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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

  1. In the Series title box, select UNESCO technical papers in marine science.
  2. Select Widen the search to all UNESCO documents/publications.
  3. Click the OK button.