[论文解读] Climate dynamics and fluid mechanics: Natural variability and related uncertainties

Michael Ghil, Mickaël D. Chekroun+1 more|Jun 15, 2010

Quantum chaos and dynamical systems被引用 23

一句话总结

该论文提出了一种随机动力系统框架，通过随机共轭对一般环流模型（GCMs）进行分类，利用圆映射中共振结构的噪声诱导平滑效应，减少气候预测中的不确定性。结果表明，噪声可使拓扑上不同的确定性系统归入同一随机类，从而实现稳健的模型比较，并有望降低气候建模中的不确定性。

ABSTRACT

The purpose of this review-and-research paper is twofold: (i) to review the role played in climate dynamics by fluid-dynamical models; and (ii) to contribute to the understanding and reduction of the uncertainties in future climate-change projections. To illustrate the first point, we focus on the large-scale, wind-driven flow of the mid-latitude oceans which contribute in a crucial way to Earth's climate, and to changes therein. We study the low-frequency variability (LFV) of the wind-driven, double-gyre circulation in mid-latitude ocean basins, via the bifurcation sequence that leads from steady states through periodic solutions and on to the chaotic, irregular flows documented in the observations. This sequence involves local, pitchfork and Hopf bifurcations, as well as global, homoclinic ones. The natural climate variability induced by the LFV of the ocean circulation is but one of the causes of uncertainties in climate projections. Another major cause of such uncertainties could reside in the structural instability in the topological sense, of the equations governing climate dynamics, including but not restricted to those of atmospheric and ocean dynamics. We propose a novel approach to understand, and possibly reduce, these uncertainties, based on the concepts and methods of random dynamical systems theory. As a very first step, we study the effect of noise on the topological classes of the Arnol'd family of circle maps, a paradigmatic model of frequency locking as occurring in the nonlinear interactions between the El Nino-Southern Oscillations (ENSO) and the seasonal cycle. It is shown that the maps' fine-grained resonant landscape is smoothed by the noise, thus permitting their coarse-grained classification. This result is consistent with stabilizing effects of stochastic parametrization obtained in modeling of ENSO phenomenon via some general circulation models.

研究动机与目标

• 解决尽管建模技术不断进步，气候变迁预测的不确定性范围仍在持续扩大的问题。
• 研究气候方程中的结构性不稳定性如何导致预测不确定性。
• 基于随机动力系统理论，为GCM族开发一种新颖的随机分类方法。
• 探讨噪声是否能平滑细尺度共振结构（如阿诺德舌），从而实现气候模型的粗粒度分类。
• 检验随机共轭是否能在噪声作用下，识别出原本不同的GCM之间具有拓扑等价行为的系统。

提出的方法

• 应用随机共轭方法比较不同GCM之间的气候模拟结果，将它们视为随机动力系统。
• 使用阿诺德族圆映射作为模型系统，研究加性噪声对共振结构的影响。
• 分析噪声如何平滑圆映射的细粒度共振景观（魔鬼阶梯），从而实现粗粒度分类。
• 采用李雅普诺夫指数分析和随机吸引子理论，评估噪声下的稳定性与双曲性。
• 应用随机动力系统的哈特曼-格罗布曼定理，建立非线性与线性化协边丛之间的全局共轭关系。
• 利用集合 $ C_{AB} $ 为余边界这一条件，确定在随机扰动下的拓扑等价性。

实验结果

研究问题

• RQ1 动力系统中共振结构的噪声诱导平滑是否能实现对气候模型的稳健、粗粒度分类？
• RQ2 加性噪声在多大程度上可使拓扑上不同的确定性系统归入同一随机类？
• RQ3 噪声强度如何影响圆映射中锁定周期态的鲁棒性？
• RQ4 随机共轭是否可用于识别尽管结构不同但具有等价动力学行为的GCM族？
• RQ5 GCM中随机参数化的形式是否显著影响其在随机分类框架中气候模拟的接近程度？

主要发现

• 噪声平滑了圆映射的细粒度共振结构（如阿诺德舌），使得原本拓扑上不同的系统可实现粗粒度分类。
• 足够高的噪声水平可破坏周期锁定，使旋转数变为无理数，系统进入严格负李雅普诺夫指数状态。
• 在强噪声下，随机吸引子退化为随机不动点，且该点处的线性化协边丛具有双曲性，从而可通过哈特曼-格罗布曼定理实现全局共轭。
• 当噪声为加性且保向时，集合 $ C_{AB} $ 为余边界，可应用定理B.3，建立非等价确定性系统间的随机共轭。
• 两个具有不同确定性动力学的GCM在适当噪声下可落入同一拓扑随机类，暗示了模型族分类的可能路径。
• GCM中随机参数化的具体形式至关重要：不同噪声模型可改变分类结果，强调了需谨慎设计参数化方案。