Error sources on InSAR: interpretation and analysis
Although we consider seasonal and inter-annual displacements detected in this study to be caused by thaw settlement/frost heave including thermokarst, there are potential error sources related to InSAR phase bias caused by turbulent atmospheric effect and soil moisture change. However, the signals we identified in the stacking processes are considered as a more robust indication of true subsidence; this is described further in the following discussions.
The turbulent atmospheric effect may affect the interferograms. However, such signals could appear regardless of land cover and are unlikely to occur at specific open areas at the same time in the interferograms. With regards to localized atmospheric phenomenon in specific land covers in this region, it is known that mist occurs on summer days after sunset over open areas. The condensation of water vapor is caused by a difference in the heat capacities of forested and open ground. However, the height of the mist is usually less than 20 m, and the effect of the propagation delay of the SAR microwave due to the localized vapor is considered negligible. Moreover, similar mist occurs at almost all open (deforested) areas in this region and is unlikely to occur systematically at particular open areas. The effect by the mist may be due to the phase change of the constituent water from vapor to liquid droplets, which is not be due to the “turbulent” atmospheric effect. In either case, we confirmed each interferogram used in the stacking, and all signals in the discussed areas showed subsidence in multiple interferograms. Therefore, it is unlikely that these signals were due to the atmospheric effects.
With regard to the change in soil moisture and its related error, there is a possibility of apparent InSAR phase change in our results. The major causes of the possible errors have been considered to be the change in penetration depth of the microwaves, and the dielectric change that induces a wavenumber shift in the microwave propagation due to changes in soil moisture (e.g., De Zan et al. 2014; Zwieback et al. 2015). Zwieback et al. (2015) examined the dependency of the InSAR phase on soil moisture using airborne L-band SAR data, and concluded that the interferogram phase could change π/2 for a change in surface moisture of 20%. This change corresponds to 2–3-cm subsidence upon the 20% moisture increase at the L-band. In our study region, fluctuation in surface soil moisture is small because of the dry continental climate and the deep active layer. During the thawing season, as the thaw depth increases water holding capacity in the active layer will increase over time, and soil water in the near-surface layer can percolate into the deeper soil layers. The SAR data used in this study were acquired in the second half of the thawing season, and rainwater can easily infiltrate into the ground, and percolate down to deeper, dry soil layers in this region. In addition, the amount of summer precipitation in this area is very low (about 150 mm) due to the continental climate. In situ soil moisture data measured at inter-alas areas in late August and September from 2005 to 2018 indicate that the average soil water content of 10-cm thick surface layer was ~ 30%, and the amplitude of the fluctuation was ~ 7%. The InSAR phase error related to the change in soil moisture was estimated to be less than 1 cm.
In addition, error analysis of the stacking treatment in Rouyet et al. (2019) was conducted in our study. Rouyet et al. (2019) estimated the standard deviation of the stacking results of 0.25–0.35 cm per summer, assuming a standard deviation of 0.5 cm per interferogram due to the atmosphere, and using Eq. 11, given by Emardson et al. (2003). We carried out a similar analysis using Eq. 10 from Emardson et al. (2003), and the standard deviations of all interferograms. The standard deviation of the phase at each interferogram was calculated by masking out the displacements (indicated by the red arrows in Fig. 4a, and solid lines in Fig. 4b, c), which we identified using qualitative interpretation. Finally, the standard deviations of the stacking results of FBD (Fig. 4a), SM3 (Fig. 4b), and SM3-inter-annual (Fig. 4c) were estimated to be 0.24, 0.11, and 0.23 cm yr−1, respectively.
Spatial distribution of subsidence and land cover
The ALOS and ALOS-2 results reveal the spatial distribution of surface subsidence in Mayya (Figs. 3, 4 and 5). The spatial variation of the displacement signals in FBD (Figs. 3a and 4a) is less clear than in SM3 (Figs. 3b and 4b, c). This is because the spatial resolution of SM3 (10 m) is twice that of FBD (20 m), and the B-perp of each SM3 interferogram was much smaller than that of FBD (Table 1; Ohki et al. 2018), leading to higher coherence (Additional file 1: Fig. S1a, b). The magnitude and location of the subsidence signals in the FBD and SM3 stacking results (Fig. 4a, b) differ for each period, which may indicate temporal changes in the subsidence rates. Moreover, the spatial variation of the displacement signals in SM1 (Figs. 3c and 6) is much clearer than that of SM3, owing to a shorter temporal baseline (14–42 days), and the SM1 images (3 m) having a much finer resolution than those of SM3. This enables us to identify the spatially smaller scale signals (~ 30 × 30 m2) not detected by the SM3 images.
We compared the distribution of the displacement signals with land cover (Fig. 2b). The distribution of the subsidence signals corresponds to that for bare ground and/or grass, and not for forested areas. This agreement implies that the SAR microwaves can reach the surface of the ground and grass in open areas, but that it may not reach the surface in the forest due to interference of trunks and branches, which may mask ground displacement. When the tree structure deforms with or without the ground-surface displacement, those areas will show decorrelation with InSAR and information on ground displacement will not be available. Another possibility is that the forested ground was stable. The forest’s vegetation layer can act as insulation to prevent permafrost from thawing (Shur et al. 2011; Iwahana et al. 2016a), which may cause little surface displacement in the forested ground. The coherence in the forest was at least moderate (Additional file 1: Figs. S1 and S2), which indicates some information on the ground surface deformation is available in the interferograms. Therefore, we believe that some of the microwaves could reach the ground surface and return as coherent signals, providing information regarding ground surface deformation.
Site visit and implications
To confirm whether the InSAR displacement signals are valid, we visited some places where the subsidence signals were detected at the end of September 2018. Figure 6a is a local photograph at A1 in Fig. 3, which is located in an alas. Alasses are considered the final geomorphological stage of old thermokarst development (e.g., van Everdingen 2005), where no further thermokarst subsidence is expected. Thus, the signal at A1 may not be caused by the thermokarst. The two subsidence areas (A1 and A2) are shown in Fig. 3 (a single interferogram showing seasonal and 1-year displacement) and Fig. 4b, c (seasonal and inter-annual displacement derived from SM3) but are almost missing in Fig. 4a (seasonal and inter-annual displacement derived from FBD). During the ALOS operation, the alasses at A1 and A2 were almost flooded, due to meteorological conditions in 2006–2009 (Iijima et al. 2010). This led to a substantial decrease in coherence at A1 and A2 in most ALOS InSAR pairs, and the missing displacement value (Fig. 4a). In contrast, during the operation period of ALOS-2 (2015–2018), the ground surface in the alasses at A1 and A2 was mostly dry; therefore, ALOS-2 InSAR obtained high coherence and detected the displacements at A1 and A2 (Fig. 4b, c). In addition, the two subsidence signals in the stacking results appear clearly in Fig. 4a, b, but less so in Fig. 4c. This suggests that the signals in A1 and A2 are caused mainly by seasonal displacement. Figures 3a, c, and 5 show the seasonal subsidence at A1 and A2 of up to 4 cm from July to September in 2009 and from mid-August to the end of September in 2018, respectively. The signals in A1 and A2 in Fig. 3b indicate positive (i.e., uplift) because we considered the magnitude of uplift due to frost heave in 2017–2018 to be greater than that of the subsidence caused by a seasonal permafrost thaw in 2018. The result from Fig. 4c was derived using the interferograms including the result in Fig. 3b, but other SM3 interferograms indicated clear subsidence, which resulted in little displacement in A1 and A2 between 2015 and 2018.
It is interesting to note that we observed new developments of polygonal subsidence in the bottom area of the alas (Fig. 6a), which implies that massive ground ice remains in the permafrost under the alasses. Polygonal texture often emerges due to preferential ground subsidence along with the location of massive ground ice after surface disturbances and following thermokarst processes (Iwahana et al. 2016b). Although no inter-annual displacement is apparent to date (Fig. 4c), the land has the potential for further thermokarst progress (Ulrich et al. 2017).
Comparison of field observations and InSAR
We compared the results of field observations in 2017–2018 (Table 2, Fig. 6b) with the InSAR results (Fig. 7). Figure 7a, b shows an enlarged view of the SM3 single interferogram obtained on September 29, 2017 and September 28, 2018 (same as Fig. 3b) in the field survey area, and on October 2, 2015 and September 28, 2018 at Plot E. A comparison of the field survey and the InSAR-based displacement is shown in Fig. 7c. The three measured values (Plots A, D, and E) are comparable to those of the InSAR measurement (Fig. 7a, b), while the two measured values (Plots B and C) are noticeably greater than those measured by InSAR (Fig. 7a) by one order of magnitude.
Frost jacking of benchmarks could be a significant source of error in permafrost regions. In our study, detailed information about the installation of the reference pipe placed in the underlying permafrost for ground temperature measurement is not available. A potential error arises from possible frost jacking of the reference pipes, and resulting in the overestimation of the measured subsidence rate. However, the differences in surface displacements between Plots A and B, and Plots C and D are significant because the same reference pipes were used for both site pairs. Plots B and C were selected from areas of relative depression with bumpy relief, which is often observed as an initial stage of thermokarst development in this region (Soloviev 1973; Bosikov 1991). In contrast, Plots A and D were selected from relatively flat and stable areas surrounding Plots B and C, respectively. Judging by the average displacement of less than 1 cm at Plots A and D, the impact of frost jacking was negligible during our study, and the greater subsidence observed at Plots B and C was relative to the surrounding stable areas.
We also do not consider that the significant differences between the InSAR and field measurements to have been caused by turbulent atmospheric effects and soil moisture changes. Significant spatial variations in atmospheric moisture content within 100 m (the distance between Plots A and B or C and D) are unlikely. However, preferential changes in soil moisture at Plots B and C could have influenced the InSAR signals. We believe that the underestimate of subsidence by InSAR for Plots B and C could be partially attributed to a local decrease in soil moisture. The decrease in surface moisture at only Plots B and C is improbable considering the relatively depressed (concaved) relief.
Based on these discussions, there are three possible reasons for the discrepancy. Firstly, the InSAR measurements in this study might not have been sensitive to the spatial variations in surface displacement measured by our ground survey at Plots B and C Thermokarst is present locally within the observation area (Figs. 2e and 6b) and causes polygonal surface subsidence. Each polygon has a diameter of ~ 5–6 m (Fig. 6b), and the magnitude of thermokarst subsidence varies at the trough (the space between polygons) and center of the polygon, where the maximum and minimum subsidence occur, respectively. Given a spatial distribution of polygons in a pixel, most parts of the pixel are occupied by the center of polygons because the area of the trough is much smaller than that of the center. InSAR may not detect the subsidence in a trough but may detect averaged subsidence in the center of polygons, which may cause underestimation of surface subsidence by InSAR in thermokarst-affected areas. Second, field measurements might have been inaccurate, and third, the spatial representativeness of surface displacement by leveling does not match that of InSAR because of the insufficient number of measurement points at Plots B and C. However, it is unlikely that only the measurements at Plots B and C were inaccurate. The validity of the distribution and number of measurement points by leveling will be discussed in future work.
The inter-annual subsidence signals detected by SM3 (T1–T5 in Fig. 4c) cover approximately 400 × 400 m2, and we identified abundant polygonal relief in each area from high-resolution optical images. The T5 subsidence signal corresponds to Plot E, and the polygonal relief was also identified from the ground survey. The results of the ground survey are in good agreement with those of the InSAR (Fig. 7b, c) and the stacking (Fig. 4c). Assuming a similar situation, the subsidence signals should be significant for the T1–T4 areas although we have no field observations.
Separating seasonal and inter-annual changes in surface subsidence
Surface displacement related to the permafrost process is composed of seasonal (thaw settlement/frost heaving) and inter-annual (thermokarst) changes. Stacking processing is a simple method to extract small displacements assuming that the displacement rate is constant for each period. Therefore, our stacking results contain both seasonal and inter-annual displacements (Fig. 4a, b).
Major InSAR time-series analysis methods, such as the small baseline subset (SBAS) approach (Berardino et al. 2002), persistent scatterer InSAR (PS-InSAR) technique (Ferretti et al. 2001), and a combination of the two (Hooper 2008), were originally applied to derive small displacements such as inter-seismic deformation (e.g., Takada et al. 2018) and land subsidence (e.g., Ishitsuka et al. 2014). These methods are useful for identifying not only linear trends of surface displacement but also cyclic trends (seasonal changes) using fitting trigonometric functions and inversion algorithms. For example, Liu et al. (2015) used the SBAS technique to examine permafrost thaw subsidence in Alaska and derived thermokarst-induced and seasonal subsidence using 18 ALOS interferograms, with the inversion algorithm described in Liu et al. (2012). The inversion algorithm requires a sufficient number of interferograms to estimate an appropriate trend; however, the number of high-quality interferograms is often limited in some areas. Chen et al. (2018b) first applied the PS-InSAR technique to ALOS/PALSAR data to derive permafrost thaw subsidence in the Qinghai-Tibet Plateau with a rate ranging from 0.3 to 3 cm yr−1 using 17 scenes of ALOS. SAR images acquired during the snow-covered season were used in the study, which may include errors associated with snow accumulation. Moreover, to extract PS points over the permafrost area, a low threshold should be set for determining the PS points, which may lead to low-quality results. In our study area, there are 17 scenes of ALOS/PALSAR data, and 12 of them were acquired in the snow-cover season. Thus, we only used five scenes obtained during the snow-free season to avoid the influence of snow accumulation. In ALOS-2/PALSAR-2, there were one or two acquisitions over Mayya until 2018 for a year, and fewer than ten acquisitions since the ALOS-2 launch. Therefore, the ALOS and ALOS-2 InSAR data (Table 1) available for time-series analysis are limited. Considering InSAR pairs for stacking, however, we derived the inter-annual displacement (Fig. 4c). This resulted from L-band data maintaining coherence over 3 years (Additional file 1: Fig. S2). We were unable to capture the complete of thaw and freeze cycle using interferograms (Fig. 5), and larger amounts of ALOS-2 data would enable us to simultaneously estimate seasonal and long-term surface displacement.
Advantages and limitations of L-band SAR for monitoring permafrost land
In the 2010s, many studies of deformation related to permafrost using SAR data have been reported (e.g., Liu et al. 2010, 2015; Short et al. 2011, 2014; Iwahana et al. 2016a; Antonova et al. 2018; Chen et al. 2018a, b; Strozzi et al. 2018), which highlighted the advantages and disadvantages of different bands (X, C, and L). X-band data such as TerraSAR-X have a high spatial resolution and a relatively short temporal revisit interval of 11 days, enabling us to generate a highly coherent interferogram. However, the temporal decrease in coherence is more rapid than that for C- and L-band data; therefore, it was used to examine only seasonal changes. Antonova et al. (2018) used TerraSAR-X SAR data to examine seasonal thaw settlement in Northern Siberia, and they detected seasonal thaw subsidence of up to 2 cm in 2013, derived from eight cumulative interferograms with moderate coherence. They demonstrated that X-band InSAR is unsuitable for monitoring inter-annual subsidence due to a quick coherence drop for even 22 days, which has already been confirmed (Short et al. 2011; Wang et al. 2017). Sentinel-1A and -1B have a C-band SAR sensor with a revisit interval of 6 or 12 days, and a wide observation swath (up to 250 km for the nominal mode), which provides us much more frequent interferometric images than ALOS-2. The coherence of Sentinel-1 interferograms spanning 48 days is moderate, and capable of capturing spatial details and identifying non-uniform seasonal displacement (Chen et al. 2018a). Although coherent interferograms spanning 1 year, using images obtained at the end of summer could be generated using Sentinel-1 C-band data in some cases (Strozzi et al. 2018), our study indicates that L-band InSAR maintains coherence over a few years (Additional file 1: Fig. S2), which could derive inter-annual subsidence (Fig. 4b), even when using a small number of interferograms, because of the low latency of ALOS-2. These coherent interferograms spanning 1–3 years are necessary to measure inter-annual subsidence, such as thermokarst and better understand the thermokarst process (Strozzi et al. 2018; Shiklomanov et al. 2013).
The moderate-to-high observation frequency of SAR satellites (shorter than 1 month) is crucial for deriving both seasonal and inter-annual displacement in permafrost dynamics. Although the 14-day revisit interval of ALOS-2 is much shorter than that of ALOS (46 days), there are some areas (e.g., Siberia) where the observation frequency of ALOS-2 is quite low. A new L-band SAR satellite, ALOS-4, will be launched in the 2021 Japanese fiscal year and will provide an observation swath of up to 200 km in high-resolution mode (3 m); therefore, the observation frequency will increase (Motohka et al. 2018). Moreover, ALOS-4 will fly in the same orbit as ALOS-2, which enables us to perform interferometry between ALOS-2 and ALOS-4 data (Motohka et al. 2018). Therefore, we expect more frequent acquisitions of L-band SAR data for a longer period. The currently operating SAtélite Argentino de Observación Con Microondas (SAOCOM) by Comisión Nacional de Actividades Espaciales (CONAE), and the upcoming National Aeronautics and Space Administration (NASA) and Indian Space Research Organization (ISRO) L-band SAR NASA ISRO synthetic aperture radar (NISAR) data will also contribute to a better understanding of permafrost dynamics. This is especially significant for the monitoring of inter-annual displacements, such as thermokarst, providing that ground observation data are obtained for a more accurate estimation of thermokarst subsidence by InSAR in Central Yakutia.