Climate variability through Koopman theory

The Earth's climate is a complex, nonlinear interplay of processes operating across a wide range of scales, giving rise to dynamic patterns of variability. Large-scale modes, such as ENSO, the Pacific Decadal Oscillation, and the North Atlantic Oscillation, play fundamental roles in shaping global climate conditions. Among these, ENSO is the dominant coupled atmosphere–ocean mode, driving global teleconnections that affect ecosystems, agriculture, and extreme events. Understanding and forecasting ENSO is therefore critical for improving climate resilience and sustainability. Traditional forecasting methods, including General Circulation Models, face limitations in simulating complex dynamics, such as ENSO. Simpler empirical approaches like Linear Inverse Models demonstrate notable skill, but rely on linear approximations which cannot fully capture its complexity. In this context, Koopman theory offers a powerful alternative, transforming nonlinear dynamics into a linear framework on a observables space, and enabling the identification of coherent structures and dominant modes within the system. This thesis applies Koopman theory to advance the understanding and predictability of ENSO and broader climate variability. Using kernel-Extended Dynamic Mode Decomposition, the study estimates Koopman spectra from tropical and global SST data. Key objectives include identifying stationary subspaces, linking dominant Koopman modes to relevant modes of climate variability, and evaluating the forecasting skill of Koopman-based methods. A new framework, Koopman Ensemble Forecasts, is proposed to address sensitivities to data record lengths, while the Residual DMD algorithm introduces an approach for assessing the reliability of Koopman modes. The findings of this thesis contribute to both fundamental and applied climate science. By addressing the structure of ENSO-related modes, this work deepens the understanding of its dynamics and highlights the potential of Koopman methods to enhance seasonal forecasting and the study of climate fluctuations. These results offer promising avenues for advancing data-driven climate modeling and developing robust tools for investigating climate variability and predictability.