A global nonhydrostatic semi-Lagrangian atmospheric model with orography

(1) where Zs is the altitude of orography, ZT is the height of the top of the model atmosphere, z is the geometrical height above the sea level, and operating D/Dt on (1), the vertical velocity in the terrain-following coordinate may be expressed as follows: ... (7) Here, Ve is the angular velocity of the rotation of the earth; i, j, and k are the unit vectors in the eastward, northward, and upward directions, respectively, and they are orthogonal to each other, that is, k is in the direction along the axis joining the center of the earth and the point of interest at the surface; and the symbols (Sy )l, (Sy )u , and (Sy )z are components of the forces in l (eastward), u (northward), and z (upward) directions, respectively.