Forecasting of Groundwater Level Using Ensemble Hybrid Wavelet–Self-adaptive Extreme Learning Machine-Based Models

Generally, the estimation and prediction of groundwater levels (GWLs) are an important challenge in the field of water resources management. In this study, for the first time, the groundwater level (GWL) of the Sarab Qanbar well located in the south of Kermanshah, Iran, is approximated using the wavelet–SAELM model. An artificial intelligence method called “self-adaptive extreme learning machine (SAELM)” and the “wavelet transform” method were implemented to develop a predictive model. First, using the autocorrelation function (ACF) and the partial autocorrelation function (PACF), the effective lags in estimating the GWL were detected and evaluated. Then, eight distinctive SAELM and WA–SAELM models were developed using the input combinations selected by the ACF and the PACF as different lags. Later, the values of the observational well were normalized to estimate the GWL. Time series data were divided into two subsamples including 70% to train the artificial intelligence (AI) techniques and 30% to test the AI models. Next, the most optimized mother wavelet was chosen for the modeling. By evaluating the results of the SAELM and WA–SAELM models, it was concluded that compared to the SAELM models, the WA–SAELM models estimate values of the objective function with higher accuracy. Then, the superior model was introduced, which was very accurate in forecasting the GWL. In the test mode, for example, the correlation coefficient, mean absolute error and the Nash–Sutcliffe efficiency coefficient for the superior model were calculated as 0.995, 0.988 and 0.990, respectively. Furthermore, an uncertainty analysis was conducted for the predictive models, revealing that the superior model has an underestimate performance.