3-D image-based numerical computations of snow permeability: links to specific surface area, density, and microstructural anisotropy

Abstract

Abstract. We used three-dimensional (3-D) images of snow microstructure to carry out numerical estimations of the full tensor of the intrinsic permeability of snow (K). This study was performed on 35 snow samples, spanning a wide range of seasonal snow types. Because the permeability is related to a characteristic length, we introduced a dimensionless tensor K*=K/ res2, where the equivalent sphere radius of ice grains (res) is computed from the specific surface area of snow (SSA) and the ice density (ρi) as follows: res=3/(SSA x ρi). Values of K*, the average of vertical and horizontal components of K*, were plotted vs. snow density (ρs) and compared to analytical models and data from the literature, showing generally a good agreement. The 35 values of K* were fitted to ρs and provide the following regression: K*=2.94 x exp(–0.013 ρs), with a correlation coefficient of 0.985. This indicates that permeability, if assumed isotropic, can be reasonably determined from SSA and ρs, which are both easily measurable in the field. However, the anisotropy coefficient of K, induced by the snow microstructure, ranges from 0.74 to 1.66 for the samples considered. This behavior is consistent with that of the effective thermal conductivity obtained in a previous work.