Many thanks for taking careful consideration of the reviews and addressing many of their points.

This paper is not ground breaking, in that it demonstrates that assimilating ice thickness into a coupled ice-ocean model does exactly what you would expect it to do, move the ice thickness estimate towards observations. A very similar paper has already been published in JGR-Ocean (Yang et al. 2014), documenting the impact of assimilating SMOS thicknesses < 1m into the MITgcm with a Kalman Filtering method. Yang et al. has more extensive validation with independent ice thickness measurements than you perform in this paper, with data sets that are available to you. It appears your results are similar to Yang et al. (2014), and I wonder if any increase in impact of SMOS is actually because your original run is actually simulating ice thickness worse than the model used in Yang et al. (2014). Given the fact that this is a reproduction of a previous study, with a similar assimilation method (some differences that are worth note) and different model, your results do not present much additional information to the reader. That said,this result is useful to the community of future sea ice forecasters and analysts who may use the TOPAZ model, which is providing medium-range forecasts unlike the seasonal forecasts of Yang et al. (2014). So I am inclined to reconsider the paper after revision.

I welcome the addition of independent thickness observations for verification, however you did not present as much verification data as is available to you. And as you point out in your response to the reviewer, the location of buoys compared against is upstream from where data is assimilated. I also find that the paper can still benefit from attention to the error characteristics of the thickness data. This is very important for understanding R in the Kalman gain. Figure A in the response to reviewers was helpful, and you could perhaps describe these error characteristics in the manuscript.

Please provide more information regarding the validation data set, used to assess skill in estimating ice thickness. Xie et al. (2016) also insufficiently describes the ice thickness data. You should describe the data density and how it varies spatially and temporally over the full time period. This paper in Ocean Science Discussions does not provide a discussion of the measurement errors, which can be substantial. Without this discussion it is impossible to assess if biases are in the model or observations (as you correctly point out in your manuscript). It is for this reason that I suggest you consider using more ice thickness data to see if you can tease this information out. However, I do understand that you may find there is limited data of thin ice thickness with which to directly verify the SMOS data set and model biases.

Only two buoy trajectories were used in this paper for validation. I assume that this is because these are the only IMB data that overlaps with your time period for model runs. There are many other data sources you can use for independent verification. Ice Bridge will be useful for March in the high Arctic, though I suspect you are not assimilating SMOS data here. There are year long moorings in the Beaufort Sea with ULS. The data, described in Krishfield et al. (2014), for these is freely available from WHOI at http://www.whoi.edu/page.do?pid=66559. Note that Krishfield processed this data, and had to filter out wave action in summer months as the Beaufort has become Marginal Ice Zone. The data processing may imply a minimum ice thickness that can be resolved, and you should check this.

Krishfield, R. A., Proshutinsky, A., Tateyama, K., Williams, W. J., Carmack, E. C., McLaughlin, F. A., & Timmermans, M. L. (2014). Deterioration of perennial sea ice in the Beaufort Gyre from 2003 to 2012 and its impact on the oceanic freshwater cycle. Journal of Geophysical Research: Oceans, 119(2), 1271-1305.

I am aware of other moorings deployed in the Beaufort Sea, in the seasonal ice zone. Consider contacting Humfrey Melling regarding this data, though it may be propriety. Shell had moorings in the Chukchi Sea and they have been providing data freely to researchers. This is information that is for your interest, as I am sure you Consider the Fram Strait moorings too, though these are not recording thin ice. Some, but not all, of these data are included in the Lindsay et al. (2013) unified sea-ice thickness product.



Minor Comments

Thank you for the largely readable and correct usage of English grammar throughout the manuscript. I have corrected a few grammatical errors and typos below.

Please expand TOPAZ where it is first introduced. Not everyone will be familiar with the model, and the brand name is not in common usage.

page 2, line 5: There are more recent references to the decrease in sea ice extent. Also, Shimada et al. is a discussion of the possible implications of reduced sea ice extent and not a presentation of the observation of reduced extent.

page 5, line 4: In the one catagory model is there a lower limit on ice thickness that is not considered open water. For example some older two level models consider ice less than 0.5m to be in the open water catagory. Please clarify, as this is exceptionally important for your assimilation scheme.

line 14-15: "which amplitude is" -> "with amplitude"

line 27: bracket -> brackets

line 31: missing f superscript from P

line 33: anomaly -> anomalies

page 6, line 1: forecastd - > forecast

Page 6: Please check you have defined all your variables.
line 10: put symbol for ensemble mean just after when you introduce it. So it is clear the equation is calculating this. Ditto for ensemble anomaly in line 12.

Equation 4: This is actually the mean difference between model and observation. While you are correct that this includes both the observation and model bias, I do not find Bias to be the most intuitive label for this quantity. However I am willing to concede provided it is very clear to the reader through out that the bias is not the model or observation bias.

page 8, line 13: Sentence incomplete

page 9, line 1: You need to describe the uncertainties. Including their magnitude, any variance and periodicity in this.

line 2: As you are disregarding all data more that 0.4m, is it not irrelevant that the upper, saturation, limit on SMOS observations is 5m. I see that you refer to this point later in the manuscript, where you point out there is very little SMOS data assimilated in the Beaufort in March. You could clarify these points when you expand the information about the SMOS uncertainty.

line 8: "within the beginnings" might read better as "at the onset"

page 11, line 11: "we are validating" -> "we validate"

page 13, line 10: Remove "the ice tethered profiles (ITP), which are"

line 13: impacts -> impact

page 14, line 18: thick -> thickness

line 27: consistently -> consistent

Fig. 5: Expand acronyms in titles. You do not explain what hice, icec is etc.

Fig. 6, caption: sea-ice -> sea ice

Dear Dr. Xie and co-authors,

Thank you very much for your thoughtful consideration of my comments. I especially appreciate your corrections on jargon and terminology, and respect your motivation to not expand TOPAZ.

Your paper is much improved, and I believe is a valuable contribution. Please note the small English corrections below, and I would suggest you take a careful proof read in case I missed some grammatical errors.

pg 3, line 30: Cryostat2 -> Cryosat2
pg 4, line 31 apply a post-processing -> apply post-processing
pg 8, line 8: What is superobed?
pg 9, line 17: at the same
pg 9, line 18: as observations
pg 9, line 26: microwaves -> microwave

pg 9, line 30 and previous sentence: do you mean assimilation is problematic for SITs thinner than 0.4m. This is what the previous sentence suggests during the melt season. Did I miss-understand your point in the previous sentence? Perhaps reword or clarify the text here.

pg 10, line 19: consider -> used, and remove 'are used' from end of sentence
pg 10, line 29: a 100 ensemble members -> 100 ensemble members
pg 15, line 11: near the location
pg 16, line 14: impact of the j'th
pg 16, line 18: the March -> March
pg 16, line 21: The profiles -> Profiles
pg 16, line 22: Arctic -> the Arctic
pg 16, line 25: impacts -> impact
pg 17, line 2: Consider starting sentence 'The study in this paper' rather than 'This study'
pg 17, line 33: These studies follow from the first ...
pg 18, line 4: spun up
pg 18, line 6: at time when -> the time period
pg 18, line 20: agreements -> agreement

You may want to check that you are happy with the text size on some of your figures. It is hard to read the very small text.

If you have any questions about my comments, please do not hesitate to contact me.

Jenny