The potential density of sea water is defined as that density which the sample would have if raised adiabatically and without change of salinity to the surface (i.e. the conditions of atmospheric pressure). A parcel of sea water under pressure will experience a slight decrease of temperature when expanded adiabatically to atmospheric pressure. The amount of temperature change is given in Tables 11, 12, 13 and 14 of The Oceans (pp. 63-65). For all practical purposes, however, the effect of this small temperature change has negligible effect on the density and, consequently, the potential density can be taken as where T and S are the temperature and salinity in situ, and the zero denotes the condition of atmospheric pressure (i.e. zero gauge pressure).
As a matter of convenience for describing the variations in this quantity we define
The sigma-t as defined above is nothing more than a way of describing the potential density. It has the units mg/cm .
The potential density is rigorously expressed as
where is the adiabatic cooling due to a reduction in pressure from the in situ value to atmospheric. The last term amounts to about 0.07 mg/cm at the greatest ( ; see Tables 9 and 12 in The Oceans). For comparison, the values of in the ocean usually lie in a range of about 20 to 30 mg/cm .
A plot of isolines of in a T-S diagram is given in Figure 3.13-1.