Filtering a statistically exactly solvable test model for turbulent tracers from partial observations

Journal of Computational Physics

Volumn 230, Issue 4, 2011, Pages 1602-1638

  Gershgorin, B ^a   Majda, A J ^a  

^a NEW YORK UNIVERSITY   (United States)

Author keywords

Data assimilation; Exactly solvable model; Nonlinear Kalman filter; Turbulent advection diffusion equation

Indexed keywords

ADVECTION; BANDPASS FILTERS; CARBON DIOXIDE; CLIMATE CHANGE; CLIMATE MODELS; GREENHOUSE GASES; NONLINEAR EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS; PASSIVE FILTERS; PROBABILITY DISTRIBUTIONS; TURBULENCE MODELS; WATER POLLUTION;

ADVECTION-DIFFUSION EQUATION; DATA ASSIMILATION; EXACTLY SOLVABLE MODEL; FILTERING ALGORITHM; NONLINEAR KALMAN FILTER; PARTIAL OBSERVATION; PASSIVE TRACERS; PROBABILITY: DISTRIBUTIONS; TEST MODELS; TURBULENT ADVECTION-DIFFUSION EQUATION;

KALMAN FILTERS;

EID: 78650533520     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2010.11.024     Document Type: Article

References (27)

1. J. Neelin, B. Lintner, B. Tian, Q. Li, L. Zhang, P. Patra, M. Chahine, S. Stechmann, Long tails in deep columns of natural and anthropogenic tropospheric tracers, Geophys. Res. Lett. 37 L05804, doi:10.1029/2009GL041726.
2. Chui C., Chen G. Kalman Filtering 1999, Springer, New York.
3. Harlim J., Majda A.J. Mathematical strategies for filtering complex systems: regularly spaced sparse observations. Journal of Computational Physics 2008, 227(10):5304-5341.
4. Anderson B., Moore J. Optimal Filtering 1979, Prentice-Hall, Englewood Cliffs, NJ.
5. Castronovo E., Harlim J., Majda A.J. Mathematical criteria for filtering complex systems: plentiful observations. J. Comput. Phys. 2008, 227(7):3678-3714.
6. Anderson J. A local least squares framework for ensemble filtering. Mon. Weather Rev. 2003, 131(4):634-642.
7. Anderson J. An ensemble adjustment Kalman filter for data assimilation. Mon. Weather Rev. 2001, 129(12):2884-2903.
8. Daley R. Atmospheric Data Analysis 1991, Cambridge University Press, New York.
9. Evensen G. Advanced data assimilation for strongly nonlinear dynamics. Mon. Weather Rev. 1997, 125:1342-1354.
10. Ghil M., Malanotte-Rizolli P. Data assimilation in meteorology and oceanography. Advances in Geophysics 1991, 33:141-266.
11. Majda A.J., Grote M. Explicit off-line criteria for stable accurate time filtering of strongly unstable spatially extended systems. Proc. Natl. Acad. Sci. 2007, 104:1124-1129.
12. Ott E., Hunt B., Szunyogh I., Zimin A., Kostelich E., Corrazza M., Kalnay E., Yorke J. A local ensemble Kalman filter for atmospheric data assimilation. Tellus A 2004, 56:415-428.
13. Jazwinski A. Stochastic Processes and Filtering Theory 1970, Academic, San Diego, California.
14. Majda A.J., Harlim J., Gershgorin B. Mathematical strategies for filtering turbulent dynamical systems. Discrete Contin. Dyn. Syst. 2010, 27(2):441-486.
15. Majda A.J., Gershgorin B. Quantifying uncertainty in climate change science through empirical information theory. Proceedings of National Academy of Sciences 2010, 107(34):14958-14963.
16. Majda A.J., Abramov R., Grote M. Information Theory and Stochastics for Multiscale Nonlinear Systems, CRM Monograph Series 2005, Vol. 25. American Mathematical Society, Providence, Rhode Island, USA.
17. Gershgorin B., Majda A.J. A nonlinear test model for filtering slow-fast systems. Commun. Math. Sci. 2008, 6(3):611-649.
18. Gershgorin B., Majda A.J. Filtering a nonlinear slow-fast system with strong fast forcing. Commun. Math. Sci. 2010, 8(1):67-92.
19. Gershgorin B., Majda A.J. A test model for fluctuation-dissipation theorems with time periodic statistics. Physica D 2010, 239(17):1741-1757.
20. Majda A.J., Kramer P. Simplified models for turbulent diffusion: theory, numerical modeling, and physical phenomena. Phys. Rep. 1999, 314:237-574.
21. Bourlioux A., Majda A.J. Elementary models with probability distribution function intermittency for passive scalars with a mean gradient. Phys. Fluid. 2002, 14:881-897.
22. Gershgorin B., Harlim J., Majda A.J. Test models for improving filtering with model errors through stochastic parameter estimation. J. Comput. Phys. 2010, 229:1-31.
23. Gershgorin B., Harlim J., Majda A.J. Improving filtering and prediction of sparsely observed spatially extended turbulent systems with model errors through stochastic parameter estimation. J. Comput. Phys. 2010, 229:32-57.
24. Harlim J., Majda A.J. Filtering turbulent sparsely observed geophysical flows. Mon. Weather Rev. 2010, 138:1050-1083.
25. Kubo R. Stochastic Liouville equations. J. Math. Phys. 1963, 4(2):174-183.
26. Gardiner C. Handbook of Stochastic Methods for Physics, Chemistry, and the Natural Sciences 1997, Springer-Verlag, New York.
27. Bensoussan A. Stochastic Control of Partially Observable Systems 2004, Cambridge University Press.