On Quasi-nondivergent Prognostic Equations and their Integration

A general two-dimensional wind-pressure relationship is obtained as the first integral of the so-called “balance equation” which requires the horizontal divergence to remain small as compared with the vertical component of the relative vorticity for the large-scale motions. This wind-pressure relationship is used in determining the initial conditions and in deriving the governing equations. The use of this general system removes the error introduced by the quasi-geostrophic approximation. An influence function is computed for a normal atmosphere. This function represents the reaction of the atmosphere to a point source perturbation and may be used to integrate the three-dimensional governing equation for arbitrary initial disturbances. A set of such functions may be computed, corresponding to different values of the parameter  , to meet different situations. DOI: 10.1111/j.2153-3490.1956.tb01235.x