Deep learning-based uncertainty quantification of groundwater level predictions

Due to the underlying uncertainty in the groundwater level (GWL) modeling, point prediction of the GWLs does not provide sufficient information for decision making and management purposes. Thus, estimating prediction intervals (PIs) for groundwater modeling can be an important step in sustainable water resources management. In this paper, PIs were estimated for GWL of selected piezometers of the Ardebil plain located in northwest of Iran and the Qorveh–Dehgolan plain located in west of Iran, using bootstrap methods based on artificial neural networks (ANNs). For this purpose, the classic feedforward neural network (FFNN) and deep learning (DL)-based long short-term memory (LSTM) were used as ANN bases and the classic bootstrap and moving blocks bootstrap (MBB) as the bootstrap variations. Monthly GWL data of some piezometers as well as hydrologic data of the related stations from both plains were used for the training and validation of the models. The results showed that the LSTM outperforms the seasonal auto regressive integrated moving average model with exogeneous data (SARIMAX), which is a linear model, and classic FFNN in point prediction task. Moreover, in terms of PIs model performance, the LSTM-based MBB (MBLSTM) achieved an average of 30% lower coverage width criterion (CWC) than the FFNN-based MBB (MBFN) and average of 40% lower CWC than the FFNN-based classic bootstrap (BFN). In addition, PIs estimated for piezometers situated in areas with high transmissivity resulted in 55% lower CWC than PIs estimated for piezometers, which are located in areas with lower transmissivity.