Prediction of Flood Frequency Factor for Gumbel Distribution Using Regression and GEP Model

Floods are the most common natural disasters that affect societies around the world. One of the major problems in water resources engineering design is the estimation of maximum flood discharges. These estimations are determined to assign hydrological and hydraulic dimensions to bridges, sewers, dam, spillway, protection embankments, weirs, detention ponds and diversion canals. Accurate estimation of flood frequency discharge increases safety of the hydraulic structures. In probability theory and statistics, flood frequency analysis is used to obtain the probability distribution of floods. The distribution models can be summarized the generalized extreme value, Gumbel or extreme value type 1, Log-Normal and the Log Pearson type III distributions. The Gumbel distribution provides the best fit according to the extreme value analysis studies. This study concentrates on prediction of flood frequency factor (K) for the Gumbel distribution using gene expression programming (GEP) and regression model. Some prediction models are presented for determining of flood frequency factor (K). The proposed regression model (Model 4) and GEP model (Model 7) give a fast and practical way of estimating the flood frequency factor. Thus, Gumbel's method has been simplified in such a predictive model that one can obtain the magnitude of a given return period for flood discharges without recourse to looking at a table. The performance of the prediction models was evaluated with an illustrative example for 2, 5, 10, 20, 50, 100, 200, 250, 500 and 1000 years flood.