Simulation of groundwater level using MODFLOW, extreme learning machine and Wavelet-Extreme Learning Machine models

Due to the need to forecast changes in groundwater systems and environment, groundwater modeling has been emerged. In this study, the groundwater level of the Kabodarahang aquifer located in Iran, Hamadan Province is simulated by means of three models: MODFLOW, Extreme Learning Machine (ELM) and Wavelet-Extreme Learning Machine (WA-ELM). At the beginning, the groundwater level simulation is carried out by MODFLOW with reasonable accuracy so that the correlation coefficient (R-2) and the scatter index (SI) are calculated 0.917 and 0.0004, respectively. After that, through different input combinations as well as the stepwise selection, 10 different models are developed as different lags for the ELM and WA-ELM models. Based on the numerical results yielded by all three models, WA-ELM is introduced as the superior model in simulating the groundwater level. For instance, the correlation coefficient (R-2) and the Nash-Sutcliffe efficiency coefficient (NSC) are computed 0.959 and 0.915, respectively. According to the uncertainty analysis, it is proved that the superior model has an underestimated performance. Furthermore, the by-products of the model such as weights and biases are then utilized to develop an explicit method for estimating the groundwater level. The developed model can be easily employed by an engineer with sufficient knowledge of matrix operation without prior information about the extreme learning machine. It is as accurate as the developed WA-ELM hybrid model and more precise than ELM and MODFLOW.