Lambert, Sébastien B., Steven L. Marcus, and Olivier de Viron. "Atmospheric Torques and Earth’s Rotation: What Drove the Millisecond-Level Length-of-Day Response to the 2015-16 El Niño?."
This figure contains the last three large El Ninos in dashed RED:
The tidal-forced model of ENSO suggests that the blue curves are lunar tidal impulses, even though the above cited paper says any tidal factors have been removed:
"To isolate as much as possible the anomalous changes due to episodic events like ENSO, we subtracted modeled zonal tides (Petit and Luzum, 2010), a multidecadal trend estimated with a 4-yr running mean and a 5.9-yr periodic term, attributed to secular tidal braking / post-glacial rebound (Hide and Dickey, 1991) and variations of the fluid core angular momentum (Hide et al., 2000; Holme and de Viron, 2013), and a mean seasonal cycle estimated over 1979-2017. The residual LOD contains essentially the fluctuation associated with anomalous AAM and oceanic currents, with the latter being less than 5%."
Their implication is that these large excursions in LOD are associated with strong El Nino events and are mountain torqueing responses to the wind resulting from the ENSO pressure dipole. This creates a drag when the wind passes over the Himalayas, thus slowing the earth's rotation for a period of time.
In comparison, this is a lunar-forced fit over the entire ENSO interval, in which no window filtering is performed:
Typically, the model will integrate the tidal forcing over a few month window to match the inertial response of ENSO. But if the window is removed, the spikiness at the resolution of a month is revealed more clearly, and these match the excursions in LOD observed in the cited paper:
The ENSO model includes a spiky biennial modulation, which is critical in providing an impulse at the end of each year, but alternately flipping in polarity to emulate the hypothesized seasonal feedback sea-saw. The reason that Lambert et al missed this factor is that they only subtracted the well-known tidal cycles, but none of the seasonal-impulse-modulated terms. Of course one can't fault them for that, because they do not know that these terms exist.
The research is missing from the climate science literature that justifiably precludes a lunar-forcing mechanism for ENSO (especially on a short time-scale). This is another case that reinforces the idea of a lunar forcing, or at the very least doesn't preclude it. As you can see from the middle figure, these lunar impulses are littered throughout the ENSO time-series and synchronize with both the El Nino + La Nina excursions and with the well-known tidal cycles that contribute to the LOD variation.
Beware that many researchers try to remove evidence of the lunar forcing from climate indices, ostensibly because they think it is a nuisance variable. Yet, I am not the only one that sees this as being problematic in determining attribution (see QBO for another case of missed lunar attribution). The web-site http://MoonClimate.org run by a former NASA JPL scientist was set up to try to correct this situation. She has many examples of published data that intentionally removes the tidal effects without an accompanying note, making it difficult to root out effects that could be tidal driven. An unsuspecting person would use the cleaned-up signal to dismiss the idea that the tides could even be a factor. It's like removing the 60 Hz term from a non-linear amplifier output and having an unsuspecting engineer puzzle over why a 120 Hz signal is appearing. They will eventually figure it out but it doesn't make their job any easier.