Advances in the Estimation of Ice Particle Fall Speeds Using Laboratory and Field Measurements

A. J. Heymsfield NCAR, Boulder, Colorado

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C. D. Westbrook Department of Meteorology, University of Reading, Reading, United Kingdom

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Abstract

Accurate estimates for the fall speed of natural hydrometeors are vital if their evolution in clouds is to be understood quantitatively. In this study, laboratory measurements of the terminal velocity υt for a variety of ice particle models settling in viscous fluids, along with wind-tunnel and field measurements of ice particles settling in air, have been analyzed and compared to common methods of computing υt from the literature. It is observed that while these methods work well for a number of particle types, they fail for particles with open geometries, specifically those particles for which the area ratio Ar is small (Ar is defined as the area of the particle projected normal to the flow divided by the area of a circumscribing disc). In particular, the fall speeds of stellar and dendritic crystals, needles, open bullet rosettes, and low-density aggregates are all overestimated. These particle types are important in many cloud types: aggregates in particular often dominate snow precipitation at the ground and vertically pointing Doppler radar measurements.

Based on the laboratory data, a simple modification to previous computational methods is proposed, based on the area ratio. This new method collapses the available drag data onto an approximately universal curve, and the resulting errors in the computed fall speeds relative to the tank data are less than 25% in all cases. Comparison with the (much more scattered) measurements of ice particles falling in air show strong support for this new method, with the area ratio bias apparently eliminated.

Corresponding author address: Dr. Andrew Heymsfield, NCAR, P.O. Box 3000, Boulder, CO 80307–3000. Email: heyms1@ucar.edu

Abstract

Accurate estimates for the fall speed of natural hydrometeors are vital if their evolution in clouds is to be understood quantitatively. In this study, laboratory measurements of the terminal velocity υt for a variety of ice particle models settling in viscous fluids, along with wind-tunnel and field measurements of ice particles settling in air, have been analyzed and compared to common methods of computing υt from the literature. It is observed that while these methods work well for a number of particle types, they fail for particles with open geometries, specifically those particles for which the area ratio Ar is small (Ar is defined as the area of the particle projected normal to the flow divided by the area of a circumscribing disc). In particular, the fall speeds of stellar and dendritic crystals, needles, open bullet rosettes, and low-density aggregates are all overestimated. These particle types are important in many cloud types: aggregates in particular often dominate snow precipitation at the ground and vertically pointing Doppler radar measurements.

Based on the laboratory data, a simple modification to previous computational methods is proposed, based on the area ratio. This new method collapses the available drag data onto an approximately universal curve, and the resulting errors in the computed fall speeds relative to the tank data are less than 25% in all cases. Comparison with the (much more scattered) measurements of ice particles falling in air show strong support for this new method, with the area ratio bias apparently eliminated.

Corresponding author address: Dr. Andrew Heymsfield, NCAR, P.O. Box 3000, Boulder, CO 80307–3000. Email: heyms1@ucar.edu

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  • Abraham, F. F., 1970: Functional dependence of drag coefficient of a sphere on Reynolds number. Phys. Fluids, 13 , 21942195.

  • Barthazy, E., and R. Schefold, 2006: Fall velocity of snowflakes of different riming degree and crystal types. Atmos. Res., 82 , 391398.

    • Search Google Scholar
    • Export Citation
  • Batchelor, G. K., 1967: An Introduction to Fluid Dynamics. Cambridge University Press, 615 pp.

  • Böhm, H. P., 1989: A general equation for the terminal fall speed of solid hydrometeors. J. Atmos. Sci., 46 , 24192427.

  • Böhm, H. P., 1992: A general hydrodynamic theory for mixed-phase microphysics. I: Drag and fall speed of hydrometeors. Atmos. Res., 27 , 253274.

    • Search Google Scholar
    • Export Citation
  • Brandes, E. A., K. Ikeda, G. Thompson, and M. Schönhuber, 2008: Aggregate terminal velocity/temperature relations. J. Appl. Meteor. Climatol., 47 , 27292736.

    • Search Google Scholar
    • Export Citation
  • Brown, P. R. A., and P. N. Francis, 1993: Measurements of the ice water content of cirrus using an evaporative technique. J. Atmos. Oceanic Technol., 10 , 579590.

    • Search Google Scholar
    • Export Citation
  • Connolly, P. R., C. P. R. Saunders, M. W. Gallagher, K. N. Bower, M. J. Flynn, T. W. Choularton, J. Whiteway, and R. P. Lawson, 2005: Aircraft observations of the influence of electric fields on the aggregation of ice crystals. Quart. J. Roy. Meteor. Soc., 131 , 16951712.

    • Search Google Scholar
    • Export Citation
  • Field, P. R., and A. J. Heymsfield, 2003: Aggregation and scaling of ice crystal distributions. J. Atmos. Sci., 60 , 544560.

  • Heymsfield, A. J., and M. Kajikawa, 1987: An improved approach to calculating terminal velocities of plate-like crystals and graupel. J. Atmos. Sci., 44 , 10881099.

    • Search Google Scholar
    • Export Citation
  • Heymsfield, A. J., and J. Iaquinta, 2000: Cirrus crystal terminal velocities. J. Atmos. Sci., 57 , 916938.

  • Heymsfield, A. J., and L. M. Miloshevich, 2003: Parameterizations for the cross-sectional area and extinction of cirrus and stratiform ice cloud particles. J. Atmos. Sci., 60 , 936956.

    • Search Google Scholar
    • Export Citation
  • Heymsfield, A. J., A. Bansemer, P. R. Field, S. L. Durden, J. Stith, J. E. Dye, W. Hall, and T. Grainger, 2002: Observations and parameterizations of particle size distributions in deep tropical cirrus and stratiform precipitating clouds: Results from in situ observations in TRMM field campaigns. J. Atmos. Sci., 59 , 34573491.

    • Search Google Scholar
    • Export Citation
  • Hobbs, P. V., S. Chang, and J. D. Locatelli, 1974: The dimensions and aggregation of ice crystals in natural clouds. J. Geophys. Res., 79 , 21992206.

    • Search Google Scholar
    • Export Citation
  • Jayaweera, K., 1972: An equivalent disc for calculating the terminal velocities of plate-like ice crystals. J. Atmos. Sci., 29 , 596598.

    • Search Google Scholar
    • Export Citation
  • Jayaweera, K., and R. E. Cottis, 1969: Fall velocities of plate-like and columnar ice crystals. Quart. J. Roy. Meteor. Soc., 95 , 703709.

    • Search Google Scholar
    • Export Citation
  • Kajikawa, M., 1971: A model experimental study on the falling velocity of ice crystals. J. Meteor. Soc. Japan, 49 , 367375.

  • Kajikawa, M., 1982: Observation of the falling motion of early snow flakes. Part I: Relationship between the free-fall pattern and the number and shape of component snow crystals. J. Meteor. Soc. Japan, 60 , 797803.

    • Search Google Scholar
    • Export Citation
  • Khvorostyanov, V. I., and J. A. Curry, 2002: Terminal velocities of droplets and crystals: Power laws with continuous parameters over the size spectrum. J. Atmos. Sci., 59 , 18721884.

    • Search Google Scholar
    • Export Citation
  • Khvorostyanov, V. I., and J. A. Curry, 2005: Fall velocities of hydrometeors in the atmosphere: Refinements to a continuous analytical power law. J. Atmos. Sci., 62 , 43434357.

    • Search Google Scholar
    • Export Citation
  • Knight, N. C., and A. J. Heymsfield, 1983: Measurement and interpretation of hailstone density and terminal velocity. J. Atmos. Sci., 40 , 15101516.

    • Search Google Scholar
    • Export Citation
  • List, R., and R. S. Schemenauer, 1971: Free-fall behavior of planar snow crystals, conical graupel and small hail. J. Atmos. Sci., 28 , 110115.

    • Search Google Scholar
    • Export Citation
  • Locatelli, J. D., and P. V. Hobbs, 1974: Fall speeds and masses of solid precipitation particles. J. Geophys. Res., 79 , 21852197.

  • Magono, C., and T. Nakamura, 1965: Aerodynamic studies of falling snowflakes. J. Meteor. Soc. Japan, 43 , 139143.

  • McDonald, J. E., 1954: The shape and aerodynamics of large raindrops. J. Meteor., 11 , 478494.

  • Mitchell, D. L., 1996: Use of mass- and area-dimensional power laws for determining precipitation particle terminal velocities. J. Atmos. Sci., 53 , 17101723.

    • Search Google Scholar
    • Export Citation
  • Mitchell, D. L., and A. J. Heymsfield, 2005: Refinements in the treatment of ice particle terminal velocities, highlighting aggregates. J. Atmos. Sci., 62 , 16371644.

    • Search Google Scholar
    • Export Citation
  • Podzimek, J., 1965: Movement of ice particles in the atmosphere. Proc. Int. Conf. on Cloud Physics, Tokyo, Japan, WMO, 224–230.

  • Pruppacher, H. R., and J. D. Klett, 1997: Microphysics of Clouds and Precipitation. 2nd ed. Kluwer, 954 pp.

  • Rutledge, S. A., and P. V. Hobbs, 1984: The mesoscale and microscale structure and organization of clouds and precipitation in midlatitude cyclones. XII: A diagnostic modeling study of precipitation development in narrow cold-frontal rainbands. J. Atmos. Sci., 41 , 29492972.

    • Search Google Scholar
    • Export Citation
  • Stith, J. L., J. A. Hagerty, A. J. Heymsfield, and C. A. Grainger, 2004: Microphysical characteristics of tropical updrafts in clean conditions. J. Appl. Meteor., 43 , 779794.

    • Search Google Scholar
    • Export Citation
  • Takahashi, T., and N. Fukuta, 1988: Supercooled cloud tunnel studies on the growth of snow crystals between −4° and −20°C. J. Meteor. Soc. Japan, 66 , 841855.

    • Search Google Scholar
    • Export Citation
  • Takahashi, T., T. Endoh, and G. Wakahama, 1991: Vapor diffusional growth of free-falling snow crystals between −3° and −23°C. J. Meteor. Soc. Japan, 69 , 1530.

    • Search Google Scholar
    • Export Citation
  • Tran-Cong, S., M. Gay, and E. E. Michaelides, 2004: Drag coefficients of irregularly shaped particles. Powder Technol., 139 , 2132.

  • Westbrook, C. D., 2005: Universality in snowflake formation. Ph.D. thesis, University of Warwick, 84 pp.

  • Westbrook, C. D., 2008: The fall speeds of sub-100μm ice crystals. Quart. J. Roy. Meteor. Soc., 134 , 12431251.

  • Westbrook, C. D., and Coauthors, 2004: A theory of growth by differential sedimentation, with application to snowflake formation. Phys. Rev. E, 70 , 021403. doi:10.1103/PhysRevE.70.021403.

    • Search Google Scholar
    • Export Citation
  • Wilson, D. R., and S. P. Ballard, 1999: A microphysically based precipitation scheme for the UK Meteorological Office Unified Model. Quart. J. Roy. Meteor. Soc., 125 , 16071636.

    • Search Google Scholar
    • Export Citation
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