I have been using the delta length-of-day (dLOD) measurements to calibrate the forcing for the ENSO model. The change in LOD is almost entirely due to tidal forcing, in so far as every LOD cycle corresponds to a well-understood lunar cycle. The dLOD is resolved enough that the overall envelope even follows the 18.6 year nodal cycle of maximum declination in the moon's orbit. Yet, I've found that the 18.6 year modulation is less critical for fitting ENSO than getting the tropical fortnightly cycle (13.66 days) and perigean anomalistic cycle (27.55 days) matched. So the timing of the cycles appears to be the critical aspect in the forcing. This makes sense in terms of the tropical/synodic cycle being critical for the localized nature of ENSO whereas the 18.6 year modulation impacts the entire earth as the longitude of maximum declination roams around. A metric that I use for timing or zero crossing is what I call an [excursion matching criteria](https://contextearth.com/2017/10/25/improved-solver-target-error-metric/), defined as :

Excursion matching criteria
\\( EMC = \frac{\sum x_i \cdot y_i}{\sum |x_i| \cdot |y_i|} \\)

The value of EMC when calculated for an ENSO tidal forcing which is calibrated to dLOD is above 0.99 (maximum=1). This agreement is the top panel in the following figure, where you can see the red trace matches the dLOD in phase, but not necessarily in amplitude. So whereas the EMC is above 0.99 (which means the sign of the excursion almost always matches), the correlation coefficient is around 0.9 (indicating the missing amplitude of the excursions).


On closer inspection, over-riding the 18.6 year nodal cycle for the ENSO model is the 19 year [Metonic cycle](https://en.wikipedia.org/wiki/Metonic_cycle), which essentially follows the pattern of eclipses (where the moon and sun are maximally aligned coinciding as a common multiple of the solar year and the synodic lunar month). This can be seen by sliding the ENSO forcing model by 57 years or 3 times the Metonic cycle, which is a particularly strong alignment of the Metonic cycle.


This works out to be a subtle effect, as the differences between an 18.6 year nodal cycle and a 19 year Metonic cycle may not always be easily distinguishable. Or with the 18 year 11 day Saros cycle, which is the well known eclipse cycle independent of time of year. More information on the [NASA eclipse page](https://eclipse.gsfc.nasa.gov/SEsaros/SEperiodicity.html).

And I should add that this interpretation is based on what the best fit is showing. In other words, calibrating the forcing to the 18.6 year modulation of the dLOD will provide a reasonable ENSO fit but not as crisp as shown above. What is reduced in amplitude is the 13.63 day (Mf') cycle which arises from the multiplication of the 27.32 tropical cycle with the 27.21 draconic cycle. In the dLOD fit this is about 1/2 the amplitude as the 13.66 day (Mf) cycle, but is much reduced in the ENSO fit.