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.
