Ocean Science www.ocean-sci.net 1812-0784 1812-0792 4 4 2008 10.5194/os-4-275-2008 http://www.ocean-sci.net/4/275/2008/ http://www.ocean-sci.net/4/275/2008/os-4-275-2008.html http://www.ocean-sci.net/4/275/2008/os-4-275-2008.pdf 275 291 2008-12-12 Mutually consistent thermodynamic potentials for fluid water, ice and seawater: a new standard for oceanography R. Feistel rainer.feistel@io-warnemuende.de D. G. Wright K. Miyagawa A. H. Harvey J. Hruby D. R. Jackett T. J. McDougall W. Wagner Leibniz Institute for Baltic Sea Research, 18119 Warnemünde, Germany Bedford Institute of Oceanography, Dartmouth, NS, Canada 4-12-11-628, Nishiogu, Arakawa-ku, Tokyo 116-0011, Japan National Institute of Standards and Technology, Boulder, CO 80305, USA Institute of Thermomechanics of the ASCR, v.v.i., Prague, Czech Republic Centre for Australian Weather and Climate Research: A partnership between CSIRO and the Bureau of Meteorology, Hobart, TAS, Australia Ruhr-Universität Bochum, 44780 Bochum, Germany A new seawater standard for oceanographic and engineering applications has been developed that consists of three independent thermodynamic potential functions, derived from extensive distinct sets of very accurate experimental data. The results have been formulated as Releases of the International Association for the Properties of Water and Steam, IAPWS (1996, 2006, 2008) and are expected to be adopted internationally by other organizations in subsequent years. In order to successfully perform computations such as phase equilibria from combinations of these potential functions, mutual compatibility and consistency of these independent mathematical functions must be ensured. In this article, a brief review of their separate development and ranges of validity is given. We analyse background details on the conditions specified at their reference states, the triple point and the standard ocean state, to ensure the mutual consistency of the different formulations, and the necessity and possibility of numerically evaluating metastable states of liquid water. Computed from this formulation in quadruple precision (128-bit floating point numbers), tables of numerical reference values are provided as anchor points for the consistent incorporation of additional potential functions in the future, and as unambiguous benchmarks to be used in the determination of numerical uncertainty estimates of double-precision implementations on different platforms that may be customized for special purposes. Asada, S., Sotani, T., Arabas, J., Kubota, H., Matsuo S., and Tanaka, Y.: Density of water at subzero temperature under high pressure: measurements and correlation, J. Phys.: Condens. Matter, 14, 11 447–11 452, 2002. Bailey, D. H., Hida, Y., Jeyabalan, K., Li, X. S., and Thompson, B.: High-precision software directory, available at: http://crd.lbl.gov/~dhbailey/mpdist/, 2008. BIPM: The International System of Units (SI), Organisation Intergouvernementale de la Convention du Mètre, Paris, available at: http://www.bipm.fr/utils/common/pdf/si_brochure_8_en.pdf, 2006. Dahlquist, A., Björck, A., and Anderson, N.: Numerical Methods, Prentice-Hall Series in Automatic Computation, 573 pp., 1974. Feistel, R.: Equilibrium thermodynamics of seawater revisited, Progr. Oceanogr., 31, 101–179, 1993. Feistel, R.: A new extended Gibbs thermodynamic potential of seawater, Progr. Oceanogr., 58, 43–114, 2003. Feistel, R.: Numerical implementation and oceanographic application of the Gibbs thermodynamic potential of seawater, Ocean Sci., 1, 9–16, available at: http://www.ocean-sci.net/1/9/2005/os-1-9-2005.html, 2005. Feistel, R.: A Gibbs function for seawater thermodynamics for −6°C to 80°C and salinity up to 120 g kg^−1, Deep-Sea Res. I, 55, 1639–1671, 2008. Feistel, R., Wright, D.G., Jackett, D. R., Miyagawa, K., Wagner, W., Overhoff, U., Guder, C., Marion, G. M., Tchijov, V., Feistel, A. and J. H. Reissmann: Numerical implementation and oceanographic application of the thermodynamic potentials of water, vapour, ice, and seawater, Part I: Background and Equations. Ocean Sci., in preparation, 2009. Feistel, R. and Hagen, E.: On the Gibbs thermodynamic potential of seawater, Progr. Oceanogr., 36, 249–327, 1995. Feistel, R. and Hagen, E.: A Gibbs thermodynamic potential of sea ice, Cold Regions Sci. Technol., 28, 83–142, 1998. Feistel, R., Nausch, G., and Wasmund, N.: State and Evolution of the Baltic Sea, 1952–2005., A Detailed 50-Year Survey of Meteorology and Climate, Physics, Chemistry, Biology, and Marine Environment, John Wiley & Sons, Inc., Hoboken, New Jersey, 2008. Feistel, R. and Wagner, W.: High-pressure thermodynamic Gibbs functions of ice and sea ice, J. Mar. Res., 63, 95–139, 2005. Feistel, R. and Wagner, W.: A new equation of state for H₂O ice Ih, J. Phys. Chem. Ref. Data, 35, 1021–1047, 2006. Feistel, R. and Wagner, W.: Sublimation pressure and sublimation enthalpy of H₂O ice Ih between 0 and 273.16 K, Geochim. Cosmochim. Acta, 71, 36–45, 2007. Feistel, R., Wagner, W., Tchijov, V., and Guder, C.: Numerical implementation and oceanographic application of the Gibbs potential of ice, Ocean Sci., 1, 29–38, available at: http://www.ocean-science.net/os/1/29, 2005. Fofonoff, N. P.: Physical properties of sea-water, in: The Sea, edited by: Hill M. N., Wiley, New York, 3–30, 1962. Fofonoff, N. P. and Millard, R. C.: Algorithms for the computation of fundamental properties of seawater, Unesco techn. pap. mar. sci., 44, 1–53, 1983. Griffies, S. M., Gnanadesikan, A., Dixon, K. W., Dunne, J. P., Gerdes, R., Harrison, M. J., Rosati, A., Russell, J. L., Samuels, B. L., Spelman, M. J., Winton, M., and Zhang, R.: Formulation of an ocean model for global climate simulations, Ocean Sci., 1, 45–79, available at: http://www.ocean-sci.net/1/45/2005/os-1-45-2005.pdf, 2005. Guildner, L. A., Johnson, D. P., and Jones. F. E.: Vapor pressure of water at its triple point, J. Res. Nat. Bur. Stand., 80A, 505–521, 1976. Haar, L., Gallagher, J. S., and Kell, G. S.: The anatomy of the thermodynamic surface of water: the formulation and comparisons with data. Proceedings of the 8th Symposium on Thermophysical Properties, edited by: Sengers, J. V., The American Society of Mechanical Engineers, New York, Vol. II, 298–302, 1982. Haar, L., Gallagher, J. S., and Kell, G. S.: NBS/NRC Steam Tables, Hemisphere, Washington, and McGraw-Hill, New York, 320 pp., 1984. Harvey, A. H., Peskin, A. P, and Klein, S. A.: NIST/ASME Steam Properties (NIST Standard Reference Database 10), Version 2.21, National Institute of Standards and Technology, Gaithersburg, MD, 2004. IAPWS: Release on the IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use, The International Association for the Properties of Water and Steam, Fredericia, Denmark, September, available at: http://www.iapws.org/relguide/IAPWS95.pdf, 1996. IAPWS: Guideline on the Use of Fundamental Physical Constants and Basic Constants of Water, The International Association for the Properties of Water and Steam, Gaithersburg, Maryland, USA, September 2001, revised September, available at: http://www.iapws.org/relguide/fundam.pdf, 2008. IAPWS: Release on an Equation of State for H₂O Ice Ih, The International Association for the Properties of Water and Steam, Witney, UK, September, available at: http://www.iapws.org/relguide/Ice.pdf, 2006. IAPWS: Release on the IAPWS Formulation 2008 for the Thermodynamic Properties of Seawater, The International Association for the Properties of Water and Steam, Berlin, Germany, September, available at http://www.iapws.org/relguide/seawater.pdf, 2008. Jackett, D. R., McDougall, T. J., Feistel, R., Wright, D. G., and Griffies, S. M.: Algorithms for density, potential temperature, conservative temperature and the freezing temperature of seawater, J. Atm. Ocean. Technol., 23, 1709–1728, 2006. Marion, G. M., Millero, F. J., and Feistel, R.: Salinity/temperature ranges for application of seawater thermodynamic models, Paper Sea-07, Proceedings of the 15th International Conference on the Properties of Water and Steam, Berlin, Germany, 7–11~September, 2008a. Marion, G. M., Millero, F. J., and Feistel, R.: Salinity/temperature ranges for application of seawater S-T-P models, Ocean Sci., submitted, 2008b. McDougall, T. J.: Potential enthalpy: A conservative oceanic variable for evaluating heat content and heat fluxes, J. Phys. Oceanogr., 33, 945–963, 2003. McDougall, T. J.: On the need for the accurate representation of seawater thermodynamics in ocean climate models, Paper Sea-01, Proceedings of the 15th International Conference on the Properties of Water and Steam, Berlin, Germany, 7–11 September, 2008. McDougall, T. J., Jackett, D. R., Wright, D. G., and Feistel, R.: Accurate and computationally efficient algorithms for potential temperature and density of seawater, J. Atm. Ocean. Technol., 20, 730–741, 2003. McDougall, T. J., Feistel, R., Jackett, D. R., Wright, D. G., Millero, F. J., King, B. A., Marion, G. M., Spitzer, P., and Chen, C.-T. A.: Oceanographic application of the Gibbs function 2008 of seawater, Deep-Sea Res., in preparation, 2009a. McDougall, T. J., Feistel, R., Millero, F. J., Jackett, D. R., Wright, D. G., King, B. A., Marion, G. M., Chen, C.-T. A., and Spitzer, P.: Calculation of Thermophysical Properties of Seawater, in: Global Ship-based Repeat Hydrography Manual, IOCCP Report No 14, ICPO Publication Series no 134, in preparation, 2009b. Millero, F. J., Feistel, R., Wright, D. G., and McDougall, T. J.: The composition of Standard Seawater and the definition of the Reference-Composition Salinity Scale, Deep-Sea Res., 55, 50–72, 2008. Millero, F. J. and Leung, W. H.: The thermodynamics of seawater at one atmosphere, Am. J. Sci., 276, 1035–1077, 1976. Nicholas, J. V., Dransfield, T. D., and White, D. R.: Isotopic composition of water used for triple point of water cells, Metrologia, 33, 265–267, 1996. Preston-Thomas, H.: The international temperature scale of 1990 (ITS-90), Metrologia, 27, 3–10, 1990. Pruß, A. and Wagner, W.: A new equation of state for water as a candidate for the New Scientific Formulation of IAPWS, in: Physical Chemistry of Aqueous Systems: Meeting the Needs of Industry, edited by: White Jr., H. J., Sengers, J. V., Neumann, D. B., and Bellows, J. C., Proceedings of the 12th International Conference on the Properties of Water and Steam. Begell House, New York, 66–77, 1995. Riethmann, T., Wagner, W., and Feistel, R.: New equations for the melting pressure and sublimation pressure of H₂O ice Ih, Paper Prop-06, Proceedings of the 15th International Conference on the Properties of Water and Steam, Berlin, Germany, 7–11 September, 2008. Rudtsch, S. and Fischer, J.: Temperature measurements according to the International Temperature Scale of 1990 and its associated uncertainties, Accred. Qual. Assur., 13, 607–609, 2008. Sotani, T., Arabas, J., Kubota, H., Kijima, M., and Asada, S.: Volumetric behaviour of water under high pressure at subzero temperature, High Temp. – High Press., 32, 433-440, 2000. Tailleux, R.: On the energetics of stratified turbulent mixing, irreversible thermodynamics, Boussinesq models, and the ocean heat engine controversy, J. Fluid Mech., submitted, 2008. Tchijov, V., Feistel, R., Cruz-León, G., and Rodríguez-Romoa, S.: Thermodynamic properties of high-pressure ices: A review, Paper Prop-07, Proceedings of the 15th International Conference on the Properties of Water and Steam, Berlin, Germany, 7–11 September, 2008a. Tchijov, V., Cruz-León, G., Rodríguez-Romoa, S., and Feistel, R.: Thermodynamics of ice at high pressures and low temperatures, J. Phys. Chem. Solids, 69, 1704–1710, 2008b. Tillner-Roth, R.: Fundamental Equations of State, Shaker Verlag, Aachen, 172 pp., 1998. Wagner, W. and Pruß, A.: The IAPWS formulation 1995 for the thermodynamic properties of ordinary water substance for general and scientific use, J. Phys. Chem. Ref. Data, 31, 387–535, 2002. White, D. R., Dransfield, T. D., Strouse, G. F., Tew, W. L., Rusby, R. L., and Gray, J.: Effects of heavy hydrogen and oxygen on the triple-point temperature of water, American Institute of Physics; CP684, Temperature: Its Measurement and Control in Science and Industry, 7, 221–226, 2003. Wright, D. G., Feistel, R., Jackett, D. R., Miyagawa, K., Feistel, A., Guder, C., Marion, G. M., Overhoff, U., Reissmann, J. H., Tchijov, V., and W. Wagner: Numerical implementation and oceanographic application of the thermodynamic potentials of water, vapour, ice, and seawater, Part II: The Library Routines, Ocean Sci., in preparation, 2009.