Haline contraction coefficient

• Comment: @Robert McClenon:, can you look into this one and determine if it is legit? Bkissin (talk) 16:14, 13 July 2021 (UTC)

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The Haline contraction coefficient i.e., β, is a coefficient that describes the change in density in the ocean due to the salinity change, while the potential temperature and the pressure are kept constant. It is a parameter in the Equation Of State (EOS) of the ocean. In literature, β is also described as the saline contraction coefficient and is measured in [kg]/[g] in the equation of seawater (EOS) that describes the ocean. An example is the TEOS-10. This is the Thermodynamic equation of state.

The haline contraction coefficient is the salinity variant of the thermal expansion coefficient α, where the density changes due to a change in temperature instead of salinity. With these two coefficients, the density ratio can be calculated. This determines the contribution of the temperature and salinity to the density of a water parcel.

β is called a contraction coefficient, because when the salinity increases, the water parcel becomes denser. While if the temperature increases, the water parcel becomes less dense.

Definition

Τhe haline contraction coefficient is defined as followed:

$\beta ={\frac {1}{\rho }}{\frac {\partial \rho }{\partial S_{A}}}{\Bigg |}_{\Theta ,p}$

ρ is the density of a water parcel in the ocean and S$_{A}$ is the absolute salinity. The subscripts Θ and p indicate that β is defined at constant potential temperature Θ and constant pressure p. The haline contraction coefficient is constant when a water parcel moves adiabatically along the isobars.

Application

The density of the ocean is mainly defined by the temperature and the salinity. The thermal expansion and haline contraction coefficients indicate how much the density is influenced by a change in salinity or temperature. This can be concluded from the density formula that is derived from the thermal wind balance.

$\rho =\rho \left(\alpha \Theta +\beta S_{A}\right)$

The Brunt–Väisälä frequency can also be defined when β is known, in combination with α, Θ and S$_{A}$. This frequency is a measure of the stratification of a fluid column and is defined over depth as

$N^{2}=g\left(\alpha {\frac {\partial \Theta }{\partial z}}-\beta {\frac {\partial S_{A}}{\partial z}}\right)$.

From the density difference and the Brunt-Väisälä frequency we can find the direction of the mixing. And if the mixing is temperature driven or salinity driven.

Computation

The haline contraction coefficient can be computed when the conserved temperature, the absolute salinity and the pressure is known from a water parcel. Python has a package called GSW, The Gibbs SeaWater (GSW) oceanographic toolbox. It contains coupled non-linear equations that are derived from the Gibbs function. These equations are formulated in the different equation of state of seawater (EOS), also called the equation of seawater. This equation relates the different thermodynamic properties of the ocean like the density, temperature, salinity and pressure to each other. These equations are based on empirical thermodynamic properties.This means that the properties of the ocean can be computed from other thermodynamic properties. The difference between the EOS and the TEOS-10 is that in the TEOS-10, the salinity is stated as the absolute salinity, while in the previous EOS version the salinity was stated as the conductivity based salinity. The absolute salinity is the salinity based on density, where it uses the mass off all non-H₂O molecules. The conductivity based salinity is the salinity that is calculated directly from conductivity measurements taken by for example bouys.

The gsw_beta(SA,CT,p) function can calculate the beta coefficient when the absolute salinity (SA), conserved temperature (CT) and the pressure are known. The conserved temperature cannot be obtained straight away from the assimilation data bases like GODAS. But these variables can also be calculated with the GSW python package.

This is the 2020 average for the haline contraction coefficient β. At the locations where the salinity is high, in the tropics, the haline contraction coefficient is low and where the salinity is low, the haline contraction coefficient is high. This means that changing the salinity will have a large effect on the density when the haline contraction coefficient is high.

Physical examples

The haline contraction coefficient is not a constant in the ocean, it mostly changes per latitude and depth. At the locations where the salinity is high, like it is in the tropics, the haline contraction coefficient is low and where the salinity is low, the haline contraction coefficient is high. A high haline contraction coefficient means that the increase in density is more than when the haline contraction coefficient is low.

This graph shows the 2020 average salinity in an intersection in the Atlantic ocean at 30W. The salinity is low near Antarctica and high in the tropics.

The effect of the haline contraction coefficient is shown in the figures. Near Antarctica, the salinity in the ocean is low. This is because the meltwater that runs off Antartica dilutes the ocean. This water is very dense, because it is very cold. The haline contraction coefficient around Antarctica is relatively high. Which corresponds with the theory, that the density increases more in this part in the ocean when the salinity increases compared to the tropics. Near Antarctica, the temperature is the main contributor for the high densities in this part of the ocean. The water near the tropics has already a high salinity. This is due to the evaporation, the salt is left behind in the ocean, making it more saline. This would indicate a higher density, but as the water temperatures are also a lot higher, the density in the tropics is lower than the density around the poles. In the tropics, salinity is the main contributor to the density in this part of the ocean.

References

Category:Oceanography