Application of bivariate extreme value distribution to flood frequency analysis: a case study of Northwestern Mexico

In Mexico, poverty has forced people to live almost on the water of rivers. This situation along with the occurrence of floods is a serious problem for the local governments. In order to protect their lives and goods, it is very important to account with a mathematical tool that may reduce the uncertainties in computing the design events for different return periods. In this paper, the Logistic model for bivariate extreme value distribution with Weibull-2 and Mixed Weibull marginals is proposed for the case of flood frequency analysis. A procedure to estimate their parameters based on the maximum likelihood method is developed. A region in Northwestern Mexico with 16 gauging stations has been selected to apply the model and regional at-site quantiles were estimated. A significant improvement occurs, measured through the use of a goodness-of-fit test, when parameters are estimated using the bivariate distribution instead of its univariate counterpart. Results suggest that it is very important to consider the Mixed Weibull distribution and its bivariate option when analyzing floods generated by a␣mixture of two populations.