| Summary: | While the physics of the El Niño–Southern Oscillation (ENSO) phenomenon in the Tropical Pacific is quite well understood, there is still debate on several more fundamental aspects. The focus of this paper is on one of these issues that deals with whether ENSO variability, within the recharge-discharge oscillator theory arising from a stochastic Hopf bifurcation, is subcritical or supercritical. Using a Reservoir Computing method, we develop a criticality index as an indicator for the presence of a limit cycle in noisy time series. The utility of this index is shown in three members of a hierarchy of ENSO models: a conceptual box model, the classical Zebiak-Cane model and a state-of-the-art Global Climate Model. Finally, the criticality index is determined from observations, leading to the result that ENSO variability appears to be subcritical.
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