Numerical Integration of the Primitive Equations on the Hemisphere

A 48-hr. forecast for the entire Northern Hemisphere of a barotropic hydrostatic atmosphere is made with the “primitive equations.” Overlapping Mercator and stereographic grids are used, together with the finite-difference scheme proposed by Eliassen. Initial data corresponded to a Haurwitz-type pattern of wave number 4. The initial wind field was nondivergent and the initial geopotential field satisfied the balance equation. The computations seem to be stable and well behaved, except for two small temporary irregularities. The amplitude of the gravity-inertia waves present in the forecast geopotential field is about 1/30 that of the large-scale field. It can be shown that this is due to the neglect, in the initial data, of the quasi-geostrophically conditioned divergence field. The computational technique itself therefore does not give any unreal prominence to the “meteorological noise.” The computational characteristics and stability criterion of the Eliassen finite-difference system are investigated for a linearized version of the equations.