Estimate the maximum depth to which frost penetrates the ground at a location where the temperature ranges between –15°C and 25°C.  Assume the temperature history at the surface is sinusoidal, and that the water content of the soil is low enough that we can ignore the latent heat associated with the phase change of water (in other words, your calculation works best in low porosity rock). Assume the thermal diffusivity of soil, k, is 0.8 mm² s^-1.;

• At this depth, how far out of phase (by what fraction of a year) will the temperature be relative to the surface. In other words, the maximum frost penetration will likely occur after the minimum in surface temperature; we are asking how much later this will occur.