We used daily AOD data during 2017–2019 from 19 sites at the Sun-sky radiometer Observation NETwork (SONET, http://www.sonet.ac.cn/), which is a ground-based CIMEL radiometer network providing long-term atmospheric aerosol characterization over China (Holben et al., 1998; Li et al., 2014; Li et al., 2018). The main instrument used is the multi-wavelength polarimetric solar radiometer CE318-DP, which observes columnar aerosol properties approximately every 15 min (Wei et al., 2020). To ensure data accuracy, regular staff services are carried out and the instruments are calibrated once a year. SONET can perform aerosol and water vapor measurements in multiple channels at different wavelengths. More than 20 aerosol parameters including AOD and single scattering albedo (SSA) are estimated. The SONET data have been fully evaluated and widely used in the analyses of particle size distribution and aerosol radiative effects (Xie et al., 2015a; Zhang et al., 2019a; Huang et al., 2020).

As of 2019, SONET built a total of 20 permanent sites, in which the data of 19 stations are used for this study. These sites are distributed unevenly with more in central and eastern China (Figure 1), especially over industrialized areas such as North China Plain (Beijing, Jiaozuo, Songshan, Yanqihu), Yangtze River Delta (Hefei, Nanjing, Shanghai, Zhoushan), Pearl River Delta (Guangzhou), and Sichuan Basin (Chengdu). In addition, nine sites are built in less populated areas with varied topography or land types, including four in the Northwest (Xian, Minqin, Zhangye, Kashi), one in the Southwest (Lhasa), one in the Northeast (Harbin), and three in the South (Sanya, Guilin, Nanning). Some sites are affected by large particles such as dust (Kashi, Minqin, Zhangye) and sea salt (Sanya, Zhoushan) aerosols. Since AOD of smaller wavelength is less sensitive to larger particles, we selected daily AOD at 440 nm for non-rainfall days to study the associations with PM_2.5. We also used SSA data on the same days at the 19 sites to explore the possible impacts of aerosol compositions on the PM_2.5-AOD relationship.

We used daily PM_2.5 mass concentration data from 1,580 sites at the China National Environmental Monitoring Center (CNEMC) network (https://air.cnemc.cn:18007/) during 2017–2019. The monitoring stations are shown in Figure 1. Continuous and automated monitoring of PM_2.5 mass concentrations is usually performed using the tapered element oscillating microbalance method (TEOM) (Chen et al., 2018; Kong et al., 2021). Data pre-processing is then performed in the laboratory to eliminate deviations. We located the CNEMC sites with the closest distance to SONET sites to represent the PM_2.5 pollution level at SONET sites. The PM_2.5 concentrations on the same days as SONET observations are collected.

We used meteorological reanalyses data of ERA5 from the European Centre for Medium-Range Weather Forecasts (ECMWF, https://cds.climate.copernicus.eu/). The ERA5 provides near-surface meteorological variables at the hourly time step from the year 1979. Compared to the previous ECMWF products (e.g., ERA-Interim), the ERA5 has improved model parameters, finer spatiotemporal resolution, and higher data accuracy (Hoffmann et al., 2019; Hersbach et al., 2020). For this study, we used air temperature (T, °C), sea level pressure (P, Pa), wind speed (W, m s⁻¹), and specific humidity (Q, g kg⁻¹) at the 0.25° × 0.25° surface grids in China during 2017–2019. Previous studies have found that boundary layer height (BLH) is an important metric influencing surface PM_2.5 (Miao et al., 2018, Miao et al.,2019; Feng et al., 2021). However, we do not include this variable in the analyses because the BLH data are in general assimilated without enough coverage of observations and show large variations among different products (Seibert, 2000; Zang et al., 2017). We also used meteorological data from the Modern-Era Retrospective analysis for Research and Applications, Version 2 (MERRA-2, https://gmao.gsfc.nasa.gov/reanalysis/MERRA-2/) as a comparison. The hourly meteorology is averaged to the daily scale and interpolated to the SONET sites for the corresponding days. Furthermore, the gridded data are used to derive the favorable weather patterns for the PM_2.5-AOD associations.

Analyses showed that changes of PM_2.5 concentrations and AOD may have both consistent and inconsistent tendencies. To facilitate the comparisons between PM_2.5 and AOD variations, we normalized both variables using the Z-score method: Z = x − μ σ (1) where x is either PM_2.5 or AOD time series, µ is the mean value and σ is the standard deviation. We then define U index as their differences: U = Z p m 2.5 − Z A O D (2)

Here, Z_pm2.5 and Z_AOD are the normalized daily PM_2.5 concentrations and AOD, respectively. The positive U value indicates that PM_2.5 is higher than the level correspondent to AOD values, and vice verse. By calculating the correlation coefficients (R) between U index and individual meteorological variables, we identified the dominant meteorology regulating the PM_2.5-AOD associations.

We built Random Forest (RF) models to predict PM_2.5 concentrations based on daily AOD and meteorological variables. The RF consists of a large number of regression trees with random attribute selections in the training process of bootstrap aggregation (Zhao et al., 2020; Chen et al., 2021). The training subset is randomly sampled with put-back to get multiple sample sets, which are then randomly selected as alternative features for decision making under the current node. During this training process, the features that best drive the training samples are selected. After obtaining the desired decision trees, the best prediction results are obtained by voting method and majority outcome method. In summary, random forest is to find the most stable and reliable results by a large number of underlying tree models (Zamani Joharestani et al., 2019; Kianian et al., 2021; Sun et al., 2021). In this study, we used AOD as the basic input for RF models to predict PM_2.5 concentrations. Different combinations of meteorological variables (T, P, W, Q) are used as additional inputs for the RF models to improve the prediction of PM_2.5 concentrations. For each RF model, 50% of the data are used as training samples and the rest are used for validations.

PM_2.5 concentrations show high values of 60–80 µg m⁻³ over the North China Plain (Figure 1), where large anthropogenic emissions locate (Quan et al., 2011; Zhao et al., 2013). Outside this center, PM_2.5 decreases gradually to 0–40 µg m⁻³ in the periphery area. Some exceptionally high PM_2.5 sites are found in the West, where dust emissions affect the local air quality and PM_2.5 concentrations (Zhao et al., 2010; Nobakht et al., 2021). For 19 SONET sites, the highest PM_2.5 of 104.4 µg m⁻³ is found at Kashi and the lowest value of 12.2 µg m⁻³ is at Lhasa (Figure 2). For most sites, monthly PM_2.5 shows higher values in winter (December-February) season than that in summer (June-August). On average, the mean PM_2.5 level in the winter is higher by 39.08 µg m⁻³ (148%) than that in summer for SONET sites, with the highest ratio of 341% at Harbin and the lowest of 59.7% at Beijing. For most sites, PM_2.5 concentrations show decreasing trend, with the largest reduction of 22.07 µg m⁻³ (28.4%) at the site Lhasa in 2019 relative to 2017.

The seasonal variation of AOD shows decoupling tendencies with PM_2.5. For 17 out of 19 SONET sites, small R of 0.03–0.60 are achieved between the daily AOD and PM_2.5. The site Kashi shows the highest R but with AOD data available for only 7 months. About half of the sites show peak AOD in summer, opposite to the winter maximum of PM_2.5 concentrations. Such difference in the seasonality of AOD and PM_2.5 data in part contributes to the low PM_2.5-AOD associations. Some sites exhibit maximum AOD in spring (e.g., Guangzhou, Guilin, and Nanning) while PM_2.5 does not show corresponding peaks. For these sites, local AOD is likely enhanced by the cross-boundary transport of biomass burning aerosols from Southeast Asia during spring seasons (Tie et al., 2001; Martin et al., 2003; Deng et al., 2008). These transported aerosols are tend to float at the high altitudes and cause limited impacts on the surface PM_2.5 concentrations. Only three sites (Chengdu, Nanjing, and Xian) show peak AOD in winter, consistent with the seasonal variations of surface PM_2.5. However, the correlation coefficients between the daily AOD and PM_2.5 are only 0.24–0.5 at these sites. In general, we found a low association between the variations of AOD and PM_2.5 at the SONET sites.

We collected daily PM_2.5, AOD, and corresponding meteorological variables at SONET sites (Figure 3). For all data samples, a low R of 0.43 is achieved between PM_2.5 and AOD. We found a general ratio of 100 between the values of PM_2.5 concentrations and AOD. Accordingly, we divided the PM_2.5-AOD pairs into three domains with an angle interval of 30° against the x axis. Within domain I, the PM_2.5-AOD ratio of >500/3 is higher than the mean state of 100, suggesting that PM_2.5 is higher than the “normal” value associated with AOD. For domain III, the PM_2.5-AOD ratio of <300/5 is lower than 100, indicating a high AOD with relatively low PM_2.5. The rest of samples are located in domain II, which represents consistent levels for AOD and PM_2.5. Ideally, if the AOD and PM_2.5 are strongly connected, most of the samples should be within domain II with nearly linear responses. Actually, 23.2% of paired samples are located in domain I, 22.2% in domain III, and 54.6% in domain II, suggesting that changes of PM_2.5 and AOD are decoupled for half of the time.

We found strong impacts of meteorology on the association between PM_2.5 and AOD. Relatively lower air humidity (Figure 3A) and temperature (Figure 3C), but higher wind speed (Figure 3B) and air pressure (Figure 3D) are found for the paired samples in domain I (high PM_2.5 with low AOD) than that in domain III (high AOD with low PM_2.5). On average, specific humidity is lower by 9.06 g kg⁻¹ (76.2%, p < 0.05) and air temperature is lower by 16.7°C (p < 0.05) at the domain I than that at the domain III. In contrast, wind speed is higher by 0.06 m s⁻¹ (1.1%, p > 0.05) and sea level pressure is higher by 8.52 hPa (0.8%, p < 0.05) at the domain I than that at the domain III. The meteorological conditions for domain II are normally within the range of that for domain I and III. We found the most significant differences in air humidity and temperature for different domains, suggesting that these two meteorological factors may act as dominant roles in regulating the associations between PM_2.5 and AOD. For specific humidity (Figure 3A), the higher water content (usually in summer) can result in the larger AOD with strong hygroscopic growth, leading to faster increase of AOD even with low PM_2.5 (domain III). For temperature (Figure 3C), the cold air (usually in winter) is normally associated with low boundary layer height, increasing surface PM_2.5 by confining more particles in the low level (domain I).

We further identified the dominant weather patterns resulting in the decoupled variations between PM_2.5 and AOD. For each of three domains (Figure 3A), we screened the typical day on which the maximum occurrence of sites is present for the same domain. As a result, a winter day (22 December 2017) with 12 sites is selected for domain I, a spring day (10 March 2017) with 12 sites is selected for domain II, and a summer day (17 July 2017) with 7 sites is selected for domain III. We then calculated the deviation of those typical days from the annual mean state (Figure 4). In Winter, the dry (Figure 4A) and cold (Figure 4C) air associated with high pressure (Figure 4D) systems (such as the Mongolian High) increases atmospheric stability and promotes the accumulation of aerosol particles at the low levels. Such weather pattern is more favorable for haze pollution with high PM_2.5 concentrations (Shi et al., 2020; Zhang et al., 2022). In summer, the humid (Figure 4I) and warm (Figure 4K) air associated with low pressure (Figure 4L) systems promotes vertical convection and increases the hygroscopic growth of aerosols, leading to relatively low PM_2.5 concentrations near surface while high AOD of the whole column (domain III). In spring or autumn, the weather pattern provides medium levels of humidity (Figure 4E) and temperature (Figure 4G) that favor the coupling between AOD and PM_2.5 concentrations (domain II). Compared to other meteorological factors, surface wind shows limited differences among the three domains over most of China except for Northeastern region (Figures 4B,F,J).

To identify the dominant meteorological variable influencing the associations between PM_2.5 and AOD, we calculated the R between individual meteorological factors and the normalized PM_2.5-AOD differences (U index). For almost all SONET sites, negative R is achieved for specific humidity and air temperature when correlating with daily U index (Figure 5). In contrast, the R is generally positive between sea level pressure and U index. The impact of surface wind speed is limited, as the R values are usually within −0.2 to 0.3. Among the four meteorological factors, specific humidity acts as the dominant driver at 14 out of 19 sites with the largest R in magnitude. As a result, the anomalous levels of air humidity are more likely resulting in the decoupled variations for PM_2.5 and AOD.

We then explored the effects of meteorological variables on the prediction of surface PM_2.5 concentrations. Figure 6A shows that when only AOD is considered in the RF model, the prediction yields a very low R of 0.49 against the observed PM_2.5. In contrast, if all the four meteorological variables are fed into the model together with AOD, the R shows a significant improvement to the value of 0.81 (Figure 6B), suggesting that inclusion of more meteorological factors can better capture the associated changes in PM_2.5 and AOD. Sensitivity tests with single meteorological variables showed that the combination of AOD and specific humidity alone can improve the R from 0.49 to 0.74 (Figure 6C), very close to the effect with all four meteorological variables. As a comparison, RF models with other individual meteorological variables such as surface air temperature (Figure 6D), sea level pressure (Figure 6E), and wind speed (Figure 6F) result in lower R from 0.60 to 0.70. Our experiments suggest that meteorological conditions, especially the specific humidity, should be considered in the retrieval of surface PM_2.5 using the AOD data in China.