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.

Bathymetry is important to shallow coral reef management. Remote sensing is one of the most important techniques for mapping bathymetry. For instance, multispectral remote sensing images have been widely used to map bathymetry of coral reefs. These physically based methods, which are able to retrieve bathymetry, water column inherent optical properties (IOPs), and benthic reflectance simultaneously, generally can achieve good bathymetry results. However, there are strong limitations when facing the scenarios of mixing benthic reflectance for bathymetry with multispectral images. In this study, aiming at handling the mixing phenomenon on the use of multispectral remote sensing images for mapping bathymetry, we propose a new unmixing-based method, namely unmixing-based multispectral optimization process exemplar method (UMOPE). The new method incorporates endmember variability with a linear combination of three fixed endmembers and the relaxation of the sum-to-one constrained. UMOPE was validated with two existing methods with in situ data and a WorldView-2 image in the South China Sea. Results from in situ data show that the proposed method performs the best, with the smallest absolute root mean square error ${\rm{(RMSE)}}$ (2.26 m) and the best agreement ( $R^{2}= {\text{0.91}}$ ) between the measured and estimated water depth. Moreover, results from WV-2 imagery demonstrate the superior performance for the UMOPE at depth range from about 9 to 26 m. Furthermore, since the errors from IOPs can propagate to bathymetry, we further take this issue into account by analyzing the rule of influence of bottom on IOPs. Finally, the result of benthic classification map from UMOPE is shown.

The log-ratio method (LRM) proposed by Stumpf et al. has been widely used to map bathymetry from multispectral imagery for oligotrophic waters, while the selection criteria of bands for the LRM have been subject to tradeoffs between maximum detectable depth and sensitivity. In this study, we first applied a method for global sensitivity analysis to a semi-analytical forward model of optically shallow waters with the WorldView-2 band-set. The results show that the sensitive wavelength band in water-leaving reflectance for water depth varies from the longer wavelength band to the shorter wavelength band with increasing water depth. Then, we developed an adaptive blended algorithm approach (ABAA) to seamlessly map bathymetry from the shallower region to the deeper region. The LRM with different band combinations was selected for the sub-algorithms of the ABAA. The sub-algorithms and depth range used for each sub-algorithm of the ABAA were automatically determined by the proposed applicable depth range analysis that considers logarithmic regression for the LRM. The ABAA was applied to WorldView-2 and Landsat-8 imagery of the Xisha Qundao. When the in-situ bathymetry data are available, compared with the LRM with the blue and green bands, the ABAA significantly improves the accuracy of the estimated depth, especially for waters shallower than 6 m (root mean square error (RMSE)=0.31 to 0.94 m for WorldView-2 data, RMSE=0.25 to 1.42 m for Landsat-8 data). When the in-situ bathymetry data are absent, the ABAA performs better than the LRM with a single band ratio and an optimization-based method overall.