An objective definition of isopycnal surfaces

The concept of density or isopycnal sufaces forms the backbone of our understanding of numerous aspects of the ocean circulation. It is central to the study of quasi-geostrophic motions, potential vorticity, lateral stirring, and the Atlantic meridional overturning circulation, among others. It is well known, however, that the identification of such surfaces is greatly complicated by the thermobaric nonlinearity of the equation of state. So far, the prevailing paradigm has been that isopycnal surfaces should be empirically constructed to be as neutral and material as feasible. Because these two properties cannot be simultaneously and exactly satisfied, isopycnal surfaces constructed in such a way necessarily include subjective elements related to the cost function necessary to define proximity to neutrality and materiality. In this work, I argue that the most natural and objective way to define isopycnal surfaces in the oceans is as the iso-surfaces of the reference pressure of fluid parcels in their state of minimum potential energy entering Lorenz theory of available potential energy. This claim will be supported by a few illustrative examples ranging from the specification of lateral stirring directions in Redi rotated diffusion tensors to the study of the meridional overturning circulation in density coordinates.