Recently obtained World Ocean Circulation Experiment (WOCE) bottle sections and a pre-WOCE bottle data set are used in a water mass mixing model. The mixing scheme comprises three intermediate water sources: Antarctic Intermediate Water (AAIW) from the northern Drake Passage, a combination source of the Indian Ocean intermediate waters entering from south of Africa, and a transformed end-member of the former two sources. I call them dAAIW, iAAIW, and aAAIW, respectively. The dAAIW originates from the southeast South Pacific, enters the South Atlantic in the northern Drake Passage, and is modified in the Falkland Current loop. The iAAIW is a combination of the Indian Ocean sources including Red Sea Intermediate Water, Indonesian Intermediate Water, and AAIW formed locally in the south central Indian Ocean and transformed dAAIW that has returned following a loop through the Indian Ocean. The aAAIW is a transformed end-member of a mixture of dAAIW and iAAIW located in the eastern tropical South Atlantic, characterized by an oxygen minimum and nutrient maxima. Although aAAIW is not an import source like dAAIW and iAAIW, it spans property fields to extrema as a result of water mass mixing and transformation processes and therefore must be included in the basin-wide water mass mixing scheme. The study is performed on five neutral surfaces that encompass the AAIW layer from 700 to 1200 dbar in the subtropical latitudes with a distance of about 100 dbar between a pair of surfaces. Four conservative variables of potential temperature, salinity, initial phosphate (PO4o), and NO and one conservative dynamical tracer fN2 (where f is the Coriolis frequency and N2 is the squared buoyancy frequency) are used as input information to the mixing model. The model-derived mixing fraction gives a quantitative description of AAIW sources when they are mapped onto neutral surfaces. The contoured pattern of mixing fraction shows water mass spreading paths, thus implying circulation and ventilation of AAIW in the South Atlantic. Results show that dAAIW is a dominant water mass and iAAIW is about 30–60% of dAAIW in the subtropical latitudes. With the mixing proportion of AAIW sources derived from the mixing model the geostrophic volume transport and dianeutral upwelling transport can be separated into the individual contributions from each AAIW source. It is found that the percentage of the transport contributed by dAAIW and iAAIW to the South Atlantic is almost constant at 64 ± 2% and 36 ± 2%, respectively. Meridional transport in the subtropical latitudes between 30° and 10°S by dAAIW and iAAIW (referenced to 2000 dbar) has a mean of 4.26 Sv northward (1 Sv = 106 m3 s−1) shared between dAAIW at 2.70 Sv (63%) and iAAIW at 1.56 Sv (37%). The mean zonal transport in the western and eastern South Atlantic between 40° and 3°S is −5.13 Sv westward, shared between dAAIW at −3.38 Sv (66%) and iAAIW at −1.75 Sv (34%). The dianeutral upwelling transport across the uppermost neutral surface σN = 27.25 in the northwest South Atlantic (north of 30°S and west of 10°W) is 2.26 Sv shared between dAAIW at 1.40 Sv (62%) and iAAIW at 0.86 Sv (38%).
 Antarctic Intermediate Water (AAIW) in the South Atlantic plays an important role in the “conveyor belt” circulation [Broecker, 1991; Schmitz, 1995] as it provides the northward return flow for North Atlantic Deep Water (NADW). However, whether NADW replacement water should be mainly supplied by thermocline or intermediate water has caused considerable debate, i.e., the so-called “warm and cold water route” issues. Gordon  showed that the warm thermocline water from the southwest Indian Ocean (the warm water route) is the main contributor. However, Rintoul  argued that the AAIW transport through the Drake Passage (the cold water route) is required by the meridional heat flux to contribute to a major part of the NADW return cell. Rintoul concluded that the warm water route does not play a major role in the return flow of NADW, contrary to the idea of the warm water route proposed by Gordon.
 Later, Gordon et al.  proposed an eastward flow of AAIW from the Drake Passage to the Indian Ocean, looping back to the South Atlantic through the Agulhas eddies, whereas the cold water route suggests a direct flow of AAIW from the Drake Passage to the Benguela Current within the South Atlantic. By invoking this hypothesis they could reconfirm their earlier assertion that the Benguela Current was mainly supplied by the water from the Indian Ocean, consistent with the idea of the warm water route in the thermocline layer. They concluded that the cold water route through Drake Passage can provide no more than one quarter of the total return cell compared with the Indian Ocean contribution. Their scheme is based on the geographical consideration that the South America continent extends to about 56°S, while Africa extends to only 37°S [see also Gordon, 1996]. Therefore the water from the Drake Passage would largely bypass the South Atlantic and flow into the Indian Ocean. Nevertheless, Gordon  also recognized a direct contribution from the northern Drake Passage but regarded it as a relatively smaller source. The debate lead Schmitz  to guess an equal contribution from the Drake Passage and the Indian Ocean. Obviously, a quantitative measure of the relative contributions from the Drake Passage and the Indian Ocean is required. The existence of these different AAIW import sources is evident in the South Atlantic in both property distribution and model results [Stramma and England, 1999; de Ruijter et al., 1999].
 As AAIW is observed crossing the equator into the North Atlantic, some northward paths must exist in the southern South Atlantic. McCartney  and Talley  suggest that the northern Drake Passage is the source of AAIW in the South Atlantic, although its origin of this water is in the southeast South Pacific (Talley suggested the same source even to the Indian Ocean). Piola and Gordon  and Provost et al.  emphasized the importance of the transformation of AAIW after Drake Passage in the southwest South Atlantic.
 Farther equatorward, the flow path of AAIW is, however, rather complicated. In the past, AAIW was considered to flow directly northward from the Falkland Current to the equator as a western boundary current [Wüst, 1935; Deacon, 1937; Defant, 1941]. However, Taft  noted the nonunidirectional flow along the western boundary; northward flow was only found south of about 40°S (the Falkland Current) and north of 25°S (under the Brazil Return Current [Zemba, 1991] and the North Brazil Undercurrent [Stramma et al., 1995]). In a comprehensive study of the total geostrophic circulation of the South Atlantic, Reid  showed two gyre-governed flows of intermediate water: a subtropical anticyclonic flow centered at about 35°S and a near-tropical cyclonic flow centered at about 10°–15°S, called Tropical Gyre by Gordon and Bosley . Reid's scheme indicates a splitting between the northward and southward western boundary flows at the Vitσria-Trindade Ridge (at about 20°S). Recent observations from neutrally buoyant float tracks (RAFOS) [Hogg et al., 1996] suggest that the separation point may be as far north as 25°S. Later, Boebel et al. [1997, 1999a] identified a divergence at 28°S from RAFOS float trajectories. Therefore it appears that the bifurcation location shifts between 25° and 30°S, presumably because of climatological variations.
 For AAIW to be a significant contributor of NADW replacement water, AAIW must be transformed into either lighter water in the upper layer or heavier water at depth when it propagates to the north. The latter case seems impossible because AAIW is observed at a shallow depth of 700 m in the western equatorial Atlantic and terminates in the tropical North Atlantic. On the other hand, Talley  noted that the AAIW salinity minimum core extends into a slightly higher density after it crosses the equator than when it is still south of the equator. You  discovered that the increase of density is caused by dianeutral mixing of cold/fresh upper Circumpolar Deep Water with AAIW, inducing diffusive convection. However, the density increase is not enough for a considerable sinking of the AAIW core to the NADW depth level. The slight density increase of the AAIW core north of the equator implies that the rising of AAIW most likely occurs before crossing the equator. This is confirmed by the recent study on dianeutral mixing, transformation, and transport of AAIW in the South Atlantic by You . He found that the AAIW sources from the northern Drake Passage and the southwestern Indian Ocean contribute to the NADW return flow by dianeutral upwelling into the South Equatorial Current (SEC). Coherent and significant dianeutral upwelling appears in the northwestern South Atlantic north of the bifurcation (about 25°S). He speculated that the AAIW sources could not obtain enough heat/buoyancy to rise until they have reached the western boundary region north of the bifurcation. With updated results, You  derived a schematic AAIW circulation in the South Atlantic that is adapted here as Figure 1. The dianeutral upwelling region is marked by a solid dot in an open circle east of the Brazil coast. The AAIW sources at the northern Drake Passage and the southwestern Indian Ocean are marked by a solid dot. The schematic shows that the northern Drake Passage source water is carried to the eastern limb of the subtropical gyre along the southern perimeter of the gyre where it merges with the northwestward spreading of the Indian Ocean source water leaked from the Agulhas Current. Then the merged water proceeds northwestward in the lower Benguela Current and the northern perimeter of the subtropical gyre. Further equatorward transit of the mixture is found in the western boundary region east of the Brazil coast and north of the bifurcation point, the branching between the Brazil Current and the Intermediate Western Boundary Current under the North Brazil Undercurrent. Dianeutral upwelling occurs during the equatorward progression of the mixture. Part of the mixture eventually crosses the equator into the tropical North Atlantic through the Western Boundary Current. The rest of the mixture turns to the east south of the equator, then southward at the eastern boundary, and back to the west in the northern Benguela Current, forming a cyclonic gyre called the South Equatorial Gyre (SEG). Here we use a different name to distinguish this circulation from the “Tropical Gyre,” the name applied by Gordon and Bosley  to the thermocline water circulation since we discuss intermediate water in this study. One will see later that the SEG does have different features. The schematic AAIW circulation depicted in Figure 1 has been partially observed recently with a series of RAFOS float tracking studies by Boebel et al. [1997, 1999a], Schmid , and Schmid et al. . Combining their observations with historical float trajectories from various independent float programs, Boebel et al. [1999b] were able to track AAIW paths to the tropical North Atlantic.
 The two import sources, the northern Drake Passage and the southwest Indian Ocean, are well defined at their entrances to the South Atlantic, compared with the situation in the Indian Ocean [You, 1998a] where the entrance of AAIW from the Southern Ocean is less well defined. Recent comprehensive studies of intermediate water mixing, circulation, and transformation in the Indian Ocean by You [1998a, 1998b] showed the percentage contribution of all Indian Ocean water masses to the Agulhas Current system. These water masses are Red Sea Intermediate Water (RSIW) including the Persian Gulf influence, Indonesian Intermediate Water (IIW), and AAIW from south central Indian Ocean and south of Australia. In this study I cannot deal with so many Indian Ocean source water masses; rather, I treat them as only one import source as a whole to the South Atlantic via south of Africa. This is reasonable when I consider only the South Atlantic basin. Readers can refer to the numerous studies dealing with the currents and water masses in the two locations, southwest and southeast South Atlantic. A good review as to how the Agulhas eddies can escape the eastward retroflection of the Agulhas Current and leak into the South Atlantic is given by Lutjeharms . For the northern Drake Passage source, one can refer to McCartney , Talley , and England . As discussed above, a quantitative estimate of the relative strength of the two import sources is crucial for resolving the debate of warm/cold water route issues. This is the main objective of the present study. On the other hand, transport and spreading of the import sources contribute to the circulation and ventilation of AAIW in the South Atlantic, therefore interpreting the proposed circulation in Figure 1. In this study I will use recently obtained World Ocean Circulation Experiment (WOCE) and pre-WOCE bottle data including potential temperature, salinity, oxygen, and nutrients in a water mass mixing model. With the mixing patterns and spreading paths known the AAIW circulation and ventilation can be inferred, and the proposed schematic AAIW circulation in Figure 1 can therefore be examined. The rest of the paper is organized as follows. The data and method used are described in section 2. To be consistent with the study by You  on dianeutral mixing, transformation, and transport of AAIW in the South Atlantic, I apply neutral surfaces as the study frame [McDougall, 1987]. The same five neutral surfaces used by You , σN = 27.25, 27.32, 27.40, 27.45, and 27.55, will be applied with the σN = 27.40 surface following the salinity minimum core of AAIW (here σN denotes the neutral density similar to σθ used for potential density). However, to avoid showing too many figures, I present the mapping of neutral surfaces and property distributions only on the AAIW core surface σN = 27.40 in section 3. A water mass mixing model is described in section 4. Our reasons for including aAAIW in the mixing model are discussed in detail in section 4. The model-derived water mass mixing fractions are presented in section 5 on each of the five neutral surfaces and in two meridional sections and one zonal section. A sensitivity study of the choice of source water masses is carried out in section 6. Given these mixing proportions, the geostrophic transport for the AAIW layer bounded by the uppermost and lowermost neutral surfaces is separated into the individual contributions from the import sources (the northern Drake Passage and the southwestern Indian Ocean) in section 7. The dianeutral upwelling transport across the uppermost neutral surface σN = 27.25 in the northwestern South Atlantic from the previous study of You  is also separated into the different import source contributions in this section. Finally, summary remarks and perspective are concluded in section 8.
2. Data and Methods
 The bottle data set used in this study is composed of various sources including both recently obtained WOCE bottle data and historical hydrography. The new WOCE bottle data include three transatlantic sections occupied by the German ship FS Meteor from 1991 to 1994: sections A8 along 11°S [Zenk and Müller, 1995], A9 along 19°S [Siedler and Zenk, 1992], and A10 along 30°S [Siedler et al., 1993]. Because of a sampling problem, A8 contains no phosphate data. Two other WOCE sections occupied by German vessels in the Southern Ocean are also included. They are sections A21 across the Drake Passage by FS Meteor [Roether et al., 1990] in 1990 and A12 from Cape Basin westward to the Antarctic by Polarstern [Lemke, 1994] in 1992. The A12 and A21 bottle data were obtained from the WOCE Hydrographic Program (WHP) Special Analysis Centre (SAC) in Hamburg, Germany. Additional relatively new bottle data from the South Atlantic Ventilation Experiment (SAVE) including legs 1, 2, and 3 [Oceanographic Data Facility, 1992a] and legs 4 and 5 [Oceanographic Data Facility, 1992b] were also obtained from WHP SAC in Hamburg. The pre-WOCE historical bottle data include (1) the Southern Ocean Atlas [Gordon and Molinelli, 1982], obtained from WHP SAC, and (2) the archived bottle data from the Center for Meteorology and Physical Oceanography, Massachusetts Institute of Technology. The latter historical data set contains a major part of J. Reid's data [Reid, 1989].
 The combined WOCE and pre-WOCE hydrographic data form the data set in Figure 2. When the data points are plotted on the lowermost neutral surface σN = 27.55, there are a total of 3116 stations. Since the number of data points decreases as the depth increases, more data stations are found on the shallower surfaces. As seen in Figure 2, the entire basin of the South Atlantic is well covered. Each bottle data station contains mostly physical-chemical observations including potential temperature θ(°C), salinity S, dissolved oxygen O2 (μmol kg−1), phosphate PO4 (μmol kg−1), silicate H4SiO4 (μmol kg−1), and nitrate NO3 (μmol kg−1). Although the data set contains a significant number of high-quality WOCE data, it also includes some historical data measured with old techniques. I have not attempted to improve the historical data to modern standards. However, after a few outliers in the property-property plot were removed I did not find any significant discrepancy between old and new data through data comparison, objective analysis, and contour plotting. Nevertheless, the measurement accuracy for modern WOCE data of potential temperature, salinity, oxygen, phosphate, silicate, and nitrate is achieved at ±2 mK, ±0.002 psu, ±0.01 μmol kg−1, ±0.01 μmol kg−1, ±0.1 μmol kg−1, and ±0.05 μmol kg−1, respectively.
 I use neutral surfaces as the study frame because neutral surfaces are more accurate than potential density surfaces and less affected by compressibility (see the demonstration figure of Figure 1 by You [1998a]). Oceanic mixing is believed to be more aligned with neutral surfaces because when a water parcel moves a small distance isentropically and adiabatically on a neutral surface, it will not experience any buoyancy restoring force. A neutral surface is defined such that α∇nθ = β∇nS, where ∇n is the lateral gradient operator on a neutral surface, α = ρ−1∂ ρ/∂θ is the appropriate thermal expansion coefficient, and β = ρ−1∂ ρ/∂S is the haline contraction coefficient [McDougall, 1987]. In this study I adopt the same five neutral surfaces used by You  (see Figure 3). I select the neutral surfaces in this way: first, I choose the σN = 27.4 surface to follow closely the salinity minimum core of AAIW; I then select two neutral surfaces σN = 27.25 and 27.55 to follow loosely the AAIW core (the upper and lower boundary surfaces of AAIW); and finally, I take additional two surfaces σN = 27.32 and 27.45 (not shown in Figure 3) between the core surface σN = 27.40 and the upper boundary surface σN = 27.25 and between the core surface σN = 27.40 and the lower boundary surface σN = 27.55 to follow the AAIW core more closely. As a result, the distance between a pair of surfaces is about 100 dbar. Tsuchiya et al.  noted that the AAIW salinity minimum along their meridional section 25°W in the South Atlantic cannot be followed by just one single potential density surface: south of 40°S, the salinity minimum is better followed by 27.15 σθ; in the subtropical latitudes between 40° and 20°S a slightly higher density of 27.2 σθ is needed to describe the salinity minimum; and farther to the tropical latitude north of 20°S, the highest density of 27.30 σθ could follow the salinity minimum better. Therefore they have to use three potential density levels to describe the AAIW salinity minimum in the South Atlantic. Talley  used a single density of 31.7 σ1 to give an approximate description of the intermediate salinity minimum for the global oceans. Obviously, the nonlinear nature of the state equation of seawater is a major factor that can cause a potential density surface to fluctuate more than a neutral surface [McDougall, 1987; You, 1998a]. Since a neutral surface has already taken these nonlinear effects into account, the AAIW salinity minimum in the South Atlantic is better followed by only a single neutral density of σN = 27.40 than by any potential density surface, as shown in Figure 3.
 I define a water mass as a body of water with a common formation history for all its contained elements. The intermediate water of the South Atlantic contains two import sources, one in the southwest South Atlantic (the Falkland Current loop) and another in the southwest Indian Ocean (the southern tip of South Africa). I call the former dAAIW, representing an inflow from the Drake Passage, and the latter iAAIW, a combination of all the Indian Ocean sources. Water mass transformation is achieved both along neutral surfaces (epineutral mixing) and across neutral surfaces (dianeutral mixing). The transformation processes convert the mixture of dAAIW and iAAIW to a rather different water mass in the eastern tropical South Atlantic, characterized by high temperature, salinity, and nutrients but low oxygen. The steady decrease of oxygen value from its maximum in the Southern Ocean to a minimum in the eastern tropical South Atlantic implies an aging process since the last contact of AAIW sources with the atmosphere. I call this transformed end-member of the dAAIW and iAAIW mixture the aAAIW. The definition of aAAIW will be discussed further in section 4. As seen in Figure 1, aAAIW is associated with the SEG. Obviously, water mass transformation of dAAIW and iAAIW is controlled also by the dynamics of the two opposing subtropical and tropical gyres. Detailed property features of these AAIW sources will be described on neutral surfaces in section 3.
 As a water mass is a physical entity of finite volume, it can be mathematically described by a functional relationship between its characteristic properties and a set of standard deviations. A water type is defined as a point in parameter space; it is only a mathematical construction and does not occupy any volume in parameter space. The functional relationships of a water mass represented by its characteristic properties can then be described by a finite set of water types that I call source water types. In practice, if the functional relationship between all parameters of a water mass is linear, the water mass can be described by a minimum of two source water types.
 These ideas are developed in a water mass analysis method called optimum multiparameter analysis (OMP) which was first proposed by Tomczak  and later further developed by Mackas et al.  and Tomczak and Large . You and Tomczak  first expanded the method to a basin-wide description of water mass mixing, circulation, and ventilation on isopycnal surfaces in the thermocline of the Indian Ocean. Later, You [1998a] applied the analysis on a physically more meaningful frame, the neutral surface frame, in the intermediate depth of the Indian Ocean because of the increasingly divergent tendency between isopycnal and neutral surfaces in the intermediate depth layer. More recently, You  combined OMP analysis with a dianeutral velocity calculation to address the renewal mechanism of NADW in the deep Indian Ocean. The earlier idea for the OMP analysis was developed from sediment composition analysis in a lake where a sediment sample is composed by the source components of discharge rivers. The idea is particularly useful for the situation of AAIW in the South Atlantic as dAAIW and iAAIW are import sources from the southeastern Pacific and southwestern Indian Ocean. Thus the intermediate water layer of the South Atlantic can be imagined as a lake where each water sample is a mixture of the two inflow sources, dAAIW and iAAIW. However, unlike sediment particles that are somewhat solid objects, oceanic water is in a fluid form that can easily move around and be affected by the surrounding environment, resulting in property exchange between different water bodies causing intrinsic property conversion. Therefore, logically, any water sample can be described by the mixing of dAAIW and iAAIW as well as the transformation process of aAAIW. Here I briefly review the method again: it solves a linear system of mixing equations for each data point in which all water masses are represented through respective water types. The linear system for any water sample is written as
where G is a matrix containing the parameter values that define the source water types, xv is a vector containing parameter values for the sample (the observations), xg is a vector containing the relative contributions or mixing ratios of the source water types to the sample, and R is a vector containing the residual of water mass conservation. The water mass conservation equation is
 The multiple tracer analysis method has been successfully applied to the South Atlantic by several studies, such as Maamaatuaiahutapu et al. [1992, 1994, 1998] for the Brazil-Malvinas confluence region and Larque et al.  using the SAVE sections for almost the whole water column. These applications are different from present study since they resolve the local water mass mixing problem in cruise sections, whereas I discuss the whole basin-scale mixing in a water mass layer bounded and spanned by neutral density surfaces. Since in a linear approach a minimum of two source water types can describe a source water mass that spans vertically across neutral surfaces, the present layered mixing model also includes dianeutral mixing implicitly as more than one source water mass is included in the model. With more source water masses involved the mixing system includes both epineutral and dianeutral mixing, thus representing a three-dimensional view of water mass structure. Further detailed description of the water mass mixing model will be provided in section 4.
 To solve equations (1) and (2) for a mixing system of three source water masses dAAIW, iAAIW, and aAAIW, at least six equations are required. With six parameters, potential temperature, salinity, dissolved oxygen, phosphate, silicate, and nitrate, and the water mass conservation equation (2) a total number of seven equations are available. Therefore the mixing system can be solved. However, among the six parameters, oxygen and nutrients are nonconservative variables. In order to use only conservative parameters in the water mass mixing model for deriving a more accurate mixing fraction, I introduce two conservative variables PO4o [Broecker et al., 1985] and NO [Broecker, 1974]:
where PO4, O2, and NO3 are the observed phosphate, oxygen, and nitrate, respectively, and O2sat is the oxygen saturation at the temperature and salinity of the sample. The coefficient Re is known as the Redfield ratio. Here I use 175 for Re as suggested by Broecker et al. . With conservative variables of potential temperature, salinity, PO4o, and NO plus the water mass conservation equation (2) I have a total of five equations. I am still short one equation for resolving the mixing of six source water types. To have an additional equation, I introduce a dynamical conservative tracer, potential vorticity (PV) fN2, where f is the Coriolis frequency and N2 is the squared buoyancy frequency. Thus I have six equations that satisfy the system (1) with all conservative parameters. This study is the first to apply the tracers NO and PV to OMP analysis.
3. Neutral Surfaces and Property Distributions
 As mentioned above, a total of five neutral surfaces are selected for AAIW in the South Atlantic, σN = 27.25, 27.32, 27.40, 27.45, and 27.55, encompassing the intermediate water layer between about 700 and 1200 dbar in the subtropical latitudes with a distance of about 100 dbar between each pair of surfaces. For mapping the neutral surfaces the Jackett and McDougall  code was used, which facilitates the determination of a neutral density surface from a hydrographic cast. Their reference cast is located in the South Pacific (16°S, 172°W) for global oceans. The density value at the reference cast is based on the Veronis  definition, which provides the name for the neutral density surface.
 Since I use ungridded hydrographic stations (Figure 2), it is necessary to apply objective mapping in order to produce contour maps. I used a length scale of about 3°–5° in latitude/longitude to derive a smoothed contour. In order to avoid showing too many figures for the property distributions on neutral surfaces, here I present only the core surface σN = 27.40 that closely follows the AAIW salinity minimum core (see Figure 3). Figures 4a–Figure 4j includes mapped pressure, potential temperature, salinity, dissolved oxygen, phosphate, silicate, nitrate, initial phosphate (or preformed phosphate), NO, and potential vorticity on the σN = 27.40 neutral surface. Figure 4a shows that this core surface lies at 900 dbar in the subtropical latitudes with a maximum pressure of 1000 dbar in the western subtropical gyre. The surface plunges steeply equatorward from the Weddell Sea where the surface outcrops with a pressure <100 dbar. In the subtropical latitudes, note that the deep part of the subtropical gyre enclosed by the isobar of 900 dbar is open to the southwest Indian Ocean. This suggests direct contact between the subtropical South Atlantic and the southwest Indian Ocean, implying a possible infloss passage of iAAIW. In the southwest South Atlantic the isobars of 600 and 700 dbar point to the north after Drake Passage near the Argentine coast, indicative of the northward Falkland Current. The isobars of 500 dbar and less immediately south of 600 dbar, however, extend northeastward, showing a bifurcation. An isolated enclosed isobar of 500 dbar north of Malvinas Island indicates a cyclonic subgyre, the Falkland Current loop (see Figure 1). Toward the equator the neutral surface shoals to a relatively uniform pressure of 700 dbar. However, the pressure inside the enclosed isobar of 700 dbar is slightly higher. This is spatially consistent with the location of the SEG as seen in Figure 1. On the shallower and deeper neutral surfaces (not shown) the enclosed isobar with slightly higher pressure inside is not so evident. Along with the different property distribution between intermediate and thermocline waters this may suggest a different tropical gyre structure between the shallow Tropical Gyre [Gordon and Bosley, 1991] and the deep intermediate gyre, i.e., SEG.
 A minimum temperature of −0.5°C is found in the Weddell Sea (Figure 4b). The temperature value then increases to a maximum of over 5°C in the tropical South Atlantic. The isothermal lines of 4.5° and 4°C extend in opposite directions in the western boundary between latitudes of 35° and 10°S, indicative of the bifurcation between the southward Brazil Current and the northward Intermediate Western Boundary Current under the North Brazil Undercurrent. The isothermal line of 4.5°C stretches westward south of Africa, suggesting the inflow of iAAIW from the southwest Indian Ocean and the Agulhas retroflection. The temperature is quite uniform over the Malvinas Current region, indicative of the formation region of Subantarctic Mode Water (SAMW) [McCartney, 1977]. Inshore, isothermal lines of 3.5° and 4.0°C extend northward from the northern Drake Passage to about 48°S. In the tropical South Atlantic, potential temperature is uniform at 5°C north of 25°S. The isothermal line is strongly tilted from the west coast of Namibia at about 25°S to the western equatorial Atlantic north of Brazil, consistent with the flow path of the northwestward lower Benguela Current that feeds the North Brazil Current (Figure 1).
 Salinity has a minimum of 33.80–33.85 in the Weddell Sea and a maximum of 34.5 in the eastern tropical South Atlantic (Figure 4c). The inflow iAAIW salinity south of Africa is 34.4 and higher. The bifurcation signal in the salinity field is indicated by isohalines of 34.3 and 34.4 in the western boundary of east Brazil. This is a rather persistent feature, as seen in other properties such as oxygen (Figure 4d), phosphate (Figure 4e), and nitrate (Figure 4g). Like temperature, isohalines of 34.2–34.3 switch to inshore in the north after the Drake Passage.
 Dissolved oxygen has a maximum of 340 μmol kg−1 in the Weddell Sea and a minimum of 100 μmol kg−1 in the east tropical South Atlantic (Figure 4d). The oxygen in the Falkland Current loop region is 240–260 μmol kg−1 and is 200 μ mol kg−1 and lower in the iAAIW inflow region south of Africa. The equatorward decrease of oxygen suggests an aging of the water mass since its last contact with the atmosphere. The slightly higher oxygen in the western boundary of the tropics suggests an exit path for tranformed AAIW to cross the equator into the North Atlantic. The oxygen minimum in the east tropical South Atlantic indicates the oldest AAIW mixture, the aAAIW. When I combine Figure 4d with Figure 1 to examine the oxygen minimum pattern, I understand that the oxygen minimum value is associated with the cyclonic flow of the SEG. Except for part of the AAIW mixture crossing the equator into the North Atlantic in the western equatorial Atlantic (see the relatively higher oxygen in the west than the east), the rest of the mixture turns to the south in the eastern boundary and resides the longest time in the gyre. Because of its long trapping time in the gyre, oxygen is continuously consumed by biological uptake. In an alternative interpretation, Reid  linked the oxygen minimum pattern with a slow coastal upwelling. This could be understood by the dynamics of SEG itself. When the southern perimeter of SEG moves westward offshore, the higher nutrient water below rises, resulting in high oxygen consumption.
 The phosphate distribution in Figure 4e shows an equatorward increase. A minimum of 1.5 μmol kg−1 is found in the Weddell Sea, while a maximum of 2.6 μmol kg−1 is located in the eastern subtropical South Atlantic. The phosphate value at the two entrances of dAAIW and iAAIW is remarkably similar at 1.9–2.0 μmol kg−1.
 Silicate has quite a different distribution, compared to temperature, salinity, oxygen, and phosphate as analyzed above. Silicate shows a maximum of 80 μmol kg−1 in the Weddell Gyre and along the Antarctic Continent (Figure 4f). However, an extremum is not found in the eastern tropical South Atlantic like oxygen and phosphate. It shows only a moderate value of 29–30 μmol kg−1. A silicate minimum of 25 μmol kg−1 is found extending eastward from the Falkland Current loop region, a good indicator for dAAIW inflow. One will see later that this silicate signal is consistent with the PV signal marking the dAAIW. In contrast, another inflow source iAAIW is characterized by a relatively high silicate of 40–45 μmol kg−1, which implies the signal of high silicate RSIW and IIW flowing into the region [You, 1998a]. North of 35°S, the silicate value is remarkably constant at 29 μmol kg−1.
 In Figure 4g, nitrate shows an equatorward increase from a minimum of 22–24 μmol kg−1 in the Weddell Sea to a maximum of 38–40 μmol kg−1 in the east tropical South Atlantic, echoing the general distribution of oxygen and phosphate. Note that nitrate data are poor east of Greenwich meridian and south of Africa. Since this study discusses mainly the mixing north of 50°S, the final result is not affected.
 In the following I analyze the calculated three conservative tracers, initial phosphate, NO, and PV, which will be used in the mixing model. The initial phosphate in Figure 4h shows a tongue of low value extending westward from south of Africa, marking the inflow of iAAIW. The phosphate tongue on this neutral surface is stronger than on the other neutral surfaces. Relatively high initial phosphate is found in the Weddell Gyre, and low values are found in the tropical South Atlantic. NO shows an equatorward decrease from its maximum of 560 μmol kg−1 in the Weddell Sea to a minimum of 440 μmol kg−1 in the tropics (Figure 4i). The PV distribution in Figure 4j shows a general poleward increase. However, a noticable feature is the low-PV tongue extending eastward from the Falkland Current loop region. This is an indication of dAAIW transformation after Drake Passage in the southwest South Atlantic, especially in the austral winter [see Piola and Gordon, 1989; Provost et al., 1995]. The low PV marks the important signal for dAAIW, a typical feature for SAMW [McCartney, 1977; Talley, 1996]. South of Africa, iAAIW enters the South Atlantic with slightly higher PV. Clearly, the low PV and initial phosphate give distinct signals to the two import sources, dAAIW and iAAIW.
 For a concluding remark to the above property distributions, dAAIW is characterized by relatively low temperature and salinity, moderate initial phosphate and NO, and a prominent low PV; iAAIW is characterized by relatively high temperature, salinity, and PV, a moderate NO value, and a prominent low initial phosphate; aAAIW exhibits extrema in most property fields in the eastern tropical South Atlantic. These property characteristics on five neutral surfaces provide useful information to the water mass mixing model that is established in section 4.
4. Model Source Water Type Definition and the Water Mass Mixing Model
 The above property distributions on neutral surfaces show that the AAIW sources are well defined. The dAAIW and iAAIW are two import sources from the northern Drake Passage and the southwestern Indian Ocean. The aAAIW is the transformed end-member of the dAAIW and iAAIW mixture with property extrema in the eastern tropical South Atlantic. Therefore it is logical to define the former two sources, dAAIW and iAAIW, at their entrances 55°–48°S, 65°–52°W and 35°–40°S, 15°–30°E, respectively. The region for aAAIW is defined at 8°–15°S, 5°–17°E in the eastern tropical South Atlantic. In the above I have briefly discussed the reason to include aAAIW in the water mass mixing model. Here I give further details of the aAAIW definition. A full sensitivity study of the choice of source water mass definition will be given in section 6. In Figure 5 I plot dAAIW, iAAIW, and aAAIW at their source regions in a property-property diagram of potential temperature–salinity (Figure 5a) and potential temperature–oxygen (Figure 5b) on the AAIW core surface σN = 27.40. Obviously, with only two import sources, dAAIW and iAAIW, the basin-scale mixing in the South Atlantic cannot be described. That is because water mass transformation has turned aAAIW to another end-member in the property-property plot, virtually a different water mass signal. In other property-property plots (not shown), aAAIW is also shown as a different water mass from dAAIW and iAAIW. The difference between dAAIW, or iAAIW, and aAAIW is that aAAIW cannot be interpreted as a moving water mass component contributing to the intermediate water circulation as dAAIW and iAAIW can. Including aAAIW is therefore required only by the water mass mixing model. On the other hand, the mixing model allows one to test different results. With only dAAIW and iAAIW included in the model an unacceptably large residual is found in the tropical region. If aAAIW was defined near the western equatorial Atlantic, there would be no AAIW crossing the equator into the North Atlantic, contrary to observations. Nevertheless, the aAAIW distribution on neutral surfaces would still have physical meaning in terms of transformation process and aging speed.
 The averaged property values in the definition regions are used as a first guess for source water types that are called initial source water types. With the properties mapped on five neutral surfaces I derive five initial source water types for each source water mass. They are shown in Figure 6 in diagrams of potential temperature against salinity (Figure 6a), potential temperature against initial phosphate (Figure 6b), potential temperature against NO (Figure 6c), and potential temperature against PV (Figure 6d). The symbol of cross is used for the initially guessed water types for dAAIW, the asterisk is used for iAAIW, and the plus is used for aAAIW. It is seen that in most cases the initial water types already show a near-linear distribution across the five neutral surfaces. The dAAIW is an exception in that a full linear distribution is achieved only in the diagram of potential temperature against NO in Figure 6c. In the rest of the property-property diagrams, there is no linear distribution because of the change in property value at the AAIW core surface σN = 27.40. On the other hand, the property distribution suggests that dAAIW is a major AAIW source, while iAAIW and aAAIW are more or less transformation sources of dAAIW. The property curvature of AAIW characteristics along σN = 27.40 surface is the strongest for dAAIW. Figure 6a shows that none of the source water mass satisfies a linear distribution in the θ-S diagram. This is caused by the characteristic salinity minimum of these source water masses at the core surface σN = 27.40.
 A similar situation was met by You [1998a] for AAIW in the Indian Ocean. To solve the nonlinear problem, the procedure of calculating the water mass contribution is applied separately for the neutral surfaces above and including the core surface σN = 27.40 and below and including the core surface σN = 27.40. The respective properties involved are θ-S, θ-PO4o, and θ-NO for dAAIW and only θ-S for iAAIW and aAAIW. Readers are referred to You and Tomczak  and You [1997, 1998a] for details of the method for handling this particular problem.
 The procedure also calculates the weights for each parameter with data points on all five neutral surfaces. The source water types used for OMP analysis (called model source water type) are derived from the best fit points through regression analysis (the best fit points are the intersection points of neutral surfaces and best fit lines). They are marked by the open circle in Figure 6. The values on the uppermost (σN = 27.25) and lowermost (σN = 27.55) neutral surfaces and on the core surface (σN = 27.40) at the breakpoints for dAAIW, iAAIW, and aAAIW are then taken as the model source water types. They are tabulated, together with weights, in Table 1. Obviously, the procedure of determining the model source water types has delineated and simplified the water mass structure in property-property diagrams. Mixing of these model source water types defined for dAAIW, iAAIW, and aAAIW constitutes the mixing model to derive the results of mixing ratios described in section 5.
Table 1. Source Water Type Definition and Parameter Weight
Water Type on Neutral Surface
Potential Temperature θ, °C
Initial Phosphate PO4o, μmol kg−1
NO, μmol kg−1
PV, × 1010 s−3
dAAIW on σN = 27.25
dAAIW on σN = 27.40
dAAIW on σN = 27.55
IAAIW on σN = 27.25
IAAIW on σN = 27.40
IAAIW on σN = 27.55
aAAIW on σN = 27.25
aAAIW on σN = 27.40
aAAIW on σN = 27.55
 Readers are reminded that such a water mass mixing system includes both epineutral and dianeutral mixing (along and across neutral surface mixing) as the model water types lie not only on the same neutral surfaces but also across the neutral surfaces. However, to single out either epineutral or dianeutral mixing from the system is impossible because all model water types are bound together in the same scheme.
5.1. On Neutral Surfaces
 The mixing scheme comprises a mixing system of two source water masses, dAAIW and iAAIW, as well as a transformation end-member aAAIW. The sum of the total water mass contributions is added to 100% plus a residual. In section 3, in order to avoid showing too many figures I presented property distributions only on the core neutral surface σN = 27.40. However, for a better description of the mixing fraction for the whole AAIW layer it is necessary to show the mixing fraction results mapped onto all five neutral surfaces. Figures 7, 8, 9, 10, and 11 show the water mass contributions and residual on five neutral surfaces. Water mass fractions are also shown on three cross sections: along 30°W in the western South Atlantic, along 5°E in the eastern South Atlantic, and along 37°S in the Southern Ocean. On the uppermost neutral surface σN = 27.25 (Figure 7a) the mixing proportion contributed by dAAIW is 100% in the Falkland Current loop region, indicative of its source region (note that in the figures, values are given as ratios, not percentages, so the number 1 in the figures is equivalent to 100%). The mixing fraction then decreases equatorward. More than 60% of dAAIW dominates the Southern Ocean south of 40°S. South of Africa, dAAIW mixing fraction significantly decreases eastward to 10%, leaving room for iAAIW to enter. In the western boundary east of Brazil the isolines of 40 and 30% bifurcate to southward and northward. About 30% of dAAIW continues equatorward, with about 20% reaching the western equatorial region, likely crossing the equator into the North Atlantic. The remaining 10% is found in the eastern tropical South Atlantic, contributing to the cyclonic SEG circulation. Thus dAAIW source water is partly converted to aAAIW along the path from its source region.
Figure 7b shows the fraction of iAAIW from the southwest Indian Ocean. At the entrance south of Africa the iAAIW contribution is close to 100%, indicating the source region of iAAIW. However, nearly 70% of iAAIW is trapped in the Agulhas retroflection. Only about 30–40% of iAAIW leaks into the subtropical latitudes between 10° and 40°S, with up to 30% reaching the South American coast. When the pattern of mixing fraction is compared with the property distribution (not shown), most iAAIW is found lying in the northern rim of the subtropical gyre, tilting northwestward. In the western boundary, about 10% of iAAIW extends to 10°S near the coast of Brazil. Compared to Figure 7a, dAAIW is clearly a dominant water mass on this uppermost neutral surface.
Figure 7c shows the fraction of aAAIW, an indication of the transformation speed of the dAAIW and iAAIW mixture. The maximum of 100% fraction in the eastern tropical South Atlantic suggests that the greatest transformation of water mass properties has occurred there. In other words, the region contains the oldest AAIW. Generally speaking, the aAAIW fraction is lower in the Southern Ocean than in the tropics because the Southern Ocean is close to the inflow region of dAAIW and iAAIW and the water is therefore less aged. Toward the equator, water mass transformation continues for longer, and the water is therefore more aged. Also, aAAIW shows a relatively lower fraction in the western boundary than in the eastern boundary. This is understandable since the water mass is less transformed in the western boundary than in the eastern boundary. A remarkable feature in Figure 7c is the rather high fraction of 50% south of Cape Town, while water at the same latitude in the western boundary is only 10% aAAIW. This suggests that the water south of Africa is older than that in the west because iAAIW itself contains largely the transformed dAAIW looping back to the South Atlantic. Oxygen distribution in the region was at least 50 μmol kg−1 lower near South Africa than at the same latitude in the western boundary. The information here suggests that iAAIW cannot be a dominant water mass for AAIW circulation and ventilation.
Figure 7d shows the water mass conservation residual. As seen in Figure 7d, north of 45°S, the residual is close to zero everywhere, suggesting that the calculated mixing fractions given above are rather accurate. A relatively high residual is found only south of 45°S, where as seen in Figure 7a, the region is largely occupied by dAAIW. A large residual occurs outside of the defined mixing domain as seen south of 45°S.
 Closer to the AAIW core on the σN = 27.32 neutral surface, dAAIW contributes about 10% more to the equatorial region than does the upper surface (Figure 8a). Meanwhile, the contribution of iAAIW to the tropical South Atlantic has also increased significantly. About the same amount of iAAIW as dAAIW spreads to the equatorial South Atlantic, so that about 10–20% of iAAIW is likely to cross the equator into the North Atlantic through the western boundary. The equatorward increase of both dAAIW and iAAIW fractions can be supported by Figure 8c, which shows that the aAAIW fraction has reduced by about 10–20% compared to the above surface. For instance, the 80% contour line in the western equatorial Atlantic is now reduced to 60% (see Figure 7a). The 90 and 100% isolines have largely retreated to the eastern boundary.
 On the AAIW core surface σN = 27.40 in Figure 9 one would expect an enhanced northward advection of AAIW sources. Evidence is found only in the western boundary north of Brazil where the dAAIW 10, 20, and 30% contribution isolines extend slightly more to the equator than on the upper and lower surfaces in Figures 8a and 10a. However, the iAAIW contribution is much less than on the upper and lower surfaces (Figure 9b). This is because dAAIW dominates the mixing proportion. The aAAIW contribution seems to retreat more northward than on the above surfaces between 30° and 40°S (see the 10 and 20% contour lines in Figure 9c). This suggests that along the core of AAIW, iAAIW and aAAIW give more room to dAAIW. In the subtropical latitudes the dAAIW contribution is actually slightly less than above surface σN = 27.32. The strong dAAIW but weak iAAIW in the tropics also suggests that the strong dianeutral upwelling found between 30° and 10°S (see also the salinity section in Figure 3) is mainly contributed by dAAIW. You  showed increasingly strong dianeutral upwelling toward the shallower neutral surfaces in this region. Water mass transformation can cause isopycnal surfaces to evolve upward or downward. Because of the strong dianeutral motion, to conclude the examination of the equatorward advection of AAIW, it is necessary to discuss the AAIW layer bounded by the σN = 27.25 and 27.55 neutral surfaces rather than only the core surface σN = 27.40.
 Below the AAIW core on the σN = 27.45 neutral surface in Figure 10, dAAIW provides about 10–20% of its water mass contribution to the western equatorial South Atlantic (Figure 10a), slightly less than above surface σN = 27.40. The contribution by iAAIW, however, reaches a maximum in the tropical South Atlantic among the five neutral surfaces. About 30% of iAAIW contribution is found north of 25°S. When the property distribution is examined on the corresponding neutral surface (not shown), an almost identical potential temperature of 4.5°C is found at the iAAIW source region south of Africa to the broad basin area north of 25°S. Other properties such as salinity, initial phosphate, and NO have values close to that in the tropical latitudes. Corresponding to the increase of iAAIW contribution in the tropical latitudes, aAAIW fraction is significantly reduced, becoming the smallest among the five neutral surfaces (Figure 10c).
 On the lowermost neutral surface σN = 27.55 the water mass contributions of two AAIW import sources, dAAIW and iAAIW, are substantially reduced (Figure 11). The dAAIW fraction to the equatorial Atlantic is at least 10% less than the above four surfaces (Figure 11a). The distribution of iAAIW fraction is patchy, suggesting an intermittent northwestward spreading. Nevertheless, iAAIW still makes about a 10–20% contribution to the western boundary at the east coast of South America (Figure 11b). Figure 11c shows a maximum of 100% ratio in the equatorial South Atlantic by aAAIW, the highest fraction among the five surfaces, with the 90% contoured line extending southward to nearly 20°S. Apparently, AAIW sources age the fastest on this lowermost neutral surface, suggesting a relative weakening of the equatorward AAIW advection near the lower boundary.
5.2. In Cross Sections
Figures 12, 13, and 14 show the water mass fraction in three cross sections, two meridional sections along 30°W in the western South Atlantic and along 5°E in the eastern South Atlantic, and one zonal section along 37°S, crossing the inflow region of iAAIW. Since basic information about water mass spreading has already been provided on all five neutral surfaces in Figures 7, 8, 9, 10, and 11, I present the mixing fraction in the cross sections in order to show the vertical structure of the water mass for further detailed analysis. For simplicity I present these sections only at constant longitude and latitude. Readers can always refer to the epineutral distribution of the fraction for detailed local distributions such as near the western and eastern boundaries along the coasts of South America and western Africa. These sections are mapped with neutral density range (kg m−3) as the vertical coordinate. Figure 12a shows the contribution by dAAIW in the western South Atlantic. Its mixing fraction is 100% south of 43°S, indicative of the source region. The fraction then decreases equatorward with 10% reaching the equator. The strongest equatorward advection of dAAIW is found at σN = 27.45 south of 37°S and at a lower neutral density of σN = 27.40 in the north, showing the core path of AAIW.
 The iAAIW source in Figure 12b does not show a successive distribution to the equator like dAAIW since iAAIW's spreading to the west is perpendicular to this section. At σN = 27.40 the iAAIW contribution is only 10%, showing a minimum at the AAIW core. This is understandable from the water mass conservation equation (2) as dAAIW takes the most proportion at σN = 27.40. Obviously, dAAIW is a dominant water mass in the western South Atlantic. In the lower and higher densities, iAAIW contribution reaches a maximum of 30%. At σN = 27.45 the 30% contour of iAAIW fraction extends to the equator, showing a significant contribution of iAAIW to the equatorial South Atlantic. Because the large fraction of iAAIW lies in the high neutral density, the dianeutral upwelling in the tropics as the contribution of AAIW to the NADW replacement flow seems mainly to be contributed by dAAIW, less by iAAIW. This will be seen even clearer later. In Figure 12c the aAAIW contribution shows a southward decrease with a maximum of 80% and more lying near the equator. The contoured isolines show three curvatures in the vertical: southward stretching at σN = 27.40 and two equatorward stretchings at σN = 27.32 and 27.45, with the strongest equatorward stretching at σN = 27.45. The poleward stretching implies that AAIW source water from the south ages fast toward the equator and vise versa for the equatorward stretching. Obviously, this transformation does not reflect the dAAIW source, as dAAIW spreads faster toward the equator at σN = 27.40 (see Figure 12a). It reflects the iAAIW source. This is because iAAIW from the Indian Ocean largely contains the already transformed dAAIW. Therefore aAAIW mostly describes the continuous transformation procedure of dAAIW → iAAIW → aAAIW.
 In the eastern South Atlantic, dAAIW shows 100% fraction close to 45°S (Figure 13a), slightly more south of the western section compared to Figure 12a. This has implications for the eastward downstream of dAAIW to the Indian Ocean. Compared to the western section, the strong spreading of the equatorward dAAIW is found at σN = 27.45 until 34°S. This is roughly the latitudinal location of the most southern tip of South Africa. Farther north, the spreading core rises significantly to σN = 27.32 until 25°S. North of 25°S, the dAAIW fraction is vertically the same. The minimum 10% fraction is up to 15°S, while it reaches the equator in the western section. Clearly, the major northward spreading path of dAAIW lies in the western boundary (north of the bifurcation).
 The iAAIW contribution shows a maximum of 40% in the lower neutral density range (σN = <27.35) centered at 35°S (Figure 13b). In Figure 12b, however, the maximum contribution is centered at 25°S, showing that iAAIW extends 10° more to the north in the eastern South Atlantic. The minimum contribution of iAAIW at σN =27.40, as seen in Figure 12b, is not so evident in Figure 13b. This is because the section is close to the source region of iAAIW. Another reason is that dAAIW does not reach a maximum along σN = 27.40 in the eastern South Atlantic. The iAAIW shows a strong northward extension at σN = 27.45 north of 30°S. The tongue corresponds to the maximum tongue of aAAIW in Figure 13c, reflecting the fast aging of iAAIW.
Figure 14 is the only zonal section shown in this study. In order to examine the westward spreading of iAAIW from the Indian Ocean the section is chosen at 37°S. Meanwhile, I can examine the dAAIW profile in the western boundary region. The section should perhaps be chosen slightly farther to the south as the eastern end of the section may cross the shallow shelf of the Agulhas Bank. However, for a basin-scale description the effect of Agulhas Bank is negligible. On the other hand, iAAIW usually flows northwestward after it enters the South Atlantic. A zonal section farther south therefore cannot describe iAAIW distribution better than the current section. As seen in Figure 14a, dAAIW shows an eastward tongue. The 100% of dAAIW contribution lies in the western boundary, suggesting that most of the water mass there is composed of dAAIW. Then the tongue extends eastward at σN = 27.45 until the Greenwich meridian. Farther east (but west of 15°E), the tongue tends slightly upward. This is the longitudinal location where dAAIW enters the South Atlantic equatorward. The slight rising of dAAIW in this band suggests that dAAIW most likely feeds to the lower Benguela Current.
 The iAAIW has a large percentage of mixing fraction up to 100% concentrated to a rather narrow longitude band of only 5° near 30°E (Figure 17b). This region is where the lower Agulhas Current is located. The iAAIW contribution then shoals westward with a large percentage found in the upper level. Another feature worth mentioning is that unlike dAAIW, which appears as a steady and continuous transition tongue, iAAIW mixing patterns are usually not continuous. This fits the general idea that the leaking of the Agulhas Current to the South Atlantic is usually in the form of sporadic eddies.
Figure 14c shows the fraction of aAAIW, which is mainly concentrated in the longitudinal band between 10° and 30°E. This is the location where dAAIW and iAAIW meet and the transformed dAAIW returns to the South Atlantic. One can thus expect an intensive mixing and water mass aging in the region. West of 10°E, the mixing fraction of aAAIW is largely zero except for the upper and lower boundaries. The distribution suggests that the northward path of AAIW sources has to be west of 10°E. This is consistent with the property distributions, which show generally northward extension of contour lines west of 10°E, while inshore, the contour lines in the eastern boundary extend southward.
6. Sensitivity Study of the Choice of Source Water Masses
 In section 4 the water mass mixing model was built on two import sources, dAAIW and iAAIW, and a transformation end-member of aAAIW. The dAAIW and iAAIW were well defined at their entrances to the South Atlantic in the Falkland Current loop region (considering the vigorous water mass transformation after Drake Passage) and south of Africa. The aAAIW was defined at the east tropical South Atlantic where property extrema are found. The mixing model showed meaningful results of water mass mixing fraction on neutral surfaces and cross sections in section 5. Water mass spreading paths can thus be identified from the contoured maps, implying the basin-scale circulation and ventilation of water masses.
 Because model results rely on the definition of model source water types that were determined from initial source water types through regression analysis, the choice of source water mass is critical. Here we want to examine the results by conducting a sensitivity study. The initial source water types were derived from the definition region as mean values. The procedure is somewhat subjective. However, You [1998a] compared the definition with that from cluster analysis and found no great difference. It is especially true in the intermediate layer of the South Atlantic where sources are imported and naturally defined at their entrances. In this study I experimented with various choices of source water types. The effect on results is summarized in the sketch diagram of Figure 15. In Figure 15a, whether or not the initial source water type is guessed from a big or small definition region (determined by the radius), the result of mixing fraction is not changed significantly so long as the cluster center is unchanged. Figure 15b shows that although two definition regions are the same, with the cluster center moved to the left the resulting whole pattern of mixing fraction moves to the left accordingly. An opposite situation occurs in Figure 15c. Figures 15b and 15c suggest that the source water masses of dAAIW and iAAIW defined slightly more inside or outside from their entrances than the current definition would affect the basin-wide distribution of mixing fractions. In other words, this is equivalent to the source water mass joining the basin-scale mixing earlier or later. Therefore I can conclude that the mixing results as shown in section 5 are subject to the definition positions of the chosen source water masses. This is understandable, for instance, if I define dAAIW in the northern Drake Passage; the mixing of dAAIW with iAAIW and aAAIW then starts from there (somewhat earlier). However, a physically more meaningful choice is to place the definition region of dAAIW in the Falkland Current loop region as carried above.
Figure 15 discusses the changes in spatial variability with the change of source water mass definition region. The mixing fraction would also be changed with the time variability of source water masses in spite of the timescale being seasonal, decadal, or even much longer scale (climotological). Maamaatuaiahutapu et al.  showed strong seasonal variability in the upper layer of the Brazil-Malvinas confluence. Since I use historical and modern WOCE data, the results shown in this study represent an annual mean situation at best. A well-covered basin-wide seasonal data set for the whole South Atlantic still needs to wait for some time to come. With an annual mean data set I cannot discuss seasonal variability in this study. On the other hand, this is not a critical issue as I study the intermediate layer that is less changed with season. The present data set does not easily permit a further longer timescale study for the source water masses. To obtain a diagnostic study of the impact of climotological variations on the changes in source water mass properties, I perform a perturbation study. I assume that the long-term climotological variability would lead to the change of source water property by 10%. This might be exaggerated for intermediate depth; at least I give an upper bound extreme. Because dAAIW is a dominant water mass, for simplicity, I carry a perturbation test of 10% change only for dAAIW. Then I will examine the responding change of iAAIW. Figure 16a shows the 100% fraction of dAAIW at its source region, varied by 10% increase (dotted line) and decrease (dashed line) of its model source water mass properties. With 10% increase the 100% fraction contour line migrates at least 5 latitudinal degrees more to the north, implying more dAAIW contribution to the mixing system (thus less iAAIW and aAAIW fraction can be expected). It is actually a slightly northward shift of the whole pattern of mixing fraction. The opposite situation occurs when the water mass property of dAAIW is changed by a 10% decrease. On the other hand, a decrease of source water mass property increases its contrast with other source water masses. Thus mixing takes a longer time, and vise versa. That is why I see the 100% source water mass fraction lying more to the south.
Figure 16b shows the impact of the corresponding change of dAAIW property on iAAIW. The response of iAAIW is opposite to the change of dAAIW (here I show 70% fraction because 100% fraction contour is hard to vision). It appears that the increase of dAAIW source water property leads to a decrease of iAAIW fraction. This can be understood that when dAAIW takes a larger proportion of mixing, less remaining proportion (minus by 100%) has to be shared by iAAIW and aAAIW. Figure 16b also shows that the response of iAAIW to the change of dAAIW property is less significant (see also the 100% contour line east of 10°E in Figure 16a). The reason is probably due to the long journey dAAIW has traveled to the Indian Ocean and back through the Agulhas Current system via south of Africa.
 In the above discussion I have not carried a study of the response of dAAIW to changes in iAAIW. I consider that dAAIW is the dominant water mass in the AAIW circulation in the South Atlantic. Therefore the above perturbation study for diagnosing the climatological variability by focusing on the change of dAAIW and response of iAAIW is adequate. Incidentally, about 5° differences of the bifurcation position in observation east of Brazil, as mentioned in section 1, can be interpreted by the perturbation study in this section. The shift of the bifurcation position is suggested because of the impact of climatological variations on dAAIW property changes. On the other hand, impact of climatological variations on the variability of AAIW properties might be smaller than 10% compared to the upper thermocline layer. For a smaller change the contoured lines of 100% mixing fraction in dotted and dashed lines would be much closer to the solid line of annual mean of this study.
7. Transport Contributed by AAIW Sources
 With the mixing proportion derived above the total geostrophic transport in the AAIW layer can thus be separated into the individual contributions of each AAIW source. This is because the whole AAIW layer in the South Atlantic is shared by these source water masses. The relative importance of the AAIW sources from the Drake Passage and the southwest Indian Ocean can therefore be counted quantitatively. As mentioned above, aAAIW describes only the transformation of the dAAIW and iAAIW mixture and therefore has no contribution to water mass transport. For water mass balance I then assume that the part of transport by aAAIW is proportionally shared by dAAIW and iAAIW. In fact, with or without this assumption the ratio of input sources dAAIW and iAAIW is unchanged. The percentage contribution of the two import sources is a major concern in this study.
 For the transport estimate I first calculate the flow stream function, the acceleration potential (10 m2 s−2), on each neutral surface. Suga and Talley  have mapped acceleration potential (referenced to 4000 dbar) on an isopycnal surface σθ = 27.3 to describe the AAIW circulation. However, their potential density surface can only follow the AAIW salinity minimum to north of 20°S. Also, they used only a limited number of cruise sections, mainly the SAVE sections. Here, I want to present the acceleration potential on neutral surfaces with better data coverage on a basin scale. Therefore more details of the AAIW circulation feature should be described.
Figure 17 shows the stream function on the AAIW core surface σN = 27.40 referenced to 2000 dbar. The identifiable flow paths have been marked with arrows. As seen in the Figure 17, most flow patterns are consistent with the sketch diagram of Figure 1. However, some details need to be added, for instance, the southward flow along the west coast of South Africa in the Cape Basin. This is a strong feature as seen both in the property fields and mixing fraction distributions. Another feature missed in Figure 1 is the westward flow right at the equator. Figure 17 shows that the eastward flow along the northern perimeter of SEG bifurcates, with some water turning to the south and some turning to the equator in the eastern tropical South Atlantic, forming the westward branch along the equator.
 With the flow stream function it is easy to calculate the geostrophic transport across 1° × 1° cubic sides. In Figure 18 I show the geostrophic transport vector by the two AAIW sources, dAAIW (Figure 18 (left)) and iAAIW (Figure 18 (right)) in Figures 18a and 18b. For detailed northward (v component) and eastward (u component) transport I separate the transport vector into the contoured components in Figures 18c–18f. The total transport is calculated for the whole AAIW layer between the neutral surfaces σN = 27.25 and 27.55 and integrated vertically for the neutral surface pairs. The contribution by each source is calculated with its mixing proportion. Thus the transport by dAAIW and iAAIW is separated quantitatively. In Figure 18a, dAAIW shows a predominant large transport south of 40°S. The iAAIW transport has a minimum in this region (Figure 18b). In the north the equatorward transport path of dAAIW is seen clearly in the western boundary north of 25°S. The relatively strong westward transport of dAAIW along the equator and southward transport along the western South Africa coast in Cape Basin are also evident in Figure 18a. The strong southwestward transport from the Indian Ocean by iAAIW is seen clearly south of Africa in Figure 18b. Along the equator, iAAIW contributes to the westward transport.
 In Figure 18c, dAAIW contributes to the eastward transport (solid line) south of 38°S and in two tropical latitudinal zones, 20°–15°S and 8°–3°S. Westward transport (dashed line) is found in the broad subtropical latitudes between 38° and 20°S, 13°–8°S, and along the equator. The westward transport components are also found at the Brazil-Malvinas confluence region. In Figure 18b a relatively strong transport path extends from south of Africa westward to the broad westward transport region in the subtropical latitudes, marking the transport path of iAAIW. The meridional transport in Figures 18e and 18f shows the major three northward paths (solid line) for dAAIW and iAAIW in the western and eastern boundaries and approximately above the mid-ocean ridge. Between these northward paths, southward transport is found (dashed line).
 With the given meridional and zonal transport components in Figure 18 I integrate the transport along five constant latitudinal lines (40°, 30°, 20°, 10°, and 5°S) and two longitudinal lines (30°W and 5°E between 40° and 3°S) for the AAIW layer. The results are shown in Figure 19a. The transport number is given separately for dAAIW and iAAIW. The meridional net transport is positive northward, and the zonal net transport is negative westward. The transport values are also shown in Table 2. A sensitivity check by changing the reference level by 500 dbar less at 1500 dbar and 500 dbar more at 2500 dbar shows an ∼30% variation. The meridional transport by dAAIW decreases steadily from 3.8 Sv at 30°S to 1.4 Sv at 5°S. Its zonal transport is westward in the western and eastern South Atlantic, and the transport value changes a little between −3.11 Sv in the west and −3.64 Sv in the east. The zonal transport for iAAIW also shows a relatively constant value between −1.58 Sv in the west and −1.93 Sv in the east. Except for the southern and northern ends the northward transport by iAAIW is less varied in the subtropical latitudes, 1.38 Sv at 30°S, 1.36 Sv at 20°S, and 1.94 Sv at 10°S. It is found that the transport percentage by the two sources is almost constant, 64% by dAAIW with a small variation of ±2 and 36% by iAAIW with the same variation of ±2%. The estimate is based on the mean transports in the subtropical latitudes. The meridional transport in the subtropical latitudes between 30° and 10°S by dAAIW and iAAIW has a mean of 4.26 Sv northward, shared by dAAIW at 2.7 Sv (63%) and by iAAIW at 1.56 Sv (37%). The mean zonal transport in the western and eastern South Atlantic between 40° and 3°S is −5.13 Sv westward, shared by dAAIW at −3.38 Sv (66%) and by iAAIW at −1.75 Sv (34%).
Table 2. Cross-Section Geostrophic Transport of AAIW Sources Between σN = 27.25 and σN = 27.55 Neutral Surfaces Referenced to 2000 dbar
Sensitivity With Reference Level Changed by 500 dbar
 In the previous study, You  showed a strong dianeutral upwelling transport across the uppermost neutral surface σN = 27.25 in the northwestern South Atlantic [see You, 1999, Figure 13a]. When the upwelling transport north of 30°S and west of 10°W is integrated, I find that the total upwelling transport by dAAIW and iAAIW is 2.26 Sv. This transport is divided proportionally into 1.40 Sv by dAAIW and 0.86 Sv by iAAIW on the basis of their mixing proportion (see Figure 19b). Interestingly, the transport percentage is 62% by dAAIW and 38% by iAAIW, close to the percentages from the geostrophic estimates. Therefore I conclude that the import transport is about 64 ± 2% by dAAIW from the Drake Passage and 36 ± 2% by iAAIW from the southwestern Indian Ocean.
8. Summary and Perspective
 In this study I used recently obtained WOCE bottle data from the German ships FS Meteor and Polarstern in the South Atlantic combined with pre-WOCE data in a water mass mixing model. The study is focused on quantitative estimate of two import sources of AAIW from the northern Drake Passage and the combined Indian Ocean intermediate waters from the southwestern Indian Ocean, called dAAIW and iAAIW, respectively. The iAAIW contains a large part of transformed dAAIW flowing into the Indian Ocean and coming back after a loop in the Indian Ocean and the intermediate water formed locally in the south central Indian Ocean. Two other smaller sources as part of iAAIW are RSIW and IIW. The mixture of dAAIW and iAAIW continues to transform toward the equator and reaches the extrema of water mass property in the eastern tropical South Atlantic with an oxygen minimum and nutrient maxima. The potential temperature-salinity diagrams in Figures 5a and 6a show a successive change of water mass from the coldest/freshest dAAIW to iAAIW with medium temperature and salinity and then to the warmest/saltiest aAAIW. Figure 5a indicates a linear transformation of dAAIW → iAAIW → aAAIW, while Figure 5b shows that the linear increase is distorted by the influence of the Indian Ocean sources in potential temperature–dissolved oxygen diagram. This implies a water mass transformation process. I called the transformation end-member aAAIW. Thus the mixing system comprises two source water masses, dAAIW and iAAIW and the transformation end-member aAAIW. Regarding the AAIW formation source, strictly speaking, there is only one real AAIW source, the dAAIW, as revealed from the above study; iAAIW and aAAIW are transformed water masses from the former. You [1998a] showed the relatively small contributions of RSIW and IIW to the southwest Indian Ocean. Nevertheless, for the purpose of estimating the quantitative water mass contribution by dAAIW and iAAIW to the AAIW circulation and ventilation in the South Atlantic it is logical to use dAAIW and iAAIW as import sources in the geographic sense and iAAIW and aAAIW as converted sources of dAAIW. The system is therefore established by two end-members dAAIW and aAAIW and a medium member iAAIW. Thus the scheme relates these three sources by mixing along and across neutral surfaces.
 Five conservative variables, potential temperature, salinity, initial phosphate, NO, and potential vorticity, are used as input information to the mixing scheme. The mixing model returns with mixing fractions as outputs. When the mixing fractions are mapped on neutral surfaces and cross sections, the relative importance of each AAIW source becomes obvious by showing the percentage contribution in the AAIW layer. The above results show that dAAIW is the predominant water mass, about 30–60% higher than iAAIW in the subtropical latitudes. Because water mass conservation requires the total fractions of dAAIW, iAAIW, and aAAIW to be added to 100%, a very strong and high dAAIW proportion along the core of AAIW in the western South Atlantic leads to a minimum distribution of iAAIW.
 Given the mixing proportion by each AAIW source, geostrophic and dianeutral upwelling transports were proportionally separated into individual contributions. It is found that the transport percentage contributed by dAAIW and iAAIW to the South Atlantic is almost constant at 64 ± 2% and 36 ± 2%, respectively. The meridional transport in the subtropical latitudes between 30° and 10°S by dAAIW and iAAIW has a mean of 4.26 Sv northward, shared by dAAIW at 2.70 Sv (63%) and by iAAIW at 1.56 Sv (37%). The mean zonal transport in the western and eastern South Atlantic between 40° and 3°S is −5.13 Sv westward, shared by dAAIW at −3.38 Sv (66%) and by iAAIW at −1.75 Sv (34%). The dianeutral upwelling transport across the uppermost neutral surface σN = 27.25 in the northwestern South Atlantic (north of 30°S and west of 10°W) derived from the previous study by You [1999, Figure 13a] is a total of 2.26 Sv, shared by dAAIW at 1.40 Sv (62%) and by iAAIW at 0.86 Sv (38%). These transport estimates conclude the relatively constant percentages, 64 ± 2% by dAAIW and 36 ± 2% by iAAIW, respectively. The Indian Ocean source iAAIW itself is 56% of the Drake Passage source dAAIW in average. A sensitivity analysis for geostrophic calculation by changing the reference pressure for 500 dbar less and more from 2000 dbar showed a roughly ±30% difference. The change of reference levels can change the magnitude of volume transport to a certain degree but does not change the percentage of the relative contribution by dAAIW and iAAIW. For the dianeutral upwelling transport, You  has already given an error band of 10–20% with a half order of magnitude change from an assumed constant vertical diffusivity.
 Now I recall the argument discussed in section 1, the so-called warm/cold water route issue. One should bear in mind that the issue actually concerns which source provides the main return water formation of NADW. In the present study the focus is somewhat different. In this study, attention is only paid to the AAIW layer (or cold water route alone). I have not discussed the main thermocline layer. The present study along with the earlier study in dianeutral mixing and transport by You  puts forward the discussion in two aspects: first, the quantitative measure of relative strength of the northern Drake Passage and the Indian Ocean has been made, and second, dianeutral upwelling in the northwest South Atlantic connects AAIW from the intermediate depth into the upper layer (SEC), thus contributing to the NADW replacement flow.
 The mixing ratios derived from the model output enable a quantitative estimate of AAIW source contribution. The contoured pattern of water mass contribution on neutral surface shows the spreading path of AAIW source, implying AAIW circulation and ventilation in the South Atlantic. Thus the results derived from this study interpret and implement the AAIW circulation proposed by You  in Figure 1.
 This study was carried out when the author was a guest investigator to the Department of Regional Oceanography, Institut für Meereskunde of Kiel University. He is grateful for the financial support and provision of facilities. The author would like to thank Victor Goureski for help in accessing the Gordon and Molinelli  data and Charmaine King for the MIT archive. The comments from Sonya Legg and two anonymous reviewers have helped to improve the presentation of the results. This is a WOCE contribution.