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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union
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Volume 14, issue 5 | Copyright
Nonlin. Processes Geophys., 14, 681-694, 2007
https://doi.org/10.5194/npg-14-681-2007
© Author(s) 2007. This work is licensed under
the Creative Commons Attribution-NonCommercial-ShareAlike 2.5 License.

  31 Oct 2007

31 Oct 2007

Fluctuation-Response Relation and modeling in systems with fast and slow dynamics

G. Lacorata1 and A. Vulpiani2 G. Lacorata and A. Vulpiani
  • 1Institute of Atmospheric and Climate Sciences, National Research Council, Str. Monteroni, 73100 Lecce, Italy
  • 2Department of Physics and INFN, University of Rome "La Sapienza", P.le A. Moro 2, 00185 Roma, Italy

Abstract. We show how a general formulation of the Fluctuation-Response Relation is able to describe in detail the connection between response properties to external perturbations and spontaneous fluctuations in systems with fast and slow variables. The method is tested by using the 360-variable Lorenz-96 model, where slow and fast variables are coupled to one another with reciprocal feedback, and a simplified low dimensional system. In the Fluctuation-Response context, the influence of the fast dynamics on the slow dynamics relies in a non trivial behavior of a suitable quadratic response function. This has important consequences for the modeling of the slow dynamics in terms of a Langevin equation: beyond a certain intrinsic time interval even the optimal model can give just statistical prediction.

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