What is the exact definition of Salinity?
The term 'salinity' is measure of 'saltiness', particularly used in reference to sea water.

The exact scientific definition has evolved over time to incorporate our ever growing understanding of physics and chemistry.

In 1889 the International Council for the Exploration of the Sea (ICES) used a measure of salinity based on the total dissolved solids of salt (g/kg) found in seawater after evaporation and drying at 480$^{o}$C.

By taking samples of ocean water from around the world and at different depths, oceanographers have determined that whilst the concentration of salts varies, the relative ionic composition remains essentially constant. The average salinity of the world's ocean water is usually stated as 35 g/kg, with the relative ionic composition of this "average sea water" made up as follows:

The major cations present in 1 kg of sea water are Na$^{+}$ (10.7653 g), Mg$^{2+}$ (1.2942 g), Ca$^{2+}$ (0.4117 g), K$^{+}$ (0.3991 g) and Sr$^{2+}$ (0.0079 g).

The major anions present in 1kg of seawater are Cl$^{-}$ (19.3534 g), SO$_{4}$$^{2-}$ (2.7124 g), HCO$_{3}$$^{-}$ (0.1178 g), CO$_{3}$$^{2-}$ (0.0122 g), Br$^{-}$ (0.0674 g), F$^{-}$ (0.0013 g), B(OH)$_{4}$$^{-}$ (0.0066 g).

The process of determining salinity from evaporation &amp; drying can be quite difficult, particularly on board ships.

In 1963, the ICES adopted a new definition based on "chlorinity" measurement (using titration). The "average sea water" with ionic composition given above was determined to have chlorinity of 19.374%. By measuring the relative chlorinity of a sample of sea water, the salinity could be calculated using the formula S = 1.80655 Cl.

In 1978, with the advent of modern electronics, the United Nations Educational, Scientific and Cultural Organization (UNESCO), International Council for the Exploration of the Sea (ICES), Scientific Committee on Oceanic Research (SCOR) and International Association for the Physical Sciences of the Oceans (IAPSO) adopted a method based on electrical conductivity measurements compensated for temperature. The Practical Salinity Scale of 1978 (PSS78) defines S (a dimensionless quantity) from conductivity and temperature measurements, in the range 2 $\leq$ S $\leq$ 42, by the following formula:

S = 0.0080 - 0.1692$K_{15}$$^{1/2}$ + 25.3851$K_{15}$ + 14.0941$K_{15}$$^{3/2}$ - 7.0261$K_{15}$$^{2}$ + 2.7081$K_{15}$$^{5/2}$

Where $K_{15}$ is the ratio of conductivity of the sea water sample to that of potassium chloride (KCl) solution of mass fraction 32.4356x10$^{-3}$, at 15$^{o}$C and atmospheric pressure.

A formula is also provided for compensation of the conductivity measurement at different temperatures (see http://unesdoc.unesco.org/images/0004/000479/047932eb.pdf)

In 2010, the Intergovernmental Oceanographic Commission released "the international thermodynamic equation of seawater (TEOS-10)" in which it recommended a return to the use of "Absolute Salinity" to take into account variations in the composition of sea water which can occur for example in regions where rivers run into the ocean or where some other regional variability results in "anomalous" sea water composition.

The rational for this approach is based on understanding the effect each chemical component of seawater has on its thermodynamic properties such as density, pressure, temperature and Gibbs function. Various measures of salinity are defined and their relationships with thermodynamic properties described.

The Added-Mass Salinity, which incorporates the Reference Composition Salinity of "standard sea water" (the Practical Salinity Scale) with an adjustment for the Absolute Salinity Anomaly (mass fraction of material which must be added to standard seawater to achieve the concentration levels in the sample) is sometimes difficult to determine in-situ.

Modern techniques for determining Absolute Salinity involve taking various other measurements such as conductivity, temperature, pressure and density by incorporating measurements from sensitive electronic and optical instruments with data-driven computer algorithms.

The Density Salinity, which is the salinity argument in the thermodynamic expression for density which gives the sample's actual measured density, can be used where accurate measurements of density are available, such as a vibrating-tube densimeter or optical refractometer. When combined with Practical Salinity, temperature and pressure measurements, this can provide an accurate and easily determined measure of the amount of dissolved material in seawater (within a certain range).

Composition anomalies can be estimated by computer algorithms which take into account longitude, latitude and depth data. The accuracy of such algorithms is dependent upon the collection of accurate data from field measurements and laboratories across the world and is therefore an evolving process.

(For more details, see: http://www.teos-10.org/).