# Presentation: 321600

## 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)

## From Rintoul et al. 2001

- From Rintoul *et al*. 2001

- From Speer *et al*. 2000

## 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?

## Outline

- Obtaining an eddy permitting Southern Ocean state estimate (SOSE): method, observations, and results
- The general Southern Ocean circulation from the SOSE
- Review Current theories of the Southern Ocean MOC
- Analyze the force balance of the MOC in the SOSE
- Conclude

## 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)

- 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)

## 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. Forget’s 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 SDSC’s
-     DataStar (IBM SP4) supercomputer

## 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 |

## 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)

## 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

## Binned cost: WOA01, MOA, SOSE (I26)

- Binned cost: WOA01, MOA, SOSE (I26)

- ARGO
- SEaOS
- A16 & P16
- aaiw05
- aaiw06

- Median Temperature Cost

- Median _x0013_Salinity Cost

- Latitude

- Latitude

- Binned median cost (weighted product - observation squared) at each longitude

- Observation

## 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

## Outline

- Obtaining an eddy permitting Southern Ocean state estimate (SOSE): method, observations, and results
- The general Southern Ocean circulation from the SOSE
- Review Current theories of the Southern Ocean MOC
- Analyze the force balance of the MOC in the SOSE
- Conclude

## Mean Horizontal Transport in SOSE

- Vertically integrated transport streamfunction [Sv]

- Weddell Gyre       Ross Gyre
-     ~40 Sv               ~ 20Sv

- ACC ~150 Sv

- ~60 Sv

- ~30 Sv

- ~30 Sv

## Eulerian mean MOC

- Inconsistent with buoyancy flux

- 2005 buoyancy flux

- From
- Cerovecki
*et al.* 2008

- Sv

## Southern Ocean MOC,                , in -space

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

- Sv

## b Flux and the MOC

- Sv m s-2

## Outline

- Obtaining an eddy permitting Southern Ocean state estimate (SOSE): method, observations, and results
- The general Southern Ocean circulation from the SOSE
- Review Current theories of the Southern Ocean MOC
- Analyze the force balance of the MOC in the SOSE
- Conclude

## SO theory

- Classic theory
- (x-avg & Rossby<<1)

- DP lats below
- Ekman layer

- Add eddies
- Johnson-Brydon

- TEM formulation
- Plumb-Ferrari

**Notes:**
Planetary geostrophic model...with winds
Along isopycnal pv flux
A nightmare in z coord....elegant in gamma

## (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

## (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

## (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

- Pressure forcing

- Ekman transport

- = Eddy forcing

## Current Theories of MOC

- Issues:
- What’s 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

## Outline

- Obtaining an eddy permitting Southern Ocean state estimate (SOSE): method, observations, and results
- The general Southern Ocean circulation from the SOSE
- Review Current theories of the Southern Ocean MOC
- Analyze the force balance of the MOC in the SOSE
- Conclude

## 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.

## The zonal mom. eqn. in  coordinates

- Lowest order temporal mean zonal mom. eqn. in ****** -space
- Previously used decomposition:
-      ...but the results here suggest:

## Southern Ocean MOC,                , in -space

- Sv

## The Force Balance of the Residual MOC

- Mechanical (wind) forcing:

- Sv

## The Force Balance of the Residual MOC

- The eddy term,    :

- Sv

## Pressure forcing:

- The Force Balance of the Residual MOC

- Sv

## 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)

- 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

- Pressure Forcing in Unblocked Latitudes

- kg m-3

## Pressure Forcing

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

- ACC streamlines on **s

- kg m-3

## The Force Balance of the Residual MOC

- The eddy term,    :

- Sv

## Mean Potential Vorticity 

- Mean Potential Vorticity

- Mean PV:

- (ms)-1

## Mean Potential Vorticity Gradient 

- Mean Potential Vorticity Gradient

- Smoothed PV gradient:

- 10-6 m-2 s-1

## Temporally and zonally averaged neutral density, 

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

## 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.

**Notes:**
 A Southern Ocean model was fit to the observed ocean in a weighted least squares sense
The state estimate was used to analyze the volume weighted zonal momentum equation in isopycnal space
Determined the force balance of the residual meridional overturning circulation
Highlighted inconsistencies of this force balance with commonly accepted theories

- Thanks!