SOME OCEAN MODEL FUNDAMENTALS
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change drastically at scales larger than 1km, or do the hydrostatic
models parameterize non-hydrostatic processes sufficiently well for
most applications at these scales? Note that the accuracy of the
hydrostatic approximation scales as the squared flow aspect ratio
(ratio of vertical to horizontal length scales). Atmospheric modelers believe their simulations will be far more realistic with an
explicit representation of non-hydrostatic dynamics, such as convection and cloud boundary layer processes. In contrast, it remains
unclear how necessary non-hydrostatic simulations are for global
ocean climate. Perhaps it will require plenty of experience running non-hydrostatic global models before we have unambiguous
answers.
Should the kinematics be based on incompressible volume conserving fluid parcels, as commonly assumed for ocean models using the Boussinesq approximation, or should the more accurate
mass conserving kinematics of the non-Boussinesq fluid be used, as
commonly assumed for the more compressible atmosphere. Ocean
model designers are moving away from the Boussinesq approximation since only a mass conserving fluid can directly represent
sea level changes due to steric effects (see Section 3.4.3 of Griffies,
2004), and because it is simple to use mass conserving kinematics
by exploiting the isomorphisms between depth and pressure discussed by DeSzoeke and Samelson, 2002, Marshall et al., 2003, and
Losch et al., 2004.
Can the upper ocean surface be fixed in time with a rigid lid, as
proposed decades ago by Bryan, 1969 and used for many years, or
should it be allowed to fluctuate with a more realistic free surface
so to provide a means to pass fresh water across the ocean surface
and to represent tidal fluctuations? Most models today employ a
free surface in order to remove the often unacceptable restrictions
of the rigid lid. Additionally, many free surface methods remove
elliptic problems from hydrostatic models. The absence of elliptic
problems from the free surface models greatly enhances their computational efficiency on parallel computers (Griffies et al., 2001).
Should tracers, such as salt, be passed across the ocean surface via
virtual tracer fluxes, as required for rigid lid models, or should the
model employ real water fluxes thus allowing for a natural dilution
and concentration of tracer upon precipitation and evaporation, respectively? As discussed more fully in Section 3.6, the advent of
free surface methods allows for modelers to jettison the unphysical
23
change drastically at scales larger than 1km, or do the hydrostatic
models parameterize non-hydrostatic processes sufficiently well for
most applications at these scales? Note that the accuracy of the
hydrostatic approximation scales as the squared flow aspect ratio
(ratio of vertical to horizontal length scales). Atmospheric modelers believe their simulations will be far more realistic with an
explicit representation of non-hydrostatic dynamics, such as convection and cloud boundary layer processes. In contrast, it remains
unclear how necessary non-hydrostatic simulations are for global
ocean climate. Perhaps it will require plenty of experience running non-hydrostatic global models before we have unambiguous
answers.
Should the kinematics be based on incompressible volume conserving fluid parcels, as commonly assumed for ocean models using the Boussinesq approximation, or should the more accurate
mass conserving kinematics of the non-Boussinesq fluid be used, as
commonly assumed for the more compressible atmosphere. Ocean
model designers are moving away from the Boussinesq approximation since only a mass conserving fluid can directly represent
sea level changes due to steric effects (see Section 3.4.3 of Griffies,
2004), and because it is simple to use mass conserving kinematics
by exploiting the isomorphisms between depth and pressure discussed by DeSzoeke and Samelson, 2002, Marshall et al., 2003, and
Losch et al., 2004.
Can the upper ocean surface be fixed in time with a rigid lid, as
proposed decades ago by Bryan, 1969 and used for many years, or
should it be allowed to fluctuate with a more realistic free surface
so to provide a means to pass fresh water across the ocean surface
and to represent tidal fluctuations? Most models today employ a
free surface in order to remove the often unacceptable restrictions
of the rigid lid. Additionally, many free surface methods remove
elliptic problems from hydrostatic models. The absence of elliptic
problems from the free surface models greatly enhances their computational efficiency on parallel computers (Griffies et al., 2001).
Should tracers, such as salt, be passed across the ocean surface via
virtual tracer fluxes, as required for rigid lid models, or should the
model employ real water fluxes thus allowing for a natural dilution
and concentration of tracer upon precipitation and evaporation, respectively? As discussed more fully in Section 3.6, the advent of
free surface methods allows for modelers to jettison the unphysical