Simulating isothermal aging of snow

A Monte Carlo algorithm to simulate the isothermal recrystallization process of snow is presented. The snow metamorphism is approximated by two mass redistribution processes: surface diffusion and sublimation-deposition. The algorithm is justified and its parametrization is determined. The simulation results are compared to experimental data, in particular, the temporal evolution of the specific surface area and the ice thickness. We find that the two effects of surface diffusion and sublimation-deposition can accurately model many aspects of the isothermal metamorphism of snow. Furthermore, it is shown that sublimation-deposition is the dominant contribution for temperatures close to the melting point, whereas surface diffusion dominates at temperatures far below the melting point. A simple approximation of gravitational compaction is implemented to simulate density change. Copyright c © EPLA, 2010 Introduction. – The structural transformation of snow as a result of recrystallization has become an increasingly investigated field of research over the past few years. Isothermal metamorphism of snow was recently studied experimentally in ref. [1], providing measurements of detailed microstructural properties. Most experiments were performed with in vitro X-ray microtomography [2], while we used in situ X-ray microtomography. This approach provides the possibility to directly analyze the evolution of the same snow crystals in space and time. Isothermal metamorphism of snow is a sintering process between the ice grains forming the snow [3]. Various studies, although not always agreeing in every point [4–7], lead to assume that amongst the possible mass redistribution processes such as sublimation-deposition, grain boundary diffusion, plastic flow, surface diffusion, viscous flow and volume diffusion, only a few processes significantly contribute to the isothermal metamorphism of snow [1]. Surface diffusion and sublimation-deposition are believed to be the most dominant ones [8,9]. Isothermal metamorphism of snow has been stated to be similar to the evolution of bicontinous interfaces during coarsening [10]. Predictive simulations by means of numerical models of isothermal recrystallization of snow are hoped to lead to a deeper understanding of the governing processes (a)E-mail: [email protected] of snow metamorphism and might become a helpful tool in applications such as avalanche forecasting. The current models [2,11] use a macroscopic approach. Here we used a model which is based on a direct simulation by means of Monte Carlo processes, similar to the model of ref. [12], but using effective ice particles instead of real molecules. The model presented in this paper implements the two dominant mass redistribution effects in isothermal metamorphism, for the effective ice particles. In order to directly compare and validate the simulation results with the experimental ones, important structural quantities, the specific surface area and the shape of the ice matrix, are measured and compared. Experiments. – Experimental data has been obtained by Kaempfer and Schneebeli [1] from four samples of freshly fallen snow, which was sieved at −20 C through a 1mm sieve and filled in cylindrical sample holders with a diameter of 18.5mm, which were sealed to avoid sublimation. The samples were kept for about 11 months in a temperature controlled environment at four different constant temperatures: −54 C, −19.1 C, −8.3 C and −1.6 C. Roughly once per month, the samples were i) weighed, ii) the snow height in the sample holders was determined, and iii) the samples were imaged with a micro computer tomograph (μCT). During the μCT measurement, the samples were exposed to a temperature of