OCEAN MODELS
101
tion proposes that this effect is best represented using the antisymmetric
part of the diffusion tensor (5), that is, by an additional advection of
the density field. They propose to make this velocity proportional to
the isopycnal slope (a pedagogical presentation of their parameterization is found in Gent et al., 1995). This parameterization was the first
physically-based original parameterization for coarse resolution ocean
model, and as such it has known a rapid success. It certainly improves
the climate model solutions especially in the Antarctic circumpolar current, although too large advective velocities for the GM parameterization
have negative effects there (Speer et al., 2000).
It is useful to consider the parameterizations in the quasigeostrophic
limit (Treguier et al., 1997), in which case GM corresponds to a mixing
of potential vorticity (more precisely, the vortex stretching contribution
to potential vorticity) along isopycnals. Therefore, the coefficient used
for the GM parameterization can be considered as a mixing coefficient
for potential vorticity, while the coefficient used for isopycnal mixing is
relevant to a passive tracer (temperature and salinity anomalies along
isopycnal surfaces). Two-dimensional turbulence emphasizes the similarity between the dynamics of vorticity and passive tracers; although no
similar studies exist with primitive equations in three dimensions there
is no physical argument to justify widely different mixing coefficients
for the two parameterizations. It is thus very surprising to find that
many modellers take coefficients for their GM parameterizations that
are spatially dependent on the level of baroclinic instability as proposed
by Treguier et al. (1997) or Visbeck et al. (1997), thus correctly taking
into account the inhomogeneity of the eddy activity in the ocean, while
they keep the isopycnal mixing coefficient constant. Maybe modellers
are reluctant to seek guidance from the quasi-geostrophic framework
because things are indeed more complex in primitive equations: for example, the GM parameterization as usually implemented is closer to a
mixing of isopycnal depth than to a mixing of potential vorticity.
A most important open question is how to represent the unresolved
part of the mesoscale eddy spectrum in eddy permitting models. First,
it is important to note that the unresolved spectrum varies with latitude.
A typical spatial scale for baroclinic instability is the first Rossby radius
R 1 . Even though model grids are often of Mercator type, refined as the
cosine of latitude, they still fall short of resolving R 1 in the Labrador
Sea and Nordic seas where it can be a few kilometers in winter. Perhaps we should be more precise about what is meant by ”resolving”. A
minimum requirement could be 12 grid points per wavelength (a first
derivative estimated with a second order finite difference scheme still
has 5% error in that case), thus δx < 2πR 1 /12 ≈ R 1 /2. Chanut (2003)
101
tion proposes that this effect is best represented using the antisymmetric
part of the diffusion tensor (5), that is, by an additional advection of
the density field. They propose to make this velocity proportional to
the isopycnal slope (a pedagogical presentation of their parameterization is found in Gent et al., 1995). This parameterization was the first
physically-based original parameterization for coarse resolution ocean
model, and as such it has known a rapid success. It certainly improves
the climate model solutions especially in the Antarctic circumpolar current, although too large advective velocities for the GM parameterization
have negative effects there (Speer et al., 2000).
It is useful to consider the parameterizations in the quasigeostrophic
limit (Treguier et al., 1997), in which case GM corresponds to a mixing
of potential vorticity (more precisely, the vortex stretching contribution
to potential vorticity) along isopycnals. Therefore, the coefficient used
for the GM parameterization can be considered as a mixing coefficient
for potential vorticity, while the coefficient used for isopycnal mixing is
relevant to a passive tracer (temperature and salinity anomalies along
isopycnal surfaces). Two-dimensional turbulence emphasizes the similarity between the dynamics of vorticity and passive tracers; although no
similar studies exist with primitive equations in three dimensions there
is no physical argument to justify widely different mixing coefficients
for the two parameterizations. It is thus very surprising to find that
many modellers take coefficients for their GM parameterizations that
are spatially dependent on the level of baroclinic instability as proposed
by Treguier et al. (1997) or Visbeck et al. (1997), thus correctly taking
into account the inhomogeneity of the eddy activity in the ocean, while
they keep the isopycnal mixing coefficient constant. Maybe modellers
are reluctant to seek guidance from the quasi-geostrophic framework
because things are indeed more complex in primitive equations: for example, the GM parameterization as usually implemented is closer to a
mixing of isopycnal depth than to a mixing of potential vorticity.
A most important open question is how to represent the unresolved
part of the mesoscale eddy spectrum in eddy permitting models. First,
it is important to note that the unresolved spectrum varies with latitude.
A typical spatial scale for baroclinic instability is the first Rossby radius
R 1 . Even though model grids are often of Mercator type, refined as the
cosine of latitude, they still fall short of resolving R 1 in the Labrador
Sea and Nordic seas where it can be a few kilometers in winter. Perhaps we should be more precise about what is meant by ”resolving”. A
minimum requirement could be 12 grid points per wavelength (a first
derivative estimated with a second order finite difference scheme still
has 5% error in that case), thus δx < 2πR 1 /12 ≈ R 1 /2. Chanut (2003)