[1] It is a function of the three state variables (salinity, temperature, and pressure) and the geographical location (longitude and latitude).
These surfaces are widely used in water mass analyses.
In practice, its construction from a given hydrographic dataset is achieved by means of a computational code (available for Matlab and Fortran), that contains the computational algorithm developed by Jackett and McDougall.
Use of this code is currently restricted to the present day ocean.
The neutral tangent plane is the plane along which a given water parcel can move infinitesimally while remaining neutrally buoyant with its immediate environment.
(related in form to hydrodynamical helicity) must be zero everywhere on that surface, a condition arising from non-linearity of the equation of state.
[3] A continuum of such neutral surfaces could be usefully represented as isosurfaces of a 3D scalar field
[6] There will always be flow through any well-defined surface caused by neutral helicity.
Therefore, it is only possible to obtain approximately neutral surfaces, which are everywhere _approximately_ perpendicular to
Numerical techniques can be used to solve the coupled system of first-order partial differential equations (2) while minimizing some norm of
has been defined, neutral density surfaces can be considered the continuous analog of the commonly used potential density surfaces, which are defined over various discrete values of pressures (see for example [9] and [10]).
This spatial dependence is a fundamental property of neutral surfaces.
on a neutral surface is a vital topological consideration.
The solution of the system for a high resolution dataset would be computationally very expensive.
In this case, the original dataset can be sub-sampled and (2) can be solved over a more limited set of data.
The authors suggested to solve this system by using a combination of the method of characteristics in nearly 85% of the ocean (the characteristic surfaces of (2) are neutral surfaces along which
The output of these calculations is a global dataset labeled with values of
values resulting from the solution of the differential system (2) satisfies (2) an order of magnitude better (on average) than the present instrumentation error in density.
values to any arbitrary hydrographic data at new locations, where values are measured as a function of depth by interpolation to the four closest points in the Levitus atlas.
The formation of neutral density surfaces from a given hydrographic observation requires only a call to a computational code that contains the algorithm developed by Jackett and McDougall.
[14] The Neutral Density code comes as a package of Matlab or as a Fortran routine.
It enables the user to fit neutral density surfaces to arbitrary hydrographic data and just 2 MBytes of storage are required to obtain an accurately pre-labelled world ocean.
Then, the code permits to interpolate the labeled data in terms of spatial location and hydrography.
By taking a weighted average of the four closest casts from the labeled data set, it enables to assign
Another function provided in the code, given a vertical profile of labeled data and
surfaces within the water column, together with error bars.
Comparisons between the approximated neutral surfaces obtained by using the variable
and the previous commonly used methods to obtain discretely referenced neutral surfaces (see for example Reid (1994),[10] that proposed to approximate neutral surfaces by a linked sequence of potential density surfaces referred to a discrete set of reference pressures) have shown an improvement of accuracy (by a factor of about 5) [15] and an easier and computationally less expensive algorithm to form neutral surfaces.
In fact, if a parcel moves around a gyre on the neutral surface and returns to its starting location, its depth at the end will differ by around 10m from the depth at the start.
[8] If potential density surfaces are used, the difference can be hundreds of meters, a far larger error.