Mathematical test criteria for filtering complex systems: Plentiful observations

Journal of Computational Physics

Volumn 227, Issue 7, 2008, Pages 3678-3714

  Castronovo, E ^a   Harlim, J ^a   Majda, A J ^a  

^a NEW YORK UNIVERSITY   (United States)

Author keywords

Data assimilation; Finite difference; Kalman filter; Turbulence

Indexed keywords

BANDPASS FILTERS; INFORMATION FILTERING; MESH GENERATION; REAL TIME SYSTEMS; STABILITY CRITERIA;

DATA ASSIMILATION; FILTERING STRATEGIES; FINITE DIFFERENCE; REAL TIME FILTERING; SCIENTIFIC ISSUES; SPATIO-TEMPORAL; STATISTICAL ACCURACY; TEST CRITERIA; TEST PROBLEM; TURBULENT SPECTRUM;

KALMAN FILTERS;

EID: 39649123724     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2007.12.016     Document Type: Article

References (30)

1. Anderson B.D., and Moore J.B. Optimal Filtering (1979), Prentice-Hall, Englewood Cliffs, NJ
2. Anderson J.L. An ensemble adjustment Kalman filter for data assimilation. Monthly Weather Review 129 12 (2001) 2884-2903
3. Anderson J.L. A local least squares framework for ensemble filtering. Monthly Weather Review 131 4 (2003) 634-642
4. Berliner L.M., Milliff R.F., and Wikle C.K. Bayesian hierarchical modeling of air-sea interaction. Journal of Geophysical Research (Oceans) 108 C4 (2003) 3104-3120
5. Bishop C.H., Etherton B.J., and Majumdar S.J. Adaptive sampling with the ensemble transform Kalman filter. Part I: The theoretical aspects. Monthly Weather Review 129 (2001) 420-436
6. J. Harlim, A.J. Majda, Mathematical strategies for filtering complex systems: regularly spaced sparse observations, J. Comp. Phys., doi:10.1016/j.jcp.2008.01.049.
7. Chorin A.J., and Krause P. Dimensional reduction for a Bayesian filter. Proceedings of the National Academy of Sciences 101 42 (2004) 15013-15017
8. Chui C.K., and Chen G. Kalman Filtering (1999), Springer, New York
9. Cohn S.E., and Dee D. Observability of discretized partial differential equations. SIAM Journal on Numerical Analysis 25 3 (1988) 586-617
10. Farrell B.F., and Ioannou P.J. State estimation using a reduced-order Kalman filter. Journal of the Atmospheric Sciences 58 23 (2001) 3666-3680
11. Farrell B.F., and Ioannou P.J. Distributed forcing of forecast and assimilation error systems. Journal of the Atmospheric Sciences 62 2 (2005) 460-475
12. Gardiner C.W. Handbook of Stochastic Methods for Physics, Chemistry, and the Natural Sciences (1997), Springer-Verlag, New York
13. Ghil M., and Malanotte-Rizzoli P. Data assimilation in meteorology and oceanography. Advances in Geophysics 33 (1991) 141-266
14. Grote M.J., and Majda A.J. Stable time filtering of strongly unstable spatially extended systems. Proceedings of the National Academy of Sciences 103 20 (2006) 7548-7553
15. J. Harlim, Errors in the initial conditions for numerical weather prediction: a study of error growth patterns and error reduction with ensemble filtering, Ph.D. Thesis, University of Maryland, 2006.
16. Harlim J., and Hunt B.R. A non-Gaussian ensemble filter for assimilating infrequent noisy observations. Tellus 59A 2 (2007) 225-237
17. J. Harlim, A.J. Majda, Filtering nonlinear dynamical systems with linear stochastic models, Nonlinearity, submitted for publication.
18. Haven K., Majda A.J., and Abramov R.V. Quantifying predictability through information theory: small sample estimation in a non-Gaussian framework. Journal of Computational Physics 206 1 (2005) 334-362
19. Jazwinski A.H. Stochastic Processes and Filtering Theory (1970), Academic Press, New York
20. Kaipio J.P., and Somersalo E. Statistical and Computational Inverse Problems (2005), Springer, New York
21. E.N. Lorenz, Predictability - a problem partly solved, in: Proceedings of the Seminar on Predictability, vol. 1, ECMWF, Reading, Berkshire, UK, 1995, pp. 1-18.
22. Majda A.J., and Grote M.J. Explicit off-line criteria for stable accurate time filtering of strongly unstable spatially extended systems. Proceedings of the National Academy of Sciences 104 4 (2007) 1124-1129
23. Majda A.J., Abramov R.V., and Grote M.J. Information Theory and Stochastics for Multiscale Nonlinear Systems (2005), American Mathematical Society
24. Majda A.J., and Wang X. Nonlinear Dynamics and Statistical Theories for Basic Geophysical Flows (2006), Cambridge University Press
25. Miller R.N., Carter E.F., and Blue S.T. Data assimilation into nonlinear stochastic models. Tellus A 51 2 (1999) 167-194
26. Ott E., Hunt B.R., Szunyogh I., Zimin A.V., Kostelich E.J., Corazza M., Kalnay E., Patil D.J., and Yorke J.A. A local ensemble kalman filter for atmospheric data assimilation. Tellus A 56 5 (2004) 415-428
27. Richtmyer R.D., and Morton K.W. Difference Methods for Initial Value Problems (1967), Wiley
28. A. Simmons, The Control of Gravity Waves in Data Assimilation, 1999. .
29. Tribbia J.J., and Baumhefner D.P. Estimates of the predictability of low-frequency variability with a spectral general circulation model. Journal of Atmospheric Science 45 (1988) 2306-2317
30. Todling R., and Ghil M. Tracking atmospheric instabilities with the Kalman Filter. Part 1: Methodology and one-layer results. Monthly Weather Review 122 1 (1994) 183-204