Low-order pressure gradient schemes in sigma coordinate models: The seamount test revisited

The original feature of this study is to reconsider the currently admitted idea that Density-Jacobian type PGFs perform better than the primitive sigma formulation discretized in a straightforward way (hereafter Straightforward-Primitive PGF). Errors on the discrete hydrostatic pressure are actually closely related to the way the density field is initialized. If a mass conserving method is preferred to a straightforward initialization, the rectangular integral of the Straightforward-Primitive PGF is likely to be more accurate than the trapezoidal rule usually involved in Density-Jacobian PGFs. Errors on the vorticity field of the Straightforward-Primitive PGF depend on the discretization of the hydrostatic correction term. A modified version of the Straightforward-Primitive PGF is shown to be in better agreement with the concept of bottom torque consistency. The seamount tests show that this so-called Modified-Primitive PGF performs globally better than the current low-order Density-Jacobian PGFs.