68
STEPHEN GRIFFIES
For a fluid with a linear equation of state, the horizontal pressure
gradient can be easily represented.
For an adiabatic fluid, the volume (for a Boussinesq fluid) or mass
(for a non-Boussinesq fluid) between isopycnals is conserved.
Some of the disadvantages are the following:
Representing the effects of a realistic (nonlinear) equation of state
is cumbersome.
The thermal wind balance is based on in situ density, not potential
density. Hence, the further away from the reference pressure, the
less accurate the pressure gradient force can be represented solely
by the isopycnal gradient of the Montgomery.
An isopycnal coordinate is inappropriate for regions where density becomes unstratified, such as mixed layers or deep convection
regions.
Figure 13 illustrates isopycnal surfaces for a section in the model used
to generate Figures 11 and 12.
6.4
Two algorithms
Adcroft and Hallberg, 2004 distinguish two classes of algorithms used
to update the model state: quasi-Eulerian and quasi-Lagrangian. The
main distinguishing characteristic of these algorithms is how they compute the dia-surface velocity component (Section 2.5). The two algorithm classes have traditionally been associated with two classes of vertical coordinates.
Quasi-Eulerian algorithms diagnose their vertical velocity component from the continuity equation. Geopotential and sigma models
have traditionally employed this approach.
Quasi-Lagrangian algorithms set the vertical velocity component
based on specified constraints, and they update the thickness betwen layers via the continuity equation to prognostically move layers around. Isopycnal vertical coordinate models typically use this
approach. For example, adiabatic simulations with isopycnal coordinates set the diapycnal velocity component to zero, thus exactly preserving the integrity of the chosen density classes. For
non-adiabatic simulations, the diapycnal flux is based on parameterizations of diabatic processes such as arise from the nonlinear
equation of state or small scale mixing. A summary of these ideas
STEPHEN GRIFFIES
For a fluid with a linear equation of state, the horizontal pressure
gradient can be easily represented.
For an adiabatic fluid, the volume (for a Boussinesq fluid) or mass
(for a non-Boussinesq fluid) between isopycnals is conserved.
Some of the disadvantages are the following:
Representing the effects of a realistic (nonlinear) equation of state
is cumbersome.
The thermal wind balance is based on in situ density, not potential
density. Hence, the further away from the reference pressure, the
less accurate the pressure gradient force can be represented solely
by the isopycnal gradient of the Montgomery.
An isopycnal coordinate is inappropriate for regions where density becomes unstratified, such as mixed layers or deep convection
regions.
Figure 13 illustrates isopycnal surfaces for a section in the model used
to generate Figures 11 and 12.
6.4
Two algorithms
Adcroft and Hallberg, 2004 distinguish two classes of algorithms used
to update the model state: quasi-Eulerian and quasi-Lagrangian. The
main distinguishing characteristic of these algorithms is how they compute the dia-surface velocity component (Section 2.5). The two algorithm classes have traditionally been associated with two classes of vertical coordinates.
Quasi-Eulerian algorithms diagnose their vertical velocity component from the continuity equation. Geopotential and sigma models
have traditionally employed this approach.
Quasi-Lagrangian algorithms set the vertical velocity component
based on specified constraints, and they update the thickness betwen layers via the continuity equation to prognostically move layers around. Isopycnal vertical coordinate models typically use this
approach. For example, adiabatic simulations with isopycnal coordinates set the diapycnal velocity component to zero, thus exactly preserving the integrity of the chosen density classes. For
non-adiabatic simulations, the diapycnal flux is based on parameterizations of diabatic processes such as arise from the nonlinear
equation of state or small scale mixing. A summary of these ideas