60
STEPHEN GRIFFIES
bottom face. This is a very inconvenient feature that limits the use
of z-coordinates.15 In particular, the following studies may require very
refined vertical resolution and/or large undulations of the surface height,
and so would not be accessible with a conventional free surface z-model.
Process studies of surface mixing and biological cycling may warrant very refined upper ocean grid cell thickness, some as refined
as lm.
Realistic tidal fluctuations in some parts of the World Ocean can
reach 10m-20m.
Coastal models tend to require refined vertical resolution to represent shallow coastal processes along the continental shelves and
near-shore.
When coupled to a sea ice model, the weight of the ice will depress
the ocean free surface.
An example of depth coordinates.
In some of the following
discussion, we illustrate aspects of vertical coordinates by diagnosing
values for the coordinates from a realistic z-model run with partial step
thicknesses. Partial steps have arbitrary thickness which are set to accurately represent the bottom topography. The partial step technology
was introduced by Adcroft et al., 1997 in the C-grid MITgcm, and further discussed by Pacanowski and Gnanadesikan, 1998 for the B-grid
Modular Ocean Model (MOM). Figure 10 compares the representation
of topography in a z-model using partial steps as realized in the MOM
code of Griffies et al., 2004. Many z-models have incorporated the partial step technology as it provides an important facility to accurately
represent flow and waves near topography.
In the representation of bottom topography, there is an artificial distinction between a vertical face of a cell and its horizontal top and bottom faces. There is no such distinction in the real ocean. As noted
in Anne Marie Treguier's lectures at this school, the block structure of
topography in z-models has the potential to affect the level of bottom
friction. The effects on bottom friction come in by noting that for a
C-grid, it is straightforward to run with free-slip side walls as well as
bottom faces. In contrast, B-grids use a no-slip side wall and free slip
151inearized free surfaces, in which the budgets for tracer and momentum are formulated
assuming a constant top cell thickness, avoid problems with vanishing top cells. However,
such models do not conserve total tracer or volume in the presence of a surface fresh water
flux (see Griffies et al., 2001, Campin et al., 2004 for discussion).
STEPHEN GRIFFIES
bottom face. This is a very inconvenient feature that limits the use
of z-coordinates.15 In particular, the following studies may require very
refined vertical resolution and/or large undulations of the surface height,
and so would not be accessible with a conventional free surface z-model.
Process studies of surface mixing and biological cycling may warrant very refined upper ocean grid cell thickness, some as refined
as lm.
Realistic tidal fluctuations in some parts of the World Ocean can
reach 10m-20m.
Coastal models tend to require refined vertical resolution to represent shallow coastal processes along the continental shelves and
near-shore.
When coupled to a sea ice model, the weight of the ice will depress
the ocean free surface.
An example of depth coordinates.
In some of the following
discussion, we illustrate aspects of vertical coordinates by diagnosing
values for the coordinates from a realistic z-model run with partial step
thicknesses. Partial steps have arbitrary thickness which are set to accurately represent the bottom topography. The partial step technology
was introduced by Adcroft et al., 1997 in the C-grid MITgcm, and further discussed by Pacanowski and Gnanadesikan, 1998 for the B-grid
Modular Ocean Model (MOM). Figure 10 compares the representation
of topography in a z-model using partial steps as realized in the MOM
code of Griffies et al., 2004. Many z-models have incorporated the partial step technology as it provides an important facility to accurately
represent flow and waves near topography.
In the representation of bottom topography, there is an artificial distinction between a vertical face of a cell and its horizontal top and bottom faces. There is no such distinction in the real ocean. As noted
in Anne Marie Treguier's lectures at this school, the block structure of
topography in z-models has the potential to affect the level of bottom
friction. The effects on bottom friction come in by noting that for a
C-grid, it is straightforward to run with free-slip side walls as well as
bottom faces. In contrast, B-grids use a no-slip side wall and free slip
151inearized free surfaces, in which the budgets for tracer and momentum are formulated
assuming a constant top cell thickness, avoid problems with vanishing top cells. However,
such models do not conserve total tracer or volume in the presence of a surface fresh water
flux (see Griffies et al., 2001, Campin et al., 2004 for discussion).