This paper reflects the authors’ commendable effort to make available to a broad scientific community a new atlas of mesoscale eddy structures in the global ocean, with a comparison of some salient features with those inferred from another atlas accepted as a good reference on the subject.

The originality of the study lies in the Lagrangian approach chosen for the diagnosis of the coherent structures, with the integration of an impressive number of numerical particles into the geostrophic velocity field that is calculated from the horizontal slopes of the AVISO sea-level product available weekly on a ¼° geographic grid.

The comparison of statistics between the two atlases sheds interesting light on the capabilities of each to account for the global mesoscale ocean activity. This comparison is all the more relevant since the source of data is the same (sea-level topography), and the results differ almost exclusively in the methodological approach for the analysis of the coherent structures (Lagrangian in the present study; Eulerian for the atlas used for comparison).

The article is well constructed, and properly illustrated. It provides useful background information for anyone wishing to work with this new inventory of oceanic mesoscale structures in the future. I find no notable flaws in the achievement of this first objective. Particular care seems to have been taken with the diversity of parameters making it possible to extract partial information from the atlas, for example for the purposes of regional studies.

As the number of atlases of equivalent nature is not high, this one cannot be reproached for being a nth newcomer: by its very availability, this atlas is an asset for the community.

Rather, my main criticisms relate first to some shortcomings in the assumptions used to promote a Lagrangian approach in the constitution of the atlas, and second to the nature of the comparison made with the reference atlas. I believe that the article will gain in quality, and the new atlas will be better understood and used if the authors carefully address the following points.

Major comment #1

The current basis of calculation of the new atlas is the sea-level topography distributed by AVISO. By construction, the eddy structures inventoried are the result of an altimeter afflicted with a form of myopia for the finer scale structures, with a resulting aliasing on the reality of the diameters and movements surveyed for the mesoscale structures. It would be interesting for the authors to discuss in more detail how this myopia affects the Lagrangian analysis they conduct: indeed, instead of having velocities fields sampled at fine spatial and temporal scales, the method has to work with the degradation already acted out in the AVISO product. Despite the use of a Runge-Kutta type numerical scheme, it is certain that some temporal and spatial scales are lost forever, and are not taken into account in the calculated displacements.

Since the authors report some experience with their method when applied to modeled velocity fields (that are able to resolve oceanic variability at finer scales), it would be appropriate to propose a reasoned discussion on the quantification, even coarse, of the errors that result from the application of their Lagrangian diagnosis.

What is missing in this paper is indeed an estimate of the methodological error committed by applying a Lagrangian methodology, which is in essence able to work on a kinematic field of excellent spatiotemporal resolution, on velocity data degraded in time and space. First, based on a fine-scale regional modeling of a fully developed eddy activity, it would be interesting to know the unbiased result of this method for identifying coherent structures and quantifying transport properties. Then, the modeled velocity field could be degraded (keeping only its geostrophic part, sampling it at a coarse weekly scale, extrapolating it on a ¼° geographic grid, etc.) and the identification and quantification conducted again. If such a sensitivity study, or an equivalent, is already present in the bibliography currently associated with the paper, it should be mentioned more explicitly.

Major comment #2

I have serious reservations about the relevance of the estimates of the transport achieved at the global scale by coherent eddies. I understand that the authors wish to rely on calculations previously proposed in the literature, but I am not convinced that the definitions they use properly enlighten us on what this transport is, and help us appreciate thoroughly the differences between the two atlases.

Let’s just focus on the use of the propagation velocity of an individual eddy, in the calculation of transport through the sections constituted by the meshes of a geographical grid of 1° resolution in latitude and longitude. With the adopted definition, two structures with identical geometric properties (same surfaces, same vertical extensions, therefore same volumes of water) will not contribute equally to the transport analysis if their mean propagation speeds (or longevities) differ. What are the physical implications of this definition? Can we agree that what truly matters is that a given volume of water (expressed in m3) is fully transmitted through a control section? Whether the transmission occurs in hours or weeks does not change the fact that the same volume transport must be inventoried at the longitude or latitude of control. Yet, in its current format and in my understanding, the definition implies that a faster or longer-lived eddy contributes more efficiently to local volume transport. If the authors intend to work with such a definition, meticulous care must be taken in presenting the meaning and utility, and in interpreting the calculated quantity.

Other specific comments

L21-22.

The introduction could give some elements justifying the relevance of a better knowledge of mesoscale oceanic eddies also for the study of marine ecosystems.

L34-35

Even with the availability of continuous images of flow fields, an Eulerian, accurate identification of eddy centers and boundaries may remain a challenge due to the complexity of interlocking dynamical scales.

L55-56

Observational studies are now focusing on exchanges along the vertical of an eddy structure, without being limited to interactions between the center of the eddy and its periphery.

L98-99

This is an important limitation of the identification, although legitimate for a global atlas. However, the paper should remind us that true oceanic eddies are not circular, may have subsurface properties more pronounced than their surface signature, have a complex organization along the vertical, may not be in solid-body rotation, are sensitive to ageostrophic motions, etc.

L108-109

The applied correction results in closed contours for trajectories within coherent structures considered as stationary. Again, the counterpart of the assumption is the omission of the vertical dynamics that exist within oceanic eddies. This point should be emphasized in the text.

L115-116

This intensive seeding strategy requires discussion in light of the temporal and spatial scales already lost in the sea-level product distributed by AVISO (see main comment #1 above).

L130-131

More care could be given to the justification of a monthly sampling of the initial positions chosen extremely loosely compared to the spatial sampling. What relationships link the two samplings, and how can these relationships be used to optimize the number of particle trajectories to be integrated?

L138-139

It should be reminded here that the coherent structures studied are, by construction of the method, idealized two-dimensional eddies.

L168-169

One may regret the empiricism of the choice of this combination of parameters. Chelton was often criticized for having too many control parameters in his eddy identification method. In the interest of fairness, this new paper could present a summary of all the adjustable parameters used for the derivation of a new eddy atlas.

Figure 5

Avoid the use of longitudes larger than 180° (please express them in °W). In the caption, the notion of subtitle more likely refers to the title of each panel.

L221-222

At the time of my review, the web page provided for the AVISO product unfortunately does not exist...

L270

Pointing out that the vertical structure of eddies is far from known and understood is a useful reminder, but should echo equivalent information to be discussed in the body of the introduction.

L280 and following lines, and possibly some parts of the conclusion

These passages should be carefully reconsidered once the definition of eddy transport has been unambiguously established (see main comment #2 above).

The Authors present a new global Lagrangian eddy dataset (GLED) containing information about various parameters like size, position, rotation, and lifetime of these coherent structures as well as trajectory data of numerical particles trapped inside these eddies. All quantitative information present in this database comes from massive numerical simulations of Lagrangian trajectories integrated from satellite-derived ocean surface current fields, covering a period of almost three decades.

I appreciate the remarkable effort made by the Authors to carry out a so challenging task although, personally, I have some doubts about the robustness of the results, for the reasons I will try to explain.

The “Lagrangian” eddy database, introduced in this work, is discussed by the Authors in comparison to pre-existing “Eulerian” eddy datasets, and the main differences between the two approaches are described with arguments that I agree with.

-Line 7 (Abstract): “… but also the trajectories of particles…”

Personally, I do not like to consider Lagrangian trajectory simulations a “product” to store in a database as happens for other kinds of data, e.g., real ocean drifter trajectories or ocean current fields. One reason is that Lagrangian trajectories are sensitive to initial conditions and to the resolution of the velocity fields.  But we will come back to this point later.    

-Lines 112-122 (Particle advection): “The first step… they never move.”

Since 2D geostrophic velocity fields are considered, because of the nature of the Eulerian data, all results relate to large scale advection on the ocean surface, and any extrapolation to smaller scales and/or to sub-surface ocean layers must be treated with caution.

A particle spacing of 1/32° is claimed to be necessary for a good resolution of the RCLVs but it should be stressed that this does not mean to improve the resolution of the dynamics but only the definition of the large-scale features of the flow (>> 1/4°).

-Lines 138-184 (Lagrangian eddy identification): “For a coherent eddy … based on satellite observations.”

The definition of LAVD fields and RCLV boundaries is supported by common sense arguments, but not much is said about the sensitivity of this eddy identification technique to the resolution of the velocity fields. For example, since the CI coefficient depends on the mean local particle separation, after a given time interval, it must be expected that, if the small scale velocity components, or part of them by means of sub grid parameterization techniques, were included in the trajectory evolution equations, the relative separation speed  between particles would increase due to the general growth of the (Lagrangian) Lyapunov exponent with the smallest resolved scale.

Looking at figure 3, I wonder if the Authors have tried to make, at least, a qualitative comparison between a simulated coherent structure evolution and the behavior of a real ocean drifter, initially “trapped” inside the eddy. The Authors do not provide information about the accuracy of their Lagrangian trajectory simulations, but I think this problem should be at least mentioned in the text.

-Lines 219-260 (General features of global coherent eddies) “To assess GLED … along the eastern boundary”

 Briefly, I find that all the differences between “Eulerian” and “Lagrangian” approach to eddy detection, here discussed, are plausible. Incidentally, there are many examples of kinematic velocity fields made of quasi stationary eddies advecting chaotic Lagrangian trajectories. So that, if the Eulerian field is analyzed, one finds out the existence of long-living coherent structures (i.e. with infinitely long Eulerian autocorrelation times) but with zero mean transport; on the other hand, the Lagrangian trajectories consist of aperiodic open pathways across the eddies and large-scale particle transport is due to chaotic diffusion. 

 -Lines 261-288 (Global mass transport by coherent eddies) “One application … live that long.”

Given that the 3D eddy structure is unknown, does it make sense to give quantitative information about the mass transport?  Is the depth factor arbitrary or is there an argument to justify its value? Moreover, the eddy lifetime d in formula (4) could be seriously overrated with respect to the real ocean, for the reasons previously mentioned.

-Lines 308-310 “To the best of … from physics to biology”

-Lines 330-333 “Although we have produced … studying mesoscale eddies.”

Personally, I find the presumed impact of this type of databases to the research activity of others is a bit overstated. While the existence of eddies is out of question, it is worth stressing that the assessment of the accuracy of the numerical simulations in reproducing the actual Lagrangian properties of real ocean tracers is a big open issue.

-Lines 334-338 “One limitation … available”

While waiting for the next oceanographic missions, to update the database, I would suggest also to consider a Lagrangian validation of the numerical trajectory dataset (see, for example, Lacorata et al., 2019, FSLE analysis and validation of Lagrangian simulations based on satellite derived GlobCurrent velocity data, Remote Sensing of the Environment). Nobody expects the simulations to perfectly agree with the observations, but it is important to outline the limits of accuracy prior to any kind of application. I think that this could be an interesting information to potential end users of the product.