## 5 Discussion  
The presence of water has been confirmed by an independent dataset in some of the urban areas mapped as flooded. To extend the analysis we further evaluate possible sources of errors of the proposed algorithm. For any procedure based on complex coherence, major errors are generally due to spatial and temporal decorrelations. The latter can be particularly critical for the case study analyzed in this paper because of the presence of vegetation within a cell and the possible occurrence of strong anthropic activities. Intense traffic conditions found in a big city such as Houston might, in  
Figure 7: Case study 3: (**a**) Intensity RGB composite, IW (R = 24 August 2017, B = G = 30 August 2017) (**b**) \(\rho\) IW, RGB composite (R = \(\rho_{\text{pre}}\), B = G = \(\rho_{\text{co}}\)). (**c**) Digital Globe VHR imagery & crowdsourcing points of flooded buildings. (**d**) Initial FEMA model assessment (the model classifies Destroyed, Major damage, Minor damage, Affected by floods from dark red to light rose) [44]. (**e**) IW: flooded buildings (dark blue), flooded bare soil (light blue), non-flooded building footprint (red), other non-flooded land cover classes (white). theory, lead to false alarms because they potentially imply a decrease in the InSAR coherence. Even the presence of debris can cause decorrelation in an event such as that which occurred in Houston in 2017. To compare the effect of the aforementioned sources of decorrelation with the effect of the presence of floodwater, several \(\rho\) maps, with different temporal and spatial baselines, were extracted and their mean values for the urban areas classified, respectively, as Flooded (F) and Non-Flooded (NF), were computed. This analysis was carried out for the most challenging dataset, i.e., the IW images, with the lowest spatial resolution for which the presence of vegetation can play a predominant role. The \(\rho\) maps were computed considering four different configurations with respect to the flooded image (30 August 2017):  
* \(\rho_{\text{pre}}\): both images were acquired before 30 August 2017. * \(\rho_{\text{post}}\): both images were acquired after 30 August 2017. * \(\rho_{\text{co}}\): one image was acquired before 30 August 2017 (the closest one) and one during the event (30 August 2017). * \(\rho_{\text{cross}}\): one image was acquired before and one after 30 August 2017. They were computed with same pre-event image as \(\rho_{\text{co}}\), and with three post-event images acquired 6, 12 and 18 days after the flooded image (30 August 2017). We averaged the above-mentioned \(\rho\) maps for F and NF classes to obtain eight different trends with respect to the perpendicular and temporal baseline, as summarized in Figure 8.  
From the graphs in Figure 8, we notice that, as expected, the lowest coherence value is obtained for F \(\rho_{\text{co}}\), where \(\rho\) reaches 0.25. This value is very close to that of open water (\(\rho_{\text{water}}=0.1\)), which is generally considered a completely decorrelated class [49]. Although \(\rho_{\text{co}}\) has the lowest temporal baseline, i.e., 6 days, from both graphs it is evident that F areas can be easily distinguished from the NF ones independently of the temporal and perpendicular baselines. Looking at the two scatterplots in Figure 8, it is clear that there is not any dependence of the InSAR coherence from the perpendicular baseline for the eight different classes, at least in the range of 0 to 90 m, while the temporal baseline is the one that affects the coherence the most, also in urban areas. From the scatterplot in Figure 8a, it is evident that the maps not affected by floods with the highest temporal baselines have lower coherence values. It is worth considering that the residential areas containing vegetation and houses are usually small in size. Hence, in 20 m resolution pixels, although the double-bounce can be detected, the influence of other scattering mechanisms is also present.