Climate seesaws that get stuck ✎

Original: "El Nino Southern Oscillation as Sporadic Oscillations between Metastable States"
· Tian Ma, Shouhong Wang
arXiv:0812.4846 · 2008-12-28 · arXiv non-exclusive · independent analysis · 3 min
El Niño and La Niña explained as two traps in the atmosphere, between which the tropical ocean wanders.

A seesaw with two children rarely balances perfectly. It tips either left or right, pausing at the extremes for a moment before swinging back. The tropical Pacific behaves similarly: it either warms up off the coast of Peru (El Niño) or cools down (La Niña), and these states can last for months, sometimes over a year. But what makes the seesaw flip from one position to the other?

For a long time, climate scientists debated whether El Niño is a random process pushed by external disturbances, or whether the ocean–atmosphere system has an internal rhythm of its own. The new work offers a third path. The atmosphere above the equator, it turns out, can exist in two stable states, like two hollows on an uneven surface. In one hollow, air circulates in a way that warms the ocean near South America, which is El Niño. In the other, cold water rises from the depths, bringing La Niña. Between the hollows lies a ridge, an unstable equilibrium, which the system must cross to switch phases.

The transition between hollows does not require an external push. The ocean surface temperature itself changes the shape of the landscape: as water warms, the ridge lowers, making it easier for the seesaw to slide into the other hollow. When water cools, the ridge grows, and the system gets stuck in its current state.

Mathematicians Tian Ma and Shouhong Wang built a model of the Walker circulation, a giant loop of air that runs along the equator from South America to Indonesia and back. They showed that with realistic parameters (troposphere height 8 kilometers, ocean surface temperature around 27 degrees), two stable states do indeed emerge. The critical Rayleigh number, which indicates how strongly air tends to rise, turned out to be about 2.7×10²¹, corresponding to a temperature difference of roughly 60 degrees between the lower and upper atmospheric layers. It is under these conditions that circulation is born, which then swings between the two extremes.

Randomness does not disappear in this picture. It hides in the initial conditions. If the system is near the boundary between the basins of attraction of the two states, even a tiny disturbance, a gust of wind or a slight change in current, can decide which hollow it will roll into. That is why El Niño and La Niña occur irregularly, even though the transition mechanism itself is deterministic. It is like a coin balanced on its edge: the physics of its fall is predictable, but which side it lands on depends on elusive details.

Previously, ENSO was thought to be either excited by external noise or a chaotic oscillator. The new theory shows that the internal properties of the atmosphere and ocean alone are enough to produce sporadic oscillations.

This view of the climate seesaw opens the door to new forecasting methods. If we can determine which hollow the system currently occupies and how close it is to the ridge, we can estimate the probability of a transition. For now, this is a theoretical possibility, but it unifies determinism and randomness in a framework that once seemed unattainable. The seesaw does not just swing; it gets stuck at the extremes, and now we are beginning to understand why.

The name 'El Niño' (Spanish for 'the Christ child') originated with Peruvian fishermen, who noticed that a warm current sometimes appeared off the coast during the Christmas season. The phenomenon has been known since the 19th century, but its global significance was only realized in the late 20th century.

The idea of metastable states and sudden transitions between them echoes the concept of 'climate tipping points' in science fiction, such as in Kim Stanley Robinson's novel 'Forty Signs of Rain', where abrupt climate changes occur when critical thresholds are crossed.

R_c = \min_{\alpha^2} \left[ \frac{(\alpha^2+\pi^2)\delta_1 + (\alpha^2+\pi^2)^3 + \pi^2(\alpha^2+\pi^2)\delta_0}{\alpha^2} \right]
The minimum value of the Rayleigh number at which bifurcation occurs and the Walker circulation emerges; depends on the friction coefficients δ₀ and δ₁.
R_c \approx \pi^2 \delta_1 + \pi^2 \delta_0 L_c^2
Approximate formula for the critical Rayleigh number for large δ₁; used to calculate the threshold for the onset of circulation.
L_c \approx \left( \frac{\delta_1}{\pi^2 + \delta_0} \right)^{1/2}
Characteristic length of the Walker cell, obtained from bifurcation analysis; with realistic parameters it gives about 7500 km.
Concepts
ENSO El Niño-Southern Oscillation Southern Oscillation Jin-Timmermann model recharge oscillator model La Niña El Niño index Multivariate ENSO Index spring predictability barrier ERSST natural variability mixed mode oscillations TAO/TRITON moorings seasonal cycle seasonal forcing equatorial wave propagation North Equatorial Countercurrent Westerly wind burst NOAA CPC ocean-atmosphere coupling