On truncation errors due to vertical differences in various numerical prediction models

Some estimates of truncation errors due to vertical finite differences are given. The truncation errors amount to at most 10 % in the phase-speed of the basic mode in a model atmosphere in which the vertical shear of the basic, zonal flow vanishes. An increase of the vertical resolution results in rapidly decreasing truncation errors in this case.

In a model atmosphere, in which the vertical windshear is different from zero, and the static stability parameter is a function of pressure, we find small truncation errors in the initial displacement of the wave, but large errors in the initial amplification.

The initial development of a baroclinic wave is evaluated in three different baroclinic models. The models differ only in the vertical variation of the static stability parameter which is a simple function of pressure in the first model, a constant in the next and zero in the third model. It is shown that the vertical variation of static stability is important for the amplification and the slope of the wave in the vertical direction.

The initial change of the kinetic energy in the models is computed as a function of wave-length. It is shown that the change of kinetic energy is larger in the models where the static stability parameter is constant or zero than in the models where it varies with pressure.

The last section contains some comments on the upper boundary condition. It is shown that the conditions ω = 0 and ϕ < ∞ (ϕ = geopotential) at the upper boundary are equivalent in certain problems.