Spectral analysis of climate dynamics with operator-theoretic approaches

Gary Froyland,Benjamin R Lintner,Dimitrios Giannakis,Joanna Slawinska,Maxwell Pike

doi:10.1038/s41467-021-26357-x

Abstract

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.

Highlights

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
Our goal is to identify a collection of observables gj : Ω ! C with two main features: cyclicity and slow correlation decay
The observables are cyclic in the sense that there is an associated period over which they approximately return to their original values

Summary

Introduction

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. It is desirable that a climatic index be as objective as possible, i.e., reveal an intrinsic pattern of climate dynamics independent of subjective choices such as data prefiltering, or details of the observation modality For oscillatory patterns such as ENSO and MJO, it is important that the indices reveal the full cycle as a sequence of observables, e.g., SST fields in the case of ENSO. We show that the operator-theoretic framework provides an effective route for identifying slowly decaying (equivalently, slowly decorrelating) observables of the climate system as dominant eigenfunctions of transfer/Koopman operators and their generator These eigenfunctions directly describe coherent climate phenomena such as ENSO, with higher dynamical consistency and physical interpretability than indices derived through conventional approaches. Complex pairs of eigenvalues and their eigenvectors directly reveal persistent cycles (see outer panels of Fig. 1) and their periods

Objectives

Methods

Results

Conclusion