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

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. For several snow samples, a significant anisotropy of permeability was detected and is consistent with that observed for the effective thermal conductivity obtained from the same samples. The anisotropy coefficient, defined as the ratio of the vertical over the horizontal components of K, ranges from 0.74 for a sample of decomposing precipitation particles collected in the field to 1.66 for a depth hoar specimen. Because the permeability is related to a characteristic length, we introduced a dimensionless tensor K*=K/r_es², where the equivalent sphere radius of ice grains (r_es) is computed from the specific surface area of snow (SSA) and the ice density (ρ_i) as follows: r_es=3/(SSA×ρ_i. We define K and K* as the average of the diagonal components of K and K*, respectively. The 35 values of K* were fitted to snow density (ρ_s) and provide the following regression: K = (3.0 ± 0.3) r_es² exp((−0.0130 ± 0.0003)ρ_s). We noted that the anisotropy of permeability does not affect significantly the proposed equation. This regression curve was applied to several independent datasets from the literature and compared to other existing regression curves or analytical models. The results show that it is probably the best currently available simple relationship linking the average value of permeability, K, to snow density and specific surface area.