Influence of the Nonlinear Equation of State on Global Estimates of Dianeutral Advection and Diffusion

Andreas Klocker CSIRO Marine and Atmospheric Research, and Antarctic Climate and Ecosystems Cooperative Research Center, and Institute of Antarctic and Southern Ocean Studies, University of Tasmania, Hobart, Tasmania, Australia

Search for other papers by Andreas Klocker in
Current site
Google Scholar
PubMed
Close
and
Trevor J. McDougall Centre for Australian Climate and Weather Research, Hobart, Tasmania, Australia

Search for other papers by Trevor J. McDougall in
Current site
Google Scholar
PubMed
Close
Restricted access

Abstract

Recent work on the global overturning circulation and its energetics assumes that processes caused by nonlinearities of the equation of state of seawater are negligible. Nonlinear processes such as cabbeling and thermobaricity cause diapycnal motion as a consequence of isopycnal mixing. The nonlinear equation of state also causes the helical nature of neutral trajectories; as a consequence of this helical nature, it is not possible to define a continuous “density” surface that aligns with neutral tangent planes. The result is an additional diapycnal advection, which needs to be accounted for in water-mass analysis. In this paper, the authors take advantage of new techniques in constructing very accurate continuous density surfaces to more precisely estimate isopycnal and diapycnal processes caused by the nonlinear equation of state. They then quantify the diapycnal advection due to each of these nonlinear processes and show that they lead in total to a significant downward diapycnal advection, particularly in the Southern Ocean. The nonlinear processes are therefore another source of dense water formation in addition to high-latitude convection. To maintain the abyssal stratification in the global ocean, these dense water masses have to be brought back toward surface layers, and this can occur by either diabatic or adiabatic processes. Including these nonlinear processes into the advection–diffusion balance, the authors show that observed diapycnal diffusivities are unlikely to be able to support the amount of dense water produced in the global ocean, thus placing more importance on the adiabatic way of bringing the deep waters back to the surface.

* Current affiliation: Massachusetts Institute of Technology, Cambridge, Massachusetts

Corresponding author address: Andreas Klocker, Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, MA 02139. Email: aklocker@mit.edu

Abstract

Recent work on the global overturning circulation and its energetics assumes that processes caused by nonlinearities of the equation of state of seawater are negligible. Nonlinear processes such as cabbeling and thermobaricity cause diapycnal motion as a consequence of isopycnal mixing. The nonlinear equation of state also causes the helical nature of neutral trajectories; as a consequence of this helical nature, it is not possible to define a continuous “density” surface that aligns with neutral tangent planes. The result is an additional diapycnal advection, which needs to be accounted for in water-mass analysis. In this paper, the authors take advantage of new techniques in constructing very accurate continuous density surfaces to more precisely estimate isopycnal and diapycnal processes caused by the nonlinear equation of state. They then quantify the diapycnal advection due to each of these nonlinear processes and show that they lead in total to a significant downward diapycnal advection, particularly in the Southern Ocean. The nonlinear processes are therefore another source of dense water formation in addition to high-latitude convection. To maintain the abyssal stratification in the global ocean, these dense water masses have to be brought back toward surface layers, and this can occur by either diabatic or adiabatic processes. Including these nonlinear processes into the advection–diffusion balance, the authors show that observed diapycnal diffusivities are unlikely to be able to support the amount of dense water produced in the global ocean, thus placing more importance on the adiabatic way of bringing the deep waters back to the surface.

* Current affiliation: Massachusetts Institute of Technology, Cambridge, Massachusetts

Corresponding author address: Andreas Klocker, Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, MA 02139. Email: aklocker@mit.edu

Save
  • Abernathey, R., J. Marshall, M. Mazloff, and E. Shuckburgh, 2010: Enhancement of mesoscale eddy stirring at steering levels in the Southern Ocean. J. Phys. Oceanogr., 40 , 170184.

    • Search Google Scholar
    • Export Citation
  • Arneborg, L., 2002: Mixing efficiencies in patchy turbulence. J. Phys. Oceanogr., 32 , 14961506.

  • Davis, R. E., 1994: Diapycnal mixing in the ocean: Equations for large-scale budgets. J. Phys. Oceanogr., 24 , 777800.

  • Gargett, A. E., 1984: Vertical eddy diffusivity in the ocean interior. J. Mar. Res., 42 , 359393.

  • Gnanadesikan, A., R. D. Slater, P. S. Swathi, and G. K. Vallis, 2005: The energetics of ocean heat transport. J. Climate, 18 , 26042616.

    • Search Google Scholar
    • Export Citation
  • Gnanadesikan, A., A. M. de Boer, and B. K. Mignone, 2007: A simple theory of the pycnocline and overturning revisited. Ocean Circulation: Mechanisms and Impacts, Geophys. Monogr., Vol. 173, Amer. Geophys. Union, 19–32.

    • Search Google Scholar
    • Export Citation
  • Gouretski, V. V., and K. P. Koltermann, 2004: WOCE global hydrographic climatology. Bundesamtes für Seeschifffahrt und Hydrographie Tech. Rep. 35, 49 pp.

    • Search Google Scholar
    • Export Citation
  • Griffies, S. M., M. J. Harrison, R. C. Pacanowski, and A. Rosati, 2004: A technical guide to MOM4. NOAA/Geophysical Fluid Dynamics Laboratory Ocean Group Tech. Rep. 5, 342 pp.

    • Search Google Scholar
    • Export Citation
  • Huang, R. X., 1999: Mixing and energetics of the oceanic thermohaline circulation. J. Phys. Oceanogr., 29 , 727746.

  • Hughes, G. O., and R. W. Griffiths, 2006: A simple convective model of the global overturning circulation, including effects of entrainment into sinking regions. Ocean Modell., 12 , 4679.

    • Search Google Scholar
    • Export Citation
  • IOC, SCOR, and IAPSO, 2010: The international thermodynamic equation of seawater—2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides 56, UNESCO, 196 pp. [Available online at http://www.TEOS-10.org].

    • Search Google Scholar
    • Export Citation
  • Iudicone, D., G. Madec, and T. J. McDougall, 2008: Water-mass transformations in a neutral density framework and the key role of light penetration. J. Phys. Oceanogr., 38 , 13571376.

    • Search Google Scholar
    • Export Citation
  • Jackett, D. R., and T. J. McDougall, 1997: A neutral density variable for the world’s oceans. J. Phys. Oceanogr., 27 , 237263.

  • Klocker, A., and T. J. McDougall, 2010: Quantifying the consequences of the ill-defined nature of neutral surfaces. J. Phys. Oceanogr., 40 , 18661880.

    • Search Google Scholar
    • Export Citation
  • Klocker, A., T. J. McDougall, and D. R. Jackett, 2009a: A new method for forming approximately neutral surfaces. Ocean Sci., 5 , 155172.

    • Search Google Scholar
    • Export Citation
  • Klocker, A., T. J. McDougall, and D. R. Jackett, 2009b: Corrigendum to “A new method for forming approximately neutral surfaces” published in Ocean Sci., 5, 155–172, 2009. Ocean Sci., 5 , 191.

    • Search Google Scholar
    • Export Citation
  • Kunze, E., E. Firing, J. M. Hoummon, T. K. Chereskin, and A. M. Thurnherr, 2006: Global abyssal mixing inferred from lowered ADCP shear and CTD strain profiles. J. Phys. Oceanogr., 36 , 15531576.

    • Search Google Scholar
    • Export Citation
  • Ledwell, J. R., A. J. Watson, and C. S. Law, 1998: Mixing of a tracer in the pycnocline. J. Geophys. Res., 103 , 2149921529.

  • Ledwell, J. R., E. T. Montgomery, K. L. Polzin, L. C. St. Laurent, R. W. Schmitt, and J. M. Toole, 2000: Evidence for enhanced mixing over rough topography in the abyssal ocean. Nature, 403 , 179182.

    • Search Google Scholar
    • Export Citation
  • Lumpkin, R., and K. Speer, 2007: Global ocean meridional overturning. J. Phys. Oceanogr., 37 , 25502562.

  • Marshall, J., and T. Radko, 2006: A model of the upper branch of the meridional overturning of the Southern Ocean. Prog. Oceanogr., 70 , 331345.

    • Search Google Scholar
    • Export Citation
  • McDougall, T. J., 1984: The relative roles of diapycnal and isopycnal mixing on subsurface water mass conversion. J. Phys. Oceanogr., 14 , 15771589.

    • Search Google Scholar
    • Export Citation
  • McDougall, T. J., 1987a: Neutral surfaces. J. Phys. Oceanogr., 17 , 19501964.

  • McDougall, T. J., 1987b: Thermobaricity, cabbeling, and water-mass conversion. J. Geophys. Res., 92 , 54485464.

  • McDougall, T. J., 1988: Some implications of ocean mixing for ocean modelling. Small-Scale Turbulence and Mixing in the Ocean, J. C. J. Nihoul and B. M. Jamart, Eds., Elsevier, 21–35.

    • Search Google Scholar
    • Export Citation
  • McDougall, T. J., 1991: Parameterizing mixing in inverse models. Dynamics of Oceanic Internal Gravity Waves: Proc. ‘Aha Huliko‘a Hawaiian Winter Workshop, Honolulu, HI, University of Hawaii at Manoa, 355–386.

    • Search Google Scholar
    • Export Citation
  • McDougall, T. J., 2003: Potential enthalpy: A conservative oceanic variable for evaluating heat content and heat fluxes. J. Phys. Oceanogr., 33 , 945963.

    • Search Google Scholar
    • Export Citation
  • McDougall, T. J., and D. R. Jackett, 1988: On the helical nature of neutral trajectories in the ocean. Prog. Oceanogr., 20 , 153183.

  • McDougall, T. J., and P. C. McIntosh, 2001: The temporal-residual-mean velocity. Part II: Isopycnal interpretation and the tracer and momentum equations. J. Phys. Oceanogr., 31 , 12221246.

    • Search Google Scholar
    • Export Citation
  • McDougall, T. J., and D. R. Jackett, 2009: Neutral surfaces and the equation of state. Encyclopaedia of Ocean Sciences, 2nd ed. J. H. Steele, K. H. Turekian, and S. A. Thorpe, Eds., Elsevier, 4097–4103.

    • Search Google Scholar
    • Export Citation
  • Munk, W. H., 1966: Abyssal recipes. Deep-Sea Res., 13 , 707730.

  • Munk, W. H., and C. Wunsch, 1998: Abyssal recipes II: Energetics of tidal and wind mixing. Deep-Sea Res. I, 45 , 19772010.

  • Naveira Garabato, A. C., D. P. Stevens, A. J. Watson, and W. Roether, 2007: Short-circuiting of the overturning circulation in the Antarctic Circumpolar Current. Nature, 447 , 194197.

    • Search Google Scholar
    • Export Citation
  • Orsi, A. H., G. C. Johnson, and J. L. Bullister, 1999: Circulation, mixing, and production of Antarctic Bottom Water. Prog. Oceanogr., 43 , 55109.

    • Search Google Scholar
    • Export Citation
  • Osborn, T. R., 1980: Estimates of the local rate of vertical diffusion from dissipation measurements. J. Phys. Oceanogr., 10 , 8389.

  • Sallée, J. B., K. Speer, R. Morrow, and R. Lumpkin, 2008: An estimate of Lagrangian eddy statistics and diffusion in the mixed layer of the Southern Ocean. J. Mar. Res., 66 , 441463.

    • Search Google Scholar
    • Export Citation
  • Sloyan, B. M., 2005: Spatial variability of mixing in the Southern Ocean. Geophys. Res. Lett., 32 , L18603. doi:10.1029/2005GL023568.

  • Sloyan, B. M., 2006: Antarctic Bottom and Lower Circumpolar Deep Water circulation in the eastern Indian Ocean. J. Geophys. Res., 111 , C02006. doi:10.1029/2005JC003011.

    • Search Google Scholar
    • Export Citation
  • Sloyan, B. M., and S. R. Rintoul, 2001: The Southern Ocean limb of the global deep overturning circulation. J. Phys. Oceanogr., 31 , 143173.

    • Search Google Scholar
    • Export Citation
  • Sloyan, B. M., and I. V. Kamenkovich, 2007: Simulation of the mode and Antarctic Intermediate Waters in climate models. J. Climate, 20 , 50615080.

    • Search Google Scholar
    • Export Citation
  • Smith, K. S., and R. Ferrari, 2009: The production and dissipation of compensated thermohaline variance by mesoscale stirring. J. Phys. Oceanogr., 39 , 24772501.

    • Search Google Scholar
    • Export Citation
  • Smyth, W. D., J. N. Moum, and D. R. Caldwell, 2001: The efficiency of mixing in turbulent patches: Inferences from direct simulations and microstructure observations. J. Phys. Oceanogr., 31 , 19691992.

    • Search Google Scholar
    • Export Citation
  • St. Laurent, L., and H. Simmons, 2006: Estimates of power consumed by mixing in the ocean interior. J. Climate, 19 , 48774890.

  • St. Laurent, L., J. M. Toole, and R. W. Schmitt, 2001: Buoyancy forcing by turbulence above rough topography in the abyssal Brazil Basin. J. Phys. Oceanogr., 31 , 34763495.

    • Search Google Scholar
    • Export Citation
  • Stommel, H., and A. B. Arons, 1960a: On the abyssal circulation of the World Ocean—I. Stationary planetary flows on a sphere. Deep-Sea Res., 6 , 140154.

    • Search Google Scholar
    • Export Citation
  • Stommel, H., and A. B. Arons, 1960b: On the abyssal circulation of the World Ocean.—II. An idealized model of the circulation pattern and amplitude in ocean basins. Deep-Sea Res., 6 , 217233.

    • Search Google Scholar
    • Export Citation
  • Toggweiler, J. R., and B. Samuels, 1995: Effect of Drake Passage on the global thermohaline circulation. Deep-Sea Res., 42 , 477500.

  • Webb, D. J., and N. Suginohara, 2001: Vertical mixing in the ocean. Nature, 406 , 37.

  • Wunsch, C., and R. Ferrari, 2004: Vertical mixing, energy, and the general circulation of the oceans. Annu. Rev. Fluid Mech., 36 , 281314.

    • Search Google Scholar
    • Export Citation
  • Wyrtki, K., 1962: The oxygen minima in relation to ocean circulation. Deep-Sea Res., 9 , 1123.

  • Zika, J. D., B. M. Sloyan, and T. J. McDougall, 2009: Diagnosing the Southern Ocean overturning from tracer fields. J. Phys. Oceanogr., 39 , 29262940.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 348 175 17
PDF Downloads 192 61 4