Extracting transient Koopman modes from short-term weather simulations with sparsity-promoting dynamic mode decomposition

Abstract

Convective features, represented here as warm bubble-like patterns, reveal essential high-level information about how short-term weather dynamics evolve within a high-dimensional state space. In this paper, we introduce a data-driven framework that uncovers transient dynamics captured by Koopman modes responsible for these structures and traces their emergence, growth, and decay. Our approach applies the sparsity-promoting dynamic mode decomposition to weather simulations, yielding a few number of selected modes whose sparse amplitudes highlight dominant transient structures. By tuning the sparsity weight, we balance reconstruction accuracy and model complexity. We illustrate the methodology on weather simulations, using the magnitude of velocity and vorticity fields as distinct observable datasets. The resulting sparse dominant Koopman modes capture the transient evolution of bubble-like pattern and can reduce the dimensionality of weather system model, offering an efficient surrogate for diagnostic and forecasting tasks.