SOME OCEAN MODEL FUNDAMENTALS
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bottom face. Hence, depending on the interior viscosity and bottom
stress parameterization, B-grid models will generally have more bottom
friction than C-grid models. With partial steps, the area of the side walls
are reduced, thus reducing the area of no-slip side walls in the B-grid.
The effective bottom friction in the B-grid is therefore less with partial
step topography.
Because of partial steps, the level next to the ocean bottom has grid
cell centers that are generally at different depths. That is, the bottom
cell in a partial step z-model is likened to a sigma-layer. All other cells,
including the surface, have grid cell centers that are at fixed depths.
Figure 11 illustrates the lines of constant partial step depth for this
model.
Figure 10. Comparison of the partial step versus full step representation of topography along the equator as realized in the z-model discussed by Griffies et al., 2005.
The model horizontal grid has one degree latitudinal resolution. The main differences are in the deep ocean in regions where the topographic slope is gradual. Steep
sloped regions, and those in the upper ocean with refined vertical resolution, show
less distinctions.
Depth deviation coordinate.
The depth deviation coordinate
s = z − η removes the restriction on upper ocean grid cell resolution
present with s = z. That is, s = 0 is the time independent coordinate
value of the ocean surface, no matter how much the free surface depresses
or grows. Hence, no surface cells vanish so long as η > −H. However,
−(H + η) ≤ s ≤ 0, and so the bottom of a column is a time dependent
surface. Consequently, by solving the problem at the ocean surface, the
deviation coordinate introduces a problem to the ocean bottom where
bottom cells can now vanish.
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bottom face. Hence, depending on the interior viscosity and bottom
stress parameterization, B-grid models will generally have more bottom
friction than C-grid models. With partial steps, the area of the side walls
are reduced, thus reducing the area of no-slip side walls in the B-grid.
The effective bottom friction in the B-grid is therefore less with partial
step topography.
Because of partial steps, the level next to the ocean bottom has grid
cell centers that are generally at different depths. That is, the bottom
cell in a partial step z-model is likened to a sigma-layer. All other cells,
including the surface, have grid cell centers that are at fixed depths.
Figure 11 illustrates the lines of constant partial step depth for this
model.
Figure 10. Comparison of the partial step versus full step representation of topography along the equator as realized in the z-model discussed by Griffies et al., 2005.
The model horizontal grid has one degree latitudinal resolution. The main differences are in the deep ocean in regions where the topographic slope is gradual. Steep
sloped regions, and those in the upper ocean with refined vertical resolution, show
less distinctions.
Depth deviation coordinate.
The depth deviation coordinate
s = z − η removes the restriction on upper ocean grid cell resolution
present with s = z. That is, s = 0 is the time independent coordinate
value of the ocean surface, no matter how much the free surface depresses
or grows. Hence, no surface cells vanish so long as η > −H. However,
−(H + η) ≤ s ≤ 0, and so the bottom of a column is a time dependent
surface. Consequently, by solving the problem at the ocean surface, the
deviation coordinate introduces a problem to the ocean bottom where
bottom cells can now vanish.