This study analyses the past and future evolution, from the Little Ice Age to 2100, of 6 ice masses localized in Kyrgyzstan. It provides detailed future changes in glacier geometry, volume and runoff under different climate scenarios highlighting significantly different responses between the studied glaciers depending on their climatology and geometry. The authors use a model of intermediate complexity based on high-order approximation of the Stokes equation to model the ice dynamics while solving for heat advection and diffusion in the ice body. The flow model is coupled to a “degree-day”-type mass balance model including the influence of incoming potential radiation and albedo difference between snow and ice.

The main strength and originality of the study is the attempt to correctly represent the surface boundary condition of the temperature field to properly model the evolution of the glacier thermal regime, and also to start the simulation from the Little Ice Age using long term reconstructed meteorological data. I also appreciate that the author combines thickness, velocity and mass balance measurements to constrain the model in order to provide, most likely, reliable estimation of the future evolution of those ice masses.

The paper is well written and organized and I think it deserves publication in The Cryosphere after addressing the points below that would be rather in the major revision category.

General comments

• Downscaling of GCM data
  
  

1. Applying a monthly bias correction to the GCM data is a necessary step to perform the future simulation. However, this may result in a change in the long-term trend of precipitation and temperature contained in the original GCM output. The trend preservation should be checked after applying the downscaling procedure. If the trend is modified, some methods have been proposed to preserve it and should be applied (e.g. Cannon et al., 2015).
2. Also, since you are using a temperature threshold to determine solid precipitation, a different precipitation distribution as a function of temperature in the GCM and in the local data may cause a bias in the modelled snow accumulation. This should be checked by plotting the precipitation distribution as a function of temperature for the GCM and for the data over the calibration period (1984-2014). This should be corrected, if necessary, by applying a precipitation correction per quantile of temperature.

• Initial steady state condition
  
  

1. Finding a steady-state glacier to match the Little Ice Age moraines is a good approach to get the initial state, but this should be done by perturbing the climate and not directly the surface mass balance (especially in a uniform way). The surface mass balance response to climate perturbation is elevation dependent and shifting the average (1820-1850) temperature (or precipitation) rather than introducing a mass balance bias would capture this easily. The introduction of a uniform mass balance bias also incorrectly affects the surface temperatures which set the boundary condition of the steady temperature field.

• Historical simulation
  
  

1. The same comment applies here. Instead of quantifying the uniform mass balance bias needed to reproduce the length change, one should quantify a precipitation or temperature bias needed to reproduce the length change. This would allow a better assessment of the model performance, and can even be used to propose a correction to the reconstructed climate data in the region.
2. I would like to see the evolution of the temperature field from the Little Ice Age steady state to the present. This would help to assess whether the surface temperature parameterization holds on long time scales.
3. To validate the model, you should compare the modelled thickness at different times using different surface DEMs (if possible). Here you show a good agreement with the data set you actually use to tune the flow parameters (unless I am wrong?). In this case, this is not a validation that the model actually captures the physics, but just a confirmation that your parameters are well tuned...

• Future simulation
  
  

1. It would be good to see and comment the evolution of the temperature field.

• Sensitivity test
  
  

1. Your study is one of the few to consider the structure and evolution of the thermal regime on long-term glacier evolution. You should take advantage of this to quantify the influence of the temperature-dependent ice viscosity on the modelled glacier and ice cap evolution. It would be interesting to run all simulations with a uniform and constant flow factor to see the difference and to discuss the necessity (or not) to model the thermal regime in future simulations (for volume/area changes assessment).

Specific comments

You will find a list of correction and specific comments embedded in the annotated PDF in attachment. Some are redundant with my general comments but may help to clarify them.

References

Cannon, A. J., Sobie, S. R., and Murdock, T. Q.: Bias Correction of GCM Precipitation by Quantile Mapping: How Well Do Methods Preserve Changes in Quantiles and Extremes?, Journal of Climate, 28, 6938–6959, https://doi.org/10.1175/JCLI-D-14-00754.1, 2015.