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The authors are responsible for the choice and the presentation of the facts contained in this publication and for the opinionsexpressed therein, which are not necessarily those of UNESCO, SCOR or IAPSO and do not commit those Organizations.For bibliographic purposes, this document should be cited as follows:The International Thermodynamic Equation of Seawater – 2010: A Summary for Policy Makers. IOC, SCOR and IAPSO, 2011(IOC. Brochures Series)TEOS-10 is published in the IOC Manuals and Guides Series:IOC, SCOR and IAPSO, 2010: The International Thermodynamic Equation of Seawater – 2010: Calculation and useof thermodynamic properties. (Manuals and Guides, 56.) (English), 196 pp. (IOC/2010/MG/56)Designer: Eric Loddé(IOC/BRO/2010/7)Printed in France© UNESCO/IOC et al. 2011

.75179 γTEOS-10: A new way to look at waterSeawater composition is a critical factor, along with temperature and pressure, in determiningthe density of the ocean and calculating its potential to contain and disperse energy. Howthese variables relate to each other is the basis for the new Thermodynamic Equation ofSeawater – 2010 (referred to as TEOS-10).The Intergovernmental Oceanographic Commission (IOC) of the United Nations Educational,Scientific, and Cultural Organization (UNESCO), the Scientific Committee on Oceanic Research(SCOR), the International Association for the Physical Sciences of the Oceans (IAPSO), andthe International Association for the Properties of Water and Steam (IAPWS) have all endorsedthe new thermodynamic approach, TEOS-10.This new method of analyzing seawater provides mutually consistent expressions for density,potential temperature, entropy, enthalpy, sound speed, chemical potential, as well as otherseawater properties — and provides an update to the Equation of State of Seawater, whichUNESCO endorsed in 1980 (referred to as EOS-80). Unlike the previous equation, however,the thermodynamic approach is also applicable to freshwater, ice, and water vapor.1

ΣΑ =The InternationalThermodynamicEquation of Seawater– 2010ΣASummary for Policy MakersWorking Group 127The people behind the equation“An equation giving internal energy in terms of entropy and specific volume,or more generally any finite equation between internal naenergy, entropy andspecific volume, for a definite quantity of any fluid, may be considered asthe fundamental thermodynamic equation of thatfluid, as fromit… maybederived all the thermodynamic properties of the fluid (so far as reversibleprocesses are concerned).”~ J. W. Gibbs, 1873The group tasked with developing the new set of highly accurate and comprehensiveformulas used in TEOS-10, the SCOR/IAPSO Working Group 127, began work in 2005and included:Trevor J. McDougall, (chair), CSIRO, Hobart, AustraliaRainer Feistel, Leibniz Institut fuer Ostseeforschung, Warnemuende, GermanyDaniel G. Wright, Bedford Institute of Oceanography, Dartmouth, CanadaRich Pawlowicz, University of British Columbia, Vancouver, CanadaFrank J. Millero, RSMAS, Florida, USA*David R. Jackett, CSIRO, Hobart, AustraliaBrian A. King, National Oceanography Centre, Southampton, UKGiles M. Marion, Desert Research Institute, Reno, USASteffen Seitz, Physikalisch-Technische Bundesanstalt (PTB), Braunschweig, GermanyPetra Spitzer, Physikalisch-Technische Bundesanstalt (PTB), Braunschweig, GermanyChen-Tung Arthur Chen, National Sun Yat-Sen University, Taiwan, R.O.C.* Member of the original committee on EOS-80Josiah Willard GibbsAs previous studies have noted, the EOS-80 equation was missing a mathematicalcomponent -- a Gibbs function which physicists had determined for a variety of fluids,except seawater. Named after American theoretical physicist, chemist, and mathematicianJosiah Willard Gibbs (1839-1903), a Gibbs function defines a fluid in termsof its energy and heat transfer, or thermodynamics. One of the first requirements theworking group had to address was incorporating a Gibbs function into the new equationfor seawater. The fundamental work of Rainer Feistel at Leibniz Institute for BalticSea Research led to the development of a Gibbs free energy function that is the backboneof the new thermodynamic equation of state (TEOS-10). Because the compositionof seawater is different in different locations around the world, another aspect ofthe new equation is the provision of a practical way to account for these spatial variations.Merging the different seawater properties into one equation, the working grouphas mixed 19 th -century theory with 21 st -century computer algorithms.2

75179 γPractical vs. Absolute SalinityA fundamentally different approach todetermining what’s in seawaterIn 1978, oceanographers agreed to use conduc-tivity as the universal method for estimating thesalinity of seawater. UNESCO endorsed thismethod, and incorporated the 1978 Practical Sa-linity Scale into its 1980 equations for calculatingthe density of seawater (EOS-80).Prior to the Practical Salinity Scale, oceanogra-phers had primarily calculated salinity using titrationmethods that measured the most commonsalt ion: chlorine (see box on page 7: The searchfor salinity). The conductivity method improvedaccuracy, as it tracked all the ions in the sea andnot just chloride. But calculating salinity fromconductivity, as opposed to traditional chemicalanalysis, required sacrificing the definition ofsalinity. This is because conductivity measuresonly free-floating ions or electrolytes, the samedissolved salts that are found in sports drinks,for example. In fact, any non-conductive material,such as dissolved silicon dioxide, is simplyignored when it comes to practical salinity.Since seawater conductivity can only be preciselyrelated to salinity for a particular chemicalcomposition, applying the 1978 Practical SalinityScale to seawater of different compositions canlead to errors. These errors are small in the openocean, but are much larger than the typical precisionof modern measurements.Water from the North Atlantic with a salinity ofabout 35 parts of salt per thousand parts waterhas traditionally been used as a control for comparingother water samples. But as the waterfrom the Atlantic ocean travels around the world,the composition of the seawater changes as aconsequence of the biogeochemical differencesin the environment. Sinking particles remineralize,adding calcium, carbon and nutrients like silicicacid and nitrate. Once seawater comes intocoastal areas, its composition will also changeas it mixes with river waters, which have dissolvedions in very different combinations fromA Taste for Salt‘In chemistry, any positive and negative ionbound together is called a salt,’ explainsmolecular geneticist and chemosensation(taste and smell) expert Hiroaki Matsunami ofDuke University in the USA. In the ocean, saltsdissolve into free-floating negative and positiveions, also known as electrolytes. Thesecharged particles are what make it possiblefor electricity to flow through water. The sameions that make up the salt used in foods —sodium (Na + ) and chloride (Cl - ) — accountfor more than 86% by weight of the 11 majorions in the sea and are what gives the oceanits salty taste. Dried, these ions form table saltand get sprinkled over food.After chloride and sodium, the ocean’s nextmost common ions are sulfate (SO 42-) andmagnesium (Mg 2+ ). How would the oceantaste if these ions were more common? ‘Itasted magnesium sulfate and it tasted reallybad but I wouldn’t call it bitter,’ Matsunamisays of the ingredient used in bath salts.seawater. Some of these added molecules addto the conductivity, but not in the same way asthe original set of ions.Unlike the Practical Salinity Scale, which accountsonly for ions, the new Absolute Salinityincorporates non-electrolytes using tables thataccount for how these additional substancesvary region by region. Once again, the latitudeand longitude at which seawater samples aretaken will play an important role in calculatingsalinity. Unlike the Practical Salinity Scale-- which, as a reference scale, has no unit ofmeasure -- Absolute Salinity is a new variablewithin the thermodynamic description and ispart of the International System of Units.3

ΣΑ = Δρ/0Σ– A Summary for Policy Makers2010ΣΑThe InternationalThermodynamicEquation of SeawaterPresent Practice for Data Storing Stays the SameData stored in national and international databasesshould, as a matter of principle, bemeasured values rather than derived quantities.Consistent with this, the working group recommendscontinuing to store the measured (in situ)temperature rather than the derived quantity,potential temperature. Similarly they recommendthat Practical Salinity (S P ) continue to bethe salinity variable that is stored in such databasessince S P is closely related to the measuredvalues of conductivity. This recommendation hasthe very important advantage that there is nochange to the present practice and so there is lesschance of transitional errors occurring in nationaland international databases because of the adoptionof Absolute Salinity (S A ) in oceanography(for more see page 9: Data Representations: Metadata requirements of TEOS-10).In 2010, the algorithm for calculating salinityincorporated for the first time more informationthan is contained in measurements of seawaterconductivity. The more accurate way of identifyingAbsolute Salinity everywhere in the oceanwas devised and incorporated into TEOS-10.The new equation incorporated the location ofthe conductivity measurements with chemicalanalysis from those regions into a new AbsoluteSalinity calculation. The working group alsoredefined how the properties of seawater arecalculated using this new Absolute Salinitymethod and combining it with the principlesbehind thermodynamics to form a single newthermodynamic equation for seawater.The re-evaluation of the 1980s equationsprovided seawater with a ‘Gibbs function’. Theprevious mathematical equations for determiningthe properties of seawater had not accountedfor water’s ability to transfer heat from warmerto cooler currents. Nor did the old equationsset a standard for comparing how difficult sucha transfer of energy might be, based on thewater’s inherent pressure and volume. The thermodynamicequation of seawater replaces theold equations with a recipe of computer algorithmsthat modellers crave.On 24 June 2009, the 25th Assembly ofUNESCO’s Intergovernmental OceanographicCommission (IOC) recommended that theoceanographic community adopt TEOS-10.The TEOS-10 method has already become anindustrial standard, approved by IAPWS. Forexample, any company interested in providingdrinking water for desert cities near the coast,is required to use the new method of calculationin building seawater desalination plants.The thermodynamic equation uses IAPWS-08and IAPWS-06 as the official descriptions forseawater and ice.Under TEOS-10 it is recognized that the compositionof seawater varies around the world andthat the thermodynamic properties of seawaterare more accurately represented as functionsof Absolute Salinity than of Practical Salinity.These new international standards were adoptedwhile recognizing that the techniques forestimating Absolute Salinity will likely improveover the coming decades. The algorithm forevaluating Absolute Salinity in terms of PracticalSalinity, latitude, longitude and pressure willbe updated on the website www.TEOS-10.orgfollowing peer-reviewed publications. Users ofthis software should always state in their publishedwork which version of the software wasused to calculate Absolute Salinity.4© CSIRO

.75179 γMotivation for an Updated ThermodynamicDescription of SeawaterThe Practical Salinity Scale and EOS-80, whichexpresses the density of seawater as a functionof Practical Salinity, temperature, and pressure,have served the oceanographic community for30 years.In recent years, however, the following aspectsof the thermodynamics of seawater, ice, andmoist air became apparent and suggested thatit was time to redefine the properties of thesesubstances. tionof State of Seawater (EOS-80) were notconsistent. The thermodynamic approacheliminates this problem. Properties of Water and Steam developed amore accurate and more broadly applicablethermodynamic description of pure water.Also higher accuracy measurements havebeen made of several properties of seawatersuch as (i) heat capacity, (ii) sound speed and(iii) the temperature of maximum density.These have been incorporated into the newthermodynamic description of seawater. standingof how variation in the compositionof seawater can change seawater density inthe different ocean basins. In order to furtherprogress this aspect of seawater, a standardmodel of seawater composition is needed toserve as a generally recognised reference fortheoretical and chemical investigations. being an integral part of the global heatengine points to the need for accurate expressionsfor the entropy, enthalpy and internalenergy of seawater so that heat fluxes can bemore accurately determined in the ocean andacross the interfaces between the ocean andthe atmosphere and ice (entropy, enthalpyand internal energy were not available fromEOS-80). tentdescription of the interactions betweenseawater, ice and moist air; in particular, theneed for accurate expressions for the latentheats of evaporation and freezing, both atthe sea surface and in the atmosphere. 1990 and TEOS-10 incorporates this revisionas well as the latest update from the InternationalUnion of Pure and Applied Chemistryfor the atomic weights of the elements.5

ΣΑ = Δρ/0The InternationalThermodynamicEquation of Seawater– 2010ΣASummary for Policy Makers0Practical Salinity vs. Absolute Salinity Part II:How the Relationship Works TogetherThe salinity input to the TEOS-10 Gibbs functionrequires knowledge of the Absolute Salinity ofseawater (S A ), which is based upon the ReferenceSalinity of seawater (S R ). The ReferenceSalinity is our best estimate of the AbsoluteSalinity of the seawater that was used to developthe Practical Salinity Scale (S P ), the equation ofstate, and the other thermodynamic propertiesof seawater. Reference Salinity is related toPractical Salinity byS R = S P –1and Absolute Salinity is related to ReferenceSalinity byδS A = S R + δS Awhere δS A is due to the added solutes in seawaterin deep waters resulting from the dissolutionof CaCO 3 (soluble) and SiO 2 (soluble), CO 2 , andnutrients like NO 3 and PO 4 from the oxidation ofplant material. The δS A values due to the addedsolutes are estimated from the differencesbetween the measured densities of seawatersamples compared with the densities calculatedfrom the TEOS-10 equation of state at the sameReference Salinity, temperature, and pressure.The values of δS A in the ocean can be estimatedfor waters at given longitude, latitude, and depthusing correlations of δS A and the concentrationof Si(OH) 4 in the waters. Other methods of estimatingδS A are also available in cases wherethe composition changes are measured or canbe modelled. The δS A values can then be usedto calculate all the thermodynamic propertiesof seawater in the major ocean basins using thenew TEOS-10.Improving the accuracyof climate modelsThe new thermodynamic equation for seawater also allows climatemodels to better account for changes in density and heat transferin the ocean. Early tests of the use of the new equation show anestimated 1% change in how the ocean circulates heat from theequator to the poles. The change in the West to East temperaturedifference in the equatorial Pacific is about 0.1°C, and this is anotheraspect which is expected to be a valuable improvement in climatemodelling.The fundamental properties of seawater — salinity,temperature and pressure, along with the freezingand boiling points, heat capacity, speed of soundand density — are intricately tied together. Beingable to measure salinity is important, as salinitylevels are indicators of climate change. They indicatehow much freshwater is evaporating from theoceans. For instance, parts of the Atlantic Oceanappear to be getting saltier. A possible explanationcould be that trapped heat from higher atmosphericconcentrations of CO 2 is causing more seawater toevaporate than before, leaving the salt behind.Salinity levels affect water density.Density especially determineswhether a current risestowards the surface or sinks towardsthe seafloor, as the denserthe seawater, the deeper itwill sink. Density depends ontemperature, pressure and theamount of dissolved materialin the water. Knowing the density of seawateris crucial to monitoring the Earth’s climate. Theocean transports heat via currents collectivelycalled the ocean conveyor belt in a processknown as thermohaline circulation. In the Arcticand Southern oceans, cool and salty waters sinkto form deep water currents. Over thousandsof years, these currents travel around the worlduntil they reach areas of upwelling which bringthem to the surface. Once at the surface, thesun-warmed, rain-freshened currents head back6

.75179 γ© Chris Linder, WHOIto the poles, where the formation of ice allowsthe cycle to continue.Several factors influence ocean circulation patterns:wind, rain, seafloor topography, the propertiesof the surrounding water, as well as theposition and distance of the moon and the rotationof the Earth. Ocean circulation models includeall of these factors and the computer algorithmsthat generate the models take weeks torun. Climate change models, which incorporatethe ocean’s ability to transport heat, take evenlonger. To see what model works best, what fitswith the Earth’s climate record from the pastthen run the model forward a century or twocan take the best part of a year, on the world’sfastest supercomputers.The Search for Salinity‘The exact chemical composition of seawater isunknown at the present time,’ says Frank Milleroof the Rosenstiel School of Marine and AtmosphericScience at the University of Miami in Working Group 127. It is not for want of trying.Marine scientists have been searching for the‘magic formula’ for measuring salinity for more Georg Forchhammer found 27 differentsubstances in seawater he sampled fromdifferent regions of the ocean. ‘Next to chlorine,oxygen and hydrogen, sodium is the most abundantelement in seawater,’ he wrote. Other majorsubstances he found included sulphuric acid,soda, potash, lime and magnesia. ‘Those whichoccur in less but still determinable quantity aresilica, phosphoric acid, carbonic acid and oxideof iron,’ he concluded. His tables were useduntil 1902 when Danish oceanographer MartinKnudsen filtered and distilled North Atlanticwater as a seawater standard that all marinescientists could use to calibrate their instrumentseasily and compare their samples fromaround the world with a control.In the 1930s, the introduction of instrumentsthat could measure seawater’s electricalconductivity set oceanographers scramblingto determine whether chemical analysis or thenew physical analysis worked better to determinesalinity. Conductivity won and by themid-1970s, deploying a rosette of samplingtubes equipped with conductivity, temperatureand depth recorders (CTDs) was becominga routine part of oceanographic cruises. Tomaintain consistency, a change to the internationalstandard for seawater was made in the1970s that allowed oceanographers to compareconductivity to a Practical Salinity Scale.Unlike the Practical Salinity Scale, whichaccounts only for ions, the new AbsoluteSalinity will incorporate non-electrolytes usingtables that account for how these additionalsubstances vary region by region. Once again,the latitude and longitude at which the seawatersamples are taken will play an important role incalculating salinity.7

ΣΑ = Δρ/0Σ– A Summary for Policy Makers2010ΣΑThe InternationalThermodynamicEquation of SeawaterAdvantages of TEOS-108© CSIROThe more prominent advantages of TEOS-10compared with EOS-80 are: lationof internal energy, entropy, enthalpy,potential enthalpy and the chemical potentialsof seawater as well as the freezingtemperature, and the latent heats of freezingand of evaporation. These quantities werenot available from the International Equationof State 1980 but are essential for the accurateaccounting of “heat” in the ocean andfor the consistent and accurate treatment ofair-sea and ice-sea heat fluxes. For example,a new temperature variable, ConservativeTemperature, can be defined as being proportionalto potential enthalpy and is a valuablemeasure of the “heat” content per unit massof seawater for use in physical oceanographyand in climate studies, as it is approximatelytwo orders of magnitude more conservativethan both potential temperature and entropy. varying composition of seawater can systematicallybe taken into account through theuse of Absolute Salinity. In the open ocean,this has a non-trivial effect on the horizontaldensity gradient computed from the equationof state, and thereby on the ocean velocitiesand heat transports calculated via the“thermal wind” relation. the new approach are totally consistent witheach other, and can now account for propertiessuch as speed of sound and the compressibilityof water with depth. measured in SI units. Moreover the treatmentof freshwater fluxes in ocean models will beconsistent with the use of Absolute Salinity,but is only approximately so for PracticalSalinity. seawater supports marine physicochemicalstudies such as the solubility of sea saltconstituents, alkalinity, pH, and ocean acidificationfrom risingspheric CO 2 .concentrations of atmo-

.75179 γData Representations:Metadata requirements of TEOS-10and Absolute Salinity AnomalyThe working group strongly recommends thatoceanographers continue to report salinity to nationaldatabases as Practical Salinity, determinedon the Practical Salinity Scale of 1978 (suitablyupdated to ITS-90 temperatures as described inappendix E of the TEOS-10 manual).There are three very good reasons for continuingto store Practical Salinity rather than Absolute Salinityin such data repositories:1. Practical Salinity is an (almost) directly measuredquantity whereas Absolute Salinity is generallya derived quantity. Practical Salinity is directlycalculated from measurements of conductivity,temperature and pressure, whereas AbsoluteSalinity is derived from a combination of thesemeasurements plus other measurements andcorrelations that are not yet well established.Practical Salinity is preferred over the measuredin situ conductivity value because of its conservativenature with respect to changes oftemperature and pressure, or dilution with purewater.2. It is imperative that confusion is not createdin national databases where a change in thereporting of salinity may be mishandled atsome stage and later be misinterpreted as areal increase in the ocean’s salinity. This secondpoint argues strongly for no change in presentpractice in the reporting of Practical Salinity innational databases of oceanographic data.the density of Standard Seawater) should beconverted to corresponding numbers of PracticalSalinity for storage. The practice of storingone type of salinity in national databases (PracticalSalinity, S P ) but using a different type ofsalinity in publications (Absolute Salinity, S A )is analogous to the present practice withtemperature; in situ temperature (t) is storedin databases (since it is a measured quantity)but the temperature variable that is used inpublications is a calculated quantity: potentialtemperature under EOS-80 or conservativetemperature under TEOS-10.3. The algorithms for determining the best estimateof Absolute Salinity of seawater withnon-standard composition are immature andwill undoubtedly change in the future, sostoring Absolute Salinity in national databasesis not recommended. Storage of an intermediatevalue, the Reference Salinity, (S R , definedto give the best estimate of Absolute Salinityof Standard Seawater), would also introduceconfusion in the stored salinity values withoutproviding any real advantage over storingPractical Salinity. Values of Reference Salinityobtained from suitable observational techniques(for example, by direct measurement ofDr Steve Rintoul and Stephanie Barrett, CSIRO.9

ΣΑ = Δρ/0The InternationalThermodynamicEquation of Seawater– 2010ΣASummary for Policy Makers0In order to improve the determination of AbsoluteSalinity oceanographers need to begin collectingand storing values of the salinity anomalyδS A =S A −S R based on measured values of density(such as can be measured with a vibratingtube densimeter). The 4-letter GF3 code DENSis currently defined for in situ measurements orcomputed values from EOS-80. It is recommendedthat the density measurements made witha vibrating beam densimeter be reported withUsing the TEOS-10:Algorithms and Programmesthe GF3 code DENS along with the laboratorytemperature (TLAB in °C) and laboratory pressure(PLAB, the sea pressure in the laboratory,usually 0 dbar). From this information and thePractical Salinity of the seawater sample, the absolutesalinity anomaly δS A =S A −S R can be calculatedusing an inversion of the TEOS-10 equationfor density to determine S A . For completeness,it is advisable to also report δS A under the newGF3 code DELS.The computer software to calculate the variousthermodynamic quantities is available from twoseparate libraries, the Seawater-Ice-Air (SIA) libraryand the Gibbs-SeaWater (GSW) library. Thefunctions in the SIA library are generally availablein basic-SI units, both for their input parametersand for the outputs of the algorithms. Some additionalroutines are included in the SIA libraryin terms of other commonly used units for theconvenience of users. The SIA library takes significantlymore computer time to evaluate mostquantities (approximately a factor of 65 morecomputer time for many quantities, comparingoptimized code in both cases) and provides significantlymore properties than does the GSW library.The SIA library uses the world-wide standardfor the thermodynamic description of pure watersubstance (IAPWS-95). Since this is defined overextended ranges of temperature and pressure,the algorithms are long and their evaluation time-consuming.The GSW library uses the Gibbsfunction of Feistel (2003) (IAPWS-09) to evaluatethe properties of pure water, and since this is validonly over the restricted ranges of temperatureand pressure appropriate for the ocean, the algorithmsare shorter and their execution is faster.The GSW library is not as comprehensive as theSIA library; for example, the properties of moistair are only available in the SIA library. In addition,computationally efficient expressions for densityρ in terms of Conservative Temperature (ratherthan in terms of in situ temperature) involvingjust 25 coefficients are also available.The input and output parameters of the GSWlibrary are in units which oceanographers willfind more familiar than basic SI units. We expectthat oceanographers will mostly use thisGSW library because of its greater simplicityand computational efficiency, and because ofthe more familiar units compared with the SIAlibrary. The library name GSW (Gibbs-SeaWater)has been chosen to be similar to, but differentfrom the existing “sw” (Sea Water) library whichis already in wide circulation. Both the SIA andGSW libraries, together with the TEOS-10 Manualand this summary are available from thewebsite www.TEOS-10.org. Initially the SIA libraryis being made available in Visual Basic andFORTRAN while the GSW library is available inMATLAB.10

.75179 γImagesCover: A CTD onboard the R/V Knorr during theRAPID/MOCHA Mooring cruise in 2005. Theworld’s first trans-basin mooring array acrossthe North Atlantic Ocean at 26 N, the array hasbeen continuously measuring Atlantic meridionaloverturning circulation since 2004. The project isa joint effort of the National Oceanography Centre,Southampton UK and the Rosenstiel Schoolof Marine and Atmospheric Science at the Universityof Miami, USA. Credit: Rosenstiel School ofMarine and Atmospheric Science.Page 1: A CTD and lowered acoustic Dopplercurrent profiler hovering just below the sea surfacewas taken south of Timor from the SouthernSurveyor in August 2003. Credit: Ann GronellThresher.Page 2: Josiah Willard Gibbs (1839-1903) CourtesyWiki ImagesReferencesLinks to papers describing the new thermodynamicformulation for the properties of seawaterand to codes implementing this new approachcan also be found online: http://www.teos-10.org/Feistel, R., 2003: A new extended Gibbs thermodynamicpotential of seawater, Progr. Oceanogr.,58, 43-114.Feistel, R., 2008: A Gibbs function for seawaterthermodynamics for −6 to 80 °C and salinity upto 120 g kg–1, Deep-Sea Res. I, 55, 1639-1671.Feistel, R., et al., 2010a: Thermodynamic propertiesof sea air. Ocean Science, 6, 91–141. http://www.oceansci.net/6/91/2010/os-6, 91-2010.pdfFeistel, R., et al., 2010b: Numerical implementationand oceanographic application of the thermodynamicpotentials of liquid water, watervapour, ice, seawater and humid air - Part 1:Background and equations. Ocean Science, 6,633/677. http://www.ocean-sci.net/6/633/2010/os-6-633-2010.pdf and http://www.oceansci.net/6/633/2010/os-6:-633-2010-supplement.pdfFeistel, R., et al., 2010c: Density and Absolute Salinityof the Baltic Sea 2006–2009. Ocean Science,6, 3–24. http://www.ocean-sci.net/6/3/2010/os-6-3-2010.pdfFeistel, R., G. M. Marion, R. Pawlowicz and D. G.Wright, 2010: Thermophysical property anomaliesof Baltic seawater. Ocean Science, 6, 949-981. http://www.ocean-sci.net/6/949/2010/IAPWS, 2009a: Revised Release on the Equationof State 2006 for H2O Ice Ih. The InternationalAssociation for the Properties of Water andSteam. Doorwerth, The Netherlands, September2009, available from http://www.iapws.org. This Release is referred to in the text asIAPWS 06.IAPWS, 2009b: Revised Release on the IAPWSFormulation 1995 for the Thermodynamic Propertiesof Ordinary Water Substance for Generaland Scientific Use. The International Associationfor the Properties of Water and Steam.Doorwerth, The Netherlands, September 2009,available from http://www.iapws.org. This Releaseis referred to in the text as IAPWS 95.IAPWS, 2009c: Supplementary Release on aComputationally Efficient Thermodynamic Formulationfor Liquid Water for OceanographicUse. The International Association for the Propertiesof Water and Steam. Doorwerth, TheNetherlands, September 2009, available fromhttp://www.iapws.org. This Release is referredto in the text as IAPWS 09.IAPWS, 2010: Guideline on an Equation of Statefor Humid Air in Contact with Seawater and Ice,Consistent with the IAPWS Formulation 2008for the Thermodynamic Properties of Seawater.The International Association for the Propertiesof Water and Steam. Niagara Falls, Canada,July 2010, available from http://www.iapws.org. This Guideline is referred to in the text asIAPWS 10.IOC, 1987: GF3- A General Formatting System forGeo-Referenced Data. Vol. 2, Technical Descriptionof the GF3 Format and Code Tables. IntergovernmentalOceanographic Commission, Manualsand Guides 17, UNESCO.IOC, SCOR and IAPSO, 2010: The internationalthermodynamic equation of seawater – 2010:Calculation and use of thermodynamic properties.Intergovernmental Oceanographic Commission,Manuals and Guides 56, UNESCO(English), 196 pp. http://www.teos-10.org/TEOS-10_Manual.pdfMcDougall, T. J., D. R. Jackett and F. J. Millero,2010a: An algorithm for estimating Absolute Salinityin the global ocean. submitted to OceanScience, a preliminary version is available atOcean Sci. Discuss., 6, 215-242. http://www.ocean-sci-discuss.net/6/215/2009/osd-6-215-2009-print.pdf and the computer software isavailable from http://www.TEOS-10.org11

ΣΑ = Δρ/0The InternationalThermodynamicEquation of Seawater– 2010ΣASummary for Policy MakersMillero, F. J., 2000. Effect of changes in the compositionof seawater on the density-salinity relationship.Deep-Sea Res. I 47, 1583-1590.Millero, F. J., J. Waters, R. Woosley, F. Huang, andM. Chanson, 2008b: The effect of compositionon the density of Indian Ocean waters, Deep-Sea Res. I, 55, 460-470.UNESCO, 1981: The Practical Salinity Scale 1978and the International Equation of State ofSeawater 1980. UNESCO technical papers inmarine science 36, 25 pp.UNESCO, 1983: Algorithms for computation offundamental properties of seawater. UNESCOtechnical papers in marine science 44, 53 pp.Pawlowicz, R., D. G. Wright and F. J. Millero,2010: The effects of biogeochemical processeson oceanic conductivity/salinity/density relationshipsand the characterization of real seawater.Ocean Science Discussions, 7, 773–836.http://www.ocean-sci-discuss.net/7/773/2010/osd-7-773-2010-print.pdfPoisson, A., and M. H. Gadhoumi, 1993: An extensionof the Practical Salinity Scale 1978 andthe Equation of State 1980 to high salinities.Deep-Sea Res. I, 40, 1689-1698.Reed, Christina. ‘A Pinch of Salt’ UNESCO newsletterA World of Science, vol. 7, no. 3, July-September2009.Wieser, M. E., 2006: Atomic weights of the elements2005 (IUPAC Technical Report). PureAppl. Chem. 78, 2051-2066. www.iupac.org/publications/pac/78/11/2051/pdf/Wright, D. G., R. Pawlowicz, T. J. McDougall,R. Feistel and G. M. Marion, 2010b: AbsoluteSalinity, “Density Salinity” and the Reference-Composition Salinity Scale: present and futureuse in the seawater standard TEOS-10. OceanSci. Discuss., 7, 1559-1625. http://www.ocean-sci-discuss.net/7/1559/2010/osd-7-1559-2010-print.pdfSampling in the Southern Ocean© B. Longworth, 200812