A simple linear model of the tropical atmosphere has been used to study the effect of meridional gradient in moist static energy on equatorially-trapped waves. The presence of a meridional gradient in moist energy causes the amplification of westward migrating mixed Rossby-gravity waves with wavelength in the range of 8000 to 9000 km and a period on the order of 4 days (10 days) when the mean zonal wind is easterly (westerly) with a speed of 10 m/sec. The predictions of this model are consistent with observed mixed Rossby-gravity waves.

A gradient of moist static energy causes a gradient in the moist gravity wave speed. The meridional variation of the moist static energy is modeled by assuming the square of the moist wave speed to vary linearly with latitude. This gradient of moist gravity wave speed divided by the moist gravity wave speed at the Equator is the parameter, denoted as gamma, which determines the effects of the variation of the moist static energy. For gamma equal to zero, the problem reverts to the adiabatic case for mixed Rossby-gravity waves, which was treated by Lindzen (1967). One effect of the gradient of moist static energy is to displace the position of the maximum of the wave toward the warmer side of the Equator. The second effect is to increase the order of the eigenvalue equation from three to seven. With a gradient of moist static energy, four additional roots appear. Two of these roots are real, corresponding to stable oscillations, and the other two are a pair of complex roots, indicating a mode which grows in time. The details by which the wave grows are examined.