the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 19 Aug 2024
Internal-wave-induced dissipation rates in the Weddell Sea Bottom Water gravity current
Abstract. This study investigates the role of wave-induced turbulence in the dynamics of the Weddell Sea Bottom Water gravity current. The current transports dense water from its formation sites on the shelf to the deep sea and is a crucial component of the Southern Ocean overturning circulation. The analysis is based on velocity records from a mooring array deployed across the continental slope between January 2017 and January 2019 and salinity and temperature (CTD) profiles measured by various ship expeditions. To quantify the importance of internal waves for entrainment into the gravity current along the continental slope, we employ three independent methods for estimating turbulence. First, we use a Thorpe scale approach to compute turbulence from density inversions in density profiles in order to calculate total, process-independent dissipation rate. Second, we apply the finestructure parameterization to estimate wave-induced mixing from vertical profiles. Third, we estimate wave energy levels from moored velocity time series and deduce turbulent kinetic energy dissipation rates by applying a formulation that is at the heart of the finestructure parameterization. On this transect, turbulence is highest on the shelf break and decreases towards the deep sea, in line with a decreasing strength of wave-induced turbulence. We observe a 2-layer structure of the gravity current, a strongly turbulent about 60–80 m thick bottom layer and an upper, more quiescent interfacial layer. In the interfacial layer, internal waves induce an important part of the dissipation rate and therefore to entrainment of warmer upper water into the gravity current. A literature comparison with turbulence measurements up- and downstream of our study site suggests that the question of which turbulent process is dominant may be dependent on the location along the Weddell Sea Bottom Water gravity current. On the shelf, trapped waves are most important, on the slope, we see the effect of breaking internal waves and in the basin, symmetric instabilities are identified as the main driver of turbulence.
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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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RC1: 'Comment on egusphere-2024-2444', Anonymous Referee #1, 22 Sep 2024
Overall, the manuscript is well-written. Their science is solid, and the results based on field observations in the Weddel Sea are pretty interesting. I’m almost satisfied with the current manuscript, but there are some sentences hard to follow. I hope the following specific comments will help improve the manuscript.
Specific comments:
L4-5: The sentence “On the continental shelves…” is hard to follow.
L65-66, Table 1, and L83: Which months were the observations conducted? The observation months should be specified in the main text for readers who want know what the "background mean" stands for. (I found the sentence “all CTD measurements were collected in the same season of austral summer” in L325. I think this information should be mentioned earlier.)
L178-182: It’s hard to follow the methodology because there are vague directives “this” and “it”.
L194: The mooring time series are 2-years long. Does the averaged CTD profiles represent the time-mean density structures?
L202-203: I could not understand the sentence “Buoyancy frequency…”. Could you rephrase it?
L212: I could not follow the sentence “A second fit …”.
L284-285: “This results in …”: I could not follow this sentence because the authors described that the CTD profiles were depth-binned at 1 or 2 dbar resolution (L68-69). They did not mention the vertical resolution of LADCP profiles.
L319-320: The finestructure parameterization can calculate TKE dissipation rates for all profiles. How did the authors use the background dissipation rates?
L466-467: This is not clear form Fig.4.
L620-621: I could not follow the sentence.
Typos:
L147: (Fig. 2a) -> (Fig. 2b)
L585, RHS of the equation (A1): The constant coefficient should be ½, not 2.
Citation: https://doi.org/10.5194/egusphere-2024-2444-RC1 -
AC1: 'Reply on RC1', Ole Pinner, 30 Oct 2024
The authors thank the reviewer for the overall very positive assessment as well as for highlighting of inconsistencies, ambiguities and the occasional lack of clarity.
Overall, we are convinced that all wording criticized for lacking clarity can be rephrased and/or extended to improve the readability of the text, following the guidance of the review.
Following the review, we looked into a possible seasonal bias of the CTD profiles and compared them to vertically interpolated profiles from the mooring records, which provide year-round data. We find that CTD profiles are able to represent the variability of temperature and salinity profiles revealed by the moored instruments. The seasonal bias in availability of CTD profiles (mostly data measured in austral summer) therefore does not translate to a seasonal bias in our dissipation rate estimates. We will point this out in the revised manuscript. However, during this analysis we found 5 (previously undetected) CTD profiles, which deviate suspiciously far from an average profile, that they were deemed physically implausible, and were therefore removed from the analysis. We find that this correction to play a minor role for the derived dissipation.We agree with the reviewer’s statement on the finestructure parameterization. The latter indeed provides complete dissipation rate profiles, any assumption of a background value is not necessary. We assured ourselves, that the actual averaging into bins is done correctly without any false background assumptions. The mistake is therefore solely in the text and not in the calculation, and we are grateful to the reviewer for spotting this. We will remove the erroneous statement.
Following the guidance, we will add the information about the vertical resolution of the LADCP to the text. Additionally, will add a clearer explanation of what the given length scales mean, namely the integration limits in the finestructure method. This will be extended by an added paragraph in the discussion, where we compare our choice of integration limits with the choices in comparable literature.
During this peer-review, we found our integration limits for the shear spectra to be relatively narrow compared to other studies. Therefore, we tested the effect of an increase of the range of wave numbers in the integration from (0,1,2,3) to (0,1,2,…,7,8) in order to be more consistent with previous applications.
The new integration limits of the shear-based finestructure parameterization lead to a slightly improved agreement of shear- and strain-based results. The corresponding figure D1 will be updated accordingly in the revised manuscript. The average shear-to-strain variance ratio R_w value changes from 7.9±10.3 to 7.8±9.2. This therefore does not impact our decision to use the literature value of R_w = 7 for the strain-based formulation. In summary, because the change to the shear integration limits does not affect the strain-based calculations, our interpretation, and discussion of the results remains unchanged.Citation: https://doi.org/10.5194/egusphere-2024-2444-AC1
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AC1: 'Reply on RC1', Ole Pinner, 30 Oct 2024
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RC2: 'Comment on egusphere-2024-2444', Anonymous Referee #2, 14 Nov 2024
This manuscript presents vertical mixing estimates near and inside a bottom water gravity current in the Weddell Sea based on three different methods to estimate the mixing, to attempt to identify the contribution of internal gravity waves to the total ocean mixing.
This work is challenging because the mixing parameterizations that are used as not straight forward and involve a lot of tuning and careful choice of parameters. In addition, the errors associated with these methods are difficult to estimate and the authors did not have ‘direct’ microstructure mixing observations to benchmark their mixing estimates.
Nevertheless, the authors have taken great care to explain the three methods well and provided an excellent discussion of assumptions and choices of parameters. While the findings about the relative role of internal waves to the mixing in the gravity current and surrounding waters are limited, the novelty of using the wave energy method to estimate the wave-induced dissipation rate from a velocity time series is one to highlight, and worth further investigating in future work.
The scientific quality of the work is excellent and so is the presentation quality. The significance of the work needs to be better presented.
Main comments:
To compare the three methods, the vertical mean profiles in Fig6 are useful but they only show the data for part of the transect and misses half of the gravity current it seems (text is a bit unclear as to what is included in the data for Fig 6; see other individual comments). It would be useful to have a similar figure showing the mean vertical mixing profiles of all the data, including closer to the shelf past 51.5oW . If you want to separate mixing estimates within and outside the gravity current (because the finestructure param doesn’t work inside the gravity current), then show two mean vertical profile figures.
If you know that in the homogenously mixed BL, the assumptions for the finescale para are violated, why still present the mixing estimates from that method for that layer in some of the figures?
Limitations and resolution of the Thorpe scale method: There are some ways to use your own dataset to work out if it’s the sampling resolution (vertical sampling of CTD) or the instrument accuracy and noise level (CTD resolution) that limit the resolvable density inversions. The parameter R can represent this (Stansfield et al., 2001 and Johnson and Garrett, 2004). Comparing your LT data with au Gaussian fit can also help you estimate how much of the Thorpe scales you have resolved in your data set. This is because the distribution of LT is expected to be lognormal since it is theoretically the result of a multiplicative series of independent events (Stansfield et al., 2001).
Great to see you didn’t estimate diffusivity and thanks for adding the small discussion you provide on this Line 471-474.
Section called ‘Connection to larger scales’: You start this section by saying that you ‘want to set our results in a greater context’. By greater context, I think of the Southern Ocean or global ocean. Restricting that discussion section to the Weddell Sea is not really connecting to ‘larger scales’ in my mind. I would suggest renaming that section to better reflect the content.
The last paragraph in your Discussion brings in the topic of climate change and discusses changes in stratification potentially leading to increased vertical mixing. Currently you seem to summarise the findings from Zhou et al. (2023). Are you able to relate better these statements to your findings? Have you tried to see if the mean mixing along the transect has increased between 1989 and 2022? Or are the uncertainties in mixing estimates too high to be able to do that?
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Specific comments:
Line 34: You might want to remove the word ‘vertical’ since all types of mixing, not just vertical, will entrain ambient waters.
Line 104-105: Add relevant references such as Dillon 1982, Crawford 1986 and Ferron et al., 1998.
Line 118: How did you estimate your density noise level of 3x10-4 kgm-3? Have you considered applying a minimum thickness test based on the Galbraith and Kelley (1996) definition which puts a limit on the resolution of the data set? This minimum height of a density overturn is defined partly on the density accuracy of the instrument.
Line 129-130: Please add a few references here of other people having successfully applied this technique.
Line 136: Is this P=10 value similar to what is usually applied?
Line 154-155: add reference to Fig 2b
Line 315-316: What do you base this statement on? ‘Luckily, these observed higher modes contain the energy that is dissipated locally through turbulence.’ How do you know this?
Line 323-324: Maybe a little more discussion around that choice of neutral density =28.40 for the gravity current definition is needed: is this a common definition used by more than Naveira et al 2002b?
Line 325: if you don’t show the approx. 100 m variation in a table or figure, please add ‘not shown’.
Line 338-342: If this is not shown in a table or figure, please add ‘not shown’
Line 345-346: That single outlier profile looks dubious. Have you got any other CTD data to check the buoyancy frequency profile from another source? Would there be any reason for such large values of dissipation at that place and that time, like increased wind forcing (storm) or something else?
Line 358: ‘around 52oW’ . The elevated mixing in the whole water column is at 53oW on Figure 4. Please either change the value in the text of fix the figure.
Line 375-376: How did you estimate variables like the dissipation rate, inside the gravity current? Did you do it qualitatively ‘by eye’ on the figures or did you quantitatively average values within the core of the current based on a core definition? I suggest you try doing the quantitative approach.
Line 388-389: Did you only use data between 48.5 and 51.5oW for Figure 6? I think that is what you mean by this sentence. If so, please add that info in Fig 6 caption.
Line 400: add a depth range for what you mean by intermittent layer in brackets please.
Line 404: same as above but for ‘interfacial layer’; pls add a depth range.
Line 464: This has been observed before. Add ref and discussion, with here or in your 5.3 ‘relation to other studies’ section, based on existing literature on this topic such as Waterman, S., K. L. Polzin, A. C. Naveira Garabato, K. L. Sheen, and A. Forryan, 2014: Suppression of Internal Wave Breaking in the Antarctic Circumpolar Current near Topography. J. Phys. Oceanogr., 44, 1466–1492, https://doi.org/10.1175/JPO-D-12-0154.1.
Line 469: Add a depth range for what you call the ‘inner water column’ please.
Line 485-494: This section would benefit from being tidied up. Currently not very convincing and unclear what you can actually demonstrate based on your data.
Line 525-530: This paragraph is maybe a bit oversimplified? There are likely some appropriate models that resolve the gravity current and in which the wave propagation would be simulated. Instead of saying it is not possible, maybe say this could be part of future studies when the right tools are identified.
Line 550-558: in this paragraph please better separate your own statements from Zhou et al (2023) findings. Can you better relate what you say here to your own results?
Line 552-553: ‘The parameterization yields results comparable in value to the long-tested method of finestructure analysis.’ This is mostly true but not completely. In the bottom layer, the IDEMIX epsi estimates and the finescale epsi estimates differ significantly in my opinion (compared to the rest of the water column), and in a way that is currently unexplained. I would suggest to temper that statement.
Line 570: add ‘… is complicated by large uncertainties in the mixing estimates, …’
Acronyms throughout: Please define acronyms the first time they are used.
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Technical corrections:
Line 28: there is something missing in that sentence, like a word and it does not make sense. Please fix that sentence.
Line 51-52: Consider rephrasing the beginning of that sentence, which is currently awkward ‘Due to its remote and difficult to access location at high latitudes, …’.
Line 719: Here and elsewhere in the references, the hyperlinks to the datasets on Pangaea currently include a comma (‘,’) at the end of the link, which makes the link invalid when you click on it. Please remove the comma from within the link so the links can be used to access the data.
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Figures:
Figure 1: Very nice. Subplot a and b would benefit from being bigger. Currently it is difficult to look at features on figure 1a as it is too small.
Figure 2b insert: What is the second most prominent frequency that is not labelled, after M2?
Figure 3: Can you remind the reader in the caption what the measurement period is? Is it January 2017 to January 2019?
Figure 4: Nice figure! It would be useful to see a contour of the core of the gravity current based on the mean velocity field shown on Fig 3. Maybe a contour of 0.30 m/s or 0.25 m/s? In the caption, add info about the grey rectangles which probably mean no data available .
Figure 5: Same as above: add a mean velocity contour to show the location of the core of the gravity current. In the caption, add info about the grey rectangles which probably mean no data available .
Figure 6: Nice figure! See main comments for more feedback.
Citation: https://doi.org/10.5194/egusphere-2024-2444-RC2 -
AC2: 'Authors response, Reply on RC2', Ole Pinner, 12 Dec 2024
We thank the reviewer for the detailed and constructive assessment of our paper, and are very grateful for the positive feedback regarding the quality of our work. In the following, we will address the main comments as well as some of the specific questions and suggestions. A detailed point-to-point response to all comments will be provided with the revised manuscript.
In the revised text, we aim to better emphasize the scientific significance of our work, especially of our newly developed method for quantifying wave-induced dissipation rates and our contribution to an improved understanding of deep water export from the Weddell Sea.
Main comments:
In the current version, Figure 6 only shows one vertical slice through the gravity current. For the revised version, we will add an additional subfigure to allow for a method comparison as well as a result comparison along the transect. We will also better clarify how the data presented in Figure 6 was computed. The corresponding description in the text will be updated
Applicability of the finestructure parameterization
The finescale parameterization assumes (a) that all observed variability is associated with internal gravity waves and, subsequently, (b) that a stratification exists (N^2/= 0) for internal gravity waves (IGWs) to exist in. The validity of these assumptions is not always given in our study region, and we agree with the reviewer that this needs to be discussed in greater detail. In the revised manuscript, we will address both, the effect of the nearly homogeneous bottom layer (BL) and the applicability of the method in the interfacial layer in the text and mark the regions accordingly in the figures 3, 4, 5 and 6.
The BL is defined as having almost zero stratification, and finescale parameterization is consequently not applicable here. But we observed a maximum height of the BL of around 60m, which is much smaller than the length of 187m of the lowest vertical segment of the finestructure parameterization. Therefore, the BL can affect the results of the bottom-most bins, but does not invalidate them completely. Due to the variability of the BL height, we avoid shifting the bins vertically to keep the segments comparable. In the revised version of the figures, we pla to hatch the bottom-most bins, to communicate their difference from the upper bins.
The question of the applicability of the finestructure parameterization in the interfacial layer (IL) is less clear. The IL likely contains turbulent processes not caused by internal waves. To mitigate their effect, we consider in the integration for strain variance only the resolved length scales associated with waves. The potential case of turbulence from other sources being misidentified as wave-induced will be discussed in more detail.
At our end of the discussion, we see a careful use of the finestructure method in the IL as justified, as long as the caveats are explicitly described.
Uncertainty of the Thorpe scale approach
We looked more into the limitations and resolution of the Thorpe scale. We investigated the measured Thorpe scales by plotting the corresponding histogram and fitting a lognormal distribution to it. As expected from the vertical resolution, the histogram is truncated at O(1m). Although Thorpe scales of few centimeters are physically possible, we expect these missing small scales to only contribute little to the overall turbulence pattern, as we resolve the large majority of the expected Thorpe scales.
The CTD measurements are accurate to 0.0005 °C in temperature and 0.002 g/kg in salinity, which results in a density resolution of similar magnitude of O(10^-3). To check if the depth or density resolution limits our results, we will use the parameter R (Stansfield et al., 2001), a smooth vertical density profile and the fixed vertical resolution of 1m. This results in the minimum value of density resolution, from where it would be the limiting factor, which we can compare to our estimated density resolution value.
To differentiate between physical overturning and noise, a rejection criterion is already used, based on a critical value of the overturn ratio developed in Gargett and Garner, 2008. (doi:10.1175/2008JTECHO541.1). We argue that the additional application of the Galbraith and Kelly test to further describe the limits of the Thorpe scale analysis would exceed the scope of this work. The discussion section of the Thorpe scale method will be extended with the above. We continue our discussion on this topic at the relevant specific comment about the chosen density noise level for the Thorpe scale approach.
Time-dependence of dissipation rates
We share the interest of the reviewer to look into potential temporal changes in the dissipation rates over the years. But mean dissipation rates for each expedition along the transect are not easily comparable, as the expeditions differ in their coverage and resolution of the continental slope. Making sure the resulting time series is as unbiased as possible exceeds the scope of this work. The temporal changes of dissipation rate estimates (longer trends, interannual and seasonal variability) is part of our ongoing work and will be dealt with in a follow-up paper.
Specific comments:
Line 136 Parameters in the Multitaper analysis
On the question if the parameter P=10 in the multitaper method is similar to what is usually applied, one has to consider that the multitaper analysis has 3 parameters which are not necessarily set by the data. The window length N in units of data points, the time-half-bandwidth product P, and the amount of Slepian tapers k. The time-half-bandwidth product is often called NW to reflect its origin as a product of window length N and the half-bandwidth W.
While non-oceanographic literature (Thomson1982, Cokelaer2017) recommend NW values between 2.5 and 4 (with a corresponding choice of 2*NW or 2*NW-1 slepian tapers), the applications to marine data we found use more varied parameter values. LeBoyer2021 et al. use for their multitaper analysis a “window length [...] chosen to be the integer number of inertial periods nearest to 30 days”, together with k=3 slepian tapers. They do not give values for the chosen half-bandwidth or time-half-bandwidth product. If we applied this condition to our measurements, the inertial period at 64° S of 13.33 hours would lead to a window length N of 30 days / 13.33 hours ≈ 54 data points.
Instead, we use a window length of the complete length of the velocity data (N = O(5*10^3), with P=NW=10 and k = 2P-1 = 19 slepian tapers. These parameters are very close to the parameters of a time-half-bandwidth product of 8, with 15 slepian tapers, Chave et al, 2019 use to resolve infragravity waves and tidal frequencies in deep ocean pressure records. The general problem persists that although multitaper is not a trivial method, its defining parameters are regularly not given completely in the main text of published literature and the corresponding research code is not easily accessible. To increase reproducibility without requiring a detailed look into our published research code, we will give all parameters of our multitaper analysis in an additional paragraph in the methods section.
Thorpe scales Line 118, 345-346:
For the computation of the Thorpe scales, we previously used a value for the density noise of 3e-4 kg/m^3. With a density resolution of O(10^-3) (see above), we see this now as slightly too low. We increased it to 5e-4 kg/m^3, but still below the density differences we can accurately resolve. This results in that previously accepted overturns, yielding in low dissipation rates of around 3*10^-10, are now reclassified as spurious and replaced by the background dissipation of 1*10^-10. This especially happens in the open water column towards the east of the transect. The numerical values given in the text are corrected to describe the updated results. The interpretation of the Thorpe scale dissipation rates remains unchanged, as the values change only minimally.
Because the outlier in the dissipation rates from the Thorpe scale approach is measured in depths around 3000m deep in the ocean, it is unlikely that wind forcing could be a physical cause of this. Additionally, profiles from the same expedition do not show segments of dissipation rate this strongly enhanced. The outlier was traced back to a single diagnosed overturn of multiple hundred meter lengths, which was not automatically rejected by the internal quality control in the Thorpe scale algorithm. We removed the large overturn as non-physical, but kept the measurements from the same profile closer to the seafloor. In the text, we will add a sentence documenting the outlier removal.
Energy distribution in vertical modes, Line 315-316:
The fact that higher vertical modes more likely lead to locally dissipated energy, while lower modes are more likely to spatially transport energy is used several times throughout the paper. We supported that in the text by a reference to Falahat et al. 2014. More previous work to this topic is for example summarised in the introduction of de Lavergne, 2019. In short, the distribution of locally available energy among vertical modes is based on time scales of nonlinear interactions. For example, in the often dominant process of parametric subharmonic instability (short PSI), the decay time decreases strongly with vertical mode numbers (Olbers et al., 2020, Fig. 13).
In the revised text, we will reference the assumption we make more extensively by adding the 2 mentioned papers as references, as well as a short explanatory sentence.
WSBW definition Line 323-324:
The definition of Weddell Sea Bottom Water is not completely unanimous, as two established definitions still coexist: as bottom-near water below a certain potential temperature (Foster1976, Orsi1999, Nicholls2009), most recently < -0.7 °C (Vernet2019, Gordon2020), or water of neutral density > 28.40 kg m^-3 (NaveiraGarabato2002b, Meredith2008, Dotto2014, Llanillo2023). We decided to use the newer classification employing neutral density, among other reasons because it automatically excludes very cold surface waters. We will extend the definition of Weddell Sea Bottom Water in the text with a short explanation.
Quantitative Averaging, Line 375-376
The dissipation rate in each region description was previously determined by averaging qualitatively ‘by eye’. For the revised version, we split the transect into 5 regions (shelf, interfacial layer, bottom layer, open ocean, air/no data) and calculate an arithmetic mean for each. Because of the strong horizontal changes (even inside a single region), this reduction to (a maximum of) 4 values each for Thorpe and Finestructure is suited best for a summary at the end of the results sections or for the conclusion. The parameterization based on velocity time series does not have the necessary resolution for meaningful averages in each region.
Waterman et al., 2014, Line 464:
We thank the reviewer for the recommendation of Waterman et al. 2014, which we missed in our literature research. They find for the Southern Ocean that bottom-near dissipation rates, predicted by the finescale parameterization, systematically overestimated microstructure estimations, especially at locations of large near-bottom flow speeds. We will add a paragraph to discuss our results in relation to the findings of Waterman et al.
Citation: https://doi.org/10.5194/egusphere-2024-2444-AC2
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AC2: 'Authors response, Reply on RC2', Ole Pinner, 12 Dec 2024
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EC1: 'Comment on egusphere-2024-2444', Bernadette Sloyan, 03 Dec 2024
Dear Ole and coauthors,
The two reviewers have provided some useful comments on your manuscript. I encourage you to address the reviewers comments and submit a revised manuscript and point-by-point reply to reviewers comments.
Regards
Bernadette
Citation: https://doi.org/10.5194/egusphere-2024-2444-EC1
Interactive discussion
Status: closed
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RC1: 'Comment on egusphere-2024-2444', Anonymous Referee #1, 22 Sep 2024
Overall, the manuscript is well-written. Their science is solid, and the results based on field observations in the Weddel Sea are pretty interesting. I’m almost satisfied with the current manuscript, but there are some sentences hard to follow. I hope the following specific comments will help improve the manuscript.
Specific comments:
L4-5: The sentence “On the continental shelves…” is hard to follow.
L65-66, Table 1, and L83: Which months were the observations conducted? The observation months should be specified in the main text for readers who want know what the "background mean" stands for. (I found the sentence “all CTD measurements were collected in the same season of austral summer” in L325. I think this information should be mentioned earlier.)
L178-182: It’s hard to follow the methodology because there are vague directives “this” and “it”.
L194: The mooring time series are 2-years long. Does the averaged CTD profiles represent the time-mean density structures?
L202-203: I could not understand the sentence “Buoyancy frequency…”. Could you rephrase it?
L212: I could not follow the sentence “A second fit …”.
L284-285: “This results in …”: I could not follow this sentence because the authors described that the CTD profiles were depth-binned at 1 or 2 dbar resolution (L68-69). They did not mention the vertical resolution of LADCP profiles.
L319-320: The finestructure parameterization can calculate TKE dissipation rates for all profiles. How did the authors use the background dissipation rates?
L466-467: This is not clear form Fig.4.
L620-621: I could not follow the sentence.
Typos:
L147: (Fig. 2a) -> (Fig. 2b)
L585, RHS of the equation (A1): The constant coefficient should be ½, not 2.
Citation: https://doi.org/10.5194/egusphere-2024-2444-RC1 -
AC1: 'Reply on RC1', Ole Pinner, 30 Oct 2024
The authors thank the reviewer for the overall very positive assessment as well as for highlighting of inconsistencies, ambiguities and the occasional lack of clarity.
Overall, we are convinced that all wording criticized for lacking clarity can be rephrased and/or extended to improve the readability of the text, following the guidance of the review.
Following the review, we looked into a possible seasonal bias of the CTD profiles and compared them to vertically interpolated profiles from the mooring records, which provide year-round data. We find that CTD profiles are able to represent the variability of temperature and salinity profiles revealed by the moored instruments. The seasonal bias in availability of CTD profiles (mostly data measured in austral summer) therefore does not translate to a seasonal bias in our dissipation rate estimates. We will point this out in the revised manuscript. However, during this analysis we found 5 (previously undetected) CTD profiles, which deviate suspiciously far from an average profile, that they were deemed physically implausible, and were therefore removed from the analysis. We find that this correction to play a minor role for the derived dissipation.We agree with the reviewer’s statement on the finestructure parameterization. The latter indeed provides complete dissipation rate profiles, any assumption of a background value is not necessary. We assured ourselves, that the actual averaging into bins is done correctly without any false background assumptions. The mistake is therefore solely in the text and not in the calculation, and we are grateful to the reviewer for spotting this. We will remove the erroneous statement.
Following the guidance, we will add the information about the vertical resolution of the LADCP to the text. Additionally, will add a clearer explanation of what the given length scales mean, namely the integration limits in the finestructure method. This will be extended by an added paragraph in the discussion, where we compare our choice of integration limits with the choices in comparable literature.
During this peer-review, we found our integration limits for the shear spectra to be relatively narrow compared to other studies. Therefore, we tested the effect of an increase of the range of wave numbers in the integration from (0,1,2,3) to (0,1,2,…,7,8) in order to be more consistent with previous applications.
The new integration limits of the shear-based finestructure parameterization lead to a slightly improved agreement of shear- and strain-based results. The corresponding figure D1 will be updated accordingly in the revised manuscript. The average shear-to-strain variance ratio R_w value changes from 7.9±10.3 to 7.8±9.2. This therefore does not impact our decision to use the literature value of R_w = 7 for the strain-based formulation. In summary, because the change to the shear integration limits does not affect the strain-based calculations, our interpretation, and discussion of the results remains unchanged.Citation: https://doi.org/10.5194/egusphere-2024-2444-AC1
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AC1: 'Reply on RC1', Ole Pinner, 30 Oct 2024
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RC2: 'Comment on egusphere-2024-2444', Anonymous Referee #2, 14 Nov 2024
This manuscript presents vertical mixing estimates near and inside a bottom water gravity current in the Weddell Sea based on three different methods to estimate the mixing, to attempt to identify the contribution of internal gravity waves to the total ocean mixing.
This work is challenging because the mixing parameterizations that are used as not straight forward and involve a lot of tuning and careful choice of parameters. In addition, the errors associated with these methods are difficult to estimate and the authors did not have ‘direct’ microstructure mixing observations to benchmark their mixing estimates.
Nevertheless, the authors have taken great care to explain the three methods well and provided an excellent discussion of assumptions and choices of parameters. While the findings about the relative role of internal waves to the mixing in the gravity current and surrounding waters are limited, the novelty of using the wave energy method to estimate the wave-induced dissipation rate from a velocity time series is one to highlight, and worth further investigating in future work.
The scientific quality of the work is excellent and so is the presentation quality. The significance of the work needs to be better presented.
Main comments:
To compare the three methods, the vertical mean profiles in Fig6 are useful but they only show the data for part of the transect and misses half of the gravity current it seems (text is a bit unclear as to what is included in the data for Fig 6; see other individual comments). It would be useful to have a similar figure showing the mean vertical mixing profiles of all the data, including closer to the shelf past 51.5oW . If you want to separate mixing estimates within and outside the gravity current (because the finestructure param doesn’t work inside the gravity current), then show two mean vertical profile figures.
If you know that in the homogenously mixed BL, the assumptions for the finescale para are violated, why still present the mixing estimates from that method for that layer in some of the figures?
Limitations and resolution of the Thorpe scale method: There are some ways to use your own dataset to work out if it’s the sampling resolution (vertical sampling of CTD) or the instrument accuracy and noise level (CTD resolution) that limit the resolvable density inversions. The parameter R can represent this (Stansfield et al., 2001 and Johnson and Garrett, 2004). Comparing your LT data with au Gaussian fit can also help you estimate how much of the Thorpe scales you have resolved in your data set. This is because the distribution of LT is expected to be lognormal since it is theoretically the result of a multiplicative series of independent events (Stansfield et al., 2001).
Great to see you didn’t estimate diffusivity and thanks for adding the small discussion you provide on this Line 471-474.
Section called ‘Connection to larger scales’: You start this section by saying that you ‘want to set our results in a greater context’. By greater context, I think of the Southern Ocean or global ocean. Restricting that discussion section to the Weddell Sea is not really connecting to ‘larger scales’ in my mind. I would suggest renaming that section to better reflect the content.
The last paragraph in your Discussion brings in the topic of climate change and discusses changes in stratification potentially leading to increased vertical mixing. Currently you seem to summarise the findings from Zhou et al. (2023). Are you able to relate better these statements to your findings? Have you tried to see if the mean mixing along the transect has increased between 1989 and 2022? Or are the uncertainties in mixing estimates too high to be able to do that?
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Specific comments:
Line 34: You might want to remove the word ‘vertical’ since all types of mixing, not just vertical, will entrain ambient waters.
Line 104-105: Add relevant references such as Dillon 1982, Crawford 1986 and Ferron et al., 1998.
Line 118: How did you estimate your density noise level of 3x10-4 kgm-3? Have you considered applying a minimum thickness test based on the Galbraith and Kelley (1996) definition which puts a limit on the resolution of the data set? This minimum height of a density overturn is defined partly on the density accuracy of the instrument.
Line 129-130: Please add a few references here of other people having successfully applied this technique.
Line 136: Is this P=10 value similar to what is usually applied?
Line 154-155: add reference to Fig 2b
Line 315-316: What do you base this statement on? ‘Luckily, these observed higher modes contain the energy that is dissipated locally through turbulence.’ How do you know this?
Line 323-324: Maybe a little more discussion around that choice of neutral density =28.40 for the gravity current definition is needed: is this a common definition used by more than Naveira et al 2002b?
Line 325: if you don’t show the approx. 100 m variation in a table or figure, please add ‘not shown’.
Line 338-342: If this is not shown in a table or figure, please add ‘not shown’
Line 345-346: That single outlier profile looks dubious. Have you got any other CTD data to check the buoyancy frequency profile from another source? Would there be any reason for such large values of dissipation at that place and that time, like increased wind forcing (storm) or something else?
Line 358: ‘around 52oW’ . The elevated mixing in the whole water column is at 53oW on Figure 4. Please either change the value in the text of fix the figure.
Line 375-376: How did you estimate variables like the dissipation rate, inside the gravity current? Did you do it qualitatively ‘by eye’ on the figures or did you quantitatively average values within the core of the current based on a core definition? I suggest you try doing the quantitative approach.
Line 388-389: Did you only use data between 48.5 and 51.5oW for Figure 6? I think that is what you mean by this sentence. If so, please add that info in Fig 6 caption.
Line 400: add a depth range for what you mean by intermittent layer in brackets please.
Line 404: same as above but for ‘interfacial layer’; pls add a depth range.
Line 464: This has been observed before. Add ref and discussion, with here or in your 5.3 ‘relation to other studies’ section, based on existing literature on this topic such as Waterman, S., K. L. Polzin, A. C. Naveira Garabato, K. L. Sheen, and A. Forryan, 2014: Suppression of Internal Wave Breaking in the Antarctic Circumpolar Current near Topography. J. Phys. Oceanogr., 44, 1466–1492, https://doi.org/10.1175/JPO-D-12-0154.1.
Line 469: Add a depth range for what you call the ‘inner water column’ please.
Line 485-494: This section would benefit from being tidied up. Currently not very convincing and unclear what you can actually demonstrate based on your data.
Line 525-530: This paragraph is maybe a bit oversimplified? There are likely some appropriate models that resolve the gravity current and in which the wave propagation would be simulated. Instead of saying it is not possible, maybe say this could be part of future studies when the right tools are identified.
Line 550-558: in this paragraph please better separate your own statements from Zhou et al (2023) findings. Can you better relate what you say here to your own results?
Line 552-553: ‘The parameterization yields results comparable in value to the long-tested method of finestructure analysis.’ This is mostly true but not completely. In the bottom layer, the IDEMIX epsi estimates and the finescale epsi estimates differ significantly in my opinion (compared to the rest of the water column), and in a way that is currently unexplained. I would suggest to temper that statement.
Line 570: add ‘… is complicated by large uncertainties in the mixing estimates, …’
Acronyms throughout: Please define acronyms the first time they are used.
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Technical corrections:
Line 28: there is something missing in that sentence, like a word and it does not make sense. Please fix that sentence.
Line 51-52: Consider rephrasing the beginning of that sentence, which is currently awkward ‘Due to its remote and difficult to access location at high latitudes, …’.
Line 719: Here and elsewhere in the references, the hyperlinks to the datasets on Pangaea currently include a comma (‘,’) at the end of the link, which makes the link invalid when you click on it. Please remove the comma from within the link so the links can be used to access the data.
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Figures:
Figure 1: Very nice. Subplot a and b would benefit from being bigger. Currently it is difficult to look at features on figure 1a as it is too small.
Figure 2b insert: What is the second most prominent frequency that is not labelled, after M2?
Figure 3: Can you remind the reader in the caption what the measurement period is? Is it January 2017 to January 2019?
Figure 4: Nice figure! It would be useful to see a contour of the core of the gravity current based on the mean velocity field shown on Fig 3. Maybe a contour of 0.30 m/s or 0.25 m/s? In the caption, add info about the grey rectangles which probably mean no data available .
Figure 5: Same as above: add a mean velocity contour to show the location of the core of the gravity current. In the caption, add info about the grey rectangles which probably mean no data available .
Figure 6: Nice figure! See main comments for more feedback.
Citation: https://doi.org/10.5194/egusphere-2024-2444-RC2 -
AC2: 'Authors response, Reply on RC2', Ole Pinner, 12 Dec 2024
We thank the reviewer for the detailed and constructive assessment of our paper, and are very grateful for the positive feedback regarding the quality of our work. In the following, we will address the main comments as well as some of the specific questions and suggestions. A detailed point-to-point response to all comments will be provided with the revised manuscript.
In the revised text, we aim to better emphasize the scientific significance of our work, especially of our newly developed method for quantifying wave-induced dissipation rates and our contribution to an improved understanding of deep water export from the Weddell Sea.
Main comments:
In the current version, Figure 6 only shows one vertical slice through the gravity current. For the revised version, we will add an additional subfigure to allow for a method comparison as well as a result comparison along the transect. We will also better clarify how the data presented in Figure 6 was computed. The corresponding description in the text will be updated
Applicability of the finestructure parameterization
The finescale parameterization assumes (a) that all observed variability is associated with internal gravity waves and, subsequently, (b) that a stratification exists (N^2/= 0) for internal gravity waves (IGWs) to exist in. The validity of these assumptions is not always given in our study region, and we agree with the reviewer that this needs to be discussed in greater detail. In the revised manuscript, we will address both, the effect of the nearly homogeneous bottom layer (BL) and the applicability of the method in the interfacial layer in the text and mark the regions accordingly in the figures 3, 4, 5 and 6.
The BL is defined as having almost zero stratification, and finescale parameterization is consequently not applicable here. But we observed a maximum height of the BL of around 60m, which is much smaller than the length of 187m of the lowest vertical segment of the finestructure parameterization. Therefore, the BL can affect the results of the bottom-most bins, but does not invalidate them completely. Due to the variability of the BL height, we avoid shifting the bins vertically to keep the segments comparable. In the revised version of the figures, we pla to hatch the bottom-most bins, to communicate their difference from the upper bins.
The question of the applicability of the finestructure parameterization in the interfacial layer (IL) is less clear. The IL likely contains turbulent processes not caused by internal waves. To mitigate their effect, we consider in the integration for strain variance only the resolved length scales associated with waves. The potential case of turbulence from other sources being misidentified as wave-induced will be discussed in more detail.
At our end of the discussion, we see a careful use of the finestructure method in the IL as justified, as long as the caveats are explicitly described.
Uncertainty of the Thorpe scale approach
We looked more into the limitations and resolution of the Thorpe scale. We investigated the measured Thorpe scales by plotting the corresponding histogram and fitting a lognormal distribution to it. As expected from the vertical resolution, the histogram is truncated at O(1m). Although Thorpe scales of few centimeters are physically possible, we expect these missing small scales to only contribute little to the overall turbulence pattern, as we resolve the large majority of the expected Thorpe scales.
The CTD measurements are accurate to 0.0005 °C in temperature and 0.002 g/kg in salinity, which results in a density resolution of similar magnitude of O(10^-3). To check if the depth or density resolution limits our results, we will use the parameter R (Stansfield et al., 2001), a smooth vertical density profile and the fixed vertical resolution of 1m. This results in the minimum value of density resolution, from where it would be the limiting factor, which we can compare to our estimated density resolution value.
To differentiate between physical overturning and noise, a rejection criterion is already used, based on a critical value of the overturn ratio developed in Gargett and Garner, 2008. (doi:10.1175/2008JTECHO541.1). We argue that the additional application of the Galbraith and Kelly test to further describe the limits of the Thorpe scale analysis would exceed the scope of this work. The discussion section of the Thorpe scale method will be extended with the above. We continue our discussion on this topic at the relevant specific comment about the chosen density noise level for the Thorpe scale approach.
Time-dependence of dissipation rates
We share the interest of the reviewer to look into potential temporal changes in the dissipation rates over the years. But mean dissipation rates for each expedition along the transect are not easily comparable, as the expeditions differ in their coverage and resolution of the continental slope. Making sure the resulting time series is as unbiased as possible exceeds the scope of this work. The temporal changes of dissipation rate estimates (longer trends, interannual and seasonal variability) is part of our ongoing work and will be dealt with in a follow-up paper.
Specific comments:
Line 136 Parameters in the Multitaper analysis
On the question if the parameter P=10 in the multitaper method is similar to what is usually applied, one has to consider that the multitaper analysis has 3 parameters which are not necessarily set by the data. The window length N in units of data points, the time-half-bandwidth product P, and the amount of Slepian tapers k. The time-half-bandwidth product is often called NW to reflect its origin as a product of window length N and the half-bandwidth W.
While non-oceanographic literature (Thomson1982, Cokelaer2017) recommend NW values between 2.5 and 4 (with a corresponding choice of 2*NW or 2*NW-1 slepian tapers), the applications to marine data we found use more varied parameter values. LeBoyer2021 et al. use for their multitaper analysis a “window length [...] chosen to be the integer number of inertial periods nearest to 30 days”, together with k=3 slepian tapers. They do not give values for the chosen half-bandwidth or time-half-bandwidth product. If we applied this condition to our measurements, the inertial period at 64° S of 13.33 hours would lead to a window length N of 30 days / 13.33 hours ≈ 54 data points.
Instead, we use a window length of the complete length of the velocity data (N = O(5*10^3), with P=NW=10 and k = 2P-1 = 19 slepian tapers. These parameters are very close to the parameters of a time-half-bandwidth product of 8, with 15 slepian tapers, Chave et al, 2019 use to resolve infragravity waves and tidal frequencies in deep ocean pressure records. The general problem persists that although multitaper is not a trivial method, its defining parameters are regularly not given completely in the main text of published literature and the corresponding research code is not easily accessible. To increase reproducibility without requiring a detailed look into our published research code, we will give all parameters of our multitaper analysis in an additional paragraph in the methods section.
Thorpe scales Line 118, 345-346:
For the computation of the Thorpe scales, we previously used a value for the density noise of 3e-4 kg/m^3. With a density resolution of O(10^-3) (see above), we see this now as slightly too low. We increased it to 5e-4 kg/m^3, but still below the density differences we can accurately resolve. This results in that previously accepted overturns, yielding in low dissipation rates of around 3*10^-10, are now reclassified as spurious and replaced by the background dissipation of 1*10^-10. This especially happens in the open water column towards the east of the transect. The numerical values given in the text are corrected to describe the updated results. The interpretation of the Thorpe scale dissipation rates remains unchanged, as the values change only minimally.
Because the outlier in the dissipation rates from the Thorpe scale approach is measured in depths around 3000m deep in the ocean, it is unlikely that wind forcing could be a physical cause of this. Additionally, profiles from the same expedition do not show segments of dissipation rate this strongly enhanced. The outlier was traced back to a single diagnosed overturn of multiple hundred meter lengths, which was not automatically rejected by the internal quality control in the Thorpe scale algorithm. We removed the large overturn as non-physical, but kept the measurements from the same profile closer to the seafloor. In the text, we will add a sentence documenting the outlier removal.
Energy distribution in vertical modes, Line 315-316:
The fact that higher vertical modes more likely lead to locally dissipated energy, while lower modes are more likely to spatially transport energy is used several times throughout the paper. We supported that in the text by a reference to Falahat et al. 2014. More previous work to this topic is for example summarised in the introduction of de Lavergne, 2019. In short, the distribution of locally available energy among vertical modes is based on time scales of nonlinear interactions. For example, in the often dominant process of parametric subharmonic instability (short PSI), the decay time decreases strongly with vertical mode numbers (Olbers et al., 2020, Fig. 13).
In the revised text, we will reference the assumption we make more extensively by adding the 2 mentioned papers as references, as well as a short explanatory sentence.
WSBW definition Line 323-324:
The definition of Weddell Sea Bottom Water is not completely unanimous, as two established definitions still coexist: as bottom-near water below a certain potential temperature (Foster1976, Orsi1999, Nicholls2009), most recently < -0.7 °C (Vernet2019, Gordon2020), or water of neutral density > 28.40 kg m^-3 (NaveiraGarabato2002b, Meredith2008, Dotto2014, Llanillo2023). We decided to use the newer classification employing neutral density, among other reasons because it automatically excludes very cold surface waters. We will extend the definition of Weddell Sea Bottom Water in the text with a short explanation.
Quantitative Averaging, Line 375-376
The dissipation rate in each region description was previously determined by averaging qualitatively ‘by eye’. For the revised version, we split the transect into 5 regions (shelf, interfacial layer, bottom layer, open ocean, air/no data) and calculate an arithmetic mean for each. Because of the strong horizontal changes (even inside a single region), this reduction to (a maximum of) 4 values each for Thorpe and Finestructure is suited best for a summary at the end of the results sections or for the conclusion. The parameterization based on velocity time series does not have the necessary resolution for meaningful averages in each region.
Waterman et al., 2014, Line 464:
We thank the reviewer for the recommendation of Waterman et al. 2014, which we missed in our literature research. They find for the Southern Ocean that bottom-near dissipation rates, predicted by the finescale parameterization, systematically overestimated microstructure estimations, especially at locations of large near-bottom flow speeds. We will add a paragraph to discuss our results in relation to the findings of Waterman et al.
Citation: https://doi.org/10.5194/egusphere-2024-2444-AC2
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AC2: 'Authors response, Reply on RC2', Ole Pinner, 12 Dec 2024
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EC1: 'Comment on egusphere-2024-2444', Bernadette Sloyan, 03 Dec 2024
Dear Ole and coauthors,
The two reviewers have provided some useful comments on your manuscript. I encourage you to address the reviewers comments and submit a revised manuscript and point-by-point reply to reviewers comments.
Regards
Bernadette
Citation: https://doi.org/10.5194/egusphere-2024-2444-EC1
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Analysis code to: Internal-wave-induced dissipation rates in the Weddell Sea Bottom Water gravity current, (Pinner et al., 2024) Ole Pinner https://doi.org/10.5281/zenodo.13134608
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