## 2 Materials and Methods
### Study Events and Data Sets  
Four different SAR images of two different flood events were studied. The locations of the three study sites in southern Britain (Wraysbury, Staines, and Tewkesbury) are shown in Figure 2[42]. The sites were chosen because they were subject to recent urban flood events for which VHR SAR, LiDAR, and independent validation data were available. Wraysbury is a village on the Thames, west of London; Staines is a town on the Thames nearer Londonwith a higher housing density, and Tewkesbury is a market town on the Severn and Avon in the west of England. As stated in [PERSON] et al. (2018) [PERSON] et al. (2018), \"The first two examples are based on the Thames flood of February 2014 in West London, which caused substantial urban flooding ([PERSON] et al., 2018). In January and February 2014, heavy and persistent rainfall left large parts of southern England under water. The flooding resulted from a long series of Atlantic depressions caused by the jet stream being further south than usual. The peak of the flooding in West London occurred around 11 February 2014, with peak flow being 404 m\({}^{3}\)/s. A substantial amount of urban flooding occurred in a number of towns, in particular Wraysbury and Staines. Three COSMO-SkyMed (CSK) (X-band) 2.5 m resolution Stripmap images of the flooding were acquired covering the flooded areas. Their processing level was GTC (Level 1D). A limited number of aerial photos acquired by the press were available to validate the SAR flood extents. These tended to cover small areas with substantial flooding. An example aerial photo showing flooding in Wraysbury is shown in Figure 3a, together with the SAR subimage for 12 February 2014 covering the area (Figure 3b). No high resolution visible band satellite (e.g., WorldView-2) data with low cloud cover were available for validation. The data acquired for the Thames flood were -  
1. a sequence of 3 CSK images showing flooding in the Wraysbury area on 12, 13 and 14 February 2014 just after the flood peak. 2. a sequence of 2 CSK images on 13 and 14 February 2014 also showing flooding in Staines, where on 13 February the flow was still only 5% less than the peak. A contemporaneous aerial photo for validation was acquired showing flooding in Blackett Close, Staines. Figure 2: Locations of the 3 study sites in southern England, at Wraysbury (51.5\({}^{\circ}\) N, 0.6\({}^{\circ}\) W), Staines (51.4\({}^{\circ}\) N, 0.5\({}^{\circ}\) W) and Tewkesbury (52\({}^{\circ}\) N, 2.2\({}^{\circ}\) W) (main rivers in blue). The third example was based upon the \(>\)1-in-100-year flood (AEP \(<\) 1.0%) that took place on the lower Severn around Tewkesbury in July 2007 [54]. This resulted in substantial flooding of urban and rural areas, about 1500 homes in Tewkesbury being flooded. Tewkesbury lies at the confluence of the Severn, flowing in from the northwest, and the Avon, flowing in from the northeast. The peak of the flood occurred on 22 July, and the river did not return to bankfull until 31 July. On 25 July, TerraSAR-X (TSX) (X-band) acquired a 3 m resolution StripMap image of the region in which urban flooding was visible. The image was multi-look ground range spatially enhanced [39]. Aerial photos of the flooding were acquired on 24 and 27 July, and these were used to validate the flood extent extracted from the TerraSAR-X image [39].\" The Tewkesbury event is included as a test of how well the FRP method performs at river confluences. Traditional flood risk management methods have typically sidestepped the issue of tributary dependence by focusing on modelling the T-year flow using a single water course. However, at river confluences, it is difficult to define a single event that will be exceeded once every T years, due to the multiple possible combinations of flow magnitude and timing on the tributaries [55]. Table 1 gives the parameters of the SAR images considered in the study.