Gumbel function parameters estimation for annual maximum precipitation data using the Whale Optimization Algorithm (WOA)

Hydrological variables frequency analysis is crucial for designing and operating hydraulic infrastructure. The Gumbel distribution is commonly used to model extreme events like floods. This study investigates the Whale Optimization Algorithm (WOA) use, a metaheuristic inspired by humpback whale hunting, to estimate the parameters of the Gumbel distribution for annual maximum precipitation data from a climatological station located at Hidalgo State, Mexico. The WOA was compared with moments method. Performance was evaluated using adjustment (EEA) standard error and root mean square error (RMSE). Results demonstrated comparable performance between these two methods. The WOA offers several advantages, including flexibility and adaptability to complex optimization problems. This study highlights the potential of the WOA as a valuable tool for parameter estimation in hydrological frequency analysis, improving the accuracy and reliability of designs for hydraulic structures under conditions of uncertainty and climate change.