Geoscience Reference
In-Depth Information
90
1
0.75
45
0.5
0
0.25
−45
0
400
−90
−400
−400
−300
−300
−200
−200
−100
−100
−20 −10
0
10
20
100
100
200
200
300
300
400
Period [d]
Fig. 11
Frequency-dependent magnitude-squared coherence
c
xy
(
black line
) and phase lag
ϕ
xy
(
blue line
) between observed polar motion excitation and equatorial angular momentum functions.
Analyzed time span: 1980 to 2010.
Red vertical lines
(at annual, semiannual and terannual periods)
indicate the prograde and retrograde seasonal bands. Spectral content at periods shorter than 100 d
has been smoothed appropriately to underline the decrease of coherence at high frequencies. The
phase lag information varies erratically at high frequencies and is thus not displayed in the
middle
panel
We complete the theoretical considerations of this section with additional remarks
on Eq. (
78
), which suggests that full variability of
ˆ
m
in the TRS is conveyed exclu-
ˆ
ˆ
sively by
p
characterizes all terrestrial perturbations of the CIP, i.e.
that outside the retrograde diurnal band
p
. By definition,
cpsd. However, the polar
motion of the instantaneous Earth rotation axis is not subject to such a spectral sepa-
ration and shows in fact substantial variations due to the celestial motion of the CIP,
see Brzezi nski and Capitaine (
1993
) for a rigorous treatment of the problem. The
mean additional term to
σ
t
∈
(
−
1
.
5
,
−
0
.
5
)
28 mas) corresponds to the well-known analytical part
of the precession-nutation model and is called
diurnal polar motion
(McClure
1973
).
Accordingly, the unpredictable portion of nutational motion, expressed by the celes-
tial pole offsets
m
(
ˆ
≈
X
,
Y
}
m
but can be virtually omitted in
view of the smallness of
X
and
Y
. A final contribution arises from the fact that the
GCRS in the above derivations has been rotated by the precession-nutation model
and thus is no more an inertial reference. As shown by Brzezi nski and Capitaine
(
1993
), the order of this effect is negligibly small (2
{
(Sect.
1.2
), is also affecting
ˆ
10
−
10
mas).
The application of the derived excitation relationships onto real data is straight-
forward. Figure
11
illustrates the differentiation approach of Eq. (
79
) in terms of a
coherence study between geodetic polar motion and its geophysical excitation as
modeled from atmospheric data. The observational time series have been extracted
from the well-known EOP 05 C04 series (Bizouard
2011
) at daily intervals from1980
to 2010. The same sampling applies on the equatorial AAM function, which has been
computed from pressure and wind analysis fields of the ECMWF. The response of
the oceans to atmospheric perturbations at large time scales is assumed to be static,
i.e. the IB-correction has been imposed on the matter term
·
p
.
Numerical differentiation of the polar motion series yields the so-called
geodetic
excitation function
(left-hand side of Eq.
79
), a complex-valued signal that can be
examined for linear dependency and phase differences with respect to the equa-
torial AAM function, e.g. within a two-sided magnitude-squared coherence plot,
augmented by the corresponding phase lag information (Fig.
11
). The displayed
χ
