GENERAL FORMS OF DYNAMIC EQUATIONS FOR ATMOSPHERE IN NUMERICAL MODELS WITH TOPOGRAPHY

The atmospheric dynamic equations have been transformed from the z-coordinate system into a generalized vertical coordinate system by using a so-called DDD transformation method. Then the general-ized system is assumed being pressure, sigma or incorporated pressure-sigma coordinate system and corre-sponding equations are obtained with the second-order accuracy. It is pointed out that the usual equations are only of the first-order accuracy when their space-differential terms are approximated by central finite differences. Therefore the usual forms of the equations may result in quite large errors on steep slopes of mountains included in a model.