Ensemble Kalman filtering without the intrinsic need for inflation

Nonlinear Processes in Geophysics

Volumn 18, Issue 5, 2011, Pages 735-750

  Bocquet, M ^a,b  

^a UNIVERSITÉ CATHOLIQUE DE L'OUEST   (France)

^b INRIA   (France)

Author keywords

[No Author keywords available]

Indexed keywords

BAYESIAN ANALYSIS; ENSEMBLE FORECASTING; ERROR ANALYSIS; GAUSSIAN METHOD; INFLATION; KALMAN FILTER; PROBABILITY DENSITY FUNCTION;

EID: 80054891746     PISSN: 10235809     EISSN: 16077946     Source Type: Journal    
DOI: 10.5194/npg-18-735-2011     Document Type: Article

References (46)

1. Anderson, J. L.: An ensemble adjustment Kalman filter for data assimilation, Mon. Weather Rev., 129, 2884-2903, 2001. (Pubitemid 34004796)
2. Anderson, J. L.: Exploring the need for localization in ensemble data assimilation using a hierarchical ensemble filter, Physica D, 230, 99-111, 2007a. (Pubitemid 46776901)
3. Anderson, J. L.: An adaptive covariance inflation error correction algorithm for ensemble filters, Tellus A, 59, 210-224, 2007b. (Pubitemid 46671846)
4. Anderson, J. L. and Anderson, S. L.: A Monte Carlo Implementation of the Nonlinear Filtering Problem to Produce Ensemble Assimilations and Forecasts, Mon. Weather Rev., 127, 2741-2758, 1999.
5. Bishop, C. H. and Hodyss, D.: Flow-adaptive moderation of spurious ensemble correlations and its use in ensemble-based data assimilation, Q. J. Roy. Meteor. Soc., 133, 2029-2044, 2007. (Pubitemid 351201443)
6. Bocquet, M., Pires, C. A., and Wu, L.: Beyond Gaussian statistical modeling in geophysical data assimilation, Mon. Weather Rev., 138, 2997-3023, 2010.
7. Brankart, J.-M., Cosme, E., Testut, C.-E., Brasseur, P., and Ver-ron, J.: Efficient adaptive error parameterization for square root or ensemble Kalman filters: application to the control of ocean mesoscale signals, Mon. Weather Rev., 138, 932-950, 2010.
8. Burgers, G., van Leeuwen, P. J., and Evensen, G.: Analysis scheme in the ensemble Kalman filter, Mon. Weather Rev., 126, 1719-1724, 1998. (Pubitemid 128597660)
9. Carrassi, A., Vannitsem, S., Zupanski, D., and Zupanski, M.: The maximum likelihood ensemble filter performances in chaotic systems, Tellus A, 61, 587-600, 2009.
10. Corazza, M., Kalnay, E., and Patil, D.: Use of the breeding technique to estimate the shape of the analysis errors of the day, J. Geophys. Res., 10, 233-243, 2002. (Pubitemid 36755753)
11. Dee, D. P.: On-line Estimation of Error Covariance Parameters for Atmospheric Data Assimilation, Mon. Weather Rev., 123, 1128-1145, 1995.
12. Desroziers, G., Berre, L., Chapnik, B., and Poli, P.: Diagnosis of observation, background and analysis-error statistics in observation space, Q. J. Roy. Meteor. Soc., 131, 3385-3396, 2005.
13. Evensen, G.: Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics, J. Geophys. Res., 99, 10143-10162, 1994.
14. Evensen, G.: Data Assimilation: The Ensemble Kalman Filter, Springer-Verlag, 2nd Edn., 2009.
15. Furrer, R. and Bengtsson, T.: Estimation of high-dimensional prior and posterior covariance matrices in Kalman filter variants, J. Multivariate Anal., 98, 227-255, 2007. (Pubitemid 44660963)
16. Gejadze, I. Y., Le Dimet, F.-X., and Shutyaev, V.: On analysis error covariances in variational data assimilation, SIAM J. Sci. Com-put., 30, 1847-1874, 2008.
17. Gottwald, G. A. and Mitchell, L., and Reich, S.: Controlling over-estimation of error covariance in ensemble Kalman filters with sparse observations: A variance-limiting Kalman filter, Mon. Weather Rev., 139, 2650-2667, 2011.
18. Hamill, T. M., Whitaker, J. S., and Snyder, C.: Distance-dependent filtering of background error covariance estimates in an ensemble Kalman filter, Mon. Weather Rev., 129, 2776-2790, 2001. (Pubitemid 33079980)
19. Harlim, J. and Hunt, B.: A non-Gaussian ensemble filter for assimilating infrequent noisy observations, Tellus A, 59, 225-237, 2007. (Pubitemid 46671847)
20. Houtekamer, P. L. and Mitchell, H. L.: Data assimilation using an ensemble Kalman filter technique, Mon. Weather Rev., 126, 796-811, 1998. (Pubitemid 128581567)
21. Houtekamer, P. L. and Mitchell, H. L.: A sequential ensemble Kalman filter for atmospheric data assimilation, Mon. Weather Rev., 129, 123-137, 2001. (Pubitemid 32180439)
22. Huber, P. J.: Robust regression: Asymptotics, conjectures, and Monte Carlo, Ann. Statist., 1, 799-821, 1973.
23. Hunt, B. R., Kostelich, E. J., and Szunyogh, I.: Efficient data assimilation for spatiotemporal chaos: A local ensemble transform Kalman filter, Physica D, 230, 112-126, 2007. (Pubitemid 46776911)
24. Jeffreys, H.: Theory of Probability, Oxford University Press, 3rd Edn., 1961.
25. Lei, J., Bickel, P., and Snyder, C.: Comparison of Ensemble Kalman Filters under Non-Gaussianity, Mon. Weather Rev., 138, 1293-1306, 2010.
26. Li, H., Kalnay, E., and Miyoshi, T.: Simultaneous estimation of covariance inflation and observation errors within an ensemble Kalman filter, Q. J. Roy. Meteor. Soc., 135, 523-533, 2009.
27. Livings, D. M., Dance, S. L., and Nichols, N. K.: Unbiased ensemble square root filters, Physica D, 237, 1021-1028, 2008.
28. Lorenz, E. N.: Deterministic nonperiodic flow, J. Atmos. Sci., 20, 130-141, 1963.
29. Lorenz, E. N. and Emmanuel, K. E.: Optimal sites for supplementary weather observations: simulation with a small model, J. At-mos. Sci., 55, 399-414, 1998.
30. Mallat, S., Papanicolaou, G., and Zhang, Z.: Adaptive covariance estimation of locally stationary processes, Ann. Stat., 26, 1-47, 1998.
31. Mitchell, H. L. and Houtekamer, P. L.: An adaptive ensemble Kalman filter, Mon. Weather Rev., 128, 416-433, 1999. (Pubitemid 30205909)
32. Mitchell, H. L. and Houtekamer, P. L.: Ensemble Kalman Filter Configurations and Their Performance with the Logistic Map, Mon. Weather Rev., 137, 4325-4343, 2009.
33. Muirhead, R. J.: Aspect of Multivariate Statistical Theory, Wiley-Interscience, 1982.
34. Myrseth, I. and Omre, H.: Hierarchical Ensemble Kalman Filter, SPE J., 15, 569-580, 2010.
35. Ott, E., Hunt, B. R., Szunyogh, I., Zimin, A. V., Kostelich, E. J., Corazza, M., Kalnay, E., Patil, D. J., and Yorke, A.: A local ensemble Kalman filter for atmospheric data assimilation, Tellus A, 56, 415-428, 2004. (Pubitemid 39533058)
36. Raynaud, L., Berre, L., and Desroziers, G.: Objective filtering of ensemble-based background-error variances, Q. J. Roy. Meteor. Soc., 135, 1177-1199, 2009.
37. Sacher, W. and Bartello, P.: Sampling Errors in Ensemble Kalman Filtering. Part I: Theory, Mon. Weather Rev., 136, 3035-3049, 2008.
38. Sakov, P. and Bertino, L.: Relation between two common localisation methods for the EnKF, Comput. Geosci., 15, 225-237, 2010.
39. Sakov, P. and Oke, P. R.: Implications of the Form of the Ensemble Transformation in the Ensemble Square Root Filters, Mon. Weather Rev., 136, 1042-1053, 2008. (Pubitemid 351753162)
40. Tippett, M. K., Anderson, J. L., Bishop, C. H., Hamill, T. M., and Whitaker, J. S.: Ensemble square root filters, Mon. Weather Rev., 131, 1485-1490, 2003. (Pubitemid 36953823)
41. van Leeuwen, P. J.: Comment on Data Assimilation Using an Ensemble Kalman Filter Technique, Mon. Weather Rev., 127, 1374-1377, 1999.
42. Wang, X., Bishop, C. H., and Julier, S. J.: Which is better, an ensemble of positive-negative pairs or a centered spherical simplex ensemble?, Mon. Weather Rev., 132, 1590-1605, 2004. (Pubitemid 39052086)
43. Whitaker, J. S. and Hamill, T. M.: Ensemble Data Assimilation without Perturbed Observations, Mon. Weather Rev., 130, 1913-1924, 2002. (Pubitemid 34825252)
44. Wick, G. C.: The Evaluation of the Collision Matrix, Phys. Rev., 80, 268-272, 1950.
45. Zhou, Y., McLaughlin, A., and Entekhabi, D.: Assessing the performance of the ensemble kalman filter for land surface data assimilation, Mon. Weather Rev., 134, 2128-2142, 2006. (Pubitemid 44275528)
46. Zupanski, M.: Maximum Likelihood Ensemble Filter: Theoretical Aspects, Mon. Weather Rev., 133, 1710-1726, 2005. (Pubitemid 41300134)