Hydrological insights from a comparative evaluation of LSTM and MC-LSTM networks in the Ebro River basin (Spain)

The northern part of the Ebro River basin, Spain. Deep learning techniques are transforming streamflow modelling by delivering state-of-the-art predictions despite persistent challenges in interpretability and adherence to physical laws. In this study, we evaluate the performance of the standard Long Short-Term Memory (LSTM) neural network alongside its physically constrained variant, the Mass-Conserving LSTM (MC-LSTM), across multiple training scenarios applied to gauging stations in the Ebro River Basin (Spain). In addition to traditional metrics such as the Nash-Sutcliffe Efficiency (NSE), our analysis uniquely disaggregates model performance by quantifying peak magnitude errors through normalized RMSE values stratified by specific return periods (T 0.5 , T 1 , T 2 , T 5 , T 10 ) and by assessing time delay errors using a wavelet coherence approach to capture temporal differences between observed and predicted discharge records. Our results indicate that while the regional LSTM model excels in predicting low and medium magnitude flows with accurate timing, its performance in modelling flood peaks is mixed. In contrast, the MC-LSTM model, leveraging its mass balance constraint as a regularization mechanism, demonstrates superior detection of high-magnitude events but exhibits distinct time lag characteristics. This integrated evaluation framework provides comprehensive insights into both the magnitude and temporal accuracy of deep learning hydrological models, underscoring the potential of incorporating physical constraints to achieve more robust and interpretable flood modelling. • Peak flow errors are evaluated using normalized RMSE for different return periods. • The MC-LSTM model shows excellent performance in flood predictions tasks. • Traditional LSTM models provide improved estimates of peak streamflow timing. • Sequence length selection is linked to dominant streamflow temporal dynamics. • The physical constraint in MC-LSTM improves generalization with less training data.