Deep learning of flood forecasting by considering interpretability and physical constraints

Abstract. Deep learning models have been proven to be effective in flood forecasting by leveraging the rich time-series information in the data. However, their limited interpretability and lack of physical mechanisms remain significant challenges. To address these limitations, this study introduces a novel model called PHY-FTMA-LSTM, which combines the feature-time-based multi-head attention mechanism with physical constraints. The PHY-FTMA-LSTM model takes four essential features of runoff, rainfall, evapotranspiration, and initial soil moisture as inputs to forecast floods in the Luan River Basin with a lead time of 1–6 h. It emphasizes the significance of relevant factors in the input features and historical moments through the feature-time attention module. Furthermore, the model enhances physical consistency by considering the monotonic relationship between the input variables and the output results. The results demonstrate that the PHY-FTMA-LSTM in most cases outperforms the original LSTM, the feature-time-based attention LSTM (FTA-LSTM), and the feature-time-based multi-head attention LSTM (FTMA-LSTM). For a lead time of t+1, the model achieves an NSE of 0.988, with KGE and R² of 0.984 and 0.988. The NSE, KGE, and R² also reach 0.908, 0.905, and 0.911 for a lead time of t+6. The proposed PHY-FTMA-LSTM model achieves excellent prediction accuracy, offering valuable insights for enhancing interpretability and physical consistency in deep learning approaches.