Hybridization between σ- andz-co-ordinates for improving the internal pressure gradient calculation in marine models with steep bottom slopes

It is discussed in this paper how the pressure gradient error in general vertical co-ordinate models (in which the σ-transformation is a special case) can be reduced by means of hybrid models. For a better understanding, the derivation of such a general vertical co-ordinate model from the Cartesian co-ordinate model is given. Two types of hybridization between σ- and z-co-ordinate models, each using one parameter specifying the degree of hydridization, are presented: (i) the mixed layer transformation with a constant number of layers which are refined near the surface and (ii) the z/σ-transformation which introduces steps near the bottom. In order to achieve good results with the models using other than σ-co-ordinates, a profile-conserving momentum advection discretization is developed. The different co-ordinate transformations are tested with 2D barotropic and baroclinic flows over a topographic bump. Those models with nearly horizontal co-ordinate surfaces in the stratified area give the best correspondence with an isopycnal reference solution.