An explainable physical-machine learning hybrid approach for inflow modelling

Accurate yet interpretable inflow forecasts are essential for hydropower operation. This study introduces modular Hydrologiska Byråns Vattenbalansavdelning-deep learning (mHBV-DL), a physics-guided hybrid deep learning framework that integrates the HBV model structure with neural networks, exposing intermediate hydrological states and fluxes alongside inflow predictions to enhance physical explainability. To systematically evaluate physics-DL integration strategies, four model configurations are constructed and compared, balancing learning flexibility with physical consistency. The best-performing mHBV-DL configuration achieved a Nash–Sutcliffe efficiency coefficient of 0.833, outperforming the standalone HBV model and remaining competitive with the architecture-matched black-box DL baselines. Its intermediate outputs also reflected expected hydrological patterns. The modular architecture and intermediate state and flux tracking enable systematic analysis of seasonal performance and model limitations. These findings establish mHBV-DL as an effective framework for combining predictive performance with physical explainability in catchment inflow modelling and provide a basis for future lead-time-based forecasting applications.