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ATMOSPHERIC AND OCEANIC EXCITATION OF THE NUTATION
ATMOSPHERIC AND OCEANIC EXCITATION OF THE NUTATION
(1984 to nowadays)



This tool allows you to study the excitation produced by the atmospheric or oceanic global circulation from 1984 until the current month. The reconstructed atmospheric or oceanic excitation ΨF is derived from the Celestial Angular Momentum (CEAM) of the fluid layer. It is compared with the Geodetic excitation ΨG calculated from celestial pole offsets (C04 series) with respect to IAU 2000/2006 conventional precession-nutation-model, only composed of luni-solar effects (updated on 2026, July 2). In these quantities, the computation of time derivative evaluated by cubic spline method.


Inverted barameter model         Non Inverted barameter model (not yet activated)            
Comparison of observed excitation with : Matter + motion terms    Matter term     Motion term

Atmospheric excitation ECMWF         Oceanic excitation MPIOM

First date : year month day     Last date : year month day

Plot and correlate X comp. of ΨG and ΨF (along vernal point)
Plot and correlate Y comp. of ΨG and ΨF(90ˆ)

  Parameters (see explanations below):

  Chandler period days   Chandler quality factor

  FCN period days         FCN quality factor       ama days   amo

Apply Vondrak frequency filter Remove parabolic trend
(P0) year    Transfer coefficient for P0 :T0= %
  • The Vondrak filter transfer function at another period P is given by :
    T=1/(1+(P0/P)6 (1-T0)/T0)
  • For the case "Select band below" the selected period is transfered with a rate of (100-T0)
Remove circular periodic components (periods in year) in both celestial excitations ΨG, ΨF and polynomial of degree before comparison      


     Produce data file of ΨG, ΨF, and χ'F
(unit : milliarcseconds ; no filtering, no fit)
              


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.