On Calculating Vorticity Balances in Primitive Equation Models

Abstract A note of caution is Provided to users of the widely-distributed Cox ocean circulation model. It is shown that the discrete conservation of vorticity equation associated with the finite difference approximations to the primitive equations on an Arakawa B grid contains a term that approximates βΔy2∂2u/∂x∂y. Although this term has no counterpart in the continuous equation, it is consistent with a beta term in which the v velocity is evaluated by a streamfunction difference over 2Δx and must be included when model velocities am used to calculate vorticity balances. Regions within ocean models where the spurious term might be significant are discussed and the relative magnitude of the term with respect to βv is calculated for a simple barotropic model of the North Pacific Ocean. It is shown that a similar spurious term can also arise with a C grid model.