Interpretable Machine Learning Quantifies Composition and Size Controls on Aerosol Spectral Absorption

Wang, Wenfang; Tian, Pengfei; Zeng, Shuhua; Zhang, Yifei; Yu, Zeren; Cui, Chen; Wu, Yunfei; Chen, Min; Zhang, Lei

doi:10.5194/egusphere-2025-6118

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https://doi.org/10.5194/egusphere-2025-6118

Preprints

09 Jan 2026

| 09 Jan 2026

Interpretable Machine Learning Quantifies Composition and Size Controls on Aerosol Spectral Absorption

Wenfang Wang, Pengfei Tian, Shuhua Zeng, Yifei Zhang, Zeren Yu, Chen Cui, Yunfei Wu, Min Chen, and Lei Zhang

Abstract. The spectral dependence of aerosol absorption, characterized by the absorption Ångström exponent (AAE), strongly influences radiative effects, yet the relative importance of controlling factors remains poorly quantified. We integrate multisource observations with an interpretable machine-learning framework (Shapley Additive Explanations, SHAP) to disentangle the roles of chemical composition and particle size in shaping AAE and to evaluate radiative impacts. Field observation in Beijing reveal that near-surface AAE is predominantly influenced by higher fine mineral dust and water-soluble inorganic ions fractions. Multi-year columnar data identify dust loading as the dominant factor, followed by carbonaceous aerosols. The fine-mode radius accounts for 29 % of size parameters cumulative importance and ranks closely with black carbon. SHAP diagnostics highlight that columnar AAE contributes to radiative forcing at the top of the atmosphere (TOA) comparably to single scattering albedo (SSA), while its impact is clearly weaker at the bottom of the atmosphere and in the atmosphere. These findings help clarify AAE determinants and reduce uncertainties in aerosol radiative effect assessments.

Received: 08 Dec 2025 – Discussion started: 09 Jan 2026

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Journal article(s) based on this preprint

13 May 2026

Interpretable machine learning quantifies composition and size influences on aerosol spectral absorption

Wenfang Wang, Pengfei Tian, Shuhua Zeng, Yifei Zhang, Zeren Yu, Chen Cui, Yunfei Wu, Min Chen, and Lei Zhang

Atmos. Chem. Phys., 26, 6471–6487, https://doi.org/10.5194/acp-26-6471-2026,https://doi.org/10.5194/acp-26-6471-2026, 2026

Short summary

Wenfang Wang, Pengfei Tian, Shuhua Zeng, Yifei Zhang, Zeren Yu, Chen Cui, Yunfei Wu, Min Chen, and Lei Zhang

Interactive discussion

Status: closed

CC1:
'Comment on egusphere-2025-6118', Xiyao Chen, 21 Jan 2026
This paper conducts a detailed study on the influencing factors of ground and atmospheric column AAE, revealing distinct patterns of influence. However, it is evident that there is a lack of correlation and comparison between the studies on the ground and atmospheric column. Furthermore, a significant portion of the text is devoted to discussing the SHAP of TOA, ATM, and BOA with respect to atmospheric column optical properties. However, are TOA, ATM, and BOA calculated based on atmospheric column optical properties and radiative transfer models? Therefore, SHAP is likely just a data-driven decomposition and description of the traditional radiative transfer simulation process. In summary, I suggest a major revision.

Major comments:
It is necessary to enhance the comparison between ground and atmospheric column AAE, especially to explain why carbonaceous aerosols and dust are not the main driving factors on the ground.

The article initially employs many correlations, followed by regression analysis using Multiple Linear Regression (MLR) for ground-based AAE, while the atmospheric column is studied using seven interpretable machine learning models for AAE and six radiative factors. There is considerable overlap in data analysis functions among correlations, MLR, and machine learning. Firstly, why isn't interpretable machine learning used for ground-based AAE? The same method makes it easier for readers to compare driving patterns between ground and column AAE.

Why does the ground-based MLR directly state in the methods section that black carbon, brown carbon, and dust are not included or as the “intercept term” (Lines 179-180)? The apparent reason for exclusion may stem from the correlation analysis in the results section (e.g., Section 3.2). I am not denying your viewpoint, on the contrary, I find it very interesting. Unfortunately, the author did not focus on analyzing possible mechanisms and instead conducted extensive repetitive analysis and modeling.

The interpretable machine learning for the six radiative quantities seems (e.g., Figs. 6-7) to merely describe the traditional radiative transfer simulation process via a data-driven machine learning method. It is suggested to move it to the Supplementary Information (SI), with only the main conclusions appearing in the main text. Is this comment correct? Perhaps you need to clarify how radiation variables are obtained, rather than just relying on literature, why machine learning is applicable, and what new discoveries machine learning has made.

Minor comments:
Lines 44-46: Provide AAE for dust and brown carbon separately.

In the Introduction, it is necessary to separately review the ground and column AAE, with fewer or unclear reviews of column AAE. Why is it necessary to study both ground and column AAE simultaneously?

Line 180, 304-307, 323-325, and so on: These are key points, but too simple. Need more discussions.

Lines 251-254, Fig. 1: It is not clear or direct for reads to understand! Perhaps Figure 1 contains a lot of information, but lacks visualization skills, making it difficult to highlight key points.

MLR and machine learning first need to report R2 and RMSE, such as in Lines 313-314. These are the most direct indicators to win the trust of readers. Please check the whole paper.

Lines 336-338: Organize sections around this point.
Citation: https://doi.org/10.5194/egusphere-2025-6118-CC1
- AC1: 'Reply on CC1', Pengfei Tian, 12 Mar 2026
  
  We thank Dr. Xiyao Chen for carefully reading and reviewing our manuscript. Our point-by-point response is uploaded as a supplement PDF.
  
  Citation: https://doi.org/10.5194/egusphere-2025-6118-AC1
RC1:
'Comment on egusphere-2025-6118', Anonymous Referee #1, 31 Jan 2026
Review of "Interpretable Machine Learning Quantifies Composition and Size Controls on Aerosol Spectral Absorption"
This manuscript by Wang et al. investigates the complex drivers of the Absorption Ångström Exponent (AAE) using a combination of high-resolution field observations in Beijing and multi-year AERONET columnar data. The study addresses a persistent challenge in atmospheric science: quantitatively disentangling the relative importance of chemical composition versus particle size in determining aerosol spectral absorption. The authors employ Shapley Additive exPlanations (SHAP) to provide a ranked attribution of AAE drivers. The study quantifies how AAE variations directly influence aerosol radiative forcing efficiency (ARFE), finding that AAE is a primary driver of cooling efficiency at the Top of the Atmosphere (TOA). The manuscript is well-structured and the methodology is fairly robust, with the caveats detailed below.
Major issues
The study relies heavily on SHAP to attribute drivers of AAE which identifies associations, not necessarily causal links. The authors acknowledge nonlinearity and collinearity among predictors, however, if two variables are highly correlated (e.g., $D_{APS}$ and FMD mass fraction, $r=0.64$), SHAP can sometimes "split" the importance between them in ways that don't reflect physical reality. The manuscript would benefit from a more explicit discussion on whether the "importance" found by the model is supported by Mie theory or other physical optical models to bridge the gap between statistical importance and physical causation.

Near-surface chemical data was collected via offline filter sampling (day/night blocks), while optical data was online (hourly). While the authors matched these temporally, the coarse resolution of the chemical data (12-hour averages) likely masks the fine-scale diurnal variability seen in the optical $AAE_{sfc}$.

The authors describe using a ‘consistent split’ for model training, testing and validation but never explicitly state what that is. Please describe the method for splitting and why that’s appropriate for this dataset.

Minor issues
The authors focus on a specific site in Beijing, which given the observational constraints seems reasonable, but it would be beneficial to include a sentence or two in the conclusion explicitly stating how these results might change (and therefore their relevance) in cleaner or more dust-dominant global regions.

Please mention the ranges quoted in the results section. Are these 1 standard deviation, or something else?

L217, "coare-mode" should be corrected to "coarse-mode".
Citation: https://doi.org/10.5194/egusphere-2025-6118-RC1
- AC2: 'Reply on RC1', Pengfei Tian, 12 Mar 2026
  
  We thank the referee for carefully reading and reviewing our manuscript. Our point-by-point response is uploaded as a supplement PDF.
  
  Citation: https://doi.org/10.5194/egusphere-2025-6118-AC2
RC2:
'Comment on egusphere-2025-6118', Anonymous Referee #2, 21 Feb 2026
This manuscript by Wang et al. investigates the relative importance of aerosol chemical composition and particle size in determining the Absorption Ångström Exponent (AAE), using both ground-based observations and column-integrated AERONET data within an interpretable machine learning framework (SHAP). This study presents a novel and insightful application of machine learning to a challenging problem in aerosol science. The quantification of the relative roles of composition and size on AAE is a significant contribution. However, the manuscript requires major revisions to address the critical issue of causality in the radiative forcing analysis, clarify key methodological steps (especially the temporal matching), and provide a more integrated and critical discussion of the multi-platform datasets. With these revisions, the paper will be well-suited for publication in Atmospheric Chemistry and Physics.
Major Comments
Causality and the Role of AAE in Radiative Forcing (Lines 224-242, 424-459, and Section 4):

The most significant conceptual issue lies in the framing of AAE's role in radiative forcing. The authors state that they aim to "elucidate the critical role of AAE in radiative effects" and later use SHAP to quantify AAE as a "driver" of ADRF and ARFE variations. This implies a causal relationship where AAE is an independent variable controlling radiative forcing.However, as the authors themselves expertly demonstrate in the first half of the paper, AAE is not a fundamental physical property; it is a diagnostic metric that is itself driven by the same factors that control radiative forcing: composition (BC, BrC, dust) and size. To then turn around and treat AAE as an independent "driver" of radiative effects is circular. The fundamental drivers are the microphysical and chemical properties (e.g., BC concentration, dust loading, fine-mode radius). AAE is a valuable observational constraint precisely because it integrates these properties, but it is a consequence, not a cause. The analysis of AAE's relationship with DRF is still scientifically valuable, but its framing must be corrected. The study should not claim to quantify AAE's "driving" role. Instead, it should be framed as an investigation into the diagnostic power of AAE. The goal should be to understand how well this convenient, measurable optical parameter can explain or predict variability in radiative forcing. For example, showing that AAE is a strong predictor of TOA forcing efficiency (as in Figure 7) is a useful result: it suggests that if you can measure or constrain AAE, you have a powerful tool for estimating the aerosol's radiative effect. This is a correlative/ diagnostic relationship, not a causal one. The language throughout Sections 3.4 and 4 must be revised to reflect this, replacing terms like "driver," "regulator," and "governs" with phrases like "is associated with," "can help predict," or "serves as a key diagnostic for."

Matching Offline and Online Measurements for Model Training (Section 2.2, Lines 175-186):

A critical methodological detail is insufficiently explained. The multiple linear regression model in Section 2.2 uses offline chemical composition data (FMD fraction, nd-WSII fraction) matched with online AAE and size distribution data. The authors state that data were "temporally matched to the corresponding online measurements based on sampling periods" (daytime 09:00-20:30; nighttime 21:00-08:30).This averaging over ~11.5-hour and ~11.5-hour periods is a significant source of uncertainty and potential bias. Within a single daytime or nighttime filter sample, the aerosol composition, size distribution, and AAE are likely highly variable due to changes in emissions (e.g., rush hour), boundary layer dynamics, and chemistry. Assigning a single, averaged composition value to the highly temporally resolved online data within that period assumes a static relationship that may not hold. The authors must: （1）Explicitly justify why this temporal resolution is sufficient to capture the relationships they are investigating. （2）Discuss the potential for "ecological fallacy" or averaging bias—where the relationship between variables at an aggregated level differs from the relationship at a high-resolution level. （3）Ideally, provide an uncertainty estimate for how this temporal mismatch might affect the regression coefficients and conclusions.

Disconnect Between Surface and Columnar Models (Sections 3.2 and 3.3):

The manuscript essentially presents two independent modeling efforts: one for surface AAE (using MLR with 4 predictors) and one for columnar AAE (using ML models with 9 predictors). The connection between these two parts is weak. The surface analysis uses direct physical measurements, while the columnar analysis uses retrieved optical properties and a chemically inverted dataset. The manuscript would be strengthened by a more explicit discussion of how these two perspectives complement each other. For instance, does the dominant role of dust at the surface (FMD) align with the importance of CAI (coarse-mode absorbing dust) in the column? How do the limitations of one dataset inform the interpretation of the other? A dedicated paragraph synthesizing these findings and acknowledging their different physical meanings would greatly improve the manuscript's coherence.

Uncertainty in AERONET-Inverted Chemical Composition (Section 2.3):

The analysis of columnar AAE relies heavily on the AERONET chemical composition product (BC, BrC, CAI, etc.). It is crucial to remind readers that these are not directly measured but are retrieved from inversions of spectral sun photometer measurements, which come with their own assumptions and uncertainties. The manuscript briefly cites Zhang et al. (2024), but a more critical discussion is warranted here, especially given the central role of these data in Figure 5. What are the primary assumptions in this retrieval? (e.g., regarding refractive indices, mixing state, particle shape). What is the estimated uncertainty for each component (BrC, BC, dust) as provided by the retrieval algorithm or the literature? A short statement acknowledging these limitations and citing key references on the uncertainties of AERONET inversions (e.g., Dubovik et al., 2000; Sinyuk et al., 2020) would provide necessary context for the robustness of the SHAP results.

Minor Comments
Line 89-90: The phrasing "an ensemble of models was initially trained, after which the optimal model was selected" is slightly ambiguous. Clarify that you trained multiple model types and selected the best-performing one (CatBoost) for the final interpretation, as described later in Section 2.4. This is good practice, but the wording could be more precise.

Line 245-247: The acronyms SMPS and APS are used but were introduced in Section 2.1.1. Since this is the start of the Results section, it might be helpful to briefly re-introduce them as "fine-mode (SMPS) and coarse-mode (APS) particle sizers" for readers who may not have the methods section fresh in mind.

Line 340-341: The sentence "The AAEcol (1.47±0.56) was also suggested to be greater than that derived from the surface field campaign" is a bit awkward. Replacing "was also suggested to be" with "was found to be" or "was also higher than" would be clearer.

Line 384: "explaining ∼50%of model performance." It would be more precise to say "explaining ∼50% of the model's predictive power (as measured by mean absolute SHAP value)" or something similar, as SHAP importance sums to the total model output, not necessarily a performance metric like R².

Figures 6 and 7: The box plots in (a-c) are very effective. The SHAP summaries in (d-f) are informative. Consider adding the sample size (n) for each AAE bin in the box plots to give the reader a sense of the statistical robustness of each category.

Line 225: Change "in determining" to "in predicting" or "in explaining the model's estimation of."

Line 424: Change "revealed a robust, layer-dependent coupling" to "revealed a robust, layer-dependent correlation."

Line 477: Change "is a key regulator of" to "is a strong predictor of" or "contains valuable information for estimating."

Line 484-486: Change "demonstrate the multifactorial control of AAE" to "demonstrate the multifactorial influences on AAE" and "highlight its pivotal role in partitioning radiative forcing" to "highlight its strong correlation with the vertical partitioning of radiative forcing."
Citation: https://doi.org/10.5194/egusphere-2025-6118-RC2
- AC3: 'Reply on RC2', Pengfei Tian, 12 Mar 2026
  
  We thank the referee for carefully reading and reviewing our manuscript. Our point-by-point response is uploaded as a supplement PDF.
  
  Citation: https://doi.org/10.5194/egusphere-2025-6118-AC3

Interactive discussion

Status: closed

CC1:
'Comment on egusphere-2025-6118', Xiyao Chen, 21 Jan 2026
This paper conducts a detailed study on the influencing factors of ground and atmospheric column AAE, revealing distinct patterns of influence. However, it is evident that there is a lack of correlation and comparison between the studies on the ground and atmospheric column. Furthermore, a significant portion of the text is devoted to discussing the SHAP of TOA, ATM, and BOA with respect to atmospheric column optical properties. However, are TOA, ATM, and BOA calculated based on atmospheric column optical properties and radiative transfer models? Therefore, SHAP is likely just a data-driven decomposition and description of the traditional radiative transfer simulation process. In summary, I suggest a major revision.

Major comments:
It is necessary to enhance the comparison between ground and atmospheric column AAE, especially to explain why carbonaceous aerosols and dust are not the main driving factors on the ground.

The article initially employs many correlations, followed by regression analysis using Multiple Linear Regression (MLR) for ground-based AAE, while the atmospheric column is studied using seven interpretable machine learning models for AAE and six radiative factors. There is considerable overlap in data analysis functions among correlations, MLR, and machine learning. Firstly, why isn't interpretable machine learning used for ground-based AAE? The same method makes it easier for readers to compare driving patterns between ground and column AAE.

Why does the ground-based MLR directly state in the methods section that black carbon, brown carbon, and dust are not included or as the “intercept term” (Lines 179-180)? The apparent reason for exclusion may stem from the correlation analysis in the results section (e.g., Section 3.2). I am not denying your viewpoint, on the contrary, I find it very interesting. Unfortunately, the author did not focus on analyzing possible mechanisms and instead conducted extensive repetitive analysis and modeling.

The interpretable machine learning for the six radiative quantities seems (e.g., Figs. 6-7) to merely describe the traditional radiative transfer simulation process via a data-driven machine learning method. It is suggested to move it to the Supplementary Information (SI), with only the main conclusions appearing in the main text. Is this comment correct? Perhaps you need to clarify how radiation variables are obtained, rather than just relying on literature, why machine learning is applicable, and what new discoveries machine learning has made.

Minor comments:
Lines 44-46: Provide AAE for dust and brown carbon separately.

In the Introduction, it is necessary to separately review the ground and column AAE, with fewer or unclear reviews of column AAE. Why is it necessary to study both ground and column AAE simultaneously?

Line 180, 304-307, 323-325, and so on: These are key points, but too simple. Need more discussions.

Lines 251-254, Fig. 1: It is not clear or direct for reads to understand! Perhaps Figure 1 contains a lot of information, but lacks visualization skills, making it difficult to highlight key points.

MLR and machine learning first need to report R2 and RMSE, such as in Lines 313-314. These are the most direct indicators to win the trust of readers. Please check the whole paper.

Lines 336-338: Organize sections around this point.
Citation: https://doi.org/10.5194/egusphere-2025-6118-CC1
- AC1: 'Reply on CC1', Pengfei Tian, 12 Mar 2026
  
  We thank Dr. Xiyao Chen for carefully reading and reviewing our manuscript. Our point-by-point response is uploaded as a supplement PDF.
  
  Citation: https://doi.org/10.5194/egusphere-2025-6118-AC1
RC1:
'Comment on egusphere-2025-6118', Anonymous Referee #1, 31 Jan 2026
Review of "Interpretable Machine Learning Quantifies Composition and Size Controls on Aerosol Spectral Absorption"
This manuscript by Wang et al. investigates the complex drivers of the Absorption Ångström Exponent (AAE) using a combination of high-resolution field observations in Beijing and multi-year AERONET columnar data. The study addresses a persistent challenge in atmospheric science: quantitatively disentangling the relative importance of chemical composition versus particle size in determining aerosol spectral absorption. The authors employ Shapley Additive exPlanations (SHAP) to provide a ranked attribution of AAE drivers. The study quantifies how AAE variations directly influence aerosol radiative forcing efficiency (ARFE), finding that AAE is a primary driver of cooling efficiency at the Top of the Atmosphere (TOA). The manuscript is well-structured and the methodology is fairly robust, with the caveats detailed below.
Major issues
The study relies heavily on SHAP to attribute drivers of AAE which identifies associations, not necessarily causal links. The authors acknowledge nonlinearity and collinearity among predictors, however, if two variables are highly correlated (e.g., $D_{APS}$ and FMD mass fraction, $r=0.64$), SHAP can sometimes "split" the importance between them in ways that don't reflect physical reality. The manuscript would benefit from a more explicit discussion on whether the "importance" found by the model is supported by Mie theory or other physical optical models to bridge the gap between statistical importance and physical causation.

Near-surface chemical data was collected via offline filter sampling (day/night blocks), while optical data was online (hourly). While the authors matched these temporally, the coarse resolution of the chemical data (12-hour averages) likely masks the fine-scale diurnal variability seen in the optical $AAE_{sfc}$.

The authors describe using a ‘consistent split’ for model training, testing and validation but never explicitly state what that is. Please describe the method for splitting and why that’s appropriate for this dataset.

Minor issues
The authors focus on a specific site in Beijing, which given the observational constraints seems reasonable, but it would be beneficial to include a sentence or two in the conclusion explicitly stating how these results might change (and therefore their relevance) in cleaner or more dust-dominant global regions.

Please mention the ranges quoted in the results section. Are these 1 standard deviation, or something else?

L217, "coare-mode" should be corrected to "coarse-mode".
Citation: https://doi.org/10.5194/egusphere-2025-6118-RC1
- AC2: 'Reply on RC1', Pengfei Tian, 12 Mar 2026
  
  We thank the referee for carefully reading and reviewing our manuscript. Our point-by-point response is uploaded as a supplement PDF.
  
  Citation: https://doi.org/10.5194/egusphere-2025-6118-AC2
RC2:
'Comment on egusphere-2025-6118', Anonymous Referee #2, 21 Feb 2026
This manuscript by Wang et al. investigates the relative importance of aerosol chemical composition and particle size in determining the Absorption Ångström Exponent (AAE), using both ground-based observations and column-integrated AERONET data within an interpretable machine learning framework (SHAP). This study presents a novel and insightful application of machine learning to a challenging problem in aerosol science. The quantification of the relative roles of composition and size on AAE is a significant contribution. However, the manuscript requires major revisions to address the critical issue of causality in the radiative forcing analysis, clarify key methodological steps (especially the temporal matching), and provide a more integrated and critical discussion of the multi-platform datasets. With these revisions, the paper will be well-suited for publication in Atmospheric Chemistry and Physics.
Major Comments
Causality and the Role of AAE in Radiative Forcing (Lines 224-242, 424-459, and Section 4):

The most significant conceptual issue lies in the framing of AAE's role in radiative forcing. The authors state that they aim to "elucidate the critical role of AAE in radiative effects" and later use SHAP to quantify AAE as a "driver" of ADRF and ARFE variations. This implies a causal relationship where AAE is an independent variable controlling radiative forcing.However, as the authors themselves expertly demonstrate in the first half of the paper, AAE is not a fundamental physical property; it is a diagnostic metric that is itself driven by the same factors that control radiative forcing: composition (BC, BrC, dust) and size. To then turn around and treat AAE as an independent "driver" of radiative effects is circular. The fundamental drivers are the microphysical and chemical properties (e.g., BC concentration, dust loading, fine-mode radius). AAE is a valuable observational constraint precisely because it integrates these properties, but it is a consequence, not a cause. The analysis of AAE's relationship with DRF is still scientifically valuable, but its framing must be corrected. The study should not claim to quantify AAE's "driving" role. Instead, it should be framed as an investigation into the diagnostic power of AAE. The goal should be to understand how well this convenient, measurable optical parameter can explain or predict variability in radiative forcing. For example, showing that AAE is a strong predictor of TOA forcing efficiency (as in Figure 7) is a useful result: it suggests that if you can measure or constrain AAE, you have a powerful tool for estimating the aerosol's radiative effect. This is a correlative/ diagnostic relationship, not a causal one. The language throughout Sections 3.4 and 4 must be revised to reflect this, replacing terms like "driver," "regulator," and "governs" with phrases like "is associated with," "can help predict," or "serves as a key diagnostic for."

Matching Offline and Online Measurements for Model Training (Section 2.2, Lines 175-186):

A critical methodological detail is insufficiently explained. The multiple linear regression model in Section 2.2 uses offline chemical composition data (FMD fraction, nd-WSII fraction) matched with online AAE and size distribution data. The authors state that data were "temporally matched to the corresponding online measurements based on sampling periods" (daytime 09:00-20:30; nighttime 21:00-08:30).This averaging over ~11.5-hour and ~11.5-hour periods is a significant source of uncertainty and potential bias. Within a single daytime or nighttime filter sample, the aerosol composition, size distribution, and AAE are likely highly variable due to changes in emissions (e.g., rush hour), boundary layer dynamics, and chemistry. Assigning a single, averaged composition value to the highly temporally resolved online data within that period assumes a static relationship that may not hold. The authors must: （1）Explicitly justify why this temporal resolution is sufficient to capture the relationships they are investigating. （2）Discuss the potential for "ecological fallacy" or averaging bias—where the relationship between variables at an aggregated level differs from the relationship at a high-resolution level. （3）Ideally, provide an uncertainty estimate for how this temporal mismatch might affect the regression coefficients and conclusions.

Disconnect Between Surface and Columnar Models (Sections 3.2 and 3.3):

The manuscript essentially presents two independent modeling efforts: one for surface AAE (using MLR with 4 predictors) and one for columnar AAE (using ML models with 9 predictors). The connection between these two parts is weak. The surface analysis uses direct physical measurements, while the columnar analysis uses retrieved optical properties and a chemically inverted dataset. The manuscript would be strengthened by a more explicit discussion of how these two perspectives complement each other. For instance, does the dominant role of dust at the surface (FMD) align with the importance of CAI (coarse-mode absorbing dust) in the column? How do the limitations of one dataset inform the interpretation of the other? A dedicated paragraph synthesizing these findings and acknowledging their different physical meanings would greatly improve the manuscript's coherence.

Uncertainty in AERONET-Inverted Chemical Composition (Section 2.3):

The analysis of columnar AAE relies heavily on the AERONET chemical composition product (BC, BrC, CAI, etc.). It is crucial to remind readers that these are not directly measured but are retrieved from inversions of spectral sun photometer measurements, which come with their own assumptions and uncertainties. The manuscript briefly cites Zhang et al. (2024), but a more critical discussion is warranted here, especially given the central role of these data in Figure 5. What are the primary assumptions in this retrieval? (e.g., regarding refractive indices, mixing state, particle shape). What is the estimated uncertainty for each component (BrC, BC, dust) as provided by the retrieval algorithm or the literature? A short statement acknowledging these limitations and citing key references on the uncertainties of AERONET inversions (e.g., Dubovik et al., 2000; Sinyuk et al., 2020) would provide necessary context for the robustness of the SHAP results.

Minor Comments
Line 89-90: The phrasing "an ensemble of models was initially trained, after which the optimal model was selected" is slightly ambiguous. Clarify that you trained multiple model types and selected the best-performing one (CatBoost) for the final interpretation, as described later in Section 2.4. This is good practice, but the wording could be more precise.

Line 245-247: The acronyms SMPS and APS are used but were introduced in Section 2.1.1. Since this is the start of the Results section, it might be helpful to briefly re-introduce them as "fine-mode (SMPS) and coarse-mode (APS) particle sizers" for readers who may not have the methods section fresh in mind.

Line 340-341: The sentence "The AAEcol (1.47±0.56) was also suggested to be greater than that derived from the surface field campaign" is a bit awkward. Replacing "was also suggested to be" with "was found to be" or "was also higher than" would be clearer.

Line 384: "explaining ∼50%of model performance." It would be more precise to say "explaining ∼50% of the model's predictive power (as measured by mean absolute SHAP value)" or something similar, as SHAP importance sums to the total model output, not necessarily a performance metric like R².

Figures 6 and 7: The box plots in (a-c) are very effective. The SHAP summaries in (d-f) are informative. Consider adding the sample size (n) for each AAE bin in the box plots to give the reader a sense of the statistical robustness of each category.

Line 225: Change "in determining" to "in predicting" or "in explaining the model's estimation of."

Line 424: Change "revealed a robust, layer-dependent coupling" to "revealed a robust, layer-dependent correlation."

Line 477: Change "is a key regulator of" to "is a strong predictor of" or "contains valuable information for estimating."

Line 484-486: Change "demonstrate the multifactorial control of AAE" to "demonstrate the multifactorial influences on AAE" and "highlight its pivotal role in partitioning radiative forcing" to "highlight its strong correlation with the vertical partitioning of radiative forcing."
Citation: https://doi.org/10.5194/egusphere-2025-6118-RC2
- AC3: 'Reply on RC2', Pengfei Tian, 12 Mar 2026
  
  We thank the referee for carefully reading and reviewing our manuscript. Our point-by-point response is uploaded as a supplement PDF.
  
  Citation: https://doi.org/10.5194/egusphere-2025-6118-AC3

Peer review completion

AR – Author's response | RR – Referee report | ED – Editor decision | EF – Editorial file upload

AR by Pengfei Tian on behalf of the Authors (12 Mar 2026) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (12 Mar 2026) by James Allan

RR by Anonymous Referee #2 (16 Mar 2026)

Suggestions for revision or reasons for rejection

The authors have addressed the majority of the previous review comments satisfactorily.
However, to further strengthen the manuscript's scientific depth and place its findings within the broader context of aerosol optics, I have a suggestion for a discussion point regarding the microphysical properties of aerosols, particularly black carbon (BC).

Discussion on Microphysical Properties (Morphology and Mixing State):
The manuscript convincingly demonstrates the importance of bulk properties like composition (BC, BrC, dust mass fractions) and size distribution parameters (e.g., Rfine) in controlling AAE. However, the optical properties of aerosols, especially light-absorbing ones like BC and BrC, are critically modulated by their microphysical characteristics, such as morphology (e.g., fractal vs. compact aggregates) and mixing state (e.g., coating thickness, uniformity, and the spatial distribution of inclusions).
Recent studies have highlighted that these microphysical properties introduce significant complexity that can influence AAE and subsequent radiative forcing estimates, sometimes in ways that are not fully captured by bulk properties alone. For instance:
Luo, J., Li, D., Wang, Y., Sun, D., Hou, W., Ren, J., Wu, H., Zhou, P., and Qiu, J.: Quantifying the effects of the microphysical properties of black carbon on the determination of brown carbon using measurements at multiple wavelengths, Atmos. Chem. Phys., 24, 427–448, https://doi.org/10.5194/acp-24-427-2024, 2024.
Luo, J., Hu, M., Luo, J., Li, C., Bi, M., Zhou, X., Geng, X., Wu, C., Li, K., and Wang, F.: Numerically quantifying the spectral dependence of the absorption enhancement of partially-coated black carbon with complex microphysical properties, Opt. Express, 32(26), 46982–46998, https://doi.org/10.1364/OE.545559, 2024.
Luo, J., Li, Z., Qiu, J., Zhang, Y., Fan, C., Li, L., Wu, H., Zhou, P., Li, K., Zhang, Q., et al.: The simulated source apportionment of light absorbing aerosols: Effects of microphysical properties of partially-coated black carbon, J. Geophys. Res.-Atmos., 128, e2022JD037291, https://doi.org/10.1029/2022JD037291, 2023.
Luo, J., Wang, W., Qiu, J., Zhang, Q., Li, C., Hou, W., Dong, X., and Hu, M.: Both non-uniform mixing states and coating structures are important for absorption enhancement and radiative effect of black carbon, Opt. Express, 33(10), 21719–21735, https://doi.org/10.1364/OE.552013, 2025.
Liu, C., Chung, C. E., Yin, Y., and Schnaiter, M.: The absorption Ångström exponent of black carbon: from numerical aspects, Atmos. Chem. Phys., 18, 6259–6273, https://doi.org/10.5194/acp-18-6259-2018, 2018.
Wang, Y., Zheng, Z., Sun, Y., Yao, Y., Ma, P. L., Zhang, A., and Li, W.: Improved representation of black carbon mixing structures suggests stronger direct radiative heating, One Earth, 8(5), https://doi.org/10.1016/j.oneear.2025.04.012, 2025.

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ED: Publish as is (06 May 2026) by James Allan

AR by Pengfei Tian on behalf of the Authors (07 May 2026) Author's response Manuscript

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13 May 2026

Interpretable machine learning quantifies composition and size influences on aerosol spectral absorption

Wenfang Wang, Pengfei Tian, Shuhua Zeng, Yifei Zhang, Zeren Yu, Chen Cui, Yunfei Wu, Min Chen, and Lei Zhang

Atmos. Chem. Phys., 26, 6471–6487, https://doi.org/10.5194/acp-26-6471-2026,https://doi.org/10.5194/acp-26-6471-2026, 2026

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Wenfang Wang, Pengfei Tian, Shuhua Zeng, Yifei Zhang, Zeren Yu, Chen Cui, Yunfei Wu, Min Chen, and Lei Zhang

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Wenfang Wang, Pengfei Tian, Shuhua Zeng, Yifei Zhang, Zeren Yu, Chen Cui, Yunfei Wu, Min Chen, and Lei Zhang

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We separated the roles of chemical composition and particle size in shaping absorption Ångström exponent (AAE) using ground and column measurements together with an interpretable machine learning. We found that near surface AAE is governed by higher fine mineral dust and inorganic ions fractions. Fine-mode effective radius has an influence close to black carbon on columnar AAE. Columnar AAE contributes to radiative forcing at the top of the atmosphere comparably to single scattering albedo.


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