Ocean Swings Connected by a Spring ✎

Original: "Coexistence of attractors in a coupled nonlinear delayed system modelling El Niño Southern Oscillations"
arXiv:1707.09853 · 2017-07-28 · arXiv non-exclusive · independent analysis · 1 min
Two regions of the Pacific Ocean can together generate El Niño, even if one of them would not oscillate on its own.

Two pendulums hang side by side, with a spring stretched between them. One might stay still on its own, but if the other swings, the spring transmits a nudge, and the first one starts swinging too.

Two regions of the Pacific Ocean work the same way. They exchange heat through waves that travel from one shore to the other. One wave is fast, the other slow, and this time difference acts like a spring. The scientists captured this in an equation and used a computer to see what happens for different coupling strengths.

Key finding: if one region tends toward stillness on its own while the other oscillates, the coupling makes both oscillate. But if the coupling is too strong, both pendulums freeze, and El Niño disappears.

Previously, scientists thought the influence of a neighboring region was random noise, like gusts of wind. Now it turns out to be a regular mechanism: one region nudges the other, and that changes the whole picture. Instead of a single threshold of 0.5 °C, they now suggest looking at a range: from 0.5 to 1.6 °C in the first region and from -0.06 to 2 °C in the second.

So two pendulums on a wall teach each other to swing, and the Pacific Ocean follows the same rules.

Kelvin and Rossby waves, which carry heat across the Pacific, travel at different speeds: the fast Kelvin wave crosses 13,350 km in 110 days, while the slow Rossby wave takes 329 days. This difference creates the delay needed for oscillations.

In Kim Stanley Robinson's novel 'Forty Signs of Rain', climate models predict abrupt changes in ocean currents. Here a similar idea appears: small changes in initial conditions can switch the system between states, as in scenarios of climate surprises.

\frac{dT}{dt} = T - T^3 - \alpha T(t-\delta)
The rate of temperature change depends on the current value, nonlinear damping, and the past value with delay δ.
\begin{aligned}\frac{dT_1}{dt} &= T_1 - T_1^3 - \alpha_1 T_1(t-\delta_1) + \gamma T_2 \\ \frac{dT_2}{dt} &= T_2 - T_2^3 - \alpha_2 T_2(t-\delta_2) + \gamma T_1\end{aligned}
Each region is described by the same equation, but with linear coupling γ to the neighboring region.
Concepts
ENSO El Niño-Southern Oscillation Jin-Timmermann model recharge oscillator model El Niño index Southern Oscillation La Niña Multivariate ENSO Index ERSST spring predictability barrier TAO/TRITON moorings relative ONI sea surface temperature Warm water volume natural variability ocean-atmosphere coupling equatorial wave propagation Westerly wind burst mixed mode oscillations sea surface temperature anomaly