Trivariate Flood Frequency Analysis Using the Gumbel–Hougaard Copula
Publication: Journal of Hydrologic Engineering
Volume 12, Issue 4
Abstract
Using the Gumbel–Hougaard copula, trivariate distributions of flood peak, volume, and duration were derived, and then conditional return periods were obtained. The derived distributions were tested using flood data from the Amite River Basin in Louisiana. A major advantage of the copula method is that marginal distributions of individual variables can be of any form and the variables can be correlated.
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References
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.
De Michele, C., Salvadori, G., Canossi, M., Petaccia, A., and Rosso, R. (2005). “Bivariate statistical approach to check adequacy of dam spillway.” J. Hydrol. Eng., 10(1), 50–57.
Favre, A.-C., Adlouni, S. E., Perreault, L., Thiéonge, N., and Bobée, B. (2004). “Multivariate hydrological frequency analysis using copulas.” Water Resour. Res., 40, W01101.
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. (1983). “Statistical inference procedures for bivariate Archimedean copulas.” J. Am. Stat. Assoc., 88, 1034–1043.
Genest, C., and Rivest, L. (1995). “A semiparametric estimation procedure of dependence parameters in multivariate families of distributions.” Biometrika, 82(3), 543–552.
Goel, N. K., Seth, S. M., and Chandra, S. (1998). “Multivariate modeling of flood flows.” J. Hydraul. Eng., 124(2), 146–155.
Griamaldi, S., Serinaldi, F., Napolitano, F., and Ubertini, L. (2005). “A 3-copula function application for design hyetograph analysis.” IAHS Publication, 293, 1–9.
Gringorten, I. I. (1963). “A plotting rule of extreme probability paper.” J. Geophys. Res., 68(3), 813–814.
Nelsen, R. B. (1999). An introduction to copulas, Springer, New York.
Salvatori, G., and De Michele, C. (2004). “Frequency analysis via copulas: Theoretical aspects and applications to hydrological events.” Water Resour. Res., 40(12), W12511.
Sklar, A. (1959). “Fonctions de repartition á n dimensions et leurs marges.” Publ. Inst. Stat. Univ. Paris, 8, 229–231.
Yevjevich, V. (1972). Probability and statistics in hydrology, Water Resources Publications, Fort Collins, Colo.
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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Information
Published In
Journal of Hydrologic Engineering
Volume 12 • Issue 4 • July 2007
Pages: 431 - 439
Copyright
© 2007 ASCE.
History
Received: Aug 29, 2006
Accepted: Aug 29, 2006
Published online: Jul 1, 2007
Published in print: Jul 2007
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