Accurate groundwater level predictions: integration of physics-driven and machine learning approaches

Accurate prediction of groundwater levels (GWLs) is crucial for groundwater resource management. Traditional numerical models, such as MODFLOW, often fail to provide precise predictions due to data limitations, while machine learning models like long short-term memory (LSTM) lack interpretability. This study proposes an integrated approach that combines MODFLOW predictions with LSTM to enhance both prediction accuracy and interpretability. The performance of the coupling model (MOD-LSTM) was tested using data from ten monitoring wells located at the top, middle, and bottom of a typical alluvial fan in the North China Plain. The results demonstrate a significant improvement in GWL prediction accuracy. During the training and validation periods, 80% of the wells achieved a Nash-Sutcliffe Efficiency (NSE) greater than 0.75. During the prediction period, the MOD-LSTM model outperformed MODFLOW, with an average increase of 0.423 in the Pearson correlation coefficient (PR) and a decrease of 0.618 m in the root mean square error (RMSE); Compared to pure LSTM model, the MOD-LSTM model showed a 0.145 increase in PR and a 0.280 m decrease in RMSE. The model also effectively captured long-term trends of GWLs, seasonal fluctuations, and rising trends following river ecological water replenishment events. Furthermore, the predictions of the MOD-LSTM model can be interpreted using the MODFLOW model, due to the similar GWL dynamics of each well. The coupling model combines physics-driven modeling with machine learning, providing a novel approach for more accurate groundwater level prediction.