Explainable Hybrid Physics-Guided Neural Network (HPGNN) for diverse Inland Lakes water quality inversion

Accurate remote sensing of optically active water quality parameters (OAWQPs) in optically complex lakes remains challenging due to similar reflectance signatures, spectral overlap, and adjacency effects, leading to non-uniqueness and sensitivity to sparse, noisy in situ observations. While Machine Learning (ML) models capture complex relationships, they often lack physical consistency, resulting in limited generalization. Whereas conventional Physics-Guide Neutral Networks (PGNNs), integrating physics-based governing equations and auxiliary information, are effective but difficult to scale to satellite-based retrieval of OAWQPs, lacking sufficient observables and governing equations. This study proposes a Hybrid PGNN (HPGNN) that integrates reflectance-native physics-guided and statistical regularization constraints with data fidelity to simultaneously enforce physical plausibility, statistical robustness, and empirical fidelity. Using Sentinel-2 remote sensing reflectance and a broadly distributed in situ dataset, HPGNN models are developed with a hybrid loss function integrating the above constraints, achieving superior performance over conventional ML and empirical algorithms across multiple OAWQPs with R 2 (0.81–0.98). Using HPGNN models, quantitative and qualitative assessment results are produced across different continents, showing multiregional generalization and practical applicability. Finally, models' interpretability is ensured through SHapley Additive exPlanations (SHAP), which elucidates the influence of spectral bands on each parameter, providing hydrological insights. The proposed HPGNN framework provides a scalable and interpretable solution, enabling multiregional OAWQPs' spatio-temporal assessment to understand lake hydrology and take management decisions.