Fluctuation-response relation and modeling in systems with fast and slow dynamics

Nonlinear Processes in Geophysics

Volumn 14, Issue 5, 2007, Pages 681-694

  Lacorata, G ^a   Vulpiani, A ^b  

^a CNR   (Italy)

^b SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

BROWNIAN MOTION; FEEDBACK MECHANISM; MODEL TEST; PERTURBATION; RECIPROCITY;

EID: 35648990543     PISSN: 10235809     EISSN: 16077946     Source Type: Journal    
DOI: 10.5194/npg-14-681-2007     Document Type: Article

References (55)

1. Abramov, R. and Majda, A.: New approximations and tests of linear fluctuation-response for chaotic nonlinear forced-dissipative dynamical systems, J. Nonlinear Sci., accepted, 2007.
2. Bell, T. L.: Climate sensitivity from, fluctuation-dissipation: some simple model tests, J. Atmos. Sci., 37, 1700-1707, 1980.
3. Biferale, L., Daumont, I., Lacorata, G., and Vulpiani, A.: Fluctuation-response relation in turbulent systems, Phys. Rev. E, 65, 016302, 016302-1-016302-7, 2002.
4. Boffetta, G., Lacorata, G., Musacchio, S., and Vulpiani, A.: Relaxation of finite perturbations: Beyond the Fluctuation-Response relation, Chaos, 13, 806-811, 2003.
5. Bohr, T., Jensen, M. H., Paladin, G., and Vulpiani, A.: Dynamical systems approach to turbulence, Cambridge University Press, UK, 1998.
6. Cane, M.: Understanding and predicting the world's climate system, Chaos in geophysical flows, Chaos in geophysical flows, edited by: Boffetta, G., Lacorata, G., Visconti, G., and Vulpiani, A., Otto Eds., Torino, Italy, 2003.
7. Cessac, B. and Sepulchre, J.-A.: Linear response, susceptibility and resonance in chaotic toy models, Physica D, 225, 13-28, 2007.
8. Cionni, I., Visconti, G., and Sassi, E: Fluctuation-dissipation theorem in a general circulation model, Geophys. Res. Lett., 31, L09206, doi:10.1029/2004GL019739, 2004.
9. Deker, U. and Haake, E: Fluctuation-dissipation theorems for classical processes, Phys. Rev. A, 11, 2043-2056, 1975.
10. Ditlevsen, P. D.: Observation of a-stable noise induced millennial climate changes from an ice-core record, Geophys. Res. Lett., 26(10), 1441-1444, 1999.
11. Dymnikov, V. P.: Potential Predictability of Large-Scale Atmospheric Processes, Izvestiya, Atmospheric and Oceanic Physics, 40(5), 513-519, 2004.
12. Dymnikov, V. P. and Gritsoun, A. S.: Climate model attractors: chaos, quasi-regularity and sensitivity to small perturbations of external forcing, Nonlin. Processes Geophys., 8, 201-209, 2001, http://www.nonlin-processes- geophys .net/8/201/2001/.
13. Dymnikov, V. P. and Gritsoun, A. S.: Current problems in the mathematical theory of climate, Izvestiya, Atmospheric and Oceanic Physics, 41, 294-314, 2005.
14. Falcioni, M., Isola, S., and Vulpiani, A.: Correlation functions and relaxation properties in chaotic dynamics and statistical mechanics, Phys. Lett. A, 144, 341-346, 1990.
15. Fraedrich, K.: Predictability: short and long-term, memory of the atmosphere, Chaos in geophysical flows, Chaos in geophysical flows, edited by: Boffetta, G., Lacorata, G., Visconti, G., and Vulpiani, A., Otto Eds., Torino, Italy, 2003.
16. Frisch, U.: Turbulence, Cambridge University Press, UK, 1995.
17. Gardiner, C. W.: Handbook, of stochastic methods for Physics, Chemistry and the Natural Sciences, Springer-Verlag, Berlin, Germany, 1990.
18. Givon, D., Kupferman, R., and Stuart, A.: Extracting macroscopic dynamics: model problems and algorithms, Nonlinearity, 17, 55-127, 2004.
19. Gritsoun, A. S.: Fluctuation-dissipation theorem, on attractors of atmospheric models, Russ. J. Numer. Analysis Math. Modelling, 16, 115-133, 2001.
20. Gritsoun, A. S. and Branstator, G.: Climate Response Using a Three-Dimensional Operator Based on the Fluctuation Dissipation Theorem, J. Atmos. Sci., 64(7), 2558-2575, 2007.
21. Gritsoun, A. S., Branstator, G., and Dymnikov, V. P.: Construction of the linear response operator of an atmospheric general, circulation model to small external forcing, Russ. J. Numer. Analysis Math. Modelling, 17, 399-416, 2002.
22. Gritsoun, A. S. and Dymnikov, V. P.: Barotropic atmosphere response to small external, action: theory and numerical experiments, Izvestiya, Atmospheric and Oceanic Physics, 35, 511-525, 1999.
23. Haskins, R., Goody, R., and Chen, L.: Radiance covariance and climate models, J. Climate, 12, 1409-1422, 1999.
24. Hohenberg, P. C. and Shraiman, B. I.: Chaotic behavior of an extended system, Physica D, 37, 109-115, 1989.
25. Imkeller, P. and von Storch, J.-S. (Eds.): Stochastic Climate Models, Birkhäuser, Basel, Switzerland, 2001.
26. Kraichnan, R. H.: Classical fluctuation-relaxation theorem, Phys.Rev., 113, 1181-1182, 1959.
27. Kraichnan, R. H.: Deviations from fluctuation-relaxation relations, Physica A, 279, 30-36, 2000.
28. Kraichnan, R. H. and Montgomery, D.: Two-dimensional turbulence, Rep. Prog. Phys., 43, 547-619, 1980.
29. Kubo, R.: The fluctuation-dissipation theorem, Rep. Prog. Phys., 29, 255-284, 1966.
30. Kubo, R.: Brownian motion and nonequilibrium statistical mechanics, Science, 233, 330-334, 1986.
31. Leith, C. E.: Climate response and fluctuation-dissipation, J. Atmos. Sci., 32, 2022-2026, 1975.
32. Leith, C. E.: Predictability of climate, Nature, 276, 352-355, 1978.
33. Lorenz, E. N.: Deterministic nonperiodic flow, J. Atmos. Sci., 20, 130-141, 1963.
34. Lorenz, E. N.: Predictability - a problem, partly solved, Proceedings, Seminar on Predictability ECMWF, 1, 1-18, 1996.
35. Loreto, V., Paladin, G., and Vulpiani, A.: On the concept of complexity for random dynamical systems, Phys. Rev. E, 53, 2087-2098, 1996.
36. Majda, A. J., Abramov, R., and Grote, M.: Information theory and stochastics for multiscale nonlinear systems, CRM monograph series 25, American Mathematical Society, 2005.
37. Majda, A. J. and Franzke, C.: Low Order Stochastic Mode Reduction for a Prototype Atmospheric GCM, J. Atmos. Sci., 63(2), 457-479, 2006.
38. Majda, A. J., Timofeyev, I., and Vanden-Eijnden, E.: Models for stochastic climate prediction, Proc. Natl. Acad. Sci. USA, 96, 14687-14691, 1999.
39. Majda, A. J., Timofeyev, I., and Vanden-Eijnden, E.: A mathematical framework for stochastic climate models, Commun. Pure Appl. Math., 54, 891-974, 2001.
40. Majda, A. J. and Wang, X.: Nonlinear Dynamics and Statistical Theories for Basic Geophysical Flows, Cambridge University Press, UK, 2006.
41. Marwan, N., Trauth, M., Vuille, M., and Kurths, J.: Comparing modern and Pleistocene ENSO-like influences in NW Argentina using nonlinear time series analysis methods, Clim. Dynam., 21, 317-326, 2003.
42. Matsumoto, K. and Tsuda, I.: Noise-induced order, J. Stat. Phys., 31, 87-106, 1983.
43. Mazzino, A., Musacchio, S., and Vulpiani, A.: Multiple scale analysis and renormalization for preasymptotic scalar transport, Phys. Rev.E, 71, 011113, 1-11, 2005.
44. McComb, W. D. and Kiyani, K.: Eulerian spectral closures for isotropic turbulence using a time-ordered fluctuation-dissipation relation, Phys. Rev. E, 72, 016309, 016309-1-016309-12, 2005.
45. Moeng, C.-H.: A Large-Eddy Simulation model for the study of planetary boundary layer turbulence, J. Atmos. Sci., 41, 2052-2062, 1984.
46. Moeng, C.-H. and Sullivan, P. P.: A comparison of shear and buoyancy driven planetary boundary layer flows, J. Atmos. Sci., 51, 999-1021, 1994.
47. North, G. R., Bell, R. E., and Hardin, J. W.: Fluctuation dissipation in a general circulation model, Clim. Dynam., 8, 259-264, 1993.
48. Paladin, G., Serva, M., and Vulpiani, A.: Complexity in dynamical systems with noise, Phys. Rev. Lett., 74, 66-69, 1995.
49. Paladin, G. and Vulpiani, A.: Anomalous scaling laws in multifractal objects, Phys. Rep., 156, 147-225, 1987.
50. Pasmanter, R. A.: On long-lived vortices in 2-D viscous flows, most probable states of inviscid 2-D flows and a soliton equation, Phys. Fluids, 6, 1236-1241, 1994.
51. Pikovsky, A., Rosenblum, M., and Kurths, J.: Synchronization: a universal concept in nonlinear sciences, Cambridge University Press, UK, 2003.
52. Rose, R. H. and Sulem, P. L.: Fully developed turbulence and statistical mechanics, J. Phys., 39, 441-484, 1978.
53. Ruelle, D.: General linear response formula in statistical mechanics, and the fluctuation-dissipation theorem far from equilibrium, Phys. Lett. A, 245, 220-224, 1998.
54. Sullivan, P. P., McWilliams, J.-C., and Moeng, C.-H.: A subgridscale model for large-eddy simulation of planetary boundary layer flows, Bound. Layer Meteorol., 71, 247-276, 1994.
55. Zeeman, E. C.: Stability of dynamical systems, Nonlinearity, 1, 115-135, 1988.