THE VEJ TIDAL-TORQUING MODEL - FURTHER CONFIRMATION

This post is an update to an earlier post found at:

http://astroclimateconnection.blogspot.com.au/2013/04/a-confirmation-of-vej-tidal-torquing.html

concerning the remarkable discovery of Paul Vaughan.

The above graph compares the deviation of the surface 
rotation velocity plot of Tlatov and Makarov (2005) 
[top graph] with the relative rotation velocities (blue 
histogram) and rotational accelerations (red histogram) 
of the outer convective layers of  the Sun that are predicted 
by the VEJ Tidal-Torquing Model [bottom graph]. 

Superimposed across the top of the lower graph are 
red lines that show the periods of time where the 
Tlatov and Makarov (2005) graph indicates that 
the Sun's near-equatorial (< 10-15 degrees away 
from the equator)  rotation rate is higher than 
normal. Similarly, superimposed across the bottom 
of the lower graph are red lines that show the periods 
of time where the Tlatov and Makarov (2005)  
graph indicates that the Sun's near-equatorial 
rotation rate is lower than normal.

What this graph shows is the rotational velocities of the
outer layers of the Sun that are predicted by the VEJ 
Tidal-Torquing Model are almost perfectly synchronized
in phase with the measured changes in rotational 
velocity on the surface of the Sun, over a period of 
100 years.

Wow!!

Long-Term Lunar Atmospheric Tides in the Southern Hemisphere

Ian R. G. Wilson and Nikolay S. SidorenkovThe Open Atmospheric Science Journal, 2013, 7, 51-76

Available as an eprint ahead of scheduled publication at:
http://benthamopen.com/contents/pdf/TOASCJ/TOASCJ-7-51.pdf

Here is a scientific summary of the main conclusions

Abstract

The longitudinal shift-and-add method is used to show that there are N=4 standing wave-like patterns in the summer (DJF) mean sea level pressure (MSLP) and sea-surface temperature (SST) anomaly maps of the Southern Hemisphere between 1947 and 1994. The patterns in the MSLP anomaly maps circumnavigate the Earth in 36, 18, and 9 years. This indicates that they are associated with the long-term lunar atmospheric tides that are either being driven by the 18.0 year Saros cycle or the 18.6 year lunar Draconic cycle. In contrast, the N=4 standing wave-like patterns in the SST anomaly maps circumnavigate the Earth once every 36, 18 and 9 years between 1947 and 1970 but then start circumnavigating the Earth once every 20.6 or 10.3 years between 1971 and 1994. The latter circumnavigation times indicate that they are being driven by the lunar Perigee-Syzygy tidal cycle. It is proposed that the different drift rates for the patterns seen in the MSLP and SST anomaly maps between 1971 and 1994 are the result of a reinforcement of the lunar Draconic cycle by the lunar Perigee-Syzygy cycle at the time of Perihelion. It is claimed that this reinforcement is part of a 31/62/93/186 year lunar tidal cycle that produces variations on time scales of 9.3 and 93 years. Finally, an N=4 standing wave-like pattern in the MSLP that circumnavigates the Southern Hemisphere every 18.6 years will naturally produce large extended regions of abnormal atmospheric pressure passing over the semi-permanent South Pacific sub-tropical high roughly once every ~ 4.5 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 may led to conditions that preferentially favor the onset of La Nina/El Nino events.

In English: What are the main results of this paper?

The NOAA SST anomaly map for the 25th of January 1981.

Available at: ftp://public.sos.noaa.gov/oceans/SST_1980-1999/2048_rolled/cyl_1981_01_25.jpg [Accessed: September 2012].

The N=4 Standing Wave Pattern in the Mean Sea-Level Atmospheric Pressure (MSLP) 

1. There are four large region of enhanced/reduced MSLP in the Southern Hemisphere, that are separated from each other by ~ 90 degrees in longitude that are slowly moving around the Earth in a retrograde (Westerly) direction, roughly once every 18.6 years.

2. These large features are part of a huge standing wave-like pattern in the atmosphere that is propagating in a westerly direction along the southern edge of the summer Sub-Tropical High Pressure Ridge. 

3. This pattern is formed by atmospheric lunar tides that are being driven by the 18.6 year Lunar Draconic cycle.

4. Roughly once every 4.65 (=18.6/4) years, the four large regions of enhanced/reduced MSLP simultaneously pass over the top of the four semi-permanent high pressure systems embedded in the summer Sub-Tropical High Pressure Ridge (their rough locations are marked by the symbol "H" in the figure above).

5. When this happens, if the four propagating regions have an enhanced MSLP, they will produce a temporary increase in the MSLPs of the four fixed semi-permanent high pressure systems. This naturally leads to enhanced warm northerly winds on the western sides of the semi-permanent highs that would produce regions of warmer-than-normal SSTs, and cooler southerly winds on the eastern sides of the semi-permanent highs that would naturally produce regions of cooler-than-normal SSTs. This is exactly what is observed in the figure above.   

Producing the necessary conditions for the onset of El Nino and La Nina Events

1. During the first climate epoch between 1947 and 1970, the pressure of the four extended propagating regions of MSLP were predominantly higher-than-normal.

  

2. During the second climate epoch between 1971 and 1994, the pressure of the four extended propagating regions of MSLP were predominantly lower-than-normal. 

3. Hence, roughly once every 4.65 years during the first climate epoch, the four main regions of enhanced atmospheric pressure passed over the four large semi-permanent high pressure systems in the summer sub-tropical high pressure ridge. When this occurred, a large moving region of enhanced atmospheric pressure increased the pressure of the South Pacific sub-tropical high hovering over Easter Island, causing a temporary strengthening of the East-Pacific Trade Winds. This could have led to conditions that favor the onset of La Nina events over El Nino events throughout the first climate.

4. Hence, roughly once every 4.65 years during the second climate epoch, the four main regions of reduced atmospheric pressure passed over the four large semi-permanent high pressure systems in the summer sub-tropical high pressure ridge. When this occurred, a large moving region of reduced atmospheric pressure decreased the pressure of the South Pacific sub-tropical high hovering over Easter Island, causing a temporary reduction in the strength of the East-Pacific trade winds. This could have led to conditions that favor the onset of El Nino events over La Nina events throughout the second climate.

A mutual reinforcement of the lunar Draconic cycle seen in the atmospheric tides and the lunar Perigee-Syzygy cycle seen in the SSTs .

1. In the second climate epoch (from 1970 to 1994) there are N=4 patterns in the MSLP anomaly profiles that have circumnavigation times that closely match the lengths of the 18.03 (tropical) year lunar Saros cycle or the 18.60 (tropical) year lunar draconic cycle. In addition, there are N=4 patterns in the SST anomaly profiles that have circumnavigation times that closely match the 20.294 (tropical) year Perigee-Syzygy lunar cycle. The fact that standing wave-like patterns in the MSLP anomalies and the SST anomalies are moving around the Earth at different rates and that the moving patterns in the MSLP anomalies appear around 1971 and then disappear roughly 24 years later around 1994, indicate that both patterns may only become visible because of a process of mutual pattern reinforcement. 

(N.B. If you have a N=4 pattern in the MSLP anomalies that is moving towards the west at 17.74° per year (corresponding to a circumnavigation time of 20.294 years), it will drift out of phase with (i.e. be 45° in longitude ahead of) an N=4 pattern in the SST anomalies that is moving towards the west at 19.97°/19.35° per year (corresponding to circumnavigation times of 18.03/18.60 years) in 20.20/27.86 years, respectively. So, on average, one pattern will drift-in and then out-of-phase with the other over a period of roughly 24 years, in good agreement with the time of visibility of the moving patterns in the MSLP and SST anomalies maps.)

2. Hence, the observational evidence suggests that we are seeing a process that is result of a mutual reinforcement of the lunar Draconic cycle seen in the atmospheric tides and the lunar Perigee-Syzygy cycle seen in the SSTs .

3. In the first climate epoch (from 1947 to 1970) there are N=4 patterns in both the MSLP and SST anomaly profiles that have circumnavigation times that closely match the length of the 18.60 year lunar Draconic cycle. There is no evidence of patterns in the SST that have circumnavigation times that match the length of the Perigee-Syzygy cycle. The fact that standing wave-like patterns in the MSLP anomalies and the SST anomalies are both moving around the Earth at the same drift rates and that these drift rates closely match the lengths of the lunar Saros or Draconic cycles, indicates that we are seeing a process where the tidal effects of the lunar Draconic cycle are no longer being reinforced by the lunar Perigee-Syzygy cycle.

          Some Supporting Figures 

Fig. (5). The relative power spectral density (PSD) for those features that have an N=4 pattern in the average longitudinal profile for latitudes between 30° and 50° S, for the shift-and-add map of the summer MSLP anomalies, plotted against westerly longitudinal drift rate. N.B. The step in westerly drift rates has been increased to 2.5° per year between 0 and 25° degrees per year for greater resolution. A solid black line drawn across the lower part of this figure indicates the minimum power spectral density that is required to rule out the possibility that the signal is generated by noise at the 0.01 (= 99 %) confidence limit. This limit was obtained by applying the Multi-Taper Method (MTM) (number of tapers =3) to each shift-and-add anomaly profile that is associated with a given drift rate in this diagram. Only those points which had spectral densities that could not be generated by chance from either white noise or AR(1) noise at the 0.01 level were accepted as being statistically significant. All points above the 99 % confidence line in this figure are statistically significant while all the points below this line are not (with the exception of the point with a drift-rate of 50° per year). It is important to note that there are strong, low frequency spatial features present in the individual spatial MSLP anomaly profiles. Under these circumstances, simple spectrogram analysis is not good at determining the true spectra noise levels that are need to test the statistical significance of spectral features. One way to circumvent this problem is to use MTM analysis, since it better able to distinguish strong low frequency signals from spectral noise.

Fig. (6). (a-c) The shift-and-add maps of the Southern Hemisphere MSLP anomalies between the latitudes of 20° and 60° S for westerly longitudinal drift rates of 0°, 10°, and 20° per year, respectively. The pressure anomalies are plotted so that lower-than-normal MSLP anomalies are displayed as positive numbers.

Fig. (14). Blue curve: The angle between the line-of-nodes of the lunar orbit and the Earth-Sun line at the time of Perihelion (phi) is plotted as a function 1/(1+ phi) between the years 1857 and 2024, in order to highlight the years in which these two axes are is close alignment. Brown curve: The angle between the line-of-apse of the lunar orbit and the Earth-Sun line at the time of perihelion (psi) plotted as the function - 1/(1+ psi), in order to highlight the years in which these two axes are is close alignment. Red curve: This is an alignment index that is designed to represent the level of reinforcement of the Draconic tidal cycle by the Perigee-Syzygy tidal cycle. This is done by plotting the values of the blue curve at times when there is a close alignment of the line-of-apse and the Earth-Sun line at perihelion (i.e. when psi <= 16°).

Fig. (A3a). The map on the right-hand side of Fig. (A3a) displays the cross-correlation functions, for all years from 1971 to 2009, which use the 1964 profile as a template, stacked together to form a map. This map is reproduced on the left-hand side of Fig. (A3a) to show that the N=4 pattern is moving towards the west over most of the period between 1971 and 1994.

A Confirmation of the VEJ Tidal-Torquing Model

                       UPDATED 30/04/2013
See the following newer post for the updates this post:

http://astroclimateconnection.blogspot.com.au/2013/04/further-confirmation-of-vej-tidal.html

The diagram below shows the solar sunspot number 

(SSN) for solar cycles 13 through  to 23, plotted against 

the net tangential torque of Jupiter acting upon the V-E tidal 

bulge. The net tangential torque was obtained by adding

Jupiter's tangential torque at one V-E inferior conjunction 

to Jupiter's tangential torque at the next V-E superior 

conjunction. In this diagram, a positive net torque means 
that the rotational speed of the Sun's equatorial convective 
layer is sped-up and a negative net torque means that the 
equatorial convective layer is slowed-down.

[N.B. The net torque curve has been smoother with a 

5th and 7th order binomial filter to isolate low frequency 

changes]       

This diagram clearly shows that:

a) The net torque of Jupiter acting on the V-E tidal bulge
     has a natural 22.4 year periodicity which matches the 22.1
     year period of the solar Hale (magnetic) cycle.

b) the equatorial convective layers of the Sun are 
     sped-up during ODD solar cycles and slowed-down 
     during EVEN solar cycles. 

Support for point b) is provided by the following 
figure which was kindly sent to me as a private
communication by Paul Vaughan. Paul has allowed 
me to use his graph here to support this post.

In this plot, Paul Vaughan has superposed the 22.1 year 
JEV cycle onto Tlatov & Makarov's (2005) Figure 3. 

Reference:
Tlatov, A.G.; & Makarov, V.I. (2005). 22-year variations 
of the solar rotation, Large-scale Structures and their 
Role in Solar Activity, ASP Conference Series,  Ed: K. 
Sankarasubramanian, Matt Penn & Alexei Pevtsov, 
Vol. 346, 

http://www.solarstation.ru/TL/PDF/tl_22.pdf

The underlying figure from Tlatov & Makarov (2005) shows 

the deviation of the surface rotation velocity of the Sun from 

its average value at corresponding latitudes. These 

measurements have been obtained from H-alpha observations 

of the Sun.  In this diagram, the regions where rotation is 

slower than normal are painted dark and the velocity is 

averaged over the northern and southern hemispheres 

(Note: The window for the spectral analysis was set to 

12 years).

Paul Vaughan's graph clearly shows the 22.1 year 
JEV cycle is almost perfectly synchronized in phase 
with the changes in rotational velocity on the 
surface of the Sun over a period of 100 years.

This is a remarkable result! 

Further confirmation of point b) is given by the following figure

which compares the deviation of the surface rotation velocity

plot of Tlatov & Makarov (2005) with the monthly solar sunspot 

number for cycles 13 through 23.

This plot  clearly shows that for all 11 solar cycles, the 
deviation of the rotation velocity of the surface of the 
Sun from its average value at corresponding latitudes, 
speeds up during ODD solar cycles and slows down 
during EVEN solar cycles.

This is a wonderful confirmation of my earlier results 
published in  the blog post of November 23rd 2012.

It also indirectly confirms the result obtained in our 2008 solar paper:

Does a Spin–Orbit Coupling Between the Sun and the Jovian Planets Govern the Solar Cycle? 

I. R. G. Wilson, B. D. Carter, and I. A. Waite

Publications of the Astronomical Society of 

Australia, 2008, 25, 85–93.



This graph from Wilson et al. 2008 (above) shows 
the moment arm of the torque for the quadrature 
Jupiter and Saturn nearest the maximum for a given 
solar cycle, plotted against the change in the average 
equatorial (spin) angular velocity of the Sun since 
the previous solar cycle (measured in μrad s−1). 
The equatorial (≤±15 deg) angular velocities published 
by Javaraiah (2003) for cycles 12 to 23 have been 
used to determine the changes in the Sun’s angular 
velocity (since the previous cycle) for cycles 13 to 23.

What these graphs clearly show is that the Sun's equatorial
angular velocity increases in ODD solar cycles and decreases
in EVEN solar cycles, in a manner that is predicted by the 
V-E-J Tidal-Torquing model.

Could This Be The Climate Smoking Gun?

Figure 1 shows amplitude spectrum of the North American temperature over a 2200 year period from:

Cyril RON, Yavor CHAPANOV and Jan VONDRÁK
SOLAR EXCITATION OF BICENTENNIAL EARTH ROTATION OSCILLATIONS
Acta Geodyn. Geomater., Vol. 9, No. 3 (167), 259–268, 2012

Figure 1

The spectrum is based upon bristle-cone pine series obtained from:

MATTHEW W. SALZER and KURT F. KIPFMUELLER
RECONSTRUCTED TEMPERATURE AND PRECIPITATION
ON A MILLENNIAL TIMESCALE FROM TREE-RINGS
IN THE SOUTHERN COLORADO PLATEAU, U.S.A.
Climatic Change (2005) 70: 465–487


Given the controversial nature of the use of Bristle-cones as a proxy for temperature, I have quoted the section of this paper dealing with methods used in constructing the tree-ring chronology that reflects past temperature variability - see the Appendix at the end of this post.

I would be the first to concede that while tree-ring widths in Bristle-cones are probably most sensitive to changes in temperature (because they grow near the tree-line), it is also likely that they are partially sensitive to changes in other climate factors such as precipitation levels, frequency of severe frosts and the amount of daily sunshine exposure etc. Hence, it is probably more accurate to say that the tree-ring widths of Bristle-cone pines are a good proxy for the general climate conditions that promote/retard the growth of these trees, chief of which is the local ambient temperature.

The important thing to note about figure 1 is that, for periods for less than or equal to 500 years, there are prominent spectral peaks at:

89 years, 104 years, ~ 150 years, 208 years, ~ 230 years, ~ 355 years and ~ 500 years.

These periods (obtained from proxy temperature data) can be compared with Fourier spectrum of solar activity qualified by the solar modulation potential and the Fourier spectrum of the planetary torque acting upon the Sun, published by:

J. A. Abreu1, J. Beer, A. Ferriz-Mas, K. G. McCracken, and F. Steinhilber
Is there a planetary influence on solar activity?
A&A 548, A88 (2012)

These spectra are based upon a time 9400 year time series of solar activity derived from observations of Be10 and C14.

Figure 2

Amazingly, the solar activity spectrum shows peaks at:

89 years, 104 years, 150 years, 208 years, ~ 230 years, ~ 355 years and  506 years.

and the planetary torque shows all of these peaks, except those at ~230 & ~ 355 years.

I believe that it is extremely unlikely that the spectral peaks for the North American temperatures are almost exactly the same as the spectral peaks for solar activity and planetary tidal torques acting upon the Sun.


The question is how do the upper-tree-line Bristlecone Pine (P. aristata) in the San Francisco Peaks know about the level of solar activity on the Sun and the planetary torques being applied to the Sun?

I claim that it indicates that the level of solar activity upon the Sun is modulated by planetary tidal-torquing acting upon the convective layer of the Sun and that it is these variations in the level of solar activity that have determined the mean temperatures of the North America continent over the last 2200 years.

APPENDIX

Figure 1A

quote:
To build a tree-ring chronology that reflects past temperature variability, upper-tree-line Bristlecone Pine (P. aristata), whose ring-width variability is a function of temperature, were sampled at timberline in the San Francisco Peaks (∼3,536 m), where temperature is most limiting to growth (Figure 2). Increment core and sawed samples were collected from living and dead Bristlecone Pine on both Agassiz Peak and Humphreys Peak. Long chronologies were constructed by cross-dating the deadwood samples with the living tree specimens. Prior to AD 659 the chronology is composed entirely from deadwood material. The individual growth rings of each sample were measured to the nearest 0.01 mm. The measured series were converted to standardized tree-ring indices by fitting a modified negative exponential curve, a straight line, or a negatively sloped line to the series. This process removes the age/size related growth trend and transforms the ring-width measurement values into ring-width index values for each individual ring in each series (Fritts, 1976). Several statistics were calculated to gauge the reliability of the tree-ring series (Cook and Kairiukstis, 1990; Wigley et al., 1984) (Table I). Through conservative standardization techniques and the use of relatively long series, care was taken to preserve low-frequency information in the chronology (Cook et al., 1995). A regional curve standardization (RCS) approach (Briffa et al. 1992a), which has been used in some dendroclimatic studies to resolve multi-decadal to centennial trends, was considered but rejected. In general, RCS was devised for chronologies built from short series that use heavy detrending. The SFP chronology was built from relatively long segment lengths (Table I) and a conservative standardization process was employed. Additionally, we could not meet the necessary assumptions critical to successfully applying this technique: it was impossible to ascertain pith or near-pith dates from the deadwood material due to the irregular growth form of Bristlecone Pine, and we are not able to demonstrate that the age structure of the samples are evenly distributed. To create the mean site chronology, the annual standardized indices of tree growth were averaged. A single chronology was developed from samples collected at two sites on Humphreys Peak and one site on Agassiz Peak. The SFP chronology extends from 663 BC–AD 1997. In total, 234 series (130 trees) are used. The period before 266 BC is considered less reliable than the rest of the chronology as six or fewer series cover this interval. The climate data used in the temperature reconstruction calibration are from the Fort Valley Experimental Research Station, which is part of the United States Historical Climatology Network. The station data, from an elevation of 2,239 m and approximately 4.5 km from the high elevation SFP tree-ring sites, span the period 1909–1994.
end quote: