Dear Authors,
After 2 in general positive reviews of the first version of the manuscript and with some rather substantial suggestions for changes/revisions of one of the reviewers, the authors undertook major revisions and added additional experiments and modelling investigations and addressed the more technical points as well. As the revisions were rather substantial the paper has been sent to 2 further re-reviews, of which one of the reviewers had already reviewed the first version of the manuscript and was happy with the revised version of the manuscript. The second new reviewer had however some additional in my view valid comments that should be addressed before publication and which I outline below (the detailed review is given further below). The main points to be addressed are in brief:

1. to clarify the difference in the model and results of this study in relation to an earlier study by VanPelt and Oerlemans (2012) who used almost the same model. This should include
-a clarification in the model difference
-some better discussion/integration of the own and maybe new findings against/with Pelt and Oerlemans (2012)
-perhaps a clearer discussion of what the implications of ‘ocean-terminating’ really changes /means (compared to the land-based VanPelt Oerlemans (2012) study).

2. Related, this study should be embedded slightly better into the surge-modelling literature in the introduction and discussion and therefore VanPelt and Oerlemans should likely be mentioned in the introduction, as their study is very close (with the difference of being land-based).

3. link to HE-events (overselling): the used geometry seems pretty generic and perhaps together with the results not too close to the real HE-case (the modelled cycle-periods also do not match and in reality there was likely a slight retrograde slope into Hudson bay which would change things quite a bit regarding groundingline motion and feedbacks). Thus although a motivation by the HE-events seems ok, maybe the title could be rethought and be less strongly linked to HE-events (HE-event ‘like’, ‘towards’ HE-event cycles….???). At the end it is the choice of the authors of how to label the manuscript but i think one should be careful to also deliver to the raised expectations.
Note, in the context of HE-event mechanisms and for completeness, in the introduction perhaps the recent literature of Alvarez-Solas (2013) and Bassis et al (2017) (see detailed references further below) are may be relevant (although not directly related to the mechanism investigated here, so not crucial).

4. the choice and implications of a rather low reference velocity (1m/y) should be addressed/ or clarified in relation to the variable flow law exponent ‘q’ (and related issues, see reviewer comment)

5. I agree with the reviewer that the ‘averaged grounded’ visualization is not that ideal, and makes it also difficult to compare to other studies (e.g. VanPelt and Oerlemans 2012). At least for some of the experiments maybe a average or max. centreline value could also be shown (as additional dashed lines or in appendix).

For details see reviewer comment below

Editor Andreas Vieli


Reviewer comment to be addressed:
In their manuscript From Heinrich events to cyclic ice streaming, the grow-and- surge instability in the Parallel Ice Sheet model, Johannes Feldmann and Anders Levermann nicely describe their findings from surge-type experiments with the Parallel Ice Sheet Model.
In this respect, this manuscript is very similar to the Van Pelt and Oerlemans 2012 publication. There is nothing fundamentally wrong with this. Testing previously obtained results is an important process in science, and it is interesting to see that and under which parameters the current version of the Parallel Ice Sheet Model shows surge-type behavior. However, it then needs to be made very clear, where previous results were (not) confrmed and where new results are obtained.
In contrast to the Author's claim, Van Pelt and Oerlemans also used a model version
that included modeled pore water as enthalpy (page 348, second paragraph). The friction laws in the two publications look very similar to me. Please point out where the ‘simpler friction law` was improved. The visible main differences between the publications are the investigation of a water-terminating glacier instead of a land- terminating one (this has no obvious effect on the surge cycle as drawn in Figure 2), the parameters that were varied, and slight changes in the treatment of basal water.

The manuscript left me a bit concerned regarding the appreciation of the authors for previous work, and a tendency towards over-selling their own results. This begins in the title where Heinrich events are mentioned right at the start, while the manuscript deals with cyclic surging in a pretty generic ocean-terminating glacier, that is not obviously set up to resemble the situation in the Hudson Bay / Hudson Strait area, the source region of Heinrich events. I would suggest cutting the title to The grow-and-surge instability in the Parallel Ice Sheet model or something similar.
While continuing through the manuscript, I would have enjoyed seeing more references to previous publications on glacier surging, and the similarities and differences in the underlying theory and results. This has already substantially improved since the first version of the manuscript, but I think it can be improved further. One example is the introduction of Figure 2 in Section 3.1, where a comparison of the model presented here to the binge-purge cycles of MacAyeal 1993 (and subsequent publications, e.g, Roberts et al, 2016) could make it easier for the reader to appreciate the additions presented in this manuscript. There also is a substantial body of research on growth-and-surge cycles in the context of mountain glaciers that could be referenced.

The newly introduced comparison of different values for the basal sliding exponent q suffers from an ill-chosen reference velocity uc = 1m/s. This is the velocity for which the basal friction _b is independent of the exponent q. For comparing different flow law exponents, this value has to be in the range of typical sliding velocities. Using numbers obtained from the surge phase in Figure 3, the basal shears stress for ice sliding at ub = 1000 m/a, and a _c value of 300 kPa varies over more than six orders of magnitude for the different values of q. It is highest for the plastic flow law with
_b = 300 kPa (q=0) and decreases via _b = 9500Pa (q=1/3 ) to _b = 9:5Pa (q=1). For lower velocities relevant for surge initiation, this contrast is even more extreme. Van Pelt and Oerlemans chose uc = 100m/a, a much more realistic value. This might explain some of the differences in the results of the two studies.

I am not convinced by averaging the values for Figs. 3, 6-9, A1, considering that
at least two thirds of the grounded domain are not affected by the surge at all. I would
probably prefer one or two point measurements in the center line, or a line-average of
this line.

references:
Alvarez-Solas, J., Robinson, A., Montoya, M. & Ritz, C. (2013) Iceberg discharges of the last glacial period driven by oceanic circulation changes. Proc. Natl Acad. Sci. USA 110, 16350–16354

Bassis et al. (2017) Heinrich events triggered by ocean forcing and modulated by isostatic adjustment. Nature 542, doi:10.1038/nature21069

Final decision of editor based on comments of two initial reviews, major revisions undertaken and two re-reviews of the revised version.

Dear J. Feldmann,
After substantial revisions in response of two initially critical but overall very positive reviews, this paper has been reviewed again (one referee of first round, one new referee), with some substantial suggestion for revisions of the new referee.
These critical points were addressed mostly very well and in detail in the 2nd revision of the manuscript and I thank the authors for their carful revisions and detailed response.
After the viewing the revised version and considering all the information from the response and reviews the manuscript seems now very close to final publication in TC.
However, before official acceptance there are a few technical details that need correcting (see list below) and one remaining point flagged in the last review that could in my view be addressed a bit better (left also to author judgment).

This last point refers to the reference to the earlier somewhat similar study by Pelt and Oerlemans (2012). In general the revised version makes the links and differences to this study much clearer (method, model, results), but personally I think it would be useful to know before the results and in the introduction what the main findings/conclusions of the vanPelt study were, as this study is so close. Currently, this is done in the final discussion, but I would personally prefer, to very briefly outline their for tis study relevant results in the introduction (besides the difference in model/methods), maybe in the last paragraph p. 2 lines 31-35.
I leave the final decision on this to the authors, but I think knowing upfront what others found/concluded would be useful here.


Detailed more technical points to correct/address:

p. 2 line 28: ‘sentence with ‘…visualized in a novel way..’ , I do not quite know which graphs/figures/visualization are referred to here and what should really be novel here. Is it the conceptual feedback loops? But seems not very ‘visually novel’ to me but rather conceptual and at least parts of it seemed familiar to me. I would simply leave this sentence away (to avoid issue of what is really ‘novel’) or at least rephrase clearer.

p. 2 line 34: I would be more specific and integrate ‘marine terminating’ or similar (instead of just ‘bed topography, boundary conditions’)

p. 7 line 15 and Fig 7: maybe I am picky but the frequency first increases from 10% to 30% and then decreases.

p. 10 line 16: I would be more explicit here to which study you compare here: e.g. something like’…differences in results compared to the PISM study of Van Pelt and Oerlemans (2012) are a …’

p. 10 line 23/24: ‘qualitatively different ICE MASSES’ seems a bit awkward, you probably mean ‘qualitatively different ice sheet GEOMTERIES or CHARACTERISTICS’?

p. 10 line 28/29: formulation is here just appears somewhat confusing (contradicting): same order of magnitude but 5 times faster; I guess you similar but still substantially different. Maybe reformulate differently.

p. 11 paragraph lines 7-15: could add how you results compares to van pelt and oerlemans (2012). In particular the found decreasing amplitude with decreasing accumulation contrasting the result of to other studies (p. 10-11 line 11), is as far as I know consistent at least with the van Pelt (although they did not exactly vary accum. But ELA). Would probably strengthen your case.

Figure 8 caption: I think the caption on (a) and (b) is here the wrong way round: (a) should be the from 10degree equilibrium to 8 degree, and (b) the increase from 8 degree to …
Currently is the other way round!?

Figure A1 caption : maybe one could add at end of caption ‘… instead of the area grounded averaged values.’

Figure A2 caption: ‘Additional timeseries to results in Fig. 3 of ….’

Figure A3 caption: should it not refer to Fig. A2: ‘…complementing Fig. A2…’ as it shows the same quantities as in fig A2 but for centreline values. Or maybe refer to both ‘Fig A2 and 3’.

Andreas Vieli (editor), 13th July 2017