United States Office of Water (4305) EPA-823-B-05-002

Environmental Protection October 2005

Agency 

AQUATOX FOR WINDOWS

A MODULAR FATE AND EFFECTS 

MODEL FOR AQUATIC ECOSYSTEMS

RELEASE 2.1

ADDENDUM TO RELEASE 2 

TECHNICAL DOCUMENTATION

 
AQUATOX Release 2.1 Technical Documentation Addendum 

AQUATOX FOR WINDOWS

A MODULAR FATE AND EFFECTS 

MODEL FOR AQUATIC ECOSYSTEMS

RELEASE 2.1 

ADDENDUM TO RELEASE 2 

TECHNICAL DOCUMENTATION 

Jonathan S. Clough, Warren Pinnacle Consulting, Inc. 

and 

Richard A. Park, Eco Modeling 

Prepared under 

EPA Contract 68-C-98-010 

with AQUA TERRA Consultants 

Prepared for 

U.S. Environmental Protection Agency 

Risk Assessment Division (7403M) 

Office of Pollution Prevention and Toxics 

Washington, D.C. 20460 

October 2005
AQUATOX Release 2.1 Technical Documentation Addendum 

TABLE OF CONTENTS

1 INTRODUCTION TO RELEASE 2.1 ...................................................................... 4 

Background.................................................................................................................... 4 

What’s New ................................................................................................................... 4

3 PHYSICAL CHARACTERISTICS .......................................................................... 5 

Dynamic Mean Depth.................................................................................................... 5

4 BIOTA ....................................................................................................................... 5 

4.1 Algae .................................................................................................................. 5 

Periphyton Code Changes.......................................................................................... 6 

Phytoplankton and Zooplankton Residence Time ..................................................... 7 

Periphyton-Phytoplankton Link................................................................................. 8 

4.4 Steinhaus Similarity Index................................................................................. 9

5 REMINERALIZATION.......................................................................................... 10 

5.2 Nitrogen ........................................................................................................... 10 

Assimilation ............................................................................................................. 11 

Nitrification and Denitrification .............................................................................. 12 

Ionization of Ammonia ............................................................................................ 14 

5.3 Phosphorus....................................................................................................... 16 

5.4 Nutrient Mass Balance..................................................................................... 17 

Variable Stoichiometry ............................................................................................ 18 

Nutrient Loading Variables...................................................................................... 18 

Nutrient Output Variables........................................................................................ 19 

Mass Balance of Nutrients....................................................................................... 19 

5.7 Modeling Dynamic pH .................................................................................... 25

7 Toxic Organic Chemicals ........................................................................................ 28 

7.6 Nonequilibrium Kinetics.................................................................................. 28 

7.7 Alternative Uptake Model: Entering BCFs, K1, and K2................................. 28 

7.8 Half Life Calculation Refinement DT50 & DT95........................................... 29

8 ECOTOXICOLOGY ............................................................................................... 30 

8.3 External Toxicity ............................................................................................. 30

9 REFERENCES ........................................................................................................ 32 
AQUATOX Release 2.1 Technical Documentation Addendum 

1 INTRODUCTION TO RELEASE 2.1 

Background 

Nutrients (nitrogen and phosphorus) are leading causes of water quality impairment in the 

Nation’s rivers, lakes and estuaries. To address this problem, states need the technical resources 

to establish nutrient criteria, adopt them into their water quality standards, and implement them

in regulatory programs. Ecosystem models such as AQUATOX that mechanistically simulate 

nutrient dynamics can be one tool for deriving and implementing nutrient criteria. 

To further assist in modeling nutrients AQUATOX has been significantly updated since EPA 

Release 2 was released. There have also been several enhancements related to toxicity, along

with improvements to the user interface. This document is an addendum to the AQUATOX

Release 2 Technical documentation (EPA-823-R-04-002, January 2004). The document 

describes changes in the model that distinguish Release 2.1 from Release 2. 

What’s New 

• The capability to model mean depth dynamically has been included. 

• Various modifications to periphyton modeling, phytoplankton modeling, and a 

periphyton-phytoplankton linkage may be found in the section on biota. 

• The capability to export Steinhaus similarity matrices has been added to provide a 

measure of community effects. 

• The fraction of ammonia that is un-ionized is estimated and reported. 

• Variable stoichiometry, new nutrient loading variables, new nutrient output variables, and 

strict mass balance of nutrients have all been added to AQUATOX since Release 2. 

• pH may now be modeled dynamically as a function of a site’s total alkalinity, carbon 

dioxide, and dissolved organic matter. 

• Additional flexibility has been added to the modeling of toxic organic chemicals

including new uptake and depuration modeling options and the ability to model toxicity 

based on external concentrations. 

• Libraries now can be viewed in a “GridMode” spreadsheet form to facilitate comparison 

of chemical or organism parameters. 

• The complete setup of a study, including state variable parameter values, loadings, and

site constants, can be exported to a text file. 

• The linkage to BASINS has been expanded to include a variety of phosphorus loadings.

A revised User’s Manual for the BASINS Extension to AQUATOX has been released

that describes these changes. (EPA-823-B-05-001, October 2005) 

4 
AQUATOX Release 2.1 Technical Documentation Addendum 

3 PHYSICAL CHARACTERISTICS 

The following should be inserted before “Habitat Disaggregation” on p. 3-6.

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 or rivers, the

depth of the system can change considerably, 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 (38);

• Calculation of biotic volumes for sloughing calculations, see (66);

• Calculation of vertical dispersion for stratification calculations, Thick in equation (18); 

• Calculation of sedimentation for plants & detritus, Thick in (135);

• Oxygen reaeration, see (158) . 

• Toxicant photolysis and volatilization, Thick in (221) and (230) 

4 BIOTA 

4.1 Algae 

(There have been minor refinements added to Algae Derivatives, and the following should 

replace equations 29 and 30 in the Release 2 Technical Documentation) 

 

3

Slough Mortality Predation Sinking Washout TurbDiff

Loading Photosynthesis Respiration Excretion

dt

dBiomassPhyto

− − ± − ± +

= + − −

 (29) 

Peri

Peri

Mortality Predation Sed

Loading Photosynthesis Respiration Excretion

dt

dBiomass

− − +

= + − − (30)

5 
AQUATOX Release 2.1 Technical Documentation Addendum 

where: 

Slough = Scour of Periphyton to Phytoplankton, see (1a); 

SedPeri = Sedimentation of Phytoplankton to Periphyton, see (7a). 

(See page 4-2 of Release 2 Technical Documenation for other terms and equations.)

Periphyton Code Changes 

The following should replace the text and equations on p 4-22 and 4-23, up to “Detrital 

Accumulation in Periphyton” on p. 4-23. 

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: 

else 0

then

If

=

= ⋅

> ⋅ ⋅

Slough

Slough Biomass FracSloughed

DragForce Suboptimal FCrit Adaptation Org Org

(1a)

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/s

2

); 

Adaptation = factor to adjust for mean discharge of site compared to reference 

site (unitless); 

Slough = biomass lost by sloughing (g/m3

); 

FracSloughed = fraction of biomass lost at one time (97%, unitless). 

If 1 then 1

20

> =

= ⋅ ⋅ ⋅

Org Org

Org Org Org Org

Suboptimal Suboptimal

Suboptimal NutrLimit LtLimit TCorr

(2a)

where: 

NutrLimit = nutrient limitation for given algal group (unitless) computed by 

AQUATOX, see (47); 

LtLimitOrg = light limitation for given algal group (unitless) computed by 

AQUATOX, see (33); and 

TCorr = temperature limitation for a given algal group (unitless) computed 

by AQUATOX, see (51); 

20 = factor to desensitize construct. 

6 
AQUATOX Release 2.1 Technical Documentation Addendum 

The sloughing construct was tested and calibrated (U.S. E.P.A., 2001) with data from 

experiments with artificial and woodland streams in Tennessee (Rosemond, 1993, ). However, 

in modeling periphyton at several sites, it was observed that sloughing appears to be triggered at 

greatly differing mean velocities. The working hypothesis is that periphyton adapt to the 

ambient conditions of a particular channel. Therefore, a factor is included to adjust for the

velocity 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: 

0.006634

2 Vel Adaptation =

(3a)

where: 

Vel = velocity for given site (m/s), see (14); 

 0.006634 = mean velocity2

 for reference experimental stream (m/s). 

The following two sections should be added to the end of Section 4.1, on p. 4-24 

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 based on watershed area based on Leopold et al. 1964. 

(4a) 0.6 TotLength = 1.609 ⋅1.4⋅(WaterShed ⋅0.386)

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 the total length or watershed area is entered as zero, the phytoplankton and zooplankton 

residence time equations are not used and Eqs. 63 and 105 of Release 2 are used to calculate 

washout. Otherwise, to simulate the inflow of plankton from upstream reaches plankton 

upstream loadings are estimated as follows: 

7 
AQUATOX Release 2.1 Technical Documentation Addendum 

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ = − TotLength SiteLength

Washout Loading Washout biota

upstream biota / (5a)

where: 

Loadingupstream = loading of plankton due to upstream production (mg/L); 

Washoutbiota = 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 being modeled 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:

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ = SiteLength

TotLength

Discharge

Volume

tresidence

(6a)

 

where: 

tresidence = residence time for floating biota within the total river length (d); 

Volume = volume of modeled segment reach (m3

); see (2, Rel. 2); 

Discharge = discharge of water from modeled reach (m3

/d); see Table 1, Rel. 2; 

TotLength = total river length (km); 

SiteLength = length of the modeled reach (km).

Periphyton-Phytoplankton Link 

Periphyton may slough or be scoured, contributing to the suspended algae; this may be reflected 

in the chlorophyll a observed in the water column. Previously, AQUATOX assumed that 

sloughed periphyton became detritus. Periphyton may now be linked to a phytoplankton 

compartment so that chlorophyll a results 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. 

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. 

=

All Linked Peri

Periphyton A

Periphyton A Phyto Mass

Mass

Sed Sink (7a) 

8 
AQUATOX Release 2.1 Technical Documentation Addendum 

where: 

SedPeriphyton A = sedimentation that goes to periphyton compartment A;

SinkPhyto = total sedimentation of linked phytoplankton compartment, see (61, 

 Rel.2); 

MassPeriphyton A = mass of periphyton compartment A; 

MassAll Linked Peri = 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. 

4.4 Steinhaus Similarity Index 

This section should be added to page 4-45. 

Within the differences graph portion of the output interface, a user may now 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 

biomass in this application) between two samples for each species. 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: 

( )

∑( )

∑

=

=

+

⋅

= n

i

i control i perturbed

n

i

i control i perturbed

Biomass Biomass

Biomass Biomass

S

1

_ _

1

_ _ 2 min ,

(8a) 

where: 

S = Steinhaus similarity index at time t; 

Biomass i_control = 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. 

9 
AQUATOX Release 2.1 Technical Documentation Addendum 

5 REMINERALIZATION 

5.2 Nitrogen 

Replace Section 5.2 with the following section. Note: equations 138 and 139 have been 

removed as they are now replaced with the Remineralization calculation below (9a). 

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 (NH3) is not modeled as a 

separate state variable but is estimated as a fraction of ammonia (10a). Ammonia is assimilated 

by algae and macrophytes and is converted to nitrate as a result of nitrification: 

- Washout TurbDiff

 = Loading + Remineralization - Nitrify - Assimilation dt

dAmmonia

Ammonia

±

(137)

where: 

dAmmonia/dt = change in concentration of ammonia with time (g/m3

⋅d); 

Loading = loading of nutrient from inflow (g/m3

⋅d); 

Remineralization = ammonia derived from detritus and biota (g/m3

⋅d), see (9a); 

Nitrify = nitrification (g/m3

⋅d), see (144); 

Assimilation = assimilation of nutrient by plants (g/m3

⋅d), see (141) and (142); 

Washout = loss of nutrient due to being carried downstream (g/m3

⋅d), see (16) 

TurbDiff = depth-averaged turbulent diffusion between epilimnion and

hypolimnion if stratified (g/m3

⋅d), see (22) and (23). 

Remineralization includes all processes by which ammonia is produced from animal, plants, and

detritus, including decomposition, excretion, and other processes required to maintain variable 

stoichiometry (see Table 2 on page 22): 

NutrRelColonization NutrRelPeriScour

NutrRelPlantSink NutrRelMortality NutrRelGameteLoss

DetritalDecomp AnimalPredation NutrRelDefecation

Remineralization = PhotoResp DarkResp AnimalResp AnimalExcr 

+ +

+ + +

+ + +

+ + +

 (9a)

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); 

10 
AQUATOX Release 2.1 Technical Documentation Addendum 

AnimalResp = excretion of ammonia due to animal respiration (g/m3

⋅d); 

AnimalExcr = animal excretion of excess nutrients to ammonia to maintain 

constant org. to n ratio as required (g/m3⋅d); 

DetritalDecomp = nitrogen release due to detrital decomposition (g/m3

⋅d); 

AnimalPredation = change in nitrogen content necessitated when an animal consumes 

prey with a different nutrient content (g/m3⋅d); 

NutrRelDefecation = ammonia released from animal defecation (g/m3

⋅d); 

NutrRelPlantSink = ammonia balance from sinking of plants and conversion to detritus 

(g/m3⋅d); 

NutrRelMortality = 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); 

NutrRelColonization = 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: 

 = Loading + Nitrify - Denitrify - Assim - Washout TurbDiff dt

dNitrate

Nitrate ± (140)

where:

dNitrate/dt = change in concentration of nitrate with time (g/m3

⋅d); 

Loading = user entered loading of nitrate, including atmospheric deposition;

and 

Denitrify = denitrification (g/m3⋅d). 

Free nitrogen can be fixed by blue-green algae. Both nitrogen fixation and denitrification are 

subject to environmental controls and are difficult to model with any accuracy; therefore, the 

nitrogen cycle is represented with considerable uncertainty. 

Assimilation 

Nitrogen compounds are assimilated by plants as a function of photosynthesis in the respective 

groups (Ambrose et al., 1991): 

 Assimilation = ( Photosynthesis Uptake NH4Pref) Ammonia Plant Plant Nitrogen Σ ⋅ ⋅ (141) 

11 
AQUATOX Release 2.1 Technical Documentation Addendum 

Assimilation = ( Photosynthesis Uptake (1- NH4Pref)) Nitrate Plant Plant Nitrogen Σ ⋅ ⋅ (142) 

where: 

Assimilation = assimilation rate for given nutrient (g/m3⋅d); 

Photosynthesis = rate of photosynthesis (g/m3

⋅d), see (31); 

UptakeNitrogen = fraction of photosynthate that is nitrogen (unitless, 0.01975 

if nitrogen-fixing, otherwise 0.079); 

NH4Pref = ammonia preference factor (unitless). 

Only 23 percent of nitrate is nitrogen, but 78 percent of ammonia is nitrogen. This results in an

apparent preference for ammonia. The preference factor is calculated with an equation

developed by Thomann and Fitzpatrick (1982) and cited and used in WASP (Ambrose et al.,

1991): 

(N2NH4 Ammonia+ N2NO3 Nitrate) (KN + N2NO3 Nitrate)

N2NH4 Ammonia KN

 

+

(KN + N2NH4 Ammonia) (KN + N2NO3 Nitrate)

N2NH4 Ammonia N2NO3 Nitrate NH4Pref =

⋅ ⋅ ⋅ ⋅

⋅ ⋅

⋅ ⋅ ⋅

⋅ ⋅ ⋅

(143)

where:

N2NH4 = ratio of nitrogen to ammonia (0.78); 

N2NO3 = ratio of nitrogen to nitrate (0.23); 

KN = half-saturation constant for nitrogen uptake (g N/m3

); 

Ammonia = concentration of ammonia (g/m3

); and 

Nitrate = concentration of nitrate (g/m3

). 

For algae other than blue-greens, Uptake is the Redfield (1958) ratio; although other ratios (cf. 

Harris, 1986) may be used by editing the parameter screen. At this time nitrogen-fixation by 

blue-greens is represented by using a smaller uptake ratio, thus "creating" nitrogen. 

Nitrification and Denitrification 

Nitrification is the conversion of ammonia to nitrite and then to nitrate by nitrifying bacteria; it 

occurs primarily at the sediment-water interface (Effler et al., 1996). The maximum rate of 

nitrification, corrected for the area to volume ratio, is reduced by limitation factors for 

suboptimal 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: 

12 
AQUATOX Release 2.1 Technical Documentation Addendum 

DOCorrection TCorr pHCorr Ammonia

Volume

Area Nitrify = KNitri ⋅ ⋅ ⋅ ⋅ ⋅ (144)

where: 

Nitrify = nitrification rate (g/m3⋅d); 

KNitri = maximum rate of nitrification (m/d); 

Area = area of site or segment (m2

); 

Volume = volume of site or segment (m3); see (2); 

DOCorrection = correction for anaerobic conditions (unitless) see (131); 

TCorr = correction for suboptimal temperature (unitless); see (51); 

pHCorr = correction for suboptimal pH (unitless), see (133); and 

Ammonia = concentration of ammonia (g/m3

). 

The nitrifying bacteria have narrow environmental optima; according to Bowie et al. (1985) they

require aerobic conditions with a pH between 7 and 9.8, an optimal temperature of 30E, and 

minimum and maximum temperatures of 10E and 60E respectively (Figure 60, Figure 61). 

 Figure 60 Figure 61 

 Response to pH, Nitrification Response to Temperature, Nitrification 

 

In contrast, denitrification (the conversion of nitrate and nitrite to free nitrogen) is an anaerobic 

process, so that DOCorrection enhances the process (Ambrose et al., 1991): 

Denitrify = KDenitri ⋅(1 - DOCorrection)⋅TCorr ⋅ pHCorr ⋅ Nitrate (145)

where: 

Denitrify = denitrification rate (g/m3

⋅d); 

KDenitri = maximum rate of denitrification (g ammonia/g nitrate); and 

Nitrate = concentration of nitrate (g/m3

). 

13 
AQUATOX Release 2.1 Technical Documentation Addendum 

Furthermore, it is accomplished by a large number of reducing bacteria under anaerobic 

conditions and with broad environmental tolerances (Bowie et al., 1985; Figure 62, Figure 63). 

 Figure 60 Figure 61 

 Response to pH, Denitrification Response to Temperature, Denitrification 

 

Ionization of Ammonia 

The un-ionized form of ammonia, NH3, 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. Previous

versions of AQUATOX did not differentiate the forms of ammonia. However, now that pH is a

dynamic variable (see new section 5.7), it is useful to report NH3 as well as total ammonia (NH3

+ NH4

+

). 

The computation of the fraction of total ammonia that is un-ionized is relatively straightforward 

(Bowie et al. 1985): 

pkh pH FracNH − + = 1 10

1 3

(10a)

NH 3 = FracNH 3 ⋅ Ammonia (11a)

TKelvin pkh 2729.92 = 0.09018 +

(12a)

where: 

FracNH3 = fraction of un-ionized ammonia (unitless); 

pkh = hydrolysis constant; 

NH3 = un-ionized ammonia (mg/L); 

Ammonia = total ammonia (mg/L); see (137, Rel. 2)

TKelvin = temperature (oK). 

The relative contributions of temperature and pH can be seen by graphing the fraction of unionized ammonia against each of those variables in simulations of Lake Onondaga (Figures 1 and 

14 
AQUATOX Release 2.1 Technical Documentation Addendum 

2). 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. 

Fraction NH3

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

Sep-88 Apr-89 Oct-89 May-90 Nov-90 Jun-91

0

5

10

15

20

25

30

Frac NH3

Temp

Figure 1. Fraction of un-ionized ammonia roughly following temperature. 

Fraction NH3

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

Sep-88 Apr-89 Oct-89 May-90 Nov-90 Jun-91

7.5

7.6

7.7

7.8

7.9

8

8.1

8.2

8.3

Frac NH3

pH

Figure 2. Fraction of un-ionized ammonia affected by extreme values of pH. 

The construct was verified with the same set of data from Lake Onondaga as was used for the pH 

verification (Effler et al. 1996). It fits the observed data well (Figure 3). 

15 
AQUATOX Release 2.1 Technical Documentation Addendum 

Fraction NH3

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

Feb89Apr89May89Jul-89 Aug89Oct89Dec89

Frac NH3

Obs frac NH3

Poly. (Obs frac NH3)

Figure 3. Comparison of predicted and observed fraction of NH3 for Lake Onondaga, NY. 

Data from (Effler et al. 1996). 

5.3 Phosphorus 

Replace Section 5.2 with the following section. Note: equations 147 and 148 have been 

removed as they are now replaced with the Remineralization calculation below (13a). 

- Washout TurbDiff

 = Loading + Remineralization - Assimilation dt

dPhosphate

Phosphate

±

(146)

where: 

dPhosphate/dt = change in concentration of phosphate with time (g/m3

⋅d); 

Loading = loading of nutrient from inflow (g/m3

⋅d); 

Remineralization = phosphate derived from detritus and biota (g/m3

⋅d), see (13a); 

Assimilation = assimilation of nutrient by plants (g/m3⋅d), see (149); 

Washout = loss of nutrient due to being carried downstream (g/m3

⋅d), see (16) 

TurbDiff = depth-averaged turbulent diffusion between epilimnion and

hypolimnion if stratified (g/m3⋅d), see (22) and (23). 

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 3 on page 

24): 

16 
AQUATOX Release 2.1 Technical Documentation Addendum 

NutrRelColonization NutrRelPeriScour

NutrRelPlantSink NutrRelMortality NutrRelGameteLoss

DetritalDecomp AnimalPredation NutrRelDefecation

Remineralization = PhotoResp DarkResp AnimalResp AnimalExcr 

+ +

+ + +

+ + +

+ + +

 (13a)

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); 

AnimalResp = excretion of phosphate due to animal respiration (g/m3

⋅d); 

AnimalExcr = animal excretion of excess nutrients to phosphate to maintain 

constant org. to p ratio as required (g/m3⋅d); 

DetritalDecomp = phosphate release due to detrital decomposition (g/m3

⋅d); 

AnimalPredation = change in phosphate content necessitated when an animal consumes 

prey with a different nutrient content (g/m3⋅d); 

NutrRelDefecation = phosphate released from animal defecation (g/m3

⋅d); 

NutrRelPlantSink = phosphate balance from sinking of plants and conversion to detritus 

(g/m3⋅d); 

NutrRelMortality = 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 future

enhancement could be to consider phosphate precipitated with calcium carbonate, which would

better represent the dynamics of marl lakes; however, that process is ignored in the current 

version. A default value is provided for average atmospheric deposition, but this should be 

adjusted for site conditions. In particular, entrainment of dust from tilled fields and new 

highway construction can cause significant increases in phosphate loadings. As with nitrogen, 

the uptake parameter is the Redfield (1958) ratio; it may be edited if a different ratio is desired 

(cf. Harris, 1986). 

 

5.4 Nutrient Mass Balance 

This section should be inserted on p. 5-17 as the new section 5.4. Current Sections 5.4 

(Dissolved Oxygen) and 5.5 (Carbon Dioxide), should be renumbered as 5.5 and 5.6, 

respectively 

17 
AQUATOX Release 2.1 Technical Documentation Addendum 

Variable Stoichiometry

A notable simplification in AQUATOX has been the assumption of constant stoichiometry 

across trophic levels. However, in order to better model nutrients, the latest version of 

AQUATOX allows the ratios of elements in organic matter to vary considerably. 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 had been

hard-wired with a value of 5. 

In order to maintain the specified ratios for each compartment, the model now explicitly

accounts for processes that balance the ratios during transfers, such as excretion coupled with 

consumption and nutrient uptake coupled with colonization. Nutritional value is not 

automatically related to stoichiometry in the model, but it is implicit in default egestion values

provided with various food sources. Table 1 shows the default stoichiometric values suggested 

for the model based on two references (Elser et al. 2000) (Sterner and Elser 2002). 

Table 1: Default Stochiometric Values in AQUATOX 

Compartment 

Frac. N 

(dry) 

Frac. P 

(dry) Reference 

Refrac. detritus 0.002 0.0002 Sterner & Elser 2002 

Labile detritus 0.059 0.007 Same as phytoplankton 

Phytoplankton 0.059 0.007 Sterner & Elser 2002 

Bl-greens 0.059 0.007 same as phytoplankton for now 

Periphyton 0.04 0.0044 Sterner & Elser 2002 

Macrophytes 0.018 0.002 Sterner & Elser 2002 

Cladocerans 0.09 0.014 Sterner & Elser 2002 

Copepods 0.09 0.006 Sterner & Elser 2002 

Zoobenthos 0.09 0.014 same as cladocerans for now 

Minnows 0.097 0.0149 Sterner 2000

Shiner 0.1 0.025 Sterner 2000

Perch 0.1 0.031 Sterner 2000

Smelt 0.1 0.016 Sterner 2000

Bluegill 0.1 0.031 same as perch for now 

Trout 0.1 0.031 same as perch for now 

Bass 0.1 0.031 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 now accept both loadings and initial 

conditions as “Total N” and “Total P.” This is made possible by accounting for the nitrogen and 

phosphorus contributed by suspended and dissolved detritus and phytoplankton and backcalculating 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: 

18 
AQUATOX Release 2.1 Technical Documentation Addendum 

N Dissolved = NTotal − NSuspendedDetritus − NSuspendedPlants (14a) 

where: 

NDissolved = bioavailable dissolved nitrogen (g/m3 d); see (137 & 140, Rel. 2); 

NTotal = loadings of total nitrogen as input by the user (g/m3 d); 

NSuspendedDetritus = nitrogen in suspended detritus loadings (g/m3 d); 

NSuspendedPlants = nitrogen in suspended plant loadings (g/m3 d). 

In acknowledgment of the way it is used in the model, the phosphorus state variable is now

designated “Total Soluble P.” Phosphorus that is not bioavailable (i.e. immobilized phosphorus/ 

acid soluble phosphorus) may be specified using the FracAvail parameter as shown here: 

( ) TSP = FracAvail PTotal − PSuspendedDetritus − PSuspendedPlants (15a) 

where: 

TSP = bioavailable phosphorus (g/m3

 d); see (146, Rel. 2); 

FracAvail = user input bioavailable fraction of phosphorus; 

PTotal = loadings of total phosphorus (g/m3

 d); 

PSuspendedDetritus = phosphorus in suspended detritus loadings (g/m3

 d); 

PSuspendedPlants = 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 

now 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 particulate organic matter are calculated and summed. 

Biochemical oxygen demand (BOD5) is computed as the sum of the contributions from

phytoplankton and labile dissolved and particulate organic matter using a conversion of 1.35

BOD/organic matter. 

Mass Balance of Nutrients 

New variables for tracking mass balance and nutrient fate have been added to 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

19 
20 

AQUATOX Release 2.1 Technical Documentation Addendum 

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 EmergeI: 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, 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 

Please 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 Figures 4 and 5. A 

full accounting of the 18 nutrient linkages and all external loads and losses for nitrogen and 

phosphorus is also provided in Tables 2 and 3. 
21 

Figure 4

detritus

dissolved in water

Nitrogen Cycle in AQUATOX

NO NH4 3

nitrification

denitrification

plants

animals

assimilation

mortality

mortality, defecation, gameteloss

Loadings 

N in pore wate

(not in model dom

macrophyte root uptake

free nitrogen

(not in model domain)

decomp.

ingestion

ingestion

excretion, respiration

excretion,respiration
22 

Nitrogen Mass Balance: Accounting

NO3 link NH4 link

Detritus, Sed.Refractory link

Detritus, Sed.Labile link

DetrDiss

Load external load Load external load Load external load Load external load Load 

Nitrif from NH4 a Nitrif to NO3 a Defecation from animal e Defecation from animal e Dec

DeNitrif external loss Assimil to plant b Plant Sedmtn from plant f Plant Sedmtn from plant f MorNO3Assim to plant b Excretion from anim/plt c,o Colonz to SedLabDetr g Colonz from SedRefrDetr g ColoWashout external loss Respiration from anim/plt m,n Predation to Animal h Predation to Animal h ExcTurbDiff layer accountg DetritalDecomp from LabileDetr d Sedimentation from PartRefrDetr i Decomp to NH4 d Was

Washout external loss Scour to PartRefrDetr j Sedimentation from PartLabDetr i Turb

TurbDiff layer accountg Burial external loss Scour to PartLabDetr j

Exposure external load Burial external loss

Exposure external load

Detritus, Particulate Refr. link

Detritus, Particulate Labile link Algae link Macrophytes link Anim

Load external load Load external load Load external load Load external load Load 

mortality from anim/plt k Decomp to NH4 d Photosyn from NO3, NH4 b Photosyn root uptake, external Con

Colonz to PartLabDetr g mortality from anim/plt k Respiration to NH4 m Respiration to NH4 m DefeWashout external loss GamLoss from Animal q Photo Resp to diss detr, NH4 l,c Photo Resp to diss detr, NH4 l,c ResPredation to Animal h Colonz from Diss,PartRefr g Mortality to Diss / Part Detr k Mortality to Part Detr k ExcSedimentation to SedRefrDetr i Washout external loss Predation to Animal h Predation to animal h TurbScour from SedRefrDetr j Predation to Animal h Washout external loss Breakage to detr., as mort k PredSinkToHyp layer accountg Sedimentation to SedLabDetr i Sedimntn (Sink) to Sed Detr f MorSinkFromEpi layer accountg Scour from SedLabDetr j TurbDiff layer accountg GamTurbDiff layer accountg SinkToHypo layer accountg SinkToHypo layer accountg Drift 

SinkFromEpi layer accountg SinkFromEpi layer accountg EntrTurbDiff layer accountg Sloughing to detr., phytoplk r Prom

ToxDislodge to detr., as mort k Rec

EmeMigr

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 breaks down 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.

l 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. 

Table 2 
Figure 5 

23 detritus

phosphate 

dissolved in water

Phosphorus Cycle in AQUATOX

plants

animals

assimilation

mortality

mortality, defecation, gameteloss

Loadings 

excretion,respiration

P in pore wate

(not in model dom

macrophyte root uptake

decomp.

ingestion

ingestion

excretion, respiration
24 

Phosphorus Mass Balance: Accounting

Total Soluble P link

Detritus, Sed. Refractory link

Detritus, Sed.Labile link

Detritus, Dissolved link

Load external load Load external load Load external load Load external load

Assimilation to plant b Defecation from animal e Defecation from animal e Decomp (labile) to TSP d

Excretion from anim/plt c,o Plant Sedmtn from plant f Plant Sedmtn from plant f Mortality from anim/plt kRespiration from anim/plt m,n Colonz to SedLabDetr g Colonz from SedRefrDetr g Colonz DissRefr->PartLab gDetritalDecomp from LabileDetr d Predation to Animal h Predation to Animal h Excretion from anim/plt lWashout external loss Sedimentation from PartRefrDetr i Decomp to TSP d Washout external loss

TurbDiff layer accountg Scour to PartRefrDetr j Sedimentation from PartLabDetr i TurbDiff layer accountg

Burial external loss Scour to PartLabDetr jExposure external load Burial external loss

Exposure external load

Detritus, Particulate Refr. link

Detritus, Particulate link Algae link Macrophytes link Ani

Load external load Load external load Load external load Load external load Loa

mortality from anim/plt k Decomp to TSP d Photosyn from TSP b Photosyn root uptake, external Con

Colonz to PartLabDetr g mortality from anim/plt k Respiration to TSP m Respiration to TSP m DefWashout external loss GamLoss from Animal q Photo Resp to diss detr, TSP l,c Photo Resp to diss detr, TSP l,c ResPredation to Animal h Colonz from Diss,PartRefr g Mortality to Diss / Part Detr k Mortality to Part Detr k ExcSedimentation to SedRefrDetr i Washout external loss Predation to Animal h Predation to animal h TurScour from SedRefrDetr j Predation to Animal h Washout external loss Breakage to detr., as mort k PreSinkToHyp layer accountg Sedimentation to SedLabDetr i Sedimntn (Sink)to Sed Detr f MorSinkFromEpi layer accountg Scour from SedLabDetr j TurbDiff layer accountg GamTurbDiff layer accountg SinkToHypo layer accountg SinkToHypo layer accountg Drif

SinkFromEpi layer accountg SinkFromEpi layer accountg EntTurbDiff layer accountg Sloughing to detr., phytoplk r Pro

ToxDislodge to detr., as mort k Rec

EmeMig

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.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 P between phases is made up using dissolved P. j 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 n ratio as required.o Animal excretion of excess nutrients to P 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 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.

Table 3 
AQUATOX Release 2.1 Technical Documentation Addendum 

There are instances in which nutrients can be moved to and from compartments that are not in 

the model domain. For example, when NO3 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 which is not

modeled in this version of AQUATOX. 

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 6. 

N Tot. Mass (kg)

N Mass Dissolved (kg)

N Mass Detritus (kg)

N Mass Animals (kg)

N Mass Plants (kg)

N Wash, Animals (kg)

N Wash, Detritus (kg)

N Wash, Plants (kg)

N Loss EmergeI (kg)

N Loss Denitrif. (kg)

N Burial (kg)

N Load as Detritus (kg)

N Load as Biota (kg)

N Root Uptake (kg)

ONONDAGA LAKE, NY (PERTURBED) 7/5/2004 7:23:35 PM

(Epilimnion Segment)

1/18/1989 5/18/1989 9/15/1989 1/13/1990 5/13/1990 9/10/1990 1/8/1991

kg

900000.0

800000.0

700000.0

600000.0

500000.0

400000.0

300000.0

200000.0

100000.0

0.0

Figure 6 Distribution of predicted mass of nitrogen in Lake Onondaga NY. 

5.7 Modeling Dynamic pH 

(add this section to the end of chapter 5) 

25 
AQUATOX Release 2.1 Technical Documentation Addendum 

Dynamic pH is important in simulations for several reasons. As demonstrated in section 5.2,

ionization of ammonia is sensitive to pH. Furthermore, hydrolysis of organic chemicals can be

sensitive to pH. Both these relationships are modeled in AQUATOX. In addition, the viability

of organisms and bioaccumulation and toxicity of organic chemicals can be dependent on pH; 

these relationships are not currently modeled by AQUATOX. 

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: 

⎟

⎠

⎞ ⎜

⎝

⎛ − ⋅ = + ⋅ C

Alkalinity DOC pHCalc A B ArcSinH 5.1

(16a)

where: 

pHCalc = pH; 

ArcSinH = inverse hyperbolic sine function; 

Alkalinity = mean Gran alkalinity (μeq CaCO3/L); 

DOC = refractory dissolved organic carbon (mg/L); calc. from (114, 115, 

Rel 2); 

5.1 = average μeq of organic ions per mg of DOC; 

A = − Log Alpha

B = 1/ ln(10)

C = 2 ⋅ Alpha

Alpha = H 2CO3* ⋅ CCO2 + pkw

(6.57 0.0118 0.00012 ) 0.92 2 3* 10− − ⋅ + ⋅ ⋅ ⋅ = T T T H CO

where: 

H2CO3* = first acidity constant; 

CCO2 = CO2 expressed as μeq/L; see (164, Rel. 2); 

pkw = ionization constant for water (1e-14); 

T = temperature (oC); see (24, Rel. 2); 

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 

26 
AQUATOX Release 2.1 Technical Documentation Addendum 

Onondaga, NY, from before and after closure of a chlor-alkali plant (Effler et al., 1996), and one 

observation in a river (Figure 7). 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. 

Observed vs. Predicted pH

6.0

6.5

7.0

7.5

8.0

8.5

9.0

9.5

10.0

6.0 7.0 8.0 9.0 10.0

Predicted pH

O b served p

H

Figure 7 Comparison of predicted and observed pHs from selected lakes. 

The construct also was verified using time-series data from Lake Onondaga, NY (Figure 8). 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. 

Predicted pH, Lake Onondaga NY

7.5

7.7

7.9

8.1

8.3

8.5

Feb89Apr89May89Jul-89 Aug89Oct89Dec89

pH

AQUATOX

Observed

Poly. (Observed)

Figure 8. Comparison of predicted and observed pH values for Lake Onondaga, NY. 

 Data from (Effler et al. 1996).

27 
AQUATOX Release 2.1 Technical Documentation Addendum 

7 Toxic Organic Chemicals 

7.6 Nonequilibrium Kinetics 

The following text and equation should replace Equation (251) on page 7-24 and the 

descriptive paragraph preceding it. 

Given the latest model formulations and testing, it is not necessary to normalize an uptake rate 

constant (Diff) based on competing uptake rates. The Runge-Kutta dufferential equation solver

effectively removes any issues of excessive chemical uptake and toxicant mass balance is 

maintained at all times. Therefore: 

Diff = 1.0 (251)

7.7 Alternative Uptake Model: Entering BCFs, K1, and K2 

The following should be added to the end of Chapter 7, on page 7-36. 

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 LogKOW of the

chemical. Uptake in plants is a function of log KOW 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 are subject to very rapid 

uptake and depuration are not effectively modeled using these relationships. 

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, K1, K2) and the third 

factor is calculated using the below relationship: 

2

1

K

K BCF =

(17a)

where: BCF = bioconcentration factor (L/kg dry); 

K1 = uptake rate constant (L/kg dry day); 

K2 = elimination rate constant (1/d). 

Given these parameters, AQUATOX calculates uptake and depuration in plants and animals as 

kinetic processes. 

Uptake = K1⋅ToxState ⋅ Biomass ⋅1e - 6 (18a)

28 
AQUATOX Release 2.1 Technical Documentation Addendum 

Depuration = K2 ⋅ToxState (19a)

where: Uptake = uptake rate within organism (μg/L day); 

K1 = uptake rate constant (L/kg dry day); 

ToxState = concentration of toxicant in organism in water (μg/L) 

Biomass = concentration organism in water (mg/L) 

 1e-6 = (kg/mg) 

 Depuration = loss rate within organism (μg/L day); 

 K2 = elimination rate constant (1/d). 

 

Dietary uptake of chemicals by animals is not affected by this alternative parameterization. 

7.8 Half Life Calculation Refinement DT50 & DT95 

The half-life estimation capability with AQUATOX has been significantly upgraded since

Release 2. AQUATOX now estimates time to 50% (half-lives, DT50s) 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.

Water

Water Water

Water Mass

Hydrolysis Photolysis Microbial Washout Volat Sorption Loss + + + + + = .

(20a) 

Sed

Sed Sed

Sed Mass

Microbial Hydrolysis Desorption Loss + + =

(21a)

where: LossMedia = loss rate within media (1/d); 

 HydrolysisMedia = hydrolysis rate in given media (μg/L d), see (212, Rel. 2); 

Photolysis = photolysis rate in the water column (μg/L d), see (219, Rel. 2); 

 MicrobialMedia = rate of microbial metabolism in given media (μg/L d), see (225, Rel. 

 2); 

 Washout = rate of toxicant washout from the water column (μg/L d); see (16, Rel. 

 2)

 Volat = rate of chemical volatilization in the water column (μg/L d), see (230, 

 Rel. 2); 

 Sorption = sorption of toxicant to detritus, plants, and animals (μg/L d), see (249, 

 Rel. 2); 

MassMedia = mass of chemical in the media (μg/L); 

Desorption = desorption of toxicant from bottom sediment, see (250, Rel. 2). 

Loss rates are converted into time to 50% and 95% loss using the following formulae for firstorder reactions: 

29 
AQUATOX Release 2.1 Technical Documentation Addendum 

DT Media LossMedia 50 = 0.693/ (22a)

DT Media LossMedia 95 = 2.996 / (23a)

where: DT50Media = time in which 50% of chemical will be lost at current loss rate (d); 

DT95Media = time in which 95% of chemical will be lost at current loss rate (d); 

LossMedia = loss rate within media (1/d); 

The following should be inserted at the end of Chapter 8, on p. 8-10 

8 ECOTOXICOLOGY 

8.3 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): 

1 exp( ) (24a) Eta CumFracKilled = − −kz

where: z = external concentration of toxicant (μg/L); 

CumFracKilled = cumulative fraction of organisms killed for a given period of exposure 

 (fraction/d); 

k and Eta = 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 Ferson,

1997): 

Eta LC

k

50

− ln(0.5) = (25a)

ln(0.5)

2 LC50 slope Eta − ⋅ ⋅ = (26a)

where: slope = slope of the cumulative mortality curve at LC50 (unitless). 

LC50 = concentration where half of individuals are affected (μg/L). 

30 
AQUATOX Release 2.1 Technical Documentation Addendum 

AQUATOX assumes that each chemical’s dose response curve has a distinct shape, relevant to 

all organisms modeled. In this manner, a single parameter describing the shape of the Weibull 

parameter can be entered in the chemical record rather than requiring the user to derive slope 

parameters for each organism modeled. 

However, 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. 

Figures 9 and 10 show two Weibull distributions with identical shapes, but with slopes that are 

significantly different due to the scales of the x axes: 

 

Weibull Distribution, LC50=1, Slope=1

0%

50%

100%

0 0.511.5 2

Concentration

Cumulative Effect

Weibull

Slope

Weibull Distribution, LC50=100, Slope=0.1

0%

50%

100%

0 50 100 150 200

Concentration

Cumulative Effect

Weibull

Slope

Figures 9 and 10: Weibull distributions with identical shapes, but with slopes that are significantly different 

due to the scales of the x axes

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.

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). 

31 
AQUATOX Release 2.1 Technical Documentation Addendum 

32 

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