When I compute sigma-density values, why are they sometimes negative?

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.


  • Sigma = (rho(t,s,p) - 1000) kg/m3
  • Sigma-t = (rho(s,t,p=0) - 1000) kg/m3 (density at atmospheric pressure)
  • Sigma-theta = (rho(t=theta,s,0) - 1000 kg/m3 (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/m3. 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/m3
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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