Internal pressure errors in sigma-coordinate ocean models due to anisotropy

Abstract

Sigma-coordinate ocean models, or models based on more generalized topography following coordinate systems, are presently widely used in oceanographic studies. Terrain following models are attractive because of their abilities to resolve the surface and bottom layers. However, the internal pressure gradient estimation is problematic in such models, and artificial pressure gradients may create artificial flow. In fine resolution studies where topography and stratification is well resolved, the artificial flow due to erroneous pressure gradients is small because the errors typically converge to zero with the square of the grid size. In coarse resolution studies, however, there may still be large erroneous pressure gradients that may create strong artificial flow. To avoid this, larger horizontal viscosities than one would like to apply from physical considerations, are often applied. This means that smaller scale phenomena in the flow will be poorly represented. The response of the flow to the pressure errors in long time simulations with low horizontal viscosity is very important and different ways to reduce these pressure errors have been suggested. The present study focus on how the grid orientation affect the internal pressure errors in sigma-coordinate ocean models. It is shown that if the internal pressure gradients are computed both along the original axes and along coordinate axes that are rotated 45° to the original axes, the erroneous velocities are substantially reduced if the two internal pressure gradient estimates are averaged properly.