Internal pressure gradient errors in sigma-coordinate ocean models: The finite volume and weighted approaches

Abstract

Terrain-following (sigma-coordinate) models are widely used. They are often advantageous when dealing with large variations in topography, and give an accurate representation of the bottom and top boundary layers. However, near steep topography, the use of these coordinates can lead to a large error in the internal pressure gradient force. Using finite differences is the traditional way of discretising the equations. However, it is possible to integrate over horizontal cells by using a finite volume approach instead. In this work, we will interpret the traditional computation of the internal pressure in the Princeton Ocean Model (Blumberg and Mellor, 1987) as a finite volume method. We will include additional points in the computantional stencil and derive higher order finite volume methods. The standard 2nd order POM method will also be combined with the rotated grid approach from Thiem and Berntsen, 2006. We will investigate the possibility of using an 'optimal weighting', with weights that depend on the topography, the stratification, and the grid size. All methods will be applied to an idealised test case - the seamount problem.