vxEPA
United States
Environmental Protection
Agency
WASP7 Benthic Algae -
Model Theory and User's Guide
RESEARCH AND DEVELOPMENT
-------
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.
-------
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 half-
saturation 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 spatially-
variable 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.
in
-------
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 (at,) 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 Eutrophi cation - 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
-------
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.
2 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.
-------
Periphyton
Phytoplankton
Oxidation
Photosynthesis and Respiration
4 —•
atmosphere
Reaeration
Settling
Uptake (Growth) and
Excretion (Respiration)
Nitrification
Inorganic Nutrients
P04
NH4
N03
DOM
CBOa
CBOU
OP
ON
Settling
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
-------
(Chapra 2005) documentation. Here, source/sink terms are denoted by "5" and are in g/d.
2
Areal rates (e.g., fluxes) [g/m -d] are denoted by "F" and are used to calculate benthic
3
algal source/sink terms. Volumetric rates [g/m -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 "#" 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, a\,, is represented as total biomass per unit area of available substrate
[gD/m2]. 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], Fob is the photosynthesis rate
[gD/m2-d], pRb is the respiration loss rate [gD/m2-d], Fob is the death rate [gD/m2-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/m2-
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 Tb Nb Lb (2)
2
where FGb2o is the maximum photosynthesis rate at 20 °C [gD/m -d], fab is the
photosynthesis temperature correction factor [dimensionless], fab is the bottom algae
nutrient attenuation factor [dimensionless number between 0 and 1], and fab 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:
F0b = kGb20 Tb Nb Lb Sb ab (3)
where kob2o is the maximum photosynthesis rate constant at 20 °C [d"1], fab 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:
-------
4n = C2° (4)
where 0Qb 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):
A ™ir, 1 ^OAT 1 m=mm 1 U1 (5)
where q^ and qp are cell quotas of nitrogen [mgN/gD] and phosphorus [mgP/gD],
respectively, and qw and qop 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(Q)e-k'H (6)
where I(H) is light intensity at depth H below the water surface [Ly/d], 1(0) is light
intensity just below the water surface [Ly/d], His 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:
T/r\\ —kpH
_ I(v)e e .
Smith's Function:
'" (8)
-------
Steele's Equation:
KLb
(9)
where KU, 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:
(10)
where a^max 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, temperature-
corrected kinetics:
FRb = kRb20 &Rb2° ab
where kRb2o is the bottom algae respiration rate constant at 20 °C [d"1] and 6Rb is the
bottom algae respiration temperature coefficient [dimensionless].
Death. Bottom algal death is also represented using first-order, temperature-corrected
kinetics:
FDh=kDh209TDh20ah (12)
where knb2o is the bottom algae death rate constant at 20 °C [d"1] and dub 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:
(13)
ah
-------
(14)
a
where qN and qP are cell quotas [mgN/gD or mgP/gD], INb is intracellular nitrogen
concentration [gN/m2], IPb is in
units conversion factor [mg/g].
concentration [gN/m2], IPb is intracellular phosphorus concentration [gP/m2], and 103 is a
The total source/sink terms for intracellular nitrogen and phosphorus in bottom algal cells
[g/d] are controlled by uptake, excretion, and death:
^bN = VUNb ~*lENb ~*'DNb)Ab (15)
^bP = VUPb ~ ^ EPb ~*lDPb)Ab (16)
where Fum 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 Fom and Fopb 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):
(18)
Where NH^ NO 3, and PO4 are external water concentrations of ammonium N, nitrate N,
and phosphate P [mgN/L and mgP/L], pmN and pmP 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], Kq^ 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 half-
saturation 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, temperature-
corrected kinetics:
TEb2°qNablO-3 (19)
TEb20qPablO-3 (20)
-------
where kEb2o is the bottom algae cell excretion rate constant at 20 °C [d"1] and 6Eb 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:
j—' -j—1 -i f\~3 /r\ -i \
FDPb=FDbqPW-3 (22)
where 10"3 is a units conversion factor [g/mg].
In the following sections, volumetric rate terms "R" [g/m3-d] are used in place of the
corresponding periphyton areal rate, or flux terms "F/' [g/m2-d]. Volumetric rates are
calculated from areal rates as follows:
Rs=Fs(Ab/V) (23)
where "s" denotes the appropriate subscripts, Ah is the active surface area [m2], and Fis
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, NO 3 [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:
~ [(RENb + RDNb ) i1 ~ foNb ) ~ RUNb PNH 4b ] V (24)
=-[RUNb(l-PNH4b)]V (25)
SP04b = [(REPb + RDPb ) i1 ~ foPb ) ~ RUPb ] V (26)
where fom andfopb are the cell nutrient organic fractions [dimensionless number between
0 and 1] andPNH4b 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)
JONb - _ -. n-3
(APC/ADC)
Jopb 7
-------
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. Pmi4b is calculated from NH4 and NO 3 concentrations:
p _
1-\TTTA-U -
(Khnxb+NH4)(Khm:b+N03) (NH4+N03)(Khnxb+N03)
where Khmb 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., CBODj 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=RDbADC-lV (30)
SmNb = RDNb foNb V (3 0
SmPb = RDPb foPb V (32)
Bottom algae affect the dissolved organic N and P pools by cell excretion:
" DONb ~ -^ENb JoNb ' \* * )
R-EPb JOPb 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
-------
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:
O
ROC ANC( /3 32>| ROC]
-- h /V, - [i — f; \rriAh l\ — x - \~-K-Dh - \y
Gb ^ NH4b Rb
--
ADC ADC 2 14 ADC)
3
where Rob is the periphyton growth rate [gD/m-d], RRI, is the periphyton respiration rate
3
[gD/m-d], ROC is oxygen to carbon ratio, 32/12 [gC>2/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:
2NO3^2NH4 + 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 gCVgN.
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 : 1 000 mgP : 1 000 mgA (3 7)
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 f\s 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.
Paiaraeter Used Scafe Faetoi j
1 Segment Scale Factor forWind \ F* 1.0000 1
2 Wind Speed Time Function to use lofSe f~ 1.0000
4 Tanpeiatuieof Segment lOeijiees Can IS" 1.0000
6 bci» Extinction tor SecimcrfiPei Dai' or t ix 10000 |
7 Ligl* Extinction Time Function to use for : H 1 0000 j
$ BCDfliDscaj' Rare Scab Facia f~ 10000 j
9 BC'OG) Decat Rate Scale Fsuot f~ 1.0000 I
TO GOE13J Decay Rate Scale Factor !~~ 10000 |
11 EB-i«cAt,-imc™Fli.ix(raa/m2/dasl [~ 1 0000 j
12 eonlhic Phosphate FluK (mg/r^/day) P 10000 j
13 Sedmient Oxygen Demarid [g/m2/da;ii f™ 1 0000 I
14 SedwenS Oxygen Demand Temperate t !~~ 10000 |
15 incoming Sola' Radiation tlangteys/dayi f^ 1 0000 ]
16 Measured Segment Reaeralnn Hate (pet P 10000
17 Zooplanklon Population !"~ 1.0000
18 Fraction Light Intercept fei Canow T 1.0000
19 Ts'/tgolo Escape Coefficient P 1 OOOQ f
20 Dam Elevator, imetete) !~ 1 0000 j
21 DamPoolWOCoetteert T 1.0000 j
J2 Dam IjpeCorfhciem l~ 1.0000 j
25 Fraction of Bottom of Segrrrenr Coveted b !W 1.0000 ]
Time Function Used
* Wdta Temperature Function 1 fCi !x"
Water Ternperatuie t-yncttcn 2 TCi F"
•Wate Temperature Fyricttori 4 f p P
•Dafe olai Radiation sLati^leysl f)?
.Fraofi n Daily Light Ifracticnl F"
jrievj^yei^ifjJonA^er^Teiipeiature Functon T ITJ
Dal« Time Vdue
1 | .'31/2004 | 0.00 2.154E.1
3 /31/2OM 2'00 2064E.1
4 /31/2004 SOO 203?E«1
5 /31/2004 4:00 2019E.1
0 .'31/2004 500 200EEt1
? .'31/2004 6:00 1.934E*!
0 .'31/2004 7:00 1 SSBEtl
9 SI/2004 3.00 2005E>1
10 /31/2004 900 2051E*1
12 /31,'2004 11:00 2223E*1
13 /31/2004 12:00 2337Ef1
14 7/31/200J 13:00 2.443E*1
15 7/31/2004 14:00 2.523E41
16 7/31/2004 15:00 25S2E*1
mAet-lfm emBn-eFunttiorHfCl
: 3*j .- ::, : , p.: ,,. - A\
: W £•:•:•* £--• •-'*=£•*• -I, --•;•:* -<&•- -;^v= -- ^
. Sat 11 StfemS? Wed@4 fri@€
i July through August, 2004
• — .-:= — D»% Set«r Ks^sli*n ttirtn^si
: 1««»1 •--;"• -"--".• :
: { _ _.«- : -:-v_
: SMS @§HI§ 13;@§ 16:SS @@:@9
: July through August, 2004
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
-------
Constant Group
Constant
1 Benthic Algae D:C Ratio (mg Dry Weight/mg C)
2 B enthic Algae N: C R atio (mg N /mg C)
3 B enthic Algae P: C R atio (mg P/rng C)
4 Benthic Algae Chi a:C Ratio (mg Chlorophyll a / mg C)
5 Benthic Algae 02:C Production (mg 02/mg C)
6 Growth Model, 0 =Zero Order; 1 = First Order
7 Max Growth Rate (gD/m2/d for 0-order growth, 1 /d for 1 -order growth)
8 Temp Coefficient for Benthic Algal Growth
9 Carrying Capacity for First Order Model (gD/m2)
10 Respiration Rate Constant (1 /day)
11 Temperature Coefficient for Benthic Algal Respiration
12 Internal Nutrient Excretion Rate Constant for Benthic Algae (1 /day)
13 Temperature Coefficient for Benthic Algal Nutrient Excretion
14 D eath R ate Constant (1 /day)
15 T emperature Coefficient for B enthic Algal D eath
16 Half Saturation Uptake Constant for Extracellular Nitrogen (mg N/L)
17 Half Saturation Uptake Constant for Extracellular Phosphorus (mg P/L)
18 Inorganic Carbon Half-Saturation Constant (not implemented) (rnoles/L)
13 LIGHT OPTION, 1=Half saturation, 2=SMITH, 3= STEELE
20 Light Constant for growth (langleys/day)
21 Benthic Algae ammonia preference (mg N/L)
22 Minimum Cell Quota of Internal Nitrogen for Growth (mgN/gDW)
23 Minimum Cell Quota of Internal Phosphorus for Growth (mgP/gDW)
24 Maximum Nitrogen Uptake Rate for Benthic Algae (mgN/gDW-day)
25 Maximum Phosphorus Uptake Rate for Benthic Algae (rngP/gDW-day)
26 Half Saturation Uptake Constant for Intracellular Nitrogen (mgN/gDW)
27 Half Saturation Uptake Constant for Intracellular Phosphorus (mgP/gDW)
iffe Copy
3 Paste I |f Fill/Gate
Cancel
2.5
Used
Rl
Rt 1.8E-1
R] 2.5E-2
Rl 2.5E-2
Ri 263
Rl 0
RI 3
Rl 1.07
n o
mi 3E-1
Ri 1.07
Rl 3E-2
Ri 1.07
Rl 1E-2
Ri 1.07
IH 2E-2
mi 1E-3
n o
Rl 2
Ri 1E+2
Ri 2.5E-2
Rl 7.2
Rt 1
R) 7.2E+2
R) 5E+1
Rl 9
Rl 1.3
Value
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:
'gP
40
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 + 16NHJ + HPC>4~ + 108H2O C^R^OnoN^?! + 107O2 + 14H+
R
so that the stoichiometric ratio in Figure 4 is determined by (Chapra 2003):
(39)
W6[moleC]xU[gC/moleC]
gC
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
-------
j __/ d ,1 ,3 JL • 1* u i A -j ^ - / * " • fe z * ti IJ la 4> 100% » * u
3j Hie |dit View Insert Farroat Tools Data Window Sheets Plots Help : •:'.-:• ''.-- -<-•'•• : r-.-?--:- •» _
-> I ~_ ~ _ --.' ••> . : - :-.' .-- - :" ""'- -:""."- '-:." '-- ' J| ; "I- : $•>'* >•' "2 <;: »/, P
G29 ' j&
: ! A : B ' C ! D
! 8
i 9 iCaibon j 40
! 10 [Nitrogen
! 11
! 12 : Dry weight
I 13
7.2
1
100
1
§€ if
iN
§P
9D
«A
! 14
! 15 |S*ttlin§ ¥«loeity
0.3
nv'd
: 16
! 17 iReaeiation
! 18 jTemp conection
• 19 :Reaeration wind effect
[ 20 !O2 for carbon oxidation
i 21 [O2forNH4
! 22 lOinygen CBOD
Internal
1.024
None
2.69
4.57
'saturation
iO->/iC
902'-gN
;w -< >• w \ Headwater ^Rates/ Temperature /Light / WASP-SS / | <
Ready
I 74
I 75
1 7B Growth
i 77 T«mp correction
i 78 -Firsi-oiidei model capacity
; 79 Respiration
| 80 Temp
i 81 Excrotion i ate
= 82 Temp correction
i 83 rate
| 84 T«mp
i 85 External nitrogen cfliistairt
86 External phosphorus half sat constant
87 Inorganic cat bon half sat constant
i 88 light model
i 89 Light
90 Ammonia preference
i 91 Siibsisfwic* fo< nitrogen
92 Subsistence foi phosphoius
= 93 for nitrogen
1 94 for
: 95
i 98 sat
Zere-order
300
1.07
1500
0.1
1.07
0.09
1.07
0.05
1.07
100
40
1.30E-05
Smith
135
25
0.72
0.1
72
5
0.9
mgA'iif.'il 01 ;'»
m§A/mf
•'(I
'd
.'d
ugN.1.
ugP'L
rnoles>'L
rngO"2«l
iiijiA
ni§i;in§A
nigP/ififA
m§i;rn§A:cI
mgP'mgA/'4
mgN''mgA
0.13|mgP;mgA
s»
iP
tD
§A
*"i
*.
rx
f^K
C*
att
**ft.'?sn:
*rt
fi*
**
&»
*«
^»
*s/»
*iWt
*'<*
*!*
*fe«*
f »/
ft!."
P.dA"
P*f
*'#
^#
E; F
G I H
to WASP7.1
2.500 gD/gC
0.180 gN/gC
0.025 gP/gC
0.025 gA-cjC
2.69 gO2/gC
NUM
WASP7.1
Zero-order
30 gD/m2-d
1.07
150 gD/m2
0.1
1.07
0.09 /d
1.07
0.05 /d
1.07
0.1 mgN/L
0.04 mgP/L
1.30E-05>moles/L
Smith
135 Ly/day
0,025 mgN/L
7.2 imjN/gD
1 mgP/gD
720 mgN/gD-d
50 mgP/gD-d
9 niiN/jjD
1.3 mgP/gD
Figure 5 Conversion of constants from QUAL2Kto 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.
Descriptor!
1 Segment Depth
2 Water Temperature
3 Wind Speed
4 Water Velocity
5 i'lO'garac Solid!
b ^PaiticuiateQiganc Mallei
? Total Solid?
S PGIQitj?
3 Salinity
10 D Solved O^gen
11 DO Minimum
12 OOMwmuro
13 DO Saturation iConc)
14 DOOe&i
1 5 Pefceni DO Saturation
16 Reaeratson
5 7 Wind Reaerafef!
1 8 Hydraulic Tieaef afeti
1 3 Sedsrrerrt Oxygen Demand
20 CBOD il) (Ultimate!
21 CBOD 1 Decay Rate
22 -CBOD!2)phmaieI
23 CBOD 2 Decay Rate
24 CBOD [3){Ultimatej
25 CBOD 3 Decay Rate
28 Dr^ol^edOrgawcC
27 'Total uBOO
Units
_*<*»*
T-
m/-xc
rn/*e>-
mg/L
mg/L
ing/L
fraction
pp!
mg/l.
mg/L
mg/L
mg/L
psr day
pe! day
pet day
mg/L
pa day
r*gA
per day
mg/t
per day
mgA.
Qulpul CSV
Bf P
Bf P.
Sf P
Bf 'P
!>c p
Ix P
« P
IS ^P
Bf P
Bf P
Bf P
Bf P
er P
Bf P
ur p
ix f .
BE n
Bf P
i^r p*j
Bf P
Bf P
Sx p
SEp f™";
Ix P
Bf P
Description
28 PhjrtoDiar^ton Carbon
23 Ph>top!ar,K>on CHoropK'll a
30 Ph=/lopiankton Growth
31 Ph5'toplar,kton Death
32 .Ph^optariKon DO Production
33 Ph^HiplanKton DO Comuniptiori
34 Phj'toplankon Carbon lo Chla Ratio
35 •Ph^topiankton Light GuMthLtmti
3& 'Ph5rtop!ar,ktor-iNuttienl Growth Limit
3? phstoplanMon Ni'jogen Growth Limit
38 . Phs'toplafilston P Growth Lmit
3 Total Light
0 Sat, Light IntfrHtji
1 .Light Top Segment
2 Light Bottom Segment
3 Calculated Light ExtretKm
4 Background t:»
5 Algal Shade fe
b Soltfc I'.e
7 :DOCKe
8 Total Nitrogen
3 Total Organic N
0 . Particulate Organic N
51 ,Dr,:olvadOrgaimN
52 ToW Inorganic N
53 .Di^olvedlnorganic-N
54 Anrrriotiia N
55 Nitrate H
Unite
rtg/L
ug/L
pet day
pe- day
mg/L;'da-y
rng/L/d*y
^/fng
1/m
1/m
1/rrr
l/rr.
1/»i
mg#l
mg/L
mg/L
rng/L
mg/L
mod.
rng/L
mg/L
Qytpul
BT
Ix
Be
IX
p<
Ix
(«
Bf
Ix
Be
Bf
p<
Ix
|»
m
Bf
Bf
Be
Ix
B<
BT
Bf
Bf
Bf
m
m
Ix
Bt
~:-m~-.*
CSV
p
p,
p
p
p
p
n
p
p
p
p
R
p
p
IK
|X:
P
P
P
P
P
p
P
P
P
P
B
m
Beseiijrtion Urals Output CSV
:56
:f'7
:5B
•S3
:eo
:61
•63
:63
:B4
:65
:66
•67
las
163
:70
:?1
J72
•73
174
: 75
•78
:??
•78
:?9
•80
;ei
:82
Total Phosphorus
Total Org-snio P
Parfcdata Otdaiiic P
Dissolved Organic P
Orthpphpsphate P
D»io!ved Inoiganio P
Hittoger.BenlhioFltix
Phojphorot BantWo Flux
Benthic Algae Biorrsa^
BentNc Algae Light Limit
BenlNc Algae Nutitent Limit
Benlhk Algae N Cell Quota
Benthk-.4l9a«F Cell Quota
Benthio Algae Chloiophyil
Benthio Algae Cell N Chi
BenthicAI0aeOIIPl7hl
Total Detriial Carbon
Re-Mdencalime
Adyective Flow
Fl&w li-tlo Segment
Flow Out ot Segment
Di-,peniwe Flow
MaKsnuriiTitrMjslep
Time Step (Used]
Volume
Biofc Solid? Producricn Rate
Biofc Sow,- DiiiiiUion Rate Cow
•mg/L
rng/l.
mg/L
mg/L
mg/L
mg/L
g/m2/dai'
e/m2/da!'
gti/o,.'
•mgN/gDW
•rngP/jDW
mgA/m2
mgN/mcA
rngP/mgA
mg/L
days
m3/«c
tn3/-'M
ro3/sec
,m3Aeo
day^
days
. cubic meters
gOW/rn3-day
ft, its
W\
'BE
:w
PB
Ixl
Be!
.IRi
BP
|X:
'm
M
m
lie:
Bf!
•|Sfi
P
'w
Bfl
155
iSf:
Bfl
m
,P
'|R
'Ix:
'f»
•|5i
P
P
P
P
Bf
Be
P
P
is-
is
Bf
Bf
Bf
Bf
Ix
Be
|Sf
p
r
r
r
p
r
p
p
r
p
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), paniculate 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, WASPS; 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, Wiley-
Interscience, 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, andN. 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=Q
(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:
06 20 gb
a =
T~20
qT-20
~Db
(41)
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-Fmb-FDm=Q (42)
UPb
EPb
DPb
Substituting in the rate expressions for these fluxes (equations 17-22) and simplifying
results in the following:
= 0 (44)
17
-------
These equations can be rearranged into the quadratic form:
ai IN + bi VN + ci = ° (46)
a2 q2p + b2 qp + c2 = 0 (47)
where:
a, = 1 (48)
«2 = 1 (49)
b,=KqN-qON (50)
^2 = KqP - qop (51)
c, = _ pm { NHt+N0l Y £» \
1 r mN TV- UTTT HT/~\ 7 /iT-20 / -oT-20 ^ ^
I ^ + NH4 +N°3A kEb20 °Eb + kDb20 °Db )
C2=-pmP\
The solutions to these quadratic equations are:
(54)
-b2±Jb2 -4a2c2
qP= ^ 2 "-^ (55)
2a2
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 q^ 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 mVd, 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 NFLi, NOs, and PC>4 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
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
Benthic Algae D:C Ratio (mg Dry Weight/mg C)
Benthic Algae N:C Ratio (mg N/mg C)
Benthic Algae P:C Ratio (mg P/mg C)
Benthic Algae Chi a:C Ratio (mg Chlorophyll a / mg C)
Benthic Algae O2:C Production (mg O2/mg C)
Growth Model, 0 = Zero Order; 1 = First Order
Max Growth Rate (gD/m2/d for 0-order growth, 1/d for 1-order growth)
Temp Coefficient for Benthic Algal Growth
Carrying Capacity for First Order Model (gD/m2)
Respiration Rate (1/day)
Temperature Coefficient for Benthic Algal Respiration
Internal Nutrient Excretion Rate Constant for Benthic Algae (1/day)
Temperature Coefficient for Benthic Algal Nutrient Excretion
Death Rate (1/day)
Temperature Coefficient for Benthic Algal Death
Half Saturation Uptake Constant for Extracellular Nitrogen (mg N/L)
Half Saturation Uptake Constant for Extracellular Phosphorus (mg P/L)
Inorganic Carbon Half-Saturation Constant (not implemented) (moles/L)
LIGHT OPTION, 1=Half saturation, 2=SMITH, 3= STEELE
Light Constant for growth (langleys/day)
Benthic Algae ammonia preference (mg N/L)
Minimum Cell Quota of Internal Nitrogen for Growth (mgN/gDW)
Minimum Cell Quota of Internal Phosphorus for Growth (mgP/gDW)
Maximum Nitrogen Uptake Rate for Benthic Algae (mgN/gDW-day)
Maximum Phosphorus Uptake Rate for Benthic Algae (mgP/gDW-day)
Half Saturation Uptake Constant for Intracellular Nitrogen (mgN/gDW)
Half Saturation Uptake Constant for Intracellular Phosphorus (mgP/gDW)
2.5
0.18
0.025
0.025
2.69
0
30
1.07
0
0.1
1.07
0.09
1.07
0.05
1.07
0.1
0.04
0
2
135
0.025
7.2
1
720
50
9
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.
1704
16M
1500
140«
13SO
1200
1100
1000
«2
Figure 8 WASP7 Calculated Nutrient and Light Limitation
20
-------
ftuj OS
Aug 12 Hug 19
July 2004 - September 2004
ftug 26
Sup 02
Cell N quota
Call P quota
Figure 9 WASP7 Simulation of Cell Nutrient Content
Table 2 Comparison of WASP7 with analytical solutions - base test conditions
Variable
Nutrient Limitation Factor
Light Limitation Factor
Total Biomass, mgA/m
Cell Nitrogen, mgN/mgA
Cell Phosphorus, mgP/mgA
Analytical
Solution
0.9382
0.9568
1795
18.68
1.619
WASP7
Solution
0.9382
0.9568
1794
18.68
1.619
Relative
Error
0.0000
0.0001
-0.0005
0.0001
0.0000
Table 3 Comparison of WASP7 with analytical solutions - low temperature & light
Variable
Nutrient Limitation Factor
Light Limitation Factor
Total Biomass, mgA/m
Cell Nitrogen, mgN/mgA
Cell Phosphorus, mgP/mgA
Analytical
Solution
0.9659
0.6351
1227
33.34
2.932
WASP7
Solution
0.9659
0.6354
1226
33.31
2.930
Relative
Error
0.0000
0.0005
-0.0010
-0.0010
-0.0007
Table 4 Comparison of WASP7 with analytical solutions - high temperature & light
Variable
Nutrient Limitation Factor
Light Limitation Factor
Total Biomass, mgA/m
Cell Nitrogen, mgN/mgA
Cell Phosphorus, mgP/mgA
Analytical
Solution
0.9064
0.9801
1777
12.65
1.069
WASP7
Solution
0.9065
0.9801
1776
12.65
1.069
Relative
Error
0.0001
0.0000
-0.0003
0.0004
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 ug/L, 1.2
ug/L, and 0.3 ug/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
Nutrient Limitation Factor
Light Limitation Factor
Total Biomass, mgA/m2
Cell Nitrogen, mgN/mgA
Cell Phosphorus, mgP/mgA
Analytical
Solution
0.3541
0.9568
678
2.14
0.155
WASP7
Solution
0.3545
0.9568
679
2.14
0.155
Relative
Error
0.0012
0.0001
0.0005
0.0008
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
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Benthic Algae D:C Ratio (mg Dry Weight/mg C)
Benthic Algae N:C Ratio (mg N/mg C)
Benthic Algae P:C Ratio (mg P/mg C)
Benthic Algae Chi a:C Ratio (mg Chlorophyll a / mg C)
Benthic Algae O2:C Production (mg O2/mg C)
Growth Model, 0 = Zero Order; 1 = First Order
Max Growth Rate (gD/m2/d for 0-order growth, 1/d for 1-order growth)
Temp Coefficient for Benthic Algal Growth
Carrying Capacity for First Order Model (gD/m2)
Respiration Rate (1/day)
Temperature Coefficient for Benthic Algal Respiration
Internal Nutrient Excretion Rate Constant for Benthic Algae (1/day)
Temperature Coefficient for Benthic Algal Nutrient Excretion
Death Rate (1/day)
Temperature Coefficient for Benthic Algal Death
2.5
0.18
0.025
0.025
2.69
0
9
1.07
0
0.3
1.07
0.09
1.07
0.01
1.07
22
-------
16
17
18
19
20
21
22
23
24
25
26
27
Half Saturation Uptake Constant for Extracellular Nitrogen (mg N/L)
Half Saturation Uptake Constant for Extracellular Phosphorus (mg P/L)
Inorganic Carbon Half-Saturation Constant (not implemented) (moles/L)
LIGHT OPTION, 1=Half saturation, 2=SMITH, 3= STEELE
Light Constant for growth (langleys/day)
Benthic Algae ammonia preference (mg N/L)
Minimum Cell Quota of Internal Nitrogen for Growth (mgN/gDW)
Minimum Cell Quota of Internal Phosphorus for Growth (mgP/gDW)
Maximum Nitrogen Uptake Rate for Benthic Algae (mgN/gDW-day)
Maximum Phosphorus Uptake Rate for Benthic Algae (mgP/gDW-day)
Half Saturation Uptake Constant for Intracellular Nitrogen (mgN/gDW)
Half Saturation Uptake Constant for Intracellular Phosphorus (mgP/gDW)
0.02
0.001
0
2
100
0.025
7.2
1
720
50
9
1.3
Table 7 Comparison of WASP7 with analytical solutions - alternate rate constants
Variable
Nutrient Limitation Factor
Light Limitation Factor
Total Biomass, mgA/m
Cell Nitrogen, mgN/mgA
Cell Phosphorus, mgP/mgA
Analytical
Solution
0.9582
0.9756
271
23.82
2.390
WASP7
Solution
0.9582
0.9756
271
23.83
2.391
Relative
Error
0.0001
0.0000
0.0003
0.0005
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 mVsec, giving a
hydraulic residence time of 83 minutes per segment. Upstream boundary concentrations
for NH4, NOs, and PC>4 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
-------
Peritest
D
27
25
24
23
22
21
20
19
Tli'i
agrees C Ly/
— ^
^-^^^
/
/
, /
.' ^-^
__
., — "~
"^
S •
""-x^
\
"X^
^••s^
0:(0 Thu MM Thn 12:00 Thn IBM Fii 0
July 2004 - August 2004
jay
2000
1500
woo
508
0
0:00
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 1 1 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.
Crmmk
- ttmmmli 4 fmtmmmmt 2)
180
110
140
120
100
10
so
40
20
0 -f
0
10
15
20
25
30
j—"Bat Alcpe (mgAftnZ} • BotAIg (mgA/in2| data
Figure 11 QUAL2K Periphyton Biomass Diel Results
24
-------
Peritest Creek.
150
MO
130
120
110
11)0
"10
rim
~ — — — -^^_
_— — '
— ,
— ~~~
^
"" — "" — ^-^^
0:(l) Thu KM Thn 12:00 Thn IBM Fii 0
August 2004
ffi JUpui
Figure 12 WASP7 Periphyton Biomass Diel Results
Pmntmmt Greek
- Msssli 4 {&/emettt 2)
30 -
21 -
20 -
15 -
10 -
5 -
Q_
---~~~~~~^~
~— — — .
^^^!s™*SSss«(™sssiaaaaasiss^
^-— — — "
0 5 10 15 20 25 31
— Int N (mgNAngA) hit P (miP/mgA)
Figure 13 QUAL2K Cell Nutrient Diel Results
Pel itest Creek.
Figure 14 WASP7 Cell Nutrient Diel Results
' -II N,
Cull P,
25
-------
10 1
9
8
7
6
5
4
3
2 -
1
0
Peritest Creek (S/5/2OO4)
- Reach 4 (element 2)
-DO|rng'L| • DO(mg'L| data DOsat Irng.LJ
25
Figure 15 QUAL2K Diel Dissolved Oxygen Results
8
6
4
2
0
Tim
^ ••
W-M Thu 0«:00 Thu 12:00 Thu 1«:00 Fil 0
August 2004
id, ™ilL
n
Figure 16 WASP7 Diel Dissolved Oxygen Results
26
------- |