4SM: A novel self-calibrated algebraic ratio method for satellite-derived bathymetry and water column correction

All empirical water column correction methods have consistently been reported to require existing depth sounding data for the purpose of calibrating a simple depth retrieval model; they yield poor results over very bright or very dark bottoms. In contrast, we set out to (i) use only the relative radiance data in the image along with published data, and several new assumptions; (ii) in order to specify and operate the simplified radiative transfer equation (RTE); (iii) for the purpose of retrieving both the satellite derived bathymetry (SDB) and the water column corrected spectral reflectance over shallow seabeds. Sea truth regressions show that SDB depths retrieved by the method only need tide correction. Therefore it shall be demonstrated that, under such new assumptions, there is no need for (i) formal atmospheric correction; (ii) conversion of relative radiance into calibrated reflectance; or (iii) existing depth sounding data, to specify the simplified RTE and produce both SDB and spectral water column corrected radiance ready for bottom typing. Moreover, the use of the panchromatic band for that purpose is introduced. Altogether, we named this process the Self-Calibrated Supervised Spectral Shallow-sea Modeler (4SM). This approach requires a trained practitioner, though, to produce its results within hours of downloading the raw image. The ideal raw image should be a “near-nadir” view, exhibit homogeneous atmosphere and water column, include some coverage of optically deep waters and bare land, and lend itself to quality removal of haze, atmospheric adjacency effect, and sun/sky glint.