Modeling active layer thickness in permafrost rock walls based on an analytical solution of the heat transport equation, Kitzsteinhorn, Hohe Tauern Range, Austria

The active layer thickness (ALT) refers to the seasonal thaw depth of a permafrost body and in high alpine environments represents an essential parameter for natural hazard analysis. The aim of this study is to model ALT based on bedrock temperature data measured in four shallow boreholes (SBs, 0.1 m deep) in the summit region of the Kitzsteinhorn (Hohe Tauern Range, Austria, Europe). We set up our heat flow model with temperature data (2016–2021) from a 30 m deep borehole (DB) drilled into bedrock at the Kitzsteinhorn north face. For modeling purposes, we assume one-dimensional conductive heat flow and present an analytical solution of the heat transport equation through sinusoidal temperature waves resulting from seasonal temperature oscillations (damping depth method). The model approach is considered successful: in the validation period (2019–2021), modeled and measured ALT differed by only 0.1 ± 0.1 m, with a root mean square error (RMSE) of 0.13 m. We then applied the DB-calibrated model to four SBs and found that the modeled seasonal ALT maximum ranged between 2.5 m (SB 2) and 10.6 m (SB 1) in the observation period (2013–2021). Due to small differences in altitude (∼ 200 m) within the study area, slope aspect had the strongest impact on ALT. To project future ALT deepening due to global warming, we integrated IPCC climate scenarios SSP1-2.6 and SSP5-8.5 into our model. By mid-century (∼ 2050), ALT is expected to increase by 48 % at SB 2 and by 62 % at DB under scenario SSP1-2.6 (56 % and 128 % under scenario SSP5-8.5), while permafrost will no longer be present at SB 1, SB 3, and SB 4. By the end of the century (∼ 2100), permafrost will only remain under scenario SSP1-2.6 with an ALT increase of 51 % at SB 2 and of 69 % at DB.