Abstract

CAMPOS-ARANDA, Daniel Francisco. Practical application of Copula functions in Bivariate Frequencies Analysis (Q,V) of Annual Floods. Ing. invest. y tecnol. [online]. 2022, vol.23, n.3, e1926.  Epub Nov 07, 2022. ISSN 2594-0732.  https://doi.org/10.22201/fi.25940732e.2022.23.3.023.

The hydrological safety study of reservoirs requires the estimation of the hydrograph of its design flood. The simplest and most approximate way to define such graph is through the bivariate frequency analysis (AFB acronym in Spanish) to obtain the maximum flow (Q) and the volume (V), associated with a certain joint design return period. Copula functions model the dependence between Q and V, at the same time, they allow the construction of the bivariate distribution based on the previously adopted marginal univariate distributions. The use of Copula functions implies two advantages, they separate the effect of the dependence between Q and V from the influence of the marginal distributions, and they are simple to apply. The AFB of the 52 annual Q and V data of the inflow floods to the Venustiano Carranza Dam (Don Martín), from the state of Coahuila, Mexico, was carried out; applying the Copula functions of Clayton, Frank, Gumbel-Hougaard and Plackett. The practical approach adopted uses Copula functions of a single fit parameter and selects the most appropriate one based on the fit errors between bivariate probabilities. Due to their importance, the search for the marginal functions was carried out with the minimum absolute distance, for the six distributions that the diagram of quotients L exposes. The calculation of the graph of the joint return period of type AND is detailed. Finally, conclusions highlight the advantages of using Copula functions in flood AFBs.

Keywords : Copula functions; Kendall's tau quotient; Spearman's rho coefficient; mean standard error; mean absolute error; joint return periods; critical events.

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