Geoscience Reference
In-Depth Information
4
C
20
VI
C
20
TL
Difference x 10
3
2
1
0
−1
−2
−3
−4
Jan
Apr
Aug
Dec
2008
Fig. 14
Time variation of the
C
20
coefficient in geoid height for the year 2008 in millimeter, in
black
following the VI approach in
blue
the TL approach, in
red
the difference multiplied by 10,
bias removed
3.3.3 Indirect Effect
The indirect effect of the atmosphere on the gravity field, i.e. the elastic deformation
of the solid Earth due to atmospheric loading, is counteracting the direct effect due
to the deformation towards the geocenter. In general, for small deformations the
additional change in the potential
Δ
V
depends linearly on the potential, following
Farrell (
1972
):
V
ind
n
Δ
=
k
n
Δ
V
,
(37)
V
tot
Δ
=
Δ
V
+
k
n
Δ
V
=
(
1
+
k
n
)Δ
V
,
(38)
n
where
k
n
denote the degree dependent
load Love numbers
and represent the defor-
mational behavior based on the rheology of the Earth.
Figure
15
shows the difference between a solutionwithout considering loading and
one which includes loading, both for the thin layer approximation. As expected only
differences at a large spatial scale appear since the Earth's elastic surface deformation
due to mass redistribution is mainly sensitive to large scale pressure variations with
wavelengths greater than 2000km, corresponding to
n
10 (Boy et al.
2001
).
This result is confirmed by the degree standard deviation expressed in geoid height
calculated for the year 2008 in Fig.
16
.
Given the fact that the differences up to degree 4 lie above the GRACE RL04 error
level and up to degree 15 above the predicted error level, the indirect effect has to be
accounted for, as it was already shown by Flechtner (
2007
). The same conclusion is
drawn looking at the difference between introducing and neglecting loading in terms
of geoid height variability for low degrees (Fig.
17
), considering the aimed precision
of GRACE to be a few micrometers for degree 3-5 (Tapley et al.
2004
).
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