This study investigates the use of surface fracture and strain rate data in constraining inversions for ice rheology. The study considers two applications – the “snapshot” inversion infers both ice viscosity and basal friction in a single timepoint and the “time-dependent” inversion infers viscosity on an ice shelf at many points in time. The study finds that the inclusion of this additional information into regularization terms can alter the estimates found by the inverse method and possibly allows for an improved physical representation of ice viscosity in the inversion. The addition of this new data appears to be most useful on floating ice.

The application of more data, particularly that of surface fracture, to constrain glaciological inversions is a potentially very useful contribution, as inverse methods are widely used to initialize models and investigate drivers of ice sheet change. The study itself is very applicable to The Cryosphere. Below I describe some comments about the work itself and the presentation.

• The study focuses on the application of these new methods to a case study of Pine Island Glacier. This makes it challenging to draw a concrete conclusion about whether this new data does improve the inversion because we don’t know what the “right answer” is. Without knowing what ice softness is in Pine Island Glacier, it’s hard to know how to compare these different cases the authors present (no regularization, heuristic regularization, data-informed regularization) rather than to say that they are different in certain ways. It seems to hamper the ability for the authors to suggest that one way is “better” than the other. One way of evaluating this is comparing the misfits to see if one regularization technique improves the optimization; however, in evaluations of Figures 2-4, there doesn’t appear to be enough of a significant difference in the misfits to suggest that the data-informed regularization can produce more physical insight than the heuristic regularization. The authors are very careful and measured in the way they speak about these comparisons, which I think is a strength of this manuscript – they do acknowledge cases where the inclusion of this data does not appear to contribute to the inversion (e.g. on grounded ice). However, I still struggle with what the takeaways should be if there is such a difficulty in comparing between these cases. Possibly a clearer approach might be to test this technique on a synthetic case that approximates the PIG case study, in which a synthetic fracture field is imposed and a relationship between that fracture field and viscosity is assumed. This would provide a more straightforward way to compare between the cases presented in the manuscript and enhance the takeaways for the reader.
• The description of the methods I found to be often hard to understand, in terms of the organization of the methods section and the wording of the explanations:
  • A bit more explanation for how fractures are identified and how those fractures are converted into a continuous field to produce f would be helpful here, especially for those that haven’t read the previous papers that describe these methods.
  • Line 44: the relationship between softness and stiffness seems to imply that stiffness is bounded between 0 and 1 – is this the case, and if so, why does this need to be the case? Stiffness appears to be simply a multiplicative factors on viscosity, in which case I don’t see why viscosity can’t vary by orders of magnitude
  • Lines 151-153 form the key description of the “snapshot” inversion and yet I found this to be challenging to understand. What is epsilon meant to represent physically? What is gamma, physically? I also found it challenging to understand xi and its relationship with phi. Having a clearer description of all these parameters would be very useful.
  • The L-curve section seems to be most applicable in the methods section, as I found myself wondering while reading how the regularization parameters were chosen and whether there was an L-curve-style approach to finding them. For example, lines 165-166 mention that there is an independent search for the regularization parameters but without further information it is hard to understand what this means.
  • The term “high” shear strain rates is used often but not defined until line 145. A definition earlier (when it is first referenced) would be useful.
  • Lines 128-130 imply that xi is a mask of only 0 and 1 values, but Figure 1 makes it seem like xi is continuous.
  • Some of the equations (especially the regularization equations, such as Equations 10 and 11) could use much more explanation to describe what the terms mean and to remind the reader what the parameters are (I had trouble, for example, remembering the distinction between f and xi).

Other Comments

• The paragraph in lines 131-139 state that there are some things to note in the fracture data that are useful to understand the stress balance of PIG but the paragraph doesn’t explain what the implications to the stress balance are
• Line 200 – “The phi fields in each case are substantively different…” – it took me a while to understand what the different “cases” were (it is clear upon looking at the figure but it may be helpful to state this in the text as well)
• Line 202 – “of even slow-flowing ice streams” – I wasn’t sure what the “ice streams” were referencing here.
• Figures 2 and 4 – it would be helpful visually to add more labels to the colorbars rather than just the top and bottom labels. It could also be a useful diagnostic to visualize the misfit as a percentage of the observed velocity, to give some context to the absolute numbers.