A Semi-Analytical–Empirical Hybrid Model for Shallow Water Bathymetry Using Multispectral Imagery Without In Situ Data

Water depth in shallow marine environments is a fundamental parameter for oceanographic research and coastal engineering applications. High-resolution satellite imagery and long-term medium-resolution imagery offer significant potential for detailed bathymetric mapping and monitoring spatiotemporal variations in bathymetry. However, most of these images contain only three visible bands (blue, green, and red), making bathymetric mapping from such images challenging in practical applications. For the empirical approach, high-quality in situ depth calibration data, which are essential for establishing a reliable empirical bathymetric model, are either unavailable or excessively expensive. For the physics-based approach, images containing only three visible bands can be problematic in accurately deriving depths. To address this limitation, this study proposes a novel semi-analytical-empirical hybrid model for water depth retrieval. The core of the proposed method is the integration of a semi-analytical model with a physics-based dual-band model. This integration quantifies the relative depth relationships among pixels and uses them as a physical constraint. Through this constraint, the method identifies physically reliable depth estimates from the multiple numerical solutions of the semi-analytical model for a subset of shallow-water pixels, which then serve as an in situ–free calibration dataset. This dataset is subsequently used to determine the empirically based optimal retrieval model, which is finally applied to generate the complete bathymetric map. The results from four typical coral reef regions—Buck Island, Yongxing Island, Kaneohe Bay, and Yongle Atoll—demonstrated that the proposed model achieved root-mean-square errors (RMSE) of 0.98–1.62 m, mean absolute errors (MAE) of 0.73–1.13 m, and coefficients of determination (R2) of 0.91–0.95 in comparison to in situ measurements. Compared to both the physics-based dual-band model and the L-S model (i.e., the bathymetry mapping approach combining Log-ratio and Semi-analytical models), the proposed model reduced the RMSE by 9–55%, reduced the MAE by 4–56%, and improved the R2 by 0.01–0.29. Additionally, the accuracy of the proposed model surpasses that of both the physics-based dual-band model and the L-S model across all depth intervals, particularly in deeper depth waters (>15 m). This study offers a robust solution for bathymetric mapping in areas lacking in situ depth data and contributes significantly to advancing optical remote sensing techniques for underwater topography detection.