Modeling spatial autocorrelation in geostatistical models with applications to siberian permafrost thaw rates

Abstract

Spatial autocorrelation the tendency of nearby locations to exhibit similar values is both a feature and a nuisance in geostatistical modeling of permafrost thaw. Ignoring it inflates standard errors and biases regression coefficients. This research models spatial autocorrelation in permafrost active layer thickness (ALT) across 138 monitoring sites in central Siberia (1998-2022) using four variogram-based geostatistical models: ordinary kriging, universal kriging, kriging with external drift, and a Bayesian geostatistical model. Moran’s I confirmed strong positive spatial autocorrelation (I = 0.67, p < 0.001). The Matérn variogram family provided the best fit across sites (mean RMSE 14.3 cm for ALT predictions). Universal kriging with mean annual air temperature as drift outperformed ordinary kriging by 18.7 percent in cross-validated RMSE. Thaw rates averaged 1.23 cm/year over the 25-year period, with the fastest rates (1.87 cm/year) in discontinuous permafrost zones. Neglecting spatial autocorrelation inflated trend standard errors by 34.2 percent, demonstrating the practical cost of ignoring spatial structure in cryospheric research.