A note on the finite differencing of the linearized primitive equations' lower boundary condition

This note examines the accuracy of finite difference solutions of the midlatitude primitive equations and the quasi-geostrophic equation. First order accurate forward differencing of the equations' lower boundary condition is shown to poorly simulate the radiating wave response to midlatitude heating. Forward differencing always exaggerates the magnitude of the radiating response. For a realistic heating height scale and for a reasonable mesh size this exaggeration is on the order of 50 percent. Central differencing of the lower boundary condition gives an error of only about 3 percent.