See attachment.

In this study, Wang et al. compare modelled velocities derived from a full-Stokes thermomechanical model (from a previous study, Huang et al., 2024) with surface velocity observations from MEaSUREs. I do not think this study is a novel contribution to the field, and found the manuscript confusing, so I do not recommend it for publication.

Major comments

In a preceding study, Huang et al. (2024) conduct full-Stokes thermomechanical simulation forced by 8 different geothermal heat flux models. The strength of this study is the comparison of the model results with an independent constraint – the radar specularity content of the bed. To make this comparison, Huang et al. perform an inversion for the basal parameters, based on modelled vs. surface velocities. So in this study, Wang et al. are calculating metrics based on the residuals of the modelled vs surface velocities, and are thus evaluating the performance of the Huang et al. inversions. While it seems reasonable that better performing inversions reflect more accurate GHF map, a range of other factors can be at play. For instance, the authors note the possible influence of anisotropic viscosity. Poorly-performing inversions could also be the result of uncertainties in the form of the basal sliding law, or in the basal topography model. Wang et al. present a ranking of GHF maps that is similar but not identical to that of Huang et al. It is unclear why Wang et al. think that this ranking is more accurate, especially given the circularity of the velocity residual argument mentioned above. It is also unclear that the Wang et al study presents results which are novel, relative to the Huang et al. study.

Wang et al. justify their study by saying that they are introducing a new method – this is misleading. They are instead introducing new terminology for “metrics” based on velocity residuals, which is a common practice in the field of glaciological inversion. One metric masks the thawed bed, another metric masks the frozen bed, but both metrics are used in the final evaluation – so it is unclear why the masking was necessary to start with. I don’t understand why you need “bidirectional constraints” when you could take the root-mean-square error. Even if they were presenting a new method, they do not provide any tests to show that this method improves upon existing ones. Finally, the terminology of these metrics is confusing, and I found did not provide me with a better physical understanding of why some models performed better than others (although this last point can be rectified with clearer language).

Minor comments

In Figure 3 & 4, I think it would be clearer to change the term “warm bed” to “thawed bed”. And in Figure 5, “cold bed” to “frozen bed”.

The authors should note where they obtain their velocity observations within the main text, and maybe plot them.

I think the authors should add a section describing the model methodology, so that the reader can understand this paper without having to read Huang et al.