## 3 Test Case and Dataset
As described in Section 2.2, we make use of the S-1 multi-temporal intensity and \(\rho\) series to generate the building maps from SAR S-1 data. For this purpose, a stack of 12 SAR images acquired between August 2016 and August 2017 (one per month) is used to derive TAI and TAC for both the IW and SM modes. An example of the TAI images for both IW and SM are shown in Figure 3a,b. During a flood event, it is not straightforward to get reliable and independent validation to assess the results of the classification. When available, VHR optical images are used, but clouds, building shadows and time delay between acquisitions often hamper consistent and meaningful comparisons. Hence, there is a necessity to gather as much information as possible from multiple data sources. To evaluate the final inundation map, we use information about the flooded buildings extracted from different data sources, namely VHR optical images, numerical models, and aerial photographs. Given the heterogeneous data and spatially discontinuous nature of the validation dataset available, a comprehensive and quantitative large-scale comparison between SAR-based products and reference data is difficult. For these reasons, we opt here for local qualitative comparisons of SAR-based floodwater maps with independent data, as they became available. On 31 August 2017, just one day after the S-1 acquisitions, a GeoEye-1 image was acquired over Houston and was made available immediately thanks to Digital Globe's Open data program. Thanks to reduced cloud coverage at the acquisition time, the image clearly shows the massive flooding in and around Houston. In addition to GeoEye-1 images, Digital Globe's Tomnod crowdsourcing team has labeled the location of damages over the city of Houston through photointerpretation, providing pointwise and independent interpretation of these images. By 31 August 2017, a total of 21,600 points had been labeled as flooded/damaged houses, flooded/damaged roads, blocked bridges, and trash heaps. Here we make use of the flooded/damaged houses points representing more than 50% of the total labels, i.e., 12,000 points, to cross-validate our results. Concerning the flood information from models, we use the results provided by the inundation model of the Federal Emergency Management Agency (FEMA) [45], available on the Internet [46]. FEMA runs inundation models immediately after a storm to provide a rapid damage assessment within days from the event. Inundation models typically feed predicted or observed rainfall amounts into standard hydrological models to calculate where the water flows along major streams. This information is overlaid with data on built structures to estimate which structures are exposed and may be damaged along the modeled streams. The damage modeling is based on parcel data and actually measured coastal and river flood gauge levels but does not account for damage that may have been caused by wind or leveee breaks, nor does it take into account that structures on a property may be elevated [46]. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Flood Image Acquisition** & \multicolumn{2}{c}{**Reference Image**} & \multirow{2}{*}{**S-1 Mode**} & \multirow{2}{*}{**Polarization**} & \multirow{2}{*}{**Resolution (m)**} \\
**Time [UTC]** & & & & & \\ \hline
2017-08-30T12:22:03 & 2017-08-24T12:22:48 & IW & VV & 20 \\
2017-08-30T00:17:40 & 2017-08-18T00:18:03 & SM & HH & 5 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: SAR Intensity images used for delineating bare soil flooded areas.