Predictability of El Ni\~no as a Nonlinear Stochastic Limit Cycle

The El Ni\~no phenomenon, synonymously El Ni\~no-Southern Oscillation (ENSO), is an anomalous climatic oscillation in the Equatorial Pacific that occurs once every 3-8 years. It affects the earth's climate on a global scale. Whether it is a cyclic or a sporadic event, or whether its apparently random behaviour can be explained by stochastic dynamics have remained matters of debate. Herein ENSO is viewed, unconventionally, as a two-dimensional dynamical system on a desktop. The main features of ENSO: irregularity, interannual variability, and the asymmetry between El Ni\~no and La Ni\~na are captured, simply, comprehensibly, quickly and cheaply, in a nonlinear stochastic limit cycle paradigm. Its predictability for ENSO compares remarkably well with that of the best state-of-the-art complex models from the European and American meteorological centres. Additionally, for the first time, by analyzing subsurface Equatorial Pacific data since 1960, this model finds that long-term variations are not caused by ENSO itself, but by external sources.