Well-posedness and accuracy of the ensemble Kalman filter in discrete and continuous time

Nonlinearity

Volumn 27, Issue 10, 2014, Pages 2579-2603

  Kelly, D T B ^a   Law, K J H ^b   Stuart, A M ^a  

^a UNIVERSITY OF WARWICK   (United Kingdom)

^b KING ABDULLAH UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Saudi Arabia)

Author keywords

data assimilation; ensemble Kalman filter; stochastic analysis

Indexed keywords

EID: 84907246706     PISSN: 09517715     EISSN: 13616544     Source Type: Journal    
DOI: 10.1088/0951-7715/27/10/2579     Document Type: Article

References (26)

1. Anderson J L 2007 An adaptive covariance inflation error correction algorithm for ensemble filters Tellus A 59 210-24
2. Bloemker D, Law K J H, Stuart A M and Zygalalkis K 2013 Accuracy and stability of the continuous-time 3DVAR filter for the Navier-Stokes equation Nonlinearity 26 2193
3. Brett C E A, Lam K F, Law K J H, McCormick D S, Scott M R and Stuart A M 2012 Accuracy, stability of filters for dissipative PDEs Phys. D: Nonlinear Phenom. 245 34-45
4. Burgers G, Van P J and Evensen G 1998 On the analysis scheme in the ensemble Kalman filter Mon. Weather Rev. 126 1719-24
5. Constantin P and Foiaş C 1988 Navier-Stokes Equations (Chicago, IL: University of Chicago Press)
6. Cox S M and Matthews P C 2002 Exponential time differencing for stiff systems J. Comput. Phys. 176 430-55
7. DaPrato G and Zabczyk J 1992 Stochastic equations in infinite dimensions Encyclopedia of Mathematics and its Applications vol 44 (Cambridge: Cambridge University Press)
8. Evensen G 2006 Data Assimilation: The Ensemble Kalman Filter (Berlin: Springer)
9. Evensen G and Van Leeuwen P J 2000 An ensemble Kalman smoother for nonlinear dynamics Mon. Weather Rev. 128 1852-67
10. Evensen G, Burgers G and van Leeuwen P J 1998 Analysis scheme in the ensemble kalman filter Mon. Weather Rev. 126 1719-24
11. Gottwald G A and Majda A J 2013 A mechanism for catastrophic filter divergence in data assimilation for sparse observation networks Nonlinear Process. Geophys. 20 705-12
12. Hesthaven J S, Gottlieb S and Gottlieb D 2007 Spectral Methods for Time-dependent Problems vol 21 (Cambridge: Cambridge University Press)
13. Ide K, Kuznetsov L and Jones C K R T 2002 Lagrangian data assimilation for point-vortex system J. Turbul. 3 53
14. Jazwinski A H 1970 Stochastic Processes and Filtering Theory vol 63 (New York: Academic)
15. Kalnay E 2003 Atmospheric Modeling, Data Assimilation and Predictability (Cambridge: Cambridge University Press)
16. Kloeden P E and Platen E 1992 Numerical solution of stochastic differential equations Applications of Mathematics vol 23 (Berlin: Springer)
17. Law K J H, Shukla A and Stuart A M 2014 Analysis of the 3DVAR filter for the partially observed Lorenz '63 model Discrete Continuous Dyn. Syst. A 34 1061-78
18. François LG, et al 2011 Large sample asymptotics for the ensemble Kalman filter Oxford Handbook of Nonlinear Filtering ed D Crisan and B Rozovskii (Oxford: Oxford University Press) pp 598-631
19. Majda A J and Harlim J 2008 Catastrophic filter divergence in filtering nonlinear dissipative systems Commun. Math. Sci. 8 27-43
20. Majda A J and Harlim J 2012 Filtering Complex Turbulent Systems (Cambridge: Cambridge University Press)
21. Majda A J and Wang X 2006 Nonlinear Dynamics and Statistical Theories for Geophysical Flows (Cambridge: Cambridge University Press)
22. Mandel J, Cobb L and Beezley J D 2011 On the convergence of the ensemble Kalman filter Appl. Math. 56 533-41
23. Mao X 1997 Stochastic Differential Equations, their Applications (Horwood Publishing Series in Mathematics and Applications) (Chichester: Horwood)
24. Moodey A J F, Lawless A S, Potthast R W E and van Leeuwen P J 2013 Nonlinear error dynamics for cycled data assimilation methods Inverse Problems 29 025002
25. Oliver D S, Reynolds A C and Liu N 2008 Inverse Theory for Petroleum Reservoir Characterization and History Matching (Cambridge: Cambridge University Press)
26. Temam R 1997 Infinite-dimensional dynamical systems in mechanics, physics Applied Mathematical Sciences vol 68 2nd edn (New York: Springer)