United States
Environmental Protection
Agency
Office of Water (4305)
EPA-823-R-09-004
August 2009
&EPA AQUATOX (RELEASE 3)
MODELING ENVIRONMENTAL FATE
AND ECOLOGICAL EFFECTS IN
AQUATIC ECOSYSTEMS
VOLUME 2: TECHNICAL DOCUMENTATION
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
AQUATOX (RELEASE 3)
MODELING ENVIRONMENTAL FATE
AND ECOLOGICAL EFFECTS IN
AQUATIC ECOSYSTEMS
VOLUME 2: TECHNICAL DOCUMENTATION
Richard A. Park
and
Jonathan S. Clough
AUGUST 2009
U.S. ENVIRONMENTAL PROTECTION AGENCY
OFFICE OF WATER
OFFICE OF SCIENCE AND TECHNOLOGY
WASHINGTON DC 20460
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
DISCLAIMER
This document describes the scientific and technical background of the aquatic ecosystem model
AQUATOX, Release 3. Anticipated users of this document include persons who are interested
in using the model, including but not limited to researchers and regulators. The model described
in this document is not required, and the document does not change any legal requirements or
impose legally binding requirements on EPA, states, tribes or the regulated community. 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.
ACKNOWLEDGMENTS
This model has been developed and documented by Dr. Richard A. Park of Eco Modeling and by
Jonathan S. Clough of Warren Pinnacle Consulting, Inc. under subcontract to Eco Modeling.
The work was funded with Federal funds from the U.S. Environmental Protection Agency,
Office of Science and Technology under contract number 68-C-01-0037 to AQUA TERRA
Consultants, Anthony Donigian, Work Assignment Manager. Integration of Interspecies
Correlation Estimation (Web-ICE) was made possible due to the work of US. EPA Office of
Research and Development Gulf Breeze, the University of Missouri-Columbia, and the US
Geological Survey.
The assistance, advice, and comments of the EPA work assignment manager, Marjorie Coombs
Wellman of the Exposure Assessment 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 David A. Mauriello, Rufus Morison, and Donald Rodier of the Office of Pollution
Prevention and Toxics is gratefully acknowledged. Marietta Echeverria, Office of Pesticide
Program, contributed to the integrity of the model through her careful analysis and comparison
with EXAMS. Release 2 of this model underwent independent peer review by Donald
DeAngelis, Robert Pastorok, and Frieda Taub; and Release 3 underwent peer review by Marty
Matlock, Damian Preziosi, and Frieda Taub. Their diligence is greatly appreciated.
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
TABLE OF CONTENTS
DISCLAIMER ii
TABLE OF CONTENTS iii
PREFACE viii
1. INTRODUCTION 1
1.1 Overview 1
1.2 Background 4
1.3 The Multi-Segment Version 5
1.4 The Estuary Model 6
1.5 The PFA Model 6
1.6 AQUATOX Release 3 Overview 6
1.7 Comparison with Other Models 7
1.8 Intended Application of AQUATOX 9
2. SIMULATION MODELING 11
2.1 Temporal and Spatial Resolution and Numerical Stability 11
2.2 Results Reporting 13
2.3 Input Data 14
2.4 Sensitivity Analysis 15
2.5 Uncertainty Analysis 16
2.6 Calibration and Validation 21
3. PHYSICAL CHARACTERISTICS 39
3.1 Morphometry 39
Volume 39
Bathymetric Approximations 42
Dynamic Mean Depth 45
Habitat Disaggregation 45
3.2 Velocity 46
3.3 Washout 47
3.4 Stratification and Mixing 48
Modeling Reservoirs and Stratification Options 52
3.5 Temperature 53
3.6 Light 54
Hourly Light 55
3.7 Wind 56
3.8 Multi Segment Model 58
Stratification and the Multi-Segment Model 59
State Variable Movement in the Multi-Segment Model 60
4. BIOTA 62
4.1 Algae 63
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
Light Limitation 67
Adaptive Light 72
Nutrient Limitation 73
Current Limitation 75
Adjustment for Suboptimal Temperature 76
Algal Respiration 77
Photorespiration 78
Algal Mortality 79
Sinking 81
Washout and Sloughing 82
Detrital Accumulation in Periphyton 86
Chlorophyll a 86
Phytoplankton and Zooplankton Residence Time 87
Periphyton-Phytoplankton Link 88
4.2 Macrophytes 89
4.3 Animals 93
Consumption, Defecation, Predation, and Fishing 95
Respiration 99
Excretion 102
Nonpredatory Mortality 103
Suspended Sediment Effects 104
Gamete Loss and Recruitment 120
Washout and Drift 122
Vertical Migration 123
Migration Across Segments 124
Promotion 125
4.4 Aquatic Dependent Vertebrates 126
4.5 Steinhaus Similarity Index 126
4.6 Biological Metrics 127
5. REMINERALIZATION 131
5.1 Detritus 131
Detrital Formation 135
Colonization 136
Decomposition 139
Sedimentation 141
5.2 Nitrogen 144
Assimilation 146
Nitrification and Denitrification 147
lonization of Ammonia 149
Ammonia Toxicity 151
5.3 Phosphorus 152
5.4 Nutrient Mass Balance 154
Variable Stoichiometry 154
Nutrient Loading Variables 154
Nutrient Output Variables 155
Mass Balance of Nutrients 156
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
5.5 Dissolved Oxygen 163
Diel Oxygen 167
Lethal Effects due to Low Oxygen 168
Non-Lethal Effects due to Low Oxygen 174
5.6 Inorganic Carbon 175
5.7 Modeling Dynamic pH 177
5.8 Modeling Calcium Carbonate Precipitation and Effects 180
6. INORGANIC SEDIMENTS 182
6.1 Sand Silt Clay Model 182
Deposition and Scour of Silt and Clay 184
Scour, Deposition and Transport of Sand 187
Suspended Inorganic Sediments in Standing Water 188
6.2 Multi-Layer Sediment Model 189
Suspended Inorganic Sediments 191
Inorganics in the Sediment Bed 191
Detritus in the Sediment Bed 193
Pore Waters in the Sediment Bed 193
Dissolved Organic Matter within Pore Waters 194
Diffusion within Pore Waters 195
Sediment Interactions 196
7. SEDIMENT DIAGENESIS 199
7.1 Sediment Fluxes 201
7.2 POC 204
7.3 PON 206
7.4 POP 206
7.5 Ammonia 206
7.6 Nitrate 208
7.7 Orthophosphate 209
7.8 Methane 210
7.9Sulfide 212
7.10 Bioavailable Silica 213
7.11 Non-Biogenic Silica 214
8. TOXIC ORGANIC CHEMICALS 216
8.1 lonization 223
8.2 Hydrolysis 224
8.3 Photolysis 226
8.4 Microbial Degradation 228
8.5 Volatilization 229
8.6 Partition Coefficients 232
Detritus 232
Algae 235
Macrophytes 236
Invertebrates 237
Fish 237
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
8.7 Nonequilibrium Kinetics 238
Sorption and Desorption to Detritus 239
Bioconcentration in Macrophytes and Algae 240
Macrophytes 240
Algae 241
Bioaccumulation in Animals 244
Gill Sorption 244
Dietary Uptake 246
Elimination 248
Linkages to Detrital Compartments 250
8.8 Alternative Uptake Model: Entering BCFs, Kl, and K2 251
8.9 Half-Life Calculation, DT50 and DT95 252
8.10 Chemical Sorption to Sediments 253
8.11 Chemicals in Pore Waters 255
8.12 Mass Balance Capabilities and Testing 257
8.13 Perfluoroalkylated Surfactants Submodel 259
Sorption 259
Biotransformation and Other Fate Processes 259
Bioaccumulation 259
Gill Uptake 260
Dietary Assimilation 261
Depuration 262
Bioconcentration Factors 263
9. ECOTOXICOLOGY 265
9.1 Lethal Toxicity of Compounds 265
Interspecies Correlation Estimates (ICE) 265
Internal Calculations 267
9.2 Sublethal Toxicity 270
9.3 External Toxicity 273
10. ESTUARINE SUBMODEL 276
10.1 Estuarine Stratification 276
10.2 Tidal Amplitude 277
10.3 Water Balance 278
10.4 Estuarine Exchange 279
10.5 Salinity Effects 280
Mortality and Gamete Loss 280
Other Biotic Processes 280
Sinking 281
Sorption 283
Volatilization 283
Reaeration 283
Migration 284
10.6 Nutrient Inputs to Lower Layer 285
11. REFERENCES 286
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APPENDIX A. GLOSSARY OF TERMS 304
APPENDIX B. USER SUPPLIED PARAMETERS AND DATA 307
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
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. Data
submitted by the States to the U.S. Environmental Protection Agency's WATERS (Watershed
Assessment, Tracking & Environmental Results) database (http://www.epa.gov/waters/)
indicate that a very high percentage of the Nations waters continue to be impaired. As of early
2009, of the waters that have been assessed, 44% of rivers and streams, 59% of lakes, reservoirs
and ponds, and 35% of estuaries were impaired for one or more of their designated uses. The
five most commonly reported causes of impairment in rivers and streams were: pathogens,
sediment, nutrients, habitat alteration and organic enrichment/dissolved oxygen depletion. In
lakes and reservoirs the five most common causes were mercury, nutrients, organic
enrichment/dissolved oxygen depletion, metals, and turbidity. In estuaries the five most
common causes were pathogens, mercury, organic enrichment/oxygen depletion, pesticides and
toxic organics. Many waters are impaired for multiple uses, by multiple causes, from multiple
sources.
New approaches and tools, including appropriate technical guidance documents, are needed to
facilitate ecosystem analyses of watersheds as required by the Clean Water Act. In particular,
there is a pressing need for refinement and release of an ecological risk methodology that
addresses the direct, indirect, and synergistic effects of nutrients, metals, toxic organic
chemicals, and non-chemical stressors on aquatic ecosystems, including streams, rivers, lakes,
and estuaries.
The ecosystem model AQUATOX is one of the few general ecological risk models that
represents the combined environmental fate and effects of toxic chemicals. The model also
represents conventional pollutants, such as nutrients and sediments, and considers several trophic
levels, including attached and planktonic algae, submerged aquatic vegetation, several types of
invertebrates, and several types of fish. It has been implemented for experimental tanks, ponds
and pond enclosures, streams, small rivers, linked river segments, lakes, reservoirs, linked
reservoir segments, and estuaries.
Vlll
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION CHAPTER 1
1. INTRODUCTION
1.1 Overview
The AQUATOX model is a general ecological risk assessment model that represents the
combined environmental fate and effects of conventional pollutants, such as nutrients and
sediments, and toxic chemicals in aquatic ecosystems. It considers several trophic levels,
including attached and planktonic algae and submerged aquatic vegetation, invertebrates, and
forage, bottom-feeding, and game fish; it also represents associated organic toxicants (Figure 1).
It can be implemented as a simple model (indeed, it has been used to simulate an abiotic flask) or
as a truly complex food-web model. Often it is desirable to model a food web rather than a food
chain, for example to examine the possibility of less tolerant organisms being replaced by more
tolerant organisms as environmental perturbations occur. "Food web models provide a means
for validation because they mechanistically describe the bioaccumulation process and ascribe
causality to observed relationships between biota and sediment or water" (Connolly and Glaser
1998). The best way to accurately assess bioaccumulation is to use more complex models, but
only if the data needs of the models can be met and there is sufficient time (Pelka 1998).
It has been implemented for experimental tanks, ponds and pond enclosures, streams, small
rivers, linked river segments, lakes, reservoirs, linked reservoir segments, and estuaries. It 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: sublethal and lethal toxicity to the
various organisms modeled; and indirect effects such as release of grazing and predation
pressure, increase in detritus and recycling of nutrients from killed organisms, dissolved oxygen
sag due to increased decomposition, and loss of food base for animals.
AQUATOX represents the aquatic ecosystem by simulating the changing concentrations (in
mg/L or g/m3) of organisms, nutrients, chemicals, and sediments in a unit volume of water
(Figure 1). As such, it differs from population models, which represent the changes in numbers
of individuals. As O'Neill et al. (1986) stated, ecosystem models and population models are
complementary; one cannot take the place of the other. Population models excel at modeling
individual species at risk and modeling fishing pressure and other age/size-specific aspects; but
recycling of nutrients, the combined fate and effects of toxic chemicals, and other
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 3) TECHNICAL DOCUMENTATION
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Figure 1. Conceptual model of ecosystem represented by AQUATOX
Suspended and
bedded sedim ents
Settling, scour
Plants
Phytoplankton
Attached algae
Macrophytes
Ingestion
Any ecosystem model consists of multiple components requiring input data. These are the
abiotic and biotic state variables or compartments being simulated (Figure 2). In AQUATOX
the biotic state variables may represent trophic levels, guilds, and/or species. The model can
represent a food web with both detrital- and algal-based trophic linkages. Closely related are
driving variables, such as temperature, light, and nutrient loadings, which force the system to
behave in certain ways. In AQUATOX state variables and driving variables are treated similarly
in the code. This provides flexibility because external loadings of state variables, such as
phytoplankton carried into a reach from upstream, may function as driving variables; and driving
variables, such as 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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Figure 2. State variables in AQUATOX as implemented for Cahaba River, Alabama.
Zoobenthos
grazers
mayfly,
riffle beetle
Refractory
Diss. Detritus
Refractory
Sed. Detritus
Bottom Fish
stoneroller
Forage Fish
shiner,
bluegill
Piscivore
bass
Zoobenthos
susp. feeders
caddisfly
'eriphyton diatom,
green
Ammonia
Zoobenthos
molluscs
snail, mussel,
Corbicula
Phytoplankton
diatom,
green
Nitrate & Nitrite
Carbon Dioxide
Predatory
Invertebrate
crayfish,
stonefly
Macrophyte
moss
Oxygen
Labile
Diss. Detritus
Labile
Sed. Detritus
Refractory
Susp. Detritus
Labile
Susp. Detritus
Buried Refrac.
tus Sed. Detritus
Sediments
sand, silt, cli
(orTSS)
The model is written in object-oriented Pascal using the Delphi programming system for
Windows. An object is a unit of computer code that can be duplicated; its characteristics and
methods also can be inherited by higher-level objects. For example, the organism object,
including variables such as the LC50 (lethal concentration of a toxicant) and process functions
such as respiration, is inherited by the plant object; that is enhanced by plant-specific variables
and functions and is duplicated for four kinds of algae; and the plant object is inherited and
modified slightly for macrophytes and moss. This modularity forms the basis for the remarkable
flexibility of the model, including the ability to add and delete given state variables interactively.
AQUATOX utilizes differential equations to represent changing values of state variables,
normally with a reporting time step of one day. These equations require starting values or initial
conditions for the beginning of the simulation. If the first day of a simulation is changed, then
the initial conditions may need to be changed. A simulation can begin with any date and may be
for any length of time from a few days, corresponding to a microcosm experiment, to decades,
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
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
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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 lakes, reservoirs, streams, small rivers, estuaries,
and ponds- and even enclosures and tanks. The generalized parameter screen is used for all these
site types, although some, such as the hypolimnion and estuary 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.
Table 1. Model Overview Summary (also see Section 2.1)
Category:
Reporting Time Step
Differentiation
Output Averaging
Conceptual Approach
Horizontal Spatial
Resolution
Vertical Spatial
Resolution
Sediment Bed
Boundary Conditions
Ecological Complexity
Chemical Complexity
Mass Balance Tracking
Summary:
Daily or Hourly
Variable time-step Runge Kutta
Variable
Kinetic; biomass model
Point model, or ID and 2D with
linked segments
Vertically stratified water
column when relevant
Multiple sediment bed options
Inflows and outflows of all state
variables (dissolved oxygen,
nutrients, biota, detritus, and
toxic organics)
Variable— user can model
representative groups or
individual species
Zero to 20 organic chemicals
For nutrients and chemicals
Notes:
time-step over which equations are solved
smaller step sizes than the reporting time-
step may be utilized to reduce relative error
editable by user
no longer a fugacity option for chemicals;
individual organisms are not modeled
modeled units can be a lake, river, reservoir,
stream segment, estuary, or enclosure
user-specified or model calculated dates of
stratification
active layer only, multi-layer sediments,
sediment diagenesis submodels
water inflow, point sources, nonpoint
sources, direct precipitation, separate
tributary inputs
can model abiotic conditions or single
macrophyte species in a water tank up to
dozens of plant and animal species in a
complex river or reservoir system
biotransformation to daughter products
may be modeled
1.2 Background
AQUATOX Release 3 is the result of an effort to combine all of the various versions of
AQUATOX into a single consolidated version. Models that have been combined to produce this
new version include:
. AQUATOX Multi Segment version
. AQUATOX Estuarine Version
. AQUATOX PFA Model (Perfloroalkylated Surfactants)
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION CHAPTER 1
Each of these versions is discussed in a separate section below.
AQUATOX is the latest in a long series of models, starting with the aquatic ecosystem model
CLEAN (Park et al., 1974) and subsequently improved in consultation with numerous
researchers at various European hydrobiological laboratories, resulting in the CLEANER series
(Park et al., 1975, 1979, 1980; Park, 1978; Scavia and Park, 1976) and LAKETRACE (Collins
and Park, 1989). The MACROPHYTE model, developed for the U.S. Army Corps of Engineers
(Collins et al., 1985), provided additional capability for representing submersed aquatic
vegetation. Another series started with the toxic fate model PEST, developed to complement
CLEANER (Park et al., 1980, 1982), and continued with the TOXTRACE model (Park, 1984)
and the spreadsheet equilibrium fugacity PART model. AQUATOX combined algorithms from
these models with ecotoxicological constructs; and additional code was written as required for a
truly integrative fate and effects model (Park, 1990, 1993). The model was then restructured and
linked to Microsoft Windows interfaces to provide greater flexibility, capacity for additional
compartments, and user friendliness (Park et al., 1995). The current version has been improved
with the addition of constructs for sublethal effects and uncertainty analysis, making it a
powerful tool for probabilistic risk assessment.
This technical documentation is intended to provide verification of individual constructs or
mathematical and programming formulations used within AQUATOX. The scientific basis of
the constructs reflects empirical and theoretical support; and precedence in the open literature
and in widely used models is noted. Units are given to confirm the dimensional analysis. The
mathematical formulations have been programmed and graphed in spreadsheets and the results
have been evaluated in terms of behavior consistent with our understanding of ecosystem
response; many of those graphs are given in the following documentation. The variable names in
the documentation correspond to those used in the program so that the mathematical
formulations and code can be compared, and the computer code has been checked for
consistency with those formulations. Much of this has been done as part of the continuing
process of internal review. Releases 2 and 3 of the AQUATOX model and documentation have
undergone successful peer reviews by external panels convened by the U.S. Environmental
Protection Agency. Release 3 has also been described in the peer-reviewed literature (Park et al.
2008).
1.3 The Multi-Segment Version
The AQUATOX Multi-Segment version was developed and applied for the EPA Office of Water
in support of the Modeling Study of PCB Contamination in the Housatonic River. Capabilities
introduced with this version include the linkage of individual AQUATOX segments into a single
simulation. Segments can be linked together in a manner that allows feedback into the upstream
segment or a one-way "cascade" linkage can be created. More information about the physical
characteristics of linked segments may be found in Section 3.8 of this document.
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION CHAPTER 1
Additionally, a sediment submodel was added to the AQUATOX model to enable tracing the
passage of toxicants within a multi-layered sediment bed. Specifications for this multi-layer
sediment model may be found in section 6.2 of this document.
1.4 The Estuarine Submodel
The Risk Assessment Division (RAD), EPA Office of Pollution Prevention and Toxics, is
responsible for assessing the human health and ecological risks of new and existing chemicals
that are regulated under the Toxic Substances Control Act (TSCA). RAD has partially funded
AQUATOX from its initial conceptualization. Many of the industrial chemicals regulated under
TSCA are discharged into estuarine environments.
Therefore, AQUATOX's capabilities were enhanced by adding salinity and other components
(including shore birds) that would be needed to simulate an estuarine environment. The estuarine
version of AQUATOX is intended to be an exploratory model for evaluating the possible fate
and effects of toxic chemicals and other pollutants in estuarine ecosystems. The model is not
intended to represent detailed, spatially varying site-specific conditions, but rather to be used in
representing the potential behavior of chemicals under average conditions. Therefore, it is best
used as a screening-level model applicable to data-poor evaluations in estuarine ecosystems.
Complete documentation for the AQUATOX estuarine submodel may be found in Chapter 10 of
this document.
1.5 The PFA Submodel
The bioaccumulation and effects of a group of chemicals known as perfluorinated surfactants has
been of recent interest. There are two major types of perfluorinated surfactants: perfluoro-
alkanesulfonates and perfluorocarboxylates. The perfluorinated compounds of interest as
bioaccumulators are the perfluorinated acids (PFAs). Perfluoroctane sulfonate (PFOS) belongs
to the sulfonate group and perfluorooctanoic acid (PFOA) belongs to the carboxylate group.
These persistent chemicals have been found in humans, fish, birds, and marine and terrestrial
mammals throughout the world. PFOS has an especially high bioconcentration factor in fish. The
principal focus was on PFOS because of its prevalence and the availability of data. Because both
chemical classes contain high- and low-chain homologs, AQUATOX will be useful in estimating
the fate and effects of a wide range of molecular weight components where actual data are not
available for every homolog.
Complete documentation for the AQUATOX Perfloroalkylated Surfactants model may be found
in Chapter 7 of this document.
1.6 AQUATOX Release 3 Overview
Additional capabilities are available in Release 3. These capabilities often require considerable
additional data, but they do not have to be used unless the application calls for them. The basic
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION CHAPTER 1
data requirements are no greater than those of Release 2.2 but with the advantage of enhanced
output. In addition to the enhancements derived from other versions and documented above,
Release 3 has significant additional capabilities:
• Link to WEB-ICE (Interspecies Correlation Estimates) database and graphics
Sediment diagenesis based on Di Toro model
Optional hourly time step with diel oxygen, light, and photosynthesis;
• Low oxygen effects
Toxicity due to ammonia
Suspended and bedded sediment effects on organisms; % embeddedness
Calcite precipitation and removal of phosphorus
• Adaptive light limitation for plants
• Linked periphyton and phytoplankton compartments
• Conversions for many units in input screens
• User-specified seasonally varying thermocline depth
• User-entered reaeration constant in addition to alternative estimation procedures
• Editable CBODu and BOD parameters
• Estuarine reaeration incorporating salinity
Sensitivity analysis with tornado diagrams
Correlation of variables in uncertainty analysis
Sediment oxygen demand (SOD) output
• Enhanced graphics including log plot, duration and exceedance graphs, and threshold
analysis
• Option to export all graphs to Microsoft Word
• Output of statistics for all graphed model results
• Output of trophic state indices and ecosystem bioenergetics such as gross primary
productivity and community respiration
• Integrated users manual and context-sensitive help files
Documentation for each of these enhancements may be found in this technical documentation
volume or in the user's manual.
1.7 Comparison with Other Models
The following comparison is taken from Park et al. (2008):
The model is perhaps the most comprehensive aquatic ecosystem simulation model available, as
can be seen by comparison with other representative dynamic models being used for risk
assessment (Table 2). All the models, with the exception of QSim and CASM, are public
7
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION CHAPTER 1
domain. The closest to AQUATOX in terms of scope is the family of CATS models developed
by Traas and others (Traas et al., 1996; Traas et al., 1998; Traas et al., 2001); these
ecotoxicology models have simple representations of growth and are not as suitable as
AQUATOX for detailed analyses of eutrophication effects. CASM (DeAngelis et al., 1989;
Bartell et al., 1999) is similar to CATS, with simplified growth terms, but it lacks a toxicant fate
component. QUAL2K (Chapra et al., 2007) and WASP (Di Toro et al., 1983; Wool et al., 2004)
are water quality models that share many functions with AQUATOX, including benthic algae
(Martin et al., 2006); WASP also models fate of toxicants. The hydraulic and water quality
models EFDC (Tetra Tech Inc., 2002) and HEM3D (Park et al., 1995a) are often combined;
EFDC has also been used to provide the flow field for linked segments in AQUATOX, resulting
in a similar representation. AQUATOX, QUAL2K, WASP, and EFDC include the sediment
diagenesis model for remineralization (Di Toro, 2001). WASP and the bioaccumulation model
QEAFdChn (Quantitative Environmental Analysis, 2001) have been combined in the Green Bay
Mass Balance (GBMB) study (U.S. Environmental Protection Agency, 1989), which Koelmans
et al. (2001) considered to be more accurate for portraying bioaccumulation than AQUATOX.
However, GBMB does not include an ecotoxicology component. BASS (Barber, 2001) is a very
detailed bioaccumulation and ecotoxicology model; it provides better resolution than
AQUATOX in modeling single species, but so far it has only been applied to fish and does not
include ecosystem dynamics. The German model QSim (Schol et al., 1999; Schol et al., 2002;
see also Rode et al., 2007) has detailed ecosystem functions and has been applied in studying
impacts of both eutrophication and hydraulics on river ecosystems. Similar to AQUATOX, it
has been used to analyze relationships between plankton and mussels and impacts of oxygen
depletion. Further comparison of models can be found in a book by Pastorok,at al. (2002).
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
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Table 2. Comparison of AQUATOX with other representative dynamic models used for risk
assessment (Park et al. 2008).
State variables and
processes
Nutrients
sediment diageuesis
Detritus
Dissolved oxygen
'DO effects on biota
PH
MM* toxidtf
Sand'sfitfclaj'
Sediment effects
Hydraulics
Heat budget
Salinity
Phytoplankton
Periphyton
Macrophytes
Zoo-plankton.
Zoobenthcs
Fish
Bacteria
Pathogens
Organic toxicant fate
Organic toxicants in
Sediments
Stratiliett sediments
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1.8 Intended Application of AQUATOX
AQUATOX is intended to be used at any one of several levels of application. Like any model, it
is best used as one of several tools in a weight-of-evidence approach. The level of required
precision, rigor, data requirements and user effort depend upon the goals of the modeling
exercise and the potential consequences of the model results.
Perhaps its most widespread use is as a screening-level model requiring few changes to default
studies and parameters. In fact, it was originally developed as an evaluative model to assess the
fate and effects of pesticides and industrial organic chemicals in representative or "canonical"
environments; these include ponds and pond enclosures, experimental streams, and a
representative estuary. It is especially useful in taking the place of expensive, labor-intensive
mesocosm tests. It has been calibrated and validated with data from pond enclosures,
experimental streams, and a polluted harbor. In one early application, AQUATOX was driven
with predicted pesticide runoff into a farm pond adjacent to a corn field using the field model
PRZM. Also, with little effort the model can provide insights into the potential impacts of
invasive species and the possible effects of control measures, such as pesticide application, on
the aquatic ecosystem.
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION CHAPTER 1
In recent years AQUATOX has been applied as part of the process of developing water quality
targets for nutrients, and comparing model-derived values with regional criteria developed
empirically. This application has involved setting up the model and calibrating with available
data for rivers and reservoirs receiving nutrients from wastewater treatment plants, agricultural
runoff, and background "natural" loadings. It has been our experience that this entails a
substantial level of effort, especially if the system is spatially heterogeneous, which then requires
application of linked segments. A certain amount of site-specific biotic, water quality and flow
data is required, as well as pollutant loading data, for calibration. However, once the model is
set up and calibrated for a site, it is relatively easy to represent a series of loading scenarios and
determine threshold nutrient levels for deleterious impacts such as nuisance algal blooms and
anoxia. This process is facilitated by the fact that the model has been calibrated across nutrient,
turbidity, and discharge gradients, resulting in robust parameter sets that span these conditions.
This is important because the intent of setting water quality targets is to model ecological
communities under changing conditions as a result of environmental management decisions; this
would give better assurance that the sometimes costly nutrient reduction actions would render
the desired environmental result.
The most intensive, time-consuming application of AQUATOX is in environmental remediation
projects, such as SUPERFUND. Because of the likely litigation and the potential for costly
remediation, this level of application requires site-specific calibration and validation using
quality-assured data collected specifically for the model. In dynamic systems, linkage to an
equally well calibrated and validated hydrodynamic model is essential to represent, for example,
burial and exhumation of contaminated sediments. Several of the more powerful features of the
model, such as the linked segments and IPX layered-sediment submodel, were developed for this
type of application. Unfortunately, the one remediation application performed by the model
developers cannot be published because of continuing litigation.
10
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Simulation Modeling: Simplifying
Assumptions
• Each modeled segment is well-
mixed
• Model is run with a daily or hourly
maximum time-step.
• Results are trapezoidally integrated
AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION CHAPTER 2
2. SIMULATION MODELING
2.1 Temporal and Spatial Resolution and Numerical Stability
AQUATOX Release 3 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
was originally designed with the simplest spatial and temporal
resolutions consistent with this objective. Release 3 may still
be run as a non-dimensional point model. However, unlike
previous versions of AQUATOX, in Release 3 spatial
segments may be linked together to form a two- or three-
dimensional model if a more complicated spatial resolution is
desired.
The reporting step, on the other hand, can be as long as several years or as short as one hour;
results are integrated to obtain the desired reporting time period.
The model generally represents average daily conditions for a well-mixed aquatic system. Each
segment in a multi-dimensional run is also assumed to be well-mixed in each time-step.
AQUATOX also represents one-dimensional vertical epilimnetic and hypolimnetic conditions
for those systems that exhibit stratification on a seasonal basis. Multi-segment systems also can
be set up with vertical stratification. Furthermore, the effects of run, riffle, and pool
environments can be represented for streams. Results may be plotted in the AQUATOX output
screen with the capability to import observed data to examine against model predictions.
While the model is generally run with a daily maximum time-step, the temporal resolution of the
model can be reduced to an hourly maximum time-step as well. This capability was added so
that AQUATOX can represent diel oxygen. See sections 3.6 and 5.5 for more information on
how this choice of hourly time-step affects AQUATOX equations.
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.
Usually the reporting time step is one day, but numerical instability is avoided by allowing the
step size of the integration to vary to achieve a predetermined accuracy in the solution. (This is a
numerical approach, and the step size is not directly related to the temporal scale of the
ecosystem simulation.) AQUATOX uses a very efficient fourth- and fifth-order Runge-Kutta
integration routine with adaptive step size to solve the differential equations (Press et al., 1986,
1992). The routine uses the fifth-order solution to determine the error associated with the fourth-
order solution; it decreases the step size (often to 15 minutes or less) when rapid changes occur
and increases the step size when there are slow changes, such as in winter. However, the step
size is constrained to a maximum of one day (or one hour in hourly simulations) so that short-
11
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
CHAPTER 2
term pollutant loadings are always detected. The reporting step, on the other hand, can be a long
as several years or as short as one hour; results are integrated to obtain the desired reporting time
period.
The temporal and spatial resolution is in keeping with the generality and realism of the model
(see Park and Collins, 1982). Careful consideration has been given to the hierarchical nature of
the system. Hierarchy theory tells us that models should have resolutions appropriate to the
objectives; phenomena with temporal and spatial scales that are significantly longer than those of
interest should be treated as constants, and phenomena with much smaller temporal and spatial
scales should be treated as steady-state properties or parameters (Figure 3, O'Neill et al., 1986).
AQUATOX uses a longer time step than dynamic hydrologic models that are concerned with
representing short-term phenomena such as storm hydrographs, and it uses a shorter time step
than fate models that may be concerned only with long-term patterns such as bioaccumulation in
large fish.
Figure 3. Position of ecosystem models such as AQUATOX in the spatial-temporal hierarchy of models.
Rule-based habitat models
succession, urbanization, sea-level rise
Ecosystem models
Population models
High-resolution
process models
flood hydrograph
diurnal pH
Changing the permissible relative error (the difference between the fourth- and fifth-order
solutions) of the simulation can affect the results. The model allows the user to set the relative
error, usually between 0.005 and 0.01. Comparison of output shows that up to a point a smaller
error can yield a marked improvement in the simulation, although execution time is longer. For
example, simulations of two pulsed doses of chlorpyrifos in a pond exhibit a spread in the first
pulse of about 0.6 ug/L dissolved toxicant between the simulation with 0.001 relative error and
the simulation with 0.05 relative error (Figure 4); this is probably due in part to differences in the
timing of the reporting step. However, if we examine the dissolved oxygen levels, which
combine the effects of photosynthesis, decomposition, and reaeration, we find that there are
pronounced differences over the entire simulation period. The simulations with 0.001 and 0.01
relative error give almost exactly the same results, suggesting that the more efficient 0.01 relative
error should be used; the simulation with 0.05 relative error exhibits instability in the oxygen
simulation; and the simulation with 0.1 error gives quite different values for dissolved oxygen
(Figure 5). The observed mean daily maximum dissolved oxygen for that period was 9.2 mg/L
12
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
CHAPTER 2
(U.S. Environmental Protection Agency, 1988), which corresponds most closely with the results
of simulation with 0.001 and 0.01 relative error.
Figure 4. Pond with chlorpyrifos in dissolved
phase.
06/19/88 06/30/88 07/12/88
06/24/88 07/06/88 07/18/88
0.001 • 0.01
0.05 - 0.1
Figure 5. Same as Figure 4 with Dissolved
Oxygen.
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2.2 Results Reporting
The AQUATOX results reporting time step may be set to any desired frequency, from a fraction
of an hour to multiple years. The Runge-Kutta differential equations solver produces a series of
results of variable frequency; this frequency may be either greater than or less than the reporting
time-step. To standardize AQUATOX output, the user has two options, the trapezoidal
integration of results (default) or the output of "instantaneous" concentrations. Using either of
these options, AQUATOX will produce output with time-stamps that match the reporting time-
step precisely.
When instantaneous concentrations are requested (in the model's setup screen) AQUATOX
returns output precisely at the requested reporting time-step through linear interpolation of the
nearest Runge-Kutta results that occur before and after the relevant reporting time-step.
When results are trapezoidally integrated, AQUATOX calculates results by summing all of the
trapezoids that can be produced by linear interpolation between Runge-Kutta results and dividing
by the results-reporting step-size to get an average result over the reporting step. In Figure 6, for
example, the areas of the four shaded trapezoids are summed together and this sum is divided by
the results reporting step to achieve an average result over that reporting step. When trapezoidal
integration is selected, AQUATOX output is time-stamped at the end of the interval over which
the integration is taking place. For example, if a user selects a 366.25 day time-step, the results
at the end of the first year will be reflective of all time-steps calculated within that year.
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
CHAPTER 2
Figure 6. An example of trapezoidal integration.
Runge Kutta
Step Size
(Variable)
Results-
Reporting Step
Results may be plotted in the AQUATOX output screen including the capability to import
observed data to examine against model predictions.
2.3 Input Data
AQUATOX accepts several forms of input data, a partial list of which follows:
• Point-estimate parameters describing animals, plants, chemicals, sites, and
remineralization. Default values for these parameters are generally available from
included databases (called "libraries"). The full list of these parameters, their units, and
their manner of reference in the interface, this document, and the source code may be
found in Appendix B of this document.
• Time series (or constant values) for nutrient-inflow, organic matter-inflow, and gas-
inflow loadings.
• Time series for inorganic sediments in water, water volume variables, and the pH, light,
and temperature climates.
• Time series of chemical inflow loadings and initial conditions.
• A feeding preference matrix must be specified to describe the food web in the simulation.
• Additional parameters may be required depending on which submodels are included (e.g.
additional sediment diagenesis parameters.)
• Nearly all point-estimate parameters may be represented by distributions when the model
is run in uncertainty mode (see section 2.5).
For more discussion of AQUATOX data requirements please see the "Data Requirements"
section in the AQUATOX Users Manual (or in the context sensitive help files included with the
model software).
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
CHAPTER 2
For time-series loadings, when a value is input for every day of a simulation, AQUATOX will
read the relevant value on each day. If missing values are encountered by the model, a linear
interpolation will be performed between the surrounding dates. If the AQUATOX simulation
time includes dates before or after the input time-series the model assumes an annual cycle and
tries to calculate the appropriate input value accordingly. Please see the "Important Note about
Dynamic Loadings" in the AQUATOX Users Manual (integrated help-file) for a complete
description of this process.
2.4 Sensitivity Analysis
"Sensitivity" refers to the variation in output of a
mathematical model with respect to changes in the values of
the model inputs (Saltelli 2001). It provides a ranking of the
model input assumptions with respect to their relative
contribution to model output variability or uncertainty (U.S.
Environmental Protection Agency 1997).
Simplifying Assumptions:
• Parameters are treated as
independent
• Feeding preference matrices are not
included
• Sensitivity is compared for the last
step of the simulation
Caution
• 10% change is appropriate, a large
change can exceed reasonable
values and give misleading results
AQUATOX includes a built-in nominal range sensitivity
analysis (Frey and Patil 2001), which may be used to examine
the sensitivity of multiple model outputs to multiple model
parameters. The user first selects which model parameters to
vary and which output variables to track. The model iteratively steps through each of the
parameters and varies them by a given percent in the positive and negative direction and saves
model results in an Excel file.
A sensitivity statistic may then be calculated such that when a 10% change in the parameter
results in a 10% change in the model result, the sensitivity is calculated as 100%.
Sensitivity =
\Resultpos-ResultBaselm\
ResultNeg-ResultBa^\
100
2 • Result,
'aseline
PctChanged
where:
Sensitivity
ReSUltscenario
PctChanged
normalized sensitivity statistic (%);
averaged AQUATOX result for a given endpoint given a positive
change in the input parameter, a negative change in the input
parameter or no change in the input parameter (baseline)
percent that the input parameter is modified in the positive and
negative directions.
Sensitivity is computed for the last time step of the simulation, so one usually sets the reporting
time step to encompass a year or the entire period of the simulation. For each output variable
tracked, model parameters may be sorted on the average sensitivity (for the positive and negative
tests) and plotted on a bar chart. The end result is referred to as a "Tornado Diagram." Tornado
diagrams may automatically be produced within the AQUATOX output window (Figure 7).
15
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
CHAPTER 2
When interpreting a tornado diagram, the vertical line at the middle of the diagram represents the
deterministic model result. Red lines represent model results when the given parameter is
reduced by the user-input percentage while blue lines represent a positive change in the
parameter.
Figure 7. An example tornado diagram showing calculated sensitivity statistic.
Sensitivity of Chironomid (g/m2 dry) to a 20% change in the 15 most sensitive (tested) parameters
220% - Site: Ave. Epilimnetic Temperature (deg C)
163% - Chironomid: Maximum Temperature (deg. C)
142% - Site: Epi Temp. Range (deg C)
137% - Peri, Green: Max Photosynthetic Rate (1/d)
115% - Temp: Multiply Loading by-
102% - Sphaerid: Maximum Temperature (deg. C)
87.2% - Peri, Green: Optimal Temperature (deg. C)-
74.8% - Chironomid: Respiration Rate: (1 /d)
68.7% - Mayfly (Baetis: Respiration Rate: (1 /d)
66.7% - Water Vol: Initial Condition (cu.m)
54.2% - Shiner: Optimal Temperature (deg. C)
42.1% - Phyt, Blue-Gre: Max Photosynthetic Rate (1/d)
33.8% - Mayfly (Baetis: Max Consumption (g /g day)
27.9% - Largemouth Ba2: Maximum Temperature (deg. C)-
27.2% - Peri High-Nut: Maximum Temperature (deg. C)
2.5 3 3.5 4
Chironomid (g/m2 dry)
4.5
2.5 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-
Uncertainty Analysis: Strengths
• Use of Latin hypercube sampling is
more efficient than brute-force
Monte Carlo analysis
• Nearly all variables and parameters
may be represented as distributions
• Variables can be correlated
Simplifying Assumptions:
• Feeding preference matrices are not
included
• Modeled correlations can not be
perfect (e.g. 1.0) due to limitations
of the Iman & Conover method
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
CHAPTER 2
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 almost 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 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 8). 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 9
exhibits the result of such a loading distribution.
Figure 8. Distribution screen for point-source loading of toxicant in water.
I Distribution Information
Distribution Type:
>~' Triangular
C Uniform
C Normal
Lognormal
Distribution Parameters
Mean
Std. Deviation
Probability r Cumulative Distribution
In an Uncertainty Run:
'• Use Above Distribution
C Use Point Estimate
Choice of distribution: A sequence of increasingly informative distributions should be
considered for most parameters. If only two values are known and nothing more can be
17
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
CHAPTER 2
assumed, the two values may be used as minimum and maximum values for a uniform
distribution (Figure 10); 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 11).
Note that the minimum and maximum values for the distribution are constraints that have zero
probability of occurrence. If additional data are available indicating both a central tendency and
spread of response, such as parameters for well-studied processes, then a normal distribution
may be most appropriate (Figure 12). The result of applying such a distribution in a simulation of
Onondaga Lake, New York, is shown in Figure 13, where simulated benthic feeding affects
decomposition and subsequently the predicted hypolimnetic anoxia. Most distributions are
truncated at zero because negative values would have no meaning (Log Kow is one exception).
Figure 9. Sensitivity of bass (g/m2) to variations in loadings of dieldrin in Coralville Lake, Iowa.
Largemouth Ba2 (g/m2
4/17/2009 2:16:20 PM
1.2
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Minimum
Maximum
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Mean + StDev
Deterministic
10/24/1969 12/23/1969 2/21/1970 4/22/1970 6/21/1970 8/20/1970
Figure 10. Uniform distribution for Henry's Law
constant for esfenvalerate.
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18
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
CHAPTER 2
Figure 12. Normal distribution for maximum consumption rate for
the detritivorous invertebrate Tubifex.
Distribution Information
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
CHAPTER 2
Efficient sampling from the distributions is obtained with the Latin hypercube method (McKay
et al., 1979; Palisade Corporation, 1991). 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 12 can be sampled as shown in
Figure 14. 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. Correlations may be imposed using the method of Iman and Conover
(1982). By varying one parameter at a time the sensitivity of the model to individual parameters
can be determined in a more rigorous way than nominal range sensitivity offers. This is done for
key parameters in the following documentation.
Figure 14. Latin hypercube sampling of a cumulative
distribution with a mean of 25 and standard deviation of 8
divided into 5 intervals.
0.8
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:
StartVal
(1)
where:
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
CHAPTER 2
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 15). Note
that there are ten points in this example, one for each iteration as the consecutive segments of the
distribution are sampled.
Figure 15. Risk to bass from dieldrin in Coralville Reservoir, Iowa.
Biomass Risk Graph
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Uncertainty analysis can also be used to perform statistical sensitivity analysis, which is much
more powerful than the screening-level nominal range sensitivity analysis. Parameters are tested
one at a time using the most appropriate distribution of observed parameter values. The time-
varying and mean coefficient of variation can be calculated in an exported Excel file using the
mean and standard deviation results for a particular endpoint. Examples will be published in a
separate report.
2.6 Calibration and Validation
Rykiel (1996) defines calibration as "the estimation and adjustment of model parameters and
constants to improve the agreement between model output and a data set" while "validation is a
demonstration that a model within its domain of applicability possesses a satisfactory range of
accuracy consistent with the intended application of the model." A related process is
verification, which is "a subjective assessment of the behavior of the model" (I0rgensen 1986).
The terms are used in those ways in our applications of AQUATOX.
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION CHAPTER 2
Endpoints for comparison of model results and data should utilize available data for various
ecosystem components, preferably covering nutrients, dissolved oxygen, and different trophic
levels, and toxic organics if they are being modeled. Although AQUATOX models a complete
food web, often the only biotic data available are chlorophyll a values. The model converts
biomass predictions to chlorophyll a values to facilitate comparison. Likewise, Secchi depth is
computed from the overall extinction coefficient for comparison with observed data.
Verification should consider process rates to confirm that the results were obtained for the
correct reasons (Wlosinski and Collins 1985). Rate information that can be assessed for
reasonableness and compared with observations includes sediment oxygen demand (SOD), the
fluxes of phosphorus, nitrogen, and dissolved oxygen, and all biotic process rates. These can be
presented in tabular and graphical form in AQUATOX.
There are several measures of model performance that can be used for both calibrations and
validations (Bartell et al. 1992, Schnoor 1996). The primary difficulty is in comparing general
model behavior over long periods to observed data from a few points in time with poorly defined
sample variability. Recognizing that evaluation is limited by the quantity and quality of data,
stringent measures of goodness of fit are often inappropriate; therefore, we follow a weight-of-
evidence approach with a sequence of increasingly rigorous tests to evaluate performance and
build confidence in the model results:
• Reasonable behavior as demonstrated by time plots of key variables—is the model
behavior reasonable based on general experience? Are the end conditions similar to the
initial conditions? This is highly subjective, but when observed data are lacking or are
sparse and restricted to short time periods it provides a limited reality check (Figure 16,
Figure 17).
• Visual inspections of data points compared to model plots—do the observations and
predictions exhibit a reasonable concordance of values (Figure 18, Figure 19)? Visual
inspection can also take into consideration if there is concordance given a slight shift in
time.
• Do model curves fall within the error bands of observed data (Figure 20)? Alternatively,
if there are limited replicates, how do the model curves compare with the spread of
observed data?
• Do point observations fall within predicted model bounds obtained through uncertainty
analysis? This has the limitation of being dependent on the precision of the model; the
greater the model uncertainty, the greater the possibility of the data being encompassed
by the error bounds (Figure 21).
• Regression of paired data and model results—does the model produce results that are free
of systematic bias? What is the correlation (R2)? See Figure 22, which corresponds to
the results shown in Figure 18.
Overlap between data and model distributions based on relative bias (rB) in combination
with the ratio of variances (F)—how much overlap is there (Figure 23)? Relative bias is
a robust measure of how well central tendencies of predicted and observed results
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
CHAPTER 2
correspond; a value of 0 indicates that the means are the same (Bartell et al. 1992). The F
test is the ratio of the variance of the model and the variance of the data. A value of 1
indicates that the variances are the same.
Do the observed and predicted values differ significantly based on their cumulative
distributions (Figure 24)? The Kolmogorov-Smirnov statistic, a non-parametric test, can
be used; however, the two datasets should represent the same time periods (for example,
one should not compare predicted values over a year with observed values taken only
during spring and summer).
Figure 16. Predicted biomass patterns for animals in a hypothetical farm pond in Missouri.
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^ 0.48
en
E 0.40
0.32
0.24
0.16
0.08
FARM POND, ESFENVAL (CONTROL)
Run on 01-25-09 10:48 AM
11.7
10.4
9.1
7.8
6.5
5.2
3.9
2.6
1.3
.0
5/16/1994
8/14/1994
11/12/1994 2/10/1995
- Daphnia(mg/Ldry)
- Mayfly (Baetis (g/m2 dry)
• Gastropod (g/m2 dry)
-Shiner (g/m2dry)
• Largemouth Bas (g/m2 dry)
- Largemouth Ba2 (g/m2 dry)
23
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
CHAPTER 2
Figure 17. Sediment oxygen demand predicted for Lake Onondaga, using Di Toro sediment diagenesis
option; this is an example of using rates for a reality check.
2.7
2.4
2.1
1.8
1.5
81.2
01
0.9
0.6
0.3
0.0
ONONDAGA LAKE, NY (CONTROL) Run on 06-20-08 2:47 PM
(Hypolimnion Segment)
| — SOD(gO2/m2d)|
1/12/1989 5/12/1989
9/9/1989
1/7/1990
5/7/1990
9/4/1990
1/2/1991
24
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
CHAPTER 2
Figure 18. Comparison of predicted and observed (Oliver and Niemi 1988) PCB congener
bioaccumulation factors in Lake Ontario lake trout.
11
10-
9 -
en
o 7H
6
5 H
4
Lake Trout
Pred/Obs = 0.97 +/- 1.03
6 7
Log KOW
8
Observed
Predicted
9
Figure 19. Predicted biomass and observed numbers of chironomid larvae in a
Duluth, Minnesota, pond dosed with 6 ug/L chlorpyrifos.
0.36
0 28
T3
CM 0 20
^016
0 12
0 08
0 04
0 00
CHLORPYRIFOS 6 ug/L (PERTURBED)
Run on 01-25-09 3'09 PM
I
I
f
I
1
6/27/1986 7/27/1986 8/26/1986
f*hirnnnmiri fn/m9 ririrt
• Obs. Chironomids (no./sample)
900
700
-500
200
25
-------
AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
CHAPTER 2
Figure 20. Predicted and observed benthic chlorophyll a in Cahaba River, Alabama;
bars indicate one standard deviation in observed data.
200
20
0
1/1/01
7/20/01
2/5/02
8/24/02
Figure 21. Visual comparison of the envelope of model uncertainty, using two standard deviations for
each of the nutrient loading distributions, with the observed data for chlorophyll a in Lake Onondaga,
NY.
120
100
-Min Chloroph (ug/L)
Mean Chloroph (ug/L)
-Max Chloroph (ug/L)
Det Chloroph (ug/L)
-ObsChl
co o) o i— (NT— CN co
? s
26
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
CHAPTER 2
Figure 22. Regression shows that the correlation between predicted and observed (Oliver and Niemi
1988) PCB congener bioaccumulation factors in Lake Ontario trout may be very good, but the slope
indicates that there is systematic bias in the relationship. See Figure 18 for another presentation of these
same results.
10
o»
o
9 -
8 H
I 7H
CL
LAKE ONTARIO TROUT
R2=0.915
7 8
Obs Log BAF
10
27
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
CHAPTER 2
Figure 23. Relative bias and F test to compare means and variances of observed data and predicted
results with AQUATOX. The isopleths correspond to the probability that the distributions of predicted
and observed, as defined by the combination of the rB and F statistics, are similar. The isopleths assume
normal distributions. This was used in validation of nonylphenol simulations in pond enclosures
(Park and Clough 2005).
Statistical Comparison of Means and Variances
_t_(Pred-Obs
Ta
j-, iJ pred
r --
obs
rB = 0.242, F = 0.400
predicted and observed
distributionsarc similar
28
-------
AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
CHAPTER 2
Figure 24. Comparison of predicted and observed chlorophyll a in Lake Onondaga, New York (U.S.
Environmental Protection Agency 2000). The Kolmogorov-Smirnov p statistic = 0.319, indicating that the
distributions are not significantly different.
I
o
100
90 \
80 i
70 i
60 i
50 ^
40 ^
30 ^
20 J
10
0 ^
0
20 40 60 80 100
Chlorophyll a (ug/L)
120
Observed
Predicted
Data are often too sparse for adequate calibration at a given site. However, AQUATOX can be
calibrated simultaneously across sites using an expanded state variable list representative of a
range of conditions and using the same parameter set. In this way the observed biotic data can be
pooled and the resulting state variable and parameter sets, being applicable to diverse sites, are
assured to be robust. This is an approach that we have used on the Cahaba River, Alabama (Park
et al. 2002); on three dissimilar rivers in Minnesota (Park et al. 2005); and on 13 diverse reaches
on the Lower Boise River Idaho (CH2M HILL et al. 2008). The Minnesota rivers application is
discussed below.
Time series of driving variables for the Minnesota rivers were obtained from several sources
with varying degrees of resolution and reliability. Results of watershed simulations with HSPF
(Hydrologic Simulation Program- Fortran, a watershed loading model) were linked to
AQUATOX, providing boundary conditions (site constants and drivers) for the Blue Earth and
Crow Wing Rivers (Donigian et al. 2005). HSPF was not run for the Rum River; however, a
U.S. Geological Survey (USGS) gage is located at the sample site and both daily discharge and
sporadic water quality data were available from the USGS Web pages (search on "National
Water Information System"). AQUATOX interpolates between points, and this feature was used
to compute daily time series of nutrient concentrations from USGS National Water Information
System (NWIS) observed data. Total suspended solids (TSS) are critical because the daily light
climate for algae is affected. Therefore, we derived a significant relationship by regressing TSS
against In-scaled discharge and used that to generate a daily time series for the Rum River (
Figure 25).
29
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
CHAPTER 2
Figure 25. TSS at Rum River: a) In-linear regression against daily flow at gage; b) resulting simulated
daily time series (line), and observed values (symbols).
a)
25
I
10
b) 140
120 -
100 -
60 H
*
400000 800DOO 1200000
Daily Mean Flow (m3/cT)
1600000
20DOOOO
01/99 05/99 03/99 12/99 04/00 08/00 12/00
After calibration we evaluated the efficacy of generating daily time series for TN using a
regression of TN on discharge. The relationship is statistically significant and yielded a more
30
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
CHAPTER 2
realistic time series than the interpolation with sparse data that we had used (Figure 26).
However, calculation of the different limitations on photosynthesis indicates that N is not
limiting in the Rum River (Figure 27), so we kept the simpler approach and did not repeat the
calibration (see section 4.1 for an explanation of the reduction factor as an expression of nutrient
limitation) . TP did not exhibit a statistically significant trend with discharge (R2 = 0.124) so the
simple interpolation was also kept.
Figure 26. TN at Rum River site: a) In-linear regression against daily flow at gage; b) interpolated TN
observations (red) and time series (black) estimated from discharge regression.
a)
1.8
1.6
1.4
i"
£ i
| 0.8
£ 0.5
0.4
0,2
0
c
. *
*
^-^^
4**^*~* *
^ * R2 = 0.6861
500000 1000000 1500000 2000000
Discharge (mi/d)
b)
i.50
-EstTN
•ObsTN
0.00
31
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
CHAPTER 2
Figure 27. Predicted nutrient limitations for the dominant algal group in the Rum River.
Note that N is not limiting.
0.9
0.8
0.7
0.6
0.5
£0.5
0.4
0.3
0.2
0.1
Rum R. 18 MN (CONTROL)
Run on 01-27-09 7:35 AM
- Peri High-Nut N_LIM (frac)
- Peri High-Nut PO4_LIM (frac)
- Peri High-Nut CO2_LIM (frac)
3/21/1999 7/19/1999 11/16/1999 3/15/2000 7/13/2000 11/10/2000
In almost all cases parameter values were chosen from ranges reported in the literature (for
example, Le Cren and Lowe-McConnell 1980, Collins and Wlosinski 1983, Home and Goldman
1994, Jorgensen et al. 2000, Wetzel 2001). However, because these often are broad ranges and
the model is very sensitive to some parameters, iterative calibration was necessary for a subset of
parameters in AQUATOX. Conversely, some parameters have well established values and
default values were used with confidence. A few parameters such as extinction coefficients and
critical force for sloughing of periphyton are poorly defined or are unique to the AQUATOX
formulations and were treated as "free" parameters subject to broad calibration. For example,
some periphyton species are able to migrate vertically through the periphyton mat, and others
have open growth forms; therefore, they could be assigned extinction coefficient values without
regard to the physics of light transmission through biomass fixed in space. As noted earlier,
sensitivity analysis can help determine how much attention needs to be paid to individual
parameters. Sensitivity analysis of five diverse studies has shown that the model is sensitive to
optimal temperature (TOpf) for algae and fish, maximum photosynthesis (PMax) for algae, %
lost in periphytic sloughing, and log octanol-water partition coefficient (KOW). It is advisable to
perform sensitivity analysis when the initial calibration is complete in order to identify
parameters and driving variables requiring additional attention. Although not used in this
application, if modeling a toxic chemical, there are several published sources (for example,
Lyman et al. 1982, Verscheuren 1983, Schwarzenbach et al. 1993), and there are a couple
excellent online references, including the US EPA ECOTOX site and the USDA ARS Pesticide
Properties Database, which can be found with an Internet search engine.
Calibration of AQUATOX for the Minnesota rivers used observed chlorophyll a as the primary
target for obtaining best fits. Because there were only five to eight sestonic chlorophyll a
32
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION CHAPTER 2
observations in each of the two target years and only one benthic chlorophyll a observation at
each location, calibration adequacy was evaluated subjectively, based on generally expected
behavior (e.g. blooms occurring during summer) and approximate concordance with observed
values (in terms of both magnitude and timing), as determined through graphical comparisons of
model output and data (Figure 28).
The central tendencies are similar for predicted and observed distributions for all three sites, as
shown by the relative bias (Figure 29). Despite the fluctuations in predicted chlorophyll a, the
predicted and observed variances are similar for the Crow Wing River and Rum River
simulations. Predicted periphyton sloughing events played a major role in determining the
timing of chlorophyll a peaks in both simulations. The variance in predicted values is too high in
the Blue Earth River simulation, where summer peak concentrations in 1999 appear to be
overestimated by a factor of about two. The reason for this is not known, but may be related to
inherent uncertainties in the simulated flow and TSS values, the sparseness of water chemistry
sampling data, and/or limitations of model algorithms. Given the wide range in degree of
enrichment among these three rivers, and the fact that the model was calibrated against all three
data sets using a single set of parameters, a two-fold error during one period of the Blue Earth
River simulation seems to be acceptable. The combined probability that the Blue Earth River
predictions and observations have the same distribution, based on both central tendency and
dispersion, is greater than 0.8. For the purpose of this analysis, we judged the calibration to be
adequate for the three rivers.
33
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
CHAPTER 2
Figure 28. Observed (symbols) and calibrated AQUATOX simulations (lines) of chlorophyll a in three
Minnesota rivers: a) Blue Earth at mile 54, b) Rum at mile 18, c) Crow Wing at mile 72. Note the order-
of-magnitude range in scale among the Figures.
400
350 -
300 -
250 -
b)
70 T
c)
30
-C
U
25 -
_20 -
r
?15 -
'no -
5 -
01/99 05/99 08/99 12/99 04/00 08/00 12/00
01/99 05/99 08/99 12/99 04/00 08/00 12/00
01/99 05/99 08/99 12/99 04/00 08/00 12/00
34
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
CHAPTER 2
Figure 29. Overlap between model and data distributions based on relative bias and ratio of variances, F;
1 = Blue Earth River, 2 = Crow Wing River, 3 = Rum River. Isopleths indicate the probability that the
predicted and observed distributions are the same, assuming normality.
-4
-202
Relative Bias
The calibrated algal model was also applied to three dissimilar sites on the Lower Boise River,
Idaho, without modification from the Minnesota calibration. This provided additional
verification of the generality of the parameter set. The three sites cover a broad range of nutrient
and turbidity conditions over 90 km. Eckert is a low-nutrient, clear-water site upstream of Boise;
Middleton receives wastewater treatment effluent and is a nutrient-enriched, clear-water site; and
Parma is a nutrient-enriched, turbid site impacted by irrigation return flow from agricultural
areas. Although the model overestimated periphyton at the Eckert site, the fit of the initial
application (Figure 30) provided an excellent basis for further river-specific calibration.
35
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
CHAPTER 2
Figure 30. Predicted (line) and observed (symbols) benthic chlorophyll a (a) at Eckert Road, (b) near
Middleton, (c) near Parma, Lower Boise River, Idaho, using Minnesota parameter set.
a)
c)
35796
1/1/S8
1/1/98
36296
36796
5/16/99
9/27/00
5/16/99
9/27/00
36
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
CHAPTER 2
As a limited validation, the calibrated model was applied to a site on the Cahaba River south of
Birmingham, Alabama, with modifications to only two parameters, critical force for periphyton
scouring and optimal temperature for algae. The Crow Wing and Rum Rivers have cobbles and
boulders and are more sensitive to higher current velocities than the bedrock outcrops in the
Cahaba River. Not only is the bedrock stable, it also provides abundant crevices and lee sides
that are protected refuges for periphyton. For these reasons greater water velocity is expected to
be required to initiate periphyton scour in the Cahaba River than in the Crow Wing and Rum
Rivers, thus the critical force (Fcrit) for scour of periphyton was more than doubled in the
Cahaba River simulation. Also, between Minnesota and Alabama one would expect different
local ecotypes in resident algal species, with differing adaptations to temperature. Based on
professional judgment, the optimum temperature values (Topt) for green algae and cyanobacteria
were therefore increased by 5°C to 31°C and 32°C respectively. The resulting fit to observed
data (Figure 20) was good. Furthermore, the fish and zoobenthos fits were acceptable (Figure 31,
see also Figure 68). Note that the bluegill are predicted to exhibit ammonia toxicity in 2001, an
observation made possible by viewing biotic process rates. (Within rates graphs, animal
mortality rates may be broken down into their various constituents, see (112)).
Figure 31. Predicted and observed fish in Cahaba River, Alabama; predicted shiner mean biomass = 0.6
g/m2 compared to observed 0.5 g/m2.
Cahaba River AL (CONTROL)
Run on 01-26-09 12:07 PM
1.4
1.3
1.2
1.1
1.0
0.9
-a 0-8
| 0.7
""0.6
0.5
0.4
0.3
0.2
0.1
0.0
-Shiner (g/m2 dry)
- Bluegill (g/m2 dry)
- Stoneroller (g/m2 dry)
- Smallmouth Bas (g/m2 dry)
Smallmouth Ba2 (g/m2 dry)
Obs stonerollers (g/m2 dry)
Obs shiners (g/m2dry)
Obs bluegill (g/m2 dry)
Obs bass (g/m2 dry)
8/26/2000 2/24/2001 8/25/2001 2/23/2002 8/24/2002
In another validation, published PCB data from New Bedford Harbor, Massachusetts, were used
to verify the generality of the estuarine ecosystem bioaccumulation model. The observed
concentrations of total PCBs in the water and bottom sediments in the Massachusetts site were
set as constant values in a simulation of Galveston Bay, Texas. The predicted PCB
concentrations in the various biotic compartments at the end of the simulation were then
compared to the observed means and standard deviations in New Bedford Harbor (Figure 32).
Considering that the sites and some of the species were different, the concordance in values
provides a validation of the model for assessing bioaccumulation of chemicals in a "canonical"
or representative estuarine environment.
37
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
CHAPTER 2
Figure 32. Predicted and observed concentrations of PCBs in selected animals based on ecosystem
calibration for Galveston Bay, Texas and exposure data (Connolly 1991) for New Bedford Harbor,
Massachusetts.
10
i
c
.3
o.i
u
0.
>•
T3
o
Si
i
o
o.oi
J>
f r jf
A third example of a validation is shown in Figure 19, which provides a visual comparison of
predicted biomass and observed numbers per sample of chironomid larvae with dosing by an
insecticide. No calibration was performed for either the fate or toxicity of the chemical.
38
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AQUATOX (RELEASE 3) 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:
Morphometry: Simplifying
Assumptions
• Evaporation does not vary
seasonally
• Base flow equation assumes a
rectangular channel
• Site shapes are represented by
idealized geometrical
approximations
• Mean Depth may be held constant
or user varying depth may be
imported
dVolume
dt
= Inflow - Discharge - Evap
(2)
where:
dVolume/dt
Inflow
Discharge
Evap
derivative for volume of water (m3/d),
inflow of water into waterbody (m3/d),
discharge of water from waterbody (m3/d), and
evaporation (m3/d), see (3).
AQUATOX cannot successfully run if the volume of water in a site falls to zero. To avoid this
condition, if the site's water volume falls below a minimum value (which is defined as a fraction
of the initial condition using the parameter "Minimum Volume Frac." from the site screen), all
differentiation of state variables is suspended (except for the water volume derivative) until the
water volume again moves above the minimum value. Differentiation of all state variables then
resumes.
Evaporation is converted from an annual value for the site to a daily value using the simple
relationship:
„ MeanEvap „„.,. .
Evap = — • 0.0254 • Area
365
(3)
where:
MeanEvap
365
0.0254
Area
mean annual evaporation (in/yr),
days per year (d/yr),
conversion from inches to meters (m/in), and
area of the waterbody (m2).
The user is given several options for computing volume including keeping the volume constant;
making the volume a dynamic function of inflow, discharge, and evaporation; using a time series
39
-------
AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
CHAPTER 3
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 3.
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 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 3. Computation of Volume, Inflow, and Discharge
Method
Constant
Dynamic
Known values
Manning
Inflow
InflowLoad
InflowLoad
InflowLoad
ManningVol - State/dt + Discharge + Evap
Discharge
InflowLoad - Evap
DischargeLoad
InflowLoad - Evap + (State -
Known Vals)/dt
DischargeLoad
The variables are defined as:
InflowLoad
DischargeLoad
State
KnownVals
dt
ManningVol
user-supplied inflow loading (m /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 (4).
Figure 33 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.
40
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
CHAPTER 3
Figure 33. Volume, inflow, and discharge for a 4-year period
in Coralville Reservoir, Iowa.
6.0E+07
O.OE+00
2.5E+08
=3
o
5.0E+07
Oct-74 Oct-75 Nov-76 Dec-77
Apr-75 May-76 Jun-77 Jul-78
O.OE+00
— Inflow
Discharge — Volume
The time-varying volume of water in a stream channel is computed as:
where:
7
CLength
Width
ManningVol = Y • CLength • Width
dynamic mean depth (m), see (5);
length of reach (m); and
width of channel (m).
(4)
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, 1973), which is
rearranged to yield:
Y = \
y/j
Q • Manning
(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 choose among the following stream types:
41
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION CHAPTER 3
. 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). The
user may also enter a value for the coefficient.
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:
IDepth5/3 • 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 mVd to m3/s:
86400
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 P
(Junge, 1966) characterizes the site, with a shape that is indicated by the ratio of mean to
maximum depth.:
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 and P = 0.6. Reservoirs and rivers generally are extreme elliptic sinusoids with values ofP
42
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION CHAPTER 3
constrained to -1.0. Lakes may be either elliptic sinusoids, with P between 0.0 and -1.0, or
elliptic hyperboloids with P between 0.0 and 1.0. Not all water bodies fit the elliptic shapes, but
the model generally is not sensitive to the deviations.
Based on these relationships, fractions of volumes and areas can be determined for any given
depth (Junge, 1966). 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 34). AreaFrac
calculates the fraction that is the donut (not the donut hole). To get the donut hole, 1 - AreaFrac
is used.
AreaFrac = (1-P) —— + P • (—^— / (9)
ZMax ZMax
VolFrac = ZMax ZMax ZMax
3.0 + P
where:
AreaFrac = fraction of area of site above given depth (unitless);
VolFrac = fraction of volume of site above given depth (unitless); and
Z = depth of interest (m).
For example, the fraction of the volume that is epilimnion can be computed by setting depth Z to
the mixing depth. Furthermore, by setting Z to the depth of the euphotic zone, where primary
production exceeds respiration, the fraction of the area available for colonization by macrophytes
and periphyton can be computed:
„ T , ZEuphotic „ (ZEuphotic\ , „
FracLit = (l-P) + P-\ (11)
ZMax \ ZMax )
A relatively deep, flat-bottomed basin would have a small littoral area and a large sublittoral area
(Figure 34).
Figure 34.
43
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
CHAPTER 3
If the site is an artificial enclosure then the available area is increased accordingly:
„ ,. , „ ,. Area + EnclWallArea
FracLittoral = FracLit
Area
otherwise
(12)
where:
FracLittoral = FracLit
FracLittoral = fraction of site area that is within the euphotic zone (unitless);
ZEuphotic = depth of the euphotic zone, is assumed to be 1% of surface light
and calculated as 4.605/Extinct (m) see (40);
Area
= site area (m ); and
EnclWallArea = area of experimental enclosure's walls (m2).
Figure 35. Area as a function of depth Figure 36. Volume as a function of depth
RESERVOIR (P = -0.6)
1357
246
) 11 13 15 17 19 21 23 25
10 12 14 16 18 20 22 24
DEPTH(m)
RESERVOIR (P = -0.6)
1357
246
) 11 13 15 17 19 21 23 25
10 12 14 16 18 20 22 24
DEPTH(m)
If a user wishes to model a simpler system, the bathymetric approximations may be bypassed in
favor of a more rudimentary set of assumptions via an option in the site parameter screen.
When the user chooses not to "use bathymetry"
• the system is assumed to have vertical walls;
• the system is assumed to have a constant area as a function of depth;
• the system's depth may be calculated at any time as water volume divided by surface
area.
This option may be useful when linking data from other models to AQUATOX as the horizontal
spatial domain of AQUATOX remains unchanged over time. However, a system will not
undergo dynamic stratification based on water temperature unless the more complex bathymetric
approximations are utilized ((8) to (11)).
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION CHAPTER 3
Dynamic Mean Depth
AQUATOX normally uses an assumption of unchanging mean depth (i.e., mean over the site
area). However, under some circumstances, and especially in the case of streams and reservoirs,
the depth of the system can change considerably over time, which could result in a significantly
different light climate for algae. For this reason, an option to import mean depth in meters has
been added. A daily time-series of mean depth values may be imported into the software (using
an interface found within the site screen by pressing the "Show Mean Depth Panel" button.) A
time-series of mean depth values can be estimated given known water volumes or can be
imported from a linked water hydrology model.
The user-input dynamic mean depth affects the following portions of AQUATOX:
. Light climate, see (43);
Calculation of biotic volumes for sloughing calculations, see (74);
Calculation of vertical dispersion for stratification calculations, Thick in equation (18);
. Calculation of sedimentation for plants & detritus, Thick in (165);
. Oxygen reaeration, see (190);
. Toxicant photolysis and volatilization, Thick in (320) and (331).
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 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.
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
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where:
HabitatLimitspedes
Preference habitat
Percenthabitat
Percent
habitat
cehabjlat>0
100
(13)
fraction of site available to organism (unitless), used to limit
ingestion, see (91), and photosynthesis, see (35), (85);
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/m 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, which is generally collected in a specific habitat type,
cannot be used as input to AQUATOX until these values have been converted to represent the
entire surface area. This is especially true in modeling habitats; for example, an animal could
have a high density within riffles, but riffles might only constitute a small portion of the entire
system.
3.2 Velocity
If the user has site-specific velocity data, this may be entered on the "site data" screen in units of
cm/s. Otherwise, velocity is calculated as a simple function of flow and cross-sectional area:
Velocity =
AvgFlow
XSecArea 86400
-•100
(14)
where
Velocity
AvgFlow
XSecArea
86400
100
velocity (cm/s),
average flow over the reach (m3/d),
cross sectional area (m2),
s/d, and
cm/m.
AvgFlow =
Inflow + Discharge
2
(15)
where:
Inflow
Discharge
flow into the reach (m3/d);
flow out of the reach (mVd).
It is assumed that this is the velocity for the run of the stream (user entered velocities are also
assumed to pertain to the run of the screen). 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
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
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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 4).
Table 4. Factors relating velocities to those of the average reach.
Flows (Q = discharge)
Q < 2.59e5 m3/d
2.59e5 m3/d < Q < 5.18e5 m3/d
5.18e5 m3/d < Q < 7.77e5 m3/d
Q > 7.77e5 m3/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
Figure 37. Predicted velocities in an Ohio stream according to habitat.
400
350
LO
CD
00
CTJ
• Run
•Riffle
• Pool
3.3 Washout
Transport out of the system, or washout, is an important loss term for nutrients, floating
organisms, and dissolved toxicants in reservoirs and streams. Although it is considered
separately for several state variables, the process is a general function of discharge:
where:
Washout
State
TTr , Discharge _,
Washout = — • State
Volume
loss due to being carried downstream (g/m3 -d), and
concentration of dissolved or floating state variable (g/m3).
(16)
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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 38); the metalimnion
zone that separates these is ignored. Instead, the
thermocline, or plane of maximum temperature change, is
taken as the separator; this is also known as the mixing
depth (Hanna, 1990). Dividing the lake into two vertical
zones follows the treatment of Imboden (1973), Park et al.
(1974), and Straskraba and Gnauck (1983). The onset of
stratification is considered to occur when the mean water
temperature exceeds 4 deg. and the difference in
temperature between the epilimnion and hypolimnion
exceeds 3 deg.. Overturn occurs when the temperature of the epilimnion is less than 3 deg.,
usually in the fall. Winter stratification is not modeled, unless manually input. For simplicity,
the thermocline is generally assumed to occur at a constant depth. Alternatively, a user-specified
time-varying thermocline depth may be specified, see the section on modeling reservoirs below.
Figure 38. Thermal stratification in a lake; terms defined in text
Stratification: Simplifying
Assumptions
• Two vertical zones modeled;
metalimnion is ignored
• Flowing waters are assumed not to
stratify
• Stratification occurs when vertical
temperature difference exceeds
three degrees
• Winter stratification is not modeled
• Thermocline occurs at constant
depth except when user enters time
series
• Wind action is implicit in vertical
dispersion calculations
Epilimnion
1-1 Thermocline —
Thick
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 Figure 39, and it is computed as (Hanna, 1990):
\og(MaxZMix) = 0.336 • \og(Length) - 0.245
(17)
where:
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
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MaxZMix
Length
maximum mixing depth under stratified conditions (thermocline
depth) for lake (m); and
maximum effective length for wave setup (m, converted from user-
supplied km).
Figure 39. Mixing depth as a function of fetch
MAXIMUM MIXING DEPTH
OK
20-
eis-
i
D.
£10-
5-
g
,.,,--•'"
/
100 11500 22900 34300
5800 17200 28600 40000
LENGTH (m)
Wind action is implicit in this formulation. Wind has been modeled explicitly by Baca and
Arnett (1976, quoted by Bowie et al., 1985), but their approach requires calibration to individual
sites, and it is not used here.
Vertical dispersion for bulk mixing is modeled as a function of the time-varying hypolimnetic
and epilimnetic temperatures, following the treatment of Thomann and Mueller (1987, p. 203;
see also Chapra and Reckhow, 1983, p. 152; Figure 40):
VertDispersion = Thick
\ HypVolume
rpt-l rr,t+l
-/ hypo ~ -/ hypo
ThermoclArea • Deltat Tepi -
(18)
Typo
where:
VertDispersion =
Thick =
vertical dispersion coefficient (m2/d);
distance between the centroid of the epilimnion and the centroid of
the hypolimnion, effectively the mean depth (m);
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
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HypVolume =
ThermoclArea =
Deltat
rp t-l rp t+l _
-* hypo ' -* hypo
rr> t rj-l t
•* epi j i hypo
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 (deg. C); and
temperature of epilimnion and hypolimnion at present time
(deg.C).
Stratification can break down temporarily as a result of high throughflow. This is represented in
the model by making the vertical dispersion coefficient between the layers a function of
discharge for sites with retention times of less than or equal to 180 days (Figure 41), rather than
temperature differences as in equation 11, based on observations by Straskraba (1973) for a
Czech reservoir:
VertDispersion = 1.37 • JO4 • Retention
-2.26V
(19)
and:
Retention =
Volume
TotDischarge
(20)
where:
Retention =
Volume =
TotDischarge =
retention time (d);
volume of site (m3); and
total discharge (m3/d).
Figure 40. Vertical dispersion as a function of temperature differences
100
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
CHAPTER 3
Figure 41. Vertical dispersion as a function of retention time
100
O
CO
tr
LU
o_
CO
Q
cr
LU
10
0.1-
VERTICAL DISPERSION
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):
where:
^ 7,, f ^ /./• VertDispersion • ThermoclArea
BulkMixCoeff =
«/«/ rr-rl • /
Thick
BulkMixCoeff = bulk vertical mixing coefficient (m3/d),
ThermoclArea = area of thermocline (m2).
(21)
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:
T hPi'ff _ BulkMixCoeff
L UtOLJlJJ . ' ( (^ OTIC compartment hypo ~ ^ OtlC compartment, epi /
Volume epi
_ BulkMixCoeff
1 UrOLJlJJ ^g • ( L, OnC compartment, epi ~ C OnC compartment, hypo/
Volumehypo
(22)
(23)
where:
TurbDiff
Volume
Cone
turbulent diffusion for a given zone (g/m3-d);
volume of given segment (m3); and
concentration of given compartment in given zone (g/m3).
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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 42).
Figure 42. Stratification and mixing in Lake Nockamixon,
Pennsylvania as shown by hypolimnetic dissolved oxygen
14
10
8
6
Q>
"5
b
2
onset of
stratification
overturn
high
throughflow
0
01/01 /82 03/07/82 05/11182 07/15/82 09/18/82 11 /22/S2
Modeling Reservoirs and Stratification Options
Stratification assumptions and equations based on lake characteristics may not be appropriate for
modeling reservoirs. Moreover, a lake may have a unique morphometry or chemical
composition that renders inappropriate the equations presented above. For this reason, a
"stratification options" screen is available (through the site screen or water-volume screen) that
allows a user to specify the following characteristics of a stratified system:
• a constant or time-varying thermocline depth;
• options as to how to route inflow and outflow water; and
• the timing of stratification.
Water volumes for each segment are calculated as a function of the overall system volume and
the thermocline depth (see (10)). Because of this, if a time-varying thermocline depth is
specified, water from one segment must usually be transferred into the other segment, along with
the state variables within that water. In this manner, specifying a time-varying thermocline depth
has the potential to promote mixing between layers. Alternatively, using the linked-mode model,
two stratified segments may be specified with water volumes that are calculated independently
from the thermocline depth; see section 3.8 for more details about stratification in linked-mode.
By default, AQUATOX routes inflow and outflow to and from both segments as weighted by
volume. For example, if the hypolimnion has twice as much volume as the epilimnion, twice as
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION CHAPTER 3
much inflow water will be routed to the hypolimnion as to the epilimnion (and twice as much
outflow water will be routed from the hypolimnion). The user has the option to route all inflow
and outflow waters to and from either segment. In this case, all of the nutrients, chemicals, and
other loadings within the inflow water will be routed directly to the specified segment and will
not be transferred to the other segment except through turbulent diffusion or overturn.
Atmospheric and point-source loadings are assumed to be routed to the epilimnion in all cases
(unless a linked-mode model is used in which case more flexibility is present).
Additionally, if a user has information about the timing of stratification, this may be specified on
the stratification-options entry screen. This can be used to specify winter stratification, for
example, or precise periods of stratification for each year modeled. If only one year of
stratification dates are entered and multiple years are modeled, all years are assumed to stratify
and overturn on the dates specified in the user input (regardless of the year specified).
3.5 Temperature
Temperature is an important controlling factor in the model. Virtually all processes are
temperature-dependent. They include stratification; biotic processes such as decomposition,
photosynthesis, consumption, respiration, reproduction, and mortality; and chemical fate
processes such as microbial degradation, volatilization, hydrolysis, and bioaccumulation. On the
other hand, temperature rarely fluctuates rapidly in aquatic systems. Default water temperature
loadings for the epilimnion and hypolimnion are represented through a simple sine
approximation for seasonal variations (Ward, 1963) based on user-supplied observed means and
ranges (Figure 43):
r + r ** / i n TempRcmge
Temperature = TempMean + (-1.0 —
• (sin(0.0174533 • (0.98 7 • (Day + PhaseShift) - 30))))]
where:
Temperature = average daily water temperature (deg. C);
TempMean = mean annual temperature (deg. C);
TempRange = annual temperature range (deg. C),
Day = Julian date (d); and
PhaseShift = time lag in heating (= 90 d).
Observed temperature loadings should be entered if responses to short-term variations are of
interest. This is especially important if the timing of the onset of stratification is critical, because
stratification is a function of the difference in hypolimnetic and epilimnetic temperatures (see
Figure 40). It also is important in streams subject to releases from reservoirs and other point-
source temperature impacts.
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
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3.6 Light
Light is important as the controlling factor for
photosynthesis and photolysis. The default incident light
function formulated for AQUATOX is a variation on the
temperature equation, but without the lag term:
Solar = LightMean
LightRange
Light: Simplifying Assumptions
• Ice cover is assumed when the
average water temperature drops
below 3 degrees centigrade.
• Photoperiod is approximated by
Julian date
• Average daily light is the program
default, although hourly light may
be simulated
2
sm(0. 0174533 • Day -1.76) • Frac
Light
(25)
where:
Solar
LightMean
LightRange
Day
FracLlRht
average daily incident light intensity (ly/d);
mean annual light intensity (ly/d);
annual range in light intensity (ly/d); and
Julian date (d, adjusted for hemisphere).
fraction of site that is un-shaded, (firac., 1.0-user input shade);
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 deg.C, the model assumes the presence of ice cover and decreases
transmitted light to 15% of incident radiation. (This has changed from 33% in Release 2.2.) This
reduction, due to the reflectivity and transmissivity of ice and snow, is an average of widely
varying values summarized by Wetzel (2001). For estuaries, average water temperature must
fall below -1.8 deg.C before the model assumes ice cover due to the influence of salinity.
Shade can be an important limitation to light, especially in riparian systems. A user input
"fraction of site that is shaded" parameter can be entered either as a constant or as a time-series
within the "Site" input screen. This parameter can be left as zero for no shading effects on light.
Photoperiod is an integral part of the photosynthesis formulation.
Julian date following the approach of Stewart (1975) (Figure 44):
It is approximated using the
12 + A- cos (380 •
Photoperiod =
365
248)
where:
Photoperiod =
A
Day
24
(26)
fraction of the day with daylight (unitless); converted from hours
by dividing by 24;
hours of daylight minus 12 (d); and
Julian date (d, converted to radians).
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
CHAPTER 3
A is the difference between the number of hours of daylight at the summer solstice at a given
latitude and the vernal equinox, and is given by a linear regression developed by Groden (1977):
where:
Latitude
Sign
A = 0.1414- Latitude - Sign -2.413
latitude (deg., decimal), negative in southern hemisphere; and
1.0 in northern hemisphere, -1.0 in southern hemisphere.
(27)
Figure 43. Annual Temperature
Figure 44. Photoperiod as a Function of Date
TEMPERATURE IN A MIDWESTERN POND
35
O
LU
77 153 229 305
39 115 191 267 343
JULIAN DAY
i • 0 65
O)
TO U'°
Q
5
ro u-=>
Q
S 04
-Q U.«
ro
LL 0 35
-~-
/ ^
/ \
\ / \
^ / \ '
y \ '
A V
/ - <'\
/ \ z \
/ "N /' \
/ V
— ' ^ — - ' ^- —
1 53 105 157 209 261 313 365
27 79 131 183 235 287 339
Julian Date
— Latitude 40 N — Latitude 40 S
Hourly Light
When the model is run with an hourly time-step, solar radiation is calculated as variable during
the course of each day. The following equation is used to distribute the average daily incident
light intensity over the portion of the day with daylight hours.
Solar,
Solar
Photoperiod
sin
71-
brae Day'Passed
1-Photoperiod
2
Photoperiod
(28)
Frac
Light
where:
Solarh0uriy
Solarda,iy
Photoperiod
solar radiation at the given time-step (ly/d);
average daily incident light intensity (ly/d), see (25);
fraction of the day with daylight (unitless); see (26);
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
CHAPTER 3
FracDayPassed =
FracLlght
fraction of the day that has passed (unitless)
fraction of site that is un-shaded, (firac., 1.0-user input shade);
A user may enter a constant or time-series shade variable in the site window ("Fraction of Site
that is Shaded"). When this input is utilized then the FracLight variable is calculated.
Figure 45: Average light per day is distributed during daylight hours
in a semi-sinusoidal pattern based on photoperiod.
1200
1000 -
800 -
600 -
400 -
200 -
0
0
10
20 30
Hours
40
50
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 also can affect the depth of
stratification for estuaries. Wind is usually measured at
meteorological stations at a height of 10 m and is 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 twelve additional harmonics seem to
effectively capture the variation (Figure 46):
Wind: Simplifying Assumptions
• If site data are not available a
Fourier series is used to represent
wind loadings
Wind = CosCoeff, + z CosCoeff n • Cos
365
+ SmCoeff Q
where:
Wind
wind speed; amplitude of the Fourier series (m/s);
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
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CosCoeffo
CosCoeffn
Day
SinCoeffn
Freqn
cosine coefficient for the 0-order harmonic, which is the mean wind
speed (default = 3 m/s);
cosine coefficient for the nth-order harmonic;
Julian date (d);
sine coefficient for the nth-order harmonic;
selected frequency for the nth- order harmonic.
This default loading is based on an annual cycle of data taken from the Buffalo, NY airport.
Therefore, it has a 365-day repeat, representative of seasonal variations in wind. Frequencies
were selected to ensure that the standard deviation of the Fourier series and the data were closely
matched. The frequency of wind-speeds of less than three meters per second were also precisely
matched to observed data as well as the periodicity of wind-events. The Fourier approach is
quite useful because the mean can be specified by the user and the variability will be imposed by
the function.
If ice cover is predicted, wind is set to 0. A user also may input a site-specific time series, which
may be important where the timing of a blue-green algal bloom or reaeration is of interest.
Figure 46. Default wind loadings for Onondaga Lake with mean = 4.17 m/s.
ONONDAGA LAKE, NY (CONTROL) Run on 04-24-08 9:07 PM
(Epilimnion Segment)
—Wind (m/s)
1/12/1989
5/12/1989
9/9/1989
1/7/1990
5/7/1990
9/4/1990
1/2/1991
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION CHAPTER 3
3.8 Multi Segment Model
AQUATOX Release 3.0 includes the capability to link AQUATOX segments together, tracking
the flow of water and the passage of state variables from segment to segment. Some general
guidelines for using this model follow:
Multi-Segment Model: Simplifying
Assumptions
• All linked segments have an
identical set of state variables
• Each segment is well mixed
• Linkages between segments may be
unidirectional or bidirectional
• Dynamic stratification does not
apply; stratified pairs of segments
All linked segments must have an identical set of
state variables. (State variables that do not occur in
one segment may be set to zero there.)
Parameters pertaining to animal, plant, and
chemical state variables (i.e. "underlying data") are
considered global to the entire linked system. If
the user changes one of these parameters in one
segment, this parameter changes within all
segments must be sPecified by me user
On the other hand, "site" parameters, initial
conditions, and boundary conditions are unique to
each segment.
State variables can pass from segment to segment through active upstream and
downstream migration, passive drift, diffusion, and bedload.
Mass balance of all state variables is maintained throughout a multi-segment simulation.
There are two types of linkages that may be specified between individual segments, "cascade
links" and "feedback links." A cascade link is unidirectional; there is no potential for water or
state variable flow back upstream. Segments that are linked together by cascade linkages are
solved separately from one another moving from upstream to downstream. This is particularly
useful when modeling faster flowing rivers and streams.
A feedback link allows for water or state variables to flow in both directions. For bookkeeping
purposes, water flows are required to be unidirectional (i.e. entered water flows over a feedback
link must not be negative). However, two feedback links may be specified simultaneously (in
opposite directions) to allow for bidirectional water flows. Feedback links may also be subject to
diffusion; a diffusion coefficient, characteristic length, and cross section must be entered for
diffusion to be calculated, see (32). Segments that are linked together by feedback links are
solved simultaneously. There may only be one contiguous set of segments linked together by
feedback linkages within a simulation (i.e. the model will not solve a "feedback" set of segments
followed by downstream cascade segments followed by more feedback segments below that.)
Figure 47 gives an example of a simulation in which cascade segments and feedback segments
are both included. In this case, AQUATOX solves the simulation from the top down, solving
each segment 1-4, 6, and 6b individually before moving on to solve the feedback segments
simultaneously. Finally, segments 11-14 are be solved individually using the results from the
simultaneous segment run.
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
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Figure 47: An example of feedback and cascade segments linked together.
x ) Feedback Seg.
*•—
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION CHAPTER 3
daily water flow between segments is greater than 30% of the total water volume in both
segments. In this case, fish are assumed to have an equal preference to both segments and they
migrate to equality in a biomass basis. (This allows fish to return to the hypolimnion if it had
earlier been vacated due to anoxia.) Another implication of a well-mixed stratified system (in
linked mode) is that a weighted average of light climate is used when calculating plant
productivity. The calculation of LightLimit for plants (38) is based on a thickness-weighted
average of algal biomass and sediment throughout the entire thickness of the system. This
prevents unreasonable model results due to the light climate in a very thin epilimnion, for
example. Because the system is well-mixed, suspended algae should instead be subject to the
light climate throughout the water column.
State Variable Movement in the Multi-Segment Model
To maintain mass balance, all state variables that are subject to washout or passive drift are also
added to any downstream linked segments. The calculation for this process is as follows:
W ,. ^ Washouty •Volumeu • FracWas^^
Washm = 2_, - - - (30)
upstream links ' ^^^^Dawstream Segment
In the case of toxicants that are absorbed to or contained within a drifting state variable, the
following equation is used:
Washin = V ^^ ' camer • • VolumeUpstrean • ,^^
ToxCarrier ^_j -rr j \ /
upstream links ' OlUm6 'Dowstream Segment
where:
Washin = inflow load from upstream segment (unit/Ldownstream'd);
Washoutjjpstream = washout from upstream segment (unit/Lupstream'd), see (16);
Volume segment = volume of given segment (m3);
fraction of upstream segment's outflow that goes to this
particular downstream segment (unitless);
inflow load of toxicant sorbed to a carrier from an upstream
segment (ng/Ld0wnstream-d);
Washoutcarrier = washout of toxicant carrier from upstream (mg/Lupstream'd);
PPBcamer = concentration of toxicant in carrier upstream (|j,g/kg), see (310);
le-6 = units conversion (kg/mg)
This Washin term is added to all derivatives for state variables that are suspended in the water
column and subject to drift or "washout."
Dissolved state variables are subject to diffusion across feedback links.
60
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION _ CHAPTER 3
n./r . DiffCoeff • Area i \
Diffusion ThlsSe = (Conc0therSeg - ConcThlsSeg ) (32)
where:
DiffusioriThisSeg = gain of state variable due to diffusive transport over the feedback link
between two segments, (unit/d);
DiffCoeff = dispersion coefficient of feedback link, (m2 /d);
Area = surface area of the feedback link (m2);
CharLength = characteristic mixing length of the feedback link, (m);
= concentration of state variable in the relevant segment, (unit/m3);
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AQUATOX (RELEASE 3) 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
and freely-floating macrophytes are modeled as special classes of macrophytes, limited by
nutrients in the water column. These differences are treated at the process level in the equations
(Table 5). All are subject to habitat availability, but to differing degrees.
Table 5. Significant Differentiating Processes for Plants
Biota: Simplifying Assumptions
• Biomass is simulated but not
numbers of individual organisms
• Responses are simulated as
averages for the entire group
Plant Type
Phytoplankton
Periphyton
Rooted
Macrophytes
Non-rooted,
Floating
Macrophytes
Bryophytes
Nutrient
Lim.
J
J
a
j
Current
Lim.
J
Sinking
J
Washout
J
a
Sloughing
J
Breakage
J
a
j
Habitat
J
J
J
a
j
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. 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 6. In addition, a bioaccumulative endpoint such as bald eagle, dolphin, or
mink that feeds on aquatic compartments can be simulated; it is defined by feeding preferences,
biomagnification factor, and clearance rate.
Table 6. Significant Differentiating Processes for Animals
Animal Type
Pelagic Invert.
Benthic Invert.
Benthic Insect
Fish
Washout
a
Drift
a
a
Entrainment
a
a
a
Emergence
a
Promotion
a
Multi-year
a
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION CHAPTER 4
4.1 Algae
The change in algal biomass—expressed as g/m3 for phytoplankton, but as g/m2 for periphyton—
is a function of the loading (especially phytoplankton from upstream), photosynthesis,
respiration, excretion or photorespiration, nonpredatory mortality, grazing or predatory mortality,
sloughing, and washout. As noted above, phytoplankton also are subject to sinking. If the
system is stratified, turbulent diffusion also affects the biomass of phytoplankton.
Plants: Simplifying Assumptions
• Photosynthesis is modeled as a maximum observed rate multiplied by reduction factors. The reduction factors are
assumed to be independent of one another.
Intracellular storage of nutrients is not modeled; constant stoichiometry within species is assumed
For each individual nutrient, saturation kinetics is assumed
Algae exhibit a nonlinear, adaptive response to temperature changes
Low temperatures are assumed not to affect algal mortality
The ratio between biovolume and biomass is assumed to be constant for a given growth form
Constant chlorophyll a to biomass ratios are assumed within algae groups
Phytoplankton-speciflc
• Phytoplankton other than blue-greens are assumed to be mixed throughout the well-mixed layer
• In the event of ice cover, all phytoplankton will occur in the top 2 m
• Sinking of phytoplankton is modeled as a function of physiological state
• Phytoplankton are subject to downstream drift as a simple function of discharge
• To model phytoplankton (and zooplankton) residence time, an implicit assumption may be made that upstream reaches
included in the "Total River Length " have identical environmental conditions as the reach being modeled
Blue-greens-specific
• Blue-greens are assumed to be located in the top 0.1 m unless limited by lack of nutrients or sufficient wind occurs in
which case they are located within the top 3 m
• Blue-greens are not severely limited by nitrogen due to facultative nitrogen fixation (if N less than 1A KN)
Periphyton-specific
• Periphyton are limited by slow currents that do not replenish nutrients and carry away senescent biomass
• Periphyton are assumed to adapt to the ambient conditions of a particular channel
• Periphyton are defined as including associated detritus; non-living biomass is modeled implicitly
Macrophyte-specific
• Macrophytes occupy the littoral zone
• Rooted macrophytes are not limited by nutrients but are assumed to take up necessary nutrients from bottom sediments
• Non-rooted, floating macrophytes are limited by nutrients but not by low light
• Bryophytes are limited by nutrients, can tolerate low light, and contain a high percentage of refractory material
dBiomassph to
— = Loading + Photosynthesis - Respiration - Excretion
- Mortality - Predation ± Sinking - Washout + Washin (33)
± TurbDiff + Diffusionseg +
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
CHAPTER 4
dBiomass
~dt
Pen = Loading + Photosynthesis - Respiration - Excretion
-Mortality - Predation + Sedperi - Slough
(34)
where:
dBiomass/dt
Loading
Photosynthesis
Respiration
Excretion
Mortality
Predation
Washout
Washin
Sinking
TurbDiff
Diffusionseg
Slough
Sedperi
change in biomass of phytoplankton and periphyton with respect to
time (g/m3-d and g/m2-d);
boundary-condition loading of algal group (g/m3-d and g/m2-d);
rate of photosynthesis (g/m3-d and g/m2-d), see (35);
respiratory loss (g/m3-d and g/m2-d), see (63);
excretion or photorespiration (g/m3-d and g/m2-d), see (64);
nonpredatory mortality (g/m3-d and g/m2-d), see (66);
herbivory (g/m3-d and g/m2-d), see (99);
loss due to being carried downstream (g/m3-d), see (129);
loadings from upstream segments (linked segment version only,
g/m3-d), see (30);
loss or gain due to sinking between layers and sedimentation to
bottom (g/m3-d), see (69);
turbulent diffusion (g/m3-d), see (22) and (23);
gain or loss due to diffusive transport over the feedback link
between two segments, (g/m3-d), see (32);
Scour loss of Periphyton or addition to linked Phytoplankton, see
(75); and
Sedimentation of Phytoplankton to Periphyton, see (83).
Figure 48 and Figure 49 are examples of the predicted changes in biomass and the processes that
contribute to these changes in a eutrophic lake. Note that photosynthesis and predation dominate
the diatom rates, with respiration much less important during the growing season.
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
CHAPTER 4
Figure 48. Predicted algal biomass in Lake Onondaga, New York
ONONDAGA LAKE, NY (PERTURBED) Run on 04-23-08 2:59 PM
(Epilimnion Segment)
6.0
5.4
4.8
4.2
3.6
3.0
2.4
1.2
.6
1/12/1989 5/12/1989 9/9/1989 1/7/1990 5/7/1990 9/4/1990 1/2/1991
• Cyclotella nan (mg/L dry)
• Greens (mg/L dry)
• Phyt, Blue-Gre (mg/L dry)
• Cryptomonad (mg/L dry)
Figure 49. Predicted process rates for diatoms in Lake Onondaga, New York
ONONDAGA LAKE, NY (PERTURBED) Run on 04-23-08 2:59 PM
(Epilimnion Segment)
110
99
88
77
66
55
44
33
22
11
S.
3/11/1989
9/9/1989
3/10/1990
9/8/1990
• Cyclotella nan Photosyn (Percent)
- Cyclotella nan Respir (Percent)
• Cyclotella nan Excret (Percent)
- Cyclotella nan Other Mort (Percent)
• Cyclotella nan Predation (Percent)
Cyclotella nan Washout (Percent)
• Cyclotella nan Sediment (Percent)
Cyclotella nan TurbDiff (Percent)
Cyclotella nan SinkToHypo (Percent)
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AQUATOX (RELEASE 3) 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 • SaltEffect (35)
The limitation of primary production in phytoplankton is:
PProdLimit = LtLimit • NutrLimit • TCorr • FracPhoto (36)
Periphyton have an additional limitation based on available substrate, which includes the littoral
bottom and the available surfaces of macrophytes. The macrophyte surface area conversion is
based on the observation of 24 m2 periphyton/m2 bottom (Wetzel, 1996) and assumes that the
observation was made with 200 g/m3 macrophytes.
PProdLimit = LtLimit • NutrLimit • VLimit • TCorr • FracPhoto
(37)
• ( FracLittoral + SurfAreaConv • BiomassMacroPhytes)
where:
Pmax = maximum photosynthetic rate (1/d);
LtLimit = light limitation (unitless), see (38);
NutrLimit = nutrient limitation (unitless), see (55);
Vlimit = current limitation for periphyton (unitless), see (56);
TCorr = limitation due to suboptimal temperature (unitless), see (59);
HabitatLimit = in streams, habitat limitation based on plant habitat preferences
(unitless), see (13).
SaltEffect = effect of salinity on photosynthesis (unitless);
FracPhoto = reduction factor for effect of toxicant on photosynthesis (unitless),
see (421);
FracLittoral = fraction of area that is within euphotic zone (unitless) see (11);
SurfAreaConv = surface area conversion for periphyton growing on macrophytes (0.12
m2/g);
= total biomass of macrophytes in system (g/m ); and
= biomass of periphytic 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; Di Toro 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 3) 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). The equation is
slightly different when the model is run with a daily versus an hourly time-step:
e • Photoperiod • (LtAtDepthDail - LtAtTopDail ) • PeriphytExt
Extinct • (DepthBottom - Depth )
/loc * .~s*^~' •"*" \-^"-i--^~r"*Daily •""•"*- ^fDaily / -i "• f"./"-•-'•<•"• tto\
LtLimitDaay = 0.85 „ ,. , .„ ,/ „ .. , (38)
e • (LtAtDepthjj , - LtAtTopH , ) • PeriphytExt
LtLimitH , = — F Hourly FHourly/ — (39)
Extinct • (DepthBottom - DepthTop )
where:
LtLimitnmeStep = light limitation (unitless);
e = the base of natural logarithms (2.71828, unitless);
Photoperiod = fraction of day with daylight (unitless), see (26);
Extinct = total light extinction (1/m), see (40), (41);
DepthBottom = maximum depth or depth of bottom of layer if stratified (m); if
periphyton or macrophyte then limited to euphotic depth;
Depthrop = depth of top of layer (m);
LtAtTop = limitation of algal growth due to light, (unitless) see (44), (45);
LtAtDepth = limitation due to insufficient light, (unitless), see (43);
PeriphytExt = extinction due to periphyton; only affects periphyton and
macrophytes (unitless), see (42).
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 to the daily formulation (Kremer and Nixon,
1978). When AQUATOX is run with an hourly time-step, the correction factor of 0.85 is not
relevant, nor the inclusion of photoperiod.
Light limitation does not apply to free-floating macrophytes as these are assumed to be located at
the surface of the water.
Even when the model is run with an hourly time-step, two algal equations utilize the daily light
limit equation (38) as most appropriate. First, when calculating algal mortality, the stress factor
for suboptimal light and nutrients (68) is expecting the input of daily light limitation (i.e. the
plants do not all die each night). Secondly, when calculating the sloughing of benthic algae (75)
67
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION _ CHAPTER 4
the calculation of suboptimal light is calibrated to daily light limitation, not the instantaneous
absence or presence of light (i.e. sloughing is not more likely to occur when it is dark).
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 suspended particulate organic matter (POM) and inorganic
sediment, and attenuation due to dissolved organic matter (DOM):
Extinct = Water Extinction + PhytoExtinction + ECoeffDOM • DOM
(40)
+ ECoefjPOM-ZPartDetr + ECoeffSed-InorgSed
where:
Water Extinction = user-supplied extinction due to water (1/m);
PhytoExtinction = user-supplied extinction due to phytoplankton and macrophytes
(1/m), see (41), (42);
ECoeffDOM = attenuation coefficient for dissolved detritus l/(m-g/m3);
DOM = concentration of dissolved organic matter (g/m3), see (143) and
(144);
ECoeffPOM = attenuation coefficient for particulate detritus l/(m-g/m3);
PartDetr = concentration of particulate detritus (g/m3), see (141) and
(142);
ECoeffSed = attenuation coefficient for suspended inorganic sediment
l/(m-g/m3); and
InorgSed = concentration of total suspended inorganic sediment (g/m3), see
(244)
For computational reasons, the value of Extinct is constrained between 5"19 and 25. Self-shading
by phytoplankton, periphyton, and macrophytes is a function of the biomass and attenuation
coefficient for each group. Extinction by periphyton is computed differently because it is not
depth-dependent but rather pertains to the growing surface:
and
PhytoExtinction = ^alga ( ECoeffPhyto alga • Biomassaiga) (41)
PeriPhytExt = e^pm (~ ECoe-ffphytop^ ' Biomass pen)
where:
EcoeffPhytOaiga = attenuation coefficient for given phytoplankton or macrophyte
(1/m-g/m3),
EcoeffPhytOpen = attenuation coefficient for given periphyton (1/m-g/m2),
Biomass = concentration of given plant (g/m3 or g/m2), and
The light limitation at depth is computed by:
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION CHAPTER 4
Tjoht -Extinct£pj-DepthTop
_ & '"TimeStep 'g -Extinct VSeg ' DepthBottom
LtAtDepthTimeStep = e LightSat-LightCorr e (43)
Light limitation at the surface of the water body is computed by:
Li8htTimeStep
LtAtTopTimeSfep = e' LightSat-LightCorr (44)
and light limitation at the top of the hypolimnion is computed by:
TimeStep - ExtinctEpi • DepthTop
LightSat-LightCorr (45)
where:
LtAtTop = limitation of algal growth due to light, (unitless multiplier, 0 being
no limitation, 1 being 100% limitation)
LtAtDepth = limitation due to insufficient light, (unitless, see LtAtTop)
Extinct= overall extinction of light in relevant vertical segment (1/m), (40)
Lightnmestep = photosynthetically active radiation (ly/d), (46);
LightCorr = Correction factor, 1.0 for a daily time-step, 1.25 for an hourly
time-step. LightSat is increased by 25% to account for
instantaneous solar radiation as opposed to daily averages;
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 (Equation (55)) and the wind is less than 3
m/s then DepthBottom for blue-greens is set to 0.1 m to account for buoyancy due to gas
vacuoles. Otherwise it is set to 3 m to represent downward transport by Langmuir circulation.
When calculating self-shading for blue-greens, the model accounts for more intense self shading
in the upper layer of the water column due to the floating concentration of blue-greens there.
The Extinct term in equation (43) is multiplied by the segment thickness and divided by the
thickness over which blue-greens occur so that the more intense self-shading effects of these blue
greens concentrated at the top of the system are properly accounted for.
Under the ice, all phytoplankton are represented as occurring in the top 2 m (cf LeCren and
Lowe-McConnell, 1980). As discussed in Section 3.6, light is decreased to 15% of incident
radiation if ice cover is predicted.
Approximately half the incident solar radiation is photosynthetically active (Edmondson, 1956):
LightTmeStep = SolarTimeStep • 0.5 (46)
where:
daily light intensity on a daily (25) or hourly (28) basis (ly/d).
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
CHAPTER 4
The light-limitation function represents both limitation for suboptimal light intensity and
photoinhibition at high light intensities (Figure 50). However, when the photoperiod for all but
the highest latitudes is factored in, photoinhibition disappears (Figure 51). When considered
over the course of the year, photoinhibition can occur in very clear, shallow systems during
summer mid-day hours (Figure 52), but it usually is not a factor when considered over 24 hours
(Figure 53).
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 7).
Table 7. Light Extinction and Attenuation Coefficients
WaterExtinction
ECoeffPhytOdiatont
ECoeffPhytoblue.ereen
ECoeffDOM
ECoeffPOM
ECoeffSed
0.02 1/m
0.14 l/m-(g/m3)
0.099 l/m-(g/m3)
0.03 l/m-(g/m3)
0.12 l/m-(g/m3)
0.17 l/m-(g/m3)
Wetzel, 1975
calibrated
Megard et al., 1979 (calc.)
Effleretal., 1985 (calc.)
Verduin, 1982
Straskraba and Gnauck,
1985
All coefficients may be user-supplied in the plant or site underlying data.
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
CHAPTER 4
Figure 50. Instantaneous Light Response
Function
Diatoms in 0.5-m Deep Pond
0.88
200 250 300 350 400 450 500
Light (ly/d)
Diatoms in 0.5-m Deep Pond
3 53 103 153 203 253 303 353
Julian Date
0.88
— Light — Limitation
Figure 51. Daily Light Response Function
n crc;
(/) U.O
_o>
~ n 4s;
5,
o
'•*-• n ^
i m
- 0.3
n 9=1
20
Diatoms in 0.5-m Deep Pond
0 250 300 350 400 45
Average Light (ly/d)
0
Figure 53. Daily Light Limitation
cnfl _
^A^C)
~o ^^u
l>i
•nW)
o>
£ -*nn
3
in ocn
9nn
%!
Diatoms in 0.5-m Deep Pond
53 103 153 203 253 303 353
Julian Date
Light Limitation
n ^G,
T?
05 o>
C
c
n A .°
2
_l
fl 0 -^
U'J ro
Q
n 9s;
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 =
Extinction
(47)
where:
Secchi
Secchi depth (m).
This relationship also could be used to back-calculate an overall Extinction coefficient if only the
Secchi depth is known for a site.
As a verification of the extinction computations, the calculated and observed Secchi depths were
compared for Lake George, New York. The Secchi depth is estimated to be 8.3 m in Lake
George, based on site data for the various components (Figure 54). This compares favorably
with observed values of 7.5 to 11 (Clifford, 1982).
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
CHAPTER 4
Figure 54. Contributions to light extinction in Lake George NY.
POM (26.13%)
Sediment (0.00%)
Water (6.97%)
Phytoplankton (1.59%)
DOM (65.32%)
Adaptive Light
Saturating light can be specified as a constant for each plant taxonomic group (classic
AQUATOX approach) or it can be adaptive based on Kremer & Nixon (1978) and similar to the
approach used in EFDC. The adaptive light saturation is the weighted average of
photosynthetically active solar radiation (PAR) at the optimal depth for growth of a given plant
group, using an approximation based on the user-specified light saturation and site solar radiation
and turbidity at the beginning of the simulation:
LightSatCalc = Q.l(LightHistl}+Q2(LightHist2}+ 0. l(LightHist3)
(48)
LightHistn=PAR-e
(-Extinct -ZOptplaM)
(49)
where:
LightSatCalc =
LightHistn =
PAR
Solar =
Extinct =
adaptive light saturation (Ly/d)
photosynthetically active radiation at optimum depth for plant
growth n days prior to simulation date (Ly/d)
photosynthetically active radiation, Solar * 0.5 (Ly/d)
incident solar radiation (Ly/d)
total light extinction computed dynamically (40).
If the LightSatCalc is greater or less than the user-entered maximum and minimum light
saturation coefficients ("Plant underlying data" screen) then the LightSatCalc is set to the user-
entered maximum or minimum. This LightSatCalc variable is then used in the LtAtDepth and
LtAtTop calculations (43)-(45).
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
CHAPTER 4
\n(LightSat I ' MaxDailyLight)
Plant
^ „• v
- Extinct
\ '
lmtcond
where:
ZOpt piant =
LightSat =
MaxDailyLight =
Extinct M
tCond
optimum depth for a given plant (a constant approximated at the
beginning of the simulation in meters);
user entered light saturation coefficient (Ly/d);
maximum daily-averaged incident solar radiation for one
calendar year forward from the start date (Ly/d);
initial condition total light extinction (unitless);
Nutrient Limitation
There are several ways that nutrient limitation has been represented in models. Algae are
capable of taking up and storing sufficient nutrients to carry them through several generations,
and models have been developed to represent this. However, if the timing of algal blooms is not
critical, intracellular storage of nutrients can be ignored, constant stoichiometry can be assumed,
and the model is much simpler. Therefore, based on the efficacy of this simplifying assumption,
nutrient limitation by external nutrient concentrations is used in AQUATOX, as in many other
models (for example, Chen, 1970; Parker, 1972; Lassen and Nielsen, 1972; Larsen et al., 1974;
Park et al., 1974; Chen and Orlob, 1975; Patten et al., 1975; Environmental Laboratory, 1982;
Ambrose et al., 1991).
For an individual nutrient, saturation kinetics is assumed, using the Michaelis-Menten or Monod
equation (Figure 55); this approach is founded on numerous studies (cf Hutchinson, 1967):
nr . .
PLimit =
Phosphorus
- -
Phosphorus + KP
__
(51)
NLrmit = •
Nitrogen
Nitrogen + KN
~T . .
CLirmt =
Carbon
Carbon + KCO2
(53)
where:
PLimit =
Phosphorus =
KP =
NLimit =
Nitrogen =
KN =
CLimit =
Carbon =
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
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
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KCO2
half-saturation constant for carbon (gC/m3).
Figure 55. 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:
where:
C2CO2
C02
Carbon = C2CO2 • CO2
ratio of carbon to carbon dioxide (0.27); and
inorganic carbon (g/m3).
(54)
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 Michaelis-Menten equation is evaluated for each nutrient, and the factor for the
nutrient that is most limiting at a particular time is used:
where:
NutrLimit
NutrLimit = min(PLimit, NLimit, CLimit)
reduction due to limiting nutrient (unitless).
(55)
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.
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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(7, RedStillWater
VelCoeff • Velocity
1 +VelCoeff-Velocity'
(56)
where:
VLimit =
RedStillWater =
VelCoeff
Velocity =
limitation or enhancement due to current velocity (unitless);
user-entered reduction in photosynthesis in absence of current
(unitless);
empirical proportionality coefficient for velocity (0.057, unitless);
and
flow rate (converted to m/s), see (14).
VLimit has a minimum value for photosynthesis in the absence of currents and increases
asymptotically to a maximum value for optimal current velocity (Figure 56). In high currents
scour can limit periphyton; see (75). 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).
Figure 56. Effect of current velocity on periphyton photosynthesis.
a:
o
o
0.8
O
0.6
0.4
a:
O
z
O
I-
u
S0.2
a:
20 40 60 80
VELOCITY (cm/s)
100
120
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION CHAPTER 4
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 VTis 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:
(TMax + Acclimation) - Temperature
V L = •
(TMax + Acclimation) - (TOpt + Acclimation)
where:
Temperature = ambient water temperature (deg. C);
TMax = maximum temperature at which process will occur (deg. C);
TOpt = optimal temperature for process to occur (deg. C); and
Acclimation = temperature acclimation (deg. 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- /^--^(T^r^-r^y (58)
where:
XM = maximum acclimation allowed (deg. 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 (deg. 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):
= VTXT-e> (59)
where:
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XT =
WT2 • (1
40/YT
400
where:
and,
where:
WT = \n(Q10) • ((TMax + Acclimation) - (TOpt + Acclimation))
YT = \n(QJO) • ((TMax + Acclimation) - (TOpt + Acclimation) + 2)
(60)
(61)
(62)
Q10 = slope or rate of change per 10°C temperature change (unitless).
This well-founded, robust algorithm for TCorr is used in AQUATOX to obtain reduction factors
for suboptimal temperatures for all biologic processes in animals and plants, with the exception
of decomposition and plant respiration. By varying the parameters, organisms with both narrow
and broad temperature tolerances can be represented (Figure 57, Figure 58).
Figure 57. Temperature response of blue-greens Figure 58. Temperature response of diatoms
STROGANOV FUNCTION
BLUE-GREENS
TOpt
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 Figure 59:
Respiration = Resp20 • 1 .
ratere-20) • Biomass
(63)
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where:
Respiration =
Resp20
1.045
Temperature =
Biomass =
dark respiration (g/m3-d);
user input respiration rate at 20°C (g/g-d);
exponential temperature coefficient (/°C);
ambient water temperature (°C); and
plant biomass (g/m3).
This construct also applies to macrophytes.
Figure 59. Respiration (Data From Collins, 1980)
DARK RESPIRATION
10 20 30
TEMPERATURE(C)
Photorespiration
Algal excretion, also referred to as photorespiration, is the release of photosynthate (dissolved
organic material) that occurs in the presence of light. Environmental conditions that inhibit cell
division but still allow photoassimilation result in release of organic compounds. This is
especially true for both low and high levels of light (Fogg et al., 1965; Watt, 1966; Nalewajko,
1966; Collins, 1980). AQUATOX uses an equation modified from one by Desormeau (1978)
that is the inverse of the light limitation:
where:
Excretion = KResp • LightStress • Photosynthesis (64)
Excretion = release of photosynthate (g/m3-d);
KResp = coefficient of proportionality between excretion and
photosynthesis at optimal light levels (unitless); and
Photosynthesis = photosynthesis (g/m3-d), see (35),
and where:
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LightStress = 1- LtLimit
(65)
where:
LtLimit
light limitation for a given plant (unitless), see (38).
Excretion is a continuous function (Figure 60) 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 60. Excretion as a fraction of photosynthesis
EFFECT OF LIGHT ON PHOTORESPIRATION
w DIATOMS IN POND
0.09
200 250
300 350 400
LIGHT (ly/d)
450 500
Algal Mortality
Nonpredatory algal mortality can occur as a response to toxic chemicals (discussed in Chapter
8) and as a response to unfavorable environmental conditions. Phytoplankton under stress may
suffer greatly increased mortality due to autolysis and parasitism (Harris, 1986). Therefore, most
phytoplankton decay occurs in the water column rather than in the sediments (DePinto, 1979).
The rapid remineralization of nutrients in the water column may result in a succession of blooms
(Harris, 1986). Sudden changes in the abiotic environment may cause the algal population to
crash; stressful changes include nutrient depletion, unfavorable temperature, and damage by light
(LeCren and Lowe-McConnell, 1980). These are represented by a mortality term in AQUATOX
that includes toxicity, high temperature (Scavia and Park, 1976), and combined nutrient and
light limitation (Collins and Park, 1989):
where:
Mortality = (KMort + Excess! + Stress) • Biomass + Poisoned
Mortality = nonpredatory mortality (g/m3-d);
Poisoned = mortality rate due to toxicant (g/m3-d), see (417);
KMort = intrinsic mortality rate (g/g-d); and
(66)
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Biomass
and where:
and:
where:
plant biomass (g/m3),
ExcessT —
(Temperature - TMax)
2
„ _ 7 _ -EMort • (1 - (NutrLimit • LtLimit))
(67)
(68)
ExcessT = factor for high temperatures (g/g-d);
TMax = maximum temperature tolerated (° C);
Stress = factor for suboptimal light and nutrients (g/g-d),
Emort = approximate maximum fraction killed per day with total limitation
(g/g-d);
NutrLimit = reduction due to limiting nutrient (unitless), see (55)
LtLimit = light limitation (unitless), see (38).
Exponential functions are used so that increasing stress leads to rapid increases in mortality,
especially with high temperature where mortality is 50% per day at the TMax (Figure 61), and, to
a much lesser degree, with suboptimal nutrients and light (Figure 62). This simulated process is
responsible in part for maintaining realistically high levels of detritus in the simulated water
body. Low temperatures are assumed not to affect algal mortality.
Figure 61. Mortality due to high temperatures
Figure 62. Mortality due to light limitation
S'ns
T3
= 06
•S°.b
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Sinking
Sinking of phytoplankton, either between layers or to the bottom sediments, is modeled as a
function of physiological state, similar to mortality. Phytoplankton that are not stressed are
considered to sink at given rates, which are based on field observations and implicitly account
for the effects of averaged water movements (cf. Scavia, 1980). Sinking also is represented as
being impeded by turbulence associated with higher discharge (but only when discharge exceeds
mean discharge):
where:
Sink =
KSed MeanDischarge
Depth Discharge
• SedAccel • Biomass
(69)
Sink
KSed
Depth
MeanDischarge
Discharge
Biomass
phytoplankton loss due to settling (g/m -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 3; 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 increase in
sinking (Figure 63), as observed by Smayda (1974), and formulated by Collins and Park (1989):
0 j A j ESed • (!- LtLimit • NutrLimit • TCorr • FracPhoto)
SedAccel — e
(70)
where:
SedAccel
ESed
LtLimit
NutrLimit
FracPhoto
TCorr
increase in sinking due to physiological stress (unitless);
exponential settling coefficient (unitless);
light limitation (unitless), see (38);
nutrient limitation (unitless), see (55); and
reduction factor for effect of toxicant on photosynthesis (unitless),
see (421);
temperature limitation (unitless), see (59).
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Figure 63. Sinking as a function of nutrient stress
SINKING IN POND
DIATOMS, DEPTH = 3 m, BIOMASS = 1
0.00 0.02 0.03 0.05 0.06 0.08 0.10
PHOSPHATE (g/cu m)
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:
Discharge
I phytoplankton -,T T
Volume
• • Biomass
(71)
where:
WashoUtphytoplankton
Discharge
Volume
Biomass
loss due to downstream drift (g/m
daily discharge (m3/d);
volume of site (m3); and
biomass of phytoplankton (g/m3).
•d),
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 better (Figure 64
and Figure 65).
Washout periphyton = Slough + Dislodge
Peri,Tax
(72)
where:
WashoUtperiphyton
Slough
= loss due to sloughing (g/m -d);
= loss due to natural causes (g/m3-d), see (75); and
= loss due to toxicant-induced sloughing (g/m3-d), see (427).
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Figure 64. 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.
Si
$
- Diatoms(g/m2) —•—Oth alg{g/m2)
Periphyton
Observed
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Figure 65. 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 D Respiration D Excretion C Mortality • Predation • Slougiiing
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 • UnitAreaf3 -IE-6
(73)
where:
DragForce
Rho
DragCoeff
Vel
BioVol
UnitArea
1E-6
drag force (kg m/s2);
density of water (kg/m3);
drag coefficient (2.53E-4, unitless);
velocity (converted to m/s) see (14);
biovolume of algae (mm3/mm2);
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):
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Biomass _, ,
BiovolD,a = ZMean
Biovolpn —
2.08E-9
Biomass
8.57E-9
•ZMean
(74)
where:
BiovolDm
Biovolpu
Biomass
ZMean
biovolume of non-filamentous algae (mm3/mm2);
\ ^
biovolume of filamentous algae (mm /mm );
biomass of given algal group (g/m2);
mean depth (m).
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 > SuboptimalOrg • FCrit0rg • Adaptation
then Slough = Biomass • FracSloughed
else Slough = 0
(75)
where:
Suboptimalorg = factor for Suboptimal nutrient, light, and temperature effect on
senescence of given periphyton group (unitless);
FCritorg = critical force necessary to dislodge given periphyton group (kg
m/s2);
Adaptation = factor to adjust for mean discharge of site compared to reference
site (unitless);
Slough = biomass lost by sloughing (g/m3);
FracSloughed = fraction of biomass lost at one time, editable.
Suboptimal0rg = NutrLimit0rg • LtLimit0rg • TCorr0rg • 20
If Suboptimal0rg > 1 then Suboptimal0rg = 1
(76)
where:
NutrLimit
LtLimitc/rg
TCorr
20
nutrient limitation for given algal group (unitless) computed by
AQUATOX; see (55);
light limitation for given algal group (unitless) computed by
AQUATOX; see (38); and
temperature limitation for a given algal group (unitless) computed
by AQUATOX; see (59).
factor to desensitize construct.
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The sloughing construct was tested and calibrated (U.S. E.P.A., 2001) with data from
experiments with artificial and woodland streams in Tennessee (Rosemond, 1993, Figure 64).
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 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:
Vel2
Adaptation =
0.006634 (77)
where:
Vel = velocity for given site (m/s), see (14);
0.006634 = mean velocity2 for reference experimental stream (m/s).
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 ugC/ug 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 ug/L; therefore, the computation is:
ll A = "Biomass gar , \^-'BiomassDiatom ^ Biomass oa,' _ 5_ J 000
~
45 28
where:
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION CHAPTER 4
ChlA = biomass as chlorophyll a (ug/L);
Biomass = biomass of given alga (mg/L);
CToOrg = ratio of carbon to biomass (0.526, unitless); and
1000 = conversion factor for mg to ug (unitless).
Periphytic chlorophyll a is computed as a 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. The conversion factor is based on the observed average ratio of chlorophyll
a to AFDW for the Cahaba River near Birmingham, Alabama (unpub. data) and also based on
data published in Biggs (1996)and Rosemond (1993).
Perichlor = AFDW -5.0 (79)
where:
PeriChlor = periphytic chlorophyll a (mg/m2);
AFDW = ash free dry weight (g/m2).
Phytoplankton and Zooplankton Residence Time
Phytoplankton and zooplankton can quickly wash out of a short reach, but they may be able to
grow over an extensive reach of a river, including its tributaries. Somehow the volume of water
occupied by the phytoplankton needs to be taken into consideration. To solve this problem,
AQUATOX takes into account the "Total Length" of the river being simulated, as opposed to the
length of the river reach, or "SiteLength" so that phytoplankton and zooplankton production
upstream can be estimated. This parameter can be directly entered on the Site Data screen or
estimated from the watershed area based on Leopold et al. (1964).
TotLength = 1.609 • 1.4 • (Watershed • 0.386)u 6 (80)
where:
TotLength = total river length (km);
Watershed = land surface area contributing to flow out of the reach (square km);
1.609 = km per mile;
0.386 = square miles per square km.
If Enhanced Phytoplankton Retention is not chosen (or the total length or watershed area is
entered as zero,) the phytoplankton and zooplankton residence time equations are not used and
Equations (71) and (129) are used to calculate washout. In this case, the phytoplankton
residence time is equal to the retention time of the system.
Otherwise, to simulate the inflow of plankton from upstream reaches plankton upstream loadings
are estimated as follows:
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION CHAPTER 4
TTr , [ Washout^ t ] , ^
Loading,.mtr,am = Washout hinta -\ £12£2 (81)
o upstream oioia rr\ ,-r ,7 / o-^ T ^.i \ v '
^ TotLength I SiteLength )
where:
Loadingupstream = loading of plankton due to upstream production (mg/L);
Washoutbtota = washout of plankton from the current reach (mg/L);
TotLength = total river length (km);
SiteLength = length of the modeled reach (km).
An integral assumption in this approach is that upstream reaches included in the total river length
have identical environmental conditions as the reach being modeled and that plankton production
in each mile up-stream will be identical to plankton production in the given reach. Residence
time for plankton within the total river length is estimated as follows:
_ Volume (TotLength ^
residence
Discharge [^SiteLength
where:
^residence = residence time for floating biota within the total river length (d);
Volume = volume of modeled segment reach (m3); see (2);
Discharge = discharge of water from modeled reach (m3/d); see Table 3;
TotLength = total river length (km);
SiteLength = length of the modeled reach (km).
Periphyton-Phytoplankton Link
Periphyton may slough or be physically scoured, contributing to the suspended algae; this may
be reflected in the chlorophyll a observed in the water column. Periphyton may be linked to a
phytoplankton compartment so that sestonic chlorophyll a reflect the results of periphyton
sloughing. One-third of periphyton is assumed to become phytoplankton and two thirds is
assumed to become suspended detritus in a sloughing event. The default is linkage to detritus
with a warning.
Additionally, when phytoplankton undergoes sedimentation it will now be incorporated into the
linked periphyton layer if such a linkage exists. If multiple periphyton species are linked to a
single phytoplankton species, biomass is distributed to periphyton weighted by the mass of each
periphyton compartment. (A single periphyton compartment cannot be linked to multiple
phytoplankton compartments.)
o J 0-7 PeriphytonA /o-»\
SedPenphytonA = Sink — - = - (83)
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION _ CHAPTER 4
where:
nA = sedimentation that goes to periphyton compartment A;
= total sedimentation of linked phytoplankton compartment, see (69);
MassperiphytonA = mass of periphyton compartment A;
Mass AH Linked Pen = mass of all periphyton compartments linked to the
relevant phytoplankton compartment.
If no linkage is present, settling phytoplankton are assumed to contribute to sedimented detritus.
4.2 Macrophytes
Submersed aquatic vegetation or macrophytes can be an important component of shallow aquatic
ecosystems. It is not unusual for the majority of the biomass in an ecosystem to be in the form of
macrophytes during the growing season. Seasonal macrophyte growth, death, and
decomposition can affect nutrient cycling, and detritus and oxygen concentrations. By forming
dense cover, they can modify habitat and provide protection from predation for invertebrates and
smaller fish (Howick et al., 1993); this function is represented in AQUATOX (see Figure 71).
Macrophytes also provide direct and indirect food sources for many species of waterfowl,
including swans, ducks, and coots (Jupp and Spence, 1977b).
AQUATOX represents rooted macrophytes as occupying the littoral zone, that area of the bottom
surface that occurs within the euphotic zone (see (11) for computation). Similar to periphyton,
the macrophyte 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 (ZEuphotic = 4.605/Extinct), the area predicted to be occupied by
macrophytes can increase or decrease depending on the clarity of the water.
The macrophyte equations are based on submodels developed for the International Biological
Program (Titus et al., 1972; Park et al., 1974) and CLEANER models (Park et al., 1980) and for
the Corps of Engineers' CE-QUAL-R1 model (Collins et al., 1985):
dBiomass T , „
- = Loading + Photosynthesis - Respiration - Excretion
dt
- Mortality - Predation - Breakage (84)
+ Washout FreeFloat - WashinFreeFloat
and:
Photosynthesis = PMax • LtLimit • TCorr • Biomass • FracLittoral
where:
(85)
• NutrLimit • FracPhoto • HabitatLimit
dBiomass/dt = change in biomass with respect to time (g/m2-d);
Loading = loading of macrophyte, usually used as a "seed" (g/m2-d);
Photosynthesis = rate of photosynthesis (g/m2-d);
Respiration = respiratory loss (g/m2-d), see (63);
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Excretion
Mortality
Predation
Breakage
PMax
LtLimit
TCorr
HabitatLimit
FracLittoral
NutrLimit
FracPhoto
Washout
FreeFloat
Washin
FreeFloat
= excretion or photorespiration(g/m2-d), see (64);
= nonpredatory mortality (g/m2-d), see (87);
= herbivory (g/m2-d), see (99);
= loss due to breakage (g/m2-d), see (88);
= maximum photosynthetic rate (1/d);
= light limitation (unitless), see (38);
= correction for suboptimal temperature (unitless), see (59);
= in streams, habitat limitation based on plant habitat preferences
(unitless), see (13);
= fraction of bottom that is in the euphotic zone (unitless) see (11);
= nutrient limitation for bryophytes or freely-floating macrophytes
(unitless), see (55);
= reduction factor for effect of toxicant on photosynthesis (unitless),
see (421);
= washout of freely floating macrophytes, see (86); and
= loadings from linked upstream segments (g/m3-d), see (30);
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. For rooted macrophytes, nutrient limitation is not modeled
at this time because macrophytes can obtain most of their nutrients from bottom sediments
(Bristow and Whitcombe, 1971; Nichols and Keeney, 1976; Barko and Smart, 1980).
Bryophytes and freely floating macrophytes assimilate nutrients from water and are subject to
nutrient limitation.
Release 3 includes free-floating macrophytes. These macrophytes are assumed to be floating at
the upper layer of the water column and therefore are not subject to light limitation.
Furthermore, free-floating macrophytes are not subject to the FracLittoral limitation to
macrophyte photosynthesis (85). On the other hand the washing of macrophytes out of the
system is affected by the carrying capacity for the species:
Washout
freefloat
, KCap I ZMean - State \ Discharge 0
1 — • State
KCap I ZMean
Volume
(86)
where:
freefloat
State
KCap
ZMean
Discharge
loss due to being carried downstream (g/m -d),
concentration of dissolved or floating state variable (g/m3),
carrying capacity (g/m2);
mean depth from site underyling data (m);
discharge (m3/d), see Table 3; and
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
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Volume
= volume of site (m3), see (2);
Simulation of macrophyte respiration and excretion utilize the same equations as algae; excretion
in rooted macrophytes results in "nutrient pumping" because the nutrients are assumed to come
from the sediments but are excreted to the water column1. Non-predatory mortality is modeled
similarly to algae as a function of suboptimal temperature (but not light). However, mortality is
a function of low as well as high temperatures, and winter die-back is represented as a result of
this control; the response is the inverse of the temperature limitation (Figure 66):
Mortality = [KMort + Poisoned + (1 - e
-^^.(i-TCorr)
. Biomass
(87)
where:
KMort
Poisoned
EMort
intrinsic mortality rate (g/g-d);
mortality rate due to toxicant (g/g-d) (417), 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 (Figure 66).
Figure 66. Mortality as a function of temperature
MACROPHYTE MORTALITY
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 (Figure 67):
where:
Breakage
„ , Velocity-VelMax _.
Breakage = Biomass
Gradual • UnitTime
macrophyte breakage (g/m -d);
(88)
1 Because nutrients are not usually explicitly modeled in bottom sediments, macrophyte root uptake can result in
loss of mass balance, particularly in shallow ponds. The optional sediment diagenesis model does include nutrients
but linkage to macrophytes through root uptake has not yet been specified and implemented. However, the total
mass of nutrients taken into the water column through macrophyte uptake can be tracked as a model output (N and P
"Root Uptake" in kg).
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Velocity = current velocity (cm/s) see (14);
VelMax = velocity at which total breakage occurs (cm/s);
Gradual = velocity scaling factor (20 cm/s);
UnitTime = unit time for simulation (1 d);
Biomass = macrophyte biomass (g/m2).
Figure 67. Breakage of macrophytes as a function of current
velocity; VelMax set to 300 cm/s.
Velocity (cm/s)
The Breakage formulation also applies to freely floating macrophytes and may be considered
entrainment in periods of high flow. As such, VelMax should be set to a relatively high value for
these organisms.
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 62% labile 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 = l^BryoConv • BiomassBry^
(89)
where:
MossChlor
BryoConv
bryophytic chlorophyll a (mg/m2);
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
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION CHAPTER 4
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
Animals: Simplifying Assumptions
• Ingestion is represented by a maximum consumption rate adjusted for conditions of food, temperature, sublethal toxicant
effects, and habitat preferences
Reproduction is implicit in the increase in biomass
Macrophytes can provide refuge from predation
AQUATOX is a food-web model including prey switching based on prey availability
Specific dynamic action (the metabolic "cost" of digesting and assimilating prey) is represented as proportional to food
assimilated
Unless spawning dates are entered by the user, spawning occurs as a function of water temperature
Zooplankton and fish will migrate vertically from an anoxic hypolimnion to the epilimnion
Promotion from one size class offish to the next is estimated as a fraction of total biomass growth
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 , _, ^ . „ „ ,
= Load + Consumption - Defecation - Respiration - Pishing
dt
- Excretion - Mortality - Predation - GameteLoss ± DiffusionSeg
- Washout + Washin ± Migration - Promotion + Recruit - Entrainment (90)
GrowthRate = Consumption - Defecation - Respiration - Excretion
where:
dBiomass/dt = change in biomass of animal with respect to time (g/m3-d);
Load = biomass loading, usually from upstream (g/m3-d);
Consumption = consumption of food (g/m3-d), see (98);
Defecation = defecation of unassimilated food (g/m3-d), see (97);
Respiration = respiration (g/m3-d), see (100);
Fishing = loss of organism due to fishing pressure (g/m3-d), user input fraction
fished multiplied by the biomass.
Excretion = excretion (g/m3-d), see (111);
Mortality = nonpredatory mortality (g/m3-d), see (112);
Predation = mortality from being preyed upon (g/m3-d), see (99);
GameteLoss = loss of gametes during spawning (g/m3-d), see (126);
Washout = loss due to being carried downstream by washout and drift (g/m3-d),
see (129) and (130);
Washin = loadings from linked upstream segments (g/m3-d), see (30);
Diffusionseg = gain or loss due to diffusive transport over the feedback link between
two segments, pelagic inverts, only (g/m3-d), see (32);
Migration = loss (or gain) due to vertical migration (g/m3-d), see (133);
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Promotion =
Recruit =
Entrainment =
GrowthRate =
promotion to next size class or emergence (g/m3-d), see (136);
recruitment from previous size class (g/m3-d), see (128);
entrainment and downstream transport by floodwaters (g/m3-d)
(132).
estimated growth rate as a function of derivative terms, output in
units of percentage per day when animal's "rates output" is turned
on.
The change in biomass (Figure 68) is a function of a number of processes (Figure 69) 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 68. Predicted changes in biomass in a stream
18.7
17.0
15.3
13.6
11.9
10.2
. 8.5
i
6.8
5.1
3.4
1.7
0.0
Cahaba River AL (CONTROL)
Run on 03-8-08 10:13 AM
Obs Corbicula (g/m2dry)
• Caddisfly,Tric (g/m2 dry)
• Corbicula (g/m2 dry)
Mussel (g/m2 dry)
Obs Snails (g/m2 dry)
Mayfly (Baetis (g/m2 dry)
Gastropod (g/m2 dry)
Obs Mayfly (g/m2 dry)
Obs Caddisfly (g/m2 dry)
2/26/2000 8/26/2000 2/24/2001 8/25/2001 2/23/2002 8/24/2002
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
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Figure 69. Predicted Process Rates for the Invasive Clam Corbicula, Expressed as Percent of Biomass;
Yellow Spikes are Entrainment During Storm Events; Consumption Depends on Sloughing Periphyton..
30.0
27.0
24.0
21.0
18.0
15.0
12.0
9.0
6.0
3.0
0.0
u^
Cahaba River AL (CONTROL)
Run on 03-8-08 10:13 AM
12/5/2000
12/5/2001
12/5/2002
• Corbicula Load (Percent)
• Corbicula Consumption (Percent)
• Corbicula Defecation (Percent)
• Corbicula Respiration (Percent)
Corbicula Excretion (Percent)
Corbicula Scour_Entrain (Percent)
• Corbicula Predation (Percent)
Corbicula Mortality (Percent)
Corbicula GameteLoss (Percent)
Consumption, Defecation, Predation, and Fishing
Several formulations have been used in various models to represent consumption of prey,
reflecting the fact that there are different modes of feeding and that experimental evidence can be
fit by any one of several equations (Mullin et al., 1975; Scavia, 1979; Straskraba and Gnauck,
1985).
Ingestion is represented in AQUATOX by a maximum consumption rate, adjusted for ambient
food, temperature, oxygen, sediment, and salinity conditions, and reduced for sublethal toxicant
effects and limitations due to habitat preferences of a given predator:
Ingestion
prey, pred
= CMaxpred • SatFeeding • TCorr pred • FoodDilution
• HabitatLimit • ToxReduction • HarmSS • SaltEffect • O2EffectFrac • Biomass
(91)
pred
where:
Ingestionprey: pred
Biomass
CMax
SatFeeding
TCorr
FoodDilution
ToxReduction
= ingestion of given prey by given predator (g/m -d);
= concentration of organism (g/m3-d);
= maximum feeding rate for predator (g/g-d);
= saturation-feeding kinetic factor, see (93);
= reduction factor for suboptimal temperature (unitless), see Figure 57;
= factor to account for dilution of available food by suspended
sediment (unitless), see (120);
= reduction due to effects of toxicant (see (424), unitless); and
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION CHAPTER 4
HarmSS = reduction due to suspended sediment effects (see (116), unitless);
SaltEffect = effect of salinity on ingestion rate (unitless), see (440);
O2EffectFrac = effect of reduced oxygen on ingestion (unitless), see (205); and
HabitatLimit = in streams, habitat limitation based on predator habitat preferences
(unitless), see (13).
The maximum consumption rate is sensitive to body size, so an alternative to specifying CMax
for fish is to compute it using an allometric equation and parameters from the Wisconsin
Bioenergetics Model (Hewett and Johnson, 1992; Hanson et al., 1997):
CMax = CA • MeanWeighf8 (92)
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 = ^^ (93)
Zprey( Preference prey,pred-Food)+ FHalJSatpred
where:
Preference = preference of predator for prey (unitless);
Food = available biomass of given prey (g/m3);
FHalfSat = half-saturation constant for feeding by a predator (g/m3).
The food actually available to a predator may be reduced in two ways:
Food = (Biomassprey - BMinpred) • Refuge (94)
where:
Refuge = reduction factor for prey hiding in macrophytes (unitless).
BMin = minimum prey biomass needed to begin feeding (g/m3); and
Search or filtration may virtually cease below a minimum prey biomass (BMin) to conserve
energy (Figure 70), so that a minimum food level is incorporated (Parsons et al., 1969; Steele,
1974; Park et al., 1974; Scavia and Park, 1976; Scavia et al., 1976; Steele and Mullin, 1977).
However, some filter feeders such as cladocerans (for example, Daphnia) must constantly filter
because the filtratory appendages also serve for respiration; therefore, in these animals there is
no minimum feeding level and BMin is set to 0.
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
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Figure 70. Saturation-kinetic consumption
BASS CONSUMPTION
BASS BIOMASS = 1 g/cu m
0.03 T-C
0 2.65 5.3 7.9510.613.2515.918.55
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 (Figure 71):
Biomassua,
Macm + Hal/Sat
where:
Hal/Sat
Biomassuacro
Refuge = 1-
half-saturation constant (20 g/m ), and
biomass of macrophyte (g/m3).
Figure 71. Refuge from predation
(95)
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
97
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION CHAPTER 4
(Bloomfield et al., 1973; Park et al., 1974; Canale et al., 1976; Scavia et al., 1976). Higher
values indicate increased preference by a given predator for a particular prey compared to the
preferences for all possible prey. In other words, the availability of the prey is weighted by the
preference factor.
The preference factors are normalized so that if a potential food source is not modeled or is
below the BMin value, the other preference factors are modified accordingly, representing
adaptive preferences:
Pref
r* f ** prey, pred sf\s-\
Preference re red = LJ1L— (96)
SumPref
where:
Preferencepreyipred = normalized preference of given predator for given prey
(unitless);
PrefPrey, pred = initial preference value from the animal parameter screen
(unitless); and
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 (153) and (154)), is indicated by a matrix of egestion
coefficients with the same structure as the preference matrix, so that defecation is computed as
(Parketal., 1974):
Defecation pred = ^prey ( EgestCoeff prey pred • Ingestion prey pred + IncrEgest • IngestNoTox ) (97)
where:
Defecationpred = total defecation for given predator (g/m3-d);
Ingestionprey, pred = ingestion of given prey by given predator (g/m3-d) (91);
EgestCoeffVKJr pred = fraction of ingested prey that is egested (unitless); and
IncrEgest = increased egestion due to toxicant (see Eq. (425), unitless);
Ingest^oTox = ingestion excluding toxic effects, calculated as Ingestion
divided by ToxReduction (see Eq. (424), g/m3-d).
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:
Consumption pred = ^prey (Ingestion prey pred) (98)
Predation p^ = l>pred (Ingestion prey pred) (99)
where
Consumption^ = total consumption rate by predator (g/m3-d); and
Predationprey = total predation on given prey (g/m3-d).
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION CHAPTER 4
Fishing pressure is represented simply as a fraction of biomass removed each day. A future
model enhancement will allow for temporally variable fishing pressures to better reflect
harvesting seasons.
Respiration
Respiration can be considered as having three components (Cui and Xie, 2000), subject to the
effects of salinity:
Respiration pred = \StdResppred + ActiveResp pred + SpecDynAction pre J • SaltEffect (100)
where:
Respirationpred = respiratory loss of given predator (g/m3-d);
StdResppred = basal respiratory loss modified by temperature (g/m3-d); see
(101);
ActiveResppred = respiratory loss associated with swimming (g/m3-d), see (104);
SpecDynActionpred = metabolic cost of processing food (g/m3-d), see (110); and
SaltEffect = effect of salinity on respiration (unitless), see (440).
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. AQUATOX
simulates standard respiration as a basal rate modified by a temperature dependence and, in fish,
a density dependence (see Kitchell et al., 1974):
StdResppred = BasalResp pred • TCorr pred • Biomass pred • DensityDep (101)
where:
BasalResppred = basal 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 Figure 57;
Biomasspred = concentration of predator (g/m3); and
DensityDep = density-dependent respiration factor used in computing standard
respiration, applicable only to fish (unitless). See (109)
As an alternative formulation, 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):
StdResppred = BasalResppred • MeanWeight predm'"d. TFnpred • Biomasspred • DensityDep (102)
where:
MeanWeightpred = mean weight for a given fish (g);
d = slope of the allometric function for a given fish;
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION CHAPTER 4
TFripred = temperature function (unitless).
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;
Hanson et al., 1997). However, the basal respiration rate in that model is expressed as g of
oxygen per g organic matter of fish per day, and this has to be converted to organic matter
respired:
BasalResp pmd = RApred • 1.5 (103)
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 Q^)
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:
ActiveResp pred = Activity pred • Biomasspred (104)
where:
Activitypred = activity factor (g/g-d).
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:
,= e(RQ.Temp) (jg^
where:
RQ = the Qio or rate of change per lOdeg. C for respiration (1/deg. C);
Temp = ambient temperature (deg. C).
This is coupled with a complex function for swimming speed as an allometric function of
temperature (Hewett and Johnson, 1992; Hanson et al., 1997):
Activity pred = e(RTO-Vel)
lfTemp>RTL Then Vel = RKl • MeanWeightRK4 (106)
Else Vel = ACT • MeanWeightRK4 • Q(BACT'Temp}
where:
RTO = coefficient for swimming speed dependence on metabolism (s/cm);
RTL = temperature below which swimming activity is an exponential function of
temperature (deg. C);
Vel = swimming velocity (cm/s);
RK1 = intercept for swimming speed above the threshold temperature (cm/s);
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION CHAPTER 4
RK4 = weight-dependent coefficient for swimming speed;
ACT = intercept for swimming speed for a 1 g fish at deg. C (cm/s); and
BACT = coefficient for swimming at low temperatures (1/deg. C),
Equation Set 2 uses the Stroganov function used elsewhere in AQUATOX:
TFn = TCorr (107)
and activity is a constant:
Activity = ACT (108)
where:
TCorr = reduction factor for suboptimal temperature (unitless), see (59);
ACT = activity factor, which is not the same as ACT'm Equation Set 1 (g/g-d).
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):
rx • ^ , IncrResp • Biomass ^««^
DensityDep = 1 + (109)
7>""'/"* / r7~\ if
KCap I ZMean
where:
IncrResp = increase in respiration at carrying capacity (0.5);
KCap = carrying capacity (g/m2);
ZMean = mean depth from site underyling data (m).
With the IncrResp value of 0.5, respiration is increased by 50% at carrying capacity (Kitchell et
al., 1974), as shown in Figure 72. This density-dependence is used only for fish, and not for
invertebrates.
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
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Figure 72. Density-dependent factor for increase in respiration as fish
biomass approaches the carrying capacity (10.0 in this example).
1.6
jj 1.5
'E 1.4
& 1-3
Q
£• 1.2
§ 1.1
4 6
Biomass (g/m3)
10
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):
SpecDynAction = KResp • (Consumption - Defecation )
(110)
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) see (98); and
DefecationpKd = egestion of unassimilated food (g/m3-d), see (97).
Excretion
As respiration occurs, biomass is lost and nitrogen and phosphorus are excreted directly to the
water (Home and Goldman 1994); see (169) and (183). 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:
where:
Excretionpred
KExCrpred
Respirationpreci
Excretionpred = KExcr pred • Respiration
pred
(111)
excretion rate (g/m -d);
proportionality constant for excretion:respiration (unitless);
respiration rate (g/m3-d), see (100).
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION _ CHAPTER 4
Excretion is approximately 17 percent of respiration, which is not an important biomass loss
term for animals, but it is important in nutrient recycling. All biomass lost due to animal
excretion is assumed to convert to dissolved labile detritus, see (151).
Nonpredatory Mortality
Nonpredatory mortality is a result of both environmental conditions and the toxicity of
pollutants:
Mortality pred = Dpred • Biomass pred + Poisoned pred + MortAmmonia
+ MortSedEffects + MortSalimty
where:
Mortalitypred = nonpredatory mortality (g/m3-d);
Dpred = environmental mortality rate; the maximum value of (113) and
(114), is used (1/d);
BiomasSpred = biomass of given animal (g/m3);
Poisoned = mortality due to toxic effects (g/m3-d), see (417);
MortAmmonia = ammonia mortality, (g/m3-d), see (179);
MortiovO2 = low oxygen mortality, (g/m3-d), see (203); and
MortsedEffects = mortality from suspended sediments, (g/m3-d), see (115)
= mortality from salinity , (g/m3-d), see (112)
Under normal conditions a baseline mortality rate is used:
Dpred = KMortpred (1 13)
where:
= normal nonpredatory mortality rate (1/d).
An exponential function is used for temperatures above the maximum (Figure 73):
Temperature -TMaXpred
Dpred = KMortpred + - T - (1 1 4)
where:
Temperature = ambient water temperature (°C); and
= maximum temperature tolerated (°C).
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Figure 73. Mortality as a function of temperature
MORTALITY OF BASS
, 1
1
£°8
Q.
D nfi
LU U.O
_j
|0.4-
O
i~ n ?
o u-^
-------
AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
CHAPTER 4
at this time.
Reduction in feeding occurs in game fish due to visual impairment (Crowe and Hay 2004). SS
of 25 mg/L seems to be threshold for response (Rowe et al. 2003). The general equation (115) is
used to represent a decrease in food due to turbidity, but without the exposure factor because the
response is instantaneous:
HarmSS = SlopeSS • \n(SS) + InterceptSS
(116)
where:
HarmSS
SlopeSS
SS
InterceptSS =
reduction factor for impairment of visual predation (unitless)
slope for suspended sediment response (-0.36, unitless)
suspended inorganic sediment concentration (mg/L). If TSS is
modeled see (244) otherwise, the sum of inorganic sediments in
the water column (e.g. Sand+Silt+Clay);
intercept for suspended sediment reponse (2.11, unitless)
The equation is parameterized using data for coho salmon with 1-hr exposure (Berry et al. 2003).
It was verified with numerous other qualitative observations for salmon, Arctic grayling, and
trout (Berry et al. 2003). This equation is used for all visual-feeding fish, especially game fish.
The user has the option of turning on this factor
Figure 74. Reduction in feeding by coho salmon (Oncorhynchus kisutch)
due to suspended sediments. Data from (Berry et al. 2003).
Reduced Feeding in Salmon
0
400
For modeling lethal effects, mortality can occur in fish over a range of suspended sediments.
Because of the lack of suitable quantitative data, these responses are divided into sensitivity
categories specific to this model and differing from Clarke and Wilber (2000) with parameters
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION _ CHAPTER 4
for surrogate species that can be considered representative for groups of organisms. The factor
also can be turned off for those organisms that are completely insensitive.
Tolerant
This category represents those species having a 24-hr LCio > 5000 mg/L SS. Generally, these
are benthic species exposed to the flocculent zone and bottom sediments. The general equation
(115) is parameterized to accommodate the 24-hr lethality observations and is extended to other
times of exposure by fitting to observed 48-hr lethal responses:
LethalSS = l.62-\n(SS) - 14.2 + 3.5-ln(r£^) (117)
where:
LethalSS = cumulative fraction killed by given exposure to a given suspended
sediment concentration (fraction/d)
TExp = time of exposure to given level of suspended sediment (d)
SS = minimum suspended inorganic sediment concentration over
exposure time (mg/L). If TSS is modeled see (244) otherwise, the
sum of inorganic sediments in the water column (e.g.
Sand+Silt+Clay).
The parameters are based on the benthic estuarine fish spot (Leiostomus xanthums), using data
compiled in Berry et al. (2003).
Due to lack of data beyond 48 hours, this equation is applied using one- and two-day exposure
times only. The maximum effect is chosen from these two equation results.
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Figure 75. Lethality of suspended sediments to spot (Leiostomus xanthurus),
a tolerant species, based on data compilation of Berry et al. (2003).
Fraction Killed
Spot Mortality
1.00 n
0.80
0.60
0.40
0.20
0.00
(
,
/
f /
1 /
) 2000 4000 6000 8000 10000 12000
SS (mg/L)
• SS 24-hr « SS 48-hr • SS 24-hr Est
A SS 48-hr Est Log. (SS 24-hr) Log. (SS 48-hr)
Sensitive
This category represents those species having 250 mg/L < 24-hr LCio <5000 mg/L SS. Small
estuarine species seem to be highly sensitive to suspended sediment (Figure 80). The general
parameters are based on a composite fit to data for bay anchovy, menhaden, and Atlantic
silversides taken from a compilation by Berry et al. (2003). The equation is:
LethalSS = 0.34 • \n(SS) -1.85 + 0.1- \n(TExp)
(118)
This equation is applied using one- and two-day exposure times along with effects from one,
two, and three weeks exposure. The maximum effect is chosen from these multiple calculations.
Figure 76 illustrates the response curve for white perch. The equation exhibits good extension to
juvenile rainbow trout with a 28-d exposure to SS (Figure 77) and Chinook salmon with a 1.5-d
exposure (Figure 78). In both cases the equation is slightly over-protective, but that is
considered appropriate.
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Figure 76. Lethality of suspended sediments to white perch (Morone americana),
a sensitive species, based on data compilation of (Berry et al. 2003).
White Perch Mortality, 24-hr
0 1000
* Observed
2000
SS (mg/L)
3000
4000
Figure 77. Lethality of suspended sediments to juvenile rainbow trout (Oncorhynchus
mykiss) using parameters for sensitive species. Data from Berry et al. (2003).
Fraction Killed
Juvenile Rainbow Trout Mortality, 19-d,
1.00 n
0.80
0.60
0.40
0.20
0.00
(
•1
•
^^—
r*
»
) 200 400 600 800 1000
-0.20 J
SS(mg/L)
• Obs « Est Log. (Obs)
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Figure 78. Lethality of suspended sediments to Chinook salmon (Oncorhynchus
tshawytscha) using parameters for sensitive species. Data from Berry et al. (2003).
Chinook Salmon Mortality, 36-hr
10000 20000 30000 40000
SS (rng/L)
50000
Obs1.5d
Est 1.5 d
•Trend
Highly Sensitive
This category represents those species having a 24-hr LCio < 250 mg/L SS. Small estuarine
species seem to be highly sensitive to suspended sediment (Figure 80). The general parameters
are based on a composite fit to data for bay anchovy, menhaden, and Atlantic silversides taken
from a compilation by (Berry et al. 2003). The equation is:
LethalSS = 0.328 • \n(SS) -1.375 + 0.1 • In(ZExp)
(119)
This equation is applied using one and two day exposure times along with effects from one two
and three weeks exposure. The maximum effect is chosen from these multiple calculations.
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Figure 79. Three dimensional plot of equation for highly sensitive fish
-\ -
o-
c?
CO
U-
Although not verified with observed data from longer exposure periods, the equation appears to
be robust; it yields reasonable predictions of mortality for a range of SS concentrations and
exposure periods.
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
CHAPTER 4
Figure 80. Response of bay anchovy to SS. Data from (Berry et al. 2003)
Composite of Highly Sensitive Spp., 24-hr
100% n
00% •*• ••• •*•
80%
70%
R0%
50%
40%
-3n%
?0%
10%
0%
^--^
^^^^
^^^
>/*
s
/
/ y = 0.3278Ln(x) - 1.3751
/ R2 = 0.7125
A / A A
7
0 200 400 600 800 1000 1200
TSS
Sediment Effects on Filter Feeders
Sediments can clog filter-feeding apparatuses in invertebrates and some fish. A 25% reduction
in feeding in Daphnia occurs with SS of 6 NTU (-22 mg/L) (Henley, 2000); rotifers are not
affected (Rowe et al. 2003). Equation (116) can be parameterized to reflect the Daphnia
response (SlopeSS = -0.46 and InterceptSS = 2.2, Figure 81).
Figure 81. Reduction in feeding by Daphnia due to suspended sediments.
Points represent LC75 and supposed LC50, and LC5 values
HarmSS Reduction
1 n
n Q
n R
n 7
n R
n 5
o 4
n 3
n ?
n 1
n
Reduced Feeding in Daphnia
\
\
\
X
V
X
x^
^x^
^^^^^
^^>
0 20 40 60 80 100 120
SS (mg/L)
Ill
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Increased turbidity can inhibit feeding by mussels; 600 to 750 mg SS/L reduced clearance rates
in several mussel species (Henley et al. 2000). This can be used to parameterize Equation (116)
(SlopeSS=-OA7 andInterceptSS = 3.1, Figure 82).
Figure 82. Reduction in clearance of sediment by freshwater mussels due to
suspended sediments. Points represent supposed LC95, LC50, and LC10 values.
Reduced Clearance in Mussels
1 -,
V)
.4
.2
200
400
SS (mg/L)
600
800
Reduced pumping was observed at SS > 1000 mg/L in the Eastern oyster (Berry et al. 2003).
This too can be used to parameterize Equation (116). (SlopeSS = -0.61 and InterceptSS = 4.72,
Figure 83).
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Figure 83. Reduced pumping in Eastern oysters (Crassostrea virginica).
Points represent supposed LC90, LC50, and LC5 values.
o
•5
3
1?
W
E
I
Reduced Pumping in Oysters
^ n x
n Q
n R
07
n R
0 5
04
0 "}
0 2
n 1
n _
\
\
\
\
X
\
\
'V
xv
^s.
^v.
^*s
0 500 1000 1500 2000 2500
SS (mg/L)
A related factor, which is treated separately in the model, is the degree to which there is dilution
of food by inorganic particles, offset by selective sorting of particles and feeding (Henley, 2000).
Mytilus edulis., the blue mussel, and Crassostrea virginica, the Eastern oyster, actively sort
particles; their food intake should not be affected by SS until very high levels that clog the filter
feeding mechanism are reached. In contrast, there is limited selective feeding among many
clear-water clams, including the surf clam Spisula solidissima, the Iceland scallop Chlamys
islandica, and probably many of the endangered freshwater mussels (Henley, 2000). The
dilution of available food for both filter feeders and grazers decreases as a proportionate function
of sediment corrected for the degree to which there is selective feeding (Figure 84):
FoodDilution =
Food
Food + Sed • Proportion • (1 - Sorting)
(120)
where:
FoodDilution =
Food =
Sed
Sorting =
Proportion =
factor to account for dilution of available food by suspended
sediment (unitless)
preferred food for filter feeders (mg/L) and for grazers (g/m2) (see
(94))
suspended sediment for filter feeders (mg/L) and deposited
sediment for benthic grazers (g/m2)
degree to which there is selective feeding (unitless)
proportionality constant, set to 0.01 for snails and grazers and set
to 1.0 for all other organisms, (unitless)
To account for the fact that snails and grazers feed on periphyton above the depositional surface,
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CHAPTER 4
a proportionality constant is utilized for those organisms.
The intermediate variable Sed depends on the computation of suspended sediment for filter
feeders and the computation of deposited sediment for benthic grazers. If the optional sediment
transport submodel (Section 6.1) is used then:
Sed = (Conc(Silt) + Conc(Clay)) or
Sed = (Deposit(Sili) + Deposit (Clay)) • Vol I Surf Area • 1000 • 1.0
where:
Sed
ConcSed
1000
Deposit^
Volume
SurfArea
1.0
(121)
suspended sediment for filter feeders (taxa = 'Susp. Feeder' or
'Clam' in units of mg/L or g/m3) and deposited sediment for
benthic grazers (taxa = 'Sed Feeder' or 'Snail' or 'Grazer' in units
of g/m2);
concentration of suspended silt or clay (mg/L) (224);
conversion factor for kg to g;
amount of sediment deposited (kg/m3 day) (230);
water volume, (m3);
surface area, (m2); and
days' accumulation of sediment (day)
If the sediment transport submodel is not used and TSS is used as a driving variable then
suspended sediment is computed for filter feeders. Additionally, when TSS is used as a driving
variable, deposited sediment (Sed) is calculated using the relationship shown in Figure 87.
Sed.
Suspended
= InorgSed
SedDeposaed=0.270\n(InorgSed60day)-0.072
(122)
where:
Sed
InorgSed
InorgSedt
60day
food dilution equation input (120), (mg/L or g/m );
suspended inorganic sediment computed from TSS (mg/L) (see
(244));
60 day average of suspended inorganic sediment computed from
TSS (mg/L) (see (244))
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Figure 84. The FoodDilution factor as a function of TSS with Food kept constant at 10
mg/L and with Sorting set to 0 and 0.5.
1.00 i
0
0.00
Sediment Dilution Factor
10
• Sorting = 0
• Sorting = 0.5
Continued high levels of SS can cause mortality in oysters as shown in Figure 85. However, this
can be interpreted as the natural consequence of reduced filtration as predicted by
parameterization of (115). Therefore, oyster mortality due to SS is not simulated separately.
Figure 85. Response of oysters to SS. Data from (Berry et al. 2003).
Fraction Killed
Eastern Oyster Mortality, 12-d Exposure
1 nn -•
n QO
0 80
n 7n
0 fiO
0 'SO
0 40
0 ^0
0 ?0
0 10
0 00
V
^^^"^
^4T
^
/*
/
r
/
j
T
0 1000 2000 3000 4000
SS (mg/L)
115
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
CHAPTER 4
Sediment Effects on Grazers
Sediment reduces preference of New Zealand mud snails and mayflies for periphyton (Suren
2005), which is ignored by the model. More important, the food quality of periphyton declines
linearly with increasing fine sediment content (Broekhuizen et al. 2001). This is represented as
food dilution by (120).
Riffle areas are degraded or lost by deposition of fine sediment, including sand (Crowe and Hay
2004). A 12-17% increase in fines in riffles areas resulted in 27-55% decrease in mayfly
abundance; this did not affect chironomids and simulids, and riffle beetles actually increased
(Crowe and Hay 2004). Drift rates doubled from 2.3%/d to 5.2%/d with a 16% increase in fine
interstitial sediments; chironomids and caddisflies were affected (Suren and Jowett 2001). This is
represented by a function in which the deposition rate is compared to a trigger value beyond
which there is accelerated drift:
where:
Drift
Dislodge
Drift = Dislodge • Biomass
loss of zoobenthos due to downstream drift (g/m3-d); and
fraction of biomass subject to drift per day (unitless).
(123)
Nocturnal drift is a natural phenomenon:
Dislodge = AvgDrift • AccelDrift
(124)
where:
AvgDrift
where:
AccelDrift
Deposit
Trigger
fraction of biomass subject to normal drift per day (unitless).
AccelDrift = e^p^-T"sg^
factor for increasing invertebrate drift due to sediment deposition
(unitless);
total rate of inorganic sediment deposition (kg/m2 day), (125b);
deposition rate at which drift is accelerated (kg/m2 day).
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
CHAPTER 4
Figure 86. AccelDrift as a function of depth-corrected
sediment deposition with Trigger = 0.2.
Drift as a Function of Sedimentation
2.500
0.000
0.2 0.4 0.6 0.8
Deposit (kg/m2 d)
1.2
The model computes daily sediment deposition rate based on suspended sediment using the
following relationship:
where:
Deposit
SS
Deposit = 2.70-\n(SS)
(125b)
total rate of inorganic sediment deposition (kg/m2 day), (125b);
suspended inorganic sediment concentration (mg/L). If TSS is
modeled see (244) otherwise, the sum of inorganic sediments in
the water column (i.e. Sand+Silt+Clay);
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION CHAPTER 4
Figure 87. Relationship of one-day sedimentation
to average TSS; data from Larkin and Slaney (1996)..
"° 1.20
1.40
1.18
y=0.2705ln(x)- 0.0723
"SB 1.00 R2 = 0.9712
•*
0.92
o.oo °'06
0 20 40 60 80
Mean Suspended Sediment (mg/L)
Ephemeroptera, Pteroptera, and Trichoptera (mayfly, stonefly, and caddisfly or EPT) diversity
declines when the fines (<0.25 mm) exceed 0.8% (Kaller and Hartman 2004). This change in
composition should result from proper parameterization of Equation (125).
Interstitial Sediments
Salmonid reproduction is adversely affected by deposition of fines, with 27% fines being a
threshold (Nelson and Platts, unpublished report, cited by Rowe et al. 2003). "Multiple age
classes of both salmonids and sculpins were uncommon where average instream surface fines
were greater than 30%, and nearly absent above 40%" (Rowe et al. 2003). Both the eggs and the
yolk-fry or alevins are sensitive to sedimentation of fines, including sand. Sedimentation in
spawning gravels can be related to average suspended sediment (TSS) concentrations (Larkin
and Slaney 1996). The relationship is logarithmic for average TSS over a 60-day period (Figure
88).
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
CHAPTER 4
Figure 88. Relationship of 60-day sedimentation to average TSS;
data from (Larkin and Slaney 1996).
o
500.00
400.00
~Z 300.00
OJ
£
in
•a
OJ
w
o
a.
OJ
Q
200.00
100.00
0.00
|y= 108.lln(x)-28.898
! R2 = 0.9712
: 471.86!
366.68
224.04
*" 221.13
23.07
10
100
Mean Suspended Sediment (mg/L)
A similar measure of fines is embeddedness, which is the extent to which sand, silt, and clay fill
the interstitial spaces among gravel and cobbles (Osmond et al. 1995). Good spawning substrate
is characterized as less than 25% embedded (Flosi et al. 1998). The data that allow us to predict
percent fines also yield an estimate of percent embeddedness (Figure 89), and that relationship is
used in the model. Although the training data only go to 34% embeddedness, the log
relationship using averaged data allows the regression to extend to any reasonable level of
suspended sediment. The user can enter an observed "baseline embeddedness" in the site record,
and that can be used as an initial condition. A corresponding embeddedness threshold value can
be entered in the animal record. If that value is exceeded then exclusion can be assumed
(mortality = 100%). Although this functionality is intended for salmonids, it can also apply to
other fish such as sculpins and to invertebrates that hide in the interstices. In practice, the
maximum 60-day moving average of suspended sediments is used to compute the percent
embeddedness; if the initial percent embeddedness is exceeded then the new simulated percent
embeddedness is used. The possibility of scour from a high-discharge event resetting the percent
embeddedness is ignored.
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION CHAPTER 4
Figure 89. Relationship of 60-day percent embeddedness to average TSS;
data from (Larkin and Slaney 1996).
40%
y=0.0777ln(x)-0.0208
R2 = 0.9712
5%
0% • "" -
0 50 100 150 200
Mean Suspended Sediment (mg/L)
Gamete Loss and Recruitment
Eggs and sperm can be a significant fraction of adult biomass; in bluegills these can be 13
percent and 5 percent, respectively (Toetz, 1967), giving an average of 9 percent if the
proportion of sexes is equal. Because only a small fraction of these gametes results in viable
young when shed at the time of spawning, the remaining fraction is lost to detritus in the model.
There are two options for determining the date or dates on which spawning will take place. A
user can specify up to three dates on which spawning will take place. Alternatively, one may use
a construct that was modified from a formulation by Kitchell et al. (1974). As a simplification,
rather than requiring species-specific spawning temperatures, it assumes that spawning occurs
when the temperature first enters the range from six tenths of the optimum temperature to 1° less
than the optimal temperature. This is based on a comparison of the optimal temperatures with the
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 + IncrMort + O2EffectFrac ) • FracAdults • PctGamete
JJ (126)
• SaltMort • Biomass
else GameteLoss = 0
where:
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Temperature =
TOpt
GameteLoss =
GMort
IncrMort =
O2EffectFrac =
PctGamete =
FracAdults =
SaltMort
Biomass =
ambient water temperature (°C);
optimum temperature (°C);
loss rate for gametes (g/m3-d);
gamete mortality (1/d);
increased gamete and embryo mortality due to toxicant (see (426),
1/d);
calculated fraction of gametes lost at a given oxygen concentration
and exposure time (1/d), see (205);
fraction of adult predator biomass that is in gametes (unitless); and
fraction of biomass that is adult (unitless);
effect of salinity on gamete loss rate (unitless), see (440); and
biomass of predator (g/m3).
As the biomass of a population reaches its carrying capacity, reproduction is usually reduced due
to stress; this results in a population that is primarily adults. Therefore, the proportion of adults
and the fraction of biomass in gametes are assumed to be at a maximum when the biomass is at
the carrying capacity (Figure 90):
Figure 90. 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
FracAdults = 1.0-
I Capacity
{KCap/ZMean ^
(127)
if Biomass > KCap / ZMean then Capacity = 0 else Capacity = KCap / ZMean - Biomass
where:
KCap = carrying capacity, the maximum sustainable biomass (g/m2);
ZMean = mean depth from site underyling data (m).
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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 gametes through recruitment:
Recruit = (1- (GMort + IncrMort)) • FracAdults • PctGamete • Biomass (128)
where:
Recruit = biomass gained from successful spawning (g/m -d).
Washout and Drift
Downstream transport is an important loss term for invertebrates. Zooplankton are subject to
transport downstream similar to phytoplankton:
where:
Washout = 1SC arge • Biomass (129)
Volume
Washout = loss of zooplankton due to downstream transport (g/m3-d);
Discharge = discharge (m3/d), see Table 3;
Volume = volume of site (m3), see (2); and
Biomass = biomass of invertebrate (g/m3).
Likewise, zoobenthos exhibit drift, which is detachment followed by washout, and it is
represented by a construct that is original with AQUATOX:
WashoutZoobenthos = Drift = Dislodge • Biomass (130)
where:
Drift = loss of zoobenthos due to downstream drift (g/m3-d); and
Dislodge = fraction of biomass subject to drift per day (unitless), see (131) and
(132)
Nocturnal drift is a natural phenomenon:
Dislodge = AvgDrift (131)
where:
AvgDrift = fraction of biomass subject to normal drift per day (unitless).
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 • MaxRate • e Oradual (132)
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where:
Entrainment
Biomass
MaxRate
Vel
VelMax
Gradual
entrainment and downstream transport (g/m -d);
biomass of given animal (g/m3);
maximum loss per day (1/d);
velocity of water (cm/s), (14);
velocity at which there is total loss of biomass (cm/s); and
slope of exponential, set to 25 (cm/s).
Figure 91. Entrainment of animals as a function of stream velocity
with VelMax of 400 cm/s
-Q
1
n s
0 6 -
04 -
0 2 -
/
/
/
/
/
/
/
/
/
_^/
0 100 200 300 400 500
Velocity (cm/s)
Entrainment is not applied to pelagic invertebrates as these organisms already passively wash out
of a system during a flood event (129).
Vertical Migration
When presented with unfavorable conditions, most animals will attempt to migrate to an adjacent
area with more favorable conditions. The current version of AQUATOX, following the example
of CLEANER (Park et al., 1980), assumes that zooplankton and fish will exhibit avoidance
behavior by migrating vertically from an anoxic hypolimnion to the epilimnion. AQUATOX
assumes that EC50growth is the best indicator of when the species has become so intolerant of the
oxygen climate that it is going to migrate. This also allows more tolerant species to spend more
time in the hypolimnion and less tolerant species to migrate earlier. 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
(133)
Migration =
HypVolume • Biomasspn
pred, hypo
Epi Volume
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where:
VSeg = vertical segment;
Hypo = hypolimnion;
Anoxic = boolean variable for anoxic conditions when O2 < EC50grawth,
Migration = rate of migration (g/m3-d);
HypVolume = volume of hypolimnion (m3), see Figure 36;
EpiVolume = volume of epilimnion (m3), see Figure 36; and
Biomasspred,hypo = biomass of given predator in hypolimnion (g/m3).
In the estuarine model, fish will also migrate vertically based on salinity cues (see Section 10.5).
In the linked-segment version of AQUATOX, fish will vertically migrate to achieve equality on
a biomass basis if the system becomes well mixed (see Section 3.).
Migration Across Segments
To simulate seasonal migration patterns animals may be set up to move from one segment to
another during a multi-segment model run. Animals may migrate to or from a segment on any
date of the year to represent an appropriate seasonal pattern; however, reaches must be linked
together with "feedback links" for migration to be enabled. The user must specify the date on
which migration occurs, the fraction of the state variable's concentration expected to migrate,
and the segment(s) involved. The calculation of state variable movement to and from each
segment must be normalized to the volume of water in the destination segment:
MigrationFromSeg = ConcSourceSeg
FracMoving
(134)
Migration
ConcSourceSeg • VolumeSourceSeg • FracMoving
ToSeg
Volume
(135)
Destination
where:
MigrationFromseg = loss of state variable in source segment (mg/LSourceSeg'd);
MigrationToSeg = gain of state variable in destination segment (mg/
Concsegment = concentration of state variable in given segment (mg/L);
Volume segment = volume of given segment (m3);
FracMoving = user input fraction of animals migrating on given date (unitless);
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Promotion and Emergence
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 = KPropred' (Consumption - Defecation - Respiration - Excretion - GameteLoss) (136)
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 (98);
Defecation = rate of defecation (g/m3-d), see (97);
Respiration = rate of respiration (g/m3-d), see (100);
Excretion = rate of excretion (g/m3-d), see (111); and
GameteLoss = loss rate for gametes (g/m3-d), see (126).
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:
If Temperature > (0.8 • TOpt} and Temperature < {TOpt -1.0) then
(137)
Emergelnsect = 2 • Promotion
where:
Emergelnsect = insect emergence (mg/L-d);
Temperature = ambient water temperature (°C); and
TOpt = optimum temperature (°C);
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION _ CHAPTER 4
Because emergence is a function of the organism's growth rate, if the temperature passes through
the optimal temperature interval while the growth rate of the organism is zero or below zero,
emergence of insects does not occur.
4.4 Aquatic-Dependent Vertebrates
Herring gulls and other shorebirds were added to AQUATOX Release 3 as a bioaccumulative
endpoint — not as a dynamic variable but as a post-processed variable reflecting dietary exposure
to a contaminant. In fact, the endpoint can be used to simulate bioaccumulation for any aquatic
feeding organism, such as bald eagles, mink, and dolphins, provided that the organism feeds
exclusively on biotic compartments modeled within AQUATOX. The user can specify a
biomagnification factor (BMP) and the preferences for various food sources so that alternate
exposures can be computed. Dietary preferences are input as fraction of total food consumed by
the modeled species and are normalized to 100% when the model is run.
The concentration of each chemical is based on the chemical concentration in prey at a given
time-step.
PPBBirdTmicant = :Pre/Prey.BMFTm.PPBPreyJm (138)
z=l
where:
PPBBirdToXicant = estimated concentration of this toxicant in bird or other organism
= biomagnification factor for this chemical in bird or other organism
(unitless);
PPBpreyjox = concentration of this chemical in prey (ug/kg), see (310).
Uptake of toxicant is assumed to be instantaneous, but depuration of the chemical is governed by
the user-input clearance rate. If the concentration of chemical is declining in shorebirds (due to
the concentrations of the chemical declining in prey), the lowest the chemical concentration in
birds can fall to at any time is calculated as follows:
PPBBirdLowestJOX = PPBBird^ (1 - ClearTox ) AJ (139)
where:
PPBBirdiowestjox = lowest cone, of this toxicant in gulls or other organism at this time-
step (ug/kg);
PPBBirdTox,t-i = concentration of this toxicant in in the previous time-step (ug/kg);
ClearTox = clearance rate for the given toxicant, (I/day)
4.5 Steinhaus Similarity Index
Within the differences graph portion of the output interface, a user may select to write a set of
Steinhaus similarity indices in Microsoft Excel format. The Steinhaus index (Legendre and
Legendre 1998) measures the concordance in values (usually numbers of individuals, but
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION CHAPTER 4
biomass in this application) between two samples for each species. Typically it is computed from
monitoring data from perturbed and unperturbed, or reference, sites. When calculated by
AQUATOX it is a measure of the difference between the control and perturbed simulations. A
Steinhaus index of 1.0 indicates that all species have identical biomass in both simulations (i.e.,
the perturbed and control simulations); an index of 0.0 indicates a complete dissimilarity
between the two simulations.
The equation for the Steinhaus index is as follows:
" /
2 • £ mm(Biomass t control , Biomass t h
S = ^ : :—
s, control + Biomass t perturbed)
'•=1 (140)
where:
S = Steinhaus similarity index at time t;
Biomass i_controi = biomass of species i, control scenario at time t;
Biomass i_perturbed = biomass of species i, perturbed scenario at time t.
A time-series of indices is written for each day of the simulation representing the similarity on
that date. Separate indices are written out for plants, all animals, invertebrates only, and fish
only.
4.6 Biological Metrics
Ecological indicators are defined as primarily biological and are measurable characteristics of the
structure, composition, and function of ecological systems (Niemi and McDonald 2004). The
term "indicator" as used by Niemi and McDonald is a rather broad one, and includes two terms
often used within the biocriteria program, "metric" and "index". A biological metric is a
numerical value that represents a quantitative community parameter, such as species diversity,
or percent EPT (see below). A multimetric index is a number that integrates several metrics to
express a site's condition or health, such as an IBI (Index of Biological Integrity). AQUATOX
has the ability to calculate numerous metrics, some of which can be compared to similar metrics
derived from monitoring data. However, there are limitations in the application of many such
metrics that reflect the differing capabilities of simulation models as opposed to field studies.
Models can predict continuing complex responses to changing conditions, while field
measurements usually represent snapshots of existing conditions with limited empirical
predictive power. Aquatic models have limited taxonomic resolution and usually represent
biomass; most metrics and indices applied in the field are based on detailed taxonomic
identifications and involve counting the numbers of individual organisms per sample. Therefore,
only a subset of possible indicators can be implemented with AQUATOX; however, given the
biologic realism of the model, the list is much more extensive than for other models.
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION CHAPTER 4
Biotic metrics and indices have been widely used for several decades, stimulated in part by
inclusion in rapid bioassessment protocols (RBP) by the US EPA (Plafkin et al. 1989). Most are
applicable to streams and wadeable rivers (Barbour et al. 1999), though there is a suite of
indices (the trophic state indices) that were developed as a measure of eutrophication in lakes.
Metrics can be calculated for algae, which indicate short-term impacts; macroinvertebrates,
which integrate short-term impacts on localized areas; and fish, which are indicators of long-term
impacts over broad reaches (Barbour et al. 1999).
Ecological indicator measures fall into several well defined categories. Those metrics that are
presently calculated in AQUATOX are shown below in boldface; the others enumerated here can
be calculated offline using exported Excel output files:
• Composition—many metrics related to community composition are suitable for
simulation with AQUATOX by selecting the appropriate "Benthic metric designation"
category on the underlying data screen; they include:
o % EPT (the following three combined) (Barbour et al. 1999)
• % Ephemeroptera (mayfly larvae) (Maloney and Feminella 2006)
• % Plecoptera (stonefly larvae) (Barbour et al. 1999)
• %Trichoptera (caddisfly larvae) (Barbour et al. 1999)
o % chironomids (midge larvae) (Barbour et al. 1999)
o % oligochaetes (aquatic worms) (Barbour et al. 1999)
o % Corbicula (invasive Asian clam) (Barbour et al. 1999)
o % Eunotia (interstitial diatom characteristic of low-nutrient conditions) (Lowe et
al. 2006)
o % blue-greens (cyanobacteria characteristic of high-nutrient, turbid conditions)
(Trimbee and Prepas 1987).
• Trophic—these include metrics that can be calculated from AQUATOX output:
o Periphytic chlorophyll a (Barbour et al. 1999)
o Sestonic chlorophyll a (Barbour et al. 1999)
o % predators (can apply to both macroinvertebrates and fish) (Barbour et al. 1999)
o % omnivores (best applied to fish in AQUATOX) (Barbour et al. 1999)
o % forage or insectivorous fish (Barbour et al. 1999)
• Trophic state—surrogates for lake and reservoir algal biomass adjusted to a common
scale (Gibson et al. 2000):
o TSI(TN) (total nitrogen)
o TSI(SD) (Secchi depth)
o TSI(CHL) (chlorophyll a)
o TSI(TP) (total phosphorus)
• Ecosystem bioenergetic—whole ecosystem metrics:
o Gross primary productivity, GPP (g O2/m2 d) (Odum 1971), more meaningful
if expressed as an annual measure (g O2/m2 yr) (Wetzel 2001)
o Community respiration, R (g O2/m2 d) (Odum 1971), more meaningful if
expressed as an annual measure (g O2/m2 yr) (Wetzel 2001)
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION CHAPTER 4
o P/R (ratio of GPP to community respiration) (Odum 1971)
o Turnover time (P/B, ratio of GPP to biomass in days) (Odum 1971)
In addition to those listed above, there are several ecological indicators that are not suitable for
simulation modeling in general or for AQUATOX in particular:
• Richness—these are based on numbers of observed taxonomic groups and are not
suitable for simulation modeling;
• Tolerance/intolerance—based on number of tolerant or intolerant species and therefore
unsuitable for modeling;
• Life cycle—percent of organisms with short or long life cycles, not easily modeled with
AQUATOX.
The trophic state indices are applicable to lakes and reservoirs. They are lognormal-transformed
values that attempt to convert environmental variables to a common value representing algal
biomass (Gibson et al. 2000):
Secchi Depth (m): TSI (SD) = 60 - 14.41 ln(SD)
Chlorophyll a (ug/L): TSI (CHL) = 9.81 In(CHL) + 30.6
Total Phosphorus (mg/L): TSI (TP) = 14.42 ln(TP) +4.15
Total Nitrogen (mg/L): TSI(TN) = 54.45 + 14.43 ln(TN)
The user can specify over what time period the indices are averaged. This enables better
comparison with field-derived TSIs, which are generally calculated from samples taken during
the growing season.
Obviously, chlorophyll a is the best representation of algal biomass, and that metric should be
used in determining the trophic state of a lake or reservoir (Table 8). However, comparing the
TSIs is also informative (Table 9).
The bioenergetic metrics are widely used by ecologists and have practical value as indicators of
accumulating organic matter (Odum 1971) and response to watershed disturbance (Dale and
Maloney 2004).
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CHAPTER 4
Table 8. Changes in Temperate Lake Attributes According to Trophic State
(Gibson et al. 2000, adapted from Carlson and Simpson 1996).
TSI
Value
<30
30-40
40-50
50-W
60-70
70-eo
>80
SD
(m)
>8
e-4
4-2
2-1
0.5-1
0.25-
0.5
<0.25
TP
(WHO
<6
6-12
12-24
24-48
4fl-96
§6-192
192-
3B4
Attributes
Oligoiropny: Clear
water, oxygen
throughout ihe year in
the riypolirrinion
Hypolimnia of shallower
lakes may become
anoxic
Mesolrophy: Water
moderately clear but
increasing probability of
hypolirnnetic anoxia
during summer
Eutroptiy: Anoxic
hypolimnia, macrophyte
problems possible
Blue-green algae
dominate, algal scums
and macroptiyta
problems
Hypereutrophy (light
limited). Dense algae
and macropnytes
Algal scums, tew
macraphytes
Water Supply
Iron and manganese
evident during the
summer. 'THM
precursors exceed
0.1 mg/L and turbidity
>1 NTU
Iron, manganese.
taste, and odor
problems worsen
Recreation
Weeds, algal
scums, and
low
transparency
discourage
swimming
and boating
Fisheries
Salmon id
fisheries
dominate
Salrnonid
fisheries in
deep lakes
Hypolimnetic
anoxia
results in
loss of
saJmonids.
W alleys may
predominate
Warm-water
fisheries
only. Bass
may be
dominant
Rough fish
dominate,
summer fish
kills possible
Table 9. Conditions Associated with Various Trophic State Index Variable Relationships
(Gibson et al. 2000).
Relationship Between TSI Variables
Conditions
TSI (CHL) = TSI(CHL) =TSI(SD>
TSI(CHL) > TSI(SD)
TSI(TP) =TSI(SD) >TS1{CHL)
TSI(SD)=TSI(CHL)>TSI(TP)
TSI(TP) >TSI(CHL) =TSI(SD)
Algae dominate light attenuation
Large particulates. such as Aphanizomenon flakes.
dominate
Nonalgal particulates or color dominate light attenuation
Phosphorus limits algal biomass (TN/TP ratio greater than
33:1)
Zooplankton grazing, nitrogen, or some factor other than
phosphorus limits algal biomass
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5. REMINERALIZATION
5.1 Detritus
For the purposes of AQUATOX, the term "detritus" is used to
include all non-living organic material and associated
decomposers (bacteria and fungi). As such, it includes both
particulate and dissolved material in the sense of Wetzel (1975),
but it also includes the microflora and is analogous to
"biodetritus" of Odum and de la Cruz (1963) . Detritus is
modeled as eight compartments: refractory (resistant) dissolved,
suspended, sedimented, and buried detritus; and labile (readily
decomposed) dissolved, suspended, sedimented, and buried
detritus (Figure 92). 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 biochemical 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 92. Detritus compartments in AQUATOX
Detritus: Simplifying Assumptions
• Refractory detritus does not
decompose directly but is
converted to labile detritus through
colonization
• Detrital sedimentation is modeled
with simplifying assumptions
(unless the sediment submodel for
streams is included)
• Biomass of bacteria is not
explicitly modeled
detr.
fm.
detr. ^
~fE L^>
s
detr.
ex
* c
Refractory
Dissolved
Refractory
Suspended
colonisation
"^X
colonization r^
u-~
ingestion r~__
U-" *
Labile
Dissolved
Labile
Suspended
A sedimentation A sedimejit.
co[ir y sco[jr y
Refractory
Sediments
A burial
po|sure y
Refractory
Buried
colonization ^
L----
ingestion r-^
U-"*
ex
Labile
Sediments
A bujial
Dopjre y
Labile
Buried
^ detr.
~^fhi~
decomp.i--^ .
^detr^
~~-Tm~
ingestion ^^
decomp.[~~-^ +
ation
.^ detr.
"^fm"
ingestion ^ ^
decomp.r-^ ,
onnection to detritivores + connection to nutrients
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION CHAPTER 5
The concentrations of detritus in these eight compartments are the result of several competing
processes:
dSuspRefrDetr T ,. ^ „ _ , . Tir , Tir , .
— = Loading + DetrFm - Colonization - Washout + Washm
dt (141)
- Sedimentation - Ingestion + Scour ± Sinking ± TurbDiff ± DiffusionSeg
dSuspLabDetr , ^ „ _ , ^
= Loading + Detrrm + Colonization - Decomposition
dt
- Washout +Washin- Sedimentation -Ingestion + Scour (142)
+ Sinking ± TurbDiff ± DiffusionSeg
dDissRefrDetr , ^ „ _ , TTr , TTr ,
= Loading + Detrrm - Colonization - Washout + Washm
dt (143)
+ TurbDiff±DiffusionSeg
dDissLabDetr T ,. ^ „ ^ . . Tir , Tir , .
= Loading + DetrFm - Decomposition - Washout + Washm
dt (144)
+ TurbDiff + Diffusion Seg
dSedRefrDetr T ,. ^ „ 0 ,. . „
= Loading + DetrFm + Sedimentation + Exposure
dt * P (145)
- Colonization - Ingestion - Scour - Burial
dSedLabileDetr , ^ „ 0 , _ ,
= Loading + Detrrm + Sedimentation + Colonization
dt S (146)
- Ingestion - Decomposition - Scour + Exposure - Burial
dBuriedRefrDetr 0 , , 0 „ ^ .-^
= Sedimentation + Burial - Scour - Exposure (147)
dt
dBuriedLabileDetr 0 , , 0 „
= Sedimentation + Burial - Scour - Exposure
dt (148)
where:
dSuspRefrDetr/dt = change in concentration of suspended refractory detritus
with respect to time (g/m3-d);
dSuspLabileDetr/dt = change in concentration of suspended labile detritus with
respect to time (g/m3-d);
dDissRefrDetr/dt = change in concentration of dissolved refractory detritus
with respect to time (g/m3-d);
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
CHAPTER 5
dDissLabDetr/dt
dSedRefrDetr/dt
dSedLabileDetr/dt
dBuriedRefrDetr/dt
dBuriedLabileDetr/dt
Loading
DetrFm
Colonization
Decomposition
Sedimentation
Scour
Exposure
Burial
Washout
Washin
Diffusionseg
Ingestion
Sinking
TurbDiff
change in concentration of dissolved labile detritus with
respect to time (g/m3-d);
change in concentration of sedimented refractory detritus
with respect to time (g/m3-d);
change in concentration of sedimented labile detritus with
respect to time (g/m3-d);
change in concentration of buried refractory detritus with
respect to time (g/m3-d);
change in concentration of buried labile detritus with
respect to time (g/m3-d);
loading of given detritus from nonpoint and point sources,
or from upstream (g/m3-d);
detrital formation (g/m3-d);
colonization of refractory detritus by decomposers (g/m3-d),
see (155);
loss due to microbial decomposition (g/m3-d), see (159);
transfer from suspended detritus to sedimented detritus by
sinking (g/m3-d); in streams with the inorganic sediment
model attached see (235), for all other systems see (165);
resuspension from sedimented detritus (g/m3-d); in streams
with the inorganic sediment model attached see (233), for
all other systems see (165) (resuspension);
transfer from buried to sedimented by scour of overlying
sediments (g/m3-d);
transfer from sedimented to deeply buried (g/m3-d), see
(167b);
loss due to being carried downstream (g/m3-d), see (16);
loadings from upstream segments (g/m3-d), see (30);
gain or loss due to diffusive transport over the feedback
link between two segments, (g/m3-d), see (32);
loss due to ingestion by detritivores and filter feeders
(g/m3-d), see (91);
detrital sinking from epilimnion and to hypolimnion under
stratified conditions, see (165); and
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. Labile detritus is then available for
both decomposition and ingestion by detritivores (organisms that feed on detritus). 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
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
CHAPTER 5
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.
AQUATOX simulates detritus as organic matter (dry weight); however, the user can input data
as organic carbon or biochemical oxygen demand (BOD) and the model will make the necessary
conversions. Organic matter is assumed to be 1.90 • organic carbon as derived from
stoichiometry (Winberg 1971). The conversion to BOD is somewhat more complex:
^/JQQS.CBOq,-
I O2Biomass
(148b)
where:
OM
BOD
BODS CBODU =
O2Biomass
organic matter input as required by AQUATOX (g OM/m -d);
biochemical demand 5-day from user input (g O2/m3-d);
BOD5 to ultimate carbonaceous BOD conversion factor, also
defined as CBODu:BODs ratio, (remineralization parameter, default
is 2.47 based on Thomann and Mueller 1987);
ratio O2 to organic matter (OM). (remineralization parameter, the
default is 0.667 based on Winberg (1971));
The equation above is used by AQUATOX when converting initial conditions and loadings in
BOD5, in estimating BOD5 for simulation output, and when linking HSPF BOD data.
The BODs to ultimate CBOD conversion factor will vary depending on the source of the BOD
loading (U.S. Environmental Protection Agency, 2000b)
Table 10. BOD5 to ultimate CBOD conversion Factor
Source, EPA 2000b, Appendix B: National Municipal Wastewater Inventory and Infrastructure
Ultimate Carbonaceous BOD (CBOD ) Conversion Factor = CBOD,,:BOD. ratios
Type Category
1.
2 .
3 .
4 .
5.
6 .
7.
8.
9.
No Discharge
Raw
Primary
Advanced Primary
Secondary
Advanced Secondary
Advanced Treatment
Secondary (No. 6 + Ho . 7
Influent
mg/Li
258
258
258
258
258
258
258
258
258
00
00
00
00
00
00
00
00
00
Effluent
rng/L
0
258
223
172
91
61
32
197
46
00
00
60
00
59
06
25
80
76
Removal Conversion
Percent Factor
100
0
13
33
64
76
87
23
81
0
0
3
3
5
3
5
3
9
1
1
1
1
2
2
3
1
2
000
200
600
600
840
840
000
600
900
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION CHAPTER 5
If it is assumed that labile detritus will thoroughly decompose in five days, and therefore is
captured by BODS, the BODS to CBODu ratio may also be utilized to determine the percentage
refractory for BOD loadings. For example, if the BOD to CBODu ratio is 1.2 this means that for
every one unit of labile organic matter there are 0.2 additional units of refractory organic matter.
Therefore, 0.2 / 1.2 can be assumed to be the refractory percentage of the BOD. If the ratio is
higher, reflecting a higher degree of treatment, a higher percentage of refractory can be used.
Detrital Formation
Detritus is formed in several ways: through mortality, gamete loss, sinking of phytoplankton,
excretion and defecation:
DetrFm suspRefrDetr = Zb,ota (Mort 2 detr, biota • Mortality^) (149)
DetrFmDlsSRefrDetr = Zb.ota (Mort 2 detr,b,ota -Mortality,^) + "Lblota(Excr2detr,blota • Excretion) (150)
DetrFmDlssLMeDetr = Zb,ota(Mort 2 detr,blota-Mortality bwta) + I.Kota(Excr 2 detr,hwta • Excretion) (151)
DetrFm SuSpLab,ieDetr = Zb,ota (Mort 2detr,biota • Mortality biota) + ^anmah GameteLoss (152)
DetrFmsedLMieDetr = I pred (Def 2 detr, pred • Defecation pred) + Zcompartment (Sinking compartment) (153)
DetrFmSedRefrDetr = I. pred (Def 2detr, pred ' Defecationpred)
\ /
+ *L compartment Sedimentation compartment' PlcintSinkToDetr)
where:
DetrFm = formation of detritus (g/m3-d);
Mort2deir, biota = fraction of given dead organism that goes to given detritus
(unitless);
Excr2detr, biota = fraction of excretion that goes to given detritus (unitless), see
Table 11;
Mortalitybtota = death rate for organism (g/m3-d), see (66), (87) and (112);
Excretion = excretion rate for organism (g/m3-d), see (64) and (111) for plants
and animals, respectively;
GameteLoss = loss rate for gametes (g/m3-d), see (126);
Def2detr: biota = fraction of defecation that goes to given detritus (unitless);
DefecationpKd = defecation rate for organism (g/m3-d), see (97);
Sedimentation = loss of phytoplankton to bottom sediments (g/m3-d), see (69); 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
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
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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 (that are not linked to periphyton compartments) are
considered to become detritus; most are consumed quickly by zoobenthos (LeCren and Lowe-
McConnell, 1980) and are not available to be resuspended.
Table 11. Mortality and Excretion to Detritus
Dissolved Labile Detritus
Dissolved Refractory Detritus
Suspended Labile Detritus
Suspended Refractory Detritus
Algal
Mortality
0.27
0.03
0.65
0.05
Macrophyte
Mortality
0.24
0.01
0.38
0.37
Bryophyte
Mortality
0.00
0.25
0.00
0.75
Animal
Mortality
0.27
0.03
0.56
0.14
Dissolved Labile Detritus
Dissolved Refractory Detritus
Algal
Excretion
0.9
0.1
Macrophyte
Excretion
0.8
0.2
Bryophyte
Excretion
0.8
0.2
Animal
Excretion
1.0
0.0
Colonization
Refractory detritus is converted to labile detritus through microbial colonization. When bacteria
and fungi colonize dissolved refractory organic matter, they are in effect turning it into
particulate matter. Detritus is usually refractory because it has a deficiency of nitrogen
compared to microbial biomass. In order for microbes to colonize refractory detritus, they have
to take up additional nitrogen from the water (Saunders et al., 1980). Thus, colonization is
nitrogen-limited, as well as being limited by suboptimal temperature, pH, and dissolved oxygen:
Colonization = ColonizeMax • DecTCorr • NLimit • pHCorr
• DOCorrection • RefrDetr
(155)
where:
Colonization =
ColonizeMax =
Nlimit =
DecTCorr =
pHCorr =
DOCorrection =
RefrDetr
rate of conversion of refractory to labile detritus (g/m -d);
maximum colonization rate under ideal conditions (g/g-d);
limitation due to suboptimal nitrogen levels (unitless), see (157);
the effect of temperature (unitless), see (156);
limitation due to suboptimal pH level (unitless), see (162);
limitation due to suboptimal oxygen level (unitless), see (160);
and
concentration of refractory detritus in suspension, sedimented, or
dissolved (g/m3).
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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 = Thetaemp~TObs where
Theta = 1.047 if Temp > 19° else
Theta = 1.185-0.00729-Temp
(156)
If Temp > TMax Then DecTCorr = 0
The resulting curve has a shoulder similar to the Stroganov curve, but the effect increases up to
the maximum rate (Figure 93).
Figure 93. Colonization and decomposition as an effect of temperature
c
4.5 :
4-
3.5-
i- 3-
o
LU-jc.
u_z-°
LU 2-
1.5-
1-
0.5-
.. ,-_ — i-" ,
/
/
y
/
/
^^
.-""•""
1 . 1 , E ,
A
/
i | t j | i | t | j
0 10 20 30 40 50 60 70
TEMPERATURE (C)
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:
NLimit = •
N-MinN
N-MmN + HalfSatN
(157)
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N = Ammonia + Nitrate (158)
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) 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).
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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 (159)
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 (160);
DecTCorr = the effect of temperature (unitless), see (156);
pHCorr = correction for suboptimal pH (unitless), see (162); and
Detritus = concentration of detritus, including dissolved but not buried (g/m3).
Note that biomass of bacteria is not explicitly modeled in AQUATOX. In some models (for
example, EXAMS, Burns et al., 1982) decomposition is represented by a second-order equation
using an empirical estimate of bacteria biomass. However, using bacterial biomass as a site
constant would constrain 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 (156), which also is used
for colonization. The function for dissolved oxygen, formulated for AQUATOX, is:
DOCorrection = Factor + (1- Factor) -- (160)
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 et al., 1982):
T- . Oxygen
Factor = - — - (161)
HalfSatO + Oxygen
and:
Factor = Michaelis-Menten factor (unitless);
KAnaerobic = decomposition rate at 0 g/m3 oxygen (g/m3-d or ug/L-d); Set to
0.3 g/m3-d for microbial degradation of sediments. For chemicals,
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Oxygen
HalfSatO
(160) is also used and the "rate of anaerobic microbial degr." from
the chemical underlying data is used (KMDegrAnaerobic).
dissolved oxygen concentration (g/m3); and
half-saturation constant for oxygen (g/m3) (0.5 g/m3 in the water
column or 8.0 g/m3 for sedimented detritus).
DOCorrection accounts for both decreased and increased (Figure 94) 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 0.5 g/m3 is used in the water column and a calibrated value of 8.0 g/m3 is
used for the sediments to force anoxic conditions.
Figure 94. Correction for dissolved oxygen
• 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 grow between pH 6
to about 9 (Alexander, 1977). Microbial oxidation is most rapid between pH 6 and 8 (Lyman et
al., 1990). Within the pH range of 5 and 8.5, therefore, pH is assumed to not affect the rate of
microbial degradation, and the suboptimal factor for pH is set to 1.0. In the absence of good data
on the rates of biodegradation under extreme pH conditions, biodegradation is represented as
decreasing exponentially beyond the optimal range (Park et al., 1980a; Park et al., 1982). If the
pH is below the lower end of the optimal range, the following equation is used:
pHCorr =
_ (pH - pHMin)
(162)
where:
pH
pHMin =
ambient pH, and
minimum pH below which limitation on biodegradation rate occurs.
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If the pH is above the upper end of the optimal range for microbial degradation, the following
equation is used:
where:
pHCorr = e(pHMma*-PH> (163)
pHMax = maximum pH above which limitation on biodegradation rate occurs.
These responses are shown in Figure 95.
Figure 95. Limitation due to pH
EFFECT OF pH
1
0.8
go.6
O
§0.4
o:
0.2
3.0 4.1 5.2 6.3 7.4 8.5 9.6 10.7
PH
Sedimentation
When the inorganic sediment model, the multiple layer sediment model, or the sediment
diagenesis model are not included in a simulation, the sedimentation of suspended particulate
detritus to bottom sediments is modeled using simplifying assumptions. The constructs are
intended to provide general responses to environmental factors, but they should not be
considered as anything more than place holders for more realistic hydrodynamic functions to be
incorporated in later versions.
When the inorganic sediment model (sand-silt-clay) is included, the sedimentation and
deposition of detritus is assumed to mimic the sedimentation and resuspension of silt (see (235)
and (233)). If the multi-layer sediment model is included (using user-input erosion and
deposition time-series) the sedimentation of detritus is calculated using the deposition velocity
for cohesives (assumed to be a surrogate for organic matter) as follows:
Sedimentation =
_ DepVel
Thick
State
(164)
In the absence of a sediment model:
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where:
Sedimentation =
KSed
DepVel =
Thick =
Decel =
State
Sedimentation = Decel • State
Thick
(165)
transfer from suspended to sedimented by sinking (g/m -d), if
negative is effectively Resuspension (see below);
sedimentation rate (m/d);
user input time-series of deposition velocities for cohesives (multi-
layer model only; m/d);
depth of water or thickness of layer if stratified (m);
deceleration factor (unitless), see (166); and
concentration of particulate detrital compartment (g/m3).
Table 12: Summary of Detrital Deposition and Resuspension in AQUATOX
Deposition of Suspended Detritus & Phytoplankton
"Classic" AQUATOX model
Sand-Silt-Clay submodel
Multi-layer Sediment Model
Sediment Diagenesis
Assumption
Sedimentation is a function of Mean Discharge
Follows "silt" in inorganic sediments model
Follows "cohesives" class, (which may be user input
or calculated using the sand-silt-clay model)
Choice of "Classic" AQUATOX or Sand-Silt-Clay
assumptions
Equation
(165)
(235)
(164);
(235)
Resuspention of Sedimented Detritus
"Classic" AQUATOX model
Sand-Silt-Clay submodel
Multi-layer Sediment Model
Sediment Diagenesis
Assumption
Resuspension is a function of Mean Discharge
Follows "silt" in inorganic sediments model
Follows "cohesives" class, (which may be user input
or calculated using the sand-silt-clay model)
Resuspension is not enabled.
Equation
(165)
(233)
(167);
(233)
If the discharge exceeds the mean discharge then sedimentation is slowed proportionately
(Figure 96):
where:
If TotDischarge > MeanDischarge then
„ , MeanDischarge
Decel = —
TotDischarge
else Decel = 1.0
TotDischarge = total epilimnetic and hypolimnetic discharge (m3/d); and
(166)
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MecmDischarge = mean discharge, recalculated on an annual basis at the beginning of
each year of the simulation (mVd).
Figure 96. Relationship ofdecel to discharge with a mean discharge of 5 m3/s.
0.4
0.2
0 2
10 12 14 16 18 20 22 24
Discharge (cu m/s)
If the depth of water is less than or equal to 1.0 m and wind speed is greater than or equal to 5.5
m/s then the sedimentation rate is negative, effectively becoming the rate of resuspension. For
plants, if the depth of water is is less than or equal to 1.0 m and wind speed is greater than or
equal to 2.5 m/s then the sedimentation rate is assumed to be zero. If there is ice cover, then the
sedimentation rate is doubled to represent the lack of turbulence.
If the multi-layer sediment model is included (using user-input erosion and deposition time-
series) the resuspension of detritus is calculated using the erosion velocity for cohesives
(assumed to be surrogate for organics) as follows
where:
Resuspension
ErodeVel
Thick
„ . ErodeVel „ 70
Resuspension = SedSiaie
T7! * /
Inick
(167)
transfer from sediment to suspended by erosion (g/m3-d);
user input time-series of cohesives erosion velocities (multi-layer
model only m/d);
depth of water or thickness of layer if stratified (m);
Daily Burial
When the quantity of refractory detritus exceeds its initial condition, it is transferred to the
deeply buried category (buried detritus).
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BurialDetntus = ABS(ConcDetntus - MtialConditionDetntu J
(167b)
where:
Burial Detritus —
ConCDetntus
InitialCondition =
daily burial of detritus (g/m -d);
sedimented detritus concentration (g/m3)
initial condition of detritus (g/m3)
5.2 Nitrogen
In the water column, 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. Un-ionized ammonia (NHa) is not modeled as a
separate state variable but is estimated as a fraction of
ammonia (177). In the sediment bed, if the optional sediment
diagenesis model is included (see chapter 7), nitrogen is
explicitly modeled; otherwise inorganic nitrogen in the
sediment bed is ignored, but organic nitrogen is implicitly modeled as a component of
sedimented detritus.
In the water column, ammonia is assimilated by algae and macrophytes and is converted to
nitrate as a result of nitrification:
Nitrogen: Simplifying Assumptions
• Nitrite is not explicitly modeled
• Nitrogen fixation and
denitrification models are subject to
uncertainty
• Lethal effects from un-ionized and
ionized ammonia are assumed
additive
• Ammonia makes up stoichiometric
imbalances between trophic levels.
dAmmonia
dt
where:
dAmmonia/dt
Loading
Remineralization =
Nitrify
Assimilation
Washout
Washin
DiffusionSeg
TurbDiff
r lUX£)ia
Loading + Remineralization - Nitrify - Assimilation Ammonia
- Washout + Washin ± TurbDiff ±DiffusionSeg + FluxDjagenesjs
(168)
change in concentration of ammonia with time (g/m -d);
loading of nutrient from inflow (g/m3-d);
ammonia derived from detritus and biota (g/m3-d), see (169);
nitrification (g/m3-d), see (174);
assimilation of nutrient by plants (g/m3-d), see (171);
loss of nutrient due to being carried downstream (g/m3-d), see (16)
loadings from linked upstream segments (g/m3-d), see (30);
gain or loss due to diffusive transport over the feedback link between
two segments, (g/m3-d), see (32);
depth-averaged turbulent diffusion between epilimnion and
hypolimnion if stratified (g/m3-d), see (22) and (23);
potential flux from the sediment diagenesis model, (g/m3-d), see (273)
Remineralization includes all processes by which ammonia is produced from animal, plants, and
detritus, including decomposition and excretion required to maintain variable stoichiometry (see
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(169)
Table 14):
Remineralization = PhotoResp + DarkResp + AnimalResp + AnimalExcr
+ DetritalDecomp + AnimalPredation + NutrRelDefecation
+ NutrRelPlantSink + NutrRelMortality + NutrRelGameteLoss
+ NutrRelColonization + NutrRelPeriScour
where:
PhotoResp = algal excretion of ammonia due to photo respiration (g/m3-d);
DarkResp = algal excretion of ammonia due to dark respiration (g/m3-d);
excretion of ammonia due to animal respiration (g/m3-d);
animal excretion of excess nutrients to ammonia to maintain
constant org. to N ratio as required (g/m3-d);
nitrogen release due to detrital decomposition (g/m3-d);
change in nitrogen content necessitated when an animal consumes
prey with a different nutrient content (g/m3-d), see discussion in
"Mass Balance of Nutrients" in Section 5.4;
ammonia released from animal defecation (g/m3-d);
ammonia balance from sinking of plants and conversion to detritus
(g/m3-d);
ammonia balance from biota mortality and conversion to detritus
(g/m3-d);
NutrRelGameteLoss = ammonia balance from gamete loss and conversion to detritus
(g/m3-d);
ammonia balance from colonization of refractory detritus into labile
detritus (g/m3-d);
NutrRelPeriScour = ammonia balance when periphyton is scoured and converted to
phytoplankton and suspended detritus. (g/m3-d);
Nitrate is assimilated by plants and is converted to free nitrogen (and lost) through
denitrification:
AnimalResp
AnimalExcr
DetritalDecomp
AnimalPredation
NutrRelDefecation
NutrRelPlantSink
NutrRelMortality
NutrRelColonization =
dNitrate
di
where:
dNitrate/dt
Washin
Diffusionseg
Loading
Denitrify
r lUX
= Loading + Nitrify - Denitrify - Assimmtrate - Washout + Washin
± TurbDiff±DiffusionSeg+FluxDwgemsjs
(170)
change in concentration of nitrate with time (g/m -d);
loadings from linked upstream segments (g/m3-d), see (30);
gain or loss due to diffusive transport over the feedback link between
two segments, (g/m3-d), see (32);
user entered loading of nitrate, including atmospheric deposition;
denitrification (g/m3-d), see (175);
potential flux from the sediment diagenesis model, (g/m3-d), see
(273)
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Free nitrogen can be fixed by blue-green algae. Both nitrogen fixation and denitrification are
subject to environmental controls and are difficult to model with any accuracy; therefore, the
nitrogen cycle is represented with considerable uncertainty.
Figure 97. Components of nitrogen remineralization
Free N (not in
model domain)
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):
Assimilation Ammoma = Lpiant( Photosynthesis plant • UptakeNn • NH4Pref)
(171)
Assimilationmtrate = Zpiant (Photosynthesis plant • Uptake en • (1 - NH4Pref)) (172)
where:
Assimilation =
Photosynthesis =
UptakeNltrogen
NH4Pref
assimilation rate for given nutrient (g/m -d);
rate of photosynthesis (g/m3-d), see (35);
fraction of photosynthate that is nitrogen (unitless, 0.01975 if
nitrogen-fixing, otherwise 0.079);
ammonia preference factor (unitless).
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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)
(173)
N2NH4 • Ammonia • KN
(N2NH4 • Ammonia + N2NO3 • Nitrate) • (KN + N2NO3 • Nitrate)
where:
N2NH4 = ratio of nitrogen to ammonia (0.78);
N2NO3 = ratio of nitrogen to nitrate (0.23);
KN = half-saturation constant for nitrogen uptake (g N/m3);
Ammonia = concentration of ammonia (g/m3); and
Nitrate = concentration of nitrate (g/m3).
For algae other than blue-greens, Uptake is the Redfield (1958) ratio; although other ratios (cf.
Harris, 1986) may be used by editing the parameter screen. At this time nitrogen-fixation by
blue-greens is represented by using a smaller uptake ratio, thus "creating" nitrogen.
Nitrification and Denitrification
Nitrification is the conversion of ammonia to nitrite and then to nitrate by nitrifying bacteria; it
occurs at the sediment-water interface (Effler et al., 1996) and in the water column (Schnoor
1996). The maximum rate of nitrification is reduced by limitation factors for suboptimal
dissolved oxygen and pH, similar to the way that decomposition is modeled, but using the more
restrictive correction for suboptimal temperature used for plants and animals:
Nitrify = KNitri • DOCorrection • TCorr • pHCorr • Ammonia (174)
where:
Nitrify = nitrification rate (g/m3-d);
KNitri = maximum rate of nitrification (m/d);
DOCorrection = correction for anaerobic conditions (unitless) see (160);
TCorr = correction for suboptimal temperature (unitless); see (59);
pHCorr = correction for suboptimal pH (unitless), see (162); and
Ammonia = concentration of ammonia (g/m3).
If the Sediment Diagenesis model is used, the KNitri value may need to be decreased to account
for sediment nitrification being represented separately. The nitrifying bacteria have narrow
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environmental optima; according to Bowie et al. (1985) they require aerobic conditions with a
pH between 7 and 9.8, an optimal temperature of 30deg., and minimum and maximum
temperatures of 10 deg. and 60 deg. respectively (Figure 98, Figure 99).
Figure 98. Response to pH, nitrification
Figure 99. Response to temperature, nitrification
EFFECT OF pH
5 6.4 7.8 9.2 10.6
5.7 7.1 8.5 9.9
PH
STROGANOV FUNCTION
NITRIFICATION
20 30 40 50
TEMPERATURE (C)
60
In contrast, denitrification (the conversion of nitrate and nitrite to free nitrogen) is an anaerobic
process, so that the assumptions are that it operates continuously at the sediment-water interface
and that low oxygen levels enhance the process when it occurs in the water column (Ambrose et
al., 1991):
Denitrify = (KDenitriBottom • Area/Volume • TCorr • pHCorr
+ KDenitriWater • (1 - DOCorrection) • TCorr • pHCorr) • Nitrate
(175)
where:
Denitrify
KDenitriBottom
Area
Volume
Nitrate
denitrification rate (g/m -d);
maximum rate of denitrification at sediment-water interface (m/d);
maximum rate of denitrification in water column (1/d);
area of site or segment (m2);
volume of site or segment (m3); see (2);
concentration of nitrate (g/m3).
KDenitriBottom is set to zero when the sediment diagenesis model is included, because
denitrification in the sediment bed is tracked within that model (see (278))
Furthermore, denitrification is accomplished by a large number of reducing bacteria under
anaerobic conditions and with broad environmental tolerances (Bowie et al., 1985; Figure 100,
Figure 101).
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Figure 100. Response to pH, denitrification
1
0.8
°0.6
O
00.4
LU
0.2
0
EFFECT OF pH
3 4.8 6.6 8.4 10.2
3.9 5.7 7.5 9.3
PH
Figure 101. Response to temperature,
STROGANOV FUNCTION
DECOMPOSITION
20 30 40 50
TEMPERATURE (C)
60
lonization of Ammonia
The un-ionized form of ammonia, NHa, is toxic to invertebrates and fish. Therefore, it is often
singled out as a water quality criterion. Un-ionized ammonia is in equilibrium with the
ammonium ion, NH4+, and the proportion is determined by pH and temperature. It is useful to
report NHa as well as total ammonia (NHa + NH4+).
The computation of the fraction of total ammonia that is un-ionized is relatively straightforward
(Bowie etal. 1985):
1
FmcNH3
NH3 =
pkh = 0.09018
FracNH3 • Ammonia
2729.92
TKelvin
where:
(176)
(177)
(178)
FracNH3
pkh
NH3
Ammonia
TKelvin
fraction of un-ionized ammonia (unitless);
hydrolysis constant;
un-ionized ammonia (mg/L);
total ammonia (mg/L) see (168);
temperature (°K).
The relative contributions of temperature and pH can be seen by graphing the fraction of un-
ionized ammonia against each of those variables in simulations of Lake Onondaga (Figure 102
and Figure 103). As inspection of the construct would suggest, un-ionized ammonia has a linear
relationship to temperature and a logarithmic relationship to pH, which causes it to be sensitive
to extremes in pH.
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Figure 102. Fraction of un-ionized ammonia roughly following temperature.
Fraction NH3
Sep-88 Apr-89 Oct-89 May-90 Nov-90 Jun-91
Figure 103. Fraction of un-ionized ammonia affected by extreme values of pH.
Fraction NH3
Sep-88 Apr-89 Oct-89 May-90 Nov-90 Jun-91
The construct was verified with the same set of data from Lake Onondaga as was used for the pH
verification (Effler et al. 1996), see section 5.7. It fits the observed data well (Figure 104).
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Figure 104. Comparison of predicted and observed fraction of NH3 for Lake Onondaga, NY.
Data from (Effler et al. 1996).
Fraction NH3
- Frac NH3
• ObsfracNHS
.Poly. (ObsfracNHS)
Feb- Apr- May- Jul-89 Aug- Oct- Dec-
89 89 89 89 89 89
Ammonia Toxicity
Lethal effects of ammonia on animals have been implemented in AQUATOX based on U.S.
EPA's Update of Ambient Water Quality Criteria for Ammonia (U.S. Environmental Protection
Agency, 1999). Based on this document, it is preferable to base toxicity on total ammonia, taking
into account the contributions from the un-ionized and ionized ammonia (LCSOu and LCSOi):
LC50,, =
R
+ -
i+io^-8 1+
(179)
LC50, =
1+
R 1
1 +
(180)
where:
LC50U
LC50,
al ammonia
LC50 for the unionized concentrations of ammonia
LC50 for the ionized concentrations of ammonia.
LC50U + LC50,
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pHT
R
LC50t8
transition pH at which LC50 is the average of the high- and low-
pH intercepts (7.204);
shape parameter defined as the ratio of the high- and low-pH
intercepts (0.00704), along with pHT, defines the shape of the
curve;
user-input LC50totaiammonia at 20 degrees centigrade and pH of 8.
LC50 parameters derived with the equations above are then applied to the external toxicity
formulation (see section 9.3, equations (429)-(431)). The slope of the Weibull curve is a
constant 0.7 for both forms of ammonia. This value produces the best general match of data
from Appendix 6 from the Ammonia Criteria update (U.S. Environmental Protection Agency,
1999). Lethal effects from un-ionized and ionized ammonia are assumed to be additive.
5.3 Phosphorus
The phosphorus cycle is simpler than the nitrogen cycle.
Decomposition, excretion, and assimilation are important
processes that are similar to those described above. As was
the case with ammonia and nitrate, if the optional sediment
diagenesis model is included (see chapter 7), flux of
phosphate from the sediment bed may be added to the water
column, especially under anoxic conditions. Additionally,
sorption to calcite may have a significant effect on phosphate predictions in high pH systems due
to precipitation of calcium carbonate. This optional formulation is important to adequately
simulate marl lakes.
Phosphorus: Simplifying
Assumption
• Total bioavailable soluble
phosphorus is modeled
• A constant sorption rate for calcite
is used
• Soluble phosphorus makes up
stoichiometric imbalances between
trophic levels.
dPhosphate
~dt
= Loading+Remineralization - Assimilationphosphate -Washout
+ Washin ± TurbDiff ± Diffusion,, - SorptionP + FluxDia,
(181)
Assimilation = ^Plant (Photosynthesis plant • Uptake phhorus)
(182)
where:
dPhosphate/dt
Loading
Remineralization
Assimilation
TurbDiff
Washin
change in concentration of phosphate with time (g/m -d);
loading of nutrient from inflow and atmospheric deposition
(g/m3-d);
phosphate derived from detritus and biota (g/m3-d), see (183);
assimilation by plants (g/m3-d);
depth-averaged turbulent diffusion between epilimnion and
hypolimnion if stratified (g/m3-d), see (22) and (23);
loadings from linked upstream segments (g/m3-d), see (30);
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
CHAPTER 5
Diffusionseg
SorptionP
r lUX£)ia
Photosynthesis
Uptake
gain or loss due to diffusive transport over the feedback link
between two segments, (g/m3-d), see (32);
rate of sorption of phosphorus to calcite (mgP/L-d), see (218);
potential flux from the sediment diagenesis model, (g/m3-d), see
(273)
rate of photosynthesis (g/m3-d), see (35), and
fraction of photosynthate that is phosphate (unitless, 0.018).
As was the case with ammonia, Remineralization includes all processes by which phosphate is
produced from animal, plants, and detritus, including decomposition, excretion, and other
processes required to maintain mass balance given variable stoichiometry (see Table 15):
(183)
Remineralization = PhotoResp + DarkResp + AnimalResp + AnimalExcr
+ DetritalDecomp + AnimalPredation + NutrRelDefecation
+ NutrRelPlantSink + NutrRelMortality + NutrRelGameteLoss
+ NutrRelColonization + NutrRelPeriScour
where:
PhotoResp = algal excretion of phosphate due to photo-respiration (g/m3-d);
DarkResp = algal excretion of phosphate due to dark respiration (g/m3-d);
excretion of phosphate due to animal respiration (g/m3-d);
animal excretion of excess nutrients to phosphate to maintain
constant org. to P ratio as required (g/m3-d);
phosphate release due to detrital decomposition (g/m3-d);
change in phosphate content necessitated when an animal consumes
prey with a different nutrient content (g/m3-d), see discussion in
"Mass Balance of Nutrients" below;
phosphate released from animal defecation (g/m3-d);
phosphate balance from sinking of plants and conversion to detritus
(g/m3-d);
phosphate balance from biota mortality and conversion to detritus
(g/m3-d);
NutrRelGameteLoss = phosphate balance from gamete loss and conversion to detritus
(g/m3-d);
NutrRelColonization = phosphate balance from colonization of refractory detritus into
labile detritus (g/m3-d);
NutrRelPeriScour = phosphate balance when periphyton is scoured and converted to
phytoplankton and suspended detritus. (g/m3-d);
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 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).
AnimalResp
AnimalExcr
DetritalDecomp
AnimalPredation
NutrRelDefecation
NutrRelPlantSink
NutrRelMortality
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CHAPTER 5
5.4 Nutrient Mass Balance
Variable Stoichiometry
The ratios of elements in organic matter are allowed to
vary among but not within compartments. This is
accomplished by providing editable fields for N:organic
matter and P:organic matter for each compartment.
Furthermore, the wet to dry ratio is editable for all
compartments; it has a default value of 5.
In order to maintain the specified ratios for each
compartment, the model explicitly accounts for processes
that balance the ratios during transfers, such as excretion
coupled with consumption and nutrient uptake coupled
with detrital colonization. Nutritional value is not
automatically related to Stoichiometry in the model, but it
is implicit in default egestion values provided with various
default stoichiometric values suggested for the model, though
Nutrient Mass Balance: Simplifying
Assumptions
• Stoichiometry within each model
compartment is constant over time
• Free nitrogen is not tracked within
AQUATOX
• Nutrients taken up by macrophyte
roots come from sources that are
outside the modeled system
• Mass balance may fail if total
nutrients in the water column drop
to zero (due to inter-organism
interactions)
• Ammonia loadings are assumed to
be 12 to 15% when total nitrate
loadings are input by the user.
• Dissolved nutrients make up
stoichiometric imbalances between
trophic levels.
food sources. Table 13 shows the
these can be edited.
Table 13: Default stochiometric values in AQUATOX
Compartment
Refrac. detritus
Labile detritus
Phytoplankton
Bl-greens
Periphyton
Macrophytes
Cladocerans
Copepods
Zoobenthos
Minnows
Shiner
Perch
Smelt
Bluegill
Trout
Bass
Frac. N
(dry)
0.002
0.079
0.059
0.059
0.04
0.018
0.09
0.09
0.09
0.097
0.1
0.1
0.1
0.1
0.1
0.1
Frac. P
(dry)
0.0002
0.018
0.007
0.007
0.0044
0.002
0.014
0.006
0.014
0.0149
0.025
0.031
0.016
0.031
0.031
0.031
Reference
Sterner & Elser 2002
Redfield (1 958) ratios
Sterner & Elser 2002
same as phytoplankton for now
Sterner & Elser 2002
Sterner & Elser 2002
Sterner & Elser 2002
Sterner & Elser 2002
same as cladocerans for now
Sterner & George 2000
Sterner & George 2000
Sterner & George 2000
Sterner & George 2000
same as perch for now
same as perch for now
same as perch for now
Nutrient Loading Variables
Often water quality data are given as total nitrogen and phosphorus. In order to improve
agreement with monitoring data, AQUATOX can accept both loadings and initial conditions as
"Total N" and "Total P." This is made possible by accounting for the nitrogen and phosphorus
154
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION _ CHAPTER 5
contributed by suspended and dissolved detritus and phytoplankton and back-calculating the
amount that must be available as freely dissolved nutrients. The precision of this conversion is
aided by the model's variable stoichiometry. For nitrogen:
^Dissolved ~ •'* Total ~ * * SuspendedD etritus ~ * * Suspended? lants V^"V
where:
= bioavailable dissolved nitrogen (g/m3 d); see (170);
= loadings of total nitrogen as input by the user (g/m3 d);
= nitrogen in suspended detritus loadings (g/m3 d);
= nitrogen in suspended plant loadings (g/m3 d).
When Total N inputs are used, based on the type of input, ammonia is assumed to be a fixed
percentage of bioavailable dissolved nitrogen:
• Inflow waters: Ammonia content of dissolved inorganic nitrogen = 12%
• Point sources: Ammonia content of dissolved inorganic nitrogen = 15%
• Non-point sources: Ammonia content of dissolved inorganic nitrogen = 12%
In acknowledgment of the way it is used in the model, the phosphorus state variable is
designated "Total Soluble P." Phosphorus that is not bioavailable (i.e. immobilized phosphorus
and acid-soluble phosphorus) may be specified using the FracAvail parameter as shown here:
TSP = FracAvail (Plotal - PSuspendedD etntus - PSuspendedP lants ) (185)
where:
TSP = bioavailable phosphorus (g/m3 d); see (181);
FracAvail = user-input bioavailable fraction of phosphorus;
P Total = loadings of total phosphorus (g/m3 d);
= phosphorus in suspended detritus loadings (g/m3 d);
= phosphorus in suspended plant loadings (g/m3 d).
Nutrient Output Variables
In order to compare model results with monitoring data, total phosphorus, and total nitrogen are
calculated as output variables. This is accomplished by the reverse of the calculations for the
loadings: the contributions of the nutrient in the freely dissolved state and tied up in
phytoplankton and dissolved and paniculate organic matter are calculated and summed.
Biochemical oxygen demand (BODs) is computed as the sum of the contributions from
phytoplankton and labile dissolved and parti culate organic matter using a conversion of 1.35
BOD/organic matter.
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION CHAPTER 5
Mass Balance of Nutrients
Variables for tracking mass balance and nutrient fate are included in the output as detailed
below. Phosphorus and Nitrogen now balance mass to machine accuracy. To maintain mass
balance, nutrients are tracked through many interactions.
The mass balance and nutrient fate tracking variables are:
Nutrient Tot. Mass: Total mass of nutrient in the system in kg
Nutrient Tot. Loss: Total loss of nutrient from system since simulation start, kg
Nutrient Tot. Washout: Total washout since simulation start, kg
Nutrient Wash, Dissolved: Washout in dissolved form since simulation start, kg
Nutrient Wash, Animals: Washout in animals since start, kg
Nutrient Wash, Detritus: Washout in detritus since start, kg
Nutrient Wash, Plants: Washout in plants since start, kg
Nutrient Loss Emergel: Loss of nutrients in emerging insects since start, kg
Nutrient Loss Denitrif.: Denitrification since start, kg
Nutrient Burial: Burial of nutrients since start, kg
Nutrient Tot. Load: Total nutrient load since start, kg
Nutrient Load, Dissolved: Dissolved nutrient load since start, kg
Nutrient Load as Detritus: Nutrient load in detritus since start, kg
Nutrient Load as Biota: Nutrient load in biota since start, kg
Nutrient Root Uptake: Load of nutrients into sytem via macrophyte roots since start. (Macrophyte root
uptake is currently assumed to occur from below the modeled sediment layer), kg
Nutrient MB Test: Mass balance test, total Mass + Loss - Load: Should stay constant
Nutrient Exposure: Exposure of buried nutrients
Nutrient Net Layer Sink: For stratified systems, sinking since start, kg
Nutrient Net TurbDiff: For stratified systems, Turbdiff since start, kg
Nutrient Net Layer Migr: For stratified systems, migration since start, kg
Nutrient Total Net Layer: Net movement over layers, kg
Nutrient Mass Dissolved: Total mass of dissolved nutrient in system, kg
Nutrient Mass Detritus: Total mass of nutrient in detritus in system, kg
Nutrient Mass Animals: Total mass of nutrient in animals in system, kg
Nutrient Mass Plants: Total mass of nutrient in plants in system, kg
It is important to make careful note of the units presented in the list above. Load and loss terms
are calculated in terms of "kg since the start of the simulation," total mass units are "kg at the
current moment."
A simplified diagram of the nitrogen and phosphorus cycles can be found in Figure 105 and
Figure 106. A full accounting of the 18 nutrient linkages and all external loads and losses for
nitrogen and phosphorus is also provided in Table 14 and Table 15.
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
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X
o
p
a
U
G
QJ
60
O
M
157
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Table 14
Nitrogen Mass Balance: Accounting
NO3 link
Load external load
Nitrif from NH4 a
De N itrif external loss
NOSAssim to plant b
Washout external loss
TurbDiff layer accountg
Detritus,
Participate Refr. link
Load external load
mortality from anim/plt k
Colonz to PartLabDetr g
Washout external loss
Predation to Animal h
Sedimentation to SedRefrDetr i
Scour from SedRefrDetr j
SinkToHyp layer accountg
SinkFromEpi layer accountg
TurbDiff layer accountg
NH4 link
Load external load
Nitrif to NO3 a
Assimil to plant b
Excretion from anim/plt c,o
Respiration from anim/plt m,n
DetritalDecomp from LabileDetr d
Washout external loss
TurbDiff layer accountg
Detritus, Participate
Labile link
Load external load
Decomp to NH4 d
mortality from anim/plt k
GamLoss from Animal q
Colonz from Diss.PartRefr g
Washout external loss
Predation to Animal h
Sedimentation to SedLabDetr i
Scour from SedLabDetr j
SinkToHypo layer accountg
SinkFromEpi layer accountg
TurbDiff layer accountg
Detritus, Sed.
Refractory link
Load external load
Defecation from animal e
Plant Sedmtn from plant f
Colonz to SedLabDetr g
Predation to Animal h
Sedimentation from PartRefrDetr i
Scour to PartRefrDetr j
Burial external loss
Exposure external load
Algae link
Load external load
Photosyn from NO3, NH4 b
Respiration to NH4 m
Photo Resp to diss detr, NH4 l,c
Mortality to Diss / Part Detr k
Predation to Animal h
Washout external loss
Sedimntn (Sink) to Sed Detr f
TurbDiff layer accountg
SinkToHypo layer accountg
SinkFromEpi layer accountg
Sloughing to detr., phytoplk r
ToxDislodge to detr., as mort k
Detritus, Sed.
Labile link
Load external load
Defecation from animal e
Plant Sedmtn from plant f
Colonz from SedRefrDetr g
Predation to Animal h
Decomp to NH4 d
Sedimentation from PartLabDetr i
Scour to PartLabDetr j
Burial external loss
Exposure external load
Macrophytes link
Load external load
Photosyn root uptake, external
Respiration to NH4 m
Photo Resp to diss detr, NH4 l,c
Mortality to Part Detr k
Predation to animal h
Breakage to detr., as mort k
Detritus,
Dissolved link
Load external load
Decomp (labile) to NH4 d
Mortality from anim/plt k
Colonz DissRefr->PartLab g
Excretion from anim/plt 1
Washout external loss
TurbDiff layer accountg
Animals link
Load external load
Consumption from anim/plt h
Defecation to sed detr e
Respiration to NH4 if req. n
Excretion to NH4 if req. o
TurbDiff layer accountg
Predation to animal h
Mortality to Part Detr k
Gamete Loss to PartLabDetr q
Drift external loss
Entrain external loss
Promotion to animal p
Recruit from animal p
Emergel external loss
Migration layer accountg
oo
Linkage Notes
a Denitrification from NH4 to NO3.
b An appropriate quantity of NO3 and NH4 are taken into a plant as part of photosynthesis so that mass balance is maintained.
c When excretion & respiration takes place in plants and animals, all nitrogen lost goes directly to dissolved NH4.
d Labile detritus breaks down and the nutrient content is released as NH4.
e Defecation is split into sedimented-labile and sed-refr detritus 50-50. Excess nitrogen is released as NH4.
f Plants sink and are split into sedimented-labile and sed-refr detritus (92-08). Excess nitrogen is released as NH4.
g Refractory detritus converts into labile detritus. Any nitrogen imbalance is balanced using NH4 in water.
h Animals eat plants and detritus. Animal homeostasis (const, org to N ratio) is managed through Respiration & Excretion.
i Suspended sediment sinks and joins bottom sediment. Any change in N between phases is made up using dissolved NH4.
j Bottom sediment is scoured up and joins suspended sediment. Any change in N between phases is made up using dissolved NH4.
k Animals and plants die and are divided up among suspended and dissolved detritus. Excess nitrogen is released as NH4.
I Plants excrete organic matter to dissolved detritus. Excess Nitrogen is released as NH4.
m Plant respiration, nutrients are released to NH4
n Animal respiration, nutrients are relased to NH4 to maintain animal constant org. to N ratio as required.
o Animal excretion of excess nutrients to NH4 to maintain constant org. to N ratio as required.
p If young and old age-classes have different ratios, a warning is raised. Prom/Recr takes place outside derivatives so ratios must match.
q Through gameteloss, biomass is converted to Part Lab Detr. Excess Nitrogen is released as NH4.
r 1/3 of periphyton sloughing goes to phytoplankton, 2/3 to detritus as mortality. Nutrients are balanced between compartments.
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
CHAPTER 5
O
D
U
O
^
PH
vo
O
0)
•_
2
CL>
"oS
^
i-H
0
ex
c
fin
;
c !
•a !
a i
-§ i
rt !
T3 ^
O I
a i
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B i
3 1
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\^_x :
159
-------
Table 15
Phosphorus Mass Balance: Accounting
Total Soluble P link
Load external load
Assimilation to plant b
Excretion from anim/plt c,o
Respiration from anim/plt m,n
DetritalDecomp from LabileDetr d
Washout external loss
TurbDiff layer accountg
Detritus,
Participate Refr. link
Load external load
mortality from anim/plt k
Colonz to PartLabDetr g
Washout external loss
Predation to Animal h
Sedimentation to SedRefrDetr i
Scour from SedRefrDetr j
SinkToHyp layer accountg
SinkFromEpi layer accountg
TurbDiff layer accountg
Detritus, Sed.
Refractory link
Load external load
Defecation from animal e
Plant Sedmtn from plant f
Colonz toSedLabDetr g
Predation to Animal h
Sedimentation from PartRefrDetr i
Scour to PartRefrDetr j
Burial external loss
Exposure external load
Detritus,
Participate link
Load external load
Decomp to TSP d
mortality from anim/plt k
GamLoss from Animal q
Colonz from Diss.PartRefr g
Washout external loss
Predation to Animal h
Sedimentation toSedLabDetr i
Scour from SedLabDetr j
SinkToHypo layer accountg
SinkFromEpi layer accountg
Tu rb Diff layer accountg
Detritus, Sed.
Labile link
Load external load
Defecation from animal e
Plant Sedmtn from plant f
Colonz from SedRefrDetr g
Predation to Animal h
Decomp to TSP d
Sedimentation from PartLabDetr i
Scour to PartLabDetr j
Burial external loss
Exposure external load
Algae link
Load external load
Photosyn from TSP b
Respiration to TSP b
Photo Resp todissdetr, TSP l,c
Mortality to Diss / Part Detr k
Predation to Animal h
Washout external loss
Sedimntn (Sink) to Sed Detr f
TurbDiff layer accountg
SinkToHypo layer accountg
SinkFromEpi layer accountg
Sloughing to detr., phytoplk r
ToxDislodge to detr., as mort k
Detritus,
Dissolved link
Load external load
Decomp (labile) to TSP d
Mortality from anim/plt k
Colonz DissRefr->PartLab g
Excretion from anim/plt 1
Washout external loss
TurbDiff layer accountg
Macrophytes link
Load external load
Photosyn root uptake, external
Respiration to TSP m
Photo Resp to diss detr, TSP l,c
Mortality to Part Detr k
Predation to animal h
Breakage to detr., as mort k
Animals link
Load external load
Consumption from anim/plt h
Defecation to sed detr e
Respiration toTSPifreq. n
Excretion to TSP if req. l,o
TurbDiff layer accountg
Predation to animal h
Mortality to Part Detr k
GameteLoss to PartLabDetr q
Drift external loss
Entrain external loss
Promotion to animal p
Recruit from animal p
Emergel external loss
Migration layer accountg
Linkage Notes
b An appropriate quantity of phosphorus is taken into a plant as part of photosynthesis so that mass balance is maintained.
c When excretion & respiration takes place in plants and animals (organic matter becomes DOM) additional P lost goes directly to dissolved P.
d Labile detritus breaks down and the nutrient content is released as dissolved P.
e Defecation is split into sedimented-labile and sed-refr detritus 50-50. Excess phosphorus is released as dissolved P.
f Plants sink and are split into sedimented-labile and sed-refr detritus (92-08). Excess phosphorus is released as dissolved P.
g Refractory detritus breaks down into labile detritus. Any P imbalance is balanced using dissolved P in water.
Animals eat plants and detritus. Animal homeostasis (const, org to P ratio) is managed through Respiration & Excretion.
Suspended sediment sinks and joins bottom sediment. Any change in P between phases is made up using dissolved P.
Bottom sediment is scoured up and joins suspended sediment. Any change in P between phases is made up using dissolved P.
k Animals and plants die and are divided up among suspended and dissolved detritus. Excess phosphorus is released as dissolved P.
l Plants and animals excrete organic matter to dissolved detritus. Excess phosphorus is released as dissolved P.
m Plant respiration, nutrients are released to dissolved phosphorus.
n Animal respiration, nutrients are relased to dissolved P to maintain animal constant org. to P ratio as required.
o Animal excretion of excess nutrients to P to maintain constant org. to P ratio as required.
p If young and old age-classes have different ratios, a warning is raised. Prom/Recr takes place outside derivatives so ratios must match.
q Through gameteloss, biomass is converted to Part Lab Detr. Excess phosphorus is released as dissolved P.
r 1/3 of periphyton sloughing goes to phytoplankton, 2/3 to detritus as mortality. Nutrients are balanced between compartments.
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION CHAPTER 5
There are instances in which nutrients can be moved to and from compartments that are not in
the model domain. For example, when NOs undergoes denitrification and becomes free nitrogen
the free nitrogen is no longer tracked within AQUATOX. An example of nutrients entering the
model domain comes with the growth of macrophytes. Rooted macrophytes are not limited by a
lack of nutrients in the water column as nutrients are derived from the sediment. Therefore,
when photosynthesis of macrophytes produces growth, the nutrient content within the leaves of
the macrophytes is assumed to originate from the pore waters of the sediments. However, this
implicit "nutrient pumping" is tracked in the mass balance output.
Additionally, some simplifications are required as a result of dietary imbalances. For example,
herbivores generally have higher nutrient concentrations than the plants that they are consuming.
When biomass is converted from a plant into an animal through consumption the imbalance has
to be satisfied to maintain mass balance. Sterner and Elser (2002) state: "There is no single way
that consumers maintain their stoichiometry in the face of imbalanced resources." As a
simplification, AQUATOX takes nutrients from the dissolved water-column compartments to
make up this difference (see AnimalPredation in (169)). However, these same herbivores ingest
plants with higher nutrient concentrations than the fecal matter that they defecate. When
biomass is converted from plants to detrital matter through defecation the model simulates a
release of nutrients into the water column (see NutrRelDefecation in (169)). These two
simplifying algorithms, therefore, balance each other for the most part, and such interactions will
have only a minor effect on predicted water-column nutrient concentrations. Likewise, nutrient-
poor refractory detritus is converted to labile detritus through microbial colonization and growth;
this is stimulated by uptake of nutrients from the water column (Sterner and Elser 2002) and is
represented in the model.
In some cases, when concentrations of nutrients in the water column drop to zero, perfect mass
balance of nutrients will not be maintained. Nutrient to organic matter ratios within organisms
do not vary over time, therefore transformation of organic matter (e.g. consumption, mortality,
sloughing, and sedimentation) occasionally requires that a nutrient difference be made up from
the water column. If there are no available nutrients in the water column, a slight loss of mass
balance is possible.
The mass associated with each component can be plotted, as in Figure 107.
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
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Figure 107 Distribution of predicted mass of nitrogen in Lake OnondagaNY.
ONONDAGA LAKE, NY (PERTURBED) Run on 03-23-09 3:29 PM
(Epilimnion Segment)
1 .OB-6
1.0B-5
1.0B-4
1.0B-3
NMass Dissolved (kg)
N Mass Susp. Detritus (kg)
N Mass Animals (kg)
— NMass Plants (kg)
N Mass Bottom Sed. (kg)
1/12/1989 5/12/1989 9/9/1989 1/7/1990 5/7/1990 9/4/1990 1/2/1991
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CHAPTER 5
5.5 Dissolved Oxygen
Oxygen is an important regulatory endpoint; very low levels
can result in mass mortality for fish and other organisms,
mobilization of nutrients and metals, and decreased
degradation of toxic organic materials. Dissolved oxygen is
usually simulated as a daily average and does not account for
diurnal fluctuations (however, see Diel Oxygen below). It is
a function of reaeration, photosynthesis, respiration,
decomposition, and nitrification:
Oxygen: Simplifying Assumptions
• Reaeration is set to zero if ice cover
is predicted
• Blue-green algal blooms limit the
depth of oxygen reaeration
dOxygen
~dt
= Loading + Reaeration + Photosynthesized - BOD -^ Respiration
- NitroDemand - Washout + Washin ± TurbDiff ± DiffusionSeg
Photosynthesized = O2Photo • ^Plant (Photosynthesis plant)
BOD = O2Biomass• (zDetntus('DecompositionDetntus) )
NitroDemand = O2N • Nitrify
where:
dOxygen/dt
Loading
Reaeration
Photosynthesized
O2Photo
BOD
NitroDemand
Washout
Washin
Diffusionseg
O2Biomass
Photosynthesis
Decomposition
£ Respiration
O2N
Nitrify
(186)
(187)
(188)
(189)
change in concentration of dissolved oxygen (g/m3-d);
loading from inflow (g/m3-d);
atmospheric exchange of oxygen (g/m3-d), see (190);
oxygen produced by photosynthesis (g/m3-d);
ratio of oxygen to photosynthesis (1.6, unitless);
instantaneous biochemical oxygen demand (g/m3-d);
oxygen taken up by nitrification (g/m3-d);
loss due to being carried downstream (g/m3-d), see (16);
loadings from linked upstream segments (g/m3-d), see (30);
gain or loss due to diffusive transport over the feedback link
between two segments, (g/m3-d), see (32);
ratio of oxygen to organic matter (unitless);
rate of photosynthesis (g/m3-d), see (35), (85);
rate of decomposition (g/m3-d), see (159);
sum of respiration for all organisms (g/m3-d), (63) and (100);
ratio of oxygen to nitrogen (unitless); and
rate of nitrification (gN/m3-d) see (174).
Reaeration is a function of the depth-averaged mass transfer coefficient KReaer, corrected for
ambient temperature, multiplied by the difference between the dissolved oxygen level and the
saturation level (cf. Bowie et al., 1985):
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION CHAPTER 5
Reaeration = KReaer • (O2Sat - Oxygen) (190)
where:
Reaeration = mass transfer of oxygen (g/m3-d);
KReaer = depth-averaged reaeration coefficient (1/d);
O2Sat = saturation concentration of oxygen (g/m3), see (198); and
Oxygen = concentration of oxygen (g/m3).
For reaeration in estuaries, see Chapter 10 and equation (445).
KReaer may be entered as a constant value within the site's "underlying data." Alternatively,
AQUATOX will calculate KReaer based on the site-type and other characteristics. In standing
water KReaer is computed as a minimum transfer velocity plus the effect of wind on the transfer
velocity (Schwarzenbach et al., 1993) divided by the thickness of the mixed layer to obtain a
depth-averaged coefficient (Figure 108):
VJ> , — 4 + 4E-5-Wind2)-864
KReaer = (191)
Thick
where:
Wind = wind velocity 10m 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 0.1 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 0.1
m. This does not affect the KReaer that is used in computing volatilization (see section 8.5).
In streams, reaeration is a function of current velocity and water depth (Figure 109) 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 (192)
else:
TransitionDepth = 4.411- Vel2'9135 (193)
where:
Vel = velocity of stream (converted to m/sec) see (14); and
TransitionDepth = intermediate variable (m).
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If Depth < 0.61 m (but > 0.06), the equation of Owens et al. (1964, cited in Ambrose et al., 1991)
is used:
KReaer = 5.349 • Vel°'67 • Depth'1'8' (194)
where:
Depth = mean depth of stream (m).
Otherwise, if Depth is > TransitionDepth, the equation of O'Connor and Dobbins (1958, cited in
Ambrose et al., 1991) is used:
KReaer = 3.93- Vela5° • Depth'1'50
Else, if Depth < TransitionDepth but not <0.60 m, the equation of Churchill et al. (1962, cited in
Ambrose et al., 1991) is used:
KReaer = 5.049 • Vel°'97 • Depth1'67 (195)
In extremely shallow streams, especially experimental streams where depth is < 0.06 m, an
equation developed by Krenkel and Orlob (1962, cited in Bowie et al. 1985) from flume data is
used:
-_ 234 .(U- Slope)0'408
KReaer = nff (196)
Tj-0.66
tl
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 <
3deg. C).
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Figure 108. Reaeration as a Function of Wind
EFFECT OF WIND
OXYGEN, DEPTH = 1 m
8 12 16
6 10 14
WIND (mis)
Figure 109. Reaeration in Streams
VELOCITY (m/sec)
DEPTH(m)
Reaeration is assumed to be representative of 20 deg. C, so it is adjusted for ambient water
temperature using (Thomann and Mueller 1987):
where:
KReaerT =
Kreaer2o =
Theta
Temperature =
T^T~* T^T~* ^n i (Temperature-20)
KReaerT = KReaer2o • Theta
Reaeration coefficient at ambient temperature (1/d);
Reaeration coefficient for 20deg. C (1/d);
temperature coefficient (1.024); and
ambient water temperature (deg. C).
(197)
In Release 3, oxygen saturation is calculated using the formulation of Thomann and Mueller
(1987, p 277) see also APHA et al (1995). Oxygen saturation is calculated as a function of
temperature (Figure 110), salinity (Figure 111), and altitude (Figure 112):
O2Sat = AltEffect • exp
where
1.57570E + 5 6.64231E +1 1.2438E + 10
-139.3441 + — + -
TKelvin
8.62195E + 11
TKelvin4
-S 0.017674-
TKelvin2 TKelvin3
10.754 2140.7
TKelvin TKelvin'
100 - (0.0035 • 3.28083 • Altitude]
AltEffect = -
100
(198)
and where:
AltEffect
TKelvin
S
Altitude
Fractional reduction in oxygen saturation due to the effects of altitude
(Thomann and Mueller 1987, from Zison et al. 1978);
Kelvin temperature;
salinity driving variable, set to zero if not included in model (ppt); and
site specific altitude (m).
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Figure 110.
Temperature
Saturation as a Function of
Oxygen Saturation
Salinity - 0 ppt, Altitude -Om
an 12.0
_£
c 10.0
o
2 8.0
^
% 6.0
10 20 30
Temperature {C)
40
Figure 111. Saturation as a Function of Salinity
10.0
9.5
9.0
8.5
8.0
7.5
7.0
Oxygen Saturation
Temperature-20C, Altitude - 0 m
10 20
Salinity {ppt)
30
40
Figure 112. Saturation as a function of altitude
Oxygen Saturation
Temperature-20C, Salinity - 0 ppt
10
c
g
'2 7
f3 (~
LO O
5
500 1000 1500
Altitude (m)
2000
Diel Oxygen
Significant fluctuations in oxygen are possible over the course of each day, particularly under
eutrophic conditions. This type of fluctuation may now be captured within AQUATOX when
the model is run with an hourly time-step. If the model is run with a larger reporting time step
(but an hourly integration time-step) the minimum and maximum oxygen concentrations will be
output on the basis of the hourly results.
The instantaneous light climate (28) affects the photosynthesis within the system and this, in
turn, affects the amount of oxygen released into the water column (187). To assist in this
simulation, hourly oxygen loadings may be input into AQUATOX if such data are available.
Alternatively, the effects of oxygen loadings and washout may be turned off, assuming that
upstream processes governing oxygen are producing water concentrations identical to the current
stream segment being modeled; in this way, in-stream processes can be analyzed without being
dominated by upstream loadings.
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Lethal Effects due to Low Oxygen
AQUATOX represents both lethal and non-lethal effects from low concentrations of dissolved
oxygen. The US EPA saltwater criteria document suggests the following general model for
estimating time to mortality based on data from two species of saltwater juvenile fish, one
species of juvenile freshwater fish, and three species of saltwater larval crustaceans (U.S.
Environmental Protection Agency, 2000, Equation 9):
LCTime = Slope _ • \n(LC24hours) + Intercept _ (199)
exptime exptime
where:
= Lethal Concentration for a given percentage of a population
over the given duration (mg/L);
Slope ^ = 0.191 • LC24hours + 0.064 (200)
exptime
and
Intercept^_ = 0.392 • LC24hours + 0.204 (201)
exptime
To produce a general model of low oxygen effects, concentrations at which different percentages
are killed (holding duration constant) also need to be related to one another. That is to say, a
model that relates LC5 to LC50 to LC95 must be produced. Examining available data (Figure
113 to Figure 115), a linear model seems appropriate
LCFracduration = Slope conc • LCKnownduration + Intercept^^ (202)
pctkilled pctkilled
where:
LCFracduration = concentration at which given percentage of organisms are killed
estimated from a known lethal concentration (holding duration
constant).
LCKnownduration = known lethal concentration for a given percentage of organisms at
the given duration.
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Further examination of available data indicates different slopes for different species (Figure
116). Most important, however, is that for all species, the range of slopes is quite narrow,
ranging from -0.001 to -0.01. This indicates that for all species and all durations, the range at
which mortality occurs due to insufficient oxygen is quite narrow. For this reason, the
intermediate value of -0.007 was chosen as it is likely to reproduce available data reasonably
well. This is preferable to having a user input this slope as these data are unlikely to be available
to most users. Given a known lethal concentration at a known duration and using this slope, the
Intercept can be calculated see (204).
Figure 113. Menhaden percent killed vs. o2 exposure concentration
Menhaden Pet Killed vs. Cones
atvarious exposure times (hours)
20
40 60
Percent Killed
80
100
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Figure 114. Blue Crab percent killed vs. O2 exposure concentration
BlueCrab Pet Killed vs. Cones, at various
exposure times (hours)
1.2
1
0.8
in
o
,90.6
O
0.4 •
0.2 •
0
y=-0.007x +1.047
y=-0.005x +0.766
•H 6-12
» 14-24
Linear (6-12)
Linear (14-24)
50 100
Percent Killed
150
Figure 115. Spot percent killed vs. O2 exposure concentration
Spot Pet. Killed vs. Cones at various
exposure times (hours)
y=-0.0019x +0.7678
y=-0.0016x +0.5778
• 1
A 4
x 24
+• 72
I inn-ir f~>\
m 2
6
• 48
- 72
20
40 60
Percent Killed
100
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Figure 116. Slope vs. species type
Slope Conc./PctKilled vs. Species Type
o
-0.002 -
•c
1 -0.004 -
£
g -0.006 -
o
O
% -0.008 -
Q.
O
CO
-0.01 -
-0 012
^ m m
j
* •
*
A
B
• Menhaden, Blue Crab
• Spot
• *
0 20 40 60 80 100 120
duration
Combining equations (199) to (202), given a user input 24-hour lethal concentration (in the
Animal underlying data screen), the model can calculate the fraction killed at a given duration
and at a given concentration.
PctKilled = -
O2Conc - 0.204 + 0.064 • \n(ExpTime)
0.191 • \n(ExpTime) + 0.392
-Intercept conc
pctkilled
-0.007
(203)
where:
Intercept conc = LCKnownduration + 0.007 • PctKilledKnown
pctkilled
(204)
and:
PctKilled
ExpTime
LCKnownduration
estimated percent killed at a given oxygen concentration and
exposure time;
concentration of oxygen (mg/L);
exposure time (hours);
user input lethal concentration (24-hour) (mg/L);
user input percentage for lethal concentration (percentage);
The model presented in equation (203) requires a user to input 24-hour lethal concentration as
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this is the basis for the general model presented in the saltwater criteria document. If a user has a
lethal concentration at a different duration, the user must estimate the 24-hour lethal
concentration, bearing in mind that the relationship between exposure time and lethal
concentrations is usually logarithmic in nature (Figure 117). There are insufficient data to
develop a general model that will estimate 24-hour lethal concentrations given different user
input durations.
AQUATOX tracks oxygen concentrations over the previous 96 hours from the current time-step.
The oxygen effects model is then applied with the durations shown below:
. 1 hour, 4 hours, 12 hours (when model is run with hourly time-step only)
• 1 day, 2 days, 4 days (relevant to both hourly and daily time-steps)
AQUATOX finds the minimum oxygen concentration over each of these time-periods and
applies it to equation (203). The maximum percent killed over all of the durations tested is then
applied to the animal biomass by increasing mortality (equations 112 and 90) .
Figure 118 shows an example of a three-dimensional response surface produced by this model.
This is a model of low oxygen lethality for Atlantic menhaden produced by entering a 24-hour
LC95 of 0.61 mg/L. Figure 119 shows model predictions using a 24 hour LC50 of 3 mg/L
overlaid on a figure from the U.S. Environmental Protection Agency's 1986 Quality Criteria for
Water. This plot shows that the default value of 3 mg/L works well for many species, but for
white bass, for example, the LC50 should be set to a lower concentration.
Figure 117. LC50 to exposure time based on data from U.S. EPA 2000
LC50 to Exposure Time Relationships,
Menhaden and Spot
y= 0.0762lnx +0.6332
y= 0.0526ln(x) +0.4773
Spot 88 mm
Atlantic menhaden 132mm
-Log.(Spot88mm)
- Log. (Atlantic menhaden 132mm)
20 40 60
Exposure Time, Hours
80
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CHAPTER 5
Figure 118. Example of low O2 lethality model- menhaden response surface
120
(Exposure
Time in
Hours)
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CHAPTER 5
Figure 119. 96-hour model predictions (in red) compared against continuous exposure data
(Data from U.S. EPA 1986, model set up using a 24-hour LC50 of 3.0mg/L)
~0
^ 1 OO
CO
•£= 00
o
0
*O 6O
,
B
tt>
CL
o 20
to o
^ 0-|°^"
* I "
V "'
r
i •
• 1
^1 i/i i
a 345
Dissolved Oxygen
O 1 1 1 1
"^^
O Largemouth Bass
O Slack Crappie
A White Sucker
v White Bass
• Northern Pike
• Channel Catfish
A Walleye
^Smallmouth Basi
1 1111
e T e 9 10
(mg/L)
Non-Lethal Effects due to Low Oxygen
The same three dimensional model used for lethal effects is utilized to calculate non-lethal low
oxygen effects (functions of exposure level and time.) In this case, EC50 reproduction affects
the fraction of gametes that are lost and EC50 growth affects consumption rates.
O2EffectFrac = •
'O2Conc - 0.204 + 0.064 • \n(ExpTime)
0.191 • \n(ExpTime) + 0.392
- Intercept
pctkilled
-0.007
(205)
and:
where:
O2EffectFrac
O2Conc
Intercept cona = EC50duratlon + 0.007 • 50
pctkilled
(206)
calculated fraction of gametes lost or reduction in growth rate at a
given oxygen concentration and exposure time;
concentration of oxygen (mg/L);
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ExpTime
= exposure time (hours);
= user input 50% effect concentration (24-hour) (mg/L);
O2EffectFrac is then applied to ingestion (91) and gamete loss (126)
5.6 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
Carbon Dioxide: Simplifying
Assumption
• Atmospheric exchange is treated
similar to that for oxygen
dt
where:
= Loading + Respired ^Decompose - Assimilation - Washout
(207)
+ Washin ± CO2AtmosExch ± TurbDiff ± Diffusion
Seg
Respired = CO2Biomass • ^Orgamsm( Respiration Orgamsm)
(208)
Assimilation = ^Piant (Photosynthesisplant • UptakeCO2) (209)
Decompose = CO2Biomass-^Detntm(DecompDetntus)
(210)
and where:
dCO2/dt
Loading
Respired
Decompose
Assimilation
Washout
Washin
Diffusionseg
CO 2A tmosExch
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 (16);
loadings from linked upstream segments (g/m3-d), see (30);
= gain or loss due to diffusive transport over
the feedback link between two segments, (g/m3-d), see (32);
interchange of carbon dioxide with atmosphere (g/m3-d);
ratio of carbon dioxide to organic matter (unitless);
rate of respiration (g/m3-d), see (63) and (100);
rate of decomposition (g/m3-d), see (159);
rate of photosynthesis (g/m3-d), see (35); and
ratio of carbon dioxide to photosynthate (= 0.53).
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Carbon dioxide also is exchanged with the atmosphere; this process is important, but is not
instantaneous: significant undersaturation and over saturation are possible (Stumm and Morgan,
1996). The treatment of atmospheric exchange is similar to that for oxygen:
CO2AtmosExch = KLiqCO2 • (CO2Sat - CO2)
(211)
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 • MolWtO
2
MolWtCO
-2
0.25
(212)
where:
CO2AtmosExch =
KLiqCO2
CO2
CO2Sat
KReaer =
MolWtO2
MolWtCO2
interchange of carbon dioxide with atmosphere (g/m -d);
depth-averaged liquid-phase mass transfer coefficient (1/d);
concentration of carbon dioxide (g/m3);
saturation concentration of carbon dioxide (g/m3), see (213);
depth-averaged reaeration coefficient for oxygen (1/d), see (191)-
(195);
molecular weight of oxygen (=32); and
molecular weight of carbon dioxide (= 44).
Keying the mass-transfer coefficient for carbon dioxide to the reaeration coefficient for oxygen
is very powerful in that the effects of wind (Figure 120) and the velocity and depth of streams
can be represented, using the oxygen equations (Equations (191)-(195)).
Figure 120. Carbon dioxide mass transfer
EFFECT OF WIND
CARBON DIOXIDE, DEPTH = 1 m
6 8 10 12 14 16
WIND (m/s)
Based on this approach, the predicted mass transfer under still conditions is 0.92, compared to
the observed value of 0.89 + 0.03 (Lyman et al., 1982). This same approach is used, with minor
modifications, to predict the volatilization of other chemicals (see Section 8.5). Computation of
saturation of carbon dioxide is based on the method in Bowie et al. (1985; see also Chapra and
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Reckhow, 1983) using Henry's law constant, with its temperature dependency (Figure 121), and
the partial pressure of carbon dioxide:
CO2Sat = CO2Henry • pCO2
where:
2385.73
CO2Henry = MCO2 • 1Q TK^
-14.0184 + 0.0152642 • TKelvin
(213)
(214)
and where:
CO2Sat
CO2Henry =
pC02
MCO2
TKelvin =
Temperature =
TKelvin = 2 73.15 + Temperature
(215)
saturation concentration of carbon dioxide (g/m );
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 deg.K, and
ambient water temperature (deg. C).
Figure 121. Saturation of carbon dioxide
CARBON DIOXIDE SATURATION
7.5
12 16.5 21 25.5 30 34.5 39
TEMPERATURE (C)
5.7 Modeling Dynamic pH
Dynamic pH is important in simulations for several reasons:
o pH affects the ionization of ammonia and potential
resulting toxicity;
o pH affects the hydrolysis and ionization of organic
chemicals which potentially has effects on chemical
fate and the degree of toxicity;
o pH also affects the decay of organic matter and denitrification of nitrate which could
eventually feed back to the animals;
Dynamic pH: Simplifying
Assumptions
• Simple semi-empirical formulation
• Computation is good for the pH
range of 4 to 8.25
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o if pH exceeds 7.5, calcite precipitation can take place which has a significant effect
on the food-web.
A user-input time-series of pH levels may be used to drive the model or AQUATOX can
calculate pH levels.
Many models follow the example of Stumm and Morgan (1996) and solve simultaneous
equations for pH, alkalinity, and the complete carbonate-bicarbonate equilibrium system.
However, this approach requires more data than are often available, and the iterative solution of
the equations entails an additional computational burden—all for a precision that is unnecessary
for ecosystem models. The alternative is to restrict the range of simulated pH to that of normal
aquatic systems and to make simplifying assumptions that allow a semi-empirical computation of
pH (Marmorek et al. 1996, Small and Sutton 1986). That is the approach taken for AQUATOX.
The computation is good for the pH range of 4 to 8.25, where the carbonate ion is negligible and
can thus be ignored. The derivation is given by Small and Sutton (1986), with a correction for
dissolved organic carbon (Marmorek et al. 1996). It incorporates a quadratic function of carbon
dioxide; and it is a nonlinear function of mean alkalinity and the concentration of refractory
dissolved organic carbon (humic and fulvic acids), by means of an inverse hyperbolic sine
function:
B • ArcSmti (^aHmty - 5.L DOC^
( C )
pHCalc = A+_
where:
(216)
pHCalc
ArcSinH
Alkalinity
DOC
5.1
pH;
inverse hyperbolic sine function;
mean Gran alkalinity (ueq CaCOs/L);
refractory dissolved organic carbon (mg/L); sum of (143), (144);
average ueq of organic ions per mg of DOC;
B = l/ln(10)
Alpha = H2CO3*-CCO2
H2CO3* = 10
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where:
H2CO3* = first acidity constant;
CCO2 = CO2 expressed as ueq/L; see (207) multiplied by conversion factor
of 22.73 (ueq/mg);
pkw = ionization constant for water (le-14);
T = temperature (°C); see (24);
0.92 = correction factor for dissolved CO2.
Calibration and verification of the construct used data from nine lakes and ponds in the National
Eutrophication Survey (U.S. Environmental Protection Agency, 1977), two observations on Lake
Onondaga, NY, from before and after closure of a chlor-alkali plant (Effler et al., 1996), and one
observation in a river (Figure 122). The correction factor for CO2 was obtained by fitting the
data to the unity line, but ignoring the two highest points because the construct does not predict
pH above 8.25.
Figure 122. Comparison of predicted and observed pHs from selected lakes.
6.0
Observed vs. Predicted pH
7.0
8.0
Predicted pH
9.0
10.0
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The construct also was verified using time-series data from Lake Onondaga, NY (Figure 123).
The observed data were interpolated from the 2-m depth pH isopleths on a graph (Effler et al.
1996), introducing some uncertainty into the comparison.
Figure 123. Comparison of predicted and observed pH values for Lake Onondaga, NY.
Data from (Effler et al. 1996).
Predicted pH, Lake Onondaga NY
•AQUATOX
• Observed
• Poly. (Observed)
Feb- Apr- May- Jul-89 Aug- Oct- Dec-
89 89 89 89 89 89
Calcite Precipitation: Simplifying
Assumptions
• Biogenic origin
• pH of 8.25 is considered as a
threshold for precipitation
• Dissolved phosphate sorbs to
calcium carbonate but desorption is
not modeled
5.8 Modeling Calcium Carbonate Precipitation and Effects
Precipitation of calcium carbonate (mostly calcite in
freshwater), with the potential for sorption and removal of
phosphorus, is modeled as an extension of the pH
approach. The prediction of pH in AQUATOX does not
extend past 8.25 because the carbonate-bicarbonate system
becomes dominant. We use the predicted pH of 7.5 as a
threshold for precipitation of calcium carbonate in
freshwater ecosystems. Almost all calcite is formed
biogenically, primarily by plants using bicarbonate as a source of carbon (McConnaughey et al.
1994). Even "whitings" (sudden precipitation of fine-grained calcite) have been shown to be a
consequence of blue-green photosynthesis (Thompson et al. 1997). Calcareous plants are
characterized by pH polarization with acidic and alkaline poles; calcification occurs at the
alkaline pole (McConnaughey et al. 1994). Proton generation leads to formation of twice as
much CO2 than is used in the process, providing CO2 that is immediately taken up for
photosynthesis. As a result, calcification and photosynthesis use equivalent moles of C, as
shown by both theory and experiments (McConnaughey et al. 1994). Three chemical reactions
represent this process:
Ca2+ + CO2 + H2O -» CaCO3 + 2H+
2H+ + 2HCO3" -» 2CO2 + 2H2O
Ca2+ + 2HCO3" -» CaCO3 + CO2 + H2O
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Not all plants can use bicarbonate. However, it is difficult to generalize; mosses do not and
many chrysophytes (golden algae) do not. Evidence suggests that other groups, including
greens, blue-greens, diatoms, and macrophytes, have species that do use bicarbonate and that
these will dominate in alkaline systems.
The algorithm simulates precipitation of calcite as being the molar equivalent to photosynthesis
of most plants and as occurring when the threshold pH of 7.5 is reached:
If pH >= 7.5 then CalcitePcpt = C2Calcite • ?'™^ (217)
C2OM
where:
pH = pH calculated by Eq. 204 or observed time series;
CalcitePcpt = calcite precipitated (mg calcite/L • d);
C2Calcite = stoichiometric constant for C and calcite (8.33, g calcite /g C);
Photosynthesis = rate of photosynthesis for a subset of plants (g/m3 • d);
PlantSubset = all plants except Bryophytes and Other Algae;
C2OM = stoichiometric constant for C and organic matter (1 .9, g C/g OM).
Precipitated calcite is protected, in part, by sorbed organic material. Therefore, it is assumed to
be insoluble — an assumption also made in the sediment diagenesis model (Di Toro 2001).
Because the settling rate is fast, it is also assumed that the calcite goes directly to the sediment.
Phosphorus is adsorbed to the surface and coprecipitates with calcium carbonate (Wetzel 2001).
The rate of coprecipitation seems to be dependent on the rate of calcite precipitation (Otsuki and
Wetzel 1972). However, the sorption is weak and can be reversed easily (Murphy et al. 1983).
Therefore, the default partition coefficient (300 L/kg) is based on equilibration experiments with
sediments from a marl lake (Van Rees et al. 1991).
SorptionP = KDP Calcite • Phosphate • CalcitePcpt • \e - 6 (218)
where:
SorptionP = rate of sorption of phosphorus to calcite (mgP/L • d);
KDPCalcite = partition coefficient for phosphorus to calcite (L/kg);
Phosphate = concentration of phosphorus in water (mg P/L) (see (181));
1 e-6 = conversion factor (kg/mg).
Ironically, precipitation is impeded by phosphorus levels that are too high. The threshold for
inhibition is about 30 mg-P/L (Neal 2001). Furthermore, dissolved organic matter also can
inhibit precipitation, with 120 mg C/L being the threshold (Neal 2001). However, these
concentrations are so high that they are ignored in the model.
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6. INORGANIC SEDIMENTS
Release 3.0 of AQUATOX contains four levels of inorganic sediment submodels:
• a very simple model based on a regression relationship between sediment deposition and
total suspended sediments, see (122).
• a simple inorganic sediments submodel described in Section 6.1
• a complex multiple-layer sediment submodel described in Section 6.2
• a sediment diagenesis model described in Section 7.
6.1 Sand Silt Clay Model
The original version was contributed by Rodolfo Camacho of
Abt Associates Inc. AQUATOX simulates scour, deposition
and transport of sediments and calculates the concentration of
i- ,-,i , 1 J_T j. i j -j.i • • River reach is short and well-mixed
sediments in the water column and sediment bed within a
Sand, Silt, Clay: Simplifying
Assumptions
Channel is rectangular
Daily average flow regime
determines scour, and deposition
Model for streams / rivers only
river reach. For running waters, the sediment is divided into
three categories according to the particle size:
• sand, with particle sizes between 0.062 to 2.0
millimeters (mm),
• silt (0.004 to 0.062 mm), and
• 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. 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.
Within the bed, the mass of sediment in each of the three sediment size classes is a function of
the mass in the previous time step, and the mass of sediment in the overlying water column lost
through deposition, and gained through scour:
MassBedsed = MassBedSed,t=-i + (DepositSed - ScourSed) • VolumeWater • TimeStep (219)
where:
MassBedsed = mass of sediment in channel bed (kg);
MassBedsed, t = -i = mass of sediment in channel bed on previous day (kg);
Depositsed = amount of suspended sediment deposited (kg/m3 d); see (230);
Scoursed = amount of silt or clay resuspended (kg/m3 d); see (227);
VolumeWater = volume of stream reach (m3); see (2); and
TimeStep = derivative time-step (d).
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The volumes of the respective sediment size classes are calculated as:
., , MassBedsed /iim
Volume sed = (22°)
RkOsed
where:
Volumesed = volume of given sediment size class (m3);
MassBedsed = mass of the given sediment size class (kg);
Rhosed = density of given sediment size class (kg/m3);
RhoSand = 2600 (kg/m3); and
Rhos.it, ciay = 2400 (kg/m3).
The porosity of the bed is calculated as the volume weighted average of the porosity of its
components:
BedPorosity = EFmcSed • Porosity Sed (221)
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 (fraction).
The total volume of the bed is calculated as:
D ^T/ 7 Volume sand + Volume siit+ VolumeCiay ,.„,
BedVolume = (222)
1-BedPorosity
where:
BedVolume = Volume of the bed (m3).
The depth of the bed is calculated as
r, ,T^ , BedVolume ,--~
BedDepth = (223)
ChannelLength • ChannelWidth
where:
BedDepth = depth of the sediment bed (m);
ChannelLength = length of the channel (m); and
ChannelWidth = width of the channel (m).
The concentrations of silt and clay suspended 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:
KgLoad- ,
ConeSed = + ConeSed, t=-i + ScourSed - DepositSed - WashSed (224)
(J • oo4UU
where:
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Concsed = concentration of silt or clay in water column (kg/m3);
Concsed, t = -i = concentration of silt or clay on previous day (kg/m3);
KgLoadsed = loading of clay or silt (kg/d);
Q = flow rate (m3/s);
86400 = conversion from m3/s to m3/d;
Scoursed = amount of silt or clay resuspended (kg/m3); see (227);
Deposited = amount of suspended sediment deposited (kg/m3); see (230); and
Wash^ed = amount of sediment lost through downstream transport (kg/m3);
see (231).
The concentration of sand is computed using a totally different approach, which is described in
the section on Sand below.
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, U.S. Environmental Protection Agency, 1991). Deposition and scour of silts and clay
are modeled using the relationships for deposition (Krone, 1962) and scour (Partheniades, 1965)
as summarized by Partheniades (1971).
Shear stress is computed as (Bicknell et al., 1992):
Tau = mODensity • Slope • HRadius (225)
where:
Tau = shear stress (kg/m2);
H2ODensity = density of water (1000 kg/m3);
Slope = slope of channel (m/m);
and hydraulic radius (HRadius) is (Colby and Mclntire, 1978):
Y-Width „„.
HRadius = (226)
2-Y + Width ^ '
where:
HRadius = hydraulic radius (m);
Y = average depth over reach (m); and
Width = channel width (m).
Resuspension or scour of bed sediments is predicted to occur when the computed shear stress is
greater than the critical shear stress for scour:
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if Tau > TauScoursed then
i ( Tau ^ (227)
Y \TauScour $ed )
where:
ScourSed = resuspension of silt or clay (kg/m3 d);
Erodibilitysed = credibility coefficient (0.244 kg/m2 d); and
TauScoursed = critical shear stress for scour of silt or clay (kg/m2).
The amount of sediment that is resuspended is constrained by the mass of sediments stored in the
bed. An intermediate variable representing the maximum potential mass that can be scoured is
calculated; if the mass available is less than the potential, then scour is set to the lower amount:
Check sed = Scour sed' Volumewater (228)
if Mass'sed ^ CheckSed then
Masssed (229)
Scour sed
Volumewater
where:
Checksed = maximum potential mass (kg); and
mass of silt or clay in bed (kg).
Deposition occurs when the computed shear stress is less than the critical depositional shear
stress:
if Tau < TauDepSed then
Deposit^ = ConcSt
-VT&j-SecPerDay
Tau
TauDep&j
(230)
where:
Depositsed = amount of sediment deposited (kg/m3 day);
TauDepsed = critical depositional shear stress (kg/m2);
Concsed = concentration of suspended silt or clay (kg/m3);
VTsed = terminal fall velocity of given sediment type (m/s); and
SecPerDay = 86400 (seconds / day).
The terminal fall velocity is specified in the site's underlying data.
Downstream transport is an important mechanism for loss of suspended sediment from a given
stream reach:
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„, , _ Disch-ConeSed ,,,,n
Washsed —— (231)
SegVolume
where:
Washsed = amount of given sediment lost to downstream transport (kg/m3
day);
Disch = discharge of water from the segment (nrVday);
Concsed = concentration of suspended sediment (kg/m3);
SegVolume = volume of segment (m3).
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:
Frac Scour Detritus= Frac Scour sat= Scour sat ~ (232)
Mass sat
Scour Detritus = Frac Scour Detritus • ConcAiisedDetntus • 1000 (233)
where:
FracScour = fraction of scour per day (fraction/day);
Scoursnt = amount of silt scoured (kg/m3 day) see (227);
VolumesHt = volume of silt initially in the bed (m3);
Masssnt = mass of silt initially in the bed (kg);
ConcAiisedDetritus = 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:
„ ^ „ „ Deposition „.,• 1000 ,.„..,
brae DepositionDetritus = brae Depositionsat = — — (234)
Cone sat
DepositionDetntus = Frac DepositionDetntus • ConeSusPDetntus (235)
where:
Depositionsnt = amount of silt deposited (kg/m3 day) see (230);
Cone snt = amount of silt initially in the water (g/m3);
FracDeposition = fraction of deposition per day (frac / day); and
(^,OnC SuspDetritus
and
DepositionDetritus = amount of detritus deposited (g/m3 day).
amount of suspended detritus initially in the water (g/m3);
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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.
. -, Rho Velocity• Slope r=—-— ^-,^
PotConcsand = 0.05 . , ' ^TauStar (236)
RhoSand-Rho \Rhosand-Rho
~' & ' Dsand' 1(J(J(J
Rho
where:
PotConcsand = potential concentration of suspended sand (kg/m3);
Rho = density of water (1000 kg/m3)
Rhosand = density of sand (2650 kg/m3);
Velocity = flow velocity (converted to m/s);
Slope = slope of stream (m/m);
Dsand = mean diameter of sand particle (0.30 mm converted to m); and
TauStar = dimensionless shear stress.
The dimensionless shear stress is calculated by:
_, 0 Rho TTr> ,. Slope „,„„<..
TauStar = -- HRadius -- - - (237)
DSand/ 1000
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:
Check sand = PotConcsand ' Volumewater (238)
MassSuspSand = Cone sand • Volumewater (239)
TotalMassSand = MassSuspSand + MassBedSand (240)
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if Checksand ^ MassSuspSand then
DepositSand = MassSuspSand - Checksand (241)
ConCSand = PotConCSand
if Checksand ^ TotalMasssand then
MassBedsand = 0 (242)
_ _ TotalMasssand
COnCSand
Volumewater
if Checksand > MassSuspSand and < TotalMasssand then
Scoursand = Checksand - MassSuspSand (243)
_ MassSuspSand + Scoursand
COnCSand
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-E Phyto - Z PartDetr (244)
where:
InorgSed = concentration of suspended inorganic sediments (g/m3);
TSS = observed concentration of total suspended solids (g/m3);
Phyto = predicted phytoplankton concentrations (g/m3); and
PartDetr = predicted suspended detritus concentrations (g/m3).
A radio button on the TSS loadings screen is used to specify whether user-input TSS loadings are
"total suspended (inorganic) sediments" or "total suspended solids." If "inorganic sediments"
are specified then equation (244) is not required as the TSS loading is not assumed to include
phytoplankton or organic matter.
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Multi-Layer Sediment
Simplifying Assumptions
Model:
6.2 Multi-Layer Sediment Model
As an alternative to the simple sand-silt-clay model
described above (section 6.1), AQUATOX also includes a
complex multiple layer sediment transport model. This
model can simulate up to ten bottom layers of sediment.
Within each sediment layer, the state variables consist of
inorganic solids, pore waters, labile and refractory dissolved
organic matter in pore waters, and sedimented detritus.
Nutrient concentrations are not modeled in the pore waters
of the sediment layers, although dissolved organic matter is.
Each of these state variables can also have up to twenty organic toxicant concentrations
associated with it. The AQUATOX sediment transport component is summarized in Figure 124.
Figure 124: Components of the AQUATOX sediment transport model and units.
Top layer is "active layer" that
interacts with the water column
Sediment layers are well-mixed
Density of each sediment layer
remains constant
Hardpan barrier assumed at the
bottom of the system
Susp. Inorg.
Solids mg/Lwc
DOM in Water
Col. mg/Lwc
Inorganic
Solids g/m
DOM in Pore
Water mg/L
Pore Water
m3/m2
Sed Detr mg/L
Pore Water
DOM in Pore
Water mg/L
Buried Detr g/m
Inorganic
Solids g/m
Buried Detr g/m2
DOM in Pore
Water mg/L
Pore Water
m3/m2
The AQUATOX sediment submodel was designed to be nearly identical in concept to IPX (In-
Place Pollutant eXport) version 2.7.4 (Velleux et. al 2000). Erosion and deposition cause
changes in the mass of sediments in the top or "active" layer. When the active layer becomes too
large or too small, a conveyor-belt action takes place moving all of the layers up or down intact
("pez dispenser" action). Because all layers are assumed well-mixed, moving partial layers up
and down and then recalculating concentrations within sediment layers would result in too much
mixing throughout the sediment layers (and advection of pollutants from the bottom layer to the
top). During development, the AQUATOX sediment submodel was closely tested against the
IPX model and precisely reproduced results from that model.
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Within AQUATOX, inorganic sediments in layered sediments are represented as three distinct
state variables: cohesives (clay), non-cohesives (silt), and non-cohesives2 (sand). These
correspond to the variables described in Section 6.1.
For each inorganic compartment, the sediment transport model accepts daily input parameters for
interactions between the top sediment layer and the water column. These interactions are input
as daily scour and daily deposition for each inorganic sediment type in units of grams per day.
The model also requires deposition and erosion velocities for cohesive inorganic sediments.
These inputs are then used to calculate the deposition and erosion of organic matter within the
system.
AQUATOX assumes that the density of each sediment layer will remain constant throughout a
simulation. Because of this, the volume and thickness of the top bed layer will vary in response
to deposition and erosion. Additionally, the surface area of the multi-layer sediment bed is set to
remain constant. Even if the sediment surface at a site grows or shrinks due to water volume
changes, this model tracks sediments under the initial-condition surface area.
When the top layer has reached a maximum thickness, it is broken into two layers. Other layers
in the system are moved down one layer without disturbing their concentrations or thicknesses.
This allows the model to maintain a toxicant concentration gradient within the sediment layers
during depositional regimes. Similarly, when the top layer has eroded to a minimum size, the
layer beneath it is joined with the active layer to form a new top layer. In this case, lower layers
are moved up one level, without changing their concentrations, densities, or thicknesses. More
details about these processes can be found in section on sediment layer interactions below.
At the bottom of the system, a hardpan barrier is assumed. The model, therefore, has no
interaction beneath its lowest layer. If enough erosion takes place so that this hardpan barrier is
exposed, no further erosion will be possible. Deposition can, however, rebuild the sediment
layer system. This hardpan bottom prevents the artificial inclusion of "clean" sediment and
organic matter into the model's simulation during erosional events. Because it is a barrier and
not a boundary, it prevents loss of toxicant to the system under depositional regimes.
AQUATOX writes output data for a fixed number of sediment layers. When, due to deposition,
a layer is buried below the fixed number of sediment layers, AQUATOX keeps track of that
layer, but does not write daily output. That deep layer is stored in memory and state variables in
that layer have the potential to move back into the system later due to erosion. When, due to
erosion, there are fewer than the fixed number of sediment layers, AQUATOX writes zeros for
all layers below the hardpan barrier.
Pore water moves up and down through the sediment system when layers move upward and
downward in the system. Substances dissolved in pore water also move through the system as a
result of diffusion.
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Suspended Inorganic Sediments
As mentioned above, inorganic sediments are broken into three sets of state variables based on
particle size. Each of these three inorganic sediment types are found in the water column as well
as in each modeled sediment layer.
For inorganic sediments suspended in the water column, the derivative looks as follows:
dSuspSediment
dt
where:
• = Loading + Scour - Deposition - Washout + Washin (245)
dSuspSediment/dt = change in concentration of suspended sediment (g/m3-d);
Loading = inflow loadings (excluding upstream segments) (g/m3-d);
Scour = scour from the active sediment layer (g/m3-d);
Deposition = deposition to the active sediment layer (g/m3-d);
Washout = loss due to being carried downstream (g/m3-d), see (16);
Washin = loadings from upstream segments (g/m3-d), see (30);
There are two options for specifying deposition to and scour from the active layer when using the
multi-layer sediment option. Deposition and scour can be simulated by a hydrodynamic model
and imported into AQUATOX. In this case, for each of the three categories of suspended
sediment, deposition to and scour from the active layer are input to AQUATOX as a daily time
series in units of g/d. These inputs are converted into units of g/m3-d by dividing by the volume
of the segment.
Alternatively, based on user specification, the model can calculate deposition and scour using the
sand-silt-clay model specifications, see (230), (227). In the "Edit Sediment Layer Data" dialog,
where cohesives or non-cohesives are being input there is a checkbox that states "use sand-silt-
clay model" to toggle between these two options.
Unlike the simple sediment model, suspended sediments can sorb organic toxicants when the
multi-layer sediment model is run. More specifications about sorption of organic chemicals to
inorganic sediments can be found in Section 8.10 of this document.
Inorganics in the Sediment Bed
Inorganic sediments are found in each sediment layer that is modeled. The derivative, however
is relevant only for the active (top) layer.
dBottomSediment . .
= Deposition - Scour + Bedload - Bedloss (246)
dt
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where:
dBottomSediment/dt = change in concentration of sediment in this bed layer (g/m2-d);
Scour = movement to the water column (g/m2-d);
Deposition = deposition from the water column (g/m2-d);
Bedload = bedload from all upstream segments (g/m2-d). Only relevant for
the active layer of sediment, see (247);
Bedloss = loss due to bedload to all downstream segments (g/m2-d). Only
relevant for the active layer of sediment, see (248).
Deposition and scour are input into the model in units of g/d. These inputs are divided by the
area of the system to get units of g/m2-d.
Bed load is input as a loading in g/d for each link between two segments, if multiple segments
are being modeled. This process is only relevant for the top layer of sediment modeled. The
total bed load for a particular segment can be calculated by summing the loadings over all
incoming links.
D JT J
BedLoad = - - — - - (247)
AvgArea
where:
2
BedLoad = total bedload from all upstream segments (g/m-d);
BedLoadUpstreamiink = bedload over one of the upstream links (g/d);
AvgArea = average area of the segment (m2);
Similarly, total bed loss is the sum of the loadings over all outgoing links:
n IT ^ "ed-L°SSUpstreamlink
BedLoss = > - - - - - (248)
AvgArea
BedLoss = total bedloss to all downstream segments (g/m2-d);
BedLossDownstreamiink = bedload over one of the downstream links (g/d);
AvgArea = average area of the segment (m2);
As mentioned above, the derivative presented is relevant only for the active layer. Inorganic
sediments below the active layer do move up and down through the system as a result of
exposure or deposition. However, these sediments move as a part of their entire intact layer
when the active layer has reached its maximum or minimum level.
When the top layer reaches a minimum thickness, the layer below the active layer is added to the
active layer to form one new layer. The inorganic sediments within these two layers do undergo
mixing during this process.
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Detritus in the Sediment Bed
State variables tracking sedimented labile and refractory detritus are also included in each layer
of sediment that is simulated. The equations for sedimented detritus in the active layer are the
same as those for "classic" AQUATOX.
Like inorganic sediments, buried detritus below the active layer only moves up and down in the
system when its layer moves up and down intact. Therefore, detritus found below the active
layer has a very simple derivative:
dBuriedDetritus ^ ,-. in^
= -Decomp (249)
dt
where:
dBuriedDetritus/dt = change in concentration of sediment on bottom (g/m2-d);
Decomp = microbial decomposition in (g/m2-d) see (159).
Pore Waters in the Sediment Bed
Pore water quantities are also tracked in the sediment bed. The derivative for pore waters is
quite straightforward:
dPoreWater .
= Gamup - LossUp (250)
where:
dPoreWater/dt = change in volume of pore water in the sediment bed normalized
per unit area (m3/m2 -d);
GainUp = gain of pore water from the water column above (m3/m2 -d);
LossUp = loss of pore water to the water column above (mVm2 -d);
In the active layer, pore waters are assumed to move into the water column when scour occurs.
To keep the bed density constant, the loss of pore waters can be solved as follows:
-^ (Erode ~ ,Density ~ ,) - (Erode~ , / BedDensity]
LoSSUp = 2^ • — -L^LL 1 ¥2. -L-L (L5\}
I _L / _016/.LXC-A/kS ii>y ) J- C O
where:
Lossup = loss of pore water to the water column above (cmV-d);
Erodesed = scour of this sediment to the water column above, (g/d);
Density sed = density of this sediment (g/m3);
BedDensity = density of the active layer (g/m3);
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le-6 = one over the density of water (m3/g);
Pore waters are taken from the water column when deposition occurs. Keeping the density
constant, the gain of pore waters can be solved as follows:
. -^ (DepositSedDensitySed)-(DepositSed I BedDemity}
amup ~ LSed,ments(\IBedDewity)- le-6(252)
where:
= gain of pore water from the water column above (cmV-d);
Deposit^ = deposit of this sediment from the water column, (g/d);
Density sed = density of this sediment (g/m3);
BedDensity = density of the active layer (g/m3);
le-6 = one over the density of water (m3/g);
When the active layer becomes too large it becomes split into two layers. During this split, the
new second layer is assumed compressed to the density of the old second layer. This
compression results in squeezing of pore water out into the water column. Details of this process
can be found in the section on sediment layer interactions, below.
Dissolved Organic Matter within Pore Waters
Another state variable tracked within the sediment bed is dissolved organic matter within pore
waters. Dissolved labile and refractory detritus within pore waters are tracked as separate state
variables. Like other dissolved detritus, these variables use units of mg/L. However, it is
important to note that these are liters of pore water and not liters in the water column.
dDOM
PoreWa- = GainDOMUp - LossDOMUp + DiffDown + DiffUp - Decomp (253)
dt
where:
dDOMporewater/dt = change in concentration of DOM in pore water in the sediment bed
normalized per unit area (mg/Lpw-d);
GainDOMup = active layer only: gain of DOM due to pore water gain from the water
column (mg/LpM/d);
LossDOMup = active layer only: loss of DOM due to pore water loss to the water
column (nig/Lp^-d);
Diffup, Diffoown = diffusion over upper or lower boundary (mg/Lpw-d), see (256);
Decomp = microbial decomposition in (mg/Lpw-d), see (159).
The increase of DOM due to pore water gain from the water column is simply the volume of
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CHAPTER 6
water that is moving from the water column above multiplied by the DOM concentration in the
above sediment layer. However, the concentration then needs to be normalized for the volume
of pore water in the current segment:
GainDOMUv = ConcDOMn ,
Up "~l
|
Pore Water Vol )
(254)
where:
GainDOMu
up
GainPW,
up
AvgArea
Ie3
PoreWaterVol
gain of DOM due to pore water gain from the layer above (mg/Lpw-d);
concentration of DOM in above layer (mg/Lupper water);
gain of pore water from above (m3upperwater/m -d);
average area of the segment (m2);
units conversion (L/m3);
pore water volume (L);
The loss of DOM in pore water to the water column is a simpler equation due to the fact that
there are no units conversions necessary:
( LossPWv
LossDOMv = ConcDOMl " " " Up
I PoreWaterConc
(255)
where:
LossDOMup
ConcDOMn
LossPW,
= loss of DOM in pore water to the layer above (mg/Lpw-d);
= concentration of DOM in this layer (mg/LpW);
= loss of pore water to above layer (m3pw/m -d);
PoreWaterConc = pore water concentration (m3pw/m2);
up
Because diffusion and decomposition of DOM in pore water occur throughout the system, not
just the active layer, the above derivative is relevant for the whole system. DOM in pore water
also moves up and down through a system when its layer moves intact due to erosion or
deposition.
Diffusion within Pore Waters
AQUATOX calculates the diffusion of dissolved organic matter within pore waters in the
sediment layers. This calculation requires that porosity be included in the diffusion equation:
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Area • AvgPor \ Concup Concd
7~1 • /*/* • -L^*// ^-'^'^-'11 1A.I \SW 1 -L * J^.-L *-SI UV ^sl-St ''^ /Jf,-\AJM y<* ^ S"\
Diffusion^ = —— — -1 dmm_ (256)
CharLength • AvgPor I Porosityup Porositydown I
where:
DiffusionUp = gain of DOM due to diffusive transport over the upper boundary of the
sediment layer, (g/d);
DiffCoeff = dispersion coefficient, (m2 /d);
Area = interfacial area of the upper boundary of the sediment layer (m2);
AvgPor = average porosity of the two layers. If the boundary is a sediment/water
boundary, AvgPor is the porosity of the sediment, (fraction);
CharLength = characteristic mixing length, see text below, (m);
Conciayer = concentration of the relevant segment, (g/m3);
PorosityLayer = porosity of the relevant layer (fraction).
For the characteristic mixing length, AQUATOX uses the distance between two benthic segment
midpoints. For pore water exchange with a surface water segment, the characteristic mixing
length is taken to be the depth of the surficial benthic segment
Equation (256) is also used to calculate the diffusion of toxicants within pore waters. In this
case, the units of Diffusionup are mg/d rather than g/d and the concentrations of toxicants within
the layers are in units of ug/L rather than mg/L.
Sediment Interactions
The mass of the top sediment layer increases and decreases as a result of deposition and scour.
Because the density of this layer remains constant, the volume and thickness of the top sediment
layer also increases and decreases. When the thickness of the top sediment layer reaches its
maximum, as defined by the user, the upper bed is split horizontally into two layers. The top of
these two layers maintains the same density it had before the layer was split up. It is assigned the
initial condition depth of the active layer.
The lower level is assumed to be compressed to the same density as the level below it. This
compression results in pore water being squeezed into the water column. The volume that is lost
as a result of this compression can be solved as follows:
BedMasspiess -(Density Lower-BedVolpieJ
VolumeLost = - - - - - (257)
\e6- Density Lmer
where:
VolumeLost = volume of active layer lost due to compaction (m3);
= mass of the new second layer before compression (g);
= volume of the new second layer before compression (m3);
Densityiower = density of the layer below the active layer (g/m3);
Ie6 = density of water (g/m3)
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The above equation also provides the quantity of pore water squeezed into the water column
because the compression of the active layer is entirely the result of pore water being squeezed
out. Toxicants, dissolved organic matter, and toxicants associated with dissolved organic matter
in the pore water also move into the water column as a result of this compression. If there is
only one layer in the system when the splitting of the active layer takes place, Densitylower is
assumed to be the initial condition density of the second layer in the system.
The volume of a sediment layer is defined as follows:
y SedMass
BedVoln = ^ (258)
BedDensity
where:
BedVoln = volume of bed at layer n (m3);
SedMass = mass of sediment type (g);
BedDensity = density of bed (g/m );
The porosity of a sediment layer is defined as:
FmcWatern=l-Y \ sed (259)
where:
FracWatern = porosity of the sediment layer (fraction);
Concsed = concentration of the sediment (g/m3);
Sedtypes = all organic and inorganic sediments
Density sed = density of the sediment (g/m3);
When the thickness of the top sediment layer reaches a minimum, as defined by the user, the two
top layers combine into one new active layer. The density of this new active layer is the
weighted average of the densities of the combined layers.
,r „ ,„ .„ Volume' -Density> + Volume -Density
NewBedDensity = — (260)
Volume Lcyer2 +Volume Lcyerl
where:
NewBedDensity = density of new joined bed (g/m3);
VolumeLayerN = volume of layer that was initially layer 1 or 2 (m3)
DensityiayerN = density of layer that was initially layer 1 or 2 (g/m3);
The height of the new layer is the sum of the heights of the two layers being joined.
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The bottom of the system is composed of a hardpan barrier. When this bottom is exposed, no
further erosion can take place. When deposition occurs on this hardpan bottom, it is rebuilt with
the density of the layer that existed previously. If enough deposition occurs so that two layers
are created, the new second layer is compressed to the density of the original second layer.
If a system starts with exposed hardpan as an initial condition, the user must still specify the
density of the top layer so that AQUATOX knows what density to create the top layer with. If
the user specifies a density for the second layer, this will be used when enough deposition occurs
so that two layers are created.
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7. SEDIMENT DIAGENESIS
AQUATOX has been modified to include a representation of
the sediment bed as presented in Di Toro's Sediment Flux
Modeling (2001). This optional sediment submodel tracks the
effects of organic matter decomposition on pore-water
nutrients, and predicts the flux of nutrients from the pore
waters to the overlying water column based on this
decomposition. It is a more realistic representation of nutrient
fluxes than the "classic" AQUATOX model. It includes silica,
which will be modeled as a nutrient for diatoms in a later
version.
The model assumes a small aerobic layer (LI) above a larger
anaerobic layer (L2). For this reason, it is best to apply this
optional submodel in eutrophic sites where anaerobic
sediments are prevalent.
Because AQUATOX simulates organic matter with
stoichiometric ratios for nutrients and Di Toro's model
simulates separate organic nutrients, the organic-nutrient
relationships are redefined for the sediments. The additional 21
sediment diagenesis model is enabled (and one driving variable)
Sediment Diagenesis Model:
Simplifying Assumptions
• Model assumes a depositional
environment (no scour is modeled).
• Two layers of sediment are
modeled.
• Aerobic (top) layer is quite thin
• Model is best suited to represent
predominantly anaerobic
sediments.
• Deposition of particulate organic
matter moves directly into Layer 2.
Particulate organic matter in Layer
1 assumed to be negligible and is
not modeled
• The fraction of POP and PON
within defecated or sedimented
matter is assumed equal to the ratio
of phosphate or nitrate to organic
matter for given species.
• All methane is oxidized or lost.
state variables added when the
are as follows:
POC (Particulate Organic Carbon) in sediment: three state variables to represent three
reactivity classes (see below). A component of the particulate organic matter (POM) that
settles from the water column into the anaerobic layer (Layer 2) and decomposes.
PON (Particulate Organic Nitrate) in sediment: as with POC, three state variables to
represent three reactivity classes in the anaerobic layer. Another component of POM.
POP (Particulate Organic Phosphate) in sediment: as with POC, three state variables to
represent three reactivity classes in the anaerobic layer. The third modeled component of
POM.
Ammonia: two state variables to represent two layers. Formed by the decomposition of
PON, this process is also called the diagenesis flux. Ammonia in sediment undergoes
nitrification and flux to or from the water column.
Nitrate: two state variables (in Layers 1 and 2). Formed by nitrification of ammonia in
the sediment bed. Undergoes denitrification and flux to or from the water column.
Orthophosphate: two state variables (in Layers 1 and 2). Formed by the decomposition
of POP in sediment (diagenesis flux). Flux to or from the water column is predicted but
may be limited by strong P sorption to oxidated ferrous iron in the aerobic layer.
Methane: (Layer 2) Methane is formed due to the decomposition of POC in the sediment
bed under low-salinity conditions. Methane undergoes oxidation resulting in increased
sediment oxygen demand.
Sulfide: two state variables (in Layers 1 and 2). Hydrogen sulfide (H2S) is formed,
rather than methane under saline conditions. Sulfide in sediment may undergo burial,
flux to the water column, or oxidation (increasing SOD).
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Bioavailable Silica: Silica in sediment is modeled using three state variables. Silica
deposited from the water column is bioavailable or "biogenic silica" and is modeled in
Layer 2. Bioavailable silica can then either undergo deep burial or dissolution to non
biogenic silica.
Non Biogenic Silica: two state variables (in Layers 1 and 2). Produced when
bioavailable silica breaks down due to dissolution. Available Silica in Layer 2 and Silica
in Layers 1 & 2. Non biogenic silica may undergo burial or flux to the water column.
COD: Driving variable for chemical oxygen demand in the water column that affects the
flux of sulfide to the water column.
Figure 125: Simplified schematic of the AQUATOX sediment diagensis model
(Diagram does not include Silica, Sulfide or COD)
Flux to
Water
fn(Oxygen)
Oxidation
CH4 kSOD
Deeply Buried
Particulate organic matter in the sediment bed (POC, PON, and POP) is divided into three
reactivity classes as follows:
• GI - reactivity class 1, equivalent to labile organic matter
• G2 - reactivity class 2, equivalent to refractory organic matter
• G3 - reactivity class 3, non reactive (lignin and humic materials)
Within the system of equations governing these state variables, sediment oxygen demand (SOD)
is a function of specific chemical reactions following the decomposition of organic matter.
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Specifically the oxidation of methane or sulfide and the nitrification of ammonia increases the
predicted SOD . This in turn has effects on the amount of oxygen present in the water column.
The amount of oxygen in the water column, however significantly affects the nitrification of
ammonia (275).
To optimize the solution of this feedback loop, an iterative solution is utilized to calculate SOD
in each time-step, (see Eq 263) An initial value of SOD (SODinitiai) is estimated. (In the first
time-step, SODInUiai is calculated by the model based on sediment initial conditions, in later time-
steps the SODimtiai is assumed to equal the SOD in the previous time-step.) Based on SODMtiai,
the concentrations of ammonia, nitrate, and sulfide or methane can be calculated by the model
Then, using those nutrient concentrations, a new estimate of SOD may be obtained. This
becomes the new "initial" estimate of SOD until the initial estimate and "new" estimate of SOD
converge (to within the relative error set in the AQUATOX setup screen).
This iterative solution is likely not mandatory within AQUATOX as the water column model is
not decoupled from the sediment diagenesis model (all differential equations are solved
simultaneously.) However, by including this iterative solution, the solution for SOD is not a
limiting factor when setting the variable differentiation time-step.
Most implementations of Di Toro's model solve state variables in the thin aerobic upper layer
(Layer 1) using an assumption of steady-state. Because the mass of nutrients are tracked within
AQUATOX and balanced to machine accuracy, this solution was not possible within
AQUATOX. If there are two interacting state variables and one is solved with a steady-state
solution and the other is solved using differential equations, the conservation of mass is not
possible. (For example, when solved under steady state, the nutrient mass in Layer 1 will change
based on the conditions prior to the time-step but that nutrient mass is not explicitly moving to or
from another state variable.)
The model was tested with the steady-state assumption for Layer 1 and found significant loss of
mass balance due to this simplification. Mass balance loss at steady state declined when the
time-step was reduced but even under very small time-steps, mass balance to machine-accuracy
was not produced. For this reason, the state variables in sediment Layer 1 are solved using
differential equations and not using a steady-state assumption. The thickness of Layer 1 (a user
input variable) may therefore have a significant effect on model run time, with larger layer
thicknesses resulting in shorter run-times.
7.1 Sediment Fluxes
State variables in the two model layers are subject to a number of fluxes to and from other
modeled and unmodeled compartments. Fluxes in the model include:
• Diffusion of the dissolved component of state variables to and from the water column;
• Diffusion of the dissolved component of the state variables between layers;
• Burial of the state variables below the lower layer and out of the modeled system; and
• Particulate mixing of the two layers and resultant exchange of state variable.
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To calculate these fluxes, the diffusion velocity between layers must be solved as well as a
particle mixing velocity between the two layers and a surface mass transfer coefficient.
Diffusion Velocity Between Layers
Diffusion between layers is specified by a diffusion coefficient, provided by the user and
adjusted for the water temperature in the system. Enhanced diffusive mixing due to bioturbation
is not currently included in the AQUATOX implementation, though direct mixing by
bioturbation is.
(261)
j-v r\ Temp -20
KL = ^—M
H2
KL = diffusion velocity between layers (m/d);
Dd = diffusion coefficient for pore water (m2/d);
$Dd = constant for temperature adjustment for Dd (unitless);
Temp = temperature of water (deg. C); and
H2 = depth of sediment layer 2 (m).
Particle Mixing Between Layers (Bioturbation)
In a departure from Di Toro's model, particle mixing between layers is a direct function of the
modeled benthic biomass in the system. Di Toro's formulation uses the assumption that benthic
biomass is proportional to the labile carbon in the sediment. As AQUATOX calculates benthic
biomass explicitly, this simplifying assumption is not required and a direct relationship to
benthic biomass is utilized.
1 r\(Log(Benthic_Biomass) -2.778151 ) -i A
<*> 1,2 = 7j (262)
H2
where:
co7,2 = particle mixing velocity between layers (m/d)
Benthic Biomass = sum of benthic invertebrate biomass (g/m2 dry);
H.2 = depth of sediment layer 2 (m); and
le-4 = pore water concentration (m2/cm2);
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Figure 126: Relationship derived from Di Toro, 2001, Figure 13.1A
"Diffusion coefficient for particle mixing versus benthic biomass"
0.1
0.01
0.001
0.1
1 10 100
Biomass (g dry/m2)
1000
Additionally, AQUATOX's calculation of benthic biomass includes benthic invertebrate
mortality due to low oxygen conditions and recovery when oxygen concentrations rise. Because
of this, Di Toro's benthic stress model incorporating accumulated stress and dissipation of stress
is not required nor included within AQUATOX.
Surface Mass Transfer Coefficient
Di Toro has advanced the idea that the diffusive surface mass transfer coefficient can be
successfully related to the sediment oxygen demand (Di Toro et al. 1990). The resulting
equation is as follows.
SOD
OxygenWi
Water
(263)
SOD = CSOD+NSOD
where:
s
SOD
CSOD
NSOD
Oxygenwater
surface diffusive transfer (m/d)
sediment oxygen demand (g Q^ / m2 d);
carbon based sediment oxygen demand (g O2 / m2 d) see (287) or
(291);
sediment oxygen demand due to nitrification (g O2 / m d) see (275),
converted into oxygen equivalent units (1.714 gO2/gN);
overlying water oxygen cone, (g O2/ m3) (186).
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As shown above, SOD is the sum of the carbon based sediment oxygen demand and sediment
oxygen demand due to nitrification..
7.2 POC
Particulate Organic Carbon in sediment is assumed to be located exclusively in the second layer
of sediment. Three state variables are utilized to represent three reactivity classes (Gi through
Gs). POC is a component of the particulate organic matter that settles from the water column
into the anaerobic layer and decomposes. It is also subject to consumption by detritivores.
Sediment = Deposition - Mineralization - Burial - Predation (264)
dt
where:
Deposition = deposition from water column (g C/ m3 d) see (266);
Mineralization = decomposition (g C/ m3 d) see (267) ;
Burial = deep burial below modeled layer (g C/ m3 d) see (265); and
Predation = predation by detritivores (g C/ m3 d) see (99);
For all state variables burial is solved as a function of the user input burial rate w2:
Burial = POM - (265)
H.
where:
Burial = burial below modeled layer (g C/ m3 d); and
POM = POP, POC, orPON(gC/m3);
w2 = user input burial rate (m/d); and
Hn = depth of sediment layer n (m).
Burial from the top layer is added to the second layer, whereas burial from the second layer is
considered deep burial out of the modeled system.
Deposition is solved as
DepositionPOM Oi= ^Def • Def2POMGi+ ^ Se d • Se d2POMGi . (266)
\^Animals Algae&Detritus j sediment
where:
DepositionpoM Gt = deposition of G; reactivity class of POP, POC, or PON from water
column (g OM/ m3 d);
Def = defecation of animals, see (97) (g OM/m3waterd);
Def2POMGl = fraction of POP, POC, or PON reaction class G; in defecated matter;
Sed = sedimentation of plants or detritus, see (165), (g OM/m3water d);
Sed2POMGi = fraction of POP, POC, or PON reaction class G; in sedimented algae
or detritus (unitless);
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Volwater = water volume (m3); and
= sediment volume (m3);
Assigning fractions of defecation to the relevant POM class (i.e., determining Def2POMoi) is a
two-part process. First, the fraction of POM, POC, or PON in the defecated material must be
determined. Second, each fraction must be again multiplied by a fraction to assign it to the three
reactivity classes (Gi to Gs). In this manner, particulate organic matter is separated into nine
different state variables in the sediment.
The fractions of POP and PON within defecated matter are assumed to equal the ratios of
phosphate or nitrate to organic matter for sedimented labile detritus; these are editable
parameters (remineralization screen). The fraction of POC within defecated matter is set to
52.6% (Winberg 1971). Defecated matter is split evenly between reactivity classes GI and G2,
with no defecation assigned to the non-reactive G?, class (Def2SedLabile=0.5).
Similarly, assigning fractions of sedimentation to reactivity classes is a two-part process. As
before, the fraction of POP and PON within sedimented matter is assumed equal to the ratio of
phosphate or nitrate to organic matter for the given species or detritus (editable parameters). The
fraction of POC within sedimented matter is again set to 52.6% (Winberg 1971). The amount of
refractory detritus that is converted to reactivity class G3 is a user entered parameter. The rest of
the refractory detritus is assigned to G2 and labile detritus becomes GI. 92% of sinking plants
are assumed to be labile (Gi) with no sinking algae being converted to the non-reactive
compartment (Gs).
The decomposition of organic matter is calculated as a first order reaction with an exponential
temperature sensitivity built in:
Mineralization^ _& = POMGl • KPOM_Gl • 9POM_G^emp^ (267)
where:
MineralizationpoM Gi = decomposition of G reactivity class of POP, POC, or PON in
the sediment bed (g/m3 d);
POMoi = concentration of POM in reactivity class G; (g/m3);
Kpotvt_Gi = decay rate of POM class (I/day);
OpoM_Gt = exponential temperature adjustment for decomposition of POM
class G (unitless); and
Temp = temperature (deg.C).
Predation on GI is calculated based on preferences for labile detritus and predation on G2 is
based on preferences for refractory detritus; these are set in the animal data screens. No
predation on Gs is assumed.
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7.3 PON
Particulate Organic Nitrogen in sediment is also assumed to be in the second layer of sediment.
Three state variables are utilized to represent three reaction classes (Gi through G^).
dPON
Sediment
dt
= Deposition - Mineralization - Burial - Predation
(268)
where:
Deposition =
Mineralization =
Burial =
Predation =
deposition from water column (g N/ m3 d) see (266);
decomposition to ammonia (g N/ m3 d) see (267) ;
deep burial below modeled layer (g N/ m3 d) see (265); and
predation by detritivores (g N/ m3 d) see (99);
7.4 POP
Particulate Organic Phosphate in sediment is solved in a very similar manner to POC and PON.
Mineralization rates may be different, however.
dPOR
Sediment
dt
= Deposition -Mineralization - Burial - Predation
(269)
where:
Deposition =
Mineralization =
Burial =
Predation =
deposition from water column (g P/ m d) see (266);
decomposition to orthophosphate (g P/ m3 d) see (267) ;
deep burial below modeled layer (g P/ m3 d) see (265); and
predation by detritivores (g P/ m3 d) see (99);
7.5 Ammonia
Ammonia in the sediment is solved using two state variables to represent the two layers.
Ammonia is formed by the decomposition of PON. Ammonia in sediment undergoes
nitrification, burial, and flux to or from the water column. The ammonia in each state variable is
the sum of dissolved and particulate ammonia. The fraction that is dissolved is solved below in
equation (274). The ammonia differential equations are as follows:
dAmmonia
L2Sed
dt
= Diag _ Flux - Burial + Flux2Anaerobic
(270)
dAmmoniaLlSed
dt
= -Nitrification - Burial - Flux2Water - Flux2 Anaerobic (271)
where:
DiagFlux = decomposition of PON, see (267) ;
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Burial = burial below relevant layer (g N/ m3 d) see (265);
Flux2Anaerobic = flux to layer 2 from layer 1 (g N/ m3 d, may be negative) see (272) ;
Flux2Water = flux to water from layer 1 (g N/ m3 d, may be negative); see (273);
Nitrification = conversion to nitrate (g N/ m3 d) see (275);
Flux2Anaerobic = -(col2 (fp2Conc2 - fplConcl)+ Kl(fd2Conc2 - fdlConcl ))HLayer (272)
where:
a>i2 = particle mixing velocity between layers (m/d), see (262);
KL = diffusion velocity between layers (m/d), see (261);
fp,iayer = particulate fraction in layer 1 or 2 (unitless); see (274)
= dissolved fraction in layer 1 or 2 (unitless); see (274)
er = total concentration of state variable in layer (g/m3); and
= depth of layer being evaluated (m);
Flux2Water = s(fdl • concl - concwater col }rll (273)
where:
s = surface diffusive transfer (m/d); (263)
fdi = dissolved fraction in layer 1;
Conciayer = total concentration of state variable in layer (g/m3); and
HI = depth of layer 1 (m);
The fraction of ammonia that is dissolved in each layer is calculated as follows:
(274)
f =1 - f
J p ammonia, layer J d ammonia, layer
where:
fdammoma,iayer = dissolved fraction in layer;
miayer = user-input solids concentration in layer (kg/L);
KdNH4 = editable partition coefficient for ammonium (L/kg); and
fp ammoma,iayer = p aiticul ate fraction in layer.
Ammonia in the top layer is converted to nitrate in the presence of oxygen, resulting in sediment
oxygen demand. Since the nitrification reaction requires oxygen, no nitrification is assumed to
occur in the lower anaerobic layer. Nitrification in the aerobic layer is calculated as follows:
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Nitrification =
2-KMm+DOm
lTemp-20
we.
(NH4,
(275)
where:
Nitrification
DOwc.
KMo2
K
s
NH4i
HI
6
Temp
conversion of ammonia to nitrate (g N/m );
dissolved oxygen in the water column (g/m3);
user-input nitrification half-saturation coefficient for ammonium
(gN/m3);
user-input nitrification half- saturation coefficient for oxygen
(g 02/m3);
reaction velocity for nitrification (m/d); (user-input, differentiating
between fresh and salt water)
surface diffusive transfer (m/d); (263)
concentration of ammonia in layer 1 (g/m3); (168)
user-input depth of layer 1 (m);
user-input exponential temperature adjustment for nitrification
(unitless); and
temperature (deg.C).
7.6 Nitrate
Nitrate is formed by the nitrification of ammonia in the top layer of the sediment bed. Nitrate in
sediment undergoes denitrification, burial and flux to or from the water column.
dNitrate L2Si
'ed
dt
= -Burial - Denitr + Flux2 Anaerobic
(276)
dNitrate
LISed
dt
= Nitrification - Denitr - Burial - Flux2Water - Flux2 Anaerobic (277)
where:
Burial
Flux2Anaerobic
Flux2Water
Nitrification
Denitr
burial to layer below modeled layer or out of the system(g N/ m3 d)
see (265);
flux to layer 2 from layer 1 (g N/ m3 d, may be negative) see (272) ;
flux to water from layer 1 (g N/ m3 d, may be negative); see (273);
conversion of ammonia to nitrate (g N/ m3 d), see (275);
denitrification of nitrate to free nitrogen (g N/ m3 d), see (278);
Nitrate is assumed to be dissolved in the sediment bed so// =1.0 andfp= 0.0.
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Denitrification is solved as follows
Temp-2Q
,-. . "~layer,NO3
Demtr = —
TT
-" laye
(278)
where:
K layer, No3
e
tl layer
NO3iayer
Temp
= user-input reaction velocity for denitrification given the layer and
salinity regime (m/d);
= user-input exponential temperature adjustment for denitrification
(unitless); and
= surface diffusive transfer (m/d); (263)
= depth of layer (m);
= concentration of nitrate in layer (g/m3); and
= temperature (deg.C).
7.7 Orthophosphate
Phosphate in the sediment is solved using two state variables to represent the two layers. Like
ammonia, the phosphate in each state variable represents the sum of dissolved and paniculate
phosphate.
dPO4 T,
2Sed
dt
= Diag _ Flux - Burial + Flux2 Anaerobic
(279)
dPO4
LISed
dt
= -Burial - Flux2Water - Flux2 Anaerobic
(280)
where:
Diag Flux
Burial
Flux2Anaerobic
Flux2Water
decomposition of POP, see (267) ;
burial to layer below modeled layer or out of the system(g P/ m3 d)
see (265);
flux to layer 2 from layer 1 (g P/ m3 d, may be negative) see (272) ;
flux to water from layer 1 (g P/ m3 d, may be negative); see (273);
When oxygen is present in the water column, the diffusion of phosphorus from sediment pore
waters is limited. This is due to strong P sorption to oxidated ferrous iron in the aerobic layer
(iron oxyhydroxide precipitate). Under conditions of anoxia, phosphorus flux from sediments
increases significantly.
Di Toro incorporates the effect of oxygen on phosphate flux into his model by making the
dissolved fraction of phosphate a function of oxygen in the water column. When the oxygen in
water passes a critical threshold the partition coefficient for phosphate is increased by a user-
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entered factor. As the oxygen goes to zero, the partition coefficient is smoothly reduced to the
anaerobic coefficient using an exponential function:
if DOwc>DOCntP04 then Kdp04l=Kdp042AKdp04
(281)
DOW
else KdP04l = KdP04aAKdP04^i
Partitioning of phosphate between the dissolved and paniculate forms will affect on the flux of
phosphate to the water column (273).
' d phosphate, layer
(282)
where:
J d phosphate, laye
Wllayer
KdpQ4,2
DOWC
DOcrit,PO4.
= dissolved fraction in layer (unitless);
= user-input solids concentration in layer (kg/L); and
= partition coefficient for phosphate in layer 2 (L/kg);
= fresh or saltwater factor to increase the aerobic (Li) partition
coefficient of PO4 relative to the anaerobic (L2) coeff. (unitless);
= dissolved oxygen in the water column (g/m3), see (186); and
= critical oxygen concentration for adjustment of partition coefficient
for inorganic P (g/m3);
7.8 Methane
Methane is formed due to the decomposition of POC in the sediment bed under low-salinity
conditions. Methane undergoes oxidation resulting in increased sediment oxygen demand.
dMethane ,9
L2Sed
dt
= Diag_FluxMetham -Flux2WaterMethane-OxidationMethane
(283)
where:
Diag Flux
Flux2Water
Oxidation
methane in the anaerobic layer expressed in oxygen equivalence
units (gO2equiv/m3)
decomposition of POC in freshwater, adjusted for the organic carbon
lost due to denitrification (g O2equiv/ m3 d) see (284);
methane flux to water (g O2equiv/ m3 d), see (288); and
oxidation of methane (CSOD) (g O2equiv/ m3 d) see (287);
In the manner of Di Toro, methane and sulfide are tracked in units of oxygen equivalents (g
O2equiv/ m3) to easily balance the model's computations.
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In fresh water conditions, decomposing POC is converted to methane which is tracked in oxygen
equivalents. In salt water, decomposing POC becomes sulfide. However, some POC is lost due
to denitrification and does not decompose:
Diag _ FluxMethanet Sulfide = Mineralizationpoc 1 — 1-2.86- Denitrification (284)
where:
Diag_FluXMethane,Sulfide
= decomposition of POC in water, adjusted for the organic carbon lost
due to denitrification (g O2equiv/ m3 d);
Mineralizationpoc = decomposition of POC in freshwater, (g POC/ m3 d) see (267) ;
Denitrification = denitrification of nitrate, (g N/ m3 d) see (278);
32/12 = conversion between POC and oxygen equivalents; and
2.86 = conversion between Nitrate and oxygen equivalents;
Oxidation of methane is solved as a function of the saturation concentration of methane in pore
water.
CH4 =
10
(285)
CSODMax = mm (/2KL-CH4sat • Diag _ Flux Methane , Diag _ FluxMethane ) (286)
K -9
'v r-u/i "-^
Oxidation
Methane
H 9
Temp-20 \\
CH4
(287)
where:
CH4sat
zmean
Temp
CSODMax
KL
Diag_FluxMethane
OxidationMethane
sech
s
6cH4
H.2
saturation concentration of methane in pore water (g O2equiv / m2);
mean depth of water column above the sediment bed (m);
temperature (deg.C);
maximum oxidation (g O2equiv/ m2);
diffusion velocity between layers (m/d); (261)
diagenesis flux of methane to water column, adjusted to be in units
of(g02equiv/m2d);
oxidation of methane (g O2equiv/ m3 d);
hyperbolic secant function
surface diffusive transfer (m/d); (263)
reaction velocity for methane oxidation(m/d);
exp. temperature adjustment for methane oxidation (unitless); and
depth of layer 2 (m); (methane mass arbitrarily tracked on the second layer)
211
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION CHAPTER 7
All methane is assumed to be oxidized or to escape from the sediment to water. Thus the
derivative for methane will remain at zero and the solution for the flux to water can be solved as
follows:
Flux2WaterMetham = Diag_FluxMethane - OxidationMethane (288)
where:
Diag Flux = decomposition of POC in freshwater, adjusted for the organic carbon
lost due to denitrification (g O2equiv / m3), see (284);
Oxidation = oxidation of methane (g O2equiv/ m3), see (287);
7.9 Sulfide
Sulfide is formed, rather than methane, under saline conditions. Sulfide in sediment may
undergo burial, flux to the water column, or oxidation, which increases SOD.
dSulfideL2Sed
= Diag _ Fluxs lfd - Burial + Flux2Anaerobic (289)
dt
dSulfideLl Sed
= -Oxidation - Burial - Flux2Water - Flux2 Anaerobic (290)
dt
where:
Sulfidem Sed = sulfide in layer n of sediment, (g O2equiv / m3);
Diag_FluxSuifide = decomposition of POC in salt water, adjusted for the organic carbon
lost due to denitrification (g O2equiv/ m3 d), see (284);
Burial = burial to layer below modeled layer or out of the system (g O2equiv /
m3 d); see (265);
Flux2Anaerobic = flux to layer 2 from layer 1 (g O2equiv / m3 d, may be neg.) see (272) ;
Flux2Water = flux to water from LI (g O2equiv / m3 d, may be neg.) (Note the
driving var. "COD" represents the water col. cone, of sulfide.) see
(273);
Oxidation = oxidation of sulfide in the active layer;
(2 _/* 2 _/* I .^\ T&mp
K-H2S,d 'Jd\~>rKH2S,p 'Jp\j^H2S
DO
Oxidation = ConcH2S L1 ^ -^ (291)
s • Hl
where:
3
Oxidationsuifide = oxidation of sulfide (g O2equiv/ m d);
212
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION _ CHAPTER 7
ConcH2S,Li = concentration of sulfide in layer 1 (g O2equiv/ m3);
KH2s,d = reaction velocity for dissolved sulfide oxidation (m/d);
KH2s,p = reaction velocity for particulate sulfide oxidation (m/d);
DOWc. = dissolved oxygen in the water column (g/m3);
KMH2S,op = sulfide oxidation normalization constant for oxygen (g O2/m3);
6H2s = exp. temperature adjustment for sulfide oxidation (unitless);
s = surface diffusive transfer (m/d); and
HI = depth of layer 1 (m);
The fraction of sulfide that is dissolved in each layer is calculated as follows:
Jd sulfide, layer ~
where:
fd mifide.iayer = dissolved fraction in layer;
miayer = solids concentration in layer (kg/L); and
KdNH4 = partition coefficient for sulfide for layer (L/kg);
The particulate fraction of sulfide in each layer is calculated as one minus the dissolved fraction.
7.10 Bioavailable Silica
Silica in sediment is modeled using three state variables. Silica deposited from the water column
is bioavailable or "biogenic silica" and is modeled in Layer 2. Bioavailable silica can then either
undergo deep burial or dissolution to non-biogenic silica. It will be modeled as a limiting
nutrient for diatoms in a later version of AQUATOX.
dAvail _ SilicaL2 Sed
= Deposition - Dissolution - Burial (293)
dt
= deposition from water column (g Si/ m3 d) see (294);
= dissolution of bioavailable silica (g Si/ m3 d)
= deep burial below modeled layer (g Si/ m3 d) see (265
where:
Deposition
Burial = deep burial below modeled layer (g Si/ m3 d) see (265); and
Deposition of silica is a function of the sinking of diatoms:
DepositionSl = ^Sed- FracSilica V° water (294)
\Diatoms J Wsediment
213
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION CHAPTER 7
where:
Deposition^ = deposition of silica from water column (g Si/ m3 d);
FracSilica = user-input fraction of silica in diatoms, (unitless);
Sed = sedimentation of diatoms, see (165), (g OM/m3water d);
Volwater = water volume (m3); and
Volsediment = sediment volume (m3);
Bioavailable silica can undergo dissolution to non-biogenic silica. This reaction can also operate
in reverse:
Dissolution = KSl8s{emp^ \ -— """'"fL \Sis« ~ fd,s,i,ca, 12' ConcSlh L2 (295)
ConcAvail Sl+KMPSl
where:
Dissolution = dissolution of bioavailable silica (g Si/ m3);
Kst = user-input reaction velocity for dissolved silica dissolution (m/d);
6 Si = user-input exponential temperature adjustment for silica dissolution
(unitless);
= concentration of available silica or silica in layer 2 (g Si/ m3);
= user input silica dissolution half-saturation constant for bioavailable
Si (g Si/m3);
Sisat = user-input saturation concentration of silica in pore water (g Si/m3);
fd silica, layer = dissolved fraction of silica in layer.
7.11 Non-Biogenic Silica
Non-biogenic silica is produced when bioavailable silica breaks down due to dissolution. Non-
biogenic silica (referred to hereafter as "silica") is modeled in two layers:
dSilica L2Sed
- = Dissolution - Burial + Flux2 Anaerobic (296)
dt
dSilica
= -Burial - Flux2Water - Flux2Anaerobic (297)
where:
Dissolution = dissolution of bioavailable silica, see (295);
Burial = burial to layer below modeled layer or out of the system (g Si / m3
d); see (265);
Flux2Anaerobic = flux to layer 2 from layer 1 (g Si/ m3 d, may be negative) see (272) ;
Flux2Water = flux to water from layer 1 (g Si/ m3 d, may be negative); see (273);
214
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION CHAPTER 7
Similar to inorganic phosphate, dissolved oxygen causes a barrier to silica flux to the water
column. This is modeled by increasing the partition coefficient by a factor when the dissolved
oxygen passes a critical threshold.
if DOwc>DOCr^Sl then KdSll=KdSl2kKdSll
(298)
DOwc
else Kdsi l = Kdsi 2AKdSi jDoCri( a
Jd Si,layer ~ , . T^ , (299)
where:
fd siiicajayer = dissolved fraction in layer (unitless);
miayer = solids concentration in layer (kg/L); and
Kdst,2 = partition coefficient for Si in layer 2 (L/kg);
= fresh or saltwater factor to increase the aerobic (Li) partition
coefficient of Si relative to the anaerobic (L2) coeff. (unitless);
= dissolved oxygen in the water column (g/m3); and
DOcrit,Si. = critical oxygen concentration for adjustment of partition coefficient
for silica (g/m3);
215
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
CHAPTER 8
8. TOXIC ORGANIC CHEMICALS
The chemical fate module of AQUATOX predicts the
partitioning of a compound between water, sediment, and biota
(Figure 127), and estimates the rate of degradation of the
compound (Figure 128). 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 no longer represented in
AQUATOX except as a constraint on sorption to detritus and
plants and as a basis for computing internal toxicity.
Partitioning to inorganic sediments is not modeled unless the
multi-layer sediment model is included.
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).
Toxic Organic Chemicals:
Simplifying Assumptions
• Kinetic model of toxicant fate
• Photolysis in sediments is not
included
• A generalized equation is used to
calculate partitioning of polar
compounds
• Direct sorption onto the body of an
animal is ignored
• The exchange of toxicant through
the gill membrane is assumed to be
facilitated by the same mechanism
as the uptake of oxygen
• Estimation of the elimination rate
constant k2 may be made based on
logKow
• Biotransformation occurs at a
constant rate throughout a
simulation
216
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
CHAPTER 8
Figure 127. In-situ uptake and release of chlorpyrifos in a pond, dominated by plants
CHLORPYRIFOS 6 ug/L (PERTURBED)
Run on 05-2-08 4:33 PM
430
387
344
301
258
215
172
129
86
43
»T1 H2OGMISorption (Percent)
• T1 H2O Depuration (Percent)
• T1 H2O DetrSorpt (Percent)
• T1 H2O Decomp (Percent)
T1 H2ODetrDesorpt (Percent)
T1 H2O PlantSorp (Percent)
6/27/1986 7/12/1986 7/27/1986 8/11/1986 8/26/1986 9/10/1986
Figure 128. In-situ degradation rates for chlorpyrifos in pond
CHLORPYRIFOS 6 ug/L (PERTURBED)
Run on 05-2-08 4:33 PM
»T1 H2O Hydrolysis (Percent)
»T1 H2O Photolysis (Percent)
»T1 H2O MicroMet (Percent)
• T1 H20Volatil (Percent)
6/27/1986 7/12/1986 7/27/1986 8/11/1986 8/26/1986 9/10/1986
217
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION CHAPTER 8
The mass balance equations follow. The change in mass of toxicant in the water includes
explicit representations of mobilization of the toxicant from sediment to water as a result of
decomposition of the labile sediment detritus compartment, sorption to and desorption from the
detrital sediment compartments, uptake by algae and macrophytes, uptake across the gills of
animals, depuration by organisms, and turbulent diffusion between epilimnion and hypolimnion:
— °X1™n Water = Loading + ^LMleDetr (Decomposition LMeDetr • PPBiameDetr • le-6)
+ I Desorption DetrTox + T. Depuration Org- T. Sorption SedTox
- J^GillUptake -Macro Uptake- J^AlgalUptakeAlga (300)
- Hydrolysis - Photolysis - MicrobialDegrdn + Volatilization
-Discharge + BiotransformMicrobIn ± TurbDiff ± Diffusion Seg
+ PorewaterAdvection + Diffusion Sedment- Washout + Washin
The equations for the toxicant associated with the two sediment detritus compartments are rather
involved, involving direct processes such as sorption and indirect conversions such as defecation.
However, photolysis is not included based on the assumption that it is not a significant process
for detrital sediments:
d Toxicant SedLabneDetr = Sorption _ Desorption + (colonization • PPB SedRefrDetr • le-6)
DefecationTox Pred P
- (Resuspension + Scour + Decomposition) • PPB sedLabiieDetr • 1 e - 6
-^PredIngeStiOnprediSedLMeDetr • PPBsedLMleDetr '16-6
+ Sedimentation • PPB SuSpLabiieDetr • 1 e - 6
+ E(Sed2Detr • SinkPhyto- PPBPlyto- le-6)
- Hydrolysis - MicrobialDegrdn - Burial + Expose
+ BiotransformMicrMal
SedRefrDetr
- - =
r, .. ^ ,.
= Sorption - Desorption
+ ILpredlLpreyk1 - Def2SedLabile) ' DefecotionTox Pmi Pre)
(Resuspension + Scour + Colonization) • PPB SedRefrDetr ' le-6
-HpredIngestionpredSedRefrDetr • PPB se^De* • le-6 (302)
+ (Sedimentation + Scour) • PPB suSpRefrDetr • le-6
+ Z(Sed2Detr • Sinkphyto • PPBphyto • le-6)
- Hydrolysis - MicrobialDegrdn - Burial + Expose
+ BiotransformMicrobial
218
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION CHAPTER 8
Similarly for the toxicant associated with suspended and dissolved detritus, the equations are:
SuspLabileDetr _
= Loading + Sorption - Desorption + WashinToxCar
dt
+ J^Qrg((Mort2Detr • Mortality0rg + GameteLoss0rg) • PPB0rg • 1 e-6)
- (Sedimentation + Deposition + Washout + Decomposition
+ T.PredIngeStiOnprecLSuspLMeDetr) • PPBsuspLabileDetr ' 1 e -6 (303)
+ Colonization • PPBSuspRefrDetr • 1 e-6 + BiotransformMicrobial
+ (Resuspension + Scour) • PPB sedLMieDetr ' 1 e -6 + SedToHyp
- Hydrolysis - Photolysis - MicrobialDegrdn ± TurbDiff ± DiffusionSeg
SuspRefrDetr
— - =
T ,. r, ,. ^ ,.
= Loading + Sorption - Desorption
dt
+ Z0rg(Mort2Ref • Mortality Org • PPB0rg • 1 e -6)
- (Sedimentation + Deposition + Washout + Colonization
± BiotransformMjcmbial + ^Pred IngestionSuspRefrDetr ) • PPBSu*PRefrDetr • 1 e -6 (304)
+ (Resuspension + Scour) • PPBsedRefrDetr • 1 e -6
± SedToHyp - Hydrolysis - Photolysis - MicrobialDegrdn
+ TurbDiff + DiffusionSeg + WashinTmCarner
dToxicantDlssLMeDetr = Loading + Sorption . Desorption + SumExcrToxToDiss0rg
+ T.0rg(Mort2Detr • Mortality Org • PPB0rg • 1 e -6)
- (Washout + Decomposition) • PPBDlssLabneDetr • 1 e -6 (305)
+ BiotransformMicmbial - Hydrolysis - Photolysis
- MicrobialDegrdn ± TurbDiff ± Diffusion Seg + WashinToxCarrier
± PorewaterAdvection ± Diffusion Sediment
d Toxicant D,ssRefrDetr Sorption _ Desorption + SumExcToxToDisSorg
+ Z0rg(Mort2Ref • Mortality Org • PPB0rg • 1 e -6)
- (Washout + Colonization) • PPBDlsSRefrDetr • 1 e -6 (306)
+ BiotransformMicrohial - Hydrolysis - Photolysis
- MicrobialDegrdn ± TurbDiff ± Diffusion Seg + WashinToxCarrier
± PorewaterAdvection ± Diffusion Sediment
219
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION CHAPTER 8
When the simple sediment model is run, there are no equations for buried detritus, as they are
considered to be sequestered and outside of the influence of any processes which would change
the concentrations of their associated toxicants. When the multi-layer sediment model is
included, equations for toxicants in pore waters and toxicants in buried sediments may be found
in sections 8.10 and 8.11.
Toxicants associated with algae are represented as:
= Loading + AlgalUptake - Depuration ± TurbDiff
d ToxicantAiga _
dt
± Diffusion Seg + WashinToxCamer (307)
- (Excretion + Washout + T.predPredationPred, Aiga + Mortality
+ Sink + SinkToHypo) • PPBAiga • 1 e -6 ± BiotransformAlga
Macrophytes are represented similarly, but reflecting the fact that they are stationary unless
specified as free-floating:
Macrophyte _
= Loading + MacroUptake - Depuration - (Excretion
dt
+ Hpred Predationpred, Macro + Mortality + WashoutFreeFloating + Breakage) (308)
• PPBMaCro ^ e-6 ± BiotmnsformMacrophyte + WashinTmCamerpreeploat
The toxicant associated with animals is represented by an involved kinetic equation because of
the various routes of exposure and transfer:
d Toxicant Ammai = Loading + GillUptake + ZPreyDietUptake + TurbDiff
- (Depuration + ^PredPredationPred,Ammai + Mortality + Spawn (309)
+ Promotion + Drift + Migration + Emergelnsect) • PPBAnimai • I e -6
± BiotransformAmmal + WashinTmCarner
where:
Toxicantwater = toxicant in dissolved phase in unit volume of water (ug/L);
ToxicantsedDetr = mass of toxicant associated with each of the two sediment
detritus compartments in unit volume of water (ug/L);
ToxicantsuspDetr = mass of toxicant associated with each of the two suspended
detritus compartments in unit volume of water (ug/L);
ToxicantoissDetr = mass of toxicant associated with each of the two dissolved
organic compartments in unit volume of water (ug/L);
ToxicantAiga = mass of toxicant associated with given alga in unit volume
of water (ug/L);
ToxicantMacmphyte = mass of toxicant associated with macrophyte in unit
volume of water(ug/L);
ToxicantAnimai = mass of toxicant associated with given animal in unit
volume of water (ug/L);
PPBsedDetr = concentration of toxicant in sediment detritus (ug/kg), see
(310);
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
CHAPTER 8
PPBsuspDetr
PPBoissDetr
PPBAlga
PPBAnimal
1 e-6
Loading
TurbDiff
Washin
WashiriToxCarner
Diffusionseg
DifJusionSedment
PorewaterAdvection
Hydrolysis
BiotransformMicrobiai
Biotransformorg
Photolysis
MicrobialDegrdn
Volatilization
Discharge
Burial
Expose
Decomposition
Depuration
Sorption
Desorption
Colonization
concentration of toxicant in suspended detritus (ug/kg);
concentration of toxicant in dissolved organics (ug/kg);
concentration of toxicant in given alga (ug/kg);
concentration of toxicant in macrophyte (ug/kg);
concentration of toxicant in given animal (ug/kg);
units conversion (kg/mg);
loading of toxicant from external sources (ug/L-d);
depth-averaged turbulent diffusion between epilimnion and
hypolimnion (ug/L-d), see (22) and (23).
loadings from linked upstream segments (g/m3-d), see (30);
inflow load of toxicant sorbed to a carrier from an upstream
segment (ug/L-d), see (31);
gain or loss due to diffusive transport over the feedback
link between two segments, (ug/L-d), see (32);
gain or loss due to diffusive transport to porewaters in the
sediment (ug/L-d), see (256);
gain or loss of toxicant to porewater due to scour or
deposition of sediment (ug/Lpw-d), see (394), (395);
rate of loss due to hydrolysis (ug/L-d), see (313);
biotransformation to or from given organic chemical in
given detrital compartment due to microbial
decomposition (ug/L-d), see (375);
biotransformation to or from given organic chemical within
the given organism (ug/L-d); (375)
rate of loss due to direct photolysis (ug/L-d), see (320);
assumed not to be significant for bottom sediments;
rate of loss due to microbial degradation (ug/L-d), see
(326);
rate of loss due to volatilization (ug/L-d), see (331);
rate of loss of toxicant due to discharge downstream
(ug/L-d), see Table 3;
rate of loss due to deposition and resultant deep burial
(ug/L-d) see (167b);
rate of exposure due to resuspension of overlying sediments
(ug/L-d),see(227);
rate of decomposition of given detritus (mg/L-d), see (159);
elimination rate for toxicant due to clearance (ug/L-d), see
(362), (363), and (372);
rate of sorption to given organic or inorganic compartment
(ug/L-d), see (350);
rate of desorption from given organic or inorganic
compartment (ug/L-d), see (351);
rate of conversion of refractory to labile detritus (g/m3-d),
see (155);
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
CHAPTER 8
DefecationToxpred, pre ~~
Def2SedLabile
Resuspension
Scour
Sedimentation
Deposition
Sed2Detr
Sink
Breakage
Mortalityorg
Mort2Detr
GameteLoss
Mort2Ref
Washout or Drift
SedToHyp
IngestionPred,prey
d, prey
ExcToxToDissorg
Excretion
SinkToHypo
AlgalUptake
MacroUptake
GillUptake
rate of transfer of toxicant due to defecation of given prey
by given predator (ug/L-d), see (379);
fraction of defecation that goes to sediment labile detritus,
= 0.5;
rate of resuspension of given sediment detritus (mg/L-d)
without the inorganic sediment model attached, see (165);
rate of resuspension of given sediment detritus (mg/L-d); in
streams with the inorganic sediment model attached, see
(233);
rate of sedimentation of given suspended detritus (mg/L-d);
without the inorganic sediment model attached, see (165);
rate of sedimentation of given suspended detritus (mg/L-d)
in streams with the inorganic sediment model attached, see
(235);
fraction of sinking phytoplankton that goes to given detrital
compartment;
loss rate of phytoplankton to bottom sediments (mg/L-d),
see (69);
loss of macrophytes due to breakage (g/m2-d), see (88);
nonpredatory mortality of given organism (mg/L-d), see
(66), (87), and (112);
fraction of dead organism that is labile (unitless);
loss rate for gametes (g/m3-d), see (126);
fraction of dead organism that is refractory (unitless);
rate of loss of given toxicant, suspended detritus or
organism due to being carried downstream (mg/L-d), see
(16), (71), (72), (130), and (131);
rate of settling loss to hypolimnion from epilimnion
(mg/L-d). May be positive or negative depending on
segment being simulated, see (69);
rate of ingestion of given food or prey by given predator
(mg/L-d), see (91);
predatory mortality by given predator on given prey
(mg/L-d), see (99);
toxicant excretion from plants to dissolved organics
(mg/L-d);
excretion rate for given organism (g/m3-d), see (64), (111);
rate of transfer of phytoplankton to hypolimnion (mg/L-d).
May be positive or negative depending on segment being
modeled, see (69);
rate of sorption by algae (ug/L - d), see (360);
rate of sorption by macrophytes (ug/L - d), see (356);
rate of absorption of toxicant by the gills (ug/L - d), see
(365);
222
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION _ CHAPTER 8
ey = rate of dietary absorption of toxicant associated with given
prey (ug/L-d), see (369);
Recruit = biomass gained from successful spawning (g/m3-d), see
(128);
Promotion = promotion from one age class to the next (mg/L-d), see
(136);
Migration = rate of migration (g/m3-d), see (133); and
Emergelnsect = insect emergence (mg/L-d), see (137).
The concentration in each carrier is given by:
ppB= ToxState, .7e6 (31Q)
CarrierStatej
where:
PPBj = concentration of chemical in carrier /' (ug/kg);
ToxStatCj = mass of chemical in carrier /' (ug/L);
CarrierState = biomass of carrier (mg/L); and
Ie6 = conversion factor (mg/kg).
8.1 lonization
Dissociation of an organic acid or base in water can have a significant effect on its environmental
properties. In particular, solubility, volatilization, photolysis, sorption, and bioconcentration of
an ionized compound can be affected. Rather than modeling ionization products, the approach
taken in AQUATOX is to represent the modifications to the fate and transport of the neutral
species, based on the fraction that is not dissociated. The acid dissociation constant is expressed
as the negative log, pKa, and the fraction that is not ionized is:
Nondissoc = - - - - (311)
1+ in(pH'pKa)
where:
Nondissoc = nondissociated fraction (unitless).
If the compound is a base then the fraction not ionized is:
Nondissoc = - - - - (312)
J+jQ(pKa-pH) ^ >
When pKa = pH half the compound is ionized and half is not (Figure 129). At ambient
environmental pH values, compounds with a pKa in the range of 4 to 9 will exhibit significant
dissociation (Figure 130).
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
CHAPTER 8
Figure 129. Dissociation of pentachlorophenol
(pKa = 4.75) at higher ph values
1
"8
•80.8
8
8 0.6
T3
C
O
ZQ.4
c
O
I 0.2
6
PH
10
Figure 130. Dissociation as a function ofpKa at
an ambient pH of 7
"S
^
0.8
o
I 0.6
T3
C
O
c
.0
I0.2
6 8
pka
10 12 14
8.2 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 • Toxicant
Phase
(313)
where:
and where:
KHyd
KAcidExp
KBaseExp
KUncat
Arrhen
KHyd = (KAcidExp + KBaseExp + KUncat) • Arrhen (314)
= overall pseudo-first-order rate constant for a given pH and
temperature (1/d);
= pseudo-first-order acid-catalyzed rate constant for a given pH
(1/d);
= pseudo-first-order base-catalyzed rate constant for a given pH
(1/d);
= the measured first-order reaction rate at pH 7 (1/d); and
= temperature adjustment (unitless), see (319).
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:
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
CHAPTER 8
where:
KAcidExp = KAcid • Hlon
(315)
and where:
KAcid
Hlon
pH
Hlon = 10~PH
acid-catalyzed rate constant (L/mol-d);
concentration of hydrogen ions (mol/L); and
pH of water column.
(316)
Likewise for base-catalyzed hydrolysis, the first-order rate constant for a reaction between the
hydroxide ion and the pollutant at a given pH (Figure 131) can be described as:
where:
and where:
KBase
OHIon
KBaseExp = KBase • OHIon
OHIon = 10pH~14
= base-catalyzed rate constant (L/mol • d); and
= concentration of hydroxide ions (mol/L).
Figure 131. Base-catalyzed hydrolysis of pentachlorophenol
(317)
(318)
6.05E-03
6.00E-03
Q 5.95E-03
£ 5.90E-03
a:
5.85E-03
5.80E-03
2
1
J
4 6 8 10
PH
Hydrolysis reaction rates are 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) is used as a default:
En
Bn
where:
En
R
Arrhen =
Arrhenius activation energy (cal/mol);
universal gas constant (cal/mol • Kelvin);
(319)
225
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION CHAPTER 8
KelvinT = temperature for which rate constant is to be predicted (Kelvin); and
TObs = temperature at which known rate constant was measured (Kelvin).
8.3 Photolysis
Direct photolysis is the process by which a compound absorbs light and undergoes
transformation:
Photolysis = KPhot • Toxicant Phase (320)
where:
Photolysis = rate of loss due to photodegradation (ug/L-d); and
KPhot = 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.
lonization may result in a significant shift in the absorption of light (Lyman et al., 1982;
Schwarzenbach et al., 1993). However, there is a general absence of information on the effects
of light on ionized species. The user provides an observed half-life for photolysis, and this is
usually determined either with distilled water or with water from a representative site, so that
ionization may be included in the calculated lumped parameter KPhot.
Based on the approach of Thomann and Mueller (1987; see also Schwarzenbach et al. 1993), the
observed first-order rate constant for the compound is modified by a light attenuation factor for
ultraviolet light so that the process as represented is depth-sensitive (Figure 132); it also is
adjusted by a factor for time-varying light:
KPhot = PhotRate • ScreeningFactor • LightFactor (321)
where:
PhotRate = direct, observed photolysis first-order rate constant (I/day);
ScreeningFactor = a light screening factor (unitless), see (322); and
LightFactor = a time-varying light factor (unitless), see (323).
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
CHAPTER 8
Figure 132. Photolysis of pentachlorophenol as a function of
light intensity and depth of water
100 200 300 400 500 600
LIGHT INTENSITY (ly/d)
DEPTH(m)
— 0.5 1 —1.5 — 2 2.5
700
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):
n 77-v • , 7 (- Extinct • Thick)
„ . „ RadDistr 7-exp(
ScreemngFactor =
RadDistrO Extinct • Thick
(322)
where:
RadDistr
RadDistrO
Extinct
Thick
radiance distribution function, which is the ratio of the average
pathlength to the depth (see Schwarzenbach et al., 1993) (taken to
be 1.6, unitless);
radiance distribution function for the top of the segment (taken to
be 1.2 for the top of the epilimnion and 1.6 for the top of the
hypolimnion, unitless);
light extinction coefficient (1/m) not including periphyton, see
(40);
thickness of the water body segment if stratified or maximum
depth if unstratified (m).
The equation presented above implicitly makes the following assumptions:
quantum yield is independent of wavelength; and,
. the value used for PhotRate is a representative near-surface, first-order rate constant for
direct photolysis.
227
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION _ CHAPTER 8
The rate is modified further to represent seasonally varying light conditions and the effect of ice
cover:
LightFactor= (323)
Ave Solar
where:
Solar 0 = 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 (default = 500 Ly/day).
If the system is unstratified or if the epilimnion is being modeled, the light intensity is the light
loading:
SolarO = Solar (324)
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:
o 7 n o 7 (-Alpha • MaxZMix) s*r\
SolarO = Solar • exp (325)
where:
Solar = incident solar radiation loading (ly/d), see (25); and
MaxZMix = depth of the mixing zone (m), see (17).
Because the ultraviolet light intensity exhibits greater seasonal variation than the visible
spectrum (Lyman et al., 1982), decreasing markedly when the angle of the sun is low, this
construct 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 (see
section 3.6) so that photolysis, as modeled, is not an important process in northern waters in the
winter.
8.4 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 (159) and supporting equations:
MicrobialDegrdn = KMDegrdnphase • DOCorrection • TCorr • pHCorr
(326)
• Toxicant phase
where:
MicrobialDegrdn = loss due to microbial degradation (g/m3-d);
KMDegrdn = maximum aerobic microbial degradation rate, either in
water column or sediments (1/d), in sediments this is
assumed to be four times the user-entered value for water;
228
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION CHAPTER 8
DOCorrection = effect of anaerobic conditions (unitless), see (160);
TCorr = effect of suboptimal temperature (unitless), see (59);
pHCorr = effect of suboptimal pH (unitless), see (162); and
Toxicant = concentration of organic toxicant (g/m3).
Microbial degradation of toxicants proceeds more quickly if the material is associated with
surficial or particulate sediments rather than dissolved 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 converted by the model to four times the user entered maximum
chemical degradation rate in the water (Max. Rate of Aerobic Microbial Degradation). 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.
8.5 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
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:
( 2 Y2i i
KLiq = KReaer • Thick • MolWtO —-— (327)
^ MolWt) Nondissoc
where:
KLiq = water-side transfer velocity (m/d);
KReaer = depth-averaged reaeration coefficient for oxygen (1/d), see (191)-
(195);
Thick = thickness of the water body segment if stratified or maximum
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 (311).
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION _ CHAPTER 8
Likewise, the thickness of the air-side stagnant boundary layer is also affected by wind. Wind
usually is measured at 10m, 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):
( o
KGas = 168-\ MolWtH2 — - — • Wind • 0.5 (328)
I, 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 resistances- the reciprocals of the air- and water-phase
mass transfer coefficients (Schwarzenbach et al., 1993), modified for the effects of ionization:
(329)
KOVol KLiq KGas • HenryLaw • Nondissoc
where:
KOVol = total mass transfer coefficient through both stagnant boundary layers
(m/d);
Henry • HLCSaltFactor ,~~n^
HenryLaw = (330)
R-TKelvin
and where:
HenryLaw = Henry's law constant (unitlessj;
Henry = Henry's law constant (atm m3 mol"1);
HLCSaltFactor= Correction factor for effect of salinity (unitless), see (444).
R = gas constant (=8.206E-5 atm m3 (mol K)"1); and
TKelvin = temperature in °K.
The Henry's law constant is applicable only to the fraction that is nondissociated because the
ionized species will not be present in the gas phase (Schwarzenbach et al., 1993, p. 179).
The atmospheric exchange of the pollutant can be expressed as the depth-averaged total mass
transfer coefficient times the difference between the concentration of the chemical and the
saturation concentration:
Volatilization = ——— • (ToxSat - Toxicantwater) (331)
Thick
230
-------
AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION CHAPTER 8
where:
Volatilization = interchange with atmosphere (ug/L-d);
Thick = depth of water or thickness of surface layer (m);
ToxSat = saturation concentration of pollutant in equilibrium with the gas
phase (ug/L), see (332); and
Toxicantwater = concentration of pollutant in water (ug/L).
Because, theoretically, toxicants can be transferred in either direction across the water-air
interface, volatilization takes a negative sign when it is a loss term and is output as such.
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 = Toxrcantair J00() (332)
HenryLaw • Nondissoc
where:
Toxicant^? = gas-phase concentration of the pollutant (g/m3); and
Nondissoc = nondissociated fraction (unitless).
Often the pollutant can be assumed to have a negligible concentration in the air and ToxSat is
zero. However, this general construct can represent the transferral of volatile pollutants into
water bodies. Because ionized species do not volatilize, the saturation level increases if
ionization is occurring.
The nondimensional Henry's law constant, which relates the concentration of a compound in the
air phase to its concentration in the water phase, strongly affects the air-phase resistance.
Depending on the value of the Henry's law constant, the water phase, the air phase or both may
control volatilization. For example, with a depth of 1 m and a wind of 1 m/s, the gas phase is
100,000 times as important as the water phase for atrazine (Henry's law constant = 3.0E-9), but
the water phase is 50 times as important as the air phase for benzene (Henry's law constant =
5.5E-3). Volatilization of atrazine exhibits a linear relationship with wind (Figure 133) in
contrast to the exponential relationship exhibited by benzene (Figure 134).
231
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
CHAPTER 8
Figure 133. Atrazine KOVol as a function of Figure 134. Benzene KOVol as a function of
Wind
VOLATILIZATION OF ATRAZINE
4E-05
3.5E-05
_ 3E-05
1 2.5E-05
5 2E-05
§ 1.5E-05
* 1E-05
5E-06
0
0 3.5 7 10.5 14 17.5 21 24.5 28
WIND (m/s)
Wind
VOLATILIZATION OF BENZENE
0 3 6 9 12 15 18 21 24 27 30
WIND (m/s)
—AQUATOX
« Schwarzenbach etal., 1993
8.6 Partition Coefficients
Although AQUATOX is a kinetic model, steady-state partition coefficients for organic pollutants
are computed in order to place constraints on competitive uptake and loss processes in detritus
and plants, speeding up computations. Bioconcentration factors also are used in computing
internal toxicity in plants and animals. 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):
0.82
(333)
where:
KOMRefrDetr
KOW
detritus-water partition coefficient (L/kg); and
octanol-water partition coefficient (unitless).
Detritus in sediments is simulated separately from inorganic sediments, rather than as a fraction
of the sediments as in other models. When the multi-layer sediment model is not included,
refractory detritus is used as a surrogate for sediments in general; and the sediment partition
coefficient KPSed, which can be entered manually by the user, is the same as
Equation (334) and the equations that follow are extended to polar compounds, following the
approach of Smejtek and Wang (1993):
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
CHAPTER 8
KOMRefrDetr = 1.38- KOW0'82 • Nondissoc
+ (1- Nondissoc) • lonCorr -1.38- KOW°'82
(334)
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 pentachorophenol as a test compound, and comparing it to octanol, the influence of pH-
mediated dissociation is seen in Figure 135. This relationship is verified by comparison with the
results of Smejtek and Wang (1993) using egg membrane. However, in the general model Eq.
(334) is used for refractory detrital sediments as well.
Figure 135. Refractory detritus-water and octanol-water partition coefficients for pentachlorophenol as a
function of pH
2
0
1E6
1E51
1E4
1E3
1E2
1E1
... ~*\.
. . ,\^
'i
3456789
PH
--- PCP KOM for refractory detritus
-•- Un-ionized PCP - octanol/water
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):
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION CHAPTER 8
KOCLabpart = 23. 44 • KOW0'61 (335)
In the model, the equation is generalized to polar compounds and transformed to an organic
matter partition coefficient:
KOMiaWetr = (23.44 • KOW™1 • Nondissoc
+ (1 - Nondissoc) • lonCorr • 23.44 • KOW°'61 ) • 0.526
where:
= partition coefficient for labile particulate organic carbon (L/kg);
= 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.
Humic acids exhibit high polarity and do not readily complex neutral compounds. Natural
humic acids from a Finnish lake with extensive marshes were spiked with a PCB, but a PCB-
humic acid complex could not be demonstrated (Maaret et al. 1992). In another study, Freidig et
al. (1998) used artificially prepared Aldrich humic acid to determine a humic acid-DOC partition
coefficient (n = 5, r2, = 0.80), although they cautioned about extrapolation to the field. Landrum
et al. (1984) found that KOC values for natural dissolved organic matter were approximately one
order of magnitude less than for Aldrich humic acids (Gobas and Zhang 1994); incorporating
that factor into the equation of Freidig et al. (1998) yields:
7 (337)
where:
refractory dissolved organic carbon partition coefficient (L/kg).
Until a better relationship is found, we are using a generalization of this equation to include polar
compounds, transformed from organic carbon to organic matter, in AQUATOX:
234
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION CHAPTER 8
KOMRefrDOM = (2.88 • KOWa67 • Nondissoc
(338)
+ (1 - Nondissoc) • lonCorr • 2.58 • KOW°'67) • 0.526
where:
KOMRefrDOM = refractory dissolved organic matter partition coefficient (L/kg).
Algae
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 (339)
which we also generalized for polar compounds and transformed:
KOMiabooM = (0-88 • KOW • Nondissoc
+ (1- Nondissoc
where:
(340)
- Nondissoc) • lonCorr • 0.88 • KOW) • 0.526
KOCiabDoc = partition coefficient for labile dissolved organic carbon (L/kg); and
= partition coefficient for labile dissolved organic matter (L/kg).
Unfortunately, older data and modeling efforts failed to distinguish between hydrophobic
compounds that were truly dissolved and those that were complexed with DOM. For example,
the PCB water concentrations for Lake Ontario, reported by Oliver 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. AQUATOX distinguishes between truly dissolved and complexed compounds;
therefore, the partition coefficients calculated by AQUATOX may be larger than those used in
older studies.
Bioaccumulation of PCBs in algae depends on solubility, hydrophobicity and molecular
configuration of the compound, and growth rate, surface area and type, and content and type of
lipid in the alga (Stange and Swackhamer 1994). Phytoplankton may double or triple in one day
and periphyton turnover may be so rapid that some PCBs will not reach equilibrium (cf Hill and
Napolitano 1997).
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
235
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION _ CHAPTER 8
1994). Algal lipids have a much stronger affinity for hydrophobic compounds than does octanol,
so that the algal BCFupid > K0w (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(BCFAlga) = 0.41 + 0.91 • LogKOW (341)
where:
a = partition coefficient between algae and water (L/kg).
Rearranging and extending to hydrophilic and ionized compounds:
BCFAiga = 2.57 • KOW°'93 • Nondissoc
+ (1- Nondissoc) • lonCorr • 0.257 • KOW°'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 (Figure 137). 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 Figure 136, which shows the effect of ionization
on binding of pentachlorophenol to various types of organic matter. The polar substrates, such
as algal detritus, have an inflection point which is one pH unit higher than that of nonpolar
substrates, such as refractory detritus. The relative importance of the substrates for binding is
also demonstrated quite clearly.
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:
Macro) = 0.98 • LogKOW - 2.24 (343)
Again, rearranging and extending to hydrophilic and ionized compounds:
BCF M^O = 0. 00575 • KOW0'98 • (Nondissoc + 0.2) (344)
236
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
CHAPTER 8
Invertebrates
For the invertebrate bioconcentration factor, the following empirical equation is used for
nondetritivores, based on 7 chemicals with LogKOWs ranging from 3.3 to 6.2 and
bioconcentration factors for Daphniapulex (r2 = 0.85; Southworth et al., 1978; see also Lyman et
al., 1982), converted to dry weight:
( BCF ^ertebraJ = (0.7520 • LogKOW - 0.4362) • WetToDry
(345)
where:
'invertebrate
WetToDry
partition coefficient between invertebrates and water (L/kg); and
wet to dry conversion factor (unitless, default = 5).
Extending and generalizing to ionized compounds:
BCF lmertehrate = 0.3663 • KOW"7"" • (Nondissoc + 0.01)
(346)
For invertebrates that are detritivores the following equation is used, based on Gobas 1993:
mC Vl KOMRefroetr • (Nondissoc + 0.01) (347)
BCF Invertebrate
where:
etritus
BCFinvertebrate = 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 (334).
Figure 136. Partitioning to Various Types of
Organic Matter as Function of Kow
Figure 137. Partitioning to Various Types of
Organic Matter as a Function of pH
1 Fin
1E9-
1 FR
1 F7
O1 Ffi
* 1E5
1 F4 '
1E3
1E2
^
£-~"
^^
--^
m^'f
*f
B'"'
•-^
mj'-f'
.-"":
^
•"
^
*-"
w^
^
_,
""
.,'-'
^^
'"
m-'"'
^
m
.
4
3456789
Log KOW
— humic acids — - algae - exudate
r algal detritus • refr. detritus • sediments
1E6
1E5-
0
1E4-
1E3
3
— humic e
- exudate
1
cid
:-=*
4
3 -
!^~l
-•—
^
^i
£
algs
algc
^
1
e
1 df
^
e
p
;trit
'
X '
"~~~l
H
us
^
^
^^i
' — » — i
— » ,
789
- octanol/water
• 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
237
-------
AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
CHAPTER 8
on the lipid content of the fish extended to hydrophilic chemicals (McCarty et al., 1992), with
provision for ionization:
where:
KBpish
Lipid
WetToDry
sh = Lipid • WetToDry • KOW • (Nondissoc + 0.01)
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).
(348)
The bioconcentration factor is adjusted for the time to reach equilibrium as a function of the
clearance or elimination rate and the time of exposure (Hawker and Connell, 1985; Connell and
Hawker, 1988; Figure 138):
BCFFlsh = KBFlsh • (J - e(-D^°"'TEl«p^>} (349)
where:
BCFptsh = quasi-equilibrium bioconcentration factor for fish (L/kg);
TElapsed = time elapsed since fish was first exposed (d); and
Depuration = clearance, which may include biotransformation, see (372) (1/d).
Figure 138. Bioconcentration factor for fish as a function
of time and log KOW
LU
O
O
O
O
ffl
1E7
1E6
1E5
1E4
1E3
log KOW = 6
log KOW = 8
log KOW = 3
0 200 400 600 800 1000 1200
DAY
8.7 Nonequilibrium Kinetics
Often there is an absence of equilibrium due to growth or insufficient exposure time, metabolic
biotransformation, dietary exposure, and nonlinear relationships for very large and/or
superhydrophobic compounds (Bertelsen et al. 1998). Although it is important to have a
knowledge of equilibrium partitioning because it is an indication of the condition toward which
systems tend (Bertelsen et al. 1998), it is often impossible to determine steady-state potential due
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION CHAPTER 8
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 = k jDetr • ToxicantWater • (Nondissoc + 0.01)
I «J3" I
• Org2C • Detr • UptakeLimit • 7e - 6
Desorption = k 2Detr • Toxicant Detr (351)
where:
Sorption = rate of sorption to given detritus compartment (ug/L-d);
klDetr = sorption rate constant (1.39 L/kg-d), see (355);
Nondissoc = fraction not ionized (unitless), see (311);
Toxicantwater = concentration of toxicant in water (ug/L);
Org2C = conversion factor for organic matter to carbon (= 0.526 g C/g
organic matter);
Detr = mass of each of the detritus compartments per unit volume (mg/L);
le -6 = units conversion (kg/mg);
Desorption = rate of desorption from given sediment detritus compartment
(ug/L-d);
k2oetr = desorption rate constant (1/d), see (354);
UptakeLimit = factor to limit uptake as equilibrium is reached (unitless) see (352);
and
Toxicantoetr = mass of toxicant in each of the detritus compartments (ug/L).
In order to limit sorption to detritus and algae as equilibrium is reached, UptakeLimit is
computed as:
TJ . j T. .. ToXiCantwater 'kp Carrier ~ Carrier /•*«<> \
UptakeLimit Carner = - — - <^ - (352)
ter earner
where:
UptakeLimitcamer = factor to limit uptake as equilibrium is reached (unitless);
kpcarrier = partition coefficient (KOM) or bioconcentration factor (BCF) for
each carrier (L/kg), see (333) to (342);
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION CHAPTER 8
= concentration of toxicant in each carrier (ug/kg), see (310).
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):
— * 0.03-24-KOM (353)
k2
So k2 is taken to be:
k2 = ^- (354)
KOM
where:
KOM = detritus-water partition coefficient (L/kg OM, see section 8.6); and
24 = conversion from hours to days.
Because the kinetic definition of the detrital partition coefficient KOM is:
kJ
KOM = — (355)
kl
the sorption rate constant kl is set to 1.39 L/kg-d.
Bioconcentration in Macrophytes and Algae
Macrophytes: As Gobas et al. (1991) have shown, submerged aquatic macrophytes take up and
release organic chemicals over a measurable period of time at rates related to the octanol-water
partition coefficient. Uptake and elimination are modeled assuming that the chemical is
transported through both aqueous and lipid phases in the plant, with rate constants using
empirical equations fit to observed data (Gobas et al., 1991), modified to account for ionization
effects (Figure 139, Figure 140):
MacroUptake = kl • Toxicant water • StVarPiant -le-6 (356)
Depurationplant = k2 • ToxicantPiant (357)
(358)
0. 0020
KOW • Nondissoc
If the user selects to estimate the elimination rate constant based on KOW (see section 8.8), the
following equation is used:
k2 = - - - (359)
1. 58 + 0. 0000 1 5 • KOW • Nondissoc
where:
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MacroUptake
Depurationpiant
StVarpiant
1 e-6
kl
k2
KOW
Nondissoc
= uptake of toxicant by plant (ug/L-d);
= clearance of toxicant from plant (ug/L-d);
= biomass of given plant (mg/L);
= units conversion (kg/mg);
= mass of toxicant in plant (ug/L);
= sorption rate constant (L/kg-d);
= elimination rate constant (1/d).
= octanol-water partition coefficient (unitless); and
= fraction of un-ionized toxicant (unitless).
Figure 139. Uptake rate constant for macrophytes
(after Gobas et al., 1991)
500
400
300
200
100
0
468
Log KOW
- Predicted » Observed
10
Figure 140. 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
468
Log KOW
Predicted - Observed
10
Algae: Aside 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% in Myriophyllum spicatum as observed by Gobas et al. (1991), which affect both
uptake and elimination of toxicants. However, the approach used by Gobas et al. (1991) in
modeling bioaccumulation in macrophytes provides a useful guide to modeling kinetic uptake in
algae.
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION CHAPTER 8
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 • ToxState • Carrier • 1 e - 6 (360)
where:
AlgalUptake = rate of sorption by algae (ug/L-d);
kl = uptake rate constant (L/kg-d), see (362);
UptakeLimitAiga = factor to limit uptake as equilibrium is reached (unitless), see
(352);
ToxState = concentration of dissolved toxicant (ug/L);
Carrier = biomass of algal compartment (mg/L); and
le-6 = conversion factor (kg/mg).
The kinetics of partitioning of toxicants to algae is based on studies on PCB congeners in The
Netherlands by Koelmans, Sijm, and colleagues and at the University of Minnesota by Skoglund
and Swackhamer. Both groups found uptake to be very rapid. Sijm et al. (1998) presented data
on several congeners that were used in this study to develop the following relationship for
phytoplankton (Figure 141):
kl = (361)
1.8 E- 6 + 1/(KOW • (Nondissoc + 0.01))
Because size-dependent passive transport is indicated (Sijm et al., 1998), uptake by periphyton is
set arbitrarily at ten percent of that for phytoplankton.
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 (362)
where:
Depuration = elimination of toxicant (ug/L-d);
State = concentration of toxicant associated with alga (ug/L); and
k2 = elimination rate constant (1/d).
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As a simplifying assumption, the depuration rate for periphyton is assumed to be two orders of
magnitude less:
Depuration = k2 • State • 0.01
(363)
The elimination rate in plants may be input in the toxicity record by the user or it may be
estimated using the following equation based in part on Skoglund et al. (1996). Unlike
Skoglund, this equation ignores surface sorption and recognizes that growth dilution is explicit in
AQUATOX (see Figure 142):
where:
LFrac
and
WetToDry
2.4E + 5
Algae
(KOW • LFrac • WetToDry)
(364)
desorption rate constant (1/d);
fraction lipid (wet weight), entered in the chemical toxicity screen;
translation from wet to dry weight (user input).
Figure 141. Algal sorption rate constant as a function
of octanol-water partition coefficient
FIT TO DATA OF SUM ET AL. 1998
600000
^500000
1*400000
^T 300000 •
T5 200000 •
5 100000 .
0 -
4 6
LOG KOW
10
ObsK1
Pred K1
Figure 142. Rate of elimination by algae as a function of
octanol-water partition coefficient
1.2
1
50.8
CN n r-
^ 0.6
"ra
•2" 0.4
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION CHAPTER 8
Bioaccumulation in Animals
Animals can absorb toxic organic chemicals directly from the water through their gills and from
contaminated food through their guts. Direct sorption onto the body is ignored as a simplifying
assumption in this version of the model. Reduction of body burdens of organic chemicals is
accomplished through excretion and biotransformation, which are often considered together as
empirically determined elimination rates. "Growth dilution" occurs when growth of the
organism is faster than accumulation of the toxicant. Gobas (1993) includes fecal egestion, but
in AQUATOX egestion is merely the amount ingested but not assimilated; it is accounted for
indirectly in DietUptake. However, fecal loss is important as an input to the detrital toxicant
pool, and it is considered later in that context. Inclusion of mortality and promotion terms is
necessary for mass balance, but emphasizes the fact that average concentrations are being
modeled for any particular compartment.
Gill Sorption: An important route of exposure is by active transport through the gills (Macek et
al., 1977). This is the route that has been measured so often in bioconcentration experiments
with fish. As the organism respires, water is passed over the outer surface of the gill and blood is
moved past the inner surface. The exchange of toxicant through the gill membrane is assumed to
be facilitated by the same mechanism as the uptake of oxygen, following the approach of
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 • Toxicantwater • FracWaterColumn (365)
T^Tr , WEffTox • Respiration • O2Biomass
KUptake = —^ *- (366)
Oxygen -WEffO2
where:
GillUptake = uptake of toxicant by gills (ug/L - d);
KUptake = uptake rate (1/d);
Toxicantwater = concentration of toxicant in water (ug/L);
FracwaterCoiumn = fraction of organism in water column (unitless), differentiates from
pore-water uptake if the multi-layer sediment model is included;
WEffTox = withdrawal efficiency for toxicant by gills (unitless), see (367);
Respiration = respiration rate (mg biomass/L-d), see (100);
O2Biomass = ratio of oxygen to organic matter (mg oxygen/mg biomass; 0.575);
Oxygen = concentration of dissolved oxygen (mg oxygen/L), see (186); 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,
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CHAPTER 8
piece-wise fit (Figure 143) to the data of McKim et al. (1985) using 750-g fish, corrected for
ionization:
If LogKOW < 1.5 then
WEffTox = Q.I
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
(367)
If 6.0 < LogKOW < 8.0 then
WEffTox = 0.1 + Nondissoc • (0.45 - 0.23 • (LogKOW - 6.0))
where:
LogKOW
Nondissoc
If LogKOW > 8.0 then
WEffTox = 0.1
log octanol-water partition coefficient (unitless); and
fraction of toxicant that is un-ionized (unitless), see (311).
Figure 143. Piece-wise fit to observed toxicant uptake data;
Modified from McKim et al., 1985
80h
345
LOG KOW
Ionization decreases the uptake efficiency (Figure 144). 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 does not seem to
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
CHAPTER 8
justify using two different constructs.
Figure 144. The Effect of Differing Fractions of Un-
ionized Chemical on Uptake Efficiency
0.6
0.5
>,
o
S 0.4
|o
iij 0.3
o>
raO.2
D.
D0.1
1.0
0.8
0.6
0.4
0.2
0.0
4 6
Log KOW
10
The user input FracWaterCoiumn parameter is only relevant if the multi-layer sediment model is
included. If so, this parameter determines how much gill uptake comes from the water column
and how much from the pore waters of the active layer. Gill uptake from pore waters is
calculated as follows and added to gill uptake from the water column:
GillUptakePoreWater = KUptake • Toxicant PoreWater • (l - FracWaterColumn\
(36g)
WaterCol
where:
GillUptake = uptake of toxicant by gills (ug/L\vaterCoi - d);
ToxicantporeWater = concentration of toxicant in pore waters (ug/LporeWater);
Volume porewater = volume of pore water (LPorewater); and
VolumewaterCoi = volume of water column (LWaterCoi)-
Dietary Uptake: Hydrophobic chemicals usually bioaccumulate primarily through absorption
from contaminated food. Persistent, highly hydrophobic chemicals demonstrate
biomagnification or increasing concentrations as they are passed up the food chain from one
trophic level to another; therefore, dietary exposure can be quite important (Gobas et al., 1993).
Uptake from contaminated prey can be computed as (Thomann and Mueller, 1987; Gobas,
1993):
where:
and:
DietUptakeprey = KDPrey • PPBPrey • 1 e - 6 (369)
KDprey = GutEffTox • GutEffRed • Ingestionprey (370)
DietUptakeprey = uptake of toxicant from given prey (ug toxicant/L-d);
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KDprey
PPBprey
1 e-6
GutEfjTox
GutEffRed
= dietary uptake rate for given prey (mg Nrey/L-d);
= cone, of toxicant in given prey (ug toxicant/kg Nrey), see (310);
= units conversion (kg/mg);
= efficiency of sorption of toxicant from gut (unitless);
= reduction in GutEffTox due to non-lethal effects, see (371); and
= ingestion of given prey (mg Nrey/L-d), see (91).
Gobas (1993) presents an empirical equation for estimating GutEffTox as a function of the
octanol-water partition coefficient. However, data published by Gobas et al. (1993) suggest that
there is no trend in efficiency between LogKOW 4.5 and 7.5 (Figure 145); 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. (Note, the PFA model uses a relationship to chain
length, see (403) and (404).)
Figure 145. GutEffTox constant based on mean value for data
from Gobas et al., 1993
Dietary Absorption Efficiency
o o
k> P ^i
o en en tn ->•
1.5
5.5 6 6.5
Log KOW
7.5
Guppies
Goldfish — Mean = 0.63
One potential non-lethal effect of toxicant exposure is an increase in the rate of egestion, see
(425). If GutEffTox is kept constant at the same time that the egestion rate is increased, toxicant
concentrations will increase too much within organisms (biomass falls but toxicant uptake
remains constant). To avoid this problem, and to reflect that the rate of toxicant uptake is more
a function of assimilated rather than total ingested food, the GutEfjTox must be reduced by the
same quantity that assimilated food is decreased.
GutEffRed = 1 - RedGrow
(371)
where:
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION CHAPTER 8
GutEffRed = reduction in GutEfJTox due to toxicant induced increased egestion
(unitless);
RedGrow = factor for reduced assimilation of food in animals (unitless); see
(422).
Despite this adjustment, if overall species growth rates become negative due to the reduced
assimilation of food in animals, toxicant concentrations in animals will still increase (a process
that is best conceived as the opposite of growth dilution.)
Elimination: Elimination or clearance includes both excretion (depuration) and
biotransformation of a toxicant by organisms. Biotransformation may cause underestimation of
elimination (McCarty et al., 1992). An overall elimination rate constant is estimated and
reported in the toxicity record. The user may then modify the value based on observed data; that
value is used in subsequent simulations. If, known, biotransformation also can be explicitly
modeled.
For any given time the clearance rate is:
Depuration Ammal = k2 • Toxicant Ammai • TCorr (372)
where:
Depuration Ammai = clearance rate (ug/L-d);
k2 = elimination rate constant (1/d);
ToxicantAnimai = mass of toxicant in given animal (ug/L); and
TCorr = correction for suboptimal temperature (unitless), see (59).
If the multi-layer sediment model is included, the amount of depuration that goes to the water
column vs. the active layer of pore waters is determined by the user input "Frac. in Water
Column" parameter.
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 in a construct unique to AQUATOX:
If WetWt < 5 g then
WpfWtRB
Log k2 = - 0.536 • Log Kow • Log NonDissoc + 0.065 • vveivvl— (373)
LipidFrac
else
WctWtRB
Log k2 = - 0.536 • Log Kow • Log NonDissoc + 0.116 • yveim— (374)
LipidFrac
where
KOW = octanol-water partition coefficient (unitless);
NonDissoc = fraction of toxicant that is un-ionized (unitless), see (311);
LipidFrac = fraction of lipid in organism (g lipid/g organism wet);
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WetWt
RB
mean wet weight of organism (g);
allometric exponent for respiration (unitless).
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 • BioRateConst orgamSm,t,
(375)
where
Biotransformation =
BioRateConst =
rate of conversion of chemical by given organism (ug/L d),
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.
A simplifying assumption of the model is that biotransformation occurs at a constant rate
throughout a simulation.
Figure 146. Depuration rate constants for invertebrates and fish
04
3
2
0
-1 -
-2
-3
-4
1
K2 for Various Animals
Log KOW
• Daphnia
• 10-gfish
- Eel
— Linear (Daphnia pred)
Diporeia
A Eel obs
— Linear (10-g fish pred)
— Linear (Diporeia pred)
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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:
BiotramformMicrobIn = -£0rgTmMicrobialDegradn0rgTm • FracAerobic • Frac0rgTox (376)
and for anaerobic conditions:
BiotramformMicrobIn = *^0rffm Microbial Degradn0rgTm • (1 - FracAerobic) • Frac0rffm (377)
where:
BiotransformMicrob in = Biotransformation to a given organic chemical in a given
detrital compartment due to microbial decomposition (ug/L d);
MicrobialDegradn = total microbial degradation of a different toxicant in this detrital
compartment (ug/L d) see (326);
FracAerobic = fraction of the microbial degradation that is aerobic (unitless),
see (378); and
FracorgTox = user input fraction of the organic toxicant that is transformed to
the current organic toxicant (inputs can differ depending on
whether the degradation is aerobic or anaerobic).
To calculate the fraction of microbial decomposition that is aerobic, the following equation is
used:
Factor
FracAerobic = (378)
DOCorrection
where:
Factor = Michaelis-Menten factor (unitless) see (161);
DOCorrection = effect of oxygen on microbial decomposition (unitless) see (160).
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 = T.(KEgestpmd,pmy • PPBPrey • / e - 6) (379)
KEgestPred,Prey = (1 - GutEffTox • GutEffRed) • IngestionpreciPrey (380)
where::
DefecationTox = rate of transfer of toxicant due to defecation (ug/L-d);
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d, Prey = fecal egestion rate for given prey by given predator (mg
prey/L-d);
PPBprey = concentration of toxicant in given prey (ug/kg), see (310);
1 e-6 = units conversion (kg/mg);
GutEfJTox = efficiency of sorption of toxicant from gut (unitless); and
GutEffRed = reduction in GutEfJTox due to non-lethal effects, see (371) ;
Inge stionp red prey = rate of ingestion of given prey by given predator (mg/L-d), see
(91)
The amount of toxicant transferred due to mortality may be large; it is a function of the
concentrations of toxicant in the dying organisms and the mortality rates:
MortTox = Zf 'Mortality Org • PPB0rg • Ie6) (381)
where:
MortTox = rate of transfer of toxicant due to mortality (ug/L-d);
Mortality org = rate of mortality of given organism (mg/L-d), see (66), (87) and
(H2);
PPBorg = concentration of toxicant in given organism (ug/kg), see (310); and
1 e-6 = units conversion (kg/mg).
8.8 Alternative Uptake Model: Entering BCFs, Kl, and K2
When performing bioaccumulation calculations, the default behavior of the AQUATOX model is
to allow the user to enter elimination rate constants (K2) for all plants and animals for a
particular organic chemical. K2 values may also be estimated based on the Log KOW of the
chemical. Uptake in plants is a function of Log K0w while gill uptake in animals is a function of
respiration and chemical uptake efficiency. The AQUATOX default model works well for a
wide variety of bioaccumulative organic chemicals, but some chemicals that are subject to very
rapid uptake and depuration are not efficiently modeled using these relationships because the
rapid rates create stiff equations that require shorter time-steps for solution. In addition, because
of the rapid rates, the chemical does approach equilibrium quickly.
For this reason, an alternative uptake model is provided to the user. In the chemical toxicity
record, the user may enter two of the three factors defining uptake (BCF, Kl, K2) and the third
factor is calculated using the below relationship:
BCF=Kl
K2
where: BCF = bioconcentration factor (L/kg dry);
Kl = uptake rate constant (L/kg dry day);
K2 = elimination rate constant (1/d).
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Given these parameters, AQUATOX calculates uptake and depuration in plants and animals as
kinetic processes.
(383)
(384)
Uptake = Kl • ToxState • Biomass • 1 e - 6
Depuration = K2 • ToxState
where: Uptake = uptake rate within organism (|J,g/L day);
Kl = uptake rate constant (L/kg dry day);
ToxState = concentration of toxicant in organism in water (|j,g/L)
Biomass = concentration organism in water (mg/L)
le-6 = (kg/mg)
Depuration = loss rate within organism (ng/L day);
K2 = elimination rate constant (1/d).
Dietary uptake of chemicals by animals is not affected by this alternative parameterization.
8.9 Half-Life Calculation, DT50 and DT95
AQUATOX estimates time to 50% (half-lives, DTSOs) and time to 95% chemical loss (DT95s)
independently in bottom sediment and in the water column. Estimates are produced at each
output time-step depending on the average loss rate during that time-step in that medium.
L°SSWater =
HydrolysisWater + Photolysis + MicrobialWater + Washout + Volatilization. + Sorption
MaSSWater
where:
LoSSMedia
HydrolysisMedia
Photolysis
MicrobialMedm
Washout
Volatilization
Sorption
MaSSuedia
Desorption
MicrobialSed + Hydrolysis Sed + Desorption
Mass
Sed
(386)
loss rate within media (1/d);
hydrolysis rate in given media (ng/L d), see (313);
photolysis rate in the water column (ng/L d), see (320);
rate of microbial metabolism in given media (ng/L d), see (326);
rate of toxicant washout from the water column (ng/L d); see (16);
rate of chemical volatilization in the water column (ng/L d), see (331);
sorption of toxicant to detritus, plants, and animals (ng/L d), see (350);
mass of chemical in the media (|j,g/L);
desorption of toxicant from bottom sediment, see (351).
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Loss rates are converted into time to 50% and 95% loss using the following formulae for first-
order reactions:
^50^=0.693/105*^
DT95Media=2.996ILossMedia
(387)
(388)
where: DT50Media
DT95uedia
LoSSuedia
= time in which 50% of chemical will be lost at current loss rate (d);
= time in which 95% of chemical will be lost at current loss rate (d);
= loss rate within media (1/d);
8.10 Chemical Sorption to Sediments
When the complex multi-layer sediment model is included, chemicals can sorb to and desorb
from suspended inorganic sediments based on user input rates that are applied to the model's
equations for sorption (249), and desorption (250). To activate this model, required rates are:
Kl uptake rate constant L/kg dry day
K2 depuration rate constant I/day
Kp partition coefficient L/kg dry
The derivative for toxicants sorbed to inorganic sediments is similar to that for suspended
organics:
dToxicant
dt
SuspSed = Load - Microbial + Sorption -Desorption
- (Deposition + Washout) • PPBsuSpsed • 1 e - 6
+ (Washin- PPBSuSpSedupstream- le-6)
(389)
+ (Scour • PPB Bottomed • le-6)
where:
ToxicantsuspSed
Load
Microbial
Sorption
Desorption
Deposition
Washout
Washin
Scour
toxicant in relevant suspended sediment size-class (ug/L);
loading of toxicant from external sources (ug/L-d);
rate of loss due to microbial degradation (ug/L-d), see (326);
rate of sorption to given compartment (ug/L-d), see (350);
rate of desorption from given compartment (ug/L-d), see (351);
rate of sedimentation of given suspended detritus (mg/L-d) in
streams with the inorganic sediment model attached, see (230);
rate of loss of from sediment being carried downstream (mg/L-d),
see (16)
rate of gain from sediment carried in from any upstream linked
segments (mg/L-d), see (30);
rate of resuspension of given sediment (mg/L-d), see (227);
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Chemicals also are tracked within inorganic sediments in the multi-layer sediment bed:
dToxicant
BottomSed _
dt
= Sorption -Desorption - Microbial
+ (Deposition- PPBSuspSed • 1 e - 6) + BedLoadTo
- (Scour • PPB BottomSed • 1 e - 6) - BedLossTm
(390)
where:
ToxicantBottomSed
Microbial
Sorption
Desorption
Deposition
Scour
BedLoadTox
BedLossTox
toxicant in bottom sediment (relevant sediment size-class ug/m2);
rate of loss due to microbial degradation (ug/m2-d), see (326);
rate of sorption to given compartment (ug/m2-d after units
conversion), see (350);
rate of desorption from given compartment (ug/m2-d after units
conversion), see (351);
rate of sedimentation of given suspended detritus (ug/m2-d after
units conversion) in streams with the inorganic sediment model
attached, see (230);
rate of resuspension of given sediment (ug/m2-d after units
conversion), see (227);
rate of bed load of given toxicant (ug/m2-d), see (391);
rate of bed loss of given toxicant (ug/m2-d), see (392).
In several cases above, units need to be converted from ug/L-d to ug/m -d when moving from
sediment suspended in the water column to bed sediment. This is done by multiplying by water
volume and then dividing by the sediment bed surface area. Toxicant mass balance has been
verified to be conservative through this process.
Toxicant movement due to bedload and bedloss are straightforward calculations:
BedLoadTox =
' BedLoadUpstreamlink ^ ^^
AvgArea
• le-:
(391)
where:
BedLoadupstreamlink
AvgArea
fft) UpstreamBed
le-3
toxicant bedload from all upstream segments (ug/m2-d);
bedload over one of the upstream links (g/d);
average area of the segment (m2);
toxicant concentration in the relevant upstream link (ug/kg)
units conversion (kg/g)
Similarly, total bed loss is the sum of the loadings over all outgoing links:
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BedLossTnv =
Tox
BedLoss
xox
AvgArea
PPBBed
le-3
Downstreamlink
4 4
AvgArea
Bed
•le-3
(392)
toxicant bedloss from current segment (ug/m -d);
bedloss over one of the downstream links (g/d);
average area of the segment (m2);
toxicant concentration in the current segment (ug/kg)
units conversion (kg/g)
8.11 Chemicals in Pore Waters
When the complex multi-layer sediment model is included, pore waters may contain toxic
organic chemicals. Chemicals in pore waters are separated into those that are freely dissolved
and those that are complexed to dissolved organic carbon within the pore waters.
dToxicant
FreelyDissolvedP. W.
~ = GainToxUp - LossToxUp ± DiffDown ± DiffUp + Decomp
- GillUptake -Microbial - Sorption + Desorption + Depuration
(393)
where:
ToxicantpreelyDissolvedP. W.
GainToxUp
LossToxup
DiffUp, DiffDown
Decomp
GillUptake
Depuration
Microbial
Sorption, Desorption
change in concentration of pore water in the sediment bed
normalized per unit area (ng/L^-d);
active layer only: gain of toxicant due to pore water gain from
the water column ((j,g/LpW-d), see (394);
active layer only: loss of toxicant due to pore water loss to the
water column ((jg/L^-d), see (395);
diffusion over upper or lower boundary ((j,g/Lpw-d), see (256);
freely dissolved toxicant gain due to microbial decomposition
of organic matter ((j,g/Lpw-d), see (159);
active layer only: uptake of toxicant into organisms that
reside at least partially in the sediment ((j,g/Lpw-d) (365);
active layer only: excretion of toxicant by organisms that
reside at least partially in the sediment ((j,g/Lpw-d), (362);
loss of toxicant in pore waters due to microbial degradation
(Hg/Lpw-d) see (326);
sorption to and desorption from organic matter and inorganic
matter in the current layer (|j,g/Lpw-d). (350), (351)
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GainToxUp =
GamUp • AreaSedLayer • ConcToxWaterCol • Ie3
Volume
PoreWater
LossToxUp =
LossUp • AreaSedLayer • ConcToxporeWater • Ie3
where:
GainToxUp
LossToxup
Volume poreWater
Ie3
Volume
(394)
(395)
'PoreWater
gain of toxicant in pore water from the water col. ((j,g/Lpw-d);
loss of toxicant in pore water to the water column above
([ig/LpW-d);
gain or loss of pore water from the water column above (m3/m2-d);
see (252), (251);
sediment layer area (m2);
concentration of toxicant in relevant media (|j,g/L);
pore water volume (Lpw);
units conversion (L/m3).
Chemicals also sorb to dissolved organic matter within pore waters:
dToxicantr
1 DOMPoreWater
dt
= GainDOMToxUp - LosSDOMToxUp ± DiffDown ± DiffUp
- (Decomp • PPB • le - 6) -Microbial - Sorption + Desorption
(3961
where:
GainDOMToxup
LossDOMToxup
DiffUp:DiffDown
Decomp
Microbial
Sorption
Desorption
gain of toxicant sorbed to DOM from the water column
(Hg/Lpw-d) see (394);
loss of toxicant sorbed to DOM in pore water to the water column
above ((j,g/Lpw-d) see (395);
diffusion over upper or lower boundary ((j,g/Lpw-d), see (256);
Decomposition of DOM ((j,g/Lpw-d), see (159);
loss of toxicant sorbed to DOM due to microbial degradation
(|j,g/Lpw-d) see (326);
sorption to DOM (ng/Lpw-d). (350)
desorption from DOM (|j,g/Lpw-d). (351)
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8.12 Mass Balance Capabilities and Testing
A chemical mass balance testing capability was added to the code during the development of the
estuarine version of AQUATOX. This capability ensured that all linkages between stratified
layers were properly developed with no loss of mass balance. New PFA formulations were also
tested for mass balance with this capability. Current testing indicates that AQUATOX balances
chemical mass to machine accuracy.
The chemical mass balance testing comprehensively tracks the mass of all chemical loadings and
losses to the system. Chemical mass balance is explicitly tested with this capability; mass
balance of state variables containing chemicals is implicitly tested. The Chemical MBTest output
variable keeps track of all chemical by the following equation:
MBTest = Chemical Mass + Chemical Loss - Chemical Load - Net Layer Exchange (397)
In this manner, the MBTest will stay constant (within machine accuracy) throughout a simulation
if mass balance is being maintained. However, the chemical mass balance function does not
work if the "Keep Freely Dissolved Contaminant Constant" option is selected within the setup
screen.
The chemical mass balance capability also provides a chemical tracking capability that allows
the user to see exactly what is happening to the chemical within the system. Chemical fate may
be tracked using the following output categories (all units are in kilograms):
Chem. MBTest:
Chem. Mass:
Mass balance test as described above, see (397).
Total chemical mass in the system including chemicals within
biota.
Chem. Loss + Mass: Chemical loss plus chemical mass in the system.
Chem. Tot Wash:
Chem. WashH2O:
Chem. WashAnim:
Chem. WashDetr:
Chem. WashPlnt:
Washout of chemical from the system since the simulation start.
The sum of the below four categories:
Washout of chemical dissolved in water
Washout of chemical in drifting animals.
Washout of chemical in suspended & dissolved detritus.
Washout of chemical in plants
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Chem. Tot Loss:
Chem. Hydrol:
Chem. Photol:
Chem. Volatil:
Chem. MicrobMet:
Chem. BioTram:
Chem. Emergel:
Chem. Fishing Loss:
Chem. Tot Load:
Chem. H2O Load:
Chem. Detr Load:
Chem. Biota Load:
Net LayerExch:
Total loss of chemical from the system since the simulation start.
The sum of the following eight categories plus washout:
Chemical loss due to hydrolysis.
Chemical loss due to photolysis.
Chemical loss due to volatilization.
Chemical loss due to microbial metabolism.
Chemical loss due to biotransformation.
Chemical loss due to the emergence of insects.
Chemical loss due to fishing.
Total loading of chemical into the system since the simulation
start. The sum of the following three categories:
Load of chemical directly into water.
Load of chemical within detritus loadings.
Load of chemical within plant and animal loadings.
The
Net of layer exchange between the other layer in the system.
sum of the below five categories:
Chem. Net Sink: Net sinking from upper to lower layer.
Chem. Net Entrain: Net entrainment of chemical.
Chem. Net TurbDiff: Net turbulent diffusion of chemical.
Chem. Net Migrate: Net migration of chemical in animals.
Chem. Delta Thick: Chemical movement due to changes in the thickness of the two
layers.
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8.13 Perfluoroalkylated Surfactants Submodel
As mentioned in the introduction (section 1.5), the perfluorinated compounds of interest as
bioaccumulators are the perfluorinated acids (PFAs). Perfluoroctane sulfonate (PFOS) belongs
to the sulfonate group and perfluorooctanoic acid (PFOA) belongs to the carboxylate group. Due
to their use in industrial manufacturing, these persistent chemicals are found in humans, fish,
birds, and marine and terrestrial mammals throughout the world. PFOS has an especially high
bioconcentration factor in fish.
Sorption
Perfluorinated surfactants are quite different from hydrocarbon surfactants. The nonpolar
perfluorocarbon tail repels both water and oil, and the perfluorinated surfactants are much more
active than their hydrocarbon counterparts (Moody and Field 2000). A field is provided for the
user to input a value for the organic matter partition coefficient ("Kom for Sediments"); this
empirical approach was taken in lieu of sufficient theory to support a mechanistic formulation.
Sorption to algae and macrophytes are also modeled empirically ("BCF for Algae" and "BCF for
Macrophytes" parameters).
Biotransformation and Other Fate Processes
PFOS and other related chemicals are anionic surfactants and, as such, they are not subject to
volatilization. However, the worldwide detection of PFOS suggests that there are one or more
precursors that are volatile. Therefore, a fate model for these compounds would not be complete
if it were not able to represent the movement and transformation of significant precursors to
PFOS and other bioaccumulative fluorinated organics. In particular, some fluorinated
compounds are subject to biodegradation of the nonfluorinated portion (Key et al. 1998, Moody
and Field 2000, Giesy and Kannan 2001); these can yield both volatile and nonvolatile
biotransformation products (Key et al. 1998). For example, 7V-EtFOSE alcohol is subject to
microbial degradation, yielding 92% PFOS and 8% PFOA (Lange 2000 cited in Cahill et al.
2003). AQUATOX has the capability of representing biotransformation from one congener or
homolog to one or more others when there are sufficient data to parameterize that part of the
model.
Bioaccumulation
PFOS and PFOA and similar compounds bioaccumulate differently than PCBs and chlorinated
pesticides (Kannan et al. 2001). The perfluorinated compounds of interest as bioaccumulators
are the acids. At least for PFOS the salts dissociate instantaneously at neutral pH (OECD 2002).
Perfluorinated acids (PFAs) are oil repelling and are taken up by protein rather than lipids
(Kannan quoted in Scientific American, March, 2001). Therefore, their kinetics cannot be
modeled as functions of the octanol-water partition coefficient. Instead, relationships based on
perfluoroalkyl chain length (Martin et al. 2003a) are used.
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Gill Uptake
Data on PFAs were insufficient at the time this submodel was developed (2005) to determine
withdrawal efficiencies and explicitly include respiration such as is done for other organic
compounds simulated by AQUATOX. Based on the data of (Martin et al. 2003a), the uptake
rate for all but the longest chain-length carboxylates can be represented as:
logArl = -5.7213+ 0.7764-ChainLength (398)
where
kJ = uptake transfer rate (L/kg d);
ChainLength = length of perfluoroalkyl chain (integer).
If chain length exceeds 11, the value for 11 is used. This uptake rate is based on wet weights,
and AQUATOX uses dry weights for most computations. Therefore, a wet-to-dry conversion of
5 is assumed within the model. Furthermore, the data were based on 5-g trout, and uptake is at
least implicitly a function of respiration, which is sensitive to size. A size correction is based on
a standard allometric relationship and the reciprocal of that value for a 5-g fish:
SizeCorr = MeanWeighr02 (399)
Sizeref
where
SizeCorr = allometric correction for size (unitless);
MeanWeight = mean wet weight of organism (g);
SizeRef = reference value (0.7248).
The respiration rate decreases with larger sizes. The size correction for a 5-g fish is, of course,
1.0; the correction for a 10-g fish is 0.63, that is, uptake is 63% that of the fish for which the hi
values were determined; the correction for a 100-g fish is 55% of the reference; and the
correction for a 1000-g fish is 35%.
Invertebrates respire more slowly than fish. As an approximation, their respiration rate is taken
to be 0.1 times that of a fish, based on the rate for mysids, the only invertebrate parameterized
for the Wisconsin Bioenergetics Model (Hewett and Johnson 1992).
Although there are only two data points for sulfonates (Martin et al. 2003a), the trend defined by
those points provides an approximation:
log&l = -6.00 + 0.966- ChainLength (400)
However, the kJ values were determined from the first few observed uptake values and not the
observations just before the depuration phase of the experiment. Adjusting the intercept actually
provides a better fit to the overall experiment:
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log kl = - 5.85 + 0.966 • ChainLength
(401)
With the greater intercept, the sulfonates are taken up more rapidly than the carboxylates, as
shown in Figure 147. The wet-weight and size corrections are used for both carboxylates and
sulfonates. Therefore, gill uptake is:
GillUptake = WetToDry • SizeCorr • kl • StVarAnimal -le-6
(402)
where:
GillUptake
WetToDry
SizeCorr
1 e-6
uptake of toxicant by gills (ng/L d);
conversion factor for wet to dry weights (5);
allometric correction for size (unitless), see (399);
biomass of given animal (mg/L);
units conversion (kg/mg).
Figure 147: Predicted and observed uptake transfer rates for carboxylates and sulfonates.
8 10 12
Perfluoroalkyl Chain Length
• Pred carboxylate
Obs carboxylate
• Pred sulfonate
x Obs sulfonate
Dietary Assimilation
Martin et al. (2003b) found that assimilation of PFAs was quite efficient, exceeding that for the
normal hydrophobic chemicals. However, many of the calculated values reported (Martin et al.
2003b) exceeded 1.0, so the observed assimilation efficiencies were normalized to a maximum
of 1.0, and equations were derived for uptake from the gut (GutEfJTox). If a carboxylate:
\ogGutEff = -0.91 + 0.085 • ChainLength r2 = 0.897
(403)
If a sulfonate:
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GutEff = -0.68 + 0.21- ChainLength
r2 =1.0 (2 points)
(404)
In the absence of information on other organisms, these equations are used for all animals.
Figure 148: Gut assimilation efficiency as a function of chain length.
1.20
1*1.00
*
~ 0.30 -\
1C
111
o.eo -
0.40 -
< 0.20
0.00
7911
Perfluoroalkyl Chain Length
13
-Pred carboxylate
-Pred/Obs su If on ate
Depuration
Based on regression of published data from experiments with juvenile trout (Martin et al. 2003a,
Martin et al. 2003b), carboxylate depuration can be estimated as:
where:
log k2 = - 0.0873 - 0.1207 • ChainLength
k2 = depuration rate (1/d).
r2 =0.98
(405)
Only four data points are available for two sulfonate compounds (Martin et al. 2003a, Martin et
al. 2003b); but they indicate that depuration is much slower than for carboxylates. The model
extrapolates from those two pairs of points, but this estimation procedure should be used with
caution (Figure 149):
log k2 = - 0.733 - 0.07 • ChainLength
r2 =0.84
(406)
Because uptake is so efficient in the gut, depuration may be largely across the gills. If this is true
then depuration rate can be related to respiration rate, providing a correction for size. The same
size correction is used for depuration as for gill uptake, see equation (399).
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In the absence of any data, this approach to modeling depuration is extended to invertebrates.
When data become available on depuration of PFAs in invertebrates, this series of constructs
may be modified.
Figure 149. Depuration rate as a function of perfluoroalkyl chain length.
n -\A
n 1 9 -
n 1 -
n n&
(N
^
n OR -
n r\A •
n 09
n
•
\
\
V
^K^
__^%j
i i i
• ObsCaboxylate
Pred Carboxylate
Obs Sulfonate
Pred Sulfonate
i
5 7 9 11 13
Perfluoroalkyl Chain Length
Available data indicate that concentrations of PFOS in wildlife are less than those known to
cause toxic effects in laboratory animals (Giesy and Kannan 2001). AQUATOX provides a
means of factoring in toxicity data as they become available for aquatic species.
Bioconcentration Factors
The steady-state bioconcentration factor (BCF) for carboxylates, used to compute time-
dependent toxicity, can be estimated by (Martin et al. 2003a):
log BCF = - 5.724 + 0.9146 • ChainLength
r2 =0.995
(407)
where
BCF =
bioconcentration factor (L/kg).
Similar to uptake, the slope for the BCFs of sulfonates closely parallels that of carboxylates but
with a different intercept (Figure 150):
log BCFsulfonate = - 5.195 + 1.03 • ChainLength r2 = 1.0 (2 points)
(408)
For compounds with perfluoroalkyl chain lengths in excess of 11, it is assumed that the BCF is
the same as that for chain length 11, as suggested by the outlier (Figure 150). Because
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AQUATOX uses dry weights in most computations, these values are multiplied by 5 to account
for the wet to dry conversion.
Figure 150. Bioconcentration factors as functions of perfluoroalkyl chain length.
Pred Cart
Pred Sulf
Obs Carboxylate
A ObsSulfonate
7 9 11 13
Perfluoroalkyl Chain Length
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9. ECOTOXICOLOGY
Unlike most ecological models, AQUATOX contains an
ecotoxicology submodel that computes both lethal and sublethal
acute toxic effects from the concentration of a toxicant in a
given organism. Furthermore, because AQUATOX is an
ecosystem model, it 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 lethal 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 sublethal toxicity responses in
50% of the population, are used to obtain factors relating the sublethal toxicities to the lethal
toxicity. Because AQUATOX can simulate as many as twenty toxic organic chemicals
simultaneously, the simplifying assumption is made that the toxic effects are additive.
Ecotoxicology: Simplifying
Assumptions
• Toxic effects of multiple chemicals
are additive
• Sublethal effects levels of
chemicals may be estimated as a
fraction of lethal effects levels
• Regressions from one species to
another are available regardless of
the mode of action
• The external toxicity model
assumes immediate toxic effect to a
level of external exposure
• Cumulative toxicity considers
differing tolerances in a population,
but ignores inherited tolerance
• Resistance to lower doses is
conferred for the lifetime of an
animal and for one year for a plant.
9.1 Lethal Toxicity of Compounds
Interspecies Correlation Estimates (ICE)
Often LC50 data will only be available for one or two of the many species that a user wishes to
include in a simulation. To alleviate this problem, a substantial database of regressions
(Interspecies Correlation Estimation, ICE) is available as developed by the US. EPA Office of
Research and Development, the University of Missouri-Columbia, and the US Geological
Survey (Asfaw and Mayer, 2003). At this time the Web-ICE database has over 2000 regressions
with over 100 aquatic species as "surrogates" (Raimondo et al. 2007). Regressions may be made
on the basis of species, families, or genera. The database also includes goodness of fit
information for regressions so their suitability for a given application may be ascertained. Only
statistically significant regressions are included in the database.
Using the ICE database and the following regression equation, the model can be parameterized
to represent a complete food web.
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Log LC50Estimated = Intercept + Slope • Log LC50obsemd (409)
where:
LC50Estimated = estimated LC50 (ug/L);
Intercept = intercept for regression (ug/L);
Slope = slope of the regression equation;
= observed LC50 (ug/L).
The ICE database is integrated into the AQUATOX user interface. A link is provided to the
Web-based (Web-ICE) site so that the user can alternatively use the web tool. The steps that a
user can take to use ICE within AQUATOX to estimate unavailable LC50 data are as follows:
• Invoke the ICE interface from the AQUATOX "Chemical Toxicity Parameter" screen;
• Choose from the six available ICE databases (species, genus, and family by either
scientific names or common names);
• Either choose a "surrogate species" that matches a species for which there is observed
LC50 data, or start with a "predicted species" that matches a species that you wish to
model;
• The list box that you did not select from in the previous step will narrow to reflect the
available surrogate or predicted species that match with your selection. Select a choice
from this list box as well. If you wish to start over again, you may select the "show all"
button next to this list box.
• Examine the goodness of fit for your model and evaluate whether it is appropriate for
your purposes. Where there are multiple surrogates for the desired predicted species,
compare the statistics and choose best surrogate/predicted pair;
• Apply the model by assigning the surrogate and predicted species to species within the
chemical's toxicity record.
Experimentally derived toxicity data for individual species should be used when available.
However, ICE may then be used to estimate toxicity for species that have not yet been studied
given a particular chemical. There are uncertainties in this estimation procedure, but the model
helps to track these uncertainties. When the ICE model is invoked, data about the goodness of fit
and confidence interval are copied back into the "LC50 comment" field. Overall model
uncertainty resulting from this estimation can then be numerically quantified — these goodness of
fit data can be utilized within an iterative AQUATOX uncertainty analysis (see section 2.5).
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Internal Calculations
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.
The same principles apply to organic toxicants and to both plants and animals.
The internal lethal concentration for a given period of exposure can be computed from reported
lethal toxicity data based on the simple relationship suggested by an algorithm in the FGETS
model (Suarez and Barber, 1992):
InternalLCSO = BCF • LC50
(410)
where:
InternalLCSO =
BCF
LC50
internal concentration that causes 50% mortality;
bioconcentration factor (L/kg), see (342) to (349); and
concentration of toxicant in water that causes 50% mortality
For compounds with aLogKOW'm excess of 5 the usual 96-hr toxicity exposure does not reach
steady state, so a time-dependent BCF is used to account for the actual internal concentration at
the end of the toxicity determination. This is applicable no matter what the length of exposure
(Figure 151, based on Figure 138).
Figure 151; Bioconcentration factor as a function of time and KOW
Q:
Z
uu
o
O
0
o
CQ
1E3 ,
0 \ 200 400 600 800 1000 1200
DAY
The internal concentration causing 50% mortality after an infinite period of exposure, LCInfmite,
can be computed by:
where:
LCInfmite = InternalLCSO • (l - e-k2'
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k2 = elimination rate constant (1/d); and
ObsTElapsed = exposure time in toxicity determination (h).
Essentially this equation determines the asymptotic toxicity relationship and provides the model
with a constant toxicity parameter for a given compound.
The model estimates k2, see (364) and (354), assuming that this k2 is the same as that measured
in bioconcentration tests; good agreement has been reported between the two (Mackay et al.,
1992). The user may then override that estimate by entering an observed value. The k2 can be
calculated off-line based on the observed half-life:
(412)
tin
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 i i^ LCInfmite ,**^
LethalConc = - J (413)
7 -k2» TElapsed ^ '
where:
LethalConc = tissue-based concentration of toxicant that causes 50% mortality
(ppb or ug/kg);
LCInfmite = ultimate internal lethal toxicant concentration after an infinitely
long exposure time (ppb);
TElapsed = period of exposure (d).
The longer the exposure the lower the internal concentration required for lethality.
Exposure is limited to the lifetime of the organism:
if TElapsed > LifeSpan then TElapsed = LifeSpan (414)
where:
LifeSpan = user-defined mean lifetime for given organism (d).
Based on an estimate of time to reach equilibrium (Connell and Hawker, 1988),
•f TJ71 ^^'+U
it I Elapsed > - then
P k2 (415)
LethalConc = LCInfmite
The fraction killed by a given internal concentration of toxicant is best estimated using the time-
dependent LethalConc in the cumulative form of the Weibull distribution (Mackay et al., 1992;
see also Christensen and Nyholm, 1984):
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CumFracKilled = l-e\
PPB
LethalConc
(416)
where:
CumFracKilled
PPB
Shape
(unitless).
fraction of organisms killed per day (g/g d),
internal concentration of toxicant (ug/kg), see (310); and
parameter expressing variability in toxic response
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.
This formulation is preferable to the empirical probit and logit equations because it is simple and
yet based on mechanistic relationships. The Shape parameter is important because it controls the
spread of mortality. The larger the value, the greater the distribution of mortality over toxicant
concentrations and time. 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. Although mercury is not currently modeled, data
on MeHg toxicity shows that the Shape parameter may take a value less than 0.1 (Figure 152).
Figure 152. The effect of Shape in fitting the observed (McKim et al., 1976)
cumulative fraction killed following continued exposure to MeHg
1
Qo.s
tu
20.6
o
o
0.4
0.2
0
Hgppb - LettialConcBg for Day 637
0 200 400 600 SCO 1000120014001600
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 been exposed to a given level of toxicant and therefore is referred to as Nonresistant.
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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
timeis computed as:
Poisoned = Resistant • Biomass • FracKilled + Nonresistant • CumFracKill (417)
where:
Poisoned = biomass of given organisms killed by exposure to toxicant at given
time (g/m3 d);
Resistant = fraction of biomass not killed by previous exposure (frac);
FracKilled = fraction killed per day in excess of the previous fraction (g/g d);
Nonresistant = biomass not previously exposed; the biomass in excess of the
resistant biomass (g/m3) = (1-Resistant)-Biomass.
New biomass is considered vulnerable, ignoring the possibility of inherited tolerance. It is
assumed for purposes of risk analysis that resistance is not conferred for an indefinite period. In
animals elapsed exposure time is capped at the average life span, which is a parameter in the
animal record. However, it is assumed that resistance persists in the population until the end of
the growing season. Macrophytes can live for an entire growing season, and algae usually
reproduce asexually as long as conditions are favorable. However, winter die-back does occur in
most macrophytes, and many algae will switch to sexual reproduction under unfavorable
conditions, especially triggered by light and temperature. As a simplifying assumption for both
animals and plants, in the northern hemisphere January 1 is taken as being the date at which
exposure and resistance are reset; in the southern hemisphere (denoted by negative latitude in the
site record) July 1 is the reset date. On this date, the variables Resitant, FracKilledPrevious, and
TElapsed are all set to zero.
9.2 Sublethal Toxicity
Organisms usually have adverse reactions to toxicants at levels significantly below those that
cause death. In fact, the lethal to sublethal ratio is commonly used to quantify this relationship.
The user supplies observed EC50 values, which can then be used to compute AFs (application
factors). For example:
ECSOGrowth
AFGrowth= (418)
LC50
where:
ECSOGrowth = external concentration of toxicant at which there is a 50%
reduction in growth (ug/L);
AFGrowth = sublethal to lethal ratio for growth (unitless); and
LC50 = external concentration of toxicant at which 50% of population is
killed (ug/L).
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If the user enters an observed EC50 value, the model provides the option of applying the
resulting AF to estimate EC50s for other organisms. The computations for AFPhoto and
AFRepro are similar:
AFPhoto =
AFRepro =
ECSOPhoto
LC50
ECSORepro
LC50
(419)
(420)
where:
ECSOPhoto
AFPhoto
ECSORepro
AFRepro
external concentration of toxicant at which there is a 50%
reduction in photosynthesis (ug/L);
sublethal to lethal ratio for photosynthesis (unitless);
external concentration of toxicant at which there is a 50%
reduction in reproduction (ug/L); and
sublethal to lethal ratio for reproduction (unitless).
Similar to computation of lethal toxicity in the model, sublethal toxicity is based on internal
concentrations of a toxicant. Often sublethal effects form a continuum with lethal 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 factors relate the observed effect to the lethal effect and
permit efficient computation of sublethal effects factors in conjunction with computation of
lethal 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 factor enters into the Weibull equation to estimate reduction factors for photosynthesis,
growth, and reproduction:
PPB
FracPhotO— e\LethalConc-AFPhoto
I/Shape
(421)
RedGrOWth — 1 - e\LethalConc -AFGrowth
PPB
I/Shape
(422)
where:
RedRepro — I - e\ LethalConc • AFRepro
PPB
I/Shape
(423)
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 (ug/kg), see (310);
LethalConc = tissue-based cone, of toxicant that causes mortality (ug/kg), see (413);
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AFPhoto = sublethal to lethal ratio for photosynthesis (unitless, default of 0.10);
AFGrowth = sublethal to lethal ratio for growth in animals (unitless, default of 0. 1 0);
AFRepro = sublethal to lethal ratio for reproduction in animals (unitless, default of
0.05);
Shape = parameter expressing variability in toxic response (unitless, default of
0.33).
The reduction factor for photosynthesis, FracPhoto, enters into the photosynthesis equation (Eq.
(35)) and it also appears in the equation for the acceleration of sinking of phytoplankton due to
stress (Eq. (69)).
The variable for reduced growth, RedGrowth, is arbitrarily split between two processes,
ingestion (Eq. (91)), where it reduces consumption by 20%:
ToxReduction = 1-(0.2- RedGrowth) (424)
and defecation (Eq. (97)), where it increases the amount of food that is not assimilated by 80%:
IncrEgest = (1 - EgestCoeff pmy prj -0.8- RedGrowth (425)
These have indirect effects on the rest of the ecosystem through reduced predation and increased
production of detritus in the form of feces.
Embryos are often more sensitive to toxicants, although reproductive failure may occur for
various reasons. As a simplification, the factor for reduced reproduction, RedRepro, is used
only to increase gamete mortality (Eq. (126)) beyond what would occur otherwise:
IncrMort = (1- GMort) • RedRepro (426)
By modeling sublethal and lethal effects, AQUATOX makes the link between chemical fate and
the functioning of the aquatic ecosystem- a pioneering approach that has been refined over the
past twenty years, following the first publications (Park et al., 1988; Park, 1990).
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 sublethal toxicity parameter, as in the equation for periphyton
sloughing:
Dislodge M Tox = MaxToxSlough • . ^ -- Biamasspal (427)
Toxicantwater + EC50Dlslodge
where:
n, Tox = periphyton sloughing due to given toxicant (g/m3 d);
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MaxToxSlough = maximum fraction of periphyton biomass lost by sloughing due to
given toxicant (fraction/d, 0.1);
Toxicantwater = concentration of toxicant dissolved in water (ug/L); see (300);
EC50Disiodge = external concentration of toxicant at which there is 50% sloughing
(ug/L); and
Biomasspen = biomass of given periphyton (g/m3); see (33).
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 sublethal toxicity parameter :
ToxicantWater - DriftThreshold
DislodgeTox = \ —
ox ToxicantWater - DriftThreshold
(428)
where:
ToxicantWater =
DriftThreshold =
concentration of toxicant in water (ug/L);
the concentration of toxicant that initiates drift (ug/L); and
concentration at which half the population is affected (ug/L).
These terms are incorporated in the respective periphyton washout (72) and zoobenthos drift
(130) equations.
9.3 External Toxicity
Chemicals that are taken up very rapidly and those that have an external mode of toxicity, such
as affecting the gills directly, are best simulated with an external toxicity construct. AQUATOX
has an alternative computation for CumFracKilled, when calculating toxic effects based on
external concentrations, using the two-parameter Weibull distribution as in Christiensen and
Nyholm (1984):
= l-exp(-kzEta)
(429)
where:
CumFracKilled
k and Eta
= external concentration of toxicant (ug/L);
= cumulative fraction of organisms killed for a given period of exposure
(fraction/d), applied to equation (417);
= fitted parameters describing the dose response curve.
Rather than require the user to fit toxicological bioassay data to determine the parameters for k
and Eta, these parameters are derived to fit the LC50 and the slope of the cumulative mortality
curve at the LC50 (in the manner of the RAMAS Ecotoxicology model, Spencer and Person,
1997):
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k =
-ln(0.5)
Eta
(430)
Eta =
-2-LC50-slope
ln(0.5)
(431)
where: slope = slope of the cumulative mortality curve at LC50 (unitless).
LC50 = concentration where half of individuals are affected (|j,g/L).
AQUATOX assumes that each chemical's dose response curve has a distinct shape, relevant to
all organisms modeled. In this manner, a single "slope factor" parameter describing the shape of
the Weibull curve can be entered in the chemical record rather than requiring the user to derive
slope parameters for each organism modeled. (Note, this is different than the shape parameter
used for internal toxicity.)
As shown below, the slope of the curve at the LC50 is both a function of the shape of the
Weibull distribution and also the magnitude of the LC50 in question. Figure 153 shows two
Weibull distributions with identical shapes, but with slopes that are significantly different due to
the scales of the x axes.
Figure 153. Weibull distributions with identical shapes, but different slopes.
For this reason, rather than have a user enter "the slope at LC50" into the chemical record,
AQUATOX asks that the user enter a "slope factor" defined as "the slope at LC50 multiplied by
LC50." In the above example, the user would enter a slope factor of 1.0 and then, given an
LC50 of 1 or an LC50 of 100, the above two curves would be generated.
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When modeling toxicity based on external concentrations, organisms are assumed to come to
equilibrium with external concentrations (or the toxicity is assumed to be based on external
effects to the organism).
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10. ESTUARINE SUBMODEL
The estuarine version of AQUATOX is intended to be an
exploratory model for evaluating the possible fate and effects
of toxic chemicals and other pollutants in estuarine ecosystems.
The model is not intended to represent detailed, spatially
varying site-specific conditions, but rather to be used in
representing the potential behavior of chemicals under average
conditions. Therefore, it is best used as a screening-level
model applicable to data-poor evaluations in estuarine
ecosystems. However, it can be calibrated for different
estuaries.
Hourly tidal fluctuations are not included in the model; the
native AQUATOX time-step is one day. Because of this, the
overall water volume of the estuary may be assumed to remain
constant over the entire simulation. The simplifying
assumption is that the water volume of the estuary is not
sensitive to the freshwater inflow. The volumes and depths of
the fresh layer and the salt wedge do vary as a function of the
daily average tidal range and freshwater flows.
10.1 Estuarine Stratification
AQUATOX Estuarine Submodel:
Simplifying Assumptions
• Estuary is a single segment that
always has two well-mixed layers
• The estuary has freshwater inflow
from upstream and saltwater inflow
from the seaward end (salt-wedge)
• Water flows at the seaward end are
estimated using the salt-balance
approach
• Effects of salinity on sorption are
minor and are not modeled
• Hourly tidal fluxes are not modeled
• Daily average volume of the
estuary is assumed to remain
constant over time
• The surface area of the lower layer
is the same as the upper layer
• Nutrient concentrations in
inflowing seawater are assumed to
be constant
• Possible salinity effects on
microbial degradation, hydrolysis,
and photolysis are ignored.
As a general case, the estuarine system is assumed to always have two layers, although at times
the layers may be essentially identical because of respective thicknesses and turbulent diffusion.
The two layers are assumed to be a function of and to vary with freshwater loadings and daily
tidal ranges. The fraction of depth in the upper layer is adjusted to account for changing volumes
due to entrainment (flow of water from lower to upper layer; see section 10.4), with a value of
1.5 based on inspection of published observations. li ResidFlow > 0 then:
FreshwaterHead =
ResidFlow
Area
(432)
FracUpper = 1.5-
FreshwaterHead
TidalAmplitude + FreshwaterHead
where:
FreshwaterHead
ResidFlow
Area
FracUpper
TidalAmplitude
height of freshwater (m/d);
inflow residual flow of fresh water minus daily evaporation,
(m3/d) user inputs;
area of the estuary taken at mean tide (m2).
fraction of mean depth that is upper layer (unitless).
tidal amplitude (m), see (434);
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IfResidFlow <= 0 thenFracUpper is taken as having a nominal value of 0.05.
The thicknesses of the two layers, and therefore the volumes of the two layers, may be calculated
as a function of FracUpper.
where:
ThickUpper
FracLower
ThickLower
MeanDepth
VolumeUpper
VolumeLower
Area
ThickUpper = FracUpper • MeanDepth
ThickLower = MeanDepth - ThickUpper
VolumeUpper = FracUpper • Area
VolumeLower = FracLower • Area
thickness of the upper layer (m);
1 -FracUpper, see (432);
thickness of the lower layer (m);
mean depth of the estuary (m);
volume of the upper layer (m3);
volume of the lower layer (m3);
area of the estuary taken at mean tide (m2).
(433)
As shown in the formulations above, layer thicknesses are a function of the daily predicted tidal
range. Given that the estuary's average daily volume is assumed to remain constant, to maintain
mass-balance of water AQUATOX moves water from one layer to the next when thicknesses
change. (This same movement of water occurs when the user specifies a variable thermocline
depth in a stratified lake or reservoir, see section 3.4 on "Modeling Reservoirs and Stratification
Options.") In order to maintain biomass, nutrient, and toxicant mass-balance AQUATOX also
transfers state variables located in the moving water from one layer to the next. This transfer can
cause minor fluctuations that are visible in some estuarine-version results (e.g. wave-like patterns
in fish biomass predictions.) Such fluctuation is predominantly an artifact of the simple manner
in which AQUATOX models estuarine water volume.
10.2 Tidal Amplitude
Tidal amplitude is calculated using the general equation found in the Manual of Harmonic
Analysis and Prediction of Tides (U.S. Department of Commerce 1994):
TidalAmplitude =
' AmPCon • NodefactorConYear • >
cos((SpeedCon • Hours) + EquilConJear - EpochCon),
(434)
where:
TidalAmplitude =
Con.
Ampcon.
Nodefactor =
Speed =
one-half the range of a constituent tide (m);
eight constituents of tidal range listed below;
user-input amplitude for each constituent (m);
node factor for each constituent for each year,
AQUATOX for 1970-2037 (deg.);
speeds of each constituent in (deg./hour), hard-wired
hard-wired into
into
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AQUATOX for each relevant constituent;
Hours = time since the start of the year (hours);
Equil = equilibrium argument for each constituent for each year in degrees
for the meridian of Greenwich, hard-wired into AQUATOX for
1970-2037 (deg.);
Epoch = user input phase lag for each constituent (deg.).
AQUATOX requires Amplitudes and Epochs for the following eight constituents of tidal range
for the modeled esturary, generally available for download from NOAA databases. These
"primary" constituents were found to have the largest effect on tidal range and will predict tidal
range to the precision as required by the estuarine submodel:
M2 - Principal lunar semidiurnal constituent
S2 - Principal solar semidiurnal constituent
N2 - Larger lunar elliptic semidiurnal constituent
Kl - Lunar diurnal constituent
Ol - Lunar diurnal constituent
SSA - Solar semiannual constituent
SA - Solar annual constituent
PI - Solar diurnal constituent
10.3 Water Balance
Water balance is computed using the salt balance approach (Ibafiez et al. 1999):
ResidFlow
Saltwater Inflow = (435)
Salinity Lower ISalinityUppper -1
ResidFlow
Outflow = (436)
1 - SalinityUpperlSalinityLower
where:
Saltwater Inflow = water entering estuary from mouth of estuary, usually into lower
level but may be into upper level if evaporation exceeds freshwater
inflow (m3/d);
Outflow = water leaving estuary at mouth (m3/d);
ResidFlow = residual flow of fresh water; may be negative if evaporation
exceeds freshwater inflow (m3/d);
SalinityLower = salinity of lower layer at mouth of estuary (psu or %o);
SalinityUpper = salinity of upper layer at mouth of estuary (psu or %o);
Programmatically, the system is modeled as a single constant-volume segment with two layers
and with freshwater inflow from upstream and saltwater inflow from the seaward end. Ice cover
is not assumed on top of estuaries unless the average water temperature falls below -1.8 deg.C.
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10.4 Estuarine Exchange
Saltwater inflow occurs to replace water that is admixed (entrained) from one layer (usually the
lower) to the other layer, producing the observed salinities of the two layers at the mouth of the
estuary. (Note that this use of the term "entrainment" differs from the downstream entrainment
of organisms, e.g. (132).) This circulation is much greater than any longitudinal mixing (see
Thomann and Mueller 1987). Therefore, effectively, entrainment is the equivalent of
Saltwater Inflow, but its derivation is informative:
„ Tr , Saltwater Inflow
Entrain)/el =
Area
VertAdvection = EntrainVel • Thick (437)
„ VertAdvection • Area
Lntrarnment =
Thick
where:
EntrainVel = entrainment velocity of lower layer into upper layer (m/d);
VertAdvectiveDisp = vertical advective dispersion (m2/d);
Entrainment = vertical flow as derived above (m3/d).
Transport of suspended and dissolved substances from the lower layer to the upper layer can then
be computed. In a truly stratified estuary turbulent diffusion will be minimal, so we will set the
bulk mixing coefficient (BulkMixCoeff) to 0.1 m2/d following the example of Koseff et al.
(1993). However, when wind exceeds 3 m/s Langmuir circulation sets up with downwelling and
upwelling extending to about 3 m. Therefore, if the thickness of the upper layer is less than 3 m
and the wind speed is greater than 3 m/s, then bulk mixing is increased by a factor of 5.
Turbulent diffusion can then be computed for each dissolved and suspended compartment:
BulkMixCoeff . i \
TurbDiff = —— Langmuir • \Conc co en - Cone }
Volumeupper
(438)
BulkMixCoeff . t \
TurbDifflower = —— Langmuir • (Cone - Cone mentjower)
Volumelower
If ThickUpper < 3 and Wind > 3 then Langmuir = 5 else Langmuir = 1
where:
TurbDiff = turbulent diffusion (g/m3-d);
BulkMixCoeff = bulk mixing coefficient (0.1 m2/d);
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Langmuir = factor for greater mixing when wind equals or exceeds 3 m/s
(unitless);
Volumeupper = volume of the upper layer (m3);
Volume iower = volume of the lower layer (m3);
Cone = concentration of given compartment in a given layer (g/m3).
10.5 Salinity Effects
Mortality and Gamete Loss
Salinity that is less than or greater than threshold values increases mortality and gamete loss:
if SalMin < Salinity < SalMax then SaltMort = 0
if Salinity < SalMin then SaltMort = SalCoeffl • eSalM>"-Sa»"> SalMaxtiusa. SaltMort = SalCoeffl • eSaUmty-SalMa:c
where:
SalMin = minimum salinity below which effect is manifested (%o);
Salinity = ambient salinity (%o);
SalMax = maximum salinity above which effect is manifested (%o);
SaltMort = mortality due to salinity (1/d);
SalCoeffl = coefficient for effect of low salinity (unitless);
SalCoeff2 = coefficient for effect of high salinity (unitless);
e = the base of natural logarithms (2.71828, unitless).
SaltMort is then applied to mortality (112) and gamete loss (126). The model assumes
reproduction is affected because eggs and sperm are not viable in abnormal salinities.
Other Biotic Processes
Salinity beyond the range of tolerance for a particular process, including photosynthesis,
ingestion, and respiration, will reduce the process:
if SalMin < Salinity < SalMax then SalEffect = 1
if Salinity < SalMin then SalEffect = SalCoeffl • eSalimty-Sam" (440)
if Salinity > SalMaxihea. SalEffect = SalCoeffl • eSalMax-Sa"mty
where:
SaltEffect = effect of salinity on given process (unitless).
In general, the ranges of tolerance of abnormal salinities in animals, going from least tolerant to
most tolerant, affects reproduction, ingestion, respiration, and mortality in that order (Figure
154). Respiration decreases because gill ventilation is depressed. SaltEffect is applied to
ingestion (91), respiration (100), and photosynthesis (35) as appropriate.
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CHAPTER 10
Figure 154. Effects of salinity on various animal processes.
£
£
Effects of Salinity
•\ i ^
.<•
= 0.8
5 n R
t
I 0.4
0.2
0
C
Inr
me
F
UVx
I
-
v;
o
4.5
4
3.5
3
9 ^
2
1.5
- 1
0.5
n
) 10 20 30 40 50 60 70 80
Salinity (ppt)
estio
n f^nn^ntn\ nr-r- D nr-in' rnt' nn ^/l«
n (jaineieLoss Kespiraiion ~ ~ ivioi
•tality
>
+j
o
Sinking
Sinking of phytoplankton and suspended detritus also is affected by salinity, more so than by
temperature (Figure 155, Figure 156). However, because ambient salinity and temperature affect
sinking by controlling density, we will compute a density factor based on the effects of both
compared to the salinity and temperature of the observed sinking rate (Thomann and Mueller
1987):
WaterDensi ty = 1 + <^ 10
-3
(28.14 - 0.0735 • Temperatur e - 0.00469 • Temperatur e2)
+ (0.802 - 0.002 • Temperatur e}- (Salinity - 35)
(441)
DemityFactor =
WaterDensityrefer(
iference
WaterDemityamhjent
(442)
Sink = DensityFactor
rr\-j • -j •/
Thick
(443)
where:
Water Density reference
density of water at temperature and salinity of observed sinking
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WaterDemityambient
Temperature
Density Factor
Sink
KSed
Thick
rate (kg/L);
density of water at ambient temperature and salinity (kg/L);
temperature of water (°C);
correction factor for water densities other than those at which
sinking rates were observed (unitless);
sinking rate of given suspended compartment (g/m3-d);
intrinsic settling rate (m/d);
thickness of water layer (m).
Figure 155. Correction factor for sinking as
a function of temperature.
Figure 156. Correction factor for sinking as a
function of salinity.
Effect of Temperature on Sinki ng
1.01
1.005
1
0.995
0.99
0 5 10 15 20 25 30 35 40 45
Temperature
Effect of Salinity on Sinking
0.93
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Sorption
The influence of seawater or "salting out" does not cause major changes in sorption of organic
compounds (Schwarzenbach et al. 1993). It varies with the compound, with greater effect on
polar compounds, but is seldom measured. Therefore, it will be ignored at the present time.
Volatilization
Volatilization is affected by salinity, and can be represented by a linear increase in the Henry's
Law constant (Eqn. 330). At 35%o salinity the average increase in the constant across tested
organic compounds is 1.4 compared to that of distilled water (Schwarzenbach et al. 1993).
Applying this relationship:
HLCSaltFactor = 1 + 0.01143 • Salinity (444)
Estuarine Reaeration
Reaeration is affected by salinity, especially through calculation of the saturation level (O2Sai).
Salinity is included in the present formulation for O2Sat. Computation of the depth-averaged
reaeration coefficient (KReaer) requires determination of the effects of both tidal velocity and
wind velocity. Thomann and Fitzpatrick (1982, see also (Chapra 1997)) combine the two in one
equation:
„ M JVelocity 0.728 -JWind -0.317 -Wind+ 0.0372-Wind2 „_
KReaer = 3.93 T-f- H (445)
Thick312 Thick
The daily average tidal velocity can be computed by a variation of a formulation presented by
(Thomann and Mueller, 1987), substituting the spring tide harmonic for the diurnal harmonic:
Velocity =
ResidFlow Vel + TidalVel • 1 + 0. 5 • sin
12
86400
(446)
r> -jr-7 IT , OutFloW ,tt-^
ResidFlow Vel = (447)
XSecArea
XSecArea = Depth • Width (448)
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CHAPTER 10
TidalVel =
TidalPrism
XSecArea
(449)
TidalPrism = 2.0- Amplitude • Area
(450)
where:
Velocity =
Wind
ResidFlowVel =
Outflow
TidalVel
Day
XSecArea =
Depth
Width
TidalPrism =
Amplitude =
Area =
water velocity (m/s);
wind velocity (m/s), see (29);
residual flow velocity of fresh water (m/d);
water leaving estuary at mouth (m3/d), see (436);
mean tidal velocity (m/d);
Julian date (d);
cross-sectional area of estuary (m2);
mean water depth (m);
width of estuary (m);
the difference in water volume between low and high tides (m3);
tidal amplitude (m), see (434);
area of site (m2).
Figure 157. Daily average water velocities based on freshwater flow and tidal flow.
Freshwater and Tidal Velocities
0.25 n
0.20
1. 0.15
o 0.10
o>
0.05
0.00
10
15
Days
20
25
30
Migration
Fish and pelagic invertebrates will also migrate vertically when the salinity level is not favorable.
284
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION CHAPTER 10
Favorable salinity is defined as the range of salinity in which no ingestion effects occur for the
animal (from the minimum to the maximum salinity tolerances for ingestion). If the salinity of
the current segment is outside that range, and the salinity of the other segment is within the range
of favorable salinity, the animal is predicted to migrate vertically to the other segment.
Entrainment for pelagic invertebrates (movement due to water movement from the lower layer to
the upper layer as predicted by the salt balance model, see (437)) will also be set to zero if the
salinity in the upper layer is outside of the favorable range. This can have significant effects on
shrimp populations, for example.
10.6 Nutrient Inputs to Lower Layer
Nutrient concentrations in ocean water flowing into the lower layer are set to temporally constant
levels, the assumption being that the chemical composition of seawater remains relatively
uniform. Nutrients and gasses in seawater may be edited using a button available in the initial
conditions and loadings screen for each relevant variable. The default nutrient and gas
composition of seawater are set as follows:
• Ammonia: 0.02 mg/L (Data from Galveston Bay, TX)
• Nitrate: 0.05 mg/L (Data from Galveston Bay, TX)
• Phosphate: 0.03 mg/L (Data from Galveston Bay, TX)
• Oxygen: 7.0 mg/L (Default oxygen inflow to lower segment)
• CO2 : 90.0 mg/L (Anthoni, 2006)
285
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION CHAPTER 11
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National Investment in Municipal Wastewater Treatment: Appendix B. EPA-832-R-00-
008, http://www.epa.gov/owtnitnet/wquality/app-b.pdf.
U.S. Environmental Protection Agency, 2002. National Water Quality Inventory: 2000 Report.
EPA-841-R-02-001.
U.S. Environmental Protection Agency, 2005. AQUATOX For Windows: A Modular Fate and
Effects Model For Aquatic Ecosystems Release 2.1 Addendum To Release 2 Technical
Documentation.
Van Rees, K. C. I, K. R. Reddy, and P. A. Moore, Jr. 1991. Lake Okeechobee Phosphorus
Dynamics Study: Biogeochemical Processes in the Sediments, Chapter 7: Phosphorus
Exchange Between Sediment and Overlying Water. Pages 7-1 to 7-26. University
Florida, Soil Science Department, Gainesville, Fl.
Velleux, M., S. Westenbroek, J. Ruppel, M. Settles, and D. Endicott. 2000. A User's Guide to
IPX, the In-Place Pollutant Export Water Quality Modeling Framework, Version 2.7.4.
U.S. Environmental Protection Agency, Office of Research and Development, National
Health and Environmental Effects Research Laboratory, Mid-Continental Ecology
Division-Duluth, Large Lakes Research Station, Grosse He, Michigan. 179 pp.
Verduin, 1982. Components Contributing to Light Extinction in Natural Waters: Method of
Isolation. Arch. Hydrobiol, 93(3):303-312.
Verscheuren, K. 1983. Handbook of Environmental Data on Organic Chemicals, Second edition.
Van Nostrand Reinhold, New York.
Ward 1963, ASCE 1989, 6:1-16
Watt, W.D. 1966. Release of Dissolved Organic Material From the Cells of Phytoplankton
Species in Natural and Mixed Populations. Proceedings of the Royal Society, London, B
164:521-525.
Weininger, D. 1978. Accumulation of PCBs by Lake Trout in Lake Michigan. Ph.D.
Dissertation, University of Wisconsin, Madison, 232 pp.
Westlake, D.F. 1967. Some Effects of Low Velocity Currents on the Metabolism of Aquatic
Macrophytes. Journal Experimental Botany 18:187-205.
Wetzel, R.G., P.H. Rich, M.C. Miller, and H.L. Allen. 1972. Metabolism of Dissolved and
Paniculate Detrital Carbon in a Temperate Hard-water Lake, in U. Melchiorri-Santolinii
and J.W. Hopton (eds.) Detritus and Its Role in Aquatic Ecosystems, Mem. 1st. Ital.
Idobiol, 29(Suppl): 185-243.
Wetzel, R.G. 1975. Limnology, W.B. Saunders, Philadelphia, 743 pp.
Wetzel, R.G. 2001. Limnology: Lake and River Ecosystems. San Diego: Academic Press, 1006
pp.
Whitman, W.G. 1923. The two-film theory of gas absorption. Chem. Metal. Eng. 29:146-148.
Winberg, G. G. 1971. Symbols, Units and Conversion Factors in Studies of Freshwater
Productivity. Pages 23. International Biological Programme Central Office, London.
Wlosinski, J. H., and C. D. Collins. 1985. Confirmation of the Water Quality Model CE-QUAL-
Rl Using Data from Eau Galle Reservoir, Wisconsin. Army Engineers Waterways
302
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION CHAPTER 11
Experiment Station, Vicksburg, Mississippi.
Wood, L.W., P. O.Keefe, and B. Bush. 1997. Similarity Analysis of PAH and PCB
Bioaccumulation Patterns in Sediment-Exposed Chironomus tentans Larvae.
Environmental Toxicology and Chemistry, 16(2):283-292.
Wool, T. A., R. B. Ambrose, J. L. Martin, and E. A. Comer. 2004. Water Quality Analysis
Simulation Program (WASP) Version 6.0 DRAFT: User's Manual. US Environmental
Protection Agency - Region 4, Atlanta GA.
303
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
APPENDICES
APPENDIX A. GLOSSARY OF TERMS
Taken in large part from: The Institute of Ecology. 1974. An Ecological Glossary for Engineers
and Resource Managers. TIE Publication #3, 50 pp.
Abiotic
Adsorption
Aerobic
Algae
Allochthonous
Algal bloom
Alluvial
Alluvium
Ambient
Anaerobic
Anoxic
Aphotic
Assimilation
Autochthonous
Benthic
Benthos
Biodegradable
Biochemical oxygen
demand (BOD)
Biomagnification
Biomass
Biota
Chlorophyll
Colloid
Consumer
Copepods
Crustacean
Decomposers
Detritus
Diatom
Diurnal
nonliving, pertaining to physico-chemical factors only
the adherence of substances to the surfaces of bodies with which they
are in contact
living, acting, or occurring in the presence of oxygen
any of a group of chlorophyll-bearing aquatic plants with no true leaves,
stems, or roots
material derived from outside a habitat or environment under
consideration
rapid and flourishing growth of algae
of alluvium
sediments deposited by running water
surrounding on all sides
capable of living or acting in the absence of oxygen
pertaining to conditions of oxygen deficiency
below the level of light penetration in water
transformation of absorbed nutrients into living matter
material derived from within a habitat, such as through plant growth
pertaining to the bottom of a water body; pertaining to organisms that
live on the bottom
those organisms that live on the bottom of a body of water
can be broken down into simple inorganic substances by the action of
decomposers (bacteria and fungi)
the amount of oxygen required to decompose a given amount of organic
matter
the step by step concentration of chemicals in successive levels of a food
chain or food web
the total weight of matter incorporated into (living and/or dead)
organisms
the fauna and flora of a habitat or region
the green, photosynthetic pigments of plants
a dispersion of particles larger than small molecules and that do not
settle out of suspension
an organism that consumes another
a large subclass of usually minute, mostly free-swimming aquatic
crustaceans
a large class of arthropods that bear a horny shell
bacteria and fungi that break down organic detritus
dead organic matter
any of class of minute algae with cases of silica
pertaining to daily occurrence
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
APPENDICES
Dynamic equilibrium
Ecology
Ecosystem
Emergent
Environment
Epilimnion
Epiphytes
Equilibrium
Euphotic
Eutrophic
Fauna
Flood plain
Flora
Fluvial
Food chain
Food web
Forage fish
Habitat
Humic
Hydrodynamics
Hypolimnion
Influent
Inorganic
Invertebrate
Limiting factor
Limnetic zone
Limnology
Littoral zone
Macrofauna
Macrophytes
Nutrients
Omnivorous
Organic chemical
Overturn
Oxygen depletion
Parameter
a state of relative balance between processes having opposite effects
the study of the interrelationships of organisms with and within their
environment
a biotic community and its (living and nonliving) environment
considered together
aquatic plants, usually rooted, which have portions above water for part
of their life cycle
the sum total of all the external conditions that act on an organism
the well mixed surficial layer of a lake; above the hypolimnion
plants that grow on other plants, but are not parasitic
a steady state in a dynamic system, with outflow balancing inflow
pertaining to the upper layers of water in which sufficient light
penetrates to permit growth of plants
aquatic systems with high nutrient input and high plant growth
the animals of a habitat or region
that part of a river valley that is covered in periods of high (flood) water
plants of a habitat or region
pertaining to a stream
animals linked by linear predator-prey relationships with plants or
detritus at the base
similar to food chain, but implies cross connections
fish eaten by other fish
the environment in which a population of plants or animals occurs
pertaining to the partial decomposition of leaves and other plant material
the study of the movement of water
the lower layer of a stratified water body, below the well mixed zone
anything flowing into a water body
pertaining to matter that is neither living nor immediately derived from
living matter
animals lacking a backbone
an environmental factor that limits the growth of an organism; the factor
that is closest to the physiological limits of tolerance of that organism
the open water zone of a lake or pond from the surface to the depth of
effective light penetration
the study of inland waters
the shoreward zone of a water body in which the light penetrates to the
bottom, thus usually supporting rooted aquatic plants
animals visible to the naked eye
large (non-microscopic), usually rooted, aquatic plants
chemical elements essential to life
feeding on a variety of organisms and organic detritus
compounds containing carbon;
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
305
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
APPENDICES
Pelagic zone
Periphyton
Oxidation
Photic zone
Phytoplankton
Plankton
Pond
Population
Predator
Prey
Producer
Production
Productivity
Productivity, primary
Productivity, secondary
Reservoir
Riverine
Rough fish
Sediment
Siltation
Stratification
Substrate
Succession
Tolerance
Trophic level
Turbidity
Volatilization
Wastewater
Wetlands
Zooplankton
open water with no association with the bottom
community of algae and associated organisms, usually small but densely
set, closely attached to surfaces on or projecting above the bottom
a reaction between molecules, ordinarily involves gain of oxygen
the region of aquatic environments in which the intensity of light is
sufficient for photosynthesis
small, mostly microscopic algae floating in the water column
small organisms floating in the water
a small, shallow lake
a group of organisms of the same species
an organism, usually an animal, that kills and consumes other organisms
an organism killed and at least partially consumed by a predator
an organism that can synthesize organic matter using inorganic materials
and an external energy source (light or chemical)
the amount of organic material produced by biological activity
the rate of production of organic matter
the rate of production by plants
the rate of production by consumers
an artificially impounded body of water
pertaining to rivers
a non-sport fish, usually omnivorous in food habits
any mineral and/or organic matter deposited by water or air
the deposition of silt-sized and clay-sized (smaller than sand-sized)
particles
division of a water body into two or more depth zones due to
temperature or density
the layer on which organisms grow; the organic substance attacked by
decomposers
the replacement of one plant assemblage with another through time
an organism's capacity to endure or adapt to unfavorable conditions
all organisms that secure their food at a common step in the food chain
condition of water resulting from suspended matter, including inorganic
and organic material and plankton
the act of passing into a gaseous state at ordinary temperatures and
pressures
water derived from a municipal or industrial waste treatment plant
land saturated or nearly saturated with water for most of the year;
usually vegetated
small aquatic animals, floating, usually with limited swimming
capability
306
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
APPENDICES
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
KOMRe&DOM
Cohesives Kl
Cohesives K2
Cohesives Kp
Non-Cohesives Kl
Non-Cohesives K2
Non-Cohesives Kp
Non-Cohesives2 Kl
INTERNAL
ChemicalRecord
ChemName
CASRegNo
MolWt
pka
Solubility
Henry
VPress
LogKow
KPSed
KOMRefrDOM
CohesivesKl
CohesivesK2
CohesivesKp
NonCohKl
NonCohK2
NonCohKp
NonCoh2Kl
TECH DOC
Chemical
Underlying Data
N/A
N/A
MolWt
pKa
N/A
Henry
N/A
LogKow
KPSed
KOMReftDOM
Kl
K2
Kp
Kl
K2
Kp
Kl
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
Reftractory DOM to Water Partition Coefficient
uptake rate constant for cohesives
depuration rate constant for cohesives
partition coefficient for cohesives
uptake rate constant for non-cohesives class 1
depuration rate constant for non-cohesives class 1
partition coefficient for non-cohesives class 1
uptake rate constant for non-cohesives class 2
UNITS
N/A
N/A
g/mol
negative log
ppm
ami m3 mo I-1
mmHg
unitless
L/kgOC
L/kgOM
L/kg dry day
day'1
L/kg dry
L/kg dry day
day'1
L/kg dry
L/kg dry day
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
APPENDICES
USER INTERFACE
Non-Cohesives2 K2
Non-Cohesives2 Kp
Activation Energy for
Temperature
Rate of Anaerobic Microbial
Degradation
Max. Rate of Aerobic
Microbial Degradation
Uncatalyzed hydrolysis
constant
Acid catalyzed hydrolysis
constant
Base catalyzed hydrolysis
constant
Photolysis Rate
Oxidation Rate Constant
Weibull Shape Parameter
Weibull Slope Factor
Chemical is a Base
This Chemical is a PFA
Type of PFA
Perfluoralkyl Chain Length
Kom for Sediments (PFA)
BCF for Algae (PFA)
BCF for Macrophytes (PFA)
INTERNAL
NonCoh2K2
NonCoh2Kp
En
KMDegr Anaerobic
KMDegrdn
KUnCat
KAcid
KBase
PhotolysisRate
OxRateConst
Weibull_Shape
WeibullSlopeF actor
ChemlsBase
IsPFA
PFAType
PFAChainLength
PFASedKom
PFAAlgBCF
PFAMacroBCF
TECH DOC
K2
Kp
En
KAnaerobic
KMDegrdn
KUncat
KAcid
KBase
KPhot
N/A
Shape (Internal Model)
Slope Factor (External
Model)
Compound is a base
Compound is a PFA
carboxylate / sulfonate
ChainLength
Kom for Sediments
BCF for Algae
BCF for Macrophytes
DESCRIPTION
depuration rate constant for non-cohesives class 2
partition coefficient for non-cohesives class 2
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
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
slope at LC50 multiplied by LC50
True if the compound is a base
True if the compound is a perfluorinated surfactant
Sulfonate group and carboxylate group
Length of perfluoroalkyl chain
Organic matter partition coefficient for the PFA
Bioconcentration Factor for the PFA to algae
Bioconcentration Factor for the PFA to macrophytes
UNITS
day'1
L/kgdry
cal/mol
1/d
1/d
1/d
L/mol • d
L/mol • d
1/d
L/mold
unitless
Unitless
True/False
True/False
carboxylate /
sulfonate
Integer
L/kg
L/kg
L/kg
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
APPENDICES
USER INTERFACE
Site Name
Max Length (or reach)
Vol.
Surface Area
Estuary Site Width
Mean Depth
Maximum Depth
Ave. Temp, (epilimnetic or
hypolimnetic)
Epilimnetic Temp. Range (or
hypolimnetic)
Latitude
Altitude (affects oxygen sat.)
Average Light
Annual Light Range
Total Alkalinity
Hardness as CaCO3
Sulfate Ion Cone
Total Dissolved Solids
Enclosure Wall Area
Mean Evaporation
INTERNAL
SiteRecord
SiteName
SiteLength
Volume
Area
SiteWidth
ZMean
ZMax
TempMean
TempRange
Latitude
Altitude
LightMean
LightRange
AlkCaCOS
HardCaCOS
SO4Conc
TotalDissSolids
EnclWallArea
MeanEvap
TECH DOC
Site Underlying
Data
N/A
Length
Volume
Area
Width
ZMean
ZMax
TempMean
TempRange
Latitude
Altitude
LightMean
LightRange
N/A
N/A
N/A
N/A
EnclWallArea
MeanEvap
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
width of estuary
mean depth, (initial condition if dynamic mean depth is selected)
maximum depth
mean annual temperature of epilimnion (or hypolimnion)
annual temperature range of epilimnion (or hypolimnion)
latitude
site specific altitude
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 experimental enclosures walls; only relevant to enclosure
mean annual evaporation
UNITS
N/A
km
m3
2
m
m
m
m
°C
°C
Deg, decimal
m
Langleys/day
Langleys/day
mg/L
mg CaCOS /L
mg/L
mg/L
m2
inches / year
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
APPENDICES
USER INTERFACE
Extinct. Coeff Water
Extinct. Coeff Sediment
Extinct. Coeff DOM
Extinct. Coeff POM
Baseline Percent
Embeddedness
Minimum Volume Frac.
Auto Select Eqn. for
reaeration
Enter KReaer
Total Length
Watershed Area
M2, Amplitude & Epoch
S2, Amplitude & Epoch
N2, Amplitude & Epoch
Kl , Amplitude & Epoch
Ol, Amplitude & Epoch
SSA, Amplitude & Epoch
SA, Amplitude & Epoch
PI , Amplitude & Epoch
INTERNAL
ECoeffWater
ECoeffSed
ECoeffDOM
ECoeffPOM
BasePercentEmbed
Min Vol Frac
UseCovar
KReaer
TotalLength
WaterShedArea
amplitude l,kl
amplitude2, k2
amplitudes, k3
amplitude4, k4
amplitudes, k5
amplitude6, k6
amplitude?, k7
amplitudes, k8
TECH DOC
ExtinctmO
ECoeffSed
ECoeffDOM
ECoeffPOM
baseline embeddedness
Minimum Volume Frac.
Covar
KReaer
TotLength
Watershed
M2
S2
N2
Kl
Ol
SSA
SA
PI
DESCRIPTION
light extinction of wavelength 312.5 nm in pure water
light extinction due to inorganic sediment in water
light extinction due to dissolved organic matter in water
light extinction due to particulate organic matter in water
observed embeddedness that is used as an initial condition
fraction of initial condition that is the minimum volume of a site
boolean to determine whether user is entering reaeration
coefficient
depth-averaged reaeration coefficient
total river length for calculating Nhytoplankton retention
watershed area for estimating total river length (above)
Estuary Only - principal lunar semidiurnal constituent
Estuary Only - principal solar semidiurnal constituent
Estuary Only - larger lunar elliptic semidiurnal constituent
Estuary Only - lunar diurnal constituent
Estuary Only - lunar diurnal constituent
Estuary Only - solar semiannual constituent
Estuary Only - solar annual constituent
Estuary Only - solar diurnal constituent
UNITS
1/m
l/(m-g/m3)
l/(m-g/m3)
l/(m-g/m3)
percent (0-100)
frac. of Initial
Condition
boolean
1/d
km
km
m, deg. Local
Siderial Time
(LST)
m, deg. LST
m, deg. LST
m, deg. LST
m, deg. LST
m, deg. LST
m, deg. LST
m, deg. LST
310
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
APPENDICES
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/m1'3
%
%
kg/m2
kg/m2
m/s
kg/m2
kg/m2
m/s
311
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
APPENDICES
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
KNitri, Max Rate of Nitrif
KDenitri Bottom (max.)
KDenitri Water (max.)
P to Organics, Labile
N to Organics, Labile
P to Organics, Refractory
N to Organics, Refractory
P to Organics, Diss. Labile
N to Organics, Diss. Labile
P to Organics, Diss. Refr.
N to Organics, Diss. Refr.
O2 : Biomass, Respiration
CBODu to BODS
conversion factor
INTERNAL
ReminRecord
DecayMax Lab
DecayMax Refr
Q10
TOpt
TMax
TRef
pHMin
pHMax
KNitri
KDenitri_Bot
KDenitri_Wat
P20rgLab
N20rgLab
P2OrgRefr
N2OrgRefr
P2OrgDissLab
N2OrgDissLab
P2OrgDissRefr
N2OrgDissRefr
O2Biomass
BOD5_CBODu
TECH DOC
Remineralization
Data
DecayMax
ColonizeMax
Q10
TOpt
TMax
TRef
pHMin
pHMax
KNitri
KDenitriBottom
KDenitriWater
P20rgLab
N20rgLab
P2OrgRefr
N2OrgRefr
P2OrgDissLab
N2OrgDissLab
P2OrgDissRefr
N2OrgDissRefr
O2Biomass
BOD5_CBODu
DESCRIPTION
For each simulation, the following Parameters are
required (pertaining to organic matter)
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 occurs.
maximum rate of nitrification
maximum rate of denitrification at the sed/water interface
maximum rate of denitrification in the water column
ratio of phosphate to labile organic matter
ratio of nitrate to labile organic matter
ratio of phosphate to refractory organic matter
ratio of nitrate to refractory organic matter
ratio of phosphate to dissolved labile organic matter
ratio of nitrate to dissolved labile organic matter
ratio of phosphate to dissolved refractory organic matter
ratio of nitrate to dissolved refractory organic matter
ratio of oxygen to organic matter
BODS to ultimate CBOD conversion factor, also defined as
CBODU:BOD5 ratio
UNITS
g/g'd
g/g'd
°C
°C
°C
PH
PH
I/day
I/day
I/day
fraction dry weight
fraction dry weight
fraction dry weight
fraction dry weight
fraction dry weight
fraction dry weight
fraction dry weight
fraction dry weight
unitless ratio
unitless ratio
312
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
APPENDICES
USER INTERFACE
O2 : N, Nitrification
Detrital Sed Rate (KSed)
Temperature of Obs. KSed
Salinity of Obs. KSed
PO4, Anaerobic Sed.
NH4, Aerobic Sed.
Wet to Dry Susp. Labile
Wet to Dry Susp. Refr
Wet to Dry Sed. Labile
Wet to Dry Sed. Refr.
KD, P to CaCO3
Animal
Animal Type
Taxonomic Type or Guild
Toxicity Record
Half Saturation Feeding
Maximum Consumption
Min Prey for Feeding
Sorting: degree to which
there is selective feeding
Susp. Sed. Affect Feeding
Slope for Sed. Response
Intercept for Sed. Resp.
INTERNAL
O2N
KSed
KSedTemp
KSedSalinity
PSedRelease
NSedRelease
Wet2DrySLab
Wet2DrySRefr
Wet2DryPLab
Wet2DryPRefr
KDPCalcite
ZooRecord
AnimalName
Animal_Type
Guild_Taxa
ToxicityRecord
FHalfSat
CMax
BMin
Sorting
SuspSedFeeding
SlopeSSFeed
InterceptSSFeed
TECH DOC
O2N
KSed
TemperatureReference
Salinity Reference
N/A
N/A
Wet2DrySLab
Wet2DrySRefr
Wet2DryPLab
Wet2DryPRefr
KD_P_Calcite
Animal Underlying
Data
N/A
Animal Type
Taxonomic type or guild
N/A
FHalfSat
CMax
BMin
Sorting
Option to use eqn.
SlopeSS
InterceptSS
DESCRIPTION
ratio of oxygen to nitrogen
intrinsic sedimentation rate
reference temperature of water for calculating detrital sinking rate
reference salinity of water for calculating detrital sinking rate
Not utilized as a parameter by the code.
Not utilized as a parameter by the code.
wet weight to dry weight ratio for suspended labile detritus
wet weight to dry weight ratio for suspended refractory detritus
wet weight to dry weight ratio for particulate labile detritus
wet weight to dry weight ratio for particulate refractory detritus
partition coefficient for phosphorus to calcite
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
fractional degree to which there is selective feeding
does suspended sediment affect feeding
slope for sediment response
intercept for sediment response
UNITS
unitless ratio
m/d
deg. c
%o
g/m -d
g/m2-d
ratio
ratio
ratio
ratio
L/kg
N/A
Choice from List
Choice from List
Choice from List
g/m3
g/g'd
g/m3 or g/m2
unitless
boolean
unitless
unitless
313
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
APPENDICES
USER INTERFACE
Temp Response Slope
Optimum Temperature
Maximum Temperature
Min Adaptation Temp
Endogenous Respiration
Specific Dynamic Action
Excretion: Respiration
N to Organics
P to Organics
Wet to Dry
Gamete : Biomass
Gamete Mortality
Mortality Coefficient
Sensitivity to Sediment
Ortanism is Sensitive to
Percent Embeddedness
Percent Embeddedness
Threshold
Carrying Capacity
Average Drift
Trigger: Deposition Rate at
which drift is accel.
Frac. in Water Column
VelMax
INTERNAL
Q10
TOpt
TMax
TRef
EndogResp
KResp
KExcr
N2Org
P20rg
Wet2Dry
PctGamete
GMort
KMort
SensToSediment
SenstoPctEmbed
PctEmbedThreshold
KCap
AveDrift
Trigger
FracInWaterCol
VelMax
TECH DOC
Q10
TOpt
TMax
TRef
EndogResp
KResp
KExcr
N2Org
P20rg
Wet2Dry
PctGamete
GMort
KMort
Sensitivity Categories
N/A
embeddedness threshold
value
KCap
Dislodge
Trigger
-T raC^tejCoijjjjm
VelMax
DESCRIPTION
slope or rate of change in 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
ratio of nitrate to organic matter for given species
ratio of phosphate to organic matter for given species
ratio of wet weight to dry weight for given species
fraction of adult predator biomass that is in gametes
gamete mortality
intrinsic mortality rate
which equation to use for mortality due to sediment
if this checkbox is checked then the organism will be sensitive to
the sites calculated embeddedness as a function of TSS
if the site's calculated embeddedness exceeds this value, mortality
for the organism is set to 100%
carrying capacity
fraction of biomass subject to drift per day
deposition rate at which drift is accelerated
fraction of organism in water column, differentiates from pore-
water uptake if the multi-layer sediment model is included
maximum water velocity tolerated
UNITS
unitless
°C
°C
°C
day'1
unitless
unitless
fraction dry weight
fraction dry weight
ratio
unitless
1/d
1/d
"Zero," "Tolerant,"
"Sensitive,"
"Highly Sensitive"
boolean
percent (0-100)
g/m2
fraction / day
kg/m day
fraction
cm/s
314
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
APPENDICES
USER INTERFACE
Removal due to Fishing
Mean lifespan
Fraction that is lipid
Mean Wet Weight
Low O2: Lethal Cone
Low O2: Pet. Killed
Low O2: EC50 Growth
Low O2: EC50 Reproduction
Ammonia Toxicity: LC50,
Total Ammonia (pH=8)
Salinity Ingestion Effects
Salinity Gamete Loss Effects
Salinity Respiration Effects
Salinity Mortality Effects
Percent in Riffle
Percent in Pool
Fish spawn automatically,
based on temperature range
INTERNAL
Fishing_Frac
LifeSpan
FishFracLipid
MeanWeight
O2_LethalConc
O2_LethalPct
O2_EC50growth
O2_EC50repro
Ammonia LC50
Salmin Ing, SalMax Ing,
Salcoeffljng, Salcoeff2_Ing
Salmin Gam, SalMax Gam,
Salcoeffl_Gam, Salcoeff2_Gam
Salmin_Rsp, SalMax_Rsp,
Salcoeffl_Rsp, Salcoeff2_Rsp
Sahnin Mort, SalMax Mort,
Salcoeffl_Mort,
Salcoeff2_Mort
PrefRiffle
PrefPool
AutoSpawn
TECH DOC
fraction fished
LifeSpan
LipidFrac
WetWt
LCKnownduratlon
PctKilledKnown
IlCjUdui-ation
-bCjOduj-atjon
LC50t,8
SalMin, SalMax,
SalCoeffl,SalCoeff2
SalMin, SalMax,
SalCoeffl,SalCoeff2
SalMin, SalMax,
SalCoeffl,SalCoeff2
SalMin, SalMax,
SalCoeffl,SalCoeff2
PreferenceHabitat
PreferenceHabitat
DESCRIPTION
daily loss of organism due to fishing Nressure
mean lifespan in days
fraction of lipid in organism
mean wet weight of organism
concentration where there is a known mortality over 24 hours
the percentage of the organisms killed at the LCKnown level
above.
concentration where there is 50% reduction in growth over 24
hours
concentration where there is 50% reduction in reproduction over
24 hours
LC50total ammo™ at 20 degrees centigrade and pH of 8
parameters used to calculate the effects of the current level of
salinity on ingestion for the given animal
parameters used to calculate the effects of the current level of
salinity on gamete loss for the given animal
parameters used to calculate the effects of the current level of
salinity on respiration for the given animal
parameters used to calculate the effects of the current level of
salinity on mortality of the given animal
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
UNITS
fraction
days
g lipid/g org. wet
g wet
mg/L (24 hour)
percentage
mg/L (24 hour)
mg/L (24 hour)
mg/L (ph=8)
%o, %o, unitless,
unitless
%o, %o, unitless
%o, %o, unitless,
unitless
%o, %o, unitless,
unitless
%
%
true/false
315
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
APPENDICES
USER INTERFACE
Fish spawn of the following
dates each year
Fish can spawn an unlimited
number of times...
Use Allometric Equation to
Calculate Maximum
Consumption
Intercept for weight
dependence
Slope for weight dependence
Use Allometric Equation to
Calculate Respiration
RA
RB
Use "Set 1" of Respiration
Equations
RQ
RTL
ACT
RTO
RK1
BACT
RTM
RK4
INTERNAL
SpawnDatel..3
UnlimitedSpawning
UseAllom_C
CA
CB
UseAllom_R
RA
RB
UseSetl
RQ
RTL
ACT
RTO
RK1
BACT
RTM
RK4
TECH DOC
RQ
RTL
ACT
RTO
RK1
BACT
RK4
DESCRIPTION
User Entered Spawn Dates
Allow fish to spawn unlimited times each year
Use Allometric Consumption Equation
Allometric Consumption Parameter
Allometric Consumption Parameter
Use Allometric Consumption Respiration
Intercept for species specific metabolism
Weight dependence coefficient
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
UNITS
date
true/false
true/false
real number
real number
true/false
real number
real number
true/false
real number
°C
cm/s
s/cm
cm/s
1/°C
real number
316
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
APPENDICES
USER INTERFACE
ACT
Preference (ratio)
Egestion (frac.)
INTERNAL
ACT
TrophIntPref[ ]
TrophInt.Egest[ ]
TECH DOC
Prefprey,pred
EgestCoeffprey,pred
DESCRIPTION
intercept of swimming speed vs. temperature and weight
initial preference value from the animal parameter screen
fraction of ingested prey that is egested
UNITS
real number
unitless
unitless
Plant
Plant Type
Macrophyte Type
Taxonomic Group
Toxicity Record
Saturating Light
Use Adaptive Light
Max. Saturating Light
Min. 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
PlantRecord
PlantName
PlantType
Macrophyte Type
Taxonomic_Type
ToxicityRecord
LightSat
UseAdaptiveLight
MaxLightSat
MinLightSat
KPO4
KN
KCarbon
Q10
TOpt
TMax
TRef
PMax
Plant Underlying
Data
Plant Type
Macrophyte Type
Taxonomic Group
N/A
LightSat
Adaptive Light
user-entered maximum
user-entered minimum
KP
KN
KC02
Q10
TOpt
TMax
TRef
PMax
For each Plant in the Simulation, the following
Parameters are required
plant's name, used for reference only.
plant type: (Phytoplankton, Periphyton, Macrophytes, Bryophytes)
Benthic, Rooted Floating, Free-Floating
taxonomic group
associates plant with appropriate toxicity data
light saturation level for photosynthesis
choice whether to use adaptive light construct
maximum light saturation allowed from adaptive light equation
minimum light saturation allowed from adaptive light equation
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
N/A
Choice from List
Choice from List
Choice from List
Choice from List
ly/d
boolean
ly/d
ly/d
gP/m3
gN/m3
gC/m3
unitless
°C
°C
°C
1/d
317
-------
AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
APPENDICES
USER INTERFACE
Photorespiration Coefficient
RespRateat20deg. C
Mortality Coefficient
Exponential Mort Coeff
P to Photosynthate
N to Photosynthate
Light Extinction
Wet to Dry
Phytoplankton:
Sedimentation Rate (KSed)
Phytoplankton: Temperature
ofObs. KSed
Phytoplankton: Salinity of
Obs. KSed
Phytoplankton: Exp.
Sedimentation Coeff
Macrophytes: Carrying
Capacity
Macrophytes: VelMax
Periphyton: Reduction in
Still Water
Periphyton: Critical Force
(FCrit)
Percent Lost in Slough Event
Percent in Riffle
Percent in Pool
INTERNAL
KResp
Resp20
KMort
EMort
P20rg
N2Org
ECoeffPhyto
Wet2Dry
KSed
KSedTemp
KSedSalinity
ESed
Carry_Capac
Macro_VelMax
Red_Still_Water
FCrit
PctSloughed
PrefRiffle
PrefPool
TECH DOC
KResp
Resp20
KMort
EMort
P20rg
N2Org
EcoeffPhyto
Wet2Dry
KSed
TemperatureReference
Salinity Reference
ESed
KCap
VelMax
RedStillWater
FCrit
FracSloughed
PrefRiffle
PrefPool
DESCRIPTION
coefficient of proportionality between, excretion and
photosynthesis at optimal light levels
respiration rate at 20°C
intrinsic mortality rate
exponential factor for suboptimal conditions
ratio of phosphate to organic matter for given species
ratio of nitrate to organic matter for given species
attenuation coefficient for given alga
ratio of wet weight to dry weight for given species
intrinsic settling rate
reference temperature of water for calculating Nhytoplankton
sinking rate
reference salinity of water for calculating Nhytoplankton sinking
rate
exponential settling coefficient
macrophyte carrying capacity, converted to g/m3 and used to
calculate washout of free-floating macrophytes
velocity at which total breakage occurs
reduction in photosynthesis in absence of current
critical force necessary to dislodge given periphyton group
fraction of biomass lost at one time
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
unitless
g/g'd
g/g'd
g/g'd
fraction dry weight
fraction dry weight
l/m-g/m3w
ratio
m/d
deg. c
%o
unitless
g/m2
cm/s
unitless
newtons (kg m/s2)
%
%
%
318
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
APPENDICES
USER INTERFACE
Salinity Photosyn. Effects
Salinity Mortality Effects
INTERNAL
Salmin_Phot, SalMax_Phot,
Salcoeffl Phot,
Salcoeff2_Phot
Salmin Mort, SalMax Mort,
Salcoeffl _Mort,
Salcoeff2_Mort
TECH DOC
SalMin, SalMax,
SalCoeffl,SalCoeff2
SalMin, SalMax,
SalCoeffI, SalCoefG
DESCRIPTION
parameters used to calculate the effects of the current level of
salinity on photosynthesis for the given plant
parameters used to calculate the effects of the current level of
salinity on mortality for the given plant
UNITS
%o, %o, unitless,
unitless
%o, %o, unitless,
unitless
319
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
APPENDICES
USER INTERFACE
LC50
LC50 exp time (h)
K2 Elim rate const
Kl Uptake const
BCF
Biotmsfm rate
EC50 growth
Growth exp (h)
EC50 repro
Repro exp time (h)
Mean wet weight (g)
Lipid Frac
Drift Threshold (ug/L)
EC50 photo
EC50 exp time (h)
INTERNAL
AnimalToxRecord
LC50
LC50_exp_time
K2
Kl
BCF
BioRateConst
EC50_growth
Growth_exp_time
EC50_repro
Repro_exp_time
Mean_wet_wt
Lipid frac
Drift_Thresh
TPlantToxRecord
EC50_photo
EC50_exp_time
TECH DOC
Animal Toxicity
Parameters
LC50
ObsTElapsed
K2
Kl
BCF
BioRateConst
ECSOGrowth
ObsTElapsed
ECSORepro
ObsTElapsed
WetWt
LipidFrac
Drift Threshold
Plant Toxicity
Parameter
ECSOPhoto
ObsTElapsed
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
uptake rate constant, only used if "Enter Kl" option is selected
Bioconcentration factor, only used if "Enter BCF" option is
selected
percentage of chemical that is bio transformed 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
UNITS
pg/L
h
1/d
L / kg dry day
L /kg dry
1/d
pg/L
h
Pg/L
h
g
g lipid/g wet wt.
Pg/L
Pg/L
h
320
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
APPENDICES
USER INTERFACE
EC50 dislodge
K2 Elim rate const
Kl Uptake const
BCF
Biotmsfm rate
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
Biotransformation
INTERNAL
EC50_dislodge
K2
Kl
BCF
BioRateConst
LC50
LC50_exp_time
Lipid_frac
TChemical
InitialCond
Tox Air
Loadings
Alt LoadingsfPointsource]
Alt_Loadings[Direct Precip]
Alt_Loadings[NonPointsource]
BioTrans[ ]
TECH DOC
ECSODislodge
K2
Kl
BCF
BioRateConst
LC50
ObsTElapsed
LipidFrac
Chemical
Parameters
Initial Condition
Toxicantair
Inflow Loadings
Point Source Loadings
Direct Precipitation Load
Non-Point Source Loading
Biotransform
DESCRIPTION
for periphyton only: external concentration of toxicant at which
there is 50% dislodge of periphyton
elimination rate constant
uptake rate constant, only used if "Enter Kl" option is selected
Bioconcentration factor, only used if "Enter BCF" option is
selected
percentage of chemical that is bio transformed to
specific daughter products
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 bio transformed to specific daughter
products
UNITS
Pg/L
1/d
L / kg dry day
L / kg dry
1/d
MS/L
h
g lipid/g org. wet
Pg/L
g/m3
Pg/L
g/d
g/m2 -d
g/dTox_AirGas-
phase
concentrationg/m3
%
321
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
APPENDICES
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_Loadings[Pointsource]
Alt_Loadings[Direct Precip]
Alt LoadingsfNonPointsource]
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
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 (TotP or TotN optional)
Daily loading as a result of the inflow of water (TotP or TotN
optional)
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
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 -d
g/d
unitless
g/m2
lig/kg
mg/L
lig/kg
322
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
APPENDICES
USER INTERFACE
Initial Condition
Initial Condition: %
Particulate
Initial Condition: %
Refractory
Inflow Loadings
Dissolved / Particulate
Breakdown
Labile / Refractory
Breakdown
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 LoadingsfPointsource]
Alt Loadings
TToxicant. InitialCond
TToxicant.Loads
TECH DOC
Susp & Dissolved
Detritus
Initial Condition
Inflow Loadings
Percent Particulate Inflow,
Point Source, Non-Point
Source
Percent Refractory Inflow,
Point Source, Non-Point
Source
Point Source Loadings
Non-Point Source Loading
Toxicant Exposure
Tox Exposure of Inflow
Loading
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
Three constant or time-series parameters; % of each type of
loading that is particulate as opposed to dissolved detritus
Three constant or time-series parameters; % of each type 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
foorganic matter' ^
foorganic matter ^
re/kg
re/kg
323
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
APPENDICES
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)
Egestion(frac.)
INTERNAL
TBuried Detritus
InitialCond
TToxicant.InitialCond
TPlant
InitialCond
Loadings
TToxicant.InitialCond
TToxicant.Loads
TAnimal
InitialCond
Loadings
Ttoxicant. InitialCond
TToxicant.Loads
TrophlntArray .Pref
TrophlntArray.ECoeff
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
EgestCoeff
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; Toxicant 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 Expo sure 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
for each prey-type ingested, the fraction of ingested prey that is
egested
UNITS
Kg/cu. m
Kg/cu. m
mg/L or g/m2 dry
mg/L or g/m2 dry
lig/kg
re/kg
mg/L or g/sq.m
also expressed as
g/m2
mg/L or g/sq. m
re/kg
re/kg
unitless
unitless
324
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
APPENDICES
USER INTERFACE
Initial Condition
Water volume
Inflow of Water
Discharge of Water
Site Type
Frac. of Site that is Shaded
Water Velocity
Site Mean Depth
Initial Condition
Could this system stratify
Valuation or loading
INTERNAL
TVolume
InitialCond
Volume
InflowLoad
DischargeLoad
Site Characteristics
SiteType
Shade
Dyn Velocity
DynZMean
Temperature
InitialCond
TECH DOC
Volume Parameters
Initial Condition
Volume
Inflow of Water
Discharge of Water
Site Characteristics
Site Type
user input shade
user entered velocity
user entered mean depth
Temperature
Initial condition
DESCRIPTION
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.
fraction of site that is shaded, time-series
optional, time series of run velocities
optional, time series of mean depth for site
Temperature Parameters Required
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
m3
cu. m
m3/d cu m/d
nrVd
Pond, Lake,
Stream, Reservoir,
Enclosure, Estuary
fraction
cm/s
m
°C
true/false
°C
325
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
APPENDICES
USER INTERFACE
Initial Condition
Mean Value
Wind Loading
Initial Condition
Loading
Photoperiod
Initial Condition
State Variable Valuation
Mean alkalinity
Sand / Silt / Clay
Initial Susp. Sed.
Frac in Bed Seds
Loadings from Inflow
INTERNAL
Wind
InitalCond
MeanValue
Wind
Light
Light
Loadsrec
Photoperiod
pH
InitialCond
PH
alkalinity
TSediment
InitialCond
FracInBed
Loadings
TECH DOC
Wind
Wind
Light
Light
Photoperiod
pH
pH
alkalinity
Inorganic Sediment
Parameters
Initial Condition
Frac Sed
Inflow Loadings
DESCRIPTION
Wind parameters required
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
Light Parameters Required
Daily parameter; avg. light intensity at segrment top; can choose
annual mean, constant loading or dynamic loadings
Fraction of day with daylight; optional, can be calculated from
latitude
pH Parameters Required
Initial pH value
pH of the segment; can choose constant or daily value.
mean Gran alkalinity (if dynamic pH option selected)
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
UNITS
m/s
m/s
m/s
ly/d
hr/d
PH
PH
Heq CaCO3/L
mg/L
Fraction
mg/L
326
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
APPENDICES
USER INTERFACE
Loadings from Point Sources
Loadings from Direct
Precipitation
Non-point source loadings
Multi-Layer Sediment
Model
Densities [Organic and
Inorganic Components]
Multi-Layer Sediment
Model
Max Thickness of Active
Layer
Min Thickness of Active
Layer
Cohesives, NonCohesives,
Daily Scour
Cohesives, NonCohesives,
Daily Deposition
Cohesives only, Erosion
Velocity
Cohesives only, Deposition
Velocity
Multi-Layer Sediment
Model
Thickness
Diffusion Coefficient for top
of sediment layer
INTERNAL
Alt LoadingsfPointsource]
Alt LoadingsfDirect Precip]
Alt LoadingsfNonPointsource]
Global SedData
Densities
Active Layer SedData
MaxUpperThick
BioTurbThick
LScour
LDeposition
LErodVel
LDepVel
Each Layer SedData
BedDepthIC
UpperDispCoeff
TECH DOC
Point Source Loadings
Direct Precipitation Loa
Non-Point Source Loading
Multi-layer
Sediment
Parameters
Density Sed
Multi-layer
Parameters
user defined maximum
thickness
user defined minimum
thickness
ErodeSed
Deposit Sed
ErodeVel
DepVel
Multi-layer
Parameters
thickness
DiffCoeff
DESCRIPTION
Daily loading from point sources
Daily loading from direct precipitation
Daily loading from non-point sources
If the multi-layer sediment model is included in
AQUATOX, the following general parameters are
required
Density of each organic and inorganic component of the sediment
bed.
If the multi-layer sediment model is included these
parameters are required for the active layer only
maximum thickness of the active layer before it becomes split into
multiple layers
minimum thickness of active layer before it is added to the layer
below it
scour of this sediment to the water column above
deposit of this sediment from the water column
user input time-series of cohesives erosion velocities, used to
calculate scour of organics
user input time-series of cohesives deposition velocities, used to
calculate deposition of organics
If the multi-layer sediment model is included these
parameters are required for each layer modeled
initial thickness of each modeled layer
dispersion coefficient
UNITS
g/d
Kg-d
g/d
g/cm3
m
m
g/d
g/d
m/d
m/d
m
m2/d
327
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
APPENDICES
USER INTERFACE
Pore Water Init. Cond.
ROOM, LOOM PoreW,
Initial Cond
Cohesives, NonCohesives,
Initial Cond
R Detr Sed, L Detr Sed,
Initial Cond
Chemical Exposures
Trophic Interactions,
BCFs for Shorebirds
Preference (ratio)
Biomagnification Factor
Clearance Rate
Link Between Two
Segments
Type of Link
Link Name
FromSeg, ToSeg
Characteristic Length
Water Flow Data
Dispersion Coeff
INTERNAL
TPoreWater.InitialCond
TDOMPorewater.InitialCond
TBottomSediment.InitialCond
TBuriedSed.InitialCond
[ComponentJTox.InitialCond
Gull Parameters
GullPref
GullBMF
GullClear
TSegmentLink
LinkType
Name
FromID, ToID
CharLength
WaterFlowData
DiffusionData
TECH DOC
Concsed Initial Cond.
Concsed Initial Cond.
Concsed Initial Cond.
Concsed Initial Cond.
ToxicantBottomSed Initial
Cond.
Shorebirds
_TicIprey5 pred
BMFTox
ClearTox
Multi Segment
Model
two types of linkages
CharLength
Discharge
DiffusionThlsSeg
DESCRIPTION
concentration of pore water initial condition
concentration of refractory or labile DOM in pore water, initial
condition
concentration of inorganic sediments in the layer, initial condition
concentration of refractory and labile organic sediments in the
layer, initial condition
concentration of relevant toxicant in element of sediment layer
If the shorebird model is included in a simulation,
the following Parameters are required
for each prey-type ingested, a preference value within the matrix
of preferences
biomagnification factor for this chemical in gull
clearance rate for the given toxicant in gulls
If the multi segment model is used for a simulation,
the following Parameters are required for each link
between segments
indicates whether linkage is unidirectional or bidirectional
used for the user to keep track of linkages
used for the model to keep track of linkages
characteristic mixing length, feedback links only
time-series of water flow from one segment to the next
time-series of dispersion coefficients between two segments,
feedback links only
UNITS
m3 water / m2
g/m3
gm2
g/m2 dry
ug/L pore water,
ug/kg solids
unitless
unitless
day'1
"cascade" or
"feedback"
string
existing segments
m
m3/d
m2/d
328
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AQUATOX (RELEASE 3) TECHNICAL DOCUMENTATION
APPENDICES
USER INTERFACE
XSection of Boundary
BedLoadImogamcs
INTERNAL
XSectionData
BedLoad
TECH DOC
Area
BedloadUpstrealnllnk
DESCRIPTION
time-series of cross sectional areas between two segments,
feedback links only
time-series of bedload from the upstream segment to the
downstream segment
UNITS
m2
g/d
329
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