Revisiting the vapor diffusion coefficient in dry snow

Abstract. A substantial degree of uncertainty surrounds the value of the diffusion coefficient for water vapor diffusing through snow under the influence of a temperature gradient. A collection of theoretical, numerical, and experimental studies suggest the value of the normalized diffusion coefficient of snow with respect to water vapor diffusing through humid air ranges from near zero to as high as 7. The challenges in quantifying the diffusion coefficient are attributed to the fact that snow is a phase changing mixture of ice and humid air. Phase changes involving sublimation and condensation of water molecules significantly alter diffusion paths that water vapor molecules must travel through in the complex ice/humid air microstructure.

I identify 4 major diffusion mechanisms caused by the introduction of an ice phase into humid air that should be accounted for in any calculation of the diffusion coefficient. Mathematical and experimentally motivated arguments enable one to estimate the physical significance of each of these diffusion mechanisms. Using this information, three separate models of increasing complexity are developed to provide estimates of the diffusion coefficient for snow. Finally, several prior studies are anchored to a formal definition of the diffusion coefficient and, if necessary, adjusted to account for the 4 diffusion mechanisms presented. The end result is a remarkable consistency in predicted values for vapor diffusion in snow, showing the normalized diffusion coefficient with respect to water vapor in air to be slightly enhanced at all densities, with typical values between 1 and 1.3. These values are consistent with the models developed herein.