Probability Distribution of Low Streamflow Series in the United States
This article has a reply.
VIEW THE REPLYPublication: Journal of Hydrologic Engineering
Volume 7, Issue 2
Abstract
Estimates of low streamflow statistics are required for a variety of water resource applications. At gauged river sites, the estimation of low streamflow statistics requires estimation of annual n-day minimum streamflows, selection of a probability distribution to describe annual minimums, and estimation of the distribution’s parameters. Using L-moment diagrams, the ability of various probability distributions to describe low streamflow series was examined at 1,505 gauged river sites in the United States. A weighted distance statistic was developed to compare the goodness-of-fit of different probability distributions for describing low streamflow series. Compared to perennial streamflow sites, a shift of L-moments ratios was observed at intermittent river sites where discharge is sometimes reported as zero. An analytical experiment compared the observed shifts in L-moment ratios at intermittent sites with theoretical L-moment ratio shifts for a number of real- and log-spaced probability distributions. Results of these experiments indicate that Pearson Type III and the 3-parameter lognormal distributions should be the recommended distributions for describing low streamflow statistics in the United States at intermittent and nonintermittent (perennial) sites, respectively.
Get full access to this article
View all available purchase options and get full access to this article.
References
Barnes, C. R. (1986). “Methods of estimating low-flow statistics for ungaged streams in the lower Hudson River Basin, NY.” U.S. Geological Survey Water Resources Investigations Rep. 85-4070, Washington, D.C.
Caruso, B. S.(2000). “Evaluation of low-flow frequency analysis methods,” J. Hydrol., 39(1), 19–47.
Chow, K. C. A., and Watt, W. E. (1994). “Practical use of L-moments.” Stochastic and statistical methods in hydrology and environmental engineering, Vol. 1, K. W. Hipel, ed., Kluwer Boston, 55–69.
Chowdhury, J. U., Stedinger, J. R., and Lu, L. H.(1991). “Goodness-of-fit tests for regional generalized extreme value flood distributions,” Water Resour. Res., 27(7), 1765–1176.
Clausen, B., and Pearson, C. P.(1995). “Regional frequency-analysis of annual maximum streamflow drought,” J. Hydrol., 173(1–4), 111–130.
Cleveland, W. S.(1979). “Robust locally weighted regression and smoothing scatterplots,” J. Am. Stat. Assoc., 74, 829–836.
Condie, R., and Nix, G. A. (1975). “Modeling of low flow frequency distributions and parameter estimation.” Int. Water Resource Symposium, Water for Arid Lands, Teheran, Iran.
Delluer, J. W., Rao, A. R., and Bell, J. M. (1988). “Criteria for the determination of minimum streamflows.” Tech. Rep. CE-HSE-88-6, School of Civil Engineering., Purdue Univ., West Lafayette, Ind.
Durrans, S. R., and Tomic, S.(1996). “Regionalization of low-flow frequency estimates: An Alabama case study,” Water Resour. Bull., 32(1), 23–37.
Durrans, S. R., Ouarda, T. B. M. J., Rasmussen, P. F., and Bobée, B.(1999). “Treatment of zeroes in tail modeling of low flows,” J. Hydrologic Eng., 4(1), 19–27.
Fill, H., and Stedinger, J. R.(1995). “Homogeneity tests based upon Gumbel distribution and a critical appraisal of Dalrymple’s test,” J. Hydrol., 166, 81–105.
Gottschalk, L., Tallaksen, L. M., and Perzyna, G.(1997). “Derivation of low flow distribution functions using recession curves,” J. Hydrol., 194(1–4), 239–262.
Haan, C. T. (1977). Statistical methods in hydrology, Iowa State Univ. Press, Ames, Iowa.
Hosking, J. R. M.(1990). “L-moments: Analysis and estimation of distributions using linear combinations or order statistics,” J. R. Stat. Soc. Ser. B. Methodol., 52, 105–124.
Hosking, J. R. M. (1991). “Approximations for use in constructing L-moment ratio diagrams.” Res. Rep. RC 16635 (#73810), IBM Research Div., T. J. Watson Research Center, Yorktown Heights, N.Y.
Hosking, J. R. M.(1992). “Moment or L moments? An example comparing two measures of distributional shape,” Am. Stat., 46(3), 186–189.
Hosking, J. R. M. (1995). “The use of L-moments in the analysis of censored data.” Recent advances in life-testing and reliability, N. Balakrishnan, ed., CRC, Boca Raton, Fla., 546–560.
Hosking, J. R. M., and Wallis, J. R.(1993). “Some statistics useful in regional frequency Analysis,” Water Resour. Res., 29(3), 271–281.
Hosking, J. R. M., and Wallis, J. R.(1995). “Comparison of unbiased and plotting position estimators of L-moments,” Water Resour. Res., 31(8), 2019–2025.
Hosking, J. R. M., and Wallis, J. R. (1997). Regional frequency analysis an approach based on L-moments, Cambridge Univ. Press, Cambridge, U.K.
Jennings, M. E., and Benson, M. A.(1969). “Frequency curves for annual flood series with some zero events or incomplete data,” Water Resour. Res., 5(1), 276–280.
Joseph, E. S.(1970). “Probability distribution of annual droughts,” J. Irrig. Drain., 96(4), 461–474.
Kroll, C. N., and Stedinger, J. R.(1996). “Estimation of distributional moments and quantiles for censored data,” Water Resour. Res., 32(4), 1,005–1,012.
Landwehr, J. M., Matalas, N. C., and Wallis, J. R.(1979). “Probability weighted moments compared with some traditional techniques in estimating Gumbel parameters and quantiles,” Water Resour. Res., 15(5), 1,055–1,064.
Matalas, N. C. (1963). “Probability distribution of low flows.” Professional Paper 434-A, U.S. Geological Survey, Washington, D.C.
Önöz, B., and Bayazit, M.(1999). “GEV-PWM model for distribution of minimum flows,” J. Hydrologic Eng., 4(3), 289–292.
Pearson, C. P.(1995). “Regional frequency analysis of low flows in New Zealand rivers,” J. Hydrol., 30(2), 53–64.
Riggs, H. C. (1968a). “Chapter A2: Frequency curves.” U.S. Geological Survey Techniques of Water Resource Investigations, Book 4, Washington, D.C.
Riggs, H. C. (1968b). “Chapter B3: Regional analyses of streamflow characteristics.” U.S. Geological Survey Techniques of Water Resource Investigations, Book 4, Washington, D.C.
Riggs, H. C. (1972). “Chapter B1: Low-flow investigations.” U.S. Geological Survey Techniques of Water Resource Investigations, Book 4, Washington, D.C.
Riggs, H. C.(1980). “Characteristics of low flows,” J. Hydraul. Eng., 106(5), 717–731.
Rumenick, R. P., and Grubbs, J. W. (1996). “Methods for estimating low-flow characteristics for ungaged streams in selected areas, northern Florida.” U.S. Geological Survey Water Resources Investigation Rep. 96–4,124, Washington, D.C.
Slack, J. R., and Landwehr, J. M. (1993). “Hydro-climatic data network (HCDN): A U.S. Geological Survey streamflow data set for the United States for the study of climate variations, 1874–1988.” U.S. Geological Survey Water Resources Investigation Rep., 93–4,076, Washington, D.C.
Stedinger, J. R., Vogel, R. M., and Foufoula-Georgiou, E. (1993). “Chapter 18: Frequency analysis of extreme events.” Handbook of hydrology, D. R. Maidment, ed., McGraw-Hill, New York.
Task Committee on Low-Flow Evaluation, Methods, and Needs of the Committee on Surface-Water Hydrology of the Hydraulics Division. (1980). “Characteristics of low flows,” J. Hydr. Div. Am. Soc. Civil Eng., 106(5), 717–731.
Tasker, G. D.(1987). “A comparison of methods for estimating low flow characteristics of streams,” Water Resour. Bull., 23(6), 1,077–1,083.
Tasker, G. D. (1989). “Regionalization of low flow characteristics using logistic and GLS regression.” New directions for surface water modeling, M. L. Kavvas, ed., IAHS Publication No. 181, 323–331.
Vogel, R. M., and Fennessey, N. M.(1993). “L-Moment diagrams should replace product moment diagrams,” Water Resour. Res., 29(6), 1,745–1,752.
Vogel, R. M., and Kroll, C. N.(1989). “Low-flow frequency analysis using probability-plot correlation coefficients,” J. Water Resour. Plan. Manage., 115(3), 338–357.
Vogel, R. M., and Wilson, I.(1996). “Probability distribution of annual maximum, mean, and minimum streamflows in the United States,” J. Hydrologic Eng., 1(2), 69–76.
Wandle, S. W., and Randall, A. D. (1993). “Effects of surfacial geology, lakes and swamps, and annual water availability on low flows of streams in central New England, and their use in low-flow estimation.” U.S. Geological Survey Water Resources Investigation Report 93–4092, Washington, D.C.
Wang, Q. J.(1990a). “Estimation of the GEV distribution from censored samples by method of partial probability weighted moments,” J. Hydrol., 120, 103–114.
Wang, Q. J.(1990b). “Unbiased estimation of probability weighted moment and partial probability weighted moments for systematic and historical flood information and their application to estimating the GEV distribution,” J. Hydrol., 120, 115–124.
Wang, Q. J.(1996). “Using partial probability weighted moments to fit the extreme value distributions to censored samples,” Water Resour. Res., 32(6), 1,767–1,771.
Werick, B. (2000). National Drought Atlas, U.S. Army Corps of Engineers, Institute for Water Resources, 〈http://www.wrsc.usace.army.mil/iwrnew/Atlas/Atlasintro.htm〉.
Zafirakou_Koulouris, A., Vogel, R. M., Craig, S. M., and Havermeier, J.(1998). “L-moment diagrams for censored observations,” Water Resour. Res., 34(5), 1,241–1,249.
Information & Authors
Information
Published In
Journal of Hydrologic Engineering
Volume 7 • Issue 2 • March 2002
Pages: 137 - 146
Copyright
Copyright © 2002 American Society of Civil Engineers.
History
Received: Mar 9, 2001
Accepted: Aug 31, 2001
Published online: Mar 1, 2002
Published in print: Mar 2002
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.