An Improved Barotropic Model and some Aspects of Using the Balance Equation for Three-dimensional Flow

A few suggestions for improving the barotropic model presented in a previous article (Bolin, 1955) have been tested. The results show that replacing the geostrophic relation by a more general balance equation improves the forecasts over 24 hours in certain respects. Furthermore the incorporation of the effects of a stratosphere in a very approximate way gives a better description of the behaviour of the largest scales of motion in the atmosphere. The application of the balance equation in numerical forecasting is extended to three-dimensional baroclin flow. It is shown that the criterion of integrability of the balance equation to obtain the stream function from a knowledge of the pressure field has to be satisfied in the course of the computations to maintain elliptic character of the equations.