Density is defined as mass per unit volume. Mass is measured in grams (g), volume in cubic meters (m3); but density is usually given in kilograms per cubic meter (kg m-3).
On earth, where all matter is exposed to gravity, objects of identical size but different density have different weight. If the objects are fluids, this results in horizontal layering; the fluids will arrange themselves such that the less dense fluid floats on top of the denser fluid. An example of this situation is oil floating on water.
The horizontal layering of fluids of different density is called stratification. The ocean is a very thin sheet of stratified fluid on the surface of the earth. Understanding the factors that determine its density is therefore essential to oceanography.
When it comes to the dynamic behaviour of matter, fluids and gases have a lot in common. (This is borne out by the fact that winds, ie movement in the atmosphere, and currents, ie movement in the ocean, follow the same laws and produce very similar circulation patterns.) The starting point for a discussion of seawater density is therefore the
ideal gas equation: $p = \rho\;R\;T$
where p is pressure, ρ is density, T is temperature in Kelvin and R is the universal gas constant. If the gas equation is arranged to give density ($\rho = p (R T)^{-1}$) we see that the density of an ideal gas is proportional to pressure and inversely proportional to temperature.
In most oceanographic applications, the density dependence on pressure is of no consequence. It is true that the density of a water parcel increases when it is moved from the sea surface to the ocean floor; but this will not disturb the stratification, since a density gain with depth is in line with the natural arrangement of fluids under gravity. What is more, the same parcel will return o its original density when it is brought back to the surface, and it will change its density whenever it is moved vertically (in proportion to the experienced pressure change).
The static stability of the water column is only disturbed if we can manage to bring a water parcel into a position where it has a higher density than the water parcels next to it. Because the pressure effect on density is so completely reversible, we can disregard its effect from now on.
Note: This is not true for all situations. Seawater density is not a linear function of pressure. In regions of extremely uniform temperature, static stability cannot be evaluated without incorporating the pressure effect on density. Such situations can occur at very great depth. In the context of this exercise, these situations are not of interest.
How well does the ideal gas equation describe the behaviour of seawater? This is best investigated by looking at the density of pure water first. (Pure water is freshwater without any impurities such as suspended minerals or sediments).
Pure water is not an ideal gas; but over a limited range of temperatures, the density dependence on temperature is close to the inverse linear relationship expressed by the ideal gas equation. The density of pure water is very close to 1000 kg m-3, which is a convenient number to remember. (Actual values are slightly less than 1000 kg m-3.)
Oceanographers are not so much interested in the absolute density of the water but in density changes in space and time. Such changes are quite small. Oceanographers therefore use the quantity
\[ \sigma_t = \rho_h - 1000 \]
(pronounced sigma-tee), which gives the density excess or deficit against a refererence density of $1000\; kg\; m^{-3}$.
In principle, $\sigma_t$ should have the same unit as $\rho (kg\; m^{-3})$; but oceanographers never give units with $\sigma_t$. Thus, freshwater has a $\sigma_t$ value just slightly less than zero.
