Advection errors in an orthogonal terrain-following coordinate: idealized 2-D experiments using steep terrains

This study illustrated the importance of smoothed vertical layers and orthogonal grids in an orthogonal terrain-following coordinate (an OTF-coordinate) in reducing advection errors over steep terrain. Three coordinates, namely, classic terrain-following coordinate, hybrid terrain-following coordinate (HTF-coordinate) and OTF-coordinate, were employed in Schar-type advection experiments for various terrains. The results demonstrated that the OTF-coordinate could diminish the grids with high skewness in the HTF-coordinate over steep terrain; the orthogonal grids share the same importance in reducing advection errors with smoothed vertical layers. Therefore, the advection errors in the OTF-coordinate are considerably reduced than those in the corresponding HTF-coordinate over steep terrain.