Two different window dimensions (64 and 128 pixels) were experimented, and produced similar results. The last columns of the table are reserved for the consistency check, which was conceived as follows. A is the result for the period 2011–2012, B that for the period 2012–2013, and C that for the period 2011–2013; reliable results should return A + B − C = 0. This is not strictly achieved, however the deviation from zero of the aforementioned equation is generally small. The distribution of the consistency check is Gaussian with a mean of about 1 cm/year and standard deviation of 42 cm/year in the 64-pixel window case. In the 128-pixel window case, the mean and standard deviation of the distribution are on the order of 2 cm/year and 42 cm/year, respectively.
The Slumgullion landslide has been widely investigated in the past literature. Most of the studies rely on field surveys [1
]. Recently, some papers exploiting remote sensing data have been presented [2
]. In this context, only Reference [2
] made use of space-borne SAR data. However, this work was focused on spotlight DInSAR methods covering one year of observations, with small insights in long-term displacement monitoring and limited validation of the presented results against literature data. All other works reviewed rely on airborne images acquired by the NASA/JPL L-band UAVSAR with 0.6- and 1.9-m spatial resolution in the azimuth and slant range directions, respectively [35
The validation of the obtained results is implemented both at landslide scale and at point scale. A perfectly consistent validation set (i.e., ground measurements acquired over the same time span covered by the SAR images used in this study) is not available, especially concerning the landslide scale. In this case, the most referenced data are relevant to the period 1985–1990 and to the year 2010. They are reported in Table 3
for the ease of the reader.
Data concerning the period 1985–1990 were produced in [29
] using photogrammetry and field surveys. Data relevant to the year 2010 were collected in [22
] through Ground-Based SAR Interferometry (GBInSAR) measurements. The latter study highlighted that, by 2010, the landslide’s velocity halved compared to its values in the 1985–1990 period, and that the landslide head was affected by the largest decrease in velocity. The authors ascribed this behavior to both geomorphological and climatic factors. At the climatic level, they suggested that the average increase in temperature and decrease in precipitation could have induced an overall slowing of the landslide. Reference [1
] showed that the movement of the Slumgullion landslide is strongly correlated to the soil moisture, and that its decreasing trend reflected the general slowing of the landslide.
From a geomorphological point of view, the observed thinning of the landslide head [36
] caused its stability to increase. The slowing of the head should have favored the overall slowing of the landslide by decreasing downslope-directed transfer of shear stresses [22
The displacement rates retrieved in this study are congruent with those reported in Table 3
in the column relevant to the GBInSAR survey implemented in 2010 [22
]. The direction of the estimated vector field (see arrows in Figure 3
) mainly follows the landslide slope profile and is qualitatively quite similar to that presented in the past literature (see as an example [31
The obtained results showed that the effect of the variation of the correlation window is negligible from the viewpoint of the estimated displacements, being for all the regions below the theoretical sensitivity of the method, which, as previously stated, is given by 1/f, where f is the applied oversampling factor. On the other hand, defining a smaller correlation window (e.g., 32 pixels) makes the frequency-domain cross-correlation less reliable, and this increases the standard deviation of the estimated displacement field (not reported here for brevity), which results in noisiness and physical inconsistency. Therefore, it is suggested to operate with the 64-pixel window. This allows a lower computational time compared to the 128-pixel window (for these experiments, the computational time was about 2.1 h per run, compared to about 45 min for each 64-pixel window run), as well as a higher level of detail and a better preservation of the landslide edges.
For the 64-pixel window, the registered values of the standard deviation range from 0.09 m/year in Region 1 (pair 2012–2013) to 0.67 m/year in Region 7 (pair 2011–2012). They are similar to those indicated in [29
It is remarkable that the noisier displacement patterns, see as an example that north of landslide Region 8, are characterized by very low values of the quality parameters considered. This means that the peak of the correlation matrix is not sharp (i.e., it is not well-defined compared with the background), thus leading to an unreliable estimate of the displacements. In the landslide area, even though the peak of the correlation matrix is not very pronounced (as expected based on the characteristics of the phenomenon under investigation), its ratio q with respect to the mean is quite high. The average values registered for the pair 2011–2012 for these quantities within the defined kinematic regions are, respectively: Region 1–0.33, 12.34; Region 2–0.39, 12.65; Region 3–0.32, 12.14; Region 4–0.30, 12.33; Region 5–0.30, 12.38; Region 6–0.28, 10.21; Region 7–0.24, 9.70; Region 8–0.23, 9.92; Region 9–0.25, 11.17; Region 10–0.28, 11.42; and Region 11–0.24, 10.27.
The consistency check involves the three pairs: August 2011–August 2012; August 2012–August 2013; and August 2011–August 2013. A consistent result should pose that the sum of the displacements is zero. As stated above, this is not strictly achieved, however the resulting distribution has a mean very close to zero either at landslide scale or within the 11 kinematic regions. The registered deviations from zero (using the 64-pixel window) range (in absolute value) from less than 1 cm/year (region 2) to 12 cm/year (region 5). Similar results were obtained using the 128-pixel window (see Table 2
In the following, the obtained results will be discussed at a finer scale exploiting data concerning 19 measurement points (MPs) installed on the landslide by the US Geological Survey (USGS) [34
]. Reference data for comparison were extracted from Reference [26
], in which the kinematics of the landslide was analyzed in the time frame August 2011–April 2012 using airborne L-band remote sensing and was compared with GPS data collected at the USGS MPs. Note that these data were reproduced through graph digitalization, and it is therefore possible that they exhibit (negligible) differences with respect to their original version.
In Figure 5
, the comparison between the results presented here (time frame August 2011–August 2012) and those from [26
] is shown. The position of the MPs with respect to one of the available SAR acquisitions is also reported (note that MP1 and MP2 are not shown in this graphic since their position falls outside the image cut considered). Airborne SAR-derived data are rendered with blue bars and GPS data with gray bars. Outcomes from this study (orange bars) were produced by taking the maximum displacement in a window of 100 × 100 meters around each MP position (only for MP1, which is expected to be immobile, the mean displacement was considered). This choice was made in order to compensate geocoding errors (some of the MPs are at the landslide borders and/or at the transition between different kinematic zones) and SPOT maps inhomogeneity/noise.
The three datasets qualitatively show a good agreement. Disagreements are concentrated, as expected, in the neck sector, where the landslide is faster. In this area, estimates from this work exhibit the highest discrepancy when compared to airborne SAR and GPS data, in particular in MP8, MP9, and MP14. For those points, the landslide displacement rate is underestimated when compared to GPS data of about 0.17 cm/day, about 0.3 cm/day, and about 0.16 cm/day, respectively. If the measurements extracted from airborne SAR images are considered, the underestimation in correspondence of the aforementioned points is on the order of 0.13 cm/day, 0.15 cm/day, and 0.17 cm/day.
Assuming that points MP1 to MP7 belong to the head, that MP8 to MP14 belong to the neck, and that MP15 to MP19 belong to the toe, the registered Root-Mean-Square Error (RMSE) of the displacement rates here estimated with respect to GPS measurements is about 0.05 cm/day for the head, 0.15 cm/day for the neck, and 0.09 cm/day for the toe.