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 λ 2 , related to the third-order term in the expansion of the two-point correlation function, and the other is the second moment µ 2 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 λ 2 . Likewise, we show that the absorption enhancement parameter B and the asymmetry factor g G , required for optical modeling, can be related to the optical diameter and µ 2 . 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 λ 2 or µ 2 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.

ABSTRACT. The structural evolution of snow under metamorphism is one of the key challenges in snow modeling. The main driving forces for metamorphism are curvature differences and temperature gradients, inducing water vapor transport and corresponding crystal growth, which is detectable by the motion of the ice/air interface. To provide quantitative means for a microscopic validation of metamorphism models, a VTK-based image analysis method is developed to track the ice/air interface in time-lapse μCT experiments to measure local interface velocities under both, isothermal and temperature gradient conditions. Using estimates of local temperatures from microstructure-based finite element simulations, a quantitative comparison of measured interface velocities with theoretical expressions is facilitated. For isothermal metamorphism, the data are compared with a kinetics and a diffusion limited growth law. In both cases the data are largely scattered but consistently show a mean curvature dependency of the interface velocity. For temperature gradient metamorphism, we confirm that the main contribution stems from the temperature gradient induced vapor flux, accompanied by effects of mean curvature as a secondary process. The scatter and uncertainties are discussed in view of the present theoretical understanding, the experimental setup and complications such as mechanical deformations.

No abstract

Presently a unified treatment of microstructure dynamics in terrestrial snow from principles of ice crystal growth is hindered by the lack of models for the evolution of the bicontinuous ice matrix. To this end we developed a rigorous microstructure upscaling scheme which is based on common pore-scale (vapor diffusion) principles of crystal growth to predict the averaged evolution of the interface morphology. We derived a coupled set of evolution equations for the (volume averaged) ice volume fraction, surface area per unit volume, Gaussian curvature and first and second moment of the mean curvature distribution and demonstrate their correctness by a comparison to interface tracking of idealized grains. In a second step we use the model as a benchmark tool without a-priori assumptions for a comparison to experiments of snow microstructure evolution via image analysis on 4D X-ray tomography data. The benchmarking allows quantifying uncertainties from local estimates of crystal growth velocities. Finally we demonstrate how the rigorous model facilitates a statistical assessment of common growth laws by combining 4D microstructure data with finite element numerics. The results show that the prediction of the surface area evolution from first principles demands further conceptual insight from ice crystal growth.

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.