Bivariate flood frequency analysis of dates of occurrence and maximum flow through Copula functions
DOI:
https://doi.org/10.24850/j-tyca-2024-04-03Keywords:
Dates of occurrence, von Mises distribution, Copula functions, Kendall's tau ratio, joint empirical probabilities, dependency on the extreme right, joint and conditional return periodsAbstract
In the center and south of the Mexican Republic, each year the hurricanes of the Caribbean Sea and the Pacific Ocean cause floods that lead to a wet season and that generally increase in magnitude and danger as the cyclone season progresses. Both conditions allow bivariate frequency analysis of their dates of occurrence and their maximum flows (Qm). In this study, the bivariate distribution was formed based on the Gumbel-Hougaard Copula function, which satisfies the observed dependency condition () and which combines the von Mises distributions as marginal distributions for the dates of occurrence in the year and for the Qm a suitable probabilistic function. The exposed theory is applied to the annual floods recorded at the Guamúchil gauging station of Hydrological Region No. 10 (Sinaloa), Mexico, in the period from 1940 to 1971. The von Mises distribution is fitted via numerical optimization with the de Rosenbrock algorithm and the ideal distribution of the Qm turned out to be the Kappa. The graph of joint return periods of the AND type of 50, 100 and 500 years was formed. In addition, conditional joint return periods of occurrence dates were estimated given that the Qm has the cited return periods. This allows estimates of the probability of exceedance of Qm in defined periods. The conclusions highlight the simplicity of these bivariate frequency analyses, by means of the Copula functions, and the practical importance of their predictions, according to the dates of occurrence.
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