Geoscience Reference
In-Depth Information
∞
Δ
p
=
g
0
Δρ
dr
=
g
0
σ,
(29)
0
Δσ
=
Δ
p
g
0
,
(30)
where
g
0
is the mean gravity acceleration at the Earth surface and
Δρ
the pressure
variation.
The atmosphere affects the Earth gravity field in two different ways: a
direct
attraction
of the atmospheric masses acting on the orbiting satellite and a much
smaller
indirect effect
introduced by the deformation of the Earths surface due to
elastic loading. Both effects are always evaluated with respect to a mean atmosphere
model. This approach is described in detail by Torge (
1989
). The following sec-
tions deal exclusively with the direct effect, the indirect effect will be addressed in
Sect.
3.3.3
.
Due to mass redistribution in the atmosphere the potential V changes with time.
This time-dependency of atmospheric density
Δρ
can be represented in terms of
time-dependent
Δ
C
nm
and
Δ
S
nm
coefficients, taking into account Eqs. (
29
) and
(
30
), as follows
Δ
cos
m
sin
∞
r
n
+
2
d
r
P
nm
(
1
C
nm
λ
=
Δρ
cos
θ)
θ
d
θ
d
λ,
Δ
S
nm
Ma
n
sin
m
λ
(
2
n
+
1
)
r
s
Earth
(31)
where
r
s
is the Earth surface radius.
3.3.1 Thin Layer Approximation
In the simplest approach for calculating AGC the vertical extent of the atmosphere is
neglected and all the atmospheric masses are concentrated in a
thin layer
(TL) at the
Earth surface. This can be done under the assumption that most of the mass changes
occur in the lower 10km of the atmosphere and act as variable loading effects on the
solid Earth's surface (Boy and Chao
2005
).
Surface loads are defined asmass per surface element; therefore the density change
in the atmosphere can be expressed in terms of surface load,
Δ
cos
m
dS
a
2
C
nm
λ
=
Δσ
P
nm
(
cos
θ)
,
(32)
Δ
S
nm
sin
m
λ
(
2
n
+
1
)
M
Earth
r
2
d
r
sin
r
2
considering that the mass element dM
=
ρ
θ
d
θ
d
λ
=
σ
sin
θ
d
θ
d
λ
=
r
2
σ
dS.
Following the definition of the surface load
in
E
q. (
30
), the surface pressure
p
s
can be introduced, whereas a mean pressure field
p
s
, representing a static mean
Δσ
