375:
31:
552:
explanation for the observed frequency-amplitude behavior would be a forced, but slowly changing quasi-periodic excitation by interannually varying atmospheric dynamics. Indeed, a quasi-14 month period has been found in coupled ocean-atmosphere general circulation models, and a regional 14-month signal in regional
327:
with m the observed amplitude (in units of mas), and ν the frequency (in units of reciprocal sidereal years) of the
Chandler wobble. In order to generate the Chandler wobble, recurring excitation is necessary. Seismic activity, groundwater movement, snow load, or atmospheric interannual dynamics have
312:
of the order of 100 years. It is a measure of the elastic reaction of the Earth. It is also the explanation for the deviation of the
Chandler period from the Euler period. However, rather than dying away, the Chandler wobble, continuously observed for more than 100 years, varies in amplitude and
571:
simulates dissipation due to the elastic reaction of the Earth's interior. As in Figure 2, the result is the sum of a prograde and a retrograde circular polarized wave. For frequencies ν < 0.9 the retrograde wave can be neglected, and there remains the circular propagating prograde wave where the
455:
the longitude of maximum pressure. The Hough function in a first approximation is proportional to sin θ cos θ. Such standing wave represents the seasonally varying spatial difference of the Earth's surface pressure. In northern winter, there is a pressure high over the North
Atlantic Ocean
394:
There is now general agreement that the annual component of polar motion is a forced motion excited predominantly by atmospheric dynamics. There exist two external forces to excite polar motion: atmospheric winds, and pressure loading. The main component is pressure forcing, which is a standing wave
385:
of the annual component of polar motion as function of year. Numbers and tick marks indicate the beginning of each calendar month. The dash-dotted line is in the direction of the major axis. The line in the direction of the minor axis is the location of the excitation function vs. time of year.
551:
It is improbable that the internal parameters of the Earth responsible for the
Chandler wobble would be time dependent on such short time intervals. Moreover, the observed stability of the annual component argues against any hypothesis of a variable Chandler resonance frequency. One possible
297:. The annual component is rather constant in amplitude, and its frequency varies by not more than 1 to 2%. The amplitude of the Chandler wobble, however, varies by a factor of three, and its frequency by up to 7%. Its maximum amplitude during the last 100 years never exceeded 230 mas.
233:
Observations show that the figure axis exhibits an annual wobble forced by surface mass displacement via atmospheric and/or ocean dynamics, while the free nutation is much larger than the Euler period and of the order of 435 to 445 sidereal days. This observed free nutation is called
230:(6,356,752.3 m). Using the geometric axis as the primary axis of a new body-fixed coordinate system, one arrives at the Euler equation of a gyroscope describing the apparent motion of the rotation axis about the geometric axis of the Earth. This is the so-called polar motion.
328:
been suggested as such recurring forces, e.g. Atmospheric excitation seems to be the most likely candidate. Others propose a combination of atmospheric and oceanic processes, with the dominant excitation mechanism being ocean‐bottom pressure fluctuations.
101:. Since about 2000, the pole has found a less extreme drift, which is roughly along the central meridian. This less dramatically westward drift of motion is attributed to the global scale mass transport between the oceans and the continents.
242:
m per year in the direction of 80° west has been observed which is due to mass redistribution within the Earth's interior by continental drift, and/or slow motions within mantle and core which gives rise to changes of the moment of inertia.
536:
It is difficult to estimate the effect of the ocean, which may slightly increase the value of maximum ground pressure necessary to generate the annual wobble. This ocean effect has been estimated to be of the order of 5–10%.
108:
cause abrupt polar motion by altering the volume distribution of the Earth's solid mass. These shifts are quite small in magnitude relative to the long-term core/mantle and isostatic rebound components of polar motion.
559:
To describe such behavior theoretically, one starts with the Euler equation with pressure loading as in eq.(3), however now with a slowly changing frequency ν, and replaces the frequency ν by a complex frequency
456:
and a pressure low over
Siberia with temperature differences of the order of 50°, and vice versa in summer, thus an unbalanced mass distribution on the surface of the Earth. The position of the vector
698:
The number of the maximum pressure amplitude is tiny, indeed. It clearly indicates the resonance amplification of
Chandler wobble in the environment of the Chandler resonance frequency.
1051:
Earth's
Rotation from Eons to Days: Proceedings of a Workshop Held at the Centre for Interdisciplinary Research (ZiF) of the University of Bielefeld, FRG. September 26-30, 1988
159:
would be its geometric axis defined by the geographic north and south pole, and identical with the axis of its polar moment of inertia. The Euler period of free nutation is
332:
132:. In the case of the Earth, it is almost identical with its axis of rotation, with the discrepancy due to shifts of mass on the planet's surface. The vector of the
313:
shows a sometimes rapid frequency shift within a few years. This reciprocal behavior between amplitude and frequency has been described by the empirical formula:
1437:
Kikuchi, I., and I. Naito 1982 Sea surface temperature analysis near the
Chandler period, Proceedings of the International Latitude Observatory of Mizusawa,
89:
The slow drift, about 20 m since 1900, is partly due to motions in the Earth's core and mantle, and partly to the redistribution of water mass as the
664:
In the range of validity of the empirical formula eq.(2), there is reasonable agreement with eq.(7). From eqs.(2) and (7), one finds the number
246:
The annual variation was discovered by Karl
Friedrich Küstner in 1885 by exact measurements of the variation of the latitude of stars, while
1501:
124:
of a rotating system remains constant and is directed toward a fixed point in space. If the earth were perfectly symmetrical and rigid,
1014:
Gross, Richard S.; Lindqwister, Ulf J. (4 May 1992). "Atmospheric excitation of polar motion during the GIG '91 Measurement
Campaign".
951:
238:. There exist, in addition, polar motions with smaller periods of the order of decades. Finally, a secular polar drift of about 0.10
439:
describing the latitude distribution of the atmospheric pressure on the ground, θ the geographic co-latitude, t the time of year, t
1066:
460:
of the annual component describes an ellipse (Figure 2). The calculated ratio between major and minor axis of the ellipse is
73:), being the pole's average location over the year 1900. It consists of three major components: a free oscillation called
978:
807:
712:
139:
of the system (or maximum principal axis, the axis which yields the largest value of moment of inertia) wobbles around
1366:
Jochmann, H., The Earth rotation as a cyclic process and as an indicator within the Earth's interior, Z. geol. Wiss.,
1094:
286:
70:
97:, i.e. the slow rise of land that was formerly burdened with ice sheets or glaciers. The drift is roughly along the
1085:
Eubanks, T.M. (1993). "Variations in the orientation of the earth". In David E. Smith; Donald L. Turcotte (eds.).
290:
1382:, The effects of the atmosphere and oceans on the Earth's wobble — I. Theory, Geophys. Res. J. R. Astr. Soc.,
749:"Free polar motion of a triaxial and elastic body in Hamiltonian formalism: Application to the Earth and Mars"
1570:"Polar Motion: A Historical Overview on the Occasion of the Centennial of the International Latitude Service"
77:
with a period of about 435 days, an annual oscillation, and an irregular drift in the direction of the 80th
336:
1403:
Hameed, S.; Currie, R.G. (1989). "Simulation of the 14-month Chandler wobble in a global climatic model".
16:
This article is about motion relative to the crust. For motion relative to an astronomical framework, see
1284:
1110:
Dickey, Jean; Eubanks, T. (July 1985). "Earth Rotation and Polar Motion: Measurements and Implications".
270:
823:
748:
53:. This is measured with respect to a reference frame in which the solid Earth is fixed (a so-called
258:
1049:
Schuh, H (1990). "Earth's rotation measured by VLBI". In Peter Brosche; Jürgen Sündermann (eds.).
553:
294:
208:
1498:
717:
188:
is the polar moment of inertia of the Earth, A is its mean equatorial moment of inertia, and
21:
767:
485:
is the Chandler resonance frequency. The result is in good agreement with the observations.
1581:
1528:
1468:
1412:
1333:
1258:
1215:
1115:
1023:
906:
862:
763:
78:
8:
1625:
1620:
1161:
Vondrak, J., Long-periodic behaviour of polar motion between 1900 and 1980, A. Geophys.,
247:
90:
46:
1585:
1532:
1472:
1416:
1345:
1337:
1262:
1219:
1119:
1027:
910:
866:
1391:
1349:
1231:
1131:
927:
894:
572:
vector of polar motion moves on a circle in anti-clockwise direction. The magnitude of
98:
1551:
1516:
1187:
Hide, 1984 Rotation of the atmosphere of the earth and planets, Phil. Trans. R. Soc.,
69:
Polar motion is defined relative to a conventionally defined reference axis, the CIO (
1599:
1556:
1486:
1310:
1235:
1090:
1062:
974:
932:
803:
727:
224:
212:
94:
1353:
1135:
1630:
1589:
1546:
1536:
1476:
1420:
1387:
1341:
1266:
1223:
1123:
1054:
1031:
922:
914:
870:
771:
129:
118:
50:
17:
261:
relative to the stars with different periods, caused mostly by the torques on the
1505:
776:
546:
379:
301:
235:
216:
204:
74:
1058:
1521:
Proceedings of the National Academy of Sciences of the United States of America
436:
251:
1594:
1569:
1481:
1456:
1174:
Runcorn, S.K., et al., The excitation of the Chandler wobble, Surv. Geophys.,
265:
due to the gravitational attraction of the Moon and Sun. They are also called
61:
reference frame). This variation is a few meters on the surface of the Earth.
1614:
1603:
1490:
1127:
282:
148:
1424:
257:
This polar motion should not be confused with the changing direction of the
1560:
1541:
1379:
936:
918:
227:
1148:
Guinot, B., The Chandlerian wobble from 1900 to 1970, Astron. Astrophys.,
250:
found the free nutation in 1891. Both periods superpose, giving rise to a
1512:
1270:
133:
105:
35:
800:
The earth's variable rotation : geophysical causes and consequences
128:
would remain aligned with its axis of symmetry, which would also be its
1227:
220:
1035:
875:
850:
215:
amounting to several meters on the surface of the Earth: 100 mas
973:(Digitally printed ed.). Cambridge: Cambridge University Press.
802:(Digitally printed ed.). Cambridge: Cambridge University Press.
722:
308:
that is excited by a source and then dies away with a time constant τ
174:= A/(C − A) sidereal days ≈ 307 sidereal days ≈ 0.84 sidereal years
598:
It is a resonance curve which can be approximated at its flanks by
305:
266:
152:
849:
Chen, J.L.; Wilson, C.R.; Ries, J.C.; Tapley, B.D. (7 June 2013).
451:
the normalized frequency of one solar year, λ the longitude, and λ
184:
is the normalized Euler frequency (in units of reciprocal years),
707:
223:
of 3.082 m, when converted to radians and multiplied by the
374:
30:
1087:
Contributions of space geodesy to geodynamics: Earth dynamics
331:
Current and historic polar motion data is available from the
262:
144:
339:. Note in using this data that the convention is to define
58:
1289:
International Earth Rotation and Reference Systems Service
1249:
Gross, R (2001). "The excitation of the Chandler Wobble".
828:
International Earth Rotation and Reference Systems Service
333:
International Earth Rotation and Reference Systems Service
195:
The observed angle between the figure axis of the Earth
27:
Motion of Earth's rotational axis relative to its crust
952:"Quake moved Japan coast 8 feet, shifted Earth's axis"
117:
In the absence of external torques, the vector of the
1206:
Volland, H (1996). "Atmosphere and Earth' Rotation".
304:
is usually considered a resonance phenomenon, a free
848:
254:
with a period of about 5 to 8 years (see Figure 1).
207:(mas). This rotation can be interpreted as a linear
38:
as function of time in days (0.1 arcsec ≈ 3 meters).
893:Adhikari, Surendra; Ivins, Erik R. (8 April 2016).
851:"Rapid ice melting drives Earth's pole to the east"
1112:IEEE Transactions on Geoscience and Remote Sensing
971:The Rotation of the Earth A Geophysical Discussion
496:, corresponding to a Chandler resonance period of
81:west, which has lately been less extremely west.
1612:
1089:. Washington, D.C.: American Geophysical Union.
1013:
969:Munk, Walter H.; MacDonald, Gordon J.F. (2009).
488:From Figure 2 together with eq.(4), one obtains
994:
992:
990:
1467:. Cambridge University Press (CUP): 221–236.
1109:
1053:. Springer Berlin Heidelberg. pp. 1–12.
999:Moritz, Helmut; Mueller, Ivan Istvan (1987).
998:
968:
892:
1402:
1291:. Federal Agency for Cartography and Geodesy
1201:
1199:
1197:
987:
830:. Federal Agency for Cartography and Geodesy
1574:International Astronomical Union Colloquium
1461:International Astronomical Union Colloquium
1324:Wahr, J.M. (1988). "The Earth's Rotation".
1580:. Cambridge University Press (CUP): 1–24.
1080:
1078:
888:
886:
507:= 441 sidereal days = 1.20 sidereal years
1593:
1550:
1540:
1499:Earth Rotation and Equatorial Coordinates
1480:
1194:
926:
874:
793:
791:
789:
787:
775:
746:
672:. The observed maximum value of m yields
155:to a good approximation, the figure axis
1517:"Twentieth century sea level: An enigma"
1454:
895:"Climate-driven polar motion: 2003–2015"
373:
29:
1205:
1084:
1075:
883:
797:
269:, except for the slowest, which is the
151:. For a rigid Earth which is an oblate
1613:
1001:Earth rotation: theory and observation
784:
525:the latitude of maximum pressure, and
350:to be positive along 0° longitude and
281:Polar motion is observed routinely by
1248:
1048:
949:
361:to be positive along 90°E longitude.
1567:
1511:
1323:
680:. Together with eq.(8), one obtains
390:on the Earth's surface at the poles)
1346:10.1146/annurev.ea.16.050188.001311
816:
388:100 mas (milliarcseconds) = 3.082 m
369:
13:
1448:
1392:10.1111/j.1365-246X.1982.tb04972.x
1311:"IERS Conventions 2010: Chapter 8"
713:International Polar Motion Service
540:
45:of the Earth is the motion of the
14:
1642:
287:very-long-baseline interferometry
71:Conventional International Origin
190:C − A = 2.61 × 10 kg m
1431:
1396:
1373:
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1317:
1303:
1277:
1242:
1181:
1168:
1155:
1142:
1103:
1042:
950:Voigt, Kevin (April 20, 2011).
276:
1007:
962:
943:
842:
740:
632:The maximum amplitude of m at
1:
733:
1457:"Polar Motion — an Overview"
1455:McCarthy, Dennis D. (2000).
1326:Annu. Rev. Earth Planet. Sci
1016:Geophysical Research Letters
337:Earth orientation parameters
186:C = 8.04 × 10 kg m
112:
7:
1059:10.1007/978-3-642-75587-3_1
701:
324:(for 0.83 < ν < 0.9)
271:precession of the equinoxes
64:
55:Earth-centered, Earth-fixed
10:
1647:
1508:". Retrieved Jun. 5, 2005.
777:10.1051/0004-6361:20041312
544:
15:
1595:10.1017/s0252921100061170
1482:10.1017/s0252921100061364
364:
199:and its angular momentum
84:
1568:Dick, Steven J. (2000).
1285:"Earth orientation data"
1128:10.1109/TGRS.1985.289427
531:= −0.07 years = −25 days
143:. This motion is called
1425:10.1029/gl016i003p00247
768:2005A&A...432.1101F
554:sea surface temperature
426:a pressure amplitude, Θ
295:satellite laser ranging
47:Earth's rotational axis
1542:10.1073/pnas.092704599
1497:Fisher, Rick (1996). "
1114:. GE-23 (4): 373–384.
919:10.1126/sciadv.1501693
798:Lambeck, Kurt (2005).
747:Folgueira, M. (2005).
391:
39:
718:Pole shift hypothesis
377:
259:Earth's rotation axis
33:
22:astronomical nutation
1271:10.1029/2000gl011450
320:m = 3.7/(ν − 0.816)
1586:2000ASPC..208....3D
1533:2002PNAS...99.6550M
1473:2000ASPC..208..223M
1417:1989GeoRL..16..247H
1338:1988AREPS..16..231W
1263:2000GeoRL..27.2329G
1220:1996SGeo...17..101V
1120:1985ITGRS..23..373D
1028:1992GeoRL..19..849G
911:2016SciA....2E1693A
867:2013GeoRL..40.2625C
556:has been observed.
291:lunar laser ranging
91:Greenland ice sheet
1504:2011-08-18 at the
1405:Geophys. Res. Lett
1251:Geophys. Res. Lett
1228:10.1007/bf01904476
855:Geophys. Res. Lett
392:
99:80th meridian west
40:
1527:(10): 6550–6555.
1068:978-3-642-75587-3
1036:10.1029/92GL00935
876:10.1002/grl.50552
861:(11): 2625–2630.
756:Astron. Astrophys
728:True polar wander
595:(for ν < 0.9)
415:(θ) cos cos(λ − λ
213:geographical pole
203:is a few hundred
95:isostatic rebound
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285:methods such as
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130:axis of rotation
119:angular momentum
49:relative to its
34:Polar motion in
18:axial precession
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1515:(14 May 2002).
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824:"Polar motion"
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1033:
1029:
1025:
1021:
1017:
1010:
1002:
995:
993:
991:
982:
976:
972:
965:
957:
953:
946:
938:
934:
929:
924:
920:
916:
912:
908:
904:
900:
896:
889:
887:
877:
872:
868:
864:
860:
856:
852:
845:
829:
825:
819:
811:
805:
801:
794:
792:
790:
788:
778:
773:
769:
765:
761:
757:
750:
743:
739:
729:
726:
724:
721:
719:
716:
714:
711:
709:
706:
705:
699:
696:
681:
662:
640:
630:
599:
596:
577:
575:
557:
555:
548:
538:
534:
508:
497:
486:
479:
461:
459:
438:
420:
396:
395:of the form:
384:
381:
376:
362:
358:
354:
347:
343:
338:
334:
329:
325:
314:
307:
303:
298:
296:
292:
288:
284:
283:space geodesy
274:
272:
268:
264:
260:
255:
253:
249:
248:S.C. Chandler
244:
237:
231:
229:
226:
222:
218:
214:
210:
206:
202:
198:
193:
175:
160:
158:
154:
150:
149:free nutation
146:
142:
138:
135:
131:
127:
123:
120:
110:
107:
102:
100:
96:
92:
82:
80:
76:
72:
62:
60:
56:
52:
48:
44:
37:
32:
23:
19:
1577:
1573:
1524:
1520:
1513:Munk, Walter
1464:
1460:
1438:
1433:
1408:
1404:
1398:
1386:, 349, 1982
1383:
1375:
1367:
1362:
1329:
1325:
1319:
1305:
1293:. Retrieved
1288:
1279:
1257:(15): 2329.
1254:
1250:
1244:
1211:
1207:
1188:
1183:
1175:
1170:
1162:
1157:
1149:
1144:
1111:
1105:
1086:
1050:
1044:
1019:
1015:
1009:
1000:
970:
964:
955:
945:
902:
898:
858:
854:
844:
832:. Retrieved
827:
818:
799:
759:
755:
742:
697:
695:≥ 100 years
682:
663:
641:
631:
600:
597:
578:
573:
558:
550:
535:
509:
498:
487:
480:
462:
457:
421:
397:
393:
382:
356:
352:
345:
341:
330:
326:
315:
299:
280:
277:Observations
256:
245:
232:
228:polar radius
209:displacement
200:
196:
194:
176:
161:
156:
140:
136:
125:
121:
116:
103:
88:
68:
54:
43:Polar motion
42:
41:
1370:, 197, 1984
1295:7 September
1178:, 419, 1988
1165:, 351, 1985
834:7 September
621:(for (ν − ν
134:figure axis
106:earthquakes
36:arc-seconds
1626:Astrometry
1621:Precession
1615:Categories
1411:(3): 247.
1380:Wahr, J.M.
1214:(1): 101.
1152:, 07, 1992
734:References
605:m ≈ 14.5 p
583:m = 14.5 p
378:Figure 2.
221:arc length
211:of either
1604:0252-9211
1491:0252-9211
1236:129884741
723:Pole tide
678:≥ 230 mas
670:∼ 0.2 hPa
576:becomes:
567:, where ν
515:= 2.2 hPa
267:nutations
113:Principle
1561:12011419
1502:Archived
1354:54540284
1136:46607194
1003:. Ungar.
937:27152348
702:See also
650:= 14.5 p
639:becomes
306:nutation
217:subtends
153:spheroid
79:meridian
65:Analysis
1631:Geodesy
1582:Bibcode
1529:Bibcode
1469:Bibcode
1413:Bibcode
1334:Bibcode
1332:: 231.
1259:Bibcode
1216:Bibcode
1116:Bibcode
1024:Bibcode
928:4846461
907:Bibcode
863:Bibcode
764:Bibcode
708:Geodesy
613:/|ν − ν
523:= −170°
481:where ν
449:= 1.003
225:Earth's
1602:
1559:
1552:124440
1549:
1489:
1352:
1234:
1134:
1093:
1065:
977:
935:
925:
806:
685:
644:
619:
603:
593:
581:
562:ν + iν
501:
494:= 0.83
465:
422:with p
400:
365:Theory
322:
318:
240:
182:= 1.19
164:
104:Major
85:Causes
1350:S2CID
1232:S2CID
1191:, 107
1132:S2CID
752:(PDF)
691:= 1/ν
634:ν = ν
625:) ≫ ν
402:p = p
263:Geoid
170:= 1/ν
145:Euler
51:crust
1600:ISSN
1557:PMID
1487:ISSN
1441:, 64
1439:21 K
1297:2015
1189:A313
1091:ISBN
1063:ISBN
975:ISBN
933:PMID
836:2015
804:ISBN
683:(9)
642:(8)
601:(7)
579:(6)
499:(5)
463:(4)
398:(3)
316:(2)
300:The
293:and
162:(1)
59:ECEF
20:and
1590:doi
1578:178
1547:PMC
1537:doi
1477:doi
1465:178
1421:doi
1388:doi
1342:doi
1267:doi
1224:doi
1124:doi
1055:doi
1032:doi
956:CNN
923:PMC
915:doi
871:doi
772:doi
760:432
676:max
648:max
475:= ν
335:'s
219:an
147:'s
57:or
1617::
1598:.
1588:.
1576:.
1572:.
1555:.
1545:.
1535:.
1525:99
1523:.
1519:.
1485:.
1475:.
1463:.
1459:.
1419:.
1409:16
1407:.
1384:70
1368:12
1348:.
1340:.
1330:16
1328:.
1287:.
1265:.
1255:27
1253:.
1230:.
1222:.
1212:17
1210:.
1196:^
1150:19
1130:.
1122:.
1077:^
1061:.
1030:.
1020:19
1018:.
989:^
954:.
931:.
921:.
913:.
901:.
897:.
885:^
869:.
859:40
857:.
853:.
826:.
786:^
770:.
758:.
754:.
658:/ν
629:)
617:|
591:/
533:.
517:,
471:/m
435:a
431:−3
419:)
411:−3
289:,
273:.
192:.
1606:.
1592::
1584::
1563:.
1539::
1531::
1493:.
1479::
1471::
1427:.
1423::
1415::
1390::
1356:.
1344::
1336::
1299:.
1273:.
1269::
1261::
1238:.
1226::
1218::
1176:9
1163:3
1138:.
1126::
1118::
1099:.
1071:.
1057::
1038:.
1034::
1026::
983:.
958:.
939:.
917::
909::
903:2
879:.
873::
865::
838:.
812:.
780:.
774::
766::
693:D
689:D
687:τ
674:m
668:0
666:p
660:D
656:C
654:ν
652:0
646:m
636:C
627:D
623:C
615:C
611:C
609:ν
607:0
589:C
587:ν
585:0
574:m
569:D
564:D
529:0
527:t
521:0
519:λ
513:0
511:p
505:C
503:τ
492:C
490:ν
483:C
477:C
473:2
469:1
467:m
458:m
453:0
447:A
445:ν
441:0
424:0
417:0
406:Θ
404:0
386:(
383:m
357:y
353:p
346:x
342:p
310:D
201:M
197:F
180:E
178:ν
172:E
168:E
166:τ
157:F
141:M
137:F
126:M
122:M
24:.
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