A few comments up [I said](#Comment_21195):

> "The folded cross-correlation of this ideal model forcing is > 0.9, so likely the LTE modulation is responsible for the multiple splitting of the peaks in the ENSO forcing response, thus degrading the symmetry to some degree."

I initially thought the Laplace's Tidal Equation (LTE) modulation may remove the spectral symmetry around the 0.5/year position, but this is definitely not the case. The symmetry is perfectly preserved independent of the amount of modulation, with more satellite peaks added the greater the modulation. This is easy to understand as only harmonics of the no-LTE fundamental forcing frequency are generated and these will preserve the +/- satellite symmetry, no matter how strong the modulation.

This brings up an interesting possibility in terms of classical tidal analysis. Early on it was realized that there were quite a few tidal constituents to deal with:

> "Darwin's harmonic developments of the tide-generating forces were later improved when A T Doodson, applying the lunar theory of E W Brown, developed the tide-generating potential (TGP) in harmonic form, distinguishing **388** tidal frequencies. Doodson's work was carried out and published in 1921."

Even though there are even more than that now, only a few are needed for short-term forecasts. Yet, the reason that so many exist is because these are all generated by combinations of all the possible products of the constituent factors. The interesting finding is that the LTE modulation will also generate all the harmonic combinations, which may explain how the harmonics come about. The LTE modulation is likely very weak for conventional tides, but if it is there at all, it will generate all the tidal harmonics tabulated.

For 4 primary tidal constituents (solar, synodic, draconic, anomalistic) and a 4 harmonic depth on each (i.e. monthly, fortnightly, 9 day, 6.5 day for lunar, and 1 year, 1/2 year, 1/3 year, etc for solar) this will generate ~4^4 = 256 additional harmonics.

> "The folded cross-correlation of this ideal model forcing is > 0.9, so likely the LTE modulation is responsible for the multiple splitting of the peaks in the ENSO forcing response, thus degrading the symmetry to some degree."

I initially thought the Laplace's Tidal Equation (LTE) modulation may remove the spectral symmetry around the 0.5/year position, but this is definitely not the case. The symmetry is perfectly preserved independent of the amount of modulation, with more satellite peaks added the greater the modulation. This is easy to understand as only harmonics of the no-LTE fundamental forcing frequency are generated and these will preserve the +/- satellite symmetry, no matter how strong the modulation.

This brings up an interesting possibility in terms of classical tidal analysis. Early on it was realized that there were quite a few tidal constituents to deal with:

> "Darwin's harmonic developments of the tide-generating forces were later improved when A T Doodson, applying the lunar theory of E W Brown, developed the tide-generating potential (TGP) in harmonic form, distinguishing **388** tidal frequencies. Doodson's work was carried out and published in 1921."

Even though there are even more than that now, only a few are needed for short-term forecasts. Yet, the reason that so many exist is because these are all generated by combinations of all the possible products of the constituent factors. The interesting finding is that the LTE modulation will also generate all the harmonic combinations, which may explain how the harmonics come about. The LTE modulation is likely very weak for conventional tides, but if it is there at all, it will generate all the tidal harmonics tabulated.

For 4 primary tidal constituents (solar, synodic, draconic, anomalistic) and a 4 harmonic depth on each (i.e. monthly, fortnightly, 9 day, 6.5 day for lunar, and 1 year, 1/2 year, 1/3 year, etc for solar) this will generate ~4^4 = 256 additional harmonics.