Neutral Surface Topology

Most oceanic mixing occurs along the neutral tangent plane, but the nonlinear equation of state of seawater prevents any well-defined "density" surface from being parallel to this plane everywhere. A poorly chosen density variable exhibits a large yet fictitious diapycnal diffusivity, caused by a component of the strong isoneutral diffusivity that projects across the density surface. It is therefore important to construct approximately neutral surfaces that minimize this fictitious diapycnal diffusivity, whether for offline analysis or for online evolution of layered models. A new class of approximately neutral surfaces, called topobaric surfaces, is presented. These are formed using a topological tool called the Reeb graph to partition the surface into regions where the in-situ density is a function of the pressure, only. Topobaric surfaces are the topologically correct extension of orthobaric density surfaces to exhibit geographic dependence, which is shown to be fundamental to neutral surfaces. Topobaric surfaces exhibit small fictitious diapycnal diffusivity, and are fast to compute. This topological theory opens new avenues of research into neutral surfaces and neutral density variables.