Latest information on the Tide Gauge / ENSO connection is here:
The model is a Mathieu DiffEq with a RHS forcing that includes annual, biannual, and biennial sinusoidal factors. The biennial is most critical, while the annual and biannual factors add detail.
I timed posting this to coincide with the People's Climate March and am getting some feedback.
Bottomline I think the reason the model is working so well is that the Tide Gauge data is more directly sensitive to sloshing of the ocean, which makes sense since sloshing is a height differential phenomena. Whereas ENSO indices such as SOI are sensitive but only though an affine transformation to the sloshing motion.
This is the latest model fit:
The correlation coefficient is "only" 0.53 (highlighted in blue) but that is one of those measures that is dependent on the structure of the data. It also depends on not encountering bad stretches such as that highlighted in yellow. These stretches essentially negate and then detract because they show almost perfect anti-correlation. The task now is to find out if there is any way that this quality of fit is merely fortuitous and coincidental. I am looking for a cookbook approach to verifying that is not the case.