The Semidiurnal Oscillation in a Thermalgeostrophic Atmosphere

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  • 1 Institute of Geophysics, University of Oslo, Norway
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Abstract

The problem of atmospheric response to tidal oscillations is re-examined for consistent and fairly general atmospheric models. An approximate extension of the separation method is developed, with an adjusting mixed factor, inherently defined through and defining a residual eigenvalue-eigenfunction problem consisting of one formally unchanged radial equation and a set of modified angular equations. The possibility of a considerably amplified S22 reappears, and the appropriate “tropospheric” first mode fits observations surprisingly well. A seasonal dependent eigensolution, equatorially asymmetric at the solstices, approaching cos3ϕ at the surface, but decreasing much faster at the tropopause, and an almost constant significantly increased equivalent depth h2,22 implying increased response and radial exponentiality, are essential features of this new S2,22. The set of angular equations incorporates a kind of nonlinearity. Although a tropospherically excited semidiurnal mode may be strongly amplified, its “stratospheric” counterpart needs not. All quoted modes comprise the whole atmosphere, however, cascading to the appropriate wave family at each successive interface, the dominant mode being analogous to the imposed one, but behaving differently. A large ozone forcing needs thus give no serious controversies, while discrepancies encountered when interpreting upper level observations as a 1-mode feature turn highly understandable in the light of the theory advanced.

Abstract

The problem of atmospheric response to tidal oscillations is re-examined for consistent and fairly general atmospheric models. An approximate extension of the separation method is developed, with an adjusting mixed factor, inherently defined through and defining a residual eigenvalue-eigenfunction problem consisting of one formally unchanged radial equation and a set of modified angular equations. The possibility of a considerably amplified S22 reappears, and the appropriate “tropospheric” first mode fits observations surprisingly well. A seasonal dependent eigensolution, equatorially asymmetric at the solstices, approaching cos3ϕ at the surface, but decreasing much faster at the tropopause, and an almost constant significantly increased equivalent depth h2,22 implying increased response and radial exponentiality, are essential features of this new S2,22. The set of angular equations incorporates a kind of nonlinearity. Although a tropospherically excited semidiurnal mode may be strongly amplified, its “stratospheric” counterpart needs not. All quoted modes comprise the whole atmosphere, however, cascading to the appropriate wave family at each successive interface, the dominant mode being analogous to the imposed one, but behaving differently. A large ozone forcing needs thus give no serious controversies, while discrepancies encountered when interpreting upper level observations as a 1-mode feature turn highly understandable in the light of the theory advanced.

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