Analysis of Tools Used to Quantify Droplet Clustering in Clouds

Brad Baker SPEC, Inc., Boulder, Colorado

Search for other papers by Brad Baker in
Current site
Google Scholar
PubMed
Close
and
R. Paul Lawson SPEC, Inc., Boulder, Colorado

Search for other papers by R. Paul Lawson in
Current site
Google Scholar
PubMed
Close
Restricted access

Abstract

The spacing of cloud droplets observed along an approximately horizontal line through a cloud may be analyzed using a variety of techniques to reveal structure on small scales, sometimes called clustering, if such structure exists. A number of techniques have been applied and others have been suggested but not yet rigorously defined and applied. In this paper techniques are studied and evaluated using synthetic droplet spacing data. For the type of small-scale structure (clustering) modeled in this study, the most promising analysis approach is to use a combination of the power spectrum and the fishing statistic. Standard deviations and confidence intervals are determined for the power spectrum, the pair correlation function, and a modified fishing statistic. The clustering index and the volume-averaged pair correlation are shown to be less usefully normalized forms of the fishing statistic.

Corresponding author address: Brad Baker, SPEC, Inc., 3022 Sterling Circle, Suite 200, Boulder, CO 80301. Email: brad@specinc.com

Abstract

The spacing of cloud droplets observed along an approximately horizontal line through a cloud may be analyzed using a variety of techniques to reveal structure on small scales, sometimes called clustering, if such structure exists. A number of techniques have been applied and others have been suggested but not yet rigorously defined and applied. In this paper techniques are studied and evaluated using synthetic droplet spacing data. For the type of small-scale structure (clustering) modeled in this study, the most promising analysis approach is to use a combination of the power spectrum and the fishing statistic. Standard deviations and confidence intervals are determined for the power spectrum, the pair correlation function, and a modified fishing statistic. The clustering index and the volume-averaged pair correlation are shown to be less usefully normalized forms of the fishing statistic.

Corresponding author address: Brad Baker, SPEC, Inc., 3022 Sterling Circle, Suite 200, Boulder, CO 80301. Email: brad@specinc.com

Save
  • Baker, B. A., 1992: Turbulent entrainment and mixing in clouds: A new observational approach. J. Atmos. Sci., 49 , 387404.

  • Chaumat, L., and J. L. Brenguier, 2001: Droplet spectra broadening in cumulus clouds. Part II: Microscale droplet concentration heterogeneities. J. Atmos. Sci., 58 , 642654.

    • Search Google Scholar
    • Export Citation
  • Cooley, J. W., and J. W. Tukey, 1965: An algorithm for the machine calculation of complex Fourier series. Math. Comput., 19 , 297301.

  • Grabowski, W. W., and P. Vaillancourt, 1999: Comments on the “Preferential concentration of cloud droplets by turbulence: Effects on the early evolution of cumulus cloud droplet spectra”. J. Atmos. Sci., 56 , 14331436.

    • Search Google Scholar
    • Export Citation
  • Knyazikhin, Y., A. Marshak, M. L. Larsen, W. J. Wiscombe, J. V. Martonchik, and R. B. Myneni, 2005: Small-scale drop size variability: Impact on estimation of cloud optical properties. J. Atmos. Sci., 62 , 25552567.

    • Search Google Scholar
    • Export Citation
  • Kostinski, A. B., and R. A. Shaw, 2001: Scale-dependent droplet clustering in turbulent clouds. J. Fluid Mech., 434 , 389398.

  • Larsen, M. L., 2007: Spatial distributions of aerosol particles: Investigation of the Poisson assumption. J. Aerosol Sci., 38 , 807822.

    • Search Google Scholar
    • Export Citation
  • Larsen, M. L., A. B. Kostinski, and A. Tokay, 2005: Observations and analysis of uncorrelated rain. J. Atmos. Sci., 62 , 40714083.

  • Lehmann, K., H. Siebert, M. Wendisch, and R. A. Shaw, 2007: Evidence for inertial droplet clustering in weakly turbulent clouds. Tellus, 59B , 5765.

    • Search Google Scholar
    • Export Citation
  • Marshak, A., Y. Knyazikhin, M. Larsen, and W. J. Wiscombe, 2005: Small-scale drop-size variability: Empirical models for drop-size-dependent clustering in clouds. J. Atmos. Sci., 62 , 551558.

    • Search Google Scholar
    • Export Citation
  • Pinsky, M., and A. P. Khain, 2001: Fine structure of cloud droplet concentration as seen from the Fast-FSSP measurements. Part I: Method of analysis and preliminary results. J. Appl. Meteor., 40 , 15151537.

    • Search Google Scholar
    • Export Citation
  • Saw, E. W., R. A. Shaw, S. Ayyalasomayajula, P. Y. Chuang, and A. Gylfason, 2008: Inertial clustering of particles in high-Reynolds-number turbulence. Phys. Rev. Lett., 100 , 214501. doi:10.1103/PhysRevLett.100.214501.

    • Search Google Scholar
    • Export Citation
  • Shaw, R. A., W. C. Reade, L. R. Collins, and J. Verlinde, 1998: Preferential concentration of cloud droplets by turbulence: Effects on the early evolution of cumulus cloud droplet spectra. J. Atmos. Sci., 55 , 19651976.

    • Search Google Scholar
    • Export Citation
  • Shaw, R. A., A. B. Kostinski, and M. L. Larsen, 2002: Towards quantifying droplet clustering in clouds. Quart. J. Roy. Meteor. Soc., 128 , 10431057.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 248 96 27
PDF Downloads 162 55 5