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W. Kosek 1 , A . Rzeszótko 1 , W . Popiński 2PowerPoint Presentation

W. Kosek 1 , A . Rzeszótko 1 , W . Popiński 2

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### 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. Popiński2

1Space Research Centre, Polish Academy of Sciences, Warsaw, Poland

2Central Statistical Office, Warsaw, Poland

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

DATA

- x, y pole coordinates data from theIERS: 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.

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:

THE MORLET WAVELET TRANSFORM excitation functionsCOHERENCE

The WT coefficients of complex-valued signal are defined as:

where are dilation and translation parameters, respectively,

is the CFT ofcomplex-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 Δt is the sampling interval.

The excitation functionsMWT 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

The excitation functionsMWT 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

Prediction of x, y pole coordinates data excitation functionsby the LS+AR method

x, y LS model

(Chandler circle + annual and semiannual ellipses + linear trend)

x, y

LSresiduals

x, y

LS extrapolation

AR prediction

Prediction of

x, y

LSresiduals

Prediction of

x, y

x, y

LS extrapolation

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

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

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

DISCRETE WAVELET TRANSFORM BAND PASS FILTER coordinates data (black), and of x, y pole coordinates model data computed from AAM+OAM (red) and AAM+OAM+HAM (purple) excitation functions

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 indexand time index

For higher frequency index and time index

The DWT frequency components of coordinates data (black), and of x, y pole coordinates model data computed from AAM+OAM (red) and AAM+OAM+HAM (purple) excitation functionsxpole coordinate data

longer period

Chandler + Annual

Semiannual

shorter period

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

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)

CONCLUSIONS 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)

- 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.

Acknowledgements 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)

This paper was supported by the Polish Ministry of Education andScience, 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

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