Geoscience Reference
In-Depth Information
Figure 2.12
Schematic of the
spectrum of constituents of
the TGF.
Semi-diurnal
Diurnal
Low
f
r
equency
0
1
2
Frequency (cycles d
-1
)
2.5.1
Tidal constituents
As the Earth rotates, the tide generating forces of the Sun and the Moon vary in a
regular fashion with periods set by the lunar and solar days. There are also more subtle
variations at other frequencies due to the orbital motions of the Moon about the Earth
and the Sun about the Earth. A rigorous mathematical analysis of the tide generating
rather large number of spectral lines at specific frequencies. These lines are mainly
concentrated in two spectral bands, termed tidal species or bands, which are centred on
1 cycle per day (the diurnal species) and 2 cycles per day (the semi-diurnal species) with
some others at low frequencies (
1 cycle per month or less). Each separate frequency
identifiable in the spectrum is referred to as a tidal constituent, and the TGF at each
point on the Earth can, therefore, be written as a sum of these individual constituents:
∼
X
N
¼
A
n
cos
ð
o
n
t
þ
a
n
Þ
ð
:
Þ
TGF
2
20
n
¼
1
where A
n
and a
n
are the constituent amplitudes and phases. The frequencies o
n
are
known accurately from the astronomically determined motions of the Sun and Moon.
The response of the global ocean to this forcing can in theory be calculated
without reference to observations if the bathymetry of the ocean is known. This
prediction of the tides from first principles, originally proposed by Laplace, has
proved very challenging and has only recently been accomplished using high reso-
lution numerical models (Egbert et al.,
2004
). The alternative, also anticipated by
Laplace (Cartwright,
1999
), is to treat the observed tide as a sum of harmonic terms
at the same frequencies as the TGF but with different amplitudes and phases:
X
N
ð
t
Þ¼
H
n
cos
ð
o
n
t
þ
a
n
g
n
Þ:
ð
2
:
21
Þ
n¼
1
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