NdGT has a point — you do see the earth’s shadow moving across the moon, but once covered, a #lunarEclipse just looks like a duller moon (similar “new moons” are also observed like clockwork and thus take the excitement out of it). Yet the alignment of tidal forces does a number on the Earth’s climate that is totally cryptic and thus overlooked. Perhaps old Dr. Neil would find more interesting tying lunar cycles to climate indices such as ENSO and the Indian Ocean Dipole? It’s all based on geophysical fluid dynamics. Oh, and a bonus — discriminate on the variability of IOD and there’s the underlying AGW trend!
BTW, a key to this IOD model fit is to apply dual annual impulses, one for each monsoon season, summer and winter. Whereas, ENSO only has the spring predictability barrier.
Several flavors of the IOD time-series available, referred to as the Dipole Mode Index (DMI). I originally used the JAMSTEC data-set : https://www.jamstec.go.jp/aplinfo/sintexf/e/iod/dipole_mode_index.html
The Climate Explorer sets are also available
A combination of the two above give the following:
Interesting about the IOD dipole mode index in contrast to ENSO indices such as NINO34 is in the number of inflection points, in the time-series. Qualitatively, by comparing the two visually, the IOD DMI appears twice as busy and thus should be correspondingly much more difficult to fit.
Yet, with the application of the semi-annual impulse, the details of the index are modelled nearly as well, with the cross-validation of the extrapolated intervals encouraging (excepting for the powerful El Nino event of 1879 not captured in the IOD model).
As with all these models, the tidal forcing input was allowed to vary from the dLOD calibration, primarily so the iterative fitting procedure could more easily not get stuck in local minima.
This is the model fit to dLOD alone
This is the dLOD model when optimizing the IOD DMI correlation with an iterated LTE modulation — i.e. both tidal forcing and LTE modulation were allowed to vary during the fitting process.
Subtle differences in the tidal factor distribution, as the correlation coefficient drops from 0.97 to ~0.93.
Some variation due to the harmonic of Mm. Mf vs Msf are cumulatively the same as they differ by the semi-annual influence of the sun. Mt’ (prime) is Mm and Mf’ interaction. Some additional forcing from the monthly Draconic and Tropical factors which is entirely plausible given the asymmetry of north vs south hemisphere.
The semi-annual impulse is really the breakthrough in this analysis, as that may be the key to modeling the faster cycling, much like it is used to model the noisy-appearing NOA and AO indices, as shown in a previous post. In retrospect, those are also impressive fits featuring a dominant LTE modulation. Will likely revisit the NOA and AO indices with the added knowledge of a dLOD calibrated IOD model.