Iterative algorithm for maximum-likelihood estimation of the observation-error covariance matrix for ensemble-based filters

Quarterly Journal of the Royal Meteorological Society

Volumn 140, Issue 678, 2014, Pages 295-315

  Ueno, Genta ^a,b   Nakamura, Nagatomo ^c  

^a INSTITUTE OF STATISTICAL MATHEMATICS   (Japan)

^b JAPAN SCIENCE AND TECHNOLOGY AGENCY   (Japan)

^c SAPPORO GAKUIN UNIVERSITY   (Japan)

Author keywords

Coupled atmosphere ocean model; Data assimilation; El ni no; Ensemble kalman filter; Observation error

Indexed keywords

ATMOSPHERIC THERMODYNAMICS; COVARIANCE MATRIX; ITERATIVE METHODS; MATRIX ALGEBRA; MAXIMUM LIKELIHOOD; MAXIMUM LIKELIHOOD ESTIMATION; MAXIMUM PRINCIPLE;

ATMOSPHERE-OCEAN MODELING; DATA ASSIMILATION; ENSEMBLE BASED DATA ASSIMILATION; ENSEMBLE KALMAN FILTER; EXPECTATION-MAXIMIZATION ALGORITHMS; ITERATIVE ALGORITHM; OBSERVATION ERRORS; OPTIMALITY CONDITIONS;

ALGORITHMS;

EID: 84927574339     PISSN: 00359009     EISSN: 1477870X     Source Type: Journal    
DOI: 10.1002/qj.2134     Document Type: Article

References (23)

1. Cohn SE. 1997 An introduction to estimation theory. J. Meteorol. Soc. Jpn 75 257-288.
2. Desroziers G, Berre L, Chapnik B, Poli P. 2005 Diagnosis of observation, background and analysis-error statistics in observation space. Q. J. R. Meteorol. Soc. 131 3385-3396. 10.1256/qj.05.108.
3. Evensen G. 2003 The ensemble Kalman filter: theoretical formulation and practical implementation. Ocean Dyn. 53 343-367.
4. Evensen G. 2009 The ensemble Kalman filter for combined state and parameter estimation. IEEE Control Systems Magazine 29 83-104.
5. Fu LL, Fukumori I, Miller RN. 1993 Fitting dynamic models to the Geosat sea level observations in the tropical Pacific Ocean. Part II: A linear, wind-driven model. J. Phys. Oceanogr. 23 2162-2181.
6. Fukumori I. 2001 Data assimilation by models. In Satellite Altimetry and Earth Sciences, Fu LL, Cazenave A (eds). International Geophysics Ser. 69: 237-265. Academic Press: New York, NY.
7. Karspeck AR, Anderson JL. 2007 Experimental implementation of an ensemble adjustment filter for an intermediate ENSO model. J. Climate 20 4638-4658. 10.1175/JCLI4245.1.
8. Kitagawa G, Gersch W. 1996 Smoothness priors analysis of time series, Lecture Notes in Statistics 116. Springer-Verlag: New York, NY.
9. Kondrashov D, Sun C, Ghil M. 2008 Data assimilation for a coupled ocean-atmosphere model. Part II: Parameter estimation. Mon. Weather Rev. 136 5062-5076. 10.1175/2008MWR2544.1.
10. Li H, Kalnay E, Miyoshi T. 2009 Simultaneous estimation of covariance inflation and observation errors within an ensemble Kalman filter. Q. J. R. Meteorol. Soc. 135 523-533.
11. Livings DM, Dance SL, Nichols NK. 2008 Unbiased ensemble square root filters. Phys. D 237 1021-1028.
12. Magnus JR, Neudecker H. 1999 Matrix Differential Calculus with Applications in Statistics and Econometrics, revised edition, Wiley Series in Probability and Statistics. John Wiley & Sons: New York, NY.
13. McLachlan G, Krishnan T. 2007 The EM Algorithm and Extensions, Wiley Series in Probability and Statistics. Wiley-Interscience: New York, NY.
14. McLachlan G, Peel D. 2000 Finite Mixture Models, Wiley Series in Probability and Statistics. Wiley-Interscience: New York, NY.
15. Miyoshi T. 2011 The Gaussian approach to adaptive covariance inflation and its implementation with the local ensemble transform Kalman filter. Mon. Weather Rev. 139 1519-1535.
16. Tippett MK, Anderson JL, Bishop CH, Hamill TM, Whitaker JS. 2003 Ensemble square root filter. Mon. Weather Rev. 131 1485-1490.
17. Ueno G, Tsuchiya T. 2009 Covariance regularization in inverse space. Q. J. R. Meteorol. Soc. 135 1133-1156. 10.1002/qj.445.
18. Ueno G, Higuchi T, Kagimoto T, Hirose N. 2006 'Prediction of ocean state by data assimilation with the ensemble Kalman filter'. In Joint 3rd International Conference on Soft Computing and Intelligent Systems and 7th International Symposium on advanced Intelligent Systems (SCIS & ISIS 2006). SOFT: Tokyo, Japan; pp 1884-1889.
19. Ueno G, Higuchi T, Kagimoto T, Hirose N. 2007 Application of the ensemble Kalman filter and smoother to a coupled atmosphere-ocean model. SOLA 3 5-8.
20. Ueno G, Higuchi T, Kagimoto T, Hirose N. 2010 Maximum likelihood estimation of error covariances in ensemble-based filters and its application to a coupled atmosphere-ocean model. Q. J. R. Meteorol. Soc. 136 1316-1343. 10.1002/qj.654.
21. van Leeuwen PJ. 2009 Particle filtering in geophysical systems. Mon. Weather Rev. 137 4089-4114. DOI:10.1175/2009MWR2835.1.
22. Zebiak SE, Cane MA. 1987 A model El Niño-Southern Oscillation. Mon. Weather Rev. 115 2262-2278.
23. Zheng F, Zhu J, Wang H, Zhang RH. 2009 Ensemble hindcasts of ENSO events over the past 130 years using a large number of ensembles. Adv. Atmos. Sci. 26 C07002. 10.1007/s00376-009-0359-7.