The development of atmospheric cyclones is studied from the viewpoint of the instability of large-scale wave perturbations superimposed on a zonal current.

A generalization of the two-dimensional spectral forecast equations is suggested, whereby the atmospheric flow field in horizontal and vertical directions is represented in terms of orthogonal functions, which are eigenfunctions of certain differential operators in the three-dimensional equations. The technique is applied to the quasi-geostrophic potential vorticity equation.

A general numerical integration formula is presented which generates many of the commonly used one-dimensional finite-difference schemes.