MERCREDI 13 OCTOBRE 2010
11 heures
Salle Séminaire 5
Centre de Physique Théorique
Marseille-Luminy

Valerio Lucarini

Title: A Statistical Mechanical Approach for the Computation of the Climatic
Response to General Forcings

Abstract: The climate belongs to the class of non-equilibrium forced and
dissipative systems, for which most results of quasi-equilibrium
statistical mechanics, including the fluctuation-dissipation theorem,
do not apply. We show for the first time how the Ruelle linear
response theory, developed for studying rigorously the impact of
perturbations on general observables of non-equilibrium statistical
mechanical systems, can be applied to analyze the climatic response.
We choose as test bed the Lorenz 96 model, which has a well-recognized
prototypical value. We recapitulate the main aspects of the response
theory and propose some new results. We then analyze the frequency
dependence of the response of both local and global observables to
perturbations with localized as well as global spatial patterns. We
derive analytically the asymptotic behaviour, validity of
Kramers-Kronig relations, and sum rules for the susceptibilities, and
related them to parameters describing the unperturbed properties of
the system. We verify the theoretical predictions from the outputs of
the simulations with great precision. The theory is used to explain
differences in the response of local and global observables, in
defining the intensive properties of the system and in generalizing
the concept of climate sensitivity to all time scales. We also show
how to reconstruct the linear Green function, which maps perturbations
of general time patterns into changes in the expectation value of the
considered observable. Finally, we propose a general methodology to
study Climate Change problems by resorting to few, well selected
simulations and discuss the specific case of surface temperature
response to changes of the CO_2 concentration. This approach may
provide a radically new perspective to study rigorously the problem of
climate sensitivity and climate change