ENSO model verification via Fourier analysis infill

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.

Fig. 1: Bottom panel of amplitude ENSO SOI spectra shows the training windows.  A primarily low-amplitude spectral signal is used to fit the model (using least-squares on the error signal). Upper spectra shows the expanded view of the out-of-band fit. This rich spectra is all due to the non-linear harmonic solution of the ENSO Laplace’s Tidal Equation solution.

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.

Fig. 2: Temporal model fit using only Fourier frequency terms shorter than 1.25 years and longer than 11 years. The correlation coefficient is 0.7 here

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?