Snow metamorphism: a fractal approach

TL;DR

This paper introduces a fractal-based model to quantitatively describe snow microstructure and density, revealing the strong dependence of fractal parameters on snow morphology and potentially aiding in the analysis of snow and ice evolution.

Contribution

It presents a novel three-dimensional fractal modeling approach for snow microstructure, linking density and morphology through the Hurst exponent.

Findings

Hurst exponent varies with snow density and morphology

Fractal models effectively simulate snow microstructure

Potential applications in snow cover and ice sheet analysis

Abstract

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.