Algorithms for Density, Potential Temperature, Conservative Temperature, and the Freezing Temperature of Seawater

Abstract

Algorithms are presented for density, potential temperature, conservative temperature, and the freezing temperature of seawater. The algorithms for potential temperature and density (in terms of potential temperature) are updates to routines recently published by McDougall et al., while the algorithms involving conservative temperature and the freezing temperatures of seawater are new. The McDougall et al. algorithms were based on the thermodynamic potential of Feistel and Hagen; the algorithms in this study are all based on the “new extended Gibbs thermodynamic potential of seawater” of Feistel. The algorithm for the computation of density in terms of salinity, pressure, and conservative temperature produces errors in density and in the corresponding thermal expansion coefficient of the same order as errors for the density equation using potential temperature, both being twice as accurate as the International Equation of State when compared with Feistel’s new equation of state. An inverse function relating potential temperature to conservative temperature is also provided. The difference between practical salinity and absolute salinity is discussed, and it is shown that the present practice of essentially ignoring the difference between these two different salinities is unlikely to cause significant errors in ocean models.

Evolution of South Atlantic density and chemical stratification across the last deglaciation

“…The modern linear relationship between salinity and δ w-ice for the Southern Ocean (21) is assumed to hold across the deglacial period (Supporting Information). In situ density was calculated from salinity and benthic temperature, using the equation of state (23).…”

The Parallelized Large-Eddy Simulation Model (PALM) version 4.0 for atmospheric and oceanic flows: model formulation, recent developments, and future perspectives

“…ρ θ is calculated from the equation of state of seawater after each time step using the algorithm proposed by Jackett et al (2006). The algorithm is based on polynomials depending on Sa, θ , and p (see Jackett et al, 2006, Table A2).…”

Residual circulation and freshwater transport in the Dutch Wadden Sea: a numerical modelling study

“…2.3. The equation of state for seawater (TEOS-10 equation of state adopted for modelling according to Jackett et al, 2006) is used to calculate the density from the salinity, temperature and pressure.…”