Unveiling the limits of deep learning models in hydrological extrapolation tasks

Abstract. Long short-term memory (LSTM) networks have shown strong performance in rainfall–runoff modeling, often surpassing conventional hydrological models in benchmark studies. However, recent studies raise questions about their ability to extrapolate, particularly under extreme conditions that exceed the range of their training data. This study examines the performance of a stand-alone LSTM trained on 196 catchments in Switzerland when subjected to synthetic design precipitation events of increasing intensity and varying duration. The model's response is compared to that of a hybrid model – a model that combines conceptual hydrological approaches with the LSTM – and evaluated against hydrological process understanding. Our study reiterates that the stand-alone LSTM is not capable of predicting discharge values above a theoretical limit (which we have calculated for this study to be 73 mm d−1), and we show that this limit is below the maximum value of 183 mm d−1 in the training data. Furthermore, the LSTM exhibits a concave runoff response under extreme precipitation, indicating that event runoff coefficients decrease with increasing design precipitation – a phenomenon not observed in the hybrid model used as a benchmark. We show that saturation of the LSTM cell states alone does not fully account for this characteristic behavior, as the LSTM does not reach full saturation, particularly for the 1 d events. Instead, its gating structures prevent new information about the current extreme precipitation from being incorporated into the cell states. Adjusting the LSTM architecture, for instance, by increasing the number of hidden states and/or using a larger, more diverse training dataset, can help mitigate the problem. However, these adjustments do not guarantee improved extrapolation performance, and the LSTM continues to predict values below the range of the training data or show unfeasible runoff responses during the 1 d design experiments. Despite these shortcomings, our findings highlight the inherent potential of stand-alone LSTMs to capture complex hydrometeorological relationships. We argue that more robust training strategies and model configurations could address the observed limitations, preserving the promise of stand-alone LSTMs for rainfall–runoff modeling.