An Evaluation of Methods for Computing Annual Water-Quality Loads

Scientific Investigations Report 2019-5084
By: , and 



The U.S. Geological Survey publishes information on the mass, or load, of water-quality constituents transported through rivers and streams sampled as part of the operation of the National Water Quality Network (NWQN). This study evaluates methods for computing annual water-quality loads, specifically with respect to procedures currently (2019) used at sites in the NWQN. Near-daily datasets of chloride, total nitrogen, nitrate plus nitrite, total phosphorus, and suspended sediment were subset to determine the accuracy of various load-estimation methods, including linear interpolation, ratio estimators, and linear and weighted-regression methods. Water-quality loads are computed under different sampling strategies and at multiple sampling sites to provide a more complete evaluation of load-estimation methods.

Estimation methods were less accurate when computing loads at annual rather than decadal time steps. Depending on the water-quality constituent, annual loads were within comparable accuracy thresholds 21 to 64 percent of the time relative to decadal loads. The accuracy of annual load estimates varied among water-quality constituents, sampling strategies, sampling sites, and estimation methods. Methods were most accurate when estimating chloride and decreased in accuracy when estimating total nitrogen, nitrate plus nitrite, total phosphorus, and suspended-sediment loads. Estimation methods were most likely to compute accurate annual loads when samples were collected frequently (26 samples per year) and when sampling strategies targeted high-flow conditions. For a given water-quality constituent, estimation accuracy differed substantially among sampling sites; estimates were more likely to be accurate at large rivers with less variability in concentration and (or) discharge conditions and were less likely to be accurate at smaller stream sites with more variable streamflow and (or) water-quality concentrations.

The Weighted Regressions on Time, Discharge, and Season method with Kalman filtering (WRTDS_K) generally produced the most accurate annual load estimates among sampling sites and water-quality constituents. Although WRTDS_K was the most accurate generally, every estimation method evaluated had the potential to produce accurate (and inaccurate) load estimates depending on the site, constituent, and water year. Linear interpolation and ratio estimators that used samples exclusively from the year being estimated were among the best performing methods for total nitrogen and nitrate plus nitrite loads but were among the least accurate when estimating annual total phosphorus and suspended-sediment loads. Ratio estimation that considered samples from previous years and stratified based on streamflow conditions produced among the most accurate total phosphorus estimates but was among the least accurate for other constituents. Regression-based methods that assumed linear or quadratic relations among the logarithm of water-quality concentrations and streamflow conditions were among the least accurate methods generally, whereas regression-based methods that considered cubic relations among the logarithm of concentration and streamflow and the Weighted Regressions on Time, Discharge, and Season (WRTDS) method were typically more accurate. Methods that adjusted daily estimates computed from regression or weighted-regression methods based on departures from sampled values, such as WRTDS_K and the composite method, improved estimate accuracy for most sites and constituents, but especially for chloride, total nitrogen, nitrate plus nitrite, and suspended-sediment estimates.

Investigation of the underlying causes of estimation method bias indicated that sites and years with more variability in concentration and loading conditions, higher slopes in the relation of the logarithm of concentration and discharge, and sampling plans that underrepresented high-flow conditions generally led to less accurate load estimates. Finally, because all methods indicated the capacity to produce biased load estimates, additional work is needed to identify the capacity of new technologies, such as continuous water-quality sensors, to improve the accuracy of annual or shorter term load estimates. Based on findings in this report, the NWQN will continue to publish water-quality loads using LOADEST-based methods that consider multiple transformations of streamflow, as well as season, time, and variables indicative of historical streamflow conditions to maintain consistent methods for stakeholders. However, the NWQN also plans to begin publishing annual load estimates using the WRTDS_K method in 2020 because this method was determined to be the most accurate for a given site, constituent, and water year.

Suggested Citation

Lee, C.J., Hirsch, R.M., and Crawford, C.G., 2019, An evaluation of methods for computing annual water-quality loads: U.S. Geological Survey Scientific Investigations Report 2019–5084, 59 p.,

ISSN: 2328-0328 (online)

Table of Contents

  • Foreword
  • Abstract
  • Introduction
  • Purpose and Scope
  • Methods
  • Results of Method Performance Evaluations
  • Discussion
  • Summary and Conclusions
  • References Cited
  • Appendix 1. Description of Weighted Regressions on Time, Discharge, and Season Method with Kalman Filtering
  • Appendix 2. Tables Indicating the Percentage of Annual Load Estimates within 10 Percent of Observed Loads among Methods and Sampling Strategies
  • Appendix 3. Plots Showing the Distribution of Errors of Annual Load-Estimation Methods among Sampling Strategies
  • Appendix 4. Plots Showing the Distribution of Errors of Annual Load-Estimation Methods among Sampling Sites
  • Appendix 5. Evaluation of Estimation Method Performance among Sampling Windows
  • Appendix 6. Evaluating Potential Improvements in Method Performance through Graphical Examination of Residuals
  • References Cited
  • Appendix 7. Description of Methods and Results from Regression-Tree Analyses
  • References Cited

Additional publication details

Publication type Report
Publication Subtype USGS Numbered Series
Title An evaluation of methods for computing annual water-quality loads
Series title Scientific Investigations Report
Series number 2019-5084
DOI 10.3133/sir20195084
Year Published 2019
Language English
Publisher U.S. Geological Survey
Publisher location Reston, VA
Contributing office(s) Kansas Water Science Center, National Water Quality Assessment Program, WMA - Observing Systems Division, Upper Midwest Water Science Center
Description Report: x, 59 p.; Appendix Figures 3–7; Data Release
First page 1-84
Online Only (Y/N) Y
Additional Online Files (Y/N) Y
Google Analytic Metrics Metrics page
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