1. Southern Ocean Fronts and eddies
Rosemary Morrow
LEGOS, Toulouse
Plan :
Monitoring frontal movements in the Southern Ocean with altimetry
(JB Sallee, K. Speer)
Eddy diffusivity in the Southern Ocean from surface drifters and altimetry (JB Sallee, K. Speer, R. Lumpkin)
3) Impact of sub-mesoscale processes (F. D’Ovidio)
4) Constraining coastal models with altimetry (P. DeMey)

2. 1. Fronts
Fronts are generally described by horizontal property gradients (T, S, O2, N2, Dyn ht, etc), either at the surface or subsurface
Dyn height ( altimetry) – SR3 Section
Neutral Density – SR3 Section
Tasmania
Antarctica
Fronts detected in September 1996 – SR3 – between Tasmania and Antarctica
Sokolov and Rintoul, 2004

3. Detecting Southern ocean fronts
Monitor front movements using absolute SL
Strong SLA gradients often peak at absolute sea level contours
ASL = (SLA + mean sea surface)
=>
Gradient of sea surface height for January 1995 SR3 (color), with selected height contours corresponding to
particular fronts
Jets merge and split, strengthen and weaken.
(Sokolov and Rintoul, JMS, 2002; JPO, 2006).
=> Southern Ocean fronts are deep-reaching – can monitor their movements using altimetric absolute sea level

4. Variability of Southern Ocean fronts i) Topographic influence along the circumpolar belt
3. Variabilité frontale
Frequency of SAF occurrence
Variabilité du SAF
SAF Variability:
Mean position +/- 1 STD
Red = low variability
Fronts remain ~fixed
Blue = strong variability :
Fronts move over a large area
Intensity (dh/dy)
Does atmospheric variability impact on the frontal positions in deep basins ?
Sallée et al. - Response of the ACC to atmospheric variability – J. Clim (2008)

5. 3. Variabilité frontale
Variability of the fronts ii) Response to the climate variability : SAM and ENSO
Atmosphere
Ocean
SLP/SAM
SLA/SAM
SLP/ENSO
SLA/ENSO
Sallée et al. - Response of the ACC to atmospheric variability - – J. Clim (2008)

6. Variability of the fronts ii) Response to the climate variability : SAM and ENSO
Covariance of PF and SAM or ENSO
SE Pac
Indian
High frequency :
(<3 month) SAM dominates
Low frequency :
(>1 year) ENSO dominates

7. Variability of the fronts iii) Mechanisms controlling the variability
Meridional Ekman transport anomaly regressed onto SAM :
Indian Ocean : Max Ekman transport SOUTH of the fronts
Response to a positive SAM event (timescale ~2 weeks)
V ekman
Sallée et al. - Response of the ACC to atmospheric variability -

8. Variability of the fronts iii) Mechanisms controlling the variability
SE Pacific basin : Max Ekman transport NORTH of fronts
Response to a positive SAM event (timescale ~2 weeks)
V ekman
Sallée et al. - Response of the ACC to atmospheric variability -

9. Fronts – future with SWOT
- Altimetry is important for monitoring subsurface frontal movements
Currently using gridded AVISO maps (limited by the optimal interpolation scales : spatial : km at mid to high latitude, temporal : days)
Hydrographic Fronts will have geostrophic adjustment at surface
Need to resolve the Rossby radius :
10-20 km at high latitude
> 3-5 days
=> Measurements every 3-5 km

10. Eddy Diffusion and the Southern Ocean mixed layer heat budget2.
J.B. Sallee, K. Speer, R. Morrow, R. Lumpkin (JMR submitted, 2008)

11. Calculating Eddy Diffusion
Effective Diffusivity (Taylor, 1921) :
In well-sampled homogeneous turbulence, k ~ constant after several integral time-scales
T is the Lagrangian timescale, related to the velocity autocorrelation function, R :
Frequently studied in theory. In practice, we need lots of lagrangian particules.

12. Calculating Lagrangian timescale (T), and velocity ACF, (R) from Global Drifter Program (GDP) and virtual drifters from altimetric currents
10 years of lagrangian drifter data
Snapshot of altimetric currents overlaid on SLA
JB – from all of the drifters in each bin you calculate the mean + STD of the ACFs, and from this packet you then extract 500 random ACFS to perform the MC ? Yes. This gives 500 results. I take the mean to get one result. And I calculate the standard error and standard deviation from the 500 exp.
2 regimes in the raw unfiltered data : (1) quadratically grow at early times and one linear grow at longer time. We are interested in the second regime. So we want to filter as short as possible to remove the noise but we need to filter at longer time than the second regime we want to get. The second regime start before 90 days. So we can filter at 90 days. It would not change the result if we filtered at 150 days : we are still in the same regime
Observed cross stream dispersion around the ACC from lagrangian GDP drifters
Linear dispersion regime

13. Cross stream eddy scales from GDP drifters
JB Are the eddy timescales this short in other studies? Yes. Very similar to Zurbas and Oh, Rupolo (2007), etc. Be confident on the point that our result are very normal compare to other studies based on Taylor (1921) approach.
Lagrangian eddy time-scales first zero crossing (days)
Lagrangian eddy space-scales (km)
Eddy diffusion and the Upper Cell of the Southern Ocean

14. Cross stream eddy diffusion
(Sallee et al., 2008)
Statistics calculated from GDP surface drifters in Southern Ocean.
higher around ACC and in western boundary currents
1-2 x 104 – order of magnitude larger than applied in climate models

15. Alongstream averages : Contribution and ErrorPF
SAF
SAF-N
Particles on drifter “grid”
Real Drifters
0.5 deg grid particles
Without WBCs
Ekman
Mesoscale geostrophic eddy contribution dominates. Ekman contribution is weak.
Higher values than previous Southern Ocean studies.
- Consistent values with Gulf Stream or Kurushio calculations from GDP drifters.
– Sallee and Speer -

16. Application : Eddy heat diffusion
Eddy heat diffusion in W.m-2
Winter mixed layer depths (m)
Note : we calculate the effective diffusivity, which is close to the diffusivity of PV. But it can be much higher than the buoyancy diffusivity (see Smith &Marshall, submitted to JPO)
This is not important for our GRL because in our GRL : we use the effective diff as a first proxy. It is maybe overestimated but even if we reduce it the eddy heat diffusion has comparable value as Air/sea fluxes and Ekman.
You do not need to speak about that. It just to be aware in case of a question. We know … effective diff is different than buoyancy diff … first approx… give the general circumpolar structure… maybe overestimated following Smith &Marshall… etc…
Here, eddy heat diffusion in the mixed layer is :
Temperature gradient derived from TMI/AMSR satellite SST data
Impact on the formation of deep winter mixed layers in the Southern Ocean
(Sallee et al; GRL, 2007)
Eddy diffusion and the Upper Cell of the Southern Ocean

17. Eddy heat fluxes around Kerguelen
Annual mean eddy heat diffusion
SAZ
STF
SAZ
SAF
-10 10
W.m-3
Eddy diffusion coefficient estimated from GDP drifters (Davis, 1991), and meridional SST gradient is from satellite TMI/AMSR
T-S Diagram of a composite of ARGO floats in the SAZ
Strong « interleaving » near Kerguelen – cooling and freshening from eddy mixing
Sallee et al. 2006, Ocean Dynamics

18. Summary – Eddy Diffusion
Surface Drifters and altimetry -> similar estimation in situ and satellite of eddy diffusion
Linear dispersion regime dominated by geostrophic mesoscale eddies
Values order 104 m2.s-1 in the western boundary current regions
Need to resolve Rossby radius

19. Submesoscale Eddies 3.
R. Morrow, F. D’Ovidio, A. Koch-Larrouy, J.B. Sallee
(Jason-II CNES/NASA Proposal)

20. Estimating sub-mesoscale circulation from ¼° AVISO velocity maps
Submesoscale Eddies
Estimating sub-mesoscale circulation from ¼° AVISO velocity maps
ALTIMETRIC EULERIAN FIELD
Simple, instantaneous description
Mesoscale structures O(100 km)
2D maps of horizontal currents used to estimate lagrangian evolution of filaments O (10 km)
LAGRANGIAN MANIFOLDS (FSLE)
Time-integrated structures
Precise localization of transport barriers and filaments
Strong mixing in submesoscale structures
Upper plot shows the horizontal geostrophic currents from altimetry.
Lower plot shows the time-integrated lagrangian structures which evolve with the gesotrophic flow. They highlight regions of convergent/Divergent flow, associated with « transport barriers ».
A red and black tracer has been released – red into the centre of an A/C eddy, black around a cyclonic eddy around 39°N.
The black filaments following strain patterns can be parallel OR perpendicular with the geostrophic currents.
These filament patterns are very well correlated with tracers fields of SST or ocean color.
With F. D’Ovidio, LMD

21. Traditional analysis : altimetric EKE Mesoscale eddies
Resolution 30 km
5 dec. 2000
Lagrangian analysis (Lyap. Exp)
Sub-mesoscale Filaments
Resolution 1-10 km
5 dec. 2000

22. DIMES campaign:
=> release Lagrangian floats close to altimetry-detected hyperbolic points, to :
"compute" in-situ the Lyapunov exponents
follow the unstable manifolds, that for short times (a week or so) can be approximated by nearby lagrangian trajectories.
The length of the unstable manifold can be related to eddy diffusion, within the formalism of the effective diffusivity.
Emily Shuckburg (BAS), Francesco d’Ovidio (LMD)

23. Constraining coastal ocean models with altimetry
Pierre De Mey, LEGOS/POC
WATER-HM/SWOT meeting
CNES HQ, Paris, February 2008

24. Non-local, structured errors in coastal current
SLA
Depth-averaged velocity
Surface salinity
Temperature
EOF-1
79.8 %
What is this? Ensemble multivariate EOFs in the Catalan Sea coastal current in response to coastal current inflow perturbations (mimicking downscaling errors).
Relevance to WATER-HM? SLA errors are small-scale (O(40km)) and strongly correlated to fine-scale (u,v,T,S) 3-dimensional errors which we can then expect to correct if SLA is observed at sufficiently fine scales.
EOF-2
11.0 %
This is from a different Ensemble.
Now these are the first 3 EOFs for an Ensemble where the depth of the current on top of the slope on the shelf break is perturbed. Therefore by perturbing the depth we also perturb the distance from coast and the width of the current. The transport is not changed.
Main features:
- The first EOF changes the mass field and overall velocity of the current (see SLA gradient)
- The following EOFs are close to harmonics of EOF-1 (add local effects)
- Again some features seem to be locked in the vicinity of strong bathymetric features
EOF-3
4.9 %
(Jordà et al., 2006)

25. Non-local, structured errors in coastal current
SLA
Depth-averaged velocity
Surface salinity
Temperature
EOF-1
79.8 %
EOF-2
11.0 %
This is from a different Ensemble.
Now these are the first 3 EOFs for an Ensemble where the depth of the current on top of the slope on the shelf break is perturbed. Therefore by perturbing the depth we also perturb the distance from coast and the width of the current. The transport is not changed.
Main features:
- The first EOF changes the mass field and overall velocity of the current (see SLA gradient)
- The following EOFs are close to harmonics of EOF-1 (add local effects)
- Again some features seem to be locked in the vicinity of strong bathymetric features
EOF-3
4.9 %
(Jordà et al., 2006)

26. Activation of coherent error features by storms
What is this? The SLA component of a particular ensemble EOF in response to atmospheric forcing errors. It is a proxy of the actual model errors. As the time series shows, it is activated during the July 7-8 storm and is characterized by a shelf-wide response, a surge response, and a mesoscale response with O(1day) time scale.
Relevance to WATER-HM? Questions 1 (mesoscale), 2 (coastal) and 3 (storm-related). We expect a wide-swath altimeter to consistently constrain the fine-scale, multivariate ocean response to those fast events, and hopefully help better predict the associated phenomena.
Ensemble EOF-3 SLA, 3D BoB model A B
July 1
2004
August 31

27. Time variations of ensemble variance
Point A: EC
Point B: BoB
SLA, Ub errors linked to local wind errors
Kelvin waves propagation in error subspace
SLA errors attributable to pressure errors

28. Wide-swath vs. nadir in Bay of Biscay Stochastic modelling with atm
Wide-swath vs. nadir in Bay of Biscay Stochastic modelling with atm. forcing perturbations in 3D BoB
(left panel)
What is this? The RM spectra plot on the left shows the number of degrees of freedom of model (forecast) error which can be detected by a particular array amidst observational noise. This is done by counting eigenvalues above 1. This is shown for three arrays (legend). Representer matrices are calculated by stochastic modelling with atmospheric forcing errors.
Relevance to WATER-HM? Questions 1 (mesoscale) and 2 (coastal). One Wide-Swath altimeter on a JASON orbit detects 4 degrees of freedom, while one nadir instrument (JASON) detects only one. The more d.o.f.’s are detected, the more critical ocean processes will be constrained.
Array Modes -- SLA
Scaled RM spectra
Top: Wide Swath (4 dof’s)
Mid: WS over deep ocean (2 dof’s)
Bottom: JASON (1 dof)
“Slosh”
Meso1
Meso2
(after Le Hénaff & De Mey, 2008)

29. (right panel)
What is this? The “array modes” of model error corresponding to the spectra to the left. For each array, mode 1 is mostly water sloshing around between shelf and deep-ocean domains; modes 2 and 3 are a mix of mesoscale & submeso response, slope current variability and shelf processes.
Relevance to WATER-HM? Questions 1 (mesoscale) and 2 (coastal). As was seen on the left panel, JASON can only detect (and constrain) the “slosh” mode. One needs a wide-swath instrument to detect (constrain) all three modes + a 4th one not shown. In this way, one can objectively demonstrate that a wide-swath instrument is needed to constrain the coastal ocean mesoscale and coastal current variability. (A collaboration between LEGOS and OSU’s OST proposals has been proposed on this topic)
Wide-swath vs. nadir in Bay of Biscay Stochastic modelling with atm. forcing perturbations in 3D BoB
Array Modes -- SLA
Scaled RM spectra
Top: Wide Swath (4 dof’s)
Mid: WS on deep ocean (2 dof’s)
Bottom: JASON (1 dof)
“Slosh”
Meso1
Meso2
(after Le Hénaff & De Mey, 2008)

30. Summary – what is needed : SWOT
Space : Resolving the Rossby radius in the Southern Ocean : km means sea level observations at 2-5 km
Time : Resolving geostrophic adjustion time-scales of 2-5 days
=>With this resolution, finer scale filaments can be determined (eg FSLEs)
Precision : cms

32. Impact of internal tides
Regions of conversion of M2 barotropic tide into baroclinic internal waves
Le Provost et al. 1994, Lyard et al., 2006
Parametrisations exist for this conversion :
- 1/3 energy dissipated locally with bottom drag
- 2/3 energy radiates away as internal tides
In small closed seas or basins, internal tides also dissipate locally

33. I. ITF - 1) Parametrisation of tidal mixing in ¼° OGCM
Koch-Larrouy et al. 2007

34. SST Impact of the internal tides on coupled ocean-atmosphere models
Koch-Larrouy et al. 2008

35. Jason-II proposal : Submesoscale Eddies and Tidal mixing
1) Analyse the role of eddy fluxes and tidal mixing in modifying SAMW and AAIW in key regions, using the DRAKKAR ¼° model
(Ariane Koch-Larrouy, Post-Doc, LEGOS, 2008)
Winter ML density, ML > 300 m,
(Sallee et al. 2007)
Kerguelen
Macquarie Ridge
Fracture Zone
Drake Passage
M2 internal tide generation sites,
(Le Provost et al. 1994, Carrère et Lyard 2003)

37. Monitoring fronts with satellite data : Meridional gradients in SSH and SST
Surface position can be offset from subsurface position
Eg. Summer stratification + strong Ekman transport can shift surface fronts northward in summer
Grad SSH :
SSS data
Grad SST :
Altimetry is important for monitoring subsurface frontal movements

38. Winter ML heat budget terms
Air-sea Flux, Q
Ekman Heat Flux
Zones clés
Eddy heat flux
Total : 3 terms
Sallee et al. 2007, GRL

39. Winter ML heat budget terms
Winter ML depth
Total heat forcing : 3 terms

40. Circumpolar evolution of winter ML
Sum of 3 forcing terms in winter – relative to the SAF-N axis
Winter ML Depth – relative to the SAF-N axis
Winter ML Density for ML > 200 m