Exploring the performance and interpretability of hybrid hydrologic model coupling physical mechanisms and deep learning

Recently, differentiable modeling techniques have emerged as a promising approach to bidirectionally integrating neural networks and hydrologic models, achieving performance levels close to deep learning models while preserving the ability to output physical states and fluxes. However, there remains a lack of systematic exploration into the performance and physical interpretability of hybrid models that use neural networks to replace the runoff generation and routing processes in regionalized modeling. This research developed 12 regionalized hybrid models based on a differentiable parameter learning (DPL) framework, utilizing the Hydrologiska Byråns Vattenbalansavdelning (HBV) model as the foundational backbone. These hybrid models incorporate neural networks to replace the various physical processes within the runoff generation and routing modules. The publicly available CAMELS dataset is employed to evaluate the performance and interpretability of these hybrid models. The results show that while the median Nash-Sutcliffe efficiency (NSE) and Kling-Gupta efficiency (KGE) coefficients for all hybrid models are lower than those of the purely data-driven regionalized long short-term memory neural network (LSTM) model (median NSE: 0.742, median KGE: 0.762), the best-performing hybrid model (median NSE: 0.731, median KGE: 0.761) approaches the LSTM model and has better physical interpretability. Embedding neural networks does not inherently guarantee improved performance and may, in some cases, even result in reduced performance. The degree of performance enhancement is not significantly correlated with the number of embedded neural networks. Compared to replacing the runoff generation process, substituting the routing process with neural networks yields more substantial performance improvements and enables the learning of different routing patterns based on the catchment’s static attributes. This study underscores the importance of reasonably balancing the location, complexity, and quantity of embedded neural networks to achieve a trade-off between model performance and interpretability in hybrid modeling. These insights contribute to advancing regionalized hybrid modeling development.