EAGER: Understanding the Dynamics of Past, Present, and Future Climates on Subseasonal to Multidecadal Timescales Based on Operator-Theoretic Techniques for Dynamical Systems

该项目探索了库普曼进化算子在气候变异性研究中的应用。20世纪30年代初，库普曼算子被用来证明关于理想化动力系统行为的一个重要定理。但在动力系统理论之外，它们在很大程度上仍然鲜为人知，直到21世纪初，人们认识到它们对复杂的数据密集型问题的有用性。从那时起，它们被应用于流体流动、电力网络稳定性分析、金融交易算法开发和大脑活动研究等数据驱动的应用程序。与这些应用程序一样，气候研究通常是由数据驱动的，涉及到对复杂系统的分析，因此库普曼算子可能是气候研究工具包的一个有价值的补充。这里进行的研究将库普曼算子框架应用于气候动力学中的三个问题：1)了解厄尔尼诺在古气候和现代气候中的变异性和结构；2)气候系统中的十年尺度变率及其对可预报性的影响；以及3)南太平洋辐合带(SPCZ)在多个时间尺度上的动力学。这些领域的研究通常依靠主成分分析等方法来描述空间格局及其时间演变的可变性。但这些方法产生的统计特征不是基于动态的，对于将变异性模式与潜在的动态过程联系起来来说，可能并不是最佳的。库普曼操作员直接表达了系统的动态，因此他们可能会被证明更有洞察力，以理解气候系统的动态如何产生我们观察到的变化形式。这项工作具有更广泛的影响，因为它有可能加强对气候系统的理解，从而改善对关注气候影响的利益相关者和决策者的指导。此外，首席调查员(PI)与罗格斯科学与工程研究(RISE)计划合作，通过该计划，他接待了来自代表性不足群体的本科生。该项目还为博士后研究助理提供支持和培训，从而为这一研究领域的未来劳动力提供支持。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

This project explores the application of Koopman evolution operators to the study of climate variability. Koopman operators were derived in the early 1930s and used to prove an important theorem on the behavior of idealized dynamical systems. But they remained largely unknown beyond dynamical systems theory until the early 2000s, when their usefulness for complicated, data intensive problems was recognized. Since that time they have been applied in such data-driven applications as fluid flow, stability analysis in power networks, the development of financial trading algorithms, and brain activity research. Like these applications, climate research is often data-driven and involves analysis of a complex system, thus Koopman operators could be a valuable addition to the climate research toolkit.Research conducted here applies the Koopman operator framework to three problems in climate dynamics: 1) Understanding the variability and structure of El Nino in paleoclimate and current climate; 2) decadal-scale variability in the climate system and its implications for predictability; and 3) dynamics of the South Pacific Convergence Zone (SPCZ) across multiple timescales. Research in these areas typically relies on methods such as principle component analysis to characterize variability in terms of spatial patterns and their time evolution. But these methods yield statistical characterizations that are not dynamically based and may not be optimal for relating the variability patterns to underlying dynamical processes. Koopman operators directly express the dynamics of the system, thus they may prove more insightful for understanding how the dynamics of the climate system give rise to the forms of variability that we observe.The work has broader impacts through its potential to enhance understanding of the climate system and thus improve the guidance available to stakeholders and decision makers concerned with climate impacts. In addition, the Principal Investigator (PI) works with the Rutgers Research in Science and Engineering (RiSE) program, through which he hosts undergraduate students from underrepresented groups. The project also provides support and training for a postdoctoral research associate, thereby providing for the future workforce in this research area.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.