The differences between ENSO and NAO are stark. ENSO has stronger cycles from 2 to 7 years, while NAO can show fluctuations at 2 or more per year. Yet, essentially the same forcing (as shown in the cross-correlation plots along the lower pane above) can model each time-series effectively.

Why this happens is that the higher-K standing waves are producing the NAO behavior, while the lower-K produce the ENSO standing waves. Because of dispersion, high-K correspond to a higher temporal frequency and thus NAO are higher frequency.


Qualitatively, the fit to NAO doesn't look as good as to ENSO, but this is at least partly due to the large number of cycles we are trying to fit to and the fact that we are at a monthly sampling which adds temporal uncertainty.