A SEMIIMPLICIT SCHEME FOR THE BAROTROPIC PRIMITIVE EQUATIONS OF ATMOSPHERIC DYNAMICS

The primitive equations of a barotropic atmosphere in isobaric co-ordi nates are reformulated, in order to express the geopotential gradient as a function of the pressure at the Earth's surface. Furthermore, the free surface equation is written in conservative form. A finite diffe rence, semi-implicit, semi-Lagrangian scheme in isobaric co-ordinates is developed. The numerical scheme is mass conservative, is proven to be stable and requires the solution of a single five-diagonal system. Numerical simulations show that the model captures the main dynamical features of large scale atmospheric motion.