A mean field model of the decrease of the specific surface area of dry snow during isothermal metamorphism

The surface area of snow that is accessible to gases is an essential parameter for quantifying the exchange of trace gases between the snowpack and the atmosphere and is called the specific surface area (SSA). Snow SSA decreases during metamorphism, but this is not described in current snow models owing to the complexity of the physics and geometry of snow. In this paper, we test whether it is possible to model snow SSA changes during isothermal metamorphism without accounting for all the complexity of the three-dimensional (3-D) structure of real snow. We have developed a mean field model of snow metamorphism under isothermal conditions, grounded in the theoretical framework of transient Ostwald ripening and representing snow as a distribution of spherical particles. Analytical expressions of the growth rates of these spheres are obtained, and the evolution of two measurable parameters that characterize snow geometry, the SSA and the distribution of radii of curvature (DRC), are simulated and compared to experimental data obtained by X-ray tomography. The qualitative effects of temperature, snow density, and the condensation coefficient on the rate of SSA decrease are examined. The model predicts very well the rate of evolution of the particle size distribution, which validates our physical description of isothermal metamorphism. In particular, we find that vapor phase diffusion is rate limiting. However, the calculation of the SSA from the DRC appears delicate and evidences too crude approximations in our description of the 3-D geometry of snow. Finally, it is stressed that the initial DRC can greatly influence the rate of SSA decrease, while experimental measurements of the rate of SSA decrease suggest that all snow types evolve in a similar way. It is thus proposed that most natural fresh snows have similar DRCs.