and their Role in the Earth Climate

1
THE SOUTHERN OCEAN CIRCULATION PROCESSES,
DYNAMICS AND MODELS
Dirk Olbers Alfred Wegener Institute for Polar
and Marine Research Germany
thanks C.Eden, R. Greatbatch, M. Visbeck, K.
Lettmann, R. Timmermann
2
SO circulation
circumpolar circulation the ACC
meridional circulation the SO overturning
3
Outline
what drives the quasi-zonal circulation of
the ACC? how to interpret eddy fluxes? what
drives the overturning circulation in the SO?
4
forcing
Ocean gains buoyancy
from SOC climatology
5
sea surface altimetry from ERS
Chris Hughes pers comm
Eddies in the SO
Hallberg and Griffies pers comm
6
mixing in the Southern Ocean
log10 K? m2 s-1 along ALBATROSS cruise track
Naveira Garabato et al 2003
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What drives the quasi-zonal circulation ?
8
Six Circumpolar Currents
driven by NCEP winds and surface buoyancy flux
driven by NCEP winds
9
depth, f/h and forcing
surf buoy flux BRIOS
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BARBI physics
barotropic momentum streamfunction baroclinic
potential energy ? perturbation density bottom
pressure baroclinic momentum
Olbers Eden 2003
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BARBI physics
vorticity balance
consistency constraint
Poisson equation
bclinic momentum balance
potential energy balance
buoyancy forcing
nabla-4 operator
12
BARBI physics waves
eigenvectors
projection vectors
flat bottom
topographic
13
NL
NO
WQ
QQ
baroclinic potential energy drives vorticity of
vertically averaged momentum via
JEBAR determines transport of shear
velocity relative to bottom
14
BT
WQ
FL
QQ
NL
NO
bottom pressure affects zonal mean balance of
zonal momentum via bottom formstress drives
vorticity of vertically integrated momentum
via bottom torque determines
geostrophic bottom velocity
15
Momentum balance zonally integrated
DP
16
NL
pressure P bottom elevation
QQ
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Momentum balance normal and parallel to
streamlines
friction
P gradient
Coriolis
wind
normal
parrallel
flat bottom FL
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Momentum balance normal and parallel to
streamlines
friction
P gradient
Coriolis
wind
normal
parrallel
homogeneous density BT
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Momentum balance normal and parallel to
streamlines
friction
P E gradient
Coriolis
wind
normal
parrallel
nonlinear NL
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Vorticity balance
topo-plan Jac
JEBAR
wind curl
friction
WQ
21
Potential energy balance
advection
btropic pump
bclinic pump
diffusion
buoy force
Ekm pump
WQ
22
What drives the circulation ?
23
What drives the circulation ?
diffusive regime
24
small bottom slope regime bclinic Stommel
problem
What drives the circulation ?
25
What drives the circulation ?
ACC regime
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What drives the circulation ?
buoy force
Ekm pump
eddy diff
direct wind
eddy visc
beta
WQ
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Summary 1

• the dynamics of ACC transport is governed by
  linear response of topographic-planetary waves
  (two gravest modes) to wind and buoyancy forcing
  (interior vertical turbulent buoyancy flux gt
  mixing)
• direct wind driving and Ekman pumping on
  stratification are of comparable size, the
  buoyancy forcing smaller (in this set-up)
• baroclinicity breaks f/h constraint and restores
  f-characteristics (but bottom pressure still
  governed by f/h)
• eddy diffusion (GM) overwhelms eddy viscosity in
  shaping circulation and transport of ACC
• JEBAR is not a good concept

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How to interprete eddy fluxes ?
29
Historical background

• Andrews and McIntyre (1976, 1978)
• - pointed out that eddy fluxes can be
  advective in
• nature the
  Transformed Eulerian Mean (TEM)

streamfunctions
DJF
Eulerian Mean Circulation
90 N
90 S
Residual Mean Circulation
90 N
90 S
30
Historical background

• Andrews and McIntyre (1976, 1978)
• - pointed out that eddy fluxes can be
  advective in
• nature the
  Transformed Eulerian Mean (TEM)
• Marshall and Shutts (1981)
• - pointed out the need to consider
  rotational fluxes

storm track
31
Historical background

• Andrews and McIntyre (1976, 1978)
• - pointed out that eddy fluxes can be
  advective in
• nature the
  Transformed Eulerian Mean (TEM)
• Marshall and Shutts (1981)
• - pointed out the need to consider
  rotational fluxes
• McDougall and McIntosh (1996, 2001)
• - tried to combine the above the Temporal
  Residual Mean (TRM)
• Tandon and Garrett (1996), Radko and Marshall
  (2003)
• - pointed out that eddy fluxes can (must)
  also be diabatic in nature
• Greatbatch (2001)
• - attempted to combine the rotational,
  advective and diffusive flux ideas into a unified
  theory
• Medvedev and Greatbatch (2004)
• - still the possibility of a negative
  diffusivity (normal flux of variance)
• Eden, Greatbatch and Olbers (2005)

32
Balances
3d density balance
Q represents diabatic processes we do zonal
averaging e.g. averaging along a latitude
circle in Southern Ocean or atmosphere but
theory works as well on horizontal plane and
can be generalised to 3d and other kinds of
averaging
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Balances
3d density balance
34
Notations
35
Classical decompositions
TEM
36
Eddy fluxes in a channel model
instantaneous temperature at 1000 m
depth

• CHANNEL-3
• modified MOM code (FLAME)
• reentrant channel, 2000 m depth
• horizontal resolution of 30 km, 20 levels of
  100 m thickness
• initial condition uniformly sloping isopycnals
  across channel
• forcing relaxation towards initial condition
  near side walls

37

• CHANNEL-6
• modified MOM code (FLAME)
• reentrant channel, 2000 m depth
• horizontal resolution of 15 km, 40 levels of
  50 m thickness
• initial condition uniformly sloping isopycnals
  across channel
• forcing relaxation towards initial condition
  near side walls

38

• CHANNEL-12
• modified MOM code (FLAME)
• reentrant channel, 2000 m depth
• horizontal resolution of 7.5 km, 80 levels of
  25 m thickness
• initial condition uniformly sloping isopycnals
  across channel
• forcing relaxation towards initial condition
  near side walls

39
Eulerian mean cross-channel flow is essentially
zero
residual streamfunction B
diffusivity K cm2/s
large negative K evidence of rotational fluxes
TEM-G
red lines are the mean b contours
40
Integral constraints
integrate over area above an isopycnal
mean
higher moments
steady conditions eddies flux diabatically to
balance mean diabatic forcing
integrated flux is zero in steady, adiabatic
conditions
41
Summary so far the diagnosed fluxes contain
nondivergent (rotational) contributions which
lead to an overestimation of diapycnal effects
and negative K the (diapycnic) eddy diffusivity
should - vanish in adiabatic and in steady
flow - reflect the dependence on the diabatic
forcing (locally ???) Mission find a
representation of eddy fluxes which acknowledges
these requirements
42
Decompositions with rotational fluxes
has zero divergence
points along mean contours
points across mean contours
43
Decompositions with rotational fluxes
44
Decomposition using all the higher moments TRM-G
(generalized TRM)
45
same reasoning applies to all orders of moment
equations
46
Decomposition using all the higher moments TRM-G
(generalized TRM)
for steady case
TRM-G
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Decomposition using all the higher moments TRM-G
(generalized TRM)
for steady case
TRM-G
steady, adiabatic K 0
but local ?
48
1st order
2nd order
TRM G for channel
3rd order
4th order
2nd order
1st order TEM-G
3rd order
4th order
49
Decomposition using all the higher moments TRM-G
(generalised TRM)
Andrews and McIntyre 1976, 1978 McDougall and
McIntosh 1996
downgradient, in general
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Summary 2

• The generalised Temporal Residual Mean (TRM-G)
  is
• a fully consistent formulation that
• (i) combines advective, diffusive and
  rotational fluxes
• (ii) gives zero diffusivity in steady,
  adiabatic conditions
• (iii) can be adapted to any kind of
  averaging, including
• isopycnal
  averaging and 3-D situations
• (iv) the diffusivity K is, in general,
  down the mean gradient
• when (a) there is growth of eddy
  variance (non-steady) or
• (b) irreversible removal of
  eddy variance (steady)

TRM-G combines TEM, TRM, Marshall and Shutts
theories into one!
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What drives the meridional overturning ?
52
CFC-12 and anthropogenic CO2 on SR3
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basic model setup
upper layer regime forcing eddies turb mixing
mixed layer
z 0
z - d
slope layer
z - a
Mode
interior regime no turb mixing adiabatic eddies
isopycnals
y yN
y 0
residual circulation
54
the ACC path mean
zonal windstress
forcing
surface density flux
NCEP
Average temperature and salinity along estimated
path of the ACC. Use 3C at 200m depth as
criterion
55
The interior regime
56
interior density balance 1/2
mixing
eddy flux
mean advection
57
interior density balance 2/2
assume
and
and zero mixing
58
momentum balance
bottom formstress
Reynolds stress
windstress
stress
Ekman transport
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estimating interior eddy diffusivities
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neutral density field
density black linesslope of isopycnals
colorpercent of blocked flow white contours
ocean interior
61
constructing ?(B)
AAIW
NADW
62
CFC inventory 8 Sv AABW 21 Sv total input to
deep ocean
Orsi et al. 2002
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eddy diffusivities from the adiabatic model
64
a prognostic model of theoverturning
65
z - d
z - a
initial condition on slope s
AAIW
isopycnals
NADW
AABW
y yN
y 0
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z 0
z - d
z - a
upper layer balances use complete density
balance and project on profiles
eddy terms mixing terms forcing terms
67
boundary conditions
z 0
z - d
z - a
Mode
AAIW
isopycnals
NADW
AABW
bc and mixing
no bc and no mixing
68
solutions
z - d
z - a
dashed and dotted SAC climatology full this
model
upper layer
ocean interior
69
K_s ?
K_i ?
parameter variations
a ?
a ?
70
Summary 3

• eddy K O(500 1000) below ML, with near
  surface maximum
• deep K relates to NADW transport
• gross features of SO overturning can be modeled
  by simple mixed layer physics (wind, surf buoy
  flux, mixing, eddies) and adiabatic ocean
  interior
• strength and depth of overturning depend on all
  parameters windstress, surface buoyancy flux,
  mixing in ML and eddy field
• wind and eddy driven overturning partially
  compensate (for the present forcing functions)
• bottom layer AABW ?

71
Review articles Rintoul, S.R., C. Hughes and D.
Olbers. The Antarctic Circumpolar Current system.
In G. Siedler, J. Church and J. Gould, editor,
Ocean Circulation and Climate, 271-302. New York,
Academic Press, 2001 Olbers, D., D. Borowski, C.
Völker and J.-O. Wolff. The dynamical balance,
transport and circulation of the Antarctic
Circumpolar Current. Antarctic Science, 16, 79
109, 2004 Olbers, D. On the role of eddy mixing
in the transport of zonal ocean currents. In
Marine Turbulence Theories, Observations, and
Models, ed. Helmut Baumert, John Simpson, and
Jürgen Sündermann, 511 - 529. Cambridge
University Press 2005 Articles Olbers, D. and
C. Eden. A simplified general circulation model
for a baroclinic ocean with topography. Part I,
Theory, waves and winddriven circulations.
Journal of Physical Oceanography, 33, 27192737,
2003 Olbers, D., and M. Visbeck A model of the
zonally averaged stratification and overturning
in the Southern Ocean. JPO, 35, 1190-1205,
2005 Eden, C., Greatbatch, R., and D. Olbers
Interpreting eddy fluxes. JPO, revised
2005 Olbers, D., K. Lettmann and R. Timmermann
Six circumpolar currents, in prep