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Coordinates over Complex Terrain in Atmospheric Model

Wen-Yih Sun

Abstract: 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.
Keywords: model / complex terrain / Agreement / Curvilinear / curl / Coordinate / Ignored

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