EPA Doc #EPA/600/R-19/241
EPA Office of Research and Development
EPA Regions 6 and 10
December 2019
Literature Review on Nutrient-Related
Rates, Constants, and Kinetics Formulations
in Surface Water Quality Modeling
U.S. Environmental Protection Agency
Office of Research and Development
Regions 6 and 10
December 2019
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Literature Review on Nutrient-Related Rates, Constants, and Kinetics Formulations
in Surface Water Quality Modeling
U.S. Environmental Protection Agency
Ben Cope
EPA Region 10
Seattle, Washington
Dr. Taimur Shaikh
EPA Region 6
Dallas, Texas
Rajbir Parmar, Project Officer
Office of Research and Development
Center for Environmental Measurement and Modeling
Athens, Georgia
The Cadmus Group
in collaboration with
HDR, Inc.
AQUA TERRA Consultants
(A Division of RESPEC Consulting and Services)
Dr. Steven Chapra, Tufts University
Dr. James Martin, Mississippi State University
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Contents
1. Introduction 1
2. Overview of Recent Developments in Rates, Constants, and Kinetic Formulations 3
2.1 WASP 3
2.2 CE-QUAL-W2 11
2.3 HSPF 16
2.4 QUAL2K and QUAL2Kw 23
3. Methodology for Identifying Relevant Literature 26
4. Summary of Available Information 29
4.1 WASP 29
Summary of Sources 29
Summary Statistics for Rates and Constants 38
Calibration Data and Approaches 45
4.2 CE-QUAL-W2 47
Summary of Sources 47
Summary Statistics for Rates and Constants 55
Calibration Data and Approaches 59
4.3 HSPF 60
Summary of Sources 60
Summary Statistics for Rates and Constants 66
Calibration Data and Approaches 72
4.4 QUAL2K and QUAL2Kw 72
Summary of Sources 72
Summary Statistics for Rates and Constants 78
Calibration Data and Approaches 85
5. Variation in Model Coefficients 85
6. Conclusions 86
7. Future Research Opportunities 90
8. References 93
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Acknowledgements
The project team is grateful for input on draft documents and/or supporting data tables by the following
individuals:
Courtesy review of preliminary draft document:
Kyle Flynn, Montana Dept. of Environmental Quality
Greg Pelletier, Washington Dept. of Ecology
Nuri Mathieu, Washington Dept. of Ecology
Jon Butcher, Tetra Tech
Steve Whitlock, EPA
EPA internal peer review:
Chris Knightes, EPA
Tim Wool, EPA
External peer review:
Kyle Flynn, CDM Smith
Scott Wells, Portland State University
Jon Butcher, Tetra Tech
Organizational Support
This report was developed under the direction of Region 6, Region 10, and the Office of Research and
Development (ORD) as a Regional Applied Research Effort (RARE project). ORD managed the EPA
contract with the Cadmus Group (Contract EP-C-11-039 [STREAMS II]).
Disclaimer
This document provides guidance to those who develop, evaluate, and apply environmental models. It
does not impose legally binding requirements; depending on the circumstances, it may not apply to a
situation. The U.S. Environmental Protection Agency (EPA) retains the discretion to adopt, on a case-by-
case basis, approaches that differ from this guidance.
This document has been reviewed by the U.S. Environmental Protection Agency, Office of Research and
Development, and approved for publication.
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1. Introduction
The 1985 Second Edition of Rates, Constants, and Kinetics Formulations in Surface Water Quality
Modeling (Bowie et al. 1985; the Rates Manual) is a widely used source of information on kinetic
formulations and associated rate constants and coefficients used in surface water quality modeling. One
of the most common applications of this type of modeling is for Total Maximum Daily Load (TMDL)
assessments conducted in support of the Clean Water Act. Advancements in water quality modeling
over the last three decades have resulted in new and updated formulations not documented in the 1985
Rates Manual. Recent modeling and water quality process studies also have provided additional
information on suitable values for rate constants and coefficients for model applications. Accordingly,
this report presents the findings of a literature review reflecting the latest information on surface water
quality modeling and rates, constants and kinetics for modeling related to several of the most commonly
used for water quality management planning and development of TMDLs. It is the first step in a more
comprehensive compilation of content for updating the entire 1985 Rates Manual.
Toward this end, EPA contracted with The Cadmus Group, Inc., in collaboration with HDR, Inc. (HDR),
AQUA TERRA Consultants, Dr. Steven Chapra of Tufts University, and Dr. James Martin of Mississippi
State University (hereafter referred to as "project team") to compile and review literature and model
rates, constants, and kinetics relevant to four water-quality models identified in the project scope of
work: the Water Quality Analysis Simulation Program (WASP; Wool et al., 2003; Ambrose and Wool,
2017); CE-QUAL-W2 (Cole and Wells, 2018); Hydrologic Simulation Program-FORTRAN (HSPF, Bicknell et
al., 2014); and the modernized stream and river quality model QUAL2K (Chapra et al., 2012) and the
closely related QUAL2Kw (Pelletier and Chapra, 2008). The literature review consists primarily of
evaluating model documentation and model application studies and will be supplemented by a more
widespread review of laboratory and field studies in the future.
This report summarizes the project team's literature compilation and review efforts. Included is a
description of recent developments in dissolved oxygen, nutrient, and algae modeling in WASP, CE-
QUAL-W2, HSPF, and QUAL2K/QUAL2Kw. These groups of parameters will be hereafter referred to as
Group 1 parameters given that they are the first part of a planned multi-phase effort to gather rates,
constants, and kinetic formulations for all the topics in the 1985 rates manual (Bowie et al., 1985). These
Group 1 parameters were defined in the project scope of work. Also included in this report is a
discussion of the literature selection and review steps that were taken to assess the applicability and
thoroughness of model reports identified and considered. Future data review and compilation efforts
may focus on other parameter groups for state-variables such as pH and alkalinity, temperature,
zooplankton, macrophytes, and bacteria.
It is important to note that the tables of model parameter values developed for this effort do not
include empirical data from experimental or laboratory studies. In this regard, the report and the tables
that included herein are not an exhaustive presentation of all possible values, but rather describe
coefficients that were used and calibrated in more recent well-documented model applications. The
project team determined that it was not feasible within the scope of this work to pursue collection of
updated field or laboratory data on rates and constants for water quality processes that are simulated in
each model. Discussion of challenges associated with tabulating empirical data, as well as future work
that could be conducted in tabulating those values, is included in Section 6 of this report.
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The information presented in this report describes an assessment of the body of literature related to the
application of the four models listed above. The report includes information on the geographic and
environmental ranges of published modeling efforts as well as any gaps, in terms of location, modeled
constituents, and environmental conditions, in the application of each model. Each model is also
described with a focus on updates since 1985 and the results of the literature review related to each
model. The second objective of this project was to review and compile rate, constant, and kinetic (RCK)
parameters from relevant literature sources and tabulate this information for use by model
practitioners.
This document and the accompanying parameter value tables do not constitute a complete replacement
for sections of the 1985 Rates Manual related to the Group 1 parameters noted above, which includes
more detail on species-specific algal rates as well as related nutrient parameters. It is important to note
that there are fundamental similarities among the four models selected for this effort. Specifically, many
of the post-1985 model enhancements to QUAL2K, CE-QUAL-W2, and WASP correspond to formulations
that were already incorporated into HSPF in 1985.
The rate tables provided in this document contain study-specific metadata for each model application
including: study location, geographic applicability, environmental conditions, purpose/model use,
calibration period, and input data sampling plan. Details on model updates since the 1985 Rates Manual,
as well as a discussion of available literature, potential data gaps, and limitations related to model
application are included within the report.
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2. Overview of Recent Developments in Rates, Constants, and Kinetic Formulations
Water quality models covered in this document along with the most recent version consulted and web
page address as of 10/8/2019 are summarized in Table 1.
Table 1. Models Summarized in this Document
Model
Version
Web Page
WASP (Water Quality Analysis
Simulation Program)
8.32 (4/2/2019)
https://www.epa.gov/ceam/water-qualitv-
analvsis-simulation-program-wasp
CE-QUAL-W2
4.2 (9/20/2019)
http://www.cee.pdx.edu/w2/
HSPF (Hydrologic Simulation
Program - FORTRAN)
12.5 (4/8/2019)
https://www.epa.gov/ceam/hvdrological-
simulation-program-fortran-hspf and
https://www.epa.gov/ceam/basins-download-
and-installation
QUAL2K
2.12bl (5/5/2016)
http://www.aual2k.com/
QUAL2KW
6 (9/22/2016)
https://ecologv.wa.gov/Research-Data/Data-
resources/Models-spreadsheets/Modeling-the-
environment/Models-tools-for-TMDLs
2.1 WASP
Model Background
The Water Quality Analysis Simulation Program, WASP (Wool et al., 2003; Ambrose and Wool, 2017),
has been used regularly both nationally and internationally since its development in the early 1980's.
WASP is a generalized modeling framework based on the finite-volume concept for quantifying fate and
transport of water quality variables in surface waters. While WASP has been applied to address a myriad
of environmental problems, including pathogens, dissolved oxygen, eutrophication, and toxic
contaminants, the focus of this project is on eutrophication and dissolved oxygen. WASP is capable of
being applied in one, two or three dimensions to virtually any type of waterbody. Initially, WASP
depended on the user to specify the model geometry and advective and dispersive transport, usually by
trial-and-error calibration to observed spatial and temporal profiles of temperature and/or salinity, but
with the latest releases of the code, WASP can use information from hydrodynamic models such as
DYNHYD5 (Ambrose et al., 1993), RIVMOD (Hossenipour and Martin, 1990), DYRESM (Imberger and
Patterson, 1981), EFDC (Hamrick, 1996), and SWMM (Rossman, 2015). This has significantly expanded
WASP's capabilities and applications to more complex riverine and estuarine systems.
WASP is EPA-supported and has a long history of development and application, beginning with its
release (DiToro et al., 1983) and continuing with its latest version, WASP8.32 (U.S. EPA, 2019;
https://www.epa.gov/ceam/water-quality-analysis-simulation-program-wasp). As constructed at the
time that the Rates Manual was published in 1985 (Bowie et al., 1985), the eutrophication kinetics
present in WASP were based on the Potomac Estuary Model (PEM) developed by HydroQual (Thomann
and Fitzpatrick, 1982). The following state variables were included in WASP at that time:
• Salinity;
• Phytoplankton biomass (two groups) as chlorophyll a or carbon;
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• Dissolved and particulate inorganic phosphorus;
• Detrital dissolved and particulate organic phosphorus;
• Ammonia nitrogen;
• Nitrate nitrogen;
• Detrital total organic nitrogen;
• Carbonaceous biochemical oxygen demand (CBOD);
• Dissolved oxygen; and
• Suspended solids.
Fluxes of sediment oxygen demand and nutrients (inorganic phosphorus, ammonia nitrogen, and nitrate
nitrogen) were specified as "boundary conditions" across the sediment-water interface.
Recent Model Additions
The most recent version of WASP has been expanded and includes the following state variables in
addition to those listed above:
• Up to five phytoplankton groups (e.g., diatoms, greens, cyanobacteria);
• Up to three macrophyte/benthic algae groups;
• Detrital and dissolved organic nitrogen;
• Detrital and dissolved organic phosphorus;
• Detrital organic carbon and five types of CBOD;
• Biogenic and dissolved silica;
• Alkalinity/pH;
• Up to 10 inorganic solids;
• Water Temperature; and
• Predictive Light Module.
Algal System Modeling
Basic algal system modeling in WASP follows formulations that were already well established at the time
of the 1985 Rates manual in which the specific algal growth rate is a function of the maximum 20 °C
growth rate at optimal light and nutrient concentrations. The maximum growth rate is modified by
multiplicative factors describing limits on growth imposed by temperature, light availability, and
concentrations of dissolved inorganic phosphorus and dissolved inorganic nitrogen. These equations are
not repeated here.
With the expansion of WASP to allow the user to model up to three phytoplankton groups, the user now
also has the option to specify an alternative approach to model the effects of temperature on algal
growth. Rather than just be limited to the traditional Arrhenius or "theta" (0) model (Equation 2-1), the
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user may also specify a set of temperature optimum curves (Equations 2-2a and 2-2b) in which the
growth rate increases with temperature up to an optimum temperature and then decreases with higher
temperatures.
fl(T) — H20 degC ' ^
T-20
Where:
H(T)
T
= algal growth rate at the ambient temperature
= temperature
H2o°c = algal growth rate at 20 °C
9 = temperature coefficient
Where:
KT) = Ht,
opt
e-/31(T-Topt)2
KT) = liTopt ¦ e foVopt T)2
TTopt
2-1
2-2a
2-2b
H(T) = the algal growth rate at the ambient temperature
Topt = optimal temperature
Pi, P2 = parameters that determine the shape of the relationship of growth to temperature
below and above the optimal temperature, respectively
With the modification of WASP to include additional phytoplankton species, rates and constants
relevant to each phytoplankton group or species modeled are required for the following:
• Algal growth and respiration rate as a function of temperature and saturating light intensities;
• Rates of phytoplankton grazing by zooplankton;
• Algal settling rates for each algal group simulated;
• Michaelis-Menten constants for algal growth limitation by inorganic nitrogen, phosphorus, and
silica; and
• Cell composition (stoichiometry) with respect to carbon, nitrogen, phosphorus, chlorophyll and,
for diatoms, silica.
The most recent version of WASP also includes include the following new processes and kinetic
formulations that impact Group 1 parameters:
• Sediment diagenesis nutrient flux model. Based on a model developed by DiToro and Fitzpatrick
(1993) and DiToro (2001), and implemented into WASP by Martin et al. (2012), the sediment
diagenesis nutrient flux model (SFM) computes the mass balance of organic and inorganic
nutrients and oxygen between the water column and the sediment bed. The SFM accounts for
the deposition of organic matter (phytoplankton and particulate organic matter [carbon,
nitrogen, phosphorus, and biogenic silica]) from the water column to the sediment bed, the
diagenesis or decomposition of this organic matter to its end-products (inorganic nitrogen,
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phosphorus, and silica, and oxygen demanding materials), and the effects of sediment
conditions on oxygen demand and nutrient fluxes to the overlying water column.
• A benthic algal model (Martin et al., 2006) that can simulate the inter-relationships between
temperature, light, nutrients, and benthic algae or periphyton. In many shallow streams and
rivers, it is the benthic algae or periphyton that are often of greater ecological and
environmental importance than water column or floating phytoplankton.
The new state variables for particulate and dissolved organic nitrogen (replacing detrital total organic
nitrogen) require rates and constants for:
• The hydrolysis of particulate organic nitrogen to dissolved organic nitrogen;
• The mineralization of dissolved organic nitrogen to ammonia nitrogen;
• The settling of particulate organic nitrogen; and
• The partitioning of phytoplankton respiration and death to particulate organic nitrogen,
dissolved organic nitrogen and ammonia nitrogen.
As a consequence of adding detrital organic carbon to the model, the user must provide hydrolysis base
rates (Khyd) at 20 °C and temperature correction coefficients (9's) for the conversion of detrital
(particulate) organic matter to dissolved organic carbon to CBOD, and the fraction of detrital organic
carbon that goes to each of the three classes of CBOD because of hydrolysis of the detrital organic
carbon.
The addition of silica state variables to the model, including the uptake and utilization of silica by diatom
phytoplankton, requires rates and constants for the dissolution of biogenic silica to dissolved silica, the
settling of biogenic silica, and the specification of the carbon to silica ratio for diatoms.
Sediment Flux Model
This section describes the governing equations for a sediment flux model (SFM) that was recently
incorporated into WASP. The SFM is similar to the sediment diagenesis or sediment flux models used in
other water quality models including QUAL2K and CE-QUAL-W2.
The SFM includes state variables for labile (Gi), refractory (G2), and relatively inert (G3) particulate
organic carbon (C), nitrogen (N), and phosphorus (P), particulate or biogenic silica (BSi), inorganic
nutrients (ammonia [NH3], nitrate [N03], phosphorus [P04], silica [Si], hydrogen sulfide [H2S], and
methane [CH4]). The rates and constants that need to be specified are related to two sets of processes
that occur in the sediment bed: diagenesis (or decomposition) of the particulate organic matter that is
delivered to the sediment bed, and the reactions that occur in the aerobic and anaerobic layers in the
sediment, and the transfer that occurs between these layers due to particulate and dissolved mixing.
The general form of the diagenesis mass balance equation follows (in implicit form) Equation 2-3,
,t+At
Gi
IY /"t+At
^diagi^Gi
2-3
Where:
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Cg' = concentration of G, (labile, refractory [relatively inert] carbon, nitrogen, or
phosphorus) in the sediment bed at time t
CGit+flt = concentration of G, (labile and refractory carbon, nitrogen, or phosphorus) in the
sediment bed at time t+At
At = time step of the water quality model
Jpomi = flux of Gifrom the overlying water column to the sediment bed
Hsed = depth of the active layer in the sediment bed
Wbur = net burial or sedimentation
Kdiagi = diagenesis rate constant for G,
The equations that govern the reactions that occur in the aerobic (layer 1) and anaerobic (layer 2) layers
of the sediment, and the particulate and dissolved mixing between the two layers are provided below
from the WASP user manual. Since the aerobic layer is quite thin, Hi =1 mm (10~3 m), and the surface
mass transfer coefficient is on the order of s « 0.1 m/day, the residence in the layer is Hi/s = 10"2 days.
Because of the depth of the upper layer, it can be assumed to be at steady state without any loss in
accuracy, and is expressed as follows (Equation 2-4):
Aerobic Layer (layer 1):
o = Mfdi.cnM - cJD + 2lT1 ~~ T LT1
i/l + il j_ pt+Atu-r /'t+At/iV I Ll~\
+Jt\ + L rz "1 Ln ("t + "i J 2-l
The anaerobic layer mass balance time-dependent implicit formula using the Euler method is in
Equation 2-5:
Anaerobic Layer (layer 2):
TT LT2 LT2 _ ( r „t+M , „t+At^
2 At ~ 12 v^ T2 "/pi6n )
is (f rt ~ At: f r>t+At\ „ rt+At I ,. p-t+&t
IKL12\fd2LrZ JdlLTl } k?lT2 + t"2LTl
, , /"t+At i it+At i /"t+At ij — i u +
^0)2LT2 +JT2 + LT1 "1 ^ LT2 k"2+"l) 2-C
Where:
s = surface transfer rate; SOD/[O2(0)], where SOD = sediment oxygen demand (SOD) rate
and O2(0) is the overlying water concentration
fdi = fraction dissolved in layer 1
fd2 = fraction dissolved in layer 2
fpi = fraction particulate in layer 1
fp2 = fraction particulate in layer 2
Cnt+At = total concentration in layer 1 at time t+At
CT2t+At = total concentration in layer 2 at time t+At
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Cn' = total concentration in layer 2 at time t
Cdot+At = concentration in overlying water column
K[_i2 = mass transfer coefficient via diffusion
CO12 = particle mixing coefficient between layers 1 and 2
C02 = sedimentation velocity for layer 2
Jnt+At = source term for total chemical in layer 1 at time t+At
JT2t+At = source term for total chemical in layer 2 at time t+At
K12 = square of reaction velocity in layer 1
k2 = reaction velocity in layer 2
Hi" = time derivative for H in layer 1 (not used; constant depth assumed)
Hi+ = time derivative for H in layer 1 (not used; constant depth assumed)
Hi = time derivative for H in layer 1 (not used; constant depth assumed)
H2 = time derivative for H in layer 2 (not used; constant depth assumed)
H2 = thickness of layer 2
At = time step
The fraction dissolved and particulate in the two layers are computed from Equations 2-6a through 2-6d:
Layer 1:
fd 1 = —"— 2-6a
JCl'1 1+7T C15i
/ = nciSl 2-6b
JP'1 1+TTciSi
Layer 2:
l + TC2^2
Where:
fd 2= 2-6c
Ja'z l+nC2S2
nC2S2
JP'Z
7tCi = partition coefficient for total chemical in layer 1
7iC2 = partition coefficient for total chemical in layer 2
51 = solids concentration in layer 1
52 = solids concentration in layer 2
(Note: a more complete description of the SFM may be found in DiToro [2001] or Martin et al. [2006].)
The rates required by the SFM include: diagenesis or decay rates and temperature coefficients for
particulate labile and refractory C, N, P, and BSi; freshwater and saltwater nitrification and
denitrification reaction velocities; oxidation velocities for H2S and CH4; partition coefficients for NH3,
P04, Si and H2S; and particulate and dissolved mixing coefficients. Note: the term "reaction velocities" is
used for nitrification, denitrification, and oxidation because these values are formulated in the model as
a product of a reaction rate times a depth, therefore having units of m/day.
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Benthic Algal Model
The benthic algal or periphyton model includes state variables for bottom algal biomass (dry weight;
DW) and internal cell nitrogen and phosphorus. The kinetic representations for benthic algae in WASP
(beginning in version 7) were adopted from the QUAL2K model (Chapra, 2005). They differ from the
representation of phytoplankton in two primary ways: (1) the benthic algal model uses an algal growth
rate that is dependent on the intracellular nutrient content, following the Droop formulation (Droop,
1973), rather than external nutrients, and (2) space limitation effects are incorporated into bottom algae
photosynthesis. As a result, there are a few more model constants or coefficients that are used to model
the intracellular nutrient dynamics.
Benthic algal simulation was not covered in detail in the 1985 Rates Manual, so additional details are
provided herein for WASP and the other three models discussed in this review. Bottom algae biomass,
ab, is represented as dry weight biomass (D) per unit area of available substrate. Bottom algal biomass
increases due to photosynthesis and decreases with respiration and death, as calculated in Equation 2-7:
Sab = (Fob ~ Fnb ~ Fob) Ab 2-7
where Sab is the total source/sink of algal biomass (g D/d [day]), FGb is the photosynthesis rate (g D/m2-d
[per day]), FRb is the respiration loss rate (gD/m2-d), FDb is the death rate (g D/m2-d), and Ab is the bottom
substrate surface area (m2).
Two options are available to represent the bottom algal photosynthesis rate, FGb [gD/m2-d], The first
option, using Equation 2-8, is a temperature-corrected, zero-order maximum rate attenuated by
nutrient and light limitation (simplified from Rutherford et al., 2000):
FGb = Fg/)20 (pTb (pNb (pLb 2"8
where FGb2ois t
he maximum photosynthesis rate at 20 °C [gD/m2-d], cpibisthe photosynthesis temperature correction
factor [dimensionless], cpNb is the bottom algae nutrient attenuation factor [dimensionless number
between 0 and 1], and tpLb is the bottom algae light attenuation coefficient [dimensionless number
between 0 and 1],
The second option, using Equation 2-9, uses a first-order, temperature-corrected rate constant,
attenuated by nutrient, light, and space limitation:
FGb = kGb20 (pTb fNb fib (psb Ob 2"9
where kGb2oisthe maximum photosynthesis rate constant at 20 °C [d1], cpsbisthe bottom algae space
attenuation coefficient [dimensionless number between 0 and 1], and other terms are as defined above.
Space limitation of the first-order growth rate is modeled as a logistic function, using Equation 2-10:
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Nutrient limitation of the photosynthesis rate is dependent on intracellular nutrient concentrations
using a formulation shown in Equation 2-11, which was originally developed by Droop (1973):
2-11
where qN and qP are cell quotas of nitrogen [mg N/gD] and phosphorus [mg P/gD], respectively, and q0N
and q0p are the minimum cell quotas of nitrogen [mg N/gD] and phosphorus [mg P/gD], respectively. The
minimum cell quotas are the levels of intracellular nutrient at which growth ceases.
Intracellular nutrient (nitrogen or phosphorus) concentrations, or cell quotas, represent the ratios of the
intracellular nutrient to the bottom algal dry weight, and are calculated using Equations 2-12a and 2-
12b, respectively:
qN = 103 ^ 2-12a
ab
qP = 103 — 2-12b
ab
where qN and qP are cell quotas [mg N/gD or mg P/gD], INb is intracellular nitrogen concentration [g
N/m2], IPb is intracellular phosphorus concentration [g P/m2], and 103 is a units conversion factor [mg/g].
The total source/sink terms for intracellular nitrogen (Equation 2-13a) and phosphorus (Equation 2-13b)
in bottom algal cells [g/d] are controlled by uptake, excretion, and death:
SbN = (FuNb ~ pENb ~ PDNb) * Ab 2-13a
$bP = (FuPb ~ ^EPb ~ pDPb) * Ab 2-13b
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 [g N/m2-d and g P/m2-d], and FDNb and FDpb are
loss rates from bottom algae death [g N/m2-d and g P/m2-d],
The N (Equation 2-14a) and P (Equation 2-14b) uptake rates depend on both external and intracellular
nutrient concentrations as in Rhee (1973):
P = in-3 „ f NH4+N03 \ f KaN \
UNh PmN U5Wb+ NH4 + NO J \KqN+ (qN- q0N}) ~b
Fm = 10-= PmF a-
2-14a
2-14b
where NH4, N03, and P04 are external water concentrations of ammonium N, nitrate N, and phosphate P
[mg N/L and mg P/L], pmN and pmP are the maximum uptake rates for nitrogen and phosphorus [mg
N/g D-d and mg P/gD-d], KsNb and KsPb are half-saturation constants for external nitrogen and
phosphorus [mg N/L and mg P/L], KqN and KqP are half-saturation constants for intracellular nitrogen and
phosphorus [mg N/gD and mg P/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.
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The internal N (Equation 2-15a) and P (Equation 2-15b) excretion rates are represented using first-order,
temperature-corrected kinetics:
Eb20 uEb
Eb20 °Eb
2-15b
2-15a
where kEb2o is the bottom algae cell excretion rate constant at 20 °C [d1] and 0Eb is the bottom algae
excretion temperature coefficient [dimensionless].
The internal N (Equation 2-16a) and P (Equation 2-16b) loss rates from benthic algal death are the
product of the algal death rate, FDb [gD/m2-d], and the cell nutrient quotas:
where 10"3 is a units conversion factor [g/mg],
WASP8 added capability to simulate floating surface and subsurface and submersed macroalgae, along
with forms of macrophytes that obtain nutrients from the water column rather than from roots in the
sediment. The kinetic formulations are similar to those for periphyton.
The additional rates and constants that need to be specified include:
• Benthic algal initial stoichiometry (i.e., DW:C, C:N, C:P and C:Chl-a ratios);
• Benthic algal growth, death, and respiration rates, and corresponding temperature coefficients;
• Saturating light intensity;
• Minimum cell quotas for internal N and P for cell growth;
• Maximum uptake rates for N and P;
• Half saturation uptake constants for intracellular and extracellular N and P; and
• Carrying capacity or maximum density for bottom biomass.
2.2 CE-QUAL-W2
CE-QUAL-W2 is a two-dimensional, laterally averaged hydrodynamic and water quality model that
describes vertical and longitudinal distributions of hydrodynamics, heat, and selected biological and
chemical materials in a water body through time. It was one of the first water quality models in which
water quality was coupled with multi-dimensional hydrodynamics.
CE-QUAL-W2 has undergone continuous development since the early 1970s, first largely by the U.S.
Army Corps of Engineers (USACE), and over the last several years by Dr. Scott Wells and others at
Portland State University. CE-QUAL-W2 Version 1.0 was released in 1986 (Environmental and Hydraulics
Laboratory, 1986) and its first application to De Gray Reservoir (Martin, 1988). Version 2 of the model
was released in 1995 (Cole and Buchak, 1995) and the latest official release is Version 4.1 released
October 2017 (Cole and Wells, 2018). The model has been widely applied throughout the world.
pDNb ~ pDb Rn 10 3
2-16a
pDPb ~ ^Db Qp 10 3
2-16b
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Portland State University (http://www.ce.pdx.edu/w2/) reports over 2,300 documented applications
worldwide, including 935 applications in the United States and Canada.
Version 1.0 of CE-QUAL-W2 (Martin, 1988) allowed for simulation of the interactive dynamics of physical
factors (such as flow and temperature regimes), chemical factors (such as nutrients), and an algal
assemblage. The model structure allowed for the simulation of up to 20 water quality constituents in
addition to temperature, density, and circulation patterns. Hydrodynamics and water temperatures
could be simulated independently of, or in conjunction with, other water quality constituents.
Since its initial release there have been substantial improvements and modifications to the original
code. Many of the modifications were related to the solution scheme, physical computations (e.g., the
model can now be applied to riverine systems), addition of particle tracking, and the graphical user
interface. However, there have been several updates and improvements to the water quality kinetics as
well. The state variables in the latest release of CE-QUAL-W2 (Version 4.1; Cole and Wells, 2018) are
tabulated in Table 2 in comparison to those from Version 1.0. In addition, model output includes over 60
derived variables (e.g., pH, TOC, DOC, TON, TOP, DOP; Cole and Wells, 2011) for comparison with
observed data. The most notable improvements in the kinetics over Version 1.0 were the addition of
multiple inorganic solids groups, dissolved inorganic and particulate biogenic silica, photodegradation of
generic constituents, N2 as a state variable to compute Total Dissolved Gas (TDG), multiple groups of
algae, zooplankton, epiphytes, macrophytes, non-conservative alkalinity, a sediment diagenesis model
(Prakash et al., 2011) including bubble formation and rise in the water column, sediment consolidation,
and a variable sediment temperature, pH, and alkalinity and new state variables of metals, H2S, and CH4
in the water column and sediment (Cole and Wells, 2018).
With regards to rates and kinetics, primary producers in Version 1.0 of CE-QUAL-W2 were simulated
using a single state variable taken to represent planktonic forms (e.g., phytoplankton). In the present
version, multiple phytoplankton groups may be simulated. The latest version allows the user to select
the number and kinds of algae and additional state variables have been added for periphyton and
macrophytes. In Version 1.0, rates of change in phytoplankton biomass were computed from an optimal
growth rate that was modified by light and nutrients and from losses due to natural mortality, dark
respiration, excretion, grazing, and settling. The approach in the present version is similar, but this
version allows for variable stoichiometry (versions prior to 3.5 used fixed stoichiometric constants for
the ratios of nitrogen and phosphorus to organic matter), losses due to grazing by zooplankton (multiple
zooplankton groups are simulated), mortality and excretion to particulate organic matter (POM) rather
than detritus (labile and refractory particulate organic carbon, nitrogen, and phosphorus), and an
ammonia preference.
The kinetic formulations for periphyton or epiphyton in the current version of CE-QUAL-W2 are based
on the balance between growth, respiration, excretion, mortality, and burial. Epiphyton growth rate
(Equation 2-17) is computed by modifying a maximum growth rate affected by epiphyton biomass,
temperature, and nutrient availability:
^eg ~ Yer Yef ^min Keg max 2-17
Where:
y„ = temperature rate multiplier for rising limb of curve
yef = temperature rate multiplier for falling limb of curve
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A,min = multiplier for limiting growth factor (minimum of phosphorus, silica, nitrogen, and
epiphyton biomass)
Keg = epiphyton growth rate, sec"1
Kegmax = maximum epiphyton growth rate, sec"1
Rate multipliers for epiphyton growth are computed based upon available light, phosphorus, nitrogen,
silica, and epiphyton biomass. Epiphyton biomass is included as a surrogate for light limited epiphyton
self-shading.
The rate multiplier for light is based upon the Steele function (Equation 2-18):
i i (f+i)
A; = — e11® >
h 2-18
Where:
I = available light, watts per square meter (W-m"2)
Is = saturating light intensity at maximum photosynthetic rate, W-m"2
A,i= light limiting factor
Rate multipliers limiting epiphyton growth due to nutrient limitations are computed using the Monod
relationship (Equation 2-19):
A; = —— 2-19
1 Pi+fi
Where:
Ai= phosphorus or nitrate + ammonium concentration, g m"3
Pi = half-saturation coefficient for phosphorus or nitrate + ammonium, g m"3
The epiphyton preference for ammonium is modeled using Equation 2-20:
p — 0 0nox | kNHa 220
NH4 NH4 (KNH4+0NH4)(KNH4+0NOx) (
-------
Epiphyton excretion is evaluated in Equation 2-22 using an inverse relation to the light rate multiplier:
^ee (1 Yer Yef
eemax
2-22
Where:
Kee = epiphyton excretion rate
Keemax = maximum excretion rate constant, sec 1
^eemax
Epiphyton mortality is defined in Equation 2-23:
^ern — Yer Yef
emmax
2-23
Where:
Kem = epiphyton mortality rate
Kemmax = maximum mortality rate, sec 1
This mortality rate represents both natural and predator mortality. Epiphyton growth does not occur in
the absence of light. Epiphyton growth is not allowed to exceed the limit imposed by nutrient supply
over a given timestep. Epiphyton excretion is not allowed to exceed epiphyton growth rates.
The epiphyton burial rate represents the burial of dead epiphyton to the organic sediment
compartment. Currently, there is no sloughing of epiphyton into the water column as a function of
velocity shear. This is a function of the biomass limitation term.
The epiphyton biomass is controlled by a biomass limitation equation based on Monod kinetics. The
biomass limitation function, f, varies from 0 to 1 and is multiplied with the growth rate. This function is
defined as in Equation 2-24:
B = epiphyton areal biomass, g/m2
Kb = epiphyton areal biomass half-saturation coefficient, g/m2
The macrophyte model in CE-QUAL-W2 can represent multiple submerged species and allows nutrients
to be obtained from the water column or the sediments. If they are obtained from the sediments, the
sediments are assumed to be an infinite pool that cannot limit growth. Plants grow upwards from the
sediment through model layers. Growth upward is accomplished by moving the growth of a layer to the
layer above if the concentration in the layer is greater than a threshold concentration and the
concentration in the upper layer is less than the same threshold concentration. Macrophyte shading is
modeled by making light attenuation as a function of macrophyte concentration. The remaining kinetics
of the macrophyte model in CE-QUAL-W2 are similar to those used to represent epiphyton, except that
macrophytes are not subject to burial.
Nutrients simulated in Version 1.0 of CE-QUAL-W2 included ammonia, nitrate-nitrogen, and inorganic
phosphorus, with source terms including phytoplankton respiration, dissolved organic matter (DOM)
decay (detritus and dissolved forms, labile and refractory), and anaerobic release from sediments (a
zeroth order rate). Nutrient losses included algal uptake during growth and phosphorus settling of
fractions sorbed to iron and solids. Nitrification and denitrification were additional losses for ammonia
B+ Kb
2-24
Where:
14
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and nitrate respectively. In the present version, dissolved and particulate biogenic silica are added as
state variables. Additional loss terms for nutrients include uptake by macrophytes and epiphytes (like
phytoplankton, there may be multiple groups of each). Additional source terms include zooplankton
respiration, a 1st order sediment release (in addition to a zeroth order rate), and decay of labile and
refractory DOM, POM, and CBOD.
For dissolved oxygen in Version 1.0, sources and sinks included phytoplankton growth and respiration,
reaeration, detritus decay, DOM decay (labile and refractory), ammonia decay, mortality, and sediment
oxygen demand (zeroth order rate). In the current version, additional sources and sinks include growth
and respiration of macrophytes and epiphytes, respiration of zooplankton, and decay of sediments,
DOM (labile and refractory), POM (labile and refractory state variables), CBOD (multiple groups), and
oxidation of CH4, H2S, and reduced metals. Several new reaeration formulations have been added that
are specific to rivers, lakes and reservoirs, estuaries, and aeration over large dam spillways/gates, small
dams, and weirs. In the current version 4.1, the sediment diagenesis model is structured based on the
equations presented in Section 2.1 and is a modification of the sediment diagenesis sub-model included
as part of the CE-QUAL-ICM model (Cerco and Cole, 1994), which incorporates a mass-balance model in
bottom sediments to predict sediment oxygen demand and nutrient flux. In addition, the model includes
prediction of bubble formation and rise in the water column, which can be used in the evaluation of
oxygen injection systems (see Martin and Cole [2000] for an example application for J. Percy Priest
Reservoir, Tennessee).
Table 2. CE-QUAL-W2 Version 1 State Variables (Martin, 1988) compared to Version 4.1 (Cole and
Wells, 2018)
Version 1.0 Variables
Version 4.1 Variables
Water Temperature (including ice)
Water Temperature (including ice)
Conservative tracer
Any number of generic constituents defined by a 0 and/or
a 1st order decay rate and/or a settling velocity and/or an
Arrhenius temperature rate multiplier and/or photo-
degradation and/or gas transfer/volatilization that can be
used to define any number of the following: conservative
tracer, water age or hydraulics residence time, coliform
bacteria, contaminants, l\h gas (for computation of TDG).
Coliform bacteria
Total dissolved solids or salinity
Total dissolved solids or salinity
Inorganic suspended solids
Inorganic suspended solids groups1
Dissolved inorganic carbon
Total Inorganic Carbon
Alkalinity (conservative)
Alkalinity (non-conservative)
Labile dissolved organic matter
Labile dissolved organic matter (three forms: N,P,C)
Refractory dissolved organic matter
Refractory dissolved organic matter (three forms: N,P,C)
Phytoplankton
Phytoplankton groups1
15
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Version 1.0 Variables
Version 4.1 Variables
Detritus
Labile particulate organic matter (three forms: N,P,C)
Refractory particulate organic matter (N,P,CO)
Phosphate-phosphorus
Bioavailable phosphorus (commonly represented by
orthophosphate or soluble reactive phosphorus)
Ammonia-nitrogen
Ammonia-nitrogen
Nitrate + nitrite-nitrogen
Nitrate + nitrite-nitrogen
Dissolved oxygen
Dissolved oxygen
Organic sediments
Organic sediments
Total Iron
Total iron
No further state variables in version 1.0; Version 4.1
included additional variables in the next column.
CBOD groups with separate settling, N, and P defined for
each group1
Dissolved silica
Particulate biogenic silica
Zooplankton groups1
Epiphyton groups1
Macrophyte groups1
Cm, SO4, H2S, reduced and oxidized Mn and Fe
1 Arbitrary number of state variables, set by user
2.3 HSPF
The Hydrological Simulation Program-FORTRAN (HSPF; Bicknell et al., 2014) is a watershed model
developed under U.S. EPA sponsorship to simulate hydrologic and water quality processes in natural and
man-made water systems. HSPF uses information such as the records of rainfall and temperature,
computed evaporation, landscape characteristics to simulate watershed processes. The initial result of
an HSPF simulation is a time series of the quantity and quality of water transported over the land
surface and through soil zones. Runoff flow rate, sediment runoff, nutrients, pesticides, toxic chemicals,
and other water quality constituent concentrations can be predicted. The model uses these runoff and
infiltration results, coupled with stream channel information, to simulate instream flow and water
quality processes. From this information, HSPF produces a time series of water quantity and quality at
any point in the watershed.
HSPF was first released publicly in 1980 as Release No. 5 (Johanson et al., 1980) by the EPA Water
Quality Modeling Center (now the Center for Exposure Assessment Modeling). Originally, HSPF was
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designed based on the Stanford Watershed Model (SWM) developed in the early 1960s. SWM was
expanded and refined in the early 1970s into the Hydrocomp Simulation Program (HSP), which built in
nonpoint source loading and water quality simulation capabilities (Donigian and Imhoff, 2006). HSPF was
developed to integrate functions of HSP, EPA's Agricultural Runoff Management model, and EPA's
Nonpoint Source model. Throughout the 1980s, 1990s, and the 2000s, HSPF underwent a series of code
and algorithm enhancements producing a continuous succession of updated code, culminating in the
major upgrade of Version No. 12.2 in 2005 (Bicknell et al., 2005). The most recent version is 12.5,
released in 2019 as part of the BASINS 4.5 package (https://www.epa.gov/ceam/better-assessment-
science-integrating-point-and-non-point-sources-basins).
The structure of HSPF features four major "application modules": PERLND for pervious land segments,
IMPLND for impervious land segments, RCHRES for river reaches and well-mixed reservoirs, and BMP for
simulating constituent removal efficiencies associated with implementing management practices. Of
these four application modules, only one (RCHRES) falls within the topical domain (i.e., surface water
quality modeling) of EPA's Rates Manual. Some processes relevant to this project are included in HSPF
application modules other than RCHRES, but are simulated using the waterbody science contained
within RCHRES, and were included in this effort where applicable. The RCHRES module is a one-
dimensional model with completely mixed segments. It incorporates state variables for inorganic and
organic forms of N and P along with phytoplankton and periphyton biomass. The basic state variables
relevant to nutrient simulation in HSPF are summarized in Table 3.
Table 3. State Variables Relevant to Instream Nutrient Simulation in HSPF
Variable Name
Definition
Units
BOD
Benthal oxygen demand at 20 °C
mg/L
DOX
Dissolved oxygen concentration
mg/L
SATDO
Dissolved oxygen saturation concentration
mg/L
NH3
Dissolved concentration of NH3
mg/L
NH4
Dissolved concentration of NH4
mg/L
N02
Dissolved concentration of NO2
mg/L
N03
Dissolved concentration of NO3
mg/L
P04
Dissolved concentration of PO4
mg/L
SN4(3)
Storage of NH4 on sand, silt, clay
mg/mg
SP04(3)
Storage of PO4 on sand, silt, clay
mg/mg
BALCLA
Benthic algal density (as chlorophyll a)
Hg/m2
BENAL
Benthic algal density (as biomass)
mg/m2
ORC
Dead refractory organic carbon
mg/L
ORN
Dead refractory organic nitrogen
mg/L
ORP
Dead refractory organic phosphorus
mg/L
PHYCLA
Phytoplankton concentration (as chlorophyll a)
M-g/L
PHYTO
Phytoplankton concentration (as biomass)
mg/L
POTBOD
Potential biochemical oxygen demand
mg/L
TORC
Total organic carbon
mg/L
TORN
Total organic nitrogen
mg/L
TORP
Total organic phosphorus
mg/L
ZOO
Zooplankton concentration
mg/L
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HSPF simulates a single phytoplankton type. HSPF first calculates a temperature-corrected maximum
algal growth rate using linear interpolation between a minimum and maximum temperature for growth.
Limitations on algal growth are then applied using a Michaelis-Menten half saturation approach to
evaluate growth reduction due to availability of inorganic nitrogen, orthophosphorus and light. Algal
growth may also be limited by insufficient water depth. Algal death rates can vary between a low and
high unit death rate. The high death rates are applied when concentrations of inorganic nitrogen or
orthophosphorus fall below a user specified limit, or when the concentration of phytoplankton (as
chlorophyll a) exceeds a specified value. In the original formulation of HSPF, benthic algae are simulated
as analogous to phytoplankton except that light availability is calculated at the bottom, rather than
middle of the water column, a maximum benthic algae density is imposed, and growth and death rates
may vary relative to phytoplankton by a fixed ratio. Unlike phytoplankton, benthic algae are not subject
to advection. Instead, when the density of benthic algae exceeds a user-specified limit the excess
benthic algal is added to the death rate to represent sloughing loss. HSPF does not explicitly simulate
macrophytes, and their effects on water quality must be approximated using the benthic algal routines.
A major enhancement to the HSPF nutrient algorithms was introduced in Version 10 in 1993. The focus
was on implementing a more robust representation of inorganic sediment-nutrient interactions for both
suspended and bed sediment. While the enhancements were a significant improvement, the approach
does not constitute a full diagenesis model. The focus of the enhancement was on a free-flowing
riverine environment, one in which the adsorptive medium was expected to be predominantly non-
organic. While the sediment-nutrient interaction enhancements were being implemented to support
the EPA Chesapeake Bay Program, an upgrade in the computation and representation of additional
nutrient processes was also introduced. In addition to model processes present in the original 1980
model, current features of the HSPF RCHRES module include:
• Adsorption/desorption of phosphate and ammonium to inorganic sediment fractions (sand, silt,
clay) is represented using a linear relationship with a kinetic transfer rate. New state variables
for concentration and mass of phosphate and ammonium in suspended sediment fractions and
concentration of phosphate and ammonium in bed sediment are introduced.
• Nutrients adsorb/desorb from suspended sediment according to user-specified water column
partition coefficients.
• Bed sediment fractions are assumed to have reach-specific, temporally constant nutrient
concentrations. When nutrients adsorbed on suspended sediment are added to the bed via
deposition, these nutrients join an infinite pool. When sediment and its adsorbed nutrients are
scoured from the bed, the amount of nutrient entering the water column is proportional to the
amount of re-suspended sediment at a constant nutrient concentration.
• Reduction of nitrate to nitrogen gas (i.e., denitrification) is represented in the water column
using a first-order, temperature-dependent formulation dependent on water column nitrate
concentration. A parameter is integrated that specifies the dissolved oxygen concentration
above which denitrification (an anaerobic process) ceases; this threshold value is user-defined.
• Ionization of ammonia to ammonium is represented in the water column. New (or re-defined)
state variables for ammonia, ammonium, and total ammonia are required.
• Ammonia volatilization is represented using a two-layer model that relates volatilization rate to
oxygen reaeration rate.
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With the modification of HSPF to include sediment-nutrient interactions, the following rates and
constants are required: constant bed concentrations of ammonia-N and orthophosphorus-P adsorbed to
each sediment fraction (sand, silt, and clay) and adsorption coefficients (Kd) for ammonia-N and
orthophosphorus-P. Addition of the denitrification process required introducing two new rates and
constants: temperature correction factor for denitrification rate, and a threshold value for DO
concentration above which denitrification ceases. Addition of the ammonia volatilization process
required constants to represent both the exponent in the gas layer and the liquid layer of the mass
transfer equation.
In addition, a more sophisticated benthic algae simulation was introduced into the HSPF surface water
quality algorithms in Version 12.2 in 2005. The new methods are based on periphyton kinetics contained
in the DSSAMt water quality model (Caupp et al., 1998), and allow effective simulation of benthic algae
in shallow streams and rivers. Up to four different algal types can be simulated simultaneously, and the
processes these algae undergo are independent of phytoplankton processes. The process equations and
assumptions are as follows:
• Benthic algae are assumed to grow only in portions of the stream that are classified by the user
as riffles.
• Algal growth is a function of available nutrients, light, temperature, and the total density of
benthic algae.
• Nitrogen-fixing (blue-green) algae can be represented, and algae are generally not permitted to
reduce nutrients below a user-defined minimum.
• Respiration is dependent on temperature.
• Algae are lost or die (i.e., are removed) through grazing/disturbance by benthic invertebrates
and through scouring or sloughing processes.
• The inorganic and organic nutrient pools in the water column reflect the growth, respiration,
and removal processes.
The new routines can represent multiple types of benthic algae, each of which is simulated in a similar
manner. For benthic algal type I, the overall mass balance equations are given by Equation 2-25:
d B™ALi = [GROBAi - RESBAi - SLOFi] * BENALi - RE MB A t 2-25
Where:
BENAU = biomass (mg biomass/m2)
GROBAi = growth or production rate (/interval)
RESBAi = respiration rate (/interval)
SLOFi = biomass removal rate from scouring (/interval)
REMBAi = removal rate (grazing and disturbance) (mg biomass/m2/interval)
The growth or production rate for type I is given by Equation 2-26:
GROBAi = MBALGRt * TCMBAGt * min{GROFNi, GROFLit GROFDj} 2-26
Where:
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MBALGR, = production under optimal conditions
TCMBAG, = temperature limitation function
GROFN, = nutrient limitation function
GROFL, = light limitation function
GROFD, = density limitation function
The temperature limitation function is computed by an Arrhenius equation characterized by a
coefficient for the temperature effect on the growth of each algal type at 20 °C.
If the inorganic nitrogen and phosphorus concentrations are greater than user-defined minimum values
for growth (NMINGR and PMINGR), then growth can occur, and the nutrient limitation function is
computed by Equation 2-27, a Michaelis-Menten equation for non-blue-green algae:
, f GROFV'PO. GROFV'MMN
GROFNi = mm |-
\.CMMPj+ GR0FV*PO4 CMMP/+ CROFVMMN } j-JJ
Where:
GROFV = velocity limitation function for benthic algal nutrient availability (-)
P04 = dissolved available phosphorus concentration (mg P/L)
CMMPi = half-saturation constant for phosphorus uptake (mg P/L)
MMN = dissolved available inorganic nitrogen concentration (mg N/L)
CMMNi = half-saturation constant for nitrogen growth f (mg N/L)
For nitrogen-fixing (blue-green) algae, if the available nitrogen concentration is greater than a user-
defined parameter (NMAXFX), fixation is suppressed and the above equation is used. Otherwise, fixation
is assumed to occur and only the orthophosphate limitation is applied.
The velocity adjustment on nutrient limitation is computed as in Equation 2-28:
GROFV = 2-28
CMMV+BALVEL
Where:
BALVEL = water velocity in riffle sections of reach (ft/s or m/s)
CMMV = half-saturation constant for velocity for algal nutrient availability (ft/s or m/s)
If the light intensity is greater than the user-specified minimum value for growth (LMINGR), then growth
can occur, and the light limitation function on growth is computed as in Equation 2-29:
rDArf BALLIT ( BALLIT\
GROFLi = * exp 1
1 CSLIT1 r V CSLIT1)
2-29
Where:
BALLIT = available light at the stream bottom (langley [ly]/interval)
CSLIT, = saturating light intensity for growth of benthic algal type i (ly/interval)
The density limitation function on growth is based on the total density of benthic algae of all types
(SUMBA) as in Equation 2-30:
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GROFD = CMMD1i*SUMBA+CMMD2i 2-30
1 SUMBA+ CMMD2t
Where:
SUMBA = total benthic algal biomass for all algal types (mg biomass/m2)
CMMDli = coefficient in equation for density-limited growth
CMMD2i = half-saturation constant for density-limited growth (mg biomass/m2)
If necessary, the growth of each benthic algal type is adjusted so that its density (mg/m2) does not go
below the minimum value given by the input parameter MINBAL.
Respiration is calculated as in Equation 2-31:
RESBAt = BALR20i * TCBALRjTw~20 + GRORESi * GROBAi 2-31
Where:
BALR20, = respiration rate at 20 °C (/interval)
TCBALR, = temperature correction coefficient for respiration
Tw = water temperature (°C)
GRORESi = fraction of respiration required to support growth
Benthic algae removal is assumed to occur as a result of grazing and disturbance by benthic
invertebrates and scouring. These processes are computed in subroutine BALREM. The total removal
rate of all benthic algae due to grazing and disturbance is computed as in Equation 2-32:
REMINV = CREMVL * TCGRAZTW~20 * * BINV 2-32
5 UMBA * C MMBI
Where:
REMINV = total removal of benthic algae (all types) due to grazing and disturbance (mg
biomass/m2/interval)
CREMVL = removal rate due to grazing and disturbance of benthic algae by invertebrates (mg
biomass/mg invertebrates/interval)
TCGRAZ = temperature correction coefficient for grazing of benthic algae by benthic
invertebrates
CMMBI = half-saturation constant for benthic invertebrate grazing (mg biomass/m2)
BINV = biomass of grazing benthic invertebrates in the reach (mg invertebrates/m2)
The scouring loss rate (/interval) for each benthic algal type is computed as in Equation 2-33:
SLOFi = CSLOFli * exp(CSL0F2i * BALVEL) 2-33
Where:
CSLOFli = rate coefficient in scour regression equation for benthic algal type (/interval)
CSLOF2i = exponent coefficient in scour regression equation for benthic algal type x (/interval)
Finally, the total removal is computed by allocating the total grazing removal to each of the types and
adding the scouring removal rate as in Equation 2-34:
21
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REMBAj = [REMINV/sUMBA + Si0Fi\ * BENALt
2-34
If necessary, the removal of each benthic algal type is adjusted so that its density (mg/m2) does not go
below the minimum value given by the input parameter MINBAL.
The following rates and constants are required when simulating benthic algae using the newer method:
• Minimum benthic algae density (as biomass);
• Coefficient for the alternative nitrogen preference equation for benthic algae;
• Fraction of non-refractory nutrients resulting from benthic algae death/removal that are
assumed to be immediately available as inorganic nutrients, plus refractory organic carbon;
• Concentration of available inorganic nitrogen in the water column above which nitrogen-fixation
by benthic algae is suppressed;
• Maximum benthic algae growth rate for each benthic algae species;
• Temperature correction coefficient for growth for each species;
• Half-saturation constants for nitrogen- and phosphorus-limited growth for each species (if the
value for the nitrogen limitation is set to zero, then growth is not limited);
• Coefficient for total benthic algae density in the density-limited growth equation for each
species;
• Half-saturation constant for density-limited growth for each species;
• Saturation light level for each species;
• Benthic algae respiration rate at 20 °C for each species;
• Temperature correction coefficient for respiration for each species;
• Rate coefficient in the benthic algae scour equation for each species;
• Multiplier of velocity in the exponent in the benthic algae scour equation for each species;
• Fraction of photorespiration needed to support growth/photosynthesis for each species;
• Annual benthic algae grazing (removal) rate by invertebrates;
• Half-saturation constant for grazing by invertebrates;
• Temperature correction coefficient for macroinvertebrate grazing;
• Biomass of grazing invertebrates in the reach;
• Coefficient and exponent in the turbidity estimation equation;
• Coefficient and exponent in the light extinction equation;
• Fraction of the reach that is composed of riffles where benthic algae can grow;
• Half-saturation constant for riffle velocity in the nutrient availability equation for benthic algae;
• Critical flow levels (3) for riffle velocity and average depth; and
• Riffle velocity multipliers corresponding to the critical flow value and depth multipliers
corresponding to the critical flow value
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2.4 QUAL2K and QUAL2Kw
Model Background
QUAL2K (or Q2K) and QUAL2Kw (or Q2Kw) are closely related river and stream water quality models,
developed primarily by Tufts University, the Washington State Department of Ecology, and the Montana
Department of Environmental Quality, that are intended to represent modernized versions of the EPA-
supported model QUAL2E (or Q2E) model (Brown and Barnwell 1987). The first version of the QUAL2K
model (Chapra, 1999) was originally developed to address several major shortcomings of Q2E. Since
then, it has been updated on a periodic basis with the current version documented by Chapra et al.
(2015).
Q2Kw (w for Washington) is an alternative expression of the model developed by Pelletier et al. (2006)
and Pelletier and Chapra (2008)1. Most of the following discussion focuses on Q2K with a separate
section devoted exclusively to the major distinguishing features of Q2Kw. For the purposes of this
document, discussions of Q2K are also relevant to Q2Kw. Post-1985 enhancements to Q2K are equally
applicable to Q2Kw, and are therefore not discussed separately. Features or components that are found
in Q2Kw but not in Q2K are discussed as being Q2Kw-specific. Enhancements specific to Q2Kw are not
specifically related to rates, constants, or kinetic formulations, as discussed in more detail later in this
section.
The original impetus for Q2K stemmed from two major overriding factors: 1) Q2E had not been updated
since it was issued in 1987 and hence had not kept up with advances in water-quality modeling and
computing; and 2) Q2E was developed primarily for larger rivers in the Eastern United States and hence
had some severe deficiencies for application in the Western United States. Key issues that needed to be
addressed were:
• Q2E could not be applied to clear and shallow streams dominated by bottom algae;
• It did not mechanistically model sediment-water fluxes of oxygen and nutrients;
• It could not be used for anoxic systems (e.g., the model did not include denitrification and it
allowed oxygen concentrations to go negative);
• It did not simulate pH and hence could not address pH-dependent processes such as ammonia
toxicity; and
• It was not designed for modern personal computers, and new software advances offered an
opportunity to move the program to a spreadsheet environment for ease of use and
transparency.
The current release of Q2K (Chapra et al., 2012) is version 2.12 (www.qual2k.com). Q2K is similar to Q2E
in the following respects:
• One dimensional - the channel is well-mixed vertically and laterally;
• Branching - the system can consist of a mainstem river with branched tributaries;
1 The current version and documentation of Q2Kw is available from the Washington State Department of Ecology
at http://www.ecy.wa.gov/programs/eap/models.html
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• Steady-state hydraulics2 - non-uniform, steady flow is simulated;
• Diel heat budget - the heat budget and temperature are simulated as a function of meteorology
on a diel time scale. Solar radiation is computed at each time step as a function of date, time,
latitude/longitude, and atmospheric conditions using solar equations;
• Diel water-quality kinetics - all water quality variables are simulated on a diel time scale; and
• Heat and mass inputs - point and non-point loads and withdrawals are simulated.
The Q2K framework includes the following elements not found in Q2E:
• Carbonaceous BOD speciation - Q2K uses two forms of carbonaceous BOD to represent organic
carbon;
• Anoxia - Q2K accommodates anoxia by reducing oxidation reactions to zero at low oxygen
levels. In addition, denitrification is modeled as a first-order reaction that becomes pronounced
at low oxygen concentrations;
• Sediment-water interactions - Sediment-water fluxes of dissolved oxygen and nutrients can be
simulated internally rather than being prescribed. That is, oxygen (SOD) and nutrient fluxes are
simulated as a function of settling particulate organic matter, reactions within the sediments,
and the concentrations of soluble forms in the overlying waters using a version of the sediment
diagenesis framework (Di Toro and Fitzpatrick, 1993; Di Toro, 2001) developed by Martin and
Wool (2012);
• Bottom algae - The model explicitly simulates attached bottom algae. These algae have variable
stoichiometry;
• Light extinction - Light extinction is calculated as a function of suspended algae, detritus, and
inorganic solids;
• pH - Both alkalinity and total inorganic carbon are simulated. The river's pH is then computed
based on these two quantities;
• Pathogens - A generic pathogen is simulated. Pathogen removal is determined as a function of
temperature, light, and settling;
• Reach-specific kinetic parameters - Q2K allows you to specify many of the kinetic parameters on
a reach-specific basis; and
• Weirs and waterfalls - The hydraulics of weirs are explicitly modeled as well as the effects of
weirs and waterfalls on gas transfers (oxygen, carbon dioxide, and unionized ammonia).
The kinetic formulation for bottom algae in QUAL2K and QUAL2Kw is the same as the formulation used
in current version of WASP and described in Section 2.1 because the WASP module was based on the
representation in QUAL2K.
The model state variables are listed in Table 4.
2 Although Q2K is limited to steady-state hydraulics, Q2Kw does not have this limitation. Q2Kw simulates non-
steady, non-uniform flow using kinematic wave flow routing. Q2Kw is capable of continuous simulation with time-
varying boundary conditions for periods of up to one year. Q2Kw also has the option to use repeating diel
conditions similar to Q2K but with either steady or non-steady flows. See subsection QUAL2Kw-Specific Features.
24
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Table 4. QUAL2K/QUAL2Kw Model State Variables
Variable
Symbol
Units
Conductivity
s
|amhos
Inorganic suspended solids
m.
mg D7L
Dissolved oxygen
0
mg O2/L
Slowly reacting CBOD
Cs
mg O2/L
Fast reacting CBOD
Cf
mg O2/L
Organic nitrogen
n0
Mg N/L
Ammonia nitrogen
na
Mg N/L
Nitrate nitrogen
nn
Mg N/L
Organic phosphorus
P°
M-g P/L
Inorganic phosphorus
Pi
M-g P/L
Phytoplankton
aP
MS AVL
Phytoplankton nitrogen
IN:
Mg N/L
Phytoplankton phosphorus
IPp
Mg P/L
Detritus
m0
mg DVL
Pathogen
X
cfu/100 mL
Alkalinity
Alk
mg CaCOs/L
Total inorganic carbon
c
mole/L
Bottom algae biomass
ab
mg AVm2
Bottom algae nitrogen
INb
mg N/m2
Bottom algae phosphorus
IPb
mg P/m2
1 In the current versions of the model, A represents mass as chlorophyll a and D represents mass as ash-free dry
weight.
QUAL2Kw-Specific Features
QUAL2Kw (Q2Kw) began in 2004 as a modification of Q2K version 1.4. The current release is version 6
(Pelletier and Chapra, 2008; https://ecology.wa.gov/Research-Data/Data-resources/Models-
spreadsheets/Modeling-the-environment/Models-tools-for-TMDLs ). The development of Q2Kw is
supported by the Washington State Department of Ecology and has occurred in parallel to development
of Q2K, and the development team for Q2Kw includes the developers of Q2K. Q2Kw is used as the main
modeling framework for TMDL studies in the state of Washington related to temperature and
eutrophication in rivers (e.g., Carroll et al., 2006). Q2Kw has also been adopted by other states (e.g.,
Turner et al., 2009) to support their TMDL programs, and it is widely used worldwide (e.g., Kannel et al.,
2011).
The parallel development of Q2Kw from 2004 to the present has led to the addition of several
capabilities that are not available in Q2K. As discussed earlier in this section, post-1985 enhancements
to Q2K related to rates, constants, and kinetic formulations are equally applicable to Q2Kw. In addition
to the features of Q2K described above, the current version of Q2Kw (version 6) also has the following
capabilities:
25
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• Non-steady, non-uniform flow using kinematic wave flow routing - Q2Kw is capable of
continuous simulation with time-varying boundary conditions for periods of up to one year.
Q2Kw also maintains the option to use steady flow with repeating diel conditions, like Q2K;
• Transient storage zones - Q2Kw has the capability to simulate water quality in hyporheic
transient storage (HTS) and/or surface transient storage (STS) zones attached to any reaches;
• Automatic calibration - Q2Kw includes a genetic algorithm to calibrate the kinetic rate
parameters automatically within user-defined ranges for each parameter. Details on the
autocalibration algorithm is included in the model manual;
• Monte Carlo simulation - Q2Kw is capable of Monte Carlo simulation to evaluate uncertainty or
sensitivity with either of the following two add-ins for Microsoft Excel: 1) an open-source add-in
called YASAIw supported by the Washington State Department of Ecology3, or 2) Oracle Crystal
Ball4; and
• Sediment Flux Model (SFM) - Q2Kw employs the same SFM framework as WASP, following the
governing equations described in Section 2.1.
The benthic and planktonic algal simulation routines are similar to those contained in the advanced
eutrophication module of WASP (since version 7). The algorithms for predicting detrital and periphyton
concentrations in WASP were adapted from the QUAL2K model. Unlike WASP, the QUAL2K and
QUAL2Kw models do not contain separate macroalgae routines.
3. Methodology for Identifying Relevant Literature
To identify literature appropriate for developing tables of rates from modeling studies since the 1985
Rates Manual, the team conducted literature searches and contacted members of the modeling
community. Internet searches were conducted using Google Scholar and Google to obtain both peer-
reviewed published literature as well as grey literature (e.g., TMDL reports). Keywords were chosen
based on our team's expertise and knowledge of the models and the water quality constituents of
interest (i.e., dissolved oxygen, nutrients, and algae). A list of primary keywords used for the literature
search is provided in Table 5. These keywords were combined and manipulated for multiple search
efforts; this is not an exhaustive list of all keyword combinations. These keywords, and other
permutations of them, were applied to Google Scholar, Web of Science, the USACE Engineering
Research and Development Center (ERDC) library, EPA'sTMDL Database, and other publication
repositories. In addition, the available lists of model-centric publications were mined for additional
literature to evaluate.
3 YASAIw, an open-source Monte Carlo simulation add-in for Microsoft Excel supported by the Washington
Department of Ecology, is available for download from http://www.ecy.wa.gov/programs/eap/models.html
4 Oracle Crystal Ball is an add-in for Microsoft Excel available from Oracle at
http://www.oracle.com/us/products/applications/crystalball/overview/index.html
26
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Table 5. Primary keywords for literature identification
Keyword
[Model name]
Phytoplankton model rates
Application of [model name]
Dissolved oxygen model rates
Modeling studies using [model name]
Nutrient rate constant surface water
Parameter values TMDL models
Freshwater nutrient recycling
TMDL [model name]
Sediment nutrient diagenesis model
Surface water model calibration results
Water quality model parameters
During the literature search and review phase, specific documents targeted included:
• TMDL modeling studies, in which one or more of the four models of interest were calibrated
and validated as part of TMDL development;
• General water quality modeling studies, in which one of the four models was used to assess
water quality separate from the development of a TMDL; and
• Laboratory or field studies, in which rates, constants, and kinetic parameters used in the
models were measured under controlled conditions.
In addition to Internet searches, the project team reached out to the modeling community to obtain
relevant literature. To do so, announcements (example shown in Exhibit 1) requesting relevant studies
were posted on professional listservs identified for three of four models (
Exhibit 2). Several listserv members contacted the project team to provide documents that appeared
relevant to this effort.
Exhibit 1. Example announcement posted to model listserv
To: HSPF-USERS@ LISTSERV. UOGUELPH.CA
Subject: Request for information for Rates, Constants, Kinect Formulations manual
Our team is supporting EPA on a research project to support updates to Rates, Constants, and Kinetic
Formulations in Surface Water Quality Monitoring (Second Edition) (EPA/600/3-85/040). If you have applied any
of the following models—QUAL2Kw, WASP, CE-QUAL-W2 or HSPF—in the development of nutrient TMDLs, we
would be interested in obtaining any reports that discuss the application of those models in the TMDL
development. In particular, we are looking for reports or peer-reviewed publications that provide information
concerning the calibration of the model, its calibration data sets, and model coefficients used. Electronic or
hard-copy versions of those reports would be appreciated.
Contact: [contact information]
Thank you.
Exhibit 2. Listservs by model
Model Name
Listserv
WASP
http://www.lsoft.com/scripts/wl.exe?SLl=WASP-USERS&H=LISTSERV. UOGUELPH.CA
HSPF
http://www.lsoft.com/scripts/wl.exe?SLl=HSPF-USERS&H= LISTSERV. UOGUELPH.CA
CE-QUAL-W2
http://w2forum. cee.pdx.edu/
27
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The documents obtained from the Internet searches were screened and narrowed down further by
applying the following criteria:
• Publication date: Studies published in 1985 or later were selected, to ensure the most recent
information is used and that it reflects updates and changes to the models since the 2nd Edition
of the Rates Manual was published. Issues may arise in comparing the values identified in the
1985 manual to values gathered for this project. In some instances, the values are not directly
comparable, as some of the model formulations have changed (see, for example, Equation 2-1
vs. Equations 2-2a and 2-2b);
• Specificity to models and constituents of interest: Only studies specific to the four models and
to Group 1 water quality constituents (dissolved oxygen, nutrients, and algae) were selected;
• Availability of data on rates, constants, and kinetic parameters: Studies that explicitly provided
values of model rates, constants, and kinetic parameters, typically identified in tables and
figures, were included; and
• Representativeness of different waterbody types: Studies that represented different
waterbody types, such as lakes, rivers, estuaries, and streams, were selected.
It was outside the scope of this effort to research formally or make judgments on the quality control
practices of the studies and reports identified through the literature review and included here as
literature and data sources. For all models, the project team assumed that state and federal agencies
and peer-reviewed journals publish studies and study data with acceptable quality control practices and
data quality. To determine whether a paper or report was suitable for inclusion in the data tables,
several criteria were considered to gauge completeness of documentation for the purposes of this
project: tabulated final calibrated parameters; information on the data used for calibration; description
of model setup and calibration procedures; and an evaluation by the authors of model output. Reports
that did not include thorough documentation were removed from consideration. A study or paper that
was deemed inappropriate for this project's data tables was not necessarily a poor-quality paper or
poorly executed study; omission may merely indicate that the authors did not provide complete
documentation of procedures and calibrated parameters, possibly due to journal space constraints or
because the goals of the paper did not require in-depth documentation. The project team found that
state and federal government reports often provide more complete descriptions of data acquisition and
model development than peer-reviewed journal articles.
Selected documents were then reviewed for information on:
• Whether measurements of water quality were used to calibrate model parameters related to
dissolved oxygen, nutrients, and algae;
• The number of years of data used for calibration of nutrients, DO, and algae; and
• Whether calibration data included measurements of water quality processes5 and, if yes, which
ones.
5 Process measurements include those that go beyond measurements of constituent concentrations (e.g.,
collection of chamber measurements of sediment oxygen demand versus reliance only on water column dissolved
oxygen concentrations).
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4. Summary of Available Information
This section summarizes the information obtained from the literature search. For each of the four
models, a similar sequence of information is provided:
• Discussion of literature search process;
• Literature table summarizing the studies obtained in the search, including author(s), year,
waterbody name, geographic area and climate, and watershed/waterbody characteristics;
• Data table with summary statistics for model rates and constants;
• Discussion of calibration data and approaches; and
• Discussion of information gaps.
It should be noted that there is overlap in some of the eutrophication kinetics employed in WASP, CE-
QUAL-W2, QUAL2K/QUAL2Kw, and HSPF. In some cases, it may be possible for a user of the data tables
to investigate parameters across all models in cases where the underlying kinetic processes in each
model are similar. However, a preliminary evaluation of governing equations across models identified
numerous issues associated with a cross-model comparison of parameters. A discussion of this
evaluation, barriers encountered, and suggested future research is included in Section 6 of this report.
Before assuming that parameter values reported for one model will meet the needs for what appear to
be similar parameters used in a second model, users should review the kinetic formulations employed in
each of the models to be sure that the associated rates and coefficients are used in a consistent kinetic
formulation across the models. Detailed information on the theoretical underpinnings of each model are
available either in the model user's manual or associated documentation. It may also be important for
the user to compare the underlying model code in situations where they are considering comparing RCK
parameters across models.
4.1 WASP
Summary of Sources
Summary of Literature sources for WASP applications found via the Google Scholar and U.S. EPA
AskWaters search engines were reviewed following the methods described in Section 3. Initial screening
activities identified approximately 150 papers. These papers were then reviewed in more detail, with
the review focusing on the following items:
• Peer-reviewed journal papers vs. grey literature - As described in Section 3, literature selection
depended on thorough documentation of model setup, calibration, and verification. Peer,
reviewed journal papers were considered high value (in terms of acceptability for this effort),
since they were reviewed by impartial and knowledgeable practitioners. Additionally, reports
prepared for states and federal agencies were included if model documentation was sufficient
or if the report was reviewed by a technical advisory committee.
• Multi-year or multi-season data sets - Modeling efforts that included calibration/validation data
sets that included more than one year or one season of data were considered to be of higher
value compared to data sets that consisted of just one year or season of data. The principal
reason for this is that it is easier to over-calibrate a model to one year (or season) of data than it
29
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is to calibrate to multi-year (or multi-season) data sets. A model that can reproduce the major
features of multi-year data sets can be considered more robust. However, models that appeared
to adjust model constants and coefficients from year to year, unless justifiable, were considered
to be of lesser value as compared to models that used a consistent set of constants and
coefficients throughout the calibration/validation period.
• Quantitative skill assessment - Papers that presented quantitative skill assessment metrics and
results were considered of higher value, assuming that the model skill could be quantified as
being good or acceptable (see Arhonditsis and Brett, 2004; Fitzpatrick, 2009), than papers that
presented just qualitative skill, i.e., time-series or spatial profiles of model versus data. Papers
that presented only qualitative skill assessment were not necessarily rejected, but required
additional review to determine their acceptability.
• Rate and coefficient values - Model rates and coefficients presented in the papers were also
reviewed as to their reasonableness and consistency with the range of values reported in the
modeling literature, previous WASP applications and the range of coefficients reported in WASP
documentation and EPA's 1985 Rates Manual. Sources reporting RCK values that deviated
significantly from acceptable ranges were eliminated from further consideration.
The tables developed for WASP were supplemented with additional information drawn from
eutrophication-based studies performed by HydroQual (now HDR), and the USACE ERDC. The reason for
including these grey-literature sources is that the sediment diagenesis/nutrient flux model (SFM) is a
recent addition to WASP and only two peer-reviewed papers were found that used the SFM (Brady et
al., 2013, Testa et al., 2013). However, since the version of SFM that is incorporated in WASP is virtually
identical to that used by HDR and the USACE ERDC, the Project Team believed that incorporating this
information was appropriate for this effort. The non-WASP models that incorporate the SFM are HDR's
RCA model code, the USACE's CE-QUAL-ICM (Cerco and Cole, 1994) model code, and CE-QUAL-W2 and
QUAL2KW.
After detailed screening, 47 papers passed relevance and criteria checks, including eight HydroQual,
HDR and USACE ERDC reports that provided information concerning the application of the SFM and
associated RCK values for eutrophication (Table 6). Of these 47 papers, 28 were peer-reviewed journal
articles, eight were TMDL reports (prepared by EPA, states, or consulting firms under contract to EPA or
states), six were reports prepared by HydroQual or HDR, two by USACE ERDC, one by USGS, one by Tetra
Tech, and one was a doctoral thesis. WASP has been used in many other TMDL studies, but the team
was not successful in locating those studies via Google, Google Scholar, or the EPA AskWATERS TMDL
search engine. For additional resources regarding WASP, see Section 9 of this report. Detailed examples
of application of the WASP model to nutrient and DO problems, along with extensive tables of relevant
rates and constants are also available in U.S. EPA (1995).
While a few of the papers used data sets of a limited time frame (i.e., a few weeks to a summer season)
for model calibration, the team decided to include them because the model appeared well-calibrated
and the model coefficients were reasonable. While several papers modeled only BOD/DO, the majority
simulated water column phytoplankton and/or attached algae or periphyton.
30
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Table 6. WASP Literature Sources
Citation
Study Location
Type of
Water body
Watershed Characteristics
Calibration period
Camacho, R., J. Martin, B. Watson, M. Paul, L Zheng, and J. Stribling,
2014. Modeling the Factors Controlling Phytoplankton in the St. Louis
Bay Estuary, Mississippi and Evaluating Estuarine Responses to
Nutrient Load Modifications. Journal of Environmental Engineering.
1943-7870.0000892.
St. Louis Bay,
Mississippi
Estuary
1,840 km2 drainage; avg depth = 1.4m; surface area =
39.8 km2; watershed undeveloped (52%-forest, 23%-
timber,15%-anthropogenic uses)
January 27, 2011-
December 31,
2011.
Canu, D., C. Solidoro, and G. Umgiesser, 2004. Modelling the
Responses of the Lagoon of Venice Ecosystem to Variations in Physical
Forcings. Ecological Modelling. 174(2).
The Lagoon of
Venice
Lagoon
avg. depth = 1 m; surface area = 550 km2
1987, 2000
Cerucci, M., G. Jaligama, and R. Ambrose, 2010. Comparison of the
Monod and Droop Methods for Dynamic Water Quality Simulations.
Journal of Environmental Engineering. 1943-7870.0000257.
Raritan River, New
Jersey
River
2,850 km2 drainage.
2003-2005
Chen, C., W. Lung, S. Li, and C. Lin, 2012. Technical Challenges with
BOD/DO Modeling of Rivers in Taiwan. Journal of Hydro-
environmental Research. 3(8).
The Danshui River
and the
Chungkang River,
Taiwan
River
Danshui River (watershed 2726 km2); Chungkang River
(watershed area of 446 km2).
October-
November 2006
Dilks, D., and T. James, 2011. Parameter Uncertainty in a Highly
Parameterized Model of Lake Okeechobee. Lake and Reservoir
Management. 27(4).
Lake Okeechobee,
Florida
Lake
surface area = 1800 km2; avg depth = 2.7 m; eutrophic
1983-2000
Dongil, S., and K. Minae, 2011. Application of EFDC and WASP7 in
Series for Water Quality Modeling of the Yongdam Lake, Korea.
Journal of Korea Water Resources Association. 44(6).
The Yongdam Lake,
South Korea
Lake
Withdrawal facilities for water supply; natural flow
through spillways; hydropower generation discharge to
Geum River
2005
Gin, K., Q. Zhang, E. Chan, and L. Chou, 2001. Three-Dimensional
Ecological-Eutrophication Model for Singapore. Journal of
environmental Engineering. 10(928).
Southwest
Monsoon, Singapore
River
Increased loading from treated industrial and domestic
effluents, urban runoff, and sedimentation
August 1998 (14
days)
Gu, R., and M. Don, 1998. Water Quality Modeling in the Watershed-
based Approach for waste Load Allocations. Water Science
Technology. 38(10).
Des Moines River,
Iowa, USA
River
4600 km2 drainage area; annual mean discharges =
1000 m3/s; 7Q10=2.8 m3/s
1975-1977
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Citation
Study Location
Type of
Water body
Watershed Characteristics
Calibration period
Huang, Y., C. Yang, and P. Tang, 2010. Water Quality Management
Scenarios for the Love River in Taiwan. International Conference on
Challenges in Environmental Science and Computer Engineering.
The Love River,
Taiwan
Stream
Catchment area of 62 km2, an urban-type tidal
stream
May 18 -
October 13, 2009
James, R.T., J. Martin, T. Wool, and P.F. Wang, 1997. A Sediment
Resuspension and Water Quality Model of Lake Okeechobee. 33(3).
Lake Okeechobee,
Florida
Lake
Lake Okeechobee is a large (surface area 1,732
km2) shallow (mean depth 2.7 m) lake
January 1,1990-
December 31,
1991
Jia, H., Y. Zhang, and Y. Guo, 2010. The Development of a Multi-
Species Algal Ecodynamic Model for Urban Surface Water Systems
and its Application. Ecological Modelling. 221(15).
Urban river system,
Beijing
River
Urban area
March - October
2004
Kardos, J., and C. Obropta, 2011. Water Quality Model Uncertainty
Analysis of a Point-Point Source Phosphorus Trading Program. Journal
of the American Water Resources Association. 47(6).
Passaic River Basin,
New Jersey
River Basin
1733 km2 and 347 km2 watershed area in New Jersey
and New York
2007
Kim, T., and Y. Sheng, 2009. Estimation of Water Quality Model
Parameters. KSCE Journal of Civil Engineering. 14(3).
Indian River Lagoon,
Florida
Lagoon
estuary
Narrow except the Inter-Coastal Waterway (0.5-7 km);
extends 255 km
Kish, S., J. Barlett, J. Warwick, A. McKay, and C. Fritsen, 2006. Long-
Term Dynamic Modeling Approach to Quantifying Attached Algal
Growth and Associated Impacts on Dissolved Oxygen in the Lower
Truckee River, Nevada. 132(10).
Truckee River,
Nevada
River
The Truckee River Basin comprises an area of about
7,925 km2. Mostly agricultural area. 195 km long
Truckee River.
August 2000-
December 2001
Lai, Y., C. Yang, C. Hsieh, C. Wu, and C. Kao, 2011. Evaluation of Non-
Point Source Pollution and River Water Quality Using a Multimedia
Two-Model System. Journal of Hydrology. 409(3-4).
The Kaoping River,
Taiwan
River
The Kaoping River Basin: 3625 km2
Forest-56%, Brdlf evergreen-7.7%, Farms-15.5%, Marsh-
5.3%, Shrub+Grassland-7.5%, Resid+commerce-2.6%
River length=171 km, Mean Flow=239 m3/s.
2008-2009
Lindenschmidt, K.E., 1. Pech, and M. Baborowski, 2009. Environmental
Risk of Dissolved Oxygen Depletion of Diverted Flood Waters in River
Polder Systems-A Quasi-2D Flood Modelling Approach. Science of the
Total Environment. 407(5).
Elbe River, Germany
River
Mean Q=153 m3/s (1998) Mean Q=228 m3/s (1999)
Mean Q=194 m3/s (2000) Mean Q=2743 m3/s (2002)
12 - 21 August of
2002, and Apr-Aug
of 1998, 1999,
2000
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Citation
Study Location
Type of
Water body
Watershed Characteristics
Calibration period
Liu, Z., W. Kingery, D. Huddleston, F. Hossain, W. Chen, N. Hashim,
and J. Kieffer, 2007. Modeling Nutrient Dynamics Under Critical Flow
Conditions in Three Tributaries of St. Louis Bay. Journal of
Environmental Science and Health, Part A. 43(6).
St. Louis Bay,
Mississippi
Bay
The drainage area is approximately
1,840 km2 with two major tributaries,
Jourdan River and Wolf River
March 16 to
July 23, 1998,
January 1 to
April 30,1999
Lundgren, R., and R. Nustad, 2008. Calibration of a Water-Quality
Model for Low-Flow Conditions on the Red River of the North at
Fargo, North Dakota, and Moorhead, Minnesota, 2003. USGS.
Scientific Investigations Report.
Red River, North
Dakota, and
Moorhead,
Minnesota
River
19.2-mi reach of the Red River
Sept. 24-27, 2003
Lung, W., and A. Nice, 2007. Eutrophication Model for the Patuxent
Estuary: Advances in Predictive Capabilities. Journal of Environmental
Engineering. 133(9).
The Patuxent
Estuary
Estuary
1997-1999
Lung, W., and H. Paerl, 1988. Modeling Blue-green Algal Blooms in the
Lower Neuse River. Water Research. 22(7).
Neuse River, North
Carolina
River
Neuse River drains approx. 25% of North Carolina's land
area, flowing through the Piedmont and Coastal Plain
regions.
1983-1985
Lung, W., 1986. Assessing Phosphorus Control in the James River
Basin. Journal of Environmental engineering. 112(1).
James River Estuary,
Virginia
Estuary
Summer 1983
Melendez, W., M. Settles, J. Pauer, and K. Rygwelski, 2009. LM3: A
High-resolution Lake Michigan Mass Balance Water Quality Model.
Grosse lie, Michigan: U.S. EPA.
Lake Michigan
Lake
1994-1995
Narasimhan, B., R, Srinivasan, S. Bednarz, M. Ernst, and P. Allen, 2010.
A Comprehensive Modeling Approach for Reservoir Water Quality
Assessment and Management Due to Point and Nonpoint Source
Pollution. Transactions of ASABE. 53(5).
Cedar Creek
reservoir, Texas
Reservoir
Reservoir surface area of
13,350 ha and a volume of 795 million m3.
1991-2001
Pauer, J., A. Anstead, W. Melendez, and R. Kreis, 2008. The Lake
Michigan Eutrophication Model, LM3 - Eutro: Model Development
and Calibration. Water Environment Research 80(9).
Lake Michigan
Lake
1994-1995
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Citation
Study Location
Type of
Water body
Watershed Characteristics
Calibration period
Sangsurasak, C., H. Hsieh, W. Wongphathanakul, and W. Wirojanagud,
2006. Water Quality Modeling in the Nam Pong River, Northeast
Thailand. ScienceAsia. 32.
Nam Pong River,
Thailand
River
Mostly agricultural land
DO= 3.1 nmol/L
1999-2000
Simachaya, W., 1999. Integrated Approaches to Water Quality
Management Using Geographic Information Systems and the WASP5
Simulation Model: Application to the Tha Chin River Basin, Thailand.
University of Guelph.
Tha Chin River Basin,
Thailand
River
Depth: 3-12m; Width: 100-600m; avg freshwater
inflow: 32 m3/s
predominantly agriculture (83%)
1995, 2014
Soyupak, S., L Mukhallalati, D. Yemisen, A. Bayar, and C. Yurteri,
1996. Evaluation of Eutrophication Control Strategies for the Keban
Dam Reservoir. Ecological Modelling. 97.
Keban Dam
Reservoir
(KDR), Anatolia,
Turkey
Reservoir
Surface Ares=675 km2, Volume=30.6E9 m3.
1992
Tetra Tech, Inc., 2009. TMDLs for Dissolved Oxygen and Nutrients in
Selected Subsegments in the Mississippi River Basin, Louisiana.
Capitol Lake, Baton
Rouge, Louisiana
Lake
60-acre freshwater lake
drainage area: 1.731 acres
predominant land use is developed (96.76%)
August 30-
September 1, 2007
Tetra Tech, Inc., 2008. Nutrient and Sediment TMDLs for the Indian
Creek Watershed, Pennsylvania: Established by the U.S.
Environmental Protection Agency.
Indian Creek,
Pennsylvania
third-order
stream
drainage area = 7 mi2, flows 6.1 miles, various degrees
of residential development scattered throughout
watershed. Middle portion of watershed is
predominantly pastures
1997-2004
Tufford, D., and H. McKellar, 1999. Spatial and Temporal
Hydrodynamic and Water Quality Modeling Analysis of a Large
Reservoir on the South Carolina (USA) Coastal Plain. Ecological
Modelling. 114.
Lake Marion, South
Carolina
Lake
Surface area: 330.7 km2; drainage area: 25,433.8 km2;
mean depth: 4 m; maximum depth: 23.4 m
1985-1990
U.S. EPA, 2000. Total Maximum Daily Load (TMDL) Development for
Dissolved Oxygen in the Taylors Creek in the Ogeechee River Basin.
Taylors Creek,
Georgia
Creek
Stream Flow=4.35cfs, DO=5.0 mg/L, BOD=2.5 mg/L,
Temp=26 °C
U.S. EPA, 2003. Modeling Report for Wissahickon Creek, Pennsylvania
Nutrient TMDL Development, including Appendix F: Technical Memo
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Wissahickon Creek,
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Creek and
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2002
34
-------
Citation
Study Location
Type of
Water body
Watershed Characteristics
Calibration period
U.S. EPA, 2005. Total Maximum Daily Load (TMDL) for Dissolved
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Butcher Pen Creek,
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St. Johns River Basin drainage = 9500 mi2
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1995-2002
U.S. EPA, 2006. Total Maximum Daily Load (TMDL) for Dissolved
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Hogan Creek, Florida
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St. Johns River Basin drainage = 9500 mi2
Hogan Creek area = 3.4 mi2. Urban and residential area-
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1996-2003
U.S. EPA Region 4, 2013. Appendix A Modeling Report Cedar Creek
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Cedar Creek, Florida
Tributary
Tributary basin to the Braden River; 5 km2; 76% Urban,
2003-2007
U.S. EPA, 2013. Model Setup and Calibration for McKay Bay.
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January 2003-
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U.S. EPA Region 4, 2013. Modeling Report Owen Creek and Myakka
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35
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Watershed Characteristics
Calibration period
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Neuse River drains approx. 25% of North Carolina's land
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October 27-28,
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Yenilmez, F., and A. Aksoy, 2013. Comparison of Phosphorus
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2000
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Satilla River Estuary,
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"blackwater" high conc. humic and tannic acids
mean depth=4 km; max depth=23 m; width=l-4 km
April 8 and 16,
1995; October
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Zou, R., S. Carter, L. Shoemaker, A. Parker, and T. Henry, 2006
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Support Nutrient Total Maximum Daily Load Development for
Wissahickon Creek, Pennsylvania. Journal of Environmental
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Wissahickon Creek,
Pennsylvania
Creek
drains 164 km2, extends 38.6 miles
2002
Zouiten, H., C. Alvarez Diaz, A. Garcia Gomez, J. Revilla Cortezon, and
J. Garcia Alba, 2013. An Advanced Tool for Eutrophication Modeling in
Coastal Lagoons: Application to the Victoria Lagoon in the North of
Spain. Ecological Modelling. 265.
Victoria Lagoon,
Spain
Lagoon
Wetlands, natural reserve, freshwater coastal lagoon
periodically becomes saline
area= 61ha: 39.5 ha marsh, 21.5 ha dunes
May 1
November 1, 2009
36
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As a model capable of being applied in one, two or three dimensions, WASP applications reported in the
tables included lakes, reservoirs, creeks, streams, rivers, lagoons, tidal embayments, and estuaries. In
many the earlier papers, the gross transport features of the waterbody were assumed to be at steady
state and/or were estimated via calibration to observed temperature and salinity profiles using
procedures developed by Pritchard (1964) or Lung and O'Connor (1984), while in more recent papers,
the waterbody transport was computed by hydrodynamic models such as DYNHYD (Ambrose et al.,
1993), DYRESM (Imberger and Patterson, 1981), or EFDC (Hamrick, 1996). In the case of the RCA model
applications, either the ECOM (Blumberg and Mellor, 1987) or EFDC (Hamrick, 1996) hydrodynamic
models have been used to provide transport information, while in the case of the CE-QUAL-ICM
application, the CH3D hydrodynamic model (Sheng, 1989) has been used.
Several more recent papers also have some discussion of linkages between WASP and watershed
models such as HSPF (Bicknell et al., 2014), SWAT (Neitsch et al., 2011), and LSPC (Tetra Tech, 2009) to
provide estimates of nutrient loadings to the waterbody under investigation. The basin sizes involved in
these applications have ranged from as small as < 10 km2 to as large as 166,000 km2. Land use has varied
from almost exclusively urban settings to largely agricultural or largely forested/timberland.
Information, where available, concerning the watershed characteristics for each included study are
contained within the RCK tables.
Climatologically, the study areas include embayments and estuaries in the Atlantic Northeast
(Massachusetts, New York, and Connecticut), humid subtropical regions (Florida, Mississippi, Alabama,
Georgia, Texas, Turkey), temperate subtropical region (Virginia and Maryland), humid continental cool
summer (Vermont), warm/hot summer continental/hemiboreal climates (North Dakota, Iowa), mixed
subtropical/tropical climate (Thailand), the Mediterranean (Italy), and semi-arid areas (Nevada).
Tabulating rates and constants values for WASP from the literature is difficult because of the many
recent changes in the model, notably including the addition of benthic algae (2006), multiple-algae
(2011), and sediment diagenesis (2017) components. These updates added many new kinetic equations
and variables and change the number of parameters, and in some cases their interpretation. As a result,
published modeling reports from one generation of WASP may not be fully applicable to the current
version, and some important parameters—such as internal half-saturation constants for nutrients in
algal cells—were not retrieved in the search process for this report.
Results of the survey of rates found in the literature on WASP are provided in Table 7 through 10. Unlike
CE-QUAL-W2, for example, the current version of WASP does not have a comprehensive user's guide
containing tables of default parameter values. Instead, default and/or example values are spread
throughout the many update reports, and are lacking for many parameters. For some rates, there are
conflicting default value recommendations among different user updates. Therefore, the tables provide
a column of "representative" values, which are intentionally not characterized as defaults. It should be
noted, however, that the WASP benthic algae representation is largely consistent with
QUAL2K/QUAL2Kw, while the multi-algae and sediment diagenesis routines share many kinetic
representations with both QUAL2K/QUAL2Kw and CE-QUAL-W2. Therefore, the WASP user may gain
additional insight on rates and constants for WASP applications by consulting the rate tables for CE-
QUAL-WQ (Table 12) and QUAL2K/QUAL2Kw (Tables 17-20).
37
-------
Summary Statistics for Rates and Constants
Table 7. WASP Rates and Constants: Nutrient Parameters
Nutrient Parameter
Count
Min
Max
Mean
Median
Representative
Values
Units
Denitrification rate at 20 °C
20
0
1.05
0.199
0.09
0.09
day1
Denitrification temperature coefficient
14
1.04
1.08
1.060
1.08
1.045
-
Dissolved organic nitrogen decay in sediment
temperature coefficient
1
1.08
1.08
1.08
1.08
-
-
Fraction of dissolved organic nitrogen
2
1
1
1
1
1.0
-
Fraction of dissolved organic phosphorous
3
0.5
1
0.833
1
0.85
-
Fraction of non-recycled organic nitrogen
2
0.15
0.4
0.275
0.275
0.5
-
Fraction of non-recycled organic phosphorus
1
0.2
0.2
0.2
0.2
0.5
-
Half saturation constant for denitrification
oxygen limitation
16
0.01
10
0.867
0.1
0.1
mg O2/L
Half saturation constant for nitrification
oxygen limitation
17
0.01
2
1.183
1
2
mg O2/L
Nitrification rate
26
0.001
2.5
0.317
0.1
0.09 -0.013
day1
Nitrification rate temperature correction
coefficient
17
1.04
1.08
1.071
1.08
1.08
-
Organic carbon mineralization rate
1
0.02
0.02
0.02
0.02
-
day1
Organic N mineralization rate at 20 °C
18
0.0033
0.5
0.096
0.065
0.075
day1
Organic N mineralization temperature
correction coefficient
14
1.04
1.08
1.072
1.08
1.08
-
Organic P mineralization rate at 20 °C
16
0.02
0.75
0.156
0.125
0.22
day1
Organic P mineralization temperature
correction coefficient
12
1.02
1.08
1.067
1.08
1.08
-
Sediment bed organic N decomposition rate at
20 °C
4
0.0004
0.1
0.033
0.0152
0.0004
day1
Sediment bed organic N decomposition
temperature correction coefficient
4
1.07
1.08
1.078
1.08
1.08
-
Sediment bed organic P decomposition rate at
20 °C
4
0
0.27
0.068
0.0002
0.0004
day1
Sediment bed organic P decomposition
temperature correction coefficient
4
0
1.08
0.808
1.075
1.08
-
Settling velocity of particulate inorganic P
1
18
18
18
18
-
m/d
Settling velocity of particulate organic N
2
0.3
0.5
0.4
0.4
-
m/d
Settling velocity of particulate organic P
2
0.3
0.5
0.4
0.4
-
m/d
38
-------
Table 8. WASP Rates and Constants: Oxygen Parameters
Oxygen parameter
Count
Min
Max
Mean
Median
Representative
Values
Units
BOD decay rate
20
0.01
0.3
0.131
0.125
0.16-0.21-
day1
BOD decay rate temperature correction
coefficient
12
1.04
1.08
1.047
1.047
1.047
day1
CBOD decay
1
0.05
0.05
0.05
0.050
-
day1
CBOD sediment decomposition rate at 20 °C
1
0.0001
0.0001
0.0001
0.000
-
day1
CBOD sediment decomposition rate
temperature correction coefficient
1
1.08
1.08
1.08
1.080
-
-
Fraction of BOD carbon source for
denitrification
1
0.1
0.1
0.1
0.100
-
-
Fraction of detritus to BOD
1
1
1
1
1.000
-
-
Fraction of dissolved CBOD
2
0.5
1
0.75
0.750
0.5
-
Half-saturation constant for oxygen limitation
9
0
0.5
0.34
0.500
0.5
mg O2/L
Oxygen to Carbon stoichiometric ratio
4
2.67
2.67
2.67
2.670
-
G 02/gC
Reaeration coefficient at 20 °C
6
0.00005
2
0.74
0.500
0.125
day1
Reaeration temperature correction coefficient
6
1.024
1.048
1.036
1.035
1.045
day1
Respiration
1
0.1
0.1
0.1
0.100
-
day1
Sediment oxygen demand
4
0
1
0.45
0.350
0.2-4.0
g/m2/day
Settling velocity of CBOD and organic matter
2
0.05
0.5
0.28
0.275
-
m/d
Settling rate for particulate CBOD
1
0.0001
0.0001
0.0001
0.0001
-
m/d
SOD temperature correction coefficient
3
1.06
1.08
1.073
1.080
1.08
-
Temperature adjustment for reaeration rate
2
1.028
1.028
1.028
1.028
-
-
Table 9. WASP Rates and Constants: Algae Parameters
Algae Group
Parameter
Count
Min
Max
Median
Representative
Values
Units
Phytoplankton
(generic)
Growth rate
30
0
4
2
2
day1
Phytoplankton
(generic)
Growth rate
temperature
correction
19
0
10
1.068
1.068
-
Phytoplankton
(generic)
Death rate
19
3.5E-07
0.2
0.1
0.02
day1
Phytoplankton
(generic)
Death rate
temperature factor
2
1
1
1
-
-
Phytoplankton
(generic)
Grazing rate
6
0
1.2
0.245
0
L/mgC/d
39
-------
Algae Group
Parameter
Count
Min
Max
Median
Representative
Values
Units
Phytoplankton
(generic)
Respiration rate
21
0.01
0.2
0.1
0.125
day1
Phytoplankton
(generic)
Respiration rate
temperature factor
13
1.045
1.08
1.068
1.045
-
Phytoplankton
(generic)
Extinction
coefficient
2
0
2
1
0.1 5
m1
Phytoplankton
(generic)
N:Chl-a
2
0.007
7
3.5035
7.2
-
Phytoplankton
(generic)
P:Chl-a
2
0.001
1
0.5005
1
-
Phytoplankton
(generic)
C:Chl-a
20
0.025
80
35
40
-
Phytoplankton
(generic)
P:C
14
0.01
0.24
0.025
0.025
-
Phytoplankton
(generic)
N:C
17
0.1
0.3
0.2
0.18
-
Phytoplankton
(generic)
Si:C
2
0.8
0.8
0.8
-
-
Phytoplankton
(generic)
C:0
4
2.67
2.67
2.67
-
-
Phytoplankton
(generic)
Half-saturation for
nutrient recycling
2
0
1
0.5
-
mg Phyt
C/L
Phytoplankton
(generic)
Half-saturation
constant for
nitrogen uptake
7
2.5E-05
25
0.025
-
mgN/L
Phytoplankton
(generic)
Half-saturation
constant for silica
uptake
2
0.03
0.05
0.04
-
mgSi/L
Phytoplankton
(generic)
Half-saturation for
phosphorus uptake
7
1.0E-06
1
0.001
-
mgP/L
Phytoplankton
(generic)
Half-saturation for
nitrogen limited
growth
11
0.005
0.4
0.025
0.025
mgN/L
Phytoplankton
(generic)
Half-saturation for
phosphorus limited
growth
14
0.0005
0.01
0.0025
0.001
mgP/L
Phytoplankton
(generic)
Half saturation
constant for
phytoplankton
limitation of
phosphorus
mineralization
2
0
1
0.5
-
mgC/L
Phytoplankton
(generic)
Organic phosphorus
mineralization rate
2
0.06
0.22
0.14
-
day1
Phytoplankton
(generic)
Fraction recycled to
organic nitrogen
pool
9
0.3
0.8
0.5
-
-
Phytoplankton
(generic)
Fraction recycled to
organic phosphorus
pool
9
0.1
0.65
0.45
-
-
Phytoplankton
(generic)
Saturation light
intensity
8
120
720
275
200 - 500
ly/d
40
-------
Algae Group
Parameter
Count
Min
Max
Median
Representative
Values
Units
Phytoplankton
(generic)
Light extinction
coefficient
13
0
5
0.35
-
m1
Phytoplankton
(generic)
Phytoplankton
optimal light
saturation
4
200
350
260
-
ly/d
Phytoplankton
(generic)
Algal settling rate
6
2.3E-07
0.5
0.04
0.1
m/d
Phytoplankton
(generic)
Mortality ratio of
phytoplankton and
zooplankton for
PON
2
0
0.5
0.25
-
-
Phytoplankton
(generic)
Phytoplankton
optimal light
saturation
4
200
350
260
-
ly/d
Phytoplankton
(generic)
Phytoplankton
Temperature
Coefficient for
Sediment Decay
2
1.08
1.08
1.08
-
-
Phytoplankton
(generic)
Phytoplankton
Phosphorus:Carbon
Ratio
3
0.025
0.025
0.025
-
-
Phytoplankton
(generic)
DOP mineralization
rate
3
0.026
0.43
0.22
-
day1
Phytoplankton
(generic)
DOP mineralization
rate
3
0.026
0.43
0.22
-
day1
Phytoplankton
(generic)
Organic phosphorus
mineralization rate
2
0.06
0.22
0.14
-
day1
Benthic algae
P:C
2
0.015
0.02
0.018
0.025
mgP/mgC
Benthic algae
Growth rate
2
2
25
13.5
9
gD/m2/d
Benthic algae
Respiration rate
2
0
0.1
0.05
0.03
day1
Benthic algae
Ammonia
preference
2
0.025
0.1
0.063
0.025
mgN/L
Blue green algae
Algal settling rate
3
1.2E-06
0.19
0.05
-
m/d
Blue green algae
Growth rate
2
1.3
2.32
1.81
-
day1
Blue green algae
Half-saturation for
nitrogen limited
growth
3
0
0.4
0.015
-
mgN/L
Diatoms
Growth rate
2
2
2.5
2.25
-
day1
Diatoms
Growth rate
temperature
correction
2
0.2
20
10.1
-
°C
Periphyton
Growth rate
7
0.6
1.52
0.85
-
day1
Periphyton
Growth rate
temperature
correction
5
1.055
1.06
1.06
1.07
-
Periphyton
Death rate
3
0.009
0.05
0.02
0.05
day1
Periphyton
Respiration rate
6
0.015
0.15
0.063
0.10
day1
41
-------
Algae Group
Parameter
Count
Min
Max
Median
Representative
Values
Units
Periphyton
Respiration rate
temperature factor
3
0.069
0.078
0.078
1.07
-
Periphyton
P:C
3
0.01
0.03
0.025
0.025
-
Periphyton
N:C
4
0.12
0.21
0.18
0.18
-
Periphyton
C:0
2
2.67
3.6
3.135
2.69
-
Periphyton
Half-saturation for
nitrogen limited
growth
3
0.01
0.025
0.025
0.02
mg/L
Periphyton
Half-saturation for
phosphorus limited
growth
2
0.005
0.005
0.005
0.001
mg/L
Periphyton
Half-saturation for
periphyton density
3
6.5
6.5
6.5
-
gC/m2
Periphyton
Periphyton Velocity
Half Saturation
2
0.25
0.25
0.25
-
m/s
Periphyton
Periphyton Velocity
Limitation Minimum
2
0.15
0.15
0.15
-
m/s
Periphyton
Carrying capacity
2
10
30
20
-
gC/m2
Table 10. WASP Rates and Constants: Sediment and Detritus Parameters
Sediment/Detritus Parameter
Count
Min
Max
Mean
Median
Representative
Values
Units
Active aerobic layer depth for phosphate flux
model (top layer)
1
0.1
0.1
0.1
0.1
-
cm
Active anaerobic layer depth for phosphate
flux model (bottom layer)
1
9.9
9.9
9.9
9.9
-
cm
Active sediment layer depth for diagenesis and
SOD/ammonia flux model
1
10
10
10
10
-
cm
Ammonia oxidation normalization constant
8
0.37
0.74
0.509
0.37
-
mg O2/L
Burial velocity for layer 2 to inactive sediments
8
0.2
1
0.338
0.25
0.25
cm/yr
Carbon-Nitrogen ratio
8
5.68
5.68
5.68
5.68
-
GC/gN
Carbon-Phosphorus ratio
8
41
41
41
41
-
GC/gP
Carbon-Silica ratio
8
2
2
2
2
-
G C/g Si
Coefficient for calculation of partition
coefficient for phosphate in aerobic layer
1
300
300
300
300
-
-
Critical Oxygen concentration for phosphate
sorption
9
2
2
2
2
2
mg O2/L
Critical Oxygen concentration for silica
sorption
8
2
2
2
2
1
mg/L
Decay constant for benthic stress
8
0.03
0.03
0.03
0.03
0.03
day1
Diagenesis rate for POC, PON, POP G1
8
0.035
0.035
0.035
0.035
0.035
day1
Diagenesis rate for POC, PON, POP G2
8
0.0018
0.0018
0.002
0.0018
0.0018
day1
42
-------
Sediment/Detritus Parameter
Count
Min
Max
Mean
Median
Representative
Values
Units
Diagenesis rate for Si
8
0.5
0.5
0.5
0.5
-
day1
Diffusion coefficient for dissolved mixing
8
5
25
13.44
8.75
-
cm2/d
Diffusion coefficient for particle mixing
9
0.6
0.6
0.6
0.6
0.6
cm2/d
Dissolution rate of particulate biogenic silica at
20 °C
8
0.5
0.75
0.531
0.5
0.5
day1
Fraction of POM in G1 reactivity class
1
0.65
0.65
0.65
0.65
-
-
Fraction of POM in G2 reactivity class
1
0.2
0.2
0.2
0.2
-
-
Fraction of POM in G3 reactivity class
1
0.15
0.15
0.15
0.15
-
-
Fraction POC to G2
8
0.2
0.25
0.206
0.2
-
-
Fraction POC to G3
8
0.1
0.15
0.144
0.15
-
-
Fraction POC, PON, POP to G1
8
0.65
0.65
0.65
0.65
0.65
-
Fraction PON to G2
8
0.25
0.25
0.25
0.25
0.25
-
Fraction PON to G3
8
0.1
0.1
0.1
0.1
-
-
Fraction POP to G2
8
0.2
0.25
0.206
0.2
0.2
-
Fraction POP to G3
8
0.05
0.15
0.138
0.15
-
-
Half-saturation coefficient for ammonia in the
nitrification reaction
8
728
728
728
728
0.728
mgN/m3
Half-saturation constant of Dissolved Silica in
dissolution reaction
8
50
100
62.5
50
-
gSi/L
Mineralization rate of POM in G1 reactivity
class at 20°C
1
0.035
0.035
0.035
0.035
-
day1
Mineralization rate of POM in G2 reactivity
class at 20°C
1
0
0
0
0
-
day1
Mineralization rate of POM in G3 reactivity
class at 20°C
1
0
0
0
0
-
day1
Particle mixing half-saturation constant for
oxygen
8
4
4
4
4
4
mg O2/L
Partition coefficient between
Dissolved/Sorbed phosphate in Layer 1
8
20
300
79.4
37.5
-
L/kg
Partition coefficient between
Dissolved/Sorbed phosphate in Layer 2
9
20
1000
171.1
100
20
L/kg
Partition coefficient between
Dissolved/Sorbed silica in Layer 1
8
5
10
9.063
10
-
L/kg
Partition coefficient between
Dissolved/Sorbed silica in Layer 2
8
15
100
83.1
100
100
L/kg
Reaction velocity for dissolved ammonia
oxidation
9
0.09
0.16
0.130
0.131
0.1313
m/d
Reaction velocity for dissolved nitrate
oxidation in Layer 1
7
0.085
0.125
0.101
0.1
0.1
m/d
Reaction velocity for dissolved nitrate
oxidation in Layer 2
7
0.25
0.25
0.25
0.25
0.25
m/d
Reaction velocity for dissolved sulfide
oxidation in Layer 1
8
0.2
0.2
0.2
0.2
0.2
m/d
43
-------
Sediment/Detritus Parameter
Count
Min
Max
Mean
Median
Representative
Values
Units
Reaction velocity for dissolved sulfide
oxidation in Layer 2
8
0.4
0.4
0.4
0.4
-
m/d
Reaction velocity for methane oxidation
1
1.25
1.25
1.25
1.25
0.7
m/day
Reference concentration of POC in reactivity
class G1 for particle mixing calculation in
phosphate flux model
1
0.1
0.1
0.1
0.1
0.2667
mgC/g
Silica detritus flux
8
0.1
100
73.8
100
-
g/m3/d-
Silica saturation concentration in porewater
8
40
40
40
40
40
mgSi/L
Solids concentration in Layer 1
7
0.5
0.95
0.56
0.5
-
kg/L
Solids concentration in Layer 2
6
0.5
1.09
0.60
0.5
-
kg/L
Sulfide oxidation normalization constant
8
4
4
4
4
4
mg O2/L
Sulfide partition coefficient
8
1
1
1
1
-
-
Sulfide partition coefficient in Layer 1
8
100
100
100
100
100
L/kg
Sulfide partition coefficient in Layer 2
8
100
100
100
100
100
L/kg
Temperature coefficient for ammonia
oxidation
16
1.123
1.125
1.124
1.124
1.123
-
Temperature coefficient for Dd
8
1.08
1.15
1.096
1.09
1.08
-
Temperature coefficient for diagenesis of POC,
PON, POP G1
8
1.1
1.1
1.1
1.1
1.1
-
Temperature coefficient for diagenesis of POC,
PON, POP G2
8
1.15
1.15
1.15
1.15
1.15
-
Temperature coefficient for diagenesis of Si
8
1.1
1.1
1.1
1.1
-
-
Temperature coefficient for Dp
8
1.08
1.15
1.107
1.117
1.117
-
Temperature coefficient for methane and
ammonia oxidation
1
1.079
1.079
1.079
1.079
1.079
-
Temperature coefficient for nitrate oxidation
8
1.08
1.1
1.083
1.08
1.08
-
Temperature coefficient for POM in G1
reactivity class
1
1.1
1.1
1.1
1.1
-
-
Temperature coefficient for POM in G2
reactivity class
1
1.15
1.15
1.15
1.15
-
-
Temperature coefficient for POM in G3
reactivity class
1
0
0
0
0
-
-
Temperature coefficient for sulfide oxidation
8
1.08
1.08
1.08
1.08
1.079
-
Temperature correction coefficient for
diffusion coefficient for dissolved phase mixing
1
1.08
1.08
1.08
1.08
-
-
Temperature correction coefficient for
diffusion coefficient for particle mixing
1
1.117
1.117
1.117
1.117
-
-
Temperature Effect on Silica dissolution
8
1.1
1.1
1.1
1.1
1.1
-
Thickness of active sediment layer
8
10
10
10
10
0.1
cm
44
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Calibration Data and Approaches
As is the case for the other models contained within this report, a primary concern with calibration of
WASP is collecting enough high-quality data, to both describe the pollutant inputs to the system as well
as make qualitative model versus data comparisons and/or perform quantitative skill assessment.
Generally, input data consists of:
• Pollutant loadings to the system, including point and non-point sources and if the surface area
of the waterbody under investigation is large enough, atmospheric sources as well;
• Boundary conditions, either at the upstream end of streams, rivers or inflows to lakes and
reservoirs, or at the downstream ends of estuaries, tidal embayments, or coastal waterbodies;
and
• Exogenous inputs such as solar radiation, winds, and light attenuation.
Although not traditionally thought of as an "input" to a water quality model, transport information
provided by a companion or coupled hydrodynamic model is an important input to a water quality
model. If the hydrodynamic model fails to reproduce the major features of transport within a
waterbody, in particular, vertical stratification due to thermal heating in lakes and reservoirs, density
driven circulation in estuarine, tidal embayments, and coastal systems, destratification due to wind-
mixing, and fall decreases in air temperatures, then the accompanying water quality model will likely not
calibrate well to the water quality variables of interest such as dissolved oxygen and phytoplankton
biomass.
As was mentioned earlier, it is generally desirable to have multiple or multi-year datasets for model
calibration. In the case of BOD/DO models, year-long data sets are generally not necessary because the
models are generally being applied to worst-case conditions, such as the "7Q10" or the lowest 7-day
average flow that occurs on average once every 10 years. However, it is good modeling practice to
calibrate and confirm model performance with a few DO surveys. In the case of more complicated
eutrophication models, especially as applied to lakes, reservoirs, and estuarine applications, model
calibration/confirmation to a few year-long or seasonal surveys or multi-year data sets is preferable, to
avoid over-calibrating a model using a dataset that is not representative of more typical or average
environmental conditions.
Most, but not all, of the WASP studies met these conditions. However, not meeting these conditions
was not sufficient to rule out a study if the calibration and the RCK values used in the model calibration
appeared reasonable based on expert judgment. Most of the phytoplankton or eutrophication modeling
studies used multi-year studies. Available datasets within these studies generally included monthly
sampling and in some cases bi-weekly sampling that occurred during the critical spring and summer
periods. Generally, these datasets also included multiple monitoring or sampling stations within the
waterbody, and qualitative and quantitative skill assessment results were presented for a subset of
these stations.
The addition of SFM capabilities to WASP and other water quality modeling programs, such as Q2K,
Q2Kw, and CE-QUAL-W2, has both removed a degree of freedom in model calibration and improved
model capability in projecting changes in future water quality in response to a management scenario.
Prior to the SFM, sediment oxygen demand (SOD) and nutrient fluxes were effectively another boundary
condition to the water column that had to be parameterized by the user. While sometimes supported by
45
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field measurements of SOD and nutrient fluxes, the sediments were generally treated as an adjustable
parameter in model calibration. The problem, however, was to predict the change in SOD and nutrient
flux that would result from implementing a management action to reduce organic matter or nutrient
inputs to the waterbody. Use of the SFM has largely removed this degree of freedom in model
calibration, since now there is a direct coupling and mass balance between the water column and the
sediment bed. SFM tracks the deposition of phytoplankton and detrital organic matter to the sediment,
its decomposition or diagenesis within the bed, and the flux of resultant end-products (SOD and
nutrients) back to the overlying water column, all within a mass balance framework. This capability is
likely most useful to systems having an abundance of fine sediments and may be less applicable to
cobble or gravel dominated river systems.
Of interest is the fact that, with a very few exceptions, the RCK values arrived at through the original
development and calibration of the SFM to Chesapeake Bay (DiToro and Fitzpatrick, 1993) and as
documented in DiToro (2001) have not changed in the various applications to different waterbodies.
Generally, the only SFM coefficients that have varied from site to site are the phosphorus partition
coefficients and the particle mixing coefficients. These values may change from model application to
model application or from site to site based on the quantities of iron that are contained in local
sediments that effect phosphorus partitioning to iron oxides, and the types and numbers of biota and
sediments that are present in the waterbody, which can affect particle mixing in the sediment bed. In
the case of the latter, sites that are dominated by the presence of combined sewer overflows (CSO) and
a limited pollution-tolerant benthic community would be expected to have less bioturbation or particle
mixing as compared to an oligotrophic or mesotrophic waterbody with a more diverse benthic
community, which could include a greater population of burrowing organisms. Given the consistent use
of the original defaults in numerous applications, potential users of the SFM should carefully consider
deviations from the reported SFM values presented in the RCK tables.
Overall, many WASP parameters in recent literature were determined through manual calibration using
default or literature starting values (from the scientific literature, site specific studies, from the EPA
1985 Rates Manual, etc.). Values for individual parameters were sometimes altered slightly, but
remained within ranges suggested in the literature and the EPA 1985 Rates Manual, and in the WASP
model manual as applicable in an effort to improve model skill (i.e., reduce relative or mean differences
and RMSE of the modeled values against observed data). For most parameters, the default values
remained unchanged during calibration. For the studies where parameters were manually calibrated,
the researchers or model practitioners followed a generally consistent procedure to achieve good
agreement between modeled and observed data, first calibrating hydrodynamics then water quality.
Generally, within each RCK category, model coefficients or parameters were manipulated in a logical
way and were not changed at random to increase model fit. There were a few cases, however, where
reaeration rates or SOD appear to have been adjusted slightly by model segment/distance or season,
the reason(s) for which were not explained in the paper. There were also a few cases where a specific
model coefficient fell outside of the range of generally acceptable bounds, but may not have affected
the calibration directly. These occurrences are documented in the RCK tables.
46
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4.2 CE-QUAL-W2
The CE-QUAL-W2 (W2) model is a 2D laterally averaged model that has been applied in a variety of
systems where longitudinal and vertical gradients are likely to exist. Because of consistent model
updates and use, there is a large body of literature that presents hydrodynamics and water quality
studies using W2. [See section 2.2 for more details.]
Summary of Sources
Literature searches returned thousands of documents that reference W2, although many were not
applications of the model. As discussed above, the methodology for identifying relevant literature was
composed of multiple culling steps that eventually resulted in a relatively small subset of papers and
reports that met all relevance criteria. From an initial pool of thousands of search results, more than 100
were pulled from searches for initial assessment, resulting in 57 papers being selected for detailed
review (Table 11). The screening process used for this task disqualified papers without electronic access,
making it likely that some papers with relevant, documented RCK values were removed from
consideration due to lack of availability. Throughout the literature evaluation process, preference was
given to documents with thorough model documentation, as described in Section 3.
Of the 57 papers and reports that were reviewed, 31 passed relevance and criteria checks. These
consisted of: 12 U.S. Geological Survey (USGS) reports; seven peer-reviewed journal articles; five
Portland State University (PSU) reports (prepared for the States of Washington and Idaho); four USACE
modeling reports; one report each by the USDA, the State of Washington, and Tetra Tech (prepared for
the State of Ohio). Many of the W2 reported model applications were led by a relatively small group of
model practitioners associated with USGS, USACE, and PSU. The remaining body of literature was not
useful for the purposes of this study (i.e., no parameter values were provided), but does show the
breadth of W2 application. For example, PSU reports more than 100 current projects utilizing W2 as a
hydrodynamic and/or water quality model and a history of more than 2,300 documented applications
worldwide. Many of these studies do not have publicly accessible calibration reports or results at this
time.
For additional resources regarding CE-QUAL-W2, see also Section 9 of this report.
47
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Table 11. CE-QUAL-W2 Literature Sources
Citation
Study
Location
Type of
Waterbody
Watershed Characteristics
Calibration period
Notes
Afshar, A., and M. Saadatpour, 2009. Reservoir
Eutrophication Modeling, Sensitivity Analysis,
and Assessment: Application to Karkheh
Reservoir, Iran. Environmental Engineering
Science. 26(7).
Karkheh
Reservoir,
Iran
(southwest)
Reservoir
50,000 km2 drainage; avg depth =
61.8 m; active storage = 3500
Mm3; primarily arid landcover
with minimal agriculture
May-December 2005
(monthly data)
Annear R., S. Wells, and C. Berger, 2005. Upper
Spokane River Model in Idaho: Boundary
Conditions and Model Setup and Calibration for
2001 and 2004. Portland State University
Technical Report EWR-02-05. Prepared for the
Washington Department of Ecology.
Upper
Spoke River,
Idaho
River
15,540 km2 drainage; avg Q =100
m3/s; primarily forested with
urban influence in City of Coeur
d1 Alene; 3 WWTP discharges
January-December
2001
Updated model from
Wells, 2003 with
additional data.
Annear, R., C. Berger, and S. Wells, 2006. Pend
Oreille River Model: Model Development and
Calibration. Portland State University Technical
Report EWR-02-06. Prepared for the Idaho
Department of Environmental Quality.
Pend Oreille
River,
Oregon
River
avg Q =600 m3/s; primarily
forested with some agriculture
and urban cover; 3 WWTP
discharges
Summer 2004, 2005
(continuous T;
variable WQ sampling
intervals)
Bales, J., K. Sarver, and M. Giorgino, 2001.
Mountain Island lake, North Carolina: Analysis of
Ambient Conditions and Simulation of
Hydrodynamics, Constituent Transport, and
Water-Quality Characteristics, 1996-1997. USGS
Water Resources Investigations Report 01-4138.
Mountain
Island Lake,
North
Carolina
Reservoir
4,820 km2 drainage; avg depth =
4.9 m; primarily forested
watershed with minor residential
and agricultural use; water level
controlled by very large upstream
reservoir
April 1996-September
1997 (continuous T,
DO, SC; periodic WQ
vertical profiles; bi-
monthly WQ grab
samples)
Berger, C., R. Annear, and S. Wells, 2001. Lower
Willamette River Model: Model Calibration.
Portland State University Department of Civil
Engineering Technical Report EWR-2-01.
Lower
Willamette
River,
Oregon
River
29,785km2 drainage; mixed
forest, agriculture, and
developed land (includes
Portland); known WWTP point
discharges; tidally influenced at
lower reaches
May-October 1993,
'94, '97, '98, '99
Berger, C., R. Annear, and S. Wells, 2003. Upper
Spokane River Model: Model Calibration, 2001.
Portland State University Department of Civil
Engineering Technical Report EWR-1-03.
Prepared for the City of Spokane.
Upper
Spokane
River,
Washington
River
avg Q =150 m3/s; mixed forested,
agriculture, clearcut; 4 point
source discharges in City of
Spokane; other details in Annear
et al, 2001 background data
report
March-September
2001 (continuous Q
periodic WQ)
Update to Berger et al.
2002 model (above).
48
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Citation
Study
Location
Type of
Waterbody
Watershed Characteristics
Calibration period
Notes
Berger, C., R. Annear, S. Wells, and T. Cole, 2002.
Upper Spokane River Model: Model Calibration,
1991 and 2000. Portland State University
Department of Civil Engineering Technical Report
EWR-01-02. Prepared for the Washington
Department of Ecology.
Upper
Spokane
River,
Washington
River
avg Q =150 m3/s; mixed forested,
agriculture, clearcut; 4 point
source discharges in City of
Spokane; other details in Annear
et al, 2001 background data
report
February-September
1991 and January-
September 2000
(continuous Qand
water level; periodic
WQ)
Cole, T., and D. Tillman, 2001. Water Quality
Model of Allatoona and West Point Reservoirs
using CE-QUAL-W2. ERDC/EL SR-01-3, U.S. Army
Engineer Research and Development Center.
Allatoona
Lake and
West Point
Lake,
Georgia
Reservoirs
Allatoona Lake: 2,845 km2
drainage; some municipal and
agricultural input
West Point Lake: 8,754 km2
drainage; abundant municipal
(Atlanta) and agricultural
influence
Allatoona Lake: 1992,
1993, 1996, 1997
(hourly inflows, daily
outflows; very limited
WQ data)
West Point Lake:
1979, 1996, 1997
(hourly inflows, daily
outflows; very limited
WQ data)
Some boundary
parameters calculated
from other available data
(inflow T calculated from
meteorological data; WQ
data set to upstream
sample).
Cole, T.M., and D.H. Tillman, 1997. "Water
Quality Modeling of Lake Monroe Using CE-
QUAL-W2," Miscellaneous Paper EL-99-1, U.S.
Army Engineer Waterways Experiment Station,
Vicksburg, Mississippi.
Lake
Monroe,
Indiana
Reservoir
1,142 km2 drainage; avg
depth=5.5-7m; residence
time=180-410 days; active
storage=300-430 Mm3; primarily
forested, minor agriculture
First calibrated to
1994 (most WQ data,
low water year); 1992,
1995,1996 added
after (more normal
water years); WQ data
available only for 1994
Relatively limited WQ
data. Some calculations
used to estimate specific
WQ concentrations.
Debele, B., R. Srinivasan, and J. Parlange, 2006.
Coupling upland watershed and downstream
waterbody hydrodynamic and water quality
models (SWAT and CE-QUAL-W2) for better
water resources management in complex river
basins. Environmental Model Assessment. 13.
135-153.
Cedar Creek
Reservoir
(and upland
watershed),
Texas
Reservoir
5,244 km2 drainage; active
storage = 698 Mm3; avg
depth=6.5 m; primarily
agricultural (64%) with mixed
forest (12%) and residential
(11%); 2 WWTP inflows
SWAT output used as
CE-QUAL-W2 input;
W2 simulation for
1997 to 2001 with
hourly boundary data
(from SWAT)
Coupled watershed
(SWAT) and waterbody
(CE-QUAL-W2) model.
Flowers, J., L. Hauck, and R. Kiesling, 2001 Water
Quality Modeling of Lake Waco Using CE-QUAL-
W2 for Assessment of Phosphorus Control
Strategies. Prepared for the USDA: Lake Waco-
Bosque River Initiative. TR0114.
Lake Waco
and Bosque
River, Texas
Reservoir
4,300 km2 drainage; avg depth -
6m; active storage = 179 Mm3;
primarily forested with 29%
agriculture and known non-point
source contamination issues
June 1996-July 1998
(monthly data)
Coupled SWAT/CE-QUAL-
W2; independent
calibration.
49
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Citation
Study
Location
Type of
Waterbody
Watershed Characteristics
Calibration period
Notes
Galloway, J., and W. Green, 2002. Simulation of
Hydrodynamics, Temperature, and Dissolved
Oxygen in Norfork Lake, Arkansas, 1994-1995.
USGS Water Resources Investigations Report 02-
4250.
Norfork
Lake,
Arkansas
Reservoir
4,683 km2 drainage; active
storage = 1,540 Mm3; avg
depth=17 m; retention time=0.9
years; mixed forested and
agricultural
January 1994 -
December 1995 (daily
T; periodic vertical
profiles and boundary
values for chemical
data)
Galloway, J., and W. Green, 2006. Analysis of
Ambient Conditions and Simulation of
Hydrodynamics and Water Quality
Characteristics in Beaver Lake, Arkansas, 2001
through 2003. USGS Scientific Investigations
Report 2006-5003.
Beaver Lake,
Arkansas
Reservoir
3087 km2 drainage; avg depth =
18m; active storage = 2040 Mm3;
mixed forest and agriculture; 3
cities with point source
discharges in watershed
April 2001-April 2003
(continuous Q
monthly WQonly
during well-mixed
conditions)
Galloway, J., and W. Green, 2003. Simulation of
Hydrodynamics, Temperature, and Dissolved
Oxygen in Bull Shoals Lake, Arkansas, 1994-1995.
USGS Water Resources Investigation Report 03-
4077.
Bull Shoals
Lake,
Arkansas
Reservoir
15,675 km2 drainage; avg min.
outflow = 4.6 m3/s; active
storage = 4194 Mm3; avg depth =
23 m; reservoir retention time =
0.75 years (avg); mixed forested
and agricultural, minor municipal
input
January 1994 -
December 1995 (daily
T; periodic vertical
profiles and boundary
values for chemical
data)
DO concentrations at
inflow set to
concentration for 100%
saturation at a given T.
Galloway, J., R. Ortiz, J. Bales, and D. Mau, 2008.
Simulation of Hydrodynamics and Water Quality
in Pueblo Reservoir, Southeastern Colorado, for
1985 through 1987 and 1999 through 2002.
USGS Scientific Investigations Report 2008-5056.
Pueblo
Reservoir,
Colorado
Reservoir
active storage = 441 Mm3; avg
inflow discharge = 22 m3/s;
primarily plains landcover with
some agriculture and minor
developed land
October 1985 to
September 1987 =
water years 1986 and
1987; daily
inflow/outflow T and
hydrodynamic data;
period WQ data,
regression model used
to interpolate loads)
Some recomputation
done to convert daily
inflow/outflow data to
hourly for use in model.
Some WQdata
interpolated from
discrete samples.
Giorgino, M., and J. Bales, 1997. Rhodhiss Lake,
North Carolina: Analysis of Ambient Conditions
and Simulation of Hydrodynamics, Constituent
Transport, and Water-Quality Characteristics,
1993-1994. USGS Water Resources
Investigations Report 97-4131.
Rhodhiss
Lake, North
Carolina
Reservoir
avg depth = 8 m; mixed-use
watershed (managed forest,
agriculture, urban/industrial,
textile mills, machinery and dye
plants, furniture manufacturing)
April 1993-March
1994 (continuous Q
and water level;
monthly WQ)
50
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Citation
Study
Location
Type of
Waterbody
Watershed Characteristics
Calibration period
Notes
Green, W., J. Galloway, J. Richards, and E.
Wesolowski, 2003. Simulation of Hydrodynamics,
Temperature, and Dissolved Oxygen in Table
Rock Lake, Missouri, 1996-1997. USGS Water
Resources Investigations Report 03-4237.
Table Rock
Lake,
Missouri
Reservoir
10,412 km2 drainage; avg min.
outflow = 4.4 m3/s; active
storage = 3330 Mm3; avg depth =
19 m; reservoir retention time =
0.8 years (avg); mixed agriculture
and forest, some municipal input
January 1996 -
December 1997
(hourly or daily T;
hourly or daily inflow
WQ periodic vertical
profiles)
DO concentrations at
non-measured inflows set
to concentration for 80%
saturation at a given T.
Gunduz, 0., S. Soyupak, and C. Yurteri, 1998.
Development of Water Quality Management
Strategies for the Proposed Isikli Reservoir.
Water Science Technology. 37(2): 369-376.
Proposed
Isikli
Reservoir,
Turkey
Reservoir
active storage = 25 Mm3; max
depth=24 m; mixed agricultural,
developed, and arid landcover
Initial conditions from
March 1995 upstream
river WQ data;
simulation period
March to October
1995
Modeling of a proposed
reservoir, so no model
validation. All coefficients
are default or literature
values.
Ha, S., and J. Lee, 2008. Application of CE-QUAL-
W2 Model to Eutrophication Simulation in
Daecheong Reservoir Stratified by Turbidity
Storms. Proceedings of TAAL2007: The 12th
World Lake Conference. 824-833.
Daecheong
Reservoir,
South Korea
Reservoir
4,166 km2 drainage; avg depth -
20 m; active storage = 790 Mm3;
primarily forested with 20%
agriculture
2003 (wet year) and
2005 (dry year)
Hart, R., W. Green, D. Westerman, J. Peterson,
and J. De Lanoi, 2013. Simulated Effects of
Hydrologic, Water Quality, and Land-Use
Changes of the Lake Maumelle Watershed,
Arkansas, 2004-2010. USGS Scientific
Investigations Report 2012-5246.
Lake
Maumelle,
Arkansas
Reservoir
355 km2 drainage; avg depth =7.6
m; active storage = 270 Mm3;
primarily forested with minor
clearcut and agriculture; no point
source discharges
2004-2010
Coupled HSPF/CE-QUAL-
W2. Outputs from HSPF
used as input to CE-QUAL
following independent
calibration.
Kuo, J., W. Lung, C. Yang, W. Liu, M. Yang, and T.
Tang, 2006. Eutrophication modeling of
reservoirs in Taiwan. Environmental Modelling &
Software. 21(6): 829-844.
Te-Chi and
Tseng-Wen
Reservoirs,
Taiwan
Reservoir
Te-Chi: 592 km2 drainage; active
storage = 183 Mm3
Tseng-Wen: 481 km2 drainage;
active storage = 659 Mm3;
numerous nonpoint nutrient
sources in both reservoirs
(agricultural)
1998-1999 (monthly
WQand vertical T
profiles; continuous
outflow T and
hydrodynamics)
Liu, W, W. Chen, and N. Kimura, 2009. Impact of
phosphorus load reduction on water quality in a
stratified reservoir-eutrophication modeling
study. Environmental Monitoring Assessment.
159:393-406.
Mingder
Reservoir,
Taiwan
Reservoir
61 km2 drainage; active storage =
165 Mm3; mixed forest,
agricultural, residential;
significant nonpoint nutrient
sources; regular algae blooms in
reservoir
2003-2004 (seasonal
WQ samples including
vertical profiles;
continuous
inflow/outflow T and
hydrodynamic data)
51
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Citation
Study
Location
Type of
Waterbody
Watershed Characteristics
Calibration period
Notes
Lung, W. and S. Bai, 2003. A Water Quality
Model for the Patuxent Estuary: Current
Conditions and Predictions under Changing Land-
use Scenarios. Estuaries. 26(2A):267-279.
Patuxent
River
estuary,
Maryland
Estuary
2,401 km2 drainage; mixed forest,
urban, and agricultural; heavily
influenced by point and nonpoint
nutrient sources; downstream of
DC and Baltimore
August 1997 - July
1998 (details on data
collection in Weller et
al. 2003)
Pickett, P. and S. Hood, 2008. Lake Whatcom
Watershed Total Phosphorus and Bacteria Total
Maximum Daily Loads. Volume 1. Water Quality
Study Findings. Department of Ecology State of
Washington. Publication No. 08-03-024, App B-F.
Lake
Whatcom,
Washington
Lake
Volume: 921 Mm3 cubic meters
Mean depth: 46 m
Surface area: 20.3 km2
Land uses are predominantly
urban, rural residential, and
forestry.
Pollution sources: manure,
fertilizers, septic systems, soil
particles, and dust particles.
Jan 2002 - Dec 2003
Coupled HSPF/CE-QUAL-
W2. Outputs from HSPF
used as input to CE-QUAL
following independent
calibration.
Calibration years:
2002 - dry year
2003 - average year
Rounds, S., and T. Wood, 2001. Modeling Water
Quality in the Tualatin River, Oregon, 1991-1997.
USGS Water-Resources Investigations Report 01-
4041; original model: Rounds, S.A., Wood, T.M.,
and Lynch, D.D., 1999, Modeling discharge,
temperature, and water quality in the Tualatin
River, Oregon: U.S. Geological Survey Water-
Supply Paper 2465-B.
Tualatin
River,
Oregon
River
Details on watershed in Rounds,
et al., 1999
Original model
calibrated to May-
October 1991-1993
Updated with May-
October 1994-1997
Expansion on a previous
model to include
additional data.
Smith, D., T. Threadgill, and C. Larson, 2012.
Modeling the Hydrodynamics and water Quality
of the Lower Minnesota River using CE-QUAL-
W2. USACE Technical Report ERDC/ELTR-12-12.
Minnesota
River (lower
40 miles),
Minnesota
River
43,771 km2 drainage; avg
discharge = 4,414 cfs; primarily
agricultural (70%) with increasing
development at river outlet (Twin
Cities); 4 large point source
discharges; lower 15 miles used
as shipping channel
First calibrated to
water year 2006;
recalibrated to 1988
data (low flow year);
validated to 1988 and
2001-2006
52
-------
Citation
Study
Location
Type of
Waterbody
Watershed Characteristics
Calibration period
Notes
Smith, E., R. Kiesling, J. Galloway, and J.
Ziegeweid,. 2014. Water Quality and Algal
Community Dynamics of Three Sentinel
Deepwater Lake in Minnesota Utilizing CE-QUAL-
W2 Models. USGS Scientific Investigations
Report 2014-5066.
Carlos (a),
Elk(b),
Trout (c)
lakes,
Minnesota
Lake
Carlos: 634 km2 drainage;
primarily forested
Elk: 8 km2 drainage; mixed
forest/prairie
Trout: 3.6 km2 drainage; dimictic;
primarily forested
Carlos: April-
November 2011;
Elk: April-November
2011;
Trout: April-October,
2010
3 separate models in 3
sentinel deepwater lakes;
Non-traditional
morphology for CE-QUAL-
W2.
Sullivan, A., and S. Rounds, 2004. Modeling
Hydrodynamics, Temperature, and Water
Quality in Henry Hagg Lake, Oregon, 2000-2003.
USGS Scientific Investigations Report 2004-5261.
Henry Hagg
Lake,
Oregon
Lake
105 km2 drainage; active storage
= 76 Mm3; primarily forested with
few (if any) contaminant sources;
high extraction demand
2000-2001
(continuous water T
and meteorology;
monthly WQ)
Sullivan, A., and S. Rounds, 2011. Modeling
Hydrodynamics, Water Temperature, and Water
Quality in the Klamath River Upstream of Keno
Dam, Oregon, 2006-2009. USGS Scientific
Investigations Report 2011-5105.
Klamath
River,
Oregon
River
Channel width =100-300 m;
depth = <1-6 m; 3 large WWTP
inputs; flow-controlled river with
irrigation diversions
April-November 2006-
2009 (continuous
monitoring;
intermittent grab
samples)
Tetra Tech, 2008. TMDLs for the Black River
Watershed, Ohio. Prepared for the State of Ohio
Environmental Protection Agency.
Lower Black
River, Ohio
River
1,217 km2 drainage; avg Q=333
cfs; mixed agricultural and highly
urbanized land uses; numerous
point source discharges and
abundant nonpoint influence;
highly impaired river
Jan 2002 - Dec 2003
Coupled HSPF/CE-QUAL-
W2. Outputs from HSPF
used as input to CE-QUAL
following independent
calibration.
Tillman, D., T. Cole, and B. Bunch, 1999. Detailed
Reservoir Water Quality Modeling (CE-QUAL-
W2), Alabama-Coosa-Tallapoosa/Apalachicola-
Chattahoochee-Flint (ACT/ACF) Comprehensive
Water Resource Study. USACE ERDC Technical
Report EL-99-15.
Weiss, Neely
Henry, and
Walter
George
Reservoirs,
Alabama
Reservoirs
Report includes engineering
characteristics of each reservoir
(water elevation, embankment
and spillway size, powerhouse
capacity, etc.)
January 1991 -
November 1994
(discontinuous
historical records
across reservoirs;
monthly samples
where available;
primarily summer/fall
sampling dates)
Model calibrated to 3
separate reservoirs. Post-
calibration parameters
identical for all.
53
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As a 2-D laterally averaged model capable of simulating vertical and longitudinal hydrodynamics and
water quality, W2 can be applied for a variety of purposes. The studies examined during this project
reflected the range of possible applications of W2, with the main trend across all studies being the
desire to model in two dimensions for both hydrodynamics (such as velocities, water level, outflow
discharge, thermal stratification, etc.) and water quality (such as nutrient loads, DO, and pH). W2 can be
used to simulate reservoir conditions under changing watershed conditions. In some cases, this can be
accomplished by coupling a separate watershed model (e.g., SWAT, HSPF) with W2 and using the output
from watershed models as the upstream boundary condition for W2. Two of the sources of RCK values
included in the data table used this coupled model method.
W2 has been applied nationwide and globally. Nationally, the studies are clustered in certain regions,
with many W2 applications in the Pacific Northwest (Washington, Oregon, Idaho) and South/Southeast
(Arkansas, Missouri, Alabama, Georgia). There were additional studies performed elsewhere in the
United States including North Carolina, Minnesota, Indiana, Texas, and Colorado. The peer-reviewed
journal articles provide the remaining geographic range, both nationally and globally, with model
applications in: Texas, Maryland, Taiwan, Turkey, Korea, and Iran. It is clear from the geographic
distribution of the W2 applications, both by government agencies and academic researchers, that the
model can be applied in many geographic regions. The only area not represented in the selected papers
was the Northeast.
As discussed above, W2 was developed and optimized for use in relatively long and narrow waterbodies,
and has been applied in reservoirs, lakes, estuaries, and linked waterbody systems (multiple reservoirs).
Most of the applications have been to reservoirs, in part due to the needs of the agency that originally
developed W2 (USACE) and since the original model was not applicable to rivers (or systems with
significant bottom slope). The W2 model was updated in 2007 (Version 3 and higher) to allow simulation
of free-flowing rivers. As a result, W2 can model linked rivers and reservoirs, which is reflected in the
literature, with many studies simulating the upstream and/or downstream water body in addition to the
reservoir. W2 has also been used in systems with non-ideal geomorphologies (e.g., small, deep lakes
with very small surface area to volume ratios) to assess its capabilities to model vertical gradients in
those systems.
Basin sizes ranged from <10 to tens of thousands of km2 with a wide range of lake/reservoir volumes
and surface areas. Land use within these basins ranged from heavily forested to agricultural and urban,
with many rivers and reservoirs impacted by nonpoint and point source pollution. Nearly all the
modeled waterbodies were influenced by some degree of runoff or WWTP pollution. Details on the
watershed characteristics for each included study are contained within Table 11. The resulting
distributions of rate values are summarized in Table 12. Note that the current release of CE-QUAL-W2
also includes separate rates for macroalgae, but none of the selected examples includes that module.
Default rates are shown as provided in Cole and Wells (2018).
54
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Summary Statistics for Rates and Constants
Table 12. CE-QUAL-W2 Rates and Constants
Group
Parameter
Description
Default
Count
Min
Max
Median
Units
ALGAL RATE
AG
Maximum algal growth rate
2
28
0.34
6.5
1.9
day1
ALGAL RATE
AR
Maximum algal respiration rate
0.04
28
0.005
0.4
0.04
day1
ALGAL RATE
AE
Maximum algal excretion rate
0.04
28
0.005
0.15
0.04
day1
ALGAL RATE
AM
Maximum algal mortality rate
0.1
28
0
0.41
0.08
day1
ALGAL RATE
AS
Algal settling rate
0.1
28
0
0.8
0.1
day1
ALGAL RATE
AHSP
Algal half-saturation for phosphorus limited growth
0.003
28
0.0005
0.042
0.003
g m"3
ALGAL RATE
AHSN
Algal half-saturation for nitrogen limited growth
0.014
28
0
0.2
0.014
g m"3
ALGAL RATE
AHSSI
Algal half-saturation for silica limited growth
0
7
0
0.003
0
g m"3
ALGAL RATE
ASAT
Light saturation intensity at maximum photosynthetic
rate
100
25
40
500
90
W m"2
ALGAL TEMP
ATI
Lower temperature for algal growth
5
23
0
16
5
°C
ALGAL TEMP
AT 2
Lower temperature for maximum algal growth
25
23
5
30
16.5
°C
ALGAL TEMP
AT 3
Upper temperature for maximum algal growth
35
24
10
35.1
25
°C
ALGAL TEMP
AT4
Upper temperature for algal growth
40
24
20
40
35
°C
ALGAL TEMP
AK1
Fraction of algal growth rate at ATI
0.1
23
0.1
0.2
0.1
ALGAL TEMP
AK2
Fraction of maximum algal growth rate at AT2
0.99
23
0.6
0.99
0.99
ALGAL TEMP
AK3
Fraction of maximum algal growth rate at AT3
0.99
23
0.95
0.99
0.99
ALGAL TEMP
AK4
Fraction of algal growth rate at AT4
0.1
22
0.01
0.3
0.1
ALG STOICH
AP
Stoichiometric equivalent between algal biomass and
phosphorus, fraction
0.005
15
0.0015
0.02268
0.005
ALG STOICH
AN
Stoichiometric equivalent between algal biomass and
nitrogen, fraction
0.08
15
0.059
0.0825
0.08
ALG STOICH
AC
Stoichiometric equivalent between algal biomass and
carbon, fraction
0.45
15
0.45
0.55
0.45
55
-------
Group
Parameter
Description
Default
Count
Min
Max
Median
Units
ALG STOICH
ASI
Stoichiometric equivalent between algal biomass and
silica, fraction
0.18
3
0.18
0.18
0.18
ALG STOICH
ACHLA
Ratio between algal biomass and chlorophyll a in terms
of mg algae/ng chl-a
0.05
11
0.031
0.4
0.094
mg algae/ng
chl-a
ALG STOICH
APOM
Fraction of algal biomass that is converted to
particulate organic matter when algae die
0.8
18
0.5
0.8
0.8
ALG STOICH
ANPR
Algal half saturation constant for ammonium
preference
0.001
3
0.001
0.003
0.001
EPI RATE
EG
maximum epiphyton/periphyton growth rate
2
5
1.2
2
1.5
day1
EPI RATE
ER
maximum epiphyton/periphyton respiration rate
0.04
5
0.04
0.15
0.04
day1
EPI RATE
EE
maximum epiphyton/periphyton excretion rate
0.04
5
0.04
0.04
0.04
day1
EPI RATE
EM
maximum epiphyton/periphyton mortality rate
0.1
5
0.1
0.1
0.1
day1
EPI RATE
EB
epiphyton/periphyton burial rate
0.001
4
0.001
0.1
0.001
EPI RATE
EHSP
epiphyton half-saturation for phosphorus limited
growth
0.003
0
N/A
N/A
N/A
g m"3
EPI RATE
EHSN
epiphyton half-saturation for nitrogen limited growth
0.014
0
N/A
N/A
N/A
g m"3
EPI RATE
EHSSI
epiphyton half-saturation for silica limited growth
-
0
N/A
N/A
N/A
g m"3
EPI HALF
ESAT
light saturation intensity at maximum photosynthetic
rate
75
5
75
150
150
W m"2
EPI HALF
EHS
biomass limitation factor
35
1
20
20
20
g m"2
TEMP
ET1
Lower temperature for periphyton growth
5
5
1
5
1
°C
TEMP
ET2
Lower temperature for maximum periphyton growth
25
5
3
25
3
°C
TEMP
ET3
Upper temperature for maximum periphyton growth
35
5
16
35
20
°C
TEMP
ET4
Upper temperature for periphyton growth
40
5
30
40
30
°C
TEMP
EK1
Fraction of periphyton growth rate at ET1
0.1
5
0.1
0.3
0.1
TEMP
EK2
Fraction of maximum periphyton growth rate at ET2
0.99
5
0.6
0.99
0.99
TEMP
EK3
Fraction of maximum periphyton growth rate at ET3
0.99
5
0.99
0.99
0.99
TEMP
EK4
Fraction of periphyton growth rate at ET4
0.1
5
0.1
0.1
0.1
EPI STOICH
EP
Stoichiometric equivalent between
epiphyton/periphyton biomass and phosphorus
0.005
4
0.003
0.005
0.0045
56
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Group
Parameter
Description
Default
Count
Min
Max
Median
Units
EPI STOICH
EN
Stoichiometric equivalent between
epiphyton/periphyton biomass and nitrogen
0.08
4
0.06
0.08
0.08
EPI STOICH
EC
Stoichiometric equivalent between
epiphyton/periphyton biomass and carbon
0.45
4
0.45
0.45
0.45
EPI STOICH
ESI
Stoichiometric equivalent between
epiphyton/periphyton biomass and silica
0.18
1
145
145
145
EPI STOICH
EPOM
Fraction of epiphyton/periphyton biomass that is
converted to particulate organic matter when
epiphyton/periphyton die
0.8
4
0.8
0.8
0.8
DOM
LDOMDK
Labile DOM decay rate
0.1
24
0.03
0.5
0.1
day1
DOM
RDOMDK
Refractory DOM decay rate
0.001
23
0.0005
0.015
0.001
day1
DOM
LRDDK
Labile to refractory DOM decay rate
0.01
22
0.001
0.01
0.001
day1
POM
LPOMDK
Labile POM decay rate
0.08
23
0.002
0.101
0.08
day1
POM
RPOMDK
Refractory POM decay rate
0.001
16
0.0005
0.01
0.001
day1
POM
LRPDK
Labile to refractory POM decay rate
0.01
8
0.001
0.02
0.0015
day1
POM
POMS
POM settling rate
0.45
22
0
2.5
0.165
day1
OM STOICH
ORGP
Stoichiometric equivalent between organic matter and
phosphorus
0.005
20
0.0005
0.02268
0.005
OM STOICH
ORGN
Stoichiometric equivalent between organic matter and
nitrogen
0.08
19
0.01
0.0825
0.08
OM STOICH
ORGC
Stoichiometric equivalent between organic matter and
carbon
0.45
16
0.45
0.6
0.45
OM STOICH
ORGSI
Stoichiometric equivalent between organic matter and
silica
0.18
2
0.18
0.18
0.18
OM RATE
OMT1
Lower temperature for organic matter decay
4
21
2
5
4
°C
OM RATE
OMT2
Upper temperature for organic matter decay
25
21
20
30
30
°C
OM RATE
OMK1
Fraction of organic matter decay rate at OMT1
0.1
21
0.05
0.2
0.1
OM RATE
OMK2
Fraction of organic matter decay rate at OMT2
0.99
21
0.9
0.99
0.99
CBOD
KBOD
5-day decay rate @ 20 °C
0.1
11
0.0186
2
0.07475
day1
57
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Group
Parameter
Description
Default
Count
Min
Max
Median
Units
CBOD
TBOD
Arrhenius Temperature coefficient
1.02
9
1.0147
1.047
1.02
CBOD
RBOD
Ratio of CBOD5 to ultimate CBOD
1.85
9
1
1.85
1
CBOD
CBODS
CBOD settling rate
0
1
0
0
0
day1
CBOD STOICH
CBODP
P stoichiometry for CBOD decay (mg P/mg O2)
0.004
7
0.002
2
0.083
mg P/mg O2
CBOD STOICH
CBODN
N stoichiometry for CBOD decay (mg N/mg O2)
0.06
6
0.06
1.047
0.08
mg N/mg O2
CBOD STOICH
CBODC
C stoichiometry for CBOD decay (mg C/mg O2)
0.32
6
0.32
1.85
0.825
mg C/mg O2
PHOSPHOR
P04R
Sediment release rate of phosphorus, fraction of SOD
0.001
22
0.0001
0.05
0.00204
PHOSPHOR
PARTP
Phosphorus partitioning coefficient for suspended
solids
0
18
0
3
0
AMMONIUM
NH4REL
Sediment release rate of ammonium, fraction of SOD
0.001
20
0.001
0.2
0.02
AMMONIUM
NH4DK
Ammonium decay rate
0.12
27
0.01
0.4
0.12
day1
NH4 RATE
NH4T1
Lower temperature for ammonia decay
5
22
4
10
5
°C
NH4 RATE
NH4T2
Lower temperature for maximum ammonia decay
25
22
20
35
25
°C
NH4 RATE
NH4K1
Fraction of nitrification rate at NH4T1
0.1
22
0.1
0.2
0.1
NH4 RATE
NH4K2
Fraction of nitrification rate at NH4T2
0.99
22
0.99
0.99
0.99
NITRATE
N03DK
Water column denitrification rate or nitrate decay rate
0.03
26
0.01
2.6
0.1
day1
NITRATE
N03S
Nitrate loss velocity to the sediments because of
sediment denitrification
0.001
5
0
0.5
0.2
m day1
N03 RATE
N03T1
Lower temperature for nitrate decay
5
21
4
5
5
°C
N03 RATE
N03T2
Lower temperature for maximum nitrate decay
25
21
20
30
25
°C
N03 RATE
N03K1
Fraction of denitrification rate at N03T1
0.1
21
0.1
0.1
0.1
N03 RATE
N03K2
Fraction of denitrification rate at N03T2
0.99
21
0.99
0.99
0.99
SILICA
DSIR
Dissolved silica sediment release rate, fraction of SOD
0.1
3
0.1
0.1
0.1
SILICA
PS IS
Particulate biogenic settling rate
1
3
0.04
1
0.1
m sec1
SILICA
PSIDK
Particulate biogenic silica decay rate
0.3
3
0.1
0.3
0.3
day1
SILICA
PARTS 1
Dissolved silica partitioning coefficient
0
2
0
0.2
0.1
58
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Calibration Data and Approaches
The primary concern with calibration of the W2 model is collecting enough high-quality input data, both
boundary conditions and in-pool conditions. W2 will not produce a well-calibrated model using only in-
pool measurements and requires boundary conditions for inflow, outflow, and tributaries to model
hydrodynamics and water quality. As described in the model manual, meteorological and inflow/outflow
hydrodynamic data should ideally be continuous for the calibration year with hourly to daily
measurements. W2 is capable of modeling diel fluctuations, which require hourly data at least for
successful calibration and simulation. Monthly in-pool sampling may be appropriate, although storm
events may warrant additional sampling attention. For this task, the length of calibration period and
spatiotemporal sampling frequency were not considered as disqualifying characteristics during literature
review, although multiple studies did mention the potential shortcomings of a limited dataset. Nearly all
the studies using W2 had sufficient input data and/or took steps to address data limitations. Details on
calibration periods for each RCK parameter source are included in Table 6.
All the W2 studies used at least a single water year for calibration, and many used multiple water years
with varying hydrologic conditions (wet/dry). In some cases, additional calibration years were added to
previously calibrated models in the same system to increase model confidence. During model
evaluation, most of the studies used multiple water years to make sure that the calibrated model could
accurately simulate a wide range of hydrologic conditions. Most of the studies had continuous
inflow/outflow temperature and hydrodynamic data (such as discharge and water level) at an hourly to
daily interval. For studies with insufficient data, nearby meteorological stations and available hydrologic
data were correlated to generate hourly to daily inflow values. Most of the studies also calibrated using
vertical profiles in addition to in-pool point samples, both of which were collected monthly with
additional storm samples. In some cases, the in-pool measurements were taken only seasonally,
although the studies included a discussion of potential issues associated with limited data. For all
studies, whenever possible, the calibration was conducted using the water year(s) with the largest
amount of available data. Generally, errors in prediction of temperatures, stratification, and transport
were commonly attributable to inadequate bathymetric data or poorly defined boundary conditions.
Many parameters in the RCK tables were determined through manual calibration using default or
literature starting values. Initial values came from other studies of similar systems, including the EPA
1985 Rates Manual, extensive tables of values included in the W2 manuals, and other literature.
Calibration strategies varied, but most commonly involved systematic variation of individual parameters
within ranges suggested in the literature and model manual to obtain the best graphical "fit" of model
predictions and observations (qualitative) and/or quantitatively reduce RMSE of the modeled values
against observed data. In many cases, the default values or literature values remained unchanged during
calibration. For the studies where parameters were manually calibrated, the researchers followed a
generally consistent procedure to achieve good agreement between modeled and observed data,
calibrating first hydrodynamics and then water quality. Within each category parameters were
manipulated in a logical way and were not changed at random to increase model fit.
59
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4.3 HSPF
As a starting point, the methods for literature searches and study selection described in Section 3 were
used for HSPF. However, the project team was aware from the onset that locating relevant values by
means of keyword-based searching would be more challenging for HSPF than for the other models.
Several factors contribute to the challenge:
• HSPF is different from the other three models in that it simulates both land surface runoff and
washoff processes and receiving water processes. Only receiving water parameters are relevant to
this update of EPA's Rates Manual. Many (likely most) search results lead to studies that utilize
HSPF's surface module PERLND as opposed to its receiving water module RCHRES.
• The majority of the RCHRES module code was created prior to 1985, and has therefore not been
treated as novel in the published literature. Within the scope of the current effort, only post-1985
information was being sought. The HSPF model has been extensively applied since 1985, with
substantial additional experience in model calibration; however, these results are present primarily
in regulatory gray literature (e.g., TMDL reports) rather than in the peer-reviewed journal
literature, making them more difficult to find.
• RCHRES offers numerous alternatives for modeling the current project's Group 1 water quality
constituents. Each of the post-1985 enhancements is structured as a modeling option; hence, even
carefully designed keyword combinations rarely guarantee that studies that are being identified
utilize the specific enhancements/options that are sought by this project.
Because of these challenges, the HSPF data table that accompanies this report has relatively few
parameter values compared with the other models, given the focus of this project on model applications
in surface water systems since 1985. Additional parameter values are available in the HSPFParm
database described under Summary of Sources.
Summary of Sources
The automated literature searches resulted in 22 pieces of literature that were deemed to be potentially
relevant to HSPF. More careful examination of these documents substantiated the weaknesses of using
a keyword-based approach to meet the needs specific to HSPF. Many of the reports documented studies
that used HSPF to simulate runoff and washoff to receiving waters (i.e., used HSPF PERLND), and
subsequently used another water quality model to simulate receiving water processes (e.g., EFDC
[Hamrick, 1996], WASP [Section 4.1], QUAL2K [Section 4.4], or CE-QUAL-W2 [Section 4.2]).
In parallel to evaluating the documents that were identified by means of automated literature search, a
supplemental approach to mining relevant parameter values was pursued. The approach relied on: 1)
mining HSPF parameter values that EPA had already collected and distributed in a published tool
(HSPFParm); and 2) accessing and mining values from studies that were known to utilize the code
enhancements of interest and were also known to have been performed by well-qualified HSPF
modelers.
The first source of relevant parameter values was U.S. EPA's HSPFParm (Donigian et al., 1999), an
interactive database of HSPF model parameters. To support an expanding community of HSPF modelers
60
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that needed a readily available source of model parameter values that can provide the best possible
starting point for developing new watershed applications, EPA funded AQUA TERRA Consultants to
collect available HSPF parameter values from applications across North America, assimilate the
parameter values into a single database, and develop an interactive interface that enables modelers to
access and utilize the database. The resulting product, named HSPFParm, contains parameter values for
model applications in more than 70 watersheds in 14 states. The parameter values that are contained in
the database characterize a broad variety of physical settings, land use practices and water quality
constituents.
The Minnesota Pollution Control Agency has subsequently funded the expansion of HSPFParm to include
input sequences that represent the State's HUC-8 watersheds and are the basis for developing the
State's TMDLs.
The studies (Table 13) that yielded relevant parameter values were the following:
• A study prepared at Portland State University entailing a model application in Oregon;
• A study prepared at Memphis State University entailing a model application in Tennessee;
• A study prepared by Maryland Department of the Environment that included parameter values
for five separate watersheds primarily in Maryland;
• A study prepared for U.S. EPA ORD detailing a model application in Pennsylvania;
• A study prepared for Minnesota Pollution Control Agency;
• The parameter values established by U.S. EPA's Chesapeake Bay program for the Phase IV
Chesapeake Bay Watershed Model;6 and
• Model input representing 19 HUC-8 watersheds in Minnesota developed by three different
contractors to Minnesota Pollution Control Agency: AQUA TERRA (9 watersheds); Tetra Tech (10
watersheds);
The second type of source for relevant parameter values was any study known to utilize the code
enhancements of interest and known to have been performed by well qualified HSPF modelers. Two
additional collections of parameter values were obtained as follows:
• Parameter values for post-1985 nutrient enhancements were mined for 14 watersheds
contained in the Puget Sound drainage.
• Parameter values for post-1985 benthic algae enhancements were mined from an application in
the Truckee River (Nevada) watershed for the Cities of Sparks and Reno.
6 Values are reported for 19 sub-watersheds within the Chesapeake drainage. This is a pivotal body of data since
HSPF's post-1985 nutrient enhancements were designed to support this effort.
61
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Table 13. HSPF Literature Sources
Citation
Study Location
Type of
Waterbody
Watershed Characteristics
Calibration
period
Notes
Aqua Terra and King County, 2003. King
County Watershed Modeling Services - Green
River Water Quality Assessment, and
Sammamish-Washington Analysis and
Modeling Program Watershed Modeling
Report. Prepared for King County Department
of Natural Resources and Parks, Water and
Land Resources Division. Seattle, WA.
Prepared by Aqua Terra Consultants, Everett,
Washington and Mountain View, California in
conjunction with King County.
Puget Sound
Drainage,
Washington
Rivers &
Streams
Forest, pasture/agriculture,
low density residential, high
density residential,
commercial/industrial (on till
soil, outwash soil, saturated
soil, and rock)
1/1991 - 12/2004
14 models - each shown
separately in RCK table
Bicknell B.R., A.S. Donigian Jr., T.H. Jobes, and
R.V. Chinnaswamy, 1996. Modeling Nitrogen
Cycling and Export in Forested Watersheds
using HSPF. Prepared for U.S. EPA; Athens,
Georgia.
Young Woman's
Creek - an 11.3-
mile creek in the
West Branch
Susquehanna
River, Pennsylvania
River
Forest
1/1984 - 12/1991
Donigian, A.S., Jr., 1997. Preliminary
Calibration Results for Blue Earth, Watonwan,
Redwood, Yellow Medicine, Cottonwood and
Hawk Watersheds. Prepared for Minnesota
Pollution Control Agency; St. Paul, Minnesota.
Minnesota
Rivers
Forest, cropland; pasture;
marsh/wetland; animal waste
application area; impervious
urban/residential
1/1986 - 12/1992
6 models developed in
study (main stem river
and tributary). Each
included separately in
RCK table.
LimnoTech, 2008. Final Draft Calibration of the
Truckee River HSPF Water Quality Model.
Prepared for the Cities of Reno and Sparks,
Nevada, January 2008.
Truckee River
Drainage, Nevada
& California
River
Coniferous forest; deciduous
forest; shrub; grassland;
pasture; golf courses; farm;
marsh; barren; low/high
density residential;
commercial; industrial;
confined feeding
1/2000 - 12/2002
A total of 43 segments
were used for this
application, Segments
range in length from 0.13
miles to 3.24 miles.
62
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Citation
Study Location
Type of
Waterbody
Watershed Characteristics
Calibration
period
Notes
MDE, 1991. Patuxent Watershed Model - Final
Report. Maryland Department of the
Environment; Baltimore, Maryland.
Patuxent River,
Maryland
Rivers & 1
Reservoir
19 separate land use
categories: forest; tillage; hay;
pasture; wetlands; residential;
commercial; industrial; major
roads; animal areas
1/1986 - 12/1990
5 separate models in this
study (Upper Patuxent,
Middle Patuxent, Lower
Patuxent, North
Patuxent, South
Patuxent). Each included
separately in RCK table.
Mishra, A., A.S. Donigian, Jr., and B.R. Bicknell,
2014. HSPF Watershed Modeling Phase 3 for
the Crow Wing, Redeye, and Long Prairie
Rivers Watersheds: Calibration and Validation
of Hydrology, Sediment, and Water Quality
Constituents. Final Report. AQUA TERRA
Consultants, Mountain View, CA. Prepared for
Minnesota Pollution Control Agency, St. Paul,
Minnesota.
Minnesota
Rivers
Forest; cropland; pasture;
marsh/wetland; animal waste
application area; impervious
urban/residential
1/2003 - 12/2009
3 models developed in
study (main stem river
and tributary). Each
included separately in
RCK table.
Moore, L.W., et al., 1992. Feasibility of an
Integrated Geographic Information/Nonpoint
Modeling System. Memphis State University;
Memphis; Tennessee.
West Sandy Creek,
Kentucky Lake
watershed, Henry
County, TN
River
11% cropland; 33% pasture and
hay; 50% forest; 6% other
(urban, quarries, gullies)
1/1987 - 12/1987
Patwardhan, A.S., R.M. Jacobson, A.S. Donigian
Jr., and R.V. Chinnaswamy, 1996. HSPF Model
Application to the LeSueur Watershed
Preliminary Findings and Recommendations.
Minnesota Pollution Control Agency; St. Paul,
Minnesota.
LeSueur River,
Minnesota
River
Forest; cropland; pasture;
marsh/wetland; animal waste
application area; impervious
urban/residential
1/1986 - 12/1992
Tang, F., 1993. Calibration and Verification of
HSPF Model for Tualatin River Basin Water
Quality. Technical Report EWR-003-93; Dept.
Civil Eng.; Portland State University; Portland,
Oregon.
Tualatin River,
western Oregon
River
Mixed land use segments
simulated including urban,
crops, forest, limited range &
wetland
1/1991 - 12/1991
63
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Citation
Study Location
Type of
Waterbody
Watershed Characteristics
Calibration
period
Notes
Tetra Tech, 2009. Minnesota River Basin
Turbidity TMDL and Lake Pepin Excessive
Nutrient TMDL Prepared for Minnesota
Pollution Control Agency; St. Paul, Minnesota.
Minnesota River
Basin, Minnesota
Rivers & 1
Reservoir
Forest; cropland; feedlots;
pasture; urban;
marsh/wetlands
1/1993 - 12/2006
10 separate models in
this study. Each included
separately in RCK table.
U.S. EPA, 1998. Chesapeake Bay Watershed
Model Application and Calculation of Nutrient
and Sediment Loadings. Phase IV Model
Documentation and Results. Prepared by
Modeling Subcommittee of CBP. February
1998.
Chesapeake Bay
Watershed, North
Central United
States
Rivers & 1
Reservoir
Forest; conventional tillage
(high till); cropland;
conservation tillage (low till);
cropland; hay; pasture;
urban/residential; animal
waste/feedlot areas;
impervious urban/residential
1/1984 - 12/1991
19 separate models in
this study. Each included
separately in RCK table.
64
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Studies selected to provide parameter values for HSPF nutrient routines represent the Pacific
Northwest, Mid-Atlantic and the Upper Midwest. These regions are characterized by streams that can
transport a significant fraction of inorganic nutrient washoff associated with inorganic sediment.
Generally, the climatic distribution of the current collection of parameter values is skewed towards
northern latitudes that experience coastal or large lake influences. The formulations in the post-1985
HSPF benthic algae enhancement are uniquely relevant to relatively shallow and clear Western streams.
Applications of the DSSAMt model (from which the formulations were adopted) also appears to be
limited to this geographic area and stream type. Hundreds of HSPF applications have occurred
throughout the United States that have not been captured by the literature search or by the alternative
effort made for this project. Relevant parameter values exist for applications in other regions, but the
materials were not identified by the search strategy used for this report and would need to be retrieved
from the gray literature such as TMDL model calibration reports. For additional resources regarding
HSPF, see also Section 9 of this report. Details on the watershed characteristics for each included study
were contained within Table 13. The resulting distributions of rates and constants values are
summarized in Table 14.
65
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Summary Statistics for Rates and Constants
Table 14. HSPF Rates and Constants
Block
Name
Description
Count
Min
Max
Mean
Median
Default
Units
CONV-
VAL1
CVBO
Conversion from mg biomass to mg
oxygen
49
1.63
5
1.65
1.63
1.98
mg/mg
CONV-
VAL1
CVBPC
Conversion from biomass expressed as
Pto C
49
106
200
106.24
106
106
mols/mol
CONV-
VAL1
CVBPN
Conversion from biomass expressed as
Pto N
49
10
16
15.98
16
16
mols/mol
CONV-
VAL1
BPCNTC
Percentage of biomass that is carbon
(by weight)
49
10
49
48.90
49
49
-
NUT-
BENPARM
BRTAM1
Benthal release rate of ammonia under
aerobic conditions
41
0
4
0.0777
0
0
mg/m2.hr
NUT-
BENPARM
BRTAM2
Benthal release rate of ammonia under
anaerobic conditions
41
0
33
0.4082
0
0
mg/m2.hr
NUT-
BENPARM
BRP041
Benthal release rate orthoP under
aerobic conditions
41
0
2.7
0.0354
0
0
mg/m2.hr
NUT-
BENPARM
BRP042
Benthal release rate of orthoP under
anaerobic conditions
41
0
2.7
0.0332
0
0
mg/m2.hr
NUT-
BENPARM
ANAER
Concentration of DO below which
anaerobic conditions exist
41
0.001
1
0.0428
0.001
0.005
mg/L
NUT-
NITDENIT
KTAM20
Nitrification rate of ammonia at 20 °C
60
0.001
0.6
0.0401
0.002
-
1/hr
NUT-
NITDENIT
KNO220
Nitrification rate of nitrite at 20 °C
50
0.001
0.05
0.0081
0.012
-
1/hr
NUT-
NITDENIT
TCNIT
Temperature correction coefficient for
nitrification
60
1
1.07
1.0647
1.04
1.07
-
NUT-
NITDENIT
KNO320
Nitrate denitrification rate
50
0.001
3.5
0.0333
0.002
-
1/hr
NUT-
NITDENIT
TCDEN
Temperature correction coefficient for
denitrification
50
1
1.07
1.0404
1.04
1.07
-
NUT-
NITDENIT
DENOXT
Threshold value for DO above which
denit. ceases
60
1
100
5.5860
5
2
mg/L
66
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Block
Name
Description
Count
Min
Max
Mean
Median
Default
Units
NUT-
NH3VOLAT
EXPNVG
Exponent in gas layer mass transfer
equation for NH3 volatilization
5
0.5
0.5
0.5000
0.5
0.5
-
NUT-
NH3VOLAT
EXPNVL
Exponent in liquid layer mass transfer
equation for NH3 volatilization
5
0.667
0.667
0.6670
0.667
0.6667
-
NUT-
BEDCONC
BRTAM(l)
Constant bed concentrations of
ammonia-N adsorbed to clay
45
0.0001
300
39.2
40
0
mg/kg
NUT-
BEDCONC
BRTAM(2)
Constant bed concentrations of
ammonia-N adsorbed to sand
45
0.0002
600
103.8
100
0
mg/kg
NUT-
BEDCONC
BRTAM(3)
Constant bed concentrations of
ammonia-N adsorbed to silt
45
0.0003
550
102.3
100
0
mg/kg
NUT-
BEDCONC
BRP04(1)
Constant bed concentrations of ortho-
phosphorus-P adsorbed to clay
45
0.00005
200
84.4
100
0
mg/kg
NUT-
BEDCONC
BRP04(2)
Constant bed concentrations of ortho-
phosphorus-P adsorbed to sand
45
0.0003
3500
457.2
250
0
mg/kg
NUT-
BEDCONC
BRP04(3)
Constant bed concentrations of ortho-
phosphorus-P adsorbed to silt
45
0.0004
1000
256.8
250
0
mg/kg
NUT-
ADSPARM
ADNHPM(1
Adsorption coefficients (Kd) for
ammonia-N adsorbed to clay
35
10
300
30.2
150
-
ml/g
NUT-
ADSPARM
ADNHPM(2
Adsorption coefficients (Kd) for
ammonia-N adsorbed to sand
20
100
4000
257.1
100
-
ml/g
NUT-
ADSPARM
ADNHPM(3
Adsorption coefficients (Kd) for
ammonia-N adsorbed to silt
35
100
4000
329.0
150
-
ml/g
NUT-
ADSPARM
ADPOPM(l
Adsorption coefficients for ortho-
phosphorus-P adsorbed to clay
20
100
9500
371.9
100
-
ml/g
NUT-
ADSPARM
ADPOPM(2
Adsorption coefficients for ortho-
phosphorus-P adsorbed to sand
20
1000
30000
2360.7
1000
-
ml/g
NUT-
ADSPARM
ADPOPM(3
Adsorption coefficients for ortho-
phosphorus-P adsorbed to silt
20
1000
100000
2607.9
1000
-
ml/g
PLNK-
PARM1
RATCLP
Ratio of chl-a content of biomass to P
content
50
0.6
0.68
0.6769
0.68
0.6
-
PLNK-
PARM1
NONREF
Non-refractory fraction of algal biomass
50
0.2
0.6
0.4713
0.5
0.5
-
67
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Block
Name
Description
Count
Min
Max
Mean
Median
Default
Units
PLNK-
PARM1
UTS ED
Multiplication factor to total sediment
concentration to determine sediment
contribution to light extinction
50
0
1
0.0032
0
0
1/mg.ft
PLNK-
PARM1
ALNPR
Fraction of N requirements for
phytoplankton growth that is satisfied
by nitrate
50
0.1
0.7
0.2560
0.25
1
-
PLNK-
PARM1
EXTB
Base extinction coefficient for light
50
0.01
0.6
0.1865
0.12
-
1/ft
PLNK-
PARM1
MALGR
Maximum unit algal growth rate
50
0.001
0.32
0.0878
0.075
0.3
1/hr
PLNK-
PARM2
CMMLT
Michaelis-Menten constant for light-
limited algal growth
49
0.000001
0.04
0.0258
0.033
0.033
ly/min
PLNK-
PARM2
CMMN
Nitrate Michaelis-Menten constant for
N-limited algal growth
49
0.000001
0.045
0.0348
0.045
0.045
mg/L
PLNK-
PARM2
CMMNP
Nitrate Michaelis-Menten constant for
P-limited algal growth
49
0.000001
0.0284
0.0041
0.0001
0.0284
mg/L
PLNK-
PARM2
CMMP
Michaelis-Menten constant for P-
limited algal growth
49
0.000001
0.05
0.0110
0.015
0.015
mg/L
PLNK-
PARM2
TALGRH
Temperature above which
phytoplankton growth ceases
49
50
95
94.4
95
95
°F
PLNK-
PARM2
TALGRL
Temperature below which
phytoplankton growth ceases
49
-110
50
-15.0
-10
43
°F
PLNK-
PARM2
TALGRM
Temperature below which
phytoplankton growth is retarded
49
50
86
79.8
77
77
°F
PLNK-
PARM3
ALR20
Phytoplankton respiration rate at 20 °C
49
0.000001
0.007
0.0049
0.005
0.004
1/hr
PLNK-
PARM3
ALDH
High phytoplankton unit death rate
49
0.000001
0.02
0.0156
0.02
0.01
1/hr
PLNK-
PARM3
ALDL
Low phytoplankton unit death rate
49
0.000001
0.003
0.0011
0.001
0.001
1/hr
PLNK-
PARM3
OXALD
Increment to phytoplankton unit death
rate due to anaerobic conditions
49
0.000001
0.03
0.0295
0.03
0.03
1/hr
PLNK-
PARM3
NALDH
Inorganic N concentration below which
high phytoplankton death rate occurs
49
0
0.025
0.0120
0.01
0
mg/L
68
-------
Block
Name
Description
Count
Min
Max
Mean
Median
Default
Units
PLNK-
PARM3
PALDH
Inorganic P concentration below which
high phytoplankton death rate occurs
49
0
0.005
0.0025
0.002
0
mg/L
PHYTO-
PARM
SEED
Minimum concentration of
phytoplankton not subject to advection
38
0.018
10
1.0272
1
-
mg/L
PHYTO-
PARM
MXSTAY
Concentration of phytoplankton not
subject to advection at low flow
48
0.05
25
2.8424
2
-
mg/L
PHYTO-
PARM
OREF
Flow at which concentration of
phytoplankton not subject to advection
is between SEED and MXSTAY
48
2
6000
202.5
100
-
cfs
PHYTO-
PARM
CLALDH
Chl-a concentration above which high
algal death rate occurs
49
15
9999
139.6
20
50
Hg/L
PHYTO-
PARM
PHYSET
Phytoplankton settling rate
49
0
0.15
0.0176
0.015
0
ft/hr
PHYTO-
PARM
REFSET
Settling rate for dead refractory
organics
49
0
1
0.0357
0.021
-
ft/hr
BENAL-
PARM
MBAL
Maximum benthic algal biomass
45
60
800000
49904
2500
600
mg/m2
BENAL-
PARM
CFBALR
Ratio of benthic algal to phytoplankton
respiration
45
0.1
1
0.3525
0.35
1
-
BENAL-
PARM
CFBALG
Ratio of benthic algal to phytoplankton
growth rate
45
0.08
1
0.9305
1
1
-
69
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For the advanced benthic algae parameters, the literature search resulted in only a single study (LimnoTech, 2008. Final Draft Calibration of the
Truckee River HSPF Water Quality Model). The benthic algae parameters from this study are listed in Table 15.
Table 15. Advanced Benthic Algae Parameters
Parameter
Module
Description
Value
Units
MINBAL
BENAL-PARM
Minimum benthic algae density (as biomass)
1000.0
mgDW/m2
CAM PR
BENAL-PARM
Coefficient in the alternative nitrogen preference equation for benthic algae
20.0
-
FRAVL
BENAL-PARM
Fraction of nonrefractory nutrients resulting from benthic algae death/removal
that are assumed to be immediately available as inorganic nutrients, plus
refractory organic carbon
0.250
-
N MAX FX
BENAL-PARM
Concentration of available inorganic nitrogen in the water column (TAM + NO3 +
NO2) above which nitrogen-fixation by benthic algae is suppressed
0.20
mg/L
MBALGR
BENAL-GROW
Maximum benthic algae base growth rate for each benthic algae species
0.120
/hr
TCBALG
BENAL-GROW
Temperature correction coefficient for growth for each species
1.067
-
CMMNB
BENAL-GROW
Half-saturation constant for nitrogen-limited growth for each species. If the value
is zero, then growth is not limited (i.e., this species fixes nitrogen)
0.0250
mg/L
CMMPB
BENAL-GROW
Half-saturation constant for phosphorus-limited growth for each species
0.0050
mg/L
CMMD1
BENAL-GROW
Coefficient for total benthic algae density in the density-limited growth equation
for each species
0.010
-
CMMD2
BENAL-GROW
Half-saturation constant for density-limited growth for each species
16000.0
mg/m2
CSLIT
BENAL-GROW
Saturation light level for each species
0.2780
ly/min
BALR20
BENAL-RESSCR
Benthic algae respiration rate at 20 C for each species
0.00550
/hr
TCBALR
BENAL-RESSCR
Temperature correction coefficient for respiration for each species
1.0670
-
CSLOF1
BENAL-RESSCR
Rate coefficient in the benthic algae scour equation for each species
0.00010
/hr
CSLOF2
BENAL-RESSCR
Multiplier of velocity in the exponent in the benthic algae scour equation for each
species
4.50
-
GRORES
BENAL-RESSCR
Fraction of photorespiration needed to support growth/photosynthesis for each
species
0.0750
-
70
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Parameter
Module
Description
Value
Units
CREMVL
BENAL-GRAZE
Annual benthic algae grazing (removal) rate by invertebrates
34.660
mg/mg/yr
CMMBI
BENAL-GRAZE
Half-saturation constant for grazing by invertebrates
10000.0
mg/m2
BINV
BENAL-GRAZE
Biomass (density) of grazing invertebrates in the reach
(2400 - 4150)
mg/m2
TCGRAZ
BENAL-GRAZE
Temperature correction coefficient for macroinvertebrate grazing
1.060
-
FRRIF
BENAL-RIFF1
Fraction of the reach that is composed of riffles where benthic algae can grow
(0.5-1.0)
-
CMMV
BENAL-RIFF1
Half-saturation constant for riffle velocity in the nutrient availability equation for
benthic algae
0.20010
ft/s
RIFCQ1
BENAL-RIFF1
Critical flow levels for riffle velocity and average depth
105.9
cfs
RIFCQ2
BENAL-RIFF1
Critical flow levels for riffle velocity and average depth
211.9
cfs
RIFCQ3
BENAL-RIFF1
Critical flow levels for riffle velocity and average depth
317.8
cfs
RIFVEL(l)
BENAL-RIFF2
Riffle velocity multipliers corresponding to the critical flow values (RIFCQ)
1.80
-
RIFVEL(2)
BENAL-RIFF2
Riffle velocity multipliers corresponding to the critical flow values (RIFCQ)
1.50
-
RIFVEL(3)
BENAL-RIFF2
Riffle velocity multipliers corresponding to the critical flow values (RIFCQ)
1.20
-
RIFVEL(4)
BENAL-RIFF2
Riffle velocity multipliers corresponding to the critical flow values (RIFCQ)
1.00
-
RIFDEP(l)
BENAL-RIFF2
Depth multipliers corresponding to the critical flow values (RIFCQ)
0.550
-
RIFDEP(2)
BENAL-RIFF2
Depth multipliers corresponding to the critical flow values (RIFCQ)
0.650
-
RIFDEP(3)
BENAL-RIFF2
Depth multipliers corresponding to the critical flow values (RIFCQ)
0.750
-
RIFDEP(4)
BENAL-RIFF2
Depth multipliers corresponding to the critical flow values (RIFCQ)
0.850
-
71
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Calibration Data and Approaches
The predominant procedure for calibration is adjustment of default values (default values are not
available for all the parameters of interest) using a systematic approach to vary parameter values
individually to increase similarity between modeled and observed data. A detailed summary of HSPF
model use and calibration is provided in Duda et al. (2012). Guidance on HSPF calibration for flow and
sediment is provided in U.S. EPA (2000) and (2006), respectively. Comprehensive national guidance on
nutrient parameters and rates for HSPF has not been developed; however, RESPEC (2018) provides
information on acceptable ranges of kinetic coefficients for application in Minnesota.
Since the enhancement of HSPF related to nutrient-sediment interactions is very dependent on
sediment scour/deposition phenomena, calibration requires comparison to monitored data for variable
flow conditions. Ideally the monitored data record extends at least over the period of several years.
Likewise, calibration of the benthic algae enhancement is best supported with monitored data for an
annual cycle of population growth/decline.
Results of the rates and constants search for nutrient-related parameters in HSPF are shown in Table 14.
Default values shown in this table are from Bicknell et al. (2014). These are the defaults that HSPF
assumes when user data are not provided and in some cases, represent nominal values that will prevent
code crashes rather than physically realistic estimates.
An advantage of utilizing the alternative method of obtaining parameter values for HSPF enhancements
that is described above (i.e., mining them from complete model input sequences) is that a full set of
parameter values can be provided for each model application. However, this data mining is resource-
intensive; it was pursued for HSPF to compensate for the limited information on parameter values for
this model in journal articles and readily discoverable technical reports.
4.4 QUAL2K and QUAL2Kw
The initial literature search for Q2K and/or Q2Kw returned more than 50 papers and reports that
discussed a modeling study using Q2K or Q2Kw and addressed nutrients, dissolved oxygen, or algae. Of
these studies, 17 (Table 16) were deemed to be appropriate for inclusion in this survey based on the
criteria noted above (tabulation of parameters; identification of parameter sources, calibration data,
and calibration procedures; evaluation of model performance).
Summary of Sources
Eight of the studies were published in peer-reviewed journals, eight were reports by state
environmental agencies or boards (California, Washington, Oregon, and Montana), and one was a Tetra
Tech report for EPA and the State of California. These selected studies contained thorough
documentation of modeling activities and calibration parameters as described in Section 3.
Studies were generally geared towards regulatory goals, with more than half undertaken to support
development of TMDLs or numeric nutrient criteria in the United States. Four studies are from outside
of the United States and are geared towards evaluating the impacts of waste discharges on river water
quality.
72
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All the Q2K applications selected from the United States were conducted in western states (California,
Montana, Oregon, Utah, and Washington). The four studies from outside of the United States were
done in China, Portugal, Nepal, and India. Climatologically, the study areas include rivers in the Pacific
Northwest (Oregon and Washington), tropical and humid subtropical regions (Deccan Plateau in India
and Zhejiang Province in China, respectively), a warm temperate region (Kathmandu Valley, Nepal), the
Mediterranean (Portugal), and subhumid (Utah) and semi-arid (southern California, Montana) areas.
The waterbodies studied are rivers and streams in a variety of basin types and sizes. For example, some
of the Q2K applications are in systems fed by snowmelt (Yellowstone River, Wenatchee River, Jordan
River); in a contrasting example, most of the flow of the New River in southern California consists of
tributary/agricultural drain and wastewater inputs. For additional resources regarding
QUAL2K/QUAL2Kw, see also Section 9 of this report. Detailed examples of application of the older
QUAL2E model along with extensive tables of relevant rates and constants are also available in U.S. EPA
(1995).
73
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Table 16. QUAL2K and QUAL2Kw Literature Sources
Citation
Study Location
Type of
Waterbody
Watershed Characteristics
Calibration period
Butkus, S., 2011. Dissolved Oxygen Model
Development and Evaluation. Memorandum for
California Regional Water Quality Control Board North
Coast Region.
Santa Rosa Creek and
Lake Jonvie, Santa
Rosa, California
River (a) and
lake (b)
(separate
models)
Details on watershed contained in Butkus, S.,
2011. Water Quality Model Development History
for the Laguna de Santa Rosa TMDL
Memorandum for California Regional Water
Quality Control Board North Coast Region.
Calibrated to 3 diel sampling
events in August 2009
Carroll, J., S. O'Neal, and S. Golding, 2006. Wenatchee
River Basin Dissolved Oxygen, pH, and Phosphorus
Total Maximum Daily Load Study. Prepared for
Washington State Department of Ecology
Environmental Assessment Program.
Wenatchee River,
northwest
Washington (east
flank of Cascades)
River (a) and
tributary (b)
(separate
models)
3555 km2 drainage; primarily forested watershed
with relatively pristine headwaters; some
agricultural and municipal runoff in lower river
reaches (two small cities)
Calibrated to 2 synoptic
surveys in 09/2002 and
10/2002
Fang, X., J. Zhang, C. Mei, and M. Wong, 2014. The
assimilative capacity of Qiantang River watershed,
China. Water and Environment Journal. 28,192-202.
Zhejiang Province,
China (eastern
coastal China)
River
Heavily populated and agricultural watershed
with thousands of point sources. 41700 km2
drainage; 14.08 million people in watershed
Calibrated to seasonal water
quality surveys from 01/2000
to 06/2005
Flynn, K., and M.W. Suplee, 2011. Using a computer
water quality model to derive 20 numeric nutrient
criteria: Lower Yellowstone River. WQPBDMSTECH-22.
Helena, MT: Montana Dept. of Environmental Quality.
A 232.9 km (144.7
mile) segment of the
lower Yellowstone
River in eastern
Montana.
River
Study area was a 232.9 km (144.7 mile) segment
of the lower Yellowstone River in eastern
Montana.
Two synoptic surveys:
August 17-26, 2007, for
calibration.
September 11-20, 2007, for
validation.
Flynn, K., M. Suplee, S. Chapra, and H. Tao, 2015.
Model-based Nitrogen and Phosphorus (Nutrient)
Criteria for Large Temperate Rivers: 1. Model
Development and Application. Journal of the American
Water Resources Association. 51(2).
Segment of the lower
Yellowstone River,
Montana
River
River segment runs from Billings to Sidney,
Montana (536 km). Flow is unregulated. Water
yield is 334 m3/s annually and base flow is 177
m3/s
August 17-26, 2007 and
August 23-30, 2000
Kannel, P.R., and S. Lee. 2007. Application of
QUAL2Kw for Water Quality Modeling and Dissolved
Oxygen Control in the River Bagmati. Environmental
Monitoring Assess. 125:201-207.
Bagmati River,
Kathmandu Valley of
Nepal
River
Study area is about 20 km of the Bagmati
between Atterkhel village and Chovar
19-20 June, 2004 (pre-
monsoon)
2-3 December, 2004 (post-
monsoon)
Kannel, P.R., Y.-S. Lee, S.R. Kannel, and G.J. Pelletier,
2007. Application of automated QUAL2Kw for water
quality modeling and management in the Bagmati
River, Nepal. Ecological Modelling, 202, 503-517.
Bagmati River in
Kathmandu. Study
area was the upper
25 km of the river.
River
Bagmati River basin in central part of Nepal. Study
covered the upper 25 km length of the Bagmati
River. Drainage area = 651 sq. km within the
Kathmandu Valley.
January 2-6 (winter)
Year uncertain - likely 2005
or 2006 based on 2007
publication date
74
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Citation
Study Location
Type of
Waterbody
Watershed Characteristics
Calibration period
Kori, B., T. Shashidhar, and S. Mise, 2013. Application
of automated Qual2kw for water quality modeling in
the River Karanja, India. Global Journal of Bio-Science
and Biotechnology, 2(2): 193-203.
Karanja River,
Pradesh state, India.
Deccan Plateau.
Stretch of river
between Karanja
Reservoir and Bhalki
pump station (21.85
km).
River
Karanja River is a tributary to the Godavari River,
in Pradesh state of India. River has a dam and a
pumping station about 21.85 km downstream of
the reservoir. Catchment area of river at proposed
dam site is 2,025.4 km2.
June 30, 2010 (pre-monsoon
season).
Mohamedali, T., and S. Lee, 2008. Bear-Evans
Watershed Temperature and Dissolved Oxygen Total
Maximum Daily Load: Water Quality Improvement
Report. Prepared for State of Washington Department
of Ecology.
Bear Creek (a), Evans
Creek (b), Cottage
Lake Creek (c),
northwest
Washington
River
57.8 km2 drainage (main stem of 132 km2 basin);
mixed-use watershed with 3 cities and ~50%
developed land (primarily residential)
Calibrated to continuous and
grab samples from 06/2006
to 10/2006
Oliveira, B., J. Bola, P. Quinteiro, H. Nadais, and L.
Arroja, 2012. Application of Qual2Kw model as a tool
for water quality management: Certima River as a case
study. Environ Monit Assess. 184. 6197-6210.
Certima River,
Portugal (west-
central)
River
Mixed-use watershed with numerous diffuse
contaminant sources.
Calibrated to full sampling
season in 2008
Pelletier, G., S. Chapra, and H. Tao, 2006. QUAL2Kw - A
Framework for Modeling Water Quality in Streams
and Rivers Using a Genetic Algorithm for Calibration.
Environmental Modelling & Software. 21:419-425.
NA
NA
NA
NA
Sargeant, D., B. Carey, M. Roberts, and S. Brock, 2006.
Henderson Inlet Watershed Fecal Coliform Bacteria,
Dissolved Oxygen, pH, and Temperature Total
Maximum Daily Load Study. Environmental
Assessment Program, Washington State Department
of Ecology.
Woodland Creek,
near Olympia,
Washington (south
Puget Sound)
River
76.8 km2 drainage; mixed urban/suburban and
forested watershed, minor agriculture. Drains into
southern Puget Sound (some tidal influence)
Calibrated to 8 storm events
and 4 dry season events in
2003; also used data from
previous studies in
Henderson Inlet.
Snouwaert, E., and T. Stuart, 2015. North Fork Palouse
River Dissolved Oxygen and pH Total Maximum Daily
Load Water Quality Improvement Report and
Implementation Plan. Department of Ecology State of
Washington. Publication No. 15-10-029 Part 1 (July).
North Fork Palouse
River, Washington
River
The North Fork Palouse River lies north of the
confluence with the South Fork Palouse River at
Colfax, in southeastern Washington. The upper
part of the watershed lies in western Idaho,
beyond Potlatch, Idaho.
July 1 - August 31, 2007;
September 1 -
September 19, 2012;
September 20 -
September 30,1987.
Tetra Tech, 2009. New River QUAL2K Water Quality
Model for the New River Dissolved Oxygen TMDL.
Prepared for U.S. EPA Region 9 and California Regional
Water Quality Control Board Colorado River Basin
Region.
New River, southern
California/Mexico
border (drains into
Salton Sea)
River
Heavily polluted (unnatural) river composed
primarily of agricultural runoff, industrial
wastewater, and municipal discharge.
Calibrated to single
07/16/2006 sampling event
(1 headwater and 17
tributary/WWTP sites).
75
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Citation
Study Location
Type of
Waterbody
Watershed Characteristics
Calibration period
Turner, D., B. Kasper, P. Heberling, B. Lindberg, M.
Wiltsey, G. Arnold, and R. Michie, 2006. Umpqua Basin
Total Maximum Daily Load (TMDL) and Water Quality
Management Plan (WQMP). Oregon Department of
Environmental Quality.
Impaired streams in
the Umpqua Basin in
southwestern
Oregon: Calapooya,
Elk, Jackson, and
Steamboat creeks
Streams in
forested
watershed
Basin is about 3.24 million acres. It is 90%
forestland. Includes fisheries, recreational uses,
and forestry.
Calibrated to synoptic
surveys:
Calapooya: July 24, 2002.
Elk: September 25, 2002
Jackson: August 26-29, 2002
Steamboat: August 9, 2000.
Turner, D., G. Pelletier, and B. Kasper, 2009. Dissolved
Oxygen and pH Modeling of a Periphyton Dominated,
Nutrient Enriched River. Journal of Environmental
Engineering. 135(8). 645-655.
South Umpqua River,
southwestern
Oregon
River
High elevation forest/mountains; lowland
agriculture and urban development
Two models calibrated and
compared for 1991 and 2004
sampling seasons.
von Stackelberg, N. 0., and B. T. Neilson, 2012.
Collaborative Approach to Calibration of a Riverine
Water Quality Model. Journal of Water Resources
Planning and Management. 140.3: 393-405.
Jordan River, Utah
River
83 km from Utah Lake to Great Salt Lake.
Water surveys were
performed for 3-day periods
in October 2006, February
2007, September 2007,
August 2009.
76
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Basin sizes range from about 58 km2 to thousands of km2. One study (Turner et al., 2006; citation in
Table 16) developed models for four waterways within a larger basin (13,112 km2). Land uses range from
heavily forested to more varied land uses, and the rivers in these sources receive inputs from nonpoint
(e.g., agricultural runoff) and point (e.g., wastewater treatment plant effluents) sources. Details on study
locations, watershed characteristics, and environmental conditions were provided in Table 16. The
resulting ranges of rates and constants are shown in Table 17 through 20. Default rates and constants
shown in Tables 17 through 20 were provided directly to the project team by Greg Pelletier, developer
of the QUAL2Kw model.
77
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Summary Statistics for Rates and Constants
Table 17. QUAL2K and QUAL2Kw Rates and Constants: Nutrient Parameters
Nutrient Parameter
Count
Min
Max
Median
Units
Default Value
C:N:P
19
N/A
N/A
N/A
gC:gN:gP
40:7.2:1
Denitrification rate
23
0
1.9
1
day1
0.1
Denitrification rate T correction
15
1.044
1.07
1.07
-
1.07
Inorganic P sediment oxygen attenuation half saturation constant
3
1.56
1.97
1.77
Mg Oz/L
1
Inorganic P settling velocity
16
0
2
0.8855
m/d
0.8
Nitrification rate
23
0.01
10
2.5
day1
0.08
Nitrification rate T correction
15
1.01
1.08
1.07
-
1.07
Organic N hydrolysis
20
0.001
4.3
0.2
day1
0.015
Organic N hydrolysis T correction
15
1.05
1.08
1.07
-
1.07
Organic N settling velocity
16
0
1.8
0.11
m/d
0.0005
Organic P hydrolysis
23
0.001
4.2
0.43
day1
0.03
Organic P hydrolysis T correction
15
1
1.07
1.07
-
1.07
Organic P settling velocity
14
0.003
1.8
0.1
m/d
0.001
Prescribed inorganic phosphorus flux
2
0
100
50
mg P/m2/d
-
Prescribed NhMlux
2
0
500
250
mg NH4/m2/d
-
-------
Table 18. QUAL2K and QUAL2Kw Rates and Constants: Oxygen Parameters
Oxygen Parameter
Count
Min
Max
Median
Units
Default Value
Slow CBOD oxidation rate
2
0.000001
0.001
0.001
day1
-
Slow CBOD oxidation rate T correction
2
1.014
1.047
1.031
-
1.024
Fast CBOD oxidation rate
20
0.016
4.3
2.5
day1
0.05-0.3
Fast CBOD oxidation rate T correction
12
1.047
1.05
1.047
-
1.047
Oxygen enhance parameter bottom algae respiration
10
0.6
0.6
0.6
L/mg O2
0.6
Oxygen enhance parameter denitrification
10
0.6
0.6
0.6
L/mg O2
0.6
Oxygen for carbon oxidation
10
2.67
2.69
2.69
g 02/g C
2.69
Oxygen for nitrification
9
4.57
4.57
4.57
g 02/g N
4.57
Oxygen inhibition parameter CBOD oxidation
10
0.6
0.6
0.6
L/mg O2
0.6
Oxygen inhibition parameter nitrification
10
0.6
0.6
0.6
L/mg O2
0.6
Oxygen inhibition parameter phytoplankton respiration
9
0.6
0.6
0.6
L/mg O2
0.6
Reaeration model T correction
10
1.024
1.05
1.024
-
1.024
Slow CBOD hydrolysis rate
16
0
3.9988
0.817
day1
0
Slow CBOD hydrolysis rate T correction
12
1
1.07
1.047
-
1.047
Slow CBOD oxidation rate
14
0
5
0.200
day1
0
Slow CBOD oxidation rate T correction
6
1.047
1.047
1.047
-
1.047
79
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Table 19. QUAL2K and QUAL2Kw Rates and Constants: Algae Parameters
Group
Algae Parameter
Count
Min
Max
Median
Units*
Default
Value
Bottom algae
Ammonia preference
20
1.2
84
25
Hg N/L
25
Bottom algae
Basal respiration rate
22
0.007
1.2
0.2
day1
0.2
Bottom algae
Bottom algae coverage
2
0
100
50
%
-
Bottom algae
C:Chl-a
5
N/A
N/A
N/A
gC:gChl-a
40:1
Bottom algae
C:N:P
4
N/A
N/A
N/A
gC:gN:gP
40:7.2:1
Bottom algae
Death rate
22
0.00095
1
0.3
day1
0.1
Bottom algae
Death rate T correction
8
1.05
1.07
1.07
-
1.07
Bottom algae
Dry Weight
4
100
100
100
mg D
100
Bottom algae
Excretion rate
20
0
0.48
0.20
day1
0.02
Bottom algae
Excretion rate T correction
8
1
1.07
1.07
-
1.07
Bottom algae
External nitrogen half sat constant
24
15
493
206
Hg N/L
300
Bottom algae
External phosphorus half sat constant
24
2.9
178
74
Hg P/L
100
Bottom algae
First-order model carrying capacity
3
77
300
200
g D/m2
-
Bottom algae
First-order model carrying capacity
8
1000
1000
1000
mg A/m2
1000
Bottom algae
Growth rate temperature correction
10
1.004
1.08
1.07
-
1.07
Bottom algae
Inorganic carbon half sat constant
20
0
0.00013
0.000013
moles/L
0.000013
Bottom algae
Internal nitrogen half sat ratio
20
0.9
9
2.2
-
0.9
Bottom algae
Internal phosphorus half sat ratio
20
0.09
4.6
1.4
-
0.13
Bottom algae
Light constant
20
1.7
100
59
langleys/d
100
Bottom algae
Maximum growth rate
11
1.3
100
15
g D/m2/d
-
Bottom algae
Maximum growth rate
13
50
500
350
mg A/m2/d
200
-------
Group
Algae Parameter
Count
Min
Max
Median
Units*
Default
Value
Bottom algae
Maximum uptake rate for nitrogen
9
100
720
364
mg N/gD/d
-
Bottom algae
Maximum uptake rate for nitrogen
13
2.8
226
72
mg N/mg A/d
72
Bottom algae
Maximum uptake rate for phosphorus
9
50
200
100
mg P/gD/d
-
Bottom algae
Maximum uptake rate for phosphorus
13
0.4
490
10
mg P/mg A/d
5
Bottom algae
Nitrogen uptake water column fraction
4
1
1
1
-
1
Bottom algae
Phosphorus uptake water column fraction
4
1
1
1
-
1
Bottom algae
Photo-respiration rate parameter
3
0.3
0.6
0.6
-
-
Bottom algae
Respiration rate temperature correction
10
1
1.07
1.07
-
1.07
Bottom algae
Subsistence quota for nitrogen
8
7.2
72
7.4
mg N/g D
-
Bottom algae
Subsistence quota for nitrogen
14
0.3
7.0
2.9
mg N/mg A
0.72
Bottom algae
Subsistence quota for phosphorus
8
1
10
2.9
mg P/g D
-
Bottom algae
Subsistence quota for phosphorus
14
0.013
7.2
0.37
mg P/mg A
0.1
Phytoplankton
Ammonia preference
16
20
80
25
Hg N/L
25
Phytoplankton
C:Chl-a
21
N/A
N/A
N/A
gC:gChl-a
40:1
Phytoplankton
C:N:P
5
N/A
N/A
N/A
gC:gN:gP
40:7.2:1
Phytoplankton
Death rate
19
0
0.59
0.05
day1
0
Phytoplankton
Death rate temperature correction
14
1
1.07
1.07
-
1.07
Phytoplankton
Dry weight
1
107
107
107
gD
100
Phytoplankton
Excretion rate
5
0
0.1
0.05
day1
0.3
Phytoplankton
Excretion rate temperature correction
5
1.07
1.07
1.07
-
1.07
Phytoplankton
External nitrogen half sat constant
16
13
50
15
Hg N/L
15
Phytoplankton
Phosphorus half sat constant
17
0
30
2
Hg P/L
2
-------
Group
Algae Parameter
Count
Min
Max
Median
Units*
Default
Value
Phytoplankton
Growth rate temperature correction
14
1.001
1.07
1.07
-
1.07
Phytoplankton
Inorganic carbon half sat constant
16
0
0.0011
0.000013
moles/L
0.000013
Phytoplankton
Internal nitrogen half sat ratio
7
2.5
9
9
-
9
Phytoplankton
Internal phosphorus half sat ratio
7
0.05
4.4
1.3
-
1.3
Phytoplankton
Light constant
18
35
100
58
langleys/d
57.6
Phytoplankton
Maximum growth rate
19
0.2
4.1
2.5
day1
2.5
Phytoplankton
Maximum uptake rate for nitrogen
6
447
1333
720
mg N/g D/d
720
Phytoplankton
Maximum uptake rate for nitrogen
2
40
40
40
mg N/mg A/d
-
Phytoplankton
Maximum uptake rate for phosphorus
6
100
169
100
mg P/g D/d
100
Phytoplankton
Maximum uptake rate for phosphorus
2
27
27
27
mg P/mg A/d
-
Phytoplankton
Respiration rate
19
0.015
0.7
0.1
day1
0.1
Phytoplankton
Respiration rate temperature correction
15
1
1.07
1.07
-
1.07
Phytoplankton
Settling velocity
19
0
2
0.15
m/d
0.15
Phytoplankton
Subsistence quota for nitrogen
2
2.5
2.5
2.5
mg N/mg A
0
Phytoplankton
Subsistence quota for phosphorus
2
0.1
0.1
0.1
mg P/mg A
0
Phytoplankton
Subsistence Quota of Intracellular N
4
7.2
7.2
7.2
mg N/g D
7.2
Phytoplankton
Subsistence Quota of Intracellular P
4
1
1
1
mg P/g D
1
* Depending on the model version, algal parameters and rates may be expressed relative to grams of dry weight biomass (g D) or relative to mg of chlorophyll a (mg A).
-------
Table 20. QUAL2K and QUAL2Kw Rates and Constants: Sediment, Detritus, and Biofilm Parameters
Sediment/Detritus/Biofilm Parameter
Count
Min
Max
Median
Units
Default Value
Ammonia preference
1
25
25
25
Hg N/L
-
Biofilm growth rate temperature correction
1
1.047
1.047
1.047
-
-
Carrying capacity
1
100
100
100
g D/m2
-
Death rate
1
0.05
0.05
0.05
day1
-
Death rate T correction
1
1.07
1.07
1.07
-
-
Detritus dissolution rate
22
0.001
5
0.63
day1
0.23
Detritus settling velocity
21
0
4.8
0.5
m/d
1
Detritus dissolution rateT correction
14
1
1.07
1.07
-
1.07
External nitrogen half sat constant
1
15
15
15
Hg N/L
-
External phosphorus half sat constant
1
2
2
2
Hg P/L
-
Fast CBOD half sat
1
0.5
0.5
0.5
mg O2/L
-
Fraction of dissolution to fast CBOD
1
1
1
1
-
1
Inorganic suspended sediment settling velocity
15
0.000001
1.9
0.61
m/d
0.1
Max biofilm growth rate
1
5
5
5
g 02/m2/d
-
Oxygen inhibition parameter
1
0.6
0.6
0.6
L/mg O2
0.6
Prescribed SOD
2
0
0
0
g 02/m2/d
-
Respiration rate
1
0.2
0.2
0.2
day1
-
Respiration rateT correction
1
1.07
1.07
1.07
-
-
Sed denitrification transfer coefficient
20
0
0.95
0.21
m/d
-
Sed denitrification transfer coefficient T correction
14
1.042
1.07
1.07
-
-
Sed P oxygen attenuation half sat constant
15
0
2.0
1.4
mg O2/L
1
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Sediment/Detritus/Biofilm Parameter
Count
Min
Max
Median
Units
Default Value
Sediment N flux
2
0.8
100
50
mg N/m2/d
-
Sediment oxygen demand
4
0
10
2.3
g 02/m2/d
-
Sediment P flux
2
0
0.9
0.45
mg P/m2/d
-
Temp correction
1
1.05
1.05
1.05
-
-
-------
Calibration Data and Approaches
There was a wide range of calibration periods for the Q2K applications, with some studies utilizing one
or two sampling events, and others utilizing more than 10. Generally, the timing of sampling events
appears to be most often targeted towards the dry or low flow season, which is consistent with the
application of Q2K as a steady-state model. No distinctions were made between Q2K and Q2Kw in the
parameter value tables that accompany this report. In some cases, applications of Q2Kw are likely to
apply the non-uniform kinematic wave function that distinguishes Q2Kw from Q2K, as well as the
autocalibration feature in Q2Kw. Calibration is most accurate when using data collected during the most
likely steady-state condition (i.e., baseflow).
Autocalibration of parameters using the genetic algorithm in QUALK2Kw was used by eight studies.
Three studies followed autocalibration with manual calibration for at least some parameters. Others
began with the model default or literature values and used the autocalibration process to generate final
parameters. Manual calibration starting with model default or literature values was done by five studies.
Three studies used experimental or literature values for calibration. Some studies used more than one
calibration approach for the various parameters.
5. Variation in Model Coefficients
The biggest variations in model coefficients can be found in phytoplankton growth rates and nutrient
recycle rates. Certainly, there is much information in the literature concerning algal growth rates, both
for individual species (often related to harmful algal blooms such as freshwater Microcystis, Anabaena,
and other cyanobacteria or blue-greens, and marine dinoflagellates such as Alexandrium, Prorocentrum,
etc.) and taxonomic groups (such as diatoms, greens, dinoflagellates, cyanobacteria, etc.). However, it is
important to recognize that individual phytoplankton taxonomic groups, as well as individual species,
may be present on an episodic basis; i.e., residing for several days to several weeks, and the reasons for
these short-term blooms and crashes are not fully understood. Furthermore, phytoplankton spatial and
temporal heterogeneity or patchiness in large lake, reservoir, or estuarine systems can be related to
flood or storm events, vertical velocities associated with wind-induced stress or Ekman-type upwelling,
aggregation of phytoplankton along tidal fronts when river flow and tides are in opposite direction, or
lake seiche driven upwelling or coastal upwelling of nutrient-rich waters associated with local-winds or
mesoscale eddies. This patchy behavior is extremely difficult to simulate with current hydrodynamic and
water quality models.
It is also important to recognize that monitoring or sampling programs are often at temporal and spatial
scales that are inconsistent with patch dynamics as opposed to more region-wide algal growth.
Furthermore, in attempting to model phytoplankton biomass, modelers are often limited to datasets
that contain only chlorophyll a as an indicator of biomass. As has been shown in the literature,
phytoplankton carbon to chlorophyll a ratios vary as a function of temperature, light, and nutrient
limitation (Chalup and Laws, 1990, Geider et al., 1997, Finenko et al., 2003). Therefore, given these
factors that can contribute to the spatial and temporal variability of phytoplankton biomass, it is not
surprising that phytoplankton growth rates used in modeling studies can vary so much from site to site
and from application to application. This natural variability is also the reason that it is recommended to
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use multi-year data sets to calibrate eutrophication models when data are available and this level of
model development is feasible under a project budget and schedule.
The other set of model coefficients that show considerable variation are nutrient recycle rates. While
the project team was able to find and report on the range of RCK values used in the modeling studies, it
was difficult to find information in the literature that described empirical studies where rates of reaction
were reported for nutrient hydrolysis (particulate organic matter conversion to dissolved organic
matter) or mineralization (dissolved organic matter conversion to its inorganic form). Therefore, these
rate coefficients tend to be treated as a "freely tunable" calibration parameter. It is also important to
recognize that there is a wide range in the "reactivity" of organic matter (Eckenfelder, 1970, Middleburg,
1989, Ogawa et al., 2011). Discharges from CSOs tend to have very high reaction rates, while oceanic
organic matter has very low reaction rates; organic matter associated with phytoplankton production
has intermediate reaction rates. Therefore, it is not surprising that these coefficients vary across sites
and model applications. In addition, with the development of the SFM, water quality modeling codes
(CE-QUAL-W2 [Section 4.2], CE-QUAL-ICM [Cerco and Cole, 1994], RCA [HydroQual, 2004]) have started
to differentiate between different forms of organic matter (particulate versus dissolved) and various
pools of reactivity (labile and refractory) (Cole and Wells, 2015; Cerco, 1994, 2004; HydroQual, 1991,
2000). Although the current version of WASP does not consider various pools of reactivity for organic
nitrogen and phosphorus, WASP does permit the modeler to utilize up to three pools of CBOD. Since it is
possible that future releases of WASP will be expanded to include labile and refractory organic nutrient
pools, the project team decided to include RCK values from model applications where labile and
refractory organic matter (C, N, P) were used in conjunction with the SFM.
6. Conclusions
Significant improvements have been made to the water quality models WASP, CE-QUAL-W2, HSPF, Q2K
and Q2Kw since 1985 including additional simulation capacity for multiple algal groups (both suspended
and benthic), and changes in the way the models represent interactions between the water column and
bed sediments. WASP, CE-QUAL-W2, and Q2Kw have incorporated complete sediment diagenesis
models that account for deposition of organic matter, diagenesis of organic matter in sediments, and
flux of end-products back to the water column. HSPF and Q2K have implemented more robust
simulations of sediment-nutrient interactions and sediment-water fluxes without adding a complete
sediment diagenesis module. There have also been major improvements to the models' treatment of
anoxic/hypoxic conditions, with all models incorporating nitrification and denitrification in the water
column and sediments as a function of oxygenation.
Model updates have generally focused on increasing the ability of the models to differentiate between
reactive and recalcitrant forms of organic matter, in particular organic nitrogen and organic phosphorus,
and incorporating this differentiation into algal growth, respiration, and mortality calculations. The
addition of multiple phytoplankton groups requires RCK parameters related to growth and respiration as
a function of temperature, nutrient limitation, stoichiometry, and settling. Therefore, the models were
updated to allow the user to specify temperature optimum curves for algal growth, respiration,
excretion, and death rates, or at a minimum, to specify temperature corrections that include upper and
lower temperature limits. The incorporation of more robust sediment-nutrient interaction simulations
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or full sediment diagenesis nutrient flux models allows the water quality models to simulate the impact
of sediment flux on algal growth and water quality in general.
Other more general model changes include computational improvements since 1985, such as the
addition of a genetic algorithm for auto-calibration of RCK parameters available in Q2Kw. Specific model
additions and changes post-1985 are presented in Table 21.
Table 21. Model Additions and Changes since 1985
Sediment
Model
Water Quality State Variables
Simulation
Other Changes
WASP
• Multiple phytoplankton groups
Sediment
• User-defined
• Dissolved organic nitrogen
diagenesis
temperature optimum
• Detrital organic carbon
nutrient flux
curves for algal rates
• 3 types of CBOD
model (SFM)
• Stream/River Transport
• Biogenic and dissolved silica
Algorithms (kinematic
• Benthic algal model
and dynamic wave)
• Macrophytes
• Hydraulics of weirs
• pH-alkalinity model
• Predictive water
• Water temperature
column light model
CE-QUAL-W2
• Multiple phytoplankton groups
Sediment
• Variable stoichiometry
• Multiple macrophyte, epiphyte, and
diagenesis
allowed (previously
zooplankton groups
nutrient flux
fixed stoichiometric
• Nitrification and denitrification
model (SFM)
constants for C:N:P)
• Decay of sediments, DOM, POM
in production
• Fish habitat analysis
• CBOD, BOD-N, BOD-P
(in current
• Particle transport
• New reaeration formulations specific
beta version)
• Hypolimnetic aeration
to rivers, lakes and reservoirs,
• Dynamic shading
estuaries, and aeration over spillways
computation
• Photo-degradation
• N2 gas for TDG simulation
• CH4, S04, H2S, reduced and oxidized
forms of Fe and Mn
• Non-conservative alkalinity
QUAL2K(w)
• CBOD speciation
Sediment-
• Hydraulics of weirs and
• Explicit simulation of attached
water fluxes
waterfalls (for gas
bottom algae
of DO and
transfer modeling)
• Light extinction parameter
nutrients
• New model
• pH simulation (as a function of
simulated
segmentation protocol
alkalinity and TOC simulations)
internally
• Genetic algorithm for
• Pathogens
(02 K);
auto-calibration
• Denitrification at low DO
Sediment
• Monte Carlo simulation
• Reach-specific kinetic parameters
diagenesis
• Transient storage
nutrient flux
zones
model (SFM)
• Computation of
(Q2 Kw)
evaporation
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Model
Water Quality State Variables
Sediment
Simulation
Other Changes
HSPF
• Simulation of up to 4 algal types
Sediment-
• Wetlands and shallow
• Nitrification and denitrification as
nutrient
water-table hydrology
water column processes
interaction
• Irrigation capabilities
• New state variables for phosphate
simulation
• Alternative simplified
and ammonium in suspended and
(adsorption
snow algorithms
bed sediment
and
• BMP and REPORT
desorption of
modules
P and N)
For all models, many of the model applications were conducted by state and federal agencies such as
USGS, USACE, and state environmental agencies. In addition, the models have also been used by
academic researchers nationally and internationally. It is very important for model practitioners to use
defensible parameter values for TMDLs and other regulatory and planning purposes. There is a potential
for misuse if model practitioners utilize abbreviated and incomplete model parameter tables without a
complete understanding of antecedent environmental conditions for the model application, geographic
scale and applicability, and other relevant study-specific information, as well as specific limitations
acknowledged by the model practitioner. Although the quality criteria review for this study disqualified
papers with no discussion of model setup and input data, some literature did report abbreviated lists of
parameter values. It is the responsibility of the modeler to assess the relevance of specific values before
use and to document all values.
There are some differences in the availability of model parameter values in the literature depending on
the model. Many of the WASP, CE-QUAL-W2, Q2K, and Q2Kw studies were conducted by federal and
state agencies with complete, publicly available reports, making the identification and extraction of RCK
parameter values relatively easy for these models. It is also standard reporting practice for some federal
and state agencies to include tables of calibrated model parameters for these models. In many cases,
these reports contained complete parameter tables as well as abundant supporting hydrologic,
environmental, climatic, and sampling information. Access to the full input sequences and metadata
allows a motivated modeler to discern the importance of hydroclimatic, hydrographic, physical,
chemical, and biotic model parameter values in relation to each other. The approach of presenting full
and complete metadata and parameter value tables may allow a modeler to develop more defensible
parameter values compared to using abbreviated tables from peer-reviewed journal papers.
Although HSPF is used extensively for TMDL modeling, fewer publicly available reports that contain
parameter tables were identified using the search strategy used for this report. The available HSPF
literature describes study setup and results; however, some literature sources, especially peer-reviewed
journal articles, often include abbreviated parameter tables and minimal amounts of supporting
information on environmental setting and model setup. By contrast, the EPA-funded database
HSPFParm contains full input sequences and metadata for model applications in more than 70
watersheds in 14 states, which can help prevent model misuse. Many of these applications are runoff
and land-surface simulations, but some studies used the receiving waters HSPF module RCHRES, which is
the relevant module for this task. Additional full parameter lists for calibrated HSPF models are included
in gray literature model calibration reports (e.g., for TMDL studies) that were not identified or selected
by the search strategy.
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All four models have been used in studies in the United States and internationally, in climates ranging
from semi-arid to tropical and in both warm and cool environments. Hydrologic regimes in the areas
studied included snowmelt dominated, storm dominated, and monsoonal, although there are few cold-
climate applications. It is unlikely that the settings represented in the literature investigated for this task
are exhaustive, and therefore do not reflect the full application capabilities of the models.
For QUAL2Kw, WASP, and certain modeling options for HSPF, the use of the model for benthic algae
simulation is focused on relatively shallow and clear Western streams. In the case of HSPF, this is a
function of the formulations used in the post-1985 benthic algae enhancements, which are optimized
for those conditions; the pre-1985 benthic algae formulations for HSPF, which are retained as a
modeling option, are more generalized in nature and therefore applicable to a wider range of settings.
It is clear that all of these models are applicable in a variety of climatic conditions and waterbody types.
Because the criteria used to select studies disqualified those papers and reports without reported RCK
parameter values and without clear documentation of model setup and calibration, the RCK data
included in the data tables were extracted from only a small subset of the universe of studies that use
these models. Nevertheless, it is possible to identify water quality processes with notable variability in
rate values. In general, the largest variation in model coefficients between studies exists in
phytoplankton and benthic algae rates, nutrient recycling rates, and nutrient partitioning coefficients.
Monitoring and sampling programs are often inconsistent with phytoplankton growth and death
dynamics, likely resulting in difficulties with model calibration. As would be expected, these difficulties
result in significant variation from site to site and application to application. Similarly, there is significant
site-specific variation in nutrient recycle rates. A problem encountered during the literature review and
population of the RCK data tables is that there are very few studies that present empirical information
to constrain rates; the majority of RCK parameters included in the studies and the data tables developed
for this effort are calibration parameters derived from the model. Future study could focus on
constraining rates with empirical data (e.g., laboratory algal growth rates for a variety of species;
nitrification rates, etc.). Given the lack of empirical parameter data, the model practitioner must rely on
the body of parameters estimated through calibration; these data are presented in the RCK data tables
created for this effort.
The largest data gap for all the models involves the data used for calibration. All the models can be
calibrated using a limited amount of data (e.g., a single sampling season), but use of limited data can
produce a model that is less able to simulate years with different hydrologic and biogeochemical
conditions accurately. Due to limited time, funding, and resources, many studies are not able to collect
multiple years of data, and studies with relatively short calibration periods were included in the data
compiled for this task if the studies presented sufficient documentation, and rates were within
reasonable ranges as determined by expert judgment. Although fewer studies calibrate using multiple
years of data, it has become increasingly common for model practitioners to revisit existing calibrated
models (i.e., calibrated for a specific river) and add additional calibration years as data become available
or it becomes clear that the calibrated model cannot accurately simulate water quality for different
hydrologic conditions.
Updates and enhancements to these models since 1985 have resulted in new RCK parameters, examples
of which should be available to model practitioners. Although the acceptable ranges for many model
parameters are still informed by the 1985 Rates Manual, changes to the models since 1985, particularly
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for algal simulation and sediment diagenesis/flux, have resulted in additional parameters that are
necessary for successful model application. The data tables in this report can serve as a reference for
model users and that can be expanded in the future to incorporate additional studies.
7. Future Research Opportunities
In addition to the literature review and parameter value compilation discussed above, the project team
considered other aspects of model parameter value compilation during the project including:
• The availability and applicability of empirically derived parameter values;
• Cross-model applicability of parameter values; and,
• Comparison and mapping of similarities and differences between the governing equations for
each model.
Information on these topics could augment the parameter value tables that accompany this report.
Preliminary considerations related to empirically derived parameter values, cross-model applicability of
values, and comparison of similarities and differences of governing equations are briefly noted below as
background for potential future research of these topics related to the update of the 1985 Rates
Manual.
Empirical Data
We conducted an initial assessment of the feasibility of compiling empirically derived rates in addition to
model application parameters, looking first at citations in the original 1985 Rates, Constants, and
Kinetics manual. Of the 116 citations in the 1985 manual, a large majority were modeling studies. Many
of these modeling studies contained references to rates and other parameters based on laboratory data,
but most of the initial rates manual was based on modeling studies, similar to this project.
Following an assessment of the 1985 Rates Manual, the research team investigated the availability of
empirical studies related to the Group 1 water quality parameters. In conducting this search, several
issues were identified that inhibited a comprehensive assessment of empirical studies and the inclusion
of empirical data in the parameter data tables. These issues included:
1. Presentation of environmental conditions - The applicability of empirically derived values was a
concern given the tight coupling of environmental conditions to algal behavior, nutrient cycling,
and sediment diagenesis. Many of the studies evaluated during the preliminary assessment of
empirical data presented multiple parameter values across a range of conditions, making it
difficult to extract a single parameter value from a report.
The parameter value tables for this project were not designed to include details on the project-
specific applicability for a given parameter. For instance, various studies focused on
representation of a single algal species and the resulting rates are applicable to the species in
question (e.g., some harmful algal bloom (HAB) species, such as Microcystis or Anabaena), but
may not be informative to a modeler who wishes to model an algal functional group such as
diatoms, greens, or dinoflagellates. This level of detail is not available in the tables presented
herein. Furthermore, studies report diverse types and levels of information, making it difficult to
extract the same information on methods and environmental conditions from all sources.
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Accurately representing the environmental or laboratory conditions for specific parameter
values is necessary, and should be a significant component of potential future projects to
identify and compile empirical values.
2. Identification and Accessibility of Literature - The preliminary assessment of the availability of
empirical parameter values indicated that it would be particularly difficult to assess the
applicability of studies based on the results of keyword searches; a comprehensive assessment
of empirical studies since 1985 would be a very large undertaking. The limited amount of
empirical parameter values proved difficult to find because they represent foundational data
that are often not published in peer-reviewed reports. Future research could focus on the
identification of the most applicable laboratory and field studies that provide empirically derived
parameters.
3. Selection of appropriate parameters - It is not possible to determine a value empirically for
every parameter listed in the parameter value tables that accompany this document; some
parameters are difficult to determine through field or laboratory experiments. Selecting the
parameters to investigate in a literature review of empirical studies was difficult given the range
of parameters in the models. For example, although there are many studies that provide
empirical values for algal parameters (e.g., growth, death, N/P requirements, etc.), it is
challenging to determine sediment flux rates in the field due to the sensitivity of sediment
diagenesis to environmental conditions such as DO, pH, and temperature, which can vary
significantly over a short distance. A comprehensive literature review of empirical studies could
potentially identify studies that did investigate the more complex or variable parameters.
4. Differences between empirical and calibration methods - The preliminary assessment of
empirical data sources indicated significant differences across empirical studies and between
empirical studies and model applications. Consistency in methods used to calculate parameters
is a factor. For example, a kinetics model for a constituent in an empirical study may not match
the method employed by one of the water quality models (e.g., zero order vs. first order
kinetics; variable models for algal growth). Similarly, many empirical studies do not report values
in the same units as the model applications, requiring careful and complete conversion and
standardization of units. Reconciling these differences and presenting metadata to explain the
differences will likely take effort and time.
For this report, an empirical data assessment and collection was deferred due to the challenges
summarized above. Future identification, assessment, and compilation of empirical parameter values
could be conducted and provided as a supplemental table to, and additional context for, those tables of
calibrated parameter values produced for this project.
Comparison of Model Kinetic Formulations
During the development of the model-specific parameter value tables that accompany this report, the
project team investigated the possibility that the values for certain parameters might be applicable
across models. For example, kinetic formulations for processes such as nitrification may be similar and
the parameters relevant to more than one model (if units are consistent). To determine the level of
consistency in the kinetic formulations across models, a selected subset of governing equations was
evaluated to identify parameters that are model-agnostic and those that are model-specific. However,
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full cross-model parameter value comparisons are difficult because each model handles kinetic
formulations in slightly different ways, including how those formulations are incorporated into the
model. It is, therefore, difficult to identify if a parameter is truly held in common between multiple
models. In some cases, the governing equations presented in model documentation are not identical to
the model code, making it difficult to compare models based on their documentation. The project team
determined that, due to the uncertainty in how similar or identical parameters are treated in each
model, parameter values should be considered model-specific for the purposes of this project and the
associated data tables.
The project team conducted a preliminary comparison of the governing equations for each model and
concluded that through this process it might be possible to identify a subset of the parameter values
that could be used in multiple models. Subsequent research could initially assess the similarities and
differences of governing equations between the different models, with a focus on identification of
parameters that can confidently be applied to any of the water quality models. Such an effort would
require both an investigation of the governing equations in the model documentation and a detailed
assessment of the model code. Important next steps would include extracting as many governing
equations as possible and linking them to the parameter data that are presented in the parameter value
tables that accompany this report. This could identify parameter values that could be removed from the
model-specific tables and used to create a model-agnostic parameter value table to facilitate cross-
model applications.
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Di Toro, D. M. 2001. Sediment Flux Modeling, Wiley-lnterscience, New York, New York. 624 pp.
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Donigian, A., J.C. Imhoff, and J. Kittle, 1999. HSPFParm: An Interactive Database of HSPF Model
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Donigian, A.S., and J.C. Imhoff, 2006. Chapter 2. History and Evolution of Watershed Modeling Derived
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