Developing numerical equality to regional intensity–duration–frequency curves using evolutionary algorithms and multi‑gene genetic programming

Abstract

This study aims to carry out regional intensity−duration−frequency (IDF) equality using the relationship with IDF obtained from point frequency analysis. Eleven empirical equations used in the literature for seven climate regions of Turkey were calibrated using particle swarm optimization (PSO) and genetic algorithm (GA) optimization techniques and the obtained results were compared. In addition, in this study, new regional IDF equations were obtained for each region utilizing MultiGene Genetic Programming (MGGP) method. Finally, Kruskal–Wallis (KW) test was applied to the IDF values obtained from the methods and the observed values. As a result of the study, it was observed that the coefcients of 11 empirical equations calibrated with PSO, and GA techniques were diferent from each other. The mean absolute error (MAE), root mean square error (RMSE), mean absolute relative error (MARE), coefcient of determination (R2 ), and Taylor diagram were used to evaluate the performances of PSO, GA, and MGGP techniques. According to the performance criteria, it has been determined that the IDF equations obtained by the MGGP method for the Eastern Anatolia, Aegean, Southeastern Anatolia, and Central Anatolia regions are more successful than the empirical equations calibrated with the PSO and GA method. The empirical IDF equations produced with PSO and the IDF equations acquired with MGGP have similar fndings in the Mediterranean, Black Sea, and Marmara. In addition, the KW test results showed that the data of all models were from the same population.