Density of Seawater from Temperature and Salinity (UNESCO 1981)

This is an equation of state: a fitted formula that returns the density of seawater from its temperature and salinity, not a law derived from first principles. It is the international equation of state of 1980 in the one-atmosphere form of Millero and Poisson (1981), with the algorithms collected by Fofonoff and Millard (UNESCO, 1983). The first term, $\rho_w(T)$, is the density of pure water. The dissolved salts add the other terms, in powers of the practical salinity $S$, with coefficients $A(T)$ and $B(T)$ that depend on temperature and a constant $C$.

Read it as pure water plus a correction for what is dissolved. Salinity is 0 for fresh water and about 35 for the open sea, and the page accepts temperatures from $-2$ to 40 °C. Standard seawater of salinity 35 comes to 1025.97 kg/m³ at 15 °C and to 1028.11 at 0 °C, so the colder water is the denser. Fresher water behaves differently: below a salinity of about 24.7 the density peaks above the freezing point, so two temperatures can give the same density. Solved for the temperature, the page returns the warmer of the two.

The page is checked against the published values of the UNESCO equation at one atmosphere (Fofonoff and Millard, 1983). At salinity 0 they are 999.96675 kg/m³ at 5 °C and 997.04796 at 25 °C. At salinity 35 they are 1027.67547 at 5 °C and 1023.34306 at 25 °C. Try the 5 °C, salinity 35 case and the result should be 1027.67547. At each temperature the gap between the fresh and salt values is what the dissolved salt contributes.

Use it for the surface: it is the one-atmosphere form, so it leaves out the effect of the greater pressure at depth. It is the density to put into a pressure, a wave energy or a buoyancy calculation for the sea; the wave power per metre is proportional to it, and the Ghyben-Herzberg lens depends on the ratio of the fresh and sea densities. For fresh water alone, Kell's page gives the same quantity from a different fit, for 0 to 100 °C.