Theory of ground ice stability in sublimation environments

Permanently stable ground ice is found beneath a permanently frost free surface on Mars, and similar conditions exist in the Antarctic Dry Valleys. This phenomenon is due to a balance of the vapor pressure of the ice with the atmospheric humidity in the presence of large amplitude temperature oscillations. An exactly solvable model example shows that the fraction of time the atmosphere needs to be saturated to stabilize the ice decreases with temperature amplitude. It is estimated that for conditions that prevail on Mars today, the mean temperature needs to be about $5\mathrm{K}$ lower than the frost point temperature for ground ice to be stable. A decomposition method to evaluate the contribution of short term weather events to ground ice stability is developed; when applied to a study site in the Dry Valleys, it reveals that the coldest periods contribute most to stabilization.

Figure 1

Schematic model system where ground ice exchanges water vapor with the atmosphere through a layer or porous soil. Temperature oscillations decay with depth, as illustrated by a set of instantaneous temperature profiles.

Figure 2

(a) Required frost point temperature $T_f$ as a function of temperature amplitude $T_a$. The mean temperature is $T_m=200\mathrm{K}$. The solid line shows the numerical solution, the dashed line is the perturbation expansion (19), and the dotted line is approximation (21). (b) The maximum fraction of time the atmosphere can be unsaturated and still stabilize the ground ice, $\pi t_1∕\omega$.

Figure 3

Required mean temperature $T_m$ and temperature amplitude $T_a$ for a frost point temperature of $T_f=200\mathrm{K}$. The required mean temperature is only a few K less than $T_f$, even for large amplitudes. The dashed and dotted lines show approximations (19, 21), respectively.

Figure 4

Stabilization index, which is a measure of the contribution of an instantaneous event to the humidity balance between the atmosphere and the ice, for meteorological data from Beacon Valley, Antarctica [19] from 2001 to 2004. A positive index indicates an above average contribution to stabilization. The vertical dashed line shows the mean temperature.