Application of the bivariate GEV distribution in the joint flood frequency analysis

Abstract

The floods in our country every year cause damage and endanger the reservoirs. Therefore, its hydrological dimensioning is based on the hydrograph of the design flood, and its most straightforward estimation is based on the joint frequency analysis of the annual peak flow and volume. In this study, the bivariate general extreme values distribution (GVEb) was adjusted to the record of the 55 annual floods at the La Cuña hydrometric station on the Río Verde of Hydrological Region No. 12-3, Mexico. This study encompasses the following nine stages: (1) selection and testing of annual records; (2) verification of the randomness of the records; (3) estimation of the joint empirical probabilities; (4) adjustment of the GVEb function through the maximum likelihood method; (5) validation of the GVEb function; (6) ratification of GVE marginal functions; (7) verification of probability constraints; (8) estimation of hybrid univariate design events, and (9) estimation of joint design events and selection of the critical subgroup. In stage 1, a simple test is applied based on the shape parameter of the marginal GVE. Stage 2 is carried out based on the Wald–Wolfowitz Test. In stage 4, the Complex algorithm is used. Stages 5 and 6 use the Kolmogorov-Smirnov Test. In stage 9, the graphs of the joint return period of type AND are used. Finally, conclusions are formulated, which highlight the maximization approach adopted and the advantages of the bivariate joint frequency analysis through the GVEb.