United States
Environmental Protection
Agency
Office of Water
(4305)
EPA-823-R-00-007
September 2000
»EPA AQUATOX FOR WINDOWS
A MODULAR FATE AND EFFECTS
MODEL FOR AQUATIC ECOSYSTEMS
RELEASE 1
VOLUME 2: TECHNICAL DOCUMENTATION
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AQUATOX FOR WINDOWS
A MODULAR FATE AND EFFECTS MODEL
FOR AQUATIC ECOSYSTEMS
RELEASE 1
VOLUME 2: TECHNICAL DOCUMENTATION
SEPTEMBER 2000
U.S. ENVIRONMENTAL PROTECTION AGENCY
OFFICE OF WATER
OFFICE OF SCIENCE AND TECHNOLOGY
WASHINGTON DC 20460
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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 a new 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;
most of the programming has been by Jonathan S. Clough under subcontract to Eco Modeling. It
was funded 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.. Work assignment
managers for The Cadmus Group have been Paul Jacobson, Jonathan Butcher, and William Warren-
Hicks; their help in expediting the contractual arrangements and in reviewing the scientific
approaches is appreciated. Revision of the documentation has been performed under subcontract
to AQUA TERRA Consultants, Anthony Donigian, Work Assignment Manager, under EPA
Contract 68-C-98-010.
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.
The assistance, advice, and comments of the EPA work assignment manager, Marjorie
Coombs Wellman of the Exposure Assessment Branch, Office of Science and Technology has been
of great value in developing this model and preparing this report. Further technical and financial
support from David A. Mauriello and Rufus Morison of the Office of Pollution Prevention and
Toxics is gratefully acknowledged..
In an earlier version of the model developed at Abt Associates, Brad Firlie facilitated the
programming; Rodolfo Camacho developed and programmed the inorganic sediment constructs; and
review was provided by Lisa Akeson, Elizabeth Fechner-Levy, and Keith Sappington.
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TABLE OF CONTENTS
1. INTRODUCTION .....-....: ;1 -1
1.1 Overview '.'.'.'..'. .'. 1 -1
1.2 Background .',.-.. .. 1 - 4
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 ......:.......... ......' 3-3
3.2 Washout '.. .'.'.'.......'.....-:' .-..'..'.';'.-.'. .'.'... . 3 - 7
3.3 Stratification and Mixing 3-7
3.4 Temperature 3-12
3.5 Light 3-13
3.6 Wind : 3-14
4. BIOTA , :... 4 -1
4.1 Algae ..'. . 4-1
Light Limitation 4-3
Nutrient Limitation : . 4-7
Current Limitation : 4-10
Adjustment for Suboptimal Temperature 4-10
Algal Respiration ; 4-12
Photorespiration 4-13
Algal Mortality : 4-14
Sinking 4-16
Washout and Entrainment 4-17
Chlorophyll a , 4-19
4.2 Macrophytes 4-19
4.3 Animals 4-22
Consumption, Defecation, and Predation 4-22
Respiration 4-27
Excretion 4-27
Nonpredatory Mortality .4-28
Gamete Loss and Recruitment .4-29
Washout and Drift 4 -. 31
Vertical Migration 4 - 32
Promotion .4-32
5. REMINERALIZATION 5 - 1
5.1 Detritus , 5.- 1
Detrital Formation ;.....,......; 5-4
Colonization 5-5
in
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Decomposition '5.7
Sedimentation 5.9
5.2 Nitrogen 5-10
Assimilation 5-12
Nitrification and Denitrification 5-13
5.3 Phosphorus 5-15
5.4 Dissolved Oxygen 5-16
5.5 Inorganic Carbon 5-20
6. INORGANIC SEDIMENTS 6-1
6.1 Deposition and Scour of Silt and Clay 6-2
6.2 Scour, Deposition and Transport of Sand 6-5
6.3 Suspended Inorganic Sediments in Standing Water 6-7
7. TOXIC ORGANIC CHEMICALS 7-1
7.1 lonization 7-6
7.2 Hydrolysis 7.7
7.3 Photolysis 7.9
7.4 Microbial Degradation 7-12
7.5 Volatilization 7-13
7.6 Partition Coefficients 7-16
7.7 Nonequilibrium Kinetics '. 7-23
Sorption and Desorption to Sedimented Detritus 7-23
Bioconcentration in Macrophytes and Algae 7-26
Macrophytes 7-26
Algae 7-27
Bioaccumulation in Animals 7-29
Gill Sorption 7-29
Dietary Uptake 7-31
Elimination 7-33
Linkages to Detrital Compartments 7-34
8. ECOTOXICOLOGY 8-1
8.1 Acute Toxicity of Compounds 8-1
8.2 Chronic Toxicity 8-4
9. REFERENCES R . 1
APPENDIXA. GLOSSARY OF TERMS ; A-1
APPENDIX B. USER-SUPPLIED PARAMETERS AND DATA B - 1
IV
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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: 1996 Report to Congress, 36 percent of assessed river lengths
and 39 percent of assessed lake areas were impaired for one or more of their designated uses '(US
EPA 1998). The most commonly reported causes of impairment in rivers and streams were siltation,
nutrients, bacteria, oxygen-depleting substances, and pesticides; in lakes and reservoirs the causes
also included metals and noxious aquatic plants. The most commonly reported sources of
impairment were agriculture, nonpoint sources, municipal point sources, atmospheric deposition,
hydrologic modification, habitat alteration and resource extraction. There were 2196 fish
consumption advisories, which may include outright bans, in 47 States, the District of Columbia and
American Samoa. Seventy-six percent of the advisories were due to mercury, with the rest due to
PCBs, chlordane, dioxin, and DDT (US EPA 1998). 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 non-
chemical 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 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 offish. It has been implemented for streams, small rivers, ponds,
lakes, and reservoirs.
The AQUATOX model 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: Validation
Studies presents three model validation studies performed for different environmental stressors and
in different waterbody types.
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AQUATOX TECHNICAL DOCUMENTATION
CHAPTER 1
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 (Figure 1). 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.
1 -1
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AQUATOX TECHNICAL DOCUMENTATION
CHAPTER 1
Figure 1. Conceptual Model of Ecosystem Represented by AQUATOX.
1imei}t
Light
Loadings
Temperature
Wind
Outflo\
Ingestion
A
Sediment ^N
surficlal,
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- andnonpoint 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.
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AQUATOX TECHNICAL DOCUMENTATION
CHAPTER 1
Figure 2. Compartments (State Variables) in AQUATOX
3
2
Herbivorous
Invertebrate
Toxicant
Forage Fish
Toxicant
Small
Game Fish
Toxicant
Predatory
Invertebrate 2
Toxicant
Large
Game Fi
Toxica
Refractory
Suspended
Detritus
toxicant
Labile
Suspended
Detritus
toxicant
' Phytopiankton or Periphyton; 2 Zooplankton or Zqobenthos;
3 Suspended, Sedimented, and Buried; 4 Surficial and buried
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^xample, 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 obj ect; 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
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.
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AQUATOX TECHNICAL DOCUMENTATION
CHAPTER 1
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
pondsand 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 M ACROPHYTE model, developed for the U.S. Army Coips 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).
The current version has been improved with the addition of constructs for chronic effects and
uncertainty analysis, making it a powerful tool for probabilistic risk assessment (see Volume 3).
This technical documentation is intended to provide verification of individual constructs or
mathematical and programming formulations used within AQUATOX. The scientific basis of the
constructs reflects empirical and theoretical support; and precedence in the open literature and in
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. This report is intended to expedite external
review as well.
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AQUATOX TECHNICAL DOCUMENTATION
CHAPTER 2
2. SIMULATION MODELING
2.1 Temporal and Spatial Resolution and Numerical Stability
AQUATOX Release 1 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 non-
dimensional point model). It also can represent one-dimensional vertical epilimnetic and
hypolimnetic conditions for those systems that exhibit stratification on a seasonal basis.
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 distributed version of the model (Version 2.00) is being developed; it will be able to
simulate several linked stream reaches.
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 short-term pollutant loadings are always detected.
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 it uses a shorter time step than fate models that may be
concerned only with long-term patterns such as bioaccumulation in large fish.
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AQUATOX TECHNICAL DOCUMENTATION
CHAPTER 2
Figure 3. Position of Ecosystem Models such as
AQUATOX in the Spatial-temporal Hierarchy of
Models.
Rule-based habitat models
succession, urbanization, sea-level rise
Ecosystem models
Population models
High-resolution
process models
flood hydrograph
diurnal pH
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 simulationalthough 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 [ig/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 andO.Ol 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.
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AOUATOX TECHNICAL DOCUMENTATION
CHAPTER 2
Figure 4. Pond with Chlorpyrifos in Dissolved
Phase.
06/19/88 06/30/88 07/12/88
06/24/88 07/06/88 07/18/88
Figure 5. Same as Figure 4 with Dissolved
Oxygen.
-0.001 « 0.01
-0.05 * 0.1
12 »
06/19/88 06/30/88 07/12/88
06/24/88 07/06/88 07/18/88
0.001 » 0.01 0.05 0.1
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 octanol-
water 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 distribution and key
statistics for a wide selection of 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 limits
of the distribution, reflecting the stochastic nature of such loadings. Distributions for dynamic
loadings may employ multiplicative factors that are sampled once each simulation (Figure 6).
Normally the multiplicative factor for a loading is set to 1, but, as seen in the example, under
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AQUATOX TECHNICAL DOCUMENTATION
CHAPTER 2
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 6. Distribution Screen for Point-Source Loading of Toxicant in Water.
(Distribution Information
M&1C
M
0.06
0.04
002
000
0673
583
< Probability r Cumulative Distribution:
Distribution Type:
r Triangular
r. Uniform ,
r Normal
& Lognormal
t*s«'t v
rt
In an Uncertainly Run:
& Use Above Distribution
C Use Point Estimate
Distribution Parameters; "J/
Mean
Std. Deviation
i
/
pi
fas' ^
} s
] ftevwp*»-*,'*fi*tf^y^vU 4
^ OK |<'JJC Cancel { ';
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 7); 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 8). Note
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 9). The result of applying such a distribution in a simulation of Onondaga Lake,
New York is shown in Figure 10, where simulated benthic feeding is seen to affect the sediment-
water interaction and subsequently the predicted hypolimnetic anoxia. All distributions are truncated
at zero because negative values would have no meaning. A non-random seed can be used for the
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AQUATOX TECHNICAL DOCUMENTATION
CHAPTER 2
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.
Figure 7. Uniform Distribution for Henry's Figure 8. Triangular Distribution for
Law Constant for Esfenvalerate. Maximum Consumption Rate for Bass.
o,oa
6.16-8
T.53E-6
ae-e
003
OJD2
001 ,
'0,00
Figure 9. Normal Distribution for Maximum Consumption Rate for Tubifex.
000
001T3
025
0483
3 I ,'* ' " ~^1
' "' tt Probability r Cumulative Distribution i»^J
''"ftijR^ "gSsft"- A''..*"-.'JJ>?'l*>,""'"^r"^'^^A
iiiiififfrfirTi. "-T .«.*....rffim I flit f i.nTiffBiMiillmi I 1' .«*....-.... 111.1111. fi-i" ^- _
Distribution Parameters-
Mean 'i 0.215
Std. Deviation
jS
'^ In anTJneertaittty Run: ._ *
ff Useftbowebist^ib«tion_(_
Use Point Estimate""
Efficient sampling from the distributions is obtained with the Latin hypercube method
(McKay etal., 1979; Palisade Corporation, 1991), using algorithms originally written in FORTRAN
(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
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AQUATOX TECHNICAL DOCUMENTATION
CHAPTER!
distribution shown in Figure 9 can be sampled as shown in Figure 11. This method is particularly
advantageous because all regions of the distribution, including the tails, are sampled. 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.
Figure 10. Sensitivity of Hypolimnetic Oxygen to
Zoobenthic Feeding in Lake Onondaga New York.
01/01/89 09/24/89 06/17/90
05/14/89 02/04/90 10/28/90
-Minimum
- Maximum
Mean
- - Deterministic
Figure 11. Latin Hypercube Sampling of a
Cumulative Distribution with a Mean of 25 and
Standard Deviation of 8 Divided into 5 Intervals.
0.2
1.58
3.17
2-6
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AOUATOX TECHNICAL DOCUMENTATION
CHAPTERS
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:
dVolume = Inflow -Discharge - Evap (1)
dt
where:
dVolume/di =
Inflow
Discharge
Evap =
derivative for volume of water (m3/d),
inflow of water into waterbody (m3/d),
discharge of water from waterbody (m3/d), and
evaporation (nrYd), see (2).
Evaporation is converted from an annual value for the site to a daily value using the simple
relationship:
= MeanEvap .
365
where:
MeanEvap =
365
0.0254
Area =
mean annual evaporation (in/yr),
days per year (yr),
conversion from inches to meters (m/in), and
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 computing volume as a function of the Manning's equation. Depending
on the method, inflow and discharge are varied, as indicated in Table 1.
Constant
Dynamic
Inflow
InflowLoad
InflowLoad
InflowLoad
ManningVol - (State + Discharge)/dt + Evap
Discharge
InflowLoad - Evap
DischargeLoad
InflowLoad - Evap + (State - KnownVals)/dt
DischargeLoad
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AQUATOX TECHNICAL DOCUMENTATION
CHAPTER 3
The variables are defined as:
InflowLoad
DischargeLoad'
State
KnownVals
dt
ManningVol
user-supplied inflow loading (m3/d);
user-supplied discharge loading (m3/d);
computed state variable value for volume (m3);
time series of known values of volume (m3);
incremental time in simulation (d); and
volume of stream reach (m3), see (3).
in
Figure 12 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
volume occur with operational releases, usually in the spring, for flood control purposes.
Figure 12. Volume, Inflow, and Discharge for a 4-year Period in
Coralville Reservoir, Iowa.
6.0E+07
5.0E+07
CO
a
£j 3.0E+07 -
° 2.0E+07
1.0E+07 -
OOE+00
JL ~~
I
. _|J~ ...,._» i
Wo
- -
-
I
fe
..;..;..!
--]"
1
Oct-74 Oct-75 Nov-76 Dec-77
Apr-75 May-76 Jun-77 Jul-7£
Inflow Discharge Volun
2.0E+08
1 .5E+08
1.0E+08 °
5.0E+07
O.OE+00
ne
The time-varying volume of water in a stream channel is computed as:
ManningVol = Y- CLength Width
(3)
where:
Y
CLength
Width
dynamic mean depth (m), see (4);
length of reach (m); and
width of channel (m).
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:
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AOUATOX TECHNICAL DOCUMENTATION
CHAPTERS
7 =
Q Manning }
Width)
3/5
(4)
where:
fi
Manning
Slope
Width
flow rate (m3/s);
Manning's roughness coefficient (s/m'/3);
slope of channel (m/m); and
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 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).
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:
IDepth513 ^Slope Width
QBase = £ v .
Manning
(5)
where:
QBase
Idepth
base flow (mYs); and
mean depth as given in site record (m).
The dynamic flow rate is calculated from the inflow loading by converting from nrVd to m3/s:
n _ Inflow
~ 86400
(6)
where:
fi
Inflow
flow rate (m3/s); and
water discharged into channel from upstream (mVd).
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
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AQUATOX TECHNICAL DOCUMENTATION
CHAPTER 3
treatment of Junge (1966; see also Straskraba 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.:
P = 6.0
ZMean
ZMax
- 3.0
(7)
Where:
ZMean
ZMax
P
mean depth (m);
maximum depth (m); and
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 andP = 0.6. Reservoirs 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 (Table 2). The model requires mean and maximum depth, but if only
the maximum depth is known, then the mean depth pan 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.
Based on these relationships, fractions of volumes and areas can be determined for any given
depth (Junge, 1966) (Figure 13-Figure 14):
AreaFrac = (1.0 + P)
ZMax
- P
ZMax
)2
(8)
6.0
VolFrac =
ZMax
- 3.0
- P)
ZMax
)2 - 2.0 P (-?_)3
3.0 + P
ZMax
(9)
where:
AreaFrac
VolFrac
Z
fraction of area of site above given depth (unitless);
fraction of volume of site above given depth (unitless); and
depth of interest (m).
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AQUATOX TECHNICAL.DOCUMENTATION
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Table 2. Examples of Morphometry of Waterbodies
Site
Lakes
Chad, Chad
Managua, Nicaragua
Michigan, U.S.-Canada
Erie, U.S.-Canada
Windermere, England
3aikal, Russia
Como, Italy
Superior, U.S.-Canada
Tahoe, CA-NV
Esrom, Denmark
Clear, CA
Crater, OR
Kinneret, Israel
Okeechobee, FL
Ontario, U.S.-Canada
Balaton, Hungary
George, Uganda
Reservoirs
DeGray, AR
Grenada, MS
Lewis and Clark, SD
Texoma, TX
Delaware, OH
Sidney Lanier, GA
Monroe, IN
Tenkiller Ferry, OK
Vlendocino, CA
Coralville, IA
Waterbury, VT
Pend Oreille, ID
Ponds
Czech Rep., fish (very old)
Czech Rep., Elbe R. backwaters
Dor Israel fish recent
ZMean/ZMax
0.13
0.26
0.27
0.33
0.36
0.43
0.45
0.47
0.50
0.56
0.57
0.60
0.60
0.67
0.69
0.75
0.80
0.25
0.21
0.31
0.27
0.22
0.33
0.30
0.36
0.36
0.37
0.43
0.50
0.43
0.50
0.67
P
-2.22
-1.42
-1.38
-1.02
-0.85
-0.42
-0.30
-0.18
0.00
0.35
0.43
0.60
0.63
1.00
1.14
1.50
1.80
-1.49
-1.74
-1.13
-1.38
-1.68
-1.01
-1.18
-0.86
-0.84
-0.80
-0.42
-0.03
-0.42
-0.03
1.00
Constrained P
-1.00
-1.00
-1.00
-1.00
-0.85
-0.42
-0.30
-0.18
0.00
0.35
0.43
0.60
0.63
1.00
1.00
1.00
1.00
-1.00
-1.00
-1.00
-1.00
-1.00
-1.00
-1.00
-0.86
-0.84
-0.80
-0.42
-0.03
-0.42
-0.03
1.00
data from Hutchinson, 1957; Hrbacek, 1966; Leidy and Jenkins, 1977;
and Home and Goldman, 1994
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 euphoric zone, the fraction of
the fraction of the area available for colonization by macrophytes and periphyton can be computed:
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AQUATOX TECHNICAL DOCUMENTATION
CHAPTER 3
FracLit = (1 + P) ZEuPhotic - P ( ZEuphoticY
,, ZMax ( ZMax )
(10)
If the site is a limnocorral (an artificial enclosure) then the available area is increased accordingly:
Area + LimnoWallArea
FracLittoral = FracLit
Area
otherwise
FracLittoral = FracLit
(11)
where:
FracLittoral
ZEuphotic
Area
Limno WallArea
fraction of site area that is within the euphotic zone (unitless);
depth of the euphotic zone, where primary production exceeds
respiration, usually calculated as a function of extinction (m);
site area (m2); and -
area of limnocorral walls (m2).
The depth of the euphotic zone, where radiation is 1% of surface radiation, is computed as (Thomann
and Mueller, 1987): .
ZEuphotic = 4.605/Extinct
(12)
where:
Extinct
the overall extinction coefficient (1/m), see (30).
Figure 13
Volume as a Function of Depth in Ponds
POND (P *-1.0)
0.25 1.75 3.25 4.75
1 2.5 4
DEPTH (m)
Figure 14
Area as a Function of Depth in Ponds
POND (P = -1.0)
0.25 1.75 3.25 4.75
1 2.5 4
DEPTH (m)
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AOUATOX TECHNICAL DOCUMENTATION
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3.2 Washout
Transport out of the system, or washout, is an important loss term for nutrients, floating
organisms, and dissolved toxicants in reservoirs and streams. Although it is considered separately
for several state variables, the process is a general function of discharge:
Washout
Discharge
Volume
State
(13)
where:
Washout
State
loss due to being carried downstream (g/m3 -d), and
concentration of dissolved or. floating state variable (g/m3).
3.3 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 15); the metalimnion zone that separates these
is ignored. Instead, the thermocline, or plane of maximum temperature 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 Straskraba 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.
Figure 15
Thermal Stratification in a Lake; Terms Defined in Text
Epilimnion
'- Thermocline
VertD/spers/on
Hypolimnion
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 =
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AQUATOX TECHNICAL DOCUMENTATION
CHAPTER 3
0.850, meaning that 85 percent of the sum of squares is explained by the regression. Its curvilinear
nature is shown in Figure 16, and it is computed as (Hanna, 1990):
log(MaxZMix) = 0.336 \og(Length) - 0.245 (14)
where:
MaxZMix
Length
maximum mixing depth for lake (m); and
maximum effective length for wave setup (m).
Wind action is implicit in this formulation. Wind has been modeled explicitly by Baca and
Amett (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 17):
VertDispersion = Thick
HypVolume
\T}
t-i
hypo
ri+l I
hypo\
ThermoclArea Deltat
rri t _
*- epi ~
hypo
(15)
where:
VertDispersion =
Thick
HypVolume =
ThermoclArea =
Deltat
if t-l rp !+/ _
* hyjn ' * hypo
' T '
'efi* 'hypo
vertical dispersion coefficient (m2/d);
distance between the centroid of the epilimnion and the centroid of the
hypolimnion, effectively the mean depth (m);
volume of the hypolimnion (m3);
area of the thermocline (m2);
time step (d);
temperature of hypolimnion.one time step before and one time step
after present time (°C); and
temperature of epilimnion and hypolimnion at present time (°C).
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AOUATOX TECHNICAL DOCUMENTATION
CHAPTERS
Figure 16
Mixing Depth as a Function of Fetch
MAXIMUM MIXING DEPTH
"100 11SOO 22900 34300
5800 17200 29800 40000
IBMGTHfnf
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 18), rather than temperature
differences as in equation 15, based on observations by Straskraba (1973) for a Czech reservoir:
VertDispersion = 1.37 1Q4 -Retention'2269
(16)
and:
Retention =
Volume
TotDischarge
(17)
where:
Retention =
Volume . =
TotDischarge =
retention time (d);
volume of site (m3); and
total discharge (nrVd).
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AQUATOX TECHNICAL DOCUMENTATION
CHAPTERS
Figure 17
Vertical Dispersion as a Function of Temperature Differences
25 -i
3" 20
1J
5n
U 10
3.
u s
0 -
^
1
onset of /
stratification / /
\^A/.,.'
s^
^
/ ,
/
12/30 02/28 04/29 06/
D>
Epilimnion Temp.
Vert. Dispersion (sc
tT
\ /
^
J
28 08/
IVY
m/d)
V
X
S
\
\
_^^..
1 ,., ,
27 10/26 12/2
Hypolimnion Temp.
4 degrees
IUU ^
£
10 1
ii
u.
0, S
0.1 z
C
001 2
LL
U
0.001 C
5
Figure 18
Vertical Dispersion as a Function of Retention
Time
VERTICAL DISPERSION
180 146 112 78 44
163 129 95 61 27
RETENTION TIME (d)
The bulk vertical mixing coefficient is computed using site characteristics and the time-varying
vertical dispersion (Thomann and Mueller, 1987):
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AQUATOX TECHNICAL DOCUMENTATION
, CHAPTERS
BulkMixCoeff = V<*tDisPersion ThermoclArea
- , , ....:. . Thick -.. .
(18)
where:
BulkMixCoeff = bulkvvertical mixing coefficient (m3/d),
ThermoclArea- area of thermocline (m2).
Turbulent diffusion between epilimnion and hypolimnion is computed separately for each
segment for each time step while there is stratification: ,
n trk-.d);
volume of given segment (m3); and
... concentration of given compartment in given zone (g/m3).
The effects of stratification, mixing due to high thf Oughflow, and overturn are well illustrated
by the pattern of dissolved oxygen levels in the hypolimnion of Lake Nockamixon, a eutrophic
reservoir in Pennsylvania (Figure 19). ,
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AQUATOX TECHNICAL DOCUMENTATION
CHAPTERS
Figure 19
Stratification and Mixing in Lake Nockamixon,
Pennsylvania as Shown by Hypolimnetic Dissolved Oxygen
14
j?10-
§> 8
*.:
o 4
0)
CO
b 2
0 -
01/0
-MX
onset of /"
stratification overturn ^
^ Y
high
throughflow
^
1 /82 03/07/82 05/1 1 /82 07/1 5/82 09/1 8/82 1 1 /22/S2
3.4 Temperature
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 20):
> Temperature = TempMean + (-1.0 TemPRanSe
2 (21)
(sin(0.0174533 (0.987 (Day + PhaseShift) - 30))))]
where:
Temperature
TempMean =
TempRange =
Day =
PhaseShift
average daily water temperature (°C);
mean annual temperature (°C);
annual temperature range (°C),
Julian date (d); and
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
18).
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AQUATOX TECHNICAL DOCUMENTATION
CHAPTER 3
3.5 Light
The default incident light function is a variation on the temperature equation, but without the
lag term:
Solar = LightMean +
sin(0.0 174533 Day - 1.76)
(22)
where:
Solar
LightMean
LightRange
Day
average daily incident light intensity (ly/d);
mean annual light intensity (ly/d);
annual range in light intensity (ly/d); and
Julian date (d).
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 cart 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 approximated using the Julian date (Figure 21):
12 + A cos(380
V
Photoperiod =
365
+ 248)
'
(23)
24
where:
Photoperiod = fraction of the day with daylight (unitless);
A = hours of daylight minus 12 (hr); and
Day = Julian date (d).
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):
A = 0.1414 Latitude - Sign 2.413
(24)
where:
Latitude
Sign
latitude (°, decimal), negative in southern hemisphere; and
1.0 in northern hemisphere, -1.0 in southern hemisphere.
3-13
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AQUATOX TECHNICAL DOCUMENTATION
CHAPTER 3
Figure 20
Annual Temperature
TEMPERATURE IN A MIDWESTERN POND
1 77 153 229 305
39 115 191 267 343
JULIAN DAY '
Figure 21
Photoperiod as a Function of Date
J=°-65
01
I1 °-6
Q
1 '
Fraction of Da
o o
0) P k f
w ** en t
-- ^ .
\ / x
/ \ /,
/ \
\ / \ /
/ \ "'
A V
/ \ /\
/ \ / \
/ \ / \
y x y \
*- - ~
53 105 157 209 261 313 365
27 79 131 183 235 287 339
Julian Date
Latitude 40 N Latitude 40 S
3.6 Wind
Wind is an important driving variable because it determines the stability of blue-green algal
blooms, and reaeration or oxygen exchange, and it controls volatilization of some organic chemicals.
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 22), 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.
Figure 22
Default Wind Loadings for Missouri Pond
WIND LOADINGS
06/13 OS/03 09/23 11/13 01/03 02/23 04/16 06/05
DATE
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AQUATOX TECHNICAL DOCUMENTATION
CHAPTER 4
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 subj ect to sinking and washout, while periphyton are subj ect to substrate limitation
and scour by currents. These are treated as process-level differences in the equations.
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, but benthic
invertebrates are not. Gamefish may be represented by both young of the year and adults, which are
connected by promotion. , . , . ,
4.1 Algae
The change in algal biomassexpressed as g/m3 for phytoplankton, but as g/m2 for
periphytonis a function of the loading (especially phytoplankton from upstream), photosynthesis,
respiration, excretion or photorespiration, nonpredatory mortality, grazing or predatory mortality, and
washout; as noted above, phytoplankton also are subject to sinking. If the system is stratified,
turbulent diffusion also affects the biomass of phytoplankton:
dBiomass
dt
= Loading + Photosynthesis - Respiration - Excretion
- Mortality - Predation ± Sinking - Washout ± TurbDiff
(25)
where:
dBiomass/dt =
Loading
Photosynthesis :
Respiration
Excretion =
Mortality
Predation
Washout
Sinking =
TurbDiff
change in biomass of algae with respect to time (g/m3'd);
loading of algal group (g/m3>d);
rate of photosynthesis (g/m3'd), see (26);
respiratory loss (g/m3-d), see (51);
excretion or photorespiration (g/m3'd), see (52);
nonpredatory mortality (g/m3'd), see (54);
herbivory (g/m3-d), see (74);
loss due to being carried downstream (g/m3>d), see (60);
loss or gain due to sinking between layers and sedimentation to bottom
(g/m3-dj, see (57); and
turbulent diffusion (g/m3-d), see (18).
Figure 23 and Figure 24 are examples, of the predicted changes in biomass and the processes
that contribute to these changes in a eutrophic lake.
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AQUATOX TECHNICAL DOCUMENTATION
CHAPTER 4
Figure 23
Change in Predicted Algal Biomass
_J
^4-
1-
z: 3
ii-
0.
|
7 J ^ ~^-^ \^
01/01/89 04/26/89 08/20/89 12/14/89
02/27/89 06/23/89 10/17/89
Diatoms Cryptomonads Greens
Figure 24
Predicted Algal Process Rates in Cryptomonads
02-Jan 20-Feb 10-Apr 29-May 17-Jul 04-Sep 23-Oct 11-Dec
| Photosynthesis ^j^ Respiration ^ Excretion
| Mortality
| Sinking
Photosynthesis is modeled as a maximum observed rate multiplied by reduction factors for
the effects of toxicants and suboptimal light, temperature, current, and nutrients:
Photosynthesis = PMax PProdLimit Biomass (26)
The limitation of primary production in phytoplankton is:
PProdLimit = LtLimit NutrLimit VLimit TCorr FracPhoto
(27)
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AQUATOX TECHNICAL DOCUMENTATION
CHAPTER 4
Periphyton have an additional limitation based on available substrate:
PProdLimit = LtLimit NutrLimit VLimit TCorr FracPhoto FracLittoral (28)
where:
Pmax = maximum photosynthetic rate (1/d);
LtLimit = light limitation (unitless), see (29);
NutrLimit = nutrient limitation (unitless), see (43);
Vlimit = current limitation for periphyton (unitless), see (44);
TCorr = limitation due to suboptimal temperature (unitless), see (47);
FracPhoto = reduction factor for effect of toxicant on photosynthesis (unitless), see
(271);
FracLittoral = fraction of area that is within euphotic zone (unitless) see (11); and
Biomass = biomass of algae (g/m3).
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; Straskraba 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; J0rgensen, 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, J0rgensen, 1979; Collins and Wlosinski, 1983; Bowie et al., 1985); they may be
modified as needed.
Light Limitation
Because it is required for photosynthesis, light is a very important limiting variable. It is
especially important iri controlling competition among plants with differing light requirements.
Similar to many other models(for example, DiToro etal., 1971; Park etal., 1974,1975,1979,1980;
Lehman et al., 1975; Canale et al., 1975, 1976; Thomann et al., 1975, 1979; Scavia et al., 1976;
Biermanetal., 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):
LtLimit = 0.85
Extinct (DepthBottom - DepthTop)
Photoperiod (LtAtDepth - LtAtTop)
(29)
where:
LtLimit = light limitation (unitless);
e = the base of natural logarithms (2.71828, unitless);
Photoperiod = fraction of day with daylight, see (23);
Extinct = total light extinction (1/m), see (30);
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AQUATOX TECHNICAL DOCUMENTATION
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DepthBottom =
DepthTop
LtAtDepth =
LtAtTop
maximum depth or depth of bottom of layer if stratified (m); if
periphyton or macrophyte then limited to euphotic depth;
depth of top of layer (m);
see (32); and
see (33), (34).
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
pure water, the so-called "self-shading" of plants, attenuation due to suspended particulate organic
matter (POM) and inorganic sediment, and attenuation due to dissolved organic matter (DOM):
Extinct = WaterExtinction + PhytoExtinction + ECoeffDOM DOM
+ ECoeffPOM ZPartDetr + ECoeffSect'- InorgSed
where:
WaterExtinction =
PhytoExtinction =
EcoeffDOM =
DOM
EcoeffPOM
PartDetr =
EcoeffSed
InorgSed =
extinction due to pure water (1/m);
extinction due to phytoplankton and periphyton (1/m), see (31);
attenuation coefficient for dissolved detritus (1/m-g/m3);
concentration of dissolved organic matter (g/m3), see (96) and (97);
attenuation coefficient for particulate detritus (1/m-g/m3);
concentration of particulate detritus (g/m3), see (94) and (95);
attenuation coefficient for suspended sediment (1/m-g/m3); and
total suspended inorganic sediment (g/m3), see (177).
For computational reasons, the value of Extinct is constrained between 5"19 and 25. Self-
shading by phytoplankton, periphyton, and macrophytes is a function of the biomass and attenuation
coefficient for each group:
PhytoExtinction = £V,ga (ECoeffPhytoalga Biomassalga)
(31)
where:
EcoeffPhyto .= attenuation coefficient for given alga (1/m-g/m3); and
Biomass = concentration of given alga (g/m3).
The light at depth is computed by:
_ Light _ e -Extinction DepOiBollom
LtAtDepth = e Li^htSat
(32)
Light at the surface of the waterbody is computed by:
Light
LtAtTop = e LishtSat
(33)
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AQUATOX TECHNICAL DOCUMENTATION
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and light at the top of the hypolimnion is computed by:
Light . -Extinction DspthTop
LtAtTop = e~
(34)
where:
Light
LightSat
photosynthetically active radiation (ly/d); and
light saturation level for photosynthesis (ly/d).
Healthy blue-green algae tend to float. Therefore, if the nutrient limitation for blue-greens is
greater than 0.25 (Equation (43)) 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. Other phytoplankton are considered to occupy all the
well mixed layer. Under the ice, 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.
1956):
Approximately half the incident solar radiation is photosynthetically active (Edmondson,
Light = Solar 0.5
(35)
where:
Solar =
average daily light intensity (ly/d), see (22).
The light-limitation function represents both limitation for suboptimal light intensity and
photoinhibition at high light intensities (Figure 25). However, when the photoperiod for all but the
highest latitudes is factored in, photoinhibition disappears (Figure 26). When considered over the
course of the year, photoinhibition can occur in very clear, shallow systems during summer mid-day
hours (Figure 27), but it usually is not a factor when considered over 24 hours (Figure 28).
The extinction coefficient for pure water varies considerably in the photosynthetically-active
400-700 nm range (Wetzel, 1975, p. 55); the value of 0.016 (1/m) is used, corresponding 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 6).
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AQUATOX TECHNICAL DOCUMENTATION
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Figure 25
Instantaneous Light Response Function
Diatoms in 0.5-m Deep Pond
0.88
200 250 300 350 400 450 500
Light (ly/d)
Figure 27
Mid-day Light Limitation
Diatoms in 0.5-m Deep Pond
200
53 103 153 203 253 303 353
Julian Date
ILight Limitation]
Figure 26
Daily Light Response Function
Diatoms in 0.5-m Deep Pond
200
250 300 350 400
Average Light (ly/d)
450
Figure 28
Daily Light Limitation
Diatoms in 0.5-m Deep Pond
500
53 103 153 203 253 303 353
Julian Date
Light Limitation I
0.55
0.5
0.45
0.4
0.35
0.3
0.25
Table 6. Light Extinction and Attenuation Coefficients
WaterExtinction
ECoeffPhyto^m
ECoeffPhytoh,,,f.^
ECoeffDOM
ECoeffPOM
ECoeffSed
0.016 1/m
0.014 l/m-(g/m3)
0.099 l/m-(g/m3)
0.03 l/m-(g/m3)
0.12 l/m-(g/m3)
0.03 l/m-(g/m3)
Wetzel, 1975
Collins and Wlosinski, 1980
Megard et al., 1979 (calc.)
Effleretal., 1985 (calc.)
Verduin, 1982
Mclntire and Colby, 1978
The Secchi depth, the depth at which a Secchi disk disappears from view, is a commonly used
indication of turbidity. It is computed as (Straskraba and Gnauck, 1985):
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AQUATOX TECHNICAL DOCUMENTATION
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Secchi =
1.9
Extinction
(36)
where:
Secchi
Secchi depth (m).
This relationship could also 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 29). This compares favorably with
observed values of 7.5 to 11 (Clifford, 1982).
Figure 29
Contributions to Light Extinction in Lake George, NY
[-Sediment (0.00%)
Water (6.97%)
Phytoplankton (1.59%)
POM (26.13%)
DOM (65.32%)
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, 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).
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AQUATOX TECHNICAL DOCUMENTATION
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For an individual nutrient, saturation kinetics is assumed, using the Michaelis-Menten or
Monod equation (Figure 30); this approach is founded on numerous studies (cf. Hutchinson, 1967):
Phosphorus
PLimit =
Phosphorus + KP
(37)
mtr°Sen
Nitrogen + KN
(38)
CLimit =
Carbon
Carbon + KCO2
(39)
where:
PLimit
Phosphorus
KP
NLimit
Nitrogen
KN
CLimit
Carbon
KCO2
limitation due to phosphorus (unitless);
available soluble phosphorus (gP/m3);
half-saturation constant for phosphorus (gP/m3);
limitation due to nitrogen (unitless);
available soluble nitrogen (gN/m3);
half-saturation constant for nitrogen (gN/m3);
limitation due to inorganic carbon (unitless);
available dissolved inorganic carbon (gC/m3); and
half-saturation constant for carbon (gC/m3).
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; therefore, the
concentration of the compound is corrected for the molar weight of the element:
Phosphorus = P2PO4 Phosphate (40)
Carbon = C2CO2 CO2
Nitrogen = N2NH4 Ammonia + N2NO3 Nitrate
(41)
(42)
where:
P2PO4
Phosphate
N2NH4
Ammonia
N2NO3
ratio of phosphorus to phosphate (0.33);
available soluble phosphate (g/m3);
ratio of nitrogen to ammonia (0.78);
available ammonia (g/m3);
ratio of nitrogen to nitrate (0.23);
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AQUATOX TECHNICAL DOCUMENTATION
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C2C02
CO2
ratio of carbon to carbon dioxide (0.27); and
inorganic carbon (g/m3).
All these conversions are built into AQUATOX.
Figure 30
Nutrient Limitation
M1CHAELIS-MENTEN RELATIONSHIP
DIATOMS
1
0.8
bO.6
1
5^0.4
0.2
0 -1
half-saturation
0.00 0.01 0.03 0.04 0.05 0.07 0.08 0.09
PHOSPHATE (mg/L)
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:
NutrLimit = ram(PLimit, NLimit, CLimit) (43)
where:
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 and macrophytes also are limited by slow currents
that do not replenish nutrients and carry away senescent biomass. Based on the work of Mclntire
(1973) and Colby and Mclntire (1978), a factor relating photosynthesis to current velocity is used for
periphyton and macrophytes:
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AQUATOX TECHNICAL DOCUMENTATION
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VLimit = min(l, RedStillWater
Velocity
1 + VelCoeff- Velocity
(44)
where:
VLimit =
RedStillWater =
VelCoeff
Velocity =
limitation or enhancement due to current velocity (unitless);
reduction in photosynthesis in absence of current (unitless);
empirical proportionality coefficient for velocity (0.057, unitless); and
flow rate (m/s), see (169).
VLimit has a minimum value for photosynthesis in the absence of currents and increases
asymptotically to a maximum value for optimal current velocity (Figure 31). In high currents
entrainment can limit periphyton; see (60). 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 Mcrntire, 1978).
Figure 31
Response to Current
ce
o 1
5
gO.8
III
O
Z
< 06
z
U]
a:
o
z 04 -
802-
/
/
/
f
/
/
/
X
^
^"
-
*~~^
K 0 20 40 60 80 100
120
VELOCITY (cm/s)
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 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
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AQUATOX TECHNICAL DOCUMENTATION
CHAPTER 4
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:
VT =
(TMax + Acclimation) - Temperature
(TMax + Acclimation) - (TOpt + Acclimation)
(45)
where:
Temperature =
TMax
TOpt
Acclimation =
ambient water temperature (°C);
maximum temperature at which process will occur (°C);
optimal temperature for process to occur (°C); and
temperature acclimation (°C), as described below.
Acclimation to changing temperature is accounted for with a modification developed by
Kitchell et al. (1972):
Acclimation = XM [1 - e<-*r MS******** -
(46)
where:
XM = maximum acclimation allowed (°C);
KT = coefficient for decreasing acclimation as temperature approaches rre/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 VTis 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):
TCorr = VT e^^1'^ (47)
where:
XT =
WT2 (1 +
40/rr )2
400
(48)
where:
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AQUATOX TECHNICAL DOCUMENTATION
CHAPTER 4
WT = ]n(Q10) ((TMax + Acclimation) - (TOpt + Acclimation))
(49)
and,
YT = ln(£>70) ((TMax + Acclimation) - (TOpt + Acclimation) + 2)
(50)
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 32, Figure 33).
Figure 32
Temperature Response of Blue-Greens
STROGANOV FUNCTION
BLUE-GREENS
10 20 30
TEMPERATURE (C)
40
Figure 33
Temperature Response of Diatoms
STROGANOV FUNCTION
DIATOMS
10 20 30
TEMPERATURE (C)
40
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 (1 980), 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 34:
Respiration = RespO e (TResP
(51)
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AOUATOX TECHNICAL DOCUMENTATION
CHAPTER 4
where:
Respiration =
RespO
TResp
Temperature =
Biomass =
dark respiration (g/m3-d);
respiration rate at 0°C (g/g'd);
exponential temperature coefficient (unitless);
ambient water temperature (°C); and ^
plant biomass (g/m3).
This construct also applies to macrophytes.
Figure 34
Respiration (Data From Collins, 1980)
DARK RESPIRATION
10 20 30
TEMPERATURE(C)
Photorespiration
Algal excretion, also referred to as photorespiration, is the release of photosynthate (dissolved
organic material) and carbon dioxide that 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:
Excretion = KResp LightStress Photosynthesis (52)
where:
Excretion
KResp
release of photosynthate (g/m3-d);
coefficient of proportionality between excretion and photosynthesis at
optimal light levels (unitless); and
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AQUATOX TECHNICAL DOCUMENTATION
CHAPTER 4
Photosynthesis = photosynthesis (g/m3-d), see (26),
and where:
LightStress = 1 - LtLimit
(53)
where:
LtLimit= light limitation for a given plant (unitless), see (28).
It is a continuous function (Figure 35) 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.
Figure 35
Photorespiration
EFFECT OF LIGHT ON PHOTORESPIRATION
w DIATOMS IN POND
W0.09
2 0.04
"- 200 250 300 350 400 450 500
LIGHT (ly/d)
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):
Mortality = (KMort + ExcessT + Stress) Biomass + Poisoned
(54)
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AOUATOX TECHNICAL DOCUMENTATION
CHAPTER 4
where:
-Mortality
Poisoned
Kmort
Biomass
and where:
nonpredatoiy mortality (g/m3-d);
mortality rate due to toxicant (g/g'd), see ((269));
intrinsic mortality rate due to high temperature (g/g'd); and
plant biomass (g/m3),
ExcessT =
, (Temperature - TMax)
(55)
and:
Stress = 1 - e 'EMort' ^ ' (NutrLimtt
(56)
where:
ExcessT
TMax
Stress
Emort
NutrLimit
LtLimit
factor for high temperatures (g/g-d);
maximum temperature tolerated (° C);
factor for suboptimal light and nutrients (g/g-d),
approximate maximum fraction killed per day; if total limitation then
value of 2 = doubled mortality (g/g-d);
reduction due to limiting nutrient (unitless), see (43)
light limitation (unitless), see (29).
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 37), and, to a
much lesser degree, with suboptimal nutrients and light (Figure 36). This 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.
Figure 37 Figure 36
Mortality Due To High Temperatures Mortality Due To Light Limitation
">*np
5
OK
-gO.6
CD
C/l
0
LLJ
2
/
/
/TMax
4 26 28 30 32 34 36 38 4
Temperature
0
ALGAL MORTALITY
DIATOMS
0.03
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AQUATOX TECHNICAL DOCUMENTATION
CHAPTER4
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:
MeanDischarge
Depth Discharge + 0.001
SedAccel Biomass
(57)
where:
Sink
Ksed
Depth
MeanDischarge
Discharge =
Biomass =
phytoplankton loss due to settling (g/m3
-------
AOUATOX TECHNICAL DOCUMENTATION
CHAPTER 4
Figure 38
Sinking as a Function of Nutrient Stress
SINKING IN POND
DIATOMS, DEPTH = 3 m, BIOMASS = 1
'0.00 0.02 0.03 0.05 0.06 0.08 0.10
PHOSPHATE (g/cu m)
This allows the model to mimic high sedimentation loss associated with the crashes of
phytoplankton blooms, as discussed by Harris (1986). The equation is parameterized so that the
sinking rate doubles as photosynthesis is totally limited, although that can be edited by the user.
Washout and Entrainment
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:
(59)
where:
Washout
Discharge
Volume
Biomass
loss due to downstream drift (g/m3-d),
daily discharge (m3/d), see Table 1;
volume of site (m3), see (1) and
biomass of phytoplankton (g/m3).
Periphyton (and macrophytes, as discussed in the next section) also may be subject to
entrainment and transport as they outgrow their substrate and as discharge increases (Mclntire, 1968,
1973):
Washout
periphyton<
= Entrainment
Discharge
Volume
Biomass
(60)
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AQUATOX TECHNICAL DOCUMENTATION
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Entrainment is a function of carrying capacity; the formulation is based on Mclntire (1973). As the
biomass increases, additional biomass is entrained (Figure 31):
Entrainment = KCapLimit
(61)
where:
Entrainment =
KCapLimit =
fraction of biomass available for transport (unitless), and
limitation due to carrying capacity (unitless), see below.
Because periphyton are limited by the area of substrate available, as the biomass approaches
the carrying capacity of the substrate, increasing quantities are dislodged and available for transport
(Figure 39):
where:
KCap
KCapLimit = 1 - KCaP " Biomass
KCap
carrying capacity of periphyton (g/m2).
Figure 39
Entrainment as a Function of Biomass
(62)
1.2 -
1
0 8
06
04
0 2
i
4
i
L_
I
/
10
{
/
20
>
f
30
r-1
r
40
S
r
50
i-*
f
60
i
r^
70
r
80
r-
I-*
90
100
r-«
1
110
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 [igC/[ig chlorophyll a for blue-greens 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
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AQUATOX TECHNICAL DOCUMENTATION
CHAPTER 4
usually most interested in the maxima. The results are presented as total chlorophyll a in [ig/L;
therefore, the computation is:
.-,, , f BiomassB!Gr CToOrg (Biomass Diatom + Biomass^ CToOrg}
Chlorophylla = ^ + J (63)
1000
where:
Chlorophyll a =
Biomass =
CToOrg
1000
4.2 Macrophytes
biomass as chlorophyll a (|J,g/L);
biomass of given alga (mg/L);
ratio of carbon to biomass (0.526, unitless); and
conversion factor for mg to |_ig (unitless).
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 45). 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 (12),
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):
dBiomass
dt
= Loading + Photosynthesis - Respiration -Excretion
- Mortality - Predation -Washout
(64)
and:
Photosynthesis = PMax LtLimit VLimit TCorr Biomass FracLittoral
FracPhoto
(65)
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AQUATOX TECHNICAL DOCUMENTATION
CHAPTER 4
where:
dBiomass/dt
Loading =
Photosynthesis =
Respiration =
Excretion =
Mortality =
Predation =
Washout =
PMax
LtLimit =
VLimit =
TCorr
FracLittoral =
FracPhoto =
change in biomass with respect to time (g/m2-d);
loading of macrophyte, usually used as a "seed" (g/m2>d);
rate of photosynthesis (g/m2-d);
respiratory loss (g/m2-d), see (51);
excretion or photorespiration(g/m2-d), see (52);
nonpredatory mortality (g/m2-d), see (66);
herbivory (g/m2-d), see (68);
loss due to entrainment (g/nr'd), see (60),
maximum photosynthetic rate (1/d),
light limitation (unitless), see (29),
current limitation (unitless), see (44),
correction for suboptimal temperature (unitless), see (47),
fraction of bottom that is in the euphotic zone (unitless) see (11); and
reduction factor for effect of toxicant on photosynthesis (unitless), see
(271).
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 because macrophytes can obtain most of 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 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.) Non-predatory mortality is modeled
similarly to algae as a function of suboptimal temperature and 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 40):
Mortality = [Poisoned + (1 - e ~m°n' (1 " LtLimit' rc°"0)] Biomass
(66)
where:
Poisoned
EMort
mortality rate due to toxicant (g/g'd) (269), and
maximum mortality due to suboptimal conditions (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 41).
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AOUATOX TECHNICAL DOCUMENTATION
CHAPTER 4
Figure 40
Mortality as a Function of Temperature
MACROPHYTE MORTALITY
00.02
10 20 30 40
TEMPERATURE (C)
Figure 41
Mortality as a Function of Light
MACROPHYTE MORTALITY
0.04
1000 2000 3000
LIGHT (ly/d)
4000
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 entramment eventually
will be modeled when wave action is simulated.
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CHAPTER 4
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:
dBiomass
It
= Load + Consumption - Defecation - Respiration
- Excretion - Death - Predation - GameteLoss
- Washout ± Migration - Promotion + Recruit
(67)
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/m3d), see (84);
Washout = loss due to being carried downstream by washout and drift (g/m3-d),
see (87) and (88);
Migration = loss (or gain) due to vertical migration (g/m3-d), see (91);
Promotion = promotion to next size class or emergence (g/m3-d), see (92); and
Recruit = recruitment from previous size class (g/m3-d), see (92).
The change in biomass (Figure 42) is a function of a number of processes (Figure 43) 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.
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; Straskraba 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:
Ingestionpreytpred = CMaxpred SatFeeding TCorr
pred
ToxReduction Biomass
pred
(68)
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CHAPTER4
Figure 42
Change in Animal Biomass in Stream
10 -
8
G"
O5
& 6-
S 4-
O
CD
2 -
0
01/0
X-v
~r 7 \
V,/ \ ' A
\
1/91 02/27/91 04/25/91 06/21/91 08/17/91 10/13/91 12/09/91
Amphipods Mayflies Bass, YOY
Bass, adult - - Minnows
Figure 43
Mayfly Processes
0 -
01/03/91 04/11/91 07/18/91 10/24/91
02/21/91 05/30/91 09/05/91 ' 12/12/91
| Consumption HI Defecation
j Excretion EIJ Predation
Drift
[ Respiration
] Mortality
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):
SatFeeding =
Preference^ pred Food
Vprey(Preferencepreypred Food) + FHalfSatpred
(69)
where:
Ingestionpreyi pn,d = ingestion of given prey by given predator (g/m3-d);
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AQUATOX TECHNICAL DOCUMENTATION
CHAPTER 4
Biomass
CMax
TCorr
Preference =
Food
FHalfSat
ToxReduction =
concentration of organism (g/m3-d);
maximum feeding rate for predator (g/g'd);
reduction factor for suboptimal temperature (unitless), see Figure 32;
preference of predator for prey (unitless);
available food (g/m3);
half-saturation constant for feeding by a predator (g/m3); and
reduction due to effects of toxicant (see Eq. (274), unitless).
The food actually available to a predator may be reduced in two ways:
Food = (Biomassprey - BMinprJ Refuge
(70)
where:
BMin
Refuge
minimum prey biomass needed to begin feeding (g/m3); and
reduction factor for prey hiding in macrophytes (unitless).
Search or filtration may virtually cease below a minimum prey biomass (BMin) to conserve
energy (Figure 44), 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, Daphnid) must constantly filter because the filtratory appendages also serve
for respiration; therefore, in these animals there is no minimum feeding level.
Macrophytes can provide refuge from predation; this is represented by a factor related to the
macrophyte biomass that is original with AQUATOX (Figure 45):
Refuge = 1 -
Biomass
Macro
BiomassMacro + HalfSat
(71)
where:
HalfSat
Biomass,
'Macro
half-saturation constant (20, g/m3), and
biomass of macrophyte (g/m3).
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AQUATOX TECHNICAL DOCUMENTATION
CHAPTER 4
Figure 44
Saturation-kinetic Consumption
BASS CONSUMPTION
BASS BIOMASS = 1 g/cu m
0.03 -iCMax
2.65 5.3 7.95 10.613.2515.918.55
PREY BIOMASS (g/cu m)
Figure 45
Refuge From Predation
100 200 300
MACROPHYTE BIOMASS
400
AQUATOX is a food-web model with multiple potential food sources. Passive size-selective
filtering (Mullin, 1963; Lam andFrost, 1976) and active raptorial selection (Burns, 1969;Bermanand
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; Parket
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.
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AQUATOX TECHNICAL DOCUMENTATION
CHAPTER 4
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:
Preferencepreytpfed =
prey,pred
SumPref
(72)
where:
Preferencepreyipred
SumPref
normalized preference of given predator for given prey
(unitless);
initial preference value from the animal parameter screen
(unitless); and
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 differentpotentials 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 (106)), 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):
Defecationpred =
IncrEgesf) Ingestion
prey pred
)
(73)
where:
Defecationpred
EgestCoeffVKy>
IncrEgest
total defecation for given predator (g/m3-d);
fraction of ingested prey that is egested (unitless); and
increased egestion due to toxicant (see Eq. (275), 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:
Consumptionpred = ^ prey(Ingestionpr^ pred) (74)
Predation
prey
(75)
where
ConsiimptionpKd
PredationfKy
total consumption rate by predator (g/m3-d); and
total predation on given prey (g/m3'd).
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Respiration
Respiration can be considered as having two components (Park et al., 1979):
Respirationpred = SpecDynActionpred + Endogenous^
(76)
where:
Respirationpml
SpecDynActionfreli
EndogenousVKA
respiratory loss of predator (g/m3>d);
respiratory loss due to activity (g/m3-d), see (78); and
basal respiratory loss modified by temperature (g/m3-d); see
(77).
Basal or endogenous respiration is a rate at resting in which the organism is expending energy
without uptake (as in overwintering), in contrast to the so-called specific dynamic action when the
organism is moving, and consuming and digesting prey. AQUATOX simulates basal respiration as
increasing with increasing temperature to a maximum value, using the adaptive temperature function
(see Hewett and Johnson, 1992):
Endogenouspred = EndogResppred TCorrpred Biomasspred (77)
where:
EndogRespVKA =
TCorrpml
basal respiration rate at 0° C for given predator (I/day); parameter
input by user as "Respiration Rate;"
Stroganov temperature function (unitless), see Figure 32; and
concentration of predator (g/m3).
Biomasspn,d =
As a simplification, specific dynamic action is represented as proportional to food assimilated
SpecDynActionpred = KResppred (Consumptionpred - Defecationpred) (78)
(Hewett and Johnson, 1992; see also Kitchell et al., 1974; Park et al., 1974):
where:
KResppn
ed
Consumption^
DefecationyKA
proportion of assimilated energy lost to specific dynamic
action (unitless); parameter input by user as "Specific Dynamic
Action;"
ingestion (g/m3-d); and
egestion of unassimilated food (g/m3
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AQUATOX TECHNICAL DOCUMENTATION
CHAPTER 4
converted by Scavia and Park (1976) to obtain a proportionality constant relating excretion to
respiration:
where:
Excretionpivd
KExcr.
pred
Respirationimd
Excretionpred = KExcrpred Respirationpred (79)
excretion rate (g/m3-d);
proportionality constant for excretion:respiration (unitless); and
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:
Deathpred = Dpred
PoisOned
pred
(80)
where:
Deathf!Cd
Dnrtd
Biomasspred
Poisoned
nonpredatory mortality (g/m3-d);
environmental mortality rate; the maximum value of three
computations, (81), (82), and (83), is used (1/d);
biomass of given animal (g/m3); and
mortality due to toxic effects (g/m3-d), see (269).
Under normal conditions a baseline mortality rate is used:
Dpred = KMortpred
(81)
where:
KMort,
lpre
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AOUATOX TECHNICAL DOCUMENTATION
CHAPTER 4
Figure 46
Mortality as a Function of Temperature
i '
a: 0.8
Q_
One
uj 0.6
d
^. n A
z; 0.4
0
1 n o
o°-2
£
0
MORTALITY OF BASS
I
f
1
TMax /
XV
3 "e "9 ' 12 15 18 21 24 27 30 33 36 39 4
TEMPERATURE
2
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 1 g/m3, recognizing that the
predicted level is an average for the entire water column or epilimnetic or hypolimnetic segment:
Dead = 1.0 if Oxygen < 1.0 (83)
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. The construct is 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 the optimum temperature to 1° less than the optimal temperature. This is
based on a comparison of the optimal temperatures with the species-specific 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, which may
or may not be realistic.
If (0.6 TOpf) < Temperature < (TOpt - 1.0) then
GameteLoss = (GMort + IncrMort) FracAdults PctGamete Biomass (84)
else GameteLoss = 0
where:
Temperature - ambient water temperature (°C);
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AQUATOX TECHNICAL DOCUMENTATION
CHAPTER 4
TOpt
GameteLoss
GMort
IncrMort
Biomass
PctGamete
FracAdults
optimum temperature (°C);
loss rate for gametes (g/m3'd);
gamete mortality (1/d);
increased gamete and embryo mortality due to toxicant (see Eq
(276),l/d);
biomass of predator (g/m3);
fraction of adult predator biomass that is in gametes (unitless); and
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 47):
FracAdults = 1.0 - { CaPacity\
( KCap )
if Biomass > KCap then Capacity = 0 else Capacity = KCap - Biomass
(85)
where:
KCap
carrying capacity (g/m3).
Figure 47
Correction for Population-Age Structure
BASS
PctGamete = 0.09, GMort = 0.1
0.1 0.7 1.3 1.9 2.5 3.1 3.7 4.3 4.9 55
BIOMASS
Spawning in large gamefish results in an increase in the biomass of small gamefish if bom
small and large size classes are of the same species. Gametes are lost from the large gamefish, and
the small gamefish gain the viable gametes through recruitment:
Recruit = (1 - (GMort + IncrMort)) ' FracAdults PctGamete Biomass
(86)
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CHAPTER 4
where:
Recruit
biomass gained from successful spawning (g/m -d).
Washout and Drift
Downstream transport is an important loss term for invertebrates. Zooplankton are subject to
transport downstream similar to phytoplankton:
Washout = DischarSe . Biomass (87)
Volume
where:
Washout
Discharge
Volume
Biomass '
loss of zooplankton due to downstream transport (g/m3-d);
discharge (m3/d), see Table 1;
volume of site (m3), see (1); and
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:
Drift = ^charge . Dislodge . Biomass (88)
Volume ,
where:
Drift
Dislodge
loss of zoobenthos due to downstream drift (g/m3-d); and
fraction of biomass subject to drift per day (unitless), see (89) and (90).
Nocturnal drift is a natural phenomenon:
Dislodge = NormalDrift
(89)
where:
NormalDrift = fraction of biomass subject to normal drift per day (unitless).
However, drift is greatly increased when zoobenthos are subjected to stress by sublethal and lethal
doses of toxic chemicals (Muirhead-Thomson, 1987), and that is represented by a saturation-kinetic
formulation:
Toxicant,,
Dislodge =
'Water
ToxicantWater + EC50Growth
(90)
where:
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AQUATOX TECHNICAL DOCUMENTATION
CHAPTER 4
Toxicant
Water
concentration of toxicant in water (g/m3); and
ECSOGrowth = concentration at which half the population is affected (g/m3).
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 followine 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. 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-
If VSeg = Hypo and Anoxic
. HypVolume Biomass ,
Migration = - _ Pred>
EpiVolume
(91)
where:
VSeg
Hypo
Anoxic
Migration
HypVolume
EpiVolume
Biomass,
'prctljiypn '
vertical segment;
hypolimnion;
boolean variable for anoxic conditions;
rate of migration (g/m3-d);
volume of hypolimnion (m3), see Figure 15;
volume of epilimnion (m3), see Figure 15; and
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
m representing the emergence of aquatic insects, and therefore loss of biomass from the system and
mpredictmg bioaccumulationofhydrophobicorganiccompounds in larger fish. Themodel 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):
Promotion = KPropred (Consumption -Defecation - Respiration - Excretion)
(92)
where:
Promotion =
KPro
Consumption =
Defecation =
rate of promotion (g/m3-d);
fraction of growth that goes to promotion or emergence (0.5, unitless);
rate of consumption (g/m3-d), see (74);
rate of defecation (g/m3-d), see (73);
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AOUATOX TECHNICAL DOCUMENTATION
CHAPTER 4
Respiration =
Excretion =
rate of respiration (g/m3>d), see (76); and
rate of excretion (g/m3>d), see (79).
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.
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, and
is represented by:
If Temperature > (0.8 TOpf) and Temperature < (TOpt - 1.0) then
Emefgelnsect = 2 Promotion
(93)
where:
Emergelnsect
Temperature
TOpt
insect emergence (mg/l/d);
ambient water temperature (°C); and
optimum temperature (°C);
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AOUATOX TECHNICAL DOCUMENTATION
CHAPTERS
5. REMINERALIZATION
5.1 Detritus
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 now modeled as eight compartments: refractory (resistant)
dissolved, suspended, sedimented, and buried detritus; and labile (readily decomposed) dissolved,
suspended, sedimented, and buried detritus (Figure 48). This disaggregation is considered necessary
to provide more realistic simulations of 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
suspendedparticulate matter in lakes and streams (Saunders, 1980), and refractory compounds usually
predominate; however, the proportions are modeled dynamically.
Figure 48
Detritus Compartments in AQUATOX
The concentrations of detritus in these eight compartments are the result of several competing
processes:
dSuspRefrDetr = Loading + DetrFm - Colonization - Washout
dt
- Sedimentation - Ingestlon + Scour ± TurbDiff
(94)
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CHAPTER 5
dSuspLabDetr , ,. n _ _ ,
= Loading + DetrFm + Colonization - Decompositi
'.on
- Washout - Sedimentation - Ingestion + Scour ± TurbDiff
(95)
dDissRefrDetr T ...
= Loading + DetrFm - Colonization - Washout ± TurbDiff (95)
dDissLabDetr , ,. _ _ ^
= Loading + DetrFm - Decomposition - Washout ± TurbDiff (97)
dSedRefrDetr , ,. _ ^
= Loading + DetrFm + Sedimentation + Exposure
- Colonization - Ingestion - Scour - Burial '.
(98)
dSedLabileDetr
dt
= Loading + DetrFm + Sedimentation + Colonization
- Ingestion - Decomposition - Scour + Exposure - Burial
(99)
dBuriedRefrDetr _ ,. .
= Sedimentation + Burial - Scour - Expo.
dt
isure
(100)
dBuriedLabileDetr
dt
= Sedimentation + Burial - Scour - Exposure
(101)
where:
dSuspRefrDetr/dt
dSuspLabileDetr/dt *=
dDissRefrDetr/dt
change in concentration of suspended refractory detritus with
respect to time (g/m3-d);
change in concentration of suspended labile detritus with
respect to time (g/m3
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AOUATOX TECHNICAL DOCUMENTATION
CHAPTER 5
dDissLabDett/dt
dSedRefrDetr/dt
dSedLabileDetr/dt
dBuriedRefrDetr/dt =
dBuriedLabileDeti/dt =
Loading =
DetrFm
Colonization =
Decomposition =
Sedimentation =
Scour =
Exposure =
Burial =
Washout
Ingestion =
TurbDiff
change in concentration of dissolved labile detritus with
respect to time (g/m3'd);
change in concentration of sedimented refractory detritus with
respect to time (g/m3-d);
change in concentration of sedimented labile detritus with
respect to time (g/m3-d);
change in concentration of buried refractory detritus with
respect to time (g/m3-d);
change in concentration of buried labile detritus with respect
to time (g/m3-d);
loading of given detritus from nonpoint and point sources, or
from upstream (g/m3-d);
detrital formation (g/m3'd);
colonization of refractory detritus by decomposers (g/m3>d),
see (108);
loss due to microbial decomposition (g/m3
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AQUATOX TECHNICAL DOCUMENTATION
CHAPTER 5
Detrital Formation
Detritus is formed in several ways: through mortality, gamete loss, sinking of phytoplankton,
excretion and defecation:
DetrFmSuSpReJrDetr = ^biota(Mort2detr, biota ' Deadbiot<) (102)
DetrFmDissRefrDetr = Zbiota(Mort2detr>biota Deadbiota) + Vbtota(Excr2detr^iota Excretion) (103)
DetrFmDissLabileDetr = ^ biota(M°rt2 detr,biota ' Deadbiotc)
'detr.biota ' Excretion) (1Q4)
= ^ biota(M°rt2detr.biota ' Deadbiota) + ^
animals
(105)
' Defecationred)
(106)
' Defecation + S
compartment
t(Sink
compartmen
(107)
where:
DetrFm
Mort2,
Excr2.
delr, biola
dtltr, biota
Excretion
GameteLoss =
tr, biota
DefecationpKA
Sink
formation of detritus (g/m3-d);
fraction of given dead organism that goes to given detritus (unitless);
fraction of excretion that goes to given detritus (unitless);
death rate for organism (g/m3-d), see (80);
excretion rate for organism (g/m3'd), see (52) and (79) for plants and
animals, respectively;
loss rate for gametes (g/m3-d), see (84);
fraction of defecation that goes to given detritus (unitless);
defecation rate for organism (g/m3-d), see (73); and
sinking rates for labile and refractory portions of phytoplankton
(g/m3-d), see (57).
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)
_
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AOUATOX TECHNICAL DOCUMENTATION
CHAPTER 5
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 Lowe-
McConnell, 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 usually 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:
Colonization = ColonizeMax DecTCorr NLimit pHCorr
DOCorrection RefrDetr
(108)
where:
rate of conversion of refractory to labile detritus (g/m3-d);
maximum colonization rate under ideal conditions (g/g'd);
limitation due to suboptimal nitrogen levels (unitless), see (110);
the effect of temperature (unitless), see (109);
limitation due to suboptimal pH level (unitless), see (115);
limitation due to suboptimal oxygen level (unitless), see (113); and
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:
Colonization =
ColonizeMax -
Nlimit
DecTCorr
pHCorr
DOCorrection =
RefrDetr
DecTCorr = ThetaTemp ' TObs where
Theta = 1.047 if Temp .:> 19° else
Theta = 1.185 - 0.00729 Temp
(109)
The resulting curve has a shoulder similar to the Stroganov curve, but the effect increases up
to the maximum rate (Figure 49).
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CHAPTER 5
Figure 49. Colonization and Decomposition as a
Function of Temperature.
DECOMPOSITION
20 30 40 50
TEMPERATURE(C)
60
The nitrogen limitation construct, which is original with AQUATOX, is computed by:
N - MtnN
NLimit =
N - MinN + HalfSatN
(110)
N = N2NH4 - Ammonia + N2NO3 Nitrate
(111)
where:
N
MinN
HalfSatN
N2NH4
N2NO3
total available nitrogen (g/m3);
minimum level of nitrogen for colonization (= 0.1 g/m3);
half-saturation constant for nitrogen stimulation (= 0.15 g/m3);
ratio of nitrogen to ammonia (= 0.78, unitless); and
ratio of nitrogen to nitrate (= 0.23, unitless).
It is parameterized using an analysis of data presented by Egglishaw (1972) for Scottish
streams. A maximum colonization rate of 6.007 (g/g'd) per day is used, based on Mchitire and Colby
(1978, after Sedell et al., 1975).
The rates of decomposition (or colonization) of refractory dissolved organic matter are
comparable to those for paniculate 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
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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):
Decomposition = DecayMax DOCorrection DecTCorr pHCorr Detritus (112)
where:
Decomposition =
DecayMax =
DOCorrection =
DecTCorr
pHCorr
Detritus =
loss due to microbial decomposition (g/m3'd);
maximum decomposition rate (g/g'd);
correction for anaerobic conditions (unitless), see (113);
the effect of temperature (unitless)., see (109);
correction for suboptimal pH (unitless), see (115); and
concentration of detritus, including dissolved but not buried (g/m3).
Note that biomass of bacteria is not explicitly modeled in AQUATOX. ,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 (109), which also is
used for colonization. The function for dissolved oxygen, formulated for AQUATOX, is:
DOCorrection = Factor + (1 - Factor) KAnaerobic (113)
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
etal.,1982): '
Oxygen
Factor =
HaljSatO + Oxygen
(114)
and:
Factor
KAnaerobic
Oxygen
HalfSatO
Michaelis-Menten factor (unitless);
decomposition rate at 0 g/m3 oxygen,
dissolved oxygen concentration (g/m3); and
half-saturation constant for oxygen (g/m3).
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It accounts for both decreased (Figure 50) and increased (Figure 51) degradation rates under
anaerobic conditions, withKAnaerobic 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 0.5 g/m3
is used as a default.
Figure 50
Correction for Dissolved Oxygen
DECREASED ANAEROBIC DEGRADATION
1
0.9-
0.8-
0.7-
0.6
$0.5
0.4 -/-
03
0.2
1.2 1.8 2.4 3
OXYGEN (mg/L)
4.2
Figure 51
Correction for Dissolved Oxygen
INCREASED ANAEROBIC DEGRADATION
1.3-
0 0.6 1.2 1.8 2.4 3 3.6 4.2
OXYGEN (mg/L)
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:
pHCorr =
(115)
where:
pH
pHMin
ambient pH, and
minimum pH below which limitation on biodegradation rate occurs.
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If the pH is above the upper end of the optimal range for microbial degradation, the following
equation is used:
pHCorr = eWMmax - pH) (116)
where:
pHMax = maximum pH above which limitation on biodegradation rate occurs.
These responses are shown in Figure 52.
Figure 52
Limitation Due To pH
EFFECT OF pH
3.0 4.1 5.2 6.3 7.4 8.5 9.6 10.7
pH
Sedimentation
In this version, sedimentation of particulate detritus is 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.
Sedimentation = Deaccel State
Thick
(117)
where:
Sedimentation =
KSed
Thick
Deaccel =
State
transfer from suspended to sedimented by sinking (g/m3
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If TotDischarge > MeanDischarge then
Deaccel = MeanDischarge
TotDischarge +
else Deaccel = 1.0
0.001
(118)
where:
TotDischarge =
MeanDischarge =
total epilimnetic and hypolimnetic discharge (m3/d); and
mean discharge over the course of the simulation (m3/d).
Figure 53. Relationship of Deaccel to Discharge
with a Mean Discharge of 5 m3/s.
0.2
2 4
6 8 10 12 14 16 18 20 22 24
Discharge (cu m/s)
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 54). 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:
dAmmonia
d7
= Loading + Excrete + Decompose
- Nitrify - Assim
Ammonia
- Washout
(119)
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where:
^Ammonia/At =
Loading =
Excrete =
Decompose
Nitrify =
Assimilation =
Washout =
change in concentration of ammonia with time (g/m3-d);
loading of nutrient from inflow (g/m3'd);
ammonia derived from excretion by animals (g/m3'd), see (121);
ammonia derived from decomposition of detritus (g/m3-d), see (120);
nitrification (g/m3'd), see (127);
assimilation of nutrient by plants (g/m3'd), see (124) and (125); and
loss of nutrient due to being carried downstream (g/m3'd), see (13).
Ammonia is a product of decomposition:
Decompose = H Detraus(Org2Ammonia DecompositionDetritu)
(120)
It is also excreted directly by organisms:
Excrete = V Biota(Org2Ammonia Excretion Organism)
(121)
where:
Org2Ammonia
Decomposition
Excretion
ratio of ammonia to organic matter (unitless);
decomposition rate of given type of detritus, (g/m3-d), see
(112); and
excretion rate of given organism (g/m3
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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.
Figure 54
Components of Nitrogen Remineralization
fixation
i assimilation
-Lassimilation
Assimilation
Nitrogen compounds are assimilated byplants as a function of photosynthesis in the respective
groups (Ambrose etal, 1991):
AssimilationAmmonia = S^(Photosynthesisplant Uptakemtrogen NH4Pref) (i24)
AssimilationNitrate = 2plant(Photosynthesisplan( Uptake mtrogen (1 - NH4Pref)) (125)
where:
Assimilation =
Photosynthesis =
Uptake =
NH4Pref
assimilation rate for given nutrient (g/m3-d);
rate of photosynthesis (g/m3>d), see (26);
fraction of photosynthate that is nutrient (unitless);
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):
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NH4Pref =
N2NH4 Ammonia N2NO3 Nitrate +
(KN + N2NH4 Ammonia) - (KN + N2NO3 Nitrate)
N2NH4 Ammonia KN
(N2NH4 Ammonia + N2NO3 Nitrate) (KN + N2NO3 Nitrate)
(126)
where:
N2NH4
N2NO3
KN
Ammonia
Nitrate
ratio of nitrogen to ammonia (0.78);
ratio of nitrogen to nitrate (0.23);
half-saturation constant for nitrogen uptake (g N/m3);
concentration of ammonia (g/m3); and
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 mtrifying bacteria.
The maximum rate of nitrification is reduced by limitation factors for suboptimal 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:
Nitrify '= KNitri DOCorrection TCorr pHCorr Ammonia (127)
where:
Nitrify =
KNitri
DOCorrection =
TCorr
pHCorr
Ammonia =
nitrification rate (g/m3-d);
maximum rate of nitrification (g nitrate/g ammonia);
correction for anaerobic conditions (unitless) see (113);
correction for suboptimal temperature (unitless); see (47);
correction for suboptimal pH (unitless), see (115);
concentration of ammonia (g/m3); and
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 55, Figure 56).
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Figure 55
Response to pH, Nitrification
EFFECT OF pH
5 6.4 7.8 9.2 10.6
5.7 7.1 8.5 9.9
PH
Figure 56
Response to Temperature, Nitrification
STROGANOV FUNCTION
NITRIFICATION
20 30 40 50
TEMPERATURE (C)
60
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):
Denitrify = KDenitri (1 - DOCorrection) TCorr pHCorr Nitrate (128)
where:
Denitrify
KDenitri
Nitrate
denitrification rate (g/m3>d);
maximum rate of denitrification (g ammonia/g nitrate); and
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 57,Figure 58).
Figure 57
Response to pH, Denitrification
EFFECT OF pH
o
1
0.8
:0.6
)
JO.4
' 0,2
0
3 4.8 6.6 8.4 10.2
3.9 5.7 7.5 9.3
pH
Figure 58
Response to Temperature, Denitrification
STROGANOV FUNCTION
DECOMPOSITION
10
20 30 40 50
TEMPERATURE (C)
60
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5.3 Phosphorus
APhosphate = Loading . FracAvail + AtmosDep + Excrete + Decompose
dt
~ ^simphosphate - Washout
(129)
The phosphorus cycle is much simpler than the nitrogen cycle. Decomposition, excretion, and
assimilation are important processes that are similar to those described above:
AtmosDep = PAtmos
Volume
(130)
Excrete = S Bjota(Org2Phosphate ExcretionBiota)
(131)
Decompose = S Detritus(Org2Phosphate Decomposition^^
(132)
Assimilation = ^^Photosynthesisplaat UptakePhosphoru)
(133)
where:
dPhosphate/dt =
Loading =
FracAvail =
AtmosDep =
Excrete
Decompose =
Assimilation
Washout =
Patmos =
Area
Volume =
Org2Phosphate =
Excretion =
Decomposition =
Photosynthesis =
Uptake
change in concentration of phosphate with time (g/m3-d);
loading of nutrient from inflow (g/m3-d);
fraction of phosphate loading that is available (unitless);
loading of nutrient directly from atmosphere (g/m3-d);
phosphate derived from excretion by biota (g/m3-d);
phosphate derived from decomposition of detritus (g/m3-d);
assimilation by plants (g/m3-d);
loss due to being carried downstream (g/m3'd), see (13);
average observed atmospheric deposition rate (g/m2'd);
area of site (m2);
volume of water at site (m3);
ratio of phosphate to organic matter (unitless);
excretion rate for given organism (g/m3-d), see (79);
decomposition rate for given detrital compartment (g/m3-d), see (112);
rate of photosynthesis (g/nrM), see (26), and
fraction of photosynthate that is phosphate (unitless).
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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 couldbe 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
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 a function of reaeration, photosynthesis, respiration,
decomposition, and nitrification:
dOxygen , ,. _
= Loading + Reaeration + Photosynthesized
- BOD - NitroDemand - Washout
(134)
Photosynthesized = O2Biomass S plant(Photosynthesisp, )
(135)
BOD - 02BiomaSS
^(Decomposition DsMJ + ^Orgaflisins(^spiratiOnOrganisJ)
NitroDemand = O2N Nitrify
(136)
(137)
where:
dOxygen/dt
Loading
Reaeration
Photosynthesized
BOD
NitroDemand
Washout
O2Biomass
Photosynthesis
Decomposition
Respiration
O2N
Nitrify
change in concentration of dissolved oxygen (g/m3-d);
loading from inflow (g/m3-d);
atmospheric exchange of oxygen (g/m3td);
oxygen produced by photosynthesis (g/m3-d);
instantaneous biological oxygen demand (g/m3'd);
oxygen taken up by nitrification (g/m3-d);
loss due to being carried downstream (g/m3-d), see (13);
ratio of oxygen to organic matter (unitless);
rate of photosynthesis (g/m3-d), see (26), (65);
rate of decomposition (g/m3-d), see (112);
rate of respiration (g/m3-d), see (76);
ratio of oxygen to nitrogen (unitless); and
rate of nitrification (g N/m3-d).
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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):
Reaeration = KReaer (O2Sat - Oxygen) (138)
where:
Reaeration =
KReaer =
O2Sat
Oxygen =
mass transfer of oxygen (g/m3>d);
depth-averaged reaeration coefficient (1/d);
saturation concentration of oxygen (g/m3), see (147); and
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 59):
KReaer =
0.346 + 0.0346 Wind2
Thick
(139)
where:
Wind
Thick
wind velocity 10 m above the water (m/sec); and
thickness of mixed layer (m).
In streams, reaeration is a function of current velocity and water depth (Figure 60) 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 WASPS code (Ambrose et al., 1991).
If Vel< 0.518:
TransitionDepth = 0
(140)
else:
TransitionDepth = 4.411 Vel
2.9135
(141)
where:
Vel
TransitionDepth
velocity of stream (m/sec); and
intermediate variable (m).
If Depth < 0.61 m, the equation of Owens et al. (1964, cited in Ambrose et al., 1991) is used:
KReaer = 5.349 Vel0-61 Depth'1*5
(142)
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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:
KReaer = 3.93 Fe/°-50 Depth'1-50 (143)
Else, if Depth <> TransitionDepth, the equation of Churchill et al. (1962, cited in Ambrose et al
1991) is used: '
KReaer = 5.049 Vel0-97 Depth-1-67 (144)
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:
KReaer =
234
i0.408
^
0.66
where:
U = velocity (fps);
Slope = longitudinal channel slope (m/m); and
H = water depth (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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CHAPTER 5
Figure 59
Reaeration as a Function of Wind
EFFECT OF WIND
OXYGEN, DEPTH = 1 m
8 12 16
6 10 14
WIND (m/s)
Figure 60 ,
Reaeration in Streams
so
VELOCITY (m/sec)
DEPTH (m)
Reaeration is assumed to be representative of 20°C, so it is adjusted for ambient water
temperature using (Thomann and Mueller 1987):
KReaerT =
~ 20)
(146)
where:
KReaerT
Kreaer20
Theta
Temperature
Reaeration coefficient at ambient temperature (1/d);
Reaeration coefficient for 20°C (1/d);
temperature coefficient (1.024); and
ambient water temperature (°C).
Oxygen saturation, as a function of both temperature (Figure 61) and salinity (Figure 62), is
based on Weiss (1970, cited in Bowie et al., 1985):
02Sat - 1.4277- exP[- 173.4927.
143.3483
TKelvin + S (-0.033096 + 0.00014259 TKelvin -1.7 10~7
-0.21849
(147)
where:
TKelvin
S
Kelvin temperature, and
salinity (ppt).
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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 ( et al., 1993). At
the present time salinity is set to 0; although, it has little effect on reaeration.
Figure 61
Saturation as a Function of Temperature
OXYGEN SATURATION
SALINITY = 0ppt
r12
ho
I
7.5
12 16.5 21 25.5 30 34.5 39
TEMPERATURE (C)
Figure 62
Saturation as a Function of Salinity
OXYGEN SATURATION
TEMPERATURE = 20 C
8.55
8.25
13.5 18 22.5 27 31.5 36
SALINITY (ppt)
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:
dCO2
dt
= Loading + Respired +Decompose
- Assimilation - Washout ± CO2AtmosExch
(148)
where:
Respired = CO2Biomass S Organism(.ResPirationOrgatiiJ
(149)
Assimilation = S plant(Photosynthesisplmt UptakeCO2)
Decompose = CO2Biomass ^Detritus(DecpmpDeMJ
(150)
(151)
and where:
dCO2/dt
Loading
change in concentration of carbon dioxide (g/m3-d);
= loading of carbon dioxide from inflow (g/m3-d);
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Respired
Decompose
Assimilation
Washout
CO2AtmosExch
CO2Biomass
Respiration
Decomposition
Photosynthesis
UptakeCO2
carbon dioxide produced by respiration (g/rh3-d);
carbon dioxide derived from decomposition (g/m3-d);
assimilation of carbon dioxide by plants (g/m3-d);
loss due to being carried downstream (g/m3-d), see (13);
interchange of carbon dioxide with atmosphere (g/m3-d);
ratio of carbon dioxide to organic matter (unitless);
rate of respiration (g/m3-d), see (76);
rate of decomposition (g/m3*d), see (112);
rate of photosynthesis (g/in3-d), see (26); and
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:
CO2AtmosExch = KLiqCO2 (CO2Sat - CO2) (152)
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):
,rr. ~ ( MolWt02 }°'25 ,,_,,.
KLl'lC02 = meaer (153)
where:
CO2AtmosExch =
KLiqCO2
CO2
CO2Sat
KReaer =
MolWtO2
MolWtCO2 =
interchange of carbon dioxide with atmosphere (g/m3-d);
depth-averaged liquid-phase mass transfer coefficient (1/d);
concentration of carbon dioxide (g/m3);
saturation concentration of carbon dioxide (g/m3), see (154);
depth-averaged reaeration coefficient for oxygen (1/d), see (139)-
(146);
molecular weight of oxygen (=32); and
molecular weight of carbon dioxide (= 44).
Keying the mass-transfer coefficient for carbon dioxide to the reaeration coefficient for
oxygen is very powerful in that the effects of wind (Figure 63) and the velocity and depth of streams
can be represented, using the oxygen equations (Equations (139)- (144)).
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Figure 63
Carbon Dioxide Mass Transfer
EFFECT OF WIND
CARBON DIOXIDE, DEPTH = 1 m
6 8 10 12 14 16
WIND (m/s)
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 64), and the
partial pressure of carbon dioxide:
CO2Sat = CO2Henry pCO2
where:
2385.73
CO2Henry = MCo2
14.0184 + 0.0152642 TKelvin
(154)
(155)
and where:
CO2Sat
CO2Henry =
pCO2
MC02
Tkelvin
Temperature =
TKelvin = 273.15 + Temperature
saturation concentration of carbon dioxide (g/m3);
Henry's law constant for carbon dioxide (g/m3-atm)
atmospheric partial pressure of carbon dioxide (= 0.00035);
mg carbon dioxide per mole (= 44000);
temperature in °K, and
ambient water temperature (°C).
(156)
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Figure 64
Saturation of Carbon Dioxide
CARBON DIOXIDE SATURATION
3 7.5
12 16.5 21 25.5 30 34.5 39
TEMPERATURE (C)
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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 -
0.062 mm), and 3) clay (0.00024 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. Rapid sedimentation can adversely affect periphyton and some zoobenthos. Scour can
also adversely affect periphyton and zoobenthos. The ratio of inorganic to organic sediments can be
used as an indicator of aerobic or anaerobic conditions in the bottom sediments.
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:
MassBedSed = MassBedSed^_v + (DepositSed - Scour
Volume
Water
(157)
where:
MassBed
Seil
DepositSed
ScourScd
VolumeWMer
mass of sediment in channel bed (kg);
mass of sediment in channel bed on previous day (kg);
amount of suspended sediment deposited (kg/m3);
amount of silt or clay resuspended (kg/m3); and
volume of stream reach (m3).
The volumes of the respective sediment size classes are calculated as:
1 Original riverine version contributed by Rodolfo Camacho of Abt Associates Inc.; not
validated
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AQUATOX TECHNICAL DOCUMENTATION
CHAPTER 6
TV 7 MassBed-.
Volume^ - Sed
Rho
Sed
(158)
where:
VolumeStld
MassJBedSed
volume of given sediment size class (m3);
mass of the given sediment size class (kg); and
density of given sediment size class (kg/m3).
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:
Cone
KgLoad,
'Sed
Sed
Q 86400
Concsed,t--i + Scour Sed - DepositSed - Wash
Sed
(159)
where:
Concs<
Cone,
Sa/.t = -l
KgLoadScd
Q
Scour,
Sal
Deposit^
WashSyd
concentration of silt or clay in water column (kg/m3);
concentration of silt or clay on previous day (kg/m3);
loading of clay or silt (kg/d);
flow rate (nrYs converted to m3/d);
amount of silt or clay resuspended (kg/m3);
amount of suspended sediment deposited (kg/m3); and
amount of sediment lost through downstream transport (kg/m3).
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):
Tau = H2ODensity Slope HRadius
(160)
where:
Tau
shear stress (kg/m2);
6-2
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AQUATOX TECHNICAL DOCUMENTATION
CHAPTER 6
H2ODensity =
Slope" .
density of water (1000 kg/m3);
slope of channel (m/m);
and hydraulic radius (HRadius) is (Colby and Mclntire, 1978):
Y Width
HRadius =
2 Y + Width
(161)
where:
HRadius
Y
Width
hydraulic radius (m);
dynamic mean depth (m); and
channel width (m).
Resuspension or scour of bed sediments is predicted to occur when the computed shear stress
is greater than the critical shear stress for scour:
Scour
if Tau > TauScourSed then
Tau
ErodibilitySed
Sed
TauScour
- 1
Sed
(162)
where:
ScourScd =
ErodibilitySal =
TauScourSed =
resuspension of silt or clay (kg/m3);
erodibility coefficient (kg/m2); and
critical shear stress for scour of silt or clay (kg/m2).
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:
CheckSed = ScourSed VolumeWater
(163)
if MassSed <, CheckSed then
Scour
Mass
Sed
Sed
(164)
Volume
Water
where:
CheckSed
MassSed
maximum potential mass (kg); and
mass of silt or clay in bed (kg).
6-3
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AQUATOX.TECHNICAL DOCUMENTATION
CHAPTER 6
stress:
Deposition occurs when the computed shear stress is less than the critical depositional shear
if Tau < TauDeps, then
DepositSd = Cone
Sed
rr,.
1 - e
i -
Tau
TauDep&
(165)
where:
DepositSctl
TauDepSed =
ConcSa, =
amount of sediment deposited (kg/m3);
critical depositional shear stress (kg/m2);
concentration of silt, clay, or sand (kg/m3); and
terminal fall velocity of given sediment type (m/s).
The settling velocity is computed from Stake's law (Schnoor, ,1987):
g
18 Vise
RhoSed - Rho
Rho
D
Sed
1000;
(166)
where:
g
Vise
Rho
= gravitational acceleration constant (9.807 m/s2);
= kinematic viscosity of water (m2/s);
= density of water (kg/m3);
= density of given sediment (kg/m3); and
DSeil = particle diameter for given sediment (mm, converted to m).
Downstream transport is an important mechanism for loss of suspended sediment from a given'
stream reach. In a steady-state simulation with constant flow and volume and with a one-day time
step, the downstream transport of sediments is simply the amount of sediments in suspension in the
previous time step:
Washv , = Cone? , , ,
!>ed Sed, t= -1
where:
Wash
Sett
amount of given sediment lost to downstream transport (kg/m3).
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
6-4
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AQUATOX TECHNICAL DOCUMENTATION
CHAPTER 6
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.
>tConcSand = 0.05
Rho
Velocity Slope
Rhov , - Rho
Sana
iTauSt
Rh°Sand ~ Rh°
Rho
8
(168)
where:
PotConcSand =
Velocity
Slope
TauStar
The flow velocity is calculated by:
Velocity =
potential concentration of suspended sand (kg/m3);
density of sand (kg/m3);
flow velocity (m/s);
slope of stream (m/m);
mean diameter of sand particle (mm converted to m); and
dimensionless shear stress.
Q
Y- Width
(169)
where:
Q
Y
Width
flow rate (m3/s);
dynamic mean depth of water (m); and
channel width (m).
The dimensionless shear stress is calculated by:
Rho
TauStar =
~ Rh°
HRadius
Slope
(170)
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:
CheckSand = PotConCSand ' VolumeWater
(171)
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AQUATOX TECHNICAL DOCUMENTATION
CHAPTER 6
MassSuspSand = ConcSand VolumeWater
(172)
TotalMassSand = MassSuspSand + MassBedSand
(173)
if CheckSand <. MassSuspSand then
DepositSand = MassSuspSand - CheckSand
ConCSand = PotC°nCSand
(174)
if CheckSand * TotalMassSand then
MassBedSand = 0
Cone
TotalMass
(175)
Sand
Sand Volume
Water
if CheckSand > MassSuspSand and < TotalMassSand then
ScOUrSand = CheckSand ~ MaSsSusPSand
Cone
Sand
MassSuspSand + ScourSand
(176)
Volume
Water
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 predicted phytoplankton and suspended detritus
concentrations:
InorgSed = TSS -^Phyto - ^PartDetr (177)
6-6
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AQUATQX TECHNICAL DOCUMENTATION
CHAPTER 6
where:
InorgSed
TSS
Phyto
PartDetr
concentration of suspended inorganic sediments (g/m3);
observed concentration of total suspended solids (g/m3);
predicted phytoplankton concentrations (g/m3); see (25) and
predicted suspended detritus concentrations (g/m3); see (94) and (95).
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 (30)).
6-7
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AQUATOX TECHNICAL DOCUMENTATION
CHAPTER 7
7. TOXIC ORGANIC CHEMICALS
The chemical fate module of AQUATOX predicts the partitioning of a compound between
water, sediment, and biota (Figure 65), and estimates the rate of degradation of the compound
(Figure 66). Microbial degradation, 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 no longer represented in
AQUATOX.
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. 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).
Figure 65
In-situ Uptake and Release of Insecticide
Figure 66
In-situ Degradation Rates for Insecticide
PARATHION IN POND
UPTAKE AND RELEASE
50
-40
_i
"3)30
UJ
20
03/09/78 03/17/78 03/25/78
03/13/78 03/21/78 03/29/78
HI GillSorption7 H Depuration/ H DetrSorpt/
Q Decomp/ US DetrDesorpt/ |H AlgalSorp7
PARATHION IN POND
DEGRADATION
09/78
03/17/78
03/25/78
03/13/78
03/21/78
03/29/78
f Hydrolysis/ H Photolysis/ HJ MicroMet/
The mass balance equations follow. 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:
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AQUATOX TECHNICAL DOCUMENTATION
CHAPTER 7
dToxicant^
dT~
Loading + ^LabileDetr (DeCOmPOsiti°n LabileDetr ' PPBLabileDetr ' le~6)
+ ^£>esorptioKDetrTox
- ^SorptionDetrTox
- E AlgalUptakeA, - Hydrolysis - Photolysis - MicrobialDegrdn
- Volatilization - Discharge + TurbDiff
PPBOrg le-6)
- X) GillUptakePred - MacroUptake
(178)
The equations for the toxicant associated with the two sediment detritus compartments are
rather involved:
dToxicantSedLabileDelr = ^^ _ ^^
dt
+ Colonization PPBSedRefi.Detr le-6
le-6
- (Resuspension + Decomposition) PPBSedLahileDetr
PPB*,,,,,^. le-6
Sedimentation PPBSuspLabileDetr le-6
Sinkphyto PPBphyto le-6)
- Hydrolysis - MicrobialDegrdn - Burial + Expose
(179)
dToxicant,
SedRefrDetr =
dt
ion - Desorption
- Def2Detr) DefecationToxpred p\
- (Resuspension + Colonization) PPBSedRefrDetr le-6
+ Sedimentation PPB'SllspRejrDetr le-6
+ Y^(Sed2Detr Sinhphyto PPBphyto le-6)
- Hydrolysis - MicrobialDegrdn - Burial + Expose
(180)
Similarly for the toxicant associated with suspended and dissolved detritus, the equations are:
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AQUATOX TECHNICAL DOCUMENTATION
CHAPTER 7
Toxicant
SvspLabileDetr =
dt
Sorption - Desorption +
'Pred
(DeftSed Defp .)
((Mort2Detr Mortality Org + GameteLossOr)
Org'
+ Decamp
'Pred *n£eSti°nPred, SuspLabileDetr) ' ??%'SuspLabileDetr ' le~6
PPBQfS le-6) - (Sedimentation + Washout
(181)
+ Colonization PPB
+ Resuspension PPB
SaspRefrDetr
i
SedLabileDetr
le-6
le-6 - SedToHyp + SedFrE,
- Hydrolysis - Photolysis - MicrobialDegrdn + TurbDiff
dToxicantSuspRefrDetr
dt
= Loading + Sorption - Desorption
+ ^0rg(Mort2Ref- MortalityOrg PPBQfg le-6)
- ^Sedimentation + Washout + Colonization
+ 7 Tw&pffinn \ PP'R 1 f» f\
t-JPred & *llu"'SuspREfrDetr> * *nSuspRefrDetr lc °
+ Resuspension PPBSedReftDetr le-6 - SedToHyp + SedFrEpi
- Hydrolysis - Photolysis - MicrobialDegrdn + TurbDiff
(182)
dToxicant
DissLabileDetr
dt
= Loading + Sorption - Desorption + 2_jExcrToxToDissOr
lL,0rg(Mort2Detr MortalityOrg PPBOrg le-6)
- (Washout + Decomposition)
+ Colonization PPBDissRefrDetr
- Hydrolysis - Photolysis - MicrobialDegrdn + TurbDiff
DissLabileDetr
le-6
(183)
dToxicant .
dt
= Loading + Sorption - Desorption
J20rg(Mort2Ref- Mortality^ PPBQrg le-6)
Org
'DissRefrDetr
le-6
- (Washout + Colonization) PPB
- Hydrolysis - Photolysis - MicrobialDegrdn + TurbDiff
(184)
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AQUATOX TECHNICAL DOCUMENTATION
CHAPTER?
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:
= Loading + AlgalUptake - Depuration + TurbDiff
+ (- Excretion - Washout - z2pred Predationpred Alga - Mortality
- Sink + SinkToHypo -SinkFrEpi) PPBAlga le-6
dt
(185)
Macrophytes are represented similarly, but reflecting the fact that they are stationary:
1-1 """" = Loading + MacroUptake - Depuration - (Excretion
Mortality) PPBMacro le-6
dt
(186)
The toxicant associated with animals is represented by an involved kinetic equation because
of the various routes of exposure and transfer:
dToxicant
dt
= Loading + GillUptake +
- (Depuration + / v
'Prey
Predation
DietUptake + TurbDiff
+ Mortality + Spawn
fPred * ' """"""Pred, Animal
± Promotion + Drift + Migration + Emergelnsect) PPBAnimal
(187)
le-6
where:
Toxicantmer
ToxicantSedDclr
ToxicantSuspDell.
ToxicantDis..Dcu.
Toxicant
Alsa
ToxicantMami,liy,e
ToxicantAnlnml
toxicant in dissolved phase in unit volume of water ((J,g/L);
mass of toxicant associated with each of the two sediment
detritus compartments in unit volume of water (|J,g/L);
mass of toxicant associated with each of the two suspended
detritus compartments in unit volume of water (|Ig/L);
mass of toxicant associated with each of the two dissolved
organic compartments in unit volume of water (p,g/L);
mass of toxicant associated with given alga in unit volume of
water (|ig/L);
mass of toxicant associated with macrophyte in unit volume
of water([lg/L);
mass of toxicant associated with given animal in unit volume
of water ([J,g/L);
concentration of toxicant in sediment detritus (|lg/kg);
concentration of toxicant in suspended detritus (|J,g/kg);
7-4
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AQUATOX TECHNICAL DOCUMENTATION
CHAPTER 7
PPBAIsa
nr>D
r * D Mmrophytc
PPBAnimal
le-6
Loading
TurbDiff
Hydrolysis
.Photolysis
MicrobialDegrdn
Volatilization
Discharge
Burial
Expose
Decomposition
Depuration
Sorption
Desorption
Colonization
Def2Detr
Sedimentation
Sed2Detr
Sink
Death
Mort2Detr
GameteLoss
Mort2Ref
Washout or Drift
SedToHyp
SedFrEpi
concentration of toxicant in dissolved organics (|0,g/kg);
concentration of toxicant in given alga (|Ig/kg);
concentration of toxicant in macrophyte (fig/kg);
concentration of toxicant in given animal (|0,g/kg);
units conversion (kg/mg);
loading of toxicant from external sources (|J,g/L-d);
depth-averaged turbulent diffusion between epilimnion and
hypolimnion (|J,g/L-d), see 11;
rate of loss due to hydrolysis ([Ig/L-d), see (190);
rate of loss due to direct photolysis (|lg/L-d), see (197);
rate of loss due to microbial degradation (jlg/L-d), see (204);
rate of loss due to volatilization (|lg/L-d), see (209);
rate of loss of toxicant due to discharge downstream (|ig/L-d),
see Table 1;
rate of loss due to deep burial (jlg/L-d) see (165);
rate of exposure due to resuspension of overlying sediments
'([Ig/L-d), see (162);
rate of decomposition of given detritus (mg/L-d), see (112);
elimination rate for toxicant due to clearance (jlg/L-d), see
(258);
rate of sorption to given compartment (|J,g/L-d), see (230);
rate of desorption from given compartment (fig/L-d), see
(231);
rate of conversion of refractory to labile detritus (g/m3-d), see
(108);
rate of transfer of toxicant due to defecation of given prey by
given predator (|J,g/L-d), see (259);
fraction of defecation that goes to given compartment;
rate of resuspension of given sediment detritus (mg/L'd);
rate of sedimentation of given suspended detritus ,(mg/L-d);
fraction of sinking phytoplankton that goes to given detrital
compartment; ^
loss rate of phytoplankton to bottom sediments (mg/I/d), see
(57);
nonpredatory mortality of given organism (mg/L-d), see (80);
fraction of dead organism that is labile (unitless);
loss rate for gametes (g/m3-d), see (84);
fraction of dead organism that is refractory (unitless);
rate of loss of given suspended detritus or organism due to
being carried downstream (mg/L-d), see (13);
rate of settling loss to hypolimnion from epilimnion (mg/L-d);
rate of gain to hypolimnion from settling out of epilimnion
(mg/L-d);
7-5
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AQUATOX TECHNICAL DOCUMENTATION
CHAPTER 7
IngestionPmLPre!.
PredationPmliPny
ExcToxToDiss0rg
Excretion
SinkToHypo
SinkFrEpi
AlgalUptake
MacroUptake
GillUptake
DietUptakePrev
Promotion
Migration
Emergelnsect
rate of ingestion of given food or prey by given predator
(mg/L-d), see (68);
predatory mortality by given predator on given prey (mg/L-d),
see (75);
toxicant excretion from plants to dissolved organics (mg/L-d); j
excretion rate for given organism (g/m3-d), see (79); ";
rate of transfer of phytoplankton to hypolimnion (mg/L'd); ,
loss rate of phytoplankton to hypolimnion (mg/L-d); j
rate of sorption by algae ([ig/L - d), see (244);
rate of sorption by macrophytes (|lg/L - d), see (240);
rate of absorption of toxicant by the gills (Hg/L - d), see (249);
rate of dietary absorption of toxicant associated with given
prey ([Ig/L-d), see (252);
promotion from one age class to the next (mg/L-d), see (92);
rate of migration (g/m3-d), see (91); and
insect emergence (mg/L-d), see (93).
7.1 lonization
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:
Nondissoc = - (188)
where:
Nondissoc = nondissociated fraction (unitless).
If the compound is a base then the fraction not ionized is:
Nondissoc =
1
a - pH)
(189)
When/7/fa =pHha\f the compound is ionized and half is not (Figure 67). At ambient environmental
pH values, compounds with apKa in the range of 4 to 9 will exhibit significant dissociation (Figure
68).
7-6
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AQUATOX TECHNICAL DOCUMENTATION
CHAPTER 7
Figure 67
Dissociation of Pentachlorophenol
(pKa = 4.75) at Higher pH Values
Figure 68
Dissociation as a Function of pKa at an Ambient
pHof7
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 modelled 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:
Hydrolysis = KHyd Toxicant,
'Phase
(190)
where:
and where:
KHyd
KAcidExp
KBaseExp
KUncat
Arrhen
KHyd = (KAcidExp + KBaseExp + KUncaf) Arrhen (191)
overall pseudo-flrst-order rate constant for a given pH and temperature
(1/d);
pseudo-flrst-order acid-catalyzed rate constant for a given pH (1/d);
pseudo-first-order base-catalyzed rate constant for a given pH (1/d);
the measured first-order reaction rate at pH 7 (1/d); and
temperature adjustment (unitless).
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AQUATOX TECHNICAL DOCUMENTATION
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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:
KAcidExp = KAcid Hlon (192)
where:
Hlon = lQ-pH
(193)
and where:
KAcid
Hlon
pH
acid-catalyzed rate constant (L/mol- d);
concentration of hydrogen ions (mol/L); and
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 69) can be described as:
KBaseExp = KBase OHIon
(194)
where:
OHIon =
(195)
and where:
KBase
OHIon
base-catalyzed rate constant (L/mol d); and
concentration of hydroxide ions (mol/L).
7-8
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AQUATOX TECHNICAL DOCUMENTATION.
CHAPTER?
Figure 69
Base-catalyzed Hydrolysis of Pentachlorophenol
6.05E-03
6.00E-03
Cj 5.95E-03
£ 5.90E-03
5.85E-03
5.80E-03
2
i i i i j
! j i L i J
"-;! : T /
._!~.; _: ; /
. _. . :^y
4 6 8 10
PH
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:
En
En \
Arrhen = e \R ' KehinT R ' TObs'
(196)
where:
En
R
Kelvin!
TObs
Arrhenius activation energy (cal/mol);
universal gas constant (cal/mol Kelvin);
temperature for which rate constant is to be predicted (Kelvin); and
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:
Photolysis = KPhot Toxicantpfmse (197)
where:
Photolysis
KPhot
rate of loss due to photodegradation (g/m3-d); and
direct photolysis first-order rate constant (I/day).
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AOUATOX TECHNICAL DOCUMENTATION
CHAPTER 7
For consistency, photolysis is computed for both the epilimnion and hypolimnion in stratified
systems. However, it is not a significant factor at hypolimnetic depths.
lonization 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 half-life for photolysis, 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 70); it also is adjusted
by a factor for time-varying light:
KPhot = PhotRate ScreeningFactor LightFactor
(198)
where:
PhotRate =
ScreeningFactor =
LightFactor =
direct, observed photolysis first-order rate constant (I/day);
a light screening factor (unitless), see (199); and
a time-varying light factor (unitless), see (201).
Figure 70
Photolysis of Pentachlorophenol as a Function of
Light Intensity and Depth of Water
100 200 300 400 500 600 700
LIGHT INTENSITY (ly/d)
-DEPTH (m)-
-1.5 2
2.5 3
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):
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ScreeningFactor =
RadDistr 1 -
mcK>
RadDistrO Alpha Thick
(199)
where:
RadDistr
RadDistrO
Alpha
Thick
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);
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);
light extinction coefficient at wavelength 312.5 run (1/m), see (200);
and
thickness of the water body segment if stratified or maximum depth if
. unstratified (m).
The extinction of light of the reference wavelength of 312.5 nm is a function of several
components, based on parameter values in Burns and Cline (1985), as given in Ambrose et al. (1991):
Alpha = ExtinctmO + AttenChl Chlorophyll + AttenDOC DOC
+ AttenSolids SuspSed
(200)
where:
ExtinctH2O
AttenChl
AttenDOC
AttenSolids
Chlorophyll
DOC
SuspSed
light extinction of wavelength 312.5 nm in pure water (1/m);
attenuation coefficient for chlorophyll a (L/mg - m);
attenuation coefficient for dissolved organic carbon (L/mg - m);
attenuation coefficient for suspended sediment (L/mg-- m);
concentration of chlorophyll a in water column (mg/L);
concentration of dissolved organic carbon in water (mg/L); and
concentration of suspended sediments (mg/L).
The equations presented above implicitly make the following assumptions:
the compound of interest absorbs light only over a relatively narrow wavelength range,
and the screening factor for wavelength 312.5 nm can be considered representative;
quantum yield is independent of wavelength; and,
the value used for PhotRate is a representative near-surface, first-order rate constant
for direct photolysis.
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The rate is modified further to represent seasonally varying light conditions and the effect of
ice cover:
LightFactor =
SolarO
AveSolar
(201)
where:
SolarO
AveSolar
time-varying average light intensity at the top of the segment (ly/day);
and
average light intensity for late spring or early summer, corresponding
to time when photolytic half-life is often measured (default = 500
Ly/day).
loading:
If the system is unstratified or if the epilimnion is being modeled, the light intensity is the light
SolarO = Solar
(202)
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:
SolarO = Solar exp(-J**a 'Max7M^ (203)
where:
Solar
MaxZMix
incident solar radiation loading (ly/d), see (22); and
depth of the mixing zone (m), see (14).
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
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 (112) and supporting equations:
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MicrobialDegrdn = KMDegrdnphase DOCorrection TCorr pHCorr
Toxicant
Phase
(204)
where:
MicrobialDegrdn
KMDegrdn
DOCorrection
TCorr
pHCorr
Toxicant
loss due to microbial degradation (g/m3'd);
maximum degradation rate, either in water column or sediments
(1/d);
effect of anaerobic conditions (unitless), see (113);
effect of suboptimal temperature (unitless), see (21);
effect of suboptimal pH (unitless), see (115); and
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 dissolved phase, the maximum degradation rate is set
arbitrarily to 25 percent of the maximum degradation rate in the sediments. The model assumes that
reported maximum microbial degradation rates are for suspended slurry or wet soil samples; if the
reported degradation value is from a flask study without additional organic matter, then the parameter
value that is entered should be four times 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 vapon 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 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: ,
KLiq = KReaer Thick
(MolWt02\0-25
( MolWt }
1
Nondissoc
(205)
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where:
KLiq
KReaer
Thick
MolWtO2
MolWt
Nondissoc
water-side transfer velocity (m/d);
depth-averaged reaeration coefficient for oxygen(l/d), see (139)-(146);
thickness of the water body segment if stratified or maximum depth if
unstratified (m);
molecular weight of oxygen (g/mol, =32);
molecular weight of pollutant (g/mol); and
nondissociated fraction (unitless), see (188).
Likewise, the thickness of the air-side stagnant boundary layer is also affected by wind. 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):
rr i*c
KGas = 168
( MolWtH2O\ °'25
-
( MolWt
_ ,
Wind
(206)
where:
KGas
Wind
MolWtH2O =
air-side transfer velocity (m/d);
wind speed ten meters above the water surface (m/s); and
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 resistancesthe reciprocals of the air- and water-phase mass
transfer coefficients (Schwarzenbach et al., 1993), modified for the effects of ionization:
1
1
1
KOVol KLiq KGas HenryLaw Nondissoc
(207)
where:
KOVol
total mass transfer coefficient through both stagnant boundary layers
(m/d);
HenryLaw =
Henry
R TKelvin
(208)
and where:
HenryLaw =
Henry =
R
Henry's law constant (unitless,),-
Henrys law constant (arm m3 mol"1);
gas constant (=8.206E-5 arm m3 (mol K)'1); and
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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:
KOVol
Volatilization =
Thick
(ToxSat - Toxicantwater)
(209)
where:
Volatilization =
Thick
ToxSat
Toxicantwaler -
interchange with atmosphere (^g/I/d);
depth of water or thickness of surface layer (m);
saturation concentration of pollutant (|lg/L); and
concentration of pollutant in water (|-lg/L).
The saturation concentration depends on the concentration of the pollutant in the air, ignoring
temperature effects (Thomann and Mueller, 1987, p. 532), but adjusting for ionization and units:
ToxSat =
Toxicant^
HenryLaw Nondissoc
1000
(210)
where:
Toxicantair =
Nondissoc =
gas-phase concentration of the pollutant (g/m3); and
nondissociated fraction (unitless).
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' iaw 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' few 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 (Henry1 fcaw constant = 3 .OE-9), but the water phase is 50
times as important as the air phase for benzene (Henry1 s law constant = 5.5E-3). Volatilization of
atrazine exhibits a linear relationship with wind (Figure 71) in contrast to the exponential relationship
exhibited by benzene (Figure 72).
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Figure 71
Atrazine KOVol as a Function of Wind
VOLATILIZATION OF ATRAZINE
4E-05
3.5E-05
3E-05-
1 2.5E-05
0 3.5
7 10.5 14 17.5 21 24.5 28
WIND (m/s)
Figure 72
Benzene KOVol as a Function of Wind
VOLATILIZATION OF BENZENE
3 6
9 12 15 18 21 24 27 30
WIND (m/s)
AQUATOX
Schwarzenbach etal., 1993
7.6 Partition Coefficients
Although AQUATOX is a kinetic model, steady-state partition coefficients for organic
pollutants are computed in order to place constraints on competitive uptake and loss processes,
speeding up computations. They are estimated from empirical regression equations and the pollutant's
octanol-water partition coefficient.
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 is a function of the octanol-water partition coefficient (N
= 34, r = 0.93; Schwarzenbach et al. 1993):
= 1.38 KOW0*2
(211)
where:
KOMKtfrDctr = detritus-water partition coefficient (L/kg); and
KOW = octanol-water partition coefficient (unitless).
This and the following equations are extended to polar compounds, following the work of
Smejtek and Wang (1993):
KOMRefrDetr
2 Nondissoc
+ (I-Nondissoc) lonCorr 1.38 KOW0-82
(212)
where:
Nondissoc = un-ionized fraction (unitless); and
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lonCorr
correction factor for decreased sorption, generally 0.1 (unitless).
Using pentachlorophenol as a test compound, and comparing it to octanol, the influence of pH-
mediated dissociation is seen in Figure 73. This relationship is verified by comparison with the results
of Smejtek and Wang (1993) using egg membrane.
Partitioning of bioaccumulative chemicals on organic carbon in sediments in Lake Ontario, as
represented by the Oliver and Niimi (1988) data, exhibits a weak relationship with KOW (US EPA
1995, Burkhard 1998):
KOC = 25 KOW
(213)
where:
KOC =
the partition coefficient for particulate organic carbon.
Converting to organic matter and generalizing to include polar compounds, this relationship
was used in AQUATOX to represent the partitioning of chemicals between water and refractory
detritus in sediments in a validation for Lake Ontario (Park, 1999c, in Volume 3):
KOM = 13 KOW + (1 - Nondissoc) lonCorr 13 KOW (214)
However, in the general model Eq. (212) is used for refractory detrital sediments as well.
Figure 73
Refractory Detritus-water and Octanol-water
Partition Coefficients as a Function of pH.
§
1E6
1E4
1E3
1E2
1E1
i- "» & ^t~
45678
pH
-*- PCP KOM for refractory detritus
» Un-ionized PCP - octanol/water
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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 (N = 3, r2 = 1.0;) is based on a study by Koelmans et
al. (1995) using fresh algal detritus:
KOCLabPart = 23'44
(215)
The equation is generalized to polar compounds and transformed to an organic matter partition
coefficient:
KOMLabDetr = (23-44 ' KOW0'61 Nondissoc
+ (1 -Nondissoc) lonCorr 23.44 KOWQM) 0.526
(216)
where:
= partition coefficient for labile particulate organic carbon (L/kg); and
= partition coefficient for labile detritus (L/kg).
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 modelled 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 PCS, 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:
- 28-84
(217)
where:
KOC
RefrDOM
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:
KOMRefrDOM = (28.84 KOW0-67 Nondissoc
+ (1 - Nondissoc) lonCorr 28.84 KOW0-67) 0.526
(218)
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:
KOCLahDOC = 0.88 KOW (219)
which we also generalized for polar compounds and transformed:
KOMLabDOM = (0.88 KOW Nondissoc
+ (1 - Nondissoc) lonCorr 0.88 KOW) 0.526
(220)
where:
KOMLuhDOM
partition coefficient for labile dissolved organic carbon (L/kg); and
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 andNiimi (1988) and used by many
subsequent researchers, included both dissolved and DOC-complexed PCBs (a fact which they
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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 PCS model, Thomann et al. (1991) again used an operational definition of dissolved PCBs.
AQUATOX distinguishes between truly dissolved and complexed compounds; therefore, the partition
coefficients calculated by AQUATOX may be larger than those used in older studies.
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 BAF,ipili > 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:
= 0.41 + 0.91 LogKOW
(221)
where:
a = partition coefficient between algae and water (L/kg).
Rearranging and extending to hydrophilic and ionized compounds:
BCFAlga = 2.57 KOW0-91 Nondissoc
+ (1 -Nondissoc) lonCorr 2.57 KOW0-91
(222)
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 74). 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 (Bjork 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).
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The influence of substrate polarity is evident in Figure 75, 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 substrates, such as
refractory detritus. The relative importance of the substrates for binding is also demonstrated quite
clearly.
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:
log(KBMacro) = 0.98 LogKOW - 2.24 (223)
Again, rearranging and extending to hydrophilic and ionized compounds:
KBMacro = 0.00575 KOWOSS (Nondissoc + 0.2)
For the invertebrate bioconcentration factor, the following empirical equation is used, based
on 7 chemicals v/ithLogKOWs ranging from 3.3 to 6.2 and bioconcentration factors forDaphniapulex
(r2 = 0.85; Southworth et al., 1978; see also Lyman et al., 1982), converted to dry weight:
loz(KBImertebrate) = (0.7520 LogKOW - 0.4362) WetToDry
(225)
where:
^*"^ invertebrate
WetToDry
partition coefficient between invertebrates and water (L/kg); and
wet to dry conversion factor (unitless, default = 5).
Extending and generalizing to ionized compounds:
KB
Invertebrate
= 0.3663 KOW°-7520 (Nondissoc + 0.01)
Figure 74
.Partitioning to Various Types of Organic
Matter as a Function of KOW
1E10
1E9-
1E8
s 1E7'
0 1E6
* 1E5
1E4
, , ^ . .
cr.'....;.«-s,j5
1E3:=£BS...
1E21
3 4
i
j
i
"^'
.."^2,
\
5
j 1
. ..^
~~,~* ...;^.^
'>
r.......
.."^pfdg^-
£*£*-*' -|
\
L
!
tr^.
^-. ...
zs&
^"*
6 7.8 9
Log KOW
humic acids -- algae
- exudate
»- algal detritus - refr. detritus -sediments
Figure 75
Partitioning to Various Types of Organic
Matter as a Function of pH
humic acids --algae octanol/water
-»- exudate « algal detritus -- refr. detritus
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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:
= LiPid ' WetToDry KOW (Nondissoc + 0.01) ,
(227)
where:
'fish ~
Lipid =
WetToDry
partition coefficient between whole fish and water (L/kg);
fraction offish that is lipid (g lipid/g fish); and
wet to dry conversion factor (unitless, default = 5).
Lipid content of fish is varied depending on the potential for growth as predicted by the
bioenergetics equations; the initial lipid values for the species are given. 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 76):
(l - (> (.-Depuration
BCF
RA
Fish
.(228)
where:
TElapsed
Depuration =
O
UJ
O
O
8
ca
quasi-equilibrium bioconcentration factor for fish (L/kg);
time elapsed since fish was first exposed (d); and
clearance, which may include biotransformation, see (258) (1/d).
Figure 76
Bioconcentration Factor for Fish
as a Function of Time and log KOW
1E3
0 200 400 600 800 1000 1200
DAY
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The concentration in each carrier is given by:
PPBt =
ToxStatel
CarrierStatei
Ie6
(229)
where:
PPBi
ToxStatei
CarrierState
Ie6
concentration of chemical in carrier i (jj,g/kg);
mass of chemical in carrier i (ug/L);
biomass of carrier (mg/L); and
conversion factor (mg/kg).
7.7 Nonequilibrium Kinetics
Often there is 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). Although 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), it is often impossible to determine steady-state potential due to changes hi
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 Sedimented Detritus
Partitioning to sediments 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. This applies to suspended detritus compartments
as well. Because of the need to represent sorption and desorption separately in detritus, kinetic
formulations are used (Thomann and Mueller, 1987), with provision for ionization:
Sorption = klD fr Toxicant
'Water
Diffl
Carrier
(Nondissoc + 0.01)
Org2C Detr le-6
(230)
Desorption = k2Detr Diff2Carrler ToxicantDetr
(231)
where:
Sorption
klr
' Den-
of sorption to given detritus compartment ([0,g/L-d);
sorption rate constant (L/kg-d);
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Nondissoc
ToxicantWater
Org2C
Detr
le-6
Desorption
Toxicant
Delr
fraction not ionized (unitless);
concentration of toxicant in water (jJ-g/L);
factor to normalize rate constant for given carrier (detritus compartment
in this case) based on all competing uptake rates (unitless);
factor to normalize loss rates (unitless);
conversion factor for organic matter to carbon (= 0.526 g C/g organic
matter);
mass of each of the detritus compartments per unit volume (mg/L);
units conversion (kg/mg);
rate of desorption from given sediment detritus compartment (jlg/L-d);
desorption rate constant (1/d); and
mass of toxicant in each of the detritus compartments (|J.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 Diffl factor is computed for
each direct uptake process, including sorption to detritus and algae, uptake by macrophytes, and uptake
across animals' gills:
Dffl
RateDiff,
Carrier
Carrier
£, RateDiff
Carrier
(232)
RateDiffCarfier = Gradientl
Carrier
kl
(233)
Gradientl
Carrier
Toxicantwater kpcarrier - PPB.
Carrier
Toxicant,
Water
kpl
Carrier
(234)
where:
1 Carrier'
RateDifflCarrler = maximum rate constant for uptake given the concentration gradient
(L/kg-d);
Gradient lrn~,,, = gradient between potential and actual concentrations of toxicant in
each carrier (unitless);
partition coefficient or bioconcentration factor for each carrier (L/kg);
concentration of toxicant in each carrier ([Ig/kg).
Likewise, the loss rate constants are normalized; the equations parallel those for uptake, with
the gradient being reversed:
,7-24
-------
AOUATOX TECHNICAL DOCUMENTATION
CHAPTER?
RateDiff2(
Carrier
Carrier
Carrier
(235)
RateDtff2Carrier = Gradient2Carrier k2
(236)
Gradient2
*PCarrJ
Carrier,
PPB
Carrier
(237)
where:
RateDiff2Cm.rie,.= maximum rate constant for loss given the concentration gradient
(L/kg-d); and
Gradient2Carrter = gradient between actual and potential concentrations of toxicant in
each carrier (unitless).
Desorption of the nonlabile or slow compartment 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 (r2 = 0.87):
~ 0.03 24 KPSed (238)
k2 ^ '
So k2 is taken to be:
k2 =
1.39
KPSed
(239)
where:
KPSed
24
detritus-water partition coefficient (L/kg, see Eq. (212)); and
conversion from hours to days.
The nonlabile compartment may be involved in 40 to 90% of the sorption so, as a
simplification, fast desorption of the labile compartment is ignored. This compensates in part for the
fact that AQUATOX models the top layer of bottom sediments as if it were in close contact with the
overlying water column (interstitial water is not modeled at this time).
The sorption rate constant kl is set to 1200 L/kg-d, representing the very fast labile sorption
of most chemicals.
7-25
-------
AQUATOX TECHNICAL DOCUMENTATION
CHAPTER 7
Bioconcentration 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 77, Figure
78):
MacroUptake = kl Difflplant Toxicant
'Water
Plant
le-6
(240)
Depuration
Plant
plmt
Diff2
plant
(241)
kl =
0.0020 +
500
KOW Nondissoc
(242)
k2 =
1
1.58 + 0.000015 KOW Nondissoc
(243)
where:
MacroUptake =
DepurationPlm =
StVarPlant
le-6
Toxicantplml =
kl
k2
DifflPlml
KOW
Nondissoc
uptake of toxicant by plant (|lg/L-d);
clearance of toxicant from plant ((J,g/L-d);
biomass of given plant (mg/L);
units conversion (kg/mg);
mass of toxicant in plant (|J.g/L);
sorption rate constant (L/kg-d);
elimination rate constant (1/d);
factor to normalize uptake rates (unitless);
factor to normalize loss rates (unitless);
octanol-water partition coefficient (unitless); and
fraction of un-ionized toxicant (unitless).
7-26
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AOUATOX TECHNICAL DOCUMENTATION
CHAPTER 7
Figure 77
Uptake Rate Constant for Macrophytes
(after Gobasetal., 1991)
Figure 78
Elimination Rate Constant for Macrophytes
(after Gobas et al., 1991)
500
400
300
:*:
200
100
r' !
.. . .,....
; ! "
|
iK
,
.r. J. -| -
o
0 2 4 6 8 10
Log KOW
Predicted » Observed
4 6
Log KOW
Predicted - Observed
AlgaeThere 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 m
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 constrained by
competitive uptake by other compartments:
AlgalUptake = kl Michaelis Diffl ToxState Carrier le-6 (244)
where:
AlgalUptake = rate of sorption by algae ((J,g/L-d);
k] = uptake rate constant (L/kg-d), see (245);
Michaelis = Michaelis-Menton construct for nonlinear uptake (unitless), see (246);
Diffl = factor to normalize uptake rates (unitless), see (232);
ToxState = concentration of dissolved toxicant (|0,g/L);
Carrier = biomass of algal compartment (mg/L); and
le-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
79):
7-27
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AQUATOX TECHNICAL DOCUMENTATION
CHAPTER 7
kl =
1.8E-6 + \I(KOW Nondissoc)
(245)
Because size-dependent passive transport is indicated (Sijm et al., 1998), uptake byperiphyton
is set arbitrarily at ten percent of that for phytoplankton.
In order to represent saturation kinetics, Michaelis is computed as:
BCF ToxState - PPB,
Michaelis = ^21
BCFAisae ToxState
(246)
where:
BCF.
PPB
Algae
'Algae
steady-state bioconcentration factor for algae (L/kg), see (222); and
concentration of toxicant in algae (mg/kg).
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:
Depuration =
State =
k2
Depuration = k2 State
elimination of toxicant (|J,g/L-d);
concentration of toxicant associated with alga (|J.g/L); and
elimination rate constant (1/d).
(247)
Based in part on Skoglund et al. (1996}, but ignoring surface sorption and recognizing that
growth dilution is explicit in AQUATOX, the elimination rate constant (Figure 80) is computed as:
kl
KOW (248)
k2 =
Aside from obvious structural differences, algae may have very high lipid content (20% for
Chlorellasp. according to J0rgensenetal., 1979) and rnacrophytes 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.
7-28
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AOUATOX TECHNICAL DOCUMENTATION
CHAPTER 7
Figure 79
Algal Sorption Rate Constant as a Function of
Octanol-water Partition Coefficient
Figure 80
Rate of Elimination by Algae as a Function of
Octanol-water Partition Coefficient
FIT
600000
S- 500000
& 400000
^300000
^ 200000
f 100000
0
C
TO DATA OF SUM ET AL. 1998
j ""
I - -
- - i
i « '~
/.*..
"'"'" ~ \ ~
. ,__._
2 4 68 10
LOG KOW
- ObsK1 -r-PredKI
. 50.8
2 0.6
(0
|> 0.4
0.2
- -
,
,
-
i _
T\^
r\
i !\
' i
__ ' - -
j . i, -
- ; -r
! "I . .
r 1
,
- 1 : -!Vj ":
,
0 2 4 6 8 10
Log KOW
Bioaccumulation in Animals
Animals can absorb toxic organic chemicals directly from the water through their gills and
from contaminated food through their guts. Direct sorption onto the body is ignored as a simplifying
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 SorptionAn 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 Fagerstrom and Asell (1973,
1975), Weininger (1978), andThomann 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):
GillUptake = KUptake Toxicant Water DifflCarrter (249)
KUptake =
WEffTox Respiration O2Biomass
Oxygen WEffO2
(250)
7-29
-------
AQUATOX TECHNICAL DOCUMENTATION
CHAPTER 7
where:
GillUptake
KUptake
ToxicantWater
WEfJTox
Respiration
O2Biomass
Oxygen
WEffO2
uptake of toxicant by gills (|J.g/L - d);
uptake rate (1/d);
concentration of toxicant in water (|ig/L);
factor to normalize rate constant for given carrier (animal compartment
in this case) based on all competing uptake rates (unitless), see (232);
withdrawal efficiency for toxicant by gills (unitless), see (251);
respiration rate (mg biomass/L-d), see (76);
ratio of oxygen to organic matter (mg oxygen/mg biomass; generally
0.575);
concentration of dissolved oxygen (mg oxygen/L); and
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 81) to the data of McKim et al. (1985) using 750-g fish, corrected for ionization:
K LogKOW < 1.5 then
WEffTox = 0.1
If 1.5 s LogKOW> 3.0 then
WEffTox = 0.1 + Nondissoc (0.3 LogKOW - 0.45)
If 3.0 <; LogKOW z 6.0 then
WEffTox = 0.1 + Nondissoc 0.45 (2S1)
If 6.0 < LogKOW < 8.0 then
WEffTox = 0.1 + Nondissoc (0.45 - 0.23 (LogKOW - 6.0))
If LogKOW ;> 8.0 then
WEffTox = 0.1
where:
LogKOW
Nondissoc =
log octanol-water partition coefficient (unitless); and
fraction of toxicant that is un-ionized (unitless), see (188).
7-30
-------
AOUATOX TECHNICAL DOCUMENTATION
CHAPTER 7
Figure 81
Piece-wise Fit to Observed Toxicant Uptake Data;
Modified from McKim et al., 1985
80|
1
z
ui
UJ60
!20-
I
345
LOG KOW
6 7 S
lonization decreases the uptake efficiency (Figure 82). 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.
Figure 82
The Effect of Differing Fractions of Un-ionized
Chemical on Uptake Efficiency
4 6
Log KOW
Dietary UptakeHydrophobic chemicals usually bioaccumulate 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):
7-31
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AQUATOX TECHNICAL DOCUMENTATION
CHAPTER 7
DietUptakeprey = KDprey- PPBPrey- le-6
(252)
KDprey = GutEffTox- Ingestionprey
(253)
where:
DietUptakePrey =
KD,
PPB,
Prey
Prev
le-6
GutEffTox
uptake of toxicant from given prey (|lg toxicant/I/d);
dietary uptake rate for given prey (mg prey/I/d);
concentration of toxicant in given prey (|J,g toxicant/kg prey);
units conversion (kg/mg);
efficiency of sorption of toxicant from gut (unitless); and
ingestion of given prey (mg prey/L'd), see (68).
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 LogKOW4.5 and 7.5 (Figure 83); this is to be expected because the
digestive system has evolved to assimilate a wide variety of organic molecules. Therefore, the mean
value of 0.63 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 0.90 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
0.3 5 is used for invertebrates in AQUATOX.
Figure 83
GutEffTox Constant Based on Mean Value for Data
from Gobas etal., 1993
>ietary Absorption Efficiency
P o
K) P . -si
3 Ol Ol Ol -J-
I-
1
" " ' ' H
B "=..'.
\
- »-
m
. . .
,...,.,.
! ! ,^
| !
'
! -.
. a" '
!'.
4.5 5 5.5 6 6.5 7 7.5
Log KOW
» Guppies m Goldfish Mean = 0.63
7-32
-------
CHAPTER?
sM^s ^ver, because biotransformation is not modeled explicitly, this is treated as
depuration for purposes of tracking the transfer of toxicant.
For purposes of estimatingelimin^^
assuming an aUometric relationship between respiration and the weight of the animal (Thomann,
1989):
kl * 1000 WetWr02 WEffTox <2S4>
where:
uptake rate constant (L/kg-d);
mean wet weight of organism (g);
units conversion (g/kg);
withdrawal efficiency for toxicant by gills, see Eq. (251) (umtless).
partition coefficient at equilibrium and zero growth, then:
kl
kl
WetWt
1000 '
WEffTox
k2 =
KOW LipidFrac WetToDry (Nondissoc + 0.1)
(255)
where:
k2
KOW
LipidFrac
Wet2Dry
Nondissoc
elimination rate constant (1/d); and
octanol-water partition coefficient (unitless);
fraction of lipid in organism (g lipid/g organism);
wet to dry weight ratio (5); and
fraction of compound un-ionized (unitless).
This simple relationship, although weak, has been used in AQUATOX for both invertebrates
manually using as guides regression equations for Daphma:
Log k2 = -0.5688 Log KOW + 3.6445
and small fish:
Log k2 = -0.503 Log KOW + 1.45
7-33
-------
AQUATQX TECHNICAL DOCUMF.NTATTOM
Figure 84
Depuration Rate Constants for Daphnia and for 10-
g Fish; see Thomann, 1989
4 6
Log KOW
Observed Fish Estimated Fish
* Observed Invert. Estimated Invert.
Daphnia regr Sm fish regr
For any given time the clearance rate is:
= k2 TOXicant
Animal
where:
Depuration^,,,
ToxicantAnlmal
clearance rate (|lg/L-d); and
mass of toxicant in given animal (|-lg/L).
(258)
Linkages to Detrital Compartments
DefecationTox =
, PPBp . ie-6)
(259)
= (1 ~ GutEffTox) Ingestion
Pred, Prey
(260)
where:
DefecationTox
rate of transfer of toxicant due to defecation (|ig/L-d);
7-34 .
-------
AQUATOX TECHNICAL DOCUMENTATION
CHAPTER?
KEgestPredi ,,rey
PPBPrev
1 e-6
GutEfjTox
Ingestionpm,:Pl.ey
fecal egestion rate for given prey by given predator (mg
prey/L-d);
concentration of toxicant 'in given prey (jig/kg);
units conversion (kg/mg);
efficiency of sorption of toxicant from gut (unitless); and
rate of ingestion of given prey by given predator (mg/I/d), see
(68).
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:
MortTox = £ (MortalityOrg PPBOrg le-6) (261)
where:
MortTox
Mortality0rs
PPB0rg
le-6
rate of transfer of toxicant due to mortality Qig/L-d);
rate of mortality of given organism (mg/I/d), see(80);
concentration of toxicant in given organism (jig/kg); and
units conversion (kg/mg).
7-35
-------
-------
AOUATOX TECHNICAL DOCUMENTATION
CHAPTER 8
8. ECOTOXICOLOGY
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
discussionbecause of the availability of excellent data. The same principles apply to organic toxicants
and to both plants and animals.
Based on the Mancini (1983) model, the lethal internal concentration of a toxicant can be
expressed as (Crommentuijn et al. (1994):
LCInfinite
LethalConc =
-i _ e - K2 TElapsed
(262)
where:
LethalConc
LCInfinite
k2
TElapsed
tissue-based concentration of toxicant that causes mortality (ppb
or Jig/kg);
ultimate internal lethal toxicant concentration after an infinitely
long exposure time (ppb);
elimination rate constant (1/d); and
period of exposure (d).
Figure 85
Lethal Concentration of MeHg hi Brook Trout as a
Function of Time; two data points from McKim et al., 1976
k2 = 9.5E-4d, LC50lnf =
700
& 600
£^500
f|400
o g 300
1&200
3 100 -
0
-_
. _i_
i _
\
i_
-
...
36-hour
\|
yK;-
^
..fir..
X:
.JS
....
...
I
L I
--.
~:U-L
_
2370 ppb
i
41.
-
-
1EO 1E1 1E2
DAYS
!
!
i
-
...
1E3 1E"
LethalConcHg calc LethalConcHg obs
,-1
-------
AQUATOX TECHNICAL DOCUMENTATION
CHAPTER 8
The model estimates k2, see (242), (248), and (255), 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 based on the observed half-life:
k2 =
0.693
'1/2
(263)
where:
where:
t% = observed half-life.
Exposure is limited to the lifetime of the organism:
If TElapsed > LifeSpan Then TElapsed = LifeSpan
LifeSpan = user-defined mean lifetime for given organism (d).
Based on an estimate of tune to reach equilibrium (Connell and Hawker, 1988),
if TElapsed >
(264)
k2
then
where:
LethalConc = LCInfinite
LCInfinite can be computed by a rearrangement of Eq. (262).
LCInfinite = LethalConc (l - e ~k2' obsTEiapsed}
ObsTElapsed = exposure time in toxicity determination (h).
(265)
(266)
The internal lethal concentration for a given period of exposure can be computed from reported
acute toxicity data based on the simple relationship suggested by an algorithm in the FGETS model
(Suarez and Barber, 1992):
LethalConc = BCF LC50
(267)
where:
BCF
LC50
bioconcentration factor (L/kg), see (222), (228); and
concentration of toxicant in water that causes 50% mortality (|J,g/L).
8-2
-------
AQUATOX TECHNICAL DOCUMENTATION
CHAPTER 8
A given LC50 can be provided by the user, or the user may choose to have the model estimate the
LC50 based on regressions from other species for which there are data (Mayer and Ellersieck, 1986,
Surer etal., 1986).
The fraction killed by a given internal concentration of toxicant and the time-dependent
LCInfinite is best estimated using the cumulative form of the Weibull distribution (Mackay et al.,
1992):
^.,».^^
(
-.
l
where:
CumFracKilled =
PPB
Shape =
cumulative fraction of organisms killed,
internal concentration of toxicant (jig/kg); and
parameter expressing variability in toxic response (unitless).
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 Shape parameter is important because it controls the spread of mortality. The larger the
value, the greater the distribution of mortality over toxicant concentrations and time. Methyl mercury
toxicity exhibits a rapid response over a short time period, so Shape has a value of about 0.1 (Figure
86). 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. Note that when the internal concentration equals the lethal concentration the
Weibull equation predicts 63% mortality.
i-3
-------
AQUATOX TECHNICAL DOCUMENTATION
CHAPTER 8
Figure 86
The Effect of Shape on the Variability of Response to a Given
Internal Concentration of MeHg
Hgppb = LethalConcHg for Day 112
100
200 300
DAYS
400
500
0.11 0.33 -»- 0.66 -*- 0.99
acute mortality accounts for the population already exposed and subject only to increased exposure,
and the newly exposed population that is more vulnerable. Mortality is computed as:
Poisoned = Resistant FracKilled + Nonresistant CumFracKilled (269)
where:
Poisoned
Resistant
FracKilled
Nonresistant
8.2 Chronic Toxicity
biomass of given organisms killed by exposure to toxicant at given time
(mg/L);
biomass not killed by previous exposure (mg/L);
fraction killed in excess of the previous fraction (unitless); and
biomass not previously exposed; the biomass in excess of the resistant
biomass (mg/L).
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. The user supplies observed EC50 values, which are used
to compute AFs. For example:
8-4
-------
AOUATOX TECHNICAL DOCUMENTATION
CHAPTER 8
AFGrowth =
ECSOGrowth
LC50
(270)
where:
ECSOGrowth =
AFGrowth
LC50
external concentration of toxicant at which there is a 50% reduction in
growth ([ig/L);
chronic to acute ratio for growth; and
external concentration of toxicant at which 50% of population is killed
(Hg/L).
If the user enters an observed EC50 value, the model provides the option of applying the resulting AF
to estimate ECSOs for other organisms. The computations for AFPhoto and AFRepro are similar.
Similar to computation of acute toxiciry 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:
FracPhotO =
PPB
_
AFPhoto
(271)
RedGrowth =
- e
PPB
JLethalCanc AFGrowth ]
(273)
RedRepro
.,-.-1
PPB Wffl«p»
f,ethalConc AFRepro]
(272)
where:
FracPhoto =
RedGrowth =
reduction factor for effect of toxicant on photosynthesis (unitless);
factor for reduced growth in animals (unitless);
-5
-------
AQUATOX TECHNICAL DOCUMENTATION
CHAPTER 8
RedRepro
PPB
LethalConc
AFPhoto
AFGrowth
AFRepro
Shape
factor for reduced reproduction in animals (unitless);
internal concentration of toxicant (|lg/kg);
tissue-based concentration of toxicant that causes mortality (|J,g/kg);
chronic to acute ratio for photosynthesis (unitless, default of 0.10);
chronic to acute ratio for growth in animals (unitless, default of 0.10);
chronic to acute ratio for reproduction in animals (unitless, default of
0.05); and
parameter expressing variability in toxic response (unitless, default of
0.33).
The reduction factor for photosynthesis, FracPhoto, enters into the photosynthesis equation
(Eq. (26)), and it also appears in the equation for the acceleration of sinking of phytoplankton due to
stress (Eq. (58)).
The variable for reduced growth, RedGrowth, is arbitrarily split between two processes,
ingestion (Eq. (68)), where it reduces consumption by 20%:
ToxReduction = 1 - (0.2 RedGrowth) (274)
and egestion (Eq. (73)), where it increases the amount of food that is not assimilated by 80%:
IncrEgest = (1 - EgestCoeffprey>pred) 0.8 RedGrowth
(275)
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 (Eq. (84)) beyond what would occur otherwise:
IncrMort = (1 - GMorf) RedRepro (276)
By modeling chronic and acute effects, AQUATOX makes the link between chemical fate and
the functioning of the aquatic ecosystema pioneering approach that has been refined over the past
twelve years, following the first publications (Park et al., 1988; Park, 1990).
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AOUATOX TECHNICAL DOCUMENTATION
APPENDIX A
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
Adsorption
Aerobic
Algae
Allochthonous
Algal bloom
Alluvial
Alluvium
Ambient
Anaerobic
Anoxic
Aphotic
Assimilation
Autochthonous
Benthic
Benthos
Biodegradable
Biochemical oxygen
demand (BOD)
Biomagnification
Biomass
Biota
Chlorophyll
Colloid
Consumer
Copepods
Crustacean
Decomposers
Detritus
Diatom
Diurnal
nonliving, pertaining to physico-chemical factors only
the adherence of substances to the surfaces of bodies with which they are in
contact
living, acting, or occurring in the presence of oxygen
any of a group of chlorophyll-bearing aquatic plants with no true leaves,
stems, or roots
material derived from outside a habitat or environment under consideration
rapid and flourishing growth of algae
of alluvium
sediments deposited by running water
surrounding on all sides
capable of living or acting in the absence of oxygen
pertaining to conditions of oxygen deficiency
below the level of light penetration in water
transformation of absorbed nutrients into living matter
material derived from within a habitat, such as through plant growth
pertaining to the bottom of a water body; pertaining to organisms that live on
the bottom
those organisms that live on the bottom of a body of water
can be broken down into simple inorganic substances by the action of
decomposers (bacteria and fungi)
the amount of oxygen required to decompose a given amount of organic
matter
the step by step concentration of chemicals in successive levels of a food
chain or food web
the total weight of matter incorporated into (living and/or dead) organisms
the fauna and flora of a habitat or region
the green, photosynthetic pigments of plants
a dispersion of particles larger than small molecules and that do not settle out
of suspension
an organism that consumes another
a large subclass of usually minute, mostly free-swimming aquatic crustaceans
a large class of arthropods that bear a horny shell
bacteria and fungi that break down organic detritus . . .
dead organic matter
any of class of minute algae with cases of silica
pertaining to daily occurrence
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AQUATQX TECHNICAL DOCUMENTATION
APPENDIX A
Dynamic
equilibrium
Ecology
Ecosystem
Emergent
Environment
Epilimnion
Epiphytes
Equilibrium
Euphotic
Eutrophic
Fauna
Flood plain
Flora
Fluvial
Food chain
Food web
Forage fish
Habitat
Humic
Hydrodynamics
Hypolimnion
Influent
Inorganic
Invertebrate
Limiting factor
Limnetic zone
Limnology
Littoral zone
Macrofauna
Macrophytes
Nutrients
Omnivorous
Organic chemical
a state of relative balance between processes having opposite effects
the study of the interrelationships of organisms with and within their
environment
a biotic community and its (living and nonliving) environment considered
together
aquatic plants, usually rooted, which have portions above water for part of
their life cycle
the sum total of all the external conditions that act on an organism
the well mixed surficial layer of a lake; above the hypolimnion
plants that grow on other plants, but are not parasitic
a steady state in a dynamic system, with outflow balancing inflow
pertaining to the upper layers of water in which sufficient light penetrates to
permit growth of plants
aquatic systems with high nutrient input and high plant growth
the animals of a habitat or region
that part of a river valley that is covered in periods of high (flood) water
plants of a habitat or region
pertaining to a stream
animals linked by linear predator-prey relationships with plants or detritus at
the base
similar to food chain, but implies cross connections
fish eaten by other fish
the environment in which a population of plants or animals occurs
pertaining to the partial decomposition of leaves and other plant material
the study of the movement of water
the lower layer of a stratified water body, below the well mixed zone
anything flowing into a water body
pertaining to matter that is neither living nor immediately derived from living
matter
animals lacking a backbone
an environmental factor that limits the growth of an organism; the factor that
is closest to the physiological limits of tolerance of that organism
the open water zone of a lake or pond from the surface to the depth of
effective light penetration
the study of inland waters
the shoreward zone of a water body in which the light penetrates to the
bottom, thus usually supporting rooted aquatic plants
animals visible to the naked eye
large (non-microscopic), usually rooted, aquatic plants
chemical elements essential to life
feeding on a variety of organisms and organic detritus
compounds containing carbon;
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AOUATOX TECHNICAL DOCUMENTATION
APPENDIX A
Overturn
Oxygen depletion
Parameter
Pelagic zone
Periphyton
Oxidation
Photic zone
Phytoplankton
Plankton
Pond
Population
Predator
Prey
Producer
Production
Productivity
Productivity,
primary
Productivity,
secondary
Reservoir
Riverine
Rough fish
Sediment
Siltation
Stratification
Substrate
Succession
Tolerance
Trophic level
Turbidity
Volatilization
Wastewater
Wetlands
the complete circulation or mixing of the upper and lower waters of a lake
when temperatures (and densities) are similar
exhaustion of oxygen by chemical or biological use
a measurable, variable quantity as distinct from a statistic
open water with no association with the bottom
community of algae and associated organisms, usually small but densely set,
closely attached to surfaces on or projecting above the bottom
a reaction between molecules, ordinarily involves gain of oxygen
the region of aquatic environments in which the intensity of light is sufficient
for photosynthesis
small, mostly microscopic algae floating in the water column
small organisms floating in the water
a small, shallow lake
a group of organisms of the same species
an organism, usually an animal, that kills and consumes other organisms
an organism killed and at least partially consumed by a predator
an organism that can synthesize organic matter using inorganic materials and
an external energy source (light or chemical)
the amount of organic material produced by biological activity
the rate of production of organic matter
the rate of production by plants
the rate of production by consumers
an artificially impounded body of water
pertaining to rivers
a non-sport fish, usually omnivorous in food habits
any mineral and/or organic matter deposited by water or air
the deposition of silt-sized and clay-sized (smaller than sand-sized) particles
division of a water body into two or more depth zones due to temperature or
density
the layer on which organisms grow; the organic substance attacked by
decomposers
the replacement of one plant assemblage with another through time
an organism's capacity to endure or adapt to unfavorable conditions
all organisms that secure their food at a common step in the food chain
condition of water resulting from suspended matter, including inorganic and
organic material and plankton
the act of passing into a gaseous state at ordinary temperatures and pressures
water derived from a municipal or industrial waste treatment plant
land saturated or nearly saturated with water for most of the year; usually
vegetated
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AQUATOX TECHNICAL DOCUMENTATION
APPENDIX A
Zooplankton t small aquatic animals, floating, usually with limited swimming capability
A-4
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AOUATOX TECHNICAL DOCUMENTATION
APPENDIXB
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, and ReminRecord, which in turn may be linked to
input forms that the user accesses through the Windows environment. Although consistency has been
a goal, some names may differ between the code and documentation
INTERNAL
ChemicalRecord
ChemName
CASRegNo
MoIWt
Solubility
Henry
pka
VPress
LogP
En
KMDegrdn
KMDegr Anaerobic
KUnCat
KAcid
KBase
PhotolysisRate
OxRateConst
KPSed
Weibull Shape
ChemlsBase
TECH DOC
Chemical Underlying
Data
N/A
N/A
MoIWt
N/A
Henry
pKa
N/A
LogKow
En
MicrobialDegrdn
KAnaerobic
KUncat
KAcidExp
KJBaseExp
KPhot
N/A
KPSed
Shape
DESCRIPTION
For each Chemical Simulated, the following
parameters are required
Chemical's Name. Used for Reference only.
CAS Registry Number. Used for Reference only.
molecular weight of pollutant
Not utilized as a parameter by the code.
Henry's law constant
acid dissociation constant
Not utilized as a parameter by the code.
log octanol-water partition coefficient
Arrhenius activation energy
rate of loss due to microbial degradation
decomposition rate at 0 g/m3 oxygen
the measured first-order reaction rate at pH 7
pseudo-first-order acid-catalyzed rate constant for a
given pH
pseudo-first-order rate constant for a given pH
direct photolysis first-order rate constant
Not utilized as a parameter by the code.
detritus-water partition coefficient
parameter expressing variability in toxic response
if the compound is a base
UNITS
N/A
N/A
(g/mol)
(ppm)
(atmm3 mol-1)
negative log
mmHg
(miitless)
(cal/mol)
(Jig/Ld)
(1/d)
(1/d)
(1/d)
(1/d)
(1/d)
(L/ mol d)
(L/kg)
(unitless)
(True/False)
B-l
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AQUATOX TECHNICAL DOCUMENTATION.
APPENDIX B
INTERNAL
SitcRccord
SiteNamc
ECocffWater
SitcLcngth
Volume
Area
ZMcan
ZMax
TempMcan
TempRange
Latitude
LightMcan
LiglitRangc
AlkCaCOS
HardCaCOS
SO4Cone
TotalDissSolids
StreamType
ChanneI_SIope
Max_ChanJDepth
ScdDepth
LininoWallArea
vlcanEvap
UseEntercdManning
Entered Manning
RcminRccord
TECH DOC
Site Underlying Data
N/A
ExtinctH2O
Length
Volume
Area
ZMean
ZMax
TempMean
TempRange
Latitude
LightMean
LightRange
N/A
N/A
N/A
N/A
Stream Type
Slope
Max_Chan_Depth
SedDepth
LimnoWallArea
VIeanEvap
vlanning
^mineralization Data
DESCRIPTION
For each Segment Simulated, the following
parameters arc required
Site's Name. Used for Reference only.
light extinction of wavelength 312.5 nm in pure water
maximum effective length for wave setup"
initial volume of site
site area
mean depth
maximum depth
mean annual temperature
annual temperature range
latitude
mean annual light intensity
annual range in light intensity
Not utilized as a parameter by the code.
Not utilized as a parameter by the code.
Not utilized as a parameter by the code.
Not utilized as a parameter by the code.
concrete channel, dredged channel, natural channel
slope of channel
depth at which flooding occurs
maximum sediment depth
area of limnocorral walls; only relevant to
limnocorral
mean annual evaporation
do not determine Manning coefficient from
streamtype
manually entered Manning coefficient.
For each simulation, the following parameters are
required
UNITS
N/A
(1/m)
(m)
(m3)
(m2)
(m)
(m)
(°C)
(°C)
(°, decimal)
(ly/d)
(ly/d)
mg/L
mg CaCO3 / L
mg/L
mg/L
Choice from
List
(m/m)
(m)
(m)
(m2)
inches / year
(true/false)
s/ml/3
B-2
-------
AOUATOX TECHNICAL DOCUMENTATION
APPENDIX B
INTERNAL
3ecayMax_Lab
Q10
TOpt
TMax
TRef
pHMin
pHMax
Org2Phosphate
Org2Ammonia
O2Biomass
O2N
KSed
PSedRelease
NSedRelease
DecayMax_Refr
ZooRecord
AnimalName
FHalfSat
CMax
BMin
Q10
TOpt
TMax
TRef
EndogResp
TECH DOC
DecayMax
NA
TOpt
TMax
NA
pHMin
pHMax
Org2Phosphate
Org2 Ammonia
O2Biomass
O2N
KSed
N/A
N/A
CoIonizeMax
Animal Underlying
Data
N/A
FHalfSat
CMax
BMin
Q10
TOpt
TMax
TRef
EndogResp
DESCRIPTION
maximum decomposition rate
-------
AQUATOX TECHNICAL DOCUMENTATION
APPENDIX B
INTERNAL
KRcsp
KExcr
PctGamete
GMort
KMort
KCap
McanWeight
FishFracLipid
LifeSpan
Animal_Type
AveDrift
AutoSpawn
SpawnDatel..3
UnlimitcdSpawning
SpawnLimit
UseAHom_C
CA
CB
UsoAllom_R
RA
RB
UseSetl
RQ
RK1
TECH DOC
KResp
KExcr
PctGamete
GMort
KMort
KCap
WetWt
LipidFrac
LifeSpan
Animal Type
Dislodge
DESCRIPTION
proportion assimilated energy lost to specific
dynamic action
proportionality constant for excretion:respiration
fraction of adult predator biomass that is in gametes
gamete mortality
intrinsic mortality rate
carrying capacity
mean wet weight of organism
fraction of lipid in organism
mean lifespan in days
Animal Type (Fish, Pelagic Invert, Benthic Invert,
Benthic Insect)
fraction of biomass subject to drift per day
Does AQUATOX calculate Spawn Dates
Automatically Entered Spawn Dates
Allow fish to spawn unlimited times each year
Number of spawns allowed for this species this year
Use Allometric Consumption Equation
Allometric Consumption Parameter
Allometric Consumption Parameter
Use Allometric Consumption Respiration
Allometric Respiration Parameter
Allometric Respiration Parameter
Use "Set 1" of Allometric Respiration Parameters
Allometric Respiration Parameter
Allometric Respiration Parameter
UNITS
(unitless)
(unitless)
(unitless)
(1/d)
(g/g'd)
(mg/L)
(g)
days
Choice from
List
fraction / day
(true/false)
(date)
(true/false)
(integer)
(true/false)
(real number)
(true/false)
(real number)
(real number)
B-4
-------
AQUATOX TECHNICAL DOCUMENTATION
APPENDIX B
INTERNAL
PlantRccord
PlantName
PlantType
LightSat
KPO4
KM
' KCarbon -
Q10
TOpt
TMax
TRef
PMax
KResp
!
KMort
EMort .
KSed
ESed ,
UptakePO4
UptakeN
ECoeffPhyto
CarryCapac
Red_StilI_Water
Macrophyte_Type
TECH DOC
Plant Underlying Data
Plant Type
LightSat '
KP
KN
KCO2
Q10 ;
TOpt
TMax
TRef
PMax
KResp
KMort '
EMort
KSed
ESed '
Uptake Phosphorus
Uptake Nitrogen
EcoeffPhyto
KCap
RedStillWater
Macrophyte Type
DESCRIPTION
For each Plant in the Simulation, the following
parameters are required
Plant's Name. Used for Reference 'only.
Plant Type: (Phytoplankton, Periphyton,
Macfophytes)
light saturation level for photosynthesis
half-saturation constant for phosphorus
half-saturation constant for nitrogen
half-saturation constant for carbon '
slope or rate of change per 1 0°C temperature change
optimum temperature
maximum temperature tolerated
adaptation temperature below which there is no
acclamation
maximum photosynthetic rate '
coefficient of proportionality btwn. excretion and
photosynthesis at optimal 1
intrinsic mortality rate
exponential factor for suboptimal1 conditions '
intrinsic settling rate
exponential settling coefficient >
fraction of photosynthate that is nutrient
fraction of photosynthate that is nutrient
attenuation coefficient for given alga
carrying capacity of periphyton
reduction in photosynthesis in absence of current
Type of macrophyte (benthic, rooted floating, free-
floating)
UNITS ' ;
N/A
Choice from
List ' ' ' '
(ly/d)
(gP/m3)
(gN/m3)
(gC/m3)
(unitless)
CO
(°C)
(°C)
(1/d)
(unitless)
(g/g'd)
(unitless) ,
(m/d)
(unitless)
(unitless)
(unitless)
(l/m-g/m3)
(g/m2)
(unitless)
Choice from
List
B-5
-------
AQUATOX TECHNICAL DOCUMENTATION
APPENDIX B
INTERNAL
AnimalToxRccord
LC50
LCSO_exp_time
K2
EC50_growth
Growth_cxp_time
EC50_repro
Rcpro_cxp_time
Ave_wet_\vt
Lipid_frac
Drift_Thresh
TPIantToxRccord
EC50_photo
EC50_oxp_time
K2
LC50
LC50_cxp_time
Lipid_frac
TChcmical
nitialCond
Loadings
TECH DOC
Animal Toxicity
Parameters
LC50
ObsTEIapsed
K2
ECSOGrowth
ObsTEIapsed
ECSORepro
ObsTEIapsed
WetWt
LipidFrac
Drift Threshold
Plant Toxicity
Parameter
EC50Photo
ObsTEIapsed
K2
LC50
ObsTEIapsed
LipidFrac
Chemical Parameters
nitial Condition
nflow Loadings
DESCRIPTION
For each Chemical Simulated, the following
parameters are required for each an
external concentration of toxicant at which 50% of
population is killed
exposure time in toxicity determination
elimination rate constant
external concentration of toxicant at which there is a
50% reduction in growth
exposure time in toxicity determination
external concentration of toxicant at which there is a
50% reduction in reprod
exposure time in toxicity determination
mean wet weight of organism
fraction of lipid in organism
concentration at which drift is initiated
For each Chemical Simulated, the following
parameters are required for each pi
external concentration of toxicant at which there is
50% reduction in photosyn
exposure time in toxicity determination
elimination rate constant
external concentration of toxicant at which 50% of
population is killed
exposure time in toxicity determination
fraction of lipid in organism
For each Chemical to be simulated, the following
aarameters are required
nitial Condition of the state variable
Daily loading as a result of the inflow of water
excluding modeled upstream r
UNITS
(H.g/L)
(h)
(1/d)
(M-g/L^
(h)
(|J.g/L)
(h)
(g)
(g lipid/g organ
(M*g/L)
(Hg/L)
(h)
(1/d)
(|ig/L)
(h)
(g lipid/g organ
M-g/L
[ig/L
B-6
-------
AQUATOX TECHNICAL DOCUMENTATION
APPENDIX B
INTERNAL
Alt_Loadings[Pointso
urce]
Alt_Loadings[Direct
Preci
Alt_Loadings[NonPoi
ntsour
Tox_Air
TRemineralize
InitialCond
Loadings
Alt_Loadings[Pointso
urce]
Alt_Loadings[Direct
Preci
AIt_Loadings[NonPoi
ntsour
TSedDetr
InitialCond
TToxicanUnitialCond
TDetritus
InitialCond
Percent_Part_IC
Percent_Refr_IC
TECH DOC
Point Source Loadings
Direct Precipitation
Loa
Non-Point Source
Loading
Gas-phase
concentration
Nutrient Parameters
Initial Condition
Inflow Loadings
Point Source Loadings
Direct Precipitation
Loa
Non-Point Source
Loading
Scd. Detritus
Parameters
Initial Condition
Toxicant Exposure
Susp & Dissolved
Detritu
Initial Condition
Percent Paniculate Init
Percent Refractory Init
DESCRIPTION
Daily loading from point sources
Daily loading from direct precipitation
Daily loading from non-point sources
For each Nutrient to be simulated, O2 and CO2,
the following parameters are re
Initial Condition of the state variable
Daily loading as a result of the inflow of water
(excluding modeled upstream r
Daily loading from point sources
Daily loading from direct precipitation
Daily loading from non-point sources
For the Labile and Refractory Sed. Detritus
compartments, the following parameters
Initial Condition of the state variable
Initial Toxicant Exposure of the state variable, for
each chemical simulated
For the Suspended and Dissolved Detritus
compartments, the following parameter
InitialCond. of susp. &diss. detritus, as organic
matter, organic carbon, or
Percent of Initial Condition that is particulate as
opposed to dissolved detri
Percent of Initial Condition that is refractory as
opposed to labile detritus
UNITS
(g/d)
(g/m2 -d)
(g/d)
(g/m3)
mg/L
mg/L
(g/d)
(g/m2 -d)
(g/d)
(g/m2)
P.g/kg
mg/L
percentage
percentage
B-7
-------
AQUATOX TECHNICAL DOCUMENTATION
APPENDIX B
INTERNAL
Loadings
Percent_Part
Percent_Refr
AlULoadings[Pointso
urce]
Percent_Part_PS
Porcent_Refr_PS
Alt_Loadings[NonPoi
ntsour
Pcrccnt_Part_NPS
Perccnt_Refr_NPS
TToxicantJnitialCond
TToxicant.Loads
TBuried Detritus
InitialCond
TToxicant.InitialCond
TPlant
InitialCond
Loadings
TToxicant.InitialCond
TToxicant.Loads
TECH DOC
Inflow Loadings
Percent Paniculate Infl
Percent Refractory
Inflo
Point Source Loadings
Percent Particulate
Poin
Percent Refractory
Point
Non-Point Source
Loading
Percent Particulate
NonP
Percent Refractory
NonPo
Toxicant Exposure
Tox Exposure of Inflow
L
Buried Detritus
Initial Condition
Toxicant Exposure
Plant Parameters
Initial Condition
Inflow Loadings
Toxicant Exposure
Tox Exposure of Inflow
L
DESCRIPTION
Daily loading as a result of the inflow of water
(excluding modeled upstream r
Daily parameter; % of loading that is particulate as
opposed to dissolved detr
Daily parameter; % of loading that is refractory as
opposed to labile detritus
Daily loading from point sources
Daily parameter; % of loading that is particulate as
opposed to dissolved detr
Daily parameter; % of loading that is refractory as
opposed to labile detritus
Daily loading from non-point sources
Daily parameter; % of loading that is particulate as
opposed to dissolved detr
Daily parameter; % of loading that is refractory as '
opposed to labile detritus
Initial Toxicant Exposure of the state variable
Daily parameter; Tox. Exposure of each type of
inflowing detritus, for each ch '
For Each Layer of Buried Detritus, the following
parameters are required
Initial Condition of the state variable
Initial Toxicant Exposure of the state variable, for
each chemical simulated
-. . . . .. -.
For each plant type simulated, the following
parameters are required
Initial Condition of the state variable
Daily loading as a result of the inflow of water
(excluding modeled upstream r
Initial Toxicant Exposure of the state variable
Daily parameter; Tox. Exposure of the Inflow
Loadings, for each chemical simul
UNITS
mg/L
percentage
percentage
(g/d)
percentage
percentage
(g/d)
percentage
percentage
Hi/kg
Hg/kg
(g/m2)
Hg/kg.
mg/L
mg/L
|J.g/kg
H-g/kg
B-i
-------
AQUATOX TECHNICAL DOCUMENTATION
APPENDIX B
INTERNAL
TAnimal
InitialCond
Loadings
TToxicant.InitialCond
TToxicant.Loads
TrophlntArray.Pref
TrophlntArray-ECoeff
TVoIume
InitialCond
InflowLoad
DischargeLoad
-,:
Site Characteristics ,
Temperature
Wind
Light .
Photoperiod
pH
Physical Geometry,
TECH DOC
Animal Parameters
Initial Condition
Inflow Loadings
Toxicant Exposure
Tox Exposure of Inflow
L
Prefprey, pred
EgestCoeff
Volume Parameters
Initial Condition
Inflow of Water
Discharge of Water
Site Characteristics
Temperature
Wind
Light
Photoperiod
pH
Physical Geometry
DESCRIPTION
For each animal type simulated, the following
parameters are required
Initial Condition of the state variable
Daily loading as a result of the inflow of water
(excluding modeled upstream r
Initial Toxicant Exposure of the state variable
Daily parameter; toxic exposure of the Inflow
Loadings, for each chemical simulated
for each prey-type ingested, a preference value within
the matrix of preferences
for each prey-type ingested, the fraction of ingested
prey that is egested
For each segment simulated, the following water
flow parameters are required
Initial Condition of the state variable
Inflow of water
Discharge of water
The following characteristics are required
Daily parameter; temperature of the segment;
Optional, can use annual mean
Daily parameter; wind velocity 10 m above the water;
Optional, default time se
Daily parameter; avg. light intensity at segment top;
Optional, can use annual
Fraction of day with daylight; Optional, can be
calculated from latitude
Daily parameter; pH of the segment.
For each segment simulated, the following physical
geometry parameters are required
UNITS '
mg/L
mg/L
Hg/kg
M.g/kg
(unitless).
(unitless)
(m3)
(m3 /d)
(m3 /d)
(°C)
(m/s)
(ly/d)
(hr/d)
(pH)
B-9
-------
AQUATOX TECHNICAL DOCUMENTATION
APPENDIX B
INTERNAL
Thickness
Surface Area
TECH DOC
Segment Thickness
Surface Area
DESCRIPTION
Thickness of the segment
Surface area of the segment
UNITS
m
(m2)
B-10
AU.S. GOVERNMENT PRINTING OFFICE:2000-523-233/95155
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