Article Type:
Research Article

Characterization of Ice Crystals in Clouds by Simple Mathematical Expressions Based on Successive Modification of Simple Shapes

Pao K. Wang Department of Atmospheric and Oceanic Sciences, University of Wisconsin–Madison, Madison, Wisconsin

Search for other papers by Pao K. Wang in
Current site
Google Scholar
PubMed Close
Print Publication:
01 Aug 1997
DOI:
https://doi.org/10.1175/1520-0469(1997)054<2035:COICIC>2.0.CO;2
Page(s):
2035–2041
Restricted access

Abstract

The technique based on the concept of successive modification of simple shapes using elementary mathematical functions to represent the shape and size of ice crystals in clouds is discussed. Two hypothetical samples of ice crystals, a single-habit sample of hexagonal plates and a multihabit crystal sample, are generated using a formula developed previously to illustrate the use of this technique in generating ice crystal ensembles in cloud models. Next, a new expression representing columnar ice crystals is described. Finally, two new expressions that can be used to generate the three-dimensional combination of bullets and spatial dendrites are described. The parameters involved in these expressions are expected to be useful in characterizing the shape and size spectra of ice crystals found in cirrus clouds.

Corresponding author address: Dr. Pao K. Wang, Department of Atmospheric and Oceanic Sciences, University of Wisconsin—Madison, 1225 W. Dayton Street, Madison, WI 53706.

Abstract

The technique based on the concept of successive modification of simple shapes using elementary mathematical functions to represent the shape and size of ice crystals in clouds is discussed. Two hypothetical samples of ice crystals, a single-habit sample of hexagonal plates and a multihabit crystal sample, are generated using a formula developed previously to illustrate the use of this technique in generating ice crystal ensembles in cloud models. Next, a new expression representing columnar ice crystals is described. Finally, two new expressions that can be used to generate the three-dimensional combination of bullets and spatial dendrites are described. The parameters involved in these expressions are expected to be useful in characterizing the shape and size spectra of ice crystals found in cirrus clouds.

Corresponding author address: Dr. Pao K. Wang, Department of Atmospheric and Oceanic Sciences, University of Wisconsin—Madison, 1225 W. Dayton Street, Madison, WI 53706.

Save
Cover Journal of the Atmospheric Sciences
Journal of the Atmospheric Sciences

  • Cotton, W. R., and R. A. Anthes, 1989: Storm and Cloud Dynamics. Academic Press, 880 pp.

  • Furukawa, Y., 1982: Structures and formation mechanisms of snow polycrystals. J. Meteor. Soc. Japan,60, 535–547.

  • Hallett, J., 1964: Experimental studies on the crystallization of supercooled water. J. Atmos. Sci.,21, 671–682.

  • Heymsfield, A., 1972: Ice crystal terminal velocities. J. Atmos. Sci.,29, 1348–1357.

  • ——, 1975: Cirrus uncinus generating cells and the evolution of cirroform clouds. Part I: Aircraft observations of the growth of ice phase. J. Atmos. Sci.,32, 799–808.

  • Hobbs, P. V., 1976: Ice Physics. Oxford University Press, 837 pp.

  • Johnson, D. E., P. K. Wang, and J. M. Straka, 1993: Numerical simulations of 2 August 1981 CCOPE supercell storm with and without ice microphysics. J. Appl. Meteor.,32, 745–759.

  • ——, ——, and ——, 1994: A study of microphysical processes in the 2 August 1981 CCOPE supercell storm. Atmos. Res.,33, 93–123.

  • Kikuchi, K., and H. Uyeda, 1979: On snow crystals of spatial dendritic type. J. Meteor. Soc. Japan,57, 282–287.

  • Kobayashi, T., Y. Furukawa, K. Kikuchi, and H. Uyeda, 1976a: On twinned structures in snow crystals. J. Cryst. Growth,32, 233–249.

  • ——, ——, ——, and ——, 1976b: Cubic structure models at the junctions in polycrystalline snow crystals. J. Cryst. Growth,35, 262–268.

  • Lee, C. W., 1972: On the crystasllographic orientation of spatial branches in natural polycrystalline snow crystals. J. Meteor. Soc. Japan,50, 171–180.

  • Liou, K. N., 1993: Radiation and Cloud Processes in the Atmosphere. Oxford University Press, 487 pp.

  • Magono, C., and C. W. Lee, 1966: Meteorological classification of natural snow crystals. J. Fac. Sci. Hokkaido Univ. Ser. VII,2, 321–335.

  • McFarquhar, G. M., and A. Heymsfield, 1996: Microphysical characteristics of three anvils sampled during the Central Equatorial Pacific Experiment. J. Atmos. Sci.,53, 2401–2423.

  • Parungo, F., 1995: Ice crystals in high clouds and contrails. Atmos. Res.,38, 249–262.

  • Pruppacher, H. R., and J. D. Klett, 1978: Microphysics of Clouds and Precipitation. D. Reidel, 714 pp.

  • Wang, P. K., 1982: Mathematical description of the shape of conical hydrometeors. J. Atmos. Sci.,39, 2615–2622.

  • ——, 1987: Two-dimensional characterization of polygonally symmetric particles. J. Colloid. Interface Sci.,117, 271–281.

  • ——, and S. M. Denzer., 1983: Mathematical description of the shape of plane hexagonal snow crystals. J. Atmos. Sci.,40, 1024–1028.

  • ——, and W. Ji, 1992: A numerical study of the diffusion growth and riming rates of ice crystals in clouds. Proc. 11th Int. Conf. on Clouds and Precipitation, Vol. I, Montreal, Quebec, Canada, ICCP/IAMAP, 76–78.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 394 235 18
PDF Downloads 155 44 1