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.

Natural snowpacks are frequently subjected to temperature gradients induced
by their environment. Due to temperature differences in the snowpack, the
morphology of snow at the microscale, i.e., the snow microstructure,
quickly evolves with time. This metamorphism, called temperature gradient
(TG) metamorphism, is mainly characterized by the reorganization of ice along
the gradient direction by sublimation of the warmest parts of the grains,
water vapor transport across the air pores, and its deposition on the coldest
zones of the ice matrix

In particular, snow properties are often expressed as functions of snow
density such as for the effective thermal conductivity

We propose addressing these issues by studying the evolution of snow
morphology together with several physical properties during a typical
experiment of TG metamorphism. The main objective consists in better
understanding the relationships between the snow microstructure and its
properties. In this context, our paper focuses on the description of the time
evolution of a snow slab of 294 kg m

The new contributions of this study lie in the following points: (i) a wide
range of snow properties (mean and Gaussian curvature distributions,
directional correlation lengths, specific surface area, air and ice
tortuosities, intrinsic permeability, effective thermal conductivity) are
investigated during the same experiment; (ii) the time evolution of most
properties computed in the

Natural snow was collected at Chamrousse (1800 m, French Alps) on
22 February 2011 and stored at

Photograph in cold room of the apparatus designed to control and monitor temperatures at the top and bottom of a snow slab. The front and side vertical polystyrene plates were removed from the device for visualization purposes.

The snow slab was sampled using a cylindrical core drill approximately every
3 days over the 3 weeks, leading to seven samples in total at the end
of the experiment. Macro photographs of snow particles were also taken to
characterize snow type. During the sampling operation, the temperature of the
cold room was temporarily held at

Illustration of the cryogenic cell used during the tomographic acquisition.

Microstructural and physical properties computed from 3-D images.
Snow types are given according to the international classification

Each core was scanned using the conical X-ray microtomograph of the 3SR lab
set with an acceleration voltage of 75 kV and a current of
100

DigiXCT:

Snow porosity

The specific surface area estimates along the

Two-point probability function

At a given time, within 3-D images of snow, we can define the following
characteristic function of the air phase:

At a given point on the surface of a 3-D object, the shape is characterized by two
principal curvatures,

Many techniques have been proposed to estimate mean and Gaussian curvatures
on either triangular or digital surfaces

The full 3-D tensors of tortuosity

Geodict:

To compute the effective thermal conductivity tensor

The tensor

As the non-diagonal terms of the tensors

The anisotropy coefficient

After sieving, the density of the snow slab exhibited slight spatial
inhomogeneities (300

We used two analytical estimates based on ellipsoidal inclusions to estimate
the physical properties of snow in the

The snow microstructure is considered here as a macroscopically
anisotropic composite, which corresponds to an assemblage of isotropic
ellipsoidal inclusions of air and ice with a major axis collinear with the

Schematic representation of the microstructure corresponding to the
two-point bounds and the self-consistent scheme. Effective thermal
conductivity versus ice volume fraction when

Thus, from Eqs. (

As an illustration, Fig.

The snow is seen as a dilute dispersion of ellipsoids of ice in a matrix of
air. The semiaxes of each ellipsoid are defined as

Figure

Microstructure evolution during the TG metamorphism. For each stage
of the evolution, the following views are given: (i) 3-D images of the snow
samples where colors represent the mean curvature of the surfaces, ranging
from

Time evolution of microstructural and physical properties of snow
during the whole temperature gradient experiment. Values in the

Time evolution of the anisotropy coefficient of the whole computed properties.

All the snow properties computed based on the 3-D images are summarized in
Table

The snow density shows no significant evolution with time and
the average value over the experiment is 294 kg m

The average value of the SSA estimates in the three directions decreases continuously with time from 27.7 to
13.4 m

The values of correlation length increase continuously during
the experiment, evolving from 71 to 181

The values of air tortuosity (

The raw values of the effective thermal conductivity, which are
referred as “computed” and depicted by the dashed lines in
Fig.

The computed values of permeability range between 0.70

Figure

The distributions of mean curvature of the upward (left panel) and downward
(right panel) surfaces of ice are presented in
Fig.

Time evolution of the mean curvature distribution computed from the
upward (left panel) and downward (right panel) surfaces of the 3-D images.
Each curvature class is 0.5 mm

Time evolution of the Gaussian curvature distribution computed from
the whole surface of the 3-D images. Each curvature class is 10 mm

Using the same representation, Fig.

The initial (left panel) and final (right panel) 3-D images of the
experiment where colors represent the Gaussian curvature of the surfaces,
ranging from

Time evolution of air tortuosity, thermal conductivity and
permeability during the whole experiment. Comparison between values computed
from 3-D images in the

Time evolution of the anisotropy coefficients of air tortuosity, thermal conductivity and permeability. Comparison between coefficients deduced from values computed on 3-D images (dashed lines) and values given by analytical estimates (solid lines).

Figure

Using the same representation, the time evolution of anisotropy coefficients
from computed values and values given by estimates of the three
properties above is shown in Fig.

From the mean curvature distributions (Fig.

From the temporal evolution of the snow (e.g., Fig.

Because the air tortuosity is about 5 times higher than the ice tortuosity
(see Fig.

Heat conduction in snow is mostly due to the conduction of ice which
conducts 100 times better than the air. Consequently, the effective
thermal conductivity of snow is strongly linked to its density and to the ice
tortuosity, as illustrated in Fig.

We observe two distinct stages in the evolution of the effective thermal
conductivity (Fig.

As already mentioned, the intrinsic permeability is proportional to

Figure

The computed effective properties of snow were compared with analytical
estimates based on basic information of the microstructure such as the snow
density and the anisotropy of heterogeneities (air and ice) through the
correlation lengths. Even if the analytical estimates fail to reflect all the
details of the microstructure (e.g., bonds between grains), our results
clearly show that they capture the overall evolution of the considered
properties with a mean of relative differences ranging from

In both of the presently proposed estimates, the time evolution of physical
properties during the metamorphism mainly depends on one parameter

An experiment of TG metamorphism was performed in
a cold room in order to monitor the evolution of microstructural and
physical properties of snow over time: seven snow samples were collected, at
regular time intervals over 3 weeks, from a snow slab subjected to
a vertical temperature gradient of 43 K m

The main results concerning the TG experiment can be summarized as follows: (i) as shown by many other studies, density remained almost constant during the whole experiment. (ii) The grains were continuously faceting at their bottom parts (deposition) while the upper parts underwent rounding due to ice sublimation. (iii) Overall, grain growth and neck growth were observed during the metamorphism. (iv) The intrinsic permeability, linked mainly to the air phase, increased continuously. (v) The snow microstructure evolved in two stages: a short period of strong modifications of the ice structure due to the TG initiation (0–73 h), where the ice tortuosity and the thermal conductivity decreased, followed by a stage of consolidation of this new structure (73–500 h), where the above properties increased gradually. (vi) The anisotropy coefficients of all properties increased during the metamorphism, with larger values in the gradient direction.

These results highlight the strong interplay between the microstructure and physical properties of snow, and confirm that the density alone, or any isotropic quantity, is not sufficient to describe the time evolution of physical properties during a TG metamorphism. To solve this problem, we applied analytical anisotropic estimates (self-consistent estimates and dilute beds of spheroids) using microstructural parameters (directional correlation lengths) that reflect the general shape of heterogeneities (size, anisotropy). The proposed analytical estimates, whose results were compared to those obtained by numerical computations, offer good estimations of the physical properties and anisotropy coefficients for our time series, without applying any fitting parameters.

In summary, this study presents numerical tools to quantitatively monitor snow properties using 3-D images and provides a detailed database describing snow under a TG metamorphism. In particular, it provides a quantification of snow anisotropy, which is a key – but challenging – parameter to access directly with physical measurements during such a process. Used as a guideline or a validation tool, this database offers new outlooks for the development of micro- and macroscale snow models.

We thank Henning Löwe, Martin Schneebeli, and three anonymous reviewers for their contributions in the improvement of this paper. Funding by Météo-France, INSU-LEFE and DigitalSnow (ANR-11-BS02-009-03) is acknowledged. We thank P. Charrier and J. Desrues of the 3SR laboratory, where the 3-D images were obtained. We are also grateful to J. Roulle, J.-M. Panel, P. Puglièse, C. Carmagnola and S. Morin of the CNRM-GAME for their support during the experiment. N. Calonne thanks S. Morin for his co-supervision of her master's internship, during which the TG experiment has been realized. CNRM-GAME/CEN is part of the Labex OSUG@2020 (ANR10 LABX56). The laboratory 3SR is part of the LabEx Tec 21 (Investissements d'Avenir – grant agreement ANR11LABX0030). Edited by: M. Schneebeli