| 03 Aug 2026
Classification-Constrained Retrieval of PM2.5 Vertical Profiles from Fluorescence–Raman–Mie Polarization Lidar
Abstract. The vertical distribution of PM2.5 during urban haze events is jointly affected by aerosol composition, boundary-layer structure, and regional transport. Empirical PM2.5 retrievals based on lidar-derived extinction coefficients can be biased by the optical contribution of coarse-mode mineral particles. This study used fluorescence–Raman–Mie polarization lidar observations in Beijing to identify anthropogenic pollution aerosols (APA), desert dust (DD), and mineral dust (MD) using the particle depolarization ratio (PDR) and fluorescence capacity (Gf). The classification results were incorporated into the construction and application of an empirical extinction–PM2.5 relationship. For mixed-aerosol samples, the APA component fraction and its associated extinction contribution were estimated before retrieving the vertical PM2.5 distribution.
To quantify the effect of classification constraints, three linear models were developed: a model without aerosol-type constraints, a PDR-only screening model, and a model constrained by combined PDR–Gf classification. Near-surface, date-separated validation using 411 hourly samples from 69 observation dates showed that the combined-classification model achieved an RMSE of 17.32 µg m−3, an MAE of 13.54 µg m−3, and a Bias of 3.30 µg m−3. Compared with the model without aerosol-type constraints, the RMSE, MAE, and Bias decreased by 38.2 %, 45.0 %, and approximately 83.0 %, respectively. Uncertainty analysis showed that classification end-member and aerosol-type-dependent lidar-ratio perturbations affected the quantitative PM2.5 estimates under mixed-aerosol conditions, whereas the residual scatter and parameter stability of the empirical extinction–PM2.5 relationship were the dominant sources of prediction uncertainty.
For a mixed-to-pollution aerosol evolution episode in Beijing in November 2024, the classification-constrained PM2.5 vertical structure was physically consistent with temperature stratification, wind fields, and backward trajectories. Seasonal testing showed no stable and consistent improvement from season-specific fitting. The proposed method provides classification-constrained estimates of the PM2.5 vertical structure under APA-dominated conditions in Beijing. Model parameters should be recalibrated using local observations when applied to regions, seasons, or aerosol conditions with substantially different composition.
The authors have substantially revised the manuscript and have addressed most of the concerns raised in my previous review. In particular, the revised manuscript now includes date-separated quantitative validation using 411 hourly near-surface samples, comparison of the classification-constrained retrieval with unconstrained and PDR-only models, sensitivity analyses of aerosol classification end-member parameters and aerosol-type-dependent lidar ratios, and a more comprehensive uncertainty analysis including model-parameter uncertainty. The discussion of aerosol chemical composition, seasonal applicability, and model generalizability has also been substantially improved.
The quantitative comparison is particularly useful. The combined PDR–Gf classification model achieves substantially lower RMSE, MAE, and bias than the model without aerosol-type constraints and the PDR-only model. These results provide much stronger quantitative evidence for the benefit of the proposed classification constraint than was available in the previous version.
The revised treatment of the extinction-partitioning assumption is also satisfactory. The authors now explicitly recognize that different aerosol components may have different lidar ratios, formulate the corresponding aerosol-type-dependent extinction partitioning, and quantify the sensitivity of the retrieved PM₂.₅ to plausible lidar-ratio variations. Similarly, the Monte Carlo analysis of PDR and fluorescence end-member parameters provides a useful assessment of the sensitivity of the retrieval to classification assumptions.
I have only a few remaining comments:
The new near-surface comparison provides important quantitative validation of the empirical retrieval model, but it should be clearly distinguished from independent validation of the complete vertical PM₂.₅ profiles. As the authors appropriately acknowledge in the Conclusions, direct vertically resolved PM₂.₅ observations from UAVs, tethered balloons, or aircraft are not available. Please ensure that the terminology used throughout the Abstract, Results, and Conclusions does not imply that the full vertical profiles have been independently validated.
The uncertainty analysis based on perturbations of the PDR and Gf end-member parameters represents sensitivity to the assumed classification parameters rather than instrument-level measurement uncertainties in PDR and Gf. The manuscript recognizes this distinction in Methods. I suggest maintaining this distinction explicitly when discussing “classification uncertainty” elsewhere in the manuscript.
I still encourage the authors to improve the data and code availability statement. At present, the lidar data, processed datasets, and analysis scripts are available upon reasonable request. If possible, the processed datasets underlying the principal figures and validation analysis, together with the relevant analysis code, should be deposited in a public repository with a persistent DOI. This would substantially improve reproducibility.
Overall, I believe that the authors have responded constructively to the major concerns of the previous review and that the methodological support for the conclusions is now considerably stronger. The remaining issues are primarily matters of clarification, terminology, and reproducibility rather than fundamental methodological concerns.