The paper takes a thoughtful approach to assess a collection of Geothermal Heat Flux (GHF) using two sets of radar sounding observations: the detection of subglacial lakes and bed echo specularity content.  The authors rightly point out that “one-sided” tests using either observable will result in the selection of the highest GHF values.  The authors are thoughtful about where they do and do not apply the specularity content in terms of upstream and downstream portions of the catchment.  The authors are also thoughtful about the difference between how the lakes and specularity observations are used in terms of “one-sided” vs. “two-sided” constraint.  However, the authors seem to view the choice as either a “one-sided” approach that only evaluates if the lakes/high-specularity correspond to thawed areas or a “two-sided” approach in which that comparison is combined with evaluation of “no lake”/low-specularity correspond to cold areas.  However, it seems like there’s another option. To “reward” the match between lakes/high-specularity and thawed areas as in the “one-sided” and then to “penalize” a mismatch between lakes/high-specularity and cold areas.  This seems like more than the “one-sided” approach and like it might not be vulnerable to the same preference for the highest meld as the pure “one-sided” approach.  However, it also seems like it has the benefit of applying to both lakes and specularity.   It has the additional benefit of allowing the specularity to be used in all regions of the catchment.  This seems additionally important because, just as the authors describe for lakes, it’s not the case that low-specularity areas have to correspond to cold areas, it can correspond to thawed areas where water is not pooled in sufficient quantities to be specular and/or form a lake.  As a result, this intermediate between “one-sided” and “two-sided” metrics could apply to both observables. 

Dear Authors, dear Editor,

 

At this stage, the manuscript needs some major edits.

The main goal of the manuscript is to evaluate GHF data sets in the Totten region using specularity results. The idea and the novelty of the method in this region are laudable and of interest, as from one data set to another, GHF values vary a lot. However, a more detailed review of the literature, statistical work, .... are needed to ascertain what the authors suggest at the moment. In addition, the whole manuscript requires technical revision work (disjointed paragraphs, figures, figures captions, ... ). There are key GHF data sets that are missing from your analysis and the seminal reference of Burton-Johnson on Review article: Geothermal heat flow in Antarctica: current and future directions https://tc.copernicus.org/articles/14/3843/2020/ is not referenced.

I would therefore suggest the following actions (general comments):

1) Describe and use all available datasets published, especially since your aim is to do a ranking of the various datasets. Doing so would add great value to your paper, especially since the missing two datasets are quite recent. However, the idea of doing a ranking of the GHF data set is also tricky in my opinion, as it depends strongly on the model resolution, the ranking parameters chosen, .... For example in your paper, you mention that the Shen et al, 2020 data set is "the best", while we can clearly see that the Martos et al, 2017 data set matches well for "warm conditions". Also, the grid resolution of all these data sets are critical in your analyses and in consequence they have to be at least listed in table 2.

The key references for the missing GHF data sets are : 1) Haeger, Carina, A. G. Petrunin, and M. K. Kaban. "Geothermal heat flow and thermal structure of the Antarctic lithosphere." Geochemistry, Geophysics, Geosystems 23.10 (2022): e2022GC010501. 2) Lösing, Mareen, and J. Ebbing. "Predicting geothermal heat flow in Antarctica with a machine learning approach." Journal of Geophysical Research: Solid Earth 126.6 (2021): e2020JB021499. 3) Stål, Tobias, et al. "Antarctic geothermal heat flow model: Aq1." Geochemistry, Geophysics, Geosystems 22.2 (2021): e2020GC009428.  

2) I strongly suggest a) adding statistical analyses to all parameters described (especially parameters shown on figure 5 to figure 7), perhaps stdev or another appropriate statistical parameter. b) adding a description of the bed roughness / topography influence. The bed topography influences the heat dissipation (difference between convex and concave bedrock shape). 

3) An interesting exercise (and fairly straightforward) to add to your work presented here would be to look at model simulation output with as input a single uniform GHF value for your whole domain of interest. This would allow you to have a base for comparaison and statistical analysis. 

4) The figures need to be clearer (see specific comments): e.g. fig 2 to 7, it would be useful to have a few geographic locations (Dome C, grounding line, Vostok, a few lat-lon) so readers can pinpoint where geographically the differences between datasets lie ; and use a thicker black / white line, we do not see it at all on the figure panels (velocity contours, ice bottom at the pressure-melting point).

5) The figure captions need to be rewritten. It's unclear as is (see specific comments). 

6) The bibliography as a whole has to be checked: some references are wrong, and some are not actually cited in the main document (see also specific comments). a) Please always mention the whole ref, i.e. Martos et al (2017) and not Martos in the text and also on the figures and tables. b) There are several references listed in the bibliography that are never cited in the main text: e.g Stearns et al, 2008 ; Cuffey, K. M., and Paterson 2010 ; Van Liefferinge et al, 2018 ; Wolovick 2021b, ... These references have to be cited explicitly in the text, especially since they support the results of the manuscript. c) There are typos in some references: e.g Van Liefferringe and Pattyn, 2013. d) Wright and Siegert, 2012 is mentioned in the text but not in the linked table, ... it lacks consistency. 

....

I attach a detailed review of the paper for the specific line-by-line comments, see attached PDF.

All the best,

Brice Van Liefferinge