A rigorous approach to the specific surface area evolution in snow during temperature gradient metamorphism

Abstract. Despite being one of the most fundamental microstructural parameters of snow, the specific surface area (SSA) dynamics during temperature gradient metamorphism (TGM) have so far been addressed only within empirical modeling. To surpass this limitation, we propose a rigorous modeling of SSA dynamics using an exact equation for the temporal evolution of the surface area, fed by pore-scale finite-element simulations of the water vapor field coupled with the temperature field on X-ray computed tomography images. The proposed methodology is derived from the first principles of physics and thus does not rely on any empirical parameter. Since the calculated evolution of the SSA is highly sensitive to fluctuations in the experimental data, we quantify the impact of these fluctuations within a stochastic error model. In our simulations, the only poorly constrained physical parameter is the condensation coefficient α. We address this problem by simulating the SSA evolution for a wide range of α values and estimate optimal values by minimizing the differences between simulations and experiments. This methodology suggests that α lies in the intermediate range 10-3<α<10-1 and slightly varies between experiments. Also, our results suggest a transition of the value of α in one TGM experiment, which can be explained by a transition in the underlying surface morphology. Overall, we are able to reproduce very subtle variations in the SSA evolution with correlations of R2=0.95 and 0.99, respectively, for the two TGM time series considered. Finally, our work highlights the necessity of including kinetic effects and of using realistic microstructures to comprehend the evolution of SSA during TGM.