There has been a recent push to understand the lunar-climate connection by none other than NASA JPL.
A former researcher at JPL, Claire Perigaud wrote a proposal a few years ago that apparently never got funded:
In that research proposal, there is a clear indication that they understood the lunar origin of the equatorial climate forcing:
The 13.606 number is half the period of the Draconic cycle (27.212 days) and one can infer that this is the same lunar acceleration vector applied to Laplace's tidal equations in the [gravity-forced QBO model](http://contextearth.com/2016/08/23/qbo-model-final-stretch/).
Perigaud is maintaining a website up called http://www.MoonClimate.org/ -- which doesn't look very active. I think this was started because they were committed to following up on the ideas that JPL would not fund
They apparently [submitted an article](http://www.moonclimate.org/docs/2011_NCC_CoverLetter.pdf) to Nature Climate Change called "Earth-Moon-Sun alignments influencing tropical climate events" in 2011 that was rejected. No sign of any article with that title or those co-authors when I googled.