Surveys in Geophysics

, Volume 17, Issue 1, pp 101–144 | Cite as

Atmosphere and Earth's rotation

  • Hans Volland


The theoretical aspects of the transfer of angular momentum between atmosphere and Earth are treated with particular emphasis on analytical solutions. This is made possible by the consequent usage of spherical harmonics of low degree and by the development of large-scale atmospheric dynamics in terms of orthogonal wave modes as solutions of Laplace's tidal equations.

An outline of the theory of atmospheric ultralong planetary waves is given leading to analytical expressions for the meridional and height structure of such waves. The properties of the atmospheric boundary layer, where the exchange of atmospheric angular momentum with the solid Earth takes place, are briefly reviewed. The characteristic coupling time is the Ekman spin-down time of about one week.

The axial component of the atmospheric angular momentum (AAM), consisting of a pressure loading component and a zonal wind component, can be described by only two spherical functions of latitude ϕ: the zonal harmonicP 2 0 (ϕ), responsible for pressure loading, and the spherical functionP 1 1 (ϕ) simulating supperrotation of the zonal wind. All other wind and pressure components merely redistributeAAM internally such that their contributions toAAM disappear if averaged over the globe. It is shown that both spherical harmonics belong to the meridional structure functions of the gravest symmetric Rossby-Haurwitz wave (0, −1)*. This wave describes retrograde rotation of the atmosphere within the tropics (the tropical easterlies), while the gravest symmetric external wave mode (0, −2) is responsible for the westerlies at midlatitudes. Applying appropriate lower boundary conditions and assuming that secular angular momentum exchange between solid Earth and atmosphere disappears, the sum of both waves leads to an analytical solution of the zonal mean flow which roughly simulates the observed zonal wind structure as a function of latitude and height. This formalism is used as a basis for a quantitative discussion of the seasonal variations of theAAM within the troposphere and middle atmosphere.

Atmospheric excitation of polar motion is due to pressure loading configurations, which contain the antisymmetric functionP 2 1 (ϕ) exp(iλ) of zonal wavenumberm=1, while the winds must have a superrotation component in a coordinate system with the polar axis within the equator. The Rossby-Haurwitz wave (1, −3)* can simulate well the atmospheric excitation of the observed polar motion of all periods from the Chandler wobble down to normal modes with periods of about 10 days. Its superrotation component disappears so that only pressure loading contributes to polar motion.

The solar gravitational semidiurnal tidal force acting on the thermally driven atmospheric solar semidiurnal tidal wave can accelerate the rotation rat of the Earth by about 0.2 ms per century. It is speculated that the viscous-like friction of the geomagnetic field at the boundary between magnetosphere and solar wind may be responsible for the westward drift of the dipole component of the internal geomagnetic field. Electromagnetic or mechanical coupling between outer core and mantle may then contribute to a decrease of the Earth's rotation rate.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Abarca del Rio, R., and A. Cazenave, Interannual variations in the Earth's polar motion for 1963–1991: Comparison with atmospheric angular momentum over 1980–1991,Geophys. Res. Lett. 21, 2361, 1994.CrossRefGoogle Scholar
  2. Akasofu, S.I., Energy coupling between solar wind and the magnetosphere,Space Sci. Rev. 28, 121, 1981.CrossRefGoogle Scholar
  3. Andrews, D.G., J.R. Holton, and C.B. Leovy,Middle Atmospheric Dynamics, Academic Press, New York, 1987.Google Scholar
  4. Barnes, R.T.H., R. Hide, A.A. White, and C.A. Wilson, Atmospheric angular momentum fluctuations, Length-of-Day changes and polar motion,Proc. R. Soy. London Ser. A 387, 31, 1983.Google Scholar
  5. Becker, G., Nonlinear coupling of Rossby-Haurwitz waves,Contr. Atm. Phys. 59, 470, 1986.Google Scholar
  6. Belmont, A.D., D.G. Dartt, and G.D. Nastrom, Periodic variations in stratospheric zonal wind from 20 to 65 km, at 80° N to 70° S.Quart J. R. Met. Soc. 100, 203, 1974.CrossRefGoogle Scholar
  7. Belmont, A.D., D.G. Dartt, and G.D. Nastrom, Variations of stratospheric zonal winds, 20–65 km, 1961–1971.J. Appl. Meteor. 14, 585, 1975.CrossRefGoogle Scholar
  8. Brosche, P. and J. Sündermann,Earth's Rotation from Eons to Days, Springer, Heidelberg, 1990.Google Scholar
  9. Brosche, P., P.J. Wünsch, A. Frische, J. Sündermann, E. Maier-Reimer, and U. Mikolajewicz, The seasonal variation of the angular momentum of the oceans,Naturwiss. 77, 185, 1990.CrossRefGoogle Scholar
  10. Carter, W.E., and D.S. Robertson, Studying the earth by very-long-baseline interferometry,Sci. American 44, Nr. 5, 225, 1986.Google Scholar
  11. Chapman, S. and R.S. Lindzen,Atmospheric Tides, D. Reidel, Dordrecht, 1970.Google Scholar
  12. Chao, B.F., On the excitation of the earth's polar motion,Geophys. Res. Lett. 12, 526, 1985.Google Scholar
  13. Choe, R.S., M. Prevot, and P. Camps, New evidence of extrordinary rapid changes of the geomagnetic field during a reversal,Nature 374, 687, 1995.CrossRefGoogle Scholar
  14. Dartt, D.G., G.D. Nastrom, and A.D. Belmont, Seasonal and solar cycle wind variations, 80–100 km,J. Atm. Terr. Phys. 45, 707, 1983.Google Scholar
  15. Dickey, J.O., Atmospheric excitation of the earth's rotation: Progress and prospects via space geodesy, in Smith, D.E., and D.L. Turcotte (eds.):Contributions of Space Geodynamics: Earth Dynamics, Geodynamic Series, Vol. 24, American Geophysical Union, Washington, D.C., 55, 1993.Google Scholar
  16. Dickey, J.O., and T.M. Eubanks, Earth rotation and polar motion: Measurements and implications,IEEE Transact. Geosci. Remote Sensing GE-23, 373, 1985.Google Scholar
  17. Dunkerton, T.J., Theory of mesopause semiannual oscillation,J. Atm. Sci. 42, 2681, 1982.CrossRefGoogle Scholar
  18. Eubanks, T.M., Variations in the orientation of the earth, in Smith, D.E., and D.L. Turcotte (eds.):Contributions of Space Geodynamics: Earth Dynamics, Geodynamic Series, vo. 24, American Geophysical Union, Washington, D.C., 1, 1993.Google Scholar
  19. Eubanks, T.M., J.A. Steppe, J.O. Dickey, and P.S. Callahan, A spectral analysis of the earth's angular momentum budget,J. Geophys. Res. 90, 5385, 1985.Google Scholar
  20. Eubanks, T.M., J.A. Steppe, and J.O. Dickey, The atmospheric excitation of rapid polar motions, in Babcock, A.K., and Wilkins, G.A. (eds.):The Earth's Rotation and Reference Frames for Geodesy and Geodynamics, Kluwer Publ., Dordrecht, 365, 1988.Google Scholar
  21. Gold, T., and S. Soter, Atmospheric tides and the resonant rotation of Venus,Icarus 11, 356, 1969.CrossRefGoogle Scholar
  22. Gold, T., and S. Soter, Atmospheric tides and the 4-day circulation of Venus,Icarus 14, 16, 1971.CrossRefGoogle Scholar
  23. Gross, R.S., and U.J. Lindqwister, Atmospheric excitation of polar motion during the GIG 91 measurement campaign,Geophys. Res. Lett. 19, 849, 1992.Google Scholar
  24. Guinot, B., The Chandlerian wobble from 1900 to 1970,Astron. Astrophys. 19, 207, 1972.Google Scholar
  25. Hameed, S., and R.G. Currie, Simulation of the 14-month Chandler wobble in a global climate model,Geophys. Res. Lett. 16, 247, 1989.Google Scholar
  26. Hamilton, K., Mean wind evolution through the quasi-biennial cycle in the tropical lower stratosphere,J. Atm. Sci. 41, 2113, 1984.CrossRefGoogle Scholar
  27. Hantel, M.. On the vertical eddy transports in the northern hemisphereJ. Geophys. Res. 81, 1577, 1976.Google Scholar
  28. Held, I.M., Stationary and quasi-stationary eddies in the extratropical troposphere, in Hoskins, B., and R. Pierce, (eds.):Large-scale Dynamic Processes in the Atmosphere, pp. 127. Academic Press, London, 1983.Google Scholar
  29. Hide, R., Rotation of the atmospheres of the Earth and planets,Phil. Trans. R. Soc. A 313, 107, 1984.Google Scholar
  30. Hide, R., Fluctuations in the earth's rotation and the topography of the core-mantle interface,Phil. Trans. R. Soc. A 328, 351, 1989.Google Scholar
  31. Hide, R., and J.O. Dickey, Earth's variable rotation,Science 235, 829, 1991.Google Scholar
  32. Hill, T.W., Inertial limit of corotation,J. Geophys. Res. 84, 6554, 1979.Google Scholar
  33. Hines, C.O., Internal atmospheric gravity waves at ionospheric heights,Can. J. Phys 38, 1441, 1960a.Google Scholar
  34. Hines, C.O., On the rotation of the polar ionospheric regions,J. Geophys. Res. 65, 141, 1960b.Google Scholar
  35. Hines, C.O., Solar wind torque as an indicator of terrestrial motion.J. Geophys. Res. 79, 1543, 1974.Google Scholar
  36. Holton, J.R.,An Introduction to Dynamic Meteorology, Academic Press, New York, 1983.Google Scholar
  37. Jochmann, H., The Earth rotation as a cyclic process and as an indicator within the Earth's interior.Z. geol. Wiss. 12 197, 1984.Google Scholar
  38. Kiehl, J.T., Clouds and their effects on the climatic system,Physics Today 11, 36, 1994.Google Scholar
  39. Kikuchi, I., and I. Naito, Sea surface temperature analyses near the Chandler period, inProceedings of the International Latitude Observatory of Mizusawa, No. 21, volume K, 64, 1982.Google Scholar
  40. Kolaczek, B., J. Nastula, D. Gambis, W. Kosek, and H. Hozakowdki, The semiannual oscillation of polar motion and its atmospheric excitation in the period of 1979–1989,Astron. Astrophys. 243, 276, 1991.Google Scholar
  41. Kundt, W., Spin and atmospheric tides of Venus,Astron. Astrophys. 60, 85, 1977.Google Scholar
  42. Kundt, W., and H. Volland, Decade fluctuations of the earth's rotation and the westward drift of the geomagnetic field,Naturwiss. 76, 305, 1989.CrossRefGoogle Scholar
  43. Lambeck, K.,The Earth's Variable Rotation, Cambridge University Press, Cambridge, 1980.Google Scholar
  44. Madden, R.A., Large intraseasonal variations in wind stress over the tropical Pacific,J. Geophys. Res. 93, 5333, 1988.Google Scholar
  45. Madden, R.A., and P.R. Julian, Observations of the 40–50 day tropical oscillations—a review,Mon. Wea. Rev. 122, 814, 1994.CrossRefGoogle Scholar
  46. Mayr, H.G., and I. Harris, Quasi-axisymmetric circulation and superrotation in planetary atmospheres,Astron. Astrophys. 121, 124, 1983.Google Scholar
  47. McAvaney, B.J., W. Bourke, and K. Puri, A global spectral model for simulation of the general circulation.J. Atm. Sci. 35, 1557, 1978.CrossRefGoogle Scholar
  48. Merriam, J.B., Meteorological excitation of the annual polar motion,Geophys. J. R. Astr. Soc. 70, 41, 1982.Google Scholar
  49. Merill, R.T., and M.W. McElhinny,The Earth' Magnetic Field, Academic Press, London, 1983.Google Scholar
  50. Moritz, H., and I. Mueller,Earth Rotation, Ungar, New York, 1987.Google Scholar
  51. Munk, W.H., and G.F.J. McDonald,The Rotation of the Earth, Cambridge University Press, Cambridge, 1960.Google Scholar
  52. Naukojat, B., An update of the observed QBO of the stratospheric winds over the tropics,J. Atmos. Sci. 43, 1873, 1986.CrossRefGoogle Scholar
  53. Newell, R.E., J.W. Kidson, D.G. Vincent, and G.J. BoerThe general circulation of the tropical atmosphere and interactions with extratropical latitudes, Vol. 1, The MIT Press, 1972.Google Scholar
  54. Nerem, R.S., B.F. Chao, J.C. Chan, S.M. Klosko, N.K. Pavlis, and R.G. Williamson, Temporal variations of the earth's gravitational field: Measurements and geophysical modeling,Ann. Geophys. 11, C110, 1993.Google Scholar
  55. Pedlosky, J.,Geophysical Fluid Dynamics, Springer, Heidelberg, 1979.Google Scholar
  56. Peixoto, J.P. and A.H. Oort,Physics of Climate, American Institute of Physics, New York, 1992.Google Scholar
  57. Ponte, R.M., Barotropic motions and exchange of angular momentum between the oceans and solid earth.J. Geophys. Res. 95, 11369, 1990.Google Scholar
  58. Reed, R.J., The quasi-biennial oscillation of the atmosphere between 30 and 50 km over Ascension Island,J. Atmos. Sci. 22, 331, 1965.CrossRefGoogle Scholar
  59. Robertson, D.S., Geophysical applications of Very-Long-Baseline Interferometry,Reviews of Modern Physics 63, 899, 1991.CrossRefGoogle Scholar
  60. Rosen, R.D., The axial momentum balance of earth and its fluid envelope.Surveys in Geophys.,14, 1, 1993.CrossRefGoogle Scholar
  61. Rosen, R.D. and D.A. Salstein, Variations in atmospheric angular momentum on global and regional scales, and the length of day,J. Geophys. Res.,88, 5451–5470, 1983.Google Scholar
  62. Rosen, D.A., D.A. Salstein, T.M. Eubanks, J.O. Dickey, and J.A. Steppe, An El Niño signal in atmospheric angular momentum and earth rotation,Science 225, 411, 1984.Google Scholar
  63. Runcorn, S.K., G.A. Wilkins, E. Groten, H. Lenhardt, J. Campbell, R. Hide, B.F. Chao, A. Souriau, J. Hinderer, H. Legros, J.-L. Le Mouel, and M. Feisel, The excitation of the Chandler wobble,Surveys in Geophys. 9, 419, 1988.CrossRefGoogle Scholar
  64. Salstein, D.A., and R.D. Rosen, Regional contributions to the excitation of rapid polar motions,J. Geophys. Res. 94, 9971, 1989.Google Scholar
  65. Salstein, D.A., D.M. Kann, A.J. Miller, and R.D. Rosen, The Sub-Bureau for Atmospheric Angular Momentum of the International Earth Rotation Service: A meteorological data center with geodetic applications,Bull. Am. Met. Soc. 74, 67, 1993.CrossRefGoogle Scholar
  66. Schuh, H., Earth's rotation measured by VLBI, in Brosche, P. and J. Sündermann (eds.),Earth's Rotation from Eons to Days, Springer, Heidelberg, 1, 1990.Google Scholar
  67. Speth, P., and R.A. Madden, Space-time spectral analysis of northern hemisphere geopotential height,J. Atm. Sci. 40, 1086, 1983.CrossRefGoogle Scholar
  68. Stacey, F.D.,Physics of the Earth, John Wiley & Sons, New York, 1977.Google Scholar
  69. Stephenson, F.R., and L.V. Morrison, Long term changes in the rotation of the earth: 700 B.C. to A.D. 1980,Phil. Trans. R. Soc. London Ser A 313, 47, 1984.Google Scholar
  70. Stix, M., and P.H. Roberts,Earth Planet. Interiors 36, 49, 1984.CrossRefGoogle Scholar
  71. Stull, R.B.,Boundary Layer Meteorology, Kluwer, Dordrecht, 1989.Google Scholar
  72. Takahashi, M., A 2-dimensional numerical model of the semiannual zonal wind oscillation. in Holton, J.R., and T. Matsuno (eds.),Dynamics of the Middle Atmosphere, D. Reidel, Dordrecht, pp. 253, 1984.Google Scholar
  73. Voigt, G.H., Magnetospheric configuration, in Volland, H. (ed.):Handbook of Atmospheric Electrodynamics, Vol II, pp. 333, CRC Press, Boca Raton, 1995.Google Scholar
  74. Volland, H., A spectral model of the zonally averaged circulation in the middle atmosphere.Quart J. R. Met. Soc. 109 479, 1983.CrossRefGoogle Scholar
  75. Volland, H.,Atmospheric Tidal and Planetary Waves, Kluwer, Dordrecht, 1988.Google Scholar
  76. Volland, H., Rossby-Haurwitz waves with zero zonal wavenumber,Contr. Phys. Atm. 62 477, 1989.Google Scholar
  77. Vondrak, J., Long-period behaviour of polar motion between 1900.0 and 1984.0,Ann. Geophys. 3, 351, 1985.Google Scholar
  78. Wahr, J.M., The effects of the atmosphere and oceans on the Earth's wobble — I. Theory,Geophys. J. R. Astr. Soc. 70, 349, 1982.Google Scholar
  79. Wahr, J.M., The effects of the atmosphere and oceans on the Earth's wobble and on the seasonal variations in the length of day—II. Results,Geophys. J. R. Astr. Soc. 74, 349, 1983.Google Scholar
  80. Wahr, J.M., The Earth's rotation,Ann. Rev. Earth Planet. Sci. 16, 231, 1988.CrossRefGoogle Scholar
  81. Wahr, J.M., and A.H. Oort, Friction- and mountain torques and atmospheric fluxes,J. Atmos. Sci. 41, 190, 1984.CrossRefGoogle Scholar
  82. Wilson, C.R., and R.A. Haubrich, Meteorological excitation of the Earth's wobble,Geophys. J. R. Astr. Soc. 46, 707, 1976.Google Scholar
  83. Wunsch, C., Bermuda sea level in relation to tides, weather and baroclinic fluctuations,Rev. Geophys. Space Phys. 10, 1, 1972.Google Scholar
  84. Wünsch, J., and U. Seiler, Theoretical amplitudes and phases of the periodic polar motion terms caused by ocean tides,Astron. Astrophys. 266, 581, 1992.Google Scholar
  85. Yoder, C.F., G.J. Williams, and M.E. Parke, Tidal variations of Earth rotation,J. Geophys. Res. 86, 881–891, 1981.Google Scholar

Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • Hans Volland
    • 1
  1. 1.Radioastronomical InstituteUniversity of BonnBonnGermany

Personalised recommendations