Geoscience Reference
In-Depth Information
Δ
I
,
h
,
Ta b l e 1
Comparison of the overall
I
33
and
h
3
coefficients as proposed by Gross (
2007
)
and Barnes et al. (
1983
). The numerical results are based on the individual parameter values of
either work
Model
Δ
Δ
I
coefficient
h
coefficient
Δ
I
33
coefficient
h
3
coefficient
1
.
608
/
(
C
−
A
)Ω
=
1
.
100
/(
C
−
A
)
=
Gross
0
.
748
/
C
m
=
0
.
998
/
[
Ω
C
m
]
=
4
.
1825
·
10
−
36
8
.
3845
·
10
−
32
1
.
0500
·
10
−
38
1
.
9212
·
10
−
34
Barnes et al. 1
.
00
/(
C
m
−
A
m
)
=
1
.
43
/
[
(
C
m
−
A
m
)Ω
]
=
0
.
70
/
C
m
=
1
/
[
Ω
C
m
]
=
4
.
2656
·
10
−
36
8
.
3650
·
10
−
32
0
.
9943
·
10
−
38
1
.
9479
·
10
−
34
is only applicable at periods significantly longer than 1d. This restriction to the low-
frequency band may also justify our tacit assumption of non-dispersive geophysical
parameters such as the Love numbers, see Dickman (
2005
) for additional remarks
on this topic. Moreover, it has to be pointed out, that the given set of correction
factors is by no means unchallengeable, as it depends on the underlying geophysical
models, the applied mathematical approach and the used numerical values. In detail,
as shown by Gross (
2007
), the angular momentum functions in Eqs. (
35
)-(
36
) agree
within 2% with that of Wahr (
2005
) and reveal similar discrepancies compared to
the approaches of Barnes et al. (
1983
), Eubanks (
1993
) or Zhou et al. (
2006
). A
compilation and discussion of the various formulations in the spotlight of different
amounts of core-mantle coupling is presented in Dickman (
2003
). Since the majority
of previous investigations concerning geophysical effects on polar motion and LOD
have used the angular momentum formulation of Barnes et al. (
1983
), we juxtapose
in Table
1
the
Δ
I
,
h
,
I
33
and
h
3
coefficients of the latter study to the respective
scaling factors of Gross (
2007
).
The two gravest approximations of the Barnes formulation—assuming an Earth
model with a fully decoupled core and neglecting feedback features except rotational
deformation plus crustal loading—are particularly apparent in thewriting of the equa-
torial terms but numerically balance each other. As a result, the overall coefficients
of
Δ
Δ
I
and
h
vary within 1-2% across the two studies. For
Δ
I
33
the discrepancy of
about 5% is down to the introduction of
α
3
, which has no correspondence in Barnes
et al. (
1983
).
Considering the long-period limitations of the presented theory, it is clear, that
investigation of geophysical excitation phenomena on short time scales, such as
daily and subdaily atmospheric signals in ERP (or EOP, more generally), requires
an adapted, frequency-dependent form of (effective) angular momentum functions.
If models exist that account for relative angular momentum of the core and mass
redistributions in the oceans—both engendered by the perturbing centrifugal forces
due to spin and wobble—on short time scales, the derivations of Sect.
2.4
could
be modified accordingly. However, this is not the case and hence, the creation of
an accurate and consistent scheme for high-frequency excitation studies is still a
pivotal topic of present Earth rotation research. The most remarkable effort in this
field has been performed by Brzezi nski (
1994
), who extended the original equatorial
relationship of polar motion excitation, given in Eq. (
30
), for the FCN (Sect.
1.2
). The
