One index that I haven't looked at is the [Indian Ocean Dipole](https://www.esrl.noaa.gov/psd/gcos_wgsp/Timeseries/DMI/) and its gradient measure the [Dipole Mode Index](http://www.jamstec.go.jp/frsgc/research/d1/iod/dmi.html). This is important because it is correlated with India subcontinent monsoons. It also shows a correlation to ENSO, which is quite apparent by comparing specific peak positions, with a correlation coefficient of 0.2.
I think the reason the correlation isn't higher is that there is likely another standing wave solution that complements the major standing wave that stretches across the equatorial Pacific. The latter contributes the majority of ENSO but only a portion of IOD, so the mystery standing wave is what generates the busier cyclic behavior o IOD.
Like with the other oceanic indices, it has a similar tidal forcing to ENSO, with R^2>0.95.
What differs from ENSO is the LTE modulation, of which IOD consists of a background similar to ENSO, but also a faster modulation that is 3 to 4 that of the background.
The fit over the entire time span is good, with the Fourier spectrum in the lower panel.
So far, the following indices highlighted in yellow have been modeled. The QBO is the only atmospheric behavior, and it has a distinct tidal forcing. Each of ENSO, PDO, AMO, NAO, and now IOD have a nearly identical set of fundamental forced tidal cycles but distinct standing mode modulations.