PHY-SDB: a dual-physics-guided deep learning framework for hyperspectral satellite-derived bathymetry

Satellite-derived bathymetry (SDB) is vital for coastal and reef ecosystem monitoring, yet conventional data-driven methods often lack physical interpretability and robustness in optically complex shallow waters. Here, we propose PHY-SDB, a dual-physics-guided deep learning framework integrating hyperspectral imagery with: (1) inherent optical properties (IOPs), including chlorophyll-a and CDOM absorption coefficients at 440 nm from a bio-optical model, and (2) a Stumpf model-inspired log-ratio loss function to enforce depth–reflectance constraints. Implemented with fully connected deep neural networks (FC-DNN) and one-dimensional convolutional neural networks (CNN-1D), PHY-SDB was trained on EnMAP hyperspectral imagery and ICESat−2 ATL03 bathymetry data. Validated against baseline models (SVR, KNN, LGBM) using in-situ depths from Lingyang Reef and Qilianyu in the South China Sea, PHY-SDB achieved superior performance. At Lingyang Reef, RMSE decreased from 1.62 m (SVR) and 1.46 m (KNN/LGBM) to 1.36 m (FC-DNN) and 1.21 m (CNN-1D). At Qilianyu, RMSE reduced from 1.02 m (SVR) to 0.94 m (FC-DNN) and 0.97 m (CNN-1D), with R² reaching 0.97 for both deep learning variants. The S-IOP-PHYLoss configuration, combining physical inputs and physics-based loss, yielded the most stable and accurate results across multiple depth intervals and repetitions. Across three complementary experiments—the radiative-transfer simulation, the deeper network test, and the cross-regional validation—PHY-SDB consistently demonstrated the effectiveness of its dual-physics design. The physics-consistency loss (PHYLoss) showed robust generalization across optical conditions, while the explicit IOP inputs were more sensitive to regional and sampling variations. Overall, PHY-SDB enhances accuracy, stability, and physical interpretability in satellite-derived bathymetry, providing a scalable framework for hyperspectral coastal mapping.