124
RAINER BLECK
coordinate models in suppressing certain types of truncation errors.The
newfound flexibility gives the user more choices in tayloring a model
to specific physical situations, but it also means that far more experimentation is required to establish optimal model configurations than is
necessary in the case of the x, y, z model class.
One example is vertical resolution. Because changes in the number
or depth of coordinate surfaces in an x, y, z model often require elaborate adjustment of the model bathymetry, the grid layout in such models typically remains frozen long enough to allow thorough “tuning”
of subgrid-scale physics parameterizations. In hybrid coordinate layer
models, changing vertical resolution is a matter of changing a few parameters like target densities and minimum layer thicknesses. Consequently,
hybrid model users are more likely to experiment with different vertical
resolutions, a degree of freedom whose exploitation can have unintended
consequences for subgrid-scale closure schemes.
The advantages offered by a hybrid vertical coordinate do not come
without a price. Foremost among the complexities introduced by variable-depth layer models is the need to cast transport equations in flux
form and to use relatively complex lateral transport operators that maintain the physical integrity of mass field tracers in situations characterized
by strong (order-one) changes in layer thickness.
Another concern is the potential in hybrid-coordinate models for excessive vertical diffusion caused by the dispersive character of vertical
advection schemes. If left uncontrolled, this diffusion can exceed that
found in z coordinate models, for the simple reason that interlayer mass
exchange can be much larger than the vertical transport rate seen in
fixed-grid models. Limiting “capricious” interface movement, which according to (1) will spawn a compensating generalized vertical velocity
of similar magnitude, therefore is an important step toward controlling
vertical diffusion. Experiments to be reported elsewhere have shown
that this diffusion is particularly noticeable in the transition zone between the isopycnic and fixed-depth coordinate subdomains, especially
if the grid generator is unable to prevent abrupt vertical changes in layer
thickness in the transition zone.
The areas of concern just mentioned must be weighed against the
unquestionable advantages of the ALE-type vertical coordinate. Some
of these advantages, listed here in no particular order, are
substantial reduction of numerically induced diapycnal fluxes due
to the presence of a sizable isopycnic subdomain;
a larger isopycnic subdomain than can be achieved by other, more
traditional “hybrid” coordinate schemes;
z-
RAINER BLECK
coordinate models in suppressing certain types of truncation errors.The
newfound flexibility gives the user more choices in tayloring a model
to specific physical situations, but it also means that far more experimentation is required to establish optimal model configurations than is
necessary in the case of the x, y, z model class.
One example is vertical resolution. Because changes in the number
or depth of coordinate surfaces in an x, y, z model often require elaborate adjustment of the model bathymetry, the grid layout in such models typically remains frozen long enough to allow thorough “tuning”
of subgrid-scale physics parameterizations. In hybrid coordinate layer
models, changing vertical resolution is a matter of changing a few parameters like target densities and minimum layer thicknesses. Consequently,
hybrid model users are more likely to experiment with different vertical
resolutions, a degree of freedom whose exploitation can have unintended
consequences for subgrid-scale closure schemes.
The advantages offered by a hybrid vertical coordinate do not come
without a price. Foremost among the complexities introduced by variable-depth layer models is the need to cast transport equations in flux
form and to use relatively complex lateral transport operators that maintain the physical integrity of mass field tracers in situations characterized
by strong (order-one) changes in layer thickness.
Another concern is the potential in hybrid-coordinate models for excessive vertical diffusion caused by the dispersive character of vertical
advection schemes. If left uncontrolled, this diffusion can exceed that
found in z coordinate models, for the simple reason that interlayer mass
exchange can be much larger than the vertical transport rate seen in
fixed-grid models. Limiting “capricious” interface movement, which according to (1) will spawn a compensating generalized vertical velocity
of similar magnitude, therefore is an important step toward controlling
vertical diffusion. Experiments to be reported elsewhere have shown
that this diffusion is particularly noticeable in the transition zone between the isopycnic and fixed-depth coordinate subdomains, especially
if the grid generator is unable to prevent abrupt vertical changes in layer
thickness in the transition zone.
The areas of concern just mentioned must be weighed against the
unquestionable advantages of the ALE-type vertical coordinate. Some
of these advantages, listed here in no particular order, are
substantial reduction of numerically induced diapycnal fluxes due
to the presence of a sizable isopycnic subdomain;
a larger isopycnic subdomain than can be achieved by other, more
traditional “hybrid” coordinate schemes;
z-