Origin of diversity in falling snow
This paper presents a systematic way to examine the origin of variety in falling snow. First, we define shape diversity as the logarithm of the number of possible distinguishable crystal forms for a given resolution and set of conditions, and then we examine three sources of diversity. Two sources are the range of initial-crystal sizes and variations in the trajectory variables. For a given set of variables, diversity is estimated using a model of a crystal falling in an updraft. The third source is temperature-updraft heterogeneities along each trajectory. To examine this source, centimeter-scale data on cloud temperature and updraft speed are used to estimate the spatial frequency (m−1) of crystal feature changes. For air-temperature heterogeneity, this frequency decays as p−0.66, where p is a measure of the temperature-deviation size. For updraft-speed heterogeneity, the decay is p−0.50. By using these frequencies, the fallpath needed per feature change is found to range from ~0.8 m, for crystals near −15°C, to ~8 m near −19°C – lengths much less than total fallpath lengths. As a result, the third source dominates the diversity, with updraft heterogeneity contributing more than temperature heterogeneity. Plotted against the crystal's initial temperature (−11 to −19°C), the diversity curve is "mitten shaped", having a broad peak near −15.4°C and a sharp subpeak at −14.4°C, both peaks arising from peaks in growth-rate sensitivity. The diversity is much less than previous estimates, yet large enough to explain observations. For example, of all snow crystals ever formed, those that began near −15°C are predicted to all appear unique to 1−μm resolution, but those that began near −11°C are not.