Koopman Operator Methods for Analysis of Tropical Climate Variability

Explore Koopman operator methods for analyzing tropical climate variability in this 48-minute conference talk by Claire Valva from the California Institute of Technology, presented at IPAM's Mathematics and Machine Learning for Earth System Simulation Workshop. Learn how 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. Discover how this framework performs feature extraction in nonlinear systems by identifying quasi-oscillatory spatial models that evolve coherently with distinct frequencies. Examine data-driven approximations of the Koopman operator as useful tools for understanding and forecasting climate systems, particularly their oscillatory components. Focus on implementations in the tropical atmosphere where these techniques identify the Quasi-Biennial and Madden–Julian oscillations, and understand how these indices enable improved analysis and prediction of these phenomena. Gain insights into advanced mathematical approaches that bridge machine learning and climate science for better earth system simulation and prediction capabilities.