# A Hybrid Bio-Optical Transformation for Satellite Bathymetry Modeling Using Sentinel-2 Imagery
## 2 Materials and Methods
### Methodology--Model Development
#### 2.3.3 Band Ratio Methodology  
The next phase of model analysis consisted of identifying the relationship between the bio-optical parameters and sea-bottom reflectance. To examine this, tests were carried out using various spectral band ratios. Previous research [20; 21] confirmed that the ratio between two spectral bands allows for more stable depth results when extracting bathymetry in coastal areas with variations in bottom albedo. In the present study, we adopted the ratio algorithm technique as shown in Equation (6), with an innovation, since initial tests indicated that it is rather difficult to estimate the exact value for the factor \(n\):  
\[z=m_{1}*\frac{\ln(n*R_{i})}{\ln\left(n*R_{j}\right)}-m_{o} \tag{6}\]  
where, \(z\) is the water depth, \(R_{i}\) and \(R_{j}\) are the reflectances of bands \(i\) (blue) and \(j\) (green), \(m_{1}\) is a constant for scaling the ratio to depth, and \(m_{o}\) is the offset for \(z=0\). The \(n\)-factor usually takes a fixed value between 500 and 10,000, ensuring that the logarithm remains positive under any seabed texture, and results in a linear correlation between ratio bands and field data. Consequently, all the possible  
Figure 5: Areas used for implementing the water column correction technique. band combinations or band ratio schemes were examined in order to estimate which one provided the best correlation to field data or--in our case--to depths derived from a nautical chart. Initial tests using ratio transformation (Equation (6)) indicated that the best results for Sentinel-2A (BOA reflectance) were obtained when implementing the ratio (Equation (7)) between the sunlight-corrected blue (_Degl_B2_) and green bands (_Degl_B3_):  
\[x=\ln\left(\frac{Degl\_B2}{Degl\_B3}\right) \tag{7}\]  
where \(x\) is the unknown term of the regression equation (Figure 7). Figure 6: The Sentinel-2A Water column corrected image (right) and the sunlight-corrected (deglinted) image (left) within the central part of the study area (see also Figure 1). Figure 7: Regression analysis in the study area between chart depths (shown onto the left panel as red dot () symbols) and the logarithm of the ratio between the sunlight-corrected blue and green bands of Sentinel-2A. An initial test was undertaken to assess the robustness of the band correlation between chart depths and the logarithmic ratio of Equation (7). For this reason, a set of training depths was selected, comprising 28 points depicted on the Greek chart no. 423/2, with depths ranging between 0.4 and 41.0 m. The ratio of Equation (7) was implemented along with regression analysis and the relevant curve fitting to provide the corresponding determination coefficient values (R\({}^{2}\)), obtaining values of 0.78 for linear, 0.84 for quadratic, and 0.85 for cubic fit (Figure 7). The chart depths refer to a variety of seabed textures and depth ranges, since the training depths were chosen arbitrarily from different seabed textures; nevertheless, the above test revealed that there is a good correlation between Sentinel-2A imagery and chart depths. Based on these results, we further investigated the effects of inherent (IOPs) and apparent optical parameters (AOPs) on depth modelling. In particular, we examined how it is possible to improve the outcome bathymetry of the ratio algorithm from data taken solely by spaceborne sensors, and using the IOPS and AOPs of coastal waters. Further trials showed that close to the coastline the remote sensing reflectance of B3 (i.e., \(R_{rs}\)(B3) green band) is greater than the equivalent reflectance of B2 (blue band) and B4 (red band). This fact revealed the existence of subsurface meadows at depths of approximately 0-8 m, which mainly consist of species such as _Posidonia oceanica_ and _Cymodcea nodosa_, the latter being characteristic species of the marine flora in the study area [22].