• Alderson, S. G., and P. D. Killworth, 2005: A preoperational scheme for calculating sea surface height by Bernoulli inverse of Argo float data in the North Atlantic. J. Atmos. Oceanic Technol., 22 , 14161422.

    • Search Google Scholar
    • Export Citation
  • Cunningham, S. A., 2000: Circulation and volume flux of the North Atlantic using synoptic hydrographic data in a Bernoulli inverse. J. Mar. Res., 58 , 135.

    • Search Google Scholar
    • Export Citation
  • Davis, R. E., 1978: On estimating velocity from hydrographic data. J. Geophys. Res., 83 , 55075509.

  • Ganachaud, A., C. Wunsch, J. Marotzke, and J. Toole, 2000: Meridional overturning and large-scale circulation of the Indian Ocean. J. Geophys. Res., 105 , 2611726134.

    • Search Google Scholar
    • Export Citation
  • Gent, P. R., J. Willebrand, T. J. McDougall, and J. C. McWilliams, 1995: Parameterizing eddy-induced tracer transports in ocean circulation models. J. Phys. Oceanogr., 25 , 463474.

    • Search Google Scholar
    • Export Citation
  • Hallberg, R. W., 2000: Time integration of diapycnal diffusion and Richardson number–dependent mixing in isopycnal coordinate ocean models. Mon. Wea. Rev., 128 , 14021419.

    • Search Google Scholar
    • Export Citation
  • Karsten, R. H., and J. Marshall, 2002: Constructing the residual circulation of the ACC from observations. J. Phys. Oceanogr., 32 , 33153327.

    • Search Google Scholar
    • Export Citation
  • Killworth, P., 1986: A Bernoulli inverse method for determining the ocean circulation. J. Phys. Oceanogr., 16 , 20312051.

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

    • Search Google Scholar
    • Export Citation
  • Kuhlbrodt, T. A., M. Griesel, A. Montoya, A. Levermann, M. Hofmann, and S. Rahmstorf, 2007: On the driving processes of the Atlantic meridional overturning circulation. Rev. Geophys., 45 , RG2001. doi:10.1029/2004RG000166.

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

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

  • McDougall, T. J., 1988: Neutral-surface potential vorticity. Prog. Oceanogr., 20 , 185221.

  • McDougall, T. J., 1991: Parameterising 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., 1995: The influence of ocean mixing on the absolute velocity vector. J. Phys. Oceanogr., 25 , 705725.

  • 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. Prog. Oceanogr., 20 , 11531183.

  • McDougall, T. J., and D. R. Jackett, 2007: The thinness of the ocean in S–Θ–p space and the implications for mean diapycnal advection. J. Phys. Oceanogr., 37 , 17141732.

    • Search Google Scholar
    • Export Citation
  • McDougall, T. J., and A. Klocker, 2009: An approximate geostrophic streamfunction for use in density surfaces. Ocean Modell., in press.

  • McIntosh, P. C., and S. R. Rintoul, 1997: Do box inverse models work? J. Phys. Oceanogr., 27 , 291308.

  • Naveira-Garabato, A., 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
  • Needler, G. T., 1985: The absolute velocity as a function of conserved measurable quantities. Prog. Oceanogr., 5 , 173182.

  • Sloyan, B. M., and S. R. Rintoul, 2000: Estimates of area-averaged diapycnal fluxes from basin-scale budgets. J. Phys. Oceanogr., 30 , 23202341.

    • Search Google Scholar
    • Export Citation
  • Stommel, H., and F. Schott, 1977: The beta spiral and the determination of the absolute velocity field from hydrographic data. Deep-Sea Res., 24 , 325329.

    • Search Google Scholar
    • Export Citation
  • Tarantola, A., 1987: Inverse Problem Theory: Methods for Data Fitting and Model Parameter Estimation. Elsevier, 613 pp.

  • Turing, A. M., 1948: Rounding-off errors in matrix processes. Quart. J. Mech. Appl. Math., 1 , 287308.

  • Veronis, G., 1975: The role of models in tracer studies. Numerical Models of Ocean Circulation, National Academy of Science, 133–146.

  • Wunsch, C., 1978: The North Atlantic general circulation west of 50°W determined by inverse methods. Rev. Geophys. Space Phys., 16 , 583620.

    • Search Google Scholar
    • Export Citation
  • Zhang, H. M., and N. G. Hogg, 1992: Circulation and water mass balance in the Brazil basin. J. Mar. Res., 50 , 385420.

  • Zika, J. D., and T. J. McDougall, 2008: Vertical and lateral mixing processes deduced from the Mediterranean water signature in the North Atlantic. J. Phys. Oceanogr., 38 , 164176.

    • Search Google Scholar
    • Export Citation
  • 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
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A Tracer-Contour Inverse Method for Estimating Ocean Circulation and Mixing

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  • 1 Climate Change Research Centre, Faculty of Science, University of New South Wales, Sydney, New South Wales, and Centre for Australian Weather and Climate Research, Hobart, Tasmania, Australia
  • | 2 Centre for Australian Weather and Climate Research, Hobart, Tasmania, Australia
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Abstract

A method is developed for estimating the along-isopycnal and vertical mixing coefficients (K and D) and the absolute velocity from time-averaged hydrographic data. The method focuses directly on transports down tracer gradients on isopycnals. When the tracer considered is salinity or an appropriate variable for heat, this downgradient transport constitutes the along-isopycnal component of the thermohaline overturning circulation. In the method, a geostrophic streamfunction is defined that is related on isopycnals by tracer contours and by the thermal wind relationship in the vertical. Volume and tracer conservation constraints are also included. The method is overdetermined and avoids much of the signal-to-noise error associated with differentiating hydrographic data in conventional inverse methods. The method is validated against output of a layered model. It is shown to resolve both K and D, the downgradient isopycnal transport, and the mean flow on isopycnals in the North Pacific and South Atlantic.

Importantly, an understanding is established of both the physics underlying the method and the circumstances necessary for an inverse method to determine the mixing rates and the absolute velocity. If mixing is neglected, the method is the Bernoulli inverse method. At the limit of zero weight on the tracer-contour equations the method is a conventional box inverse method. Comparisons are drawn between each method and their relative merits are discussed. A new closed expression for the absolute velocity is also presented.

Corresponding author address: Jan Zika, Laboratoire des écoulements géophysiques et industriels, BP 53, 38041, Grenoble, CEDEX 9, France. Email: jan.zika@hmg.inpg.fr

Abstract

A method is developed for estimating the along-isopycnal and vertical mixing coefficients (K and D) and the absolute velocity from time-averaged hydrographic data. The method focuses directly on transports down tracer gradients on isopycnals. When the tracer considered is salinity or an appropriate variable for heat, this downgradient transport constitutes the along-isopycnal component of the thermohaline overturning circulation. In the method, a geostrophic streamfunction is defined that is related on isopycnals by tracer contours and by the thermal wind relationship in the vertical. Volume and tracer conservation constraints are also included. The method is overdetermined and avoids much of the signal-to-noise error associated with differentiating hydrographic data in conventional inverse methods. The method is validated against output of a layered model. It is shown to resolve both K and D, the downgradient isopycnal transport, and the mean flow on isopycnals in the North Pacific and South Atlantic.

Importantly, an understanding is established of both the physics underlying the method and the circumstances necessary for an inverse method to determine the mixing rates and the absolute velocity. If mixing is neglected, the method is the Bernoulli inverse method. At the limit of zero weight on the tracer-contour equations the method is a conventional box inverse method. Comparisons are drawn between each method and their relative merits are discussed. A new closed expression for the absolute velocity is also presented.

Corresponding author address: Jan Zika, Laboratoire des écoulements géophysiques et industriels, BP 53, 38041, Grenoble, CEDEX 9, France. Email: jan.zika@hmg.inpg.fr

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