Janosi et al. apply their proxy-vortex method in diagnosing the effective eddy radius and westward propagation of mesoscale eddies globally. It has been know for some time that mesoscale eddies in the real ocean are larger than the Rossby deformation radius. However, what substitutes the Rossby radius as a better metric for describing their size has been a subject of debate. Their method of estimating the effective eddy radii will be a good addition to this debate and I recommend their manuscript for publication with only minor comments listed below.

• Sections 2.3 and 3.1: It would be interesting to have a physics-based discussion on why one would expect a temporal correlation between the area-integrated eddy kinetic energy and enstrophy;
• Equations 6 and 8: The notation of the mean of I_EKE and I_Z are denoted with an overbar while the temporal mean of the nominator is in angle brackets. I would suggest unifying the notation one way or the other for representing the mean;
• Line 243: In the later -> latter;
• Lines 322-323: The notation E_ec is EKE_ec in Figure 6. Please unify the notation.

The paper presents a reasonable method for analyzing mesoscale eddies. It is based on an observed correlation between the enstrophy and kinetic energy and assumes that eddies have a Gaussian profile. The paper presents application of these ideas to global AVISO data. I am generally favorable of the work but have a few comments and questions that I hope the authors can address.

1. In the abstract, please consider replacing "super vortex proxy" with "vortex proxy." As you mention in the text, the word "super" may be an overstatement.
2. In Fig. 1, it is unclear from the caption if the quantity being visualized in (b) is |v_g-v'_g|^2 or |v_g|^2-|v'_g|^2 . Please be more explicit.
3. On line 74, you compare the results to the dataset of Faghmous (2015). Is there a reason? Have you considered also using Chelton et al dataset? Can you please comment in the paper? Would doing so constitute too much additional work?
4. In eqs. 1,2,3,4, do you use absolute or anomalous values? I suspect you are using SLA, but it is confusing when you use v'_g to represent anomalies in Fig. 1 and v_g (sometimes v, without subscript) to represent the same thing in the text and equations.
5. In eq. 5, you essentially define R_eff as the ratio of the EKE to Z. But in eq. 2, R is a parameter representing the radius of the eddy. Can you please comment on the relation between R_eff and R?
6. Line 122, the word "inevitable" is perhaps better replaced with another word? I could not understand the sentence.