Physics of flood frequency analysis. II. Convective diffusion model versus lognormal model

• Autorzy: Strupczewski W. , Singh V. , Węglarczyk S. , Mitosek H.
• Języki publikacji: EN

Abstrakty

EN

The similarity between the convective diffusion (CD) model and the lognormal (LN) distribution is shown by comparison of their moment estimates. Both models are tested using annual peak discharges observed at 39 gauging-sections of Polish rivers. The average value of the ration of the coefficient of skew ness to the coefficient of variation equals about 2.52, a value closer to the ration of the CD model than to the gamma or the lognormal model. The likelihood ratio indicates the preference of the CD over the LN model for 27 out of 39 cases. Applying the maximum likelihood (ML) method, one should take into account the consequence of the wrong distributional assumption on the estimate of moments. In the case of CD, the ML-estimate of the means is unbiased for any true distribution, which is not the case with the LN model, moreover the ML-estimate of the two fist moments of CD remains asymptotically unbiased if LN is true, while there is small bias in the opposite case. To check the objectivity of our inferences from empirical findings, a simulation experiment was carried out, which comprised generated CD- and LN- distributed samples and both the moment and likelihood criteria for the distribution choice. Its results clearly show that normal hydrological sample sizes are far too small for selecting the true distribution.

Słowa kluczowe

EN

flood frequency; probability distribution; convective diffusion model lognormal model; parameter estimation; model selection; asymptotic bias; Monte Carlo simulation; statistical tests; time series; Poland

• Wydawca: Instytut Geofizyki PAN
• Czasopismo: Acta Geophysica Polonica
• Rocznik: 2003
• Tom: Vol. 51, nr 1
• Strony: 85--106
• Opis fizyczny: Bibliogr. 23 poz.

Twórcy

autor

Strupczewski W.

• Water Resources Department Insitute of Geophysics, Polish Academy of Sciences, ul. Księcia Janusza 64, 01-452 Warszawa

autor

Singh V.

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

autor

Węglarczyk S.

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

autor

Mitosek H.

• Water Resources Department Insitute of Geophysics, Polish Academy of Sciences, ul. Księcia Janusza 64, 01-452 Warszawa

Bibliografia

• 1. Cunnane, C., 1989, Statistical distributions for flood frequency analysis, WMO Operational Report No. 33, WMO-No. 718.
• 2. Fisz, M., 1963, Probability Theory and Mathematical Statistics. Chap. 11, John Wiley and Sons Inc., New York.
• 3. Interagency Advisory Committee on Water Data, 1982, Guidelines for Determining Flood Flow Frequency, Bulletin 17B, U.S. Department of the Interior, U.S. Geological Survey, Office of Water Data Coordination, Reston, Va.
• 4. Johnson, N.L., and S. Kotz, 1970, Distribution in Statistics: Continuous Univariate Distributions l, Houghton-Mifflin, Boston, Mass.
• 5. Katsnelson, J., and S. Kotz, 1957, On the upper limits of some measures of variability, Archiv. F. Meteor., Geophys. U. Bioklimat. (B), 8, 103.
• 6. Kendall, M.G., and A. Stuart, 1969, The advanced theory of Statistics. Vol. 1. Distribution Theory, Charles Griffin & Company Ltd., London, 70 p.
• 7. Kendall, M.G., and A. Stuart, 1973, The advanced theory of Statistics. Vol. 2 Inference and Relationship, pp. 12, 26, 67, Charles Griffin & Company Ltd., London.
• 8. Kirby, W., 1974, Algebraic boundness of sample Statistics, Water Resour. Res. 10, 2, 220-222.
• 9. Kuczera, G., 1982, Robust flood frequency models, Water Resour. Res. 18, 2, 315-324.
• 10. Landwehr, J.M., N.C. Matalas and J.R. Wallis, 1980, Quantile estimation with more or less flood like distributions, Water Resour. Res. 16, 1, 547-555.
• 11. Lombard, F., 1988, Detecting change points by Fourier analysis, Technometrics 30, 3,305-310.
• 12. Mann, H.B., 1945, Nonparametric tests against trend, Econometrics 13, 245-259.
• 13. Mitosek, H.T., and W.G. Strupczewski, 1996, Can series of maximal annual flow discharges be treated as realizations of stationary process? Acta Geophys. Pol. 44, 61-77.
• 14. Pettitt, A.N., 1979, A nonparametric approach to the change-point problem, Appl. Statistics 28,2,126-135.
• 15. Pilgrim, D.H. (ed.), 1987, Australian Rainfall and Run off. A Guide to Flood Estimation. Vol. 1, The Institute of Engineers, Barton ACT, Australia (revised edition).
• 16. Rao, A.R., and K.H. Hamed, 2000, Flood Frequency Analysis, CRC Press, Boca Raton, Florida.
• 17. Robson, A., and D. Reed, 1999, Flood Estimation Handbook, V.3. Statistical procedures for flood frequency estimation, Institute of Hydrology, Crowmarsh Gifford, Wallingford.
• 18. Strupczewski, W.G., V.P. Singh and S. Węglarczyk, 2002a, Asymptotic bias of estimation methods caused by the assumption of false probability distribution, J. Hydrol. 258, 1-4, 122-148.
• 19. Strupczewski, W.G., V.P. Singh and S. Węglarczyk, 2002b, Physics of flood frequency analysis. Part I. Linear convective diffusion wave model, Acta Geophys. Pol. 50,433-455.
• 20. Wallis, J.R., N.C. Matalas and J.R. Slack, 1974, Just a moment, Water Resour. Res. 10, 211-219.
• 21. Węglarczyk, S., and W.G. Strupczewski, 2001, Relative asymptotic bias of mean, variance and quantiles caused by the assumption of false probability distribution, 77 p., Institute Geophysics, Pol. Acad. Sc. (unpublished memorandum).
• 22. Węglarczyk, S., W.G. Strupczewski and V.P. Singh, 2002, A note on the applicability of log-Gumbel and log-logistic probability distributions in hydrological analyses. Port, Assumed pdf, Hydrol. Sci. J. 47, 1, 123-137.
• 23. WMO, 1988, Analyzing long time series of hydrological data with respect to climate variability. Project description, WCAP Report No. 3. WMO/TD - No. 224.