• Benoit, R., , J. M. Desgagné, , P. Pellerin, , S. Pellerin, , Y. Chartier, , and S. Desjardins, 1997: The Canadian MC2: A semi-Lagrangian, semi-implicit wideband atmospheric model suited for finescale process studies and simulation. Mon. Wea. Rev., 125 , 23822415.

    • Search Google Scholar
    • Export Citation
  • Berry, E., , and R. Reinhardt, 1974: An analysis of cloud drop growth by collection. Part II: Single initial distributions. J. Atmos. Sci., 31 , 18251831.

    • Search Google Scholar
    • Export Citation
  • Bigg, E. K., 1953: The supercooling of water. Proc. Phys. Soc. London, B66 , 668694.

  • Byers, H. R., 1965: Elements of Cloud Physics. The University of Chicago Press, 191 pp.

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

    • Search Google Scholar
    • Export Citation
  • Cohard, J-M., , and J-P. Pinty, 2000b: A comprehensive two-moment warm microphysical bulk scheme. II: 2D experiments with a non-hydrostatic model. Quart. J. Roy. Meteor. Soc., 126 , 18431859.

    • Search Google Scholar
    • Export Citation
  • Cohard, J-M., , J-P. Pinty, , and C. Bedos, 1998: Extending Twomey’s analytical estimate of nucleated cloud droplet concentrations from CCN spectra. J. Atmos. Sci., 55 , 33483357.

    • 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
  • DeMott, P. J., , M. P. Meyers, , and W. R. Cotton, 1994: Parameterization and impact of ice initiation processes relevant to numerical model simulations of cirrus clouds. J. Atmos. Sci., 51 , 7790.

    • 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. Tau, , 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
  • Hallet, J., , and S. C. Mossop, 1974: Production of secondary ice particles during the riming process. Nature, 249 , 2628.

  • Harrington, J. Y., , M. P. Meyers, , R. L. Walko, , and W. R. Cotton, 1995: Parameterization of ice crystal conversion processes due to vapor deposition for mesoscale models using double-moment basis functions. Part I: Basic formulation and parcel model results. J. Atmos. Sci., 52 , 43444366.

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

  • Lesins, G., , R. List, , and P. Joe, 1980: Ice accretions. Part I: Testing of new atmospheric icing concepts. J. Rech. Atmos., 14 , 347356.

    • Search Google Scholar
    • Export Citation
  • 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
  • Long, A. B., 1974: Solutions to the droplet collection equation for polynomial kernels. J. Atmos. Sci., 31 , 10401052.

  • Macklin, W. C., , and I. H. Bailey, 1966: On the critical liquid water concentrations of large hailstones. Quart. J. Roy. Meteor. Soc., 92 , 297300.

    • Search Google Scholar
    • Export Citation
  • McCumber, M., , W-K. Tao, , and J. Simpson, 1991: Comparison of ice-phase microphysical parameterization schemes using numerical simulations of tropical convection. J. Appl. Meteor., 30 , 9851004.

    • Search Google Scholar
    • Export Citation
  • Meyers, M. P., , P. J. DeMott, , and W. R. Cotton, 1992: New primary ice-nucleation parameterizations in an explicit cloud model. J. Climate Appl. Meteor., 31 , 708721.

    • Search Google Scholar
    • Export Citation
  • 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, 2005a: A multimoment bulk microphysics parameterization. Part I: Analysis of the role of the spectral shape parameter. J. Atmos. Sci., 62 , 30513064.

    • 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
  • Musil, D. J., 1970: Computer modeling of hailstone growth in feeder clouds. J. Atmos. Sci., 27 , 474482.

  • Rasmussen, R. M., , and A. J. Heymsfield, 1987: Melting and shedding of graupel and hail. Part II: Sensitivity study. J. Atmos. Sci., 44 , 27642782.

    • Search Google Scholar
    • Export Citation
  • Reisner, J., , R. M. Rasmussen, , and T. Bruintjes, 1998: Explicit forecasting of supercooled liquid water in winter storms using the MM5 mesoscale model. Quart. J. Roy. Meteor. Soc., 124 , 10711107.

    • Search Google Scholar
    • Export Citation
  • Walko, R. L., , W. R. Cotton, , M. P. Meyers, , and J. Y. Harrington, 1995: New RAMS cloud microphysics. Part I: The one-moment scheme. Atmos. Res., 38 , 2962.

    • Search Google Scholar
    • Export Citation
  • Wisner, C., , R. D. Orville, , and C. Myers, 1972: A numerical model of a hail-bearing cloud. J. Atmos. Sci., 29 , 11601181.

  • Young, K. C., 1974: The role of contact nucleation in ice phase initiation in clouds. J. Atmos. Sci., 31 , 17351748.

  • Young, K. C., 1993: Microphysical Processes in Clouds. Oxford University Press, 427 pp.

  • 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
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 132 132 33
PDF Downloads 91 91 26

A Multimoment Bulk Microphysics Parameterization. Part II: A Proposed Three-Moment Closure and Scheme Description

View More View Less
  • 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
© Get Permissions
Restricted access

Abstract

Many two-moment bulk schemes use a three-parameter gamma distribution of the form N(D) = N0DαeλD to describe the size spectrum of a given hydrometeor category. These schemes predict changes to the mass content and the total number concentration thereby allowing N0 and λ to vary as prognostic parameters while fixing the shape parameter, α. As was shown in Part I of this study, the shape parameter, which represents the relative dispersion of the hydrometeor size spectrum, plays an important role in the computation of sedimentation and instantaneous growth rates in bulk microphysics schemes. Significant improvement was shown by allowing α to vary as a diagnostic function of the predicted moments rather than using a fixed-value approach. Ideally, however, α should be an independent prognostic parameter.

In this paper, a closure formulation is developed for calculating the source and sink terms of a third moment of the size distribution—the radar reflectivity. With predictive equations for the mass content, total number concentration, and radar reflectivity, α becomes a fully prognostic variable and a three-moment parameterization becomes feasible. A new bulk microphysics scheme is presented and described. The full version of the scheme predicts three moments for all precipitating hydrometeor categories.

Simulations of an idealized hailstorm in the context of a 1D kinematic cloud model employing the one-moment, two-moment, and three-moment versions of the scheme are compared. The vertical distribution of the hydrometeor mass contents using the two-moment version with diagnostic-α relations are much closer to the three-moment than the one-moment simulation. However, the evolution of the surface precipitation rate is notably different between the three-moment and two-moment schemes.

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

Many two-moment bulk schemes use a three-parameter gamma distribution of the form N(D) = N0DαeλD to describe the size spectrum of a given hydrometeor category. These schemes predict changes to the mass content and the total number concentration thereby allowing N0 and λ to vary as prognostic parameters while fixing the shape parameter, α. As was shown in Part I of this study, the shape parameter, which represents the relative dispersion of the hydrometeor size spectrum, plays an important role in the computation of sedimentation and instantaneous growth rates in bulk microphysics schemes. Significant improvement was shown by allowing α to vary as a diagnostic function of the predicted moments rather than using a fixed-value approach. Ideally, however, α should be an independent prognostic parameter.

In this paper, a closure formulation is developed for calculating the source and sink terms of a third moment of the size distribution—the radar reflectivity. With predictive equations for the mass content, total number concentration, and radar reflectivity, α becomes a fully prognostic variable and a three-moment parameterization becomes feasible. A new bulk microphysics scheme is presented and described. The full version of the scheme predicts three moments for all precipitating hydrometeor categories.

Simulations of an idealized hailstorm in the context of a 1D kinematic cloud model employing the one-moment, two-moment, and three-moment versions of the scheme are compared. The vertical distribution of the hydrometeor mass contents using the two-moment version with diagnostic-α relations are much closer to the three-moment than the one-moment simulation. However, the evolution of the surface precipitation rate is notably different between the three-moment and two-moment schemes.

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

Save