JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 96, NO. C2, PAGES 2675-2692, FEBRUARY 15, 1991
South Atlantic Interbasin Exchange
STEPHEN RICH RINTOUL 1
Centerfor Meteorologyand PhysicalOceanography,MassachusettsInstitute of Technology,Cambridge
Hydrographicdata and inversemethodsare usedto estimatethe exchangeof massand heat between
the South Atlantic polewardof 32øSand the neighboringocean basins.The Antarctic Circumpolar
Current (ACC) carriesa surplusof intermediatewater into the SouthAtlantic throughDrake Passage,
which is compensatedby a surplusof deep and bottom water leaving the basin south of Africa. As a
result,theACCloses0.25_+0.18x 1015W ofheatincrossing
theAtlantic.At 32øS
themeridional
flux
of heatis 0.25-+0.12x 1015W equatorward,
consistent
in signbutsmaller
in magnitude
thanother
recent estimates. Attempts to force the system to carry a larger heat flux across 32øS led to
unreasonablecirculations.The meridionalheat flux is carriedprimarily by an overturningcell in which
theexportof 17x 106 m3 s-1 ofNorthAtlanticDeepWater(NADW)isbalanced
byanequatorward
return flow equallysplit betweenthe surfacelayers, and the intermediateand bottom water. No input
of warm Indian Ocean thermoclinewater is necessaryto accountfor the equatorwardheat flux across
32øS; in fact, a large transfer of warm water from the Indian Ocean to the Atlantic is shown to be
inconsistentwith the presentdata set. Togethertheseresultsdemonstratethat the globalthermohaline
cell associatedwith the formationand export of NADW is closedprimarily by a "cold water path,"
in which deep water leaving the Atlantic ultimately returns as intermediatewater enteringthe basin
through Drake Passage.
1.
INTRODUCTION
The South Atlantic is uniquein beingthe only major ocean
basin in which the meridional flux of heat is equatorward in
mid-latitudes, counter to the global requirement that the
ocean-atmospheresystem carry heat from the equator to the
depth, southwardflow of salineNADW at deeper levels, and
a thin layer of cold fresh Antarctic Bottom Water (AABW) at
abyssal depths, also moving to the north.
W/ist was apparently aware that such a scheme implied a
heat transport of the "wrong" sign, but found such a result
too strong a violation of his intuition to mention in his
poles[Model, 1950;Jung, 1955;Bryan, 1962;Bennett, 1978; discussionof the Meteor data (letter from W/ist's research
Hastenrath, 1982]. This heat transportis primarily the result assistantto H. Stommel, 1980). The first study to comment
of an overturning meridional cell in which warm water flows on the anomalous heat transport implied by the oceanonorthward in the upper layers of the ocean, is made more graphicobservations
wasthat of Model [1950]15yearslater.
denseby cooling and evaporationin the North Atlantic, and Since the early work of Model [1952] and Jung [1955],
returns southward at depth as North Atlantic Deep Water several studies, using a variety of methods, have confirmed
(NADW) [Jung, 1952, 1955;Bryan, 1962].The secondmajor that the meridional flux of heat in the South Atlantic is
source of cold water to the world ocean, Antarctic Bottom
Water formed in the Weddell Sea, is also found in the
Atlantic. Since the ocean basins are nearly closed to the
north, the South Atlantic acts as a conduit throughwhich the
dense water masses formed in the Atlantic
are introduced to
the other oceans, and through which water must return to
close the global thermohaline cell. Determining the general
circulation of the South Atlantic is therefore an important
step toward a better understanding of the thermohaline
circulation and, in turn, the role of the ocean in the global
climate system.
equatorward [Bryan, 1962, 1982; Hastenrath, 1980, 1982;
Fu, 1981; Bunker, 1980; Georgi and Toole, 1982; Hsiung,
1985]. However, estimates of the magnitude of the heat flux
vary over a wide range, as seen in Figure 9.
Although W/ist's assumption of a predominantly meridional circulation was limiting [Reid, 1981], his picture of the
vertical-meridional
circulation
has survived
intact
to the
present day. However, his core layer argumentscould not
determine the strength of the meridional cell, or the formation rates and transports of individual water masses.Derant
[ 1941]was the first to use the density field and geostrophyto
The meridional circulation in the South Atlantic was first
try and quantify the circulation in the South Atlantic. Subdescribed by Wast [1935]. Using the zonal sections of the
sequentestimatesof volume transportsin the literature have
Meteor expeditions, he identified various property extrema,
varied over a wide range, depending on each investigator's
or "core layers," which he interpreted as the primary
"spreading path" of each water mass away from its source choice of reference level, or on values assumedfor poorly
region. The circulation scheme he derived from these obser- known quantities such as the net air-sea heat flux. In this
paper the inverse method of Wunsch [1978] is used to
vations consistedof a stack of layers moving alternately to
combine a variety of constraintsand a priori information to
the north and south: northward flow of surface water and
better
determine the mass and heat transports of the major
relatively fresh Antarctic Intermediate Water (AAIW) at mid
water massesand boundary currents in the South Atlantic.
In particular, we focus on the exchange of mass and heat
1NowatCommonwealth
Scientific
andIndustrial
Research
Orga- between the South Atlantic and the neighboring ocean
nization, Division of Oceanography,Hobart, Tasmania, Australia.
basins,in order to gain some insight into how the deepwater
Copyright 1991 by the American GeophysicalUnion.
formation processesoccurring within the Atlantic are linked
to the global thermohaline circulation. The distribution of
Paper number 90JC02422.
0148-0227/91/90JC-02422505.00
properties in the deep ocean clearly shows that some ex2675
2676
RINTOUL:
SOUTH ATLANTIC
INTERBASIN
0o
changetakes placeßReid and Lynn [1971], for example, were
able to trace the salinity maximum of the NADW into low
latitudes
of the South Pacific.
EXCHANGE
15øS
Since the ocean basins are
nearly closed to the north, the strong eastward flow in the
Antarctic Circumpolar Current (ACC) is the primary means
by which such exchange is achieved.
•
Several studies of interbasin exchange with the South
Atlantic have appearedin recent years. Fu [1981]discussed
the exchangeof massand heat between the SouthernOcean
and the rest of the Atlantic north of 32øS in a study of the
subtropical South Atlantic circulation. Fu found a meridional cell carrying 20 Sv of NADW poleward across 32øS
balanced by an equatorward flow of equal magnitudein the
upper layers, resulting in an equatorward heat flux of 0.66-
30 ø
40ø
i
ß
60 ø
ß
ß........
- DRAKE':
......
ß ,:.'........ W-'•
75øS
90ow
He also demonstrated
that
forcing a poleward heat transportacross32øSresultedin an
unreasonable
III
'
:
30 ø
0o
30 ø
60øE
LONGITUDE
Fig. 1. Station locationsfor the five hydrographicsectionsusedto
define three closed regions (I, II, III) used in the inverse model.
circulation.
Georgi and Toole [1982] consideredthe Southern Ocean
as a whole and asked whether the ACC gained or lost heat
and fresh water as it traversed
each of the ocean basins. In
the Atlantic the ACC was found to lose heat and gain fresh
water, but the uncertainties were large, and neither estimate
could be distinguishedfrom zero. Georgi and Toole inferred
from their estimate of the heat divergence and estimates of
the air-sea heat exchange in the Southern Ocean that the
meridional heat flux across40øSwas 0.175 PW equatorward.
They noted, however, that their estimates were possibly
sensitive to horizontal variations in the unknown barotropic
velocity field.
The most recent discussion of the problem of interbasin
exchangeand its relation to the global thermohalinecirculation is Gordon's [1986] study of the fate of NADW exported
from the North Atlantic. He suggested that the global
thermohaline
!
i
ß
I
60 ø
consistingof zonal flow in the interior and strong boundary
in the east and west.
:
:
II
0.88 PW (PW = 10]5 W), and a horizontalcirculation
currents
,.,30OE
:
cell
associated
with
NADW
formation
is
closed primarily by a "warm water path:" NADW leaving
the Atlantic upwells uniformly into the thermocline of the
Pacific and Indian oceans, flows westward through the
Indonesian Passagesand across the tropical Indian Ocean,
and ultimately reenters the Atlantic via a branch of the
Agulhas Current that does not complete the retroflection.
Gordon concluded that the "cold water path," in which
water leaving the Atlantic returns through Drake Passagein
the ACC, could account for no more than 25% of the return
flow.
This hypothesisis consideredin detail in section4. It will
be seen that the argument used to demonstrate the dominance of the warm water path is not conclusive and that the
models presentedhere suggestthat a significantfraction of
the return flow does reenter the Atlantic through Drake
Passage.
The designof the inverse models is describedin section2.
Section 3 presentsthe results of a standard model, which
representsa "best estimate" of the circulation. These resultsare comparedto thoseof other studiesin section4, and
several additional experiments designedto test the compatibility of the data with the heat or masstransportestimatesof
other investigatorsare described. The main conclusionsare
summarized
in section
5.
2.
THE MODEL
Five hydrographicsectionsare used to divide the area of
the South Atlantic poleward of 32øS into three closed regions, as shown in Figure 1. The potential temperature,
salinity, and potential density distributions at most of these
sections have been discussedpreviously in the references
given in Table 1. The AJAX section at 0øE includes seven
stations from leg I of the AJAX expedition between the
African coast and the beginning of leg II at 50øS, IøE. There
is a 2-month gap between legs I and II. The 32øSsectionwas
taken from the Fuglister [1960] atlas; however, several
questionablesalinity values in the deep water of the eastern
basin, thought to be due to a leaky replacement bottle
[Fuglister, 1960],were replaced by constructinga ©-S curve
for all other deep observationsin the Cape Basin and reading
off the salinity values correspondingto the observedtemperatures.
Within each region defined by these sections the water
TABLE 1. Hydrographic Sections Used in the Model
Section
Name
Reference
Date
Drake Passage
Ajax 0øE
Feb.-March 1975
Jan. 1984
Nowlin et al. [1977]
Whitworth and Nowfin [1987]
Conrad
Jan.-Feb.
Jacobs and Georgi [1977]
ScrippsInstitute of Oceanography/
Texas A&M University [ 1985]
Fuglister [ 1960]
30øE
1974
Ajax Weddell-Scotia
Feb. 1984
IGY 32øS
April-June 1959
See Figure 1 for location of the sections.
RINTOUL: SOUTH ATLANTIC INTERBASIN EXCHANGE
TABLE
2.
2677
Nominal Layer Boundaries (See Text) and Layer Average Potential Temperature and Salinity (Italicized Values) at Each
Section
Layer
1
2
Upper
Boundary
Lower
Boundary
surface
rr0 = 26.20
rr0 = 26.20
3
26.80
4
27.20
26.80
27.20
rr• = 32.00
5
32.00
32.16
6
32.16
32.36
7
32.36
8
37.00
rr2 = 37.00
rr3 = 41.50
9
41.50
41.54
10
41.54
41.60
11
41.60
41.66
12
41.66
13
46.14
rr4 = 46.14
bottom
Drake
0øE
30øE
WeddellScotia
32øS
*
16.80
16.98
*
18.27
ß
35.288
35.250
*
35.661
6.82
10.21
10.37
*
13.05
34.070
34.635
34.629
*
35.227
4.18
34.137
5.85
34.332
5.66
34.319
1.93
33.918
6.73
34.489
2.72
3.02
3.18
34.220
34.245
34.286
34.038
1.00
34.321
3.54
2.39
34.392
2.10
34.583
2.45
34.403
2.26
34.603
2.46
34.407
2.14
34.589
0.48
34.160
0.57
34.394
2.91
34.454
2.76
34.648
1.80
2.21
2.05
1.15
2.67
34.698
34.766
34.745
34.566
34.832
1.50
1.87
1.80
0.83
2.32
34.724
1.23
34.726
0.85
34.799
1.49
34.780
0.92
34.785
1.39
34.759
0.98
34.548
0.90
34.585
0.93
34.876
1.91
34.859
1.32
34.719
34.734
34.732
34.661
34.804
0.37
34.705
0.40
34.696
0.40
34.700
0.33
34.6 78
0.66
34.736
-0.33
-0.26
-0.32
-0.09
34.661
-0.73
34.652
34.668
-0.64
34.655
34.660
-0.72
34.650
34.674
*
*
0.06
34.687
*
ß
Temperatures are in degrees Celsius, salinities in psu.
*No water in this layer in this section.
column was divided into 13 layers defined by approximate
neutral surfaces. The surfaces were constructed by varying
the reference pressureused to calculate potential density as
the surface underwent large vertical excursions [Rintoul,
1988]. The nominal layer boundaries are listed in Table 2
along with the layer-average temperature and salinity at each
section. These layers were chosento resolve the major water
massesand for the most part correspondto the definitionsof
Reid et al. [ 1977]. Experiments run with more than 13 layers
gave similar results.
We assume the flow is in thermal wind balance, that the
sections are representative of the mean state of the ocean,
and that mass is approximately conserved in each layer in
each region. The mass conservation equation in each layer
takes the form
N
• •jAxj
pm(Vrel
+ b)jdp+ (w*a)m
- (w*a)m
+1• 0
decomposition (SVD)[Lanczos, 1961; Wunsch, 1978]. Before doing the SVD, the rows and columns of the coefficient
matrix are weighted. The columns are divided by the square
root of their length to remove the bias introduced by variable
station spacing and water depth. The rows are weighted by
the expected error in each equation so that each equation has
unit variance. Errors in the near-conservation equations
result from measurement and interpolation errors in temperature, pressure, and salinity and errors introduced in extrapolating the shear below the deepest common observed
depth. Perhaps the most difficult source of error to estimate
is that due to the fact that the sectionsused are not synoptic.
The uncertainty in each equation due to these sources of
error was roughly estimated to be ---2 Sv in each layer.
In addition, layers that outcrop within a region receive
lower weights than those that do not reach the sea surface, to
account for possibletransfers of mass between layers due to
exchangeof buoyancywith the atmosphere.In the Weddell
Sea, where even the densestlayers reach the sea surface and
(1)
buoyancy loss to the atmosphere drives active AABW
where N is the numberof stationpairs, Pro,Pm+l are depths formation, all the layers are strongly downweighted. Only
of isopycnalsurfacesbounding
layer m, •ij is unit normal, total mass is required to be conserved, thus allowing for
(Vrel)/isthermalwindvelocityat pairj, relativeto theinitial exchangebetween individual layers in region II. The weights
j
1
m
reference
level,bj isreference
levelvelocityat stationpairj, chosen for the layers in regions I and III are roughly
Axjis stationspacing
at pairj, (w*a)mis netcross-isopycnalproportional to the outcrop area of each layer. The values
massflux acrossinterface m, and Pmis density.
The conservation equations for each layer in each area,
along with the supplementary constraints discussedbelow,
give 42 equations to be solved for the 190 unknowns (the
listed in Table 3 are rough guessesof the uncertainty in each
conservation equation due to all sourcesof error. The results
of several experiments testing different weights suggested
that the solution was insensitive to small (1-2 Sv) changesin
referencelevel velocitiesbj at 154 stationpairs and 36
the estimated
cross-interfacetransferswin).
The system of equations is solved using the singularvalue
In addition to the massconservationequations,a variety of
other informationis incorporatedinto the model in the form of
errors.
2678
RINTOUL:
TABLE
3.
SOUTH ATLANTIC
Constraints (_ Estimated Uncertainty) for the
Standard
Model
Uncertainty
Total mass conserved in regions I, II, and III
_+2Sv
Mass conserved in 13 layers in I and III
Layers 1-4,
_+4Sv
Layers 5-8
-+3 Sv
Layers 9-13
-+2 Sv
Total transport across Drake Passage, 0øE and 30øE 130 _+ 13 Sv
Net transport across 32øSand the Weddell-Scotia
0 _+2 Sv
section
Net transport across 32øSbelow sill depth east of
Walvis Ridge
Net transport between Africa and the Agulhas
Plateau below sill depth
Transport of bottom water across 32øSwest of MidAtlantic Ridge
Heat
flux across the Weddell-Scotia
section
0 -+ 2 Sv
0 _+2 Sv
INTERBASIN
EXCHANGE
port includes both the geostrophic and Ekman transports.
However, in this casethe Ekman transportsacrosseach of the
sectionsis small:the 32øSsectionis nearly coincidentwith the
zero line of the wind stress,the winds are weak in the Weddell
Sea, and the strong zonal winds over the ACC drive only a
small flux across the three meridional
The final constraint
across
the
Weddell-Scotia
section.
The
Weddell
Sea is
thought to be the major source of AABW to the world's
oceans, but estimates of the rate at which this water mass is
produced vary over a wide range [Gill, 1973;Killworth, 1977;
Carmack and Foster, 1975; Gordon, 1978]. Because of the
uncertainty in the transport estimates, the a priori information that the Weddell
4 _+ 1.2 Sv
sections.
listed in Table 3 concerns the heat flux
Sea should be a source of bottom water
was included by setting the heat flux across the WeddellScotia section equal in magnitude to the heat lost by the
ocean to the atmosphere in the Weddell Sea. Gordon [1981a]
estimated the net annual heat loss by the ocean between 60ø
0.1 -+ 0.05
x 1015W
(see text)
and70øSto be 31 W m-2. Thisvalueintegrated
overthe
linear constraints. The additional constraints used in the standard case are summarized
in Table 3 and discussed below.
During the International Southern Ocean Studies (ISOS)
program, several extensive current meter and pressure sensor arrays were deployed in Drake Passageto measure the
transport of the ACC. Nowlin and Klinck [1986] have
recently reviewed these estimates and report a mean transport of 130 Sv with an uncertainty of not more than 10%.
Since the Atlantic basin is closed to the north except for a
weak inflow from the Pacific (1 Sv [Coachman et al., 1975]),
the net transport across the sections running from Africa to
Antarctica at 0ø and 30øE must equal the transport at Drake
Passage.Therefore constraintswere added requiring that the
total transport across each of these three sectionsbe 130 -+
13 Sv.
The current meter observations of Hogg et al. [ 1982] in the
Vema Channel also provide useful constraints on the flow.
The Vema Channel is a narrow, deep passage through the
Rio Grande Rise at 30øSwhich provides the only path for the
exchange of bottom water between the Argentine and Brazil
basins. (Whether the poorly surveyed Hunter Channel to the
eagtis also deep enoughto permit someflow of bottom water
between the basins is unknown, and its contribution is
assumed to be small in this model.) The northward volume
transport of AABW found by dynamic calculations and
direct
current
measurements
was 4 _+ 1.2 Sv. Therefore
a
constraint was added requiring that the net flux of AABW
across 32øS west of the Mid-Atlantic Ridge be equal to the
flux observed by Hogg et al., to within estimated error.
Several more constraints are suggestedby the basin geometry. The Walvis Ridge crosses the 32øS section at 5øW
and continues to the northeast to the African coast, closing
the Cape Basin to the north. Thus there can be little net flow
of water below the sill depth (3500 m) of the Walvis Ridge
across the eastern portion of the 32øSsection. Similarly, the
basin between the Agulhas Plateau and the African coast is
closed to the east below 4000 m, and the net flow below this
depth across this part of the Conrad section must be small.
There is a similar requirement that the total transport across
the 32øS and Weddell-Scotia sections be close to zero, since
the Atlantic as a whole is nearly closed to the north and the
Weddell-Scotiasectionspansthe Weddell Sea. The total trans-
surface of region II implies a poleward heat transport of 0.1
PW by the ocean across this section. Estimates of air-sea
exchange in this region are poor, but still are perhaps better
known than the transports of the deeper layers across each
section. Moreover, in this way we can at least determine the
bottom water productions rates implied by different values
of the heat flux. The impact of this constraint on the solution
is considered in section 3. (Note that it is assumed that the
heat lost to the atmosphereis balanced by heat carried in by
the geostrophicflow. Although eddies are thought to make
an important contribution to the meridional heat flux across
the Polar Front [Bryden, 1979; de Szoeke and Levine, 1981],
the meridional temperature gradient in the Weddell Sea itself
is small, and the eddy contribution is unlikely to significantly
alter the results.)
The geostrophicshear in the ACC fronts extends nearly to
the bottom and the transport estimates in Drake Passage
obtained by referencing dynamic calculations to direct current meter measurements
confirm
that the eastward
flow of
the ACC reaches to great depth. Therefore most investigators studying the ACC have chosen a deep reference level
[Jacobs and Georgi, 1977; Georgi and Toole, 1982; Whitworth, 1983; Whitworth and Nowlin, 1987]. A deep reference
level also seems to be appropriate at 32øS. Wright [1969]
suggestedthat a kink in the O-Scurve at •2.0øC marking the
boundary between the AABW and NADW was a good
reference level choice; this surface lies at 3400-3800 m at
32øS. Subsequentstudies have also found that a deep level
leads to a more consistent deep circulation pattern in the
southwest Atlantic [Johnson et al., 1976; Reid et al., 1977;
Georgi, 1981; Hogg et al., 1982; Fu, 1981].
After some experimentation, an initial reference level of
3500 dbar was chosenfor the standard case. For station pairs
at which the bottom depth was less than 3500 dbar the
reference level was taken to be at the deepest common
sample depth. Results of runs with different initial reference
levels are discussedalong with those of the standard model
in the next section.
3.
RESULTS OF THE STANDARD
MODEL
Errors
There are several sources of uncertainty in the mass and
heat transport estimates. Errors in the estimates of the
RINTOUL: SOUTHATLANTIC INTERBASINEXCHANGE
reference
level velocities
arise from noise in the observa-
2679
found in the northernmostjet correspondingto the Subant-
tions and because we have insufficient information to fully
arctic Front. The flow is to the west near the bottom in the
resolve the velocities [Wiggins, 1972; Wunsch, 1978]. The
error due to noise can be estimated from the problem
residuals(see the appendix). In this case, the error due to
northern portion of the section and over the continental
slopeat the southernendof the passage.The velocityfieldin
Figure 2a is very similarto that obtainedby Nowlin et al.
observational
noiseis negligible:
<0.1 cm s-• at Drake [1977] (see their Figure 11), who used short-term current
meter measurementsto reference geostrophic calculations
Passage
and<0.01cms-1 for mostof theremaining
bi.
The uncertainty in the individual model parametersdue to
the lack of resolution is larger than that due to data noise.
basedon the samehydrographyused here (Melville, section
Typically the diagonalelementsof the resolutionmatrix are
<0.2. For the standard model the number of independent
The velocity field at the AJAX sectioncrossingthe ACC at
0øE is shown in Figure 2b. The initial reference level used
II, FDRAKE75).
equations (i.e., the rank) is about 32, so that with the
gavea net transportequalto 134Sv, and little adjustmentof
available information we are able to determine only 32
the reference level velocity was required to satisfy the
weightedaveragesof the 190unknownsin the problem. The
resolution, however, is generally compact' the solution at
each station pair is a weighted average of the (unknown)
"true" velocity at physicallyadjacentpairs, not pairs from
different sections, or distant parts of the same section.
Station pairs with similar ratios of layer depthstend to be
groupedtogether,or resolvedas a unit, by the SVD solution.
In this case the local, or compact, nature of the resolutionis
due to the strongvariation in layer geometryboth alongeach
sectionand between sections:for example, the ratio of layer
depths at a station pair from the northern end of Drake
Passageis very differentfrom that at a pair from the southern
end of the section, due to the steep meridional slope to the
isopycnalsassociatedwith the zonal flow of the ACC.
Likewise, the relative thickness of the layers at Drake
Passageis very differentfrom stationpairs at 32øSor in the
transportand massconservationconstraints.At this longitude, most of the transport of the ACC occurs in two jets
Weddell Sea. The solution found is thus a spatially smoothed
version of the real reference level velocity field. The length
scale of the smoothing varies along each section, from
roughly500-800 km in the interior to 100-200km near the
boundaries and in Drake Passage.
The extent to which the unresolved components of the
associated with the Subantarctic Front (SAF) and Polar
Front (PF). Both the SAF and the PF are broader at 0øEthan
in Drake Passageand result in less intenseflows. However,
Nowlin and Clifford [ 1982]and Whitworthand Nowlin [1987]
have shownthat at both longitudesthe cross-frontalscaleis
roughly twice the local deformationradius. The ACC is
found mostly to the north of the Mid-Ocean Ridge. Further
south is a third jet of eastward flow, much weaker than the
SAF and PF, which correspondsto the boundary between
the ACC and the cyclonic Weddell gyre to the south [Whitworth and Nowlin, 1987]. Near the African coast there is a
strong
flowto thewest(maximum
speed> 15cms-1) over
the continentalslope. Further offshorethe flow is weak and
alternatesin signuntil the edge of the ACC is reached at the
SAF
at 45øS.
At 30øE(Figure 2c) the ACC appearsto be broader and
weaker than at 0øE, but this may be partially due to the wide
stationspacingalongthis section.Two distinctfronts or jets
of eastwardflow can still be seen, separatedby a thin band
of westward velocities. Toward Antarctica the sense of the
flow mightcontributeto the heat flux acrossa sectioncan be
estimated by consideringthe projection of the total heat
content onto the vectors of the null space, as shown by
flow reverses, increasingin strengthnear the coast to form
the Antarctic Coastal Current [Gill, 1973]. By far, the most
intense flows at this section are the Agulhas and Agulhas
Wunsch et al. [ 1983]. The details are shown in the appendix.
Return Currents at the northern end of the section, with
In this case, the projection onto the null space is small,
maximumspeeds>70 cm s-1. The AgulhasCurrentis
indicatingthat the depth-integrated
temperaturevariesalong separatedfrom the African coastby a narroweastwardflow.
Dynamic topographymaps constructedfrom historical
eachsectionprimarily on the broad scaleswe have resolved.
A more difficult source of error to evaluate is that due to
data suggestthat the middepthcirculationin the subtropical
South Atlantic consists of an anticyclonic gyre with poleward flow along the western boundary, mostly zonal flow
along 32øSin the interior, and equatorward flow near the
easternboundary [Defant, 1961;Montgomery and Pollock,
1942; Buscaglia, 1971; Reid et al., 1977; Tsuchiya, 1985].
These maps also show a return flow or recirculationjust
heat between the ocean basins hold for each of the models
offshoreof the western boundary current, analogousto the
discussedbelow is taken as evidence that the assumptions recirculation gyre of the Gulf Stream system [Tsuchiya,
the aliasingof time variability by combininghydrographic
sectionstaken in different years. Observationsof the volume
transportof the ACC, for example, show significanttemporal variability (see Peterson [1988] for a recent review). In
the absence of a truly synoptic data set, the fact that the
major conclusionsconcerningthe net exchangeof massand
made are valid.
1985; Worthington, 1976].
For a more detailed discussion of the model design,
resolution, and error analysis, see Rintoul [1988].
The velocity field shown in Figure 2d is consistentwith
this picture, showingstrongboundarycurrentsin the east
The Velocity Field
The geostrophicvelocity at each sectionfor the standard
modelis shownin Figures2a-2e. The velocity field at Drake
Passageis shown in Figure 2a. The ACC appearsas four
deepjets with horizontalscalesof O(100 km) and maximum
and west and weak alternating flows in the interior. The
polewardflow extendingfrom the sea surfaceto the bottom
alongthe westernboundaryhastraditionally(and arbitrarily)
been divided into two currents: the Brazil Current in the
upperlayers, correspondingto the westernboundarycurrent
of the wind-driven subtropical gyre, and a deep western
boundary current resultingfrom the thermohalinecircula-
velocities
greaterthan25cms-•. Thejetsareseparated
by tion. The top-to-bottomtransportin the western boundary
regionsof slowereastwardflow. The strongestvelocitiesare
current is 63 Sv; of this, 33 Sv is returned to the north in the
2680
RINTOUL'
2.5
20
15
1000-
25 10 2 25
•
1.5
tO
-
,o •
•
SOUTH ATLANTIC INTERBASIN EXCHANGE
1000-
10 •
,._•_o
5
5
2000-
5
2000-
Z
•_5
5
3000-
3000-
4000400058øS
5000
0
60øS
200
5000-
S
400
600
81•0
i
'
0
lO•O
Fig. 2a
ß70!525
60øS
,i
2doo
30b0
, i
70øS
i
,
4000
i
i
5000
DISTANCE (km)
o
lOOO-
50øS
40øS
6000
DISTANCE (km)
2102 2
Fig.
2b
o
10002000-
2000-
3000'
• 3000-
4000'
40005000'
6000
40øS
11
0
1•00
45?
,
i
50øS
60
65
i I 55øS•
i
iøs
,
iøs
I
2000
3000
5000'
4000
6000
DISTANCE (km)
Fig. 2c
0 -
-
0
,
40•W, 30øW
iI
, 20øW
i ,
,10øW
i i
,0
iø , 10øE
,i
2000
4000
60•0
DISTANCE (km)
-
Fig. 2d
2000
40001
6000
I
40ow
20øW
oo
8000
,
0
,'
1000
,
' ,
20'00
3dO0
I
4000
DISTANCE (km)
Fig. 2.
Fig. 2e
Geostrophicvelocity for the standardmodel. Southwardor westward flow is shaded. Contour interval is 5
cms-i. Upperplotisreference
levelvelocity
forthissolution.
(a)DrakePassage,
(b)0øE,(c)30øE,(d)32øS,
and(e)
Weddell-Scotia.
counterflowoffshore.The transportof NADW in the band of
poleward flow near the coast is 19 Sv, while the weak eddies
in the interior of the westernbasinresult in a smallflux (2 Sv)
to the north.
flow within 1000km of the African coast. At abyssaldepths
in the Cape Basin there is a cyclonic gyre carrying •3 Sv.
The velocity field along the section crossingthe Weddell
and Scotia Seas is shown in Figure 2e. The Weddell gyre is
There is substantial northward flow along the coast of not symmetric at this section: the broad westward flow in the
Africa, but it is difficultto distinguishbetweenthe Benguela interior of the basin returns to the east in a narrow jet near
Current and isolated eddies. Wooster and Reid [1963] de- the northern boundary of the basin. This jet is thoughtto be
fined the Bengeula Current as the flow above 1000 m and the open ocean expressionof the western boundary current
within 1000 km of the coast, and estimateda transport of of the Weddell gyre [Gordon et al., 1981]. To the north there
15.7 Sv at 28.5øSusingthe Meteor data. For comparison,the is a tightly confinedanticyclonic gyre of strongflow which
net transport above 1000 m and within 1000 km of the coast reaches to the bottom and appears to be related to the
in this modelis 28.7 Sv. At deeperlevels in the easternbasin, bathymetry of the South Sandwich Trench. Within the
there is southward flow above and to the east of the
ScotiaSea the flow is strongand alternatesin signas the ship
Mid-Atlantic Ridge, which is compensatedby a northward track runs from the South Scotia Ridge into the Scotia Sea
RINTOUL:
transport
(Sv)
10
i
SOUTH ATLANTIC INTERBASIN EXCHANGE
transport
20
i
i
30
i
-10
0
i
,
transport
(Sv)
10
ß
2681
20
,
i
-lO
30
.
0
(Sv)
10
20
I
1
1
2
3
4
4
5
5
layer
layer
layer
$
7
7
8
/
9
10
10
11
13
/
/
I
1
I
I
11
12
13
o
EAST
30
EAST
Fig. 3. Volumeflux in eachlayer integratedalongeachsectioncrossingthe ACC for the standardmodel(Sv). Positive
fluxes are to the east. (a) Drake Passage,(b) 0øE, and (c) 30øE.
and back again across the Weddell-Scotia Confluence [Gordon et al., 1977].
Net Mass and Heat Transport
Across
Each
Section
The estimate of the absolute velocity field found in the
standardcase and presentedin Figure 2 is not unique, and
with the available information, we have been able to resolve
the reference level componentof the velocity field only on
broad scales.However, the primary focus of this paper is on
the net exchangeof water massesbetween the ocean basins,
and the net transportsacrosseach sectionare better determined than the details of the velocity field itself. One way to
demonstratethis is to simply comparethe resultsof different
models, as done below. A more formal way to demonstrate
that the fluxes have been well resolved is by consideringthe
contribution by the null space, as shown in the appendix.
The integratedtransportin eachlayer for each of the three
sectionscrossingthe ACC showsa similar pattern, as seenin
Figure 3. The net transport is to the east in all but the first
layer and concentrated near the sea surface. Roughly twothirds of the transport into the Atlantic through Drake
Passageoccurs in layers 3-6, correspondingto the Intermediate Water and upper branch of the Circumpolar Water
described by Reid et al. [1977]. (For the remainder of the
discussion these layers will be referred to collectively as
(lower case) intermediate water).
At 32øS the zonal integral of the circulation consists of
northward flow of surface and intermediate water, south-
ward flow of deep water, and northward flow of bottom
water (Figure 4a). Note that although the synoptic velocity
field shown in Figure 2d bears little resemblance to the
layered circulation described by Wiist [1935], the zonal
integral of the velocity is consistentwith the picture Wast
derived from analysis of the property fields. The equatorward flow of warm water and poleward flow of cooler deep
water results in a net equatorwardheat flux of 0.25 PW in the
standard
model.
The integral of the flow acrossthe Weddell-Scotia section
also reveals an overturning cell (Figure 4b): poleward flow of
deep water into the Weddell Sea balanced by an equatorward transport of bottom water in layers 12 and 13. Recall
that in this model
the heat flux
across
this section
was
required to equal the heat lost to the atmospherewithin the
Weddell Sea. The constraint that the ocean carry 0.1 PW of
heat into the Weddell Sea leads to a poleward transport of
•9 Sv of CDW balancedby an export of cooler AABW from
the Weddell
Sea. When
the constraint
was altered
to force
the ocean to carry 0.2 PW of heat into the Weddell Sea, the
export of AABW was also doubled.
These results are summarized
in the "circulation
cartoon"
shownin Figure 5. In this figure the net transport acrosseach
sectionhas been summedin groups of layers corresponding
to different water massesand plotted as a bar whose length
is proportional to the transport.
Despite the similarity of the plots in Figure 3 and the fact
that the total transportfor each sectioncrossingthe ACC is
constrainedto be 130 Sv, the transport in individual layers is
not the same across each section. More intermediate
water
enters the Atlantic through Drake Passagethan leaves south
of Africa. To keep the total transport across each section
equal, the deficit of intermediate water is made up by a
surplusof deep and bottom water leaving the basin across0ø
and 30øE. Thus the Atlantic as a whole converts intermediate
water into deep and bottom water.
Also presented in Figure 5 are estimates of the net
temperatureflux acrosseach section, relative to 0øC. The
shift in transport in the ACC from intermediate to cooler
deep and bottom water resultsin a smaller temperatureflux
at 0ø and 30øE than at Drake Passage, and a net heat
divergenceof •0.20 PW in the Atlantic. Note, however, that
this heat divergenceis not due to local cooling of waters in
the ACC. In fact, summingthe heat flux across each of the
four sectionsboundingregion I implies that the ocean gains
a small amount of heat (0.1 PW) from the atmospherein this
area. The heat divergence actually reflects the heat lost by
2682
RINTOUL: SOUTH ATLANTIC INTERBASIN EXCHANGE
transport
-10
-5
(Sv)
o
transport
5
lO
-4
-6
ß
/
.
i
-2
,
,
i
(Sv)
0
2
....
i
4
.
.
!
6
.
.
i
1
2
3
4
5
layer
layer
l
6
7
8
9
lO
/
l
11
12
13
32
Fig. 4.
SOUTH
AJAX
WEDDELL-SCOTIA
Integratedvolumetransportacrossthe (a) 32øSand (b) Weddell-Scotiasection.Positivefluxesare to the north
and east.
the oceanin the formationof deepand bottomwater at high
dbar the transportthroughDrake Passageis > 100 Sv to the
west). However, the transports differ from the standard
One way to get a feeling for the uncertaintyin these model by only a few Sverdrups. In particular, the main
transport estimates is to examine the sensitivity of the resultsdiscussedabove are unchanged:a surplusof interresults to the initial model assumed.In Figures 6 and 7 the mediate water enters the Atlantic in the ACC and is balanced
results of running the model with initial reference levels at by an increasein the transport of deep and bottom water
700 dbar and the bottom, respectively,are summarized.The leaving the basin; the ACC loses heat in crossingthe
solution norm is increased significantlyin both cases, as Atlantic; and at 32øSthere is an overturningcell of 0(15 Sv)
either choiceleadsto an initial statethat is far from satisfy- which carries an equatorward heat flux of 0.13-0.25 PW.
ing the constraints(e.g., with an initial referencelevel at 700
The exportof BW from the Weddell Sea is alsounchanged
when different reference levels are used. In fact, the translatitude.
port of CDW and BW across the Weddell-Scotia section
øø ,
........................................
•.5os ::':iiiiiii:•iiiiii!iii!iiiiiii:
variedby less than 1 Sv for all the modelsconsidered
:ii!iiiiiiiiiiiiiiii•
demonstrating
that fixingthe heat flux placesa strong
iiiiiii!ii!!iiiiiiiii!ii
i
iiiiiiiiiii!!!11iiil
•:i constraint
on
the
system.
This
section
has
particula
little
30ø
.iiii::i::ii!!iiiii!
e s
ii::!::!"
4
i::!::i::i::i::i::i'
•7
0o
.5 S
"•'
"' o
60 TF=--•
•
7F
s
49
17
.................
.......
:::..:
................
:::::::::::::::::::::::::::
:::::::::::::::::::::
::::iiii::!::ii::i::!!i"
6s s
30ø ii ;i!! ""• '
•
o
...................
'
......................................
'.......................
'.........
90øW
60 ø
30 ø
0o
30 ø
60oE
LONGITUDE
Standard
Model
bTb=1200
75øS
•ß =•ur[•e• w•r [l•y•r• 1-•}
:intermediatewater (layers3-6)
Fig. 5.
•=d•
l=bottom
w•r
[l•y•r• 7-11}
90øW
60ø
water (layers12-13)
units of øC Sv.
0ø
30ø
60ø•
LONGITUDE
Schematic circulation cartoon for the standard model.
Length of each bar is proportionalto the net transportacrosseach
section in sum of layers correspondingto each water mass (see
legend).Numbersat end of each bar give transportin Sv. Also
shownis the temperatureflux acrosseachsection(relativeto 0øC)in
30ø
Reference
Level=700
db
bTb=10,480
Fig. 6.
As in Figure 5, for model with initial reference level at
700dbar;brb is thenondimensional
solution
normforcomparison
to standard
case.
RINTOUL: SOUTH ATLANTIC INTERBASIN EXCHANGE
0o
still roughly in balance, but layers 2 and 3 show large
residuals of opposite sign in region I. The "upwelling"
across the interface between these two layers is the only w*
term that carries a significant mass flux (5 Sv). Indeed,
allowing transfer across this isopycnal is essential to find a
consistent solution' an experiment in which the w* term was
removed from the mass conservation equations resulted in a
solution that could not balance mass without unreasonably
large reference level velocities.
Although w* enters the mass conservation equations (1) as
a velocity-like term, it is properly interpreted as a proxy for
the net effect of a variety of processes which may act to
transfer mass across the layer boundaries. This transfer may
be due to true upwelling in the ocean interior, or for layers
15øS
30 ø
40 ø
60 ø
75øS
90øW
60 ø
30 ø
0o
30 ø
60OE
which
outcrop
withina box,it maybetheresult
ofair-sea
LONGITUDE
Reference
interactionalteringthe densityof waterexposedat'the sea
Level at the Bottom
bTb=2500
Fig. 7.
2683
As in Figure 5, for model with initial reference level at the
bottom.
freedom to partition the layer transports to carry this heat
flux, since only the densest layers have a significantarea at
this latitude, and the temperature difference between them is
small (Table 2).
surface. In this section it is argued that the transfer from
layer 3 to layer 2 found in this model results from the latter
of these two processes.
Bunker's [1988] map of net annual heat gain by the ocean
shows that, outside the narrow poleward extensions of the
western boundary currents, the South Atlantic between 30ø
and 60øSis a region of net heat gain, in strong contrast to the
North Atlantic. In particular, there is a broad, relatively
weak maximum at 50-55øS, 10øW-20øE, and a stronger
maximum
related
to theequatorward
flowing
Malvinas
Current alongthe SouthAmericancoast[.Taylor et al. [1978]
Interpretation of the Residuals
also found a region of oceanic heat gain north of the Polar
The residuals in the mass conservation equations in region
I are shown in Figure 8a. For each layer the residuals are
small and appear randomly distributed, demonstrating that
the physical model is adequate to account for the observations. Shown in Figure 8b is a second set of residuals, which
give the imbalance left in each layer by the horizontal
advection terms alone. When the mass flux carried by the
cross-isopycnaltransfer term is removed, the deep layers are
Front.
transport
The difference in the pattern of heat gain in the two basins
is in part due to the large .volumeof warm water carried to
high latitudes by the near-surface currents in the North
Atlantic. Although both oceans gain a similar amount of heat
through radiation, the warmer North Atlantic evaporates
more easily and experiences a much larger latent heat loss
[Bunker, 1988]. The larger land area in the northern hemi-
transport
(Sv)
a
-8
-4
0
4
8
1
2
layer
(Sv)
b
layere
e
Iø
l
1
I
lO
1
11
12
13
LAYERRESIDUALS
Fig. 8.
RESIDUALS:
LATERAL
ADVECTION
ONLY
(a) Mass residualsin each layer in region I for the standardmodel (Sv). (b) Mass residuals in region I from sum
over "horizontal"
advection
terms alone.
2684
RINTOUL'.
SOUTH ATLANTIC
sphere also contributesto the high latent heat loss through
outbreaks of cold, dry continental air over the North Atlan-
INTERBASIN EXCHANGE
[]
x
ß
+
Fu (1981)
Hsiung(1985)
Hastenrath(1982)
Hastenrath(1980)
O
Bunker(1976)
1.5
tic.
The outcrop area of layer 3 correspondsclosely to the area
of heat gain on Bunker's map, includingthe strongmaximum
near South America [Rintoul, 1988]. The latitude band in
which layer 3 outcropsalso correspondsto the maximumof
the westerly wind stress, which drives an equatorward
Ekman
flow. South of the wind stress maximum
1.0
m
Bennett(1978)
A
Georgi+ Toole(1982)
I•
Standard
Case
ß
Bryan(1962)
the net
divergenceof massin the Ekman layer causesupwellingof
cooler water to the surface, which in turn results in a gain of
heat by the ocean.
0.5-
The fact that the ocean south of the wind stress maximum
is a region of net heat gain is not surprising.If the pattern of
annual mean near-surface temperature is to remain steady
despite Ekman suction of colder waters from below, and
equatorwardtransport of these waters in the Ekman layer,
there must be a source of heat.
In the North
Atlantic
it
appears that the heat is supplied by horizontal advection of
relatively warm waters from the south; that is, the nearsurface flow, consisting of the sum of the Ekman and
geostrophicflow, has a significantpoleward component. In
the South Atlantic the poleward penetration of warm water
is blocked by the strong zonal flow of the ACC, and the
required heat must be suppliedby the atmosphere.
Thus the meteorologicalevidence supportsthe notion that
in this density range the net effect of air-sea interactionsis to
warm the surface waters and drive them to the north. While
this is not a demonstration
of the existence of such a water
mass modification mechanism, a rough calculation shows
that the numbers
are reasonable.
To warm 5 Sv of water
25
30
35
latitude
45
(øS)
Fig. 9. Comparisonof estimatesof meridional heat transport in
the South Atlantic.
above 1200m. Of the 24 Sv carried to the southin layers 3-5
in the Brazil Current, half is compensatedby this return
flow. The most intensesalinityminimum signalof the AAIW
is in fact foundjust offshoreof the Brazil Current [Fuglister,
1960]. The net flux of water in this density range in the
interior is weakly to the north (1 Sv). Further east, 16 Sv of
IW is carried to the north by the strong flows near the
easternboundary, resulting in a net flux of 5 Sv to the north
across the section. Note that the net flux across the section
entering the South Atlantic through Drake Passageat an
average temperature of 4.2øC in layer 3 to layer 2 water with
an average temperature of 10.2øC (the average temperature
of the isopycnalboundinglayers 2 and 3 at 32øS)requires
is a relatively small residual of the strong flows in the
opposingboundary currents. The minimum salinity values
found in the equatorward flow in the east are 0.1%ohigher
than in the western part of the section. This may be
0.12PW, or about19W m-2 overtheoutcrop
areaof layer indicative of mixing with the more saline waters above and
3. This value is of the same order of magnitude as the below this layer as the IW crosses the Atlantic from Drake
estimatesof Bunker [1988] and Taylor et al. [1978] for this Passagesouth of 32øS.Thus the transport of IW across 32øS
region.
occurs primarily in narrow flows near the boundaries, with
the northward flow near the western boundary found just
4.
DISCUSSION
seaward of the Brazil Current, rather than as a counterflow
beneath the core of the surface current.
Transport of Antarctic Intermediate Water
The path by which the intermediate water (IW) enters the
Atlantic from the SouthernOceanhasbeen a topic of debate
for several decades.The early view was that the northward
flow of AAIW was concentratedalongthe westernboundary
[e.g., Wl;ist,1935]. Later, severalinvestigatorsconcludedon
the basis of maps of dynamic topography that the AAIW
followed the coast only as far as the Brazil-Malvinas Confluence at 40øS,there turning to the east and following the
path of the anticyclonic subtropical gyre into the South
Atlantic [Martineau, 1953;Reid, 1965;Buscaglia, 1971].The
Meridional Flux of Heat Across 32øS
The overturningcell at 32øSresultsin an equatorwardheat
flux of 0.25 PW in the standard model. This estimate can be
comparedto the estimatesof other investigatorsin Figure 9.
The range of values is very broad, from a minimum of 0.04
PW [Hsiung, 1985] to a maximum of 1.15 PW [Hastenrath,
1980]. (Interestingly enough, both of the extreme values are
obtained by similar bulk-formula integrations of air-sea
exchange estimates.) The heat flux found in the standard
casefalls toward the low end of this range. The projection of
first direct velocity measurements[Evans and Signorini, the total heat content onto the null space vectors for this
1985], however, showed northward flow of AAIW near the sectionis small (<2%), suggestingthat the potential contricoast at 23øS, supporting the earlier ideas of W•ist at least at bution of the unresolved componentsof the flow to the heat
this latitude.
flux is also small. Experiments run with different initial
The results of this model suggest that both paths are referencelevels confirmedthis point: using700 dbar and the
important.As mentionedabove, immediatelyadjacentto the bottom as initial levels resulted in slightly smaller heat
western boundary, poleward flow extends to the bottom in fluxes, showing that the heat flux estimate is stable in the
the Brazil Current and deep western boundary current. sense of not being sensitive to the choice of initial model.
However, just offshore there is a return flow to the north Alternatively, one can use the inverse machineryto explore
RINTOUL'
SOUTH ATLANTIC INTERBASIN EXCHANGE
2685
(Sv)
'transport
0o
-'5
-10
-5
I
!
0
5
10
I
I
1
2
3
400
6
55168
4
5
ø
Layer
6
7
8
9
90ow
60 ø
30 ø
0o
30 ø
.88 PW
.69 PW
standard
60øE
lO
LONGITUDE
11
32ø5 Heat Flux=.69 PW
bTb=6300
12
Fig. 10. As in Figure 5, for the experimentwith the heat flux
Fig. 11. Zonallyintegratedvolumetransportacross32øSfor the
across32øSfixed at 0.69 PW [Hastenrath, 1982].
standardcase, the 0.69 PW case, and the 0.88 PW case.
the consequencesof forcing the system to accommodatea
larger equatorward heat flux.
The model was run again with an additional constraint
forcingthe systemto carry a specifiedheat flux across32øS.
The constraintrequiringthat there be no net massflux across
this latitude was upweighted slightly to ensure that the
system did not satisfy the heat flux constraint by simply
carryinga net flux of massto the north. All other constraints
which the heat flux was set equal to the estimates of
Hastenrath [1982] (0.69 PW) and Fu [1981] (0.88 PW). Figure
were as in the standard
model.
The results obtained when the heat flux is set equal to
Hastenrath' s [ 1982]estimate of 0.69 PW are shownin Figure
11 showsthe integratedmasstransport across32øSfor the
three models. The magnitude of the heat flux and the
strengthof the overturningcell are clearly tightly coupled.
Note, however, that the relative contribution made by each
water massto the total transport remains roughly the same.
The layer geometryimposesstronglimits on the responseof
the systemto the requirementfor an increasedheat flux: the
strengthof the wholecell mustbe increased,ratherthan,for
example,keepingthe volumeunchangedbut maximizingthe
temperature difference by concentrating the flow in the
10. Satisfyingthe heat flux constraintrequiresan increasein
energy of the reference level velocity by a factor of 5. In warmest and coldest layers.
Another useful way to examine how the heat flux conparticular, increasingthe heat flux to 0.69 PW requires a
much more vigorousoverturningcell at 32øS,and the export straint is met is to compare the total mass transport inteof NADW is increased from 17 to 27 Sv. The compensating gratedfrom west to east along the 32øSsection(Figure 12).
equatorwardflow is roughlyevenlysplitbetweenthe ther- The integratedtransportsdiffer substantiallyin the western
mocline and intermediate layers, as in the standard case.
basin. Specifically,to satisfy the requirementfor an inThetransports
atthesections
crossing
theACCreflectthe creasedequatorward heat flux, strong northward velocities
increasedproductionrate of NADW implied by the stronger at the reference level are introduced near the western
overturning cell. The divergenceof IW in the ACC between boundary, decreasingthe poleward flow in the Brazil Curcurrentby a factorof 3.
Drake Passageand 0øEis increasedto 21 Sv, 11 Sv of which rentandthedeepwesternboundary
must be converted to surface or thermocline water before
East of where the Walvis Ridge crosses the section the
leavingthe box to the north across32øS.Thus increasingthe solutionsare nearly identical becausethe constraintrequirexportof heat across32øSrequiresan increaseby a factorof ing no net flux of deep water acrossthis portion of the
øn largelyfixesthereference
levelvelocities
there.To
2 in the net heatingof the oceanby the atmospherein region secti
I. The large flux of NADW enteringregion I at 32øSturns to balancethe northwardflow near the easternboundaryand
the east and leaves the basin as part of the ACC. In the upper keep the total transportequal to zero, the model including
layers, the net flow is slightly decreasedin magnitudeat 0ø the heat flux constraint introduces strong southward flows
and 30øE but is still to the east.
between the Mid-Atlantic Ridge and the Walvis Ridge,
temperature
is lowrelativeto that
Thesechangesin the'patternof masstransportdiver- wherethedepth-averaged
gencesin various water massesalter the heat fluxes as well. in the west. For thismodel,then, the primarypathby which
To supportthe large flux of heat to the north across32øS, NADW leaves to the south is not along the western boundmore heat is carried into the basin at Drake Passageand less ary, where the most intense salinity maximum water is
is removed south of Africa. The difference in heat carried in
found, but just east of the Mid-Atlantic Ridge.
The discrepancybetween the standard model and Fu's
and out of the basin by the ACC is thus increasedby a factor
of 3 from the standard case.
results at first seems surprisingly large, given that both
Further insight into how the system responds to the models use the same IGY section at 32øS and similar
requirement for a larger heat flux can be gained by compar- methods. However, there are several important differences
ing the results of the standardmodel with experimentsin between the calculations. Fu' s heat flux estimate includes an
2686
RINTOUL: SOUTH ATLANTIC INTERBASIN EXCHANGE
32 SOUTH
standard
........ß
k .....
2o]
ternpflux= -168
ternpflux= -214
-20
-60
-80
......
0
2000
4000
6000
distance (km)
Fig. 12. Total masstransportintegratedalong32øSfrom west to eastfor the heat flux experimentsand the standard
case.
Ekman contributionof .28 PW, due to an equatorwardmass North Atlantic Deep Water and the
transport of 5 Sv. Fu realized that this value was probably Thermohaline Circulation
very uncertainand suggestedit be taken as an upperbound,
since it was based on the wind stress values of Hellerman
[1967], which were thought to be overestimated[Saunders,
1976]. The more recent compilationsof Han and Lee [1981]
and Hellerman and Rosenstein[ 1983]in fact suggestthat the
Ekman transport is less than 1 Sv to the north at 32øS.
A second way in which the standard model differs from
that of Fu is in the additionin this caseof a constraintforcing
the net equatorward flux of bottom water (BW) across32øS
to be 4 _+1 Sv, as estimatedby Hogg et al. (1982)from direct
current observations.Fu found the net transportof BW to be
about 1 Sv. By shiftinga larger fraction of the equatorward
flow to the relatively cold BW layers, the BW constraint
effectively decreasesthe equatorward heat flux in the standard model. When the present model was run with this
Traditionally, studies of the thermohaline circulation have
focused on the processand rate of deepwaterformation.
And yet the way in which this deep water returns in the
upper ocean to close the global thermohaline cell is also an
importantpart of the problem, as this may play a role in
determining the rate at which the thermohaline "mill"
grinds. The recent work of Gordon [1985, 1986] has rekindled interest in the path taken by the upwelled water as it
returns to the North Atlantic to balance the export of
NADW.
Gordon [1986] has proposed that this return flow occurs
constraint removed the BW flux was reduced to 1 Sv and the
primarilywithin the warm upper layers of the ocean.In this
schemeNADW reachingthe Pacific upwells into the thermocline, flows westward through the Indonesianpassages
and acrossthe tropical Indian Ocean, where it is joined by
heat flux was increased to 0.4 PW, close to the value Fu
NADW upwelled into the Indian Ocean thermocline, and
obtainedfor the geostrophiccomponentof the heattransport ultimately reentersthe Atlantic via a branch of the Agulhas
(0.38 PW, with the 4000-dbar reference level). Thus the Current that does not complete the retroflection. He condifference in the heat flux estimates of Fu [1981] and the cludedthat the alternative "cold water path," in which the
standard model are due to Fu's overestimate of the Ekman
flow of NADW out of the Atlantic is balancedby water
contribution,and the additionof a constraintin the present entering from the Pacific through Drake Passage, could
modelforcingthe BW flow to be consistentwith the Hogg et account for no more than 25% of the return flow. Gordon
al. current meter results at 32øS.
[1985] also suggestedthat the injection of warm Indian
Driving the systemto accomodatethe meridionalheat flux
estimates of Hastenrath [1982] and Fu [1981] thus leads to
dramatic and unreasonable changes in the circulation at
32øS. Satisfying the heat flux constraint requires a large
increase in the reference level velocities, a near-reversal of
the Brazil Current and the deep western boundarycurrent,
and a much more vigorous overturningcell. We conclude
that the data are inconsistentwith an equatorwardheat flux
of this magnitude at 32øS.
Ocean water at the southeastern
corner of the basin was
responsible for the "anomalous" equatorward heat flux
observed in the South Atlantic.
Gordon called on a variety of evidence to supportthis
hypothesis. The linchpin in his argument was a demonstration that the mean temperatureof the water moving to the
north to balancethe export of NADW was too warm to have
come through Drake Passage. Assuming Hastenrath's estimate of the heat flux (0.69 PW) and an outflow of 16 Sv of
RINTOUL: SOUTH ATLANTIC INTERBASIN EXCHANGE
II8TF[•
3
ii::j
s•
.•s
,54
75øSl
'-'"--....-'
..............
/I I
90øW
60 ø
30 ø
0o
30 ø
60øE
LONGITUDE
Warm
Water
the west.
NADW at 2øC, Gordon estimated the mean temperature of
flow to be 15.4øC. Since the warmest water in
Drake Passageis about 8øC [Gordon and Molinelli, 1982], he
concluded
that most of the return
from the Indian
flow must be thermocline
Ocean.
However, the results of the inverse models suggestedthat
the above argument is not internally consistent. In particular, the heat flux experiments showed that the heat flux
across 32øS is tightly tied to the strength of the meridional
cell. As a result, the magnitude of the heat flux and the
transport of NADW cannot be specifiedindependently. The
flaw in the box-model argument is that the values assumed
for the heat flux and the NADW transport are not consistent
with
each
other:
if one
insists
that
a weak
meridional
circulation carry a large heat flux, an unreasonably high
temperature for the warm return flow is required.
The
inversion
results
flow of intermediate
demonstrated
that
the northward
and bottom water from the Antarctic
plays an important role in closingthe meridional circulation'
independent of the strength of the overturning cell, one half
of the NADW leaving the Atlantic across 32øS returns at
depth in these layers. None of the models showed a net
import of warm Indian Ocean water into the Atlantic. Even
when the system was forced to carry an equatorward heat
flux 4 times that of the standard model, the system responded by increasing the vigor of the overturning cell, not
by introducing an influx of warm thermocline water from the
Indian Ocean. To test directly whether the data set used here
was consistent with a large inflow of Indian Ocean thermocline water, the model was run again with a constraint
forcing a net flux of 13 Sv of warm water (tr0 < 26.8; layers
1 and 2) to the west across the 0ø and 30øE sections.
The results of the warm water path experiment are summarized in Figure 13. Forcing the system to carry a large flux
of warm water into the South Atlantic requires an increasein
the solution norm by an order of magnitude, and reference
level velocities >35 cm s-• near the African coast. To
maintain a total transport across 0ø and 30øE of 130 Sv,
despite a net westward flow of warm water, requires an
increase in the flux of deep and bottom water carried by the
ACC of •35
level velocities
sufficient
to reverse
the 4-6 Sv of eastward
case to a westward
flow of 13 Sv
carry an even larger transport of deep and bottom water to
Path
Fig. 13. As in Figure 5 for the warm water path experiment.
water derived
in sign, leading to a net loss of > 1 PW in region I in contrast
to air-sea exchange estimates, which show this region of the
South Atlantic gaining heat.
An even more dramatic illustration of the large changesin
the flow field required to satisfy the constraint is provided by
comparing the total mass transport integrated along each
section in this model to the standard case (Figure 14). To
carry more warm water into the Atlantic across 0ø and 30øE,
the system introduces reference level velocities to the west
in the northern end of the sections, where these layers are
thickest. In turn, eastward velocities are required in the
southernhalf of the section to keep the total transport equal
to 130 Sv. However, the upper layers are relatively thin and
occupy only a small fraction of the water column; reference
flow found in the standard
bTb=17,400
the northward
2687
Sv. The heat flux across 0 ø and 30øE is reversed
The
effect
on the circulation
is to introduce
a
recirculation of very large transport with westward flow in
the north and eastward flow in the southern part of each
section crossing the ACC. At Drake Passage, for example,
the velocities are large enough to nearly reverse the strong
jet associated with the Subantarctic Front. The transport
acrossthe first 8 station pairs of the 0øE section is more than
200 Sv to the west in this model, compared to roughly zero
net transport for these pairs in the standard case.
Imposing a large net transfer of thermocline water from
the Indian
to the Atlantic
Ocean thus leads to unreasonable
changes in the circulation, and the present data set is
incompatible with an interocean exchange of the magnitude
required by the warm water path hypothesis. This does not
mean, of course, that Indian Ocean water does not enter the
South Atlantic. The constraint required that there be a net
flux of warm
water
across the sections
south of Africa:
an
arbitrarily large amount of warm water could enter the South
Atlantic
and return
to the Indian
Ocean
within
the same
density range and not affect the constraint imposed. That is,
the data are not inconsistent
with the thermoclines
of the two
oceans being connected, as suggested by the similar O-S
relation in each basin [McCartney, 1977; Gordon, 1981b] and
some numerical model results [de Ruijter, 1982; de Ruijter
and Boudra, 1985].
Furthermore, these results do not rule out intermittent
exhange. Indeed, there is good evidence that some Indian
Ocean water enters the Atlantic, but the magnitude of the
exchange and the fate of this water are uncertain. Eddies
formed in the Agulhas Retroflection region have been observed in satellite imagery to enter the South Atlantic
[Harris et al., 1978; Gordon, 1985; Lutjeharms, 1981; Olson
and Evans, 1986]. Olson and Evans [1986] estimate that one
ring per year amounts to a transport of less than 0.5 Sv.
Lutjeharms and Ballegooyen [1988] concluded from a study
of 4 years of daily satellite imagery that rings are shed from
the Agulhas retroflection loop at intervals of 1.5-2 months. If
all rings formed enter the South Atlantic, this formation rate
implies a transport of 3-4 Sv.
In any case, the inverse models show that a large import of
warm water is not necessary to explain the observed equatorward heat transport in the South Atlantic. Several additional piecesof evidencefurther supportthe casefor the cold
water path playing an essential role in the global thermohaline circulation.
The budget of fresh water in the Atlantic apparently
2688
RINTOUL'
SOUTH ATLANTIC
INTERBASIN EXCHANGE
30EAST
standard
warm path
DRAKE
PASSAGE
200
standard
warm path
150
100
5o
-loo
O'
o
-50
'
0
2•0
'
4•0
'
6•0
'
8•0
1 ooo
2000
' 10'00
3000
4000
5000
distance
(km}
distance (krn}
32 SOUTH
standard
warmpath
0 EAST
4OO
standard
wa
3OO
-2O
o
c•
i-
0
1000
20'00
30'00
40'00
20'00
50'00
distance(km)
40'00
60'00
distance(km)
Fig. 14. Total masstransportintegratedfrom southto north alongeach sectionfor the warm water path experiment
and the standard
case.
requires a significantequatorwardtransportof intermediate provided the O-S curve is relatively tight, the transportsof
water across 32øS,following an argument of $tommel [ 1980]. heat and fresh water carried by an overturning meridional
Stommel noted that the shapeof the O-S relation imposed cell are coupled. If the volume-transport-weightedtemperacertain constraints on the meridional flux of heat and freshwater in the ocean. A O-S curve constructed from the mean
layer values at 32øSis shown in Figure 15. It is clear that,
10øC,then a line on the O-S curve connectingthis water with
the poleward flow of NADW has a positive slope, implying
that the meridional flux of fresh water is poleward. If the
transport-weighted
temperature
of thereturnflowis • 15øC,
2O
15
10
3 ß
4 I
6
8
ß
ß
-5
34
ture of the equatorward return flow is warmer than about
0
3•.$
3•.0
3•.$
3•.0
salinity (psu)
Fig. 15. Potential temperature-salinitydiagram constructedfrom
the layer average values at 32øS.
as suggestedby Gordon [1986], then the transport-weighted
salinity is much greater than that of the poleward fl0w,
resultingin a large poleward flux of fresh water. Estimatesof
the net fresh water balance of the Atlantic using bulk
formulae, on the other hand, suggest that the Atlantic as a
whole loses fresh water to the atmosphere [Baumgartner
and Reichel, 1975; Schmitt et al., 1989]. To carry fresh water
into the Atlantic across 32øSand balance the water budget,
the return flow must be sufficiently cold, and hence the
contribution of the subthermoclinewater must be significant.
Broecker and Peng [1982] have also argued that the
nutrient balance of the North Atlantic requires a contribution from the AAIW. Since there is no large sourceor sink of
nutrients in the northern North Atlantic, the upper layer
water feeding the NADW formation regions must have about
the same nutrient concentrations as the NADW leaving.
RINTOUL.' SOUTH ATLANTIC INTERBASINEXCHANGE
2689
about one kilometer depth [at 30øN]. This feature is likely
generatedby the isopycnaltransport of silicaterich water all
the way from the Antarctic Ocean!" (p. 346). A source of
feed water to the formation region at this depth is also
supportedby the radiocarbon data, they continued, as the
observed •14C of NADW is low relative to that of the
equatorward return flow balancing the export of NADW at
32øSis evenly split between the thermocline and the intermediate and bottom water layers, and the surplus of intermediate water entering the basin in the ACC is balanced by
a net export of deep water. Thus both the standard model
and the heat flux tests supportthe notion that the Atlantic as
a whole converts intermediate water entering the basin
through Drake Passageinto deep and bottom water leaving
near-surface
the basin south of Africa.
Broecker and Peng suggestedthat "the most likely candidate
for the feed water is the silicate maximum
water
in the North
water...
found at
Atlantic.
The distribution of AAIW in the ocean is also suggestive
of a link between the intermediate water and the global cell
associated with NADW formation. As Jacobs and Georgi
[1977] noted, the distribution of intermediate water is not
uniform
in the three oceans: the 34.4%o isohaline reaches to
These results are in conflict with Gordon's [1986] recent
suggestionthat the global thermohaline circulation associated with the formation of NADW is closed primarily by a
"warm water path," in which the export of NADW is
compensatedby an inflow of warm Indian Ocean thermo-
cline water south of Africa. To test directly whether the data
set used here was consistent with the warm water path, the
model was run with a contraint added requiring a net flux of
13 Sv [Gordon, 1985] of warm water from the Indian to the
additional source of AAIW within the South Atlantic, or to
Atlantic. Satisfying this constraint required drastic changes
topographic control. Alternatively, the results presented in the circulation, including reference level velocities >35
here suggestthat the AAIW is drawn into the Atlantic by the cm s -1 at 3500 dbar and the introduction of a horizontal
formation of NADW: the AAIW tongue extends further into recirculation of > 150 Sv at the 0 ø and 30øE sections. The
40øSin the Indian Ocean, and to 35-45øS in the Pacific, while
in the Atlantic the same isohaline extends to 5øS. They
suggestedthat the disparity in the degree of penetration of
AAIW in each ocean might be due to the presence of an
the Atlantic
than the other oceans because the Atlantic
is the
only ocean with a significantnorthern sourceof deep water.
Broecker and Takahashi [1981] were led to a similar hypothesis in their study of the intermediate waters in the central
Atlantic.
5.
SUMMARY
AND CONCLUSIONS
presentdata set is thus inconsistentwith a net transfer of
warm water of this magnitudefrom the Indian Ocean to the
South Atlantic.
This does not mean that warm Indian Ocean
water never enters the South Atlantic (flow from the Indian
to the Atlantic and back within a density layer is not
restricted by this model) but rather suggeststhat the import
of Indian Ocean thermocline water does not play a major
part in the globaloverturningcell associatedwith the forma-
An inverse method and historical hydrographic data have
been used to estimate the absolute velocity field in the South
Atlantic poleward of 32øS, with a particular focus on the
exchangeof mass and heat between the South Atlantic and
the neighboring ocean basins.
All the models show a divergence of intermediate water
and a convergenceof deep and bottom water in the ACC
during its transit of the South Atlantic. The shift in transport
from intermediate to deep layers in the ACC results in a net
divergenceof heat carried by the current. The magnitudeof
the divergence, 0.25 --- 0.18 PW, is similar to that found by
Georgi and Toole [1982]. The "loss" of heat is not due to
local cooling of the waters in the ACC, however, but rather
reflects the heat lost in the high-latitude regions in the
formation of deep and bottom water.
The surplusIW carried into the Atlantic leavesthe box to
the north across 32øS, with 5 Sv first gaining heat from the
atmosphereover the broad outcrop area of layer 3 (26.8 < cr0
< 27.2). The equatorward flow of thermocline and IW across
32øSis balancedby a poleward flow of 17 Sv of NADW in the
deepwesternboundarycurrent. This overturningcell results
in an equatorward meridional heat flux of 0.25 PW across
32øS. Forcing the system to be compatible with the larger
heat flux estimates of Hastenrath [1982] and Fu [1981] led to
dramatic changes in the solution: a large increase in the
solution norm, a near-reversal of the western boundary
current, and a doubling in strength of the meridional cell.
These changeswere considered to be unrealistic, and the
hypothesisthat the heat flux across32øSwas as large as 0.69
PW was rejected.
Even when the system is forced to carry an unreasonably
large heat flux across 32øS, however, the water mass trans-
tion of NADW.
ports show the samepattern as in the standardmodel. The
paper.
Taken together, the results of the inverse models make a
strongcasefor the cold water path playinga dominantrole in
closing the thermohaline circulation. Such a role is also
apparentlyrequired by the freshwater and nutrient budgets
of the Atlantic.
Inverse methodshave proved to be particularly useful in
this study of interbasin exchange. By consideringbudgets
for a set of density layers it was possible to make the first
estimates of the transports and transport divergences of
individual water massesin the ACC. These budgets in turn
revealedthe importantrole played by the intermediatewater
in the global thermohalinecirculation. The flexibility of the
method was also used to advantage, enabling us to include a
variety of a priori informationin the model, and to test the
consistencyof specifichypotheseswith the observationsin
an explicit and straightforwardmanner. These results suggest, furthermore, that much could be learned about the
global thermohalinecirculationby applying similar methods
to study the circulationat high latitudes of the South Indian
and South Pacific oceans. In particular, one may hope to
shedsomelight on the poorly understoodupwellingbranch
of the circulation, in which the NADW that has left the
Atlantic
is modified
to become intermediate
water
before
reentering the basin.
APPENDIX:
SENSITIVITY
OF THE FLUX ESTIMATES
The discussion of the errors in the property fluxes pre-
sentedhere summarizesthe presentationof Wunschet al.
[1983] and is included here for completeness;those interested in a more complete treatment are referred to that
2690
RINTOUL: SOUTH ATLANTIC INTERBASIN EXCHANGE
The "true"
velocity at a hydrographic section can be
written
N
To estimate the error in B4, we first use the fact that the V
and Q vectors form a complete set to rewrite the vector of
(vertically integrated) tracer concentrations C:
k
N
C -- Z (CtVl)Vl-• Z
/=k+l
/=1
or
v = A1 + A2 + A3 + A4
where Q are the "null space" vectors [Wunsch and Grant,
1982], vR is the relative velocity, vœis the Ekman velocity,
and b is the reference level velocity. The flux of a tracer C
(CtQl)Ql
/=k+l
Wunschet al. [1983] show that the squaredmagnitudeof B 4
is then given by
(•//2)CtQQtC
lB4
2_< a CtC
• ct
ß
across a section becomes
Fc= B1 + B2 + B3 + B4
where B1,2,3,
4 are the fluxesobtainedby integratingthe
velocities
A 1,2,3,4
timestheconcentrations
alongthe section.
B 3 and B4 can be written
CtQQtC
k
ctc
B• = Ctb= Y• -•2tv•
ctc
whereC tvvtc is the squaredprojectionof C ontothe range
1=1
N
B4= •
CtVVtC
otlCtQlß
/=k+l
Errors in Fc result from errors in each of the individual
componentsof the flux. B1, the flux contribution from the
thermal wind, has errors due to noise in the observations,
navigatioherrors, and interpolationerrors, as discussedin
the text. Errors in B 2 arise from errors in the wind stress.
Thecontribution
fromthereference
levelvelocity
B3 also
contains errors resulting from noise in the observations. The
singular value decomposition provides a formal estimate of
the error in the bi due to data noise,whichcan be converted
intoanestimate
of theerrorin thefluxdueto thissource,
as
seen below. B 4 represents the flux due to the unresolved
components of the flow lying in the null space of the
coefficient matrix A. Since the set of eigenvectorsof A (V, Q)
form a complete set, B 4 representsthe differencebetween all
of A. If the problem is fully determinedand there is no null
space, then A = 0, and this uncertainty is zero. For the
problems consideredhere, the projection of C onto the null
spacetends to be small. The error estimatesgiven in the text
are the change in the transport of each property that would
result from an increase in the rms null space velocity (i.e.,
a2) of 1 cm S-1 .
Acknowledgments. Carl Wunsch provided valuable ideas and
suggestionsthroughout the course of this work, which was completed while the author was a student in the MassachusettsInstitute
of Technology/WoodsHole OceanographicInstitute Joint Program
in Oceanography. W. Nowlin and J. Reid allowed the use of the
AJAX data prior to publication and provided useful comments on
the manuscript. Many thanks to Barbara Grant for computing
assistance.Support was provided by National Science Foundation
grant OCE-8521685 and National Aeronautics and Space Administration grant NAG5-534.
models based on the same data and constraints.
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Z Fl._i_
V•j
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0'2-- Z
i= • (M- lO
where M is the total number
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i j•.
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(Received March 10, 1989;
revised September 10, 1990;
accepted July 6, 1989.)