Analysis of data from the Levitus (1982) atlas shows that the application of the Montgomery streamfunction to the potential density surfaces induces an error which cannot be ignored in some regions in the ocean. The error arises from the variation of the specific volume anomaly along isopycnal surfaces. By including the major part of this effect, new streamfunctions, named the "pressure anomaly" and "mean pressure" streamfunctions, are suggested for use in potential density coordinates. By including the variations of specific volume anomaly and pressure along isopycnal surfaces, the inverse model proposed by Hogg (1987) is modified for increased accuracy and then applied to the Brazil Basin to study the circulation, diffusion and water mass balances. The system of equations with constraints of positive diffusivities and oxygen consumption rates is solved by the inverse method. By using multiple tracers and controlling the scale of variation of the diffusion coefficients we are able to construct an overdetermined system whose solution is by a least-square approach. The results indicate that the circulation in the upper ocean is consistent with previous work, but that in the deep ocean differs from some previous analyses. In the NADW depth, we find a coincidence of flow with tongues of water properties. The diffusivities and diapycnal velocities seem stronger in the region near the equator than in the south, with reasonable values. Diffusion plays an important role in the water property balances. Examples show that similar property patterns may result from different processes.