A theory for the excitation mechanism of stratospheric equatorial waves is proposed. The theory states that the tropical atmosphere is under the marginally stable state with respect to wave-CISK mechanism and that equatorial waves are forced ones under such circumstances.
It is shown from this theory that only the mode with the equivalent depth equal to that of the free wave in the marginal state or the slightly longer one is selectively excited, regardless of the profile of a forcing. Although the selected equivalent depth is shorter than the observed one when the Arakawa-Schubert's theory is used as the cumulus parameterization, the dominant periods in the stratosphere, at least, coincide with observed ones. Further considerations suggest that, under some devices of more complete parameterization, the longer equivalent depth seems to be selected. Then the dominant periods at the tropopause are close to those in the stratosphere, so that the vertical structure in the troposphere of the selected waves in the stratosphere may agree well with observations.
Assuming a lateral forcing as the excitation source of mixed Rossby-gravity waves and imposing the forcing in the form of a body forcing confined in mid-latitudes (not a boundary forcing), the selectivity for wavenumber is examined. With large meridional scale forcing, the waves with wavenumber 1 or 2 are not dominant and the waves of middle wavenumbers (3-7) are selected corresponding to those observed. Concerning the horizontal structure of the dominant waves, they also show a phase difference of about 90°between meridional wind and geopotential in agreement with observations. It is difficult to specify the excitation source of Kelvin waves, but if thermal forcing is assumed to be the source at least, wavenumber 1 is selected.
Thus, this theory seems to explain well the characteristics of stratospheric equatorial waves, with a more complete parameterization of cumulus ensemble.
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