Waves and Instabilities for Model Tropical Convective Parameterizations

Abstract

Models of the tropical atmosphere with crude vertical resolution are important as intermediate models for understanding convectively coupled wave hierarchies and also as simplified models for studying various strategies for parameterizing convection and convectively coupled waves. Simplified models are utilized in a detailed analytical study of the waves and instabilities for model convective parameterizations. Three convection schemes are analyzed: a strict quasi-equilibrium (QE) scheme and two schemes that attempt to model the departures from quasi equilibrium by including the shorter timescale effects of penetrative convection, the Lagrangian parcel adjustment (LPA) scheme and a new instantaneous convective available potential energy (CAPE) adjustment (ICAPE) scheme. Unlike the QE parameterization scheme, both the LPA and ICAPE schemes have scale-selective finite bands of unstable wavelengths centered around typical cluster and supercluster scales with virtually identical growth rates and wave structure. However, the LPA scheme has, in addition, two nonphysical superfast parasitic waves that are artifacts of this parameterization while such waves are completely absent in the new ICAPE parameterization. Another topic studied here is the fashion in which an imposed barotropic mean wind triggers a transition to instability in the Tropics through suitable convectively coupled waves; this is the simplest analytical problem for studying the influence of midlatitudes on convectively coupled waves. For an easterly barotropic mean flow with the effect of rotation included, both supercluster-scale moist Kelvin waves and cluster-scale moist mixed Rossby‐gravity waves participate in the transition to instability. The wave and stability properties of the ICAPE parameterization with rotation are studied through a novel procedure involving complete zonal resolution but low-order meridional truncation. Besides moist Kelvin, mixed Rossby‐gravity, and equatorial Rossby waves, this approximation retains other slowly propagating moist gravity waves in a consistent fashion.