Integration of the reptile search algorithm and the adaptive neuro-fuzzy inference system enhances standardized precipitation evapotranspiration index forecasting

A novel metaheuristic algorithm called the reptile search algorithm (RSA) was introduced in conjunction with artificial neural fuzzy inference system (ANFIS) for the estimation of standardized precipitation evapotranspiration index (SPEI). The model was tested in three different climates: arid and super-cold, semi-arid and cold, and semi-arid and moderate climate across Iran by combining meteorological indices (minimum temperature, maximum temperature, average temperature, precipitation, and potential evapotranspiration) and large-scale climate signals (North Atlantic Oscillation, Arctic Oscillation, Pacific Decadal Oscillation, and Southern Oscillation Index). The results of the ANFIS + RSA model were compared with those of the ANFIS + WOA and ANFIS + GWO models for evaluation. Based on the estimation results and error evaluation criteria, the performance of the ANFIS + RSA model is considered appropriate, showing a higher relative accuracy compared to ANFIS, ANFIS + GWO, and ANFIS + WOA. In semi-arid and moderate climates, the ANFIS + RSA model exhibited the highest prediction accuracy, with RMSE = 0.28, MAE = 0.20, CA = 0.19, and NASH = 0.91. In semi-arid and cold climates, the model's accuracy was slightly lower, with RMSE = 0.33, MAE = 0.23, CA = 0.23, and NASH = 0.85. In arid and super-cold climates, the model's accuracy remained relatively consistent, with RMSE = 0.24, MAE = 0.18, CA = 0.19, and NASH = 0.84. Furthermore, the promising results of the hybrid ANFIS + RSA model can be further evaluated in other regions and climates to assess its overall effectiveness.