Analytical solution for the periodic temperature field in frozen ground with account for variation in mean daily air temperature

This paper presents an analytical solution for temperature waves in a two-layer medium consisting of frozen ground and snow cover. Temperature waves represent diurnal temperature fluctuations relative to the mean daily value. In the literature they are known for a constant mean daily temperature value. In this paper, a solution is obtained for periodic temperature of the ground–snow system with account for variations in mean daily air temperature over the entire winter. The solution can be used in estimating the effect of snow cover on the thermal state of frozen ground in the cold season.

► Periodic temperature of frozen ground is calculated at the presence of snow cover.
► Boundary condition is set at snow cover surface.
► Variation in mean daily snow surface temperature through winter is taken into account.