Improving streamflow prediction across China by hydrological modelling together with machine learning

Predicting streamflow is key for water resource planning, flood and drought risk assessment, and pollution mitigation at regional, national, and global scales. There is a long-standing history of developing physically or conceptually catchment rainfall-runoff models that have been continuously refined over time to include more physical processes and enhance their spatial resolution. On the other hand, machine learning methods, particularly neural networks, have demonstrated exceptional accuracy and extrapolation capabilities in time-series prediction. Both approaches exhibit their strengths and limitations. This leads to a research question: how to effectively balance model complexity and physical interpretability while maintaining a certain level of predictive accuracy. This study aims to effectively combine a conceptual hydrological model, HBV, with machine learning (Transformer, Long Short-Term Memory (LSTM)) using a differentiable modeling framework strategy, tailored to predicting streamflow under diverse climatic and geographical conditions across China. Utilizing the Transformer to optimize and replace certain parameterization processes in the HBV model, a deep integration of neural networks and the HBV model is achieved. This integration not only captures the non-linear relationships that traditional hydrological models struggle to express, but also maintains the physical interpretability of the model. Preliminary application results show that the proposed framework outperforms traditional HBV model and pure LSTM model in streamflow prediction across 68 catchments in China. Based on the test results from different catchments, we have adjusted and optimized the model structure or parameters to better adapt to the unique hydrological processes of each catchment. The application of self-attention mechanisms and a differentiable programming framework significantly enhances the model's ability to capture spatiotemporal dynamics. It is likely that the proposed framework can be widely used for streamflow prediction somewhere else.