The statistical properties and possible causes of polar motion prediction errors

1
The statistical properties and possible causes of
polar motion prediction errors
Wieslaw Kosek(1) , Maciej Kalarus(2), Agnieszka
Wnek(1), Maria Zbylut(1) (1) Environmental
Engineering and Land Surveying, University of
Agriculture in Krakow, Poland (2) Space Research
Centre, Polish Academy of Sciences, Warsaw,
Poland
XXIX General Assembly, Honolulu, Hawaii - August
3 - 14, 2015
2

• 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.

3
EOP Prediction international cooperation

• Earth Orientation Parameters Prediction
  Comparison Campaign (EOPPCC)
• (Oct. 2005 Mar. 2008) H. Schuh (Chair),
  W. Kosek, M. Kalarus
• The goal comparison of the EOP prediction
  results from different methods . 10 participants,
  Weekly predictions.
• IERS Working Group on Predictions (WGP)
  
• (Apr. 2006 Oct. 2009) W. Wooden
  (Chair), T. Van Dam (input data) , W. Kosek
  (algorithms)
• The goal to show advantages and disadvantages
  of different prediction algorithms and quality of
  different data
• IERS Workshop on EOP Combination and Prediction
• (Warsaw, 19-21 October 2009) W. Kosek, B. Wooden
  (Chairs)
• Recommendations
• set goals for EOP prediction accuracy
• create a short (two week) prediction series and
  a longer (one year) prediction series
• investigate the feasibility of initiating
  operational ensemble EOP predictions
• investigate ensemble geophysical analyses and
  forecasts with the goal of creating operational
  ensemble geophysical analysis and forecasts
• Earth Orientation Parameters Combination of
  Prediction Pilot Project (EOPCPPP)
• (Oct. 2010 now ) Chair B. Luzum,
  co-chair W. Kosek,
• The goal To determine the feasibility and
  benefits of combining EOP predictions on a daily
  basis and to determine the best algorithms for
  EOP predictions combinations.

4
DATA

• x, y from the IERS EOPC04_IAU2000.62-now (1962.0
  - 2015.6), ?t 1 day, http//hpiers.obspm.fr/ier
  s/eop/eopc04_05/,
• Long term earth orientation data EOP C01 IAU2000
  (1846-now) http//www.iers.org/IERS/EN/DataProduct
  s/EarthOrientationData/eop.html
• x,y pole coordinates data prediction results from
  different participants of the EOPCPPP, ?t 1
  day, http//www.cbk.waw.pl/eopcppp/
• http//maia.usno.navy.mil/eopcppp/eopcppp.htm
  l
• 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,

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EOPPCC (2005-2008) RESULTS

• Mean prediction errors (in mas) of x, y pole
  coordinates data computed from prediction results
  of different participants in the EOPPCC.

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The participants of the EOPCPPP and their
contribution to x,y predictions.
Author Institute Total number of computed predictions of x, y
Brian Luzum (BL) U.S. Naval Observatory, Washington DC, USA 1630 1083 comb
Daniel Gambis (DG) Paris Observatory, Paris, France 1740
Leonid Zotov (LZ) Sternberg Astronomical Institute of Moscow State University, Department of Gravimetry, Moscow, Russia 1360 1360 1360
Maciej Kalarus (MK) Space Research Centre, PAS, Warsaw, Poland 1591
Richard Gross (RG) Jet Propulsion Laboratory, Pasadena, California, USA 1663
Viktor Tissen (VT) Siberian Scientific Research Institute of Metrology and Siberian State Geodetic Academy, Russia 1667
Wieslaw Kosek (WK) Space Research Centre, PAS, Warsaw, Poland 1782
Xu Xueqing (XX) Shanghai Astronomical Observatory, China 1532
Zinovy Malkin (ZM) Pulkovo Observatory, Russia 1777
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EOPCPPP (from 2010) RESULTS

• An example of 90-day polar motion predictions at
  different starting prediction epochs from
  different participants of the EOPCPPP

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Standard deviation (SDE)
Mean absolute error (MAE)
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Skewness (SKE)
skewness is a measure of the asymmetry of the
probability distribution of a real-valued random
variable. Negative skew indicates that the tail
on the left side of the probability density
function is longer than the right side. If the
distribution is symmetric then skewness is zero.

- third moment about the mean
- standard deviation error
- the expectation operator.
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Kurtosis (CUR)
(Gr. ???t??, ang. bulging) is a measure of the
"peakedness" of the probability distribution of a
real-valued random variable,
- fourth moment about the mean
- standard deviation error
- the expectation operator.
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Mean absolute error (MAE), standard deviation
(SDE), skewness and kurtosis together with their
error bars of x (blue), y (red) predictions
computed by Brian Luzum.
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Mean absolute error (MAE), standard deviation
(SDE), skewness and kurtosis together with their
error bars of x (blue), y (red) predictions
computed by Valery Tissen.
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Mean absolute error (MAE), standard deviation
(SDE), skewness and kurtosis together with their
error bars of x (blue), y (red) predictions
computed by Zinovy Malkin.
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Mean absolute error (MAE), standard deviation
(SDE), skewness and kurtosis together with their
error bars of x (blue), y (red) predictions
computed by Wieslaw Kosek.
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Mean absolute error (MAE), standard deviation
(SDE), skewness and kurtosis together with their
error bars of x (blue), y (red) predictions
computed by Maciej Kalarus.
17
Absolute values of the differences between the
IERS x, y pole coordinates data and their LSAR
predictions and the SDE, MAE, SKE and KUR of
these differences in 1986.5 - 2015.5
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LSAR prediction errors of IERS x, y pole
coordinates data and of x, y pole coordinates
model data computed from AAMOAM and AAM
excitation functions
- pole coordinates model data,

• equatorial fluid excitation functions (AAM, OAM),

• complex-valued Chandler frequency,
• where and
  is the quality factor

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EOPPCC
EOPCPPP
Cor_coef0.595 0.022
Cor_coef0.549 0.022
The differences between the IERS x,y pole
coordinates data and their LSAR 90-day
predictions and time series of these differences
for one (purple) and two (green) weeks in the
future.
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The mean FTBPF amplitude spectra (?0.0003) of
the differences between the IERS x-iy pole
coordinates data and their LSAR predictions at
1, 2 and 4 weeks in the future
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Time variable FTBPF amplitude spectra (?0.001)
of the differences between the IERS x-iy pole
coordinates data and their LSAR predictions at
1, 2 and 4 weeks in the future
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Combination of complex demodulation and the
Fourier transform low pass filter (CDFTLPF)
1. Multiplication of the time series by
complex-valued harmonic with frequency
2. Filtration of the transformed signal using
FTLPF of complex-valued time series 3.
Computation of instantaneous phases
.

• transmittance function,

? - window halfwidth
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Amplitudes and phases of the Chandler (green) and
Annual (x-blue, y-red) oscillations computed by
combination of complex demodulation and the
Fourier transform low pass filter (CDFTLPF)
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First differences of amplitudes (x-red, y-orange)
and the products of amplitudes and phase
differences (x-navy blue, y-blue) of the
Chandler, annual and semi-annual oscillations
computed by the CDFTLPF combination.
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CONCLUSIONS
The pole coordinates data mean prediction errors
for different participants of the EOPCPPP are
different due to different prediction techniques
applied as well as different time span of data to
compute them. The skewness and kurtosic values
of the differences between pole coordinates data
and their predictions for different prediction
lengths and for different participants of the
EOPCPPP are close to 0 and 3 for , respectively
which means that they follow normal distribution.
The increase of the differences between pole
coordinates data and their prediction with the
prediction length is caused by mismodelling of
the irregular Chandler and annual oscillations in
the forecast models.
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IERS Rapid Service/Prediction Centre

• Wyznaczaniem prognoz EOP zajmuje sie IERS RS/PC w
  US Naval Observatory w Waszyngtonie
  
• UT1-UTC prognozowany jest z wykorzystaniem
  prognozy skladowej osiowej momentu pedu atmosfery
  (Johnson et al., 2005) otrzymywanej w procesie
  dynamicznego wyznaczenia modelu cyrkulacji
  atmosfery.
  
  
  
• wspólrzedne x, y bieguna prognozowane sa
  kombinacja metody najmniejszych kwadratów i
  autoregresji (LSAR) (Kosek i in., 2004).
  
  
  
  
• obecna dokladnosc modelu precesji-nutacji IAU
  2006/2000A jest bardzo wysoka dlatego residua
  precesji-nutacji dX, dY pokazuja jedynie
  niedeterministyczny sygnal z okresem ok. 430 dni
  i o amplitudzie rzedu 0.3 mas pochodzacy od
  rotacji cieklego jadra Ziemi. Prognoza precesji i
  nutacji wyznaczana jest jako ekstrapolacja modelu
  IAU 2006/2000A.

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PROGNOZOWANIE ZMIAN EOP

• W celu uzyskania informacji o pozycji obiektu
  znajdujacego sie poza rotujaca Ziemia nalezy
  wiedziec jak maja sie do siebie wspólrzedne
  stacji obserwacyjnej okreslone w ukladzie
  ziemskim wzgledem wspólrzednych tego obiektu
  okreslonych w ukladzie niebieskim. Obserwacje
  technikami VLBI, SLR, GNSS, DORIS pozwalaja
  obecnie na wyznaczanie ukladów niebieskiego i
  ziemskiego z wysoka dokladnoscia, jednak nie
  pozwalaja na wyznaczenie parametrów orientacji
  Ziemi w czasie rzeczywistym. Nawiazanie ukladów w
  czasie rzeczywistym jest mozliwe dzieki prognozom
  parametrów orientacji Ziemi (x, y, UT1-UTC, dX,
  dY).
• Prognozy EOP wykorzystywane sa miedzy innymi
  przez NASA Deep Space Network (DSN), która jest
  siecia anten sluzacych do kontroli
• - misji miedzyplanetarnych (Cassini,
  Opportunity, Spirit, Mars Global Serveyor,
  Rosetta, Stardust, Voyager-1, Voyager-2).,
• - radiowych i radarowych obserwacji
  astronomicznych,
• - niektórych okoloziemskich misji
  kosmicznych.
• DSN jako najwiekszy i najlepiej wyposazonym
  systemem telekomunikacyjny na swiecie sklada sie
  z trzech kompleksów komunikacyjnych
• - Goldstone, California, pustynia Mojave
• - Madrid, Spain
• - Canberra, Australia.

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The mean LSAR prediction errors of IERS x, y
pole coordinates data (black), and of x, y pole
coordinates model data computed from AAMOAM
(red) excitation functions as well as by summing
the DWTBPF components corresponding to Chandler,
annual and shorter period oscillations (green)