64
STEPHEN GRIFFIES
deeper than the ocean bottom (i.e., so long as q > - H ) , then all cells
remain nonvanishing. l6
In addition to not worrying about vanishing grid cells, some key advantages of sigma models are the following.
They provide a natural framework to represent bottom influenced
flow and to parameterize bottom boundary layer processes.
Thermodynamic effects associated with the equation of state are
well represented.
However, some of the disadvantages are the following:
As with the x-models, the representation of the quasi-adiabatic interior is cumbersome due to numerical truncation errors inducing
unphysically large levels of spurious mixing, especially in the presence of vigorous mesoscale eddies. Parameterization of these processes using neutral physics schemes may be more difficult numerically than in the x-models. The reason is that neutral directions
generally have slopes less than 1/100 relative to the horizontal, but
can have order unity slopes relative to sigma surfaces. The larger
relative slopes precludes the small slope approximation commonly
made with x-model implementations of neutral physics. The small
slope approximation provides for simplification of the schemes, and
improves computational efficiency.
Sigma models have difficulty accurately representing the horizontal
pressure gradient in the presence of realistic topography, where
slopes are commonly larger than 1/100.
Although there are regional simulations using terrain following models, Griffies et al., 2000a notes that there are few examples of global
climate models running with this vertical coordinate. Diansky et al.,
2002 is the only exception known to the author. This situation is largely
due to problems representing realistic topography without incurring unacceptable pressure gradient errors, as well as difficulties implementing
parameterizations of neutral physical processes. There are notable efforts to resolve these problems, such as the pressure gradient work of
Shchepetkin and McWilliams, 2002. Continued efforts along these lines
may soon facilitate the more common use of terrain following coordinates
for global ocean climate modelling.
161f q < -H, besides drying up a region of ocean, the specific thickness z,s = H + q changes
sign, which signals a singularity in the vertical grid definition. The same problem occurs for
the z* coordinate.
STEPHEN GRIFFIES
deeper than the ocean bottom (i.e., so long as q > - H ) , then all cells
remain nonvanishing. l6
In addition to not worrying about vanishing grid cells, some key advantages of sigma models are the following.
They provide a natural framework to represent bottom influenced
flow and to parameterize bottom boundary layer processes.
Thermodynamic effects associated with the equation of state are
well represented.
However, some of the disadvantages are the following:
As with the x-models, the representation of the quasi-adiabatic interior is cumbersome due to numerical truncation errors inducing
unphysically large levels of spurious mixing, especially in the presence of vigorous mesoscale eddies. Parameterization of these processes using neutral physics schemes may be more difficult numerically than in the x-models. The reason is that neutral directions
generally have slopes less than 1/100 relative to the horizontal, but
can have order unity slopes relative to sigma surfaces. The larger
relative slopes precludes the small slope approximation commonly
made with x-model implementations of neutral physics. The small
slope approximation provides for simplification of the schemes, and
improves computational efficiency.
Sigma models have difficulty accurately representing the horizontal
pressure gradient in the presence of realistic topography, where
slopes are commonly larger than 1/100.
Although there are regional simulations using terrain following models, Griffies et al., 2000a notes that there are few examples of global
climate models running with this vertical coordinate. Diansky et al.,
2002 is the only exception known to the author. This situation is largely
due to problems representing realistic topography without incurring unacceptable pressure gradient errors, as well as difficulties implementing
parameterizations of neutral physical processes. There are notable efforts to resolve these problems, such as the pressure gradient work of
Shchepetkin and McWilliams, 2002. Continued efforts along these lines
may soon facilitate the more common use of terrain following coordinates
for global ocean climate modelling.
161f q < -H, besides drying up a region of ocean, the specific thickness z,s = H + q changes
sign, which signals a singularity in the vertical grid definition. The same problem occurs for
the z* coordinate.