Practical salinity of seawater
Since it is not possible to directly measure the absolute salinity of seawater (the ratio of the mass of dissolved material to the mass of seawater), it is necessary to work in terms of practical salinity, which can be determined from measurable properties of seawater.
This is defined in "Algorithms for computation of fundamental properties of seawater", by N. P. Fofonoff and R. C. Millard Jr.:
The practical salinity, symbol S, of a sample of sea water, is defined in terms of the ratio K of the electrical conductivity of a sea water sample of 15°C and the pressure of one standard atmosphere, to that of a potassium chloride (KCl) solution, in which the mass fraction of KCl is 0.0324356, at the same temperature and pressure. The K value exactly equal to one corresponds, by definition, to a practical salinity equal to 35.
The practical salinity of seawater can be calculated from three measurable parameters: electrical conductivity, temperature, and pressure. Each of the three parameters is necessary for the salinity calculation since the electrical conductivity of seawater changes with temperature and pressure. Electrical conductivity of seawater is dependent upon the number of dissolved ions per volume (salinity), as well as the mobility of those ions (affected by temperature and pressure). The accuracy of the salinity 'measurement' depends on the accuracy to which the three principal parameters can be measured.
The Practical Salinity Scale of 1978, endorsed by UNESCO/IAPSO, is currently the world standard for salinity calculation. It is used by all RBR CTD instruments and software for the calculation of seawater salinity, using the equations given below; these are taken from "IEEE Journal of Oceanic Engineering", Vol. OE-5, No. 1, January 1980, page 14. Practical salinity, S, is given by
where ΔS is a temperature correction term given by
where Fn(RT) is the polynomial function
and T is the in-situ temperature according to the International Temperature Scale of 1968 (ITS-68). All RBR loggers and software use the more recent ITS-90 scale, but make the simple conversion to ITS-68 for salinity calculations.
RT is a term representing a ratio of conductivities, with further corrections applied for temperature and pressure.
R is the ratio of the conductivity of the sample of seawater (measured by the logger) to the conductivity of standard seawater at S = 35, T = 15ºC, and P = 0: Conductivity(35, 15, 0) = 42.914 mS/cm.
Rp and rT are correction terms to adjust for in-situ pressure and temperature respectively.
where P is the in-situ hydrostatic pressure measured in bars (RBR loggers and software account for the conversion from decibars).
The table below gives all the coefficients required in all the above equations. These values have been empirically determined, and are fixed: they do not need to be programmed into a data logger in any way by end users.
Table 1. Coefficients for the PSS78 equations
a | b | c | d | e | |
|---|---|---|---|---|---|
0 | 0.0080 | 0.0005 | 0.6766097 | ||
1 | -0.1692 | -0.0056 | 2.00564e-2 | 3.426e-2 | 2.070e-5 |
2 | 25.3851 | -0.0066 | 1.104259e-4 | 4.464e-4 | -6.370e-10 |
3 | 14.0941 | -0.0375 | -6.968e-7 | 0.4215 | 3.989e-15 |
4 | -7.0261 | 0.0636 | 1.0031e-9 | -3.107e-3 | |
5 | 2.7081 | -0.0144 |