Increased Numerical Accuracy of Terrain Slope Amplifies Advection Errors in Idealized 2D Experiments Under Terrain‐Following Coordinate

This study investigates the impact of numerical accuracy of terrain slope on advection errors under Gal‐Chen and Somerville terrain‐following coordinates. Through a series of idealized 2D linear advection experiments, we demonstrate that increasing the numerical accuracy of terrain slope (from second‐ to fourth‐order) amplifies advection errors under steep topographic conditions, irrespective of the numerical accuracy of other spatial differences in the advection equation. Mechanistic analysis reveals that this error amplification is predominantly caused by the horizontal advection process, wherein higher‐order accuracy terrain slope introduces intensified unresolved small‐scale topographic forcings, which manifest as spurious waves through aliasing. These findings indicate that increased numerical accuracy does not invariably enhance model performance and highlight the need for careful attention to terrain representation in the model.