History of the equation of state of seawater

Frank J. Millero

Research output: Contribution to journalReview articlepeer-review

48 Scopus citations


As one of few who have been involved in the equation of state of seawater over the last 40 years, I was invited to review some of the history behind its early development and also the more recent thermodynamic equation of state. The article first reviews early (late 1800s) work by Knudsen and others in defining the concept of salinity. This summary leads into the development of the practical salinity scale. Our studies at the University of Miami Rosenstiel School, along with the work of Alain Poisson's group at Laboratoire de Physique et Chimie, Université Pierre et Marie Curie, and that of Alvin Bradshaw and Karl Schleicher at Woods Hole Oceanographic Institution, were instrumental in deriving the 1980 equation of state (EOS-80) that has been used for 30 years. The fundamental work of Ranier Feistel at Leibniz Institute for Baltic Sea Research led to the development of a Gibbs free energy function that is the backbone of the new thermodynamic equation of state (TEOS-10). It can be used to determine all of the thermodynamic properties of seawater. The salinity input to the TEOS-10 Gibbs function requires knowledge of the absolute salinity of seawater (SA), which is based upon the reference salinity of seawater (SR). The reference salinity is our best estimate of the absolute salinity of the seawater that was used to develop the practical salinity scale (SP), the equation of state, and the other thermodynamic properties of seawater. Reference salinity is related to practical salinity by SR = SP (35.16504/35.000) g kg-1 and absolute salinity is related to reference salinity by SA = SR + δSA, where δSA is due to the added solutes in seawater in deep waters resulting from the dissolution of CaCO3(s) and SiO2(s), CO2, and nutrients like NO3 and PO4 from the oxidation of plant material. The δSA values due to the added solutes are estimated from the differences between the measured densities of seawater samples compared with the densities calculated from the TEOS-10 equation of state (Δρ) at the same reference salinity, temperature, and pressure, using δSA = Δρ/0.75179 g kg-1. The values of δSA in the ocean can be estimated for waters at given longitude, latitude, and depth using correlations of δSA and the concentration of Si(OH)4 in the waters. The SA values can then be used to calculate all the thermodynamic properties of seawater in the major oceans using the new TEOS-10. It will be very useful to modelers examining the entropy and enthalpy of seawater.

Original languageEnglish (US)
Pages (from-to)18-33
Number of pages16
Issue number3
StatePublished - Sep 2010

ASJC Scopus subject areas

  • Oceanography


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