In this study, a coupled ocean-sea ice 3Dvar system is extended to include the assimilation of sea ice concentration and sea ice thickness. OSISAF sea ice concentrations and sources of sea ice thickness from CryoSat-2 and SMOS are assimilated in various configurations. The assimilation of OSISAF sic data alongside L4 C2SMOS SIT data with a Desroziers’ OE factor of 1 performs best in comparison to both assimilated and independent moorings.

Overall I believe this to be a good paper with strong scientific basis and quality, particularly with strong implementation of a robust data assimilation scheme and good statistical assessment of the results. The plots show the results well. My main concern is that a bit more validation would improve the impact of the paper strongly alongside some discussion of the results.

General comments:

In your analysis of the validation against BGEP ULS moorings you also mention the RMSE and BIAS but do not show these results which would be useful to see. I think it would be useful to extend the validation to also look at Operation IceBridge data, which also covers the time period of your experiments, and has a higher spatial coverage than the BGEP ULS moorings do. Although the data only cover March and April it would be useful to show a comparison to them with, for example, BIAS, RMSE or scatter plots of the different runs against the OIB data available during your experimental time period.

The authors use a relatively simple 1 category sea ice model but achieve good results with the sea ice assimilation, it would be good to have a discussion of how using a more complex sea ice model might improve or change the results. Some discussion that compares your results to those seen in the other sea ice data assimilation studies you mention in the introduction would also be useful, as well as the reason for any differences or similarities.

Why is SIT RMSE only shown for February, it would be good also to see for maybe sometime earlier in Winter (November?)

Specific comments:

Throughout the paper: You use ingestion or ingesting many times when assimilation or assimilating sounds fine, ingestion sounds quite strange and not correct.

In quite a few places you have used Cryosat-2 when you should use CryoSat-2

The abstract feels a little clumsy in presentation and wording and could be rewritten in a clearer way, there are also many grammatical/spelling errors in the abstract highlighted below

Line 1: cryoshopere -> the cryosphere, evolution over time -> evolution

Line 6: those variables are treated -> these variables are treated

Line 9: the assimilation of the sole Cryosat-2 -> The sole assimilation of Cryosat-2 sea ice thickness

 Line 10: along the year -> throughout the year

Line 11: The use of merged L4 product -> The use of the merged L4 product

Line 15: have been offering -> have offered

Line 16: Thickness extimates were firstly derived -> Thickness estimates were first derived

Line 23: general agreement in the extension -> I assume you mean general agreement in the sea ice extent?

Line 28: while the assimilation of the sole concentration -> while the sole assimilation of sea ice concentration

Line 35: routinely -> routine

Line 38: gaussianity -> gaussian

Line 54: Change sentence to begin with “In the past few decades” instead of using “in the last decades” in middle of sentence.

Line 56-57: Laxon et al., 2013 should be referenced here also in terms of the CryoSat-2 SIT retrieval 

Line 66: year-round product that guesses -> year round product that estimates

Line 122: The number of sampling -> The sample size

Line 142: The sentence is difficult to understand, I am not sure what

Line 152: will be possibly investigated -> may be investigated

Figure 3 title: Diagnosys -> Diagnosis

Figure 4 and 5: very difficult to see SICDE1 in plot due to colour scheme chosen, suggest choose a different scheme for this experiment. Could also change x axis labels in RHS plots from numbers to month initials (i.e. 2, 4, 6 etc to J, F, M, A, M…).

Line 209: significative -> significant

Line 214: “While THE L4DE1 provides the best skill score, the other two experiments show similar spatial RMSE and BIAS” – It looks to me like the spatial pattern is different with L4DE1 having higher RMSE further from the east coast of Greenland, whereas in the other two experiments it is closer, and they also have high RMSE in Beaufort/CAA, whereas L4DE1 does not have this spatial pattern.

Line 219: fairy well -> fairly well

Line 227: reanalysis purpose -> the purpose of reanalysis

Figure 6: The colour scheme uses white for both lowest and highest RMSE, therefore within the ice pack I am not sure if the white colour is indicating highest or lowest RMSE values?

 Line 251: This sharp jump -> This sharp discontinuity or increment

Figure 8: Very difficult to see L4DE30 in plot due to colour chosen for this line.

 Line 276: extimates -> estimates

Line 281: jumps -> increments/discontinuities

Sentence Line 284-285 “The reasons can be sought in the peculiar aspects of sea-ice variables that prevent a smooth ingestion in global analysis/reanalysis systems already in place.” This sentence sounds very strange and not correct, needs rewording.

Line 292: routinely production -> routine production

Line 293: “to cope with” -> “to benefit from”

Laxon, S.W., Giles, K.A., Ridout, A.L., Wingham, D.J., Willatt, R., Cullen, R., Kwok, R., Schweiger, A., Zhang, J., Haas, C. and Hendricks, S., 2013. CryoSat‐2 estimates of Arctic sea ice thickness and volume. Geophysical Research Letters 40, no. 4 (2013): 732-737

Review on “Bivariate sea-ice assimilation for global ocean Analysis/Reanalysis”, by Andrea Cipollone, Deep Sankar Banerjee, Doroteaciro Iovino, Ali Aydogdu, and Simona Masina, submitted for publication in EGUsphere.

General comments :

The paper presents experiments where sea ice concentration and thickness observations are assimilated in a coupled ice-ocean model. The correlation between sea ice concentration and thickness observations is taken into account. The method of Desroziers (2005) is used to better characterize the observation-error statistics. Also the Degrees of Freedom for Signal (DFS) developed by Cardinali et al. (2004) is used to measure the influence of the observations on the analysis.

The results of the experiments are first compared to one of the same sea ice observations dataset that were assimilated. Since only the analyses and not the forecasts are verified, the exercise is more to verify the assimilation methodology than the accuracy of the analyses. Fortunately, the experiments are also verified against independent observations of ice thickness in the Beaufort Sea.

In the section describing the assimilation method, we see gICE and gSIC that are used interchangeably. I think it would be better to have just one expression throughout, if these point to the same thing.

Figures 10 and 11 seem to be identical. Please remove figure 11 and only refer to figure 10 in the text. Also please revise the caption for this figure. Currently the caption for figure 10 and 11 are slightly different but I am not sure which one is more correct.

Specific comments:

Line 20: What about the first CryoSat mission ?

Line 65: “contest” or “context” ?

Line 88: ‘x’ should be called the state vector, and ‘x_a’ is the final analysis state (the value of ‘x’ that minimize the cost function).

Line 113: Please define “CVT”.

Line 146: Should “V_ICE→gICE” be “V^T_ICE→gICE” ?

Line 151: I think that “that it has been shown” should be “that has been shown”.

Technical corrections

Line 122: “31-year-long” should be “31-year long” for consistency with the caption of figure 1.

Figure 1: In the caption, “Panel g and f show the same as e,f for September” should be “Panels g and h show the same as e,f for September”.

Figure 4: In the caption, “Panels” should be “panels”.

Line 203: “Beaufourt” should be “Beaufort”.

Line 219: “0.5 * 10¹³km” should be “0.5 * 10¹³ m³”

Line 253: “is usual higher” should be “is usually higher”.

Line 255: “…contribute to the modify the model…” should be “…contribute to modify the model…”.

Line 275: “indestion” should be “ingestion”.