Because the ENSO model generates precise temporal harmonics via a non-linear solution to Laplace’s Tidal Equations, it may in practice be trivially easy to verify. By only using higher-frequency harmonics (T<1.25y) during spectral training (with a small window of low-frequency signal to stabilize the solution, T>11y), the model essentially fills in the missing bulk of the signal frequency spectrum, 1.25y < T < 11y. This is shown below in Figure 1.
This agreement is statistically unlikely (nee impossible) to occur unless the out-of-band signal had knowledge of the fundamental harmonics (i.e. the highest amplitude terms in the meat of the spectra) that are contributing to the higher harmonics.
Figure 2 is the underlying temporal fit. Although not as good a fit as what we can achieve using more of the primary Fourier terms, it is still striking.
The consensus claim is that ENSO is a chaotic process with no long-term coherence. Yet, this shows excellent agreement with a forced lunisolar model showing very long-term coherence. An issue to raise is: why has the obvious deterministic forcing model been abandoned as a plausible physical mechanism so long ago?
4 thoughts on “ENSO model verification via Fourier analysis infill”
Improving the long-lead predictability of El Niño using a novel forecasting scheme based on a dynamic components model
Appears to be a good predictor yet they use wind stress as a regression variable (possibly not independent) and it is only 6 months in advance as shown below.
A full model fit to shortest component 0.4y.
The residual of the fit across the entire spectrum (Nyquist T = 1/6 y) appears to be flat white noise
No use trying to improve the fit beyond this point —
Interesting Fourier analysis for paleo data here:
Autumn-winter minimum temperature changes in the southern Sikhote-Alin mountain range of northeastern Asia since 1529 AD
Note below the strong biennial component right at the Nyquist limit, and that they do not even discuss in the text!
Pingback: Unified ENSO Proxy | context/Earth