Future improvements in EOP prediction

1
Future improvements in EOP prediction

• Wieslaw 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 of x, y and UT1-UTC
(EOPC04_IAU2000.62-now) data in 1968-2008
YEARS 1968 1973 1978 1983 1988 1993 1998 2003 2008
x mas 20.0 15.0 15.0 2.05 0.959 0.232 0.105 0.066 0.011
y mas 20.0 15.0 15.0 2.05 0.926 0.192 0.106 0.067 0.014
UT1 ms 1.50 1.90 1.90 0.400 0.021 0.009 0.007 0.006 0.005
34 mm
EOP mean prediction errors and their ratio to
determination errors in 2008
Days in the future 1 7 20 40 80
x, y mas UT1-UTC ms 0.5 0.12 2.7 0.7 6.3 3.6 11 6.9 17 13
prediction to determination errors ratio x, y _________________________UT1-UTC 40 24 200 140 500 720 900 1400 1400 2600
4

• Future EOP data are needed to 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 ? data from the IERS
  EOPC04_IAU2000.62-now (1962 - 2009.6), ?t
  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) ?t 0.25
  day, ftp//ftp.aer.com/pub/anon_collaborations/sba
  /,
• Equatorial components of ocean angular momentum
  
  
  c20010701.oam (Jan. 1980 - Mar. 2002) ?t 1
  day, ECCO_kf066b.oam (Jan. 1993 - Dec.
  2008), ?t 1 day, http//euler.jpl.nasa.gov/sbo/
  sbo_data.html,

6
Prediction of x, y by combination of the LSAR
method
x, y LS residuals
x, y LS model
x, y
AR
LS
Prediction of x, y
AR prediction of x, y residuals
LS extrapolation of x, y
7
Prediction of UT1-UTC by combination of the LSAR
method

diff

UT1-UTC
-- leap seconds
UT1-TAI
?
-- Tides
?- d? LS residuals
?- d? LS model
?- d?
AR
LS
Prediction of ?- d?
AR prediction of ?- d? residuals
LS extrapolation of ?- d?
Tides
Prediction of UT1-TAI
Prediction of UT1-UTC
Prediction of ?
int
leap seconds
8
Prediction of UT1-UTC by combination of the
DWTAC method

diff

UT1-UTC
-- leap seconds
UT1-TAI
?
-- Tides
DWT BPF
?- d?
?-d?(?1), ?-d?(?2),, ?-d?(?p)
AC
AC
AC
Prediction of ?- d?
?-d?(?1) ?-d?(?2) ?-d?(?p)
Tides
Prediction of UT1-TAI
Prediction of UT1-UTC
Prediction of ?
int
leap seconds
9
Prediction errors of x, y pole coordinates data
computed by the LS and LSAR methods
10
Mean prediction errors of x (thin line), y
(dashed line) pole coordinates data computed by
the LS and LSAR methods in 1984-2009
11
Prediction errors of UT1-UTC data computed by the
LSAR method
12
Mean prediction errors of UT1-UTC data computed
by the LSAR 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 ? 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 ?-d? 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
LSAR prediction errors of IERS x, y pole
coordinates data and of x, y pole coordinates
model data computed from AAM, OAM and AAMOAM
excitation functions
19
The mean LSAR prediction errors of IERS x, y
pole coordinates data (black), and of x, y pole
coordinates model data computed from AAM, OAM and
AAMOAM excitation functions
20
x, y pole coordinates data prediction by the
Kalman filter
The linear state equation (Gelb 1974)
- 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 LSAR method
22
Prediction of ?-?R data by LSAR and LSMAR
algorithms (Niedzielski and Kosek, J. Geodes 2008)
e(?-?R) residuals
?-?R LS model
eAAM?3 residuals
AAM?3 LS model

?-?R
AAM?3
AR
LS
AR prediction e(?-?R)
MAR
?-?R LS extrapolation
Prediction of ?-?R
MAR prediction e(?-?R)
23
LS, LSAR and LSMAR prediction errors of UT1-UTC
and ? data
24
The frequency components of x (black), y (blue)
pole coordinates data computed by the Shannon
wavelet decomposition






longer period



ChAn

Sa



shorter period






25
The mean LSAR 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 ?-d? data with
indices i1,...,13, computed by the Meyer wavelet
decomposition




longer period


An
Sa


shorter period




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