Snow anisotropy enables more precise determination of thermal conductivity via second-order bounds
Abstract
The evolution of macroscopic physical properties of snow and their relation to microstructural parameters is a key aspect for virtually all applications in cryospheric sciences. Snow properties are usually parametrized phenomenologically, e.g. in terms of the density (ice volume fraction) as the most important microstructural parameter which correlates well with physical properties. However, a large scatter usually remains if properties are solely constrained on density. We show that the broad range of anisotropy in natural snow, if formalized by appropriate means, can be exploited to reduce the scatter. To this end we address the effective thermal conductivity tensor of snow via known rigorous, second-order bounds. The bounds predict the relevance of a microstructural anisotropy parameter Q which is given by an integral over the two-point correlation function and thereby unambiguously defined for arbitrary microstructures. For validation we compiled a comprehensive data set of 167 snow samples. These comprise individual samples of various seasonal snow types and several time series of metamorphism experiments under isothermal conditions (duration: one year) and temperature gradient conditions (duration: weeks to months) with emphasis on depth hoar. All samples were reconstructed by micro-computed tomography to facilitate a comparison of the theory with microstructure-based Finite Element simulations of conductive heat transport. Compared to purely density based parametrizations, the incorporation of Q yields a considerably smaller error. Our systematic approach quantifies the influence of snow anisotropy and constitutes a generalizable route to incorporate snow microstructure into macroscopic snow models. By mathematical analogy, we indicate the expected impact of anisotropy on the dielectric tensor, permeability and the adsorption rate of diffusing species in the pore space.
- Publication:
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AGU Fall Meeting Abstracts
- Pub Date:
- December 2012
- Bibcode:
- 2012AGUFM.C53D..02L
- Keywords:
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- 0736 CRYOSPHERE / Snow;
- 0798 CRYOSPHERE / Modeling