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σ
cw
σ
cw
−
σ
p
ˆ
(σ )
=
χ,
(93)
which is an equivalent representation of Eq. (
79
) in frequency domain. In turn, we
can also give a time domain representation of the extended model in Eq. (
90
)
∂
t
−
σ
cw
∂
t
−
σ
f
i
i
p
ˆ
=
σ
cw
∂
t
−
σ
cw
a
p
χ
w
σ
f
χ
w
+
∂
t
−
p
P
−
i
i
+
χ
i
+
a
w
χ
(94)
Alas, the practical implementation of this expression would require computing time
derivatives of quickly-varying, empirical functions and thus might increase their
initial inaccuracies (Moritz and Müller
1987
).
Figure
15
portrays the application of the broadband frequency-domain formula
(Eq.
90
) onto the 30-year record of equatorial AAM values, which has already been
utilized in Sect.
3.1
. Complex-valued (non-IB) pressure and wind terms have been
convolved with the corresponding transfer function, yielding Fourier coefficients of
ˆ
σ
t
in cycles per day. By aid of the basic relation in
Eq. (
2
), the spectral content has been transfered to celestial frequencies
p
(σ )
at terrestrial frequencies
σ
t
in cpy
(cycles per year). From the resulting amplitude spectrum one clearly recognizes
the resonance peak at the FCN frequency located at
T
f
=
σ
f
−
1
2 cpd.
Moreover, large excitation amplitudes can be attributed to atmospheric tides which
would be centered around the retrograde diurnal frequency in the terrestrial reference
frame. Such global-scale atmospheric waves are chiefly of thermal origin, with their
labeling identical to that of the coherent gravitational tides (Brzezi nski et al.
2002
):
S
1
represents themain diurnal tidal component and contributes to the prograde annual
nutational motion, while
=−
430
.
are side lobes that modulate
S
1
and cause
additional peaks in nutation at frequencies
{
ψ
1
,
K
1
,
P
1
,π
1
}
cpy. The amplitude values
discernable from Fig.
15
may be compared to different findings in literature, e.g.
with that of Brzezi nski et al. (
2002
) or Vondrák and Ron (
2010
). Prerequisite for
such cross checking is to analyze the same time span as in the comparative study,
due to the fact that amplitude and phase values of atmospheric tides are time-variable
quantities. Further discrepancies between the estimates of each study are basically
down to insufficiencies in the underlying general circulation models for atmospheric
and oceanic processes.
There are some critical issues to the presented extended model that need to be
addressed more precisely. Firstly, the applied angular momentum function formalism
of Barnes et al. (
1983
) is not consistent in its treatment of core-mantle coupling, see
Dickman (
2003
). In detail, Eqs. (
85
)-(
87
) exclusively use the moments of inertia of
the mantle, whereas all remaining parameters (
k
2
,
k
2
and
k
s
) are assigned values
appropriate to the whole Earth, cf. the tabulations of Barnes et al. (
1983
, pp. 46,
71). Coincidentally, the free wobble frequency of the mantle
{−
1
,
0
,
2
,
3
}
σ
e
, resulting from the
theoretically erroneous Eq. (
85
), represents an exceptionally good estimate of the true
Chandler frequency. Adapting the involved Love numbers to mantle-only quantities
