A Baroclinic Model of the Atmosphere Applicable to the Problem of Numerical Forecasting in Three Dimensions. I

A three-dimensional baroclinic model of the atmosphere is presented. This model is completely determined by 4 parameters, three of which specify the field of temperature. The main difference between this model and other models so far published is that it allows for a non-uniform temperature lapse-rate in the horizontal. Moreover, it takes into account the observed division of the atmosphere into a troposphere and a stratosphere.

A simplification is introduced by utilizing the synoptic experience that the horizontal temperature gradient is usually reversed when traversing the tropopause. This essentially reduces the number of parameters to three.

This simplified version of the model is used for integrating the vorticity equation along the vertical, and the coefficients of the resulting two-dimensional equation are discussed in some detail. Examination of the coefficients give some valuable information regarding the levels of mean wind and non-divergence.

The main results are that in middle latitudes the level of mean wind may vary from 2.5–6.5 km and that the level of of non-divergence is always higher than the former, the difference amounting to 0.5–3.0 km. On the average, the level of mean wind lies below and the level of non-divergence above the 500 mb surface. One is therefore lead to the conclusion that this surface might be used to approximate each of the two levels mentioned.

The consequence of this for the practical procedures for numerical forecasting is that the height changes at this particular level could alternatively be predicted in the two following ways:

1. By use of the barotropic vorticity equation, thereby assuming that the level of non-divergence can be replaced by the 500 mb surface.
2. By use of an integrated vorticity equation applicable to the level of mean wind. In this case one replaces the level of mean wind with the 500 mb surface.