Based on the Levitus atlas, we find that the application of the Montgomery streamfunction
to the isopycnal surfaces induces an error which can not be ignored in some regions
in the ocean. The error arises from the sloping effect of the specific volume anomaly
along isopycnal surfaces. By including the major part of this effect, new streamfunctions,
namely the pressure anomaly and main pressure streamfunctions, are suggested
for the use in potential density coordinates.
By using the newly proposed streamfunction and by including the variations of
specific volume anomaly along isopycnal surfaces, the inverse model proposed by Hogg
(1987) is modified for increasing accuracy and applied to the Brazil Basin to study the
circulation, diffusion and water mass balances. The equations in the model, i.e. the
dynamic equation, continuity equation, integrated vorticity equation, and conservation
equations for heat, salt and oxygen (in which a consumption sink term is allowed), are
written in centered finite difference form with lateral steps of 2 degree latitude and
longitude and 8 levels in the vertical. This system of equations with constraints of positive
diffusivities and oxygen consumption rates is solved by the inverse method. The results
indicate that the circulation in the upper oceans is consistent with previous works, but
that in the deep ocean is quite different. In the NADW region, we find a coincidence of
the flows with the 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 mass balance. Examples show that similar
property fields may results from different processes.