- The observed (or geodetic) celestial equatorial excitation functions
are computed from the IERS C04 series (sampling of 1 day, fluctuations
> 6 days). Let P=dX + idY be the Celestial Pole Offsets, referred
to nutation model UAI 2000, the complex form of those functions is :
= P + i ( 1/σ'FCN+ 1/σ'C)
dP/dt - 1/(σ'C σ'FCN)d2P/dt2
where σ'FCN = 2π
/ TFCN (1 + i/2QFCN) ; σ'C
= Ω + 2π / TC
(1 + i/2QC) with Ω the Earth angular
The celestial equatorial excitation functions are based upon the knowledge
of the Chandler term period TC and its quality factor QC,
the Free Core Nutation (FCN) period TFCN and its quality factor
QFCN. As these parameters are affected by large uncertainties,
we let you the possibility to tune them within the allowed bands (426
<TC<439 days; 50<QC<200, 420<TFCN<440
days; 1000<QFCN<40000). The excitation function is mostly
sensible to FCN parameters, especially around the FCN period of 430
- Celestial Atmospheric/Oceanic (CEAM/CEOM) functions are derived
from the equatorial AAM/OAM functions χA/O
provided by the Special Bureau for Atmosphere of the IERS (NCEP-NCAR
reanalysis time series, 6-hours time resolution). They are defined by
χ'F = χ'A/O = -χA/O
where GMST is the Greenwhich Mean Sideral Time.
The Celestial Oceanic Momentum (CEOM) functions are defined similarly.
The CEAM/CEOM functions are filtered and sampled before comparison to
have the consistency with C04 series.
- The effect of CEAM (or CEOM) on χ'G
is given by the quantity:
χ''F = i σC/
dχ'F/dt + σC/σ'C
χ'F + i σC/
(ap dχ'F(matter)/dt +aw
dχ'F(motion)/dt) + σC/σ'FCN
(apχ'F(matter) + awχ'F(motion))
where "(matter)" means that the CEAM/CEOM is restricted to
the "matter term" (pressure/water height), and "(motion)"
means that the CEAM/CEOM is restricted to the motion term (wind/current).
The pressure term is associated with oceans reacting either as "Inverted
Barometer" (IB) or non inverted barameter (NIB) in
front of the pressure variations. The parameters ap and aw, which depends
on rheological properties of the Earth and core-mantle coupling, can
Basic equation expressing angular momentum conservation is :
χ'G = χ''F
This formalism is exposed in more details in Brzezinski (1994): Polar
Motion excitation by variations of the effective angular momentum, II
: extented model, Manuscripta Geodetica 19, 157-171.