This is a review of the manuscript "Subglacial hydrology regulates oscillations in marine ice streams" by Haseloff et al. for publication in The Cryosphere, prepared by Alexander Robel. This paper describes a 1D model and corresponding results on the coupled variability of marine ice stream flow and subglacial hydrology. It extends prior work by myself and others, considering water flow within subglacial hydrological systems which leads to the emergence of more rapid surge-like ice flow variability in realistic parameter regimes that may help to address certain shortcomings of past models. I think the manuscript is overall well written and the scientific results are robust and thoughtfully laid out. I see no barrier to publication of this in The Cryosphere after some minor revisions.

Conceptual suggestions:

1. I think perhaps one of the more underplayed implications of the results is that the model produces variability at multi-centennial time scales at values of till hydraulic conductivity that may reasonably be expected to occur in reality. Prior models (i.e., Robel et al. 2013, 2014) which do not include subglacial water flow cannot produce ice stream flow oscillations on time scales less than 900 years or so. The best observations we have of ice stream flow variability in the present day (or at least the late holocene) is the Siple Coast, where most evidence points to periodicity in stagnation-activation cycles of 300-500 years. So, this is a very exciting result since it may resolve this issue. It would be worth spending more time on this in the discussion, and also comparing to the results of Mantelli et al. 2016 which is able to produce quasi-periodic variability at similar time-scales by forcing the system with stochastic climate noise.

2. I think you a being too non-committal on the question of what K_d is in reality. On line 298, you say "these values are not straightforwardly transferable to the values of Kd used here. These values do not take the formation of subglacial conduits into account." But you basically have reasonable values for the case where flow occurs entirely through microporous till (K small limit) and where channelization may enhance these values (K intermediate to large). Other studies (Warburton et al. 2020) besides those that you have cited indicate that till under shear in W. Antarctica may have these higher conductivities (without specific evidence for channelization). You should translate these to Kappa in the discussion in 4.3 so readers can understand what these till values mean in the context of your prior results. Ultimately, the strength of these results will rest on whether the reader understands the conditions under which they can be applied to reality, even if uncertainty remains in what exact parameter values are.

3. I see that there is some discussion of the numerics in the appendix, but it would be useful to summarize in the model description sections how the equations are discretized and solved (seemingly some large nonlinear solve in Petsc). Particularly because activation/surge-type behavior in models is notoriously resolution dependent and you do reference the computational intensity of these simulations in your discussion.

Minor suggestions:

L1: semicolon unnecessary

L6: is there a good reason to use "surge" and "oscillation" terminology separately here. It gives the false impression that these are strongly different phenomena.

L12: mass discharge occurs in regions

L44: here and throughout this is referred to as the "undrained bed model", but historically Tulaczyk called this the "undrained plastic bed model". Is there a reason for dropping "plastic"?

L45: subglacial water discharge

L51: due to flow, water freezes and the ice

Figure 1 - great figure!

L64: indicate here that this limit goes to the solution given by Tsai

L68: at intermediate hydraulic conductivities

L76: This is confusing because it implies that the glacier length is a constant 1000 km, but this is merely the scale, and the grounding line evolves (as you explain below). Perhaps reword this.

L99: only a few models

L100: subglacial water mass

L109: could reword this to point out that this isn't actually a canal model, just a model for down-gradient porous water flow through till which could incorporate the bulk effect of canals through increased hydraulic conductivity

L142: sediment from freezing

Figure 2: Its a bit confuding as to whether the two columns in the intermediate Kappa range are for different values of Kappa? Perhaps should indicate they are different ranges within the intermediate range?

L149: Please provide a physical justification for why it makes sense that effective pressure goes to zero at the grounding line

L170: please indicate the time scales of the upstream traveling wave

L172: different regimes

L184: N is indicate in row (a), not row (b)?

L188: combine this paragraph with the previous one?

L190: leads to a local build up in the

L204: "mechanical barrier upstream of the grounding line" you explain what you mean by this later, but it would be more useful to describe exactly what you mean by this here

L209: a few sentences could be added here describing the variation in oscillation period in more detail - it varies from X yrs to y years over this range of kappa...

Figure 4: not sure what the N_c is doing above the colobar for the N column

L226: see comment for L204 about the "buttress" which is a different term than was used before

L249: would be prudent to also cite Fowler & Schiavi 1998 where many of these ideas originated

Figure 5b/e: I don't think the y-axis needs a log-scale, obscures some of the variation that occurs here

L263: yes, but you hold everything else constant, so this line reads as a bit absolute given that you don't (in this study) vary other parameters

L270: surging mountain glaciers?

L274: basal temperature gradient?

L276: by upstream-traveling activation waves

L282: in some sense your study shows this as well, since climatic and gemoetric factors also enter into Kappa, which is the relevant parameter of this study

L288: do no always apply when basal

L289: The study by Robel et al. 2016 in TC shows that thermal oscillations can temporarily mitigate a positive feedback of grounding line flux and thickness on retrograde slopes. May be useful to make the connection to MISI-style arguments here

L291: can change on decadal to centennial time scales (since this is the time scale for passage of activation/deactivation waves, not necessarily the full period of an oscillation)

L293: uncertainty in how

L294: similar point to #3 above - your model can be used to speak to the computational requirements for simulating these kinds of variability, which currently is a bit glossed over in appendix and not discussed much at all in main text. Would be useful for modelers interested in incorporating these dynamics in large-scale models to have a sense for resolution they should be aiming for.

L333: there is an interesting literature on interactions between ice streams, particularly the water piracy hypothesis (Anadakrishnan and Alley papers 1994 and 1997) that would be worth discussing in the context of your results

L347: steady-streaming

L349: at period from a few centuries to millennia

L356: O(\Delta x) accuracy