Atmospheric and oceanic excitation of the polar motion and length of day
updated : March 2019      

Inverted barameter model         Non Inverted barameter model             Civil date for graphics

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

Atmosphere         Oceans:         Continental water:

Plots and correlation       Dimension du graphe : X English French

     Plot and correlate χGEOD and χGEOPH Plot differences χGEODGEOPH: Plot χGEOPH

        x components (along Greenwhich) y components (90°E) Excess of length-of-day (z)
        2D x/y equatorial components

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)

  • Spectral analysis (FFT, complex for 2D signal) Amplitude (Ampl.)2   Log scale
    min. frequency       max. frequency (in cycle per year)

    x (along Greenwhich)  y (90°E)  z (axial)  2D x - i y   Geodetic Geophysical excitation
    Produce data file :

        x/y/z components of the Geodetic (χGEOD) and Geophysical excitations (χGEOPH) functions (not filtered)
        x/y/z components χGEOD - χGEOPH
       Chandler period : days

       Chandler quality factor :

    Starting date : year month day

    Ending date :   year month day
       Coefficients of the effective angular momentum function (by default: from Gross et al, JGR, 2005):

       Matter-equatorial    Matter-axial    Motion-equatorial    Motion-axial


    This tool allows you to compute the excitation functions of the Earth rotation χ1, χ2, χ3 (according to the "Euler-Liouville" formalism) and to compare them to the geophysical excitation functions, as far as these later ones are available. Comparison is done through visual plot and computation of the correlation coefficients.
    • The observed excitation functionsx, χy, χz) are computed from the pole coordinates (x,y) and length of day changes ΔLOD of the IERS C04 series (sampling of 1 day, fluctuations > 6 days) according to the equations : χx + i χy=(x-i y) + i/σc d(x-iy)/dt where σc is the Chandler angular frequency : (σc = 2π/T ( 1 + i / 2 Q), T Chandler period, Q quality factor) and χz=ΔLOD (actually the true adimensionel axial excitation function is ΔLOD / LOD with LOD =86400 s TAI). The equatorial excitation function χx + i χy is computed according to an algorithm such as the one introduced by Wilson and Vicente (1981,1985,2002) .

    • Comparison can be done with :

      • Atmospheric Angular Momentum Functions provided by the Special Bureau for Atmosphere of the IERS (NCEP-NCAR reanalysis time series) ( from 1962 to 2016/1/1 (see readme). From 2016/1/1 up to the current week these data are completed by those of the operational NCEP model ( In March 2019 we add the operational ECWMF series as computed by GFZ, daily updated and spanning the period 1976-one day back from now

      • Oceanic Angular Momentum (OAM) functions of the ECCO model : file ECCO_50yr.chi (10 day values from 1962 to 1993 daily interpolated at 0hUTC) + file ECCO_kf080 (daily values from 1993 to 2016, assimilation of altimetric measurements of the sea surface, NCEP/NCAR atmospheric forcing), provided by the Special Bureau for Oceans of IERS (responsible : Richard Gross). In March 2019 we add the operational OMCT series, as computed by GFZ, daily updated and spanning the period 1976-one day back from now

      • Hydrological Angular Momentum (HAM) functions (since March 2019). HAM series of the LSDM model, as estimated by GFZ, daily updated and spanning the period 1976-one day back from now

    • For the observed axial excitation the effect of zonal gravitational tides is removed.

    • The atmospheric and oceanic angular momentum functions are filtered and sampled before comparison. By default the pressure term is associated with oceans reacting as "Inverted Barometer" (IB) in front of the pressure variations : this is a realist approximation for variations larger than 10 days (for rough pressure term click the button "Non IB").

    • Geodetic Excitation functions are derived from combined series C04 using an algorithm based upon trapezoidal integration of the geodetic excitation function.

    • The equatorial excitation function is based upon the knowledge of the Chandler term period T and its quality factor Q. As these parameters are affected by large uncertainties, we let you the possibility to tune them within the allowed bands (426 <T<439 days; 50<Q<200). The excitation function in the Chandler frequency band can be spoiled by bad choice of these parameters. Outside this band the choice of these parameter is not critic.

    • From March 2019 user can fix by himself the coefficients of the effective angular momentum functions.
    Thanks to Henryk Dobslaw and Robert Dill for fruitful discussion pertaining to GFZ angular momentum series. Thanks to David Salstein (Atmospheric and Environmental Research, Boston) and Olivier de Viron (Institut de Physique du Globe de Paris) for their respective advices. C. Bizouard