From AMS Glossary
(Symbol σS'T'p.) The density ρ (in kg m-3) that seawater of salinity S and temperature T would have at pressure p, less 1000 kg m-3.
where p is the atmospheric pressure relative to that at the sea surface. This definition includes the effects of compressibility in calculating the density but does not include the effects of adiabatic warming due to compression.