Investigating the Formation of Submesoscale Structures along Mesoscale Fronts and Estimating Kinematic Quantities Using Lagrangian Drifters

Round 1

Reviewer 1 Report

The authors utilise X-band radar, ship based hydrographic measurements, drifter and remote sensing data deployed in two campaigns in the Gulf of Mexico (LASER programme) and the western Mediterranean (CALYPSO programme) to qualitatively and quantitatively characterise and contrast the sub-mesoscale dynamics (e.g. eddies and filaments) in each region.

A variant of the statistical technique (GPR), reported elsewhere in the refereed literature, is utilised to analyse the drogue drifter trajectories. My questions on this technique are:

1. In eqn. (5) the covariance function is the sum of two exponential functions. Why two? Almost certainly because the more hyperparameters you introduce the more difficult it will be to assign values to them.
2. Do the spatial and temporal hyperparameters relate to the dynamics of the ocean circulation? This is not rigorously addressed in this study. Why not collaborate with an OGCM modeller to conduct controlled numerical experiments with the statistical method, where the spatial and temporal scales of the flow are known? As it stands, the relevance of the hyperparameters to flow dynamics is left in doubt.
3. Define ALL symbols - P and N in (1) and (2), respectively. 
4. Lines 506 and 507; can you not remove the background (mean) flow to better reveal the eddy?
5. One has to use a degree of imagination to see the eddy in Fig15 and the reported upwelling at its base? It is debatable whether an eddy is present in the density field, for example.
6. The results in Fig 12 are of limited use as the algorithm produces acceptable fields in small disjoint regions. More generally, the authors speak in the most general terms about the origins of the sub-mesoscale dynamics shedding no insights about the instability mechanisms operating within the front. The study would be more substantial if the authors collaborated with OGCM modellers who could provide insight into the dynamics at play.
7. In section 3.4 I contend that the drifters in Fig 3 converge on a front with distinct curvature. Rather than treating this front as locally linear you could use curvilinear coordinates to more accurately capture the frontal dynamics.
8. The regions where fields of divergence and relative vorticity are produced by the GPR method are extremely limited. They are centred on the front and this calls into question how well you can estimate the cross-frontal spatial derivative.
9.  What has this study told me about the sub-mesoscale dynamics of the Alboran Gyre? We obtain snapshots of the dynamics in limited spatial domains. However, there is no advance in understanding the generation, evolution and dissipation of the sub-mesoscale dynamics. The other concern I have is that a great deal of a priori knowledge about the mesoscale and sub-mesoscale dynamics of the region of interest is required to implement the variants of the GPR method discussed in this paper
10. Line 570 states convergence along the front is apparent in Fig 16. It is visible but given the highly elongated domain, how reliable is this result?
11. Lines 585-586; discussion of Fig 17 in terms of filaments is not convincing.
12. I think Section 4 can be shortened as it contains a lot of what has already been noted earlier. A discussion about the relationship (tenuous) between the calculated hyperparameter values and dynamical length and time scales of the ocean dynamics is required. Note the reference to baroclinic instability on page 38 and its role on the drifter trajectories is speculation. There is a rigorous theoretical framework to test whether a vertically sheared flow is baroclinically unstable in the linear regime.
13. Line 233; is the same equation of state used to calculate density in both field campaigns?
14. Consecutive sentences on lines 395 and 396 begin "In comparison..."
15. Typos; line 188 "tested"; line 772 "extends"
16. I do not think it is insightful to refer to K-H instability as an analogue to the instabilities that operate at an ocean front. 

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Reviewer 2 Report

This manuscript develops and tests four different methods of deriving horizontal velocities from drifters in convergent front and eddy zones. Then, the authors applied the methods in three different flow regimes, i.e., the unstable mesoscale front in the Gulf of Mexico, the subsequent submesoscale eddy of the front and the relatively stable mesoscale eddy front in the Mediterranean. They calculated the divergence and the vorticity from the derived horizontal velocities and compare the dynamics process in three different situations. Basically, the manuscript is quite technical in the methods, and less dynamics in phenoma analysis. Here are some suggestions for further improvements.

• The calculated divergence and the vorticity depend on the velocity shear not the velocity itself. Thus, the spatial distribution of the differences between the x-band velocities and the derived velocities are necessary. As shown in Figures 8 and 9, thought the RMSD between the two velocities are smaller, the direct differences reaches -0.1 and 0.2 m s^-1, which might induce horizontal velocity error to 0.3 m s^-1 and then large error in shear. Furthermore, the accuracy of the x-band velocities is important but not shown in the manuscript.  
• The authors emphasize the importance of the vertical motion of the submesoscale processes. However, there is no quantitative results of the vertical velocity in the manuscript. The relation between the vertical velocity wand the divergence δ and the vorticity ζ need to be clarified.
• It would be better to add more dynamic analysis instead of qualitative description for the comparison of three flow regimes. 

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Reviewer 3 Report

This long, technical and ambitious paper describes methodology for calculating Eulerian velocity fields from surface drifter trajectories and applies the method to groups of drifter trajectories released near frontal features in the Gulf of Mexico and the western Mediterranean. A general objective is to compare and contrast processes including frontogenesis, subduction, instability, and submesoscale processes in general.  To test the methodology, data from X-band radar velocity fields from the Gulf of Mexico region were compared with four different versions of the Gaussian Process Regression method (GPR) used to calculate the Eulerian velocity fields.  Surface convergence and vorticity were calculated from the derived velocity fields and the results considered along said hydrographic sections across the fronts that were made during the experiment. Overall the authors have undertaken an difficult application because of the rapid convergence and shearing that occurs near a front causes the drifters to become aligned and separated.  This means that the area over which a reliable conversion to Eulerian velocities shrinks and becomes patchy as time progresses.  Although I do not understand all of the technical aspects of the GPR technique (and leave that to other reviewers), I do believe that the authors have been very careful in their analysis, and straightforward in their descriptions of the advantages and limitations of the approach. Some of the dynamical interpretations are speculative and accompanied by terms like “seem” and “appear” to, but this is mostly due to the lack of the kind of 3D picture that one would get from a model.  The contrast between the Gulf of Mexico features, which exhibit strong sub-mesoscale characteristics, and the WAG front, which is more strongly influenced by mesoscale dynamics, is interesting.  I recommend publication with just a few modifications:

Line 198. “testes”

Fig. 2 caption. I can’t tell from the caption what are the start point, what are the end points, and what the green and magenta dots indicate. (The caption just refers to the fixed dots as drifters.) Same remark for Fig. 3.

Line 249.  If I understand this correctly, you are compiling individual velocity measurements from the drifters as a group, and throwing away information about individual trajectories. I wonder if there is a way of somehow including this info and whether it would make much of a difference.

Line 409.  The meaning of “entirely constrained” is not clear. So you mean that mixing only occurs on the cold side.

Figure 17 shows hydgrography that is consistent with the southward movement and subduction of a patch of cool, salty water into the WAG. This is consistent with pictures of turnstile lobes produced in a model by Brett et al. (JPO, submitted).

Eq. 1.  The operators “script_G and script_P” are not defined. Same remark for “script_N” in (3)

Line 772 “extents”

Line 814:  more non-divergent = less divergent ?

 

 

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Round 2

Reviewer 1 Report

What are the relative merits of the GPR method compared with the Principle Component analysis technique? The readers of this paper could be interested in the answer to this question.

The authors of this paper have done a decent job in addressing my questions and comments about the original version of the manuscript. I still come away from this study feeling that there is a degree of "artistic licence" in the experimental design of the GPR method.

I recommend that the revised version of this manuscript is published in "Fluids".

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Reviewer 2 Report

The authors have improved the manuscript according to the previous comments. I still have concern on the vertical velocity which is derived with the conitinuty equation and has quite large values on order of 0.01 ms^-1.  

(1) The calculation of the vertical velocity is ambiguous. How is the divergence of horizontal velocity below the surface is calcualte? As I unstander, the x-band radar can only observe the surface velocities. Furthmore, the horzionalt varaition of the vertical velocity is not given. Maybe the value in Table 4 is the average of each case.

(2) The diagnose of vertical velocity from observations is quite a state-of-art technology. As shown in previous stuides, Omega equation is generally used instead of continuty equation. Here, the error should be discussed. 

 

 

 

 

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