Global Positioning System Reference
In-Depth Information
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periodicities can be directly derived from the motion of the celestial bodies, similar
to nutation (see below). The solid earth tides generate periodic site displacements
of stations that depend on latitude. The tidal variation can be as much as 30 cm in
the vertical and 5 cm in the horizontal. McCarthy (1996, p. 61) lists the following
expression:
h
2
e
3
e
e
(2.5)
3
4
2
r
j
·
e
2
3
l
2
r
j
·
e
r
j
−
r
j
·
GM
E
GM
j
r
E
1
2
∆
x
=
−
+
r
j
3
j
=
2
In
this expression,
GM
E
is the gravitational constant of the earth,
GM
j
is the one for
th
e moon (subscript
j
3),
e
is the unit vector of the station
in
the geocentric coordinate system
(
x
)
, and
r
denotes the unit vector of the celestial
bo
dy.
h
2
and
l
2
are the nominal degree 2 Love and Shida numbers that describe elastic
pr
operties of the earth model. Equation (2.5) gives the solid earth tides accurate to at
lea
st 5 mm. For additional expressions concerning higher-order terms or expressions
fo
r the permanent tide, see McCarthy (1996).
=
2) and the sun (
j
=
[19
Lin
—
3.5
——
Cu
PgE
2.1.4 Ocean Loading
Oc
ean loading refers to the deformation of the sea floor and coastal land that results
fro
m the redistribution of ocean water that takes place during the ocean tide. The
ea
rth's crust yields under the weight of the tidal water. McCarthy (1996, p. 53) lists
th
e following expression for the site displacement components
∆
c
(where the
c
refers
to
the radial, west, and south component) at a particular site at time
t
,
[19
f
j
A
cj
cos
ω
cj
∆
c
=
j
t
+ χ
j
+
u
j
− Φ
(2.6)
j
Th
e summation over
j
represents eleven tidal waves traditionally designated as semi-
di
urnal
M
2
,S
2
,N
2
,K
2
, diurnal
K
1
,O
1
,P
1
, and long-periodic
M
f
,M
m
,S
sa
. The
sy
mbols
ω
j
and
χ
j
denote the angular velocities and the astronomic arguments at
0
h
. The fundamental arguments
time
t
χ
j
reflect the position of the sun and the
m
oon (see nutations below).
f
j
and
u
j
depend on the longitude of the lunar node.
Th
e station-specific amplitudes
A
cj
and phases
=
Φ
cj
can be computed using ocean
tid
e models and coastal outline data. The IERS makes these values available for most
IT
RF reference stations. Typically the
M
2
loading deformations are largest, but they
do
not exceed 5 cm in the vertical and 2 cm in the horizontal.
2.
2 CONVENTIONAL CELESTIAL REFERENCE SYSTEM
Dy
namical equations of motion are solved in this inertial frame. The equator, ecliptic,
an
d pole of the rotation of the earth historically defined the celestial reference frame.
Tw
o-dimensional coordinates of a large number of stars realized it. Present-day ICRF
