# Atmosphere and Earth's rotation

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DOI: 10.1007/BF01904476

- Cite this article as:
- Volland, H. Surv Geophys (1996) 17: 101. doi:10.1007/BF01904476

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## Abstract

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 harmonic*P*_{2}^{0}(ϕ), responsible for pressure loading, and the spherical function*P*_{1}^{1}(ϕ) simulating supperrotation of the zonal wind. All other wind and pressure components merely redistribute*AAM* internally such that their contributions to*AAM* 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 the*AAM* within the troposphere and middle atmosphere.

Atmospheric excitation of polar motion is due to pressure loading configurations, which contain the antisymmetric function*P*_{2}^{1}(ϕ) exp(*i*λ) of zonal wavenumber*m*=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.