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Future improvements in EOP prediction

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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 (Kalarus et al., prepared to Δ data from the EOPPCC (Kalarus et al., prepared to J. Geodesy)

Amplitudes and phases of the most energetic oscillations in (Kalarus et al., prepared to 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 (Kalarus et al., prepared to 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 coordinates data (black), and of x, y pole coordinates model data computed from AAM, OAM and AAM+OAM excitation functions(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 Kalman filter and LS+AR methodΔ-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)

LS, LS+AR and LS+MAR prediction errors of UT1-UTC and Kalman filter and LS+AR methodΔ data

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- coordinates data, and x, y pole coordinates model data computed by summing the chosen DWTBPF componentsδΔ 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 coordinates data, and x, y pole coordinates model data computed by summing the chosen DWTBPF componentsUT1-UTC data, and UT1-UTC model data computed by summing the chosen DWTBPF frequency components

CONCLUSIONS coordinates data, and x, y pole coordinates model data computed by summing the chosen DWTBPF components

- 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 coordinates data, and x, y pole coordinates model data computed by summing the chosen DWTBPF components

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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