Summary of review
This manuscript addresses submarine melting at tidewater glaciers using simple plume models. This topic is of great current interest due to its potential importance for Greenland ice sheet dynamics, and these simple plume models are now a common tool for examining ice-ocean interaction processes. The results in this manuscript can be split into three sections: the first describing key factors driving variability in submarine melt rate as calculated using the plume model, the second comparing the plume models to similar studies using general circulation models, and the third comparing melt rate obtained using the plume models with field estimates from the literature.
I am in agreement with the previous reviewers of this manuscript, and am not convinced that this revised version of the manuscript has adequately addressed their concerns, hence I have raised some of these again. But I also have a significant number of additional concerns. At present, there are a large number of grammatical and typographical errors, numerical inconsistencies and references used incorrectly. Furthermore, in many places the results of this manuscript are poorly discussed. I am sorry for the length of this review but there are errors in many aspects of the manuscript.
I have concerns with each of the results sections, in some cases serious. Some parts of the first section are not particularly novel, and the parts which are novel could be better presented/discussed. The comparison to GCMs in the second section feels rather superficial as the authors are not able to offer any insight into perceived model disagreement (particularly whether it is real disagreement or just different set-ups), so I am not sure what the reader is supposed to take from this. My most serious concerns are with the final section: at present I believe this is presented in an inappropriate fashion, and that the conclusion reached is overly simplistic and far too bold. This conclusion is reached based on matching highly uncertain field estimates with a plume model where parameters are pushed to their limits; in short such a comparison has huge uncertainties and is not a basis on which to reach the strong conclusions stated here. What is particularly lacking is an appreciation or discussion of whether a line plume is even appropriate for the subglacial hydrology we are beginning to uncover at tidewater glaciers, or whether there might be substantial melting outside of plumes. At the moment it feels as if the authors are just matching two uncertain numbers without consideration of process at all.
I found the appendix to be perhaps the best part of this manuscript, with some elegant and insightful derivations. I think there is a good case for moving some of this material into the main manuscript.
I have detailed my concerns in detail below. This manuscript might be able to make a contribution to the literature, but in my opinion significant revisions are needed to improve the quality of the manuscript, to bring out the novel elements and to undertake the model-observation comparison in a more appropriate manner and with more discussion of process.
Major comments:
Plume model sensitivities: Sensitivity to subglacial discharge and ambient fjord conditions have already received much attention (e.g. Jenkins, 2011; Xu et al., 2012; Sciascia et al., 2013; Xu et al., 2013; Cowton et al., 2015; Slater et al., 2016), and this manuscript reaches many of the same conclusions with the same method as some of the quoted papers, so I am not sure what is new here. This first section is most novel in its presentation of sensitivities to entrainment rate and glacier front angle, but the presentation of these sections could be much improved (see suggestions below) with more detailed discussion/analysis. Perhaps some of the interesting material from the appendix could be brought into these sections, replacing material which is similar to previous work?
Comparison of plume models to GCMs: Where the plume models disagree with the GCMs the authors are not able to offer any insight into why this might be; in particular it is not clear whether the disagreement arises from genuine disagreement in plume dynamics, or is just due to model set-up, or whether the disagreement arises because the GCMs are simulating processes beyond those in the plume model. For example, GCMs often simulate elevated melt rates just outside the plume where water is being entrained into the plume, a process which is not included in the plume model melt rates. Xu et al. (2013) also included “background” heat and salt transfer coefficients which may affect their results (see the supplementary information to their paper). The higher discharge results in Xu et al. 2013 also use a low and wide subglacial channel so that the plume might be better compared with a line plume than cone plume. None of these issues are critically evaluated here, and perhaps it is not possible to do so without detailed interrogation of the GCMs. Therefore I do not find the conclusions on your scaling factors (3.4, 2.46 etc) to be very insightful, and I am not sure what the reader gains from this section. I also don’t understand why you have to apply a scaling factor of 0.48 to match the results of Sciascia et al. (2013), when Sciascia et al. (2013) obtain much better agreement with a line plume model in their Figure 5.
Comparison of plume models to observations: This section culminates in the final line of the abstract: “Our results show that the line plume model is more appropriate than the cone plume model for simulating submarine melt rates of real glaciers in Greenland”. This is a sweeping, bold and overly-simplistic conclusion. There are so many uncertainties in comparisons between modelled and observed melt rates that any conclusions should be drawn very cautiously. Uncertainties in the estimation of melt rates from fjord flux gates have been analysed by Jackson & Straneo (2016) and I think the points made therein should receive greater respect/discussion here. Some of the glaciers discussed in this manuscript are known to have large distinct channels for which a cone plume model (or narrow line plume model) is presumably more appropriate than the full-glacier width line plume model (e.g. to use the abbreviations from Table 6, KS has several channels (Fried et al., 2015), KAS and ST also have distinct channels (Rignot et al., 2015)). In fact applying just a line plume model to KS will clearly not capture the many discrete channels inferred to lead to substantial heterogeneity in melt rate. Stevens et al (2016) considers a different glacier to those in this paper, but provides another example of a glacier where a glacier-wide line plume would not be the most appropriate.
I agree that when spatially averaged over the calving front, melt rates from a few cone plumes are much smaller than the observations (e.g. Slater et al., 2015; Fried et al., 2015; Carroll et al., 2016), so that (taking the observations at face value) front-wide melting may be dominated by melting outside of these cone plumes. But this does not necessarily mean that we should apply a line plume to the whole calving front. Melting outside of the cone plumes might be controlled by entrainment of water into the cone plumes, or by other fjord circulation processes which we have not yet understood. Or it might be that we should apply a low discharge line plume to these regions, we just don’t know yet.
A further issue is that in order to make the line plume-modelled and observed melt rates match, the entrainment parameter takes a very low value (0.036) and the heat transfer coefficient is doubled. I am not sure there is much support for the use of this low value of entrainment coefficient for near-vertical plumes (I think this low value was originally artificially lowered to crudely represent the effect of Coriolis on ice shelf plumes – see Jenkins (1991) and more comments below). Of course, there is so little data on plumes at tidewater glaciers that the values of parameters adopted might ultimately prove to be about right, but they are not a basis on which to reach the strong conclusions presented in this paper.
In my opinion then, this section needs substantial rethinking to take account of what is known of the subglacial hydrology at the glaciers presented, to acknowledge the potential for melting outside of plumes, and to respect the very many uncertainties currently present in comparisons of model and observation.
Minor comments:
P1L3-5: Suggest toning this down a little – the importance of submarine melting is not yet clear – maybe change “submarine melt plays a crucial role” to “submarine melt may play a crucial role” and “submarine melt will increase and outlet glaciers will retreat, contributing…” to “submarine melt will increase, potentially driving outlet glacier retreat and contributing…”
P2L16-17: “These large uncertainties are associated with the parameterisation of the rate of submarine melt” – surely there are many more reasons for the uncertainty e.g. the representation of calving and basal sliding, lack of resolution – it would be good to acknowledge here that representation of submarine melting is not the only reason for uncertainty in future projections.
P2L25-26: “the influence of fjord circulation … were investigated with the 3D models” – do you mean the influence of fjord circulation on submarine melting? I don’t think any of the 3D papers you cited looked at this. Maybe remove this line?
P2L29: for clarity, maybe change “the second one is localized (the…” to “the second one has localized subglacial discharge (the…”
P2L32: “these simulations” – which simulations do you mean? It’s not clear at the moment – please clarify.
P3L2: “where geostrophic flow becomes significant” – the importance of Coriolis is not fundamentally what drives the quadratic dependence, so this statement is misplaced. The quadratic dependence comes from the fact that mixed layer velocity increases significantly with ocean temperature (Holland et al., 2007), which is not the case for plumes driven by large volumes of subglacial discharge (e.g. Slater et al., 2016). Perhaps either remove the reference to geostrophic flow or summarise the reason for the linear-quadratic dependence difference.
P3L8-9: “Simulations with 3D models, which differ with respect to boundary conditions and turbulence parameters” – I presume that “differ” refers to the difference between 3D and 2D models? I don’t think that 2D and 3D models differ fundamentally in their boundary conditions and turbulence parameters – please clarify and be more specific.
P3L9-11: I don’t think there is much reason to bring up the differing melt profiles unless you outline why the profiles differ. I’d suggest either removing this section or explaining why the profiles differ (presumably it’s because Kimura et al., 2014 assumed an unstratified fjord while the other two studies assumed a stratified fjord).
P3L15 (and throughout the manuscript): I am not sure I would call the plume model a “parameterization”. Perhaps this is a matter of opinion, but I would imagine a “parameterization” to be even simpler than a plume model. I’d maybe consider referring to the plume model by its name rather than calling it a “parameterization”. If you agree, you’ll need to change it throughout the manuscript. E.g. on P3L16 could change “parameterization” to “a method”.
P3L16: “in a 1D ice stream models” – this should be corrected to “in 1D ice stream models”. But I would also argue that plume models could be used in any form of ice flow model (not just 1D), so you could generalise a bit more here if wanted.
P3L24: I find the use of “ice tongue” here a bit odd. I think “geometry of the calving front” would be more appropriate.
P3L30: For clarity, I’d suggest changing “additional melting … glacier front, and” to “submarine melting of the ice-ocean interface, and”.
P4L9: For clarity, I’d suggest changing “along the glacier” to “along the calving front”.
P4L11: For clarity, I’d suggest changing “along the glacier front” to “up the glacier front”, because two lines above, you used “along” to refer to the across-glacier direction.
P4L11-14: It’d be good to insert a reference to Fig. 1 in this paragraph.
P4L20 and L28: The notation here is a bit confusing (or the equation is missing a factor) because ∆ρ should be divided by a reference density (see e.g. Jenkins, 2011; his Eq. 2). In line 28 it looks like you equate ∆ρ=β_S (S_a-S)-β_T (T_a-T) but really it should be ∆ρ/ρ_0=β_S (S_a-S)-β_T (T_a-T), again see Jenkins, 2011, his Eq. 5. Dividing by the reference density is needed to make your Eq. 2 dimensionally correct.
P5L4-5: I don’t think it says anywhere what your values for Ti and Si are – maybe you could include these in Table 1?
P5L13: what exactly do you mean by this “freezing point”? Do you mean equation (7) with Sb set to 0, or equation (7) with Sb set to the ambient value Sa? I think Jenkins (2011) uses the latter? Please clarify.
P5L17: “dependence of the melt rate on plume velocity” – surely the melt rate is always linearly dependent on the plume velocity (see your equations 5 and 6). Do you mean something else here?
P5L25: As for the line plume equations (see comment above), I believe you may be missing a factor of ρ_0 in the momentum equation.
P6L6: “for glaciers with floating tongues” – I think sin(alpha) can vary without the glacier having a full floating tongue – for example if it is undercut. I’d suggest removing this phrase.
P6L28 and 30: In these expressions, the density difference ρ_0 should again be divided by a reference density so that the dimensions work out.
P7L7: Even for the highest velocities the melt rate is still lowest at the grounding line so arguably the highest velocities might lead to a toe too. I’d suggest rephrasing this.
P7L14-120: In the present position, this paragraph is a bit confusing because you define a value for qsg but then use a different value just below. It might be better to move this paragraph to below section 2.5 as it would avoid confusion and it leads naturally into section 3.
P7L22-26: this paragraph concerns the comparison of line and conical plume models, so it would perhaps be better in the next section (2.5).
P7L22: “defined per unit length” – would be clearer as “defined per unit width of grounding line”
P7L28: “local melt rate is higher in the CP model than in the LP model practically for all depths” – Fig. 4 shows this is true for the parameters you have picked, but is it true regardless of Q and for all stratifications? This section would be more meaningful if it could be said that this statement holds more generally than the single example you have plotted.
P8L10-12: it would be worth citing Magorrian & Wells, 2016 here and including the phrase “melt-driven convection”
P8L13-15: I find these sentences very difficult to follow: please explain more explicitly/carefully and check grammar/typos. For example, you suggest that the melt rate is linearly dependent on the plume velocity in a well-mixed fjord. But this is true in any situation (due to the form of the three-equation melt rate parameterisation).
P8L19-21: If it’s to be included, this section needs expanding (i.e. explain more explicitly what Table 2 actually shows). There are a number of problems with Table 2, which I’ve detailed elsewhere in this review.
P8L29-31: At present, this sentence says that all of the cited studies derived values for the entrainment coefficient from laboratory results. They didn’t, so this needs rephrasing.
P8L30: I am not sure that the value 0.036 is appropriate as quoted. The value 0.036 comes from Jenkins (1991), and to quote from that paper: “adopting the value for E0 of 0.072 given by Bo Pederson (1980) will lead to an overestimate of entrainment. This is because the Coriolis force, which is not incorporated in this simple one-dimensional treatment, will tend to deflect the flow across the basal slope, hence reducing the sinθ term. To compensate for this effect, the value of E0 used is half the figure quoted above.” In other words, the value 0.036 is artificially small to try to account for Coriolis effects which become important beneath broad ice shelves. Since your manuscript mostly looks at vertical plumes, the Coriolis force is not important (Kimura et al., 2014), and a value 0.036 is probably not appropriate. For the vertical plumes studied here I think it would be more appropriate to use values thought to be more suited to vertical plumes (e.g. 0.07 to 0.16 according to Kimura et al., 2014). I think this issue is particularly relevant to section 5, which I have discussed in the major comments above. Of course, I acknowledge there is much uncertainty in the value of E0 due to lack of field measurements, and therefore using 0.036 is not wrong per se (it is interesting to include it in the sensitivity analysis), but the above issue should be discussed. In particular, the reaching of the strong conclusions for vertical plumes in section 5 based on the value E0=0.036 is, in my opinion, not appropriate.
P9L1-9: I think this section could be expanded with the results explained in more detail. At present Fig. 6 (which has a great deal of information on it) is only briefly mentioned. Fig. 7 is referred to before Fig. 6 so these figures should be swapped.
P9L13-14: The effect of temperature variation on melt rate has been looked at using methods other than 3d circulation models (i.e. with 2d circulation models and plume theory) – it’d be good to acknowledge that here, and include citations to relevant papers.
P9L20-21: It’d be good to refer to Table 3 here, and to change q to qsg for consistency of notation.
P9L22: “the cone plume model seems not to show this change in power law for analytical solutions”. As far as I can tell from Table 3, this statement is referenced to Slater et al., 2016. This is inappropriate as Slater et al., 2016 only considered the high discharge regime (i.e. that in which melting does not matter for the dynamics of the plume), and did not consider the low discharge regime at all. A number of other issues with Table 3 are outlined elsewhere.
P9L29-32: This discussion of the impact of glacier front angle is poor and needs to give much more insight into how the front angle affects plume dynamics and melting. The Magorrian & Wells (2016) results only apply for very low (negligible) discharge, so are not readily applicable to your results.
P10L6: “strongly overestimate plume velocity and melt rate” – can you provide a reference for this statement?
P10L11: “the models contain the right physics to simulate plume dynamics” – this statement is a bit odd as simple plume models also contain the “right physics”. I’d suggest removing this phrase.
P10L16: Xu et al 2013 will not have resolved all of the turbulence, just a bit more than the coarser resolution models. It’d be good to clarify this here.
P10L24: “this simulation” – it’s not clear whether this refers to the Sciascia et al 2013 simulations or your plume model – please clarify.
P11L4-5: this sentence implies that the results of Xu et al., 2013 agree well with plume theory. They may do, but I don’t think Xu et al., 2013 did this comparison. Does this statement come from your results? If so, it might be better to leave it till later.
P12L3-5: this is a very inadequate (and incorrect) description of the issue of reliability of fjord heat flux estimates of submarine melting. Please improve and expand.
P12L12: “velocity measurements and mass balance” – I think “ice flux divergence” is clearer.
P12L7-23: some discussion of across-fjord variability would add to this section. Is the ‘observed’ melt rate which is the blue line in Fig. 12 an across-fjord average? Is it representative of the channels you mention or the ice in between?
Section 5.2: I don’t think you say where your discharge estimates come from – please add.
P13L10: “a shelf of 3km length” – I’m a bit confused by this as I don’t think Kangerlussuup Sermia has a floating tongue (according to Fried et al 2015 it is undercut but only by a few hundred metres).
P14L9-12: you need to explain these methods more clearly – at the moment this is very confusing.
P15L4: would be clearer as “future changes in subglacial discharge and fjord temperature”.
P15L26: “such discrepancy is not surprising given the highly simplified parameterization of the LP and CP models compared to GCMs” – I disagree strongly with this statement. The plume models and the GCMs are simulating the same phenomenon with the same physics. If they disagree it is because of how the models are set up or run rather than because one is simpler than the other.
P15L31: “due to the missing Coriolis force in the plume models” – I think this statement needs to be backed up with a reference or some analysis (see similar comment above).
Appendix:
P16L11: I think analytical solutions for the line plume model have been presented by Linden et al (1990), Straneo & Cenedese (2015) and Slater et al (2016) – it might be worth including these references.
P18L5-7: I wasn’t quite able to follow these derivations. Could you add some more detail/intermediate steps to make it more obvious?
P18L16: expression for b – as for my other comments above, I think this needs a factor of the reference density in the denominator.
Eq A15: I couldn’t see where this expression comes from. Could you explain more?
Eq A20: I couldn’t quite follow the final integration – could you add an intermediate step or explain? In the discussion which follows it would be good to refer to Figure 5.
P20L15: “background melting” – I think this is more often called “melt-driven convection” – it would be good to add this phrase.
Figures and Tables:
Figure 1: “ice shelf an slope” should presumably by “ice shelf at slope”? “Melting mdot occurs on the glacier…. salinity Sb” – this sentence doesn’t make sense at the moment – consider rephrasing. In the second last line of the caption you have two “ands”. In general this whole caption could be clearer.
Figure 2: “U0 = 3.5 ms-3” – I guess this should be “U0 = 3.5 x 10-3 ms-1”?
Figure 3: the y-axis label is confusing, suggest changing to “cumulative melt in % of melt when U0=U*0”.
Figure 4: change “total discharge occur through” to “total discharge is delivered through”. In the fourth line of the caption, “acrosss” should be “across”. Use of “entire glacier” in the last two lines – I think it would be better to say “across the full width W”.
Figure 5: I guess the legend should say “Qsg1/3” rather than “**1/3”? First and second line of caption: no need for “(a)”. Change “for red line” to “the red line”. The equation in the caption is not the same as the line on the plot (maybe it’s the units?). If I take Qsg = 1 m2/s then according to your plot I would get a melt rate of ~0.04 m3/d but according to your equation I would get 7.2 x 10-5 so something is wrong. Are the units on the y-axis correct? Should they not be m2/s?
Figure 7: Change “in dependence of” to “as a function of”. Figure legend should say Ta rather than T. You quote a discharge of 10-3 m2/s – is this right? In Fig. 6a, where I presume Ta = 4, the line with a discharge 10-3 m2/s shows a cumulative melt of ~600 m2/d for E0=0.1 whereas for the same parameters, this figure gives a cumulative melt of ~1600 m2/d. So it looks to me like Fig. 6 and 7 are inconsistent?
Figure 10: Legend: last entry should presumably be 1.1˚ rather than 0.02?
Figure 11: plots labels (a) and (b) need to be swapped. “Same temperature profile as Xu” – presumably also the same salinity profile? Might be better then to say “same stratification”?
Figure 12: Legends and caption: in the text (P12L14) you say the maximum E0 value is 0.08 but here you say 0.16 – needs fixing. In the text (P12L14) you quota a discharge 10-4 but here you say 10-5 – please fix. Line 2 of caption: “entrainement” should be “entrainment”.
Figure 13: The units are a bit odd on the temperature plot. It might also be worth plotting the salinity profile here?
Figure 14: “Sutherland et al” should be “Sutherland and Straneo, 2012”? In the caption, “with and” should be “with a”.
Figure 15: Caption line 1: remove “in”, and “sublgacial” should be “subglacial”. “Motyka model” and “Gade model” – I think these are better referred to as “methods”. Line 2: I think “melt rate estimates” would be better than “melt rate profiles”. Line 3: insert “line” after “red dotted” and “blue dotted”.
Figure 16: How have you calculated the 1-sigma uncertainty range? It looks rather narrow compared to the spread in the data. Could you quote what the value of the “scaling coefficient” in line 2 is?
Table 1: 4th line of table: typo: “inital” should be “initial”. 6th line of table – I presume this should be the initial plume salinity rather than the ambient salinity?
Table 2: Grammar: replace “of melt rate on discharge Q” with “in”. Typo: “seperate” should be “separate”. I believe you may have mixed up the Qc values – I think in Xu et al., 2013, Qc = 4.34 m3/s?
Table 3: I have serious concerns about this table. Firstly, the grammar and typos need fixing in the caption. Second, I do not understand the separation into “experimental” and “theoretical” – all the quoted studies including yours are models of some sort. Most seriously, you have split discharge values into high and low, and then attributed the quoted studies into these categories. But as far as I know most of these studies (Jenkins, 2011; Magorrian & Wells, (2016); Slater et al., (2016)) make no distinction between high and low discharge, and even if they did they wouldn’t have the same discharge boundaries as your results, so the attribution of results from the literature in this table is very questionable. For example, Slater et al., 2016 have no results on low discharge cases, so I don’t understand where the central “1e” entry in the table comes from. I also don’t think Magorrian & Wells (2016) considered high discharges, so I don’t understand where that entry comes from either. Lastly, I think the Xu et al (2013) discharge boundary is wrong again – it should be 4.34 m3/s right? This table needs a complete rethink, probably by removing all of the literature references and just sticking to results from this manuscript. There could maybe be a discussion in the text comparing results from this manuscript to the literature, but the categorisation of other papers in this table is, I believe, incorrect.
Table 6: I think “Estimated subglacial discharge” is more appropriate than “measured subglacial discharge”. Line 3: typo: “sublacial” should be “subglacial”. GammaT and GammaS values need “x 10-2” and units.
Typos:
There are typos on P1L10 (suit), P1L19 (0.33 ± 8 mm/yr – the uncertainty value here must be a typo?), P3L16 (submarime), P4L7 and P4L17 and P6L19 (Fig. 1 should presumably be Fig. 1a), P4L14 (should 0.9 x 10-9 actually be 0.9 x 10-6?), P6L9 (euqation), P9L3 (stong), P9L26 (plume thoery), P11L19 (intoroduced), P11L20 (malt), P12L18 (domintad), P13L16 (averged), P13L19 (closet), P13L31 (Semerlik), P14L11 (coloumn), P14L11 (tempreature), P14L15 (accomodate), P14L27 (obervations), P15L14 (explenation), P16L5 (futue), P16L15 (greenladic), P17L3 (salininty), P20L10 (wit).
Grammar, numerical inconsistencies, incorrect references:
P1L1: “Two hundreds of marine-terminating” should be “Two hundred marine-terminating”
P1L5: “is hampered” should be “are hampered”
P1L5-7: rethink the structure of this sentence – it doesn’t read well at the moment
P1L9: change “using” to “the use”
P1L10: change “parameterization” to “a parameterization”
P2L4: remove “of” from “most of Greenland”
P2L10-11: “Nick et al (2013), using the same flowline model implemented” reads better as “Using the same flowline model, Nick et al (2013) implemented”
P2L19: “taken to estimate” is better than “derived to calculate”
P2L20: Rignot et al., 2015 did not present estimates of submarine melt rate from ocean data – I presume this should be Rignot et al., 2010, Nature Geoscience?
P2L21: Holland et al., 2008a is not a general circulation modelling paper – I presume you mean Holland et al., 2007, Journal of Climate?
P2L22: Sciascia et al., 2013 is a 2d general circulation model, not a 3d model
P2L23: I think Holland et al., 2008b should actually be Holland et al., 2007, Journal of Climate?
P2L23-24: I think you have mixed up hydrostatic and non-hydrostatic. The Holland and Little papers were hydrostatic, Sciascia et al., 2013 was non-hydrostatic.
P2L25: “pattern, vertical” should be “pattern and vertical”
P3L25: “3D ocean models” – at the moment you also compare with 2D models (your section 4.2)
P3L22: “There we” would be better as “We then”
P3L31: “They act to” would be better as “These processes act to”
P4L3: change “during summer season” to “during the summer season”
P4L8: change “they can be a number of them” to “there can be a number of them”
P4L24: “in lateral direction” should be “in the lateral direction”
P4L11: change “Solving for equations” to “Solving equations”
P5L15 and 17: I presume “Annex” should be “Appendix”
P7L16: “maximal melting conditions for Greenlands fjord” – I presume you mean that these ambient conditions are the fjord waters found in Greenland which would give the highest melt rates. Maybe state this more explicitly as it’s not very clear at the moment. Or at least change “Greenlands fjord” to “Greenlandic fjords”.
P7L18-19: “Greenland fjords, most of them do not have a floating tongue (tidewater glaciers) and we therrfore generally perform…” – this sentence has many errors. I’d suggest changing to “glaciers in Greenland, most of which do not have a floating tongue, and we therefore generally…”
P7L29: “(i.e. integral of the melt rate across entire surface area of the glacier front, of width W)” should be “(i.e the integral of the melt rate across the entire surface area of the glacier front, of width W)”. But I also find this confusing because it sort of suggests that the conical plume covers the whole width W, so it might be better to say what the cumulative melt rate is separately for the line and conical plumes.
P8L3: “there are more than one channel” should be “there is more than one channel”
P8L8: “can already be determined by the look on the balance velocities” reads better as “is already suggested by the form of the balance velocities”
P8L24-25: “Slower velocity as a result negatively affects melting” would be better as “Reduced velocity in turn reduces melting”
P10L12-13: grammar: “in order not to resolve the small-scale turbulences” would be better as “in order to represent the small-scale turbulence which is not resolved”
P10L19-20: insert “the” before “simple plume parameterization” in line 19 and “our” before “plume parameterization” in line 20
P10L23: insert “fjord” before “with a resolution”
P11L8: change “to Store” to “of Store” and in line 8 insert “the” before “same”
P11L21: “without a background melting and 1.7 with background melting” – it’s not clear what you mean here – please be more explicit.
P12L8: “of along the floating tongue” should be something like “incised into the underside of the floating tongue”
P12L22: “but correction for Coriolis effect” should be “but a correction for the Coriolis effect”
P13L9: add “the” before “previously”
P13L16: change “2 magnitudes” to “2 orders of magnitude”
P13L28-29: “might be diluted…” – this sentence says that the derivation might be diluted, but actually you mean that the CTD profile might be diluted, so this needs reforming.
P13L33: I don’t think “section 7” exists?
P15L6: “marine-terminated” should be “marine-terminating”
P15L9: I think the correct reference is Slater et al (2015). Change “At last” to “Lastly”.
P15L17: “that was used parameterization of the turbulence of the plume” should be something like “that was used to parameterize turbulent entrainment into the plume”.
P16L19: insert “slowly varying” before “ice temperature”
References (only those not cited in the manuscript)
Holland, P. R., A. Jenkins, and D. M. Holland (2007), The response of ice shelf basal melting to variations in ocean temperature, Journal of Climate, doi: 10.1175/2007JCLI1909.1.
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