50
STEPHEN GRIFFIES
In general, it is not possible to make this identification. Instead, we
must settle for the general expression
The above results lead to the thickness weighted tracer budget for the
ocean surface grid cell
and the corresponding mass budget
3.6
Surface boundary condition for salt
We close this section by mentioning the free ocean surface boundary
condition for salt and other material tracers. Salt is transferred into
the ocean with brackish river water and ice melt of nonzero salinity.
Yet evaporation and precipitation generally leave the salt content of the
ocean unchanged. In these latter cases, the boundary layer tracer flux
(85) vanishes
salt) = 0.
(90)
This trivial boundary condition is also appropriate for many other material tracers, such as those encountered with ocean biogeochemical processes. In these cases, the tracer concentration is not altered via the
passage of tracer across the surface. Instead, it is altered via the transport of fresh water across the ocean free surface which acts to dilute or
concentrate the tracer.
The boundary condition (90) is often replaced in ocean models by a
virtual tracer flux condition, whereby tracer is transferred into the model
in lieu of altering the ocean water mass via the transport of fresh water. Virtual tracer flux boundary conditions are required for rigid lid
models (Bryan, 1969) that maintain a constant volume and so cannot
incorporate surface fresh water fluxes. However, there remain few rigid
lid models in use today, and there is no reason to maintain the virtual
tracer flux in the more commonly used free surface models. The differences in solution may be minor for many purposes, especially short
STEPHEN GRIFFIES
In general, it is not possible to make this identification. Instead, we
must settle for the general expression
The above results lead to the thickness weighted tracer budget for the
ocean surface grid cell
and the corresponding mass budget
3.6
Surface boundary condition for salt
We close this section by mentioning the free ocean surface boundary
condition for salt and other material tracers. Salt is transferred into
the ocean with brackish river water and ice melt of nonzero salinity.
Yet evaporation and precipitation generally leave the salt content of the
ocean unchanged. In these latter cases, the boundary layer tracer flux
(85) vanishes
salt) = 0.
(90)
This trivial boundary condition is also appropriate for many other material tracers, such as those encountered with ocean biogeochemical processes. In these cases, the tracer concentration is not altered via the
passage of tracer across the surface. Instead, it is altered via the transport of fresh water across the ocean free surface which acts to dilute or
concentrate the tracer.
The boundary condition (90) is often replaced in ocean models by a
virtual tracer flux condition, whereby tracer is transferred into the model
in lieu of altering the ocean water mass via the transport of fresh water. Virtual tracer flux boundary conditions are required for rigid lid
models (Bryan, 1969) that maintain a constant volume and so cannot
incorporate surface fresh water fluxes. However, there remain few rigid
lid models in use today, and there is no reason to maintain the virtual
tracer flux in the more commonly used free surface models. The differences in solution may be minor for many purposes, especially short