Seawater Equation of State Teos 10 Calculator

TEOS-10 differs from earlier equations of state in that every property is derived from a single Gibbs function rather than from independent empirical fits. Once that thermodynamic potential is specified in terms of Absolute Salinity SA, temperature, and pressure, density, entropy, enthalpy, sound speed, thermal expansion, haline contraction, and freezing point all follow by differentiation, and they are guaranteed mutually consistent. The framework also replaces the two variables oceanographers had long used. Absolute Salinity in grams per kilogram replaces Practical Salinity, differing from it by roughly 0.165 g/kg on average and by a spatially varying composition anomaly of up to about 0.03 g/kg that is largest in the North Pacific. Conservative Temperature replaces potential temperature because it is proportional to potential enthalpy and is therefore genuinely conserved under mixing, whereas potential temperature is not. The practical significance is that using SA and CT rather than SP and potential temperature removes density errors that were large enough to distort computed ocean circulation. In the deep North Pacific the composition anomaly alters density by around 0.010 kg per cubic meter, comparable to the density contrasts that drive abyssal flow. Typical outputs are density 1020 to 1070 kg per cubic meter over the full pressure range, sigma-0 of 21 to 28 in the open ocean, and sound speed 1450 to 1550 m/s. The formulation is valid over the full oceanographic range including ice and seawater equilibrium, but the Absolute Salinity conversion depends on a lookup atlas of composition anomaly that is poorly constrained in coastal and estuarine waters.

The move beyond EOS-80 began with accumulating evidence of its limitations. Frank Millero and colleagues documented during the 1990s and 2000s that the relationship between conductivity-based Practical Salinity and true dissolved mass varies regionally, particularly with silicate and total alkalinity, so two samples with identical Practical Salinity could differ measurably in density. Separately, Trevor McDougall showed in 2003 that potential temperature is not conserved when water masses mix, and introduced Conservative Temperature as the properly conserved alternative derived from potential enthalpy. The Gibbs function approach was developed principally by Rainer Feistel at the Leibniz Institute for Baltic Sea Research in Warnemunde, who published successive thermodynamic potentials for seawater through the 1990s and 2000s, culminating in a formulation covering seawater, ice, and humid air. SCOR and IAPSO convened Working Group 127 on the Thermodynamics and Equation of State of Seawater in 2005, chaired by Trevor McDougall, and its work produced the Thermodynamic Equation of Seawater 2010. The Intergovernmental Oceanographic Commission of UNESCO formally adopted TEOS-10 at its 25th Assembly in June 2009, recommending it replace EOS-80 from 2010. The associated Gibbs SeaWater Oceanographic Toolbox, released in MATLAB, C, Python, and Fortran, made the standard usable in practice, and TEOS-10 is now required for CLIVAR and GO-SHIP hydrographic data and for the CMIP class of climate models.