A Simple Multicloud Parameterization for Convectively Coupled Tropical Waves. Part I: Linear Analysis

Abstract

Recent observational analysis reveals the central role of three multicloud types, congestus, stratiform, and deep convective cumulus clouds, in the dynamics of large-scale convectively coupled Kelvin waves, westward-propagating two-day waves, and the Madden–Julian oscillation. A systematic model convective parameterization highlighting the dynamic role of the three cloud types is developed here through two baroclinic modes of vertical structure: a deep convective heating mode and a second mode with low-level heating and cooling corresponding respectively to congestus and stratiform clouds. A systematic moisture equation is developed where the lower troposphere moisture increases through detrainment of shallow cumulus clouds, evaporation of stratiform rain, and moisture convergence and decreases through deep convective precipitation. A nonlinear switch is developed that favors either deep or congestus convection depending on the relative dryness of the troposphere; in particular, a dry troposphere with large convective available potential energy (CAPE) has no deep convection and only congestus clouds. The properties of the multicloud model parameterization are tested by linearized analysis in a two-dimensional setup with no rotation with constant sea surface temperature. In particular, the present study reveals new mechanisms for the large-scale instability of moist gravity waves with features resembling observed convectively coupled Kelvin waves in realistic parameter regimes without any effect of wind-induced surface heat exchange (WISHE). A detailed dynamical analysis for the linear waves is given herein and idealized nonlinear numerical simulations are reported in a companion paper. A maximum congestus heating leads during the dry phase of the wave. It is followed by an increase of the boundary layer θe, that is, CAPE, and lower troposphere moistening that precondition the upper troposphere for the next deep convective episode. In turn, deep convection consumes CAPE and removes moisture, thus yielding the dry episode.