*2.5. Spaceborne Bathymetric DSM*

The creation of the satellite-based bathymetric DSM relies on the use of a single multispectral imagery that needs to be both radiometrically and geometrically corrected, as well as pansharpened. The imagery #2 was selected for this purpose since it displayed the lowest off-nadir viewing angle (Table 2). Following the radiometric correction (see Section 2.4), the VIS+NIR multispectral reflectance imagery was orthorectified using the RPCs and the 20 ground control points, as well as the corresponding panchromatic reflectance imagery. Among seven sharpening methods, the Gram-Schmidt pansharpening procedure yielded the best visual results, and it was then implemented so as to produce a VIS+NIR dataset at 0.3 m pixel size (see [5] for details). The resulting sub-metre eight-band dataset was subjected to the radiative transfer model, called the ratio transform [29]. This standard bathymetric model makes use of the fact that light absorption by water varies with wavebands. It can thereafter determine the bathymetry (*z*), as follows:

$$z = a\_1 \left( \frac{\ln[R\_w(\lambda\_i) - R\_\infty(\lambda\_i)]}{\ln\left[R\_w(\lambda\_j) - R\_\infty(\lambda\_j)\right]} \right) - a\_0 \tag{1}$$

where *a*<sup>0</sup> is the intercept to match the mean sea level, *a*<sup>1</sup> is the slope converting the relative to absolute bathymetry (20 calibration sea control points), *Rw* is the reflectance related to the waveband *λi*, and *R*<sup>∞</sup> is the reflectance over deep water. The MAE and RMSE bathymetric validation (*N* = 15) accuracy reached 0.74 and 0.89 m, echoing the findings from previous WorldView-3 studies [15,24].

**Figure 4.** (**a**) Natural-coloured orthorectified WorldView-3 imagery of the study area; (**b**) topobathymetric digital surface model (in m) derived from the combination of a photogrammetry-based stereo-panchromatic imagery for land and a ratio transform model for sea, both derived from the same WorldView-3 stereo-imagery. The colour scale on the right indicates the estimated height and depth below sea-level of different parts of the image.
