Comparison of polar motion prediction results supplied by the IERS Sub-bureau for Rapid Service and Predictions and results of other prediction methods

1
Comparison of polar motion prediction results
supplied by the IERS Sub-bureau for Rapid
Service and Predictions and results of other
prediction methods

• W. Kosek1, D.D. McCarthy2, T.J. Johnson2, M.
  Kalarus1
• 1Space Research Centre, PAS, Warsaw, Poland
• 2U.S. Naval Observatory, Washington D.C., USA

Journees 2003 Systemes de Reference
Spatio-Temporels, 22-25 September 2003, St.
Petersburg, Russia.
2
Data

• EOPC01 (1846.0 - 2000.0), ?t 0.05 years
  http//hpiers.obspm.fr/eop-pc/
• EOPC04 (1962.0 - 2003.5), ?t 1 day
  http//hpiers.obspm.fr/eop-pc/
• USNO (1976.0 - 2003.5), ?t 1 day (finals.all )
  http//maia.usno.navy.mil/bulletin-a.html

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Accuracy of polar motion prediction depends on
For short period prediction
For longer period prediction

• amplitude variations of the Chandler
  oscillation,
• irregular phase and amplitude variations of the
  annual oscillation,
• irregular decadal and secular variations.

• irregular amplitudes and phases of short period
  oscillations with periods less than 1 year,

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The Chandler and annual oscillations filtered by
the FTBPF from pole coordinates data
Chandler
Annual
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Time-frequency FTBPF amplitude spectra (prograde
part) with different frequency bandwidths of
complex-valued USNO pole coordinate data
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The current polar motion prediction computed by
the IERS Sub-Bureau for Rapid Service and
Prediction is the LS extrapolation of the
circular Chandler and elliptic annual and
semiannual oscillations. The LS extrapolation
model is fit to the last year of the pole
coordinates data and predicted for one year in
the future.
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The amplitude and phase variations of the
Chandler circle and annual elliptic oscillations
computed by the LS in one year time intervals
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Two ways of polar motion prediction

• A prediction method is applied directly to x, y
  pole coordinates data. Before the prediction is
  applied the linear trend is removed and the trend
  extrapolation model is added to the computed
  forecast.

• A prediction method is applied in polar
  coordinate system to the polar motion radius and
  angular velocity and then their forecasts are
  transformed to the pole coordinate prediction
  using linear intersection. The radius and its
  prediction must be referred to the mean pole and
  its prediction.

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The following prediction methods using two ways
of prediction were applied
1) Least-squares (LS) extrapolation (1 and 2
dimensions) 2) Autocovariance (2 dimensions)
(Kosek 1997) 3) Autoregressive (AR) (2
dimensions) (Brzezinski 1995) 4) Neural networks
(NN) (1 dimension)
Different combinations of the two prediction
methods that compute the forecast as the sum of
the LS extrapolation and the autocovariance,
autoregressive and neural networks prediction of
the LS extrapolation residuals were also tested.
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Transformation of pole coordinates data to polar
coordinate system
mean pole
angular velocity
radius
the length of polar motion path (integrated
angular velocity)
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Transformation of the prediction of radius and
angular velocity from the polar to the Cartesian
pole coordinate system
mean pole prediction
Linear intersection formula
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The mean pole using Ormsby LPF
- pole coordinates data,
- number of data,
- filter length,
- cutoff frequency, - cutoff
period,
- cutoff frequency roll off termination
frequency.
1849
2003
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Corr. Coeff. 1900-2003 0.864 1950-2003 0.899
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The FTBPF time-frequency amplitude spectra of
polar motion radius and angular velocity
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The FTBPF amplitude spectra of polar motion
radius and angular velocity
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Time-frequency FTBPF amplitude spectra of polar
motion radius, angular velocity and integrated
angular velocity
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Autocovariance prediction
Let be
stationary complex-valued time series
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The absolute values of the difference between x,
y pole coordinates data, the radius R and
integrated angular velocity L and their
autocovariance predictions in the polar
coordinate system
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The absolute value of the difference between x, y
pole coordinates data and their IERS and
autocovariance predictions computed in the polar
coordinate system
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The mean prediction error of x, y pole
coordinates data, the radius R, angular velocity
A and integrated angular velocity L in
1984.0-2003.5 computed from the autocovariance
predictions in the polar coordinate system
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The mean prediction error of x, y pole
coordinates data in 1984.0-2003.5 computed from
the autocovariance predictions in the polar
coordinate system and by the IERS Sub-bureau for
Rapid Service and Predictions
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Prediction by combination of the LS and a
stochastic methodin the Cartesian pole
coordinate system
x, y LS extrapolation residuals
x, y pole coordinates data
x, y LS model
AUTOCOVARIANCE AR NN
Prediction of x, y LS extrapolation residuals
LS extrapolation of x, y
Prediction of x, y
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Prediction of x, y pole coordinates data by
combination of the LS and a stochastic method in
the polar coordinate system
x, y pole coordinates data
mean pole its LS prediction
transformation
R, A LS extrapolation residuals
R, A LS model
R radius A angular velocity
AUTOCOVARIANCE AR
Prediction of R, A LS extrapolation residuals
R, A LS extrapolation
Prediction of R, A
Prediction of R, A
linear intersection
Prediction of x, y
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The mean prediction error of x, y pole
coordinates data, the radius, angular velocity A
and integrated angular velocity L in
1984.0-2003.5 computed by the combination of the
LS method and the autoregressive prediction of
the LS extrapolation residuals in the polar
coordinate system
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The mean prediction error in 1984.0-2003.5 of x,
y pole coordinates data computed from the LS
predictions of the IERS Sub-Bureau for Rapid
Service and Predictions (x - blue and y - red)
and from the combination of the LS extrapolation
of complex-valued pole coordinate data and the AR
prediction of the complex-valued LS extrapolation
residuals (x - green, y - yellow)
USNO
LS AR
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The absolute value of the difference between x, y
pole coordinates data and their IERS and LSAR
predictions
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The mean prediction error in 1984.0-2003.5 of x,
y pole coordinates data computed from the LS
predictions of the IERS Sub-Bureau for Rapid
Service and Predictions (x - blue and y - red)
and from the combination of the LS extrapolation
of complex-valued pole coordinate data and the NN
prediction of the real-valued LS extrapolation
residuals (x - green, y - yellow)
USNO
LS NN
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The absolute value of the difference between x, y
pole coordinates data and their IERS and LSNN
predictions
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Conclusions

• The mean prediction errors of x, y pole
  coordinates data for prediction length less than
  50 days in the future of the IERS prediction and
  the autocovariance prediction in polar coordinate
  system are of the same order.
• The problem of any prediction method of pole
  coordinates data in the polar coordinate system
  is a significant error in the prediction of the
  integrated angular velocity.
• The accuracy of prediction of x, y pole
  coordinates data by combination of the LS
  extrapolation and the AR or NN predictions of the
  LS extrapolation residuals is better than the
  accuracy of prediction carried out by the IERS
  Sub-Bureau for Rapid Service and Prediction.