oceanic density and pressure

oceanic density and pressure The density of sea water is a complex and non-linear function of temperature, salinity, and pressure. (This can be seen in Fig. 1 of the entry on ocean water, where the lines of equal density do not follow straight line.) At temperatures above 20 °C, temperature and salinity generally have an approximately equal control on the density of sea water. As temperatures decrease, the control of density is passed to salinity. As temperature falls, the maximum density of fresh water is reached at 3.98 °C; above and below this temperature the density of fresh water is lower. In the ocean, however, the addition of salt to the system alters the behaviour and when the salt content is greater than 24.7 practical salinity units (PSU) (as in virtually all of the world's oceans) the density of the sea water increases with salt content as temperatures approach the freezing point.

Density is expressed in kilograms per cubic metre. For typical ocean depths of up to 4 km the density typical ranges between 1020 and 1030 kg m⁻³ (kilograms per cubic metre). Oceanographers use a unit σ_t (pronounced sigma-t), which is the density minus 1000 kg m⁻³. Throughout the ocean σ_t generally varies between 20 and 30 kg m⁻³. For 80 per cent of the worlds ocean water σ_t ranges between 26 and 28.5 kg m⁻³. The temperature and salinity values used for the calculation of σ_t are called the in situ values, and this introduces a problem. The compression of sea water under pressure is significant. Consider a volume of sea water with a salinity of 35 PSU and a temperature of 5 °C at 4000 m, which is raised to the surface adiabatically (i.e. without exchange of heat with its surroundings). As pressure decreases, the volume will increase and the temperature will fall, in this example to 4.56 °C. The temperature of 5 °C is the temperature value in situ. To take into account the variation of temperature with pressure we calculate the density using the temperature that the volume of water would have at the surface (4.56 °C); this is called the potential temperature (θ).

When density is calculated using the potential temperature it is termed the potential density σθ (pronounced sigma theta). The potential density does not have to be calculated relative to the surface. If we use potential density for comparing the density of water in the deep ocean, it is usual to calculate the potential density at a comparable pressure level. For example, if we were comparing the densities of water at a depth of 3000 m it would be usual to calculate the potential density relative to 3000 m, which would be called σ₃ (sigma 3), or even σ_2.5, which would be relative to 2500 m; and so on.

For a particular depth in the ocean the hydrostatic pressure is equal to the height of the water column in metres above our point, multiplied by the density of the water and the acceleration due to gravity. As a first approximation it is usual to assume the acceleration due to gravity as 10 m s⁻² and the density of sea water as 1000 kg m⁻³; pressure in Newtons per metre squared is then 1000 times the depth. In reality the pressure is greater than this, and a uniform depth will not have equal pressure throughout the ocean as it is dependent on the density of water above the depth. A CTD (conductivity, temperature, depth) measurement usually shows the density increasing with depth except in special circumstances.

The surface density of water also varies with latitude (Fig. 1) because of the different temperatures and salinities encountered in different climatic zones. Surface density is greatest in the Southern Ocean south of the Antarctic Circumpolar Current, decreasing to a minimum just north of the Equator before rising again with latitude. The surface density then falls towards and under the permanent ice cover of the Arctic because of the decrease in sea-surface salinity due to melting of sea ice and freshwater input from rivers. This variation has important consequences for the interiors of the oceans. The dense surface water at high latitudes can descend along density surfaces into the interior of the more temperate oceans and can be tracked using temperature, salinity, and potential vorticity. Changes in the surface waters at high latitudes can therefore be responsible for determining the water properties of the interior of the oceans, making the polar oceans important in climate change.

Mark A. Brandon

Bibliography

Pickard, G. L. and and Emergy, W. J. (1982) Descriptive physical oceanography. Pergamon Press, Oxford.