Salby, M. L., and R. R. Garcia, 1987: Transient response to localized episodic heating in the tropics. Part I: Excitation and short-time near-field behavior. Journal of the Atmospheric Sciences, 44(2), 458-498.

Abstract: The dynamical response to localized, unsteady tropical heating is studied in a stochastic framework. Spectral statistics of the random wave response are derived from those of tropical convection using the primitive equations for a spherical baroclinic atmosphere.

Short-time near-field behavior emerges in the form of a transient wavepacket which disperses away from the source region. Two principal components characterize the response: 1) a projection response which matches the vertical scale of the heating and 2) a barotropic response involving Rossby normal modes. The projection response consists of a continuum of frequencies and vertical scales centered about vertical wavelengths twice the effective depth of the heating. This scale discrimination is shown to be insensitive to variations in the heating distribution. The associated disturbance is trapped laterally about the equator but radiates vertically away from the source region. It corresponds to the tropical waves traditionally studied on the equatorial beta-plane. The barotropic component, on the other hand, radiates latitudinally into middle and high latitudes but is vertically trapped. This component of the response corresponds to planetary Rossby waves usually developed with the barotropic vorticity equation on the sphere. Because of the complementary nature of these two components, far-field tropospheric behavior is dominated by the barotropic contribution.

These elements of the response are presented in both local and more conventional modal descriptions. Vertical radiation and dispersion are evaluated for several modes. The wavepacket associated with the Kelvin mode completes less than one circuit around the globe before propagating completely out of the troposphere. Higher frequency components of the projection continuum radiate out of the source region even more quickly.

For short-term heating fluctuations, typical of tropical convection, the response at tropopause level is in accord with classical observations of the Wallace and Kousky Kelvin wave. The fast and ultra-fast Kelvin waves are secondary ingredients of the initial wave spectrum. In the case of slow transitional heating, e.g., the seasonal drift in monsoon activity between hemispheres, the Kelvin response assumes the form of a damped transient Walker circulation. This eastward migrating cell captures the salient characteristics of Madden and Julian's composite of the 40-day wave in the tropical Pacific Ocean.