OS Ocean Science OS Ocean Sci. 1812-0792 Copernicus Publications Göttingen, Germany 10.5194/os-6-91-2010 Thermodynamic properties of sea air Feistel R. 1 Wright D. G. 2 Kretzschmar H.-J. 3 Hagen E. 1 Herrmann S. 3 Span R. 4 Leibniz Institute for Baltic Sea Research, 18119 Warnemünde, Germany Bedford Institute of Oceanography, Dartmouth, NS, Canada Department of Technical Thermodynamics, Zittau/Görlitz University of Applied Sciences, 02763 Zittau, Germany Lehrstuhl für Thermodynamik, Ruhr-Universität Bochum, 44780 Bochum, Germany 01 02 2010 6 1 91 141 Copyright: © 2010 R. Feistel et al. 2010 This work is licensed under the Creative Commons Attribution 3.0 Unported License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/3.0/ This article is available from https://os.copernicus.org/articles/6/91/2010/os-6-91-2010.html The full text article is available as a PDF file from https://os.copernicus.org/articles/6/91/2010/os-6-91-2010.pdf

Very accurate thermodynamic potential functions are available for fluid water, ice, seawater and humid air covering wide ranges of temperature and pressure conditions. They permit the consistent computation of all equilibrium properties as, for example, required for coupled atmosphere-ocean models or the analysis of observational or experimental data. With the exception of humid air, these potential functions are already formulated as international standards released by the International Association for the Properties of Water and Steam (IAPWS), and have been adopted in 2009 for oceanography by IOC/UNESCO. <br><br> In this paper, we derive a collection of formulas for important quantities expressed in terms of the thermodynamic potentials, valid for typical phase transitions and composite systems of humid air and water/ice/seawater. Particular attention is given to equilibria between seawater and humid air, referred to as "sea air" here. In a related initiative, these formulas will soon be implemented in a source-code library for easy practical use. The library is primarily aimed at oceanographic applications but will be relevant to air-sea interaction and meteorology as well. <br><br> The formulas provided are valid for any consistent set of suitable thermodynamic potential functions. Here we adopt potential functions from previous publications in which they are constructed from theoretical laws and empirical data; they are briefly summarized in the appendix. The formulas make use of the full accuracy of these thermodynamic potentials, without additional approximations or empirical coefficients. They are expressed in the temperature scale ITS-90 and the 2008 Reference-Composition Salinity Scale.

 References Alberty, R. A.: Use of Legendre transforms in chemical thermodynamics, Pure Appl. Chem., 73, 1349–1380, 2001. Alexandrov, A. A. and Orlov, K. A.: The thermodynamic properties of humid air at high pressure and temperature, Thermal Eng., 54, 548–551, 2007. Ambrose, D. and Lawrenson, I. J.: The vapour pressure of water, J. Chem. Thermodyn., 4, 755–761, 1972. Arons, A. B. and Kientzler, C. F.: Vapor pressure of sea-salt solutions, Trans. Am. Geophys. Union, 35, 722–728, 1954. Baosen, L.: The latent and sensible heat fluxes over the western tropical Pacific and its relationship to ENSO, Adv. Atmosph. Sci., 6, 467–474, 1989. Battino, R., Rettich, T. R., and Tominaga, T.: The solubility of nitrogen and air in liquids, J. Phys. Chem. Ref. Data, 13, 563–600, 1984. Bezold, W. v.: Zur Thermodynamik der Atmosphaere. Zweite Mittheilung. Potentielle Temperatur. Verticaler Temperaturgradient. Zusammengesetzte Convection, Sitz. ber. Königl. Preuss. Akad. Wiss. Berlin, 46, 1189–1206, online available at: <a href="http://bibliothek.bbaw.de/bibliothek-digital/digitalequellen/schriften/anzeige/index_html?band=10-sitz/1888-2&seite:int=530">http://bibliothek.bbaw.de/bibliothek-digital/digitalequellen/schriften/anzeige/index_html?band=10-sitz/1888-2&seite:int=530</a>, 1888. Blandamer, M. J., Engberts, J. B. F. N., Gleeson, P. T., and Reis, J. C. R.: Activity of water in aqueous systems; A frequently neglected property, Chem. Soc. Rev. 34, 440–458, 2005. Bolton, D.: The computation of equivalent potential temperature, Mon. Weather Rev., 108, 1046–1053, 1980. Calvert, J. G.: Glossary of atmospheric chemistry terms (Recommendations 1990), Pure Appl. Chem., 62, 2167–2219, 1990. Cochrane, T. T. and Cochrane, T. A.: Sea Water Dilution and its Influence on Climatic Change, J. Climatic Change, submitted, 2009. Cooper, J. R.: Representation of the ideal-gas thermodynamic properties of water, Int. J. Thermophys., 3, 35–43, 1982. Curry, R., Dickson, B., and Yashayev, I.: A change in the freshwater balance of the Atlantic Ocean over the past four decades, Nature, 426, 826–829, 2003. Dai, A.: Recent Climatology, Variability, and Trends in Global Surface Humidity, J. Climate, 19, 3589–3605, 2006. Davis, R. S.: Equation for the determination of the density of moist air (1981/91), Metrologia, 29, 67–70, 1992. Defant, A.: Physical Oceanography, Vol. I, Pergamon Press, Oxford, 1961. De Groot, S. R. and Mazur, P.: Non-equilibrium thermodynamics, Dover Publications, New York, 1984. Dietrich, G., Kalle, K., Krauss, W., and Siedler, G.: Allgemeine Meereskunde, Gebr. Bornträger, Berlin, Stuttgart, 1975. Doherty, B. T. and Kester, D. R.: Freezing Point of Seawater, J. Mar. Res., 32, 285–300, 1974. Dressler, A. E., Zhang, Z., and Yang, P.: Water-vapor climate feedback inferred from climate fluctuations. 2003–2008, Geophys. Res. Lett., 35, L20704, https://doi.org/10.1029/2008GL035333, 2008. Durack, P. J. and Wijffels, S. E.: Fifty-year trends in global ocean salinities and their relationship to broadscale warming, J. Climate, submitted, 2009. Ebeling, W. and Feistel, R.: Physik der Selbstorganisation und Evolution, Akademie-Verlag, Berlin, 1982. Emanuel, K. A.: Atmospheric convection, University Press, New York, Oxford, 1994. Ewing, M. B., Lilley, T. H., Olofsson, G. M., Ratzsch, M. T., and Somsen, G.: Standard quantities in chemical thermodynamics. Fugacities, activities and equilibrium constants for pure and mixed phases (IUPAC Recommendations 1994), Pure Appl. Chem., 66, 533–552, 1994. Falkenhagen, H., Ebeling, W., and Hertz, H. G.: Theorie der Elektrolyte, S. Hirzel, Leipzig, 1971. Feistel, R.: Equilibrium thermodynamics of seawater revisited, Progr. Oceanogr., 31, 101–179, 1993. Feistel, R.: A Gibbs Function for Seawater Thermodynamics for −6 to 80 °C and Salinity up to 120 g/kg, Deep-Sea Res. I, 55, 1639–1671, 2008a. Feistel, R.: Thermodynamics of Water, Vapour, Ice and Seawater, Accred. Qual. Assur., 13, 593–599, 2008b. Feistel, R.: Extended Equation of State for Seawater at Elevated Temperature and Salinity, Desalination, 250, 14–18, 2010. Feistel, R. and Feistel, S.: Die Ostsee als thermodynamisches System, in: L. Schimansky-Geier, H. Malchow, T. Pöschel (Hrsg.), Irreversible Prozesse und Selbstorganisation, Logos-Verlag, Berlin, 247–264, 2006. 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 Reg. Sci. Technol., 28, 83–142, 1998. Feistel, R. and Marion, G. M.: A Gibbs-Pitzer Function for High-Salinity Seawater Thermodynamics, Prog. Oceanogr., 74, 515–539, 2007. 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 H<sub>2</sub>O ice Ih, J. Phys. Chem. Ref. Data, 35, 1021–1047, 2006. Feistel, R. and Wagner, W.: Sublimation pressure and sublimation enthalpy of H<sub>2</sub>O ice Ih between 0 and 273.16 K, Geochim. Cosmochim. Acta, 71, 36–45, 2007. Feistel, R., Wright, D. G., Jackett, D. R., Miyagawa, K., Reissmann, J. H., Wagner, W., Overhoff, U., Guder, C., Tchijov, V., Feistel, A., and Marion, G. M.: Numerical implementation and oceanographic application of the thermodynamic potentials of water, vapour, ice, seawater and air. Part I: Background and Equations, Ocean Sci., submitted, 2009. Feistel, R., Feistel, S., Nausch, G., Szaron, J., Lysiak-Pastuszak, E., and Ǽrtebjerg, G.: BALTIC: Monthly time series 1900–2005, in: State and Evolution of the Baltic Sea, 1952 – 2005. A Detailed 50-Year Survey of Meteorology and Climate, Physics, Chemistry, Biology, and Marine Environment, edited by: Feistel, R., Nausch, G., and Wasmund, N., John Wiley & Sons, Inc., Hoboken, 311–336, 2008a. Feistel, R., Wright, D. G., Miyagawa, K., Harvey, A. H., Hruby, J., Jackett, D. R., McDougall, T. J., and Wagner, W.: Mutually consistent thermodynamic potentials for fluid water, ice and seawater: a new standard for oceanography, Ocean Sci., 4, 275–291, 2008b. 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, online available at: <a href="http://unesdoc.unesco.org/images/0005/000598/059832EB.pdf">http://unesdoc.unesco.org/images/0005/000598/059832EB.pdf</a>, 1983. Gatley, D. P.: Understanding Psychrometrics, 2nd ed., American Society of Heating, Refrigerating and Air-Conditioning ASHRAE, Atlanta, 2005. Giacomo, P.: Equation for the determination of the density of moist air (1981), Metrologia, 18, 33–40, 1982. Gibbs, J. W.: Graphical methods in the thermodynamics of fluids, Trans. Connecticut Acad. Arts Sci., 2, 309–342, 1873. Gill, A. E.: Atmosphere Ocean Dynamics, Academic Press, San Diego, 1982. Glansdorff, P. and Prigogine, I.: Thermodynamic Theory of Structure, Stability, and Fluctuations, Wiley Interscience, New York, 1971. Glasstone, S.: Thermodynamics for Chemists, D. van Nostrand Company, Inc., Princeton, NJ, USA, 1947. Goldberg, R. N. and Weir, R. D.: Conversion of temperatures and thermodynamic properties to the basis of the International Temperature Scale of 1990, Pure Appl. Chem., 64, 1545–1562, 1992. Goodstein, D. L.: States of matter, Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1975. Guggenheim, E. A.: Thermodynamics. An advanced treatment for chemists and physicists, North-Holland Physics Publishing, Amsterdam, 1967. Hagen, E., Zülicke, Ch., and Feistel, R.: Near surface structures in the Cape Ghir filament off Morocco, Oceanol. Acta, 19, 577–597, 1996. Hantel, M. and Mayer, P.: Skriptum Theoretische Meteorologie I. Wiener Meteorologische Schriften, Heft 3, Facultas Universitätsverlag, Wien, 2006. Harvey, A. H. and Huang, P. H.: First-Principles Calculation of the Air-Water Second Virial Coefficient, Int. J. Thermophys., 28, 556–565, 2007. Helland-Hansen, B.: The Ocean Waters. International Review on Hydrobiological Hydrographic, Hydrog. Supp. Ser. 1 No. 2, Leipzig, 1912. Hellmuth, O.: Columnar modelling of nucleation burst evolution in the convective boundary layer – first results from a feasibility study Part I: Modelling approach, Atmos. Chem. Phys., 6, 4175–4214, 2006. Helmholtz, H. v.: Ueber atmosphaerische Bewegungen, Sitz. ber. Königl. Preuss. Akad. Wiss. Berlin, 46, 647–663, online available at: <a href="http://bibliothek.bbaw.de/bibliothek-digital/digitalequellen/schriften/anzeige/index_html?band=10-sitz/1888-1&seite:int=665">http://bibliothek.bbaw.de/bibliothek-digital/digitalequellen/schriften/anzeige/index_html?band=10-sitz/1888-1&seite:int=665</a>, 1888. Henry, P. S. H.: The Specific Heats of Air, Oxygen, Nitrogen from 20 °C to 370 °C, Proc. Roy. Soc. London, A133, 492–506, 1931. Herrmann, S., Kretzschmar, H.-J., and Gatley, D. P.: Thermodynamic Properties of Real Moist Air, Dry Air, Steam, Water, and Ice, ASHRAE RP-1485, American Society of Heating, Refrigeration, and Air-Conditioning Engineers, Inc., Atlanta, GA, online available at: <a href="http://www.ashrae.org">http://www.ashrae.org</a>, 2009a. Herrmann, S., Kretzschmar, H.-J., and Gatley, D. P.: Thermodynamic Properties of Real Moist Air, Dry Air, Steam, Water, and Ice, HVAC{&}R Research, 15, 961–986, 2009b. Herrmann, S., Kretzschmar, H.-J., Teske, V., Vogel, E., Ulbig, P., Span, R., and Gatley, D. P.: Determination of Thermodynamic and Transport Properties of Humid Air for Power-Cycle Calculations, Report PTB-CP-3, Physikalisch-Technische Bundesanstalt, Braunschweig und Berlin, Germany, 2009c. Herrmann, S., Kretzschmar, H.-J., Teske, V., Vogel, E., Ulbig, P., Span, R., and Gatley, D. P.: Properties of Humid Air for Calculating Power Cycles, J. Eng. Gas Turbines Power, in press, 2010. Higashi, K., Nakamura, K., and Hara, R.: The specific gravities and the vapour pressures of the concentrated sea water at 0 °–17 °C (in Japanese), J. Soc. Chem. Ind. Japan, 34, 166–172, 1931. Hofmann, G.: Die Thermodynamik der Taubildung, Ber. Deutsch. Wetterd., 18, 1–45, 1955. Hofmann, G.: Verdunstung und Tau als Glieder des Wärmehaushalts, Planta, 47, 303–322, 1956. Hyland, R. W. and Wexler, A.: The Enhancement of Water Vapor in Carbon Dioxide-Free Air at 30, 40, and 50 °C, J. Res. NBS, 77A, 115–131, 1973. Hyland, R. W: A Correlation for the Second Interaction Virial Coefficients and Enhancement Factors for Humid Air, J. Res. NBS, 79A, 551–560, 1975. Hyland, R. W. and Wexler, A.: Formulations for the Thermodynamic Properties of the Saturated Phases of H<sub>2</sub>O From 173.15 K to 473.15 K, ASHRAE Transact., 89, 500–519, 1983a. Hyland, R. W. and Wexler, A.: Formulations for the thermodynamic properties of dry air from 173.15 K to 473.15 K, and of saturated moist air from 173.15 K to 372.15 K, at pressures up to 5 MPa, ASHRAE Transact., 89, 520–535, 1983b. 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, Mayland, USA, September 2001, Revision July 2005, online available at: <a href="http://www.iapws.org">http://www.iapws.org</a>, 2005. IAPWS: Guideline on the Henry's Constant and Vapor-Liquid Distribution Constant for Gases in H<sub>2</sub>O and D<sub>2</sub>O at High Temperatures. The International Association for the Properties of Water and Steam, 2004, online available at: <a href="http://www.iapws.org">http://www.iapws.org</a>, 2004. 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 2008, online available at: <a href="http://www.iapws.org">http://www.iapws.org</a>, 2008a. IAPWS: Revised Release on the Pressure along the Melting and Sublimation Curves of Ordinary Water Substance. The International Association of the Properties of Water and Steam, Berlin, Germany, September 2008, onlien available at: <a href="http://www.iapws.org">http://www.iapws.org</a>, 2008b. IAPWS: Revised 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. Doorwerth, The Netherlands, September 2009, online available at: <a href="http://www.iapws.org">http://www.iapws.org</a>, 2009a. IAPWS: Revised Release on the Equation of State 2006 for H<sub>2</sub>O Ice Ih. The International Association for the Properties of Water and Steam, Doorwerth, The Netherlands, September 2009, online available at: <a href="http://www.iapws.org">http://www.iapws.org</a>, 2009b. IAPWS: Guideline on an Equation of State for Humid Air in Contact with Seawater and Ice, Consistent with the IAPWS Formulation 2008 for the Thermodynamic Properties of Seawater. The International Association for the Properties of Water and Steam. Niagara Falls, Canada, July 2010, in preparation, 2010. IOC: Resolution XXV-7, INTERNATIONAL THERMODYNAMIC EQUATION OF SEAWATER (TEOS-10), INTERGOVERNMENTAL OCEANOGRAPHIC COMMISSION (of UNESCO), Twenty-fifth Session of the Assembly, Paris, 16–25 June 2009. IOC: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties, Intergovernmental Oceanographic Commission, Manuals and Guides, UNESCO (English), online available at: <a href="http://www.TEOS-10.org">http://www.TEOS-10.org</a>), in preparation, 2010. IUPAC: Compendium of Chemical Terminology, 2nd ed. (the "Gold Book"), compiled by: A. D. McNaught and A. Wilkinsonm, Blackwell Scientific Publications, Oxford 1997, XML on-line corrected version: <a href="http://goldbook.iupac.org">http://goldbook.iupac.org</a> (2006) created by: Nic, M., Jirat, J., and Kosata, B., updates compiled by: Jenkins, A., ISBN 0-9678550-9-8, https://doi.org/10.1351/goldbook, 1997. Jacobsen, R. T., Clarke, W. P., Penoncello, S. G., and McCarthy, R. D.: A Thermodynamic Property Formulation for Air. I. Single-Phase Equation of State from 60 to 873 K at Pressures to 70 MPa, Int. J. Thermophys., 11, 169–177, 1990. Jacobson, M. Z.: Fundamentals of Atmospheric Modeling, 2nd Edition, University Press, Cambridge, 2005. Kammer, H. and Schwabe, K.: Einführung in die statistische Thermodynamik, Akademie-Verlag, Berlin, 1971. Kennish, M. J.: Practical Handbook of Marine Science, CRC Press, Boca Raton, 2001. Kittel, C.: Thermal Physics. John Wiley & Sons, Inc., New York, 1969. Köhler, H.: The nucleus in and the growth of hygroscopic droplets, T. Faraday Soc., 43, 1152–1161, 1936. Korolev, A. and Isaac, G. A.: Relative humidity in liquid, mixed-phase, and ice clouds, J. Atmos. Sci., 63, 2865–2880, 2006. Kraus, E. B.: Atmosphere-Ocean Interaction, Oxford University Press, London, New York, 1972. Landau, L. D. and Lifschitz, I. M.: Hydrodynamik, Akademie-Verlag, Berlin, 1974. Landau, L. D. and Lifschitz, I. M.: Statistische Physik, Akademie-Verlag, Berlin, 1987. Lehmann, H. P., Fuentes-Arderiu, X., and Bertello, L. F.: Glossary of terms in quantities and units in Clinical Chemistry (IUPAC-IFCC Recommendations 1996), Pure Appl. Chem., 68, 957–1000, 1996. Lemmon, E. W., Jacobsen, R. T., Penoncello, S. G., and Friend, D. G.: Thermodynamic Properties of Air and Mixtures of Nitrogen, Argon and Oxygen From 60 to 2000 K at Pressures to 2000 MPa, J. Phys. Chem. Ref. Data, 29, 331–362, 2000. Lewis, G. L.: The osmotic pressure of concentrated solutions, and the laws of the perfect solution, J. Am. Chem. Soc., 30, 668–683, 1908. Linke, F. and Baur, F.: Meteorologisches Taschenbuch, Geest & Portig, Leipzig, 1970. List, R. J.: Smithsonian Meteorological Tables, Smithson. Misc. Collect. 114, Smithson. Inst., Washington DC, 1951. Lunt, D. J., Foster, G. L., Haywood, A. M., and Stone, E. J.: Late Pliocene Greenland glaciation controlled by a decline in atmospheric CO<sub>2</sub> levels, Nature, 454, 1102–1105, 2008. Magee, J. W.: Molar Heat Capacity at Constant Volume for Air from 67 to 300 K at Pressures to 35 MPa, Int. J. Thermophys., 15, 849–861, 1994. Margenau, H. and Murphy, G. M.: The Mathematics of Physics and Chemistry, D. van Nostrand Company, Inc., New York, 1943. Marion, G. M., Millero, F. J., and Feistel, R.: Precipitation of solid phase calcium carbonates and their effect on application of seawater $S_A-T-P$ models, Ocean Sci., 5, 285–291, 2009. 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. and Feistel, R.: What Causes the Adiabatic Lapse Rate?, Deep-Sea Res. I, 50, 1523–1535, 2003. Millero, F. J.: The thermodynamics of seawater. Part II. Thermochemical properties, Ocean Sci. Eng., 8, 1–40, 1983. Millero, F. J.: Physical Chemistry of Natural Waters, Wiley-Interscience, New York, 2001. Millero, F. J.: Chemical Oceanography, CRC Press, Boca Raton, 1996. 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. I, 55, 50–72, 2008. Millero, F. J. and Huang, F.: The density of seawater as a function of salinity (5 to 70 g kg<sup>−1</sup>) and temperature (273.15 to 363.15 K), Ocean Sci., 5, 91–100, 2009. Millero, F. J. and Leung, W. H.: The thermodynamics of seawater at one atmosphere, Am. J. Sci., 276, 1035–1077, 1976. Möbius, H.-H. and Dürselen, W.: Chemische Thermodynamik, VEB Deutscher Verlag für Grundstoffindustrie, Leipzig, 1973. Montgomery, R. B.: Observations of vertical humidity distribution above the ocean surface and their relation to evaporation, Pap. Phys. Oceanogr. Meteor., 7, 1–30, 1940. Morris, V., Clemente-Colón, P., Nalli, N. R., Joseph, E., Armstrong, R. A., Detrés, Y., Goldberg, M. D., Minnett, P. J., and Rick Lumpkin, R.: Measuring Trans-Atlantic Aerosol Transport From Africa, Eos, 87, 565–571, 2006. Nalli, N. R., Clemente-Colon, P., Morris, V., Joseph, E., Szczodrak, M., Minnett, P. J., Shannahoff, J., Goldberg, M. D., Barnet, C., Wolf, W. W., Feltz, W. F., and Knuteson, R. O.: Profile observations of the Saharan air layer during AEROSE 2004, Geophys. Res. Lett., 32, L05815, 1–5, 2005. O'Dowd, C. D., Smith, M. H., Consterdine, I. E., and Lowe, J. A.: Marine aerosol, sea-salt, and the marine sulphur cycle: A short review, Atmos. Environ., 31, 73–80, 1997. Ostwald, W.: Lehrbuch der Allgemeinen Chemie, Leipzig, 1896. Panin, G. N. and Brezgunov, V. S.: Influence of the Salinity of Water on its Evaporation, Izvestiya, Atmos. Ocean. Phys., 43, 663–665, 2007. Pauluis, O., Czaja, A., and Korty, R.: The Global Atmospheric Circulation on Moist Isentropes, Science, 321, 1075–1078, 2008. Picard, A., Davis, R. S., Gläser, M., and Fujii, K.: Revised formula for the density of moist air (CIPM-2007), Metrologia, 45, 149–155, 2008. Pollitzer, F. and Strebel, E.: Over the Influence of Indifferent Gases on the Saturation Steam Concentration of Liquids, Z. Phys. Chem., 110, 768–785, 1924 (in German). Preston-Thomas, H.: The international temperature scale of 1990 (ITS-90), Metrologia, 27, 3–10, 1990. Prigogine, I. and Defay, R.: Chemical Thermodynamics, Longmans Green, London, 1954. Pruppacher, H. R. and Klett, J. D.: Microphysics of Clouds and Precipitation. Second Revised and Enlarged Edition with an Introduction to Cloud Chemistry and Cloud Electricity, Kluwer Academic Publishers, Dordrecht/Boston/London, 1997. Reif, F.: Fundamentals of Statistical and Thermal Physics, McGraw-Hill Book Co., Singapore, 1965. Robinson, R. A.: The vapour pressure and osmotic equivalence of sea water, J. Mar. Biol. Ass. United Kingdom, 33, 449–455, 1954. Rogers, R. R. and Yau, M. K.: Short Course in Cloud Physics, Third Edition, Butterworth-Heinemann, Oxford, 1989. Safarov, J., Millero, F., Feistel, R., Heintz, A., and Hassel, E.: Thermodynamic properties of standard seawater: extensions to high temperatures and pressures, Ocean Sci., 5, 235–246, 2009. Santer, B. D., Mears, C., Wentz, F. J., Taylor, K. E., Gleckler, P. J., Wigley, T. M. L., Barnett, T. P., Boyle, J. S., Brüggemann, W., Gillett, N. P., Klein, S. A., Meehl, G. A., Nozawa, T., Pierce, D. W., Stott, P. A., Washington, W. M., and Wehner, M. F.: Identification of human-induced changes in atmospheric moisture content, P. Natl. Acad. Sci. USA, 104, 15248–15253, 2007. Schmelzer, J. and Schweitzer, F.: Ostwald ripening of bubbles in liquid-gas solutions, J. Non-Equilib. Thermodyn., 12, 255–270, 1987. Shaw, A. N.: The Derivation of Thermodynamical Relations for a Simple System, Philos. T. Roy. Soc. London A, 234, 299–328, 1935. Seinfeld, J. H. and Pandis, S. N.: Atmospheric Chemistry & Physics: From Air Pollution to Climate Change, John Wiley & Sons, New York, 1998. Siedler, G. and Peters, H.: Properties of Sea Water: Physical Properties, in: Oceanography, edited by: Sündermann, J., Landolt-Börnstein V/3a, Springer, Berlin, Heidelberg, 1986. Smith, S. D.: Coefficients for the sea surface wind stress, heat flux, and wind profiles as a function of wind speed and temperature, J. Geophys. Res., 93(C12), 15467–15472, 1988. Sonntag, D.: Formeln verschiedenen Genauigkeitsgrades zur Berechnung des Sättigungsdampfdruckes über Wasser und über Eis und ihre Anwendung auf einige praktische Feuchteme{ß}aufgaben, Abh. Met. Dienst. DDR, 17, 1–59, 1982. Sonntag, D.: Important new Values of the Physical Constants of 1986, Vapour Pressure Formulations based on the ITS-90, and Psychrometer Formulae, Z. Meteorol., 40, 340–344, 1990. Sonntag, D.: The History of Formulations and Measurements of Saturated Water Vapour Pressure. Third International Symposium on Humidity and Moisture, National Physical Laboratory, Teddington, Middlesex, UK, April 1998, Vol. 1, 93–102, 1998. Span, R., Lemmon, E. W., Jacobsen, R. T., Wagner, W., and Yokozeki, A.: A Reference Equation of State for the Thermodynamic Properties of Nitrogen for Temperatures from 63.151 to 1000 K and Pressures to 2200 MPa, J. Phys. Chem. Ref. Data, 29, 1361–1433, 2000. Stanley, E. H.: Introduction to Phase Transitions and Critical Phenomena, Clarendon Press, Oxford, 1971. Stewart, R. B., Jacobsen, R. T., and Wagner, W.: Thermodynamic Properties of Oxygen from the Triple Point to 300 K with Pressures to 80 MPa, J. Phys. Chem. Ref. Data, 20, 917–1021, 1991. Stott, R. A., Sutton, R. T., and Smith, D. M.: Detection and attribution of Atlantic salinity changes, Geophys. Res. Lett., 35, L21702, https://doi.org/10.1029/2008GL035874, 2008. Stull, R. B.: An Introduction to Boundary Layer Meteorology, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2003. Sun, R., Hu, W., and Duan, Z.: Prediction of Nitrogen Solubility in Pure Water and Aqueous NaCl Solutions up to High Temperature, Pressure, and Ionic Strength, J. Solution Chem., 30, 561–573, 2004. Tegeler, Ch., Span, R., and Wagner, W.: A New Equation of State for Argon Covering the Fluid Region for Temperatures From the Melting Line to 700 K at Pressures up to 1000 MPa, J. Phys. Chem. Ref. Data, 28, 779–850, 1999. Tetens, O.: Über einige meteorologische Begriffe, Z. Geophys., 6, 297–309, 1930. Tillner-Roth, R.: Fundamental Equations of State, Shaker Verlag, Aachen, 1998. Trenberth, K. E., Caron, J. M., and Stepaniak, D. P.: The atmospheric energy budget and implications for surface fluxes and ocean heat transports, Clim. Dynam., 17, 259–276, 2001. Unesco: The Practical Salinity Scale 1978 and the International Equation of State of Seawater 1980, Unesco techn. pap. mar. sci., 36, 8–25, online available at: <a href="http://unesdoc.unesco.org/images/0004/000461/046148eb.pdf">http://unesdoc.unesco.org/images/0004/000461/046148eb.pdf</a>, 1981. Van Wylen, G. J. and Sonntag, R. E.: Fundamentals of Classical Thermodynamics, John Wiley & Sons, Inc., New York, 1965. Wagner, W. and de Reuck, M.: International thermodynamic tables of the fluid state-9, oxygen, Blackwell Scientific, Oxford, 1987. Wagner, W. and Kretzschmar, H.-J.: International Steam Tables, 2nd edition. Springer Verlag, Berlin, Heidelberg, 2008. Wagner, W. and Pru{ß}, 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. Walton Smith, F. G.: Handbook of Marine Science, Vol. I. CRC Press, Cleveland, 1974. Weare, B. C., Strub, P. T., and Samuel, M. D.: Annual mean surface heat fluxes in the tropical Pacific Ocean, J. Phys. Oceanogr., 2, 705–717, 1981. Webster, T. J.: The Effect on Water Vapour Pressure of Superimposed Air Pressure, J. Soc. Chem. Ind. London, 69, 343–346, 1950. Weiss, R. F.: The solubility of nitrogen, oxygen and argon in water and seawater, Deep-Sea Res., 17, 721–735, 1970. Weiss, R. F. and Price, B. A.: Nitrous oxide solubility in water and seawater, Mar. Chem., 8, 347–359, 1980. Weller, R. A., Bradley, E. F., Edson, J. B., Fairall, C. W., Brooks, I., Yelland, M. J., and Pascal, R. W.: Sensors for physical fluxes at the sea surface: energy, heat, water, salt, Ocean Sci., 4, 247–263, 2008. Wells, N. C. and King-Hele, S.: Parametrization of tropical ocean heat flux, Q. J. Roy. Meteorol. Soc., 116, 1213–1224, 1990. Wieser, M. E.: Atomic Weights of the elements (IUPAC Technical Report), Pure Appl. Chem., 78, 2051–2066, online available at: <a href="http://www.iupac.org/publications/pac/78/11/2051/">http://www.iupac.org/publications/pac/78/11/2051/</a>, 2006. Willett, K. M., Gillett, N. P., Jones, P. D., and Thorne, P. W.: Attribution of observed surface humidity changes to human influence, Nature, 44(9), 710–712, 2007. Witting, R.: Untersuchungen zur Kenntnis der Wasserbewegungen und der Wasserumsetzung in den Finnland umgebenden Meeren, I, Der Bottnische Meerbusen in den Jahren 1904 und 1905, Erster Teil, Finnl. Hydrogr.-Biol. Unters., 2, 1–246, 1908. Woolley, H. W.: Thermodynamic properties for H<sub>2</sub>O in the ideal gas state, in: Water and Steam, edited by: Straub, J. and Scheffler, K., Proceedings of the 9th International Conference on the Properties of Steam, München, 1979, Pergamon Press, Oxford-New York-Toronto-Sydney-Paris-Frankfurt, 166–175, 1980. Wright, D. G., Feistel, R., Jackett, D. R., Miyagawa, K., Reissmann, J. H., Wagner, W., Overhoff, U., Guder, C., Tchijov, V., Feistel, A., and Marion, G. M.: Numerical implementation and oceanographic application of the thermodynamic potentials of water, vapour, ice, seawater and air. Part II: The Library Routines, Ocean Sci., submitted, 2009. Wylie, R. G. and Fisher, R. S.: Molecular Interaction of Water Vapor and Air, J. Chem. Eng. Data, 41, 133–142, 1996.