Spectral analysis of climate dynamics with operator-theoretic approaches

We present a framework based on operator-theoretic techniques from ergodic theory, combined with methods from data science, to identify modes of variability of the climate system with two main features: slow correlation decay and cyclicity. These modes are approximate eigenfunctions of Koopman evolution operators, estimated from high-dimensional time series data using kernel methods. We discuss methodological aspects of this approach, and present applications to identification of coherent modes of climate dynamics on seasonal to interannual timescales, focusing on ENSO and its teleconnections to Antarctic circumpolar waves