Construction and application of covariance functions with variable length-fields

Quarterly Journal of the Royal Meteorological Society

Volumn 132, Issue 619, 2006, Pages 1815-1838

  Gaspari, Gregory ^a,b,c   Cohn, Stephen E ^b   Guo, Jing ^a,b   Pawson, Steven ^b  

^a SAIC FREDERICK INC   (United States)

^b NASA GODDARD SPACE FLIGHT CENTER   (United States)

^c SCIENCE APPLICATIONS INTERNATIONAL CORPORATION   (United States)

Author keywords

Correlation functions; Correlation length scale; Data assimilation; Non separable; Quasi Biennial Oscillation

Indexed keywords

ATMOSPHERIC TURBULENCE; DATA PROCESSING; RADIOSONDES; STATISTICAL METHODS; UPPER ATMOSPHERE;

MULTI-LEVEL COVARIANCE FUNCTIONS; QUASI-BIENNIAL OSCILLATION (QBO); VERTICAL WIND SHEAR;

CLIMATOLOGY;

COVARIANCE ANALYSIS; DATA ASSIMILATION; EOS; QUASI-BIENNIAL OSCILLATION;

EID: 33750120394     PISSN: 00359009     EISSN: None     Source Type: Journal    
DOI: 10.1256/qj.05.08     Document Type: Article

References (29)

1. Andersson, E., Haseler, J., Undén, P., Courtier, P., Kelly, G., Vasiljević, D., Branković, C., Cardinali, C., Gaffard, C., Hollingsworth, A., Jakob, C., Janssen, P., Klinker, E., Laanzinger, A., P., Miller, M., Rabier, F., Simmons, A., Strauss, B., Thépaut, J.-N. and Viterbo, P. 1998 The ECMWF implementation of three dimensional variational assimilation (3D-Var). Part III: Experimental results. Q.J.R. Meteorol. Soc., 124, 1831-1860
2. Baldwin, M. P., Gray, L. J., Dunkerton, T. J., Hamilton, K., Haynes, P. H., Randel, W. J., Holton, J. R., Alexander, M. J., Hirota, I., Horinouchi, T., Jones, D. B. A., Kinnersley, J. S., Marquardt, C., Sato, K. and Takahashi, M. 2001 The Quasi-Biennial Oscillation. Rev. Geophys., 39(2), 179-229
3. Bartello, P. and Mitchell, H. L. 1992 A continuous three-dimensional model of short-range forecast error covariances. Tellus, 44A, 217-235
4. Belmont, A. D. and Dartt, D. G. 1968 Variation with longitude of the quasi-biennial oscillation. Mon. Weather Rev., 96, 767-777
5. Bloom, S., da Silva, A., Dee, D., Bosilovich, M., Chem, J.-D., Pawson, S., Schubert, S., Sicnkiewicz, M., Štajner, I., Tan, W.-W. and Wu, M.-L. 2005 Documentation and validation of the Goddard Earth Observing System (GEOS) Data Assimilation System-Version 4. NASA Technical Memo. No. 2005-104606, 26, http://gmao.gsfc.nasa.gov/pubs/tm/
6. Churchill, R. V. and Brown, J. W. 1984 Complex variables and applications, 4th edition. McGraw-Hill, New York
7. Cohn, S. E., da Silva, A., Guo, J., Sienkiewicz, M. and Lamich, D. 1998 Assessing the effects of data selection with the DAO Physicalspace Statistical Analysis System. Mon. Weather Rev., 126, 2913-2926
8. Courtier, R, Andersson, E., Heckley, W., Pailleux, J., Vasiljević, D., Hamrud, M., Hollingsworth, A., Rabier, F. and Fisher, M. 1998 The ECMWF implementation of three-dimensional variational assimilation (3D-Var). Part I: Formulation. Q.J.R. Meteorol. Soc., 124, 1783-1808
9. Crameŕ, H. 1940 On the theory of stationary random processes. Ann. Math., 41, 215-230
10. Daley, R. 1991 Atmospheric data analysis. Cambridge University Press, New York
11. Daley, R. and Barker, E. 2001 NAVDAS: Formulation and diagnostics. Mon. Weather Rev., 129, 869-883
12. Folland, G. B. 1992 Fourier analysis and its applications. Wadsworth & Brooks, Pacific-Grove, CA
13. Gaspari, G. and Cohn, S. E. 1999 Construction of correlation functions in two and three dimensions. Q.J.R. Meteorol. Soc., 125, 723-757
14. Hamilton, K., Hertzog, A., Vial, F. and Stenchikov, G. 2004 Longitudinal variation of the stratospheric quasi-biennial oscillation. J. Atmos. Sci., 61, 383-402
15. Hannan, E. J. 1970 Multiple time series. Wiley, New York
16. Hollingsworth, A. and Lönnberg, P. 1986 The statistical structure of short-range forecast errors as determined from radiosonde data. Part I: The wind field. Tellus, 38A, 111-136
17. Holton, J. R. 1992 An introduction to dynamic meteorology. Academic Press, New York
18. Loève, M. 1963 Probability theory, 3rd edition. Van Nostrand, Princeton, USA
19. Lönnberg, P. and Hollingsworth, A. 1986 The statistical structure of short-range forecast errors as determined from radiosonde data, Part II: The covariance of height and wind errors. Tellus, 38A, 137-161
20. Ménard, R., Cohn, S. E., Chang, L.-P. and Lyster, P. M. 2000 Assimilation of stratospheric chemical tracer observations using a Kalman filter. Part I: Formulation. Mon. Weather Rev., 128, 2654-2671
21. Parrish, D. F. and Derber, J. C. 1992 The National Meteorological Center's spectral statistical interpolation analysis system. Mon. Weather Rev., 120, 1747-1763
22. Pawson, S. and Fiorino, M. 1998 A comparison of reanalyses in the tropical stratosphere. Part 2: The quasi-biennial oscillation. Clim. Dyn., 14, 645-658
23. Phillips, N. A. 1986 The spatial statistics of random geostrophic modes and first-guess errors. Tellus, 38A, 314-332
24. Rabier, F., McNally, A., Andersson, E., Courtier, P., Undén, P., Eyre, J., Hollingsworth, A. and Bouttier, F. 1998 The ECMWF implementation of three-dimensional variational assimilation (3D-Var). Part II: Structure functions. Q. J. R. Meteorol. Soc., 124, 1809-1830
25. Randel, W., Udelhofen, P., Fleming, E., Geller, M., Gelman, M., Hamliton, K., Karoly, D., Ortland, D., Pawson, S., Swinbank, R., Wu, F., Baldwin, M., Chanin, M.-L., Keckhut, P., Labitzke, K., Remsberg, E., Simmons, A. and Wu, D. 2004 The SPARC intercomparison of middle-atmosphere climatologies. J. Climate, 17, 986-1003
26. Segers, A. J., Eskes, H. J., Van Der, A. R. J., Van Oss, R. F. and Van Velthoven, P. F. J. 2005 Assimilation of GOME ozone profiles and a global chemistry-transport model using a Kalman filter with anisotropic covariance. Q. J. R. Meteorol. Soc., 131, 477-502
27. Štajner, I., Riishøjgaard, L. P. and Rood, R. B. 2001 The GEOS ozone data assimilation system: Specification of error statistics. Q. J. R. Meteorol. Soc., 127, 1069-1094
28. Yaglom, A. M. 1987 Correlation theory of stationary and related random functions, Vol. I: Basic Results. Springer-Verlag, New York
29. Žagar, N., Andersson, E. and Fisher, M. 2005 Balanced tropical data assimilation based on a study of equatorial waves in ECMWF short-range forecast errors. Q. J. R. Meteorol. Soc., 131, 987-1011