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 (<b>K</b>). 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 <b>K</b>, 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 <b>K</b>*=<b>K</b>/<i>r</i><sub>es</sub><sup>2</sup>, where the equivalent sphere radius of ice grains (<i>r</i><sub>es</sub>) is computed from the specific surface area of snow (SSA) and the ice density (ρ<sub>i</sub>) as follows: <i>r</i><sub>es</sub>=3/(SSA×ρ<sub>i</sub>. We define <i>K</i> and <i>K</i>* as the average of the diagonal components of <b>K</b> and <b>K</b>*, respectively. The 35 values of <i>K</i>* were fitted to snow density (ρ<sub>s</sub>) and provide the following regression: <i>K</i> = (3.0 ± 0.3) <i>r</i><sub>es</sub><sup>2</sup> exp((−0.0130 ± 0.0003)ρ<sub>s</sub>). 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, <i>K</i>, to snow density and specific surface area

Numerical homogenization of the viscoplastic behavior of snow based on X-ray tomography images

“…The original 3-D images used in this study are further described in the Supplement of Calonne et al (2012) and Wautier et al (2015). They can be obtained on request (frederic.flin@meteo.fr) after signing an agreement with Météo-France.…”

“…Thanks to the recent application of X-ray tomography to snow (Brzoska et al, 1999;Schneebeli, 2004;Kaempfer et al, 2005;Flin and Brzoska, 2008;Chen and Baker, 2010; A. Wautier et al: Numerical homogenization of the viscoplastic behavior of snow Srivastava et al, 2010;Pinzer et al, 2012;Wang and Baker, 2013;Adams and Walters, 2014;Calonne et al, 2015) good databases of 3-D images for the main snow types reported in the international classification (Fierz et al, 2009) are now available (Calonne et al, 2012;Löwe et al, 2013). Given these extensive geometrical descriptions of snow, its corresponding macroscopic behavior can be upscaled in a more systematic way thanks to the use of techniques derived from the homogenization theory (Dormieux and Bourgeois, 2002;Auriault et al, 2010).…”

Anisotropy of seasonal snow measured by polarimetric phase differences in radar time series

“…The transformation to vertical structures from initially horizontal structures has been observed in laboratory samples when vertical temperature gradients have been applied (Schneebeli and Sokratov, 2004;Riche et al, 2013;Calonne et al, 2014). Vertical as well as horizontal structures have been found in artificial snow from the cold laboratory as well as in natural seasonal snow (Calonne et al, 2012). In polar firn, vertical structures are commonly found in firn cores at different depths (e.g., Hörhold et al, 2009;Fujita et al, 2009;Lomonaco et al, 2011).…”

Rainwater propagation through snowpack during rain-on-snow sprinkling experiments under different snow conditions

“…These processes entail a higher hydraulic conductivity and snow permeability which lead to faster water flow (Calonne et al, 2012;Conway and Benedict, 1994). Rainwater introduced to the snowpack during ROS represents an important additional source of liquid water besides snowmelt which can contribute to the generation of snowpack runoff.…”

“…The hydraulic conductivity is connected to the intrinsic permeability of snow, which increases as the snow density decreases (Calonne et al, 2012). The snow in Ex.…”