Figure 10. Non-dimensional heave rate profiles of an ice lens as a function of its boundary position, based on the analytical model by Rempel et al (2004). Five cases of non-dimensional overburden pressure \(p_{0}\) and porosity \(\phi\) are shown.
In order to interpret the detected frost heave signal on the basis of the theory by Rempel et al (2004), we first examine the sensitivity of the heave rate on the normalized overburden pressure \(p_{0}\) and porosity \(\phi\). Figure 10 shows five cases of non-dimensional heave rate profiles as a function of the ice lens boundary position\(\xi_{l}\), indicating that the maximum heave rate is mainly controlled by the normalized overburden pressure \(p_{0}\) and is somewhat insensitive to the porosity \(\phi\). Details of the heave rate profiles will depend on the assumed models of permeability and ice saturation, but the qualitative characteristics are not altered (Rempel et al., 2004). There exist two positions that give the same heave rate, but only the branch with smaller \(\xi_{l}\) is stable (Worster and Wettlaufer, 1999; Rempel et al., 2004).
We can attribute the clear contrast in the frost heave signals inside and outside the burned area to the differences in the normalized overburden pressure \(p_{0}\). Because the mechanical overburden pressure \(P_{0}\) will not significantly differ from the inside to the outside of the burned area, the larger frost heave rate in the burned area would be caused by larger temperature gradient \(G\) and/or deeper frozen depth \(z_{f}\). Owing to the removal of vegetations and surface organic layers over the burned area, the larger temperature gradient\(G\) than that of the unburned area is likely more marked in the early freezing season and may generate a greater thermomolecular force that will effectively reduce the normalized overburden pressure. We may also interpret the absence of frost heave signals in mid-winter as due, probably, to the smaller temperature gradient \(G\) than that in late fall/early winter; if frost heave were controlled by temperature instead of temperature gradient, we would expect even more significant signals during the much colder part of the season. The deeper frozen depth\(z_{f}\) is also likely due to the loss of surface vegetation and should supply more water for frost heave.
From the end of September to the middle of November 2017, Figure 6 shows LOS changes by approximately 1.5 cm over 12 days toward the satellite that corresponds to an approximate 1.9 cm uplift. Assuming a constant-rate frost heave, this corresponds to a heave rate of 1.8\(\times\ \)10-8 (m/s). The most critical parameter controlling heave rate is the permeability for ice-free soil \(k_{0}\), which can vary by orders-of-magnitude, while other parameters are well-constrained. We may fit our observed heave rate with the ice-free permeability, \(k_{0}\)~10-17(m2), which is a likely value in view of the three cases in Rempel (2007).
Here we comment on the modeling of uplift signals as caused by in situ freezing of pore water into ice (Hu et al., 2018). The in situ freezing model is simple, and can explain the timing, duration, and magnitude of uplift signals, if one assumes such pore water in the active layer. However, because the Stefan function approach in Hu et al (2018) is essentially controlled by atmospheric (or ground) temperature that is rather homogeneous over this spatial scale, it is difficult to account for the observed heterogeneous distribution of uplift signals. The distribution of uplift signals was closely correlated with that of subsiding signals, which led us to interpret that the permafrost thaw and its incomplete drainage could become a water reservoir for ice lens formation and frost-heave. The frozen pore ice within the soil and the ice lens formed by water migration are totally different in terms of their formation mechanisms and subsequent forms of ice. From a geomorphological perspective, the presence of ice lenses will play a role in reducing the strength of soil and potentially initiating ALDS, because porewater pressure will increase at the front of thawing, whereas pore ice within the soil would simply stay as pore water with little impact on the landform.
We also recognize, however, that the microphysics-based theory adopted in this study is developed in 1-D geometry and is based on the assumption of “frozen fringe”, a region where liquid freezes into ice through the pores of soil. Some laboratory experiments did not support the presence of frozen fringe (e.g., Watanabe and Mizoguchi, 2000), and the “fringe free” frost heave theory has also been proposed; see Peppin and Style (2013) for review. In addition to the controlled lab experiments and theoretical developments, more detailed observations of natural frost heave signals are becoming possible and might help better understand the physics of frost heave and its geomorphological consequences.
6 Conclusions
We used L-band and C-band InSAR to detect post-wildfire ground deformation at Batagay in Sakha Republic, showing not only subsidence signal during the thawing season, but also uplift during the early freezing season and virtually no deformation in midwinter without loss of coherence. Time series analysis allowed us to estimate cumulative displacements and their temporal evolution, as quality interferograms could be obtained even in the winter season. We found that the thawing of permafrost in the burned area lasted three years after the fire, but apparently slowed down after five years. During the studied period, no significant slope-parallel sliding was detected, and the post-wildfire deformation was mostly subsidence. Despite the rather homogeneous burn severity, the cumulative subsidence magnitude was larger on the east-facing slopes and showed a clear correlation with the development of gullies, suggesting that the east-facing active layers might have been originally thinner. Short-term interferograms (2017–2018) indicated that the subsidence and uplift was clearly enhanced compared with the unburned site. We have thus interpreted the frost heave signals within a framework of premelting dynamics. Post-wildfire areas are a focus of permafrost degradation in the Arctic region.
Acknowledgments, Samples, and Data
This study is supported by Researcher’s Community Support Projects of Japan Arctic Research Network Center in 2016-2019, and by KAKENHI (19K03982). PALSAR2 level 1.1 data are provided by the PALSAR Interferometry Consortium to Study our Evolving Land Surface (PIXEL) and the ALOS2 RA6 project (3021) under cooperative research contracts with the JAXA. Sentinel-1 SLC data are freely available. TanDEM-X DEM copyrighted by DLR and were provided under TSX proposal DEM_GLAC1864. Climate data at Verkhoyansk, Russia, are available from ClimatView site; http://ds.data.jma.go.jp/tcc/tcc/products/climate/climatview/outline.html. We thank Go Iwahana for discussing our preliminary results. We also acknowledge Lin Liu, two anonymous reviewers and the editors, Joel B. Sankey and Amy East, for their extensive and constructive comments, which were helpful in improving the original manuscript.
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Table 1. Data list of ALOS2 for interferograms in Figures 4a-4e and Figure 7.