Relating optical and microwave grain metrics of snow: the relevance of grain shape

Quirine Krol,Henning Löwe

doi:10.5194/tc-10-2847-2016

Abstract

Abstract. Grain shape is commonly understood as a morphological characteristic of snow that is independent of the optical diameter (or specific surface area) influencing its physical properties. In this study we use tomography images to investigate two objectively defined metrics of grain shape that naturally extend the characterization of snow in terms of the optical diameter. One is the curvature length λ2, related to the third-order term in the expansion of the two-point correlation function, and the other is the second moment μ2 of the chord length distributions. We show that the exponential correlation length, widely used for microwave modeling, can be related to the optical diameter and λ2. Likewise, we show that the absorption enhancement parameter B and the asymmetry factor gG, required for optical modeling, can be related to the optical diameter and μ2. We establish various statistical relations between all size metrics obtained from the two-point correlation function and the chord length distribution. Overall our results suggest that the characterization of grain shape via λ2 or μ2 is virtually equivalent since both capture similar aspects of size dispersity. Our results provide a common ground for the different grain metrics required for optical and microwave modeling of snow.

Highlights

Linking physical properties of snow to the microstructure always requires the identification of appropriate metrics of grain size
To provide confidence of the interpretation of the curvature metrics derived from the two-point correlation function, we present an independent validation of these quantities via the triangulation of the ice–air interface
In contrast to λ1 and λ2, the interpretation of first and second moments of the chord length distribution, μ1 and μ2, is rather straightforward, where μ1 is directly related to the optical diameter dopt, and μ2 is a measure of the variations of this size metric

Summary

Introduction

Linking physical properties of snow to the microstructure always requires the identification of appropriate metrics of grain size In this regard the two-point correlation function has become a key quantity for the prediction of various properties such as thermal conductivity, permeability and electromagnetic properties of snow (Wiesmann and Mätzler, 1999; Löwe et al, 2013; Calonne et al, 2014b; Löwe and Picard, 2015). The analysis of two-point correlation functions was already used in the era before micro-computed tomography (μCT), where thin section data and stereology were employed to obtain the required information (Vallese and Kong, 1981; Zurk et al, 1997; Mätzler and Wiesmann, 1999). The relevance of the two-point correlation function for microwave modeling originates from the connection between its Fourier transform and the scattering phase function in the Born approximation for small scatterers (Mätzler, 1998; Ding et al, 2010; Löwe and Picard, 2015) or the connection to the effective dielectric tensor via depolarization factors (Leinss et al, 2016)

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Discussion

Conclusion