A Generalization of the SLEVE Vertical Coordinate

Most atmospheric models use terrain-following coordinates, and it is well known that the associated deformation of the computational mesh leads to numerical inaccuracies. In a previous study, the authors proposed a new terrain-following coordinate formulation [the smooth level vertical (SLEVE) coordinate], which yields smooth vertical coordinate levels at mid and upper levels and thereby considerably reduces numerical errors in the simulation of flow past complex topography. In the current paper, a generalization of the SLEVE coordinate is presented by using a modified vertical decay of the topographic signature with height. The new formulation enables an almost uniform thickness of the lowermost computational layers, while preserving the fast transition to smooth levels in the mid and upper atmosphere. This allows for a more consistent and more stable coupling with planetary boundary layer schemes, while retaining the advantages over classic sigma coordinates at upper levels. The generalized SLEVE coordinate is implemented and successfully tested in real-case simulations using an operational nonhydrostatic atmospheric model.