Earth Rotation

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Earth Rotation
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Earths revolution around the Sun
Automn
Spring
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Precession of the Equinoxes
Motion of mean rotation axis and angular
momentum vector of whole Earth in space. Note
position of North Pole, where rotation vector
intersect Earths surface, doesnt change
Image university of Hong Kong, Dept of physics
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Change in Earths ellipticity
Observed changes in J2 (Cox and Chao, Science,
2002)
Decrease of Earths ellipticity due to GIA
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True Polar wander
Change in the location of rotation axis with
respect to fixed point at surface
Mass excess Mass deficit

change in moment of inertia
Rotation axis stays aligned with largest
principal moment of inertia
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True Polar wander
Directly observed in last 100 years
3.5 mas/yr in the direction of Greenland
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True polar wander
Indirectly observed (from paleomagnetism assuming
GAD) for the last few hundred million years
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True polar wander
Mantle convection can explain TPW over past
50-100 million years
Can also explain about 40 of the current
rate Post-glacial rebound, Ice-mass variations
and sea-level change can explain the difference.

Steinberger OConnell, Nature, 1997
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Polar motion
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Polar motion
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Polar motion
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Polar motion
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Doom!!!!

• Michael Mandeville, in his report titled "The
  Earths Wobble Has Paused

"For the past 21 days there has been no
discernable wobble motion in the Earth. Have we
come to a profound change in the geophysics of
the Earth? Why this sudden change in what usually
has been for the past 100 years or more a fairly
regular, fairly predictable wobble track. As is
well known, the wobble is generated by the
differential pulling of the Moon and the Sun on
the Earth's equatorial bulge (and any other
concentrations of mass in or on the Earth). This
differential pulling is caused by the oblique
angles of the orbital planes which bring the Sun
and the Moon alternatively above and below the
equator, thus tending through orbital time to
push one side of the Earth or the other to move
faster or slower than the other side to the North
or to the South.The Earth's Wobble has a 7 year
cycle . But suddenly at the beginning of
November 2005, the track of the location of the
spin axis veered at a very sharp right angle to
its circling motion. The track of the spin axis
began to slow down and by about January 8, 2006,
it ceased nearly all relative motion on the x and
y coordinates which are used to define the daily
changing location of the spin axis.
Taken from christian-forum.net, where it is
further suggested that the imminent total
collapse of our world is at hand
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Polar motion
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Polar motion
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Polar motion
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Polar motion
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Annual wobble
Driven primarily by the atmospheric pressure
high over Siberia during NH winter
From The Atmosphere, Lutgens and Tarbuck
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Annual wobble
Driven primarily by the atmospheric pressure
high over Siberia during NH winter
From The Atmosphere, Lutgens and Tarbuck
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Free core nutation
From Palmer Smylie, PEPI, 2005
Measured by VLBI. Amplitude 0.26 mas Observed
period 417 days (in celestial frame) (Mathews,
Herring, Buffett observed period 430
days) Theoretical period 455-460 days
Excess CMB ellipticity of 500 m compared to
hydrostatic

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Chandler Wobble
observed period, T 435 days
Rigid Earth T 305 days elasticity T
447 days core T 400 days
oceans T 427 days dissipation T 435
days
Seth Carlo Chandler
Dissipation observed Q 170 (half-life of 70
yrs)
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Forced nutations
P precession N nutation
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Observed nutations
In celestial frame
From Herring et al, JGR, 1986
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Observed nutations
In terrestrial frame
From Herring et al, JGR, 1986
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Electromagnetic coupling at CMB and ICB inferred
from forced nutations
From Buffett et al, JGR, 2002
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Polar motion

• Secular change true polar wander (mantle
  convection, post-glacial rebound)
• Chandler Wobble
• Annual wobble (atmosphere, ocean)

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Polar motion

• Secular change true polar wander (mantle
  convection, post-glacial rebound)
• Chandler Wobble
• Annual wobble (atmosphere, ocean)
• Daily variations (ocean tides)
• Inter-annual variations (oceans, atmosphere)
• Decadal variations (??)

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Credit BF Chao
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Polar motion at daily subdaily timescales
From ocean tides
From Chao et al, JGR, 1996
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Decadal polar motion?
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Decadal polar motion Markowitz wobble
From Dumberry, GJI, 2008
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Changes in length of day (amplitude of rotation)

• Secular change (tidal friction)
• Daily variations (oceans tides)
• Seasonal variations (oceans, atmosphere)
• Decadal variations (core flows)
• Millennial variations (core flows?)

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Secular change Tidal friction
Earths rotation is indeed slowing down at a
present rate of 0.0018 seconds per century
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Lunar and solar eclipses recorded by ancient
civilizations
Babylon, solar eclipse of April 15 136 BC
China, lunar eclipse Sept 4/5 434 AD
Images from Stephenson, Astron. Geophys., 2003
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Lunar and solar eclipses recorded by ancient
civilizations
Offset between predicted and observed
eclipse path when Earths rotation rate is
constant
from Stephenson, Astron. Geophys., 2003
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Lunar and solar eclipses recorded by ancient
civilizations
Reconstruction of past Earths rotation rate
from Stephenson, Astron. Geophys., 2003
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Lunar and solar eclipses recorded by ancient
civilizations
Reconstruction of past Earths rotation rate
From LLR difference with mean observed change is
from GIA
from Stephenson, Astron. Geophys., 2003
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Paleorotation
From Williams, Rev. Geophys., 2000
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Paleorotation
From Williams, Rev. Geophys., 2000
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LOD changes at daily timescales
Mostly due to ocean tides
From Chao, EOS, 2003
From Chao et al, JGR, 1996
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LOD changes at seasonal annual timescales
From Gross et al, JGR, 2004
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LOD changes at inter-annual timescales
From Gross et al, JGR, 2004
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LOD changes at decadal timescales
From Chao, EOS, 2003
Tides (18.6 yr) contribute to 0.15 ms Oceans and
atmosphere less than 0.5 ms
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Torsional oscillations
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Torsional oscillations
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Torsional oscillations
Recovered from time changes in the geomagnetic
field
From Zatman Bloxham, nature, 1997
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LOD changes at decadal timescales
From Chao, EOS, 2003
From Jault et al, nature 1988 Jackson et al,
AGU, 1993
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What is the torque?

• Topographic?
• Viscous?
• Gravitational (inner core)?
• Electromagnetic?

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Free modes of torsional oscillations?
Period and decay of free modes for different EM
coupling at CMB
Br gufm1, conductance 108 S
nutation constraints
From Dumberry Mound, JGR, 2008
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LOD changes at millennial timescales
From Chao, EOS, 2003
Changes at 1500 yr timescale. Caused by core
flows?
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Magnetic field changes at millennial timescales
Latitude 60N
From Dumberry Finlay, EPSL, 2007
Episodes of westward and eastward drifts
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Predicted changes in LODassuming rigid
cylindrical flows
From Dumberry Bloxham, GJII, 2006
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Predicted changes in LODassuming non-rigid flows
From Dumberry Bloxham, GJI, 2006