Abstract

CAMPOS-ARANDA, Daniel Francisco. Stages of the joint flood frequencies analysis with the bivariate GEV distribution. Ing. invest. y tecnol. [online]. 2023, vol.24, n.2.  Epub May 19, 2023. ISSN 2594-0732.  https://doi.org/10.22201/fi.25940732e.2023.24.2.011.

The floods that occur in our country every year, cause damages and endanger the hydraulic infrastructure of the reservoirs. Therefore, its safety hydrological dimensioning is based on the hydrograph of the design flood, its simplest estimation is made with the joint frequency analysis of the annual peak flow and volume. In this study, the bivariate General Extreme Values distribution (GEVb) was adjusted to the record of the 52 annual floods of entry to the Venustiano Carranza Dam, in the state of Coahuila, Mexico. This process encompasses eight stages: 1) verification of the randomness of the annual records; 2) estimation of the joint empirical probabilities; 3) adjustment of the GEVb function through the maximum likelihood method; 4) validation of the GEVb function; 5) ratification of GEV marginal functions; 6) verification of probability constraints; 7) estimation of hybrid univariate design events and 8) estimation of joint design events and selection of the critical subgroup. Stage 4 is the most important, due to the contrast between theoretical and empirical joint probabilities; the first ones estimated with the GEVb and the second ones obtained in the two-dimensional plane. Stage 1 is carried out based on the Wald-Wolfowitz Test. In stage 3 the Complex algorithm is used. Stages 4 and 5 use the Kolmogorov-Smirnov Test. In stage 8, the graphs of the joint return period of type AND are used. Finally, Conclusions are formulated, which highlight the advantages of applying the GEVb.

Keywords : GEVb distribution; conditional distributions; joint empirical probabilities; Complex algorithm; GEVb validation; joint return periods; critical events.

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