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

This paper revisits the classic seamount test used in numerous previous studies to evidence the sigma errors of the pressure gradient force (PGF) and their long-term effects on circulation. Two kinds of analysis are developed. We first consider the initial PGF errors. Then, the global level of erroneous kinetic energy is computed along a 180-day simulation. The long-term circulation appears to be better correlated to the initial vorticity errors than to the initial error diagnostics. iginal 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.