Snow densification stores water in alpine regions and transforms snow into ice on the surface of glaciers. Despite its importance in determining snow-water equivalent and glacier-induced sea level rise, we still lack a complete understanding of the physical mechanisms underlying snow compaction. In essence, compaction is a rheological process, where the rheology evolves with depth due to variation in temperature, pressure, humidity, and meltwater. The rheology of snow compaction can be determined in a few ways, for example, through empirical investigations (e.g., Herron and Langway, 1980), by microstructural considerations (e.g., Alley, 1987), or by measuring the rheology directly, which is the approach we take here. Using a “French-press” or “cafetière-à-piston” compression stage, Wang and Baker (2013) compressed numerous snow samples of different densities. Here we derive a mixture theory for compaction and airflow through the porous snow to compare against these experimental data. We find that a plastic compaction law explains experimental results. Taking standard forms for the permeability and effective pressure as functions of the porosity, we show that this compaction mode persists for a range of densities and overburden loads. These findings suggest that measuring compaction in the lab is a promising direction for determining the rheology of snow through its many stages of densification.

Snow densification in alpine and polar regions transforms snowflakes into ice crystals. On the surface of glaciers and ice sheets, fresh snow is buried by new snow each winter, thereby slowly transforming into firn and then glacial ice as it compresses and descends. In cold and dry environments (e.g., melt-free accumulation areas of mountain glaciers, interior Greenland, and Antarctica), surface snow evolves due to temperature gradient metamorphism and atmospheric interactions

An important reason for studying snow compaction on glaciers, ice sheets, and snowfields is to connect a change in surface elevation to a volume of stored water. The total water volume stored in glaciers and snowpacks is important to know for current as well as future water resources and sea level rise considerations. Additionally, compaction is important for ice core analysis

In one-dimensional compaction, the body force acting on the snow is gravity, leading to an overburden pressure

The standard compaction law applied to most glaciers and ice sheets is a one-dimensional relationship for the rate of change of snow density

We now summarize the outline of the paper. In Sect.

Initial values of density and specific surface area for the four sintered low-temperature snow samples used in

To understand the microstructural origin of macroscopic snow material properties, the role of snow microstructure in avalanche initiation, and snow metamorphosis,

Schematic diagram of the snow French press:

Compaction occurs in a variety of natural and industrial processes, such as sedimentary basin formation, paper pulp dewatering, and particle flocculation, and has motivated numerous experiments and mathematical models

For dry snow that is composed of solely air and ice particles, snow density

Now from the expression in Eq. (

In the

Force balance in the vertical direction is given as

Effective pressure

Equation (

The dependence of effective pressure on the porosity of a sample has not to our knowledge been measured for snow or firn. In other systems

As shown in Fig.

At the bottom of the sample

The initial condition is that the snow sample starts with a uniform porosity throughout; i.e.,

Additionally, the height of the snow sample evolves as a free boundary during compaction according to

Compaction profiles for the theoretical model showing solid fraction change (

In our theory for the snow compaction experiments of

We solve Eqs. (

Comparison of theory with French-press experiments from

Here we compare the predictions of the theory outlined in the previous section with the experimental data of

The model, therefore, contains three inputs and seven parameters. The most important and most uncertain parameter is

The values of the fixed parameters used for the theory lines in Fig.

In general, there is excellent agreement between the theoretical predictions and the experimental data. For the bottom two samples, SLT-3 and SLT-4, the theory captures all of the major data trends and all falls well within any experimental scatter. For the top sample SLT-1, the theory does a reasonable job in capturing the data trend, yet for these parameters it does not follow the data points exactly. A better fit can be obtained by changing the parameters, indicating that this sample may be a different compaction regime than SLT-3 or SLT-4. However, the fit is reasonable enough that this sample is likely just on the edge of a new regime, if at all. In contrast to the other samples, the theory does not adequately capture the data trend of the middle sample, SLT-2. This sample is interesting because it has almost the same density and specific surface area as SLT-3, yet it responded very differently to compression loading. Due to the small size of the samples, i.e., 15.7 mm in diameter and 18 mm tall, the likelihood of defects or inhomogeneities dominating the results is quite high. Thus, the snow bonds in SLT-2 from prior sintering could have been particularly stubborn, requiring more load for a given displacement.

Another possibility for why the two snow samples SLT-1 and SLT-2 did not agree as well with the theory as SLT-3 and SLT-4 is that pressure sintering during the experiment allowed for greater bonding of snow crystals. Adding pressure is an efficient method of accelerating the rate of sintering and can lead to sinter rates that are orders of magnitude faster than by ambient surface energy differences alone

The plastic compaction theory presented here can be related back to the general firn compaction model given in Eq. (

For generalized viscous compaction,

In this paper, we articulated a mathematical model to describe the snow compaction experiments of

The data used in this paper are published and the numerical model is publicly available at

CRM and KMK started the project. CRM performed the numerical simulations, compared the model to the

The authors declare that they have no conflict of interest.

We wish to thank Alden Adolph and Xuan Wang for providing the data for Figs.

This paper was edited by Guillaume Chambon and reviewed by two anonymous referees.