Are parsimonious FF models more reliable than true ones? II. Comparative assessment of the performance of simple models versus the parent distributions

• Autorzy: Kochanek K. , Strupczewski W. G. , Singh V. P. , Węglarczyk S.
• Języki publikacji: EN

Abstrakty

EN

Applying the methodology described in Strupczewski et al. (2005a; this issue), the performance of various parsimonious models combined with three estima-tion methods versus Flood Parent Distributions is comparatively assessed by simulation experiments. Moments (MOM), L-moments (LMM) and maximum likelihood (MLM) are used as alternative methods. Five four-parameter Specific Wakeby Distributions (SWaD) are employed to serve as Flood Parent Distributions and forty Distribution/Estimation (D/E) procedures are included in respect to the estimation of upper quantiles. The relative bias (RB), relative root mean square error (RRMSE) and reliability of procedures are used for the assessment of the relative performance of alternative procedures. Parsimonious two-parameter models generally perform better for hydrological sample sizes than their three-parameter counterparts with respect to RRMSE. How-ever, the best performing procedures differ for various SWaDs. As far as estimation methods are concerned, MOM usually produces the smallest values of both RB and RRMSE of upper quantiles for all competing methods. The second place in rank is occupied by LMM, whereas, MLM produces usually the highest values. Considerable influence of sampling bias on the value of the total bias has been ascertained. The improper choice of a model fitted to SWaD samples causes that the reliability of some three-parameter parsimonious D/E procedures does not always rise with the sample size. Also odd is that True model does not always give one hundred percent reliability for very large samples, as it should. This means that estimating algorithms still require improvements.

Słowa kluczowe

EN

flood frequency analysis; Monte Carlo; probability distribution; estimation methods; quantiles; bias

• Wydawca: Instytut Geofizyki PAN
• Czasopismo: Acta Geophysica Polonica
• Rocznik: 2005
• Tom: Vol. 53, nr 4
• Strony: 437--457
• Opis fizyczny: Bibliogr. 17 poz.

Twórcy

autor

Kochanek K.

• Institute of Geophysics, Polish Academy of Sciences, Księcia Janusza 64, 01-452 Warszawa, Poland

autor

Strupczewski W. G.

• Institute of Geophysics, Polish Academy of Sciences, Księcia Janusza 64, 01-452 Warszawa, Poland

autor

Singh V. P.

• Department of Civil and Environmental Engineering, Louisiana State University Baton Rouge, LA 70803-6405, USA

autor

Węglarczyk S.

• Institute of Water Engineering and Water Management, Cracow University of Technology ul. Warszawska 24, 31-155 Kraków, Poland

Bibliografia

• Cunnane, C, 1989: "Statistical distribution for flood frequency analysis", World Meteorological Organisation, Operational Hydrology, Report No. 33, pp. 73 + Appendices. Flood Estimation Handbook, 1999: Institute of Hydrology, Wallingford, UK.
• Greenenwood, J.A., J.M. Landwehr, N.C. Matalas and J.R. Wallis, 1979: "Probability weighted moments: definition and relation to parameters of several distributions expressible in inverse form", Water Resour. Res. 15 (5), pp. 1049-54.
• Hosking J-R-M., 1991: Fortran routines for use with the method of L-moments, Version 2, Res. Rep. RC 17079, IBM Research Division, York-town Heights, NY 10598.
• Katz RW., M.B. Pariange and P. Naveau, 2002: "Statistics of extremes in hydrology". Adv. in Water Resour. 25, pp. 1287-1304.
• Kite, G.W., 1988: "Frequency and risk analysis in hydrology". Water Research Publications, Littleton, Colorado, pp. 257.
• Klemeš v., 2000a: "Tall tales about tails of hydrological distributions, I", J. Hydrol. Eng. 5 '(3), pp. 227-231.
• Klemeš, v., 2000b: "Tall tales about tails of hydrological distributions, 11", J. Hydrol. Eng. 5 (3), pp. 232-239.
• Kochanek, K., 2002: Manual of accuracy of quantiles and moments estimation (AQME), Soft Package, Internal Report of Inst. Geophys. Pol. Acad. Sc. (in Polish, unpublished).
• Kuczera, G., 1982: "Robust flood frequency models". Water Resour. Res. 18 (2), 315-324.
• Landwehr, J.M., N.C. Matalas and J.R. Wallis, 1980: "Quantile estimation with More or Less Floodlike Distributions", Water Resour. Res. 16 (3), pp. 547-555.
• Perrault, L., B. Bobee and P.F. Rasmussen, 1999a: Halphen distribution system, I: Mathematical and statistical properties, J. Hydrol. Eng.-ASCE, 4 (3), pp. 189-199.
• Perrault, L., B. Bobee and P.F. Rasmussen, 1999b: Halphen distribution system, II: Parameter and quantile estimation, J. Hydrol. Eng.-ASCE, 4 (3), pp. 200-208.
• Rao, A.R., and K.H. Hamed, 2000, Flood frequency analysis, CRC Press LLC. pp. 350.
• Rossi, F., M. Fiorentino and P. Versace, 1984: "Two-component extreme value distribution for flood frequency analysis". Water Resour. Res. 20, pp. 847-56.
• Strupczewski, W.G., K. Kochanek, V.P. Singh and S. Węglarczyk, 2005: Are parsimonious FF models more reliable than true ones? I. Accuracy of Quantiles and Moments Estimation (AQME) - method of assessment (submitted).
• Węglarczyk, S., and W.G. Strupczewski, 2002: Asymptotic relative bias of mean, δ(EfX), variance, δ(varfX) and quantile, δ((XpF) resulting from improper pdf assumption F with respect to estimation method when True pdf is known. Internal Report of Institute of Geophysics, Polish Academy of Sciences (in Polish, unpublished).