An analysis of frictional feedback on a moist equatorial Kelvin mode

A simple theoretical model of the tropical troposphere is used to study whe ther boundary layer friction is destabilizing to the Madden-Julian oscillat ion (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 c onvective parameterization. The troposphere is divided into a frictional bo undary 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 pro blem that is barely computationally tractable. A scaling analysis appropria te for low-frequency, long wavelength modes, such as the. MJO, leads to a m uch simpler eigenvalue problem. Friction is found to be modestly destabilizing for the moist Kelvin mode, i ncreasing its growth rate by 0.03 day(-1). It also has a smaller destabiliz ing effect on the gravest moist Rossby mode. Frictionally forced boundary l ayer convergence promotes wave amplification by enhancing convective heatin g 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 c onvective parameterization and a two-layer free troposphere. The much stron ger frictional amplification that they found is traced to an unrealisticall y large surface drag coefficient in their model. When their drag is reduced to the same value used in the current study, comparable frictional destabi lization is found. This suggests that the effect of frictional feedback may be fairly insensitive to the convective parameterization used.