Several neutral surfaces are mapped in this paper and their properties are contrasted with those of potential density surfaces. It is shown that the Pacific is relatively forgiving to the use of potential density, while more care must be taken in the Atlantic and Indian oceans because of the larger compensating lateral gradients of potential temperature and salinity along neutral surfaces in these oceans. The dynamically important tracer, neutral-surface potential vorticity (NSPV), defined to be proportional to f/h (where f is the Coriolis frequency and h is the height between two neutral surfaces), is mapped on several neutral surfaces in each of the world's oceans. At a depth of 1000 m in the Atlantic and Indian oceans, the epineutral gradient of NSPV is different to the isopycnal variations of fN2 by as much as a factor of two (here N is the buoyancy frequency). Maps of isopycnal potential vorticity (IPV) resemble those of fN2, but the values of IPV are less by the simple factor μ, defined by μ=c<R&rgr;-1>/<R&rgr;-c>, where R&rgr; is the stability ratio of the water column and c is the ratio of the values of α/β at the in situ pressure to that at the reference pressure (α and β being the thermal expansion and saline contraction coefficients, respectively). Layered models of the ocean circulation often take the vertical shear between layers (the thermal wind) to be given by the product of the interface slope and the contrast of potential density across the interface. The true thermal wind equation involves the interfacial difference of in situ density, which is larger than the corresponding difference of potential density by the factor μ that is mapped in this paper, taking values up to 1.25 at a depth of 1000 m.

This implies that the thermal wind is currently underestimated by up to 25% in layered ocean models. The differences between the slopes of neutral surfaces and potential density surfaces can be quantified using the factor μ. The magnitudes of these slopes are illustrated here with contour maps and with vertical profiles. One would think that by choosing the reference pressure of potential density to be at the central pressure of a data set, the conservation equation of potential vorticity could be expressed with respect to these potential density surfaces with sufficient accuracy. Here it is shown that even the best potential density variable is significantly in error at thermoclinic frontal regions. This is linked to the fact that diapycnal velocities are not simply due to vertical mixing processes, but are also partly caused by epineutral mixing. ¿ American Geophysical Union 1990