Saturday, October 31, 2015

Part B: Are Lunar Tides Responsible for Most of the Observed Variation in the Globally Averaged Historical Temperature Anomalies?

RETRACTION: The claim made in this blog post that the peak differential lunar force across the Earth's diameter (that is parallel to the Earth’s equator) produces an annually aliased signal with a period of 20.58 years is incorrect. The 384 day period in the peak differential lunar tidal force data that is used to establish 20.58 year bi-decadal period only exists for periods around the 4.53 year long term maxima in lunar tidal force. It turns out that the long term mean spacing between the short-term peaks in the differential tidal force is close to length of the Full Moon cycle, which is equal to 1.12743 tropical years. Hence, the 384 day spacing between peaks does not last long enough for the beat period of 20.58 years to physically meaningful. I would like to thank Paul Vaughan for pointing out this stupid mistake upon my part. In my next post, I will explain why the bi-decadal oscillation is more likely to be explained by a 20.85 tropical year period related to annual aliasing of the lunar tropical and anomalistic months. 
    
PART B: A Mechanism for the Luni-Solar Tidal Explanation 
PART A: Evidence for a Luni-Solar Tidal Explanation
[Please see the last post]

PART B: A Mechanism for the 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 Bid-Decadel 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 [1] 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.

     It is generally accepted that the ~ 9.1 - 9.2 year spectral feature is caused by luni-solar tidal cycles associated with the first sub-multiple of the 18.6 year Draconic cycle 9.3 (=18.6/2) = 9.3 years, possibly merged with the 8.85 year lunar apsidal  precession cycle, such that (8.85 + 9.3)/2 = 9.08 years . Hence the question really is: 


Can a plausible luni-solar tidal explanation be given for the 20.68 yr bi-decadal oscillation?

B.  A Potential Luni-Solar Tidal Mechanism  

     Wilson [2] 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 findings provides observational evidence to support the hypothesis that the lunar tidal cycles are primarily responsible for the onset of El Nino events.  

     If this finding is confirmed by further study then it would reasonable to assume that changes in the level of generation of  PPMJO's is related the changes in the overall level of tidal stress acting upon the equatorial regions of the Earth. A good indicator of the magnitude of these tidal stresses is the peak differential luni-solar tidal force acting across the Earth's diameter, that is parallel to the Earth's equator.  

     The peak differential tidal force of the Moon (dF) (in Newtons) acting across the Earth's diameter (dR = 1.2742 x 10^7 m), 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. that 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:


where R is the distance of the Moon and Dec(M) is the declination of the Moon.

     In like manner, the component of the peak differential tidal force of the Sun (in Newtons) acting across the Earth's diameter that is parallel to the Earth's equator is:


where Rs is the distance of the Earth from the Sun and Dec(S) is the declination of the Sun.

     The relatively rapid daily rotation of the Earth compared to the length of lunar month means that the effects upon the Earth of two differential tidal forces only changes slightly during any given single day. Hence, it is possible to define a slowly changing peak luni-solar differential tidal force acting across the Earth's diameter that is parallel to the Earth's equator, by simply adding each of the two forces above vectorially.

     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 day designated period (JPL Horizons on-Line Ephemeris System v3.32f 2008, DE-0431LE-0431 [3].) . 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:

Figure 1a


     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:

Figure 1b.


C. Discussion

     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 a 4.53 years. This is very close to half the 9.08 year quasi-decadal oscillation. It also shows that around these 4.53 peaks in tidal stress, the individual peaks in tidal stress are almost precisely separated by 13 Synodic months.

     Wilson [4] 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 [4] 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) = 7516.06.07 days = 20.58 tropical years          

This is remarkable close to the 20.68 year bi-decadal oscillation seen by Copeland and Watts [1] in their sinusoidal model fit to the first difference of the HP smoothed HadCRUT3 global monthly temperature anomaly series.

   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 [5] 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 Drconic 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 only about 7.3 days longer than precisely 93.0 tropical years.

Keeling Whorf [5] claimed that 93 period 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 observed between 1900 and 1945.

APPENDIX

      It could be argued, however, that Keeling and Whorf's figure 03 [reproduced as figure 02 below] actually points a hiatus period between about 1920 and 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:

Figure 2

    
Wilson [6] 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 lineonce every 4.425 years [the brown line in figure 3 below]. They 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 1950's.        

Figure 3


















Finally, Wilson [6] 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 [6] 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."

Figure 4














 References

[1] 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:
http://wattsupwiththat.com/2009/05/23/evidence-of-a-lunisolar-influence-on-decadal-and-bidecadal-oscillations-in-globally-averaged-temperature-trends/
[2] 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.

[3] 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.

[4] 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.

[5] 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.

[6] Wilson, I.R.G. (2013), Long-Term Lunar Atmospheric Tides in the Southern Hemisphere, The Open Atmospheric Science Journal, 7, pp. 51-76.











Wednesday, October 28, 2015

Are Lunar Tides Responsible for Most of the Observed Variation in the Globally Averaged Historical Temperature Anomalies?

PART A: Evidence for a Luni-Solar Tidal Explanation
PART B: The Mechanism for a Luni-Solar Tidal Explanation 
[Please see the next post] 

PART A: Evidence for a Luni-Solar Tidal Explanation

1. Background

A. Keeling and Whorf
     Keeling and Whorf [2] "present evidence that global temperature has fluctuated quasi-decadally since 1855, except for an interruption between about 1900 and 1945, thus supporting previous claims of failures of weather phenomena to maintain a correlation with the sunspot cycle near 1920. This interruption, although difficult to explain by a sunspot mechanism, does not rule out a tidal mechanism, because the astronomically driven tide raising forces since 1855 have exhibited strong 9-year periodicity only when quasi-decadal periodicity was evident in temperature data. Furthermore, unlike the perplexing shift in the phase of quasi-decadal temperature fluctuations with the sunspot cycle between the 19th and 20th centuries, there was no such shift in phase with respect to tidal forcing."

[N.B. Figure 3 of Keeling and Whorf [http://www.pnas.org/content/94/16/8321.full.pdf] clearly shows the 180 degree phase shift between the mean sunspot number and decadal band-pass of global surface temperature between about 1900 and 1945.]




















     Keeling and Whorf [1,2], working with globally averaged temperature data for both land and sea (expressed as an anomaly beginning in 1855 and updated through mid-1995), report strong spectral peaks at 9.3, 15.2, and 21.7 years.  They refer to the 9.3 period as the quasi-decadal signal and the 21.7 year period as the bi-decadal signal.

     Keeling and Whorf [1,2] show that the "near[quasi]*-decadal variations in global air temperature are characteristic of the past 141 years [1885 - 1995]*, except for a roughly 45-year interruption centered near 1920 [i.e. 1900 - 1945]*. This pattern has also emerged using spectral analysis, specifically from the beating of two frequencies found to be close to the 9th and 10th harmonics of the lunisolar tidal cycle of 93 years. Furthermore, temperature oscillations with periods near 6 years were found in the temperature record by spectral analysis near the time of interference of the two near-decadal oscillations [i.e. 1900 - 1945]*, and thus close in period to the 6-year repeat period of another prominent lunisolar tidal cycle."

[N.B. bracketed text with a "*" next to it are my additions to the original quote.]

B. Copland and Watts

     Copeland and Watts [3] show ..."that decadal and bidecadal oscillations in globally averaged temperature show patterns of alternating weak and strong warming rates, and that these [warming rates]* underwent a phase change [with respect to the solar cycle]* around 1920.  Prior to that time, the lunar [tidal]* influence dominates, while after that time the solar influence dominates.  While these show signs of being correlated with the broad secular variation in atmospheric circulation patterns over time, the persistent influence of the lunar nodal cycle, even when the solar cycle dominates the warming rate cycles, implicates oceanic [tidal]* influences on secular trends in terrestrial climate."

     Copeland and Watts [3] ... "pick up where Keeling and Whorf [1,2]* leave off, insofar as documenting decadal and bidecadal oscillations in globally averaged temperature trends is concerned, but...[claim]* ...that these are likely the result of a combined lunisolar influence, and not simply the result of lunar nodal and tidal influences [as claimed by Keeling and Whorf]*." 

     Figure 4 of Copeland and Watts [3] shows the MTM spectrum analysis of the unfiltered HadCRUT3 monthly global temperature anomaly time series between January 1850 and November 2008 [4]. Copeland and Watts [3] find a "“quasi-oscillatory” cycle with a peak at 8.98 years, and a “harmonic” signal centered at 21.33 years." They also find that ..."The harmonic at 21.33 years in Figure 4 encompasses a range from 18.96 to 24.38 years, and the quasi-oscillatory signal that peaks at 8.93 [sic] years has sidebands above the 99% significance level that range from 8.53 to 10.04 years. 

     Copeland and  Watts [3] claim that ..."A bidecadal frequency of 20.68 years is too short to be attributed solely to the double sunspot cycle, and too long to be attributed solely to the 18.6 year lunar nodal cycle.  Instead, they prefer that ..."a better attribution is the beat cycle explanation proposed by Bell [5]*, i.e. a cycle representing the combined influence of the 22 year double sunspot cycle and the 18.6 year lunar nodal cycle."

C. Evidence For and Against Solar Driven Variations in World Mean Temperature  

Evidence AGAINST the Solar Explanation for the Quasi-Decadal and Bi-Decadal Oscillations

1. It is generally agreed that the ~ 9.0 year peak seen in the spectral analysis of the historical world monthly temperature anomaly data is likely to be the result of forcing caused by a combination of the 9.3 (= 18.6 / 2) year lunar nodal tidal cycle and the 8.85 year lunar anomalistic tidal cycle (i.e. (9.30 + 8.85)/2 = 9.08 years).

2. This means that there is little or no evidence for the 11.1 year sunspot number cycle in the historical world monthly temperature anomaly data. Such a signal should be visible if variations in the Total Solar Irradiance (TSI) have a direct influence upon the world's mean temperatures.

3. The solar explanation does not explain the hiatus in the quasi-decadal oscillations in the historical world monthly temperature anomaly data between 1900 and 1945, nor the reversion to a 6 year period of oscillation during this period.

4. The solar explanation cannot easily explain why the observed anti-correlation between the sunspot number and the world mean temperature anomalies prior to 1900, disappears between 1900 and 1945, and then changes phase by 180 degrees after 1950.

Evidence FOR the Solar Explanation for the Quasi-Decadal and Bi-Decadal Oscillations

1. Henrik Svenmark [6,7] has proposed that that 22 year variation in the strength of the Sun's magnetic field modulates the albedo of the Earth through cosmic ray seeding of cloud formation.
If this theory is correct it could give support to the solar attribution for the 21.33 year bi-decadal oscillation seen in the historical world monthly temperature anomaly data. However there are at least two arguments against this explanation being correct:

a. The Svenmark Cosmic-Ray Cloud Model is still unable to overcome counter-arguments 3 and 4
above against a solar attribution for the 21.33 year bi-decadal oscillation.

b. Laken et al. [8] have used new high quality satellite data to show that the El NiƱo Southern Oscillation [ENSO] is responsible for most changes in cloud cover at the global and regional levels. They also found that galactic cosmic rays, and total solar irradiance did not have any statistically significant influence on changes in cloud cover.

     The evidence cited above clearly does not support the solar explanation for the Quasi-Decadal and Bid-Decadel Oscillations. Indeed, if anything, it implies that the lunar tidal explanation is by far the stronger of the two options.

     Additionally, Laken et al. [8] claims that the ENSO is responsible for much of the changes in cloud cover at regional and global levels. If this is true, then it would be much more plausible to propose that variations observed in the historical world monthly temperature anomalies data should be determined by whatever mechanism controls the long-term variations in the ENSO.

      Evidence is beginning to mount that the ENSO climate phenomenon is being primarily driven by by the long-term luni-solar tidal cycles. The purpose of this blog post is to further investigate this possibility.    

2. The Luni-Solar Tidal Explanation

A. Evidence that the onset of El Nino events are driven by the Luni-solar tides.

     Here is a quick summary of the evidence to support the claim that the timing for the onset of El Nino events is determined by the luni-solar tidal cycles:

1. Sidorenkov [10,11] has found that the SOI index that is used to monitor El Nino Southern Oscillation (ENSO) climate variations has significant spectral components that are remarkably close to the sub-harmonics of the free nutation period of the Earth's poles (i.e. the 1.185 tropical year Chandler Wobble) and the super-harmonics of the Earth's forced nutation (i.e. the 18.60 tropical year lunar nodal precession cycle). Specifically, Sidorenkov finds that the periods of the n = 2, 3, 4 and 5 sub-harmonics of the Chandler Wobble (CW) at 2.37, 3.56, 4.74, 5.93 years, closely match the periods of the n = 3, 4, 5 and 8 super-harmonics of the lunar nodal precession at 6.20, 4.65, 3.72, 2.33 years.
     Sidorenkov argues that external forcing by the lunar-solar tides, acting at the super-harmonics of the Earth's forced nutation produce non-linear enhancements of the oscillations in the Earth’s atmosphere-ocean system that closely match those seen in the ENSO indices. He also asserts that the resultant ENSO climate variations excite the CW through a resonant coupling with the sub-harmonics of the free nutation period of the Earth's pole. In essence, Sidorenkov is proposing that the ~ 4.5 year variations that are seen in the ENSO climate system are being driven by external forcing on the Earth’s atmosphere-ocean system by the lunar-solar tides. 


2. Li [14], Li and Zong [15], Li et. al. [16], and Krahenbuhl [17] clearly show that luni/solar induced atmospheric tides are present at altitudes above about 3000 m.
3. Wilson [18] shows that if you control for the changes in the mean (atmospheric) sea-level pressure (MSLP) of the Southern Hemisphere Sub-Tropical High Pressure Ridge that are caused by the Sun (i.e. the seasonal cycle), then it possible to see the much smaller long-term changes caused by the luni-solar tides.
4. Wilson [19] shows that lunar atmospheric tides can produce small but significant long term changes in the overall pressure of the four main semi-permanent sub-tropical high pressures systems in the Southern Hemisphere. Wilson shows that an N=4 standing wave-like pattern in the MSLP circumnavigates the Southern Hemisphere once every every 18 or 18.6 years. This standing wave will naturally produce large extended regions of abnormal atmospheric pressure passing over the semi-permanent South Pacific subtropical high roughly once every ~ 4.5 - 4.7 years. These moving regions of higher/lower than normal atmospheric pressure will increase/decrease the MSLP of this semi-permanent high pressure system, temporarily increasing/reducing the strength of the East-Pacific trade winds. This could led to conditions that preferentially favor the onset of La Nina/El Nino events.
5. Wilson [20] has also shown that based upon the premise that the 31/62 year Perigy-Syzygy seasonal tidal cycle plays a significant role in sequencing the triggering of El NiƱevents, its effects for the following three new moon epochs:
New Moon Epochs:
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

[The New Moon Epochs have peak seasonal tides that are dominated by new moons that are predominately in the northern hemisphere]


should be noticeably different from its effects for the following full moon 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

[The Full Moon Epochs have peak seasonal tides that are dominated by full moons that are predominately in the southern hemisphere]

Wilson found that:

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

and these simple rules explain the onset years for all but five of the 27 moderate to strong El nino events that have occurred since 1865-70 when directly measured world-wide sea-surface temperatures have become available.
6. Following in the footsteps of Sidorenkov [9-13] and Wilson [18-20] , Paul Pukite [21] has found that he can generate both the QBO and the SOI index using the luni-solar tidal forcing upon the Earth. He accomplishes this by allowing for the aliasing of the tidal signal caused by the seasonal (yearly) cycles. 
     Using the seasonally aliased tidal forcing as his forcing term for the QBO, Pukite is able to accurately reproduce the historical observed QBO time series.  Pukite claims that:
 "The rationale for this is that the faster lunar cycles will not cause the stratospheric winds to change direction, but if these cycles are provoked with a seasonal peak in energy, then a longer-term multi-year period will emerge. This is a well-known mechanism that occurs in many different natural phenomena."
In essence, he is adopting the principle laid out in Wilson [18] which proposed that effects of the long-term tides upon the Earths's atmosphere (and oceans) are amplified by annual (i.e. seasonal) aliasing. This principle states that:
"The most significant of the 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."
There are two steps to Pukite's model:

(1) Determine the lunar gravitational potential as a function of time, and

(2) plot the potential in units of 1 month or 1 year.

Pukite indicates that this last part is critical, as that emulates the aliasing required to remove the sub-monthly cycles in the lunar forcing.

Finally, he says that:

"If one then matches this plot against the QBO time-series, you will find a high correlation coefficient. If the lunar potential is tweaked away from its stationary set of parameters, the fit degrades rapidly."

7. It known that persistent Westerly Wind Bursts associated with the penetration of Madden Julian Oscillations into the Western Pacific ocean are responsible for wide-spread reversal of the westerly Equatorial trade winds which are associated with the onset or triggering of El Nino events.

     Lian et al. [22] and Chen et al. [23] have shown that for every major El Nino event since 1964, the drop off in easterly trade wind strength has been preceded by a marked increase in westerly wind bursts (WWB) in the western equatorial Pacific Ocean. These authors contend that the WWB generate easterly moving equatorial surface currents which transport warm water from the warm pool region into the central Pacific. In addition, the WWB create down-welling Kelvin waves in the western Pacific that propagate towards the eastern Pacific where they produce intense localized warming [McPhaden 24]. It is this warming that plays a crucial in the onset of El Nino events through its weakening of the westerly trade winds associated with the Walker circulation.

     Wilson [2016] 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 findings provide strong observational evidence that the lunar tidal cycles are primarily responsible for the onset of El Nino events.  (This paragraph was updated on 11/01/2015)

References

[1] Keeling, CD.  and Whorf,  TP. (1996), Decadal oscillations in global temperature and atmospheric carbon dioxide.  In: Natural climate variability on decade-to-century time scales.  Climate Research Committee, National Research Council. Washington, DC:The National Academies., pp. 97-110.


[2] 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.
[3] 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:
http://wattsupwiththat.com/2009/05/23/evidence-of-a-lunisolar-influence-on-decadal-and-bidecadal-oscillations-in-globally-averaged-temperature-trends/

[4] Brohan, P.  Kennedy, J.  Harris, I.  Tett, S.  Jones, P. (2006), Uncertainty estimates in regional and global observed temperature changes: a new data set from 1860.,  Journal of Geophysical Research., 111, D12106, data retrieved at: http://hadobs.metoffice.com/hadcrut3/diagnostics/

[5] Bell, PR.  (1981), The combined solar and tidal influence on climate. In: Sofia, SS, editor.  Variations of the Solar Constant.  Washington, DC: National Aeronautics and Space Administration, pp. 241–256.

[6] Svensmark, H. (1998), Influence of Cosmic Rays on Earth's Climate"., Physical Review Letters 81 (22), pp. 5027–5030

[7] Svensmark , H. (2007), Astronomy & Geophysics Cosmoclimatology: a new theory emerges., Astronomy & Geophysics, 48 (1), pp. 1.18–1.24.

[8] Laken, B., Palle, E., and Miyahara, H., (2012), A Decade of the Moderate Resolution Imaging Spectroradiometer: Is a Solar–Cloud Link Detectable?, Journal of Climate, (25), pp. 4430 - 4440,
retrieved at: journals.ametsoc.org/doi/pdf/10.1175/JCLI-D-11-00306.1

[9] Sidorenkov, NS. (2000), Chandler Wobble of the poles as part of the nutation of the Atmosphere, Ocean, Earth system. Astron Rep, 44 (6), pp. 414-419.

[10] Sidorenkov NS. (1992), Excitation mechanism of Chandler polar motion. Astron J., 69 (4), pp. 905-909.

[11] Sidorenkov N S. The effect of the El Nino Southern oscillation on the excitation of the Chandler motion of the Earth's pole. Astron Rep 1997; 41(5): 705-708.

[12] Sidorenkov NS. Physics of the Earth’s rotation instabilities. Astron Astrophys Transact 2005; 24(5): 425-439.

[13] Sidorenkov N., (2014) The Chandler wobble of the poles and its amplitude modulation, 
http://syrte.obspm.fr/jsr/journees2014/pdf/

[14] Li, G. (2005), 27.3-day and 13.6-day atmospheric tide and lunar forcing on atmospheric circulation., Adv Atmos Sci., 22(3), pp. 359-374.


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[16] Li, G, Zong, H, Zhang, Q. (2011), 27.3-day and average 13.6-day periodic oscillations in the earth’s rotation rate and atmospheric pressure fields due to celestial gravitation forcing., Adv Atmos, 28(1), pp. 45-58.

[17] Krahenbuhl D.S., Pace,  M.B., Cerveny, R.S., and Balling Jr, R.C. (2011), Monthly lunar declination extremes’ influence on tropospheric circulation patterns., J Geophys Res, 116, pp. D23121-6.

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Tuesday, October 6, 2015

There is a direct connection between the synodic period of Venus and the Earth and the rates of precession of the lunar line-of-nodes and the lunar line-of-apse - factors that are known to influence the levels of tidal stress upon the Earth's atmosphere and oceans

Minor Updates: 12/Oct/2015

SUMMARY
The two periods that control the precession of the tilt (i.e. the Draconic year = DY) and elongation (i.e. the Full Moon Cycle = FMC) of the lunar orbit are directly related synodic period of Venus and the Earth (T (VE)) via the formula.

4.0 DY x 1.0 FMC / (4.0 DY - 1.0 FMC) = T (VE)

This shows that there is a direct connection between the relative planetary orbital periods of Venus and the Earth and factors which control level of tidal stresses upon the Earth's atmosphere and oceans, namely the rates of precession of the lunar line-of-nodes and the lunar line-of-apse. 
BLOG POST
From the previous blog post I have found that:
if the minimum period between peaks in the rate of change in tidal stresses upon the Earth caused by the change in strength of the lunar tides (i.e. 10.14686 tropical years) amplitude modulates the minimum period between of the rate of changes in tidal stresses upon the Earth caused by the change in direction of the lunar tides (i.e. 1.89803 tropical years), you find that the 1.89803 year tidal forcing term is split into a positive and a negative side-lobe, such that: 
Positive side-lobe
[10.1469 x 1.89803] / [10.1469 – 1.89803] = 2.334(7) tropical yrs = 28.0 months

Negative side-lobe
[10.1469 x 1.89803] / [10.1469 + 1.89803] = 1.598(9) tropical yrs 

The time period of the positive side-lobe is almost exactly the same as that of the Quasi-Biennial Oscillation (QBO). The QBO is a quasi-periodic oscillation in the equatorial stratospheric zonal winds that has an average period of oscillation of 28 months, although it can vary between 24 and 30 months (Giorgetta and Doege 2004).
However, the important period that is discussed in this post is the 1.589(9) tropical year negative side-lobe period. This just happens to be synodic period of Venus and the Earth = 583.92063 days = 1.5987 tropical years, to within an error of ~ 1.8 hours).

Interestingly, the negative side-lobe period can also be obtained by the beat period between 4.0 Draconic years = 4.0 DY = 3.79606 tropical years and 1.0 Full Moon Cycles = 1.0 FMC = 411.78445 days = 1.1274 tropical years.

4.0 DY x 1.0 FMC / (4.0 DY - 1.0 FMC) = 585.7530 days = 1.6037 tropical years

Where 1.0 Draconic years is the time it takes the lunar line-of-nodes to re-synchronize with the lunar phase (synodic) cycle. 

This beat period differs from the Venus Earth Synodic period by 0.005 tropical years = 1.84 days.

[N.B. The 3.79606 tropical year period is part of the 19.0 year Metonic Cycle with the Moon's phase returning to new moon at a node after 1387.481264 days (=3.79606 tropical years). This happens because 47 Synodic months = 1387.937678 days and 51 Draconic months = 1387.82322 days. With this cycle, the synodic lunar cycle realigns with the seasonal calendar once every 4 tropical years, 4 + 4 = 8 tropical years, 4 + 4 + 3 = 11 tropical years, 4 + 4 + 3 + 4 = 15 tropical years and 4 + 4 + 3 + 4 + 4 = 19.0 tropical years. to give and average spacing of roughly (4 + 4 + 3 + 4 + 4)/5 = 3.8 years.]

1.0 Full Moon Cycles is the time it takes for the lunar line-of-apse to re-synchronize with the lunar phase (synodic) cycle.

A Full Moon Cycle (FMC) is the time required for the Perigean end of the lunar line-of-apse to re-align with the Sun close to a new moon:

1.0 Full Moon Cycle = 1.0 FMC = 411.78445 days = 1.1274 tropical years    (1)

The Moon almost returns to being New at perigee after 1.0 FMC because 14 Synodic months = 413.42824 days and 15 anomalistic months = 413.31825 days.

Hence, the two periods that control the precession of the tilt (i.e. the Draconic year) and elongation (i.e. the Full Moon Cycle) of the lunar orbit are directly related synodic period of Venus and the Earth (T(VE)) via the formula.

4.0 DY x 1.0 FMC / (4.0 DY - 1.0 FMC) = T(VE)

This shows that there is a direct connection between the relative planetary orbital periods of Venus and the Earth and factors which control level of tidal stresses upon the Earth's atmosphere and oceans, namely the rates of precession of the lunar line-of-nodes and the lunar line-of-apse. 

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Updated 12/Oct/2015

[NB: The lunar and planetary periods used in this post:

Lunar J2000.0 (1 January 2000 12:00 TT) values:
Synodic month = 29.5305889 days
Anomalistic month = 27.554550 days
Draconic month = 27.212221 days

Tropical Year = 365.242189 days

Planetary Values:
Sidereal orbital period of the Earth = 365.256363 days
Sidereal orbital period of Venus = 224.70069 days

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