USGS Enhances Statistical Techniques to Assess Water-Quality Trends

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The USGS has completed more enhancements to our innovative technique to assess water-quality trends. The WRTDS (Weighted Regressions on Time Discharge and Season) method was first published in 2010 as an exploratory data analysis technique for understanding trends in surface water. Subsequently, we published the EGRET (Exploration and Graphics for RivEr Trends) software which implements the WRTDS method as well as other exploratory methods for understanding trends in streamflow and water quality. The method has seen a good deal of use to date (including many projects inside and outside of the USGS) but one thing that many users have wanted was a way to describe the uncertainty of the results.


The USGS has enhanced WRTDS and the EGRET software to document uncertainty and deliver a suite of techniques that provides for statistical testing of trends in both flow-normalized concentration and flow-normalized flux for any two points in time. Users can now graphically portray the long term trend and the confidence intervals around that estimated trend. The enhanced technique will be used to determine loads and trends for sites in the Chesapeake Bay watershed.

A team led by Robert Hirsch, USGS research hydrologist, has published the paper “A bootstrap method for estimating uncertainty of water quality trends" by Robert Hirsch, Stacey Archfield, and Laura DeCicco. The paper is available on line at: and will appear in print in a few months in the journal Environmental Modelling and Software. In conjunction with the publication of the paper the associated software is now available from CRAN (Comprehensive R Archive Network). The name of the software is EGRETci (because it is used in conjunction with the existing EGRET package and the "ci" stands for confidence intervals). The suite of supporting water-quality packages are:

  • dataRetrieval: which can retrieve USGS and EPA water quality and hydrologic data.
  • EGRET: which retrieves daily discharge data and water quality sample data and performs a wide range of exploratory analyses of these data sets particularly aimed at describing long term trends in streamflow and in water quality. The WRTDS method is a significant component of the EGRET software.
  • EGRETci: which provides a variety of uncertainty analyses associated with the WRTDS method as implemented in EGRET.

USGS has a Web page that describes these packages at Questions about the software or the underlying methods can be addressed to us at


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