## 3 Methodology
### Extraction of Flood Coverage  
After the pre-processing was completed, water was extracted using our proposed automatic thresholding method. It consists of the following four main steps. First, the 30 m cDSWE was aggregated to 20 km grids. Particularly, the proportion of water area within each 20 km grid was calculated using the cDSWE with 30 m-resolution. Then, stratified sampling was used to randomly select three grids in three classifications (high \(>\) 66%; medium, 33-66%; low, 0-33%, respectively). A total of nine grids for the three classes were chosen for calculating the thresholds (Figure A2).  
Second, the cDSWE was used to determine the histogram type and the threshold value. According to the probability of water area calculated by cDSWE, water was classified into three classes--persistent water, persistent land, and partial (water: 45-100%; land: 1-20%; partial: 21-44%)--and the percentage of each class (\(N_{W}\), \(N_{L}\), \(N_{P}\)) was calculated at the same time. In an image with some small water bodies (inland watersheds with few lakes) or little land coverage, the histogram showed unimodally (\(N_{P}\leq\alpha N_{W}+\beta N_{L}\)); when the proportion of land to water was close, the histogram showed bimodally (\(N_{P}>\alpha N_{W}+\beta N_{L}\)) (Figure 4). The relationship between the water body probability and the histogram type was obtained by determining the value of \(\alpha,\beta\). The histogram was unimodal because of the large difference between the area of the water body and the land in the image, so we further classified the unimodal histogram into two situations (\(N_{W}>N_{L}\) and \(N_{W}<N_{L}\)). Thus, the threshold value was automatically calculated; the specific formula of the threshold for each 20 km grid (T) was as follows:  
\[\text{T}=\left\{\begin{array}{cc}H_{valley},N_{P}>\alpha N_{W}+\beta N_{L}\\ \mu+3\sigma,N_{P}\leq\alpha N_{W}+\beta N_{L}\,\ N_{W}>N_{L}\\ \mu-3\sigma,N_{P}\leq\alpha N_{W}+\beta N_{L}\,\ N_{W}<N_{L}\end{array}\right. \tag{2}\]  
\(N_{W},N_{L},N_{P}\) are the proportion of water, land, and partial, respectively; \(H_{valley}\) is the valley of the histogram; \(\alpha,\beta\) are adjustable factors; and \(\mu\), \(\sigma\) are the mean and variance, respectively.  
Next, the thresholds in three bands (\(T_{VV}\), \(T_{VH}\), \(T_{VVVH}\)) were determined using the threshold calculated with Formula (2) using each selected grid (\(T_{VVi}\), \(T_{VHi}\), \(T_{VVVHi}\)), with the following equation:  
Figure 3: The pre-processing process for Sentinel-1 data. (**a**) Location of the study area, (**b**) original image, (**c**) pre-processed images.  
\[\left\{\begin{array}{l}T_{VV}>mean(T_{VVi})\\ T_{VH}>mean(T_{VHi})\\ T_{VVVH}>max(T_{VVVHi})\end{array}\right. \tag{3}\]  
\(T_{VV}\), \(T_{VH}\), \(T_{VVVH}\) denote the threshold values of the \(VV\), \(VH\), and \(VVVH\) bands, respectively, while \(T_{VVi}\), \(T_{VHi}\), \(T_{VVVHi}\) are the thresholds of the selected nine grids.  
The morphological opening using a 3 \(\times\) 3 square structuring element was used to eliminate noise and fragmented water, and then spliced into \(1^{\circ}\times 1^{\circ}\) tiles according to the selected date. The output product was in the form of a GeoTIFF without geographic projection, and the resolution was approximately 25 m in the mid-latitude area.  
Finally, the persistent open-water extent obtained in Section 3.1, and the results obtained in the above steps, were superimposed to calculate the inundation area:  
\[R_{I}=R_{W}-R_{P} \tag{4}\]  
\(R_{\text{IV}}\) is the water extracted from images and \(R_{P}\) is the range of the persistent open-water extent.