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

Abstract

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.

A framework for multivariate data-based at-site flood frequency analysis: Essentiality of the conjugal application of parametric and nonparametric approaches

“…In the same study, the researchers concluded that these two distributions provided the same joint return periods and may be useful for representing the joint statistical properties of the two random variables. Yue and Rasmussen (2002) and Sandoval (2007) used the bivariate extreme value distribution to determine the joint probability and return period of the correlated flood variables. Apart from above mentioned, numerous studies were conducted using different bivariate distributions (Fig.…”

Validation of methods to estimate design discharge flow rates for dam spillways with large regulating capacity

“…The general equation for bivariate distributions of extreme values (the logistic model, also named the Gumbel-Hougaard copula, Shiau et al 2006), according to Gumbel (Raynal and Salas 1987, Escalante-Sandoval 1998, Ramírez and Aldama 2000, Escalante-Sandoval and Reyes-Chávez 2002, Escalante-Sandoval 2007, is given by:…”

“…Some procedures consider the peak flow rate and the volume of the flood on a joint basis, applying bivariate distribution functions (Hiemstra and Francis 1979, Yue et al 1999, Domínguez 2000, Ramírez-Aldama 2000, Jiménez 2000, Aldama and Ramírez 2002, Escalante-Sandoval 2007, and the use of copulas for the multivariate flood analysis has been recently applied (Favre et al 2004, Grimaldi and Serinaldi 2006, Shiau et al 2006, Genest et al 2007), but they have some differences in the definition of the most suitable region for the integration of the bivariate distributions, the inherent subjectivity in the estimation of the duration of the floods and, therefore, the volume of the maximum historical floods, the shape of the design flood, etc.…”

Bivariate estimation of extreme wind speeds

“…By considering the G, RW and GEV as marginal distributions of (1) the following bivariate (B) models are proposed to analyze EWS samples: B(G, G), B(G, GEV), B(GEV, G), B(GEV, GEV), B(RW, RW), B(G, RW), and B(RW, G). In fact, the first five models have already been applied in flood frequency analysis [12,14].…”