## 3 Methodology  
### Surface Water Information from the Sentinel-1 SAR Images  
Flat water surfaces act like mirrors and reflect almost all incoming energy in the specular direction, thus providing very low backscatter. With this physical principle, detection of surface water is often based, at least partly, on the application of a threshold on the SAR backscatter coefficient, with the low backscatter values attributed to water bodies [6; 7; 16; 17]. However, SAR backscatter coefficients over water surfaces are also affected by several mechanisms related to the interaction of the signal with vegetation or with possible surface roughness. The backscattered signals over flooded vegetation in wetlands can be enhanced due to the double-bounce scattering mechanism [26; 27; 28]. On the other side, the backscatter coefficients can be affected by vegetation canopy (e.g., rice) above the water surfaces due to volume scattering from the plant components (stems or leaves) [29]. The backscatter coefficients (especially the VV polarization) can also be influenced by the wind-induced surface roughness over open water [17; 30]. Finally, there might be ambiguities between surface water and other very flat surfaces (such as arid regions), that could provide very similar backscatter signatures [31].  
Based on a reference water mask derived from Landsat-8 NDVI, Figure 3 presents the histograms of the backscatter coefficients for VH and VV polarizations, separately for water and non-water pixels over the incidence angle range of 30\({}^{\circ}\)-45\({}^{\circ}\) for the area shown in Figure 2. For both polarizations, the water and non-water histograms are rather well separated, with thresholds of \(-22\) dB and \(-15\) dB for the VH and VV polarizations, respectively. Using these thresholds, the surface water has been classified separately for each polarization. The classification derived from the VH polarized image had a stronger spatial linear correlation with the reference water mask than the one derived from the VV polarized image (72% compared to 62%), confirming a higher sensitivity of the VH polarization to the presence of surface water [19]. Using both polarizations for the classification increased the correlation (76%), confirming that the two polarizations carry different information and that using both of them increases the retrieval accuracy. These findings confirmed the study by [32] where water detection with VV polarization was further refined using multiple-polarization.  
Figure 3: For surface water delineated with Landsat-8, histograms of the water and non-water pixels for the SAR backscatter coefficients in VH and VV polarizations for the area shown in Figure 2 (over the incidence angle range of 30\({}^{\circ}\) to 45\({}^{\circ}\)).  
The effect of the backscatter incidence angle is also tested here. For a collection of pixels located over water (rivers, reservoirs, or lakes), the backscatter coefficient is plotted as a function of the incidence angle between \(30^{\circ}\) and \(45^{\circ}\) (Figure 4). Similar negative correlations between incidence angle and backscatter coefficients can also be found in [13] with ASAR data over water bodies (from \(\sim\)\(-5\) dB at \(20^{\circ}\) to \(\sim\)\(-20\) dB at \(45^{\circ}\) of incidence angle).  
As a conclusion, the SAR backscatter coefficients (VH and VV polarizations) are both sensitive to the presence of water, but with slightly different sensitivities. The effect of the incidence angle, although rather limited within the \(29^{\circ}\)-\(46^{\circ}\) range of Sentinel-1 SAR, has to be accounted for if a high detection accuracy is required. Simple tests on thresholding techniques illustrated the limitations of these approaches and here we suggest developing a new scheme to delineate the surface water based on Neural Networks.  
The temporal dynamics of the backscatter coefficients can also be a source of information and can help disentangle the influence of the other surface parameters [13]. However, this temporal information will not be investigated here.