4SM: A Novel Self-Calibrated Algebraic Ratio Method for Satellite-Derived Bathymetry and Water Column Correction

Abstract

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.

The Contribution of Multispectral Satellite Image to Shallow Water Bathymetry Mapping on the Coast of Misano Adriatico, Italy

“…Bathymetry from Earth observation data has been explored by many authors [27][28][29][30][31][32][33][34][35] under various domains, such as underwater archaeology [25] and natural disaster evaluation [34]. The authors of [36] used a simplified radiative transfer equation to retrieve both SDB and water column in shallow waters without the need for a formal atmospheric correction technique (i.e., the conversion of relative radiance into calibrated reflectance) or the use of existing depth sounding data. However, they noted that some sensor configurations (e.g., near-nadir view angle) and environmental conditions-including a clear sky, the time the sun is highest in the sky, and less suspended water particles (clear water)-must be respected in order to obtain a good quality satellite image with less atmospheric and glint effects for SDB study.…”

4SM Method Tested in the Gulf of California Suggests Field Data are Not Needed to Derive Satellite Bathymetry

“…To this extent, and from many tests made in the development of 4SM (see www.watercolumncorrection.com , and [23]) it can be said that 4SM is not site-specific, and is capable of delivering both a bathymetric map and a water column corrected image in units of image's DN over many different water types, in different location of the world, when the high cost of collecting similar data in the field is simply not affordable. While an empirical method (e.g.…”

“…As presented by Morel and Favoretto [23] and at www.watercolumncorrection.com, it is possible to retrieve from the image all the information needed for the calibration of the simplified RTE. Solving for Z and LB in equation (2) requires four spectral parameters which are estimated from the image itself: 1) the deep water reflectance Lsw; 2) the Soil Line; 3) the water volume reflectance Lw; 4) the Brightest Pixels Line.…”

“…The inversion of the model is achieved by increasing Z term in equation 2 until the ratio LBi/LBj matches that of the Soil Line. As detailed by Morel and Favoretto [23], for a Landsat-8 or WorldView-2 image, several solutions are available: the NIR solution, the Red solution, the Green solution, and the PAN solution. In practice, the PAN solution is preferred, as it carries several distinct advantages.…”

“…As regards the accuracy of 4SM depths, pixels with both groundtruthed depths and satellite derived depths are selected and these depth pairs are assigned to bins in decimeters [23]. Bins with few data pairs are excluded as outliers and plotted as red points in the scatterplots of Figure 6: these outliers are generated by various alien features and must be excluded for a fair regression calculation.…”