• Cheng, L., , and M. English, 1983: A relationship between hailstone concentration and size. J. Atmos. Sci., 40 , 204213.

  • Cohard, J-M., , and J-P. Pinty, 2000: A comprehensive two-moment warm microphysical bulk scheme. I: Description and tests. Quart. J. Roy. Meteor. Soc., 126 , 18151842.

    • Search Google Scholar
    • Export Citation
  • Cotton, W. R., , G. J. Tripoli, , R. M. Rauber, , and E. A. Mulvihill, 1986: Numerical simulation of the effects of varying ice crystal nucleation rates and aggregation processes on orographic snowfall. J. Climate Appl. Meteor., 25 , 16581680.

    • Search Google Scholar
    • Export Citation
  • Feingold, G., , R. L. Walko, , B. Stevens, , and W. R. Cotton, 1998: Simulations of marine stratocumulus using a new microphysical parameterization. Atmos. Res., 47-48 , 505528.

    • Search Google Scholar
    • Export Citation
  • Ferrier, B. S., 1994: A two-moment multiple-phase four-class bulk ice scheme. Part I: Description. J. Atmos. Sci., 51 , 249280.

  • Ferrier, B. S., , W-K. Tao, , and J. Simpson, 1995: A two-moment multiple-phase four-class bulk ice scheme. Part II: Simulations of convective storms in different large-scale environments and comparisons with other bulk parameterizations. J. Atmos. Sci., 52 , 10011033.

    • Search Google Scholar
    • Export Citation
  • Ivanova, D., , D. L. Mitchell, , W. P. Arnott, , and M. Poellot, 2001: A GCM parameterization for bimodal size spectra and ice mass removal rates in mid-latitude cirrus clouds. Atmos. Res., 59-60 , 89113.

    • Search Google Scholar
    • Export Citation
  • Kessler, E., 1969: On the Distribution and Continuity of Water Substance in Atmospheric Circulation. Meteor. Monogr., No. 32, Amer. Meteor. Soc., 84 pp.

  • Kong, F., , and M. K. Yau, 1997: An explicit approach to microphysics in MC2. Atmos. Ocean., 33 , 257291.

  • Lin, Y-L., , R. D. Farley, , and H. D. Orville, 1983: Bulk parameterization of the snow field in a cloud model. J. Climate Appl. Meteor., 22 , 10651092.

    • Search Google Scholar
    • Export Citation
  • Marshall, J. S., , and W. Mc K. Palmer, 1948: The distribution of raindrops with size. J. Atmos. Sci., 5 , 165166.

  • Meyers, M. P., , R. L. Walko, , J. Y. Harrington, , and W. R. Cotton, 1997: New RAMS cloud microphysics. Part II: The two-moment scheme. Atmos. Res., 45 , 339.

    • Search Google Scholar
    • Export Citation
  • Milbrandt, J. A., , and M. K. Yau, 2005: A multimoment bulk microphysics parameterization. Part II: A proposed three-moment closure and scheme description. J. Atmos. Sci., 62 , 30653081.

    • Search Google Scholar
    • Export Citation
  • Murakami, M., 1990: Numerical modeling of dynamical and microphysical evolution of an isolated convective cloud—The 19 July 1981 CCOPE cloud. J. Meteor. Soc. Japan, 68 , 107128.

    • Search Google Scholar
    • Export Citation
  • Sekhon, R. S., , and R. C. Srivastava, 1970: Snow spectra and radar reflectivity. J. Atmos. Sci., 27 , 299307.

  • Srivastava, R. C., 1978: Parameterization of raindrop size distributions. J. Atmos. Sci., 35 , 108117.

  • Uijlenhoet, R., , M. Steiner, , and J. A. Smith, 2003: Variability of raindrop size distributions in a squall line and implications for radar rainfall estimation. J. Hydrometeor., 4 , 4361.

    • Search Google Scholar
    • Export Citation
  • Ulbrich, C. W., 1983: Natural variations in the analytical form of the raindrop size distribution. J. Climate Appl. Meteor., 22 , 17641775.

    • Search Google Scholar
    • Export Citation
  • Wacker, U., , and A. Seifert, 2001: Evolution of rain water profiles resulting from pure sedimentation: Spectral vs. parameterized description. Atmos. Res., 58 , 1939.

    • Search Google Scholar
    • Export Citation
  • Waldvogel, A., 1974: The N0 jump of raindrop spectra. J. Atmos. Sci., 31 , 10671078.

  • Yu, W., , L. Garand, , and A. P. Dastoor, 1997: Evaluation of model clouds and radiation at 100 km scale using GOES data. Tellus, 49A , 246262.

    • Search Google Scholar
    • Export Citation
  • Ziegler, C. L., 1985: Retrieval of thermal and microphysical variables in observed convective storms. Part 1: Model development and preliminary testing. J. Atmos. Sci., 42 , 14971509.

    • Search Google Scholar
    • Export Citation
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A Multimoment Bulk Microphysics Parameterization. Part I: Analysis of the Role of the Spectral Shape Parameter

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  • 1 Department of Atmospheric and Oceanic Sciences, McGill University, Montreal, and Recherche en Prévision Numérique, Meteorological Service of Canada, Dorval, Quebec, Canada
  • 2 Department of Atmospheric and Oceanic Sciences, McGill University, Montreal, Quebec, Canada
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Abstract

With increasing computer power, explicit microphysics schemes are becoming increasingly important in atmospheric models. Many schemes have followed the approach of Kessler in which one moment of the hydrometeor size distribution, proportional to the mass content, is predicted. More recently, the two-moment method has been introduced in which both the mass and the total number concentration of the hydrometeor categories are independently predicted.

In bulk schemes, the size spectrum of each hydrometeor category is often described by a three-parameter gamma distribution function, N(D) = N0DαeλD. Two-moment schemes generally treat N0 and λ as prognostic parameters while holding α constant. In this paper, the role of the spectral shape parameter, α, is investigated by examining its effects on sedimentation and microphysical growth rates. An approach is introduced for a two-moment scheme where α is allowed to vary diagnostically as a function of the mean-mass diameter. Comparisons are made between calculations using various bulk approaches—a one-moment, a two-moment, and a three-moment method—and an analytic bin model. It is found that the size-sorting mechanism, which exists in a bulk scheme when different fall velocities are applied to advect the different predicted moments, is significantly different amongst the schemes. The shape parameter plays an important role in determining the rate of size sorting. Likewise, instantaneous growth rates related to the moments are shown to be significantly affected by this parameter.

Corresponding author address: Dr. Jason A. Milbrandt, Meteorological Research Branch, Environment Canada, 2121 Trans-Canada Highway, 5th Floor, Dorval, QC H9P 1J3 Canada. Email: jason.milbrandt@mcgill.ca

Abstract

With increasing computer power, explicit microphysics schemes are becoming increasingly important in atmospheric models. Many schemes have followed the approach of Kessler in which one moment of the hydrometeor size distribution, proportional to the mass content, is predicted. More recently, the two-moment method has been introduced in which both the mass and the total number concentration of the hydrometeor categories are independently predicted.

In bulk schemes, the size spectrum of each hydrometeor category is often described by a three-parameter gamma distribution function, N(D) = N0DαeλD. Two-moment schemes generally treat N0 and λ as prognostic parameters while holding α constant. In this paper, the role of the spectral shape parameter, α, is investigated by examining its effects on sedimentation and microphysical growth rates. An approach is introduced for a two-moment scheme where α is allowed to vary diagnostically as a function of the mean-mass diameter. Comparisons are made between calculations using various bulk approaches—a one-moment, a two-moment, and a three-moment method—and an analytic bin model. It is found that the size-sorting mechanism, which exists in a bulk scheme when different fall velocities are applied to advect the different predicted moments, is significantly different amongst the schemes. The shape parameter plays an important role in determining the rate of size sorting. Likewise, instantaneous growth rates related to the moments are shown to be significantly affected by this parameter.

Corresponding author address: Dr. Jason A. Milbrandt, Meteorological Research Branch, Environment Canada, 2121 Trans-Canada Highway, 5th Floor, Dorval, QC H9P 1J3 Canada. Email: jason.milbrandt@mcgill.ca

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