After spending several years (edit: part-time) on formulating a model of ENSO (then and now), I decided to test out the formulation on another standing wave oscillation — specifically, the Atlantic Multidecadal Oscillation (AMO). All the optimization infrastructure was in place, with the tidal factors fully parameterized for automated model fitting.
This fit is for a training interval 1900-1980:
The ~60 year oscillation is a hallmark of AMO, and according to the results, this arises primarily from the anomalistic lunar forcing cycle modulated by a biennial seasonal modulation. Because of the spiked biennial modulation, we do not get a single long-period cycle but one that is also modulated by the forcing monthly tidal periods. As with ENSO, second-order effects in the anomalistic cycle described by lunar evection and variation is critical.
Outside of the training interval, the cross-validated test interval matches the AMO data arguably well. Since AMO is based on SST anomalies, it's possible that strong ENSO episodes and volcanic perturbations (e.g. post 1991 Pinatubo eruption) can have an impact on the AMO measure.
This is a typical fit over the entire interval.
This is the day after I started working on the AMO model, so these results are preliminary but also promising. AMO has a completely different character than ENSO and is more of an upper latitude phenomenon, which means that the tidal forces have a different impact than the equatorial ENSO cycle. Some more work may reveal whether the volcanic or ENSO forcing overrides the tidal forcing in certain intervals.