Lyapunov vectors and assimilation in the unstable subspace: Theory and applications

Journal of Physics A: Mathematical and Theoretical

Volumn 46, Issue 25, 2013, Pages

  Palatella, Luigi ^a   Carrassi, Alberto ^b   Trevisan, Anna ^c  

^a CNR   (Italy)

^b Institut Catalá de Ciéncies del Clima IC3   (Spain)

^c INSTITUTE OF ATMOSPHERIC SCIENCES AND CLIMATE   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84878891469     PISSN: 17518113     EISSN: 17518121     Source Type: Journal    
DOI: 10.1088/1751-8113/46/25/254020     Document Type: Article

References (40)

1. Jazwinski A H 1970 Stochastic Processes and Filtering Theory (New York: Academic)
2. Daley R 1991 Atmospheric Data Analysis (Cambridge: Cambridge University Press)
3. Kalnay E 2003 Atmospheric Modeling, Data Assimilation and Predictability (Cambridge: Cambridge University Press)
4. Talagrand O 1997 Assimilation of observations, an introduction J. Meteorol. Soc. Japan 75 191-209 (Pubitemid 127712496)
5. Kalman R 1960 A new approach to linear filtering and prediction problems Trans. ASME D 82 3545
6. Ghil M and Malanotte-Rizzoli P 1991 Data assimilation in meteorology and oceanography Adv. Geophys. 33 141-266
7. Miller R N, Ghil M and Gauthier F 1994 Advanced data assimilation in strongly nonlinear dynamical systems J. Atmos. Sci. 51 1037-56
8. Pires C, Vautard R and Talagrand O 1996 On extending the limits of variational assimilation in nonlinear chaotic systems Tellus A 48 96-121
9. Trevisan A and Uboldi F 2004 Assimilation of standard and targeted observations within the unstable subspace of the observation-analysis-forecast cycle system J. Atmos. Sci. 61 103-13 (Pubitemid 38185097)
10. Uboldi F and Trevisan A 2006 Detecting unstable structures and controlling error growth by assimilation of standard and adaptive observations in a primitive equation ocean model Nonlinear Process. Geophys. 16 67-81
11. Carrassi A, Trevisan A, Descamps L, Talagrand O and Uboldi F 2008 Controlling instabilities along a 3DVar analysis cycle by assimilating in the unstable subspace: a comparison with the EnKF Nonlinear Process. Geophys. 15 503-21
12. Trevisan A, D'Isidoro M and Talagrand O 2010 Four-dimensional variational assimilation in the unstable subspace and the optimal subspace dimension Q. J. R. Meteorol. Soc. 136 487-96
13. Trevisan A and Palatella L 2011 On the Kalman filter error covariance collapse into the unstable subspace Nonlinear Process. Geophys. 18 243-50
14. Tremolet Y 2007 Model-error estimation in 4D-Var Q. J. R. Meteorol. Soc. 133 1267-80 (Pubitemid 47316574)
15. Carrassi A and Vannitsem S 2010 Accounting for model error in variational data assimilation: a deterministic formulation Mon. Weather Rev. 138 3369-86
16. Talagrand O and Courtier P 1987 Variational assimilation of observations with the adjoint vorticity equations Q. J. R. Meteorol. Soc. 113 1311-28
17. Le Dimet F X and Talagrand O 1986 Variational algorithms for analysis and assimilation of meteorological observations - theoretical aspects Tellus 38 97-110
18. Tsuyuki T and Miyoshi T 2007 Recent progress of data assimilation methods in meteorology J. Meteorol. Soc. Japan B 85 331-61 (Pubitemid 47506051)
19. Lorenc A C 2003 The potential of the ensemble Kalman filter for NWP - a comparison with 4DVAR Q. J. R. Meteorol. Soc. 129 3183-293 (Pubitemid 38034055)
20. Kalnay E, Li H, Miyoshi T, Yang S-C and Ballabrera-Poy J 2007 4DVar or ensemble Kalman filter? Tellus A 59 758-73 (Pubitemid 47434011)
21. Gustafsson N 2007 Discussion on '4DVar or EnKF'? Tellus A 59 774-7 (Pubitemid 47434012)
22. Benettin G, Galgani L, Giorgilli A and Strelcyn J M 1980 Lyapunov characteristic exponents for smooth dynamical systems and for Hamiltonian systems, a method for computing them Meccanica 15 9-21
23. Trevisan A and Pancotti F 1998 Periodic orbits, Lyapunov vectors, and singular vectors in the Lorenz system J. Atmos. Sci. 55 390-8
24. Ginelli F, Poggi P, Turchi A, Chatè H, Livi R and Politi A 2007 Characterizing dynamics with covariant Lyapunov vectors Phys. Rev. Lett. 99 130601 (Pubitemid 47480005)
25. Wolfe C L and Samelson R M 2007 An efficient method for recovering Lyapunov vectors from singular vectors Tellus A 59 355-66 (Pubitemid 46605431)
26. Kuptsov P V and Parlitz U 2012 Theory and computation of covariant Lyapunov vectors J. Nonlinear Sci. 22 727-62
27. Carrassi A, Trevisan A and Uboldi F 2007 Adaptive observations and assimilation on the unstable subspace by breeding on the data assimilation system Tellus A 59 101-13 (Pubitemid 46111270)
28. Toth Z and Kalnay E 1993 Ensemble forecasting at NMC: the generation of perturbations Bull. Am. Meteorol. Soc. 74 2317-30
29. Toth Z and Kalnay E 1997 Ensemble forecasting at NCEP and the breeding method Mon. Weather Rev. 125 3297-319 (Pubitemid 127667540)
30. Trevisan A and Palatella L 2010 The extended Kalman filter and its reduction to the unstable subspace Ecodyc 2010: Inf. Workshop on Exploring Complex Dynamics in High-Dimensional Chaotic Systems: From Weather Forecasting to Oceanic Flows (Dresden, Germany,) www.mpipks-dresden.mpg.de/∼ecodyc10/ Contributions/Trevisan.pdf
31. Bannister R N 2008 A review of forecast error covariance statistics in atmospheric variational data assimilation. I: characteristics and measurements of forecast error covariances Q. J. R. Meteorol. Soc. 134 1951-70
32. Swanson K L, Palmer T N and Vautard R 2000 Observational error structures and the value of advanced assimilation techniques J. Atmos. Sci. 57 1327-40 (Pubitemid 30343823)
33. Lorenz E N 1996 Predictability: a problem partly solved Proc. Seminar on Predictability. European Center for Medium-Range Weather Forecasting (Shinfield Park, Reading, UK,) pp 1-18
34. Thornton C L and Bierman G J 1976 A numerical comparison of discrete Kalman filtering algorithms: an orbit determination case study JPL Tech. Memo. 33 771
35. Hamill T M and Whitaker J S 2011 What constrains spread growth in forecasts initialized from ensemble Kalman filters? Mon. Weather Rev. 139 117-31
36. Carrassi A, Vannitsem S, Zupanski D and Zupanski M 2009 The maximum likelihood ensemble filter performances in chaotic systems Tellus 61 587-600
37. Bocquet M 2011 Ensemble Kalman filtering without the intrinsic need for inflation Nonlinear Process. Geophys. 18 735-50
38. Ng G-H C, McLaughlin D, Entekhabi D and Ahanin A 2011 The role of model dynamics in ensemble Kalman filter performance for chaotic systems Tellus A 63 958-77
39. Palatella L and Trevisan A 2012 Nonlinear stability of traffic models and the use of Lyapunov vectors for estimating the traffic state Phys. Rev. E submitted
40. Orosz G, Krauskopf B and Wilson R E 2005 Bifurcations and multiple traffic jams in a car-following model with reaction time delay Physica D 211 277-93 (Pubitemid 41550117)