Chapter 2 Temperature, Salinity, Density, and the Oceanic Pressure
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Chapter 2 Approximate Thermodynamics
Chapter 2 Approximate Thermodynamics 2.1 Atmosphere Various texts (Byers 1965, Wallace and Hobbs 2006) provide elementary treatments of at- mospheric thermodynamics, while Iribarne and Godson (1981) and Emanuel (1994) present more advanced treatments. We provide only an approximate treatment which is accept- able for idealized calculations, but must be replaced by a more accurate representation if quantitative comparisons with the real world are desired. 2.1.1 Dry entropy In an atmosphere without moisture the ideal gas law for dry air is p = R T (2.1) ρ d where p is the pressure, ρ is the air density, T is the absolute temperature, and Rd = R/md, R being the universal gas constant and md the molecular weight of dry air. If moisture is present there are minor modications to this equation, which we ignore here. The dry entropy per unit mass of air is sd = Cp ln(T/TR) − Rd ln(p/pR) (2.2) where Cp is the mass (not molar) specic heat of dry air at constant pressure, TR is a constant reference temperature (say 300 K), and pR is a constant reference pressure (say 1000 hPa). Recall that the specic heats at constant pressure and volume (Cv) are related to the gas constant by Cp − Cv = Rd. (2.3) A variable related to the dry entropy is the potential temperature θ, which is dened Rd/Cp θ = TR exp(sd/Cp) = T (pR/p) . (2.4) The potential temperature is the temperature air would have if it were compressed or ex- panded (without condensation of water) in a reversible adiabatic fashion to the reference pressure pR. -
Gibbs Seawater (GSW) Oceanographic Toolbox of TEOS–10
Gibbs SeaWater (GSW) Oceanographic Toolbox of TEOS–10 documentation set density and enthalpy, based on the 48-term expression for density, gsw_front_page front page to the GSW Oceanographic Toolbox The functions in this group ending in “_CT” may also be called without “_CT”. gsw_contents contents of the GSW Oceanographic Toolbox gsw_check_functions checks that all the GSW functions work correctly gsw_rho_CT in-situ density, and potential density gsw_demo demonstrates many GSW functions and features gsw_alpha_CT thermal expansion coefficient with respect to CT gsw_beta_CT saline contraction coefficient at constant CT Practical Salinity (SP), PSS-78 gsw_rho_alpha_beta_CT in-situ density, thermal expansion & saline contraction coefficients gsw_specvol_CT specific volume gsw_SP_from_C Practical Salinity from conductivity, C (incl. for SP < 2) gsw_specvol_anom_CT specific volume anomaly gsw_C_from_SP conductivity, C, from Practical Salinity (incl. for SP < 2) gsw_sigma0_CT sigma0 from CT with reference pressure of 0 dbar gsw_SP_from_R Practical Salinity from conductivity ratio, R (incl. for SP < 2) gsw_sigma1_CT sigma1 from CT with reference pressure of 1000 dbar gsw_R_from_SP conductivity ratio, R, from Practical Salinity (incl. for SP < 2) gsw_sigma2_CT sigma2 from CT with reference pressure of 2000 dbar gsw_SP_salinometer Practical Salinity from a laboratory salinometer (incl. for SP < 2) gsw_sigma3_CT sigma3 from CT with reference pressure of 3000 dbar gsw_sigma4_CT sigma4 from CT with reference pressure of 4000 dbar Absolute Salinity -
Spiciness Theory Revisited, with New Views on Neutral Density, Orthogonality, and Passiveness
Ocean Sci., 17, 203–219, 2021 https://doi.org/10.5194/os-17-203-2021 © Author(s) 2021. This work is distributed under the Creative Commons Attribution 4.0 License. Spiciness theory revisited, with new views on neutral density, orthogonality, and passiveness Rémi Tailleux Dept. of Meteorology, University of Reading, Earley Gate, RG6 6ET Reading, United Kingdom Correspondence: Rémi Tailleux ([email protected]) Received: 26 April 2020 – Discussion started: 20 May 2020 Revised: 8 December 2020 – Accepted: 9 December 2020 – Published: 28 January 2021 Abstract. This paper clarifies the theoretical basis for con- 1 Introduction structing spiciness variables optimal for characterising ocean water masses. Three essential ingredients are identified: (1) a As is well known, three independent variables are needed to material density variable γ that is as neutral as feasible, (2) a fully characterise the thermodynamic state of a fluid parcel in material state function ξ independent of γ but otherwise ar- the standard approximation of seawater as a binary fluid. The bitrary, and (3) an empirically determined reference function standard description usually relies on the use of a tempera- ξr(γ / of γ representing the imagined behaviour of ξ in a ture variable (such as potential temperature θ, in situ temper- notional spiceless ocean. Ingredient (1) is required because ature T , or Conservative Temperature 2), a salinity variable contrary to what is often assumed, it is not the properties im- (such as reference composition salinity S or Absolute Salin- posed on ξ (such as orthogonality) that determine its dynam- ity SA), and pressure p. -
Equations of Motion Using Thermodynamic Coordinates
2814 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 30 Equations of Motion Using Thermodynamic Coordinates ROLAND A. DE SZOEKE College of Oceanic and Atmospheric Sciences, Oregon State University, Corvallis, Oregon (Manuscript received 21 October 1998, in ®nal form 30 December 1999) ABSTRACT The forms of the primitive equations of motion and continuity are obtained when an arbitrary thermodynamic state variableÐrestricted only to be vertically monotonicÐis used as the vertical coordinate. Natural general- izations of the Montgomery and Exner functions suggest themselves. For a multicomponent ¯uid like seawater the dependence of the coordinate on salinity, coupled with the thermobaric effect, generates contributions to the momentum balance from the salinity gradient, multiplied by a thermodynamic coef®cient that can be com- pletely described given the coordinate variable and the equation of state. In the vorticity balance this term produces a contribution identi®ed with the baroclinicity vector. Only when the coordinate variable is a function only of pressure and in situ speci®c volume does the coef®cient of salinity gradient vanish and the baroclinicity vector disappear. This coef®cient is explicitly calculated and displayed for potential speci®c volume as thermodynamic coor- dinate, and for patched potential speci®c volume, where different reference pressures are used in various pressure subranges. Except within a few hundred decibars of the reference pressures, the salinity-gradient coef®cient is not negligible and ought to be taken into account in ocean circulation models. 1. Introduction perature surfaces is a potential for the acceleration ®eld, Potential temperature, the temperature a ¯uid parcel when friction is negligible. Because the gradient of this would have if removed adiabatically and reversibly from function gives the geostrophic ¯ow when it balances ambient pressure to a reference pressure, is a valuable Coriolis force, it is also called the geostrophic stream- concept in the study of the atmosphere and oceans. -
Recovery of Temperature, Salinity, and Potential Density from Ocean
PUBLICATIONS Journal of Geophysical Research: Oceans RESEARCH ARTICLE Recovery of temperature, salinity, and potential density from 10.1002/2013JC009662 ocean reflectivity Key Points: Berta Biescas1,2, Barry R. Ruddick1, Mladen R. Nedimovic3,4,5, Valentı Sallare`s2, Guillermo Bornstein2, Recovery of oceanic T, S, and and Jhon F. Mojica2 potential density from acoustic reflectivity data 1Department of Oceanography, Dalhousie University, Halifax, Nova Scotia, Canada, 2Department of Marine Geology, Thermal anomalies observations at 3 the Mediterranean tongue level Institut de Cie`ncies del Mar ICM-CSIC, Barcelona, Spain, Department of Earth’s Sciences, Dalhousie University, Halifax, 4 5 Comparison between acoustic Nova Scotia, Canada, Lamont-Doherty Earth Observatory of Columbia University, Palisades, New York, USA, University of reflectors in the ocean and isopycnals Texas Institute for Geophysics, Austin, Texas, USA Supporting Information: Methods Abstract This work explores a method to recover temperature, salinity, and potential density of the Supporting figures ocean using acoustic reflectivity data and time and space coincident expendable bathythermographs (XBT). The acoustically derived (vertical frequency >10 Hz) and the XBT-derived (vertical frequency <10 Hz) impe- Correspondence to: dances are summed in the time domain to form impedance profiles. Temperature (T) and salinity (S) are B. Biescas, then calculated from impedance using the international thermodynamics equations of seawater (GSW [email protected] TEOS-10) and an empirical T-S relation derived with neural networks; and finally potential density (q) is cal- culated from T and S. The main difference between this method and previous inversion works done from Citation: Biescas, B., B. R. Ruddick, M. R. real multichannel seismic reflection (MCS) data recorded in the ocean, is that it inverts density and it does Nedimovic, V. -
Physical Properties of Seawater
CHAPTER 3 Physical Properties of Seawater 3.1. MOLECULAR PROPERTIES in the oceans, because water is such an effective OF WATER heat reservoir (see Section S15.6 located on the textbook Web site Many of the unique characteristics of the ; “S” denotes supplemental ocean can be ascribed to the nature of water material). itself. Consisting of two positively charged As seawater is heated, molecular activity hydrogen ions and a single negatively charged increases and thermal expansion occurs, oxygen ion, water is arranged as a polar mole- reducing the density. In freshwater, as tempera- cule having positive and negative sides. This ture increases from the freezing point up to about molecular polarity leads to water’s high dielec- 4C, the added heat energy forms molecular tric constant (ability to withstand or balance an chains whose alignment causes the water to electric field). Water is able to dissolve many shrink, increasing the density. As temperature substances because the polar water molecules increases above this point, the chains break align to shield each ion, resisting the recombina- down and thermal expansion takes over; this tion of the ions. The ocean’s salty character is explains why fresh water has a density maximum due to the abundance of dissolved ions. at about 4C rather than at its freezing point. In The polar nature of the water molecule seawater, these molecular effects are combined causes it to form polymer-like chains of up to with the influence of salt, which inhibits the eight molecules. Approximately 90% of the formation of the chains. For the normal range of water molecules are found in these chains. -
Is the Neutral Surface Really Neutral? a Close Examination of Energetics of Along Isopycnal Mixing
Is the neutral surface really neutral? A close examination of energetics of along isopycnal mixing Rui Xin Huang Department of Physical Oceanography Woods Hole Oceanographic Institution Woods Hole, MA 02543, USA April 19, 2010 Abstract The concept of along-isopycnal (along-neutral-surface) mixing has been one of the foundations of the classical large-scale oceanic circulation framework. Neutral surface has been defined a surface that a water parcel move a small distance along such a surface does not require work against buoyancy. A close examination reveals two important issues. First, due to mass continuity it is meaningless to discuss the consequence of moving a single water parcel. Instead, we have to deal with at least two parcels in discussing the movement of water masses and energy change of the system. Second, movement along the so-called neutral surface or isopycnal surface in most cases is associated with changes in the total gravitational potential energy of the ocean. In light of this discovery, neutral surface may be treated as a preferred surface for the lateral mixing in the ocean. However, there is no neutral surface even at the infinitesimal sense. Thus, although approximate neutral surfaces can be defined for the global oceans and used in analysis of global thermohaline circulation, they are not the surface along which water parcels actually travel. In this sense, thus, any approximate neutral surface can be used, and their function is virtually the same. Since the structure of the global thermohaline circulation change with time, the most suitable option of quasi-neutral surface is the one which is most flexible and easy to be implemented in numerical models. -
The All-Atlantic Temperature-Salinity-Pressure Relation and Patched Potential Density
Journal of Marine Research, 63, 59–93, 2005 The all-Atlantic temperature-salinity-pressure relation and patched potential density by Roland A. de Szoeke1 and Scott R. Springer2 ABSTRACT The relation between temperature, salinity, and pressure in the Atlantic Ocean is examined. Most of the Atlantic resolves itself into three two-dimensional manifolds of three-dimensional thermody- namic space: a northern, more saline, branch, and a southern, fresher, branch, each quite independent of pressure, and between them a bridge, on which density is uniform at constant pressure. The properties of the branches are crucial to the construction of joint potential density surfaces, patched together at 1000 db intervals. By resolving more finely in pressure (illustrated with 200 db spacing), a finer system of patched potential density surfaces can be obtained, and indeed the continuous limit can be taken. This limit gives a form of orthobaric density, regionally differentiated because it is based on the duplicate regional branches. A mapping can be devised, using the properties of the bridge waters, that links the southern and northern forms of orthobaric density across the boundary between their respective regions of validity. The parallel of patched potential density surfaces to orthobaric density surfaces permits the use of measures developed for the latter to estimate quantitative measures of the material nature (or otherwise) of the former. Simply put, within the waters of the respective branches the patched isopycnals, or orthobaric isopycnals, are very nearly material, limited only by inherent irreversible mixing processes. However, where these isopycnals cross the bridge waters, significant, reversible, material exchange across them may occur. -
Orthobaric Density: a Thermodynamic Variable for Ocean Circulation Studies
2830 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 30 Orthobaric Density: A Thermodynamic Variable for Ocean Circulation Studies ROLAND A. DE SZOEKE,SCOTT R. SPRINGER, AND DAVID M. OXILIA College of Oceanic and Atmospheric Sciences, Oregon State University, Corvallis, Oregon (Manuscript received 21 October 1998, in ®nal form 30 December 1999) ABSTRACT A new density variable, empirically corrected for pressure, is constructed. This is done by ®rst ®tting com- pressibility (or sound speed) computed from global ocean datasets to an empirical function of pressure and in situ density (or speci®c volume). Then, by replacing true compressibility by this best-®t virtual compressibility in the thermodynamic density equation, an exact integral of a Pfaf®an differential form can be found; this is called orthobaric density. The compressibility anomaly (true minus best-®t) is not neglected, but used to develop a gain factor c on the irreversible processes that contribute to the density equation and drive diapycnal motion. The complement of the gain factor, c 2 1, multiplies the reversible motion of orthobaric density surfaces to make a second contribution to diapycnal motion. The gain factor is a diagnostic of the materiality of orthobaric density: gain factors of 1 would indicate that orthobaric density surfaces are as material as potential density surfaces. Calculations of the gain factor for extensive north±south ocean sections in the Atlantic and Paci®c show that it generally lies between 0.8 and 1.2. Orthobaric density in the ocean possesses advantages over potential density that commend its use as a vertical coordinate for both descriptive and modeling purposes. -
Reduction of Density and Pressure Gradient Errors in Ocean Simulations
JULY 2001 NOTES AND CORRESPONDENCE 1915 Reduction of Density and Pressure Gradient Errors in Ocean Simulations JOHN K. DUKOWICZ Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 23 October 2000 and 30 January 2001 ABSTRACT Existing ocean models often contain errors associated with the computation of the density and the associated 21 21 pressure gradient. Boussinesq models approximate the pressure gradient force, r =p, by r 0 =p, where r0 is a constant reference density. The error associated with this approximation can be as large as 5%. In addition, Cartesian and sigma-coordinate models usually compute density from an equation of state where its pressure dependence is replaced by a depth dependence through an approximate conversion of depth to pressure to avoid the solution of a nonlinear hydrostatic equation. The dynamic consequences of this approximation and the associated errors can be signi®cant. Here it is shown that it is possible to derive an equivalent but ``stiffer'' equation of state by the use of modi®ed density and pressure, r* and p*, obtained by eliminating the contribution of the pressure-dependent part of the adiabatic compressibility (about 90% of the total). By doing this, the errors associated with both approximations are reduced by an order of magnitude, while changes to the code or to the code structure are minimal. 1. Introduction approximation to (3) in ®xed vertical coordinate models is Consider the horizontal pressure force in ocean mod- els: r ø r(S, u,p0(z)), (5) 1 where p (z) is a speci®ed depth-to-pressure conversion PGF 5 =p, (1) 0 r function such as that proposed by Fofonoff and Millard (1983), for example. -
A New Algorithm to Accurately Calculate Neutral Tracer Gradients and Their
1 A new algorithm to accurately calculate neutral tracer gradients and their 2 impacts on vertical heat transport and water mass transformation ∗ 3 Sjoerd Groeskamp and Paul M. Barker and Trevor J. McDougall 4 School of Mathematics and Statistics, University of New South Wales, Sydney, New South Wales, 5 Australia 6 Ryan P. Abernathey 7 Columbia University, Lamont-Doherty Earth Observatory, New York City, NY, USA 8 Stephen M. Griffies 9 NOAA Geophysical Fluid Dynamics Laboratory & Princeton University Program in Atmospheric 10 and Oceanic Sciences, Princeton, USA ∗ 11 Corresponding author address: Sjoerd Groeskamp, School of Mathematics and Statistics UNSW 12 Sydney, NSW, 2052, Australia 13 E-mail: [email protected] Generated using v4.3.2 of the AMS LATEX template 1 ABSTRACT 14 Mesoscale eddies stir along the neutral plane, and the resulting neutral diffu- 15 sion is a fundamental aspect of subgrid scale tracer transport in ocean models. 16 Calculating neutral diffusion traditionally involves calculating neutral slopes 17 and three-dimensional tracer gradients. The calculation of the neutral slope 18 usually occurs by computing the ratio of the horizontal to vertical locally ref- 19 erenced potential density derivative. This approach is problematic in regions 20 of weak vertical stratification, prompting the use of a variety of ad hoc reg- 21 ularization methods that can lead to rather nonphysical dependencies for the 22 resulting neutral tracer gradients. We here propose an alternative method that 23 is based on a search algorithm that requires no ad hoc regularization. Com- 24 paring results from this new method to the traditional method reveals large 25 differences in spurious diffusion, heat transport and water mass transforma- 26 tion rates that may all affect the physics of, for example, a numerical ocean 27 model. -
Adiabatic Density Surface, Neutral Density Surface, Potential Density Surface, and Mixing Path*
热带海洋学报 JOURNAL OF TROPICAL OCEANOGRAPHY 2014 年 第 33 卷 第 4 期: 1−19 海洋水文学 doi:10.3969/j.issn.1009-5470.2014.04.001 http://www.jto.ac.cn Adiabatic density surface, neutral density surface, potential * density surface, and mixing path HUANG Rui-xin Department of Physical Oceanography, Woods Hole Oceanographic Institution, Woods Hole, MA 02543, USA Abstract: In this paper, adiabatic density surface, neutral density surface and potential density surface are compared. The adiabatic density surface is defined as the surface on which a water parcel can move adiabatically, without changing its potential temperature and salinity. For a water parcel taken at a given station and pressure level, the corresponding adiabatic density surface can be determined through simple calculations. This family of surface is neutrally buoyant in the world ocean, and different from other surfaces that are not truly neutrally buoyant. In order to explore mixing path in the ocean, a mixing ratio m is introduced, which is defined as the portion of potential temperature and salinity of a water parcel that has exchanged with the environment during a segment of migration in the ocean. Two extreme situations of mixing path in the ocean are m=0 (no mixing), which is represented by the adiabatic density curve, and m=1, where the original information is completely lost through mixing. The latter is represented by the neutral density curve. The reality lies in between, namely, 0<m<1. In the turbulent ocean, there are potentially infinite mixing paths, some of which may be identified by using different tracers (or their combinations) and different mixing criteria.