How Order Emerges from Chaos: Simple Models of El Niño ✎

Original: "Rigorous Derivation of Stochastic Conceptual Models for the El Niño-Southern Oscillation from a Spatially-Extended Dynamical System"
· Nan Chen, Yinling Zhang
arXiv:2212.14179 · 2022-12-29 · arXiv non-exclusive · independent analysis · 2 min
Scientists derived simple equations for El Niño from a complex ocean-atmosphere model.

Every few years, the water in the Pacific Ocean becomes warmer than usual, triggering floods in some countries and droughts in others. This is El Niño, a phenomenon that recurs irregularly, every 3–7 years. Scientists want to predict it, but complex ocean-atmosphere models require enormous computing power. Simple models with a couple of equations would be more convenient, but previously they were devised by intuition. Now researchers have shown how to derive such simple models from the complex system rigorously, without guesswork.

Imagine an orchestra where each instrument plays its own part. To hear the main melody, you need to pick it out from the overall noise. Similarly, from the many oscillations of the ocean and atmosphere, two principal motions are extracted.

In the complex model, the ocean and atmosphere are coupled, and random wind gusts add noise. The scientists identified special directions along which the system oscillates independently, much like finding the principal axes in a dance. It turns out that two such directions, with a period of about 4.6 years, explain almost everything. Projecting the noise onto these directions yields two simple equations. These equations reproduce El Niño's frequency, its strength, and even rare but intense events. The correlation with real observations exceeds 0.85.

Previously, simple models were like hand-drawn sketches, but now they are derived from the full picture. This means we better understand why El Niño behaves the way it does. The resulting models can be used for rapid forecasting and for testing new ideas in more complex climate models. Thus, order emerges from chaos, and from a symphony, a simple melody arises.

The phase shift between sea surface temperature in the east and thermocline depth in the west is 122 degrees, not 90, as one might expect for a simple harmonic oscillator. This detail is important for correctly reproducing the time delay in the delayed oscillator.

\frac{d\tilde{a}}{dt} = -d_o \tilde{a} + \tilde{c}_{11} \tilde{a} + \tilde{c}_{12} \tilde{b} + 2g_{a,Re}, \quad \frac{d\tilde{b}}{dt} = -d_o \tilde{b} + \tilde{c}_{21} \tilde{a} + \tilde{c}_{22} \tilde{b} + 2g_{b,Re}
General form of the low-dimensional conceptual model after projection onto the two leading modes; coefficients are expressed in terms of eigenvalues and eigenvectors.
\frac{dT_E(t)}{dt} = -d_o T_E(t) + \tilde{c}_{11} T_E(t) + \tilde{c}_{12} c_y e^{-d_o \phi / \omega_o} T_E(t - \phi/\omega_o) + \alpha_{T_E} a_p(t) + \text{интегральный член}
Stochastic version of the delayed oscillator with exponential damping of the delayed term and a noise contribution with memory.
Concepts
ENSO El Niño-Southern Oscillation Jin-Timmermann model El Niño index Multivariate ENSO Index recharge oscillator model spring predictability barrier La Niña Southern Oscillation TAO/TRITON moorings ERSST natural variability stochastic dynamical system Warm water volume Westerly wind burst relative ONI NOAA CPC Indian Ocean capacitor effect North Equatorial Countercurrent equatorial wave propagation