Note that this is a review on the revised version of the manuscript only. Note also, that I have not previously reviewed the initial submission but I have read the two reviews (ref1 and ref2) of the initial submission and the author response as well as the re-review of the revised manuscript of one of the previous reviewers (ref1).
However, I first tried to judge this revised manuscript on its own, but I could not get around relating here or there to the earlier very critical reviews, in particular with regard to novelty and value of the paper and the choice and limitations of the model.
In my view, this is an interesting manuscript that investigates the dynamic retreat behaviour of Jakobshavn Isbrae in Greenland since the little ice age (LIA) using a simple flow model with a fully dynamic treatment of the calving front (ocean boundary) and importantly compares it to the observed retreat behaviour.
While several attempts of modelling the flow and dynamic changes of Jakobshavb Isbrae have been undertaken (including an early study with a similar model by myself), these earlier works focussed on the time period after 1990 and partly into the future and they did not all use a fully dynamic calving model (partly prescribed retreat to study upstream propagation of thinning/velocity).
The novelty of this study here clearly lies with the longer time perspective considered in which it attempts to explain (through flow modelling) to determine the essential controls of the observed step-wise and non-linear retreat behaviour from the LIA (1850) into the present.
While I agree with the earlier reviewers that the found sensitivity to fjord geometry (mainly water depth) has long been proposed and investigated, comparing detailed observed retreat behaviour with a fully dynamic flow model (moving calving front) over century time scales is still lacking (apart from Lea et al 2014, JG, but with much coarser data and on a much smaller glacier). The understanding and model capability of dynamic retreat over century time scales is however crucial given the current rapid changes and that predictions into the future typically should span a century or two and
Further, the modelling also goes beyond the argument of water depth as a control for non-linear retreat and demonstrates that the width of the fjord is for the retreat since the LIA the more dominant control for the retreat pattern, which has not been explicitly investigated before.
The strongly simplified forcing (slow linear changing forcing) in the modelling still produces very robustly (extensive sensitivity study) the highly non-linear retreat pattern which highlights the potential importance of long-term transient effects (inherent) in addition the response to the current rapid warming.
Thus, I have no doubt that this study is, although using a relatively simple flow model (but with all essential ingredients), clearly novel and a first in combining longer-term (centuries) observations successfully with dynamic flow modelling of marine outlet glacier behaviour.
This is not only crucial for understanding and putting current dramatic dynamic changes into a longer-term perspective but also highly valuable for interpreting the palaeo record (reconstructions).
There are a couple of points that one can criticise (as done in the other reviews) which I comment on below in more detail, and some of them should be addressed, but in my view they do not substantially affect the main conclusions of the paper and therefore I have the strong view that this is a valuable contribution for TC and of wider interest (modellers, contemporary glaciology, palaeo-reconstruction community).
1) typos/editing/use of language:
In general here and there are some editing issues, typos or inaccurate use of language (see minor points below) which is somewhat unfortunate for a revised version but maybe just a result of the major rewriting in the revisions. Thus, the manuscript should be carefully proof-read again (ideally from native English speaker).
2) The model used here:
both earlier reviewers to some degree criticise the used flow-model as not fully appropriate, as too simple for such a complex outlet glacier. I agree that the model is relatively 'simple' and reduced and clearly has some limitations, but in my view such a model does not necessarily have to be inappropriate. It just depends on the question one asks and what processes are expected to be included. For a reduced question (of less complexity: e.g. a simple channel, only retreat pattern…) and simpler model may be appropriate.
In this case, I think one just has to be clear about the assumptions made (which could be improved a bit). Basically, the flowline model sees a channel, with variable width though, it includes longitudinal stress gradients and lateral drag from the side (given a width) as well as a fully dynamic marine boundary (calving criterion and capable to form a floating tongue, (which has been tested on several contemporary outlets against data)). Yes, all is vertically and width averaged but for the outer fjord channel (LIA position to recent terminus position) and given the high basal motion this seems to me a valid approach. Also note that with buttressing from a floating tongue or a narrowing channel it is perfectly capable of producing stable positions in retrograde slopes (consistent with Gudmundsson et al (2012) and unlike stated by reviewer1 (which to me seems from the comments in the review, not really to understand the used model here)).
Of course one should then not expect to reproduce details related to complex lateral topography variations… and not really interpret the continuation of the modelling runs into the future (as the stream retreats back into the ice sheet, a fair point of the earlier reviewers).
For addressing the question of what the effect of fjord geometry (bed AND width) are on the longer-term retreat pattern since the LIA, to me the model seems perfectly adequate, if the assumptions (what is in the model) are made clear. Simpler models sometimes also make it easier to tease out the essential things (zero-order) rather than hangup on details (2nd ortder).
Perhaps the authors could clarify this point a bit and make clearer somewhere that: 'assuming these and these stresses/processes are important and included in the model we test whether we can reproduce the general pattern of retreat as observed'.
Also the assumptions and a general statement about what terms/processes in the model could maybe at the beginning of the methods be clarified. In the moment it is a bit spread out and one has almost to already 'know' the model to know what is roughly in there.
Yes, I agree with the other reviewers that future work should start to use improved models, likely 3d and with additional processes in (e.g. shear softening, which I actually explored for JAKO already in an adhoc way in the 2011 paper with a similar flowline model) and in particular for future projections. The authors already addressed this latter issue well in the revisions.
One should also note that more complex models (3d, more processes) also need better/more input data to constrain parameters or geometry, which for example for the ice-fjord channel here is simply not there. Further, for example the groundingline issue related to the sliding formulation (hinted on be re-review 1) does not go away when using more complexe models. On that note, the grounding line migration of the used model is actually pretty robust and fully consistent with schoof (2007) (successful in the MISMIP 1-d comparison exercise).
Model calibration/experiment setup
A further point related to the model is the calibration of the parameters and experiment setup. As mentioned by reviewer 2 as well, I somewhat struggled a bit how the parameters have been chosen. I think most is there but it could structured and formulated a bit better (see detailed comments below).
Regarding the waterdepth parameter (mentioned in the re-review 1) I am also a bit puzzled about the very high values used, in earlier papers they are usually below 100m for the calving model using surface and bottom crevasses (which is still high). Anyway, what is more important here is to make clear that this is not necessarily a 'real' water depth but rather a model parameter in the calving relation that can be used to perturb/force the model (calving) (with some relation to the surface e melt), see Nick et al 2010. This should be clarified.
The issue of calibration to the observations (see reviewer 2) has mostly been addressed well by making clear that only start and end position are used as constraints and the retreat in between is free to evolve.
I agree that one should be clear about model limitations but in the moment this section is more like a description what the model can not do with little justification why this is still ok and does not affect the main conclusions.
It would be useful to explain why the authors think the results are still ok for their conclusions/question and to defend what their simple model can do and that this is ok for the given question. Again, just needs some reformulations and justifications (see some suggestions in comments below).
Moraine build up proxy
I partly agree with re-review 1 that the conclusion of using the model to locate potential moraine build up locations is not that useful. I agree that such retreat slow downs will likely be coincident with submarine moraines but I do not think they replace bathymetric or radar surveys. I would phrase the thread of conclusion just slightly different. The found very robust influence of width on the retreat patterns means that looking at fjord geometry, and in the case of Jako in particular fjord width, allows to pin down locations of expected slow-downs or step changes in retreat which is extremely useful for interpreting paleo records, for example from adjacent land-records (moraines) etc. this will be useful for reconstructions and pale-record interpretations.
So basically, this study is very helpful of interpreting the past changes and paleo-record, but also for interpreting current high spatial and temporal variability in outlet glacier retreat/mass loss. But this could maybe made clearer/be highlighted a bit.
Discussion of terminus versus grline (and floating tongue):
In general, in the discussion of the results, a slightly more differentiated discussion of the influence of the dominance of width over the bed (in this case) maybe useful and add value to the study. Or am I wrong in this interpretation.
Further the formation of the floating tongue before the rapid step retreat (or lack of a floating tongue in the phase before compared to observations, see fig 4) should in my view be commented a bit more, as the shown run in fig 4 differs the observations somewhat (extensive floating tongue in 1980-90s). It may well be an issue of underestimated water depth in the fjord…? Or is it simply because you crevasse depth perturbations are so high that hardly any floating tongue is able to form. Maybe your extensive forcing sensitivity study gives an answer on this (from fig 4 it seems that some runs seem to form a floating tongue well before the rapid retreat (similar as observed.
Another point related to maybe discuss a bit more (or have I missed it?) is that the more stepped and pronounced 'resting' points of the grounding line compared to the terminus (see fig. 4 and as described in section 4.3 maybe indicates that the groundingline retreat pattern is a bit stronger related to the bed topography whereas the terminus (at most times floating) rather reflects the width variations (narrowings/widening…). and the floatng tongue makes the difference between the terminus and grline retreat pattern.
Maybe this differential behavuiour needs a little be more anaylsis or thought, but some more differentiated discussion/analysis of the effect of width and bed topography maybe useful and mare this study more valuable (to counteract the mentioned 'lack of novelty by the earlier reviewers ('we know the bed is important').
More detailed specific comments.
Introduction p. 2, bottom paragraph: I would emphasise here so far missing longer-term perspective constraint by observations (century scale).
p. 3 line 2: I think this should be Vieli et al. 2005 (as in the 2001 paper I used a full stokes model!!!).
p. 3 lines 5-7: rephrase this a bit, I am not sure the 'validation' is fully appropriate here. Yes application to real world is important but also that compared to longer-term retreat…
p. 3 line 13-14: could refer to Pattyn et al (2012, TC) paper on the statement of the robust grline treatment
p. 4 line 12: '…submarine melt below the floating tongue described…'
p. 4 lines 21 and 22: the formulation of '…to tune the…' is a bit awkward, as you would have to say to what constraints you tune the model.
Maybe just say they are model parameters (basal sliding coefficient, lateral enhancement factor to reduce lateral resistance…) that adjusted to roughly match the observed flow for the present geometry.
Is a constant every where or is there also some water pressure (peff) dependency built in? faezeh used this in here nature paper as far as I remember.
p. 4 line 26: '…300m initially, and due to using a stretched grid, it reduces to ???m when retreat to the present position.
p. 4 line 31: '(dsc and dbe, respectively)
p. 5 line 1: '…crevasses is dependent on the tensile…'
p. 6 top half: this is maybe more of a personal preference, but I would avoid double letter subscripts (e.g. d_cw, d_sc, rho_fw,…).
Similar within the text (also on page before) I think you do not need the brackets around the variables (line 1, 6 ,..) at least be consistent everywhere.
p. 6 line 1: maybe clarify that water depth in crevasses not necessarily a 'real' quantity but rather a forcing parameter within the calving model.
p. 6 line 1/before eqn. the variable 'd_sc' is not 'named' yet. Maybe add before eqn text: 'The crevasse depth d_sc is given by…'
p. 6 lines 3-8: I find this explanation a bit confusing, maybe rewrite and restructure this explanation of the horizontal stretching rate. Maybe first explain the important stresses/terms and then the forcing parameters.
p. 6 line 6 and 7: the sentence explaining the factor f_si should be moved to after the eqn starting with e_xx.
p. 6 line 14: add what the basis for the SMB of Box 2013 is (meteo station records?
p. 6 paragraph on atmospheric forcing: I find this explanation and variation in forcing rather difficult to understand. Am I right you actually change the mass balance gradient in the ablation area? Maybe a figure illustrating the SMB along x (before and after change) would be useful (maybe in appendix). And what is s_o? the ELA? or did I miss this? add s_o to to table 1. And again why use a 2 letter subscript for the vertical gradien 'G_a1'?
p. 6 line 21: '…as a vertical melt rate at the base of the floating tongue and that is assumed to be spatially uniform. Sensitivity analysis with along-flow variations in submarine melt showed similar results.'
p. 6 line 25: clarify the that you do this to get a 'realistic mass flux in the lower channel'. Note that Nick et al 2013, Jamieson et al (2014) and Nick et al (2013) did something similar.
p. 7 line 8: '..and realistic FORCING', is this really so, you strongly simplify/modify the forcing to linear! Maybe rephrase and clarify.
p. 7 line 10-11 and next paragraph (3.1): I would be more specific how you do this tuning and which parameters you tuned.
p. 7 line13: IMPORTANTLY, during the retreat the calving front…'
p. 7 line 14: exactly 43 km? or approximately?
p. 7/8 section 3.1 Model initialization in general: in particular last paragraph on p. 7 and two pragraphs on p. 8 should be clarified and maybe structured and explained more logically. I struggled to follow (see some more specific points below). E.g. make clearer that LIA extent and trimline used as constraint for initial LIA geometry and present extent, surface and velocity for geometry and basal sliding coefficient.
p. 7 line 24: basal sliding changes - the surface slope and hence ice thickness? Do you mean the choice of the basal sliding coefficient influences flow, and hence surface slope and divide thickness?
p. 7 line 28: 'reference height'??? do you mean 'is used as elevation constraint for the LIA surface'?
p. 7 line 30: again is the sliding parameter independent ofg peff (effective pressure/water pressure)
p. 8: line 3-4: maybe rephrase by saying: 'The steady state surface profile is …. A uniform lateral…'. Question, did you apply it up to the divide? Or just in the fjord part? May need some explanation. This also rises the question of what with you used upstream…? The cahnnel or the catchment width?
p. 8 line 9 and line 12-13: again the crevasse water depth is rather a calving parameter than a 'real' quantity.
p. 8 line 15-19: explain better how you vary SMB 'linearly'. At what rate, how? Before and further down you say you use Box dataset, but then you perturb it here??? But always the same way? Maybe show the SMB profiles in the appendix.
p. 8 line 20-24: maybe check and refer to these referneces who also considered ice-melang buttressing (walter et al 2012 Ann Glaciol, Todd 2014 TC, Todd 2018 JGR,…)
p. 8. Line 33: '…may be related…' (comparable would mean water deoth and runoff have same units!)
table 2: I would add and clearly label the unperturbed steady state parameters as well, so one can see the step change applied.
p. 9: '…to reach observed retreat position in 2015'
p. 9 line 11: awkward phrasiung 'high amount of observations', better: 'high NUMBER of …'
p. 9 line 13: delete 'Nevertheless' is not needed
p. 9 line 15: I can not foillow this 'mean latitudinal' ? do you mean you define a centreline along flow and then take the front perpendicular to it? 'latutudinal' refers to geographix coordinates.
p. 10 line 4: you could be more specific here: '…we also try to investigate the effect of fjord geometry and the relative importance of bed topography versus channel width….'
p. 11 line 12: '…reaches about 400m compared to 300m…'.; and refer to Fig. 3a here.
p. 11 are these values (stresses) from LIA or today?
p. 11 line 17: 'In comparison, other modelling studies obtained lower basal resistance (joughin…)' and but they are from present??
p. 11 line 23: '…retreats a further…'
p. 11 line 29: how do the 65 km^3 compare to todays observed flux?
p. 12 line 1: '…that are approximately an interpolation of those…' awkward formulation, rephrase ('are inbetween?').
p. 12 line 3: '…the simulated temporal retreat patternof the glacier front…'
p. 12 line 5: '…in the timing of the phases of rapid retreat…'?
p. 12 line 7: what do you mean with 'the simulated frontal positions from the observations???'
p. 12, fig 3: this figure clearly shows that it is not just BED TOPO that is important for retreat pattern but that width (widening/narrowing)m seems here even more dominant influence. Should be mentioned and discussed later.
Figure 3: how does it fit with earls 1990s velocity data, pre-rapid acceleration (joughin 2003)?
p. 13 line 3: 'The forcing parameter combinations thereby determine the …'
p. 13 line 5: this section is not just on grline but also on front retreat, so adjust title to: 'Control….on front and groundingline retreat'
p. 13 whole bottom paragraph: maybe 'stability' and 'stabilization' are not quite the right terms here as these are mathematically not fully stable, but rather slow downs in retreat.
I am somewhat surprised that the grline position doe not change when the front is retreating. Do you measure here how long the front is within the same 'bin' (grid size)?
Clarify how you measure stability.
Also in caption of fig 5: maybe 'residence time' or 'still stand time' is more appropriate as '0stabilization'.
p. 13 line 10 : add a 'space' between 'position' and '(Fig., 5b)'
p. 13 line 12: '…forcing as with the original…'
p. 13 caption fig 4: add in caption what grey shaded line is.
p. 14 whole paragraph. Maybe the jamieson (2012) paper is relevant here.
p. 15, fig 6: maybe adding the grline positions as well (as in Fig 4) would be useful here.
p. 15/16 Improve/differentiate discussion of terminus versus grline: see main comments
p. 15 line 2: 'At the example of JI, our results show.…and THEIR implications…' and delete first sentence on line 3.
p. 15 line 7: '…fjord geometry and fjord width in particular to a large degree controls the retreat pattern history…'
p. 15 line 8: '…magnitude controls the onset…'
p. 15 line 5: these references refer to large scale ice sheets/shelves and in the case of Schoof without a floating tongue. I would add some tidewater calving example as well
p. 15 line 16: width not just affects lateral drag but also the flux cross section (narrowing leads to a jamming of ice flux and thus along flow thicknening/steeoeninG).
p. 15 line 13-14: 'they use shorter time periods' or ' use a short short time pertiod'
p. 15 line 21-22: the jamieson (2014) paper maybe relevant here.
p. 16 first paragraph: maybe one could highlight importance of width here (in comparison to bed topo).
p. 16 line 9: 'reasonable' range? 340m of water depth in crevasses seems not necessarily 'reasonable to me.
p. 16 line 14: related to comment just above, yes, water depth in crevasses is not necessarily a 'real' quantity, but a model parameter. I am still puzzled why you had to use such big values, was it so hard to push/force it of the LIA position?
p. 16: line 14: 'vertical'? do you mean 'horizontal submarine melt'? at the vertical calving face?
p. 16 line 18-20: again would be useful to see this SMB profile (add figure maybe in appendix)
p. 16 line 22: '…than the local SMB…'
p. 16/17 model limitations: I would mention the 'comparison to observations' as well in the subtitle and maybe say a bit more there how it matches or not matches the observed geometry change (forming of floating tongues …). Basically a little bit more on the 'details' mentioned on line 27. But keep it positive, meaning first say in the things it does well and what it still captures and not only a list of what it does not do. And regarding the limitations some more justification why these limitations are not crucial for the main conclusion/question of the study would be useful. (see main comments).
p. 17 line 2: note that Bondzio actually did prescribe the front position over time…
p. 17 line 6: 'This asymmetry causes in reality…'
p. 17 line 8: 'treated as STRAIGHT…' (rather than flat)
most would agree that SSA is a reasonable approximation for flow.
p. 17 line 7-9: depends on the question but for here I think
p. 17 line 10: yes ice viscisity evolution may change with acceleration but this is unlikely to affect the stepped retreat pattern as it is a response to the rapid dynamic changes rather than a cause (it may change the timing and average retreat rate later a bit though).
p. 17 lines 12-13: did you test the sensitivity to this effect out, if so this may help to support your case. I think we did that in the jamieson et al (2012/2014) papers and did not see much effect on the stepped retreat pattern.
p. 17 line 15: 'outputs annual'? you mean you do not consider seasonal variations? Maybe clarify, but again including seasonal changes is unlikely to change your retreat pattern/main conclusions.
p.17 line 18-19: with regard to data uncertainties I would also mention the relatively poorly constrained bathymetry data in the fjord.
p. 17 section 5.4: see my main comment in general comments.
I would not focus too much on 'predicting moraine positions' (and hence change title) but rather towards how it helps for interpretation of palaeo records and to do reconstruction (e.g. looking at the fjord width tells you an awful lot)
p. 18 line 7: '…has been RELATED to increased…' ('correlation' is a statistical technique and would require a coefficient and significance….)
p. 18 in the conclusions I would say a bit more what comes out/what it means at the end (fjord topo crucial and very robust for longer.-term retreat pattern) rather than what you did. For example the relative importance of the width and grline for the retreat pattern would be useful.
p. 18 line 12: '…is highly non-linear …which is a robust feature of the modelling sensitivity study and consistent with longer-term (century scale) observations'