Fifteen Years of WRTDS for Advancing Water-Quality Science: A Review of Methodological Developments and Global Applications
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Fifteen Years of WRTDS for Advancing Water-Quality Science: A Review of Methodological Developments and Global Applications
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Environmental Science & Technology

Cite this: Environ. Sci. Technol. 2026, XXXX, XXX, XXX-XXX
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https://doi.org/10.1021/acs.est.5c12895
Published April 7, 2026

© 2026 The Authors. Published by American Chemical Society. This publication is licensed under

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Abstract

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Contamination by nutrients, major ions, and metals poses a major threat to global water sustainability. Understanding how these pollutants vary across time and space requires long-term monitoring and robust statistical approaches. Traditional methods, however, often struggle to account for streamflow variability, seasonality, and nonlinear responses. Introduced in 2010, the Weighted Regressions on Time, Discharge, and Season (WRTDS) method offers a flexible, data-driven framework that generates both observed and flow-normalized estimates of concentration and load. Over the past 15 years, WRTDS has become a state-of-the-art tool for water-quality science and management, with applications spanning a wide range of hydrologic, climatic, and policy contexts─including major watersheds across North America, Europe, Asia, Australia, and the Arctic. In this review of WRTDS, we document the method’s major advancements, examine its expanding geographic and thematic applications, and summarize its relevance to water-quality management programs and policies worldwide. We also discuss its performance relative to other regression and machine-learning approaches. Finally, we identify key priorities for future development to support the continued evolution of WRTDS as a trusted and practical tool for scientists and managers working to protect and sustain water resources.

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1. Introduction

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Contamination by nutrients, major ions, and metals threatens freshwater and coastal ecosystems worldwide. (1−3) Examples of impacted systems include major rivers such as the Mississippi River and Yangtze River, (4,5) as well as estuaries and lakes such as the Chesapeake Bay, Great Lakes, Gulf of America (also known as Gulf of Mexico), and Baltic Sea. (6−9)
Despite decades of scientific investigation, tracking and explaining water-quality patterns and their drivers remains a challenge. Solutions rely on sustained investment in high-quality data, robust analytical methods, and long-term monitoring networks that are strategically placed and consistently maintained. (10) These monitoring data form the foundation of science-based management. However, translating complex data sets into actionable information remains a key challenge. Robust analysis methods are therefore needed to extract meaningful insights from these data. These approaches are most successful when accounting for confounding factors such as seasonality and nonlinear responses and distinguishing anthropogenic signals from natural variability. (11−13)
Historically, analyses of water-quality loads and trends in rivers and streams relied on methods developed in the 1980s and 1990s. (12,13) Mann-Kendall and Seasonal Kendall approaches are widely used for trend analyses due to their simplicity and robustness. However, these nonparametric methods assume monotonic trends, which may not reflect the complexity of river water quality. In addition, they are not designed to account for streamflow variability or censored values. (14,15) LOADEST, a parametric method developed in the late 1980s, marked a significant step forward by explicitly accounting for the effects of streamflow and seasonal variations. (16,17) Yet, its fixed functional form is too rigid for use with multidecadal data sets. This type of parametric approach is based on assumptions that concentration-discharge relationships maintain the same shape over time, that seasonal patterns never change, and that trends follow some defined functional forms (e.g., linear or quadratic). (18,19)
These methodological limitations underscored the need for more flexible and interpretable approaches in water-quality analysis. In response, Weighted Regressions on Time, Discharge, and Season (WRTDS) was developed in 2010. (20) WRTDS estimates water-quality concentrations as a smooth function of time, discharge, and season using locally weighted regression. It was designed to accommodate shifting seasonal cycles and capture nonmonotonic trends. (20) In addition, WRTDS includes a built-in “flow-normalization” algorithm to remove the noise of natural hydrologic variability, which can help reveal water-quality changes related to management actions. In rivers, streamflow and water-quality concentrations are often correlated, and thus a sequence of wet or dry years may induce an apparent trend that reverses direction once conditions return to normal. Flow-normalization addresses this issue, providing trend estimates that are more robust to weather-driven fluctuations. Failure to consider these interannual streamflow variations can weaken the statistical power for trend detection and, in some cases, lead to misleading interpretations when observed changes primarily reflect short-term hydrologic conditions near the beginning or end of the record. (20)
Over the past 15 years, WRTDS has emerged as a widely used tool for water-quality trend and load analysis. Through the Exploration and Graphics for RivEr Trends (EGRET) R package, which offers a user-friendly interface and a broad set of diagnostic and visualization tools, WRTDS has become highly accessible to researchers and water managers. This accessibility has driven its expansion well beyond its original focus on nitrogen and phosphorus in rivers, enabling applications to a wide range of water-quality constituents, including major ions and metals, and new environmental settings.
In this review of WRTDS, we document the method’s major advancements, examine its expanding geographic and thematic applications, and summarize its relevance to water-quality management programs and policies worldwide. We also discuss its limitations and strengths, including its performance relative to other regression and machine-learning approaches. Finally, we identify key priorities for future development to support the continued evolution of WRTDS as a trusted and practical tool for scientists and managers.

2. Overview of the WRTDS Model Framework

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WRTDS is a flexible regression method developed for estimating water-quality concentrations and loads based on routine discrete sampling data (20) (Figure 1). It requires two input data sets: a complete daily streamflow record and a time series of concentration observations, typically collected monthly or quarterly. To ensure robust model performance, at least 10 years and 100 concentration samples, collected to represent the seasonal and hydrologic variability of the location, are recommended for trend studies. For load estimation, however, as little as five years may be sufficient. (20) Like other established methods, WRTDS models log-transformed constituent concentrations as a function of time, discharge, and season, which capture the long-term, flow, and seasonal effects, respectively. (20) The logarithmic transformation prevents negative predictions and is more consistent with the statistical distribution of the concentration observations.

Figure 1

Figure 1. Conceptual overview of WRTDS: model features, software, inputs, and outputs.

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Inspired by the Locally Estimated Scatterplot Smoothing (LOESS) technique, (21) WRTDS applies a locally weighted regression approach that gives higher weight to observations that are similar in time, discharge, and season to each point of estimation. In contrast to LOADEST, which fits a single global regression model, WRTDS generates a unique local regression for each estimation point by dynamically recalibrating weights and coefficients. These weights are determined by the distance of each observation from the estimation point in time, discharge, and season, as well as by user-defined half-window widths. Observations closer to the estimation point are assigned higher weights, while those beyond the half-window widths are excluded from the local fit. To make the estimation computationally feasible, WRTDS constructs a two-dimensional grid over time (16 “time intervals” per year) and log-discharge (14 “flow intervals” covering the flow range) and makes predictions at each intersection of this grid. Bilinear interpolation is then used to estimate concentrations across the full time-discharge space. The result of this innovative framework is called the “regression surface,” which offers a detailed representation of how concentrations evolve over time, discharge, and season. (20) This framework makes WRTDS data-driven, responsive to local conditions, and capable of capturing nonlinear patterns. (20)
WRTDS produces two types of estimates on a daily resolution that can be aggregated to monthly, seasonal, or annual resolutions (Figure 1). The first type, “true-condition” estimates, reflect actual streamflow conditions on a given day. These estimates are useful for quantifying nutrient budgets, calibrating watershed models, and assessing downstream impacts. The second type, “flow-normalized” estimates, remove the effects of interannual streamflow variability by considering the statistical distribution of streamflow over an annual cycle. These estimates are especially useful for detecting long-term water-quality changes that are related to human activities and management actions.
WRTDS is implemented through the EGRET R package. (22) This package supports automated data retrieval from the United States Geological Survey (USGS) Water Data for the Nation (10.5066/F7P55KJN), the Water Quality Portal (10.5066/P9QRKUVJ), or user-supplied data files. EGRET also provides a wide range of graphical tools for evaluating data inputs, assessing model performance, visualizing the regression surface, and summarizing model estimates. Full details of WRTDS are available in its foundational publication, (20) the official user manual for the EGRET R package, (23) and a number of tutorial presentations and articles on the EGRET Web site (https://rconnect.usgs.gov/EGRET/).
Despite its many strengths, WRTDS came with a few important assumptions and limitations in its initial release. Notably, WRTDS assumed that the concentration-discharge relationship changes in a gradual manner, which reflects the cumulative influence of evolving hydrologic, biogeochemical, and anthropogenic processes. In addition, WRTDS did not account for antecedent conditions, flow hysteresis, or any other covariates beyond time, discharge, and season. Moreover, the flow-normalization procedure assumed that the streamflow regime remains stationary over time, but this assumption is increasingly challenged by climate change and hydrologic modifications. (24) In these regards, Hirsch et al. (20) outlined several directions for further improving WRTDS, including:

  • Incorporating censored data (i.e., values below detection limits),

  • Considering antecedent discharge conditions as explanatory variables,

  • Extending flow-normalization to address nonstationary flow regimes,

  • Estimating exceedance probabilities for thresholds relevant to human and ecosystem health,

  • Modeling multiple constituents simultaneously (e.g., nitrogen subspecies),

  • Optimizing the selection of half-window widths, and

  • Quantifying uncertainties in model estimates, particularly for flow-normalized trends.

These priorities have guided many of the advancements made to WRTDS over the past 15 years, as described in the following section.

3. Historical Development and Advancements

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3.1. Introduction and Early Applications (2010–2013)

In the foundational paper of WRTDS, Hirsch et al. (20) estimated long-term loads and trends of nitrogen and phosphorus in nine major tributaries of Chesapeake Bay (Figure 2). Early applications extended the method to several other major river systems, including the Mississippi River, (25) Susquehanna River, (26,27) and Lake Champlain tributaries. (28) During this initial period, most studies focused on characterizing long-term trends in nitrogen and phosphorus.

Figure 2

Figure 2. Key milestones in the development and enhancement of the WRTDS method.

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3.2. Method Assessment and Software Development (2012–2015)

Parallel to its early applications, research efforts focused on method assessment. Moyer et al. (18) compared WRTDS and LOADEST for nine Chesapeake Bay tributaries. They found that WRTDS outperformed LOADEST in most cases, especially when concentration-discharge relationships were nonlinear. Subsequently, WRTDS was adopted as the primary tool by the Chesapeake Bay Program for riverine loads and trends reporting. Hirsch (19) further showed that LOADEST was prone to bias in conditions such as poor model fit, seasonal variation in concentration-discharge relationships, and heteroscedastic residuals. In comparison, WRTDS showed greater resistance to bias due to its flexible structure.
To improve accessibility and reproducibility, the EGRET R package was released (23) and has been routinely updated (22) (Figure 2). EGRET introduced a streamlined workflow for importing input data, executing and assessing the WRTDS model (which now also accommodates censored data), and generating informative and customizable visualizations of model inputs, outputs, and performance. These features have made WRTDS more widely accessible to both researchers and water managers.

3.3. Model Enhancements (2015–2025)

Following its early applications, WRTDS has undergone several major enhancements that addressed earlier limitations and adapted WRTDS to more complex data sets (Figure 2).

3.3.1. WRTDS-Bootstrap Method for Uncertainty Estimation (wBT):

Hirsch et al. (29) developed wBT for calculating confidence intervals around the flow-normalized trends. Implemented with the EGRETci R package, (30) wBT can report flow-normalized trends with likelihood qualifiers pertaining to the direction of change such as “Highly Likely” or “Highly Unlikely,” which has addressed a long-standing need by water managers and has been widely adopted. (31−33) Since 2015, the EGRETci package has expanded the set of methods for uncertainty evaluation, using the functions runPairsBoot, runGroupsBoot, and ciCalculations, which provide several enhancements to the original wBT method. The first of these functions compares flow-normalized values between any two selected years, the second of these compares flow-normalized values between two groups of years, and the third creates confidence intervals as they evolve over a period of years.

3.3.2. Generalized Flow-Normalization (GFN):

Choquette et al. (34) introduced GFN to relax the assumption of streamflow stationarity and address situations where the streamflow itself has a substantial (i.e., statistically significant) trend over two or more decades. In parallel, Murphy and Sprague (35) presented a conceptual framework for GFN and demonstrated the use of “trend components”─the discharge trend component and the concentration-discharge (i.e., “management”) trend component─for disentangling broad-scale drivers of water quality trends. GFN is particularly relevant to systems affected by changes in streamflow regimes, dam construction or removal, or long-term shifts in hydrologic response due to landscape modification (e.g., artificial drainage, increased impervious area). (35,36)

3.3.3. WRTDSplus for Incorporating Antecedent Discharge Conditions or Other Covariates:

Murphy et al. (37) demonstrated that flow-anomaly variables, which capture periods of nitrate accumulation or depletion, helped explain the residuals from WRTDS. Zhang and Ball (38) expanded this effort by evaluating 12 flow-history metrics across six constituents. These studies provided concrete support for incorporating antecedent discharge conditions into WRTDS. Recently, DeCicco et al. (39) released the WRTDSplus R package, which allows users to incorporate an additional covariate beyond time, discharge, and season or substitute daily discharge with a measure that is more correlated with water quality, like quick flow from a baseflow separation. The initial application of WRTDSplus was for estimating loads and trends for suspended sediment in the lower Mississippi and Atchafalaya Rivers. (40)

3.3.4. WRTDS with Kalman Filtering (WRTDS-K):

Zhang and Hirsch (41) developed WRTDS-K to improve estimation accuracy by leveraging the autocorrelation structure of model residuals. This postprocessing procedure provides daily estimates that rely more heavily on observations when available and on WRTDS model output when observations are not available. Evaluations across multiple sites and constituents showed that WRTDS-K can improve short-term (e.g., daily) concentration and load estimation. Consistently, Lee et al. (42) confirmed that WRTDS-K generally outperformed other methods in estimating annual loads. WRTDS-K is intended for generating improved true-condition estimates, which help quantify nutrient budgets, calibrate watershed models, and assess downstream impacts. It has been applied in numerous studies. (43−45)

3.3.5. Flow-Normalization by Flow Classes (FN2Q):

FN2Q was introduced by Zhang et al. (46) to partition flow-normalized trends into low-flow and high-flow components, thereby revealing how trends differ across hydrologic regimes. This disaggregation of flow-normalized trends enables more nuanced interpretation of trend drivers. For example, application of FN2Q in the South Fork Shenandoah River showed declines in low-flow FN loads of total nitrogen, which were likely linked to major wastewater-treatment upgrades. FN2Q has since been applied successfully in multiple investigations. (47−49)

3.3.6. The “Wall”:

This concept addresses abrupt changes in the concentration-discharge relationship that are not well-represented by WRTDS’s core assumption of gradual evolution. Such abrupt changes may arise from point source upgrades, dam removals, or lasting impacts of extreme events. This concept was first described in the EGRET online documentation (https://doi-usgs.github.io/EGRET/articles/Enhancements.html#the-wall) as an optional enhancement to the standard WRTDS framework. In practice, the “wall” can be implemented through the “runPairs” function in the EGRET R package, which enables users to compare distinct periods before and after a step change. For example, Rumsey et al. (36) used it to account for abrupt changes in the Colorado River following a 1980 pollution control policy. Ruckhaus et al. (50) also used a variation to estimate the impacts of a large wildfire on nutrient concentrations.

3.3.7. WRTDS for Projection (WRTDS-P):

WRTDS has traditionally been used for retrospective analysis rather than future forecasting. WRTDS-P, a recent methodological advancement, extends the framework to enable forward projection of daily water quality under changing hydrologic conditions using commonly available discrete monitoring data. A pilot application (51) across the Delaware River Basin demonstrated strong predictive performance for specific conductance, nitrate, magnesium, and calcium, indicating that WRTDS-P can robustly estimate future water-quality responses to hydrologic variability. This development provides a practical tool for scenario analysis and risk assessment in a changing climate.

4. Expanding Footprint: United States and Global Applications

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WRTDS has evolved into a globally adopted framework for water-quality assessment and management. In the United States, WRTDS has become central to national water-quality assessments led by the USGS. One major effort by the USGS National Water-Quality Assessment team compiled nationwide data for rivers and streams from federal, state, and other sources for the period 1972–2012. (52) Flow-normalized trends were estimated for nutrients, sediment, major ions, salinity, and carbon for four time periods, resulting in approximately 12,000 trend results. This synthesis identified several national-scale patterns. Nutrient loads generally decreased at urbanized sites but showed little change at agricultural sites. In addition, rapid salinization of freshwater was observed at sites across all human-dominated land uses, with implications for biological, ecological, and human health. (31)
Sensitivity analyses of WRTDS were also conducted to evaluate the influence of storm sampling, sample density, rounding of concentration values, and the incorporation of new calibration data. These analyses informed data screening procedures and model specifications. For example, storm-sampling analyses provided criteria to identify sites with sufficient high-flow representation in water-quality records─a necessary consideration for accurate load estimates of particulate-bound constituents. (52)
Flow-normalized trends were further analyzed to identify potential drivers. (31,35,53−55) For example, widespread decreases in suspended sediment concentrations were associated with landscape and management changes rather than changes in flow regime, and were correlated with factors such as changes in low- to medium-density development, row-cropped acreage, and conservation program enrollment. (53)
The national-level assessments have been extended through 2017 (56) and 2022. (57) Since 2017, the USGS has adopted WRTDS as the primary method for computing water-quality loads at National Water Quality Network sites, (58) ensuring that this consistently sampled, long-term monitoring network is supported by robust statistical analysis methods.
Although initially developed for application to major nutrients, WRTDS has also been applied to a broader range of water-quality constituents in human-impacted systems. These include contaminants associated with mining activities (e.g., metals, mercury); (59−61) road deicing (chloride); (62,63) and coal mining (selenium). (64)
Globally, WRTDS has been applied in a wide range of hydrologic and climatic settings. Below, we provide a chronological synthesis of the first WRTDS applications in selected countries, illustrating the method’s growing international reach (Figure 3). These applications demonstrate WRTDS’s adaptability to diverse settings spanning temperate, semiarid, and Arctic landscapes.

  • Finland: Rankinen et al. (65) applied WRTDS to assess nutrient concentrations and loads in 20 tributaries of the Baltic Sea. They documented declines in both nitrogen and phosphorus loads, which likely reflected management efforts.

  • Canada: Van Meter and Basu (66) analyzed 16 nested subwatersheds in Southern Ontario, which revealed nonlinear nitrogen input-output relationships and multiyear lags. Van Meter et al. (67) applied WRTDS to estimate nitrate and phosphorus concentrations for over 200 sites in the Great Lakes Basin to characterize seasonal nutrient regimes and dominant watershed controls. Yates et al. (68) applied WRTDS to nutrient and suspended solids at 18 monitoring locations in the Lake Winnipeg basin.

  • Germany: Ehrhardt et al. (69) assessed nitrate in the Holtemme catchment from 1970 to 2016. Their results demonstrated nutrient input-output imbalances, long lag times, and limited denitrification.

  • France: Dupas et al. (70) studied nitrogen in 16 Brittany catchments from 1976 to 2015. They found that 45–88% of net nitrogen input was retained, largely due to top-soil accumulations (i.e., soil biogeochemical legacies).

  • Russia: Zolkos et al. (71) evaluated particulate mercury export from eight Russian rivers in the pan-Arctic basin (ca. 1975–2010). Declines of 70–90% in particulate mercury were linked to pollution controls and reservoir sedimentation. Their results also suggested Russian rivers’ dominance in mercury inputs to the Arctic Ocean.

  • China: Wu et al. (49) examined nitrogen trends in the Yongan River watershed from 1980 to 2019. They showed effective point-source controls and persistent nonpoint-source challenges due to legacy nutrients.

  • India: Sinha et al. (72) analyzed nitrogen runoff in seven major rivers across peninsular India (1981–2014). Their findings revealed strong seasonal and interannual variability in nitrogen runoff, driven largely by precipitation. They raised concerns given projected future increases in precipitation and seasonal monsoons.

  • Australia: Guo et al. (73) conducted the first national-scale WRTDS application in Oceania, assessing water-quality trends in 287 catchments from 2000–2019. In particular, the authors reported declining salinity, phosphorus, and sediment in the Murray–Darling Basin, which likely reflect drought conditions and salinity management programs.

  • New Zealand: McDowell et al. (74) used WRTDS to estimate total yields of nitrate, total nitrogen, total phosphorus, and Escherichia coli (E. coli) at over 300 long-term sites in New Zealand. They reported that high flows (≥90th percentile) accounted for 51–74% of annual yields.

Figure 3

Figure 3. First published WRTDS applications across continents and countries, highlighting its global adoption. Colors are used to clarify the boundaries between neighboring countries. Base map source: MapChart (https://www.mapchart.net), licensed under CC BY-SA 4.0.

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5. Linking Science to Practice: Supporting Management Programs and Policies

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WRTDS has been widely used to track water-quality patterns and changes across diverse ecological and jurisdictional contexts. In many applications, it has effectively linked long-term monitoring data with regulatory and management frameworks. This broad applicability reflects the range of methods within the WRTDS framework that can be tailored to support load estimation, flow-normalized trends, or management-relevant assessments. While the preceding section summarizes the geographic expansion of WRTDS applications, this section focuses on how these applications have been used to support water-quality management and policy frameworks in the United States (Figure 4) and worldwide.

Figure 4

Figure 4. Distribution of WRTDS applications across United States. Base map source: NOAA (https://www.ncei.noaa.gov/access/monitoring/reference-maps/us-river-basins), public domain.

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5.1. United States Programs and Management Applications

5.1.1. Chesapeake Bay Program

WRTDS has been used to estimate nitrogen, phosphorus, and sediment loads at hundreds of monitoring stations within the Bay watershed. (18,75) These estimates directly inform efforts to restore the nation’s largest estuary and meet its Total Maximum Daily Load (TMDL) goals. (47,76) Notably, a series of studies revealed the declining trapping performance of the Conowingo Reservoir after nearly a century of filling; these findings were subsequently integrated into the TMDL policy framework. (26,27,77)

5.1.2. Great Lakes Restoration Initiative

WRTDS has been used to track nutrient loads in rivers draining into Lake Erie (34,78,79) and the other Great Lakes. (80) These analyses have played an important role in supporting the binational Great Lakes Water Quality Agreement (GLWQA) and the Great Lakes Restoration Initiative (GLRI) led by the United States Environmental Protection Agency (USEPA).

5.1.3. Gulf Hypoxia Task Force

In 2018, this coalition of Federal and State partners working to reduce the size of the hypoxic zone in the Gulf of America added WRTDS as a tool for tracking progress toward nutrient loading reduction goals. (81) Each year the USGS provides annual total nitrogen and total phosphorus loads computed using WRTDS to the Task Force which are compared to reduction goals.

5.1.4. State-Level Nutrient Loss Reduction Strategies

WRTDS supports nutrient trend assessments in key Mississippi River tributaries including the Upper Mississippi, Missouri, Ohio, and Arkansas Rivers. (25,33,82,83) These findings inform state-level nutrient loss reduction strategies aimed at curbing nitrogen and phosphorus runoff throughout the Mississippi River Basin. For example, Illinois used WRTDS in their computation of watershed-scale loads to identify areas of the state with high nutrient yields and notable increases or decreases. (84) WRTDS applications in the Des Moines (Iowa) and Illinois Rivers (Illinois) estimated long-term nitrate trends and evaluated the impacts of tile drainage and best management practices. (85) These findings are relevant to the Gulf Hypoxia Task Force to coordinate efforts to reduce the dead zone in the Gulf of America.

5.1.5. California Nonpoint Source Pollution Control Policies

WRTDS supports nonpoint source pollution control policies toward meeting TMDL goals in the Sacramento-San Joaquin River Delta, part of the largest estuary on the West Coast. (86,87)

5.1.6. Colorado River Basin Salinity Control Program

WRTDS has been used to track long-term trends in dissolved solids and salinity. (36,88) These results support water-quality management under the Colorado River Basin Salinity Control Program, which is aimed at protecting water quality for human and ecological uses in a water-scarce region.

5.1.7. State-Level Water Quality Protection Programs in the Northeast

WRTDS supports water-quality assessments in the Delaware River Basin (DRB) (63,89) and across New England. (90) These insights support the DRB Special Protection Water Program and the Connecticut Nitrogen Credit Exchange Program, respectively.

5.1.8. Water-Quality Protection Programs in Florida

WRTDS applications in the Tampa Bay (91) and Upper St. Johns River (92) provide information to help local programs like the Tampa Bay Estuary Program and the St. Johns River Basin Management Program prioritize actions and track progress over time.

5.2. Global Programs and Management Applications

5.2.1. Transboundary Management (Canada and United States)

WRTDS informs quantification of legacy nitrogen across the Grand River Watershed (93) and nutrient concentrations across the Great Lakes Basin, (67) supporting transboundary management efforts under the GLWQA and GLRI. In another study, WRTDS attributes increasing solute concentrations in Lake Koocanusa to coal mining in the Elk River Valley, British Columbia, highlighting transboundary water-quality challenges. (64)

5.2.2. Baltic Sea Action Plan (Finland)

In Finnish rivers discharging into the Baltic Sea, WRTDS reveals nutrient load reductions, which reflect the effectiveness of the Finnish Agri-Environmental Program and support the goals of the HELCOM Baltic Sea Action Plan. (65)

5.2.3. EU Water Framework Directive (Germany and France)

In agricultural catchments across Central and Western Europe, WRTDS has helped reveal nutrient imbalances, legacy effects, and shifting sources in agricultural catchments. (69,70,94) These insights directly inform strategies under the EU Water Framework Directive.

5.2.4. Pollution Control Programs in Russia

WRTDS indicates decadal-scale mercury reductions in major rivers flowing to the Arctic Ocean, highlighting success in pollution controls and the value of long-term riverine monitoring programs in Arctic rivers. (71)

5.2.5. Pollution Control Programs in China

WRTDS demonstrates the effects of point-source pollution controls under national- and state-level regulations (e.g., Action Plan for Water Pollution Prevention and Control) and highlights the challenges of nutrient legacies. (49,95) Recently, WRTDS provided evidence on the effectiveness of China’s Ecological Compensation Program. (96)

5.2.6. Water-Quality Management in Australia

A nationwide study reveals the effectiveness of regional land management practices, water-quality interventions, and salinity management schemes, especially in the Murray–Darling Basin. (73)

6. Global Adoption and Impact: A Bibliometric Analysis

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This section presents selected bibliometric insights into the global adoption of WRTDS. We compiled peer-reviewed publications (n = 511 as of December 2025) from the Web of Science Core Collection that cite at least one of the four core method papers of WRTDS, (20,29,34,41) and conducted a bibliometric analysis using the bibliometrix R package. (97)

6.1. Publications and Software Downloads

Since its introduction in 2010, WRTDS-related publications have grown rapidly based on records from the Web of Science Core Collection. These publications span hydrology, biogeochemistry, ecology, and environmental science. Publication counts grew steadily through the early 2010s and accelerated after 2017, coinciding with the release and broader use of the EGRET and EGRETci R packages. As of December 2025, these packages have been downloaded over 83,000 and 46,500 times, respectively, from the Comprehensive R Archive Network.

6.2. Thematic Expansions

WRTDS publications have revealed three major thematic expansions, reflecting its use across different pollutant classes, ecosystem types, and environmental challenges. The first thematic expansion is the adaptation of WRTDS to a wide range of water-quality parameters beyond major nutrients like nitrogen and phosphorus. Notable applications include:

  • carbon (e.g., organic carbon) in temperate and Arctic rivers; (90,98,99)

  • dissolved solids in salinity-impacted systems; (36,88,100)

  • chloride in areas impacted by snow and road salts; (62,101,102)

  • trace metals (e.g., mercury, selenium) in regions impacted by mining and industrial activities; (59,64,71,103)

  • dissolved silicon in rivers around the globe─from polar to tropical regions; (104) and

  • biological indicators (e.g., chlorophyll-a) in eutrophic lakes and estuaries. (98)

Second, WRTDS is now widely applied to assess long-term changes in lakes and reservoirs, which include inflow/outflow dynamics and biogeochemical cycling. (77,103) As mentioned above, it has been used to quantify long-term trends in nitrogen, phosphorus, and sediment mass balances in the Conowingo Reservoir on the Susquehanna River, providing evidence of the reservoir’s declining trapping efficiency and highlighting a new challenge for the Chesapeake Bay restoration effort. (26,27,77)
Lastly, WRTDS has become a common benchmark for estimating riverine concentrations and loads. It is now routinely used to compute true-condition loads that are utilized within other models (e.g., SPAtially-Referenced Regression On Watershed attributes [SPARROW]) and to support investigations beyond trend assessment (e.g., Zhao et al. (105)). In addition, its estimation accuracy has been compared with machine learning approaches, including Random Forest, gradient boosting, and Long Short-Term Memory (LSTM) models. (106−108)

7. Comparison with Regression and Machine Learning Methods

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In this section, we compare WRTDS with traditional regression methods and newer machine-learning approaches, highlighting strengths and limitations across methods.

7.1. Comparison with Regression Methods

WRTDS was initially developed to address the limitations of traditional regression methods like LOADEST, which were constrained by rigid model structures. Early evaluations demonstrated generally improved performance of WRTDS in estimating nutrient loads across a range of settings. (18,19) These improvements were apparent in cases with nonlinear or seasonally varying concentration-discharge patterns. Focused on decadal mean loads, Lee et al. (109) provided a broader evaluation across water-quality constituents and monitoring scenarios. WRTDS and Beale’s ratio estimator (110) typically yielded higher accuracy and lower bias than other methods. However, not all comparisons and metrics favored WRTDS─e.g., for nitrate in the Maumee River, WRTDS had significantly lower bias than LOADEST and linear interpolation, but its root-mean-square error (RMSE) and coefficient of determination (R2) performance were less favorable. (111) In a study comparing various methods for estimating annual loads, (42) WRTDS-K was found to generally perform as well as, or better than, other methods, including linear interpolation, Beale’s ratio estimator, and LOADEST.
In estuarine settings, WRTDS has been compared with other flexible statistical models such as the Generalized Additive Model (GAM). Beck and Murphy (112) analyzed chlorophyll-a in the Patuxent River estuary and found that WRTDS and GAMs provided similar long-term trends and predictive accuracy. While GAMs offered more flexibility in modeling irregular patterns, they lacked WRTDS’s built-in diagnostics and tools for interpreting the output. Beck and Hagy (91) also adapted WRTDS’s flow-normalization procedure (WRTDStidal) to evaluate long-term changes in Tampa Bay. They used estuarine salinity values as an indicator of hydrologic conditions in place of the discharge variable used in WRTDS. This adaptation enabled better differentiation between natural variability and anthropogenic impacts.

7.2. Comparison with Machine Learning Methods

With the growing adoption of machine learning techniques, several studies have compared WRTDS with models like Random Forest, gradient boosting (e.g., XGBest), and LSTM. Isles (106) compared WRTDS and Random Forest across 17 tributaries of Lake Champlain. Random Forest outperformed WRTDS and WRTDS-K in most cases, partly due to inclusion of discharge derivatives and antecedent discharges─findings consistent with earlier studies. (37,38) However, Isles (106) noted that WRTDS remains useful because of its interpretability, diagnostic features, and flow-normalization. Jain et al. (107) compared WRTDS, LOADEST, and XGBest for 499 stations in the eastern United States. XGBest achieved higher predictive accuracy by integrating 29 climate and landscape covariates. However, many of these ancillary inputs are not readily available at routine monitoring locations. WRTDS requires only discharge and concentration data, which makes it more broadly applicable for long-term monitoring programs.
Deep learning models, particularly LSTM, have also been compared with WRTDS. Jung et al. (113) applied LSTM to nitrate data in seven rivers in the United States and reported better performance than WRTDS, especially under high-frequency sampling. This is not surprising given the additional covariates leveraged by LSTM. Similarly, Saha et al. (114) reported better performance of LSTM than WRTDS-K in nitrate estimation, particularly at sites with sparse observations (<50 observations). However, WRTDS-K performed comparably in estimating annual nitrate loads. Fang et al. (108) provided the most comprehensive comparison between WRTDS and LSTM to date. They analyzed 20 water-quality parameters for nearly 500 catchments in the United States and found generally similar performance between the two models. LSTM performed better for nutrients but not for weathering-derived solutes. The authors pointed out WRTDS’s distinct advantages in interpretability, stability, and ease of implementation.
In summary, machine learning methods can sometimes yield more accurate predictions, particularly when trained on large sets of explanatory variables. However, their predictive success often offers limited insight into the underlying processes that control water-quality dynamics. In contrast, a key strength of WRTDS lies in its interpretability and diagnostic capabilities. Specifically, the model’s structure enables direct examination of how concentrations respond to time, discharge, and season, allowing users to assess and validate component contributions, identify temporal shifts, and develop new hypotheses about system behavior and change. Beyond estimating concentrations and loads, WRTDS serves as a diagnostic framework for understanding water-quality patterns and drivers─an attribute that distinguishes it from many black-box machine-learning approaches. These interpretability and diagnostic capabilities, together with its relatively modest data requirements, help explain why WRTDS remains widely used for both scientific inference and management applications (Figure 5).

Figure 5

Figure 5. Conceptual comparison of WRTDS with regression and machine-learning models, illustrating tradeoffs between interpretability/transparency (vertical axis) and data requirements/model complexity (horizontal axis). WRTDS combines high interpretability and transparency with relatively low data requirements and complexity.

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8. Synthesis and Future Directions

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Over the past 15 years, WRTDS has supported a wide range of environmental applications globally. Its flexible modeling framework and ability to account for streamflow variations make it well suited for tracking loads and trends in nutrients, sediment, major ions, and other contaminants. Compared to traditional regression methods, WRTDS offers greater interpretability and, in many reported applications, comparable or improved performance. Machine learning models may surpass WRTDS in predictive accuracy, especially in data-rich situations, but WRTDS remains useful for its strong interpretability, powerful diagnostic strengths, and comparatively low demand for input data. Many of the priorities identified at the method’s inception have now been addressed, including uncertainty quantification techniques, integration of flow history, and improved handling of nonstationary hydrology. The EGRET and EGRETci R packages have supported global adoption across diverse regions and settings, and WRTDS has been extended to new pollutants, diverse ecosystem types, and emerging environmental challenges. Looking ahead, we highlight several methodological, operational, and collaborative opportunities to guide the next phase of WRTDS development and applications.
From a methodological perspective, several limitations of the current framework point to important avenues for improvement. First, WRTDS has limited ability to capture short-term (i.e., subdaily) dynamics because it operates at a daily time step. Additionally, existing uncertainty-quantification techniques (e.g., wBT) are currently applicable at individual stations but do not extend naturally to multisite analyses such as load aggregation or mass-balance assessments. Moreover, WRTDS models total streamflow and therefore cannot explicitly separate baseflow and surface runoff contributions, limiting mechanistic interpretation. Finally, WRTDS was originally designed for retrospective analysis; although recent efforts have begun to extend the framework toward projection (e.g., WRTDS-P), its performance under future, nonstationary hydroclimatic conditions remains an open challenge. Addressing these limitations would strengthen the robustness and interpretive power of WRTDS under changing hydroclimatic conditions.
At the same time, water-quality monitoring data sets are becoming increasingly information-rich, incorporating high-frequency sensor observations and subdaily discharge records that extend well beyond the traditional monitoring data for which WRTDS was developed. While the WRTDS framework offers a useful conceptual foundation for analyzing such data, fully utilizing these richer data sets will require substantial methodological development to address challenges such as gaps in high-frequency data, biases in sensor values as estimates of analyte concentrations, and potential drift in sensor-analyte relationships.
From an operational standpoint, WRTDS is already widely used in both scientific and policy-related applications, many of which are described above. However, continued relevance will depend on the ability to provide meaningful model outputs that are relevant to decision making. Integrating WRTDS with complementary data and analytical tools, including high-frequency observations, remote-sensing products, and machine-learning approaches, creates new opportunities to translate complex information into actionable insights. Leveraging spatially and temporally dense data sets within WRTDS could help characterize storm-event responses, extend analyses into sparsely monitored areas, and improve anomaly detection while preserving the method’s transparency and interpretability.
Finally, continued progress will depend on building an active global WRTDS community engaged in evaluating, improving, and standardizing the model and its workflows. The cocreation of unified guidelines, documentation, user interfaces, and data-sharing platforms can support consistency, reproducibility, and comparability across regions and management contexts. These methodological, operational, and collaborative directions are described in greater detail in a companion publication. (115) These advancements can help ensure that WRTDS continues to meet evolving scientific and management needs and remains a practical tool supporting global efforts to protect and sustain water resources.

Author Information

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  • Corresponding Author
  • Authors
  • Author Contributions

    Q.Z. and R.M.H. developed the manuscript outline. Q.Z. drafted the original manuscript and prepared the figures. R.M.H., L.A.D., and J.C.M. revised and validated the manuscript.

  • Notes
    The authors declare no competing financial interest.

Acknowledgments

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This work was supported by funding from the United States Environmental Protection Agency and the United States Geological Survey. We would like to express our sincere gratitude to Jeff Chanat for developing the code for the interpolation scheme in WRTDS, and to Tim Cohn for his foundational work on the code that drives WRTDS-Kalman. We are deeply thankful to the broader community of researchers who have applied, tested, and advanced WRTDS over the past 15 years. We also thank Gretchen Olsner for providing constructive comments on an early version of the manuscript. This is UMCES contribution number 6501. Any use of trade, firm, or product names is for descriptive purposes only and does not imply endorsement by the United States Government.

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  • Abstract

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    Figure 1

    Figure 1. Conceptual overview of WRTDS: model features, software, inputs, and outputs.

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    Figure 2

    Figure 2. Key milestones in the development and enhancement of the WRTDS method.

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    Figure 3

    Figure 3. First published WRTDS applications across continents and countries, highlighting its global adoption. Colors are used to clarify the boundaries between neighboring countries. Base map source: MapChart (https://www.mapchart.net), licensed under CC BY-SA 4.0.

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    Figure 4

    Figure 4. Distribution of WRTDS applications across United States. Base map source: NOAA (https://www.ncei.noaa.gov/access/monitoring/reference-maps/us-river-basins), public domain.

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    Figure 5

    Figure 5. Conceptual comparison of WRTDS with regression and machine-learning models, illustrating tradeoffs between interpretability/transparency (vertical axis) and data requirements/model complexity (horizontal axis). WRTDS combines high interpretability and transparency with relatively low data requirements and complexity.

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