Frictional Feedbacks on Large-Scale Equatorially Trapped Waves

A simple theoretical model of the tropical troposphere is used to study whether boundary layer friction is destabilizing to the Madden-Julian Oscillation (MJO) and other convectively coupled moist equatorially trapped Kelvin-like modes. A linear stability analysis is performed on an equatorial beta-plane with a continuously stratified atmosphere using a Betts-Miller-like convective parameterization. The troposphere is divided into a frictional boundary layer close to the surface and a frictionless free troposphere. The basic state is horizontally homogeneous and uniformly convecting.

Friction is found to be modestly destabilizing for the moist Kelvin mode, increasing its growth rate by 0.03 day^{-1}. It also has a smaller destabilizing effect on the gravest moist Rossby mode. Frictionally forced boundary layer convergence promotes wave amplification by enhancing convective heating along the equator in the warm sector of the wave. With a radiation upper boundary condition, the longest waves have the largest growth rate. A rigid lid boundary condition slightly favors short wavelengths.

The frictional boundary layer model, which relates boundary layer convergence to low-level pressure gradients, is tested by comparison with reanalysis data. In addition, we explore the sensitivity of the modelled moist Kelvin mode to correlations between large-scale vertical motion, mid-tropospheric relative humidity, and net tropospheric radiative cooling empirically derived from TOGA COARE.