Novel reliable model by integrating the adaptive neuro-fuzzy inference systems with wavelet transform and firefly algorithms for rainfall forecasting in the north of Iran

Abstract Rainfall is perhaps the most important source of drinking and agriculture water for inhabitants different parts world, particularly in arid semi-arid area like Iran. Hence, simulation this hydrological phenomenon crucial. The current research attempts to reproduce long-term monthly precipitation Ardabil, Iran, during 44 years from 1976 2020 first time via a hybrid fuzzy technique. For developing model (WANFIS-FA), adaptive neuro-fuzzy inference system (ANFIS), firefly algorithm wavelet transform were integrated. Firstly, impacting lags series data recognized by using autocorrelation function 14 WANFIS-FA models defined them. Then, results evaluated best influencing found. example, variance accounted index (VAF), correlation coefficient ( R ) Nash–Sutcliffe (NSC) values superior computed be 98.082, 0.990 0.980, respectively. In addition, t − 1), 2), 3) 12) effective ones. Next, members mother tested finally demy was selected as an optimal wavelet. Also, analysis outcomes demonstrated that meaningfully enhanced efficiency model. Finally, compared with ANFIS, WANFIS ANFIS-FA, which displayed performed better.