3 Processing Dissipation Rates obtained aboard AUV Abyss
3.3 Noise and Error Estimate
17:04 17:06 17:08 17:10 17:12 17:14 17:16 17:18 17:20 17:22 17:24 17:26 10−9
10−8 10−7
UTC 24/08/2010
Dissipation [W/kg]
ε hybrid ε filtered
Figure 3.2: Dissipation rate segment from Dive 8 determined from the hybrid spectrum and from the filtered spectrum (for k > 10 cpm). The black, dashed, vertical lines indicate the two examples shown in Figure 3.1. The black, horizontal line indicates the noise level for Dive 8. The resolution is 6 s corresponding to 9 m.
were 2·10−9W/kg higher than those computed using the hybrid method. This discrepancy is mainly associated with a reduction of the noise level inherent to the hybrid method. In a low-turbulent environment ( <1·10−9W/kg), limited shear variance resides in the high k band (k > 10 cpm) and the inclusion of the low k band between k1 and k2 contributes to reduce noise in the dissipation rate estimates. In this thesis, dissipation rates determined from the hybrid spectrum ΦH will be used as those estimates rely on a larger bandwidth constrained by observations and the shape of the hybrid spectra shows reasonable agreement with the corresponding Nasmyth spectra. Spatial structures of the resulting dissipation rate distribution are robust among the two methods (Fig. 3.2).
The resulting dissipation rate time series has a resolution of 6 s corresponding to 9 m along-track resolution (speed of the AUV approximately 1.5 m/s). As two Airfoil probes were deployed simultaneously the mean of both sensors is used.
3.3 Noise and Error Estimate
The dissipation rate time-series of Dives 7 to 9 showed intervals of low and uniform dissipation rates. In these intervals, shear spectra no longer follow the Nasmyth spectrum for k > 4 cpm and are noise dominated (Fig. 3.1b). As the processing algorithm always uses the k range between 10 cpm and 15 cpm, fitted Nasmyth spectra cannot be much lower than those Φf intersecting the shear noise in that k-range (between 10 cpm and 15 cpm). Thus, using the hybrid spectra much lower dissipation rates cannot be estimated and it is expected to find potentially lower
3 Processing Dissipation Rates obtained aboard AUV Abyss
values biased high. This is illustrated by the histogram of the dissipation rates for Dive 8 (Fig. 3.3) which show an accumulation at low dissipation rates. This inter-pretation is supported by the microstructure data of St. Laurent and Thurnherr (2007) who also observed dissipation rates in the eastern channel of the Lucky Strike segment in the bottom boundary layer. Their dissipation rates fall substan-tially below the lowest estimates based on the hybrid spectrum (Fig. 3.3). Thus, the most frequently observed dissipation rate was chosen as the noise level n for the hybrid method (mode of the logarithm of the dissipation rates).
The noise level was estimated for each dive separately to be n = 7·10−10W/kg for Dive 8 and n = 2.5·10−9W/kg for Dives 7 and 9. The difference between Dives 7 and 8 originates from an improvement in the mounting of the MR, while the difference between Dives 8 and 9 originates most likely from different dive modes. Dives 7 and 8 were carried out in the staircase mode (Section 2.3.4), while the AUV followed the topography at a constant altitude during Dive 9. This dive mode is accompanied by increased vertical movements of the AUV and therefore by a higher level of vibrations. In data visualization the different noise levels are account for by setting all values below the noise level to a tenth of the noise level for each dive separately (Section 4).
The error of a single dissipation rate estimate is determined from the error of each
1e−11 1e−10 1e−09 1e−08 1e−07 1e−06
0 0.05 0.1 0.15 0.2 0.25 0.3
ε [W/kg]
DMP, St. Laurent & Thurnherr Dive 8
Figure 3.3:Histogram of the dissipation rates in logarithmic space of Dive 8 (gray) and the deepest 150 m from the deep microstructure profiler (DMP) profiles (black) normalized by the number of measurements. Vertical black, dashed lines mark the noise level atn= 7·10−10W/kg for Dive 8 andn= 1·10−10W/kg for the DMP.
42
3.3 Noise and Error Estimate parameter in Equation 2.1 and from the error arising from the spectral analysis in computing the dissipation rate. Here, the error of the output voltage Vs, the MR Gain G, the sensor sensitivity S and the AUV speed through the water are unknown. The error of the AUV speed can be estimated to be on the order of a few cm/s. This estimation is based on the in-situ calibration of the conversion factor cf, which revealed a difference in the flow velocity determined from the moorings and from the AUV of a few cm/s only (Section 2.4). Estimates of the dissipation rate which are commonly averaged over 1 s intervals for free-falling instruments usually have an uncertainty of about 50 % but the single dissipation rate estimates are subject to variations on a few orders of magnitude on short spatial and temporal scales and thus the uncertainty of a single estimate is often less important (Thorpe, 2005). Here, on the one hand averaging was performed over 3 independent intervals of 2 s length which might reduce the uncertainty but on the other hand, the error of the speed of the AUV through the water might introduce a larger uncertainty as the dissipation rate depends on the speed through the water to the power of 4 (Equation 2.1 and 3.1). The estimation of an error for the single dissipation rate values thus is itself uncertain and was not attempted.
A direct measurement of the speed through the water and sensor calibration at different temperatures (Section 2.3.3) is expected reduce the uncertainty.
The error of the spatially and temporally averaged dissipation rate (Section 4.1.2) can be estimated with the bootstrap method (Efron, 1979) and will be given in the respective sections where the averaged dissipation rates are discussed.