Spectral analysis of climate dynamics with operator-theoretic approaches

Funding Information: This research was initiated during a 2-week visit of D.G. to UNSW in 2018, supported by GF’s Future Fellowship, and further developed during a 5-week visit by G.F. to NYU in 2019, supported by the UNSW Faculty of Science’s and School of Mathematics and Statistics’ Special Studies Program, and an ARC Discovery Project. G.F. also thanks the Courant Institute for hospitality during this visit. D.G. received support from NSF grants 1842538 and DMS 1854383 and ONR YIP grant N00014-16-1-2649. BRL and MP received support from NSF grant 1842543. J.S. received support from NSF grant 1842538. J.S. also acknowledges support from the core funding of the Helsinki Institute for Information Technology (HIIT) and the Institute for Basic Sciences (IBS), Republic of Korea, under IBS-R028-D1. Publisher Copyright: © 2021, The Author(s).The Earth’s climate system is a classical example of a multiscale, multiphysics dynamical system with an extremely large number of active degrees of freedom, exhibiting variability on scales ranging from micrometers and seconds in cloud microphysics, to thousands of kilometers and centuries in ocean dynamics. Yet, despite this dynamical complexity, climate dynamics is known to exhibit coherent modes of variability. A primary example is the El Niño Southern Oscillation (ENSO), the dominant mode of interannual (3–5 yr) variability in the climate system. The objective and robust characterization of this and other important phenomena presents a long-standing challenge in Earth system science, the resolution of which would lead to improved scientific understanding and prediction of climate dynamics, as well as assessment of their impacts on human and natural systems. Here, we show that the spectral theory of dynamical systems, combined with techniques from data science, provides an effective means for extracting coherent modes of climate variability from high-dimensional model and observational data, requiring no frequency prefiltering, but recovering multiple timescales and their interactions. Lifecycle composites of ENSO are shown to improve upon results from conventional indices in terms of dynamical consistency and physical interpretability. In addition, the role of combination modes between ENSO and the annual cycle in ENSO diversity is elucidated.Peer reviewe