Why El Niño Arrives Late ✎

Original: "Derivation of Delay Equation Climate Models Using the Mori-Zwanzig Formalism"
arXiv:1902.03198 · 2019-02-08 · arXiv non-exclusive · independent analysis · 1 min
The ocean remembers its past states, and this memory shapes the climate.

A wave crosses the Pacific Ocean, bounces off the shore, and returns to change the water temperature. This journey takes about six months. That is why El Niño arrives not immediately but with a delay. Scientists have built an equation that accounts for this delay, and they did so not by guesswork but through rigorous calculation.

Earlier models of El Niño were based on assumptions. Now the delay is derived from the equations of ocean motion, which changes forecast accuracy.

The new model shows that temperature oscillations become slower and closer to what is observed in reality. The period increased from 2–3 years to 3.5–4.5 years, while real El Niño occurs every 4–7 years. This means the equation better reflects nature. This approach can also be applied to other climate phenomena where the past influences the future.

The delay in the El Niño model corresponds to the time it takes for Rossby waves to cross the Pacific basin, reflect off the western boundary, and return as Kelvin waves. This journey takes about half a year.

\frac{dT}{dt} = T(t) - T(t)^3 - \alpha T(t-\delta) (1 - \gamma T(t)^2)
The rate of change of temperature is determined by an instantaneous nonlinearity and a delayed effect with a cubic correction.
Concepts
delay differential equation Jin-Timmermann model delayed oscillator theory El Niño-Southern Oscillation recharge oscillator model ENSO reanalysis Pacific decadal oscillation spring predictability barrier time delay TAO/TRITON moorings seasonal forcing Dynamical Systems Multivariate ENSO Index mixed mode oscillations NOAA PMEL / TAO Indian Ocean capacitor effect El Niño index finite element method seasonal cycle