Fine Structure of Vertical Density Distribution in the Black Sea and Its Relationship with Vertical Turbulent Exchange

Round 1

Reviewer 1 Report

A very good dataset including time series profiles of flow velocity, conductivity, temperature and depth (CTD) is used in the paper. The authors analyze these data in order to understand the vertical turbulent exchange in the Black Sea.

General comments

It is good that the authors base their analyses on many of their previous works, but I would suggest that they rationalize their analyses and argumentation using some important references in the English literature. For example, Zaron and Moum (2009, see also the reference list in this paper) give some considerations on the use of the Pi theorem. They say, "“…there are not enough dimensional groups in S2 , N2 , and Kh to provide a relation between Kh and Ri that is invariant to the dimensional units. To make a complete, universally valid, parameterization for Kh requires other parameters". Furthermore, as I understand from the notations in their manuscript, the Cox number (Eq. 2) and Ri are not independent by definition, so the statement "Cox number (C) is a power function of the Richardson number (Ri)" sounds a bit trivial. Perhaps the authors should reconsider this statement, which appears first in the Abstract.

Specific comments

1.     Citations: Because this paper largely addresses intrusions in the Black Sea, when referring to ecological aspects, authors could consider citing Stanev et al. (2017). In connection with “The reliable evidence for such intrusions was found recently, based on the analysis of vertical profiles of temperature, salinity and dissolved oxygen obtained using the Argo floats [27, 28]”, you can also consider citing Stanev et al., (2018; 2021)

2.      Line 51: “Podymov et al. [19,20] estimated the values of Kρ…”. Please explain what is the difference of present paper compared to these two published ones. What is the step forward?

3.     Line 78 “concentration of passive tracers, etc.” Also non-passive tracers.

4.     Line 85: “The FS of temperature, salinity and density fields is called as the thermohaline fine structure of the ocean”. Is that a definition of authors or they cite something? Make this clear.

5.     Line 123. “FS intensity”, and further in text, seems an unclear term, please rephrase or define it clearly (units). Processes are usually characterized by intensity. May be some aspects of structures, too, but the structures themselves?

6.     Line 127:  “extracting a required “turbulent mixing signal”” does not sound correct. Required by whom? Consider rephrasing.

7.     Lines 246-247 “Since the density of water in the Black Sea increases on average with depth, the inversion layers were those where the density decreased with depth.” Does density or its gradient decrease? Do you observe unstable stratification?

8.     Line 260 “To estimate the non-dimensional intensity of the FS density gradient pulsations we used a kind of the Cox number [41]:” I don’t find in this publication what you cite as “Cox number”. May be you should cite Osborn and Cox (1972), but there, this number has not been given this name.

9.     Please, check carefully what belongs to Introduction and what should be presented in the remaining sections. Example: “Forryan et al. [17] analyzed the parameterization (3) using the data of direct observations of vertical turbulent diffusivity from three separate ocean regions in the North Atlantic and Southern Ocean. It was found that equation (3) is robust for Ri > 1 at depths below the ocean near-surface boundary layer. In particular, when the equation (3) was fitted to all of the data for turbulent diffusivity from all three data sets simultaneously, then the best fit was for a smoothing window of 56 m with the parameter values as …” presents what others did. Consider moving this phrase, or part of it, in the Introduction.

10.  Could authors consider adding to Fig. 10 Ri time-depth diagram? For readers it would also be interesting to see similar N^2 and S^2 diagrams. May be add a new figure with these three characteristics.

11.   Line 420: “It also helps to demonstrate a possibility of using <Ri> to assess the stability of a stratified flow”. For that N^2 is more appropriate. Ri<0.25 demonstrates that there are conditions for mixing.

12.  Lines 485-486 “Therefore, it might be possible in the future to provide K estimations for the Rim Current zone of the Black Sea using only values of the FS Cox number, without any calculations of the Richardson number.” This statement would need that you give a measure of the expected error. If the error is too big, the method would not be useful.

13.  English grammar needs substantial improvement.

References:

Osborn, T.R., & C. S. Cox (1972) Oceanic fine structure, Geophysical Fluid Dynamics, 3:4, 321-345, DOI: 10.1080/03091927208236085

Stanev, E. V., Chtirkova, B., & Peneva, E. (2021). Geothermal convection and double diffusion based on profiling floats in the Black Sea. Geophysical Research Letters, 48, e2020GL091788

Stanev, E., Grayek, S., Claustre, H., Schmechtig, C., & Poteau, A. Water intrusions and particle signatures in the Black Sea: a Biogeochemical-Argo float investigation. Ocean Dynamics 67, 1119–1136 (2017).

Stanev, E. V., Poulain, P.-M., Grayek, S., Johnson, K. S., Claustre, H., & Murray, J. W. (2018). Understanding the dynamics of the oxic-anoxic interface in the Black Sea. Geophysical Research Letters, 45, 864–871.

Zaron, E. D., and J. N. Moum, 2009: A new look at Richardson number mixing schemes for equatorial ocean modeling. J. Phys. Oceanogr., 39, 2652–2664

Author Response

REVIEWER 1 RESPONSE.

A very good dataset including time series profiles of flow velocity, conductivity, temperature and depth (CTD) is used in the paper. The authors analyze these data in order to understand the vertical turbulent exchange in the Black Sea.

It is good that the authors base their analyses on many of their previous works, but I would suggest that they rationalize their analyses and argumentation using some important references in the English literature. For example, Zaron and Moum (2009, see also the reference list in this paper) give some considerations on the use of the Pi theorem. They say, "“…there are not enough dimensional groups in S2 , N2 , and Kh to provide a relation between Kh and Ri that is invariant to the dimensional units. To make a complete, universally valid, parameterization for Kh requires other parameters". Furthermore, as I understand from the notations in their manuscript, the Cox number (Eq. 2) and Ri are not independent by definition, so the statement "Cox number (C) is a power function of the Richardson number (Ri)" sounds a bit trivial. Perhaps the authors should reconsider this statement, which appears first in the Abstract.

Authors are very thankful to the reviewer for his helpful comments and remarks. The mentioned paper by Zaron and Moum (2009) is indeed a very important, showing that there are not enough dimensional groups in S², N² and K_ρ to provide a relation between K_ρ and Ri that is invariant to the dimensional units. In order to overcome this difficulty Zaron and Moum proposed a new parameterization which is based not only on Ri, but also includes the shear length scale and the kinetic energy of the background flow. Relevant paragraph is added to the Introduction, mentioning our intention to try this approach in the future work.

While both C and Ri depend on density and its gradient, there are no further apparent connection between these parameters. And unlike C, Ri is also a function of vertical velocity shear, which can vary significantly in the studied layer. In the end, it took both vertical and temporal data smoothing to find a Ri-based approximation of the Cox number in the form of a power function, so it doesn't seem that trivial to the authors.

Specific comments

1. Citations: Because this paper largely addresses intrusions in the Black Sea, when referring to ecological aspects, authors could consider citing Stanev et al. (2017). In connection with “The reliable evidence for such intrusions was found recently, based on the analysis of vertical profiles of temperature, salinity and dissolved oxygen obtained using the Argo floats [27, 28]”, you can also consider citing Stanev et al., (2018; 2021)

Thank you, the suggested citations have been added.

2. Line 51: “Podymov et al. [19,20] estimated the values of Kρ…”. Please explain what is the difference of present paper compared to these two published ones. What is the step forward?

      The previous studies were about calculations of the vertical turbulent exchange coefficient, trying to provide a simple and effective method to estimate Kr in the Black Sea main pycnohalocline, based on modified formula of Munk and Anderson. This paper is centered on the characteristics of the vertical fine structure of density profiles and attempts to use these characteristics to find an approach to Kr estimation without costly and relatively rare measurements of current velocity profiles.

3. Line 78 “concentration of passive tracers, etc.” Also non-passive tracers.

      Thank you, added.

4. Line 85: “The FS of temperature, salinity and density fields is called as the thermohaline fine structure of the ocean”. Is that a definition of authors or they cite something? Make this clear.

We removed this phrase from the manuscript and cited Fedorov (1978) the first time the term “fine structure” (FS) was mentioned.

5. Line 123. “FS intensity”, and further in text, seems an unclear term, please rephrase or define it clearly (units). Processes are usually characterized by intensity. May be some aspects of structures, too, but the structures themselves?

      The first time “FS intensity” appears in the manuscript, we explain what we mean (“a deviation of the smoothed temperature, salinity and density profiles from the original measurement data”). The wording was slightly changed (“…a magnitude of deviation…”). The term is probably not the best, but we couldn’t find a better alternative.

6. Line 127: “extracting a required “turbulent mixing signal”” does not sound correct. Required by whom? Consider rephrasing.

      Wording was made clearer.

7. Lines 246-247 “Since the density of water in the Black Sea increases on average with depth, the inversion layers were those where the density decreased with depth.” Does density or its gradient decrease? Do you observe unstable stratification?

      It’s density decrease, and yes, it means a local instability in the water stratification. A decrease of the density gradient alone (unless it becomes negative) doesn’t signal an inversion layer.

8. Line 260 “To estimate the non-dimensional intensity of the FS density gradient pulsations we used a kind of the Cox number [41]:” I don’t find in this publication what you cite as “Cox number”. May be you should cite Osborn and Cox (1972), but there, this number has not been given this name.

The parameter named as “Cox number” was described in “Introduction to Ocean Turbulence” by S. A. Thorpe (2007). The reference was fixed. However, the Cox number in Thorpe's book is somewhat different from what we use. Thorpe defined it as the sum of the squares of microstructural temperature fluctuations in all three dimensions, divided by the square of the mean gradient. We used the square of density gradient fluctuation in one dimension (depth), divided by the square of the average gradient in the analyzed layer. We called this number the fine structure analog of the microstructural Cox number.

9. Please, check carefully what belongs to Introduction and what should be presented in the remaining sections. Example: “Forryan et al. [17] analyzed the parameterization (3) using the data of direct observations of vertical turbulent diffusivity from three separate ocean regions in the North Atlantic and Southern Ocean. It was found that equation (3) is robust for Ri > 1 at depths below the ocean near-surface boundary layer. In particular, when the equation (3) was fitted to all of the data for turbulent diffusivity from all three data sets simultaneously, then the best fit was for a smoothing window of 56 m with the parameter values as …” presents what others did. Consider moving this phrase, or part of it, in the Introduction.

      The entire phrase was moved to the Introduction.

10. Could authors consider adding to Fig. 10 Ri time-depth diagram? For readers it would also be interesting to see similar N^2 and S^2 diagrams. May be add a new figure with these three characteristics.

We decided to change Fig. 10 entirely, removing the original diagram as low-informative. Its only purpose was to demonstrate that an additional temporal smoothing is needed to find a correlation between the Richardson and Cox numbers (similar procedure was performed by Thorpe in “An Introduction to Ocean Turbulence”, 2007), and the resulted data is already presented in Fig. 11. As suggested, new Fig. 10 now shows the time-depth diagrams of <Ri>, <N^2> and <S^2>.

11. Line 420: “It also helps to demonstrate a possibility of using <Ri> to assess the stability of a stratified flow”. For that N^2 is more appropriate. Ri<0.25 demonstrates that there are conditions for mixing.

      The questionable phrase was removed.

12. Lines 485-486 “Therefore, it might be possible in the future to provide Kr estimations for the Rim Current zone of the Black Sea using only values of the FS Cox number, without any calculations of the Richardson number.” This statement would need that you give a measure of the expected error. If the error is too big, the method would not be useful.

We added to the manuscript the root mean square error (RMSE) between the Ri-based Kr values and the C-based approximation (RMSE = 5·10^-5). The approximation formula could be improved in the future.

13. English grammar needs substantial improvement.

      The manuscript was proofread by a colleague with native English.

 

Author Response File: Author Response.pdf

Reviewer 2 Report

This paper describes the relation between Krho, Ri and a Cox number calculated from a vertical profiler in the Black Sea. It is clearly presented.

Nothing seems wrong but the paper as it stands seems to have missed a part of the literature, and either the analysis, or at least the discussion, would greatly benefit from more references to past work, and from a comparison with these past works.

In particular, in the introduction and in the text, lateral intrusions have been studied in detail by Terry Joyce (JPO, 1977) and many papers by Barry Ruddick (in particular his review in Progress in Oceanography)

I asked the JMSE editing board to forward you these papers that I sent them.

Further, it would be of interest to compare your vertical scale h to the Ellison scale and to the Thorpe length. Again the relation between these lengths, the Cox number, the Richardson number have been studied in detail in the literature. Again I sent to the JMSE editors the necessary papers (in particular that by Cimatoribus et al 1994). I asked them to forward these papers to you.

Technically, this paper is well written apart from two places where the article "the" is missing (lines 9 and 73). 

In summary I recommend a moderate revision to enrich the paper contents with a more in depth review of the literature and a comparison of the present results with past theory and analyses.

Author Response

REVIEWER 2 RESPONSE.

 This paper describes the relation between Kr, Ri and a Cox number calculated from a vertical profiler in the Black Sea. It is clearly presented.

Nothing seems wrong but the paper as it stands seems to have missed a part of the literature, and either the analysis, or at least the discussion, would greatly benefit from more references to past work, and from a comparison with these past works.

In particular, in the introduction and in the text, lateral intrusions have been studied in detail by Terry Joyce (JPO, 1977) and many papers by Barry Ruddick (in particular his review in Progress in Oceanography)

A paragraph about the study of intrusions in the World Ocean has been added to the manuscript, with links to the recommended references. However, we should note that the Black Sea thermohaline intrusions are not the subject of our paper, so we cannot pay much attention to them.

I asked the JMSE editing board to forward you these papers that I sent them.

Thank you very much for this kind support. We used the provided publications to improve the Introduction chapter and to deepen and expand the discussion of the results.

Further, it would be of interest to compare your vertical scale h to the Ellison scale and to the Thorpe length. Again the relation between these lengths, the Cox number, the Richardson number have been studied in detail in the literature. Again I sent to the JMSE editors the necessary papers (in particular that by Cimatoribus et al 1994). I asked them to forward these papers to you.

It is a good idea to compare the fine structure inhomogeneities calculated in different scales. Unfortunately, we were given a very limited amount of time to revise the manuscript, and experiments with two additional different methods, their analysis and comparison, seem like a subject for a separate paper. In future we are planning to conduct a detailed analysis of different approaches for estimation of the vertical turbulent exchange, including the scales of Thorpe and Ellison.

Technically, this paper is well written apart from two places where the article "the" is missing (lines 9 and 73). 

Fixed. However, another reviewer suggested that English in the manuscript needed a substantial improvement, so we had to ask a native speaker to check the grammars.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Most of my comments werw sufficiently addressed.

Reviewer 2 Report

the paper has been revised according to the referees' remarks

my remarks have received answers

except for the very few typos that I mentioned, and a few new ones

that I list below

Publication is recommended

these typos should be corrected by the authors or the journal:

abstract:

This paper IS CONCERNED with THE analysis of long-term...., measured by A moored autonomous profiler...

line 65 that is invariant to the dimensional units --> that is independent of the dimensional units

line 68 appears to be very perspective --> provide an interesting perspective on

line 92 on THE analysis of the fine structure

line 265 the original CTD data were binned into 10cm vertical cells:

I DO NOT UNDERSTAND WHY THERE IS A BINNING:

THE AQUALOG PROFILER MOVES AT 20CM/S VERTICALLY AND ACQUIRES DATA AT 2 HZ

THEREFORE THE VERTICAL RESOLUTION OF DATA IS 10CM.

THUS THERE IS ONE DATUM PER "BIN"

--> the original CTD data were spaced vertically by 10 cm

line 276 and h_inv intervals, (comma)

line 278 After that, (comma)

line 358 spanning 20 profiles (not "for")

line 401 on the vertical turbulence exchange, BUT THE COEFFICIENTS OF THIS RELATION MAY VARY IN SPACE AND WITH TIME

----------------------------

finally - but this is not necessary for the final version: there clearly are wedges in figure 12; perhaps this is a signature of IGW; you mention that tides are small, but they are not the only mechanism which produces IGW