6.1: Definition of Salinity

At the simplest level, salinity is the total amount of dissolved material in grams in one kilogram of sea water. Thus salinity is a dimensionless quantity. It has no units. The variability of dissolved salt is very small, and we must be very careful to define salinity in ways that are accurate and practical. To better understand the need for accuracy, look at figure \(\PageIndex{1}\). Notice that the range of salinity for most of the ocean’s water is from 34.60 to 34.80 parts per thousand, which is 200 parts per million. The variability in the deep North Pacific is even smaller, about 20 parts per million. If we want to classify water with different salinity, we need definitions and instruments accurate to about one part per million. Notice that the range of temperature is much larger, about \(1^{\circ}\text{C}\), and temperature is easier to measure.

Writing a practical definition of salinity that has useful accuracy is difficult (see Lewis, 1980, for the details), and various definitions have been used.

Figure \(\PageIndex{1}\): Histogram of temperature and salinity of ocean water colder than 4\(^{\circ}\)C. Height is proportional to volume. Height of highest peak corresponds to a volume of 26 million cubic kilometers per bivariate class of 0.1\(^{\circ}\)C and 0.01. After Worthington (1981: 47).

A Simple Definition

Originally salinity was defined to be the “Total amount of dissolved material in grams in one kilogram of sea water.” This is not useful because the dissolved material is almost impossible to measure in practice. For example, how do we measure volatile material like gasses? Nor can we evaporate seawater to dryness because chlorides are lost in the last stages of drying (Sverdrup, Johnson, and Fleming, 1942: 50).

A More Complete Definition

To avoid these difficulties, the International Council for the Exploration of the Sea set up a commission in 1889 which recommended that salinity be defined as the “Total amount of solid materials in grams dissolved in one kilogram of sea water when all the carbonate has been converted to oxide, the bromine and iodine replaced by chlorine and all organic matter completely oxidized.” The definition was published in 1902. This is useful but difficult to use routinely.

Salinity Based on Chlorinity

Because the above definition was difficult to implement in practice, because salinity is directly proportional to the amount of chlorine in sea water, and because chlorine can be measured accurately by a simple chemical analysis, salinity \(S\) was redefined using chlorinity: \[S = 0.03 + 1.805 \ Cl \nonumber \]

where chlorinity \(Cl\) is defined as “the mass of silver required to precipitate completely the halogens in 0.328 523 4 kg of the sea-water sample.” As more and more accurate measurements were made, equation \((\PageIndex{1})\) turned out to be too inaccurate. In 1964 UNESCO and other international organizations appointed a Joint Panel on Oceanographic Tables and Standards to produce a more accurate definition. The Joint Panel recommended in 1966 (Wooster, Lee, and Dietrich, 1969) that salinity and chlorinity be related using: \[S = 1.806 \ 55 \ Cl \nonumber \]

This is the same as equation \((\PageIndex{1})\) for \(S = 35\).

Salinity Based on Conductivity

At the same time \((\PageIndex{2})\) was adopted, oceanographers had began using conductivity meters to measure salinity. The meters were very precise and relatively easy to use compared with the chemical techniques used to measure chlorinity. As a result, the Joint Panel also recommended that salinity be related to conductivity of sea water using: \[\begin{align} S &= - 0.089 \ 96 + 28.297 \ 29 \ R_{15} + 12.808 \ 32 \ R_{15}^{2} \nonumber \\ &\quad -10.678 \ 69 \ R_{15}^{3} + 5.986 \ 24 \ R_{15}^{4} - 1.323 \ 11 \ R_{15}^{5} \\ R_{15} &= C(S, 15, 0) / C(35, 15, 0) \end{align} \nonumber \]

where \(C(S, 15, 0)\) is the conductivity of the sea-water sample at 15\(^{\circ}\)C and atmospheric pressure, having a salinity \(S\) derived from \((\PageIndex{5})\), and \(C(35, 15, 0)\) is the conductivity of standard “Copenhagen” sea water. Millero (1996) points out that \((\PageIndex{3})\) is not a new definition of salinity, it merely gives chlorinity as a function of conductivity of seawater relative to standard seawater.

Practical Salinity Scale of 1978

By the early 1970s, accurate conductivity meters could be deployed from ships to measure conductivity at depth. The need to re-evaluate the salinity scale led the Joint Panel to recommend in 1981 (JPOTS, 1981; Lewis, 1980) that salinity be defined using only conductivity, breaking the link with chlorinity. All water samples with the same conductivity ratio have the same salinity even though the their chlorinity may differ.

The Practical Salinity Scale of 1978 is now the official definition: \[\begin{align} S &= 0.0080 - 0.1692 \ K_{15}^{1/2} + 25.3851 \ K_{15} + 14.0941 \ K_{15}^{3/2} \nonumber \\ &\quad - 7.0261 \ K_{15}^{2} + 2.7081 \ K_{15}^{5/2} \\ K_{15} &= C(S, 15, 0) / C(KCl, 15, 0) \\ 2 \leq &S \leq 42 \nonumber \end{align} \nonumber \]

where \(C(S, 15, 0)\) is the conductivity of the sea-water sample at a temperature of 14.996\(^{\circ}\)C on the International Temperature Scale of 1990 (ITS-90, see Section 6.2) and standard atmospheric pressure of 101,325 Pa. \(C(KCl, 15, 0)\) is the conductivity of the standard potassium chloride (KCl) solution at a temperature of 15\(^{\circ}\)C and standard atmospheric pressure. The standard KCl solution contains a mass of 32.4356 grams of KCl in a mass of 1.000 000 kg of solution. Millero (1996: 72) and Lewis (1980) give equations for calculating salinity at other pressures and temperatures.

Comments

The various definitions of salinity work well because the ratios of the various ions in sea water are nearly independent of salinity and location in the ocean (Table \(\PageIndex{1}\)). Only very fresh waters, such as are found in estuaries, have significantly different ratios. The result is based on Dittmar’s (1884) chemical analysis of 77 samples of sea water collected by the Challenger Expedition and further studies by Carritt and Carpenter (1959).

“The importance of this result cannot be over emphasized, as upon it depends the validity of the chlorinity: salinity: density relationships and, hence, the accuracy of all conclusions based on the distribution of density where the latter is determined by chemical or indirect physical methods such as electrical conductivity. . .”

—Sverdrup, Johnson, Fleming (1942).

The relationship between conductivity and salinity has an accuracy of around ±0.003 in salinity. The very small error is caused by variations in constituents such as SiO₂ which cause small changes in density but no change in conductivity.

Table \(\PageIndex{1}\). Major Constituents of Sea Water.

	Ion		Atoms
55.3%	Chlorine	55.3%	Chlorine
30.8%	Sodium	30.8%	Sodium
7.7%	Sulfate	3.7%	Magnesium
3.7%	Magnesium	2.6%	Sulfur
1.2%	Calcium	1.2%	Calcium
1.1%	Potassium	1.1%	Potassium

Reference Seawater and Salinity

The Practical Salinity Scale of 1978 introduced several small problems. It led to confusion about units and to the use of “practical salinity units” that are not part of the definition of Practical Salinity. In addition, absolute salinity differs from salinity by about 0.5%. And, the composition of seawater differs slightly from place to place in the ocean, leading to small errors in measuring salinity.

To avoid these and other problems, Millero et al (2008) defined a new measure of salinity, the Reference Salinity, that accurately represents the Absolute Salinity of an artificial seawater solution. It is based on a Reference Composition of seawater that is much more accurate than the values in Table \(\PageIndex{1}\) above. The Reference Composition of the artificial seawater is defined by a list of solutes and their mole fractions given in Table 4 of their paper. From this, they defined artificial Reference Seawater to be seawater having a Reference Composition solute dissolved in pure water as the solvent, and adjusted to its thermodynamic equilibrium state. Finally, the Reference Salinity of Reference Seawater was defined to be exactly \(35.16504 \ \text{g kg}^{-1}\).

With these definitions, plus many details described in their paper, Millero et al (2008) show Reference Salinity is related to Practical Salinity by: \[S_{R} \approx (35.16504/35) \ \text{g kg}^{-1} \times S \nonumber \]

The equation is exact at \(S = 35\). Reference Salinity is approximately 0.47% larger than Practical Salinity. Reference Salinity, \(S_{R}\), is intended to be used as an SI-based extension of Practical Salinity.