Review Report on “Probabilistic projections of the Amery Ice Shelf catchment,

Antarctica, under high ice-shelf basal melt conditions”

The manuscript discusses the calibration of the MPAS-Albany Land Ice (MALI) model to reduce parametric uncertainties and generate more constrained future projections. Based on a perturbed physics ensemble with 200 runs, the authors have built a GP emulator and used it for Bayesian calibration following the framework of Kennedy and O’Hagan (2001, hereafter referred to as KOH). To propagate the quantified parametric uncertainty in future projections, another set of emulators is used: a PCA-based emulator for the entire trajectory and scalar emulators for certain future time points. The results show that, under the high emission scenario (SSP5), the Amery sector may significantly contribute to sea level rise after the year 2100.

Overall, the statistical approaches used for emulation and calibration are well-designed, and the scientific results are an important contribution to the literature on the future of Antarctica. Therefore, the manuscript is suitable for publication in The Cryosphere. I have only a few minor comments:

1. Two hundred ensemble members seem to be quite small given that the number of parameters being calibrated is six. Some comments on how the number of ensemble members was determined would be useful.
   
   
   
   
2. In Section 3.4, the three observed variables are assumed to be independent when defining the likelihood function. I think some comments or justification is needed on this point.
   
   
   
   
3. The covariance function for the GP emulator is defined as the Matérn with a smoothness of 2.5, for which I commend the authors for avoiding the common mistake of using the squared exponential function. I think it would be even better if they added a brief statement on the implication of this choice, noting that the resulting GP is twice mean square differentiable and hence highly smooth.

This study seeks to evaluate the future contribution to sea-level rise of the Amery Ice Shelf catchment, and in particular this study takes a Bayesian approach and accounts for parametric uncertainty of AmIS response under different climate scenarios. The authors use Gaussian process emulators to calibrate ensembles of uncertain parameters and then use a second set of emulators to propagate this uncertainty to future sea-level rise contribution. Ultimately, they find that AmIS has the potential to contribute to sea-level rise significantly. The methodology is sensible and well-justified, the results are of great interest to the glaciology community, and the manuscript is well-written. I have a handful of comments below:

[1] Ensemble filtering: The authors seem to have removed RELX ensemble members that lie in parts of the parameter space that the emulators may struggle with. I am curious what these parts of the parameter space are, and whether the removal of these regions of the parameter space may affect estimates of posterior uncertainty? This filtering step also seems to have removed a significant portion of the ensemble members (resulting in only 119 members, if I’m understanding the text correctly), which seems to be low. Is this still an appropriate number of members to conduct the calibration?

[2] Effect of parametric uncertainty: the authors study the bulk effect of all parametric uncertainty (listed in Table 1) on projections of glacier behavior. Are the authors able to say anything about the contributions of uncertainty in individual parameters on sea-level rise contribution? Does one parameter contribute more than others? If the existing simulations cannot provide this detail, I don’t believe the authors need to include it, as there is already quite a bit in this manuscript and the focus is on quantifying overall uncertainty and SLR contribution, but if the existing runs can provide this, this would be useful detail to include.

[3] In general, the axes labels on the figures are faint, making it difficult to read. If possible, it would be good to bold the text to make it clearer.

[4] Figure 8: I did not quite understand what subplot c added to this figure – is it showing the same information as subplot b?

[5] Figure 11: the colorbar labels in subplots b and c are very small and hard to read