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On secular polar motion
Chinese Astronomy and Astrophysics 5 (1981) 68-70 Act. Astron Sin&a -21 119801 69-72
ON SECULAR
POLAR
MOTION
Pergamon Press. Printed in Great Britain 0146..6364/81/0301-0068-$07.50/o
*
Zhao Ming and Zheng Da-wei Shanghai L%servatory,Academia Sin&a
Received 1978 November 4
ABSTRACT Using the auto-regressive technique, we have analysed data of polar motion, Earth's rotation and excitation function of Earth's atmosphere and obtained their low frequency spectra. These spectra have some periods in common and this fact suggests that these periods are probably real.
The ILS polar data have been analysed before for periods of tens of years with somewhat different results. Markowitz [l] gave a period of 24 yr, Poverbio [2] gave one of 26 yr and Vicente gave one of 30 yr.
In this paper we have re-analysed the same data using the
the auto-regressive technique and have compared the results with those for the Earth's rotation and the excitation function of the Earth's atmosphere.
1. The low Frequency Spectrum of the ILS polar coordinates 1
Data used:
the ILS polar coordinates at 0.1 yr intervals for the period 1900-1975.
The data for 1900-1968 is taken directly from Vicente and Yumi [4], and for 1969 and after, from the IPMS Anna1 Reports. 2
Elimination of the linear term: during this period, the avarage linear motion of
the ILS coordinates is O"OO35 yr-’ in the direction 79'W; this is removed from the raw data. 3
Method of analysis: to study a low frequency spectrum, it is necessary to use a
method with a high resolution. We shall use the auto-regressive technique, taking the prediction error filter length to be 70% of the data lenth. For details, see [S]. 4
Period correction and determination of amplitude: near zero frequency, the peaks
in an auto-regressive spectrum may suffer large frequency shifts. Also, this method does not give the amplitudes. Hence, we complemented it with a least squares fitting for the corrections to the periods of the peaks near zero frequency and for a determination of the amplitudes of all the peaks. The results for z,y components separately and for their mean are given in Table 1. 5
Comparison with the spectrum of Earth's rotation: The long period component in
the rate of rotation of Earth was analysed by Luo Shi-fang et al. [6] using a periodgram technique. The same data was analysed by us [5] using the auto-regressive technique. As compared with polar motion,Earth's rotation has many more peaks. However, for each peak found in the polar motion spectrum, we can find a corresponding peak in the Earth's rotation spectrum. These are shown in the last line of Table 1. * Condensed translation
Polar Motion
Table 1
Long-Period
Components in Polar
Period (yr) z-component amplitude (Ol’OOl) period (Yrj Y-Component amplitude (O!‘OOl)
period
in rotation I
2. The low-freguency Many factors oceans,
excite
Iiaubrich
calculations
12.6
9.4
7.9
6.8
9
30
6
9
7
3
54
32
12.4
9.1
7.7
6.8
12
24
4
7
3
9
31.5
12.5
9.2
7.8
6.8
31
12.2
60
the rotation
,
I
are expressed
function
We have calculated and imaginary parts
period CurI amplitude (O!‘rKU)
real part
imaginary part
atmosphere
motion in the atmosphere and
excitation
in complex form with the real
and the imaginary axis to 90’E.
Long-Period
is given in [7].
function
axis pointing
the low frequency
for
range of the auto-
Function
30
12.9
9.2
7.7
O.’
0.2
0.4
0.5
0.6
period (Yr)
44
Z?
14.6 11.5
9.2
7.6
amplitude (0!‘001>
1.9
0.8
0.5
1.1
the linear
motion of 0”-0001
yr -I
Their
separately.
Components in the Atmosphere Excitation
0.9
1901-1970.
to Greenwich Meridian
55
After deducting
6.9
,
causing the annual polar motion and Wilson and
regressive
Table 2
of Earth’s
material
the monthly atmospheric
spectrum for the real
8.0
I
A comprehensive description
etc.
motion is the main factor
9.1
,
of Earth, including
in the ice-cover
[S] have published
Rotation
31
spectrum of the excitation
the variation
The atmospheric
f’otion and Earth’s
55
54.5
mean period
x,y
69
0.7
in the direction
Slow, the results
are
given in Table 2. 3. Discussions I at least stations.
Table 1 shows that these periods We stress
so that the variations
that the polar are global
of some of the long periods,
largest
amplitude of O”.O3. Our results
Hence in addition
nor by local
motion and the rotation
in character.
reality 2
are found in 3 different
says that these peaks are not caused by noise,
particularly
show that the long period
to random excitations,
there
This fact
variations
of some ILS
are two independent
We are therefore the period polar
data series.
inclined
to
of about 31 yr,
motion is not entirely
must exist
some systematic
quantities,
beleive
in the
as it has the irregular.
and periodic
Polar
70
excitation
factors. The atmosphere
3
data.
linear
motion.
For the be nearly
This
equal
to
the
can only
agreement of
between
does
portion forcing
account the
geogphysical
function
is not only
agreement
low frequency
excitation
complex
excitation
The agreement
motion
the
Motion
not
in
the
a small
two seems
a spectrum
in good but
main period,
agreement
also
in
the
with
the
polar
direction
of
the
seem to be accidental. the
considered, amplitude,
for
has
hence part
of
significant,
forced
component
from Table the
long
perhaps
of
2 we see period they
the that
polar are
polar
will
atmospheric
motion.
both
motion
caused
Even so, by
the
same
factors.
REFERENCES
[‘I1 r21 131 [41
PI
[61
Mmkoktz, W., Latitude and Longitude and the Secular Motion of the Pole. in Methods a~1 Techniques in Geophysics, ed. & K. R.uncorn, Interscience. New York (1960). 325. Proverbio, E., Secular and Long-term Variations of the Polar Motion, IAU S~ntposi~lm No. 48 (1972), 97. Vice&e, R. 0. $ Currie, R. G., Maximum Entropy Spectrum of Long-period Polar Motion, Ge@Ys* J. R. A&. $00. 46(1976), 67. ProveFbio, E. & Queeada, V., Homogeneous Systems of Polar Coordinates. Circolari Della Stazione Astronomica Internazional di Latitudine Carloforte-Cagliari, Serie B(5). NO. 6(1979). Zheng Da-wei,
Zhan Ming,
4 (1980) 298-304 iuo Shi-fang et (1977) 221-227.
al.
Acta Astron, Sir&a 20 (1979)
Acta. Astron. Sinica -15 (1974)
301-307;
79-85
Eng.
Eng. tr.
tr.
in Chin. Astron.
in Chin. 4stron. _1
[‘iI Munk, W. H. & MacDonald, G. J. F., The Rotation of the Earth (1960). 181 Wla’W C. B. & Haubrich, R. A., Atmospheric contributions to the Excitation of t.ke Barth’s Wobble 1901-1970,Geophya. J. B. dstr.
Sm.,
46(1976),
745.
ON SECULAR
POLAR
MOTION
Pergamon Press. Printed in Great Britain 0146..6364/81/0301-0068-$07.50/o
*
Zhao Ming and Zheng Da-wei Shanghai L%servatory,Academia Sin&a
Received 1978 November 4
ABSTRACT Using the auto-regressive technique, we have analysed data of polar motion, Earth's rotation and excitation function of Earth's atmosphere and obtained their low frequency spectra. These spectra have some periods in common and this fact suggests that these periods are probably real.
The ILS polar data have been analysed before for periods of tens of years with somewhat different results. Markowitz [l] gave a period of 24 yr, Poverbio [2] gave one of 26 yr and Vicente gave one of 30 yr.
In this paper we have re-analysed the same data using the
the auto-regressive technique and have compared the results with those for the Earth's rotation and the excitation function of the Earth's atmosphere.
1. The low Frequency Spectrum of the ILS polar coordinates 1
Data used:
the ILS polar coordinates at 0.1 yr intervals for the period 1900-1975.
The data for 1900-1968 is taken directly from Vicente and Yumi [4], and for 1969 and after, from the IPMS Anna1 Reports. 2
Elimination of the linear term: during this period, the avarage linear motion of
the ILS coordinates is O"OO35 yr-’ in the direction 79'W; this is removed from the raw data. 3
Method of analysis: to study a low frequency spectrum, it is necessary to use a
method with a high resolution. We shall use the auto-regressive technique, taking the prediction error filter length to be 70% of the data lenth. For details, see [S]. 4
Period correction and determination of amplitude: near zero frequency, the peaks
in an auto-regressive spectrum may suffer large frequency shifts. Also, this method does not give the amplitudes. Hence, we complemented it with a least squares fitting for the corrections to the periods of the peaks near zero frequency and for a determination of the amplitudes of all the peaks. The results for z,y components separately and for their mean are given in Table 1. 5
Comparison with the spectrum of Earth's rotation: The long period component in
the rate of rotation of Earth was analysed by Luo Shi-fang et al. [6] using a periodgram technique. The same data was analysed by us [5] using the auto-regressive technique. As compared with polar motion,Earth's rotation has many more peaks. However, for each peak found in the polar motion spectrum, we can find a corresponding peak in the Earth's rotation spectrum. These are shown in the last line of Table 1. * Condensed translation
Polar Motion
Table 1
Long-Period
Components in Polar
Period (yr) z-component amplitude (Ol’OOl) period (Yrj Y-Component amplitude (O!‘OOl)
period
in rotation I
2. The low-freguency Many factors oceans,
excite
Iiaubrich
calculations
12.6
9.4
7.9
6.8
9
30
6
9
7
3
54
32
12.4
9.1
7.7
6.8
12
24
4
7
3
9
31.5
12.5
9.2
7.8
6.8
31
12.2
60
the rotation
,
I
are expressed
function
We have calculated and imaginary parts
period CurI amplitude (O!‘rKU)
real part
imaginary part
atmosphere
motion in the atmosphere and
excitation
in complex form with the real
and the imaginary axis to 90’E.
Long-Period
is given in [7].
function
axis pointing
the low frequency
for
range of the auto-
Function
30
12.9
9.2
7.7
O.’
0.2
0.4
0.5
0.6
period (Yr)
44
Z?
14.6 11.5
9.2
7.6
amplitude (0!‘001>
1.9
0.8
0.5
1.1
the linear
motion of 0”-0001
yr -I
Their
separately.
Components in the Atmosphere Excitation
0.9
1901-1970.
to Greenwich Meridian
55
After deducting
6.9
,
causing the annual polar motion and Wilson and
regressive
Table 2
of Earth’s
material
the monthly atmospheric
spectrum for the real
8.0
I
A comprehensive description
etc.
motion is the main factor
9.1
,
of Earth, including
in the ice-cover
[S] have published
Rotation
31
spectrum of the excitation
the variation
The atmospheric
f’otion and Earth’s
55
54.5
mean period
x,y
69
0.7
in the direction
Slow, the results
are
given in Table 2. 3. Discussions I at least stations.
Table 1 shows that these periods We stress
so that the variations
that the polar are global
of some of the long periods,
largest
amplitude of O”.O3. Our results
Hence in addition
nor by local
motion and the rotation
in character.
reality 2
are found in 3 different
says that these peaks are not caused by noise,
particularly
show that the long period
to random excitations,
there
This fact
variations
of some ILS
are two independent
We are therefore the period polar
data series.
inclined
to
of about 31 yr,
motion is not entirely
must exist
some systematic
quantities,
beleive
in the
as it has the irregular.
and periodic
Polar
70
excitation
factors. The atmosphere
3
data.
linear
motion.
For the be nearly
This
equal
to
the
can only
agreement of
between
does
portion forcing
account the
geogphysical
function
is not only
agreement
low frequency
excitation
complex
excitation
The agreement
motion
the
Motion
not
in
the
a small
two seems
a spectrum
in good but
main period,
agreement
also
in
the
with
the
polar
direction
of
the
seem to be accidental. the
considered, amplitude,
for
has
hence part
of
significant,
forced
component
from Table the
long
perhaps
of
2 we see period they
the that
polar are
polar
will
atmospheric
motion.
both
motion
caused
Even so, by
the
same
factors.
REFERENCES
[‘I1 r21 131 [41
PI
[61
Mmkoktz, W., Latitude and Longitude and the Secular Motion of the Pole. in Methods a~1 Techniques in Geophysics, ed. & K. R.uncorn, Interscience. New York (1960). 325. Proverbio, E., Secular and Long-term Variations of the Polar Motion, IAU S~ntposi~lm No. 48 (1972), 97. Vice&e, R. 0. $ Currie, R. G., Maximum Entropy Spectrum of Long-period Polar Motion, Ge@Ys* J. R. A&. $00. 46(1976), 67. ProveFbio, E. & Queeada, V., Homogeneous Systems of Polar Coordinates. Circolari Della Stazione Astronomica Internazional di Latitudine Carloforte-Cagliari, Serie B(5). NO. 6(1979). Zheng Da-wei,
Zhan Ming,
4 (1980) 298-304 iuo Shi-fang et (1977) 221-227.
al.
Acta Astron, Sir&a 20 (1979)
Acta. Astron. Sinica -15 (1974)
301-307;
79-85
Eng.
Eng. tr.
tr.
in Chin. Astron.
in Chin. 4stron. _1
[‘iI Munk, W. H. & MacDonald, G. J. F., The Rotation of the Earth (1960). 181 Wla’W C. B. & Haubrich, R. A., Atmospheric contributions to the Excitation of t.ke Barth’s Wobble 1901-1970,Geophya. J. B. dstr.
Sm.,
46(1976),
745.