We thank the reviewer for the work and insightful comments. Form the review, it is clear that there is the need to revise the MS to be more clear and readable. Below each point of the reviewer is answered paragraph by paragraph. Our answers are written italic.

The manuscript seeks to address an important topic of contributions of different sources of uncertainty to sea ice thickness observations relevant to past, current and future altimetry missions. There are some potentially useful insights from this analysis. However, the manuscript is difficult to read and suffers from three major issues:

1. The objective(s) are unclear, and not given in the abstract. What is the overall aim? Which values (line 4) are being compared to which, and for what purpose?

The values being compared are model parameters for snow thickness, sea ice density and water density, as stated in line 3-4 in the abstract and in the title. The purpose is to evaluate the modeled values (for snow thickness, sea ice density and water density) against observations and the values used in the CryoSat-2 weekly sea ice thickness product from AWI. In addition, the study evaluates how much the sea ice thickness varies based on the difference between the model and AWI data. We will work on the clarity of the manuscript, since this was not clear to the reviewer.

2. There are previous studies e.g. by Landy and Mallett which address some of the questions the study seeks to answer, however, these are not referenced  - they should be discussed in the introduction with an explanation of how this work builds on them and/or differs to them.

Assuming that the reviewer refers to “Faster decline and higher variability in the sea ice thickness of the marginal Arctic seas when accounting for dynamic snow cover” discussing the W99 snow climatology compared against modeled snow thickness from SnowModel-LG and NESOSIM, we will integrate this study in the introduction along with a discussion. “A year-round satellite sea-ice thickness record from CryoSat-2” by Landy is already mentioned in the introduction part that discusses other studies using modeled snow thickness, and to our knowledge there are no studies to our knowledge that discuss the sea ice density nor water density by the mentioned authors.

3. The methodology is very difficult to understand, there are number of observational datasets, model assimilation and outputs being discussed but it is not clear how these were selected, what is being compared to what etc. and as above, for what purpose. It seems as though everything is being investigated/varied at once without a clear strategy.

We will rewrite the methodology and clarify the steps taken to analyses the data, as well as review the descriptions of the data sets used in this study.

It seems likely there could be some value of this study, though previous studies have already investigated some of this and it will need to be clarified how this is distinct. In particular the findings relating to water density could be of interest to the community. In the current form it is not possible for a reader to gain this understanding from the manuscript.

We thank the reviewer for their comments. From the review it is clear that there is need for a rewrite of the methods and clarifications on the overall aim of this study. We will address this in the review. This study aim at showing that the modeled values can be a substitute to poorly constrained variables of snow thickness, sea ice density and water density. In addition to the points in the current manuscript we will add a section presenting an improved sea ice density parameterization further strengthening our point.

We thank the reviewer for the work and insightful comments. For the review we will revise the MS and clarify exactly what the aim and outcome is. Below, each point of the reviewer is answered paragraph by paragraph. Our answers are written bold italic.

Review of “The Variability of CryoSat-2 derived Sea Ice Thickness introduced by modelled vs. empirical snow thickness, sea ice density and water density” by Sievers et al.

The MS is evaluating the sea ice thickness retrieval uncertainty from the radar freeboard due to the buoyancy effects of snow thickness, sea ice density and ocean water density. The list of literature describing the uncertainties when deriving sea ice thickness from the radar freeboard is long and a narrow selection of those articles are presented in the introduction. The main novelty of the MS is the “overlooked” ocean density variability in previous studies.

The topic is definitely relevant and actual and the future assimilation of radar freeboards in sea ice and ocean models has a large potential. However, the presentation of the results is raw, starting already in the abstract, it is difficult grasp what the MS is presenting and the figures are missing units and consistent ranges of the color scales for comparison. These things can be handled in a revision; however, my main concern is the large ocean water density variability in the model (C6N4), the novelty here. The water column of the sea ice covered parts of the Arctic Ocean have the so called “polar waters” on top of the “Pacific” or “Atlantic” waters underneath in a very stable stratification. Does the ocean model (C6N4) replicate the polar waters and that stratification? And how does the model compare to surface salinity (CTD) measurements?

We will investigate which additional in situ observations could be used for evaluating the model halocline. In the current version we did not include subsurface processes, because we did not deem them important, since we are mainly interested in the surface density. However, we also feel the need to point out that the study does compare the model surface density to observations (derived from salinity observations) and that the observations are even more variable than the model (comp figure 7 upper right).

The surface water density colorbar (I presume in [kg/m3]) in figure 7 (top row) varies between 1018 kg/m3 and 1028 kg/m3. This corresponds to a salinity range between about 23 and 35 psu. The AWI value of 1024 kg/m3 corresponds to approximately 30 psu. 35 psu corresponds approx. to the Atlantic Water salinity. It might be useful to also show that density/salinity of the waters not covered by sea ice. I could be wrong, but I am skeptical about the large range of salinities (densities) for the polar waters and it would be reassuring to make a comparison with in situ CTD measurements (fx. MOSAiC data) to see if C6N4 is capturing the Arctic Ocean halocline.

We agree that evaluating the models simulation of the halocline would be a good addition. From the review it is not clear, if the reviewer is aware that the WOA data in figure 7 consist of observations. This observation data set also shows the strongest surface density gradient in the Arctic, which is not as strongly pronounced in the modeled data. The WOA data was chosen because it consist of a comprehensive amount of observations and because it is a climatology, which is compared to a 10 year mean of model data.

Selected specific comments (I think that the MS needs a complete rewrite with attention to clarity and even grammar, here are some suggestions):

We thank the reviewer for the detailed comments and will change the manuscript accordingly. Below only comments which we felt like we needed to clarify were commented. All other comments will be incorporated in the review.

P7,T1: This table is difficult to understand. Why is the “disagreement” metric constrained to the interval 0-2? And what is the unit [m]?

The disagreement is calculated from the integral of two PDFs. The PDFs are dimension less and the integral is always 1. The disagreement excludes the area in which they overlap, so if they are in perfect agreement disagreement is 0 and the snow is distributed equally in both data sets. This metric was chosen to compare two data sets that are existing on different spacial and temporal scales. We will add a better description in the method section in the review.

P10,F3: use same scale on colorbar, what is the unit [m?], give meaningful heading to lower left figure, why does the SIT difference plot only have positive values?

We will adjust the figures accordingly. The positive values in the SIT difference plot are there because the difference was calculated from the mean absolute difference. We will reevaluate if this is a relevant metric.

P11,L231: Does the IceBird derived densities include snow? AWI and C6N4?

Assuming that the reviewer asks if IceBird is deriving bulk density values for snow and ice together: No IceBird derives sea ice densities under the assumption of constant snow density.

Yes figure 4 displays the relation between both IceBird and AWI and IceBird and C6N4. The relation between AWI and Icebird are blue and the relation between C6N4 is orange.

P13:F5: What are the trend-lines for? I don’t see a trend except that the density increases at the onset of melt. I think that those different densities would result in a systematic uncertainty, why do you quantify it as a RMSD? Please add the AWI density.

The Figure will be revised, since we found an error in the calculation of the observed sea ice density.

P20,L404: water density variation by 10 kg/m3, you should really check with observations.

WOA is a climatology calculated from observations. We will evaluate which other observations are relevant.

We thank the reviewer for the work and insightful comments. For the review we will revise the MS and clarify exactly what the aim and outcome is. Below, each point of the reviewer is answered paragraph by paragraph. Our answers are written bold italic.

This manuscript, titled “The Variability of CryoSat-2 derived Sea Ice Thickness introduced by modelled vs. empirical snow thickness, sea ice density and water density”, carries out evaluation of the sea ice thickness retrievals based on CS2 radar altimeter. The topic studied here, the uncertainty of satellite radar altimetry, specifically that involved during the conversion from freeboard to thickness, is a key and pending issue. Hence the paper is highly relevant to the journal. A comprehensive study of the various parameters during the retrieval is carried out, and the results constitute a good contribution and update to our current understanding of the issue. I have the following major comments before the manuscript be considered accepted by the journal. 

First, I find the paper’s name to be inadequate, regarding its current content. The major contribution of the paper is the uncertainty analysis, rather the analysis of the sea ice thickness (or its variability). The title should be more accurate and informative of the main purpose of the manuscript. Example could be: “Uncertainty Analysis of the CryoSat-2 Sea Ice Thickness Retrieval based on Modeled and Empirical Parameters”. 

We will consider the suggested title changes. However, we believe that uncertainties might be misleading, since the analysis examines differences between the model variables and typically used variables in CryoSat-2 SIT products. A more detailed explanation is included in the answer to the fourth question of the reviewer.

Second, I find the introduction of the model (named C6N4) lacking key details. I resort to the reference provided (i.e., Sievers et al., TC, 2023) for details, but have not found every relevant piece of information. For example: What is the resolution of the model? How the mushy layer thermodynamic model is configured? Has the drift validated to the Lagrangian locations during MOSAiC? How snow-ice is treated in the model (which could be very relevant in the Atlantic part)? These information, in my opinion, are all relevant to the intercomparison and should be covered. 

In the revised manuscript we will include a more detailed description of the model to address the reviewers remarks. The resolution is 10x10km, the mushy layer thermodynamic follows Feltham et al. 2006 (https://doi.org/10.1029/2006GL026290), The model drift has not been evaluated at the MOSAiC locations and snow-ice formation is calculated from freeboard calculations that is not using the newly introduced sea ice density.

Third, the systematic underestimation of ice density from the model to those in the altimetry community is worth to be investigated more thoroughly. How does the raw thickness fields compare? Is there a systematic bias in the thickness itself between the model and the AWI’s observation? Is it density bias related to ice (thickness) type? These info could be very helpful in delineating the actual cause of the difference. Furthermore, the difference in the ice density variability from observations and model results (i.e. Sec. 3.2 and Fig. 4) is really interesting. The model’s `effective resolution’ in simulating the ice density, and how it compares with the observations at different spatial scales may holds invaluable information about both the model’s performance and the various contributing processes of the ice physics.

The sea ice density presented in the manuscript has no influence on the model thickness. It has only an influence on the modeled freeboard. Both the freeboard and the sea ice density are model diagnostic variables introduced in Sievers et al., TC, 2023. Diagnostic meaning, variables that are not used in the core equations of the model, but for output. We are however planning to add a new section in the review where we investigate the in the outlook suggested improved sea ice density. An analysis of the modeled freeboard in comparison to the satellite derived freeboard and the freeboard originating from the current, too low sea ice density would probably be in line with what the reviewer had in mind and will be investigated for the reviewed manuscript.

Besides, what is the motivation of using the specific methodology in Eq. 5, rather than the traditional way of propagating of the uncertainty (i.e., Kwok, 2010, J. Glaciol.)? Does it yield more trustworthy results due to nonlinearity of Eq. 1? 

The motivation to use eq. 5 is that we are not actually using uncertainties, but analyzing the differences between the model values and the AWI data values. Both the AWI data and the model would have their own uncertainties. This analysis for example allows us to come to the conclusion that the water density uncertainty generally is underestimated. If we would use uncertainties this would not have been the case.

Finally, I find that the language usage and the format of reference needs to be examined thoroughly. Parentheses for referencing the papers should be used properly (many cases to be corrected across the manuscript). Some extra examples are given below.

We will review the manuscripts grammar and spelling thoroughly in the review and thank the reviewer for their remarks.