In this study, radar imagery was used from two satellite systems. Sentinel-1 uses C-band radar (wavelength ∼ 5.6 cm), whilst ALOS-2 PALSAR-2 uses lower-frequency L-band radar (wavelength ∼ 24 cm). The difference in wavelength between the two systems means that, in forested areas, L-band radar penetrates further into the canopy than C-band. The shorter wavelength of C-band radar means it is sensitive to surface modifications on a smaller spatial scale. For example, in a forest, C-band radar data may detect change in the location or orientation of leaves, while L-band is sensitive instead to changes in the location and orientation of branches. L-band InSAR is often more useful in vegetated areas as its deeper penetration allows it to retain higher coherence in the absence of major vegetation changes .

Radar systems acquire data at an oblique angle to the vertical on near-polar ascending and descending orbital tracks (referred to here as a and d), which are acquired on different dates. The satellite look direction is perpendicular to the orbit direction. The data used in this study were acquired at an angle of between 31.4 and 43.8∘ to vertical. This oblique acquisition angle means that on a given track, some hillsides will be more favourably oriented to the sensor than others, and so information from ascending and descending tracks can be combined to obtain more complete coverage of an event. As it is impossible to calculate a combined coherence surface using data from two tracks, and in some cases imagery will only be acquired on one track within 2 weeks of an event, here we considered each track separately. We will refer to tracks according to their sensor, track number and orbit direction, for example, A018d (ALOS-2, track 18, descending orbit).

We used four case study events: the 2015 Mw=7.8 Gorkha, Nepal, earthquake (Fig. a and d); the Mw=6.6 2018 Hokkaido, Japan, earthquake (Fig. b and e); and two Mw=6.8 and 6.9 earthquakes from the 2018 Lombok, Indonesia, sequence (Fig. c and f). These four events have several traits in common which made them suitable for this study. First, they were all large earthquakes, triggering thousands of landslides, making them of interest from an emergency response perspective. This also meant that the earthquakes and associated landslides had previously been investigated, and inventories of triggered landslides had been compiled from optical satellite imagery, enabling direct testing of the radar methods against these independent datasets . Second, while the vegetation types differ between the three regions, the presence of dense vegetation across each region meant that we could expect landslide and non-landslide pixels to have a similar first-order signal in the radar data across the events. Third, ascending- and descending-track Sentinel-1 data and at least one track of high-resolution ALOS-2 data (acquired in stripmap mode at a resolution of 3–10 m) were available for all case study areas. Finally, the type of landslides triggered by our four case study earthquakes were typical of landslides triggered by earthquakes . The majority of ground failures in the four earthquakes were slides. In Nepal, ground failures were primarily a mixture of slides and falls, with the exception of a large debris avalanche in the Langtang Valley. For all four earthquakes, failure surfaces were at shallow depths in most cases, with a small number of exceptions .

The Mw=7.8 2015 Gorkha, Nepal, earthquake (Fig. a) occurred on 25 April 2015 and triggered around 25 000 landslides over an area hundreds of kilometres wide, as mapped by . Sentinel-1 imagery was acquired on tracks S019d and S085a. ALOS-2 data on track A157a were divided into subtracks, with acquisitions on different dates, shown as separate polygons in Fig. a, which are referred to as east (E), central (C) and west (W).

The Mw=6.6 2018 Hokkaido, Japan, earthquake (Fig. b) occurred on 5 September 2018. Two inventories have been published for this event: one containing 7837 landslides and one containing 5265 . Neither provided information on the mapping extent, so we assumed that this could be approximated by the convex hull of the data locations. As the inventory of has the largest convex hull, we used this inventory for validation of the radar methods. Both descending and ascending ALOS-2 data were available for this event, with a higher spatial and temporal frequency than for the other events. The earthquake occurred the day after Typhoon Jebi passed over Hokkaido, and so this case study was also an opportunity to test landslide detection methods following a rainfall event, with the advantage that because the typhoon and earthquake occurred 1 d apart, and aerial imagery of the triggered landslides was acquired immediately afterwards, we know more precisely when the landslides occurred . This is important if SAR methods are to be used in the future for mapping storm-triggered landslides because factors such as wind damage and the water content of the soil are known to affect SAR coherence and amplitude .

The 2018 Lombok earthquake sequence comprised four earthquakes with Mw>6: Mw=6.4 on 28 July, Mw=6.8 on 5 August, and Mw=6.3 and 6.9 on 19 August. generated two landslide inventories for this sequence. Although cloud-free imagery was not available across the whole affected area following the earthquake on 28 July, no landslides were visible in the areas that could be mapped. thus presented their first inventory of 4823 landslides triggered following the 5 August earthquake and a second inventory of 9319 landslides, which had been triggered by the end of the sequence. We refer to the 5 August inventory as Lombok-1 (Fig. c) and the 19 August inventory as Lombok-2 (Fig. c, inset).

There are several key ways in which the events differed. First, the triggered landslides had very different spatial patterns, with the Gorkha earthquake triggering landslides across an area spanning hundreds of kilometres, while the Lombok and Hokkaido earthquakes triggered landslides across only a few kilometres. It can be seen in Fig.  that much denser landsliding was triggered by the Hokkaido earthquake than by the other events. Second, the sizes and shapes of the landslides were very different between events: the Lombok earthquakes triggered a large number of small landslides, with a median landslide area of 460 m2 for Lombok-1 and 580 m2 for Lombok-2, compared to equivalent median areas of 4350 m2 for Hokkaido and 1070 m2 for Nepal (measured from the inventories of ; ; and ). Third, the events occurred under different weather conditions: the Hokkaido earthquake followed months of heavy rain and occurred 1 d after Typhoon Jebi, while the Gorkha and Lombok earthquakes occurred during the dry season. Finally, the topographic relief in the three case study areas varied significantly. In Nepal the majority of landslides occurred on slopes of over 40∘ . For the Hokkaido event, the proportion of slopes > 40∘ was very low, and so the majority of landslides occurred on much shallower slopes , with Lombok lying between these two extremes. This is highly relevant to the application of SAR coherence methods to landslide detection. Steep slopes can lead to distortion of the radar image, and coherence is also dependent on the geometry of the hillslope and radar sensor. Therefore, we might expect that, as hillslopes in Hokkaido and Lombok are shallower than in Nepal, landslide detection using SAR may be more successful in these areas. These differences between the four events made them ideal for testing the wider applicability of SAR-coherence-based landslide detection methods in vegetated areas. If a method is to be widely applied in the future, we need to be confident that its performance is consistent across differing events and settings.

We tested two existing methods: the co-event coherence loss (CECL) method of and the boxcar–sibling method of . Each of these existing methods uses a single post-event SAR image. We also present three new methods that incorporated a second post-event image: the post-event coherence increase (PECI), the sum of the coherence increase and decrease (ΔC_sum), and the maximum of coherence increase or decrease (ΔC_max). A “boxcar” coherence estimate is used for CECL, PECI, ΔC_sum and ΔC_max.

SAR data were processed using GAMMA, with the LiCSAR processing software used for Sentinel-1 . The data were multilooked by a factor of 5 in range and 1 in azimuth (Sentinel-1) or by 5 in both range and azimuth (ALOS-2) to improve the signal-to-noise ratio. See Table  for information on the data resolution and pixel size at various stages of the processing. For geometric coregistration, we used the 1-arcsecond Shuttle Radar Topography Mission (SRTM) digital elevation model .

The boxcar coherence estimate used in all methods was calculated using a 3×3 px moving window (Table ). The sibling-based coherence estimate used for the Bx–S method was calculated using the RapidSAR algorithm of . Siblings were calculated based on all pre-event images shown in Fig.  (a minimum of six images). For every pixel, between 15 and 50 siblings were identified within an 81×81 px window based on their amplitude and amplitude variability (window sizes in Table ). Unfortunately, insufficient pre-event ALOS-2 data were available to carry out this calculation in the case of the 2015 Gorkha earthquake, and so the Bx–S method could not be tested for this case.

In most cases, we used the co-event, pre-event and post-event coherences with the shortest temporal baseline; however for the inventory provided by for the landslides triggered by the Lombok earthquake on 19 August, we used a co-event image that spans this earthquake and the 5 August earthquake as the landslide inventory contains landslides triggered by both events. After calculating each landslide classification surface from the methods described in Sect. , we used the GAMMA software to convert the surfaces to a geographic coordinate system. This process, involving reprojection and interpolation, results in uniform pixel size (20 m × 22 m). We then normalised the values of each surface by the theoretical maximum and minimum value that could be obtained from each method, resulting in a set of classification surfaces with values between 0 and 1, with 1 most likely to be a landslide.

Before statistical testing, we removed distorted pixels. The oblique angle at which SAR imagery is acquired meant that some pixels were distorted by topography and were badly imaged by the SAR system, experiencing shadow, foreshortening, or layover and decorrelation of γspatial (Sect. ). Following , we masked these according to the area in geographic coordinates that contributes to the pixel in radar geometry, removing pixels with an area of 0 and those where this area was over 6 times larger than their multilooked pixel spacing in radar coordinates (see Table ).

We carried out statistical testing of the results at two resolutions: first, at the initial resolution of the processed radar data in geographical coordinates (20 m × 22 m), with the vector landslide inventories of , and rasterised at this resolution, and second, at an aggregated resolution of 200 m × 220 m, calculated by amalgamating 10×10 grids of the 20 m × 22 m pixels. Aggregated classifier pixels were given the mean value of the unmasked pixels in the 10×10 grid. If over 95 % of an aggregate pixel was made up of masked pixels, the aggregate pixel was masked. This high threshold of 95 % was chosen to minimise the loss of spatial coverage due to the masks. Varying the threshold between 95 % and 5 % had little difference in terms of the number of pixels used in the analysis in Hokkaido and Lombok (<5 %), but in Nepal, where more pixels were masked due to distortion on steep slopes, decreasing the threshold to 5 % resulted in a loss of coverage of around 40 % on S085a. Altering this threshold made very little difference to the results presented in Sect. 4.1.

In this study, we did not attempt to map SAR classification surface values directly to landslide areal density values as this has not been attempted in previous studies e.g. and may not be possible due to differences in viewing geometry, land cover and, particularly with the ALOS-2 data used here, differences in temporal baseline between events. Thus, a binary ground truth was preferable, which we generated by assigning aggregate pixels as “landslide” if they were composed of over 25 % landslide by area according to the rasterised landslide inventories we used for verification. We explore the effect that this choice of a 25 % threshold to define a landslide pixel has on our results in the Supplement, but varying this threshold between 1 % and 50 % was found to have little effect on the relative performance of the different classifiers.

The aggregation process was done for several reasons. First, the boxcar coherence estimation has the effect of blurring neighbouring pixels so that the minimum size of an object we could resolve was dependent on the size of the 3×3 boxcar (see Table ). In all cases this was larger than the 20 m × 22 m pixel spacing in geographic coordinates. Second, it has already been demonstrated that SAR-coherence-based methods perform better at lower resolutions . Third, when comparing landslide inventories, for example those of and for the Hokkaido earthquake, there is often some variation in the exact shape and location of individual polygons. We expect this effect to be decreased when inventories are downsampled. We therefore chose a resolution that was larger than the boxcar window but that resulted in enough mapped landslide and non-landslide aggregate pixels for analysis. This is similar to the resolution of other landslide products generated for emergency response e.g.

We used the receiver operating characteristic (ROC) area under the curve (AUC) to evaluate and compare the classification ability of each surface. For each classification surface, a threshold was set for which no pixels were classified as landslides and then incrementally decreased until it reached a value where all pixels were classified as landslides. At each incremental threshold, the false-positive rate (the ratio of false positives to real non-landslide pixels) was plotted against the true positive rate (the ratio of true positives to real landslide pixels) to form an ROC curve. The area under this curve is equal to the probability that if a landslide pixel and a non-landslide pixel were randomly selected from the dataset, the classifier would rank them correctly . For a randomly generated surface with no classification ability, the AUC = 0.5. For a perfect classifier, the AUC = 1.0.

On all SAR tracks, there are many more non-landslide than landslide pixels. It has been suggested that for such imbalanced data, precision-recall curves can better represent classification ability than ROC AUC . Here, we chose to use ROC analysis since precision-recall curves do not allow comparison between datasets with different proportions of landslide and non-landslide pixels and therefore between different earthquakes and SAR tracks. However, when considering the relative performance of classifiers for each track independently, we found the same conclusions could be drawn from precision-recall curves as from ROC curves. A recreation of Fig. a using precision-recall rather than ROC AUC values can be found in the Supplement.

Figure  shows the ROC AUC values for each classification method described in Sect.  and each track of radar data shown in Fig. . The cells are coloured so that the best-performing classification surfaces are shown in green and the weakest in red. A classifier that performs well for all events and both sensors should therefore appear as a green row. The eastern and western tracks of S157a and data for Lombok-2 on track A129a have been omitted as the waiting times for the first post-event image were very long (77, 63 and 139 d, respectively). This long time window resulted in widespread co-event coherence loss that adversely affected classifier performance. Such a long waiting time would make it extremely unlikely that these data could be used in emergency response, and the poor performance is unlikely to be representative of classifier behaviour when using more timely imagery.

The methods are grouped by the number of post-event images that are required, and the waiting time in days for this imagery for each event and SAR track is also given. As the primary scientific use for post-event ALOS-2 imagery is to form a co-event interferogram, only one post-event image was acquired immediately following the Lombok-1 and Nepal earthquakes, with the waiting time for the second post-event image being considerably longer. We still include these results as the waiting time for L-band radar data is likely to decrease in the future with the planned NASA–ISRO synthetic aperture radar (NISAR) satellite constellation, which is expected to launch in 2022, acquiring data globally with a 12 d repeat time .

If we consider only data acquired within the 2-week emergency response window , the highest AUC in Hokkaido was initially 0.58 on day 0 using the Bx–S method on S046d, rising to 0.89 after 1 d with data from track A018d and the CECL method. In Nepal, the first radar data were acquired on day 4 on track S019d, from which the highest AUC of 0.74 was obtained using the Bx–S method. On day 7, the first ALOS-2 image was acquired on A157a, and more accurate information could have been generated using CECL (AUC 0.81), although this ALOS-2 scene covers a smaller area than the Sentinel-1 data (Fig. ). In Lombok, the 6 d Sentinel-1 acquisition repeat time meant that a large volume of data was available within 2 weeks of these events. The best data and method for Lombok-1 evolved as follows: CECL, S032d (day 0, AUC 0.56); CECL or Bx–S, S156a (day 3, AUC 0.64); PECI, S032d (day 6, AUC 0.69); ΔC_max, S156a (day 9, AUC 0.72); CECL, A129a (day 13, AUC 0.88). The corresponding classification surfaces for this evolution are plotted in Fig. . For Lombok-2, the first Sentinel-1 image was acquired on day 1, track S156a, and had an AUC of 0.67 using the Bx–S method, which could be slightly improved upon using the second post-event image that was acquired on day 7 using PECI (AUC 0.68). No ALOS-2 data were available within 2 weeks of this earthquake. Therefore in most cases, initially only Sentinel-1 data are available, and the best option is the Bx–S method. This can then be improved upon when the first ALOS-2 image becomes available using CECL. For Lombok-1 and Lombok-2, where two post-event Sentinel-1 images became available before the first ALOS-2 image, incorporating these data also improved on the accuracy of the result.

With a single L-band post-event image from ALOS-2, CECL was the best-performing landslide classification surface in all cases. An improvement was seen when an additional post-event image was acquired, and methods requiring this image were used for the case of Lombok and Nepal but not for Hokkaido. When a single C-band post-event image was used, the Bx–S method outperformed CECL for Hokkaido, Gorkha and Lombok-2 and had a similar performance for Lombok-1. The addition of a second post-event image and adoption of methods that used this image showed an improvement in Hokkaido and Lombok-1 but not in Nepal. However, when considering Fig. a as a whole, methods that used a second post-event image were both better-performing and more consistent across event and sensor type. When looking across all three events, the best option in terms of AUC was to use the ΔC_sum method with L-band imagery. When grouped by event and radar look direction and ranked according to AUC, ΔC_sum using ALOS-2 was ranked 3rd out of 10 classification surfaces for descending imagery over Hokkaido, 1st out of 9 for ascending imagery over Nepal and 2nd out of 10 for ascending imagery over Lombok-1. A comparison cannot be made for ascending track data in Hokkaido as A116a and S085a had different look directions (westwards and eastwards, respectively).

Figure  shows the landslide classification surfaces calculated using the ΔC_sum method and ALOS-2 data of each event alongside the aggregated validation landslide data. In Fig. b, d and f, cells made up of <1 % landslide by area are masked. In order to recreate this in the radar surface, it was necessary to threshold and plot only pixels that were most likely to be landslides based on their classifier value. Here we applied a threshold such that the number of pixels plotted in Fig. a, c and e is the same as the number in Fig. b, d and f, respectively. These threshold values were similar but not identical, and we expect that more case study sites would be required to determine a more general threshold for application in future events. However, in each case, the spatial pattern of landsliding in Fig. b, d and f was recreated using the radar surfaces in Fig. a, c and e, which would allow the worst-affected areas to be identified for emergency response even without strict definition of this threshold.

Our results show significant variation across event and sensor type. L-band radar outperformed C-band in the majority of cases, but for some methods, we observed additional effects causing differences in performance.

For methods relying on a co-event vs. pre-event coherence decrease (i.e. CECL, ΔC_sum, ΔC_max), landslides associated with Lombok-2 were more difficult to predict than Lombok-1 (Fig. ). This is likely to be due to the co-event acquisition time window, which was 6 d for the first inventory but had to be increased to 18 d on track S156a and 24 d on S032d in order to span both earthquakes. This will have caused temporal decorrelation of vegetated non-landslide pixels, resulting in a smaller difference between landslide and non-landslide co-event coherence and making it more difficult for the classifier to distinguish between these. The same effect was seen in Nepal, where 12 d interferograms were used for S019d, but 24 d pre-event and co-event interferograms were used for S085a.

Generally, the Bx–S method was more consistent across sensor type than the CECL method. The CECL method performed better than the Bx–S method with ALOS-2 data but worse with Sentinel-1. There are several possible reasons for this. First, the longer wavelength of L-band SAR meant that it was able to maintain a higher coherence in the pre-event interferogram so that the coherence difference for a landslide pixel in a pre-event and co-event interferogram was larger, resulting in better performance from CECL. Second, in the Bx–S method, siblings are identified using pre-event imagery. As Sentinel-1 imagery is acquired every 12 d, more images were available for this calculation and were acquired over a shorter time period. This allows less time for pixels to be altered by changes to the ground surface, meaning that, for non-landslide pixels, a pixel and its siblings are likely to be more similar. In this way, the siblings selected by RapidSAR for Sentinel-1 imagery may have been of a higher quality than those for ALOS-2, giving a more reliable coherence estimate.

While the main aim of this study was not to map individual landslides, we also show results at a 20 m × 22 m scale (the resolution of the classification surfaces in geographic coordinates), with pixels that are sufficiently small to resolve individual landslides. Our results show that SAR methods were less successful at this resolution than when downsampled, with AUC on average 16 % lower using Sentinel-1 data and 11 % lower using ALOS-2 data. Using Sentinel-1 data, AUC values were low, ranging from 0.49 (CECL, Lombok-2) to 0.61 (PECI, Hokkaido). From this we conclude that mapping individual landslides with Sentinel-1 data was not possible using the methods tested here, which supports similar preliminary findings by .

Classification surfaces using ALOS-2 are more promising, with AUC up to 0.80 (ΔC_max, Lombok-1). As in Sect. , ΔC_sum performed best, having the highest AUC on tracks A116a and A157a and an AUC of only 0.01 less than the best-performing classification surface on tracks A018d and A129a. Figure  shows small regions of this surface overlain with landslide polygons for each event. While the landslides generally coincide spatially with high classifier values, it is clear that it would not have been possible in most cases to map the landslide polygons using the radar data. Some large landslides (Fig. b and d) contain pixels with high classifier values. However, in Fig. d, there are also areas of mapped landslides that do not have high classifier values, and in Fig. a and c the landslides are too small. Therefore we conclude that, while radar coherence methods show promise in individual landslide detection, it was not possible using the methods tested here, and there is likely to be a minimum detectable landslide size.

We have demonstrated that the classification ability of a method can vary significantly based on the data used, the nature of the triggering event and the resolution of the analysis. For example, the Bx–S method performed significantly better in the case of Nepal than Hokkaido, and CECL was up to 32 % more successful when using ALOS-2 compared to Sentinel-1 data with the same event and look direction. Thus, it is clear that any future SAR-based classification method must be widely tested on multiple events, and it cannot be assumed that a method performing well with one SAR dataset will be equally successful using data from a different sensor.

While we tested ascending and descending tracks separately, a more complete picture would be obtained through combining these two tracks as hillslopes that are unfavourably oriented to the satellite in one track are likely to be more favourably oriented in the other track. A complete map would be easier to interpret for emergency responders than two maps, each of which is missing landslides on unfavourably oriented slopes. This is particularly important since landslides are most likely on steep slopes, where these orientation effects are likely to be most severe.

Although we selected earthquakes to use as case studies, SAR methods could be equally useful in the case of rainfall-triggered landslides, where cloud cover may also cause delays to mapping using optical satellite imagery. We have shown that SAR methods performed well in Hokkaido, where the co-event coherence maps spanned both an earthquake and a typhoon. This demonstrates that the alterations in SAR coherence and amplitude that can result from changes in soil moisture content are not prohibitive to the application of SAR methods to rainfall-triggered landslides, although some false positives may have been caused by wind damage.

The Lombok case studies demonstrate the importance of knowing the timing of the landslides when applying current methods. When moving from Lombok-1, in which all landslides were assumed to have been triggered by a single earthquake, to Lombok-2, which contained landslides triggered by a series of earthquakes over a 2-week period, it was necessary to increase the time span of the Sentinel-1 co-event interferograms from 6 to 24 d on track S032d and 18 d on track S156a, which significantly reduced the AUC of the classification methods. Therefore, if we wish to apply radar methods more widely to landslide triggering events that are dispersed through time, such as long rainfall events (e.g. those associated with the monsoon) or earthquake sequences, more work will be required on the characterisation of the signals of landslides in radar imagery through time.

Finally, here we assessed classifier performance using ROC analysis, which does not require a threshold to be applied to the classification surface. However, if SAR methods are to be applied to future events for emergency response, it will be necessary to set a threshold between “landslide” and “non-landslide”. In this study, the time between image acquisitions varied significantly between events, making it unlikely that a threshold could be selected that would work well for both Sentinel-1 and ALOS-2 across all events. However, this may be possible in the future when more events have been studied, and SAR data with more regular acquisitions are available. Further work is therefore needed to establish such thresholds, which will be determined according to the requirements of emergency responders and their relative tolerance for false positives and false negatives.