(1984 to nowadays)

updated : May 2010

The following tool allows you to study the atmospheric and oceanic excitation of the nutation. Equatorial excitation functions associated with the nutation of the Earth are compared to the Celestial Atmospheric Angular Momentum (CEAM) and Celestial Oceanic Angular Momentum (COAM) functions through visual plot and computation of the correlation coefficients. Both quantities can be taken into separately or added up.

Inverted barameter model         Non Inverted barameter model             Civil date for graphics

Comparison of observed excitation with : Matter + motion terms    Matter term     Motion term

Atmospheric excitation NCEP (1984-current year)        Oceanic excitation ECCO (1993-2009)

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

Plot and correlate X comp. of χ'G and χ''A/O (along vernal point)
Plot and correlate Y comp. of χ'G and χ''A/O (90°)
  Parameters of observed celestial equatorial excitation functions (see explanations below):

  Chandler period days   Chandler quality factor

  FCN period days         FCN quality factor       ap days   aw

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 functions χ'G and χ''Fand polynomial of degree before comparison      

Produce data file χ'G /χ'A/O χ''A/O
(unit : milliarcseconds ; no filtering, no fit)


  • 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 :

          χ'G = 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 velocity
    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 days.

  • 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 ei GMST

    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/ (σ'Cσ'FCN) dχ'F/dt + σC/σ'C χ'F + i σC/ (σ'Cσ'FCN) (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 be tuned.

    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.