The Extrapolation Dilemma in Hydrology: Unveiling the extrapolation properties of data-driven models

Long Short-Term Memory (LSTM) networks have shown strong performance in rainfall–runoff modelling, 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 and evaluated against hydrological process understanding. Our study reiterates that the stand-alone LSTM is characterised by a theoretical prediction limit, and we show that this limit is below the range of the data the model was trained on. We show that saturation of the LSTM cell states alone does not fully account for this characteristic behaviour, as the LSTM does not reach full saturation, particularly for the 1-day events. Instead, its gating mechanisms 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 hydrologically unfeasible runoff responses during the 1-day design experiments. Despite these shortcomings, our findings highlight the inherent potential of stand-alone LSTMs to capture complex hydro-meteorological relationships. We argue that more robust training strategies and model configurations could address the observed limitations, ensuring the promise of stand-alone LSTMs for rainfall–runoff modelling.