Barotropic Divergence and Very Long Atmospheric Waves

The problem of spurious retrogression of very long waves by the non-divergent barotropic forecasts is shown to be the same problem discussed extensively by Rossby, Yeh, and Bolin. This difficulty is due to the failure of the non-divergent model to allow properly for the mutual adjustment of wind and pressure fields. The equation of continuity for a homogeneous incompressible fluid with an upper free surface, proposed as a remedy by Rossby nearly 20 years ago, removes much of the difficulty. Further improvements are obtained by inclusion of a tropopause in the manner adopted by Bolin. The results of a series of 10 test forecasts are shown in verification of the function of the divergence in a barotropic model.