Combining inflation-free and iterative ensemble Kalman filters for strongly nonlinear systems

Nonlinear Processes in Geophysics

Volumn 19, Issue 3, 2012, Pages 383-399

  Bocquet, M ^a,b   Sakov, P ^c  

^a UNIVERSITÉ CATHOLIQUE DE L'OUEST   (France)

^b INRIA   (France)

^c NANSEN ENVIRONMENTAL AND REMOTE SENSING CENTER   (Norway)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHM; KALMAN FILTER; NONLINEARITY; NUMERICAL MODEL;

EID: 84863313070     PISSN: 10235809     EISSN: 16077946     Source Type: Journal    
DOI: 10.5194/npg-19-383-2012     Document Type: Article

References (21)

1. 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.
2. Bocquet, M.: Ensemble Kalman filtering without the intrinsic need for inflation, Nonlin. Processes Geophys., 18, 735-750, doi:10.5194/npg-18-735-2011, 2011.
3. Borwein, J. M. and Lewis, A. S.: Convex analysis and nonlinear optimization: theory and examples, Springer, 2000.
4. Byrd, R. H., Lu, P., and Nocedal, J.: A Limited Memory Algorithm for Bound Constrained Optimization, J. Sci. Stat. Comput., 16, 1190-1208, 1995.
5. Gu, Y. and Oliver, D. S.: An Iterative Ensemble Kalman Filter for Multiphase Fluid Flow Data Assimilation, Soc. Petrol. Eng. J., 12, 438-446, 2007.
6. Harlim, J. and Hunt, B.: A non-Gaussian ensemble filter for assimilating infrequent noisy observations, Tellus A, 59, 225-237, 2007. (Pubitemid 46671847)
7. 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)
8. Jazwinski, A. H.: Stochastic Processes and Filtering Theory, Academic Press, 1970.
9. Kalnay, E. and Yang, S.-C.: Accelerating the spin-up of Ensemble Kalman Filtering, Q. J. Roy. Meteor. Soc., 136, 1644-1651, 2010.
10. Levenberg, K.: A Method for the Solution of Certain Problems in Least Squares, Quart. Appl. Math., 2, 164-168, 1944.
11. Lorenz, E. N.: Deterministic nonperiodic flow, J. Atmos. Sci., 20, 130-141, 1963.
12. Lorenz, E. N. and Emmanuel, K. E.: Optimal sites for supplementary weather observations: simulation with a small model, J. Atmos. Sci., 55, 399-414, 1998.
13. Madsen, K., Nielsen, H. B., and Tingleff, O.: Methods for nonlinear least square problems, Tech. rep., Informatics and Mathematical Modelling, Technical University of Denmark, 2nd Edn., 2004.
14. Marquardt, D.: An Algorithm for Least-Squares Estimation of Nonlinear Parameters, SIAM J. Appl. Math., 11, 431-441, 1963.
15. Nocedal, J. and Wright, S. J.: Numerical Optimization, Springer Series in Operations Research, Springer, 2006.
16. Pires, C., Vautard, R., and Talagrand, O.: On extending the limits of variational assimilation in nonlinear chaotic systems, Tellus A, 48, 96-121, 1996.
17. 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)
18. Sakov, P., Oliver, D., and Bertino, L.: An iterative EnKF for strongly nonlinear systems, Mon. Weather Rev., 140, 1988-2004, doi:10.1175/MWR-D-11- 00145.1, 2012.
19. Tarantola, A.: Inverse Problem Theory and Methods for Model Parameter Estimation, SIAM, 352 pp., 2005.
20. Wishner, R. P., Tabaczynski, J. A., and Athans, M.: A Comparison of Three Non-Linear Filters, Automatica, 5, 487-496, 1969.
21. Zupanski, M.: Maximum Likelihood Ensemble Filter: Theoretical Aspects, Mon. Weather Rev., 133, 1710-1726, 2005. (Pubitemid 41300134)