Applying the analytical solution to Laplace’s tidal equations, we can isolate the parts of the Southern Oscillation Index signal that appear quite noisy (i.e. 1880-1885, 1900-1905, etc).
#WednesdayWisdom becoming clear that the Southern Oscillation index of El Nino behavior is tied to lunar cycles. Early period training (1880-1950) predicts later behavior (1950-now) https://t.co/CC8evcAFxa #AGU2017 #AGU pic.twitter.com/MTkRxA6lIe
— Paul Pukite (@WHUT) November 8, 2017
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For this 3-month averaged SOI fit, it’s a sin(sin(f(t))) function in the ENSO model that generates the folded signal which appears as a rapidly fluctuating and noisy signal. Although my simplification of Laplace’s equation was originally applied to QBO, it is applicable to other equatorial standing wave phenomenon such as ENSO, of which the SOI is a measure. The SOI signal has always been considered noisy — especially in contrast to other ENSO measures such as NINO34 — but perhaps this needs to be rethought, as the higher frequency components may be real signal.
These results will be presented at next month’s AGU meeting:
The presentation for the 2017 AGU Fall Meeting:
Biennial-Aligned Lunisolar-Forcing of ENSO: Implications for Simplified Climate Models 🌜🌊🌛
https://t.co/FWFQJpu1Vk— Paul Pukite (@WHUT) November 8, 2017
GeoEnergy Math 
Another paper that claims to find the “heartbeat” of ENSO
J. T. Bruun, J. Allen, and T. J. Smyth, “Heartbeat of the Southern Oscillation explains ENSO climatic resonances,” Journal of Geophysical Research: Oceans, 2017.
http://onlinelibrary.wiley.com/doi/10.1002/2017JC012892/full
And recently reported “reduced predictability” for ENSO
“ENSO forecasts near the spring predictability barrier and possible
reasons for the recently reduced predictability”
http://journals.ametsoc.org/doi/10.1175/JCLI-D-17-0180.1
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Am I correct that the Bruun (et al) paper finds some of the resonant frequencies, but completely fails to hypothesize the drivers?
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The ones I noted they found are {2.5, 3.8, 5, 12, 65} years. Yet, I would not consider these resonant frequencies, as the system is forced to begin with. The impulse response of the diffEq I am using has a weak resonance at 1 year and that is more from the 1-year delay differential than anything else.
So you have the correct interpretation, in that this paper has completely failed to determine the real drivers. ENSO is no different than ocean tides when it comes to its fundamental behavior — all the periods observed are forced from external drivers, in both cases arising from the influence of the moon and the sun.
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