DOCSLIB.ORG

An Assessment of Orthobaric Density in the Global Ocean

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
An Assessment of Orthobaric Density in the Global Ocean 2054 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 35 An Assessment of Orthobaric Density in the Global Ocean TREVOR J. MCDOUGALL AND DAVID R. JACKETT CSIRO Marine Research, Hobart, Australia (Manuscript received 20 May 2004, in final form 18 April 2005) ABSTRACT Orthobaric density has recently been advanced as a new density variable for displaying ocean data and as a coordinate for ocean modeling. Here the extent to which orthobaric density surfaces are neutral is quantified and it is found that orthobaric density surfaces are less neutral in the World Ocean than are potential density surfaces referenced to 2000 dbar. Another property that is important for a vertical coordinate of a layered model is the quasi-material nature of the coordinate and it is shown that orthobaric density surfaces are significantly non-quasi-material. These limitations of orthobaric density arise because of its inability to accurately accommodate differences between water masses at fixed values of pressure and in situ density such as occur between the Northern and Southern Hemisphere portions of the World Ocean. It is shown that special forms of orthobaric density can be quite accurate if they are formed for an individual ocean basin and used only in that basin. While orthobaric density can be made to be approximately neutral in a single ocean basin, this is not possible in both the Northern and Southern Hemisphere portions of the Atlantic Ocean. While the helical nature of neutral trajectories (equivalently, the ill-defined nature of neutral surfaces) limits the neutrality of all types of density surface, the inability of orthobaric density surfaces to accurately accommodate more than one ocean basin is a much greater limitation. 1. Introduction The density of seawater is a significantly nonlinear Density is used in oceanography for a variety of pur- function of temperature, pressure, and salinity, and the poses. Its horizontal gradient is used to deduce the ver- nonlinearity that causes oceanographers the most tical shear of horizontal velocity (assuming geostrophic trouble is the so-called thermobaric nonlinearity, which balance) and, because small-scale turbulent mixing is so is primarily due to the pressure dependence of the ther- weak compared with the lateral mixing of mesoscale mal expansion coefficient (or equivalently, the tem- eddies, it is important to be able to calculate the sur- perature dependence of the sound speed). The idea faces along which this strong lateral diffusion occurs. that properties are mixed predominately along isopyc- Oceanographers assume that the strong mixing of heat nals has a long history in oceanography, and the ther- and salt that is achieved by mesoscale eddies occurs mobaric nature of seawater led Reid and Lynn (1971) along the locally referenced potential density surfaces. to form a series of potential density surfaces referenced Shrinking this argument to a point defines the so-called to a series of different pressures in order to better ap- neutral tangent plane and the smallness of the observed proximate the surfaces along which the ocean mixes dissipation of mechanical energy in the ocean gives tracers. Following de Szoeke et al. (2000) we call these strong support to this being the correct plane in which isopycnals of Reid and Lynn’s (1971) patched potential the strong mesoscale mixing occurs (McDougall and density surfaces. Jackett 2005b). Oceanographers would like to analyze McDougall (1987a) defined the concept of a neutral data and run layered ocean models with respect to sur- tangent plane along which fluid parcels could be ex- faces that everywhere coincide with neutral tangent changed without feeling any buoyant forces. While planes, but the equation of state dictates that this is not these neutral tangent planes are well defined, they do possible and various compromises must be made. not link up to form a well-defined neutral surface be- cause of the thermobaric terms in the equation of state. Corresponding author address: Trevor McDougall, CSIRO Ma- The ill-defined nature of a neutral surface was dis- rine Research, Castray Esplanade, Hobart, TAS 7001, Australia. cussed by McDougall and Jackett (1988) who showed E-mail: [email protected] that individual neutral trajectories in the ocean are © 2005 American Meteorological Society Unauthenticated | Downloaded 09/30/21 02:37 PM UTC JPO2796 NOVEMBER 2005 MCDOUGALL AND JACKETT 2055 helical in nature. Nevertheless, McDougall and Jackett We “road test” orthobaric density in the global (1988) and later Jackett and McDougall (1997; the neu- ocean, finding that it is significantly less neutral than is tral density software was available online at http://www. potential density referenced to 2000 dbar. Also, ortho- ml.csiro.au/ϳjackett/NeutralDensity) showed that, baric density is significantly non–quasi material ␴ while the helical nature of neutral trajectories may al- whereas 2 is 100% quasi material. low a significant mass flux to move vertically through In this paper we regard in situ density ␳ ϭ ␳(S, ⌰, p) the ocean without the need for small-scale mixing ac- to be a function of salinity S (expressed on the practical tivity, the ill-defined nature of neutral surfaces is small salinity scale), conservative temperature ⌰, and pres- in the sense that a well-defined surface [such as can be sure p [p is absolute pressure minus 0.101 325 MPa ϭ calculated with the neutral density algorithm ␥ n of 10.1325 dbar; see Feistel (2003) and Jackett et al. (2005, Jackett and McDougall (1997)] can be found that is manuscript submitted to J. Atmos. Oceanic Technol.)]. almost neutral everywhere; this statement will be fur- Conservative temperature (McDougall 2003) is propor- ϭ ther quantified in this paper (see Figs. 4 and 5). tional to potential enthalpy (referenced to p 0 MPa) De Szoeke et al. (2000) sought a density variable, and is a factor of more than 100 closer to being pro- portional to the heat content of seawater than is poten- called orthobaric density ␳␷ that is as neutral as possible ␪ ⌰ ␪ but is restricted to be a function only of pressure and in tial temperature . The difference between and is not central to the present paper and we shall sometimes situ density, that is, ␳␷ ϭ ␳␷(p, ␳). Such a pycnotropic ⌰ variable has the desirable properties that (i) a geo- simply refer to as temperature. In sections 2–4, we quantify the nonneutral and non- strophic streamfunction can be found in each ␳␷ surface so that the horizontal pressure gradient can be ex- quasi-material aspects of orthobaric density surfaces and compare these attributes with those of other types pressed in the convenient and numerically accurate of density surfaces. The reason for the irreducible and form of a divergence along the orthobaric density sur- significant nonneutral behavior of orthobaric density is face and (ii) the potential vorticity equation written in isolated in sections 5 and 6. One of the main conclu- terms of gradients of orthobaric density does not con- Ϫ2 sions of de Szoeke et al. (2000) is that the non-quasi- ١p ١␳ ϫ · ١␳␷ tain the baroclinic production term ␳ material nature of orthobaric density also characterizes since this is zero. finely patched potential density surfaces. In sections 5 Orthobaric density is a clever combination of pres- and 6 we show that this is incorrect; the explanation sure and in situ density that has the property that, so involves the important distinction between local helic- long as water mass variations occur in a monotonic way ity and the interhemispheric water mass contrasts. The with pressure (see section 5 below), ␳␷ can be made to paper ends with a discussion section. be quite neutral. We will show that in practice this means that it is possible to tune the orthobaric density variable so that it is a good approximation to neutral 2. Orthobaric density and vertical stability density surfaces in a single ocean basin. However, a Orthobaric specific volume ␯ is defined by the fol- major point of the present paper is that ␳␷ cannot be made to be approximately neutral in the global ocean. lowing relationship between total differentials (de Here we seek quantitative answers to the following Szoeke et al. 2000): three questions: (i) how close is the vertical gradient of 1 orthobaric density to being proportional to N2, the ␾d␯ ϭ d͑1ր␳͒ ϩ dp, ͑1͒ ␳2 2 square of the buoyancy frequency, (ii) how neutral are c0 orthobaric density surfaces, and (iii) how quasi material where c0 can be regarded as an approximation to the is orthobaric density? A variable is said to be quasi sound speed that is restricted to be a function only of material if it only changes when irreversible mixing oc- ϭ ␳ pressure and density, that is, c0 c0 (p, ), and the curs. If a fluid parcel does not change its salinity and boundary condition ␯ ϭ 1/␳ is applied at p ϭ 0 dbar. conservative temperature, then the value of a quasi- Orthobaric specific volume ␯ and the integrating factor material variable of the fluid parcel will also be un- ␾ are also functions only of pressure and density, that changed. Examples of quasi-material variables are en- is, ␾ ϭ ␾(p, ␳) and ␯ ϭ ␯(p, ␳). tropy, salinity, potential temperature, potential enthal- Here we discuss orthobaric density, ␳␷ ϵ 1/␷, rather py, and conservative temperature (see McDougall than orthobaric specific volume. The corresponding to- 2003). Variables such as density that vary with pressure, tal differential form is even for fixed values of salinity and conservative tem- ⌽ ␳ ϭ ␳ Ϫ ⌫ ͑ ͒ perature, are said to be non–quasi material. d ␯ d 0dp, 2 Unauthenticated | Downloaded 09/30/21 02:37 PM UTC 2056 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 35 ␳ ϭ ␳ ϭ Ϫ ϭ ␳ Ϫ ␳ ⌰ and the boundary condition ␷ is applied at p 0 c0 c c0(p, ) c(p, , ). The derivation of the last 2 dbar, the integrating factor ⌽ϭ␾(␳/␳␷) is also a func- expression in (5) followed the same route as that of de ␳ ␳Ϫ1⌫ tion of only p and , 0 is an approximation to the Szoeke et al.
Load more

Recommended publications
  • Rapid Mixing and Exchange of Deep-Ocean Waters in an Abyssal Boundary Current
    Rapid mixing and exchange of deep-ocean waters in an abyssal boundary current Alberto C. Naveira Garabatoa,1, Eleanor E. Frajka-Williamsb, Carl P. Spingysa, Sonya Leggc, Kurt L. Polzind, Alexander Forryana, E. Povl Abrahamsene, Christian E. Buckinghame, Stephen M. Griffiesc, Stephen D. McPhailb, Keith W. Nichollse, Leif N. Thomasf, and Michael P. Meredithe aOcean and Earth Science, National Oceanography Centre, University of Southampton, SO14 3ZH Southampton, United Kingdom; bNational Oceanography Centre, SO14 3ZH Southampton, United Kingdom; cNational Oceanic and Atmospheric Administration Geophysical Fluid Dynamics Laboratory & Atmospheric and Oceanic Sciences Program, Princeton University, Princeton, NJ 08544; dDepartment of Physical Oceanography, Woods Hole Oceanographic Institution, Woods Hole, MA 02543; ePolar Oceans, British Antarctic Survey, CB3 0ET Cambridge, United Kingdom; and fDepartment of Earth System Science, Stanford University, Stanford, CA 94305 Edited by Eric Guilyardi, Laboratoire d’Océanographie et du Climat: Expérimentations et Approches Numériques, Institute Pierre Simon Laplace, Paris, France, and accepted by Editorial Board Member Jean Jouzel May 26, 2019 (received for review March 8, 2019) The overturning circulation of the global ocean is critically shaped UK–US Dynamics of the Orkney Passage Outflow (DynOPO) by deep-ocean mixing, which transforms cold waters sinking at high project (17), and consisted of two core elements: a series of fifteen latitudes into warmer, shallower waters. The effectiveness of mixing 6- to 128-km-long vessel-based sections of profile measurements in driving this transformation is jointly set by two factors: the crossing the boundary current at an unusually high horizontal – – ∼ intensity of turbulence near topography and the rate at which well- resolution (Fig.
    [Show full text]
  • Hydrographic Atlas of the World Ocean Circulation Experiment (WOCE) Volume 2: Pacific Ocean
    Hydrographic Atlas of the World Ocean Circulation Experiment (WOCE) Volume 2: Pacific Ocean Lynne D. Talley Series edited by Michael Sparrow, Piers Chapman and John Gould Hydrographic Atlas of the World Ocean Circulation Experiment (WOCE) Volume 2: Pacific Ocean Lynne D. Talley Scripps Institution of Oceanography, University of San Diego, La Jolla, California, USA. Series edited by Michael Sparrow, Piers Chapman and John Gould. Compilation funded by the US National Science Foundation, Ocean Science division grant OCE-9712209. Publication supported by BP. Cover Picture: The photo on the front cover was kindly supplied by Akihisa Otsuki. It shows squalls in the northernmost area of the Mariana Islands and was taken on June 12, 1993. Cover design: Signature Design in association with the atlas editors, Principal Investigators and BP. Printed by: ATAR Roto Presse SA, Geneva,Switzerland. DVD production: ODS Business Services Limited, Swindon, UK. Published by: National Oceanography Centre, Southampton, UK. Recommended form of citation: 1. For this volume: Talley, L. D., Hydrographic Atlas of the World Ocean Circulation Experiment (WOCE). Volume 2: Pacific Ocean (eds. M. Sparrow, P. Chapman and J. Gould), International WOCE Project Office, Southampton, UK, ISBN 0-904175-54-5. 2007 2. For the whole series: Sparrow, M., P. Chapman, J. Gould (eds.), The World Ocean Circulation Experiment (WOCE) Hydrographic Atlas Series (4 vol- umes), International WOCE Project Office, Southampton, UK, 2005-2007 WOCE is a project of the World Climate Research Programme (WCRP) which is sponsored by the World Meteorological Organization (WMO), the International Council for Science (ICSU) and the Intergovernmental Oceanographic Commission (IOC) of UNESCO.
    [Show full text]
  • 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.
    [Show full text]
  • 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.
    [Show full text]
  • 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.
    [Show full text]
  • MIMOC: a Global Monthly Isopycnal Upperocean Climatology with Mixed
    JOURNAL OF GEOPHYSICAL RESEARCH: OCEANS, VOL. 118, 1658–1672, doi:10.1002/jgrc.20122, 2013 MIMOC: A global monthly isopycnal upper-ocean climatology with mixed layers Sunke Schmidtko,1,2 Gregory C. Johnson,1 and John M. Lyman1,3 Received 23 November 2012; revised 7 February 2013; accepted 8 February 2013; published 3 April 2013. [1] A monthly, isopycnal/mixed-layer ocean climatology (MIMOC), global from 0 to 1950 dbar, is compared with other monthly ocean climatologies. All available quality- controlled profiles of temperature (T) and salinity (S) versus pressure (P) collected by conductivity-temperature-depth (CTD) instruments from the Argo Program, Ice-Tethered Profilers, and archived in the World Ocean Database are used. MIMOC provides maps of mixed layer properties (conservative temperature, Y, absolute salinity, SA, and maximum P) as well as maps of interior ocean properties (Y, SA, and P) to 1950 dbar on isopycnal surfaces. A third product merges the two onto a pressure grid spanning the upper 1950 dbar, adding more familiar potential temperature (θ) and practical salinity (S) maps. All maps are at monthly 0.5 Â 0.5 resolution, spanning from 80Sto90N. Objective mapping routines used and described here incorporate an isobath-following component using a “Fast Marching” algorithm, as well as front-sharpening components in both the mixed layer and on interior isopycnals. Recent data are emphasized in the mapping. The goal is to compute a climatology that looks as much as possible like synoptic surveys sampled circa 2007–2011 during all phases of the seasonal cycle, minimizing transient eddy and wave signatures.
    [Show full text]
  • Spiciness Theory Revisited, with New Views on Neutral Density
    Spiciness theory revisited, with new views on neutral density, orthogonality and passiveness Rémi Tailleux1 1Dept of Meteorology, University of Reading, Earley Gate, PO Box 243, RG6 6BB Reading, United Kingdom Correspondence: Rémi Tailleux ([email protected]) Abstract. This paper clarifies the theoretical basis for constructing spiciness variables optimal for characterising ocean water masses. Three essential ingredients are identified: 1) a material density variable γ that is as neutral as feasible; 2) a material state function ξ independent of γ, but otherwise arbitrary; 3) an empirically determined reference function ξr(γ) of γ representing the imagined behaviour of ξ in a notional spiceless ocean. Ingredient 1) is required, because contrary to what is often assumed, 5 it is not the properties imposed on ξ (such as orthogonality) that determine its dynamical inertness but the degree of neutrality of 0 γ. The first key result is that it is the anomaly ξ = ξ −ξr(γ), rather than ξ, that is the variable the most suited for characterising ocean water masses, as originally proposed by McDougall and Giles (1987). The second key result is that oceanic sections of normalised ξ0 appear to be relatively insensitive to the choice of ξ, as first suggested by Jackett and McDougall (1985), based on the comparison of very different choices of ξ. It is also argued that orthogonality of rξ0 to rγ in physical space is more 10 germane to spiciness theory than orthogonality in thermohaline space, although how to use it to constrain the choices of ξ and ξr(γ) remains to be fully elucidated.
    [Show full text]
  • Ertel Potential Vorticity Versus Bernoulli Potential on Approximately Neutral Surfaces in the Antarctic Circumpolar Current
    SEPTEMBER 2020 S T A N L E Y E T A L . 2621 Ertel Potential Vorticity versus Bernoulli Potential on Approximately Neutral Surfaces in the Antarctic Circumpolar Current GEOFFREY J. STANLEY School of Mathematics and Statistics, University of New South Wales, Sydney, New South Wales, Australia TIMOTHY E. DOWLING Department of Physics and Astronomy, University of Louisville, Louisville, Kentucky MARY E. BRADLEY Department of Mathematics, University of Louisville, Louisville, Kentucky DAVID P. MARSHALL Department of Physics, University of Oxford, Oxford, United Kingdom (Manuscript received 20 June 2019, in final form 4 July 2020) ABSTRACT We investigate the relationship between Ertel potential vorticity Q and Bernoulli potential B on orthobaric density surfaces in the Antarctic Circumpolar Current (ACC), using the Southern Ocean State Estimate. Similar to the extratropical atmospheres of Earth and Mars, Q and B correlate in the ACC in a function-like manner with modest scatter. Below the near-surface, the underlying function relating Q and B appears to be nearly linear. Nondimensionalizing its slope yields ‘‘Ma,’’ a ‘‘Mach’’ number for long Rossby waves, the ratio of the local flow speed to the intrinsic long Rossby wave speed. We empirically estimate the latter using established and novel techniques that yield qualitatively consistent results. Previous work related ‘‘Ma’’ to the degree of homogeneity of Q and to Arnol’d’s shear stability criteria. Estimates of ‘‘Ma’’ for the whole ACC are notably positive, implying inhomogeneous Q, on all circumpolar buoyancy surfaces studied. Upper layers generally exhibit ‘‘Ma’’ slightly less than unity, suggesting that shear instability may operate within these layers.
    [Show full text]
  • 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.
    [Show full text]
  • Approximating Isoneutral Ocean Transport Via the Temporal Residual Mean
    fluids Article Approximating Isoneutral Ocean Transport via the Temporal Residual Mean Andrew L. Stewart Department of Atmospheric and Oceanic Sciences, University of California, Los Angeles, CA 90095, USA; [email protected] Received: 28 July 2019; Accepted: 27 September 2019; Published: 2 October 2019 Abstract: Ocean volume and tracer transports are commonly computed on density surfaces because doing so approximates the semi-Lagrangian mean advective transport. The resulting density-averaged transport can be related approximately to Eulerian-averaged quantities via the Temporal Residual Mean (TRM), valid in the limit of small isopycnal height fluctuations. This article builds on a formulation of the TRM for volume fluxes within Neutral Density surfaces, (the “NDTRM”), selected because Neutral Density surfaces are constructed to be as neutral as possible while still forming well-defined surfaces. This article derives a TRM, referred to as the “Neutral TRM” (NTRM), that approximates volume fluxes within surfaces whose vertical fluctuations are defined directly by the neutral relation. The purpose of the NTRM is to more closely approximate the semi-Lagrangian mean transport than the NDTRM, because the latter introduces errors associated with differences between the instantaneous state of the modeled/observed ocean and the reference climatology used to assign the Neutral Density variable. It is shown that the NDTRM collapses to the NTRM in the limiting case of a Neutral Density variable defined with reference to the Eulerian-mean salinity, potential temperature and pressure, rather than an external reference climatology, and therefore that the NTRM approximately advects this density variable. This prediction is verified directly using output from an idealized eddy-resolving numerical model.
    [Show full text]
  • Hydrographic Atlas of the World Ocean Circulation Experiment (WOCE) Volume 3: Atlantic Ocean
    Hydrographic Atlas of the World Ocean Circulation Experiment (WOCE) Volume 3: Atlantic Ocean Klaus Peter Koltermann, Viktor Gouretski and Kai Jancke Bundesamt für Seeschifffahrt und Hydrographie, Hamburg, Germany Series edited by Michael Sparrow, Piers Chapman and John Gould Federal Ministry of Education and Research Hydrographic Atlas of the World Ocean Circulation Experiment (WOCE) Volume 3: Atlantic Ocean Klaus Peter Koltermann (1), Viktor Gouretski (2) and Kai Jancke Bundesamt für Seeschifffahrt und Hydrographie, Hamburg, Germany (1) now Natural Risk Assessment Laboratory, Geography Faculty, Moscow State University, Moscow, Russia (2) now KlimaCampus, Universität Hamburg, Hamburg, Germany Series edited by Michael Sparrow, Piers Chapman and John Gould. Compilation funded by German Bundesministerium für Forschung und Technologie, BMFT. Publication supported by BP. Cover Picture: The photo on the front cover was kindly supplied by Olaf Boebel. It was taken in mid December 1992, during the Meteor 22/4 cruise in the South Atlantic. Cover design: Signature Design in association with the atlas editors, Principal Investigators and BP. Printed by: Nauchnyi Mir Publishers, Moscow, Russia DVD production: Reel Picture, San Deigo, CA Published by: National Oceanography Centre, Southampton, UK. Recommended form of citation: 1. For this volume: Koltermann, K.P., V.V. Gouretski and K. Jancke. Hydrographic Atlas of the World Ocean Circulation Experiment (WOCE). Volume 3: Atlantic Ocean (eds. M. Sparrow, P. Chapman and J. Gould). International WOCE Project Office, Southampton, UK, ISBN 090417557X. 2011 2. For the whole series: Sparrow, M., P. Chapman, J. Gould (eds.), The World Ocean Circulation Experiment (WOCE) Hydrographic Atlas Series (4 vol- umes), International WOCE Project Office, Southampton, UK, 2005-2011.
    [Show full text]
  • Climatological Mean Distribution of Specific Entropy in the Oceans
    Ocean Sci. Discuss., 4, 129–144, 2007 Ocean Science www.ocean-sci-discuss.net/4/129/2007/ Discussions © Author(s) 2007. This work is licensed under a Creative Commons License. Papers published in Ocean Science Discussions are under open-access review for the journal Ocean Science Climatological mean distribution of specific entropy in the oceans Z. Gan, Y. Yan, and Y. Qi LED, South China Sea Institute of Oceanology, Chinese Academy of Sciences, Guangzhou, China Received: 5 December 2006 – Accepted: 24 January 2007 – Published: 31 January 2007 Correspondence to: Y. Yan ([email protected]) 129 Abstract Entropy as an important state function can be considered to provide insight into the thermodynamic properties of seawater. In this paper, the spatial-temporal distribution of specific entropy in the oceans is presented, using a new Gibbs thermodynamic po- 5 tential function of seawater, which is proposed by R. Feistel. An important result is found that the distribution of specific entropy is surprisingly different from that of poten- tial density or neutral density surfaces. By contrast, the distribution of specific entropy is quite similar to that of potential temperature in the oceans. This result is not con- sistent with the traditional assumption that isopycnal or isoneutral surfaces could be 10 approximately regarded as isentropic surfaces in the physical oceanography. 1 Introduction Entropy, as enthalpy, internal energy of seawater is scientifically interesting thermo- dynamic state function of seawater. The concept of entropy and particularly the rate of entropy production form the central core of thermodynamic theory since entropy is 15 a measure for the amount of “disorder” or “chaos” in a system (Feistel and Ebeling, 1989).
    [Show full text]