fine-structure methods for estimating diapycnal diffusivity in the Southern
5.4 Results and discussion
5.4.4 Quantifying diffusivity
A second test of a successful fine-structure parameterization is whether it provides reasonable quantitative estimates of the vertical diffusivity. Ledwell et al.
(2011) found a factor of two difference between tracer-derived diffusivity and microstructure diffusivity, which might be attributable to temporal variability but could also indicate the presence of physical processes that generate mixing in ways that are not readily measured by microstructure probes. Similarly, Waterman et al.’s (2012b) ratios of microstructure and shear/strain fine-structure diffusivities computed near the Kerguelen Plateau indicate that the shear/strain estimates typically exceed microstructure by a factor of 2 to 3 in the top 1000 m of the ocean in regions of flow over rough topography. The Ledwell et al. (2011) and Waterman et al. (2012b) results suggest that density-based fine-structure diffusivities might be expected to provide order-of-magnitude agreement with microstructure diffusivities, but that we probably cannot expect them to agree by better than a factor of two or three.
Figure 5.6 shows ratios of fine-structure diffusivity to microstructure diffusivity for the two regions. For both the Thorpe scale (Figure 5.6a-b) and strain (Figure 5.6c-d) estimates, the XCTD diffusivity exceeds the microstructure diffusivity (blue). For the Thorpe scale approach, differences can be as much as two orders of magnitude, while the strain diffusivities provide a better match but can still exceed the microstructure by an order of magnitude or more at some depths. The Thorpe-scale over-estimates are consistent with indications that instrument noise in XCTD measurements leads to inflated estimates of diffusivity, with the Thorpe scale estimates being more affected than the strain estimates.
The CTD-derived fine-structure estimates provide a better quantitative match (green lines in Figure 5.6), but can still differ from microstructureκs by an order of magnitude, particularly for the Thorpe-scale method in the low diffusivity region of the southeastern Pacific (Figure 5.6a). The best fine-structure/microstructure agreement appears to occur for the Thorpe-scale based analysis of CTD data collected in Drake Passage, where microstructure measurements reflect the presence of enhanced mixing. However, the fact that Thorpe scales do not perform well in regions of lower mixing means that Thorpe scales are probably ill-suited for analyzing observations spanning regions of low stratification and low mixing. For
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Figure 5.6: The ratios of Thorpe scale (top row) and strain (bottom row) estimates ofκ to microstructure estimates for CTD and XCTD in (a, c) southeast Pacific and (b, d) Drake Passage.
the strain method, CTD-derivedκ’s usually agree with microstructure derived κ’s within statistical uncertainty, though the statistical uncertainties can be large. The ratios of CTD strain estimates to microstructure estimates are within one order of magnitude for all depth bins except for the topmost bin in Drake Passage.
5.5 Summary 105
5.5 Summary
Fine-structure estimates of diapycnal diffusivities in the Southern Ocean were computed from CTD and XCTD data sampled during the DIMES survey in January and February of 2010. Both the Thorpe scale and the vertical strain method produced values of κ on the order of 10−4 to 10−3 m2 s−1. The fine-structure methods for the CTD and the XCTD tend to overestimate κ, compared with microstructure shear estimates, by at least an order of magnitude, except in Drake Passage, where the strain method for the CTD tends to underestimateκ compared with microstructure shear estimates.
A close examination of the noise characteristics of CTD and XCTD data indicates that once the data have been processed to minimize instrument noise, salinity spiking and ship effects, the minimum size of resolvable density overturns for Thorpe scales is approximately 1.5 m for CTD data and 20 m for the XCTD.
Such a resolution is insufficient for the Thorpe scale method to resolve the small overturns that generate most of the mixing in the survey region. The XCTD-Thorpe scaleκ estimates exceed the microstructure shear estimates by up to two orders of magnitude, while microstructure and CTD-Thorpe scale estimates match within an order of magnitude in Drake Passage.
The strain method produces more consistentκ estimates than does the Thorpe-scale method, and the CTD estimates match microstructure more closely than the XCTD. Neither the XCTD nor the CTD precisely reproduce the differences in diffusivity that have been previously measured between Drake Passage and the low-mixing region in the eastern Pacific section of the survey (Ledwell et al., 2011;
St. Laurent et al., 2012), though the strain estimates provide a more consistent representation of the spatial variations, and the CTD yields more robust results with smaller statistical uncertainties than the XCTD. However, even with the CTD data, the strain method still leaves considerable uncertainty inκ, with values often overestimated in the southeastern Pacific and underestimated in Drake Passage.
Our analysis implies that CTD and XCTD measurements do not precisely replicate the microstructure estimates of small-scale mixing in the low-stratification regime characteristic of the Southern Ocean. However, both the Thorpe scale and the strain method have the potential to produce accurate estimates in regions where the stratification is high and mixing is characterized by large density overturns.
Additional methods, such as a shear/strain approach based on a combination of CTD and LADCP data, may offer more possibilities for minimizing discrepancies between microstructure and fine-structure diffusivity estimates.