WASP7 Benthic Algae -

Model Theory and User's Guide 

R E S E A R C H A N D D E V E L O P M E N T
EPA 600/R-06/106 

September 2006 

www.epa.gov 

WASP7 Benthic Algae -

Model Theory and User's 

Guide 

Supplement to Water Quality Analysis 

Simulation Program (WASP) User 

Documentation 

Robert B. Ambrose, Jr., P.E. 

U.S. EPA, Office of Research and Development 

National Exposure Research Laboratory 

Ecosystems Research Division 

Athens, Georgia 

James L. Martin, Ph.D., P.E. 

Mississippi State University 

Starkville, Mississippi 

Tim A. Wool 

U.S. EPA, Region 4 

Water Management Division 

Atlanta, Georgia 

U.S. Environmental Protection Agency 

Office of Research and Development 

Washington, DC 20460 
NOTICE 

The U.S. Environmental Protection Agency (EPA) through its Office of Research and 

Development (ORD) funded and managed the research described herein. It has been 

subjected to the Agency’s peer and administrative review and has been approved for 

publication as an EPA document. Mention of trade names or commercial products does 

not constitute endorsement or recommendation for use. 

ii 
ABSTRACT

The standard WASP7 eutrophication module includes nitrogen and phosphorus cycling, 

dissolved oxygen-organic matter interactions, and phytoplankton kinetics. In many 

shallow streams and rivers, however, the attached algae (benthic algae, or periphyton, 

attached to submerged substrates) are often of greater importance than phytoplankton. 

These attached plants affect water quality in various ways, and their impact must often be 

considered in order to properly evaluate riverine water quality conditions. 

An advanced WASP7 eutrophication module has been developed to handle streams and 

rivers with bottom algae. This supplemental user manual documents the new bottom 

algae algorithms, including the kinetic equations, the additional model input and output, 

and a series of model verification tests. 

This advanced WASP7 module, named “periphyton,” includes the standard WASP7 

eutrophication algorithms, and incorporates bottom algae, with three additional state 

variables: bottom algal biomass, bottom algal cell nitrogen, and bottom algal cell 

phosphorus. Bottom algae are not subject to advective and dispersive transport. Sources 

and sinks include nutrient uptake, growth, nutrient excretion, death, and respiration. 

Nutrient uptake rates are driven by concentrations of inorganic nitrogen and phosphorus 

in the water column and within algal cells, and are controlled by cell minimum and halfsaturation parameters. Biomass growth is computed from a maximum zero or first-order 

rate constant that is adjusted internally by water temperature, bottom light intensity, 

internal nutrient concentrations, and maximum carrying capacity. Nutrient excretion, 

death, and respiration are represented by first-order, temperature dependent rates. 

Growth, respiration, and death rates affect other model state variables, including 

dissolved oxygen and nutrients. The algorithms for predicting bottom algal biomass and 

nutrient concentrations are based upon the periphyton routines included in the QUAL2K 

model (Chapra 2005). 

To run the WASP7 periphyton module, the user must supply initial concentrations of 

algal biomass and cell nitrogen and phosphorus content by segment. In addition, some 

model parameters, time functions, and constants must be specified. A new spatiallyvariable parameter represents the fraction of bottom area suitable for growth. Standard 

WASP7 parameters and time functions representing water temperature and incident light 

intensity are used. A periphyton constant group was added, with 27 new rate constants 

and coefficients that must be specified. 

The WASP7 periphyton module adds 8 new output variables to the standard 

eutrophication output available for examination in the post-processor. Simulated algal 

biomass per unit area of substrate is expressed both on a dry weight basis and as 

chlorophyll a. Internal cell nitrogen and phosphorus values are expressed as fractions of 

total biomass and as ratios with chlorophyll a. Finally, calculated light and nutrient 

growth limitation factors are provided. 

iii 
Table of Contents 

Abstract ........................................................................................iii

List of Figures ............................................................................... v

List of Tables................................................................................. v

1 Introduction ............................................................................... 1

2 Background ................................................................................ 2

3 Development of Equations ........................................................ 4

3.1 Bottom algal biomass (ab)....................................................................... 4 

3.1.1 Photosynthesis..................................................................................... 4 

3.1.2 Losses.................................................................................................. 6 

3.2 Bottom Algal Cell Nutrients (qN, qP)...................................................... 6 

3.3 External Inorganic Nutrients................................................................... 8 

3.4 External Organic Matter ......................................................................... 9 

3.5 Dissolved Oxygen................................................................................... 9 

4 Bottom Algae Model Inputs .................................................... 10

4.1 Initial Conditions and Model Parameters ............................................. 10 

4.2 Model Parameters and Time Functions ................................................ 11 

4.3 Model Constants and Reaction Coefficients......................................... 11 

5 Bottom Algae Model Outputs ................................................. 15

6 References................................................................................. 16

7 Appendix 1: Model Verification Tests ................................... 17

7.1 Development of Equations.................................................................... 17 

7.2 Verification Test Results....................................................................... 18 

7.3 Model Comparison Test........................................................................ 23 

iv 
List of Figures 

Figure 1 Phytoplankton and Periphyton ................................................................. 1 

Figure 2 WASP Version 7 Eutrophication Kinetics .............................................. 3 

Figure 3 Model Parameters and Time Functions.................................................. 11 

Figure 4 Model Constants for Benthic Algae ....................................................... 12 

Figure 5 Conversion of constants from QUAL2K to WASP7.1 .......................... 14 

Figure 6 Output Variables for Eutrophication – Bottom Algae Module ............. 15 

Figure 7 WASP7 Simulation of Benthic Algal Density ...................................... 20 

Figure 8 WASP7 Calculated Nutrient and Light Limitation ................................ 20 

Figure 9 WASP7 Simulation of Cell Nutrient Content ....................................... 21 

Figure 10 WASP Diel Temperature and Light Functions .................................... 24 

Figure 11 QUAL2K Periphyton Biomass Diel Results ........................................ 24 

Figure 12 WASP7 Periphyton Biomass Diel Results........................................... 25 

Figure 13 QUAL2K Cell Nutrient Diel Results .................................................. 25 

Figure 14 WASP7 Cell Nutrient Diel Results ...................................................... 25 

Figure 15 QUAL2K Diel Dissolved Oxygen Results........................................... 26 

Figure 16 WASP7 Diel Dissolved Oxygen Results.............................................. 26 

List of Tables 

Table 1 Kinetic coefficients for bottom algae................................................................... 19 

Table 2 Comparison of WASP7 with analytical solutions – base test conditions............ 21 

Table 3 Comparison of WASP7 with analytical solutions – low temperature & light..... 21 

Table 4 Comparison of WASP7 with analytical solutions – high temperature & light.... 21 

Table 5 Comparison of WASP7 with analytical solutions – low nutrients ...................... 22 

Table 6 Alternate kinetic coefficients for bottom algae.................................................... 22 

Table 7 Comparison of WASP7 with analytical solutions – alternate rate constants....... 23 

v 
1 Introduction 

Phytoplankton (floating plants) are commonly included as state variables in water quality 

models, such as WASP, both because they impact dissolved oxygen and material cycling 

in water bodies and because excessive phytoplankton populations are of environmental 

concern. However, in many shallow streams and rivers it is the attached algae (benthic 

algae, or periphyton, attached to submerged substrates) that are often of greater 

importance. These attached plants affect water quality in various ways, and their impact 

must often be considered in order to properly evaluate riverine water quality conditions. 

Though the term “periphyton” includes both bottom algae and associated detritus and 

bacteria, in this document “benthic algae” and “periphyton” are used to designate the 

algal community attached to bottom rocks and stable sand surfaces. 

As with phytoplankton, periphyton growth is impacted by temperature, light and 

nutrients. The growth of periphyton consumes nutrients and produces oxygen. 

Periphyton, like phytoplankton, also excrete cell contents and die, recycling dissolved 

and particulate organic matter to the stream’s carbon and nutrient pools. While the 

modeling approaches used for phytoplankton and periphyton are similar, periphyton 

differ from phytoplankton in a number of fundamental ways, as illustrated in Figure 1 : 

• Periphyton do not move with the water current, as do phytoplankton, 

• Periphyton typically dwell on or near the bottom, so are not impacted by the average 

light in the water column but the light reaching the bottom (substrate). 

• Periphyton are limited by the amount of substrate available for growth. 

• There is typically a maximum density for attached plants. 

Figure 1 Phytoplankton and Periphyton 

The importance of periphyton and need for incorporation of periphyton routines into the 

WASP modeling framework has long been recognized. Because of the impact of 

1
2 

periphyton on water quality, Chapra (1997) suggested that eutrophication frameworks 

should include both phytoplankton and periphyton. As a result of the need to simulate 

either or both phytoplankton and periphyton in the WASP framework, studies were 

initiated to review available routines, select the routine(s) and then incorporate 

periphyton routines into WASP. For incorporation of periphyton routines into WASP, 

two periphyton models were reviewed: the Jackson River periphyton model developed by 

HydroQual (HydroQual 2003, reviewed by Martin 2003) and the periphyton routines 

incorporated into the QUAL2K model (Chapra 2003). The QUAL2K routines were 

ultimately selected and incorporated into WASP7. The more detailed HydroQual 

routines may be incorporated in part or in whole in later versions. 

Background 

WASP7 includes two eutrophication modules. The standard module (Ambrose, et al., 

1993, Wool et al., 2001) includes the following state variables: 

• Ammonia 

• Nitrate 

• Orthophosphate 

• Phytoplankton 

• Detrital carbon 

• Detrital nitrogen 

• Detrital phosphorus 

• CBOD type 1 

• CBOD type 2 

• CBOD type 3 

• Dissolved Oxygen 

• Dissolved Organic Nitrogen 

• Dissolved Organic Phosphorus 

• Salinity 

• Inorganic Solids 

The advanced stream eutrophication module incorporates bottom algae, with the 

following additional state variables: 

• Bottom algae biomass 

• Internal cell nitrogen 

• Internal cell phosphorus 

The relationship between WASP state variables is illustrated in Figure 2. 

2
Figure 2 WASP Version 7 Eutrophication Kinetics 

Each of the above state variables is represented using a general mass balance equation of 

the form of: 

accumulation = ± advective transport ± diffusive transport + external load ± sources/sinks. 

where accumulation is the rate of change in the mass of the constituent and sources/sinks 

result from reactions and transfer mechanisms. Periphyton state variables do not move 

with the flow of water, and their mass balance equations are reduced to: 

accumulation = ± sources/sinks. 

Sources and sinks for periphyton include growth, death, and respiration. Growth is 

computed from a maximum rate that is then modified based upon available light and 

internal nutrients. Unlike phytoplankton, bottom light rather than average water column 

light is used in the computation of growth. Rates of death and respiration are temperature 

dependent. Rates of growth, respiration, and death impact other model state variables 

including dissolved oxygen and nutrients. 

The algorithms for predicting variations in detrital and periphyton concentrations were 

based upon routines included in the QUAL2K model (Chapra 2005). The kinetic 

formulations provided in the following text were taken largely from the QUAL2K 

3
(Chapra 2005) documentation. Here, source/sink terms are denoted by “S” and are in g/d. 

Areal rates (e.g., fluxes) [g/m

2

-d] are denoted by “F” and are used to calculate benthic 

algal source/sink terms. Volumetric rates [g/m3-d] are denoted by “R” and are used to 

calculate source/sink terms for most WASP variables. Volumetric rates are the product 

of areal rates and active surface area divided by segment volume. Rate constants are 

denoted by “k” and are in units of d-1. Mass units are qualified by D, C, N, P, and A, 

which refer to dry weight, carbon, nitrogen, phosphorus, and chlorophyll a, respectively. 

3 Development of Equations 

3.1 Bottom algal biomass (ab) 

Bottom algae, ab, is represented as total biomass per unit area of available substrate 

[gD/m

2

]. Bottom algal biomass increases due to photosynthesis and decreases with 

respiration and death: 

Sab = (FGb − FRb − FDb ) Ab (1) 

where Sab is the total source/sink of algal biomass [gD/d], FGb is the photosynthesis rate 

[gD/m

2

-d], FRb is the respiration loss rate [gD/m2-d], FDb is the death rate [gD/m

2

-d], and 

Ab is the bottom substrate surface area [m2]. 

3.1.1 Photosynthesis 

Two options are available to represent the bottom algal photosynthesis rate, FGb [gD/m

2

-

d]. The first option is a temperature-corrected, zero-order maximum rate attenuated by 

nutrient and light limitation (simplied from Rutherford et al., 2000): 

FGb = FGb20 φ Tb φ Nb φ Lb (2) 

where FGb20 is the maximum photosynthesis rate at 20 °C [gD/m

2

-d], φTb is the 

photosynthesis temperature correction factor [dimensionless], φNb is the bottom algae 

nutrient attenuation factor [dimensionless number between 0 and 1], and φLb is the bottom 

algae light attenuation coefficient [dimensionless number between 0 and 1]. 

The second option uses a first-order, temperature-corrected rate constant, attenuated by 

nutrient, light, and space limitation: 

FGb = kGb20 φTb φ Nb φ Lb φSb ab (3) 

where kGb20 is the maximum photosynthesis rate constant at 20 °C [d-1], φSb is the bottom 

algae space attenuation coefficient [dimensionless number between 0 and 1], and other 

terms are as defined above. 

Temperature Effect. An Arrhenius model is employed to quantify the effect of 

temperature on bottom algae photosynthesis: 

4
T −20 φTb = θ Gb (4) 

where 2Gb is the photosynthesis temperature coefficient [dimensionless]. 

Nutrient Limitation Effect. Nutrient limitation of the photosynthesis rate is dependent 

on intracellular nutrient concentrations using a formulation originally developed by 

Droop (1974): 

φ Nb = min 

⎡

⎢

⎛

⎜

⎜1− q0 N ⎞

⎟

⎟, 

⎛

⎜

⎜1− q0P ⎞

⎟

⎟

⎤

⎥ (5) 

⎣⎝ qN ⎠ ⎝ qP ⎠⎦

where qN and qP are cell quotas of nitrogen [mgN/gD] and phosphorus [mgP/gD], 

respectively, and q0N and q0P are the minimum cell quotas of nitrogen [mgN/gD] and 

phosphorus [mgP/gD], respectively. The minimum cell quotas are the levels of 

intracellular nutrient at which growth ceases. 

Nutrient cell quotas are state variables calculated by WASP. Their mass balance 

equations are described in a later section. 

Light Limitation Effect. Light limitation is determined by the amount of 

photosynthetically-active radiation (PAR) reaching the bottom of the water column. This 

quantity is computed with the Beer-Lambert law evaluated at the bottom of the river: 

I (H ) = I(0)e −keH (6) 

where I(H) is light intensity at depth H below the water surface [Ly/d], I(0) is light 

intensity just below the water surface [Ly/d], H is depth [m], and ke is the light extinction 

coefficient [d-1]. 

Three models are used to characterize the impact of light on bottom algae photosynthesis. 

Substituting the above formulation into these models yields the following formulas for 

the bottom algae light attenuation coefficient: 

Half-Saturation Light Model: 

φ Lb = KLb

I (

+

0

I 

)e 

(0

−k 

) 

e

e

H 

−keH (7) 

Smith’s Function: 

φ Lb = I (0)e−keH (8) 

2 K e

Lb + (I (0)e −k H )

2 

5
Steele’s Equation: 

⎛ I (0)e−keH ⎞

φ Lb = I (0)e−keH e 

⎜

⎜

⎝

1+ KLb ⎟

⎟

⎠ (9) KLb 

where KLb is the appropriate bottom algae light parameter for each light model. 

Space Limitation Effect. Bottom algal densities are limited by their carrying capacity, 

or maximum density. Space limitation of the first-order growth rate is modeled as a 

logistic function: 

φSb = 1 − ab (10)

ab max 

where abmax is the bottom algae carrying capacity, or maximum density [gD/m2

]. 

3.1.2 Losses 

Bottom algal biomass decreases due to respiration and death. 

Respiration. Bottom algal respiration is represented using first-order, temperaturecorrected kinetics: 

T −20 FRb = kRb20 θ Rb ab (11) 

where kRb20 is the bottom algae respiration rate constant at 20 °C [d-1] and 2Rb is the 

bottom algae respiration temperature coefficient [dimensionless]. 

Death. Bottom algal death is also represented using first-order, temperature-corrected 

kinetics: 

F = k θT −20 a (12) Db Db20 Db b 

where kDb20 is the bottom algae death rate constant at 20 °C [d-1] and 2Db is the bottom 

algae death temperature coefficient [dimensionless]. 

3.2 Bottom Algal Cell Nutrients (qN, qP) 

Intracellular nutrient concentrations, or cell quotas, represent the ratios of the intracellular 

nutrient to the bottom algal dry weight: 

qN = 103 INb (13)

ab 

6
qP = 103 IPb (14)

ab 

where qN and qP are cell quotas [mgN/gD or mgP/gD], INb is intracellular nitrogen 

concentration [gN/m2

], IPb is intracellular phosphorus concentration [gP/m2], and 103 is a 

units conversion factor [mg/g]. 

The total source/sink terms for intracellular nitrogen and phosphorus in bottom algal cells 

[g/d] are controlled by uptake, excretion, and death: 

SbN = (FUNb − FENb − FDNb ) Ab (15) 

SbP = (FUPb − FEPb − FDPb ) Ab (16) 

where FUNb and FUPb are uptake rates for nitrogen and phosphorus by bottom algae 

[gN/m2

-d and gP/m2-d], FENb and FEPb are the bottom algae cell excretion rates [gN/m2-d 

and gP/m2

-d], and FDNb and FDPb are loss rates from bottom algae death [gN/m2-d and 

gP/m2

-d]. 

The N and P uptake rates depend on both external and intracellular nutrient 

concentrations as in Rhee (1973): 

F =10−3 ρ

⎛ NH4 + NO3 ⎞⎛

⎜ KqN ⎞

⎟ a (17) UNb mN ⎜

⎜

⎝ KsNb + NH4 + NO3 

⎟

⎟

⎠

⎜

⎝ KqN + (qN − q0N ) ⎟

⎠ b 

− FUPb =10 3 ρ mP 

⎛

⎜

⎜ PO4 ⎞

⎟

⎟

⎛

⎜

⎜ KqP ⎞

⎟

⎟ ab (18)

⎝ KsPb + PO4 ⎠⎝ KqP + (qP − q0P ) ⎠

Where NH4, NO3, and PO4 are external water concentrations of ammonium N, nitrate N, 

and phosphate P [mgN/L and mgP/L], ρmN and ρmP are the maximum uptake rates for 

nitrogen and phosphorus [mgN/gD-d and mgP/gD-d], KsNb and KsPb are half-saturation 

constants for external nitrogen and phosphorus [mgN/L and mgP/L], KqN and KqP are 

half-saturation constants for intracellular nitrogen and phosphorus [mgN/gD and 

mgP/gD], and 10-3 is a units conversion factor [g/mg]. Note that nutrient uptake rates fall 

to half of their maximum values when external nutrient concentrations decline to the halfsaturation constants, or when excess internal nutrient concentrations rise to the internal 

half-saturation constants. 

The internal N and P excretion rates are represented using first-order, temperaturecorrected kinetics: 

F = k θT −20 q a 10−3 (19) ENb Eb20 Eb N b 

T −20 3 FEPb = kEb20 θ Eb qP ab 10− (20) 

7
where kEb20 is the bottom algae cell excretion rate constant at 20 °C [d-1] and 2Eb is the 

bottom algae excretion temperature coefficient [dimensionless]. 

The internal N and P loss rates from benthic algal death are the product of the algal death 

rate, FDb [gD/m2

-d], and the cell nutrient quotas: 

FDNb = FDb qN 10−3 (21) 

FDPb = FDb qP 10−3 (22) 

where 10-3 is a units conversion factor [g/mg]. 

In the following sections, volumetric rate terms “Rs” [g/m3

-d] are used in place of the 

corresponding periphyton areal rate, or flux terms “Fs” [g/m2

-d]. Volumetric rates are 

calculated from areal rates as follows: 

Rs = Fs (Ab /V ) (23) 

where “s” denotes the appropriate subscripts, Ab is the active surface area [m2

], and V is 

the segment volume [m3

]. 

3.3 External Inorganic Nutrients 

External inorganic nutrients, found in the water column around the benthic algae, include 

ammonia nitrogen, NH4 [mgN/L], nitrate nitrogen, NO3 [mgN/L], and orthophosphate, 

PO4 [mgP/L]. Bottom algae affect these nutrient concentrations by cell uptake and cell 

excretion. The source/sink terms in the inorganic nutrient mass balance equations 

include the following benthic algal terms: 

S NH 4b = [(RENb + RDNb )(1− fONb ) − RUNb PNH 4b ]V (24) 

S NO3b = − [RUNb (1− PNH 4b )]V (25) 

SPO4b = [(REPb + RDPb )(1− fOPb ) − RUPb ]V (26) 

where fONb and fOPb are the cell nutrient organic fractions [dimensionless number between 

0 and 1] and PNH4b is the benthic algae ammonia preference factor [dimensionless number 

between 0 and 1]. The cell nutrient organic fractions are calculated as ratios of the 

stoichiometric nutrient fraction to the total cell nutrient fraction: 

(ANC / ADC) fONb = (27)

qN 10−3 

(APC / ADC) fOPb = (28)

qP 10−3 

8
where ANC, APC, and ADC are specified stoichiometric nitrogen to carbon, phosphorus 

to carbon, and dry weight to carbon ratios [gN/gC, gP/gC, and gD/gC], qN and qP are the 

calculated total cell nitrogen and phosphorus cell quotas [mgN/gD and mgP/gD], and 10-3 

is a units conversion factor [g/mg]. Whenever the calculated cell nutrient fractions fall 

below the specified stoichiometric nutrient fractions, the nutrient organic fractions are set 

to 1.0. 

The ammonia preference factor reflects the preference of benthic algae for ammonium as 

a nitrogen source. PNH4b is calculated from NH4 and NO3 concentrations: 

P = NH4 ×NO3 +

NH4 ×Khnxb (29) NH 4b (Khnxb + NH4 )(Khnxb + NO3 ) (NH4 + NO3 )(Khnxb + NO3 ) 

where Khnxb is the preference coefficient of bottom algae for ammonium [mgN/L]. 

3.4 External Organic Matter 

External organic matter includes particulate and dissolved forms. Particulate organic 

matter is derived from algal death, and is transformed to dissolved organic matter by 

bacterial dissolution. Dissolved organic matter is further mineralized to inorganic forms. 

WASP7 simulates detrital carbon, nitrogen, and phosphorus [mgC/L, mgN/L, and 

mgP/L], dissolved organic nitrogen [mgN/L], and dissolved organic phosphorus [mgP/L]. 

WASP7 also simulates three forms of dissolved organic carbon in terms of their oxygen 

equivalents (i.e., CBODi in mgO2/L). These carbonaceous variables are formed only by 

detrital dissolution, and are not linked directly to algal cell excretion or death. 

Bottom algae affect the particulate detrital C, N, and P pools by death: 

SmCb = RDb ADC −1 V (30) 

SmNb = RDNb fONb V (31) 

SmPb = RDPb fOPb V (32) 

Bottom algae affect the dissolved organic N and P pools by cell excretion: 

S DONb = RENb fONb V (33) 

S DOPb = REPb fOPb V (34) 

3.5 Dissolved Oxygen 

Bottom algae affect dissolved oxygen levels directly through photosynthesis and 

respiration, and indirectly through the production of detrital organic carbon, which is 

subsequently dissolved and oxidized. The indirect effects of organic matter on dissolved 

9
oxygen are covered in the WASP6 user manual, and will be documented in a WASP7 

supplement on dissolved oxygen. The production of oxygen by periphyton is given by 

the following equation: 

SO2Peri = ⎛

⎜

⎜RGb 

ROC 

+ RGb 

ANC (1− PNH 4b )

⎛

⎜

3 

×

32 ⎞

⎟ − RRb 

ROC ⎞

⎟

⎟V (35) ⎝ ADC ADC ⎝ 2 14 ⎠ ADC ⎠

where RGb is the periphyton growth rate [gD/m3

-d], RRb is the periphyton respiration rate 

[gD/m3

-d], ROC is oxygen to carbon ratio, 32/12 [gO2/gC], ADC is periphyton dry mass 

to carbon ratio [gD/gC], and ANC is periphyton nitrogen to carbon ratio [gN/gC]. The 

first term gives the production of oxygen during photosynthesis. The third term gives the 

consumption of oxygen by respiration. The second term represents the evolution of 

oxygen with the reduction of nitrate to ammonium. It is based on the following reaction: 

2 NO3 → 2 NH4 + 3O2 (36) 

in which 3 moles of oxygen are produced when 2 moles of nitrate are reduced. The term 

32/14 converts this molar ratio to the mass ratio of gO2/gN. 

4 Bottom Algae Model Inputs 

The data required to support the application of a model of periphyton include initial 

conditions (for total biomass, cell nitrogen, and cell phosphorus), model parameters, and 

reaction constants and coefficients. Each of these is briefly described in the sections 

below. 

4.1 Initial Conditions and Model Parameters 

Initial conditions are required for bottom algal biomass [gD/m2], cell nitrogen quota 

[mgN/gD], and cell phosphorus quota [mgP/gD]. If initial conditions are not specified 

for cell N and P in a segment with bottom algal biomass, WASP will initialize these 

variables to the minimum cell quotas specified in the constants section 4.3. Boundary 

conditions are not required for bottom algae variables. 

The initial conditions can be based on measurements or estimated by modeling. The 

modeling estimations are typically based on steady state or quasi-dynamic calculations. 

Estimates of initial periphyton biomass can also be made using direct measurements or 

artificial substrate studies. If the periphyton biomass is estimated in units other than ash 

free dry weight (e.g. carbon or chlorophyll a) it will be necessary to convert the units 

using some representative stoichiometry. The following representation is suggested as a 

first approximation (Redfield et al. 1963, Chapra 1997, Chapra 2005), 

100 gD: 40 gC:7200 mgN:1000 mgP:1000 mgA (37) 

10
where gX is mass of element X [g] and mgY is mass of element Y [mg]. It should be 

noted that chlorophyll a is the most variable of these quantities with a range of 

approximately 500-2000 mgA (Laws and Chalup 1990, Chapra 1997). 

4.2 Model Parameters and Time Functions 

To implement bottom algae simulations, segment-specific values for the bottom substrate 

surface area Ab are required for equation 1. In WASP the plan surface area of a model 

segment Asurf is computed by dividing the computed volume by the computed depth. 

Only a fraction of this area, however, may provide adequate substrate. Alternatively, in 

some reaches, the substrate (such as rocks) may provide more available area for growth 

than is represented by the plan area. To account for the effects of available substrate, the 

spatially-variable parameter fAS was added to WASP representing the fraction of bottom 

area in each segment providing suitable substrate for growth (parameter 23). The user 

must specify segment-specific values for fAS, and the model will compute the available 

substrate area Ab as the product of fAS and Asurf. If no substrate fraction is specified for a 

segment, the value defaults to 0 and no bottom algae will be supported. 

Bottom algal simulations also require the specification of parameters and time functions 

representing temperature and light. An example is provided in Figure 3. 

Figure 3 Model Parameters and Time Functions 

4.3 Model Constants and Reaction Coefficients 

Several kinetic constants and reaction coefficients control benthic algal dynamics. The 

WASP7 model constants related to bottom algae are listed Figure 4. The correspondence 

between the QUAL2K constants and the WASP7 constants is provided in Figure 5. 

11
Figure 4 Model Constants for Benthic Algae 

The stoichiometric coefficients (constants 1-4) reflect the measured or assumed 

stoichiometry of benthic algal organic matter. They correspond to variables ADC, ANC, 

and APC in the treatment on page 8. The following organic matter representation is 

suggested as a first approximation (Redfield et al. 1963, Chapra 1997): 

12 
100 gD : 40 gC : 7200 mgN : 1000 mgP 

The terms D, C, N, P, and A refer to dry weight, carbon, nitrogen, phosphorus, and 

chlorophyll a, respectively. These values are then combined to determine stoichiometric 

ratios [gX / gY]. For example, the amount of organic phosphorus that is released due to 

the death of periphyton expressed in carbon units is: 

−3 1000[mgP]×10 [gP / mgP] ⎡ gP ⎤ APC = 40[gC] = 0.025 ⎢

⎣ gC ⎥⎦ (38) 

The stoichiometric ratio for oxygen production and consumption (ROC, constant 5) is 

based upon a typical chemical reaction for plant photosynthesis (P) and respiration (R) 

assuming that ammonia is used as a substrate (Chapra 1997): 

P ⎯⎯→

106CO2 +16NH+

4 + HPO24 

− +108H2O C106H263O110N16P1 +107O2 +14H+

←⎯⎯R 

so that the stoichiometric ratio in Figure 4 is determined by (Chapra 2003): 

107[moleO2 ]× 32[g O2 / moleO2 ] ⎡ g O2 ⎤ ROC = 106[moleC]×12[g C / moleC] = 2.69 ⎢

⎣ g C ⎥

⎦

(39) 

Periphyton growth (equations 2-9) is computed from a maximum growth rate (constant 7) 

that is modified by the impacts of temperature (constant 8), light (constants 19, 20), and 

the ratios of cell nutrient concentration to minimum cell quota (constants 22, 23). The 

impact of light on periphyton is computed using the quantity of light reaching the bottom 

of a WASP segment. The maximum growth rate is typically on the order of 30 g/m2

-d, 

with a range of 10-100. The nutrient half-saturation constants tend to be higher than in 

phytoplankton by a factor of 10 to 100 (Chapra, personal communication). 

Bottom algal biomass declines with respiration and death (equations 11-12). Rates are 

calculated from first-order, 20 °C rate constants (constants 10, 14) and temperature 

coefficients (constants 11, 15). Typical values of the respiration rate constant are on the 

order of 0.1 d-1 with a range of 0.05-0.2. Death rate constants have typical values of 0.05 

d-1 with ranges of 0.01-0.5. Death rates during sloughing events could be greater 

(Chapra, personal communication). 

Cell nutrient concentrations are controlled by uptake, excretion, and death rates 

(equations 15-22). Ambient nutrient uptake is a function of the maximum uptake rate 

(constants 24, 25), the external nutrient half-saturation constants (constants 16, 17), and 

the internal nutrient half-saturation constants (constants 26, 27). Excretion is calculated 

from a first-order, 20 °C rate constant and a temperature coefficient (constants 12, 13). 

13
Figure 5 Conversion of constants from QUAL2K to WASP7.1 

14
5 Bottom Algae Model Outputs 

Output variables from the algal water quality module are listed in Figure 6. Variables 

checked in the “Output” box will be available to the WASP7 graphical post-processing 

software. For each variable with a checked “CSV” box, WASP7 will produce a separate 

comma-delimited file containing output for all segments and all output times. In this 

example, checked CSV output variables are related directly or indirectly to the benthic 

algal simulation. 

Figure 6 Output Variables for Eutrophication – Bottom Algae Module 

Output variables 64 – 71 are directly related to the benthic algae. Algal biomass per unit 

area of substrate is expressed both on a dry weight basis (64) and as chlorophyll a (69). 

Internal cell nitrogen and phosphorus concentrations are expressed as fractions of total 

biomass (67 and 68) and as ratios with chlorophyll a (70 and 71). Finally, the calculated 

light and nutrient growth limitation factors are provided (65 and 66). 

Many other water quality variables will be of interest when calibrating a benthic algae 

model. Those directly affecting benthic algal nutrients and biomass include bottom light 

(42), ammonia nitrogen (54), nitrate nitrogen (55), and orthophosphate phosphorus (60). 

Variables that are directly affected by benthic algae include ammonia and phosphate, 

detrital carbon (72), particulate organic nitrogen (50), particulate organic phosphorus 

(58), dissolved organic nitrogen (51), dissolved organic phosphorus (59), and dissolved 

oxygen (10). Users are encouraged to explore patterns and relationships among these 

variables to better understand the dynamics controlling water quality in their water body. 

15
6 References 

Ambrose, R.B., Jr., T.A. Wool, and J.L. Martin. 1993. The Water Quality Analysis 

Simulation Program, WASP5; Part A: Model Documentation. Internal Report 

Distributed by USEPA Center for Exposure Assessment Modeling, U.S. Environmental 

Protection Agency, Athens, GA, June, 1993. 

Chapra, S.C. 1997. Surface Water-Quality Modeling, McGraw-Hill, New York, New 

York, 844 pp. 

Chapra, S.C. 2003. QUAL2K: A Modeling Framework for Simulating River and Stream 

Water Quality (Beta Version): Documentation and Users Manual. Civil and 

Environmental Engineering Dept., Tufts University, Medford, MA. 

Chapra, S.C. and G.J. Pelletier. 2004. QUAL2K: A Modeling Framework for Simulating 

River and Stream Water Quality, Version 1.3: Documentation and Users Manual. Civil 

and Environmental Engineering Dept., Tufts University, Medford, MA. 

Droop, M.R. 1974. The Nutrient Status of Algal Cells in Continuous Culture. J. Mar. 

Biol. Assoc. UK. 54:825-855. 

HydroQual. 2003. "Development and Calibration of the Jackson River Periphyton 

Model," Prepared for MEAD-WESTVACO Corporation. HydroQual Project No: 

WEST0092, June, 2003. 

Laws, E. A. and M.S. Chalup. 1990. A Microalgal Growth Model. Limnol. Oceanogr. 

35(3):597-608. 

Martin, J. L. 2003. “Review of the HydroQual Jackson River Periphyton Model," 

Contract report prepared for Tetra Tech, Inc., Atlanta, GA. 

Redfield, A.C., B.H. Ketchum, and F.A. Richards. 1963. The Influence of Organisms on 

the Composition of Seawater, in The Sea, M.N. Hill, ed. Vol. 2, pp. 27-46, WileyInterscience, NY. 

Rhee, G-Y. 1973. A Continuous Culture Study of Phosphate Uptake, Growth Rate, and 

Polyphosphate in Scenedesmus sp. J. Phycol. 9:495-506. 

Rutherford, J.C., M.R. Scarsbrook, and N. Broekhuizen. 2000. Grazer Control of Stream 

Algae: Modeling Temperature and Flood Effects. J. Environ. Eng. 126(4):331-339. 

Wool, T.A., R.B. Ambrose, and J. L. Martin. 2001. “The Water Analysis Simulation 

Program, User Documentation for Version 6.0,” Distributed by USEPA Watershed and 

Water Quality Modeling Technical Support Center, Athens, GA. 

16
7 Appendix 1: Model Verification Tests 

Model verification tests were designed to assure that the equations are implemented 

correctly in the model code. In this section, analytical solutions are derived for cell 

nitrogen, cell phosphorus, and algal biomass concentrations under steady-state 

conditions. WASP7 simulations were run for 2 months under steady flow, temperature, 

and light conditions until simulated concentrations reached steady state. The simulated 

results were then compared to the analytical solutions. 

7.1 Development of Equations 

First, we solved for total biomass. Setting the source/sink term Sab to 0 in equation 1 

gives the controlling steady-state equation: 

FGb − FRb − FDb = 0 (40) 

Substituting the kinetic expressions for growth (using the zero-order model with the 

Smith light formulation), respiration, and death developed in Section 3.1 into equation 

40, the following equation is derived for bottom algal biomass density: 

e 

T −20 ⎡⎛ q0N ⎞ ⎛ q0P ⎞⎤ ⎛

⎜ I (0)e−k H ⎞

⎟ FGb20 θ gb ×min 

⎣

⎢

⎝

⎜

⎜1− qN ⎠

⎟

⎟, 

⎝

⎜

⎜1− qP ⎠

⎟

⎟

⎦

⎥×

⎜

⎜ 2

K 2 + (I(0)e−keH ) ⎟

⎟

⎝ Lb ⎠ a (41) b = T −20 T −20 kRb20 θ Rb + kDb20 θ Db 

This equation gives the steady-state algal biomass density [gD/m2

] as a function of cell N 

and P content, a set of reaction constants, and ambient environmental conditions, 

including light intensity just below the water surface, water temperature, and depth. 

Cell N and P content can be solved by setting the source/sink terms SbN and SbP equal to 0 

in equations 15 and 16. The resulting equations control cell nitrogen and phosphorus 

concentrations under steady-state conditions: 

FUNb − FENb − FDNb = 0 (42) 

FUPb − FEPb − FDPb = 0 (43) 

Substituting in the rate expressions for these fluxes (equations 17-22) and simplifying 

results in the following: 

⎛ NH + NO ⎞⎛ KqN ⎞ T −20 T −20 ρ mN ⎜

⎜ 4 3 ⎟⎟⎜ ⎟

⎟ − kEb20 θ Eb qN − kDb20 θ Db qN = 0 (44)

⎝ KsNb + NH4 + NO3 ⎠⎝

⎜ KqN + (qN − q0N ) ⎠

⎛ PO ⎞⎛ KqP ⎞ T −20 T −20 ρ mP ⎝

⎜

⎜

KsPb +

4 

PO4 ⎠

⎟

⎟

⎝

⎜

⎜

KqP + (qP − q0P ) ⎠

⎟

⎟

−kEb20 θ Eb qP − kDb20 θ Db qP = 0 (45) 

17
These equations can be rearranged into the quadratic form: 

a1 qN

2 + b1 qN + c1 = 0 (46) 

a2 qP

2 + b2 qP + c2 = 0 (47) 

where: 

a1 =1 (48) 

a2 =1 (49) 

b1 = KqN − q0N (50) 

b2 = KqP − q0P (51) 

c1 = − ρ mN 

⎛

⎜

⎜ NH4 + NO3 ⎞

⎟

⎟

⎛

⎜

⎜ T −20 

KqN 

T −20 

⎞

⎟

⎟ (52)

⎝ KsNb + NH4 + NO3 ⎠⎝ kEb20 θ Eb + kDb20 θ Db ⎠

c2 = − ρ mP 

⎛

⎜

⎜ PO4 ⎞

⎟

⎟

⎛

⎜

⎜ T −20 

KqP 

T −20 

⎞

⎟

⎟ (53)

⎝ KsPb + PO4 ⎠⎝ kEb20 θ Eb + kDb20 θ Db ⎠

The solutions to these quadratic equations are: 

− b1 ± b1

2 − 4 a1 c1 

q (54) N = 2 a1 

− b2 ± b2

2 − 4 a2 c2

qP = (55) 2 a2 

These equations give the steady-state cell nutrient content as a function of external 

nutrient concentrations, a set of reaction constants, and water temperature. The external 

nutrient concentrations will depend on upstream flow and boundary concentrations, as 

well as the segment volume. Substituting the values for qN and qP from equations 54 and 

55 into equation 41 gives the value for bottom algal biomass density at steady-state. 

7.2 Verification Test Results 

For verification testing, a single reach was set up with a depth of 0.5 m and a volume of 

5000 m3

. The advective flow was set to 50,000 m3/d, giving a hydraulic residence time 

of 0.1 days. With this large through-flow, ambient nutrient concentrations will remain 

close to the specified upstream boundary concentrations. 

The first verification test is based on the kinetic coefficients in Table 1. Temperature was 

set at a constant value of 22.63 °C. Incident light was set at a constant value of 519 Ly/d, 

and the light extinction coefficient was set to 0.1 m-1. In WASP, light just below the 

water surface is set to 90% of incident light to account for reflectance. In WASP, 

boundary concentrations for NH4, NO3, and PO4 were set to 0.1 mg/L, 1 mg/L, and 0.1 

18
mg/L, respectively, resulting in calculated ambient concentrations of 0.072, 0.930, and 

0.088 mg/L, respectively. These concentrations were used to drive the analytical 

solutions for cell nutrient content and biomass density. 

Table 1 Kinetic coefficients for bottom algae. 

No. Constant Value 

1 Benthic Algae D:C Ratio (mg Dry Weight/mg C) 2.5 

2 Benthic Algae N:C Ratio (mg N/mg C) 0.18 

3 Benthic Algae P:C Ratio (mg P/mg C) 0.025 

4 Benthic Algae Chl a:C Ratio (mg Chlorophyll a / mg C) 0.025 

5 Benthic Algae O2:C Production (mg O2/mg C) 2.69 

6 Growth Model, 0 = Zero Order; 1 = First Order 0 

7 Max Growth Rate (gD/m2/d for 0-order growth, 1/d for 1-order growth) 30 

8 Temp Coefficient for Benthic Algal Growth 1.07 

9 Carrying Capacity for First Order Model (gD/m2) 0 

10 Respiration Rate (1/day) 0.1 

11 Temperature Coefficient for Benthic Algal Respiration 1.07 

12 Internal Nutrient Excretion Rate Constant for Benthic Algae (1/day) 0.09 

13 Temperature Coefficient for Benthic Algal Nutrient Excretion 1.07 

14 Death Rate (1/day) 0.05 

15 Temperature Coefficient for Benthic Algal Death 1.07 

16 Half Saturation Uptake Constant for Extracellular Nitrogen (mg N/L) 0.1 

17 Half Saturation Uptake Constant for Extracellular Phosphorus (mg P/L) 0.04 

18 Inorganic Carbon Half-Saturation Constant (not implemented) (moles/L) 0 

19 LIGHT OPTION, 1=Half saturation, 2=SMITH, 3= STEELE 2 

20 Light Constant for growth (langleys/day) 135 

21 Benthic Algae ammonia preference (mg N/L) 0.025 

22 Minimum Cell Quota of Internal Nitrogen for Growth (mgN/gDW) 7.2 

23 Minimum Cell Quota of Internal Phosphorus for Growth (mgP/gDW) 1 

24 Maximum Nitrogen Uptake Rate for Benthic Algae (mgN/gDW-day) 720 

25 Maximum Phosphorus Uptake Rate for Benthic Algae (mgP/gDW-day) 50 

26 Half Saturation Uptake Constant for Intracellular Nitrogen (mgN/gDW) 9 

27 Half Saturation Uptake Constant for Intracellular Phosphorus (mgP/gDW) 1.3 

The first month’s output from this WASP7 verification simulation is illustrated in Figure 

7, Figure 8, and Figure 9. At the end of the first month, calculated variables were close to 

steady-state conditions. A comparison of these simulated variables after 4 months with 

the analytical solutions is provided in Table 2. WASP7 deviates from the analytical 

solutions by 0.05% for total biomass, and 0.01% or less for cell nutrients and limitation 

factors. 

The second verification run tested WASP7 output under low temperature and low light 

conditions. Temperature and incident light intensity were reduced by a factor of 4 to 5.7 

°C and 130 Ly/d, and the model was re-run. Table 3 shows WASP7 deviating from the 

analytical solutions by 0.1% or less. Because of the low temperature conditions, the 

WASP7 solution was probably not quite to steady-state. 

The third verification run tested WASP output under high temperature and high light 

conditions. Temperature and incident light intensity were increased by 50% to 34 °C and 

19
778 Ly/d, and the model was re-run. Table 4 shows WASP7 deviating from the 

analytical solutions by 0.05% or less. 

Figure 7 WASP7 Simulation of Benthic Algal Density 

Figure 8 WASP7 Calculated Nutrient and Light Limitation 

20
Figure 9 WASP7 Simulation of Cell Nutrient Content 

Table 2 Comparison of WASP7 with analytical solutions – base test conditions 

Variable Analytical 

Solution 

WASP7 

Solution 

Relative 

Error 

Nutrient Limitation Factor 0.9382 0.9382 0.0000 

Light Limitation Factor 0.9568 0.9568 0.0001 

Total Biomass, mgA/m2 1795 1794 -0.0005 

Cell Nitrogen, mgN/mgA 18.68 18.68 0.0001 

Cell Phosphorus, mgP/mgA 1.619 1.619 0.0000 

Table 3 Comparison of WASP7 with analytical solutions – low temperature & light 

Variable Analytical 

Solution 

WASP7 

Solution 

Relative 

Error 

Nutrient Limitation Factor 0.9659 0.9659 0.0000 

Light Limitation Factor 0.6351 0.6354 0.0005 

Total Biomass, mgA/m2 1227 1226 -0.0010 

Cell Nitrogen, mgN/mgA 33.34 33.31 -0.0010 

Cell Phosphorus, mgP/mgA 2.932 2.930 -0.0007 

Table 4 Comparison of WASP7 with analytical solutions – high temperature & light 

Variable Analytical 

Solution 

WASP7 

Solution 

Relative 

Error 

Nutrient Limitation Factor 0.9064 0.9065 0.0001 

Light Limitation Factor 0.9801 0.9801 0.0000 

Total Biomass, mgA/m2 1777 1776 -0.0003 

Cell Nitrogen, mgN/mgA 12.65 12.65 0.0004 

Cell Phosphorus, mgP/mgA 1.069 1.069 0.0005 

21
The fourth verification run tested WASP output under low nutrient conditions. In 

WASP, incoming ammonia, nitrate, and phosphate boundary concentrations were 

reduced by a factor of 100, resulting in calculated ambient concentrations of 0.1 μg/L, 1.2 

μg/L, and 0.3 μg/L, respectively. These concentrations were used in the analytical 

solutions for cell nutrient content and cell biomass density. Table 5 shows WASP7 

deviating from the analytical solutions by 0.05% for biomass, 0.1% for cell nitrogen, and 

0.05% for cell phosphorus, the limiting nutrient. The WASP nutrient limitation term 

differs from the analytical solution by 0.1% in this simulation. 

Table 5 Comparison of WASP7 with analytical solutions – low nutrients 

Variable Analytical 

Solution 

WASP7 

Solution 

Relative 

Error 

Nutrient Limitation Factor 0.3541 0.3545 0.0012 

Light Limitation Factor 0.9568 0.9568 0.0001 

Total Biomass, mgA/m2 678 679 0.0005 

Cell Nitrogen, mgN/mgA 2.14 2.14 0.0008 

Cell Phosphorus, mgP/mgA 0.155 0.155 0.0005 

The fifth verification run tested WASP output under base temperature and light 

conditions, but with a different set of rate constants (Table 6). The maximum growth rate 

was reduced to 9 gD/m2

-d, while the respiration rate was increased to 0.3 d-1 and the 

death rate was reduced to 0.01 d-1. The half-saturation constants for extracellular 

nitrogen and phosphorus were reduced to 0.02 and 0.001 mg/L, and the Smith light 

constant was reduced to 100 Ly/d. The model was re-run, with results summarized in 

Table 7. With lower growth and higher respiration rates, biomass declined by more than a 

factor of 6 from the base simulation, while the lower death rate caused cell nutrient 

concentrations to increase. WASP7 deviates from the analytical solutions by less than 

0.06%. 

Table 6 Alternate kinetic coefficients for bottom algae 

No. Constant Value 

1 Benthic Algae D:C Ratio (mg Dry Weight/mg C) 2.5 

2 Benthic Algae N:C Ratio (mg N/mg C) 0.18 

3 Benthic Algae P:C Ratio (mg P/mg C) 0.025 

4 Benthic Algae Chl a:C Ratio (mg Chlorophyll a / mg C) 0.025 

5 Benthic Algae O2:C Production (mg O2/mg C) 2.69 

6 Growth Model, 0 = Zero Order; 1 = First Order 0 

7 Max Growth Rate (gD/m2/d for 0-order growth, 1/d for 1-order growth) 9 

8 Temp Coefficient for Benthic Algal Growth 1.07 

9 Carrying Capacity for First Order Model (gD/m2) 0 

10 Respiration Rate (1/day) 0.3 

11 Temperature Coefficient for Benthic Algal Respiration 1.07 

12 Internal Nutrient Excretion Rate Constant for Benthic Algae (1/day) 0.09 

13 Temperature Coefficient for Benthic Algal Nutrient Excretion 1.07 

14 Death Rate (1/day) 0.01 

15 Temperature Coefficient for Benthic Algal Death 1.07 

22
16 Half Saturation Uptake Constant for Extracellular Nitrogen (mg N/L) 0.02 

17 Half Saturation Uptake Constant for Extracellular Phosphorus (mg P/L) 0.001 

18 Inorganic Carbon Half-Saturation Constant (not implemented) (moles/L) 0 

19 LIGHT OPTION, 1=Half saturation, 2=SMITH, 3= STEELE 2 

20 Light Constant for growth (langleys/day) 100 

21 Benthic Algae ammonia preference (mg N/L) 0.025 

22 Minimum Cell Quota of Internal Nitrogen for Growth (mgN/gDW) 7.2 

23 Minimum Cell Quota of Internal Phosphorus for Growth (mgP/gDW) 1 

24 Maximum Nitrogen Uptake Rate for Benthic Algae (mgN/gDW-day) 720 

25 Maximum Phosphorus Uptake Rate for Benthic Algae (mgP/gDW-day) 50 

26 Half Saturation Uptake Constant for Intracellular Nitrogen (mgN/gDW) 9 

27 Half Saturation Uptake Constant for Intracellular Phosphorus (mgP/gDW) 1.3 

Table 7 Comparison of WASP7 with analytical solutions – alternate rate constants 

Variable Analytical 

Solution 

WASP7 

Solution 

Relative 

Error 

Nutrient Limitation Factor 0.9582 0.9582 0.0001 

Light Limitation Factor 0.9756 0.9756 0.0000 

Total Biomass, mgA/m2 271 271 0.0003 

Cell Nitrogen, mgN/mgA 23.82 23.83 0.0005 

Cell Phosphorus, mgP/mgA 2.390 2.391 0.0006 

7.3 Model Comparison Test 

Further testing of the new WASP7 formulation was conducted by comparing case study 

results with QUAL2K. This is a hypothetical case study with no observed data. A single 

reach with 4 computational elements was set up in QUAL2K. An equivalent 4 segment 

network was set up with WASP7. Each segment and computational element had a depth 

of 0.5 m and a volume of 5000 m3

. The advective flow was set to 1 m3/sec, giving a 

hydraulic residence time of 83 minutes per segment. Upstream boundary concentrations 

for NH4, NO3, and PO4 were set to 0.1 mg/L, 1 mg/L, and 0.1 mg/L, respectively. Model 

constants and coefficients from Table 6 were used in this test. A diel temperature 

function (Figure 10) was specified with a daily average equal to 22.63 °C to match the 

previous analytical solutions. 

Setting up comparable incident solar radiation in the two models proved to be 

problematic, since QUAL2K calculates light internally. The site location of 42.5 N, 72 

W was specified, and the simulation date was set to August 5. The WASP7 diel light 

function, illustrated in Figure 10, averages 519 Ly/d, with a peak of 1830, which is 

typical of clear skies at 40 N during late summer. The light function in Figure 10 is 

adjusted for surface reflectance loss, which is assumed to be 10%. 

23
Figure 10 WASP Diel Temperature and Light Functions 

Starting with nutrient and biomass initial conditions of zero, QUAL2K was run for a 

period of 60 days to assure a steady-state initial solution. WASP7 was run for 28 days 

with initial benthic algal densities set to 10 gD/m2

. Algal densities and cell nutrient 

concentrations converged to a repeating diel solution within 3 to 4 weeks. 

Simulation results for the two models are illustrated in the following figures. Results are 

illustrated from midnight to midnight (hour 0 to 24 in QUAL2K, time 00:00 to 00:00 in 

WASP7). For the specified incident light, WASP7 reproduced the QUAL2K diel biomass 

trend well, with minimum and maximum values higher by 2.4% and 1.0%, respectively 

(Figure 11 and Figure 12). Cell nutrient dynamics were also reproduced well, with 

WASP7 exceeding QUAL2K by 4% for the diel minimum and 2.4% for the diel 

maximum (Figure 13 and Figure 14). Finally, the diel dissolved oxygen dynamics in 

Figure 15 and Figure 16 compare favorably. The small percentage differences could be 

due to slightly different model inputs, specifically including incident light. Nevertheless, 

this case study basically confirms that the new WASP7 benthic algae routines have been 

implemented correctly. 

Figure 11 QUAL2K Periphyton Biomass Diel Results 

24
Figure 12 WASP7 Periphyton Biomass Diel Results 

Figure 13 QUAL2K Cell Nutrient Diel Results 

Figure 14 WASP7 Cell Nutrient Diel Results 

25
Figure 15 QUAL2K Diel Dissolved Oxygen Results 

Figure 16 WASP7 Diel Dissolved Oxygen Results 

26