Estimation of secondary PM 2 . 5 in China and the United States using a multi-tracer approach

. PM 2 . 5 , generated via both direct emission and secondary formation, can have varying environmental impacts due to different physical and chemical properties of its components. However, traditional methods to quantify different PM 2 . 5 components are often based on online or ofﬂine observations and numerical models, which are generally high economic cost- or labor-intensive. In this study, we develop


Introduction
Fine particulate matter (PM 2.5 , with an aerodynamic diameter of less than 2.5 µm) can be categorized into primary and secondary PM 2.5 according to its formation processes. Primary PM 2.5 (PPM), including primary organic aerosol (POA), elemental carbon (EC), sea salt and mineral dust, is a direct emission product from the combustion of fossil or biomass fuel, dust blowing and sea spray. Secondary PM 2.5 (SPM) is mainly generated by the further oxidation of gaseous precursors emitted in anthropogenic and biogenic activities Wang et al., 2019). SPM consists of secondary organic aerosol (SOA) and secondary inorganic aerosol (SIA, including sulfate, nitrate and ammonium). The primary and secondary components of PM 2.5 have different environmental impacts on air quality, human health and climate change. For example, EC is a typical PPM that can severely reduce atmospheric visibility and greatly influence the weather and climate due to its strong absorption of solar radiation (Bond et al., 2013;IPCC, 2013;. Sulfate, a critical hygroscopic component of secondary PM 2.5 (SPM), can be rapidly formed in high relative humidity and further leads to grievous air pollution Guo et al., 2014;Quan et al., 2015). Furthermore, sulfate and other hygroscopic PM 2.5 exert considerable influences on climate change, mostly by changing cloud properties (Leng et al., 2013;von Schneidemesser et al., 2015). In addition, different PM 2.5 components also have various deleterious impacts on human health due to their toxicities Khan et al., 2016;Maji et al., 2018).
To understand the severe PM 2.5 pollution characteristics in China over the past several years Song et al., 2017;Yang et al., 2016), many observational studies have been conducted on PM 2.5 components. The basic methods used in such studies are offline laboratory analysis and online instrument measurements, such as those made using an aerosol mass spectrometer (AMS). Observational studies are crucial for exactly identifying aerosol chemical compositions. They represent the most widely used offline approach (Ming et al., 2017;Tang et al., 2017;Tao et al., 2017;Gao et al., 2018;Wang et al., 2018;Zhang et al., 2018;Xu et al., 2019;Yu et al., 2019), and have been successfully applied to investigate the interannual variations of different aerosol chemical species (Ding et al., 2019;. In terms of online approaches, the AMS is a state-of-the-art method for analyzing different chemical species with high time resolution, and has great application value for diagnosing the causes of haze events in China over the past decade (R. J. Huang et al., 2014;Quan et al., 2015;Guo et al., 2014;Yang et al., 2021;Gao et al., 2021;Hu et al., 2021;. Nevertheless, both online and offline measurements require high levels of manpower and are economically costly; for these reasons, these methods are expensive and rarely applied in large-scale regions or for long periods. A chemical transport model (CTM) is another useful tool to identify the composition characteristics of PM 2.5 . The simulation predicted by a CTM features high spatiotemporal resolution (Geng et al., 2021). Meanwhile, it also provides vertical profiles of diverse chemical species . However, the results of a CTM are largely dependent on external inputs such as emission inventories, boundary conditions, and initial conditions. The internal parameterizations of itself also significantly influence the final model results , which leads to uncertainty in the simulated PM 2.5 and its composition. In addition, the burden of their high computational cost and high storage requirement hinders the universal use of CTMs.
In this study, we develop a novel method, Multi-Tracer Estimation Algorithm (MTEA), with the aim of distinguishing the primary and secondary compositions of PM 2.5 from routine observation of the PM 2.5 concentration. Different from traditional CTMs, the MTEA proposed by this study is based on statistical assumption and works in a more convenient way. This algorithm and its application are tested in China and the United States. In Sect. 2, we introduce the structure and principle of MTEA. In Sect. 3, we evaluate the MTEA results, comparing three PM 2.5 composition datasets: (1) short-term measurements in 16 cities in China from 2012 to 2016, as reported in previous studies; (2) continuous longterm measurements in Beijing and Shanghai from 2014 to 2018; and (3) the IMPROVE network in the United States during 2014 and 2018. Additionally, we compare the MTEA model with one of the most advanced datasets from a CTM in China. Subsequently, in Sect. 4, we investigate the spatiotemporal characteristics of PPM and SPM concentrations in China, explain the unexpected haze events in several cities of China during the COVID-19 lockdown, and discuss the complicated correlation between PM and O 3 . This study differs from previous works as follows: (1) we develop an efficient approach to explore PPM and SPM with low economic or technique costs and a low computational burden, and (2) we apply this approach to observation data from the MEE (China Ministry of Ecology and Environment) network, offering an unprecedented opportunity to quantify the PM 2.5 components at large spatial and time scales.

Multi-Tracer Estimation Algorithm (MTEA)
In order to distinguish PPM and SPM efficiently from the observed PM 2.5 , we develop a new approach, named Multi-Tracer Estimation Algorithm (MTEA). The multi-tracer (denoted X) is defined as representing multiple primary contributions to PM 2.5 , which mainly results from incomplete combustion of carbonaceous material and flying dust. We select the typical combustion product CO as one tracer to represent the combustion process, and the particles in coarse mode (PM coarse , denoted PMC, where PMC = PM 10 − PM 2.5 ) as the other tracer to track flying dust. Then we combine the CO and PMC to generate the multi-tracer X (Eq. 1), which can represent hybrid primary contributions to PM 2.5 .
As shown in Eq.
(1), we use a and b to quantify the relative contributions of combustion and dust processes to the PPM. Given that a complicated process such as the combustion of multiple sources is hard to represent via current routine CO observations, we avoid considering the correlation among these sources but focus on the relative weights of the combustion process and flying dust. Meanwhile, the uncertainty resulting from the apportioning coefficients a and b will be further discussed in Sect. 4.5. The values of these coefficients depend on the ratio of the emission intensities of POA + EC (combustion products) and fine-mode dust, as shown below:  (Seinfeld and Pandis, 2006), and we quantify sulfate and nitrate emissions by multiplying the PM 2.5 emission by an investigative coefficient of 0.1 (Zhang, 2019). However, this investigative coefficient for quantifying primary sulfate and nitrate emissions may be relatively high compared to empirical coefficients (0.01-0.05) used in previous simulation studies. We evaluated the potential effect of the coefficient by conducting a set of comparative simulations with a coefficient of 0.03 and found that the final estimated SPM was not sensitive to this coefficient (Table S1 in the Supplement). Thus, we concluded that the uncertainty of primary sulfate and nitrate emissions did not significantly influence the final estimation of the MTEA model. Other uncertainties of X that are dependent on emission intensities or tracer concentrations are discussed later, in Sect. 4.5. The aim of including coefficient b is to reflect the activity intensity of fine-mode dust by counting the emissions of this dust. However, the MEIC does not directly provide fine-mode dust emissions. It is included in the emissions of total PM 2.5 (M. Li et al., 2017a). Thus, we inferred the fine-mode dust emission by deducting the emis-sions of EC, POA, sulfate and nitrate from the PM 2.5 emissions. Based on Eq.
(2), we establish a dynamic a and b value database that reflects the specific changes in PM 2.5 sources among years, seasons, hours and regions. With the help of the multi-tracer X, we can describe secondary PM 2.5 as follows: Here, PM 2.5 is the observed PM 2.5 concentration, and the multi-tracer X can be calculated from the observed CO, PM 2.5 and PM 10 concentrations. The original concentrations of CO, PM 2.5 and PM 10 are normalized to avoid any influence of their initial levels. To calculate the SPM, the key step is to find the target ratio of PPM/X. In the MTEA method, we give the PPM/X ratio a reasonable range (0-400 is used in this work) and then scan the ratio with an interval of 1. For more precise results, a smaller scanning step can be applied, although this may lead to a larger calculation cost. As a result, each varying ratio may give a series of SPM, along with a coefficient of determination (R 2 ) between SPM and X ( Fig. S1 in the Supplement). If we assume that the PPM and SPM came from different sources or processes, then the appropriate PPM/X ratio should be the one that corresponds to weak correlation between SPM and the tracer X. To aid understanding of the principle of the MTEA approach, we show a flow chart in Fig. 1. We also provide the MTEA software package and input datasets at http: //nuistairquality.com/m_tea (last access: 1 August 2021). The MTEA approach makes some improvements by using a similar principle and similar assumptions to the modified EC-tracer method developed by Hu et al. (2012). They estimated primary and secondary organic carbon (denoted POC and SOC) concentrations by adopting a POC/EC ratio when SOC was least strongly correlated with EC. However, this assumption may be too hard to achieve in the real atmosphere. Therefore, in the MTEA approach, we take a range of proper ratios of PPM/X when SPM correlates with the tracer X nonsignificantly (with a p-value greater than 0.05). As a result, the calculated SPM concentration for each case is a range ( Table S2 in the Supplement). We employ the concentration ranges to represent the severity of secondary pollution and discuss its uncertainties in the following discussions. For quantitative calculations, the mean values of the concentration ranges are used for the final estimation.  (Table S3 in the Supplement). Except for Guyuan, the mean PM 2.5 concentration in each regional background city is less than 35.0 µg m −3 (Chinese National Ambient Air Quality Standard level II, NAAQS), indicating that they are only slightly impacted by anthropogenic activities. By comparing the populous cities with the regional background cities, we can reveal the discrepancy in PPM and SPM between regions that suffer from different levels of PM 2.5 pollution. The geographical distribution of these populous and regional background cities is shown in Fig. 2a.

PM
Recently, the Chinese government carried out a series of control policies, such as the elimination of backward industry, desulfurization and denitration of flue gas, as well as restrictions on motor vehicles Wu et al., 2017). Consequently, the concentrations of the major gaseous and particle pollutants have been decreasing year by year Shen et al., 2020). Taking PM 2.5 as an example, previous studies revealed that the annual mean PM 2.5 decreased by 30 %-50 % across China during the period of 2013-2018.

PM 2.5 composition measurements in China
Numerous studies focusing on the aerosol chemical composition in China have employed offline filter-based observations coupled with laboratory analysis to obtain detailed information on PM 2.5 compositions. To directly compare the estimated with the measured PPM or SPM in China, we per-formed an evaluation based on two long-term time series of in situ measurements taken in Beijing (Peking University, PKU) and Shanghai (Shanghai Academy of Environmental Sciences, SAES) during 2014-2018 Tan et al., 2018). The chemical composition measurements included ions (NH + 4 , Na + , K + Mg 2+ , Ca 2+ , SO 2− 4 , NO − 3 and Cl − , measured by ion chromatography), elements (Al, Si, Ti, Ca, Ti, Mn, etc., measured by X-ray fluorescence spectrometry) and carbonaceous components (EC and organic carbon, measured using a thermal-optical transmittance carbon analyzer). After accessing the chemical compositions, we categorized them into PPM and SPM for further evaluation. Specifically, SOA was roughly identified from organic matter (OM) by the EC-tracer model . SPM concentrations were calculated by summing the SO 2− 4 , NO − 3 , NH + 4 and SOA concentrations. Then PPM was calculated by deducting SPM from PM 2.5 . In addition, we investigated observation-based analyses of PM 2.5 components in 16 cities in China during 2012-2016 from 32 published studies. This survey offered an opportunity to compare the estimations from MTEA with past measurements of the secondary fraction of PM 2.5 . SOA concentrations in the literature were roughly estimated by multiplying the OM by 0.5 because of limited access to the source data. Meanwhile, it should be noted that the factor that can convert OC (organic carbon) to OM is dependent on the definitions used in a specific observation study.

PM 2.5 composition measurements from the IMPROVE network in the United States
The Interagency Monitoring of Protected Visual Environments (IMPROVE) aerosol network has continuous records of PM 10 and PM 2.5 and PM 2.5 chemical speciation in the United States since 1987. The specific aerosol chemical compositions include ammonium sulfate, ammonium nitrate, organic carbon, EC, soil dust and mineral dust. The catego-   (Geng et al., 2021(Geng et al., , 2017. The TAP reanalysis dataset is originally based on CMAQ (Community Multiscale Air Quality) simulation and is further assimilated by ground measurements, satellite remote sensing retrievals and emission inventories with the aid of machine learning algorithm. We collected the monthly mean concentrations of aerosol species during 2014-2018 from TAP, including SO 2− 4 , NO − 3 , NH + 4 , OM, BC (black carbon) and total PM 2.5 . SOA was further calculated from OM by the EC-tracer model . SPM concentrations were inferred by summing SO 2− 4 , NO − 3 , NH + 4 and SOA. PPM concentrations were then obtained by deducting SPM from PM 2.5 .

Comparison with continuous long-term measurements in Beijing and Shanghai
We compared the MTEA results with the two sets of longterm in situ measurements in Beijing and Shanghai, China, and the evaluations are shown in Fig. 3. Reduced major axis (RMA) regression was applied to fit the data. Given the discrepancy in PM 2.5 concentrations between the in situ measurements at a single site and multiple MEE national sites, we first preprocessed the data for further evaluation. In data preprocessing, we removed the in situ daily measurements with values that were over 30 µg m −3 higher than the city average (from MEE). Comparisons between the estimated and observed PPM in the two cities are given in Fig. 3a and c. The correlation coefficient r for predicted PPM versus observed PPM is 0.85 for Beijing and 0.87 for Shanghai. The slope of the regression is 1.29 for Beijing and 0.73 for Shanghai, which indicates an overestimation (NMB = 32 %) and underestimation (NMB = −9 %) for these two cities, respectively. For SPM, the regression line for Shanghai is quite close to the 1 : 1 ratio line (s = 1.13, d = −2.3), and its statistical correlation is up to 0.89. The estimated SPM in Beijing also shows a high correlation with the observed SPM, with its r value exceeding 0.80, though the fitting formula indicates an underestimation of 27 %. These discrepancies can be explained by the fact that the observations of primary emission tracers and PM 2.5 are obtained from different sites. Specifically, the CO and PMC observations are obtained from 12 monitoring MEE sites in Beijing, while the PM 2.5 component measurements are from a single spot at PKU that is away from crowded streets (Tan et al., 2018). The MTEA predictions based on the data from MEE sites located in districts with high emission densities may lead to considerable overestimation of PPM concentrations.
Overall, the MTEA model performed satisfactorily in the comparison with long-term in situ measurements in Beijing and Shanghai. Nearly all the points in the plots are located at the range between the ratios 2 : 1 and 1 : 2. It is believed that our model is able to capture the magnitudes and variations of PPM and SPM. The estimated and the observed interannual variations in PPM and SPM are further compared in Sect. 4.2.2.

Comparison with various short-term measurements
To evaluate the reliability of the MTEA approach, we also conducted a  Ming et al., 2017;Niu et al., 2016;Tan et al., 2016;Tang et al., 2017;Tao et al., 2017Tao et al., , 2015Tian et al., 2015;Wang et al., 2018;Wu et al., 2016;Xu et al., 2019;Yu et al., 2019;Zhang et al., , 2018Zhao et al., 2015). Most field measurements focused on regions in eastern China and on episodes during the winter. We list the observed concentrations of PM 2.5 , SO 2− 4 , NO − 3 , NH + 4 and SOA from these studies in Table S4 in the Supplement. It should be noted that there may be inconsistencies between the observations due to differences in sampling locations, observation times and analytical instruments between studies.
The estimated PPM and SPM from MTEA show reasonable agreement with the observation-based PM 2.5 component analyses in China. The MTEA-estimated secondary proportions of PM 2.5 (i.e., secondary PM 2.5 / total PM 2.5 ) vary in the range of 41 % to 67 % and are higher in eastern cities in China, consistent with the observational results. However, we find that there are still a few discrepancies between the estimated and observation-based results. For example, we overestimated the secondary proportions of PM 2.5 in cities such as Haikou, Lanzhou and Lhasa. Though all of these show considerable overestimations of over 20 %, the cause of this bias may be quite different for each city. In the coastal city of Haikou, we may attribute this discrepancy between MTEA and observations to the neglect of the contribution of sea salt aerosols. Offline PM 2.5 measurements in 2015 showed that the contribution of sea salt aerosols to the ambient PM 2.5 mass concentration in Haikou is 3.6 %-8.3 % . Secondly, the overestimation phenomenon in Lanzhou, which is a typical inland city located in northwestern China, can be explained by the neglect of the contribution of natural dust to PM 2.5 speciation. Generally, both sea salt and natural dust are categorized as non-anthropogenic processes, and are not accounted for by the anthropogenic emission inventory, resulting in an underestimation of the primary process intensity. Finally, for Lhasa, the observation-based results are derived from too few samplers, leading to a controversial comparison with the MTEA model.

Comparison with the CTM simulation
In addition to evaluating our model via PPM and SPM measurements in China, we also provide a comparison between MTEA estimation and CTM simulation for 31 populous cities based on monthly mean PM concentrations. As shown in Fig. 4a-b, the correlation coefficient r for TAP versus MTEA is 0.86 in terms of PPM concentration and 0.91 in terms of SPM concentration, showing a strongly positive correlation between the two models. At the same time, both the slopes (1.26 and 0.89) and intercepts (−3.7 and 1.9 µg m −3 ) of the regressions about PPM and SPM illustrate that most of the scattered points are distributed around the 1 : 1 ratio line.
Moreover, we further compared MTEA and TAP in terms of the long-term trends in the PPM and SPM concentrations averaged across 31 populous cities (Fig. 4c-d). Both MTEA and TAP exhibit descending interannual trends in the PPM concentration, with rates of −2.0 and −1.9 µg m −3 yr −1 for MTEA and TAP, respectively. For the SPM concentration, the rates of decline are −2.9 and −2.8 µg m −3 yr −1 , respectively. Meanwhile, the statistical correlations between the two interannual variations are 0.98 (PPM) and 0.99 (SPM), which are both quite close to 1, showing good agreement.
Thus, comparisons of the PPM and SPM concentration magnitudes and interannual variations between the two kinds of models suggest that our statistical model can infer similar estimations to those given by a traditional CTM. Meanwhile, they again highlight that our model is capable of capturing reasonable PPM and SPM concentrations. Furthermore, they also show that MTEA can track primary and secondary components of PM 2.5 using a proxy at a much lower cost when compared to traditional air quality model simulations.

Evaluation in the United States
Based on the chemical component measurements of the IMPROVE network, we evaluated the performance of the MTEA model for the United States. Figure 5 presents scatter plots of the evaluation results, with the x axis indicating the observed concentrations and the y axis indicating the estimated concentrations. Temporal, spatial and spatiotemporal validations were performed. Each dot represents a monthly mean observed or estimated PM concentration.
Almost all of the dots are located in the region between the 2 : 1 and 1 : 2 dashed lines, indicating that our model is capable of predicting the magnitudes of PPM and SPM in the United States. Based on correlation analysis, we find that the correlation coefficient r for PPM ranges from 0.69 (spatiotemporal validation) to 0.75 (temporal validation), while r reaches up to 0.98 (temporal validation) for SPM. The results reveal that the MTEA approach successfully captured the spatial and temporal variations of PPM and SPM in the United States.
The majority of the dots are distributed around the 1 : 1 dashed line. Based on the fitting results, the slopes for the regression lines vary from 1.12 (spatial validation) to 1.15 (temporal validation) for PPM and from 0.92 (temporal validation) to 0.93 (spatiotemporal validation) for SPM. In general, PPM and SPM show slight overestimation and underestimation, respectively. These discrepancies may result from the influences of the emission inventory. It is reported that emissions of PMC and CO in the United States continuously declined over the past decade (https://www.statista.com/statistics/501298/ volume-of-particulate-matter-2-5-emissions-us/, last access: 2 October 2021). Thus, the coefficients a and b derived from the HTAP global emission inventory in 2010 overestimate the contribution of primary emissions during the study period. However, these emissions inevitably have an impact, and we will discuss the uncertainty of the emission inventory  in Sect. 4.5. In addition, the intercepts of the regression lines for both PPM and SPM are less than ±0.1 µg m −3 . The verification results strongly show that our model can reasonably reproduce the monthly averaged concentrations of PPM and SPM in the United States.

Results and discussion
We used the MTEA approach and the MEE observation data to estimate PPM and SPM concentrations in China for the period of 2014-2018. Observations during severe haze events (the top 10 % of days for CO and PMC pollution) were excluded to avoid the influence of unfavorable meteorological conditions and extremely high primary emission cases. Unfavorable meteorological conditions are major causes of haze events. Under these unfavored meteorological conditions, PPM may have a considerably collinear relationship with total PM 2.5 . The concentration of SPM from complicated formation pathways is then underestimated. Therefore, we excluded these polluted days to focus more attention on the general characteristics of the PPM and SPM concentrations. Figure 6 shows spatial patterns of the MTEA-estimated PPM and SPM concentrations over China averaged for the period of 2014-2018. Sixteen populous cities and nine regional background cities in the north, and 15 populous cities and 10 regional background cities in the south (the north and south are separated by the Qinling-Huaihe line) are involved in the following discussions.

Spatial distribution
In populous cities, the concentrations of both PPM and SPM in the north (the 5-year average is 21.5 for PPM and 26.6 µg m −3 for SPM) are 15 %-43 % higher than those in the south (the 5-year average is 15.0 for PPM and 23.2 µg m −3 for SPM). The north-south difference is mainly caused by the higher energy consumption and consequent stronger pollutant emission in northern populous regions. Nevertheless, in background regions, the difference is relatively small for SPM. The SPM in the south (12.5 µg m −3 ) is only 1 % higher than that in the north (12.4 µg m −3 ).
In terms of the secondary proportion of PM 2.5 , the MTEA approach speculates that it is higher in southern regions (63.5 %) than in northern regions (57.1 %). This result confirms the fact that the atmospheric conditions in the south are more favorable for secondary pollutant formation than those in the north. In addition, the MTEA approach captures the difference in the secondary proportion of PM 2.5 between populous and regional background cities reasonably well. As shown in Fig. 6e and f, the secondary proportion of PM 2.5 in regional background cities is 19 % higher than that in populous cities, consistent with recent observational studies (Z. . Secondary aerosols can affect a larger area than primary aerosols, mostly due to the diffusion of their gaseous precursors. Thus, for regional background cities, the role of secondary PM 2.5 tends to be more important, mainly due to the secondary pollutants transmitted from surrounding populous regions.

Seasonal variation
We compare seasonal mean concentrations of the MTEAestimated PPM and SPM in 31 populous cities and 19 regional background cities in Table 1. The concentrations of both PPM and SPM are the highest in winter, with a seasonal mean concentration of 16.6 for PPM and 24.9 µg m −3 for SPM across China. This phenomenon can be mainly explained by adverse diffusion conditions, such as a low boundary layer height and strong temperature inversion (Zhao et al., 2013), as well as fossil-fuel and biofuel usage for winter home heating (Zhang et al., 2009;. Summer is the least polluted season of the year, with a seasonal mean PPM of 10.2 µg m −3 and SPM of 15.8 µg m −3 nationwide, largely due to the benefits of a higher boundary layer (Guo et al., 2019) and abundant precipitation.
We also compared the secondary proportions of PM 2.5 in different seasons and in the 50 Chinese cities considered in this work (Table 1). The MTEA approach estimates that the secondary proportion tends to be lowest in fall, with a seasonal mean value of 56.1 % nationwide, while the seasonal proportions stay at around 61 % for the other three seasons. At the same time, the seasonality of the secondary proportion varies among regions. In the north of China, the secondary proportions are higher in spring and summer, which is attributed to the stronger atmospheric oxidizing capacity (AOC) in the warmer seasons. But, in the south of China, the highest secondary proportions occur in winter, which is mainly explained by the tremendous amounts of pollutants (secondary particles and their gaseous precursors) transported from northern China in the presence of the monsoon. Figure 7 illustrates the interannual variations of the estimated PPM and SPM based on MTEA in the 31 populous cities and 19 regional background cities of China. We analyzed the MEE observational data during 2014-2018 but excluded the data for 2014 in the regional background regions due to data deficiencies for several cities.

Interannual variation
The observed PM 2.5 concentrations in populous cities have continuously and significantly reduced since 2014, largely due to a series of emission control measures led by the governments, such as the Action Plan on Prevention and Control of Air Pollution (Chinese State Council, 2013). Using the MTEA approach, we find that both PPM and SPM decreased simultaneously at annual rates of decrease of 1.9 and 2.7 µg m −3 yr −1 , respectively.   secondary proportion of PM 2.5 remains relatively constant (56.4 %-58.5 %), but it presents a consistent increasing trend (from 58.5 % to 59.2 %) in summer during the study period, which can be attributed to the continuing worsening O 3 pollution (Tang et al., 2022). However, for regional background cities, the MTEA approach reports different features of the PM 2.5 mitigation. The estimated SPM is considerably reduced by 1.1 µg m −3 yr −1 in regional background cities, while the PPM remains nearly unchanged (the rate of decrease is 0.2 µg m −3 yr −1 ). This is because the SPM in regional background cities is largely contributed by pollutant transport from surrounding populous regions, where the air quality is getting better as a result of the aforementioned emission controls. However, the PPM mostly derives from local sources and is rarely affected by those emission controls, which mostly focus on densely populated and industrialized cities, not on background regions. We investigated the interannual variations of PPM and SPM concentrations on the basis of long-term in situ observations in Beijing and Shanghai as well. As Fig. 8 shows, long-term measurements demonstrate a decline in the total PM 2.5 by 4.0 µg m −3 yr −1 in Beijing (1.6 for PPM and 2.4 µg m −3 yr −1 for SPM) and by 3.9 µg m −3 yr −1 in Shanghai (1.7 for PM and 2.2 µg m −3 yr −1 for SPM). The observed secondary proportion of PM 2.5 shows a slight decrease of −0.4 % yr −1 in Beijing but a small increase of 0.8 % yr −1 in Shanghai. Applying the MTEA model to this case, we are delighted to find that our model not only successfully reproduces the consistent decreasing trends in PPM and SPM in Beijing and Shanghai (the correlation coefficient r of observation versus estimation ranges from 0.83 to 0.89), but it also captures the different trends in the secondary proportion of PM 2.5 in the two cities (−0.6 % yr −1 in Beijing and 0.3 % yr −1 in Shanghai).

Application during the COVID-19 lockdown
To curb the spread of the novel coronavirus disease 2019  pandemic, China conducted the first entire city lockdown in Wuhan, Hubei on 23 January 2020. Other provinces also gradually implemented this restriction in the following three weeks (Le et al., 2020). The lockdown greatly limited traffic and outdoor activities, which directly reduced the emissions of primary pollutants (Huang et al., 2020). By analyzing the MEE monitoring data obtained before (1-23 January 2020) and during (24 January to 17 February 2020) the nationwide lockdown ( Fig. 9 and Fig. S2 in the Supplement), we show that the national mean NO 2 , PM 2.5 and CO concentrations were decreased by 56 %, 30 % and 24 %, respectively, while O 3 showed an increase (of 34 %) in general, which would have efficiently promoted the AOC. However, the surface monitoring network still observed unexpected PM 2.5 pollution in cities over the Beijing-Tianjin-Hebei (BTH) region during the lockdown. Especially in Beijing, the mean PM 2.5 concentration was increased by ∼ 100 % compared to its average value (41 µg m −3 ) before the nationwide lockdown.
Exploring this unexpected air pollution, we find that the enhanced secondary pollution could be the major factor; this even offset the reduction of primary emissions in the BTH region during the lockdown. With the help of MTEA, we tracked variations of the secondary proportion of PM 2.5  in East China before and during the COVID-19 lockdown (Fig. 9d-f). The specific emission reductions owing to the national lockdown were derived from Huang et al. (2020). Based on bottom-up dynamic estimation, provincial emissions of CO, NO x , SO 2 , VOC, PM 2.5 , BC and OC decreased by 13 %-41 %, 29 %-57 %, 15 %-42 %, 28 %-46 %, 9 %-34 %, 13 %-54 % and 3 %-42 %, respectively, during the lockdown period. The secondary proportions in the BTH region show evident increases of 7 %-34 %, which highlight the importance of secondary formation during the lockdown. Our result is consistent with recent observation and simulation studies (Chang et al., 2020;Huang et al., 2020;Le et al., 2020) that suggested that the reduced NO 2 resulted in O 3 enhancement, further increasing the AOC and facilitating secondary aerosol formation. In addition, another cause of the air pollution was the unfavorable atmospheric diffusion conditions. CO, a nonreactive pollutant, was increased by 22 % in Beijing during the lockdown, even given the considerable reduction in its emission.
For other regions of China, the MTEA approach suggests that the secondary proportion of PM 2.5 increased by 20 % over the Yangtze River Delta (YRD) region but decreased by 32 % over Central China. Although O 3 and AOC enhanced in all these regions, the unprecedented reductions in precursors ultimately resulted in a net drop in secondary pollution.

Correlation analysis with O 3
PM 2.5 and O 3 are closely correlated with each other. One reason for this is that PM 2.5 and O 3 have similar precursors, i.e., NO x and VOCs. Besides, PM 2.5 can impact O 3 formation by adjusting the radiation balance  and affecting the radical level via aerosol chemistry . There is therefore a complicated interaction between PM 2.5 and O 3 . Our study utilized the MTEA approach to explore the relationship between PM and O 3 from the perspective of exploring the statistical correlation. Figure S3 in the Supplement illustrates the hourly correlations between the estimated SPM and the observed O 3 averaged for 31 populous cities in China (cities that failed to pass the significance test were excluded) in summer. In general, SPM and O 3 show a positive relationship nationwide, especially during the afternoon (during 14:00-18:00, r is up to 0.56). This phenomenon might be explained by noting that the production of O 3 and that of SPM are simultaneously affected by AOC; thus, a higher correlation tends to occur when the AOC is stronger. Moreover, the hourly correlations between SPM and O 3 are higher than those between PPM and O 3 throughout the day, suggesting that secondary oxidation processes may be captured well by the MTEA method.
A series of recent studies have focused on the correlation between PM 2.5 and O 3 , and many of them have agreed that the correlation varies greatly among different regions of China. Specifically, the statistical correlation is more positive in southern cities compared to northern cities (Chu et al., 2020). Because of this significant difference, a question arises: is the difference mostly caused by PPM, by SPM, or by both of them? To address this question, we compared the correlations of daily PPM, SPM and total PM 2.5 with O 3 in the Beijing-Tianjin-Hebei (BTH) and the Yangtze River Delta (YRD) regions during the study period with the help of the MTEA approach. The O 3 diurnal formation regime can be destroyed because of the suppressed radiative condition under precipitation. The local O 3 concentration level is mainly dominated by background fields. Here, we would like to focus our attention on the secondary formation relationship between daily PM 2.5 and O 3 . Therefore, the cases during which precipitation took place were removed to avoid the cleaning impacts of wet deposition on MDA8 (maximum daily 8 h average) O 3 concentrations. Precipitation data were based on the ERA5 reanalysis database from the European Centre for Medium-Range Weather Forecasts (ECMWF, https://www.ecmwf.int/, last access: 1 August 2021).
As shown in Fig. 10, the correlations between total PM 2.5 and O 3 are positive and stronger in YRD (r = 0.14) than in BTH (r = 0.09). However, compared with total PM 2.5 , the correlations between SPM and O 3 are much stronger (r = 0.21-0.24) and show minor regional differences. The correlation of PPM with O 3 is not significant (p-value >0.05) in either region. The correlation between SPM and O 3 is higher mostly because both of them are secondary oxidation products. A higher ambient O 3 concentration indicates a stronger AOC, which leads to more SPM generation. However, for PPM, its effect on O 3 is mainly to inhibit the production of O 3 by adjusting the radiation balance and affecting the radical level. Hence, we suggest that the regional differences in the correlation between total PM 2.5 and O 3 are mainly caused by the different PPM levels in the BTH and YRD regions.

Uncertainties
Based on the previous evaluation and discussions, we believe that MTEA can successfully capture the magnitudes and spatiotemporal variations of PPM and SPM in China. However, there are still some uncertainties in the model estimation and its application in China.
Firstly, the assumption of nonsignificant correlation between PPM and SPM may be violated by the fact that SO 2 and NO x emitted from combustion will further generate secondary sulfate and nitrate particulates. Nevertheless, the combustion processes for generating SO 2 and NO x and PPM are still different. PPM, i.e., BC and POC, mainly comes from incomplete combustion in residential activities, such as burning biofuels and coal (Long et al., 2013), but SO 2 and NO x mainly come from the complete combustion of industrial and transportation sources, such as coal, gasoline and diesel (Lu et al., 2011;M. Li et al., 2017a;Tang et al., 2019). In addition, the MTEA approach uses the assumption of non- significant correlation rather than irrelevance. Such processing also reduces the uncertainty to a certain extent.
Secondly, natural sources of PPM, such as fine dust from desert and sea salt, are not taken into account in the MTEA approach. As a result, the PPM in a city near a desert or sea could be underestimated. For example, the PM 2.5 component observational campaign conducted in 2015 showed that the contribution of sea salt aerosols to the ambient PM 2.5 mass concentration in Haikou is 3.6 %-8.3 % .
Thirdly, current bottom-up emission inventories are generally outdated, with a time lag of at least 1-2 years, mainly due to a lack of timely and accurate statistics. Consequently, a corresponding uncertainty in MTEA estimation is inevitable. To evaluate the uncertainty, a comparison test was conducted by adjusting the apportioning coefficients (a and b in Eq. 1) with a disturbance of ±0.1. Firstly, we decreased the value of a in each populous city by 0.1. Meanwhile, the coefficient b was increased by 0.1. This scenario indicates an overestimation of the contribution of combustion-related processes to the primary PM 2.5 or an underestimation of the contribution of dust-related processes. Secondly, we increased the value of a in each populous city by 0.1 (and decreased b by 0.1) to check the opposite case. The results are presented in Table S5 in the Supplement, and they point out that the estimated secondary proportions of PM 2.5 varied by less than ±3 % in the most populous cities due to the changes in the apportioning coefficients. This sensitivity experiment highlights that the apportioning coefficients, which depend on the emissions, have a limited impact on the final estimation results. Generally, the uncertainty of the apportioning coefficients is one of two factors that directly affect the tracer X. The other one is the concentrations of CO and PMC themselves. Hence, we also conducted a similar test to check the impacts of tracer X on the model estimation by changing the tracer concentrations mentioned in Eq. (1). Specifically, we (1) increased the CO concentration by 10 % and decreased the PMC concentration by 10 % and (2) decreased the CO concentration by 10 % and increased the PMC concentration by 10 %. Both sets of adjustments yield changes of within ±2 % in the estimated secondary proportions of PM 2.5 in all cities except for Urumqi (Table S6 in the Supplement). This phenomenon from the perspective of tracer concentration also supports the idea that the impact of the tracer X on the final model results is limited. In summary, we believe that the factor that is most determinative of the final results of our model is the principle of minimum correlation between PPM and SPM, not the tracer X, which relies on emissions or concentrations.

Conclusions
In this study, we developed a new approach, MTEA, to distinguish the primary and secondary compositions of PM 2.5 efficiently from routine observation of the PM 2.5 concentration with a much lower computation cost than traditional CTMs. By comparing MTEA results with long-term and short-term measurements of aerosol chemical components in China as well as an aerosol composition network in the United States, we showed that MTEA was able to capture variations of PPM and SPM concentrations. Meanwhile, our model showed great agreement with the reanalysis dataset from one of the most advanced CTMs in China as well.
The method was then applied to the surface air pollutant concentrations from the MEE observation network in China, and was found to offer an effective way to understand the characteristics of PPM and SPM across a wide area. In terms of the spatial pattern, MTEA reveals that SPM accounts for 63.5 % of the total PM 2.5 in southern cities averaged for 2014-2018, while the proportion drops to 57.1 % in the north. It should be noted that the secondary proportion in regional background regions is ∼ 19 % higher than that in populous regions. In terms of seasonality, the estimated national averaged secondary proportion is the lowest in fall (56.1 %), and remains around 61 % during the other three seasons.
Moreover, we applied MTEA to explore the changes in the secondary proportion of PM 2.5 in China. In recent years, the PM 2.5 pollution in China has been significantly alleviated, mainly due to a series of emission control measures. The MTEA results suggest that both PPM and SPM decreased simultaneously in populous regions, while for regional background regions, the reduction in secondary PM 2.5 was much more notable than that in the PPM. The secondary proportion of PM 2.5 in populous cities during 2014-2018 remained constant (56.4 %-58.5 %) in general on an annual average scale, but it showed a slight but consistent increase in summer, mostly due to the elevated O 3 and stronger photochemical pollution in China. In addition, with the help of MTEA, we found that the secondary PM 2.5 proportion in Beijing significantly increased (by 34 %) during the COVID-19 lockdown, which might be the main reason for the observed unexpected PM pollution in this special period.
Finally, we applied MTEA to explore the synergistic correlation between PM 2.5 and O 3 . Estimated results demonstrate that PPM is weakly correlated with O 3 ; its effect on O 3 is mainly to inhibit the production of O 3 by adjusting the radiation balance and affecting the radical level. SPM is positively correlated with O 3 in the presence of the effect of AOC. A higher ambient O 3 concentration indicates a stronger AOC, leading to more SPM generation. We suggest that regional differences in the correlation between total PM 2.5 and O 3 are mainly caused by the different PPM levels in the BTH and YRD regions.
We also discussed the uncertainties of the MTEA method. MTEA may overestimate the secondary fractions of PM 2.5 in regions near to the desert or sea by ∼ 20 %, as it fails to take natural dust into consideration. In addition, a sensitivity experiment in which a reasonable disturbance of emissions and tracer concentrations was imposed also showed that such a disturbance has limited impacts on the final estimation. Overall, the factor that is most determinative of our model estimate is the principle of minimum correlation between PPM and SPM.
China has been plagued by PM 2.5 pollution in recent years. Different PM 2.5 compositions may have different impacts on the environment, climate and health, due to their different sources and generation pathways. Therefore, it is of great importance to quantify PPM and SPM for pollution recognition and prevention. The methods that are used to quantify different PM 2.5 components are often based on either lab analysis of offline filter samplings or online observation instruments such as AMS. However, these methods are often labor intensive, highly technical and have a high economic cost. CTM is another useful tool to reveal the composition characteristics of PM 2.5 . However, traditional CTMs also have high hardware requirements. Our study has developed an efficient, lower-cost approach based on a statistical principle to explore PPM and SPM, and applying this approach to large-scale observation networks, such as the MEE network, can offer an unprecedented opportunity to quantify the PM 2.5 components at large spatial and time scales.
Code and data availability. The MTEA software package and input datasets are available at http://nuistairquality.com/m_tea . Observational datasets and modeling results described in the text are available upon request from the corresponding author (linan@nuist.edu.cn).
Author contributions. NL designed this study. NL and HL supervised this work. HZ and KT established, performed and improved the MTEA model. HZ and NL interpreted the data and wrote the original draft. CH, HW, SG and MH provided the long-term measurements of aerosol compositions. HL, CS, JH, XG, MC, ZL and HY provided useful comments on the paper, and all authors contributed to the revision of the manuscript.
Competing interests. The contact author has declared that neither they nor their co-authors have any competing interests.
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Acknowledgements. The numerical calculations reported in this paper were done on the supercomputing system in the Supercomputing Center of Nanjing University of Information Science & Technology. Review statement. This paper was edited by Ivan Kourtchev and reviewed by four anonymous referees.