I am adding a web server app to do automated ENSO model fitting. Here is an example of a model that uses the QBO-folded tidal components, long-range tidal factors, and a Chandler wobble component.
The fitting interval is rather narrow, from 1995 to 2013. You can see that it is a very tight fit in this interval, yet when the model is back-extrapolated to 1880, the validated interval from 1880 to 1980 is impressive. Most of the peaks and valleys line up and often with the right amplitude. The model flipped the sign of the broad ElNino valley centered at 1941, which is indicated by the up arrow. And the interval from 1980 to 1995 also out-of-phase.
What I am going to do is provide interactive options for users to adjust the model periods and fitting intervals. Hopefully they can use the model to find other interesting correlations.
The current parameter set is
1. Long term tidal periods of 9.03, 18.613, and 4.424 years
2. Chandler wobble period of 6.48 years
3. Folded tidal periods of 2.245, 2.091, 2.765 (Synodic) years averaging to the Draconic 2.368 years along with a strong 2.33 year period
4. A lunar spin-orbit coupling of 2.9 years
Surfers know the 9-year cycle well http://www.severn-bore.co.uk/bore_cycle.html
My premise is that the standing wave in the Pacific ocean known as the Southern Oscillation is caused by sloshing of the thermocline and this sloshing is incredibly sensitive to any kind of angular momentum changes in the earth's rotation. And because of the large inertial mass of the ocean, the long-term periods have a greater observable impact than the short-term parameters.
And the same thing holds for the standing wave in the stratosphere known as the Quasi-Biennial Oscillation. But in this case, the parameters 3 and 4 are more important as the response time of the low-density stratosphere favors shorter periods due to its smaller inertial mass. That is also why the QBO appears less erratic as well, since the long term forcing factors won't introduce complex beat patterns.