Fig. 6: Active layer thaw depth estimate.

Thaw depth scaled by the D₉₀ Particle Size = 0.096 m for two surface air temperature warming events. The blue curve indicates a thought experiment where a typical July surface air temperature increase of 5 °C drives active layer thaw conductively for 10 days before a relatively sharp (stepwise) 10 °C warming event is imparted at the surface. The thermal effect of this powerful warming event diffuses to the depth of the melting front over about 4 days, driving enhanced penetration of the melting front over the rest of the month. This step increase in surface temperature increases the depth of the July thaw by approximately 40%. In addition to increasing the depth of the active layer thickness by the end of the melt season, which enhances potential soil mobility, an important consequence for the subsequent melt seasons is an increase in the soil porosity and, in turn, the potential for enhanced subsurface hydrologic storage¹⁹ and potentially steeper hydraulic gradients in and around channelizing reaches within interconnected polygon trough regions. We propose that enhanced melting with channelization could introduce a positive feedback to this overall process, which would effectively contribute to advancing the seasonal thaw front even deeper into the ground, driving additional permafrost degradation¹¹. In the Muskox Valley context, we also provide an estimate of the flows associated with the equivalent lake draining time scale, assuming a lake volume loss of 10⁴−10⁵ m³ (“Methods”). Calculations assume the thermal properties of a saturated, vertically homogeneous gravelly-sand substrate. See the “Methods” section for the calculation procedure using a solution to the Stefan problem⁴⁹ scaled for the volumetric water content, and the online repository for a Jupyter Notebook detailing the parameter values, calculations and plotting of this figure.