Preliminary study: Parameterisation of Eddy Transfer Properties in Eddy Permitting Ocean Models Real

1
Preliminary study Parameterisation of Eddy
Transfer Properties in Eddy Permitting Ocean
ModelsRealisation Nick Hall (nick.hall_at_hmg.inpg.
fr), Jérôme Chanut (jerome.chanut_at_hmg.inpg.fr),
Jean-Marc Molines (LEGI)
DRAKKAR
Multi-scale Ocean Modelling Project
Context Mesoscale eddies are only properly
resolved by models with grid spacing less than
about 1/15o. Global ocean models usually not
resolve the eddies at all. In these models the
eddies are parameterised with a diffusion law and
advection of mean properties by the trasformed
Eulerian mean flow (Gent and McWilliams, 1990,
GM). Here we discuss the eddy permitting 1/3o and
1/6o CLIPPER simulations, which to some degree
represent eddy transfer processes explicitly.
Since the representation is incomplete, we
consider how it may be augmented by such
parameterizations.
We show diagnostics from a 20-year 1/6o CLIPPER
integration with repeated-annual-cycle forcing.
Transient eddy fluxes of density are calculated,
leading to eddy sources and sinks of mass, the
eddy advecting velocity and the diffusion
coefficient.
JFM
Eddy density flux

• Transient eddy density fluxes and their
  horizontal divergence are here compared with the
  advecting bolus' velocity v, and the associated
  advection of mean density.
• Negative values correspond to creation of dense
  water. Differences between these two quantities
  derive from vertical eddy fluxes and diapycnal
  transports.
• The divergent eddy flux and the bolus advection
  are broadly comparable, but their annual cycles
  differ.

eddy density flux divergence
AMJ
The diffusion coefficient k has been diagnosed
from the horizontal transient eddy density flux
and mean density gradients using two methods. The
first method includes the effect of the
rotational part of the flux and is exact. The
second method uses only the divergent part of the
flux but assumes that local variations in k are
small. Both methods display considerable noise
and significant areas of negative k.
Bolus velocity
JAS
Bolus advection of mean density
OND
Conclusion
Different eddy diffusivity coefficients k are
appropriate for different regions. The table to
the right shows eddy resolvability as a function
of latitude. At high latitudes there are no
resolved eddy fluxes and a large k is needed.
This would be too diffusive in the Gulf Stream
region. In defining k we must consider the
following 1) Spatial variations in eddy
resolvability by an eddy permitting model. 2)
Spatial variations in diffusivity deduced from
higher resolution runs. 3) Seasonal variations in
diffusivity. The optimal solution may be partial
parameterisation', in which k varies
discontinuously.
Latitude Rossby Radius Grid Size 60oN
10 km 18 km
45oN 20 km
26 km 30oN 40 km
32 km 10oN
90 km 36 km Eddy size and grid
size as a function of latitude for a 1/3o model
1/3
1/15
kgm1200 m2.s-1
kgm800 m2.s-1
kgm400 m2.s-1
kgm0 m2.s-1
A high resolution (1/15o) model of the Labrador
Sea has been embedded in a 1/3o North Atlantic
simulation. The eddies are resolved and they are
responsible for restratification after deep
convection. A mean value of k 800 m2s-1 has
been deduced.
Instantaneous potential temperature at -182m in
the refined model.
Potential temperature (top) and salinity (bottom)
at station Bravo (red star on the figure on the
left) versus time and depth. The 1/3 model is
initialised from the refined model at the
beginning of the last restratification phase
(April). Increasing values of the GM diffusivity
(kgm) are tested against the 1/15 results.
In the 1/3o model, eddies in the Labrador Sea are
not resolved. Restratification is only possible
if the eddies are parameterised. GM experiments
with several values of k show a relatively high
value is needed for restratification.
Density fluxes at 350 m diagnosed from the 1/15
model during restratification.