## 2 Assumptions and Methods
### Building Detection  
To extract the double-bounce objects, we use an approach developed for mapping buildings at the global scale by means of S-1 data and proposed by [PERSON] et al. (2016). It is based on a hierarchical split-based approach described in [PERSON] et al. (2016). In the following paragraph, only the main underlying principles are summarized, and we refer to the relevant bibliography for details. The method in [PERSON] et al. (2016) is based on the fact that in the co-polarization channel, buildings are characterized by a high backscattering, as well a high degree of correlation in time between images. To increase the potential for detecting buildings when the LoS is not orthogonal to the building facade, cross-polarization backscattering is also used, as it rises when rotated dihedrals are present ([PERSON] et al., 2016). High backscattering values can also occur in the case of vegetation. In the cross-polarization channel, the high backscattering values rise when the volumetric scattering is dominant, while in the co-polarization channel, high vegetation backscatter is associated with the increase of double-bounce, e.g., when water beneath vegetation is present, as exemplified by [PERSON] et al. (2016) for rice fields. To cope with false alarms generated by vegetated areas, the algorithm exploits \(\rho\). Indeed, \(\rho\) has a contrasting behavior in vegetated and built-up areas, respectively, as buildings are stable structures, unlike vegetation. Another risk of a false alarm is caused by the layover in mountainous areas. By means of a DEM and the geometry of the SAR acquisition, the local incidence angle (LIA) is computed and the layover areas are masked out ([PERSON] et al., 2016). The algorithm is composed of two steps: (i) discrimination of bright pixels in co- and cross-polarization channels, making use of a statistical modeling-based adaptive thresholding approach; (ii) removal of false alarms by using \(\rho\) and the LIA. When handling SAR data, it is worth emphasizing the importance of accounting for speckle noise that is known to hamper, in general, a straightforward image classification when only using backscatter values on a pixel basis. In [PERSON] et al. (2016) a temporal averaging is adopted, by exploiting  
Figure 1: Block diagram of the floodwater mapping algorithm, which is composed of different elements: bare soil floodwater mapping (light blue), urban area floodwater mapping (dark blue) and building detection (red). the availability of the S-1 temporal series with a frequency of up to 6 days. The temporal average is performed on a stack of images from the same orbit and acquired at different times. Its main advantage is that, contrary to the multi-looking and textural approaches that decrease the spatial resolution, the speckle is reduced without decreasing resolution. Considering that we are interested in classifying a temporally coherent target, i.e., buildings, this type of approach is sensible. The algorithm generates building maps at the highest possible resolution, i.e., that of the sensor, with a temporal resolution of a few months. Similarly, \(\rho\) values extracted from the successive interferometric image pairs are averaged to obtain the temporal average coherence, TACvv, which is used to mask out bright vegetation. In summary, the following steps constitute the overall procedure:  
1. Generate the temporal average intensity (TAI) using 12 different images of the co- and cross-polarization backscattering (TAI\({}_{\text{VV}}\) and TAI\({}_{\text{VH}}\)) and the TAC\({}_{\text{VV}}\) separately;
2. Remove layover areas using LIA;
3. Identify the bright pixels from TAI\({}_{\text{VV}}\) and TAI\({}_{\text{VH}}\) that are representative of buildings by making use of a hierarchical split-based approach (HSBA, Chini el. [16]);
4. Filter false alarms from the built-up area maps by considering only TAC\({}_{\text{VV}}\) above a threshold;
5. Merge the two built-up area maps corresponding to TAI\({}_{\text{VV}}\) and TAI\({}_{\text{VH}}\) using a logical OR function.