Enhancing process-based hydrological model with embedded residual neural networks: A hybrid modeling approach for hourly flood simulation

Study region Chenda, Yutan, Yongding, Guanyinqiao and Longmen catchments located in Fujian Province, China. Study focus This study focused on enhancing the physical interpretability and predictive performance of hydrological simulations by proposing a novel hybrid framework based on an Embedded Residual Neural Network (ERNN) integrated within the HBV model structure. The framework was rigorously evaluated using hourly flood data from five catchments, demonstrating superior accuracy and stability compared to conventional embedded neural network approaches. New hydrological insights This study proposes a novel hybrid framework based on an Embedded Residual Neural Network (ERNN) to enhance the HBV model. Instead of directly replacing empirical equations, our method integrates residual connections within the internal modules of the model, allowing the neural network to learn corrective residuals while preserving the physical consistency of the original hydrological structure. The model was evaluated using hourly flood data from five small and medium-sized catchments in Fujian Province, China. Results show that the proposed ERNN-based model significantly outperforms conventional embedded neural network approaches, achieving higher accuracy and more stable simulations. Furthermore, model performance improves progressively as the number of residual modules increases. The approach also maintains physical coherence in key hydrological state variables, and reduces the model outputs uncertainty across multiple training runs.