Ensemble data assimilation for hyperbolic systems

Physica D: Nonlinear Phenomena

Volumn 243, Issue 1, 2013, Pages 128-142

  González Tokman, Cecilia ^a   Hunt, Brian R ^b  

^a UNIVERSITY OF NEW SOUTH WALES   (Australia)

^b University of Maryland   (United States)

Author keywords

Data assimilation; Ensemble Kalman filtering; Hyperbolic dynamical systems

Indexed keywords

DYNAMICAL SYSTEMS; LYAPUNOV METHODS; ONE DIMENSIONAL;

COMPUTATIONAL STUDIES; DATA ASSIMILATION; ENSEMBLE DATA ASSIMILATION; ENSEMBLE KALMAN FILTER; ENSEMBLE KALMAN FILTERING; ENSEMBLE-BASED METHOD; HIGH-DIMENSIONAL SYSTEMS; MODEL LINEARIZATION;

KALMAN FILTERS;

EID: 84870063507     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2012.10.005     Document Type: Article

References (30)

1. H.E. Nusse, and J.A. Yorke A procedure for finding numerical trajectories on chaotic saddles Phys. D: Nonlinear Phenomena 36 1-2 1989 137 156 URL http://www.sciencedirect.com/science/article/B6TVK-46X4M29-B/2/ bf50634d9fe6315e334610a128df5de4
2. P. Moresco, and S.P. Dawson The pim-simplex method: an extension of the pim-triple method to saddles with an arbitrary number of expanding directions Phys. D: Nonlinear Phenomena 126 1-2 1999 38 48 URL http://www.sciencedirect. com/science/article/B6TVK-3WWCDFX-4/2/f516f855454ae514b9dfdc931b0c0c34
3. E. Kalnay Atmospheric Modeling, Data Assimilation and Predictability 2002 Cambridge University Press
4. G. Evensen Data Assimilation second ed. 2009 Springer-Verlag Berlin 10.1007/978-3-642-03711-5 the ensemble Kalman filter
5. I. Szunyogh, E. Kostelich, G. Gyarmati, E. Kalnay, B. Hunt, E. Ott, E. Satterfield, and J. Yorke A local ensemble transform Kalman filter data assimilation system for the NCEP global model Tellus A 60 1 2008
6. J. Whitaker, T. Hamill, X. Wei, Y. Song, and Z. Toth Ensemble data assimilation with the NCEP global forecast system Mon. Weather Rev. 136 2 2008 463 482 URL http://journals.ametsoc.org/doi/abs/10.1175/2007MWR2018.1
7. B. Hunt, E. Kostelich, and I. Szunyogh Efficient data assimilation for spatiotemporal chaos: a local ensemble transform Kalman filter Phys. D 230 1-2 2007 112 126 10.1016/j.physd.2006.11.008
8. R. Kalman A new approach to linear filtering and prediction problems Trans. ASME J. Basic Eng. 1960 35 45
9. A. Jazwinski, Stochastic processes and filtering theory, Reprint 2007 Edition, Dover, 1970.
10. G. Evensen Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics J. Geophys. Res. 99 1994 10143 10162
11. G. Burgers, P. van Leeuwen, and G. Evensen Analysis scheme in the ensemble Kalman filter Mon. Weather Rev. 126 6 1998 1719 1724 URL http://journals.ametsoc.org/doi/abs/10.1175/1520- 0493%281998%29126%3C1719%3AASITEK%3E2.0.CO%3B2
12. P. Houtekamer, and H. Mitchell Data assimilation using an ensemble Kalman filter technique Mon. Weather Rev. 126 3 1998 796 811 URL http://journals. ametsoc.org/doi/abs/10.1175/1520-0493%281998%29126%3CO796%3ADAUAEK%3E2.0.CO%3B2
13. J. Anderson An ensemble adjustment kalman filter for data assimilation Mon. Weather Rev. 129 2001 2884 2903
14. C. Bishop, B. Etherton, and S. Majumdar Adaptive sampling with the ensemble transform Kalman filter, part I: theoretical aspects Mon. Weather Rev. 129 2001 420 436
15. E. Ott, B. Hunt, I. Szunyogh, A. Zimin, E.J. Kostelich, M. Corazza, E. Kalnay, D. Patil, and J. Yorke A local ensemble Kalman filter for atmospheric data assimilation Tellus Ser. A: Dyn. Meteorol. Oceanogr. 56 5 2004 415 428
16. M. Tippett, J. Anderson, C. Bishop, T. Hamill, and J. Whitaker Ensemble square root filters Mon. Weather Rev. 131 7 2003 1485 1490 URL http://journals.ametsoc.org/doi/abs/10.1175/1520- 0493%282003%29131%3C1485%3AESRF%3E2.0.CO%3B2
17. X. Wang, C. Bishop, and S. Julier Which is better, an ensemble of positive-negative pairs or a centered spherical simplex ensemble? Mon. Weather Rev. 132 7 2004 1590 1605 URL http://journals.ametsoc.org/doi/abs/10.1175/1520- 0493%282004%29132%3C1590%33AWIBAEO%3E2.0.CO%3B2
18. J. Whitaker, and T. Hamill Ensemble data assimilation without perturbed observations Mon. Weather Rev. 130 2002 1913 1924
19. K. Reif, S. Gunther, E. Yaz, and R. Unbehauen Stochastic stability of the discrete-time extended Kalman filter IEEE Trans. Autom. Control 44 4 1999 714 728
20. L.M. Pecora, and T.L. Carroll Synchronization in chaotic systems Phys. Rev. Lett. 64 8 1990 821 824 10.1103/PhysRevLett.64.821
21. K. Hayden, E. Olson, and E.S. Titi Discrete data assimilation in the Lorenz and 2D Navier-Stokes equations Phys. D: Nonlinear Phenomena 240 18 2011 1416 1425 URL http://www.sciencedirect.com/science/article/pii/S016727891100114X
22. A. Katok, and B. Hasselblatt Introduction to the Modern Theory of Dynamical Systems Encyclopedia of Mathematics and its Applications vol. 54 1995 Cambridge University Press Cambridge with a supplementary chapter by Katok and Leonardo Mendoza
23. F. Takens Detecting strange attractors in turbulence Dynamical Systems and Turbulence, Warwick 1980 (Coventry, 1979/1980) Lecture Notes in Math. vol. 898 1981 Springer Berlin 366 381
24. V. Oseledec A multiplicative ergodic theorem, characteristic Ljapunov, exponents of dynamical systems Trudy Moskov. Mat. Obšč. 19 1968 179 210
25. I. Shimada, and T. Nagashima A numerical approach to ergodic problem of dissipative dynamical systems Prog. Theor. Phys. 61 1979 1605 1616
26. F. Ginelli, P. Poggi, A. Turchi, H. Chaté, R. Livi, and A. Politi Characterizing dynamics with covariant Lyapunov vectors Phys. Rev. Lett. 99 13 2007 130601
27. L. Barreira, and Y. Pesin Smooth ergodic theory and nonuniformly hyperbolic dynamics Handbook of Dynamical Systems, Vol. 1B 2006 Elsevier B.V. Amsterdam 57 263 10.1016/S1874-575X(06)80027-5 with an appendix by Omri Sarig
28. T. Sauer, J.A. Yorke, and M. Casdagli Embedology J. Stat. Phys. 65 1991 579 616
29. P. Maybeck, Stochastics Models, Estimation, and Control: Introduction, 1979.
30. G. Bierman Factorization Methods for Discrete Sequential Estimation Mathematics in Science and Engineering vol. 128 1977 Academic Press.