated with suspended and dissolved detritus,

with deposition or sedimentation, depending on whether or not inorganic sediments are modeled:
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(204)

(205)

(206)

Note that there are no equations for buried detritus, as they are considered to be sequestered

and outside of the influence of any processes which would change the concentrations of their

associated toxicants.

Algae are represented as:

Macrophytes are represented similarly, but reflecting the fact that they are stationary:
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The toxicant associated with animals is represented by an involved kinetic equation because

of the various routes of exposure and transfer:

where:

ToxicantWater = toxicant in dissolved phase in unit volume of water (:g/L);

ToxicantSedDetr = mass of toxicant associated with each of the two sediment

detritus compartments in unit volume of water (:g/L);

ToxicantSuspDetr = mass of toxicant associated with each of the two suspended

detritus compartments in unit volume of water (:g/L);

ToxicantDissDetr = mass of toxicant associated with each of the two dissolved

organic compartments in unit volume of water (:g/L);

ToxicantAlga = mass of toxicant associated with given alga in unit volume of

water (:g/L);

ToxicantMacrophyte = mass of toxicant associated with macrophyte in unit volume

of water (:g/L);

ToxicantAnimal = mass of toxicant associated with given animal in unit volume

of water (:g/L);

PPBSedDetr = concentration of toxicant in sediment detritus (:g/kg), see

(209);

PPBSuspDetr = concentration of toxicant in suspended detritus (:g/kg);

PPBDissDetr = concentration of toxicant in dissolved organics (:g/kg);

PPBAlga = concentration of toxicant in given alga (:g/kg);

PPBMacrophyte = concentration of toxicant in macrophyte (:g/kg);

PPBAnimal = concentration of toxicant in given animal (:g/kg);

1 e -6 = units conversion (kg/mg);

Loading = loading of toxicant from external sources (:g/L"d);

TurbDiff = depth-averaged turbulent diffusion between epilimnion and

hypolimnion (:g/L"d), see (22) and (23).

Hydrolysis = rate of loss due to hydrolysis (:g/L"d), see (212);

BiotransformMicrobial = biotransformation to or from given organic chemical in given

detrital compartment due to microbial decomposition

(:g/L"d), see (273);
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BiotransformOrg = biotransformation to or from given organic chemical within

the given organism (:g/L"d);

Photolysis = rate of loss due to direct photolysis (:g/L"d), see (219);

assumed not to be significant for bottom sediments;

MicrobialDegrdn = rate of loss due to microbial degradation (:g/L"d), see (225);

Volatilization = rate of loss due to volatilization (:g/L"d), see (230);

Discharge = rate of loss of toxicant due to discharge downstream

(:g/L"d), see Table 1;

Burial = rate of loss due to deep burial (:g/L"d) see (184);

Expose = rate of exposure due to resuspension of overlying sediments

(:g/L"d), see (181);

Decomposition = rate of decomposition of given detritus (mg/L"d), see (130);

Depuration = elimination rate for toxicant due to clearance (:g/L"d), see

(262) and (269);

Sorption = rate of sorption to given compartment (:g/L"d), see (249);

Desorption = rate of desorption from given compartment (:g/L"d), see

(250);

Colonization = rate of conversion of refractory to labile detritus (g/m3"d), see

(126);

DefecationToxPred, Prey = rate of transfer of toxicant due to defecation of given prey by

given predator (:g/L"d), see (276);

Def2SedLabile = fraction of defecation that goes to sediment labile detritus;

Resuspension = rate of resuspension of given sediment detritus (mg/L"d)

without the inorganic sediment model attached, see (135);

Scour = rate of resuspension of given sediment detritus (mg/L"d) in

streams with the inorganic sediment model attached, see

(187);

Sedimentation = rate of sedimentation of given suspended detritus (mg/L"d),

 without the inorganic sediment model attached, see (135);

Deposition = rate of sedimentation of given suspended detritus (mg/L"d) 

in streams with the inorganic sediment model attached, see

(189);

Sed2Detr = fraction of sinking phytoplankton that goes to given detrital

compartment;

Sink = loss rate of phytoplankton to bottom sediments (mg/L"d), see

(61);

MortalityOrg = nonpredatory mortality of given organism (mg/L"d), see (98);

Mort2Detr = fraction of dead organism that is labile (unitless);

GameteLoss = loss rate for gametes (g/m3

"d), see (102);

Mort2Ref = fraction of dead organism that is refractory (unitless);

Washout or Drift = rate of loss of given suspended detritus or organism due to

being carried downstream (mg/L"d), see (16), (63), (67),

(105), and (106);

SedToHyp = rate of settling loss to hypolimnion from epilimnion (mg/L"d).

May be positive or negative depending on segment being

simulated;
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IngestionPred, Prey = rate of ingestion of given food or prey by given predator

(mg/L"d), see (78);

PredationPred, Prey = predatory mortality by given predator on given prey

(mg/L"d), see (86);

ExcToxToDissOrg = toxicant excretion from plants to dissolved organics

(mg/L"d);

Excretion = excretion rate for given plant (g/m3

"d), see (97);

SinkToHypo = rate of transfer of phytoplankton to hypolimnion (mg/L"d).

May be positive or negative depending on segment being

modeled;

AlgalUptake = rate of sorption by algae (:g/L - d), see (260);

MacroUptake = rate of sorption by macrophytes (:g/L - d), see (256);

GillUptake = rate of absorption of toxicant by the gills (:g/L - d), see (265);

DietUptakePrey = rate of dietary absorption of toxicant associated with given

prey (:g/L"d), see (268);

Recruit = biomass gained from successful spawning (g/m3

"d), see (104);

Promotion = promotion from one age class to the next (mg/L"d), see (110);

Migration = rate of migration (g/m3"d), see (109); and

EmergeInsect = insect emergence (mg/L"d), see (111).

The concentration in each carrier is given by:

where:

PPBi = concentration of chemical in carrier i (:g/kg);

ToxStatei = mass of chemical in carrier i (ug/L);

CarrierState = biomass of carrier (mg/L); and

1e6 = conversion factor (mg/kg).

7.1 Ionization

Dissociation of an organic acid or base in water can have a significant effect on its

environmental properties. In particular, solubility, volatilization, photolysis, sorption, and

bioconcentration of an ionized compound can be affected. Rather than modeling ionization

products, the approach taken in AQUATOX is to represent the modifications to the fate and

transport of the neutral species, based on the fraction that is not dissociated. The acid dissociation

constant is expressed as the negative log, pKa, and the fraction that is not ionized is:
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(211)

Figure 72

Dissociation of Pentachlorophenol 

(pKa = 4.75) at Higher pH Values

Figure 73

Dissociation as a Function of pKa at an

Ambient pH of 7

(212)

where:

Nondissoc = nondissociated fraction (unitless).

If the compound is a base then the fraction not ionized is:

When pKa = pH half the compound is ionized and half is not (Figure 72). At ambient

environmental pH values, compounds with a pKa in the range of 4 to 9 will exhibit significant

dissociation (Figure 73).

7.2 Hydrolysis

Hydrolysis is the degradation of a compound through reaction with water. During

hydrolysis, both a pollutant molecule and a water molecule are split, and the two water molecule

fragments (H+

 and OH-) join to the two pollutant fragments to form new chemicals. Neutral and

acid- and base-catalyzed hydrolysis are modeled using the approach of Mabey and Mill (1978) in

which an overall pseudo-first-order rate constant is computed for a given pH, adjusted for the

ambient temperature of the water:

where:
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(213)

(214)

(215)

(216)

(217)

and where:

KHyd = overall pseudo-first-order rate constant for a given pH and

temperature (1/d);

KAcidExp = pseudo-first-order acid-catalyzed rate constant for a given pH (1/d);

KBaseExp = pseudo-first-order base-catalyzed rate constant for a given pH (1/d);

KUncat = the measured first-order reaction rate at pH 7 (1/d); and

Arrhen = temperature adjustment (unitless), see (218).

There are three types of hydrolysis: acid-catalyzed, base-catalyzed, and neutral. In neutral

hydrolysis reactions, the pollutant reacts with a water molecule (H2O) and the concentration of water

is usually included in KUncat. In acid-catalyzed hydrolysis, the hydrogen ion reacts with the

pollutant, and a first-order decay rate for a given pH can be estimated as follows:

where:

and where:

KAcid = acid-catalyzed rate constant (L/mol@ d);

HIon = concentration of hydrogen ions (mol/L); and

pH = pH of water column.

Likewise for base-catalyzed hydrolysis, the first-order rate constant for a reaction between

the hydroxide ion and the pollutant at a given pH (Figure 74) can be described as:

where:

and where:

KBase = base-catalyzed rate constant (L/mol @ d); and

OHIon = concentration of hydroxide ions (mol/L).
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Figure 74

Base-catalyzed Hydrolysis of Pentachlorophenol

(218)

(219)

Hydrolysis reaction rates were adjusted for the temperature of the waterbody being modeled

by using the Arrhenius rate law (Hemond and Fechner 1994). An activation energy value of 18,000

cal/mol (a mid-range value for organic chemicals) was used as a default:

where:

En = Arrhenius activation energy (cal/mol);

R = universal gas constant (cal/mol @ Kelvin);

KelvinT = temperature for which rate constant is to be predicted (Kelvin); and

TObs = temperature at which known rate constant was measured (Kelvin).

7.3 Photolysis

Direct photolysis is the process by which a compound absorbs light and undergoes

transformation:

where:

Photolysis = rate of loss due to photodegradation (:g/L"d); and

KPhot = direct photolysis first-order rate constant (1/day).

For consistency, photolysis is computed for both the epilimnion and hypolimnion in stratified

systems. However, it is not a significant factor at hypolimnetic depths.
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Figure 75 

Photolysis of Pentachlorophenol as a Function of

Light Intensity and Depth of Water

(221)

Ionization may result in a significant shift in the absorption of light (Lyman et al., 1982;

Schwarzenbach et al., 1993). However, there is a general absence of information on the effects of

light on ionized species. The user provides an observed rate constant for photolysis (PhotRate), and

this is usually determined either with distilled water or with water from a representative site, so that

ionization may be included in the calculated lumped parameter KPhot.

Based on the approach of Thomann and Mueller (1987; see also Schwarzenbach et al. 1993),

the observed first-order rate constant for the compound is modified by a light attenuation factor for

ultraviolet light so that the process as represented is depth-sensitive (Figure 75); it also is adjusted

by a factor for time-varying light: 

where:

PhotRate = direct, observed photolysis first-order rate constant (1/day);

ScreeningFactor = a light screening factor (unitless), see (221); and

LightFactor = a time-varying light factor (unitless), see (222).

A light screening factor adjusts the observed laboratory photolytic transformation rate of a

given pollutant for field conditions with variable light attenuation and depth (Thomann and Mueller,

1987):

where:
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(223)

(224)

RadDistr = radiance distribution function, which is the ratio of the average

pathlength to the depth (see Schwarzenbach et al., 1993) (taken to be

1.6, unitless);

RadDistr0 = radiance distribution function for the top of the segment (taken to be

1.2 for the top of the epilimnion and 1.6 for the top of the

hypolimnion, unitless);

Extinct = light extinction coefficient (1/m) not including periphyton, see (30);

and

Thick = thickness of the water body segment if stratified or maximum depth

if unstratified (m).

The equation presented above implicitly makes the following assumptions:

@ quantum yield is independent of wavelength; and,

@ the value used for PhotRate is a representative near-surface, first-order rate constant

for direct photolysis.

The rate is modified further to represent seasonally varying light conditions and the effect

of ice cover:

where:

Solar0 = time-varying average light intensity at the top of the segment

(ly/day); and

AveSolar = average light intensity for late spring or early summer, corresponding

to time when photolytic half-life is often measured (500 Ly/day).

If the system is unstratified or if the epilimnion is being modeled, the light intensity is the

light loading:

otherwise we are interested in the intensity at the top of the hypolimnion and the attenuation of light

is given as a logarithmic decrease over the thickness of the epilimnion:

where:

Solar = incident solar radiation loading (ly/d), see (25); and

MaxZMix = depth of the mixing zone (m), see (17).

Because the ultraviolet light intensity exhibits greater seasonal variation than the visible

spectrum (Lyman et al., 1982), decreasing markedly when the angle of the sun is low, this construct
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could predict higher rates of photolysis in the winter than might actually occur. However, the model

also accounts for significant attenuation of light due to ice cover so that photolysis, as modeled, is

not an important process in northern waters in the winter.

7.4 Microbial Degradation

Not only can microorganisms decompose the detrital organic material in ecosystems, they

also can degrade xenobiotic organic compounds such as fuels, solvents, and pesticides to obtain

energy. In AQUATOX this process of biodegradation of pollutants, whether they are dissolved in

the water column or adsorbed to organic detritus in the water column or sediments, is modeled using

the same equations as for decomposition of detritus, substituting the pollutant and its degradation

parameters for detritus in Equation (130) and supporting equations:

where:

MicrobialDegrdn = loss due to microbial degradation (g/m3

"d);

KMDegrdn = maximum degradation rate, either in water column or

sediments (1/d);

DOCorrection = effect of anaerobic conditions (unitless), see (131);

TCorr = effect of suboptimal temperature (unitless), see (24);

pHCorr = effect of suboptimal pH (unitless), see (133); and

Toxicant = concentration of organic toxicant (g/m3).

Microbial degradation proceeds more quickly if the material is associated with surficial

sediments rather than suspended in the water column (Godshalk and Barko, 1985); thus, in

calculating the loss due to microbial degradation in the sorbed phase, the maximum degradation rate

is set to four times the maximum degradation rate in the water. The model assumes that reported

maximum microbial degradation rates are for the dissolved phase; if the reported degradation value

is from a study with additional organic matter, such as suspended slurry or wet soil samples, then

the parameter value that is entered should be one-fourth that reported. 

7.5 Volatilization

Volatilization is modeled using the "stagnant boundary theory", or two-film model, in which

a pollutant molecule must diffuse across both a stagnant water layer and a stagnant air layer to

volatilize out of a waterbody (Whitman, 1923; Liss and Slater, 1974). Diffusion rates of pollutants

in these stagnant boundary layers can be related to the known diffusion rates of chemicals such as

oxygen and water vapor. The thickness of the stagnant boundary layers must also be taken into

account to estimate the volatile flux of a chemical out of (or into) the waterbody.

The time required for a pollutant to diffuse through the stagnant water layer in a waterbody

is based on the well-established equations for the reaeration of oxygen, corrected for the difference
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(227)

(228)

in diffusivity as indicated by the respective molecular weights (Thomann and Mueller, 1987, p. 533).

The diffusivity through the water film is greatly enhanced by the degree of ionization

(Schwarzenbach et al., 1993, p. 243), and the depth-averaged reaeration coefficient is multiplied by

the thickness of the well-mixed zone: 

where:

KLiq = water-side transfer velocity (m/d);

KReaer = depth-averaged reaeration coefficient for oxygen (1/d), see (155)-

(162);

Thick = mean thickness of the water body segment if stratified or men depth

if unstratified (m);

MolWtO2 = molecular weight of oxygen (g/mol, =32);

MolWt = molecular weight of pollutant (g/mol); and

Nondissoc = nondissociated fraction (unitless), see (210).

Likewise, the thickness of the air-side stagnant boundary layer is also affected by wind.

Wind usually is measured at 10 m, and laboratory experiments are based on wind measured at 10

cm, so a conversion is necessary (Banks, 1975). To estimate the air-side transfer velocity of a

pollutant, we used the following empirical equation based on the evaporation of water, corrected for

the difference in diffusivity of water vapor compared to the toxicant (Thomann and Mueller, 1987,

p. 534):

where:

KGas = air-side transfer velocity (m/d);

Wind = wind speed ten meters above the water surface (m/s); 

0.5 = conversion factor (wind at 10 cm/wind at 10 m); and

MolWtH2O = molecular weight of water (g/mol, =18).

The total resistance to the mass transfer of the pollutant through both the stagnant boundary

layers can be expressed as the sum of the resistances—the reciprocals of the air- and water-phase

mass transfer coefficients (Schwarzenbach et al., 1993), modified for the effects of ionization:

where:
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KOVol = total mass transfer coefficient through both stagnant boundary layers

(m/d); 

and where:

HenryLaw = Henry's law constant (unitless);

Henry = Henry's law constant (atm m3

 mol-1);

R = gas constant (=8.206E-5 atm m3 (mol K)-1); and

TKelvin = temperature in /K.

The Henry’s law constant is applicable only to the fraction that is nondissociated because

the ionized species will not be present in the gas phase (Schwarzenbach et al., 1993, p. 179).

The atmospheric exchange of the pollutant can be expressed as the depth-averaged total mass

transfer coefficient times the difference between the concentration of the chemical and the saturation

concentration:

where:

Volatilization = interchange with atmosphere (:g/L"d);

Thick = depth of water or thickness of surface layer (m);

ToxSat = saturation concentration of pollutant in equilibrium with the gas

phase (:g/L); and

Toxicantwater = concentration of pollutant in water (:g/L).

Because theoretically toxicants can be transferred in either direction across the water-air

interface, Eq. 209 is formulated so that volatilization takes a negative sign when it is a loss term.

The saturation concentration depends on the concentration of the pollutant in the air, ignoring

temperature effects (Thomann and Mueller, 1987, p. 532; see also Schnoor, 1996), but adjusting for

ionization and units:

where:

Toxicantair = user-supplied gas-phase concentration of the pollutant (g/m3); and

Nondissoc = nondissociated fraction (unitless).
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Figure 76

Atrazine KOVol as a Function of Wind

Figure 77

Benzene KOVol as a Function of Wind

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Often the pollutant can be assumed to have a negligible concentration in the air and ToxSat

is zero. However, this general construct can represent the transferral of volatile pollutants into water

bodies. Because ionized species do not volatilize, the saturation level increases if ionization is

occurring.

The nondimensional Henry's law constant, which relates the concentration of a compound

in the air phase to its concentration in the water phase, strongly affects the air-phase resistance.

Depending on the value of the Henry's law constant, the water phase, the air phase or both may

control volatilization. For example, with a depth of 1 m and a wind of 1 m/s, the gas phase is

100,000 times as important as the water phase for atrazine (Henry's law constant = 3.0E-9), but the

water phase is 50 times as important as the air phase for benzene (Henry's law constant = 5.5E-3).

Volatilization of atrazine exhibits a linear relationship with wind (Figure 76) in contrast to the

exponential relationship exhibited by benzene (Figure 77).

7.6 Partition Coefficients

Although AQUATOX is a kinetic model, steady-state partition coefficients for organic

pollutants are computed in order to constrain sorption to detritus and algae (252), and to compute

internal toxicities (279). They are estimated from empirical regression equations and the pollutant's

octanol-water partition coefficient. 

Detritus

Natural organic matter is the primary sorbent for neutral organic pollutants. Hydrophobic

chemicals partition primarily in nonpolar organic matter (Abbott et al. 1995). Refractory detritus

is relatively nonpolar; its partition coefficient (in the non-dissolved phase) is a function of the

octanol-water partition coefficient (N = 34, r2 = 0.93; Schwarzenbach et al. 1993):
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Figure 78 

Refractory Detritus-water and Octanol-water Partition

Coefficients for Pentachlorophenol as a Function of pH.

where:

KOMRefrDetr = detritus-water partition coefficient (L/kg); and

KOW = octanol-water partition coefficient (L/kg).

Detritus in sediments is simulated separately from inorganic sediments, rather than as a

fraction of the sediments as in other models. At this time AQUATOX does not simulate sorption

to inorganic sediments. Therefore, refractory detritus is used as a surrogate for sediments in general;

and the sediment partition coefficient KPSed, which can be entered manually by the user, is the same

as KOMRefrDetr.

Equation (232) and the equations that follow are extended to polar compounds, following

the approach of Smejtek and Wang (1993):

where:

Nondissoc = un-ionized fraction (unitless); and

IonCorr = correction factor for decreased sorption, 0.01 for chemicals that are

bases and 0.1 for acids. (unitless).

Using pentachlorophenol as a test compound, and comparing it to octanol, the influence of

pH-mediated dissociation is seen in Figure 78. This relationship is verified by comparison with the

results of Smejtek and Wang (1993) using egg membrane. However, in the general model Eq. (233)

is used for refractory detrital sediments as well.
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There appears to be a dichotomy in partitioning; data in the literature suggest that labile

detritus does not take up hydrophobic compounds as rapidly as refractory detritus. Algal cell

membranes contain polar lipids, and it is likely that this polarity is retained in the early stages of

decomposition. KOC does not remain the same upon aging, death, and decomposition, probably

because of polarity changes. In an experiment using fresh and aged algal detritus, there was a 100%

increase in KOC with aging (Koelmans et al., 1995). KOC increased as the C/N ratio increased,

indicating that the material was becoming more refractory. In another study, KOC doubled between

day 2 and day 34, probably due to deeper penetration into the organic matrix and lower polarity

(Cornelissen et al., 1997).

Polar substrates increase the pKa of the compound (Smejtek and Wang, 1993). This is

represented in the model by lowering the pH of polar particulate material by one pH unit, which

changes the dissociation accordingly. 

The partition equation for labile detritus (non-dissolved) is based on a study by Koelmans

et al. (1995) using fresh algal detritus (N = 3, r2 = 1.0):

The equation is generalized to polar compounds and transformed to an organic matter partition

coefficient:

where:

KOCLabPart = partition coefficient for labile particulate organic carbon (L/kg);

KOMLabDetr = partition coefficient for labile detritus (L/kg);

IonCorr = correction factor for decreased sorption, 0.01 for chemicals that are

bases and 0.1 for acids. (unitless); and

0.526 = conversion from KOC to KOM (g OC/g OM).

O’Connor and Connolly (1980; see also Ambrose et al., 1991) found that the sediment

partition coefficient is the inverse of the mass of suspended sediment, and Di Toro (1985) developed

a construct to represent the relationship. However, AQUATOX models partitioning directly to

organic detritus and ignores inorganic sediments, which are seldom involved directly in sorption of

neutral organic pollutants. Therefore, the partition coefficient is not corrected for mass of sediment.

Association of hydrophobic compounds with colloidal and dissolved organic matter (DOM)

reduces bioavailability; such contaminants are unavailable for uptake by organisms (Stange and

Swackhamer 1994, Gilek et al. 1996). Therefore, it is imperative that complexation of organic

chemicals with DOM be modeled correctly. In particular, contradictory research results can be

reconciled by considering that DOM is not homogeneous. For instance, refractory humic acids,

derived from decomposition of terrestrial and wetland organic material, are quite different from

labile exudates from algae and other indigenous organisms. 
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 Humic acids exhibit high polarity and do not readily complex neutral compounds. Natural

humic acids from a Finnish lake with extensive marshes were spiked with a PCB, but a PCB-humic

acid complex could not be demonstrated (Maaret et al. 1992). In another study, Freidig et al. (1998)

used artificially prepared Aldrich humic acid to determine a humic acid-DOC partition coefficient

(n = 5, r2

, = 0.80), although they cautioned about extrapolation to the field:

where:

KOCRefrDOM = refractory dissolved organic carbon partition coefficient (L/kg).

Until a better relationship is found, we are using a generalization of their equation to include

polar compounds, transformed from organic carbon to organic matter, in AQUATOX:

where:

KOMRefrDOM = refractory dissolved organic matter partition coefficient (L/kg).

Nonpolar lipids in algae occur in the cell contents, and it is likely that they constitute part

of the labile dissolved exudate, which may be both excreted and lysed material. Therefore, the

stronger relationship reported by Koelmans and Heugens (1998) for partitioning to algal exudate (n

= 6, r2 = 0.926) is:

 which we also generalized for polar compounds and transformed:

where:

KOCLabDOC = partition coefficient for labile dissolved organic carbon (L/kg); and

KOMLabDOM = partition coefficient for labile dissolved organic matter (L/kg).

Unfortunately, older data and modeling efforts failed to distinguish between hydrophobic

compounds that were truly dissolved and those that were complexed with DOM. For example, the

PCB water concentrations for Lake Ontario, reported by Oliver and Niimi (1988) and used by many

subsequent researchers, included both dissolved and DOC-complexed PCBs (a fact which they

recognized). In their steady-state model of PCBs in the Great Lakes, Thomann and Mueller (1983)

defined “dissolved” as that which is not particulate (passing a 0.45 micron filter). In their Hudson

River PCB model, Thomann et al. (1991) again used an operational definition of dissolved PCBs.
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AQUATOX distinguishes between truly dissolved and complexed compounds; therefore, the

partition coefficients calculated by AQUATOX may be larger than those used in older studies.

Algae

Bioaccumulation of PCBs in algae depends on solubility, hydrophobicity and molecular

configuration of the compound, and growth rate, surface area and type, and content and type of lipid

in the alga (Stange and Swackhamer 1994). Phytoplankton may double or triple in one day and

periphyton turnover may be so rapid that some PCBs will not reach equilibrium (cf. Hill and

Napolitano 1997); therefore, one should use the term “bioaccumulation factor” (BAF) rather than

“bioconcentration factor,” which implies equilibrium (Stange and Swackhamer 1994).

Hydrophobic compounds partition to lipids in algae, but the relationship is not a simple one.

Phytoplankton lipids can range from 3 to 30% by weight (Swackhamer and Skoglund 1991), and

 not all lipids are the same. Polar phospholipids occur on the surface. Hydrophobic compounds

preferentially partition to internal neutral lipids, but those are usually a minor fraction of the total

lipids, and they vary depending on growth conditions and species (Stange and Swackhamer 1994).

Algal lipids have a much stronger affinity for hydrophobic compounds than does octanol, so that the

algal BAFlipid > KOW (Stange and Swackhamer 1994, Koelmans et al. 1995, Sijm et al. 1998). 

For algae, the approximation to estimate the dry-weight bioaccumulation factor (r2 = 0.87),

computed from Swackhamer and Skoglund’s (1993) study of numerous PCB congeners, is:

where:

BAFAlga = partition coefficient between algae and water (L/kg).

Rearranging and extending to hydrophilic and ionized compounds:

Comparing the results of using these coefficients, we see that they are consistent with the

relative importance of the various substrates in binding organic chemicals (Figure 79). Binding

capacity of detritus is greater than dissolved organic matter in Great Lakes waters (Stange and

Swackhamer 1994, Gilek et al. 1996). In a study using Baltic Sea water, less than 7% PCBs were

associated with dissolved organic matter and most were associated with algae (Björk and Gilek

1999). In contrast, in a study using algal exudate and a PCB, 98% of the dissolved concentration

was as a dissolved organic matter complex and only 2% was bioavailable (Koelmans and Heugens

1998).

The influence of substrate polarity is evident in Figure 80, which shows the effect of

ionization on binding of pentachlorophenol to various types of organic matter. The polar substrates,

such as algal detritus, have an inflection point which is one pH unit higher than that of nonpolar
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substrates, such as refractory detritus. The relative importance of the substrates for binding is also

demonstrated quite clearly.

Macrophytes

For macrophytes, an empirical relationship reported by Gobas et al. (1991) for 9 chemicals

with LogKOWs of 4 to 8.3 (r2 = 0.97) is used:

Again, rearranging and extending to hydrophilic and ionized compounds:

Invertebrates

For the invertebrate bioconcentration factor, the following empirical equation is used for

nondetritivores, based on 7 chemicals with LogKOWs ranging from 3.3 to 6.2 and bioconcentration

factors for Daphnia pulex (r2

 = 0.85; Southworth et al., 1978; see also Lyman et al., 1982), converted

to dry weight :

where:

KBInvertebrate = partition coefficient between invertebrates and water (L/kg); and

WetToDry = wet to dry conversion factor (unitless, default = 5).

Extending and generalizing to ionized compounds:

For invertebrates that are detritivores the following equation is used, based on Gobas 1993:

where:

KBInvertebrate = partition coefficient between invertebrates and water (L/kg);

FracLipid = fraction of lipid within the organism; 

FracOCDetritus = fraction of organic carbon in detritus (= 0.526); 

KOMRefrDetr = partition coefficient for refractory sediment detritus (L/kg), see (233).
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Figure 79

Partitioning to Various Types of Organic

Matter as a Function of KOW

Figure 80

Partitioning to Various Types of Organic

Matter as a Function of pH

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Fish

Fish take longer to reach equilibrium with the surrounding water; therefore, a nonequilibrium

bioconcentration factor is used. For each pollutant, a whole-fish bioconcentration factor is based

on the lipid content of the fish extended to hydrophilic chemicals (McCarty et al., 1992), with

provision for ionization:

where:

KBFish = partition coefficient between whole fish and water (L/kg);

Lipid = fraction of fish that is lipid (g lipid/g fish); and

WetToDry = wet to dry conversion factor (unitless, default = 5).

Lipid content of fish is either held constant or is computed depending on the potential for

growth as predicted by the bioenergetics equations; the initial lipid values for the species are entered

by the user. The bioconcentration factor is adjusted for the time to reach equilibrium as a function

of the clearance or elimination rate and the time of exposure (Hawker and Connell, 1985; Connell

and Hawker, 1988; Figure 81):

where:

BCFFish = quasi-equilibrium bioconcentration factor for fish (L/kg);

TElapsed = time elapsed since fish was first exposed (d); and

Depuration = clearance, which may include biotransformation, see (269) (1/d).
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Figure 81

Bioconcentration Factor for Fish 

as a Function of Time and log KOW

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7.7 Nonequilibrium Kinetics

Although partition coefficients are computed in AQUATOX in order to provide constraints

on sorption and to compute internal toxicities, the model is basically a kinetic model. In nature there

is often an absence of equilibrium due to growth or insufficient exposure time, metabolic

biotransformation, dietary exposure, and nonlinear relationships for very large and/or

superhydrophobic compounds (Bertelsen et al. 1998). It is important to have a knowledge of

equilibrium partitioning because it is an indication of the condition toward which systems tend

(Bertelsen et al. 1998), but steady-state potential is often not achieved due to changes in

bioavailability and physiology (Landrum 1998). For example, PCBs may not be at steady state even

in large systems such as Lake Ontario that have been polluted over a long period of time. In fact,

PCBs in Lake Ontario exhibit a 25-fold disequilibrium (Cook and Burkhard 1998). The challenge

is to obtain sufficient data for a kinetic model (Gobas et al. 1995). 

Sorption and Desorption to Detritus

Partitioning to detritus appears to involve rapid sorption to particle surfaces, followed by

slow movement into, and out of, organic matter and porous aggregates (Karickhoff and Morris,

1985). Therefore attainment of equilibrium may be slow. Because of the need to represent sorption

and desorption separately in detritus, kinetic formulations are used (Thomann and Mueller, 1987),

with provision for ionization:
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where:

Sorption = rate of sorption to given detritus compartment (:g/L"d);

k1Detr = sorption rate constant (1.39 L/kg"d);

Nondissoc = fraction not ionized (unitless); 

ToxicantWater = concentration of toxicant in water (:g/L);

Diff = factor to normalize rate constant based on all competing uptake rates

(unitless), see (251);

Org2C = conversion factor for organic matter to carbon (= 0.526 g C/g organic

matter);

Detr = mass of each of the detritus compartments per unit volume (mg/L);

1e -6 = units conversion (kg/mg);

Desorption = rate of desorption from given sediment detritus compartment

(:g/L"d);

k2Detr = desorption rate constant (1/d), see (254);

UptakeLimit = factor to limit uptake as equilibrium is reached (unitless); see (252)

and

ToxicantDetr = mass of toxicant in each of the detritus compartments (:g/L).

Because there are several processes competing for the dissolved toxicant, the rate constants

for these processes are normalized in order to preserve mass balance. The Diff factor is computed

considering all direct uptake processes, including sorption to detritus and algae, uptake by

macrophytes, and uptake across animal gills. If the sum of the competing processes per day is less

than the mass available in the water then Diff = 1, otherwise:

where:

SorptionDetritus = rate of sorption to given detrital group (:g/L"d), see (249);

PlantUptakePlant = rate of uptake by given plant group (:g/L"d), see (256),

(260);

GillUptakeAnimal = rate of uptake by given animal group (:g/L"d), see (265); and

dt = time step (d).

In order to limit sorption to detritus and algae as equilibrium is reached, UptakeLimit

is computed as:
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where:

UptakeLimitCarrier = factor to limit uptake as equilibrium is reached (unitless);

kpCarrier = partition coefficient or bioconcentration factor for each carrier (L/kg),

see (233) to (241);

PPBCarrier = concentration of toxicant in each carrier (:g/kg), see (209).

Desorption of the detrital compartments is the reciprocal of the reaction time, which

Karickhoff and Morris (1985) found to be a linear function of the partition coefficient over three

orders of magnitude (r

2

 = 0.87):

So k2 is taken to be:

where:

KOMRefrDetr = detritus-water partition coefficient (L/kg OM, see section

7.1); and

Because the kinetic definition of the detrital partition coefficient KOM is:

the sorption rate constant k1 is set to 1.39 L/kg"d.

Bioaccumulation in Macrophytes and Algae

Macrophytes—As Gobas et al. (1991) have shown, submerged aquatic macrophytes take up and

release organic chemicals over a measurable period of time at rates related to the octanol-water

partition coefficient. Uptake and elimination are modeled assuming that the chemical is transported

through both aqueous and lipid phases in the plant, with rate constants using empirical equations fit

to observed data (Gobas et al., 1991), modified to account for ionization effects (Figure 82, Figure

83):
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Figure 82

Uptake Rate Constant for Macrophytes

(after Gobas et al., 1991)

Figure 83

Elimination Rate Constant for Macrophytes

(after Gobas et al., 1991)

If the user selects to estimate the elimination rate constant based on KOW, the following equation

is used:

where:

MacroUptake = uptake of toxicant by plant (:g/L"d);

DepurationPlant= clearance of toxicant from plant (:g/L"d);

StVarPlant = biomass of given plant (mg/L);

1 e -6 = units conversion (kg/mg);

ToxicantPlant = mass of toxicant in plant (:g/L);

k1 = sorption rate constant (L/kg"d);

k2 = elimination rate constant (1/d).

Diff = factor to normalize uptake rates (unitless), see (251);

KOW = octanol-water partition coefficient (unitless);

Nondissoc = fraction of un-ionized toxicant (unitless): and

DissocFactor = constrained factor based on Nondissoc (unitless).
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Algae—Aside from obvious structural differences, algae may have very high lipid content (20% for

Chlorella sp. according to Jørgensen et al., 1979) and macrophytes have a very low lipid content

(0.2% in Myriophyllum spicatum as observed by Gobas et al. (1991), which affect both uptake and

elimination of toxicants. However, the approach used by Gobas et al. (1991) in modeling

bioaccumulation in macrophytes provides a useful guide to modeling kinetic uptake in algae.

There is probably a two-step algal bioaccumulation mechanism for hydrophobic compounds,

with rapid surface sorption of 40-90% within 24 hours and then a small, steady increase with transfer

to interior lipids for the duration of the exposure (Swackhamer and Skoglund 1991). Uptake

increases with increase in the surface area of algae (Wang et al. 1997). Therefore, the smaller the

organism the larger the uptake rate constant (Sijm et al. 1998). However, in small phytoplankton,

such as the nannoplankton that dominate the Great lakes, a high surface to volume ratio can increase

sorption, but high growth rates can limit internal contaminant concentrations (Swackhamer and

Skoglund 1991). The combination of lipid content, surface area, and growth rate results in species

differences in bioaccumulation factors among algae (Wood et al. 1997). Uptake of toxicants is a

function of the uptake rate constant and the concentration of toxicant truly dissolved in the water,

and is constrained by competitive uptake by other compartments; also, because it is fast, it is limited

as it approaches equilibrium, similar to sorption to detritus :

where:

AlgalUptake = rate of sorption by algae (:g/L-d);

k1 = uptake rate constant (L/kg-d), see (261);

UptakeLimitAlga = factor to limit uptake as equilibrium is reached (unitless), see (252);

Diff = factor to normalize uptake rates (unitless), see (251);

ToxState = concentration of dissolved toxicant (:g/L);

Carrier = biomass of algal compartment (mg/L); and

1e-6 = conversion factor (kg/mg).

The kinetics of partitioning of toxicants to algae is based on studies on PCB congeners in

The Netherlands by Koelmans, Sijm, and colleagues and at the University of Minnesota by

Skoglund and Swackhamer. Both groups found uptake to be very rapid. Sijm et al. (1998) presented

data on several congeners that were used in this study to develop the following relationship for

phytoplankton (Figure 84):

Depuration is modeled as a linear function; it does not include loss due to excretion of

photosynthate with associated toxicant, which is modeled separately:

where:
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Figure 84 

Algal Sorption Rate Constant as a Function of

Octanol-water Partition Coefficient

Figure 85 

Rate of Elimination by Algae as a Function of

Octanol-water Partition Coefficient

Depuration = elimination of toxicant (:g/L-d);

State = concentration of toxicant associated with alga (:g/L); and

k2 = elimination rate constant (1/d).

The elimination rate in plants may be input in the toxicity record by the user or it may be estimated

using the following equation based in part on Skoglund et al. (1996). Unlike Skoglund, this equation

ignores surface sorption and recognizes that growth dilution is explicit in AQUATOX (see Figure

85):

where:

k2Akgae = desorption rate constant (1/d);

LFrac = fraction lipid, as entered in the chemical toxicity screen; and

WetToDry = translation from wet to dry weight (5.0).

If more than 20% of the compound is ionized, the k2Algae is estimated from the k1 and BCF

values:

Bioaccumulation in Animals

Animals can absorb toxic organic chemicals directly from the water through their gills and

from contaminated food through their guts, hence they bioaccumulate, and seldom is steady-state

bioconcentration an important factor. Direct sorption onto the body is ignored as a simplifying
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assumption in this version of the model. Reduction of body burdens of organic chemicals is

accomplished through excretion and biotransformation, which are often considered together as

empirically determined elimination rates. “Growth dilution” occurs when growth of the organism

is faster than accumulation of the toxicant. Gobas (1993) includes fecal egestion, but in AQUATOX

egestion is merely the amount ingested but not assimilated; it is accounted for indirectly in

DietUptake. However, fecal loss is important as an input to the detrital toxicant pool, and it is

considered later in that context. Inclusion of mortality and promotion terms is necessary for mass

balance, but emphasizes the fact that average concentrations are being modeled for any particular

compartment.

Gill Sorption—An important route of exposure is by active transport through the gills (Macek et

al., 1977). This is the route that has been measured so often in bioconcentration experiments with

fish. As the organism respires, water is passed over the outer surface of the gill and blood is moved

past the inner surface. The exchange of toxicant through the gill membrane is assumed to be

facilitated by the same mechanism as the uptake of oxygen, following the approach of Fagerström

and Åsell (1973, 1975), Weininger (1978), and Thomann and Mueller (1987; see also Thomann,

1989). Therefore, the uptake rate for each animal can be calculated as a function of respiration

(Leung, 1978; Park et al., 1980):

where:

GillUptake = uptake of toxicant by gills (:g/L - d);

KUptake = uptake rate (1/d);

ToxicantWater = concentration of toxicant in water (:g/L);

Diff = factor to normalize rate constant based on all competing uptake rates

(unitless), see (251);

WEffTox = withdrawal efficiency for toxicant by gills (unitless), see (267);

Respiration = respiration rate (mg biomass/L"d), see (87);

O2Biomass = ratio of oxygen to organic matter (mg oxygen/mg biomass; 0.575);

Oxygen = concentration of dissolved oxygen (mg oxygen/L), see (150); and

WEffO2 = withdrawal efficiency for oxygen (unitless, generally 0.62).

The oxygen uptake efficiency WEffO2 is assigned a constant value of 0.62 based on

observations of McKim et al. (1985). The toxicant uptake efficiency, WEffTox, can be expected to

have a sigmoidal relationship to the log octanol-water partition coefficient based on aqueous and

lipid transport (Spacie and Hamelink, 1982). This is represented by an inelegant but reasonable,

piece-wise fit (Figure 86) to the data of McKim et al. (1985) using 750-g fish, corrected for

ionization:
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Figure 86

Piece-wise Fit to Observed Toxicant Uptake Data;

Modified from McKim et al., 1985

where:

LogKOW = log octanol-water partition coefficient (unitless); and

Nondissoc = fraction of toxicant that is un-ionized (unitless), see (210).

Ionization decreases the uptake efficiency (Figure 87). This same algorithm is used for

invertebrates. Thomann (1989) has proposed a similar construct for these same data and a slightly

different construct for small organisms, but the scatter in the data do not seem to justify using two

different constructs.
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Figure 87

The Effect of Differing Fractions of Un-ionized

Chemical on Uptake Efficiency

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Dietary Uptake—Hydrophobic chemicals usually bioaccumulate in larger animals primarily

through absorption from contaminated food. Persistent, highly hydrophobic chemicals demonstrate

biomagnification or increasing concentrations as they are passed up the food chain from one trophic

level to another; therefore, dietary exposure can be quite important (Gobas et al., 1993). Uptake

from contaminated prey can be computed as (Thomann and Mueller, 1987; Gobas, 1993):

where:

DietUptakePrey = uptake of toxicant from given prey (:g toxicant/L"d);

GutEffTox = efficiency of sorption of toxicant from gut (unitless); and

PPBPrey = concentration of toxicant in given prey (:g toxicant/kg prey), see

(209);

IngestionPrey = ingestion of given prey (mg prey/L"d), see (78).

1 e-6 = units conversion (kg/mg);

Gobas (1993) presents an empirical equation for estimating GutEffTox as a function of the

octanol-water partition coefficient. However, data published by Gobas et al. (1993) suggest that

there is no trend in efficiency between LogKOW 4.5 and 7.5 (Figure 88); this is to be expected

because the digestive system has evolved to assimilate a wide variety of organic molecules.

Therefore, the mean value of 0.62 is used in AQUATOX as a constant for small fish. Nichols et al.

(1998) demonstrated that uptake is more efficient in larger fish; therefore, a value of 0.92 is used

for large game fish because of their size. Invertebrates generally exhibit lower efficiencies;

Landrum and Robbins (1990) showed that values ranged from 0.42 to 0.24 for chemicals with log

KOWs from 4.4 to 6.7; the mean value of 0.35 is used for invertebrates in AQUATOX. These

values cannot be edited at this time.
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 7

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Figure 88

GutEffTox Constant Based on Mean Value for Data

from Gobas et al., 1993

(269)

(270)

Elimination—Elimination or clearance includes both excretion (depuration) and biotransformation

of a toxicant by organisms. Biotransformation may cause underestimation of elimination (McCarty

et al., 1992). An overall elimination rate constant is estimated and reported in the toxicity record.

The user may then modify the value based on observed data; that value is used in subsequent

simulations. If known, biotransformation also can be explicitly modeled.

For any given time the clearance rate is:

where:

DepurationAnimal = clearance rate (:g/L"d); 

k2 = elimination rate constant (1/d); 

ToxicantAnimal = mass of toxicant in given animal (:g/L); and

TCorr = correction for suboptimal temperature (unitless), see (51).

Because much animal depuration is across the gills, estimation of the elimination rate

constant k2 is based on a slope related to log KOW and an intercept that is a direct function of

respiration, assuming an allometric relationship between respiration and the weight of the animal

(Figure 89, Thomann, 1989), and an inverse function of the lipid content:

If WetWt < 5 g then 

else
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(272)

where

KOW = octanol-water partition coefficient (unitless);

LipidFrac = fraction of lipid in organism (g lipid/g organism); 

WetWt = mean wet weight of organism (g);

RB = allometric exponent for respiration (unitless);

DissocFactor = constrained factor for Nondissoc, see (259).

The other gain and loss terms in equation (208) (TurbDiff, Predation, Mortality, Migration,

Recruit, GameteLoss, Promotion, Drift, Migration, and EmergeInsect) are all simply multiplied by

the appropriate toxicant concentration to complete the computation of the overall toxicant

concentration in the animal.

Biotransformation

Biotransformation can cause the conversion of a toxicant to another toxicant or to a harmless

daughter product through a variety of pathways. Internal biotransformation to given daughter

products by plants and animals is modeled by means of empirical rate constants provided by the user

in the Chemical Biotransformation screen:

where

Biotransformation = rate of conversion of chemical by given organism (:g/L d),

BioRateConst = biotransformation rate constant to a given toxicant, provided

by user (1/day)

with the model keeping track of both the loss and the gains to various daughter compartments.
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 7

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K2 for Various Animals

-4

-3

-2

-1

0

1

2

3

4

123456789

Log KOW

Log K2

Daphnia Diporeia

10-g fish Eel obs

Eel Linear (10-g fish pred)

Linear (Daphnia pred) Linear (Diporeia pred)

Figure 89

Depuration Rate Constants for Invertebrates and Fish 

(273)

(274)

Biotransformation also can take place as a consequence of microbial decomposition. The

percentage of microbial biotransformation from and into each of the organic chemicals in a

simulation can be specified, with different values for aerobic and anaerobic decomposition. The

amount of biotransformation into a given chemical can then be calculated as follows for aerobic

conditions:

and for anaerobic conditions:

where

BiotransformMicrobIn = Biotransformation to a given organic chemical in a given

detrital compartment due to microbial decomposition (:g/L

d);
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(275)

(276)

(277)

(278)

MicrobialDegradn = total microbial degradation of a different toxicant in this

detrital compartment (:g/L d) see (225);

FracAerobic = fraction of the microbial degradation that is aerobic (unitless),

see (275); and

FracOrgTox = user input fraction of the organic toxicant that is transformed

to the current organic toxicant (inputs can differ depending on

whether the degradation is aerobic or anaerobic). 

To calculate the fraction of microbial decomposition that is aerobic, the following equation

is used:

where

Factor = Michaelis-Menten factor (unitless) see (132);

DoCorr = effect of oxygen on microbial decomposition (unitless) see (131).

Linkages to Detrital Compartments

Toxicants are transferred from organismal to detrital compartments through defecation and

mortality. The amount transferred due to defecation is the unassimilated portion of the toxicant that

is ingested:

where:

DefecationTox = rate of transfer of toxicant due to defecation (:g/L"d);

KEgestPred, Prey = fecal egestion rate for given prey by given predator (mg

prey/L"d);

PPBPrey = concentration of toxicant in given prey (:g/kg), see (209);

1 e-6 = units conversion (kg/mg);

GutEffTox = efficiency of sorption of toxicant from gut (unitless), see page

7-31; and

IngestionPred, Prey = rate of ingestion of given prey by given predator (mg/L"d),

see (78).

The amount of toxicant transferred due to mortality may be large; it is a function of the

concentrations of toxicant in the dying organisms and the mortality rates. The general equation is:
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 7

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where:

MortToxDetr = rate of transfer of toxicant to a given detrital compartment due to

mortality (:g/L"d);

MortalityOrg = rate of mortality of given organism (mg/L"d), see (58), (74) and (98);

PPBOrg = concentration of toxicant in given organism (:g/kg), see (209); and

1 e-6 = units conversion (kg/mg).
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8 ECOTOXICOLOGY

Unlike most models, AQUATOX contains an ecotoxicology submodel that computes acute

and chronic toxic effects from the concentration of a toxicant in a given organism, using the critical

body residue approach (McCarty 1986, McCarty and Mackay 1993). Because the model simulates

toxicity based on internal concentrations as a consequence of bioaccumulation, both water and

dietary exposure pathways are represented equally well. Furthermore, as an ecosystem model,

AQUATOX can simulate indirect effects such as loss of forage base, reduction in predation, and

anoxia due to decomposition following a fish kill. 

User-supplied values for LC50, the concentration of a toxicant in water that causes 50%

mortality, form the basis for a sequence of computations that lead to estimates of the biomass of a

given organism lost through acute toxicity each day. The sequence, which is documented in this

chapter, is to compute:

! the internal concentration causing 50% mortality for a given period of exposure;

! the internal concentration causing 50% mortality after an infinite period of time based on an

asymptotic concentration-response relationship;

! the time-varying lethal internal concentration of a chemical;

! the cumulative mortality for a given internal concentration;

! the biomass lost per day as an increment to the cumulative mortality.

The user-supplied EC50s, the concentrations in water eliciting chronic toxicity responses in

50% of the population, are used to obtain application factors relating the chronic toxicities to the

acute toxicity. Because AQUATOX can simulate as many as twenty toxic organic chemicals

simultaneously, the simplifying assumption is made that the toxic effects are additive.

8.1 Acute Toxicity of Compounds

Toxicity is based on the internal concentration of the toxicant in the specified organism.

Many compounds, especially those with higher octanol-water partition coefficients, take appreciable

time to accumulate in the tissue. Therefore, length of exposure is critical in determining toxicity.

Although AQUATOX cannot currently model mercury, mercury is used as an example in the

following discussion because of the availability of excellent data. The same principles apply to

organic toxicants and to both plants and animals.

The internal lethal concentration or lethal body residue can be computed from reported acute

toxicity data for the reported period of exposure based on the simple relationship suggested by an

algorithm in the FGETS model (Suárez and Barber, 1992):

where:

InternalLC50 = internal concentration that causes 50% mortality for a given period

of exposure (:g/kg);
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 8

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Figure 85

Bioconcentration Factor as a Function of Time and KOW

(280)

BCF = time-dependent bioconcentration factor (L/kg), see (241), (248); and

LC50 = concentration of toxicant in water that causes 50% mortality for a

given period of exposure (:g/L).

Note that time is implicit in the toxicity parameters. For compounds with a LogKOW in

excess of 5 the usual 96-hr toxicity exposure does not reach steady state, so a time-dependent BCF

is used to account for the actual internal concentration at the end of the toxicity determination. This

is applicable no matter what the length of exposure (Figure 85, based on Figure 81).

A given LC50 can be provided by the user, or the user may choose to have the model

estimate the LC50 from other species or groups for which there are data based on linear regressions

(Mayer and Ellersieck, 1986) and maximum likelihood estimators (Suter et al., 1986). In this way

the model can be parameterized to represent a complete food web (Table 7).

where:

CalcLC50 = estimated LC50 (:g/L);

Intercept = intercept for regression (:g/L);

Slope = slope of the regression equation;

LC50 = external concentration of toxicant at which 50% of population is

killed (:g/L).
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 8

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Table 7. Interspecies regression parameters.

From To Intercept Slope Correl. r

minnow trout -0.09 0.947 0.95 Mayer and Ellersieck,

1986

minnow bass -0.433 0.972 0.93 Mayer and Ellersieck,

1986

minnow catfish 0.954 0.832 0.88 Mayer and Ellersieck,

1986

minnow bluegill 0.018 0.954 0.93 Mayer and Ellersieck,

1986

bluegill trout 0.44 0.898 0.96 Mayer and Ellersieck,

1986

bluegill bass 0.051 1.003 0.98 Mayer and Ellersieck,

1986

bluegill catfish 1.918 0.713 0.78 Mayer and Ellersieck,

1986

bluegill minnow 0.947 0.883 0.92 Mayer and Ellersieck,

1986

trout bass 0.258 0.983 0.96 Mayer and Ellersieck,

1986

trout catfish 1.391 0.802 0.82 Mayer and Ellersieck,

1986

trout bluegill 0.135 1.005 0.96 Mayer and Ellersieck,

1986

trout minnow 0.796 0.928 0.94 Mayer and Ellersieck,

1986

Daphnia chironomid 0.802 0.846 0.86 Mayer and Ellersieck,

1986

Daphnia stonefly 1.475 0.667 0.65 Mayer and Ellersieck,

1986

Daphnia ostracod 0.79 0.62 Suter et al., 1986

Daphnia amphipod -0.462 1.01 0.82 Mayer and Ellersieck,

1986
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(281)

(282)

(283)

 A constant toxicity parameter independent of time is obtained by determining the

asymptotic toxicity relationship, which is a rearrangement of (283) for the special case of observed

toxicity data: 

where:

LCInfinite = internal concentration causing 50% mortality after an infinite period

of exposure (:g/kg);

k2 = elimination rate constant (1/d); and

ObsTElapsed = exposure time in toxicity determination (h converted to d).

The model estimates k2, see (258), (263), (270) and (271), assuming that this k2 is the same

as that measured in bioconcentration tests; good agreement has been reported between the two

(Mackay et al., 1992). The user may then override that estimate by entering an observed value. The

k2 can be calculated off-line by the user based on the observed half-life:

where:

t1⁄2 = observed half-life.

Based on the Mancini (1983) model, the lethal internal concentration of a toxicant for a given

exposure period can be expressed as (Crommentuijn et al. (1994):

where:

LethalConc = time-varying tissue-based concentration of toxicant that

causes 50% mortality (ppb or :g/kg), used in (286) to

compute fraction killed;

LCInfinite = ultimate internal lethal toxicant concentration after an

infinitely long exposure time (:g/kg);

TElapsed = time elapsed since beginning of exposure to toxicant (d).

The longer the exposure the lower the internal concentration required for lethality (Figure

86).
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 8

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Figure 86

Lethal concentration of MeHg in brook trout as a function of

time; two data points from McKim et al., 1976

(284)

(285)

(286)

Exposure is limited to the lifetime of the organism:

where:

LifeSpan = user-defined mean lifetime for given organism (d).

Based on an estimate of time to reach equilibrium (Connell and Hawker, 1988),

The fraction killed by a given internal concentration of toxicant is best estimated using the

time-dependent LethalConc in the cumulative form of the Weibull distribution (Mackay et al., 1992;

see also Christensen and Nyholm, 1984):

where:

CumFracKilled = cumulative fraction of organisms killed for a given period of

exposure (fraction/d),

PPB = internal concentration of toxicant (:g/kg), see (209); and
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 8

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Figure 87

The effect of Shape in fitting the observed (McKim et al., 1976)

cumulative fraction killed following continued exposure to MeHg

Shape = parameter expressing variability or spread in toxic response

(unitless, default = 0.33).

As a practical matter, if CumFracKilled exceeds 95%, then it is set to 100% to avoid

complex computations with small numbers. By setting organismal loadings to very small numbers,

seed values can be maintained in the simulation.

The probit, logit, and Weibull equations yield similar results over most of the range of

distributions, but the Weibull formulation is preferable because it is algebraically simple and yet

based on mechanistic relationships (Mackay et al., 1992), and it is most sensitive to the tails of the

distribution–the EC10 and EC90 values (Christensen and Nyholm, 1984). The Shape parameter is

important because it controls the spread of mortality, providing a probabilistic response. The larger

the value, the greater the spread of mortality over toxicant concentrations and time. For example,

methyl mercury toxicity exhibits a rapid response over a short time period with most of the fish

dying when a threshold internal concentration is reached, so Shape has a value of less than 0.1

(Figure 87). However, Mackay et al. (1992) found that a value of 0.33 gave the best fit to data on

toxicity of 21 narcotic chemicals to fathead minnows. This value is used as a default in AQUATOX,

but it can be changed by the user. 

The biomass killed per day is computed by disaggregating the cumulative mortality. Think

of the biomass at any given time as consisting of two types: biomass that has already been exposed

to the toxicant previously, which is called Resistant because it represents the fraction that was not

killed; and new biomass that has formed through growth, reproduction, and migration and has not
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 8

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(288)

(289)

(290)

(291)

been exposed to a given level of toxicant and therefore is referred to as Nonresistant. Then think

of the cumulative distribution as being the total CumFracKilled, which includes the FracKilled that

is in excess of the cumulative amount on the previous day if the internal concentration of toxicant

increases. A conservative estimate of the biomass killed at a given time, ignoring the possibility of

inherited tolerance, is computed as:

where:

Poisoned = biomass of given organisms killed by exposure to toxicant at given

time (g/m3

 d);

Resistant = biomass not killed by previous exposure (g/m3);

FracKill = fraction killed per day in excess of the previous fraction (fraction/d);

FracKillt - 1 = fraction killed previous day (fraction/d);

Nonresistant = biomass not previously exposed; the biomass in excess of the

resistant biomass (g/m3).

Poisoned then becomes a term in the mortality equations (58), (74), and (98).

8.2 Chronic Toxicity

Organisms usually have adverse reactions to toxicants at levels significantly below those that

cause death. In fact, the acute to chronic ratio is commonly used to quantify this relationship.

Application factors (AFs), which are the inverse of the acute to chronic ratio, are employed in the

model to predict chronic effect responses for both plants and animals. The user can supply observed

EC50 and LC50 values, which are used to compute AFs. For example:

where:

EC50Growth = external concentration of toxicant at which there is a 50% reduction

in growth in animals (:g/L);

AFGrowth = chronic to acute ratio for growth (unitless); and
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 8

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(293)

(294)

(295)

LC50 = external concentration of toxicant at which 50% of population is

killed (:g/L).

If the user enters observed EC50 and LC50 values for a given species, the model provides

the option of applying the resulting AF to estimate EC50s for other animals. One is more likely to

have LC50 data for animals and EC50 data for plants, so the model will estimate LC50s for plants

given EC50s and a computed AF.

The computations for AFRepro and AFPhoto are similar:

where:

EC50Repro = external concentration of toxicant at which there is a 50% reduction

in reproduction in animals (:g/L); 

AFRepro = chronic to acute ratio for reproduction (unitless);

EC50Photo = external concentration of toxicant at which there is a 50% reduction

in photosynthesis (:g/L); and

AFPhoto = chronic to acute ratio for photosynthesis (unitless).

Similar to computation of acute toxicity in the model, chronic toxicity is based on internal

concentrations of a toxicant. Often chronic effects form a continuum with acute effects and the

difference is merely one of degree (Mackay et al., 1992). Regardless of whether or not the mode

of action is the same, the computed application factors relate the observed effect to the acute effect

and permit efficient computation of chronic effects factors in conjunction with computation of acute

effects. Because AQUATOX simulates biomass, no distinction is made between reduction in a

process in an individual and the fraction of the population exhibiting that response. The commonly

measured reduction in photosynthesis is a good example: the data only indicate that a given

reduction takes place at a given concentration, not whether all individuals are affected. The

application factor enters into the Weibull equation to estimate reduction factors for photosynthesis,

growth, and reproduction:
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 8

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(296)

(297)

(298)

(299)

where:

FracPhoto = reduction factor for effect of toxicant on photosynthesis (unitless);

RedGrowth = factor for reduced growth in animals (unitless); 

RedRepro = factor for reduced reproduction in animals (unitless);

PPB = internal concentration of toxicant (:g/kg), see (209);

LethalConc = time-varying tissue-based concentration of toxicant that causes 50%

mortality (ppb or :g/kg), see (283);

AFPhoto = chronic to acute ratio for photosynthesis (unitless, default of 0.10);

AFGrowth = chronic to acute ratio for growth in animals (unitless, default of 0.10);

AFRepro = chronic to acute ratio for reproduction in animals (unitless, default of

0.05); and

Shape = parameter expressing variability in toxic response (unitless, default

of 0.33).

The reduction factor for photosynthesis, FracPhoto, enters into the photosynthesis equation

(31), and it also appears in the equation for the acceleration of sinking of phytoplankton due to stress

(62).

The variable for reduced growth, RedGrowth, is arbitrarily split, based on calibration,

between two processes, ingestion (78), where it reduces consumption by 20%:

and egestion (84), where it increases the amount of food that is not assimilated by 80%:

These have indirect effects on the rest of the ecosystem through reduced predation and

increased production of detritus in the form of feces.

Embryos are often more sensitive to toxicants, although reproductive failure may occur for

various reasons. As a simplification, the factor for reduced reproduction, RedRepro, is used only

to increase gamete mortality (102) beyond what would occur otherwise:

where:

IncrMort = increased gamete and embryo mortality due to toxicant (1/d).
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(301)

Sloughing of periphyton and drift of invertebrates also can be elicited by toxicants. For

example, sloughing can be caused by a surfactant that disrupts the adhesion of the periphyton, or an

invertebrate may release its hold on the substrate when irritated by a toxicant. Often the response

is immediate so that these responses can be modeled as dependent on dissolved concentrations of

toxicants with an available chronic toxicity parameter, as in the equation for periphyton sloughing:

where:

DislodgePeri, Tox = periphyton sloughing due to given toxicant (g/m3

 d);

MaxToxSlough = maximum fraction of periphyton biomass lost by sloughing

due to given toxicant (fraction/d, 0.1);

ToxicantWater = concentration of toxicant dissolved in water (:g/L); see (199);

EC50_Dislodge = external concentration of toxicant at which there is 50%

sloughing (:g/L); and

BiomassPeri = biomass of given periphyton (g/m3); see (30).

Likewise, drift is greatly increased when zoobenthos are subjected to stress by sublethal

doses of toxic chemicals (Muirhead-Thomson, 1987), and that is represented by a saturation-kinetic

formulation that utilizes an analogous chronic toxicity parameter :

where:

ToxicantWater = concentration of toxicant in water (:g/L); 

DriftThreshold = the concentration of toxicant that initiates drift (:g/L); and

EC50Growth = concentration at which half the population is affected (:g/L).

These terms are incorporated in the respective sloughing (64) and drift (106) equations.

By modeling chronic and acute effects, AQUATOX makes the link between chemical fate

and the functioning of the aquatic ecosystem—a pioneering approach that has been refined over the

past fifteen years, following the first publications (Park et al., 1988; Park, 1990).
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION REFERENCES

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R - 16

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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION REFERENCES

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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION REFERENCES

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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION APPENDIX A

A - 1

APPENDIX A. GLOSSARY OF TERMS

Taken in large part from: The Institute of Ecology. 1974. An Ecological Glossary for Engineers

and Resource Managers. TIE Publication #3, 50 pp.

Abiotic nonliving, pertaining to physico-chemical factors only

Adsorption the adherence of substances to the surfaces of bodies with which they are

in contact

Aerobic living, acting, or occurring in the presence of oxygen

Algae any of a group of chlorophyll-bearing aquatic plants with no true leaves,

stems, or roots

Allochthonous material derived from outside a habitat or environment under

consideration

Algal bloom rapid and flourishing growth of algae

Alluvial of alluvium

Alluvium sediments deposited by running water

Ambient surrounding on all sides

Anaerobic capable of living or acting in the absence of oxygen

Anoxic pertaining to conditions of oxygen deficiency

Aphotic below the level of light penetration in water

Assimilation transformation of absorbed nutrients into living matter

Autochthonous material derived from within a habitat, such as through plant growth

Benthic pertaining to the bottom of a water body; pertaining to organisms that live

on the bottom

Benthos those organisms that live on the bottom of a body of water

Biodegradable can be broken down into simple inorganic substances by the action of

decomposers (bacteria and fungi)

Biochemical oxygen

demand (BOD)

the amount of oxygen required to decompose a given amount of organic

matter

Bioaccumulation the uptake of contaminants from all sources including direct sorption to

the body, transport across gill membranes, and through ingestion of prey

and sediments

Bioavailability the existence of a chemical in a form that it can be readily integrated into

an organism by means of any form of intake or attachment

Biodegradation the process of breaking down into simple organic substances by

decomposers (bacteria and fungi)

Biomagnification the step by step concentration of chemicals in successive levels of a food

chain or food web

Biomass the total weight of matter incorporated into (living and/or dead) organisms

Biota the fauna and flora of a habitat or region

Biotransformation the permanent changing of a substance from one chemical identity to

another by means of biotically driven processes

Chlorophyll the green, photosynthetic pigments of plants
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION APPENDIX A

A - 2

Colloid a dispersion of particles larger than small molecules and that do not settle

out of suspension

Consumer an organism that consumes another

Copepods a large subclass of usually minute, mostly free-swimming aquatic

crustaceans

Crustacean a large class of arthropods that bear a horny shell

Decomposers bacteria and fungi that break down organic detritus

Depuration excretion of contaminant by an organism

Desorption the process by which chemicals are detached and released from solid

surfaces; the opposite of adsorption

Detritus dead organic matter

Diatom any of class of minute algae with cases of silica

Diurnal pertaining to daily occurrence

Dynamic

equilibrium

a state of relative balance between processes having opposite effects

Ecology the study of the interrelationships of organisms with and within their

environment

Ecosystem a biotic community and its (living and nonliving) environment considered

together

Emergent aquatic plants, usually rooted, which have portions above water for part of

their life cycle

Environment the sum total of all the external conditions that act on an organism

Epilimnion the well mixed surficial layer of a lake; above the hypolimnion

Epiphytes plants that grow on other plants, but are not parasitic

Equilibrium a steady state in a dynamic system, with outflow balancing inflow

Euphotic pertaining to the upper layers of water in which sufficient light penetrates

to permit growth of plants

Eutrophic aquatic systems with high nutrient input and high plant growth

Fauna the animals of a habitat or region

Flood plain that part of a river valley that is covered in periods of high (flood) water

Flora plants of a habitat or region

Fluvial pertaining to a stream

Food chain animals linked by linear predator-prey relationships with plants or detritus

at the base

Food web similar to food chain, but implies cross connections

Forage fish fish eaten by other fish

Habitat the environment in which a population of plants or animals occurs

Humic pertaining to the partial decomposition of leaves and other plant material

Hydrodynamics the study of the movement of water

Hypolimnion the lower layer of a stratified water body, below the well mixed zone

Influent anything flowing into a water body

Inorganic pertaining to matter that is neither living nor immediately derived from

living matter

Invertebrate animals lacking a backbone
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION APPENDIX A

A - 3

Kinetic processes description of the dynamic rate and mode of change in the transformation

or degradation of a substance in an ecosystem

Kinetic reaction a physical, chemical or biological transformation/reaction that is best

represented using a formulation that is time-dependent

Limiting factor an environmental factor that limits the growth of an organism; the factor

that is closest to the physiological limits of tolerance of that organism

Limnetic zone the open water zone of a lake or pond from the surface to the depth of

effective light penetration

Limnology the study of inland waters

Lipids structural components of the cell that are fatty or waxy

Littoral zone the shoreward zone of a water body in which the light penetrates to the

bottom, thus usually supporting rooted aquatic plants

Macrofauna animals visible to the naked eye

Macrophytes large (non-microscopic), usually rooted, aquatic plants

Mass balance an equation that accounts for the flux of mass going into a defined area

and the flux of mass leaving the defined area; the flux in must equal the

flux out

Migration movement of an organism from one location to another

Nutrients chemical elements essential to life

Omnivorous feeding on a variety of organisms and organic detritus

Organic chemical compounds containing carbon;

Overturn the complete circulation or mixing of the upper and lower waters of a lake

when temperatures (and densities) are similar

Oxygen depletion exhaustion of oxygen by chemical or biological use

Parameter a measurable, variable quantity as distinct from a statistic 

Pelagic zone open water with no association with the bottom

Periphyton community of algae and associated organisms, usually small but densely

set, closely attached to surfaces on or projecting above the bottom

Oxidation a reaction between molecules, ordinarily involves gain of oxygen

Photic zone the region of aquatic environments in which the intensity of light is

sufficient for photosynthesis

Phytoplankton small, mostly microscopic algae floating in the water column

Plankton small organisms floating in the water

Pond a small, shallow lake

Population a group of organisms of the same species

Predator an organism, usually an animal, that kills and consumes other organisms

Prey an organism killed and at least partially consumed by a predator

Producer an organism that can synthesize organic matter using inorganic materials

and an external energy source (light or chemical)

Production the amount of organic material produced by biological activity

Productivity the rate of production of organic matter

Productivity,

primary

the rate of production by plants
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION APPENDIX A

A - 4

Productivity,

secondary

the rate of production by consumers 

Reservoir an artificially impounded body of water

Riverine pertaining to rivers

Rough fish a non-sport fish, usually omnivorous in food habits

Sediment any mineral and/or organic matter deposited by water or air

Siltation the deposition of silt-sized and clay-sized (smaller than sand-sized)

particles

Stratification division of a water body into two or more depth zones due to temperature

or density

Substrate the layer on which organisms grow; the organic substance attacked by

decomposers

Succession the replacement of one plant assemblage with another through time

Tolerance an organism’s capacity to endure or adapt to unfavorable conditions

Trophic level all organisms that secure their food at a common step in the food chain

Turbidity condition of water resulting from suspended matter, including inorganic

and organic material and plankton

Volatilization the act of passing into a gaseous state at ordinary temperatures and

pressures

Wastewater water derived from a municipal or industrial waste treatment plant

Wetlands land saturated or nearly saturated with water for most of the year; usually

vegetated

Zooplankton small aquatic animals, floating, usually with limited swimming capability
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION 

B - 1

APPENDIX B. USER-SUPPLIED PARAMETERS AND DATA

The model has many parameters and internal variables. Most of these are linked to data structures such as ChemicalRecord, SiteRecord, an

turn may be linked to input forms that the user accesses through the Windows environment. Although consistency has been a goal, some names may 

user interface, and the technical documentation

USER INTERFACE INTERNAL TECH DOC DESCRIPTION UN

ChemicalRecord Chemical

Underlying Data

For each chemical simulated, the followingparameters are required

Chemical ChemName N / A Chemical's Name. Used for Reference only. N CAS Registry No. CASRegNo N / A CAS Registry Number. Used for Reference only. N Molecular Weight MolWt MolWt molecular weight of pollutant (g/Dissociation Constant pka pKa acid dissociation constant neSolubility Solubility N / A Not utilized as a parameter by the code. (pHenry's Law Constant Henry Henry Henry's law constant (atVapor Pressure VPress N / A Not utilized as a parameter by the code. mm Octanol-water partitioncoefficient

LogP LogKow log octanol-water partition coefficient (u

KPSED KPSed KPSed detritus-water partition coefficient (LActivation Energy forTemperature

En En Arrhenius activation energy (ca

Rate of Anaerobic MicrobialDegradation

KMDegrAnaerobic KAnaerobic decomposition rate at 0 g/m3 oxygen (1

Max. Rate of Aerobic MicrobialDegradation

KMDegrdn KMDegrdn Maximum (microbial) degradation rate (1/ 

Uncatalyzed hydrolysis constant KUnCat KUncat the measured first-order reaction rate at pH 7 (1Acid catalyzed hydrolysisconstant

KAcid KAcidExp pseudo-first-order acid-catalyzed rate constant for a

given pH

(1/
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION 

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B - 2

Base catalyzed hydrolysisconstant

KBase KBaseExp pseudo-first-order rate constant for a given pH (1/

Photolysis Rate PhotolysisRate KPhot direct photolysis first-order rate constant (1Oxidation Rate Constant OxRateConst N / A Not utilized as a parameter by the code. (LWeibull Shape Parameter Weibull_Shape Shape parameter expressing variability in toxic response;

default is 0.33

(u

Chemical is a Base ChemIsBase if the compound is

a base

if the compound is a base (T
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION 

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B - 3

SiteRecord Site Underlying

Data

For each water body simulated, the followingparameters are required

Site Name SiteName N / A Site's Name. Used for Reference only. N Max Length (or reach) SiteLength Length maximum effective length for wave setup (kVol. Volume Volume initial volume of site (must be copied into state var.) (mSurface Area Area Area site area (mMean Depth ZMean ZMean mean depth (mMaximum Depth ZMax ZMax maximum depth (mAve. Temp. (epilimnetic orhypolimnetic) 

TempMean TempMean mean annual temperature of epilimnion (or

hypolimnion) 

(°C

Epilimnetic Temp. Range (orhypolimnetic)

TempRange TempRange annual temperature range of epilimnion (or

hypolimnion)

(°C

Latitude Latitude Latitude latitude (DAverage Light LightMean LightMean mean annual light intensity LaAnnual Light Range LightRange LightRange annual range in light intensity LaTotal Alkalinity AlkCaCO3 N / A Not utilized as a parameter by the code. mgHardness as CaCO3 HardCaCO3 N / A Not utilized as a parameter by the code. mg 

Sulfate Ion Conc SO4Conc N / A Not utilized as a parameter by the code. mgTotal Dissolved Solids TotalDissSolids N / A Not utilized as a parameter by the code. mgLimnocorral Wall Area LimnoWallArea LimnoWallArea area of limnocorral walls; only relevant to limnocorral (mMean Evaporation MeanEvap MeanEvap mean annual evaporation inc

Extinct. Coeff Water ECoeffWater ExtinctH2O light extinction of wavelength 312.5 nm in pure water (1/
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION 

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B - 4

SiteRecord (StreamSpecific) Site Underlying Data For each stream simulated, the following parameters are required

Channel Slope Channel_Slope Slope slope of channel (mMaximum Channel DepthBefore Flooding

Max_Chan_Depth Max_Chan_Depth depth at which flooding occurs (m

Sediment Depth SedDepth SedDepth maximum sediment depth (mStream Type StreamType Stream Type concrete channel, dredged channel, natural channel Ch

use the below value UseEnteredManning do not determine Manning coefficient from streamtype (trMannings Coefficient EnteredManning Manning manually entered Manning coefficient. s / 

Percent Riffle PctRiffle Riffle percent riffle in stream reach %Percent Pool PctPool Pool percent pool in stream reach %

SiteRecord (SandSilt-Clay Specific) Site Underlying Data For each stream with the inorganic sediments model included, the following parameters are required

Silt: Critical Shear Stress forScour

ts_silt TauScourSed critical shear stress for scour of silt (k

Silt: Critical Shear Stress forDeposition

tdep_silt TauDepSed critical shear stress for deposition of silt (k

Silt: Fall Velocity FallVel_silt VTSed terminal fall velocity of silt (mClay: Critical Shear Stress forScour

ts_clay TauScourSed critical shear stress for scour of clay (k

Clay: Critical Shear Stress forDeposition

tdep_clay TauDepSed critical shear stress for deposition of clay (k

Clay: Fall Velocity FallVel_clay VTSed terminal fall velocity of clay (m
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION 

USER INTERFACE INTERNAL TECH DOC DESCRIPTION UN

B - 5

ReminRecord Remineralization

Data

For each simulation, the following parameters arerequired

Max. Degrdn Rate, labile DecayMax_Lab DecayMax maximum decomposition rate (g

Max Degrdn Rate, Refrac DecayMax_Refr ColonizeMax maximum colonization rate under ideal conditions (g/Temp. Response Slope Q10 Q10 Not utilized as a parameter by the code. (uOptimum Temperature TOpt TOpt optimum temperature for degredation to occur (°CMaximum Temperature TMax TMax maximum temperature at which degradation will occur (°CMin. Adaptation Temp TRef TRef Not utilized as a parameter by the code. (°CMin pH for Degradation pHMin pHMin minimum pH below which limitation on biodegradation

rate occurs.

pH

Max pH for Degradation pHMax pHMax maximum pH above which limitation on biodegradation

rate occurs.

pH

Organics to Phosphate Org2Phosphate Org2Phosphate ratio of phosphate to organic matter (unitless) (uOrganics to Ammonia Org2Ammonia Org2Ammonia ratio of ammonia to organic matter (uO2 : Biomass, Respiration O2Biomass O2Biomass ratio of oxygen to organic matter (uO2: N, Nitrification O2N O2N ratio of oxygen to nitrogen (uDetrital Sed Rate KSed KSed intrinsic sedimentation rate (mPO4, Anaerobic Sed. PSedRelease N / A Not utilized as a parameter by the code. (g

NH4, Aerobic Sed. NSedRelease N / A Not utilized as a parameter by the code. (g
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION 

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B - 6

ZooRecord Animal

Underlying Data

For each animal in the simulation, the followingparameters are required

Animal AnimalName N / A Animal's Name. Used for Reference only. N Animal Type Animal_Type Animal Type Animal Type (Fish, Pelagic Invert, Benthic Invert,

Benthic Insect)

Ch

Taxonomic Type or Guild Guild_Taxa Taxonomic type or

guild

Taxonomic type or trophic guild Ch

Toxicity Record ToxicityRecord N / A associates animal with appropriate toxicity data ChHalf Saturation Feeding FHalfSat FHalfSat half-saturation constant for feeding by a predator (g/Maximum Consumption CMax CMax maximum feeding rate for predator (g/

Min Prey for Feeding BMin BMin minimum prey biomass needed to begin feeding (g/Temp Response Slope Q10 Q10 slope or rate of change in given process per 10°C

temperature change 

(u

Optimum Temperature TOpt TOpt optimum temperature for given process (°CMaximum Temperature TMax TMax maximum temperature tolerated (°CMin Adaptation Temp TRef TRef adaptation temperature below which there is no

acclimation

(°C

Respiration Rate EndogResp EndogResp basal respiration rate at 0° C for given predator (1/Specific Dynamic Action KResp KResp proportion assimilated energy lost to specific dynamic

action

(u

Excretion:Respiration KExcr KExcr proportionality constant for excretion:respiration (uGamete : Biomass PctGamete PctGamete fraction of adult predator biomass that is in gametes (uGamete Mortality GMort GMort gamete mortality (1/Mortality Coefficient KMort KMort intrinsic mortality rate (1Carrying Capacity KCap KCap carrying capacity g/
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Average Drift AveDrift Dislodge fraction of biomass subject to drift per day fraVelMax VelMax VelMax maximum water velocity tolerated (cmMean lifespan LifeSpan LifeSpan mean lifespan in days daInitial fraction that is lipid FishFracLipid LipidFrac fraction of lipid in organism (g Mean Weight MeanWeight WetWt mean wet weight of organism (gPercent in Riffle PrefRiffle PreferenceHabitat Percentage of biomass of animal that is in riffle, as

opposed to run or pool

%

Percent in Pool PrefPool PreferenceHabitat percentage of biomass of animal that is in pool, as

opposed to run or riffle

%

Fish spawn automatically, basedon temperature range

AutoSpawn Does AQUATOX calculate Spawn Dates (tr

Fish spawn of the followingdates each year

SpawnDate1..3 User Entered Spawn Dates (d

Fish can spawn an unlimitednumber of times...

UnlimitedSpawning Allow fish to spawn unlimited times each year (tr

Fish can only spawn... SpawnLimit Number of spawns allowed for this species this year (inUse Allometric Equation toCalculate MaximumConsumption

UseAllom_C Use Allometric Consumption Equation (tr

Intercept for weight dependence CA CA Allometric Consumption Parameter (reSlope for weight dependence CB CB Allometric Consumption Parameter (reUse Allometric Equation toCalculate Respiration

UseAllom_R Use Allometric Consumption Respiration (tr

RA RA RA Intercept for species specific metabolism (reRB RB RB Weight dependence coefficient (re
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Use “Set 1" of RespirationEquations

UseSet1 Use "Set 1" of Allometric Respiration Parameters (tr

RQ RQ RQ Allometric Respiration Parameter (reRTL RTL RTL temperature below which swimming activity is an

exponential function of temperature

(°C

ACT ACT ACT intercept for swimming speed for a 1g fish (cmRTO RTO RTO coefficient for swimming speed dependence on

metabolism 

(s/

RK1 RK1 RK1 intercept for swimming speed above the threshold

temperature

(cm

BACT BACT BACT coefficient for swimming at low temperatures (1RTM RTM not currently used as a parameter by the codeRK4 RK4 RK4 weight-dependent coefficient for swimming speed (reACT ACT ACT intercept of swimming speed vs. temperature and

weight

(re

Preference (ratio) TrophInt.Pref[ ] Prefprey,pred initial preference value from the animal parameter

screen

(u

Egestion (frac.) TrophInt.Egest[ ] EgestCoeffprey,pred fraction of ingested prey that is egested (u
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PlantRecord Plant Underlying

Data

For each Plant in the Simulation, the followingparameters are required

Plant PlantName Plant's Name. Used for Reference only. N Plant Type PlantType Plant Type Plant Type: (Phytoplankton, Periphyton, Macrophytes,

Bryophytes)

Ch

Taxonomic Group Taxonomic_Type Taxonomic Group Taxonomic group ChToxicity Record ToxicityRecord N / A associates plant with appropriate toxicity data ChSaturating Light LightSat LightSat light saturation level for photosynthesis (lyP Half-saturation KPO4 KP half-saturation constant for phosphorus (gN Half-saturation KN KN half-saturation constant for nitrogen (gInorg C Half-saturation KCarbon KCO2 half-saturation constant for carbon (gTemp Response Slope Q10 Q10 slope or rate of change per 10°C temperature change (uOptimum Temperature TOpt TOpt optimum temperature (°CMaximum Temperature TMax TMax maximum temperature tolerated (°CMin. Adaptation Temp TRef TRef adaptation temperature below which there is no

acclimation

(°C

Max. Photosynthesis Rate PMax PMax maximum photosynthetic rate (1Respiration Coefficient KResp KResp coefficient of proportionality between. excretion and

photosynthesis at optimal light levels

(u

Mortality Coefficient KMort KMort intrinsic mortality rate (g

Exponential Mort Coeff EMort EMort exponential factor for suboptimal conditions (uP : Photosynthate UptakePO4 Uptake Phosphorus fraction of photosynthate that is nutrient (P) (uN: Photosynthate UptakeN Uptake Nitrogen fraction of photosynthate that is nutrient (N) (uLight Extinction ECoeffPhyto EcoeffPhyto attenuation coefficient for given alga (1/
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Sedimentation Rate KSed KSed intrinsic settling rate (mExp. Sedimentation Coefficient ESed ESed exponential settling coefficient (uCarrying Capacity N A N A not used by the code (g/Reduction in Still Water Red_Still_Water RedStillWater reduction in photosynthesis in absence of current (uVelMax for macrophytes Macro_VelMax VelMax velocity at which total breakage occurs (cmCritical Force (Fcrit forperiphyton only)

FCrit Fcrit critical force necessary to dislodge given periphyton

group

(k

Percent in Riffle PrefRiffle PrefRiffle Percentage of biomass of plant that is in riffle, as

opposed to run or pool

(%

Percent in Pool PrefPool PrefPool Percentage of biomass of plant that is in pool, as

opposed to run or riffle

(%
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AnimalToxRecord Animal Toxicity

Parameters

For each Chemical Simulated, the followingparameters are required for each animal simulated

LC50 LC50 LC50 concentration of toxicant in water that causes 50%

mortality 

(:

LC50 exp time (h) LC50_exp_time ObsTElapsed exposure time in toxicity determination (hElim rate const K2 K2 elimination rate constant (1/Biotrnsfm rate BioTrans[ ] Biotransform percentage of chemical that is biotransformed to

specific daughter products 

(1/

EC50 growth EC50_growth EC50Growth external concentration of toxicant at which there is a

50% reduction in growth

(:

Growth exp (h) Growth_exp_time ObsTElapsed exposure time in toxicity determination (hEC50 repro EC50_repro EC50Repro external concentration of toxicant at which there is a

50% reduction in reprod

(:

Repro exp time (h) Repro_exp_time ObsTElapsed exposure time in toxicity determination (hAve. wet wt. (g) Ave_wet_wt WetWt mean wet weight of organism (gLipid Frac Lipid_frac LipidFrac fraction of lipid in organism (g Drift Threshold (ug/L) Drift_Thresh Drift Threshold concentration at which drift is initiated (:

TPlantToxRecord Plant Toxicity

Parameter

For each Chemical Simulated, the followingparameters are required for each plant simulated

EC50 photo EC50_photo EC50Photo external concentration of toxicant at which there is 50%

reduction in photosynthesis

(:

EC50 exp time (h) EC50_exp_time ObsTElapsed exposure time in toxicity determination (hEC50 dislodge EC50_dislodge EC50Dislodge for periphyton only: external concentration of toxicant

at which there is 50% dislodge of periphyton

(:

Elim rate const K2 K2 elimination rate constant (1
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LC50 LC50 LC50 concentration of toxicant in water that causes 50%

mortality 

(:

LC50 exp.time (h) LC50_exp_time ObsTElapsed exposure time in toxicity determination (hLipid Frac Lipid_frac LipidFrac fraction of lipid in organism (g 

TChemical Chemical

Parameters

For each Chemical to be simulated, the followingparameters are required

Initial Condition InitialCond Initial Condition Initial Condition of the state variable :g

Gas-phase conc. Tox_Air Toxicantair gas-phase concentration of the pollutant g/m

Loadings from Inflow Loadings Inflow Loadings Daily loading as a result of the inflow of water :g

Loadings from Point Sources Alt_Loadings[Pointso

urce]

Point SourceLoadings

Daily loading from point sources (g/

Loadings from DirectPrecipitation

Alt_Loadings[DirectPrecip]

Direct PrecipitationLoad

Daily loading from direct precipitation (g

Nonpoint-source Loadings Alt_Loadings[NonPoi

ntsource]

Non-Point SourceLoading

Daily loading from non-point sources (g/

phco

Biotrnsfm rate BioTrans[ ] Biotransform percentage of chemical that is biotransformed to

specific daughter products 

%
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TRemineralize Nutrient

Parameters

For each Nutrient to be simulated, O2 and CO2, the

following parameters are required

Initial Condition InitialCond Initial Condition Initial Condition of the state variable mg

Loadings Inflow Loadings Daily loading as a result of the inflow of water mg

Loadings from Point Sources Alt_Loadings[Pointso

urce]

Point SourceLoadings

Daily loading from point sources (g/

Loadings from DirectPrecipitation

Alt_Loadings[DirectPrecip]

Direct PrecipitationLoa

Daily loading from direct precipitation (g

Non-point source loadings Alt_Loadings[NonPoi

ntsource]

Non-Point SourceLoading

Daily loading from non-point sources (g

Fraction of Phosphate Available FracAvail FracAvail Fraction of phosphate loadings that is available versus

that which is tied up in minerals

(u

TSedDetr Sed. Detritus

Parameters

For the Labile and Refractory Sedimented Detrituscompartments, the following parameters arerequired

Initial Condition InitialCond Initial Condition Initial Condition of the labile or refractory sedimented

detritus

(g/

Initial Condition TToxicant.InitialCond Toxicant Exposure Initial Toxicant Exposure of the state variable, for each

chemical simulated

:g

Loadings from Inflow Loadings Inflow Loadings Daily loading of the sedimented detritus as a result of

the inflow of water

mg

(Toxicant) Loadings TToxicant.Loads Tox Exposure of

Inflow L

Daily parameter; Toxicant Exposure of each type ofinflowing detritus, for each chemical

:g
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TDetritus Susp & Dissolved

Detritus

For the Suspended and Dissolved Detrituscompartments, the following parameters arerequired

Initial Condition InitialCond Initial Condition Initial Condition of suspended & dissolved detritus, as

organic matter, organic carbon, or biochemical oxygendemand

mg

Initial Condition: % Particulate Percent_Part_IC Percent of Initial Condition that is particulate as

opposed to dissolved detritus

pe

Initial Condition: % Refractory Percent_Refr_IC Percent of Initial Condition that is refractory as opposed

to labile detritus

pe

Inflow Loadings Loadings Inflow Loadings Daily loading as a result of the inflow of water mgAll Loadings: % Particulate Percent_Part Percent Particulate

Infl

Daily parameter; % of all loadings that are particulateas opposed to dissolved detritus

pe

All Loadings: % Refractory Percent_Refr Percent Refractory

Inflo

Daily parameter; % of loading that is refractory asopposed to labile detritus

pe

Loadings from Point Sources Alt_Loadings[Pointso

urce]

Point SourceLoadings

Daily loading from point sources (g/

Nonpoint-source Loadings(Associated with OrganicMatter)

Alt_Loadings[NonPointsource]

Non-Point SourceLoading

Daily loading from non-point sources (g

(Toxicant) Initial Condition TToxicant.InitialCond Toxicant Exposure Initial Toxicant Exposure of the suspended and

dissolved detritus 

:g

(Toxicant) Loadings (associatedwith Organic Matter)

TToxicant.Loads Tox Exposure of

Inflow L

Daily parameter; Toxicant Exposure of each type ofinflowing detritus, for each chemical 

:g
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TBuried Detritus Buried Detritus For Each Type of Buried Detritus, the following

parameters are required

Initial Condition InitialCond Initial Condition Initial Condition of the labile and refractory buried

detruitus 

(g/Kg

(Toxicant) Initial Condition TToxicant.InitialCond Toxicant Exposure Initial Toxicant Exposure of the labile and refractory

buried detritus , for each chemical simulated

:g

sc

TPlant Plant Parameters For each plant type simulated, the following

parameters are required

Initial Condition InitialCond Initial Condition Initial Condition of the plant mgLoadings from Inflow Loadings Inflow Loadings Daily loading as a result of the inflow of water mg(Toxicant) Initial Condition TToxicant.InitialCond Toxicant Exposure Initial Toxicant Exposure of the plant :g(Toxicant) Loadings TToxicant.Loads Tox Exposure of

Inflow L

Daily parameter; Tox.icant exposure of the InflowLoadings, for each chemical simulated

:g

TAnimal Animal

Parameters

For each animal type simulated, the followingparameters are required

Initial Condition InitialCond Initial Condition Initial Condition of the animal mg

ex

Loadings from Inflow Loadings Inflow Loadings Daily loading as a result of the inflow of water mg(Toxicant) Initial Condition Ttoxicant.InitialCond Toxicant Exposure Initial Toxicant Exposure of the animal :g

(Toxicant) Loadings TToxicant.Loads Tox Exposure of

Inflow L

Daily parameter; toxic exposure of the InflowLoadings, for each chemical simulated

:g

Preference (ratio) TrophIntArray.Pref Prefprey, pred for each prey-type ingested, a preference value within

the matrix of preferences

(u
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Egestion (frac.) TrophIntArray.ECoeff EgestCoeff for each prey-type ingested, the fraction of ingested

prey that is egested

(u

TVolume Volume

Parameters

For each segment simulated, the following waterflow parameters are required

Initial Condition InitialCond Initial Condition Initial Condition of the water volume . (mWater volume Volume Volume Choose method of calculating volume; choose between

Manning’s equation, constant volume, variabledepending upon inflow and discharge, or use knownvalues

cu

Inflow of Water InflowLoad Inflow of Water Inflow of water; daily parameter, can choose between

constant and dynamic loadings

(m

Discharge of Water DischargeLoad Discharge of Water Discharge of water; daily parameter, can choose

between constant and dynamic loadings

(m

Site Characteristics Site

Characteristics

The following parameters are required

Site Type SiteType Site Type Site type affects many portions of the model. Po

Re

TemperatureInitial Condition InitialCond Initial condition Initial temperature of the segment or layer (if vertically

stratified

(°C

Could this system stratify could system vertically stratify truValuation or loading Temperature of the segment. Can use annual means for

each stratum and constant or dynamic values

(°C
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WindInitial Condition InitalCond Initial wind velocity 10 m above the water (mMean Value Wind(MeanValue) CosCoeff0 Mean wind velocity (m

Wind Loading Wind Wind Daily parameter; wind velocity 10 m above the water; l,

can choose default time series, constant or dynamicloadings

(m

LightInitial Condition Light Light (lyLoading Loadsrec Daily parameter; avg. light intensity at segrment top;

can choose annual mean, constant loading or dynamicloadings 

Photoperiod Photoperiod Photoperiod Fraction of day with daylight; optional, can be

calculated from latitude

(h

pHInitial Condition InitialCond Initial pH value (pState Variable Valuation pH pH pH of the segment; can choose constant or daily value. (p
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Sand / Silt / Clay TSediment Inorganic

SedimentParameters

If the inorganic sediments model is included inAQUATOX, the following parameters are requiredfor sand, silt, and clay

Initial Susp. Sed. InitialCond Initial Condition Initial Condition of the sand, silt, or clay (mFrac in Bed Seds FracInBed FracSed Fraction of the bed that is composed of this inorganic

sediment. Fractions of sand, silt, and clay must add to1.0

(fr

Loadings from Inflow Loadings Inflow Loadings Daily sediment loading as a result of the inflow of water mgLoadings from Point Sources Alt_Loadings[Point

source]

Point SourceLoadings

Daily loading from point sources (g/

Loadings from DirectPrecipitation

Alt_Loadings[DirectPrecip]

Direct PrecipitationLoa

Daily loading from direct precipitation (K

Non-point source loadings Alt_Loadings[Non

Pointsource]

Non-Point SourceLoading

Daily loading from non-point sources (g