the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 08 May 2026
Estimating cross-stream isopycnal eddy diffusivity from mooring observations
Abstract. We present a method to derive distributions of cross-stream isopycnal eddy diffusivities in the Antarctic Circumpolar Current (ACC) from data measured by a mooring. This method transforms the time series measured by the mooring to spatial (cross-stream) distributions using dynamic height as the cross-stream coordinate. For this transformation, the relation between dynamic height and cross-stream location must be inferred from a spatial data set, such as hydrographic section measurements or reanalysis data along a transect through the mooring. From the distribution of temperature as a function of neutral density and cross-stream distance, the isopycnal temperature properties and fluctuations can be determined, and a mixing length and eddy diffusivity can be inferred. We apply this method to a mooring in Drake Passage and compare the resulting distributions with those derived from hydrographic section data. The mooring and section data yield very similar distributions of the mean isopycnal temperature field as well as the root mean square (rms) temperature fluctuations along isopycnals, which provide a metric of isopycnal stirring. The mooring-derived eddy diffusivity distributions capture some key features predicted by kinematic theories: reduced diffusivities at the Sub-Antarctic Front jet and increased diffusivities at mid-depths, both in line with mean flow suppression theory. The results presented here show that the methodology can be a valuable tool to study cross-stream isopycnal mixing properties from mooring data, especially in equivalent-barotropic systems and for moorings with a high vertical resolution.
Competing interests: At least one of the (co-)authors is a member of the editorial board of Ocean Science.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors. Views expressed in the text are those of the authors and do not necessarily reflect the views of the publisher.- Preprint
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Status: final response (author comments only)
- RC1: 'Comment on egusphere-2026-2566', Anonymous Referee #1, 21 Jul 2026
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RC2: 'Comment on egusphere-2026-2566', Anonymous Referee #2, 02 Sep 2026
The authors present an observational framework that transforms mooring time series into spatial, cross-stream distributions, which are used to estimate isopycnal eddy diffusivity from mixing lengths in the Antarctic Circumpolar Current. Overall this work is interesting and very relevant to property distributions in the Southern Ocean. My main reservation is technical and related to the assumptions of the mixing length method. An ad hoc cutoff is used, which seems inadequate or at the very least needs some more justification. A second reservation is that the length scales measured in the various datasets is not clear and these length scales will affect gradients. Lastly, there are a few comments to improve presentation, which is for the authors to consider rather than a requirement. These suggestions include: reducing subplots and plotting in density coordinates. Overall, it is an excellent start and with a little more work this manuscript will be a solid contribution.
Major comments:
1. Do the assumptions required for the mixing length method hold? Are eddies doing most of the mixing? Is no variance advected from upstream? Does the background vary slowly over the mixing length?
Maybe some of the data are obtained in the mixed layer, in which case the mixing is not due to eddies. The mixed layer should be excluded from the calculations. Argo could be used to examine the advection of tracer variance in the area- maybe this is already in Cole et al (2015) or Roach et al (2018). If the mixing length is 1000 km and the section is only 200 km over which we see isopycnal shoaling, then the mixing length is probably not valid because the background is changing over 200 km. More explanation is needed to show how the data over a limited range can support much larger mixing lengths.
2. In the same vein, about 2/3 of the data for section SR1b is below the cutoff (Fig 7a) and so it’s not clear how useful these data are. Argo seems better but certain depth ranges near 1500 m and 3000 m seem unviable too (Fig 7b, c).
So is this a problem with the low gradient cutoff? Or is it a more serious problem with the method? Maybe it’s not possible to convert time variability to spatial variability because the assumptions of the mixing length method do not hold here.
The Argo climatology is objectively mapped using certain time and length scales. How do these compare to section SR1b. The differences in their methods of making a gridded dataset will make a difference in the gradients used here. These should be explicitly mentioned somewhere,
Could some of these problems be mitigated with coarser binning in density and coarser binning in space? Then there are more data points per bin. Or would finer binning in density help in converting depth to density and vice versa?
3. Why does Fig 7 only extend south of the mooring? Are there no streamline displacements to the north?
4. To make the manuscript more concise, I think some of the comparisons to the various data/climatologies could be moved to supporting info and the number of virtually identical subplots in a figure could be reduced. Much of what is the appendices could also go in supporting info.
These various datasets strongly support the main point but are not essential to understanding it. Having these multiple additional subplots in the figures in the main text is an extra burden on a reader. A similar argument is on lines 260-266.
So maybe just chose your favorite conversion.
Continuing in the same vein, there are places where all the various subplots are described, such as Section 5.2. The description is all valid but the main idea is maybe a bit lost in all the descriptions here and elsewhere. I believe the main point is on lines 10-13: “The mooring-derived eddy diffusivity distributions capture some key features predicted by kinematic theories: reduced diffusivities at the Sub-Antarctic Front jet and increased diffusivities at mid-depths, both in line with mean flow suppression theory.” It should be clear in each sub-/section how that section contributes to this main point.
5. All of the figures are presented as lat vs depth. I wonder if you should not convert to depth and just use lat vs density. The isopycnals are tilted and so averaging in density coordinates makes more sense, as you have done except not in the figures. What do the mean profiles (averaged in the y direction) look like in density coordinates? It may aid your interpretation and more easily accommodate error bars. This is a suggestion not a requirement.
6. Typical values of diffusivity at scales of 100 km are of order 100 m^2/s from Okubo (1971). With results 10-100x that in Fig 9 from your estimates and those by others, it’s worth some explanation.
Comments by line number:
36 - how big is the deformation radius?
40 - how big is the diffusivity? Later in the manuscript values are much bigger than expected for open ocean from Okubo (1971). Please explain why the mixing here is much bigger.
65 - what is the value of gamma? how do you obtain it? It’s mentioned later in the manuscript but could go here.
76 - do these assumptions hold? “the gradient does not vary significantly over the mixing length (i.e. there is a scale separation between the eddy and mean flow scales) and that the temperature fluctuations are generated locally, not transported in from regions upstream.” Also the background gradient should be uniform over the mixing length.
110 - while applicable to the ACC and its equivalent barotropic current, maybe it is worth pointing out that this will not work in other places. Or that another variable can be used to make the cross-stream coordinate, which you mention later
121 - some numbers here would help here as would some idea of how how variable this adjustment is
Fig 1 - we just need the location of C and so could omit the inset
168 - Cole et al (2015) is a similar method. You should compare to that dataset too. Roach et al (2018) made a comparison and found the magnitude was different but the spatial variability was similar. Roach’s diffusivity data are available online too. They have spatial coverage and could show how representative your location is of a wider area.
212 - smoothing factor is not explained. This is an important detail since you are converting temporal variability to spatial variability.
233 - can you convert these minimum gradient to maximum distances? How do these max distances compare to length/time scales in your observations? Since your results for K are big, does this suggest a larger minimum gradient?
241- How about a figure of U_e? Fig B4a could go in the paper or at least be referenced.
255 - I prefer the topic sentence of a paragraph like: “the four different data sets used to transform the mooring profiles to spatial coordinates using the fit..” instead of “Fig 5 shows something” as you have it now. This is a matter of style and so up to you, Similarly line 284 and likely elsewhere in the manuscript.
Fig 6b, c - These seem very similar and so one could be moved to the appendix or even supporting material.
Fig 7- align color map with the limit. eg, Fig 7c has a lot of dark blue but only some of it is excluded. Hard to tell if the stripes extend over the whole region of drak blue. Maybe use dots instead or just blank out the “bad” data with the colormap
273 - AAIW?
294 - “From the hydrographic properties presented in the previous sections, we can derive the mixing length from equation (3)” (Figure 7g–i).
There are numerous statements like ”This is shown in Figure 7”- just put the figure reference in brackets. It’s more concise.
301 - Large mixing lengths in regions of low gradient. Does this result suggest a problem with the low gradient cutoff or even the method?
302 - delete “can” and add equation reference
307 - any thoughts on why the fronts don’t correspond to high U_e?
Fig 9 - The other methods in Fig 9c, d look like you could make a mean profile. They do not vary much by latitude. You could try making mean profiles for your results in Fig 9a, b. And then give some thought about error bars. Overall the Argo and SR1b results look pretty similar. Error bars can help determine if the differences are significant. Making the mean profiles in density coordinates is probably best. You could make a few mean profiles- one at the PF, one at the SAF, and one in the north or something similar. Your results are a bit patchy when plotted as lat vs depth. Making mean profiles provides more averaging which may help.
342 - “Differences in the isopycnal gradients.” Gradients depend on the scale they are evaluated on. The Argo section and the hydrographic section are constructed differently. It would be good to be explicit about what scales they measure. Daily mooring values in 1 m/s current are 86 km scales for example. The hydrographic section may have 30 profiles per 10 degrees and so has 30 km scales but then is averaged over many years. So the equivalent length scale is no doubt much bigger than 30 km but what is it? Argo has a grid resolution is 1 degree, but the data have been objectively mapped in space and time. Even if a model has finer resolution, numerical diffusion and averaging of the results affects the resolved spatial scales. There are several places whee high spatial or temporal resolution is noted. Instead just quote the actual number. The best comparison would be using the same spatial scale for all the data- models, hydrographic section, Argo, and mooring. If that is not feasible, then stating the actual scales they are measuring would be second best.
345 - “On the other hand, numerical inaccuracies and sensitivity of the spline fits may play a role.” Numerical inaccuracy is probably not the problem. Spline fits maybe are an explanation, but 3 of the 4 seem pretty close. Maybe plotting d(dyn ht)/dy might show where the conversion is going to be the most sensitive.
412 - the gradient cutoff is indeed a problem. It cuts off a lot of data as noted earlier and it is ad hoc. I suspect the resulting mixing lengths are very sensitive to the gradient as you approach 0. Some further careful consideration/justification of this value is in order.
414 - it should be verified somehow that the assumptions for the mixing length are valid.
426 - don’t -> do not
430 - while the averaging period may matter, it may not. Eddy transport might be pretty steady averaged over a year. However, gradients calculated over 1 km or 100 km will be very different. Differing spatial scales may be affecting the various calculations and comparisons.
Citation: https://doi.org/10.5194/egusphere-2026-2566-RC2
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“Estimating cross-stream isopycnal eddy diffusivity from mooring observations” by Miriam F. Sterl et al.
This manuscript is a very clever new innovation that yields estimates of epineutral diffusivities. It certainly deserves to be published.
The paper extends the work of Naveira Garabato et al. (2011) [which used data from ocean sections] to apply to data from a single ocean mooring. It relies on situations where the flow is close to being “equivalent barotropic”.
To be picky, I note that IOC, SCOR and IAPSO, as well as all the main oceanographic journals (JPO, Deep-Sea Research etc) say the Absolute Salinity and Conservative Temperature should have upper case letters. This is because, for example, there are 5 different contenders that could be called absolute salinity, and Absolute Salinity indicates that you are talking about the one that TEOS-10 is based on.