# A New Method for Large-Scale Landslide Classification from Satellite Radar
## 2 Materials and Methods
### Theory: Landslide Detection with SAR
#### 2.1.4 Sibling-Based Coherence Method  
The new method we have developed is outlined in Figure 5. As with the ARIA method, the aim is to produce an expected landslide-free coherence surface, which is subtracted from the co-event coherence map. However, where [PERSON] et al. [21; 39] subtract a pre-event coherence map, we subtract a co-event coherence map that is calculated in such a way as to be less sensitive to localised decreases in coherence such as landslides. Unlike the ARIA method, the new method is not based on the change in coherence through time and so is expected to have fewer false positives caused by variations in temporal coherence unrelated to landsl. As an alternative to the boxcar coherence described in Section 2.1 and used in the absolute and ARIA methods, SAR coherence can be calculated based on ensembles of'sibling' pixels, which exhibit similar behaviour to the target pixel, e.g., [42; 43; 44]. Here, we use the RapidSAR algorithm of [PERSON] [44] for this process. For every pixel, a search is performed within a window of a given size, centred on that pixel, for pixels behaving similarly in terms of amplitude and amplitude variability throughout a time series of pre-event imagery. These pixels are designated as'siblings'. The sibling ensemble of each pixel is then used in place of the boxcar of adjacent pixels in the summations in Equation (1). Figure 4: Workflow of the ARIA method [21; 39] for identifying ‘damaged’ pixels, for example those which correspond to collapsed buildings or landslides given in 3 steps: (**a**) Generate coherence maps C\({}_{12}\), C\({}_{23}\). (**b**) Histogram match C\({}_{23}\) to C\({}_{21}\). (**c**) Calculate the difference between the two coherence maps. Darker grey pixels in (**c**) have a lower coherence in C\({}_{23\text{m}}\) and C\({}_{12}\) and negative pixels in the classification surface are identified as ‘damaged’, i.e., those for which C\({}_{23\text{m}}\) \(<\) C\({}_{12}\). Figure 5: Workflow for the Bx-S method, in which the difference between sibling-based and boxcar coherence estimates is used in landslide classification. When using a boxcar ensemble in estimating the coherence of a pixel that lies within a landslide, the pixels used in the summation are adjacent and so are likely to also lie within the landslide when the landslide in question is similar in size or larger than the boxcar. Since a landslide modifies the scattering properties of the Earth's surface, giving pixels within the landslide random \(\Delta\varphi\), the ensemble is expected to sum destructively, resulting in a low coherence estimate. Additionally, any coherent pixels within the landslide will still be estimated as low coherence due to the random \(\Delta\varphi\) of their neighbours. However, the sibling-based coherence estimate calculated using RapidSAR uses an ensemble of pixels dispersed throughout a window much larger than the size of a boxcar and specified to be larger than the expected size of individual landslides. Compared to the boxcar ensemble, we expect that proportionally fewer siblings of a landslide pixel will lie within the landslide. Pixels lying outside the landslide will not experience the random \(\Delta\varphi\) associated with it and so may sum constructively. The landslide pixel is thus given an estimated coherence value that is more dependent upon its siblings which lie outside the landslide. The sibling-based coherence calculated by RapidSAR is relatively insensitive to small spatial scale changes in the ground surface such as landslides. This map can therefore be thought of as the co-event coherence map we would expect if there were no landslides. The method we propose is to subtract this sibling-based coherence map from the co-event boxcar map, producing a classification surface, which will be referred to subsequently as boxcar-sibling (Bx-S). Landslide pixels should have a lower boxcar coherence than sibling-based coherence and so be negative in the Bx-S surface.