Coordinates over Complex Terrain in Atmospheric Model

Wen-Yih Sun (Department of Earth, Atmospheric and Planetary Sciences, Purdue University, W. Lafayette, IN, 47907, USA;Department of Atmospheric Sciences, National Central University, Chung-Li, Taoyuan, 320, Taiwan;Institute for Space-Earth Environmental Research, Nagoya University, Nagoya, 464-8601, Japan)


In the terrain following coordinate, Gal-Chen and Somerville and other proposed a vertical coordinate   and constant spatial intervals of  and  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.


Navier-Stokes equations;Cartesian;Curvilinear;Covariant;Contravariant;Terrain following

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