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Appraisal of regional and index flood quantile estimators

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Abstract

Our results illustrate the performance of at-site and regional GEV/PWM flood quantile estimators in regions with different coefficients of variation, degrees of regional heterogeneity, record lengths, and number of sites. Analytic approximations of bias and variance are employed. For realistic GEV distributions and short records, the index-flood quantile estimator performs better than a 2-parameter GEV/PWM quantile estimator with a regional shape parameter, or a 3-parameter at-site GEV/PWM quantile estimator, in both humid and especially in arid regions, as long as the degree of regional heterogeneity is moderate. As regional heterogeneity or record lengths increases, 2-parameter estimators quickly dominate. Flood frequency models that assign probabilities larger than 2% to negative flows are unrealistic; experiments employing such distributions provide questionable results. This appraisal generally demonstrates the value of regionalizing estimators of the shape of a flood distribution, and sometimes the coefficient of variation.

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References

  • Acreman, M.C.; Sinclair, C.D. 1986: Classification of drainage basins according to their physical characteristics: An application for flood frequency analysis in Scotland, J. of Hydrol. 84, 365–380

    Google Scholar 

  • Arnell, N.W.; Gabriele, S. 1988: The performance of the two-compoent extreme value distribution in regional flood frequency analysis, Water Resour. Res. 24(6), 879–887

    Google Scholar 

  • Benson, M.A. 1962 Evolution of methods for evaluating the occurrence of floods, U.S. Geol. Survey Water Supply Pap. 1580-A, 30 pp

  • Bobeé, B.; Cavadias, G.; Ashkar, F.; Bernier J.; Rasmussen, P. 1993: Toward a systematic approach to comparing distributions used in flood frequency analysis, J. of Hydrol. 142, 121–136

    Google Scholar 

  • Boes, D.C.; Heo, J.H.; Salas, J. D. 1989: Regional flood frequency modeling and estimation, Water Resour. Res. 25(5), 979–990

    Google Scholar 

  • Burn, D.H. 1989: Cluster analysis as applied to regional flood frequency, J. of Water Resour. Plann. and Manage. ASCE 115(5), 567–582

    Google Scholar 

  • Burn, D.H. 1990: Evaluation of regional flood frequency analysis with a region of influence approach, Water Resour. Res. 26(10), pp. 2257–2265

    Google Scholar 

  • Chowdhury, J.U.; Stedinger, J. R.; Lu, L-H. (1991): Goodness-of-fit tests for regional GEV flood distributions, Water Resour. Res. 27(7), 1765–1776

    Google Scholar 

  • Cohn, T.A.; Stedinger, J.R. 1987: Use of historical information in a maximum-likelihood framework, J. of Hydrol. 96(1–4), 215–23

    Google Scholar 

  • Cong, S.; Li, Y.; Vogel, J.L.; Schaake, Jr. J.C. 1993: Identification of the underlying distributional form of precipitation by using regional data, Water Resour. Res. 29(4); 1103–1111

    Google Scholar 

  • Cunnane, C. 1987: Review of Statistical Models for Flood Frequency Estimation, Regional Flood Frequency Analysis, ed. by V.P. Singh, D. Reidel Publishing Company

  • Cunnane, C. 1988: Methods and merits of regional flood frequency analysis, J. of Hydrol. 100, 269–290

    Google Scholar 

  • Dalrymple, T. 1960: Flood frequency analyses, USGS, Water Supply Paper 1543A, 11–51

    Google Scholar 

  • Farquharson, F.A.K.; Green, C.S.; Meigh, J.R.; Sutcliffe, J.V. 1987: Comparison of Flood Frequency Curves for Many Different Regions of the World, Regional Flood Frequency Analysis, ed. by V. P. Singh, D. Reidel Publishing Company, 223–256

  • Fill, H.D. 1994: Improving Flood Quantile Estimates using Regional information, Ph.D. Dissertation, Cornell University, Ithaca, New York

    Google Scholar 

  • Fill, H.D.; Stedinger, J.R. 1994: Homogeneity tests based upon Gumbel distribution and a critical appraisal of Dalrymple's test, to appear J. of Hydrol.

  • Gabriele, S.; Arnell, N. 1991: A hierarchical approach to regional flood frequency analysis, Water Resour. Res. 27(6), 1281–1289

    Google Scholar 

  • Greenwood, J.A.; Landwehr, J.M.; Matalas, N.C.; Wallis, J.R. 1979: Probability weighted moments: Definitions and relation to parameters of several distributions expressed in inverse form, Water Resour. Res. 15(6), 1049–54

    Google Scholar 

  • Greis, N.P.; Wood, E.F. 1981: Regional flood frequency estimation and network design, Water Resour. Res. 17(4), 1167–1177

    Google Scholar 

  • Greis, N.P.; Wood, E.F. 1983: Correction to ‘Regional flood frequency estimation and network design’, Water Resour. Res. 19(2), 589–90

    Google Scholar 

  • Guo, X.; Salas, J.D.; Boes, D.C. 1990: Regional flood frequency analysis, Water Resources Paper, Engineering Research Center, Colorado State University

  • Hebson, C.S.; Cunnane, C. 1987: Assessment of Use of At-site and Regional Flood Data for Flood Frequency Estimation, Hydrologic Frequency Modeling, ed. by V. P. Singh, D. Reidel Publishing Company, 433–448

  • Hosking, J.R.M.; Wallis, J.R. 1993: Some statistics useful in regional frequency analysis, Water Resour. Res. 29(2), 271–281

    Google Scholar 

  • Hosking, J.R.M. 1990: L-moments: Analysis and estimation of distributions using linear combinations of order statistics, J. Royal Stat. Soc. 52(1), 105–124

    Google Scholar 

  • Hosking, J.R.M.; Wallis, J.R. 1988: The effect of intersite dependence on regional flood frequency analysis, Water Resour. Res. 24(4), 588–600

    Google Scholar 

  • Hosking, J.R.M. 1986: The theory of probability weighted moments, Res. Report RC12210, IBM Research, Yorktown Heights

  • Hosking, J.R.M.; Wallis, J.R. 1986a: Paleoflood hydrology and flood frequency analysis, Water Resour. Res. 22(4), 543–550

    Google Scholar 

  • Hosking, J.R.M.; Wallis, J.R. 1986b: The value of historical data in flood frequency analysis, Water Resour. Res. 22(11), 1606–1612

    Google Scholar 

  • Hosking, J.R.M.; Wallis, J.R.; Wood, E.F. 1985a: An appraisal of the regional flood frequency procedure in the UK Flood Studies Report, Hydol. Sci. Jour. 30(1), 85–109

    Google Scholar 

  • Hosking, J.R.M.; Wallis, J.R.; Wood, E.F. 1985b: Estimation of the generalized extreme-value distribution by the method of probability-weighted moments, Technometrics, 27(3), 251–261

    Google Scholar 

  • Jenkinson, A.F. 1955: The frequency distribution of the annual maximum (or minimum) of metcorological elements, Quarterly Journal of the Royal Meteorological Society 81, 158–171

    Google Scholar 

  • Jin, M.; Stedinger, J.R. 1989: Flood frequency analysis with regional and historical information, Water Resour. Res. 25(5), 925–36

    Google Scholar 

  • Kuczera, G. 1982a: Combining site-specific and regional information, an empirical Bayes approach, Water Resour. Res. 18(2), 306–314

    Google Scholar 

  • Kuczera, G. 1982b: Robust flood frequency models, Water Resour. Res. 18(2), 315–324

    Google Scholar 

  • Landwehr, J.M.; Tasker, G.D.; Jarrett, R.D. 1987: Discussion on relative accuracy of log Pearson III procedures by J.R. Wallis and E.F. Wood, J. of Hydraul. Eng. 113(7), 1206–1210

    Google Scholar 

  • Landwehr J.M.; Matalas, N.C.; Wallis, J.R. 1978: Some comparison of flood statistics in real and log space, Water Resour. Res. 14(5), 902–920

    Google Scholar 

  • Landwehr, J.M.: Matalas, N.C.; Wallis, J.R. 1979: Probability weighted moments compared with some traditional techniques in estimating Gumbel parameters and quantiles, Water Resour. Res. 15(5), 1055–1064

    Google Scholar 

  • Lettenmaier, D.P.; Potter, K.W. 1985: Testing flood frequency estimation methods using a regional flood generation model, Water Resour. Res. 21(12), 1903–1914

    Google Scholar 

  • Lettenmaier, D.P.; Wallis, J.R.; Wood, E.F. 1987: Effect of regional heterogeneity on flood frequency estimation, Water Resour. Res. 23(2), 313–323

    Google Scholar 

  • Lu, L.H. 1991: Statistical methods for regional flood frequency investigations, Ph.D. Dissertation, Cornell University, Ithaca, New York

    Google Scholar 

  • Lu, L.H.; Stedinger, J.R. 1992a: Sampling variance of normalized GEV/PWM quantile estimators and a regional homogeneity test, J. of Hydrol. 138, 223–245

    Google Scholar 

  • Lu, L.H.; Stedinger, J.R. 1992b: Variance of two and three-parameter GEV/PWM quantile estimators: Formulae, confidence intervals, and a comparison, J. of Hydrol. 138, 247–267

    Google Scholar 

  • Natural Environmental Research Council (NERC) 1975: Flood Studies Report, Vol. 1–5, NERC, London

    Google Scholar 

  • Phien, H. N. 1987: A review of methods of parameter estimation for the extreme value type-1 distribution, J. of Hydrol. 90, 251–268

    Google Scholar 

  • Pilon, P.J.; Adamowski, K. 1992: The value of regional information to flood frequency analysis using the method of L-moments, Can. J. Civ. Eng. 19(1), 137–147

    Google Scholar 

  • Potter, K. W.; Lettenmaier, D. P. 1990: A comparison of regional flood frequency estimation methods using a resampling method, Water Resour. Res. 26(3), 415–424

    Google Scholar 

  • Potter, K.W. 1987: Research on flood frequency analysis: 1983–86, Reviews of Geophysics, 25(2), 113–118

    Google Scholar 

  • Schaefer, M.G. 1990: Regional analysis of precipitation annual maxima in Washington State, Water Resour. Res. 26(1), 119–131

    Google Scholar 

  • Smith, J.A. 1989: Regional flood frequency analysis using extreme order statistics of the annual peak record, Water Resour. Res. 25(2), 311–317

    Google Scholar 

  • Stedinger, J.R.; Vogel, R. M.; Georgiou, E.F. 1993: Frequency analysis of extreme events, In: Handbook of Hydrology, Chapt. 18, editor in chief D. J. Maidment, McGraw Hill, New York

    Google Scholar 

  • Stedinger, J.R.; Cohn, T. A. 1986: Flood frequency analysis with historical and paleoflood information, Water Resour. Res. 22(5), 785–793

    Google Scholar 

  • Stedinger, J.R.; Potter, K.; Kibler, D.F.; Tasker, G. 1983: Comments on regional flood frequency estimation and network design, Water Resour. Res. 19(5), 1343–1345

    Google Scholar 

  • Stedinger, J.R. 1983: Estimating a regional flood frequency distribution, Water Resour. Res. 19(2), 503–510, 1983.

    Google Scholar 

  • Stedinger, J.R. 1980: Fitting log normal distributions to hydrologic data, Water Resour. Res. 16(3), 481–490

    Google Scholar 

  • Tasker, G.D.; Stedinger, J.R. 1986: Estimating generalized skew with weighted least squares regression, J. of Water Resour. Plan. and Manage. 112(2), 225–237

    Google Scholar 

  • U.S. Water Resources Council Hydrology Committee 1982: Guidelines for Determining Flood Flow Frequency, Bulletin #17B, U.S. Govt. Printing Office, Washington, D.C.

    Google Scholar 

  • Vogel, R.M.; Fennessey, N.M. 1993: L-moment diagrams should replace product moment diagrams, Water Resour. Res. 29(6), 1745–1752

    Google Scholar 

  • Wallis, J.R. 1993: Regional frequency studies using L-moments, In: Concise Encyclopedia of Environmental Systens, editor P. C. Young, Pergamon Press, New York

    Google Scholar 

  • Wallis, J.R. 1988: Catastrophes, computing and containment: Living in our restless habitat, Speculation in Sci. and Tech. 11(4), 295–315

    Google Scholar 

  • Wallis, J.R.; Wood, E.F. 1985: Relative accuracy of log Pearson III procedures, J. of Hydr. Engineering 111(7), 1043–56, (with discussion and closure J. of Hydr. Engineering 113(7), 1205–14, 1987)

    Google Scholar 

  • Wallis, J.R. 1980 Risk and uncertainties in the evaluation of flood events for the design of hydraulic structures in: Pinene e Siccita, editors: E. Guggino, G. Rossi and E. Todini pp. 3–36, Fondazione Politecnica del Mediterraneo, Catania, Italy

    Google Scholar 

  • Wiltshire, S.E. 1986a: Identification of homogeneous regions for flood frequency analysis, J. of Hydrol. 84, 287–302

    Google Scholar 

  • Wiltshire, S.E. 1986b Regional flood frequency analysis I: Homogeneity statistics, Hydrol. Sci. Jour. 31(3), 321–333

    Google Scholar 

  • Zrinji, Z.; Burn, D.H. 1994: Flood frequency analysis for ungauged sites using a region of influence approach, J. of Hydrology 153, 1–21

    Google Scholar 

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  1. School of Civil and Environmental Engineering Hollister Hall, Cornell University, 14853-3501, Ithaca, NY, USA

    J. R. Stedinger & L. -H. Lu

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  1. J. R. Stedinger
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Stedinger, J.R., Lu, L.H. Appraisal of regional and index flood quantile estimators. Stochastic Hydrol Hydraul 9, 49–75 (1995). https://doi.org/10.1007/BF01581758

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