Temperature Error Sensitivity

We test the sensitivity of the Thorpe scale analysis to random measurement errors. The Seabird SBE 39 thermistors have a nominal accuracy of 2 millidegrees. This error value is provided by the instrument manufacturer, and independent calibrations have shown this value to realistically describe this instrument performance (Lukas 2005 Pers. comm.). A significant fraction of the dissipation at both moorings is contributed by overturns spanning a temperature difference between instruments larger than the instrument error of 2 millidegree (Figures 5.3 and 5.5). For the largest overturns detected ( $\ge 100 m$ ), at both moorings, this temperature error does not affect the detection of these overturns (Figures 5.4 and 5.6).

To quantify the sensitivity of our analysis to the instrument error, we perform a Monte-Carlo simulation on a series of profiles from mooring DN with a synthetic noise added. We use a sub-sample of the entire dataset containing 6000 vertical temperature profiles ( $\sim21 days$ ). In this subsample, $12.5\%$ of the profiles contain at least one overturn. The average dissipation for the subsample is $1.91\times10^{-9}Wkg^{-1}$ . We added synthetic instrument noise to these profiles by adding a normally distributed random number with a zero mean and a standard deviation equal to the instrument nominal accuracy of 2 millidegree. We infer salinity from the temperature after adding the noise. Averaged over 1000 such profile time-series, $21 \%$ of the profiles contained one or more overturn (up from $12.5\%$ ), and the average dissipation increased to $3.32\times10^{-9}Wkg^{-1}$ (up from $1.91\times10^{-9}Wkg^{-1}$ ).

For mooring DS, with a subsample of 10000 profiles, the dissipation increases from $8.05\times10^{-9}$ to $10.10\times10^{-9}Wkg^{-1}$ , and the percentage of profiles showing overturns increases to $43\%$ from $31\%$ .

In conclusion, the synthetic instrument noise raised the mean dissipation by $1.4\times10^{-9}Wkg^{-1}$ , a $\sim 50\%$ increase at DN and a $25\%$ increase at DS. The synthetic profiles contain high vertical wavenumber noise that is not a feature of the original profiles. We believe that the error estimate is an upper bound on the effect of instrument noise on the Thorpe scale analysis. We conclude that random instrument noise alone cannot account for the strength of the infered overturns. The uncertainty of the mixing estimates obtained with this analysis is much smaller than the factor 10 difference in the overall average of dissipation between the two moorings.