On Barotropic and Baroclinic Models, With Special Emphasis on Ultra-Long Waves

The problem of control of the ultra-long waves in numerical prediction is considered. Sections 2–4 contain a discussion of the one-level forecasts. It is shown that the vertical variation of the horizontal wind and the static stability are the main factors in determining the value of divergence a t 500 mb. An independent estimate of the size of the term governing the ultra-long waves in the atmosphere agrees well with the one determined by Cressman on an empirical basis. Section 5 points out that any two-parameter model has to contain an effect similar to the one contained in the one-parameter model controlling the ultra-long waves. A modification of a two-parameter model is made in such a way that the ultra-long wares are controlled. Section 6 describes a perturbation analysis of the model developed in Section 5 in order to investigate the effect of the modification also on the shorter waves. It is found that a certain stabilization of the shorter waves is produced. Baroclinic instability and growth rate are investigated. Sections 7 and 8 contain a justification of certain approximations used in the earlier sections regarding the vertical variation of static stability and the profile of vertical velocity.