Please see attached pdf comments.

The manuscript "Numerical issues in modeling ice sheet instabilities such as binge-purge type cyclic ice stream surging" by Hank et al. is a study of numerical issues associated with modeling thermal oscillations in ice stream flow. It utilizes the GSM and PISM models, and varies many aspects of the numerical implementation including various details of the thermal and sliding models, resolution in time and space, and a variety of parameters. The central goal of this paper is to demonstrate which aspects of the model implementation are most critical to correctly simulate thermal (aka "binge-purge" oscillations).

The goal of this study is a worthy one, and though the general topic of simulating thermal oscillations in ice sheet models has recieved considerable attention over three decades, a systematic study of the dependence of oscillation characteristics on choices in the numerical implementation has not been done. The main issue I see is that the manuscript in its current form is very challenging to read. It is organized more like a reference guide to a large number of simulations, rather than a discussion of the link between real physical processes, numerical choices and clear recommendations for how to remedy these issues in future simulations. In order to be publishable in a form that will be usable by other researchers, the manuscript needs substantial re-organization, reduction in length and re-writing in places. Below the major issues are listed in more detail (I will wait to comment on minor issues in a subsequent revision):

Major issues:

1. Currently, the organization of the manuscript feels like a laundry list of simulations completed and a description of the results, without prioritizing the most important and revealing simulations and little discussion for what the results mean and how they relate to other studies. The study also seems to currently have about 10-15 areas of focus, making it challenging to see which end up actually being important. My recommendation would be to take all the description of simulations where numerical choices don't appear to have much influence on the results and move them into a supplement. They can be summarized in a few sentences perhaps at the end of the results section, but right now they add too much extra to the manuscript making it longer and hard to get through. This includes the sediment-hard bed transition, basal hydrology, basal hydrology instead of temperature ramp and the max time step.

2. The way the results are currently described and presented also contributes to the challenge of reading through this manuscript. There are 15 tables, and it is difficult to understand what all the numbers in the tables mean. Figures 4 and 6 seem like a more intuitive way to present this information (though all the markers and line and shading in Figure 6 need explicit descriptions in the caption and perhaps a legend to be interpretable). There really shouldn't be more than a few tables in the main text of this manuscript, the rest should be relegated to a supplement.

3. The "such as" in the title of the paper is misleading. The only type of ice sheet instability discussed and tested in this paper is a thermal oscillatory instability (or B-P). A more accurate title would be simpler: "Numerical issues in modeling binge-purge type cyclic ice stream surging"

4. Related to #3 and throughout - the term "binge-purge" oscillations has largely fallen out of favor in the ice sheet modeling community. These are more commonly called thermal oscillations or ice stream activation-stagnation cycles. It is OK to mention in the introduction that these have historically been referred to as binge-purge, but it isn't in keeping with the field to continue to refer to them as such throughout.

5. I am quite confused over how numerical noise is defined in this manuscript. It seems in section 3.1.3 that to quantify numerical noise that different solver choices are used. However, depending on the number of iterations occuring between the different tolerances (and the details of how the solver works) it would seem that this method could yield strongly different estimates for the "noise". Additionally, it is unclear why this is the correct bar for determining whether a change is "important", instead of a more physically meaningful quantity. Additionally, the rationale behind the set of simulations detailed in Table 6 is confusing. In a bitwise reproducible code, I don't see why the number of cores used in a simulation should have any influence on the simulations. This makes me concerned about the robustness of other simulations if the number of cores has such an important influence on the results. How reproducible are these results by other researchers? If the same setup is run on a different cluster architecture would the results be different?

6. In section 4 I see the summary of results, but very little discussion of what they mean (in some cases but not others). This seems to me to be the main missing piece of the manuscript to be useful to other researches, a discussion of how these results relate to the theory of thermal oscillations (from Schiavi, Mantelli, Robel, MacAyeal, etc.) and how they might relate to other ice sheet models.