• Anderson, A., and A. Kostinski, 2010: Reversible record breaking and variability: Temperature distributions across the globe. J. Appl. Meteor. Climatol., 49, 16811691.

    • Search Google Scholar
    • Export Citation
  • Baker, B., 1992: Turbulent entrainment and mixing in clouds: A new observational approach. J. Atmos. Sci., 49, 387404.

  • Baker, B., and R. Lawson, 2010: Analysis of tools used to quantify droplet clustering in clouds. J. Atmos. Sci., 67, 33553367.

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

    • Search Google Scholar
    • Export Citation
  • Cox, D., and V. Isham, 1980: Point Processes. Chapman and Hall, 188 pp.

  • Grandell, J., 1976: Doubly Stochastic Poisson Processes. Springer-Verlag, 234 pp.

  • Jameson, A., and A. Kostinski, 2000: Fluctuation properties of precipitation. Part VI: Observations of hyperfine clustering and drop size distribution structures in three-dimensional rain. J. Atmos. Sci., 57, 373388.

    • Search Google Scholar
    • Export Citation
  • Knyazikhin, Y., A. Marshak, M. Larsen, W. Wiscombe, J. Martonchik, and R. 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., 2001: On the extinction of radiation by a homogeneous but spatially correlated random medium. J. Opt. Soc. Amer., A18, 19291933.

    • Search Google Scholar
    • Export Citation
  • Kostinski, A., and A. Jameson, 1997: Fluctuation properties of precipitation. Part I: On deviations of single-size drop counts from the Poisson distribution. J. Atmos. Sci., 54, 21742186.

    • Search Google Scholar
    • Export Citation
  • Kostinski, A., and A. Jameson, 2000: On the spatial distribution of cloud particles. J. Atmos. Sci., 57, 901915.

  • Kostinski, A., and R. Shaw, 2001: Scale-dependent droplet clustering in turbulent clouds. J. Fluid Mech., 434, 389398.

  • Kostinski, A., and R. Shaw, 2005: Fluctuations and luck in droplet growth by coalescence. Bull. Amer. Meteor. Soc., 86, 235244.

  • Kostinski, A., M. Larsen, and A. Jameson, 2006: The texture of rain: Exploring stochastic microstructure at small scales. J. Hydrol., 328, 3845.

    • Search Google Scholar
    • Export Citation
  • Larsen, M., 2006: Studies of discrete fluctuations in atmospheric phenomena. Ph.D. dissertation, Michigan Technological University, 220 pp.

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

  • Larsen, M., and A. Kostinski, 2009: Simple dead-time corrections for discrete time series of non-Poisson data. Meas. Sci. Technol., 20, 095101, doi:10.1088/0957-0233/20/9/095101.

    • Search Google Scholar
    • Export Citation
  • Larsen, M., W. Cantrell, J. Kannosto, and A. Kostinski, 2003: Detection of spatial correlations among aerosol particles. Aerosol Sci. Technol., 37, 476485.

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

  • Larsen, M., A. Clark, M. Noffke, G. Saltzgaber, and A. Steele, 2010: Identifying the scaling properties of rainfall accumulation as measured by a tipping-bucket rain gauge network. Atmos. Res., 96, 149158.

    • Search Google Scholar
    • Export Citation
  • Lavergnat, J., and P. Gole, 1998: A stochastic raindrop time distribution model. J. Appl. Meteor., 37, 805818.

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

    • Search Google Scholar
    • Export Citation
  • Lovejoy, S., M. Lilly, N. Desaulniers-Soucy, and D. Schertzer, 2003: Large particle number limit in rain. Phys. Rev., E68, 025301, doi:10.1103/PhysRevE.68.025301.

    • Search Google Scholar
    • Export Citation
  • Marshak, A., Y. Knyazikhin, M. Larsen, and W. 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
  • Martinez, V., and E. Saar, 2002: Statistics of the Galaxy Distribution. Chapman and Hall/CRC, 432 pp.

  • Neyman, J., and E. Scott, 1958: Statistical approach to problems of cosmology. J. Roy. Stat. Soc., B20, 143.

  • Picinbono, B., and C. Bendjaballah, 2005: Characterization of nonclassical optical fields by photodetection statistics. Phys. Rev., A71, 013812, doi:10.1103/PhysRevA.71.013812.

    • Search Google Scholar
    • Export Citation
  • Pinsky, M., and A. 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
  • Preining, O., 1983: Optical single-particle counters to obtain the spatial inhomogeneity of particulate clouds. Aerosol Sci. Technol., 2, 7990.

    • Search Google Scholar
    • Export Citation
  • Santaló, L., 1976: Integral Geometry and Geometric Probability. Addison-Wesley, 404 pp.

  • Shaw, R., 2003: Particle-turbulence interactions in atmospheric clouds. Annu. Rev. Fluid Mech., 35, 183227.

  • Shaw, R., W. Reade, L. 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. Kostinski, and M. Larsen, 2002: Towards quantifying droplet clustering in clouds. Quart. J. Roy. Meteor. Soc., 128, 10431057.

    • Search Google Scholar
    • Export Citation
  • Stoyan, D., and H. Stoyan, 1994: Fractals, Random Shapes and Point Fields: Methods of Geometrical Statistics. John Wiley and Sons, 389 pp.

  • Uijlenhoet, R., J. Stricker, P. Torfs, and J.-D. Creutin, 1999: Towards a stochastic model of rainfall for radar hydrology: Testing the Poisson homogeneity hypothesis. Phys. Chem. Earth, 24B, 747755.

    • Search Google Scholar
    • Export Citation
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Scale Localization of Cloud Particle Clustering Statistics

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  • 1 Department of Physics and Astronomy, College of Charleston, Charleston, South Carolina
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Abstract

Recent work has examined the spatial distribution of droplets within a cloud. Experimentally, most studies analyze interevent times from static probes flown linearly through a cloud, allowing the spatial information to be conveyed through a time series of particle detections. Analysis of these data has shown unequivocally that most clouds have nontrivial spatial structure. There is still debate as to which of many different possible statistical descriptions is most appropriate for characterizing this spatial structure and for identifying spatiotemporal scales of physical significance from the data record. This paper seeks to clarify some pervasive misunderstandings and to outline more carefully the range of validity for several of these statistical tools. Simulations are used to explore the relative scale-localizing capabilities of various commonly used statistical tools.

Corresponding author address: Michael L. Larsen, Department of Physics and Astronomy, College of Charleston, Charleston, SC 29424. E-mail: larsenml@cofc.edu

Abstract

Recent work has examined the spatial distribution of droplets within a cloud. Experimentally, most studies analyze interevent times from static probes flown linearly through a cloud, allowing the spatial information to be conveyed through a time series of particle detections. Analysis of these data has shown unequivocally that most clouds have nontrivial spatial structure. There is still debate as to which of many different possible statistical descriptions is most appropriate for characterizing this spatial structure and for identifying spatiotemporal scales of physical significance from the data record. This paper seeks to clarify some pervasive misunderstandings and to outline more carefully the range of validity for several of these statistical tools. Simulations are used to explore the relative scale-localizing capabilities of various commonly used statistical tools.

Corresponding author address: Michael L. Larsen, Department of Physics and Astronomy, College of Charleston, Charleston, SC 29424. E-mail: larsenml@cofc.edu
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