Reduction of the Tropical Atmospheric Dynamics Into Shallow‐Water Analogs: A Formulation Analysis

Abstract The shallow‐water analogue models for the tropical atmosphere are examined from a formulational point of view. The normal‐mode approach provides a formal procedure to reduce the primitive equation system to a shallow‐water analogue, although approaches based on vertical integrals of the primitive equation system may be more intuitively appealing. Under a general framework of the latter, classical models by Gill (1980, https://doi.org/10.1256/smsqj.44904 ) and Lindzen and Nigam (1987, 2.0.co;2>https://doi.org/10.1175/1520‐0469(1987)044<2418:otross>2.0.co;2 ) are derived in a deductive manner, by elucidating their limitations, implications, as well physical processes assumed. Major advantage of shallow‐water analogue models is that after a vertical integral, the determination of convective heating rate simply reduces to that of a precipitation rate. Consequently, the question of representing convection also almost reduces to that of precipitation. This fact leads to confusions in literature about distinction between large‐scale precipitation and subgrid‐scale convection. This framework further supports a popular notion of the moisture as a key variable for describing convection. By reviewing the existing formulations, it is shown that convection can be parameterized without moisture under the limit of the parcel‐environment quasi‐equilibrium.