Summary

This article describes a new method for representing the effect of subgrid variability of cloud ice in the calculation of ice aggregation in the ICON-AES general circulation model. This stochastic method is based on using a random sample from a distribution of ice water content as input to the ice aggregation equation. The distribution of ice water content that is sampled is consistent with the ICON-AES cloud scheme.

The authors compare the ICON-AES mean cloud ice water content and the cloud scheme cloud ice water content variance to DARDAR satellite observations (with appropriate sampling to remove convective cloud and precipitating cloud from DARDAR). They argue that the consistency between the two demonstrates that it is reasonable to use the cloud scheme ice condensate variance as in their method for accounting for subgrid variability. They then demonstrate that including the effect of subgrid variability of cloud ice in the aggregation rate reduces the mean ice water content in ICON-AES, due to an increase in aggregation rate, which is partially offset by a decrease in the accretion rate in the model.

General Comments

This article is well structured and clear, and the language is fluent and precise. While there is a significant body of literature detailing methods for and consequences of accounting for subgrid variability of cloud water content in atmospheric model radiation calculations and warm rain processes, to my knowledge there are no previous studies on accounting for subgrid variability of cloud ice in microphysical process calculations. The methods are clearly described, and the results support the interpretation and conclusions.

My main concern with the article is that I think this is quite a minor advance in modelling science – in the authors’ own words, this produces “no important change in radiation”.  The title of the article suggests a broad analysis of subgrid scale variability of cloud ice in the model, but the study is limited to a single process. I think this paper would be more signicant if it considered other processes. Do any of the other ice microphysics processes in the model have a nonlinear dependence on ice water content? If so, can this method be extended to those processes? What about the model radiative transfer calculations? Do they account for subgrid-scale variability of cloud ice and if so, do they use the same variability as used for ice aggregation here?

Specific Comments

1. It would be good to include analytically derived corrections (e.g., Morrison and Gettelman, 2008; Larson and Griffin, 2012; Boutle et al, 2014) in the discussion of how the effects of subgrid variability of cloud water content on microphysical process rates have been represented in previous studies. Although most of this literature focuses on warm rain microphysics rather than ice, I think it is relevant to the discussion. Is it possible to derive an analytical correction to the ice aggregation rate?
2. Can you explain why you only apply a representation of the effects of subgrid variability of ice water to the aggregation calculation? Do other ice microphysical processes in ICON-AES depend nonlinearly on ice water content?
3. Does the ICON-AES radiation scheme include the effect of subgrid variability of ice water content on radiative fluxes and heating rates? If so, what does it use for the subgrid variability? Assuming the radiation scheme does not already use ice cloud water content variability that is consistent with the cloud scheme, what difference would this make?
4. I am not convinced that the comparison between DARDAR and the model is particularly useful. I think it would be more useful to compare aggregation rates calculated using the cloud scheme subgrid ice variance, aggregation rates calculated using the “true” variance (i.e., values derived from DARDAR) and aggregation rates calculated using only the mean value (i.e., a similar analysis to that done for figure 8). This could be an additional plot and, in my opinion, would better demonstrate the utility of the cloud scheme subgrid ice cloud variance.
5. I’m not sure how fair it is to compare the variance along a 1D line through a cloud (i.e., what DARDAR sees) with that in a 3D gridbox (ICON-AES). For example, Hill et al (2015) estimated that the standard deviation of water content in a 2D cloud would be approximately 1.3 times larger than that in a 1D cross-section through the cloud. Can you comment on how this might affect your DARDAR – model comparison?
6. I’m not entirely convinced that the way that the DARDAR data is sampled (I.e., removing convective and precipitating ice) achieves the aim of making it more consistent with the model. It would be interesting to see how much difference removing convective and precipitating ice makes to the variance of ice water content calculated from DARDAR. It would also be interesting to try some alternative comparisons between the two. For example, precipitating ice is removed from DARDAR based on a surface precipitation flag. What difference would it make if you removed ICON points with nonzero surface precipitation from the comparison?
7. For Figure. 2 and 3 a third column showing the difference between the two would be really useful. If necessary, you could plot this at lower resolution to reduce noise.
8. You state that there is “No important change in radiation”. Is this also true for precipitation rates? If this doesn’t lead to any important changes then is it worth implementing in the model?
9. I think it may better to have figure 8 and the discussion of the change in aggregation rate before figure 5, to demonstrate that the stochastic method does a good job or reproducing the unbiased aggregation rate before showing the effect of the stochastic method in the model.
10. The paper is quite concise already but could be made more so by removing table 1, which in my opinion does not add a great deal.

Technical Corrections

L5: “For a realistic comparison … removed from the observational data set.” I think this is more technical detail than is needed for an abstract and suggest removing this sentence.

L6: “The global patterns of … despite some regional differences”. This is a bit vague, and I would add some more specific details e.g., quantify the % difference between the model and observations.

L39: “Instead of taking a grid-box mean … with a randomly chosen cloud ice mass”. I think it might be clearer to rewrite this as: “… with a cloud ice mass randomly chosen from the distribution of cloud ice mass assumed in the cloud scheme”.

L57: Change “with an instantaneously output” to “with instantaneous diagnostics output”

L86: Change “which allows biases” to “which introduces biases”.

L171: “see the supplement material” should be “see the supplementary material”. However, I was not able to find any supplementary material to view anyway.

L177: typo “at the same lebvels”.

L179: Change “Therefore it is usable for” to “Therefore it is suitable for use in”.

L188: typo: “averaged aggregattion rate”

References

Morrison, H. and Gettelman, A., 2008. A new two-moment bulk stratiform cloud microphysics scheme in the Community Atmosphere Model, version 3 (CAM3). Part I: Description and numerical tests. Journal of Climate, 21(15), pp.3642-3659.

Larson, V.E. and Griffin, B.M., 2013. Analytic upscaling of a local microphysics scheme. Part I: Derivation. Quarterly Journal of the Royal Meteorological Society, 139(670), pp.46-57.

Boutle, I.A., Abel, S.J., Hill, P.G. and Morcrette, C.J., 2014. Spatial variability of liquid cloud and rain: Observations and microphysical effects. Quarterly Journal of the Royal Meteorological Society, 140(679), pp.583-594.

Hill, P.G., Morcrette, C.J. and Boutle, I.A., 2015. A regime‐dependent parametrization of subgrid‐scale cloud water content variability. Quarterly Journal of the Royal Meteorological Society, 141(691), pp.1975-1986.

General comments:

This study developed a new scheme for the cloud ice aggregation process, which considers subgrid-scale variability based on a stochastic approach. The authors introduced the scheme into ICON-AES, and evaluated the impact on cloud ice representation against the CloudSat/CALIPSO-based DARDAR product. The new scheme enhances the aggregation rate to reduce cloud ice, which is compensated by decreasing the accretion of ice. Although it was reported that the impact of the new scheme on cloud and radiation fields is not significant, the new approach could provide an important advance in the subgrid-scale representation of ice clouds in future studies.

I feel that the appropriately revised manuscript after the authors include the minor suggestions below may be suitable for publication in Geoscientific Model Development.

Specific comments:

Introduction: There are some previous studies for correcting microphysical process rates by considering subgrid-scale variabilities of hydrometeors, though the approach and target differ from the present study. For example, the analytical formulas for modifying autoconversion and accretion rates in the liquid phase have been developed (Lebsock et al., 2013; Boutle et al., 2014), but I do not know any methods for ice-phase clouds. Adding brief discussions for these previous studies would be helpful for readers and for clearing up the novelty.

Line 57-58: Could you describe model configurations and parameterizations in more detail? For example, “… for a period from 2005 to 2009 …” may imply nudged configuration, right? Please also add information on the spin-up period and model time-step.

Line 57: “with an instantaneously output every …” => “with instantaneous output every …”

Line 60-61: Could you add more specific information about the diagnostic cloud cover scheme?

Line 62: How does the model treat precipitating hydrometeors? As far as I know, ECHAM6 physics includes prognostic rain and snow based on Sant et al. (2015), or optional? Please add a brief description of the treatment of precipitation (diagnostic or prognostic) because ice microphysical processes, which is the main focus of this paper, depend strongly on how models treat snowflakes (Michibata et al., 2020).

Equations (4) and (5): Typo? Please check the symbol “X” in equation (4), and symbols “p₀” and “p” in equation (5).

Line 132-134: Consider adding references for CloudSat and CALIPSO missions (e.g., Stephens et al., 2002; Winker et al., 2010).

• Winker, D. M. et. al.: The CALIPSO Mission, B. Am. Meteorol. Soc., 91, 1211–1230, https://doi.org/10.1175/2010BAMS3009.1, 2010.
• Stephens, G. L. et al.: THE CLOUDSAT MISSION AND THE A-TRAIN, B. Am. Meteorol. Soc., 83, 1771–1790, https://doi.org/10.1175/BAMS-83-12-1771, 2002.

Line 141-145: I do not have a complaint about the analysis method, but I believe that the comparison between model and observation without separating clouds and precipitating ice is more straightforward. Ice-to-snow conversion is continuous and therefore CALIPSO retrievals cannot separate between cloud ice and snowflake even though using the “precipitation flag”. Noting possible uncertainty would be valuable for readers. And again, how does the model treat snowfall?

Line 150: “… and cloud ice mixing ratio (q_i).” => “… and cloud ice mixing ratio (q_i) obtained from the DARDAR product.”

Line 151: “higher levels” and “lower levels”: This is unclear. Please clearly state by adding pressure levels.

Line 160: The result section starts with “2.4”. Please correct the editorial error in the LaTeX commands.

Line 168-169 and Figure 3: Although the model seems to perform well in representing cloud ice distribution, how about column integrated water path (CIWP)? I am slightly concerned about how much the model overestimates CIWP, which directly affects process rates.

Line 169: Start a new paragraph from “Figure 4 shows …”.

Line 177: Please correct the typo “lebvels”.

Line 184: In the caption of Figure 5, the CTRL result was from Tromel et al. (2021). Just to check, were the tuning parameters between CTRL and AGGstoch the same? Please consider adding a note to the main text or figure caption.

Line 201-203: How does the model represent the riming process and Bergeron-Findeisen process? These microphysical processes are also the important source terms for cloud ice and thus snowfall (Gettelman, 2015; Michibata et al., 2020).

Line 206: Insert comma, between “aggregation process rate” and “accretion rate”.

Line 212: Typo “8,9 %” => “8.9 %”

Line 214 “no important change in radiation is visible (not shown here)”: Consider adding changes in global mean shortwave, longwave, and net radiation at the top-of-the-atmosphere, which would be helpful as a more intuitive metric.

Line 233-234 “Overall we show …”: Start a new paragraph here.

Line 241-242: I feel that a 20% change in the process rate is not significant enough to largely affect radiation and cloud fields. Some studies often show that significant changes in cloud, precipitation, and radiation require modifications of microphysical process rates by a factor of 2 or more (e.g., Imura and Michibata, 2022). In the present study, the authors applied the stochastic method to the aggregation process alone, but it could be extended to other ice microphysics as well (e.g., riming process, accretion among droplets, crystals, and snowflakes) in future studies. When such a framework is incorporated into the model, the impact of the scheme on radiation would be larger than the current model. Please consider adding such brief discussions to the revised manuscript.

References

Boutle I., S. J. Abel, P. G. Hill, and C. J. Morcrette: Spatial variability of liquid cloud and rain: observations and microphysical effects. Q. J. R. Meteorol. Soc., 140, 583–594. DOI:10.1002/qj.2140, 2014.

Gettelman, A.: Putting the clouds back in aerosol–cloud interactions. Atmos. Chem. Phys., 15, 12397–12411, https://doi.org/10.5194/acp-15-12397-2015, 2015.

Imura, Y., and T. Michibata: Too frequent and too light Arctic snowfall with incorrect precipitation phase partitioning in the MIROC6 GCM. J. Adv. Model. Earth Syst., 14, e2022MS003046, https://doi. org/10.1029/2022MS003046, 2022.

Lebsock M., H. Morrison, A. Gettelman: Microphysical implications of cloud-precipitation covariance derived from satellite remote sensing. J. Geophys. Res. -Atmos., 118, 6521–6533, https://doi.org/10.1002/jgrd.50347, 2013.

Michibata T., K. Suzuki, T. Takemura: Snow-induced buffering in aerosol-cloud interactions. Atmos. Chem. Phys., 20, 13771–13780, https://doi.org/10.5194/acp-20-13771-2020, 2020.

Sant V., R. Posselt, and U. Lohmann: Prognostic precipitation with three liquid water classes in the ECHAM5–HAM GCM, Atmos. Chem. Phys., 15, 8717–8738. https://doi.org/10.5194/acp-15- 8717-2015, 2015.

Stephens, G. L. et al.: THE CLOUDSAT MISSION AND THE A-TRAIN, B. Am. Meteorol. Soc., 83, 1771–1790, https://doi.org/10.1175/BAMS-83-12-1771, 2002.

Trömel, S. et al.: Overview: Fusion of radar polarimetry and numerical atmospheric modelling towards an improved understanding of cloud and precipitation processes, Atmos. Chem. Phys., 21, 291–17314, https://doi.org/10.5194/acp-21-17291-2021, 2021.

Winker, D. M. et. al.: The CALIPSO Mission, B. Am. Meteorol. Soc., 91, 1211–1230, https://doi.org/10.1175/2010BAMS3009.1, 2010.