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David R. Jackett, Trevor J. McDougall, Rainer Feistel, Daniel G. Wright, and Stephen M. Griffies

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.

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Trevor J. McDougall, David R. Jackett, Daniel G. Wright, and Rainer Feistel

Abstract

An equation of state for seawater is presented that contains 25 terms and is an excellent fit to the Feistel and Hagen equation of state. It is written in terms of potential temperature (rather than in situ temperature), as required for efficient ocean model integrations. The maximum density error of the fit is 3 × 10–3 kg m–3 in the oceanographic ranges of temperature, salinity, and pressure. The corresponding maximum error in the thermal expansion coefficient is 4 × 10–7 °C–1, which is a factor of 12 less than the corresponding maximum difference between the Feistel and Hagen equation of state and the widely used but less accurate international equation of state.

A method is presented to convert between potential temperature and in situ temperature using specific entropy based on the Gibbs function of Feistel and Hagen. The resulting values of potential temperature are substantially more accurate than those based on the lapse rate derived from the international equation of state.

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Trevor J. McDougall, Paul M. Barker, Rainer Feistel, and Ben K. Galton-Fenzi

Abstract

The thermodynamic consequences of the melting of ice and sea ice into seawater are considered. The International Thermodynamic Equation Of Seawater—2010 (TEOS-10) is used to derive the changes in the Conservative Temperature and Absolute Salinity of seawater that occurs as a consequence of the melting of ice and sea ice into seawater. Also, a study of the thermodynamic relationships involved in the formation of frazil ice enables the calculation of the magnitudes of the Conservative Temperature and Absolute Salinity changes with pressure when frazil ice is present in a seawater parcel, assuming that the frazil ice crystals are sufficiently small that their relative vertical velocity can be ignored. The main results of this paper are the equations that describe the changes to these quantities when ice and seawater interact, and these equations can be evaluated using computer software that the authors have developed and is publicly available in the Gibbs SeaWater (GSW) Oceanographic Toolbox of TEOS-10.

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