A Review of Watershed and Water Quality Tools for Nutrient Fate and Transport

EPA 600/R-19/232 | December 2019 | www.epa.gov/research

Office of Research and Development Center for Environmental Solutions & Emergency Response | Groundwater Characterization & Remediation Division 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 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,” (QA ID #: G-GWERD- 0031787-QP-1-1), 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 3.01d.

ii 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

iii Acronyms

AGNPS Agricultural NonPoint Source Pollution NCCHE National Center for Computational Model Hydroscience and Engineering

AGWA Automated Geospatial Watershed NH4 Ammonium Assessment Tool NO2 Nitrite AnnAGNPS Annualized Agricultural NonPoint Source Pollution Model NO3 Nitrate BASINS Better Assessment Science Integrating NOAA National Oceanic and Atmospheric Point and Nonpoint Sources Administration BMPs Best Management Practices NPS NonPoint Source BOD Biological Oxygen Demand N-SPECT NonPoint Source Pollution and Erosion CAT Climate Assessment Tool Comparison Tool CEAM Center Exposure Assessment Models OpenNSPECT Open NonPoint Source Pollution and Erosion Comparison Tool CORMIX Cornell Mixing Zone Expert System P Phosphorus CWA Clean Water Act PLOAD Pollutant Loading Estimator DEM Digital Elevation Model PO4 Phosphate DO Dissolved Oxygen RHEM Rangeland Hydrology and Erosion Model DOC Dissolved Organic Carbon RUSLE Revised Universal Soil Loss Equation EAAMOD Everglades Agricultural Area Model SCS-CN Soil Conservation Service Curve Number ECM Export Coefficient Model SLAMM Source Loading and Management Model EFDC Environmental Fluid Dynamics Code SUTRA Saturated-Unsaturated Transport EMC Event Mean Concentration SWAT Soil and Water Assessment Tool EPA Environmental Protection Agency SWET Soil and Water Engineering Technology, GenScn GENeration and Analysis of Model Inc. Simulation SCeNarios SWMM Stormwater Management Model GEPD Georgia Environmental Protection Division TKN Total Kjeldahl Nitrogen GIS Geographic Information System TMDL Total Maximum Daily Load GLEAMS Groundwater Loading Effects of Agricultural Management Systems TN Total Nitrogen GWLF Generalized Watershed Loading Function TP Total Phosphorus HEC-RAS Hydrologic Engineering Center’s River TSS Total Suspended Solids Analysis System USACE United States Army Corps of Engineers HRU Hydrologic Response Units USDA-ARS United States Department of Agriculture - HSPF Hydrologic Simulation Program - Fortran Agricultural Research Service HST3D Heat- and Solute-Transport Program USGS United States Geological Survey HUSLE Hydro-geomorphic Universal Soil Loss USLE Universal Soil Loss Equation Equation VP Visual Plume KINEROS2 Kinematic Runoff and Erosion 2 WAM Watershed Assessment Model LID Low Impact Development WARMF Watershed Analysis Risk Management LSPC Loading Simulation Program Frame L-THIA The Long-Term Hydrologic Impact WASP Water Quality Analysis Simulation Program Assessment WDMUtil Watershed Data Management Utility MUSLE Modified Universal Soil Loss Equation WMS Watershed Modeling System N Nitrogen WQM Water Quality Management

iv 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, database, 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 commonly 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. 1 2.0 Background 2.1 Overview of Water Quality Management Major activities in water quality management (WQM) include adopting water quality standards, monitoring and assessing 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 priority 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 assimilative 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 standards.

TMDL action plans are implemented to achieve the intended water quality improvements. Pollution load is controlled 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 preferred 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 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 difficult to explain through the observational approaches alone. Thus, models can help us better understand the complex 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 factors 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.

3 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 Represented Intended Use Environment of Models Processes Watershed 14 Delivery mechanisms To identify pollution Watershed Loading of pollution load sources, simulate from land surface to processes, and surface water calculate the loading Mixing 4 Physical mixing and To analyze water Surface water near dilution of pollutants quality condition in discharge location in receiving water the mixing zone Surface Water 12 Transport To analyze surface Surface water mechanisms and water response to transformation point and nonpoint of pollutants in source pollution load receiving water Groundwater 8 Pollutants fate To assess solute Groundwater and transport in contaminant fate in the subsurface the groundwater environment

4 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 agriculture, 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, erosion 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 equation 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 component in most watershed loading models. A water balance equation in a closed system can be described as equation 1 (Todd and Mays, 2005): (Eq 1)

Where R is runoff, P is precipitation, ET is evapotranspiration, ΔS is a change in soil water or groundwater.

5 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 primarily considers three factors: the rainfall, soil infiltration, and hydrologic soil group. CN method is applied to calculate direct runoff from a single-event rainfall.

if (P – Ia) ≤ 0, then Q = 0 (Eq 2)

(Eq 3)

(Eq 4)

Where, Q 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 evapotranspiration. The basic form of the Penman-Monteith method is expressed as Equation 5 (Monteith, 1965):

(Eq 5)

Where λE is latent heat flux of vaporization (MJ/m2d), λ is the latent heat of vaporization (MJ/kg), Δ is a slope 2 2 of the saturated vapor pressure curve (kPa/°C), Rn is net radiance flux (MJ/m d), G is soil heat flux (MJ/m d),

usually difficult to measure, γ is Psychrometric constant (γ ≈ 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:

(Eq 6)

Where Ea is daily potential evapotranspiration (mm/d), λ is the latent heat of vaporization (MJ/kg), α is a model coefficient, s is the slope of the saturation vapor density curve (kPa/°C), γ is the Psychrometric constant 2 2 (kPa/°C), Rn is net radiation (MJ/m d), and G is ground heat flux (MJ/m d).

6 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):

(Eq 7)

Where f(t) is infiltration rate for time t (mm/hr), Ke is effective hydraulic conductivity, ψ is wetting front matric

potential (mm), Δθ is a variation of soil water content, f(t) is cumulative infiltration (mm).

Horton’s method (Horton, 1933): (Eq 8)

Where ft is the infiltration rate at time t, fo 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.

7 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 average annual soil erosion throughout the world for over 50 years.

(Eq 9)

Where, A is average annual soil loss (t/a), R is rainfall erosivity index, K is soil erodibility factor, LS is a topographic 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 assessment. 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:

(Eq 10)

Where Y is sediment yield (ton/ha), X is the energy factor, EK is soil erodibility factor, CVF is a crop management 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: (Eq 11)

Where Q is runoff volume (mm), qp is the peak runoff rate (mm/hr), Wa is the watershed area (ha). Q can be

calculated by the SCS-CN method. qp is calculated by the rational method expressed as equation 12:

(Eq 12)

Where q is peak flow rate, C is the runoff coefficient representing watershed characteristics, i is rainfall intensity for the watershed’s time of concentration, A is the watershed area.

8 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 integration, 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):

(Eq 13)

Where EMC is event mean concentration (mg/L), V is total runoff volume per event (L), Vi is runoff volume

proportional to the flow rate at the time i, Ci is pollutant concentration at sample time i and n is a total number 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 defined as Equation 14 (Fei Dong et at., 2017):

(Eq 14)

Where Load is the annual loss of nutrients (kg/yr), Ei is the export coefficient for the nutrient source i 2 2 (kg/km ·year), Ai is the area occupied by land-use type i (km ), Ii 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.

9 AGNPS/AnnAGNPS 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, sediment, 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 transport, 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 simplification 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 quality. 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).

10 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 extension 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 potential sediment or pollution source areas and generate alternative future land-use/cover scenarios and compare 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 provides 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.

11 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 plugins to 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 limitation of BASINS is a steep learning curve because it involves a lot of watershed science theories and technical knowledge.

12 GWLF GWLF (Generalized Watershed Loading Function) was developed by Haith & Shoemaker (1987). GWLF version 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 streamflow 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 complex 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.

13 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 supporting 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 assess 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-water 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 reservoirs. 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 urbanization 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 calibration. 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).

14 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 download 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) algorithm. 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 transformation 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 components 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 system. 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-groundwater interactions.

15 L-THIA L-THIA (Long-Term Hydrologic Impact Assessment), developed by Purdue University, was initially implemented 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 http://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 runoff 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 runoff 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 operate 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.

16 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 erosion 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 coefficients method to estimate pollutant flux, and applies RUSLE and MULSE to calculate erosion rates and sediment 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 pollutant 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, erosion, 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.

17 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 download WinSLAMM from https://www.usgs.gov/centers/wisconsin-water-science-center/science/slamm?qt- 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 sources 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.

18 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 https://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 management 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 impacts 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.

19 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 impervious 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, hydraulic 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.

20 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: http://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 phosphorus 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 hydrologic, 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.

21 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 developing 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 module, 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 calculate 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 variables consist of temperature, pH, major cations and anions, total dissolved solids, ammonia (NH4), nitrate

(NO3), phosphate (PO4), 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 drainage, 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, despite 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).

22 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 software 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-introduction. 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 spatiotemporal 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, automated/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. et al., 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 generated 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.

23 3.2 Mixing Models Continuous or instantaneous discharge of effluent from point sources to surface water is subjected to physical mixing (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 water, 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 diffusion. 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.

(Eq 15)

Where q is the flow field property (flow rate, temperature, density, or mass), u is the rate of change, and u. ∇ is the operator applied to each flow property change. For a three-dimensional space, the operator is represented by Equation 16. (Eq 16)

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 constituent 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). (Eq 17)

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).

(Eq 18)

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 Dy is the lateral diffusion coefficient.

24 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 developed 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 viscosity, 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.

25 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 surface 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 currently 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 outfalls 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 pollutant type (conservative or non-conservative), concentration, coefficient of decay for non-conservative pollutants, and temperature. The primary data required from ambient water conditions are background concentration, 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 modification 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 geometrics, and ambient conditions.

26 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 locator (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 discharge through tributary channels. The outfall geometry in the PDSW simulator is approximated to a rectangular 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 characteristics, 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 Submerged (single and 3D Model for Windows multiport) outfall NRFIELD Near-field Multiport (4 or more ports) 3D FRFIELD Far-field Submerged or surface 2D discharge UM3 Three-Dimensional Updated Submerged (single and 3D Merge multiport) outfall PDSW Prych, Davis, Shirazi Model Surface discharge 3D for Windows DOS PLUMES DOS operating system- Submerged (single and 2D based Plumes multiport)

27 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):

(Eq 19)

Where ρ is water density, ρT is pure water density as a function of temperature T, ΔρS is the change of water density related to salinity S, ΔρC 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):

(Eq 20)

Water quality is affected and controlled by water hydrodynamic processes, including its physical, chemical, biological, 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):

(Eq 21)

Where ρ is water density, v is velocity vector, and ∇ 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.

28 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):

(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, Ky, Kz are turbulent diffusive coefficient in x, y 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 discharged to surface water in various forms. Some forms of nutrients (ammonia and nitrate) are consumed by phytoplankton (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):

(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 models 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.

29 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 program 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.

30 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 conventional 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 https://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 carbon, nitrogen, phosphorus, and oxygen cycles. It can be used to describe physical factors governing biogeochemical 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 using 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-RIV1 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-RIV1 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- RIV1 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/riv1info.html. The program is supported in Windows operating systems.

CE-QUAL-RIV1 is a one-dimensional model developed to simulate twelve water quality variables, which include 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-RIV1 model, vertical and lateral water quality variation in a riverine environment is assumed insignificant when compared to the longitudinal.

The key inputs for CE-QUAL-RIV1 simulator are an initial concentration of water constituents, flow, meteorological 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.

31 CE-QUAL-W2 CE-QUAL-W2 was developed at the Hydraulic and Environmental laboratory of the USACE WES by modifying 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 hydrodynamic 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/w2/. 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 temperature. 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 parameters (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 module 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 calibrate 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.

32 EPD-RIV1 EPD-RIV1 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-RIV1. EPD-RIV1 consists of the hydrodynamic (RIV1H) and water quality (RIV1Q) models. The program is currently maintained by Georgia EPD. The software and documentation are available free of charge from Georgia EPD page at http://epdsoftware.wileng. com/. The software is supported by Windows operating systems.

EPD-RIV1 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 module can simulate the interaction of 16 water quality state variables, including 7 nutrient variables (nitrogenous biochemical oxygen demand, organic nitrogen, ammonia, nitrate, nitrite, organic phosphorus, phosphates, and algae).

To predict water quality state variables, the hydrodynamic model runs first, then the results are linked to the water quality module. EPD-RIV1 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 maintained 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 supported 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, ammonia, 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 nutrient 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, atmospheric data, and rate constants for nutrients.

33 HSPF The Hydrological Simulation Program Fortran (HSPF) is a comprehensive model applicable to watershed loading 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 water 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 https://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 groundwater, 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-11. 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 simulate 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.

34 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 https://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 component 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 several 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 https:// 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 versions 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, dissolved 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-dimensional 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 parameters, and chemical constants.

35 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 processes before it reaches the aquifer, (2) contaminants in the porous media move very slowly and transit time estimation 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 contaminant transport.

Despite numerous factors controlling contaminant fate, groundwater models represent only relevant transformation and transport mechanisms (Bear and Cheng, 2010). The movement of dissolved contaminants in groundwater 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 represented by Equation 24 (Whitaker, 1986).

(Eq 24)

Where Q 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).

(Eq 25)

Where K is the hydraulic conductivity along the x, y, z domain space, Q is the water flux store change from

the source or sink, and Ss is a specific storage coefficient representing the water released from porous media storage.

36 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 reaction 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.

(Eq 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.

(Eq 27)

Where K and Ki are the denitrification rate constants for nitrate and its transformation forms (nitrite, nitrous

oxide, and nitrogen gas), C and Ci 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 groundwater 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.

37 ANALGWST ANALGWST is a suite of programs developed at the USGS in 1990 to simulate solute transport in groundwater (Wexler, 1992). Firstly, the individual programs are one-dimensional solute transport in finite or semi-infinite 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 solute 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_wrdapp?biomoc. The software 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 contaminant 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.

38 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 saturated 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 particularly 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 solute 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 https://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 transformation (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.

39 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/gwsoftware/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 information for technical support are available free of charge from the USGS page at https://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 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 functions and the most recent modification was released as version 3.4.0 in 2017. The software is currently maintained 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 freshwater 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 transport, 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 simulate heat and multiple-solute transport. SutraPrep and SutraPlot are SUTRA pre- and post-processing packages. 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 https://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 environment. 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 concentration, 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 condition can be modeled for the saturated or saturated-unsaturated system.

41 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 represent 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 application. 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 watershed 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 development 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 watershed model in the world, the Stanford Watershed Model, developed in the 1960s. Finally, SWAT and HSPF have active user communities.

Figure 1. Instances of watershed loading model records in the literature (May 2019). 42 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 summary 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 accuracy 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.

43 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.

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 environment (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 variations 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 constituents 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 mixing analysis.

44 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 example, 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 estimation 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-Fernández 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 4.3 Surface Water Quality Models Surface water quality models reported here have been applied for a long time in water quality management programs. 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 literature (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.

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 riverine 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.

46 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 nutrient 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 phosphate 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 models unsuitable for a site scale mixing analysis.

47 4.4 Groundwater Quality Models Groundwater models have been applied to simulate the fate and transport of contaminants in a subsurface environment. 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 investigation, 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.

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 evaluating 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 selenium 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 variety 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 environment.

48 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 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 problem 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 understanding 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 water 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 guidance 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 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, temporal 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 compared based on selected features (Table 3).

Table 3. Comparison of model characteristics for nutrient fate and transport simulation

Water quality Resolution Type Model Processes Environment Availability State variables Spatial Temporal HSPF Dissolved oxygen, A few Long-term Flow, Rural or urban Public BOD, Pesticides, acres to a continuous Sediment watershed Fecal coliforms, large river dynamic detachment Sediment, basin and transport, Nitrite-nitrate, Nutrient fate Organic Nitrogen, and transport Orthophosphate, Organic Phosphorus, Phytoplankton LSPC Sediment, No preset No Flow, Rural or urban Public Nutrients, limit inherent Sediment, watershed Dissolved Oxygen for the limit for General water watershed temporal quality size resolution SWMM TSS, BOD, COD, From Single Pollutant Urban Public TP, Soluble P, TKN, single events or a buildup, watershed

NO2/NO3, Total lots up to continuous Washoff, Non- Cu, Total Pb, Total hundreds dynamic runoff loads

Watershed Loading Model Watershed Zn of acres simulation AGNPS Sediment, Total No Daily Runoff, Rural Public N, Total P, COD, limitation time step, Sediment, watershed organic carbon for Continuous Soil erosion, watershed simulation Nutrients, size Pesticide AGWA N and P simulated From one From event Runoff, Rural Public through SWAT hectare to or daily to Sediment, watershed sub-model thousands yearly Nutrient fate integrated into of square and transport AGWA kilometers

51 Table 3. (cont.) Comparison of model characteristics for nutrient fate and transport simulation

Water quality Resolution Type Model Processes Environment Availability State variables Spatial Temporal GWLF N, P in Mid-range Monthly Runoff, Rural or urban Public surface water, watersheds sediment Sediment, watershed groundwater, and and Nutrient sediment pollution loading output with daily step WMS The same Flexible Continuous Flow, Sediment Rural or urban Private processes watershed simulation detachment watershed simulated with size and transport, HSPF Nutrient fate and transport WARMF N, P, TSS, DO, Flexible for Daily Flow, Soil Urban Public Ammonia, Nitrate, watershed continuous erosion and watershed Coliform bacteria, size, simulation sediment, 3 algal species, typically Nutrient

Periphyton, pH, resolution uptake, CO2 Phosphate, Iron, is 11-digit exchange Zinc, Manganese, HRU set by Copper the USGS WAM N, P, TSS, BOD A small to Daily Flow, Erosion/ Rural or urban Public/ medium continuous sediment watershed Private watershed simulation yield, Nutrient transport/ Watershed Loading Model Watershed Plant nutrients SLAMM TSS, Total Large Stormwater Flow, Urban Private Dissolved Solids, watershed runoff Particulate watershed COD, TP, Filtered including simulation accumulation, P, TKN, Cu, Pb, Zn, urban Particulate

NO3 + NO2, Fecal areas washoff, coliforms Pollutant associations, Street cleaning N-SPECT/ N, P, Lead, Zinc Medium- Long-term Runoff, Coastal and Public Open- to-large continuous Sediment, near the NSECT watersheds simulation Soil erosion, noncoastal Pollutant area loads and concentrations

52 Table 3. (cont.) Comparison of model characteristics for nutrient fate and transport simulation

Water quality Resolution Type Model Processes Environment Availability State variables Spatial Temporal L-THIA TN, TP, Dissolved A large Long-term Runoff, Soil Urban and Public P, TSS, Dissolved watershed simulation erosion and suburban Solids, Total Lead, such as sediment areas delg Mo delg Total Copper, Great Lakes yield, Total Zinc, Total Watershed Pollutant Chromium, Total loads Nickel, BOD Loadin SWAT Sediment, N, From a Long-term Surface runoff, Rural Public P, Pesticides, small continuous Groundwater, watershed Bacteria, Carbon watershed simulation Nutrient

Watershed to the entire with a sub- loading and European daily time transportation continent step CORMIX Effluents with 2D or 3D Steady- Plume Near-field and Private conservative, visualization state trajectory and far-field non-conservative, dilution heated, brine discharge or suspended sediment constituents VISJET Multiple 3D Steady- Path and Near-field Private

Mixing constituents visualization state mixing of from buoyant buoyant wastewater jets, effluent discharges discharge Visual Multiple 2D or 3D Steady- Initial dilution Near-field and Public Plumes constituents state of plume far-field from wastewater discharges

53 Table 3. (cont.) Comparison of model characteristics for nutrient fate and transport simulation

Water quality Resolution Type Model Processes Environment Availability State variables Spatial Temporal BATHTUB Chlorophyll-a, 1D Steady- Water and Lake Public eutrophication state nutrient mass response to nitrogen and phosphorus CCHE3D Ammonia 2D or 3D Steady and Flow, transport Rivers, lakes, Private nitrogen, nitrate dynamic estuaries and nitrogen, state oceans inorganic phosphorus, phytoplankton, organic nitrogen, and organic phosphorus CE-QUAL- Nitrogenous 1D Steady and Flow, transport River Public RIV1 biochemical dynamic oxygen demand, state organic nitrogen, ammonia nitrogen, nitrate, nitrite nitrogen, organic phosphorus,

Surface Water Quality Water Surface phosphates, and algae CE-QUAL- Nitrogen and 1D, 2D, or Steady and Transport River, lake, Public ICM phosphorus 3D dynamic estuary biogeochemical state cycles CE- Ammonia, nitrate, 2D Steady and Flow, transport River, estuary Public QUAL-W2 nitrite, organic dynamic nitrogen and state phosphorus in dissolved and particulate forms, algae EFDC Nitrogen and 1D, 2D, or Steady and Flow, transport River, lake, Public phosphorus cycles 3D dynamic estuary, ocean in eutrophication state processes

54 Table 3. (cont.) Comparison of model characteristics for nutrient fate and transport simulation

Water quality Resolution Type Model Processes Environment Availability State variables Spatial Temporal EPD-RIV1 Nitrogenous 1D Steady and Flow, River Public biochemical dynamic transport oxygen demand, state organic nitrogen, ammonia nitrogen, nitrate, nitrite nitrogen, organic phosphorus, phosphates, and algae HEC-RAS Orthophosphate, Flow 2D, Steady- Flow, River Public organic transport state transport phosphorus, 1D dissolved ammonia, nitrate, nitrite, and organic nitrogen HSPF Ammonia, 1D Steady and Flow, River, Public nitrite-nitrate, dynamic transport watershed organic nitrogen, state orthophosphate, and organic phosphorus MIKE-11 Nitrogen and 1D Steady and Flow, River Private phosphorus dynamic transport Surface Water Quality Water Surface concentration and state their cycles in the eutrophication process QUAL2KW Total Kjeldahl 1D Dynamic Flow, River Public nitrogen, State transport ammonia, nitrate, nitrite, total phosphorus, and orthophosphate WASP Ammonia, 1D, 2D, or Dynamic Transport River, lake, Public nitrogen, nitrate 3D State estuary nitrogen, inorganic phosphorus, phytoplankton, organic nitrogen, and organic phosphorus

55 Table 3. (cont.) Comparison of model characteristics for nutrient fate and transport simulation

Water quality Resolution Type Model Processes Environment Availability State variables Spatial Temporal ANALG Multiple species 1D, 2D, or Steady state Transport, Unsaturated Public WST solutes 3D chemical and saturated transformation groundwater flow BIOMOC Multiple solute 1D, 2D, or Steady and Flow, trans- Groundwater Public species 3D Transient port, biotrans- State formation HST3D Multiple solute 3D Steady and Flow, transport Saturated Public species and heat Transient groundwater State flow MT3D Multiple solute 3D Steady and Transport, Unsaturated Public species Transient biological and and State geochemical groundwater transformation flow, solute exchange with streams and lakes MODFLOW Multi solute 3D Steady and Flow, transport Saturated Public -GWT species Transient groundwater Groundwater Quality Groundwater State flow SEAWAT Multiple species 3D Steady and Flow, transport Saturated Public solute and heat transient groundwater state flow PHAST Multicomponent 3D Steady and Flow, solute Saturated Public reactive solutes transient transport, groundwater state multicomponent flow geochemical reactions SUTRA Multiple dissolved 2D or 3D Steady and Flow, transport Unsaturated Public species transient and saturated state groundwater flow

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 monitoring 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 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 effectiveness 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 relevant 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 selection criteria should be primarily based on model suitability to the nature of the water quality problem. Time, resources needed, as well as familiarity with the model, which often dictates model selection, should be secondary considerations.

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64 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 relatively 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 A1.

Table A1. 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”

A1 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 15 4 1 “nutrients” “Automated Geospatial Watershed Assessment Tool” and 5 0 1 “nutrients” “Bett er Assessment Science Integrati ng Point and 37 3 2 Nonpoint Sources” and “nutrients” “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 80 85 “nutrients” “Open NonPoint Source Pollution and Erosion Comparison Tool” 1 0 2 and “nutrients” “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 “eﬄ uent” 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 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 Office of Research and Development Washington, DC 20460