## 4 Results
### Test Case 1: Kingwood Area  
The first case study contains an area in the north-west of Lake Houston. This includes the Kingwood area, where more than 3000 houses were damaged during Harvey (2017). This area was imaged by S-1 with both acquisition modes, SM and IW. In Figure 4a,b, we show the SAR intensity as a red, green and blue (RGB) composite of the reference (R) and flood (B = G) images. From this data set, we can clearly see (in red) all changes due to the flooding on bare soil, as the appearance of floodwater led to a decrease of the backscattering. We can also see some changes within built-up areas, which are depicted in cyan. The related backscatter increase is arguably caused by an increase in the double-bounce effect in areas where buildings are surrounded by water. However, since this effect is strongly dependent on the alignment of buildings with respect to the SAR flight line, its usage for identifying flooded buildings remains rather limited. To overcome this limitation and the ambiguity of the intensity signature, we make use of the information given by \(\rho\). Figure 4c,d illustrate the multi-temporal behavior of \(\rho\) over the same area, with an RGB composite (\(\rho_{\text{pre}}\) = R, \(\rho_{\text{co}}\) = B = G) layer. Focusing our analysis on the built-up areas, we notice a significant change in the \(\rho\) values for both IW and SM. Before the flooding occurs, \(\rho\) usually presents high values due to the temporal stability of buildings. However, in the event of floodwater appearance, this characteristic is no longer apparent and \(\rho\) drops off significantly, resulting in the condition \(\rho_{\text{pre}}>\rho_{\text{co}}\), as depicted by areas in red color. Since other land classes, such as vegetation areas, exhibit similar behavior (note that red areas are spread all over the scene and have an overall big extension), the information given by \(\rho\) cannot be used in isolation to identify flooded buildings. For this reason, we make use of the building footprint presented in Section 2.2. This layer is intersected with the areas that show a decrease of \(\rho\) to identify flooded buildings. The first case study contains an area to the north-west of the lake. The results obtained are given in Figure 4g,h and depicted in dark blue. Most buildings, labeled as 'flooded' by the algorithm, are identified in both IW and SM images. Figure 4e illustrates the Digital Globe VHR imagery along with the crowdsourcing points depicting damaged/flooded areas. The coherence-based algorithm detects most of the flooded buildings and appends them to the flooded bare soil areas identified by the initial step of the procedure (see Figure 1). For example, this is the case of some houses located in the proximity of the lake border. As shown in the AOIs 2 and 3, in the areas containing many Digital Globe labels, our methodology detects a significant amount of flooded buildings. Moreover, the results of the proposed method present some additional flooded built-up areas with respect to crowdsourcing points. For instance, as depicted in AOI 1 from Figure 4e, we notice that this area does not contain any Digital Globe labels. However, our method detects flooded buildings, as shown in AOI 1 from both IW and SM images (Figure 4g,h). The latter are confirmed by aerial pictures taken over the respective areas on August 30, some examples being given in Figure 5. The apparent misdetection of crowdsourcing is due to the fact that Digital Globe imagery was acquired 24 h after the S-1 IW image acquisition, and 36 h after the S-1 SM one. If we compare our results with damaged and affected built-up areas extracted from the FEMA inundation model (Figure 4f), there is a good agreement between the two datasets. In particular, when looking at AOIs 1 and 2 in our maps (Figure 4g,h) we notice that flooded buildings largely correspond to FEMA results from Figure 4f. Moreover, as mentioned above, for AOI 1, the presence of floodwater is confirmed by aerial photos taken on August 30 (see Figure 5).