A simple one-layer, quasi-geostrophic model of vertical motion and surface pressure tendency is derived and used to illustrate relationships between various parameters such as stability, latitude, wind speed, and the sea-level pressure tendency for sinusoidal disturbances in a baroclinic current. It is shown in the model that the wavelength at which the maximum surface pressure tendency occurs varies with the Rossby radius of deformation, as well as with the zonal wind speed and amplitude of the disturbance. In the case of a simulated polar cyclone, which exists at high latitudes under conditions of low static stability and shallow atmospheric depth, the wavelength of maximum growth rate is relatively short.
The primary virtue of this model is that it can be used as a pedagogical tool for explaining quantitatively, but without lengthy calculations, the behavior of surface pressure systems.
