Bivariate Flood Frequency Analysis Using the Copula Method
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VIEW THE REPLYPublication: Journal of Hydrologic Engineering
Volume 11, Issue 2
Abstract
Using the copula method, bivariate distributions of flood peak and volume, and flood volume and duration were derived. A major advantage of this method is that marginal distributions of individual variables (i.e., flood peak, volume, and duration) can be of any form and the variables can be correlated. The copula method was applied to obtain the conditional return periods that are needed for hydrologic design. The derived distributions were tested using flood data from Amite River at Denham Springs, La., and the Ashuapmushuan River at Saguenay, Quebec, Canada. The derived distributions were also compared with the Gumbel mixed and the bivariate Box–Cox transformed normal distributions. The copula-based distributions were found to be in better agreement with plotting position-based frequency estimates than were other distributions.
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References
Adamowski, K. (1985). “Nonparametric kernel estimation of flood frequencies.” Water Resour. Res., 21(11), 1585–1590.
Akaike, H. (1974). “A new look at the statistical model identification.” IEEE Trans. Autom. Control, AC-19(6), 716–722.
Ashkar, F., and Rousselle, J. (1982). “A multivariate statistical analysis of flood magnitude, duration and volume.” Statistical analysis of rainfall and runoff, V. P. Singh, ed., Water Resource publication, Fort Collins, Colo., 659–669.
Correia, F. N. (1987). “Multivariate partial duration series in flood risk analysis.” Hydrologic frequency modeling, V. P. Singh, ed., Reidel, Dordrecht, The Netherlands, 541–554.
Cunnane, C. (1978). “Unbiased plotting positions—A review.” J. Hydrol., 37(3), 205–222.
Cunnane, C. (1987). “Review of statistical models for flood frequency estiamtion.” Hydrologic frequency modeling, V. P. Singh, ed., Reidel, Dordrecht, The Netherlands, 49–95.
Genest, C., and MacKay, L. (1986). “The joy of copulas: bivariate distributions with uniform marginals.” Am. Stat., 40, 280–283.
Genest, C., and Rivest, L. (1993). “Statistical inference procedures for bivariate Archimedean copulas.” J. Am. Stat. Assoc., 88, 1034–1043.
Goel, N. K., Seth, S. M., and Chandra, S. (1998). “Multivariate modeling of flood flows.” J. Hydraul. Eng., 124(2), 146–155.
Gringorten, I. I. (1963). “A plotting rule of extreme probability paper.” J. Geophys. Res., 68(3), 813–814.
Gumbel, E. J., and Mustafi, C. K. (1967). “Some analytical properties of bivariate extreme distributions.” J. Am. Stat. Assoc., 62, 569–588.
Kite, G. W. (1978). Frequency and risk analysis in hydrology, Water resource publications, Fort Collins, Colo.
Krstanovic, P. F., and Singh, V. P. (1987). “A multivariate stochastic flood analysis using entropy.” Hydrologic frequency modeling, V. P. Singh, ed., Reidel, Dordrecht, The Netherlands, 515–539.
Nelsen, R. B. (1999). An introduction to copulas, Springer, New York.
Rao, A. R., and Hamed, K. H. (2000). Flood frequency analysis, CRC, Boca Raton, Fla.
Sackl, B., and Bergmann, H. (1987). “A bivariate flood model and its application.” Hydrologic frequency modeling, V. P. Singh, ed., Dreidel, Dordrecht, The Netherlands, 571–582.
Singh, K., and Singh, V. P. (1991). “Derivation of bivariate probability density functions with exponential marginals.” Stochastic Hydrol. Hydr., 5, 55–68.
Sklar, A. (1959). “Fonctions de repartition à n dimensions et leurs marges.” Publ. Inst. Stat. Univ. Paris, 8, 229–231.
U.S. Water Resources Council. (1981). “Guidelines for determining flood flow frequency.” Bulletin 17B (revised), Hydrology Committee, Washington, D.C.
Yue, S. (2001a). “A bivariate extreme value distribution applied to flood frequency analysis.” Nord. Hydrol., 32(1), 49–64.
Yue, S. (2001b). “The bivariate lognormal distribution to model a multivariate flood episode.” Hydrolog. Process., 14, 2575–2588.
Yue, S., Ouarda, T. B. M. J., Bobée, B., Legendre, P., and Bruneau, P. (1999). “The gumbel mixed model for flood frequency analysis.” J. Hydrol., 226, 88–100.
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Published In
Journal of Hydrologic Engineering
Volume 11 • Issue 2 • March 2006
Pages: 150 - 164
Copyright
© 2006 ASCE.
History
Received: May 6, 2003
Accepted: Jul 15, 2005
Published online: Mar 1, 2006
Published in print: Mar 2006
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