This tool compares the two members of the second order differential equation (with respect to celestial pole offset P) ΨG = ΨF,
expressing angular momentum conservation of the system composed of the solid Earth and of the fluid
layer, where :
- ΨG is the observed (or geodetic) celestial equatorial excitation functions,
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, we have:
ΨG
= P + i ( 1/σ'f+ 1/σ'c)
dP/dt - 1/(σ'c σ'f)d2P/dt2
where σ'f = 2π / Tf (1 + i/2Qf) ; σ'C
= Ω + 2π / Tc
(1 + i/2Qc) with Ω the Earth angular
velocity. Thus, ΨG is based upon the knowledge
of the Chandler term period Tc and its quality factor Qc,
the Free Core Nutation (FCN) period Tf and its quality factor
Qf. 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<Tf<440
days; 1000<Qf<40000). The excitation function is mostly
sensible to FCN parameters, especially around the FCN period of 430
days.
- ΨF is the modelled excitation given by :
ΨF = i σc/
(σ'cσ'f)
dχ'/dt + σc/σ'c
χ' + i σc/
(σ'cσ'f)
(ama dχ'ma/dt +amo
dχ'mo/dt) + σc/σ'f
(ama χ'ma+ amoχ'mo)
where "ma" means that the Celestial Effective Angular Momentum Functions (CEAMF) χ' restricted to
the "matter term" (pressure/water height), and "mo"
means that the CEAMF 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. Currently only the IB model is considered.
The parameters ama and amo, which depends
on rheological properties of the Earth and core-mantle coupling, can
be tuned.
- Celestial Effective Angular Momentum Functions CEAMF χ'=χ'F functions are derived
from the equatorial AAM/OAM functions χF provided by the GFZ (from the ECMWF model for the atmosphere, from MPIOM for the oceans).
They are defined by :
χ'F = -χF ei GMST
where GMST is the Greenwhich Mean Sideral Time.
The CEAMF functions are filtered and daily sampled before comparison to
have the consistency with C04 series.
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.
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