As water-quality challenges intensify, the widely used Weighted Regressions on Time, Discharge, and Season (WRTDS) method offers an adaptable and practical framework for global water-quality science and management.
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References
Helsel, D. R. et al. Statistical Methods in Water Resources (USGS, 2020); https://doi.org/10.3133/tm4a3.
Hirsch, R. M. et al. Weighted Regressions on Time, Discharge, and Season (WRTDS), with an application to Chesapeake Bay river inputs. J. Am. Water Resour. Assoc. 46, 857–880 (2010).
Hirsch, R. M. et al. A bootstrap method for estimating uncertainty of water quality trends. Environ. Model. Softw. 73, 148–166 (2015).
Choquette, A. F. et al. Tracking changes in nutrient delivery to western Lake Erie: Approaches to compensate for variability and trends in streamflow. J. Great Lakes Res. 45, 21–39 (2019).
Zhang, Q. & Hirsch, R. M. River water‐quality concentration and flux estimation can be improved by accounting for serial correlation through an autoregressive model. Water Resour. Res. 55, 9705–9723 (2019).
Pellerin, B. A. et al. Mississippi River nitrate loads from high frequency sensor measurements and regression-based load estimation. Environ. Sci. Technol. 48, 12612–12619 (2014).
DeCicco, L. A. et al. WRTDSplus: Extensions to the WRTDS Method (USGS, 2024); https://doi.org/10.5066/P14PE5AN.
Green, C. T. et al. Projecting stream water quality using Weighted Regression on Time, Discharge, and Season (WRTDS): An example with drought conditions in the Delaware River Basin. Sci. Total Environ. 999, 180286 (2025).
Vecchia, A. V. et al. Modeling variability and trends in pesticide concentrations in streams. J. Am. Water Resour. Assoc. 44, 1308–1324 (2008).
Fang, K. et al. Modeling continental US stream water quality using long-short term memory and weighted regressions on time, discharge, and season. Front. Water 6, 1456647 (2024).
Acknowledgements
The research of the authors is supported by funding from the US Environmental Protection Agency and the US Geological Survey. The authors thank the broader community of researchers who have applied, tested and advanced WRTDS over the past 15 years. Any use of trade, firm, or product names is for descriptive purposes only and does not imply endorsement by the US Government. This is UMCES contribution number 6481.
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EGRET webpage: https://rconnect.usgs.gov/EGRET/
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Zhang, Q., Hirsch, R.M., DeCicco, L.A. et al. Advancing an adaptable and practical framework to address water quality challenges in a changing world. Nat Rev Earth Environ 7, 1–3 (2026). https://doi.org/10.1038/s43017-025-00753-z
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DOI: https://doi.org/10.1038/s43017-025-00753-z