A Generalization of a Sigma Coordinate Ocean Model and an Intercomparison of Model Vertical Grids

Abstract

Numerical ocean models increasingly make use of σ — coordinate systems. A paper by Gerdes (1993) shows that these coordinate systems can be more general; he termed the generalized form an “s — coordinate” system. The main advantage of the σ or s — system is that, when cast in a finite difference form, a smooth representation of the bottom topography is obtained; one can also easily incorporate a bottom boundary layer as well as a surface boundary layer in those coordinate systems. This is intuitively appealing and Gerdes has shown that superior numerical results are obtained relative to a z — level system. However, in regions of steep topography and crude resolution — a limiting case would be a seamount represented by a single grid point surrounded by a flat bottom — the so-called sigma coordinate pressure gradient error exists (Haney 1991, Mellor et al. 1994, 1998) and at least locally a z — level coordinate system might be preferred. On the other hand, in a recent study, Bell (1997) has shown that the step structure of z — level models lead to vorticity errors and consequent errors in the barotropic component of the flow which, he reports, cause rather large temperature errors (3 to 4° C) on a 1° x 1° grid of an Atlantic Ocean model after 3 months of integration. And it is difficult to model bottom boundary layers in a z — level model (Winton et al. 1998).