Atmosphere Ocean Science Friday Seminar

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Data-driven approximation of Koopman operators for analysis of climate variability

Speaker: Claire Valva, CAOS

Location: Warren Weaver Hall 1314

Date: Friday, April 22, 2022, 4 p.m.

Notes:

We often wish to identify and characterize coherent modes of climate variability — such as the El Niño-Southern Oscillation or the Quasi-Biennial Oscillation (QBO) — to improve our understanding and prediction of the earth system. Koopman operator-theoretic formalism can be used as an approach for coherent feature extraction in dynamical systems and is particularly well suited for quasi-oscillatory features such as the QBO. In this talk, I will discuss the spectral decomposition of Koopman operators, including current work in which I approximate the Koopman generator by a “compactification” of its resolvent. The extraction of approximate Koopman eigenfunctions (and the associated eigenfrequencies) from an unknown system without spectral pollution can be a nontrivial task, particularly if the system has mixed or dense spectra. I will also explore implementation of these techniques using data (i.e. observables sampled along dynamical trajectories) and show how we can use these techniques to begin to detect and characterize the QBO.