Representation of 3D heterogeneous cloud fields using copulas: Theory for water clouds

Quarterly Journal of the Royal Meteorological Society

Volumn 134, Issue 636, 2008, Pages 1843-1864

  Norris, Peter M ^a,b   Oreopoulos, Lazaros ^a,b   Hou, Arthur Y ^b   Tao, Wei Kuo ^b   Zeng, Xiping ^a,b  

^a UNIVERSITY OF MARYLAND BALTIMORE COUNTY   (United States)

^b NASA GODDARD SPACE FLIGHT CENTER   (United States)

Author keywords

Cloud heterogeneity; Cloud overlap; Radiative transfer; Rank statistics; Statistical cloud parametrizations

Indexed keywords

ASTROPHYSICS; CLOUDS; MOISTURE; PROBABILITY DISTRIBUTIONS; REGRESSION ANALYSIS; SPEECH RECOGNITION; STATISTICS; THREE DIMENSIONAL; TRELLIS CODES; WIRELESS TELECOMMUNICATION SYSTEMS;

ATMOSPHERIC COLUMNS; CLOUD FIELDS; CLOUD FRACTIONS; CLOUD HETEROGENEITY; CLOUD OVERLAP; CLOUD OVERLAPS; CONDENSED WATERS; CONVECTIVE CLOUDS; COPULA APPROACHES; DEPENDENCE STRUCTURES; GAUSSIAN COPULA MODELS; GAUSSIAN COPULAS; GENERAL SPECIFICATIONS; GLOBAL ANALYSES; HIGH RESOLUTIONS; MODEL SIMULATIONS; MULTIVARIATE SYSTEMS; PARAMETRIZATION; PARAMETRIZATIONS; PRELIMINARY TESTS; PROBABILITY DENSITIES; RANK STATISTICS; SATELLITE OBSERVATIONS; STATISTICAL CLOUD PARAMETRIZATIONS; STATISTICAL FRAMEWORKS; STATISTICAL FUNCTIONS; STATISTICAL INFORMATIONS; SUB GRIDS; WATER CLOUDS;

PROBABILITY DENSITY FUNCTION;

CLOUD MICROPHYSICS; CLOUD RADIATIVE FORCING; CLOUD WATER; CONVECTIVE CLOUD; CORRELATION; ENCAPSULATION; GAUSSIAN METHOD; GENERAL CIRCULATION MODEL; MULTIVARIATE ANALYSIS; PARAMETERIZATION; PROBABILITY DENSITY FUNCTION; RADIATIVE TRANSFER; THREE-DIMENSIONAL MODELING;

EID: 57349120785     PISSN: 00359009     EISSN: None     Source Type: Journal    
DOI: 10.1002/qj.321     Document Type: Article

References (40)

1. Chakak A, Koehler KJ. 1995. A strategy for constructing multivariate distributions. Commun. Stat. Simulat. 24: 537-550.
2. Cherubini U, Luciano E, Vecchiato W. 2004. Copula methods in finance. John Wiley & Sons, Ltd.
3. Chou M-D, Suarez MJ. 1999. 'A shortwave radiation parameterization for atmospheric studies'. NASA Tech Memo 15-104 606. NASA/Goddard: Greenbelt, Maryland, USA.
4. Chou M-D, Suarez MJ, Ho C-H, Yan MM-H, Lee K-T. 1998. Parameterizations for cloud overlapping and shortwave single-scattering properties for use in general circulation and cloud ensemble models. J. Climate 11: 202-214.
5. Chou M-D, Suarez MJ, Liang X-Z, Yan MM-H. 2001. 'A thermal infrared radiation parameterization for atmospheric studies'. NASA Tech Memo 19-104 606. NASA/Goddard: Greenbelt, Maryland, USA.
6. Dee DP, da Silva AM. 1999. Maximum-likelihood estimation of forecast and observation error covariance parameters. Part I: Methodology. Mon. Weather Rev. 127: 1822-1834.
7. Dee DP, Gaspari G, Redder C, Rukhovets L, da Silva AM. 1999. Maximum-likelihood estimation of forecast and observation error covariance parameters. Part II: Applications. Mon. Weather Rev. 127: 1835-1849.
8. Demarta S, McNeil AJ. 2005. The t copula and related copulas. Internat. Statist. Rev. 73: 111-129.
9. Drezner Z. 1994. Computation of the trivariate normal integral. Math. Comput. 63: 289-294.
10. Drezner Z, Wesolowsky GO. 1989. On the computation of the bivariate normal integral. J. Statist. Comput. Simulat. 35: 101-107.
11. Dupuis DJ. 2007. Using copulas in hydrology: Benefits, cautions, and issues. J. Hydrol. Eng. 12: 381-393.
12. Gaspari G, Cohn SE. 1999. Construction of correlation functions in two and three dimensions. Q. J. R. Meteorol. Soc. 125: 723-757.
13. Gaspari G, Cohn SE, Guo J, Pawson S. 2006. Construction and application of covariance functions with variable length-fields. Q. J. R. Meteorol. Soc. 132: 1815-1838.
14. Geleyn J-F, Hollingsworth A. 1979. An economical analytic method for the computation of the interaction between scattering and line absorption of radiation. Beitr. Phys. Atmos. 52: 1-16.
15. Genest C, Favre A-C. 2007. Everything you always wanted to know about copula modeling but were afraid to ask. J. Hydrol. Eng. 12: 347-368.
16. Genz A. 2004. Numerical computation of rectangular bivariate and trivariate normal and t probabilities. Statist. Comput. 14: 251-260.
17. Genz A, Bretz F. 1999. Numerical computation of multivariate t probabilities with application to power calculation of multiple contrasts. J. Statist. Comput. Simulat. 63: 361-378.
18. Genz A, Bretz F. 2002. Comparison of methods for the computation of multivariate t probabilities. J. Comput. Graph. Statist. 11: 950-971.
19. Golaz J-C, Larson VE, Cotton WR. 2002. A PDF-based model of boundary layer clouds. Part I: Method and model description. J. Atmos. Sci. 59: 3540-3551.
20. Hogan RJ, Illingworth AJ. 2000. Deriving cloud overlap statistics from radar. Q. J. R. Meteorol. Soc. 126: 2903-2909.
21. Jakob C, Klein SA. 1999. The role of vertically varying cloud fraction in the parametrization of microphysical processes in the ECMWF model. Q. J. R. Meteorol. Soc. 125: 941-965.
22. Larson VE. 2007. From cloud overlap to PDF overlap. Q. J. R. Meteorol. Soc. 133: 1877-1891.
23. Larson VE, Wood R, Field PR, Golaz J-C, Vonder Haar TH, Cotton WR. 2001. Small-scale and mesoscale variability of scalars in cloudy boundary layers: One-dimensional probability density functions. J. Atmos. Sci. 58: 1978-1994.
24. Mace GG, Benson-Troth S. 2002. Cloud-layer overlap characteristics derived from long-term cloud radar. J. Climate 15: 2505-2515.
25. Monaghan JJ, Lattanzio JC. 1985. A refined particle method for astrophysical problems. Astron. Astrophys. 149: 135-143.
26. Nelsen RB. 2006. An Introduction to Copulas. 2nd ed. Springer Science + Business Media, LLC: New York.
27. Norris PM, da Silva AM. 2007. Assimilation of satellite cloud data into the GMAO Finite Volume Data Assimilation System using a parameter estimation method. J. Atmos. Sci. 64: 3880-3895.
28. Oreopoulos L, Khairoutdinov M. 2003. Overlap properties of clouds generated by a cloud-resolving model. J. Geophys. Res. 108: 4479, DOI: 10.1029/2002JD003329.
29. Pincus R, Hannay C, Klein SA, Xu K-M, Hemler R. 2005. Overlap assumptions for assumed-PDF cloud schemes in large-scale models. J. Geophys. Res. 110: D15S09.
30. Räisänen P, Barker HW. 2004. Evaluation and optimization of sampling errors for the Monte Carlo Independent Column Approximation. Q. J. R. Meteorol. Soc. 130: 2069-2085.
31. Räisänen P, Barker HW, Cole JNS. 2005. The Monte Carlo Independent Column Approximation's conditional random noise: Impact on simulated climate. J. Climate 18: 4715-4730.
32. Räisänen P, Barker HW, Khairoutdinov MF, Li J, Randall DA. 2004. Stochastic generation of subgrid-scale cloudy columns for large-scale models. Q. J. R. Meteorol. Soc. 130: 2047-2068.
33. Rienecker MM, Suarez MJ, Todling R, Bacmeister J, Takacs L, Liu HC, Gu W, Sienkiewicz M, Koster RD, Gelaro R, Stajner I, Nielsen E. 2007. 'The GEOS-5 Data Assimilation System - Documentation of versions 5.0.1, 5.1.0, and 5.2.0'. Technical Report Series on Global Modeling and Data Assimilation NASA/TM-2007-104 606, 27: Suarez MJ (ed.) National Aeronautics and Space Administration: Available at http://gmao.gsfc.nasa.gov/pubs/docs/GEOS-5.0.1_-Documentation_r3.pdf.
34. Salvadori G, De Michele C. 2007. On the use of copulas in hydrology: Theory and practice. J. Hydrol. Eng. 12: 369-380.
35. Smith RNB. 1990. A scheme for predicting layer clouds and their water content in a general circulation model. Q. J. R. Meteorol. Soc. 116: 435-460.
36. Snedecor GW, Cochran WG. 1980. Statistical Methods, 7th ed. Iowa State Univ. Press: Ames, Iowa, USA.
37. Tian L, Curry JA. 1989. Cloud overlap statistics. J. Geophys. Res. 94: 9925-9935.
38. Tompkins AM. 2002. A prognostic parameterization for the subgrid-scale variability of water vapor and clouds in large-scale models and its use to diagnose cloud cover. J. Atmos. Sci. 59: 1917-1942.
39. Xu K-M, Randall DA. 1996. Evaluation of statistically based cloudiness parameterizations used in climate models. J. Atmos. Sci. 53: 3103-3119.
40. Zeng X, Tao W-K, Zhang M-H, Peters-Lidard C, Lang S, Simpson J, Kumar S, Xie S-C, Eastman JL, Shie C-L, Geiger JV. 2007. Evaluating clouds in long-term cloud-resolving model simulations with observations. J. Atmos. Sci. 64: 4153-4177.