## 2 Materials, Methods, and Discussion
### Topographic Constraints  
The visibility of the landmass to the radar satellite sensor depends on the orientation of the employed satellite line-of-sight (LOS) and radar acquisition geometry with respect to that of the imaged terrain. Visibility varies within different portions of the same Sentinel-1 IW scene depending on local terrain slope (\(\beta\)) and aspect (\(\alpha\)), local incident angle (\(\theta\)), which varies between 29.1\({}^{\circ}\) and 46\({}^{\circ}\) from the near to the far range and is \(\sim\)37.5\({}^{\circ}\) at scene centre, and the satellite heading angle (\(\gamma\)), which is 9.1\({}^{\circ}\) on average at the latitudes of Great Britain. We extract the terrain slope and aspect from the Shuttle Radar Topography Mission (SRTM) digital surface model (DSM) at 90 m resolution which--in terms of spatial resolution--is the closest one to the Sentinel-1 ground range resolution after multi-looking using the factors of 22 and 5 in range and azimuth, respectively, as adopted by [28]. Figure 4: Sentinel-1 IW image availability over path 30 for Doncaster during the period between January and October 2016. Depending on their effects, range geometrical distortions can be classified as foreshortening, layover (Lv), and shadow (Sh) (e.g., [29; 30]). Their presence hampers the application of both interferometric and non-interferometric techniques (e.g., [31]). A priori identification of these distortions is, therefore, essential to plan InSAR analyses, especially over the foreslope of hilly and mountainous regions where the assessment of the most suitable LOS geometry ensures that the target area is visible prior to the acquisition of long SAR imagery stacks. To identify Sentinel-1 IW geometrical distortions in the ascending and descending acquisition modes in Great Britain, we calculated the R-Index (RI) [10; 32]:  
\[\text{RI}=\sin\left[\theta-\beta\times\sin\left(\text{A}\right)\right] \tag{1}\]  
where A is the aspect correction factor, which is computed as A = \(\alpha-\gamma\) for descending mode data, and A = \(\alpha+\gamma+180^{\circ}\) for ascending mode data. Essentially RI, represents the ratio between the pixel size in slant and ground range geometry and its values range between \(-1\) and \(+1\). Areas of foreshortening show RI above 0 and up to \(\sin\left(\theta\right)\). The latter represents the specific threshold to discriminate foreshortening from good visibility regions, and is identified as RI\({}_{0}\)[10]. Radar layover affects slopes facing the sensor, where \(\theta<\beta\) and, therefore, RI takes on negative values between 0 and \(-1\), whilst shadow occurs when slopes facing away from the sensor are characterised by \(\beta\geq 90^{\circ}-\theta\). Since passive layover (Lv) and shadow (Sh) cannot be discriminated on backslopes by using the sole R-Index, Lv and Sh are separately calculated by using the formula from [32], and eventually masked out to obtain the visibility map by multiplying the RI by a reclassified binary map where pixels take on values of 0 and 1 where Lv or Sh occur and do not, respectively, as follows:  
\[\text{Visibility}=\text{RI}\times\text{Lv}\times\text{Sh} \tag{2}\]  
The total areas of shadow within Great Britain were found to be as small as 9.6 km\({}^{2}\) in ascending, and 8.8 km\({}^{2}\) in descending, mode due to the presence of very few areas characterised by slopes steeper than 52.5\({}^{\circ}\) (Figure 5). Total areas of layover (including active and passive) are 8805 km\({}^{2}\) in ascending and 7939 km\({}^{2}\) in descending mode (Figure 5). Of these, 10.5 km\({}^{2}\) in ascending and 11.2 km\({}^{2}\) in descending mode are active layover regions, which were determined as a subset of total layover, by considering DSM pixels showing R between \(-1\) and 0. Total extension of layover and shadow distortions for the landmass is \(\sim\)1.0% in each imaging mode (Figure 6).