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### 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

- 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

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

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.

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,

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

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

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

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

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

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

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

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

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

Amplitudes and phases of the most energetic oscillations in Δ-δΔ data

Amplitudes

Annual

Semi-annual

Semi-annual

Phases

Annual

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:

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

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

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

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

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)

The frequency components of x (black), y (blue) pole coordinates data computed by the Shannon wavelet decomposition

longer

period

Ch+An

Sa

shorter

period

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

The frequency components of Δ-δΔ data with indices i=1,...,13,computed by the Meyer wavelet decomposition

longer

period

An

Sa

shorter

period

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

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.

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.

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