ENSO models best with alternating sign semi-annual pulses. Operating on the Mf tidal factor this generates a tight forcing with average period 3.8 years.

AMO models best with an annual pulse. Because of the Mt tidal factor the forcing slowly wanders with a period of ~120 years.

PDO models best with an annual pulse but fast decay. Because of the Mt tidal factor the forcing would wander like AMO, but instead it makes biased excursions.

To summarize, the models of ENSO, AMO, and PDO depend on the specific forcing character while keeping the LOD tidal calibration fixed. ENSO likely requires this alternating semi-annual because it is aligned along the equator and so alternates with northern and southern nodal swings. AMO and PDO may require an annual impulse because it’s essentially a northern hemisphere behavior. Why the decay is faster for PDO, or what exactly sets the decay rate after an integrating impulse, is not clear. Perhaps the larger the inertial push the slower the response.