An Analysis of Frictional Feedback on a Moist Equatorial Kelvin Mode

Abstract

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. The full linear stability problem can be discretized into an eigenvalue problem that is barely computationally tractable. A scaling analysis appropriate for low-frequency, long wavelength modes, such as the MJO, leads to a much simpler eigenvalue problem. 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. Results are compared to a similar study by Wang and Rui using a different convective parameterization and a two-layer free troposphere. The much stronger frictional amplification that they found is traced to an unrealistically large surface drag coefficient in their model. When their drag is reduced to the same value used in the current study, comparable frictional destabilization is found. This suggests that the effect of frictional feedback may be fairly insensitive to the convective parameterization used.