Reposted from Ian Wilson’s Astro-Climate Connection blog.
PART B: A Mechanism for the Luni-Solar Tidal Explanation
PART A: Evidence for a Luni-Solar Tidal Explanation
A. Brief Summary of the Main Conclusions of Part A.
Evidence was presented in Part A to show that the solar explanation for the Quasi-Decadal and Bi-Decadal Oscillations was essentially untenable. It was concluded that the lunar tidal explanation was by far the most probable explanation for both features.
In addition, it was concluded that observed variations in the historical world monthly temperature anomalies data were most likely determined by factors that control the long-term variations in the ENSO phenomenon.
Further evidence was presented in Part A to support the claim that the ENSO climate phenomenon was being primarily driven by variations in the long-term luni-solar tidal cycles, leading to the possibility that variations in the luni-solar tides are responsible for the observed variations in the historical world monthly temperature anomaly data.
Copeland and Watts  did a sinusoidal model fit to the first difference of the HP smoothed HadCRUT3 global monthly temperature anomaly series and found that the top two frequencies in the data, in order of significance, were at 20.68 and 9.22 years.
B. A Potential Luni-Solar Tidal Mechanism
Wilson  has found that the times when Pacific-Penetrating Madden Julian Oscillations (PPMJO) are generated in the Western Indian Ocean are related to the phase and declination of the Moon. This finding provides observational evidence to support the hypothesis that the lunar tidal cycles are primarily responsible for the onset of El Nino events.
The peak differential tidal force of the Moon (dF) (in Newtons) acting across the Earth’s diameter (dR = 1.2742 x 10^7m), along a line joining the centre of the two bodies, is given by:
where G is the Universal Gravitational Constant (= 6.67408 x 10^-11 MKSI Units), M(E) is the mass of the Earth (= 5.972 x 10^24 Kg), m(M) is the mass of the Moon (= 7.3477 x 10^22 Kg), and R is the lunar distance (in metres) (N.B. The negative sign in front of the terms on the right hand side of this equation just indicates that the gravitational force of the Moon decreases from the side of the Earth nearest to the Moon towards the side of the Earth that faces away from the Moon.)
Hence, the component of this peak differential lunar force (in Newtons) that is parallel to the Earth’s equator is:
The geocentric solar and lunar distances, solar and lunar declinations and Sun-Earth-Moon angles were calculated at 0:00, 06:00, 12:00, and 18:00 hours UTC for each daily designated period (JPL Horizons on-Line Ephemeris System v3.32f 2008, DE-0431LE-0431 .) . This data was then used to calculate the peak differential luni-solar tidal force using the equations cited above. Figure 1a shows the calculated peak differential luni-solar tidal force for the period from Jan 1st 1996 to Dec 31 2015:
This plot shows that luni-solar differential tidal force reaches maximum strength roughly every 4.53 years (i.e every 60 anomalistic lunar months = 1653.273 days or every 56 Synodic lunar months = 1653.713 days), with the individual short term peaks near these 4.53 year maximums being separated by almost precisely 384 days (or more precisely 13 Synodic months = 383.8977 days). In order to emphasize this point, figure 1a is re-plotted in figure 1b for the time period spanning from 2000.0 to 2004.5:
What figures 1a and 1b show is that peak luni-solar differential tidal stress acting upon the Earth’s equatorial regions reaches maximum strength roughly every 4.53 years. This is very close to half the 9.08 year quasi-decadal oscillation. It also shows that around these 4.53 year peaks in tidal stress, the individual peaks in tidal stress are almost precisely separated by 13 Synodic months.
Wilson  has proposed that:
“The most significant large-scale systematic variations of the atmospheric surface pressure, on an inter-annual to decadal time scale, are those caused by the seasons. These variations are predominantly driven by changes in the level of solar insolation with latitude that are produced by the effects of the Earth’s obliquity and its annual motion around the Sun. This raises the possibility that the lunar tides could act in “resonance” with (i.e. subordinate to) the atmospheric pressure changes caused by the far more dominant solar-driven seasonal cycles. With this type of simple “resonance” model, it is not so much, ‘in what years do the lunar tides reach their maximum strength?’, but whether or not there are peaks in the strength of the lunar tides that re-occur at the same time within the annual seasonal cycle.”
In essence, what Wilson  is saying is that we should be looking at tidal stresses upon the Earth that are in resonance with the seasons. (i.e. annually aliased). If we do just that, we find that the peaks in luni-solar differential tidal stressing every 13 synodic months (= 383.8977 days) will realign with the seasons once every:
(383.8977 x 365.242189) / (383.8977 – 365.242189) = 7516.0607 days = 20.58 tropical years
Hence, it is plausible to propose that the 9.08 year quasi-decadal oscillation and the 20.68 year bi-decadal oscillation can both be explained by variations in the tidal stresses on the Earth’s equatorial oceans and atmosphere caused by the peak differential luni-solar tidal force acting across the Earth’s diameter that is parallel to the Earth’s equator.
Keeling and Whorf  gives support to this hypothesis by noting that the realignment time (or beat period) between half of a 20.666 tropical year bi-decadal oscillation and the 9.3 year Draconic cycle is simply 5 times the 18.6 year Draconic cycle:
(10.333 x 9.30) / (10.333 – 9.30) = 93.02 years = 5 x 18.6 tropical years
which is a well known seasonal alignment cycle of the lunar tidal cycles where:
1150.5 Synodic months = 33974.94253 days = 93.020 tropical years
1233.0 anomalistic months = 33974.76015 days = 93.020 tropical years
1248.5 Draconic months = 33974.45667 days = 93.019 tropical years
which is only about 7.3 days longer than precisely 93.0 tropical years.
Keeling and Whorf  claimed that the 93 tropical year lunar tidal cycle is able to naturally re-produce the hiatus in the quasi-decadal oscillations of the rate-of-change of the smoothed global temperature anomalies that matched those observed between 1900 and 1945.
It could be argued, however, that Keeling and Whorf’s figure 3 [reproduced as figure 2 below] actually points to a hiatus period between about 1920 and the 1950’s, as this is the period over which the phase changes, between the mean solar sunspot number and the peaks in their temperature anomaly curve:
Wilson  made a more accurate determination of the times at which the lunar-line-of-nodes aligned with the Earth-Sun line roughly once every 9.3 years [the blue line in figure 3 below], and when the lunar line-of-apse aligned with the Earth-Sun line once every 4.425 years [the brown line in figure 3 below]. He then used this to determine the 93 year cycle over which these two alignment cycles constructively and destructively interfered with each other [the red line in figure 3 below]. showing that the period of destructive interference actually extended from about 1920 to the 1950’s.
Finally, Wilson  presented some data that showed that there was circumstantial evidence that the 93 year lunar tidal cycle does in fact influence temperature here on Earth.
Wilson  found that “…when the Draconic tidal cycle is predicted to be mutually enhanced by the
Perigee-Syzygy tidal cycle there are observable effects upon the climate variables in the South Eastern part of Australia. Figure 4 below shows the median summer time (December 1st to March 15th) maximum temperature anomaly (The Australian BOM High Quality Data Sets 2010), averaged for the cities of Melbourne (1857 to 2009 – Melbourne Regional Office – Site Number: 086071) and Adelaide (1879 to 2009 – Adelaide West Terrace – Site Number 023000 combined with Adelaide Kent Town – Site Number 023090), Australia, between 1857 and 2009 (blue curve).
Superimposed on figure 4 is the alignment index curve from figure 3, (the red line). A comparison between these two curves reveals that on almost every occasion where there has been a strong alignment between the Draconic and Perigee-Syzygy tidal cycles, there has been a noticeable increase in the median maximum summer-time temperature, averaged for the cities of Melbourne and Adelaide. Hence, if the mutual reinforcing tidal model is correct then this data set would predict that the median maximum summer time temperatures in Melbourne and Adelaide should be noticeably above normal during southern summer of 2018/19.”
 Copeland, B. and Watts, A. (2009), Evidence of a Luni-Solar Influence on the Decadal and Bidecadal Oscillations in Globally Averaged Temperature Trends, retrieved at:
 Wilson, I.R.G. (2016) Do lunar tides influence the onset of El Nino events via their modulation of Pacific-Penetrating MAdden Julian Oscillations?, submitted to the The Open Atmospheric Science Journal.
 JPL Horizons on-Line Ephemeris System v3.32f 2008, DE-0431LE-0431 – JPL Solar System Dynamics Group, JPL Pasadena California, available at: http://ssd.jpl.nasa.gov/horizons.cgi, Jul 31, 2013.
 Wilson, I.R.G. (2012), Lunar Tides and the Long-Term Variation of the Peak Latitude Anomaly of the Summer Sub-Tropical High Pressure Ridge over Eastern Australia., The Open Atmospheric Science Journal, 6, pp. 49-60. Keeling, CD. and Whorf, TP. (1997), Possible forcing of global temperature by the oceanic tides. Proceedings of the National Academy of Sciences., 94(16), pp. 8321-8328.
 Wilson, I.R.G. (2013), Long-Term Lunar Atmospheric Tides in the Southern Hemisphere, The Open Atmospheric Science Journal, 7, pp. 51-76