Investigating the thermal state of permafrost with Bayesian inverse modeling of heat transfer

Abstract. Long-term measurements of permafrost temperatures do not provide a complete picture of the Arctic subsurface thermal regime. Regions with warmer permafrost often show little to no long-term change in ground temperature due to the uptake and release of latent heat during freezing and thawing. Thus, regions where the least warming is observed may also be the most vulnerable to permafrost degradation. Since direct measurements of ice and liquid water contents in the permafrost layer are not widely available, thermal modeling of the subsurface plays a crucial role in understanding how permafrost responds to changes in the local energy balance. In this work, we first analyze trends in observed air and permafrost temperatures at four sites within the continuous permafrost zone, where we find substantial variation in the apparent relationship between long-term changes in permafrost temperatures (0.02–0.16 K yr−1) and air temperature (0.09–0.11 K yr−1). We then apply recently developed Bayesian inversion methods to link observed changes in borehole temperatures to unobserved changes in latent heat and active layer thickness using a transient model of heat conduction with phase change. Our results suggest that the degree to which recent warming trends correlate with permafrost thaw depends strongly on both soil freezing characteristics and historical climatology. At the warmest site, a 9 m borehole near Ny-Ålesund, Svalbard, modeled active layer thickness increases by an average of 13 ± 1 cm K−1 rise in mean annual ground temperature. In stark contrast, modeled rates of thaw at one of the colder sites, a borehole on Samoylov Island in the Lena River delta, appear far less sensitive to temperature change, with a negligible effect of 1 ± 1 cm K−1. Although our study is limited to just four sites, the results urge caution in the interpretation and comparison of warming trends in Arctic boreholes, indicating significant uncertainty in their implications for the current and future thermal state of permafrost.