Sparsity-Promoting Dynamic Mode Decomposition Applied to Sea Surface Temperature Fields

Abstract: In this paper, we leverage Koopman mode decomposition to analyze the nonlinear and high-dimensional climate systems acting on the observed data space. The dynamics of atmospheric systems are assumed to be equation-free, with the linear evolution of observables derived from measured historical long-term time-series data snapshots, such as monthly sea surface temperature records, to construct a purely data-driven climate dynamics. In particular, sparsity-promoting dynamic mode decomposition is exploited to extract the dominant spatial and temporal modes, which are among the most significant coherent structures underlying climate variability, enabling a more efficient, interpretable, and low-dimensional representation of the system dynamics. We hope that the combined use of Koopman modes and sparsity-promoting techniques will provide insights into the significant climate modes, enabling reduced-order modeling of the climate system and offering a potential framework for predicting and controlling weather and climate variability.