Predicting Climate Change Via the Fluctuation -Dissipation Theorem: A Practical Computational Strategy for Linear Response on a Chaotic Attractor

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The response of climate dynamics on the planetary scale to changes of various global physical parameters is an area which is being extensively studied in contemporary atmospheric and ocean science. The physical parameters controlling the planetary climate dynamics range from solar radiation, to volcanic activity, greenhouse gas, ozone, polar ice melting, and many others, which are normally modeled via direct numerical simulation for an appropriate climate model, which is typically a complex nonlinear partial differential equation or a system of such equations. In the context of the Fluctuation-Dissipation Theorem, the main idea is to model the statistical behavior of planetary climate dynamics under the tacit assumption that the dynamics is close to its statistical equilibrium, and then to apply the fluctuation-response formula, which is the key part of the Theorem, to predict the average climate response (the response of various statistical quantities of the climate state) to small changes of the physical parameters of the climate dynamics. Unlike a straightforward numerical simulation, this approach does not require one to actually simulate each appropriate scenario of climate development for various changes of parameters (which usually poses a computational problem of substantial complexity), instead providing the whole variety of possible responses to a wide range of small parameter changes for just a single numerical simulation with a climate model. Obviously, this latter property will facilitate climate response modeling to a great extent. However, the classical Fluctuation-Dissipation Theorem as formulated in statistical physics is not directly applicable to climate modeling due to the fundamental mathematical incompatibility of the statistical states of virtually all nontrivial climate models with the classical version of the Theorem. Here we propose a novel mathematical framework to perform climate response modeling with a suitably amended version of the Fluctuation-Dissipation Theorem, which is designed to circumvent these difficulties. However, this framework requires extensive further development of mathematical and computational approaches to become practically usable for climate response modeling. The detailed strategy for this development is set forth in the current proposal.