Relay of Chaos: How Warm Pacific Waters Make Weather Unpredictable ✎

Original: "The Effects of El Niño on the Global Weather and Climate"
arXiv:1801.00891 · 2018-01-03 · arXiv non-exclusive · independent analysis · 3 min
Mathematicians have found that El Niño chaos can jump from ocean to atmosphere and infect neighboring regions, turning local unpredictability into a global phenomenon.

In the 1960s, meteorologist Edward Lorenz discovered that the air above our planet behaves like a crowd at a sale: the slightest nudge can change everything. His famous question about a butterfly in Brazil causing a tornado in Texas became a symbol of chaos in the atmosphere. But Lorenz only looked at the air. He left the ocean, which covers seven-tenths of the globe, out of the picture. Yet it is the ocean that warms and cools the atmosphere, and it is the ocean that triggers El Niño, the warm current that every few years turns weather upside down on every continent.

New work shows that chaos can travel. Picture a relay race where runners pass not a baton but unpredictability. One runner is the warm water off the coast of Peru, another is the winds over Australia, and a third is the currents in the Atlantic. Mathematicians linked three simple models: an equation describing heat transport by ocean currents, an El Niño model, and the classic Lorenz system for the atmosphere. It turns out that if you inject a chaotic signal into one of these systems, the neighboring system, which on its own was calm and predictable, begins to behave erratically.

The numbers speak for themselves. In the Lorenz system, parameter r=0.35 means stability, but once connected to a chaotic ocean, it produces irregular oscillations. The El Niño model with parameters B=20, C=7 behaves as steadily as a pendulum until it is linked to a chaotic neighbor, and then it breaks into a dance.

This is not just a mathematical trick. Warm Pacific waters exchange heat with the air, wind rubs against the water surface, and currents carry heat thousands of kilometers. If chaos arises in one link of this chain, it spreads along the entire chain like a crack through glass. That is why forecasting weather a week ahead is always a guessing game, even with perfect satellites and supercomputers. Chaos does not sit in one place; it is spread across the whole planet.

The study offers a fresh perspective on an old problem. Previously, scientists looked for the source of unpredictability in individual models, asking whether the atmosphere is chaotic on its own or whether El Niño confuses it. Now it is clear that the issue is not the source but the connections. Chaos is contagious, and the climate system is a vast network where unpredictability runs from node to node like a signal through wires.

For now, this is pure knowledge, with no immediate benefit for forecasting. But it changes the very framing of the question. Instead of asking “where is chaos born?”, we should ask “how does it spread?”. And then, perhaps, we might find a way to dampen it, like putting out a fire by preventing it from jumping to neighboring houses. Meanwhile, the butterfly in Brazil flaps its wings, and its flutter, passing through the warm waters of the Pacific, might turn into a downpour in Moscow.

Lorenz, who discovered chaos in the atmosphere, posed the famous question: 'Does the flap of a butterfly's wings in Brazil set off a tornado in Texas?' This work shows that chaos can also travel through the ocean: warm water in the Pacific can make weather in the distant Atlantic unpredictable.

The idea of global climate connectivity echoes Kim Stanley Robinson's novel 'Forty Signs of Rain', where scientists try to understand and predict abrupt climate changes caused by nonlinear interactions between ocean and atmosphere.

\frac{dx}{dt} = -\sigma x + \sigma y, \quad \frac{dy}{dt} = rx - xz - y, \quad \frac{dz}{dt} = xy - bz
Classic model of atmospheric convection, exhibiting chaos for certain parameters.
\frac{du}{dt} = B T_d - C u, \quad \frac{dT_d}{dt} = u T_s - T_d, \quad \frac{dT_s}{dt} = -u T_d - T_s + 1
Simplified El Niño model that reduces to the Lorenz system; variables are zonal velocity and the difference/sum of sea surface temperatures.
\frac{\partial T}{\partial t} + u \frac{\partial T}{\partial x} + v \frac{\partial T}{\partial y} + w \frac{\partial T}{\partial z} = f(t,x,y,z,T)
Describes the transport of sea surface temperature by currents; the source f includes heat fluxes between ocean and atmosphere.
Concepts
ENSO El Niño-Southern Oscillation El Niño spring predictability barrier Jin-Timmermann model La Niña Multivariate ENSO Index natural variability ERSST Southern Oscillation equatorial wave propagation TAO/TRITON moorings interannual variability recharge oscillator model Warm water volume seasonal cycle Indian Ocean capacitor effect NOAA CPC relative ONI sea surface temperature