Abstract

This study designs a novel terrain-following coordinate, called the Orthogonal curvilinear terrain-following coordinate (Orthogonal sigma coordinate, OS-coordinate), which has the ability to handle both the well-known high level errors and the pressure gradient force (PGF) errors above the steep terrain in the classic terrain-following coordinate (sigma-coordinate).

The OS-coordinate is proposed through a way quite different from and against the sigma-coordinate. The basis vectors of OS-coordinate which is unit and terrain-following are firstly designed, and then the corresponding definitions of every coordinates are solved, so that the scalar equations of OS-coordinate are solved. The PGF computational form has only one term in each momentum equation of OS-coordinate, thereby avoiding the PGF problem completely.

Finally, a unified framework is proposed to combine the equations of the Cartesian coordinate, sigma-coordinate and OS-coordinate together via an on-off, and is used to implement idealized advection experiments for testing the OS-coordinate. The evaluation on the experimental results show the vertical coordinate surfaces in the OS-coordinate can be much smoother than those in the sigma-coordinate, and therefore the OS-coordinate outperforms all along the sigma-coordinate. This new coordinate can be used for oceanic models as well, and needs to be tested in both the idealized and real-case experiments.