Gaps in Water Quality Modeling of Hydrologic Systems

Lucas, Lisa V.; Brown, Craig J.; Robertson, Dale M.; Baker, Nancy T.; Johnson, Zachary C.; Green, Christopher T.; Cho, Se Jong; Erickson, Melinda L.; Gellis, Allen C.; Jasmann, Jeramy R.; Knowles, Noah; Prein, Andreas F.; Stackelberg, Paul E.

doi:10.3390/w17081200

Open AccessReview

Gaps in Water Quality Modeling of Hydrologic Systems

by

Lisa V. Lucas

^1,*

,

Craig J. Brown

²,

Dale M. Robertson

³,

Nancy T. Baker

⁴,

Zachary C. Johnson

⁵

,

Christopher T. Green

¹,

Se Jong Cho

⁶,

Melinda L. Erickson

⁷

,

Allen C. Gellis

⁶,

Jeramy R. Jasmann

⁸

,

Noah Knowles

¹,

Andreas F. Prein

^9,10

and

Paul E. Stackelberg

¹¹

¹

Integrated Modeling and Prediction Division, Water Resources Mission Area, U.S. Geological Survey, P.O. Box 158, Moffett Field, CA 94035, USA

²

New England Water Science Center, U.S. Geological Survey, 339 Main Street, East Hartford, CT 06108, USA

³

Upper Midwest Water Science Center, U.S. Geological Survey, 1 Gifford Pinchot Drive, Madison, WI 53726, USA

⁴

Ohio-Kentucky-Indiana Water Science Center, U.S. Geological Survey, 5957 Lakeside Boulevard, Indianapolis, IN 46278, USA

⁵

Washington Water Science Center, U.S. Geological Survey, 934 Broadway, Suite 300, Tacoma, WA 98402, USA

⁶

Earth System Processes Division, Water Resources Mission Area, U.S. Geological Survey, 12201 Sunrise Valley Dr., Reston, VA 20192, USA

⁷

Upper Midwest Water Science Center, U.S. Geological Survey, 2280 Woodale Drive, Mounds View, MN 55112, USA

⁸

Laboratory and Analytical Services Division, Water Resources Mission Area, U.S. Geological Survey, 3215 Marine St., Suite E127, Boulder, CO 80303, USA

⁹

Institute for Atmospheric and Climate Science, ETH Zürich, 8092 Zurich, Switzerland

¹⁰

Mesoscale & Microscale Meteorology Laboratory, NSF National Center for Atmospheric Research, 3090 Center Green Drive, Boulder, CO 80301, USA

¹¹

Earth System Processes Division, Water Resources Mission Area, U.S. Geological Survey, 425 Jordan Road, Troy, NY 12180, USA

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^*

Author to whom correspondence should be addressed.

Water 2025, 17(8), 1200; https://doi.org/10.3390/w17081200

Submission received: 29 January 2025 / Accepted: 28 February 2025 / Published: 16 April 2025

(This article belongs to the Section Hydrology)

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Abstract

:

This review assesses gaps in water quality modeling, emphasizing opportunities to improve next-generation models that are essential for managing water quality and are integral to meeting goals of scientific and management agencies. In particular, this paper identifies gaps in water quality modeling capabilities that, if addressed, could support assessments, projections, and evaluations of management alternatives to support ecosystem health and human beneficial use of water resources. It covers surface water and groundwater quality modeling, dealing with a broad suite of physical, biogeochemical, and anthropogenic drivers. Modeling capabilities for six constituents (or constituent categories) are explored: water temperature, salinity, nutrients, sediment, geogenic constituents, and contaminants of emerging concern. Each constituent was followed through the coupled atmospheric-hydrologic-human system, with prominent modeling gaps described for a diverse array of relevant inputs, processes, and human activities. Commonly identified modeling gaps primarily fall under three types: (1) model gaps, (2) data gaps, and (3) process understanding gaps. In addition to potential solutions for addressing specific individual modeling limitations, some broad approaches (e.g., enhanced data collection and compilation, machine learning, reduced-complexity modeling) are discussed as ways forward for tackling multiple gaps. This gap analysis establishes a framework of diverse approaches that may support improved process representation, scale, and accuracy of models for a wide range of water quality issues.

Keywords:

water quality; water-quality; model; surface water; groundwater; temperature; salinity; nutrient; sediment; geogenic; contaminants of emerging concern

1. Introduction

1.1. Background

Water is one of the world’s most essential natural resources. Preserving and protecting water resources not only requires an assessment and understanding of water quantity but also of water quality. This necessitates quantification of existing water quality, understanding of the factors affecting water quality, and development of the ability to forecast water quality changes in the future. Water quality models represent some of the primary tools to address societal and economic effects of water quality degradation; manage water availability for beneficial use and ecosystem health; understand sources, transport, and processing of water quality constituents in the environment; and forecast the response of water quality to various changes in environmental conditions and anthropogenic forcings [1,2,3,4,5,6,7]. Substantial gaps remain, however, in understanding water quality processes and in the application of modeling tools to protect water resources effectively.

This review assesses gaps in water quality modeling, emphasizing opportunities to improve next-generation models that may support water quality management and are integral to goals of scientific and management agencies [8,9,10]. In particular, this paper identifies gaps in water quality modeling capabilities that, if addressed, could support assessments, projections, and evaluation of management alternatives to support ecosystem health and human beneficial use of water resources [9,10]. This team of authors was assembled by the U.S. Geological Survey (USGS) to assess current capabilities and gaps related to modeling of key water quality constituents, parameters, and properties (hereafter “constituents”) across hydrologic systems. The initial motivation was to support planning and development of next-generation water quality models to better enable water availability assessments and projections, as well as evaluation of management alternatives to support ecosystem health and human beneficial uses in the United States (U.S.). However, our findings apply more broadly, assessing surface water and groundwater quality modeling capabilities in relation to a broad suite of physical and biogeochemical drivers and natural and anthropogenic inputs, processes, and activities, with timescales ranging from days to decades and spatial scales ranging from local to continental.

Many developers and practitioners consider “water quality models” as quantitative tools that relate external loads to water quality responses in receiving water bodies, a definition linked with the field’s origin in the need to determine waste-load allocations [11,12]. In this paper, the term “water quality models” (or “modeling”) is used in a subtly different, and perhaps broader, sense: (the use of) quantitative tools that describe the dynamics of water quality constituents through hydrologic systems, incorporating the effects of sources, transport, and transformations on concentrations. Despite the difference in definitions, the modeling tools discussed herein can be (and in many cases are) implemented to perform “water quality modeling” in the more traditional sense.

To holistically model, understand, and manage water quality—and more broadly, water availability—we consider not only natural influences but also societal uses of water and how those uses influence water quality. A critical aspect of this paper is its focus on capabilities for modeling the quality of water as a resource supporting and affected by a diverse array of ecological and human beneficial uses. In 2015, human water use in the U.S. totaled 1.2 billion cubic meters per day (m³/d)—approximately the daily discharge of the Mississippi River at its mouth [13]—and was being used for thermoelectric power (41%, although just 3% was consumptive use due to once-through cooling), irrigation (37%), public supply (12%), domestic self-supply (1%), livestock and aquaculture (3%), and mining and industrial self-supply (6%) [14,15]. These uses also represent influences on water quality, quantity, and availability and are therefore considered in the assessment herein.

Several constituents in water pose problems for human uses and ecosystem function (see Table 1 for examples). At the same time, many natural and anthropogenic inputs, processes, and activities operating across the hydrologic system potentially alter the distributions and concentrations of constituents in water, sometimes to harmful levels (see Figure 1). Table 2 indicates which of these processes and activities (shown in Figure 1) influence specific constituents, emphasizing that the quality of water used by humans and ecosystems is controlled by a complex combination of natural and anthropogenic factors distributed in space and across hydrologic compartments. Figure 1 thus visually depicts the general framework within which we investigated the capabilities and gaps in modeling tools for describing the influence of an activity, process, or input on a constituent. It should be noted that coastal storms (e.g., hurricanes) are not listed explicitly in the 45 processes and activities in Figure 1 and Table 2; however, as is discussed in later sections, they influence many of those processes and activities, which in turn affect sources, mobilization, and distribution of constituents. In this review, modeling capabilities and gaps are examined for the following six key water quality constituents, or groups of constituents, which either directly or indirectly impact the suitability of water for human and ecological uses [16,17]: temperature, salinity, nutrients such as nitrogen and phosphorus, suspended sediment, geogenic constituents such as arsenic, selenium, and other trace elements, and contaminants of emerging concern (CECs). CECs can include chemicals that are truly new with little known about them, as well as legacy chemicals with renewed attention due to new information about occurrence, exposure pathways, or adverse health effects. Additionally, gaps are assessed for several key “cross-cutting” model-related capabilities influencing more than one of the water quality constituents considered herein.

Table 1. Water quality constituents that affect specific human and ecosystem uses and benefits. An X indicates that the constituent (column 1) affects specific human and ecosystem uses and benefits (top row). Boldface font is used for the six constituent categories that are the primary focus of this article. Bioactive CECs: biologically active contaminants of emerging concern. PFAS: per- and polyfluoroalkyl substances. ED Chemicals: endocrine-disrupting chemicals (e.g., natural and synthetic hormones). Household chemicals: chemicals found in consumer products and include chemicals such as bisphenol A, phthalates, 1,4-dioxane, surfactants, disinfectants, and flame retardants. “Other Industry” includes mining, oil and gas development, and manufacturing. Shell fishing and fin fishing are included in “Other Industry” and “Recreation”. “Recreation” includes fishing and hunting game species. Subsets of salinity and CECs are indicated with italics and with a dagger (†) or asterisk (*), respectively. Citations relevant to each row are provided in the footnote.

Constituent	Potable Drinking Water	Irrigation	Thermoelectric Cooling	Other Industry	Recreation	Ecosystem Health	Livestock	Aquaculture
Temperature ^a		X	X	X	X	X		X
Salinity ^b	X	X	X	X	X	X	X	X
Corrosivity ^c^†	X	X	X	X		X	X	X
Nutrients ^d	X	X		X	X	X	X	X
Sediment ^e	X	X	X	X	X	X	X	X
Geogenics (e.g., metals) ^f	X	X	X	X	X	X	X	X
Bioactive CECs ^g	X	X		X	X	X	X	X
Pathogens ^h*	X	X		X	X	X	X	X
Algal toxins ⁱ*	X	X		X	X	X	X	X
PFAS ^j*	X	X		X	X	X	X	X
Microplastics ^k*	X	X		X	X	X	X	X
Pesticides ^l*	X	X		X	X	X	X	X
ED Chemicals ^m*	X			X	X	X	X	X
Pharmaceuticals ⁿ*	X			X	X	X	X	X
Household Chemicals ^o*	X	X		X	X	X	X	X

^a [18,19,20]; ^b [16,17,21,22]; ^c [22,23,24,25,26]; ^d [17,27,28,29,30,31,32,33]; ^e [16,33,34,35]; ^f [21,27,35,36,37,38,39,40,41,42,43]; ^g [22,35,44,45,46,47,48,49,50,51,52,53,54]; ^h [22,49,50,55,56,57,58,59,60]; ⁱ [22,49,50,61,62,63,64,65,66,67]; ^j [22,44,49,50,51,68,69,70,71,72,73,74]; ^k [22,44,49,50,64,66,72,75,76,77,78,79,80,81,82,83,84,85,86,87,88]; ^l [17,22,45,49,50,52,83,86,87,89,90,91,92,93,94,95]; ^m [17,22,44,45,46,49,50,52,92,96,97,98]; ⁿ [17,22,44,45,46,49,50,52,99,100]; ^o [17,22,44,45,46,49,50,52,99,100,101].

Figure 1. Graphic depicts natural and anthropogenic inputs, processes, and activities (1–45) potentially affecting constituents of interest across the hydrologic system, which is divided into ten compartments (labeled I–X). Specific constituents affected by individual inputs, processes, and activities are indicated in Table 2. Detailed information regarding the availability of modeling capabilities for describing such process-constituent connections is presented in the companion data release [102].

1.2. Model Types

There are three broad types of models considered herein: process-based models, statistical models, and hybrid models. Process-based models (Table A1 in Appendix A) include mathematical representations of some or many of the individual processes mechanistically linking one or more response variables (effects) to one or more predictor variables (causes); such representations may be based on first principles (e.g., conservation of mass or momentum) and/or empirical relationships [152] (e.g., Monod kinetics). Process-based models are often applied at smaller spatial scales (e.g., ecosystem scale or less) where many of the factors affecting the individual processes can be described, although there are also global hydrologic models with simplified process representation [153] (see Section 4.2.4 herein for a discussion of “Reduced Complexity Models”). Advantages of process models include enhanced model transferability, interpretability, and the ability to support process understanding, ecosystem diagnosis, and process sensitivity analysis. However, particularly complex models can require many input parameters that are unknown for the situation of interest and are consequently determined through the process of model calibration, potentially leading to “equifinality” [154].

While process-based models are more effective at helping us understand how and why driving processes control water quality, statistical (also known as “empirical” or “data driven”) models (Table A2) can be particularly useful for identifying driving processes and where those processes are most important. Statistical models are non-mechanistic mathematical representations of observed data. Typically, there is either a continuous or categorical outcome that is to be predicted using a set of features (predictor variables). Linear and logistic regression methods are effective for making these predictions when there are linear relations between the outcome and set of features. Machine learning (ML; see Table A2) approaches, such as tree-based models (e.g., random forest) and neural network models, can be more effective for making predictions when complex, non-linear relations exist between the outcome and set of features—as is often the case in large datasets representing heterogenous environmental phenomena [155]. Statistical models can provide uncertainty estimates around model outputs; however, they do not represent processes mechanistically as in process-based models.

As an alternative to purely process-based or statistical models, hybrid models (Table A3) contain combinations of components from process models and statistical models and blend both their benefits and drawbacks. For example, statistical model features, structures, and fitting algorithms can incorporate information from process-based models to help constrain predictions in what is often referred to as a “hybrid” or “process-guided” modeling approach [156,157,158,159]. Because they typically strive for a more parsimonious mechanistic structure than process-based models, hybrid models often require less information about the factors driving changes in water quality. However, because less detailed information is needed for hybrid models, they can be applied over large spatial areas and still provide information on the specific processes that are incorporated into the models. In addition, hybrid ML-process models can sometimes make more accurate predictions (i.e., estimates, interpolations, and extrapolations), provided sufficient training data are available.

These three model delineations represent zones along a continuum of modeling types [160]. Each type of model can span a broad range of complexity, with the simplest models of any category sometimes termed “reduced complexity models”, or “RCMs” [161]. RCMs are predictive mathematical tools characterized by relatively simple model structure and parametrization requirements, a high degree of transparency, and the incorporation of a key set of critical processes, behaviors, or drivers [162,163]. The simplicity of these models can offer computational efficiency and circumvent the problem of model overparameterization (see more discussion of RCMs in Section 4.2.4).

1.3. Objective and Approach

The objective of this paper is to identify gaps and limitations in water quality modeling capabilities as they relate to water availability for human beneficial uses and ecosystem health. In order to identify modeling gaps, we first identified capabilities. Our assessment approach was to follow each constituent (or constituent group) of interest (temperature, salinity, nutrients, sediment, geogenic constituents (“geogenics”), and CECs; Table 3, left) through the coupled atmospheric-hydrologic-terrestrial-human system and, at each step, assess the availability of modeling capabilities that characterize the key inputs, processes, or activities affecting the constituent. Spatial domains in which water quality is of interest herein include inland waters (rivers, streams, watersheds, and lakes), the subsurface (saturated and unsaturated zones), and estuaries (italic items in Table 4), although processes influencing water quality in those domains may operate in, or provide a connection to, adjacent compartments (e.g., atmosphere, terrestrial, and coastal ocean; normal type items in Table 4). The schematic in Figure 1 provides a simple, generic depiction of many inputs, processes, and activities affecting constituent transport, transformations, distributions, and/or concentrations (numbers 1–45 in Figure 1) across the ten hydrologic “compartments” considered. Through the course of our assessment, it became evident that some model-related capabilities are relevant to more than one, or in some cases every, constituent under consideration. Such capabilities are what we have termed “cross-cutting” capabilities (Table 3, right). To streamline the ultimate discussion of modeling gaps for each constituent, we first discuss capabilities and gaps associated with those nine key cross-cutting topics.

Generally, there are three fundamental components to process-based (and some hybrid) water quality modeling, regardless of the hydrologic compartment of interest: (1) the physics of water movement (also known as hydrodynamics or hydraulics), (2) the transport of water quality constituents by the moving water (i.e., advection and/or dispersion), and (3) the sources, sinks, and transformations of reactive (i.e., non-conservative) constituents. A credible model of the flow physics (#1 above) is necessary to establish a solid foundation for the transport (#2 above) of constituents. Hydrodynamic models compute the physical information (e.g., velocities and/or discharges, water levels, and mixing or dispersion coefficients) that is used in the constituent transport equations to “move the constituent around”. Often, constituent reactions and transformations (#3 above) are added as extra terms to transport equations. In this paper, modeling capabilities addressing all three fundamental modeling components are addressed.

This paper is organized as follows. In Section 1, we provide relevant background, the motivation for this study, and introduce our approach. In Section 2, we describe the importance, existing capabilities, and gaps pertinent to nine cross-cutting areas. In Section 3, we describe for each constituent of interest examples of existing, widely used modeling capabilities and then focus on identifying gaps in modeling tools, data, or fundamental understanding that, if addressed, could help move modeling of that constituent forward. In both Section 2 and Section 3, the importance of individual modeling gaps is discussed, and opportunities for addressing those gaps are presented. In Section 4, we summarize common water quality modeling gaps identified in the foregoing sections, recognizing three primary categories, or “types”, into which the prominent gaps fall: modeling gaps (i.e., gaps in model code, incorporation of processes, computing resources, etc.), data gaps (e.g., limitations in the availability of data for model calibration, validation, or parameter specification), and process understanding gaps (i.e., limitations in our collective understanding of critical processes affecting water quality that in turn limit our ability to incorporate those processes into models). We then summarize broadly applicable approaches for moving water quality modeling forward and provide a few concluding remarks.

As mentioned above, the emphasis of this manuscript is on the identification of water quality modeling gaps and limitations, but identification of those gaps necessitated examination of a collection of models that are sufficiently representative of the state-of-the-art and state-of-the-science. Thus, our review of contemporary and representative modeling capabilities—presented in detail in a companion data release [102] and only briefly summarized in the text—is extensive, though non-exhaustive; that database of relevant model and data resources provides information on the principal models we considered in order to identify modeling gaps. The authors’ assessment of water quality modeling capabilities and gaps incorporated their own knowledge of and research on available modeling capabilities, consultation with colleagues who are experts in the individual fields discussed in Section 2 and Section 3, and extensive expert colleague review (see Acknowledgements). Moreover, the representativeness of our collection of models as “state-of-the-art” and “state-of-the-science” is supported by the considerable overlap between our collection and the models cited in water quality model reviews, compendia, and reports (e.g., [1,2,3,4,5,6,7,164,165,166,167]). The reader is referred to such works for more complete lists of available models, valuable model insight, and guidance on model selection or application. For the present purpose, models originating anywhere—in government, academia, non-governmental organizations, and private industry—are considered if they have been used to support understanding, prediction, or management of water quality problems. We emphasize models that are widely used, open source, and representative of the state-of-the-art; additionally, models that are published in the literature and/or for which documentation is easily available on the internet were considered. The authors acknowledge a potential bias in modeling resources cited related to the authors’ U.S. and/or USGS point of view. Moreover, process-based and hybrid models are emphasized in this gap analysis; in the discussion, ML approaches are discussed as a potential path toward filling gaps left by process-based and hybrid models.

Although the initial impetus of this gap analysis was to support planning and development of next-generation models for the U.S., many of the models considered are used around the globe; therefore, we expect our findings to transcend national boundaries. Our intention is that the gaps identified herein will highlight key areas for future research, data gathering, and model development for agencies, academia, institutes, and private industry to move the science, practice, and effectiveness of water quality modeling forward.

2. Cross-Cutting Modeling Capabilities and Gaps

This section describes capabilities and gaps associated with nine “cross-cutting” model-related needs for modeling water quality across the hydrologic system, with “cross-cutting” defined as having relevance to more than one constituent considered herein. Cross-cutting models may not be models of water quality per se but may represent foundationally necessary tools for modeling water quality in some part of the hydrologic system. First, brief overviews of the importance of these cross-cutting capabilities and summaries of existing representative tools are presented. Next, gaps for each cross-cutting need are discussed and summarized in a table. Each of the current section’s cross-cutting topics is associated with its own table in the companion data release [102], which provides detailed information on existing relevant modeling capabilities and resources. Numbers in parentheses refer to the numbered inputs, processes, and activities in Figure 1 and Table 2.

2.1. Meteorologic and Climatic Forcing

Accurate meteorological forcings are essential for modeling water quality since precipitation, air temperature, solar radiation, and winds strongly affect the transport of pollutants into water bodies, the rate of chemical and biological processes, and water circulation and mixing [168]. Meteorological and climatic forcings for simulations of hydrology, hydrodynamics, and water quality can come from three sources: (1) observations, (2) models, or (3) analyses that blend both [169].

While being the backbone of our understanding of the hydrologic cycle, observation based products are often subject to limitations in the length of the recorded time series, as well as the sparseness of station networks [170]. The lack of spatial coverage is particularly problematic in many mountain regions and the global south [171]. Additionally, only a limited number of variables are typically measured, making it difficult to close budgets and understand process interactions. Furthermore, interpolating station observations onto a grid introduces additional uncertainties, particularly for variables that are spatially inhomogeneous (e.g., precipitation) and in regions with strong climate gradients (e.g., mountains, coastlines) [172]. Some forcing datasets attempt to explicitly estimate the latter uncertainties by generating ensemble-based products, e.g., [173]. Another approach that largely improves the spatial accuracy of datasets is to merge multiple in-situ and remote sensing products to derive better estimates of forcing variables. The Multi-Radar Multi-Sensor (MRMS) dataset [174], for instance, blends multiple radar datasets with precipitation gauges to produce high spatio-temporal resolution precipitation estimates over the Contiguous U.S. (CONUS). However, such blended products typically have limited areal coverage and are often only available for recent time periods. Lastly, observations can have systematic biases, which are typically small for most variables but can become significant in some situations. A prominent example is precipitation under-catch, which can be up to 80% in snow-dominated and exposed locations [172,175]. For climate-change applications, observational datasets can be problematic due to inhomogeneities in their record that usually stem from changing observational methods (e.g., measurement sensors), station density, location of stations, or changes in the surroundings of stations (e.g., buildings close to stations) [176,177].

Model-based forcing datasets typically have complementary strengths and weaknesses compared to observation-based products. Models can provide continuous four-dimensional data of atmospheric states that are physically consistent. The major limitations of model-based forcing datasets are biases in the simulated fields, e.g., [178,179], and the coarse grid spacings that inhibit regional and local-scale analyses, e.g., [180]. These two limitations are partly related since resolving small-scale features in weather and climate models, such as thunderstorms, coastlines, and orography, can reduce systematic biases in forcing fields, e.g., [181]. However, kilometer-scale grid spacings or smaller are needed to realistically resolve land-surface features and relevant atmospheric processes, such as orographic precipitation and thunderstorms. Such simulations are computationally very expensive and currently only available for few regions globally, mostly focused on the U.S. and Europe. An example of such a dataset is the CONUS404 product that provides hourly three-dimensional (3-D) forcing data at a 4 km grid for the entire CONUS for the period September 1979 to close to 2023 [182,183]. However, even kilometer-scale models have systematic biases that can significantly affect hydrologic modeling studies. Bias correction methods are, therefore, frequently used to adjust the model output to observational fields, e.g., [184]. While these corrections are useful, they are based on the assumption that model biases are stationary and do not change under future climate conditions, which can deteriorate model-based forcing data for assessments of future climate, e.g., [185]. Additionally, such bias corrections might deteriorate the quality of high-resolution modeling output, particularly in regions with low observational density and high mountain regions where the skill of kilometer-scale models can outperform our ability to measure meteorological fields, e.g., precipitation [183,186]. Model output can also be statistically downscaled to an even higher resolution to, for example, better account for geographic effects on surface variables. This is frequently performed for near-surface temperature and surface pressure since both fields strongly vary with elevation [187], while downscaling fields that have a less clear dependency on topography, such as precipitation, is more difficult.

For modeling studies focusing on future climate impact assessments, forcings from modeling datasets are the only option. Raw or statistically downscaled data from the Sixth version of the Coupled Model Intercomparison Project (CMIP6) [180,188] are widely used since they provide global coverage and easy access. However, important hydrologic processes such as precipitation, evapotranspiration, or radiation are not well simulated in these models due to their coarse grid spacing. Regional modeling efforts such as the Coordinated Regional Downscaling Experiment (CORDEX) provide higher resolution data but with smaller ensemble sizes for many regions [189]. CORDEX simulations can improve the representation of regional processes, especially over complex topography, but frequently suffer from similar biases as global models [190,191]. Climate projections with kilometer-scale models are promising tools to improve long-standing model biases and provide more physically sound regional and local information, e.g., [181]. Such datasets are limited to small regions and single simulations but will become more widely accessible within the next five to ten years [183,192,193]. A summary of the relative strengths and weaknesses of these and other meteorological forcing datasets is shown in Figure 2.

Forcing datasets that blend observational and model data are becoming increasingly used since they can take advantage of the complementary strengths of both approaches. The most popular datasets in this category are reanalysis products such as MERRA-2 [203], the NCEP climate forecast system reanalysis [204], and ERA5 [201]. Reanalyses assimilate a vast amount of in situ and remote sensing observations into numerical weather prediction models, which helps to keep the modeled weather consistent with observations while being able to fill in gaps between observations or derive unobserved variables in a physically sound way. However, reanalyses ingest some of the limitations from observations and modeling, such as inhomogeneous time series due to changing observational information over time, e.g., [205,206], which makes their application for studies of future climate problematic. Reanalyses also suffer from model biases, particularly in areas with low observational densities, for variables that are not directly assimilated, and in representing regional and local-scale processes that cannot be well captured in coarse resolution models. Regional reanalyses are promising tools to improve model biases particularly on regional and local scales, but such datasets are not widely available yet [207,208].

An overview of the characteristics of widely used forcing datasets can be found in Table 1 within the companion data release [102]. Gaps and limitations with respect to meteorological forcing to drive water quality models are summarized in Table 5 herein.

2.2. Geochemical and Biogeochemical Modeling

The constituents of concern in water are affected by chemical, physical, and biological reactions in different ways as they pass through the hydrologic system, including by changes in temperature, pH, redox chemistry, and interactions with gases, solids, other waters, and biota. Water quality models can be used to assess and understand biogeochemical processes through simulations assuming thermodynamic equilibrium (thermodynamic models) and/or simulations that include reaction rates and mechanisms (kinetic models); collectively, these are commonly referred to as geochemical models and are used to assess and understand water quality processes and ecosystems in waters at the land surface, in the subsurface, and in water-related infrastructure such as water treatment plants (Figure 1; Table 2 in the companion data release [102]). Thermodynamic data, for example, are critical for use in models used to interpret the geochemistry of contaminants such as arsenic because they provide the equations and parameters necessary to calculate aqueous speciation, sorption, and solubilities of arsenic-bearing minerals [209]. Kinetic data are important when reaction rates are important, such as with phosphorus mobilization and subsequent algal growth [210]. It remains a persistent challenge to obtain accurate parameter values for key reaction rates, such as site- and time-specific algal growth rate (which influences nutrient concentrations) or nutrient remineralization rate. This uncertainty can significantly impact the prediction of potential impacts of future climate. The composition of organic matter plays a vital role in the biogeochemical processes, where labile particulate organic matter is remineralized at a faster rate compared to refractory organic matter. For water quality models that do not incorporate thermodynamic or kinetic equations but must necessarily simplify complex hydrobiogeochemical processes [211], the model can benefit by directly or indirectly incorporating the output of geochemical models [212,213,214]. Biological effects may not be directly relevant to equilibrium models, but the metabolic activity of biota has large effects on pH and concentrations of O₂ and CO₂ that affect other reaction rates in hydrologic systems, including surface and groundwater chemistry, the composition of the sediment or aquifer matrix, and the movement of contaminants [215,216]. For example, numerous biogeochemical processes can affect pH [217], which in turn can affect reaction rates such as Fe(II) oxidation and aqueous complexation and sorption of metals in both surface water and groundwater. Aqueous kinetics are complicated by biotic metabolism because of the many associated factors, such as temperature, nutrient concentrations, carbon sources, redox, and enzyme inhibitors and catalysts, in addition to microbial competition, symbiosis, predator-prey dynamics, and dynamic changes in water saturation [215,216]. Further complications to aqueous kinetics include various nutrient cycling pathways by animals in freshwater ecosystems (such as excretion [218]) and trophic cascades [219].

Various software programs have been developed to model the chemistry of aqueous solutions interacting with minerals, gases, solid solutions, exchangers, and sorption surfaces under equilibrium conditions, as well as with aquatic organisms (Table 2 in the companion data release [102]). The early geochemical models were developed to provide thermodynamic descriptions of multicomponent systems without regard to transport [220]. Commonly used contemporary geochemical modeling programs include PHREEQC (the “pH-redox-equilibrium model in the C programming language” model) [221,222], Visual MINTEQ (VM) [223], TOUGHREACT [224], CrunchFlow [225], The Geochemist’s Workbench [226], and AquaEnv [227]. PHREEQC, one of the most commonly used codes for a variety of studies of water chemistry, has been coupled with groundwater flow and solute transport models for reactive transport simulations [228,229,230] and hydrologic models to simulate fluxes of water and solutes through watersheds on a daily time step [231].

Biogeochemical models that characterize sources, sinks, and interactions between constituents such as nutrients, algae, dissolved oxygen, and/or secondary producers in surface water need to consider biological and geochemical processes, as well as (in many cases) physical transport. These models can be used to diagnose, understand, or predict processes connected to algal blooms and eutrophication, nutrient limitation, hypoxia/anoxia, trophic transfer of contaminants, and extent of periphyton growth downstream of a point nutrient source [232]. Numerous models exist for characterizing such biogeochemical dynamics, many of which couple to—or are embedded in—models of flow physics. A few commonly used examples are the CE-QUAL family of models [233,234], D-Water Quality (also known as Delft3D-WAQ or “DELWAQ”) [235], SWAT [236], and CoSiNE [237]. AQUATOX is an ecosystem model that simulates pollutants, including nutrients and sediments, in aquatic systems and estimates the environmental fate of these pollutants on resident organisms [167]. The degree of biogeochemical model complexity can vary widely, with the most complex models computing concentrations and interactions between numerous constituents, usually requiring the specification of large numbers of model parameters, many of which may not be known for the water body of interest.

The accuracy and relevance of water quality models could be enhanced by the incorporation of key processes that play significant roles in aquatic ecosystems. One such crucial process is mixotrophy (a phenomenon whereby an organism can use a mix of different sources of energy and carbon) [238], which has recently gained attention in the field of algal studies. The emerging understanding of mixotrophy challenges the conventional model that rigidly separates producers and consumers in marine biogeochemical cycles and that fails to capture the true complexity of marine microbial communities [239]. Mixotrophy is also present in freshwaters [240]. Mixotrophy can affect standing stocks and cycling of nutrients, as well as planktonic biomass [239]. More sophisticated and comprehensive models could represent the intricate interactions within marine ecosystems more accurately, such as with HABs (harmful algal blooms) [62]. Most current water quality models have yet to integrate mixotrophy, mainly due to limited available data on this complex process (see [62] for an exception). This gap could be addressed by laboratory experiments aimed at understanding important parameters to be incorporated in future water quality models that include mixotrophy.

Geochemical and biogeochemical models aid in the development of conceptual and reactive transport models and help us better understand water quality problems. Because limited conceptual understanding leads to greater uncertainty in model parameters, water quality managers (e.g., drinking water suppliers and regulatory agencies) could benefit from increased availability and quality of data to advance biogeochemical modeling capabilities [241]. For example, geochemical modeling codes such as PHREEQC, together with major ion data, are commonly not considered in studies but could be used to quickly generate mineral saturation indices and water types that relate to corrosivity and information on water sources and pathways that might not otherwise be evident. Currently, gaps exist in thermodynamic and kinetic data for reactions under natural, varied, and site-specific conditions, and information is sparse for several important trace elements such as Mo and Se (Table 6). Additional thermodynamic and kinetic data (in addition to surface complexation models) could be generated (or compiled based on existing literature) for varying conditions and new aqueous species or modified existing species. Furthermore, process formulations built into multidisciplinary models (e.g., aquatic ecosystem models) could be compared with output from geochemical models to ensure model understanding and adequate functionality. Data with which to specify boundary conditions, evaluate model performance, and specify critical site- and species-specific source or loss rates (e.g., grazing rates on phytoplankton [242]) are often sparse or non-existent.

2.3. Watershed Modeling

Watershed models describe the transport of water and various constituents (commonly sediment and nutrients) from where they originate or are introduced on the landscape to the river or groundwater network, and ultimately to downstream water bodies or the ocean. Delivery from the landscape to nearby streams is based on both static and dynamic factors including topography, soils, weather, land cover, and land use. Watershed models can be combined with river, lake, and reservoir models to describe the transport and fate of various constituents. Specifically, watershed models are often used to describe: (1) boundary fluxes of water and solutes including precipitation, evapotranspiration, and exports of surface and groundwater; (2) internal fluxes such as snowmelt, overland flow, infiltration, preferential flow, recharge, and baseflow; (3) the spatial and temporal variability in the contributions of specific constituents throughout the watershed and thus provide information on where and when actions would be most beneficial, (4) the relative importance of various sources of the constituent and thus provide information on what types of actions would be most beneficial to reduce constituent transport, (5) the factors affecting the delivery of specific constituents, and (6) the effects of specific management actions and practices and environmental changes, including projected climate and land use change (e.g., agricultural to developed).

Watershed models range in complexity from simple statistical models to complex dynamic, process-based models that describe the transport of a constituent from where it originates to where it is delivered. Many models incorporate aspects of both of these extremes and are referred to as semi-mechanistic hybrid models that use a combination of statistical relations and physically based process relations. The various types of watershed models have been described previously by other authors (e.g., [160,243,244,245,246,247]). Statistical watershed models are typically driven by relations found between a specific constituent (e.g., phosphorus load) and various characteristics describing the catchment (e.g., percentage of agricultural area) and are typically expressed as a series of land-use export coefficients or yields [248]. Many of these statistical relations have been incorporated into the Spreadsheet Tool for Estimating Pollutant Loads (STEPL) [249] used for agricultural fields and the Source Loading and Management Model (WinSLAMM) [250,251] used for urban areas. Process-based hydrologic watershed models are typically based on a series of mathematical relations describing the physical mechanisms involved in driving changes in the constituent(s) of interest, such as the effects of landscape slope, rainfall, hydrology, geology, land uses, vegetation, and land-management practices. The USEPA Storm Water Management Model (SWMM) is a dynamic rainfall-runoff model used for single-event or long-term simulation of runoff quantity and quality that is widely used for planning, analysis, and design related to drainage systems in urban areas [252]. TOPMODEL is another commonly used topography-based rainfall-runoff watershed model that reflects the dynamic nature of runoff-contributing areas [253]. A one-dimensional (1-D) reactive transport model, OTIS [254], accounts for transient storage in side pockets or in porous media, as well as sorption and first-order decay; OTEQ couples OTIS with a chemical equilibrium model, MINTEQ [255,256]. Two commonly used process-based surface water hydrologic models include WRF-Hydro [257] and the Precipitation-Runoff Modeling System (PRMS; [258]). WRF-Hydro is an open-source community model developed by the National Center for Atmospheric Research (NCAR) for hydrologic prediction, hydroclimatic impacts, seasonal forecasting of water resources, and land-atmospheric coupling studies. WRF-Hydro is the core of the NCAR National Water Modeling System (NWM) that is used for simulating hydrologic conditions over the entire CONUS. PRMS is also an open-source, deterministic, distributed-parameter model developed by the USGS to evaluate the response of various combinations of climate and land use on streamflow and general watershed hydrology. PRMS includes representation of the canopy, snowpack, and unsaturated zone with simplistic representation of groundwater. PRMS is used within the USGS National Hydrologic Model (NHM), which is also used to simulate hydrologic conditions over the entire CONUS. A commonly used process-based groundwater model is MODFLOW [259]. MODFLOW is an open-source finite-difference flow model used to simulate groundwater flow through aquifers having a series of vertical layers. GSFLOW [260] links PRMS and MODFLOW to leverage the strengths of each model. Where the fluids of interest are of variable density, as in product spills for energy development, injections of wastewater, melting permafrost, or seawater intrusions of coastal aquifers, models such as SUTRA [261] or VS2DT [262] are available. A few commonly used process-based hydrologic models with additional capabilities to simulate the effects of biota (crop production) and anthropogenic activities on streamflow and sediment and nutrient yields include the Soil and Water Assessment Tool (SWAT; [263]), the Agricultural Policy/Environmental eXtender (APEX; [264]), and the Hydrologic Simulation Program (HSPF; [265]). Examples of commonly used hybrid watershed models include the Spatially Referenced Regression on Watershed attributes model (SPARROW; [266]) and the Catchment Land-Use for Environmental Sustainability model (CLUES; [267]). In hybrid models such as SPARROW, the specific processes affecting constituent transport are simplified into simple fractions of each source or delivery rate per unit area being delivered downstream, which in SPARROW are functions of various landscape characteristics (i.e., land-to-water delivery variables) and modified by instream/reservoir decay variables. Please see Table 3 in the companion data release [102] for additional watershed models.

Watershed models are used to describe the movement of water and/or the transport of various constituents in various sized areas (from fields to large basins) and over various time frames (days to decades). Therefore, these models require information describing the sources of the constituents and the factors affecting their delivery that can vary over a range of spatial and temporal scales. A variety of factors affect the hydrology and the transport and fate of specific constituents. If the model is simulating changes on a daily time step, then it requires daily input data describing weather and the daily management practices. If this information is not available, then the specific processes included in the model may not perform properly. Recent CONUS-scale flow models, including the National Hydrologic Model [258] and the National Water Model [268] described above, have been calibrated using 40 years of retrospective atmospheric inputs at a subdaily timestep at 4-km resolution with hillslope hydrology simulated by WRF-Hydro [257] or PRMS [182], respectively.

There are several important gaps that limit the use of watershed models (Table 7). One of the most important limitations is the lack of information describing the specific timing of short-term practices (e.g., agricultural management practices) and the spatial extent of long-term practices (e.g., tile drains). Most watershed models simulate flow and water quality changes based on inputs of selected sources and include the primary processes affecting their delivery, but few models include all the important sources and processes affecting specific water quality constituents. Thus, quantifying the effects of these secondary sources and processes is an important gap to fill to develop justified cause-and-effect relations. Watershed models commonly rely on extensive monitoring data that provide defensible quantitative values of flow and constituent fluxes (loads) for regional mass balance computations and model calibration. More extensive spatially distributed monitoring data than are currently available, especially at sites describing the effects of specific management practices and at sites on main river systems, would be useful. Most statistical and hybrid watershed models provide long-term mean output (such as mean annual fluxes). Dynamic hybrid models that simulate changes in water quality at fine temporal scales (days to seasons) would improve short-term predictions. Statistical and hybrid watershed models use their statistically based relations to provide a technique for quantifying a level of certainty (or margin of error). Usage of process-based models, such as SWAT and HSPF, would be strengthened by associating a level of true certainty with their results. Some watershed models are linked to a downstream reservoir model. However, most watershed models do not include the effects of reservoirs that intercept the river network throughout the upstream areas being modeled, or they include such effects in a simplified manner, such as with a simple settling velocity [269]. Watershed modeling conducted in large basins, such as at a continental scale, especially on a short (e.g., daily or seasonal) time step, would be improved by incorporating the effects of lakes and reservoirs on water quality. Please see Section 2.5 “Lake and Reservoir Water Quality Modeling” and Section 2.6 “Reservoir Operations and Outflow Modeling” for a detailed relevant discussion. Soil type/properties and the implementation of tile drains and irrigation are often a key source of uncertainty in partitioning precipitation into runoff versus infiltration [270]. Oftentimes, mobilization of various constituents from the subsurface into streams is mischaracterized because of these uncertainties [270]. Use of remote sensing may help better define soil properties and the use of tile drains and irrigation [270].

2.4. River Modeling

Watershed models (Section 2.3) typically focus on complex factors affecting the movement of water and constituents from upstream contributing land and subsurface flow paths to receiving bodies of water while generalizing channel dynamics. River models, on the other hand, explore complex channel dynamics in more detail while often generalizing or ignoring surface and subsurface contributing area factors. Due to the inclusion of detailed in-channel physical and/or biogeochemical processes, river models (as defined herein) are applicable at river or reach scales. One may think of river models as instream flow and transport models. There are three primary aspects of river water quality modeling (which also apply to such modeling in other spatial compartments): (1) the physics of water movement (also known as hydrodynamics or hydraulics), (2) the transport of water quality constituents by the moving water (i.e., advection and/or dispersion), and (3) the sources, sinks, and transformations of reactive (i.e., non-conservative) constituents. River models discussed in this section characterize one or more of those three model components. Hydrodynamic river models (#1) provide the physical underpinning (i.e., velocities or discharges, water levels, and mixing or dispersion coefficients) for transport-reaction models (i.e., solvers of the advection-diffusion-reaction equation, or “ADR”) for individual constituents such as sediment, nutrients, temperature, dissolved oxygen, and CECs. (The ADR melds both aspects #2 and #3 above into a single equation.) River water quality models may be used to predict pollutant concentrations and arrival times, location and duration of exceedance of regulatory thresholds [271], waste load allocations [11,12], and habitat suitability for fish [272]. Depending on the dimensionality and specific processes incorporated, river models may be used to investigate cross-stream variations in hydrodynamics and constituent concentrations, hyporheic zone transport and retention, and floodplain inundation. River models can be 1-D, 2-D, or 3-D, depending on factors such as cross-sectional homogeneity, the scientific questions of interest, and assumptions made by the modeler.

Regarding the first aspect of river modeling listed above, examples of prominent river hydrodynamic modeling software include EFDC (Environmental Fluid Dynamics Code; e.g., [273]), SCHISM (Semi-implicit Cross-scale Hydroscience Integrated System Model; [274]), D-Flow FM [275] (flexible mesh successor to Delft3D-FLOW [276]), and multiple codes available from other sources [272,277]. With respect to the third aspect listed above (water quality reactions), some models used in rivers (e.g., MINTEQ [256], PHREEQC [222], AQUATOX [167,278]) perform such computations and require linkage to a transport model in order to calculate the combined effects of (especially realistic) transport and transformations. Many water quality models for rivers perform computations of combined reactions and transport (i.e., #s 2 and 3 above) by solving some form of an ADR equation. 1-D examples include OTEQ [255] (which links the OTIS [254] transport model to the chemical equilibrium model MINTEQ), QUAL2K (an updated version of QUAL2E, which also includes channel hydraulics, i.e., #1) [279], and recent transport-reaction models that include mass exchange and reactions in the hyporheic zone [280,281]. Multidimensional transport-reaction models that may be applied in rivers include CE-QUAL-ICM [166,233] and WASP [282], which rely on hydrodynamic models such as EFDC [273] or DYNHYD [283] to provide physics data to support transport computations. Integrated modeling suites that perform computations of aspects #1–3 and may be applied in rivers include the Delft3D FM Suite [284] (successor of the Delft3D Suite [285]) and SCHISM-ICM [286]. Many of the above models or coupled modeling frameworks can be used to compute water temperature, sediment, nutrients, metals, and/or contaminants. Details of available river models are provided in Table 4 of the companion data release [102].

There are a number of gaps and limitations associated with river modeling (Table 8). As is the case for hydrodynamic models of other domains (e.g., see Section 2.7 “Estuary Modeling”), high-quality bathymetric data are fundamental to building a high-skill physical model, yet these data are expensive and time-consuming to gather. Moreover, high-accuracy stage and discharge (or velocity) boundary conditions and calibration-validation data at higher spatial resolution than are currently available in many systems would be valuable, as existing gauges may be far from model boundaries or may not capture important spatial gradients in velocity. Bottom roughness, which is typically a calibration parameter in hydrodynamic models and may capture scales from grain sizes to the plan form of the channel, is complicated to estimate. Improved bottom roughness estimation methods and the aforementioned bathymetry data would contribute to improved river modeling capabilities.

Process understanding and availability of data characterizing groundwater-surface water interactions [287], preferential flow, system heterogeneity [287], and floodplain dynamics are also gaps that, if filled, could pave the way for advancements in river modeling; these are all areas influencing water quality in rivers and water supplies. River modeling would be further bolstered by additional research on sediment and biogeochemical processes occurring in intermittent rivers and groundwater-surface water interactions in non-flowing states, as well as intensified model development for intermittent rivers [288,289]. Constituent degradation rates, reactions, and by-products of new chemicals are to a significant degree unknown. Furthermore, as Strokal et al. [290] state, “a better understanding is still needed how different pollutants can affect each other…and what their combined impacts are on ecosystems”; more research in this area will help improve “multi-pollutant” modeling approaches in rivers [290]. Expanded measurement of constituent concentrations would support specification of model boundary conditions, calibration, and validation. 1-D water quality models have been shown to exhibit significant sensitivity to the longitudinal dispersion coefficient; avenues for tackling this challenge include using dye-tracing studies spanning a range of flow rates, better understanding and quantification of the effect of detailed river features on dispersion, or implementation of 2-D models [291]. Table 8 summarizes river modeling gaps and potential solutions for addressing them.

Table 8. Gaps and limitations associated with river modeling, as well as the importance of those gaps and opportunities for addressing them. CECs: contaminants of emerging concern. AI: artificial intelligence. IR: intermittent river.

Gap or Limitation	Importance	Opportunities
1-Lack of understanding, data, and predictive ability related to floodplain dynamics and groundwater-surface water interactions (including preferential flow).	1-These processes and features can result in very long or very short contaminant transport times between spatial domains. Enhanced information and capability in these areas could reduce uncertainty of contaminant transport times.	1-Increase studies and long-term monitoring of floodplains and groundwater-surface water interactions with high temporal resolution, spanning pre- and post-flood conditions. Incorporate these processes into models.
2-Limited understanding of and data describing constituent reaction rates and biogeochemical interactions between constituents, particularly CECs.	2-Understanding and quantification of reaction rates and biogeochemical interactions are required for models to incorporate those processes and realistically depict water quality in rivers.	2-More research on constituent reaction rates and how they interact with each other biogeochemically in rivers [290].
3-Lack of constituent time series data for prescribing model boundary conditions and for calibration/validation.	3-These data are required to force the model and quantify performance. In advectively dominated conditions, boundary conditions can dominate concentrations within the model domain.	3-Increase collection of constituent time series and spatially variable data. Harmonize datasets from various sources. Employ advanced approaches (e.g., remote sensing [292]).
4-Lack of high accuracy, high-resolution bathymetry, stage, discharge, and/or velocity data to setup, drive, calibrate, and validate hydrodynamic models of rivers. Bottom roughness is challenging to estimate.	4-These data are fundamental to high-quality hydrodynamic modeling, which provides a basis for computing the transport of water- quality constituents.	4-AI [293] or inverse hydraulic modeling and data assimilation [294,295] for estimating or inferring bathymetry. Use of inexpensive, rapidly deployed pressure transducers or other methods for stage measurements. Continue research into remotely sensed discharge.
5-Lack of understanding, data, and appropriate tools for IRs.	5-IRs make up a large proportion of inland waters and can critically affect biogeochemical processing.	5-Expand research on sediment and biogeochemical processes occurring during dry, wet, and transitional phases of IRs; increase model development for IRs.

2.5. Lake and Reservoir Water Quality Modeling

During downstream transport, water often travels through natural lakes and reservoirs (collectively referred to herein as reservoirs) (#39). As water travels through reservoirs, there are several factors that affect water quality, such as a reduction in water velocity (which affects the amount of turbulent mixing) and anthropogenic control (e.g., types of withdrawal). These modifications in the amount and type of mixing in reservoirs can affect its physical (temperature), chemical (redox conditions affecting internal recycling, especially in deeper zones of the reservoirs and biodegradation), and biological conditions (macrophyte and algal growth). Therefore, quantifying and describing (i.e., modeling) the effects that reservoirs have on water quality supports large-scale modeling and description of the changes in water quality during transport through large watersheds.

There are four general types of reservoir water quality models: statistical models, process-based physical (hydrodynamic) models, process-based physical/chemical/biological (hydrodynamic water quality) models, and hybrid models. Many statistical models have been developed to estimate specific water quality characteristics in lakes (see [296] for a summary of the statistical models used to simulate water temperatures). The purely statistical approaches were advanced to create load-response models to estimate summer mean total phosphorus concentrations, chlorophyll-a concentrations, and water clarity (Secchi depth) by including phosphorus loading from the watershed, lake residence time, and the morphometry of the lake [297,298,299]. Many different load-response models have been developed based on different datasets. A few of the statistical load-response models are included in the Wisconsin Lakes Modeling Suite (WiLMS) [300] and the U.S. Army Corps of Engineers BATHTUB model [301]. These load-response models have been used to develop lake management plans and total maximum daily loads (TMDLs) for various water bodies [302].

Process-based models were originally developed to describe changes in the physical (primarily water temperature) structure of deep 1-D (horizontally uniform) reservoirs [303]. Process-based models gradually became more complex by further describing specific processes, such as in the Dynamic Reservoir Simulation Model (DYRESM) [304] and MinLake model [305]. These models continued to become more complicated and simulated reservoirs in 2 dimensions (e.g., CE-QUAL-W2 [306]) and 3 dimensions (e.g., Estuary and Lake Computer Model, ELCOM [307] and the Finite Volume Community Ocean Model, FVCOM [308]). Increasingly complex chemical and biological sub-models were added to the process-based models, resulting in such models as the Water Quality Analysis Simulation Program (WASP) [282], General Lake Model coupled to the Aquatic Ecodynamics modeling library (GLM-AED) [138,309], General Ocean Turbulence Model (GOTM) [310], Multiyear Lake simulation model (MyLake) [311], and CE-QUAL-W2 [306], just to name a few. Various water quality submodels with different levels of process description have also been incorporated into hybrid models. The BATHTUB hybrid model [301] contains several statistical water quality relations, such as the load-response models, within a mechanistic hydrologic structure that accounts for long-term mean advective transport, diffusive transport, and nutrient sedimentation as water and nutrients travel throughout a series of mixed (zero-dimensional) reservoirs. Statistical (ML) models have also been coupled with process-based models—thus creating hybrid models—to improve model predictability [312]. A more extensive list of reservoir models is provided in Table 5 of the companion data release [102].

Much of what is known about changes in water quality that occur within reservoirs and as water travels through reservoirs has been incorporated into statistical, process-driven, and hybrid reservoir models. However, there are several key gaps that, if filled, could improve understanding and modeling of the quality of water as it passes through reservoirs (Table 9). Feedback effects between the biology and physics are often not considered in reservoir models (e.g., biological changes can affect water clarity that can then affect the physical dynamics of reservoirs [313]). Often modeling is performed in a sequential manner: physical modeling is followed by chemical and biological modeling, with little feedback between the modules [314]. Indirect effects of changes in the biological community are often not considered in long-term modeling studies (e.g., the planktonic and fish communities are assumed to remain unchanged even though in reality they often change as the trophic state of the lake changes) [315]. Thus, reservoir models may not forecast the full effects of changes in nutrient loading, projected future climate, or changes in other factors being simulated. The short-term effects or transitional changes in water quality following management actions are often not considered in reservoir models. For example, changes in sediment chemistry associated with legacy sources that affect internal nutrient and metal release rates are often considered to remain unchanged in models [315,316]. By neglecting the effects of these other non-included sources and sinks, their effects are often indirectly incorporated into the processes that are considered in the model during model calibration.

Process-driven reservoir models are often highly parameterized and have many coefficients to calibrate. A systematic calibration process could help ensure that model results are not driven by the calibration process or the abilities of the modeler. Poor calibration techniques often result in poor predictions and an underestimation of the full capabilities of the model [317]. Although it is possible to simulate how reservoirs affect water quality using complex site-specific reservoir models, these changes in water quality are typically only considered at the downstream end of large watershed models and usually not considered in the reservoirs that are in the upstream areas of large-scale watershed models [318]. In large-scale watershed models such as SPARROW and SWAT, the effects of reservoirs on water quality throughout the watershed are typically not considered, or the effects are simulated using simple settling velocities [120,269]. In many modeling efforts, especially those simulating changes in large basins, it is difficult to obtain much of the physical data that reservoir models require, including bathymetry and operations information. Much of these data—particularly for large reservoirs such as those that provide hydropower—are often not publicly available throughout the area being modeled. Without simulating the processes within the reservoir and the effects of all upstream reservoirs (e.g., withdrawal depths and volumes, stratification, water quality, and contaminant attenuation), large-scale watershed models are not likely to accurately simulate the seasonal dynamics in water quality that exist throughout the watershed.

2.6. Reservoir Operations and Outflow Modeling

Dams and other operational structures are used to generate hydroelectric power, provide recreation, facilitate downstream navigation, supply ecologically beneficial flows, control water temperature, control floods, and supply water for various needs (#39 in Figure 1 and Table 2). Models are used to simulate changes to flow rates caused by dams and other operations, information that can then be used to understand reservoir impacts on downstream dilution and residence times, channel erosion, sediment resuspension, salinity, and other aspects of water quality. Across the U.S., there are many types of managed systems, from single-reservoir basins to multiple reservoirs operated jointly, and from reservoirs managed for a single purpose, such as flood control, to reservoirs managed with multiple objectives. Reservoir operations can also be coupled to hydrologic conditions throughout a watershed because the operational criteria are dependent on flows and other quantities in the downstream watershed.

“Loose coupling” of operations models and water quality models (i.e., feeding operations model flow outputs as inputs to a dedicated water quality model, described in the previous section) may not suffice in cases where operations are linked to water quality indices (Table 10). For example, when reservoir releases are used to meet downstream water quality requirements, water quality model results would need to be fed back into the operations model. In such cases a “tight coupling” would be required (including inter-model feedbacks at each time step). Also, since most operations models include only simplistic representations of hydrological processes, tight coupling with a more sophisticated hydrological model may provide significant improvements in accuracy [319]. Such improvements could be facilitated by an operations model that allows for coupling with other models and is generally extensible. This quality is inherent in models whose source code is available (see column E in Table 6 of the companion data release [102]). However, even in models for which source code is not available, the ability to customize and extend model capabilities can be offered through an appropriate interface [320].

Many models simulate operations by solving, at each time step, for a set of decisions (e.g., releases and pumping rates) subject to a set of weighted objectives (e.g., maintaining flood-control space) and inputs (upstream inflows). Other models more directly simulate the movement of water through the different components of the managed system and the processes affecting the water budget. Key outputs from operations models typically include reservoir releases and other managed flows throughout a river basin. There are multiple solution methods implemented in modern models [321,322,323]. Commonly used operations models are listed in Table 6 of the companion data release [102]. All of these models are sufficiently flexible and comprehensive to simulate managed flows in a wide range of management configurations. Although water quantity is typically the focus of such models [324], limited water quality simulation capabilities are included in some of these models. See the previous section for a discussion of reservoir models that focus on water quality.

Since multiple capable reservoir systems models are available, the choice of which model to use often comes down to the availability of previously developed models in a given system and/or which model’s experts one has access to. If no sufficient models exist in a system of interest, model configuration and development may be needed. This can be time- and resource-intensive and requires operations data that are not always readily available.

A major gap in reservoir operations modeling at the regional and national scales is the lack of a national database of detailed reservoir operating parameters and policies for reservoirs (e.g., rule curves, hydropower rules, joint operations, depths and amounts of withdrawal); such information would support the development of robust reservoir modeling capabilities (Table 10). Historically, static databases have provided the only dam or reservoir data available to modelers (e.g., NID [325], NABD [326], GDW (Global Dam Watch) [327], HILARRI [328]), and their data provide a very limited characterization of operations. ResOpsUS [329] is a first-of-its-kind basic dynamic dataset that includes time-series data describing inflow, storage volume, water elevation, and outflow for many reservoirs across CONUS. Such time-series data are useful for analysis, model calibration and evaluation, and development of empirical operations models (e.g., STARFIT [330]). However, efforts to include more robust reservoir models within regional- and national-scale hydrologic models could benefit from the development of a database focused on the criteria that constrain operational decisions for individual reservoirs and multi-reservoir systems. A first step in such an effort was the National Reservoir Data Symposium, held in Fort Collins, Colorado (USA), in February 2024, at which approaches to assembling national reservoir operations data were discussed.

2.7. Estuary Modeling

Estuaries—where surface freshwater and saltwater meet—are dynamic, complex, and subject to multiple forcings such as river flow, tides, horizontal density gradients, atmospheric heating, wind, waves, atmospheric pressure, and anthropogenic operations. These physical drivers, which can vary on sub-hourly to interannual timescales, interact with bathymetry and bottom roughness to generate hydrodynamic processes such as (1) density stratification, (2) residual transport such as gravitational circulation, (3) turbulent mixing, (4) horizontal dispersion, and (5) hourly varying water levels and currents (tides). As the foundation for modeling estuarine water quality, an estuarine hydrodynamic model—which typically computes water surface elevation, velocity, discharge, and (if the vertical dimension is resolved) vertical turbulent diffusivity—can characterize all of the above processes. Estuarine hydrodynamic models often include embedded solvers of advection-diffusion equations for salt and temperature (and in some cases sediment [331]), because variations in water density driven by those parameters can affect the hydrodynamics, and vice versa. The fate and transport of most other water quality constituents can be computed “offline”, i.e., using saved hydrodynamic model outputs as input to the water quality model (which solves transport-reaction equations for constituents), without any needed feedbacks to the hydrodynamics [161]. Constituent-specific reaction rates may be computed within the water quality model as a function of other modeled and/or imposed parameters describing the estuarine environment (e.g., turbidity, temperature, solar radiation, nutrient concentrations) [332,333,334].

Multiple high-quality and freely accessible estuary models exist. For hydrodynamics, prominent examples include SCHISM [274]; EFDC [335,336,337]; Delft3D-FLOW (structured mesh) [276]; D-Flow FM (flexible mesh) [275,338]; Regional Ocean Modeling System (ROMS) [331,339]; ADvanced CIRCulation model (ADCIRC) [340]; Finite Volume Community Ocean Model (FVCOM) [308]; General Estuarine Transport Model (GETM) [341]; Estuary, Lake and Coastal Ocean Model (ELCOM) [307]; and Stanford Unstructured-Grid Non-hydrostatic Terrain-following Adaptive Navier-Stokes Simulator (SUNTANS) [342]. All of these can solve for salinity and temperature as well as the typical hydrodynamic quantities mentioned above. (See [343] for a more exhaustive list of hydrodynamic models implemented in the coastal zone.)

Hydrodynamic models such as those listed above can produce hydrodynamic outputs that can then be used as input to water quality models (e.g., WASP [283], CoSINE [237,344,345,346], CE-QUAL-ICM [233,286], D-Water Quality, also known as DELWAQ [235], and CAEDYM [347]) to support transport computations of water quality constituents. Many of those hydrodynamic models provide the physical backbone of integrated modeling frameworks (e.g., Coupled Ocean–Atmosphere–Wave–Sediment Transport Modeling System (COAWST) [348], the SCHISM Modeling System [274], Delft3D-FM Suite [284], HEM-3D [349]), most of which include or link to one or more models for computing the transport and transformation of constituents such as nutrients, sediment, contaminants, and tracers (e.g., [350,351]). Some coupled hydrodynamic-water quality models used in estuaries incorporate critical fluxes of nutrients and other constituents between the water column and the sediment [333,351,352]. Other model coupling configurations include linkages between hydrodynamics, water quality, and vegetation [333,353]. Details on available estuarine models are provided in Table 7 of the companion data release [102].

A number of challenges in estuarine and coastal hydrodynamic modeling exist, including numerical issues [354,355,356,357], computational cost, parametrization of key physical processes [343], uncertainty estimation [343], subjectivity in model implementation [343], and the need for more, and more highly resolved, data (e.g., bathymetry [355]). Regardless of these challenges, models of estuarine physics commonly perform very well [338,358], assuming accurate bathymetric and forcing data are available and experienced modelers are at the helm. As in other surface water systems, the farther a model departs from computations of purely hydrodynamic quantities (water level, discharge, velocity), generally the more uncertainty enters the modeling process, particularly for the computation of reactive water quality constituents. Reactive constituents, especially CECs, are particularly challenging to model accurately, given the necessity to rely on empirical relationships and parameters for describing reactions and transformations. Important limitations in the capability to model water quality in estuaries include (in addition to those listed above for estuarine hydrodynamic models): (1) water quality data needs (e.g., long-term data sets, data in hard-to-monitor areas, and data to support modeling of the impact of coastal storms on water quality [359,360]); (2) numerical challenges (e.g., mass conservation difficulties in areas that wet and dry [361,362]); (3) accumulation of small errors over time in forecasting models; (4) the need for increased two-way coupling of hydrodynamics and biota (e.g., vegetation and benthic fauna) and coupling of hydrodynamic, wave, and water quality models; (5) overparameterization of complex biogeochemical models [161], and (6) the need for water quality coupling across different hydrologic compartments (e.g., groundwater-surface water and watershed-estuary-coastal ocean).

Many estuarine water quality models do not account for groundwater flow or constituent sources, yet groundwater discharge to estuaries and coastal seawater constitutes a significant part of the continental mass balance in certain regions of continental boundaries [363,364]. Furthermore, submarine groundwater discharge (SGD) can be important for the transport of nutrients and contaminants and for the distribution of salinity and biological zonation in coastal estuaries [364,365,366]. The SGD pathway was neglected for many years because of the difficulty in assessment and the perception that the process was unimportant [367]. Measurement of SGD has been measured directly or using tracers such as radon-222, dissolved organic matter, silica, and stable isotopes of carbon and nitrogen, but the often high spatial and temporal variability makes assessment difficult [367,368]. Variable density groundwater flow models have not been commonly used to estimate SGD in estuarine models because of limitations in computer speed, data availability, and availability of a simulation tool that can minimize numerical dispersion [363,369]. However, integrated or coupled modeling approaches have been increasingly used to simulate groundwater contributions to estuaries [102,363,370,371]. This is an area of model coupling that could significantly improve estuary model performance for systems and constituents for which exchange between surface and subsurface waters is significant.

With regard to coupling across the watershed-estuary-coastal ocean continuum, while many multidimensional estuarine hydrodynamic and salt transport models can accurately capture saltwater intrusion and salt fields if high-quality boundary condition and bathymetry data are available (e.g., [338,358,372]), the ability to model salinity and other water quality responses to the compound effects of extreme coastal storms (e.g., storm surge and high river flow) at large scales across the watershed-estuary-coastal ocean domain is in its infancy. This capability, which depends on dynamic two-way coupling of hydrologic and hydrodynamic models, was recently accomplished, apparently for the first time, for salinity [373] and for suspended sediment [374]. In this case, the WRF-Hydro (Weather Research and Forecasting Model Hydrological modeling system; [257]) atmospheric and terrestrial hydrology model was dynamically coupled to the ROMS [339] coastal hydrodynamic and transport model within the COAWST modeling system [348,375,376].

Details, importance, and potential solutions to estuary modeling gaps are provided in Table 11.

2.8. Groundwater Modeling

Groundwater models simulate water quality processes in aquifers, which indirectly influence surface water bodies. Dissolved and colloidal constituents in groundwater affect the quality of drinking water in community and private systems as well as ecosystem health and surface water beneficial uses via groundwater discharge to lakes, rivers, and estuaries (#36 in Figure 1 and Table 2). The optimal approaches to address these issues depend on the receptor, the constituent, and the type of information sought. In the last few decades, 3-D process models have been used often for groundwater quality modeling [378,379] (Table 8 of the companion data release [102]). Key process information can be synthesized in reduced complexity models (RCMs) to allow efficient analysis across larger scales [380,381,382,383]. More recently, machine learning and statistical methods have emerged as valuable tools to characterize groundwater quality processes [156,384,385,386,387]. Combinations of these methods show promise for advancing the goal of large-scale, next-generation groundwater quality analysis [157,382,388,389,390,391,392].

Groundwater modeling capabilities can be divided among distributed parameter process models such as MODFLOW-6 [393], MT3D-USGS [394,395], or PFLOTRAN [396]; reduced complexity models such as the Vertical Flux Method for nonpoint source solutes [382]; and data-driven approaches such as machine learning (ML) and statistical methods. Distributed parameter models require large numbers of parameters to characterize detailed hydrogeological heterogeneity [397,398], particularly the combined effects of varying hydrology and geochemistry [399,400]. Because of the computational and data demands of distributed parameter models, upscaling to regional models requires volume averaging of parameters [401,402] or simplification of the model structure to include key processes in a more efficient RCM [157,158,390,391,401,403,404,405,406]. The travel time distribution approach—sometimes generated from particle tracking models and combined with convolution algorithms—is a key example of an RCM that allows efficient estimation at local and regional scales in aquifers [401,403,404,405,406], at groundwater-surface water interfaces [407,408], and in the unsaturated zone [382,409]. The efficiency of RCMs allows evaluation of alternative conceptual scenarios through multimodel approaches [410,411,412]. Recently, hybrid approaches have combined machine learning, statistical, reduced complexity, and/or distributed parameter model frameworks [157,382,390,391,392]. The simple mechanistic or hybrid approaches can be used for testing the significance of upscaled processes, such as the relative effects of source histories, reactions, and mixing on predicted concentrations, as well as assessing the current status of groundwater quality.

Gaps in understanding of groundwater quality relate to extreme variability of the spatiotemporal characteristics of constituent sources, geological features controlling transport, and reactions (Table 12). Spatially or temporally simplified transport estimates may be adequate for providing insight into the general availability of groundwater resources [404] or estimating inputs into a well-mixed surface water body [63]. Numerous experiments in realistically complex settings find, however, that early and late-time tails resulting from mixing are inconsistent with classical Fickian macrodispersion and can affect forecasts of groundwater quality responses to changing natural or anthropogenic factors [413,414,415,416]. This effect can be dominant in predictions of concentrations orders of magnitude below the source concentrations for contaminants such as viruses and other pathogens, pesticides, PFAS, pharmaceutical and personal care products, and petroleum and transformation products. Arrival times in wells or at the water table from the unsaturated zone may be controlled by the early-time breakthrough (relating to transport in a few highly conductive interconnected pathways) rather than the bulk movement of water [56]. Similarly, the late-time tail may affect concentrations of geogenic constituents that accumulate during transport as well as the long-term response of contaminants to remediation and mitigation efforts [402].

Reactions (#43) in groundwater are another important gap affecting water quality modeling. Accurate predictions depend on detailed understanding of the reaction processes, as addressed in detail in Section 2.2. A key challenge for groundwater contaminants is to integrate into models the heterogeneity of physical, chemical, and biological features and to simulate how these pore- and local-scale features interact to produce water quality trends at larger scales [417]. For non-point source solutes, the dispersed sources can reduce the effects of mixing in small-scale features lateral to the direction of flow, but the scale of non-point source domains is often too large for detailed simulation, and so require upscaling of reaction processes [417,418,419]. Improved process understanding of reactivity and other aquifer processes would support the development of robust RCMs for predictions across large scales.

2.9. De Facto Wastewater Reuse and Chemical Transport Modeling

Important gaps in de facto wastewater reuse and chemical transport modeling are represented by the following inputs, processes, and activities: #1, 8, 13–17, 19–22, 24–25, 27, 29–30, 33–41, and 43, as illustrated in Figure 1 and detailed in Table 2.

Watershed models can synthesize atmospheric inputs to the watershed, along with landscape runoff affected by local topography, land surface/geology characteristics, and environmental conditions to simulate streamflow [420,421]. As described in Section 2.3, these watershed models can be used to describe the transport of various natural and anthropogenic constituents from where they are introduced to the river or groundwater network and ultimately to a downstream waterbody. However, watershed and associated water quality and solute transport models (#40, 41, 43) are commonly constrained to temperature, salinity, nutrients, sediments, and geogenic constituents, and incidentally exclude comprehensive simulations or assessments of unregulated contaminants of emerging concern [422]. Contaminants of emerging concern (CECs) are defined by the U.S. Department of Defense as chemicals that (i) have a possible pathway(s) to enter the environment, (ii) present a perceived or real threat to human health or the environment, and (iii) have new or changing health levels and regulatory standards due to lower detection capabilities, revised toxicity values, or new science describing previously unknown sources, environmental fate, or exposure pathways [423].

As water scarcity issues have continued, municipalities and water resource managers have turned to more innovative water management strategies, including non-potable and potable water reuse, to address increasing stress on drinking water supplies and habitat health for aquatic organisms [424,425]. Potable reuse occurs when drinking water contains a component of wastewater as a source. Planned potable reuse includes either indirect potable reuse (IPR) or direct potable reuse (DPR). IPR projects have been somewhat common in the U.S. and elsewhere since these include tertiary or advanced water treatment followed by an environmental buffer, such as a surface water reservoir (#39), wetland (#40), or groundwater infiltration regime (#28, 34, 36–38) prior to conventional drinking water treatment to improve water quality through pathogen inactivation and contaminant dilution/adsorption [49,57,424,425]. In contrast, DPR projects allow wastewater treated with tertiary or advanced treatment technologies to enter a drinking water supply without an environmental buffer step. These advanced treatment technologies include, but are not limited to, membrane technologies such as reverse osmosis and ultrafiltration, activated carbon filtration, and advanced oxidation reactions catalyzed by hydroxyl radicals produced through ozone, photocatalysis, or electrocatalysis treatment [426,427,428,429,430]. These advanced treatments supplement the conventional secondary (e.g., activated sludge) treatment in wastewater treatment plants (WWTPs) to remove highly persistent contaminants that are recalcitrant in nature or toxic to microorganisms/aquatic life [99,431]. In the past, DPR projects were rare. However, through outreach that draws on the science of water reuse and new government policies such as USEPA’s National Water Reuse Action Plan (WRAP), many more water use communities are developing and implementing DPR projects [425].

The most common type of wastewater reuse for drinking water treatment plants (DWTPs) is the unplanned, inadvertent potable reuse. This is also known as “de facto” wastewater reuse, defined as the incidental presence of treated wastewater effluent in a drinking water supply source (#24, 35) [424,432], septage recharge of groundwater supply (#22, 34, 39) to a public well [433], or treated wastewater and its contaminant load that is unavoidably intermixed with the habitat for aquatic life downstream. De facto potable water reuse is geographically widespread, and the quantity has been steadily increasing over the past four decades [424,425]. For example, Rice, Wutich, and Westerhoff [50], who conducted an assessment of de facto potable water reuse across the U.S., found that the top 25 most impacted DWTPs contained 2% to 16% wastewater discharges from upstream locations in 1980, but by 2008 these same DWTP supplies ranged from 7% to 100%, indicating how important this contribution is to maintaining sustainable water supplies. In a follow-up study by those authors [50] that analyzed 2056 surface water intakes serving 1210 DWTPs in 18 USGS-defined Hydrologic Regions across the U.S. [434], the percentage of DWTP intakes impacted by de facto wastewater reuse ranged from 5% in New England (region 1) to 90% in the Texas Gulf (region 12), and up to 100% in the Souris-Red-Rain region (region 9) of North Dakota and Minnesota. Other watersheds with high percentages of DWTP intakes impacted by de facto reuse include 96% in Lower Colorado/Arizona (region 15), 85% in the Great Lakes (region 4), 85% in the Lower Mississippi (region 8), and 65% in Ohio and surrounding states (region 5). Higher wastewater fractions of total stream flow can serve as a proxy for higher incidence of CEC occurrence, which could present greater challenges for managers of drinking water sources or aquatic habitats downstream [84,85,435,436,437,438,439]. Coupling existing hydrologic transport models, such as SPARROW [266] or CLUES [267], with existing wastewater models such as those described later in this section could support management decisions in these regions.

The initial national studies performed by USEPA to assess de facto wastewater reuse resulted in some of the first geospatial models capable of predicting wastewater-impacted streams. The De Facto Reuse in our Nations’ Consumable Supply (DRINCS) model calculated accumulated wastewater (percentage of streamflow from total upstream WWTP discharges) at the intake locations of public water systems (PWSs) supplied by stream waters [50,96,432,436]. Screening-level exposure models have expanded the use of wastewater discharges to calculate predicted environmental concentrations (PECs) of contaminants in the effluent and receiving streams. These approaches incorporate chemical-specific information (e.g., per capita use for pharmaceuticals or chemical production data for pesticides/personal care products) and environmental fate and transport behavior to estimate effluent contaminant loads discharged to surface waters (when direct effluent concentrations are not available) and account for cumulative upstream contributions, dilution, and instream decay during transport. Examples of screening-level exposure models include the: Geography-referenced Regional Exposure Assessment Tool for European Rivers (GREAT-ER) model [101,440,441]; Pharmaceutical Assessment and Transport Evaluation (PhATE^TM) model [437,442,443]; Global River Network Routing Hydro-ecological (HydroROUT) model [444,445,446]; in-STREam Exposure Model (iSTREEM^®) [438,447]; Shenandoah Accumulated Wastewater (ACCWW) model [84,448]; Potomac ACCWW model [85,435]; and stochastic risk modeling of Muddy Creek in Iowa [449]. Table 9 in the companion data release [102] provides a summary of relevant features for the above wastewater and exposure models affecting de facto wastewater reuse and contaminants of emerging concern.

A major challenge in assessing ecological and human health risks of CECs in surface water is the gaps in understanding the dynamic environmental fate and exposure pathways controlled by hydrological and biogeochemical processes (Supporting Information in [84]). When empirical data for environmental fate parameters and toxicity thresholds are unavailable or uncertain, lab-based thermodynamic and kinetic data can be used by process-based models to directly incorporate targeted CECs into their models. Since lab-based data generated under defined boundary conditions (e.g., temperature, pH, ionic strength, UV-light exposure, consistent and finite amounts of sorption sites) may not always transfer well to the complex aqueous mixtures observed in the natural environment, ground-truthing of the model outputs with measurement science could be valuable for optimal tuning and calibration. Additionally, in silico, computational models or simulations can be used for generating input variables. Computational tools, such as those found with the EPI Suite^TM interface [450], applied to fate and toxicity estimations for organic chemical contaminants, often rely on Quantitative Structure-Activity Relationship (QSAR) models [451].

The use of a combination of stream-based, lab-based, and in silico-derived environmental fate parameters and acute and chronic toxicity thresholds as input parameters for hybrid wastewater-hydrologic transport models would permit prediction of CEC concentrations, building of toxicity-based vulnerability indices for aquatic life and drinking water sources, and using GIS (Geographic Information System) tools to layer these outputs geospatially onto watershed maps [50,84,85,424,425,432,435,452,453]. With emergent models, clearly defining the conceptual model considered, along with any model assumptions and constraints, allows understanding of strengths and weaknesses. Eventually, systematic evaluation of in-stream attenuation rates and mechanistic explanations through Lagrangian longitudinal sampling of CECs within streams from different geologic and hydrologic landscapes may support better understanding and constrain in situ fate parameters to optimize model outputs. Regulatory agencies and PWSs can contribute to de facto wastewater and CEC modeling efforts by maintaining open-access, machine readable databases of CEC source types, periodic discharge concentrations of CECs, and physicochemical and kinetic data relevant to fate, transport, and aquatic toxicity. These databases could build upon vetted tables of environmental fate parameters and in-stream decay rates in the supporting information provided by [84,85,435] and could be used in harmony with other database platforms such as STEPL [90] for agriculture fields and WinSLAMM [91,92] for urban areas. Coordination of open access to relevant modeling code, standard sources of input data, and scripts for data mining and cleaning to improve the efficiency of data interpretation and development of hydrologic transport modeling for de facto wastewater reuse simulations could help streamline the modeling process. These simulations can identify “at-risk” stream reaches to prioritize future contaminant monitoring, conduct process-based studies for improving model parameterization, and inform risk-assessment decisions made by water resource managers.

For example, the ACCWW model [85,435,448] has been used to identify “at-risk” stream reaches in the Shenandoah and Potomac River Watersheds with respect to de facto wastewater reuse. The ACCWW model incorporates a variety of parameters describing watershed hydrology, wastewater treatment facilities, and contaminants of emerging concern that may be present in wastewater effluent to estimate the following for each NHDPlus V2 [454] non-tidal stream segment in a watershed: (1) accumulated wastewater as a percentage of total streamflow and (2) PECs of municipal wastewater-derived contaminants (Figure 3). The ACCWW model was used in the Shenandoah River watershed to evaluate endocrine-disrupting chemicals and estrogenicity effects found in streams [448,455]. Color-coded model outputs displayed on watershed maps were used to prioritize “at-risk” stream reaches for monitoring and future studies based upon higher percentages of accumulated wastewater in the stream (i.e., red and dark orange stream reaches in Figure 3, map A), higher estimated levels of a CEC such as the pharmaceutical carbamazepine (Figure 3, map B), or estrogenic capacity measured as 17β-estradiol equivalency (E2EQ, Figure 3, map D). Ongoing curation of thermodynamic and rate parameter inputs for CECs and improvements to the ACCWW code have resulted in the expansion of capabilities for predicting environmental concentrations and ecotoxicity vulnerabilities for over 70 different CECs [85,435,439].

Model outputs have been applied: (1) to evaluate de facto reuse and propensity for disinfection by-product formation (#24, 35) in drinking water systems [456,457] and (2) to provide screening level assessment of potential ecological risk within a stream reach or watershed [84,85,458,459]. In one type of risk assessment approach, risk quotients (RQs) are calculated as a ratio of the PEC over the predicted no-effect concentration or quasi-equivalent converted toxicity concentration (PNEC_eq), where RQ = PEC/PNEC_eq [84,85]. This approach links constituent concentrations to potential adverse biological effects and allows comparison of individual contaminants, both within and across contaminant classes. In [85], RQ values were then summed (assuming the most simplistic additive risk model) to produce a risk index (RI) for each stream segment. High RI values indicate higher risk to aquatic life, with RI > 0.1 indicating some potential for “risk” and RI > 100 indicating “high risk” for adverse effects on aquatic life. ACCWW model outputs can then illustrate (a) the percent of stream kilometers with greater risk from impacts of wastewater contaminants and (b) watershed maps showing the mean-annual RI values (based on mixture of up to 51 municipal wastewater-derived contaminants) across the watershed (Figure 4). As determined in previous studies [85,435], six percent (1479 km) of the total stream kilometers in the Potomac River watershed had mean-annual RI_PNEC (predicted no-effect concentration equivalent risk index) values >100 using this approach, indicating “high risk” of potential effects for the most sensitive aquatic species (Figure 4A,B). This is just one example of how wastewater models coupled with hydrologic transport models can be used for assessments of water quality in watersheds. Improved model inputs and mechanistic forcing parameters would support expansion of such simulations of de facto wastewater reuse into more watersheds and model application to the many water quality challenges accompanying water scarcity expected in the future.

Identified gaps and limitations, as well as possible options for closing those gaps, are listed in Table 13.

Figure 3. (A) Map of Shenandoah River Watershed showing accumulated municipal and industrial wastewater discharge as percentage of total stream flow. Additionally, maps of Shenandoah River Watershed showing predicted environmental concentrations (PECs, shown as stream segment lines) for CECs derived from municipal wastewater treatment plant discharges using mean August streamflow and measured environmental concentrations (MECs, shown as circles) from mobile laboratory samplings for (B) pharmaceutical carbamazepine, (C) endocrine-disrupting compound estrone, and (D) 17B-estradiol equivalency quotient (E2EQ) used as a proxy for estrogenic capacity of the water. ACCWW: percent of accumulated wastewater. DWTP: drinking water treatment plant. CECs: contaminants of emerging concern. MDL: method detection limit. (This figure is adapted from and combines excerpts from Figure 2 and Figure 5 in [448], with permission of the corresponding author. Reprinted with permission from Barber, L.B.; Rapp, J.L.; Kandel, C.; Keefe, S.H.; Rice, J.; Westerhoff, P.; Bertolatus, D.W.; Vajda, A.M., Integrated Assessment of Wastewater Reuse, Exposure Risk, and Fish Endocrine Disruption in the Shenandoah River Watershed. Environ. Sci. Technol. 2019, 53, 3429–3440. https://doi.org/10.1021/acs.est.8b05655, American Chemical Society.). The related USGS data release is Barber et al. [460].

Figure 4. (A) Percent of impacted river kilometers as a function of the predicted no-effect concentration equivalent risk index (RI_PNEC) risk category, flow condition, and Strahler stream order. (B) Watershed risk map showing mean-annual RI_PNEC values across the Potomac River watershed, shown as stream segment lines scaled by Strahler stream order (RI_PNEC values represent a mixture of 51 municipal wastewater-derived chemicals across impacted streams; streamflow conditions represent mean gage-adjusted EROM (Enhanced Runoff Method) estimates for the period from 1971 to 2000 [454]; map projection used: Albers equal area and North American datum, 1983). (This figure is adapted from Figure 7 in Faunce et al. (2023) [85] published under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Used and adapted with permission of the corresponding author.).

3. Capabilities and Gaps for Modeling Priority Constituents

This section describes a large collection of inputs, processes, and activities affecting each constituent or constituent group (i.e., water temperature, salinity, nutrients, sediment, geogenic constituents, and contaminants of emerging concern) considered herein across the atmospheric-terrestrial-hydrologic-human system and thus influencing water quality for ecosystem and human beneficial uses. Both natural and anthropogenic drivers of each constituent are considered. After providing brief overviews of the importance of each constituent and summarizing existing relevant modeling tools, gaps in the modeling of each constituent are discussed and summarized in a table, alongside the gaps’ importance and opportunities for addressing them. Each of the constituents considered is associated with its own table within the companion data release [102], which provides detailed information on existing relevant modeling capabilities. Numbers in parentheses refer to the numbered inputs, processes, and activities in Figure 1 and Table 2.

3.1. Water Temperature

Water temperature is a principal ecological and water quality variable that determines the overall health of aquatic ecosystems [461] by affecting fish growth, reproduction, and locomotion [462], invertebrate individual performance and communities [463], instream biogeochemical processes [463], and the emergence of HABs [464]. Water temperature also affects gas solubility (e.g., O₂ and CO₂) and rates of reactions [463,465]. It is accepted that average water temperatures in many locations will increase over time with increased air temperature associated with projected future climate [466,467,468,469]; this process is expected to be exacerbated by expanding impervious area and increasing water withdrawals to satisfy growing human needs. It is well documented that anthropogenic modifications change the amount and timing of heat load delivered to streams and that streams differ in their sensitivity to these modifications and their assimilative capacity for heat [18,104,466]. Urbanization increases surface water temperatures through urban heat island effects, deforestation and loss of riparian vegetation (#4), runoff from impervious surfaces (#33), discharges from power plants (#31), industrial and wastewater treatment facilities (#21, #25), and warming of waters in shallow retention basins [466]. Groundwater recharge (#34) is often reduced in urban environments, causing a reduction in baseflow (#38), thereby affecting the temperature-buffering capacity provided by groundwater flow to streams. Runoff from agricultural land (#17) is higher and faster than from naturally vegetated lands, resulting in stream temperature responses similar to those found in urban environments; however, surface water and groundwater are more strongly interconnected in agricultural watersheds (#38).

Water temperature is a widely measured and modeled aquatic parameter, and most local to regional water and energy budget processes affecting water temperature are generally well understood. The atmospheric components of energy budgets combined with the effects of discharge, bed properties, and topographic characteristics are well documented and widely modeled (see Table 10 in the companion data release [102] for summaries and details of modeling capabilities for inputs, processes, and activities affecting water temperature). Atmospheric conditions, especially incoming shortwave radiation (#3), are generally the most important factors affecting surface heat exchange and are relatively easy to model (HeatSource [123] and SHADE-HSPF [470]). Stream discharge is a function of surface and subsurface inflows and outflows (#38) and mainly affects the volumetric heating or cooling capacity of a river (example models include DHSVM-RBM [471] and HFLUX [472]). Topography affects atmospheric heating of water, depending on riparian vegetation, upland shading (#4), stream orientation, and other factors such as latitude, altitude, and geology (models that incorporate these factors include GIS/LIDAR methods [473], DHSVM-RBM [471], and OTIS [254]). Streambed properties such as channel dimensions (i.e., width and depth), sediment conduction, hyporheic exchange (#42), and groundwater input (#38) affect heat exchange processes between the surface and subsurface (example models include MODFLOW [393], GSFLOW and SNTEMP [474], and OTIS [254]). Many surface water hydrodynamic models for rivers, lakes, and estuaries compute water temperature, as temperature influences density, which in turn affects hydrodynamics; such two-way coupling of temperature and hydrodynamics is typical of models such as EFDC [335], D-FLOW Flexible Mesh [275], and SCHISM [274].

Although many processes affecting water temperature are well understood, significant barriers exist for observing or parameterizing many components that affect water temperature at broad scales, especially for aquatic populations and headwater streams. In the U.S., present-day temperature sensor locations are typically biased toward higher-order confluence reaches, with limited coverage of lake and reservoir temperature data nationwide [312,475,476]. This strains temperature prediction capabilities to accurately model low-order stream and waterbody temperatures at the CONUS scale. Merging of datasets collected by various organizations could help address some of these measurement gaps; however, differences in quality standards may limit such merging. Consolidating the multitude of water temperature datasets collected by various sources is no small feat, but efforts such as the joint National Water Quality Monitoring Council/USEPA/USGS Water Quality Portal [477] and the U.S. Forest Service’s NorWeST database [478] are setting examples of how this could be accomplished. For example, a recent data release collated stream temperature observations from across the United States from four data sources [479], which was then used in a subsequent effort to calculate a large set of annual metrics between 1948 and 2022 and long-term monotonic trends [480].

Groundwater can greatly affect stream temperatures and is highly relevant to aquatic organisms, but its location and relative influence is highly heterogeneous at small (e.g., reach) to large (e.g., region) spatial scales. Accurately predicting locations of groundwater discharge and the relative influence on stream temperature at those locations at resolutions required by stakeholders is beyond our current ability. However, progress has been made recently inferring groundwater discharge contribution to streams at broad scales with a diagnostic tool, which can aid improved predictions of stream responses to perturbations such as changing climate, wildfire, and land use conditions [481,482,483]. Another critical factor is dam operations (#39), which play an important role in controlling downstream temperatures; however, specific information regarding these operations, such as reservoir temperatures and the mixture of water from different intake depths, has only recently been organized into a standardized multi-agency dataset [329].

Data-related challenges associated with modeling water temperature likely vary from country to country. However, in the U.S., locally relevant national-scale temperature predictions or observational datasets are lacking; resource managers could use these data to optimize drinking water plants [484], predict evaporative water losses (#5), decide which fish to stock (#18), and design thermoelectric plants (#31) under climate and regulatory uncertainty. More mechanistic research, data collection, and model incorporation in the following areas could support management decisions: the water-temperature effects of groundwater-surface water interactions (#38); snow, ice, and glacier melt (#7); human activities such as wastewater treatment (#21) and power generation (#31); and projected future climate (e.g., resilience of hypolimnetic cold water in reservoirs and dam releases to streams) (#39) [19]. Another advancement would be expanded understanding and definition of thermal refugia for aquatic populations [485], including vertical temperature structure of the water column, the role of groundwater and hyporheic flow (#36, #38), mechanistic understanding of cold-water patches, data on thermal refuges at regional to global scale, and (ultimately) the ability to predict their development and distribution. Development and assessment of relevant metrics could help establish species-independent thermal thresholds and exceedances to be used alongside other information to predict eutrophication and habitat conditions. Integration of deterministic model outputs with fisheries information and ecosystem dynamics could help improve understanding of the role that physical habitat structure and complexity play in aquatic species’ population resilience to thermal stresses.

A list of identified gaps and limitations associated with temperature modeling is provided in Table 14 herein.

3.2. Salinity

Elevated salinity is a worsening problem for human beneficial use and ecosystem health, historically problematic in arid regions and coastal areas, and more recently in temperate humid regions as well [26,486]. Salinity is a measure of the mass of dissolved salts in a given mass of solution [487]. Specific conductance can be used as a proxy measurement for salinity and total dissolved solids, but the most comprehensive method of measurement is to sum the constituent concentrations using a geochemical speciation code such as PHREEQC because it accounts for the chemical speciation of all constituents [222,488]. Although most classification schemes define freshwater for general use as less than 1000 mg/L of dissolved solid content [21,489], the USEPA has defined a secondary drinking-water standard of 500 mg/L [22]. Freshwater naturally contains dissolved constituents that originate from atmospheric deposition (#1) and water-rock interactions (#11, #12), but large increases in salt ion concentrations currently occur due to anthropogenic sources or activities (#13, #15, #17, #19, #20–27) [26,488,490,491,492]. These sources or activities can mobilize contaminants from soil/sediment/rocks or by corrosion of plumbing and distribution lines and can, therefore, negatively affect drinking water quality and aquatic life [493,494,495,496] as well as infrastructure and agricultural returns [491,492,497,498]. Widespread changes in water temperatures, salinity, alkalinity, and pH have been documented in inland waters of North America and affect ion exchange, weathering rates, chemical solubility, and contaminant toxicity [493]. Increasing major ion concentrations linked with salinization (Ca²⁺, Mg²⁺, Na⁺, Cl⁻, and SO₄²⁻, HCO₃⁻) contribute to multiple stressors such as changing the acid-base status in streams and rivers and mobilization of chemical mixtures, such as those associated with brownification or eutrophication, resulting in freshwater salinization syndrome [26,499]. Furthermore, high concentrations of dissolved solids enter groundwater (#36), which can become dominant water sources at baseflow (#38) and thereby affect ecosystem health and the quality of water for human uses during low-flow times of the year when the ecosystem may be most sensitive to fluctuations in water quality [494].

The modeled processes affecting salinity are most widely available for soil and unsaturated zone transport, riverine and estuarine hydrodynamics and transport (#40, #41), saltwater intrusion in both surface water and groundwater (#45) [26,500], groundwater flow and transport (#40, #41), and geogenic sources/hydrogeochemical interactions (#43). (Existing models and tools for these processes are listed in Table 11 of the companion data release [102]. See also Section 2.2, Section 2.4, Section 2.7, and Section 2.8 herein). In arid areas where crops require irrigation, models such as HYDRUS [501] are widely available that simulate the concentration and long-term accumulation of salts in soils that result in decreased yield [502,503,504,505]. SALTMOD is an agro-hydro-salinity model that has been used to predict the long-term impacts of salinity on soils and understand the complicated interrelations between irrigation and agricultural practices [505]. Several models (e.g., WASP [283], HEC-RAS [506], OTIS [254], CE-QUAL-W2 [137], EFDC [335]) are also available to simulate salinity and biogeochemical transformations in riverine transport. Salinity in lakes and reservoirs, as well as dam operations and biogeochemical transformations, can be modeled using CE-QUAL-W2 [137], EFDC [335], ModSim [319], and HEC-ResSim [507]. Multiple estuarine hydrodynamic models (e.g., D-Flow FM [275,338], ROMS [331,339], SCHISM [274]) are used to accurately compute temporally changing salt fields as a function of gravitational circulation, river flow, tidal advection and dispersion, wind, and other processes, given high-quality boundary condition data to drive simulations (e.g., [338,372,508]). However, in extreme coastal storm events, salinity fields can be rapidly and significantly impacted by bi-directional forcings [359,509]; the ability to dynamically model these interacting processes crossing the watershed-coastal domain is very recent [373].

For the groundwater domain, the effects of brines (#12), saltwater intrusion (#45), road deicer contamination (#27), mine waste (#30), agricultural recharge (#34), artificial recharge (#28), or sea level rise (#44) on the hydrobiogeochemistry can be modeled using geochemical models such as MINTEQ [223] and PHREEQC [222]. Seawater intrusion (#45), which will become progressively more common with sea level rise (#44) [107,510,511], affects freshwater chemistry through mixing, mineral dissolution or precipitation (#12), adsorption, and ion exchange (#43) [500] that can be understood through numerical modeling, geochemical modeling, and reactive transport codes [512,513]. The effects of the sources and processes listed above on groundwater flow and transport of salinity can be modeled using variable-density groundwater-flow models such as SEAWAT [370], a computer program that simulates flow using a modified version of MODFLOW-2000 [514] and simulates transport with a version of MT3DMS [515]. The effects of sea-level rise and subsequent increases in freshwater salinity on aquatic habitat and drinking-water quality are not well understood. The inundation of estuaries and aquifer sediments by seawater, for example, can be simulated to determine (1) the effects on pH, redox chemistry, and dissolved oxygen, and the release of nutrients, metals, and organic carbon, and (2) the biological response to these changes [516,517,518].

Water quality models that consider and incorporate geochemical processes such as cation exchange and mineral dissolution or precipitation support better understanding of the unintended consequences of increasing salinity [21,519,520,521,522]. Understanding the water quality changes that result from the mixing of waters with varying salinities or compositions can inform water or land-use management or policy decisions that invoke these changes [26,493]. These water quality changes can be modeled to help characterize and understand consequential biogeochemical reactions. For example, water quality changes (and associated salinity increases) can have unintended and potentially dire consequences for drinking water quality and aquatic ecosystems [493,523]. Such changes can be brought about by agricultural practices (#13–20) [524], evaporative concentration of salt ions (#5), desalination or blending of water with differing compositions (#24) [525], sediment and weathering-related processes (#8–12), application of road deicers (#27) [522], and seawater intrusion (#45) from sea-level rise (#44) or over-pumping (#37) [26,526]. Expanded availability of biogeochemical reaction (#43) parameters would improve and support modeling capabilities and the understanding of interactions between multiple constituents associated with salinity and with the aquatic ecosystem and their effects on human toxicity [21,519,520,521,522].

Because saline water use will become increasingly important in the future, it is important to understand the baseline chemistry of entire aquifers where feasible [21]. Data could be compiled from multiple sources (local reports, databases, geophysical and lithologic logs, and numerical models) that provide estimates of needed parameters for regional assessments of priority principal aquifers for the generation of maps and geochemical data [21]. Baseline understanding includes developing knowledge of links between source-water geochemistry, required water treatment and distribution, and potential end users with the aid of geochemical modeling and simulations in different hydrogeologic settings [497].

Identified gaps and limitations in the modeling of salinity, as well as their importance and potential solutions for closing those gaps, are listed in Table 15 herein.

3.3. Nutrients

Nutrients are essential for ecosystem health but, when overly abundant, can lead to accelerated eutrophication, i.e., excessive algal and/or macrophyte growth [529], taste and odor problems, hypoxia or anoxia and consequent loss of aquatic life, HABs (e.g., if species such as cyanobacteria produce toxins), and degradation of drinking water [529,530]. Nitrogen and phosphorus are typically the nutrients of most interest because they often limit primary productivity in aquatic environments, and when they are in the form of nitrite, nitrate, and ammonia, they can affect human and biological health [531]. Nutrients enter aquatic systems from many different natural and anthropogenic sources. Important natural sources of nutrients include decay of plants and minerals [532], atmospheric deposition for nitrogen (#1) (which has increased due to fossil fuel combustion [533]), and erosion for phosphorus (#8) (which has been greatly increased due to changes in land use and certain types of land management). There are many other anthropogenic sources of nitrogen and phosphorus, such as fertilizers (#13), manure (#14), wastewater treatment plants (WWTPs; #21), septic systems (#22), and mine discharges (#30). There are also legacy sources stored in various hydrogeologic compartments, such as groundwater, agricultural fields (#13–14, #17), streambanks (#10), shorelines, stream channels, wetlands, and sediments of impounded water bodies, estuaries, and the coastal ocean (#42). During field-to-stream and downstream transport, several key processes change the amount and form of nutrients. Examples include physical processes such as erosion from fields (#8), streambanks (#10), and channel bottoms (#9), drainage and water movement from tile drains (#19) and irrigation (#20), sedimentation (#9), and seawater intrusion (#45). In addition, important biogeochemical processes affecting the form and concentrations of nutrients include changes in redox conditions and pH (#43), nutrient uptake by primary producers, nitrification, and denitrification (#43). Nutrients are also transported in groundwater and released from groundwater to streams (#36) and from streams back to groundwater (#38); this is referred to as “hyporheic exchange”, which may be especially important in “losing” stream reaches and lake recharge areas. Many events and processes occurring in the watershed, such as floods, droughts, fires (#6), agricultural management practices (#17), and irrigation (#16), as well as urban construction activity (#26), can increase the delivery of nutrients to surface and groundwater. Complex ocean-watershed interaction processes, such as those induced by hurricanes, can significantly influence nutrient distributions, concentrations, and speciation [359]. Increased nutrient concentrations in water bodies often lead to increased photosynthesis, accelerated eutrophication, elevated pH, and depletion of dissolved oxygen that can increase nutrient release from bottom sediments of lakes and reservoirs (#42) (i.e., positive feedback mechanisms).

Several approaches are used to quantify the nutrient inputs to the landscape, as well as the form of these nutrients, information that is needed in modeling. Nutrient inputs in urban areas are often difficult to quantify other than from point sources such as WWTPs (#21) and commercial and industrial operations (#25) that are required by U.S. law to be quantified for specific nutrients. Point-source inputs can be estimated from data contained in the Integrated Compliance Information System database [534]. However, the quality of these data is often inconsistent, nitrogen releases are rarely documented, and release data from small facilities are often not available. Inputs from septic systems (#22) are rarely directly measured and, therefore, are often neglected in many modeling exercises or estimated from simple empirical relations. An example of an approach to estimate the input of nutrients from septic systems is the Reckhow, Beaulac, and Simpson [248] relation based on the number of people using septic systems as well as the soil type [94]. Nutrient inputs to agricultural areas (#13–14, #17) are typically estimated on a farm-to-farm basis or from county fertilizer sales [535] and farm livestock population estimates [536]; however, the timing of fertilizer application and land management practices are typically not available, especially on a large scale [537]. For the U.S., atmospheric inputs of nitrogen (#1) are measured by the National Atmospheric Deposition Program [538], and the individual sources of that nitrogen have been modeled by the U.S. Environmental Protection Agency Community Multiscale Air Quality (CMAQ) program [539]. However, estimates of atmospheric inputs of phosphorus are limited, except from site-specific studies [540]. Many of the minor sources of nutrients, such as septic systems (#22), urban fertilizers (#13), and atmospheric phosphorus inputs (#1), are often ignored in many modeling studies [120].

Export of nutrients from the landscape is often estimated using empirical models, such as general land-use-specific export rates [248] that may be adjusted using specific land-use management effectiveness rates (e.g., the Spreadsheet Tool for Estimating Pollutant Loads, (STEPL) [249]). Export of nutrients and the form of these nutrients (i.e., particulate or dissolved forms and organic versus inorganic fractions) are also estimated with process-based watershed models, such as the commonly used Soil and Water Assessment Tool (SWAT) [236,263] or Hydrologic Simulation Program (HSPF) [541], which require detailed information describing the landscape, nutrient inputs, and management actions. Two models used to estimate nonpoint nutrient losses from urban areas are the Source Loading and Management Model (WinSLAMM) [250] and P8 [542], which use detailed land-use and management-control device information in the basin. Groundwater flow and transport of nutrients are often modeled using (1) process-based groundwater-flow models such as MODFLOW [514] coupled with a particle tracking model (e.g., MODPATH [543] or MT3DMS [515]); (2) integrated flow and transport models, such as MODFLOW-6 [393], MT3D-USGS [394], or PFLOTRAN [396]; or (3) reduced-complexity models, such as travel time distribution models [382,383,544]. Several models have been used to describe the transport of nutrients in selected rivers (i.e., small-scale transport). Examples are the process-based Hydrologic Engineering Center River Analysis System (HEC-RAS) [506] model that can be used to simulate 1-D and 2-D steady and unsteady flow hydraulics and nutrient transport and fate; the CE-QUAL-RIV1 model that can be used to simulate 1-D transport for unsteady flows [545]; P8 [542]; and the 2-D CE-QUAL-W2 transport model [306], which uses detailed land use in the basin and reservoir operation information. Other models and coupled modeling frameworks are used to compute detailed nutrient transport and transformation processes in rivers and estuaries (e.g., WASP [282], DELWAQ (or “D-Water Quality”, module of Delft3D or Delft3D FM) [235], SCHISM-ICM [286], CoSINE [237]). Large-scale nutrient transport has been estimated with the hybrid Spatially Referenced Regression on Watershed attributes (SPARROW) model [120,266], the Catchment Land-Use for Environmental Sustainability (CLUES) model [120,266,267], and large-scale SWAT models [546,547]. During downstream transport, flow is often intercepted by lakes and reservoirs, which affect the amount and form of nutrients resulting from stratification (#40), sedimentation, internal nutrient releases (#42), biological productivity (#43), and reservoir management (#39) (withdrawal depths and volumes). Please see Section 2.6 (Lake and Reservoir Water Quality Modeling) for a more detailed description of nutrient modeling in lakes and reservoirs. A more detailed list of nutrient models is provided in Table 12 in the companion data release [102].

Daily nutrient fluxes in streams used for model calibration and validation are typically computed based on flows and water quality concentrations measured at specific locations using numerical algorithms such as GCLAS [548], LOADEST [549], Fluxmaster [266], Flux32 [550], or the Weighted Regressions on Time, Discharge, and Season (WRTDS) [551,552,553]. WRTDS has been particularly useful for estimating long-term trends in water quality after adjusting for the effects of changes in discharge and seasonal variations.

There are several gaps that, if filled, would improve the ability to simulate the transport of nutrients from where sources are applied to fields or from where point sources are directly added to rivers to the downstream receiving aquifers and water bodies, as well as the changes in nutrient concentrations during this transport. Most watershed models simulate nutrient concentrations based on inputs from the individual sources; however, some inputs are not well known and are therefore neglected in many model applications. Omitting inputs of specific nutrient sources can result in a misrepresentation of the importance of other sources that are included in the model, especially when statistical models are used [554]. If inputs of a source are not included, their importance is attributed to the other variables that are included in the model so that the simulated loads better match the loads used to calibrate the model. More accurate source apportionment by models would be supported by quantification of these typically neglected sources, such as atmospheric phosphorus inputs (#1), nutrients from construction sites (#26), nutrients from commercial and industrial plants (#25), phosphorus added to drinking water to inhibit the release of lead (#23), nutrients released from septic systems (#22) and transferred via irrigation (#20), nitrogen from biologic fixation and losses from denitrification (#43), and nutrients from legacy sources, such as soil, groundwater (#36), streambanks, and bottom sediments of channels and reservoirs (#42). Nitrogen in WWTP effluent (#21) has not been frequently measured, although such measurements have been made more recently [555]. Although considerable effort has been made to quantify phosphorus (and more recently nitrogen) in the effluent of WWTPs [556] and to incorporate and quantify the relative importance of WWTP inputs [554], little has been done to incorporate the inputs of nutrients from WWTP byproducts (sludge) into watershed models. More could be done to quantify the inputs of nutrients from sludge and where it is applied to the land [557]. Without including this sludge as a source in a model, its importance could be allocated to other agricultural sources where the sludge is applied. Septic systems are often only considered as a source of nitrogen and phosphorus when the systems are considered to be failing; however, all septic systems could be considered [558,559] sources of nitrogen and phosphorus [560]. Inputs from septic systems can be especially important when the systems are located on the nearshore of lakes [561]. Many agricultural management actions, including specific field practices (#17) and fertilizer (#13) and manure (#14) application rates and patterns, alter the hydrology and are used to reduce the delivery of nutrients to nearby streams. However, detailed information describing the implemented management practices and the specific amounts and timing of fertilizer and manure application for large areas is only available at a relatively coarse scale (such as a HUC04 scale [562] or county scale [537]), and fine-scale information is not typically available without contacting individual farmers. (“HUC” refers to Hydrologic Unit Code [434].) Many U.S. Department of Agriculture—Natural Resources Conservation Service programs require farmers to provide specific land management information; however, this fine-scale information is kept confidential [563]. Fine-scale application rates and management information could be used to better simulate the effects of management actions [564] and forecast the impacts of changing those land practices.

Continued improvement of process-based and hybrid models could expand our understanding of how nutrients are delivered to streams, what the major sources of nutrients delivered to streams are, and which areas contribute the highest amounts of nutrients (i.e., hotspot identification). Hybrid models, such as SPARROW, have been typically used to estimate long-term mean annual nutrient transport over very large areas, such as the CONUS [266,565] and the Mississippi River Basin [558,559]. Continued development of dynamic SPARROW models [566] to incorporate intra- and inter-annual variability in transport that is typically only simulated with process-driven watershed models could help characterize nutrient delivery at seasonal scales and describe the importance of legacy sources of nutrients. Empirical and hybrid nutrient models typically only simulate the delivery of total nitrogen and total phosphorus; however, studies have shown that dissolved forms of these nutrients can be important in driving stream and reservoir productivity [567]. Many factors affect the downstream transport of nutrients, including the magnitude of streamflow used to simulate instream decay, aquatic plant uptake and release, settling, internal nutrient release from the bottom sediments (#42), and denitrification; however, flow management and its effects have not been well documented or simulated at large spatial scales. Currently, wide-scale flow estimates that are available throughout the U.S., such as from the National Hydrologic Model [568], do not account for anthropogenic effects (i.e., reservoirs and their management). Improved streamflow estimates at unmonitored reaches throughout the country could enable better estimates of velocity, which are used for instream decay in some models. Various anthropogenic features, such as reservoirs, affect flow [569] and instream nutrient transport [120]. Specific information for each reservoir, such as its morphometry, release timing, and depth of release (#39), would support quantification of the effects of reservoirs [570,571]. Much of the information on reservoir management can be obtained for an individual reservoir, but this information is not assembled in a database for ready use in large-scale nutrient modeling studies. More thorough incorporation of the effects that reservoirs have on water quality into large-scale watershed models could enable more accurate simulation of the downstream transport of nutrients over large areas. See Section 2.5 (Lake and Reservoir Water Quality Modeling) and Section 2.6 (Reservoir Operations and Outflow Modeling) for further related discussion.

Similar to other constituents, monitoring data describing nutrient concentrations and loads are often limited. Additional collection of nutrient data in streams, groundwater, and reservoirs would potentially improve model calibration and verification, especially if collected in areas where specific management practices have been implemented. There have been recent advances in approaches to compute loads. The WRTDS load program that uses daily flow inputs has been improved to account for model residuals and their autocorrelation structure [553]. Additional improvement in the computation of loads could be possible if WRTDS and other load-estimation approaches considered subdaily flows and subdaily changes in water quality. Identified gaps and limitations in modeling of nutrients, as well as their importance and potential solutions for closing those gaps, are listed in Table 16 herein.

3.4. Sediment

Fluvial sediment is transported as suspended load or bedload [572]. Sediment in transport is a product of weathering (#11), soil erosion (#8) and delivery to the channel, streambank erosion (#10), and channel bed and bar resuspension and deposition (#9), which are often described through the “sediment cycle” [573]. Sediment models address some or all portions of this cycle, including topsoil erosion (#8), streambank erosion (#10), and delivery and transport of sediment (suspended and/or bedload (#9)) [572,573]. Please see Table 13 in the companion data release [102] for details of modeling capabilities for inputs, processes, and activities affecting fluvial sediment across the hydroscape.

Rivers naturally transport sediment, but human activity can both elevate and decrease sediment loads to detrimental levels. High sediment loads and sediment concentrations in streams can degrade ecologic habitat, reduce reservoir storage, foul drinking water intakes, bury navigation channels, and provide a conveyor for other contaminants such as metals and nutrients [574,575] (see Table 1 herein for water quality constituents that affect specific human and ecosystem uses and benefits). In some aquatic systems, very low suspended sediment concentrations can have negative ecosystem ramifications such as (1) increased light availability for algal growth and consequent increase in the risk of eutrophication [576], (2) diminishment of habitat quality for sensitive species requiring turbid conditions (e.g., effects of turbidity on trout species [577]), (3) insufficient delivery of nutrient and sediment in rivers, floodplains, and deltas, and (4) lowered sustainability of tidal marshes facing drowning by rising sea levels [578]. Additionally, lower suspended sediment loads, such as below dams, can (5) affect the equilibrium state between water and sediment, leading to channel downcutting [579], and (6) expose legacy contaminants as surface sediments erode [580]. Excess sediment can result from land-use practices and natural causes (e.g., agriculture and landslides), with a wide range of water quality and ecological impacts, including: (1) clogging stream channels and reservoirs, (2) conveyance of nutrients and pesticides, (3) limiting light penetration and the ability of aquatic plants to conduct photosynthesis, (4) clogging of the gills of aquatic organisms, and (5) suffocation of fish eggs and macroinvertebrates through covering of coarse substrates and deposition in pools [581,582]. Understanding of sediment-related problems and development of management strategies for stakeholders could be supported by expanded knowledge of sediment processes and linkages, namely the sources of sediment, storage areas, and loads [577,578,579,580].

In general, sediment sources can be separated into the two general categories of upland soil erosion (#8) and channel erosion (#9). Soil is a product of chemical and physical weathering and the erosion of soil, which can be exacerbated by natural (e.g., hurricanes [359] and wildfires (#6) [583]) and anthropogenic impacts (e.g., construction (#26) and agricultural activities (#17, 19)). Channel sources are related to the erosion of the stream channel (bed, banks, and floodplain) and are affected by large flood events and anthropogenic activities (e.g., dams (#39), channelization). The identification of upland and channel sediment sources can hold substantial economic importance for stakeholders who face decisions on whether to focus on soil conservation efforts or stream restoration [103].

Sediment models can be generally grouped into statistical, process-based, and hybrid models, where sediment is modeled at the reach, river, or watershed scale with temporal scales ranging from hours to years to millennia. Multiple reviews of sediment models have been presented [584], and several sediment models and tools are cataloged with suggested appropriate uses on the USEPA website [585]. Additionally, a range of mechanistic local-scale models of morphodynamics have been developed to simulate processes ranging from bank erosion during flood events to landscape evolution [586]. Statistical models range from simple regression (e.g., sediment rating curve of discharge versus sediment loads) to parametric and non-parametric classification models (e.g., multivariate adaptive regression splines or classification and regression tree) [587]. Hybrid approaches between statistics (e.g., sediment rating curve) and physical process modeling can describe sediment transport with reduced complexity and lower computational cost and data requirements (e.g., [588]). For example, SPAtially Referenced Regression On Watershed attributes (SPARROW) is an empirical, regression-based model constrained by mass balance calculation to predict in-stream water quality relevant to spatially referenced watershed characteristics [565]. More recently, the application of Ensemble Machine Learning (ML) to surface hydrological processes, including river water quality, debris flow, and sediment transport, has shown improvements in predictive capability in the advent of higher computational efficiency and environmental data availability [589]. For example, Lund, et al. [590] applied extreme gradient boosting ML models, trained by physically collected samples with publicly available geospatial data as feature variables, to predict suspended sediment and bedload.

Soil erosion and transport mechanisms are often included in watershed-scale process-based simulation models. For example, the relatively simple Erosion Productivity Impact Calculator (EPIC) is a field-scale continuous simulation model that assesses the effects of soil erosion on agricultural productivity and water quality [591]. Similarly, the Agricultural Policy/Environmental eXtender (APEX) model dynamically performs long-term simulation of farming practices and associated sediment impact on water quality [592]. More complex watershed-scale models offer a comprehensive process ensemble, including simulation of water quantity and quality for a wide range of pollutants from complex watersheds to receiving waters [592]. For example, Hydrological Simulation Program-Fortran (HSPF) and Soil and Water Assessment Tool (SWAT) are watershed scale models that simulate sediment yield given land management practices using physical processes (e.g., critical shear stress exerted by the water) associated with water movement, soil erosion, and transport both upland and in-channel [269,593]. Many models, including those described above, rely on some version of the Universal Soil Loss Equation (USLE) [269,593].

Though this section focuses primarily on freshwater, non-tidal sediment modeling, here we cover some relevant coastal and estuarine sediment models. For example, at the local, reach, and system scale, a number of detailed, multidimensional process-based models for rivers and estuaries exist for computing suspended sediment concentrations (e.g., EFDC [335,336,337], WASP8 [282,594], and in some cases also geomorphic change (e.g., Delft3D FM Suite [284], COAWST [348], FVCOM [595]), with many other models accessible through the iRIC platform [272,277]. Coastal and estuarine sediment models typically compute the transport of three or more size classes, each with its own settling velocity [343]. Some state-of-the-art coastal sediment modeling frameworks couple to wave models due to the important combined influence of waves and currents on bottom shear stress [584]. Indeed, some coupled hydrodynamic-sediment-geomorphic models also incorporate two-way coupling to vegetation [353,584,596], and tight coupling of watershed and ocean models has recently been achieved to capture the non-linear interactions between overland runoff, coastal dynamics, and sediment transport as a result of extreme weather events such as hurricanes [374].

In many models, it is unclear whether sediment yield pertains to suspended or bedload transport as they compute the total-load transport equation, which combines bed- and suspended-load transport equations to reduce computational costs (e.g., HEC_RAS) [597]. On the other hand, the USDA Forest Service bedload model BAGS requires bed material size gradations and channel cross-section geometry to explicitly estimate bedload [598]. Only a few models estimate and differentiate upland sediment sources (erosion from various land use/land covers) versus sources near- and in-channel (e.g., streambank erosion). Models that do examine streambank erosion at the reach scale include the Bank Stability and Toe Erosion Model (BSTEM) [599] and the Bank Erosion Hazard Index (BEHI) [598]. These models also incorporate vegetation information, such as root density. At the watershed scale, only few models handle in-channel processes, including SWAT [236,263], which contains an excess shear stress approach to estimate streambank erosion, and the WARSSS model [600], which identifies hillslope, hydrologic, and channel (#33) processes responsible for significant changes in erosion (#8), sedimentation (#9), and related stream channel instability. Recently, modeling efforts have considered spatially explicit source areas. For example, a network-based river routing model with specific sediment source area attributes incorporates network topology, channel characteristics, and transport-process dynamics to simulate transport of fines, sand, and gravel [601]. Additionally, a watershed-scale topography-driven sediment delivery model was developed to explicitly consider spatially explicit and distinct upland versus near-/in-channel sources, and the simulation results were used to recommend effective sediment management strategies [602,603].

Thus, one important gap in current sediment modeling is the capability to identify and quantify sediment contributions, not only from upland sources, but also from near- and in-channel sources. Many factors control sediment storage and transport in river channels, including both exogenous (i.e., sediment supply) and endogenous (i.e., channel hydraulics) processes, as well as anthropogenic forcing (e.g., land use, channelization, and dams) [604]. This gap could be addressed and a more complete understanding of sediment processes could be built with multiple lines of catchment data, including not only sediment source fingerprinting and sediment budget investigation but also ecological and anthropogenic impacts on sediment sourcing, storage, and transport [604,605]. For instance, Refs. [606,607,608] developed the Sediment Source Assessment Tool (Sed_SAT) to “fingerprint” the sources of watershed-derived sediment. The Sed_SAT model requires robust field collection of sediment sources and target geochemical data and uses a parametric statistical procedure to estimate sediment contributions. Additionally, remote-sensing detection and cataloging of river morphology (i.e., meander, widening, and incision) can provide insight into near- and in-channel sediment source contribution (e.g., Interferometric Synthetic Aperture Radar (InSAR) analysis from satellite imagery to map aggradation/degradation along the stream network [609,610]).

Another gap in sediment modeling is appropriate representation of environmental interfaces—i.e., biological, chemical, and physical processes at air-water, water-sediment and water-vegetation interfaces—in predicting sediment loading [10]. Sediment processes occur at the environmental interfaces, but we lack a comprehensive understanding of the interface mechanisms that affect soil erosion, storage, residence time, and loading, and as a result, most models do not simulate the physical, chemical, and biological processes that may be accelerated within these interfaces [10]. For instance, the coupling between turbulence and sediment transport is experimentally difficult to investigate, leading to an incomplete representation of bed load transport and suspended transport in mechanistic models [611]. Soil condition can also significantly impact sediment processes, and its interface with biology and biogeochemistry, as well as land management, is related to the water cycle and sediment dynamics. Most models, while simulating surface processes associated with rainfall runoff, erosion, and transport, do not adequately represent soil water storage and surface roughness and their combined impact on sediment sourcing, delivery, and storage [10]. For example, though the incipient motion criterion is well established for calculating critical shear stress (CSS) for cohesionless uniform sediments, CSS is still under investigation for cohesive clayey non-uniform sediment [612]. Also, more detailed understanding of sediment trapping processes in floodplains, wetlands, and aquatic vegetation is required for reliable sediment modeling [613]. Flocculation processes, which can be particularly important in estuaries [614], are not included in most models, but they influence settling velocity, aggregation, and fragmentation of sediment particles, influencing storage of sediment in fluvial and estuarine ecosystems [334]. Coastal and estuarine models that do incorporate flocculation do not, as far as we are aware, couple biological models to sediment transport models at field scale to characterize the biological material that promotes aggregation [343,615].

Representation of sediment residence time and storage in the landscape on hillslopes [616], channel beds [617], and on floodplains [618] is another gap in current sediment process understanding and modeling capability. Great quantities of sediment can be eroded and transported episodically during high runoff events such as during river flooding. At the same time, sediment can spend longer periods of time in storage than in motion, and to account for spatial variability within the watershed system and the various time constants involved, the simple sediment delivery ratio could be replaced with a model that recognizes the various processes involved in the movement of sediment from the source area to the outlet [619]. Frameworks for simulating stochastic bedload transport processes [620] and suspended sediment delivery, deposition, and storage in the river system [621] provide a theoretical foundation for capturing sediment dynamics across a watershed. Such modeling applications could be supported by observations of the fate of sediment eroded from the land surface and various pathways and timeframes of sediment transport and storage mechanisms in the catchment [622]. Improved observation and characterization of riverbed and grain size distribution (e.g., high-frequency hydroacoustic instruments [623] and remote-sensing imaging technology [623,624]) and sediment flux, including suspended and bedload (e.g., long-term continuous acoustical instruments [625]), will likely improve predictive capabilities of sediment routing modeling.

Sediment modeling involves uncertainties associated with the model itself (conceptualization, process formulation, and parametrization) and with system observations used to drive the model [10]. Particularly, process-based sediment transport models require selection of parameters that are poorly constrained by observations, especially when extrapolating from local-scale, highly detailed mechanistic models to larger-scale watershed or river segment-scale modeling. Additionally, uncertainty in model predictions arises due to a lack of appropriate calibration data and the assumptions and parametrizations that are unsuitable for local conditions [626]. Coastal sediment models often have very little information on sediment boundary conditions associated with river inflows, and they are similarly limited by a lack of knowledge regarding spatio-temporal variability in sediment properties [343]. Even simpler statistical models, such as sediment rating curves, and more advanced machine-learning models are subject to limited predictive accuracy if long-term observations are not available to capture the changing environmental conditions [627,628]. Though uncertainty analysis is rarely conducted in water quality modeling, it could be used to inform decision processes that involve risk estimation associated with management scenarios from model predictions. Additionally, in order to adequately transfer knowledge from sediment modeling to water quality management, improved accessibility and distribution of modeling tools could be helpful [10]. Gaps in sediment modeling are summarized, along with their importance and opportunities for addressing them, in Table 17.

3.5. Geogenic Constituents

Geogenic constituents, which are generally related to geologic sources and include many trace elements and radionuclides, are among the most prevalent water contaminants in the U.S. and globally [629,630]. Geogenic constituent sources can be considered in three generalized categories: (1) natural sources distributed by natural processes (e.g., arsenic (As) and manganese (Mn) contamination in glacial and coastal plain aquifers [386,631,632]); (2) natural sources distributed by anthropogenic activities (e.g., As contamination in bedrock aquifers due to water table drawdown [633]); and (3) anthropogenic sources distributed by natural processes or anthropogenic activities (e.g., heavy metal contamination from mining or oil and gas production wastes or iron fouling in a pumping well [25,149,386,631,632,634]). These categories can overlap and change, creating ongoing challenges. Because geogenic constituents are ubiquitous in upper-crustal materials, dissolution of just small fractions during water-rock interaction can result in high concentrations, exceeding human health thresholds [37]. Geogenic constituent mobilization can be exacerbated by anthropogenic activities such as mining (#30), oil and gas development (#29), irrigation (#20), agricultural chemicals (#13–17), wastewater releases (#21, 22), landfills (#25), organic chemical spills (#25), and managed aquifer recharge (#28) (see Figure 1 and Table 2 herein). Atmospheric deposition (#1) can be a major or dominant solute source in both surface water and groundwater for constituents including oxyanions, chloride, nutrients, and metals. Atmospheric salts (#1) that have accumulated naturally in unsaturated zones over geological time scales can be leached suddenly by irrigation (#20) and managed aquifer recharge (MAR, #28), causing large and sometimes problematic concentrations in groundwater (e.g., nitrate, perchlorate, other salts). Additionally, other natural or human-enhanced processes can redistribute or enhance the mobilization of geogenic contaminants (e.g., flooding [635], saltwater intrusion (#45), road deicers (#27), wildfire (#6) [583], coastal storms [636], or CO₂ sequestration [637,638]).

Models based on the theoretical mobility of geogenic constituents and aquifer geochemistry are well recognized [209,639] and incorporate important drivers and processes such as (1) redox conditions, (2) pH, (3) sorption processes and ion competition for sorption sites, (4) formation of soluble complexes, (5) evaporative concentration, and (6) mixing and dilution. In practice, however, the behavior of geogenic constituents is difficult to predict, especially when the natural system is altered. Anthropogenic alterations exacerbate the complex interplay of multiple controlling factors. One key driver for many geogenic constituents is redox potential, especially for redox-active constituents with solubilities dependent upon oxidation state. Recent reactive transport model simulations at an oil spill site, for example, indicate that mobilization of geogenic arsenic will contaminate a larger groundwater volume and could pose a greater long-term water quality threat than benzene [640]. Processes that affect the distribution and mobility of geogenic constituents in groundwater and surface water include atmospheric deposition of geogenic constituents (#1) and hydrodynamics and transport in surface runoff (#33), groundwater recharge (#28, #34), rivers, and estuaries (#40, #41). There is varying availability of relevant data to inform models and availability of process or predictive models themselves; for example, the National Geochemical Database [641] includes geochemical analyses of over 1.4 million samples of geologic material such as soils, stream sediments, and rocks.

Table 18 herein summarizes some of the most important geogenic-related gaps in model capabilities and data/process understanding, along with opportunities to fill those model capability gaps. See Table 14 in the companion data release [102] for details of available modeling capabilities for geogenics (referred to as “geologically sourced” constituents therein). Substantial model capability gaps or data gaps exist for numerous processes that affect geogenic constituent distribution and mobility, as summarized in Table 18. MAR (methods such as an infiltration basin or aquifer storage and recovery) is used here as an example of a model deficiency for contaminant-related activities or inputs that result in geogenic-related groundwater-source drinking water quality degradation. MAR allows storage of excess water in aquifers during wet periods to potentially be used later and is increasingly considered a viable solution to certain water availability problems in both dry and humid areas. MAR can improve the quality of the injected water through filtration of pathogens, degradation of organics, sorption of trace elements, or precipitation of solids containing undesirable solutes. Injection of water that differs in composition from the ambient groundwater can, however, degrade ambient groundwater quality by mobilizing geogenic constituents [25]. Lack of appropriate models and data, lack of modeling expertise, and misapplication (or no application) of existing models has led to groundwater quality degradation. For example, a recent MAR review paper shows that 26 percent of the MAR projects in the U.S. have been abandoned, and 21 percent of the wells were abandoned owing to water quality issues, with half of those abandoned because of elevated arsenic concentrations [642]. Mobilization of numerous native geogenic constituents, including V, Mn, Fe, Ni, Zn, As, F, and U, has degraded ambient groundwater quality during MAR at sites in the U.S. [642]. Use of MAR is expanding to include diverse sources of water, such as recycled wastewater that has been purified by advanced treatment; low quality water, including treated wastewater from oil and gas development; injection of fresh water into brackish aquifers; and injection of water to store thermal energy. These methods introduce the possibility of heretofore unencountered issues related to coupled hydrologic and biogeochemical processes that can trigger mobilization of geogenic constituents, which in turn can deteriorate water quality to the point where the water quality is too poor for its intended use (see also Section 3.2 on Salinity). Improvements in models and thermodynamic databases could allow more comprehensive simulation and prediction of transient and steady-state conditions at variable density and temperature for MAR and thermal energy storage sites. Such modeling could be empowered by expanded thermodynamic data at variable temperatures and pressure; at high ionic strengths rather than for only dilute solutions; and for additional chemical species and redox reactions that control solubility and mobility of geogenic constituents [37]. TOUGHREACT [643] is a multiphase reactive transport code that can be applied to a wide range of conditions, including high temperatures and dissolved solids concentrations. PHAST [230] is a public domain code for simulating groundwater flow, multicomponent transport, and equilibrium and kinetic chemical reactions and uses PhreeqcRM [644] for the reaction engine. While PHAST has been used for simulating ASR [25], it is restricted to constant fluid density and constant temperature. PHT3D [228,645] uses MODFLOW [514] to set up a flow field prior to simulating reactive transport by coupling MT3DMS [515] with PHREEQC. However, PHT3D was linked to an old version of MODFLOW without variable density; a newly developed MODFLOW API [646] could allow coupling of the PhreeqcRM reaction module [644] with MODFLOW 6 [393], which allows variable density; efforts are underway to integrate PHREEQC capabilities into MODFLOW 6 via the API: https://github.com/MODFLOW-USGS/modflow6/discussions/1352. With more complete thermodynamic databases and isotopic composition information suitable for variable density and temperature fluids, geochemical and other modeling techniques could be used to apportion types of water, sources of water [525,647], and source composition to appropriately simulate geogenic constituent mobilization risk.

3.6. Contaminants of Emerging Concern

Currently, many watershed models and conceptual diagrams of the water cycle ignore some, or all, of the human interactions with water use and return flows that introduce CECs into freshwater and impact the quality and availability of water for beneficial uses. Human water use, along with shifts in climate and land conversion, has created a water crisis for billions of people and many ecosystems worldwide, with 80% of the world’s population facing water insecurity or severe water scarcity [48,648,649]. Human freshwater appropriation now equals 50% of global river discharge [48], and, once appropriated by humans, the return flows into surface waters contain anthropogenic contaminants introduced from municipal and industrial WWTP discharges (#21, 25) [46,650], stormwater runoff (#26, 27, 33) [55,651], and agricultural point and non-point sources (#13–17, 19, 20) [86,87,89].

Although the three main sources of CECs listed above are critical to include in national scale models, local and regional studies could improve our understanding of the lesser-known water quality impacts that come from energy generation (#31) [148], aquaculture (#18) [151], oil and gas production/refining (#29) [149,150], and mining/milling of mineral resources (#30) [147], all of which use water and return it to the hydrologic environment via direct or indirect discharges. Additional water quality research gaps are described in [652]. For example, high-capacity batteries and electric cars can introduce various contaminants into the environment through their production, use, and disposal [653]. Some potential contaminants include toxic heavy metals, such as lead, cadmium, and nickel in electric vehicle batteries or bismuth used in braking components; fluorinated compounds used in lithium-ion batteries; and microplastic releases from battery components and packaging material. There are many research gaps related to chemical impacts on non-target aquatic organisms coming from chemicals such as antibiotics and pharmaceuticals used for disease prevention, pesticides for controlling parasites, and feed additives with growth enhancers. Additionally, more comprehensive research into organic contaminants associated with mining and milling operations could be especially valuable since little is known about all the organic extractants (e.g., trioctylamine) and chelating agents (e.g., ethylenediaminetetraacetic acid, EDTA) used to extract and isolate minerals and metals of interest [17,147]. Hydrologic transport models investigating the mobility and bioavailability of certain toxic metals could benefit from knowing the concentrations of strong metal binding reagents such as EDTA. Deeper investigations into the environmental fate of emerging contaminants from all source types, particularly regarding integration into hydrologic and bioavailability models, will be essential for developing more accurate assessments of their long-term ecological and human health risks.

Water pollution caused by CECs is a central problem in the global and national water crisis, so semi-mechanistic hybrid wastewater models could provide predicted fate and concentration levels to improve risk assessments for humans and aquatic organism health and assist in water management decisions [48,85,101,435,449]. Complex mixtures of CECs and other contaminants coming from wastewater effluent (#21, 22), stormwater (#25–27, 33, 41), and agricultural runoff (#13–17, 19, 20) have been shown to increase the risk to aquatic organisms through interactive or cumulative effects (#43) [84,97,654,655]. Extreme events such as wildfires [583] and coastal storms [359,652,656] add more complexity by influencing the mobilization, conveyance, and concentrations of CECs along with mobilized sediment, nutrients, and dissolved organic carbon (DOC) into aquatic systems. For example, wildfires can cause thermal degradation of plastic pipes and leaching of carcinogenic benzene (a polycyclic aromatic hydrocarbon or “PAH”) and other volatile organic chemicals into the water transported within the pipes [657,658]; the reaction of chlorine and DOC in treated drinking water can lead to the formation of potentially carcinogenic trihalomethanes or other disinfection byproducts [659]. Seasonal or drought-induced low-flow conditions may increase stream vulnerability to CECs by reducing in-stream dilution [45,651,660]. Thus, enhancing understanding of the sources, environmental pathways, transport mechanisms, and mitigation strategies for CECs could support ecological protection and water quality management decisions in the face of increasing environmental stressors. Existing gaps in accurate modeling of emerging contaminants encompass the understanding of multiple inputs, processes, and activities illustrated in Figure 1: #1, 6–8, 13–22, 24–31, 33–41, and 43.

CECs can include chemicals that are truly new and emerging with little known about them, as well as legacy chemicals with renewed attention due to new information about occurrence, exposure pathways, or adverse health effects. For example, 1,4-dioxane and poly- and perfluoroalkyl substances (PFAS) have been used extensively for industrial purposes (#25, 34, 36–38) and in consumer products (#21, 22, 24) since the 1950s. Recent findings have highlighted emerging ecological and human health risks, underscoring the need for improved mitigation and treatment of PFAS due to the widespread occurrence, persistence, and multiple exposure pathways in surface water and groundwater [51,68,69,70]. Another example is shown by studies on two residual crude oil groundwater plumes in Minnesota that found that a subsequent plume of polar organic metabolites of crude oil is headed towards a lakeshore, and these organic chemicals pose a health risk to aquatic and mammalian species [150].

Statistically based and process-based watershed models are commonly used to quantify and understand existing water quality conditions and simulate seasonal dynamics (#1) or responses to climatic (#1, 6, 7) or management changes. Unfortunately, many CECs discharged from wastewater effluent [45,70,453], storm runoff (#25–27, 33) [651], and agricultural runoff (#8, 13–17, 19, 33) [86] are left out of existing watershed and groundwater models. CECs are often unregulated at the federal level [47] and can require costly, advanced analytical techniques to accurately measure them. Without federal mandates for regular monitoring, many CECs lack consistent, long-term, and geographically widespread data on their groundwater (#34, 36–38) and surface water (#35, 40, 41) concentrations, thus limiting the ability to support statistically based watershed modeling. Additionally, the enormous variety of CECs and widespread uses of specific CECs in multiple products lead to an incomplete understanding of all major sources of environmental exposure, variables that drive fate and transport, and limited access to the timing of environmental discharge events.

For example, cross-purpose uses of many pesticides and other chemicals for consumer or industrial products are very common. The insecticide fipronil has two major sources with two different timings of discharge: a dominant summer signal of fipronil found in domestic wastewater effluent due to its use for flea and tick treatment versus its intermittent or unknown discharge timing from its use in agriculture as a seed coating or in granular soil treatments through landscape runoff [661].

The marginal availability of consistent, long-term CEC concentration data and environmental discharge timing makes it difficult to develop accurate statistical relations between targeted CECs and specific forcing variables that are required for statistically based watershed and transport models [662]. Regular spatial and temporal monitoring of CEC concentrations and their seasonal (#1, 12, 15, 17, 20) or diurnal changes in flux (#21) across the U.S. could better constrain the timing and impacts of environment discharge events. However, alternative factors driving water contamination must sometimes be used for statistical model simulations to improve risk assessment and inform management practices. A successful example of using alternative factors was demonstrated in a recent study [663] using an extreme gradient boosting (XGBoost) model to predict PFAS occurrence in groundwater at depths used for drinking water across the contiguous United States with an accuracy of 78% under standard thresholds. The XGBoost model was based on factors such as urban land use, well depth, soil composition (including those with biosolids amendments from WWTPs), and proximity to PFAS sources. This model predicted urbanization and shallow well depths significantly increased the likelihood of PFAS presence, while areas with high clay content and low natural groundwater recharge were also associated with higher contamination risks. It was determined that an estimated 71 to 95 million people in the U.S. rely on groundwater with detectable PFAS concentrations for drinking water [663]. This is an example of successfully using modeling to improve risk assessment capabilities.

The process-based hydrologic groundwater models such as MODFLOW [259] or surface water models such as PRMS, SWAT, and HSPF [258,263,265] are typically based on a series of known mathematical relations describing each of the physical mechanisms (or groups of processes) involved in driving changes in the constituent(s) of interest. Process-based models require accurate thermodynamic constants and kinetic rate data for each constituent of interest along with its dominant sources, timing of environmental discharge (e.g., seasonal herbicide treatments, field application of biosolids), and environmental interactions that follow (i.e., biodegradation, photolysis, volatilization, and sorption).

A fair amount of literature discussing the surface water concentrations and water quality impacts of specific pesticide chemicals can be used for hydrologic transport model inputs from irrigation (#15, 20), tile drainage (#19), or storm runoff events (#8, 33) [86,87,89,91]. Additionally, tools such as STEPL can be used to estimate pesticide loads from agricultural fields [91]. However, there still exists a multitude of other insecticides, herbicides, fungicides, and their transformation products whose occurrence, sources (e.g., agriculture, aquaculture, municipal/commercial WWTPs, urban stormwater), and synergistic effects on aquatic organisms, potentially at critical life stages [86,87,89,91], are not well documented. Moreover, there are countless other emerging contaminants from other chemical classes (e.g., pharmaceuticals, hormones, consumer product chemicals, flame retardants, disinfection byproducts) with knowledge gaps regarding land use sources and mechanistic drivers of their environmental fate and health impacts. These pesticide knowledge gaps, when better understood, could improve the accuracy of hydrologic transport modeling of pesticide CECs and risk assessments. For example, better risk assessment has been achieved through new research on biogeochemical reactions (#43) with pesticides such as fipronil or chlorpyrifos that result in transformation products fipronil-sulfone and 3,5,6-trichloro-2-pyridinol, respectively, which are also toxic to freshwater organisms [91,661,664]. One pathway to prioritization of future CEC research is to utilize the Unregulated Contaminant Monitoring Rule (UCMR) [47] curated every five years by the U.S. EPA and consisting of ~30 new unregulated, understudied chemical contaminants to be monitored by PWSs. Recent and past UCMR lists, along with input from local stakeholders, may support the determination of “priority CECs” to monitor, investigate, or develop best management practices for diminishing exposure risks. Over time, a large database of thermodynamic, kinetic, and toxicity data for prioritized CECs in the aquatic environment could be compiled to make these data easily accessible and machine-readable to promote use within other hydrologic transport (#40, 41, 43) and ecological/toxicity models. These models could be used to run different management scenarios to support the decision-making by water resource managers.

Treated municipal and industrial wastewaters are continuous loading sources of CECs added to surface water, resulting in complex effects on water quality and degraded suitability for downstream use by humans and aquatic organisms [46,50,665,666]. WWTP discharges and septic systems can load surface water and groundwater with multiple classes of micropollutants and toxins including endocrine disrupting chemicals (EDCs), domestically used pesticides (e.g., weed and pest control, mold removal, pet protection), pharmaceuticals and person care product (PPCP) chemicals, organic precursors for disinfection by-products (DBPs), toxic metals, as well as nutrient loads and pathogens that all can pose ecological and human health risks [45,46,651,660,665,667]. The transport-reaction models (or other modeling frameworks) capable of simulating some form of CECs include [44]: ACCWW [85,435], DELWAQ (or “D-Water Quality”, module of Delft3D or Delft3D FM) [235], SWAT [236], WASP [282,283], and EFDC [335] (this is not an exhaustive list).

Many of the gaps and limitations identified for CECs, as well as their importance and opportunities for closing those gaps, are listed in Table 19 herein. Further descriptions of gaps and opportunities related to de facto wastewater reuse and aquatic transport of CECs can be found in Section 2.9. Also see Table 9 (“Water Reuse Modeling”) in the companion data release [102] for a summary and details of modeling capabilities for inputs, processes, and activities affecting contaminants of emerging concern.

4. Discussion and Conclusions

In Section 2 and Section 3, gaps and challenges limiting the ability to model six water quality constituents or constituent categories (temperature, salinity, nutrients, sediment, geogenics, and CECs) were discussed. Those assessments primarily focused on process-based and hybrid models. In this section, we synthesize those gaps, highlighting key challenges relevant to the modeling of water quality. We then discuss broad approaches that may pose solutions for addressing some of the key challenges confronting the field of water quality modeling.

4.1. Synthesis of Gaps

The water quality modeling gaps identified in this study can be classified as belonging to one or more of three primary types: (1) Model Gaps—gaps related to models themselves or the practice of modeling, (2) Data Gaps—gaps related to the availability of data to support the development, forcing, parameterization, scaling, or evaluation of models, and (3) Process Understanding Gaps—limitations in understanding of fundamental mechanisms that, if addressed, could permit advancements in modeling. In Table 20, we synthesize the gaps that are common across many (at least five) constituents and/or cross-cutting capabilities described in the previous sections. Those common gaps are grouped into eight themes.

Prominent challenges directly related to models and modeling, which were identified for multiple cross-cutting topics (Section 2) and constituents (Section 3), include inadequate coupling of models across spatial compartments and across disciplinary boundaries, limited ability to represent effects of reservoir and dam operations in large-scale water quality models, and the limited inclusion of anthropogenic influences in many models. Data related gaps are extensive and include the nearly universal need for improved datasets for model calibration, validation, and specification of boundary conditions; biogeochemical thermodynamic and kinetic rate parameters; constituent sources; and data describing the physical setting (hydrogeology and bathymetry, respectively) for groundwater and surface water flow models. Enhanced process understanding in areas such as constituent interactions, interactions between spatial compartments (e.g., groundwater-surface water), anthropogenic influences, and constituent sources could provide significant support to model development and implementation. Such process research could augment the understanding of potentially critical mechanisms or constituent inputs and our ability to robustly characterize them in models. Areas in which investment on all three fronts (models, data, understanding) could pave the way for water quality modeling advancement include (A) the impacts of projected future climate and extreme events on water quality, (B) model coupling, and (C) anthropogenic influences.

4.2. Some Ways Forward—Summary of Key Opportunities

The gaps and challenges identified herein suggest several actions and approaches that, if implemented, could have far-reaching positive effects on the collective ability to model water quality. In this sub-section, we discuss four such areas of action.

4.2.1. Data Collection, Compilation, and Harmonization

First, continued and new data collection, including programs to develop and employ advanced technologies such as remote sensing and environmental proxies (e.g., [673]) could support significant progress in water quality modeling. The compilation and harmonization of existing, ongoing, and new datasets across various organizations, methods (e.g., remote sensing, vessel based, sensors, discrete samples, and laboratory derived), and spatial and temporal domains and resolutions would present a considerable advancement. This could include intensified and targeted data collection to capture effects of anthropogenic actions on water quality, the influence of extreme events, processes at domain interfaces (to support related model coupling), and geophysical settings. These actions could advance the availability of constituent data for calibrating models, evaluating model skill, prescribing boundary conditions, and establishing baseline conditions. Additionally, enhanced data compilation could support the construction and extension of data bases of reservoir operations and of thermodynamic and kinetic coefficients required for reactive constituent modeling; these coefficients may emanate from field experiments, laboratory experiments, the literature, and/or other models (see “Machine Learning” below). Optimally, compiled databases would be harmonized, quality-controlled, open-access, well-documented, and machine-readable. Finally, as noted by other authors, the modeling enterprise could benefit from tighter coordination between observation, experiment, and modeling [10,161,343].

4.2.2. Process Research

Investments in process research could also substantially advance water quality modeling. Research could support understanding and modeling of biogeochemical interactions between, and the combined effects of, multiple water quality constituents emanating from and affected by a range of human activities [290]. Research at, and spanning, environmental interfaces would improve understanding of important processes, gradients, and constituent sources that are often located at interfaces and transition zones such as the sediment-water interface, the hyporheic zone, the vegetation-water interface, the transition between inland hydrologic systems and estuarine/coastal systems, and the land-water interface [10]. The spatial locations of such interfaces may move over time, as with intermittent rivers [289]. Improved understanding of these processes could support cross-domain model coupling or at least incorporation of source/sink terms associated with the adjacent domain. In the subsurface realm, research on theories of macroscopic mixing would support water quality modeling in realistically heterogeneous aquifer systems. Biological feedback processes (e.g., drag induced by aquatic vegetation) onto hydrodynamics is also an area where further research and data collection could support wider inclusion of such mechanisms into models [10]. Furthermore, process research could also fill gaps in quantification of biogeochemical parameters, assessing the importance of antecedent events, and understanding of how climate-induced changes (e.g., increases in sea level) may affect drinking water, aquatic habitat, and contaminant mobilization by wildfire and floods.

4.2.3. Machine Learning

Machine learning (ML) methods could help fill some gaps associated with process-based or hybrid models. Although ML models generally benefit from large amounts of data, the types of data they require are less specific than for process-based models. ML methods could be useful in addressing the pervasive need to specify parameters for use in process-based models [343,674,675]. This is a burgeoning area of research which, though dependent on adequate training data, holds promise for filling this major modeling gap [675] and, thereby, addressing other limitations such as modeler subjectivity and model uncertainty associated with parameter uncertainty [343]. Moreover, ML methods such as neural networks or random forests can be used to address problems that involve multiple complex processes and for scaling information from small-scale, process-based models to larger spatial extents [384,676]. They can address complex, non-linear relations and provide improved predictive capability for various surface- and groundwater applications over large areas [677,678,679]. ML methods can be particularly useful for identifying driving processes and where those processes are most important [384]. Process-based models are more effective at helping us understand how and why these driving processes control water quality. ML models, however, can be trained on the input and output from process-based models to bridge the divide between the purely empirical method (ML) and the more theoretical approach (process-based models) [156,157,158,159,388,477,680,681,682,683], thereby integrating information on controlling processes or conditions into ML models and, thus, helping guide ML predictions. Doing so encourages the ML model to predict similarly to the process-based model in a wider range of conditions, which burdens the ML model with some weaknesses of the process-based model but may improve ML accuracy when the training data otherwise fail to capture novel conditions of interest and the process-based model is accurate in those conditions. Current and future studies in water quality modeling could continue to take advantage of both process-based and ML models by bringing more mechanistic representation to ML models and transforming statistical models into hybrid models. This additional information may improve model performance for unmeasured regions and future predictions of water quality [10,684].

4.2.4. Reduced Complexity Models

As mentioned herein and elsewhere [10,161,343,397,685], very complex process-based models are frequently subject to limitations such as significant data requirements, overparameterization, difficulties in upscaling, high computational demand, bigdata storage demands, lack of interpretability, long model development times, and limitation of model use to experts only. An alternative exists with “reduced complexity” models (RCMs). RCMs present opportunities for transparent interpretation of model component behavior and predictions to broad groups of end-users including stakeholders and policy makers [603], have lower data requirements, and may be computationally trivial to run and simple to implement [162,163]. RCMs generally have flexible model structure and encompass process-based, data-driven, or hybrid models, often invoking simplifying assumptions (e.g., steady state, well-mixedness) or simplifying techniques such as spatial and/or temporal averaging, lumping of multiple processes into a single composite rate parameter, use of timescales to reduce complexity and problem dimensionality [686], and winnowing of included processes and drivers down to only those judged essential based on available data or system understanding (e.g., [687]) or most relevant to the driving questions (e.g., [242,688]). RCMs (or predictive metrics derived from them) have been implemented for modeling estuarine salt front location [358,689,690], water temperature [691,692], nutrient dynamics [299,382,391,693,694,695,696], phytoplankton biomass concentration (e.g., [242,298,688,697,698,699,700,701]), location of harmful algal bloom initiation [61], dissolved oxygen concentration [687], hypoxia occurrence [702], and contaminant trends in water supply wells [703]. Many RCMs rely on “transport timescales” such as water age or residence time to encapsulate the complexity of the hydrodynamic setting and provide a common currency with which to compare and combine with timescales for biogeochemical processes [163]. Expanded transport timescale estimation across water body types and spatial scales could enable more extensive application of water quality RCMs. In addition to RCMs’ transparency, tractability, and utility in decision support (e.g., [242]), education [161], and stakeholder engagement (e.g., [161,242,603]), their simplicity offers an option for circumventing model overparameterization [161,685] and intensive data needs, and their inherent computational efficiency provides promise as water quality modelers strive to scale up from local scales to continental and global scales, as well as perform large ensembles of runs for estimating uncertainty. (Uncertainty estimation is another challenge in water quality modeling identified herein and elsewhere [161,704,705]).

4.3. Conclusions

Sound, cutting-edge, interdisciplinary modeling is strengthened when performed in tandem with process research and data collection [10,161,343]. So, although many of the water quality modeling gaps identified herein are predominantly related to data or computation or process research, our ability to confront some of the most important water quality challenges would be buttressed by a holistic approach for addressing all three (Figure 5). For example, the ability to “scale up” models from smaller to larger scales will rely on data collection and compilation, field and laboratory process research, and advances in software development and computing technology. Those three areas of effort are especially powerful if used in tandem: (1) models can be used as tools to help design data collection programs and guide process research; (2) research can motivate model development, provide insights on model structure, and define further data needs; and (3) data collection can spawn research ideas and provide the raw materials from which to build and test models (see [688,706] as examples). All three components of this triumvirate (models, data, and research) can be used iteratively to generate hypotheses to be tested by the others (Figure 5). Data intensive, process-based, site-specific case studies provide golden opportunities on which to build (a) interdisciplinary mechanistic understanding, (b) intensive, synoptic data sets, and (c) modeling efforts that are well-equipped with data to drive and evaluate models, conceptual models to inform their construction, and science questions to be addressed. If these three realms interact with and influence each other—reversibly and iteratively—they can collectively accelerate scientific advancement.

Figure 5. Conceptual diagram of the relationships and dependencies between water quality modeling, data collection and compilation, and process research to enhance mechanistic understanding. Interaction between the three activities drives collective advancement (e.g., see [688,706]).

Author Contributions

Conceptualization, L.V.L. and C.J.B.; writing—original draft preparation, L.V.L., C.J.B., D.M.R. N.T.B., Z.C.J., C.T.G., M.L.E., A.C.G., J.R.J., A.F.P. and P.E.S.; writing—review and editing, L.V.L., C.J.B., D.M.R., N.T.B., Z.C.J., C.T.G., S.J.C., M.L.E., A.C.G., J.R.J., N.K., A.F.P. and P.E.S.; All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Data Availability Statement

The database of model and data resources referred to in the study is openly available at https://doi.org/10.5066/P13GTPTF.

Acknowledgments

This work was funded by the U.S. Geological Survey (USGS) Water Mission Area Water Quality Processes Program and was produced as a part of the National Gap Analysis of Water-Quality Understanding and Predictive Capabilities project for the USGS. We are grateful to Alison Appling, Barbara Bekins, Ken Belitz, David Bjerklie, John Karl Bohlke, Jesse Dickenson, John Engott, Hedeff Essaid, Rebecca Gorney, Karl Haase, Steffanie Keefe, Doug Kent, R. Steve Regan, Samuel Rendon, Katherine Ransom (ORCaS Inc.), Jordan Read (CUAHSI), Jared Smith, Jeffrey Starn, Beth Tomaszewski, Roland Viger, and Jake Zwart—all currently or formerly of the U.S. Geological Survey unless otherwise noted—for their invaluable pre-reviews and/or consultation provided in the compilation of this article and/or its earlier versions. We thank Kimber Petersen (USGS Visual Information Specialist) for creating the original artwork for the Figure 1 graphic. We gratefully acknowledge all the reviewers for their constructive comments and reviews of this manuscript. We extend special thanks to Scott W. Ator (U.S. Geological Survey) and Victor J. Bierman (Senior Scientist Emeritus of Limno Tech) for their comprehensive reviews of the entire volume of this work. The following experts generously reviewed selected sections of an earlier version of this manuscript (all are current or former USGS affiliates unless noted otherwise): Alison P. Appling: Introduction, Discussion and Conclusions, Appendix A; John Karl Bohlke: Introduction, Geochemical and Biogeochemical Modeling, Groundwater Modeling, Salinity, Nutrients, Discussion and Conclusions; Christopher H. Conaway: Salinity; Salme E. Cook: Estuary Modeling, Salinity; Charles A. Cravotta III (Cravotta Geochemical Consulting): Geochemical and Biogeochemical Modeling, Watershed Modeling, Lake and Reservoir Water quality Modeling, De Facto Wastewater Reuse and Chemical Transport Modeling, Temperature, Salinity, Nutrients, Geogenic Constituents; Hedeff I. Essaid: Watershed Modeling, River Modeling; Kayce Faunce: De Facto Wastewater Reuse and Chemical Transport Modeling, Contaminants of Emerging Concern; Neil K. Ganju: Estuary Modeling, Sediment; Joe Grim (U.S. National Science Foundation National Center for Atmospheric Research): Meteorologic and Climatic Forcing; Jennifer L. Keisman: Introduction, Discussion and Conclusions; Jessica R. Lacy: Sediment; Steven L. Markstrom: Temperature; Richard R. McDonald: River Modeling, Sediment; Matthew P. Miller: Introduction, Watershed Modeling, River Modeling, Salinity, Nutrients, Discussion and Conclusions; Olivia L. Miller: Watershed Modeling, Salinity; Pradeep Mugunthan (San Francisco Estuary Institute): Introduction, Geochemical and Biogeochemical Modeling, Watershed Modeling, River Modeling, Reservoir Operations and Outflow Modeling, Lake and Reservoir Water quality Modeling, Estuary Modeling, Groundwater Modeling, Temperature, Nutrients, Contaminants of Emerging Concern; Ramon C. Naranjo: River Modeling, Temperature; Kees Nederhoff (Deltares USA): River Modeling, Estuary Modeling, Temperature, Salinity, Sediment; Samantha K. Oliver: Introduction, Lake and Reservoir Water quality Modeling, Temperature; Qubin Qin (East Carolina University): Geochemical and Biogeochemical Modeling, Estuary Modeling; Robert L. Runkel: River Modeling; David A. Saad: Introduction, Watershed Modeling, Nutrients; Megan E. Saksa: Introduction, Salinity; Gerard L. Salter: River Modeling, Sediment; Jian Shen (Virginia Institute of Marine Science, College of William & Mary): Estuary Modeling; Mick van der Wegen (Deltares): Introduction, Estuary Modeling, Temperature, Salinity, Sediment; John C. Warner: Introduction, Estuary Modeling, Temperature, Salinity, Sediment; Richard M. Webb: Meteorologic and Climatic Forcing, Watershed Modeling, River Modeling, Nutrients; Jacob A. Zwart: Geochemical and Biogeochemical Modeling, Lake and Reservoir Water quality Monitoring, Geogenic Constituents. Any use of trade, firm, or product names is for descriptive purposes only and does not imply endorsement by the U.S. Government.

Conflicts of Interest

The authors declare no conflict of interest.

Appendix A

Table A1. Process-based water quality model sub-types and their associated characteristics, strengths, and limitations [162,163,241,603]. Broadly, these are models that use mathematical relations to describe one or more processes affecting water quality; they can be used to perform sensitivity analyses, but it is often difficult to place confidence limits on model results because of unknown structural errors in the model construction [3,211,243].

Model Sub-Type	Specific Type	Characteristics	Strengths	Limitations
General process model	General processes	Simplified process model; only most important processes included	Requires less types of data, and often easier to calibrate	Many processes not included, and specific processes can act as surrogates for others
Detailed process model	Detailed processes	Detailed process model; important and known less important processes included	Can describe the relative importance of all processes involved. Describes interactions among specific processes	Requires more types of data, more computational power, and often harder to calibrate because of equifinality of various model calibrations.
Local area model	Local area	Small spatial scale model	Describes changes over small spatial scales	Only provides local descriptions
Broad regional model	Broad regional area	Large spatial scale model	Provides better spatial and temporal descriptions of factors affecting water quality	Usually does not include fine detail over large areas
Reduced-complexity model	Analytical	Focuses on key processes; idealized spatial domain; simplifying assumptions such as well-mixed, steady-state	Computationally efficient, transparent, interpretable, accessible to non-experts, low data requirements	Lacks fine spatial and/or temporal detail

Table A2. Statistical (empirical and data-driven) water quality model sub-types and their associated characteristics, strengths, and limitations [707]. Broadly, these are described as statistical approaches that relate one or more response variables to one or more explanatory variables [707,708,709].

Model Sub-Type	Specific Type	Characteristics	Strengths	Limitations
Mean Value ^a	Field studies with direct manipulation of existing conditions	Direct measurement of specific actions on a field plot or basin	Direct cause and effect. Directly applicable to area being studied	Results may or may not be transferable to other areas
Linear Regression ^b	Simple linear regression	One dependent (output) variable and one independent (input) variable	Simplest approach to relate dependent variable to various independent variables one at a time	Requires linear relations, unless data are transformed. Correlations do not always translate to causation
	Multiple linear regression	One dependent variable but multiple independent variables	Simplest approach to examine multiple independent variables all at once	Often important variables not included. Hard to determine the effects of less important variables.
	Autoregressive	Used when dependent variable is correlated through time	Explains changes in the dependent variable through time	Typically, only applied at a selected location(s) and more difficult to apply to unmonitored sites
Classification ^c	Logistic regression	Often, though not exclusively, used when dependent variable dichotomous or binary	Predicting the probability of the outcome being in a particular class	The linear relationship is assumed between the logistic-transformed probability of the dependent variable and the independent variable
	Discriminant analysis	Dependent variable has a series of categories	Describes the maximum difference between predefined groups	Assumes you know the predefined groups
	Ensemble Tree based (e.g., random forest or gradient boosting)	Predictions generated sequentially (gradient boosting) or in aggregate (random forest); determines different groups of dependent variables	Good at determining main factors causing the different groups. Does not assume linear relations	Difficult to work with gradual linear changes in a variable (i.e., non-categorical)
Unsupervised learning ^d	Principal Component Analysis, K-means clustering, and hierarchical clustering	Exploratory tool to detect patterns	Used to eliminate variables not causing much variability, regionalize parameters, or detect patterns	Strongly dependent on the variables chosen in the analysis
Machine Learning (with various above sub-types) ^e	Neural network	Uses a large number of interconnected nodes that transform and combine predictor data to estimate values of dependent variables	Provides predictions for linear and nonlinear relations. Ability to work with incomplete knowledge of processes involved	Can be difficult to interpret and to understand or anticipate weaknesses in the model
Bayesian ^f	Bayesian linear regression, Bayesian estimator, Markov chain Monte Carlo	A method that combines prior information about a population parameter with evidence from a sample to guide statistical inference	Provides likelihood of the prediction, based on all of the uncertainties included	Very intensive computationally. Selection of appropriate likelihoods and priors must be evaluated during model building

^a [248]; ^b Determines best linear relation between the dependent and independent variable(s) [708,709]; ^c Examines categories of data rather than linear relations [710]; ^d An algorithm that learns patterns and describes clusters in a data set [711]; ^e [712]. Uses several of the above statistical techniques, which can be used with normal and non-normally distributed data. Pros: This approach can provide better predictive power than other approaches. Cons: Strongly dependent on the quality and inclusivity of the training dataset. It is a complicated approach that often requires an experienced modeler to use; ^f [713].

Table A3. Hybrid water quality model sub-types and their associated characteristics, strengths, and limitations [707]. These models use a combination of process-driven and statistical models or combination of various types of models, and thereby may include many of the strengths and weaknesses of both statistical and process-driven models.

Model Sub-Type	Specific Type	Characteristics	Strengths	Limitations
Combination of process-based and statistical submodules ^a	Process hydrologic model combined with statistical water quality	Process transport model with water quality described using statistical relations	Specific components or outputs of the model are often described very well. Simpler to calibrate and apply than a full process model	Specific outputs or components are often greatly simplified and not described very well. Causes of changes in water quality are hard to determine
Models that only include statistically significant variables that are chosen based on process understanding ^b	General spatially explicit models describing sources and transport of various constituents	Parsimonious structure with only variables describing processes that can be statistically derived	Describes most important input variables and provides confidence limits on model results	Often processes are lumped together (hard to ascertain cause and effect relations). Many of the limitations of statistical models
Machine learning guided by process models or process constraints ^c	A machine learning model that incorporates elements of process representation	Machine learning model with process-based equations in the model structure and/or training process	May result in a more reliable model than the process model or the machine learning model. May be useful for making predictions at scales impractical for process models alone.	Many of the limitations of statistical models and process-based models.
Differentiable modeling ^d	Hybrid process-based and neural network model all implemented with (typically) automatic differentiation	Process components alternating with neural network components	Enables rapid learning of parameters from covariates and output signals. Facilitates testing of alternate process representations	Nascent approach with unknowns about best practices for model design and risks of equifinality

^a [707]; ^b [266]; ^c [312,714]; ^d [675].

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Figure 2. Qualitative assessment of the strengths and weaknesses of meteorological forcing datasets used for water quantity and quality assessments. Assessments are relative between forcing datasets (rows), showing better-performing forcings in green and sub-optimally performing approaches in red for different categories (columns); adapted from [183]. Additional info on named meteorological forcing datasets is provided in Table 1 of the companion data release [102]. Specific datasets: PRISM [194]; Livneh [195]; Daymet [196]; AORC [197]; NLDAS [198]; gridMET [199]; NARR [200]; ERA5 [201]; MERRA2 [202]; CONUS404 [183]; CMIP6 [180,188]; CORDEX [189].

Table 2. Examples of inputs, processes, and activities that can affect concentrations, loads, and delivery of specific water quality constituents. An X indicates that the particular input/process/activity influences the constituent (listed on the top row); a dash (-) indicates that it is a very minor factor; and a blank cell indicates either that the input/process/activity is not a factor or that there is no known literature supporting its being a factor. Temp: water temperature. Sal: salinity. SS: suspended sediment. P: phosphorus. N: nitrogen. Geo: geogenic constituents (e.g., metals). HABs: harmful algal blooms. Pest: pesticides. Path: pathogens. MP: microplastics. PFAS: per- and polyfluoroalkyl substances. CECs: biologically active contaminants of emerging concern. Numbers 1–45 correspond to the numbers assigned to individual inputs, processes, or activities depicted in Figure 1. Citations relevant to each row are provided in the footnote.

Category	Input/Process/Activity	Process Number	Temp ^a	Sal ^b	SS ^c	P ^d	N ^e	Geo ^f	HABs ^g	Pest ^h	Path ⁱ	MP ^j	PFAS ^k	CECs ^l
Atmospheric	Atmospheric deposition *	1	X	X	X	X	X	X	X	X	-	X	X	X
	Lightning	2	-	-	-		X	-
	Solar radiation	3	X	-	-			-	X	X	-	X	-	-
	Shade	4	X	-	X			-	X
	Evapotranspiration	5	X	X	-			-
Climatic	Fires	6	X	-	X	X	X	X	X	X		X	X	X
Climatic	Snowpack/ice melt	7	X			X	-					-	-	-
Sediment/ Weathering	Soil erosion *	8	X		X	X	X	X	-	X	-	X	-	-
	Sediment erosion and/or deposition	9	X		X	X	X	X	X	-	-	-	-	-
	Streambank erosion	10	X		X	X	X	X			-
	Sediment weathering (chemical)	11	-			X	X	X	-	-	-		-	-
	Aquifer weathering *	12	-	X	-	X	X	X	-	-	-		X	X
Agriculture	Fertilizer	13	-	X	X	X	X	X	X	X		X	X	X
	Manure	14	-	X		X	X	X	X		X		-	X
	Pesticides	15	-			X	-	X	X	X	X		X	X
	Feed additives/hormones	16	-			X	X	X	X	X	X	-	-	X
	Land management *	17	X	X	X	X	X	X	X	X	-	X	X	X
	Aquaculture	18	X	X	X	X	X		X	X	X	-		X
	Tile drains	19	X	X	X	X	X	X		X	-	-	-	X
	Irrigation	20	X	X	X	X	X	X	X	X	-	X	X	X
Urban/ Industrial	Treated wastewater	21	X	X	X	X	X	X	X	X	X	X	X	X
	Septic systems	22	-	X	X	X	X	X	X	-	X	-	X	X
	Plumbing/distribution	23	-	X		X	-	X		-	-	-	-	-
	Drinking-water treatment *	24	-	X	-	-	-	X	-	-	X	-	X	X
	Industrial point sources/landfills/spills	25	-	X	-	X	X	X	X	X	-	X	X	X
	Construction	26	-	-	X	X	X	X		X	-	X	X	X
	Road applications/deicers/sand/debris, automobiles	27	-	X	X	X	X	X			-	X	X	X
	Managed aquifer recharge/ASR *	28	X			-	X	X		-		-	-	-
Energy	Oil/gas development	29	-	X	X	-	-	X	-	-	-	-		X
	Mining	30	-	X	X	X	-	X	-	-	-	-	X	X
	Power generation *	31	X	X	-	-	-	X	X		-	-		-
	Geothermal	32	X			-	-	X	-		-	-
Transport	Surface runoff/stormwater	33	X	X	X	X	X	X	X	X	X	X	X	X
	Groundwater recharge/infiltration	34				X	X	X		-	-	-	X	X
	Surface water withdrawal	35				X	X			X	-	X	X	X
	Groundwater discharge	36	X	X		X	X	X	-	-	-	-	X	X
	Groundwater withdrawal	37	-	X	-	X	X	X		X	-	-	X	X
	Surface water/groundwater interaction *	38	X	X	X	X	X	X	X	X	-	-	X	X
	Dam/weir/gate/pump operations *	39	X	X	X	X	X	X	X	X	X	X	X	X
	Hydrodynamics (including density) *	40	X	X	X	X	X	X	X	X	X	X	X	X
	Constituent transport *	41	X	X	X	X	X	X	X	X	X	X	X	X
	Bottom diffusion *	42				X	X	X		-			-	-
Transformations	Biogeochemical reactions	43				X	X	X	X	X	-	X	-	X
Oceanic	Sea-level rise	44	X	X	X	X	X	X	X			-
Oceanic	Seawater intrusion *	45	X	X	X	X	X	X	X			-

* Notes by Process Number: 1. Includes wet fall/rain and dry fall. 8. Includes landslides. 12. Includes brine. 13. Includes sewage sludge. 17. Includes field practices. 24. Includes desalination. 28. ASR refers to aquifer storage and recovery. 31. Includes thermoelectric. 38. Includes hyporheic exchange. 39. Includes water diversion projects. 40. Includes surface water and groundwater movement. 41. Includes advection and diffusion/dispersion. 42. Constituents in sediment porewater that diffuse into the water column. 45. Surface water and groundwater. ^a [18,103,104,105]; ^b [36,37,106,107]; ^c [107,108,109,110,111,112,113,114,115,116,117,118,119]; ^d [120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141]; ^e [120,121,122,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141]; ^f [21,27,35,36,37,38,39,40,41,142]; ^g [22,49,50,61,62,63,64,65,66,143,144]; ^h [17,22,45,49,50,83,86,87,89,90,91,92,93,94,95]; ⁱ [22,49,50,55,56,57,58,59,145,146]; ^j [22,44,49,50,64,66,72,75,76,77,78,79,80,81,82,83,84,85,86,87]; ^k [22,44,49,50,51,68,69,70,71,72,73,147]; ^l [22,35,44,45,46,47,48,49,50,51,147,148,149,150,151].

Table 3. Lists of water quality constituents (see Section 3) and cross-cutting model-related capabilities (Section 2) addressed in this paper. N and P, respectively, refer to nitrogen and phosphorus.

Water Quality Constituents of Interest	Cross-Cutting Modeling Capabilities
1-Water temperature 2-Salinity 3-Nutrients (N and P) 4-Sediment 5-Geogenic constituents 6-Contaminants of emerging concern (CECs)	1-Meteorologic and climatic forcing
	2-Geochemical and biogeochemical modeling
	3-Watershed modeling
	4-River modeling
	5-Lake and reservoir water quality modeling
	6-Reservoir operations and outflow modeling
	7-Estuary modeling
	8-Groundwater modeling
	9-Water reuse and chemical transport modeling

Table 4. List of hydrologic compartments referenced in Figure 1 and in the companion data release [102]. Italic compartments are those in which water quality is of primary interest herein. Normal font indicates compartments are adjacent domains that can influence water quality in the italic compartments.

Compartment Number	Hydrologic Compartment
I	Atmosphere
II	Terrestrial
III	Rivers
IV	Hyporheic Zone
V	Wetlands
VI	Lakes and Reservoirs
VII	Unsaturated Zone
VIII	Saturated Zone
IX	Estuaries
X	Coastal Ocean

Table 5. Gaps and limitations associated with meteorological and climatic forcing for water quality models, as well as the importance of those gaps and opportunities for addressing them.

Gap or Limitation	Importance	Opportunities
1-Limitations in observational capabilities (top row in Figure 2).	1-High quality in-situ observations, long record lengths, and measurements that allow assessment of budgets (e.g., water and energy) could support understanding of climate impacts on the hydrosphere.	1-Investments in observational networks for improved process level studies. Development of observational high-resolution modeling fusion products.
2-Limitations in physically sound uncertainty information about future local and regional climate (row 4–6 in Figure 2).	2-Watershed level climate information could support actionable mitigation and adaptation research under future climate.	2-More coordinated high-resolution modeling efforts and enhanced collaborations between research disciplines.
3-Insufficient computer resources to perform high-resolution climate projections and advanced data storage capabilities.	3-Ensemble high-resolution climate projections could support uncertainty assessment at local scales. Insufficient computational capacity can limit record length.	3-Investments in future computer & storage systems and upgrading existing climate model code to run on future high performance computing architectures.
4-Climate models simulate the natural water cycle and neglect human influences (third column from right in Figure 2).	4-Humans have a profound impact on the quantity and quality of local water resources that is largely not represented in climate models.	4-Incorporation of human interventions on the water and energy cycle in climate models.

Table 6. Gaps and limitations associated with geochemical and biogeochemical modeling, as well as the importance of those gaps and opportunities for addressing them. PHREEQC: pH-redox-equilibrium model in the C programming language; HABs: harmful algal blooms.

Gap or Limitation	Importance	Opportunities
1-Thermodynamic data for geochemical reactions under natural conditions are almost completely absent for important trace elements.	1-Mobility and toxicity of species are affected differently depending upon their valence states under natural and varying conditions.	1-Generate and (or) compile additional thermodynamic data for parameters in water quality models.
2-Geochemical modeling codes such as PHREEQC are underutilized for testing of conceptual water quality models.	2-Geochemical process modeling is necessary to predict occurrence, mobility, bioavailability, and toxicity of contaminants.	2-Provide/maintain capability of geochemical modeling codes to couple with reactive transport, biological, and mass balance codes.
3-Most current biogeochemical models don’t incorporate mixotrophy.	3-Mixotrophy is critical to understand aquatic ecosystems, particularly HABs, and can significantly affect nutrient concentrations and processes.	3-Derive biogeochemical modeling code parameters from lab measurements using cultured isolates of HAB species, etc.
4-Limited understanding of biogeochemical reaction kinetics for use in models.	4-Kinetics play a role in important societal issues such as carbon sequestration, nuclear waste disposal, HABs, and remediation of environmental contaminants.	4-Generate and/or compile additional kinetic data for parameters in water quality models.
5-Field and laboratory data, as well as process understanding, on which to base critical source and sink terms in biogeochemical modeling codes. Such rates of growth or loss/decay vary in space, time, and across systems.	5-Source and loss terms for modeled biogeochemical constituents are critical to the overall mass balance governing concentrations.	5-Expand and develop advanced data collection methods for some of the key kinetic and mass transfer questions that may be only partially represented in simplistic lab experiments.
6-Data on which to base model boundary conditions and with which to compare modeled constituents to support calibration and evaluation of model performance.	6-Realistic specification of constituent concentrations at open model boundaries, and the ability to quantitatively compare a model to observations, are fundamental to the development of a quantitatively reliable model.	6-Expand data collection and develop advanced data collection methods (e.g., remote sensing) for modeled constituents of interest, over space and time. Compile datasets across various sources and methods.

Table 7. Gaps and limitations associated with watershed modeling, as well as the importance of those gaps and opportunities for addressing them. WWTP: wastewater treatment plant.

Gap or Limitation	Importance	Opportunities
1-Limited data describing inputs of sources of constituents, especially secondary sources, over large areas.	1-Required for model development and source apportionment.	1-Dedicate resources to obtain detailed application rates and WWTP effluent concentrations and flows.
2-Limited information describing land management practices over large areas.	2-Management practices are a major factor affecting flow and constituent transport.	2-Agencies report management practices into accessible database.
3-Insufficient detailed monitoring/calibration data (fluxes at key locations).	3-Required for model calibration.	3-Additional resources dedicated to monitoring basic water quality and contaminants of emerging concern. Publish sampling frequency/standards.
4-Lack of dynamic empirical models.	4-Would enhance ability to simulate intra- and inter-annual variability.	4-Dedicate resources to high resolution monitoring and further model development.
5-Uncertainty in process-model output is often not estimated.	5-Needed to put confidence limits on model output.	5-Further model development.
6-Effects of reservoirs are not typically included in large-scale watershed models.	6-Affects models’ ability to simulate seasonal changes in water quality downstream of reservoirs.	6-Develop algorithms to describe the effects of each reservoir in the watershed.
7-Limited ability to simulate less important secondary sources (such as legacy sources) and processes.	7-Limits ability to make proper cause-and-effect relations.	7-Dedicate resources to mechanistic research and further model development.
8-Soil type, tile drain, and irrigation information are often limited.	8-Limited information on soil properties adds uncertainty to partitioning precipitation into runoff and infiltration.	8-Obtain improved soil, tile drain, and irrigation coverages, possibly through the use of remote sensing.

Table 9. Gaps and limitations associated with lake and reservoir water quality modeling, as well as the importance of those gaps and opportunities for addressing them.

Gap or Limitation	Importance	Opportunities
1-Indirect biological and chemical changes are not typically considered.	1-Biological and chemical changes can modify the full effects of management changes.	1-Incorporate indirect biological and chemical changes in reservoir models.
2-Legacy sources (internal sources, sediment loading, and groundwater inputs) are often not considered.	2-Legacy sources can delay the effects of watershed changes.	2-Incorporate legacy sources into reservoir models.
3-Full reservoir effects are usually not considered in large-scale watershed models.	3-Reservoirs affect downstream transport of many constituents (daily changes, seasonal releases, and permanent attenuation).	3-Incorporate reservoir models into watershed models. Expand research on contaminant attenuation rates in reservoirs.
4-Calibration is often dependent upon modeler abilities.	4-Simulations are often performed with a poorly calibrated model.	4-Develop consistent calibration protocols for lake/reservoir models.
5-Physical data for many reservoirs is difficult to obtain.	5-Simulations are difficult without knowing this information.	5-Incorporate full morphometric characteristics and operations of reservoirs into a national database.

Table 10. Gaps and limitations associated with modeling of reservoir operations, as well as the importance of those gaps and opportunities for addressing them. AI: artificial intelligence.

Gap or Limitation	Importance	Opportunities
1-System-specific information (e.g., depths and amounts of withdrawal and other operational parameters such as rule curves, hydropower rules, joint operations, diversion policies, downstream water quality objectives, etc.) can be difficult to obtain for many reservoirs included in regional and national models.	1,2,3,4,5-Water quality (e.g., temperature, sediment, nutrients) downstream of reservoirs can be strongly affected by site-specific operational practices. Regional- and national-scale modeling of reservoir operations and waters downstream of reservoirs is limited by this information/capability gap.	1,2-Make efforts to obtain reservoir water levels, depths of withdrawal, rules information, morphometry, and other operational parameters. Develop a national-scale database of detailed reservoir operating parameters and policies. 3,4,5-Phased development of reservoir modeling capacity, building from simple (e.g., replacement of streamflow, temperature, etc. below reservoirs to account for reservoir operation or use of empirical models) to more complex approaches, such as loosely and ultimately tightly coupled modeling approaches. 5-Tightly couple operations and water quality models.
2-Morphometry and water levels are not easily available for reservoirs over large regions and over time. Elevation-to-storage curves used in reservoir operations models are often dated and do not reflect current reservoir storage, leading to uncertainty in operational decisions.
3-Most operations models include only simplistic representations of hydrological processes.
4-The applicability of an operations model to a particular system depends on many system-specific factors. Configuration or modification for a specific system, which may be required for realistic water quality modeling, can necessitate significant investments.
5-Loose coupling of operations models (focused on water quantity) to water quality models may not be sufficient in cases where operations are linked to water quality requirements, and feedback is thus needed.

Table 11. Gaps and limitations associated with estuary modeling, as well as the importance of those gaps and opportunities for addressing them. ML: machine learning. AI: artificial intelligence. CECs: contaminants of emerging concern.

Gap or Limitation	Importance	Opportunities
1-Multiple data needs, including spatially comprehensive long-term water quality calibration and validation data, especially in areas that are difficult to monitor (e.g., shallows); reaction rates; sediment loads and composition; higher resolution atmospheric forcing and bathymetry data; time-changing boundary conditions; bathymetry; and vegetation data.	1-Water quality and its controlling processes can exhibit sharp spatial and temporal gradients. Data needed to drive and evaluate those models are often unavailable or do not capture gradients and temporal changes.	1-Increase water quality monitoring to capture critical gradients and changes over multiple timescales. Augment the use of advanced in situ instrumentation and remote sensing (with possible coupling to AI algorithms) to fill data gaps. Continue and expand on long time series datasets.
2-Limited ability to characterize, understand, and predict the impacts of extreme events (e.g., hurricanes) on water quality.	2-Flooding induced by major coastal storms can result in the release, intrusion, and mixing of multiple water quality constituents from a large range of hydrologic and terrestrial sources [360].	2-Expand the collection of datasets capturing water quality responses (for a range of constituents) to extreme climatic events [359]. Incorporate water quality into models that couple coastal hydrodynamics and inland hydrology. Include land use (indicative of anticipated chemicals or biological waste) in flooding models.
3-Significant parameterization and tuning of small-scale physical processes not resolved by physical models [343].	3-Fine-scale physical processes (e.g., horizontal diffusion and bottom drag) are critical in determining fluxes and distributions of water quality constituents in three dimensions.	3-Improve computational algorithms and resources to increase the resolution of small-scale physical processes in field-scale models. Directly compare parameterizations against high-resolution measurements and models [343]. Conversely, improve parametrizations to the benefit of coarser grids, lower time resolution, and faster computations.
4-Numerical challenges such as mass conservation difficulties in areas that wet and dry [356].	4-Computed constituent concentrations in intertidal areas or floodplains may be nonsensical if robust wetting/drying algorithms are not employed.	4-Expanded research and development into numerical methods for improved water quality computations in areas that wet and dry.
5-CECs and reactive constituents are difficult to model accurately in tidal zones due to the complex circulation patterns.	5-Complex tidal zone mixing and circulation, combined with shifting biogeochemical conditions, confound reactive constituent transport and attenuation processes.	5-Improve understanding and quantification of transport timescales (e.g., residence time and exposure time [163,377]) in tidal systems in order to better parameterize water quality models not capturing detailed intratidal transport.
6-Need for expanded model coupling (e.g., tight coupling of hydrodynamics and biota, groundwater-surface water-water quality, hydrodynamics-waves-water quality, and watershed-estuary-coastal ocean) and associated computational resources.	6-Biota such as vegetation and benthic fauna can influence the hydrodynamics, which in turn influences water quality. Water quality constituents (e.g., nutrients and CECs) can be exchanged between groundwater and surface waters and between inland and coastal waters, particularly during extreme weather events.	6-Incorporate into models the feedback effects of biological processes on hydrodynamics, e.g., as biologically induced drag. Link ground- and surface water models of transport and water quality. Incorporate water quality dynamics into dynamically coupled models spanning the land-estuary-ocean continuum.
7-Small errors in forecasting models of water quality can accumulate over time.	7-Errors in forecasted water quality can be large.	7-Incorporate data assimilation methods into water quality models to keep improving the “initial condition” and produce higher-quality forecasts [161].

Table 12. Gaps and limitations associated with groundwater modeling, as well as the importance of those gaps and opportunities for addressing them. WQ: water quality. RCM: reduced complexity model. ML: machine learning. TTD: transit time distribution.

Gap or Limitation	Importance	Opportunities
1-High uncertainty of estimated spatiotemporal fluxes to and from groundwater.	1-Essential to forecasting the availability of groundwater resources for beneficial uses as well as the effects of groundwater on surface water quality.	1-Expanded spatiotemporal measurements of age tracers, salinity, nutrients, and associated water quality parameters. Improved characterization of hydrogeologic setting through hydraulic tests, geological investigations, and geophysics. Methods development of hybrid and machine learning approaches to interpolate physical and chemical properties.
2-Integration of small-scale geological heterogeneity is impractical for models for characterizing WQ trends at larger scales.	2-Uncertainty stemming from geological variability is a key determinant of local constituent fluxes.	2-Develop RCMs and ML methods to bridge the gap between spatially and temporally averaged non-Fickian mixing processes at large scales and detailed representations at local scales. Develop TTD-based models for wells and streams, including transient conditions.
3-The classical approach of representing transport as Fickian diffusion is inadequate in realistically complex settings.	3-Affects prediction of contaminant plume concentrations, early arrival times, and long-term response to remediation. Affects estimates of geochemical reactions.	3-Continue development and implementation of alternative theories of macroscopic mixing in realistically heterogeneous aquifer systems.

Table 13. Gaps and limitations associated with modeling of water reuse return flows, as well as the importance of those gaps and opportunities for addressing them. NPDES: National Pollution Discharge Elimination System. CWNS: USEPA’s Clean Water Needs Survey. SIC codes: standard industrial classification codes. CECs: contaminants of emerging concern. GIS: geographic information system. WWTP: wastewater treatment plant.

Gap or Limitation	Importance	Opportunities
1-Limited availability of long-term, geographically widespread environmental concentration data.	1-Lack of data for model calibration and defining statistical relations to forcing variables.	1-Enhance and increase monitoring and data collection programs.
2-Limited availability of source input data from municipal and especially industrial wastewater effluent concentrations.	2-Specification of CEC loading inputs requires wastewater effluent concentrations to go along with known WWTP discharge volumes.	2-Add effluent measurements whenever and wherever stream measurements of CECs are performed. Obtain better access to industrial wastewater CEC loads through NPDES, CWNS, or SIC code applications.
3-Limited availability of quantitative (quantity and timing), location-specific chemical/biosolid applications to agricultural fields.	3-Quantitative data changes dispersed pollution variables into point-source pollution variables, greatly improving CEC source appropriation and model certainty.	3-Currently limited to using per county chemical (e.g., pesticide) purchasing log extrapolated into load applied to nearby agriculture land; opportunity to collect and compile better documentation.
4-Insufficient mechanistic data of thermodynamic constants and kinetic rates under natural conditions (e.g., in-stream attenuation coefficients).	4-Transport, fate, and toxicity of CECs are affected differently under natural and varying conditions. Such data help constrain input variables and optimize simulations for process-based and hybrid models.	4-Perform lab and field-based studies and (or) compile additional CEC thermodynamic and kinetic data for varying conditions to create a vetted, open-access database.
5-Wastewater models such as ACCWW, DRINCS, PhATE, and Global HydroROUT are underutilized in studies.	5-Accumulated wastewater modeling can predict concentration, mobility, and toxicity of CECs.	5-Maintain wastewater modeling codes and provide coupling with reaction-transport, GIS, and biological models/codes.
6-Limited to no access to the timing of environmental discharge events.	6-Knowing the timing of management practices and product ingredients could improve source appropriation capabilities.	6-Obtain greater transparency and availability of product ingredients and timing of agricultural and water management practices, e.g., application of herbicide or biosolids.
7-Lack of dynamic empirical models.	7-Could enable simulation of changes through time and near real-time simulations of environmental concentrations and potential adverse effects.	7-Dedicate resources to high resolution monitoring, more transparent access to daily WWTP discharge volumes (not just annualized averages or treatment capacity values).
8-Effects of reservoirs are not typically included in large-scale wastewater or watershed models.	8-Without correct representation of reservoir effects, models will incorrectly apply in-stream attenuation rates to long or unknown residence times in reservoirs, thus rendering them incapable of simulating water quality of labile CECs downstream of reservoirs.	8-Develop simple algorithms to describe the effects of each reservoir in the watershed. Perform tracer studies to better understand CEC residence times and transport.

Table 14. Gaps and limitations associated with modeling of water temperature, as well as the importance of those gaps and opportunities for addressing them.

Gap or Limitation	Importance	Opportunities
1-Lack of predictive ability and mechanistic understanding of thermal refugia such as cold-water patches, including the role of groundwater and hyporheic flow (#38) and stratification. Dearth of appropriate data for regional to global scale analyses of mechanisms contributing to thermal refuges and how such refuges have been/can be expanded and protected to benefit aquatic biota.	1-Relevant to thermal stress on ecosystems and the role of thermal refuges. Identification of sites with long-term buffering from increases in air temperature could support management of temperature-dependent species and ecosystems.	1-Integrate data relevant to thermal refuges from various sources such as remote sensing, logger networks, and fiber-optic distributed temperature sensing and from different measurement locations (i.e., within channel, streambed, groundwater). Increase research into mechanisms influencing the dynamics of thermal refuges.
2-Lack of data, predictive ability, and mechanistic understanding of the overall influence of many hydrologic and climatic processes such as groundwater discharge (#36), groundwater-surface water interactions (#38) (e.g., hyporheic exchange), future projected climate, snow/ice/glacier melt (#7), and dam operations (#39) (e.g., release depth and volume) on downstream thermal regimes of rivers.	2-Each of these processes can represent a dominant control on water temperature at various spatiotemporal scales and are vulnerable to human activities and changes in climate to different degrees. Improved water temperature predictive ability would be supported by increased representation of these processes in local- to continental-scale models.	2-Integrate existing hydrologic, geologic, climatic, and operational data from various sources as well as expand efforts to measure physical aspects of these processes (e.g., high-resolution continental-scale depth to bedrock for groundwater source depth information).
3-Lack of complete long-term time series data.	3-Required for model calibration/validation.	3-Maintain long-term continuous monitoring stations.
4-Temperature networks are typically focused on higher-order confluence reaches, and coverage of lake and reservoir temperature data nationwide is limited.	4-The current ability to accurately model low-order stream and waterbody temperatures at broad, continental scales is limited but can be enhanced by including these smaller water bodies in national temperature networks.	4-Focus prediction initially on large rivers, but support headwater research to improve process representations and ultimately include in continental-scale models. Merge and consolidate datasets from various organizations.
5-Paired upper and lower water column measurements in streams and lakes for assessing thermal stratification are not common.	5-Thermal stratification is a critical physical process commonly linked to important water quality processes and events (e.g., HABs, hypoxia). Stratification may become more prevalent with projected future warming.	5-Increase the number of paired upper and lower water column temperature sensors in regions susceptible to stratification. These types of sensors are relatively inexpensive and easy to deploy.
6-Lack of temperature measurements in shallow water, such as the shoals of estuaries and rivers.	6-Shallow water environments can function very differently from deeper regions—both physically and ecologically. Lack of shallow water temperature data can preclude thorough model calibration/validation.	6-Increase temperature observations in shallow regions.

Table 15. Gaps and limitations associated with modeling of salinity, as well as the importance of those gaps and opportunities for addressing them. TDS: total dissolved solids. CONUS: contiguous U.S. NaCl: sodium chloride. CaCl₂: calcium chloride. MgCl₂: magnesium chloride.

Gap or Limitation	Importance	Opportunities
1-Lack of understanding of the effects of increasing salinity and mixing of waters of varying compositions. Biogeochemical reaction parameters are needed to help model and understand interactions between multiple constituents associated with salinity.	1-Changes in hydrobiogeochemical conditions from salinity can introduce considerable risk to water quality, agriculture, and human or ecosystem health. Ecological models could be strengthened by geochemical modeling results.	1-Assess processes resulting from salinity changes such as mixing, ion exchange, and mineral dissolution or precipitation using geochemical or reaction-transport models and incorporate them into other water quality models. Ecological models can be coupled to hydrodynamic and thermodynamic models and (or) use their output.
2-Limited understanding of the effects of rising global sea levels and extreme events (e.g., coastal storms) on salinity in surface and subsurface waters.	2-Water for human, agricultural, or industrial use, as well as for ecosystems, is impacted by increasing sea levels and salinity.	2-Assess driving processes and effects of increasing salinity on human water use and aquatic habitat.
3-Geochemical and hydrogeologic data for saline aquifers are sparse and limit effective modeling.	3-As saline groundwater use becomes increasingly important, it is important to understand the resources and baseline chemistry.	3-Hydrogeologic and geochemical datasets could be compiled to estimate groundwater salinity at regional and national scales at various depths.
4-Lack of inorganic chemical analysis of water samples, including major ions, silica, nutrients, and important trace constituents (e.g., bromide, boron, iron, manganese).	4- Such analyses would support geochemical modeling and calculation of TDS and salinity through speciation and summation. They would also allow evaluation of water types, chemical source signatures, and saturation index.	4-Perform complete water sample analysis to provide the best estimate of TDS and salinity [488] and evaluation of causes and effects of salinity changes.
5-High-resolution national-scale estimates of deicing application are not currently available. The best available data are derived from salt (NaCl) sales and do not include other deicing materials. In addition, estimates are made for roads and do not include other impervious surfaces [527].	5-Deicing application accounts for the majority of chloride inputs to streams in temperate climates.	5-Obtain/develop higher resolution CONUS scale estimates of all types of deicing materials (NaCl, CaCl₂, and MgCl₂), along with application rates for all types of impervious surfaces (roads, parking lots, sidewalks, and driveways) [528].

Table 16. Gaps and limitations associated with modeling of nutrients, as well as the importance of those gaps and opportunities for addressing them. P: phosphorus. N: nitrogen. WWTP: Wastewater treatment plant. USDA: U.S. Department of Agriculture. NRCS: Natural Resources Conservation Service. 3-D: three-dimensional.

Gap or Limitation	Importance	Opportunities
1-Insufficient quantification of individual nutrient sources, e.g., atmospheric P inputs (#1), construction sites (#26), N from WWTPs, commercial and industrial sources (#25), drinking water treatment nutrient additions (#23), septic systems (#22), and irrigation (#20), N fixation and denitrification (#43), legacy sources including soils and bottom sediments (#42).	1-Inclusion of important inputs is necessary for a model to properly represent the relative importance of individual sources and describe the actions that may improve water quality.	1-Quantify individual nutrient sources and their various forms under a range of hydrologic conditions. In situ flux studies and sediment trap studies may help define specific sources.
2-Limited fine-scale information describing implemented land management activities over large areas (#17).	2-Would support simulating the effects of specific management actions and forecasting the impacts of changing practices.	2-Obtain access to management data assembled by USDA/NRCS.
3-Hybrid nutrient models are only now beginning to describe inter- and intra-annual variability in water quality.	3-Would support understanding of intra- and inter-annual changes and trends in water quality.	3-Further develop dynamic models to incorporate intra- and inter-annual variability in transport.
4-Effects of reservoirs are not usually incorporated into large-scale watershed models.	4-Cannot accurately simulate intra-annual changes in nutrient concentrations over large scales without incorporating the effects of reservoirs.	4-Assemble databases providing reservoir management information (e.g., morphometry, release timing, and release depth) for individual reservoirs across large (e.g., regional and national) scales. Develop simple algorithms to describe the changes in nutrient concentrations caused by reservoirs and incorporate these algorithms in watershed models.
5-Empirical and hybrid models typically only simulate total nitrogen and phosphorus delivery.	5-Dissolved forms of nitrogen and phosphorus often drive productivity in streams and reservoirs.	5-Further empirical and hybrid model development for various forms of nutrients.
6-Only limited water quality data are available in many areas, especially in areas where specific management practices are implemented.	6-Such data would support understanding of how specific management actions affect water quality.	6-Additional flow and nutrient data collection to improve watershed model calibration and verification.
7-Limited 3-D data exist for hydrogeologic/geochemical controls of nutrient speciation and transport in the saturated zone.	7-Would support improved description of nutrient transport through the unsaturated zone and in groundwater.	7- Obtain better 3-D data describing the saturated zone.

Table 17. Gaps and limitations associated with modeling of sediment, as well as the importance of those gaps and opportunities for addressing them.

Gap or Limitation	Importance	Opportunities
1-Lack of understanding and ability to model streambank erosion at the watershed scale.	1-Critical for land managers and researchers in identifying contributions from important sediment source(s).	1- Field and photogrammetric (including Lidar) monitoring and mapping of streambank changes at the watershed scale, with flow data, leading to modeling studies.
2-Estimation of upland versus channel sources.	2-Critical for managers to target sediment sources to reduce sediment.	2-Research into sediment fingerprinting, including field, laboratory, and statistical modeling.
3-Lack of understanding and modeling related to sediment storage and residence time.	3-Sediment transport (transit times) and residence time depend on the spatial distribution of storage or buffers and the hydraulic properties of the stream channel. To fully account for delivery of sediment from its source to sink, deposition, and yield in a modeling framework, it is important to explain sediment storage and transport mechanisms operating within a catchment.	3-Investigations into approaches to date fluvial sediment, including radionuclides and other time markers. Field and laboratory experiments augmented by biogeochemical and numerical analyses and the development of a framework to incorporate various processes involved in sediment movement from source to outlet over various spatial distributions and timeframes.
4-Lack of communication of uncertainty and limitations of models.	4-To adequately transfer knowledge from modeling to water quality management plans, it is important to effectively communicate model uncertainty and limitations of data and models.	4-Enhance our ability to identify and constrain sources of model uncertainty, both from the modeling framework, assumptions, and input data and parametrization. Advance uncertainty quantification and attribution techniques, combined with qualitative description to communicate uncertainty.
5-Limited accessibility of models for managers and planners.	5-Model accessibility and distribution are important for the transfer of knowledge to support water quality management and planning.	5-Bridge the gap between science (modelers) and management (stakeholders) through engaging stakeholders and the public in the data collection and model development process.
6-Lack of representation of environmental interfaces.	6-Interfaces in hydrology, oceanography, geomorphology, biology, geochemistry, and human systems influence sediment sourcing, delivery, storage, and loading.	6-Adopt a coupling framework in sediment modeling to simulate environmental interface dynamics.
7-Lack of data and understanding of how soil condition interacts with biology, biogeochemistry, and land management.	7-Soil condition and land management influence various environmental interfaces as well as sediment erosion, sourcing, delivery, and storage.	7-Field and laboratory experiments with environmental tracers to understand the relationships among hydrodynamics, soil biology, chemical properties, and soil conditions. Enhanced geospatial digital soil mapping. High resolution water quality monitoring.

Table 18. Gaps and limitations associated with modeling of geogenic constituents, as well as the importance of those gaps and opportunities for addressing them. Additional detail is provided in [37]. Numbers in parentheses (e.g., (#43)) refer to processes in Figure 1 and Table 2 herein.

Gap or Limitation	Importance	Opportunities
1-Limited thermodynamic and kinetic data for biogeochemical reactions and exchanges (#43).	1-Crucial for the development of appropriate models and management tools.	1-Field and laboratory experiments to augment thermodynamic and kinetic databases.
2-Limited data and process understanding of mineralogy and geochemical composition of naturally occurring soils, sediments, and rocks that can mobilize geogenic constituents.	2-Crucial for the development of appropriate models, management tools, and biogeochemical understanding of sources and mobilization of geogenic constituents. Geospatial datasets would support the upscaling of local-scale geogenic models.	2-Field and laboratory experiments to augment existing data sets and process understanding; compile relevant geospatial data sets. Collect more mineralogy and geochemical composition data for aquifer material to complement the National Geochemical Dataset.
3-Traditional statistical models of geogenic constituent concentrations and distribution in aquifers are limited in accuracy and/or spatial scale.	3-More accurate models could guide predictions, mapping, and management for geogenic contaminants that present a risk to human or ecosystem health.	3-Expand the application of machine learning methods and hybrid modeling, which have fewer data requirements and improved predictive capability; used together with geochemical models and (or) reactive transport models, these models provide greater understanding of driving processes.
4-Limited knowledge of the effects of agricultural practices and evaporative accumulation (#5, 13–17, 19–20).	4-Crucial for the development of appropriate models and management tools.	4-Develop hydrologic and biogeochemical models that incorporate anthropogenic activities to predict potential water quality limitations to beneficial use.
5-Limited process understanding of effects of projected future climate (e.g., #11, 12, 44), extreme events (e.g., #6), and water table fluctuation (#40).	5-Crucial for understanding the effects of projected future climate and extreme events on the inundation and/or mobilization of geogenic contaminants; development of appropriate models and management tools.	5-Develop conceptual models for the effects of projected future climate (flood inundation frequency and extent, extended drought conditions, sea level change, and inundation) and extreme events and how the changes redistribute or alter the mobility of geogenic constituents either directly or indirectly.
6-Limited knowledge of geochemical composition, location, and timeframe of spills and waste discharges (#25), mines and mine waste discharge (#12, 30), wastewater and septic system discharges (#21, 22), salinity from road deicers (#27), and wastes from oil and gas development (#29).	6-Crucial for understanding human-induced exacerbation of water availability problems from high concentrations of geogenic constituents. Crucial for the development of appropriate models, strategies, and other management tools to anticipate, quantify, and respond.	6-Compile relevant temporal and geospatial data sets from these human sources and drivers.
7-Limited process understanding of groundwater-surface water (hyporheic) interactions (#38).	7-Crucial for the development of appropriate models and management tools.	7-Develop coupled transient hydrologic and biogeochemical process models that incorporate density effects; collect/compile relevant thermodynamic and field data.
8-Limited knowledge of water-chemistry composition affecting corrosion of water distribution piping (#23).	8-Lead and copper contamination of tap water.	8-Compile infrastructure data sets and source water geochemistry data sets.
9-Limited process understanding of managed aquifer recharge (MAR) (#28).	9-Offers the opportunity to store water in aquifers. Absent appropriate design, MAR systems are abandoned due to induced groundwater quality problems.	9-Develop coupled transient hydrologic and biogeochemical process models; collect/compile relevant thermodynamic and field data.
10-The need exists for a coupled public domain reactive transport model that could be used to assess geogenic mobilization at variable temperature and salinity.	10-Reactive transport models integrate chemical reactions with the transport of fluids and are necessary to understand geochemical mobilization at high temperatures (for geothermal sites) and/or with high dissolved solids concentrations (e.g., brackish groundwater sites).	10-Add geochemical modeling capability (e.g., couple with PhreeqcRM) to the MODFLOW framework and maintain it with future updates.

Table 19. Gaps and limitations associated with modeling of contaminants of emerging concern, as well as the importance of those gaps and opportunities for addressing them. CEC: contaminant of emerging concern, PEC: model predicted environmental concentration. MEC: empirically measured environment concentration. WWTP: wastewater treatment plant. WWE: wastewater effluent. PNEC: Predicted No Effect Concentration. SIC codes: Standard Industrial Classification codes used in discharge permits. EC10: the concentration at which 10% of the organisms tested exhibit a statistically significant effect of the chemical. MEC: empirically measured environmental concentration. PEC: hydrologic model’s predicted environmental concentration. USEPA: U.S. Environmental Protection Agency. RCRA: Resource Conservation and Recovery Act. CWNS: USEPA’s 2012 Clean Watersheds Needs Survey [44,668]. NPDES: National Pollutant Discharge Elimination System [669]. EPI Suite^TM: Estimation Programs Interface Suite of physicochemical property and environmental fate estimation programs [450]. EcoTOX: Ecotoxicological Knowledgebase providing single chemical environmental toxicity data [670]. ECHO: USEPA’s Enforcement and Compliance History Online [671]. WQP: Water Quality Portal [672].

Gap or Limitation	Importance	Opportunities
1-Uncertainty (or unknowns) associated with underlying fate and transport for CECs.	1-Quantitative understanding of thermodynamic properties and mechanistic processes (e.g., partition coefficients, decay rates) would support more accurate fate and transport model simulations. Would also constrain input variables and optimize simulations for process-based and hybrid models.	1-Develop and maintain an open-access, machine-readable database of CEC source types, typical discharge concentrations, and physicochemical and kinetic data relevant to environmental fate and transport.
2-Limited amount of municipal WWTP effluent concentrations for CECs, especially at facilities serving < 10,000 people.	2-More WWE concentrations for CEC loading inputs improves accuracy of PECs in hydrologic models and simulations of potential adverse effects.	2-Engage local stakeholders to assist in obtaining MECs of “priority CECs” from domestic and industrial wastewater effluent in more water quality studies and upload them into accessible, machine-readable database(s).
3-Chemical loads from industrial WWTP discharges are largely missing from current hydrologic and chemical transport models.	3-Industry effluent is a significant point source of surface water contaminants and having data on chemical concentrations in effluent would greatly improve the accuracy of PECs and environmental risk assessments.	3-Engage with industry, regulatory and discharge permitting agencies to develop timely, consistent presentation of accessible, machine-readable data on average or expected chemical concentrations (with correlations to their SIC codes) and discharge volumes (e.g., NDPES, USEPA CWNS, and ECHO).
4-Lack of consistent, long-term occurrence data for many CECs.	4-Would support the development of statistical relations between controlling variables and environmental responses.	4-Perform higher resolution monitoring of CECs at regular intervals in keystone watershed types. Curate alternative land cover, land use, and management practice activities to improve the accuracy of model simulations.
5-Lack of toxic-effect threshold concentrations for CECs (with the exception of pesticides).	5- PECs of CECs can be compared to toxic-effect threshold concentrations for human or aquatic organism health to evaluate potential adverse effects; existing or proposed water management practices can be simulated by models to provide risk assessments from PECs.	5-Perform more effects-based toxicity tests (i.e., PNEC, EC10) and bioassays for CECs; utilize computational toxicology tools such as EPI Suite and EcoTOX.
6-Limited availability of timely and accessible descriptions of WWTP treatment type, daily discharge, and population served.	6-WWTP removal efficiencies and populations served can help generate discharge loads for CECs if only per capita use of chemicals or influent concentrations are known.	6-Develop and share scripts for data mining and cleaning of WWTP-relevant databases such as ECHO and WQP; speed up CWNS and NDPES reporting.
7-Insufficient data regarding timing and quantities of agricultural applications.	7-Improved descriptions of agriculture management activities and timing would help constrain agriculture discharge to become pseudo-point-source inputs.	7-Request/find data source for timing and quantities of agriculture applications (i.e., fertilizer, pesticides, biosolids).
8-Limited understanding of the effects of extreme events on CECs.	8-Wildfires, floods, and hurricanes can influence mobilization, loads, transport, and concentrations of CECs.	8-Increase monitoring and research on CECs before, during, and after extreme events.

Table 20. Synthesis of water quality modeling gaps that were common to multiple cross-cutting capabilities and/or constituents assessed in Section 2 and Section 3. Gaps are categorized as belonging to at least one of three types: data gaps (D), process understanding gaps (U), and model or modeling gaps (M). These common gaps are grouped into eight themes. CEC: contaminant of emerging concern. ML: machine learning. RCM: reduced complexity model.

Gap Theme	Description	Why It’s an Issue	Type of Gap (D,U,M)	Opportunities
1-Calibration/validation/boundary condition data	1-Long-term, spatially comprehensive water quality and hydrodynamic data to support prescription of boundary conditions, improved calibration of model parameters, and evaluation of model skill.	1-Specified concentration boundary conditions can dominate over other processes especially in strongly advective situations. Constituent concentrations and the processes affecting them can display sharp spatial and temporal gradients not captured by routine sampling programs.	D	1-Increase water quality monitoring to capture critical gradients and changes over multiple timescales, especially in areas where management actions occur. Compile and harmonize data from various sources. Augment use of advanced in situ instrumentation, remote sensing (with possible coupling to AI algorithms), and environmental proxies to fill data gaps. Continue and augment long time series datasets. Intensify data collection for CECs. Where appropriate, implement RCMs, which have lower data requirements.
2-Reservoir operations	2-Lack of reservoir operations data, rule curves, morphometry, water levels, etc. for many reservoirs included in regional and larger scale models. Lack of capacity to model reservoir operations.	2-Reservoir outflow rate, timing, and depth can strongly influence water quality (e.g., temperature, sediment, and nutrients) in downstream water bodies. Large-scale water quality models (e.g., of watersheds) are limited by the lack of reservoir operations information.	D,M	2-Obtain reservoir operations and other relevant data and compile a national-scale database of detailed reservoir operating parameters and policies. Phased development of reservoir modeling capacity. Couple real-time water quality information to reservoir operations to develop operational rules. Tightly couple operations and water quality models.
3-Extreme events and projected future climate	3-Limited ability to quantitatively describe, understand, and predict impacts of extreme events and projected future climate on water quality and the effect of those changes on human water uses and aquatic species.	3-Processes influenced by climate (e.g., sea level rise, glacier melt, drought, flooding, and water table fluctuation) and extreme events (e.g., hurricanes and wildfire) can influence the mobilization, intrusion, and mixing of multiple water quality constituents from a broad range of hydrologic and terrestrial sources, inducing changes in water chemistry, quality of water for human uses, and aquatic habitat.	D,U,M	3-Invest in long observational records and high-resolution climate scenario modeling to support understanding of potential impacts of projected future climate on the hydrosphere, water quality projections, and adaptation and mitigation research. Expand collection, integration, and analysis of datasets capturing water quality responses to extreme events and describing climate-driven processes affecting water quality and habitat. Incorporate water quality into models that couple coastal hydrodynamics and inland hydrology. Include land use and water quality in flooding models. Develop understanding of climate induced mobilization of geogenic contaminants.
4-Thermodynamic and kinetic rate data	4-Thermodynamic and kinetic rate data are missing or inadequate for use in many water quality models. These parameters can be location- and time-specific and/or unknown for many constituents. Available parameters may not represent natural conditions or interactions between constituents.	4-Required to parameterize (bio)geochemical transformation processes in models predicting fate and transport of constituents.	D,U,M	4-Generate additional and compile thermodynamic and kinetic data for parameters in water quality models. Perform research to understand and quantify interactions between constituents and how parameters vary across space and time. Explore use of ML methods for estimating parameters for use in process-based models. Where appropriate, implement RCMs, which may have lower parameterization requirements due to process lumping.
5-Model coupling	5-Limited availability of water quality models that couple hydrologic compartments (e.g., surface water-groundwater and watershed-estuary-coastal ocean) as well as across disciplinary boundaries (e.g., effects of biology on hydraulic physics, bio-removal of constituents, and effects of waves on water quality).	5-Constituents can be exchanged between spatial compartments, affecting water quality and aquatic habitat. Critical feedbacks from biological to physical processes can strongly influence constituent fate and transport and overall water quality. Wave induced resuspension of sediment can influence suspended sediment concentrations and sorbed constituents.	D,U,M	5-Couple physical and water quality models across spatial compartments. Incorporate into models the feedback effects of biological processes on hydrodynamics (e.g., biologically induced drag) and constituent biodegradation or sorption. Invest in process research and data collection to describe, understand, and parameterize those processes in models.
6-Anthropogenic influences	6-Incomplete quantification, understanding, and model-inclusion of anthropogenic influences on water and energy cycles and on water quality.	6-Understanding and quantification of human influences on physical, chemical, and biological systems would allow holistic modeling, prediction, and management of water availability.	D,U,M	6-Obtain, compile, and release data describing human influences (e.g., water and land use, agricultural practices, and construction) so those influences may be included in water quality models. Incorporate human influences (e.g., on land use, water management) into climate models.
7-Physical setting	7-Detailed data describing the hydrogeologic setting (for groundwater flow modeling) and bathymetry (for surface hydrodynamic modeling) are often inadequate but difficult and expensive to collect.	7-Data describing the geologic and bathymetric setting are fundamental to accurate modeling of physical water flow and circulation patterns and, in turn, constituent transport.	D	7-Invest in augmented field data collection and/or advanced computational approaches to infer, estimate, or interpolate bathymetry and subsurface hydrogeology.
8-Sources	8-Natural, anthropogenic, and legacy sources of constituents to waters are often unknown, poorly understood, unquantified, and thus neglected in models.	8-Quantification of sources is important for developing justified cause-and-effect relationships, mass balances, accurate estimates of source apportionment, and projections of management effects. Omission of sources in a model can result in their importance being attributed to other variables that are included in the model (especially in statistical or calibrated models).	D,U	8-Obtain, compile, and release data describing natural and anthropogenic constituent sources (e.g., municipal and industrial wastewater effluents, deicers, agricultural applications, and management actions) so they may be incorporated into water quality models. Expand research on critical sources (e.g., legacy nutrients in soils and, for sediments, streambank erosion), biogeochemical reaction kinetics, and mobilization processes.

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Lucas, L.V.; Brown, C.J.; Robertson, D.M.; Baker, N.T.; Johnson, Z.C.; Green, C.T.; Cho, S.J.; Erickson, M.L.; Gellis, A.C.; Jasmann, J.R.; et al. Gaps in Water Quality Modeling of Hydrologic Systems. Water 2025, 17, 1200. https://doi.org/10.3390/w17081200

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Lucas LV, Brown CJ, Robertson DM, Baker NT, Johnson ZC, Green CT, Cho SJ, Erickson ML, Gellis AC, Jasmann JR, et al. Gaps in Water Quality Modeling of Hydrologic Systems. Water. 2025; 17(8):1200. https://doi.org/10.3390/w17081200

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Lucas, Lisa V., Craig J. Brown, Dale M. Robertson, Nancy T. Baker, Zachary C. Johnson, Christopher T. Green, Se Jong Cho, Melinda L. Erickson, Allen C. Gellis, Jeramy R. Jasmann, and et al. 2025. "Gaps in Water Quality Modeling of Hydrologic Systems" Water 17, no. 8: 1200. https://doi.org/10.3390/w17081200

APA Style

Lucas, L. V., Brown, C. J., Robertson, D. M., Baker, N. T., Johnson, Z. C., Green, C. T., Cho, S. J., Erickson, M. L., Gellis, A. C., Jasmann, J. R., Knowles, N., Prein, A. F., & Stackelberg, P. E. (2025). Gaps in Water Quality Modeling of Hydrologic Systems. Water, 17(8), 1200. https://doi.org/10.3390/w17081200

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Gaps in Water Quality Modeling of Hydrologic Systems

Abstract

1. Introduction

1.1. Background

1.2. Model Types

1.3. Objective and Approach

2. Cross-Cutting Modeling Capabilities and Gaps

2.1. Meteorologic and Climatic Forcing

2.2. Geochemical and Biogeochemical Modeling

2.3. Watershed Modeling

2.4. River Modeling

2.5. Lake and Reservoir Water Quality Modeling

2.6. Reservoir Operations and Outflow Modeling

2.7. Estuary Modeling

2.8. Groundwater Modeling

2.9. De Facto Wastewater Reuse and Chemical Transport Modeling

3. Capabilities and Gaps for Modeling Priority Constituents

3.1. Water Temperature

3.2. Salinity

3.3. Nutrients

3.4. Sediment

3.5. Geogenic Constituents

3.6. Contaminants of Emerging Concern

4. Discussion and Conclusions

4.1. Synthesis of Gaps

4.2. Some Ways Forward—Summary of Key Opportunities

4.2.1. Data Collection, Compilation, and Harmonization

4.2.2. Process Research

4.2.3. Machine Learning

4.2.4. Reduced Complexity Models

4.3. Conclusions

Author Contributions

Funding

Data Availability Statement

Acknowledgments

Conflicts of Interest

Appendix A

References

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