• Beheng, K. D., , K. Jellinghaus, , W. Sander, , N. Roth, , and B. Weigand, 2006: Investigation of collision-induced breakup of raindrops by numerical simulations: First results. Geophys. Res. Lett., 33 , L10811. doi:10.1029/2005GL025519.

    • Search Google Scholar
    • Export Citation
  • Best, A. C., 1950: Empirical formulae for the terminal velocity of water drops falling through the atmosphere. Quart. J. Roy. Meteor. Soc., 76 , 302311.

    • Search Google Scholar
    • Export Citation
  • Brown Jr., P. S., 1988: The effects of filament, sheet, and disk breakup upon the drop spectrum. J. Atmos. Sci., 45 , 712718.

  • Fung, C., 1984: Raindrop collisions under low pressure, experiments and parameterization. Ph.D. thesis, University of Toronto, 136 pp.

  • Gelbard, F., , and J. H. Seinfeld, 1978: Numerical solution of the dynamic equation for particulate systems. J. Comput. Phys., 28 , 357375.

    • Search Google Scholar
    • Export Citation
  • Gillespie, J. R., , and R. List, 1978: Effects of collision-induced breakup on drop size distributions in steady-state rain shafts. Pure Appl. Geophys., 117 , 599626.

    • Search Google Scholar
    • Export Citation
  • List, R., 1988: A linear radar reflectivity–rainrate relationship for steady tropical rain. J. Atmos. Sci., 45 , 35643572.

  • List, R., , and G. M. McFarquhar, 1990: The role of breakup and coalescence in the three-peak equilibrium distribution of raindrops. J. Atmos. Sci., 47 , 22742292.

    • Search Google Scholar
    • Export Citation
  • List, R., , N. R. Donaldson, , and R. E. Stewart, 1987: Temporal evolution of drop spectra to collisional equilibrium in steady and pulsating rain. J. Atmos. Sci., 44 , 362372.

    • Search Google Scholar
    • Export Citation
  • List, R., , C. Fung, , and R. Nissen, 2009: Effects of pressure on collision, coalescence, and breakup of raindrops. Part I: Experiments at 50 kPa. J. Atmos. Sci., 66 , 21902203.

    • Search Google Scholar
    • Export Citation
  • Low, T. B., , and R. List, 1982: Collision, coalescence and breakup of raindrops: Part II: Parameterization of fragment distributions. J. Atmos. Sci., 39 , 16071618.

    • Search Google Scholar
    • Export Citation
  • McFarquhar, G. M., 2004: A new representation of collision-induced breakup of raindrops and its implication for the shape of raindrop size distributions. J. Atmos. Sci., 61 , 777794.

    • Search Google Scholar
    • Export Citation
  • McTaggart-Cowan, J. D., , and R. List, 1975: Collision and breakup of water drops at terminal velocity. J. Atmos. Sci., 32 , 14011411.

  • Nissen, R. P., 1996: Effects of air pressure on raindrop size distributions: Modeling and field data verification. Ph.D. thesis, University of Toronto, 140 pp.

  • Nissen, R. P., , R. List, , D. Hudak, , G. M. McFarquhar, , R. P. Lawson, , N. P. Tung, , S. K. Soo, , and T. S. Kang, 2005: Constant raindrop fall speed profile derived from Doppler radar data analyses for steady nonconvective precipitation. J. Atmos. Sci., 62 , 220230.

    • Search Google Scholar
    • Export Citation
  • Valdez, M. P., , and K. C. Young, 1985: Number fluxes in equilibrium raindrop populations: A Markov chain analysis. J. Atmos. Sci., 42 , 10241036.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 11 11 1
PDF Downloads 5 5 1

Effects of Pressure on Collision, Coalescence, and Breakup of Raindrops. Part II: Parameterization and Spectra Evolution at 50 and 100 kPa

View More View Less
  • 1 Department of Physics, University of Toronto, Toronto, Ontario, Canada
  • | 2 Environment Canada, Vancouver, British Columbia, Canada
  • | 3 Environmental Protection Department, Hong Kong, China
© Get Permissions
Restricted access

Abstract

Fragment size distributions, experimentally obtained for six drop pairs colliding at 50 kPa, are parameterized similarly to the 100-kPa drop pair experiments by Low and List. This information is then introduced into a box model to allow assessment of the spectra evolution and a comparison of the two datasets taken at the two pressures. The differences in breakup patterns include the following: The contributions to mass transfer by breakup and coalescence are very similar at the two pressures, with larger values at lower pressure; the overall mass evolution is not particularly sensitive to pressure; and disk breakup plays an “erratic” role. The situation for the number concentration, however, is totally different and develops gradually. At 50 kPa there is also no three-peak equilibrium developing as for 100 kPa. The times to reach equilibrium are ∼12 h. Note that the box model does not include accretion of cloud droplets—which may well be more important than growth by accretion of fragments.

Application of the new parameterization is not beneficial for low rain rates, but it is strongly recommended for large rain rates (>50 mm h−1).

Corresponding author address: Prof. Roland List, Department of Physics, University of Toronto, Toronto, ON M5S 1A7, Canada. Email: list@atmosp.physics.utoronto.ca

Abstract

Fragment size distributions, experimentally obtained for six drop pairs colliding at 50 kPa, are parameterized similarly to the 100-kPa drop pair experiments by Low and List. This information is then introduced into a box model to allow assessment of the spectra evolution and a comparison of the two datasets taken at the two pressures. The differences in breakup patterns include the following: The contributions to mass transfer by breakup and coalescence are very similar at the two pressures, with larger values at lower pressure; the overall mass evolution is not particularly sensitive to pressure; and disk breakup plays an “erratic” role. The situation for the number concentration, however, is totally different and develops gradually. At 50 kPa there is also no three-peak equilibrium developing as for 100 kPa. The times to reach equilibrium are ∼12 h. Note that the box model does not include accretion of cloud droplets—which may well be more important than growth by accretion of fragments.

Application of the new parameterization is not beneficial for low rain rates, but it is strongly recommended for large rain rates (>50 mm h−1).

Corresponding author address: Prof. Roland List, Department of Physics, University of Toronto, Toronto, ON M5S 1A7, Canada. Email: list@atmosp.physics.utoronto.ca

Save