the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 08 Aug 2023
Impact of melt pond and floe size on the optical properties of Arctic sea ice
Abstract. Melt ponds are usually modelled as horizontally infinite water layer overlaying on level ice. Then the albedo of summer Arctic sea ice can be determined by a linear combination of melt pond and bare ice albedo weighted by their areal coverage. However, this simulation does not reflect actual reality, in which ponds always have a limited size. In the present study, a Monte Carlo (MC) model was employed to investigate the influence of melt pond and floe size on the apparent optical properties of summer sea ice. The results showed that albedo and bottom transmittance mainly depended on the melt pond fraction (MPF) and ice thickness, respectively. The radiation absorbed by pond water depended on both pond depth and MPF. The radiation absorbed by ice depended on both pond depth and ice thickness. Two new parameters, the ratio of albedo (Kα) and transmittance (KT) of the linear combination to the MC model, are proposed to present the accuracy of the linear combination. For small-sized floe, Kα and KT decreased from 1.33 to 1.02 and from 3.96 to 1.05, respectively, as floe size increased from 2 to 40 m with an MPF of 50 %. Kα increased from 1.10 to 2.00 as MPF increased from 0 to 100 % with a floe size of 2 m. Solar radiation is more likely to penetrating into the lateral ocean in small floes than in large floes, and the small MPF, which has a high albedo, prevents solar energy from entering the floe. To reduce these uncertainties, new parameterization formulas for Kα and KT at different latitudes and different melting stages are provided. In the marginal ice zone, the average Kα and KT are about 1.03 and 1.12, respectively. During the melting season, the difference of Kα for MC model and linear combination could reach up to 34 % with the ice size 2 m for first-year ice. The results of this study can be used in future research to correct in situ data obtained via linear combination for floe sizes smaller than 20 m.
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RC1: 'Comment on egusphere-2023-1758', Anonymous Referee #1, 16 Aug 2023
The overall premise of the paper seems to be that melt pond and bare ice apparent optical properties (that is albedo and transmittance) are impacted by the scale of the feature. AND the authors assert that this means that a linear combination of the ‘pure’ melt pond and bare ice AOP’s, based on Melt Pond Fraction (MPF) does not represent the overall average albedo correctly. The reviewer is not convinced that the authors have shown this fundamental finding to be true.
- It IS true that observations of melt ponds and bare ice collected in field experiments cited in the paper are impacted by the size of the melt pond or bare ice. However this has two causes.
- Field of view: The first and likely most significant is simply the relative positioning of the sensor off the ground and its field of view. Most of the observations cited are collected with cosine-weighted collectors 1-2m off the ground. In this configuration ice that is over a meter away from nadir can have a significant impact on the overall reading. This is NOT due to a ‘true’ change in the AOP of the surface beneath the sensor – it is a contamination of the signal with the light from the adjacent surface. Lowering the sensor and reducing its footprint would provide a signal of only the surface. However, this is usually not done because surface shadowing from the sensor itself becomes significant and challenging to correct for. The field of view contamination, however, should not be interpreted as a change in the AOP.
- Lateral Scattering: The second cause is due to light scattering away from or toward the adjacent surface type within the media. This is the phenomena that the authors appear to be interested in. The concept that a melt pond immediately adjacent to bare ice may well be brighter because of the laterally scattered light entering the pond ice from the adjacent bare ice and being scattered out from there. Undoubtedly this also occurs. The question then is whether it produces a nonlinear effect. For the impact to be nonlinear, the scattering of light into melt ponds and away from melt ponds would have to not cancel out. (or similarly scattering of light laterally into the ocean would have to not be canceled out by transmission of light into the ice from the ocean.)
The key piece of evidence the authors provide for this being non-linear is the value of the ratios Ka and Kt which are found to deviate from unity, particularly at very small floe sizes. These represent the ratio of the albedo in an infinite linear mixing to the albedo in the modeled case, or the transmission in an infinite linear mixing to the transmission in the modeled case, respectively. The difference between 𝛼𝑙𝑖𝑛𝑒/ and 𝛼 appears to be driven by lateral loss of light out the boundary of the model domain.
And herein lies what appears to be a fundamental flaw with this study – there is no mechanism for allowing light IN at the lateral boundary. A lowering of albedo of ice because is adjacent to open water may in fact be offset by the INCREASE in albedo that would be apparent in the adjacent ocean due to light scattering laterally into the ocean. This could well compensate for the decrease in albedo of the ice. In other words a one-way flux is assumed at the lateral boundary by the authors, rather than the net of a two way flux across the lateral boundary. Given the diffuse light incident, and scatterers present in the adjacent ice/pond/water, there is undoubtedly a two way flux at the lateral floe boundary and a calculation of the net flux would be required before the Ka and Kt value could be meaningful for the purpose it is being used for here. This would likely require a more sophisticated modeling approach.
Regrettably this necessitates the paper be rejected. There is a foundation of quite a bit of work here and the authors will likely find value in fixing their model and submitting a new writeup, which will likely have different conclusions.
Other comments:
Large portions of the solution space being explored are physically infeasible. 100% pond coverage is extremely rare, and it has been shown that areas around the edges of floes tend to have lower pond coverage – meaning small floes rarely have pond coverage above 30%. Similarly floe sizes of 2 m do not commonly make up a significant fraction of the overall ice pack (there are definitely exceptions, but these are uncommon). So much of the small floe and high melt pond fraction solution space explored is simply non-existent in nature.
Line 130. The reviewer is unable to find where this paper concludes that AOPs are affected by MPF. Though that dataset observes meltpond fraction changes and AOP changes, no causative connection is made.
Line 176 and elsewhere… as Hp increases, the transmittance decreases slightly and the albedo decreases slightly. Caution is warranted here. The way this test is being conducted is not reflective of the real world evolution where melt ponds deepen due to ongoing melt. In an evolution sense, as pond depth increases, generally the underlying ice is melting to produce the pond water. So increasing pond depth while holding ice thickness constant is not expected. As a result these outcomes could be misinterpreted easily to say that as ponds deepen little change in albedo will occur. In reality that is not the case. As ponds deepen, underlying ice thins and albedo declines rapidly.
Diffuse conditions are indeed common in summer in the Arctic but still represent only 60-80% of the time. How does direct insolation impact the results?
Floes of size <100m are not uncommon but generally do not represent a large fraction of the coverage. Are the deviations here ever significant in the real world?
Line 350 “black ice” this is not a term in common usage. Please clarify what it is you are referring to.
Line 359 “Arctic floe size always increases with Latitude” – this is false and must be removed.
Line 440-450 other authors have noted considerable issues with these MPF determination schemes based on considerably more extensive validation. Simply put, pond albedo varies too much for spectral unmixing to be reliable. See for example Wright and Polashenski 2020.
Line 473 – The reviewer is not aware of any long term record of floe size, unless the authors have a citation or evidence to support this statement on the trend in floe size, it is speculative and will need to be removed.
Throughout the paper would benefit from a thorough editing by a native English speaker. There are lots of missing definite adjectives (a, the) and plural/singular context mismatches as well as some general stylistic issues.
Citation: https://doi.org/10.5194/egusphere-2023-1758-RC1 -
RC2: 'Review of egusphere-2023-1758', Anonymous Referee #2, 24 Aug 2023
The manuscript “Impact of melt pond and floe size on the optical properties of Arctic sea ice” by Zhang et al. uses a radiative transfer model to explore the impact of different geometric properties of sea ice on the partitioning of solar radiation. In particular, they test the response to melt pond and floe depth/thickness, floe diameter, and melt pond fraction, all with (I believe) a constant floe geometry. The results primary test the degree to which the modeled results agree with a linear combination of pond and ice albedos, and they find that the modeled optical properties more closely match a linear combination with larger floe size and lower melt pond fractions. They suggest that these results are useful for interpreting observational data, likely especially satellite observations, though it is not clear in what way.
Some of the analyses regarding sensitivity to floe size are novel and could be useful for thinking about the impact of incorporating these parameters into new sea ice models. Overall, however, I am confused by the motivation and potential applications of this work. The problem that this manuscript seeks to solve needs to be clarified before it is possible to evaluate whether this manuscript is publishable in The Cryosphere. Regardless, major revisions will be needed to clarify the results and improve presentation. I cannot comment specifically on the accuracy of the model, so hopefully another reviewer has the expertise to evaluate the details within section 2.2.
Major concerns:
- As currently written, I do not understand the question that the work is trying to answer. The authors motivate the work by saying that melt ponds are “assumed as a plane-parallel layer with infinite pure water in most models”, but I understand that most global climate models (such as CICE, which they base many parameter choices on) use a radiative transfer model which represents pond thickness and fraction, as is done here. The end of the discussion (L443-446) seems to include some possible applications in terms of satellite albedo retrievals, but the results are not discussed in specific reference to this type of data. From my perspective, a potentially novel aspect is the exploration of floe size with this model, especially with the development of coupled floe size models (e.g., Roach et al., 2021), so this could be expanded on.
- Section 4.1 presents a variety of comparisons with existing models and prior observations. Perhaps I have missed the point of this section, but if the primary goal is validation of the model, it seems that it should be included in methods (or just after) rather than as results/discussion. In fact, these plots seem to show that the model is in some cases replicating results that have already been published elsewhere. Additionally, the results and comparisons that are shown should be better motivated by/connected to the results shown. Is Figure 10 necessary here? (Or, could it be moved to supplemental material?)
- Validity of conclusions. The authors state that “These results provide a theoretical basis for using satellite remote sensing to calculate the albedo of Arctic floe surface with a large horizontal extent” (L231-232). It is not made clear how directly the linear combination method they compare to is for these retrievals; is this the main way albedo is retrieved from satellite observations? As such, it is not clear how these results can be applied to do so. In addition, what parts of the parameter space explored are realistic for the Arctic? It may be helpful to contextualize the results in terms of Ka and Kt with typical Arctic conditions. E.g., how much of an impact could this “improved” model make on the Arctic scale?
Minor concerns (line-by-line):
- L10-11: rewrite to clarify that this has been well-shown by prior studies (e.g., Webster et al., 2015, and others)
- L21: How widely applicable are results if primarily benefit correction for floe sizes less than 20 m? What fraction of data covers this area?
- L25: add “average” before “albedo”, and change values to ~0.85 and 0.45 (or similar) to reflect average albedo in cited references OR edit sentence to reflect that the cited albedos are for the typical bare ice and a particularly dark pond.
- L30: Need to add definition of albedo and transmittance early in the introduction
- L33: change “twice” to “two times”
- L40: I am not sure I agree with the statement that this is how it’s represented in “most models”. Are you referring to climate-scale sea ice models (e.g., CMIP6)? If so, need to add citation to overview mansucripts, e.g., Keen et al., 2020 and note which models.
- L42: Even after reading the manuscript, I’m still a bit confused by this statement. How does the pond size impact the albedo? Do you mean it impacts measured albedo because of the typical footprint of observations depending on height (cosine response)? If so, the paper needs to be clarified throughout that the goal here is to address measurement interpretation issues, and how this depends on measurement height.
- L67: sea-ice models that I am familiar with (e.g., the Briegleb and Light parameterization used in CICE) resolve 5 layers but with no SSL beneath ponded ice. It would be helpful to mention the similarities and differences between the modeling setup used here and that in common sea ice models and the likely impact on the results.
- Figure 1: Some clarification on geometry would be helpful. In particular, are the ponds always assume centered on the floe? Is the bottom transmission an average over an area (of some size) or at a point?
- L97: “have died” doesn’t seem like appropriate phrasing here; please revise
- L102: “photo” to “photon”
- L109: please revise “It is obvious that…” – this may not be obvious to all readers!
- L116: please revise “So do Tice…”
- L118: why was the model limited to these wavelengths? 70-80% is a significant fraction of incident solar energy, but it seems feasible to extend these limits to include a more significant fraction.
- L123: reference for these scattering coefficients?
- L129: How were these ranges chosen? Are there parts of this parameter space you don’t expect to be physically realistic? (e.g., .5 m pond with .5 m ice?)
- L130: Somewhere it needs to be stated that the IOPs of ice (bare ice and under ponds) also plays an impact. In particular, it has been observed that the albedo of ponds is largely impacted by scattering of the ice below, not just the thickness parameters as noted (e.g., Light et al., 2022). How does this impact the results and conclusions?
- L142: By “sensible” do you mean “reasonable”? In what way?
- Figure 2-4: Please add labels (such as titles) on each subpanel stating the parameter shown, such as “albedo”, “bottom transmittance”, etc.
- L149: replace “in relation to” with “into”
- L150: as noted on figure 1, it would be helpful to clarify the area that parameters such as albedo and transmittance are calculated over. It seems like these are floe-averaged?
- L174: The choice of 2.5 m thick ice for investigating MPF and Hp seems questionable. That is quite thick for the Arctic (especially these days), as most level first-year ice would likely be in the 1.5m range. Would the conclusions change if you explored difference ice thickness within the reasonable range? I assume that the response to Hp would be greater with thinner ice.
- L176: Why increase to 100%? Is this physically possible?
- Figure 5. Label with “MPF=100” and “MPF=0”. Also, why use 100% and 0%? Neither are particularly realistic, so it would be more interesting to see the extremes within observe range (maybe 5-50%?)
- Figure 5. Check the x-axis label. In the schematic in Fig. 1 “d” is defined as depth/thickness but these seem like diameters/floe size, so should be Sp and Si?
- L209: Perhaps replace “AOPs” with partitioning of solar radiation”
- L231-2: How is this true? In what types of measurements does albedo depend on the floe size? This needs to be further justified and expanded on to say how these results can be applied.
- Figure 6/L234-235: What other parameters are used here?
- L245-247: What does “open pond” mean here?
- L256: by “pure pond” do you mean just from the pond itself, rather than averaged over the floe?
- L260: missing “absorbed” after “rapidly”?
- L264: decapitalize “comparing”
- L265-266: It would be helpful contextualize how the impact of floe size on optical properties interacts with other processes that depend on floe size, e.g. lateral melt (Horvat et al., 2016 and others)
- L271: what is meant by “interlayer”?
- Figure 7: To be honest I remain a bit confused how Case 1 can be so different than Case 2 where the only difference is an increase in floe size. Perhaps this is because of some detail in the depth of spectral net irradiance that is being analyzed, or the averaging interval? Please expand on this.
- Figure 7(d): would be helpful to label the depths of “pond” and “ice”, etc. Also, it may be helpful to make these colors more distinct.
- Figure 8: I am confused how this is a comparison. (a) shows albedo from the BL model and (b) shows the transmission for the MC model. Can you show both models on both panels?
- What is the additional benefit of this model compared to other commonly-used models (e.g., BL) if the outputs compare well?
- L294: add (“H”) after ice thickness
- L333: “not well enough” to “poor due to small range”
- L342: “melting of sea ice” to “sea ice melted”
- L348: was snowfall observed? If so, include a reference.
- L353: Does this justify having more variable IOPs in your model (or, exploring sensitivity to other values)?
- L359: Floe size does not always increase with latitude; this is seasonally and regionally variable. Please revise.
- L366: revise “part of the ice concentration”
- Figure 13c: convert this to meters. Perhaps a log scale would help show the full range?
- Figure 14: I would find it more helpful to show the distribution of partitioning along different parts of the transect. Can this be re-framed to show how partitioning varies spatially as a function of changes in ice characteristics?
- L387: I am struggling to understand the physical reasoning for why lateral transmittance decreases with smaller floes. Is this because the ice is thinner, as well? It would be helpful to state more clearly the biggest factors in modeled variability.
- L404: I am confused by this physical interpretation; shouldn’t more photons make it to the bottom boundary of the floe with thinner ice?
- Figure 15: fix spelling of “latitude”
- Figure 15: I am not convinced that latitude is the correct framing for this parameterization, and the physical interpretation does not seem well founded. Perhaps I could be more convinced that this parameterization could be applied if done as a function of floe size or distance from the ice edge.
- L421: (“The smaller the floe…”) This seems to disagree with the statement at L387
- L435: Again, would be helpful to clarify when the infinite parallel plane assumption is used? Does this imply 100% MPF?
- L440: How common are ponds on floes 20 m or smaller? I don’t feel like I have commonly observed ponds in the MIZ, so would be helpful to cite references with imagery or observations of this phenomena.
- L443-446: These sentences seem to me to provide the main motivation for the study. If so, it would be good to introduce this more clearly in the introduction.
- L450: Add space before “8”
- L469-470: As noted previously, the latitude is not the controlling factor here (especially in a changing climate!) so this is not a useful or robust parameterization, currently.
Citation: https://doi.org/10.5194/egusphere-2023-1758-RC2 -
RC3: 'Comment on egusphere-2023-1758', Anonymous Referee #3, 19 Sep 2023
The paper is dedicated to investigations of the impact of the floe size onto the observed optical properties of ponded sea ice, and suggests that the semi-infinite ice layer and a linear mixture of ponds and sea ice currently used in published literature is not sufficient to represent the optical properties of sea ice correctly i.e. that the e.g. melt pond fraction inaccuracies stem from not accounting for the floe size effects.
The paper is somewhat sparsely written so that I have a feeling that some important details have been left out. I therefore have some open questions and major concerns: Unfortunately, it is not convincing to me that the presented approach is good enough to represent sea ice as a dense, low absorbing, highly scattering medium, where higher orders of scattering still have a lot of weight and any single scattering inaccuracies will inevitably accumulate. It would be good to show intermittent results in form of a medium phase function, where the distribution of the exiting radiation is shown e.g. in the principal plane. If you aim at recommendations for satellite studies, you need to include not only diffuse but direct radiation (sun as a light source), otherwise your results are not applicable, and especially for the Arctic and MPF, low sun elevation angles need to be considered. How does the medium phase function look like? Is the forward scattering prevalent or the backscattering? How does the medium phase function depend upon different sea ice parameters e.g. effective grain size? Which orders of scattering are most important? How does the result compare with e. g. BRDF measurements or models for at just sea ice without ponding at first? I am sorry, I believe all these steps should be taken before one can go further, and certainly before recommendations and conclusions.
I could not understand whether the surrounding water around the discrete ice floe and the neighbor floes have been represented as well, and whether incoming multiply scattered radiation, e g. “floe2-floe1”, “floe1-floe2-floe1”, “floe1-floe2-water-floe1”, “floe1-floe2-atmosphere-floe1”and so forth, have been accounted for and till which order of scattering. If you are going to apply your findings to satellite data, you need to model the atmospheric adjacency effects and multiple scattering therein as well. Note that Zege et al 2015 uses radiative transfer to correct for the atmospheric effects and long-term proven approximation of the radiative transfer in a dense medium to calculate the sea ice part which is able to give correct angular distribution of directional reflectance, which is only later is hemispherically integrated to give spectral albedo. You compare just the albedo (Fig 9) but this is not sufficient to demonstrate good angular correspondence, which is crucial to evaluate a Monte-Carlo approach. Another good test is to check that the integral of your incoming and outgoing/absorbed radiation are exactly the same i.e. you do not lose photons. Why do you remove the photons that reached the side and bottom ice borders? Would not they be reflected back into the medium from this flat border according to Fresnel equations, with total internal reflection at the critical angle? And when transmitted, would not they be reflected back by the neighbor floe and then potentially serve as incoming radiation to the floe under investigations?
For the validation against in situ measurements, when it, after addressing the above concerns, comes to the actual study of the effect of the floe sizes, I believe not the ship cruises but some very high resolution satellite imagery should be used (possibly of 1m resolution, e.g. declassified Global Fiducials Library images), for the reason that they provide an objective information on pond size and floe size. But frankly, I think what you are simulating is the different height of your sensor above the surface, as I could not recognize rigorous accounting for adjacency effects of neighboring ice floes. Of course it is possible that the text simply lacks some important details so that I have misunderstood. In this case, please make sure to reformulate your text clearer in this respect, or to add corresponding investigations should they have been omitted. Without them, the drawn conclusions are misleading at best.
I recommend to withdraw and resubmit when ready, or a major revision with another round of reviews, according the editor’s decision.
Citation: https://doi.org/10.5194/egusphere-2023-1758-RC3
Status: closed
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RC1: 'Comment on egusphere-2023-1758', Anonymous Referee #1, 16 Aug 2023
The overall premise of the paper seems to be that melt pond and bare ice apparent optical properties (that is albedo and transmittance) are impacted by the scale of the feature. AND the authors assert that this means that a linear combination of the ‘pure’ melt pond and bare ice AOP’s, based on Melt Pond Fraction (MPF) does not represent the overall average albedo correctly. The reviewer is not convinced that the authors have shown this fundamental finding to be true.
- It IS true that observations of melt ponds and bare ice collected in field experiments cited in the paper are impacted by the size of the melt pond or bare ice. However this has two causes.
- Field of view: The first and likely most significant is simply the relative positioning of the sensor off the ground and its field of view. Most of the observations cited are collected with cosine-weighted collectors 1-2m off the ground. In this configuration ice that is over a meter away from nadir can have a significant impact on the overall reading. This is NOT due to a ‘true’ change in the AOP of the surface beneath the sensor – it is a contamination of the signal with the light from the adjacent surface. Lowering the sensor and reducing its footprint would provide a signal of only the surface. However, this is usually not done because surface shadowing from the sensor itself becomes significant and challenging to correct for. The field of view contamination, however, should not be interpreted as a change in the AOP.
- Lateral Scattering: The second cause is due to light scattering away from or toward the adjacent surface type within the media. This is the phenomena that the authors appear to be interested in. The concept that a melt pond immediately adjacent to bare ice may well be brighter because of the laterally scattered light entering the pond ice from the adjacent bare ice and being scattered out from there. Undoubtedly this also occurs. The question then is whether it produces a nonlinear effect. For the impact to be nonlinear, the scattering of light into melt ponds and away from melt ponds would have to not cancel out. (or similarly scattering of light laterally into the ocean would have to not be canceled out by transmission of light into the ice from the ocean.)
The key piece of evidence the authors provide for this being non-linear is the value of the ratios Ka and Kt which are found to deviate from unity, particularly at very small floe sizes. These represent the ratio of the albedo in an infinite linear mixing to the albedo in the modeled case, or the transmission in an infinite linear mixing to the transmission in the modeled case, respectively. The difference between 𝛼𝑙𝑖𝑛𝑒/ and 𝛼 appears to be driven by lateral loss of light out the boundary of the model domain.
And herein lies what appears to be a fundamental flaw with this study – there is no mechanism for allowing light IN at the lateral boundary. A lowering of albedo of ice because is adjacent to open water may in fact be offset by the INCREASE in albedo that would be apparent in the adjacent ocean due to light scattering laterally into the ocean. This could well compensate for the decrease in albedo of the ice. In other words a one-way flux is assumed at the lateral boundary by the authors, rather than the net of a two way flux across the lateral boundary. Given the diffuse light incident, and scatterers present in the adjacent ice/pond/water, there is undoubtedly a two way flux at the lateral floe boundary and a calculation of the net flux would be required before the Ka and Kt value could be meaningful for the purpose it is being used for here. This would likely require a more sophisticated modeling approach.
Regrettably this necessitates the paper be rejected. There is a foundation of quite a bit of work here and the authors will likely find value in fixing their model and submitting a new writeup, which will likely have different conclusions.
Other comments:
Large portions of the solution space being explored are physically infeasible. 100% pond coverage is extremely rare, and it has been shown that areas around the edges of floes tend to have lower pond coverage – meaning small floes rarely have pond coverage above 30%. Similarly floe sizes of 2 m do not commonly make up a significant fraction of the overall ice pack (there are definitely exceptions, but these are uncommon). So much of the small floe and high melt pond fraction solution space explored is simply non-existent in nature.
Line 130. The reviewer is unable to find where this paper concludes that AOPs are affected by MPF. Though that dataset observes meltpond fraction changes and AOP changes, no causative connection is made.
Line 176 and elsewhere… as Hp increases, the transmittance decreases slightly and the albedo decreases slightly. Caution is warranted here. The way this test is being conducted is not reflective of the real world evolution where melt ponds deepen due to ongoing melt. In an evolution sense, as pond depth increases, generally the underlying ice is melting to produce the pond water. So increasing pond depth while holding ice thickness constant is not expected. As a result these outcomes could be misinterpreted easily to say that as ponds deepen little change in albedo will occur. In reality that is not the case. As ponds deepen, underlying ice thins and albedo declines rapidly.
Diffuse conditions are indeed common in summer in the Arctic but still represent only 60-80% of the time. How does direct insolation impact the results?
Floes of size <100m are not uncommon but generally do not represent a large fraction of the coverage. Are the deviations here ever significant in the real world?
Line 350 “black ice” this is not a term in common usage. Please clarify what it is you are referring to.
Line 359 “Arctic floe size always increases with Latitude” – this is false and must be removed.
Line 440-450 other authors have noted considerable issues with these MPF determination schemes based on considerably more extensive validation. Simply put, pond albedo varies too much for spectral unmixing to be reliable. See for example Wright and Polashenski 2020.
Line 473 – The reviewer is not aware of any long term record of floe size, unless the authors have a citation or evidence to support this statement on the trend in floe size, it is speculative and will need to be removed.
Throughout the paper would benefit from a thorough editing by a native English speaker. There are lots of missing definite adjectives (a, the) and plural/singular context mismatches as well as some general stylistic issues.
Citation: https://doi.org/10.5194/egusphere-2023-1758-RC1 -
RC2: 'Review of egusphere-2023-1758', Anonymous Referee #2, 24 Aug 2023
The manuscript “Impact of melt pond and floe size on the optical properties of Arctic sea ice” by Zhang et al. uses a radiative transfer model to explore the impact of different geometric properties of sea ice on the partitioning of solar radiation. In particular, they test the response to melt pond and floe depth/thickness, floe diameter, and melt pond fraction, all with (I believe) a constant floe geometry. The results primary test the degree to which the modeled results agree with a linear combination of pond and ice albedos, and they find that the modeled optical properties more closely match a linear combination with larger floe size and lower melt pond fractions. They suggest that these results are useful for interpreting observational data, likely especially satellite observations, though it is not clear in what way.
Some of the analyses regarding sensitivity to floe size are novel and could be useful for thinking about the impact of incorporating these parameters into new sea ice models. Overall, however, I am confused by the motivation and potential applications of this work. The problem that this manuscript seeks to solve needs to be clarified before it is possible to evaluate whether this manuscript is publishable in The Cryosphere. Regardless, major revisions will be needed to clarify the results and improve presentation. I cannot comment specifically on the accuracy of the model, so hopefully another reviewer has the expertise to evaluate the details within section 2.2.
Major concerns:
- As currently written, I do not understand the question that the work is trying to answer. The authors motivate the work by saying that melt ponds are “assumed as a plane-parallel layer with infinite pure water in most models”, but I understand that most global climate models (such as CICE, which they base many parameter choices on) use a radiative transfer model which represents pond thickness and fraction, as is done here. The end of the discussion (L443-446) seems to include some possible applications in terms of satellite albedo retrievals, but the results are not discussed in specific reference to this type of data. From my perspective, a potentially novel aspect is the exploration of floe size with this model, especially with the development of coupled floe size models (e.g., Roach et al., 2021), so this could be expanded on.
- Section 4.1 presents a variety of comparisons with existing models and prior observations. Perhaps I have missed the point of this section, but if the primary goal is validation of the model, it seems that it should be included in methods (or just after) rather than as results/discussion. In fact, these plots seem to show that the model is in some cases replicating results that have already been published elsewhere. Additionally, the results and comparisons that are shown should be better motivated by/connected to the results shown. Is Figure 10 necessary here? (Or, could it be moved to supplemental material?)
- Validity of conclusions. The authors state that “These results provide a theoretical basis for using satellite remote sensing to calculate the albedo of Arctic floe surface with a large horizontal extent” (L231-232). It is not made clear how directly the linear combination method they compare to is for these retrievals; is this the main way albedo is retrieved from satellite observations? As such, it is not clear how these results can be applied to do so. In addition, what parts of the parameter space explored are realistic for the Arctic? It may be helpful to contextualize the results in terms of Ka and Kt with typical Arctic conditions. E.g., how much of an impact could this “improved” model make on the Arctic scale?
Minor concerns (line-by-line):
- L10-11: rewrite to clarify that this has been well-shown by prior studies (e.g., Webster et al., 2015, and others)
- L21: How widely applicable are results if primarily benefit correction for floe sizes less than 20 m? What fraction of data covers this area?
- L25: add “average” before “albedo”, and change values to ~0.85 and 0.45 (or similar) to reflect average albedo in cited references OR edit sentence to reflect that the cited albedos are for the typical bare ice and a particularly dark pond.
- L30: Need to add definition of albedo and transmittance early in the introduction
- L33: change “twice” to “two times”
- L40: I am not sure I agree with the statement that this is how it’s represented in “most models”. Are you referring to climate-scale sea ice models (e.g., CMIP6)? If so, need to add citation to overview mansucripts, e.g., Keen et al., 2020 and note which models.
- L42: Even after reading the manuscript, I’m still a bit confused by this statement. How does the pond size impact the albedo? Do you mean it impacts measured albedo because of the typical footprint of observations depending on height (cosine response)? If so, the paper needs to be clarified throughout that the goal here is to address measurement interpretation issues, and how this depends on measurement height.
- L67: sea-ice models that I am familiar with (e.g., the Briegleb and Light parameterization used in CICE) resolve 5 layers but with no SSL beneath ponded ice. It would be helpful to mention the similarities and differences between the modeling setup used here and that in common sea ice models and the likely impact on the results.
- Figure 1: Some clarification on geometry would be helpful. In particular, are the ponds always assume centered on the floe? Is the bottom transmission an average over an area (of some size) or at a point?
- L97: “have died” doesn’t seem like appropriate phrasing here; please revise
- L102: “photo” to “photon”
- L109: please revise “It is obvious that…” – this may not be obvious to all readers!
- L116: please revise “So do Tice…”
- L118: why was the model limited to these wavelengths? 70-80% is a significant fraction of incident solar energy, but it seems feasible to extend these limits to include a more significant fraction.
- L123: reference for these scattering coefficients?
- L129: How were these ranges chosen? Are there parts of this parameter space you don’t expect to be physically realistic? (e.g., .5 m pond with .5 m ice?)
- L130: Somewhere it needs to be stated that the IOPs of ice (bare ice and under ponds) also plays an impact. In particular, it has been observed that the albedo of ponds is largely impacted by scattering of the ice below, not just the thickness parameters as noted (e.g., Light et al., 2022). How does this impact the results and conclusions?
- L142: By “sensible” do you mean “reasonable”? In what way?
- Figure 2-4: Please add labels (such as titles) on each subpanel stating the parameter shown, such as “albedo”, “bottom transmittance”, etc.
- L149: replace “in relation to” with “into”
- L150: as noted on figure 1, it would be helpful to clarify the area that parameters such as albedo and transmittance are calculated over. It seems like these are floe-averaged?
- L174: The choice of 2.5 m thick ice for investigating MPF and Hp seems questionable. That is quite thick for the Arctic (especially these days), as most level first-year ice would likely be in the 1.5m range. Would the conclusions change if you explored difference ice thickness within the reasonable range? I assume that the response to Hp would be greater with thinner ice.
- L176: Why increase to 100%? Is this physically possible?
- Figure 5. Label with “MPF=100” and “MPF=0”. Also, why use 100% and 0%? Neither are particularly realistic, so it would be more interesting to see the extremes within observe range (maybe 5-50%?)
- Figure 5. Check the x-axis label. In the schematic in Fig. 1 “d” is defined as depth/thickness but these seem like diameters/floe size, so should be Sp and Si?
- L209: Perhaps replace “AOPs” with partitioning of solar radiation”
- L231-2: How is this true? In what types of measurements does albedo depend on the floe size? This needs to be further justified and expanded on to say how these results can be applied.
- Figure 6/L234-235: What other parameters are used here?
- L245-247: What does “open pond” mean here?
- L256: by “pure pond” do you mean just from the pond itself, rather than averaged over the floe?
- L260: missing “absorbed” after “rapidly”?
- L264: decapitalize “comparing”
- L265-266: It would be helpful contextualize how the impact of floe size on optical properties interacts with other processes that depend on floe size, e.g. lateral melt (Horvat et al., 2016 and others)
- L271: what is meant by “interlayer”?
- Figure 7: To be honest I remain a bit confused how Case 1 can be so different than Case 2 where the only difference is an increase in floe size. Perhaps this is because of some detail in the depth of spectral net irradiance that is being analyzed, or the averaging interval? Please expand on this.
- Figure 7(d): would be helpful to label the depths of “pond” and “ice”, etc. Also, it may be helpful to make these colors more distinct.
- Figure 8: I am confused how this is a comparison. (a) shows albedo from the BL model and (b) shows the transmission for the MC model. Can you show both models on both panels?
- What is the additional benefit of this model compared to other commonly-used models (e.g., BL) if the outputs compare well?
- L294: add (“H”) after ice thickness
- L333: “not well enough” to “poor due to small range”
- L342: “melting of sea ice” to “sea ice melted”
- L348: was snowfall observed? If so, include a reference.
- L353: Does this justify having more variable IOPs in your model (or, exploring sensitivity to other values)?
- L359: Floe size does not always increase with latitude; this is seasonally and regionally variable. Please revise.
- L366: revise “part of the ice concentration”
- Figure 13c: convert this to meters. Perhaps a log scale would help show the full range?
- Figure 14: I would find it more helpful to show the distribution of partitioning along different parts of the transect. Can this be re-framed to show how partitioning varies spatially as a function of changes in ice characteristics?
- L387: I am struggling to understand the physical reasoning for why lateral transmittance decreases with smaller floes. Is this because the ice is thinner, as well? It would be helpful to state more clearly the biggest factors in modeled variability.
- L404: I am confused by this physical interpretation; shouldn’t more photons make it to the bottom boundary of the floe with thinner ice?
- Figure 15: fix spelling of “latitude”
- Figure 15: I am not convinced that latitude is the correct framing for this parameterization, and the physical interpretation does not seem well founded. Perhaps I could be more convinced that this parameterization could be applied if done as a function of floe size or distance from the ice edge.
- L421: (“The smaller the floe…”) This seems to disagree with the statement at L387
- L435: Again, would be helpful to clarify when the infinite parallel plane assumption is used? Does this imply 100% MPF?
- L440: How common are ponds on floes 20 m or smaller? I don’t feel like I have commonly observed ponds in the MIZ, so would be helpful to cite references with imagery or observations of this phenomena.
- L443-446: These sentences seem to me to provide the main motivation for the study. If so, it would be good to introduce this more clearly in the introduction.
- L450: Add space before “8”
- L469-470: As noted previously, the latitude is not the controlling factor here (especially in a changing climate!) so this is not a useful or robust parameterization, currently.
Citation: https://doi.org/10.5194/egusphere-2023-1758-RC2 -
RC3: 'Comment on egusphere-2023-1758', Anonymous Referee #3, 19 Sep 2023
The paper is dedicated to investigations of the impact of the floe size onto the observed optical properties of ponded sea ice, and suggests that the semi-infinite ice layer and a linear mixture of ponds and sea ice currently used in published literature is not sufficient to represent the optical properties of sea ice correctly i.e. that the e.g. melt pond fraction inaccuracies stem from not accounting for the floe size effects.
The paper is somewhat sparsely written so that I have a feeling that some important details have been left out. I therefore have some open questions and major concerns: Unfortunately, it is not convincing to me that the presented approach is good enough to represent sea ice as a dense, low absorbing, highly scattering medium, where higher orders of scattering still have a lot of weight and any single scattering inaccuracies will inevitably accumulate. It would be good to show intermittent results in form of a medium phase function, where the distribution of the exiting radiation is shown e.g. in the principal plane. If you aim at recommendations for satellite studies, you need to include not only diffuse but direct radiation (sun as a light source), otherwise your results are not applicable, and especially for the Arctic and MPF, low sun elevation angles need to be considered. How does the medium phase function look like? Is the forward scattering prevalent or the backscattering? How does the medium phase function depend upon different sea ice parameters e.g. effective grain size? Which orders of scattering are most important? How does the result compare with e. g. BRDF measurements or models for at just sea ice without ponding at first? I am sorry, I believe all these steps should be taken before one can go further, and certainly before recommendations and conclusions.
I could not understand whether the surrounding water around the discrete ice floe and the neighbor floes have been represented as well, and whether incoming multiply scattered radiation, e g. “floe2-floe1”, “floe1-floe2-floe1”, “floe1-floe2-water-floe1”, “floe1-floe2-atmosphere-floe1”and so forth, have been accounted for and till which order of scattering. If you are going to apply your findings to satellite data, you need to model the atmospheric adjacency effects and multiple scattering therein as well. Note that Zege et al 2015 uses radiative transfer to correct for the atmospheric effects and long-term proven approximation of the radiative transfer in a dense medium to calculate the sea ice part which is able to give correct angular distribution of directional reflectance, which is only later is hemispherically integrated to give spectral albedo. You compare just the albedo (Fig 9) but this is not sufficient to demonstrate good angular correspondence, which is crucial to evaluate a Monte-Carlo approach. Another good test is to check that the integral of your incoming and outgoing/absorbed radiation are exactly the same i.e. you do not lose photons. Why do you remove the photons that reached the side and bottom ice borders? Would not they be reflected back into the medium from this flat border according to Fresnel equations, with total internal reflection at the critical angle? And when transmitted, would not they be reflected back by the neighbor floe and then potentially serve as incoming radiation to the floe under investigations?
For the validation against in situ measurements, when it, after addressing the above concerns, comes to the actual study of the effect of the floe sizes, I believe not the ship cruises but some very high resolution satellite imagery should be used (possibly of 1m resolution, e.g. declassified Global Fiducials Library images), for the reason that they provide an objective information on pond size and floe size. But frankly, I think what you are simulating is the different height of your sensor above the surface, as I could not recognize rigorous accounting for adjacency effects of neighboring ice floes. Of course it is possible that the text simply lacks some important details so that I have misunderstood. In this case, please make sure to reformulate your text clearer in this respect, or to add corresponding investigations should they have been omitted. Without them, the drawn conclusions are misleading at best.
I recommend to withdraw and resubmit when ready, or a major revision with another round of reviews, according the editor’s decision.
Citation: https://doi.org/10.5194/egusphere-2023-1758-RC3
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