Coordinates over Complex Terrain in Atmospheric Model

In the terrain following coordinate, Gal-Chen and Somerville (1975) and other proposed a vertical coordinate  z*=(z-zb)/(zt-zb) and constant spatial intervals of dx* and  dy*along the other directions.  Because the variation of  and  was ignored, their coordinate does not really follow the terrain.  It fails to reproduce the divergence and curl over a complex terrain.  Aligning the coordinate with real terrain, the divergence and curl we obtained from the curvilinear coordinate are consistent with the Cartesian coordinate.  With a modification, the simulated total mass, energy, and momentum from the Navier-Stokes equations are conserved and in agreement with those calculated from Cartesian coordinate.