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.
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
- The observed excitation functions (χx, 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 :
- Effective Atmospheric Angular Momentum Functions provided
by the Special Bureau for Atmosphere of the IERS (NCEP-NCAR reanalysis
time series) (http://files.aer.com/aerweb/AAM)
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
- 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),
by the Special Bureau for Oceans of IERS (responsible : Richard Gross).
- 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
- Geodetic Excitation functions are derived from combined series
C04 using an algorithm based upon trapezoidal integration of the geodetic
- 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.