Editorial Type:
Article
Article Type:
Research Article

Cellular Statistical Models of Broken Cloud Fields. Part II: Comparison with a Dynamical Model and Statistics of Diverse Ensembles

Mikhail D. Alexandrov Department of Applied Physics and Applied Mathematics, Columbia University, and NASA Goddard Institute for Space Studies, New York, New York

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Andrew S. Ackerman NASA Goddard Institute for Space Studies, New York, New York

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Alexander Marshak NASA Goddard Space Flight Center, Greenbelt, Maryland

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Print Publication:
01 Jul 2010
DOI:
https://doi.org/10.1175/2010JAS3365.1
Page(s):
2152–2170
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Abstract

Cellular statistical models are designed to provide a simple two-parameter characterization of the structure of broken cloud fields described through distributions of cloud fraction and of chord lengths for clouds and clear gaps. In these analytical models cloud fields are assumed to occur on a semiregular grid of cells (which can be vaguely interpreted as atmospheric convective cells). In a simple, discrete cell model, cell size is fixed and each cell can either be completely filled with cloud with some probability or remain empty. Extending the discrete model to a continuous case provides more realism by allowing arbitrary cloud and gap sizes. Here the continuous cellular model is tested by comparing its statistics with those from large-eddy simulations (LES) of marine boundary layer clouds based on case studies from three trade-cumulus field projects. The statistics largely agree with some differences in small sizes approaching the LES model grid spacing. Exponential chord-length distributions follow from the assumption that the probability of any cell being cloudy is constant, appropriate for a given meteorological state (narrow sampling). Relaxing that assumption, and instead allowing this probability to have its own distribution, leads to a power-law distribution of chord lengths, appropriate to a broader sample of meteorological states (diverse sampling).

Corresponding author address: Mikhail Alexandrov, NASA Goddard Institute for Space Studies, 2880 Broadway, New York, NY 10025. Email: malexandrov@giss.nasa.gov

Abstract

Cellular statistical models are designed to provide a simple two-parameter characterization of the structure of broken cloud fields described through distributions of cloud fraction and of chord lengths for clouds and clear gaps. In these analytical models cloud fields are assumed to occur on a semiregular grid of cells (which can be vaguely interpreted as atmospheric convective cells). In a simple, discrete cell model, cell size is fixed and each cell can either be completely filled with cloud with some probability or remain empty. Extending the discrete model to a continuous case provides more realism by allowing arbitrary cloud and gap sizes. Here the continuous cellular model is tested by comparing its statistics with those from large-eddy simulations (LES) of marine boundary layer clouds based on case studies from three trade-cumulus field projects. The statistics largely agree with some differences in small sizes approaching the LES model grid spacing. Exponential chord-length distributions follow from the assumption that the probability of any cell being cloudy is constant, appropriate for a given meteorological state (narrow sampling). Relaxing that assumption, and instead allowing this probability to have its own distribution, leads to a power-law distribution of chord lengths, appropriate to a broader sample of meteorological states (diverse sampling).

Corresponding author address: Mikhail Alexandrov, NASA Goddard Institute for Space Studies, 2880 Broadway, New York, NY 10025. Email: malexandrov@giss.nasa.gov

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  • Abrams, M., 2000: The Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER): Data products for the high spatial resolution imager on NASA’s Terra platform. Int. J. Remote Sens., 21 , 847–859.

    • Search Google Scholar
    • Export Citation

  • Ackerman, A. S., M. P. Kirkpatrick, D. E. Stevens, and O. B. Toon, 2004: The impact of humidity above stratiform clouds on indirect aerosol climate forcing. Nature, 432 , 1014–1017.

    • Search Google Scholar
    • Export Citation

  • Alexandrov, M. D., A. Marshak, and A. S. Ackerman, 2010: Cellular statistical models of broken cloud fields. Part I: Theory. J. Atmos. Sci., 67 , 2125–2151.

    • Search Google Scholar
    • Export Citation

  • Astin, I., and B. G. Latter, 1998: A case for exponential cloud fields? J. Appl. Meteor., 37 , 1375–1382.

  • Astin, I., and L. Di Girolamo, 1999: A general formalism for the distribution of the total length of a geophysical parameter along a finite transect. IEEE Trans. Geosci. Remote Sens., 37 , 508–512.

    • Search Google Scholar
    • Export Citation

  • Augstein, E., H. Riehl, F. Ostapoff, and V. Wagner, 1973: Mass and energy transports in an undisturbed Atlantic trade wind flow. Mon. Wea. Rev., 101 , 101–111.

    • Search Google Scholar
    • Export Citation

  • Berg, L. K., and E. I. Kassianov, 2008: Temporal variability of fair-weather cumulus statistics at the ACRF SGP site. J. Climate, 21 , 3344–3358.

    • Search Google Scholar
    • Export Citation

  • Byrne, N., 2005: 3D radiative transfer in stochastic media. Three-Dimensional Radiative Transfer in Cloudy Atmospheres, A. Marshak and A. B. Davis, Eds., Springer, 385–424.

    • Search Google Scholar
    • Export Citation

  • Cahalan, R. F., 1994: Bounded cascade clouds: Albedo and effective thickness. Nonlinear Processes Geophys., 1 , 156–167.

  • Cahalan, R. F., and J. H. Joseph, 1989: Fractal statistics of cloud fields. Mon. Wea. Rev., 117 , 261–272.

  • Conover, W. J., 1980: Practical Nonparametric Statistics. 2nd ed. J. Wiley and Sons, 507 pp.

  • Dey, S., L. Di Girolamo, and G. Zhao, 2008: Scale effect on statistics of the macrophysical properties of trade wind cumuli over the tropical western Atlantic during RICO. J. Geophys. Res., 113 , D24214. doi:10.1029/2008JD010295.

    • Search Google Scholar
    • Export Citation

  • Evans, K. F., and W. J. Wiscombe, 2004: An algorithm for generating stochastic cloud fields from radar profile statistics. Atmos. Res., 72 , 263–289.

    • Search Google Scholar
    • Export Citation

  • Falls, L. W., 1974: The beta distribution: A statistical model for world cloud cover. J. Geophys. Res., 79 , 1261–1264.

  • Gradshteyn, I. S., and I. M. Ryzhik, 1965: Table of Integrals, Series, and Products. Academic Press, 1130 pp.

  • Hogan, R. J., and S. F. Kew, 2005: A 3D stochastic cloud model for investigating the radiative properties of inhomogeneous cirrus clouds. Quart. J. Roy. Meteor. Soc., 131 , 2585–2608.

    • Search Google Scholar
    • Export Citation

  • Isichenko, M. B., 1992: Percolation, statistical topography, and transport in random media. Rev. Mod. Phys., 64 , 961–1043.

  • Jones, P. A., 1992: Cloud-cover distributions and correlations. J. Appl. Meteor., 31 , 732–741.

  • Joseph, J. H., and R. F. Cahalan, 1990: Nearest neighbor spacing of fair weather cumulus clouds. J. Appl. Meteor., 29 , 793–805.

  • Koren, I., L. Oreopoulos, G. Feingold, L. A. Remer, and O. Altaratz, 2008: How small is a small cloud? Atmos. Chem. Phys., 8 , 3855–3864.

    • Search Google Scholar
    • Export Citation

  • Lane, D. E., K. Goris, and R. C. J. Somerville, 2002: Radiative transfer through broken clouds: Observations and model validation. J. Climate, 15 , 2921–2933.

    • Search Google Scholar
    • Export Citation

  • Marshak, A., A. Davis, R. F. Cahalan, and W. J. Wiscombe, 1994: Bounded cascade models as nonstationary multifractals. Phys. Rev. E, 49 , 55–69.

    • Search Google Scholar
    • Export Citation

  • Nagel, K., and E. Raschke, 1992: Self-organizing criticality in cloud formation? Physica A, 182 , 519–531.

  • Nicholls, S., 1989: The structure of radiatively driven convection in stratocumulus. Quart. J. Roy. Meteor. Soc., 115 , 487–511.

  • Nitta, T., and S. Esbensen, 1974: Heat and moisture budget analyses using BOMEX data. Mon. Wea. Rev., 102 , 17–28.

  • Plank, V. G., 1969: The size distribution of cumulus clouds in representative Florida populations. J. Appl. Meteor., 8 , 46–67.

  • Prigarin, S. M., and A. Marshak, 2009: A simple stochastic model for generating broken cloud optical depth and cloud-top height fields. J. Atmos. Sci., 66 , 92–104.

    • Search Google Scholar
    • Export Citation

  • Prigarin, S. M., T. B. Zhuravleva, and P. B. Volikova, 2002: Poisson model of broken multilayer cloudiness. Atmos. Ocean. Opt., 15 , 947–954.

    • Search Google Scholar
    • Export Citation

  • Prudnikov, A. P., Y. A. Brychkov, and O. I. Marichev, 1992: Direct Laplace Transforms. Vol. 4, Integrals and Series, Gordon and Breach, 637 pp.

    • 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

  • Rodts, S. M. A., P. G. Duynkerke, and H. J. J. Jonker, 2003: Size distributions and dynamical properties of shallow cumulus clouds from aircraft observations and satellite data. J. Atmos. Sci., 60 , 1895–1912.

    • Search Google Scholar
    • Export Citation

  • Sánchez, A., T. F. Smith, and W. F. Krajewski, 1994: A three-dimensional atmospheric radiative transfer model based on the discrete-ordinates method. Atmos. Res., 33 , 283–308.

    • Search Google Scholar
    • Export Citation

  • Schertzer, D., and S. Lovejoy, 1987: Physical modeling and analysis of rain and clouds by anisotropic scaling multiplicative processes. J. Geophys. Res., 92 , 9693–9714.

    • Search Google Scholar
    • Export Citation

  • Schmidt, K. S., V. Venema, F. D. Giuseppe, R. Scheirer, M. Wendisch, and P. Pilewski, 2007: Reproducing cloud microphysics and irradiance measurements using three 3D cloud generators. Quart. J. Roy. Meteor. Soc., 133 , 765–780.

    • Search Google Scholar
    • Export Citation

  • Siebesma, A. P., and Coauthors, 2003: A large-eddy simulation intercomparison study of shallow cumulus convection. J. Atmos. Sci., 60 , 1201–1219.

    • 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.

  • Su, B. J., and G. C. Pomraning, 1994: A stochastic description of a broken cloud field. J. Atmos. Sci., 51 , 1969–1977.

  • Venema, V., S. Bachner, H. W. Rust, and C. Simmer, 2006: Statistical characteristics of surrogate data based on geophysical measurements. Nonlinear Processes Geophys., 13 , 449–466.

    • Search Google Scholar
    • Export Citation

  • Wielicki, B. A., and R. M. Welch, 1986: Cumulus cloud properties derived using Landsat satellite data. J. Climate Appl. Meteor., 25 , 261–276.

    • Search Google Scholar
    • Export Citation

  • Zhao, G., and L. Di Girolamo, 2007: Statistics on the macrophysical properties of trade wind cumuli over the tropical western Atlantic. J. Geophys. Res., 112 , D10204. doi:10.1029/2006JD007371.

    • Search Google Scholar
    • Export Citation

  • Zuev, V. E., and G. A. Titov, 1995: Radiative transfer in cloud fields with random geometry. J. Atmos. Sci., 52 , 176–190.

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