Two Ocean Pendulums Sing in Unison ✎

Original: "Coexistence of attractors in a coupled nonlinear delayed system modelling El Niño Southern Oscillations"

· Chandrakala Meena, Elena Surovyatkina, Sudeshna Sinha

arXiv:1707.09853 · 2017-07-28 · arXiv non-exclusive · independent analysis · 2 min

Coupled regions of the Pacific Ocean can jointly generate El Niño oscillations, even if one region alone would settle into equilibrium.

Two pendulums hang from the same wall, with a spring stretched between them. Each on its own can swing or stay still, but connect them and a shared dance begins: one nudges the other, and oscillations spread through the whole setup.

That's how the Pacific Ocean works, where two neighboring regions exchange heat through waves. Ocean water doesn't stay put: wind piles it up, generating waves that travel from one shore to the other. One wave, fast, crosses the ocean in 110 days. Another, slow, takes 329 days. This time difference is the very spring that couples the regions.

The equation for each region looks like this: \\( \\frac{dT}{dt} = T - T^3 - \\alpha T(t-\\delta) + \\gamma T_{\\text{other}} \\). Here \\(T\\) is the temperature deviation from the mean, \\(\\delta\\) is the time it takes a wave to reach the region, and \\(\\gamma\\) is the coupling strength between regions.

Scientists solved this equation on a computer, varying the coupling strength and the delay. It turned out that if one region on its own tends toward rest while the other oscillates, the coupling makes both oscillate. Conversely, if the coupling is too strong, both pendulums freeze, and El Niño disappears.

Previously, the influence of neighboring regions was treated as random noise, like gusts of wind that alternately amplify or dampen the swing. Now, instead of noise, there is a deterministic mechanism: one region regularly nudges the other, and this changes the whole picture.

Usually, El Niño is declared when the temperature anomaly in a certain zone exceeds 0.5 °C. The new model suggests looking at a range: in the first region from 0.5 to 1.6 °C, and in the second from -0.06 to 2 °C.

Basin-of-attraction maps show which initial conditions lead to El Niño, which to La Niña, and which to a quiet state. It's like a road map: if you know where you stand, you can estimate where you'll be carried. Such maps are already used to assess the probability of El Niño, and they could improve forecasts from meteorological agencies.

The two pendulums on the wall don't just swing; they teach each other to swing. And the Pacific Ocean, with its waves and delays, follows the same rules.

Whole graph →

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

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Two Ocean Pendulums Sing in Unison ✎