An Ocean Like a Plucked String: Why El Niño Comes in Two Flavors

Original: "A spatiotemporal oscillator model for ENSO"

arXiv:2306.04074 · 2023-06-07 · CC BY 4.0 · 3 min

The temperature swings of the Pacific Ocean can be broken down into two tones, much like the sound of a guitar string, and their combination gives rise to every variety of El Niño.

In 1982, fishermen off the coast of Peru found their nets empty, while on the other side of the Pacific, in Australia, drought set in. That was the first time El Niño made itself loudly known: a warm current that, every few years, turns the world's weather upside down. Since then, it has been studied from ships, satellites, and buoys, but one puzzle remained unsolved: why does warm water sometimes pile up near the shores of South America, and at other times in the very middle of the ocean? Climate scientists even split these cases into two different types, but they could not explain where such diversity comes from.

The ocean is like a stretched guitar string. When you pluck a string, it does not sound a single pure tone but several at once: the fundamental and overtones. In the same way, when the surface of the Pacific Ocean is "plucked" by a gust of wind, it starts to oscillate not in one way but in several simultaneously.

The new model, built on the equations of motion for ocean water, shows that the Pacific has two main "tones." The first tone, the lowest, oscillates with a period of 4.3 years. In this mode, water becomes warmer in the east and cooler in the west: this is the classic El Niño, which brings rain to the Atacama Desert and drought to Indonesia. The second tone is higher, with a period of 2.3 years, and in it a warm patch appears in the center of the ocean, between two cold zones. This tone is responsible for the "central" El Niño, which has been observed particularly often over the last two decades.

By mixing the two tones in different proportions, you can get any event. If the first tone is loud and the second is quiet, you get a giant like the 1997 El Niño, which raised ocean temperatures by three degrees. If both tones are nearly equal, the event turns out weak and smeared across the whole basin.

The model does more than describe the past: it explains why El Niño is so irregular. External forces, such as solar heating or random wind gusts, act like a guitarist's hand, which plucks the string sometimes harder, sometimes softer. So some years pass quietly, while in others the ocean "sounds" deafeningly. Moreover, the model predicts that the oscillations travel across the ocean at about a quarter of a meter per second, roughly the speed of a leisurely walker, and this matches observations.

Once, El Niño seemed like a simple warm current off the coast of Peru. Now, thanks to this string analogy, it appears as a complex symphony in which two tones intertwine in endless variations. And if we learn to hear each tone separately, perhaps one day we will be able to predict what melody will play next year.

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The period of the second mode is exactly half that of the first, reminiscent of overtones in music: the fundamental tone and its octave create a complex melody of climate oscillations.

\frac{\partial^2 T'}{\partial t^2} = c^2 \frac{\partial^2 T'}{\partial x^2} + \frac{\partial Q'}{\partial t}

The temperature anomaly propagates as a wave with speed c, and external heating Q' acts as a source.

\omega_n = c \lambda_n = \frac{n \pi c}{L}

The oscillation frequency of each mode is determined by the wave speed and the basin size L; for n=1 the period is about 4.3 years, for n=2 it is 2.3 years.

\omega^2 - 2 u k \omega - c^2 k^2 - i \alpha_k \omega = 0

Relates frequency and wavenumber; shows that waves decay or grow depending on the sign of the coefficient α_k, which is related to heating.

Concepts

ENSO El Niño-Southern Oscillation recharge oscillator model Jin-Timmermann model La Niña El Niño index Southern Oscillation ERSST Multivariate ENSO Index spring predictability barrier TAO/TRITON moorings Warm water volume equatorial wave propagation sea surface temperature relative ONI natural variability North Equatorial Countercurrent Westerly wind burst sea surface temperature anomaly Kelvin wave

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An Ocean Like a Plucked String: Why El Niño Comes in Two Flavors