Figure 9. Panels (a–d) indicate the time series of LOS changes at each point indicated in Figure 8. Sites (a) and (b) are located at the east facing slope. Site (c) is located at the ridge, where no deformation signal was detected by original interferograms. Site (d) is at the west facing slope.
4.3 Estimating the total volume of thawed excess ice
Post-wildfire deformation over a permafrost area presumably consists of two contributions: (1) irreversible subsidence due to melting of ice-rich permafrost below the active layer, and (2) seasonally cyclic subsidence and uplift due to freeze-thaw of the active layer (Liu et al., 2014, 2015; Molan et al., 2018). In order to separate the two processes from the observed deformation data, Liu et al (2014) used independent ground-measured ALT data to predict the ALT contribution to total subsidence. Ground-measured pre-fire ALT data were not available at this study site. Given the temporal evolution of post-wildfire deformation data (Figures 9a-9d), however, we may regard the cumulative deformation in Figure 8a as being due to irreversible subsidence during the period between October 2015 and June 2019, and estimate the total thawed volume as 3.56 \(\pm\) 2.24 \(\times\ \)106m3; the error bar is based on the root mean square of the no-deformation signals outside the burned area, which is multiplied by the burned area. However, in view of the temporal evolution in Figure 9, we could speculate that a much larger deformation was also taking place immediately after the 2014 fire until October 2015, during which, unfortunately, no deformation data are available. Thus, this estimate should be viewed as a lower estimate, with the actual volume of thawed permafrost possibly being much greater.
Nevertheless, despite its much smaller area size (Figure 1b), the thawed volume at the Batagaika megaslump is greater than 2.5\(\times\ \)107 m3 (Günther et al., 2016), an order-of-magnitude larger than our estimate above. Moreover, the thaw-subsidence rate at the fire scar is slowing down (Figure 9). We discuss the possibility of the another megaslump emergence at the fire scar in section 5.2.
5 Discussion
5.1 Similarities and differences in the ALOS-2 and Sentinel-1 interferograms: implication for insignificant slope-parallel sliding
Taking into account the imaging geometries of the ALOS2 and Sentinel-1, we could comprehensively interpret the differences in Figure 5 and also infer the actual deformation processes. The weights multiplied to the 3D-displacements, (Uew, Uns, Uud), to compute LOS changes were +0.573, +0.132, and −0.809 for ALOS2 and −0.583, +0.236, and −0.777 for Sentinel-1, respectively; eastward, northward and upward displacements were taken to be positive. Assuming the LOS changes of the two sensors are identical (which is roughly the case in Figure 4), and no north-south displacement Uns, the constraint on the east-west and up-down displacements can be derived as Uew:Uud= 0.032:1.156. The assumption of zero Uns might appear unrealistic but can be reasonable over the east- and west-facing slopes, which incidentally cover a broad area of the fire scar. As this constraint indicates the dominance of vertical displacement, we can infer that slope-parallel sliding did not take place over the east- and west-facing slopes.
In the thawing season when the vertical displacement is downward (negative), the previous constraint on the two displacements also indicates that the east-west displacement should always be westward (negative), regardless of the slope. As this is physically implausible, we may assume that east-west displacements were virtually zero over both the east- and west-facing slopes. We can thus infer a pure vertical subsidence without any east-west displacements during the thaw season. Hence, the differences between ALOS2 and Sentinel-1 in the thawing seasons (Figures 5a and 5b) will be simply equal to −0.032Uud. Therefore, we can expect systematically positive differences in the thawing season, regardless of the east- and west-facing slopes, which appear consistent with observations (Figures 5a and 5b). Quantitatively, however, the mean differences of 0.5-0.7 cm are too large to be attributable to the geometric difference alone, on account of the subsidence by as much as 5 cm or more. Here, we hypothesize the possible impact of soil-moisture changes, which can reach ~10 % of the carrier wavelength (Zwieback et al., 2015, 2016). As changes in soil moisture generate larger apparent LOS changes in L-band than in C-band InSAR, the observed differences can be likely.
In contrast to thaw subsidence frost-heave is more likely to occur towards the slope normal direction. Assuming the magnitude of slope-normal uplift, Uf, over a slope with gradientθ , the differences between ALOS2 and Sentinel-1 would be Uf (1.156 sinθ −0.032cosθ) assuming zero Uns. We estimated |θ |=1.58°, which corresponds to 55 m height difference over 2 km horizontal distance and was fairly consistent with the slope of the studied area. Meanwhile, the differences can also be considered 1.156Uew−0.032Uud, which indicates additional positive and negative effects on the east- and west-facing slope, respectively. Indeed, Figure 5c appears to depict clearer contrasts in sign on the east- and west-facing slopes. Moreover, the impact of changes in soil moisture are likely much smaller in the colder season than in the thaw season, which may explain the smaller differences in freezing seasons.
As we derived the differences over the no-deformation season (Figure 5d), we can attribute them to the atmospheric effect on ALOS2 and Sentinel-1 interferogram (Figures 4d and 4i). The overall positive differences are likely because the spatial scale of atmospheric delay was greater than the fire scar area.
Previous reports of thermokarst subsidence after fire have focused on relatively flat areas as those at the 2002 tundra fire in the central Seward Peninsula, Alaska (Iwahana et al., 2016b), the 2007 Anaktuvuk River tundra fire (Liu et al., 2014; Jones et al., 2015; Iwahana et al., 2016a), and the 2009 Big Creek Fire in the Alaskan Yukon River basin (Molan et al., 2018). As such, in addition to the broad subsidence detected by InSAR, polygonal patterns associated with ice wedge degradation became clearly visible 4-7 years after the fire by high-resolution optical and LiDAR remote sensing (Jones et al., 2015; Iwahana et al., 2016b). At the studied hillslopes, in contrast, no such polygonal patterns are likely to be detected. Nonetheless, the dominance of vertical displacements with little slope-parallel sliding indicate that rapid active-layer detachment sliding (ALDS) events were insignificant. In contrast, many ALDS events triggered by fire have been mapped at Mackenzie Valley, Canada, whose length could sometimes reach hundreds of meters (Lewkowicz and Harris, 2005). If ALDS event with such length occurred, we could have observed significant loss of interferometric coherence. It is possible, however, that local ALDS events occurred but were undetected because of the coarse resolution (~10 m) of InSAR images. Because the subsidence was caused by thawing of ice-rich permafrost, meltwater should have been supplied at the base of active layer. Considering the mechanisms of ALDS (Lewkowicz, 2007), porewater pressure increase might have been not enough to reduce the effective overburden stress and to initiate significant slope-parallel sliding. This is possibly because the meltwater could have drained through the gullies. However, in view of the significant uplift signals over the burned area even years after the fire, the meltwater is still likely to be undrained on the slope. If there were further enough water input by, for instance, warmer days and/or heavy rain, significant ALDS events may take place in the future.
5.2 What controls the heterogeneous distribution of subsidence magnitude? Possible emergence of another megaslump
The cumulative subsidence magnitude was spatially variable but showed some systematic changes. In addition to the ridges and peaks the west-facing slopes showed significantly smaller subsidence than the east-facing slopes (Figures 4 and 8a). To interpret the spatially heterogeneous subsidence, we associated burn severity and local landform with the cumulative subsidence (Figure 8). In light of the inferred dNBR (Figure 8b), which ranged from 0.2 to 0.4, the burn severity was moderate rather than high. Also, the burn severities were spatially less heterogeneous than those of cumulative subsidence and local landform. In fact, we could even identify deformation-free areas having even higher burn severity. Thus, although the fire undoubtedly initiated the subsidence, the burn severity did not control the subsequent cumulative magnitude.
Notably, however, gullies were clearly more developed on the east-facing slopes than on the west-facing slopes (Figure 8c), which were confirmed to be present at least back in 1991 by Landsat image. Considering the striking correlation between the development of gullies and the larger subsidence, there is high likelihood of a causal relationship between them. Similar dependence on the slope aspect was reported by Lacelle et al (2010, 2015), who found that hillslope thaw slumps in the Richardson Mountains–Peel Plateau, northwest Canada, predominantly developed on the east-facing slope. Lacelle et al (2015) interpreted that the active layer on the east-facing slope might be thinner because of lower amount of insolation than on the south- and west-facing slopes, which promoted a triggering mechanisms of thaw slumps because the ice-rich permafrost was closer to the surface. Although the broadly subsiding areas are not so-called thaw slumps, thinner active layers on the east-facing slope are likely and can consistently explain both the larger subsidence and the rich development of gullies. This hypothesis can be tested either by examining the surface deformations at the 2018 and 2019 fire scars and other fire scars across Siberia and other boreal regions or by performing field-based thaw-depths measurement.
The recent slowdown of the subsidence rate (Figure 9) may suggest that the 2014 fire scar could stabilize in the near future. However, although it depends on how quickly the vegetation is recovered, we do not preclude the possible emergence of another megaslump particularly on the east-facing slopes. In order to initiate thaw slumps, ice-rich permafrost needs to be exposed at the surface (Kokelj and Jorgenson, 2013), at which the initial headwall and slump floor are formed. In contrast to the thaw slumps near shorelines, coastlines and riverbanks (e.g., Burn and Lewkowicz, 1990; Kokelj et al., 2009), no mechanical erosions by waves and currents are effective on hillslopes like the studied area. For the development of retrogressive thaw slumps (RTS) on hillslopes, Lacelle et al. (2010) suggested that ALDS triggered by meteorological events could remove the overlying active layer and expose the ice-rich permafrost. Although no large-scale ALDS events were detected during the studied period, they might take place as discussed in the previous section. Moreover, Figure 8a indicates that the subsidence magnitude becomes larger toward upslope, and there are clear boundaries between the subsiding and non-subsiding portions, where an initial headwall for RTS could be exposed. Once an initial headwall has formed, subsequent retreat rate is rapid on the order of several meters per year (Burn and Lewkowicz, 1990; Lacelle et al., 2015). Thus, in order to monitor the early formation process of RTS in more detail, long-term radar remote sensing with higher spatial and temporal resolution would be necessary and promising.
5.3 Interpretation of frost-heave signals