Stochastic Modeling of Permafrost Ground Deformation Based on High-resolution InSAR Data

Permafrost ground deformation is a disturbance process with high spatial heterogeneity. With the advent of InSAR (Interferometric Synthetic Aperture Radar) monitoring of permafrost ground deformation at meter scale, statistical approaches are becoming crucial for revealing characteristics hidden in large datasets.

For this study, we use ALOS PALSAR-2 data, covering four regions and at least three years each: Central North Slope, Mackenzie River Delta, Noatak River Basin and Yamal. Building on the approach from our previous study, we represent all meter-scale deformation data in km-scale grids using data distributions. The variance of cumulative annual permafrost ground deformation shows an approximately linear relationship with the number of years in all regions. Based on this linearity, we establish a simple stochastic model for permafrost ground deformation. With this conceptual model, the probability of a region reaching a given threshold (cm) of subsidence within a specified number of years can be derived.

We calculate Pearson correlation coefficients between ERA climate forcings and statistical moments of the ground-deformation distributions at 10 km resolution. Climatic and topographic factors at 10 km show substantially higher correlations with deformation variance and kurtosis than with mean deformation. We hypothesize that climatic impacts influence permafrost ground deformation not primarily deterministically, but through the volatility term of the stochastic process.

In addition, we quantify the intrinsic temporal memory of permafrost ground deformation using an ensemble approach.  Due to the limited time-series length, we calculate the lag-1 and lag-2 correlation coefficients by treating deformation data within the same environment condition as an ensemble in a fixed state.

This study demonstrates statistical features present in meter-scale InSAR data. Our results highlight the perspective of treating permafrost ground deformation as a stochastic process and demonstrate a potential pathway for linking km-scale climate forcings to meter-scale permafrost disturbances.