Department of Atmospheric and Oceanic Sciences and Institute of Geophysics and Planetary Physics, University of California, Los Angeles, CA 90095.
Proc Natl Acad Sci U S A. 2014 Feb 4;111(5):1684-90. doi: 10.1073/pnas.1321816111. Epub 2014 Jan 17.
Despite the importance of uncertainties encountered in climate model simulations, the fundamental mechanisms at the origin of sensitive behavior of long-term model statistics remain unclear. Variability of turbulent flows in the atmosphere and oceans exhibits recurrent large-scale patterns. These patterns, while evolving irregularly in time, manifest characteristic frequencies across a large range of time scales, from intraseasonal through interdecadal. Based on modern spectral theory of chaotic and dissipative dynamical systems, the associated low-frequency variability may be formulated in terms of Ruelle-Pollicott (RP) resonances. RP resonances encode information on the nonlinear dynamics of the system, and an approach for estimating them--as filtered through an observable of the system--is proposed. This approach relies on an appropriate Markov representation of the dynamics associated with a given observable. It is shown that, within this representation, the spectral gap--defined as the distance between the subdominant RP resonance and the unit circle--plays a major role in the roughness of parameter dependences. The model statistics are the most sensitive for the smallest spectral gaps; such small gaps turn out to correspond to regimes where the low-frequency variability is more pronounced, whereas autocorrelations decay more slowly. The present approach is applied to analyze the rough parameter dependence encountered in key statistics of an El-Niño-Southern Oscillation model of intermediate complexity. Theoretical arguments, however, strongly suggest that such links between model sensitivity and the decay of correlation properties are not limited to this particular model and could hold much more generally.
尽管气候模式模拟中存在不确定性很重要，但长期模式统计数据敏感行为的根本机制仍不清楚。大气和海洋中湍流的可变性表现出周期性的大规模模式。这些模式虽然不规则地随时间演变，但在很大的时间尺度范围内表现出特征频率，从季节内到十年际。基于混沌和耗散动力系统的现代谱理论，可以用瑞利-波利科特（Ruelle-Pollicott，RP）共振来表述相关的低频可变性。RP 共振编码了系统非线性动力学的信息，并且提出了一种通过系统的可观测量来估计它们的方法。该方法依赖于与给定可观测量相关的动力学的适当马尔可夫表示。结果表明，在该表示中，谱隙（定义为次主导 RP 共振与单位圆之间的距离）在参数依赖性的粗糙度中起着重要作用。对于最小的谱隙，模型统计数据最敏感；这种小的间隙与低频可变性更明显的情况相对应，而自相关则衰减得更慢。本方法应用于分析中间复杂度厄尔尼诺-南方涛动模型的关键统计数据中遇到的粗糙参数依赖性。然而，理论论证强烈表明，模型敏感性与相关性衰减之间的这种联系不仅限于这个特定的模型，而且可能具有更普遍的适用性。
