Transcript Prezentacja programu PowerPoint

Possible excitation of the
Chandler wobble by the
geophysical annual cycle
Kosek Wiesław
Space Research Centre, Polish Academy of Sciences
Warsaw, POLAND
http://www.cbk.waw.pl/~kosek
ECGS / Chandler Wobble Workshop
April 21-23, 2004, Luxembourg
Chandler wobble excitation

Electromagnetic torques
(Rochester and Smylie 1965).

Earthquakes

Atmosphere
(O’Connel and Dziewonski 1976; Mansinha et al. 1979; Souriau and Cazenave
1985, Gross 1986).
(Ooe 1978; Hameed and Currie 1989; Furuya et al. 1996; Aoyama and Naito
2001).

Atmosphere + ocean
(Ponte et al. 1998; Ponte and Stammer 1999; Celaya et al. 1999; Brzeziński and
Nastula 2002; Gross 2000, Gross et al. 2003).
Data

x, y pole coordinates data
- EOPC04 in 1962.0 - 2004.0
- EOPC01 in 1846.0 - 2002.0
http://hpiers.obspm.fr/eop-pc/

χAAM wind+pressure+IB, in 1948.0-2003.8
NCEP/NCAR reanalysis,
http://ftp.aer.com/pub/collaborations/sba/

χOAM mass+motion, Jan 1980 to Mar 2002,
Ocean model: ECCO (based on MITgcm).
http://euler.jpl.nasa.gov/sbo/sbo_data.html
1962.0
mas
2004.0
GE
100
0
-100
-200
-300
-400
-500
1
2
33000
36000
39000
mas
500 1948
400
300
200
100
0
-100
33000
42000
45000
48000
51000
AAM (w+p+ib)
2AAM
1AAM
36000
39000
42000
45000
48000
51000
mas
500
400
300
200
100
0
-100
OAM (mass+motion)
2OAM
2002.2
1OAM
1980
33000
36000
39000
42000
MJD
45000
48000
51000
GE & AAM
500
300
0.9
100
2E+003
2E+003
2E+003
2E+003
2E+003
2E+003
0.8
-200
0.7
period (days)
-400
0.6
-600
1970
1975
1980
1985
1990
1995
GE & (AAM + OAM)
GE & AAM
500
0.5
0.4
0.3
300
0.2
100
2E+003
2E+003
2E+003
2E+003
2E+003
2E+003
1970
1975
1980
1985
1990
1995
0.1
-200
-400
-600
The Morlet Wavelet Transform spectro-temporal coherences between the complex-valued
geodetic (GE) and the atmospheric (AAM) as well as the geodetic and the sum of the
atmospheric and oceanic (AAM+OAM) excitation functions.
arcsec
Chandler
0.30
0.20
0.10
0.00
Ch x
-0.10
-0.20
-0.30
1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000
0.30
0.20
0.10
0.00
Ch y
-0.10
-0.20
-0.30
1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000
Annual
0.20
0.10
An x
0.00
-0.10
-0.20
1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000
0.20
0.10
An y
0.00
-0.10
-0.20
1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000
The LS amplitudes and phases of the Chandler and annual oscillations in 3
year time intervals
arcsec
0.25
amplitudes
0.20
0.15
Ch x/y
An x
An y
0.10
0.05
1977
1980
1983
1986
1989
1992
1995
1998
2001
phases
o
Ch x/y
An y
350
300
250
An x
200
150
1977
1980
1983
1986
1989
1992
1995
1998
2001
The Chandler amplitude and its change computed from x–iy data by the
FTBPF and LS in 5 year time intervals
arcsec
Chandler amplitude
0.30
0.25
LS
0.20
0.15
FTBPF
0.10
0.05
0.00
1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000
mas/day
0.2
FTBPF
LS
0.1
0.0
-0.1
-0.2
1900
1910
1920
1930
1940
1950
1960
1970
1980
1990
2000
Polar motion radius
x ,y
t t

Rt
xtm , ytm 
 xt  1, yt  1
Rt 1
 xt  2 , yt  2
mean pole
Rt 

 

m 2
m 2
xt  x t
 yt  yt
,
t  1, 2,..., N
The mean pole computed by the Ormsby LPF
 xtm  L  xt k  cos(2kc )  cos(2kt )
t  L,2,..., N  L
 m    y 
2
2(t  c )(k )
 yt  k  L  t k 
L - filter length,
N - number of data,
xt , yt
- pole coordinates data,
c  t / Tc - cutoff frequency, Tc  18yr - cutoff period,
c  t  3.15E  04, t - roll-off termination frequency.
0.4
0.3
y
0.2
0.1
0.0
-0.1
-0.1
arcsec
1849 0.0
arcsec
2003
0.1
x
The radius and its time-frequency FTBPF amplitude spectra
arcsec
0.4
Radius
0.3
0.2
0.1
period (days)
0.0
1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000
0.0001
3500
2500
6
1500
3
500
1920
1930
1940
1950
1960
1970
50
40
30
20
10
1980
0.0005
period (days)
yr mas
9 60
yr mas
8
500
1.5
300
1.0
4
0.5
2
100
1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001
6
Beat period of the Chandler and annual oscillations
2  t
T
  mean   (t ) 
mean
2  t
T
mean
 T (t )

mean
 const
- from the phase variations of the Chandler and annual oscillations
1
1
1


Tbeat (t ) TAn  TAn (t ) TCh  TCh (t )
- from the phase variations of the 6-7 yr oscillation of the radius
2  t
Tbeat (t ) 
2  t / Tbeat   (t )
TAn  365.2422 days, TCh  434.0 days, Tbeat  6,31 years
Beat period computed from the LS phases of the Chandler and annual oscillations
o
350
phases
5 years
Ch x/y
An y
300
250
An x
200
1977 1980 1983 1986 1989 1992 1995 1998 2001
periods
days
440
420
400
380
360
340
years
8
7
6
5
4
Ch x/y
An y
An x
1977 1980 1983 1986 1989 1992 1995 1998 2001
beat period
1977 1980 1983 1986 1989 1992 1995 1998 2001
o
Nino 1+2
C
Nino 3
Nino 4
4
2
0
-2
1977
1980
1983
1986
1989
1992
1995
1998
2001
The LS amplitudes and phases of the 6-7 yr oscillation in the radius and the beat period
arcsec
LS amplitude of 6-7yr oscillation
0.16
0.12
0.08
0.04
1950
280
270
260
250
240
230
220
210
1950
years
6.8
6.6
6.4
6.2
6.0
5.8
1950
1960
1960
1970
1980
LS phase of 6-7yr oscillation
1970
1980
1990
2000
1990
2000
Period of 6-7yr oscillation computed from the LS phase
1960
1970
1980
1990
2000
The beat period of the Chandler and annual oscillations and the change of the
Chandler amplitude
years
6.8
Period of 6-7yr oscillation computed from the radius
6.6
Corr. Coeff.
1984-1997
6.4
6.2
1980
years
8
1984
1988
1992
1996
2000
0.510
beat period of the Chandler and annual oscillations
7
6
5
4
1980
1984
mas/day
1988
1992
1996
2000
change of the Chandler amplitude
0.10
Corr. Coeff.
1984-2000
0.654
0.05
0.00
-0.05
-0.10
1980
1984
1988
1992
1996
2000
4,5,6,12,13 yr
The LS phase variations of the annual oscillation computed
from the AAM+OAM excitation functions
o
250
AAM + OAM
200
4
3
150
1980
1984
o
1988
1992
1996
2000
AAM + OAM (retrograde)
310
300
290
1980
4
3
1984
1988
1992
1996
2000
The change of the Chandler amplitude, beat period and the LS phase of the annual
oscillation in the AAM+OAM excitation functions
mas/day
change of the Chandler amplitude
0.10
0.05
0.00
-0.05
-0.10
1980
years
8
corr. coeff.
1984
1988
1992
1996
1984-2000
0.654
2000
beat period of the Chandler and annual oscillations
7
corr.coef.
1984-2000
-0.592
6
5
4
1980
1984
o
250
1988
1992
1996
2000
AAM + OAM
200
150
1980
4
3
1984
1988
1992
1996
2000
The excitation mechanism of the Chandler wobble
Decrease
of the annual oscillation
phase in the AAM+OAM
Decrease of the phase
(increase of the period)
of the annual oscillation
in PM
Increase of the beat period
of the Chandler and annual
oscillations
TAn
1
Tbeat
TCh
1
1


TAn TCh
Increase of the
Chandler amplitude
change
Conclusions



Amplitudes and phases of the Chandler oscillation are smoother than
those of the annual oscillation.
The change of the Chandler amplitude increases with the increase of
the beat period of the annual and Chandler oscillations and decreases
with the phase of the annual oscillation of the coupled
atmospheric/ocean excitation. The increase of the beat period means
that the period of the annual oscillation increases and becomes closer
to the Chandler one. Thus, the Chandler amplitude increases during
decrease of the phase of the annual oscillation of polar motion and of
the sum of the atmospheric and oceanic angular momentum
excitation functions. Thus, the Chandler wobble is excited during
decrease of the phase of the annual geophysical cycle.
The beat period was a minimum before the biggest 1982/83 and
1997/98 El Niño events and started to increase during these El Niño
events, because the phase of the annual oscillation in the
AAM+OAM was decreasing. Thus, the Chandler oscillation can be
excited during big El Niño events.
The LS phase variations of the annual oscillation in the geodetic,
atmospheric and atmospheric + oceanic excitation functions.
o
300
250
GE
200
AAM + OAM
AAM
150
100
1980
1984
1988
1992
1996
2000
2004
o
300
GE
AAM + OAM
AAM
250
200
1980
1984
1988
1992
1996
2000
2004
4 yr