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.

This paper introduces multi-angular imagery into physics-based bathymetry in order to compensate for the shortage of bathymetric spectral bands caused by the low spectral resolution of current high-spatial-resolution satellite multispectral imagery. The focus is to propose a selective bathymetric retrieval method to eliminate the negative effect of non-optimal image data on depth retrieval in multi-angular imagery-based bathymetry. The elimination of the negative effect is implemented by excluding non-optimal pixels in every individual image from bathymetric retrieval. An empirical criterion is designed for the determination of non-optimal pixels. The proposed method can uses multi-angular image data selectively, avoiding situations where bathymetric retrieval results from the whole multi-angular imagery are poorer than that from part of the individual images. The method was tested in two typical areas within the Xisha (Paracel) Islands of the South China Sea using two-angle WorldView-2 multispectral images. The test showed that the derived depths of the method (i.e., depths derived from the selective image data) provided a better fit to the validation depths than those from the entirety of both images. The underestimation of depths derived from the entirety of both images was also improved to some extent.

Bathymetric inversions constitute a key preliminary step when characterizing coral topography. The Ice, Cloud, and Land Elevation Satellite-2 (ICESat-2) is poised to provide true values for satellite-derived bathymetry (SDB) in the absence of measured data. Nevertheless, the influences of the different available algorithms and atmospheric correction (AC) processes applied to construct SDB over coral reef waters are still poorly understood. In this research, three empirical-based bathymetric algorithms (the linear ratio model (LRM), polynomial ratio model (PRM), and exponential ratio model (ERM)) and three ACs (ACOLITE, SeaDAS, and Sen2Cor) are evaluated with Sentinel-2A/B multispectral imagery to achieve fine-spatial-resolution bathymetric information. The bathymetry estimates produced by fusing the Sentinel-2A/B and ICESat-2 datasets using the three models exhibit sufficient accuracies, with low percent errors and mean absolute errors (MAEs) between 0.44 and 0.74 m and root mean square errors (RMSEs) between 0.61 and 0.96 m. In all cases, the PRM outperforms the ERM and LRM. The AC method comparisons show that the performance of ACOLITE is better than those of Sen2Cor and SeaDAS. The obtained depth estimates are less sensitive to the impacts of the AC methods in relatively shallow waters than in relatively deep waters, and ACOLITE performs more stably. Overall, the PRM coupled with the ACOLITE method performs best. With depths extracted from ICESat-2, high-spatial-resolution SDB data capable of supporting the long-range goal of coral topography analyses are attainable even without in situ datasets.

Mapping bathymetry with satellite-based imagery for optically shallow waters is important for the management of coastal areas. However, mapping ultra-high-spatial-resolution bathymetry (spatial-resolution < 5 m) for a wide range of coastal optically shallow waters is limited by high cost and the absence of in situ data. Therefore, in this study, a new downscaled bathymetric mapping approach (DBMA-RGB) was established using freely accessed Landsat-8 (spatial-resolution = 30 m) and cost-effective Google Earth Pro-exported ultra-high-spatial-resolution red-green-blue (RGB) imagery. The new approach introduced the scale-invariance assumption that the log-ratio model (LRM) which is calibrated at a high scale is valid at a low scale. To reduce the inversion errors from Landsat-8 imagery, a theoretical maximum detection depth (MDD) model was proposed for the optimization-based inversion method, which is the foundation of DBMA-RGB for working without in situ bathymetric data. The theoretical MDDs overall matched the true MDDs except for the abnormal values, with root mean square error and correlation coefficient values of 3.30 m and 0.68, respectively. Additionally, a set of correction coefficients was obtained to improve the accuracy of the water depth derived from Landsat-8 imagery. Finally, the DBMA-RGB was applied to the RGB imagery of sixteen coastal areas around the world, incorporating the bathymetric results from Landsat-8 imagery. The comparison results indicated that the DBMA-RGB yielded similar results to the LRM calibrated using in situ bathymetric data. In summary, DBMA-RGB demonstrated its feature in accurately mapping ultra-high-spatial-resolution bathymetry for a wide range of coastal optically shallow waters without in situ bathymetric data.