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

行星尺度上的气候动力学对各种全球物理参数变化的响应是当代大气和海洋科学中广泛研究的一个领域。控制行星气候动力学的物理参数范围从太阳辐射到火山活动、温室气体、臭氧、极地冰川融化和许多其他，这些通常是通过适当的气候模型的直接数值模拟来模拟的，这通常是一个复杂的非线性偏微分方程组或这样的方程组。在涨落耗散定理的背景下，其主要思想是在行星气候动力学接近其统计平衡的默示假设下模拟气候动力学的统计行为，然后应用涨落响应公式来预测平均气候响应(气候状态的各种统计量的响应)对气候动力学物理参数的微小变化的响应。与直接的数值模拟不同，这种方法不需要针对各种参数的变化实际模拟气候发展的每一种适当情景(这通常会带来相当复杂的计算问题)，而是仅针对气候模型的单一数值模拟提供对各种小参数变化的所有可能的响应。显然，后一种特性将在很大程度上促进气候响应建模。然而，统计物理中的经典涨落耗散定理并不直接适用于气候模拟，因为几乎所有非平凡气候模型的统计状态在数学上都与经典版的该定理不相容。在这里，我们提出了一种新的数学框架来执行气候响应建模，该框架使用适当修改的涨落耗散定理版本，旨在绕过这些困难。然而，这一框架需要广泛地进一步发展数学和计算方法，才能实际用于气候响应建模。目前的提案阐述了这一发展的详细战略。

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.