Transcript S - clivar
TEOS-10, the new Thermodynamic definition of Seawater: what it is and how to use it Trevor J McDougall CSIRO, Hobart, Australia CLIVAR WGOMD Workshop on Ocean Mesoscale Eddies, Exeter, April 2009 The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology Background • The existing 1980 International Equation of State (EOS-80) has served the community very well for almost 30 years. • EOS-80 provides algorithms for density, sound speed, heat capacity and freezing temperature. • However, it does not provide expressions for entropy, internal energy and enthalpy. • All these things are best derived from a single Gibbs function from which all these thermodynamic quantities, as well as potential temperature, can be found in a consistent manner. • Also, there is a little more data that has now been incorporated, making the algorithms more accurate. The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology Main Terms of Reference for WG127 • To examine the results of recent research in ocean thermodynamics with a view to recommending a change to the existing internationally accepted algorithms for evaluating density and related quantities including enthalpy, entropy and potential temperature. • To examine the feasibility of using simple functions of threedimensional space to take account of the influence of composition anomalies on the determination of density in the ocean. The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology SCOR/IAPSO Working Group 127 SCOR/IAPSO WG127 on The Thermodynamics and Equation of State of Seawater Trevor J. McDougall, Chair (Australia) Rainer Feistel (Germany) Chen-Tung Arthur Chen (Taiwan) David R. Jackett (Australia) Brian A. King (UK) Giles M. Marion (USA) Frank J. Millero (USA) Petra Spitzer (Germany) Dan Wright (Canada) Associate member, Peter Tremaine (Canada) The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology Features of the new TEOS-10 Thermodynamic Equation Of Seawater - 2010 • SCOR/IAPSO Working Group 127 has settled on a definition of The Reference Composition of seawater. This was a necessary first step in order to define the Gibbs function at very low salinities. This Reference Composition, consisting of the major components of Standard Seawater, has been determined from earlier analytical measurements. • The definition of the Reference Composition enabled the calculation of the Absolute Salinity of seawater that has this Reference Composition (making use of modern atomic weights). The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology Solute Reference Composition Chemical Composition of Standard Seawater – the Reference Composition Using the available information and 2005 atomic weight estimates, mole fractions of standard seawater can be determined. The Na+ contribution is determined by the requirement achieve exact charge balance. The resulting “Reference Composition” is shown to the right. Millero, F. J., R. Feistel, D. G. Wright and T. J. McDougall, 2008: The composition of Standard Seawater and the definition of the ReferenceComposition Salinity Scale. Deep-Sea Research I, 55, 50-72. Mole fraction Mass fraction Na+ .4188071 .3065958 Mg2+ .0471678 .0365055 Ca2+ .0091823 .0117186 K+ .0091159 .0113495 Sr2+ .0000810 .0002260 Cl– .4874839 .5503396 SO42– .0252152 .0771319 HCO3– .0015340 .0029805 Br– .0007520 .0019130 CO32– .0002134 .0004078 B(OH)4– .0000900 .0002259 F– .0000610 .0000369 OH– .0000071 B(OH)3 CO2 .0000038 .0002807 .0005527 .0000086 .0000121 The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology 1.0000000 Sum 1.0000000 Reference Salinity as a stepping stone to Absolute Salinity • Reference Salinity SR is defined to provide the best available estimate of the Absolute Salinity SA of both (i) seawater of Reference Composition, (ii) of Standard Seawater (North Atlantic surface seawater). • SR can be related to Practical Salinity SP (which is based on conductivity ratio) by SR = (35.165 04/35) g kg–1 x SP. • The difference between the new and old salinities of ~0.165 04 g kg–1 (~0.47%) is about 80 times as large as the accuracy with which we can measure SP at sea. The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology Absolute Salinity Anomaly • Practical Salinity SP reflects the conductivity of seawater whereas the thermodynamic properties are more accurately expressed in terms of the concentrations of all the components of sea salt. For example, non-ionic species contribute to density but not to conductivity. • The Gibbs function is expressed in terms of the Absolute Salinity SA (mass fraction of dissolved material) rather than the Practical Salinity SP of seawater. • SA = (35.165 04/35) g kg–1 x SP + dSA(x,y,p) The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology Determining Absolute Salinity The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology Absolute Salinity Anomaly • The Absolute Salinity Anomaly dSA is determined by accurately measuring the density of a seawater sample in the laboratory using a vibrating beam densimeter. • This density is compared to the density calculated from the sample’s Practical Salinity to give an estimate of dSA • We have done this to date on 811 seawater samples from around the global ocean. • We exploit a correlation between dSA and the slicicate concentration of seawater to arrive at a computer algorithm to estimate dSA= dSA(x,y,p). SA = (35.165 04/35) g kg–1 x SP + dSA(x,y,p) The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology Absolute Salinity Anomaly The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology Absolute Salinity Anomaly The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology Absolute Salinity Anomaly The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology Absolute Salinity Anomaly The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology Why adopt Absolute Salinity SA? • The freshwater content of seawater is (1 – 0.001SA) not (1 – 0.001SP), and SA and SP are known to differ by about 0.47%. There seems no good reason for continuing to ignore this known difference in ocean models. • Practical Salinity expressed in the PSS-78 scale is outside the system of SI units. • PSS-78 is limited to the salinity range 2 to 42. • Density of seawater is a function of SA not of SP. Hence we need to use Absolute Salinity in order to accurately determine the horizontal density gradients (for use in the “thermal wind” equation). The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology What is a Gibbs Function? From a Gibbs function, all of the thermodynamic properties of seawater can be determined by simple differentiation and algebraic manipulation. Formulas for properties of seawater and ice expressed in terms of the Gibbs functions g(SA, T, p) for seawater and g(T, p) for ice. 3 Property Symbol Expression in g(S, T, p) of seawater Expression in g(T, p) of ice specific Gibbs energy g g g specific enthalpy h g − T gT g − T gT specific Helmholtz energy f g − p gp g − p gp specific internal energy u g − T gT − p gp g − T g T − p gp Specific entropy s − gT − gT pressure p p p density ρ 1 / gp 1 / gp specific isobaric heat capacity cp −T gTT −T gTT thermal expansion α gTp / gp gTp / gp isothermal compressibility κT isentropic compressibility κs g −gpp / gp 2 tp gtt g pp / g p gtt g −gpp / gp 2 tp gtt g pp / g p gtt Sound speed w g p gtt / g gtt g pp chemical potential of water µW g − SA gS g pressure coefficient for ice β − −gTp / gpp 2 tp − J. Willard Gibbs The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology New and old definitions of seawater Seawater: EOS-80 EOS-80 Density S , t, p Heat Capacity cP cP S , t, p Sound Speed U U S , t , p Freezing Point t f t f S , p Seawater: TEOS-10 g g Fresh t , p g S SA , t , p Temperature: ITS-90 Salinity: RCSS-08 Fluid Water: IAPWS-95 Temperature: IPTS-68 Salinity: Ice Ih: IAPWS-06 PSS-78 The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology Percentage error in the horizontal density gradient • Measurement of the horizontal gradient of density is the main way that oceanographers are able to estimate the ocean circulation (the “thermal wind” equation). • These are actually differences in density at constant pressure, so what is dynamically important is 1 p p SA p SA S R p SR p The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology Percentage error in the horizontal density gradient • This figure is for data from the world ocean below 10 Mpa ~ 1000 m. • 60% of the data is improved by more than 2%. • This improvement is mainly due to including the effects of seawater composition on the horizontal density gradient. • The effect of having a better in TEOS-10 vs EOS-80 is a factor of six smaller (the red data uses SR in place of SA). The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology Improvements in Freezing Temperature at high pressure The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology Present practice regarding “heat” in oceanography • To date oceanographers treat potential temperature q as a conservative variable. • We also mix water masses on S - q diagrams as though both salinity and potential temperature are conserved on mixing. • Air-sea heat fluxes result in a change in an ocean model’s potential temperature using a constant specific heat capacity. • That is, we treat “heat” as being a constant times q. • How good are these assumptions? • Can we do better? The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology The First Law of Thermodynamics in terms of q The First Law of Thermodynamics is written in terms of enthalpy as dh 1 dp F R FQ dt dt We would like the bracket here to be a total derivative, for then we would have a variable that would be advected and mixed in the ocean as a conservative variable whose surface flux is the air-sea heat flux. If we take h SA ,q , p , thermodynamic reasoning leads to T0 t dq dS c p pr p T0 t T pr A F R FQ dt d t T0 q The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology The specific heat capacity of seawater at p = 0 dbar Specific heat capacity J kg-1 K-1 The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology The concept of potential enthalpy h0 Just as q is the temperature calculated after an adiabatic change in pressure, so potential enthalpy is the enthalpy of a fluid parcel after the same adiabatic change in pressure. h SA ,q ,0 h SA ,q , p 0 0 1 SA ,q , p dp. p Taking the material derivative of this leads to dh 1 d p d h0 d q dt dt dt dt SA ,q , p dp d S p SA ,q , p dp , 0 SA ,q , p d t 0 SA ,q , p p and the last two terms are very small, being no more than 0.15% of the leading term, even at a pressure of 40 MPa = 4,000 dbar. This means that the First Law of Thermodynamics can be written as d h0 d c 0p F R F Q . dt dt The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology The difference between potential and conservative temperatures, q S The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology Error C in using entropy as a heat-like variable S The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology Improving Heat Conservation in Ocean Models In order to implement Conservative Temperature in an ocean model • we interpret the model’s temperature variable as , and • provide a polynomial for density in the form (SA,,p), and • provide the forward and inverse algorithms (SA,q) and q(SA,). Then heat fluxes are simply fluxes of times the constant c 0p . Similarly, models should be initialized with Absolute Salinity SA and the output should be compared to observations of SA, not of Practical Salinity SP. The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology Improving Heat Conservation in Ocean Models • Conservative temperature is 100 times closer to being “heat” than is potential temperature. • The algorithm for conservative temperature has been imported into the MOM4 code and it is available as an option when running the MOM4 code. • The figures show the expected influence of sea-surface temperature in the annual mean, and seasonally. The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology Improving Heat Conservation in Ocean Models The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology Improving Heat Conservation in Ocean Models The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology Recommended changes to oceanographic practice • Adopt the TEOS-10 definition of the Gibbs function for seawater, requiring the use of its new algorithms for density, sound speed, enthalpy, etc, (these algorithms are available on the TEOS-10 web site) • Adopt Absolute Salinity SA; requiring the use of the new algorithm to go from the present conductivity-based measure of salinity, SP, to SA (McDougall, Jackett & Millero, Ocean Science, 2009). • Continue to report Practical Salinity SP to national data bases because (i) SP is a measured parameter and (ii) we need to maintain continuity in these data bases. • Note that this treatment of salinity is similar to what we presently do for temperature; we store in situ temperature, but we publish potential temperature. The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology