5.1. SAR Interferometry
For single measurements at C-band, an error of 6 to 7 mm, partly attributed to noise (1 to 2 mm) and partly to atmospheric artifacts (5 to 6 mm), was estimated in a major validation project over urban areas [80
], where a similar high degree of coherence over a multiannual period is typically observed as in 6 to 12 days over rock glaciers. This error translates to a LOS measurement uncertainty of ±0.4 m/a for Sentinel-1 interferograms over six days and of ±0.2 m/a for Sentinel-1 interferograms over 12 days. A similar phase error of one quarter of a phase cycle due to signal noise and atmospheric artefacts is typically observed also at X-band [68
]. For TerraSAR-X interferograms over 11 days, this error corresponds to a measurement uncertainty in LOS displacement of ±0.1 m/a. At L-band the total phase error is minor [81
], for example, one eighth of a phase cycle, leading to an error in LOS displacement of the JERS-1 interferogram over 88 days of ±0.1 m/a.
One of the permanent mono-frequency GNSS stations over Becs-de-Bosson rock glacier, BdB2, which was installed in 2016 at a location where velocities are rather spatially homogeneous (Figure 6
), was used for a direct validation of the Sentinel-1 InSAR measurements. In local differential mode, with differential postprocessing computed with respect to a permanent local basis, the estimated accuracy of the mean planimetric and altimetric GNSS positioning over 24 h is in the order of +/−2 mm and that of the velocity over a 6 day period in the order of +/−0.24 m/a [43
]. The 3D GNSS velocities computed with the average daily positions corresponding to the acquisition dates of the Sentinel-1 images are plotted together with the velocities along the maximum slope direction from Sentinel-1 InSAR in Figure 12
a. For the 41 coincident measurement points (Figure 12
b), the standard deviation of the velocity difference is 0.21 m/a, while average, minimum, and maximum of the velocity difference are −0.08 m/a, −0.67 m/a, and 0.33 m/a, respectively. Sentinel-1 InSAR is slightly underestimating the GNSS velocities, possibly because the rock glacier is not exactly moving along the steepest slope or as a result of the InSAR spatial resolution on the order of 15 m.
On the one hand, over the Tsarmine rock glacier the permanent mono-frequency GNSS station operates in a local differential mode. It is, however, located in a section where the Sentinel-1 interferograms are decorrelated, because the late summer rates of motion are overpassing, since 2015, 6 m/a, i.e., amount to nearly 9 cm in six days (Figure 4
). Displacement measurements using GNSS campaigns carried out seasonally, on the other hand, are performed on about 60 positions, including the locations of the permanent GNSS station and the spot of the Sentinel-1 InSAR time-series of Figure 5
b. Considering that during the last three years (2016 to 2018) the ratio between the annual rates of motion of these two positions remained constant (factor 0.54), we plotted in Figure 13
a the scaled 3D GNSS velocities computed with the average daily positions corresponding to the acquisition dates of the Sentinel-1 images together with the velocities along the maximum slope direction from Sentinel-1 InSAR. Taking into account the scaling of the continuous GNSS data, the correspondence to the Sentinel-1 InSAR results is impressive. The scatter plot of scaled GNSS and Sentinel-1 velocities (Figure 13
b) indicates even more clearly the very good accordance. For the 45 coincident measurement points, the standard deviation of the velocity difference is 0.22 m/a, whereas average, minimum, and maximum velocity differences are 0.03 m/a, −0.40 m/a, and 0.50 m/a, respectively. The results of the displacement measurements from the GNSS campaigns carried out seasonally are also shown in Figure 13
a. In real-time GNSS kinematic mode, with the receiver left calculating its position for a few seconds, the standard deviation of positioning during this time lapse is usually less than 1 cm in the horizontal component and less than 2 cm in the vertical one [82
]. As expected, differential GNSS measurements miss the strong seasonal variations, but the order of magnitude of the rate of motion fits the Sentinel-1 InSAR results.
Standard normalized image cross-correlation techniques enable surface displacement measurements from repeat optical images at subpixel horizontal accuracy [83
]. We matched repeat orthorectified aerial images provided by Swisstopo, the Swiss national mapping agency, with a spatial resolution of 0.4 m acquired on 03.09.2014 and 21.09.2017 over the Distelhorn rock glacier. From matches over stable ground outside the rock glacier we estimate a displacement accuracy of ±0.15 m, that is, ±0.05 m/a. The horizontal displacement field from offset tracking in repeat orthoimages is compared to the Sentinel-1 InSAR LOS displacement field from 02.08.2018 to 08.08.2018 in Figure 14
along with the difference map between the two measurements. The results of Figure 14
indicate a good spatial correspondence between aerial photo matching and Sentinel-1 InSAR, but on the southern tip of the rock glacier the interferogram was not correctly unwrapped. Further discrepancies can be observed on the edges of the fastest moving parts of the rock glacier front. The scatter plot of the aerial photo matching and Sentinel-1 LOS velocities (Figure 15
a) indicates the effect of the different time intervals (three years as compared with six days) and of the satellite look direction. In Figure 15
b, we empirically fitted the Sentinel-1 LOS velocities to the aerial photo matching velocities by scaling them with a factor of −1.23 in order to maximize the one-to-one match and account, therefore, for these two effects. After scaling, the standard deviation of the velocity difference for the 2237 coincident measurement points is 0.30 m/a, while average, minimum and maximum velocity differences are 0.01 m/a, −2.09 m/a, and 2.84 m/a, respectively. After removal of the 17 wrongly unwrapped Sentinel-1 InSAR points in the southern tip of the rock glacier, the standard deviation of the velocity difference is 0.25 m/a, while average, minimum, and maximum velocity differences are 0.00 m/a, −1.28 m/a, and 1.50 m/a, respectively.
5.2. SAR Offset Tracking
Delaloye at al. [36
] investigated the accuracy of SAR offset tracking for ice surface velocity estimation in various aspects, including a formal description of the error terms, matching on stable ground, comparison against results from SAR image data of equal or better resolution, and ground-based measurements from GNSS. They estimated the reliability of the cross-correlation algorithm to return coregistration parameters in the order of 1/10th of a SAR image pixel. This corresponds for the TerraSAR-X and Cosmo-SkyMed data of our study (Table 1
) to an accuracy of about 0.3 m in measuring horizontal displacement.
Offset tracking based on TerraSAR-X images over the Distelhorn rock glacier was performed with time intervals of about two years. Therefore, a coregistration precision of 1/10th of a SAR image pixel would correspond to 0.15 m/a in measuring horizontal displacement. Statistical measures of displacement were computed for every TerraSAR-X image pair over 55,580 points on stable terrain surrounding the rock glacier. The mean of the horizontal velocities for the four image pairs 24.09.2008 to 20.09.2010, 09.09.2010 to 04.09.2012, 15.09.2012 to 22.09.2014, and 11.09.2014 to 06.09.2016 were 0.42 m, 0.43 m, 0.42 m, and 0.48 m, respectively, on average 0.22 m/a. The standard deviations of the estimates for the four image pairs were 0.45 m, 0.54 m, 0.44 m, and 0.46 m, respectively, on average 0.24 m/a. A visual comparison to the matching of aerial optical images acquired on 03.09.2014 and 21.09.2017 was drawn, as shown in Figure 16
. These results clearly point to the lower spatial resolution of TerraSAR-X offset tracking with respect to matching of aerial optical images, with large discrepancies on the edges of the fastest moving parts of the rock glacier. The scatter plot of the aerial photo matching and TerraSAR-X velocities (Figure 17
) also indicates a bias of the offset tracking results, which are generally lower than those from the matching of aerial images as a result of the larger cross-correlation window size used with SAR images. The standard deviation of the velocity difference for the 2197 coincident measurement points is 0.34 m/a, while average, minimum, and maximum velocity differences are −0.22 m/a, −2.61 m/a, and 1.87 m/a, respectively.
Offset tracking with Cosmo-SkyMed images over the Tsarmine rock glacier was performed with time intervals of about one year. Therefore, a coregistration precision of 1/10th of a SAR image pixel would correspond to 0.30 m/a in measuring horizontal displacement on the ground. Statistical measures of displacement were also computed for every Cosmo-SkyMed image pair over 20,326 points on stable terrain surrounding the rock glacier. The mean of the horizontal velocities for the eight image pairs 23.07.2009 to 10.14.2010, 27.08.2010 to 14.08.2011, 13.07.2011 to 29.06.2012, 15.07.2012 to 04.09.2013, 02.07.2013 to 21.07.2014, 22.08.2014 to 22.06.2015, 26.09.2015 to 27.08.2016, and 10.10.2016 to 13.07.2017 were 0.18 m, 0.18 m, 0.19 m, 0.17 m, 0.19 m, 0.20 m, 0.32 m, and 0.29 m, respectively, on average 0.21 m/a. The standard deviations of the estimates for the eight image pairs were 0.17 m, 0.20 m, 0.25 m, 0.29 m, 0.26 m, 0.30 m, 0.84 m, and 0.42 m, respectively, on average 0.34 m/a. Horizontal displacements for the central sector of the rock glacier assessed by GNSS campaigns carried out annually (points 022, 023, and 024 which are within about 40 m of each other) are well representative of the velocity evolution over time for the central sector of the rock glacier. The GNSS horizontal velocities over time averaged for the three points are compared to the velocities from Cosmo-SkyMed offset tracking in Figure 18
a, while the scatter plot of GNSS and Cosmo-SkyMed velocities is presented in Figure 18
b. For the eight coincident measurement points, the standard deviation of the velocity difference is 1.00 m/a, while average, minimum and maximum velocity differences are 0.40 m/a, −1.36 m/a, and 1.86 m/a, respectively. In Figure 18
a,b we also observed that the deviation between GNSS and Cosmo-SkyMed velocities increases for larger values.
In summary, we note that rock glaciers in the Swiss Alps are rather small objects (e.g., 0.5 km long and 100 to 200 m width) and offset tracking is at the limit of its applicability even with very high-resolution SAR images with a resolution of about 2 m. The measurement uncertainty is, thus, larger than assessed over fast-flowing (e.g., >300 m/a) and large (e.g., >10 km) Arctic glaciers over shorter (e.g., few days) time periods [36
]. For the TerraSAR-X images used for offset tracking over two years with image matching windows of 64 × 64 pixels, corresponding to a resolution of about 125 meters on the ground, the assessed measurement uncertainty over the Distelhorn rock glacier is about 0.3 m/a. For the Cosmo-SkyMed images used for offset tracking over one year with image matching windows of 64 × 64 pixels over the Tsarmine rock glacier, the assessed measurement uncertainty is in the order of 1.0 m/a. The Tsarmine rock glacier is only 150 m in width as compared with the width of about 300 m of the Distelhorn rock glacier, and the performance of SAR offset tracking is, therefore, well expected to be worse.