New vertical coordinateThe model can now be used in either a level mode, or as a hybrid level and sigma layer mode. The original Gent-Cane version of this model was reduced gravity, with 'sigma' layers from the free surface to the layer of no motion. In this model, we have switched to a level model with the reduced gravity assumptions replaced by a rigid lid and rigid bottom assumption, with a barotropic stream function solver. The levels can be augmented near the surface with a variable depth mixed layer, patched to the deep levels with intermediate sigma layers. The motivation for this change was our project to study decadal variability in the North Atlantic. This requires modeling the important topographic effects of the sills connecting the North Atlantic to the GIN sea.
Level Coordinate SystemFor the simple level coordinate system, we allow various options for the representing the bathymetry.
Hybrid Coordinate SystemFor the hybrid sigma-z coordinate option, we assume that the mixed layer and topography do not intersect. This is not so great, for example, in the Arctic Ocean, but doesn't unduly upset us in our current work. However, we did not want to abandon Dake's vertical mixing parameterization which requires a variable depth mixed layer. So a hybrid vertical structure was implemented - a variable depth mixed layer, patched to a z-coordinate lower ocean by a predetermined division of the intermediate water into sigma layers.
|Hybrid coordinate system|
patched to z levels using
intermediate sigma levels
z levels which can
In this example,
In order to preserve the condition
we must satisfy the compatibility condition
The remaining degree of freedom was used to place the first value of z in the center of the first layer, so that z(1) = h(1)/2. This allows easy coordinate transformations between h and z.