Using the same approach on the other major climate index, the PDO, a pattern is starting to emerge. The PDO has a significant LTE sin() modulation that is the same as ENSO, but also has a strong factor with a wavenumber that is 5 times as rapid. In contrast the AMO wavenumber modulation is 3 times as fast as ENSO (with a much weaker modulation that's the same as ENSO).


The odd-number multiplicative scaling may be related to properties of [inversion symmetry in the medium]( So if there was an even harmonic among the standing waves, it would be imbalanced with respect to positive and negative excursions.

Again, the tidal forcing matches to a correlation above 0.99 for years greater than 1920. The AMO fit extends back to 1856 so the mean forcing appears to stay closer to zero for those years, so is flatter.