## DRAFT "How do we measure the density of sea water?

In oceanographic terms, density is the weight of the water relative to that of purely fresh water. Since fresh water weighs about 1000 kilograms per cubic meter and seawater weighs about 1.026 times that, we say that the typical seawater density is 1026 kg/m3. Even though many people will say that density is a unitless quantity, many oceanographers will assign the units of kilograms per cubic meters.

"Sigma-t" is simply density minus 1000 (without the effect of pressure). Since the variations in seawater "density" varies only in the last few significant figures, we subtract 1000 for convenience in order to carry less numbers around. Hence, typical sigma-t is 26.0. Note that density (and sigma-t) varies with temperature and salinity but the typical values we find on the shelf range between 23.0 and 28.0. Note that the units on sigma-t are now "kg/m3-1000".

There is another density measure sometimes denoted "sigma_0" (where the last digit, a zero, is used to represent the greek letter theta). This is important in deep water (I think) where a water parcel's1 temperature varies due to the affect of pressure. When it is taken to a reference pressure, the density is different. This altered density which takes into account adiabatic heating/cooling2 with changes in pressure is called the "potential density". I never worry about this quantity in shelf environments.

We normally calculate "sigma-t" given observations of temperature and salinity. Since it is a "derived quantity" , it is not always posted on data servers. In these cases, code is available in MATLAB and FORTRAN on request.

Jim Manning
jmanning@whsun1.wh.whoi.edu

References
See, for example, Pond and Pickard discussion in "Intro. to Dynamical Oceanography" pages 6-11.

For a Matlab routine to compute sigma-t, see http://globec.whoi.edu/globec-dir/sigmat-calc-matlab.html.

Footnotes
1A water parcel is "a little finite chunk of water."

2If you move a parcel of water from one pressure (depth) to another it will undergo a slight change in temperature. This is why is it is important to understand what pressure is used when calculating the water parcel's density from temperature and salinity.

Contributed by: Jim Manning, Feb. 2001