  Snow is a porous disordered medium consisting of air and three water phases:
ice, vapour and liquid. The ice phase consists of an assemblage of grains, ice
matrix, initially arranged over a random load bearing skeleton. The
quantitative relationship between density and morphological characteristics of
different snow microstructures is still an open issue. In this work, a
three-dimensional fractal description of density corresponding to different
snow microstructure is put forward. First, snow density is simulated in terms
of a generalized Menger sponge model. Then, a fully three-dimensional compact
stochastic fractal model is adopted. The latter approach yields a quantitative
map of the randomness of the snow texture, which is described as a
three-dimensional fractional Brownian field with the Hurst exponent H varying
as continuous parameter. The Hurst exponent is found to be strongly dependent
on snow morphology and density. The approach might be applied to all those
cases where the morphological evolution of snow cover or ice sheets should be
conveniently described at a quantitative level.
