An arbitrary isobaric surface and the level of non-divergence constitute the two levels of the proposed model. The vorticity equation consistent with the quasi-geostrophic assumptions is applied at two levels. The thermodynamic energy equation for adiabatic motion is applied to the layer between the two levels. A parabolic profile for the vertical motion is assumed. The vertical motion is eliminated between the vorticity and the thermodynamic energy equations to obtain prognostic equations. The prognostic equations are solved by a generalized graphical forecast scheme of successive approximations. Forecasts and forecast errors in a selected meteorological situation are discussed.