Multiscale modelling of snow microstructure

A three-dimensional multiscale spatial model of snow with evolving microstructure is presented. Many engineering and environmental problems require a comprehensive understanding of snow behavior which arises as a consequence of phenomena spanning a wide spectrum of spatial length scales. Snow is classically described as a granular heterogeneous medium consisting of air and three water phases: ice, vapor, and liquid. The ice phase consists of grains arranged on a matrix according to a random load-bearing skeleton. The challenge is to achieve a detailed description of the mechanical and morphological characteristics of different snow microstructures that may have the same global density. Snow density can be determined by in situ measurements with quite good accuracy, and by means of the box-counting method, the fractal dimension of snow samples characterized by grains with different diameters could be determined. It was suggested that the fractal dimension can be adopted as a relevant parameter for quantifying snow morphology, in terms of the distribution of voids, and density over a wide range of spatial scales. In this work this concept is further developed. Snow density is simulated by means of a lacunar fractal, namely, a generalized Menger sponge. Then, a fully three- dimensional invasive stochastic fractal model is adopted. This model performs a three-dimensional mapping of the snow density to a three-dimensional fractional Brownian field. In particular, snow samples with evolving microstructure are quantified as a continuous function of the fractal dimension.