the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
CESM2/CARMA Cloud and CARMA Aerosol Model Descriptions
Abstract. The Community Aerosol and Radiation Model for Atmospheres (CARMA) is a sectional microphysical model widely used to understand the formation of aerosols and clouds. This paper is an updated description of the CARMA model algorithms since Toon et al 1988, with examples from the newly developed CARMA Cloud model. This paper describes the general algorithms and solvers for nucleation, condensation/evaporation, coagulation, and sedimentation shared among all CARMA aerosols and clouds models; specific microphysical processes needed for water droplet and ice; how the CARMA Cloud is set up and how it interacts with other processes inside the Community Earth System Model.
Status: final response (author comments only)
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CEC1: 'Comment on egusphere-2026-1185', Astrid Kerkweg, 01 Apr 2026
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AC1: 'Reply on CEC1', Yunqian Zhu, 01 Apr 2026
Dear Editor, thank you for the comments.
1. the CARMA version is version 4, which will be add to the title during the revision.
2. We created a new permanent doi to archive the model code:
NCAR CARMA Group, & Owen Brian Toon Research group. (2026). Community Aerosol and Radiation Model for Atmospheres (CARMA) standalone 4.11 code. University of Colorado Boulder. https://doi.org/10.25810/SNMH-NW733. And the data for the output are achived at: Zhu, Y. (2026). CARMA Cloud model standalone test results [Data set]. Zenodo. https://doi.org/10.5281/zenodo.19373048
Citation: https://doi.org/10.5194/egusphere-2026-1185-AC1
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AC1: 'Reply on CEC1', Yunqian Zhu, 01 Apr 2026
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RC1: 'Comment on egusphere-2026-1185', Parker Case, 06 Apr 2026
This paper is an impressive description of a highly complex and detailed microphysical model. The paper represents a triumph in moving forward the CESM model. For the most part the paper is well written, technically correct, and ready for publication. Below I outline a few general comments as well as smaller "in-line" comments. The primary issue with the manuscript as is is that the naming conventions for the various models is inconsistent and unclear. Once the below comments are rectified, this manuscript should be published.
General comments
What is the name of the overall model you are presenting? Does CARMA Cloud Model refer to the CESM2 configuration or just the configuration of CARMA?
Make sure it is clear, for each of the given experiments (sedimentation, coagulation, etc.) what the model is you’re using. Is it the box-model? Is it the 1-d column model?
Throughout the paper, CARMA Cloud is, I think, being contrasted with other CESM2 modules. I’ve made line-specific comments below about this but in general, make it clear when you are contrasting a something to your novel CARMA Cloud model.
Some processes (contact nucleation, for example) are mentioned but either not implemented in the CARMA Cloud codebase or not turned on. An explanation as to why these design choices were made would clarify the paper significantly.
1 Introduction:
Line 60-76: The second sentence of this paragraph seems to be restating something that is clear from the first sentence. I suggest removing it.
There is some amount of confusion about the naming of the different configurations you are considering here as well. At the beginning of the paragraph, you refer to “CESM2 CARMA Cloud” but later say “this paper links CARMA Cloud with the MAM4 model aerosol model”. Are these referring to the same thing? Make sure it is clear when you are talking about a full model configuration (like a configuration of CESM2) versus the individual components (like CARMA or MAM4).
Line 90-91: For readability, this sentence should read, “CARMA has also been developed and applied to study planetary atmospheres”
Line 96-98: The final sentence of this paragraph means nothing to someone who doesn’t use CESM2—I don’t know what the namelist is. Could it be removed?
2 General Model Structure
Lines 122-134: Processes, like “When ice particles fall, they redistribute dust and sulfate,” should be in the body of the paper, not the figure description. Make sure that all of the colors and symbols in the figure are described.
Lines 136-137: Model naming conventions: here it seems that “CARMA Cloud model” is actually referring to a configuration of CESM2 that includes the cloud-enabled version of CARMA.
Lines 169-170: Does the extra size information from CARMA improve the representation of the optical properties for ice/graupel or are the same assumptions made as MG?
Line 184: Should be RRTMG, not RRTGM
Lines 190-233: This is an excellent overview of the CARMA module and routines!
Lines 247-263: This description of the number concentration element/numerical problem should be its own paragraph, not attached to the discussion of grids above.
3 CARMA Continuity Equation Algorithms and Solvers
Lines 309-313: Is the cldfrc scaling used only when converting CARMA-calculated values to CESM2? Or do you scale the values inside CARMA?
Lines 324-325: Wording, I suggest, “Coagulation is expensive to compute and slow, therefore it is often time split.”
Line 324-335: Are you using coalescence and coagulation interchangeably here? It might be good to be consistent or to define the difference explicitly.
Line 414: These sedimentation tests are done in the standalone, 1-d CARMA? It might be good to explicitly mention this.
Line 510: “Avoid” should be “Avoids”
Lines 519-520: This sentence is confusingly worded. I suggest “To conserve mass between the vapor and particle phases, particles are not allowed to grow out of the largest mass bin”
Lines 539-542: “In Nature” should be “In nature”. Additionally “lead to broadening the size distribution or make it multimodal” could be simplified for clarity to “broaden the size distribution or make it multimodal”.
Lines 549-558: How often does the sub stepping happen? i.e. for a given time-step, how much of the global grid is sub stepping?
Lines 564-566: The parenthetical on this sentence is hard to understand—what does it mean to “setup the convergence criteria to do that”?
Lines 571-585: Are there physical inconsistencies in the way that CLUBB treats the bulk variables that CARMA passes it during this process? In other words, does CLUBB make its own size assumptions for any processes that are different than the size information inside of CARMA?
Lines 608-609: Is Ak=1 and g1 = 0 okay because of the size? Could you explain these choices?
Lines 633-636: Some additional information is needed in this caption about what each frame of the figure means, especially (j) and (k).
Lines 687-689: How were these parameters chosen?
Line 715: This shows the same experiment as Figure 11, just with different parameters, correct? This sentence makes it sound like it is entirely separate.
Lines 738-739: This sentence does not make sense, “The model uses 100 vertical levels resolutions in a Cartesian coordinate system.” Perhaps remove “resolutions”?
4 Physical Process Equations
Lines 780-782: “at every time” should be “at every tilmestep”.
Lines 782-785: This sentence is unclear. Are these the options in CESM/CARMA? The third option (where everything except coagulation is updated) is complex and maybe warrants its own sentence.
Lines 789-791: There’s certainly a more recent version of Seinfeld and Pandis than 1998—it seems preferable to cite a more recent/updated version.
Figure 16: Why not include the Beard (1976) values on the right panel?
Lines 853-854: “Oddly, this term is not discussed in textbooks when coalescence is considered despite being dominant in some size ranges”. This is not clear from Figure 18. “cbr” does not seem to be dominant in any of the size ranges shown.
Lines 862-864: “The collision efficiencies of liquid cloud, ice, and raindrops based on the table in (Hall, 1980) can be used in CARMA Cloud since they are widely used in other models”. This is a poor reason. Maybe “they have been widely validated in other models”? Similar for the “Ecoalescence” value a few sentences later.
Lines 890-893: This comment, I assume, is about the non-CARMA cloud models in CESM2. This should be made explicit.
Lines 942-947: The Gettleman and Morrison model is not used if CARMA Cloud is being used, correct? Is this meant to contrast with CARMA Cloud?
Lines 989-991: How common is this process? How big of a problem is it that CARMA Cloud does not return the sulfate in melting ice particles to liquid droplets?
Line 1042: “That model uses” should be “Those models use,” referring to both Bardeen’s model and M&G.
Lines 1053-1057: “We’ve comment out these nucleation processes”. The verb tenses don’t make sense. I think it should be “We’ve commented out”.
5 Conclusions
Line 1088: “Cloud sized particle” should be “cloud sized particles”.
Line 1099: “MG” has not been defined up to this point, it has previously been referred to as Gettelman and Morris or Morris and Gettelman.
Citation: https://doi.org/10.5194/egusphere-2026-1185-RC1 -
AC2: 'Reply on RC1', Yunqian Zhu, 29 May 2026
This paper is an impressive description of a highly complex and detailed microphysical model. The paper represents a triumph in moving forward the CESM model. For the most part the paper is well written, technically correct, and ready for publication. Below I outline a few general comments as well as smaller "in-line" comments. The primary issue with the manuscript as is is that the naming conventions for the various models is inconsistent and unclear. Once the below comments are rectified, this manuscript should be published.
Thank you very much for your time to provide suggestions to our manuscript. We appreciate your valuable insight.
General comments
What is the name of the overall model you are presenting? Does CARMA Cloud Model refer to the CESM2 configuration or just the configuration of CARMA?
The overall model we present is CARMA v4, which is used in all standalone version, CESM2/CARMA Cloud and Aerosol models. We fixed the title and also went through the whole content to try to make these definitions clear.
Now we have Section 2 (starting from line 157) to explain these definitions: 2. Introduction of CARMA v4 and its Usage in the Community Earth System Model (CESM2)
Make sure it is clear, for each of the given experiments (sedimentation, coagulation, etc.) what the model is you’re using. Is it the box-model? Is it the 1-d column model?
Line 777: changed to “Sedimentation tests, illustrated in Figure 4 and Figure A2, were performed using the stand-alone 1-D column CARMA model with two different vertical grid settings: one is a uniform vertical grid with levels spaced every 100 m in a Cartesian coordinate system, and the other is the much coarser and irregularly spaced hybrid grid (32-level) employed in the CESM2/CARMA Cloud configuration.”
Line 1142: changed to “Figure 7 illustrates the growth across the bin for a cloud particle using the stand-alone 1-D CARMA box model.”
Line 1305: changed to “Figures 10-14 illustrate a set of simulations of warm rain formation to test coagulation, and test coagulation-sedimentation processes using the stand-alone 1-D CARMA column model.”
Throughout the paper, CARMA Cloud is, I think, being contrasted with other CESM2 modules. I’ve made line-specific comments below about this but in general, make it clear when you are contrasting a something to your novel CARMA Cloud model.
We respond below with line-specific comments.
Some processes (contact nucleation, for example) are mentioned but either not implemented in the CARMA Cloud codebase or not turned on. An explanation as to why these design choices were made would clarify the paper significantly.
Line 1842: add “since the probability of contact nucleation is highly uncertain, and we await new laboratory data.”
1 Introduction:
Line 60-76: The second sentence of this paragraph seems to be restating something that is clear from the first sentence. I suggest removing it.
The second sentence is removed.
There is some amount of confusion about the naming of the different configurations you are considering here as well. At the beginning of the paragraph, you refer to “CESM2 CARMA Cloud” but later say “this paper links CARMA Cloud with the MAM4 model aerosol model”. Are these referring to the same thing? Make sure it is clear when you are talking about a full model configuration (like a configuration of CESM2) versus the individual components (like CARMA or MAM4).
Line 183: add “The full configuration of the CESM2/CARMA Aerosol model uses CARMA as the aerosol module and the Gettelman and Morrison (MG) two-moment scheme as the cloud module. Conversely, the full configuration of the CESM2/CARMA Cloud model uses CARMA as the cloud model and the four-mode Modal Aerosol Model (MAM4) (Liu et al., 2016) as the aerosol module.”
Line 90-91: For readability, this sentence should read, “CARMA has also been developed and applied to study planetary atmospheres”
Fixed.
Line 96-98: The final sentence of this paragraph means nothing to someone who doesn’t use CESM2—I don’t know what the namelist is. Could it be removed?
Removed.
2 General Model Structure
Lines 122-134: Processes, like “When ice particles fall, they redistribute dust and sulfate,” should be in the body of the paper, not the figure description. Make sure that all of the colors and symbols in the figure are described.
Remove the sentence “When ice particles fall, they redistribute dust and sulfate. When ice evaporates, it releases the aerosols back into the aerosol bins, and eventually back to MAM modes.” And modify line 270 to “After CARMA microphysics, the aerosol released by the sublimation of falling ice particles is passed back to MAM.” And we double checked the description to make sure all processes are included in the caption.
Lines 136-137: Model naming conventions: here it seems that “CARMA Cloud model” is actually referring to a configuration of CESM2 that includes the cloud-enabled version of CARMA.
I hope adding line 157 “Section 2 Introduction of CARMA v4 and its Usage in the Community Earth System Model (CESM2)” made it clear. “CARMA Cloud model” is a configuration in CESM2.
Lines 169-170: Does the extra size information from CARMA improve the representation of the optical properties for ice/graupel or are the same assumptions made as MG?
Mie theory does not work because ice particles are not spheres. So, we use the same optical files as MG and pass the mass and effective diameter into the RRTMG the same way as MG, so the CARMA size distribution is not used. This could be improved in the future.
Line 329: add “with CARMA providing the accumulated mass and effective diameter”.
Line 184: Should be RRTMG, not RRTGM
Fixed.
Lines 190-233: This is an excellent overview of the CARMA module and routines!
Thank you.
Lines 247-263: This description of the number concentration element/numerical problem should be its own paragraph, not attached to the discussion of grids above.
The number concentration definition is actually connected with the CARMA bin and elements closely. So, we decided to keep them together.
3 CARMA Continuity Equation Algorithms and Solvers
Lines 309-313: Is the cldfrc scaling used only when converting CARMA-calculated values to CESM2? Or do you scale the values inside CARMA?
CARMA uses the in-cloud value for the subroutines marked by the purple bracket in Figure 3. Outside this bracket and also when passing back to CESM, the grid average values are used.
To make it more clear, we explain these lines with more detail starting at line 569: “Equation (3) can be solved using in-cloud concentrations scaled by the cloud fraction (for the subroutines marked by the purple bracket in Figure 3), which are then scaled back outside the purple bracket in Figure 3 to grid-average values used by most of CESM2.”Lines 324-325: Wording, I suggest, “Coagulation is expensive to compute and slow, therefore it is often time split.”
Fixed as suggested.
Line 324-335: Are you using coalescence and coagulation interchangeably here? It might be good to be consistent or to define the difference explicitly.
Coalescence is a type of coagulation. So we change the “coalescence” in line 588 to “coagulation”.
Line 414: These sedimentation tests are done in the standalone, 1-d CARMA? It might be good to explicitly mention this.
Line 511: add “In this section, we explain how the continuity equations are solved in CARMA algorithms and demonstrate the results using the CARMA standalone box model or the column model if vertical levels need to be considered.”
Line 510: “Avoid” should be “Avoids”
Fixed.
Lines 519-520: This sentence is confusingly worded. I suggest “To conserve mass between the vapor and particle phases, particles are not allowed to grow out of the largest mass bin”
Sentence replaced as suggested.
Lines 539-542: “In Nature” should be “In nature”. Additionally “lead to broadening the size distribution or make it multimodal” could be simplified for clarity to “broaden the size distribution or make it multimodal”.
Fixed.
Lines 549-558: How often does the sub stepping happen? i.e. for a given time-step, how much of the global grid is sub stepping?
Add sentence line 1084: “The average number of sub-steps in CESM2 CARMA Cloud is ~ 6.”
Lines 564-566: The parenthetical on this sentence is hard to understand—what does it mean to “setup the convergence criteria to do that”?
Line 1092: add “the saturation change is limited to 20% for each sub-step”.
Lines 571-585: Are there physical inconsistencies in the way that CLUBB treats the bulk variables that CARMA passes it during this process? In other words, does CLUBB make its own size assumptions for any processes that are different than the size information inside of CARMA?
Basically, no. CLUBB doesn’t assume size but determines the mass needed to achieve saturation and passes it to MG. MG determines the number of new cloud particles from the activation code in MAM4. Together mass and number are all the size information in the Morrison and Gettelman model. CARMA condenses the vapor onto the existing size distribution and on newly activated particles.
Lines 608-609: Is Ak=1 and g1 = 0 okay because of the size? Could you explain these choices?
Line 1173: add “The Kelvin correction to the vapor pressure and the offsetting impact of soluble aerosol particles on the vapor pressure are essential for activation. However, cloud particles are large enough that the Kelvin correction, and aerosol solubility corrections are small. Since the aerosols are not currently included inside the cloud drops we simply ignore both corrections.”
Lines 633-636: Some additional information is needed in this caption about what each frame of the figure means, especially (j) and (k).
Explanations for j and k are added.
Lines 687-689: How were these parameters chosen?
The number of size bins is chosen to span the range of masses that are important, with enough resolution to have accurate simulations. From previous experience, we find good resolution of the size distribution for optical and other calculations requires about 10 bins per log radius increment. We need to cover the range of 0.5 um to mm to span the range from activated aerosols to rain drops. In the future we plan to explore the tradeoffs between resolution accuracy and computational cost in CESM2/Carma Cloud.
Line 225: add “CARMA Cloud currently uses 48 mass bins in each group, spanning each decade of radius with about 10-11 bins. From previous experience, we find good resolution of the size distribution for optical and other calculations requires about 10 bins per log radius increment. We need to cover the range of 0.5 um to mm to span the range from activated aerosols to rain drops. In the future we plan to explore the tradeoffs between resolution accuracy and computational cost in CESM2/CARMA Cloud.”
Line 715: This shows the same experiment as Figure 11, just with different parameters, correct? This sentence makes it sound like it is entirely separate.
Line 1348: Change to “Figure 11 illustrates simulations similar as Figure 10 but includes the sedimentation process.”
Lines 738-739: This sentence does not make sense, “The model uses 100 vertical levels resolutions in a Cartesian coordinate system.” Perhaps remove “resolutions”?
Figure 12 caption: Change to “100-meter vertical resolution”
4 Physical Process Equations
Lines 780-782: “at every time” should be “at every tilmestep”.
Fixed.
Lines 782-785: This sentence is unclear. Are these the options in CESM/CARMA? The third option (where everything except coagulation is updated) is complex and maybe warrants its own sentence.
Line 1473 and forward: We add “stand-alone” to make is clear that the previous sentence is for stand-alone CARMA and the later sentence is for CESM/CARMA. And changed the later sentence to “In CESM/CARMA, users can choose to update these quantities only at the start of the run, or at every time and location, or to update everything except for coagulation at every time and location while coagulation is updated for one column within a computational chunk at every time step (see CARMA flags in Table A2).”.
Lines 789-791: There’s certainly a more recent version of Seinfeld and Pandis than 1998—it seems preferable to cite a more recent/updated version.
Change to Seinfeld and Pandis 2016.
Figure 16: Why not include the Beard (1976) values on the right panel?
We add Beard 1976 to the right panel.
Lines 853-854: “Oddly, this term is not discussed in textbooks when coalescence is considered despite being dominant in some size ranges”. This is not clear from Figure 18. “cbr” does not seem to be dominant in any of the size ranges shown.
That’s right. “cbr” is only dominant during aerosol washout and in turbulent environments while Figure 18 is not for any of these special scenarios.
Lines 862-864: “The collision efficiencies of liquid cloud, ice, and raindrops based on the table in (Hall, 1980) used in CARMA Cloud since they are widely used in other models”. This is a poor reason. Maybe “they have been widely validated in other models”? Similar for the “Ecoalescence” value a few sentences later.
Line 1597: Changed to “The collision and collection efficiencies of liquid cloud, ice, and raindrops based on the table in (Hall, 1980) are used in CARMA Cloud since they are widely used in other models that are regional or cloud scale. No global model we know about computes the coagulation rate from first principles, so no other global model even uses collision and collection efficiencies. We are not aware of modern data that validate the Hall (1980) values particularly for particles smaller than 50 µm radius. We believe new laboratory measurements are needed for collision and collection efficiencies.”
Lines 890-893: This comment, I assume, is about the non-CARMA cloud models in CESM2. This should be made explicit.
Line 1667: Add “standard CESM2 model (non-CARMA),”
Lines 942-947: The Gettleman and Morrison model is not used if CARMA Cloud is being used, correct? Is this meant to contrast with CARMA Cloud?
Line 1747: add “In contrast,”
Lines 989-991: How common is this process? How big of a problem is it that CARMA Cloud does not return the sulfate in melting ice particles to liquid droplets?
Line 1804: add “In the real atmosphere, since only a very small fraction of aerosol particles acts as nuclei to form ice clouds, we do not expect this loss to affect the global aerosol burden.” The interaction of aerosols and liquid clouds in CESM2 should be improved so that the aerosols are carried within the liquid drops. This would allow the aerosols to change size as drops coalesce, and to be moved to other grid cells as liquid drops move to other grid cells and evaporate. Both processes are neglected in the current version of CESM2 for both the CARMA Cloud model and the Morrison and Gettleman model. However, CARMA Cloud is capable of treating these processes in the future, while the MG model is not.
Line 1042: “That model uses” should be “Those models use,” referring to both Bardeen’s model and M&G.
Fixed.
Lines 1053-1057: “We’ve comment out these nucleation processes”. The verb tenses don’t make sense. I think it should be “We’ve commented out”.
Fixed.
5 Conclusions
Line 1088: “Cloud sized particle” should be “cloud sized particles”.
Fixed.
Line 1099: “MG” has not been defined up to this point, it has previously been referred to as Gettelman and Morris or Morris and Gettelman.
It is defined at Line 185.
Citation: https://doi.org/10.5194/egusphere-2026-1185-AC2
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AC2: 'Reply on RC1', Yunqian Zhu, 29 May 2026
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RC2: 'Comment on egusphere-2026-1185', Anonymous Referee #2, 28 Apr 2026
First, I apologize to the editor and the authors for the delay.
I like this manuscript and I recommend it for prompt publication after some minor improvements here and there. I have some comments below that will hopefully improve the manuscript, but none should be treated as blocking — all optional. I would love to read a paragraph discussing if the added complexity and cost end up actually worthwhile. I say that as someone who goes between wanting more realism on the one hand but fearing for lost interpretability on the other hand.
One meta comment is that the paper is not very well written and can be significantly improved. At the very end, I wrote what I would do if I were you…
General
- I am not a fan of inserting code jargon into the main text — stuff like "the radius is defined in setupbins" — so for better readability the authors should figure out a way to describe this without resorting to mixing regular language with code_blocks. See next comment.
- All equations and figures can be improved substantially. There's a better way to write pseudo-code or a pseudo-equation that doesn't look like rmass of bin i = rmassmin × rmrat^(i-1), which frankly doesn't look good, and reflects badly on an otherwise esteemed list of authors. At a minimum, code identifiers should be monospaced and equations should be set in math font. Equation (5) in particular is, as written, essentially unreviewable — please render it properly with aligned terms and consistent subscripting.
- The manuscript oscillates between really detailed (and at times tedious) descriptions of algorithms and growth bookkeeping, and barely addressing entire sections from 4.4 onward. The model description appears to lose steam right where the physics gets interesting (nucleation, immersion freezing, contact freezing, mixed-phase). It reads like the authors ran out of time. The same uneven density also makes Section 2 feel like it belongs in a code reference manual rather than a GMD paper.
Specific comments I wrote while (re)reading the manuscript
- L 33: "the code is flexible and extensible" jumps out of nowhere with no evidence. Either remove or dedicate a paragraph to actually substantiating it — the following sentence is about runtime options, which is not really what "code flexibility and extensibility" means.
- L 56: to get this right, all these people cited above use CARMA but nobody has ever described it? It seems that's what the authors are suggesting, or maybe what they mean is that they're putting all the descriptions in one place. Either way, situate this manuscript in context of prior descriptions more clearly, and make explicit what is new here vs. updated vs. consolidated.
- L 96: can these be combined? Did all the users in the previous paragraph contribute their code back to the main CARMA codebase, or are there many divergent forks? This affects what "the CARMA model" even refers to in this paper.
- L 99: the authors keep saying "the code has been updated" (and derivatives) and it's a bit jarring because there is zero evidence about what the updates actually were. The previous paragraph started with the same line. Is this a code paper? If so, framing should be different — and in any case, "updated" and "improved" without specifics should be replaced with concrete deltas relative to prior works.
- L 105–107: delete. The manuscript is already long, and listing what each section will discuss adds zero value when readers can just look at the section titles.
- Fig 1: any story behind 48 bins for everything? 48 appears six times in the figure with different ranges — is this a coding artifact (e.g., aligning with NBIN as a compile-time constant), a memory/throughput optimization, or a physically motivated choice? A sentence would help.
- Fig 3 and the associated discussion: if I were the authors, I would move this to the supplement. A few-sentence paragraph describing the run flow suffices in the main text.
- Eq 1 and Eq 2: the format changes between the two equations, which feeds into the general disarray of the math typesetting. Please make consistent.
- L 303: "a mixing ratio" of what units? kg-substance / kg-air? Better explain this.
- L 304: concentration in what units? Number per cm³? Per cm² per scaled z? The text introduces both within a few lines without saying which.
- L 307: "ρ = ρ_z times z_met" — does this mean ρ = ρ_z · z_met, or something else? Use a multiplication symbol.
- L 382–383: to be clear, this paragraph is only about vertical movement, right? Say that here.
- Eq 5: as noted in the General comments, this is essentially unreviewable as typeset. Please render with aligned terms and consistent subscripting; I cannot say whether the equation is correct in its present form.
- Fig 5: hard to parse as a single figure
- Eq 6: the form ∂C/∂t = ∂(g_m C)/∂m reads as if it has the same sign on both sides — i.e., the opposite of the analogous flux-divergence form in Eq. (1). I assume this is a typesetting issue, but please verify.
- L 492: be careful with the word "flux" — g_m × C in Eq. (6) is the flux across the mass coordinate (in the continuum sense), so reusing the word for the bin-edge fluxes can confuse.
- L 501: does this implicit solver have a name? It looks like a backward-Euler step on a linear loss term — if there's a textbook reference, cite it.
- L 526: all true, but the presentation makes dr/dt ∝ 1/r seem trivially known. Cite or explain — there is plenty of literature deriving how g_m scales with r (gets messy at very small r, but that's not the issue here). Also: are we talking about aerosols here, or cloud and rain droplets? The paragraph slides between them. And while you're at it, remind readers why the mean free path is being introduced (continuum vs. kinetic regimes).
- L 543: "vapor concentration" needs unpacking — available vapor mass per unit volume? Above some saturation reference? It's used as if obvious.
- L 590–593: dropping every activated aerosol into bin 4 (~0.56 µm) is a tuning that throws away activation-size information. What is the sensitivity of CDNC, autoconversion, and rainfall to carma_dropact_bin?
- L 601: please cite.
- Eq 9: please cite — this is the Smoluchowski binary coagulation equation.
- Eq 12: please cite, and use notation consistent with K_c. Also: do the authors consider effects of turbulence (e.g., turbulent enhancement of collision rates inside convection) to be part of c_gr, c_cd, or absent? The next equation answers this implicitly, but it should be stated explicitly here.
- Eq 14: answers the previous comment — but please state directly that turbulence-enhanced collision is not represented.
- L 863: "can be used in CARMA Cloud since they are widely used in other models" is a poor justification.
- L 888: please cite the coalescence-kernel literature. Also, the fact that the data are forty to fifty years old is an observation, not a justification.
- L 942–947: the Gettelman & Morrison model is not used when CARMA Cloud is on, correct? Is this paragraph meant as a contrast? If so, say so.
- L 1083–1084: "modified Slingo scheme" without a Slingo citation.
- L 1132 (disclosure): good to see the disclosure. In revision, I would actually recommend feeding both the PDF of this manuscript as well as reviewer comments straight into an LLM to help triage them — many of the surface-level complaints above are easily addressable that way, and the authors' time is better spent on the substantive scientific points.
Citation: https://doi.org/10.5194/egusphere-2026-1185-RC2 -
AC3: 'Reply on RC2', Yunqian Zhu, 29 May 2026
Thank you very much for your time and energy to review our paper. We appreciate your insight to improve our manuscript.
First, I apologize to the editor and the authors for the delay.
I like this manuscript and I recommend it for prompt publication after some minor improvements here and there. I have some comments below that will hopefully improve the manuscript, but none should be treated as blocking — all optional. I would love to read a paragraph discussing if the added complexity and cost end up actually worthwhile. I say that as someone who goes between wanting more realism on the one hand but fearing for lost interpretability on the other hand.
We have a companion paper describes the computational cost and how the CARMA and MG (computationally cheaper) simulations compare with observations (Liu et al., 2026, https://doi.org/10.22541/essoar.176824045.59749413/v1). The paper pointed out several advantages of using CARMA and has a detailed chart for the cost in Figure 20. We find, for instance, that the Morrison and Gettelman model is missing clouds with particle sizes between 30 and 50 µm radius. MODIS also misses these particles, which in our model average 30% of the cloud mass. Such particles are found in recent aircraft data. Following Maloney et al (2019, 2022) we also find it is important to carry dust and sulfates inside ice crystals, which redistribute these aerosols.
One meta comment is that the paper is not very well written and can be significantly improved. At the very end, I wrote what I would do if I were you…
We took your advice and made substantial changes to the English expressions for the whole manuscript.
General
- I am not a fan of inserting code jargon into the main text — stuff like "the radius is defined in setupbins"— so for better readability the authors should figure out a way to describe this without resorting to mixing regular language with code_blocks. See next comment.
We modified the whole manuscript to ensure that the code jargon only appears inside parentheses and use the monospace font. For example, this is the first place (Line 366) we mention the code and explain how we will write them throughout the manuscript: “The radius grid is defined during the initial configuration of the mass bins (setupbins; we provide subroutine and variable names in parentheses for easier code search, see Appendix 2 and 3).”
- All equations and figures can be improved substantially. There's a better way to write pseudo-code or a pseudo-equation that doesn't look like rmass of bin i = rmassmin × rmrat^(i-1), which frankly doesn't look good, and reflects badly on an otherwise esteemed list of authors. At a minimum, code identifiers should be monospaced and equations should be set in math font. Equation (5) in particular is, as written, essentially unreviewable — please render it properly with aligned terms and consistent subscripting.
We modified the code identifiers to monospaced font throughout the space. We also went through all the equations and made changes to avoid using code identifiers in there, especially for equation (5) and other equations in Section 4.2.
- The manuscript oscillates between really detailed (and at times tedious) descriptions of algorithms and growth bookkeeping, and barely addressing entire sections from 4.4 onward. The model description appears to lose steam right where the physics gets interesting (nucleation, immersion freezing, contact freezing, mixed-phase). It reads like the authors ran out of time. The same uneven density also makes Section 2 feel like it belongs in a code reference manual rather than a GMD paper.
The physics part and the activation and interactions of mixed-phase clouds of the CARMA Cloud model is described in Liu et al. (2026) and simulations with the aerosol model are described by Tilmes et al. 2024. For this paper, we are focusing on the algorithms. We add a sentence in the abstract: “Comparisons of simulations with observations and analysis are described in Liu et al. 2026 for the CARMA Cloud model and in Tilmes et al. 2024 for the CARMA Aerosol model.”
Specific comments I wrote while (re)reading the manuscript
- L 33:"the code is flexible and extensible"jumps out of nowhere with no evidence. Either remove or dedicate a paragraph to actually substantiating it — the following sentence is about runtime options, which is not really what "code flexibility and extensibility" means.
Line 42: Change to: “Furthermore, the code is flexible and extensible: users can adapt to different vertical structures, change numbers of CARMA mass bins and their size ranges, and combine microphysical algorithms to explore the results of time-splitting for the accuracy of the solutions and computational cost”.
- L 56:to get this right, all these people cited above use CARMA but nobody has ever described it? It seems that's what the authors are suggesting, or maybe what they mean is that they're putting all the descriptions in one place. Either way, situate this manuscript in context of prior descriptions more clearly, and make explicit what is new here vs. updated vs. consolidated.
Line 159: Add “While the CARMA algorithms have undergone continuous updates since the last comprehensive description by Toon et al. (1988), these changes have not been formally documented in a single, accessible location. Descriptions of processes found in various individual papers (mentioned above) may or may not be assembled into the current main CARMA codebase. To improve community accessibility, this paper describes the CARMA algorithms developed since 1988 based on the latest published version used by the Earth science community (CARMA v4 standalone, which is also integrated into CESM2; Tilmes et al., 2023). The main changes are for the transport scheme: in 1988, the model was developed using a 3-D transport scheme; while CARMA v4 has a new vertical transport scheme for sedimentation and treats Brownian diffusion., The global model framework (e.g. CESM) handles the transport for resolved winds. Furthermore, we detail the newly developed CESM2/CARMA Cloud model, which simulates both liquid and ice clouds. In a companion paper (Liu et al., 2026), we compare simulations from this new cloud model (hereafter referred to as CARMA Cloud) with observations and with the default two-moment cloud model in CESM2.”
- L 96:can these be combined? Did all the users in the previous paragraph contribute their code back to the main CARMA codebase, or are there many divergent forks? This affects what "the CARMA model" even refers to in this paper.
No. These packages cannot be combined. However, efforts have been done to combine different aerosol types into one package such as Yu et al., 2015. And as we mentioned in the previous answer, not all code has been checked in the main CARMA codebase because it takes time and more tests to guarantee the accuracy before a package can be merged. I think we also address your concern here in our previous answer to clarify what CARMA model means in this paper.
- L 99:the authors keep saying "the code has been updated"(and derivatives) and it's a bit jarring because there is zero evidence about what the updates actually were. The previous paragraph started with the same line. Is this a code paper? If so, framing should be different — and in any case, "updated" and "improved" without specifics should be replaced with concrete deltas relative to prior works.
This paragraph is redundant since we wrote it already. To make the paragraph flow better, we rearranged the first section into two: 1. Model history; 2. Introduction of CARMA v4 and usage in the Community Climate Model CESM2.
What has been updated since 1988? In 1988, it was a model using a three-dimensional transport scheme. In the current version, we allow the global model framework to handle the horizontal transport and we get rid of the horizontal transport scheme inside CARMA. We now allow CESM to do all transport for resolved winds. We do not allow CESM to do sub-grid transport in CLUBB just like MAM, but use CLUBB diffusion coefficients in CARMA vertical routines. We have a new vertical transport scheme for sedimentation and treat Brownian diffusion in CARMA. We add one sentence in line 165: “The main changes are the for the transport scheme: in 1988, the model was developed using a 3-D transport scheme; while CARMA v4 has a new vertical transport scheme for sedimentation and treats Brownian diffusion. The global model framework (e.g. CESM) handles the transport for resolved winds.”
- L 105–107: The manuscript is already long, and listing what each section will discuss adds zero value when readers can just look at the section titles.
Paragraph deleted.
- Fig 1:any story behind 48 bins for everything? 48 appears six times in the figure with different ranges — is this a coding artifact (e.g., aligning with NBIN as a compile-time constant), a memory/throughput optimization, or a physically motivated choice? A sentence would help.
Line 226: add “CARMA Cloud currently uses 48 mass bins in each group, spanning each decade of radius with about 10-11 bins. From previous experience, we find good resolution of the size distribution for optical and other calculations requires about 10 bins per log radius increment. We need to cover the range of 0.5 um to mm to span the range from activated aerosols to rain drops. In the future we plan to explore the tradeoffs between resolution accuracy and computational cost in CESM2/CARMA Cloud.”
- Fig 3 and the associated discussion:if I were the authors, I would move this to the supplement. A few-sentence paragraph describing the run flow suffices in the main text.
Text and figure 3 are moved to Appendix 2: CARMA code structure.
Line 354: Add “The CARMA model utilizes an object-oriented interface designed for flexibility across various model frameworks, operating through two primary phases: one-time initialization and timestep execution. During initialization, the model establishes the necessary microphysical components—such as particle groups, elements, and condensing gases—and defines the rules for their interactions. At each timestep, the module ingests the current atmospheric state, sequentially computes time-split microphysical processes (including nucleation, coagulation, growth, and vertical transport), and returns the newly calculated state back to the parent model. A detailed flowchart of this run sequence, along with specific subroutine descriptions, is provided in Appendix 2 and Figure A1.”
- Eq 1 and Eq 2:the format changes between the two equations, which feeds into the general disarray of the math typesetting. Please make consistent.
Eq2 format changed to match Eq1.
- L 303:"a mixing ratio"of what units? kg-substance / kg-air? Better explain this.
Line 525: Add “(kg/kg or mol/mol)”
- L 304:concentration in what units? Number per cm³? Per cm² per scaled z? The text introduces both within a few lines without saying which.
Line 526: Add “gram or number per cm3”
- L 307:"ρ = ρ_z times z_met"— does this mean ρ = ρ_z · z_met, or something else? Use a multiplication symbol.
Fixed.
- L 382–383:to be clear, this paragraph is only about vertical movement, right? Say that here.
Line 640: Add “vertical”
- Eq 5:as noted in the General comments, this is essentially unreviewable as typeset. Please render with aligned terms and consistent subscripting; I cannot say whether the equation is correct in its present form.
Eq.5 fixed.
- Fig 5:hard to parse as a single figure
We put the bottom two panels into the appendix.
- Eq 6:the form ∂C/∂t = ∂(g_m C)/∂m reads as if it has the same sign on both sides — i.e., the opposite of the analogous flux-divergence form in Eq. (1). I assume this is a typesetting issue, but please verify.
We add the negative sign on the right side of Eqn (6) to properly reflect Euler continuity equation.
In CARMA, in the vertical transport Vfall is defined to be positive, which introduces a negative sign in front of the derivative. The growth equation gm can have either sign and has a positive sign in front of the spatial, r, derivative.
- L 492:be careful with the word "flux" — g_m × C in Eq. (6) is the flux across the mass coordinate (in the continuum sense), so reusing the word for the bin-edge fluxes can confuse.
Line 957, we change the sentence to “To compute the mass transferred out of a given bin, we use a piecewise polynomial to accurately estimate the transport at the edge of the mass bin”.
- L 501:does this implicit solver have a name? It looks like a backward-Euler step on a linear loss term — if there's a textbook reference, cite it.
Line 971: Add “(Colella and Woodward, 1984)”.
- L 526:all true, but the presentation makes dr/dt ∝ 1/r seem trivially known. Cite or explain — there is plenty of literature deriving how g_m scales with r (gets messy at very small r, but that's not the issue here). Also: are we talking about aerosols here, or cloud and rain droplets? The paragraph slides between them. And while you're at it, remind readers whythe mean free path is being introduced (continuum vs. kinetic regimes).
Line 1041, now the sentence read as: “Unlike vertical advection, for which the vertical velocity for clouds and rain is nearly independent of distance, the radius growth rate is faster for smaller particles than for larger ones when the cloud and rain particles are larger than the mean free path of air (i.e., continuum regime), because is proportional to 1/r (Pruppacher and Klett, 1997).” I bold the text that we changed.
- L 543:"vapor concentration" needs unpacking — available vapor mass per unit volume? Above some saturation reference? It's used as if obvious.
Change it to the supersaturation. Line 1069 now read as: “The growth rate is proportional to the ambient vapor supersaturation”.
- L 590–593:dropping every activated aerosol into bin 4 (~0.56 µm) is a tuning that throws away activation-size information. What is the sensitivity of CDNC, autoconversion, and rainfall to carma_dropact_bin?
In the standard CESM framework, the activated aerosol number concentration calculated by MAM is passed directly to the MG microphysics scheme, which treats the entire value as a bulk addition to the total cloud droplet number. Because MG is a bulk scheme, it does not require explicit activation-size information. However, because CARMA explicitly resolves particle growth and evaporation across discrete size bins based on ambient supersaturation, we must designate a specific size bin to receive these newly activated droplets. Based on classical Köhler theory for typical atmospheric conditions (e.g., Seinfeld and Pandis, 1998, Fig. 15.5), a radius of ~0.56 µm (Bin 4) safely exceeds the critical radius for activation. Injecting droplets at this size ensures they behave physically as activated cloud water—continuing to grow via condensation—rather than evaporating back. If we were to choose a smaller value for carma_dropact_bin, these droplets would fall below the critical radius and evaporate, resulting in an artificially lower cloud droplet number concentration (CDNC). Consequently, choosing a smaller bin would cause the activation rate explicitly calculated by MAM to lose its meaning, effectively breaking the consistency between MG and CARMA.
We do not currently carry the dissolved aerosol in the cloud water, so we cannot deal with the competition between the Kelvin effect and the solute effect. We simply put the activates particles into a large enough bin that the ambient supersaturation is likely large enough for them to grow without accounting for the solute.
In the paper, Line 1138, we add “Based on classical Köhler theory (e.g., Seinfeld and Pandis, 2016), this radius safely exceeds the critical activation radius for typical atmospheric conditions, ensuring the droplets continue to grow rather than evaporating back.”
- L 601:please cite.
Line 1158: Add “Toon et al., 1989”
- Eq 9:please cite — this is the Smoluchowski binary coagulation equation.
Line 1255 add (Smoluchowski, 1916)
Citation added: “Von Smoluchowski, M. (1916). Drei Vorträge über Diffusion, Brownsche Molekularbewegung und Koagulation von Kolloidteilchen. Physikalische Zeitschrift, 17, 557–571, 585–599.”
- Eq 12:please cite, and use notation consistent with K_c. Also: do the authors consider effects of turbulence (e.g., turbulent enhancement of collision rates inside convection) to be part of c_gr, c_cd, or absent? The next equation answers this implicitly, but it should be stated explicitly here.
Line 1564: Citation added: (Pruppacher and Klett, 1997; Toon et al., 1988)
Line 1567: add “without considering the turbulence-enhanced effects”
- Eq 14:answers the previous comment — but please state directly that turbulence-enhanced collision is not represented.
Line 1603: add “The turbulence-enhanced collision factor is not considered in Eq. (14).”
- L 863:"can be used in CARMA Cloud since they are widely used in other models"is a poor justification.
Line 1597: Changed to “The collision and collection efficiencies of liquid cloud, ice, and raindrops based on the table in (Hall, 1980) are used in CARMA Cloud since they are widely used in other models that are regional or cloud scale. No global model we know about computes the coagulation rate from first principles, so no other global model even uses collision and collection efficiencies. We are not aware of modern data that validate the Hall (1980) values particularly for particles smaller than 50 µm radius. We believe new laboratory measurements are needed for collision and collection efficiencies.”
- L 888:please cite the coalescence-kernel literature. Also, the fact that the data are forty to fifty years old is an observation, not a justification.
Line 1638: we change the sentence to “The gravitational collection kernels in the model rely on classical hydrodynamic collision efficiency calculations (e.g., Hall, 1980). While these values remain a standard baseline, their reliability for droplets below 50 μm is highly uncertain. In this size range, the collision efficiency curve exhibits a very steep slope with respect to droplet radius, making the production of precipitation highly sensitive to minor kernel variations.”
- L 942–947:the Gettelman & Morrison model is not used when CARMA Cloud is on, correct? Is this paragraph meant as a contrast? If so, say so.
Correct., MG is not on when CARMA is on. Add “(Note that when CARMA is on, MG is off)” in line 1749.
- L 1083–1084:"modified Slingo scheme" without a Slingo citation.
Line 1928: Add “Slingo 1987”
- L 1132 (disclosure):good to see the disclosure. In revision, I would actually recommend feeding both the PDF of this manuscript as well as reviewer comments straight into an LLM to help triage them — many of the surface-level complaints above are easily addressable that way, and the authors' time is better spent on the substantive scientific points.
Thank you. We modified according to your suggestions.
Citation: https://doi.org/10.5194/egusphere-2026-1185-AC3
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- 1
Dear authors,
in my role as Executive editor of GMD, I would like to bring to your attention our Editorial version 1.2: https://www.geosci-model-dev.net/12/2215/2019/
This highlights some requirements of papers published in GMD, which is also available on the GMD website in the ‘Manuscript Types’ section: http://www.geoscientific-model-development.net/submission/manuscript_types.html
In particular, please note that for your paper, the following requirement has not been met in the Discussions paper:
Please provide the version number of CARMA in the title of your revised manuscript.
As GitHub is not a persistent archive, please provide a persistent release for the exact source code versions for CARMA and CESM/CARMA used for the publication in this paper. As explained in https://www.geoscientific-model-development.net/about/manuscript\_types.html the preferred reference to this release is through the use of a DOI which then can be cited in the paper. For projects in GitHub a DOI for a released code version can easily be created using Zenodo, see https://guides.github.com/activities/citable-code/ for details. Finally note, that according to our new Editorial (v1.2) all data and analysis / plotting scripts should be made available.
Additionally, the part of the model output on which the results of your paper are based need to be made pupblicly available.
Yours,
Astrid Kerkweg