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

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).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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.