Possible excitation of the Chandler wobble by the annual oscillation of polar motion
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Possible excitation of the Possible excitation of the Chandler wobble by the annual Chandler wobble by the annual
oscillation of polar motionoscillation of polar motion
Kosek Wiesław
Space Research Centre, Polish Academy of Sciences
Annual Seminar of Commission of Satellite Geodesy, Committee Space Research PAS Section of Geodetic Networks, Committee of Geodesy PAS, Section of Geodynamics,
Committee of Geodesy PAS, Space Research Centre PAS.EARTH ROTATION AND SATELLITE GEODESY - FROM ASTROMETRY TO GNSS
Warsaw, 18-19 September 2003
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Chandler wobble excitationChandler wobble excitation The atmospheric wind and IB pressure variations maintain a major
part of the observed Chandler Wobble. However the wind signal dominates over the IB pressure term in the vicinity of the Chandler frequency (Furuya et al. 1996; Aoyama and Naito 2001).
Celaya et al. (1999) using the results of a coupled atmosphere-ocean-land climate model, concluded that some combination of atmospheric and oceanic processes probably have enough power to excite the Chandler wobble.
Using an 11-year time series of the OAM Brzeziński and Nastula (2002) concluded that, within the limits of accuracy, the coupled system atmosphere/ocean fully explains the observed Chandler wobble during the period 1985-1996.
The most important mechanism exciting the Chandler wobble in 1985-1996 was ocean-bottom pressure fluctuations, which contribute about twice as much excitation power as do atmospheric pressure fluctuations (Gross 2002).
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Data EOPC01 (1846.0 - 2000.0), Δt =0.05 yr http://hpiers.obspm.fr/eop-pc/ EOPC04 (1962.0 - 2003.6), Δ t = 1 day http://hpiers.obspm.fr/eop-pc/ USNO (1976.0 - 2003.6), Δ t = 1 day (finals.all )
http://maia.usno.navy.mil/bulletin-a.html
1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000-0.50-0.40-0.30-0.20-0.100.000.100.200.300.400.50
x
arcsec
1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000-0.40-0.30-0.20-0.100.000.100.200.300.400.500.60
y
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The mean determination error of x, y pole coordinates data
1860 1880 1900 1920 1940 1960 1980 20000.00
0.04
0.08
0.12
0.16
0.20 I ER S EOPC01 arcsec
x
y
1984 1986 1988 1990 1992 1994 1996 1998 2000 20020.0000
0.0002
0.0004
0.0006
0.0008
0.0010
0.0012
0.0014
0.0016
0.0018
0.0020
USNO
arcsec
x
y
1976 1980 1984 1988 1992 1996 20000.00
0.01
0.02
0.03
0.04
0.05
USNO
arcsec
x
y
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The FTBPF amplitude spectra of complex-valued pole coordinate data in 1900-2003
-1 .8 -1.6 -1.4 -1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8period (years)
0
40
80
120
160m as x - i y
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The most energetic oscillations of polar motion computed by the FTBPFThe most energetic oscillations of polar motion computed by the FTBPF
1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000-0.30-0.20-0.100.000.100.200.30
Ch x
arcsec
1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000-0.30-0.20-0.100.000.100.200.30
Ch y
1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000-0.20-0.100.000.100.20
An x
1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000-0.20-0.100.000.100.20
An y
Chandler
Annual
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The amplitudes and phases of the Chandler and annual oscillations computed The amplitudes and phases of the Chandler and annual oscillations computed by the LS in 3 year time intervals, the Niby the LS in 3 year time intervals, the Niñño indiceso indices
1977 1980 1983 1986 1989 1992 1995 1998 20010.05
0.10
0.15
0.20
0.25arcsec
am plitudes
Ch x/ yAn xAn y
1977 1980 1983 1986 1989 1992 1995 1998 2001-2
0
2
4
oC Nino 1+2 Nino 3 Nino 4
1977 1980 1983 1986 1989 1992 1995 1998 2001150
200
250
300
350o
phases
Ch x/ yAn y
An x
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The amplitude of the Chandler oscillation computed from the x, y data by the
FTBPF and from the x – i y data by the LS method in 5 year time intervals
1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 20000.00
0.05
0.10
0.15
0.20
0.25
0.30
x FTBPFy FTBPF
x/y LS
arcsec Chandler amplitude
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Transformation of x, y pole coordinates data to polar coordinate systemTransformation of x, y pole coordinates data to polar coordinate system
ntt
kkAtL ,...,3,2,
2
ty
tx ,
tR
ntmtyty
mtxtxtR ,...,2,1,
22
nttytytxtxtA ,...,3,2,2
12
1
radius
angular velocity
length of polar motion path
mty
mtx ,
tA
1,
1 ty
tx
mean pole
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The mean pole computed by the Ormsby LPF
LNLtkct
tkck
ktyktx
mty
mtx L
Lk
,...,2,2))((2
)2cos()2cos(
L N- filter length, - number of data,
cc Tt / - cutoff frequency, - cutoff period, yrTc 18,0415.3 Etc - roll-off termination frequency.
tt yx , - pole coordinates data,
t-0.10.00.10.20.30.4
-0.1
0.0
0.1x
yarcsec
arcsec
1849
2003
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1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 20000.0
0.1
0.2
0.3
0.4Radiusarcsec
1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 20000.000
0.002
0.004
0.006
0.008Angular velocityarcsec/day
Corr. Coeff.1900-2003
0.8641950-2003
0.899
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The FTBPF time-frequency amplitude spectra of polar motion radius and angular velocity
1920 1930 1940 1950 1960 1970 1980years
500
1500
2500
3500
per
iod
(day
s)
0.2
0.4
0.6
0.8
1.0
1 9 20 19 3 0 1 9 4 0 1 95 0 1 9 6 0 1 9 70 1 9 8 0
500
1500
2500
3500
1 02 03 04 05 06 0
3
6
9
yr m asrad ius
angular ve locity m as/day
3
6
9
0.0001
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The time-frequency coherence between the radius and angular velocity computed using the Morlet Wavelet Transform
2
4
6
8yrM W T coherence R , A
1
3
5
7
1910 1920 1930 1940 1950 1960 1970 1980 1990years
500
1000
1500
2000
2500
3000
perio
d (d
ays)
0 .1
0 .2
0 .3
0 .4
0 .5
0 .6
0 .7
0 .8
0 .9
red noise coherence
0 500 1000 1500 2000 2500 3000period (days)
0 . 00 . 20 . 40 . 60 . 81 . 0
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The length of polar motion path and the envelope of the Chandler oscillationThe length of polar motion path and the envelope of the Chandler oscillation
1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000years
-600-400-200
0200400
arcsec sum of the Chandler envelope - linear trendS
t
t
kkt ES
1
~
t
kkt AL
1
~
trendLL tt ~
trendSS tt ~
1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000-0.3-0.2-0.10.00.10.20.3
arcsec Chandler
xy
E t
1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000-6.0-4.0-2.00.02.0
arcsec length of polar m otion path - linear trendL
t
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LS Phases computed in 5 year time intervals of the Chandler and annual oscillations, periods estimated from them and the beat period
1977 1980 1983 1986 1989 1992 1995 1998 2001
200
250
300
350 phasesCh x/yAn y
An x
5 yearso
1977 1980 1983 1986 1989 1992 1995 1998 2001
340360380400420440
periods
Ch x/y
An yAn x
days ,
22constt
TTt
T
ChChAnAnbeat TTTTT
111
1977 1980 1983 1986 1989 1992 1995 1998 200145678
years beat period
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The beat period of the Chandler and annual oscillation computed from their LS phases in 5 and 6 year time intervals. First derivative of the Chandler amplitude computed by the LS
in 5 year time intervals and by the FTBPF. The NiNiññoo indices.
1950 1960 1970 1980 1990 2000-0.1
0.0
0.1m as/day
change of the Chandler amplitude x FTBPFy FTBPF
x/y LS
1950 1960 1970 1980 1990 2000-2
0
2
4
oC Nino 1+2 Nino 3 Nino 4
1950 1960 1970 1980 1990 2000468
10years beat period
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The amplitudes and phases of 6-7yr oscillation in the radius computed in 12, 13 year time intervals by the LS method. The periods computed from the phases
1950 1960 1970 1980 1990 20005.86.06.26.46.66.8 Period of 6-7yr oscillation computed from the LS phase
years
1950 1960 1970 1980 1990 20000.04
0.08
0.12
0.16 LS amplitude of 6-7yr oscillation arcsec
1950 1960 1970 1980 1990 2000210220230240250260270280 LS phase of 6-7yr oscillation
,22
consttTT
tT
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The periods of the 6-7 yr oscillation in the radius computed from the LS phases in 12, 13 year time intervals. Beat period of the Chandler and annual oscillations computed from the LS
phases in 5 and 6 year time intervals. First derivative of the Chandler amplitudes computed by the LS in 4, 5 and 6 year time intervals.
1980 1984 1988 1992 1996 2000-0.10
-0.05
0.00
0.05
0.10mas/day Daily change of the Chandler amplitude
1980 1984 1988 1992 1996 20006.2
6.4
6.6
6.8 Period of 6-7yr oscillation com puted from the radius years
1980 1984 1988 1992 1996 20004
5
6
7
8years
beat period of the Chandler and annual oscillations
0.654
Corr. Coeff.1984-2000
Corr. Coeff.1984-1997
0.510
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ConclusionsConclusions Amplitudes and phases of the Chandler oscillation are smoother
than those of the annual oscillation. The phase of the annual oscillation had maximum values and the
beat period of the Chandler and annual oscillation had minimum values before the biggest 1982/83 and 1997/98 El Niño events.
Long period variations with periods greater than 6 years in the length of polar motion path are due to variable amplitude of the Chandler oscillation.
The increase of the Chandler oscillation amplitude is associated with the increase of the beat period of the Chandler and annual oscillations. It means that the annual oscillation period gets closer to the Chandler one. Thus, the Chandler amplitude increases during increase of the period (decrease of the phase) of the annual oscillation. The Chandler oscillation can be excited by variable annual oscillation.