I have been using the Azimuth Project Forum as a sounding board for the ENSO Model [1,2,3,4,5,6,7,8]. The audience there is very science-savvy so are not easily convinced of the worth of any particular finding (and whether it is correct in the first place). They also tend to prefer pure math because that can be sufficiently detached from the muddy world of applied physics such that one can avoid being labeled as “right” or “wrong”. With math one can always come up with a formulation that can exist on its own terms, separate from a practical application.
So trying to convince those folks in the validity of the ENSO model is difficult at best.
Recently the advice has been to do statistical validation on the model. One participant recommended I try an experimental approach
“I still don’t have the spare cycles to address this fully, but given that one of the two terms of an AIC or BIC is the log likelihood and there is not a closed form representation of the likelihood in this case, I’d probably explore either the empirical likelihood work of Art Owen and his students, for one thing as packaged in the emplik R package, or possibly Approximate Bayesian Computation (ABC; see also and here).”
I am not going to go to the trouble of “exploring” some unaccepted statistical validation procedure, when I am having enough of a challenge defending the ENSO model physics. What am I supposed to do — defend someone else’s empirical statistical research in addition to defending my own work? No thanks.
It seems to be always about #RaisingTheBar to see what someone will do to defend their results.
So I will in this post show an overwhelming piece of evidence that the modeling work is on the right track.
This involves using coral proxy data that has been calibrated against modern day (1880-1978) ENSO records. The calibration of the proxy data to ENSO indices is very good, hovering in the range of 0.8 and higher for correlation coefficient.
One set of proxy data is called the Unified ENSO Proxy (UEP), which is an aggregate of a number of research efforts. What this gives us is an out-of-band time series that extends from 1650 to 1880, a span of 230 years that we can use to validate the ENSO model previously tuned for the time span 1880 to 1980.
If the back-extrapolated fit has a correlation coefficient of close to 0.4 or above, this is a result that is extremely unlikely due to chance alone. As many researchers think that ENSO is a red-noise process, the randomness would give a correlation coefficient for a sample run of anywhere between -0.2 and 0.2 — in other words no phase coherence over an interval that didn’t overlap the fitting interval.
Yet, with a non-random deterministic model, the sinusoidal variation should extrapolate backwards, maintaining a coherent phase relationship that depends on how precise the underlying model frequencies match the physical cycles of tides and wobbles. And as you can see from the multiple-regression model below, the agreement is beyond promising.
The correlation coefficient is very high over the training interval, almost reaching 0.8 and it is about 0.53 over the entire interval. Remember, the fit to the model is over a region that is less than a third of the entire interval. One spike in temperature that covered two years after the massive Laki volcanic eruption of 1783 was removed.
The bar has been raised for others.