Short-time linear response with reduced-rank tangent map

Chinese Annals of Mathematics. Series B

Volumn 30, Issue 5, 2009, Pages 447-462

  Abramov, Rafail V ^a  

^a UNIVERSITY OF ILLINOIS AT CHICAGO   (United States)

Author keywords

Fluctuation dissipation theorem; Linear response

Indexed keywords

EID: 76249089567     PISSN: 02529599     EISSN: 18606261     Source Type: Journal    
DOI: 10.1007/s11401-009-0088-3     Document Type: Article

References (27)

1. Abramov, R. and Majda, A., Blended response algorithms for linear fluctuation-dissipation for complex nonlinear dynamical systems, Nonlinearity, 20, 2007, 2793-2821.
2. Abramov, R. and Majda, A., A new algorithm for low-frequency climate response, J. Atmos. Sci., 66(2), 2009, 286-309.
3. Abramov, R. and Majda, A., New approximations and tests of linear fluctuation-response for chaotic nonlinear forced-dissipative dynamical systems, J. Nonlinear Sci., 18(3), 2008, 303-341.
4. Abramov, R., Majda, A. and Kleeman, R., Information theory and predictability for low frequency variability, J. Atmos. Sci., 62(1), 2005, 65-87.
5. Bell, T., Climate sensitivity from fluctuation dissipation: Some simple model tests, J. Atmos. Sci., 37(8), 1980, 1700-1708.
6. Carnevale, G., Falcioni, M., Isola, S., et al, Fluctuation-response in systems with chaotic behavior, Phys. Fluids A, 3(9), 1991, 2247-2254.
7. Cohen, B. and Craig, G., The response time of a convective cloud ensemble to a change in forcing, Quart. J. Roy. Met. Soc., 130(598), 2004, 933-944.
8. Crommelin, D. and Vanden-Eijnden, E., Subgrid scale parameterization with conditional Markov chains, J. Atmos. Sci., 65(8), 2008, 2661-2675.
9. Eckmann, J. and Ruelle, D., Ergodic theory of chaos and strange attractors, Rev. Mod. Phys., 57(3), 1985, 617-656.
10. Evans, D. and Morriss, G., Statistical Mechanics of Nonequilibrium Liquids, Academic Press, New York, 1990.
11. Fatkullin, I. and Vanden-Eijnden, E., A computational strategy for multiscale systems with applications to Lorenz 96 model, J. Comput. Phys., 200(2), 2004, 605-638.
12. Franzke, C., Dynamics of low-frequency variability: Barotropic mode, J. Atmos. Sci., 59(20), 2002, 2897-2909.
13. Gritsun, A., Fluctuation-dissipation theorem on attractors of atmospheric models, Russ. J. Numer. Math. Modeling, 16(2), 2001, 115-133.
14. Gritsun, A. and Branstator, G., Climate response using a three-dimensional operator based on the fluctuation-dissipation theorem, J. Atmos. Sci., 64(7), 2007, 2558-2575.
15. Gritsun, A., Branstator, G. and Dymnikov, V., Construction of the linear response operator of an atmospheric general circulation model to small external forcing, Num. Anal. Math. Modeling, 17, 2002, 399-416.
16. Gritsun, A., Branstator, G. and Majda, A., Climate response of linear and quadratic functionals using the fluctuation dissipation theorem, J. Atmos. Sci., 65(9), 2008, 2824-2841.
17. Gritsun, A. and Dymnikov, V., Barotropic atmosphere response to small external actions: theory and numerical experiments, Atmos. Ocean Phys., 35(5), 1999, 511-525.
18. Kubo, R., Toda, M. and Hashitsume, N., Statistical Physics II: Nonequilibrium Statistical Mechanics, Springer-Verlag, New York, 1985.
19. Leith, C., Climate response and fluctuation-dissipation, J. Atmos. Sci., 32(10), 1975, 2022-2026.
20. Lorenz, E., Predictability: a problem partly solved, Proceedings of the Seminar on Predictability, European Centre for Medium-Range Weather Forecast, Shinfield Park, Reading, England, 1996.
21. Lorenz, E. and Emanuel, K., Optimal sites for supplementary weather observations, J. Atmos. Sci., 55(3), 1998, 399-414.
22. Majda, A., Abramov, R. and Grote, M., Information Theory and Stochastics for Multiscale Nonlinear Systems, CRM Monograph Series, 25, A. M. S., Providence, RI, 2005.
23. Risken, F., The Fokker-Planck Equation, Second Edition, Springer-Verlag, New York, 1988.
24. Ruelle, D., Differentiation of SRB states, Comm. Math. Phys., 187(1), 1997, 227-241.
25. Ruelle, D., General linear response formula in statistical mechanics, and the fluctuation-dissipation theorem far from equilibrium, Phys. Lett. A, 245(3-4), 1998, 220-224.
26. Selten, F., An efficient description of the dynamics of barotropic flow, J. Atmos. Sci., 52(7), 1995, 915-936.
27. Young, L.-S., What are SRB measures, and which dynamical systems have them? J. Stat. Phys., 108(5-6), 2002, 733-754.