Why El Niño Doesn't Stick to a Schedule ✎

Original: "Hidden and unstable periodic orbits as a result of homoclinic bifurcations in the Suarez-Schopf delayed oscillator and the irregularity of ENSO"
· Mikhail Anikushin, Andrey Romanov
arXiv:2102.11711 · 2021-02-23 · arXiv non-exclusive · independent analysis · 1 min
Even in a calm model of the ocean, several hidden rhythms lurk, and switching between them looks like chaos.

Every few years, the water off the coast of Peru turns unusually warm, an event known as El Niño. It doesn't stick to a schedule: sometimes it appears twice in a row, sometimes it vanishes for years. Previously, researchers blamed random wind gusts. New work shows that the irregularity may be built into the system itself, like several tunes playing in turn.

Imagine a swing. If you push it gently, it stops. Push hard, and it keeps swinging for a long time. The same goes for the El Niño model: there is a 'calm' zone where small disturbances fade away, but there are also hidden cycles that only start from a strong push. Scientists found such hidden cycles and showed that there are several. Switching between them looks like chaos, but in fact it is a deterministic process.

A hidden cycle in the El Niño model is like a swing that rocks itself, but only if pushed hard enough. A small push dies out, while a strong one sends the system into a sustained cycle that doesn't disappear.

This discovery changes the approach to forecasting. Even if we know the ocean's state precisely today, we cannot predict which hidden rhythm will kick in a year from now. So long-term El Niño forecasts will always carry an element of uncertainty, and that is not a data shortcoming but a property of the system itself.

The period of hidden oscillations in the model can vary from 3.85 to 5.37 years depending on parameters, which covers the observed range of real El Niño events.

\dot{x}(t) = x(t) - \alpha x(t-\tau) - x^3(t)
The rate of change of the temperature anomaly depends on the current value, the delayed value, and nonlinear damping.
Concepts
periodic orbit hopf bifurcation saddle node bifurcation El Niño-Southern Oscillation innermost stable circular orbit delayed oscillator theory