Please find the attached.

I found this to be an interesting exploration of the subglacial heat flow conditions required to maintain depressions on an ice cap surface. At first glance, the inferred local basal melt rates seem phenomenally high to me. I have some questions about the simulation approach, but the general idea of using an ice-flow model to constrain the basal heat required to maintain a surface ice-cap depression seems feasible to me.

1. Term Convention – The V_z term in equation 2 is referred to as “outflow velocity”. I think this would more probably be called the “basal vertical ice velocity”, or even most conventions would probably refer to this as “basal mass balance”, and denote it more analogous to the B-dot surface mass balance term. Later, it seems that the “V_z” in Eq 2 is being denoted “UZ” in Section 2.3 and beyond. It seems UZ(UZ_0) is applied within the caldera, but it is not clear if there is a basal mass balance applied outside the Gaussian representation of the caldera. The reader could use some clarity on this term, both regarding the notation and the written description.
2. Heat Flow Units – The peak “outflow velocity” (or peak basal mass balance) of the simulations are given in m/yr, and then area-integrated heat flow in W. It would be quite helpful to have the UZ_0 also given in W/m2, which is the more conventional units with discussing heat flow. This would allow the heat flows being reported here to be more directly compared with extreme values in the International Heat Flow Database, for example. At first glance, basal melt on the order of 1000 m/yr seems phenomenally high, perhaps even unrealistically high.
3. Simulation Type – I would be interested to see the heat flow inferred by a steady-state simulation (i.e. maintaining a supraglacial caldera depression over centuries). It can be difficult to entirely attribute simulated changes in ice geometry to specific processes over a 1-year transient simulation, as I guess there would be some underlying transient drift or model relaxation. I see mention of a “heat sources off” simulation (L234), which may be akin to a relaxation simulation, but this simulation suggests the depression only in-fills by 15 m. I am therefore wondering how 15 m of ice dynamic infill requires 100s of m/yr of basal melt to maintain the depression. Or simply put, why is 15 m/yr of infill not just balanced by 15 m/yr of basal melt?
4. Subglacial Water Storage – The assumption that basal melt flows away immediately, and there is no change in subglacial water storage during the simulation year seems quite important, as changes in basal water storage can directly influence the surface modelling target. The authors write “In contrast to observations from a GNSS station, operated at K6 in the summers of 2016 and 2017, revealing seasonal water storage and drainage under the simulated cauldron, we assume continuous and instant water drainage underneath the glacier.” It would seem useful to show such a GPS vertical displacement record and provide more description of the water storage signal (i.e. magnitude and temporal variability).