The transports across the hydrographic lines were determined using an inversion procedure based on conservation constraints in the boxes defined in Figure 2. A detailed presentation of the method is found in Wienders et al. (2000). Volume, heat, salinity, silicate, and the parameters NO and PO (Broecker, 1974) were conserved in the whole water column and in isopycnal water mass layers, with uncertainties based on typical vertical velocities O(10^-6 ms^-1).

Figure 2: Definitions of the boxes where property conservation was imposed. S, C, and N are full-depth boxes limited by the hydrographic lines and the coast. BS, BC, and BN (shaded) are "bottom" boxes used for abyssal waters blocked by the topography.

A prefered solution was selected after a detailed study of the solution sensitivity to the inversion parameters and comparison with previous local results along the western boundary. As an example, Figure 3 shows the solution sensitivity to variations of the a priori reference isopycnals. The differences are minor in the two upper layers. Though more important in the UCPW layer (locally 5 Sv), they do not affect the curve patterns. In the NADW and AABW layers, local differences in the flow direction itself allowed us to discard some reference isopycnals (S₂, S₃). The mutual compatibility of the solutions in this test (and in those relative to other parameters) was quantified to within 5 Sv, except for the AABW in the Argentine Basin, and the NADW north of the equator, where it was closer to 10 Sv.

The inversion led to higher constraint residuals in the northern (equatorial) box than in the two others, probably due to the pronounced temporal variability of the equatorial region, not taken into account in the inversion model.

Figure 3: Solution sensitivity to the choice of a priori reference isopycnals. The curves show the northward accumulated transports across A17 in the main water masses: Central Water (SACW), Intermediate Water (AAIW), Upper Circumpolar Water (UCPW), North Atlantic Deep water (NADW), and Antarctic Bottom water (AABW). The selected solution (S₀) and three other solutions corresponding to reference isopycnals at the top of the NADW, base of the NADW, and top of the Weddell Sea Deep Water (WSDW), are shown.