1. Contribution of wide-band oscillations excited by the fluid excitation functions to the prediction errors of the pole coordinates data W. Kosek 1, A. Rzeszótko 1, W. Popiński 2 1 Space Research Centre, Polish Academy of Sciences, Warsaw, Poland 2 Central Statistical Office, Warsaw, Poland Journées "Systèmes de référence spatio-temporels" and X. Lohrmann-Kolloquium 22, 23, 24 September 2008 - Dresden, Germany

2. x, y pole coordinates data from the IERS: EOPC04_IAU2000.62-now (1962.0 - 2008.6), Δt = 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) Δt = 0.25 day, ftp://ftp.aer.com/pub/anon_collaborations/sba/, Equatorial components of ocean angular momentum (mass + motion): 1) c20010701.oam (gross03.oam) (Jan. 1980 - Mar. 2002) Δt = 1 day, 2) ECCO_kf049f.oam (Mar. 2002 - Mar. 2006), Δt = 1 day, http://euler.jpl.nasa.gov/sbo/sbo_data.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, Δt = 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:

4. THE MORLET WAVELET TRANSFORM COHERENCE The WT coefficients of complex-valued signal are defined as: is the CFT of complex-valued Morlet wavelet function: where are dilation and translation parameters, respectively, Spectro-temporal coherence between and time series is defined as: where M is a positive integer and Δt is the sampling interval. and is the CFT of

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, AAM+OAM and AAM+OAM+HAM excitation functions

7. Prediction of x, y pole coordinates data by the LS+AR method x, y LS residuals Prediction of x, y LS residuals x, y LS extrapolation Prediction of x, y AR prediction x, y x, y LS model (Chandler circle + annual and semiannual ellipses + linear trend) LS extrapolation

8. LS+AR 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 LS+AR 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 LS+AR prediction errors of IERS x, y pole coordinates data (black), and of x, y pole coordinates model data computed from AAM+OAM (red) and AAM+OAM+HAM (purple) excitation functions

11. DISCRETE WAVELET TRANSFORM BAND PASS FILTER - the DWT coefficients, The DWT j-th frequency component of the complex valued signal x(t) is given by: - discrete Shannon wavelets. Signal reconstruction: For fixed lowest frequency index and time index For higher frequency index and time index

12. The DWT frequency components of x pole coordinate data Chandler + Annual Semiannual longer period shorter period

13. The mean LS+AR 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 LS+AR prediction errors of IERS x, y pole coordinates data (black), and of x, y pole coordinates model data computed from AAM+OAM (red) excitation functions as well as by summing the DWTBPF components corresponding to Chandler, annual and shorter period oscillations (green)

15. 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 80÷90% 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/~kosek