Abstract
Abstract. The microstructure of a dry alpine snowpack is a dynamic environment where microstructural evolution is driven by seasonal density profiles and weather conditions. Notably, temperature gradients on the order of 10–20 K m−1, or larger, are known to produce a faceted snow microstructure exhibiting little strength. However, while strong temperature gradients are widely accepted as the primary driver for kinetic growth, they do not fully account for the range of experimental observations. An additional factor influencing snow metamorphism is believed to be the rate of mass transfer at the macroscale. We develop a mixture theory capable of predicting macroscale deposition and/or sublimation in a snow cover under temperature gradient conditions. Temperature gradients and mass exchange are tracked over periods ranging from 1 to 10 days. Interesting heat and mass transfer behavior is observed near the ground, near the surface, as well as immediately above and below dense ice crusts. Information about deposition (condensation) and sublimation rates may help explain snow metamorphism phenomena that cannot be accounted for by temperature gradients alone. The macroscale heat and mass transfer analysis requires accurate representations of the effective thermal conductivity and the effective mass diffusion coefficient for snow. We develop analytical models for these parameters based on first principles at the microscale. The expressions derived contain no empirical adjustments, and further, provide self consistent values for effective thermal conductivity and the effective diffusion coefficient for the limiting cases of air and solid ice. The predicted values for these macroscale material parameters are also in excellent agreement with numerical results based on microscale finite element analyses of representative volume elements generated from X-ray tomography.
Highlights
The thermodynamically active nature of snow, coupled with unusual high porosities, poses significant challenges to modeling heat and mass transfer in a snow cover
Snow metamorphism, induced by strong temperature gradients in a snow cover, is known to produce a highly faceted microstructure, the presence of which results in extremely weak layers in a snow cover
While strong temperature gradients are widely accepted as the primary driver in temperature gradient metamorphism (TGM), they do not fully account for the range of experimental observations
Summary
The thermodynamically active nature of snow, coupled with unusual high porosities, poses significant challenges to modeling heat and mass transfer in a snow cover. Macroscopic variables of interest include density, temperature, temperature gradient, as well as the mass flux of water vapor and the resulting deposition and sublimation that will occur within a snow cover These macroscopic variables are fundamental drivers for snow structure evolution occurring at the microscale, thereby coupling local phenomena driving snow metamorphism with macroscale heat and mass transfer. The thermal properties of the humid air may be taken to be those of dry air, and the heat capacity of dry air is constant for the temperature variations seen at the microscale This condition leads to a volume average definition for the temperature of the humid air constituent given by θha = Vha θmdV. When macroscale temperature gradients are presented as computed by the mixture theory analysis, it is not unreasonable to assume the microscale temperature gradients may be an order of magnitude higher in some areas of the RVE
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