The Southern Ocean Meridional Overturning Circulation as Diagnosed from an Eddy Permitting State Estimate

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The Southern Ocean Meridional Overturning
Circulation as Diagnosed from an Eddy Permitting
State Estimate

• Matt Mazloff
• Scripps Institution of Oceanography
• Raffaele Ferrari (MIT)
• Patrick Heimbach (MIT)
• Carl Wunsch (MIT)

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From Rintoul et al. 2001
From Speer et al. 2000
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Thesis Questions

• Small scale (eddy) dynamics are thought to play
  an essential role in the Southern Ocean dynamics.
  Can we find an eddy permitting model solution of
  the Southern Ocean that is consistent with the
  observed ocean?
• What is the force balance of the Southern Ocean
  meridional overturning circulation (MOC)? Is the
  balance assumed in current theories of the MOC
  representative of the true Southern Ocean?

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Outline

1. Obtaining an eddy permitting Southern Ocean state
   estimate (SOSE) method, observations, and
   results
2. The general Southern Ocean circulation from the
   SOSE
3. Review Current theories of the Southern Ocean MOC
4. Analyze the force balance of the MOC in the SOSE
5. Conclude

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• State estimation a weighted least squares fit of
  a model to observations using the method of
  Lagrange multipliers
• Sensitivity of weighted data-model misfit with
  respect to the model inputs is made known via the
  adjoint model
• This sensitivity information is used to
  iteratively perturbed the model inputs and reduce
  the misfit
• The model solution is dynamically realistic (no
  nudging)

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Southern Ocean State Estimate Configuration

• 780 South to 24.70 South
• 1/60 Horizontal resolution (eddy permitting)
• 42 depth levels (partial cells)
• initial conditions and open boundary
• conditions derived from, and con-
• strained to, G. Forgets 1o resolution
• global state estimate (MOA)
• atmospheric boundary layer scheme
• constrained to NCEP re-analysis
• atmospheric state
• adjoint generated via AD tool TAF
• sea-ice model
• KPP, GM/Redi parameterizations
• currently optimizing years 2005-06
• 600 processor adjoint on SDSCs
• DataStar (IBM SP4) supercomputer

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Observational Constraints
observation instrument product
Mean dynamic topography (MDT) GRACE SM004-GRACE3 CLS/GFZ (A.M. Rio) 1.1x107
Sea level anomaly (SLA) Jason ENVISAT GFO PO.DAAC AVISO NOAA, USN 4.3x107 7.3x106 3.9x106
SST AVHRR TMI AMSR-E NOAA/Reynolds Remote Sensing System 1.3x107 1.1x107
In-situ T, S Argo XBT CTD SEaOS Ifremer S. Behringer (NCEP) Various SMRU BAS (UK) 4.2x106 4.7x104 6.2x104 3.8x105
Climatological T,S WOA01 (upper 300 m) WOCE Conkright et al., 2002 Gouretski Koltermann, 2004 2.5x107
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Observational Coverage

• In situ profile coverage for 2005 - 2006. Total
  number of observations in parentheses
• SEaOS (3.8x105)
• ARGO (4.2x106)
• XBT (1.2x104)
• CTD (2.5x104)

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Change in SST misfit
Iteration 0 (Control run)
Iteration 23
Time average of model solution minus observations
oC Observations are combined mean from
infrared (AVHRR) and microwave (TMI AMSR-E)
radiometers Exponential color axis
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Binned cost WOA01, MOA, SOSE (I26)
Binned median cost (weighted product -
observation squared) at each longitude
Observation
Median Temperature Cost
Median Salinity Cost
ARGO SEaOS A16 P16 aaiw05 aaiw06
Latitude
Latitude
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SOSE Results

• The adjoint method optimization is converging
  towards consistency at eddy permitting resolution
• Perturbations to input variables similar to those
  found in coarse state estimates
• Largely consistent with all individual
  observations and previous static inverse models
• A better fit to the 2005-2006 in situ
  observations than the WOA01, and with realistic
  dynamics

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Outline

1. Obtaining an eddy permitting Southern Ocean state
   estimate (SOSE) method, observations, and
   results
2. The general Southern Ocean circulation from the
   SOSE
3. Review Current theories of the Southern Ocean MOC
4. Analyze the force balance of the MOC in the SOSE
5. Conclude

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Mean Horizontal Transport in SOSE
Vertically integrated transport streamfunction
Sv
30 Sv
30 Sv
60 Sv
Weddell Gyre Ross Gyre 40 Sv
20Sv
ACC 150 Sv
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Eulerian mean MOC

• Inconsistent with buoyancy flux

2005 buoyancy flux
From Cerovecki et al. 2008
Sv
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Southern Ocean MOC, , in ?-space

• Döös and Webb (1994) showed Deacon Cell results
  from changes of ? in z-space

Sv
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b Flux and the MOC
Sv m s-2
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Outline

1. Obtaining an eddy permitting Southern Ocean state
   estimate (SOSE) method, observations, and
   results
2. The general Southern Ocean circulation from the
   SOSE
3. Review Current theories of the Southern Ocean MOC
4. Analyze the force balance of the MOC in the SOSE
5. Conclude

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SO theory
DP lats below Ekman layer
Add eddies Johnson-Brydon
TEM formulation Plumb-Ferrari
Classic theory (x-avg Rossbyltlt1)
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(1) TEM Developed for Atmosphere

• Net flow is a residual between mean and eddy flow
• The QG case of Andrews and McIntyre (1976) is
• gives rise to the transformed Eulerian mean
  (TEM) eqns.
• In the TEM framework
• explicit eddy fluxes are removed from the
  buoyancy budget
• eddies forcing on the mean flow takes the form of
  a PV flux
• The residual circulation relates to the mass
  weighted circulation in isopycnal coordinates,
  , where
• , as the above
  conditions (a b) hold true

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(2) TEM Framework Applied to Ocean

• Johnson and Bryden (1989) assumed MOC is
  negligible
• mean
  circulation eddy circulation
• Assumed mean streamfunction is set by wind
  stress
• Assumed eddy streamfunction is equal to an
  interfacial form stress (IFS)
• IFS provides a mechanism to close the buoyancy,
  mass,
• and momentum budgets locally and adiabatically
• Eddy parameterizations then allow one to compare
  the stratification to the zonal wind stress

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(3) Use TEM to Reconstruct the Residual MOC

• Marshall and Radko (2003) reconstructed
  from knowledge of surface buoyancy flux and wind
  stress

Buoyancy input
Buoyancy loss
Eddy forcing
Ekman transport
Pressure forcing
Eddy forcing
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Current Theories of MOC

• Issues
• Whats the circulation in the non-ventilated
  layers?
• Assumptions made
• near surface a balance between eddies and wind
  stress
• abyss a balance between eddies and pressure
  gradients
• Are these appropriate in theorizing about the SO?
• And is the parameterized eddy circulation
  realistic?
• To address these issues, the force balance of the
  MOC was analyzed in isopycnal (?) coordinates
  using the Southern Ocean state estimate

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Outline

1. Obtaining an eddy permitting Southern Ocean state
   estimate (SOSE) method, observations, and
   results
2. The general Southern Ocean circulation from the
   SOSE
3. Review Current theories of the Southern Ocean MOC
4. Analyze the force balance of the MOC in the SOSE
5. Conclude

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The zonal mom. eqn. in ? coordinates

• Temporal mean zonal mom. eqn. in isopycnal
  coordinates
• where is a thickness weighted
  time mean
• And a hat denotes a deviation from this mean
• The potential vorticity (PV) is
• is the pressure forcing.
• is the mechanical (wind) forcing.

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The zonal mom. eqn. in ? coordinates

• Lowest order temporal mean zonal mom. eqn. in ?
  -space
• Previously used decomposition
• but the results here suggest

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Southern Ocean MOC, , in ?-space
Sv
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The Force Balance of the Residual MOC
Mechanical (wind) forcing
Sv
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The Force Balance of the Residual MOC

• The eddy term,

Sv
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The Force Balance of the Residual MOC

• Pressure forcing

Sv
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Pressure Forcing in Unblocked Latitudes

• Geostrophic transport,
  , vanishes when zonally integrated at constant
  depth, but not when integrated at constant ?, ?,
  or S. (AAIW moves equatorward while UCDW
  poleward)
• Spring averaged ? at latitude 580S (? contours
  27.63 27.9 kg m3)

L
H
kg m-3
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Pressure Forcing

• Pressure forcing is still significant for
• Streamwise integration
• Coordinate rotation into along and across
  streamlines

ACC streamlines on ?s
kg m-3
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The Force Balance of the Residual MOC

• The eddy term,

Sv
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Mean Potential Vorticity

• Mean PV

(ms)-1
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Mean Potential Vorticity Gradient

• Smoothed PV gradient

10-6 m-2 s-1
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• Temporally and zonally averaged neutral density, ?

Eddies homogenize PV, resulting in a Stokes drift
from weakly stratified regions to highly
stratified region
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Conclusions

• A 2 year Southern Ocean state estimate (SOSE) was
  produced at eddy permitting resolution
• A step towards goal of eddy resolving global
  state estimates
• Provides a useful data set to study the Southern
  Ocean
• Some users R. Abernathy, I. Cerovecki, J.
  Ledwell, T. Ito
• Eddy PV fluxes
• drive an equatorward flow in the most buoyant
  waters
• derive part of their energy from direct wind
  stirring
• are rather insignificant in the ocean interior
• Pressure forcing is lowest order everywhere in
  the Southern Ocean residual circulation force
  balance.

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Thanks!