events are triggered by the Moon.
This series of posts will provide evidence that will eventually be used in a peer-reviewed paper that
will discuss the properties of the lunar orbit that are potentially responsible for the onset of El Niño events.
The five blog posts will cover the following topics:
I. The Changing Aspect of the Lunar Orbit and its impact Upon the Earth's Length of Day (LOD).
II. Seasonal Peak Tides - The 31/62 year Perigee-Syzygy Tidal Cycle.
III. The Sample - Strong El Niños between 1865 and 2014.
IV. The triggering mechanism for El Niños: The alignment of the lunar line-of-apse with the Equinoxes and Solstices of the Earth's orbit.
Plus - Predictions for the Future - The 2015/2016 El Nino and more.
I. The Changing Aspect of the Lunar Orbit and its Impact Upon the Earth's Length of Day (LOD).
a. Inter-Annual Changes in the Earth's LOD
The blue curves in figures 1a, 1b, and 1c (below) show the Earth's LOD over a six year period from January 1966 through to December 1971. These plots use daily LOD values that are available online from the International Rotation and Earth Reference System Service (IERS) covering the period from January 1962 until the present. This data can downloaded at:
http://datacenter.iers.org/eop/-/somos/5Rgv/latest/214
It is evident from these three figures that there are abrupt periodic slow downs in the Earth's rotation rate (corresponding to an increase in LOD) once every 13.7 days that are accompanied by much smoother longer-term changes in LOD that are associated with the annual seasonal cycle (red curves).
The smoother longer-term seasonal variations in LOD are primarily the result of changes in the angular momentum of the Earth that are a response to the slow (north-south) seasonal movement of the Earth's atmosphere and its wind patterns.
Figure 1a
Figure 1b
Figure 1c
A very crude attempt has been made in figures 1a, 1b, and 1c, to remove the longer-term seasonal component from the LOD measurements. This has been done by calculating the running median and standard deviation for a +15/-14 day time interval about a point and then subtracting 1.3 times the
standard deviation from that median. The resulting red curve (which has been smoothed by a 6th order binomial filter) has then been subtracted from the blue LOD curve to produce the de-trended LOD (green) curve.
Having removed the longer-term seasonal changes in LOD, we are left with the abrupt slow downs in the Earth's rotation rate (roughly) once every 13.7 days. More detailed investigations show that the spikes in LOD occur within a day or two of the time that the Moon crosses the Earth's Equator. This tells you that the slow down in the rotation rate is a direct result of the lunar tidal bulge in the Earth's oceans (and atmosphere) being dragged across the Earth's Equator by the Moon. The slow down occurs for much the same reason that a twirling ice-skater slows down their rate of spin by extending their arms i.e. by the conservation of angular momentum.
A more detailed comparison of the tidally induced peaks in LOD in figures 1a, 1b and 1c shows that in early 1966 (figure 1a) the peaks in LOD associated with transits of the Moon across the Equator from the northern to the southern hemisphere, are roughly twice as large as the next peaks in LOD (13.7 days later) that are associated with transits of the Moon across the Equator from the southern to the northern hemisphere. By the first three months of 1969 (figure 1b), the consecutive peaks in LOD are almost equal in size. And finally, bye late 1971 (figure 1c), the peaks in LOD that are associated with transits of the Moon across the Equator from the southern to the northern hemisphere, are roughly twice as large as the next peaks in LOD (13.7 days later) that are associated with transits of the Moon across the Equator from the northern to the southern hemisphere.
b. Factors That Influence the Slow Changes in the Ratio of the Consecutive Peaks in LOD.
The reason for the slowly changing ratios of consecutive peaks in LOD with time is evident from figures 2, 3 and 4.
Figure 2 shows the ratio of the size of consecutive peaks in LOD for the years 1962 to 1987.
Figure 2
Figure 3 shows the ratio of consecutive peaks in LOD versus lunar distance (in kilometres) for the numerator of the ratio, for the years from 1966 to 1971.
Figure 3
Figure 4 shows the size of the LOD peaks versus lunar distance (in kilometres), for the years from 1966 to 1971.
Figure 4
Figure 4 indicates that the size of the peaks in LOD (seen in figures 1a, 1b, and 1c) are primarily determined by the Moon's distance from the Earth as it crosses the Equator.
Figures 2 and 3 indicate that whenever the ratio of consecutive peaks in LOD is close to 1.0, the distance of the Moon from the Earth at consecutive transit crossings of the Equator are close to the
Moon's average distance from the Earth of approximately 380,000 km. However, whenever the ratio of consecutive peaks in LOD is far from 1.0 (i.e. either 2.0 or 0.5), the distance of the Moon from the Earth at one transit crossing is at the distance of closest approach (i.e. the distance of lunar perigee = 356,000 km), and the distance of the Moon at the other transit crossing is at its furthest from the Earth (i.e the distance of lunar apogee = 407,000 km).
Hence, it is evident from these figures that main factor that governs the size of the peaks in LOD seen in figures 1a, 1b and 1c, is the distance of the Moon from the Earth, at the time of its transit across the Equator. Similarly, these figures show that the slow change in the relative size of consecutive peaks in LOD are primarily driven by the slow drift of the lunar line-of-apse with respect to the stars. That is, whenever the Perigean end of the lunar line-of-apse aligns with the Sun at or near the time of the June or December Solstice (i.e. on the 21st of June or the 21 st of December), the ratio of the peaks in LOD is close to 1.0. However, whenever the perigee end of the lunar line-of-apse aligns with the Sun at or near the time of the March or September Equinoxes (i.e. on the 21st of march or the 21 st of September), the ratio of the peaks in LOD is either close to 0.5 or close to 2.0.
In order to highlight this latter point, the times at which the Perigean end of the lunar line-of-apse aligns with the Equinoxes (i.e. in March and September) and the times at which it aligns with the Solstices (i.e. in December and June) are marked along the bottom of figure 2. These markers show that the relative size of consecutive peaks in LOD are determined by the slow 8.85 year drift of the lunar line-of-apse with respect to the stars.
[Note: It is clear from figure 2 that the relative size of consecutive peaks in LOD are also affected by the slow drift in the tilt of the lunar orbit with respect to the plane of the ecliptic, over the 18.6 year Draconic cycle. In the preliminary analysis presented here, this secondary modulation is ignored, although it will be discussed in the peer-reviewed paper that is based upon these series of posts.]
c. Conclusions[Note: It is clear from figure 2 that the relative size of consecutive peaks in LOD are also affected by the slow drift in the tilt of the lunar orbit with respect to the plane of the ecliptic, over the 18.6 year Draconic cycle. In the preliminary analysis presented here, this secondary modulation is ignored, although it will be discussed in the peer-reviewed paper that is based upon these series of posts.]
In part I it has been established that:
a) The distance of the Moon from the Earth during its passage across the Earth's Equator determines the size of the 13.7 day peaks in LOD (i.e. the periodic slow-downs in the rate of the Earth's rotation).
b) The relative sizes of consecutive peaks in LOD are determined by the slow precession of the lunar line-of-apse with respect to the stars, once every 8.85 years.
c) In the years where the lunar line-of-apse are closely aligned with the Solstices, the ratio of the peaks in LOD are close to 1.0 and in the years where the lunar line-of-apse were closely aligned with the Equinoxes, the ratio of the peaks in LOD were far from 1.0 (i.e. either at 0.5 or 2.0).
d. Using a Proxy to Extending the Analysis to Dates Prior to 1962.
This study will be investigating El Nino events as far back as 1868. Unfortunately, there is little good quality daily LOD data prior to 1962, so a proxy is needed for the ratio in peaks of LOD prior to this date.
Figure 5
One such proxy, that is useful for keeping track of the relative orientation of the lunar line-of-apse compared to the Solstices and the Equinoxes is shown in figure 5. This plot shows the difference in lunar distance between consecutive transits of the Equator between the years 1962 and 1976. Superimposed upon this graph are the years in which the lunar line-of-apse is aligned with the Solstices and the Equinoxes. A comparison with figure 2 shows that this quantity is an excellent proxy for this parameter,
