A sigma-coordinate primitive equation model for studying the circulation in the South Atlantic. Part I: Model configuration with error estimates

This paper describes the configuration of a topography-following (sigma) coordinate, numerical ocean model for studying the circulation in the South Atlantic. An analysis is performed (i) to ensure that the model configuration does not introduce a numerical bias in the model solution and (ii) to give estimates of numerical errors. The model is the Semi-spectral Primitive Equation Model (SPEM) from Rutgers University (Haidvogel et al., 1991). Two important issues relating to the sigma-coordinate are investigated: the pressure gradient calculation and the diffusion of tracers. Errors in the pressure gradient calculation are investigated by simulating an ocean at rest, and the choice is made to reduce errors by smoothing the bathymetry. A smoothing criterion is derived that permits a limitation of the errors in the pressure gradient calculation to an acceptable level (i.e. maximum errors on velocities below a millimeter per second). It is applied to define the model bottom topography. Errors in the tracer fields, induced by a diffusion scheme operating along constant sigma surfaces, generates large unrealistic velocities (of the order of 10 cm/s). A rotation of the diffusion tensor into geopotential coordinates is proposed. Tests show that errors are then reduced to an insignificant level. The rotation of the diffusion tensor is therefore retained. The numerical treatment of the open boundaries and the flux conditions that yields the most realistic circulation is also described. Open boundary conditions are based on radiation conditions and relaxation to climatology. They appear to be numerically robust, and to be able to bring into the South Atlantic basin the necessary information from the outer oceans. A configuration of the SPEM model to study the large scale circulation in the South Atlantic is then obtained. Errors due to model configuration are shown to be small compared to the signal one wants to simulate, and their spatial pattern is known, which will facilitate the interpretation of the model simulations presented in following papers.