24
STEPHEN GRIFFIES
virtual tracer methods of the rigid lid. Nonetheless, virtual tracer
fluxes remain one of the unnecessary legacy approximations plaguing some modern ocean models using free surface methods. The
potential problems with virtual tracer fluxes are enhanced as the
time scales of the integration go to the decade to century climate
scale.
What is the desired manner to write the discrete momentum equation: advective, as commonly done in B-grid models, or vector invariant, as commonly in C-grid models? The answer to this question may be based more on subjective notions of elegance than
clear numerical advantage.
How accurate should the thermodynamics be, such as the equation
of state and the model’s “heat” tracer? The work of McDougall
and collaborators provides some guidance on these questions (McDougall, 2003, McDougall et al., 2003, Jackett et al., 2004). How
important is it to get these things accurate? The perspective taken
here is that it is useful to be more accurate and flexible with present
day ocean climate models, since the temperature and salinity range
over which they are used is quite wide, thus making the older approximations less valid. Additionally, many of the more accurate
approaches have been refined to reduce their costs, thus making
their use nearly painless.
After deciding on a set of model equations, further questions arise
concerning how to cast the continuum partial differential equations onto
a finite grid. First, we ask questions about the vertical coordinates.
Which one to use?
Geopotential (z-coordinate): This coordinate is natural for Boussinesq or volume conserving kinematics and is most commonly used
in present-day global ocean climate models.
Pressure: This coordinate is natural for non-Boussinesq or mass
conserving kinematics and is commonly used in atmospheric models. As mentioned earlier, the isomorphism between pressure and
depth allow for a straightforward transformation of depth coordinates to pressure coordinates, thus removing the Boussinesq approximation from having any practical basis. We return to this
point in Section 6.
Terrain following sigma coordinates: This coordinate is commonly
used for coastal and estuarine models, with some recent efforts
aimed as using it for global modelling (Diansky et al., 2002).
STEPHEN GRIFFIES
virtual tracer methods of the rigid lid. Nonetheless, virtual tracer
fluxes remain one of the unnecessary legacy approximations plaguing some modern ocean models using free surface methods. The
potential problems with virtual tracer fluxes are enhanced as the
time scales of the integration go to the decade to century climate
scale.
What is the desired manner to write the discrete momentum equation: advective, as commonly done in B-grid models, or vector invariant, as commonly in C-grid models? The answer to this question may be based more on subjective notions of elegance than
clear numerical advantage.
How accurate should the thermodynamics be, such as the equation
of state and the model’s “heat” tracer? The work of McDougall
and collaborators provides some guidance on these questions (McDougall, 2003, McDougall et al., 2003, Jackett et al., 2004). How
important is it to get these things accurate? The perspective taken
here is that it is useful to be more accurate and flexible with present
day ocean climate models, since the temperature and salinity range
over which they are used is quite wide, thus making the older approximations less valid. Additionally, many of the more accurate
approaches have been refined to reduce their costs, thus making
their use nearly painless.
After deciding on a set of model equations, further questions arise
concerning how to cast the continuum partial differential equations onto
a finite grid. First, we ask questions about the vertical coordinates.
Which one to use?
Geopotential (z-coordinate): This coordinate is natural for Boussinesq or volume conserving kinematics and is most commonly used
in present-day global ocean climate models.
Pressure: This coordinate is natural for non-Boussinesq or mass
conserving kinematics and is commonly used in atmospheric models. As mentioned earlier, the isomorphism between pressure and
depth allow for a straightforward transformation of depth coordinates to pressure coordinates, thus removing the Boussinesq approximation from having any practical basis. We return to this
point in Section 6.
Terrain following sigma coordinates: This coordinate is commonly
used for coastal and estuarine models, with some recent efforts
aimed as using it for global modelling (Diansky et al., 2002).