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| Titel |
A statistical mechanical approach for the computation of the climatic response to general forcings |
| VerfasserIn |
V. Lucarini, S. Sarno |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
1023-5809
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| Digitales Dokument |
URL |
| Erschienen |
In: Nonlinear Processes in Geophysics ; 18, no. 1 ; Nr. 18, no. 1 (2011-01-12), S.7-28 |
| Datensatznummer |
250013864
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| Publikation (Nr.) |
 copernicus.org/npg-18-7-2011.pdf |
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| Zusammenfassung |
| 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. In this paper 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 with great
success to analyze the climatic response to general forcings. The crucial
value of the Ruelle theory lies in the fact that it allows to compute the
response of the system in terms of expectation values of explicit and
computable functions of the phase space averaged over the invariant measure
of the unperturbed state. We choose as test bed a classical version of the
Lorenz 96 model, which, in spite of its simplicity, has a well-recognized
prototypical value as it is a spatially extended one-dimensional model and
presents the basic ingredients, such as dissipation, advection and the
presence of an external forcing, of the actual atmosphere. We recapitulate
the main aspects of the general response theory and propose some new general
results. We then analyze the frequency dependence of the response of both
local and global observables to perturbations having localized as well as
global spatial patterns. We derive analytically several properties of the
corresponding susceptibilities, such as asymptotic behavior, validity of
Kramers-Kronig relations, and sum rules, whose main ingredient is the
causality principle. We show that all the coefficients of the leading
asymptotic expansions as well as the integral constraints can be written as
linear function of parameters that describe the unperturbed properties of the
system, such as its average energy. Some newly obtained empirical closure
equations for such parameters allow to define such properties as an explicit
function of the unperturbed forcing parameter alone for a general class of
chaotic Lorenz 96 models. We then verify the theoretical predictions from the
outputs of the simulations up to a high degree of precision. The theory is
used to explain differences in the response of local and global observables,
to define the intensive properties of the system, which do not depend on the spatial resolution of the Lorenz
96 model, and to generalize 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 for finite as well as infinite time. Finally, we propose a simple
yet general methodology to study general Climate Change problems on virtually
any time scale by resorting to only well selected simulations, and by taking
full advantage of ensemble methods. The specific case of globally averaged
surface temperature response to a general pattern of change of the CO2
concentration is discussed. We believe that the proposed approach may
constitute a mathematically rigorous and practically very effective way to
approach the problem of climate sensitivity, climate prediction, and climate
change from a radically new perspective. |
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