Abstract
The finite-difference scheme of the primitive equations was derived and tested in the so-called x, y, σ-coordinate system which contains the ground as a coordinate surface. The system is suitable for taking into consideration the effect of orography upon the atmospheric motion.
The numerical test was attempted for the flow against the bellshaped mountain in a homogeneous and incompressible atmosphere. The results showed the reasonable patterns of pressure and wind, that is, the configuration of trough, ridge, jet core, divergence and vorticity as expected. According to the numerical solution we obtained, our finite-difference scheme seems to be computationally stable and there appears no trouble through 48-hour forecast. Besides, the conservation of the total energy in the forecasting domain was satisfied so accurately that it varied within the range less than 0.03% of the initial value at 48-hour forecast.
