Thursday, May 19, 2016

Changes to the Earth's albedo appear to lead the SOI Index by approximately 6 months

Figures 1a shows the mean monthly apparent albedo anomalies from December 1998 to December 2014 as measured by ground-based earth-shine observations. The anomalies are calculated over the mean of the full period and positive anomalies are shown in red and negative in blue. The averaged standard deviation (error) of the monthly data is also indicated in the lower right corner.

Ref:
Palle, E., et al. (2016), Earth’s albedo variations 1998–2014 as measured
from ground-based earth-shine observations, Geophys. Res. Lett., 43, 
doi:10.1002/2016GL068025

Figure 1a and 1b



































Figure 1b shows the monthly Southern Oscillation Index (SOI) published by the Australian Bureau of Meterology (BOM) at:

ftp://ftp.bom.gov.au/anon/home/ncc/www/sco/soi/soiplaintext.html

The SOI has be shifted backward in time by 6 months.

Not withstanding the large error bars associated with the mean monthly apparent albedo anomalies, and the gap in the albedo anomaly data between June 2005 and December 2006, there appears to be rough correlation between the retarded SOI and the monthly apparent albedo anomaly.

If this correlation has any validity then I would predict that the Earth's mean monthly albedo anomaly will remain in negative territory from late 2014 till the end of 2015. 

The next few of years of data from the Earth-shine project should be very interesting if it does. 


Saturday, May 7, 2016

Moderate to strong El Nino events are triggered by the inter-annual variability in the lunar tides.

Moderate to strong El Nino events are triggered by long-term (i.e. inter-annual) variability in the lunar tides. Specifically, the timing of these events is directly related to 31/62 year Perigee/Syzygy lunar tidal cycle.
I do not have all the answers as to how this actually happens but the best answer that I can come up with is that slow forcings applied to the Earth by the lunar tides influences the formation and subsequent propagation of Madden-Julian Oscillations (MJO) along the Equatorial Indian Ocean and Pacific Oceans.
A MJO consists of a large-scale coupling between the atmospheric circulation and atmospheric deep convection. When a MJO is at its strongest, between the western Indian and western Pacific Oceans, it exhibits characteristics that approximate those of a hybrid-cross between a convectively-coupled Kelvin wave and an Equatorial Rossby wave. When a MJO moves from the western Indian Ocean into the western Pacific Ocean, it generally accelerates, becomes less strongly coupled to convection, and transitions into a convectively de-coupled (i.e. dry) Kelvin wave.
Periodically (i.e. roughly once every 4.5 years), the precise alignments of the lunar tidal forcings produce the right conditions that result an upsurge in the number and magnitude of what I call Pacific Penetrating MJO. These are MJO events that travel from the Eastern equatorial Indian Ocean, along the Equator, all the way into the Western Pacific Ocean, where they initiate Westerly Wind Bursts (WWB’s).
The spawning of these WWB’s takes place as the MJO event is transitioning from a hybrid-cross between, a convectively-coupled Kelvin wave and an Equatorial Rossby wave, and a convectively de-coupled (i.e. dry) Kelvin wave. The spawning of the WWB’s occurs in the Western Equatorial Pacific Ocean, somewhere between 60 deg E and 150 deg W longitude. The actual process involves the formation of a typhoon/cyclone pair straddling the equator which produces an intense WWB between the two intense low pressure cells.
The onset of El Nino event are marked by the weakening of the easterly trade winds associated with the Walker circulation. The actual drop off in easterly trade wind strength is always preceded by a marked increase in WWB’s in the western equatorial Pacific Ocean. The WWB’s help initiate an El Nino event by creating downwelling Kelvin waves in the western Pacific that propagate towards the eastern Pacific, where they produce intense localized warming, as well as by generating easterly moving equatorial surface currents which transport warm water from the warm pool region into the central Pacific.
The net result of the Moon’s involvement in the initiation of El Nino events means that:
El Niño events in New Moon epochs preferentially occur near times when the lunar line-of-apse aligns with the Sun at the times of the Solstices.
El Niño events in the Full Moon epochs preferentially occur near times when the lunar line-of-apse aligns with the Sun at the times of the Equinoxes.
For a full description of the meaning of Full and New Moon Epochs please read:

Are we looking in the wrong place for the connection between solar insolation and the world's mean temperature?

I propose that it is the lunar tidal modulation of the seasonal variations in the solar flux, coupled with the hemispherical asymmetry of the Earth’s surface properties (i.e. Nth Hemisphere – dominated by continents, St Hemisphere – dominated by oceans) that is responsible for setting the world's mean temperature.

On inter-annual time scales:

There are periodic slow downs in the Earth’s rotation rate every 13.66 days. These slows downs are caused by the passage of the lunar tidal bulge across the Earth’s equator once every half lunar tropical month = 13. 66 days. The ratio in the magnitude of the increase in Length Of Day (LOD) at one crossing with respect to the magnitude of the increase in LOD at the next is primarily governed by the orientation of the lunar line-of-apse with respect to the seasonal cycle as marked by the solstices and equinoxes (there is also a secondary effect caused by the 5 degree tilt of lunar obit with respect to the ecliptic). Please see:


On decadal time scales:

The climate variation is driven by the ratio in strength and frequency of El Nino to La Nina events – This is dominated by the 31/62 year lunar tidal cycle. For 31 years, El Ninos start in years when lunar line-of-apse is pointed at the Sun near the Winter/Summer solstices, then for next 31 years, El Ninos start in years when lunar line-of-apse is pointed at the Sun near the Vernal/Autumnal equinoxes.


On centennial to millennial time scales:

The climate variation appear to be correlated with variations in the overall strength of the Sun’s magnetic field as indicated by Be10 and C14 proxies. These primarily occur at 88.5 years (Gleissberg cycle), 208 years (de Vries Cycle), 354 years, 510 years, 708 years, 980 years (Eddy Cycle) and 2300 years (Hallstatt Cycle). It just so happens that these cycles in the Sun’s magnetic field strength are matched by the times at which the lunar line-of-apse points at the Sun at either the solstices or equinoxes of the Earth’s seasonal calendar (in a reference frame that is fixed with respect to the Earth’s orbit).

This produces a long term 21,000 year climate forcing which when coupled with the Milankovitch orbital forcing and the formation and melting of ice sheets at the Earth’s poles, produces the ice-age cycles.

There is a natural 208 year de Vries-like cycle in the Lunar Tidal Forces acting upon the Earth

1. The Defacto 13 year Lunar tidal cycle

There is a defacto 13 year lunar tidal cycle created by the difference 
between 31 perigee/syzygy cycle and the 18 year Saros cycle, such that:

13 years = 31 – 18 years

Now the reason for the 18.03 sidereal year Saros cycle is:

223 Synodic months______= 18.02931 sidereal years
239 anomalistic months___ = 18.02990 sidereal years
242 Draconic months______= 18.02941 sidereal years
[with closest alignment between Synodic and Draconic cycles,
though the anomalistic cycle is not far off]

while the reason for the 31 year cycle is:

383.5 Synodic months______= 31.005568 sidereal years
411.0 anomalistic months___ = 31.005401 sidereal years
416.0 Draconic months_____= 30.992708 sidereal years
[with closest alignment between Synodic and anomalistic cycles]

hence, the defacto 13 year cycle possibly comes about because:

160.5 Synodic months______= 12.976254 sidereal years
172.0 anomalistic months___= 12.9754963 sidereal years
174.0 Draconic months_____= 12.9632963 sidereal years
[with closest alignment between Synodic and anomalistic cycles]

2. The 208 year de Vries Cycle
Now 
16 x 13 years = 208 years
Thus, this would indicate that a possible reason for the ~ 208 de Vries cycle is:
16 x 160.5 = 2568.0 Synodic cycles________= 207.6200718 sidereal years
16 x 172.0 = 2752.0 anomalistic cycles_____= 207.6079414 sidereal years 

16 x 174.0 = 2784.0 Draconic cycles_______= 207.4127406 sidereal years

or with a drift of 3.0 Draconic cycles in roughly 208 years you get:
2787.0 Draconic cycles___= 207.6362457 sidereal years 
[with closest alignment between Synodic and anomalistic cycles]

Finally, if you allow for a slight drift of 4.5 Synodic cycles and 5.0 anomalistic and
Draconic cycles you get:

2572.5 Synodic cycles___= 207.98389 sidereal yrs_____= 207.99196 tropical yrs
2757.0 anomalistic cycles_= 207.98514 sidereal yrs____= 207.99321 tropical yrs
2792.0 Draconic cycles___= 208.00875 sidereal yrs____= 208.01682 tropical yrs

Of course, the drift required to realign the sidereal/tropical reference frame 
with the seasonal year of 4.5 synodic = 5.0 anomalistic = 5.0 Draconic cycles 
over 208 tropical years is not arbitrary since this is equivalent to:

132.887 days in 75970.375 days = 0.0017492 of a full cycle in 208 tropical years.

which for the Earth’s orbit is 0.6297133 degrees in 208.0 tropical years
or 10.90 ~ 11 arc second per tropical year!

This is just the (pro-grade) rate of precession of the perihelion of the Earth’s orbit 
which is currently about:

11.45 arc seconds per year – theoretical
11.62 arc seconds per year – observed epoch 2000.

CONCLUSION 
Hence, If we look at times where the perigee of the lunar orbit points at the 
Sun, they will realign with the seasons in (almost) precisely 208.0 tropical 
years or one de Vries Cycle, if you measure the alignment in a reference 
frame that is fixed with the Earth’s orbit (i.e. a frame that is tracking the 
perihelion precession of the Earth’s orbit).

Thursday, March 24, 2016

There is a natural Gleissberg-like Cycle in the Lunar tidal stresses placed upon the Earth

Preamble

1. There is a lunar tidal cycle that synchronizes the slow precession of the lunar line-of-apse with the seasons and the Synodic cycle (i.e. the Moon's phases). 

The tidal cycle 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.

It is highly recommended that readers go to the following link to get a fuller understanding of the parameters that are used to define the lunar orbit as well a better understanding of the 31/62 year Perigee-Syzygy tidal cycle, before proceeding with this post.

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

2. The current post needs to be read in the light of the fact that a previous post at:


claimed that:

El Niño events in New Moon epochs preferentially occur near times when the lunar line-of-apse aligns with the Sun at the times of the Solstices..

El Niño events in the Full Moon epochs preferentially occur near times when the lunar line-of-apse aligns with the Sun at the times of the Equinoxes. 

CURRENT POST

The Changing Aspect of the Lunar Orbit & its Impact Upon the Earth's Length of Day.

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.


1a   LOD - 1966 to 1968


















1b   LOD – 1968 to 1970


















1c   LOD – 1970 to 1972


















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 ~ 1 msec) once every 13.66 days (blue curve)* 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.

The green LOD curve is a crude seasonally de-trended version of the blue LOD curve.

[Note: Half of a lunar tropical month = 27.32158 /2 = 13.66079 days.*]

b. Reason for the Peaks in the Earth's LOD

A more detailed investigation show that the spikes in LOD (in the blue and green curves) 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) passing across the Earth's Equator.

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.















c. The Change in the Ratio of Consecutive Peaks in LOD


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 (13.66 days later) that are associated with transits of the
Moon across the Equator from the southern to the northern hemisphere.

By early 1969 (figure 1b), the consecutive peaks in LOD are almost equal in size

By 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 (13.66 days later) that are associated
with transits of the Moon across the Equator from the northern to the southern
hemisphere.

2. 



Figure 2 shows that the absolute size of the slow down in the Earth’s rotation rate is
determined by the proximity of the Moon as its crosses the Earth’s Equator 

3.


















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.

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).

4. 



Figure 4 shows the difference in lunar distance for consecutive transits of the Earth’s
Equator from 1962 to 1976.

Figure 4 confirms that whenever the perigee of the lunar orbit is pointed at Sun at the time of the
Summer or Winter solstices, the difference in lunar distance for consecutive transits of the Earth’s
equator is near zero kilometres i.e. the ratio of consecutive peaks in LOD are ~ 1.0 because the lunar
 distances at consecutive crossings are both close to the average lunar distance of 380,000 km

Similarly, figure 4 confirms that whenever the perigee of the lunar orbit is pointed at Sun at the time
of the Vernal or Autumnal equinoxes, the difference in lunar distance for consecutive transits of the
Earth’s equator approaches the maximum 50,000 km i.e. the ratio of consecutive peaks in LOD are
far from 1.0 because the Moon is near perigee and apogee at consecutive crossings.

d. Reason for the Change in the Ratio of Consecutive Peaks.

5. Lunar Perigee pointing at the Sun near Summer or Winter Solstices



























The yellow tilted elliptical orbits in figure 5 above, represent the apparent movement of the Sun about
the sky as seen from the Earth. The Sun takes a full tropical year (365.242189 days) to move once
about the yellow orbit, crossing the Earth’s equatorial plane (the grey plane) once every
six months at the Spring and Autumnal (Fall) equinox, respectively.

The red tilted elliptical orbits above, represent the apparent movement of the Moon about the sky
as seen from the Earth. The Moon takes a full tropical month (27.32158 days) to move once about
the red orbit, crossing the Earth’s equatorial plane roughly once every 13.66 days where the red
orbit crosses the black line [N.B. the ~ 5 degree tilt of the lunar orbit with respect to the ecliptic is
ignored as a second order effect at this stage of the argument.] 

Clearly, if the perigee of the lunar orbit points at the Sun at either the Winter (i.e. the top diagram)
or Summer Solstice (i.e. the bottom diagram), the Moon will be roughly at or near its average
distance from the Earth (i.e. ~ 380,000 km). This means that when it crosses the Earth’s equatorial
plane at consecutive transits of the Equator (i.e. the intersection of the red orbit and the black line),
the difference in lunar distance for consecutive transits will approach zero (i.e. the ratio of
consecutive peaks in LOD will be close to 1.0) 

6. Lunar Perigee pointing at the Sun near Vernal or Autumnal Equinox


   






















The yellow tilted elliptical orbits in figure 6 above represent the apparent movement of the Sun about
the sky as seen from the Earth. The Sun takes a full tropical year (365.242189 days) to move once
about the yellow orbit, crossing the Earth’s equatorial plane (the grey plane) once every six
months at the Spring and Autumnal (Fall) equinox, respectively.

The red tilted elliptical orbits above, represent the apparent movement of the Moon about the sky
as seen from the Earth. The Moon takes a full tropical month (27.32158 days) to move once about
the red orbit, crossing the Earth’s equatorial plane roughly once every 13.66 days where the red
orbit crosses the black line.

Clearly, if the perigee of the lunar orbit points at the Sun at either the Vernal (i.e. the bottom
diagram) or Autumnal Equinox (i.e. the top diagram), the Moon will be at or near perigee and apogee
at consecutive transits of the equatorial plane (i.e. where the red orbit crosses the black line).

This means that when it crosses the Earth’s equatorial plane at consecutive transits, the difference in
lunar distance for consecutive transits will approach its maximum value of 50,000 km (i.e. the ratio
of consecutive peaks in LOD will be as far from 1.0 as possible).

Hence, figure 4 tells us that the perigee moves from pointing at the Sun at a Solstice(/Equinox)
to pointing at the Sun at the following Equinox(/Solstice) in the seasonal calendar once every  
2.0 Full Moon Cycles (FMC) = 2.0 x 411.78444836 days 2.2547695 sidereal years = 2.2548570
tropical years

e. The 9.019 Tropical Year Cycle

7. 


















Figure 7 shows the ratio of the consecutive 13.66 day peaks in LOD from 1962 to 1988.

It is evident from this plot that the long-term variation in the ratio of consecutive peaks is dominated
by a periodicity of ~ 9.0 years. In addition, there is an approximate 18.0 year periodicity that
modulates the ~ 9 year periodicity.  

The 9.0 periodicity results from the fact that 4.0 x 2 FMC = 9.019428 tropical years  is the
time required for slowly drifting perigee of the lunar orbit to return to pointing at the Sun at the same
Solstice or Equinox (since it takes 2.2548570 topical years for the alignment of the perigee with the
Sun at a Solstice/Equinox to move to the following Equinox/Solstice in the seasonal calendar.

(N.B. The ~  9.0 period is close to but not necessarily the same as the 8.85 years that it takes the
lunar line-of-apse to precess once around the Earth with respect to the star. In addition, the
~ 18.0 periodic modulation of the 9.0 year period is close to but not necessarily the same as the 18.6
year period that it takes the lunar line-of-nodes to precess once around the Earth with respect to the
stars. The 18.6 year period is caused by the slowly changing tilt of the Moon’s orbit with respect to
the Earth’s equator caused by precession of the lunar-line-of-nodes - Please see the Addendum at the
end of this post about the possible long-term interaction of these two lunar cycles).

f. A Gleissberg Cycle in the Ratio of Consecutive Peaks in LOD.

The slow pro-grade precession of the perigee of the lunar orbit through the seasonal calendar leads to
the perigee moving from pointing at the Sun at one Solstice(/Equinox) to pointing at the Sun at the
following Equinox(/Solstice) once every 2.0 Full Moon Cycles (FMC) = 2.0 x 411.78445750
days = 2.2547695 sidereal years2.2548570 topical years.

However, since 2.0 FMC is longer than 2.00 sidereal years (by 0.2547695 sidereal years), the perigee
of the lunar orbit will slowly drift from pointing at the Sun at a given point in the seasonal calendar,
only re-synchronizing with the seasonal calendar after:
  
(2.0000000 x 2.2547695) / (2.2547695 - 2.0000000) 17.70046823 sidereal years 

This comes about because there are 8.850234 lots of 2.00 sidereal year cycles in 17.70046823
sidereal years and 7.850234 lots of 2.2547695 sidereal year cycles in 17.70046823 sidereal years.

In effect, what this means is that there will be a precise realignment between when the lunar perigee
points at the Sun at a given Solstice/Equinox and when it does so again at the same point in the
seasonal calendar (i.e. the same Solstice/Equinox), once every 354.000 years:    

157 x 2.0 FMC = 353.9988071 354.00 sidereal years

Of course, it would take half of this time i.e. 177.0 sidereal years, if we broaden our criterion to
include the cases where the lunar Perigee points directly away from the Sun:

157 x 1.0 FMC = 176.9999404 ≈  177.000 sidereal years

And it would take half of this time again i.e. 88.5 years, if we only make the constraint that the
Perigee of the lunar orbit move from one Solstice/Equinox to the next, rather than go through the full
seasonal calendar:

157 x 0.5 FMC = 88.499702 ≈  88.500 sidereal years 

Hence, the long-term variations of the ratio of the strength of the consecutive (13.66 day) slow
downs in the Earth’s LOD that are caused by the Moon transiting across the Earth’s Equator,
have a natural long term repetition cycle with respect to the seasons that matches that of the:

88 year Gleissberg Cycle 


~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Addendum 1 - A Possible 2340 Year Hallstatt-like Cycle 

In this blog post we have established that there is a quasi 9.0 year periodicity in the ratio of
consecutive increases in the Earth’s LOD that result from transits of the Moon across the Earth’s
Equatorial plane every 13.66 days.

There is a possibility that the quasi 9.0 periodicity could be the harmonic mean of the two factors in
figure 7 that are influencing the long-term variations in the ratio of consecutive increases in the
Earth’s LOD  i.e. the 8.8505 tropical year precession of the lunar line-of-apse (i.e. the Lunar
Anomalistic Cycle - LAC) and the 9.3001 (= 18.6002/2.0) tropical year half cycle for the precession
of the lunar-line of nodes (i.e. the half Lunar Nodical Cycle - LNC) such that:

2.0 x (9.3001 x 8.8505) / (9.3001 + 8.8505) = 9.0697(3) tropical years

Since 9.0697(3) tropical years is slightly longer than 9.00 tropical years, it slowly drifts by 0.0697(3)
tropical years once every 9.06973 years, resulting in a forward shift by
one full tropical year once every:

9.06973 / (9.06973 9.00000) 9.06973 / 0.06973 ≈ 130.069267 tropical years

In addition, the beat period between 9.0697(3) tropical year and 9.00000 tropical year gives:

9.00 x 9.06973 / (9.06973 – 9.00) = 1170.623 tropical year  ≈  9.0 x 130.069267 tropical years

Which is half of a Hallstatt-like cycle of 2341.247 tropical years. 

Hence, the interaction between the LAC with LNC naturally produces a Hallstatt-like cycle.

Addendum 2 - Some More Information on the 31 Year Perigee-Syzygy Lunar Tidal Cycle

A1

















Figure A1 shows the offset in days from a New/Full Moon at each instant where the Perigee of the
lunar orbit points either towards or away from the Sun - up to 27.5 FMC = 31.00308 sidereal years.
This figure shows us that phase of the Moon goes from:

New --- Full --- New --- Full    every

0.0 --- 9.00 --- 18.00 --- 27.00 FMC's

0.0 --- 10.146463 --- 20.292925 --- 30.439388 sidereal years

with the Moon being less than one day past Full Moon at 27.5 FMC = 31.00308 sidereal years.

A2

















Figure A2 shows the offset of the Moon from the lunar line-of-apse at each instant where the Perigee
of the lunar orbit points either towards or away from the the Sun - up to 27.5 FMC = 31.00308
sidereal years (N.B. the Perigee alternates between point directly at the Sun to pointing directly away
from the Sun once every 0.5 FMC).

Hence

New Perigee --- Full Apogee --- New Perigee --- Full Apogee    every

0.0 --- 9.00 --- 18.00 --- 27.00 FMC's

0.0 --- 10.146463 --- 20.292925 --- 30.439388 sidereal years

with the Moon returning to perigee, less than one day past Full Moon, at 27.5 FMC = 31.00308
sidereal years.