The authors of this manuscript should conduct a more comprehensive review of the extant literature on material frame-indifferent (i.e., objective) coherent vortex detection. The manuscript contains several inaccurate or unsubstantiated statements, including the following:

1) 'Flierl (1981) showed that when the tangential velocity of the vortex is higher than its translational velocity, fluid particles are trapped in the vortex core.' This claim is more an expression of belief rather than a rigorous conclusion, as velocity is dependent on the observer.

2) 'In particular, MC theory ignores the fact that water masses at the edge of eddies can change their properties due to various types of instabilities.' This statement is incorrect because, if a vortex is characterized as materially coherent, no fluid can traverse its boundary. More precisely, no material surface can be intersected by fluid flow since it is flow-invariant, regardless of its coherence.

3) 'Furthermore, MC theory is based only on fluid flow and does not consider the potential permeability of the eddy boundary due to diffusion processes or lateral intrusion (Joyce, 1977, 1984; Ruddick et al., 2010).' This is inaccurate since the boundaries of geodesically-detected coherent material vortices serve as minimizers of diffusion (refer to the Annual Review of Fluid Mechanics paper by Haller).

4) 'We revisited coherence definitions and checked data accuracy.'  This manuscript does not encompass an examination of coherent material vortex framing. Indeed, the manuscript lacks any explicit articulation or statement concerning this subject matter.

5) 'Comparing the horizontal positions of these core anomalies with eddy surface signatures revealed that surface data alone are insufficient for characterizing the eddy material coherence.' This is plausible, but to assess it, time-dependent flow data must be analyzed using an objective method.

Beyond these imprecise statements, the TC criterion remains nebulous and can only be regarded as qualitative in nature; temporal flow data are imperative to establish coherence. All criteria (gradients; potential vorticity — an observer-dependent quantity; pythagorean arguments) are applied to instantaneous snapshots of observed mass fields. A temporal history is requisite to ascertain if the 'gradient of a property of some kind' is conserved under advection by the flow. It is evident that transect data are unsuitable for this type of analysis.

In conclusion, I am unable to endorse the publication of this manuscript. I acknowledge the significant effort expended by the author in analyzing in-situ oceanographic campaign data, which holds intrinsic value. However, I urge the author to consider presenting their analysis within an alternative context, as the current application towards assessing material coherence is not appropriate for the available data.

Please see attached supplement.

This manuscript details the analysis of in situ float data along with CTD sections to asses how eddies transport material.  This work represents a valuable contribution to the study of eddy dynamics and can be strengthened by the addition of specific derivations to go along w the text.  My suggestion is that the authors consider my comments and maybe add some proofs that the methods of defining material coherence are similar or different.  If this is addressed it is my opinion that this paper be published.

My recommendation is to back up the arguments made in to the introduction.  The authors compare multiple methods to estimate eddy transport and do so only describing similarities and differences.  This section needs to be analytical and needs to show mathematically what is described in the text.  At the present it is not sufficient to just say two methods are the same or different with out showing it.

As to the analysis and results, I find them truly interesting and am excited to have them become part of the literature.  The strengthening of the introduction in my opinion would make this a very valuable paper.