General Comments

This paper revisits the longstanding parameterisation of lateral melt used within the CICE (Los Alamos) sea ice model and explores how assumptions about the representation of lateral melting impacts sea ice within a coupled climate model (in this case CESM2.0). As the authors note, significant progress has been made recently in terms of representation of floe size within sea ice models, but there has been a corresponding lack of attention paid to the lateral melting parameterisation. Whilst other studies have explored similar themes exploring sea ice model sensitivity to floe size and lateral melting e.g. Steele et al. (1992), and more recently Bateson et al. (2020), this is the first study I am aware of that addresses the assumption of a constant lateral melt rate across all sea ice thickness categories. The application of the concept of open water formation efficiency to provide further understanding of how lateral and basal melting processes impact the sea ice cover is a particularly strong and valuable feature of this work. I therefore believe that this paper initiates an important and valuable discussion into the lateral melting parameterisation in sea ice models and will make a valuable contribution to the literature.

The scientific quality of the work presented is generally strong, with good associated analysis and discussion. The methodology could be more thorough in terms of the details provided, and there is perhaps insufficient consideration of the limitations of the conclusions reached. I am also unconvinced that some aspects of the conclusions reached are justified by the results presented and these either need to modified or further evidence provided. The figures are of a good quality and appropriate to the discussion. I have suggested a couple of additional figures that might be helpful to illustrate some of the discussion, but this is not essential. Similarly, the structure generally seems fine, though I do have some questions about whether some of the discussion should be moved to the results section, and some of the conclusion section then moved to the discussion. The paper reads well, is clear in its conclusions, and also has a representative abstract and title.

Overall, I believe that this paper is within the scope of The Cryosphere and, with some moderate edits, merits publishing. 

Specific Comments

• P2 L52-53: Could you add further details on what you mean by the following: ‘such as related to model resolution,’?
• P2 L58: Re following, ‘i.e. Bateson et al., 2020)’. e.g. would probably be better here rather than i.e. since the study referred to is one of several on this theme.
• P3 L62-64: Re following statement, ‘different results might be expected in a coupled climate model that allows feedbacks related to the formation of open water’. There is some evidence of this in Fig. 5 in Roach et al. (2019). Simulations with a standalone sea ice model generally showed a reduction in lateral melt and increase in basal melt of comparable magnitude, but in a coupled sea ice-ocean setup the reduction in basal melt was significantly smaller than the increase in lateral melt. Might be worth referring to this?
• P3 L74-76: I am unconvinced you have achieved the final aspect of this objective with the results presented: ‘as a result of ice-albedo feedback’. Later comments will further address this. You may need to modify this paragraph depending on how you decide to address some of the later comments.
• P3-4 L79-96: I think in general this section would benefit from a more complete discussion of details of the model setup that are pertinent to this study e.g. additional details of the SOM (given the importance of surface ocean properties to lateral and basal melt rates), a more complete description of the forcing and how it is applied, and details on how the sea ice is initiated.
• P3 L80-89: Given the significant focus in this paper on the ice-albedo feedback, I think some discussion is required here or elsewhere about the possible impact of using a prescribed mixed-layer depth without a full representation of sea ice-ocean feedbacks.
• P3 L85: Re following statement, ‘although not specifically constrained in the model’. Can you clarify what you mean by this?
• P4 L93-94: It would be helpful to add a brief comment on the tuned albedos. How are they different from standard values used?
• P5 L127: Re following statement, ‘if it does, reductions are made to the lateral and basal melt rates by a constant factor’. A more detailed explanation would be helpful here on how the limits to the lateral and basal melt rates are calculated and applied.
• P6 L144: Can you provide more details on why you specifically selected this form of lateral melt redistribution (as opposed to an inverted r_n, or higher / lower spread of values for r_n)?
• P6 L145: Re following statement, ‘these values were distributed around 1 with the aim of keeping the total lateral melt volume approximately the same, such that the effect of the redistribution can be uniquely observed’. Does this not rely on an equal distribution of ice volume between thickness categories? In locations dominated by thin or thick ice, would this setup not produce abnormally high or low lateral melt rates?
• P7 L179-180: Re following statement, ‘lateral melting rate is applied to all categories equally’. You should clarify that this is for the standard lateral melt parameterisation only, not the simulation using Eq. (4).
• P8 L196-197: Re following statement, ‘contrary to intuition, increasing the lateral melt does not necessarily reduce sea ice area and volume’. My understanding from Fig. 3 is that in both simulations where the lateral melt rate is increased, the sea ice area is reduced, and the same is true for volume from March to August? I think this statement should be reworded to better reflect the results presented in Fig. 3.
• P9 L202-205: A map plot showing differences in sea ice concentration might be useful here to illustrate how the differences vary across the sea ice cover.
• P9 L211-212: Have you done any analysis of the model output to confirm that the available heat content in the surface ocean is the limiting factor for basal / lateral melting? This is not the only mechanism for the basal melt compensation effect in response to an increase in lateral melt in sea ice models e.g. in Bateson et al. (2020), it is demonstrated that the primary mechanism in standalone CICE is from the physical reduction in available sea ice area for basal melt (see Figs 4-5 in that paper). I think you either need to do some additional analysis to confirm that the mechanism suggested is the primary mechanism driving the basal melt compensation effect or acknowledge that it is not the only possible mechanism.
• P10 L221-222: I do not think you have presented sufficient evidence to demonstrate a significant ice-albedo feedback effect. There are other mechanisms that could plausibly result in a change to the sea ice mean state, particularly for simulations evaluated over decadal timescales e.g. a change in how sea ice is distributed between thickness categories, particularly since sea ice vertical growth rates are sensitive to the existing sea ice thickness, or more efficient use of available surface ocean heat content for sea ice melting. Can you directly isolate and quantify the change in sea ice mean state that can be attributed to the ice-albedo feedback mechanism here? Otherwise, you should acknowledge that the ice-albedo feedback is not the only possible mechanism that could cause a change in the mean sea ice state, and further analysis / studies are required to quantify its impact.
• P10 L223-227: Or due to non-equal distribution of sea ice volume between thickness categories? See earlier comment.
• P13 L298-300: Re following statement, ‘increasing the lateral melt rate results in similar rates of heat flux from the ocean to the ice in most areas of the Antarctic, but over the smaller resulting ice-covered area (not shown)’. A map plot would be useful here to illustrate this point.
• P13-14 L310-311: Re following statement, ‘here, ice-albedo feedback is not the main reason for why increasing lateral melting results in lower sea ice mean state.’ I may have missed or misunderstood something here, but it is not clear to me what you propose as the mechanism driving changes in the Antarctic sea ice mean state.
• P17 L352-355 & L359-361: As discussed above, I think you need to modify these conclusions given there are plausible mechanisms other than the ice-albedo feedback to explain why increases in lateral melt change the mean sea ice state.
• P18 L387-388: I suggest you put e.g. in the list of references here, given this is a non-exhaustive list of the different FSD model developments in existence.
• General comment about paper structure: It is not obvious to me why section 4.1 and 4.2 (particularly the former) are classified as discussion sections rather than results sections. Similarly, the final three paragraphs in the conclusions section could be moved to the discussion section since they introduce new material and discussion.
• General comment about conclusions: It would be useful to have some reflection on the limits of these conclusions e.g. the limitations of using the SOM.

Technical Corrections

• P1 L11: The phrase ‘well representing’ here is somewhat awkward. Maybe replace well with accurately?
• P2 L36: Should be 1980s, rather than 1980’s.
• P2 L38: The )’s setup of ‘Josberger and Martin (1981)’s formulation’ is awkward. Maybe replace with ‘the formulation of Josberger and Martin (1981)’.
• Figure 2 caption: ‘ncat’ is not referred to or defined anywhere else in this manuscript.
• P4 L108: Maybe replace ‘Lipscomb (2001) (Eq. 22)’ with ‘Eq. (22) in Lipscomb (2001)’.
• P5 L124: I do not think you have defined V_ice,n in this equation.
• P6 L135: In some places you have not followed The Cryosphere journal style guide e.g. here Eq. 3 should be Eq. (3), and section 2.3 below (L148) should be Sect. 2.3. Also, Fig 2 should be Fig. 2 on L150, and Figure 1 should be Fig. 1 on P7 L179. Similar issues are present elsewhere.
• P6 L147: Should this be ‘per unit volume’ rather than ‘per volume’?
• Figure 3 caption (and other figures): it would be helpful to clarify the number of years the results have been averaged over in the figure caption.
• P10 L230: Should ‘open water efficiency’ be ‘open water formation efficiency’.
• P11 L280: Seasonal should be season?

References

Bateson, A. W., Feltham, D. L., Schröder, D., Hosekova, L., Ridley, J. K. and Aksenov, Y.: Impact of sea ice floe size distribution on seasonal fragmentation and melt of Arctic sea ice, Cryosphere, 14, 403–428, doi:10.5194/tc-14-403-2020, 2020.

Roach, L. A., Bitz, C. M., Horvat, C. and Dean, S. M.: Advances in Modeling Interactions Between Sea Ice and Ocean Surface Waves, J. Adv. Model. Earth Syst., 11, 4167–4181, doi:10.1029/2019MS001836, 2019.

Steele, M.: Sea ice melting and floe geometry in a simple ice-ocean model, J. Geophys. Res.-Oceans, 97, 17729–17738, https://doi.org/10.1029/92JC01755, 1992.

Review of Arctic sea ice sensitivity to lateral melting representation in a coupled climate model

This paper assesses the importance of lateral melting in the context the coupled model CESM. By modifying the parameterization of lateral melting in a coupled model the authors can quantify the contribution of this process in the albedo feedback mechanism. The authors present an elegant quantification of the relative impact of lateral melt in term of efficiency at forming open water compared to the bottom melt efficiency.  This is potentially interesting for climate applications via the well known albedo feedback process. I would like the authors to discuss further this impact in terms of a potential increased contribution of lateral melt throughout the 21st century. I am also a little worried that the sensitivity study proposed is not well justified (why is it ok to vary the lateral melt scale by a factor 100) and not very well constrained by observations (in situ constraints or satellite observations of FSD). I am a little worried as well that the results presented here are only representative of this specific model configuration and in particular of the prescribed mixed layer depth (this could be particularly problematic for the Southern Ocean). As is often the case with such modelling sensitivity studies the paper asks more questions than offers insights and answers. The paper introduces a lot of model experiments but they remain at a qualitative level (arbitrary r_n function, extreme sensitivity lateral melt scale factor, unclear partition between lateral and bottom melt, prescribed mixed layer). As such it could be argued that the paper is more suitable for a modelling journal such as Ocean Modelling or GMD. In short I find the authors have presented an elegant modelling study of the contribution of lateral melt to the open water formation efficiency, are clearly well versed in the workings of the model (CICE/CESM), and in the processes controlling lateral melting but do not offer a significant new model development or model constraint from observations. Provided the authors improve on some (most) of the general comments below the paper could make a useful contribution to the community. Alternatively the authors could resubmit this fine modelling study to a modelling journal.

General comments:

1) Highlight main results better in the abstract (rewrite) as it is too generic at the moment

2) Include in the introduction a review of how lateral melting vs vertical melting is currently represented in CMIP6 (Keen et al 2020)

3) You use factors 10x and 100x without much discussion as to the validity of such choices. This correspond to changing the mean floe size by a factor 10 or 100 which is consistent with spatial gradients from pack ice to MIZ. Please explain all this a bit more and why a spatially constant scaling makes sense in your view. Discuss also impact of FSD as in Tsamados, Bateson or Horvat.

4) The participation between lateral and bottom melt in CICE (CESM) is not critically reviewed in my opinion

5) The authors introduce an ‘arbitrarily’ category dependent lateral melt redistribution function r_n. This is qualitative and not robustly justified or quantified.

6) On a related point this lateral melting scale is a dynamical quantity as more lateral melt leads to a reduction of floe sizes which in turn leads to more lateral melt. I am not sure that you fixed scale approach captures all this complexity and positive feedback.

7) Explain role of ocean and mixed layer heat reservoir in redistributing between vertical and lateral melt. I would like to see how sensitive your results are to this. With this in mind, are the results for the SO really meaningful (there the MLD can vary a lot and reach 100s of metres - definitely not a constant 10m as in your model)

8) Can you please constrain your results by comparing to more recent observations of floe size distributions. For example is it possible to assess which of 100x or control is more realistic in terms of relative distribution between vertical and lateral melt?

Specific comments:

P1 L24 “Vertical melt processes (surface and basal) can only form open water once the ice is very thin, while lateral melt can directly form open water area regardless of ice thickness” are you aware of MOSAiC experiments planning to re-evaluate the relevance of this statement.

P3 L81 How critical is the depth of the this SOB for your results? Sensitivity? I.e. how much of the heat in the SOB would have been lost to the lower ocean?

P4 L104 where all are

P4 L110 cite Massonnet, François, et al. "On the discretization of the ice thickness distribution in the NEMO3. 6-LIM3 global ocean–sea ice model." Geoscientific Model Development 12.8 (2019): 3745-3758.

P5 L120 D=300 as a default. Please discuss this approximation and why it could not be turned into a dynamical variables.

P5 L126 in addition

Figure 2 2 orders of magnitude of changes in the lateral melt rates ’scale’ seems very unconstrained by observations to me

P7 L164 to clarify definition of dV/dt_lat,n add these terms in eq (4)

P7 L165 remove as n already defined

P7 L169 to the average…in the control

Figure 1 I quite like the drawing but it does not represent ‘key melt processes’ but rather fluxes and variables of interest. Also I feel that it does not express all the quantities described in the paper as discussed in P7 L179

P7 L180 ‘open water forms equally in all categories’ seems in contradiction with r_n -> clarify this entire last paragraph.

P9 L201 minima

P9 L209 this communicating vase issue is crucial and I am worried that there is not enough discussion on how the relative basal to lateral ratio of melt is affected by the SOB characteristics (depth value) and lack of dynamics (fixed depth)

P11 L250 what about then a 10x & distribution sensitivity run

P11 L262 you mean efficiency in terms of open water formation but other aspects might still be affected (more winter growth…) -> clarify sentence

P12 L276 so which of 100x or control is more realistic?  Why not do a 1000x run or a 0.1x run as at present you do not seem to constrain these sensitivity runs at all from observations.

P12 L287 is your SOB appropriate for the SO where MLD can be much larger than 10m

P14 L310 on what basis you state this? Clarify

P16 L334 realistic as in consistent with observations? You have not discussed that much here at all.