Paper I
Wilson I.R.G. and Sidorenkov, N.S., 2018, A Luni-Solar Connection to Weather and Climate I: Centennial Times Scales, J Earth Sci Clim Change 2018, 9:2
https://www.omicsonline.org/open-access/a-lunisolar-connection-to-weather-and-climate-i-centennial-times-scales-2157-7617-1000446.pdf
Paper II
Wilson, I.R.G. and Sidorenkov, N.S., 2019, A Luni-Solar Connection to Weather and Climate II: Extreme Perigean New/Full Moons and El Niño Events, The General Science Journal, Jan 2019, 7637. DOI: 10.13140/RG.2.2.20846.87362
http://gsjournal.net/Science-Journals/Research%20Papers-Climate%20Studies/Download/7637
Abstract
Paper I showed that the epochs when the lunar line-of-apse points directly towards/away from the Sun, at times that were closely aligned with the Equinoxes and Solstices (i.e. seasonal boundaries), exhibited distinct periodicities at 28.75, 31.00, 88.50 (Gleissberg cycle), 148.25, and 208.00 (de Vries cycle) years. The caveat being that the alignments had to be observed in a frame of reference that was fixed with respect to the Perihelion of the Earth’s orbit.
This study expands upon the findings of paper I by showing that the long-term periodicities exhibited by the alignments of the lunar line-of apse with the seasonal boundaries have effectively the same periodicities as the alignments of the Perigean New/Full moons with the seasonal boundaries (provided both are viewed in a frame of reference that was fixed with respect to the Perihelion of the Earth’s orbit).
In addition, this study establishes that the very process of selecting the times when the Perigean New/Full moons occur at or near seasonal boundaries, is in fact equivalent to selecting the times when the strongest Perigean New/Full moon tidal events cross the Earth’s equator or when they are at their furthest distance from the Earth’s equator (i.e. lunar standstill).
The strongest spring tidal events that occur close to either the nominal Vernal Equinox (i.e. 0.00 UT March 21st) or the nominal Autumnal Equinox (i.e. 0.00 UT September 21st) that have peak tides at latitudes that are close to the Earth’s equator are selected. Similarly, the strongest spring tidal events that occur close to either the nominal Summer Solstice (i.e. 0.00 UT June 21st) or the nominal Winter Solstice (i.e. 0.00 UT December 21st) that have peak tides at latitudes that are close to those of the lunar standstills are selected, as well.
Collectively, the selected sample shows that the tidal events closest to the Vernal Equinox naturally divides into five 31-year epochs that start in the years 1870, 1901, 1932, 1963, and 1994. The three lunar tidal epochs that start in 1870, 1932, and 1994 begin with a Perigean Full moon, so they are designated as Full Moon epochs. Similarly, the remining two epochs that start in 1901 and 1963 begin with a Perigean New moon, so they are designated as New Moon epochs. In addition, the selected sample shows that the actual starting date for each of the 31-year epochs is dependent upon the specific seasonal boundary that is chosen. The net effect of this is a gradual transition between one lunar epoch and the next that spans a 9.0- year period which is centred upon the time when the strongest spring tide is most closely aligned with the Spring Equinox.
It turns out that the times when strongest tidal peaks cross the Earth’s equator [i.e. the Equinox spring tides, which are the strongest spring tidal events that are nearest to the times of the nominal Equinoxes] or the times when the strongest peaks reach their greatest distances from the Equator [i.e. the Solstice spring tides, which are the strongest spring tidal events that are nearest to the times of the nominal Solstices], correspond to the times when the lunar-induced rotational acceleration of the Earth changes sign. This leads to the question, can the tidally induced changes in the sign of the Earth’s rotational acceleration be link to an atmospheric/oceanic phenomenon that is known to influence changes in the Earth’s global mean temperature? Further investigation shows that the meteorological phenomenon that meets these requirements is the starting dates of moderate to strong El Nino events.
If a comparison is made between the starting dates for moderate to strong El Nino events and the times when the strongest spring tides are near to the Earth’s equator [i.e. Equinox spring tides], there is an alignment between the two phenomena during Full Moon epochs (i.e. those starting in 1870, 1932, and 1994). Similarly, if a comparison is made between the starting dates for moderate to strong El Nino events and the times when the strongest spring tides are at their furthest distance from the Earth’s equator [i.e. Solstice spring tides], there is an alignment during the New Moon epochs (i.e. those starting in 1901 and 1963).
Hence, we can conclude that, during the Full Moon epochs, there is a significant alignment between the starting dates of moderate to strong El Ninos and the times when Equinox spring tidal events occur and that, during New Moon epochs, there is a significant alignment between the starting dates of moderate to strong El Ninos and the times when Solstice spring tidal events occur. This implies that there must be a connection between the times of strongest Equinox/Solstice spring tidal events and the onset of El Ninos.
Extract 1:
Figure 4
Figure 4 shows all the pseudo-cycles that are generated by the interaction between the 2.25, 4.5, 6.75, and 9.00-year lunar cycles with the 31.0-year Perigean New/Full lunar cycle. Firstly, the 2.25-year cycle generates the 28.75, 59.75, and 90.75-year pseudo-cycles. Secondly, the 4.50-year cycle generates the 88.5, 119.5, 150.5, and 181.5-year pseudo-cycles. Thirdly, the 6.75-year cycle generates the 148.25, 179.25, and 210.25-year pseudo-cycles, and finally, the 9.00-year cycle generates the 115, 146, 177, 208, and 239-year pseudo-cycles.
In order for a Perigean New/Full moon cycle to be aligned with the seasons, it would have to lie on or close to the red horizontal line in figure 4 [Note that the lunar cycles that are on this line are fixed in a reference frame that is precessing at the same rate as the rotation axis of the Earth]. Figure 4 shows that the cycles that best fit this description are all simple whole multiples of the sum of the 28.75-year and 31.00-year lunar cycles i.e. they are those with periods of 59.75, 119.5, 179.25 and 239.0 years. This means that, on inter-decadal to centennial time scales, the Perigean New/Full moon events that are best aligned with the seasonal calendar reoccur at intervals of 59.75 years, which is very close to 60 years.
Alternatively, if Perigean New/Full moon cycle is viewed in a frame of reference that aligns with the Perihelion of the Earth’s orbit, they would lie along the red dashed line in figure 4. The cycles that best fit this description in this figure are the 59.75, 88.5, 148.25 and 208.0-year cycles [N.B. the 119.5-year cycle is just a multiple of the 59.75-year cycle]. These are exactly the same as the periods that were found for luni-solar alignments in paper I, when these alignments were viewed in a frame of reference that was fixed with respect to the Perihelion of the Earth’s orbit.
Hence, we have shown that the Perigean New/Full moons reoccur in cycles that show the same periodicities as the luni-solar alignments discussed in paper I, provided both are viewed in a frame-of-reference that is fixed with respect to the Perihelion of the Earth’s.
Extract 2:
Consequently, the following analysis will consider two possible options. The first is that the four exceptional El Nino events are assumed to be associated with the Full Moon epochs (i.e. the “With Assumption” option), which can be considered as the most favourable case. The second is that the four exceptional El Nino events are assumed to be associated with the New Moon epochs (i.e. the “Without Assumption” option) which can be considered as the least favourable case.
Hence, given the two option being considered, there are two possible null hypotheses which can be proven or disproven using a given a Chi-Squared test.
e) Using a Chi-Squared test to disprove the Null Hypothesis
The first null hypothesis (H1O) assumes that all four exceptional El Nino events are a part of the Full Moon epochs, while the second null hypothesis (H2O) assumes that all four exceptional El Nino events are a part of the New Moon epochs. Both null hypotheses propose that: The absolute time difference in years between the starting months of the El Ninos and
1) the times of Equinox spring tidal events during the Full moon epochs, AND
2) the times of Solstice spring tidal events during the New moon epochs,
randomly lies somewhere between 0.0 and 2.0 years. These null hypotheses should be true if there is no connection between the starting times for El Nino events and the times of Equinox or Solstice spring tidal events
Table 4a shows that, in the most favourable case, the likelihood that H1O is correct is p < 0.0001. This means that little doubt that we can reject the (first) null hypothesis (χ2 = 21.692, degrees of freedom (df) = 3). In like manner, table 4b shows that, in the least favourable case, the likelihood that H2O is correct is p < 0.05. This means that even in the least favourable case (i.e. all four of the exceptional El Nino events are considered part of the New Moon epoch) we can reject the (second) null hypothesis (χ2 = 7.846, df = 3). Hence, we can conclude that, even in the least favourable case, there is a distinct preference for El Nino events to start near the times when Equinox spring tidal events occur during the Full Moon epochs and to start near the times when Solstice spring tidal events occur during New Moon epochs. This means that there must some connection between strongest Equinox/Solstice spring tidal events and the onset of El Nino events.
It is obvious, however, that the robustness of this claim is diminished to some degree by the small sample size. Indeed, it would only take one or two additional El Nino events that did not follow the observed pattern for p to exceed 0.05, rendering the result null and void for the least favourable case. Ideally, we will need a slightly larger sample size before we can feel more confident about this result.
