# A Hybrid Bio-Optical Transformation for Satellite Bathymetry Modeling Using Sentinel-2 Imagery
## 3 Results
### Satellite Derived Bathymetry (SDB) Results  
In order to examine the robustness of the HBT methodology, statistical tests were undertaken by considering as field observations the depths depicted on the official large-scale hydrographic chart (no. 423/2) that covers the coastal area of interest. A small number (i.e., \(<\)10) of map depths was used as training data for extracting seabed-classified SDB by implementing either the band deglint ratios (Equation (7)) or the ratios of the modelled bio-optical properties. Linear and quadratic regression analyses were then applied to the SDB results, according to which of the five seabed classes these results belonged to. There was no need for tide reduction in the SDB outcome, since the regression analysis was based on chart (reduced) data. Table 3 presents the best correlation (after removal of two-three erroneous data points, i.e., errors caused due to remaining glint on some pixels) obtained for each seabed class between, on one hand, the training depths and, on the other hand, the SDB retrieved either from the band deglint or the bio-optical properties ratios. We find that in areas of suspended particles, or dense or sparse flora, SDB exhibits best correlation with the training chart data when implementing the bio-optical properties ratios; over offshore waters, however, the best correlation between the SDB and the training map data is obtained when applying the band-deglint ratios. Overall, the quadratic regression analysis results in a better correlation compared to the linear regression for all seabed classes. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Bio-Optical Parameter** & **Units** & **Band** & **Min** & **Max** \\ \hline \multirow{4}{*}{Backscattering Coefficient \(b_{b}\)} & \multirow{4}{*}{(\(m^{-1}\))} & B1 & 0.11 & 0.42 \\  & & B2 & 0.09 & 0.35 \\  & & B3 & 0.07 & 0.25 \\  & & B4 & 0.05 & 0.18 \\  & & B1 & 0.14 & 0.51 \\  & & B2 & 0.11 & 0.48 \\  & & B3 & 0.07 & 0.38 \\  & & B4 & 0.44 & 0.49 \\  & & B1 & 0.74 & 2.10 \\ Diffuse Attenuation Coefficient \(K_{d}\) & Unitless & B2 & 0.24 & 1.50 \\  & & B3 & 0.17 & 1.22 \\  & & B4 & 0.74 & 1.23 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Statistical variation of the computed bio-optical parameters. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Seabed Class** & **Ratio** & \
\begin{tabular}{c} \(\mathbf{R^{2}}\) \\ **(Linear)** \\ \end{tabular} &
\begin{tabular}{c} \(\mathbf{R^{2}}\) \\ **(Quadratic)** \\ \end{tabular} \\ \hline \multirow{2}{*}{Suspended particles} & \(ln\Big{(}\frac{a(B1)}{a(B4)}\Big{)}\) & 0.960 & 0.969 \\  & \(ln\Big{(}\frac{a(B3)}{a(B2)}\Big{)}\) & 0.878 & 0.931 \\  & \(ln\Big{(}\frac{a(B3)}{a(B2)}\Big{)}\) & 0.903 & 0.908 \\  & \(ln\Big{(}\frac{Degl(B2)}{Degl(B3)}\Big{)}\) & 0.880 & 0.935 \\  & \(ln\Big{(}\frac{Degl(B1)}{Degl(B2)}\Big{)}\) & 0.909 & 0.973 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Statistical analysis on each seabed classification type. The validation set comprised 20 depths that were also depicted on the official nautical chart covering the strait between Paros and Antiparos Islands, within the range from 0.4 to 41.00 m. These depths were arbitrarily chosen, and for all seabed classes contained some of the data used to configure the ratio transformation (Figure 7). By comparing the coefficients of determination (R\({}^{2}\)) of each seabed class, we find that the HBT bathymetry seems to be correlated better with the chart data at an average of approximately 13% when a linear regression is applied, and approximately 10% when a quadratic regression analysis is implemented. Depths are calculated with adequate accuracy up to 30 m.  
Finally, the bathymetries extracted from each class were merged to create the total bathymetric model for the area of interest (Figure 9). For validation purposes, the HBT results were compared with the bathymetry derived from the ratio transformation.