Editorial Type:
Article
Article Type:
Research Article

A PDF-Based Microphysics Parameterization for Simulation of Drizzling Boundary Layer Clouds

Anning Cheng AS&M, Inc., Hampton, Virginia

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Kuan-Man Xu Climate Science Branch, NASA Langley Research Center, Hampton, Virginia

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Print Publication:
01 Aug 2009
DOI:
https://doi.org/10.1175/2009JAS2944.1
Page(s):
2317–2334
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Abstract

Formulating the contribution of subgrid-scale (SGS) variability to microphysical processes in boundary layer and deep convective cloud parameterizations is a challenging task because of the complexity of microphysical processes and the lack of subgrid-scale information. In this study, a warm-rain microphysics parameterization that is based on a joint double-Gaussian distribution of vertical velocity, liquid water potential temperature, total water mixing ratio, and perturbation of rainwater mixing ratio is developed to simulate drizzling boundary layer clouds with a single column model (SCM). The probability distribution function (PDF) is assumed, but its parameters evolve according to equations that invoke higher-order turbulence closure. These parameters are determined from the first-, second-, and third-order moments and are then used to derive analytical expressions for autoconversion, collection, and evaporation rates. The analytical expressions show that correlation between rainwater and liquid water mixing ratios of the Gaussians enhances the collection rate whereas that between saturation deficit and rainwater mixing ratios of the Gaussians enhances the evaporation rate. Cases of drizzling shallow cumulus and stratocumulus are simulated with large-eddy simulation (LES) and SCM runs (SCM-CNTL and SCM-M): LES explicitly resolves SGS variability, SCM-CNTL parameterizes SGS variability with the PDF-based scheme, but SCM-M uses the grid-mean profiles to calculate the conversion rates of microphysical processes. SCM-CNTL can well reproduce the autoconversion, collection, and evaporation rates from LES. Comparisons between the two SCM experiments showed improvements in mean profiles of potential temperature, total water mixing ratio, liquid water, and cloud amount in the simulations considering SGS variability. A 3-week integration using the PDF-based microphysics scheme indicates that the scheme is stable for long-term simulations.

Corresponding author address: Dr. Anning Cheng, 1 Enterprise Parkway, Suite 300, Hampton, VA 23666. Email: anning-cheng@ssaihq.com

Abstract

Formulating the contribution of subgrid-scale (SGS) variability to microphysical processes in boundary layer and deep convective cloud parameterizations is a challenging task because of the complexity of microphysical processes and the lack of subgrid-scale information. In this study, a warm-rain microphysics parameterization that is based on a joint double-Gaussian distribution of vertical velocity, liquid water potential temperature, total water mixing ratio, and perturbation of rainwater mixing ratio is developed to simulate drizzling boundary layer clouds with a single column model (SCM). The probability distribution function (PDF) is assumed, but its parameters evolve according to equations that invoke higher-order turbulence closure. These parameters are determined from the first-, second-, and third-order moments and are then used to derive analytical expressions for autoconversion, collection, and evaporation rates. The analytical expressions show that correlation between rainwater and liquid water mixing ratios of the Gaussians enhances the collection rate whereas that between saturation deficit and rainwater mixing ratios of the Gaussians enhances the evaporation rate. Cases of drizzling shallow cumulus and stratocumulus are simulated with large-eddy simulation (LES) and SCM runs (SCM-CNTL and SCM-M): LES explicitly resolves SGS variability, SCM-CNTL parameterizes SGS variability with the PDF-based scheme, but SCM-M uses the grid-mean profiles to calculate the conversion rates of microphysical processes. SCM-CNTL can well reproduce the autoconversion, collection, and evaporation rates from LES. Comparisons between the two SCM experiments showed improvements in mean profiles of potential temperature, total water mixing ratio, liquid water, and cloud amount in the simulations considering SGS variability. A 3-week integration using the PDF-based microphysics scheme indicates that the scheme is stable for long-term simulations.

Corresponding author address: Dr. Anning Cheng, 1 Enterprise Parkway, Suite 300, Hampton, VA 23666. Email: anning-cheng@ssaihq.com

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  • Bechtold, P., J. P. Pinty, and P. Mascart, 1993: The use of partial cloudiness in a warm-rain parameterization: A subgrid-scale precipitation scheme. Mon. Wea. Rev., 121 , 3301–3311.

    • Search Google Scholar
    • Export Citation

  • Bougeault, P., 1981: Modeling the trade-wind cumulus boundary-layer. Part I: Testing the ensemble cloud relations against numerical data. J. Atmos. Sci., 38 , 2414–2428.

    • Search Google Scholar
    • Export Citation

  • Bretherton, C. S., and Coauthors, 1999: An intercomparison of radiatively driven entrainment and turbulence in a smoke cloud, as simulated by different numerical models. Quart. J. Roy. Meteor. Soc., 125 , 391–423.

    • Search Google Scholar
    • Export Citation

  • Chen, J-M., 1991: Turbulence-scale condensation parameterization. J. Atmos. Sci., 48 , 1510–1512.

  • Cheng, A., and K-M. Xu, 2006: Simulation of shallow cumuli and their transition to deep convective clouds by cloud-resolving models with different third-order turbulence closures. Quart. J. Roy. Meteor. Soc., 132 , 359–382.

    • Search Google Scholar
    • Export Citation

  • Cheng, A., and K-M. Xu, 2008: Simulation of boundary-layer cumulus and stratocumulus clouds using a cloud-resolving model with low and third-order turbulence closures. J. Meteor. Soc. Japan, 86A , 67–86.

    • Search Google Scholar
    • Export Citation

  • Cheng, A., K-M. Xu, and J-C. Golaz, 2004: Liquid water oscillation in modeling boundary-layer cumuli with third-order turbulence closure models. J. Atmos. Sci., 61 , 1621–1629.

    • Search Google Scholar
    • Export Citation

  • de Roode, S. R., and P. G. Duynkerke, 1997: Observed Lagrangian transition of stratocumulus into cumulus during ASTEX: Mean state and turbulence structure. J. Atmos. Sci., 54 , 2157–2173.

    • Search Google Scholar
    • Export Citation

  • Golaz, J-C., V. E. Larson, and W. R. Cotton, 2002a: A PDF-based model for boundary layer clouds. Part I: Method and model description. J. Atmos. Sci., 59 , 3540–3551.

    • Search Google Scholar
    • Export Citation

  • Golaz, J-C., V. E. Larson, and W. R. Cotton, 2002b: A PDF-based model for boundary layer clouds. Part II: Model results. J. Atmos. Sci., 59 , 3552–3571.

    • Search Google Scholar
    • Export Citation

  • Jakob, C., and S. A. Klein, 2000: A parameterization of the effects of cloud and precipitation overlap for use in general-circulation models. Quart. J. Roy. Meteor. Soc., 126 , 2525–2544.

    • Search Google Scholar
    • Export Citation

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

    • Search Google Scholar
    • Export Citation

  • Khairoutdinov, M. F., and D. A. Randall, 2003: Cloud resolving modeling of the ARM summer 1997 IOP: Model formulation, results, uncertainties, and sensitivities. J. Atmos. Sci., 60 , 607–625.

    • Search Google Scholar
    • Export Citation

  • Klemp, J. B., and R. Wilhelmson, 1978: The simulation of three-dimensional convective storm dynamics. J. Atmos. Sci., 35 , 1070–1096.

    • Search Google Scholar
    • Export Citation

  • Larson, V. E., R. Wood, P. R. Field, J-C. Golaz, and T. H. Vonder Haar, 2001a: Systematic biases in the microphysics and thermodynamics of numerical models that ignore subgrid-scale variability. J. Atmos. Sci., 58 , 1117–1128.

    • Search Google Scholar
    • Export Citation

  • Larson, V. E., R. Wood, P. R. Field, J-C. Golaz, T. H. Vonder Haar, and W. R. Cotton, 2001b: Small-scale and mesoscale variability of scalars in cloudy boundary layers: One-dimensional probability density functions. J. Atmos. Sci., 58 , 1978–1994.

    • Search Google Scholar
    • Export Citation

  • Larson, V. E., J-C. Golaz, and W. R. Cotton, 2002: Small-scale and mesoscale variability in cloudy boundary layers: Joint probability density functions. J. Atmos. Sci., 59 , 3519–3539.

    • Search Google Scholar
    • Export Citation

  • Larson, V. E., J-C. Golaz, H. Jiang, and W. R. Cotton, 2005: Supplying local microphysics parameterizations with information about subgrid variability: Latin hypercube sampling. J. Atmos. Sci., 62 , 4010–4026.

    • Search Google Scholar
    • Export Citation

  • Lewellen, W. S., and S. Yoh, 1993: Binormal model of ensemble partial cloudiness. J. Atmos. Sci., 50 , 1228–1237.

  • Marshall, J. S., and W. M. Palmer, 1948: The distribution of raindrops with size. J. Meteor., 5 , 165–166.

  • Mellor, G. L., 1977: The Gaussian cloud model relations. J. Atmos. Sci., 34 , 356–359.

  • Pincus, R., and S. A. Klein, 2000: Unresolved spatial variability and microphysical process rates in large-scale models. J. Geophys. Res., 105 , 27059–27065.

    • Search Google Scholar
    • Export Citation

  • Pincus, R., H. W. Barker, and J-J. Morcrette, 2003: A fast, flexible, approximate technique for computing radiative transfer in inhomogeneous cloud fields. J. Geophys. Res., 108 , 4376. doi:10.1029/2002JD003322.

    • Search Google Scholar
    • Export Citation

  • Räisänen, P., and H. W. Barker, 2004: Evaluation and optimization of sampling errors for the Monte Carlo independent column approximation. Quart. J. Roy. Meteor. Soc., 130 , 2069–2085.

    • Search Google Scholar
    • Export Citation

  • Rauber, R. M., and Coauthors, 2007: Rain in shallow cumulus over the ocean: The RICO campaign. Bull. Amer. Meteor. Soc., 88 , 1912–1928.

    • Search Google Scholar
    • Export Citation

  • Smith, R. N. B., 1990: A scheme for predicting layer clouds and their water-content in a general-circulation model. Quart. J. Roy. Meteor. Soc., 116 , 435–460.

    • Search Google Scholar
    • Export Citation

  • Sommeria, G., and J. W. Deardorff, 1977: Subgrid-scale condensation in models of nonprecipitating clouds. J. Atmos. Sci., 34 , 344–355.

    • Search Google Scholar
    • Export Citation

  • Stevens, B., and Coauthors, 2001: Simulations of trade wind cumuli under a strong inversion. J. Atmos. Sci., 58 , 1870–1891.

  • Sundqvist, H., 1978: A parameterization scheme for non-convective condensation including prediction of cloud water content. Quart. J. Roy. Meteor. Soc., 104 , 677–690.

    • Search Google Scholar
    • Export Citation

  • Tompkins, A. M., 2002: A prognostic parameterization for the subgrid-scale variability of water vapor and clouds in large-scale models and its use to diagnose cloud cover. J. Atmos. Sci., 59 , 1917–1942.

    • Search Google Scholar
    • Export Citation

  • Woods, R., P. R. Field, and W. R. Cotton, 2002: Autoconversion rate biases in stratiform boundary layer cloud parameterizations. Atmos. Res., 65 , 109–128. doi:10.1016/S0169-8095(02)00071-6.

    • Search Google Scholar
    • Export Citation

  • Xu, K-M., and D. A. Randall, 1995: Impact of interactive radiative transfer on the macroscopic behavior of cumulus ensembles. Part I: Radiation parameterization and sensitivity tests. J. Atmos. Sci., 52 , 785–799.

    • Search Google Scholar
    • Export Citation

  • Zhang, J., U. Lohmann, and B. Lin, 2002: A new statistically based autoconversion rate parameterization for use in large-scale model. J. Geophys. Res., 107 , 4750. doi:10.1029/2001JD001484.

    • Search Google Scholar
    • Export Citation

  • Zhu, P., and Coauthors, 2005: Intercomparison and interpretation of single-column model simulations of a nocturnal stratocumulus-topped marine boundary layer. Mon. Wea. Rev., 133 , 2741–2758.

    • Search Google Scholar
    • Export Citation
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