Extraction and classification of convectively coupled convective waves through eigendecomposition of Koopman operators

We study spatiotemporal patterns of convective organization using a recently developed technique for feature extraction and mode decomposition of spatiotemporal data generated by ergodic dynamical systems. The method relies on constructing low-dimensional representations (feature maps) of spatiotemporal signals using eigenfunctions of the Koopman operator governing the evolution of observables in ergodic dynamical systems. This operator is estimated from time-ordered unprocessed data through a Galerkin scheme applied to basis functions computed via the diffusion maps algorithm.

We apply this approach to brightness temperature data from the CLAUS archive and extract a multiscale hierarchy of spatiotemporal patterns on timescales spanning years to days, including the MJO but also traveling waves on temporal and spatial scales characteristic of convectively coupled equatorial waves (CCEWs). In particular, we find that the activity of certain types of CCEWs is modulated by intraseasonal modes such as the MJO and the boreal summer intraseasonal oscillation. We discuss various properties of waves in this hierarchy focusing on their association with the MJO structure and its temporal evolution.