The statistical properties and possible causes of polar motion prediction errors

1. The statistical properties and possible causes of polar motion prediction errors Wiesław Kosek(1) , Maciej Kalarus(2), Agnieszka Wnęk(1), Maria Zbylut-Górska(1) (1) Environmental Engineering and Land Surveying, University of Agriculture in Krakow,Poland (2) Space Research Centre, Polish Academy of Sciences, Warsaw, Poland XXIX General Assembly, Honolulu, Hawaii - August 3 - 14, 2015

2. Future EOP data are neededto compute real time transformation between the CRF and TRF. This transformation realized by predictions of x, y, UT1-UTC and a precesion-nutation extrapolation modelis important for the NASA Deep Space Network, which is an international network of antennas that supports: - interplanetary spacecraft missions, - radio and radar astronomy observations, - selected Earth-orbiting missions.

3. EOP Prediction – international cooperation Earth Orientation Parameters Prediction Comparison Campaign (EOPPCC) (Oct. 2005 – Mar. 2008) [H. Schuh (Chair), W. Kosek, M. Kalarus] The goal: comparison of the EOP prediction results from different methods and input data. 10 participants submitted weekly predictions. IERS Working Group on Predictions (WGP) (Apr. 2006 – Oct. 2009) [W. Wooden (Chair), T. Van Dam (input data) , W. Kosek (algorithms)] The goal: to show advantages and disadvantages of different prediction algorithms and quality of different input data. IERS Workshop on EOP Combination and Prediction (Warsaw, 19-21 October 2009) [W. Kosek, B. Wooden (Chairs)] This Workshop generatedabout 20 recommendations related to observations, analysis and prediction of the EOPs. Earth Orientation Parameters Combination of Prediction Pilot Project (EOPCPPP) (Oct. 2010 – now ) [Chair: B. Luzum, co-chair: W. Kosek], The goal: To determine the feasibility and benefits of combining EOP predictions on a daily basis and to determine the best algorithms for EOP predictions combinations. 9 participants submitted daily predictions.

4. DATA • x, yfrom IERS: EOPC04_IAU2000.62-now (1962.0 - now), Δt = 1 day,http://hpiers.obspm.fr/iers/eop/eopc04_05/, • Long term earth orientation data EOP C01 IAU2000 (1890 -now),Δt = 0.05 yearshttp://www.iers.org/IERS/EN/DataProducts/EarthOrientationData/eop.html • x,y pole coordinates data prediction results from different participants of the Earth Orientation Parameters Combination of Prediction Pilot Project (Oct.2010 – now),Δt = 1 day,http://www.cbk.waw.pl/eopcppp/http://maia.usno.navy.mil/eopcppp/eopcppp.html

5. Time variable amplitude spectrum of complex-valued pole coordinates data computed by the Fourier transform band pass filter

6. The participants of the EOPCPPP and their contribution to x,y predictions.

7. 90-day polar motion predictions at different starting prediction epochs in 2012 from different participants of the EOPCPPP

8. Standard deviation (SDE) Mean absolute error (MAE) Skewness (SKE) Kurtosis (KUR)

9. x, y Mean absolute error (MAE), standard deviation (SDE), skewness and kurtosis together with their error bars of x (blue), y (red) predictions computed by Brian Luzum.

10. x, y Mean absolute error (MAE), standard deviation (SDE), skewness and kurtosis together with their error bars of x (blue), y (red) predictions computed by Viktor Tissen.

11. x, y Mean absolute error (MAE), standard deviation (SDE), skewness and kurtosis together with their error bars of x (blue), y (red) predictions computed by Zinovy Malkin.

12. x, y Mean absolute error (MAE), standard deviation (SDE), skewness and kurtosis together with their error bars of x (blue), y (red) predictions computed by Wieslaw Kosek.

13. x, y Mean absolute error (MAE), standard deviation (SDE), skewness and kurtosis together with their error bars of x (blue), y (red) predictions computed by Maciej Kalarus.

14. Cor_coef=0.595 ± 0.022 Cor_coef=0.549 ± 0.022 The differences between the IERS x,y pole coordinates data and their LS+AR 90-day predictions and time series of these differences for one (purple) and two (green) weeks in the future.

15. The mean FTBPF amplitude spectra (λ=0.0003) of the differences between the IERS x-iy pole coordinates data and their LS+AR predictions at 2, 4 and 8 weeks in the future

16. Time variable FTBPF amplitude spectra (λ=0.001)of the differences between the IERS x-iy pole coordinates data and their LS+AR predictions at 1 day and 1, 2, 4 weeks in the future

17. Amplitudes and phases of the Chandler (green) and Annual (x-blue, y-red) oscillations computed by combination of complex demodulation and the Fourier transform band pass filter

18. First differences of amplitudes (x-red, y-orange) and the products of amplitudes and phase differences (x-navy blue, y-blue) of the Chandler, annual and semi-annual oscillations computed by the CD+FTLPF combination.

19. CONCLUSIONS The skewness and kurtosic values of the differences between pole coordinates data and their predictions for different prediction lengths and for different participants of the Earth Orientation Parameters Combination of Prediction Pilot Project are close to 0 and 3, respectively which means that they follow normal distribution. The increase of the differences between pole coordinates data and their prediction with the prediction length is caused by mismodelling of the irregular Chandler and annual oscillations in the LS+AR forecast models.