Since this thread is devoted to revisiting previous discussions of ENSO, I thought to revisit [this Azimuth Forum thread](
) on ENSO proxies.

Early on I discovered that there is a wealth of coral proxy data that has been calibrated to match 20th century SOI and NINO34 measures. The climate scientists thus have the ability to go back hundreds of years to estimate the strength and timing of the southern ocean oscillations.

As a substantiation for the SOI model that I have been analyzing, it is straightforward to get reasonable agreement to the proxy data sets by assuming roughly periodic QBO and CW as forcing factors. The following figure was a fit from last year to the coral proxy data set referred to as the Universal ENSO Proxy (UEP):


More recently, I thought to use an optimized model fit (see msg #80 above) for the last 130 years to the NINO34 and SOI and then apply that *unmodified* to the coral proxy data extending back to 1650:

This is the unadorned match from 1880 to 1970 (where the proxy records end):

The correlation coefficient is 0.48, which should be considered in the context that the data only has yearly resolution. This is essentially a calibration confirmation that the model fit to NINO34 transitively applies to the UEP data.

Now let's take a different 90 year slice, this one starting from 1700 and extending to 1790.

In essence, the 1880 to 1970 fit was used as the training interval, and we solved the DiffEq in reverse, by integrating backwards in time.
The fit is very good considering that we are going back in time almost 200 years before the start of the 20th century. The histogram shows the number of excursions that match in sign between model and data. A nearly 2-out-of-3 predictive count is certainly outside of chance, and is actually *greater* than the calibrated training set.

In practice, it is difficult to maintain coherence over this long a time range, as small deviations in the modeled periodicities will amplify the further back one goes. Due to the imprecision in an estimated period, such as for QBO or the Chandler wobble, one might expect the agreement to potentially go in and out of phase.

And what do you know ... the fit for the 90 year interval from 1790 to 1880 appears out-of-phase with the model.


I have been evaluating a machine learning run on this data and it is indeed finding the 2.33 year QBO periodicity, but perhaps closer to being between 2.34 and 2.35 year over the complete interval, which might be enough to lose a cycle over a 100 year time span. And this missing cycle, as well as other possible phase slips would be enough to generate an interval that loses phase coherence.

What is also interesting is that I have seen coral proxy records that extend back to 1150 AD and find the same coherence over intervals ranging from 70 to 100 years (none of the records extend for extremely long periods so I am using these intervals as is). A blog post describing this is [here]( Again, the same basic DiffEq model was used, but in this case, I fit the individual data sets independently wihout using the present-day training interval. What would be nice to have is an continuous (i.e. unbroken) set of data that extends back 1000 years, in which case the SOI model could really be put through the paces.

But then again, consider that the science of EL Nino prediction is still in the primitive stage of only being able to predict a few months to a year in advance. I think it is understood that there is a definite distinction between the ENSO quasi-cycles and having a full-blown El Nino, and imagine some of this has to do with getting the strength accurately predicted, not just predicting the peak at the correct time.

In any case, I am going with the premise that working the model against historical data can only help the short-term predictions.

And the agreement that we do see between model, proxy data, and modern-day data is well beyond being a fortuitous match. So what more will it take to establish this as a standard model of ENSO?