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

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.