Flood frequency analysis with the GEV distribution for r-annual events

Abstract

Floods are the maximum annual flows of a river and their frequency analysis are statistical techniques that allow estimating values associated with low probabilities of being exceeded. Such predictions allow the hydrological design and review of hydraulic works. The fundamental stage of frequency analysis is the selection and fit, to the available data or sample, of a probability distribution function to make predictions. The generalized extreme value (GEV) distribution has theoretical bases that make it a probabilistic model suitable for floods, maximum sea levels, extreme wind speeds, etc. Due to its genesis, the GEV processes one data per year, the maximum. This disadvantage has been overcome with the method of the r annual maximum events. Such procedure is described and applied to the adjustment of the GEV function, through the maximum likelihood method, using the Complex algorithm of multiple restricted variables, for numerical maximization. Five records of floods with five events per year were integrated from hydrometric stations of the Hydrological Region No. 10 (Sinaloa), Mexico. Also, two records of maximum sea levels with r = 5 were processed, taken from specialized literature; one of them is non-stationary since it shows a trend. Results were analyzed and the predictions of the GEV adjustment with r annual events, were compared against those of the classical methods of moments L and LH. Finally, conclusions are formulated, which highlight the convenience of the described method and point out the advantages of using the Complex algorithm as a numerical technique; due to the above, the systematic application of the described procedure is recommended.