Estimation of the local response to a forcing in a high dimensional system using the fluctuation-dissipation theorem

Nonlinear Processes in Geophysics

Volumn 20, Issue 2, 2013, Pages 239-248

  Cooper, F C ^a   Esler, J G ^b   Haynes, P H ^c  

^a UNIVERSITY OF OXFORD   (United Kingdom)

^b UNIVERSITY COLLEGE LONDON   (United Kingdom)

^c UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHM; ATMOSPHERIC FORCING; EMPIRICAL ANALYSIS; ESTIMATION METHOD; NUMERICAL MODEL; STOCHASTICITY; THEORETICAL STUDY;

EID: 84879007307     PISSN: 10235809     EISSN: 16077946     Source Type: Journal    
DOI: 10.5194/npg-20-239-2013     Document Type: Article

References (19)

1. Abramov, R. V. and Majda, A. J.: Blended response algorithms for linear fluctuation-dissipation for complex nonlinear dynamical systems, Nonlinearity, 20, 2793-2821, doi:10.1088/0951-7715/20/12/004, 2007.
2. Boffetta, G., Lacorata, G., Musacchio, S., and Vulpiani, A.: Relaxation of finite perturbations: Beyond the fluctuation-response relation, Chaos, 13, 806-811, doi:10.1063/1.1579643, 2003. (Pubitemid 37180730)
3. Cooper, F. C. and Haynes, P. H.: Climate Sensitivity via a Nonparametric Fluctuation-Dissipation Theorem, J. Atmos. Sci., 68, 937-953, doi:10.1175/2010JAS3633.1, 2011.
4. Cooper, F. C. and Haynes, P. H.: Assessment of the fluctuationdissipation theorem as an estimator of the response of the tropospheric response to forcing, Q. J. Roy. Meteor. Soc., submitted, 2013.
5. Davies, T., Cullen, M. J. P., Malcolm, A. J., Mawson, M. H., Staniforth, A., White, A., and Wood, N.: A new dynamical core for the Met Office's global and regional modelling of the atmosphere, Q. J. Roy. Meteor. Soc., 131, 1759-1782, doi:10.1256/qj.04.101, 2005. (Pubitemid 41573492)
6. Eyink, G. L., Haine, T. W. N., and Lea, D. J.: Ruelle's linear response formula, ensemble adjoint schemes and Ĺevy flights, Nonlinearity, 17, 1867-1889, doi:10.1088/0951-7715/17/5/016, 2004. (Pubitemid 39289023)
7. Gritsun, A. and Branstator, G.: Climate Response Using a Three-Dimensional Operator Based on the Fluctuation-Dissipation Theorem, J. Atmos. Sci., 64, 2558-2575, doi:10.1175/JAS3943.1, 2007. (Pubitemid 47233151)
8. Joliffe, I. T.: Principal Component Analysis, Springer Series in Statistics, 2nd Edn., 2002.
9. Lacorata, G. and Vulpiani, A.: Fluctuation-Response Relation and modeling in systems with fast and slow dynamics, Nonlin. Processes Geophys., 14, 681-694, doi:10.5194/npg-14-681-2007, 2007. (Pubitemid 350025435)
10. Lorenz, E. N.: Predictability: a problem partly solved, Proceedings from the ECMWF Seminar on Predictability, volume Vol. I, ECMWF, Reading, UK, 1995.
11. Lucarini, V. and Sarno, S.: A statistical mechanical approach for the computation of the climatic response to general forcings, Nonlin. Processes Geophys., 18, 7-28, doi:10.5194/npg-18-7-2011, 2011.
12. Majda, A. J., Gershgorin, B., and Yuan, Y.: Low-Frequency Climate Response and Fluctuation-Dissipation Theorems: Theory and Practice, J. Atmos. Sci., 67, 1186-1201, doi:10.1175/2009JAS3264.1, 2010.
13. Marconi, U. M. B., Puglisi, A., Rondoni, L., and Vulpiani, A.: Fluctuation-dissipation: Response theory in statistical physics, Physics Reports, 461, 111-195, doi:10.1016/j.physrep.2008.02.002, 2008.
14. Matsumoto, M. and Nishimura, T.: Mersenne Twister: A 623-dimensionally equidistributed uniform pseudorandom number generator, ACM T. Model. Comput. S., 8, 3-30, 1998.
15. Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P.: Numerical Recipes in C++: The Art of Scientific Computing, Cambridge University Press, UK, 2002.
16. Ring, M. and Plumb, R. A.: The Response of a Simplified GCM to Axisymmetric Forcings: Applicability of the Fluctuation-Dissipation Theorem, J. Atmos. Sci., 65, 3880-3898, doio:10.1175/2008JAS2773.1, 2008.
17. Ruelle, D.: General linear response formula in statistical mechanics, and the fluctuation-dissipation theorem far from equilibrium, Phys. Lett. A, 245, 220-224, doi:10.1016/S0375-9601(98)00419-8, 1998. (Pubitemid 128399519)
18. R̈umelin,W.: Numerical Treatment of Stochastic Differential Equations, SIAM J. Numer. Anal., 19, 604-613, 1982.
19. Silverman, B. W.: Density Estimation for Statistics and Data Analysis, Mg. Stat. Pro., Vol. 26, Chapman and Hall, 1986.