Why Weather Can't Be Predicted: Chaos Spreads Like a Cold ✎

Original: "The Effects of El Niño on the Global Weather and Climate"
arXiv:1801.00891 · 2018-01-03 · arXiv non-exclusive · independent analysis · 2 min
Scientists have shown that weather unpredictability can pass from ocean to air like an infection, making accurate forecasts beyond a few days impossible.

Every few years, the warm El Niño current in the Pacific Ocean alters weather worldwide: in some places, rains flood fields; in others, the sun scorches crops. Scientists have long known that the atmosphere behaves chaotically: a tiny change today can lead to a storm a week later. But now it turns out that chaos can spread from ocean to air and back again, like a cold in a crowded bus.

Mathematicians took three simple models: one for warm water carried by currents, another for El Niño, and a third for the air. They linked them together and ran them on a computer. It turned out that if you add a bit of chaos to one model, the neighboring model, previously calm and predictable, also starts behaving erratically. Chaos propagates along the chain, like a crack spreading through glass.

Example from the calculations: the air model with parameter r=0.35 is stable on its own, but after coupling to a chaotic ocean, it begins producing irregular oscillations. Another El Niño model with parameters B=20, C=7 behaves steadily until linked to a chaotic neighbor, at which point it breaks into a dance.

Previously, scientists thought unpredictability originated in a single place: either in the atmosphere or in the ocean. Now it's clear that it's not about location but about connections. The climate system is a network where chaos runs from node to node. Therefore, accurate weather forecasts beyond a few days are impossible, even with perfect instruments. This knowledge doesn't yet help predict weather better, but it changes the question itself: instead of "where does chaos originate?" we now ask "how does it spread?"

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