One of the long-standing theories in climate science has to do with the topic of atmospheric tides. Similar to the more-familiar concept of ocean tides, these can be measured as regular fluctuations in wind, temperature, density and pressure throughout the atmosphere, with the effect more pronounced at higher altitudes as the lower density requires less energy to create an impact. The on-going theory states that the 24-hour solar cycle is the greatest contributor to the periodic atmospheric tidal effect . Note that the theory appears to have (at least partially) originated with the famed AGW skeptic Richard Lindzen.
Yet some recent research appears to be challenging these ideas of a principally solar influence, especially in regards to features that obviously don’t match the periods expected of the solar cycle . The counter theory is that of it being a lunar (gravitational) origin rather than a solar (thermal) origin. This is all based on the rich detail in the data available from length-of-day measurements  and the credible fits of the countervailing theory to that data.
First, let me quote the assertions of the recent findings :
“Studies of atmospheric tides also deal with global-scale periodic oscillations of the atmosphere. According to current tidal theories (Chapman and Lindzen, 1970; Forbes el al., 2003; Hagan et al., 2003; Hagan and Forbes, 2003; Lindzen, 2005), atmospheric tides are excited primarily by the Sun’s heating of the atmosphere, whereas ocean tides are excited primarily by the Moon’s gravitational pull. This means that atmospheric tides have oscillation periods related to a 24-h length of the solar day, whereas ocean tides have longer oscillation periods related to a lunar day (time between successive lunar transits) of about 24 h and 51 min. Atmospheric tides can be detected as regular but small oscillations in surface pressure with periods of 24 and 12 h. This is the way the term “atmospheric tide” is described and explained in textbooks, dictionaries and encyclopedias; however, the atmospheric tide produced by lunar gravitation pull has never been observed in the Earth’s atmosphere, whereas the tides in oceans and the Earth’s crust, excited by lunar gravitation pull, appear so strong.” 
The researcher Li ends with the rather obvious question of why is the ocean tidal effect so strong yet the atmospheric effect so weak as to be almost unnoticeable? Beyond the fact that the atmosphere’s density is well below that of liquid water and therefore not as sensitive to gravitational effects, this is a good question. The 12-hour cycle is also curious and has been explained away as being due to a nonlinear square wave modulation (for example) contributing higher-frequency Fourier spectral components to the observations.
The other recent article covers the same ground :
” … this is contrary to conclusions of previous researchers [Lindzen, 2005; Forbes et al., 2003; Hagan and Forbes, 2003; Hagan et al., 2003; Chapman and Lindzen, 1970] who have speculated that atmospheric tides are primarily excited by the solar heating of the atmosphere, whereas ocean tides are primarily induced by the Moon’s gravitation pull. The complete variation in lunar declination occurs over a 27.3 day interval [Burroughs, 2003]. That variation produces a switch of the hemisphere which is under the lunar declinational extreme every 13.66 days.”
The key appears to be the identification of the 27.3 and 13.6 day periodicity corresponding to the sidereal lunar month. This period, combined with 27.2 day draconic month produces the longer 18.6 year beat frequency period corresponding to the lunar standstill. The lunar monthly periods are strikingly observable in high-resolution measurements of the length-of-day (LOD) measurements in the earth’s rotation periods, and Li has provided some elementary formulas to show agreement with the lunar theory . This extends to agreement, albeit less striking, with reanalysis results of historic geopotential height estimates, see figure below.These geopotential height oscillations correspond to the atmospheric tide that has apparently mislead researchers such as Lindzen until now.
Interactive views of the LOD results are available from the INTERNATIONAL EARTH ROTATION & REFERENCE SYSTEMS SERVICE operated by the Paris Observatory. This also extends to polar motion .
“An overall spectrum reveals cycles principally at 20, 13.6 (fortnightly tidal period) and 10 days (corresponding to the normal atmospheric mode, but this is only an averaged feature hiding its strong variability over seasonal time scales. This explains why it is so delicate to determine an empirical model of the tidal effect on polar motion. The variability in both amplitude and phase of the 13.6-day term is probably caused by a lunar barometric effect, modulated by some sub-seasonal thermal processes. The irregularities of the prominent cycles of the short-term polar motion are well explained by the atmospheric and oceanic excitations. The oceanic variability reinforces the atmospheric one, as they were triggered by the same agent, maybe seasonal and inter-annual thermal variations.” 
One of the challenges of deconstructing phenomena such as ENSO is that one doesn’t exactly know where to start from. There is enough variation in the predictions from assorted ENSO models that one realizes that the foundation may be a bit shaky, if not otherwise governed by chaotic uncertainty. Yet the agreement of closely related phenomena such as atmospheric tides to fundamental theories of forcing functions (ala lunar gravitational effects) provide hope that these promising leads will amount to something that generates better short or long-term predictions. I am definitely seeing these lunar monthly periods in aliased forcing of both SOI and QBO models, and so will keep my eye on these recent developments.
And then the existential question is how will Richard Lindzen respond to being so wrong in the theory that he built his reputation on? From 1970 until now is 40+ years of potential misinterpretation. Or have I misread this completely?
 Chapman, S., and R. S. Lindzen, 1970: AtmosphericTides: Thermal and Gravitational. D. Reidel Publishing Company, Dordrecht, Holland, 200pp.
 Li, G., Zong, H., & Zhang, Q. (2011). 27.3-day and average 13.6-day periodic oscillations in the Earth’s rotation rate and atmospheric pressure fields due to celestial gravitation forcing. Advances in Atmospheric Sciences, 28, 45-58.
 Krahenbuhl, D. S., Pace, M. B., Cerveny, R. S., & Balling, R. C. (2011). Monthly lunar declination extremes’ influence on tropospheric circulation patterns. Journal of Geophysical Research: Atmospheres (1984–2012), 116(D23).
 Bizouard, C., & Seoane, L. (2010). Atmospheric and oceanic forcing of the rapid polar motion. Journal of Geodesy, 84(1), 19-30.