| 07 Jul 2026
Differentiable Hybrid Hydrological Model for Short-Term Flood Forecasting with Future Meteorological Information
Abstract. Short-term flood forecasting is essential for flood control operation and risk warning in small- and medium-sized basins, yet its accuracy is constrained by rainfall uncertainty, hydrological model structural limitations, and watershed physical response characteristics. To address these challenges, this study developed a differentiable hybrid hydrological forecasting framework that coupled future meteorological information with physically representations of runoff generation, baseflow recession, flow concentration, and channel routing. A physics-informed neural architecture search (PINAS) routing scheme was further proposed and systematically compared with differentiable Muskingum routing and convolutional unit-hydrograph routing, while a purely data-driven LSTM model was used as the benchmark. The framework was evaluated in three representative watersheds in Hebei Province, China, namely the Shahe basin (2210 km2), Jumahe basin (1760 km2), and Liulin basin (57.4 km2), using rainfall–runoff observations from the flood seasons of 2000–2023 and radar-echo data from 2018–2023. Multi-lead flood forecasting experiments were conducted for lead times of 0.5–2.0 h. The results showed that the LSTM benchmark achieves high numerical accuracy in some high-peak flood events, but lacks explicit physical constraints. In contrast, the model with PINAS routing exhibited the most stable overall performance among the hybrid hydrological models, achieving a more balanced representation of flood-peak propagation, hydrograph smoothing, and recession preservation. The data-dependency analysis indicated that increasing the amount of training data improved forecasting stability, but model skill does not increase strictly monotonically with sample size, sample representativeness and flood-type coverage were also critical. SHAP interpretability analysis further revealed that forecasts in the Shahe and Jumahe basins were mainly controlled by radar echoes and their extrapolated features, whereas the small Liulin Basin was more strongly influenced by measured areal rainfall and gauge rainfall. These findings demonstrated that integrating physical constraints, differentiable runoff–routing structures, and future meteorological information can improve the stability, physical consistency, and hydrological interpretability of short-term flood forecasting in small- and medium-sized basins.
