# A Tool for Pre-Operational Daily Mapping of Floods and Permanent Water Using Sentinel-1 Data
## 3 Methods
### The Floodwater/Permanent Water Mapping Algorithm
#### 3.2.3 Discrimination between Open Floodwater and Permanent Water  
To identify floodwater, the BFE approach is applied to the difference image, i.e., to the map of \(\Delta\sigma_{VV}^{0}=\sigma_{VV}^{0}\left(t_{2}\right)-\sigma_{VV}^{0}(t_{1})\), as schematized in the right panel of Figure 7. In this case, the objects belonging to the cluster presenting the lowest median of the values of \(\Delta\sigma_{VV}^{0}\) are selected and labelled as the clustering-derived flooded area (CDFA). The latter is then modified to include only the objects that contain open water according to the classification applied to \(\sigma_{VV}^{0}(t_{2})\), but do not contain permanent water bodies according to the reference water mask. In this way the modified clustering-derived flooded area (MCDFA) likely contains only flooded pixels, i.e., pixels whose backscattering coefficient significantly decreased with respect to that measured at time \(t_{1}\). The Roberts filter is then applied to detect the floodwater-land edge and two buffer zones are created around the edge to select a set of pixels exhibiting a bimodal histogram of the \(\Delta\sigma_{VV}^{0}\) values. For the same example considered in Figure 8, Figure 10 shows the floodwater-land edge and the buffer zones created around it.  
A GMM has been assumed for the distribution of flooded and non-flooded pixels in the difference image (even the distribution of the log-ratio SAR image is expected to follow the Gaussian model [24]). For the population of pixels included in the two buffer zones, the bimodality test is performed in a similar way to that described in the previous paragraph. If the bimodality check is passed, a threshold value (_ThUtsu_,_f_) is computed through the [PERSON]'s method. Then, the following relationships are used to derive the seed region and the tolerance:  
\[i\in\textit{seed region}\implies\Delta\sigma_{VV}^{0}(i)<\Delta\sigma_{VV\_ seed}^{0}=0.5\cdot\left(Th_{\textit{Otsu\_f}}+\mu_{f}\right) \tag{3}\]  
\[\Delta\sigma_{VV\_Tolerance}^{0}=\left(\mu_{f}+2s_{f}\right) \tag{4}\]  
where \(\mu_{f}\) and \(s_{f}\) are the mean value and standard deviation of the Gaussian distribution fitting the histogram of the \(\Delta\sigma_{VV}^{0}\) values of the pixels in the buffer zone included in the MCDFA. Through Equations (3) and (4), the thresholding-derived flooded area (TDFA) is identified.  
Figure 10: Same as Figure 8c, but with superimposed the land-floodwater edge (yellow), the buffer zone included in the MCDFA (cyan) and the buffer zone included neither in the MCDFA, nor in the CDFA (green).  
The original CDFA and the TDFA are combined to obtain the map of flooded pixels based on the following scheme:  
* pixels belonging to both the CDFA and the TDFA are assigned to the class of flooded pixels;
* pixels belonging only to the TDFA are assigned to the class of flooded pixels if they are located in a buffer zone of buffering distance 1 km created around the flooded area determined according to previous point.  
The outputs of the two BFE procedures are finally combined to perform the discrimination between open floodwater and permanent water (final classification box in Figure 7). The following scheme is used by AUTOWADE:  
* pixels belonging to class of open water are finally classified as open floodwater if they also belong to the class of flooded pixels, or if they have been classified as open floodwater at time \(t_{1}\) (old map, see Figure 7);
* pixels belonging to class of open water are finally classified as permanent water if they also belong to the reference water mask, or if they are adjacent to the reference water mask and do not belong to the class of flooded pixels, or if they have been classified as permanent water at time \(t_{1}\) (old map at the bottom of Figure 7).  
All the flooded pixels grouped in patches smaller than 20,000 m\({}^{2}\) (50 pixels) are filtered out, thus assuming 20,000 m\({}^{2}\) as minimum mapping unit. Obviously, pixels comprised in the exclusion mask cannot be classified as open floodwater or permanent water.