Diagnosis and impacts of non-Gaussianity of innovations in data assimilation

Physica D: Nonlinear Phenomena

Volumn 239, Issue 17, 2010, Pages 1701-1717

  Pires, Carlos A ^a   Talagrand, Olivier ^b   Bocquet, Marc ^c,d  

^a UNIVERSITY OF LISBON   (Portugal)

^b ECOLE NORMALE SUPÉRIEURE   (France)

^c UNIVERSITÉ CATHOLIQUE DE L'OUEST   (France)

^d INRIA   (France)

Author keywords

Data assimilation; Innovation statistics; Maximum entropy method; Non Gaussianity

Indexed keywords

ERROR STATISTICS; GAUSSIAN NOISE (ELECTRONIC); HIGHER ORDER STATISTICS; MAXIMUM ENTROPY METHODS; PROBABILITY DENSITY FUNCTION; STATISTICS;

BAYESIAN DATA ASSIMILATIONS; BEST LINEAR UNBIASED ESTIMATOR; DATA ASSIMILATION; HIGH-RESOLUTION INFRARED SOUNDERS; MINIMUM VARIANCE UNBIASED ESTIMATOR; NONGAUSSIANITY; PROBABILITY DENSITY FUNCTIONS (PDFS); SPATIOTEMPORAL VARIABILITY;

ERRORS;

EID: 77955419239     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2010.05.006     Document Type: Article

References (38)

1. O. Talagrand Bayesian estimation. Optimal interpolation. Statistical linear estimation R. Swinbank, V. Shutyaev, W. Lahoz, Data Assimilation for the Earth System 2002 Kluwer Academic Publishers 21 35
2. Q. Errera, and D. Fonteyn Four-dimensional variational chemical assimilation of crista stratospheric measurements J. Geophys. Res. 106 2001 12253
3. H. Elbern, and H. Schmidt Ozone episode analysis by four-dimensional variational chemistry data assimilation J. Geophys. Res. 106 2001 3569
4. N.B. Ingleby, and A.C. Lorenc Bayesian quality control using multivariate normal distributions Q. J. R. Meteorol. Soc. 119 1993 1195
5. M. Bocquet, C.A. Pires, L. Wu, Beyond Gaussian statistical modeling in geophysical data assimilation, Mon. Weather Rev. (2010), in press (doi:10.1175/2010MWR3164.1 ).
6. S.J. Fletcher, and M. Zupanski A hybrid normal and lognormal distribution for data assimilation Atmos. Sci. Lett. 7 2006 43
7. S.J. Fletcher, and M. Zupanski A data assimilation method for log-normally distributed observational errors Q. J. R. Meteorol. Soc. 132 2006 2505
8. M. Bocquet High resolution reconstruction of a tracer dispersion event Q. J. R. Meteorol. Soc. 133 2007 1013
9. S. Fletcher Mixed Gaussian-lognormal four-dimensional data assimilation Tellus 62 3 2010 266
10. D.P. Dee Bias and data assimilation Q. J. R. Meteorol. Soc. 131 2005 3323
11. E. Holm, Revision of the ECMWF humidity analysis: construction of a Gaussian control variable, in: Proceedings of the ECMWF/GEWEX Workshop on Humidity Analysis, 2002, pp. 16.
12. E.T. Jaynes Information statistics and statistical mechanics I Phys. Rev. 106 1957 620
13. E.T. Jaynes Information statistics and statistical mechanics II Phys. Rev. 108 1957 171
14. Thomas M. Cover, and A. Thomas Elements of Information Theory Wiley Series on Communications 1991
15. J. Derber, and F. Bouttier A reformulation of the background error covariance in the ECMWF global data assimilation system Tellus 51 1999 195
16. E. Anderson, M. Fisher, R. Munro, A. McNally, Diagnosis of background errors for radiances and other observable quantities in the variational data assimilation scheme and the explanation of a case of poor convergence, ECMWF Technical Memorandum, 1999, p. 296.
17. X. Wu Calculation of maximum entropy densities with application to income distribution J. Econometrics 115 2003 347
18. P. Comon Independent component analysis, a new concept? Signal Process. 36 1994 287
19. J.F. Kenney, and E.S. Keeping Cumulants and the cumulant-generating function, additive property of cumulants, and Sheppard's correction Mathematics of Statistics 1951 Van Nostrand 77 82
20. G. Maurice, A. Stuart, J.K. Ord, and A. O'Hagan Kendall's Advanced Theory of Statistics 6th ed. 1999 Edward Arnold
21. G. Desroziers, and S. Ivanov Diagnosis and adaptative tuning of information error parameters in variational assimilation Q. J. R. Meteorol. Soc. 127 2001 1433
22. B. Chapnik, G. Desroziers, F. Rabier, and O. Talagrand Properties and first application of an error-statistics tuning method in variational assimilation Q. J. R. Meteorol. Soc. 130 2004 2253
23. V. Rudin Real and Complex Analysis 1987 McGraw-Hill
24. G.M. Clarke, and D. Cooke A Basic Course in Statistics 1991 Oxford University Press New York, USA
25. C.E. Shannon The mathematical theory of communication Bell Syst. Tech. J. 27 1948 379
26. B. Urban Humidity profile retrieval using a maximum entropy principle Mon. Weather Rev. 123 1995 1185
27. M. Bocquet Reconstruction of an atmospheric tracer source using the principle of maximum entropy I Q. J. R. Meteorol. Soc. 131 2005 2191
28. M. Bocquet Reconstruction of an atmospheric tracer source using the principle of maximum entropy II Q. J. R. Meteorol. Soc. 131 2005 2209
29. M. Bocquet Inverse modelling of atmospheric tracers: non-Gaussian methods and second-order sensitivity analysis Nonlinear Process. Geophys. 15 2005 127
30. O. Barndorff-Nielsen Information and Exponential Families in Statistical Theory Wiley Series in Probability and Mathematical Statistics 1978 John Wiley and Sons Ltd.
31. M. Rockinger, and E. Jondeau Entropy densities with an application to autoregressive conditional skewness and kurtosis J. Econometrics 106 2002 119
32. C. Pires, and R. Perdigo Non-gaussianity and asymmetry of the winter monthly precipitation estimation from NAO Mon. Weather Rev. 135 2007 430 10.1175/MWR3407.1
33. o Simpsio de Meteorologia e Geofsica da APMG, Associao Portuguesa de Meteorologia e Geofsica, 2003, p. 220.
34. A. Gelb Applied Optimal Estimation. The Analytical Sciences Corporation 1974 MIT Press
35. M. Dqu Continuous variables I. Jollife, D. Stephenson, A Practitioner's Guide in Atmospheric Science 2003 John Wiley and Sons England 97 119
36. J.C. Gilbert, and C. Le Marchal Some numerical experiments with variable storage quasi-Newton algorithms Math. Program. 45 1989 407
37. I. Takafumi On a measure of multivariate skewness and a test for multivariate normality Ann. Inst. Statist. Math. 34 1982 531
38. D. Ormoneit, and H. White An efficient algorithm to compute maximum entropy densities Econometric Rev. 18 1999 127