This is a very nice study that assesses surface albedo from the MOASAiC campaign versus the HIRHAM-NAOSIM model. Maybe a lot of it is my misunderstanding of what was done here. The pieces are mostly here and I do think this is a worthwhile study, but I have some fairly significant concerns here.

1. In terms of originality, Light et al. have recently published a similar study in Elementa. While there is more emphasis on the model results here, I still think some additional contrast to what they found would be useful here.

2. My biggest concern is the bias in absorbed shortwave (irradiance), Figure 8. Did the authors compare the incoming shortwave between the model and observations? The albedo could be perfectly correct, but if the incoming shortwave is biased, then the absorbed will be similarly biased. I am not an expert in atmospheric radiation, but I think it would be helpful to see a comparison of incoming and outgoing shortwave. Perhaps this was mentioned, but I think this could be expanded upon.

3. On a similar note, the authors talk about the importance of albedo for climate model simulations. However, related to point 2, we often have to adjust the snow albedo to compensate for biases in the incoming shortwave. So, it is possible to have the "correct" albedo, but for the wrong reasons.

4. What is the temporal resolution here? It wasn't obvious to be if these are instantaneous, hourly, etc. I assume the model is saving the fields at the same temporal resolution? How is albedo defined when there is no sun?

5. I'm very confused about the use of "online" and "offline" models here. Is the difference that one has prognostic radiation and the other has specified radiation? I would like the authors to expand upon the description of these. I think this is where you are trying to get at the question raised earlier about whether the incoming shortwave is biased, or the albedo is biased. I think a bit more could added to section 4.2 to help alleviate these concerns.

Minor points.

1. In figure 3, the panels that show the surface type are hard to see (a, g, c, i). Maybe just lines instead of filled contours. The red of melt ponds in particular is hard to see.

2. In figure 4, I prefer you not use the description of "violin" plot. While this might describe the shape it doesn't say anything about what you are showing. Just a description of what you are showing is sufficient. Also, you could refine the Y-axis. Everything below 0.6 is not interesting in spring and summer.

3. Similarly in Figure 5c. Are you simply reflecting the same information on both sides of the line? 

4. Figure 7b is a similar issue to point 1. I find that these "stacked" plots are kind of tricky to interpret. Maybe line plots are better here.

General comment

I this paper, the Arctic surface albedo simulated with the coupled regional climate model HIRHAM-NAOSIM is evaluated with aircraft and surface-based observations collected during several field campaigns. The study is very relevant for the polar modelling community, the applied method is convincing, and the observational dataset used for the model validation is outstanding. However, I have few major concerns:

1. The text in Sect 3 and 4 is hardly readable, the expressions are unclear, the language is not suitable for scientific publication and needs to be extensively rewritten. In my detailed comments I only point to few examples, but almost all the sentences require improvement.
2. In some cases, the interpretation of the results needs to be deepened (see my detailed comments). Some results depend on the selected regions and time of the year and cannot be generalized (such as the relative impact of clouds or albedo biases on the bias in surface net irradiance).
3. In my view, one of the most striking results is the model underestimation of surface albedo after the onset of melting (Fig 7). The underestimation is explained as due to the fact that, when snow disappears, the ice surface is represented as bare ice and not as the surface scattering layer that forms during the melting. This result deserves more discussion.

I therefore request a major revision of the paper.

Detailed comments:

Abstract: the result related to the lack of proper representation of the surface scattering layer over melting sea ice is missing from the abstract. I believe it is relevant to include it.

line 176: “…where sea ice is further divided into snow-covered ice (subscript s), bare ice (subscript bi), and melt ponds (subscript mp)”: could you please add a comment on which ice category the “surface scattering layer (SSL)” (also called “white ice”) belongs to? It is not snow but very much resembles it, being much more reflective than bare ice (for the definition of SSL see e.g. https://online.ucpress.edu/elementa/article/11/1/00103/195863/Evolution-of-the-microstructure-and-reflectance-of and https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2006JC003977). From your Table 3, the surface scattering layer would belong to “snow-covered ice” category when looking at the albedo intervals.

Fig 4: very nice Figure!!

Sect 3 and 4: reading these sections is extremely painful because of the unclear text and imprecise vocabulary. The logical rigor of the sentences is poor as there are often missing logical steps in the explanations. The text is not suitable for scientific publication and needs to be extensively rewritten. I provide here only some examples of poor sentences

line 300-301: “From that, we assume that the distribution shown for the modeled surface albedo is biased to higher values, since the cloud cover is overestimated.” This is a quite badly expressed sentence and concept. Maybe you mean something like “Based on these results, we argue that the match between satellite- and model-derived surface albedo medians results from the compensation of two opposite model biases: the overestimation of modelled clouds, which caused a positive bias in modelled albedo, was compensated by a negative bias in modelled clear-sky albedo.” Do you agree?

lines 315-316. “At end of March, a distinct minimum of sea ice coverage (0.86) was simulated for the area covered by the flight on 3 April 2018 leading directly to the minimum of the surface albedo.” Totally unclear sentence, I did not manage to guess what you mean.

line 316-318: “The corresponding measured areal-averaged surface albedo shows, on the one hand, a much greater spatial variability and, on the other hand, a clear tendency towards smaller surface albedo values. This tendency…” Please rephrase, and not use the word “tendency” if you are not showing a decreasing/increasing trend in your time series, it is very misleading. Do you mean that area-averaged modeled albedo is positively biased compared to area-averaged aircraft observations? If so, write it clearly.

lines 332-333: “This partly explains the difference in the distribution of modeled and measured surface albedo, in particular for the surveyed regions on September 8 and 13.” You did not show this result: either you show the plot, or you remove this sentence.

line 336: “Cloud effects are small, as mostly a full cloud coverage was modeled by HIRHAM-NAOSIM.” This sentence cannot be understood if you don’t include all the logical steps. Do you mean that “Clouds did not significantly affect the temporal variability of modeled and observed surface albedo because both observations and model simulations were carried out in overcast conditions”?

line 337-338: “The measured areal-averaged surface albedo shows best agreement for the region overflown on September 2, although parts of the northernmost section of this flight path were underestimated by the model.” It seems to me that part of the northernmost section of that flight is overestimated by the model (the western part) and part is underestimated (the eastern part).

Sect 3.3.3: it would be good to explain why you decided to use the data from one RAMSES spectral albedo station and not from other albedo stations (there were several broadband albedo stations and other RAMSES stations), especially because for this study the spectral to broadband albedo conversion. Wouldn’t be more straightforward to apply broadband observations? How representative of the MOSAiC ice floe surface the data collected at the selected station are?

line 359: the reference (Tao et al., 2023) is missing.

line 368-370: “On June 21 and June 22, both data sets showed a similar surface albedo, even though the spatial variation of the satellite product was smaller than the temporal variability of the ground-based surface albedo measurement within a day.” In my opinion, comparing spatial variability of one data with temporal variability of another data is not meaningful. You need to better elaborate, otherwise the comparison between in situ and satellite data is meaningless.

line 391, eq. 10: the way in which the equation is presented is misleading: the difference between measured and modelled net irradiance does not depend on albedo alone but also on the incoming irradiance. Please correct.

Sect 4.1, lines 406-417: the authors did a linear regression analysis to assess the relative impact of biases in albedo, solar zenith angle and modelled cloud water path on the bias in modelled net shortwave irradiance. I think that the results are very much dependent on the considered dataset (March-April and September observations). A different dateset, with different spatial and temporal variability in albedo and cloud properties would provide different standard deviations with respect to model simulations, yielding a completely different result. For instance, I would expect that in summer, when albedo is lowest, cloud optical thickness is largest, and shortwave cloud radiative forcing is largest (most negative), the cloud std may cause a larger error in surface net shortwave irradiance than the std in albedo. Hence, I recommend considering the results from the perspective of the analyzed dataset and discuss the implication of different albedo and clouds conditions.

Sect 4.2 and related text in Sect 5: often the expressions “surface albedo forcing” or “surface albedo effect” on the net shortwave irradiance are improperly used, as in reality you meant “impact of the surface albedo bias on the calculated net shortwave irradiance”. This is very confusing. I recommend rewriting the text paying particular attention to the precision of the used vocabulary and espressions.

lines 445-446: “This indicates that a surface albedo bias in spring is less relevant for the absolute amount of the solar energy budget at surface than in summer.”, and 495-497: “Since the maximum surface albedo effect on the net irradiance was derived for cloudless summer conditions, it can be concluded that the surface albedo bias is more relevant to the absolute amount to the solar energy budget in summer than in spring.” Even if the surface albedo bias causes a larger bias in clear-sky surface net irradiance when the incoming irradiance il largest (in summer), it does not mean that it is more relevant for the summer than for the spring surface energy budget. In fact, cloudless skies are much more frequent in spring than in summer. However, the freezing temperatures make the albedo spatial and temporal variability and, thus, the bias in modelled albedo, much smaller in spring than in summer. I wish the authors could expand the discussion on this result, including references to previous studies.

lines 472-473: “We conclude that a functional dependence, rather than a pure discrimination between cloudy and cloudless conditions, is required to properly describe the cloud effect on surface albedo.” The advocated physical dependence of the broadband albedo parameterization on cloud properties (optical thickness) is much less physically consistent than the waveband-dependent albedo parameterization would be. Only a waveband-dependent albedo parameterization that at least distinguishes between visible and infrared regions can account for the cloud impact on albedo in a manner that retains the coupling and dependencies between the physical variables. Could this solution be applied in HIRHAM-NAOSIM? I invite the authors to consider this solution or at least to comment on it.

lines 488-489: “In particular, the surface albedo of the scattering layer classified as bare ice seemed to be underestimated.” This is a critical issue: currently, in all sea ice schemes that I am aware of, the albedo of ice without snow is simulated as the albedo of bare ice, which is much lower than the albedo of the surface scattering layer. The surface scattering layer is completely ignored in the sea ice surface schemes, with the consequences that you have illustrated. I invite the authors to expand on this issue: what is the impact of ignoring the surface scattering layer on the surface energy budget? Could the surface scattering layer be modelled? Please refer to Macfarlane et al: https://online.ucpress.edu/elementa/article/11/1/00103/195863/Evolution-of-the-microstructure-and-reflectance-of