• Brewer, P. G., , and Bradshaw A. , 1975: The effect of the non-ideal composition of sea water on salinity and density. J. Mar. Res., 33 , 157175.

    • Search Google Scholar
    • Export Citation
  • Caldwell, D. R., 1978: The maximum density points of pure and saline water. Deep-Sea Res., 25 , 175181.

  • Del Grosso, V. A., 1974: New equation for the speed of sound in natural waters (with comparisons to other equations). J. Acoust. Soc. Amer., 56 , 10841091.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Feistel, R., 1993: Equilibrium thermodynamics of seawater revisited. Progress in Oceanography, Vol. 31, Pergamon, 101–179.

  • Feistel, R., , and Hagen E. , 1995: On the GIBBS thermodynamic potential of seawater. Progress in Oceanography, Vol. 36, Pergamon, 249–327.

    • Search Google Scholar
    • Export Citation
  • Fofonoff, N. P., 1977: Computation of potential temperature of seawater for an arbitrary reference pressure. Deep-Sea Res., 24 , 489491.

  • Fofonoff, N. P., 1985: Physical properties of seawater: A new salinity scale and equation of state for seawater. J. Geophys. Res., 90 , 33323342.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Fofonoff, N. P., , and Millard R. C. , 1983: Algorithms for computation of fundamental properties of seawater. UNESCO Technical Papers in Marine Science, Vol. 44, UNESCO, 53 pp.

    • Search Google Scholar
    • Export Citation
  • Gradshteyn, I. S., , and Ryzhik I. M. , 1980: Tables of Integrals, Series and Products. Academic Press, 1160 pp.

  • Griffies, S. M., , Boning C. , , Bryan F. O. , , Chassignet E. P. , , Gerdes R. , , Hasumi H. , , Hirst A. , , Treguier A. M. , , and Webb D. , 2000: Developments in ocean climate modeling. Ocean Modell., 2 , 123192.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • IMSL, 1991: Fortran Subroutines for Mathematical Applications. IMSL Inc., 1372 pp.

  • Jackett, D. R., , and McDougall T. J. , 1995: Minimal adjustment of hydrographic profiles to achieve static stability. J. Atmos. Oceanic Technol., 12 , 381389.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Levitus, S., 1982: Climatological Atlas of the World Ocean. NOAA Prof. Paper 13, 173 pp. and 17 microfiche.

  • Millero, F. J., 2000: Effect of changes in the composition of seawater on the density–salinity relationship. Deep-Sea Res., 47 , 15831590.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Preston-Thomas, H., 1990: The international temperature scale of 1990 (ITS-90). Metrologia, 27 , 310.

  • Wolfram, S., 1991: Mathematica: A System for Doing Mathematics by Computer. Addison-Wesley, 961 pp.

  • Wright, D. G., 1997: An equation of state for use in ocean models: Eckart’s formula revisited. J. Atmos. Oceanic Technol., 14 , 735740.

    • Crossref
    • Search Google Scholar
    • Export Citation
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Accurate and Computationally Efficient Algorithms for Potential Temperature and Density of Seawater

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  • 1 CSIRO Marine Research, Hobart, Tasmania, Australia
  • | 2 Department of Fisheries and Oceans, Bedford Institute of Oceanography, Dartmouth, Nova Scotia, Canada
  • | 3 Institut für Ostseeforschung, Warnemünde, Germany
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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.

Corresponding author address: Dr. Trevor J. McDougall, CSIRO Division of Marine Research, GPO Box 1538, Hobart, Tasmania 7001, Australia. Email: trevor.mcdougall@csiro.au

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.

Corresponding author address: Dr. Trevor J. McDougall, CSIRO Division of Marine Research, GPO Box 1538, Hobart, Tasmania 7001, Australia. Email: trevor.mcdougall@csiro.au

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