On the Problem of Initial Data for the Primitive Equations

It is first demonstrated that in a forecast with the primitive equations, pure geostrophic or purely non-divergent initial wind fields will result in noticeable meteorological “noise”, especially in a baroclinic atmosphere. It is then shown in a linear example that this noise is greatly suppressed if the divergence of the initial wind field is set equal to the divergence implied by the usual geostrophic theory of numerical weather prediction. The absence of noise in Charney’s 1955 test computation with non-divergent “balanced” initial data is explained.

Finally, the quasi-geostrophic expansion is used to define initial data for a non-linear forecast with the primitive equations. Two cases are considered, that where only the geopotential is known from observations, and that where only the non-divergent part of the wind is known from observation. It is shown that the initial tendencies computed from initial data of this kind preserve the assumed geostrophic character of the flow, and thereby make it possible to get more accurate forecasts with the primitive equations.