Seawater density

Introduction

Density gradients play a prominent role in marine hydrodynamics. The large-scale long-term mean currents in the ocean and in estuaries largely depend on the density differences between water masses. The same holds for the small-scale turbulent velocity fluctuations that are responsible for mixing processes in oceans, shelf seas and estuaries. Knowledge of the seawater density is therefore prerequisite for understanding and modelling marine processes.

The seawater density [math]\rho[/math] in the ocean mainly depends on salinity [math]S[/math], temperature [math]T[/math] and pressure [math]p[/math]. Pressure effects are usually small for shallow coastal applications, but should be included for deeper shelf waters, for comparison of water masses at different depths, and for precise CTD-based density calculations. Because of the primary focus of the Coastal Wiki on coastal waters, the dependency on pressure will be ignored in this article. Salinity in this article is the dimensionless Practical Salinity, see the article Salinity.

Salinity-temperature dependence of seawater density

Fig. 1. Curves of density anomaly [math]\sigma=\rho-1000[/math] kg m^-3 for temperatures in the range 0-30°C , salinities in the range 0-40 and atmospheric pressure, based on the EOS-80 polynomial Eq. (1). The dotted line indicates the temperature of maximum density for low salinity.

An accurate empirical expression for the density-salinity-temperature relationship for coastal waters at atmospheric pressure has been derived by Fofonoff and Millard (1983):

[math]\rho = \rho_0 + (0.8245-4.1\, 10^{-3} \,T+7.64\, 10^{-5} \,T^2-8.25\, 10^{-7} \,T^3+5.4\, 10^{-9} \,T^4)\times S \\ +(-5.7\, 10^{-3} \,+10^{-4} \,T-1.65\, 10^{-6} \,T^2)\times S^{3/2} + 4.8\, 10^{-4}\,S^2 \, , \qquad (1)[/math]

[math]\rho_0 =999.84+6.8 \, 10^{-2} \, T - 9.1\, 10^{-3} \, T^2+10^{-4} \, T^3-1.1 \, 10^{-6} \, T^4+6.5\, 10^{-9} \, T^5 \, . \qquad (2)[/math]

The density-salinity-temperature relationship is plotted in Fig. 1. The equations (1) and (2) are often designated 'EOS-80' and are valid over the ranges of temperature (-2 to 35 °C), and Practical Salinity (2-42) in the world ocean. This expression remains accurate for pressures lower than [math]p\lt 10[/math] bar.

For quick estimates in coastal waters, the following approximation gives the density to about 1 kg m^-3 over much of the usual salinity–temperature range, but it should not be used for precise stratification calculations.

[math]\rho = 999.1+ 0.77 \, (S-\Large\frac{T-15}{5.13}-\frac{(T-15)^2}{128}\normalsize) \, . \qquad (3)[/math]

In highly turbid waters, suspended mineral particles also increase the bulk density of the water–sediment mixture. If the dry sediment mass concentration is [math]C_s[/math] and the particle density is [math]\rho_s[/math], the increase in mixture density is approximately [math]C_s (1- \rho/\rho_s)[/math], when [math]C_s[/math] is expressed as mass per unit mixture volume.

Modern oceanographic calculations use TEOS-10 instead of EOS-80. Density is calculated from Absolute Salinity [math]S_A[/math], Conservative Temperature [math]\Theta[/math] or in-situ temperature, and pressure. For many shallow coastal applications, the older EOS-80 zero-pressure formula remains sufficiently accurate for explanation and rough estimates, but TEOS-10 should be used for precise CTD data processing, water-mass analysis and density-stratification calculations.

Processes induced by density differences

The sensitivity of density to temperature and salinity is described by the thermal expansion coefficient and the haline contraction coefficient. Their ratio determines how much temperature change is needed to compensate a given salinity change. Seawater density decreases with increasing temperature and increases with increasing salinity (Fig. 1). In fresh and weakly brackish water, density has a maximum at low positive temperature, whereas at normal seawater salinity the freezing point is reached before a density maximum occurs. According to Eq. (3), an increase of one Practical Salinity unit has about the same effect on the seawater density as a decrease of 4-5 °C in temperature. Warm, low salinity water tends to stay near the surface whereas cool, high salinity water tends to stay near the bottom. Evaporation of a warm surface layer increases its salinity, in which case it may sink; this occurs in the North Atlantic. Partial freezing of a low salinity surface layer may also induce sinking by increasing the salinity of the unfrozen water; this occurs in the polar regions. In both examples sinking is enhanced by cooling. Sinking of surface layers implies that subsurface layers of lower density will emerge; this process is called 'overturning'. The balance between small changes in salinity and temperature has great importance for the large-scale ocean circulation.

Fig. 2. Schematic picture of estuarine circulation in a vertical-longitudinal section of the estuary. Red=seawater, blue=fresh water.

In estuaries, the density effect of salinity gradients is generally much greater than the density effect of temperature gradients, producing vertical salinity stratification and the well-known estuarine circulation, which is driven by the density gradient along the estuarine axis, see Fig. 2. In contrast, in oceans, the density effect of temperature generally dominates the effect of salinity. In many parts of the oceans, both temperature and salinity decrease with depth.

Stratification

Fig. 3. Well-mixed (left) and stratified (right) water column. Blue=lower density, red=higher density.

A body of water is referred to as 'stable' when the density decreases from bottom to surface. This is the usual situation, also in cases where strong mixing occurs over the water column. Mixing is mainly caused by turbulence, which is generated by frictional shear stresses at the bottom and the water surface. When the production of turbulent energy in an estuary decreases, inflowing river water and seawater will be less mixed: vertical density differences force the water column into a more stratified state, with the vertical density difference concentrated around a transition layer, the so-called pycnocline, see Fig. 3. Stratification suppresses turbulence because vertical displacements of water parcels work against buoyancy forces. These buoyancy forces dampen turbulent fluid fluctuations around the pycnocline; the turbulent energy production needed for mixing increases as the stratification increases.

The suppression of mixing in stratified water bodies between the surface layer and the water layer below the pycnocline can have serious consequences for the aeration of the lower layer, because this is where the most mineralization takes place and thus the oxygen demand is greatest. Especially when the water is eutrophic (high organic content) and turbid, the oxygen demand in the lower layer leads to hypoxia, resulting in severe mortality of benthic organisms in particular (see also the article Estuarine turbidity maximum).

Water and salt cannot spontaneously unmix from an existing solution (this would be contrary to the second law of thermodynamics), but a suspension of fine sediment can unmix by settling. Settling of fine sediment in turbid coastal waters can increase the density in the lower part of the water column such that a pycnocline starts to develop. Damping of turbulence around the pycnocline furthers the settling process, which can eventually lead to the formation of a fluid mud layer (see the articles Dynamics of mud transport and Fluid mud).

Overturning

Fig. 4. Schematic picture of salt fingers. Red=warm salty water. Blue=colder less salty water.

When denser (salty, cold) water is advected over less dense water by wind-driven or tide-driven currents, the water column becomes unstable. The denser surface water will sink through the underlying less dense water layer. This process is called convective overturning and contributes to the mixing of water masses of different density. It can occur, for example, when seawater enters a partially mixed estuary and a strong near-surface flood current carries dense saline water over the underlying, less saline estuarine water (see also Estuarine circulation).

Overturning processes can also occur when surface water is heated by the sun and salinity is increased by evaporation. The density of the warm salty surface water may then exceed the density of the underlying layer of cooler water, in which case the warm salty surface water will sink through this cooler layer. The downward motion is sustained, because the salty surface water is cooled while sinking. Such an overturning process drives deep-water formation in the North Atlantic and is crucial for the large-scale thermohaline ocean circulation.

Accelerated sinking of salty warm surface water parcels through rapid cooling by underlying less salty cooler water is an instability mechanism leading to the formation of so-called 'salt fingers', see Fig. 4. Salt fingers can be triggered by small downward displacements of surface water parcels when the water column is in a state of marginal static equilibrium. Salt fingers may cause some deeper waters to rise to the surface, stimulating primary production with nutrient-rich water.

Related articles

Salinity

Ocean circulation

Thermohaline circulation of the oceans

Estuarine circulation

Salt wedge estuaries

References

The main author of this article is Job Dronkers Please note that others may also have edited the contents of this article. Citation: Job Dronkers (2026): Seawater density. Available from http://www.coastalwiki.org/wiki/Seawater_density [accessed on 8-07-2026] For other articles by this author see Category:Articles by Job Dronkers For an overview of contributions by this author see Special:Contributions/Dronkers J