This manuscript describes the procedures used to create and validate V3.1 of the BEC Arctic surface salinity product:  Arctic+ SMOS SSS v3.1.   The description is reasonably complete and well written.  The following comments are offered in the spirit of improving the description:

1. Lines 28-29: “L-band frequency is the region of the electromagnetic spectrum offering the most sensitivity to salinity variations”.  It is optimum from a remote sensing perspective (protected spectrum and reasonable sensitivity), but the maximum sensitivity occurs at lower frequency (500-900 MHz depending on temperature, incidence angle and polarization).

2. Line 51: “available [with] prior registration” ?

3. Line 53: “L1B product contains TB Fourier components”:  It is not clear in the text whether the starting point is “visibilities” or an image.  If starting from the Fourier components, details of the inversion to an image of TB need to be included.

4. Line 67: A better reference (better than 2018) for corrections to the Meissner-Wentz model for the dielectric constant of sea water is:  T. Meissner and F. J. Wentz, “The emissivity of the ocean surface between 6 and 90 GHz over a large range of wind speeds and Earth incidence angles,” IEEE Trans. Geosci. Remote Sens., vol. 50, no. 8, pp. 3004–3026, Aug. 2012.

5. Line 117: Why this choice?  For example, how does this compare with the model of Yin et al: “Roughness and foam signature on SMOS-MIRAS brightness temperatures: A semitheoretical approach,” Remote Sens. Environ., vol. 180, pp. 221–233, Jul. 2016.

6. Line 121: “first Stokes parameter (I = TBx + TBy), parameter used to perform the TB inversion”.  Details needed.  For example, how is the roughness correction (which depends on polarization) made?

7. Line 152: Typo:  “starting from”

8. Line 183: See comment 4 above.

9. Line 184: “conductivity equation Debye (1970)”  The expression attributed to Debye is for the resonance of the water molecule, not conductivity. 

10. Lines 184-185: “Therefore, we have used the MW model to derive the high latitudes SSS.”  This certainly is reasonable, but perhaps it should be noted that the MW model has been shown to result in an SST-dependent bias in the retrieved SSS. 

11. Line 227: Typo:  measured TB

12. Line 242-243: “Assuming … high radiometric error …”  There might be other sources of error in addition to noise in the radiometer.

13. Line 301-302: “It should be noticed the greater coverage and detail of the gradients of Arctic+ v3.1 product to that obtained from the previous BEC Arctic v2.0 product (fig. 5 a-c and 6).”  Wording could be improved.

14. Line 318-319: “However, a comparison with punctual measurements can not evaluate the improved data coverage neither spatial resolution.”   Something is missing.

15. Line 365: Typo: extra series:  should be "to have a long enough series of ..."

16. Line 378: “applied the CTC”.  Are there limits on the amount of correlation permitted and how it affects the conclusion?  This could be important since V2 and V3 are so closely related.

17. Line 443-445: “As the method extracts the expected natural variability from the common information between the compared products, it means that the fraction of information in the Arctic+ v3.1 product is the largest of the three products.”  Has this statement about “information” been demonstrated?  Perhaps a reference is needed here.

18. Line 449: “at smaller scales than SMAP and BEC v2.0”.  With the exception of Fig 13a, this does not appear to be true for SMAP.

The paper describes the updated SSS- SMOS derived data set. Inversion algorithm, comparison with other products, including the one previously developed by the same consortium, and partial data validation are described. The paper is clear and the description of process used to move from data to product is appropriate. The main advantage of the new product is its finer resolution which could be relevant for oceanographic processes description. The paper is almost ready for publication except for some minor suggestions which can improve its readability.  

Lines 14-15  : there is a repetition here. Please check.

Line 16.19 : you can improve the readability  of manuscript here by merging/reformulating the different short sentences.

Lines 20-21 :  sentence “…better monitoring the observed changes in the freshwater fluxes”. Please add reference for the observed changes which, in my understanding, differs from L-band radiometry.

-Line 28-29 : “ Whilst L-band frequency is the region of the electromagnetic spectrum offering the most sensitivity to salinity variations, it decreases rapidly in cold waters “ this is not true. Recent paper (e.g.  10.1109/TGRS.2021.3101962) proves that other frequencies work better and efforts are made to promote it from space ( DOI: 10.1109/JSTARS.2021.3073286)

-Line 31-32 – LSC: you  can simply mention that the problem is due to the large footprint on the ground (interferometer is obviously worst).

-Line 58 : could you provide an estimate of error introduced by the  interpolation process?

-Line 67 – the sentence “The SSS and SST are converted to TB “sounds a bit strange, I guess that you meant that SSS and SST are used as inputs in an e.m model to generate simulated Tb values.

-Line 69_ you mention that data “generated from measurements of the 2005-2017 period” are used as reference but SMOS data refers to 2011-2019 period. Did you evaluate if there is an impact on the obtained the results if the same overlapping period is used?

-Line 90: could you add an accuracy estimate for Tara data?

-Line 104-105: could you estimate/quantifying the differences in considering 64x64 instead of 128x128 point? You mention “without loss of information/resolution “.

-Line 119-120; is not clear if the ionosphere correction is applied. Since 1^st Stokes parameter is used for the inversion

-Line 133-135: if I understood correctly you use, as reference, the SSS value obtained from the WOA instead to the one obtained from SMOS (average value). If so, which is the estimated differences between these values? Could you provide an example for some specific regions where the coast contamination is /or isn’t relevant?

-Line 173 : the sentence “Only latitudes above 50◦N are considered” can be eliminated since it is repetition of line 159.

-Line 189- For the minimization did you use different approaches? For instance, did you check if the introduction of a regularization term could be beneficial?

-Line 203 – 206 why using 100 , 7 and 2 as criteria? Could you better justify it? (i.e. Why not 90 or 110?)

-Line 230-233: Also here : could you better explain how the thresholds were selected?

-line 260: The 12 psu bias has, in my view, severe implication. It implies that the retrieval largely overestimates the retrieved SSS besides the numerous procedures, averaging, de-bias which were conducted to derive it. Did you have an explanation for the bias? There is a problem of representativeness of SSS retrieved by SMOS and what provided by HYCOM? Or there is an absolute error on HYCOM only as bias but it didn’t affect the temporal variability? At the end you plan to use it for the temporal correction.

-line 276: how much the number differs from zero? This could be a useful information for the reader.

-figure 5: why the error is only represented for radiometric uncertainty? you have different factors that contribute to the error computation. This is bit reductive.

-Argo validation: not clear to me why BEC V2.0 data provides better results in 2011 -2012. If SMOS is affected by RFI (as the authors mention) this impact on all the products. Moreover, for BECV3.1 you develop an approach which is devoted to mitigate RFI effects.

-Tara Validation: from table it seems to me that the affirmation “Arctic+ v3.1 product, better than the previous BEC v2.0 product in most of the seas” is questionable. I see a clear advantage in two cases only (Kara and Beaufort).

-Spectral Analysis : the difference between SMAP and BECV3.1 seems to me very small in the figure then my conclusion is that both method provide similar results. It is correct?

-Lie 427: while I recognize that validation for 3 days product require additional effort, although it could be very interesting for potential users, I believe that validation at 18 days should be simple and can be easily implemented.