Since we have plenty of data on actual tides and know the orbits of the Moon and Earth around the Sun, we have fairly accurate tide tables. Wind shifts though can change the inertia of the water delaying or advancing tides at any given location.
Tides are what many would call a "chaotic" problem. You can "solve" tides but there are "other" factors that cannot always be considered in advance. If for whatever reason someone cut a canal through Florida wide enough, it would have an impact on the Gulf State tides by allowing more flow from a different tidal reference.
Very few people think about tides as being chaotic. They have tide tables and are used to them being close but not exact. Weather is chaotic, people are used to weather forecasts being close but not exact. When it comes to climate though, chaos seems to be an ugly word.
Energy transfer in the atmosphere and oceans also have inertia and would have "tidal" cycles similar to the plain vanilla ocean tides.
A term I may have coined is tidal stutter. It is nothing but the shift in any mixed semidiurnal or semidi-annual or semidi-preccessional shift from di whatever to semidi whatever "tidal" cycle. This is based on the accepted tidal cycles like those discussed by NOAA. There are other possible cycles but these are the "commonly" accepted variations in tidal patterns. If you can wrap your head around your local tides you should be able to wrap your head around thermal energy tides. Specific Heat Capacity is often called thermal inertia, which for this analogy you just accept as being a real inertia as if it involves mass. It does, but it is thermal mass.
If you look at the last chart the LS is lower stratosphere energy approximated from UAH LSTand SS"E" is sea surface energy instead of sea surface temperature. The atmosphere and oceans have hugely different thermal inertia and are coupled as in one influences the other. The Sun provides the energy and its response in the LS and SS"E" are lagged at differing rates due to their relative inertia.
Buried it what may appear to be noise is a basic mixed semidi-annual tidal cycle not much different than the NOAA basic example. It is more complex because of the larger differences in thermal inertia, but very similar.
If you pick just one region like the Nino3.4 you would have a different tide table than for the Persian Gulf. If you are fishing you would want your local tide table not one for Portland, Oregon. How ever if you are concern with western Pacific coast weather you would want to know the Pacific Decadal "Tides" and for England the Atlantic Multi-decadal "Tides". If you are concern with "global" climate you should want to use the equatorial "tides".
This is the reason I have spent so much time on the Tropical Ocean Peak Temperature reconstruction. Peak would be the high thermal tide. Once you know the approximate high tide you can more easily predict the low and mid-range tides.
This graph of the Berger et al. solar cycle estimate for the equator should be what paces the equatorial thermal tides. The Jun version would be a di-orbital "tide" and the Equ. Peak a semidi-orbital "tide". So using what should pace equatorial climate one should be able to find the exceptions that have to exist.
The Arabian Sea most likely would not have the same exceptions as the combined Tropical Oceans,
but there should be more similarities than differences. Remember there is a lot of uncertainty not only in the SST data but the orbital approximation as well. The precessional cycle is not fixed, but it is the data that we have and provides a reference to work from. Here I have included a "global" solar peak with the Equatorial Tropical Ocean peak. The northern/southern hemisphere thermal tides can impact the equatorial thermal tides because the system is coupled. If I finish, you will have a thermal tide table that just like the local tide tables are close but rarely right on the money.
That is what happens with a chaotic problem, you can get reasonably close but never exact, just "probably" in the right ballpark. Figuring out the area of the ballpark is another problem.