90
ANNE-MARIE TREGUIER
the fact that changing tunable constants within one parameterization
package has significant effects (Matteoli, 2003). This lack of thorough
sensitivity studies, especially for eddy permitting models, will stand out
as we discuss the different processes leading to vertical mixing.
2.2
Convection
Early primitive equation models (Cox, 1984) represented convection
by an iterative adjustment, which modified temperature and salinity in
a water column. Adjustment schemes have convergence problems in
some cases and tend to be costly; moreover the time scale of adjustment
is one time step, which is too short in high resolution configurations.
Despite these shortcomings, they are still in use in some forecasting
models (Table 2).
Nowadays convective adjustment is more frequently represented by
increasing the vertical mixing coefficient to a very large value in the
case of convection. This procedure has been found to be a satisfactory
parameterization of the effect of convective plumes by Klinger et al.
(1996), with a mixing coefficient of 10 m 2 .s −1 . Scalings suggest values up
to 50 m 2 .s −1 (Send and K¨ ase, 1998). The PSY2 model uses a coefficient
of 1 m 2 .s −1 (table 2); the ORCA2 model uses 100 m 2 .s −1 . Users of the
KPP scheme take values from 0.1 to 10 m 2 .s −1 .
The criterion for the onset of convection varies among models; convection is active as soon as the Vaisala frequency N 2 is negative in some
models (PSY2) while the criterion in KPP is N 2 < −0.2 10 −4 s −2 . The
relative mixing of momentum and tracers also varies between models.
Momentum should be mixed like tracers in convective plumes if the
time scale t mix for a parcel to move down the plume is shorter than the
1/f , the time for geostrophic adjustment. With plume vertical velocities
w of order 3 to 10 cm/s (Klinger et al., 1996), t mix = h/w reaches 12 h
for deep convection, thus comparable to 1/f . Tests performed with the
ORCA2 model (Matteoli, 2003) show important differences in mean surface velocities (up to 10 cm.s −1 ) in the Antarctic circumpolar current,
with and without momentum mixing in the case of convection.
2.3
Interior mixing
As emphasized in the review by J. Toole (Toole, 1998), observations
have shown increased levels of mixing in the abyss and over rough topography, compared with the low values found in the thermocline by
microstructure measurements and tracer releases. More recently, the
role of internal tides as an energy source for mixing has been empha-
ANNE-MARIE TREGUIER
the fact that changing tunable constants within one parameterization
package has significant effects (Matteoli, 2003). This lack of thorough
sensitivity studies, especially for eddy permitting models, will stand out
as we discuss the different processes leading to vertical mixing.
2.2
Convection
Early primitive equation models (Cox, 1984) represented convection
by an iterative adjustment, which modified temperature and salinity in
a water column. Adjustment schemes have convergence problems in
some cases and tend to be costly; moreover the time scale of adjustment
is one time step, which is too short in high resolution configurations.
Despite these shortcomings, they are still in use in some forecasting
models (Table 2).
Nowadays convective adjustment is more frequently represented by
increasing the vertical mixing coefficient to a very large value in the
case of convection. This procedure has been found to be a satisfactory
parameterization of the effect of convective plumes by Klinger et al.
(1996), with a mixing coefficient of 10 m 2 .s −1 . Scalings suggest values up
to 50 m 2 .s −1 (Send and K¨ ase, 1998). The PSY2 model uses a coefficient
of 1 m 2 .s −1 (table 2); the ORCA2 model uses 100 m 2 .s −1 . Users of the
KPP scheme take values from 0.1 to 10 m 2 .s −1 .
The criterion for the onset of convection varies among models; convection is active as soon as the Vaisala frequency N 2 is negative in some
models (PSY2) while the criterion in KPP is N 2 < −0.2 10 −4 s −2 . The
relative mixing of momentum and tracers also varies between models.
Momentum should be mixed like tracers in convective plumes if the
time scale t mix for a parcel to move down the plume is shorter than the
1/f , the time for geostrophic adjustment. With plume vertical velocities
w of order 3 to 10 cm/s (Klinger et al., 1996), t mix = h/w reaches 12 h
for deep convection, thus comparable to 1/f . Tests performed with the
ORCA2 model (Matteoli, 2003) show important differences in mean surface velocities (up to 10 cm.s −1 ) in the Antarctic circumpolar current,
with and without momentum mixing in the case of convection.
2.3
Interior mixing
As emphasized in the review by J. Toole (Toole, 1998), observations
have shown increased levels of mixing in the abyss and over rough topography, compared with the low values found in the thermocline by
microstructure measurements and tracer releases. More recently, the
role of internal tides as an energy source for mixing has been empha-