Comparison of terrain following and cut cell grids using a non-hydrostatic model

Terrain following coordinates are widely used in operational models but the cut cell method has been proposed as an alternative that can more accurately represent atmospheric dynamics over steep orography. Because the type of grid is usually chosen during model implementation, it becomes necessary to use different models to compare the accuracy of different grids. In contrast, here a C-grid finite volume model enables a like-for-like comparison of terrain following and cut cell grids. A series of standard two-dimensional tests using idealised terrain are performed: tracer advection in a prescribed horizontal velocity field, a test starting from resting initial conditions, and orographically induced gravity waves described by nonhydrostatic dynamics. In addition, three new tests are formulated: a more challenging resting atmosphere case, and two new advection tests having a velocity field that is everywhere tangential to the terrain following coordinate surfaces. These new tests present a challenge on cut cell grids. The results of the advection tests demonstrate that accuracy depends primarily upon alignment of the flow with the grid rather than grid orthogonality. A resting atmosphere is well-maintained on all grids. In the gravity waves test, results on all grids are in good agreement with existing results from the literature, although terrain following velocity fields lead to errors on cut cell grids. Due to semi-implicit timestepping and an upwind-biased, explicit advection scheme, there are no timestep restrictions associated with small cut cells. We do not find the significant advantages of cut cells or smoothed coordinates that other authors find.