Researches on predictions of Earth ... - Observatoire de Paris（1） Introduction of EOP prediction...

Researches on predictions of Earth

orientation parameters

Xueqing Xu Yonghong Zhou

17 –Sep--2013

Paris

2

Contents

Introduction of EOP prediction

Our work about EOP prediction

Participation of EOPC PPP

JOURNÉES 2013 SYSTÈMES DE RÉFÉRENCE SPATIO-TEMPORELS

3

（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 ).


4

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



5

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



6

• 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.



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Fig 3. short term prediction accuracy（MAE）of PMX and

PMY（Kalarus et al., 2010）



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Fig 4. short term prediction accuracy（MAE）of UT1-UTC and

△LOD（Kalarus et al., 2010）



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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 .



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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).



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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.



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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



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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)



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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


1970 1980 1990 2000 2010-500

0

500

mas


1970 1980 1990 2000 2010-100

0

100

T/a

mas


Extension EOP sequence from both ends by LSTSA

Fig 8. Extension series of △LOD and PMX sequence by LSTSA model



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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


1970 1980 1990 2000 2010-500

0

500

mas


1970 1980 1990 2000 2010-100

0

100

T/am

as


Fig 9. Improvement of edge effect in △LOD and PMX residual sequence by

LSTSA model



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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



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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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RMS of 90 day UT1-UTC Predictions


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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.

21 JOURNÉES 2013 SYSTÈMES DE RÉFÉRENCE SPATIO-TEMPORELS

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Thanks for your attention！

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