the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 05 Feb 2024
An improved firn densification model by integrating the Bucket scheme and Darcy’s law over the Greenland Ice Sheet
Abstract. Modelling firn densification is conducive to enhancing the accuracy of monitoring glacier mass changes from satellite altimetry and extracting climate records from ice cores. As snowmelt is increasing in a warming climate on the Greenland Ice Sheet (GrIS), quantifying the role of liquid water within the firn layer becomes critical for simulating firn properties. Nevertheless, previously published firn densification models do not accurarely capture the extensive density fluctuations caused by liquid water refreezing in observations. In this study, an improved firn densification model is developed by integrating the Bucket scheme and Darcy’s law to assess the capillary retention, refreezing, and runoff of liquid water within the firn layer. Moreover, the improved model is employed for two study sites, KAN_U and Dye-2, over the GrIS to evaluate its performance. At the KAN_U site, characterized by high snowfall and snowmelt rates, the model captures high-density peaks (~917 kg · m-3) caused by the refreezing of liquid water, which corresponds to the formation of ice lenses or ice layers. At Dye-2 with comparatively limited liquid water, the model also captures the features of high-density layers resulting from refreezing. In general, the modelled firn depth-density profiles at the two study sites agree well with the in situ measurements obtained from 12 firn cores drilled between 2012 and 2019. For the regions with limited liquid water, low-density peaks are probably overestimated due to excess refreezing or limited knowledge of ice lenses or ice layers. Future work is expected to enhance the understanding and further improve numerical simulation of the mechanisms involved in firn densification, and subsequently integrate data-driven and physical mechanisms into firn densification modelling.
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Status: closed
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RC1: 'Review of firn modelling manuscript by Zhang et al.', Anonymous Referee #1, 11 Mar 2024
Review of "An improved firn densification model by integrating the bucket scheme and Darcy's law over the Greenland Ice Sheet"", submitted for publication to The Cryosphere Discussions by Xueyu Zhang et al.
GENERAL
This paper presents a combination of firn modelling techniques in order to improve the model representation of the formation of ice lenses, ice slabs and other heterogeneous density features. The authors present a modeling framework that combines the bucket scheme on one hand, and Darcy's law for any meltwater above the irreducible water content on the other hand. They test the model at two sites on the Greenland Ice Sheet.
The paper is generally well written and its structure is good. Also, the topic is relevant since hydrology in firn has been identified previously as a major challenge in improving firn models.
However, unfortunately, (1) I find the novelty of the model limited; (2) the improvement that is claimed is not sufficiently evident from the presented material; and (3) the analysis of the model results is, to my opinion, insufficient.
Therefore, although I am really reluctant with this judgment, I recommend the editor to reject this manuscript but with the encouragement to the authors to resubmit a more mature and elaborate paper in the future.
MOTIVATION
(1) The authors present a combination of the LZ2011 model with Darcy's law. A very similar combination was presented in 2017 by Langen et al., and the representation of Darcy's law in this manuscript and the Langen paper is nearly identical. The combination of a bucket scheme and a description of Darcy's law for water above the irreducible water content has been implemented, tested and analyzed before. Therefore, I find the novelty of this paper a bit limited. Or at least, the novelty does not lie in the combination of modeling techniques like the title and narrative of the paper suggests.
(2) In the title and elsewhere in the manuscript, the incorporation of Darcy's law in a bucket scheme is described as an improvement. But the manuscript does not provide evidence for the improvement. It is not currently possible to judge how the model would perform without Darcy's law. It is also difficult to quantify the comparison of other models in section 5.1, since no quantitative results from those models are presented to compare the present model with. Langen et al. do provide a quantitative comparison and finds that Darcy's law changes the density at a detailed level, but not at a large scale. Also the thermodynamics are relatively unaffected. Such an analysis is lacking in this manuscript.
(3) The model performance is measured mainly with the metrics presented in tables 3 and 4, showing the mean density over three depth ranges. But is mean density the preferred quantity to compare? Should it not be ice layer content, firn air content, density variability?
And what about the different observations in time? There are several cores from Dye-2 and KAN_U over a time span of several years. The observations seem to show substantial differences from one observation to the next. The model however, simulates a very comparable density profile throughout the simulation. It begs the question whether the densification physics is sufficient to capture such differences. I know that simulating density variability with existing, semi-empirical densification models is very tricky. But it is difficult for me to confirm several statements in the manuscript, like the one that "the modelled density profiles reprodue the occurrence of ice slabs and compare will within unvertainties to punctual in situ measurements of the firn column" (Line 460) and elsewhere.
What I think is needed for an improved version of this manuscript are at least(1) a demonstration of the improvement provided by this model compared to existing models, and with/without the Darcy law incorporated
(2) an evaluation of the model at a number of locations, including from different climatic regimes, like for example the locations presented in the RetMIP intercomparison project (Vandecrux et al.).
(3) a more in-depth analysis of the model results, compared to observations, and conclusions about this analysis that can inform the reader about improvements and limitations of the model. Care should be given to the quantities used for a model evaluation.SPECIFIC POINTS
line 10: add: understanding ice sheet hydrology
line 21: replace "the regions with limited liquid water" by "Dye-2"
line 22: probably overestimated -> overestimated, probably ...
line 23-25: Remove last sentence of the abstract. This is more appropriate for the conclusions section.
line 27: Add something like "Numerous observational techniques exist, but to extend our knowledge on firn over the entire ice sheet, the characteristics of firn are pytically obtained through the modelling of firn densification....."
line 32: add (iii) improving the estimates of meltwater runoff.line 32: volume change estimates are accurate and robust for laser, not necessarily so for radar. Due to the density conversion, I would be a bit reluctant to call altimetry accurate and robust. Rater something more neutral here, like "a remote-sensing approach".
line 36: apart from the citation of Brils et al., please provide some more historical embedding here.
line 42: physical mechanisms implemented -> the number of implemented physical mechanisms.
line 45: utilizing -> using (Nobody ever uses the word utilize apart from scientists)
line 49: utilize -> are based on
line 55: with -> due to, and decade -> decades
line 65: cite e.g. Culberg et al.
line 67: through two levels -> in two ways
line 68: besides -> second
line 71: the Bucket percolation scheme -> a so-called bucket scheme for percolation (bucket is without a capital letter throughout the manuscript)
line 90: here I miss a rationale for what the bucket method is, what Darcy's law is, and why a combination of the two could or should lead to an improvement.
line 93: put in present tense: assume, behaves, influence
line 94: afterward -> in our approach
line 104: use present tense: are.
line 129: are the stated temperature values observations or model results? And please round off to 1 decimal.
line 130/136: round off to whole numbers (283, 146, 676 mm w.e.)
line 139: render -> make it a representative location for the percolation zoneline 141: into ice lenses -> as ice lenses
line 153: combine figures 2 and 3 into one figure
line 164: included -> includes
line 164: on both ice sheets -> across the ice sheet
line 194: how are ice lenses thinner than dz treated? How should we interpret the density profiles in this regard? Do the results depend on vertical resolution?
line 196-200: use present tense: is, is, is.
line 200: utilized -> used
line 201: liquid water scheme -> the liquid water scheme
line 239: why divide by 3? Not 4 pi r^2?
lines 254-274: this seems a bit excessive. I think a reference to Calonne suffices here, without the need to reproduce their equations here.
line 276: remove "as mentioned above"
line 294: force -> impact
line 364: can you be a bit more explicit about where q_lim comes from and how it is computed?
line 402: how does this choice of computing time steps work for locations with little snowfall, like the dry accumulation zone? Is there a risk for numerical instability for long time steps and/or thin layers?
line 422: this is a bit messy and inconsistent with units. It reads like computer code. Consider writing the density evolution in time derivaties: drho/dt = (drho/dt)_dry + (drho/dt)_refreeze
line 433: could you please explain the choice of not enabling the liquid water scheme during spin-up? Doesn't it introduce unwanted initial densification? After all, the firn layer at the start of the simulation is not truly in equilibrium. I would then expect model drift and an erroneous densification rate.
line 459: as mentioned above, there seems little temporal variation in the model firn as opposed to the observations. Why?
Citation: https://doi.org/10.5194/egusphere-2024-122-RC1 -
RC2: 'Comment on egusphere-2024-122', Anonymous Referee #2, 11 Mar 2024
Review of “An improved firn densification model by integrating the Bucket scheme and Darcy’s law over the Greenland Ice Sheet” by Xueyu Zhang et al.
The manuscript describes a water transport mechanism for a model that is based on the Community Firn Model, to simulate firn profiles on the Greenland Ice Sheet. The model is then applied on two field sites in the percolation zone on the GrIS, where firn cores for validation are available. The model generally produces the depth-density profiles very well.
Even though the manuscript is very well written, would fit the journal very well, and generally the topic is highly relevant, I still think substantial more work is needed to make it publishable. In fact, as I will point out below, there is currently not sufficient validation of the simulations, and the materials in the manuscript provide insufficient insights in the workings of the proposed water transport scheme, that it is difficult to judge if the proposed water transport scheme is indeed better than existing ones, as claimed. This means that if I were to receive a revision for review, I would basically treat it as a new submission when reviewing.
My main concern is that there is only one simulation setup compared to the firn cores, arguing that the new water transport scheme works really well. Even though some discussion is provided with previously published results, it would have been better to show alternative model setups in the figures, to really demonstrate that the new water transport scheme is better. I think it is also a bit problematic that not all relevant literature is discussed. For example, in Section 5.1., where the simulation results are contrasted with literature values, an important paper, Vandecrux et al. 2020b (doi: 10.5194/tc-14-3785-2020) is not discussed. Some simulations in that manuscript show similar behavior as the ones shown in the manuscript. Thus, it is not clear to what extent the proposed water transport scheme is truly a step forward. Comparisons are made with the simulations presented by Verjans et al., 2019. But it is really not obvious from comparing their results with the results presented in this manuscript, that the proposed water transport scheme is really better than what has been used before. It leaves a lot of the heavy-lifting to be done by the reader, by comparing figures across different papers, with different scales, coloring, etc. I think that the authors should work more on this aspect to make the paper acceptable for publication.
Second, some discussion of results is not that convincingly argued. For example, on L450-455, it is argued how the water transport scheme has an effect on the simulated density profiles. However, I see a similar pattern in the results presented by Vandecrux et al., 2020b. That means that it is likely that at least part of the effect seen in the simulated density profiles may have another cause, possibly unrelated to the water transport scheme. For example, the firn deeper down was buried longer ago, which is important when there is a climatic trend in the forcing data. So here, maybe a sensitivity study is required, for percolation across ice slabs for example.
Third, the figures provide relatively little insight into the workings of the water transport scheme. For example, in L520-522, it is mentioned that thick ice layers prevented deeper percolation. But that would imply that those layers should still be visible in Fig. 6 and 8. So maybe indicate in the figures which layers were too thick to allow for downward percolation. I think the authors should think about alternative and more extensive ways to demonstrate the workings of the water transport scheme. For me, it is not clear now for example, why in Fig. 6, the simulated profile before and after the melt event in 2012 looks very similar, while a big effect can be seen near the surface in the observed profile. Is this an effect of overestimated runoff?
Minor comments:
- The abstract should mention that the work builds upon the Community Firn Model. I think that also in the manuscript, it is reported too late in the manuscript (first mention of CFM on L386) that the work builds upon the CFM model.
- While the source code from the CFM model is cited, it is not clear where the modifications made by the authors can be obtained.
- L50-54: “Both empirical, semi-empirical, and physical firn models have been used in Greenland and Antarctica. Nevertheless, these models usually ignore or provide simplified representations of processes associated with liquid water, thereby having certain limitations when applied to sites with substantial liquid water (Thompson-Munson et al., 2023).” I find this sentence too abstract. Please provide details of these “simplified representations”. Also explain more the “certain limitations” that these representations cause.
- L65-66: “Upon encountering a thick ice slab, liquid water reduces or even stops percolation, thus leaving the firn column through runoff.” Or firn aquifer formation is also a possibility, depending on climatology and terrain.
- L72 "water tips from": I think this is not the best phrasing. I have heard the bucket model being referred to as a tipping bucket, as with tipping bucket rain gauges. However, a tipping bucket would indicate complete emptying of the bucket, once the threshold is passed, whereas most models implement the bucket scheme as overflowing buckets. I.e., onl excess water above the threshold is routed downward. I would pick phrasing here that reflects that.
- I find some of the mathematics confusing. I would appreciate when a revision includes units for all variables. In L311, P is defined as 1 - rho/rho_ice, which means it is unitless. phi is then defined as (L312): phi = P * dz, which yields units [m]. Then in L319, dz is canceling out again, meaning that this way of presenting it is more confusing than it needs to be.
- Fig. 2 and 3, upper panel: better to make the y-axis read "Temperature (K)", instead of "Value (K)". It would also be good to label the panels (a) and (b), in order to refer to them from the caption and the text.
- L185: "The solid input of the firn column is derived from the difference between snowfall and sublimation". Please note that above, accumulation was defined as also subtracting snowmelt. I think it should be made more explicit if snowmelt is subtracted to derive accumulation, and later added as a liquid water input flux from rain, or if snowmelt is treated as melting part of the ice matrix that is already there. I would argue that the latter approach is more correct, as the mass of snowmelt was added as ice to the column at some point, impacting densification.
- L187-189: "Every individual firn layer is partitioned into distinct contributions from firn, ice, and liquid water, with each component expressed in terms of m w.e. units. Due to the varying proportions of these three components, firn properties change from layer to layer."
- I assume that the three components "firn, ice and liquid water", should be "firn air, ice, and liquid water"?
- L189-190: "However, within each layer, firn properties are assumed to remain constant."
- Eq. 1: Here, the problem is that such relationships based on observed density and annual air-temperature implicitly considers densification from melt. For their model, which explicitly treats melting and refreezing, an "accumulation surface density" would be needed. I don't think it's a huge deal, but something that would need to be discussed.
- L221-L226: I think this is too much detail, and it is lacking appropriate references. I would shorten significantly, and point to the appropriate references.
- L373-375. Note that the quote from Vandecrux et al., 2020a is not consistent. In Vandecrux et al., they write: “The *meltwater retention capacity* of the firn depends on three physical characteristics: (i) the availability of pore space to host the meltwater, (ii) the availability of cold content to refreeze the meltwater and (iii) the possibility for meltwater to percolate in deeper firn where conditions (i) and (ii) are met.” Not the *refreezing amount*.
- L396-398: This explanation is very confusing. Especially the part: “In fact, a smaller amount of snowfall within a time step is more susceptible to being influenced by wind and is blown from the surface of the firn column, failing to engage in firn densification fully.“ There are not many models that treat explicit removal of snow from erosion. And then it’s also not ideal that there is a timestep dependency. Are there any citations that can be provided to support this statement?
- Eq 27 is confusing since rho and rho_dry are basically both dry firn density. I think section 3.6 would benefit from a bit of rewriting to avoid these kinds of discrepancies.
- L433-435: It’s not clear why the spinup procedure would not include the liquid water scheme.
- L492-494: See my major comment #2. The painted contrast between Dye-2 and KAN_U only holds when the opposite can be shown for KAN_U.
- L501: I would avoid using the word “Regrettably” when discussing scientific results.
- L541: “inappropriate” doesn’t work for “predictions”. It doesn’t fit with the meaning of inappropriate.
Citation: https://doi.org/10.5194/egusphere-2024-122-RC2
Status: closed
-
RC1: 'Review of firn modelling manuscript by Zhang et al.', Anonymous Referee #1, 11 Mar 2024
Review of "An improved firn densification model by integrating the bucket scheme and Darcy's law over the Greenland Ice Sheet"", submitted for publication to The Cryosphere Discussions by Xueyu Zhang et al.
GENERAL
This paper presents a combination of firn modelling techniques in order to improve the model representation of the formation of ice lenses, ice slabs and other heterogeneous density features. The authors present a modeling framework that combines the bucket scheme on one hand, and Darcy's law for any meltwater above the irreducible water content on the other hand. They test the model at two sites on the Greenland Ice Sheet.
The paper is generally well written and its structure is good. Also, the topic is relevant since hydrology in firn has been identified previously as a major challenge in improving firn models.
However, unfortunately, (1) I find the novelty of the model limited; (2) the improvement that is claimed is not sufficiently evident from the presented material; and (3) the analysis of the model results is, to my opinion, insufficient.
Therefore, although I am really reluctant with this judgment, I recommend the editor to reject this manuscript but with the encouragement to the authors to resubmit a more mature and elaborate paper in the future.
MOTIVATION
(1) The authors present a combination of the LZ2011 model with Darcy's law. A very similar combination was presented in 2017 by Langen et al., and the representation of Darcy's law in this manuscript and the Langen paper is nearly identical. The combination of a bucket scheme and a description of Darcy's law for water above the irreducible water content has been implemented, tested and analyzed before. Therefore, I find the novelty of this paper a bit limited. Or at least, the novelty does not lie in the combination of modeling techniques like the title and narrative of the paper suggests.
(2) In the title and elsewhere in the manuscript, the incorporation of Darcy's law in a bucket scheme is described as an improvement. But the manuscript does not provide evidence for the improvement. It is not currently possible to judge how the model would perform without Darcy's law. It is also difficult to quantify the comparison of other models in section 5.1, since no quantitative results from those models are presented to compare the present model with. Langen et al. do provide a quantitative comparison and finds that Darcy's law changes the density at a detailed level, but not at a large scale. Also the thermodynamics are relatively unaffected. Such an analysis is lacking in this manuscript.
(3) The model performance is measured mainly with the metrics presented in tables 3 and 4, showing the mean density over three depth ranges. But is mean density the preferred quantity to compare? Should it not be ice layer content, firn air content, density variability?
And what about the different observations in time? There are several cores from Dye-2 and KAN_U over a time span of several years. The observations seem to show substantial differences from one observation to the next. The model however, simulates a very comparable density profile throughout the simulation. It begs the question whether the densification physics is sufficient to capture such differences. I know that simulating density variability with existing, semi-empirical densification models is very tricky. But it is difficult for me to confirm several statements in the manuscript, like the one that "the modelled density profiles reprodue the occurrence of ice slabs and compare will within unvertainties to punctual in situ measurements of the firn column" (Line 460) and elsewhere.
What I think is needed for an improved version of this manuscript are at least(1) a demonstration of the improvement provided by this model compared to existing models, and with/without the Darcy law incorporated
(2) an evaluation of the model at a number of locations, including from different climatic regimes, like for example the locations presented in the RetMIP intercomparison project (Vandecrux et al.).
(3) a more in-depth analysis of the model results, compared to observations, and conclusions about this analysis that can inform the reader about improvements and limitations of the model. Care should be given to the quantities used for a model evaluation.SPECIFIC POINTS
line 10: add: understanding ice sheet hydrology
line 21: replace "the regions with limited liquid water" by "Dye-2"
line 22: probably overestimated -> overestimated, probably ...
line 23-25: Remove last sentence of the abstract. This is more appropriate for the conclusions section.
line 27: Add something like "Numerous observational techniques exist, but to extend our knowledge on firn over the entire ice sheet, the characteristics of firn are pytically obtained through the modelling of firn densification....."
line 32: add (iii) improving the estimates of meltwater runoff.line 32: volume change estimates are accurate and robust for laser, not necessarily so for radar. Due to the density conversion, I would be a bit reluctant to call altimetry accurate and robust. Rater something more neutral here, like "a remote-sensing approach".
line 36: apart from the citation of Brils et al., please provide some more historical embedding here.
line 42: physical mechanisms implemented -> the number of implemented physical mechanisms.
line 45: utilizing -> using (Nobody ever uses the word utilize apart from scientists)
line 49: utilize -> are based on
line 55: with -> due to, and decade -> decades
line 65: cite e.g. Culberg et al.
line 67: through two levels -> in two ways
line 68: besides -> second
line 71: the Bucket percolation scheme -> a so-called bucket scheme for percolation (bucket is without a capital letter throughout the manuscript)
line 90: here I miss a rationale for what the bucket method is, what Darcy's law is, and why a combination of the two could or should lead to an improvement.
line 93: put in present tense: assume, behaves, influence
line 94: afterward -> in our approach
line 104: use present tense: are.
line 129: are the stated temperature values observations or model results? And please round off to 1 decimal.
line 130/136: round off to whole numbers (283, 146, 676 mm w.e.)
line 139: render -> make it a representative location for the percolation zoneline 141: into ice lenses -> as ice lenses
line 153: combine figures 2 and 3 into one figure
line 164: included -> includes
line 164: on both ice sheets -> across the ice sheet
line 194: how are ice lenses thinner than dz treated? How should we interpret the density profiles in this regard? Do the results depend on vertical resolution?
line 196-200: use present tense: is, is, is.
line 200: utilized -> used
line 201: liquid water scheme -> the liquid water scheme
line 239: why divide by 3? Not 4 pi r^2?
lines 254-274: this seems a bit excessive. I think a reference to Calonne suffices here, without the need to reproduce their equations here.
line 276: remove "as mentioned above"
line 294: force -> impact
line 364: can you be a bit more explicit about where q_lim comes from and how it is computed?
line 402: how does this choice of computing time steps work for locations with little snowfall, like the dry accumulation zone? Is there a risk for numerical instability for long time steps and/or thin layers?
line 422: this is a bit messy and inconsistent with units. It reads like computer code. Consider writing the density evolution in time derivaties: drho/dt = (drho/dt)_dry + (drho/dt)_refreeze
line 433: could you please explain the choice of not enabling the liquid water scheme during spin-up? Doesn't it introduce unwanted initial densification? After all, the firn layer at the start of the simulation is not truly in equilibrium. I would then expect model drift and an erroneous densification rate.
line 459: as mentioned above, there seems little temporal variation in the model firn as opposed to the observations. Why?
Citation: https://doi.org/10.5194/egusphere-2024-122-RC1 -
RC2: 'Comment on egusphere-2024-122', Anonymous Referee #2, 11 Mar 2024
Review of “An improved firn densification model by integrating the Bucket scheme and Darcy’s law over the Greenland Ice Sheet” by Xueyu Zhang et al.
The manuscript describes a water transport mechanism for a model that is based on the Community Firn Model, to simulate firn profiles on the Greenland Ice Sheet. The model is then applied on two field sites in the percolation zone on the GrIS, where firn cores for validation are available. The model generally produces the depth-density profiles very well.
Even though the manuscript is very well written, would fit the journal very well, and generally the topic is highly relevant, I still think substantial more work is needed to make it publishable. In fact, as I will point out below, there is currently not sufficient validation of the simulations, and the materials in the manuscript provide insufficient insights in the workings of the proposed water transport scheme, that it is difficult to judge if the proposed water transport scheme is indeed better than existing ones, as claimed. This means that if I were to receive a revision for review, I would basically treat it as a new submission when reviewing.
My main concern is that there is only one simulation setup compared to the firn cores, arguing that the new water transport scheme works really well. Even though some discussion is provided with previously published results, it would have been better to show alternative model setups in the figures, to really demonstrate that the new water transport scheme is better. I think it is also a bit problematic that not all relevant literature is discussed. For example, in Section 5.1., where the simulation results are contrasted with literature values, an important paper, Vandecrux et al. 2020b (doi: 10.5194/tc-14-3785-2020) is not discussed. Some simulations in that manuscript show similar behavior as the ones shown in the manuscript. Thus, it is not clear to what extent the proposed water transport scheme is truly a step forward. Comparisons are made with the simulations presented by Verjans et al., 2019. But it is really not obvious from comparing their results with the results presented in this manuscript, that the proposed water transport scheme is really better than what has been used before. It leaves a lot of the heavy-lifting to be done by the reader, by comparing figures across different papers, with different scales, coloring, etc. I think that the authors should work more on this aspect to make the paper acceptable for publication.
Second, some discussion of results is not that convincingly argued. For example, on L450-455, it is argued how the water transport scheme has an effect on the simulated density profiles. However, I see a similar pattern in the results presented by Vandecrux et al., 2020b. That means that it is likely that at least part of the effect seen in the simulated density profiles may have another cause, possibly unrelated to the water transport scheme. For example, the firn deeper down was buried longer ago, which is important when there is a climatic trend in the forcing data. So here, maybe a sensitivity study is required, for percolation across ice slabs for example.
Third, the figures provide relatively little insight into the workings of the water transport scheme. For example, in L520-522, it is mentioned that thick ice layers prevented deeper percolation. But that would imply that those layers should still be visible in Fig. 6 and 8. So maybe indicate in the figures which layers were too thick to allow for downward percolation. I think the authors should think about alternative and more extensive ways to demonstrate the workings of the water transport scheme. For me, it is not clear now for example, why in Fig. 6, the simulated profile before and after the melt event in 2012 looks very similar, while a big effect can be seen near the surface in the observed profile. Is this an effect of overestimated runoff?
Minor comments:
- The abstract should mention that the work builds upon the Community Firn Model. I think that also in the manuscript, it is reported too late in the manuscript (first mention of CFM on L386) that the work builds upon the CFM model.
- While the source code from the CFM model is cited, it is not clear where the modifications made by the authors can be obtained.
- L50-54: “Both empirical, semi-empirical, and physical firn models have been used in Greenland and Antarctica. Nevertheless, these models usually ignore or provide simplified representations of processes associated with liquid water, thereby having certain limitations when applied to sites with substantial liquid water (Thompson-Munson et al., 2023).” I find this sentence too abstract. Please provide details of these “simplified representations”. Also explain more the “certain limitations” that these representations cause.
- L65-66: “Upon encountering a thick ice slab, liquid water reduces or even stops percolation, thus leaving the firn column through runoff.” Or firn aquifer formation is also a possibility, depending on climatology and terrain.
- L72 "water tips from": I think this is not the best phrasing. I have heard the bucket model being referred to as a tipping bucket, as with tipping bucket rain gauges. However, a tipping bucket would indicate complete emptying of the bucket, once the threshold is passed, whereas most models implement the bucket scheme as overflowing buckets. I.e., onl excess water above the threshold is routed downward. I would pick phrasing here that reflects that.
- I find some of the mathematics confusing. I would appreciate when a revision includes units for all variables. In L311, P is defined as 1 - rho/rho_ice, which means it is unitless. phi is then defined as (L312): phi = P * dz, which yields units [m]. Then in L319, dz is canceling out again, meaning that this way of presenting it is more confusing than it needs to be.
- Fig. 2 and 3, upper panel: better to make the y-axis read "Temperature (K)", instead of "Value (K)". It would also be good to label the panels (a) and (b), in order to refer to them from the caption and the text.
- L185: "The solid input of the firn column is derived from the difference between snowfall and sublimation". Please note that above, accumulation was defined as also subtracting snowmelt. I think it should be made more explicit if snowmelt is subtracted to derive accumulation, and later added as a liquid water input flux from rain, or if snowmelt is treated as melting part of the ice matrix that is already there. I would argue that the latter approach is more correct, as the mass of snowmelt was added as ice to the column at some point, impacting densification.
- L187-189: "Every individual firn layer is partitioned into distinct contributions from firn, ice, and liquid water, with each component expressed in terms of m w.e. units. Due to the varying proportions of these three components, firn properties change from layer to layer."
- I assume that the three components "firn, ice and liquid water", should be "firn air, ice, and liquid water"?
- L189-190: "However, within each layer, firn properties are assumed to remain constant."
- Eq. 1: Here, the problem is that such relationships based on observed density and annual air-temperature implicitly considers densification from melt. For their model, which explicitly treats melting and refreezing, an "accumulation surface density" would be needed. I don't think it's a huge deal, but something that would need to be discussed.
- L221-L226: I think this is too much detail, and it is lacking appropriate references. I would shorten significantly, and point to the appropriate references.
- L373-375. Note that the quote from Vandecrux et al., 2020a is not consistent. In Vandecrux et al., they write: “The *meltwater retention capacity* of the firn depends on three physical characteristics: (i) the availability of pore space to host the meltwater, (ii) the availability of cold content to refreeze the meltwater and (iii) the possibility for meltwater to percolate in deeper firn where conditions (i) and (ii) are met.” Not the *refreezing amount*.
- L396-398: This explanation is very confusing. Especially the part: “In fact, a smaller amount of snowfall within a time step is more susceptible to being influenced by wind and is blown from the surface of the firn column, failing to engage in firn densification fully.“ There are not many models that treat explicit removal of snow from erosion. And then it’s also not ideal that there is a timestep dependency. Are there any citations that can be provided to support this statement?
- Eq 27 is confusing since rho and rho_dry are basically both dry firn density. I think section 3.6 would benefit from a bit of rewriting to avoid these kinds of discrepancies.
- L433-435: It’s not clear why the spinup procedure would not include the liquid water scheme.
- L492-494: See my major comment #2. The painted contrast between Dye-2 and KAN_U only holds when the opposite can be shown for KAN_U.
- L501: I would avoid using the word “Regrettably” when discussing scientific results.
- L541: “inappropriate” doesn’t work for “predictions”. It doesn’t fit with the meaning of inappropriate.
Citation: https://doi.org/10.5194/egusphere-2024-122-RC2
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