Effects of Noise on Thorpe Scales and Run Lengths

Helen L. Johnson Ocean Physics, School of Earth and Ocean Sciences, University of Victoria, British Columbia, Canada

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Chris Garrett Ocean Physics, School of Earth and Ocean Sciences, University of Victoria, British Columbia, Canada

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Abstract

Estimating the diapycnal mixing rate from standard CTD data by identifying overturning regions in the water column (the Thorpe-scale approach) provides good spatial and temporal coverage but is sometimes limited by instrument noise. This noise leads to spurious density inversions that are difficult to distinguish from real turbulent overturns. Previous efforts to eliminate noise may have overcorrected and hence underestimated the level of mixing. Here idealized density profiles are used to identify the magnitude and characteristics of overturning regions arising entirely from instrument noise, in order to establish a standard against which CTD data can be compared. The key nondimensional parameters are 1) the amplitude of the noise scaled by the density change over the section of profile considered, and 2) the number of data points in the section of profile. In some cases the product of these, which is equal to the amplitude of the noise scaled by the average density difference between consecutive measurements, is more useful than the second parameter. The probability distribution of “run length,” a useful diagnostic, varies significantly across this parameter space. Reasons for this are discussed, and it is shown that CTD data very rarely lie in a region of parameter space where comparison with the probability density function (PDF) of run lengths for a random uncorrelated series, or its rms value 6, is appropriate. The distribution of Thorpe displacements arising entirely from instrument noise, as well as the Thorpe scale and the statistics of density inversions, is also discussed. Analysis of CTD data from the interfaces of the thermohaline staircase in the deep Canada Basin illustrates how the results can be applied in practice to help to distinguish between signal and noise in marginal regimes. Density inversions seen in these data are shown to be no different from those that would result from instrument noise.

Corresponding author address: Dr. Helen L. Johnson, School of Earth and Ocean Sciences, University of Victoria, P.O. Box 3055, Victoria, BC V8W 3P6, Canada. Email: helenj@uvic.ca

Abstract

Estimating the diapycnal mixing rate from standard CTD data by identifying overturning regions in the water column (the Thorpe-scale approach) provides good spatial and temporal coverage but is sometimes limited by instrument noise. This noise leads to spurious density inversions that are difficult to distinguish from real turbulent overturns. Previous efforts to eliminate noise may have overcorrected and hence underestimated the level of mixing. Here idealized density profiles are used to identify the magnitude and characteristics of overturning regions arising entirely from instrument noise, in order to establish a standard against which CTD data can be compared. The key nondimensional parameters are 1) the amplitude of the noise scaled by the density change over the section of profile considered, and 2) the number of data points in the section of profile. In some cases the product of these, which is equal to the amplitude of the noise scaled by the average density difference between consecutive measurements, is more useful than the second parameter. The probability distribution of “run length,” a useful diagnostic, varies significantly across this parameter space. Reasons for this are discussed, and it is shown that CTD data very rarely lie in a region of parameter space where comparison with the probability density function (PDF) of run lengths for a random uncorrelated series, or its rms value 6, is appropriate. The distribution of Thorpe displacements arising entirely from instrument noise, as well as the Thorpe scale and the statistics of density inversions, is also discussed. Analysis of CTD data from the interfaces of the thermohaline staircase in the deep Canada Basin illustrates how the results can be applied in practice to help to distinguish between signal and noise in marginal regimes. Density inversions seen in these data are shown to be no different from those that would result from instrument noise.

Corresponding author address: Dr. Helen L. Johnson, School of Earth and Ocean Sciences, University of Victoria, P.O. Box 3055, Victoria, BC V8W 3P6, Canada. Email: helenj@uvic.ca

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  • Alford, M. H., and R. Pinkel, 2000: Observations of overturning in the thermocline: The context of ocean mixing. J. Phys. Oceanogr, 30 , 805832.

    • Search Google Scholar
    • Export Citation
  • Baumert, H., and H. Peters, 2000: Second-order closures and length scales for weakly stratified turbulent shear flows. J. Geophys. Res, 105 , 64536468.

    • Search Google Scholar
    • Export Citation
  • Bryan, F. O., 1987: Parameter sensitivity of primitive equation ocean general circulation models. J. Phys. Oceanogr, 17 , 970985.

  • Crawford, W. R., 1986: A comparison of length scales and decay times of turbulence in stably stratified flows. J. Phys. Oceanogr, 16 , 18471854.

    • Search Google Scholar
    • Export Citation
  • Dillon, T. M., 1982: Vertical overturns: A comparison of Thorpe and Ozmidov scales. J. Geophys. Res, 87 , 96019613.

  • Ferron, B., H. Mercier, K. Speer, A. Gargett, and K. Polzin, 1998: Mixing in the Romanche Fracture Zone. J. Phys. Oceanogr, 28 , 19291945.

    • Search Google Scholar
    • Export Citation
  • Finnigan, T. D., D. S. Luther, and R. Lukas, 2002: Observations of enhanced diapycnal mixing near the Hawaiian Ridge. J. Phys. Oceanogr, 32 , 29883002.

    • Search Google Scholar
    • Export Citation
  • Galbraith, P. S., and D. E. Kelley, 1996: Identifying overturns in CTD profiles. J. Atmos. Oceanic Technol, 13 , 688702.

  • Gregg, M. C., 1989: Scaling turbulent dissipation in the thermocline. J. Geophys. Res, 94 , 96869698.

  • Gregg, M. C., T. B. Sanford, and D. P. Winkel, 2003: Reduced mixing from the breaking of internal waves in equatorial waters. Nature, 422 , 513515.

    • Search Google Scholar
    • Export Citation
  • Kelley, D. E., 1988: Explaining effective diffusivities within diffusive oceanic staircases. Small-Scale Turbulence and Mixing in the Ocean, J. C. J. Nihoul and B. M. Jamart, Eds., Elsevier Science, 481–502.

    • Search Google Scholar
    • Export Citation
  • Kunze, E., L. K. Rosenfeld, G. S. Carter, and M. C. Gregg, 2002: Internal waves in Monterey Submarine Canyon. J. Phys. Oceanogr, 32 , 18901913.

    • Search Google Scholar
    • Export Citation
  • Lorke, A., and A. Wüest, 2002: Probability density of displacement and overturning length scales under diverse stratification. J. Geophys. Res.,107, 3214, doi:10.1029/2001JC001154.

    • Search Google Scholar
    • Export Citation
  • Marotzke, J., 1997: Boundary mixing and the dynamics of three-dimensional thermohaline circulations. J. Phys. Oceanogr, 27 , 17131728.

    • Search Google Scholar
    • Export Citation
  • Oakey, N. S., 1982: Determination of the rate of dissipation of turbulent energy from simultaneous temperature and velocity shear microstructure measurements. J. Phys. Oceanogr, 12 , 256271.

    • Search Google Scholar
    • Export Citation
  • Ozmidov, R. V., 1965: On the turbulent exchange in a stably stratified ocean. Izv. Acad. Sci. USSR, Atmos. Oceanic Phys, 1 , 861871.

  • Polzin, K. L., J. M. Toole, and R. W. Schmitt, 1995: Finescale parameterization of turbulent dissipation. J. Phys. Oceanogr, 25 , 306328.

    • Search Google Scholar
    • Export Citation
  • Stansfield, K., C. Garrett, and R. Dewey, 2001: The probability distribution of the Thorpe displacement within overturns in Juan de Fuca Strait. J. Phys. Oceanogr, 31 , 34213434.

    • Search Google Scholar
    • Export Citation
  • St. Laurent, L., and R. W. Schmitt, 1999: The contribution of salt fingers to vertical mixing in the North Atlantic Tracer Release Experiment. J. Phys. Oceanogr, 29 , 14041424.

    • Search Google Scholar
    • Export Citation
  • Thorpe, S. A., 1977: Turbulence and mixing in a Scottish loch. Philos. Trans. Roy. Soc. London, 286A , 125181.

  • Timmermans, M-L., C. Garrett, and E. Carmack, 2003: the thermohaline structure and evolution of the deep waters in the Canada Basin, Arctic Ocean. Deep-Sea Res, 50A , 13051321.

    • Search Google Scholar
    • Export Citation
  • Welander, P., 1986: Thermohaline effects in the ocean circulation and related simple models. Large-Scale Transport Processes in the Oceans and Atmosphere, J. Willebrand and D. L. T. Anderson, Eds., D. Reidel, 163–200.

    • Search Google Scholar
    • Export Citation
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