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

本项目探讨Koopman演化算子在气候变率研究中的应用。库普曼算子在20世纪30年代早期被推导出来，并被用来证明关于理想动力系统行为的一个重要定理。但直到21世纪初，它们在动力系统理论之外的大部分领域仍不为人所知，直到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，它们被应用于数据驱动的应用，如流体流动、电网稳定性分析、金融交易算法的开发和大脑活动研究。与这些应用程序一样，气候研究通常是数据驱动的，涉及对复杂系统的分析，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。本文将Koopman算子框架应用于气候动力学中的三个问题：1)理解厄尔尼诺在古气候和现代气候中的变率和结构；2)气候系统的年代际变率及其对可预测性的影响；3)南太平洋辐合带（SPCZ）多时间尺度的动力学特征。这些领域的研究通常依靠诸如主成分分析等方法来描述空间格局及其时间演变方面的变异性。但是，这些方法产生的统计特征不是基于动态的，并且可能不是将变异性模式与潜在的动态过程联系起来的最佳方法。库普曼算符直接表达了系统的动力学，因此它们对于理解气候系统的动力学如何引起我们所观察到的变率形式可能更有洞察力。这项工作具有更广泛的影响，因为它有可能增进对气候系统的了解，从而改善有关气候影响的利益攸关方和决策者可获得的指导。此外，首席研究员（PI）与罗格斯大学科学与工程研究（RiSE）项目合作，通过该项目，他接待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，从而为该研究领域的未来劳动力提供支持。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值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.