## 1. Introduction

[2] Snow on the ground is a complex porous medium made of air and up to three phases of water (ice, water vapor and liquid water). Understanding heat and mass transfer through the snowpack is critical to assess the climatic and hydrological role of snow in the cryosphere. It is also needed to predict morphological changes in snow crystals [*Brzoska et al.*, 2008; *Flin and Brzoska*, 2008; *Kaempfer and Plapp*, 2009; *Pinzer and Schneebeli*, 2009], the vertical distribution of which governs, for example, the surface energy balance and the mechanical stability of the snowpack [*Armstrong and Brun*, 2008].

[3] Heat transfer through snow proceeds by conduction through ice and air, but is also potentially affected by phase change effects, water vapor diffusion and air convection in the pores [*Arons and Colbeck*, 1995; *Sturm et al.*, 1997]. Defining in a physically sound manner the thermal conductivity of snow, i.e., the tensor (**k**) linking the macroscopic temperature gradient (*T*) and the heat flux (**F**) through the Fourier's law (**F** = −**k***T*), is thus challenging because conductive and nonconductive processes both contribute to heat transfer through snow. From experimental relationships between *T* and **F**, many investigators have derived an apparent thermal conductivity **k**^{☆}, which in general is treated as a scalar, *k*^{☆}, either assuming the medium to be isotropic, or at most focusing on its vertical component [*Yen*, 1981; *Sturm et al.*, 1997; *Kaempfer et al.*, 2005; *Morin et al.*, 2010; *Riche and Schneebeli*, 2010].

[4] To meet the needs of applications that require the thermal properties of snow to be estimated based on other physical variables (e.g., numerical snowpack models), experimental fits between *k*^{☆} and snow density (*ρ*) have been proposed [*Yen*, 1981; *Sturm et al.*, 1997; *Domine et al.*, 2011]. Such regression curves differ widely: there is up to a factor of two difference between the regression curve of *Sturm et al.* [1997] and *Yen* [1981]. In addition, a considerable scatter of measured *k*^{☆} values is found around the best fitting curve between *k*^{☆} and *ρ* [*Sturm et al.*, 1997]. Both of these issues highlight the need for a re-assessment of the variables related to *k*^{☆}, the partitioning between the various physical processes involved in heat transfer, and the experimental methods used to infer *k*^{☆}.

[5] To contribute to this effort, we carried out numerical simulations of the conductivity of snow from its microstructure. This was done using 30 different 3D images of snow obtained by means of microtomography [*Brzoska et al.*, 1999; *Coléou et al.*, 2001; *Schneebeli and Sokratov*, 2004; *Kaempfer et al.*, 2005]. Only conduction through ice and air was considered in the heat transfer, leading to computing the true effective thermal conductivity tensor of snow (**k**_{eff}) from a material science perspective [*Rolland du Roscoat et al.*, 2008]. This work follows the pioneering developments of *Kaempfer et al.* [2005], who first reported computations of the vertical component of **k**_{eff} from tomographic images and compared them to experimental data. The main differences lie in the fact that our study considers a wide range of snow types, uses the periodic homogenization method [*Auriault et al.*, 2009] and evaluates the anisotropy of **k**_{eff}. In addition, it includes thermal conduction in interstitial air, which was neglected by *Kaempfer et al.* [2005] and, more recently, by *Shertzer and Adams* [2011].