Experiment to compare training runs from 1880 to 1980 of the ENSO model against both the NINO34 time-series data and the SOI data. The solid red-curves are the extrapolated cross-validation interval..
NINO34
SOI
Many interesting inferences one can potentially draw from these comparisons. The SOI signal appears more noisy, but that could actually be signal. For example, the NINO34 extrapolation pulls out a split peak near 2013-2014, which does show up in the SOI data. And a discrepancy in the NINO34 data near 1934-1935 which predicts a minor peak, is essentially noise in the SOI data. The 1984-1986 flat valley region is much lower in NINO34 than in SOI, where it hovers around 0. The model splits the difference in that interval, doing a bit of both. And the 1991-1992 valley predicted in the model is not clear in the NINO34 data, but does show up in the SOI data.
Of course these are subjectively picked samples, yet there may be some better combination of SOI and NINO34 that one can conceive of to get a better handle on the true ENSO signal.
Interesting when the training interval is set to post-1980 data. This is a much shorter interval to do training, yet the backwards cross-validation is apparent.
NINO34
SOI
GeoEnergy Math 
I am gaining confidence that the higher wavenumber activity along the equator shown here is that of the higher magnitude A solutions in the sin(A sin()) formulation
The magnitude of A is directly proportional to the wavenumber of the solution
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https://www.sciencedirect.com/science/article/pii/S0960148117312739
Study of inter-correlations of solar radiation, wind speed and precipitation under the influence of El Niño Southern Oscillation (ENSO) in California
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