geophysical causes of pole coordinates data prediction errors
DESCRIPTION
Geophysical causes of pole coordinates data prediction errors. Wiesław Kosek 1) Environmental Engineering and Land Surveying Department, Agriculture University of Krakow, Poland 2) Space Research Centre, Polish Academy of Sciences, Warsaw, Poland. - PowerPoint PPT PresentationTRANSCRIPT
Geophysical causes of pole coordinates data prediction errors
Wiesław Kosek
1) Environmental Engineering and Land Surveying Department, Agriculture University of Krakow, Poland
2) Space Research Centre, Polish Academy of Sciences, Warsaw, Poland
European Geosciences Union, General Assembly, Vienna, Austria, 22 – 27 April 2012
SUMMARY• introductionintroduction• input data input data • wavelet based comparison of complex-valued wavelet based comparison of complex-valued
time series applied to geodetic and fluid time series applied to geodetic and fluid excitation functions and corresponding to them excitation functions and corresponding to them pole coordinates data pole coordinates data
• prediction of pole coordinates data by the prediction of pole coordinates data by the LS+AR method and wavelet based comparison LS+AR method and wavelet based comparison of prediction errors. of prediction errors.
• conclusionsconclusions
The exact knowledge of the EOP is important for many investigations in astronomy and geodesy. For some tasks the 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.
DATA• x,y pole coordinates data from the IERS: EOPC04_IAU2000.62-now (1962 – 2012.15), Δt = 1 day,
http://hpiers.obspm.fr/iers/eop/eopc04/
• Equatorial components of atmospheric angular momentum from NCEP/NCAR (mass+motion),
aam.ncep.reanalysis.* (1948 - 2012.15) Δt = 0.25 day, ftp://ftp.aer.com/pub/anon_collaborations/sba/,
• Equatorial excitation functions of global ocean angular momentum (mass+motion):
ECCO_kf080.chi ECCO_JPL (Jan. 1993 - Dec. 2011), Δt = 1 day, c20010701.chi ECCO_JPL (Jan. 1980 - Mar. 2002) Δt = 1 day,
ECCO_50yr.chi ECCO_JPL (Jan 1949 - Dec 2002) Δt = 10 days http://euler.jpl.nasa.gov/sbo/sbo_data.html,
IERS C04_IAU2000 x,y pole coordinates data, their determination errors and recent ratio of the prediction to the determination errors
< 3 mm
1
3
5
1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012years
1
3
5
da
ys in
the
futu
re
01020304050607080
ratio
x
y
1965 1970 1975 1980 1985 1990 1995 2000 2005 2010-0.20.00.20.40.6mas
x
y
1998 2000 2002 2004 2006 2008 2010 2012years
0.0000
0.0001
0.0002arcsec determ ination errors in x & y
Equatorial components of AAM and connected OAM excitation functions
33000 36000 39000 42000 45000 48000 51000 54000-100
0
100
200
300
400 AAM aam.ncep.reanalysismas
33000 36000 39000 42000 45000 48000 51000 54000MJD
- 6 0- 4 0- 2 0
02 04 06 0 OAM
19801949 20121993ECCO_kf080.chic20010701.chi ECCO_50yr.chi
mas
)/2(exp)/2()(1),(ˆ2/
12/
nbinaxn
aabXn
n
)(x 2/,12/,...,12/ nnn
)(tx
)(
)4/224exp()2/2exp(2)22/2exp()2exp(21)(
tttit
The wavelet transform coefficients of complex-valued signal defined:
where
- Discrete Fourier Transforms (DFT)
of time series
, - Continuous Fourier Transform (CFT) of the modified Morlet wavelet function given by the following time domain formula (Schmitz-Hübsch and Schuh 1999):
WAVELET TRANSFORM COEFFICIENTS
- dilation and translation parameters
)(tx
1,...,1,0,0 nba
WAVELET TRANSFORM SPECTRUM AND POLARISATION
SPECTRUM:
12,2/1,...,12/),(ˆ),(ˆ ,22/
12/
nmmnmtabtXatS
m
mbxx
POLARISATION: ,),(ˆ),(ˆ),(ˆ),(ˆ
),(ˆatSatSatSatSatxxp
yyxx
xxxx
0),(ˆ atxxp
1),(ˆ atxxp1),(ˆ atxxp 1),(ˆ0 atxxp0),(ˆ1 atxxpretrograde prograde
ellipticcircular circular
the shape of ellipse degenerates to a line
...5,3,1r )(tx )(ty 1,...,1,0 nt
12,2/1,...,12/)),(ˆ(cos),(ˆ),(ˆ , nmmnmtatxyatxyatxy rr
),(ˆ),(ˆ/),(ˆ),(ˆ atSatSatSatxy yyxxxy
),(ˆ),(ˆ/]),(ˆ),(ˆ[1arg),(ˆ 2/
12/
abtYabtXabtYabtXm
atm
mbxy
WAVELET TRANSFORM SEMBLANCE
, between and
,
time series is defined as:
where - wavelet coherence,
- wavelet phase synchronization,
- wavelet spectrum of
The wavelet semblance of the order
mabtYabtXatSm
mbxy /),(ˆ),(ˆ),(ˆ 2/
12/
- wavelet cross-spectrum
)/2(exp)/2()(1),(ˆ2/
12/
nbinayn
aabYn
n
)(y - DFT of )(ty
,2
),(ˆ),(ˆ 2/
12/abtYatS
m
mbyy
)(ty
The wavelet semblance (order=1) between geodetic excitation functions computed from x-iy IERS pole coordinates data and equatorial components of the fluid excitation functions (AAM, OAM and AAM+OAM).
psi /chi IERS, AAM
psi/chi IERS, OAM
psi/chi IERS, AAM+OAM
200
400
1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005
-400
-200
200
400
1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005
-400
-200
P
erio
d (d
ays)
200
400
1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005years
-400
-200
-1
-0.5
0
0.5
1semblance (order 1)
x,y pole coordinates model data computed from fluid excitation functions
)()()( ttmtmich
)()()( tiytxtm
)(2)(1)( titt
Qi
Tchch 212 daysTch 433 170Q
tittttititmttm ch
chch exp)()(2exp)()(
Differential equation of polar motion:
- model pole coordinates
- equatorial excitation functions corresponding to AAM, OAM, and AAM+OAM excitation functions
- complex-valued frequency, where and
Approximate solution of this equation in discrete time moments can be obtained using the trapezoidal rule of numerical integration:
38000 40000 42000 44000 46000 48000 50000 52000 54000 56000-0.40-0.200.000.200.40arcsec x
38000 40000 42000 44000 46000 48000 50000 52000 54000 56000MJD
-0.200.000.200.400.60 y
The IERS x,y pole coordinates and the x,y pole coordinates model data computed from fluid excitation functions in 1962 - 2012.
IERS, AAM, AAM+OAM, OAM
The wavelet spectra of x-iy IERS pole coordinates data and pole coordinates model data computed from fluid excitation functions.
50
100
01000200030004000500060007000
1980 1984 1988 1992 1996 2000 2004 2008-100
-50
50
100
per
iod
(day
s)
1980 1984 1988 1992 1996 2000 2004 2008-100
-50
50
100
1980 1984 1988 1992 1996 2000 2004 2008-100
-50
x,y IERS
x, y AAM+OAM
x, y AAM
50
100
1980 1984 1988 1992 1996 2000 2004 2008-100
-50
x, y OAM
The wavelet polarization functions of x-iy IERS pole coordinates data and pole coordinates model data computed from fluid excitation functions.
200
400
p
erio
d (d
ays)
-1
-0.5
0
0.5
1
200
400
x,y AAM
x,y AAM+OAM
1965 1970 1975 1980 1985 1990 1995 2000 2005 2010years
200
400
x,y OAM
200
400
x,y IERS
prograde
retrograde
The mean (1980-2011) wavelet polarization functions of IERS x-iy pole coordinates data and pole coordinates model data computed from fluid excitation functions (AAM, OAM, AAM+OAM).
0 40 80 120 160 200 240 280period (days)-0.2
0.0
0.2
0.4
0.6
0.8
1.0
x,y IERSx,y AAMx,y OAMx,y AAM+OAM
Prediction of x, y pole coordinates data by the LS+AR method
x, y LS residuals
Prediction ofx, y
LS residuals
x, yLS extrapolation
Prediction of x, y
AR prediction
x, y
x, y LS model (Chandler circle + annual and semiannual ellipses +
linear trend)
LS extrapolation
Prediction errors of the IERS pole coordinates data and pole coordinates model data computed from fluid (AAM, AAM+OAM) excitation functions for 30 and 60 days in the future, together with the correlation coefficients between these errors in 1990-2012.
-0.03-0.02-0.010.000.010.020.03arcsec x - 30 day prediction differences IERS AAM AAM+OAM
1992 1996 2000 2004 2008 2012-0.03-0.02-0.010.000.010.020.03 y - 30 day prediction differences IERS AAM AAM+OAM
-0.03-0.02-0.010.000.010.020.03arcsec x - 60 day prediction differences IERS AAM AAM+OAM
1992 1996 2000 2004 2008 2012-0.03-0.02-0.010.000.010.020.03 y - 60 day prediction differences IERS AAM AAM+OAM
Correlation coefficents IERS/AAM IERS/AAM+OAM
0.56 0.86
0.52 0.76
0.48 0.84
0.51 0.75
Prediction errors of x IERS pole coordinate and x pole coordinate model data computed from fluid excitation functions from one day to one year in the future
x
IERS
AAM
AAM+OAM
0100200300
0100200300
0100200300
day
s in
the
futu
re
1980 1985 1990 1995 2000 2005 2010years
0100200300
OAM
-0.1
-0.05
0
0.05
0.1mas
Prediction errors of y IERS pole coordinate and y pole coordinate model data computed from fluid excitation functions from one day to one year in the future
y
IERS
AAM+OAM
AAM
0100200300
0100200300
0100200300
d
ays
in th
e fu
ture
1980 1985 1990 1995 2000 2005 2010years
0100200300
OAM
-0.1
-0.05
0
0.05
0.1mas
Mean prediction errors of x,y IERS pole coordinates and pole coordinates model data computed from fluid excitation functions (AAM, OAM, AAM+OAM)
0 50 100 150 200 250 300 350 400days in the fu ture
0.00
0.01
0.02
0.03
0.04IERS
arcsec
AAM
AAM+OAM
OAM
x
0 50 100 150 200 250 300 350 400days in the fu ture
0.00
0.01
0.02
0.03
0.04IERS
arcsec
AAM
AAM+OAM
OAM
y
The wavelet spectrum of complex-valued prediction errors of the IERS x,y pole coordinates data
306090
120
0
40000
80000
120000
prograderetrogradeWavelet spectrum of x-iy IERS prediction errors
100 200 300 400 500 600 700 800period (days)
0200400600800
-800 -700 -600 -500 -400 -300 -200 -100period (days)
369
da
ys in
the
futu
re
The wavelet spectra of the complex-valued prediction errors of the IERS x,y pole coordinates data and pole coordinates model data computed from fluid excitation functions (AAM, OAM, AAM+OAM)
100 200 300 400 500 600 700 800
period (days)
306090
120
306090
120
306090
120
d
ays
in th
e fu
ture
-800 -700 -600 -500 -400 -300 -200 -100
period (days)
306090
120
0
40000
80000
120000x, y IERS pred err
x,y AAM+OAM pred err
x, y AAM pred err
x,y OAM pred err
prograderetrograde
The wavelet polarizations of complex-valued prediction errors of the IERS pole coordinates data and pole coordinates model data computed from fluid excitation functions (AAM, OAM, AAM+OAM)
x,y IERS pred err
30
60
90
120
30
60
90
120
x,y AAM+OAM pred err
30
60
90
120
d
ays
in th
e fu
ture
x,y AAM pred err
50 100 150 200 250 300 350 400 450 500period (days)
30
60
90
120
x,y OAM pred err
-1
-0.5
0
0.5
1prograde
retrograde
CONCLUSIONSCONCLUSIONS• The wavelet polarization function of complex-valued IERS pole coordinates data
and pole coordinates model data computed from fluid excitation functions, show that oscillations in them with periods greater than ~30 days are mostly prograde and become more circular when the period increases. Oscillations with periods less than ~30 days are more retrograde than prograde.
• The wavelet semblance (order=1) between complex-valued geodetic excitation functions computed from the IERS pole coordinates data and fluid excitation functions are greater for the joint atmospheric-ocean excitation than for the atmospheric or ocean ones. The annual oscillations in geodetic and ocean excitation functions are out of phase.
• The contributions of atmosphere and ocean angular momentum excitation functions to the mean prediction errors of pole coordinates data is similar and of the order of 55-60% of the total mean prediction error of pole coordinates data.
• The contribution of the joint atmospheric-ocean angular momentum excitation to the mean prediction errors of pole coordinates data is of the order of 70 to 80 % of the total mean prediction error of these data.
• The wavelet spectra and polarization of time series of prediction errors of pole coordinates data show that oscillations in them are mostly prograde. These prediction errors are mostly caused by short period wide band elliptic oscillations in joint ocean atmospheric excitation function and wide band prograde oscillations in the Chandler and annual frequency band caused by mismodelling of the Chandler and annual oscillations in the prediction algorithm.
The wavelet coherence between geodetic excitation functions computed from x-iy IERS pole coordinates data and equatorial components of the fluid excitation functions.
-500 -400 -300 -200 -100 0 100 200 300 400 500period (days)
0 . 0
0 . 2
0 . 4
0 . 6
0 . 8
1 . 0
err
AAM + OAM / IERSAAM / IERSOAM / IERS
coherence chi/psi (1980-2011)
Skewness (SKE)
MiSD
xxn
xxn
SDxx
ESKEin
i jiobspred
ji
n
i jiobspred
ji
i
jiobspred
jii ,...,2,1,
)(1
)(1
33
2/3
12
,,
13
,,3
,,
3
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
iSD - standard deviation error
- the expectation operator. E pi nSKE /6)(ˆ
Kurtosis (CUR)
33)(1
)(1
3 44
2
12
,,
14
,,4
,,
in
i jiobspred
ji
n
i jiobspred
ji
i
jiobspred
jii SD
xxn
xxn
SDxx
EKUR
4
(Gr. κυρτός, ang. bulging) is a measure of the "peakedness" of the probability distribution of a real-valued random variable,
- fourth moment about the mean
iSD - standard deviation error
- the expectation operator. E
pi nKUR /24)(ˆ
Skewness and kurtosis of prediction errors of the IERS x,y pole coordinates and pole coordinates model data computed from fluid excitation functions (AAM, OAM, AAM+OAM)
0 20 40 60 80 100 120days in the future
- 6
- 4
- 2
0
2
4
6 SKE y
0 20 40 60 80 100 120days in the future
05
1015202530 KUR x
0 20 40 60 80 100 120days in the future
- 6
- 4
- 2
0
2
4
6 SKE x IERSAAM+OAMAAMOAM
0 20 40 60 80 100 120days in the future
05
1015202530 KUR y
Mean absolute errors (MAE) and standard deviations (SD) computed by different participants of the project. Ensemble prediction (red).
EOPCPPP (Oct 2010 – Dec 2011)
Pole coordinates spectra
The Morlet wavelet spectra of x,y IERS 08C04 pole coordinates data computed for different σ parameter values. Time span of data: 1962 – 2012.
-500 -400 -300 -200 -100 0 100 200 300 400 500period (days)
0.0E+02.0E+94.0E+96.0E+98.0E+9
1.0E+101.2E+101.4E+10 Morlet W avelet spectra
-400 -350 -300 -250 -200 -150 -100 -50 0 50 100 150 200 250 300period (days)
0E+0
1E+7
2E+7
3E+7 Morlet W avelet spectra
1900 1920 1940 1960 1980 2000
0.04
0.08
0.12
0.16
0.20
0.24arcsec
1900 1920 1940 1960 1980 2000years
0.00
0.01
0.02
1900 1920 1940 1960 1980 2000years
-240-200-160-120
-80-40
04080
120160200240 o
Amplitudes
Phases
Chandler
Annual
Semi-annual
Chandler
AnnualSemi-annual
Amplitudes and phases of the most energetic oscillations in x, y pole coordinates data
bold line – progradethin line - retrograde
EOP prediction – international activity
Earth Orientation Parameters Prediction Comparison Campaign (EOPPCC) (Oct. 2005 – Mar. 2008). The main idea of this campaign was to compare the various prediction techniques that can be applied to the EOP prediction.
IERS Working Group on Predictions (04. 2006 – EGU). The main idea of the WGP is to investigate the optimum input data sets for the EOP predictions and the strengths and weaknesses of the various prediction algorithms.
EOP prediction – international activity
Earth Orientation Parameters Prediction Comparison Campaign (EOPPCC) (Oct. 2005 – Mar. 2008) [H. Schuh (Chair), W. Kosek, M. Kalarus]
The main idea of this campaign was to compare the various prediction techniques that can be applied to the EOP prediction. During the EOPPCC about 10 participating groups/methods were submitting prediction results of pole coordinates, UT1- UTC, LOD, and celestial pole offsets.
IERS Working Group on Predictions (WGP) (04. 2006 – EGU) [W. Wooden (Chair), T. Van Dam (input data) , W. Kosek (algorithms)] The main idea of the WGP is to investigate the optimum input data sets for the
EOP predictions and the strengths and weaknesses of the various prediction algorithms. The WGP was formed to investigate the properties of different prediction algorithms, qualities of the input data, and the interactions between input data and prediction algorithms.
Future EOP data are neededFuture EOP data are needed to compute real-time transformation to compute real-time transformation between the celestial and terrestrial reference frames. This between the celestial and terrestrial reference frames. This transformation is important for the NASA Deep Space Network, transformation is important for the NASA Deep Space Network, which is an international network of antennas that supports: which is an international network of antennas that supports: - interplanetary spacecraft missions, - interplanetary spacecraft missions, - radio and radar astronomy observations, - radio and radar astronomy observations, - selected Earth-orbiting missions.- selected Earth-orbiting missions.
1989 - IERS Rapid Service Sub-bureau. 2001 - IERS Rapid Service/Prediction Centre (IERS RS/PC)
Goldstone, California, Goldstone, California, pustynia Mojavepustynia Mojave
Madrid, SpainMadrid, Spain
Canberra, Australia.Canberra, Australia.
Deep Space Network