Relating optical and microwave grain metrics of snow: The relevance of grain shape
Abstract. While optical properties of snow are predominantly determined by the specific surface area (SSA), microwave measurements are often analyzed in terms of the exponential correlation length ξ. A statistical relation between both is commonly employed to facilitate forcing of microwave models by optical measurements. To improve the understanding of ξ and establish a link between optical and microwave grain metrics we analyzed the third order term in the expansion of the correlation function that can be regarded as a shape parameter related to mean and Gaussian curvature. We show that the statistical prediction of the correlation length via SSA is considerably improved by including the shape metric. In a second step we address the chord-length distribution as a key quantity for geometrical optics. We show that the second moment of the distribution can be accurately related to density, SSA and the shape parameter. This empirical finding is supported by a theoretical relation between the chord length distribution and the correlation function as suggested by small angle scattering methods. As a practical implication, we compute the optical shape factor $B$ from tomography data. Our results indicate a possibility of estimating ξ by a careful analysis of shape corrections in geometrical optics.