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Ocean Tides and the Earth's Rotation
An Introductory Discussion Courtesy of the
IERS Special Bureau for Tides
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Tides affect the earth's rotation in two sharply contrasting ways.
One way, caused by tidal friction, produces an extremely slow secular
change in rotation. The other way, caused by the continual movements
of the tides about the planet, produces very small but very rapid
changes in rotation. These rapid changes occur at exactly the same
periods as the tides themselves -- half-daily, daily, etc. (The IERS
Special Bureau for Tides is concerned primarily with the rapid
changes, but some of our data have implications for the secular
changes.)
Secular Tidal Braking of Earth Rotation
The secular change in the planet's rotation is a classical topic in
geophysics. It goes back some 300 years to when Sir Edmond Halley
first hypothesized that the moon was accelerating in its orbit. Most
of Halley's lunar acceleration was only apparent. It was actually the
earth's rotation slowing down, making the moon appear to accelerate.
The moon does accelerate (strictly, it decelerates), but the larger
effect is the earth's rotational braking. This braking is caused by
tidal friction. Throughout the earth's history tidal braking has
played, and it will continue to play, a dominant role in the
rotation. Currently the secular change in the rotation rate increases
the length of day by some 2.3 milliseconds per day per century.
To see what that means, consider this example: suppose the rotating
earth is our clock and it's been 100 years since that clock's
"standard second" was set to correspond to an atomic clock's second
(which is actually almost the case, notwithstanding that atomic
clocks weren't around until 1955). Then after 1000 days our earth
clock loses about 2.3 seconds, falling further behind the atomic
clock. This long-term slowing of the rotation is a primary reason for
periodically inserting leap seconds into our timekeeping. Of course,
there are other contributors to the changing rotation rate such as
the changing atmosphere and the motions of the fluid core; one can't
blame just tides for our timekeeping difficulties.
The tidal braking in the earth's rotation is actually caused
primarily by friction in the oceans, where ``friction'' may refer to
any number of physical mechanisms which have yet to be determined
definitively. For example, bottom friction, induced by tidal currents
flowing across the seabed, various kinds of wave breaking, and
scattering of tidal waves into oceanic internal waves are all thought
to play a role. For a recent overview of this subject, look up Walter
Munk's paper ``Once again: once again--tidal friction,'' published in
Progress in Oceanography, vol. 40, pp. 7-36, 1997.
Rapid Tidal Variations in Earth Rotation
Only in the last few years has this subject come to the fore, as our
abilities to measure daily and even subdaily variations in rotation
have been developed and improved. An example is shown on the
following figure, which displays very rapid variations in the
rotation rate (in terms of Universal Time) as observed by hourly
measurements and as predicted by a numerical model of ocean tides.
The measurements are from an intensive campaign of Very Long Baseline
Interferometry (VLBI) observations, analyzed and provided courtesy of
Chopo Ma and John Gipson (NASA/GSFC). The ocean predictions are from
one of the models provided in the Special Bureau for Tides web pages.
[ut1_jan94]
Rapid variations in Universal Time as measured by VLBI and as
predicted by a numerical ocean model.
As can be seen, both diurnal and semidiurnal variations are present
in UT1, and they appear to be quite well represented by the ocean
model. There are two ways that the ocean tides can cause such rapid
variations. (1) As the tides move water around the globe, the moment
of inertia of the earth changes. By conservation of angular momentum,
the solid earth changes its rotation rate accordingly. (2) As the
tidal currents slow down or speed up, they exchange angular momentum
with the solid earth, which is manifested in the rotation rate.
Mechanism (2) is slightly more important for rotation rate
variations; both mechanisms are about equally important for polar
motion variations. Hence, to predict tidal variations in earth
rotation, similar to the solid curve in the figure, requires a global
model of both tidal heights and tidal currents. The relevant
information from several such models is provided in these web pages
of the Special Bureau for Tides.
Finally, there are also tidal variations in rotation rate and polar
motion caused by the near-equilibrium long-period tides, which have
periods from about 9 days to 18.6 years. For rotation rate, the
dominant contributor is in fact the solid-earth tides. But
perturbations from the ocean are still significant. See this
additional information.
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Some classic books on tides and on Earth rotation
These books are a bit obsolete in places, since obviously they cannot
discuss the most up-to-date accuracies, measurements, and theories.
But they are nonetheless classics of the literature and provide the
starting point for all further study. In particular, Munk and
MacDonald, more than anyone since Lord Kelvin, shaped the contours of
the entire modern subject, and they laid the foundation for the
succeeding 40 years of work. Their book, which justifiably won the
AAAS Monograph Prize for 1959, touched on nearly all aspects of the
present-day subject, save perhaps for the one addressed in these web
pages: extremely rapid (daily and faster) variations.
Munk, W. H. and G. J. F. MacDonald, The Rotation of the Earth: A
Geophysical Discussion, Cambridge Univ. Press, 1960.
Lambeck, K., The Earth's Variable Rotation: Geophysical Causes and
Consequences, Cambridge Univ. Press, 1980.
Doodson, A. T. and H. D. Warburg, Admiralty Manual of Tides, HMSO,
1941.
A Few Modern Citations
Tidal Variations in Earth Rotation
Brosche, P., U. Seiler, J. Suendermann, and J. Wuensch, Periodic
changes in the Earth's rotation due to oceanic tides, Astronomy and
Astrophysics, 220, 318-320, 1989.
Chao, B. F. and R. D. Ray, Oceanic tidal angular momentum and Earth's
rotational variations, Progress in Oceanography, 40, 399-422, 1997.
Eubanks, T. M., Variation in the orientation of the Earth, in
Contributions of Space Geodesy to Geodynamics: Earth Dynamics, pp.
1-54, Amer. Geophys. Union, Washington, 1993.
Gross, R. S., The effect of ocean tides on the Earth's rotation as
predicted by the results of an ocean tide model, Geophysical Research
Letters, 20, 293-296, 1993.
Herring, T. A. and D. Dong, Measurement of diurnal and semidiurnal
rotational variations and tidal parameters of the Earth, Journal of
Geophysical Research, 99, 18051-18071, 1994.
Ray, R. D., D. J. Steinberg, B. F. Chao, and D. E. Cartwright,
Diurnal and semidiurnal variations in the Earth's rotation rate
induced by oceanic tides, Science, 264, 830-832, 1994.
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Last Updated: May 15, 2001
Website Author and Curator: Richard Ray