Evidence that Strong El Nino Events are Triggered by the Moon - II

II. Seasonal Peak Tides - The 31/62 year Perigee-Syzygy
     Tidal Cycle.

     In part I it was established that:

a) The lunar distance during its passage across the Earth's
     Equator determined the size of the (13.7 day) peaks in
     LOD (i.e. the magnitude of the periodic slow-downs in
     the rate of the Earth's rotation).

b) The relative sizes of consecutive peaks in LOD were
     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 were closely
     aligned with the Solstices, the ratio of the peaks in LOD
     were 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. near
     either 0.5 or 2.0).

     This raise the question: Is there a lunar tidal cycle that
synchronizes the slow precession of the lunar line-of-apse
[which governs the lunar distance as the Moon crosses the
Equator] with the Synodic cycle (i.e the Moon's phases)
and the seasons? If there is, then it is clear that the
repetition period for such a long-term tidal cycle would
determine the time required for the largest (13.7 day)
peaks in LOD to reoccur, at the same point within the
seasonal calendar.

     The is such a cycle and it is called the 31/62 year 
Perigee-Syzygy Cycle. This tidal cycle is the time required
for a full (or new moon) at Perigee to re-occur at or very
near to the same point in the seasonal calendar.

     However, additional (background) information is
needed in order to fully understand  why this is the
case. This information will cover the following topics:

a) Perigean Spring Tides
b) The 8.85 year Cycle of Lunar Perigee and
c) The Full Moon Cycle (FMC)
d) The 20.293 year Perigee-Syzygy Cycle

A. The Perigean Spring Tides

     The phases of the Moon are caused by the fact the Moon
goes around the Earth once with respect to the Sun roughly
once every 29.53 days. Whenever the Moon, Earth and Sun are
lined up at New or Full Moon (i.e. syzygy) they produce
higher-than-normal variations in the heights of the tides that
are known as Spring Tides.

      The point in the Moon's orbit where the Moon is closest to
the Earth is known as Perigee, and the point where it is furthest
is known as Apogee. The line joining these two points is known
as the Line-of-Apse of the lunar orbit (see figure 1).

Figure 1

      Spring tides are strengthened when a Full or New Moon 

occurs at Perigee. This happens when the lunar line-of-apse 

is pointing at (or directly away from) the Sun. These stronger 
than normal Spring Tides are known as Perigean Spring Tides 
(see figure 2).

Figure 2

Perigean spring tides reoccur roughly once every 206
days (or once every 0.5 FMC - see below).

B. The 8.85 year Cycle of Lunar Perigee

     As the Earth revolves around the Sun, the line-of-apse 
slowly turns in a pro-grade direction (i.e. clockwise direction
in the figures shown in this post). This motion is caused by 
the precession of the line-of-apse of the lunar orbit about the 
Earth, once every 8.8501 sidereal years, as measured with 
respect to the stars. It is known as the Cycle of Lunar Perigee.

C. The Full Moon Cycle (FMC)

    The following five figures show the Earth moving in a 
clock-wise direction about the Sun. Figure 3a shows the 
location of the Earth in its orbit on January 1st. Superimposed 
upon the image of the Earth is an arrow showing the direction 
of the lunar line-of-apse – N.B. Perigee is pointing toward 
the Sun.

     As the Earth revolves around the Sun, the line-of-apse 

slowly precesses in a clock-wise direction. Figures 3b, 3c, 

3d, and 3e, show the position of the Earth and the lunar 

line-of-apse after 0.25, 0.50, 0.75 and 1.00 FMC, respectively.

   

Figure 3a

Figure 3b

Figure 3c

Figure 3d

Figure 3e

One Full Moon Cycle has passed after the 
Perigean-end of the line-of-apse points 
towards the Sun once again. Figure 3e 
shows that:

1.0 FMC = 411.78 days = 1.1274 tropical years

D. The 20.293 Perigee-Syzygy Cycle

If you have a new or full moon at closest
perigee (i.e. ~ 357,000 km) then it will again
be at closest perigee 20.293 years later. The
reason for this is that:


18 FMC  = 251 Synodic Months 
               = 269 Anomalistic Months 
               = 20.293 Tropical Years

Now the 20.293 year Perigee-Syzygy cycle
will realign with the seasons after:

(3 x 18 FMC)     + 1.0 FMC    = 55 FMC

(3 x 20.293 yrs) + 1.2174 yrs  = 62.006 yrs

Hence, it is this re-alignment that produces the 31/62 year 
Perigee-Syzygy seasonal tidal cycle.

E. The 31/62 Year Perigee-Syzygy Seasonal Tidal Cycle

     Alternatively, it is possible to see the 31/62 year

Perigee-Syzygy seasonal cycle as a realignment of the FMC 
with the seasonal calender. Figure 4 explains why this is the 
case.

Figure 4


     If we start out with the conditions shown in
figure 3a i.e the Earth at its January 1st position 
in its orbit and the perigee end of the lunar 
line-of-apse is pointing at the Sun, after 5.5 
FMC the perigee end of the lunar line-of-apse 
will be pointing directly away from the Sun 
and the Earth will have moved 6.2 orbits. This 
means that after five of these time intervals i.e.

5 x 5.50 FMC       = 27.5 FMC 
5 x 6.20086 years = 31.003 tropical years

the Earth will again be located at its January 1st
orbital position but with the perigee end of the lunar
line-of-apse pointing directly away from the Sun.

     Of course, to return to the original configuration
seen in figure 3a, with the perigee end of the lunar 
line-of-apse pointing directly towards the 
Sun, it will take twice as long i.e. 62.006 years. 

Figure 5 shows how the FMC and 20.293 year 

Perigee-Syzygy cycle are linked together and
how they re-synchronize with the seasons to
produce the 31/62 year Perigee-Syzygy seasonal 
tidal cycle. 

Figure 5

     The top part of figure 5 shows that if you start out
with a new moon at closest perigee, 20.293 years
(18 FMC) later you will get another new moon
at closest perigee. However, after 10.71 years (9.5
FMC) you have a Full Moon at closest perigee that
will also reoccur after 31.00 years (27.5 FMC),
achieving re-alignment with the seasonal calender.

     Again, it takes two of these 31 year time intervals
(i.e. 62.00 years = 55 FMC) to return a new moon at
closest perigee at the same point in the seasonal
calender.

F.  What are the Implications for the Triggering of 
      El Nino Events?

     The 31/62 year Lunar Perigee/Syzygy Seasonal tidal
cycle is the one that synchronizes the slow precession of
the lunar line-of-apse [which governs the distance of the
Moon as it crosses the Earth's Equator] with the Moon's
phases and with the seasons.

     Hence, if El Nino events are triggered by a phenomenon
that is associated with the abrupt slow downs in the Earth's
rotation rate once every 13.7 days, you might expect that
the 31/62 year seasonal tidal cycle would be evident in the
sequencing of the El Nino events.

     This study covers all the strong El Nino events between
1865 and 2014. A detailed investigation of the precise
alignments between the lunar synodic [lunar phase] cycle
and the 31/62 year Perigee-Syzygy cycle, over the time
period considered, shows that it naturally breaks-up
into six 31 year epochs each of which has a distinctly
different tidal property. The second 31 year interval
starts with the precise alignment on the 15th of April
1870 with the subsequent epoch boundaries occurring
every 31 years after that. :

Epoch 1 - Prior to 15th April  1870
Epoch 2 - 15th April 1870 to 18th April 1901
Epoch 3 - 8th April 1901 to 20th April 1932
Epoch 4 - 20th April 1932 to 23rd April 1963
Epoch 5 - 23rd April 1963 to 25th April 1994
Epoch 6 - 25th April 1994 to 27th April 2025

     The following discussion uses Epochs 2 and 3 to highlight
the reasons why each of these 31 year epochs have distinctly
different tidal properties.

     Figure 6 shows all of the tidal events between the 15th
of April 1870 and the 18th of April 1901 where a new of full
moon occurred within +/- 2.5 hours of Perigee. In essence,
this diagram shows the strongest two or three tidal events in
any given month of the year, over the full 31 year epoch.

[NOTE: It is important to recognize that the pattern that
 is seen for the strongest tidal events is representative of
 what is happening with the underlying weaker tidal events
 as well.]

     Figure 6 shows that in epoch 2, the strongest tidal events
between April and November are full moons, while those
between December and March are new moons. In addition,
it turns out that almost all of these strong tidal events (both
new and full moon) occur in the southern hemisphere.

     The pattern that is seen in the seasonal peak tidal events
in epoch 2 (i.e. in figure 6) are also repeated in epochs 4
and 6.
       

Figure 6

      Figure 7 shows all of the tidal events between the 18th
of April 19010 and the 20th of April 1932 where a new of full
moon occurred within +/- 2.5 hours of Perigee. As with figure
6, this diagram shows the strongest two or three tidal events in
any given month of the year, over the full 31 year epoch.

     Figure 6 shows that in epoch 3, the strongest tidal events
between April and November are new moons, while those
between December and March are full moons. In addition,
it turns out that almost all of these strong tidal events (both
new and full moon) occur in the northern hemisphere.

     The pattern that is seen in the seasonal peak tidal events
in epoch 3 (i.e. in figure 7) are also repeated in epochs 1
and 5.

Figure 7

     Hence, you would expect that the distinctly different tidal
properties for the 31 year epochs 1, 3, and 5 compared to the
31 year epochs 2, 4 and 6 should be evident in the sequencing
of El Nino events over the period from 1865 to the present.

      Thus, if the 31/62 year seasonal tidal cycle plays a
significant role in sequencing the triggering of El Nino events
it would be reasonable to expect that its effects for the
following three epochs:

New Moon Epoch:
Epoch 1 - Prior to 15th April  1870
Epoch 3 - 8th April 1901 to 20th April 1932
Epoch 5 - 23rd April 1963 to 25th April 1994

[That have peak seasonal tides that are dominated
  by new moons that are predominately in the
  northern hemisphere]

should be noticeably different to its effects for these
three epochs:

Full Moon Epochs:
Epoch 2 - 15th April 1870 to 18th April 1901
Epoch 4 - 20th April 1932 to 23rd April 1963
Epoch 6 - 25th April 1994 to 27th April 2025

[That have peak seasonal tides that are dominated by
  full moons that are predominately in the southern
  hemisphere]