Future improvements in EOP prediction

1. Future improvements in EOP prediction Wiesław Kosek Space Research Centre, Polish Academy of Sciences, Warsaw, Poland Geodesy for Planet Earth, Buenos Aires , Aug. 31 – Sep. 4, 2009

2. Summary: - introduction - input data - EOP prediction algorithms - EOPPCC results - possible causes of EOP prediction errors - prediction of PM by Kalman filter - MAR prediction of UT1-UTC - application of the wavelet transform filter - conclusions

3. Determination errors ofx, y and UT1-UTC (EOPC04_IAU2000.62-now)data in 1968-2008 ~3÷4 mm EOP mean prediction errors and their ratio to determination errors in 2008

4. Future EOP data are neededto compute real-time transformation between the celestial and terrestrial reference frames. This transformation is 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.

5. DATA • x, y, UT1-UTC and Δdata from the IERS: EOPC04_IAU2000.62-now (1962 - 2009.6), Δt = 1 day, http://hpiers.obspm.fr/iers/eop/eopc04_05/, • Equatorial and axial components of atmospheric angular momentum from NCEP/NCAR, aam.ncep.reanalysis.* (1948 - 2009.3) Δt = 0.25 day, ftp://ftp.aer.com/pub/anon_collaborations/sba/, • Equatorial components of ocean angular momentum: c20010701.oam (Jan. 1980 - Mar. 2002) Δt = 1 day, ECCO_kf066b.oam (Jan. 1993 - Dec. 2008), Δt = 1 day, http://euler.jpl.nasa.gov/sbo/sbo_data.html,

6. Prediction of x, y by combination of the LS+AR method x, y LS model x, y LSresiduals x, y LS AR Prediction of x, y LS extrapolation of x, y AR prediction of x, y residuals

7. Prediction of UT1-UTC by combination of the LS+AR method diff Δ UT1-TAI -- leap seconds UT1-UTC -- Tides Δ- δΔ LS model Δ- δΔ LSresiduals Δ- δΔ LS AR Prediction of Δ- δΔ LS extrapolation ofΔ- δΔ AR prediction of Δ- δΔ residuals + Tides Prediction of Δ Prediction of UT1-TAI Prediction of UT1-UTC int + leap seconds

8. Prediction of UT1-UTC by combination of the DWT+AC method diff Δ UT1-TAI -- leap seconds UT1-UTC -- Tides DWT BPF Δ- δΔ Δ-δΔ(ω1), Δ-δΔ(ω2),…, Δ-δΔ(ωp) AC AC AC Prediction of Δ- δΔ Δ-δΔ(ω1) + Δ-δΔ(ω2) + … + Δ-δΔ(ωp) + Tides Prediction of Δ Prediction of UT1-TAI Prediction of UT1-UTC int + leap seconds

9. Prediction errors of x, y pole coordinates data computed by the LS and LS+AR methods

10. Mean prediction errors of x (thin line), y (dashed line) pole coordinates data computed by the LS and LS+AR methods in 1984-2009

11. Prediction errors of UT1-UTC data computed by the LS+AR method

12. Mean prediction errors of UT1-UTC data computed by the LS+AR method in 1984-2009

13. The chosen MAE of pole coordinates data from the EOPPCC (Kalarus et al., prepared to J. Geodesy)

14. The chosen MAE of UT1-UTC and Δ data from the EOPPCC (Kalarus et al., prepared to J. Geodesy)

15. Amplitudes and phases of the most energetic oscillations in x, y pole coordinates data Chandler Amplitudes Annual Semi-annual bold line – prograde thin line - retrograde Chandler Phases Annual Semi-annual

16. Amplitudes and phases of the most energetic oscillations in Δ-δΔ data Amplitudes Annual Semi-annual Semi-annual Phases Annual

17. x, y pole coordinates model data computed from fluid excitation functions Differential equation of polar motion: - pole coordinates, • equatorial fluid excitation functions (AAM, OAM), • complex-valued Chandler frequency, • where and is the quality factor Approximate solution of this equation in discrete time moments can be obtained using the trapezoidal rule of numerical integration:

18. LS+AR prediction errors of IERS x, y pole coordinates data and of x, y pole coordinates model data computed from AAM, OAM and AAM+OAM excitation functions

19. 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 and AAM+OAM excitation functions

20. The linear state equation (Gelb 1974): x, y pole coordinates data prediction by the Kalman filter - state vector - observation vector equatorial excitation functions residual excitation functions pole coordinates - constant coefficient matrix, - constant coefficients - zero mean excitation process satisfying: prediction of the state vector: variances of white noise processes

21. Prediction errors of x, y pole coordinates computed by Kalman filter and LS+AR method

22. Prediction of Δ-ΔR data by LS+AR and LS+MAR algorithms (Niedzielski and Kosek, J. Geodes 2008) εAAMχ3 residuals AAMχ3 LS model Δ-ΔRLSmodel ε(Δ-ΔR) residuals & Δ-ΔR AAMχ3 AR LS AR prediction ε(Δ-ΔR) MAR Δ-ΔR LS extrapolation Prediction of Δ-ΔR MAR prediction ε(Δ-ΔR)

23. LS, LS+AR and LS+MAR prediction errors of UT1-UTC and Δ data

24. The frequency components of x (black), y (blue) pole coordinates data computed by the Shannon wavelet decomposition longer period Ch+An Sa shorter period

25. The mean LS+AR prediction errors of IERS x, y pole coordinates data, and x, y pole coordinates model data computed by summing the chosen DWTBPF components

26. The frequency components of Δ-δΔ data with indices i=1,...,13,computed by the Meyer wavelet decomposition longer period An Sa shorter period

27. The mean LS+AR prediction errors of IERS UT1-UTC data, and UT1-UTC model data computed by summing the chosen DWTBPF frequency components

28. CONCLUSIONS • The influence of variable amplitudes and phases of the most energetic oscillations in EOP data on their short term prediction errors is negligible. • Short term prediction errors of pole coordinates data are caused by wideband short period oscillations in these data. Some big prediction errors of pole coordinates data in 1981-82 are caused by wideband oscillations in ocean excitation functions and in 2006-07 are caused by wideband oscillations in joint atmospheric-ocean excitation functions. • Short term prediction errors of UT1-UTC are caused by short period wideband oscillations in these data. • Recommended prediction method for pole coordinates data is the combination of the least squares and autoregressive prediction. • Recommended prediction method for UT1-UTC data is the Kalman filter. • Longer term variations of UT1-UTC data can be predicted successfully by combination of the LS and multivariate autoregressive method. • To reduced short term EOP prediction errors Wavelet transform low pass filter can be used.

29. Thank You Acknowledgements The research was financed by Polish Ministry of Science and Education through the grant no. N N526 160136 under leadership of Dr Tomasz Niedzielski.