A new method based on artificial bee colony programming for the regional standardized intensity–duration‒frequency relationship

The aim of this study was to develop new analytical models to defne the regional rainfall intensity−duration−frequency (IDF) relationship for the Inland Anatolia Region, which is determined discretely by the L-Moments method at many values of rainfall durations and frequencies. First, the parameters of each one of nine commonly used empirical equations were calibrated to provide the best possible defnition of the IDF relationship for the Inland Anatolia Region. Next, analytical models best ftted to the IDF relationship of the L-Moments method were generated by the artifcial bee colony programming (ABCP) approach, such that a combination of nine diferent sets were simulated, taking into account three cost functions and three maximum depths. Mean absolute error, root mean square error, mean square error, Nash–Sutclife efciency coefcient, Willmott’s refned index, performance index, and coefcient of determination were computed to assess the accuracies of the empirical equations and of the ABCP models. These criteria revealed that the ABCP models defned the IDF relationship better than the empirical equations over the entire range of frequencies from 2 to 10,000 years. The accuracy of the empirical equations is much worse than the ABCP model, especially for frequencies smaller than 2000 years. Finally, Kruskal−Wallis tests were applied on all of the IDF relationships given by (1) the L-Moments method, (2) the empirical equations, and (3) the ABCP approach. These results indicated that the numerical values of these three models were from the same population.