Cellular statistical models of broken cloud fields. Part I: Theory

Journal of the Atmospheric Sciences

Volumn 67, Issue 7, 2010, Pages 2125-2151

  Alexandrov, Mikhail D ^a,b   Marshak, Alexander ^c   Ackerman, Andrew S ^b  

^a Columbia University ^*  (United States)

^b NASA GODDARD INSTITUTE FOR SPACE STUDIES   (United States)

^c NASA GODDARD SPACE FLIGHT CENTER   (United States)

Author keywords

Cloud parameterization; Cloud resolving models; Clouds; Numerical analysis modeling; Statistical techniques

Indexed keywords

CELL SIZE; CLOUD FIELDS; CLOUD FRACTION; CLOUD RESOLVING MODEL; CLOUD RESOLVING MODELS; CONVECTIVE CELL; DISCRETE MODELS; FINITE SAMPLES; GAP SIZE; GRID OF CELLS; INTEGER NUMBERS; STATISTICAL MODELS; STATISTICAL TECHNIQUES; TWO PARAMETER;

ATMOSPHERIC STRUCTURE; CLOUDS; PROBABILITY DENSITY FUNCTION; SAMPLING;

PROBABILITY DISTRIBUTIONS;

ATMOSPHERIC CONVECTION; CLOUD; MATHEMATICAL ANALYSIS; NUMERICAL MODEL; PARAMETERIZATION; STATISTICAL ANALYSIS;

EID: 77955586989     PISSN: 00224928     EISSN: None     Source Type: Journal    
DOI: 10.1175/2010JAS3364.1     Document Type: Article

References (55)

1. Aida, M., 1977: Scatter of solar radiation as a function of cloud dimensions and orientations. J. Quant. Spectrosc. Radiat. Transfer, 17, 303-310.
2. Alexandrov, M. D., A. Marshak, B. Cairns, A. A. Lacis, and B. E. Carlson, 2004: Automated cloud screening algorithm for MFRSR data. Geophys. Res. Lett., 31, L04118, doi:10.1029/2003GL019105.
3. Alexandrov, M. D, A. S. Ackerman, and A. Marshak, 2010: Cellular statistical models of broken cloud fields. Part II: Comparison with a dynamical model and statistics of diverse ensembles. J. Atmos. Sci., 67, 2152-2170.
4. Astin, I., and B. G. Latter, 1998: A case for exponential cloud fields? J. Appl. Meteor., 37, 1375-1382.
5. 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.
6. Astin, I., and L. Di Girolamo, and H. M. van de Poll, 2001: Bayesian confidence intervals for true fractional coverage from finite transect measurements: Implications for cloud studies from space. J. Geophys. Res., 106, 17 303-17 310.
7. Baxter, R. J., 1982: Exactly Solved Models in Statistical Mechanics. Academic Press, 498 pp.
8. Berg, L. K., and E. I. Kassianov, 2008: Temporal variability of fairweather cumulus statistics at the ACRF SGP site. J. Climate, 21, 3344-3358.
9. Breon, F.-M., 1992: Reflectance of broken cloud fields: Simulation and parameterization. J. Atmos. Sci., 49, 1221-1232.
10. 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.
11. Cahalan, R. F., 1994: Bounded cascade clouds: Albedo and effective thickness. Nonlinear Processes Geophys., 1, 156-167.
12. Cahalan, R. F., and J. H. Joseph, 1989: Fractal statistics of cloud fields. Mon. Wea. Rev., 117, 261-272.
13. Conolly, B. W., 1971: On randomized random walks. SIAM Rev., 13, 81-99.
14. Ellingson, R. G., 1982: On the effects of cumulus dimensions on longwave irradiance and heating rate calculations. J. Atmos. Sci., 39, 886-896.
15. Evans, K. F., and W. J. Wiscombe, 2004: An algorithm for generating stochastic cloud fields from radar profile statistics. Atmos. Res., 72, 263-289.
16. Gradshteyn, I. S., and I. M. Ryzhik, 1965: Table of Integrals, Series, and Products. Academic Press, 1130 pp.
17. Harrison, L., J. Michalsky, and J. Berndt, 1994: Automated multifilter rotating shadow-band radiometer: An instrument for optical depth and radiation measurements. Appl. Opt., 33, 5118-5125.
18. 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.
19. Holben, B. N., and Coauthors, 1998: Aeronet-A federated instrument network and data archive for aerosol characterization. Remote Sens. Environ., 66, 1-16.
20. Isichenko, M. B., 1992: Percolation, statistical topography, and transport in random media. Rev. Mod. Phys., 64, 961-1043.
21. Joseph, J. H., and R. F. Cahalan, 1990: Nearest neighbor spacing of fair weather cumulus clouds. J. Appl.Meteor., 29, 793-805.
22. Kassianov, E., 2003: Stochastic radiative transfer in multilayer broken clouds. Part I: Markovian approach. J. Quant. Spectrosc. Radiat. Transfer, 77, 373-394.
23. Kite, A., 1987: The albedo of broken cloud fields. Quart. J. Roy. Meteor. Soc., 113, 517-531.
24. 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.
25. 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.
26. Lane-Veron, D. E., and R. C. J. Somerville, 2004: Stochastic theory of radiative transfer through generalized cloud field. J. Geophys. Res., 109, D18113, doi:10.1029/2004JD004524.
27. Malvagi, F., R. N. Byrne, G. Pomraning, and R. C. J. Somerville, 1993: Stochastic radiative transfer in a partially cloudy atmosphere. J. Atmos. Sci., 50, 2146-2158.
28. Marshak, A., A. Davis, R. F. Cahalan, and W. J. Wiscombe, 1994: Bounded cascade models as nonstationary multifractals. Phys. Rev. E, 49, 55-69.
29. Metropolis, N., A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, 1953: Equation of state calculations by fast computing machines. J. Chem. Phys., 21, 1087-1092.
30. Nagel, K., and E. Raschke, 1992: Self-organizing criticality in cloud formation? Physica A, 182, 519-531.
31. Nicholls, S., 1989: The structure of radiatively driven convection in stratocumulus. Quart. J. Roy. Meteor. Soc., 115, 487-511.
32. Plank, V. G., 1969: The size distribution of cumulus clouds in representative Florida populations. J. Appl. Meteor., 8, 46-67.
33. 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.
34. Prigarin, S. M., T. B. Zhuravleva, and P. B. Volikova, 2002: Poisson model of broken multilayer cloudiness. Atmos. Ocean. Opt., 15, 947- 954.
35. Prudnikov, A. P., Y. A. Brychkov, and O. I. Marichev, 1986: Elementary Functions. Vol. 1, Integrals and Series, Gordon and Breach, 806 pp.
36. Prudnikov, A. P., Y. A. Brychkov, and O. I. Marichev, 2002: Special Functions. Vol. 2, Integrals and Series, Taylor and Francis, 758 pp.
37. Ramirez, J. A., and R. L. Bras, 1990: Clustered or regular cumulus cloud fields: The statistical character of observed and simulated cloud fields. J. Geophys. Res., 95, 2035-2045.
38. Randall, D. A., and G. J. Huffman, 1980: A stochastic model of cumulus clumping. J. Atmos. Sci., 37, 2068-2078.
39. 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.
40. Sanchez, A., T. F. Smith, and W. F. Krajewski, 1994: A threedimensional atmospheric radiative transfer model based on the discrete-ordinates method. Atmos. Res., 33, 283-308.
41. Sauvageot, H., F. Mesnard, and R. S. Tenorio, 1999: The relation between the area-average rain rate and the rain cell size distribution parameters. J. Atmos. Sci., 56, 57-70.
42. 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.
43. Schmidt, K. S., V. Venema, F. D. Giuseppe, R. Scheirer, M. Wendisch, and P. Pilewskie, 2007: Reproducing cloud microphysics and irradiance measurements using three 3D cloud generators. Quart. J. Roy. Meteor. Soc., 133, 765-780.
44. Settle, J. J., and H. M. van de Poll, 2007: On the Bayesian estimation of cloud fraction from lidar transects. J. Geophys. Res., 112, D09211, doi:10.1029/2006JD007251.
45. Smirnov, A., B. N. Holben, T. F. Eck, O. Dubovik, and I. Slutsker, 2000: Cloud screening and quality control algorithms for the AERONET database. Remote Sens. Environ., 73, 337-349.
46. Su, B. J., and G. C. Pomraning, 1994: A stochastic description of a broken cloud field. J. Atmos. Sci., 51, 1969-1977.
47. Swendsen, R. H., and J.-S. Wang, 1987: Nonuniversal critical dynamics in Monte Carlo simulations. Phys. Rev. Lett., 58, 86-88.
48. Takacs, L., 1957: On certain sojourn time problems in the theory of stochastic processes. Acta Math. Acad. Sci. Hung., 8, 169-191.
49. Titov, G. A., 1990: Statistical description of radiation transfer in clouds. J. Atmos. Sci., 47, 24-38.
50. Van de Poll, H. M., H. Grubb, and I. Astin, 2006: Uncertainty properties of cloud fraction estimates from random transect observations. J. Geophys. Res., 111, D22218, doi:10.1029/2006JD007189.
51. 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.
52. Wielicki, B. A., and R. M. Welch, 1986: Cumulus cloud properties derived using Landsat satellite data. J. Climate Appl. Meteor., 25, 261-276.
53. Wolff, U., 1989: Collective Monte Carlo updating for spin systems. Phys. Rev. Lett., 62, 361-364.
54. Yau, M. K., and R. R. Rogers, 1984: An inversion problem on inferring the size distribution of precipitation areas from raingage measurements. J. Atmos. Sci., 41, 439-447.
55. Zuev, V. E., and G. A. Titov, 1995: Radiative transfer in cloud fields with random geometry. J. Atmos. Sci., 52, 176-190.