Broadening of Cloud Droplet Spectra through Eddy Hopping: Turbulent Entraining Parcel Simulations

Gustavo C. Abade Institute of Geophysics, Faculty of Physics, University of Warsaw, Warsaw, Poland

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Wojciech W. Grabowski National Center for Atmospheric Research, Boulder, Colorado

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Hanna Pawlowska Institute of Geophysics, Faculty of Physics, University of Warsaw, Warsaw, Poland

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Abstract

This paper discusses the effects of cloud turbulence, turbulent entrainment, and entrained cloud condensation nuclei (CCN) activation on the evolution of the cloud droplet size spectrum. We simulate an ensemble of idealized turbulent cloud parcels that are subject to entrainment events modeled as a random process. Entrainment events, subsequent turbulent mixing inside the parcel, supersaturation fluctuations, and the resulting stochastic droplet activation and growth by condensation are simulated using a Monte Carlo scheme. Quantities characterizing the turbulence intensity, entrainment rate, CCN concentration, and the mean fraction of environmental air entrained in an event are all specified as independent external parameters. Cloud microphysics is described by applying Lagrangian particles, the so-called superdroplets. These are either unactivated CCN or cloud droplets that grow from activated CCN. The model accounts for the addition of environmental CCN into the cloud by entraining eddies at the cloud edge. Turbulent mixing of the entrained dry air with cloudy air is described using the classical linear relaxation to the mean model. We show that turbulence plays an important role in aiding entrained CCN to activate, and thus broadening the droplet size distribution. These findings are consistent with previous large-eddy simulations (LESs) that consider the impact of variable droplet growth histories on the droplet size spectra in small cumuli. The scheme developed in this work is ready to be used as a stochastic subgrid-scale scheme in LESs of natural clouds.

© 2018 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Gustavo C. Abade, gustavo.abade@fuw.edu.pl

Abstract

This paper discusses the effects of cloud turbulence, turbulent entrainment, and entrained cloud condensation nuclei (CCN) activation on the evolution of the cloud droplet size spectrum. We simulate an ensemble of idealized turbulent cloud parcels that are subject to entrainment events modeled as a random process. Entrainment events, subsequent turbulent mixing inside the parcel, supersaturation fluctuations, and the resulting stochastic droplet activation and growth by condensation are simulated using a Monte Carlo scheme. Quantities characterizing the turbulence intensity, entrainment rate, CCN concentration, and the mean fraction of environmental air entrained in an event are all specified as independent external parameters. Cloud microphysics is described by applying Lagrangian particles, the so-called superdroplets. These are either unactivated CCN or cloud droplets that grow from activated CCN. The model accounts for the addition of environmental CCN into the cloud by entraining eddies at the cloud edge. Turbulent mixing of the entrained dry air with cloudy air is described using the classical linear relaxation to the mean model. We show that turbulence plays an important role in aiding entrained CCN to activate, and thus broadening the droplet size distribution. These findings are consistent with previous large-eddy simulations (LESs) that consider the impact of variable droplet growth histories on the droplet size spectra in small cumuli. The scheme developed in this work is ready to be used as a stochastic subgrid-scale scheme in LESs of natural clouds.

© 2018 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Gustavo C. Abade, gustavo.abade@fuw.edu.pl
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  • Andrejczuk, M., W. W. Grabowski, J. Reisner, and A. Gadian, 2010: Cloud-aerosol interactions for boundary layer stratocumulus in the Lagrangian Cloud Model. J. Geophys. Res., 115, D22214, https://doi.org/10.1029/2010JD014248.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Arabas, S., and S.-I. Shima, 2017: On the CCN (de)activation nonlinearities. Nonlinear Processes Geophys., 24, 535542, https://doi.org/10.5194/npg-24-535-2017.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Arabas, S., A. Jaruga, H. Pawlowska, and W. W. Grabowski, 2015: Libcloudph++ 1.0: a single-moment bulk, double-moment bulk, and particle-based warm-rain microphysics library in C++. Geosci. Model Dev., 8, 16771707, https://doi.org/10.5194/gmd-8-1677-2015.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Celani, A., A. Mazzino, and M. Tizzi, 2008: The equivalent size of cloud condensation nuclei. New J. Phys., 10, 075021, https://doi.org/10.1088/1367-2630/10/7/075021.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Celani, A., A. Mazzino, and M. Tizzi, 2009: Droplet feedback on vapor in a warm cloud. Int. J. Mod. Phys., 23B, 54345443, https://doi.org/10.1142/S0217979209063754.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chandrakar, K. K., W. Cantrel, K. C. Chang, D. Ciochetto, D. Niedermeier, M. Ovchinnikov, R. A. Shaw, and F. Yang, 2016: Aerosol indirect effect from turbulence-induced broadening of cloud-droplet size distributions. Proc. Natl. Acad. Sci. USA, 113, 14 24314 248, https://doi.org/10.1073/pnas.1612686113.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Cooper, W. A., 1989: Effects of variable droplet growth histories on droplet size distributions. Part I: Theory. J. Atmos. Sci., 46, 13011311, https://doi.org/10.1175/1520-0469(1989)046<1301:EOVDGH>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Field, P. R., A. A. Hill, K. Furtado, and A. Koroloev, 2014: Mixed-phase clouds in a turbulent environment. Part 2: Analytic treatment. Quart. J. Roy. Meteor. Soc., 140, 870880, https://doi.org/10.1002/qj.2175.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Fuchs, N. A., and A. G. Sutugin, 1970: Highly Dispersed Aerosols. Israel Program for Scientific Translations, 105 pp.

    • Crossref
    • Export Citation
  • Furtado, K., P. R. Field, I. A. Boutle, C. J. Morcrette, and J. M. Wilkinson, 2016: A physically based subgrid parametrization for the production and maintenance of mixed-phase clouds in a general circulation model. J. Atmos. Sci., 73, 279291, https://doi.org/10.1175/JAS-D-15-0021.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Grabowski, W. W., and G. C. Abade, 2017: Broadening of cloud droplet spectra through eddy hopping: Turbulent adiabatic parcel simulations. J. Atmos. Sci., 74, 14851493, https://doi.org/10.1175/JAS-D-17-0043.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Grabowski, W. W., P. Dziekan, and H. Pawlowska, 2018: Lagrangian condensation microphysics with Twomey CCN activation. Geosci. Model Dev., 11, 103120, https://doi.org/10.5194/gmd-11-103-2018.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Heus, T., and Coauthors, 2010: Formulation of the Dutch Atmospheric Large-Eddy Simulation (DALES) and overview of its applications. Geosci. Model Dev., 3, 415444, https://doi.org/10.5194/gmd-3-415-2010.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hoffmann, F., 2016: The effect of spurious cloud edge supersaturations in Lagrangian cloud models: An analytical and numerical study. Mon. Wea. Rev., 144, 107118, https://doi.org/10.1175/MWR-D-15-0234.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hoffmann, F., Y. Noh, and S. Raasch, 2017: The route to raindrop formation in a shallow cumulus cloud simulated by a Lagrangian cloud model. J. Atmos. Sci., 74, 21252142, https://doi.org/10.1175/JAS-D-16-0220.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jensen, J., P. Austin, M. B. Baker, and A. M. Blyth, 1985: Turbulent mixing, spectral evolution and dynamics in a warm cumulus cloud. J. Atmos. Sci., 42, 173192, https://doi.org/10.1175/1520-0469(1985)042<0173:TMSEAD>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kloeden, P. E., and E. Platen, 1992: Numerical Solution of Stochastic Differential Equations. Springer-Verlag, 632 pp.

    • Crossref
    • Export Citation
  • Krueger, S. K., C.-W. Su, and P. A. McMurty, 1997: Modeling entrainment and finescale mixing in cumulus clouds. J. Atmos. Sci., 54, 26972712, https://doi.org/10.1175/1520-0469(1997)054<2697:MEAFMI>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kulmala, M., U. Rannik, E. L. Zapadinsky, and C. F. Clement, 1997: The effect of saturation fluctuations on droplet growth. J. Aerosol Sci., 28, 13951409, https://doi.org/10.1016/S0021-8502(97)00015-3.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Laaksonen, A., T. Vesala, M. Kulmala, P. M. Winkler, and P. E. Wagner, 2005: Commentary on cloud modelling and the mass accommodation coefficient of water. Atmos. Chem. Phys., 5, 461464, https://doi.org/10.5194/acp-5-461-2005.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lasher-Trapp, S. G., W. A. Cooper, and A. M. Blyth, 2005: Broadening of droplet size distributions from entrainment and mixing in a cumulus cloud. Quart. J. Roy. Meteor. Soc., 131, 195220, https://doi.org/10.1256/qj.03.199.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Paoli, R., and K. Shariff, 2009: Turbulent condensation of droplets: Direct simulation and a stochastic model. J. Atmos. Sci., 66, 723740, https://doi.org/10.1175/2008JAS2734.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Pawlowska, H., W. W. Grabowski, and J.-L. Brenguier, 2006: Observations of the width of cloud droplet spectra in stratocumulus. Geophys. Res. Lett., 33, L19810, https://doi.org/10.1029/2006GL026841.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Petters, M., and S. Kreidenweis, 2007: A single parameter representation of hygroscopic growth and cloud condensation nucleus activity. Atmos. Chem. Phys., 7, 19611971, https://doi.org/10.5194/acp-7-1961-2007.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Pope, S. B., 2000: Turbulent Flows. Cambridge University Press, 771 pp.

    • Crossref
    • Export Citation
  • Pope, S. B., 2011: Simple models of turbulent flows. Phys. Fluids, 23, 011301, https://doi.org/10.1063/1.3531744.

  • Pruppacher, H. R., and J. D. Klett, 1997: Microphysics of Clouds and Precipitation. 2nd ed. Kluwer Academics, 954 pp.

  • Riechelmann, T., Y. Noh, and S. Raasch, 2012: A new method for large-eddy simulations of clouds with Lagrangian droplets including the effects of turbulent collision. New J. Phys., 14, 065008, https://doi.org/10.1088/1367-2630/14/6/065008.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rogers, R. R., and M. K. Yau, 1989: A Short Course in Cloud Physics. 3rd ed. Butterworth-Heinemann, 293 pp.

  • Romps, D. M., and Z. Kuang, 2010: Nature versus nurture in shallow convection. J. Atmos. Sci., 67, 16551666, https://doi.org/10.1175/2009JAS3307.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sardina, G., F. Picano, L. Brandt, and R. Caballero, 2015: Continuous growth of droplet size variance due to condensation in turbulent clouds. Phys. Rev. Lett., 115, 184501, https://doi.org/10.1103/PhysRevLett.115.184501.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sardina, G., S. Poulain, L. Brandt, and R. Caballero, 2018: Broadening of cloud droplet size spectra by stochastic condensation: effects of mean updraft velocity and CCN activation. J. Atmos. Sci., 75, 451467, https://doi.org/10.1175/JAS-D-17-0241.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Schumann, U., 1991: Subgrid length-scales for large-eddy simulation of stratified turbulence. Theor. Comput. Fluid Dyn., 2, 279290, https://doi.org/10.1007/BF00271468.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Shima, S., K. Kusano, A. Kawano, T. Sugiyama, and S. Kawahara, 2009: The super-droplet method for the numerical simulation of clouds and precipitation: A particle-based and probabilistic microphysics model coupled with a non-hydrostatic model. Quart. J. Roy. Meteor. Soc., 135, 13071320, https://doi.org/10.1002/qj.441.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Siebert, H., K. Lehmann, and M. Wendisch, 2006: Observations of small-scale turbulence and energy dissipation rates in the cloudy boundary layer. J. Atmos. Sci., 63, 14511466, https://doi.org/10.1175/JAS3687.1.

    • Crossref
    • 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, https://doi.org/10.1007/BF01993560.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zapadinsky, E., K. Sabelfeld, M. Kulmala, B. Gorbunov, and D. Rackimgulova, 1995: Heterogeneous nucleation in non-uniform media: Numerical simulations. J. Aerosol Sci., 26, 11891195, https://doi.org/10.1016/0021-8502(95)00527-7.

    • Crossref
    • Search Google Scholar
    • Export Citation
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