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Abstract: The climate belongs to the class of non-equilibrium forced and dissipativesystems, for which most results of quasi-equilibrium statistical mechanics,including the fluctuation-dissipation theorem, do not apply. We show for thefirst time how the Ruelle linear response theory, developed for studyingrigorously the impact of perturbations on general observables ofnon-equilibrium statistical mechanical systems, can be applied to analyze theclimatic response. We choose as test bed the Lorenz 96 model, which has awell-recognized prototypical value. We recapitulate the main aspects of theresponse theory and propose some new results. We then analyze the frequencydependence of the response of both local and global observables toperturbations with localized as well as global spatial patterns. We deriveanalytically the asymptotic behaviour, validity of Kramers-Kronig relations,and sum rules for the susceptibilities, and related them to parametersdescribing the unperturbed properties of the system. We verify the theoreticalpredictions from the outputs of the simulations with great precision. Thetheory is used to explain differences in the response of local and globalobservables, in defining the intensive properties of the system and ingeneralizing the concept of climate sensitivity to all time scales. We alsoshow how to reconstruct the linear Green function, which maps perturbations ofgeneral time patterns into changes in the expectation value of the consideredobservable. Finally, we propose a general methodology to study Climate Changeproblems by resorting to few, well selected simulations and discuss thespecific case of surface temperature response to changes of the $CO 2$concentration. This approach may provide a radically new perspective to studyrigorously the problem of climate sensitivity and climate change.



Autor: Valerio Lucarini, Stefania Sarno

Fuente: https://arxiv.org/







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