  We study nonlinear dynamics of the Earth's tropical climate system. For that,
we apply 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 (temporal
patterns) of signals using eigenfunctions of Koopman operators governing the
evolution of observables in ergodic dynamical systems. We apply this technique
to a variety of tropical climate datasets and extract a multiscale hierarchy of
spatiotemporal patterns on diurnal to interannual timescales. In particular, we
detect without prefiltering the input data modes operating on intraseasonal and
shorter timescales that correspond to propagation of organized convection. We
discuss the salient properties of these propagating features and in particular
we focus on how the activity of certain types of these traveling patterns is
related to lower-frequency dynamics. As an extension of this work, we discuss
their potential predictability based on a range of nonparametric techniques and
potential advances related to understanding the deterministic and stochastic
aspects of the variability of these modes.
