Propagation and evolution of stationary baroclinic planetary waves from the perspective of wave ray theory

The three-dimensional propagation of stationary planetary waves in the linearized baroclinic quasi-geostrophic model is investigated by applying wave propagation theory. The variations in wave energy and amplitude along energy propagation paths or called rays are further derived by applying a method that can resolve changes in the magnitude of the group velocity. The results suggest that there exists a meridional wave guide in the middle troposphere, where waves mainly propagate meridionally and are reflected by two turning altitudes that are located in the lower and upper troposphere, respectively. There also exists a vertical wave guide in high latitudes to permit vertical propagation for rays. This wave guide is a key region for enabling interactions between the troposphere and stratosphere, particularly favoring waves with larger scales. Besides, the vertical propagation of waves is modulated by seasonal variations in the zonal basic flow and temperature. Both wave energy and amplitude can approach to the local maxima at turning altitudes and latitudes if the basic state undergoes minor changes, indicating that waves may have a substantial development when they move toward these turning locations. By defining an instability criterion and specifying a simple zonal basic flow such as a jet prototype, the instability of baroclinic waves can be further explored.