Monday, December 10, 2012

Scientific Publications & Presentations

                         UPDATED 16/04/2013

The following is a list of my recent scientific publications
and presentations. I am placing the list on my blog so that
others can have easy access.


Wilson, I. R. G., 2006, Possible Evidence of the 
De Vries, Gleissberg and Hale Cycles in the Sun’s 
Barycentric Motion, Australian Institute of Physics 17th
National Congress 2006, Brisbane, 3rd -8th December 
2006 (No longer available on the web)


Wilson, I.R.G., Carter, B.D., and Waite, I.A., 2008
Does a Spin-Orbit Coupling Between the Sun and the 
Jovian Planets Govern the Solar Cycle?,
Publications of the Astronomical Society of Australia
2008, 25, 85 – 93.

N.S. Sidorenkov, Ian Wilson. The decadal fluctuations 
in the Earth’s rotation and in the climate characteristics
In: Proceedings of the "Journees 2008 Systemes de reference 
spatio-temporels", M. Soffel and N. Capitaine (eds.), 
Lohrmann-Observatorium and Observatoire de Paris. 
2009, pp. 174-177 

Which Came First? - The Chicken or the Egg?

A Presentation to the 2008 Annual General Meeting of the
Lavoisier Society by Ian Wilson


Wilson, Ian R.G., 2009, Can We Predict the Next Indian 
Mega-Famine?, Energy and Environment, Vol 20, 
Numbers 1-2, pp. 11-24.

El Ninos and Extreme Proxigean Spring Tides

A lecture by Ian Wilson at the Natural Climate Change
Symposium in Melbourne on June 17th 2009.


N. Sidorenkov, I.R.G. Wilson and A.I. Kchlystov, 2009, The 
decadal variations in the geophysical processes and the 
asymmetries in the solar motion about the barycentre. 
Geophysical Research Abstracts Vol. 12, EGU2010-9559, 
2010. EGU General Assembly 2010 © Author(s) 2010


Wilson, I.R.G., 2011, Are Changes in the Earth’s Rotation 
Rate Externally Driven and Do They Affect Climate? 
The General Science Journal, Dec 2011, 3811.

Wilson, I.R.G., 2011, Do Periodic peaks in the Planetary Tidal 
Forces Acting Upon the Sun Influence the Sunspot Cycle? 
The General Science Journal, Dec 2011, 3812.

[Note: This paper was actually written by October-November 2007 and submitted to the New Astronomy (peer-reviewed) Journal in early 2008 where it was rejected for publication. It was resubmitted to the (peer-reviewed) PASP Journal in 2009 where it was rejected again. It was eventually published in the (non-peer reviewed) General Science Journal in 2010.]


Wilson, I.R.G., 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, 2012, 6, 49-60

Wilson, I.R.G., Changes in the Earth's Rotation in relation 
to the Barycenter and climatic effect.  Recent Global Changes 
of the Natural Environment. Vol. 3, Factors of Recent 
Global Changes. – M.: Scientific World, 2012. – 78 p. [In Russian].

This paper is the Russian translation of my 2011 paper
Are Changes in the Earth’s Rotation Rate Externally 
Driven and Do They Affect Climate? 
The General Science Journal, Dec 2011, 3811. 

Friday, November 23, 2012

V-E-J Tidal-Torquing Model

See the bottom of this post for essential background 
reading if you knowledge of the formulation and 
evolution of the V-E_J Tidal-Torquing Model is 
not up-to-date :


The problem with the collective blog postings about the 
Spin-Orbit Coupling or Tidal-Torquing Model that are described 
at the end of this post is that they only look at the tidal-torquing 
(i.e. the pushing and pulling of Jupiter upon the Venus-Earth 
tidal bulge in the Solar convective zone) when Venus and Earth 
are inferior conjunction (i.e. when Venus and Earth are on the 
same side of the Sun). However, a tidal bulge is also produced  
when Venus and the Earth align on opposites sides of the Sun, 
as well (i.e  at superior conjunction).

This means that in the real world, tidal bulges are induced in 
the convective layer of the Sun once every 0.8 years rather 
than every 1.6 years, as assumed in the original basic model. 
This is achieved by a sequence of alternating conjunctions 
of Venus and the Earth:

IC --> SC --> IC --> SC --> IC --> etc.. 

[where IC = Inferior conjunction & SC = Superior conjunction]  

Unfortunately, logic tells you the gravitational pushing/pulling 
of Jupiter on the V-E tidal bulge at a given inferior conjunction 
will be roughly equal opposite to the pushing/pulling that occurs
at the next superior conjunction. At first glance, this would seem 
to destroy any chance for the gravitational force of Jupiter (acting 
on the V-E tidal bulge) to produce any nett spin in the outer 
convective layers of the Sun. However, it turns out that the 
gravitational tugging of Jupiter at inferior V-E conjunction is
not completely cancelled by the tugging at the next superior 
V-E conjunction. This lack of cancellation is primarily related 
to the changing orientation and tilts of the respective orbits 
of Venus and Jupiter.

The diagram immediately below shows sunspot number 
(SSN) for solar cycles 0 through  to 9. Plotted below the
sunspot number curve in this figure is the net tangential torque
of Jupiter acting the V-E tidal bulge, where Jupiter's tangential 
torque at one V-E inferior conjunction is added to Jupiter's
 tangential torque at the next V-E superior conjunction to 
get the nett tangential torque. In this diagram, a positive 
nett torque means that the rotational speed of the Sun's
equatorial convective layer is sped-up and a negative 
nett torque means that the equatorial convective layer 
is slowed-down.

[N.B. The nett torque curve has been smoother with a 
5th and 7th order binomial filter to isolate low frequency 

Some important things to note are:

a) The nett torque of Jupiter acting on the V-E tidal bulge
     has a natural 22 year peridocity which matches the 22
     year hale (magnetic) cycle of solar activity.

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

These two points provide a logical explanation for the
Gnevyshev−Ohl (G−O) Rule for the Sun.

This rule states that if you sum up the mean annual Wolf
sunspot number over an 11 year solar cycle, you find
that the sum for a given even numbered sunspot cycle is
usually less than that for the following odd numbered
sunspot cycle (Gnevyshev and Ohl 1948). The physical
significance of the G−O rule is that the fundamental activity
cycle of the Sun is the 22 year magnetic Hale cycle, which
consists of two 11 year Schwabe cycles, the first of
which is an even number cycle (Obridko 1995). While
this empirical rule generally holds, there are occasional
exceptions such as cycle 23 which was noticeably weaker
than cycle 22.

These two points are also in agreement with the results of
Wilson et al. 2008.

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.

Figure 8 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 this graph clearly shows is that the Sun's equatorial
angular velocity increases in ODD solar cycles and decreases
in EVEN solar cycles, in agreement with the V-E-J
Tidal-Torquing model.

c) The 11 year solar sunspot cycle cycle constantly tries to
    synchronize itself with the Jupiter's nett tidal torque.

The original figure plotted at the top of this blog post is
reproduced here with superimpose blue and red vertical
lines showing the times where the Jupiter's nett torque
(acting on the V-E tidal bulge) changes sign (i.e. direction
with respect the axis of the Sun's rotation). The points
of sign change in Jupter's nett torque that occur just
before solar sunspot minimum are marked by blue lines
while the points that occur after solar minimum are
marked by red lines. The figure below shows that

i) Normally their is a phase-lock between the time of sign
    change in Jupiter's torque and solar minimum.

ii) As soon as this phase-lock is broken (i.e. around about 1777)
    22 years later (i.e. one Hale cycle) after the loss of lock, there is
     a collapse in the strength of the solar sunspot cycle.

The graph below shows if you plot the torque of Jupiter upon
the V-E tidal bulge at each inferior and superior conjunction of
Venus and Earth (rather than their consecutive sum), the actual
magnitude of Jupiter's torque is greatest at the times that are at
or near solar minimum. However, even though Jupiter's torque
are a maximum at these times, the consecutive torques at the
inferior and superior conjunctions of Venus and the Earth almost
exactly cancel each other out.

It is interesting to speculate whether the rapid fluctuations at
times when Jupiter's torque is strongest could explain why the
solar magnetic cycle is driven to synchronize with the Jupiter's
tidal torquing force.


1. Gnevyshev, M. N. and Ohl, A. I., 1948, Astron. Zh., 25, 18
2. Obridko, V.N., 1995, Solar Phys., 156, 179
3. Javaraiah, J., 2003, SoPh, 212, 23
4. Wilson I.R.G, Carter B.D, and Waite I.A., 2008, 
     Publications of the Astronomical Society of 
     Australia, 25, 85–93.
5. Wilson, I. R. G., 2010, General Science Journal

Essential background reading if you knowledge of
the evolution of this model is not up-to-date :

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.

Do Periodic Peaks in the Planetary Tidal Forces Acting Upon the Sun Influence the Sunspot Cycle?

I.R.G. Wilson
A free download of the paper is available in the General 
Science Journal were it was published in 2010 

Two blog entries that give a basic explanation of the 
V-E-J Tidal-Torquing Model

Six blog entries that investigate the properties of the  
V-E-J Tidal-Torquing Model

Tuesday, June 26, 2012

Singular Spectral Analysis of the Summer (DJF) Median Maximum Temperature for Adelaide between 1888 and 2011

Figure 1 (below) shows the maximum daily temperature 
for the South Australian capital city of Adelaide for the
summer of 2009-10. The data comes from the High-
Quality Australian Daily Temperature Data Set

Figure 1:

Summers in Adelaide are characterized by frequent
hot-spells with maximum temperatures exceeding 35
degrees celsius. These hot-spells generally last for a
day or 
two before temperatures are moderated by 
flows of colder air from the south. 

The highly variable nature of maximum summer 
temperatures in Adelaide means that the best way
to characterize the average summer [December/
January/February (DJF)] maximum temperature 
is to use the median rather than the mean. 
 Figure 2 (below) shows the summer-time (DJF)
median maximum temperature for Adelaide between
1888 and 2011.  

Figure 2

Singular Spectral Analysis (SSA)
Preliminary Results:
If you use SSA to investigate the de-trended maximum 
temperature time series (see figure 2), you find that there 
are spectral peaks at all sub-multiples of the 22.3 year
Hale (H) cycle from H/2 to H/10. The most prominent
sub-harmonics are those at H/3, H/6, H/9 and H/10.

This result strongly suggests that the long-term median 
summer time maximum temperatures in Adelaide are
primarily being driven by factors that are associated 
with the 22.3 year Solar Hale Cycle. 

The presence of sub-harmonics in the temperature record
is indicative of the fact that the ~ 22 year forcing term
must have a broadened temporal structure that is 
triangular like in appearance.     

Figure 3

This result is broad general agreement with the results of
Thresher (2002) who finds that the variability in the strength
of the zonal west winds (along their northern margins) broadly
correlate with the 22 year sunspot cycle [see abstract below]. 

Hence, the most likely causation sequence is:

22 Hale cycle ---> strength of zonal west winds --->
the median summer maximum temperatures in Adelaide

with the strength of the zonal west winds depending directly
on the strength of the wind vorticity around low and high 
pressure cells in the Southern Hemisphere.


Int. J. Climatol. 22: 901–915 (2002)

Royal Meteorological Society.



Atmospheric circulation in the southern mid-latitudes is
dominated by strong circum-Antarctic zonal west winds
(ZWW) over the latitude range of 35 to 60 °S. These 
winds exhibit coherent seasonal and interannual variability, 
which has been related both to Antarctic (e.g. polar ice) 
and low-latitude climate (e.g. El Ni˜no–southern oscillation) 
parameters. Historical and recent studies suggest that, 
at its northern margins, variability in the ZWW also has 
a marked quasi-decadal component. Analysis of sea-level 
pressure and rainfall data for the Australian region, South 
Africa and South America confirms frequent indications 
of quasi-decadal variability in parameters associated with 
the ZWW, which appears to be in phase around the 
hemisphere. This variation broadly correlates with the 
sunspot cycle, and specifically appears to reflect 
sunspot-correlated, seasonally modulated shifts in the 
latitude range each year of the sub-tropical ridge over 
eastern Australia. Sunspot-correlated variability in the 
southern mid-latitudes is likely to have substantial effects 
on temperate climate and ecology and is consistent with 
recent models of solar effects on upper atmospheric climate, 
though the mechanisms that link these to winds and rainfall 
at sea level remain obscure. 

Wednesday, June 20, 2012


Hypothesis: The -12.57 μsec change in the length-of-day 
(LOD) associated with the 18.6 year Draconic lunar tides
is a direct result of a systematic one degree shift to the 
South/North by the Southern/Northern Summer Sub-Tropical 
High Pressure Ridge that is produced by lunar atmospheric 

A. The Mass of Summer Sub-Tropical 
_______High-Pressure Ridge

The ideal gas equation states that:

__________P = ρRT/M___________(1)

where P is the atmospheric pressure, ρ is the atmospheric 
density, R is the Universal Gas Constant (= 8.31432 
Nm/Mole), T is the temperature and M is the molar 
mass of air (= 2.89644 x 10-2).

If we assume that in the vertical direction (z) the 
atmosphere is hydrostatic equilibrium then:

_________dP = −ρ g dz___________(2)

where dP is the change in pressure with change in 
height dz and g (=9.80 m/s2) is the acceleration due 
to gravity (N.B. g = 9.80665 m/sec2 at 0 m, 
g = 9.797 m/sec2 at 3000 m, and g =  9.776 m/sec2 
at 10000 m).

Hence, from equations (1) and (2) we find that:

________dP/P = −ρ g dz M / ρRT = −gMdz / RT___(3)

which gives the barometric formula as its solution:

________P = PO exp [−gMdz/RTO]_____________(4)

where PO (in Pascals) and TO (in Kelvin) are the pressure 
and temperature at the Earth’s surface and dz = (h – hO
where h is the height in metres above some reference height hO.

Now Newton’s Second Law tells us that:

________P = MAT g / A_____________________(5)

where MAT is the mass of atmosphere above a given area 
A of the Earth’s surface, above a given height h. 

Combining equations (4) and (5) we get:

_____MAT = [PG A /g] x {1 − exp [−gMh/RTG]}__(6)

where [PG A /g] is the total mass of the atmosphere above 
a given area A of the Earth’s surface, PG and TG are the
 pressure and temperature at ground level  
(i.e. TG = 288.15 K (15 CO) and PG = 101,325 Pascals), 
respectively, and h is the height above ground level in metres.

If we take A to be the surface area of the whole Earth = 4πRR,
 R = 6.371 x 106 m, we get:

Area of the Earth’s Surface
(1014 m2)
Height (m)
Mass of atmosphere  above height h 
(1018 Kg)
Mass Faction

where the data in the second last row uses the pressure 
value derived from the barometric formula while the data
 in the last row uses the value for the US Standard Atmosphere. 
All of the values for TO, are those for the US standard atmosphere.
     The actual NCAR value for the total mass of the atmosphere 
that is derived from sophisticated models is 5.1480 x 1018 kg for 
wet air (+/- 1.2 to 1.5 x 1015 kg due to water vapour) and 
5.1352 x 1018 kg for dry air. Our simple model gives a value 
of 5.270 x 1018 kg  most of the difference explained by the 
reduction of volume due to mountain ranges.
     The surface area of the Earth’s southern summer sub-tropical
 high pressure ridges can be obtained by assuming that bottom 
surface area this body of air is a zone of a sphere with the radius 
of the Earth, centred at 40O ± 10O South of the Equator.

__________Area = 2 π R h_______________(7)

where h = height of the zone = R (sin LU – sin LL) and LU 
and LL are the latitudes of the bottom and top arcs of the zone.

_________Area = 2 π R2 (sin 50O – sin 30O)__(8)

which gives and area of 6.7850 x 1013 m2 (approximately 
13.3024 % of the area of the whole Earth’s surface).

Area Earth’s Sub-Tropical high pressure ridge.
(1013 m2)
Height (m)
Mass of atmosphere  above height h 
(1017 Kg)
Mass Faction

B. Change in Angular Momentum of the Earth

CASE A: The Summer Southern Sub-Tropical 
High-Pressure Ridge shifts south by 1O.

Let X = the radius of circle of latitude of the Earth at latitude L.

____________X = R cos L___________(9)

___________ΔX = -R sin L ΔL________(10)

for ΔL = 1O = 0.017453293 radians and L = 40O
ΔX = 71.48 km

(N.B. In winter time the corresponding numbers would be:
for ΔL = 1O = 0.017453293 radians and L = 30O                 
ΔX = 55.60 km)

Now the Total Angular Momentum of the Earth (L) is 
given by:

___________L = I ω_______________(11)

where I = MAT X2, ω = VT/R is the angular frequency 
of rotation of the Earth and VT  is the tangential velocity 
of rotation of the Earth’s surface (in m s-1)  then:

__________L = MAT X2 ω__________(12)

____________= MAT X VT___________(13)

The movement of the Summer Southern Sub-Tropical 
High-Pressure Ridge 1O south means that there is 
decrease in the total angular momentum of the Earth’s 
atmosphere since part its mass (i.e. the sub-tropical ridge) 
is now rotating about the Earth’s axis of rotation at a 
radius that is 71.48 km smaller. This decrease in 
atmospheric angular momentum is compensated 
for by an increase in the angular momentum of the 
solid-Earth so that the total change in the Earth’s 
overall angular momentum (ΔL) remains unchanged 
(i.e. ΔL = 0): 
_____MAT VT  ΔRAT = - ME RE ΔVT___(14)
or_ΔVT (Earth) 
___= - (MAT/ME) (ΔRAT /RE) VT(Atmosphere)__(15)

Now_______VT = (2 π R cos L)/LOD______(16)

where the nominal length-of-day (LOD) is 86400 seconds. 
So for L = 40O VT = 354.91773191286 m s-1
Then if MAT = 2.098 x 1017 kg, ME = 5.9722 x 1024 kg, 
RE = 6.371 x 106 m, ΔRAT = 7.148 x 104 m:

____ΔVT (Earth) = 1.398865 x 10-7 m s-1

and since the new length-of-day (LOD /) is given by:

_____LOD/ = 2 π RE cos L /VT / (Earth)_____(17)

where the new lower velocity VT / (Earth) is equal to 
354.91773191286 m s-1 + 1.398865 x 10-7 m s-1
then the change in LOD (ΔLOD) is:

____ΔLOD = LOD / - 86400 = - 0.0341 ms____(18)

CASE B: The Winter Northern Sub-Tropical 
High-Pressure Ridge shifts south by 1O at the 
same time.

At this stage we have not taken into account a comparable
shift (i.e. ~ 1O) towards the equator by the northern 
sub-tropical high pressure ridge, which is likely to 
normally be located at its winter position 30O North of 
the Equator. The movement of the Winter Northern 
Sub-Tropical High-Pressure Ridge 1O south means 
that there is increase in the total angular momentum 
of the Earth’s atmosphere since part its mass (i.e. 
the sub-tropical ridge) is now rotating about the Earth’s 
axis of rotation at a radius that is 55.60 km larger. 
This increase in atmospheric angular momentum is 
compensated for by an decrease in the angular 
momentum of the solid-Earth so that the total 
change in the Earth’s overall angular momentum 
(ΔL) remains unchanged (i.e. ΔL = 0):  

From equation 16 the nominal speed of rotation 
of the Earth at 30O North is:

___________VT = 401.24013019223 m s-1

So for L = 30O VT = 401.2401301922 m s-1
if MAT = 2.098 x 1017 kg, ME = 5.9722 x 1024 kg, 
RE = 6.371 x 106 m, ΔRAT = 5.560 x 104 m, then 
the Earth’s rotation speed slows down by:
__________ΔVT (Earth) = 1.2301064334 x 10-7 m s-1

Therefore from equation 17:

_________LOD / = 86400.000026488012 seconds
and so____ΔLOD = LOD - 86400 = +0.0264 ms

Hence, the combined movements of both the Northern 
and Southern Tropical High-Pressure ridges will produce 
a change in the Earth’s rotation rate at the 9.3/18.6
year time scale of:

_____ΔLODTOT = (-0.0341 + 0.0264) ms
______________= -0.0077 ms
______________= -7.7 μsec

Note that ΔLODTOT would be zero if both the northern 
and southern sub-tropical ridges where at the same 
absolute latitudes (i.e. in Spring and Autumn/Fall). However, 
this is not the case during the  Northern and Southern 
Summers and Winters, so it will probably be non-zero 
during these seasons. This compares with the -12.57 μsec 
change in the length-of-day that is associated with the 
effect of 18.6 years lunar tides upon the earth’s rotation.  
Remember that this is only a back-of-the-envelope 
calculations with many assumptions thrown in, so it is 
amazing the it come out to within a factor of two.



Tidal wave___Period (days)__Δ_LOD___Erot
 ______________________(10-4 sec )_(1020 J)
18.6 year____6798.37______-0.1257__3.100
Sa _____________365.26_______0.0222__0.547
Mf ______________13.66_______0.3008__7.4200

So the 18.6 year period changes to the Earth’s LOD 
could produce movements of the sub-tropical high 
pressure ridges in both hemispheres by ~ 1O every
9.3/18.6 years, which is what we observed.