Machine learning models combined with wavelet transform and phase space reconstruction for groundwater level forecasting

Abstract

Reliable forecasting of groundwater levels plays an important role in water resource management and the prevention of environmental problems. This study aims to introduce a novel hybrid model combining machine learning with wavelet transform (WT) and phase space reconstruction (PSR) for groundwater level forecasting. The development of the proposed hybrid model consists of two levels. Firstly, a popular data-driven nonlinear artificial neural network (ANN) model was selected as the base model. Thereafter, the WT is used to decompose the groundwater level time series. In addition, the PSR method is further adopted to select the suitable sub-series components resulting from the WT decomposition processes. At the first level, the hybrid model only combines the WT with ANN (WT-ANN). At the second level, a two-step preprocessing process, WT coupled with PSR, is implemented before the ANN, namely WT-PSR-ANN. Meanwhile, three mother wavelets (Daubechies, Symlets, and Dmeyer) are selected to further investigate the effect of wavelet type. Finally, the model's performance is evaluated using visual analysis and statistical metrics (root means square error, correlation coefficient, and the Nash-Sutcliffe efficiency coefficient). The results show that the WT-ANN model outperformed the vanilla ANN model. Furthermore, the WT-PSR-ANN model achieved the best accuracy for all selected mother wavelets. The most suitable mother wavelet is specific to each well, and there is no one-size-fits-all answer. This study highlights the effectiveness of PSR combined with WT as a data preprocessing step when the ANN model is applied for groundwater level forecasting.