Two Pacific Ocean Pendulums: How Linked Regions Give Birth to and Quench El Niño ✎

Original: "Effect of Heterogeneity in Models of El-Niño Southern Oscillations"
arXiv:1705.08171 · 2017-05-23 · arXiv non-exclusive · independent analysis · 2 min
Two regions of the Pacific Ocean, coupled like pendulums joined by a spring, can swing each other up or grind to a halt together.

Two pendulums hang side by side, connected by a spring. Give one a push, and through the spring the other starts to swing. That's how the two regions of the equatorial Pacific are arranged, where sea-surface temperature rises and falls in the rhythm of El Niño.

Each region on its own resembles a pendulum with a delay: the water warms, the warm current drifts west, and a few months later a wave returns to cool the surface. The return time ranges from 237 to 439 days, depending on the basin's width. When the regions are linked, as if by a spring, one can pass its rhythm to the other.

Since 1899, 29 El Niño events have been recorded, with an average interval of about 3.7 years, but the gaps jump from two to seven years.

The scientists built a model of two coupled pendulums with different delays and self-damping strengths. It turns out that a too-stiff spring, meaning strong coupling between the regions, damps oscillations in both: the pendulums freeze. A weak spring, by contrast, lets the region with the longer delay swing its neighbor, which on its own would have settled long ago. That's how irregular but persistent temperature oscillations arise.

Moreover, the regions don't have to be identical. If their parameters differ, more often than not one pendulum freezes while the other keeps swinging, or both come to rest at different positions. When oscillations do occur, their period is shared by both, even if the delays differ.

Previously, El Niño's irregularity was blamed on random atmospheric noise. The new model shows that a complex pattern can emerge on its own, from the coupling of two dissimilar regions.

This work changes how we view the predictability of climate oscillations. If the ocean's two pendulums are weakly linked, the system stays sensitive to the slightest nudges without falling apart. Understanding which regions influence each other more strongly will help climatologists better interpret observational data and anticipate where synchronous temperature anomalies might appear. The pendulum analogy brings us back to a simple rule: sometimes, to make a system oscillate, you need to weaken the coupling, not strengthen it.

Since 1899, 29 El Niño events have been recorded, giving an average period of about 3.7 years, though intervals range from two to seven years.

\frac{dT}{dt} = T - T^3 - \alpha T(t-\delta)
The rate of change of temperature anomaly is determined by positive feedback (T), cubic damping (-T^3), and delayed negative feedback (-\alpha T(t-\delta)).
\frac{dT_1}{dt} = T_1 - T_1^3 - \alpha_1 T_1(t-\delta_1) + \gamma T_2, \quad \frac{dT_2}{dt} = T_2 - T_2^3 - \alpha_2 T_2(t-\delta_2) + \gamma T_1
Each region is described by the same equation as the single oscillator, but with an additional linear coupling term (\gamma T_j) modeling energy flux between regions.
Concepts
El Niño-Southern Oscillation ENSO Southern Oscillation recharge oscillator model Jin-Timmermann model Multivariate ENSO Index El Niño index La Niña spring predictability barrier ocean-atmosphere coupling TAO/TRITON moorings Bjerknes feedback North Equatorial Countercurrent equatorial wave propagation Indian Ocean capacitor effect Westerly wind burst mixed mode oscillations ERSST delayed oscillator theory Warm water volume