ABSTRACT:
The climate is a complex, chaotic, non-equilibrium system featuring a limited horizon of predictability, variability on a vast range of temporal and spatial scales, instabilities resulting into energy transformations, and mixing and dissipative processes resulting into entropy production. Despite great progresses, we still do not have a complete theory of climate dynamics able to encompass instabilities, equilibration processes, and response to changing parameters of the system. We will outline some possible applications of the response theory developed by Ruelle for non-equilibrium statistical mechanical systems, showing how it allows for setting on firm ground and on a coherent framework concepts like climate sensitivity, climate response, and climate tipping points. We will show results for simple yet instructive models such as that presented by Lorenz in 1996, and for comprehensive global circulation models. The results are promising in terms of suggesting new ways for approaching the problem of climate change prediction and for using more efficiently the enormous amounts of data produced by modeling groups around the world. We will then show how response theory can be used for constructing parametrizations for multiscale systems, providing explicit formulas for the effective dynamics identical to what can be obtained using a perturbative Mori-Zwanzig approach. This might be relevant for constructing practical parametrizations for weather and climate models.
References
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J. Wouters, V. Lucarini, Multi-level dynamical systems: Connecting the Ruelle response theory and the Mori-Zwanzig approach. J. Stat. Phys. 151, 850-860 (2013)
V. Lucarini, R. Blender, C. Herbert, F. Ragone, S. Pascale, J. Wouters, Mathematical and Physical Ideas for Climate Science, Reviews of Geophysics doi: 10.1002/2013RG000446 (2014)
F. Ragone, V. Lucarini, F. Lunkeit, A new framework for climate sensitivity and prediction, arXiv:1403.4908 (2014)