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Rapid estimation of bathymetry from multispectral imagery without in situ bathymetry data.

Optimization-based semi-analytical methods (OSMs) and empirical methods (EMs) have been developed to derive bathymetry maps from satellite-based multispectral data of coral reefs, allowing for the management, monitoring, and protection of coral reefs. However, OSMs are often criticized due to the time-consuming requirements of iterative computations, yet they are praised for working without the need for in situ bathymetry data. EMs are praised for their time-saving characteristics and criticized for their need for in situ measurements. To estimate the water depth from multispectral data quickly without in situ bathymetry data, we provide a new EM that combines our previously developed OSM called the unmixing-based multispectral optimization process exemplar method (UMOPE) and an EM called Stumpf's ratio method (SRM). In the new method, reflectance values from a small number of sampled pixels and the corresponding water depths estimated by UMOPE are used to determine the regression parameters for SRM. Thus, SRM determines the upper limit of accuracy for the new method, and UMOPE determines the possibility of reaching the upper limit. The new method was evaluated using three types of imagery of Xisha Islands, namely, WorldView-2 imagery with three traditional visible bands (WV-2a), Landsat 8 imagery with four visible bands, and WV-2 imagery with six visible bands (WV-2b). The results show that the new method can perform as well as SRM for Landsat 8 data and WV-2b data with similar root mean square error values at different depths. The lack of a coastal band in WV-2a imagery may cause large errors for the new method in deep water regions, especially when the water-leaving reflectance is noise perturbed. We found that even though the depths estimated by UMOPE are not error free at different ranges of water depth, if the regression line between the depths estimated by UMOPE and the measured depths is near the 1:1 line, the new method can perform as well as SRM. The new method may facilitate the rapid estimation of bathymetry from free Landsat 8 data of optically shallow waters around the world without in situ bathymetry data.