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


B.A. in Geology from Earlham College, 1971

M.S. in Geology from the University of Washington, 1974

Ph.D. from the Johns Hopkins University Department of Geography and Environmental Engineering, 1976.

Professional Studies/Experience

I am a Research Hydrologist Emeritus with the U.S. Geological Survey (USGS) located at the USGS headquarters in Reston, Virginia. I began my USGS career in 1976 and has conducted research on water supply, water quality, pollutant transport, and flood frequency analysis. My work involved significant involvement in teaching statistical methods to USGS hydrologists (an effort that continues to the present), it also involved development of concept for a National Water Quality Assessment (NAWQA) Program and working within the federal government and with stakeholders to launch that effort.  In 1993-1994 I served as Acting Director of the USGS.  From 1994 through 2008, I served as the Chief Hydrologist of the USGS. In this capacity, I was responsible for all USGS water science programs. These programs encompass research and monitoring of the nation’s ground water and surface water resources including issues of water quantity and quality.  In 2008 I returned to a research position and since that time I have focused efforts on describing long-term changes in streamflow and river water quality.  This includes exploring century-scale trends in flooding nationwide.  It also includes the development and applications of new methods for characterizing trends in river water quality in many regions of the US.  I have published applications of these methods to issues including nutrients and salinity in the watersheds of Chesapeake Bay, Lake Erie, Lake Champlain, and the Mississippi River. This research has provided important insights on causes of the observed trends and has also resulted in the development of software (the EGRET R-Package “Exploration and Graphics for RivEr Trends”) to help scientists analyze long-term water quality and quantity records.  I retired from the USGS in 2018 but continue to collaborate with colleagues inside and outside the USGS as a scientist emeritus.


Professional societies/affiliations/committees/editorial boards

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.  I also served for 8 years on the Science and Technical Advisory Committee (STAC) of the Chesapeake Bay Program.

Honors, awards, recognition, elected offices  Presented the Langbein Lecture at the 2017 American Geophysical Union, Fall meeting ( 

Scientific/Oral Presentations, Abstracts (a selected list of publications)

Blum, A.G., Archfield, S.A., Hirsch, R.M., Vogel, R.M., Kiang, J.E. and Dudley, R.W., 2019. Updating estimates of low-streamflow statistics to account for possible trends. Hydrological Sciences Journal, pp.1-11.

Lee, C.J., Hirsch, R.M. and Crawford, C.G., 2019. An evaluation of methods for computing annual water-quality loads (SIR 2019-5084, pp. 1-84). US Geological Survey.

Zhang, Q. and Hirsch, R.M., 2019. River water‐quality concentration and flux estimation can be improved by accounting for serial correlation through an autoregressive model. Water Resources Research.

Dudley, R.W., Hirsch, R.M., Archfield, S.A., Blum, A.G. and Renard, B., 2019. Low streamflow trends at human-impacted and reference basins in the United States. Journal of Hydrology, p.124254.

Fanelli, R.M., Blomquist, J.D. and Hirsch, R.M., 2019. Point sources and agricultural practices control spatial-temporal patterns of orthophosphate in tributaries to Chesapeake Bay. Science of The Total Environment, 652, pp.422-433.

Choquette, A.F., Hirsch, R.M., Murphy, J.C., Johnson, L.T. and Confesor Jr, R.B., 2019. Tracking changes in nutrient delivery to western Lake Erie: Approaches to compensate for variability and trends in streamflow. Journal of Great Lakes Research, 45(1), pp.21-39.

Kleinman, P.J., Fanelli, R.M., Hirsch, R.M., Buda, A.R., Easton, Z.M., Wainger, L.A., Brosch, C., Lowenfish, M., Collick, A.S., Shirmohammadi, A. and Boomer, K., 2019. Phosphorus and the Chesapeake Bay: Lingering issues and emerging concerns for agriculture. Journal of Environmental Quality, 48(5), pp.1191-1203.

Choquette, A.F., Hirsch, R.M., and Murphy, J.C., 2018, Nutrient and streamflow model-input data (1974-2016) and trend results (1987-2016) for selected Lake Erie tributaries: U.S. Geological Survey data release,

Lee, C.J., Hirsch, R.M., Schwarz, G.E., Holtschlag, D.J., Preston, S.D., Crawford, C.G. and Vecchia, A.V., 2016. An evaluation of methods for estimating decadal stream loads. Journal of Hydrology, 542, pp.185-203.

Zhang, Q., Hirsch, R.M. and Ball, W.P., 2016. Long-term changes in sediment and nutrient delivery from Conowingo dam to Chesapeake Bay: effects of reservoir sedimentation. Environmental science & technology, 50(4), pp.1877-1886.

Archfield, S.A., Hirsch, R.M., Viglione, A. and Blöschl, G., 2016. Fragmented patterns of flood change across the United States. Geophysical Research Letters, 43(19).

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.