Koopman operators and transfer operators transform nonlinear dynamics in phase space to linear dynamics on spaces of observables, enabling the use of spectral techniques without modeling constraints such as linearity. This framework can be used to perform feature extraction in nonlinear systems, where we can identify quasi-oscillatory spatial models that evolve coherently with distinct frequencies.
Data-driven approximations of the Koopman operator can be useful tools for the understanding and forecasting of the climate system, particularly its oscillatory components. I will discuss implementations of this technique in the tropical atmosphere, where we are to identify the Quasi-Biennial and Madden–Julian oscillations, and use these indices for improved analysis and prediction of these phenomena.
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