A pressure-invariant Neutral Density variable for the World's Oceans

We present a new method to label the neutral density of an arbitrary water parcel that depends only on its salinity, potential temperature, latitude, and longitude. In particular, its neutral density is independent of the pressure or depth of the parcel, and is therefore independent of heave in observations or high-resolution models. To do so, we move the parcel, adiabatically and isentropically like a Submesoscale Coherent Vortex (SCV), to its level of neutral buoyancy in a nearby water column of a climatological atlas. The parcel's neutral density γ^SCV is interpolated from pre-labelled neutral density values surrounding this resting location in the climatological atlas. This method is similar to γⁿ of Jackett and McDougall (1997): their discretization of the neutral relationship equated two parcel's potential density referenced to their average pressure, whereas our discretization equates two parcel's potential density referenced to the pressure of the climatological parcel. We compare the material derivative of γ^SCV with that of γⁿ, finding the contributions from irreversible mixing are similar, that lateral advection materially changes γ^SCV by roughly twice the amount it changes γⁿ, and that (by construction) vertical advection has no material effect on γ^SCV. We find similar variations of γⁿ and γ^SCV on the ω-surfaces of Klocker et al. (2009). Finally, we find that isosurfaces of γⁿ and γ^SCV deviate from the neutral tangent plane to a similar degree.