Low dimensional chaos explains ENSO asymmetry and period

Fundamental features of the El Niño-Southern Oscillation (ENSO) phenomenon, such as its 4 year period and its asymmetric temporal evolution, remain poorly understood despite decades of research. We study the chaotic dynamics of ENSO by reconstructing its phase space using high frequency sea-surface temperature observations. We find that ENSO’s strange attractor can be characterized by a set of unstable periodic orbits, with periods of 1-4 years. By visiting these orbits the system rapidly explores the warm region of the phase space (El Niño to La Niña transitions) and slowly visits the cold region of the phase space (La Niña to El Niño transitions), which leads to the attractor to curl in a specific way. Based on this result we propose that ENSO dynamics can be modeled with a periodically forced Takens-Bogdanov bifurcation. The asymmetric oscillation obtained with the Takens-Bogdanov bifurcation mathematically models the thermocline coupling and the periodic forcing the influence of the annual cycle. This low-dimensional chaotic system explains the occurrence of multi-year La Niñas and the mean period of 4 years of the oscillation. The proposed dynamics is consistent with previous studies, which show that the annual cycle can synchronize with the slow decay of La Niña, which is in turn controlled by the nonlinearity of the thermocline feedback. We find that the majority of the state-of-the-art CMIP models present an accurate ENSO dynamics, which we show by analyzing the topology of their ENSO phase space and comparing it to the observed. Differences among models are associated with the persistence of the unstable periodic orbits and the interplay between chaotic behavior and noise, which characterizes the complexity of the resulting signal. These different behaviors can be modeled with the same low dimensional model under slightly different forcing parameters, thus, the proposed underlying dynamics is appropriate to describe all model behaviors.