Figure 3. Temporal distribution of interferograms for the time-series
analysis. 50 interferograms were generated from 15 ALOS2 SAR images.
3.2 Multispectral remote sensing of burn severity
Normalized burn ratio (NBR) is a useful multispectral remote sensing
index to assess the impact of wildfire on vegetation. Vegetation
reflects more strongly in the near-infrared (NIR) than in the shortwave
infrared (SWIR) region, while a fire scar reflects more strongly in the
SWIR. Utilizing this property, NBR is defined as
NBR=(NIR−SWIR)/(NIR+SWIR). The difference NBR (dNBR), i.e., the
difference between prefire NBR and postfire NBR, indicates burn severity
(Key and Benson, 2006; Miller and Thode, 2007). Generally, when dNBR is
greater than 0.66 the fire is regarded as “highly severe”. We computed
dNBR for the 2014 fire using Landsat 8, Band 5 (850-880 nm) and Band 7
(2110-2290 nm) images for near-infrared and shortwave-infrared,
respectively, to associate the inferred subsidence distribution with
burn severity.
3.3 One dimensional frost-heave theory based on premelting dynamics
We used the one-dimensional frost-heave theory as a tool to interpret
the observed uplift signals. Inspired by one-way frost heave experiments
(Mutou et al., 1998; Watanabe and Mizoguchi, 2000), Worster and
Wettlaufer (1999) and Rempel et al (2004) derived a steady-state heave
rate \(V_{l}\) of an ice lens, considering the force balance among
thermo-molecular force \(F_{T}\), hydrodynamic force \(F_{\mu}\), and
overburden force \(F_{O}\) (pressure \(P_{0}\)). Here, we assumed a
constant heave rate \(V_{l}\), which may not necessarily reflect the
actual observations shown below as well as in Hu et al (2018). However,
this assumption simplified the theory, and we assumed that the observed
heave rate did not change drastically over time. Rempel et al (2004)
proposed a non-dimensional heave rate \(v_{l}\) of an ice lens as a
function of its boundary position \(\xi_{l}\) given:
\begin{equation}
v_{l}\equiv\frac{\mu V_{l}}{k_{0}\text{ρG}}=\left[\int_{0}^{\xi_{l}}{\left(1-\phi S_{s}\right)\text{dξ}}-p_{o}\right]\left[\int_{\xi_{h}}^{\xi_{l}}{\frac{\left(1-\phi S_{s}\right)^{2}}{\tilde{k}}\text{dξ}}\right]^{-1},\nonumber \\
\end{equation}where \(\mu\), \(k_{0}\), and \(\rho\) are the viscosity of water, the
permeability of ice-free soil, density of water, respectively. The
quantity\(G\equiv\left(\frac{L}{T_{m}}\right)\left\langle\nabla T\right\rangle\)has the same dimension as gravity and indicates thermo-molecular force
when multiplied by the mass of displaced ice; \(L\) is the latent heat
of fusion and \(T_{m}\) is the bulk melting temperature. The first and
second term in the bracketed numerator are proportional to \(F_{T}\) and\(F_{O}\), respectively, while the bracketed denominator is proportional
to \(F_{\mu}\). The integral is performed along\(\xi\equiv\frac{z}{z_{f},}\) where \(z_{f}\) is the position above
(below) where ice saturation \(S_{s}\) becomes non-zero (zero);\(z_{h}\) indicates the position where hydrostatic pressure is achieved,
and \(\phi\) is the porosity of soil. The normalized overburden pressure
and permeability are defined as\(p_{0}\equiv\frac{P_{0}}{\text{ρG}z_{f}}\) and\(\tilde{k}\equiv\frac{k}{k_{0}}\geq 1\), respectively.
4 Results
We performed an inter-comparison of ALOS2/Sentinel-1 interferograms,
focusing on the seasonal changes in surface deformation. We then showed
short-term deformation derived by Sentinel-1 and long-term deformation
derived by time-series analysis of ALOS-2. Subsequently, we estimated
the total volume of thawed excess ice. Although both satellite images
covered the Batagaika megaslump we did not observe clear LOS changes as
detected at the fire scar, which could be due to the lack of spatial
resolution of the InSAR images.
4.1 Seasonal deformation and comparison of ALOS2/Sentinel-1
interferograms