In this paper the energy propagation through dispersive waves in four atmospheric models is investigated. These waves are characterized by an approximate geostrophic balance. Diagrams showing the relation between group velocity, wave velocity, and wave length in the four types of atmosphere are given. It is found that: 1. In each of the four models there is always a range of wave length for which group velocity is larger than wave velocity, so that new waves can be formed ahead of initial waves. 2. Both divergence or convergence and horizontal solenoids give rise to waves with negative group velocity. But only in the presence of solenoids is there a range of wave length for which the speed of propagation of energy upstream is greater than the wave speed in the same direction. This means that only the horizontal solenoids make possible the formation of new waves upstream. A graphical method is used to construct the distribution of phase resulting from an instantaneous point-source disturbance. The... Abstract In this paper the energy propagation through dispersive waves in four atmospheric models is investigated. These waves are characterized by an approximate geostrophic balance. Diagrams showing the relation between group velocity, wave velocity, and wave length in the four types of atmosphere are given. It is found that: 1. In each of the four models there is always a range of wave length for which group velocity is larger than wave velocity, so that new waves can be formed ahead of initial waves. 2. Both divergence or convergence and horizontal solenoids give rise to waves with negative group velocity. But only in the presence of solenoids is there a range of wave length for which the speed of propagation of energy upstream is greater than the wave speed in the same direction. This means that only the horizontal solenoids make possible the formation of new waves upstream. A graphical method is used to construct the distribution of phase resulting from an instantaneous point-source disturbance. The...