Prediction of Rainfall in Babolsar Station by Using Optimized Wavelet-Extreme Learning Machine

In this study, the long-term rainfall in Babolsar city was simulated by means of an optimized AI model. To do this, the extreme learning machine (ELM) and the wavelet transform (WT) were combined. It should be stated that the monthly rainfall values from 1951 to 2019 were applied, meaning that 70% of the observed values were employed to training the AI models and 30% of rest were utilized to testing these models. Firstly, the activation functions of the ELM models were evaluated; as a result, the sigmoid was chosen as the best activation function. Moreover, the lags of time series were introduced using the autocorrelation function (ACF) that four ELM models were defined through those identified lags. By performing a sensitivity analysis, the superior ELM model was introduced. The values of correlation coefficient (R), variance accounted for (VAF), and scatter index (SI) for the ELM model were respectively computed to be 0.524, 27.064, and 0.819. Furthermore, different mother wavelets were examined and the “dmey” was opted as the best mother wavelet. The wavelet transform enhanced the accuracy of the simulations significantly. For instance, the VAF index for the hybrid WELM model equaled to 86.461. It is noteworthy that the hybrid model was evaluated for different decomposition levels (DL) and then the best one was detected. Also, the (t-1) and (t-12) lags were identified as the most effective input lags.