Robert M Hirsch

My main interest is improving the analysis of hydrologic data, particularly streamflow data and surface water quality data.  My major recent contributions are the EGRET software (Exploration and Graphic for River Trends) and the publication of "Statistical Methods in Water Resources" 2020.  The pdf and the hard copy of this text are available at


I am a research hydrologist.  The focus of my research is the description and understanding of long-term variability and change in surface-water quality and streamflow.  I develop and apply new statistical tools to help characterize these changes to gain the best possible understanding of the nature of the change and its implications from a policy perspective (for example with respect to water quality improvement, ecosystem restoration, flood hazard mitigation, water supply planning, or provision of in-stream flow).  I am the lead developer  of a software package called EGRET (Exploration and Graphics for RivEr Trends) which is now an approved USGS model (written in R - an open source computer language).  It is available from CRAN and is described on our EGRET project web page at  The statistical method (Weighted Regressions on Time, Discharge, and Season - WRTDS) has been used in a number of studies of water quality trends in the US (Chesapeake Bay Watershed, Mississipi River Basin, Lake Champlain Basin, and elsewhere) to describe and better understand changing concentrations and fluxes of nutrients in river systems.  There are also tools in the package and on the web page for analysis of long term trends in daily streamflow.  

My other major recent contribution is the publication of "Statistical Methods in Water Resources" the 2020 edition.  The authors are Dennis Helsel, myself, Karen Ryberg, Stacey Archfield, and Ed Gilroy.  This text book builds on the sucess of the 1992 version authored by Dennis Helsel and myself.  In addition to the book being available free from the USGS as a pdf ( it is also available in a printed version of Statistical Methods in Water Resources as a hard back book at  In addition to the pdf and the printed book, the text has on-line resources which include all of the data sets used as examples in the book, all of the R code used in the analysis of those data, and all of the R code used to produce the graphics in the book.  We hope the book will be used in many university courses and USGS courses on statistical analysis of water data.


Recent Accomplishments


Professional Studies/Experience


Professional societies/affiliations/committees/editorial boards

Honors, awards, recognition, elected offices  Presented the Langbein Lecture at the 2017 American Geophysical Union, Fall meeting (  I have served on three different study committees of the Water Science and Technology Board of the National Academies of Science, Engineering and Medicine.  I am currently serving as a member of the Water Science and Technology Board.

Scientific/Oral Presentations, Abstracts

Hirsch, R.M, and Archfield, S.A., 2015, Flood trends: Not higher but more often, Nature Climate Change, 5, 198-199, doi:10.1038/nclimate2551. [Link]

Hirsch, Robert M., Archfield, Stacey A., and DeCicco, Laura A., 2015, A bootstrap method for estimating uncertainty of water quality trends, Environmental Modelling and Software, 73, 148-166. [Link]

Milly, P. C. D., Julio Betancourt, Malin Falkenmark, Robert M. Hirsch, Zbigniew W. Kundzewicz, Dennis P. Lettenmaier, Ronald J. Stouffer, Michael D. Dettinger, and Valentina Krysanova. "Comment on critiques of “Stationarity is dead: Whither water management?”." Water Resources Research (2015). [Link]

Hirsch, R. M., and De Cicco, L. A., 2014, User Guide to Exploration and Graphic for RivEr Trends (EGRET) and dataRetrieval: R Packages for Hydrologic Data, USGS Techniques and Methods 4-A10, 95p. [Link]

Green, C. T., B. A. Bekins, S. J. Kalkhoff, R. M. Hirsch, L. Liao, and K. K. Barnes, 2014, Decadal surface water quality trends under variable climate, land use, and hydrogeochemical setting in Iowa, USA, Water Resour. Res., 50, 2425–2443, [Link]

Murphy, J. C., Hirsch, R. M., and Sprague, L. A.: 2014, Antecedent flow conditions and nitrate concentrations in the Mississippi River basin, Hydrol. Earth Syst. Sci., 18, 967-979 [Link]

Hirsch, R. M., (2014) Large Biases in Regression-Based Constituent Flux Estimates: Causes and Diagnostic Tools, Journal of the American Water Resources Association. [Link]

Corsi, S.R., De Cicco, L.A., Lutz, M.A., and Hirsch, R.M., 2014, River chloride trends in snow-affected urban watersheds: increasing concentrations outpace urban growth rate and are common among all seasons. Science of the Total Environment, 508, 1 March 2015, 448-497. [Link]

Hirsch, Robert M., and Gary T. Fisher. "Past, present, and future of water data delivery from the US Geological Survey." Journal of Contemporary Water Research & Education 153.1 (2014): 4-15. [Link]

Murphy, J.C., Hirsch, R.M., and Sprague, L.A., 2013, Nitrate in the Mississippi River and its tributaries, 1980–2010—An update: U.S. Geological Survey Scientific Investigations Report 2013–5169, 31 p [Link]

Peterson, T.C., Heim, R.R., Hirsch, R., Kaiser, D.P., Brooks, H., Diffenbaught N.S., Dole, R.M., Giovannettone, J.P., Guirguis, K., Karl, T.R., Katz, R.W., Kunkel, K., Lettenmaier, D., McCabe, G.J., Paciorek, C.J., Ryberg, K.R., Schubert, S., Silva, V.B.S., Stewart, B.C., Vecchia, A.V., Villarini, G., Vose, R.S., Walsh, J., Wehner, M., Wolock, D., Wolter, K., Woodhouse, C.A., and Wuebbles, D., 2013, Monitoring and Understanding Changes in Heat Waves, Cold Waves, Floods and Droughts in the United States: State of Knowledge. Bulletin American Meteorology Society, June 2013, p 821-834 [Link]

Hirsch, R.M., 2012, The Science, Information, and Engineering Needed to Manage Water Availability and Quality in 2050, in "Toward a Sustainable Water Future: Visions for 2050" pp 217-226, editors Grayman, Loucks, and Saito, American Society of Civil Engineers, Reston, VA, 398 pp.

Hirsch, R.M. and Ryberg, K.R., 2012, Has the magnitude of floods across the USA changed with global CO2 levels?, Hydrological Sciences Journal, Vol 57, Issue 1. [Link]

Medalie, L., Hirsch, R.M., and Archfield, S.A., 2012, Use of flow-normalization to evaluate nutrient concentration and flux changes in Lake Champlain tributaries, 1990-2009, Journal of Great Lakes Research, 38, Supplement 1, p. 58-67. [Link]

Rice, K.C. and Hirsch, R.M., 2012, Spatial and Temporal Trends in Runoff at Long-Term Streamgages within and near the Chesapeake Bay Watershed, U.S. Geological Survey, Scientific Investigations Report, 2012-5151, 55 p. [Link]

Hirsch, R.M., 2012, Flux of Nitrogen, Phosphorus, and Suspended Sediment from the Susquehanna River Basin to the Chesapeake Bay during Tropical Storm Lee, September 2011, as an Indicator of the Effects of Reservoir Sedimentation on Water Quality, U.S. Geological Survey, Scientific Investigations Report 2012-5185, 17 p. [Link]

Moyer, D.L., Hirsch, R.M., and Hyer, K.E., 2012, Comparison of two regression-based approaches for determining nutrient and sediment fluxes and trends in the Chesapeake Bay watershed: U.S. Geological Survey Scientific Investigations Report 2012-5244, 118 p. [Link]

Sprague, Lori A.; Hirsch, Robert M.; Aulenbach, Brent T., 2011. Nitrate in the Mississippi River and its tributaries, 1980 to 2008: Are we making progress?. ACS Publications , 8 p. [Link]

Hirsch, R.M., 2011, A Perspective on Nonstationarity and Water Management, Journal of the American Water Resources Association, 47, 436-446. [Download File]

Lins, Harry F.; Hirsch, Robert M.; Kiang, Julie, 2010. Water-the Nation's Fundamental Climate Issue A White Paper on the U.S. Geological Survey Role and Capabilities. U.S. Geological Survey Circular 1347, iv, 9 p. [Link]

Hirsch, R.M, Moyer, D.L., and Archfield, S.A., 2010, Weighted Regressions on Time, Discharge, and Season (WRTDS), with an Application to Chesapeake Bay River Inputs, Journal of the American Water Resources Association p. 857-880. [Link]

Milly, P.C.D., Betancourt, J, Falkenmark, M., Hirsch, R.M., Kundzewicz, Z.W., Lettenmaier, D.P., and Stouffer, R.J., 2008, Stationarity is Dead: Whither Water Management?: Science, vol. 319, p. 573-574. [Download File]

Helsel, Dennis R.; Hirsch, Robert M., 2002. Statistical Methods in Water Resources. Techniques of Water-Resource Investigation 04-A3, 523 p. [Link]

Hirsch, R.M., Alexander, R.B., and Smith, R.A., 1991, Selection of methods for the detection and estimation of trends in water quality: Water Resources Research, v. 27, no. 5, p. 803-813. [Download File]

Hirsch, Robert M.; Alley, William M.; Wilber, William G. , 1988. Concepts for a National Water-Quality Assessment Program. U.S. G.P.O., Circular 1021, vii, 42 p. :ill., maps ;28 cm.

Hirsch, R.M., and Slack, J.R., 1984, A nonparametric trend test for seasonal data with serial dependence: Water Resources Research, v. 20, no. 6, p. 727-732. [Download File]

Hirsch, R.M., Slack, J.R., and Smith, RA., 1982. Techniques of trend analysis for monthly water-quality data: Water Resources Research, v. 18, no. 1, p. 107-121. [Download File]

Hirsch, Robert M.; Slack, James Richard; Smith, Richard A., 1981. Techniques of trend analysis for monthly water-quality data. U.S. Geological Survey, Open-File Report 81-488, 33 p. :ill. ;28 cm.