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.

中文翻译：

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雪中​​冰晶生长动力学的升级：严格的建模和与 4D X 射线断层扫描数据的比较

摘要 目前，由于缺乏双连续冰基质演化模型，从冰晶生长原理统一处理地雪微观结构动力学受到阻碍。为此，我们开发了一种严格的微观结构放大方案，该方案基于晶体生长的常见孔隙尺度（蒸汽扩散）原理，以预测界面形态的平均演变。我们为（体积平均）冰体积分数、每单位体积的表面积、高斯曲率和平均曲率分布的一阶和二阶矩推导出了一组耦合演化方程，并通过与理想化颗粒的界面跟踪进行比较来证明它们的正确性。在第二步中，我们将该模型用作没有先验假设的基准工具，通过对 4D X 射线断层扫描数据的图像分析与雪微结构演化实验进行比较。基准测试允许从晶体生长速度的局部估计中量化不确定性。最后，我们展示了严格的模型如何通过将 4D 微观结构数据与有限元数值相结合来促进对常见生长规律的统计评估。结果表明，从第一性原理预测表面积演变需要从冰晶生长中获得进一步的概念洞察。最后，我们展示了严格的模型如何通过将 4D 微观结构数据与有限元数值相结合来促进对常见生长规律的统计评估。结果表明，从第一性原理预测表面积演变需要从冰晶生长中获得进一步的概念洞察。最后，我们展示了严格的模型如何通过将 4D 微观结构数据与有限元数值相结合来促进对常见生长规律的统计评估。结果表明，从第一性原理预测表面积演变需要从冰晶生长中获得进一步的概念洞察。