&EPA
United States
Environmental Protection
Agency
Office of Water (4305)
EPA-823-R-04-002
January 2004
AQUATOX (RELEASE 2)
MODELING ENVIRONMENTAL FATE
AND ECOLOGICAL EFFECTS IN
AQUATIC ECOSYSTEMS
VOLUME 2: TECHNICAL DOCUMENTATION
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AQUATOX (RELEASE 2)
MODELING ENVIRONMENTAL FATE
AND ECOLOGICAL EFFECTS
IN AQUATIC ECOSYSTEMS
VOLUME 2: TECHNICAL DOCUMENTATION
Richard A. Park
and
Jonathan S. Clough
JANUARY 2004
U.S. ENVIRONMENTAL PROTECTION AGENCY
OFFICE OF WATER
OFFICE OF SCIENCE AND TECHNOLOGY (MAIL CODE 4305T)
WASHINGTON DC 20460
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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 an aquatic ecosystem simulation model. It is not intended to serve as
guidance or regulation, nor is the use of this model in any way required. This document cannot
impose legally binding requirements on EPA, States, Tribes, or the regulated community.
ACKNOWLEDGMENTS
This model has been developed and documented by Dr. Richard A. Park of Eco Modeling
and Jonathan S. Clough of Warren Pinnacle Consulting, Inc. under subcontract to Eco Modeling.
It was funded originally with Federal funds from the U.S. Environmental Protection Agency, Office
of Science and Technology under contract number 68-C4-0051 to The Cadmus Group, Inc.
Significant enhancements to the model and revision of the documentation has been performed under
subcontract to AQUA TERRA Consultants, Anthony Donigian, Work Assignment Manager, under
EPA Contracts 68-C-98-010 and
68-C-01-0037.
Additional Federal funding for program development has come from the U. S. Environmental
Protection Agency, Office of Pollution Prevention and Toxics, through Purchase Orders 7W-0227-
NASA and 7W-4330-NALX to Eco Modeling and a Work Assignment to AQUA TERRA
Consultants.
The assistance, advice, and comments of the EPA work assignment manager, Marjorie
Coombs Wellman of the Health Protection and Modeling Branch, Office of Science and Technology
have been of great value in developing this model and preparing this report. Further technical and
financial support from Donald Rodier of the Office of Pollution Prevention and Toxics and David
A. Mauriello, and Rufus Morison formerly of that Office, is gratefully acknowledged. Marietta
Echeverria, Office of Pesticide Program, contributed to the integrity of the model through her careful
analysis and comparison with EXAMS. The model underwent independent peer review by Donald
DeAngelis, Robert Pastorok, and Frieda Taub, whose diligence is greatly appreciated.
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TABLE OF CONTENTS
TABLE OF CONTENTS
PREFACE
1 INTRODUCTION
1.1 Overview
1.2 Background
1.3 What's New
Enhanced Scientific Capabilities
Additional User Interfaces
Corrected Errors
2 SIMULATION MODELING
2.1 Temporal and Spatial Resolution and Numerical Stability
2.2 Uncertainty Analysis
3 PHYSICAL CHARACTERISTICS
3.1 Morphometry
Volume
Bathymetric Approximations
Habitat Disaggregation
3.2 Velocity
3.3 Washout
3.4 Stratification and Mixing
3.5 Temperature
3.6 Light
3.7 Wind
4 BIOTA
4.1 Algae
Light Limitation
Nutrient Limitation
Current Limitation
Adjustment for Suboptimal Temperature
Algal Respiration
Photorespiration and Excretion
Algal Mortality
Sinking
Washout and Sloughing
Detrital Accumulation in Periphyton
Chlorophyll a
4.2 Macrophytes
4.3 Animals
in
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Consumption, Defecation, and Predation
Respiration
Excretion
Nonpredatory Mortality
Gamete Loss and Recruitment
Washout, Drift, and Entrainment
Vertical Migration
Promotion
5 REMINERALIZATION
5.1 Detritus
Detrital Formation
Colonization
Decomposition
Sedimentation and Resuspension
5.2 Nitrogen
Assimilation
Nitrification and Denitrification
5.3 Phosphorus
5.4 Dissolved Oxygen
5.5 Inorganic Carbon
6 INORGANIC SEDIMENTS
6.1 Deposition and Scour of Silt and Clay
6.2 Scour, Deposition and Transport of Sand
6.3 Suspended Inorganic Sediments in Standing Water
7 TOXIC ORGANIC CHEMICALS
7.1 lonization
7.2 Hydrolysis
7.3 Photolysis
7.4 Microbial Degradation
7.5 Volatilization
7.6 Partition Coefficients
Detritus
Algae
Macrophytes
Invertebrates
Fish
7.7 Nonequilibrium Kinetics
Sorption and Desorption to Detritus
Bioaccumulation in Macrophytes and Algae . . .
Macrophytes
Algae
Bioaccumulation in Animals
IV
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Gill Sorption
Dietary Uptake
Elimination
Biotransformation
Linkages to Detrital Compartments
8 ECOTOXICOLOGY
8.1 Acute Toxicity of Compounds
8.2 Chronic Toxicity
REFERENCES
APPENDIX A. GLOSSARY OF TERMS
APPENDIX B. USER-SUPPLIED PARAMETERS AND DATA
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VI
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PREFACE
The Clean Water Act formally the Federal Water Pollution Control Act Amendments of
1972 (Public Law 92-50), and subsequent amendments in 1977,1979,1980,1981,1983, and 1987
calls for the identification, control, and prevention of pollution of the nation's waters. In the
National Water Quality Inventory: 2000 Report (US EPA, 2002), 40 percent of assessed river
lengths and 45 percent of assessed lake areas were impaired for one or more of their designated uses.
The most commonly reported causes of impairment in rivers and streams were pathogens, siltation,
habitat alterations, oxygen-depleting substances, nutrients, thermal modifications, metals (primarily
mercury), and flow alterations; in lakes and reservoirs the primary causes included nutrients,
metals, siltation, total dissolved solids, oxygen-depleting substances, excess algal growth and
pesticides. The most commonly reported sources of impairment were agriculture, hydrologic
modifications, habitat modification, urban runoff/storm sewers, forestry, nonpoint sources,
municipal point sources, atmospheric deposition, resource extraction and land disposal. There were
2838 fish consumption advisories, which may include outright bans, in 48 States, the District of
Columbia and American Samoa. Of these 2838 advisories, 2242 were due to mercury, with the
rest due to PCBs, chlordane, dioxin, and DDT (US EPA, 2002). States are not required to report fish
kills for the National Inventory; however, available information for 1992 indicated 1620 incidents
in 43 States, of which 930 were attributed to pollution, particularly oxygen-depleting substances,
pesticides, manure, oil and gas, chlorine, and ammonia.
New approaches and tools, including appropriate technical guidance documents, are needed
to facilitate ecosystem analyses of watersheds as required by the Clean Water Act. In particular,
there is a pressing need for refinement and release of an ecological risk methodology that addresses
the direct, indirect, and synergistic effects of nutrients, metals, toxic organic chemicals, and 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 organic chemicals. The model also
represents conventional pollutants, such as nutrients and sediments, and considers several trophic
levels, including attached and planktonic algae, submerged aquatic vegetation, several types of
invertebrates, and several types offish. It has been implemented for streams, small rivers, ponds,
lakes, and reservoirs.
AQUATOX Release 2 is described in these documents. Volume 1: User's Manual
describes the usage of the model. Because the model is menu-driven and runs under Microsoft
Windows on microcomputers, it is user-friendly and little guidance is required. Volume 2:
Technical Documentation provides detailed documentation of the concepts and constructs of the
model so that its suitability for given applications can be determined. Volume 3: BASINS
AQUATOX Extension Documentation describes how AQUATOX can be run with site
characteristics and loadings input directly from the BASINS data layers or from the HSPF and
SWAT watershed models.
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AQUATOX (RELEASE 2) 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. 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
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 interdependences
in the aquatic ecosystem are important aspects that AQUATOX represents and that cannot be
addressed by a population model.
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION
CHAPTER 1
Figure 1. Conceptual model of ecosystem represented by AQUATOX
Loadings
Light
Atmos. Dep.
Temperature
Wind
Inflow
Plants
Phytoplankton
Periphyton
Macrophytes
Outflow
Inorganic Sediment
Any ecosystem model consists of multiple components requiring input data. These are the
abiotic and biotic state variables or compartments being simulated In AQUATOX the
biotic state variables may represent trophic levels, guilds, and/or species. The model can represent
a food web with both detrital- and algal-based trophic linkages. Closely related are driving
variables, such as temperature, light, and nutrient loadings, which force the system to behave in
certain ways. In AQUATOX state variables and driving variables are treated similarly in the code.
This provides flexibility because external loadings of state variables, such as phytoplankton carried
into a reach from upstream, may function as driving variables; and driving variables, such as pH and
temperature, could be treated as dynamic state variables in a future implementation. Constant,
dynamic, and multiplicative loadings can be specified for atmospheric, point- and nonpoint sources.
Loadings of pollutants can be turned off at the click of a button to obtain a control simulation for
comparison with the perturbed simulation.
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION
CHAPTER 1
Figure 2. State Variables in AQUATOX as implemented for Coralville Reservoir, Iowa.
Phytoplankton
Blue-green
Toxicant
Zoobenthos
midges,
oligochaetes
Toxicant
Bottom Fish
catfish,
buffalofish
Toxicant
Refractory
Diss. Detritus
Toxicant
Refractory
Sed. Detritus
Toxicant
Phytoplankton
Diatom
Toxicant
Macrophyte
water milfoil,
Toxicant
Zoobenthos
Grazer: snails
Toxicant
Forage Fish
shad,
bluegill
Toxicant
T
Labile
Diss. Detritus
Toxicant
Herbivorous
Zooplankton
cladocerans
Toxicant
Piscivore
walleye
Toxicant
Predatory
Invertebrate
zooplankton
Toxicant
Refractory
Susp. Detritus
Toxicant
Multi-aged
Piscivore
bass
Toxicant
Labile
Susp. Detritus
Toxicant
Labile
Sed. Detritus
Toxicant
Buried Refrac.
Sed. Detritus
Toxicant
Total Susp.
Solids
(minus algae)
The model is written in object-oriented Pascal using the Delphi programming system for
Windows. An object is a unit of computer code that can be duplicated; its characteristics and
methods also can be inherited by higher-level objects. For example, the organism object, including
variables such as the LC50 (lethal concentration of a toxicant) and process functions such as
respiration, is inherited by the plant 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
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 1
length of time from a few days, corresponding to a microcosm experiment, to several years,
corresponding to an extreme event followed by long-term recovery.
The process equations contain another class of input variables: the parameters or
coefficients that allow the user to specify key process characteristics. For example, the maximum
consumption rate is a critical parameter characterizing various consumers. AQUATOX is a
mechanistic model with many parameters; however, default values are available so that the analyst
only has to be concerned with those parameters necessary for a specific risk analysis, such as
characterization of a new chemical. In the pages that follow, differential equations for the state
variables will be followed by process equations and parameter definitions.
Finally, the system being modeled is characterized by site constants, such as mean and
maximum depths. At present one can model small lakes, reservoirs, streams, small rivers, and
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 MACROPHYTE model, developed for the U.S. Army Corps of Engineers (Collins etal., 1985),
provided additional capability for representing submersed aquatic vegetation. Another series started
with the toxic fate model PEST, developed to complement CLEANER (Park etal., 1980,1982), and
continued with the TOXTRACE model (Park, 1984) and the spreadsheet equilibrium fugacity PART
model. AQUATOX combined algorithms from these models with ecotoxicological constructs; and
additional code was written as required for a truly integrative fate and effects model (Park, 1990,
1993). The model was then restructured and linked to Microsoft Windows interfaces to provide
greater flexibility, capacity for additional compartments, and user friendliness (Park et al., 1995).
Release 1 from the U.S. Environmental Protection Agency (US EPA) was improved with the
addition of constructs for chronic effects and uncertainty analysis, making it a powerful tool for
probabilistic risk assessment (US EPA, 2000a, b, c). Release 1.1 (US EPA 2001a, b) provided a
much enhanced periphyton submodel and minor enhancements for macrophytes, fish, and dissolved
oxygen. This technical documentation describes Release 2, which has a number of major
enhancements (see 1.3 What's New).
This document is intended to provide verification of individual constructs or mathematical
and formulations programming algorithms used in AQUATOX. The scientific basis of the
constructs reflects empirical and theoretical support; and precedence in the open literature and in
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 1
widely used models is noted. Units are given to confirm the dimensional analysis. The mathematical
formulations have been programmed and graphed in spreadsheets and the results have been
evaluated in terms of behavior consistent with our understanding of ecosystem response; many of
those graphs are given in the following documentation. The variable names in the documentation
correspond to those used in the program so that the mathematical formulations and code can be
compared, and the computer code has been checked for consistency with those formulations. Much
of this has been done as part of the continuing process of internal review. The model and
documentation also have undergone successful peer review by an external panel convened by the
U.S. Environmental Protection Agency.
1.3 What's New
AQUATOX Release 2 has numerous enhancements and a few corrections from Release 1.
Some of these appeared in Release 1.1 and were documented in an Addendum, and some have
occurred since the Release 2 Beta Test version was posted on the developers' Web site. The
changes fall in three categories.
Enhanced Scientific Capabilities
The model is much more powerful and can better represent a variety of environments,
especially streams and rivers compared to Release 1. Specific enhancements include:
a large increase in the number of biotic state variables, with two representatives for each
taxonomic group or ecologic guild;
the addition of bryophytes as a special type of macrophyte;
a multi-age fish category with up to fifteen age classes for age-dependent bioaccumulation
and limited population modeling;
an increase in the number of toxicants from one to a maximum of twenty, with the capability
for modeling daughter products due to biotransformations;
disaggregation of stream habitats into riffle, run, and pool;
mechanistic current- and stress-induced sloughing, light extinction, and accumulation of
detritus in periphyton;
macrophyte breakage due to currents;
computation of chlorophyll a for periphyton and bryophytes, as well as for phytoplankton;
fish biomass is entered and tracked in g/m2;
entrainment and washout of animals, including fish, can occur during high flow;
the options of computing respiration and maximum consumption in fish as functions of mean
individual weight using allometric parameters from the Wisconsin Bioenergetics Model;
respiration in fish is density-dependent;
fish spawning can occur on user-specified dates as an alternative to temperature-cued
spawning;
elimination of toxicants is more robust;
settling and erosional velocities for inorganic sediments are user-supplied parameters;
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 1
uncertainty analysis now covers all parameters and loadings;
biotic risk graphs are provided as an alternative means of portraying probabilistic results;
limitation factors for photosynthesis are output along with the biotic rates; and
AQUATOX is now an extension to BASINS, providing linkages to geographic information
system data, and HSPF and SWAT simulations.
Additional User Interfaces
The model is even more user-friendly, taking full advantage of current Windows capabilities
on modern high-speed personal computers. Capabilities include:
a Wizard to guide the user through the setup for a new study;
context-sensitive Help screens;
multiple windows for simultaneous simulations and input and output screens;
a task bar that can be customized by the user;
enhanced graphics, including secondary Y axes; and
a hierarchical tree structure for choosing variables for uncertainty analysis.
Corrected Errors
Several errors were discovered and corrected during the course of continuing model
evaluation. Some of these may require recalibration of studies. The example studies provided with
the software have been recalibrated, but users may wish to check their own calibrations in upgrading
from various versions. The corrections include:
a change in the bathymetric computations affecting the areas of the thermocline and littoral
zone (Release 1);
removal of an unnecessary conversion from phosphate and nitrate, assuming that all nutrient
input is in terms of N and P; this could affect nutrient limitations (all versions);
inclusion of an oxygen to organic matter conversion factor (a factor of 1.5) and inclusion of
specific dynamic action in the allometric computation offish respiration (Release 2 Beta
Test only);
adding a second-to-day conversion factor for inorganic sediment deposition; previously,
deposition of suspended sediments was much slower than expected (all versions);
adding a conversion factor for wind measured at 10 m height to wind occurring at 10 cm
above the water surface in the volatilization computations; for some compounds this could
result in a two-fold reduction in volatilization (all versions);
nitrification is formulated to occur only at the sediment-water interface (Release 1); and
bioaccumulation, and hence toxicity, are constrained by the life span of an animal (all
versions).
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 2
2 SIMULATION MODELING
2.1 Temporal and Spatial Resolution and Numerical Stability
AQUATOX Release 2 is designed to be a general, realistic model of the fate and effects of
pollutants in aquatic ecosystems. In order to be fast, easy to use, and verifiable, it has been designed
with the simplest spatial and temporal resolutions consistent with this objective. It is designed to
represent average daily conditions for a well-mixed aquatic system (in other words, a 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.
Furthermore, the effects of run, riffle, and pool environments can be represented for streams.
According to Ford and Thornton (1979), a one-dimensional model is appropriate for
reservoirs that are between 0.5 and 10 km in length; if larger, then a two-dimensional model
disaggregated along the long axis is indicated. The one-dimensional assumption is also appropriate
for many lakes (Stefan and Fang, 1994). Similarly, one can consider a single reach or stretch of
river at a time. A spatially-distributed version of the model (Version 3.00) that is able to simulate
linked segments also has been developed, but has not been released.
Usually the reporting time step is one day, but numerical instability is avoided by allowing
the step size of the integration to vary to achieve a predetermined accuracy in the solution. This is
a numerical approach, and the step size is not directly related to the temporal scale of the ecosystem
simulation. AQUATOX uses a very efficient fourth- and fifth-order Runge-Kutta integration routine
with adaptive step size to solve the differential equations (Press etal., 1986,1992). The routine uses
the fifth-order solution to determine the error associated with the fourth-order solution; it decreases
the step size (often to 15 minutes or less) when rapid changes occur and increases the step size when
there are slow changes, such as in winter. However, the step size is constrained to a maximum of
one day so that daily pollutant loadings are always detected. The reporting step, on the other hand,
can be as long as 99 days or as short as 0.1 day; the results are integrated to obtain the desired
reporting time period.
The temporal and spatial resolution is in keeping with the generality and realism of the model
(see Park and Collins, 1982). Careful consideration has been given to the hierarchical nature of the
system. Hierarchy theory tells us that models should have resolutions appropriate to the obj ectives;
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 O'Neill et al., 1986). The model uses a
longer time step than dynamic hydrologic models that are concerned with representing short-term
phenomena such as storm hydrographs (and, indeed, it is not intended to capture fully the dynamics
of short-term pulses less than once per day), and it uses a shorter time step than fate models that may
be concerned only with long-term patterns such as bioaccumulation in large fish.
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AQUATOX (RELEASE 2) 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 hydro graph
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 g/L dissolved toxicant between the simulation with 0.001 relative error and the
simulation with 0.05 relative error this is probably due in part to differences in the
timing of the reporting step. However, if we examine the dissolved oxygen levels, which combine
the effects of photosynthesis, decomposition, and reaeration, we find that there are pronounced
differences over the entire simulation period. The simulations with 0.001 and 0.01 relative error
give almost exactly the same results, suggesting that the more efficient 0.001 relative error should
be used; the simulation with 0.05 relative error exhibits instability in the oxygen simulation; and the
simulation with 0.1 error gives quite different values for dissolved oxygen 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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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION
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Figure 4. Pond with Chlorpyrifos in Dissolved Figure 5. Same as Eigure_4 with Dissolved
Phase. Oxygen.
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
12
11
>
§
d
c
o
O
'10
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 distributions and
key statistics for any and all input variables. Depending on the specific variable and the amount of
available information, any one of several distributions may be most appropriate. A lognormal
distribution is the default for environmental and pollutant loadings. In the uncertainty analysis, the
distributions for constant loadings are sampled daily, providing day-to-day variation within the
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION
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limits of the distribution, reflecting the stochastic nature of such loadings. A useful tool in testing
scenarios is the multiplicative loading factor, which can be applied to all loads. Distributions for
dynamic loadings may employ multiplicative factors that are sampled once each iteration (Figure
6). Normally the multiplicative factor for a loading is set to 1, but, as seen in the example, under
extreme conditions the loading may be ten times as great. In this way the user could represent
unexpected conditions such as pesticides being applied inadvertently just before each large storm
of the season. Loadings usually exhibit a lognormal distribution, and that is suggested in these
applications, unless there is information to the contrary. Figure 7 exhibits the result of such a
loading distribution.
Figure 6. Distribution Screen for Point-Source Loading of Toxicant in Water.
Distribution Information
0.00
0.673
5.8;
>>" Probability c Cumulative Distribution
In an Uncertainty Run:
''*" Use Above Distribution
C Use Point Estimate
Distribution Type:
c Triangular
c Uniform
c Normal
( Lognormal
Distribution Parameters:
Mean fl
Std. Deviation 0.6
A sequence of increasingly informative distributions should be considered for most
parameters (see Volume 1: User's Manual.) If only two values are known and nothing more can
be assumed, the two values may be used as minimum and maximum values for a uniform
distribution (Figure 8): this is often used for parameters where only two values are known. If
minimal information is available but there is reason to accept a particular value as most likely,
perhaps based on calibration, then a triangular distribution may be most suitable (Figure 9). Note
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that the minimum and maximum values for the distribution are constraints that have zero probability
of occurrence. If additional data are available indicating both a central tendency and spread of
response, such as parameters for well-studied processes, then a normal distribution may be most
appropriate (Figure 10) The result of applying such a distribution in a simulation of Onondaga
Lake, New York, is shown in Figure 11. where simulated benthic feeding affects decomposition and
subsequently the predicted hypolimnetic anoxia. All distributions are truncated at zero because
negative values would have no meaning.
Figure 7. Sensitivity of bass (g/m2) to variations in loadings of dieldrin in Coralville Lake,
Iowa.
Largemouth Ba2 (g/sq.
6/13/2003 2:02:03PM
Mean
Minimum
Maximum
Mean -StDev
Mean + StDev
Deterministic
5/9/1969
7/8/1969
9/6/1969
11/5/1969
1/4/1970
3/5/1970
5/4/1970
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION
CHAPTER 2
Figure 8. Uniform Distribution for Henry's
Law Constant for Esfenvalerate.
0.00
6.1 E-8
1.53E-6
3E-6
Figure 9. Triangular Distribution for
Maximum Consumption Rate for Bass.
0.01
0.00
0.015
0.0425
0.07
Figure 10. Normal Distribution for Maximum Consumption Rate
for the Detritivorous Invertebrate Tubifex.
Distribution Information
D invert: Max Consumption: (g/g
0.25
0.483
Probability r Cumulative Distribution
In an Uncertainty Run:
( Use Above Distribution
r Use Point Estimate
Distribution Type:
r Triangular
C Uniform
'' Normal
r Lognormal
Distribution Parameters:
Mean |o.25
Std. Deviation [M
\/ OK j X Cancel
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION
CHAPTER 2
Figure 11. Sensitivity of Hypolimnetic Oxygen in Lake
Onondaga to Variations in Maximum Consumption Rates of
Detritivores.
01/01/89 09/24/89 06/17/90
05/14/89 02/04/90 10/28/90
Minimum
Maximum
Mean
- - Deterministic
Efficient sampling from the distributions is obtained with the Latin hypercube method
(McKay et al., 1979; Palisade Corporation, 1991), using algorithms originally written in FORTRAN
((Iman and Shortencarier 1984)Anonymous, 1988). Depending on how many iterations are chosen
for the analysis, each cumulative distribution is subdivided into that many equal segments. Then
a uniform random value is chosen within each segment and used in one of the subsequent simulation
runs. For example, the distribution shown in Figure 10 can be sampled as shown in Figure 12.
This method is particularly advantageous because all regions of the distribution, including the tails,
are sampled. A non-random seed can be used for the random number generator, causing the same
sequence of numbers to be picked in successive applications; this is useful if you want to be able to
duplicate the results exactly. The default is twenty iterations, meaning that twenty simulations will
be performed with sampled input values; this should be considered the minimum number to provide
any reliability. The optimal number can be determined experimentally by noting the number
required to obtain convergence of mean response values for key state variables; in other words, at
what point do additional iterations not result in significant changes in the results? As many variables
may be represented by distributions as desired, but the method assumes that they are independently
distributed. By varying one parameter at a time the sensitivity of the model to individual parameters
can be determined. This is done for key parameters in the following documentation.
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CHAPTER 2
Figure 12. Latin Hypercube Sampling of a
Cumulative Distribution with a Mean of 25 and
Standard Deviation of 8 Divided into 5 Intervals.
1
0.8
0.6
0.4
0.2
1.58
3.17
An alternate way of presenting uncertainty is by means of a biomass risk graph, which plots
the probability that biomass will be reduced by a given percentage by the end of the simulation
(Mauriello and Park 2002). In practice, AQUATOX compares the end value with the initial
condition for each state variable, expressing the result as a percent decline:
EndVal}
Decline = 1 -
StartVal)
100
where:
Decline
EndVal
StartVal
percent decline in biomass for a given state variable (%);
value at the end of the simulation for a given state variable (units
depend on state variable);
initial condition for given state variable.
The results from each iteration are sorted and plotted in a cumulative distribution so that the
probability that a particular percent decline will be exceeded can be evaluated (Figure 13). Note
that there are ten points in this example, one for each iteration as the consecutive segments of the
distribution are sampled.
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION
CHAPTER 2
Figure 13. Risk to bass from dieldrin in Coralville Reservoir, Iowa.
Biomass Risk Graph
6/13/2003 2:03:53PM
[-- Largemouth Ba2|
50
55
60
65
70
75
Percent Decline at Simulation End
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 2
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 3
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 T r>- / E-
= Inflow - Discharge - Evap (2)
where:
dVolume/dt = derivative for volume of water (m3/d),
Inflow = inflow of water into waterbody (m3/d),
Discharge = discharge of water from waterbody (m3/d), and
Evap = evaporation (m3/d), see |3|.
Evaporation is converted from an annual value for the site to a daily value using the simple
relationship:
MeanEvap nn^r* A
f (Illy i4 " A ₯&fl /"^\
365 ' ( >
where:
MeanEvap = mean annual evaporation (in/yr),
365 = days per year (d/yr),
0.0254 = conversion from inches to meters (m/in), and
Area = area of the waterbody (m2).
The user is given several options for computing volume including keeping the volume
constant; making the volume a dynamic function of inflow, discharge, and evaporation; using a time
series of known values; and, for flowing waters, computing volume as a function of the Manning's
equation. Depending on the method, inflow and discharge are varied, as indicated in Table 1. As
shown in equation (2), an evaporation term is present in each of these volume calculation options.
In order to keep the volume constant, given a known inflow loading, evaporation must be subtracted
from discharge. This will reduce the quantity of state variables that wash out of the system. In the
dynamic formulation, evaporation is part of the differential equation, but neither inflow nor
discharge is a function of evaporation as they are both entered by the user. When setting the volume
of a water body to a known value, evaporation must again be subtracted from discharge for the
volume solution to be correct. Finally, when using the Manning's volume equation, given a known
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CHAPTER 3
discharge loading, the effects of evaporation must be added to the inflow loading so that the proper
Manning's volume is achieved. (This could increase the amount of inflow loadings of toxicants and
sediments to the system, although not significantly.)
Table 1. Computation of Volume, Inflow, and Discharge
Method
Constant
Dynamic
Known values
Manning
Inflow
InflowLoad
InflowLoad
InflowLoad
ManningVol - State/ 'dt + DischargeLoad + Evap
Discharge
InflowLoad - Evap
DischargeLoad
Inflow Load - Evap + (State - KnownVals)/dt
DischargeLoad
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 fj[|.
l:i. illustrates time-varying volumes and inflow loadings specified by the user and
discharge computed by the model for a run-of-the-river reservoir. Note that significant drops in
volume occur with operational releases, usually in the spring, for flood control purposes.
The time-varying volume of water in a stream channel is computed as:
ManningVol = Y CLength Width
(4)
where:
7
CLength
Width
dynamic mean depth (m), see
length of reach (m); and
width of channel (m).
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CHAPTER 3
Figure 14. Volume, Inflow, and Discharge for a 4-year Period
in Coralville Reservoir, Iowa.
6.0E+07
2.5E+08
2.0E+08
1.5E+08
1 .OE+08
5.0E+07
E
13
O
O.OE+00
Oct-74 Oct-75 Nov-76 Dec-77
Apr-75 May-76 Jyn-77 Jul-78
O.OE+00
Inflow
Discharge Volume
In streams the depth of water and flow rate are key variables in computing the transport,
scour, and deposition of sediments. Time-varying water depth is a function of the flow rate, channel
roughness, slope, and channel width using Manning's equation ((Gregory and Walling 1973)), which
is rearranged to yield:
7 =
Q Manning \
{Slope Width]
(5)
where:
Q
Manning
Slope
Width
flow rate (m3/s);
Manning's roughness coefficient (s/m1/3);
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 enter a value or can choose among the
following stream types:
concrete channel (with a default Manning's coefficient of 0.020);
dredged channel, such as ditches and channelized streams (default coefficient of 0.030); and
natural channel (default coefficient of 0.040).
These generalities are based on Chow's (1959) tabulated values as given by Hoggan (1989).
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 3
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 JSlope Width
QBase = £ ./ / (6)
Manning
where:
QBase = base flow (m3/s); and
Idepth = mean depth as given in site record (m).
The dynamic flow rate is calculated from the inflow loading by converting from m3/d to m3/s:
^ _ Inflow
^ ~ 86400 (7)
where:
Q = flow rate (m3/s); and
Inflow = water discharged into channel from upstream (m3/d).
Bathymetric Approximations
The depth distribution of a water body is important because it determines the areas and
volumes subject to mixing and light penetration. The shapes of ponds, lakes, reservoirs, and streams
are represented in the model by idealized geometrical approximations, following the topological
treatment of Junge (1966; see also Straskraba and Gnauck, 1985). The shape parameter/1 (Junge,
1966) characterizes the site, with a shape that is indicated by the ratio of mean to maximum depth:
, ZMean ~ n
P = 6.0 - 3.0 (8
ZMax
Where:
ZMean = mean depth (m);
ZMax = maximum depth (m); and
P = characterizing parameter for shape (unitless); P is constrained
between -1.0 and 1.0.
Shallow constructed ponds and ditches may be approximated by an ellipsoid where Z/ZMax
= 0.6 andP = 0.6. Reservoirs and rivers generally are extreme elliptic sinusoids with values ofP
constrained to -1.0. Lakes may be either elliptic sinusoids, with P between 0.0 and -1.0, or elliptic
hyperboloids with/1 between 0.0 and 1.0. The model requires mean and maximum depth, but if only
the maximum depth is known, then the mean depth can be estimated by multiplying ZMax by the
representative ratio. Not all water bodies fit the elliptic shapes, but the model generally is not
sensitive to the deviations.
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CHAPTER 3
Based on these relationships, fractions of volumes and areas can be determined for any given
depth (!Figure_l5, £igure_L6; Junge, 1966). The AreaFrac function returns the fraction of surface
area that is at depth Z given Zmax and P, which defines the morphometry of the water body. For
example, if the water body were an inverted cone, when horizontal slices were made through the
cone looking down from the top one could see both the surface area and the water/sediment
boundary where the slice was made. This would look like a circle within a circle, or a donut (Figure
17). AreaFrac calculates the fraction that is the donut (not the donut hole). To get the donut hole,
1 - AreaFrac is used.
Figure 15
Area as a Function of Depth
RiSiRVOIR (P = -6.S)
1 3 5 7 9 11 13 IS 17 19 21 23 25
2 4 6 8 10 12 14 16 18 20 22 24
DEPTH(m)
Figure 16
Volume as a Function of Depth
RESERVOIR (P = -0.6)
1 3 5 7 9 11 13 15 17 19 21 23 25
3 4 6 8 10 12 14 16 18 20 22 24
DEPTH (rn)
AreaFrac = (1 - P)
ZMax
^ZMax
)2
(9)
VolFrac =
6.0
Z
ZMax
3.0
' (1
.0
}
3
D) '
.0 -
( Z )2
ZMax
H P
9
.0
P
( z )3
ZMax
(10)
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).
For example, the fraction of the volume that is epilimnion can be computed by setting depth
Zto the mixing depth. Furthermore, by setting Zto the depth of the euphotic zone, the fraction of
the area available for colonization by macrophytes and periphyton can be computed:
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CHAPTER 3
/ \ '
j-, T.. ,-. m ZEuphotic D ZEuphotic 1
FracLit = (1 - P) + P \
ZMax ( ZMax )
(11)
A relatively deep, flat-bottomed basin would have a small littoral area and a large sublittoral
area (Figure 17).
Figure 17
If the site is a limnocorral (an artificial enclosure) then the available area is increased accordingly:
Area + LimnoWallArea
FracLittoral = FracLit
Area
otherwise
FracLittoral = FracLit
(12)
where:
FracLittoral
ZEuphotic
Area
Limno Wall Area
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).
Habitat Disaggregation
Riverine environments are seldom homogeneous. Organisms often exhibit definite
preferences for habitats. Therefore, when modeling streams or rivers, animal and plant habitats are
broken down into three categories: "riffle," "run," and "pool." The combination of these three
habitat categories make up 100% of the available habitat within a riverine simulation. The preferred
percentage of each organism that resides within these three habitat types can be set within the animal
3 -6
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CHAPTER 3
or plant data. Within the site data, the percentage of the river that is composed of each of these
three habitat categories also can be set. It should be noted that the habitat percentages are
considered constant over time, and thus would not capture significant changes in channel
morphology and habitat distribution due to major flooding events.
These habitats affect the simulations in two ways: as limitations on photosynthesis and
consumption and as weighting factors for water velocity (see 3.2 Velocity). Each animal and plant
is exposed to a weighted average water velocity depending on its location within the three habitats.
This weighted velocity affects all velocity-mediated processes including entrainment of invertebrates
and fish, breakage of macrophytes and scour of periphyton. The reaeration of the system also is
affected by the habitat-weighted velocities.
Limitations on photosynthesis and consumption are calculated depending on a species'
preferences for habitats and the available habitats within the water body. If the species preference
for a particular habitat is equal to zero then the portion of the water body that contains that particular
habitat limits the amount of consumption or photosynthesis accordingly.
HabitatLimit = /
'Preferencehabitat > 0
Percenthabitat}
100 J
(13)
where:
HabitatLimitSpea
Preference habltat
Percenthabltat
fraction of site available to organism (unitless), used to limit
ingestion, see and photosynthesis, see
preference of animal or plant for the habitat in question
(percentage); and
percentage of site composed of the habitat in question
(percentage).
It is important to note that the initial condition for an animal that is entered in g/m2 is an
indication of the total mass of the animal over the total surface area of the river. Because of this,
density data for various benthic organisms cannot be used as input to AQUATOX until these values
have been converted to representthe entire surface area. This is especially true in modeling habitats;
for example, an animal could have a high density within riffles, but riffles might only constitute a
small portion of the entire system.
3.2 Velocity
Velocity is calculated as a simple function of flow and cross-sectional area:
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CHAPTER 3
T. , ., AvgFlow 1
Velocity =
XSecArea 86400
100
(14)
where
Velocity
AvgFlow
XSecArea
86400
100
where:
Inflow
Discharge
velocity (cm/s),
flow (m3/d),
cross sectional area (m2),
s/d, and
cm/m.
A j-,, Inflow + Discharge
AvgFlow =
flow into the reach (m3/d);
flow out of the reach (m3/d).
(15)
It is assumed that this is the velocity for the run of the stream. No distinction is made in
terms of vertical differences in velocity in the stream. Following the approach and values used in
the DSAMMt model (Caupp et al. 1995), the riffle velocity is obtained by using a conversion factor
that is dependent on the discharge. Unlike the DSAMMt model, pools also are modeled, so a
conversion factor is used to obtain the pool velocity as well (Table 2). The consequence of these
habitat controls on velocity is shown in
Table 2. Factors relating velocities to those of the average reach.
Flows (Q = discharge)
Q < 2.59e5 nf/d
2.59e5 m3/d -Q < 5.18e5 nf/d
5.18e5 nf/d -Q < 7.77e5 nf/d
Q -7.77e5 nf/d
Run
Velocity
1.0
1.0
1.0
1.0
Riffle
Velocity
1.6
1.3
1.1
1.0
Pool
Velocity
0.36
0.46
0.56
0.66
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION
CHAPTER 3
Figure 18
Predicted velocities in an Ohio stream according to habitat
400
O)O)O)O)O)O)O)O)O)O)O)O)
O5O5O5O5O5O5O5O5O5O5O5O5
C\i CO
in CD r- oo CD
Run
Riffle
Pool
3.3 Washout
Transport out of the system, or washout, is an important loss term for nutrients, floating
organisms, dissolved toxicants, and suspended detritus and sediments in reservoirs and streams.
Although it is considered separately for several state variables, the process is a general function
of discharge:
Washout = DischarSe
Volume
State
(16)
where:
Washout
Discharge
Volume
State
loss due to being carried downstream (g/m3 *d);
flow out of the reach (m3/d), see Table 1;
volume of stream reach (m3), see (2): and
concentration of dissolved or floating state variable (g/m3).
3.4 Stratification and Mixing
Thermal stratification is handled in the simplest form consistent with the goals of
forecasting the effects of nutrients and toxicants. Lakes and reservoirs are considered in the
model to have two vertical zones: epilimnion and hypolimnion (Figure 19): the metalimnion
zone that separates these is ignored. Instead, the thermocline, or plane of maximum temperature
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CHAPTER 3
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 19
Thermal Stratification in a Lake; Terms Defined in Text
Epilimnion
Thermocline
VertDispersion
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 = 0.850, meaning that 85 percent of the sum of squares is explained by the
regression. Its curvilinear nature is shown in ?, and it is computed as (Hanna, 1990):
log(MoxZMx) = 0.336 \og(Length) - 0.245 (17)
where:
MaxZMix
Length
maximum mixing depth for lake (m); and
maximum effective length for wave setup (m, converted from user-
supplied km).
Wind action is implicit in this formulation. Wind has been modeled explicitly by Baca
and Arnett (1976, quoted by Bowie et al., 1985), but their approach requires calibration to
individual sites, and it is not used here.
Vertical dispersion for bulk mixing is modeled as a function of the time-varying
hypolimnetic and epilimnetic temperatures, following the treatment of Thomann and Mueller
(1987, p. 203; see also Chapra and Reckhow, 1983, p. 152;
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CHAPTER 3
VertDispersion = Thick
HypVolume
ThermoclArea Deltat
rt-l
lhypo
rf+1i
lhypo\
rrr * rri t
epi hypo
(18)
where:
VertDispersion
Thick
HypVolume
ThermoclArea
Deltat
rr t-1 rr
ho '
hypo
hypo
T t T t
epi > 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).
Figure 20
Mixing depth as a function of fetch
MAXIMUM MIXING DEPTH
100 11500 22900 34300
5800 17200 28600 40000
LENGTH (m)
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
rather than temperature differences as in equation 11, based on observations by Straskraba
(1973) for a Czech reservoir:
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VertDispersion = 1.37 104 Retention ~2'269
(19)
and:
Retention =
Volume
TotDischarge
(20)
where:
Retention =
Volume =
TotDischarge =
retention time (d);
volume of site (m3); and
combined discharge of epilimnion and hypolimnion (m3/d); see
Table 1
Figure 21
Vertical dispersion as a function of temperature differences
100
H 0.001
12/30 02/28 04/29 06/28 08/27 10/26 12/25
DAY
Epilimnion Temp. -»- Hypolimnion Temp.
Vert. Dispersion (sq m/d) - 4 degrees
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CHAPTER 3
Figure 22
Vertical Dispersion as a Function of Retention Time
VERTICAL DISPERSION
100
;o
E
LLJ
I
Q
10
ce
LU
0.1
180 162 144 126 108 90 72 54 36
171 153 135 117 99 81 63 45 27
RETENTION TIME (d)
The bulk vertical mixing coefficient is computed using site characteristics and the time-
varying vertical dispersion (Thomann and Mueller, 1987):
7? IkM' r ff - VertDispersion ThermoclArea
Thick
(21)
where:
BulkMixCoeff =
ThermoclArea =
bulk vertical mixing coefficient (m3/d),
area of thermocline (m2).
Turbulent diffusion of biota and other material between epilimnion and hypolimnion is
computed separately for each segment for each time step while there is stratification:
TurbDiffepi = yolume ' (COHC compartment, hypo ~ C°HC compartment, epl*
(22)
BulkMixCoeff fr,
^- (Cone
Volume^
compartment, epi
- Cone
compartment, hypo'
(23)
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CHAPTER 3
where:
TurbDiff
Volume
Cone
turbulent diffusion for a given zone (g/m3«d) see and
volume of given segment (m3); and
concentration of given compartment in given zone (g/m3).
The effects of stratification, mixing due to high throughflow, and overturn are well
illustrated by the pattern of dissolved oxygen levels in the hypolimnion of Lake Nockamixon, a
eutrophic reservoir in Pennsylvania (Figure_23).
Figure 23
Stratification and mixing in Lake Nockamixon,
Pennsylvania as shown by hypolimnetic dissolved oxygen
10
c
ffl
D3
X
O
T3
(B
"5
high
throughflow
0 ;
01701782 03/07/82 05/11782 07/15/82 09/18782 11722/82
3.5 Temperature
Temperature is an important controlling factor in the model. Virtually all processes are
temperature-dependent. These include stratification; biotic processes such as decomposition,
photosynthesis, consumption, respiration, reproduction, and mortality; and chemical fate
processes such as microbial degradation, volatilization, hydrolysis, and bioaccumulation. On the
other hand, temperature rarely fluctuates rapidly in aquatic systems. Default water temperature
loadings for the epilimnion and hypolimnion are represented through a simple sine
approximation for seasonal variations (Ward, 1963) based on user-supplied observed means and
ranges (Fjgure_24):
Temperature = TempMean + (-1.0
P P ^ 2 (24)
(sin(0.0174533 (0.987 (Day + PhaseShift) - 30))))]
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where:
Temperature = average daily water temperature (°C);
TempMean = mean annual temperature (°C);
TempRange = annual temperature range (°C),
Day = Julian date (d); and
PhaseShift = time lag in heating (= 90 d).
Observed temperature loadings should be entered if responses to short-term variations are
of interest. This is especially important if the timing of the onset of stratification is critical,
because stratification is a function of the difference in hypolimnetic and epilimnetic temperatures
(see It also is important in streams subject to releases from reservoirs and other
point-source temperature impacts.
3.6 Light
Light is important as the controlling factor for photosynthesis and photolysis. The
default incident light function was formulated for AQUATOX and is a variation on the
temperature equation, but without the lag term:
Solar = LightMean + Li8htRanSe . sin(0.0174533 Day - 1.76) (25)
where:
Solar = average daily incident light intensity (ly/d);
LightMean = mean annual light intensity (ly/d);
LightRange = annual range in light intensity (ly/d); and
Day = Julian date (d, adjusted for hemisphere).
The derived values are given as average light intensity in Langleys per day (Ly/d =10
kcal/m2*d). An observed time-series of light also can be supplied by the user; this is especially
important if the effects of daily climatic conditions are of interest. If the average water
temperature drops below 3°C, the model assumes the presence of ice cover and decreases light to
33% of incident radiation. This reduction, due to the reflectivity and transmissivity of ice and
snow, is an average of widely varying values summarized by Wetzel (1975; also see LeCren and
Lowe-McConnell, 1980). The model does not automatically adjust for shading by riparian
vegetation, so a times-series should probably be supplied if modeling a narrow stream.
Photoperiod is an integral part of the photosynthesis formulation. It is approximated
using the Julian date following the approach of (Stewart 1975)
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CHAPTER 3
12 + A - cos (380
Photoperiod =
365
+ 248)
(26)
24
where:
Photoperiod =
A
Day
fraction of the day with daylight (unitless); converted from hours
by dividing by 24;
hours of daylight minus 12 (hr); and
Julian date (d, converted to radians).
A is the difference between the number of hours of daylight at the summer solstice at a given
latitude and the vernal equinox, and is given by a linear regression developed by Groden (1977):
A = 0.1414 Latitude - Sign 2.413
(27)
where:
Latitude
Sign
latitude (°, decimal), negative in southern hemisphere; and
1.0 in northern hemisphere, -1.0 in southern hemisphere.
Figure 24
Annual Temperature
TEMPERATURE IN A MIDWESTERN POND
35
O
1 77 153 229 305
39 115 191 267 343
JULIAN DAY
Figure 25
Photoperiod as a Function of Date
53 105 157 209 261 313 365
2? 79 131 183 235 287 339
Julian Date
Latitude 40 N Latitude 40 S
3.7 Wind
Wind is an important driving variable because it determines the stability of blue-green
algal blooms, affects reaeration or oxygen exchange, and controls volatilization of some organic
chemicals. Wind is usually measured at meteorological stations at a height of 10 m and is
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION _ CHAPTER 3
expressed as m/s. If site data are not available, default variable wind speeds are represented
through a Fourier series of sine and cosine terms; the mean and first ten harmonics seem to
capture the variation adequately
Wind = CosCoeff^
n n ff n ( 1 ' K Day}
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION
CHAPTER 3
Figure 26
Default Wind Loadings for Missouri Pond with Mean = 3 m/s
WIND LOADINGS
06/13 08/03 09/23 11/13 01/03 02/23 04/15 06/05
DATE
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AQUATOX (RELEASE 2) 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 subject to sinking and washout, while periphyton are subject to
substrate limitation and scour by currents. Bryophytes are modeled as a special class of
macrophytes, limited by nutrients in the water column. These differences are treated at the
process level in the equations (Table 3). All are subject to habitat availability, but to differing
degrees. Plants also are characterized by taxonomic group, which is primarily a way of
organizing preferences for grazing and to identify blue-green phytoplankton as floating.
Table 3. Significant Differentiating Processes for Plants
Plant Type
Phytoplankton
Periphyton
Macrophytes
Bryophytes
Nutrient
Lim.
Current
Lim.
Sinking
Washout
Sloughing
Breakage
Habitat
Animals are subdivided into invertebrates and fish; the invertebrates may be pelagic
invertebrates, benthic insects or other benthic invertebrates. These groups are represented by
different parameter values and by variations in the equations. Insects are subject to emergence
and therefore are lost from the system, but benthic invertebrates are not. Any fish may be
represented by both juveniles and adults, which are connected by promotion. One fish species
can be designated as multi-year with up to 15 age classes connected by promotion. Differences
are shown in Table 4. Feeding preferences are very flexible and can accommodate combinations
of grazing on plants, detritus feeding, and predation ("predation" is used in the following pages
to refer to any type of feeding by animals). Animals also are characterized by taxonomic type or
guild, primarily as a way of organizing feeding preferences; these types can be overridden.
Table 4. Significant Differentiating Processes for Animals
Animal Type
Pelagic Invert.
Benthic Invert.
Benthic Insect
Fish
Washout
Drift
Entrainment
Emergence
Promotion
Multi-year
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4.1 Algae
The change in algal biomassexpressed as ash-free dry weight in 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, sloughing, and washout; as noted above,
phytoplankton also are subject to sinking. If the system is stratified, turbulent diffusion from one
layer to the other also affects the biomass of phytoplankton:
dBiomass
dt
dBiomass
= Loading + Photosynthesis - Respiration - Excretion
- Mortality - Predation ± Sinking - Washout ± TurbDiff
peri
dt
= Loading + Photosynthesis - Respiration - Excretion
- Mortality - Predation - Slough
(29)
(30)
where:
dBiomass/dt =
Loading =
Photosynthesis =
Respiration =
Excretion =
Mortality =
Predation =
Washout =
Sinking =
TurbDiff
Slough =
change in biomass of phytoplankton and periphyton with respect to
time (g/m3«d and g/m2«d);
loading of algal group (g/m3*d and g/m2*d);
rate of photosynthesis (g/m3«d and g/m2«d), see ;.,!.:..;;
respiratory loss (g/m3*d and g/m2*d), see i.;:.v;
excretion or photorespiration (g/m3«d and g/m2«d), see ;;±.;.;
nonpredatory mortality (g/m3*d and g/m2*d), see ;,;;);
herbivory (g/m3«d and g/m2«d), see ; ;i;;j;
loss due to being carried downstream (g/m3*d), see ; >'o;;
loss or gain due to sinking between layers and sedimentation to
bottom (g/m3«d), see ;'{;J. j;
turbulent diffusion (g/m3*d), see ; } :;, and (:K;;;; and
loss due to sloughing (g/m2«d), see ;< ;/j.
< '.yu .'; .;' and / ^^^J.h are examples of the predicted changes in biomass and the
processes that contribute to these changes in a eutrophic lake. In this and following examples,
rates are plotted as a percentage of biomass in an area graph (j',.-,; .-. .;'';). The thickness of the
band at any particular date is an indication of the magnitude of a given rate. Because both
positive and negative rates are plotted as positive areas, the percentage on a particular date may
exceed 100%. Discontinuities in rates may indicate stratification, turnover, anoxia, or high
turbidity and washout due to storms.
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CHAPTER 4
Figure 27. Predicted Algal Biomass in Lake Onondaga, New York
ft 55 o
Si S
Figure 28. Predicted Process Rates for Cryptomonads in Lake Onondaga, New York
140.00%
120.00%
100.00%
Si
£
80.00%
60.00%
40.00%
20.00%
0.00%
COCOCOCOCOCOCOCOCOCOCOCOCT)
DLoad DPhotosynthesis DRespiration DExcretion DMortality DPredation BWashout DSinking BTurb. Diffusion
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 4
Photosynthesis is modeled as a maximum observed rate multiplied by reduction factors
for the effects of toxicants, habitat, and suboptimal light, temperature, current, and nutrients:
Photosynthesis = PMax PProdLimit Biomass HabitatLimit (31)
The limitation of primary production in phytoplankton is:
PProdLimit = LtLimit NutrLimit TCorr FracPhoto (32)
Periphyton have an additional limitation based on available substrate, which includes the
littoral bottom and the available surfaces of macrophytes. The macrophyte conversion is based
on the observation of 24 m2 periphyton/m2 bottom (Wetzel, 1996) and assumes that the
observation was made with 200 g/m2 macrophytes.
PProdLimit = LtLimit - NutrLimit VLimit TCorr FracPhoto
(FracLittoral + SurfAreaConv BiomassMacro) ' '
where:
Pmax = maximum photosynthetic rate (1/d);
PProdLimit = limitation on productivity (unitless);
LtLimit = light limitation (unitless), see
NutrLimit = nutrient limitation (unitless), see 147};
Vlimit = current limitation for periphyton (unitless), see
TCorr = limitation due to suboptimal temperature (unitless), see £511;
HabitatLimit = in streams, habitat limitation based on plant habitat preferences
(unitless), see £11).
FracPhoto = reduction factor for effect of toxicant on photosynthesis (unitless),
see
FracLittoral = fraction of area that is within euphotic zone (unitless) see ill],;
SurfAreaConv = surface area conversion (0.12 m2/g);
BiomassMacm = total biomass of macrophytes in system (g/m2); and
Biomass = biomass of algae (g/m2).
Under optimal conditions, a reduction factor has a value of 1; otherwise, it has a
fractional value. Use of a multiplicative construct implies that the factors are independent.
Several authors (for example, Collins, 1980; 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.
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 4
Light Limitation
Because it is required for photosynthesis, light is a very important limiting variable. It is
especially important in controlling competition among plants with differing light requirements.
Similar to many other models (for example, Di Toro et al., 1971; Park et al., 1974, 1975, 1979,
1980; Lehman et al., 1975; Canale et al., 1975, 1976; Thomann et al., 1975, 1979; Scavia et al.,
1976; Bierman et al., 1980; O'Connor et al., 1981), AQUATOX uses the Steele (1962)
formulation for light limitation. Light is specified as average daily radiation. The average
radiation is multiplied by the photoperiod, or the fraction of the day with sunlight, based on a
simplification of Steele's (1962) equation proposed by Di Toro et al. (1971):
LtL' 't = 0 85 e ' PhotoPeriod ' (LtAtDepth-LtAtTop) PeriphytExt
Extinct (DepthBottom-DepthTop ) <34>
where:
LtLimit = light limitation (unitless);
e = the base of natural logarithms (2.71828, unitless);
Photoperiod = fraction of day with daylight (unitless), see
Extinct = total light extinction (1/m), see
DepthBottom = maximum depth or depth of bottom of layer if stratified (m); if
periphyton or macrophyte then limited to euphotic depth;
DepthTop = depth of top of layer (m);
LtAtDepth = intermediate variable for photosynthetic light integral at the bottom
of a layer, see
LtAtTop = intermediate variable for photosynthetic light integral at the top of
a layer, see and
PeriphytExt = extinction due to periphyton; only affects periphyton and
macrophytes (unitless).
Because the equation overestimates by 15 percent the cumulative effect of light limitation
over a 24-hour day, a correction factor of 0.85 is applied (Kremer and Nixon, 1978).
Extinction of light is based on several additive terms: the baseline extinction coefficient
for water (which may include suspended sediment if it is not modeled explicitly), the so-called
"self-shading" of plants, attenuation due to dissolved organic matter (DOM), and attenuation due
to suspended particulate organic matter (POM) and inorganic sediment:
Extinct = WaterExtinction + PhytoExtinction + ECoeffDOM DOM
+ ECoeffPOM ^PartDetr + ECoeffSed InorgSed
where:
WaterExtinction = user-supplied extinction due to water (1/m);
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PhytoExtinction =
EcoeffDOM =
DOM
EcoeffPOM
PartDetr
EcoefjSed
InorgSed =
user-supplied extinction due to phytoplankton and macrophytes
(1/m), see
attenuation coefficient for dissolved detritus (0.03/m-g/m3);
concentration of labile and refractory dissolved organic matter
(g/m3), see and(JM5);
attenuation coefficient for particulate detritus (0.12/m-g/m3);
concentration of labile and refractory particulate detritus (g/m3),
see and UMl;
attenuation coefficient for suspended inorganic sediment (0.17/m-
g/m3); and
concentration of total suspended inorganic sediment (g/m3), see
For computational reasons, the value of Extinct is constrained between 5"19 and 25. Light
extinction by phytoplankton, periphyton, and macrophytes is a function of the biomass and
attenuation coefficient for each group. Not only does this place a constraint in the form of self-
shading, but it represents a mechanism for competition and succession among plant taxa. For
example, in the model as in nature, an early phytoplankton bloom can restrict growth in
macrophytes. Extinction by periphyton is computed differently because it is not depth-
dependent but rather pertains to the growing surface:
PhytoExtinction =
PeriPhytExt = e
(ECoeffPhytoplant Biomassplan)
(36)
(37)
where:
ECoeffPhytoplant
ECoeffPhytopen
Biomass
attenuation coefficient for given phytoplankton or
macrophyte (1/m-g/m3),
attenuation coefficient for given periphyton (1/m-g/m2),
concentration of given plant (g/m3 or g/m2), and
The light effect at depth is computed by:
L
LtAtDepth = e LightSat
(38)
Light effect at the surface of the water body is computed by:
Light
LtAtTop = e LightSat
(39)
and light effect at the top of the hypolimnion is computed by:
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 4
_ Light _ -Extinction DepthTop
J~ttATl Op = Q
where:
Light = photosynthetically active radiation (ly/d); and
LightSat = light saturation level for photosynthesis (ly/d).
Phytoplankton other than blue-greens are assumed to be mixed throughout the well
mixed layer, although subject to sinking. However, healthy blue-green algae tend to float.
Therefore, if the nutrient limitation for blue-greens is greater than 0.25 and the wind is less
than 3 m/s then DepthBottom for blue-greens is set to 0.25 m to account for buoyancy due to gas
vacuoles. Otherwise it is set to 3 m to represent downward transport by Langmuir circulation.
Under the ice, all phytoplankton are represented as occurring in the top 2 m (cf. LeCren and
Lowe-McConnell, 1980). As discussed in Section 3.5, light is decreased to 33% of incident
radiation if ice cover is predicted.
Approximately half the incident solar radiation is photosynthetically active (Edmondson,
1956):
Light = Solar 0.5 (41)
where:
Solar = average daily light intensity (ly/d), see i, I
The light-limitation function represents both limitation for suboptimal light intensity and
photoinhibition at high light intensities (:-'i-;;i- t ! ) However, when the photoperiod for all but
the highest latitudes is factored in, photoinhibition disappears (: '/ ;:'). When considered
over the course of the year, photoinhibition can occur in very clear, shallow systems during
summer mid-day hours (: . ' :-), but it usually is not a factor when considered over 24 hours
( 7 :- - )
The extinction coefficient for pure water varies considerably in the photosynthetically-
active 400-700 nm range (Wetzel, 1975, p. 55); a value of 0.016 (1/m) correspond to the
extinction of green light. In many models dissolved organic matter and suspended sediment are
not considered separately, so a much larger extinction coefficient is used for "water" than in
AQUATOX. The attenuation coefficients have units of l/m-(g/m3) because they represent the
amount of extinction caused by a given concentration (Table 5).
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Figure 29
Instantaneous Light Response Function
Diatoms in 0.5-m Deep Pond
250
300 350 400
Light (ly/d)
450 500
Figure 30
Daily Light Response Function
Diatoms in 0.5-m Deep Pond
250 300 350 400
Average Light (ly/d)
450
Figure 31
Mid-day Light Limitation
Diatoms in 0.5-m Deep Pond
500
"250
200
53 103 153 203 253 303 353
Julian Date
Light Limitation
0.88
200
Figure 32
Daily Light Limitation
Diatoms in 0.5-m Deep Pond
3 53 103 153 203 253 303 353
Julian Date
Light Limitation
0.55
0.5
0.45
0.4
0.35
0.3
0.25
ra
Q
Table 5. Light Extinction and Attenuation Coefficients
WaterExtinction *
ECoeffPhyto^*
ECoeffPhyto,,,^^ *
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
* user-supplied
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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):
Secchi =
1.9
Extinct
(42)
where:
Secchi
Secchi depth (m).
This relationship also could be used to back-calculate an overall Extinction coefficient if only
the Secchi depth is known for a site.
As a verification of the extinction computations, the calculated and observed Secchi
depths were compared for Lake George, New York. The Secchi depth is estimated to be 8.3 m
in Lake George, based on site data for the various components This compares
favorably with observed values of 7.5 to 11 (Clifford, 1982).
Figure 33
Contributions to Light Extinction in Lake George, NY
POM (26.13%)
Sediment (0.00%)
Water (6.97%)
Phytoplankton (1.59%)
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,
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nutrient limitation by external nutrient concentrations is used in AQUATOX, as in many other
models (for example, Chen, 1970; Parker, 1972; Lassen and Nielsen, 1972; Larsen et al., 1974;
Park et al., 1974; Chen and Orlob, 1975; Patten et al., 1975; Environmental Laboratory, 1982;
Ambrose et al., 1991).
For an individual nutrient, saturation kinetics is assumed, using the Michaelis-Menten or
Monod equation this approach is founded on numerous studies (cf. Hutchinson,
1967):
PLimit =
Phosphorus
Phosphorus + KP
(43)
ATT * Nitrogen
NLimit =
Nitrogen + KN
(44)
CLimit =
Carbon
Carbon + KCO2
(45)
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).
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Figure 34
Nutrient Limitation
MICHAELIS-MENTEN RELATIONSHIP
DIATOMS
0.00 0.01 0.03 0.04 0.05 0.07 0.08 0.09
PHOSPHATE (mg/L)
Nitrogen fixation in blue-green algae is handled by setting NLimit to 1.0 if Nitrogen is
less than half the KN value. Otherwise, it is assumed that nitrogen fixation is not operable, and
NLimit is computed as for the other algae.
Concentrations must be expressed in terms of the chemical element. Because carbon
dioxide is computed internally, the concentration of carbon is corrected for the molar weight of
the element:
Carbon = C2CO2 CO2 (46)
where:
C2CO2
CO2
ratio of carbon to carbon dioxide (0.27); and
inorganic carbon (g/m3).
Like many models (for example, Larsen et al., 1973; Baca and Arnett, 1976; Scavia et
al., 1976; Smith, 1978; Bierman et al., 1980; Park et al., 1980; Johanson et al., 1980; Grenney
and Kraszewski, 1981; Ambrose et al., 1991), AQUATOX uses the minimum limiting nutrient,
whereby the Monod equation is evaluated for each nutrient, and the factor for the nutrient that is
most limiting at a particular time is used:
NutrLimit = mm(PLitnit, NLimit, CLimit) (47)
where:
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION _ CHAPTER 4
NutrLimit = reduction due to limiting nutrient (unitless).
Alternative formulations used in other models include multiplicative and harmonic-mean
constructs, but the minimum limiting nutrient construct is well-founded in laboratory studies
with individual species.
Current Limitation
Because they are fixed in space, periphyton also are limited by slow currents that do not
replenish nutrients and carry away senescent biomass. Based on the work of Mclntire (1973)
and Colby and Mclntire (1978), a factor relating photosynthesis to current velocity is used for
periphyton:
VLimit = min(l, RedStillWater + VelCoeff '
1 + VelCoeff Velocity
where:
VLimit = limitation or enhancement due to current velocity (unitless);
RedStillWater = reduction in photosynthesis in absence of current (unitless);
VelCoeff = empirical proportionality coefficient for velocity (0.057, unitless);
and
Velocity = flow rate (converted to m/s), see
VLimit has a minimum value for photosynthesis in the absence of currents and increases
asymptotically to a maximum value for optimal current velocity (?). In high currents scour can
limit periphyton; see 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 Mclntire, 1978).
Adjustment for Suboptimal Temperature
AQUATOX uses a general but complex formulation to represent the effects of
temperature. All organisms exhibit a nonlinear, adaptive response to temperature changes (the
so-called Stroganov function). Process rates other than algal respiration increase as the ambient
temperature increases until the optimal temperature for the organism is reached; beyond that
optimum, process rates decrease until the lethal temperature is reached. This effect is
represented by a complex algorithm developed by O'Neill et al. (1972) and modified slightly for
application to aquatic systems (Park et al., 1974). An intermediate variable FJis computed first;
it is the ratio of the difference between the maximum temperature at which a process will occur
and the ambient temperature over the difference between the maximum temperature and the
optimal temperature for the process:
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 4
T/T (TMax + Acclimation) - Temperature
(TMax + Acclimation) - (TOpt + Acclimation)
where:
Temperature = ambient water temperature (°C);
TMax = maximum temperature at which process will occur (°C);
TOpt = optimal temperature for process to occur (°C); and
Acclimation = temperature acclimation (°C), as described below.
Acclimation to both increasing and decreasing temperature is accounted for with a
modification developed by Kitchell et al. (1972):
Acclimation = XM [1 - e(~KT' *W«**»* ~ TR<*»] (50)
where:
XM = maximum acclimation allowed (°C);
KT = coefficient for decreasing acclimation as temperature approaches Tref
(unitless);
ABS = function to obtain absolute value; and
TRef = "adaptation" temperature below which there is no acclimation (°C).
The mathematical sign of the variable Acclimation is negative if the ambient temperature
is below the temperature at which there is no acclimation; otherwise, it is positive.
If the variable 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 eexr-d-w)) (51)
where:
TCorr = limitation due to suboptimal temperature (unitless); and
yi + 40/yr )2
400 l '
where:
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WT = \n(Q10) ((TMax + Acclimation) - (TOpt + Acclimation))
(53)
and
YT = \n(Q10) ((TMax + Acclimation) - (TOpt + Acclimation) + 2)
(54)
where:
Q10
slope or rate of change per IOC 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 (£igure_35,
Figure 35
Temperature Response of Blue-Greens
Figure 36
Temperature Response of Diatoms
STROGANOV FUNCTION
BLUE-GREENS
10 20 30
TEMPERATURE(C)
40
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 (1980), maximum
respiration is constrained to 60% of photosynthesis. Laboratory experiments in support of the
CLEANER model confirmed the empirical relationship and provided additional evidence of the
correct parameter values (Collins, 1980), as demonstrated by : .: /:
, (TResp Temperature)
Respiration = RespO e(
Biomass
(55)
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where:
Respiration =
RespO
TResp
Temperature =
Biomass =
dark respiration (g/m3«d);
respiration rate at 0»C (g/g*d);
exponential temperature coefficient (0.065/»C);
ambient water temperature (»C); and
plant biomass (g/m3).
This construct also applies to macrophytes. The values for RespO are given in Table 6.
Table 6. Values for respiration rate at 0*C.
Plant group
Diatoms
Greens
Blue-greens
Other algae
Macrophytes
RespO
0.022
0.006
0.072
0.006
0.015
Reference
LeCren & Lowe-McConnell, 1980, p. 189
LeCren & Lowe-McConnell, 1980, p. 189
Collins, 1980
arbitrarily set to the same as greens
LeCren & Lowe-McConnell, 1980, p. 195
Figure 37
Respiration (Data From Collins, 1980)
DARK RESPIRATION
10 20 30
TEMPERATURE(C)
40
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CHAPTER 4
Photorespiration and Excretion
Photorespiration, with the release of carbon dioxide and the concomitant excretion of
dissolved organic material, occurs in the presence of light. Environmental conditions that inhibit
cell division but still allow photoassimilation result in release of organic compounds. This is
especially true for both low and high levels of light (Fogg et al., 1965; Watt, 1966; Nalewajko,
1966; Collins, 1980). AQUATOX uses an equation modified from one by Desormeau (1978)
that is the inverse of the light limitation:
Excretion = KResp LightStress Photosynthesis (56)
where:
Excretion =
KResp
Photosynthesis =
and where:
release of photosynthate (g/m3*d);
coefficient of proportionality between excretion and
photosynthesis at optimal light levels (unitless); and
photosynthesis (g/m3«d), see
LightStress = 1 - LtLimit
(57)
where:
LtLimit= light limitation for a given plant (unitless), see
It is a continuous function 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 38
Photorespiration
EFFECT OF LIGHT ON PHOTORESPIRATION
w DIATOMS IN POND
W0.09
I
tjO.08
00.07
§0.06
00.05
30.04
200 250
300 350 400
LIGHT (ly/d)
450 500
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION
CHAPTER 4
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 + Excess! + Stress) Biomass + Poisoned
(58)
where:
Mortality
Poisoned
KMort
Biomass
and where:
nonpredatory mortality (g/m3«d);
mortality rate due to toxicant (g/m3*d), see (£287));
intrinsic mortality rate (g/g*d); and
plant biomass (g/m3),
Excess! =
(Temperature - TMax)
(59)
and:
Stress = 1 - e ~EMort ' (J ~ (NutrLimit LtLimit))
(60)
where:
Excess!
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 with total limitation
(g/g-d);
reduction due to limiting nutrient (unitless), see
light limitation (unitless), see
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
39). and, to a much lesser degree, with suboptimal nutrients and light (Fj
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION
CHAPTER 4
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 39
Mortality Due To High Temperatures
Hfna
1
O
(0
$
^0.2
LU
r
/
/
/TMax
24 26 28 30 32 34 36 38 40
Temperature
Figure 40
Mortality Due To Light Limitation
ALGAL MORTALITY
DIATOMS
0.03
0028
-E? 0026
t: 0024
0.022
0.02
0.018
200
300 350 400
LIGHT (ly/d)
Sinking
Sinking of phytoplankton, either between layers or to the bottom sediments, is modeled
as a function of physiological state, similar to mortality. Phytoplankton that are not stressed are
considered to sink at given rates, which are based on field observations and implicitly account
for the effects of averaged water movements (cf. Scavia, 1980). Sinking also is represented as
being impeded by turbulence associated with higher discharge (but only when discharge exceeds
mean discharge):
p. , KSed MeanDischarge 0 ,A , .
Sink = SedAccel Biomass
Depth Discharge
(61)
where:
Sink
KSed
Depth
MeanDischarge
Discharge
Biomass
phytoplankton loss due to settling (g/m3«d);
intrinsic settling rate (m/d);
depth of water or, if stratified, thickness of layer (m);
mean annual discharge (m3/d);
daily discharge (m3/d), see Table 1; and
phytoplankton biomass (g/m3).
The model is able to mimic high sedimentation loss associated with the crashes of
phytoplankton blooms, as discussed by Harris (1986). As the phytoplankton are stressed by
toxicants and suboptimal light, nutrients, and temperature, the model computes an exponential
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION
CHAPTER 4
increase in sinking (. ;. :. v ), as observed by Smayda (1974), and formulated by Collins and
Park (1989):
SedAccel = eESed' ^ ~ LtLimit' NutrLimit TCorr
(62)
where:
SedAccel
ESed
LtLimit
NutrLimit
FracPhoto
TCorr
increase in sinking due to physiological stress (unitless);
exponential settling coefficient (unitless);
light limitation (unitless), see OiJ;
nutrient limitation (unitless), see L47j;; and
reduction factor for effect of toxicant on photosynthesis (unitless),
see -' -i ;
temperature limitation (unitless), see ' ...
Figure 41
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
PHOSPHATE (g/cu m)
0.10
Washout and Sloughing
Phytoplankton are subject to downstream drift. In streams and in lakes and reservoirs
with low retention times this may be a significant factor in reducing or even precluding
phytoplankton populations (LeCren and Lowe-McConnell, 1980). The process is modeled as a
simple function of discharge:
WaShout
phytoplankton
Biomass
(63)
where:
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION
CHAPTER 4
Washoutplytoplankton
Discharge
Volume
Biomass
loss due to downstream drift (g/m3«d);
daily discharge (m3/d);
volume of site (m3); and
biomass of phytoplankton (g/m3).
Periphyton often exhibit a pattern of buildup and then a sharp decline in biomass due to
sloughing. Based on extensive experimental data from Walker Branch, Tennessee (Rosemond,
1993), a complex sloughing formulation, extending the approach of Asaeda and Son (2000), was
implemented. This function was able to represent a wide range of conditions (Figure 42 and
Figure 43V
WashoutPeriphyton = Slough + DislodgeperiTox (64)
where:
Washout,
'Periphyton
Slough
Dislodgepm Tox
loss due to sloughing (g/m3*d);
loss due to natural causes (g/m3«d), see (67): and
loss due to toxicant-induced sloughing (g/m3*d), see (300)
Figure 42. Comparison of predicted biomass of periphyton, constituent
algae, and observed biomass of periphyton (Rosemond, 1993) in Walker
Branch, Tennessee, with addition of both N and P and removal of grazers
in Spring, 1989.
* s s a Fq
-Diatoms(g/m2)
- Oth alg(g/m2)
Periphyton X Observed
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION
CHAPTER 4
Figure 43. Predicted rates for diatoms in Walker Branch, Tennessee, with
addition of both N and P and removal of grazers in Spring, 1989. Note the
importance of periodic sloughing. Rates expressed as g/m2 d.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48
D Photosynthesis Respiration D Excretion D Mortality Predation D Sloigfing
Natural sloughing is a function of senescence due to suboptimal conditions and the drag
force of currents acting on exposed biomass. Drag increases as both biomass and velocity
increase:
DragForce = Rho DragCoeff Vel2 (BioVol UnitArea)2'3 IE-6 (65)
where:
DragForce
Rho
DragCoeff
Vel
BioVol
UnitArea
1E-6
drag force (kg m/s2);
density (kg/m3);
drag coefficient (2.53E-4, unitless);
velocity (converted to m/s) see (14):
biovolume of algae (mnrVmm2);
unit area (mm2);
conversion factor (m2/mm2).
Biovolume is not modeled directly by AQUATOX, so a simplifying assumption is that
the empirical relationship between biomass and biovolume is constant for a given growth form,
based on observed data from Rosemond (1993):
Biovol
Dia
BiovolFil =
Biomass
2.08E-9
Biomass
8.57E-9
(66)
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION _ CHAPTER 4
where:
BiovolDia = biovolume of diatoms (mm3/mm2);
Biovolpn = biovolume of filamentous algae (mm3/mm2);
Biomass = biomass of given algal group (g/m2).
Suboptimal light, nutrients, and temperature cause senescence of cells that bind the
periphyton and keep them attached to the substrate. This effect is represented by a factor,
Suboptimal, which is computed in modeling the effects of environmental conditions on
photosynthesis. Suboptimal decreases the critical force necessary to cause sloughing. If the drag
force exceeds the critical force for a given algal group modified by the Suboptimal factor and an
adaptation factor, then sloughing occurs:
If DragForce > Suboptimal o FCrit* Adaptation
then Slough = Biomass FracSloughed (67)
else Slough = 0
where:
Suboptimal0rg = factor for Suboptimal nutrient, light, and temperature effect on
senescence of given periphyton group (unitless);
FCrit0rg = critical force necessary to dislodge given periphyton group (kg
m/s2);
Adaptation = factor to adjust for mean discharge of site compared to reference
site (unitless);
Slough = biomass lost by sloughing (g/m3);
FracSloughed = fraction of biomass lost at one time (97%, unitless).
Suboptimal * = NutrLimit ~ LtLimit^ TCorr
If Suboptimal^ > 1 then Suboptimal^ = 1
where:
NutrLimit = nutrient limitation for given algal group (unitless) computed by
AQUATOX; see (M;
LtLimit0rg = light limitation for given algal group (unitless) computed by
AQUATOX; see |M1; and
TCorr = temperature limitation for a given algal group (unitless) computed by
AQUATOX; see Ml.
The sloughing construct was tested and calibrated (U.S. E.P.A., 2001) with data from
experiments with artificial and woodland streams in Tennessee (Rosemond, 1993,
However, in modeling periphyton at several sites, it was observed that sloughing appears to be
triggered at greatly differing mean velocities. The working hypothesis is that periphyton adapt to
the ambient conditions of a particular channel. Therefore, a factor is included to adjust for the mean
discharge of a given site compared to the reference site in Tennessee. It is still necessary to calibrate
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 4
FCrit for each site to account for intangible differences in channel and flow conditions, analogous
to the calibration of shear stress by sediment modelers, but the range of calibration needed is reduced
by the Adaptation factor:
., ... MeanDischarge
Adaptation = (59)
Re/Discharge
where:
MeanDischarge = mean discharge for given site, computed over the period of
the simulation (m3/d);
RefDischarge = mean di scharge for reference experimental stream (3.5 m3/d).
Detrital Accumulation in Periphyton
In phytoplankton, mortality results in immediate production of detritus, and that transfer is
modeled. However, for purposes of modeling, periphyton are defined as including associated
detritus. The accumulation of non-living biomass is modeled implicitly by not simulating mortality
due to suboptimal conditions. Rather, in the simulation biomass builds up, causing increased self-
shading, which in turn makes the periphyton more vulnerable to sudden loss due to sloughing. The
fact that part of the biomass is non-living is ignored as a simplification of the model.
Chlorophyll a
Chlorophyll a is not simulated directly. However, because chlorophyll a is commonly
measured in aquatic systems and because water quality managers are accustomed to thinking of it
as an index of water quality, the model converts phytoplankton biomass estimates into approximate
values for chlorophyll a. The ratio of carbon to chlorophyll a exhibits a wide range of values
depending on the nutrient status of the algae (Harris, 1986); blue-green algae often have higher
values (cf. Megard et al., 1979). AQUATOX uses a value of 45 gC/» g chlorophyll a for 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 usually most interested in the maxima. The results are presented as total
chlorophyll a in g/L; therefore, the computation is:
ChlA =
45 28
1000 (7°)
where:
ChlA = biomass as chlorophyll a ( g/L);
BiomassmGr = biomass of blue-green algae (mg/L);
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION _ CHAPTER 4
Biomassoihets = biomass of algae other than blue-greens (mg/L);
CToOrg = ratio of carbon to biomass (0.526, unitless); and
1000 = conversion factor for mg to g (unitless).
Periphytic chlorophyll a is computed as a linear conversion from the ash-free dry weight
(AFDW) of periphyton; because periphyton can collect inorganic sediments, it is important to
measure and model it as AFDW. All biomass computations in AQUATOX are as AFDW. The
conversion factor is based on the observed average ratio of chlorophyll a to AFDW for the Cahaba
River near Birmingham, Alabama (unpub. data).
Perichlor = ^petiPeriConv Biomass^. (71)
where:
PeriChlor = periphytic chlorophyll a (mg/m2);
PeriConv = conversion from periphyton AFDW to chlorophyll a (6.1 mg/m2:
g/m2);
BiomassPeri = biomass of given periphyton (AFDW in g/m2).
4.2 Macrophytes
Submersed aquatic vegetation or macrophytes can be an important component of shallow
aquatic ecosystems. It is not unusual for the majority of the biomass in an ecosystem to be in the
form of macrophytes during the growing season. Seasonal macrophyte growth, death, and
decomposition can affect nutrient cycling, and detritus and oxygen concentrations. By forming
dense cover, they can modify habitat and provide protection from predation for invertebrates and
smaller fish (Howick et al., 1993); this function is represented in AQUATOX (see
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 i 1 ; 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
the area predicted to be occupied by macrophytes can increase or decrease depending on the clarity
of the water.
The macrophyte equations are based on submodels developed for the International Biological
Program (Titus et al., 1972; Park et al., 1974) and CLEANER models (Park et al., 1980) and for the
Corps of Engineers' CE-QUAL-R1 model (Collins et al., 1985):
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION
CHAPTER 4
dBiomass
dt
= Loading + Photosynthesis - Respiration -Excretion
- Mortality - Predation - Breakage
(72)
and:
Photosynthesis = PMax LtLimit TCorr Biomass FracLittoral
NutrLimit FracPhoto HabitatLimit
(73)
where:
change in biomass with respect to time (g/m2«d);
loading of macrophyte, usually used as a "seed" in the simulation;
may be a moderate value if there is rapid regrowth from rhizomes
following breakage or die-back (g/m2*d);
rate of photosynthesis (g/m2*d);
respiratory loss (g/m2«d), see '.:....i);
excretion or photorespiration(g/m2*d), see /'';;
nonpredatory mortality (g/m2«d), see ( >'.;
herbivory (g/m2*d), see hl6;;
loss due to breakage (g/m2«d), see :" ;
maximum photosynthetic rate (1/d);
light limitation (unitless), see '.;:;
correction for suboptimal temperature (unitless), see i: ;:;
in streams, habitat limitation based on plant habitat preferences
(unitless), see : , ;
fraction of bottom that is in the euphotic zone (unitless) see ^ : ;; and
nutrient limitation for bryophytes only (unitless), see. i. ;
reduction factor for effect of toxicant on photosynthesis (unitless),
see ' '; .
They share many of the constructs with the algal submodel described above. Temperature
limitation is modeled similarly, but with different parameter values. Light limitation also is handled
similarly, using the Steele (1962) formulation; the application of this equation has been verified with
laboratory data (Collins et al., 1985). Periphyton are epiphytic in the presence of macrophytes; by
growing on the leaves they contribute to the light extinction for the macrophytes (Sand-Jensen,
1977). Extinction due to periphyton biomass is computed in AQUATOX, by inclusion in LtLimit.
Nutrient limitation is not modeled at this time except for bryophytes because most macrophytes can
obtain their nutrients from bottom sediments (Bristow and Whitcombe, 1971; Nichols and Keeney,
1976; Barko and Smart, 1980).
Simulation of respiration and excretion utilize the same equations as algae; excretion results
in "nutrient pumping" because the nutrients are assumed to come from the sediments but are
dBiomass/dt =
Loading =
Photosynthesis =
Respiration =
Excretion =
Mortality =
Predation =
Breakage =
PMax
LtLimit =
TCorr =
HabitatLimit =
FracLittoral =
NutrLimit =
FracPhoto =
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION
CHAPTER 4
excreted to the water column. (Because nutrients are not explicitly modeled in bottom sediments,
this can result in loss of mass balance, particularly in shallow ponds. This will be addressed in a
future version.) Non-predatory mortality is modeled similarly to algae as a function of suboptimal
temperature (but not light). However, mortality is a function of low as well as high temperatures,
and winter die-back is represented as a result of this control; the response is the inverse of the
temperature limitation ( . v::>. I):
Mortality = [KMort + Poisoned + (1 - e
(74)
where:
KMort
Poisoned
EMort
intrinsic mortality rate (g/g*d);
mortality rate due to toxicant (g/g*d) :r , and
maximum mortality due to suboptimal temperature (g/g*d).
Sloughing of dead leaves can be a significant loss (LeCren and Lowe-McConnell, 1980); it
is simulated as an implicit result of mortality ((liiyiiiiil:!).
Figure 44
Mortality as a Function of Temperature
MACROPHYTE MORTALITY
00.02
10 20 30 40
TEMPERATURE (C)
50
Macrophytes are subject to breakage due to higher water velocities; this breakage of live
material is different from the sloughing of dead leaves. Although breakage is a function of shoot
length and growth form as well as currents (Bartell et al., 2000; Hudon et al., 2000), a simpler
construct was developed for AQUATOX ( .-: :, ."):
where:
Breakage
D , Velocity - VelMax D.
Breakage = Biomass
Gradual UnitTime
macrophyte breakage (g/m2
(75)
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION
CHAPTER 4
Velocity = current velocity (cm/s) see fjLlj;
VelMax = velocity at which total breakage occurs (cm/s);
Gradual = velocity scaling factor (20 cm/s);
UnitTime = unit time for simulation (1 d);
Biomass = macrophyte biomass (g/m2).
Figure 45. Breakage of macrophytes as a function of current
velocity; VelMax set to 300 cm/s.
1.2
? 1
£ 0.8
O)
70-6
D)
3 0.4
8
z
z
Velocity (cm/s)
At this time there is no provision for computing velocity due to wave action, so that
macrophyte biomass may be overestimated in water bodies where there is significant wave action.
Bryophytes (mosses and liverworts) are a special class of macrophytes that attach to hard
substrates, are stimulated by and take up nutrients directly from the water, are resistant to breakage,
and decompose very slowly (Stream Bryophyte Group, 1999). Nutrient limitation is enabled when
the "Bryophytes" plant type is selected, just as it is for algae. The model assumes that when a
bryophyte breaks or dies the result is 75% particulate and 25% dissolved refractory detritus; in
contrast, other macrophytes are assumed to yield 38% particulate and 24% dissolved labile detritus
and the rest (38%) as refractory detritus. All other differences between bryophytes and other
macrophytes in AQUATOX are based on differences in parameter values. These include low
saturating light levels, low optimum temperature, very low mortality rates, moderate resistance to
breakage, and resistance to herbivory (Arscott et al., 1998; Stream Bryophyte Group, 1999).
Because in the field it is difficult to separate bryophyte chlorophyll from that of periphyton, it is
computed so that the two can be combined and related to field values:
MossChlor = ^(BryoConv BiomassB )
Bryo->
(76)
where:
MossChlor
bryophytic chlorophyll a (mg/m2);
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION
CHAPTER 4
BryoConv
Biomass
Bryo
conversion from bryophyte AFDW to chlorophyll a (8.9 mg/m2:
g/m2);
biomass of given bryophyte (AFDW in g/m2).
Currents and wave agitation can both stimulate and retard macrophyte growth. These effects
will be modeled in a future version. Similar to the effect on periphyton, water movement can
stimulate photosynthesis in macrophytes (Westlake, 1967); the same function could be used for
macrophytes as for periphyton, although with different parameter values. Jupp and Spence (1977b)
have shown that wave agitation can severely limit macrophytes; time-varying breakage eventually
will be modeled when wave action is simulated.
4.3 Animals
Zooplankton, benthic invertebrates, benthic insects, and fish are modeled, with only slight
differences in formulations, with a generalized animal submodel that is parameterized to represent
different groups:
dBiomass
dt
= Load + Consumption - Defecation - Respiration
- Excretion - Mortality - Predation - GameteLoss
- Washout ± Migration - Promotion + Recruit - Entrainment
(77)
where:
dBiomass/dt =
Load =
Consumption =
Defecation =
Respiration =
Excretion =
Mortality =
Predation =
GameteLoss =
Washout =
Migration =
Promotion =
Recruit =
Entrainment =
change in biomass of animal with respect to time (g/m3*d);
biomass loading, usually from upstream (g/m3«d);
consumption of food (g/m3*d), see iMj
defecation of unassimilated food (g/m3«d), see = ;;4j;
respiration (g/m3*d), see {£/;!;
excretion (g/m3«d), see t;ia;
nonpredatory mortality (g/m3*d), see Li'i;;
predatory mortality (g/m3«d), see if-y;
loss of gametes during spawning (g/m3*d), see [],:}.,; j;
loss due to being carried downstream by washout and drift (g/m3*d),
see iljiiL and ijiiia;
loss (or gain) due to vertical migration (g/m3*d), see noli;
promotion to next size class or emergence (g/m3«d), see Hill!.; and
recruitment from previous size class or through reproduction
(g/m3«d), see ijj, J j;
entrainment and downstream transport with flood waters (g/m3*d), see
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION
CHAPTER 4
The change in biomass (£[jii!j,v,.;i!j) is a function of a number of processes (.Li^ILlJ!) that
are subject to environmental factors, including biotic interactions. Similar to the way algae are
treated, parameters for different species of invertebrates and fish are loaded and available for editing
by means of the entry screens. Biomass of zoobenthos and fish is expressed as g/m2 instead of g/m3.
Figure 46. Predicted Changes in Biomass in a Stream
?3 ^ (^c^^SicSr^cSaSo
o5^LSc3r^c3a5o
Corbicula (g/sq.m) Gastropod g_m2 (g/sq.m) Shiner (g/sq.m) Bluegill (g/sq.m)
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION
CHAPTER 4
Figure 47. Predicted Process Rates for the Invasive Clam Corbicula, Expressed as
Percent of Biomass; Spikes are Entrainment During Storm Events
I Consumption Defecation D Respiration Excretion Predation Mortality H Gamete Loss Entrainment
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 (Mullinetal., 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 and limitations
due to habitat preferences of a given predator or herbivore:
Ingestionprey pred = CMaxpred SatFeedmg TCorrpred
HabitatLimit ToxReduction Biomass
'pred
(78)
where:
Ingestionpreypred =
BiomassweA
CMax
SatFeedmg =
TCorr =
ToxReduction =
ingestion of given prey by given predator or herbivore (g/m3*d);
concentration of predator or herbivore (g/m3*d);
maximum feeding rate for predator or herbivore (g/g*d);
saturation-feeding kinetic factor, see
reduction factor for suboptimal temperature (unitless), see ;
reduction due to effects of toxicant (see Eq. 1297}, unitless); and
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 4
HabitatLimit = in streams, habitat limitation based on predator habitat preferences
(unitless), see
The maximum consumption rate is sensitive to body size, so an alternative to specifying
CMax for fish is to compute it using an allometric equation and parameters from the Wisconsin
Bioenergetics Model (Hewett and Johnson, 1992; Hanson et al., 1997):
CMax = CA MeanWeightCB (79)
where:
CA = maximum consumption for a 1 -g fish at optimal temperature (g/g*d);
MeanWeight = mean weight for a given fish species (g);
CB = slope of the allometric function for a given fish species.
Many animals adjust their search or filtration in accordance with the concentration of prey;
therefore, a saturation-kinetic term is used (Park et al., 1974, 1980; Scavia and Park, 1976):
Preference,^, , Food
SatFeeding = prey'pred (80)
pred Food) + FHal/Satpred l }
where:
Preference = preference of predator for prey (unitless);
Food = available biomass of given prey (g/m3);
FHalJSat = half-saturation constant for feeding by a predator (g/m3).
The food actually available to a predator may be reduced in two ways:
Food = (Biomassprey - BMinpred) Refuge (81)
where:
BMin = minimum prey biomass needed to begin feeding (g/m3); and
Refuge = reduction factor for prey hiding in macrophytes (unitless).
Search or filtration may virtually cease below a minimum prey biomass (BMin) to conserve
so that a minimum food level is incorporated (Parsons etal., 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 and BMin is set
toO.
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION
CHAPTER 4
Figure 48
Saturation-kinetic Consumption
BASS CONSUMPTION
BASS BIOMASS = 1 g/cu m
0.03
0.025
-CMax
2.65 5.3 7.95 10.613.2515.918.55
PREY BIOMASS (g/cu m)
Macrophytes can provide refuge from predation; this is represented by a factor related to the
macrophyte biomass that is original with AQUATOX
Refuge = 1 -
Biomass
Macro
BiomassM + HalfSat
(82)
where:
HalfSat
Biomass,
'Macro
half-saturation constant (20, g/m3), and
biomass of macrophyte (g/m3).
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION
CHAPTER 4
Figure 49
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 and Frost, 1976) and active raptorial selection (Burns, 1969; Berman
and Richman, 1974; Bogdan and McNaught, 1975; Brandl and Fernando, 1975) occur among
aquatic organisms. Relative preferences are represented in AQUATOX by a matrix of preference
parameters first proposed by O'Neill (1969) and used in several aquatic models (Bloomfield et al.,
1973; Park et al., 1974; Canale et al., 1976; Scavia et al., 1976). Higher values indicate increased
preference by a given predator for a particular prey compared to the preferences for all possible prey.
In other words, the availability of the prey is weighted by the preference factor.
The preference factors are normalized so that if a potential food source is not modeled or is
below theBMin value, the other preference factors are modified accordingly, representing adaptive
preferences:
PreferenCeprey,pred =
prey,pred
SumPref
(83)
where:
Preferencepreypred
Jprey, pred
normalized preference of given predator for given prey
(unitless);
initial preference value from the animal parameter screen
(unitless); and
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION _ CHAPTER 4
SumPref = sum of preference values for all food sources that are present
above the minimum biomass level for feeding during a
particular time step (unitless).
Similarly, different prey types have different potentials for assimilation by different
predators. The fraction of ingested prey that is egested as feces or discarded (and which is treated
as a source of detritus by the model, see . - '.), 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):
Defecation^ = ^(EgestCoeff^^ + IncrEgesf) Ingestionprey^^ (84)
where:
Defecationpred = total defecation for given predator (g/m3«d);
EgestCoeffpKytpKd = fraction of ingested prey that is egested (unitless); and
IncrEgest = increased egestion due to toxicant (see Eq. 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 = Xprey(Ingestionpreypred) (85)
(86)
where
Consumption^ = total consumption rate by predator (g/m3«d); and
Predationptey = total predation or grazing on given prey (g/m3*d).
Respiration
Respiration can be considered as having three components. Standard respiration is a rate at
resting in which the organism is expending energy without consumption. Active respiration is
modeled only in fish and only when allometric (weight-dependent) equations are used, so standard
respiration can be considered as a composite "routine" respiration for invertebrates and in the
simpler implementation for fish. The so-called specific dynamic action is the metabolic cost of
digesting and assimilating prey. In the model active respiration is combined with standard
respiration by means of an activity factor, and specific dynamic action is an additive term (Kitchell
etal., 1974):
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 4
Respiration^ = StdResppred Activity*pred + SpecDynActionpred (87)
where:
Respirationpred = respiratory loss of given predator (g/m3*d);
StdResppred = basal respiratory loss modified by temperature (g/m3*d); see
(88) and '-. ;
Activitypred = a factor for respiratory loss associated with swimming
(unitless), see ^ :; and : : '. ; and
SpecDynAction^eA = metabolic cost of processing food (g/m3«d), see -..
AQUATOX simulates standard respiration as an optimal observed rate modified by a
temperature dependence and, in fish, a density dependence (see Kitchell et al., 1974):
StdResppred = RoutineResppred TCorrpred Biomasspred DensityDep
where:
RoiitineResppted = routine respiration rate at optimal temperature for given predator
(g/g*d); parameter input by user as "Respiration Rate" or computed
as a function of the weight of the animal (see below);
TCorrpred = Stroganov temperature function (unitless), see; ilj;
Biomasspred = concentration of predator (g/m3); and
DensityDep = density-dependent respiration factor used in computing standard
respiration, applicable only to fish (unitless). See .(:;..jj
As an alternative formulation, standard respiration in fish can be modeled as a function of
the weight of the fish using an allometric equation (Hewett and Johnson, 1992; Hanson et al., 1997):
DD
StdResPpred = BasalResppred-MeanWeightpred "red-TFnpred-Biomasspred-DensityDep (89)
where:
BasalResppKd = basal respiration rate for given predator (g/g*d); computed as
a function of the weight of the animal, see > ;
MeanWeightpred = mean weight for a given fish (g);
RBpred = slope of the allometric function for a given fish (1/g);
TFnp[ed = temperature function (unitless), see. '! ', , ' :!.
The allometric functions are based on the well known Wisconsin Bioenergetics Model and,
for convenience, use the published parameter values for that model (Hewett and Johnson, 1992;
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION _ CHAPTER 4
Hanson et al., 1997). However, the basal respiration rate in that model is expressed as g of oxygen
per g organic matter offish per day, and this has to be converted to organic matter respired:
BasalResppred = RApred 1.5 (90)
where:
RApred = basal respiration rate, characterized as the "intercept of the allometric
mass function" in the Wisconsin Bioenergetics Model documentation
(g O2/g organic matter *d);
1.5 = conversion factor (g organic matter/g O2).
Swimming activity may be large and variable (Hanson et al., 1997) and is subject to
calibration for a particular site, considering currents and other factors. Activity can be a complex
function of temperature. The Wisconsin Bioenergetics Model (Hewett and Johnson, 1992; Hanson
et al., 1997) provides two alternatives. Equation Set 1 uses an exponential temperature function:
TFn = e^'*' (91)
where:
RQ = the Q10 or rate of change per 10° C for respiration (l/° C);
Temp = ambient temperature (° C).
TFn is then factored into the calculation of StdResppred , which is in turn modified by an
Activity factor as part of the calculation of Respiration Activity is a complex function for
swimming speed as an allometric function of temperature (Hewett and Johnson, 1992; Hanson et
al., 1997):
If Temp > RTL Then Vel = RK1 MeanWeight **4 (92)
Else Vel = ACT MeanWeight4 e^01 - Temp)
where:
RTO = coefficient for swimming speed dependence on metabolism (s/cm);
RTL = temperature below which swimming activity is an exponential function of
temperature (° C);
Vel = swimming velocity (cm/s);
RK1 = intercept for swimming speed above the threshold temperature (cm/s);
RK4 = weight-dependent coefficient for swimming speed;
ACT = intercept for swimming speed for a 1 g fish at ° C (cm/s); and
BACT = coefficient for swimming at low temperatures (l/° C),
Equation Set 2 uses the Stroganov function used elsewhere in AQUATOX, see ', :
TFn = TCorr (93)
and activity is a constant:
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION
CHAPTER 4
Activity = ACT
(94)
where:
ACT =
activity factor, which is not the same as ACT in Equation Set 1 (g/g).
Standard respiration in fish increases with crowding due to competition for spawning sites,
interference in feeding, and other factors. This adverse intraspecific interaction helps to constrain
the population to the carrying capacity; as the biomass approaches the carrying capacity for a given
species the respiration is increased proportionately (Kitchell et al., 1974):
DensityDep = 1 +
IncrResp Biomass
KCap
(95)
where:
IncrResp
KCap
increase in respiration at carrying capacity (0.25);
carrying capacity (g/m3).
With the IncrResp value of 0.25, which is a conservative estimate, respiration is increased
by 25% at carrying capacity (Kitchell et al., 1974), as shown in i . This density-
dependence is used only for fish, and not for invertebrates.
Figure 50. Density-dependent factor for increase in respiration as fish
biomass approaches the carrying capacity (10.0 in this example).
1.3 i
"$ 1.25
0)
E 1.2
1.15
.e 1.1
1.05
A
Biomass (g/m2)
As a simplification, specific dynamic action is represented as proportional to food assimilated
(Hewett and Johnson, 1992; see also Kitchell et al., 1974; Park et al., 1974):
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 4
SpecDynAction^ = KResppred (Consumption^ - Defecation^J (96)
where:
KResppred = proportion of assimilated energy lost to specific dynamic
action (unitless); parameter input by user as "Specific
Dynamic Action;"
Consumption^ = ingestion (g/m3«d); and
Defecation^ = egestion of unassimilated food (g/m3«d).
Excretion
As respiration occurs, biomass is lost and nitrogen and phosphorus are excreted directly to
the water (Home and Goldman 1994); see and Ganf and Blazka (1974) have reported
that this process is important to the dynamics of the Lake George, Uganda, ecosystem. Their data
were converted by Scavia and Park (1976) to obtain a proportionality constant relating excretion to
respiration:
Excretionpred = KExcrpred Respirationpred (97)
Excretionpred = excretion rate (g/m3*d);
where:
KExcrpred = proportionality constant for excretion:respiration (unitless);
and
Respirationpred = respiration rate (g/m3«d).
Excretion is approximately 17 percent of respiration, which is not an important biomass loss
term for animals, but it is important in nutrient recycling.
Nonpredatory Mortality
Nonpredatory mortality is a result of both environmental conditions and the toxicity of
pollutants:
Mortality^ = Dpred Biomasspred + Poisonedpred (93)
where:
Mortalitypred = nonpredatory mortality (g/m3«d);
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION
CHAPTER 4
Biomasspred
Poisoned
environmental mortality rate; the maximum value of three
computations,:'^ ;., : : ;' , and , is used (1/d);
biomass of given animal (g/m3); and
mortality due to toxic effects (g/m3«d), see il§T:.
Under normal conditions a baseline mortality rate is used:
(99)
where:
KMortpred
normal nonpredatory mortality rate (1/d).
An exponential function is used for temperatures above the maximum (
DPred = KM°rtpred
> Temperature - TMaxpred
(100)
where:
Temperature =
TMax
'pred
ambient water temperature (); and
maximum temperature tolerated ().
Figure 51
Mortality as a Function of Temperature
MORTALITY OF BASS
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 4
Dead = 1.0 if Oxygen < 0.25 (101)
Gamete Loss and Recruitment
Eggs and sperm can be a significant fraction of adult biomass; in bluegills these can be 13
percent and 5 percent, respectively (Toetz, 1967), giving an average of 9 percent if the proportion
of sexes is equal. Because only a small fraction of these gametes results in viable young when shed
at the time of spawning, the remaining fraction is lost to detritus in the model.
There are two options for determining the date or dates on which spawning will take place.
A user can specify up to three dates on which spawning will take place. Alternatively, one may use
a construct that was modified from a formulation by Kitchell et al. (1974). As a simplification,
rather than requiring species-specific spawning temperatures, it assumes that spawning occurs when
the temperature first enters the range from six tenths of the optimum temperature to l»4ess 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 when a simple sinusoidal temperature function is used. However, the user
also can specify a maximum number of spawnings.
If (0.6 TOpf) < Temperature < (TOpt - 1.0) then
GameteLoss = (GMort + IncrMorf) FracAdults PctGamete Biomass (102)
else GameteLoss = 0
where:
Temperature = ambient water temperature ();
TOpt = optimum temperature ();
GameteLoss = loss rate for gametes (g/m3*d);
GMort = gamete mortality (1/d);
IncrMort = increased gamete and embryo mortality due to toxicant (1/d); see
Biomass = biomass of predator (g/m3);
PctGamete = fraction of adult predator biomass that is in gametes (unitless); and
FracAdults = fraction of biomass that is adult (unitless).
As the biomass of a population reaches its carrying capacity, reproduction is usually reduced
due to stress; this results in a population that is primarily adults. Therefore, the proportion of adults
and the fraction of biomass in gametes are assumed to be at a maximum when the biomass is at the
carrying capacity
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION
CHAPTER 4
FracAdults = 1.0 - CaPacity\
( KCap )
if Biomass > KCap then Capacity = 0 else Capacity = KCap - Biomass
(103)
where:
KCap
carrying capacity (g/m3).
Figure 52
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 5.5
BIOMASS
Spawning in large fish results in an increase in the biomass of small fish if both small and
large size classes are of the same species. Gametes are lost from the large fish, and the small fish
gain the viable biomass through recruitment:
Recruit = (1 - (GMort + IncrMorf)) FracAdults PctGamete Biomass (104)
where:
Recruit
biomass gained from successful spawning (g/m3«d).
Washout, Drift, and Entrainment
Downstream transport is an important loss term for invertebrates. Zooplankton are subject
to transport downstream similar to phytoplankton:
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 4
Washout = Biomass (105)
Volume v '
where:
Washout = loss of zooplankton due to downstream transport (g/m3*d);
Discharge = discharge (m3/d), see Table 1;
Volume = volume of site (m3), see and
Biomass = biomass of invertebrate (g/m3).
Likewise, zoobenthos exhibit drift, which is detachment followed by washout, and it is
represented by a construct that is original with AQUATOX:
Drift = (Dislodge + Dislodge Tox) Biomass (106)
where:
Drift = loss of zoobenthos due to downstream drift (g/m3«d);
Dislodge = fraction of biomass subj ect to drift per day (fraction/d), see and
DislodgeTox = fraction of biomass subj ect to drift per day because of toxicant stress
(fraction/d), see
Nocturnal drift is a natural phenomenon:
Dislodge = AveDrift (107)
where:
AveDrift = fraction of biomass subject to normal drift per day (fraction/d).
Animals also are subject to entrainment and downstream transport in flood waters. In fact,
annual variations in fish populations in streams are due largely to variations in flow, with almost
100% loss during large floods in Shenandoah National Park (NFS, 1997). A simple exponential loss
function was developed for AQUATOX:
Vel - VelMax
Entrainment = Biomass MaxRateer Gra&ai (108>
where:
Entrainment = entrainment and downstream transport (g/m3*d);
Biomass = biomass of given animal (g/m3);
MaxRate = maximum loss per day (1/d);
Vel = velocity of water (cm/s),
VelMax = velocity at which there is total loss of biomass (cm/s); and
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION
CHAPTER 4
Gradual
slope of exponential, set to 25 (cm/s).
Figure 53
Entrainment of animals as a function of stream velocity
with VelMax of 400 cm/s
o 4-
100
200 300
Velocity (cm/s)
400
500
Vertical Migration
When presented with unfavorable conditions, most animals will attempt to migrate to an
adjacent area with more favorable conditions. The current version of AQUATOX, following the
example of CLEANER (Park etal., 1980), assumes that zooplankton and fish will exhibit avoidance
behavior by migrating vertically from an anoxic hypolimnion to the epilimnion. Anoxic conditions
are taken to occur when dissolved oxygen levels are less than 0.25 mg/L. The assumption is that
anoxic conditions will persist until overturn. The construct calculates the absolute mass of the given
group of organisms in the hypolimnion, then divides by the volume of the epilimnion to obtain the
biomass being added to the epilimnion:
If VSeg = Hypo and Anoxic
Migration =
HypVolume Biomass
pred, hypo
(109)
EpiVolume
where:
VSeg
Hypo =
Anoxic =
Migration =
HypVolume =
vertical segment;
hypolimnion;
boolean variable for anoxic conditions when O2 < 0.25 mg/L;
rate of migration (g/m3«d);
volume of hypolimnion (m3), see : - ;
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 4
EpiVolume = volume of epilimnion (m3), see JlifurejJ); and
Biomasspredhypo = biomass of given predator in hypolimnion (g/m3).
This does not include horizontal migration or avoidance of toxicants and stressful temperatures.
Promotion
Although AQUATOX is an ecosystem model, promotion to the next size class is important
in representing the emergence of aquatic insects, and therefore loss of biomass from the system, and
in predicting bioaccumulation of hydrophobic organic compounds in larger fish. The model
assumes that promotion is determined by the rate of growth. Growth is considered to be the sum of
consumption and the loss terms other than mortality and migration; a fraction of the growth goes
into promotion to the next size class (cf. Park et al., 1980):
Promotion = KPro , (Consumption - Defecation - Respiration - Excretion - GameteLoss) (110)
where:
Promotion = rate of promotion (g/m3*d);
KPro = fraction of growth that goes to promotion or emergence (0.5, unitless);
Consumption = rate of consumption (g/m3*d), see
Defecation = rate of defecation (g/m3«d), see
Respiration = rate of respiration (g/m3*d), see
Excretion = rate of excretion (g/m3*d), see ([97}; and
GameteLoss = loss rate for gametes (g/m3*d), see
This is a simplification of a complex response that depends on the mean weight of the
individuals. However, simulation of mean weight would require modeling both biomass and
numbers of individuals (Park et al., 1979, 1980), and that is beyond the scope of this model at
present.
Promotion of multi-age fish is straightforward; each age class is promoted to the next age
class on the first spawning date each year. The oldest age class merely increments biomass from
the previous age class to any remaining biomass in the class. Of course, any associated toxicant is
transferred to the next class as well. Recruitment to the youngest age class is the fraction of gametes
that are not subject to mortality at spawning. Note that the user specifies the age at which spawning
begins on the multi-age fish screen.
Insect emergence can be an important factor in the dynamics of an aquatic ecosystem. Often
there is synchrony in the emergence; in AQUATOX this is assumed to be cued to temperature with
additional forcing as twice the promotion that would ordinarily be computed, and is represented by:
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 4
If Temperature > (0.8 TOpt) and Temperature < (TOpt - 1.0) then
(111)
Emergelnsect = 2 Promotion
where:
Emergelnsect = insect emergence (mg/L*d);
Temperature = ambient water temperature (); and
TOpt = optimum temperature ();
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION
CHAPTER 5
5 REMINERALIZATION
5.1 Detritus
For the purposes of AQUATOX, the term "detritus" is used to include all non-living organic
material and associated decomposers (bacteria and fungi). As such, it includes both particulate and
dissolved material in the sense of Wetzel (1975), but it also includes the microflora and is analogous
to "biodetritus" of Odum and de la Cruz (1963) . Detritus is modeled as eight compartments:
refractory (resistant) dissolved, suspended, sedimented, and buried detritus; and labile (readily
decomposed) dissolved, suspended, sedimented, and buried detritus CL^UA;:\.. .f;0- This degree of
disaggregation is considered necessary to provide more realistic simulations of the detrital food web;
the bioavailability of toxicants, with orders-of-magnitude differences in partitioning; and biological
oxygen demand, which depends largely on the decomposition rates. Buried detritus is considered
to be taken out of active participation in the functioning of the ecosystem. In general, dissolved
organic material is about ten times that of suspended particulate matter in lakes and streams
(Saunders, 1980), and refractory compounds usually predominate; however, the proportions are
modeled dynamically.
Figure 54
Detritus Compartments in AQUATOX
detr.
~ftn. ^
detr. ^
"ftrT ^
s
detr.
ex
* c
Refractory
Dissolved
Refractory
Suspended
coteiization
colonization ,~^
L~-~
ingestion ^ ^
U - *
Labile
Dissolved
Labile
Suspended
A sedimentation A sedimejitc
copr y sccjir y
Refractory
Sediments
A bunal
Dosure y
Refractory
Buried
colonization ^_
U-"
ingestion r-_
L-*
ex
Labile
Sediments
A bujial
Dopure y
Labile
Buried
^ detr.
^fm.
decomp.r-^ +
detr.
"^Trri~
ingestion ^t
decomp.[^_ +
jtion
detr.
"^^fm"
ingestion p^^
decomp.r-^ j^
onnection to detritivores + connection to nutrients
The concentrations of detritus in these eight compartments are the result of several
competing processes:
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 5
= Loading + DetrFm - Colonization - Washout
dt (112)
- Sedimentation - Ingestion + Scour ± Sinking ± TurbDiff
= Loading + DetrFm + Colonization - Decomposit,
ion
- Washout - Sedimentation - Ingestion + Scour ± Sinking
± TurbDiff
= Loading + DetrFm - Colonization - Washout ± TurbDiff (114)
= Loading + DetrFm - Decomposition - Washout ± TurbDiff (115)
= Loading + DetrFm + Sedimentation + Exposure
dt (116)
- Colonization - Ingestion - Scour - Burial
dSedLabileDetr T ,. _. _,-, 0 ,. . .. ,-, , . ..
= Loading + DetrFm + Sedimentation + Colonization
dt (117)
- Ingestion - Decomposition - Scour + Exposure - Burial
= Sedimentation + Burial - Scour - Exposure (118)
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dBuriedLabileDetr
dt
= Sedimentation + Burial - Scour - Exposure
(119)
where:
dSuspRefrDetr/dt
dSuspLabileDetr/dt
dDissRefrDetr/dt
dDissLabDetr/dt
dSedRefrDetr/dt
dSedLabileDetr/dt
dBuriedRefrDetr/dt
dBuriedLabileDetr/dt
Loading
DetrFm
Colonization
Decomposition
Sedimentation
Scour
Exposure
Burial
Washout
Ingestion
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*d);
change in concentration of dissolved refractory detritus with
respect to time (g/m3*d);
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 : ; ;
loss due to microbial decomposition (g/m3*d), see ( : !;
transfer from suspended detritus to sedimented detritus by
sinking (g/m3*d); in streams with the inorganic sediment
model attached see ':;'! ;, for all other systems see (1.1:-.};
resuspension from sedimented detritus (g/m3*d); in streams
with the inorganic sediment model attached see :1 , for all
other systems see (11;*) (resuspension);
transfer from buried to sedimented by scour of overlying
sediments (g/m3*d);
transfer from sedimented to buried due to deposition of
sediments (g/m3«d), see ':; '.;
loss due to being carried downstream (g/m3*d), see r...tj;
loss due to ingestion by detritivores and filter feeders
(g/m3*d), see ' ;
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION _ CHAPTER 5
Sinking = detrital sinking from epilimnion and to hypolimnion under
stratified conditions, see and
TurbDiff = transfer between epilimnion and hypolimnion due to turbulent
diffusion (g/m3«d), see (22) and (23).
As a simplification, refractory detritus is considered not to decompose directly, but rather
to be converted to labile detritus through microbial colonization, especially through ingestion then
egestion by detritivores (organisms that feed on detritus). Labile detritus is then available for both
decomposition and assimilation by detritivores. Because detritivores digest microbes and defecate
the remaining organic material, detritus has to be conditioned through microbial colonization before
it is suitable food. Therefore, the assimilation efficiency of detritivores for refractory material is
usually set to 0.0, and the assimilation efficiency for labile material is increased accordingly.
Sedimentation and scour, or resuspension, are opposite processes. In shallow systems there may be
no long-term sedimentation (Wetzel et al., 1972), while in deep systems there may be little
resuspension. In this version sedimentation is a function of flow, ice cover and, in very shallow
water, wind based on simplifying assumptions. Burial, scour and exposure are applicable only in
streams where they are keyed to the behavior of clay and silt. Scour as an explicit function of wave
and current action is not implemented.
Detrital Formation
Detritus is formed in several ways: through mortality, gamete loss, sinking of phytoplankton,
excretion and defecation:
DetrFmSuSpRefrDetr = ^biotaWortldetr, biota ' Mortality '^J (120)
DetrFmDissRefrDetr = ^ biota(Mort2 detr^iota Mortality biota) + S biota(Excr2 detf^iota - Excretion)
DetrFmDissLaMeDetr = 2biota(Mort2detr
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 5
DetrFmSedRefrDetr = 2prJDef2detr>pred Defecationprj
PlantSinkToDetr)
where:
DetrFm = formation of detritus (g/m3*d);
Mort2dett jbiota = fraction of given dead organism that goes to given detritus (unitless);
Excr2detfr biota = fraction of excretion that goes to given detritus (unitless);
Mortality biota = death rate for organism (g/m3*d), see .' ", ',,...and ; .....>..;
Excretion = excretion rate for organism (g/m3«d), see ; and; for plants and
animals, respectively;
GameteLoss = loss rate for gametes (g/m3*d), see * ' :';
Def2detr biota = fraction of defecation that goes to given detritus (unitless);
Defecation^ = defecation rate for organism (g/m3«d), see " ;
Sedimentation = loss of phytoplankton to bottom sediments (g/m3*d), see , *:; and
PlantSinkToDetr = labile and refractory portions of phytoplankton (unitless, 0.92 and
0.08 respectively).
A fraction of mortality, including sloughing of leaves from macrophytes, is assumed to go
to refractory detritus; a much larger fraction goes to labile detritus. Excreted material goes to both
refractory and labile detritus, while gametes are considered to be labile. Half the defecated material
is assumed to be labile because of the conditioning due to ingestion and subsequent inoculation with
bacteria in the gut (LeCren and Lowe-McConnell, 1980); fecal pellets sink rapidly (Smayda, 1971),
so defecation is treated as if it were directly to sediments. Phytoplankton that sink to the bottom are
considered to become detritus; most are consumed quickly by zoobenthos (LeCren and 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 often refractory because it has a deficiency of nitrogen compared to
microbial biomass. In order for microbes to colonize refractory detritus, they have to take up
additional nitrogen from the water (Saunders et al., 1980). Thus, colonization is nitrogen-limited,
as well as being limited by suboptimal temperature, pH, and dissolved oxygen:
Colonization = ColonizeMax DecTCorr NLimit pHCorr
DOCorrection RefrDetr (126)
where:
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Colonization = rate of conversion of refractory to labile detritus (g/m3*d);
Figure 55. Colonization and Decomposition as
an Effect of Temperature
c
4.5-
4-
3.5-
w? <=>-
LJ_ J--^
Hi 2-
1.5-
1-
0.5-
- ^^_^^
^'
^^
/
/
7
/
/
/
/
0 10 20 30 40 50 60 70
TEMPERATURE (C)
ColonizeMax =
Nlimit =
DecTCorr =
pHCorr
DOCorrection =
RefrDetr
maximum colonization rate under ideal conditions (g/g*d);
limitation due to suboptimal nitrogen levels (unitless), see
the effect of temperature (unitless), see illli;
limitation due to suboptimal pH level (unitless), see ' '. .;
limitation due to suboptimal oxygen level (unitless), see
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:
DecTCorr = Thetalemp ~ 1Ubs where
Theta = 1.047 if Temp ^ 19° else
Theta = 1.185 - 0.00729 Temp
If Temv > TMax Then DecTCorr = 0
(127)
The resulting curve has a shoulder similar to the Stroganov curve, but the effect increases
up to the maximum rate (:'.' -... > ).
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The nitrogen limitation construct, which is original with AQUATOX, is parameterized using
an analysis of data presented by Egglishaw (1972) for Scottish streams. It is computed by:
, . v N - MinN
NLimit = (128)
N - MinN + HalfSatN l '
N = Ammonia + Nitrate (129)
where:
N = total available nitrogen (g/m3);
MinN = minimum level of nitrogen for colonization (= 0.1 g/m3);
HalfSatN = half-saturation constant for nitrogen stimulation (=0.15 g/m3);
Ammonia = concentration of ammonia (g/m3); and
Nitrate = concentration of nitrite and nitrate (g/m3).
Although it can be changed by the user, a default maximum colonization rate of 0.007
(g/g*d) per day is provided, based on Mclntire and Colby (1978, after Sedell et al., 1975).
The rates of decomposition (or colonization) of refractory dissolved organic matter are
comparable to those for particulate matter. Saunders (1980) reported values of 0.007 (g/g*d) for a
eutrophic lake and 0.008 (g/g*d) for a tundra pond. Anaerobic rates were reported by Gunnison et
al. (1985).
Decomposition
Decomposition is the process by which detritus is broken down by bacteria and fungi,
yielding constituent nutrients, including nitrogen, phosphorus, and inorganic carbon. Therefore, it
is a critical process in modeling nutrient recycling. In AQUATOX, following a concept first
advanced by Park et al. (1974), the process is modeled as a first-order equation with multiplicative
limitations for suboptimal environmental conditions (see section 4.1 for a discussion of similar
construct for photosynthesis):
Decomposition = DecayMax DOCorrection DecTCorr pHCorr Detritus (130)
where:
Decomposition = loss due to microbial decomposition (g/m3*d);
DecayMax = maximum decomposition rate under aerobic conditions (g/g*d);
DOCorrection = correction for anaerobic conditions (unitless), see .. " " ;
DecTCorr = the effect of temperature (unitless), see
pHCorr = correction for suboptimal pH (unitless), see UU ,", ; and
Detritus = concentration of detritus, including dissolved but not buried (g/m3).
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 5
Note that biomass of bacteria is not explicitly modeled in AQUATOX, rather it is considered
part of the detritus. In some models (for example, EXAMS, Burns et al., 1982) decomposition is
represented by a second-order equation using an empirical estimate of bacteria biomass. However,
using bacterial biomass as a site constant constrains the model, potentially forcing the rate.
Decomposers were modeled explicitly as a part of the CLEAN model (Clesceri et al., 1977).
However, if conditions are favorable, decomposers can double in 20 minutes; this can result in stiff
equations, adding significantly to the computational time. Ordinarily, decomposers will grow
rapidly as long as conditions are favorable. The only time the biomass of decomposers might need
to be considered explicitly is when a new organic chemical is introduced and the microbial
assemblage requires time to become adapted to using it as a substrate.
The effect of temperature on biodegradation is represented by Equation which also
is used for colonization. The function for dissolved oxygen, formulated for AQUATOX, is:
r\/^/^ * T? + /-1 i7 * \ KAnaerobic
DOCorrection = Factor + (1 - Factor) (131)
DecayMax
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 = ^
HalfSatO + Oxygen
and:
Factor = Michaelis-Menten factor (unitless);
KAnaerobic = decomposition rate at 0 g/m3 oxygen (g/g*d);
Oxygen = dissolved oxygen concentration (g/m3); and
HalfSatO = half-saturation constant for oxygen (g/m3).
DOCorrection accounts for both decreased and increased degradation rates
under anaerobic conditions, with KAnaerobic/DecayMax having values less than one and greater
than one, respectively. Detritus will always decompose more slowly under anaerobic conditions;
but some organic chemicals, such as some halogenated compounds (Hill and McCarty, 1967), will
degrade more rapidly. Half-saturation constants of 0.1 to 1.4 g/m3 have been reported (Bowie et al.,
1985); a value of 0.1 g/m3 is used.
(132)
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Figure 56. Correction for Dissolved Oxygen
8
34567
Dissolved Oxygen
10
KAnaerobic = 1.3
KAnaerobic = 0.3
- KAnaerobic = 0
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 growbetween 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 =
~ pHMn)
(133)
where:
pH
pHMin
ambient pH, and
minimum pH below which limitation on biodegradation rate occurs.
If the pH is above the upper end of the optimal range for microbial degradation, the
following equation is used:
pHCorr = e^0* " pH}
(134)
where:
pHMax
maximum pH above which limitation on biodegradation rate
occurs.
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These responses are shown in |;1;;
Figure 57
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 and Resuspension
When the inorganic sediment model is not included in a simulation, the sedimentation of
suspended particulate detritus to bottom sediments and the resuspension of bottom sediments to
suspended detritus are modeled using simplifying assumptions. The constructs are intended to
provide general responses to environmental factors, but they should not be considered as anything
more than place holders for more realistic hydrodynamic functions to be incorporated in later
versions. When the inorganic sediment model is included, the sedimentation and deposition of
detritus is assumed to mimic the sedimentation and resuspension of silt (see i!Ji/i and .).
Otherwise:
Sedimentation =
Thick
Decel State
(135)
where:
Sedimentation =
KSed
Thick =
Decel =
State
transfer from suspended to sedimented by sinking (g/m3*d), see
sedimentation rate (m/d);
depth of water or thickness of layer if stratified (m);
deceleration factor (unitless), see ; and
concentration of particulate detrital compartment (g/m3).
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If the discharge exceeds the mean discharge then sedimentation is slowed proportionately
If TotDischarge > MeanDischarge then
~ , MeanDischarge
TotDischarge
else Decel = 1.0
(136)
where:
TotDischarge =
MeanDischarge =
total epilimnetic and hypolimnetic discharge (m3/d); and
mean discharge over the course of the simulation (m3/d).
If the depth of water is less than or equal to 1.0 m and wind speed is greater than or equal
to 5.5 m/s then the sedimentation rate is negative, effectively becoming the rate of resuspension.
If there is ice cover, then the sedimentation rate is doubled to represent the lack of turbulence.
Figure 58. Relationship of Decel to Discharge with
a Mean Discharge of 5 m3/s.
1.2
0.4
0.2
Mean
discharge
10 12 14 16 18 20 22 24
Discharge (cu m/s)
5.2 Nitrogen
Two nitrogen compartments, ammonia and nitrate, are modeled Nitrite occurs
in very low concentrations and is rapidly transformed through nitrification and denitrification
(Wetzel, 1975); therefore, it is modeled with nitrate. Likewise, un-ionized ammonia (NH3) is not
modeled as a separate state variable. Ammonia is assimilated by algae and macrophytes and is
converted to nitrate as a result of nitrification:
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 5
dAmmonia T ,. ,-, . ~
= Loading + Excrete + Decompose
dt F (137)
- Nitrify - AssimilationAmmonia - Washout ± TurbDiff
where:
dAmmonia/dt = change in concentration of ammonia with time (g/m3*d);
Loading = loading of nutrient from inflow (g/m3*d);
Excrete = ammonia derived from excretion by animals (g/m3*d), see ;
Decompose = ammonia derived from decomposition of detritus (g/m3*d), see ; ;
Nitrify = nitrification (g/m3*d), see : ,;
Assimilation = assimilation of nutrient by plants (g/m3*d), see ; ? and { > ;
Washout = loss of nutrient due to being carried downstream (g/m3*d), see : ;
and;
TurbDiff = depth-averaged turbulent diffusion between epilimnion and
hypolimnion if stratified (g/m3«d), see (I ':. and ( ; jj.
Ammonia is a product of decomposition:
Decompose = I,Detritus(Org2Ammonia DecompositionDetritJ (133)
It also is excreted directly by animals:
Excrete = SBiota(Org2Ammonia ExcretionOrganlsJ (139)
where:
Org2Ammonia = ratio of ammonia to organic matter (unitless);
Decomposition = decomposition rate of given type of detritus, (g/m3«d), see
; i ..:'fi'.'-: and
Excretion = excretion rate of given animal (g/m3*d), see '''.
Nitrate is assimilated by plants and is converted to free nitrogen (and lost) through
denitrification:
= Loading + Nitrify - Denitrify - Assimilationmtrate - Washout ± TurbDiff (140)
where:
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dNitrate/dt
Loading =
Denitrify =
change in concentration of nitrate with time (g/m3«d);
user entered loading of nitrate, including atmospheric deposition; and
denitrification (g/m3*d); see (145).
Free nitrogen can be fixed by blue-green algae. Both nitrogen fixation and denitrification
are subject to environmental controls and are difficult to model with any accuracy; therefore, the
nitrogen cycle is represented with considerable uncertainty.
Figure 59. Components of Nitrogen Remineralization
Decomposition
Excretion
Denitrification
Ammonia
Nitrification
Assimilation
Assimilation
Assimilation
Nitrogen compounds are assimilated by plants as a function of photosynthesis in the
respective groups (Ambrose et al., 1991):
AssimilationAmmonia = Xplant(Photosynthesisplant UptakeNitrogen NH4Pref) (141)
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AssimilationNfr . = ?jpl (Photosynthesis
'Plant
Uptake
Nitrogen
(1 - NH4Prefj)
(142)
where:
Assimilation =
Photosynthesis =
Uptake mtrogen =
NH4Pref
assimilation rate for given nutrient (g/m3«d);
rate of photosynthesis (g/m3*d), see
fraction of photosynthate that is nitrogen (unitless, 0.01975 if
nitrogen-fixing, otherwise 0.079);
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):
N2NH4 Ammonia N2NO3 Nitrate
NH4Pref =
(KN + N2NH4 Ammonia) (KN + N2NO3 Nitrate)
N2NH4 Ammonia KN
(N2NH4 Ammonia + N2NO3 Nitrate) (KN + N2NO3 Nitrate)
(143)
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 nitrifying bacteria;
it occurs primarily at the sediment-water interface (Effler et al., 1996). The maximum rate of
nitrification, corrected for the area to volume ratio, is reduced by limitation factors for suboptimal
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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
Area
Volume
DOCorrection TCorr pHCorr Ammonia
(144)
where:
Nitrify
KNitri
Area
Volume
DOCorrection :
TCorr
pHCorr
Ammonia
nitrification rate (g/m3«d);
maximum rate of nitrification (0.135 m/d, according to Effler et al.,
1996);
area of site or segment (m2);
volume of site or segment (m3); see . ;;
correction for anaerobic conditions (unitless) see ;
correction for suboptimal temperature (unitless); see ; .,;
correction for suboptimal pH (unitless), see ; -. ; and
concentration of ammonia (g/m3).
The nitrifying bacteria have narrow environmental optima; according to Bowie et al.
(1985) they require aerobic conditions with a pH between 7 and 9.8, an optimal temperature of 30°,
and minimum and maximum temperatures of 10° and 60° respectively (iijyiii :;dl, jLl^iiLlLI!).
Figure 60
Response to pH, Nitrification
EFFECT OF pH
5 6.4 7.8 92 10.6
5.7 7.1 8.5 9.9
pH
Figure 61
Response to Temperature, Nitrification
STROGANOV FUNCTION
NITRIFICATION
TOpt
10 20 30 40 50 60
TEMPERATURE (C)
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 (145)
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where:
Denitrify
KDenitri
Nitrate
denitrification rate (g/m3«d);
maximum rate of denitrification (0.1 m/d, according to Di Toro,
2001); 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; FjjyireJ^,Figiire_63).
Figure 62
Response to pH, Denitrification
3.9
EFFECT OF pH
6.6 8.4 10.2
5.7 7.5 9.3
pH
Figure 63
Response to Temperature, Denitrification
o
STROGANOV FUNCTION
DECOMPOSITION
TOpt
10
20 30 40 50
TEMPERATURE(C)
60
5.3 Phosphorus
The phosphorus cycle is much simpler than the nitrogen cycle. Decomposition, excretion,
and assimilation are important processes that are similar to those described above:
= Loading FracAvail + Excrete + Decompose
dt
- Assimilationphosphate - Washout ± TurbDiff
(146)
Excrete = SBiota(Org2Phosphate ExcretionBiota)
(147)
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Decompose = SDetritus(Org2Phosphate Decomposition Detritw)
(148)
Assimilation = Splant(Photosynthesisplant UptakePhosphorJ
(149)
where:
dPhosphate/dt =
Loading =
FracAvail =
Excrete =
Decompose =
Assimilation =
Washout =
Area =
Volume =
Org2Phosphate =
Excretion =
Decomposition =
Photosynthesis =
Uptake =
change in concentration of phosphate with time (g/m3«d);
loading of nutrient from inflow and atmospheric deposition (g/m3«d);
fraction of phosphate loading that is available (unitless);
phosphate derived from excretion by biota (g/m3«d); see and
for plants and animals, respectively;
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 IJjil;
area of site (m2);
volume of water at site (m3); see
ratio of phosphate to organic matter (unitless);
excretion rate for given organism (g/m3«d), see ' * - and if?) for
plants and animals, respectively;
decomposition rate for given detrital compartment (g/m3«d), see
rate of photosynthesis (g/m3«d), see ilJJt, and
fraction of photosynthate that is phosphate (unitless, 0.018).
At this time AQUATOX models only phosphate available for plants; a correction factor in
the loading screen allows the user to scale total phosphate loadings to available phosphate. A future
enhancement could be to consider phosphate precipitated with calcium carbonate, which would
better represent the dynamics of marl lakes; however, that process is ignored in the current version.
A default value is provided for average atmospheric deposition, but this should be adjusted for site
conditions. In particular, entrainment of dust from tilled fields and new highway construction can
cause significant increases in phosphate loadings. As with nitrogen, the uptake parameter is the
Redfield (1958) ratio; it may be edited if a different ratio is desired (cf Harris, 1986).
-2^ = Loading + Reaeration + Photosynthesized
dt
- BOD - NitroDemand - Washout ± TurbDiff
(150)
5.4 Dissolved Oxygen
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Oxygen is an important regulatory endpoint; very low levels can result in mass mortality for
fish and other organisms, mobilization of nutrients and metals, and decreased degradation of toxic
organic materials. Dissolved oxygen is simulated as a daily average and does not account for diurnal
fluctuations. It is a function of reaeration, photosynthesis, respiration, decomposition, and
nitrification:
Photosynthesized = O2Photo 2jplant(Photosynthesisplant)
(151)
BOD = 02Biomass &Detritm(DecompositionDetritus) +
(i52)
NitroDemand = O2N Nitrify
(153)
where:
dOxygen/dt
Loading
Reaeration
Photosynthesized
O2Photo
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/m3*d);
oxygen produced by photosynthesis (g/m3«d);
ratio of oxygen to photosynthesis (1.6, unitless);
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
ratio of oxygen to organic matter (mg oxygen/mg biomass;
0.575, but user can change in remineralization screen);
rate of photosynthesis (g/m3*d), see IIH;
rate of decomposition (g/m3«d), see
rate of respiration (g/m3*d), see and
ratio of oxygen to nitrogen (unitless; 4.57, but user can
change in remineralization screen); and
rate of nitrification (gN/m3«d).
Reaeration is a function of the depth-averaged mass transfer coefficient KReaer, corrected
for ambient temperature, multiplied by the difference between the dissolved oxygen level and the
saturation level (cf. Bowie et al., 1985):
Reaeration = KReaer (O2Sat - Oxygen) (154)
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where:
Reaeration = mass transfer of oxygen (g/m3*d);
KReaer = depth-averaged reaeration coefficient (1/d);
O2Sat = saturation concentration of oxygen (g/m3), see £163); and
Oxygen = concentration of oxygen (g/m3).
In standing water KReaer is computed as a minimum transfer velocity plus the effect of wind
on the transfer velocity (Schwarzenbach et al., 1993) divided by the thickness of the mixed layer to
obtain a depth-averaged coefficient (jFigiire_64):
~D (4E-4 + 4E-5 Wind2) 864 __
KReaer = ± '- (155)
Thick y '
where:
Wind = wind velocity 10 m above the water (m/sec);
864 = conversion factor (cm/sec to m/d); and
Thick = thickness of mixed layer (m).
Algal blooms can generate dissolved oxygen levels that are as much as 400% of saturation
(Wetzel, 2001). However, near-surface blue-green algal blooms, which are modeled as being in the
top 0.33 m, produce high levels of oxygen that do not extend significantly into deeper water. An
adjustment is made in the code so that if the blue-green algal biomass exceeds 1 mg/L and is greater
than other phytoplankton biomass, the thickness subject to oxygen reaeration is set to 0.33 m. This
does not affect the KReaer that is used in computing volatilization.
In streams, reaeration is a function of current velocity and water depth (. - ",) 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 m/sec:
TransitionDepth = 0 (156)
else:
TransitionDepth = 4.411 Vel2'9135 (157)
where:
Vel = velocity of stream (converted to m/sec) see fJJl; and
TransitionDepth = intermediate variable (m).
If Depth < 0.61 m, the equation of Owens et al. (1964, cited in Ambrose et al., 1991) is used:
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 5
KReaer = 5.349 Vel0-61 Depth'1*5 (158)
where:
Depth = mean depth of stream (m).
Otherwise, if Depth is > TmnsitionDepth, the equation of O'Connor and Dobbins (1958, cited in
Ambrose et al., 1991) is used:
KReaer = 3.93 Vel0'50 Depth'1'50 (159)
Else, if Depth 'TransitionDepth, the equation of Churchill et al. (1962, cited in Ambrose et al.,
1991) is used:
KReaer = 5.049 Vel0-91 Depth'1*1 (160)
In extremely shallow streams, especially experimental streams where depth is < 0.06 m, an
equation developed by Krenkel andOrlob (1962, cited in Bowie etal. 1985) from flume data is used:
,0.408
234 (U Slope)
KReaer = ^ *-*-
ffO.66
where:
U = velocity (converted to fps);
Slope = longitudinal channel slope (m/m); and
H = water depth (converted to ft).
If reaeration due to wind exceeds that due to current velocity, the equation for standing water
is used. Reaeration is set to 0 if ice cover is expected (i.e., when the depth-averaged temperature
< 3°C).
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Figure 64
Reaeration as a Function of Wind
10
. 8
o:
EFFECT OF WIND
OXYGEN, DEPTH = 1 m
6 10
WIND (m/s)
12 16
14
Figure 65
Reaeration in Streams
1E-3 C ^ ,,
0,1 ,;, -,
l.j if--' an
50
VELOCITY (m/sec)
0.1
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 = KReaer20 Theta(Temperature ~ 20)
(162)
where:
KReaerT = Reaeration coefficient at ambient temperature (1/d);
Kreaer20 = Reaeration coefficient for 20°C (1/d);
Theta = temperature coefficient (1.024); and
Temperature = ambient water temperature (°C).
Oxygen saturation, as a function of both temperature and salinity
is based on Weiss (1970, cited in Bowie et al., 1985):
O2Sat = 1.4277-exp[-173.4927+ 2496339 + 143.3483 ln| TKelvm\ -0.21849
TKelvin
100
(163)
TKelvin + S (-0.033096 + 0.00014259 TKelvin -1.7 10"7 jTKelvin)]
where:
TKelvin
S
Kelvin temperature, and
salinity (ppt).
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION
CHAPTER 5
According to Bowie et al. (1985), it gives results that are not significantly different from
those computed by the more complex APHA (1985) equations that are used in WASP (Ambrose et
al., 1993). At the present time salinity is set to 0; although, it has little effect on reaeration.
Figure 66
Saturation as a Function of Temperature
OXYGEN SATURATION
SALINITY = 0 ppt
7.5
12 16.5 21 25.5 30 34.5 39
TEMPERATURE (C)
Figure 67
Saturation as a Function of Salinity
OXYGEN SATURATION
TEMPERATURE = 20C
8.55
8.5
8.45
8.35
8.3
8.25
4.5 9 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 ± TurbDiff
(164)
where:
Respired = CO2Biomass VOrganism(ResPirationOrganiJ
(165)
Assimilation = Splant(Photosynthesisplant UptakeCO2)
(166)
Decompose = CO2Biomass
'Detritus
itJDecomp DetritJ
(167)
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION
CHAPTER 5
and where:
dCO2/dt
Loading
Respired
Decompose
Assimilation
Washout
CO 2A tmosExch
TurbDiff
CO2Biomass
Respiration
Decomposition
Photosynthesis
UptakeCO2
change in concentration of carbon dioxide (g/m3«d);
loading of carbon dioxide from inflow (g/m3*d);
carbon dioxide produced by respiration (g/m3«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 r is I;
interchange of carbon dioxide with atmosphere (g/m3«d);
depth-averaged turbulent diffusion between epilimnion and
hypolimnion if stratified (g/m3*d), see / :; and ( : : ;
ratio of carbon dioxide to organic matter (unitless; 0.526,
according to Winberg, 1971);
rate of respiration (g/m3*d), see ; " and I'-'.';;
rate of decomposition (g/m3«d), see ; ;:';
rate of photosynthesis (g/m3*d), see , : ;; 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 under saturation and over saturation are possible (Stumm and Morgan,
1996). The treatment of atmospheric exchange is similar to that for oxygen:
CO2AtmosExch = KLiqCO2 (CO2Sat - CO2)
(168)
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):
KLiqCO2 = KReaer
MolWtO2
MolWtCO2\
, 0.25
(169)
where:
CO2AtmosExch
KLiqCO2
C02
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 '; i ;
depth-averaged reaeration coefficient for oxygen (1/d), see
molecular weight of oxygen (=32); and
molecular weight of carbon dioxide (= 44).
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION
CHAPTER 5
Keying the mass-transfer coefficient for carbon dioxide to the reaeration coefficient for
oxygen is very powerful in that the effects of wind (' . ) and the velocity and depth of streams
can be represented, using the oxygen equations (Equations ;" >. :-, .).
Figure 68
Carbon Dioxide Mass Transfer
EFFECT OF WIND
CARBON DIOXIDE, DEPTH = 1 m
10
6 8 10
WIND (mis)
12 14 16
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 ( " . :'), and the
partial pressure of carbon dioxide:
CO2Sat = CO2Henry pCO2 (170)
where:
CO2Henry = MCO2 10
2385.73
TKelvin
- 14.0184 + 0.0152642 TKelvin
(171)
TKelvin = 273.15 + Temperature
(172)
and where:
CO2Sat
CO2Henry =
pC02
MCO2
TKelvin =
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).
5-24
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION
CHAPTER 5
Figure 69
Saturation of Carbon Dioxide
CARBON DIOXIDE SATURATION
7,5
12 16.5 21 25.5 30 34.5 39
TEMPERATURE (C)
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 5
5-26
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 6
6 INORGANIC SEDIMENTS1
The sediment transport component of AQUATOX simulates scour, deposition and transport
of sediments and calculates the concentration of sediments in the water column and sediment bed
within a river reach. For running waters, the sediment is divided into three categories according to
the particle size: 1) sand, with particle sizes between 0.062 to 2.0 millimeters (mm), 2) silt (0.004
to 0.062 mm), and 3) clay (0.00024 to 0.004 mm). Wash load (primarily clay and silt) is deposited
or eroded within the channel reach depending on the daily flow regime. Sand transport is also
computed within the channel reach. At present, inorganic sediments in standing water are computed
based on total suspended solids loadings, described in section 6.3.
The river reach is assumed to be short and well mixed so that concentration does not vary
longitudinally. Flow routing is not performed within the river reach. The daily average flow regime
determines the amount of scour, deposition and transport of sediment. Scour, deposition and
transport quantities are also limited by the amount of solids available in the bed sediments and the
water column.
Inorganic sediments are important to the functioning of natural and perturbed ecosystems
for several reasons. When suspended, they increase light extinction and decrease photosynthesis.
When sedimented, they can temporarily or permanently remove toxicants from the active ecosystem
through deep burial. Scour can adversely affect periphyton and zoobenthos. All these processes are
represented to a certain degree in AQUATOX. In addition, rapid sedimentation also can adversely
affect periphyton and some zoobenthos; and the ratio of inorganic to organic sediments can be used
as an indicator of aerobic or anaerobic conditions in the bottom sediments. These are not simulated
in the model at this time.
The mass of sediment in each of the three sediment size classes is a function of the previous
mass, and the mass of sediment in the overlying water column lost through deposition, and gained
through scour:
MassBedSed = MassBedSed_ ,=_j + (DepositSed - ScoursJ VolumeWater (173)
where:
MassBedSed = mass of sediment in channel bed (kg);
MassBedSed t = _} = mass of sediment in channel bed on previous day (kg);
DepositSed = amount of suspended sediment deposited (kg/m3); see
ScourSed = amount of silt or clay resuspended (kg/m3); see and
VolumeWater = volume of stream reach (m3); see page 3-1.
1 Original version contributed by Rodolfo Camacho of Abt Associates Inc.
6- 1
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 6
The volumes of the respective sediment size classes are calculated as:
MassBeds ,
Volume^ = (174)
Rh°Sed
where:
VolumeSed = volume of given sediment size class (m3);
MassBedSed = mass of the given sediment size class (kg); see
Rh°$eA = density of given sediment size class (kg/m3);
RhoSmd = 2600 (kg/m3); and
i\t, Clay
2400 (kg/m3).
The porosity of the bed is calculated as the volume weighted average of the porosity of its
components:
BedPorosity = ^ FracSed ' Porositysed (175)
where:
BedPorosity = porosity of the bed (fraction);
FracSed = fraction of the bed that is composed of given sediment class; and
PorositySed = porosity of given sediment class.
The total volume of the bed is calculated as:
Volume? , + Volume?.,, + Volume^,
BedVolume = ^ ^ ^ (176)
1 -BedPorosity
where:
BedVolume = volume of the bed (m3).
The depth of the bed is calculated as
D , ., BedVolume
BedDepth = (177)
ChannelLength ChannelWidth y '
where:
BedDepth = depth of the sediment bed (m);
ChannelLength = length of the channel (m); and
ChannelWidth = width of the channel (m).
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION
CHAPTER 6
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:
dConc
Sed
dt
= LoadSed + ScourSed - DepositSed - WashSed
(178)
where:
ConcSed
LoadSed
ScourSed
DepositSed
WashSed
concentration of silt or clay in water column (kg/m3);
loading of clay or silt (kg/m3 d);
amount of silt or clay resuspended (kg/m3 d); see ;1O;
amount of suspended sediment deposited (kg/m3 d); see and
amount of sediment lost through downstream transport (kg/m3 d); see
The concentration of sand is computed using atotally 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):
Tan = H2ODensity Slope HRadius
(179)
where:
Tau =
mODensity =
Slope =
shear stress (kg/m2);
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
(180)
where:
HRadius
Y
Width
hydraulic radius (m);
average depth over reach (m); and
channel width (m).
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION _ CHAPTER 6
Resuspension or scour of bed sediments is predicted to occur when the computed shear stress
is greater than the critical shear stress for scour:
if Tau > TauScour Sed then
= Erodibilitysed ( Tau
Sed
TauScour^
where:
ScourSed = resuspension of silt or clay (kg/m3); see also
ErodibilitySed = erodibility coefficient, (0.244 kg/m2); and
TauScourSed = critical shear stress for scour of silt or clay (kg/m2); default values are
given in stream data screen, but may be changed by the user.
The amount of sediment that is resuspended is constrained by the mass of sediments stored
in the bed. An intermediate variable representing the maximum potential mass that can be scoured
is calculated; if the mass available is less than the potential, then scour is set to the lower amount:
CheckSed = ScOUrSed ' V°lumeWater (182)
if MassSed < CheckSed then
Scour
sed
VolumeWater
where:
CheckSed = maximum potential mass (kg); and
MassSed = mass of silt or clay in bed (kg); see lOj-
Deposition occurs when the computed shear stress is less than the critical depositional shear
stress:
if Tau < TauDepSed then
ay _ Tau
Deposit^ = Concsed 1 - e Y TailDlf»
where:
DepositSed = amount of sediment deposited (kg/m3 day);
TauDepSed = critical depositional shear stress (kg/m2); default values are given in
stream data screen, but may be changed by the user;
6-4
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 6
ConcSed = concentration of suspended silt or clay (kg/m3); see
VTSed = terminal fall velocity of given sediment type (m/s); default values are
given in stream data screen, but may be changed by the user; and
SecPerDay = 86400 (seconds / day).
Downstream transport is an important mechanism for loss of suspended sediment from a
given stream reach:
Disch Concv ,
Wash,, = (185)
Sed SegVolume l '
where:
WashSed = amount of given sediment lost to downstream transport (kg/m3 day);
Disch = discharge of water from the segment (m3/day);
ConcSed = concentration of suspended sediment (kg/m3);
SegVolume = volume of segment (m3); see page 3-1.
When the inorganic sediment model is included in an AQUATOX stream simulation, the
deposition and erosion of detritus mimics the deposition and erosion of silt. The fraction of detritus
that is being scoured or deposited is assumed to equal the fraction of silt that is being scoured or
deposited. The following equations are used to calculate the scour and deposition of detritus:
Volumes.lt
FracScourDetritus = FracScourSilt = Scourm (186)
= FC ScOUrDetritus ' C°nC'AllSedDetritus ' 100° (187)
where:
FracScour = fraction of scour per day (fraction/day);
ScourSilt = amount of silt scoured (kg/m3 day) see ; .:: ;
VolumeSih = volume of silt in the bed (m3); see ' -';
MassSilt = mass of silt in the bed (kg); see ; ,,";
ConcAllSedDetritus = all sedimented detritus (labile and refractory) in the stream
bed (kg/m3);
ScourDetritus = amount of detritus scoured (g/m3 day); and
1000 = conversion of kg to g.
The equations for deposition of detritus are similar:
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION
CHAPTER 6
FracDepositionDetritus = Frac Deposition Silt =
DepositionSilt 1000
Concsat
(188)
DepositionDetritus = Frac DepositionDetritm ConcSuspDetritus
(189)
where:
DepositionSilt
Concm
FracDeposition
SuspDetritus
DepositionDetntus
amount of silt deposited (kg/m3 day) see
amount of silt initially in the water (g/m3);
fraction of deposition per day (firac / day); and
amount of suspended detritus initially in the water (g/m3); and
amount of detritus deposited (g/m3 day).
6.2 Scour, Deposition and Transport of Sand
Scour, deposition and transport of sand are simulated using the Engelund and Hansen (1967)
sediment transport relationships as presented by Brownlie (1981). This relationship was selected
because of its simplicity and accuracy. Brownlie (1981) shows that this relationship gives good
results when compared to 13 others using a field and laboratory data set of about 7,000 records.
PotConcSand = 0.05
Rho
Velocity
RhoSand - Rho
\
RhOy , - Rho
'g'D /1 000
Rho
^TauStar
(190)
where:
PotConcSand
Rho
KhoSand
Velocity
Slope
l^Sand
TauStar
potential concentration of suspended sand (kg/m3);
density of water (1000 kg/m3)
density of sand (2650 kg/m3);
flow velocity (converted to m/s);
slope of stream (m/m);
mean diameter of sand particle (0.30 mm converted to m); and
dimensionless shear stress.
The dimensionless shear stress is calculated by:
Rho
TauStar =
Rh°Sand ~ Rk°
HRadius
Slope
(191)
6-6
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION
CHAPTER 6
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 = PotC°nCSand ' V°lumeWater
(192)
MassSuspSand = ConcSand VolumeWater
(193)
TotalMassSand = MassSuspSand + MassBedSand
(194)
if CheckSand < MassSuspSand then
DepositSand = MassSuspSand - CheckSand
C°nCSand = PotC°nCSand
(195)
if Check
Sand
TotalMass Sand then
MassBedSand = 0
Cone
TotalMass
Sand
Sand
Volume
Water
(196)
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 6
if CheckSand > MassSuspSand and < TotalMassSand then
ScOUrSand = CheckSa«d ~ MaSsSuSPSand
= MaSsSuSPSand + ScOUrSand
VolumeWater
where:
CheckSand = maximum potential mass (kg);
MassBedSand = mass of sand in bed (kg);
MassSuspSand = mass of sand in water column (kg);
ConcSand = concentration of sand in water column (kg/m3);
ScourSand = amount of sand resuspended (kg/m3 d);
DepositSand = amount of suspended sand deposited (kg/m3 d);
PotConcSand = potential concentration of suspended sand (kg/m3); see
Volume = volume of reach (m3); see page 3-1.
6.3 Suspended Inorganic Sediments in Standing Water
At present, AQUATOX does not compute settling of inorganic sediments in standing water
or scour as a function of wave action. However, suspended sediments are important in creating
turbidity and limiting light, especially in reservoirs and shallow lakes. Therefore, the user can
provide loadings of total suspended solids (TSS), and the model will back-calculate suspended
inorganic sediment concentrations by subtracting the simulated phytoplankton and suspended
detritus concentrations:
InorgSed = TSS -^Phyto - ^PartDetr (198)
where:
InorgSed = concentration of suspended inorganic sediments (g/m3);
TSS = observed concentration of total suspended solids (g/m3);
Phyto = predicted phytoplankton concentrations (g/m3), see \, '' ; and
PartDetr = predicted suspended detritus concentrations (g/m3), see : %, : .. ,..
The concentration of suspended inorganic sediments is used solely to calculate their
contribution to the extinction coefficient, which affects the depth of the euphotic zone and the Secchi
depth (see (35
6-8
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AQUATOX (RELEASE 2) 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 70). and estimates the rate of degradation of the compound
(Figure 71). Microbial degradation, biotransformation, photolysis, hydrolysis, and volatilization
are modeled in AQUATOX. Each of these processes is described generally, and again in more detail
below.
Nonequilibrium concentrations, as represented by kinetic equations, depend on sorption,
desorption, and elimination as functions of the chemical and exposure through water and food as a
function of bioenergetics of the organism. Equilibrium partitioning is computed as a constraint on
sorption and for purposes of computing critical body residues for ecotoxicity, but it is no longer an
output from AQUATOX. Partitioning to inorganic sediments is not modeled at this time.
Microbial degradation is modeled by entering a maximum biodegradation rate for a
particular organic toxicant, which is subsequently reduced to account for suboptimal temperature,
pH, and dissolved oxygen. Biotransformation is represented by user-supplied first-order rate
constants with the option of also modeling multiple daughter products. Photolysis is modeled by
using a light screening factor (Schwarzenbach et al., 1993) and the near-surface, direct photolysis
first-order rate constant for each pollutant. The light screening factor is a function of both the
diffuse attenuation coefficient near the surface and the average diffuse attenuation coefficient for
the whole water column. For those organic chemicals that undergo hydrolysis, neutral, acid-, and
base-catalyzed reaction rates are entered into AQUATOX as applicable. Volatilization is modeled
using a stagnant two-film model, with the air and water transfer velocities approximated by
empirical equations based on reaeration of oxygen (Schwarzenbach et al., 1993).
Figure 70. In-situ Uptake and Release of Chlorpyrifos in a Pond
250.00%
Plant Sorption
Depuration
D Gill Sorption D Depuration D Detrital Sorption D Decomposition Detrital Desorption D Plant Sorption
7- 1
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION
CHAPTER 7
Figure 71. In-situ Degradation Rates for Chlorpyrifos in Pond
o
*J
7.00%
4.00% -
2.00% -
0.00%
Volatilization
Hydrolysis
-------
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION _ CHAPTER 7
°XWan SedLabileDetr = Sorption - Desorption + (Colonization PPBSedRefrDetr le-6)
- (Resuspension + Scour + Decomposition) PPB SedLabUeDetr
' le-6 - ^p^IngestionpredtSeajMUDetr PPBSedLabileDetr le-6 (200)
+ (Sedimentation + Deposition) PPB SuspLabileDetr le-6
+ Yi(Sed2Detr Sinkphyto PPBphyto le-6)
- Hydrolysis - MicrobialDegrdn - Burial + Expose
± BiotransformMicrobial
dToxicantv , , n ^
SedRe^Detr = Sorption - Desorption
dt
+ E.wEa^O - Def2SedLabile)
- (Resuspension + Scour + Colonization) PPBSedReft.Detr le-6
- Y,PredIngeSti0nPred,SedRefrDetr ' PPBSedRefrDetr ' le~6 (201)
+ (Sedimentation + Deposition) PPBSuspRefrDetr le-6
+ Y,(Sed2Detr Sinkphyto PPBphyto le-6)
- Hydrolysis - MicrobialDegrdn - Burial + Expose
± BiotransformMicrMal
The equations are similar for the toxicant associated with suspended and dissolved detritus,
with deposition or sedimentation, depending on whether or not inorganic sediments are modeled:
oxicantSuspLaMeDetf = Loadfng + Sorption _ Desorption + J^ ((Mort2Detr
Mortality^ + GameteLoss^) PPEQrs le-6)
- {Sedimentation + Deposition + Washout + Decomposition
+ 2^/pred In8estlOnPred, SuspLabileDetr) ' **" SuspLabileDetr ' 1 e ~ 6
+ Colonization PPBSuspRefrDetr ' le-6 ± BiotransformMcrobial
+ (Resuspension + Scour) PPBSedLabileDetr'le-6 ± SedToHyp
- Hydrolysis - Photolysis - MicrobialDegrdn ± TurbDiff
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 7
°XlCan SusPRefiDetr = Loading + Sorption - Desorption
+ Y
-------
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION
CHAPTER 7
dToxicant
Macrophyte _
dt
= Loading + MacroUptake - Depuration - (Excretion
, Macro
+ Mortality + Breakage) PPB
le-6 ±
Macro
<208>
dToxicantAnimal
dt
= Loading + GillUptake
'Prey
DietUptake ± TurbDiff
- (Depuration + Z^/pred Predationpred Animai + Mortality + Recruit
± Promotion + GameteLoss + Drift + Migration + Emergelnsecf)
(207)
PPB
Animal
1 e -6 ± Biotransform
'Animal
The toxicant associated with animals is represented by an involved kinetic equation because
of the various routes of exposure and transfer:
where:
Toxicant^
Toxicant
Water
'SedDetr
Toxicant
SuspDetr
Toxicant
'DissDetr
Toxicant
'Alga
Toxicant,
'Macrophyte
Toxicant
'Animal
SedDetr
""-^
SuspDetr
PPE
± ± ^Macrophyte
PPR
1 ± n 'Animal
1 e-6
Loading
TurbDiff
Hydrolysis
BiotransformMlcrobml
toxicant in dissolved phase in unit volume of water ( g/L);
mass of toxicant associated with each of the two sediment
detritus compartments in unit volume of water ( g/L);
mass of toxicant associated with each of the two suspended
detritus compartments in unit volume of water ( g/L);
mass of toxicant associated with each of the two dissolved
organic compartments in unit volume of water ( g/L);
mass of toxicant associated with given alga in unit volume of
water ( g/L);
mass of toxicant associated with macrophyte in unit volume
of water ( g/L);
mass of toxicant associated with given animal in unit volume
of water ( g/L);
concentration of toxicant in sediment detritus ( g/kg), see
concentration of toxicant in suspended detritus ( g/kg);
concentration of toxicant in dissolved organics ( g/kg);
concentration of toxicant in given alga ( g/kg);
concentration of toxicant in macrophyte ( g/kg);
concentration of toxicant in given animal ( g/kg);
units conversion (kg/mg);
loading of toxicant from external sources ( g/L*d);
depth-averaged turbulent diffusion between epilimnion and
hypolimnion ( g/L«d), see and
rate of loss due to hydrolysis ( g/L*d), see ''- ::':;
biotransformation to or from given organic chemical in given
detrital compartment due to microbial decomposition
( g/L«d), see
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION
CHAPTER 7
Biotr am/or m0rg
Photolysis
MicrobialDegrdn
Volatilization
Discharge
Burial
Expose
Decomposition
Depuration
Sorption
Desorption
Colonization
Defecation ToxPred:
i, Prey
Def2SedLabile
Resuspension
Scour
Sedimentation
Deposition
Sed2Detr
Sink
Mortality0rg
Mort2Detr
GameteLoss
Mort2Ref
Washout or Drift
SedToHyp
biotransformation to or from given organic chemical within
the given organism ( g/L*d);
rate of loss due to direct photolysis ( g/L«d), see ;
assumed not to be significant for bottom sediments;
rate of loss due to microbial degradation ( g/L*d), see ;
rate of loss due to volatilization ( g/L«d), see , ;
rate of loss of toxicant due to discharge downstream
( g/L«d), see Table 1;
rate of loss due to deep burial ( g/L«d) see i ;;
rate of exposure due to resuspension of overlying sediments
( g/Lfl), see ;
rate of decomposition of given detritus (mg/L*d), see ;
elimination rate for toxicant due to clearance ( g/L*d), see
and ;
rate of sorption to given compartment ( g/L*d), see ;
rate of desorption from given compartment ( g/L*d), see
rate of conversion of refractory to labile detritus (g/m3«d), see
rate of transfer of toxicant due to defecation of given prey by
given predator ( g/L«d), see (276);
fraction of defecation that goes to sediment labile detritus;
rate of resuspension of given sediment detritus (mg/L*d)
without the inorganic sediment model attached, see ;
rate of resuspension of given sediment detritus (mg/L«d) in
streams with the inorganic sediment model attached, see
rate of sedimentation of given suspended detritus (mg/L«d),
without the inorganic sediment model attached, see ;
rate of sedimentation of given suspended detritus (mg/L*d)
in streams with the inorganic sediment model attached, see
fraction of sinking phytoplankton that goes to given detrital
compartment;
loss rate of phytoplankton to bottom sediments (mg/L*d), see
nonpredatory mortality of given organism (mg/L*d), see : ;
fraction of dead organism that is labile (unitless);
loss rate for gametes (g/m3«d), see ;
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 ,
, and ;
rate of settling loss to hypolimnion from epilimnion (mg/L*d).
May be positive or negative depending on segment being
simulated;
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IngestionPredPre
Predation
Pred, Prey
ExcToxToDiss,
Excretion
SinkToHypo
AlgalUptake
MacroUptake
GillUptake
DietUptakePrey
Recruit
Promotion
Migration
Emergelnsect
Org
rate of ingestion of given food or prey by given predator
(mg/L-d), see :; ;;U;
predatory mortality by given predator on given prey
(mg/L«d), see .^oj;
toxicant excretion from plants to dissolved organics
(mg/L-d);
excretion rate for given plant (g/m3«d), see ; *J ?j;
rate of transfer of phytoplankton to hypolimnion (mg/L*d).
May be positive or negative depending on segment being
modeled;
rate of sorption by algae ( g/L - d), see :l:iLu;
rate of sorption by macrophytes ( g/L - d), see , ~.;Hj;
rate of absorption of toxicant by the gills ( g/L - d), see ijliiii;
rate of dietary absorption of toxicant associated with given
prey ( g/L«d), see u,:>i;;;
biomass gained from successful spawning (g/m3«d), see c|j>v >;
promotion from one age class to the next (mg/L*d), see >.\±\;\\
rate of migration (g/m3«d), see ' ..I.! ..;)>; and
insect emergence (mg/L*d), seefill,}-
The concentration in each carrier is given by:
PPEi =
ToxState{
Carrier State,
Ie6
(209)
where:
PPB,
ToxStatei
CarrierState
Ie6
7.1 lonization
concentration of chemical in carrier /' ( g/kg);
mass of chemical in carrier /' (ug/L);
biomass of carrier (mg/L); and
conversion factor (mg/kg).
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 \og,pKa., and the fraction that is not ionized is:
Nondissoc =
1
(210)
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CHAPTER 7
where:
Nondissoc = nondissociated fraction (unitless).
If the compound is a base then the fraction not ionized is:
Nondissoc =
1
(211)
When pKa = pH half the compound is ionized and half is not (I";; j-: .'.''). At ambient
environmental pH values, compounds with a pKa in the range of 4 to 9 will exhibit significant
dissociation O'r H ,).
Figure 72
Dissociation of Pentachlorophenol
(pKa = 4.75) at Higher pH Values
1 -
T>
0)
ra 0.8
.<2 0.6
"O
C
o
Z0.4
c
o
0.2
6
pH
10
Figure 73
Dissociation as a Function ofpKa at an
Ambient pH of 7
T>
Q>
ra 0.8
.<20.6
1
o
z 0.4
c
o
6 8
pka
10 12 14
7.2 Hydrolysis
Hydrolysis is the degradation of a compound through reaction with water. During
hydrolysis, both a pollutant molecule and a water molecule are split, and the two water molecule
fragments (H+ and OH") join to the two pollutant fragments to form new chemicals. Neutral and
acid- and base-catalyzed hydrolysis are modeled using the approach of Mabey and Mill (1978) in
which an overall pseudo-first-order rate constant is computed for a given pH, adjusted for the
ambient temperature of the water:
Hydrolysis = KHyd Toxicantphase
(212)
where:
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 7
KHyd = (KAcidExp + KBaseExp + KUncaf) Arrhen (213)
and where:
KHyd = overall pseudo-first-order rate constant for a given pH and
temperature (1/d);
KAcidExp = pseudo-first-order acid-catalyzed rate constant for a given pH (1/d);
KBaseExp = pseudo-first-order base-catalyzed rate constant for a given pH (1/d);
KUncat = the measured first-order reaction rate at pH 7 (1/d); and
Arrhen = temperature adjustment (unitless), see
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 (214)
where:
Hlon = lQ-pH (215)
and where:
KAcid = acid-catalyzed rate constant (L/mol^);
Hlon = concentration of hydrogen ions (mol/L); and
pH = pH of water column.
Likewise for base-catalyzed hydrolysis, the first-order rate constant for a reaction between
the hydroxide ion and the pollutant at a given pH can be described as:
KBaseExp = KBase OHIon (216)
where:
OHIon = \(PH ~ u (217)
and where:
KBase = base-catalyzed rate constant (L/mol "id); and
OHIon = concentration of hydroxide ions (mol/L).
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Figure 74
Base-catalyzed Hydrolysis of Pentachlorophenol
6.05E-03
6.00E-03
P
Q 5.95E-03
£ 5.90E-03
5.85E-03
5.80E-03
' ' ' I
/
/
_y
2 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 KelvinT R TObs
(218)
where:
En
R
KelvinT
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 Toxicant
Phase
(219)
where:
Photolysis
KPhot
rate of loss due to photodegradation ( g/L*d); and
direct photolysis first-order rate constant (I/day).
For consistency, photolysis is computed for both the epilimnion and hypolimnion in stratified
systems. However, it is not a significant factor at hypolimnetic depths.
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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 rate constant for photolysis (PhotRate), and
this is usually determined either with distilled water or with water from a representative site, so that
ionization may be included in the calculated lumped parameter KPhot.
Based on the approach of Thomann and Mueller (1987; see also Schwarzenbach et al. 1993),
the observed first-order rate constant for the compound is modified by a light attenuation factor for
ultraviolet light so that the process as represented is depth-sensitive (=''"<:..-.. : / >); it also is adjusted
by a factor for time-varying light:
KPhot = PhotRate ScreeningFactor LightFactor
(220)
where:
PhotRate
ScreeningFactor =
LightFactor =
direct, observed photolysis first-order rate constant (I/day);
a light screening factor (unitless), see ; and
a time-varying light factor (unitless), see ' .
Figure 75
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)
0.5 1 1.5 2 2.5
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):
ScreeningFactor =
RadDistr
RadDistrO
Extinct Thick
(221)
where:
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RadDistr = radiance distribution function, which is the ratio of the average
pathlength to the depth (see Schwarzenbach et al., 1993) (taken to be
1.6, unitless);
RadDistrO = radiance distribution function for the top of the segment (taken to be
1.2 for the top of the epilimnion and 1.6 for the top of the
hypolimnion, unitless);
Extinct = light extinction coefficient (1/m) not including periphyton, see (30);
and
Thick = thickness of the water body segment if stratified or maximum depth
if unstratified (m).
The equation presented above implicitly makes the following assumptions:
quantum yield is independent of wavelength; and,
the value used forPhotRate is a representative near-surface, first-order rate constant
for direct photolysis.
The rate is modified further to represent seasonally varying light conditions and the effect
of ice cover:
T i *T? * SolarO
LightFactor = (222)
AveSolar ^ '
where:
SolarO = time-varying average light intensity at the top of the segment
(ly/day); and
AveSolar = average light intensity for late spring or early summer, corresponding
to time when photolytic half-life is often measured (500 Ly/day).
If the system is unstratified or if the epilimnion is being modeled, the light intensity is the
light loading:
SolarO = Solar (223)
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(^^fl ' M"ZMte> (224)
where:
Solar = incident solar radiation loading (ly/d), see and
MaxZMix = depth of the mixing zone (m), see ' .
Because the ultraviolet light intensity exhibits greater seasonal variation than the visible
spectrum (Lyman et al., 1982), decreasing markedly when the angle of the sun is low, this construct
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could predict higher rates of photolysis in the winter than might actually occur. However, the model
also accounts for significant attenuation of light due to ice cover so that photolysis, as modeled, is
not an important process in northern waters in the winter.
7.4 Microbial Degradation
Not only can microorganisms decompose the detrital organic material in ecosystems, they
also can degrade xenobiotic organic compounds such as fuels, solvents, and pesticides to obtain
energy. In AQUATOX this process of biodegradation of pollutants, whether they are dissolved in
the water column or adsorbed to organic detritus in the water column or sediments, is modeled using
the same equations as for decomposition of detritus, substituting the pollutant and its degradation
parameters for detritus in Equation and supporting equations:
MicrobialDegrdn = KMDegrdnphase DOCorrection TCorr pHCorr
' T°xicantPhase
where:
MicrobialDegrdn = loss due to microbial degradation (g/m3*d);
KMDegrdn = maximum degradation rate, either in water column or
sediments (1/d);
DOCorrection = effect of anaerobic conditions (unitless), see till j;
TCorr = effect of suboptimal temperature (unitless), see iMl;
pHCorr = effect of suboptimal pH (unitless), see 033 V and
Toxicant = concentration of organic toxicant (g/m3).
Microbial degradation proceeds more quickly if the material is associated with surficial
sediments rather than suspended in the water column (Godshalk and Barko, 1985); thus, in
calculating the loss due to microbial degradation in the sorbed phase, the maximum degradation rate
is set to four times the maximum degradation rate in the water. The model assumes that reported
maximum microbial degradation rates are for the dissolved phase; if the reported degradation value
is from a study with additional organic matter, such as suspended slurry or wet soil samples, then
the parameter value that is entered should be one-fourth that reported.
7.5 Volatilization
Volatilization is modeled using the "stagnant boundary theory", or two-film model, in which
a pollutant molecule must diffuse across both a stagnant water layer and a stagnant air layer to
volatilize out of a waterbody (Whitman, 1923; Liss and Slater, 1974). Diffusion rates of pollutants
in these stagnant boundary layers can be related to the known diffusion rates of chemicals such as
oxygen and water vapor. The thickness of the stagnant boundary layers must also be taken into
account to estimate the volatile flux of a chemical out of (or into) the waterbody.
The time required for a pollutant to diffuse through the stagnant water layer in a waterbody
is based on the well-established equations for the reaeration of oxygen, corrected for the difference
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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:
Vj- n- i ( MolWtO2}025 1 .
KLiq = KReaer Thick (226)
( MolWt i Nondissoc
where:
KLiq = water-side transfer velocity (m/d);
KReaer = depth-averaged reaeration coefficient for oxygen (1/d), see
Thick = mean thickness of the water body segment if stratified or men depth
if unstratified (m);
MolWtO2 = molecular weight of oxygen (g/mol, =32);
MolWt = molecular weight of pollutant (g/mol); and
Nondissoc = nondissociated fraction (unitless), see
Likewise, the thickness of the air-side stagnant boundary layer is also affected by wind.
Wind usually is measured at 10 m, and laboratory experiments are based on wind measured at 10
cm, so a conversion is necessary (Banks, 1975). To estimate the air-side transfer velocity of a
pollutant, we used the following empirical equation based on the evaporation of water, corrected for
the difference in diffusivity of water vapor compared to the toxicant (Thomann and Mueller, 1987,
p. 534):
rr 1« ( MolWtH20] °'25 ur , ft. ..
KGas = 168 Wind 0.5 (227)
MolWt ^ '
where:
KGas = air-side transfer velocity (m/d);
Wind = wind speed ten meters above the water surface (m/s);
0.5 = conversion factor (wind at 10 cm/wind at 10 m); and
MolWtH2O = molecular weight of water (g/mol, =18).
The total resistance to the mass transfer of the pollutant through both the stagnant boundary
layers can be expressed as the sum of the 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
where:
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KOVol
total mass transfer coefficient through both stagnant boundary layers
(m/d);
HenryLaw =
Henry
R TKelvin
(229)
and where:
HenryLaw
Henry
R
TKelvin
Henry's law constant (unitlessj;
Henry's law constant (atm m3 mol"1);
gas constant (=8.206E-5 atm m3 (mol K)"1); and
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:
Volatilization = : ToxSat - Toxicant^
(230)
where:
Volatilization =
Thick
ToxSat =
Toxicantwater =
interchange with atmosphere ( g/L*d);
depth of water or thickness of surface layer (m);
saturation concentration of pollutant in equilibrium with the gas
phase ( g/L); and
concentration of pollutant in water ( g/L).
Because theoretically toxicants can be transferred in either direction across the water-air
interface, Eq. 209 is formulated so that volatilization takes a negative sign when it is a loss term.
The saturation concentration depends on the concentration of the pollutant in the air, ignoring
temperature effects (Thomann and Mueller, 1987, p. 532; see also Schnoor, 1996), but adjusting for
ionization and units:
ToxSat =
Toxicantair
HenryLaw Nondissoc
1000
(231)
where:
Toxicantair
Nondissoc
user-supplied gas-phase concentration of the pollutant (g/m3); and
nondissociated fraction (unitless).
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Often the pollutant can be assumed to have a negligible concentration in the air and ToxSat
is zero. However, this general construct can represent the transferral of volatile pollutants into water
bodies. Because ionized species do not volatilize, the saturation level increases if ionization is
occurring.
The nondimensional Henry's law constant, which relates the concentration of a compound
in the air phase to its concentration in the water phase, strongly affects the air-phase resistance.
Depending on the value of the Henry's law constant, the water phase, the air phase or both may
control volatilization. For example, with a depth of 1 m and a wind of 1 m/s, the gas phase is
100,000 times as important as the water phase for atrazine (Henry's law constant = 3.0E-9), but the
water phase is 50 times as important as the air phase for benzene (Henry's law constant = 5.5E-3).
Volatilization of atrazine exhibits a linear relationship with wind (i:i?£Mi:i 1:1) in contrast to the
exponential relationship exhibited by benzene (Oiiiiiii 12).
Figure 76
Atrazine KOVol as a Function of Wind
VOLATILIZATION OF ATRAZINE
4E-05 I
3.5E-05
3E-05
7 10,5 14 17.5 21 24.5 28
WIND (m/s)
Figure 77
Benzene KOVol as a Function of Wind
VOLATILIZATION OF BENZENE
6 9 12 15 18 21 24 27 30
WIND (m/s)
| AQUATOX I
I Schwarzenbachetal., 1993
7.6 Partition Coefficients
Although AQUATOX is a kinetic model, steady-state partition coefficients for organic
pollutants are computed in order to constrain sorption to detritus and algae ' ' , and to compute
internal toxicities [17:; |, They are estimated from empirical regression equations and the pollutant's
octanol-water partition coefficient.
Detritus
Natural organic matter is the primary sorbent for neutral organic pollutants. Hydrophobic
chemicals partition primarily in nonpolar organic matter (Abbott et al. 1995). Refractory detritus
is relatively nonpolar; its partition coefficient (in the non-dissolved phase) is a function of the
octanol-water partition coefficient (N = 34, r2 = 0.93; Schwarzenbach et al. 1993):
KOM,
RefrDetr
= 1.38 KOW0*2
(232)
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where:
KOMr
KOW
RefrDetr
detritus-water partition coefficient (L/kg); and
octanol-water partition coefficient (L/kg).
Detritus in sediments is simulated separately from inorganic sediments, rather than as a
fraction of the sediments as in other models. At this time AQUATOX does not simulate sorption
to inorganic sediments. Therefore, refractory detritus is used as a surrogate for sediments in general;
and the sediment partition coefficientKPSed, which can be entered manually by the user, is the same
as KOMRefrDetr
Equation and the equations that follow are extended to polar compounds, following
the approach of Smejtek and Wang (1993):
KOW0'82
(233)
KOMRefrDetr = 1.38
Nondissoc
+ (1 -Nondissoc) lonCorr 1.38 KOW0*2
where:
Nondissoc
lonCorr
un-ionized fraction (unitless); and
correction factor for decreased sorption, 0.01 for chemicals that are
bases and 0.1 for acids, (unitless).
Using pentachlorophenol as a test compound, and comparing it to octanol, the influence of
pH-mediated dissociation is seen in This relationship is verified by comparison with the
results of Smejtek and Wang (1993) using egg membrane. However, in the general model Eq.
is used for refractory detrital sediments as well.
Figure 78
Refractory Detritus-water and Octanol-water Partition
Coefficients for Pentachlorophenol as a Function of pH.
O
1E6 |
1E5-!
1E4J
1E3 |
1E2
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 (non-dissolved) is based on a study by Koelmans
et al. (1995) using fresh algal detritus (N = 3, r2 = 1.0):
KOCLabPart = 23.44 KOW0-61 (234)
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 KOWOM) 0.526 l '
where:
KOCLabPart = partition coefficient for labile particulate organic carbon (L/kg);
KOMLabDetr = partition coefficient for labile detritus (L/kg);
lonCorr = correction factor for decreased sorption, 0.01 for chemicals that are
bases and 0.1 for acids, (unitless); and
0.526 = conversion from KOC to KOM (g OC/g OM).
O'Connor and Connolly (1980; see also Ambrose et al., 1991) found that the sediment
partition coefficient is the inverse of the mass of suspended sediment, and Di Toro (1985) developed
a construct to represent the relationship. However, AQUATOX models partitioning directly to
organic detritus and ignores inorganic sediments, which are seldom involved directly in sorption of
neutral organic pollutants. Therefore, the partition coefficient is not corrected for mass of sediment.
Association of hydrophobic compounds with colloidal and dissolved organic matter (DOM)
reduces bioavailability; such contaminants are unavailable for uptake by organisms (Stange and
Swackhamer 1994, Gilek et al. 1996). Therefore, it is imperative that complexation of organic
chemicals with DOM be modeled correctly. In particular, contradictory research results can be
reconciled by considering that DOM is not homogeneous. For instance, refractory humic acids,
derived from decomposition of terrestrial and wetland organic material, are quite different from
labile exudates from algae and other indigenous organisms.
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Humic acids exhibit high polarity and do not readily complex neutral compounds. Natural
humic acids from a Finnish lake with extensive marshes were spiked with a PCB, but a PCB-humic
acid complex could not be demonstrated (Maaretetal. 1992). In another study, Freidig etal. (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:
KOCRefrDOM = 28.84 KOW (236)
where:
KOCRefrDOM = refractory dissolved organic carbon partition coefficient (L/kg).
Until a better relationship is found, we are using a generalization of their equation to include
polar compounds, transformed from organic carbon to organic matter, in AQUATOX:
KOMp,nnM = (28.84 KOW0-61 Nondissoc
KejrlJUM ^ / ^ -5 *j \
+ (1 - Nondissoc) lonCorr 28.84 KOW0'67) 0.526
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:
KOCLabDOC = 0.88 KOW (238)
which we also generalized for polar compounds and transformed:
KOM, hnnu = (0.88 KOW Nondissoc
LaoDUM ^
+ (1 - Nondissoc) lonCorr 0.88 KOW) 0.526
where:
KOCLahDOC = partition coefficient for labile dissolved organic carbon (L/kg); and
KOMLabDOM = partition coefficient for labile dissolved organic matter (L/kg).
Unfortunately, older data and modeling efforts failed to distinguish between hydrophobic
compounds that were truly dissolved and those that were complexed with DOM. For example, the
PCB water concentrations for Lake Ontario, reported by Oliver and Niimi (1988) and used by many
subsequent researchers, included both dissolved and DOC-complexed PCBs (a fact which they
recognized). In their steady-state model of PCBs in the Great Lakes, Thomann and Mueller (1983)
defined "dissolved" as that which is not particulate (passing a 0.45 micron filter). In their Hudson
River PCB model, Thomann et al. (1991) again used an operational definition of dissolved PCBs.
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 7
AQUATOX distinguishes between truly dissolved and complexed compounds; therefore, the
partition coefficients calculated by AQUATOX may be larger than those used in older studies.
Algae
Bioaccumulation of PCBs in algae depends on solubility, hydrophobicity and molecular
configuration of the compound, and growth rate, surface area and type, and content and type of lipid
in the alga (Stange and Swackhamer 1994). Phytoplankton may double or triple in one day and
periphyton turnover may be so rapid that some PCBs will not reach equilibrium (cf Hill and
Napolitano 1997); therefore, one should use the term "bioaccumulation factor" (BAF) rather than
"bioconcentration factor," which implies equilibrium (Stange and Swackhamer 1994).
Hydrophobic compounds partition to lipids in algae, but the relationship is not a simple one.
Phytoplankton lipids can range from 3 to 30% by weight (Swackhamer and Skoglund 1991), and
not all lipids are the same. Polar phospholipids occur on the surface. Hydrophobic compounds
preferentially partition to internal neutral lipids, but those are usually a minor fraction of the total
lipids, and they vary depending on growth conditions and species (Stange and Swackhamer 1994).
Algal lipids have a much stronger affinity for hydrophobic compounds than does octanol, so that the
algal BAFlipid > Kow (Stange and Swackhamer 1994, Koelmans et al. 1995, Sijm et al. 1998).
For algae, the approximation to estimate the dry-weight bioaccumulation factor (r2 = 0.87),
computed from Swackhamer and Skoglund's (1993) study of numerous PCB congeners, is:
\og(BAFAlga} = 0.41 + 0.91 LogKOW (240)
where:
BAFAlga = partition coefficient between algae and water (L/kg).
Rearranging and extending to hydrophilic and ionized compounds:
BAF,, = 2.57 KOW0-93 Nondissoc
g (241)
+ (I-Nondissoc) 0.257 KOW0-93
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 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).
The influence of substrate polarity is evident in 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
7-20
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 7
substrates, such as refractory detritus. The relative importance of the substrates for binding is also
demonstrated quite clearly.
Macrophytes
For macrophytes, an empirical relationship reported by Gobas et al. (1991) for 9 chemicals
with LogKOWs of 4 to 8.3 (r2 = 0.97) is used:
\og(KBMacro) = 0.98 LogKOW - 2.24 (242)
Again, rearranging and extending to hydrophilic and ionized compounds:
KBMacro = 0.00575 KOW0-9* (Nondissoc + 0.2) (243)
Invertebrates
For the invertebrate bioconcentration factor, the following empirical equation is used for
nondetritivores, based on 7 chemicals with LogKOWs ranging from 3.3 to 6.2 and bioconcentration
f actor sf or Daphniapulex(r2 = 0.85; Southworthetal., 1978; seealsoLymanetal., 1982), converted
to dry weight :
\og(KBImertebrate) = (0.7520 LogKOW - 0.4362) WetToDry (244)
where:
invertebrate partition coefficient between invertebrates and water (L/kg); and
WetToDry = wet to dry conversion factor (unitless, default = 5).
Extending and generalizing to ionized compounds:
= °'3663 ' KOW*'1 ' (NondisSOC + 0.01) (245)
For invertebrates that are detritivores the following equation is used, based on Gobas 1993 :
' KOMRefrDetr ' (NondiSSoc+Q.Ol) (246)
Detritus
where:
KB invertebrate = partition coefficient between invertebrates and water (L/kg);
FracLipid = fraction of lipid within the organism;
FracOCDetritus = fraction of organic carbon in detritus (= 0.526);
KOMRefrDetr = partition coefficient for refractory sediment detritus (L/kg), see
7-21
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION
CHAPTER 7
Figure 79
Partitioning to Various Types of Organic
Matter as a Function of KOW
Figure 80
Partitioning to Various Types of Organic
Matter as a Function of pH
5
O
1E10
1E9
1E8
1E7 ,
1E6;
1E5 i
1E4i
1E3i
1E2*
3
456789
Log KOW
humic acids algae exudate
* algal detritus - refr. detritus sediments
o
1E6
1E5 :
1E4
1E3
6
PH
humic acids algae octanol/water
* exudate algal detritus refr, detritus
Fish
Fish take longer to reach equilibrium with the surrounding water; therefore, a nonequilibrium
bioconcentration factor is used. For each pollutant, a whole-fish bioconcentration factor is based
on the lipid content of the fish extended to hydrophilic chemicals (McCarty et al., 1992), with
provision for ionization:
KBFish = Lipid WetToDry KOW (Nondissoc + 0.01)
(247)
where:
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 offish is either held constant or is computed depending on the potential for
growth as predicted by the bioenergetics equations; the initial lipid values for the species are entered
by the user. The bioconcentration factor is adjusted for the time to reach equilibrium as a function
of the clearance or elimination rate and the time of exposure (Hawker and Connell, 1985; Connell
and Hawker, 1988; 81):
BCF
Fish
Fish -
1 - e(-Depwation TElapsed)
(248)
where:
BCFFlsh
TElapsed
Depuration
quasi-equilibrium bioconcentration factor for fish (L/kg);
time elapsed since fish was first exposed (d); and
clearance, which may include biotransformation, see
(1/d).
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION
CHAPTER 7
Figure 81
Bioconcentration Factor for Fish
as a Function of Time and log KOW
1E7-
~z_
o
I- 1E6 =
££
l
m 1E5-
O
0 1E4
O
4 po
0
=a^
y-
^
j\
***
.s
r
20
loq
""'
~^*
luy
Inn
0
K( )
**
Ku
k"o
40
A/ =
t/V -
A/ -
0
H
.
8
o
6C
D/
i »
0
\Y
,. *
80
0
10
m^~
DO
1200
7.7 Nonequilibrium Kinetics
Although partition coefficients are computed in AQUATOX in order to provide constraints
on sorption and to compute internal toxicities, the model is basically a kinetic model. In nature there
is often an absence of equilibrium due to growth or insufficient exposure time, metabolic
biotransformation, dietary exposure, and nonlinear relationships for very large and/or
superhydrophobic compounds (Bertelsen et al. 1998). It is important to have a knowledge of
equilibrium partitioning because it is an indication of the condition toward which systems tend
(Bertelsen et al. 1998), but steady-state potential is often not achieved due to changes in
bioavailability and physiology (Landrum 1998). For example, PCBs may not be at steady state even
in large systems such as Lake Ontario that have been polluted over a long period of time. In fact,
PCBs in Lake Ontario exhibit a 25-fold disequilibrium (Cook and Burkhard 1998). The challenge
is to obtain sufficient data for a kinetic model (Gobas et al. 1995).
Sorption and Desorption to Detritus
Partitioning to detritus appears to involve rapid sorption to particle surfaces, followed by
slow movement into, and out of, organic matter and porous aggregates (Karickhoff and Morris,
1985). Therefore attainment of equilibrium may be slow. Because of the need to represent sorption
and desorption separately in detritus, kinetic formulations are used (Thomann and Mueller, 1987),
with provision for ionization:
Sorption = klDetr ToxicantWater DiffCarrier (Nondissoc
Org2C Detr UptakeLimit le-6
0.01)
(249)
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION
CHAPTER 7
Desorption = k2D Toxicant
lDetr
(250)
where:
Sorption =
Nondissoc =
ToxicantWater =
Wf
Org2C
Detr
le-6
Desorption =
k2Detr
UptakeLimit =
Toxicant
'Detr
rate of sorption to given detritus compartment ( g/L«d);
sorption rate constant (1.39 L/kg«d);
fraction not ionized (unitless);
concentration of toxicant in water ( g/L);
factor to normalize rate constant based on all competing uptake rates
(unitless), see ;;
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
C g/L-d);
desorption rate constant (l/d), see ! :- :;
factor to limit uptake as equilibrium is reached (unitless); see . :'.
and
mass of toxicant in each of the detritus compartments ( g/L).
Because there are several processes competing for the dissolved toxicant, the rate constants
for these processes are normalized in order to preserve mass balance. The Diff'factor is computed
considering all direct uptake processes, including sorption to detritus and algae, uptake by
macrophytes, and uptake across animal gills. If the sum of the competing processes per day is less
than the mass available in the water then Diff= 1, otherwise:
Diff =
Toxicant
Water
(/; Sorption
'Detritus
2^PlantUptake
plant
GillUptakeAnimal) dt
(251)
where:
SorptionDetntm
PlantUptakePlant
GillUptakeAmmal
dt
rate of sorption to given detrital group ( g/L«d), see ;' ! : ;
rate of uptake by given plant group ( g/L*d), see :.".,
rate of uptake by given animal group ( g/L*d), see ," ';.;; and
time step (d).
is computed as:
In order to limit sorption to detritus and algae as equilibrium is reached, UptakeLimit
UptakeLimit(
ToxicantWater kpCarrier - PPBCarrier
Carrier
Toxicant
Water
kp,
(252)
Carrier
7-24
-------
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 7
where:
UptakeLimitCarrier = factor to limit uptake as equilibrium is reached (unitless);
kpcomer = partition coefficient or bioconcentration factor for each carrier (L/kg),
see /.'. to ;' ;
PPBCarrier = concentration of toxicant in each carrier ( g/kg), see .-' '...
Desorption of the detrital compartments is the reciprocal of the reaction time, which
Karickhoff and Morris (1985) found to be a linear function of the partition coefficient over three
orders of magnitude (r2 = 0.87):
-1 0.72 KOM (253)
So £2 is taken to be:
1.39
,,
=
where:
KOMRefrDetr = detritus-water partition coefficient (L/kg OM, see section
7.1); and
Because the kinetic definition of the detrital partition coefficient KOM is:
KOM = | (255)
the sorption rate constant kl is set to 1.39 L/kg*d.
Bioaccumulation in Macrophytes and Algae
MacrophytesAs 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 (Gob as etal., 1991), modified to account for ionizati on effects ( \,,:,',, :,,',", ,.;.'..:,
MacroUptake = kl Diff ToxicantWater StVarplant le-6 (256)
Depurationplant = k2 Toxicantplant (257)
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION
CHAPTER 7
If the user selects to estimate the elimination rate constant based on KOW, the following equation
is used:
k2 =
1
1.58 + 0.000015 KOW DissocFactor
(258)
kl =
0.0020 +
500
KOW DissocFactor
(259)
if Nondissoc < 0.01 then DissocFactor = 0.01
else DissocFactor = Nondissoc
where:
MacroUptake =
Depurationplant=
StVarPlant
1 e-6
Toxicantplant =
kl
k2
Diff
KOW
Nondissoc =
DissocFactor =
uptake of toxicant by plant ( g/L*d);
clearance of toxicant from plant ( g/L«d);
biomass of given plant (mg/L);
units conversion (kg/mg);
mass of toxicant in plant ( g/L);
sorption rate constant (L/kg*d);
elimination rate constant (1/d).
factor to normalize uptake rates (unitless), see
octanol-water partition coefficient (unitless);
fraction of un-ionized toxicant (unitless): and
constrained factor based on Nondissoc (unitless).
Figure 82
Uptake Rate Constant for Macrophytes
(after Gobas et al., 1991)
500
400
300
200
100
0
2468
Log KOW
Predicted » Observed
10
Figure 83
Elimination Rate Constant for Macrophytes
(after Gobas et al., 1991)
0.7
0.6
0.5
,0.4
' 0.3
0.2
0.1
0
4 6
Log KOW
10
Predicted
Observed
7-26
-------
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 7
AlgaeAside from obvious structural differences, algae may have very high lipid content (20% for
Chlorella sp. according to J0rgensen et al., 1979) and macrophytes have a very low lipid content
(0.2% mMyriophyllum spicatum as observed by Gobas et al. (1991), which affect both uptake and
elimination of toxicants. However, the approach used by Gobas et al. (1991) in modeling
bioaccumulation in macrophytes provides a useful guide to modeling kinetic uptake in algae.
There is probably a two-step algal bioaccumulation mechanism for hydrophobic compounds,
with rapid surface sorption of 40-90% within 24 hours and then a small, steady increase with transfer
to interior lipids for the duration of the exposure (Swackhamer and Skoglund 1991). Uptake
increases with increase in the surface area of algae (Wang et al. 1997). Therefore, the smaller the
organism the larger the uptake rate constant (Sijm et al. 1998). However, in small phytoplankton,
such as the nannoplankton that dominate the Great lakes, a high surface to volume ratio can increase
sorption, but high growth rates can limit internal contaminant concentrations (Swackhamer and
Skoglund 1991). The combination of lipid content, surface area, and growth rate results in species
differences in bioaccumulation factors among algae (Wood et al. 1997). Uptake of toxicants is a
function of the uptake rate constant and the concentration of toxicant truly dissolved in the water,
and is constrained by competitive uptake by other compartments; also, because it is fast, it is limited
as it approaches equilibrium, similar to sorption to detritus :
AlgalUptake = kl UptakeLimitAlga - Diff ToxState Carrier 1 e - 6 (260)
where:
AlgalUptake = rate of sorption by algae ( g/L-d);
kl = uptake rate constant (L/kg-d), see
UptakeLimitAlga = factor to limit uptake as equilibrium is reached (unitless), see
Diff = factor to normalize uptake rates (unitless), see
ToxState = concentration of dissolved toxicant ( 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. Sijmetal. (1998) presented
data on several congeners that were used in this study to develop the following relationship for
phytoplankton
" 1.8E-6 + \I(KOW DissocFactor) (261)
Depuration is modeled as a linear function; it does not include loss due to excretion of
photosynthate with associated toxicant, which is modeled separately:
Depuration = k2 State (262)
where:
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-------
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION
CHAPTER 7
Depuration =
State
k2
elimination of toxicant ( g/L-d);
concentration of toxicant associated with alga ( g/L); and
elimination rate constant (1/d).
The elimination rate in plants may be input in the toxicity record by the user or it may be estimated
using the following equation based in part on Skoglund et al. (1996). Unlike Skoglund, this equation
ignores surface sorption and recognizes that growth dilution is explicit in AQUATOX (see Pj i
k2
Algae
2.4E + 5
(KOW DissocFactor LFrac WetToDry)
(263)
where:
LFrac
WetToDry
desorption rate constant (1/d);
fraction lipid, as entered in the chemical toxicity screen; and
translation from wet to dry weight (5.0).
If more than 20% of the compound is ionized, the k2Al is estimated from the kl and BCF
values:
k2 =
kl
BCF
(264)
Figure 84
Algal Sorption Rate Constant as a Function of
Octanol-water Partition Coefficient
I
FIT TO DATA OF SUM ET AL. 1998
600000 ,
500000
400000
300000
200000
100000
4 6
LOG KOW
ObsK1 PredKI
10
Figure 85
Rate of Elimination by Algae as a Function of
Octanol-water Partition Coefficient
246
Log KOW
10
Bioaccumulation in Animals
Animals can absorb toxic organic chemicals directly from the water through their gills and
from contaminated food through their guts, hence they bioaccumulate, and seldom is steady-state
bioconcentration an important factor. Direct sorption onto the body is ignored as a simplifying
7-28
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 7
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), and Thomann and Mueller (1987; see also Thomann,
1989). Therefore, the uptake rate for each animal can be calculated as a function of respiration
(Leung, 1978; Park et al., 1980):
GillUptake = KUptake ToxicantlWater ' Diff (265)
^rr . , WEffTox Respiration O2Biomass
KUptake = ^ ±-
P Oxygen WEffO2
where:
GillUptake = uptake of toxicant by gills ( g/L - d);
KUptake = uptake rate (1/d);
ToxicantWater = concentration of toxicant in water ( g/L);
Diff = factor to normalize rate constant based on all competing uptake rates
(unitless), see 1,2511;
WEffTox = withdrawal efficiency for toxicant by gills (unitless), see £267};
Respiration = respiration rate (mg biomass/L«d), see (87);
O2Biomass = ratio of oxygen to organic matter (mg oxygen/mg biomass; 0.575);
Oxygen = concentration of dissolved oxygen (mg oxygen/L), see ' ,; and
WEffO2 = withdrawal efficiency for oxygen (unitless, generally 0.62).
The oxygen uptake efficiency WEffO2 is assigned a constant value of 0.62 based on
observations of McKim et al. (1985). The toxicant uptake efficiency, WEfJTox, 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 ( .'-. --. '..") to the data of McKim et al. (1985) using 750-g fish, corrected for
ionization:
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION
CHAPTER 7
IfLogKOW< 1.5 then
WEffTox = 0.1
If 1.5 < LogKOW > 3.0 then
WEffTox = 0.1 + Nondissoc (0.3 LogKOW - 0.45)
If 3.0 < LogKOW < 6.0 then
WEffTox = 0.1 + Nondissoc 0.45
If 6.0 < LogKOW < 8.0 then
WEffTox = 0.1 + Nondissoc (0.45 - 0.23 (Log^CW - 6.0))
If LogKOW > 8.0 then
WEffTox = 0.1
(267)
where:
LogKOW
Nondissoc
log octanol-water partition coefficient (unitless); and
fraction of toxicant that is un-ionized (unitless), see
Figure 86
Piece-wise Fit to Observed Toxicant Uptake Data;
Modified from McKim et al., 1985
80
£60
K
LU I
Q.
£
S1
LL.
U.
UJ
Ul
1
o-l
2O ~
f
45
LOG KOW
lonization decreases the uptake efficiency This same algorithm is used for
invertebrates. Thomann (1989) has proposed a similar construct for these same data and a slightly
different construct for small organisms, but the scatter in the data do not seem to justify using two
different constructs.
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION
CHAPTER 7
Figure 87
The Effect of Differing Fractions of Un-ionized
Chemical on Uptake Efficiency
0.6
0.5
0.4
Q.
D
0.1
0
1.0
0.8
0,6
0.4
0.2
0.0
246
Log KOW
10
Dietary UptakeHydrophobic chemicals usually bioaccumulate in larger animals primarily
through absorption from contaminated food. Persistent, highly hydrophobic chemicals demonstrate
biomagnification or increasing concentrations as they are passed up the food chain from one trophic
level to another; therefore, dietary exposure can be quite important (Gobas et al., 1993). Uptake
from contaminated prey can be computed as (Thomann and Mueller, 1987; Gobas, 1993):
DietUptakeprey = GutEffTox PPBprey Ingestionprey le-6 (268)
where:
DietUptakePrey =
GutEffTox
PPB
Prey
IngestionPrey =
1 e-6
uptake of toxicant from given prey ( g toxicant/L*d);
efficiency of sorption of toxicant from gut (unitless); and
concentration of toxicant in given prey ( g toxicant/kg prey), see
ingestion of given prey (mg prey/L*d), see
units conversion (kg/mg);
Gobas (1993) presents an empirical equation for estimating GutEffTox as a function of the
octanol-water partition coefficient. However, data published by Gobas et al. (1993) suggest that
there is no trend in efficiency between LogKOW 4.5 and 7.5 this is to be expected
because the digestive system has evolved to assimilate a wide variety of organic molecules.
Therefore, the mean value of 0.62 is used in AQUATOX as a constant for small fish. Nichols et al.
(1998) demonstrated that uptake is more efficient in larger fish; therefore, a value of 0.92 is used
for large game fish because of their size. Invertebrates generally exhibit lower efficiencies;
Landrum and Robbins (1990) showed that values ranged from 0.42 to 0.24 for chemicals with log
KOWs from 4.4 to 6.7; the mean value of 0.35 is used for invertebrates in AQUATOX. These
values cannot be edited at this time.
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION
CHAPTER 7
Figure 88
GutEfJTox Constant Based on Mean Value for Data
from Gobas et al., 1993
o
0)
o
LU
0
5
J3
a
0.75 ili n »
LJ | | i
0.5 a i
0.25 . . . .
l»
o !
4.5 5 5.5 6 6.5 7 7.5
Log KOW
Guppies i Goldfish Mean = 0,63
EliminationElimination or clearance includes both excretion (depuration) and biotransformation
of a toxicant by organisms. Biotransformation may cause underestimation of elimination (McCarty
et al., 1992). An overall elimination rate constant is estimated and reported in the toxicity record.
The user may then modify the value based on observed data; that value is used in subsequent
simulations. If known, biotransformation also can be explicitly modeled.
For any given time the clearance rate is:
DepurationAnimal = k2 - ToxicantAnimal TCorr (269)
where:
DepurationAmmal
k2
ToxicantAmmal
TCorr
clearance rate ( g/L*d);
elimination rate constant (1/d);
mass of toxicant in given animal ( g/L); and
correction for suboptimal temperature (unitless), see i5_Q.
Because much animal depuration is across the gills, estimation of the elimination rate
constant k2 is based on a slope related to log KOW and an intercept that is a direct function of
respiration, assuming an allometric relationship between respiration and the weight of the animal
Thomann, 1989), and an inverse function of the lipid content:
If WetWt <5g then
Log k2 = - 0.536 Log KOW - Log DissocFactor + 0.065
WetWtm
LipidFrac
(270)
else
7-32
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION _ CHAPTER 7
WptWt m
Log k2 = -0.536 Log KOW - Log DissocFactor + 0.116 (271)
LipidFrac
where
£CW = octanol-water partition coefficient (unitless);
LipidFrac = fraction of lipid in organism (g lipid/g organism);
WetWt = mean wet weight of organism (g);
RB = allometric exponent for respiration (unitless);
DissocFactor = constrained factor for Nondissoc, see
The other gain and loss terms in equation (208) (TurbDiff, Predation, Mortality, Migration,
Recruit, GameteLoss, Promotion, Drift, Migration, and Emergelnsect) are all simply multiplied by
the appropriate toxicant concentration to complete the computation of the overall toxicant
concentration in the animal.
Biotransformation
Biotransformation can cause the conversion of a toxicant to another toxicant or to a harmless
daughter product through a variety of pathways. Internal biotransformation to given daughter
products by plants and animals is modeled by means of empirical rate constants provided by the user
in the Chemical Biotransformation screen:
Biotransformation = Toxicant organism BioRateConstorganism>tox (272)
where
Biotransformation = rate of conversion of chemical by given organism ( g/L d),
BioRateConst = biotransformation rate constant to a given toxicant, provided
by user (I/day)
with the model keeping track of both the loss and the gains to various daughter compartments.
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION
CHAPTER 7
Figure 89
Depuration Rate Constants for Invertebrates and Fish
es
X
O)
o
3 -
2 -
1
0 -
-1 -
-2 -
-3 -
-4
1
K2 for Various Animals
456
Log KOW
Daphnia
10-gfish
. Eel
Linear (Daphnia pred)
Diporeia
Eel obs
Linear (10-g fish pred)
Linear (Diporeia pred)
Biotransformation also can take place as a consequence of microbial decomposition. The
percentage of microbial biotransformation from and into each of the organic chemicals in a
simulation can be specified, with different values for aerobic and anaerobic decomposition. The
amount of biotransformation into a given chemical can then be calculated as follows for aerobic
conditions:
Biotransformm
mcrMn
FracAerobic Frac
OrgTox
(273)
and for anaerobic conditions:
BiotransformMicrohIn =
where
BiotransformMlcrobIn =
MicrobialDegradn^^ (1- FracAerobic) FracOrgTox(214)
Biotransformation to a given organic chemical in a given
detrital compartment due to microbial decomposition ( g/L
d);
7-34
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 7
MicrobialDegradn = total microbial degradation of a different toxicant in this
detrital compartment ( g/L d) see
FracAerobic = fraction of the microbial degradation that is aerobic (unitless),
see {2751; and
Frac0rgTox = user input fraction of the organic toxicant that is transformed
to the current organic toxicant (inputs can differ depending on
whether the degradation is aerobic or anaerobic).
To calculate the fraction of microbial decomposition that is aerobic, the following equation
is used:
j-, A ,. Factor
FracAerobic = (215)
DoCorr l '
where
Factor = Michaelis-Menten factor (unitless) see 1132,1;
DoCorr = effect of oxygen on microbial decomposition (unitless) see : ,.
Linkages to Detrital Compartments
Toxicants are transferred from organismal to detrital compartments through defecation and
mortality. The amount transferred due to defecation is the unassimilated portion of the toxicant that
is ingested:
DefecationTox = £) (KEgestpred Prey PPBprey le-6) (276)
KE^estpred, Prey = (l - GutEffTox) Ingestionpred ^ (277)
where:
DefecationTox = rate of transfer of toxicant due to defecation ( g/L«d);
KEgestPred Prey = fecal egestion rate for given prey by given predator (mg
prey/L-d);
PPBPrey = concentration of toxicant in given prey ( g/kg), see
1 e-6 = units conversion (kg/mg);
GutEffTox = efficiency of sorption of toxicant from gut (unitless), see page
7-M; and
IngestionPmd Prey = rate of ingestion of given prey by given predator (mg/L«d),
see £78.1
The amount of toxicant transferred due to mortality may be large; it is a function of the
concentrations of toxicant in the dying organisms and the mortality rates. The general equation is:
MortToxDetr = ^ (Mortality^ PPBOrg le-6) (278)
7-35
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 7
where:
MortToxDetr = rate of transfer of toxicant to a given detrital compartment due to
mortality ( g/L«d);
Mortality Org = rate of mortality of given organism (mg/L«d), see :;£!:}, ;J-:j and Hi:];;
PPB0rg = concentration of toxicant in given organism ( g/kg), see i20.2K and
1 e-6 = units conversion (kg/mg).
7-36
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 8
8 ECOTOXICOLOGY
Unlike most models, AQUATOX contains an ecotoxicology submodel that computes acute
and chronic toxic effects from the concentration of a toxicant in a given organism, using the critical
body residue approach (McCarty 1986, McCarty and Mackay 1993). Because the model simulates
toxicity based on internal concentrations as a consequence of bioaccumulation, both water and
dietary exposure pathways are represented equally well. Furthermore, as an ecosystem model,
AQUATOX can simulate indirect effects such as loss of forage base, reduction in predation, and
anoxia due to decomposition following a fish kill.
User-supplied values for LC50, the concentration of a toxicant in water that causes 50%
mortality, form the basis for a sequence of computations that lead to estimates of the biomass of a
given organism lost through acute toxicity each day. The sequence, which is documented in this
chapter, is to compute:
the internal concentration causing 50% mortality for a given period of exposure;
the internal concentration causing 50% mortality after an infinite period of time based on an
asymptotic concentration-response relationship;
the time-varying lethal internal concentration of a chemical;
the cumulative mortality for a given internal concentration;
the biomass lost per day as an increment to the cumulative mortality.
The user-supplied ECSOs, the concentrations in water eliciting chronic toxicity responses in
50% of the population, are used to obtain application factors relating the chronic toxicities to the
acute toxicity. Because AQUATOX can simulate as many as twenty toxic organic chemicals
simultaneously, the simplifying assumption is made that the toxic effects are additive.
8.1 Acute Toxicity of Compounds
Toxicity is based on the internal concentration of the toxicant in the specified organism.
Many compounds, especially those with higher octanol-water partition coefficients, take appreciable
time to accumulate in the tissue. Therefore, length of exposure is critical in determining toxicity.
Although AQUATOX cannot currently model mercury, mercury is used as an example in the
following discussion because of the availability of excellent data. The same principles apply to
organic toxicants and to both plants and animals.
InternalLCSO = BCF - LC50 (279)
The internal lethal concentration or lethal body residue can be computed from reported acute
toxicity data for the reported period of exposure based on the simple relationship suggested by an
algorithm in the FGETS model (Suarez and Barber, 1992):
where:
InternalLCSO = internal concentration that causes 50% mortality for a given period
of exposure ( g/kg);
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION
CHAPTER 8
BCF
LC50
time-dependentbioconcentrationfactor (L/kg), see : >:: I',...": -^; and
concentration of toxicant in water that causes 50% mortality for a
given period of exposure ( g/L).
Note that time is implicit in the toxicity parameters. For compounds with a LogKOWin
excess of 5 the usual 96-hr toxicity exposure does not reach steady state, so a time-dependent BCF
is used to account for the actual internal concentration at the end of the toxicity determination. This
is applicable no matter what the length of exposure (V;.;;i£J; :l , based on I :, ! i-").
Figure 85
Bioconcentration Factor as a Function of Time and KOW
Z
Q
fe
EC
ULI
o
o
o
o
00
1E4
1E3
0 \ 200 400 600 800 1000 1200
DAY
(96hr)
A given LC50 can be provided by the user, or the user may choose to have the model
estimate the LC50 from other species or groups for which there are data based on linear regressions
(Mayer and Ellersieck, 1986) and maximum likelihood estimators (Suter et al., 1986). In this way
the model can be parameterized to represent a complete food web (Table 7).
Log CalcLCSO = Intercept + Slope Log LC50
(280)
where:
CalcLCSO
Intercept
Slope
LC50
estimated LC50 ( g/L);
intercept for regression ( g/L);
slope of the regression equation;
external concentration of toxicant at which 50% of population is
killed ( g/L).
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION
CHAPTER 8
Table 7. Interspecies regression parameters.
From
minnow
minnow
minnow
minnow
bluegill
bluegill
bluegill
bluegill
trout
trout
trout
trout
Daphnia
Daphnia
Daphnia
Daphnia
To
trout
bass
catfish
bluegill
trout
bass
catfish
minnow
bass
catfish
bluegill
minnow
chironomid
stonefly
ostracod
amphipod
Intercept
-0.09
-0.433
0.954
0.018
0.44
0.051
1.918
0.947
0.258
1.391
0.135
0.796
0.802
1.475
0.79
-0.462
Slope
0.947
0.972
0.832
0.954
0.898
1.003
0.713
0.883
0.983
0.802
1.005
0.928
0.846
0.667
0.62
1.01
Correl. r
0.95
0.93
0.88
0.93
0.96
0.98
0.78
0.92
0.96
0.82
0.96
0.94
0.86
0.65
0.82
Mayer and Ellersieck,
1986
Mayer and Ellersieck,
1986
Mayer and Ellersieck,
1986
Mayer and Ellersieck,
1986
Mayer and Ellersieck,
1986
Mayer and Ellersieck,
1986
Mayer and Ellersieck,
1986
Mayer and Ellersieck,
1986
Mayer and Ellersieck,
1986
Mayer and Ellersieck,
1986
Mayer and Ellersieck,
1986
Mayer and Ellersieck,
1986
Mayer and Ellersieck,
1986
Mayer and Ellersieck,
1986
Suteretal., 1986
Mayer and Ellersieck,
1986
8-3
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 8
A constant toxicity parameter independent of time is obtained by determining the
asymptotic toxicity relationship, which is a rearrangement of: ijij i for the special case of observed
toxicity data:
LCInfmite = InternalLCSO (1 - e ~k2 ' obsTElaP<1) (281)
where:
LCInfmite = internal concentration causing 50% mortality after an infinite period
of exposure ( g/kg);
k2 = elimination rate constant (1/d); and
ObsTElapsed = exposure time in toxicity determination (h converted to d).
The model estimates k2, see ' :" ., : : ",,//'; and ' :, ^ :, assuming that this k2 is the same
as that measured in bioconcentration tests; good agreement has been reported between the two
(Mackayetal., 1992). The user may then override that estimate by entering an observed value. The
k2 can be calculated off-line by the user based on the observed half-life:
,, _ 0.693
k2 ; (282)
'1/2
where:
t,/2 = observed half-life.
Based on the Mancini (1983) model, the lethal internal concentration of a toxicant for a given
exposure period can be expressed as (Crommentuijn et al. (1994):
T ., 1f~, LCInfmite
LethalConc =
1 - k2 TElapsed
where:
LethalConc = time-varying tissue-based concentration of toxicant that
causes 50% mortality (ppb or g/kg), used in : : f to
compute fraction killed;
LCInfmite = ultimate internal lethal toxicant concentration after an
infinitely long exposure time ( g/kg);
TElapsed = time elapsed since beginning of exposure to toxicant (d).
The longer the exposure the lower the internal concentration required for lethality ( ' '
86).
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION
CHAPTER 8
Figure 86
Lethal concentration of MeHg in brook trout as a function of
time; two data points from McKim et al., 1976
k2 = 9.5E-4 d, LCSOInfinite = 2.37 ppm
700 -|
BOO -
500 -
a.
400 -
o
c
o
1 300-
.J
200 -
100 -
0 -
/90'hour
\
\
\
\
\
* m
10 100 1000 10000
Days
LethalConc calculated LslhalConc observed
Exposure is limited to the lifetime of the organism:
If TElapsed > LifeSpan Then TElapsed = LifeSpan
(284)
where:
LifeSpan = user-defined mean lifetime for given organism (d).
Based on an estimate of time to reach equilibrium (Connell and Hawker, 1988),
if TElapsed >
k2
then
(285)
LethalConc = LCInfinite
The fraction killed by a given internal concentration of toxicant is best estimated using the
time-dependent LethalConc in the cumulative form of the Weibull distribution (Mackay et al., 1992;
see also Christensen andNyholm, 1984):
PPB
i
Shape
CumFracKilled = 1 - e LethalConc
(286)
where:
CumFracKilled
PPB
cumulative fraction of organisms killed for a given period of
exposure (fraction/d),
internal concentration of toxicant ( g/kg), see and
-5
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION
CHAPTER 8
Shape
parameter expressing variability or spread in toxic response
(unitless, default = 0.33).
As a practical matter, if CumFracKilled exceeds 95%, then it is set to 100% to avoid
complex computations with small numbers. By setting organismal loadings to very small numbers,
seed values can be maintained in the simulation.
The probit, logit, and Weibull equations yield similar results over most of the range of
distributions, but the Weibull formulation is preferable because it is algebraically simple and yet
based on mechanistic relationships (Mackay et al., 1992), and it is most sensitive to the tails of the
distribution-the EC10 and EC90 values (Christensen and Nyholm, 1984). The Shape parameter is
important because it controls the spread of mortality, providing a probabilistic response. The larger
the value, the greater the spread of mortality over toxicant concentrations and time. For example,
methyl mercury toxicity exhibits a rapid response over a short time period with most of the fish
dying when a threshold internal concentration is reached, so Shape has a value of less than 0.1
(Figure 87). However, Mackay et al. (1992) found that a value of 0.33 gave the best fit to data on
toxicity of 21 narcotic chemicals to fathead minnows. This value is used as a default in AQUATOX,
but it can be changed by the user.
Figure 87
The effect of Shape in fitting the observed (McKim et al., 1976)
cumulative fraction killed following continued exposure to MeHg
O
<
^ //! / / H9P?b - LethaSConcHg for Day 637
^ 0-2 / / L
0 200 400 600 SOO 1000 12001400 1600
DAYS
The biomass killed per day is computed by disaggregating the cumulative mortality. Think
of the biomass at any given time as consisting of two types: biomass that has already been exposed
to the toxicant previously, which is called Resistant because it represents the fraction that was not
killed; and new biomass that has formed through growth, reproduction, and migration and has not
-6
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 8
been exposed to a given level of toxicant and therefore is referred to as Nonresistant. Then think
of the cumulative distribution as being the total CumFracKilled, which includes the FracKilled that
is in excess of the cumulative amount on the previous day if the internal concentration of toxicant
increases. A conservative estimate of the biomass killed at a given time, ignoring the possibility of
inherited tolerance, is computed as:
Poisoned = Resistant FracKill + Nonresistant CumFracKill (287)
Resistant = Biomasst_v - Poisonedt_v (288)
If Resistant < Biomass then
Nonresident = Biomass - Resistant ^ '
If FracKill^ > CumFracKill then FracKill = 0
else FracKill = CumFracKill - FracKUl^ (290)
where:
Poisoned = biomass of given organisms killed by exposure to toxicant at given
time (g/m3 d);
Resistant = biomass not killed by previous exposure (g/m3);
FracKill = fraction killed per day in excess of the previous fraction (fraction/d);
FracKill^.^ = fraction killed previous day (fraction/d);
Nonresistant = biomass not previously exposed; the biomass in excess of the
resistant biomass (g/m3).
Poisoned then becomes a term in the mortality equations and
8.2 Chronic Toxicity
Organisms usually have adverse reactions to toxicants at levels significantly below those that
cause death. In fact, the acute to chronic ratio is commonly used to quantify this relationship.
Application factors (AFs), which are the inverse of the acute to chronic ratio, are employed in the
model to predict chronic effect responses for both plants and animals. The user can supply observed
EC50 and LC50 values, which are used to compute AFs. For example:
A vr*
-------
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION
CHAPTER 8
LC50
external concentration of toxicant at which 50% of population is
killed ( g/L).
If the user enters observed EC50 and LC50 values for a given species, the model provides
the option of applying the resulting AF to estimate ECSOs for other animals. One is more likely to
have LC50 data for animals and EC50 data for plants, so the model will estimate LCSOs for plants
given ECSOs and a computed AF.
The computations for AFRepro andAFPhoto are similar:
ECSORepro
AFRepro
LC50
(292)
AFPhoto =
ECSOPhoto
LC50
(293)
where:
ECSORepro =
AFRepro =
ECSOPhoto =
AFPhoto
external concentration of toxicant at which there is a 50% reduction
in reproduction in animals ( g/L);
chronic to acute ratio for reproduction (unitless);
external concentration of toxicant at which there is a 50% reduction
in photosynthesis ( g/L); and
chronic to acute ratio for photosynthesis (unitless).
Similar to computation of acute toxicity in the model, chronic toxicity is based on internal
concentrations of a toxicant. Often chronic effects form a continuum with acute effects and the
difference is merely one of degree (Mackay et al., 1992). Regardless of whether or not the mode
of action is the same, the computed application factors relate the observed effect to the acute effect
and permit efficient computation of chronic effects factors in conjunction with computation of acute
effects. Because AQUATOX simulates biomass, no distinction is made between reduction in a
process in an individual and the fraction of the population exhibiting that response. The commonly
measured reduction in photosynthesis is a good example: the data only indicate that a given
reduction takes place at a given concentration, not whether all individuals are affected. The
application factor enters into the Weibull equation to estimate reduction factors for photosynthesis,
growth, and reproduction:
PPB
\IShope
FmcPhotO =
LethalConc AFPhoto
(294)
PPB
I/Shape
RedGrowth = 1 - e LethalConc'
(295)
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 8
PPB I/Shape
LethalConc ' ****" <296>
RedRepro = 1 - e
where:
FracPhoto = reduction factor for effect of toxicant on photosynthesis (unitless);
RedGrowth = factor for reduced growth in animals (unitless);
RedRepro = factor for reduced reproduction in animals (unitless);
PPB = internal concentration of toxicant ( g/kg), see
LethalConc = time-varying tissue-based concentration of toxicant that causes 50%
mortality (ppb or g/kg), see
AFPhoto = chronic to acute ratio for photosynthesis (unitless, default of 0. 10);
AFGrowth = chronic to acute ratio for growth in animals (unitless, default of 0. 1 0);
AFRepro = chronic to acute ratio for reproduction in animals (unitless, default of
0.05); and
Shape = parameter expressing variability in toxic response (unitless, default
ofO.33).
The reduction factor for photosynthesis, FracPhoto, enters into the photosynthesis equation
; _ '_, and it also appears in the equation for the acceleration of sinking of phytoplankton due to stress
The variable for reduced growth, RedGrowth, is arbitrarily split, based on calibration,
between two processes, ingestion £78}, where it reduces consumption by 20%:
ToxReduction = 1 - (0.2 RedGrowth) (297)
and egestion where it increases the amount of food that is not assimilated by 80%:
IncrEgest = (1 - EgestCoeffprey>prJ 0.8 RedGrowth (298)
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 beyond what would occur otherwise:
IncrMort = (1 - GMorf) RedRepro (299)
where:
IncrMort = increased gamete and embryo mortality due to toxicant (1/d).
8-9
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION CHAPTER 8
Sloughing of periphyton and drift of invertebrates also can be elicited by toxicants. For
example, sloughing can be caused by a surfactant that disrupts the adhesion of the periphyton, or an
invertebrate may release its hold on the substrate when irritated by a toxicant. Often the response
is immediate so that these responses can be modeled as dependent on dissolved concentrations of
toxicants with an available chronic toxicity parameter, as in the equation for periphyton sloughing:
Toxicantw
DislodgepeHTox = MaxToxSlough -_ Biomassperi (300)
10XlCam Water ^^Dislodge
where:
Dislodge Peri Tox = periphyton sloughing due to given toxicant (g/m3 d);
MaxToxSlough = maximum fraction of periphyton biomass lost by sloughing
due to given toxicant (fraction/d, 0.1);
ToxicantWater = concentration of toxicant dissolved in water ( g/L); see
EC50 Dislodge = external concentration of toxicant at which there is 50%
sloughing ( g/L); and
BiomassPeri = biomass of given periphyton (g/m3); see
Likewise, drift is greatly increased when zoobenthos are subjected to stress by sublethal
doses of toxic chemicals (Muirhead-Thomson, 1987), and that is represented by a saturation-kinetic
formulation that utilizes an analogous chronic toxicity parameter :
Y^ Toxican tWater - DriftThreshold
8eTOX ~ 2^tox - EC50Growth (301)
where:
ToxicantWater = concentration of toxicant in water ( g/L);
DriftThreshold = the concentration of toxicant that initiates drift ( g/L); and
ECSOGrowth = concentration at which half the population is affected ( g/L).
These terms are incorporated in the respective sloughing and drift equations.
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 fifteen years, following the first publications (Park et al., 1988; Park, 1990).
8- 10
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION REFERENCES
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National Oceanic and Atmospheric Administration, Boulder, Colorado.
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R- 14
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R- 15
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R- 16
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION REFERENCES
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R- 17
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION REFERENCES
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Chemistry, 16(2):283-292.
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AQUATOX (RELEASE 2) 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)
Bioaccumulation
Bioavailability
Biodegradation
Biomagnification
Biomass
Biota
Biotransformation
Chlorophyll
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 uptake of contaminants from all sources including direct sorption to
the body, transport across gill membranes, and through ingestion of prey
and sediments
the existence of a chemical in a form that it can be readily integrated into
an organism by means of any form of intake or attachment
the process of breaking down into simple organic substances by
decomposers (bacteria and fungi)
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 permanent changing of a substance from one chemical identity to
another by means of biotically driven processes
the green, photosynthetic pigments of plants
A- 1
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION
APPENDIX A
Colloid
Consumer
Copepods
Crustacean
Decomposers
Depuration
Desorption
Detritus
Diatom
Diurnal
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
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
excretion of contaminant by an organism
the process by which chemicals are detached and released from solid
surfaces; the opposite of adsorption
dead organic matter
any of class of minute algae with cases of silica
pertaining to daily occurrence
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
A-2
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION
APPENDIX A
Kinetic processes
Kinetic reaction
Limiting factor
Limnetic zone
Limnology
Lipids
Littoral zone
Macrofauna
Macrophytes
Mass balance
Migration
Nutrients
Omnivorous
Organic chemical
Overturn
Oxygen depletion
Parameter
Pelagic zone
Periphyton
Oxidation
Photic zone
Phytoplankton
Plankton
Pond
Population
Predator
Prey
Producer
Production
Productivity
Productivity,
primary
description of the dynamic rate and mode of change in the transformation
or degradation of a substance in an ecosystem
a physical, chemical or biological transformation/reaction that is best
represented using a formulation that is time-dependent
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
structural components of the cell that are fatty or waxy
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
an equation that accounts for the flux of mass going into a defined area
and the flux of mass leaving the defined area; the flux in must equal the
flux out
movement of an organism from one location to another
chemical elements essential to life
feeding on a variety of organisms and organic detritus
compounds containing carbon;
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
A-3
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION
APPENDIX A
Productivity,
secondary
Reservoir
Riverine
Rough fish
Sediment
Siltation
Stratification
Substrate
Succession
Tolerance
Trophic level
Turbidity
Volatilization
Wastewater
Wetlands
Zooplankton
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
small aquatic animals, floating, usually with limited swimming capability
A-4
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION
APPENDIX B
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, the
user interface, and the technical documentation
USER INTERFACE
Chemical
CAS Registry No.
Molecular Weight
Dissociation Constant
Solubility
Henry's Law Constant
Vapor Pressure
Octanol- water partition
coefficient
KPSED
Activation Energy for
Temperature
Rate of Anaerobic Microbial
Degradation
Max. Rate of Aerobic Microbial
Degradation
Uncatalyzed hydrolysis constant
Acid catalyzed hydrolysis
constant
INTERNAL
ChemicalRecord
ChemName
CASRegNo
MolWt
pka
Solubility
Henry
VPress
LogP
KPSed
En
KMDegrAnaerobic
KMDegrdn
KUnCat
KAcid
TECH DOC
Chemical
Underlying Data
N/A
N/A
MolWt
pKa
N/A
Henry
N/A
LogKow
KPSed
En
KAnaerobic
KMDegrdn
KUncat
KAcidExp
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
acid dissociation constant
Not utilized as a parameter by the code.
Henry's law constant
Not utilized as a parameter by the code.
log octanol- water partition coefficient
detritus- water partition coefficient
Arrhenius activation energy
decomposition rate at 0 g/m3 oxygen
Maximum (microbial) degradation rate
the measured first-order reaction rate at pH 7
pseudo-first-order acid-catalyzed rate constant for a
given pH
UNITS
N/A
N/A
(g/mol)
negative log
(ppm)
(atmm3 mol-1)
mmHg
(unitless)
(L/kg)
(cal/mol)
(1/d)
(1/d)
(1/d)
(1/d)
B- 1
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION
APPENDIX B
USER INTERFACE
Base catalyzed hydrolysis
constant
Photolysis Rate
Oxidation Rate Constant
Weibull Shape Parameter
Chemical is a Base
INTERNAL
KBase
PhotolysisRate
OxRateConst
Weibull_Shape
ChemlsBase
TECH DOC
KBaseExp
KPhot
N/A
Shape
if the compound is
abase
DESCRIPTION
pseudo-first-order rate constant for a given pH
direct photolysis first-order rate constant
Not utilized as a parameter by the code.
parameter expressing variability in toxic response;
default is 0.33
if the compound is a base
UNITS
(1/d)
(1/d)
(L/mold)
(unitless)
(True/False)
B-2
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION
APPENDIX B
USER INTERFACE
Site Name
Max Length (or reach)
Vol.
Surface Area
Mean Depth
Maximum Depth
Ave. Temp, (epilimnetic or
hypolimnetic)
Epilimnetic Temp. Range (or
hypolimnetic)
Latitude
Average Light
Annual Light Range
Total Alkalinity
Hardness as CaCO3
Sulfate Ion Cone
Total Dissolved Solids
Limnocorral Wall Area
Mean Evaporation
Extinct. Coeff Water
INTERNAL
SiteRecord
SiteName
SiteLength
Volume
Area
ZMean
ZMax
TempMean
TempRange
Latitude
LightMean
LightRange
AlkCaCOS
HardCaCOS
SO4Conc
TotalDissSolids
LimnoWallArea
MeanEvap
ECoeffWater
TECH DOC
Site Underlying
Data
N/A
Length
Volume
Area
ZMean
ZMax
TempMean
TempRange
Latitude
LightMean
LightRange
N/A
N/A
N/A
N/A
LimnoWallArea
MeanEvap
ExtinctffiO
DESCRIPTION
For each water body simulated, the following
parameters are required
Site's Name. Used for Reference only.
maximum effective length for wave setup
initial volume of site (must be copied into state var.)
site area
mean depth
maximum depth
mean annual temperature of epilimnion (or
hypolimnion)
annual temperature range of epilimnion (or
hypolimnion)
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.
area of limnocorral walls; only relevant to limnocorral
mean annual evaporation
light extinction of wavelength 312.5 nm in pure water
UNITS
N/A
(km)
(m3)
(m2)
(m)
(m)
(°C)
(°C)
(Deg, decimal)
Langleys/day (ly/d)
Langleys/day (ly/d)
mg/L
mg CaCO3 / L
mg/L
mg/L
(m2)
inches / year
(1/m)
B-3
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION
APPENDIX B
USER INTERFACE
Channel Slope
Maximum Channel Depth
Before Flooding
Sediment Depth
Stream Type
use the below value
Mannings Coefficient
Percent Riffle
Percent Pool
Silt: Critical Shear Stress for
Scour
Silt: Critical Shear Stress for
Deposition
Silt: Fall Velocity
Clay: Critical Shear Stress for
Scour
Clay: Critical Shear Stress for
Deposition
Clay: Fall Velocity
INTERNAL
SiteRecord (Stream-
Specific)
Channel_Slope
Max Chan Depth
SedDepth
StreamType
UseEnteredManning
EnteredManning
PctRiffle
PctPool
SiteRecord (Sand-
Silt-Clay Specific)
ts_silt
tdep silt
FallVel_silt
ts_clay
tdep_clay
FallVel_clay
TECH DOC
Site Underlying
Data
Slope
Max Chan Depth
SedDepth
Stream Type
Manning
Riffle
Pool
Site Underlying
Data
TauScourSed
TauDepSed
VTSed
TauScourSed
TauDepSed
VTSed
DESCRIPTION
For each stream simulated, the following parameters
are required
slope of channel
depth at which flooding occurs
maximum sediment depth
concrete channel, dredged channel, natural channel
do not determine Manning coefficient from streamtype
manually entered Manning coefficient.
percent riffle in stream reach
percent pool in stream reach
For each stream with the inorganic sediments model
included, the following parameters are required
critical shear stress for scour of silt
critical shear stress for deposition of silt
terminal fall velocity of silt
critical shear stress for scour of clay
critical shear stress for deposition of clay
terminal fall velocity of clay
UNITS
(m/m)
(m)
(m)
Choice from List
(true/false)
s/ml'3
%
%
(kg/m3)
(kg/m3)
(m/s)
(kg/m3)
(kg/m3)
(m/s)
B-4
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AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION
APPENDIX B
USER INTERFACE
Max. Degrdn Rate, labile
Max Degrdn Rate, Refrac
Temp. Response Slope
Optimum Temperature
Maximum Temperature
Min. Adaptation Temp
Min pH for Degradation
Max pH for Degradation
Organics to Phosphate
Organics to Ammonia
O2 : Biomass, Respiration
O2 : N, Nitrification
Detrital Sed Rate
PO4, Anaerobic Sed.
NH4, Aerobic Sed.
INTERNAL
ReminRecord
DecayMax_Lab
DecayMax Refr
Q10
TOpt
TMax
TRef
pHMin
pHMax
Org2Phosphate
Org2Ammonia
O2Biomass
O2N
KSed
PSedRelease
NSedRelease
TECH DOC
Remineralization
Data
DecayMax
ColonizeMax
Q10
TOpt
TMax
TRef
pHMin
pHMax
Org2Phosphate
Org2Ammonia
O2Biomass
O2N
KSed
N/A
N/A
DESCRIPTION
For each simulation, the following parameters are
required
maximum decomposition rate
maximum colonization rate under ideal conditions
Not utilized as a parameter by the code.
optimum temperature for degredation to occur
maximum temperature at which degradation will occur
Not utilized as a parameter by the code.
minimum pH below which limitation on biodegradation
rate occurs.
maximum pH above which limitation on biodegradation
rate occurs.
ratio of phosphate to organic matter (unitless)
ratio of ammonia to organic matter
ratio of oxygen to organic matter
ratio of oxygen to nitrogen
intrinsic sedimentation rate
Not utilized as a parameter by the code.
Not utilized as a parameter by the code.
UNITS
(g/gtl)
(g/g*)
(unitless)
(°C)
(°C)
(°C)
pH
PH
(unitless)
(unitless)
(unitless)
(unitless)
(m/d)
(g/m2M)
(g/m2-d)
B-5
-------
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION
APPENDIX B
USER INTERFACE
Animal
Animal Type
Taxonomic Type or Guild
Toxicity Record
Half Saturation Feeding
Maximum Consumption
Min Prey for Feeding
Temp Response Slope
Optimum Temperature
Maximum Temperature
Min Adaptation Temp
Respiration Rate
Specific Dynamic Action
Excretion: Respiration
Gamete : Biomass
Gamete Mortality
Mortality Coefficient
Carrying Capacity
INTERNAL
ZooRecord
AnimalName
Animal Type
Guild Taxa
ToxicityRecord
FHalfSat
CMax
BMin
Q10
TOpt
TMax
TRef
EndogResp
KResp
KExcr
PctGamete
GMort
KMort
KCap
TECH DOC
Animal
Underlying Data
N/A
Animal Type
Taxonomic type or
guild
N/A
FHalfSat
CMax
BMin
Q10
TOpt
TMax
TRef
EndogResp
KResp
KExcr
PctGamete
GMort
KMort
KCap
DESCRIPTION
For each animal in the simulation, the following
parameters are required
Animal's Name. Used for Reference only.
Animal Type (Fish, Pelagic Invert, Benthic Invert,
Benthic Insect)
Taxonomic type or trophic guild
associates animal with appropriate toxicity data
half- saturation constant for feeding by a predator
maximum feeding rate for predator
minimum prey biomass needed to begin feeding
slope or rate of change in given process per 10°C
temperature change
optimum temperature for given process
maximum temperature tolerated
adaptation temperature below which there is no
acclimation
basal respiration rate at 0° C for given predator
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
UNITS
N/A
Choice from List
Choice from List
Choice from List
(g/m3)
(g/g*)
(g/m3) (or g/m2)
(unitless)
(°C)
(°C)
(°C)
(I/day)
(unitless)
(unitless)
(unitless)
(1/d)
(1/d)
g/m3
B-6
-------
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION
APPENDIX B
USER INTERFACE
Average Drift
VelMax
Mean lifespan
Initial fraction that is lipid
Mean Weight
Percent in Riffle
Percent in Pool
Fish spawn automatically, based
on temperature range
Fish spawn of the following
dates each year
Fish can spawn an unlimited
number of times. . .
Fish can only spawn...
Use Allometric Equation to
Calculate Maximum
Consumption
Intercept for weight dependence
Slope for weight dependence
Use Allometric Equation to
Calculate Respiration
RA
RB
INTERNAL
AveDrift
VelMax
LifeSpan
FishFracLipid
MeanWeight
PrefRiffle
PrefPool
Auto Spawn
SpawnDatel..3
UnlimitedSpawning
SpawnLimit
UseAllom_C
CA
CB
UseAllom_R
RA
RB
TECH DOC
Dislodge
VelMax
LifeSpan
LipidFrac
WetWt
Preferences,^
Preferences,^
CA
CB
RA
RB
DESCRIPTION
fraction of biomass subject to drift per day
maximum water velocity tolerated
mean lifespan in days
fraction of lipid in organism
mean wet weight of organism
Percentage of biomass of animal that is in riffle, as
opposed to run or pool
percentage of biomass of animal that is in pool, as
opposed to run or riffle
Does AQUATOX calculate Spawn Dates
User 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
Intercept for species specific metabolism
Weight dependence coefficient
UNITS
fraction / day
(cm/s)
days
(g lipid/g organism)
(g)
%
%
(true/false)
(date)
(true/false)
(integer)
(true/false)
(real number)
(real number)
(true/false)
(real number)
(real number)
B-7
-------
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION
APPENDIX B
USER INTERFACE
Use "Set 1" of Respiration
Equations
RQ
RTL
ACT
RTO
RK1
BACT
RTM
RK4
ACT
Preference (ratio)
Egestion (frac.)
INTERNAL
UseSetl
RQ
RTL
ACT
RTO
RK1
BACT
RTM
RK4
ACT
TrophlntPrefl ]
TrophInt.Egest[ ]
TECH DOC
RQ
RTL
ACT
RTO
RK1
BACT
RK4
ACT
Prefprey,pred
EgestCoeffprey pred
DESCRIPTION
Use "Set 1" of Allometric Respiration Parameters
Allometric Respiration Parameter
temperature below which swimming activity is an
exponential function of temperature
intercept for swimming speed for a Ig fish
coefficient for swimming speed dependence on
metabolism
intercept for swimming speed above the threshold
temperature
coefficient for swimming at low temperatures
not currently used as a parameter by the code
weight-dependent coefficient for swimming speed
intercept of swimming speed vs. temperature and
weight
initial preference value from the animal parameter
screen
fraction of ingested prey that is egested
UNITS
(true/false)
(real number)
(°C)
(cm/s)
(s/cm)
(cm/s)
(1/°C)
(real number)
(real number)
(unitless)
(unitless)
B-8
-------
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION
APPENDIX B
USER INTERFACE
Plant
Plant Type
Taxonomic Group
Toxicity Record
Saturating Light
P Half- saturation
N Half- saturation
Inorg C Half- saturation
Temp Response Slope
Optimum Temperature
Maximum Temperature
Min. Adaptation Temp
Max. Photosynthesis Rate
Respiration Coefficient
Mortality Coefficient
Exponential Mort Coeff
P : Photosynthate
N: Photosynthate
Light Extinction
INTERNAL
PlantRecord
PlantName
PlantType
Taxonomic Type
ToxicityRecord
LightSat
KPO4
KN
KCarbon
Q10
TOpt
TMax
TRef
PMax
KResp
KMort
EMort
UptakePO4
UptakeN
ECoeffPhyto
TECH DOC
Plant Underlying
Data
Plant Type
Taxonomic Group
N/A
LightSat
KP
KN
KCO2
Q10
TOpt
TMax
TRef
PMax
KResp
KMort
EMort
Uptake Phosphorus
Uptake Nitrogen
EcoeffPhyto
DESCRIPTION
For each Plant in the Simulation, the following
parameters are required
Plant's Name. Used for Reference only.
Plant Type: (Phytoplankton, Periphyton, Macrophytes,
Bryophytes)
Taxonomic group
associates plant with appropriate toxicity data
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 10°C temperature change
optimum temperature
maximum temperature tolerated
adaptation temperature below which there is no
acclimation
maximum photo synthetic rate
coefficient of proportionality between, excretion and
photosynthesis at optimal light levels
intrinsic mortality rate
exponential factor for suboptimal conditions
fraction of photosynthate that is nutrient (P)
fraction of photosynthate that is nutrient (N)
attenuation coefficient for given alga
UNITS
N/A
Choice from List
Choice from List
Choice from List
(ly/d)
(gP/m3)
(gN/m3)
(gC/m3)
(unitless)
(°C)
(°C)
(°C)
(1/d)
(unitless)
(g/g*)
(unitless)
(unitless)
(unitless)
(l/m-g/m3)vv
B-9
-------
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION
APPENDIX B
USER INTERFACE
Sedimentation Rate
Exp. Sedimentation Coefficient
Carrying Capacity
Reduction in Still Water
VelMax for macrophytes
Critical Force (Fcrit for
periphyton only)
Percent in Riffle
Percent in Pool
INTERNAL
KSed
ESed
NA
Red_Still_Water
Macro_VelMax
FCrit
PrefRiffle
PrefPool
TECH DOC
KSed
ESed
NA
RedStillWater
VelMax
Fcrit
PrefRiffle
PrefPool
DESCRIPTION
intrinsic settling rate
exponential settling coefficient
not used by the code
reduction in photosynthesis in absence of current
velocity at which total breakage occurs
critical force necessary to dislodge given periphyton
group
Percentage of biomass of plant that is in riffle, as
opposed to run or pool
Percentage of biomass of plant that is in pool, as
opposed to run or riffle
UNITS
(m/d)
(unitless)
(g/m2)
(unitless)
(cm/s)
(kg m/s2)
(%)
(%)
B- 10
-------
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION
APPENDIX B
USER INTERFACE
LC50
LC50 exp time (h)
Elim rate const
Biotmsfm rate
EC50 growth
Growth exp (h)
EC 50 repro
Repro exp time (h)
Ave. wet wt. (g)
Lipid Frac
Drift Threshold (ug/L)
EC50 photo
EC50 exp time (h)
EC50 dislodge
Elim rate const
INTERNAL
AnimalToxRecord
LC50
LC50_exp_time
K2
BioTrans[ ]
EC50_growth
Growth exp time
EC50_repro
Repro_exp_time
Ave wet wt
Lipid_frac
Drift_Thresh
TPlantToxRecord
EC50_photo
EC 50 exp time
EC50_dislodge
K2
TECH DOC
Animal Toxicity
Parameters
LC50
ObsTElapsed
K2
Biotransform
ECSOGrowth
ObsTElapsed
ECSORepro
ObsTElapsed
WetWt
LipidFrac
Drift Threshold
Plant Toxicity
Parameter
ECSOPhoto
ObsTElapsed
ECSODislodge
K2
DESCRIPTION
For each Chemical Simulated, the following
parameters are required for each animal simulated
concentration of toxicant in water that causes 50%
mortality
exposure time in toxicity determination
elimination rate constant
percentage of chemical that is biotransformed to
specific daughter products
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 plant simulated
external concentration of toxicant at which there is 50%
reduction in photosynthesis
exposure time in toxicity determination
for periphyton only: external concentration of toxicant
at which there is 50% dislodge of periphyton
elimination rate constant
UNITS
Cg/L)
(h)
(1/d)
(1/d)
Cg/L)
(h)
Cg/L)
(h)
(g)
(g lipid/g organ)
Cg/L)
Cg/L)
(h)
Cg/L)
(1/d)
B- 11
-------
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION
APPENDIX B
USER INTERFACE
LC50
LC50 exp.time (h)
Lipid Frac
Initial Condition
Gas-phase cone.
Loadings from Inflow
Loadings from Point Sources
Loadings from Direct
Precipitation
Nonpoint-source Loadings
Biotmsfm rate
INTERNAL
LC50
LC50_exp_time
Lipid frac
TChemical
InitialCond
Tox Air
Loadings
Alt LoadingsfPointso
urce]
Alt LoadingsfDirect
Precip]
Alt_Loadings[NonPoi
ntsource]
BioTrans[ ]
TECH DOC
LC50
ObsTElapsed
LipidFrac
Chemical
Parameters
Initial Condition
Toxicant^
Inflow Loadings
Point Source
Loadings
Direct Precipitation
Load
Non-Point Source
Loading
Biotransform
DESCRIPTION
concentration of toxicant in water that causes 50%
mortality
exposure time in toxicity determination
fraction of lipid in organism
For each Chemical to be simulated, the following
parameters are required
Initial Condition of the state variable
gas-phase concentration of the pollutant
Daily loading as a result of the inflow of water
Daily loading from point sources
Daily loading from direct precipitation
Daily loading from non-point sources
percentage of chemical that is biotransformed to
specific daughter products
UNITS
CB/L)
(h)
(g lipid/g organ
S/L
g/m3
S/L
(g/d)
(g/m2 -A)
(g/d)Tox_AirGas-
phase
concentration(g/m3 )
%
B- 12
-------
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION
APPENDIX B
USER INTERFACE
Initial Condition
Loadings from Point Sources
Loadings from Direct
Precipitation
Non-point source loadings
Fraction of Phosphate Available
Initial Condition
Initial Condition
Loadings from Inflow
(Toxicant) Loadings
INTERNAL
TRemineralize
InitialCond
Loadings
Alt LoadingsfPointso
urce]
Alt_Loadings[Direct
Precip]
Alt_Loadings[NonPoi
ntsource]
FracAvail
TSedDetr
InitialCond
TToxicant.InitialCond
Loadings
TToxicant.Loads
TECH DOC
Nutrient
Parameters
Initial Condition
Inflow Loadings
Point Source
Loadings
Direct Precipitation
Loa
Non-Point Source
Loading
FracAvail
Sed. Detritus
Parameters
Initial Condition
Toxicant Exposure
Inflow Loadings
Tox Exposure of
Inflow L
DESCRIPTION
For each Nutrient to be simulated, O2 and CO2, the
following parameters are required
Initial Condition of the state variable
Daily loading as a result of the inflow of water
Daily loading from point sources
Daily loading from direct precipitation
Daily loading from non-point sources
Fraction of phosphate loadings that is available versus
that which is tied up in minerals
For the Labile and Refractory Sedimented Detritus
compartments, the following parameters are
required
Initial Condition of the labile or refractory sedimented
detritus
Initial Toxicant Exposure of the state variable, for each
chemical simulated
Daily loading of the sedimented detritus as a result of
the inflow of water
Daily parameter; Toxicant Exposure of each type of
inflowing detritus, for each chemical
UNITS
mg/L
mg/L
(g/d)
(g/m2 -A)
(g/d)
(unitless)
(g/m2)
I/kg
mg/L
I/kg
B- 13
-------
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION
APPENDIX B
USER INTERFACE
Initial Condition
Initial Condition: % Particulate
Initial Condition: % Refractory
Inflow Loadings
All Loadings: % Particulate
All Loadings: % Refractory
Loadings from Point Sources
Nonpoint-source Loadings
(Associated with Organic
Matter)
(Toxicant) Initial Condition
(Toxicant) Loadings (associated
with Organic Matter)
INTERNAL
TDetritus
InitialCond
Percent_Part_IC
Percent_Refr_IC
Loadings
Percent_Part
Percent_Refr
Alt LoadingsfPointso
urce]
Alt Loadings
[NonPointsource]
TToxicant.InitialCond
TToxicant.Loads
TECH DOC
Susp & Dissolved
Detritus
Initial Condition
Inflow Loadings
Percent Particulate
Ml
Percent Refractory
Inflo
Point Source
Loadings
Non-Point Source
Loading
Toxicant Exposure
Tox Exposure of
Inflow L
DESCRIPTION
For the Suspended and Dissolved Detritus
compartments, the following parameters are
required
Initial Condition of suspended & dissolved detritus, as
organic matter, organic carbon, or biochemical oxygen
demand
Percent of Initial Condition that is particulate as
opposed to dissolved detritus
Percent of Initial Condition that is refractory as opposed
to labile detritus
Daily loading as a result of the inflow of water
Daily parameter; % of all loadings that are particulate
as opposed to dissolved detritus
Daily parameter; % of loading that is refractory as
opposed to labile detritus
Daily loading from point sources
Daily loading from non-point sources
Initial Toxicant Exposure of the suspended and
dissolved detritus
Daily parameter; Toxicant Exposure of each type of
inflowing detritus, for each chemical
UNITS
mg/L
percentage
percentage
mg/L
percentage
percentage
(g/d)
(g/d)
I/kg
I/kg
B- 14
-------
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION
APPENDIX B
USER INTERFACE
Initial Condition
(Toxicant) Initial Condition
Initial Condition
Loadings from Inflow
(Toxicant) Initial Condition
(Toxicant) Loadings
Initial Condition
Loadings from Inflow
(Toxicant) Initial Condition
(Toxicant) Loadings
Preference (ratio)
INTERNAL
TBuried Detritus
InitialCond
TToxicant.InitialCond
TPlant
InitialCond
Loadings
TToxicant.InitialCond
TToxicant.Loads
TAnimal
InitialCond
Loadings
Ttoxicant. InitialCond
TToxicant.Loads
TrophlntArray . Pref
TECH DOC
Buried Detritus
Initial Condition
Toxicant Exposure
Plant Parameters
Initial Condition
Inflow Loadings
Toxicant Exposure
Tox Exposure of
Inflow L
Animal
Parameters
Initial Condition
Inflow Loadings
Toxicant Exposure
Tox Exposure of
Inflow L
Prefprey, pred
DESCRIPTION
For Each Type of Buried Detritus, the following
parameters are required
Initial Condition of the labile and refractory buried
detruitus
Initial Toxicant Exposure of the labile and refractory
buried detritus , for each chemical simulated
For each plant type simulated, the following
parameters are required
Initial Condition of the plant
Daily loading as a result of the inflow of water
Initial Toxicant Exposure of the plant
Daily parameter; Tox.icant exposure of the Inflow
Loadings, for each chemical simulated
For each animal type simulated, the following
parameters are required
Initial Condition of the animal
Daily loading as a result of the inflow of water
Initial Toxicant Exposure of the animal
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
UNITS
(g/m2)
Kg/cu.m (on screen)
g/kg (Kg/cu. m on
screen)
mg/L
mg/L
g/kg
g/kg
mg/L or g/sq m) also
expressed as g/m2)
mg/L or g/sq. m
g/kg
g/kg
(unitless)
B- 15
-------
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION
APPENDIX B
USER INTERFACE
Egestion (frac.)
Initial Condition
Water volume
Inflow of Water
Discharge of Water
Site Type
Temperature
Initial Condition
Could this system stratify
Valuation or loading
INTERNAL
TrophlntArray.ECoeff
TVolume
InitialCond
Volume
InflowLoad
DischargeLoad
Site Characteristics
SiteType
InitialCond
TECH DOC
EgestCoeff
Volume
Parameters
Initial Condition
Volume
Inflow of Water
Discharge of Water
Site
Characteristics
Site Type
Initial condition
DESCRIPTION
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 water volume .
Choose method of calculating volume; choose between
Manning's equation, constant volume, variable
depending upon inflow and discharge, or use known
values
Inflow of water; daily parameter, can choose between
constant and dynamic loadings
Discharge of water; daily parameter, can choose
between constant and dynamic loadings
The following parameters are required
Site type affects many portions of the model.
Initial temperature of the segment or layer (if vertically
stratified
could system vertically stratify
Temperature of the segment. Can use annual means for
each stratum and constant or dynamic values
UNITS
(unitless)
(m3)
cu. m
(m3 /d) (cu m/d)
(m3 /d)
Pond, Lake, Stream,
Reservoir, Limnocorral
(°C)
true/false
(°C)
B- 16
-------
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION
APPENDIX B
USER INTERFACE
Wind
Initial Condition
Mean Value
Wind Loading
Light
Initial Condition
Loading
Photoperiod
PH
Initial Condition
State Variable Valuation
INTERNAL
InitalCond
Wind(Mean Value)
Wind
Light
Loadsrec
Photoperiod
InitialCond
PH
TECH DOC
CosCoeff0
Wind
Light
Photoperiod
PH
DESCRIPTION
Initial wind velocity 10m above the water
Mean wind velocity
Daily parameter; wind velocity 10m above the water; 1,
can choose default time series, constant or dynamic
loadings
Daily parameter; avg. light intensity at segment top;
can choose annual mean, constant loading or dynamic
loadings
Fraction of day with daylight; optional, can be
calculated from latitude
Initial pH value
pH of the segment; can choose constant or daily value.
UNITS
(m/s)
(m/s)
(m/s)
(ly/d)
(hr/d)
(PH)
(PH)
B- 17
-------
AQUATOX (RELEASE 2) TECHNICAL DOCUMENTATION
APPENDIX B
USER INTERFACE
Sand / Silt / Clay
Initial Susp. Sed.
Frac in Bed Seds
Loadings from Inflow
Loadings from Point Sources
Loadings from Direct
Precipitation
Non-point source loadings
INTERNAL
TSediment
InitialCond
FracInBed
Loadings
Alt LoadingsfPoint
source]
Alt_Loadings[Direct
Precip]
Alt_Loadings[Non
Pointsource]
TECH DOC
Inorganic
Sediment
Parameters
Initial Condition
FracSed
Inflow Loadings
Point Source
Loadings
Direct Precipitation
Loa
Non-Point Source
Loading
DESCRIPTION
If the inorganic sediments model is included in
AQUATOX, the following parameters are required
for sand, silt, and clay
Initial Condition of the sand, silt, or clay
Fraction of the bed that is composed of this inorganic
sediment. Fractions of sand, silt, and clay must add to
1.0
Daily sediment loading as a result of the inflow of water
Daily loading from point sources
Daily loading from direct precipitation
Daily loading from non-point sources
UNITS
(mg/L)
(fraction)
mg/L
(g/d)
(Kg*)
(g/d)
B- 18
------- |