Evaluating the extrapolation capability of deep learning in rainfall-runoff

Deep learning, a prominent artificial intelligence method, is increasingly applied in research addressing the impacts of global warming in the future. However, it is widely acknowledged that deep learning exhibits limitations in extrapolation, as it typically predicts accurately only within the range of the training data. When future scenarios extend beyond this range, the reliability of predictions can diminish significantly. In Japan, for example, the annual maximum precipitation is reported to be increasing, according to the Japan Meteorological Agency, indicating a potential for future values to exceed historical records. Despite this, limited studies have explored the extent to which deep learning methods can reliably extrapolate beyond the training data range. This study quantitatively evaluates the extrapolation capability of deep learning in hydrology, specifically focusing on rainfall-runoff modeling at the watershed scale. Meteorological data, including precipitation and temperature, are utilized as inputs, while river flow serves as the output. The Long Short-Term Memory (LSTM) model, which is well-suited for time-series data, was employed as the deep learning framework. Data were partitioned into training, validation, and test datasets, with river flow values categorized using threshold percentiles of 90, 95, 97, 98, and 99, rather than conventional time-based splits. This approach allows for a focused investigation into the range of accurate extrapolation beyond the training dataset. Preliminary findings reveal that the LSTM model successfully captured peak river flows up to 250.1% higher than the maximum values of the observed river flow discharge in the training-validation dataset. These results demonstrate the potential for deep learning to extrapolate in hydrological modeling, though further research is necessary to assess the performance of alternative deep learning methods and additional case studies.