HYBRID VERTICAL COORDINATES
113
ent in the ALE concept allows it to maximize the size of the isopycnic
subdomain in the model. This is a major advantage.
2.
The grid generator
At the core of ALE-type hybrid models is a utility called the vertical grid generator. Most efforts to produce a robust hybrid model are
directed at refining and "shockproofing" this unique utility. A thorough discussion of the grid generator used in HYCOM is therefore in
order. For the convenience of the reader, some details already presented
in Bleck (2002) will be repeated here, but emphasis will be on recent
improvements.
Models like HYCOM belong to the so-called layer model class where,
as mentioned earlier in the context of isopycnic-coordinate models, the
depth z of coordinate surfaces is treated as a dependent variable.' Having lost z as independent variable, layer models need a new independent
variable capable of representing the 3rd (vertical) model dimension. This
variable is traditionally called "s" .
With the number of unknowns increased by one (namely, layer interface depth), the model needs one additional diagnostic equation. The
logical choice is an equation linking s to the other model variables. In
purely isopycnic coordinate models, s is equated with potential density.
In ALE-type hybrid ocean models, s becomes a "target" potential density value assigned to each coordinate layer. The grid generator's task is
to move the coordinate layer toward the depth where the target density
is observed to occur. Once a layer is aligned with its target isopycnal, it
becomes a material layer whose subsequent evolution is no longer governed by the grid generator until interior mixing or surface thermohaline
forcing cause the density to drift away from its target value.
If the target density lies outside the density range in the water column, the layer set in motion by the grid generator will encounter the
sea surface or sea floor before finding its target density, depending on
whether the target density lies below or above the density range found
in the column. Instead of rendering layers whose target density does not
exist dynamically invisible by deflating them, the grid generator is designed to impose a minimum layer thickness. This constraint also affects
layers which during their vertical migration impinge on layers already
converted to fixed-depth layers.
'MICOM and HYCOM actually express layer depth in terms of pressure p, the weight per
unit area of the water column. Replacing z by p simplifies matters if the vertical model
dimension is expressed in terms of a thermodynamic variable. This also means that the
Boussinesq approximation is not needed in these models.
113
ent in the ALE concept allows it to maximize the size of the isopycnic
subdomain in the model. This is a major advantage.
2.
The grid generator
At the core of ALE-type hybrid models is a utility called the vertical grid generator. Most efforts to produce a robust hybrid model are
directed at refining and "shockproofing" this unique utility. A thorough discussion of the grid generator used in HYCOM is therefore in
order. For the convenience of the reader, some details already presented
in Bleck (2002) will be repeated here, but emphasis will be on recent
improvements.
Models like HYCOM belong to the so-called layer model class where,
as mentioned earlier in the context of isopycnic-coordinate models, the
depth z of coordinate surfaces is treated as a dependent variable.' Having lost z as independent variable, layer models need a new independent
variable capable of representing the 3rd (vertical) model dimension. This
variable is traditionally called "s" .
With the number of unknowns increased by one (namely, layer interface depth), the model needs one additional diagnostic equation. The
logical choice is an equation linking s to the other model variables. In
purely isopycnic coordinate models, s is equated with potential density.
In ALE-type hybrid ocean models, s becomes a "target" potential density value assigned to each coordinate layer. The grid generator's task is
to move the coordinate layer toward the depth where the target density
is observed to occur. Once a layer is aligned with its target isopycnal, it
becomes a material layer whose subsequent evolution is no longer governed by the grid generator until interior mixing or surface thermohaline
forcing cause the density to drift away from its target value.
If the target density lies outside the density range in the water column, the layer set in motion by the grid generator will encounter the
sea surface or sea floor before finding its target density, depending on
whether the target density lies below or above the density range found
in the column. Instead of rendering layers whose target density does not
exist dynamically invisible by deflating them, the grid generator is designed to impose a minimum layer thickness. This constraint also affects
layers which during their vertical migration impinge on layers already
converted to fixed-depth layers.
'MICOM and HYCOM actually express layer depth in terms of pressure p, the weight per
unit area of the water column. Replacing z by p simplifies matters if the vertical model
dimension is expressed in terms of a thermodynamic variable. This also means that the
Boussinesq approximation is not needed in these models.