Editor decision after re-reviews of revised revision.

Dear H. Akesson et al.,
The revised version of the manuscript was sent out to review again (comments further below), and both reviews were positive about the revisions undertaken and indicated that the revised version has strongly improved. Although they mentioned that overall the approach could perhaps have been more thorough and dig more systematically into the feedback mechanisms they both indicated that there are interesting results, it has a clear contribution to the general topic, it is well focussed and is well written. However, they both had some general (although rather minor) and some more specific/detailed points that should together with some very minor typos spotted by me (see list below) be addressed. The more general points are:

General points by reviewer 1:
-Try to include some of the literature mentioned by reviewer where relevant (both on the recent work on ice caps and on the issue of elevation feedback, see comments below):
-SMB-Profile: not so clear how derived could maybe be clarified a bit more

General points by reviewer 2:
-phrasing of Hardangerjokulen GREW….


Further address all further rather minor detailed comments of both reviewers (mainly reviewer 1, see list below) in a re-revised version and please proofread and re-check the manuscript before resubmission and comment all the changes and revisions undertaken.
.
The editor A. Vieli, 15 Dec 2016


Reviewer comments:

Reviewer 1

The manuscript is generally well written, flows nicely and is easy to follow and now has a clear(er) focus. The authors have carefully addressed the reviewers' comments. While the reviewer's comment "This setup, with a focus on the long-term evolution of the ice cap, is interesting to get an insight in the dynamics of this ice cap and the important role of the surface mass balance (SMB) and its feedback with elevation. However, the authors do not really dig into these concepts" still holds true, though to a lesser degree, the authors explicitly state their focus on long term reconstruction.

My main comment is that the manuscript could be made more relevant and broadly appealing by putting the results in a wider context and contrasting/comparing their findings with other recent work on ice caps and icefields. For example, recent publications assess the stability of the Juneau Icefield (Ziemen et al, 2016) and Yakutat Glacier (Truessel et al, 2015). Both glaciers are in south-east Alaska in a similar climate setting, but Yakutat Glacier is expected to disappear by the end of the 21st century while the Juneau Icefield is expected to survive. Ziemen et al (2016) have done many modeling experiments that are quite similar to this study (e.g. sensitivity to sliding, regrowth capability under different climate scenarios). I find it very interesting that for present-day climate, Hardangerjøkulen ice cap only grows to 20% to its current volume when starting from ice free conditions, while the Juneau Icefield's regrowth volumes are close to the steady-state volumes when starting from present-day (Fig 11 in Ziemen). Other similarities include the sparseness of the ice thickness data. Ziemen showed, using a very crude sensitivity experiment, that uncertainties in ice thickness have a strong impact on the simulated volume evolution. Very recently, Gilbert et al (2016) studied the evolution of the Barnes Ice Cap on Baffin Island, corroborating some of the findings of Mahaffy's seminal 1976 paper, and concluded that the ice cap will disappear within this millennium. I hope this will help expand on the concluding statement (P20,L14) "We expect that ice caps with comparable geometry elsewhere may display similar sensitivity and hysteresis".

Figure 2, SMB-altitude profile and P15, L19-20: I'm not quite able to figure out how the profile was derived from observations without reading all the underlying literature, so this might be a red herring: looking at the geographical setting, I can imagine that the ice cap experiences orographic precipitation at least to some degree, where the windward side receives higher precipitation than the lee side. If more high-altitude area is in the lee side, averaging could lead to a decrease in SMB at high altitude. Schuler et al (2008) studied orographic precipitation effects on the Svartisen ice cap further north using the Smith and Barstad (2004) linear theory of orographic precipitation model.


A side note: The authors' statement in the response letter "In addition, we think that the dependency of initial conditions for ice caps (hysteresis), illustrated in Fig. 11, has not received much attention in the literature and is relevant for modeling and reconstructing paleo-ice caps and predicting future ice cap evolution." may be true for small(er) glaciers, but not for ice sheets. We've been pushing this idea for more than 5 years now; see Aschwanden, Aðalgeirsdóttir, and Khroulev (2013) and Aðalgeirsdóttir et al (2014).

Detailed comments:

P1, L13-14: "... that the surface mass balance-altitude feedback and ice cap hypsometry are essential to this sensitivity." The surface mass balance-altitude feedback and the glacier hypsometry are not independent of each other (or am I missing something?), the hypsometry of a glacier determines how strong the surface mass balance-altitude feedback is. If memory serves me well, this was beautifully illustrated by Rivera and Cassa (1999)

P2, L3: their sea level equivalents (e.g. Grinsted, 2013; Bahr et al., 2015). It's a good practice to also cite the first manuscript that introduces a new concept (here V-A scaling).

P3, L7: ...ranges form 1020 to 1865 m a.s.l....

P6, L21: ...on a scaling analysis of the Stokes equations... ("full Stokes" still makes me cringe)

P7, L15-20: I do not want to go off on a tangent, but why do you acknowledge that SIA is only valid for no-slip conditions and then go on and combine it with Weertman sliding? See Appendix in Bueler and Brown (2009) why this should be avoided. I do not expect this to influence your general conclusions though (in fact, you will most likely get very similar sensitivities when strictly using no-slip). Along the same lines, I agree with the discussion in the previous reviews that using a more complex stress balance is not needed here.

P7, L23-24: "In this study, the basal sliding parameter β is assumed spatially and temporally constant. In reality, sliding likely varies in space and time according aforementioned factors." This two sentences do not make sense the way they are written, one gets the impression that using a constant β leads to a constant in time and space sliding, which is not true. I think you can just delete the second sentence.

P7, L25-27: There is a much stronger argument against deriving the basal friction parameter from surface properties. Inversions for β are only valid at or around the time stamp of the data sets used for inversion. Consequently, β fields are snap shots and should not used for prognostic simulations at all, but this would be all the more severe for the long time scales (millennia) considered in this study.

P8, L22: Define your steady-state. See Ziemen et al (2016) near Eq. 4 why this is important to correctly interpret your results.

P10, L2: ...sensitivity to the choice of...

P12, L19,22: should be Figure 11a,b not 10

P12, 31: Our Holocene simulations shows...

P19, L2-5: This is a rather broad brush over a large field. At least provide references (there is a wealth of literature on simple, analytical models by glaciologists including, but not limited, to: J. Oerlemans, G. Roe, W. Harrison, M. Luethi).




Reviewer 2:
Suggestions for revision or reasons for rejection (will be published if the paper is accepted for final publication)
Having read the initial reviews and the authors responses to them, I can see that the authors have made a concerted effort to simplify, clarify, and improve the paper. The major shortcoming of the study appears to be that the model implementation (using just the SIA) may produce results that are unrealistic. I think this concern still persists, but in my view the study is sufficiently conceptual that the results can be considered simply in terms of anomalies - that is, the relative changes are of interest, even if the absolute geometries and dynamics are open to question. To help convey this, one small but important modification might be to change the tense used throughout the paper when discussing the results. Rather than stating emphatically (for example), "...Hardangerjøkulen GREW from ice-free conditions in the mid-Holocene.." (L5) it might be preferable to use the present tense, and couch the statement in terms of the model results, e.g. "in our simulations Hardangerjøkulen GROWS from ice-free conditions in the mid-Holocene..:. This change of tense throughout the manuscript would make it clear that the ideas being put forward are based solely on the experimental results, and that the authors aren't making direct claims about the 'real' ice cap. Other than this suggestion I can find little else to comment on that the two original reviewers haven't already picked up. I agree with them that the findings concerning SMB feedbacks and hysteresis etc aren't particularly novel, but they are interesting nonetheless and in the revised manuscript the balance between results and speculative discussion seems ok. The figures are good and clear and the paper should be of interest to others investigating Holocene fluctuations of glaciers and ice caps elsewhere.

N R Golledge 28th Nov 2016


Very minor comments/corrections by editor
-p. 4 line 29: ‘experienced’ (not ‘experieneced’)
-p. 11, line 16: ‘faster sliding’: a bit awkward, ‘enhanced sliding’ maybe better.
-p. 14 line 29: should be ‘were’ not able … rather than ‘was’ as there are two authors.
-p. 19 line 3: again should be ‘…assumptions do’ rather than ‘‘…assumptions does’
-please acknowledge the reviewers in the acknowledgements


References:

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abstract = {Validation is a critical component of model devel- opment, yet notoriously challenging in ice sheet modeling. Here we evaluate how an ice sheet system model responds to a given forcing. We show that hindcasting, i.e. forcing a model with known or closely estimated inputs for past events to see how well the output matches observations, is a viable method of assessing model performance. By simulat- ing the recent past of Greenland, and comparing to obser- vations of ice thickness, ice discharge, surface speeds, mass loss and surface elevation changes for validation, we find that the short term model response is strongly influenced by the initial state. We show that the thermal and dynamical states (i.e. the distribution of internal energy and momentum) can be misrepresented despite a good agreement with some observations, stressing the importance of using multiple obser- vations. In particular we identify rates of change of spatially dense observations as preferred validation metrics. Hindcast- ing enables a qualitative assessment of model performance relative to observed rates of change. It thereby reduces the number of admissible initial states more rigorously than validation efforts that do not take advantage of observed rates of change.},
author = {Aschwanden, Andy and Aðalgeirsd{\'{o}}ttir, G. and Khroulev, Constantine},
doi = {10.5194/tc-7-1083-2013},
file = {:Users/andy/pdfs//Aschwanden, Aðalgeirsd{\'{o}}ttir, Khroulev - 2013 - Hindcasting to measure ice sheet model sensitivity to initial states.pdf:pdf;:Users/andy/pdfs//Aschwanden, Aðalgeirsd{\'{o}}ttir, Khroulev - 2013 - Hindcasting to measure ice sheet model sensitivity to initial states.pdf:pdf},
journal = {The Cryosphere},
pages = {1083--1093},
title = {{Hindcasting to measure ice sheet model sensitivity to initial states}},
volume = {7},
year = {2013}
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@article{Adalgeirsdottir2014,
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abstract = {We study the evolution of the Juneau Icefield, one of the largest icefields in North America (>3700 km 2 ), using the Parallel Ice Sheet Model (PISM). We test two climate datasets: 20 km Weather Research and Forecasting Model (WRF) output, and data from the Scenarios Network for Alaska Planning (SNAP), derived from spatial interpolation of observations. Good agreement between simulated and observed surface mass balance was achieved only after substantially adjusting WRF precipitation to account for unresolved orographic effects, while SNAP's climate pattern is incompatible with observations of surface mass balance. Using the WRF data forced with the RCP6.0 emission scenario, the model projects a decrease in ice volume by 58–68% and a 57–63% area loss by 2099 compared with 2010. If the modeled 2070–99 climate is held constant beyond 2099, the icefield is eliminated by 2200. With constant 1971–2010 climate, the icefield stabilizes at 86% of its present-day volume. Experiments started from an ice-free state indicate that steady-state volumes are largely independent of the initial ice volume when forced by identical scenarios of climate stabilization. Despite large projected volume losses, the complex high-mountain topography makes the Juneau Icefield less susceptible to climate warming than low-lying Alaskan icefields.},
author = {ZIEMEN, FLORIAN A. and HOCK, REGINE and ASCHWANDEN, ANDY and KHROULEV, CONSTANTINE and KIENHOLZ, CHRISTIAN and MELKONIAN, ANDREW and ZHANG, JING},
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journal = {Journal of Glaciology},
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number = {231},
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year = {2016}
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Decision of editor based on comments of two reviews on revised manuscript and subsequent minor revisions undertaken.

Dear Henning Akesson et al.,
After substantial revisions following rather critical reviews of the initial manuscript, this paper has been reviewed by two further referees which were in general rather positive still but had some suggestions for minor revisions. These minor concerns have now almost entirely been addressed but there is one issue regarding the description of the used mass balance function remaining that after closer inspection I think should be addressed before publication (see details below).This issue can however easily be addressed through technical corrections. I am therefore very happy to inform you that the paper will be accepted after correction of this issue (details below) and I thank the authors for their thorough and careful revisions.

Minor technical correction:

Reviewer 1 (of revised version), raised the issue of limited explanation of used mass balance relationship with elevation (in particular decrease in higher accumulation elevations).
Although the authors rewrote parts of the text there I do not think it is in any way clearer and there is no new information in there, rather one line (explaning the varianles in eqn 6) has been shifted a few lines down, making it rather more difficult to follow the explanations.

Further, and I apologies that I have not spotted this earlier, the term ‘mass balance gradient’ for ‘B_Ref’ ( and ‘B(z,t)’) is misleading if not even incorrect (appears on p. 9, line 10 and page 10 line 21). A ‘mass balance gradient’ refers in glaciology usually to the change of B with elevation (e.g. dB/dz), and I think you mean here rather the ‘mass balance function with elevation’ or ‘mass balance relationship with elevation’.
Further, the additional explanation of this mass balance function is currently in the figure caption (fig 2) but I would think this should be in the methods (in order there to clarify things as suggested by reviewer 1) and maybe one should even add why Giesen and Oerlemans (??) think that the accumulation decreases in high elevations (wind-effects/erosion?).

The editor
Andreas Vieli