This paper examines the roles of soot (black carbon, BC) and mineral dust as ice-nucleating particles (INPs) in shaping cirrus cloud properties and their global radiative impacts. The authors first use a cloud parcel model to perform 5.5 million simulations under a wide range of conditions, including variations in cloud-base temperature, pressure, updraft velocity, and aerosol (dust, soot, sulfate, and sea salt) mass concentrations. These simulations provide process-level insights into how soot and dust influence ice formation in cirrus clouds. The results are then incorporated into a global climate model to assess large-scale effects. The study finds that soot increases global mean ice crystal number concentration (ICNC) by about 5%, with regional enhancements of up to 90% in the upper troposphere. Furthermore, BC INPs strengthen the global longwave cloud radiative effect and lead to a statistically significant net warming during polar winters in both hemispheres. Overall, I appreciate the comprehensive simulations and analyses conducted by the authors. The results might provide valuable insights into the influence of BC INPs on cirrus cloud formation and radiative forcing at both global and regional scales. However, I think major revisions are needed to especially clarify the model configuration so that readers can better understand and assess the simulation results.

Major comments:

1. Section 2.1. Some key model configurations are either missing or insufficiently described. I recommend that the authors explicitly present these details, so readers can clearly understand the model framework and better interpret the results later presented in this paper.
   • Line 103. What are the corresponding number concentrations? Number concentration has a more direct connection to ice number concentration.
   • Line 105. What are the ranges of initial RH_ice and RH_w? I’m curious to know whether cirrus cloud starts to form at the beginning of the simulation or form after the parcel reaches a certain altitude.
   • Since there are sulfate and sea salt, can supercooled liquid droplets formed in the parcel model if the air is supersaturated with respect to water?
   • Lines 108-123. What are the parameterization equations used in the parcel model for homogeneous and heterogeneous nucleation (soot, dust, sulfate, sea salt)? Please add them in the main text or supplementary materials.
   • Lines 124-133. Please add the ice growth equation used in the parcel model in the main text or SI.
   • Section 2.1.2. List parameterization equations for INAS used in the parcel model.
   • Line 149. People might not be familiar with “the U-shaped curves”. Need to add more explanations or rephrase this sentence.
   • It is not clear to me what microphysical scheme is used in the parcel model, Lagrangian, bin, or bulk?
2. Section 2.2. Need more details about how parcel model results are implemented in AM4-MG2.
   • Line 188. “Within the GCM at each time step”. What is the time step, 30 minutes (physical time step) or 2.5 minutes (dynamic core)?
   • Line 192. “the GCM interpolates linearly for pressure and temperature, and logarithmically for updraft velocity and the aerosol mass concentration”. Are there any conditions that you need to extrapolate values outside the ranges of the box model?
   • More details are needed to explain how parcel model results are implemented in AM4-MG2. My understanding is that if you know the updraft velocity, pressure, temperature, and mass concentrations of dust, soot, sulfate, and sea salt, you can calculate the number concentration of ice crystals nucleated on dust and black carbon from a lookup take based on the parcel model results. Are those ice crystals diagnostic or prognostic variables? Will the formed ice particles have the feedback on temperature and water vapor in AM4-MG2? The lookup take is based on simulation results at 2.5 minutes or 30 minutes? If cirrus cloud already exists in What about the ice crystal size? It is from the lookup table or assigned in AM4-MG2?
3. Figure 1. It seems that homogeneous ice nucleation is ignorable, am I correct? Is it because water vapor is consumed by the formation and growth of ice particles formed by heterogeneous ice nucleation on soot and dust?
4. Figure 5. What might be the reason for the negative value of Delta_ICNC in b?
5. Is semi-direct effect of BC considered in AM4-MG2?

Minor comments:

1. Figure 1. Since BC is used to represent soot in this study, change "C_m,soot" to "C_m,BC" in the figure, the caption, and the text (e.g., line 215).
2. Line 144: should it be “ice nucleation active surface site density”?
3. K is used in Figure 2 and degree C is used in Figure 3. Please be consistent with the units used in the figure and main text.
4. Table A1: “sulfate concentration”->“sulfate mass concentration”?
5. Figure A11. The unit of BC is "mmr". Change it to "ng m-3"?

This study uses a parcel model to find relationships on the competition between homogeneous and heterogeneous nucleation based upon a large variety of black carbon and dust concentration. The resulting findings are inserted into the GFDL AM4-MG2 model to examine how black carbon and mineral dust impacts cirrus clouds globally. Black carbon enhances global ice crystal number concentration and significantly increases the annual global longwave cloud radiative effect, causing warming, particularly during polar winters. The results emphasize the roles of soot and dust and the need to assess the climate impact of increasing wildfire emissions on atmospheric ice processes. The paper is very well written, and conclusions are well supported. I have only minor comments. 

In the abstract, line 8: I like to reserve the word observe to real observations. I wonder if the sentence could be rephrased to something like “The strongest enhancements are found during boreal” 

Page 4, lines 118-123: The diameters and standard deviations of the aerosol size distribution are fixed. Could varying the size and shape of the size distributions change your results?

Page 5, line 147: Add “of” ….where N_aer is the number density of ice nucleating….

Page 7, line 199. It is stated that the AMIP simulation is run through 2006. Why is the analysis period only to 2005 and not through 2006?

Page 7, line 209. ICNC has only been defined in the abstract, but not in the main text yet.

Section 3.1.2 You describe the ICNC dependence on aerosol composition. But there is no mention about the competition between homogeneous and heterogeneous dependence on aerosol composition. I am not sure how to present it, but it would be interesting to have a figure showing how the change in composition impacts homogeneous freezing.

Page 11, Figure 3. The In-situ Heymsfield symbols are difficult to see, special in the green region.  The dotted lines could also be slightly enhanced. It would also be interesting to see how the model performs without the BC in this figure.

Conclusion: Lines 480-485. The authors have based their conclusion on one dust and BC parameterization. There are other parameterizations out there that can lead to different results. For example, how is the temperature dependent active site density in other parameterizations and how could this impact the results?

Figures 5 and 8 are very small and hard to read on printed paper.