Abstract

Abstract A linearized version of the cumulus parameterization theory of Arakawa and Schubert (1974) is used in an equatorial wave model to test the wave-CISK hypothesis under the quasi-equilibrium assumption. A unique relationship between cumulus heating and large-scale vertical motion at all levels is derived. The waves are modelled by the linearized primitive equations for an equatorial beta-plane, without surface friction and for a resting, conditionally unstable basic state. The stability of the waves, and of the ensemble of cumulus clouds embedded in them, is examined by solving the vertical structure equation as an eigenvalue problem. We find that the waves are neutral, unless the precipitation efficiency of the clouds is unrealistically large.

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