Dear Sebastian,

First, apologies for a delay in responding. Thank you for your revised manuscript. Both referees have commented on the revisions. Unfortunately, the manuscript is not yet at a stage where we can publish it in The Cryosphere. The main reason for this is that Referee #1 has questioned the physical rationale behind using the creep closure and melting terms to adjust the conductivity in the Darcy model.

During the first round of review, both referees questioned this matter.

Referee #1: “Unfortunately, I think that this viewpoint lacks physical justification. The primary way in which this paper departs from previous subglacial hydrology modelling efforts is that differences in flux are accounted for by changes in the conductivity, rather than a change in the average cavity size. However, the equations for evolving cavity size (which are well understood from a theoretical perspective) are used to model the change in conductivity, with units made to match by simply multiplying by the conductivity. How is this justified?”

Referee #2: “The model description is unclear about how to conceptually understand this model. I am puzzled about the motivation and physical interpretation of scaling K with channel opening/closing while the aquifer is unconfined.”

The revised manuscript has still not satisfied Referee #1 on this question.

I am afraid that until a much more clearly reasoned physical argument for this approach is provided, or the simulations are repeated for a system of equations that does have such a clear physical justification I will not be able to accept this manuscript for publication.

The reason I would insist on a physical rationale for the approach is that the model is relatively unconstrained by data (largely and unavoidably because of by the inaccessible nature of the subglacial environment). This means there is a risk that a non-physical model does not behave realistically outside the range covered by the limited calibration opportunities afforded by SHMIP models and NEGIS data.

I invite you to resubmit, but I still consider this to be at the level of major revisions.

This concern is quite fundamental, but I would encourage you that in most other respects the paper is of a sufficient quality to publish. Please take care though to address the other outstanding concerns of referee #2 in any revised submission.

Yours sincerely,

Robert Arthern

Dear Sebastian,

I think we could publish this version, subject to several technical corrections. Please include the technical corrections as described below. Thank you for your efforts to improve the clarity of this manuscript and congratulations on getting the manuscript to this stage.

Best regards,

Robert Arthern


P3. Line 13. Without subglacial hydrology models, the ice models simply take the ice overburden pressure as effective pressure completely neglecting water pressure.

I am not sure that this is true of most models. Often the effective pressure is simply absorbed into the sliding coefficient C, such that tau_b= C u^m.

P17. Line 8. Basal drag tau_b is defined in a Coulomb-like friction law.

A Coulomb law has no velocity dependence. This is more commonly referred to as a Budd sliding law.

P20. Line 16. We assume that changes within the channel network (e.g. the increase/decrease of cross-sectional area of one, some or many channels or just by the variation in the number of channels) can be translated into a large-scale/average change in equivalent transmissivity.

As discussed previously. This is one of the key assumptions of this paper, and it still has rather little in the way of physical justification. I think you need to be clearer about that.

At the very least you need to provide some clarification along the following lines:

i) You need to say that the precise relationship between channel/cavity opening and closing and the effective transmissivity is likely to be complicated and this paper does not provide a full physical treatment of those complications.

ii) You need to say that here you have assumed the simplest possible monotonic relationship, which is that the transmissivity of the confined system increases or decreases in direct proportion with the volume of subglacial water in cavities or channels.

iii) You need to say that this model should only be considered as a preliminary attempt to explore the qualitative dynamics of the system, until a more robust and physically-based closure scheme between cavity/channel volume and transmissivity can be determined.