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.

Estimating thermal conductivity of snow, firn, and porous ice is key for modeling the thermal regime of alpine and polar glaciers. Whereas thermal conductivity of snow was widely investigated, studies on firn and porous ice are very scarce. This study presents the effective thermal conductivity tensor computed from 64 3‐D images of microstructures of snow, antarctic firn, and porous ice at −3, −20, and −60°C. We show that, in contrast with snow, conductivity of firn and porous ice correlates linearly with density, is approximately isotropic, and is largely impacted by temperature. We report that performances of commonly used estimates of thermal conductivity vary largely with density. In particular, formulas designed for snow lead to significant underestimations when applied to denser ice structures. We present a new formulation to accurately estimate the thermal conductivity throughout the whole density range, from fresh snow to bubbly ice, and for any temperature conditions encountered in glaciers.

Snow, from its fall until its full melting, undergoes a structural metamorphism that is governed by temperature and humidity fields. Among the many possible mechanisms that contribute to snow metamorphism, those that depend only on curvature are the most accessible to modelling. In this paper, techniques of volume data analysis adapted to the complex geometry of snow are introduced and then applied to experimental tomographic data coming from the isothermal metamorphism of snow near 0°C. In particular, an adaptive algorithm of curvature computation is described. Present results on the evolution of specific surface area and anisotropy already show that such image-analysis methods are relevant tools for the characterization of real snow microstructures. Moreover, the evolution of the curvature distribution with time provides valuable information for the development of sintering models, in the same way as a possible quantitative calibration of snow-grain coarsening laws.

We carried out a study to monitor the time evolution of microstructural and physical properties of snow during temperature gradient metamorphism: a snow slab was subjected to a constant temperature gradient in the vertical direction for 3 weeks in a cold room, and regularly sampled in order to obtain a series of three-dimensional (3-D) images using X-ray microtomography. A large set of properties was then computed from this series of 3-D images: density, specific surface area, correlation lengths, mean and Gaussian curvature distributions, air and ice tortuosities, effective thermal conductivity, and intrinsic permeability. Whenever possible, specific attention was paid to assess these properties along the vertical and horizontal directions, and an anisotropy coefficient defined as the ratio of the vertical over the horizontal values was deduced. The time evolution of these properties, as well as their anisotropy coefficients, was investigated, showing the development of a strong anisotropic behavior during the experiment. Most of the computed physical properties of snow were then compared with two analytical estimates (self-consistent estimates and dilute beds of spheroids) based on the snow density, and the size and anisotropy of the microstructure through the correlation lengths. These models, which require only basic microstructural information, offer rather good estimates of the properties and anisotropy coefficients for our experiment without any fitting parameters. Our results highlight the interplay between the microstructure and physical properties, showing that the physical properties of snow subjected to a temperature gradient cannot be described accurately using only isotropic parameters such as the density and require more refined information. Furthermore, this study constitutes a detailed database on the evolution of snow properties under a temperature gradient, which can be used as a guideline and a validation tool for snow metamorphism models at the micro- or macroscale.

X-ray microtomography has become an essential tool for investigating the mechanical and physical properties of snow, which are tied to its microstructure. To allow a quantitative characterization of the microstructure, the grayscale X-ray attenuation coefficient image has to be segmented into a binary ice/pore image. This step, called binary segmentation, is crucial and affects all subsequent analysis and modeling. Common segmentation methods are based on thresholding. In practice, these methods present some drawbacks and often require time-consuming manual post-processing. Here we present a binary segmentation algorithm based on the minimization of a segmentation energy. This energy is composed of a data fidelity term and a regularization term penalizing large interface area, which is of particular interest for snow where sintering naturally tends to reduce the surface energy. The accuracy of the method is demonstrated on a synthetic image. The method is then successfully applied on microtomographic images of snow and compared to the threshold-based segmentation. The main advantage of the presented approach is that it benefits from local spatial information. Moreover, the effective resolution of the segmented image is clearly defined and can be chosen a priori.