The study is novel and could be worth publication after minor-to-major revisions.

General comments:

The presentation of the major findings and results as associated with the key figures should be more adequately outlined and addressed. Now it often appears too brief as it rushes from one figure and relative short explanation and discussion to the next. This should be improved.

Does the choice of the 1.5 layer QG model impact the results in any way? In other words, are there other modes than the first baroclinic mode that might be influecing the dynamics and variability in the greater Agulhas Current region? Is it possible to find discussion of this in the literature?  Need some more consideration.

Line 210  comments on the Agulhas Current area and claim that it is characterized by weak advection of the frontal structures. However, in view of the area (Figure 9) the presence of Natal pulses can propagate southwestward on the nearshore side of the Agulhas Current core while  highly rich and complicated dynamics occur in the retroflection area where eddies are often shed and also sometimes reintegrated into the retroflection. These areas are characterized by advection and sometimes rapid occurrances and closing of frontal structures. So the statement must be refined to better balance these conditions.

In Figure 10: The black line in the 3 panels seems to be contours of the land-ocean boundary. Must be explained. A bit strange to see values within boxes that are completely inland.

In the discussion and conclusion it would be worthwhile to comment on possible use of SWOT and Sentinel-1 image data to further strengthen this study approach.

Specific editorial comments:

The submitted paper is attached with red-markings suggesting update of the text.

Additional edisotrial comments:

Agulhas Current should always be with captial C.

Be consistent in use of reference to figures (Fig., Figure, figure, I prefer Figure).

Equation 10: The expressions in the exponent should have larger font. Difficult to see properly.

The space scale symbol D (in equation 10) must for consistency also be used in Table 1 (nudging space scale ).

This paper considers a technique for obtaining geostrophic circulation from SSH maps (BFN-QG) and applies it to real altimetric SSH data. This method is compared to another method (DUACS) and shown to improve the mapping of short energetic mesoscale structures, producing finer scale coherent structures. While the method improves the mapping of smaller scale high energy structures where there is high variability, it does not perform well for larger structures when the variability is low. Overall this paper is scientifically sound, well written and merits publication in this journal. I have not found any major issues with the paper, and believe it is almost ready for publication, but below I list a couple of minor points that should be taken onboard before final submission.

Minor comments:

page 3 - equation (4): The authors might consider using a different symbol for SSH when applying it in the mathematical formulas, for example maybe using H for SSH, and then make subscripts for when referring to the MDT and SLA part, like H_{MDT}, H_{SLA}.

page 4 - equations (7a) and (7b): You have switched the symbol for the Coriolis parameter from f to f_0. I presume we are considering the f-plane here, i.e. f=constant, this should be stated in the text.

page 7 - table 1: Typo - nudging space scale should be denoted as D instead of tau which is used for time scale.

page 7 - equation 11: confusing use of the square brackets containing the letter i, would be better to apply i as a subscript, i.e. SLA_i, and then have brackets all around the delta SLA term, then apply square, i.e. [\Delta SLA_i]^2.

page 11 - equation for flow crossing: This equation is not well defined, what is v[P_i] (presumably the velocity vector) and what is the angled symbol on the RHS inside the cosine term, even if referenced the equation variables needs to be defined here.