## 2 Assumptions and Methods  
The VHR SAR missions such as CSK and TSX gave an important boost to the identification of floods in urban environments. The increased resolution of SAR X-band sensors up to one meter allows the identification of different scattering mechanisms that are characteristic of a building, enabling to isolate the one that can provide most useful information about the presence or not of water, i.e., the double-bounce. The double-bounce is due to the dihedral reflector composed of the building facade and its surrounding ground area. At metric resolution, it produces a very bright line that appears on the side of the wall that is illuminated by the radar [35]. It is worth mentioning that the length of the double-bounce path is equal to the slant range of the intersection between the ground and the front wall of the building. Even if the building is surrounded by asphalt surfaces that are as smooth as water surfaces, the increase of reflectivity due to the high dielectric constant of the water implies a considerable increase of the double-bounce return. Therefore, TSX images (3 m resolution) were used in conjunction with a high-resolution light detection and ranging (LiDAR) height map of the urban area [19]. The position of the double-bounce areas was first extracted using a SAR simulator. Then, the predictions from an electromagnetic scattering model were compared to radar observations of double-bounce backscattering enhancement to detect floodwater [19]. The increase of the double-bounce backscatter is mainly related to the geometric arrangement of the SAR line of sight (LoS) and the building facade. The increase of the backscatter is high when the LoS is orthogonal to the horizontal alignment of the building facade, while it rapidly decreases moving away from the orthogonal direction. The SAR LoS that is unfavorable with respect to the building facade was highlighted in [PERSON] et al. [22] as a possible source of under-detection when relying only on SAR intensity. In [PERSON] et al. [21], a decrease of \(\rho\) was observed using VHR CSK X-band images of the flood event caused by the tsunami that hit Japan on 2011. This was tentatively associated with the presence of standing water. [PERSON] et al. [22] further developed the idea using a flood event that occurred in Italy in 2014 and introduced \(\rho\) as a solution to enable the detection of water in the areas that include such double-bounce objects. The method relayed on VHR CSK data and demonstrated its capability to significantly reduce the under-detection committed when only SAR intensity images were used. The rationale is that an urban settlement is a very steady target characterized by high \(\rho\), even at large temporal baselines, and the appearance of floodwater implies a significant decrease of the coherence between pairs of VHR images. For lower resolution SAR data, \(\rho\) has not yet been considered. This may be due to the lower repeat cycle of past satellites and the high temporal baseline between acquisitions. This is an important factor for decreasing \(\rho\), especially at lower spatial resolution. In fact, in addition to the double-bounce effect, other scattering mechanisms from different land cover classes (e.g., vegetation) may occur within an individual pixel. Moreover, the spatial baseline can also cause a decrease of \(\rho\) with the increase of its perpendicular component [36]. Indeed, the SAR spatial resolution plays an important role on the paradigm definition of how buildings are represented, what urban areas look like and consequently how changes can be detected. In VHR images, the double-bounce can be identified as the only contribution in a pixel, while in medium resolution images it can be mixed with contributions from other target categories. In the latter case, the other scattering mechanisms that take place can mask the double-bounce, thus attenuating its main characteristics, i.e., the coherence in time and the high-intensity value.