OCEAN MODELS
91
sized. Maps of energy flux have been derived from tidal models leading
to parameterizations of vertical mixing (Laurent et al., 2002)
Spatially variable vertical mixing coefficients based on topographic
roughness or tidal mixing have yet to be tested extensively in models.
Studies by Hasumi and Suginohara (1999) and Simmons et al. (2004)
show modest improvements in coarse resolution models integrated to
equilibrium. The effect of such parameterizations over shorter time
scales in higher resolution models needs to be assessed, since uniform
mixing coefficients are clearly not acceptable based on the observations.
One has to be aware that z coordinate models have difficulty achieving
the vertical mixing coefficients of order 10 −5 m 2 .s −1 in the thermocline,
depending on their advections scheme (Griffies et al., 2000b). Since
the last decade modellers tend to abandon centered advection schemes,
which lead to the generation of unphysical temperatures and salinities
near fronts (note, for example, that the ATL6 model of Fig. 4 has one
grid point with temperatures lower than -3 ◦ C at the bottom of the Faroe
Bank channel outflow; salinities close to 42 PSU are found downstream
of Gibraltar in the 1/10 ◦ model of Smith et al., 2000). Diffusive schemes
like FCT (Flux Corrected Transport) avoid such problems, but in eddy
permitting z-models they can cause a large amount of diapycnal mixing
(Griffies et al., 2000b). The same is true for non-eddy resolving models
when the western boundary current is marginally resolved: Griffies
et al. (2000b) find spurious diapycnal mixing of 3 10 −4 m 2 .s −1 due to the
advection scheme in that case.
2.4
Double diffusive mixing
Double diffusion occurs in stably stratified situations, either when
warm and salty water overlies cold, fresh water (salt fingering) or when
cold, fresh water overlies warm and salty water (diffusive convection).
Those processes generate turbulent mixing of heat and salt with different
coefficients, dependent on the density ratio R ρ = α∂ z T/β∂ z S, where α
and β are coefficients of thermal expansion and saline contraction. A
parameterization has been proposed by Large et al. (1994) but it has not
been thoroughly tested. A slightly different one has been proposed by
Merryfield et al. (1999) and tested in a coarse resolution model, showing
and improvement in the representation of water mass temperature and
salinity although the effect on the circulation was small. None of the
forecasting models listed in Table 2 uses a parameterization for double
diffusion, even though this dynamical process is important in the ocean
(Schmitt, 1998). A better and cleaner representation of “background”
interior vertical mixing may be needed in z-coordinate models before
91
sized. Maps of energy flux have been derived from tidal models leading
to parameterizations of vertical mixing (Laurent et al., 2002)
Spatially variable vertical mixing coefficients based on topographic
roughness or tidal mixing have yet to be tested extensively in models.
Studies by Hasumi and Suginohara (1999) and Simmons et al. (2004)
show modest improvements in coarse resolution models integrated to
equilibrium. The effect of such parameterizations over shorter time
scales in higher resolution models needs to be assessed, since uniform
mixing coefficients are clearly not acceptable based on the observations.
One has to be aware that z coordinate models have difficulty achieving
the vertical mixing coefficients of order 10 −5 m 2 .s −1 in the thermocline,
depending on their advections scheme (Griffies et al., 2000b). Since
the last decade modellers tend to abandon centered advection schemes,
which lead to the generation of unphysical temperatures and salinities
near fronts (note, for example, that the ATL6 model of Fig. 4 has one
grid point with temperatures lower than -3 ◦ C at the bottom of the Faroe
Bank channel outflow; salinities close to 42 PSU are found downstream
of Gibraltar in the 1/10 ◦ model of Smith et al., 2000). Diffusive schemes
like FCT (Flux Corrected Transport) avoid such problems, but in eddy
permitting z-models they can cause a large amount of diapycnal mixing
(Griffies et al., 2000b). The same is true for non-eddy resolving models
when the western boundary current is marginally resolved: Griffies
et al. (2000b) find spurious diapycnal mixing of 3 10 −4 m 2 .s −1 due to the
advection scheme in that case.
2.4
Double diffusive mixing
Double diffusion occurs in stably stratified situations, either when
warm and salty water overlies cold, fresh water (salt fingering) or when
cold, fresh water overlies warm and salty water (diffusive convection).
Those processes generate turbulent mixing of heat and salt with different
coefficients, dependent on the density ratio R ρ = α∂ z T/β∂ z S, where α
and β are coefficients of thermal expansion and saline contraction. A
parameterization has been proposed by Large et al. (1994) but it has not
been thoroughly tested. A slightly different one has been proposed by
Merryfield et al. (1999) and tested in a coarse resolution model, showing
and improvement in the representation of water mass temperature and
salinity although the effect on the circulation was small. None of the
forecasting models listed in Table 2 uses a parameterization for double
diffusion, even though this dynamical process is important in the ocean
(Schmitt, 1998). A better and cleaner representation of “background”
interior vertical mixing may be needed in z-coordinate models before