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.

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:

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.

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.