• Ackerman, A. S., M. P. Kirkpatrick, D. E. Stevens, and O. B. Toon, 2004: The impact of humidity above stratiform clouds on indirect climate forcing. Nature, 432 , 10141017.

    • Search Google Scholar
    • Export Citation
  • Andrejczuk, M., W. W. Grabowski, S. P. Malinowski, and P. K. Smolarkiewicz, 2009: Numerical simulation of cloud–clear air interfacial mixing: Homogeneous versus inhomogeneous mixing. J. Atmos. Sci., 66 , 24932500.

    • Search Google Scholar
    • Export Citation
  • Baker, M. B., and J. Latham, 1979: The evolution of droplet spectra and the rate of production of embryonic raindrops in small cumulus clouds. J. Atmos. Sci., 36 , 16121615.

    • Search Google Scholar
    • Export Citation
  • Baker, M. B., R. G. Corbin, and J. Latham, 1980: The influence of entrainment on the evolution of cloud droplet spectra: I. A model of inhomogeneous mixing. Quart. J. Roy. Meteor. Soc., 106 , 581598.

    • Search Google Scholar
    • Export Citation
  • Berry, E. X., and R. L. Reinhardt, 1974: An analysis of cloud drop growth by collection: Part I. Double distributions. J. Atmos. Sci., 31 , 18141824.

    • Search Google Scholar
    • Export Citation
  • Bott, A., 1998: A flux method for the numerical solution of the stochastic collection equation. J. Atmos. Sci., 55 , 22842293.

  • Brenguier, J-L., and W. W. Grabowski, 1993: Cumulus entrainment and cloud droplet spectra: A numerical model within a two-dimensional dynamical framework. J. Atmos. Sci., 50 , 120136.

    • Search Google Scholar
    • Export Citation
  • Bretherton, C. S., P. N. Blossey, and J. Uchida, 2007: Cloud droplet sedimentation, entrainment efficiency, and subtropical stratocumulus albedo. Geophys. Res. Lett., 34 , L03813. doi:10.1029/2006GL027648.

    • Search Google Scholar
    • Export Citation
  • Burnet, F., and J. L. Brenguier, 2007: Observational study of the entrainment-mixing process in warm convective clouds. J. Atmos. Sci., 64 , 19952011.

    • Search Google Scholar
    • Export Citation
  • Clark, T. L., 1973: Numerical modeling of the dynamics and microphysics of warm cumulus convection. J. Atmos. Sci., 30 , 857878.

  • Clark, T. L., 1974: On modelling nucleation and condensation theory in Eulerian spatial domain. J. Atmos. Sci., 31 , 20992117.

  • 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
  • Feingold, G., S. Tzivion, and Z. Levin, 1988: Evolution of raindrop spectra. Part I: Solution to the stochastic collection/breakup equation using the method of moments. J. Atmos. Sci., 45 , 33873399.

    • Search Google Scholar
    • Export Citation
  • Feingold, G., B. Stevens, W. R. Cotton, and R. L. Walko, 1994: An explicit cloud microphysics/LES model designed to simulate the Twomey effect. Atmos. Res., 33 , 207233.

    • Search Google Scholar
    • Export Citation
  • Ghan, S. J., C. C. Chuang, and J. E. Penner, 1993: A parameterization of cloud droplet nucleation. Part I: Single aerosol type. Atmos. Res., 30 , 197221.

    • Search Google Scholar
    • Export Citation
  • Grabowski, W. W., 1989: Numerical experiments on the dynamics of the cloud–environment interface: Small cumulus in a shear-free environment. J. Atmos. Sci., 46 , 35133541.

    • Search Google Scholar
    • Export Citation
  • Grabowski, W. W., 1998: Toward cloud resolving modeling of large-scale tropical circulations: A simple cloud microphysics parameterization. J. Atmos. Sci., 55 , 32833298.

    • Search Google Scholar
    • Export Citation
  • Grabowski, W. W., 2001: Coupling cloud processes with the large-scale dynamics using the cloud-resolving convection parameterization (CRCP). J. Atmos. Sci., 58 , 978997.

    • Search Google Scholar
    • Export Citation
  • Grabowski, W. W., 2004: An improved framework for superparameterization. J. Atmos. Sci., 61 , 19401952.

  • Grabowski, W. W., 2006: Indirect impact of atmospheric aerosols in idealized simulations of convective–radiative quasi equilibrium. J. Climate, 19 , 46644682.

    • Search Google Scholar
    • Export Citation
  • Grabowski, W. W., 2007: Representation of turbulent mixing and buoyancy reversal in bulk cloud models. J. Atmos. Sci., 64 , 36663680.

  • Grabowski, W. W., and P. K. Smolarkiewicz, 1990: Monotone finite-difference approximations to the advection–condensation problem. Mon. Wea. Rev., 118 , 20822098.

    • Search Google Scholar
    • Export Citation
  • Grabowski, W. W., and P. K. Smolarkiewicz, 1999: CRCP: A cloud-resolving convection parameterization for modeling the tropical convecting atmosphere. Physica D, 133 , 171178.

    • Search Google Scholar
    • Export Citation
  • Grabowski, W. W., and H. Morrison, 2008: Toward the mitigation of spurious cloud-edge supersaturation in cloud models. Mon. Wea. Rev., 136 , 12241234.

    • Search Google Scholar
    • Export Citation
  • Grabowski, W. W., and L-P. Wang, 2009: Diffusional and accretional growth of water drops in a rising adiabatic parcel: Effects of the turbulent collision kernel. Atmos. Chem. Phys., 9 , 23352353.

    • Search Google Scholar
    • Export Citation
  • Hall, W. D., 1980: A detailed microphysical model within a two-dimensional dynamic framework: Model description and preliminary results. J. Atmos. Sci., 37 , 24862507.

    • Search Google Scholar
    • Export Citation
  • Jarecka, D., W. W. Grabowski, and H. Pawlowska, 2009: Modeling of subgrid-scale mixing in large-eddy simulation of shallow convection. J. Atmos. Sci., 66 , 21252133.

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

    • Search Google Scholar
    • Export Citation
  • Khairoutdinov, M., and Y. Kogan, 2000: A new cloud physics parameterization in a large-eddy simulation model of marine stratocumulus. Mon. Wea. Rev., 128 , 229243.

    • Search Google Scholar
    • Export Citation
  • Klaassen, G. P., and T. L. Clark, 1985: Dynamics of the cloud–environment interface and entrainment in small cumuli: Two-dimensional simulations in the absence of ambient shear. J. Atmos. Sci., 42 , 26212642.

    • Search Google Scholar
    • Export Citation
  • Kogan, Y. L., 1991: The simulation of a convective cloud in a 3-D model with explicit microphysics. Part I: Model description and sensitivity experiments. J. Atmos. Sci., 48 , 11601189.

    • Search Google Scholar
    • Export Citation
  • Meyers, M. P., R. L. Walko, J. Y. Harrington, and W. R. Cotton, 1997: New RAMS cloud microphysics parameterization. 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 I: Analysis of the role of the spectral shape parameter. J. Atmos. Sci., 62 , 30513064.

    • Search Google Scholar
    • Export Citation
  • Morrison, H., and W. W. Grabowski, 2007: Comparison of bulk and bin warm-rain microphysics models using a kinematic framework. J. Atmos. Sci., 64 , 28392861.

    • Search Google Scholar
    • Export Citation
  • Morrison, H., and W. W. Grabowski, 2008: Modeling supersaturation and subgrid-scale mixing with two-moment bulk warm microphysics. J. Atmos. Sci., 65 , 792812.

    • Search Google Scholar
    • Export Citation
  • Morrison, H., J. A. Curry, and V. I. Khvorostyanov, 2005: A new double-moment microphysics parameterization for application in cloud and climate models. Part I: Description. J. Atmos. Sci., 62 , 16651677.

    • Search Google Scholar
    • Export Citation
  • Pruppacher, H. R., and J. D. Klett, 1997: Microphysics of Clouds and Precipitation. Kluwer Academic, 954 pp.

  • Seifert, A., and K. D. Beheng, 2001: A double-moment parameterization for simulating autoconversion, accretion and self-collection. Atmos. Res., 59–60 , 265281.

    • Search Google Scholar
    • Export Citation
  • Simmel, M., and S. Wurzler, 2006: Condensation and activation in sectional cloud microphysical models. Atmos. Res., 80 , 218236.

  • Smolarkiewicz, P. K., 1984: A fully multidimensional positive definite advection transport algorithm with small implicit diffusion. J. Comput. Phys., 54 , 325362.

    • Search Google Scholar
    • Export Citation
  • Smolarkiewicz, P. K., and L. G. Margolin, 1997: On forward-in-time differencing for fluids: An Eulerian/semi-Lagrangian nonhydrostatic model for stratified flows. Atmos.-Ocean, 35 , 127152.

    • Search Google Scholar
    • Export Citation
  • Smoluchowski, M., 1916: Drei Vorträge über Diffusion, Brownsche Molekularbewegung und Koagulation von Kolloidteilchen. Phys. Z., 17 , 557585.

    • Search Google Scholar
    • Export Citation
  • Stevens, B., R. L. Walko, W. R. Cotton, and G. Feingold, 1996: The spurious production of cloud-edge supersaturation by Eulerian models. Mon. Wea. Rev., 124 , 10341041.

    • Search Google Scholar
    • Export Citation
  • Twomey, S., 1959: The nuclei of natural cloud formation. Part II: The supersaturation in natural clouds and the variation of cloud droplet concentration. Pure Appl. Geophys., 43 , 243249.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 61 22 2
PDF Downloads 37 13 0

A Hybrid Bulk–Bin Approach to Model Warm-Rain Processes

Wojciech W. GrabowskiNational Center for Atmospheric Research,* Boulder, Colorado

Search for other papers by Wojciech W. Grabowski in
Current site
Google Scholar
PubMed
Close
,
Odile ThouronCNRM/GAME Météo-France/CNRS, Toulouse, France

Search for other papers by Odile Thouron in
Current site
Google Scholar
PubMed
Close
,
Jean-Pierre PintyLaboratoire d’Aérologie, University of Toulouse, and CNRS, Toulouse, France

Search for other papers by Jean-Pierre Pinty in
Current site
Google Scholar
PubMed
Close
, and
Jean-Louis BrenguierCNRM/GAME Météo-France/CNRS, Toulouse, France

Search for other papers by Jean-Louis Brenguier in
Current site
Google Scholar
PubMed
Close
Restricted access

Abstract

This paper presents a hybrid approach to model warm-rain processes, merging the diverse schemes of bulk and detailed (bin) microphysics. In the bulk scheme, the key assumption is that the exact saturation is maintained inside a cloud. In contrast, the supersaturation inside a cloud is predicted in the bin scheme and is applied to calculate the diffusional growth of cloud droplets. Predicting the supersaturation is numerically cumbersome, however, and typically requires spatial and temporal resolutions that are significantly higher than those that can be applied in the bulk scheme. At the same time, supersaturations inside clouds are small, and the condensate amounts in bulk and bin schemes differ insignificantly. This critical observation forms a starting point for the hybrid bulk–bin approach. In this approach, when the cloud water first appears, the activation scheme inserts cloud droplets at the low end of the bin representation. Subsequent diffusional and eventually accretional growth shift the spectrum toward larger sizes so that the saturation inside a cloud is maintained. Details of the hybrid approach are discussed in this paper, and the validation against the traditional bin scheme in a framework of the adiabatic rising parcel is presented.

Before the scheme can be applied to the multidimensional cloud model, a 1D advection–condensation problem of Grabowski and Smolarkiewicz is used to address the issue of the numerical difficulties that finite-difference schemes experience near cloud edges. In the bulk case, these are in the form of condensation rate overshoots and undershoots; and this aspect requires special attention in the hybrid scheme. A novel approach is developed that provides a physically consistent solution near cloud edges using the hybrid bulk–bin scheme. The key is to allow grid boxes near the edges to be partly cloudy and to include spectral changes of cloud droplets that take this into account. Application of the hybrid scheme to an idealized 2D problem of moist thermal rising from rest and producing rain illustrates the application of the scheme to practical problems of cloud dynamics and warm-rain microphysics.

Corresponding author address: Wojciech W. Grabowski, NCAR/MMM, P.O. Box 3000, Boulder, CO 80307–3000. Email: grabow@ncar.ucar.edu

Abstract

This paper presents a hybrid approach to model warm-rain processes, merging the diverse schemes of bulk and detailed (bin) microphysics. In the bulk scheme, the key assumption is that the exact saturation is maintained inside a cloud. In contrast, the supersaturation inside a cloud is predicted in the bin scheme and is applied to calculate the diffusional growth of cloud droplets. Predicting the supersaturation is numerically cumbersome, however, and typically requires spatial and temporal resolutions that are significantly higher than those that can be applied in the bulk scheme. At the same time, supersaturations inside clouds are small, and the condensate amounts in bulk and bin schemes differ insignificantly. This critical observation forms a starting point for the hybrid bulk–bin approach. In this approach, when the cloud water first appears, the activation scheme inserts cloud droplets at the low end of the bin representation. Subsequent diffusional and eventually accretional growth shift the spectrum toward larger sizes so that the saturation inside a cloud is maintained. Details of the hybrid approach are discussed in this paper, and the validation against the traditional bin scheme in a framework of the adiabatic rising parcel is presented.

Before the scheme can be applied to the multidimensional cloud model, a 1D advection–condensation problem of Grabowski and Smolarkiewicz is used to address the issue of the numerical difficulties that finite-difference schemes experience near cloud edges. In the bulk case, these are in the form of condensation rate overshoots and undershoots; and this aspect requires special attention in the hybrid scheme. A novel approach is developed that provides a physically consistent solution near cloud edges using the hybrid bulk–bin scheme. The key is to allow grid boxes near the edges to be partly cloudy and to include spectral changes of cloud droplets that take this into account. Application of the hybrid scheme to an idealized 2D problem of moist thermal rising from rest and producing rain illustrates the application of the scheme to practical problems of cloud dynamics and warm-rain microphysics.

Corresponding author address: Wojciech W. Grabowski, NCAR/MMM, P.O. Box 3000, Boulder, CO 80307–3000. Email: grabow@ncar.ucar.edu

Save