For convenience while examining differences in density between two water parcels, Sigma-density values are typically used by oceanographers. Sigma-density values allow the oceanographer to focus on the last 6 to 7 digits in the density value (when assuming 5 decimal place resolution), as this is where most of the variation in density occurs. Sigma-density values are also a shorthand way for representing density of a water parcel with some specific modification to one of the density computational inputs, like pressure or temperature.

*Examples:*

*Sigma = (rho(t,s,p) – 1000) kg/m*^{3}*Sigma-t = (rho(s,t,p=0) – 1000) kg/m*^{3}(density at atmospheric pressure)*Sigma-theta = (rho(t=theta,s,0) – 1000 kg/m*^{3}(density with effect of adiabatic cooling/heating effect [using potential temperature] and the pressure effect removed).

So, though the true density of water is always a value that is non-negative, when testing instruments on the bench (zero salinity) or in freshwater systems, the computed density can be < 1000 kg/m^{3}. In this situation, when converting density to a Sigma-density value, it is possible for the Sigma-density value to be negative.

*Example: S = 0, t = 5 deg C, and pressure = 0*

*rho(S,t,pressure) = 999.96675 kg/m ^{3} Sigma-t (t,S,0) = – 0.03325*

For more information on the Practical Salinity Scale (1978) and the Equation of State for Seawater (EOS-80), refer to UNESCO Technical Papers of Marine Science 44.

*Note: Many UNESCO marine science publications are available through UNESCO’s website. Go to http://unesdoc.unesco.org/ulis/ioc/.*

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