The vertical profile of PM_2.5 is important for understanding its secondary formation, transport, and deposition at high altitudes; it also provides important data support for studying the causes and sources of PM_2.5 near the ground. Based on machine learning methods, this study fully utilized simultaneous Multi-Axis Differential Optical Absorption Spectroscopy measurements of multiple air pollutants in the atmosphere and employed the measured vertical profiles of aerosol extinction—as well as the vertical profiles of precursors such as NO₂ and SO₂—to evaluate the vertical distribution of PM_2.5 concentration. Three machine learning models (eXtreme Gradient Boosting, Random Forest, and back-propagation neural network) were evaluated using Multi-Axis Differential Optical Absorption Spectroscopy instruments in four typical cities in China: Beijing, Lanzhou, Guangzhou, and Hefei. According to the comparison between estimated PM_2.5 and in situ measurements on the ground surface in the four cities, the eXtreme Gradient Boosting model has the best estimation performance, with the Pearson correlation coefficient reaching 0.91. In addition, the in situ instrument mounted on the meteorological observation tower in Beijing was used to validate the estimated PM_2.5 profile, and the Pearson correlation coefficient at each height was greater than 0.7. The average PM_2.5 vertical profiles in the four typical cities all show an exponential pattern. In Beijing and Guangzhou, PM_2.5 can diffuse to high altitudes between 500 and 1000 m; in Lanzhou, it can diffuse to around 1500 m, while it is primarily distributed between the near surface and 500 m in Hefei. Based on the vertical distribution of PM_2.5 mass concentration in Beijing, a high-altitude PM_2.5 pollutant transport event was identified from January 19th to 21st, 2021, which was not detected by ground-based in situ instruments. During this process, PM_2.5 was transported from the 200 to 1500 m altitude level and then sank to the near surface, causing the concentration on the ground surface to continuously increase. The sinking process contributes to approximately 7% of the ground surface PM_2.5 every hour.

Monitoring the horizontal distribution of PM_2.5 within urban areas is of great significance, not only for environmental management but also for providing essential data to understand the distribution, formation, transport, and transformation of PM_2.5 within cities. This study proposes a novel approach—the Spectral Analysis-based PM_2.5 Estimation Machine Learning (SAPML) model. This method uses a machine learning model trained with features derived from multi-azimuth and multi-elevation MAX-DOAS observations, specifically the oxygen dimer (O₄) differential slant column densities (O₄ dSCDs), and labels provided by near-surface ground measurements corresponding to each azimuthal direction, to estimate near-surface PM_2.5 concentrations. This approach does not rely on meteorological data and enables multi-directional near-surface PM_2.5 monitoring using only a single independent instrument. SAPML bypasses the intermediate retrieval of aerosol extinction coefficients and directly estimates PM_2.5 concentrations from spectral analysis results, thereby avoiding the accumulation of errors. Using O₄ dSCD data from multiple MAX-DOAS stations for model training eliminates inter-station conversion differences, allowing a single model to be applied across multiple sites. Station-based k-fold cross-validation yielded an average Pearson correlation coefficient (R) of 0.782, demonstrating the robustness and transferability of the method across major regions in China. Among the machine learning algorithms evaluated, Extreme Gradient Boosting (XGBoost) exhibited the best performance. Feature optimization based on importance ranking reduced data collection time by approximately 30%, while the correlation coefficient (R) of the estimation results decreased by only about 1.3%. The trained SAPML model was further applied to two MAX-DOAS stations in Hefei, HF-HD, and HFC, successfully resolving the near-surface PM_2.5 spatial distribution at both sites. The results revealed clear intra-urban heterogeneity, with higher PM_2.5 concentrations observed in the western industrial park area. During the same observation period, an east-to-west PM_2.5 pollution transport event was captured: PM_2.5 increases were first detected in the upwind direction at HF-HD, followed by the downwind direction at the same station, and finally at the downwind station HFC. These results indicate that the SAPML model is an effective approach for monitoring intra-urban PM_2.5 distributions.