Effects of noise on Thorpe scales and run lengths

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 root6, 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.