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Abstract The Earth’s climate system is a classical example of a multiscale, multiphysics dynamical system with an extremely large number of active degrees of freedom, exhibiting variability on scales ranging from micrometers and seconds in cloud microphysics, to thousands of kilometers and centuries in ocean dynamics. Yet, despite this dynamical complexity, climate dynamics is known to exhibit coherent modes of variability. A primary example is the El Niño Southern Oscillation (ENSO), the dominant mode of interannual (3–5 yr) variability in the climate system. The objective and robust characterization of this and other important phenomena presents a long-standing challenge in Earth system science, the resolution of which would lead to improved scientific understanding and prediction of climate dynamics, as well as assessment of their impacts on human and natural systems. Here, we show that the spectral theory of dynamical systems, combined with techniques from data science, provides an effective means for extracting coherent modes of climate variability from high-dimensional model and observational data, requiring no frequency prefiltering, but recovering multiple timescales and their interactions. Lifecycle composites of ENSO are shown to improve upon results from conventional indices in terms of dynamical consistency and physical interpretability. In addition, the role of combination modes between ENSO and the annual cycle in ENSO diversity is elucidated. 

Understanding multiscale rainfall variability in the South Pacific convergence zone (SPCZ), a southeastward-oriented band of precipitating deep convection in the South Pacific, is critical for both the human and natural systems dependent on its rainfall, and for interpreting similar off-equatorial diagonal convection zones around the globe. A k-means clustering method is applied to daily austral summer (December–February) Tropical Rainfall Measuring Mission (TRMM) satellite rainfall to extract representative spatial patterns of rainfall over the SPCZ region for the period 1998–2013. For a k = 4 clustering, pairs of clusters differ predominantly via spatial translation of the SPCZ diagonal, reflecting either warm or cool phases of El Niño–Southern Oscillation (ENSO). Within each of these ENSO phase pairs, one cluster exhibits intense precipitation along the SPCZ while the other features weakened rainfall. Cluster temporal behavior is analyzed to investigate higher-frequency forcings (e.g., the Madden–Julian oscillation and synoptic-scale disturbances) that trigger deep convection where SSTs are sufficiently warm. Pressure-level winds and specific humidity from the Climate Forecast System Reanalysis are composited with respect to daily cluster assignment to investigate differences between active and quiescent SPCZ conditions to reveal the conditions supporting enhanced or suppressed SPCZ precipitation, such as low-level poleward moisture transport from the equator. Empirical orthogonal functions (EOFs) of TRMM precipitation are computed to relate the “modal view” of SPCZ variability associated with the EOFs to the “state view” associated with the clusters. Finally, the cluster number is increased to illustrate the change in TRMM rainfall patterns as additional degrees of freedom are permitted.