Variability of seasonal thaw depth in permafrost regions: a stochastic modeling approach

The uppermost layer of seasonal thawing above permafrost (the active layer) is an important regulator of energy and mass fluxes between the surface and the atmosphere in the polar regions. The active layer exhibits pronounced spatial variability in complex terrain, even within relatively small areas. A stochastic model was developed and used to calculate the probability density function of active-layer thickness (ALT). Equations for the mean value, variance, and higher statistical moments of ALT were derived by applying stochastic averaging to a semi-empirical model of seasonal thawing. The stochastic model was applied in a case study in the Kuparuk river region of north-central Alaska. Data on ALT collected in the period 1995–1999 at several georeferenced sites were used to calculate landcover-specific statistics of ALT. The stochastic model was used with a digital map of landforms and gridded climatological data to construct probability maps of ALT for the Kuparuk region. Results compare favorably with semi-empirical estimates of the volume of thawed soil in the Kuparuk region, but provide additional information about uncertainties associated with estimating procedures.