Exploring the generalisation ability and interpretability of Long Short-Term Memory (LSTM) networks for large-sample groundwater level predictions

Abstract. Deep Learning (DL) models, particularly Long Short-Term Memory (LSTM) networks, have shown similar or even superior performance to process-based models in estimating streamflow particularly at ungauged locations. However, their ability to extrapolate groundwater levels across time and space is less understood, as the number of studies addressing this issue is so far relatively limited. Here, we exploit the unique availability of a large-sample dataset of groundwater level observations across England to contribute to filling this gap. We configured two LSTM model variants: one using static environmental attributes (LSTM_ENV) and one using random integers as unique identifiers of places (LSTM_RND). Both models were trained using data from 636 stations over the period 1971-2014 and tested over 2015-2019 at both the training stations (in-sample test) and at 341 unseen stations (out-of-sample). Our results indicate that the two configurations achieved comparable performance in in-sample test, but their performances significantly diverge at unseen stations. To put the LSTM models’ performance into context, we also compared them to the performance of a process-based surface-groundwater model at 124 unseen stations. We found that both models effectively capture temporal fluctuations but struggle to accurately reproduce the mean and variability of the water table depth. This systematic bias frequently resulted in negative NSE values despite high temporal correlation, suggesting that evaluating LSTM performance using NSE solely can be misleading. We also found that the LSTM_ENV model performs better at stations characterised by higher specific yield and transmissivity, and that it mostly uses meteorological input features (e.g. precipitation) and topographic features (e.g. elevation and height above nearest drainage) to make predictions at unseen stations. These findings highlight the potential of LSTMs for regional groundwater level predictions and the value of interpretability tools for understanding how such models achieve their performance and whether the environmental features used are informative.