Abstract
Abstract. Finding relevant microstructural parameters beyond density is a longstanding problem which hinders the formulation of accurate parameterizations of physical properties of snow. Towards a remedy, we address the effective thermal conductivity tensor of snow via anisotropic, second-order bounds. The bound provides an explicit expression for the thermal conductivity and predicts the relevance of a microstructural anisotropy parameter Q, which is given by an integral over the two-point correlation function and unambiguously defined for arbitrary snow structures. For validation we compiled a comprehensive data set of 167 snow samples. The set comprises individual samples of various snow types and entire time series of metamorphism experiments under isothermal and temperature gradient conditions. All samples were digitally reconstructed by micro-computed tomography to perform microstructure-based simulations of heat transport. The incorporation of anisotropy via Q considerably reduces the root mean square error over the usual density-based parameterization. The systematic quantification of anisotropy via the two-point correlation function suggests a generalizable route to incorporate microstructure into snowpack models. We indicate the inter-relation of the conductivity to other properties and outline a potential impact of Q on dielectric constant, permeability and adsorption rate of diffusing species in the pore space.
Highlights
The inter-relation between different physical properties of snow and their microstructural origin is crucial for a broad range of cryospheric applications, e.g. thermal conductivity and dielectric properties for microwave signatures (Barber and Nghiem, 1999), thermal conductivity and air permeability for mega-dune formation (Courville et al, 2007) or thermal conductivity and shear strength for field characterization (Domine et al, 2011)
The sample TGM-2 was measured in the snow breeder (Pinzer and Schneebeli, 2009) with a temperature gradient of 100 K m−1; depth hoar (DH)-1 and DH-2 are taken from Riche et al (2013)
We have shown that second-order bounds for anisotropic materials provide such an approach, which benefits from the strong, naturally occurring differences in snow anisotropy
Summary
The inter-relation between different physical properties of snow and their microstructural origin is crucial for a broad range of cryospheric applications, e.g. thermal conductivity and dielectric properties for microwave signatures (Barber and Nghiem, 1999), thermal conductivity and air permeability for mega-dune formation (Courville et al, 2007) or thermal conductivity and shear strength for field characterization (Domine et al, 2011). The ice volume fraction φi, which is proportional to the snow density, is the most important microstructural quantity which correlates well with physical properties. A large scatter remains if properties are constrained on density as e.g. revealed for the thermal conductivity in (Sturm et al, 1997; Domine et al, 2012). This scatter was recently investigated by simulations and experiments in a comprehensive study by Calonne et al (2011). The authors hypothesized that the remaining scatter in the thermal conductivity is caused by microstructural anisotropy. Anisotropy has a severe impact on thermal conductivity and can be utilized quantitatively, if formalized by appropriate means
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
