New vertical coordinate

The 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 System

For the simple level coordinate system, we allow various options for the representing the bathymetry.

+Bathtype 0 : pure level model
+Bathtype 1 : partial cell, no smaller then +Bath_fac of level thickness, no larger than full cell
+Bathtype 2 : partial cell, unlimited
+Bathtype 3 : partial cell in last level only

Hybrid Coordinate System

For 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
variable depth mixed layer patched to z levels using intermediate sigma levels z levels which can intersect topography		In this example, `Nz = 6` and `Nsigma = 4` (i.e., upper 4 layers are of variable thickness)

The major difference between vertical discretizations of this version and previous versions is the relative placement of the z value for each layer. In the previous versions, z, the distance from the surface of a layer, was assumed to be at the center of the layer. In this version, the layer interface is centered between z values. In the above diagram, the solid blue lines are the layer interfaces, and the dashed magenta lines are the z surfaces for each layer. The new configuration can be seen by looking at layer 5. The implication of this is that vertical derivatives, which are computed at layer interfaces are now centered differences, leading to an improved discretization.

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.