Growth-deviation model to understand the perceived variety of falling snow

Abstract

Abstract. What is the source of snow-crystal variety? This question is answered using a model of snow-crystal growth in a cloud. In the model, crystals start under various initial cloud-crystal conditions, and then encounter growth perturbations from random air-temperature deviations along simple crystal trajectories. To obtain distributions of these deviations, I analyzed recent high-resolution measurements of cloud updrafts and temperatures. The trajectories and distributions are used to estimate the number of possible snow crystal shapes, to a given viewing resolution, from a range of initial conditions. The logarithm of this number, defined here as the perceived shape variety or "diversity", is dominated not by the range of conditions, but rather by the air-temperature deviations along a trajectory. This qualitative result is independent of the viewing resolution. Thus, temperature deviations are the main source of crystal diversity. When plotted against the crystal's initial temperature (here –11 to –19°C), the curve is mitten-shaped, with a main peak at –15.4°C and a smaller, sharper peak near –14.4°C. The mitten shape arises from temperature trends in the crystal's terminal fallspeed and prism-face growth rate. Specifically, the two diversity peaks are due to maxima in growth-rate sensitivity to temperature near –15.4 and –14.0°C. Applying the results to all snow crystals ever formed, then, to 1-μm resolution, all crystals that began near –15°C would appear unique, but some that began near –11°C would not.