Investigate the rainfall-runoff relationship and hydrological concepts inside LSTM

Recent studies have shown that LSTM performs well in runoff prediction in large sample regional modeling and can estimate hydrological concepts based on its internal information. However, compared to process-based models, it still produces erroneous predictions that violate the physical laws. To explore the reasons for the above phenomenon, this study analyzes the evolution of LSTM’s performance in predicting runoff and estimating hydrological concepts when trained on a large basinscale dataset. Findings demonstrated that LSTM’s representation of the rainfall-runoff relationship lags behind the formation of hydrological concepts. The representations of relations and concepts do not consistently increase with the number of training basins. There is a model that achieves the best representation of the rainfall-runoff relationship and hydrological concepts, ensuring physical consistency even under extreme conditions. These results suggest that LSTM, like process-based models, learns the rainfall-runoff relationship and hydrological concepts, but its confusion about these concepts may lead to inaccurate predictions. • Rainfall - runoff relationship learned by LSTM lags behind its formation of hydrological concepts. • Rainfall - runoff relationship and hydrological concepts learned by LSTM don't consistently benefit from the increasing training set. • The LSTM with well-formed hydrological concepts predicted a more physically realistic runoff response, although the model performance was not optimal at this point.