Contribution of wide-band oscillations excited by the fluid excitation functions to the prediction errors of the pole coordinates data

1
Contribution of wide-band oscillations excited
by the fluid excitation functions to the
prediction errors of the pole coordinates data

• W. Kosek1, A. Rzeszótko1 , W. Popinski2
• 1Space Research Centre, Polish Academy of
  Sciences, Warsaw, Poland
• 2Central Statistical Office, Warsaw, Poland

Journées "Systčmes de référence
spatio-temporels"and X. Lohrmann-Kolloquium 22,
23, 24 September 2008 - Dresden, Germany
2
DATA

• x, y pole coordinates data from the IERS
  EOPC04_IAU2000.62-now (1962.0 -
  2008.6), ?t 1 day,
  http//hpiers.obspm.fr/iers/eop/eopc04_05/,
• Equatorial components of atmospheric angular
  momentum from NCEP/NCAR, aam.ncep.reanalysis.
  (1948 - 2008.6) ?t 0.25 day, ftp//ftp.aer.com/p
  ub/anon_collaborations/sba/,
• Equatorial components of ocean angular momentum
  (mass motion)
  
  1) c20010701.oam
  (gross03.oam) (Jan. 1980 - Mar. 2002) ?t 1 day,
  2) ECCO_kf049f.oam (Mar. 2002 - Mar. 2006),
  ?t 1 day, http//euler.jpl.nasa.gov/sbo/sbo_dat
  a.html,
• Equatorial components of effective angular
  momentum function of the hydrology obtained by
  numerical integration of water storage data from
  NCEP water_ncep_1979.dat, water_ncep_1980.dat,
  , water_ncep_2004.dat, ?t 1 day,
  ftp//ftp.csr.utexas.edu/pub/ggfc/water/NCEP.

3
x, y pole coordinates model data computed from
fluid excitation functions
Differential equation of polar motion
- pole coordinates,

• equatorial excitation functions corresponding to
  AAM, OAM
• and HAM,

• complex-valued Chandler frequency,
• where and

Approximate solution of this equation in discrete
time moments can be obtained using the
trapezoidal rule of numerical integration
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THE MORLET WAVELET TRANSFORM COHERENCE
The WT coefficients of complex-valued signal
are defined as
where are dilation and
translation parameters, respectively,
is the CFT of complex-valued Morlet wavelet
function
and is the CFT of
Spectro-temporal coherence between and
time series is defined as
where M is a positive integer and ?t is the
sampling interval.
5
The MWT spectro-temporal coherence between IERS
x, y pole coordinates data and x, y pole
coordinates model data computed from AAM, OAM and
HAM excitation functions
6
The MWT spectro-temporal coherence between IERS
x, y pole coordinates data and x, y pole
coordinates model data computed from AAM, AAMOAM
and AAMOAMHAM excitation functions
7
Prediction of x, y pole coordinates data by the
LSAR method
x, y LS model (Chandler circle annual and
semiannual ellipses linear trend)
x, y LS residuals
x, y
AR prediction
LS extrapolation
Prediction of x, y LS residuals
x, y LS extrapolation
Prediction of x, y
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LSAR prediction errors of IERS x, y pole
coordinates data and of x, y pole coordinates
model data computed from AAM, OAM and HAM
excitation functions
9
The mean LSAR prediction errors of IERS x, y
pole coordinates data (black), and of x, y pole
coordinates model data computed from AAM
(orange), OAM (blue) and HAM (green) excitation
functions
10
The mean LSAR prediction errors of IERS x, y
pole coordinates data (black), and of x, y pole
coordinates model data computed from AAMOAM
(red) and AAMOAMHAM (purple) excitation
functions
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DISCRETE WAVELET TRANSFORM BAND PASS FILTER
The DWT j-th frequency component of the complex
valued signal x(t) is given by
Signal reconstruction

- the DWT coefficients,
- discrete Shannon wavelets.
For fixed lowest frequency index
and time index
For higher frequency index
and time index
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The DWT frequency components of x pole
coordinate data
longer period

Chandler Annual
Semiannual
shorter period
13
The mean LSAR prediction errors of IERS x, y
pole coordinates data (black), and of x, y pole
coordinates model data computed by summing the
chosen DWTBPF components
14
The mean LSAR prediction errors of IERS x, y
pole coordinates data (black), and of x, y pole
coordinates model data computed from AAMOAM
(red) excitation functions as well as by summing
the DWTBPF components corresponding to Chandler,
annual and shorter period oscillations (green)
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CONCLUSIONS

• The contributions of atmospheric or ocean angular
  momentum excitation functions to the mean
  prediction errors of x, y pole coordinates data
  from 1 to about 100 days in the future is
  similar and of the order of 60 of the total
  prediction error.
• The contribution of ocean angular momentum
  excitation function to the mean prediction errors
  of x, y pole coordinates data for prediction
  lengths greater than 100 days becomes greater
  than the contribution of the atmospheric
  excitation function.
• The contribution of the joint atmosphere and
  ocean angular momentum excitation to the mean
  prediction errors of x, y pole coordinates data
  is almost equal to the contribution of the sum of
  Chandler annual and shorter period frequency
  components. Both contributions explain about
  8090 of the total prediction error.
• Big prediction errors of IERS x, y pole
  coordinates data in 1981-1982 and in 2006-2007
  are mostly caused by wide-band ocean and
  atmospheric excitation, respectively.
• The contribution of the hydrologic angular
  momentum excitation to the mean prediction errors
  of x, y pole coordinates data is negligible.

16
Acknowledgements

• This paper was supported by the Polish
  Ministry of Education and Science, project No
  8T12E 039 29 under the leadership of Dr. W.
  Kosek. The authors of this poster are also
  supported by the Organizers of Journées "Systemes
  de référence spatio-temporels" and X.
  Lohrmann-Kolloquium.
• poster available http//www.cbk.waw.pl/kose
  k