Geoscience Reference
In-Depth Information
3.3 Length of Day Variations
The conversion of the axial angular momentum function
χ
3
into variations of length
of day and vice versa is derived following Barnes et al. (
1983
). At first, the third
component of Eq. (
11
) is written explicitly
ω
3
=
Ω (
1
+
m
3
) .
(95)
Understandably,
ω
3
relates to the actual length of the sidereal day
Λ
, which, in turn,
is composed of the nominal length of the day
Λ
0
plus a minute excess
∂Λ
.
2
π
Λ
π
Λ
0
+
∂Λ
2
ω
3
=
=
2
π
Λ
0
1
+
∂
Λ
0
=
1
=
Ω
+
∂
Λ
0
1
1
−
∂Λ
Λ
0
⇒
ω
3
≈
Ω
.
(96)
The ratio between
and the nominal length of day is sufficiently small to justify
the employed approximation in Eq. (
96
). By comparing the obtained expression to
Eq. (
95
) and recalling the axial solution of the Liouville equations, we find
∂Λ
m
3
=
∂Λ
LOD
86400 s
+
χ
3
=−
Λ
0
+
const
=
const
(97)
d
d
t
(
=−
UT1
−
UTC
)
+
const
,
where LOD is the quantity conventionally reported by Earth rotation measurement
services. It designates the excess length of day with respect to the mean solar day of
length 86400 s. The absence of any frequency-dependent transfer function in Eq. (
97
)
represents a certain advantage when studying the impact of geodynamical processes
on Earth's rotation rate.
As an illustration, Fig.
16
compares daily values of observed variations in LOD
from the EOP 05 C04 series (Bizouard
2011
) with a 30-year record of axial
atmospheric angular momentum that has been obtained from ECMWF data. As
periods longer than two days are looked at, it is safe to revert to the IB-corrected
matter term of AAM functions,
p
3
. In order to facilitate the comparison with pure
atmospheric excitation, the measured changes in LOD have to be cleared of a sec-
ular signal, decadal fluctuations due to angular momentum exchange between core
and mantle, and pronounced harmonic variations induced by solid Earth tides. Refer
to Sect.
1.4
and Seitz and Schuh (
2010
) for a further discussion on these effects.
χ
