Researches on predictions of Earth
orientation parameters
Xueqing Xu Yonghong Zhou
17 –Sep--2013
Paris
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Contents
Introduction of EOP prediction
Our work about EOP prediction
Participation of EOPC PPP
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(1) Introduction of EOP prediction
Earth's rotation and EOP
• The Earth's rotation characterized the overall state of the Earth
motion, and reflects the coupling process between the solid Earth
and Various geophysical factors.
• Earth orientation parameters (EOP) mainly contains UT1-UTC,
△LOD (Length of day change), PMX and PMY (Polar motion
component ).
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Fig 1. △LOD sequence and multiple time scale changes
1965 1970 1975 1980 1985 1990 1995 2000 2005 2010-10
-5
0
5x 10
-3
s
Time/year
Residual
Long-term change
Annual change
Seasonal change
LOD Serie
(1) Introduction of EOP prediction
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Fig 2. PMX sequence and multiple time scale changes
1900 1920 1940 1960 1980 2000-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5as
T/a
Trend term
Chandler term
Annual term
Residual
PMX Serie
(1) Introduction of EOP prediction
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• Earth orientation parameters (EOP) is essential for transformation
between the celestial and terrestrial coordinate systems.
• The Earth Orientation Parameters Prediction Comparison Campaign,
abbreviated as EOP PCC.
• Attracted 11 participants, and collected almost 6500 submissions .
• Estimating the accuracy of the EOP predictions and provoke the
improvement.
(1) Introduction of EOP prediction
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Fig 3. short term prediction accuracy(MAE)of PMX and
PMY(Kalarus et al., 2010)
(1) Introduction of EOP prediction
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Fig 4. short term prediction accuracy(MAE)of UT1-UTC and
△LOD(Kalarus et al., 2010)
(1) Introduction of EOP prediction
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• Result shows that no single forecasting method works as
good for all the parameters and all the time spans
(Kalarus et al., 2010;XQ. Xu et al., 2012).
• Get a joint solutions of variety forecasting methods to
improve the accuracy and stability of EOP prediction .
(1) Introduction of EOP prediction
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(2) Our work about EOP prediction
AR+Kalman method
• we employ for the first time a combination of AR model
and Kalman filter (AR+Kalman) in short-term EOP
prediction.
• The combination of AR model and Kalman filter shows a
significant improvement in short-term EOP prediction.
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0 10 20 30 40 500
5
10
15
20
days
MAE[mas]:PMX
0 10 20 30 40 500
5
10
15
20
days
MAE[mas]:PMY
0 10 20 30 40 500
5
10
days
MAE[ms]:UT1-UTC
0 10 20 30 40 500
0.1
0.2
0.3
0.4
days
MAE[ms]:LOD
Fig 5. MAE for different prediction intervals for x and y components of polar motion (PMX,
PMY),UT1-UTC, △LOD from this study and the EOP prediction comparison campaign (EOP
PCC) (Kalarus et al., 2010). Blue curve and dots: this study using AR model; Red curve and
dots: this study using AR +Kalman model; others(EOP PCC)(XQ .Xu., et al., 2012; Kalarus et
al., 2010).
(2) Our work about EOP prediction
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2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010-0.2
0
0.2
0.4
0.6( a) PMX
year
as
2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 20100
0.2
0.4
0.6
0.8(b)PMY
year
as
Fig 6. PMX, PMY observations during Jan.1, 2000 ~ Dec. 20, 2009 (green curve), and the
30-day polar motion (PMX, PMY) predictions by means of AR (blue curve) and
AR+Kalman (red curve) methods starting from 2008.
(2) Our work about EOP prediction
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Edge effect in EOP decomposition series
1970 1980 1990 2000 2010-2
0
2
4
ms
LOD Series(black line) and Its Fitting series(red line)
1970 1980 1990 2000 2010-1
0
1
T/a
ms
Residual Series of LOD
1970 1980 1990 2000 2010-500
0
500
mas
PMX Series(black line) and Its Fitting series(red line)
1970 1980 1990 2000 2010-100
0
100
T/am
as
Residual Series of PMX
Fig 7. Edge effect in the residual series of △LOD and PMX sequence
(2) Our work about EOP prediction
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( ) 1,2,...,p
n n n n n pZ D S E Z U p h
Dn ─ Deterministic model, including bias, trend and stable periodic
signals.
Sn ─ Stochastic model such as an autoregressive (AR), autoregressive
moving average(ARMA), or nonlinear model.
En ─ Additive white noise.
Up ─ The pth leap-step domain of time series Zn .
LSTSA(Leap-Step Time Series Analysis model)
(2) Our work about EOP prediction
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1970 1980 1990 2000 2010-2
0
2
4LOD Series(black line) and Its Fitting series(red line)
ms
1970 1980 1990 2000 2010-1
0
1
T/a
ms
Residual Series of LOD
1970 1980 1990 2000 2010-500
0
500
mas
PMX Series(black line) and Its Fitting series(red line)
1970 1980 1990 2000 2010-100
0
100
T/a
mas
Residual Series of PMX
Extension EOP sequence from both ends by LSTSA
Fig 8. Extension series of △LOD and PMX sequence by LSTSA model
(2) Our work about EOP prediction
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Improvement of edge effect by LSTSA
1970 1980 1990 2000 2010-2
0
2
4LOD Series(black line) and Its Fitting series(red line)
ms
1970 1980 1990 2000 2010-1
0
1
T/a
ms
Residual Series of LOD
1970 1980 1990 2000 2010-500
0
500
mas
PMX Series(black line) and Its Fitting series(red line)
1970 1980 1990 2000 2010-100
0
100
T/am
as
Residual Series of PMX
Fig 9. Improvement of edge effect in △LOD and PMX residual sequence by
LSTSA model
(2) Our work about EOP prediction
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0 10 20 30 40 50 60 70 80 90300
350
400
450m
as
PMX
0 10 20 30 40 50 60 70 80 90-0.5
0
0.5
1
1.5
x-day prediction
ms
Observations
Predictions
Predictions After Improving Edge Effect
Fig 10. PMX and △LOD observations and predictions before and after
improvement of edge effect
(2) Our work about EOP prediction
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(3) Participation of EOPC PPP
EOPC PPP
• Earth Orientation Parameter Combination of Prediction
Pilot Project,abbreviated as EOPC PPP.
• China participate in the activities for the first time .
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(3) Participation of EOPC PPP
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RMS of 90 day UT1-UTC Predictions
(3) Participation of EOPC PPP
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RMS of 90 day PMY Predictions
PMY (Combined)
summary
• AR+Kalman is an effective method for EOP Prediction.
• LSTSA model can improve edge effect in EOP
decomposition series and enhance prediction accuracy
significantly.
• Higher precision EOP prediction needs more cooperation.
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Thanks for your attention!