On the convergence and error problems of the calculation of the pressure gradient force in sigma coordinate models

Abstract

The problem of the calculation of the pressure gradient force in sigma (terrain following) coordinate models is reviewed. It is pointed out that one of the well known schemes, the scheme of Corby et al. (1972), does not result in a convergent difference analogue of the pressure gradient force. Some other schemes, such as the one of Burridge and Haseler (1977) used at the European Centre for Medium Range Weather Forecasts, have a convergence condition, requiring thickness of sigma layers greater than (or equal to) a given threshold value. The two-term error problem of these analogues is reexamined. A numerical example is given, showing that, in accordance with the convergence condition, an increase in vertical resolution will generally not result in a reduction of the error.