The effect of change in thermal properties on the propagation of a periodic thermal wave: Application to a snowburied rocky outcrop

The propagation of a periodic thermal wave into snow is significantly altered by the presense of a shallow rock interface because of the large difference in thermal properties of the two media. The temperature distribution is modeled using classical heat conduction equations subject to a periodic diurnal or seasonal surface heat flux condition, jump conditions at the interface, and insulating conditions in the far-field. The natural length scale (skin depth) over which order unity changes in temperature occur is proportional to the square root of the timescale of the surface temperature variations. If the interface lies close to or within the skin depth then large temperature gradients can be sustained in the snow before temperature oscillations are forced through to the underlying rock. These features are explained by an analytic one-dimensional periodic solution. A numerical algorithm is constructed to solve for the temperature around plane two-dimensional rock geometries. The results show that during a period of atmospheric cooling the presence of a buried rocky outcrop increases the snow temperature and temperature gradients simultaneously to produce very favorable conditions for crystal growth and avalanche formation.