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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