Least-Squares-Based Deep Learning for Sentinel-2 Derived Bathymetry: A Case Study on Anegada's Southern Coast

Satellite-derived bathymetry (SDB) provides a cost-effective solution for coastal mapping, but challenges remain in model interpretability and uncertainty quantification. This study investigates the applicability of the least-squares-based deep learning (LSBDL) framework for SDB, leveraging its hybrid structure that integrates neural networks with the available least-squares theory to enhance model transparency. ICESat-2 photon-counting LiDAR was used to train depth estimation from Sentinel-2 multispectral imagery over an approximately 30 km × 30 km region of near-coastal bathymetry at Anegada, British Virgin Islands. ICESat-2 provided high-precision depth information, of which 80% were used for training and the remainder for validation. LBSDL depth estimation achieved a root-mean-square error (RMSE) of 2.74 m, representing around 10% of the maximum observed depth, with the best performance in the 2–15 m depth range. These findings demonstrate the potential of LSBDL for interpretable and reliable bathymetric mapping, highlighting ICESat-2 as a globally accessible training and validation source and advancing SDB capabilities for data-sparse coastal regions.