This is as good as any tidal analysis I have ever seen. Notice the perturbation right around 1980 is now gone. It turns out that may have been a red herring, as the past fitting routines were missing the secret ingredient.
This is a short summary I wrote to respond to someone:
In fact there is a magical differential equation that is part Mathieu equation
and part delay-differential
that captures the sloshing dynamics perfectly. Mathieu equations are favored by hydrodynamics engineers that study sloshing of volumes of water, while delay-differential equations are favored by ocean climatologists studying ENSO. So I figured why not put the two together and try to solve it on a spreadsheet?
Of course a magical equation needs magical ingredients, so as stimulus I provided the only known forcing that could plausibly cause the thermocline sloshing -- the lunar long-period tidal pull. These have to be exact in period and phase or else the signals will destructively interfere over many years.
It looks as if the noise in the ENSO signal is minimal. Just about any interval of the time-series can reconstruct any other interval. That's the hallmark of an ergodic stationary process with strong deterministic properties. It's essentially what oceanographers do with conventional tidal analysis -- train an interval of measured sea-level height gauge measurements against the known lunar periods and out pops an extrapolated tidal prediction algorithm. Basically what this infers is that Curry and Tsonis and the other deniers are flat wrong when they say that climate change on this multidecadal scale is chaotic.
Perhaps the climate is only complex when dealing with vortices, i.e. hurricanes, etc. A standing wave behavior like ENSO is not a vortex and it has a chance to be simplified. Anyone that has done any physics has learned this from their undergrad classes. And the QBO behavior may be an anti-vortex type of standing wave, which also can be simplified.
Yet, who knows if various other vortex patterns can't at least be partially simplified. I spent some time discussing with a poster presenter at last year's AGU why he was looking at analyzing jet-stream patterns at higher latitudes while the behavior at the equator (i.e. the QBO) has a much better chance of being simplified. And then that could be used for evaluating higher latitude behavior as a stimulus. Recall that these vortices peel off the equator before developing into larger patterns. He didn't have a good answer.