Atmospheric Chemistry and Physics Discussions www.atmos-chem-phys-discuss.net 1680-7367 1680-7375 8 2 2008 10.5194/acpd-8-4407-2008 http://www.atmos-chem-phys-discuss.net/8/4407/2008/ http://www.atmos-chem-phys-discuss.net/8/4407/2008/acpd-8-4407-2008.html http://www.atmos-chem-phys-discuss.net/8/4407/2008/acpd-8-4407-2008.pdf 4407 4437 2008-03-04 Growth-deviation model to understand the perceived variety of falling snow J. Nelson jnelson@se.ritsumei.ac.jp College of Science and Engineering, Ritsumeikan University, Nojihigashi 1-1-1, Kusatsu 525-8577, Japan 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. Bentley, W. A.: Twenty years' study of snow crystals, Mon. Weather Rev. 21, 212–214, 1901. Feller, W.: An Introduction to Probability Theory and its Applications, Vol I, 3rd Edition, John Wiley & Sons, NY, 1968 (see end of § II.3.). Frank, F. C.: Snow crystals, Contemp. Phys., 23, 3–22, 1982. Hallett, J.: How snow crystals grow, Am. Sci., 72, 582–589, 1984. Hallett, J. and Knight, C. A.: On the symmetry of snow dendrites, Atmos. Res., 32, 1–11, 1994. Knight, C. and Knight, N.: Snow crystals, Sci. Am., 228 (1), 100–107, 1973. Korolev, A. and Isaac, G. A.: Relative Humidity in Liquid, Mixed-Phase, and Ice Clouds, J. Atmos. Sci., 63, 2865–2880, 2006. Nakaya, U.: Snow Crystals Natural and Artificial, Harvard University Press, Cambridge, 1954. Nelson, J.: Branch growth and sidebranching in snow crystals, Cryst. Growth Des., 5, 1509–1525, 2005. Shaw, R. A.: Supersaturation intermittency in turbulent clouds, J. Atmos. Sci., 57, 3452–3456, 2000. Siebert, H., Wendisch, M., Conrath, T., Teichmann, U., Heintzenberg, J.: A New Tethered Balloon-Borne Payload for Fine-Scale Observations in the Cloudy Boundary Layer, Bound.-Lay. Meteorol., 106, 461–482, 2003. Takahashi, T., Endoh, T., Wakahama, G., Fukuta, N.: Vapor diffusional growth of free-falling snow crystals between –3 and –23°C, J. Meteorol. Soc. Jpn., 69, 15–30, 1991. Wolde, M. and Vali, G.: Polarimetric Signatures from Ice Crystals Observed at 95 GHz in Winter Clouds, Part II: Frequencies of Occurrence, J. Atmos. Sci., 58, 842–849, 2001. Wood, S., Baker, M., and Calhoun, D.: New Model for the Vapor Growth of Hexagonal Ice Crystals in the Atmosphere, J. Geophys. Res., 106, 4845–4870, 2001. Yamashita, A.: On the trigonal growth of ice crystals, J. Meteorol. Soc. Jpn., 51, 307–317, 1973.