A method for computing horizontal pressure‐gradient force in an oceanic model with a nonaligned vertical coordinate

Discretization of the pressure‐gradient force is a long‐standing problem in terrain‐following (or σ) coordinate oceanic modeling. When the isosurfaces of the vertical coordinate are not aligned with either geopotential surfaces or isopycnals, the horizontal pressure gradient consists of two large terms that tend to cancel; the associated pressure‐gradient error stems from interference of the discretization errors of these terms. The situation is further complicated by the nonorthogonality of the coordinate system and by the common practice of using highly nonuniform stretching for the vertical grids, which, unless special precautions are taken, causes both a loss of discretization accuracy overall and an…