Summary:

This study demonstrates the observed turbulent energy dissipation rate along a transect in the North Atlantic, which includes the microstructure observations of the deep ocean turbulence. The authors compare the microstructure measurements with the finescale parameterizations and the Thorpe sorting method, which can be estimated using the standard CTD data. Thought these comparisons, they suggest some recommendations and restrictions for applying both parameterizations in a deep ocean weakly turbulent environment. While the paper is well-motivated and contributes to the science, I believe the manuscript requires substantial revision before it can be considered for publication.  

Major comments:

I found this paper is concise and readable and the methods on the whole easy to follow. The comparison between the microstructure measurement and parameterization in the deep ocean is a good contribution to the existing literature, and most of the method is sound and adequately explained. However, for readers slightly removed from this field, I think that it would be useful to provide a further discussion in the Introduction about previous comparisons of finescale parameterizations and Thorpe methods to direct microstructure measurements. Section 8 of the current manuscript is mostly a summary of the results, but I think more discussion should be provided on the reasons why the finescale parameterization and Thorpe scale method deviates from microstructure observations in some regions of the present study, based on a discussion in the Introduction about previous comparisons. For example, the overestimations of the parameterization shown in Figure 5 and Figure 6 are currently interpreted as being due to iso-neutral stirring, but the influence of other physical mechanisms (e.g., double diffusion) should also be discussed. It has also been pointed out by previous studies that there the limitations of the finescale parameterization due to the fixed R_omega and that the low-resolution of the CTD may not capture small overturns leading to the overestimation of Thorpe-method (Sheehan et al., 2023). After the revision of the introduction and discussion part, I believe that this paper will more accurately provide  the science significance of this study in the context of other literature.

My other comments are mostly on details that could be improved.

Minor comments:

Line 35: Units used in parentheses should not be italicized here.

Line 39: ‘temperature variance’. Consider replacing it with “thermal variance dissipation rate’/’the rate of decrease of thermal variance’ etc.

Line 54: ‘fine-scale’but ‘finescale’ in the other parts. Please check for consistent spelling.

Line 71: ‘strain rates’. Please rephrase it ‘strain variance’ or ‘strain’.

Line 97: Estimates of εµU (εµT) were yielded from one distinct shear (FP07) probe? If they were obtained from multiple probes, are they averaged between them?

Section 3: Showing some example spectra (or composite spectra) for the shear and FP07 method in the appendix would be very helpful. Plotting the observed spectra with the fitted theoretical curves and some characteristics wavenumber (e.g., Batchelor wavenumber) would also make it easier for readers to follow the explanation of the methods for the estimates of εµU and εµT .

Line 125: (Fer et al. (2014)) - > (Fer et al., 2014)

Figure 3: typo in the legend of Figure 3b.’ perrcentile’ -> ’ percentile’. Also, plotting the lines of shear probe noise floors in Figs. 3a, c as well as Figs. 3b, d would be helpful.

Table 1: Why the values of the mode (Scheifele et al., 2018) is smaller than the 5^th percentiles (Piccolroaz et al., 2021). Please confirm it.

Line 155: The citations should be inside the parentheses.

Line 156: Please include references.

Line 157: What is ‘x %’ in this sentence?

Line 160: Was the correction method to compensate for the insufficient temporal response (Lueck et al. 1977; Gregg and Meagher 1980; Oakey 1982; Gregg 1999) used in this study? Did you use the same correction method as Piccolroaz et al. (2021)? This should be clearly stated in the main manuscript.

Line 206: (Waterman et al. (2013); Chin et al. (2016); Fine et al. (2021))  - > (Waterman et al., 2013; Chin et al., 2016; Fine et al., 2021)

Line 213: I think that this sentence is not clear. How can we interpret the relationship between R_omega and the depths from Fig. 4? Please consider rephrasing this sentence (or revising Fig. 4).

Line 221: How did you define ‘the surface mixed layer’ here? Did you just omit the several bins close to the surface?

Line 229: I think that it would be very helpful to plot vertical profiles of temperature, salinity, and R_rho and/or T-S diagrams to show the water mass variability in the present study. These plotting would be useful when you discuss how the region, where parameterizations were over(under)estimated, correspond to the finescale watermass variabilities. Also, when interpreting the results hereafter, it is important to indicate whether the water column is susceptible to double diffusion or not.

Line 234: Why does salinity noise at weak stratification lead to the ‘underestimation’ of parameterization? Please explain it in more detail.

Line 305: App.D3 is not found in the manuscript.

Line 326: I’m confused by this condition. As far as I can tell, the condition R_rho>1 corresponds to the salt-fingering-favorable regime (e.g., Schmitt, 1994). Why did you not include R_rho<-1 (doubly-stable regime). Under the condition R_rho>1, I’m afraid that the temperature change would capture the structure of the staircases and intrusions due to double diffusion rather than mechanical turbulence. Please explain this part in more detail.

Line 358: Did the vertical size of the overturn larger than 25m exist?

Line 377: Since the overestimation and underestimation were considered together in Table 2, it would be helpful to have scatterplots (eps_TP versus eps_VPM) to look at overestimation and underestimation separately.

Subsection 5.5.2: As shown in Fig. 6, the criterion 4 mainly works as a rejection of overestimate beyond a factor of 10 (When assuming  the criterion 4 leads to the removal of the overturn for which eps_TP< 1/25 eps_VMP and eps_TP > 25 eps_VMP ). What is the cause of these overestimations?

Line 385: Does St.2 and 3 in this line refer to St. NP2 and NP3? How can we interpret from Fig.2 that ‘parameterized estimate (εTP?)’ tends to be more similar to  than ? Please consider rephrasing it.

Line 393: ‘about 30-40% is removed’ by which method among Method 1-4?

Line 453: What did you use as D in calculating /in Fig7? Is it the same as in Eq.12? If so, please define here.

Line 462: I think that it is necessary to discuss the possibility that the high values of  is affected by the double diffusion rather than the isopycnal stirring. I understand that it is difficult to conclude it, but it would be useful to discuss various possible mechanisms other than the mechanical turbulence.

Line 465: I understand that it is difficult to see horizontal T/S variations from the observations due to the sparce locations, but I think it would be useful to show the vertical distribution of temperature, salinity, and Rrho. Is there any interleaving patterns in temperature and/or salinity in the vertical profiles of T,S?

Line 510: Does ‘St. 4-8’ mean St. NP4-8?

Line 542: ‘temperature-based’

The authors provide a very detailed analysis of a series of microstructure profiles collected in the North Atlantic. They provide a detailed breakdown of the data and technical analysis of the performance of the instrument and comparison against non-microstructure approaches to estimating turbulent parameters. Through this they provide advice on the applicability and analysis of both microstructure and CTD data for turbulence. This includes considering the limitations of both fine scale parameterisations and Thorpe scale analysis which the authors interpret as being driven by the methods not accounting for isoneutral mixing processes. In general, this is a very detailed manuscript which is well written and provides interesting insight. The discussion nicely summarises the results and recommendations from this study however it would be much stronger if there was a discussion of how the recommendations made here compare with the results of other studies. 

Detailed comments 

Line 72 – space missing between deep and sea 

Line 157 – “Only x% of” missing value 

Line 193 – I suggest to clarify what you mean by shear as you did collect microstructure shear data so I assume you mean LADCP based shear. I suggest “shear” > “large-scale shear” 

Around line 275 – Is it true that your CTD is measuring at 8cm vertical resolution? I would be concerned about the impact of the thermal mass of your platform and the flushing time of CTD. I saw you quote the response time given by SeaBird in the appendix however that is not the time for the sensor to give the “true” value. I think the more relevant value is the settling time which can be quite a bit longer. These potential constraints should at least be mentioned. 

Line 349 – I think the full stop is meant to be a comma, as what follows isn’t a sentence 

Line 366 – I think the labels for alpha for each method are the wrong way round 

Line 510 – The statement that the values are “likely unrealistically high” should be justified or removed. Whilst the authors might believe this, if it is to appear in a published paper it need to be driven by either data or some other evidence e.g. a scaling that shows that such values are not consistent with our existing understanding of the deep ocean. The authors compare with the profiles of Groeskamp et al 2020 however that approach also contains many assumptions and it is not clear to me a priori that one approach is more robust than the other. 

Line 613 –Typo lenght > length 

This paper is a fairly thorough look at microstructure measurements from a small number of profiles (approx 10) spanning a transect across the Atlantic Ocean. The amount of analysis done is impressive, and the methodological summaries are a useful resource for anyone new to the field. However, having read the paper twice now, I have some major comments; and recommend major revisions.

1. A lot of effort is spent in explaining the methods, so much so that it is hard to draw strong conclusions. Some of the shear-strain ratio analysis, and the less compelling Thorpe scale based estimates might be better suited to supplementary material.The discussion section needs some some context on how these results might be novel; or if not, how they support an existing body of work in to weak turbulence regimes. In general, drawing strong conclusions from a small number of turbulence profiles is hard; so it might be useful to bring in previous datasets from the NSF microstructure database to provide extra context.
2. Much of the paper focuses on very low ε & χ values. It is not clear to me how the noise floor of the thermistor is being handled. At some point, there is no "overturning turbulence", and (to me) the only sensible thing to do is apply molecular diffusivities and set ε to 0. See Cherian et al (2020) for references (including Gregg et al 2012; Itsweire et al 1988). If you "discard" too many of these low turbulence segments, you will bias the mean. From the text it doesn't appear as if this is actually biasing the mean, but it would be good to be sure and to disccuss the work of Itsweire and Gregg here.
3. The "triple decomposition" analysis in Section 6 doesn't add much to the paper, and could be removed in my opinion. I completely agree with the conclusion (lines 510-520) that it is not useful over much of the data. But that is to be expected from an analysis method that relies on residuals. Combining that with uncertainties in estimating the very small isopyncal density gradient in the abyss, the resulting diffusivity values cannot be good. A formal uncertainty analysis should indicate that your residuals are indistinguishable from 0, but isn't worth the effort in my opinion. In my experience, it is quite hard to extract the signal even from very well sampled measurement campaigns like NATRE. Outside of spicy isopycnals, where there is very low isopyncal stirring, you will simply get junk if attempting to estimate a residual (this is easily visble in Ferrari and Polzin, 2005). If you'd really like to do the comparison, I'd recommend limiting yourself to regions where "spiciness" is large, and avoiding diffusivity and comparing χ instead (if the χ residual proves to be significant).