Froyland Gary, Giannakis Dimitrios, Luna Edoardo, Slawinska Joanna
School of Mathematics and Statistics, University of New South Wales, Sydney, NSW, 2052, Australia.
Department of Mathematics, Dartmouth College, Hanover, NH, 03755, USA.
Nat Commun. 2024 May 20;15(1):4268. doi: 10.1038/s41467-024-48033-6.
An important problem in modern applied science is to characterize the behavior of systems with complex internal dynamics subjected to external forcings. Many existing approaches rely on ensembles to generate information from the external forcings, making them unsuitable to study natural systems where only a single realization is observed. A prominent example is climate dynamics, where an objective identification of signals in the observational record attributable to natural variability and climate change is crucial for making climate projections for the coming decades. Here, we show that operator-theoretic techniques previously developed to identify slowly decorrelating observables of autonomous dynamical systems provide a powerful means for identifying nonlinear trends and persistent cycles of non-autonomous systems using data from a single trajectory of the system. We apply our framework to real-world examples from climate dynamics: Variability of sea surface temperature over the industrial era and the mid-Pleistocene transition of Quaternary glaciation cycles.
现代应用科学中的一个重要问题是刻画具有复杂内部动力学的系统在外部强迫作用下的行为。许多现有方法依靠系综从外部强迫中生成信息，这使得它们不适用于研究仅观察到单个实现的自然系统。一个突出的例子是气候动力学，在其中客观识别观测记录中可归因于自然变率和气候变化的信号对于进行未来几十年的气候预测至关重要。在这里，我们表明，先前开发的用于识别自治动力系统中缓慢去相关可观测量的算子理论技术，为使用来自系统单个轨迹的数据识别非自治系统的非线性趋势和持续周期提供了一种强大的手段。我们将我们的框架应用于气候动力学的实际例子：工业时代海表面温度的变率以及第四纪冰川周期的中更新世过渡。
