&EPA
EPA 600/R-19/232 | December 2019 | www.epa.gov/research
United States
Environmental Protection
Agency
A Review of Watershed
and Water Quality Tools for
Nutrient Fate and Transport
Office of Research and Development
Center for Environmental Solutions & Emergency Response | Groundwater Characterization & Remediation Division
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EPA 600/R-19/232
December 2019
A Review of Watershed
and Water Quality Tools for
Nutrient Fate and Transport
Tadesse Sinshaw
National Research Council Resident Research Associate
United States Environmental Protection Agency
Robert S. Kerr Environmental Research Center
919 Kerr Research Drive, Ada, OK 74820, USA
Lifeng Yuan
National Research Council Resident Research Associate
United States Environmental Protection Agency
Robert S. Kerr Environmental Research Center
919 Kerr Research Drive, Ada, OK 74820, USA
Kenneth J. Forshay
Project Officer
United States Environmental Protection Agency
Office of Research and Development
Center for Environmental Solutions and Emergency Response
Groundwater Characterization and Remediation Division
919 Kerr Research Drive, Ada, OK 74820, USA
Office of Research and Development
Center for Environmental Solutions & Emergency Response | Groundwater Characterization & Remediation Division
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Disclaimer
This document has been reviewed by the U.S. Environmental Protection Agency,
Office of Research and Development, and it has been approved for publication as an
EPA document. This technical report presents the result of work directed by Project
Officer Kenneth J. Forshay (EPA). The research described in this report has been funded
wholly or in part by the U.S. Environmental Protection Agency including support for
National Research Council Research Associateship Program Fellows Tadesse Sinshaw
and Lifeng Yuan. Mention of trade names or commercial products does not constitute
endorsement or recommendation for use.
Quality Assurance
This work was performed under an EPA-approved quality assurance project plan,
"A Review of Tools for Nutrient Fate and Transport Simulation/' (OA ID #: G-GWERD-
0031787-QP-l-l), approved September 24, 2018. Generally, the report contains
description and evaluation of existing tools and literature. Primary data collection
for this work is limited to publicly available database search results as described in
Appendix 1. The data and information used in this document have been assessed by
the EPA for this review. Neither the EPA, EPA contractors, nor any other organizations
cooperating with the EPA are responsible for inaccuracies in the original data that may
be present.
Acknowledgements
We sincerely thank Dr. Chayan Lahiri for his review and constructive suggestion on
revisions of this report. We also express gratitude to other reviewers of this report,
including Dr. Jessica Brumley, Dr. David Burden, and Pat Bush. Dr. Tadesse Sinshaw and
Dr. Lifeng Yuan appreciate support from the NRC Research Associateship award funded
by the U.S. EPA while in residency at the U.S. EPA's Robert S. Kerr Environmental
Research Center, Ada, OK 74820. This work is part of the Office of Research and
Development, Safe and Sustainable Water Resources National Program, Project No.
SSWR 3.Old.
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Contents
Acronyms iv
1.0 Introduction 1
1.1 Purpose of the Report 1
1.2 Organizational Framework 1
2.0 Background 2
2.1 Overview of Water Quality Management 2
2.2 Roles of Models in Water Quality Management 2
3.0 Models for Nutrient Fate and Transport 4
3.1 Watershed Loading Models 5
3.2 Mixing Models 24
3.3 Surface Water Quality Models 28
3.4 Groundwater Quality Models 36
4.0 Findings from Past Applications 42
4.1 Watershed Loading Models 42
4.2 Mixing Models 44
4.3 Surface Water Quality Models 46
4.4 Groundwater Quality Models 48
5.0 Recommended Strategy for Model Selection 50
6.0 Conclusions 57
References 58
Appendix 1: Model Search Strategy A1
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Acronyms
AGNPS
Agricultural NonPoint Source Pollution
Model
AGWA
Automated Geospatial Watershed
Assessment Tool
AnnAGNPS
Annualized Agricultural NonPoint Source
Pollution Model
BASINS
Better Assessment Science Integrating
Point and Nonpoint Sources
BMPs
Best Management Practices
BOD
Biological Oxygen Demand
CAT
Climate Assessment Tool
CEAM
Center Exposure Assessment Models
CORMIX
Cornell Mixing Zone Expert System
CWA
Clean Water Act
DEM
Digital Elevation Model
DO
Dissolved Oxygen
DOC
Dissolved Organic Carbon
EAAMOD
Everglades Agricultural Area Model
ECM
Export Coefficient Model
EFDC
Environmental Fluid Dynamics Code
EMC
Event Mean Concentration
EPA
Environmental Protection Agency
GenScn
GENeration and Analysis of Model
Simulation SCeNarios
GEPD
Georgia Environmental Protection Division
GIS
Geographic Information System
GLEAMS
Groundwater Loading Effects of
Agricultural Management Systems
GWLF
Generalized Watershed Loading Function
HEC-RAS
Hydrologic Engineering Center's River
Analysis System
HRU
Hydrologic Response Units
HSPF
Hydrologic Simulation Program - Fortran
HST3D
Heat- and Solute-Transport Program
HUSLE
Hydro-geomorphic Universal Soil Loss
Equation
KINEROS2
Kinematic Runoff and Erosion 2
LID
Low Impact Development
LSPC
Loading Simulation Program
L-THIA
The Long-Term Hydrologic Impact
Assessment
MUSLE
Modified Universal Soil Loss Equation
N
Nitrogen
NCCHE
National Center for Computational
Hydroscience and Engineering
nh4
Ammonium
no2
Nitrite
no3
Nitrate
NOAA
National Oceanic and Atmospheric
Administration
NPS
NonPoint Source
N-SPECT
NonPoint Source Pollution and Erosion
Comparison Tool
OpenNSPECT
Open NonPoint Source Pollution and
Erosion Comparison Tool
P
Phosphorus
PLOAD
Pollutant Loading Estimator
P04
Phosphate
RHEM
Rangeland Hydrology and Erosion Model
RUSLE
Revised Universal Soil Loss Equation
SCS-CN
Soil Conservation Service Curve Number
SLAMM
Source Loading and Management Model
SUTRA
Saturated-Unsaturated Transport
SWAT
Soil and Water Assessment Tool
SWET
Soil and Water Engineering Technology,
Inc.
SWMM
Stormwater Management Model
TKN
Total Kjeldahl Nitrogen
TMDL
Total Maximum Daily Load
TN
Total Nitrogen
TP
Total Phosphorus
TSS
Total Suspended Solids
USACE
United States Army Corps of Engineers
USDA-ARS
United States Department of Agriculture -
Agricultural Research Service
USGS
United States Geological Survey
USLE
Universal Soil Loss Equation
VP
Visual Plume
WAM
Watershed Assessment Model
WARMF
Watershed Analysis Risk Management
Frame
WASP
Water Quality Analysis Simulation Program
WDMUtil
Watershed Data Management Utility
WMS
Watershed Modeling System
WQM
Water Quality Management
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1.0
Introduction
1.1 Purpose of the Report
The purpose of this report is to provide an overview of common watershed and water quality tools and models that
are used to estimate water quality, nutrient fate and transport, and non-point source (NPS) pollution. Watershed
and water quality management activities are supported by various tools. Tools integrate multiple approaches and
techniques to describe a watershed system and its natural processes. A tool can be a method, technique, data-
base, or model that is used to study a watershed system. Many watershed and water quality models have been
developed to help improve our understanding of watershed processes. These models simplify complex physical
processes through mathematical, empirical or statistical relationships and construct the conceptual framework of
primary physical processes to represent natural processes that exist in a watershed. Watershed and water quality
models help watershed managers generate useful information that assists in environmental decision making. The
core of some tools is a mathematical model that represent an abstract of a real system with a series of equations
and algorithms built in an interactive interface of software and a general understanding of these structures can
help improve tool selection or understanding of strengths and limitations of a tool. Models are useful for many
tasks including hydrologic investigation, water quality assessment, future scenario projections, permit and trading
options analysis, management practice evaluations, total maximum daily loads (TMDLs) development, and other
policy-making or management decisions for a watershed. Thus, clear insight to the most common tools and their
core structure and function is needed to apply a watershed and water quality tool correctly.
Many watershed and water quality models exist to solve varied environmental issues. Although each model is
unique and is designed to solve a specific problem, the presence of many models makes the model selection a
challenge for model users. Thus, model and tool selection require a careful examination of suitability before it is
applied in practice. A review of commonly used models can provide a general guideline of model selection for users
to understand the function of an individual or class of models, which is essential to clarify its intended use, and to
avoid misinterpretation or misapplication. This report provides a brief description of the major features of com-
monly applied models that are used primarily for watershed management and water quality problems. These major
features include each model's intended use, components, spatial and temporal resolution, pollutants represented,
and availability.
This report describes existing models that are useful for communities that intend to enhance water quality as well
as resilience and sustainability in watersheds. Thirty-seven tools that are widely used for watershed and water
quality modeling were reviewed. These reviewed models were selected based on the professional judgment of the
authors and various sources, primarily from open-source literature, since this selection approach is intrinsically
biased, a description of their frequency of appearance in primary literature is provided to show how often the use
of these tools appear in practice. Literature can be dominated by publications from academic research rather than
applied research. Therefore, the presented models are those more popular in academic research than management
applications, but likely represent the tools generally applied in practice. This approach is not exhaustive or com-
plete but does provide a good overview of tools available and starting point for those interested in learning more or
selecting appropriate tools for certain applications.
1.2 Organizational Framework
This report provides a brief description of existing watershed and water quality models that can inform the decision
in nutrient management. The report is presented in six chapters. Chapter 1 introduces the purpose, scope, and out-
line of the report. Chapter 2 provides background information on main activities in water quality management and
the role of models to support watershed management and planning. Chapter 3 introduces information on model
features, summarized from models' documentation and open literature. Chapter 4 provides a literature review
based on past applications. Chapter 5 presents the recommended strategies to guide model selection. Chapter 6
provides a summary and concluding remarks of the report.
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2.0
Background
2.1 Overview of Water Quality Management
Major activities in water quality management (WQM) include adopting water quality standards, monitoring and as-
sessing water quality conditions, prioritizing water bodies management, developing TMDLs, and restoring impaired
water bodies. A water quality standard is a desired and an attainable water quality condition established to protect
designated use or to ensure waters stay at a higher quality. Water quality goals are defined for each designated use,
such as public drinking water supply, recreation, aquatic, wildlife support, and agricultural, industrial, or naviga-
tional. Criteria to protect a designated use can be numeric (maximum pollutant concentration) or narrative (desired
water quality condition, such as free from the specific adverse condition) criteria.
WQM activities are often supported by varying amounts of data and information. These activities may also include
further monitoring to provide the data that are needed for management activities and decisions. The monitored
data is used to assess overall water quality condition, track water quality change over time, identify critical areas,
evaluate the level of protection, refine existing water quality standards, or evaluate the effectiveness of existing
projects and programs. Often these assessments are conducted by application of models or tools. Assessed waters
are labeled as healthy, threatened, or impaired depending on the specific case. To aid in the interpretation and
summary of these data, determination of the appropriate tools or models can help inform these classifications.
Appropriate tools can also assist in the prioritization of restoration or management action. Many impaired waters
can exist in a given geographical unit. Time and resource availability often limit the implementation of restoration
activities for all impaired water bodies at one time. A watershed manager needs to decide which waters are a prior-
ity among the list of impaired waters. Priority waters are determined based on user-defined criteria that are specific
to local settings. Priorities can be assigned based on human health consideration, groundwater activity, ecosystem
integrity, or various specific goals.
TMDL is the total maximum daily pollutant load that a water body can receive from point and nonpoint sources
(NPS) and that still meet the water quality standard for a specific pollutant. TMDL development involves identifying
a contaminant of concern, determining the water body assimilative capacity, quantifying the current pollutant load,
estimating the target pollutant load, and allocating a margin of safety. Watershed models play an essential role in
TMDL analysis in linking the pollution source to receiving water body. It helps to assess a contaminant of concern
and to quantify the pollution load. Water quality models are also key tools in TMDL analysis to determine the as-
similative capacity of a water body by simulating pollutant transformation in the receiving waters. TMDL analysis
provides information on how pollution loading from various sources can be reduced to meet water quality stan-
dards.
TMDL action plans are implemented to achieve the intended water quality improvements. Pollution load is con-
trolled by implementing NPS Best Management Practices (BMPs) and point source control permits. To control NPS,
such as nutrients, coordinating restoration efforts at a watershed level is considered a practical approach.
2.2 Roles of Models in Water Quality Management
It should be made clear that model predictions and calculation generally depend on high-quality field measured
data. Each activity of a WQM program, discussed in Section 2.1, is supported by varying amounts of data. Water
quality data can be obtained from field observation, but also benefits from the inclusion of modeling approaches
that can generate secondary or synthesized data that helps aid in data collection. Field monitored data is often pre-
ferred over model predictions as it provides first-hand verifiable and certifiable information by a chain of custody
and regulatory approved analysis techniques and quality assurance. A model prediction is an alternative option
2
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when the field site is not accessible for observation, resources limit extensive monitoring, or other factors that pre-
clude field sampling. Moreover, the linkage between the watershed system and water quality are complex and diffi-
cult to explain through the observational approaches alone. Thus, models can help us better understand the com-
plex watershed system. Ideally, the most effective source of data for decision making is obtained by integrating field
monitoring and modeling approaches. Field monitoring is complementary to modeling and vice versa. For instance,
field measurement can be applied to assess water quality changes over time, whereas a model computation can be
used to identify pollution sources, evaluate the effectiveness of alternative management practices, or describe fac-
tors controlling water quality changes. A discussion of model selection is also included but should not be construed
as a recommendation or affirmation of a particular tool or model, but more a description of which water quality
or data parameters are appropriate for a given approach. Here, we describe tools for WQM decisions, specifically
nutrient fate and transport, along with a brief description of how they work and how they are commonly used.
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3.0
Models for Nutrient Fate and Transport
Models presented in this report were identified from several literature sources, such as from federal and state
agencies, private companies, non-governmental organizations, universities, research centers, and open literature
databases. Most of these models are documented in U.S. EPA, United States Geological Survey (USGS), United
States Army Corps of Engineers (USACE), and United States Department of Agriculture (USDA) literature resources.
Models differ in many aspects and can be characterized in many ways, but here an effort was made to simplify
and categorize common watershed model applications. In this report, we classified models based on the intended
use along with the physical system they represent to provide clear information for model users on their suitability.
Based on the intended use, models were grouped into four categories - watershed loading, mixing, surface water,
and groundwater (Table 1).
Watershed loading models are developed to describe pollution source areas and estimate pollutants loading to
surface waters. Mixing models are a particular type of surface water models designed to analyze pollutant physical
mixing processes near the discharge zone. Surface and groundwater models are developed to simulate pollutant
transport and transformation in surface waters and subsurface environments, respectively. A brief description of
each category of models is provided in the introduction sections 3.1-3.4. For each presented model, the following
elements are described.
• General information - model history, availability, documentation/website sources, and technology
compatibility
• Model components, intended use, and capacity
• Key data requirements
Table 1. Summary of Reviewed Models
Category
Number
of Models
Represented
Processes
Intended Use
Environment
Watershed
Loading
14
Delivery mechanisms
of pollution load
from land surface to
surface water
To identify pollution
sources, simulate
processes, and
calculate the loading
Watershed
Mixing
4
Physical mixing and
dilution of pollutants
in receiving water
To analyze water
quality condition in
the mixing zone
Surface water near
discharge location
Surface Water
12
Transport
mechanisms and
transformation
of pollutants in
receiving water
To analyze surface
water response to
point and nonpoint
source pollution load
Surface water
Groundwater
8
Pollutants fate
and transport in
the subsurface
environment
To assess solute
contaminant fate in
the groundwater
Groundwater
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3.1 Watershed Loading Models
The water quality of water bodies is highly linked with the activities of the watershed system. Many watershed
activities, such as domestic, industrial, agriculture, thermal, and oil production, cause water quality deterioration
of water bodies in a watershed. These pollution sources are commonly classified as point and nonpoint sources
(NPS). Point sources, such as domestic and cooling power plants, are often discharged directly into surface water.
NPS, such as agricultural waste, are introduced to surface water through runoff from the land surface. The quantity
of pollutant mass delivered to water bodies is defined as pollution load. The load from point sources is relatively
easier to monitor and control, whereas the diffusive nature of NPS makes it challenging to assess the pollution load.
Watershed loading models (or called NPS pollution model) are developed to assist in identifying and quantifying
pollution load at a watershed scale.
NPS pollution phenomena are controlled by a range of watershed factors, including topography, soil, precipitation,
vegetation cover, stream network, and land management practices. For example, chemical fertilizer used in agricul-
ture, and the process of urbanization enrich soil nutrient on the land surface. Subsequently, pollutants picked up by
runoff, rainfall or snowmelt, and delivered to nearby rivers, lakes, reservoirs, wetlands, and other water bodies, can
cause water quality pollution at the local and regional scale.
Watershed loading models describe the NPS pollution processes mathematically. These models were build-based
on multiple sciences including land hydrology, soil erosion, sediment, and environmental chemistry. They are useful
analytical tools to predict pollution loading at different spatiotemporal scale, explain the delivery mechanism, and
describe the impact of watershed factors on pollution processes. Different governing equations are used to control
various physical processes. Generally, most watershed loading models include three components: hydrologic, ero-
sion and sediment yield, and nutrient fate and transport. Each component corresponding physical processes need
to be expressed mathematically. For example, in the hydrologic component, models use the water balance equa-
tion to calculate the volume of surface runoff. Main physical processes involve surface runoff, evapotranspiration,
and infiltration. In the erosion and sediment component, main processes include soil erosion and sediment yield.
Detailed below are the governing equations used in most watershed loading models, which focus on mass loads
calculation rather than complex transport processes.
Water Balance Equation
Water balance uses a principle of conservation of mass, which represents the volume of water that flows in
and out of a watershed system, maintaining balance. It is a basis of the construction of the hydrologic com-
ponent in most watershed loading models. A water balance equation in a closed system can be described as
equation 1 (Todd and Mays, 2005):
R = P-ET-AS (Eq!)
Where R is runoff, P is precipitation, ET is evapotranspiration, AS is a change in soil water or groundwater.
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Flow-Governing Equation
Flow supplies a power source for NPS pollution while it plays a role as a transport medium for pollutants.
Thus, mathematical equations of governing surface runoff are essential for driving hydrology and NPS models.
Soil Conservation Service - Curve Number (SCS-CN) method (NRCS,1986) was widely applied in numerous
watershed loading models to estimate direct runoff. The calculation of the Curve Number (CN) method pri-
marily considers three factors: the rainfall, soil infiltration, and hydrologic soil group. CN method is applied to
calculate direct runoff from a single-event rainfall.
Q = (P ~'a)2/[(P ~'a) + S] if(P-/„)<0,thenO = 0 (Eq 2)
Ia = 0.2 X S (Eq 3)
S = 25.4((1000/CW) - 10) (Eq 4)
Where, O is rainfall (inch), S is potential maximum retention after runoff begins (inch), I is initial abstraction
(inch), and CN is runoff curve number. A value of CN ranges from 30 to 100. The lower CN value refers to the
higher soil infiltration capability. Many watershed models use the SCS-CN method to calculate surface runoff,
including Long-Term Hydrologic Impact Assessment (L-THIA), Nonpoint Source Pollution and Erosion Compari-
son Tool or Open Nonpoint Source Pollution and Erosion Comparison Tool (NSPECT/OpenSPECT), Generalized
Watershed Loading Function (GWLF), Agricultural NonPoint Source pollution model (AGNPS), Soil and Water
Assessment Tool (SWAT), Watershed Assessment Model (WAM). SCS-CN method is easy to integrate with GIS
and conduct distributed calculations due to its simple structure.
Evaporation-Governing Equation
Evaporation is an essential mechanism of water loss from an open water surface. The Penman-Monteith and
Priestley-Taylor equations are widely applied in many watershed loading models to calculate potential evapo-
transpiration. The basic form of the Penman-Monteith method is expressed as Equation 5 (Monteith, 1965):
= m-gI±oaŁg)
A+y
Where AE is latent heat flux of vaporization (MJ/m2d), A is the latent heat of vaporization (MJ/kg), A is a slope
of the saturated vapor pressure curve (kPa/°C), R„ is net radiance flux (MJ/m2d), G is soil heat flux (MJ/m2d),
usually difficult to measure, y is Psychrometric constant (y ~ 66kPa/°C), Ea is the vapor transport flux (mm/d).
Priestley and Taylor method (1972) developed a modification of the Penman-Monteith equation with less
dependence on observed variables, given in Equation 6:
AEa = a^(Rn-G)(Eq 6)
Where Ea is daily potential evapotranspiration (mm/d), A is the latent heat of vaporization (MJ/kg), a is a mod-
el coefficient, 5 is the slope of the saturation vapor density curve (kPa/°C), y is the Psychrometric constant
(kPa/°C), R„ is net radiation (MJ/m2d), and G is ground heat flux (MJ/m2d).
6
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Infiltration-Governing Equation
The surface runoff comes from the difference that rainfall rate subtracts infiltration capacity during rainfall
period. Infiltration capacity represents the water volume of the rainfall that can be absorbed by soil without
running off.
Green-Ampt Mein-Larson infiltration method (Green and Ampt, 1911; Mein and Larson, 1973):
fm = Ke( 1 + ^2) (Eq 7)
J F(t)
Where f(t) is infiltration rate for time t (mm/hr), Ke is effective hydraulic conductivity, iff is wetting front matric
potential (mm), AO is a variation of soil water content, f(t) is cumulative infiltration (mm).
Horton's method (Horton, 1933):
ft = fc + C/o - fo)e-kt (Eq 8)
Where f is the infiltration rate at time t, fQ is the initial infiltration rate or maximum infiltration rate, fc is the
constant or equilibrium infiltration rate after the saturated soil or minimum infiltration rate, k is the decay
constant specific to the soil.
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Erosion-Governing Equation
Soil erosion processes play an essential role in the watershed loading model. Rainfall and runoff strip valuable
topsoil away and subsequent sediment flows into nearby streams or water bodies, ultimately contributing to
on-site land degradation and downstream water quality contamination, including nonpoint source pollution,
the siltation of reservoirs and lakes.
Average annual soil loss
Universal Soil Erosion Equation (USLE) (Wischmeier and Smith, 1978) has been widely used to evaluate aver-
age annual soil erosion throughout the world for over 50 years.
A = R-K-LS-C -P (Eq 9)
Where, A is average annual soil loss (t/a), R is rainfall erosivity index, K is soil erodibility factor, LS is a topo-
graphic factor, L is for slope length and S is for slope, C is cropping factor, P is conservation practice factor.
Revised Universal Soil Erosion Equation (RUSLE) is a variant of the original USLE for annual erosion assess-
ment. The RUSLE model keeps the same form with an original USLE, but it uses R (rainfall/runoff erosivity
factor) to calculate average annual soil loss and consider the impact of runoff factor on yearly soil loss. The
AGNPS model uses RUSLE to calculate sheet and rill soil loss.
A storm single-event soil loss
Some watershed loading models such as SWAT, NSPECT/OpenNSPECT use the modified universal soil loss
equation (MULSE) (Williams, 1975) to calculate sediment yield in a single rainfall event given as Equation 10:
Y = X x EK x CVF xPExSLx ROKF (Eq 10)
Where Y is sediment yield (ton/ha), Xis the energy factor, EK is soil erodibility factor, CVF is a crop manage-
ment factor that captures the effectiveness of soil and crop management systems in preventing soil loss, PE is
erosion control factor, SL is slope length and steepness factor, ROKF is coarse fragment factor. In MUSLE, the
energy factor, X, is calculated as Equation 11:
X = 1.586 X (QX X (Eq 11)
Where O is runoff volume (mm), qp is the peak runoff rate (mm/hr), Wa is the watershed area (ha). O can be
calculated by the SCS-CN method. qp is calculated by the rational method expressed as equation 12:
q = C X i X A (Eq 12)
Where q is peak flow rate, C is the runoff coefficient representing watershed characteristics, i is rainfall inten-
sity for the watershed's time of concentration, A is the watershed area.
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Pollutant Load-Governing Equation
Pollutant load refers to the mass of pollutant transported in a specific time unit from pollutant source areas to
a waterbody. The loading rate (or flux) is the rate at which a pollutant is passing a point of specific reference
on a river in mass/time unit. Methods used to calculate pollutant load of a watershed include numeric inte-
gration, worked record procedure, averaging approaches, ratio estimators, regression approaches, and flow-
proportional sampling. The two most commonly used methods to evaluate pollutant load are:
Event Mean Concentration (EMC) method
EMC is a method to calculate the total pollutant load during a single rainfall-runoff event. The expression of
EMC method listed as Equation 13 (Maniquiz et al., 2010):
total pollutant loading per event ZjLi Vi^i ^3)
total runoff volume per event V
Where EMC is event mean concentration (mg/L), V is total runoff volume per event (L), Vt is runoff volume
proportional to the flow rate at the time /, C, is pollutant concentration at sample time i and n is a total num-
ber of samples during a single storm event. EMC method was applied into L-THIA.
Export Coefficient Model (ECM) method
ECM is another popular method for pollutant load estimation in watershed modeling. ECM uses an export
coefficient that can represent an amount of load per unit area per unit time on a type of land use to simply
calculate the average nonpoint load from a watershed. A mathematical expression of the ECM method is de-
fined as Equation 14 (Fei Dong et at., 2017):
Load = YJEi[Ai (/,)] + ? (Eq 14)
i
Where Load is the annual loss of nutrients (kg/yr), Et is the export coefficient for the nutrient source i
(kg/km2 -year), At is the area occupied by land-use type i (km2), /, is an input of pollutants to the source i
(kg), p is the input of pollutant from precipitation (kg). N-SPECT/OpenNSPECT model applied ECM to estimate
total pollutant load.
Watershed load modeling started in the 1950s with the advent of the digital computer. The Stanford Water-
shed Model, developed from 1959 through 1966, was the first model used to support watershed hydrology
analysis and modeling (Crawford and Linsley, 1966). Before the 1970s, few studies were conducted to describe
the NPS pollution phenomenon and focused only on cause-and-effect relationship analysis between land use
and rainfall-runoff. With the development of watershed science, computer technology and environmental
legislation, numerous NPS pollution models have been developed and/or been integrated into watershed
models (Imhoff and Donigian, 2005). Most of the existing watershed loading models were developed from the
1970s to the 1990s. After the 1990s, more attention is given to NPS pollution modeling as people are aware
that sediment, nutrients and pesticides being the leading cause of water quality deterioration. The integration
of models, data management, geographic information system (GIS), remote sensing, and other analytical tools
became a developmental trend of watershed loading models. In this report, fourteen watershed load models
are presented as follows.
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AG N PS/An nAG NPS
AGNPS (Agricultural Non-Point Source Pollution Model) was jointly developed by USDA-Agricultural Research
Service (ARS) and Natural Resources Conservation Service. AnnAGNPS is an advanced version of AGNPS.
After the mid-1990s, AGNPS was upgraded from a model focused on simulating a single rainfall event NPS
pollution to AnnAGNPS (Annualized Agricultural Non-Point Source Pollution Model), a modeling system that
continuously simulates the movement of water, sediment and chemical loading within a watershed (Young et
al., 1989, Bingner et al., 2018). In AnnAGNPS, the user can still use the AGNPS algorithm to simulate a single
rainfall event. AnnAGNPS was written in standard ANSI Fortran 2015. The most current version of AnnAGNPS
is 5.5, released in 2018. The AnnAGNPS and AGNPS documentation are available without cost from the link:
http://go.usa.gov/KFO.
AGNPS can predict NPS pollutant load during a single rainfall event in an agricultural watershed. The model
can be used to evaluate the effect of land management practices on water, sediment and chemical loadings
under a single event within a watershed ranging from a few hectares to upwards of 20,000 ha (Young et al.,
1989).
AnnAGNPS is a distributed, physically-based, continuously-simulated model, which can simulate runoff, sedi-
ment, nutrients, and pesticides at a daily time step and evaluate the long-term effects of NPS pollution in
very large-scale watersheds (Bingner et al., 2009). AnnAGNPS discretize a watershed by using a cell approach
that divides the watershed into homogeneous grid cells by specific spatial resolution (Bingner et al., 2018).
The four main components of AnnAGNPS are: hydrology, erosion and sediment, nutrient and pesticide trans-
port, and wetland nitrogen removal. The model uses SCS-CN to simulate surface runoff and applies RUSLE
to determine soil erosion and conduct Hydro-geomorphic Universal Soil Loss Equation (HUSLE) to calculate
sediment delivery flow into streams or rivers (Chahor et al., 2014). The nutrients recognized by AnnAGNPS
include nitrogen (N), phosphorus (P), and organic carbon. The soil nitrogen considered in the model includes:
stable organic N, active organic N, and inorganic N. Nitrogen loss in simulation processes include soluble
inorganic N in runoff, leaching, denitrification, and sediment-bound organic N from soil erosion. AnnAGNPS
uses a simple crop growth stage index method to simulate plant uptake of nitrogen. Nitrogen residue return,
and decomposition are simulated by RUSLE. AnnAGNPS considers mineral P and organic P and applies a sim-
plification of the EPIC phosphorus model to simulate phosphorus processes. Primary input data for AnnAG-
NPS includes weather, soil, digital elevation model (DEM), and land use.
AnnAGPNS can simulate the spatial distribution of soil erosion and the impact of soil erosion on water qual-
ity. Sediment and nutrient loading prediction performed better at a large time scale such as monthly, sea-
sonal and annual than on a small-time scale daily. AnnAGNPS underestimated daily streamflow during a dry
period since it does not consider the baseflow. It can be applied to choose and determine BMPs, analyze risk
and cost/benefit, and assist TMDL development (Chahor et al., 2014). The cell grid in AnnAGNPS requires
many input parameters. Also, AnnAGNPS is not suitable for application or assessments in the winter season
(Fred Theurer and Bingner, 2018).
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AGWA
AGWA [Automated Geospatial Watershed Assessment Tool), jointly developed by the U.S. Environmental Pro-
tection Agency (EPA), the USDA-ARS, the University of Arizona and the University of Wyoming, is a GIS-based
hydrologic modeling tool. AGWA integrated RHEM (Rangeland Hydrology and Erosion Model), KINEROS2
{Kinematic Runoff and Erosion), KINEROS-OPUS, SWAT2000, and SWAT2005 models into a plug-in exten-
sion tool of ArcGIS to support watershed and water quality studies. AGWA has been upgraded from 1.5 for
ArcView 3.x, 2.0 for ArcGIS 9.x, to 3.x for ArcGIS 10.x. The latest AGWA 3.x software and documentation are
available without charge from https://www.tucson.ars.ag.gov/agwa/.
AGWA supports simulation of hydrology processes from a small to large watershed and helps watershed
managers and scientists understand the watershed processes (USDA-ARS, 2017). AGWA integrates GIS data
commonly used across the world and applies these GIS data to parameterize, execute, and visualize output
results from RHEM, KINEROS2, KINEROS-OPUS, SWAT2000, or SWAT2005 models. AGWA can identify poten-
tial sediment or pollution source areas and generate alternative future land-use/cover scenarios and com-
pare possible differences between simulation outputs. Input data for AGWA include DEM, land use and land
cover, soils, and precipitation data. Output files from the KINEROS model have channel infiltration, plane
infiltration, runoff, sediment yield, peak flow, channel scour, and sediment discharge. Output files from SWAT
include precipitation, evapotranspiration, percolation, runoff, transmission losses, water yield, sediment
yield, nitrate in surface runoff, and phosphorous in surface runoff (Goodrich et al., 2011).
AGWA can shorten the time at each process during model setup, watershed delineation, model execution
and result analysis. For example, AGWA uses common and attainable GIS data as model input and pro-
vides a simple and repeatable methodology for hydrologic model setup. AGWA makes hydrologic modeling
workflow easier through a unified GIS. The tool is suitable for scenario development and alternative future
modeling work at multiple spatiotemporal scales. However, it does not support the latest SWAT2012 version
running on ArcGIS 10.
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BASINS
BASINS {Better Assessment Science Integrating Point and Nonpoint Sources) was developed by U.S. EPA in
1996. BASINS 4.5 is the latest version, released in 2019. An open-source MapWindow GIS software package
works as the GIS frame for BASINS. BASINS is a comprehensive watershed modeling system. It is available
free of charge from https://www.epa.gov/ceam/basins-download-and-installation. BASINS is maintained by
EPA Center Exposure Assessment Models (CEAM).
BASINS is a physically-based model system that integrates environmental data acquisition, watershed and
water quality models, and various analytical tools, which is used to evaluate point and nonpoint source
pollution in multiple spatiotemporal scales (U.S. EPA, 2004). BASINS integrate multiple models such as HSPF
{Hydrologic Simulation Program-Fortran), SWAT, SWMM (Stormwater Management Model), GWLF-E, PLOAD
(Pollutant Loading Estimator), and instream and water quality models such as AQUATOX and WASP (Water
Quality Analysis Simulation Program) as pluginsto an open-source MapWindows GIS platform. BASINS is
also comprised of some analytical tools that allow pre- and post-processing of data for various models (US
EPA, 2015). These tools include TauDEM for geo-analysis and postprocessing, DFLOW for flow data analysis,
manual/automatic watershed delineation tool, land use reclassification tool, PEST for the Parameter Opti-
mization, time series functions, CAT (Climate Assessment Tool), GenScn (GENeration and analysis of model
simulation SceNarios), and WDMUtil (Watershed Data Management Utility). Four major data components of
BASINS include base cartographic data, environmental background data, monitoring data and point source
data. The input data include DEM, Land Use, Soil and Weather data. Output files have maps, graphs, and
tables summarizing point and non-point source pollution in a watershed (US EPA, 2015).
BASINS is a powerful modeling system since it integrates online data acquirement, various watershed models
and tools all in one unified GIS interface. This decreases data collecting and processing time, which reduces
model execution steps, and minimizing error caused by incompatible data format. The strengths of BASINS
are to analyze and develop TMDL standards and guidelines nationwide (Crossette et al., 2015). One limita-
tion of BASINS is a steep learning curve because it involves a lot of watershed science theories and technical
knowledge.
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GWLF
GWLF (Generalized Watershed Loading Function) was developed by Haith & Shoemaker (1987). GWLF ver-
sion 2.0 was published in 1992. The latest version is GWLF-E version 1.5.1 that has been incorporated into
Mapshed model. GWLF-E can be downloaded with no charge from http://www.mapshed.psu.edu/download.
htm. Currently, GWLF-E is developed and maintained by Pennsylvania State University.
GWLF can evaluate monthly time-step dissolved and solid-phase nitrogen and phosphorus loads in stream-
flow and groundwater from a complex mid-range urban or rural watershed with various land use (Wu and
Lin, 2015, Niraula et al., 2013). GWLF uses SCS-CN method with daily weather data to calculate surface
runoff, applies the USLE algorithm with monthly rainfall-runoff coefficient to assess erosion and sediment
yield, and uses the sediment delivery ratio method to determine sediment yield for each source area. Ad-
ditionally, GWLF applies dissolved N and P coefficients methods and incorporates the volume of surface
runoff to determine surface nutrient losses. GWLF considers urban nutrient inputs as solid-phase and uses
an exponential accumulation and washoff function to calculate these loadings. The input data of the GWLF
model includes daily precipitation, temperature data, runoff sources, transport, and chemical parameters
(Wu et al., 2015). The output data of GWLF has monthly time-scale streamflow, erosion and sediment yield,
total nitrogen and phosphorus loads in streamflow, yearly time-scale erosion, nitrogen and phosphorus loads
from each land-use type and presents simulation results in tables as well as in graphs (Schneiderman et al.,
2002, Haith et al., 1992).
GWLF is easy to use and requires less complicated data compared to the required data used by SWAT and
HSPF (Gene, 2004). GWLF was designed for optional calibration. If users decide to calibrate in the GWLF
model, the calibration process has a significant effect on GWLF application (Qi et al., 2017). Furthermore, the
model can simulate most of the critical mechanisms controlling nutrient fluxes within a watershed, therefore
considering more physical processes. GWLF shows its simplicity of operation compared with that of a com-
plex physical model (Du et al., 2016). However, GWLF cannot reflect spatial variability of runoff, sediment
and pollutant loads. This is due to the algorithm's lack of the channel route, and its applicable spatial scale is
limited, thus making GWLF inappropriate for a large size watershed.
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HSPF
HSPF {Hydrological Simulation Program-Fortran) was jointly developed by the U.S. EPA and the U.S. Geo-
logical Survey (USGS). The HSPF was initially released in 1974. HSPF 12.2 is the latest version and can be
downloaded at no charge from https://www.epa.gov/ceam/basins-download-and-installation. This version
of HSPF has been entirely integrated into BASINS as a core module. The user can also download a standalone
version of HSPF via the USGS website https://water.usgs.gov/software/HSPF/. Some ancillary utilities for sup-
porting the running of the HSPF are available from http://www.aquaterra.com/resources/hspfsupport/index.
php.
HSPF is designed to easily apply to most watersheds by using existing meteorological and hydrologic data,
soil, topography, land use, drainage, physical or humanmade system characteristics. HSPF can also simulate
conventional or toxic organic pollutant for a watershed and predict flow and water quality routing in the one-
dimensional river and well-mixed lakes and impoundments (Bicknell et al., 1993). HSPF has been used to as-
sess point or nonpoint source pollution from various land use types as well as nutrient fate and transport in
streams and lakes (Duda et al., 2012). The time scale of HSPF is from a few minutes to several hundred years
by using a time step ranging from sub-hourly to daily. The spatial scale of HSPF ranges from a small area (a
few acres) to a large watershed (the Chesapeake Bay with roughly 160,000 km2).
HSPF considers various physical processes, such as surface runoff, interflow, base flow, sediment yield, soil
moisture and temperature, evapotranspiration, snowmelt, snowpack depth and water content, ground-wa-
ter recharge, pesticides, conservatives, sediment detachment, nutrient fate and transport (Duda et al., 2012).
The HSPF model consists of three main components: PERLND, IMPLND, RCHRES, and six utility modules:
COPY, PLTGEN, DISPLY, DURANL, GENER, MUTSIN. PERLND and IMPLND modules simulate the runoff and
water quality from pervious areas and connect impervious land areas of a watershed. The RCHRES module is
used to route runoff and water quality constituents simulated by PERLND and IMPLND modules. HSPF needs
continuous records like precipitation, DEM, soil, land cover, and potential evapotranspiration for streamflow
simulation. Related parameters include land area, river channels, water quantities, sediment types and res-
ervoirs. The output results of HSPF are a time series of water quantity and quality transported over the land
surface and go through various soil zones down to the groundwater aquifers (Bicknell et al., 2005).
HSPF can predict yearly and monthly streamflow, sediment and nutrient yields except for the month with
severe weather conditions. Daily streamflow simulation is generally acceptable except during extreme flow
events. HSPF is suitable for an urban or an agricultural watershed. HSPF is useful to study the impact of ur-
banization and different point and nonpoint source pollution management scenarios (Skahill, 2004). Howev-
er, the data required for HSPF is intensive. And, the processes of calibration and validation of the HSPF model
are time-intensive due to the parameterization of many input parameters, especially for sediment calibra-
tion. HSPF is inadequate for simulating an intense single-event storm for large sub-basins and long channels.
Additionally, HSPF cannot represent single-event flood waves (Borah and Bera, 2003, 2004; Munson, 1998).
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LSPC
LSPC (Loading Simulation Program) was developed by Tetra Tech Inc. with funding from the U.S. EPA. LSPC
5.0 is the latest version and was released in 2015. The core algorithms of LSPC model originated from HSPF.
The model executable, database and source code are distributed and maintained by EPA. Users can down-
load LSPC 5.0 without cost and its user manual from the link: https://github.com/USEPA/LSPC-Loading-Simu-
lation-Program.
LSPC is a watershed model that included a streamlined Hydrologic Simulation Program Fortran (HSPF) algo-
rithm. LSPC and HSPF have the same core algorithms. The model can simulate hydrology, snowmelt, water
temperature, sediment erosion and transport, general water quality processes and biochemical transfor-
mation from both upland contributing areas and receiving streams or rivers. LSPC can calculate TMDL and
allocate source areas as well. LSPC is potential for an application of large-scale modeling, such as provincial/
state scale, and time scale range from an hour, daily, or to year intervals (Tetra Tech, 2017).
LSPC differs from HSPF in several key ways, including model structure, input file structure and organization,
model segmentation and meteorological linkage, data input/output, routines/capabilities in LSPC that are
not present in HSPF, and vice versa. LSPC uses a Microsoft Access database to manage data. Model compo-
nents of LSPC include hydrology, sediment and water quality. The hydrology component considers hydrology,
snow and water temperature. The water quality component has GQUAL (general quality), DO-BOD (Dissolved
Oxygen-Biological Oxygen Demand), nutrients, plankton, and so on. The model inputs include DEM, soil, land
use, meteorological data such as rainfall, air temperature, humidity. The model outputs include a time series
of pollutant loadings, hydrographs, and impacts of Best Management Practices (BMPs). Outputs from LSPC
can be linked to other water quality models such as EFDC, WASP, and CE-QUAL-W2 (Tetra Tech, 2017).
LSPC was designed to facilitate data management, organization, and modeling for a large and complex sys-
tem. LSPC overcomes many of the difficulties experienced with large-scale watershed simulation due to its
C++ programming architecture. The GIS design of LSPC can be compatible with ArcView shapefile file, so it
can use with ArcView together. However, LSPC cannot supply complex groundwater routing, nor simulate
complex surface-ground water interactions.
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L-THIA
L-THIA (Long-Term Hydrologic Impact Assessment), developed by Purdue University, was initially implement-
ed as a spreadsheet application and integrated into ArcView 3.0, and later upgraded to ArcGIS 9.x. A GIS-
based L-THIA version was developed in the ArcGIS 10.1 platform to estimate long-term direct runoff and NPS
pollution loads. Users can download ArcGIS-based L-THIA and its theory documentation from ittp://npslab.
kongju.ac.kr/#service. Light online L-THIA version is accessible from the link https://engineering.purdue.
edu/~lthia/.
L-THIA can be used to estimate the change in the runoff, recharge, and NPS pollution from past or proposed
development and evaluate long-term average annual runoff for a complex watershed, based on long-term
climate monitoring data (Zhang et al., 2011). The L-THIA model is integrated with GIS to estimate direct run-
off and generate an NPS pollution map from some primary input data, such as daily rainfall, land uses, and
hydrologic soil group. L-THIA can be applied to a large watershed, state or province scale.
Based on long-term weather data in the United States, L-THIA was designed to evaluate average annual run-
off volume, depth and NPS pollution loading flowing into water bodies from urban and non-urban areas. The
model can display the output in tables and graphs. L-THIA includes two components: hydrology and water
quality. In the hydrology component, L-THIA uses the curve number (CN) method to estimate runoff. In the
water quality component, it uses EMC method to evaluate the pollutants load from the estimated surface
runoff (Lim et al., 2006).
L-THIA is a quick screen tool for evaluating NPS pollution loads for a large spatial scale. L-THIA is easy to op-
erate since it does not require detailed data support and profound GIS knowledge. It can also provide "what-
if" alternative estimation scenarios (Purdue University, 2015). However, the output results of L-THIA, average
annual runoff volume and pollutant loading, are usually challenging to obtain at study areas. Therefore, the
validation of simulation results from L-THIA is still a challenging task. L-THIA does not take detailed physical
processes (e.g. neglected snow, permafrost, variation in moisture conditions in calculations) into account.
L-THIA should not be applied to stormwater drainage system planning.
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N-SPECT
N-SPECT {Nonpoint Source Pollution and Erosion Comparison Tool) was developed by the National Oceanic
and Atmospheric Administration (NOAA) Coastal Services Center. N-SPECT was initially designed as an ArcGIS
8.x extension tool, then OpenNSPECT was created in 2011. OpenNSPECT, an open-source version of N-SPECT,
is a plug-in extension for the open-source MapWindow GIS software package. Users can freely download
OpenNSPECT or the old version NSPECT for ArcGIS 9.x. from https://coast.noaa.gov/digitalcoast/tools/
opennspect.html.
N-SPECT allows users to quickly examine relationships between land cover, nonpoint source pollution and
soil erosion, and evaluate nearshore ecological health. N-SPECT is a useful tool to assess the long-term
impact of management decisions on water quality. N-SPECT was designed to be broadly applicable, but the
model operates most accurately in medium-to-large watersheds having moderate topographic relief (NOAA,
2008).
N-SPECT can estimate runoff volume, sediment loads, pollutant loads and concentrations, identify soil ero-
sion by high-risk water areas, and estimate the impacts of land-use changes with scenario analysis (NOAA,
2008). The model uses SCS curve number (CN) method to determine runoff, applies pollutant loading coeffi-
cients method to estimate pollutant flux, and applies RUSLE and MULSE to calculate erosion rates and sedi-
ment yield. The stream network within each watershed or sub-watershed will be assigned a specific water
quality rating by comparing estimated total pollutant and sediment concentrations to local water quality
standards. Primary inputs of N-SPECT include DEM, land use, rainfall and soil data, R-factor data, local pollut-
ant coefficient, and water quality standards. Output data include runoff volume, runoff depth, runoff curve
number, accumulated pollutant, pollutant concentration, comparison to pollutant standard, sediment loss,
and accumulate sediment yield (NOAA, 2008; Carter and Eslinger, 2008).
N-SPECT/OpenNSPECT is a screening tool for water quality and NPS pollution assessment, and is a flexible,
quick and easy-to-use tool for watershed managers. The models solved an issue of watershed delineation
on relevant plain coastal areas where there is no significant relief (Middleton and Libes, 2007). However, N-
SPECT/OpenNSPECT is an empirical-based tool that does not consider the physical processes of runoff, ero-
sion, and nutrient fate and transport. N-SPECT model cannot dynamically express runoff and pollutant time
series. Moreover, pollutant estimation of N-SPECT does not explicitly consider the duration or intensity of
rainfall and pollutant contribution from upstream cells, nor does it account for the fate of pollutants in their
complex interactions with sediments and water bodies.
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SLAMM
SLAMM (Source Loading and Management Model) was developed by Dr. Robert Pitt and John Voorhees in
the mid-1970s (Pitt, 1998). The U.S. Geological Survey (USGS) and the Wisconsin Department of Natural
Resources conducted cooperative research to develop WinSLAMM for stormwater runoff and NPS pollution
simulation in urban areas. The latest version of SLAMM is a Windows-based WinSLAMM. Users can down-
load WinSLAMM from https://www.usgs.gov/centers/wisconsin-water-science-center/science/slammPqt-
science_center_objects=0#qt-science_center_objects,
SLAMM is a stormwater runoff model for urban water quality management and planning. SLAMM was
developed to identify critical source areas of stormwater contamination, efficiently evaluate stormwater
management practices, and predict various pollutants concentration and loadings. SLAMM is a continuous
sequential event-based model that predicts flow and pollutant discharges in an urban drainage area (Pitt and
Voorhees, 2002).
SLAMM simulates runoff volume and pollutant loads for ten standards and six user-defined pollutants. The
model can be applied for alternative land use scenarios as well (Pitt and Voorhees, 2000). Urban land use of
SLAMM includes residential, institutional, commercial, industrial, open space, and freeways. Each land use
corresponds to 14 source areas (Panuska, 2000). The model uses the water volume and suspended solids
concentrations at the outfall to estimate pollutant concentrations and loads. SLAMM calculates dissolved
pollutant concentrations and loadings based on the percentage of the water volume of each source. SLAMM
focuses on small storm hydrology and particulate washoff. SLAMM is firmly based on actual field observa-
tions rather than theoretical processes.
SLAMM considers many stormwater controls such as affecting source areas, drainage systems, and outfalls
for long-term rainfall event series. Users commonly use SLAMM as a planning-level tool to understand sourc-
es of urban runoff pollutants and their control and obtain relatively simple answers. However, WinSLAMM
does not account for snowmelt conditions during the processes of urban runoff calculation. The model can
evaluate surface runoff characteristics at source areas but does not consider instream processes that can
remove or transform pollutants.
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SWAT
SWAT {Soil and Water Assessment Tool) was developed by USDA-ARS at the Grassland, Soil and Water Re-
search Laboratory in Temple, Texas, and Texas A & M University. The current SWAT version is SWAT2012 rev.
670 released in October 2018. A SWAT executable file and its auxiliary software can be downloaded with no
charge from ittps://swat.tamu.edu/software/. Currently, several graphical user interfaces can be chosen for
SWAT such as ArcSWAT, AVSWAT, QSWAT, MWSWAT, VIZSWAT. A SWAT literature online database for peer-
reviewed journal articles can be accessed from https://www.card.iastate.edu/swat_articles/.
SWAT is a continuous, physically-based, river basin-scale hydrological model used to predict the effectiveness
of land use management practice and climate change on water, sediment, crop growth, nutrient cycling and
pesticide yield with reliable accuracy on an ungagged watershed with varying soils, land use, and manage-
ment conditions (Arnold, J. G. 2012). The time scale of SWAT running ranges from sub-daily to yearly and the
spatial scale of the application can be from a small watershed to an entire European continent (Abbaspour,
2015, Gassman, P.W. et al., 2007).
SWAT has been widely applied in hydrology modeling, non-point source pollution control, water quality
evaluation, groundwater simulation, soil erosion assessment, the impact of land use management practices
on water quality, assist TMDL development, and predict hydropeaking (Chiogna et al., 2018, Mittelstet et al.,
2016, Stehr et al., 2010). A watershed is discretized into many sub-basins, and these sub-basins are further
divided into more hydrological response units (HRUs) where all land areas have unique combination with
land use, soil property, and slope. In each HRU, land areas have specific land use, soil property, and slope
combinations and hydrological components are calculated for surface water and groundwater. SWAT uses
the SCS-CN method to calculate surface runoff, Penman-Monteith, Priestley-Taylor or Hargreaves method
to estimate evapotranspiration, MUSLE or USLE to assess sediment yield within a drainage system. SWAT
requires input data such as topography, soil, weather, and land use. The output files of SWAT include the
standard output file (.std), the HRU output file (.sbs), the subbasin output file(.bsb) and the main channel or
reach output file(.rch) (Neitsch et al., 2011).
SWAT can get a reliable result when predicting yearly flow volumes and sediment and nutrient loads, and
monthly streamflow predictions are generally reliable. SWAT is applicable in several aspects such as the im-
pacts of climate changes on long-term water yield, and the impacts of management scenarios on long-term
sediment and nutrient load. However, the calibration and validation of the SWAT model are time-consuming
processes. The alternative solution is to download a standalone software SWAT-CUP and implement an
auto-calibration of SWAT (Abbaspour, et al., 2015). SWAT-CUP can be download at https://swat.tamu.edu/
software/swat-cup/. Also, it is hard to get a high accuracy while using SWAT to predict under an extreme
hydrologic condition such as flood or use it to predict daily sediment and nutrient loadings. SWAT assumes
vegetation growth is insensitive to season change, which often causes the accuracy of SWAT prediction in the
dry season to be low. One solution is to divide the wet and dry season, which can efficiently improve SWAT
simulation accuracy.
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SWMM
SWMM (Storm Water Management Model) was developed by EPA in 1971 and has been upgraded several
times. The current version SWMM is 5.1 and released in September 2015. SWMM users can download
model software and user's manual without charge from https://www.epa.gov/water-research/storm-water-
management-model-swmm.
SWMM is a physically-based urban stormwater runoff model. Users can use SWMM to design drainage
system components, generate non-point source pollutant loads for TMDL, evaluate BMPs, design LID (Low
Impact Development) stormwater controls to meet sustainability goals, and control flooding of the natural
watershed or urban areas (Rossman, 2015). It can simulate a single rainfall event or long-term continuous
change of runoff quality and quantity on hourly or sub-hourly rainfall time step. The spatial scale of SWMM
ranges from separate lots up to hundreds of acres.
SWMM runs on a collection of sub-catchments regions that receive precipitation and generate runoff and
pollutant loads. These sub-catchments are basic hydrological units that are divided into pervious and imper-
vious areas. The model considers physical processes such as surface runoff, infiltration, groundwater, flow
routing, water quality routing, snowmelt, and surface ponding. In the hydrologic component, SWMM uses
Horton Curve, Green-Ampt method or SCS Curve method to calculate infiltration, uses nonlinear reservoir
model to assess overland flow, applies localized tow-zone flux model to estimate groundwater, and heat
balance model to simulate snowmelt. In the hydraulic component, SWMM use nodes and links concepts
to describe drainage elements, 20 common conduit shapes, irregular open channels and closed conduits.
SWMM applies steady flow, kinematic wave and dynamic wave to model flow routing. In the water quality
component, SWMM uses power, exponential or saturation function of time to calculate pollutant buildup,
applies EMC, rating curve method or exponential method to calculate pollutant washoff. SWMM requires
inputs of buildup and washes off parameters to model stormwater quality and produce pollutographs at any
point in the watershed. Pollutants simulated have total nitrogen, total phosphorus, suspended solids, settle-
able solids, oil/grease, BOD, total coliform and other user-specified pollutants (Kikoyo D. and Singh V., 2007;
Obropta and Kardos, 2007).
The SWMM model has been widely applied in analysis and design in the stormwater drainage system, hy-
draulic modeling, hydrologic processes simulation, and pollutant load estimation, especially in urban areas
(Jang et al., 2007, Tikkanen, 2013, Tuomela et al., 2019, Zhang et al., 2018). However, SWMM is not a design
tool and cannot model manholes or inlet loss directly.
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WAM
WAM {Watershed Assessment Model) was developed and maintained by Soil and Water Engineering Tech-
nology, Inc in Florida. WAM worked as an add-in extension in the ArcGIS desktop environment. The latest
WAM version support by ArcGIS 10.4.1 version. Users can download software and its theoretical document
free of charge from the link: ittp://www.swet.com/wam-for-arcmap-100/.
WAM is a physically-based watershed model. It can be used to evaluate the impacts of land-use changes
on surface water and groundwater quality, estimate pollution loads, track pollutants in streams, and assist
BMPs development in an agricultural or urban watershed with a combination of various land use, soils, and
land-use practices (SWET, 2015). WAM continuously simulates the hydrologic and chemical processes at the
individual field level to determine runoff and nutrients that are routed across a stream network to an outlet
of watershed.
WAM discretizes the watershed into many grid cells. In each cell, WAM calculates surface and subsurface
flow volume, and nutrient concentrations load. Then, the model routes surface water and groundwater
flow from cells to assess flow and phosphorus levels across the watershed. Water quality variables of WAM
include particulate and soluble phosphorus, particulate and soluble nitrogen, TSS (total suspended solids),
and BOD. WAM integrates GLEAMS (Groundwater Loading Effects of Agricultural Management Systems),
EAAMOD (Everglades Agricultural Area Model) (SWET, 2018) and Special Case model to estimate soil and
plant processes affecting water quality on agricultural lands (Bottcher et al., 2012). In GLEAMS, surface
runoff generated from daily rainfall is simulated by a modified SCS-CN method; the model uses USLE method
to compute sediment yield; the model applies the plant-nutrient component to simulate nitrogen and phos-
phorus cycles. EAAMOD is suitable to simulate N and P movement in soil areas with a high-water table. In
EAAMOD, surface runoff is calculated by a vertical two-dimensional hydrologic model. The phosphorus and
nitrogen sub-models (PMOVE and NUTMOD) is used to simulate P and N loss. Primary input data of the
WAM model include land use, soils, topography, climate data, and point sources data. The outputs of WAM
include surface runoff, groundwater source loads, a ranking of land use by load source, the time history of
daily flows and pollutants, and displays of different BMP/Management scenarios (SWET, 2018).
WAM can simulate complicated surface and subsurface hydrologic and nutrient loading processes in the Ar-
cGIS environment. It can describe spatial and hydraulic details and is flexible to accommodate varied hydro-
logic, water quality, land and water management processes, and conduct scenario analysis. However, WAM
has few applications out of Florida and cannot simulate small-scale, and short-term storm events.
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WARMF
WARMF {Watershed Analysis Risk Management Framework) was developed by the Electric Power Research
Institute in California, the Duke Power Company, the US Bureau of Reclamation, and other state agencies.
WARMF works as a decision support tool for watershed management intended to facilitate TMDL analysis
and water quality plans (Herr and Chen, 2012). WARMF is not a public domain software and is maintained
by Systech Water Resources, Inc. Users can obtain its trial from http://systechwater.com/warmf_software/
software-access/ or http://warmf.com/home/.
WARMF can be used for short and long-term watershed management. WARMF assist stakeholders in devel-
oping management plans for water quality protection in any river-scale basin (Chen et al., 2001). The final
product of WARMF is a TMDL implementation plan or watershed management plan that introduced point
and non-point source pollution control.
WARMF has five modules: the engineering module, the consensus module, data module, knowledge mod-
ule, and TMDL module. The engineering module is a primary model for simulating hydrology and water
quality. The consensus module is used to evaluate management practice alternatives. The data module puts
the input data into graphs and spreadsheets for viewing and editing. The knowledge module is mainly used
for the collection of the watershed information. The TMDL module provides a step-by-step guide to calcu-
late TMDLs within the watershed (Chen, et al., 2001). In WARMF, the simulated hydrologic variables include
flow, depth, reservoir surface elevation, evapotranspiration, and snow water depth. The water quality vari-
ables consist of temperature, pH, major cations and anions, total dissolved solids, ammonia (NH4), nitrate
(N03), phosphate (P04), organic and sediment adsorbed nutrients, BOD, DO, TSS, DOC, coliform bacteria,
three types of algae, and other metals. WARMF requires DEM, land use, soil characteristics, fertilizer, point-
source discharge, observed streamflow, water quality, and atmospheric chemistry as input data, and needs
observed streamflow, water quality data and nonpoint source data for model calibration and validation (Herr
and Chen, 2012).
WARMF has been designed to handle water quality and NPS pollution problems involving acid mine drain-
age, mercury pollution, and on-site wastewater systems. WARMF integrates models, databases, application
modules and graphical software into a built-in GIS. However, WARMF neglects a tile drainage system and
does not model deep groundwater aquifers or groundwater quality. The model tends to be simplistic, de-
spite the groundwater flow component (Dayyani et al., 2010). In the TMDL module, the algorithm reduces all
upstream sources by the same percentage if the point source load reductions are taken into account. Then,
the stakeholders can determine the allocation of the individual point source reductions (McCray, 2006).
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WMS
WMS (Watershed Modeling System) was developed by the AQUAVEO company. WMS was initially developed
at the Engineering Computer Graphics Laboratory at Brigham Young University in the early 1990s. The soft-
ware was sold by Brigham Young University commercially in 2007. The current version is WMS 11.0. WMS
website can be accessed from http://www.aquaveo.com/software/wms-watershed-modeling-system-intro-
duction. Users can download the latest WMS 11.0 free trial version or purchase a software license.
WMS is a comprehensive hydrology and hydraulics modeling system with a built-in GIS for various spatio-
temporal scale watersheds. The eight modules of WMS include the terrain data module, drainage module,
map module, a hydrologic module, a hydraulic module, GIS module, 2D grid module, and a 2D scatter point
module. Each module corresponds to one of the primary data types or modeling environments supported by
WMS. WMS integrates GIS tools, web-based data acquisition tools, terrain data import and editing tools, au-
tomated/manual watershed delineation, and hydrologic modeling. WMS supports many industries standard
hydrologic modeling, hydraulic modeling flood plain mapping, and storm drain modeling. Hydrologic models
supported by WMS version 11.0 include HEC-1, HEC-HMS, NSS, TR-20, TR-55, Rational Method, OC (Orange
County) Rational, OC hydrographic, HSPF, SWMM, XP-SWMM, SMPDBK, GSSHA, CE-QUAL-W2, HY-8, HY-12,
Hydraulic Toolbox, EPANET ( Daniel, Edsel B. etal., 2011).
The WMS model is compatible with various data formats. The model supports a very flexible watershed
delineation method. Users can use any streaming network, regardless of whether it is automatically gener-
ated or manually digitized with a land surface to delineate drainage areas (AQUAVEO, 2019). However, WMS
is not a public domain software, and users need to purchase a license in WMS for use. Currently, the number
of practical applications relevant to WMS is insufficient.
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3.2 Mixing Models
Continuous or instantaneous discharge of effluent from point sources to surface water is subjected to physical mix-
ing (Fischer et al., 2013). The mixing process dilutes effluent near the discharge location (known as mixing zone)
and minimizes the immediate environmental impact. The water quality standard can be exceeded in the mixing
zone; however, the effluent is expected to meet the legal limit within a specific reach. A mixing zone analysis is
carried out to characterize the extent of mixing in the regulatory zone. A mixing study generates information on
the availability of dilution water, the discharge characteristics, and any potential adverse impacts on the receiving
water.
Mixing is commonly estimated as the amount of ambient water entrained into the discharge by the combined
effect of momentum flux, buoyancy flux, and molecular diffusion. Effluent mixes with ambient water at different
velocities and concentration profiles. It can be discharged as a jet, with a higher velocity relative to the ambient wa-
ter, or as a plume, with a relatively lower velocity. The momentum exchanged between discharge and an ambient
condition greatly shapes mixing behavior. In a stratified water environment, the relative density difference between
effluent and ambient water induces a buoyant flux where the lighter mass is mixed upward. The relative pollutant
concentration difference between the discharge and the ambient water also drives mixing through molecular diffu-
sion. These processes are mathematically represented in mixing models.
In fluid mechanics, the property of the fluid in motion (such as velocity, density, and mass) is by Lagrangian and Eu-
lerian approaches. In the Lagrangian approach, fluid movement and associated changes in its property are studied
by tracking the motion, whereas in the Eulerian approach the fluid properties are monitored in a fixed location.
The mathematical derivative for these two approaches, presented in Equation 15 (Ferziger and Peric, 2012), serves
as the basis for mixing models.
^ = 1 + (u. V)<7 (Eq 15)
dt t y
Where q is the flow field property (flow rate, temperature, density, or mass), u is the rate of change, and u. V
is the operator applied to each flow property change. For a three-dimensional space, the operator is repre-
sented by Equation 16. F) F) F)
v= if+ jf+ if (Ecl16)
ox ay ay
Mixing models widely used for regulatory mixing zone studies such as, CORMIX and Visual Plume, are Eulerian
models where the flow field properties (physical mixing) are analyzed for a fixed location. The water constitu-
ent concentration is the key flow property in mixing analysis and commonly estimated using the advective
diffusion governing equation, as shown in Equation 17 (Socolofsky et al., 2005).
dS+uiŁ = ±(D ŁŁU ±(D ŁŁU L(d dS\ (Eqi7)
dt dx dx \ x dx) + dy l >' dyl + 3z V z dz)
Where C is mass concentration, U is velocity field, and D is a diffusion coefficient in a three-dimensional
space. Mixing is primarily driven by turbulence (velocity field) or molecular diffusion, depending on the type
of flow.
A widely used analytical solution to advective diffusion equation is shown in Equation 18 (Wu et al., 2011).
(uy\
c^= ijikT/xptDyX (Eql8)
Where C is concentration (the effluent minus the background concentration), x and y are the ordinates along
the flow and the transverse direction, respectively, q is discharged per unit time, h is the average water depth,
and Dv is the lateral diffusion coefficient.
24
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Mixing is simulated based on the ambient condition and discharge information (Horner-Devine et al., 2015). The
ambient condition includes channel geometry, flow rate, temperature, mass, and density of the receiving water
near the discharge point. The discharge characteristics include the type of outfall (surface or submerged), angle of
jet or orientation of flow for surface discharge, discharge port geometry, temperature, mass, and density. An outfall
is designed as a surface or submerged port (single or multiport). Mixing processes differ greatly near the discharge
location (called near-field) and a distance away from the outfall (far-field regions). Mixing in the near-field is pre-
dominately controlled by discharge characteristics. In a far-field region, the effect of discharge characteristics on
mixing becomes insignificant and the ambient condition will be the more influential factor.
Mixing models have been developed for outfall dilution modeling in surface water since 1970 (Frick et al., 2010).
These models adopted a different approach to represent the physical mixing processes. In this section, we present
widely used mixing models.
CCHE-CHEM
CCHE is an interface of numerical models developed at the National Center for Computational Hydroscience
and Engineering (NCCHE) in collaboration with USDA-ARS (Chao et al., 2006). The original model was devel-
oped in the 1990s to analyze flow and sediment. The model has been updated to accommodate technology
compatibility and to integrate additional functions. The latest version supports simulation of flow and water
quality in a two- or three-dimensional space. It consisted of FLOW, FLOOD, SED, CHEM, WQ, and COAST
models. The CHEM model was developed in 2013 to primarily simulate a chemical's fate in a water column
and sediment bed layer during a spill incident. The program is currently maintained by the NCCHE. Access
to the software and technical support requires a license. The software and contact information are available
from the NCCHE page at https://www.ncche.olemiss.edu/cche2d3d-chem/. The software is supported by
Windows Vista 7/8/10 operating systems.
CCHE-CHEM was developed to analyze a chemical dissolved in a water column and absorbed in suspended
and bed sediments. It can be applied to simulate the spatial and temporal variations of a chemical under
steady and unsteady conditions. The exchange of a chemical between dissolved and particulate forms
through sorption and desorption is assumed to reach an equilibrium state in CHEM model. The predicted
concentration of a chemical represents the equilibrium state.
CCHE is a finite element-based numerical model where the space domain is divided into finite meshes (grids)
for computation. CCHE is built with a Mesh Generator tool. Geometrical data, such as bathymetry, will be
interpreted from finite meshes. The trajectory and fate of a chemical spill are estimated based on data on
the flow field, sediment, and chemical characteristics. The critical data inputs are water depth, eddy viscos-
ity, velocity, bed change rates, suspended and bed sediment concentrations, the decay rate of a chemical of
interest, the molecular weight of a chemical, and ambient chemical concentration.
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CORMIX
The Cornell Mixing Zone Expert System (CORMIX) was developed under a cooperative agreement between
the U.S. EPA and the Cornell University for mixing zone analysis (Jirka et al., 1996). CORMIX is a Eulerian
model developed with semi-empirical equations. The first version, CORMIX 1.0, was developed during the
1985-1995 period. The second version, CORMIX 2.1, integrated with CORMIX 1, CORMIX 2, and CORMIX 3,
was designed to analyze discharge from submerged single port, submerged multiple port, and buoyant sur-
face discharges, respectively. In the third version, CORMIX 3.0, a far-field locator, plume graphics, and other
capabilities were added. Other versions, 4.0-10.0, were evolved with significant enhancements of the far-
field mixing simulator. The most recent version, CORMIX 11.0, was released in June 2018. CORMIX is current-
ly maintained by MixZon, Inc. and license are required for software access and technical support. Contact
information and documentation are available from MixZon page at http://www.mixzon.com/. The software
requires Windows Vista/7/8/10 operating systems.
CORMIX can be applied to simulate plume behavior in a mixing zone. It is designed to predict a steady-state
plume trajectory, shape, and dilution. CORMIX is applicable for discharges from submerged or surface out-
falls with support analysis in a near- and far-field region and can be applied in a two- or three-dimensional
space. CORMIX is designed to analyze discharge from municipal wastewater, power plant cooling waters,
desalinization facilities, or drilling rig brines. Applying the CORMIX model requires information on discharge
characteristics and ambient condition. The key discharge characteristics are flow rate, density, target pollut-
ant type (conservative or non-conservative), concentration, coefficient of decay for non-conservative pollut-
ants, and temperature. The primary data required from ambient water conditions are background concentra-
tion, cross-section, bathymetry, current, and flow rate.
VISJET
VISJET is a Lagrangian jet model developed at the Area of Excellence Water Environmental Engineering, the
University of Hong Kong, to predict the environmental impact of effluent discharge (Lee et al., 2000). VISJET
is a modified version of the UOUTPLM model (originally developed at the U.S. EPA in 1984). The modifica-
tion upgraded the plume trajectory predictive capacity from two- to three-dimensional and advanced its
prediction capability to a variable crossflow. The first version, VISJET 1.5, was released in April 2001. VISJET
was updated in 2009 and released as version 2.5. Software access and technical support require a license.
Contact information and documentation are available from the University of Hong Kong page at http://www.
aoe-water.hku.hk/visjet/visjet.htm. The program is supported in Windows operating systems.
VISJET can be applied in environmental impact assessments and outfall design for discharge from cities,
thermal from power stations, hydrothermal vents from the ocean floor, and chimney smoke (Cheung et al.,
2000). VISJET is a near-field model designed to predict the path and mixing of an arbitrary inclined (single or
group) buoyant discharge in a three-dimensional space. VISJET enables the user to visualize a jet or plume
evolution over time. It predicts the size of the mixing zone and the composite dilution at any location of
interest. The key inputs required to run VISJET model include effluent characteristics, outfall geometries, and
ambient conditions.
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Visual Plumes
A Visual Plume (VP) is an interface for a suite of six integrated models (DKHW, NRFIELD, FRFIELD, UM3,
PDSW, and DOS PLUMES) developed at the U.S. EPA to simulate plume mixing in the receiving water (Frick
et al., 2004). The current version is 1.0. The model was updated in 2005 and added functions for plume con-
touring, Coliform bacteria mortality predictor, far-field progressive vector diagram, and arbitrary source loca-
tor (Frick et al., 2004). VP software and documentation are available free of charge from the U.S. EPA Center
for Exposure Assessment Modeling (CEAM) page at https://www.epa.gov/ceam/visual-plumes. The current
version is supported by Windows 98, NT, 2000 (XP but not beyond XP) and Linux operating systems.
VP is designed to simulate various plume mixing behaviors, such as plume radius, dilution, and rise. The six
integrated models allow VP to operate under different mixing conditions (see the characteristics of the six
models in Table 2). DKHW (Eulerian integral model), UM3, FRFIELD, and DOS PLUMES are designed for single
or multiport submerged outfalls, whereas PDSW (Eulerian integral flux model) is designed for surface dis-
charge through tributary channels. The outfall geometry in the PDSW simulator is approximated to a rectan-
gular conduit. NRFIELD is applicable for submerged outfalls when at least four ports are specified. FRFIELD
estimates the long-term distribution of plumes near an outfall but it is not currently functional. DOS PLUMES
is the predecessor for Windows-based, which is included in the current VP package to allow an analysis of
project files developed with the DOS version and for additional unique capabilities. These models can be run
simultaneously to generate comparable results to verify their performance. VP applicability is limited to a
steady-state condition.
VP can be applied to visualize the isopleths of a contaminant concentration, estimate the movement of a
plume in the far-field, and locate plume sources. The key input data are geometrical data, discharge charac-
teristics, and ambient conditions. The outfall is characterized by a number of ports, port size, port spacing,
vertical discharge angle, compass orientation, flow rate, and effluent concentration (target contaminant,
salinity, or temperature). The ambient condition data includes receiving water geometry, flow rate, current,
salinity, temperature, and target concentration as a function of depth.
Table 2. Summary of Visual Plumes Model Packages
Model
Acronym Description
Applicability
Spatial Resolution
DKHW
Davis, Kannberg, Hirst
Model for Windows
Submerged (single and
multiport) outfall
3D
NRFIELD
Near-field
Multiport (4 or more ports)
3D
FRFIELD
Far-field
Submerged or surface
discharge
2D
UM3
Three-Dimensional Updated
Merge
Submerged (single and
multiport) outfall
3D
PDSW
Prych, Davis, Shirazi Model
for Windows
Surface discharge
3D
DOS PLUMES
DOS operating system-
based Plumes
Submerged (single and
multiport)
2D
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3.3 Surface Water Quality Models
A pollutant in the surface water is subjected to physical, chemical, and biological transformations. Moving water
spreads a pollutant and changes the spatial distribution, described as a hydrodynamic process. The hydrodynamic
process describes the motion of water along with its ability to transport and assimilate substances. The main at-
tributes of water in hydrodynamics include water density and its viscosity, which are key parameters for most water
quality models. Water density can be formulated as Equation 19 (Liu L.B., 2018):
p = pT + ApS + ApC (Eq 19)
Where p is water density, pT is pure water density as a function of temperature T, ApS is the change of water
density related to salinity S, ApC is the change of water density due to total suspended sediments C.
The viscosity of water refers to the internal friction of water and can be described in Equation 20 as a function of
water temperature T (Wu W.M., 2008):
vis = (1.785 - 0.0584r + 0.00116 T2 0.0000102 x 10"6 (Eq 20)
Water quality is affected and controlled by water hydrodynamic processes, including its physical, chemical, biologi-
cal, and other characteristics and mechanisms. The water quality dynamics in surface water models are solved by
applying the conservation of mass and momentum theories. The conservation of mass is essential to estimate the
spatial and temporal mass variation of a pollutant. According to the conservation of mass theory, a pollutant mass
entering, leaving, or transforming in a controlled volume of water should be conserved. The continuity equation of
pollutants in mass conservation form can be described as Equation 21 (Ji, Z.G., 2017):
+ P • ipv) = 0 (Eq 21)
Where p is water density, v is velocity vector, and V is gradient operator.
The conservation of momentum is useful to understand the force acting on the moving water. The transportation
of a pollutant is mainly determined based on the force acting on the mass flow, computed as momentum flux. The
conservation of momentum of pollutants in water obeys Newton's second law. Advection and diffusion are the two
mechanisms that govern pollutant transport in surface water. Advection refers to the pollutant transport along with
the flow. Diffusion refers to the spread of a pollutant mass from a higher to a lower concentration. These processes
modify the spatial and temporal concentration of a pollutant in the receiving water.
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To represent the advective and diffusive processes of pollutants in water mathematically, all the variables of water
quality such as algae, nutrients, and DO, can be described by using a set of coupled mass conservation equations.
Thus, all governing equation for water quality processes have a similar form as Equation 22 (Ji, Z.G., 2017):
dC + d(uC) ^ d(vC) + d(wC)
dt dx
By
dz
3_
dx
( v dC \
d
f
dc
a
f
K —
+—
Ki
+—
K
X
^ ox y
dy
y
V
fy J
dz
z
V
dz J
+ S,
(Eq 22)
Where C is a concentration of a water quality state variable, u, v, w are velocity components in x,y and z
directions, Kx, Kv, Kz are turbulent diffusive coefficient in x,v and z directions, respectively, and Sc is internal
and external sources and sinks per unit volume. Equation 22 integrates physical transport due to flow
advection and dispersion, external pollutant inputs, and the kinetic interactions between the water quality
variables. The first term reflects the net change of pollutant concentration; the second to fourth terms
account for the diffusion transport. The fifth to seventh terms are the advection transport; the last term
represents the kinetic process and external loads for each variable.
A pollutant in water can undergo a various type of chemical and biological reactions. For example, a nutrient is dis-
charged to surface water in various forms. Some forms of nutrients (ammonia and nitrate) are consumed by phyto-
plankton (Domingues et al., 2011) and/or transformed through the denitrification process. The hydrodynamic and
biochemical transformations control the fate of a pollutant in surface water. This information is useful to determine
a water body's assimilative capacity that is defined as the ability of a water body to clean itself, which sets a founda-
tion of TMDL development. Surface water quality models are simplified representations of these processes. Unlike
mixing models, surface water quality model's simulation capacity extends beyond the point of discharge to a larger
span and represents varied types of pollutant transformation.
Excluding advection and diffusion, when a pollutant changes in water due to chemical, biochemical, and biological
mechanisms, it can be represented mathematically by Equation 23 below (JI, Z.G., 2018):
dC_
dt
= -kCn
(Eq 23)
Where m is the order of reaction with m = 0,1 and 2 in natural water, k is rate constant of the m th-order
reaction. Equation 23 is only a basic form of change of a single reactant in water.
Surface water quality models have been developed since the 1920s. The first water quality model is the S-P model,
developed in the 1920s to predict oxygen balance and BOD decay in Ohio, U.S. (Phelps and Streeter, 1958). In the
1970s, U.S. EPA developed the QUAL river models. After the 1970s, the development of surface water quality mod-
els has shown significant progress over time. Many water quality models that exist today differ in many aspects. In
this section, models that are applicable for nutrient simulation in surface waters are presented.
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BATHTUB
BATHTUB was developed at the Environmental Laboratory of the USACE WES (Walker, 2006). The program
was translated from MS-DOS Fortran to a Windows-based program in 1996. BATHTUB has been updated
several times. The most recent version, 6.0, integrates empirical methods to account for advective transport,
diffusive transport, and nutrient sedimentation processes. BATHTUB consists of two programs, FLUX is used
to estimate tributary nutrient loading and PROFILE is used to analyze changes of in-lake concentrations. The
program is currently maintained by WES USACE. Software and documentation are available free of charge
from USACE WES page at https://el.erdc.dren.mil/elmodels/emiinfo.html. The software is supported in Win-
dows operating systems.
BATHTUB is a steady-state water quality model developed to simulate water and nutrient mass balance in a
spatially segmented hydraulic network of lakes and reservoirs. It predicts eutrophication conditions based
on empirical relationships of total phosphorus, total nitrogen, chlorophyll a, transparency, organic nitrogen,
non-ortho-phosphorus, and hypolimnetic oxygen depletion rate. It can be used to compute mass load, assess
overall lake conditions, and evaluate selected management alternatives. The key input data are watershed
characteristics, flow data, nutrient loads, lake or reservoir morphology, and observed water quality data.
CCHE-WQ
CCHE-WQ is in the same family of CCHE models (discussed in mixing model section). It was developed in
2006 to predict phytoplankton, nutrients, and dissolved oxygen concentrations (Chao et al., 2018). The pro-
gram is currently maintained by the NCCHE. Access to the software and technical support requires licensing.
Software information is available from NCCHE page at https://www.ncche.olemiss.edu/cche2d3d-wq/.
CCHE-WQ module was developed to simulate eight water-quality constituents, five of them are nutrients
(ammonia-nitrogen, nitrate-nitrogen, organic-nitrogen, inorganic-phosphorus, and organic-phosphorus). It
allows users to run a single or multiple water quality constituent(s) at one time. It then gives known values
or gives the option to be bypassed for each run.
CCHE-WQ is a finite element-based numerical model where the space domain is divided into finite meshes
(grids) for computation. A mesh is generated from topographic data using the CCHE Mesh Generator. Geo-
metrical data, such as bathymetry, is interpreted from finite meshes. Data on a water quality constituent,
flow field, and kinetic coefficients are required for the CCHE-WQ simulation.
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CE-QUAL-ICM
CE-QUAL-ICM was developed at the Environmental Laboratory of USACE in the 1990s (Cerco and Cole, 1995;
Cerco and Noel, 2013). The model was developed as a eutrophication component of the Chesapeake Bay
Environmental Modeling Package. The model has been enhanced to incorporate a component for many con-
ventional pollutants and living resources (zooplankton, SAV, benthos). CE-QUAL-ICM is operational at one-,
two-, or three-dimensional space. CE-QUAL-ICM is currently maintained by the Engineer Research and Devel-
opment Center (ERDC) at USACE. The software is available with no charge from the page ittps://www.erdc.
usace.army.mil/Media/Fact-Sheets/Fact-Sheet-Article-View/Article/547416/ce-qual-icm-icm/. The software
is supported by Windows operating systems.
CE-QUAL-ICM was primarily developed to simulate multiple biogeochemical cycles, such as the aquatic car-
bon, nitrogen, phosphorus, and oxygen cycles. It can be used to describe physical factors governing biogeo-
chemical cycles, including salinity, temperature and suspended solids.
CE-QUAL-ICM was not built with a flow simulator (hydrodynamic component). To run the CE-QUAL-ICM
model, the hydrodynamics parameters (flows, diffusion coefficients, and volumes) must be computed us-
ing hydrodynamic models in a compatible format. The key data inputs are geometrical data, meteorological
data, boundary conditions, water quality state variables load, atmospheric load, light, benthic flux, and algal
growth rate.
CE-QUAL-RIV1
CE-QUAL-RIVl is a one-dimensional model developed at Ohio State University, at the request of the U.S. EPA,
to analyze water quality associated with stormwater runoff (Dortch et al., 1990). CE-QUAL-RIVl was modified
at the U.S. Army Corps of Engineer Waterways Experiment Station (USCAE WES) in 1991, released as version
1.0 and in 1995, released as version 2.0. The current version integrates the hydrodynamic code (RIV1H), for
water transport simulation and the water quality code (RIV1Q), for water constituent's prediction. CE-QUAL-
RIVl is currently maintained by the USAE WES. The software is available free of charge from the USAE WES
page at https://el.erdc.dren.mil/elmodels/rivlinfo.html. The program is supported in Windows operating
systems.
CE-QUAL-RIVl is a one-dimensional model developed to simulate twelve water quality variables, which in-
clude seven nutrient species (organic nitrogen, ammonia, nitrate, nitrite, organic phosphorus, and dissolved
phosphates). It can be applied to predict the longitudinal water quality variation in unsteady flows. In the
CE-QUAL-RIVl model, vertical and lateral water quality variation in a riverine environment is assumed insig-
nificant when compared to the longitudinal.
The key inputs for CE-QUAL-RIVl simulator are an initial concentration of water constituents, flow, meteoro-
logical and concentration boundary conditions, kinetic data (such as rate constants), and later water flows.
The RIV1H module predicts flow, depth, velocity, and other hydraulic characteristics and results are then
used by the RIV1Q to predict the variation of water quality variables.
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CE-QUAL-W2
CE-QUAL-W2 was developed at the Hydraulic and Environmental laboratory of the USACE WES by modify-
ing the Laterally Averaged Reservoir Model (LARM model) (Cole and Wells, 2015). The first version, 1.0, was
released in 1986. CE-QUAL-W2 has been modified several times, released as version 2.0, 3.0-3.7, and 4.0-4.1
with improved computational capacity, added functions to simulate any state of water quality variables, and
extend its applicability to all types of surface waters. The current version, 4.1, incorporates the hydrodynam-
ic and water quality modules. The program is currently maintained by the Water Quality Research Group at
Portland State University and the software is available free of charge from the page at http://www.cee.pdx.
edu/w2y. The software is supported by Windows Vista 7/8/10 operating systems.
CE-QUAL-W2 was developed to predict water quality variation for stratified and non-stratified systems in a
two-dimensional capacity. The hydrodynamic module predicts water surface elevation, velocity, and tem-
perature. The water quality module uses results from the hydrodynamic module to simulate over 60 derived
water quality variables. The nutrient-related variables included in CE-QUAL-W2 are ammonia, nitrate, nitrite,
the nitrogen forms of organic matter, and bioavailable phosphorus and the phosphorus forms of organic
matter.
The CE-QUAL-W2 simulator requires various data for the hydrodynamic and water quality components. The
key inputs are geometry data, initial and boundary conditions for flow field and water quality constituents,
hydraulic parameters (such as dispersion coefficients for momentum and temperature), and kinematic pa-
rameters (coefficients for the water quality module to describe biochemical reactions).
EFDC
The Environmental Fluid Dynamics Code (EFDC) was developed at the Virginia Institute of Marine Science in
1988 (Hamrick, 1996; Tetra Tech, 2007). EFDC has been modified with the support from the U.S. EPA, Tetra
Tech, and the National Oceanic and Atmospheric Administration's Sea Grant Program. The current version
integrates hydrodynamic, sediment and contaminant, and water quality modules. The water quality mod-
ule was added in 1995. The program is currently maintained by the U.S. EPA CEAM. Software and technical
support are available free of charge from CEAM page at https://www.epa.gov/ceam/environmental-fluid-
dynamics-code-efdc. The software is supported by Windows 98, NT, 2000, or recent operating systems.
EFDC simulates flow and water quality constituent in a three-dimensional capacity. The water quality module
of EFDC is built with the eutrophication component and simulates the interaction of 21 water quality state
variables. Nitrogen and phosphorus in a dissolved, labile particulate, and refractory particulate forms are
included in the EFDC eutrophication component.
The key inputs for the EFDC simulator are elevation data, the initial condition of water quality constituents,
the boundary condition for flow and water quality constituents (monitored data on the 21 state variables),
and kinetic coefficients. EFDC has a pre-processor that can be applied to generate a grid from elevational
data. Once the data is collected and prepared, the user can easily follow the web-based user interface to cali-
brate the model and to predict the eutrophication level. The hydrodynamic module executes simultaneously
with the eutrophication module, predicts velocity, transports fields and elevation for the free water surface.
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EPD-RIV1
EPD-RIVl was developed at the Georgia Environmental Protection Division (GEPD) by modifying the CE-
QUAL-RIV1 model in 1993 (Martin and Wool, 2002; Sharma and Kansal, 2013). Compared to the original
CE-QUAL-RIV1 model, multiple functions were added to EPD-RIVl. EPD-RIVl consists of the hydrodynamic
(RIV1H) and water quality (RIV1Q) models. The program is currently maintained by Georgia EPD. The soft-
ware and documentation are available free of charge from Georgia EPD page at ittp://epdsoftware.wileng.
com/. The software is supported by Windows operating systems.
EPD-RIVl was developed to simulate the water quality dynamic under unsteady flow in a one-dimensional
capacity. The model is designed to support TMDL analysis in a riverine environment. The water quality mod-
ule can simulate the interaction of 16 water quality state variables, including 7 nutrient variables (nitrog-
enous biochemical oxygen demand, organic nitrogen, ammonia, nitrate, nitrite, organic phosphorus, phos-
phates, and algae).
To predict water quality state variables, the hydrodynamic model runs first, then the results are linked to the
water quality module. EPD-RIVl supports simulation in a time-varying flow, elevation, and concentrations of
water quality constituents. The key inputs are geometrical data, initial and boundary conditions (flow and
water quality variables), water depth, hydraulic parameters, and control parameters (coefficients and time
steps).
HEC-RAS
HEC-RAS was developed at the Hydraulic Engineering Center in the USACE to support river flow and water
quality modeling (Brunner, 2015). HEC-RAS was released in 1995. The model has been modified and released
as versions 1.1 - 4.1, with the most recent updated version as 5.0 in 2015. The program is currently main-
tained by the Hydrologic Engineering Center of the USCAE. The software and technical support are available
free of charge from the USACE page at http://www.hec.usace.army.mil/software/hec-ras/. HEC-RAS is sup-
ported by Windows 7, 8, and 10 operating systems.
HEC-RAS was developed to support river water analysis in a steady flow, one or two-dimensional unsteady
flow, movable boundary sediment transport computation, and a one-dimensional water quality analysis. The
water quality analysis module can be used to simulate dissolved orthophosphate, organic phosphorus, am-
monia, nitrate, nitrite, and organic nitrogen variations.
In the water quality analysis module, the flow module of HEC-RAS needs to be calibrated by using flow data
and boundary conditions. The water quality module organizes water constituents into temperature and nu-
trient modeling groups. The water temperature is simulated or set to a fixed value prior to nutrient modeling
as nutrient rate constants are temperature dependent. The input data for nutrient modeling groups are the
boundary condition of the target water constituent, dispersion coefficients, meteorological data, atmospher-
ic data, and rate constants for nutrients.
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HSPF
The Hydrological Simulation Program Fortran (HSPF) is a comprehensive model applicable to watershed load-
ing and surface water quality analysis. General information about the HSPF model is provided in Section 3.1.
The water quality component of HSPF was added in the 1970s. The most recent updated version of the wa-
ter quality module was released as HSPF 12.4. The water quality component covers several conventional and
toxic organic pollutants including ammonia, nitrite, nitrate, organic orthophosphate, and organic phosphorus
constituents. The software and documentation are available free of charge from the U.S. EPA page at https://
www.epa.gov/ceam/hydrological-simulation-program-fortran-hspf or from nttps://water.usgs.gov/software/
HSPF/. HSPF is supported by Windows XP, Vista, 7, and 8 operating systems.
MIKE 11
MIKE (MIKE HYDRO River) is a suite of models developed at the Danish Hydraulic Institute (DHI) in the 1990s
(DHI, 2017). MIKE integrates tools including MIKE SHE for an integrated analysis of surface water and ground-
water, MIKE-11 for unlimited river modeling, and MIKE 21C for river hydraulics and hydrology modeling.
MIKE 11 consists of advection-dispersion, water quality, and sediment transport modules that are designed
to assess water quality in rivers and wetlands. MIKE 11 is currently under significant modification and its
successor MIKE HYDRO River is expected to be released. MIKE 11 is currently maintained by DHI. Access to
the software and technical support requires a license. Contact information and model documentation can
be found from DHI page at https://www.mikepoweredbydhi.com/products/mike-ll. MIKE 11 is supported in
Windows operating systems.
MIKE-11 can be applied to water quality analysis from simple to complex rivers, channels, and reservoirs.
The water quality module of the MIKE 11 model has three submodules, namely WQ, EU and HM. The WQ
submodule allows simulation of nitrogen and phosphorus transport in rivers and their retention process in
wetlands. It covers most nutrient processes in the riverine system. The EU submodule is developed to simu-
late eutrophication, which covers nutrient cycle. The HU submodule is designed to simulate heavy metals.
The key input data required for the MIKE 11 simulator are geometrical data, initial and boundary conditions,
reaction rates for water quality parameters, temperature, and state variable concentrations.
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QUAL2KW
QUAL2KW is a member of the QUAL model family developed under a collaboration agreement between
Tufts University and the U.S. EPA Center for Water Quality Modeling in 1985 (Pelletier et al., 2006). QUAL
model was developed in 1970. QUAL has been modified multiple times and released as QUAL I, QUAL,
QUAL2E, QUAL2EU, and QUAL2KW. QUAL2KW is the current version, 6.0, developed with hydrodynamic and
water quality modules. QUAL2KW is currently maintained by the State of Washington Department of Ecology
(WDE). The software is available with no charge from WDE page at ittps://ecology.wa.gov/Research-Data/
Data-resources/Models-spreadsheets/Modeling-the-environment/Models-tools-for-TMDLs. The software is
supported by Windows operating systems.
QUAL2KW is a one-dimensional model developed to simulate water quality, under unsteady and non-
uniform flow, in a riverine environment. It is mainly designed to assist in TMDL analysis. QUAL2KW can be
applied to simulate the interaction of 15 water quality variables, such as temperature, dissolved oxygen,
nutrients, pH, periphyton, macrophytes, phytoplankton, and sediment diagnoses. All water quality variables
are simulated on a continuously varying time scale. The nutrient variables included in QUAL2KW are total
Kjeldahl nitrogen, ammonia, nitrate, nitrite, total phosphorus, and orthophosphate.
The key input required for water quality analysis is geometrical data, metrological data, initial and boundary
conditions, concentrations in water quality state variables, and kinetic constants. The hydrodynamic compo-
nent simulates flow, travel time, velocity, depth, and reaeration. The water quality module simulates single
or multiple variables at a time.
WASP
The Water Quality Analysis Simulation Program (WASP) is a dynamic water quality model developed at Hy-
droscience, Inc. (now named as HydroQual, Inc.) in 1970 (Di Toro et al., 1983). WASP has been upgraded sev-
eral times with the most recent version, 8.2, released in 2018. WASP is currently maintained by the U.S. EPA
CEAM. The software and documentation are available free of charge from U.S. EPA CEAM page at nttps://
www.epa.gov/ceam/water-quality-analysis-simulation-program-wasp. It is also available from Tim Wool's,
developer at U.S. EPA Region 4, page at http://epawasp.twool.com/. The software is supported by early ver-
sions of Windows, 64-bit Windows 7 or higher, Mac OS, and Linux Ubuntu operating systems.
WASP represents a time-varying process of advection, dispersion, point and diffuse mass loading, and
boundary exchange to model a variety of pollutant types in three modules, namely Eutrophication, Organic
Chemical, and Mercury. The water quality variables covered in these modules are nitrogen, phosphorus, dis-
solved oxygen, biological oxygen demand, sediment oxygen demand, algae, periphyton, organic chemicals,
metals, mercury, pathogens, and temperature. WASP is described in the U.S. EPA CEAM web page as the
most widely used water quality model for TMDL analysis. It can be applied in one-, two-, or three-dimension-
al capacities.
For water quality simulation, WASP should be linked to a hydrodynamic model to provide input of flow,
depth, temperature, salinity, and sediment flux. Main inputs for the WASP water quality module are the
boundary concentration of state variables, physical characteristics of water, sediment, environmental param-
eters, and chemical constants.
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3.4 Groundwater Quality Models
Inorganic and organic contaminants are introduced to the groundwater from a wide variety of sources, such as
agricultural chemicals, untreated wastewater disposal in the land, and accidental spills of chemicals. The fate and
transport of contaminants in groundwater is complex (Bear and Cheng, 2010) when compared to surface water.
This is because (1) a contaminant in the subsurface environment undergoes various chemical and biological pro-
cesses before it reaches the aquifer, (2) contaminants in the porous media move very slowly and transit time es-
timation is difficult, and (3) aquifers are hydrologically interrelated to their adjacent surface waters that influence
the contaminant's fate. Contaminant transport in groundwater is studied by thorough information on geological,
hydrological, and biochemical characteristics of the surface and subsurface environment. Groundwater models are
developed with several sets of assumptions to approximate groundwater flow rate and direction as well as contami-
nant transport.
Despite numerous factors controlling contaminant fate, groundwater models represent only relevant transforma-
tion and transport mechanisms (Bear and Cheng, 2010). The movement of dissolved contaminants in ground-
water is controlled mainly by advection and hydrodynamic dispersion processes. Advection is the transport of
contaminants in groundwater by the bulk flow, whereas hydrodynamic dispersion refers to mechanical mixing and
molecular diffusion of a contaminant in the longitudinal and transverse direction of the flow. A contaminant in
groundwater is also influenced by microorganisms and reactions created by aquifer materials. The relevant process
controlling a contaminant in groundwater varies with the type of contaminant and environmental conditions. For
example, biologically induced denitrification is the most relevant transformation for nitrate in groundwater (His-
cock, et al., 1991).
The flow characteristics, contaminant transport, and geochemical transformation are the three essential processes
represented in groundwater models. The governing equation for most groundwater models is established based on
Darcy's law for flow behavior and advection-dispersion theory for contaminant transport. Darcy's law establishes
a relationship between flow rate, hydraulic head difference, and hydraulic conductivity for a porous medium. This
empirical relationship is utilized to derive the groundwater flow equation. Darcy's law is mathematically represent-
ed by Equation 24 (Whitaker, 1986).
Q = —K (A^-) (Eq 24)
Where O is volume flow rate, A is a flow cross-sectional area, K is hydraulic conductivity, and h is the
hydraulic head.
The general flow equation is translated from a mass balance approach where water moving in and out of a smaller
unit in a system is analyzed. The general flow equation derived for a three-dimensional and smaller volumetric
space is shown in Equation 25 (Owais et al, 2008).
Ł (** Ł) -+ Yy{*> 25)
Where K is the hydraulic conductivity along the x, v, z domain space, O is the water flux store change from
the source or sink, and Ss is a specific storage coefficient representing the water released from porous me-
dia storage.
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Contaminant transport—the transport and dispersion of reactive contaminants with the reactive component is
simulated by solving advection-dispersion equations, shown in Equations 26 and 27 (Smith et al., 2004). Equation
26 represents the general advective-dispersion equation in a one-dimensional space whereas Equation 27 is a reac-
tion term for nitrogen species for a groundwater system. The reaction term represents the various transformations
of a contaminant that produces or consumes a given species.
%=Udt)-txw-r (Ec'26»
Where c is the concentration of a solute, D is the dispersion coefficient, v is the contaminant velocity, and R
is the reaction term for nonconservative contaminants.
The dispersion coefficient is the combined effect of hydrodynamic dispersion (due to turbulence) and
molecular diffusion of a contaminant constituent.
KC KiCi /r.
R = + -LJ- (Eq 27)
nCr n
Where K and Kf are the denitrification rate constants for nitrate and its transformation forms (nitrite, nitrous
oxide, and nitrogen gas), C and C, are solute concentrations for nitrate and its transformation forms (nitrite,
nitrous oxide, and nitrogen gas), n is the porosity, and Cr is the concentration of total nitrogen.
These governing equations are solved analytically or numerically to approximate variable flow and contaminant
transport conditions. Analytical models use a direct solution with simplified assumptions when the groundwater
system conditions are simple to characterize (e.g., when the aquifer is relatively homogeneous, or the velocity is
linear). Numerical models use a numerical approximation (finite differencing approach) of the governing equation
for complex groundwater systems. The numerical solution is widely used in groundwater flow and transport models
as it simulates variable system conditions, such as saturated or unsaturated and steady or unsteady. Most ground-
water models presented in this report are numerical models.
Groundwater models have been developed to understand contaminant transport mechanisms and to estimate the
spatial concentration of contaminants in the subsurface environment. The groundwater models presented below
are widely applied for nutrient transport and its fate in the subsurface environment.
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ANALGWST
ANALGWST is a suite of programs developed at the USGS in 1990 to simulate solute transport in groundwa-
ter (Wexler, 1992). Firstly, the individual programs are one-dimensional solute transport in finite or semi-infi-
nite systems. Secondly, two-dimensional solute transport in an infinite system for a continuous point source
or in a finite-width system with a finite-width solute source, in an infinite-width system with finite-width sol-
ute sources, or in an infinite-width system with a solute source having a Gaussian concentration distribution.
Finally, three-dimensional solute transport in an infinite system for a continuous point source and a finite or
infinite-width system and finite or infinite-height with a finite or infinite-width and finite or infinite-height
solute source. The model was last updated in 1996 and released as version 1.1. The program is currently
maintained by the USGS and the software is available free of charge from the USGS page at https://water.
usgs.gov/software/ANALGWST/. The software is supported by the UNIX operating system.
ANALGWST was primarily developed to simulate solute transport in groundwater systems under a uniform
flow condition. The one-dimensional program was designed to predict solute dispersion in a soil media (in
an unsaturated zone), whereas the two-and three-dimensional transport models simulate a contaminant
plume's fate in a relatively thin and thicker aquifer. The key input for each of the integrated programs is initial
conditions, advective velocity, dispersion coefficients, spatial information, temporal information, boundary
concentrations, and optionally a first-order solute decay coefficient.
BIOMOC
BIOMOC is a two-dimensional numerical model developed at the USGS by modifying the Method of Char-
acteristics (MOC) model in 1999 (Essaid and Bekins, 1997; Essaid and Bekins, 1998). BIOMOC consists of a
transport component and groundwater flow. The program is currently maintained by the USGS. The software
is available free of charge from USGS page at https://water.usgs.gov/cgi-bin/man_wrdappPbiomoc. The soft-
ware is supported by UNIX, DOS, or Windows 2000 and higher operating systems.
BIOMOC is designed to simulate the transport and biotransformation of multiple reacting solutes in a one-
and two-dimensional areal aquifer. The simulator represents advection, hydrodynamic dispersion, fluid
sources, retardation, decay (zero-order or first-order approximation), and biodegradation processes. BIO-
MOC can be applied to develop mass balances for contaminants, assess the potential of bioremediation at
a contaminated site, examine the relative contributions of competing for biodegradation processes to con-
taminant attenuation, and compare remediation schemes.
The key inputs for BIOMOC are flow characteristics, the geometry of the domain, boundary condition, and
information on the biodegradation mediating process (substrates, reactants, products, and the microbial
population). The flow and transport processes are discretized in a uniformly spaced finite-difference grid.
Particle movement is tracked based on the average linear velocity.
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HST3D
The Heat- and Solute-Transport Program (HST3D) is a groundwater quality model developed at the USGS by
modifying the Survey Waste Injection Program (Kipp, 1997). The first version 1.0 was released in the 1980s.
HST3D was upgraded from version 1.0 to 2.5. The current version 2.5.3 is a numerical solution of the satu-
rated groundwater flow, heat-transfer, and solute-transport equations. The program is currently maintained
by the USGS. The software and documentation are available free of charge from the USGS page at https://
wwwbrr.cr.usgs.gov/projects/GW_Solute/hst/. The source code is supported in Unix and Linux operating
systems, and compatible executables are available for Windows operating systems.
HST3D was developed to simulate heat and solute transport in three-dimensional groundwater flow. It is par-
ticularly designed for analyzing waste injection into fresh or saline aquifers, contaminant plume movement,
saltwater intrusion in coastal regions, brine disposal, freshwater storage in saline aquifers, heat storage in
aquifers, liquid-phase geothermal systems, and similar transport situations.
The key data inputs for HST3D simulators are initial conditions, boundary conditions, property functions, and
transport coefficients. The initial conditions for pressure, temperature, and mass-fraction field need to be
specified. Boundary conditions are determined based on information about fluid properties, porous-medium
properties, and transport coefficients.
MT3D
MT3D (-USGS) is a groundwater solute transportation model, family of the MODFLOW-related programs,
developed at the USGS in 2016 (Bedekar et al., 2016). MT3D is an updated version of the MT3DMS model
(Zheng and Wang, 1999), modified to keep pace with the advancement of MODFLOW, and to expand the sol-
ute transport simulator functionality for complex water quality issues. The program is currently maintained
by the USGS. The software is available free of charge from the USGS page at ittps://water.usgs.gov/ogw/
mt3d-usgs/. The program is supported in the Windows operating system.
MT3D represents processes of advection, dispersion/diffusion, and chemical reactions of contaminants in
groundwater flow systems under general hydrogeologic conditions. MT3D was developed with the Basic
Transport package, which routes solute mass transportation in groundwater flow, the Reaction Package to
simulate inter-species interactions and their kinetics, the Dispersion Simulator package, and the Hydrocarbon
Spill Source Tracer package to delineate hydrocarbon mass load zones. MT3D can be used to simulate the
exchange of solutes between the hydrologically connected surface and subsurface environment. Also, it can
be used for multi-component reactive solute analysis. MT3D consists of nitrate transport and a transforma-
tion (denitrification) component.
To route solute mass transport, MT3D requires a link to MODFLOW to simulate groundwater flow. For the
flow modeling component, the boundary conditions, such as the head, should be specified. For the solute
transport model, the initial solute concentration and concentration along a boundary must be specified. The
key inputs are topographic, hydrogeology, climate, aquifer characteristics, and water chemistry.
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MODFLOW-GWT
MODFLOW-GWT (also named as MF2K-GWT) is a three-dimensional solute transport package, part of the
MODFLOW model family developed at the USGS (Winston et al., 2018). The Groundwater Transport Process
(GWT) package is an enhanced version of MOC3D (Method of Characteristics for 3-Dimensional) model, first
released in 2001. MODFLOW-related programs are designed for simulating groundwater flow, groundwater-
surface water system interaction, solute transport, variable-density flow (including saltwater), and aquifer-
system compaction and land subsidence. The model has been modified several times and the most recent
modification was in March 2018, which was released as version 1.10. The program is currently maintained
by USGS. The software is available free of charge from the USGS page at https://water.usgs.gov/nrp/gwsoft-
ware/mf2k_gwt/mf2k_gwt.html. The software package is supported by Windows operating systems.
MODFLOW-GWT represents advection, hydrodynamic dispersion, retardation, decay, matrix diffusion, and
mixing processes. It is designed to simulate solute transport and spatial concentration of a contaminant
originating from multiple fluid sources. MODFLOW-GWT can also be applied to track a mass concentration of
a particle originating in varying pore volume through a volume-weighted particle.
The data required for the MODFLOW-GWT simulator are aquifer properties, the initial concentration of a
solute, sources of contamination, flow boundary conditions, and groundwater chemistry. The predictions can
be represented in several maps showing the spatial distribution of a single solute concentration at various
times or a single map displaying a comparative change in a solute concentration on a specific time. It also
supports a graphical comparison of concentration change at a given point.
SEAWAT
SEAWAT is a three-dimensional groundwater model developed at the USGS by combining MODFLOW and
MT3DMS into a single program (Langevin et al., 2008). It is developed with the flow and solute transport
component. The first version, 1.1, was released in 1998. SEAWAT has been modified to keep pace with the
updated versions of MODFLOW and MT3DMS. The most recent version, 4.0, was released in 2012. The
software is currently maintained by the USGS. The software, user guide, source code, and contact informa-
tion for technical support are available free of charge from the USGS page at ittps://water.usgs.gov/ogw/
seawat/. The software package is supported by the Windows operating systems.
SEAWAT is designed to simulate flow, multi-species solute, and heat transport in variable-density saturated
groundwater. It can be used to simulate solute and heat transport simultaneous to evaluate the combined
effects of concentration and temperature on variable-density flow. The solute transport component in the
SEAWAT model and the MT3D model are similar to each other. SEAWAT and MT3DMS use similar key data
and information for their simulator. For input requirement, refer the information discussed under the MT3D
(which is the modified version of MT3DMS) model description.
40
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PHAST
PHAST is a three-dimensional groundwater flow and solute transport model developed at the USGS
(Parkhurst et al., 2010). The flow and transport components of PHAST are a modified version of the HST3D
model. The first version, 1.0, was released in 2004. Significant revisions have been made for additional func-
tions and the most recent modification was released as version 3.4.0 in 2017. The software is currently main-
tained by the USGS. The software and user guide are available free of charge from the USGS page at
https://wwwbrr.cr.usgs.gov/projects/GWC_coupled/phast/. The software is supported by Windows, Linux
and Unix operating systems.
PHAST was designed to simulate multicomponent reactive solute transport in saturated groundwater. It can
be applied under various equilibrium and kinetic geochemical reactions in a groundwater system. PHAST can
simulate the effluent arsenic concentrations in laboratory column experiments, the migration of dissolved
organic compounds, the migration of nutrients in a sewage plume in a sandy aquifer, the storage of fresh-
water in a slightly saline aquifer, and an examination of natural mineral and exchange reactions in a regional
aquifer. PHAST is not applicable for unsaturated-zone flow, multiphase flow, and density and temperature-
dependent flow.
Key inputs required for reactive solute transport simulation are water chemistry and thermodynamic data.
PHAST allows manipulation of spatial data in map or grid coordinate system. The required input data, such
as initial chemical composition, flow boundary condition and porous-media properties, can be interpolated
from the spatial data. During model run time, flow velocities are calculated first, followed by solute trans-
port, and lastly the calculation of geochemical reactions.
SUTRA
The Saturated-Unsaturated Transport (SUTRA) is a groundwater simulation model developed at the USGS in
1984 (Voss and Provost, 2002; Hughes and Sanford, 2005). SUTRA has been upgraded and multiple packages
added (SUTRA-MS, SutraPrep, and SutraPlot). SUTRA-MS is a recent modification of SUTRA designed to simu-
late heat and multiple-solute transport. SutraPrep and SutraPlot are SUTRA pre- and post-processing pack-
ages. The most current version is SUTRA 2.2, released in 2010. The software is currently maintained by the
USGS. The software and user guide are available free of charge from the USGS page at ttps://water.usgs.
gov/nrp/gwsoftware/sutra.html. The software is supported by Windows, Linux and Unix operating systems.
SUTRA is designed to simulate flow, heat, and multiple dissolved species transported in a subsurface environ-
ment. SUTRA supports modeling variable density fluid in both saturated and unsaturated groundwater flow.
Transport of a solute and transport of thermal energy in the solid matrix of an aquifer and the groundwater
are subject to both first-order and zero-order production or decay. The flow and transport simulation can be
applied at a single time step solution for a steady-state or a series of time steps solution for a time-varying
system. It can be used in one, two, and three-dimensional capacity.
The key inputs required for the SUTRA simulator are aquifer properties, fluid properties, initial concentra-
tion, pressure and temperature, flow and concentration boundary conditions. The user must define the
distribution of porosity, permeability (or hydraulic conductivity), dispersive, initial pressure (or initial head),
initial concentration (or initial temperature), and thickness throughout the 2D model domain. The flow con-
dition can be modeled for the saturated or saturated-unsaturated system.
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4.0
Findings from Past Applications
The models presented in Section 3.2 have been applied to solve nutrient-related water quality problems. Literature
on the model application was reviewed to identify the most recognized models, the type of problems solved, and
the model's strengths and limitations. A description of the literature search strategy is provided in Appendix 1. The
reader should be aware that industry and consultants may have different approaches or preferred tools and this
report does not suggest other tools or modifications of other tools are inappropriate. Simply, these queries repre-
sent presence in journal articles. Although research literature database queries do represent presence in primary
academic literature, these indicators of use may be a poor representation of actual practitioner or management ap-
plication. However, in the absence of extensive practitioner surveys or other available metrics, presence in primary
literature in common research databases does provide a reasonable surrogate and indicator of model use.
Case studies were searched from the Web of Science and ScienceDirect literature databases using "Model type"
and "nutrient" (for mixing also using "effluent") keywords. The number of model records from the two search
engines was used to rank models based on the popularity of the literature. Case studies from each category of
watershed and water quality models on the three most popular models were reviewed to understand the nature of
problems solved, the approach used, and model's capabilities and limitations.
4.1 Watershed Loading Models
The search results for watershed loading models are presented in Figure 1. SWAT and HSPF have many case studies
compared to other models. The results showed the number of SWAT and HSPF applications far exceed other water-
shed loading models while analyzing water quality issues caused by nutrients within a watershed. There are many
reasons that both SWAT and HSPF can be broadly applied. Some reasons include free and open-source software,
giving users easy access to acquire and use them. Watershed loading models integrate physically-based, empirical,
and statistical methods to simulate various nonpoint source pollution processes at multiple spatiotemporal scales.
SWAT and HSPF are two commonly used watershed models. SWAT and HSPF have experienced long-term develop-
ment and continuous upgrading over a long period of time. SWAT's predecessor was SWRRB (the Simulator for
Water Resources in Rural Basins) which was developed in the early 1980s. The precursor of HSPF was the first wa-
tershed model in the world, the Stanford Watershed Model, developed in the 1960s. Finally, SWAT and HSPF have
active user communities.
¦ ScienceDirect ¦ Web of Science
AGNPS
AnnAGNPS
f
AGWA
i
BASINS
1-
GWLF
r
HSPF
LSPC
L-THIA
r
N-SPECT
p
OpenNSPECT
i
SLAMM
QW AT
¦
o W/\ 1
SWMM
r
WAM
r
WARMF
WMS
n
0 200 400 600 800 1000
Instances of Record in Literature
Figure 1. Instances of watershed loading model records in the literature (May 2019).
42
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SWAT has been widely applied in many fields such as hydrologic simulation, surface and subsurface water quality
evaluation, soil erosion assessment and control, the impact of climate change and land use management practices
on hydrology cycle, hydropeaking prediction, and so on (Stehr, et al., 2010, Mittelstet, et al., 2016, Chiogna, et al.,
2018). According to the record of the official SWAT literature database, the number of articles relevant to SWAT has
been more than 1,300 during 2016-2019 (https://www.card.iastate.edu/swat_articles/, access at 02-27-2019).
HSPF has also been widely applied all over the world to evaluate the effects of land-use change, reservoir opera-
tions, point and nonpoint source treatment alternatives, and streamflow prediction. An early HSPF literature sum-
mary can be found at http://www.aquaterra.com/resources/hspfsupport/hspfbib.php. Kim, et al. (2014) integrated
HSPF with maximum likelihood filter to improve the water quality forecast in the Kumho catchment (23,384 km2)
in South Korea and found the accuracy of short-range water quality prediction can be enhanced through coupling
HSPF and a data assimilation procedure. Huo, et al. (2015) used HSPF and a fuzzy model to evaluate nonpoint
source water quality in the Feitsui reservoir watershed (303 km2) in Taiwan and concluded that supplement rainfall
data with the fuzzy method would improve the prediction accuracy of water quality.
AGNPS is the third favorite watershed model in the world after SWAT and HSPF. AGNPS has been widely used to
simulate runoff, sediment, nutrients, and pesticides in different watersheds throughout the world. Chahor, et al.
(2014) evaluated the capabilities of the AnnAGNPS model to simulate runoff and sediment loading in a Mediter-
ranean agricultural watershed (207 ha) in Spain. Li, et al. (2015) applied AnnAGNPS to simulate yearly streamflow
and monthly nutrient loading in the Taihu Lake watershed in China. The results showed that the AnnAGNPS model
is adequately accurate for annual streamflow simulation, and monthly nitrogen loading evaluation has higher ac-
curacy than monthly phosphorus loading. Karki, et al. (2017) applied AnnAGNPS to evaluate runoff, nutrients, and
sediment from an agricultural watershed of 30.3 ha in East-Central Mississippi. Then, AnnAGNPS was used as a BMP
to assess nutrient and sediment control from a farming field within the same catchment area. This study showed
that AnnAGNPS performed better for runoff and sediment assessment when evaluated for a longer time scale. The
accuracy of the model prediction dramatically depends on the available measured data for calibration. AnnAGNPS
was not able to accurately estimate nitrogen loading due to the lack of input data for nitrogen.
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4.2 Mixing Models
As shown in Figure 2, the three most popular mixing models are CORMIX, Visual Plumes (VP), and VISJET. These
models are applied to track plume movement from its source, characterize mixing behavior in the near- and far-
field regions, estimate initial dilution, design discharging port, and examine the regulatory zone.
"CORMIX" and "effluent"
"CORMIX" and "nutrient"
"CCHE2D/3D-Chem" and "effluent"
"CCHE2D/3D-Chem" and "nutrient"
"Visual Plumes" and "effluent"
"Visual Plumes" and "nutrient"
"VISJET" and "effluent"
"VISJET" and "nutrient"
—
0 10 20 30 40 50
Instances of Records in Literature
Figure 2. Instances of mixing model records in the literature (May 2019).
Examples of case studies supported by CORMIX are many thermal plume mixing in a large river and estuaries under
varying tidal conditions (Schreiner et al., 2002), described the mixing and transport of wastewater discharge to a
coastal water (Bleninger and Jirka, 2004), simulated heated brine dilution in a coastal marine environment (Pur-
nama, 2012), simulated the trajectory and geometry for an effluent discharged to an unstratified-stagnant environ-
ment (Abessi et al., 2012). In these studies, CORMIX was successfully applied to analyze the near-, intermediate-
and far-field mixing in a steady-state condition. Notice from these studies that CORMIX is an appropriate model
when the temporal dynamics are less important in the mixing processes. Also note that the CORMIX simulation
capacity for the far-field was limited to the length and vertical scale. Therefore, CORMIX cannot provide reasonable
predictions when lateral dilution is significant.
Hunt et al. (2010) applied VP to track wastewater plume movement to estimate initial dilution in a stratified
ocean. VP was also used to evaluate ocean tide effects on mixing of a nutrient-rich effluent in a harbor area (Xu
et al., 2011), and to predict wastewater dilution and bacteria concentration variation in a deep-sea outfall system
(Muhammetoglu et al., 2012). In these studies, VP provided an adequate mixing prediction for near- and far-field
regions. VP applications were limited to steady-state conditions, particularly when the spatial and temporal varia-
tions of the velocity field were insignificant. The VP far-field module was described as unsuitable for interpreting
vertical mixing as it uses a rough approximation. VP was also described as incapable of characterizing mixing in the
intermediate-field.
VISJET was applied to characterize the near-field dilution behavior for an effluent discharged into variable water
environments (Etemad-Shahidi and Azimi, 2003), to determine the trajectory of ammonia and phosphate constitu-
ents of sewage plume in a tidal stream (Xu et al., 2011), to predict the behavior of a partially treated wastewater in
a coastal water (Lai et al., 2011), and to understand partially treated wastewater plume mixing in a coastal water
(Xu et al., 2018). VISJET was successfully applied to simulate buoyant jet mixing in stratified and uniform flow in the
near-field region. However, in these studies, VISJET was described as unsuitable for intermediate- and far-field mix-
ing analysis.
-------
From peer-reviewed papers, the strengths and limitations of the three models were evaluated. The three mixing
models were successfully applied for near-field analysis under a stratified ambient layer of salinity, temperature,
density, velocity, and currents. These models were developed with several assumptions that make them unsuitable
for specific conditions. The first common assumption is a simplified representation of the physical system. For ex-
ample, the actual geometry of the channel for a surface discharge outfall is approximated to a rectangular conduit
as in the case of CORMIX. Therefore, it is crucial that simulation results for surface discharge can be a rough estima-
tion of mixing conditions. Next, physical mixing is assumed as the only process controlling water quality processes
near the discharge location. And finally, effluent constituents are considered conservative substances, or follow
linear decay as in the case of the coliform bacteria module within the CORMIX model. These assumptions may not
be valid for nutrient parameters when there is sufficient resident time for transformation. For this reason, mixing
models may not provide a reasonable prediction when the chemical and biological process of the receiving water is
significant near the discharge region. The three models' applicability is also limited to a steady-state condition. For
a time-dependent mixing analysis, these models can be applied with numerous time steps to predict the average
mixing behavior.
CORMIX, VISJET, and Visual Plumes performances were also tested for a brine jet trajectory and dilution process
from desalination plants discharge (Loya-Fernandez et al., 2012; Palomar et al., 2012). On near-field mixing, each
model was observed to be sensitive to the effluent flow rate and discharge port geometry.
45
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4.3 Surface Water Quality Models
Surface water quality models reported here have been applied for a long time in water quality management pro-
grams. These models were previously applied to a wide variety of waters, such as streams, rivers, lakes, estuaries,
and coastal waters. WASP, HSPF, and BATHTUB are the most recognized surface water quality models in the litera-
ture (Figure 3). The nature of the problems studied ranges from a single nutrient species simulation to analysis of
complex water quality problem, such as eutrophication processes.
¦ ScienceDirect ¦ Web of Science
CE-QUAL-RIV1
¦
CCHE3D
CE-QUAL-W2
CE-QUAL-ICM
EFDC
EPD-RIV1
1
HEC-RAS
MIKE-11
QUAL2KW
r™
BATHTUB
HSPF
WASP
0 50 100 150 200 250 300 350 400
Instances of Records in Literature
Figure 3. Instances of surface water quality model records in the literature (May 2019).
WASP was applied by Nikolaidis et al. (2006), to simulate nutrient dynamics in coastal waters and to understand
phytoplankton evolution. To predict nitrate, phosphate, and chlorophyll-a concentrations in a lake environment
(Moses et al., 2015), analyze sensitivity of in-stream nutrient transformation during ice-covered and ice-free sea-
sons (Hosseini et al., 2017), and predict nutrient and chlorophyll-a concentrations in a riverine system (Mbuh et al.,
2018). In these studies, WASP was successfully applied to capture the daily nutrient variation, which can be used
to make a general or specific conclusion on the water quality conditions. WASP was applied in these studies under
unsteady conditions. The reviewed literature demonstrated that carbon to nitrogen and carbon to Chlorophyll-a
ratios are most influential WASP model parameters for nitrogen and phosphorus predictions. Moreover, nitrogen
was described as being the most sensitive to N-mineralization and nitrification, whereas phosphorus is the most
sensitive to phytoplankton growth. Reviewed literature also showed that WASP was unable to capture the spatial
variations as much as the temporal variations. This limitation was described as a mode assumption that the effluent
will thoroughly mix immediately at the point of discharge.
HSPF was applied to investigate nutrient transformation under various moisture conditions of sediments in a river-
ine system (Topalova et al., 2009), simulate the impact of a wastewater load in an in-stream concentration (Fonseca
et al., 2014), to forecast water quality in conjunction with an ensemble data assimilation technique (Kim et al.,
2014), and to simulate in-stream phosphate and chlorophyll-a concentrations in conjunction with the EFDC model
(Kim et al., 2014). These studies demonstrated that HSPF could reproduce observed concentrations of phosphorus
and nitrogen species. Some deviations were observed for nitrate, nitrite, and ammonia predictions as shown by
Kim et al. (2014). It was discussed that the long-term biological process in the real condition is not accounted for
in HSPF. For improving the predictions using HSPF model, these studies suggest performing a rigorous parameter
optimization. For this reason, HSPF is not recommended when water quality and hydrologic data are scarce.
-------
BATHTUB was applied in conjunction with the AnnAGNPS model to simulate chlorophyll-a concentration as part of
a nitrogen and phosphorus TMDL analysis (Wang et al., 2005), to determine the effect a phosphorus load reduction
has on a lake eutrophication (Robertson and Schladow, 2008), and simulate a lake eutrophication response to nutri-
ent loading (Brennan et al., 2016). In the reviewed literature, BATHTUB was successfully applied for eutrophication
modeling in reservoirs and lakes. The BATHTUB eutrophication module is also a simplified model that requires less
amount of data when compared to other surface water quality models. However, its applicability is limited to a
steady-state condition. Like WASP, BATHTUB was developed with the assumption that the effluent will mix entirely
at the point of discharge.
In past applications, surface water quality models were applied to simulate nitrite, nitrate, ammonia, and phos-
phate constituents. Total nitrogen and total phosphorus along with chlorophyll-a variations were also modeled
to determine eutrophication level. Now, surface water quality models cover comprehensive modules that allow a
broader and deeper analysis of water quality. In the reviewed literature, a major limitation of surface water quality
models is that the effluent is assumed to mix completely upon discharge, which makes surface water quality mod-
els unsuitable for a site scale mixing analysis.
47
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4.4 Groundwater Quality Models
Groundwater models have been applied to simulate the fate and transport of contaminants in a subsurface en-
vironment. MODFLOW, SEAWAT, and MT3D are the most recognized groundwater models (Figure 4). Literature
records for SUTRA and SEAWAT models are the most prevalent next to MODFLOW. However, through further inves-
tigation, and researching "SUTRA/PHAST Groundwater Nutrients" keywords, we noticed that search results do not
reflect the actual number of publications and SUTRA and PHAST models are excluded from the comparison.
¦ ScienceDirect ¦ Web of Science
ANALGWST
BIOMOC
-
HST3D
¦
MT3D
MODFLOW
SEAWAT
PHAST
SUTRA
0 50
100 150 200 250 300 350 400
Instances of Records in Literature
Figure 4. Instances of groundwater quality model records in the literature (May 2019).
MODFLOW, with a GTW package and linked with other models, is the most widely applied model in groundwater
studies. MODFLOW was linked with the Nitrogen Soil Model and MT3D to estimate nitrate leaching to groundwater
from both point and nonpoint sources (Almasri and Kaluarachchi, 2007). MODFLOW-GTW was applied for evaluat-
ing the vulnerability of a public water supply well, screened in unconfined and confined units, to assess soluble
contaminants (Clark et al., 2016). MODFLOW was also coupled with UZF-RT3D to simulate reactive transport of se-
lenium and nitrogen in a coupled groundwater-surface water system (Bailey et al., 2013; Shultz et al., 2018). These
example studies show that MODFLOW can interface directly with many other models, such as with UZF-RT3D,
Nitrogen Soil Model, and MT3D. The direct interface of MODFLOW to other models makes it suitable to solve a va-
riety of groundwater quality problems. In the reviewed literature, MODFLOW was applied successfully to simulate
groundwater-stream exchange and to characterize the hydrochemistry of a hyporheic zone. Simplification of com-
plexities within space, time discretization, and large data requirements was mentioned as limitations of MODFLOW.
MT3D has linked to MODFLOW to model nutrient in a groundwater system. Example case studies supporting the
linking of MT3D with MODFLOW include analyzing groundwater and surface water flux mixing in the hyporheic
zone, which helps to identify the hydro-chemically active hyporheic zone (Lautz and Siegel, 2006), studying nitrate
transport and attenuation within a groundwater of a riparian floodplain (Krause et al., 2008), and evaluating the
impact of best management practices in the groundwater quality (Cho et al., 2010). In these case studies, MT3D
was successfully applied to estimate the spatial and temporal variation of nitrate. The literature described that the
MT3D nitrate module represented the denitrification process in accurate resolution. Nitrate prediction using MT3D
model is also described as more sensitive to denitrification than the advection and mechanical dispersion. From
this, it can be generalized that MT3D is a suitable model for nitrate transport and attenuation in a subsurface envi-
ronment.
-------
SEAWAT also belongs in the family of MODFLOW and is widely used in groundwater quality studies. SEAWAT has
been applied to flow and solute transport simulation in a deep saline aquifer with varying density (Dausman et al.,
2010). SEAWAT was linked with the PHT3D model to evaluate the influence of tides and waves in the transport and
transformation of nutrients (nitrate, ammonia, and phosphate) in a nearshore unconfined aquifer (Anwar et al.,
2014). Moreover, SEAWAT was successfully applied to investigate coastal groundwater flow processes in Southern
Florida for seven hydrological problems (related to the availability of brackish groundwater, saltwater intrusion,
surface water and groundwater interactions, submarine groundwater discharge, and effectiveness of salinity bar-
riers) (Guo et al., 2001). In these applications, SEAWAT was able to simulate fresh and saline groundwater mixing
processes. Therefore, it is possible that SEAWAT could be a suitable model for a coastal aquifer when a variable
density groundwater flow exists.
49
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5.0
Recommended Strategy for Model Selection
As noted in Section 3.2, models differ significantly in the approach used to govern processes, assumptions adopted,
and type and quantity of data needs. Models are developed to represent relevant processes controlling pollutant
transport and transformation. From case studies supported by modeling, each problem solved was unique and
several assumptions were adopted. Generally, a single model cannot meet all information to support a given water
quality goal. There is also considerable ambiguity about which model should be selected. Therefore, a strategic
model selection procedure is necessary.
We suggest the model of choice should be selected primarily on model characteristics and the nature of the prob-
lem to be addressed. It is essential that the model is suitable to the level of complexity of the problem and should
be critically evaluated. From the reviewed literature, the following general criteria are a useful guide for model
selection and consideration.
Nature of the problem
The first and most crucial step of watershed and water quality modeling is to select a suitable model. A solid under-
standing of processes governing the system to be modeled is essential to define clear criteria for model selection.
Theories and concepts about the nature of the water quality problem are well documented in the literature and can
help to understand these governing processes. For example, various natural processes control nutrient fate in a wa-
ter environment, these are conceptualized by breaking down the system components into loading, transport, and
transformation processes. These theories are linked to most of the water quality models and thus, provides guid-
ance to evaluate what processes are represented in each model. The following steps are suggested when evaluating
the nature of the problem and defining the model selection criteria.
• Each water quality problem exhibits unique characteristics that fall into a specific category. Insight from
previous modeling efforts can help explore the problem and identify individual needs. The processes
controlling water quality problems are complex to understand. Water quality models are a simplified version
of reality and they differ in the controlling processes they represent. For this reason, controlling processes
should be prioritized in order of most to least relevant. This provides critical information on the major
processes to be of major consideration for model selection. If the tools are not suited to answer the question,
an understanding of this potential limitation is critical.
• Water quality models presented in this report include modules to support the simulation of various water
quality variables. Water quality problems are analyzed by modeling indicator variables. For example,
eutrophication is estimated by treating either nitrogen or phosphorus as a critical variable. In such
circumstances, the usefulness of the indicator variable to the water quality problem should be carefully
examined.
50
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Model characteristics
Each model is developed for a specific purpose and cannot provide an answer to all water quality questions. The
ability of models to solve a specific water quality problem needs to be examined. A wide variety of criteria can be
considered when examining model suitability, such as water quality constituents it can simulate, data needs, tem-
poral and spatial scale, level of complexity, availability, processes described, modeling environment, and technical
support. To provide preliminary guidance on model characteristics, the models presented in this report were com-
pared based on selected features (Table 3).
Table 3. Comparison of model characteristics for nutrient fate and transport simulation
Type
Model
Water quality
State variables
Resolution
Processes
Environment
Availability
Spatial
Temporal
Watershed Loading Model
HSPF
Dissolved oxygen,
BOD, Pesticides,
Fecal coliforms,
Sediment,
Nitrite-nitrate,
Organic Nitrogen,
Orthophosphate,
Organic
Phosphorus,
Phytoplankton
A few
acres to a
large river
basin
Long-term
continuous
dynamic
Flow,
Sediment
detachment
and transport,
Nutrient fate
and transport
Rural or urban
watershed
Public
LSPC
Sediment,
Nutrients,
Dissolved Oxygen
No preset
limit
for the
watershed
size
No
inherent
limit for
temporal
resolution
Flow,
Sediment,
General water
quality
Rural or urban
watershed
Public
SWMM
TSS, BOD, COD,
TP, Soluble P, TKN,
N02/N03, Total
Cu, Total Pb, Total
Zn
From
single
lots up to
hundreds
of acres
Single
events or a
continuous
dynamic
simulation
Pollutant
buildup,
Washoff, Non-
runoff loads
Urban
watershed
Public
AGNPS
Sediment, Total
N, Total P, COD,
organic carbon
No
limitation
for
watershed
size
Daily
time step,
Continuous
simulation
Runoff,
Sediment,
Soil erosion,
Nutrients,
Pesticide
Rural
watershed
Public
AGWA
N and P simulated
through SWAT
sub-model
integrated into
AGWA
From one
hectare to
thousands
of square
kilometers
From event
or daily to
yearly
Runoff,
Sediment,
Nutrient fate
and transport
Rural
watershed
Public
-------
Table 3. (cont.) Comparison of model characteristics for nutrient fate and transport simulation
Type
Model
Water quality
State variables
Resolution
Processes
Environment
Availability
Spatial
Temporal
Watershed Loading Model
GWLF
N, P in
surface water,
groundwater, and
sediment
Mid-range
watersheds
Monthly
sediment
and
pollution
output with
daily step
Runoff,
Sediment,
Nutrient
loading
Rural or urban
watershed
Public
WMS
The same
processes
simulated with
HSPF
Flexible
watershed
size
Continuous
simulation
Flow, Sediment
detachment
and transport,
Nutrient fate
and transport
Rural or urban
watershed
Private
WARMF
N, P, TSS, DO,
Ammonia, Nitrate,
Coliform bacteria,
3 algal species,
Periphyton, pH,
Phosphate, Iron,
Zinc, Manganese,
Copper
Flexible for
watershed
size,
typically
resolution
is 11-digit
HRU set by
the USGS
Daily
continuous
simulation
Flow, Soil
erosion and
sediment,
Nutrient
uptake, CO2
exchange
Urban
watershed
Public
WAM
N, P, TSS, BOD
A small to
medium
watershed
Daily
continuous
simulation
Flow, Erosion/
sediment
yield, Nutrient
transport/
Plant nutrients
Rural or urban
watershed
Public/
Private
SLAMM
TSS, Total
Dissolved Solids,
COD, TP, Filtered
P, TKN, Cu, Pb, Zn,
N03 + N02, Fecal
coliforms
Large
watershed
including
urban
areas
Stormwater
runoff
simulation
Flow,
Particulate
accumulation,
Particulate
wash off,
Pollutant
associations,
Street cleaning
Urban
watershed
Private
N-SPECT/
Open-
NSECT
N, P, Lead, Zinc
Medium-
to-large
watersheds
Long-term
continuous
simulation
Runoff,
Sediment,
Soil erosion,
Pollutant
loads and
concentrations
Coastal and
near the
noncoastal
area
Public
-------
Table 3. (cont.) Comparison of model characteristics for nutrient fate and transport simulation
Type
Model
Water quality
State variables
Resolution
Processes
Environment
Availability
Spatial
Temporal
Watershed Loading Model
L-THIA
TN, TP, Dissolved
P, TSS, Dissolved
Solids, Total Lead,
Total Copper,
Total Zinc, Total
Chromium, Total
Nickel, BOD
A large
watershed
such as
Great Lakes
Watershed
Long-term
simulation
Runoff, Soil
erosion and
sediment
yield,
Pollutant
loads
Urban and
suburban
areas
Public
SWAT
Sediment, N,
P, Pesticides,
Bacteria, Carbon
From a
small
watershed
to the entire
European
continent
Long-term
continuous
simulation
with a sub-
daily time
step
Surface runoff,
Groundwater,
Nutrient
loading and
transportation
Rural
watershed
Public
Mixing
CORMIX
Effluents with
conservative,
non-conservative,
heated, brine
discharge or
suspended
sediment
constituents
2D or 3D
visualization
Steady-
state
Plume
trajectory and
dilution
Near-field and
far-field
Private
VISJET
Multiple
constituents
from buoyant
wastewater
discharges
3D
visualization
Steady-
state
Path and
mixing of
buoyant
jets, effluent
discharge
Near-field
Private
Visual
Plumes
Multiple
constituents
from wastewater
discharges
2D or 3D
Steady-
state
Initial dilution
of plume
Near-field and
far-field
Public
-------
Table 3. (cont.) Comparison of model characteristics for nutrient fate and transport simulation
Type
Model
Water quality
State variables
Resolution
Processes
Environment
Availability
Spatial
Temporal
Surface Water Quality
BATHTUB
Chlorophyll-a,
eutrophication
response to
nitrogen and
phosphorus
ID
Steady-
state
Water and
nutrient mass
Lake
Public
CCHE3D
Ammonia
nitrogen, nitrate
nitrogen,
inorganic
phosphorus,
phytoplankton,
organic nitrogen,
and organic
phosphorus
2D or 3D
Steady and
dynamic
state
Flow, transport
Rivers, lakes,
estuaries and
oceans
Private
CE-QUAL-
RIV1
Nitrogenous
biochemical
oxygen demand,
organic nitrogen,
ammonia
nitrogen,
nitrate, nitrite
nitrogen, organic
phosphorus,
phosphates, and
algae
ID
Steady and
dynamic
state
Flow, transport
River
Public
CE-QUAL-
ICM
Nitrogen and
phosphorus
biogeochemical
cycles
ID, 2D, or
3D
Steady and
dynamic
state
Transport
River, lake,
estuary
Public
CE-
QUAL-W2
Ammonia, nitrate,
nitrite, organic
nitrogen and
phosphorus in
dissolved and
particulate forms,
algae
2D
Steady and
dynamic
state
Flow, transport
River, estuary
Public
EFDC
Nitrogen and
phosphorus cycles
in eutrophication
processes
ID, 2D, or
3D
Steady and
dynamic
state
Flow, transport
River, lake,
estuary, ocean
Public
-------
Table 3. (cont.) Comparison of model characteristics for nutrient fate and transport simulation
Type
Model
Water quality
State variables
Resolution
Processes
Environment
Availability
Spatial
Temporal
Surface Water Quality
EPD-RIV1
Nitrogenous
biochemical
oxygen demand,
organic nitrogen,
ammonia nitrogen,
nitrate, nitrite
nitrogen, organic
phosphorus,
phosphates, and
algae
ID
Steady and
dynamic
state
Flow,
transport
River
Public
HEC-RAS
Orthophosphate,
organic
phosphorus,
dissolved
ammonia, nitrate,
nitrite, and organic
nitrogen
Flow 2D,
transport
ID
Steady-
state
Flow,
transport
River
Public
HSPF
Ammonia,
nitrite-nitrate,
organic nitrogen,
orthophosphate,
and organic
phosphorus
ID
Steady and
dynamic
state
Flow,
transport
River,
watershed
Public
MIKE-11
Nitrogen and
phosphorus
concentration and
their cycles in the
eutrophication
process
ID
Steady and
dynamic
state
Flow,
transport
River
Private
QUAL2KW
Total Kjeldahl
nitrogen,
ammonia, nitrate,
nitrite, total
phosphorus, and
orthophosphate
ID
Dynamic
State
Flow,
transport
River
Public
WASP
Ammonia,
nitrogen, nitrate
nitrogen, inorganic
phosphorus,
phytoplankton,
organic nitrogen,
and organic
phosphorus
ID, 2D, or
3D
Dynamic
State
Transport
River, lake,
estuary
Public
-------
Table 3. (cont.) Comparison of model characteristics for nutrient fate and transport simulation
Type
Model
Water quality
State variables
Resolution
Processes
Environment
Availability
Spatial
Temporal
ANALG
WST
Multiple species
solutes
ID, 2D, or
3D
Steady state
Transport,
chemical
transformation
Unsaturated
and saturated
groundwater
flow
Public
BIOMOC
Multiple solute
species
ID, 2D, or
3D
Steady and
Transient
State
Flow, trans-
port, biotrans-
formation
Groundwater
Public
HST3D
Multiple solute
species and heat
3D
Steady and
Transient
State
Flow, transport
Saturated
groundwater
flow
Public
>
"ro
3
a
01
4-*
CD
5
MT3D
Multiple solute
species
3D
Steady and
Transient
State
Transport,
biological and
geochemical
transformation
Unsaturated
and
groundwater
flow, solute
exchange with
streams and
lakes
Public
"O
c
3
O
u
MODFLOW
-GWT
Multi solute
species
3D
Steady and
Transient
State
Flow, transport
Saturated
groundwater
flow
Public
SEAWAT
Multiple species
solute and heat
3D
Steady and
transient
state
Flow, transport
Saturated
groundwater
flow
Public
PHAST
Multicomponent
reactive solutes
3D
Steady and
transient
state
Flow, solute
transport,
multicomponent
geochemical
reactions
Saturated
groundwater
flow
Public
SUTRA
Multiple dissolved
species
2D or 3D
Steady and
transient
state
Flow, transport
Unsaturated
and saturated
groundwater
flow
Public
Other considerations
There are many other factors that need to be considered in model selection other than the above discussion. For
example, watershed and water quality modeling activities need a lot of data support, so the availability of monitor-
ing data required needs to be considered prior to modeling. Resource limitations such as time, available funding,
and modeling expertise can limit the flexibility of the model selection. Modelers often prefer to use a model they
are familiar with based on previous experience, as it can save a considerable amount of time. Therefore, we suggest
time, available funding, user's expertise about the model, availability of previous monitoring data, and other factors
are secondary considerations when watershed and water quality managers select the most appropriate one among
the existing models.
56
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6.0
Conclusions
This report presented watershed and water quality models useful to nutrient fate and transport simulation. Based
on modeling objectives (activities ranging from assessing overall water quality condition to evaluating the effective-
ness of management practices), models were grouped into watershed loading, mixing, surface water quality, and
groundwater categories. A description of each model's characteristics was summarized from their documentation.
Model capabilities and limitations were further evaluated using reviewed case studies based on past applications to
solve nutrient-related water quality problems.
Each model was developed for a particular purpose, and varies with respect to their applicability, data need, level
of complexity, availability, resolution, and in many other aspects. These models are applicable to different water
environments (river, lake, estuary, ocean, or groundwater) and cover various water quality variables (biological,
chemical, or physical constituents). Each model is developed under certain assumptions and represents only rel-
evant water quality processes. Thus, the modeling approach cannot answer all water quality-related questions.
These models have been applied to solve water quality problems in different capacities. In the reviewed literature,
the type of water quality problem solved was different and there is a noticeable variation of the model's strength
and weakness in regard to solve each problem. Therefore, identifying the most suitable model can be a challenge.
Model selection is a critical step towards achieving the water quality objective. Appropriateness of a model should
be examined in consideration with specific criteria of the problem. As we observed from reviewed information,
each water quality problem is unique, and each model handles the problem differently. We recommend the selec-
tion criteria should be primarily based on model suitability to the nature of the water quality problem. Time, re-
sources needed, as well as familiarity with the model, which often dictates model selection, should be secondary
considerations.
57
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Appendix 1
Model Search Strategy
This appendix contains the summary of strategies used to search case studies from previous model applications. All
of the search results were completed in May 2019. The number of applications for each model will be changed over
time. The case study search focuses on studies supported by water quality modeling involving nutrient pollution-
related problems. The following literature sources were considered.
1. Federal and State agency website resources involved in developing and applying water quality models.
2. Academic and research institutions with active research in water quality modeling.
3. Scientific databases.
4. Model user communities—few models have a well-established publication database.
The original goal of the case study search was to identify the most widely used model, to find the common type of
problems solved, and to understand models' strengths and limitations. However, from preliminary search results,
such questions are difficult to answer as there is no even-handed information for all reviewed models. For this
reason, we decided to use scientific databases as the only literature sources. The case study search was completed
in three steps.
Step 1: Select Search Engine
There are several literature search engines used to find published case studies, these can make case studies rela-
tively even-handed. We used the three most popular literature search engines in the field of environment, Science-
Direct, Web of Science, and Google Scholar.
Step 2: Define Keywords for Searching
Keywords considered for case study searches are the model name and water quality search terms (alternatives to
the search terms: water quality, nutrient pollution, effluents, and nutrients). The search engines searched literature
with a different subset of keywords for each category of models using the "AND" Boolean operator. The best subset
of keywords that captured instances of a model record in the literature related to nutrient is presented in Table Al.
Table Al. Case Study Search Keywords
Model Category
Best Keywords
Watershed Models
"model name" and "nutrients"
Mixing Models
"model name" and "nutrients"
"model name" and "effluent"
Surface Water Quality Models
"model name" and "nutrients"
Groundwater Quality Models
"model name" and "nutrients"
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Step 3: Summarize Search Results
The case study search results are presented in Tables A2-A5. For a given search criterion, literature from a Google
Scholar search is much larger than the other two search engines. Upon further investigation, it was noted that
Google Scholar gathered literature when either of the keywords was used in the literature. Therefore, we decided
to exclude the Google Scholar search results from further discussion.
Table A2. Number of Literature Records in Watershed Models
Keywords
ScienceDirect
Web of Science
Google Scholar
"Agricultural Non-Point Source Pollution Model" and "nutrients"
66
9
1
"Annualized Agricultural Non-Point Source Pollution Model" and
"nutrients"
15
4
1
"Automated Geospatial Watershed Assessment Tool" and
"nutrients"
5
0
1
"Better Assessment Science Integrating Point and
Nonpoint Sources" and "nutrients"
37
3
2
"Generalized Watershed Loading Function" and "nutrients"
44
24
355
"Hydrologic Simulation Program-Fortran" and "nutrients"
191
9
1110
"Loading Simulation Program C" and "nutrients"
2
1
6
"The Long-Term Hydrologic Impact Assessment" and "nutrients"
27
3
120
"NonPoint Source Pollution and Erosion Comparison Tool" and
"nutrients"
8
0
85
"Open NonPoint Source Pollution and Erosion Comparison Tool"
and "nutrients"
1
0
2
"Source Loading and Management Model" and "nutrients"
8
0
196
"Soil and Water Assessment Tool" and "nutrients"
1040
336
7040
"Stormwater Management Model" and "nutrients"
33
1
563
"Watershed Assessment Model" and "nutrients"
15
6
158
"Watershed Analysis Risk Management Frame" and "nutrients"
0
0
2
"Watershed Modeling System" and "nutrients"
25
1
264
Table A3. Number of Literature Records in Mixing Models
Keywords
ScienceDirect
Web of Science
Google Scholar
"VISJET" and "nutrient"
4
0
24
"VISJET" and "effluent"
17
6
84
"Visual Plumes" and "nutrient"
11
0
68
"Visual Plumes" and "effluent"
31
2
105
"CCHE2D/3D-Chem" and "nutrient"
0
0
0
"CCHE2D/3D-Chem" and "effluent"
0
0
0
"CORMIX" and "nutrient"
10
0
207
"CORMIX" and "effluent"
44
10
401
A2
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Table A4. Number of Literature Records in Surface Water Quality Models
Keywords
ScienceDirect
Web of Science
Google Scholar
"CE-QUAL-RIV1" and "nutrients"
9
0
124
"CCHE3D-WQ" and "nutrients"
1
2
7
"CE-QUAL-W2" and "nutrients"
95
26
1210
"CE-QUAL-ICM" and "nutrients"
49
5
466
"Environmental Fluid Dynamics Code" and "nutrients"
115
18
601
"EPD-RIV1" and "nutrients"
2
0
50
"HEC-RAS" and "nutrients"
115
5
1310
"MIKE-11" and "nutrients"
66
7
809
"QUAL2KW" and "nutrients"
20
4
227
"BATHTUB" and "nutrients"
354
6
5030
"Hydrological Simulation Program - FORTRAN" and "nutrients"
191
23
1590
"WASP" and "nutrients"
92
12
894
Table A5. Number of Literature Records in Groundwater Quality Models
Keywords
ScienceDirect
Web of Science
Google Scholar
"ANALGWST" and "nutrients"
0
0
1
"BIOMOC" and "nutrients"
18
1
71
"HST3D" and "nutrients"
17
0
70
"MT3D" and "nutrients"
51
1
527
"MODFLOW" and "nutrients"
370
13
3220
"SEAWAT" and "nutrients"
55
1
405
"PHAST" and "nutrients"
194
0
1030
"SUTRA" and "nutrients"
133
0
2750
ScienceDirect and Web of Science were investigated further to filter relevant search results. Literature with PHAST
and SUTRA words are also popular in other fields, such as health. This makes it difficult to search for PHAST and
SUTRA literature relevant to the topic of this report. Search engines also gathered literature when a model is either:
• Cited in the literature
• Described in a model review paper
• Applied to support a component of a study
• Fully implemented to solve a given problem
Based on the search results above, the populated literature does not necessarily indicate model applications.
These results only indicate instances of models mentioned in the literature and it is impossible to draw a conclusion
to answer the original case study search goals. Therefore, we decided to discuss the three most popular models for
each category.
A3
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oEPA
United States
Environmental Protection
Agency
Office of Research and Development
Washington, DC 20460
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