Integrating Physical Parameterization and Attention Mechanisms in Recurrent Neural Networks for Hydrological Modeling: Quantification of Storage Layers Dynamics and Meteorological Responses Within the PRNN Model Framework

Abstract With the advancement of deep neural networks and physics‐data‐driven coupling methods, significant new opportunities have emerged for improving watershed hydrological simulations. Attention mechanisms (AM) and physical process‐wrapped recurrent neural networks (PRNN) enhance model performance by dynamically highlighting key hydrological features and integrating physical concepts to learn complex processes. However, in PRNN models where runoff relies on storage‐driven hydrological processes, the potential of employing AM to quantify and interpret respective contributions of aquifer‐delineated storage layers remains underexplored. This study addresses this gap by integrating an AM into a PRNN based on the Hydrologiska Byråns Vattenbalansavdelning, yielding a diagnostic framework to assess whether the model's internal representations are consistent with established hydrological principles. Validated on 451 catchment attributes and meteorology for large‐sample studies basins, the proposed PRNN‐θaf‐A variant yields a median Nash‐Sutcliffe efficiency of 0.72. The diagnostic analysis reveals two key findings: (a) the soil moisture layer (S3) is the dominant contributor to runoff generation, accounting for a mean annual attention weight of 0.53; (b) the model's seasonal behavior is systematically linked to basin climate, demonstrated by a strong correlation ( R 2 = 0.68) between the seasonal attention shift for snowpack (S1) and the basin snow fraction. These results illustrate the potential of the framework to produce internal representations that are physically plausible and consistent with established hydrological principles, thereby bridging the gap between process‐based understanding and data‐driven modeling.