A simple theoretical analysis on the stability of a resting tropical atmosphere to semigeostrophic perturbations is given using a free atmosphere–boundary layer coupled model on an equatorial β-plane.

An unstable mode emerges when sea surface temperature is higher than a critical value. The growing mode is a moist Kelvin wave modified through coupling with a Rossby wave of the lowest meridional index. The modified Rossby modes, however, remain damped even for high SST. The unstable mode selection can be explained in terms of wave energy generation due to the latent heating induced by frictional moisture convergence.

The horizontal mode-coupling has profound impacts on wave instability. It favors the amplification of long planetary-scale waves, slows down eastward propagation, and suppresses unrealistically fast growth of the uncoupled moist Kelvin mode by creating substantial meridional flows. These effects make the coupled unstable mode more resemble observed equatorial intraseasonal disturbances.

The results also demonstrate that when maximum SST moves from the equator to 7.5°N, the growth rate of the unstable wave is significantly reduced, suggesting that the annual march of the “thermal equator” and associated convective heating is likely responsible for annual variations of the equatorial 40–50 day wave activity.