1 Introduction

Secondary organic aerosols (SOA) are an important component of ambient submicron aerosols, which account for a substantial fraction of organic aerosols in urban atmospheres (Weber et al. 2007; Zhang et al. 2007; Tsimpidi et al. 2010; Hayes et al. 2015). Compared to primary organic aerosols (POA) that are emitted into the atmosphere directly in the particulate phase, SOA are formed in the atmosphere from the gas-to-particle partitioning of multi-generational oxidation products of gas-phase hydrocarbons. For example, biogenic or anthropogenic nonmethane volatile organic compounds (NMVOCs) can be oxidized by atmospheric oxidants such as hydroxyl radicals, ozone, and nitrate radicals to form SOA in situ by condensation of low vapor pressure products of the oxidation of NMVOCs onto preexisting particles (Claeys et al. 2004; Ye et al. 2016). The chemical composition, sources, and formation mechanism of SOA have attracted increasing attention due to the potential impacts of SOA on human health and radiative climate forcing (Chung and Seinfeld 2002; Pöschl et al. 2005). Based on Aerosol Mass Spectrometer measurements, it has been reported that biomass burning can lead to substantial SOA formation in areas such as Mexico city (Salcedo et al. 2006) and Xianghe, a suburban site near Beijing (Sun et al. 2016), while biogenic emission was the main source of SOA precursors in areas such as the southeastern United States, leading to abundant SOA formed in the atmosphere especially in summer (Liu et al. 2017; Zhang et al. 2018a). Besides, based on the vertical measurement of oxygenated organic aerosols, it was found that the SOA concentration at 260m altitude was higher than that at the ground level in urban Beijing (Sun et al. 2015), indicating the intensified formation of SOA at elevated altitude as well as potential regional transport of SOA.

Chemical transport models have been widely used to investigate the formation, chemical evolution and removal processes of atmospheric pollutants in regional scale. Two methods have been commonly used for SOA simulation, i.e., the two-product approach that is primarily based on gas-particle partition and parameterization of two oxidation products of different volatilities (Pankow, 1994a, b; Odum et al. 1996), and the volatility basis set (VBS) approach that accounts for the semi-volatile nature of POA and chemical aging by separating the precursors into several classes according to their volatilities (Donahue et al. 2006). The two-product approach has two main limitations, i.e., the POA emission is considered non-volatile and non-reactive and the aging process of SOA is not taken into account (Lee-Taylor et al. 2011; Giani et al. 2019). Such deficiencies led to the development of the VBS framework. The first generation VBS model used one dimensional basis set (1-D VBS) in which organic compounds are grouped only by volatility and thus is unable to describe the varying degrees of oxidation observed in atmospheric organic aerosols of similar volatility. To overcome this shortcoming, the two dimensional VBS (2-D VBS) model was developed, in which organic compounds are grouped by both oxidation state and volatility as the two dimensions (Donahue et al. 2011, 2012). However, the use of 2-D VBS has been limited due to high computational cost. By simplifying the 2-D VBS model, the 1.5-D VBS approach has been developed, which compromises the organic oxidation state and volatility in response to chemical aging. The chemical aging of SOA and oxygenated POA is modeled by shifting the organic aerosol (OA) mass along a pre-defined pathway of the oxygenated organic aerosol (OOA) basis set, which reduces the volatility while increasing oxidation state. The implementation of the VBS approach has remarkably better model performance than the traditional two-product approach (Lane et al., 2008; Feng et al. 2016; Han et al. 2016; Lin et al. 2016). However, there are still large uncertainties in SOA simulation due to the associated chemical complexity and process nonlinearity, especially during the haze periods with high pollutant loading in the atmosphere (Chen et al. 2017).

SOA modeling has remained a challenge and model studies have shown systematically underestimated ambient SOA concentrations compared to the observed values (Vutukuru et al. 2006; Volkamer et al. 2006; Zhang et al. 2014; Ait-Helal et al. 2014). Much work has attempted to improve the accuracy of the predicted concentrations of SOA and crucial understanding about SOA formation and evolution has been demonstrated. For instance, semi-volatile and intermediate VOCs (S/IVOCs) of primary emissions were not usually accounted for as SOA precursors and POA has traditionally been assumed to be non-reactive and non-volatile (Lee-Taylor et al. 2011). However, in fact, S/IVOCs can be transformed into SOA through photochemical reactions, while a considerable proportion of particulate organic matter may evaporate rapidly (Kuhn et al. 2005; Robinson et al. 2007). Most model simulations accounted for the oxidation of speciated NMVOCs only (Jathar et al. 2014), while neglecting the part of SOA formed from the unspeciated precursors (IVOCs). The absence of important precursors in the existing inventory is therefore an important reason for the poor model performance (Shrivastava et al., 2008). In addition, the accuracy of emission inventories for the existing speciated precursors would also affect the model result. Except for the uncertainties resulted from emission inputs above, other factors can also affect the SOA simulation, such as the aging rate constant (Jo et al. 2013), OH radical concentration (Salo et al. 2011), NOx level (Ng et al. 2007), and the uncertainties of meteorological parameters (Bei et al. 2012). Recent studies in China have been committed to reduce the model-measurement discrepancies, taking into account the underestimated precursor emissions and yield parameters (Li et al. 2017a; Yang et al. 2019), the effects of HONO sources (Zhang et al. 2019), and the contributions of heterogeneous formation processes (Xing et al. 2019).

Beijing is surrounded by Tianjin and Hebei province in the North China Plain (NCP), residing in the largest city cluster in China. Due to the large anthropogenic emissions, severe regional haze episodes characterized by high concentrations of PM2.5 frequently occur in the Beijing-Tianjin-Hebei (BTH) region, especially under unfavorable weather conditions (Zhang et al. 2018b 2018a). In addition to the enhanced production of secondary inorganic aerosols, the organic aerosols also account for a remarkable fraction of the PM2.5 mass during haze episodes (Zheng et al. 2015; Ji et al. 2016; Yu et al. 2019). While SOA simulation through chemical transport models is effective in revealing the sources, concentrations and formation processes of SOA in regional scale, it is essential to improve the model performance and reduce the discrepancies between observed SOA concentrations and the modeled ones. In this work, in order to identify the major uncertainties and improve the model performance, we performed a series of model tests based on the 1.5D-VBS approach to assess the sensitivity of model prediction to the key factors, including precursor emission, radical concentration, chemical aging rate and SOA yield. Using the optimized model, source apportionment of SOA in Beijing was also conducted to investigate the potential contribution from different source sectors and areas. The results of this work would therefore improve the model performance for SOA simulation and provide more accurate results for identifying the sources of SOA so as to efficiently reduce the SOA concentration in the atmosphere.

2 Method

2.1 Model configuration

The CAMx model with the newly released version of 6.5 was used for model simulation. The meteorological inputs were created using WRFv3.8, with the meteorological initial and boundary conditions from the reanalysis data of the National Centers for Environmental Prediction Final Analysis (NCEP-FNL). Time series of temperature (T), humidity (H), wind speed (WS), and wind direction (WD) in the North China Plain during the study period are shown in Fig. S1. As shown in Fig. 1, two-level domains were used for the CAMx simulation and the horizontal resolution was 36 km and 12 km, respectively. The first domain covered most areas in East Asia, providing boundary conditions for the second domain. The initial and boundary conditions of chemical species (including NO, NO2, O3, elemental carbon, etc.) for the first domain were obtained from the global chemistry transport model MOZART-v4 (Emmons et al. 2010). The simulation study focused on the second domain, which covered the North China Plain including Beijing, Tianjin, Hebei, Henan, Shanxi, Shandong, Inner Mongolia, and Other area. The vertical layer was divided into 14 unequal layers, 7 of which were below 1 km to better describe the vertical structure of the atmospheric boundary layer. The CB6 photochemical mechanism was applied for the gas-phase photochemical mechanism. In addition, several physical mechanisms were applied, including the horizontal diffusion of K theory and advection scheme (PPM), implicit Euler vertical convection scheme, and EBI calculation method. The photolysis rates were calculated using the CAMx pre-processor, which incorporated the Tropospheric Ultraviolet and Visible (TUV) radiative transfer model (NCAR, 2011). Partitioning of inorganic aerosols between the gas and aerosol phases was calculated using the ISORROPIA thermodynamic model (Nenes et al. 1998). Aqueous sulfate and nitrate formation in cloud water were modeled using the RADM aqueous chemistry algorithm (Chang et al. 1987). The monthly anthropogenic emissions in China were obtained from the 2016 Multi-resolution Emission Inventory for China (MEIC, v1.3) (http://www.meicmodel.org) with a spatial resolution of 0.25°×0.25°, which included five source sectors: power, industry, residential, transportation, and agriculture. Emissions from other regions were obtained from the MIX anthropogenic emission inventory (Li et al. 2017b 2017a). The anthropogenic emissions were re-gridded into the two domains with the grid-based spatial proxies (including population density, gross domestic product, and road network) in Geographic Information System (GIS). The biogenic emissions were estimated using the Model of Emissions of Gases and Aerosols from Nature (MEGAN v2.1) (Guenther et al. 2012) driven by the meteorological variables.

Fig. 1
figure 1

Two domains of the model simulation: the first domain (36km, left) covers most areas in East Asia and the second domain (12km, right) covers the North China Plain including Beijing, Tianjin, Hebei, Shanxi, Shandong, Henan, Inner Mongolia, and Other area (the remaining unnamed areas)

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Severe haze episodes frequently occurred in winter in Beijing and the North China Plain due to the enhanced emissions of domestic heating and the occurrence of stagnant weather conditions, showing high loading of SOA in the atmosphere (Yu et al. 2019). Therefore, the study period was chosen in winter between January 2nd and 13th, 2017, covering a haze period (2nd-7th January, P1) and a relatively clean period (8th-13th January, P2). Both model simulation and field observation were conducted. For SOA simulation, a spin-up period of 5 days was used to minimize the influence of uncertain initial conditions. Both the 1.5-D VBS approach and two-product approach were used as a subroutine of the CAMx model for SOA simulation. A series of sensitivity tests were conducted in P1 period using the 1.5-D VBS approach in order to identify the major uncertainties of SOA simulation and improve the model performance. The sensitivity of model prediction to the key factors, including precursor emission, radical concentration, chemical aging rate and SOA yield, was assessed. Because the concentration of biogenic SOA during the wintertime was generally low (less than 1μg·m-3) and the increase of SOA was highly associated with the enhancement of anthropogenic emissions such as coal consumption for household heating (Huang et al. 2014; Ding et al. 2017; Wang et al. 2018), the sensitivity analysis mainly focused on anthropogenic emissions by varying anthropogenic precursors. Source apportionment of SOA was investigated using the brute-force method to quantify the contributions from different source sectors and areas.

2.2 Description of 1.5-D VBS scheme

The 1.5D-VBS scheme was used to treat organics for the most part. Details of the approach can be found elsewhere (Koo et al. 2014; Woody et al. 2016). Briefly, the 1.5D-VBS scheme separated a wide variety of atmospheric organic compounds into three groups according to the logarithmically spaced effective saturation concentration (C*), including semivolatile POA (nonvolatile OA with C*=10-1 μg·m-3 and SVOCs with 100 μg·m-3≤C*≤103 μg·m-3), IVOCs (104 μg·m-3≤C*≤106 μg·m-3), and VOCs (gas-phase organic precursors, C*≥107 μg·m-3). POA originated from nonvolatile OA emissions and gas-particle partition of SVOCs. SOA was formed through the oxidizing or aging of precursors, including traditional VOCs, IVOCs and SVOCs, and was represented by five surrogate compounds with C* values of 0.1, 1, 10, 100, and 1000 μg·m-3. The traditional VOC precursors included anthropogenic precursors benzene, toluene and xylene, and biogenic precursors isoprene, monoterpenes and sesquiterpenes. SOA production from benzene, toluene, xylene, isoprene, and monoterpenes had specific high- and low-NOx yields, while there was no NOx dependence for SOA yield from sesquiterpenes and IVOCs. SVOCs were allocated from POA emissions and a portion of SVOCs were transferred to SOA too. Table 1 summarized the species-specific basis yields of SOA from different precursors (ENVIRON, 2018). The OH reaction rate constant was 4×10−11 cm3·molec−1·s−1 for initial aging of primary SVOCs and IVOCs (Robinson et al. 2007), and 2×10−11 cm3·molec−1·s−1 for the subsequent multigenerational aging of oxidation products (Murphy and Pandis 2009). Each aging process resulted in an order of magnitude reduction in volatility. Aging of biogenic SOA was disabled by default (Lane et al. 2008).

Table 1 CAMx SOA mass yield parameters (ppm/ppm) for CB06 chemical mechanism
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In addition to the 1.5D-VBS scheme, the two-product scheme was also employed for comparative study of SOA simulation, in which SOA species existed in equilibrium with condensable gases that could be produced through gas-phase oxidation chemistry (Strader et al. 1999). The aerosol yield data from smog chamber studies were used (Zhang et al. 2014), and water solubility of the condensable gas species was modeled based on parameterization of volatility-dependent Henry’s law constants (Hodzic et al. 2014; Knote et al. 2015). POA was assumed as non-volatile species in the two-product scheme while the photolytic loss of SOA was included and calculated by a first-order decay reaction with a photolysis rate derived by scaling the NO2 photolysis rate (Henry and Donahue 2012; Hodzic et al. 2016). Compared to the 1.5-D VBS scheme, the two-product scheme only focused on the first generation of oxidation of traditional VOCs and IVOCs.

2.3 Observational data and model evaluation

The simulated SOA was compared and evaluated by the estimated SOA from filter-based measurements. During the study period of January 2nd-13th, 2017, 12-h PM2.5 samples were collected at both an urban site (N = 23) in Beijing Normal University and a suburban site (N = 21) in the University of Chinese Academy of Sciences in Huairou District of Beijing. The contents of organic carbon (OC) and elemental carbon (EC) in PM2.5 were measured with a DRI 2001A carbon analyzer following the IMPROVE thermal/optical reflectance (TOR) protocol. The SOA concentration from measurement was estimated by the traditional minimum OC/EC ratio method and calculated by the following equation (Castro et al. 1999; Strader et al. 1999): SOA = 1.6*(OC - EC×(OC/EC)min). The OC/EC ratio varied from 2.0 to 7.3 with an average of 4.2 at the urban site, and the OC/EC ratio varied from 1.2 to 6.1 with an average of 3.4 at the suburban site. The lowest 10% percentile of the OC/EC ratio was used to determine (OC/EC)min, which was 2.2 and 1.3 for the urban and suburban sites respectively.

The hourly PM2.5, CO, O3 and NO2 concentrations in Beijing and other cities in North China Plain were collected from China National Environmental Monitoring Center. The modeled PM2.5 in 7 cities of North China Plain were evaluated using the observation data from multiple national control sites (Figs. S3 and S4). The hourly meteorological data in Beijing, including temperature, solar radiation, relative humidity, wind speed and wind direction, were recorded by an automatic meteorological station at the BNU site. The model evaluation regarding meteorological fields (including temperature, humidity, wind speed, and wind direction) was performed in terms of domain-wide performance statistics, and compared with the hourly observations from dataset ds461.0 of the NCEP ADP Global Surface Observational Weather Data.

3 Results and discussion

3.1 Field observation and model evaluation

Figure 2 shows the temporal variations of the measured PM2.5, CO, O3 and NO2 concentrations, and the measured as well as simulated meteorological parameters in urban Beijing during the study period of January, 2017. Generally, the study period can be divided into a polluted period (P1) and a clean period (P2). Compared to the clean period (P2), the polluted period (P1) was characterized with high PM2.5 concentration and stagnant meteorological conditions with an average PM2.5 concentration of 260.2 μg·m-3 and an average temperature, relative humidity, and wind speed of 2.9°C, 70.1%, and 0.6 m·s-1, respectively. Beginning on January 2nd, southerly wind with humid and polluted air masses from southern Hebei led to elevated relative humidity and sharp increase in PM2.5 concentration with hourly peak concentration up to 607 μg·m-3. Besides, persistent low wind speed and low planetary boundary layer (PBL) favored the accumulation of pollutants in the P1 period. Contrary to PM2.5, CO and NO2, O3 showed lower concentration in P1 due to the NOx titration effect and suppressed photochemical activities (Feng et al. 2016). As also shown in Fig. 2, the Ox (NO2 + O3) production was higher in the P1 period, indicating higher atmospheric oxidation capacity during the polluted period. Beginning on January 8th, the PM2.5 concentration declined dramatically in the P2 period with an average of 38.3 μg·m-3. The average temperature, relative humidity, and wind speed were 1.9°C, 40.8%, 1.5 m·s-1 respectively in P2, which were favorable for atmospheric diffusion and unfavorable for the secondary formation of aerosols (Chen et al. 2014). However, when the wind direction changed to southwest on January 9th, the PM2.5 concentration showed a sharp increase from 8 μg·m-3 to 138.5 μg·m-3, probably due to the regional transport of polluted air masses from the surrounding areas (Liu et al. 2013).

Fig. 2
figure 2

Time series of measured pollutant concentrations (PM2.5, CO, O3 and NO2), and measured and simulated meteorological parameters (solar radiation, planetary boundary layer, temperature, relative humidity, wind direction and speed) in urban Beijing in the study period of January, 2017. The arrow lines in the wind speed graph show the wind direction as well as wind speed

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The modeled 2 m-height temperature, 2 m-height humidity and 10 m-height wind speed in urban Beijing were compared with the meteorological measurements in Fig. 2. In addition, the results of WRF simulation were also compared with the NCEP weather data across the second domain covering the North China Plain (Table S1, Figs. S1-S4). Overall, the WRF simulation performed reasonably and agreed well with the observation data across the NCP. In urban Beijing, however, the meteorological parameters showed less agreement between the simulated and measured values, with underestimated temperature (MB: -2.8°C) and humidity (NMB: -17%) and overestimated wind speed (NMB: 8%). While the variation trends were well captured by the model, the overestimated wind speed might result in underestimated pollution level, and the bias in temperature and humidity would affect the calculated chemical transformation rates (Tuccella et al. 2012). The simulated PM2.5 in urban Beijing showed similar variation trend with the measured PM2.5 (R: 0.79) but an obvious overestimation (NMB: 26%). In the context of stringent air pollution control in the North China Plain, the magnitude and spatial distribution of emissions have changed rapidly in Beijing and the surrounding regions in recent years (Qin et al. 2019). Therefore, the overestimation of PM2.5 in urban Beijing was partially due to the uncertainties of the 2016 MEIC emission inventory used in the simulation.

3.2 SOA simulation and evaluation

3.2.1 SOA concentrations at the urban and suburban sites

The estimated SOA concentrations based on filter measurement and the simulated SOA concentrations based on the VBS scheme at the urban and suburban sites of Beijing are shown in Fig. 3 and Table 2. The correlation coefficient between the estimated and simulated SOA concentrations was 0.84 and 0.72 at the urban and suburban sites respectively, indicating that the simulation result was able to capture the trend of SOA. However, the ratio of the average simulated and estimated SOA concentrations was 0.51 and 0.59 in the P1 and P2 periods respectively at the urban site, and 0.28 (P1) and 0.14 (P2) at the suburban site, showing obvious underestimation of the model results especially for the suburban site in the P2 period. Such underestimation of model results could be attributed to the uncertainties of source and meteorological inputs as well as SOA formation mechanism. For example, the more overestimated wind speed at the suburban site could result in higher removal efficiency of SOA and thus lower SOA concentration from simulation. Besides, both the proportion of SOA in OA (Table 2) and the proportion of SOA with C*<=100 μg·m-3 (Fig. 3) were higher at the suburban site those at the urban site, indicating that the precursors would undergo more oxidation steps before forming SOA at the suburban site.

Fig. 3
figure 3

Estimated (based on filter measurement) and predicted (based on VBS scheme) 12-h average SOA concentrations and the corresponding volatility distributions (inlet) at the urban and suburban sites of Beijing during the study period

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Table 2 Estimated (based on filter measurement) and simulated (based on VBS scheme) SOA concentrations (mean and range, μg·m-3) and the respective ratios of SOA/OA (mean and range) over the polluted (P1) and clean (P2) periods at the urban and suburban sites of Beijing
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Based on the filter measurement estimation, the mean SOA concentration at the urban site was about 1.4 times of that at the suburban site and the mean SOA concentrations in the P1 period were nearly an order of magnitude higher than those in P2 at both sites. In addition, it is worth noting that the SOA/OA ratio also showed a significantly higher value during the P1 period at the urban site, indicating higher formation capacity of SOA with the accumulation of pollutants under unfavorable dispersion conditions.

3.2.2 Temporal variation and spatial distribution of simulated SOA with the VBS scheme

The modeled average diurnal profiles of POA and SOA in urban Beijing in the P1 and P2 periods are shown in Fig. 4. Due to elevated POA emissions, the peaks in POA concentration generally occurred at morning rush hours around 07:00 Beijing time (BJT) and evening rush hours around 19:00 BJT. In addition, due to the traffic regulations in Beijing, the heavy-duty diesel trucks were active at night and the associated heavy emissions contributed to the elevated POA at night. Similar to the results reported by Li et al. (2017a), the daily variation of SOA differed from POA and peaks in the afternoon around 14:00 BJT as a result of peak photochemical activity. However, compared to the P2 period, the SOA concentration remained at a high level till night during the P1 period, which could be partially attributable to the low atmospheric dispersion capacity as indicated by the high CO concentration shown in Fig. 4. The formation of SOA might also be enhanced due to the accumulation of oxidants at night during the P1 period.

Fig. 4
figure 4

Average diurnal variations of simulated POA and SOA concentrations as well as observed CO concentration during the P1 and P2 periods in urban Beijing

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Figure 5 shows the maps of modeled average concentrations of POA and SOA during the P1 and P2 periods. Higher POA concentrations were predicted in southern Beijing and Hebei, northern Henan, and western Shandong with values larger than 30 μg·m-3 during the P1 period. SOA peaked in northern Henan with a value larger than 20 μg·m-3, but the average predicted SOA concentrations in most areas of NCP during the P1 period were relatively low (around 8 μg·m-3) compared to POA. While overestimation of POA and underestimation of SOA by simulation were observed, the low temperature and oxidant levels in winter might lead to large fractions of primary organics partitioning into the particle phase and less production of SOA (Shrivastava et al. 2008). Due to the favorable dispersion conditions in the P2 period, the average modeled concentrations of POA and SOA in most areas of NCP were less than 30 and 15 μg·m-3, respectively.

Fig. 5
figure 5

Spatial distributions of average SOA and POA concentrations modeled with the VBS scheme during the P1 (a, b) and P2 (c, d) periods

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3.2.3 Comparison of SOA simulation with two-product and VBS schemes

The SOA as well as POA simulation results with the two-product and VBS schemes are shown in Fig. 6 for comparison. The average POA and SOA concentrations in the P1 period by experimental estimation, VBS simulation and two-product simulation were 25.9 and 35.1, 52.7 and 18.0, and 84.9 and 4.9 μg·m-3, respectively. The average POA and SOA concentrations in the P2 period by experimental estimation, VBS simulation and two-product simulation were 6.8 and 3.9, 12.3 and 2.3, and 24.3 and 1.0 μg·m-3, respectively. While SOA was underestimated, POA was overestimated with both the two-product and VBS schemes. The average simulated POA concentration with the two-product scheme at the urban site was overall 68.0% higher than that with the VBS scheme, but the average SOA concentrations with the two-product scheme in the P1 and P2 periods accounted for only 27.2% and 43.4% of that with the VBS scheme and explained only 14.0% and 25.6% of estimated SOA concentration, respectively. Compared to the VBS scheme, the higher POA and lower SOA simulated via the two-product scheme were consistent with the fact that the two-product scheme supposes POA as non-volatile and non-reactive (Meroni et al. 2017). Previous studies have also shown that the VBS scheme produces higher SOA than the traditional two-product scheme (Feng et al. 2016; Lin et al. 2016). Partly due to the overestimation of POA emissions in the current emission inventories, the modeled total OA (POA+SOA) with the VBS scheme over-predicted the estimated OA concentration by 15.9% and 36.4% in the P1 and P2 periods respectively, and that with the two-product scheme over-predicted OA by 46.7% (P1) and 136.4% (P2).

Fig. 6
figure 6

Time series of modeled SOA and POA concentrations in urban Beijing with the two-product and VBS schemes during the study period and the spatial distributions of average SOA concentration in the P1 period with different precursors (traditional VOCs or traditional VOCs plus IVOCs) included in the two-product and VBS schemes

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Figure 6 also shows the spatial distributions of average SOA concentration in the P1 period with different precursors (traditional VOCs or traditional VOCs plus IVOCs) included in the two-product or VBS schemes. When the simulation was conducted with traditional VOC emission only and the aging rate constants were zero, the average SOA concentration in urban Beijing in the P1 period was 3.7 and 4.1 μg·m-3 with the two-product and VBS schemes, respectively. The slight difference of simulated SOA concentrations with the two-product and VBS schemes might be caused by the difference of yields in these two schemes and the photolytic loss of SOA contained in the two-product scheme. After adding the IVOC emission, however, the average SOA concentration in P1 with the two-product scheme increased to 4.9 μg·m-3, while it increased to 12.5 μg·m-3 with the VBS scheme, showing the significant impact of IVOC emission on the simulation results with the VBS scheme. The roles of affecting factors such as IVOCs, SVOCs, and multi-stage aging were furthered investigated and shown in Sec. 3.3 of sensitivity analysis with the VBS scheme.

3.3 Sensitivity analysis of SOA simulation with the VBS scheme

3.3.1 Sensitivity analysis with varying parameters

A series of simulations based on the VBS scheme were conducted to investigate the sensitivity of the model predictions to the uncertain inputs over the polluted period. Table 3 shows the simulated SOA concentrations in urban Beijing in the P1 period with varying parameters, including precursor emissions, yields, aging rates, and oxidant levels. Figure 7 shows the spatial distribution of average SOA concentrations in the base case as well as the absolute changes of average surface SOA concentrations between the different sensitivity simulations and the base case. According to the SOA as well as POA simulation results shown in Section 3.2 and previous literature reports (Lu et al. 2012; Zhao et al. 2016; Li et al. 2017a), anthropogenic VOCs, IVOC emissions, aging rates, and oxidant levels may have been underestimated in the base case, while the POA emissions may have been overestimated. Therefore, the effects of enhanced anthropogenic VOCs, IVOCs, aging rates and oxidant levels and reduced POA emissions were investigated in different sensitivity scenarios.

Table 3 Simulated SOA concentrations in urban Beijing in the P1 period with varying parameters
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Fig. 7
figure 7

Spatial distribution of average SOA concentrations with the VBS scheme during the P1 period in the base case (a) and absolute changes of average surface SOA concentrations between the different sensitivity simulations and the base case (b-l)

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As shown in Table 3 and Fig. 7, the increase in anthropogenic VOCs (benzene, toluene, xylene) and IVOCs both significantly enhanced the levels of SOA, particularly in those regions with relatively high anthropogenic emissions such as Hebei, Henan, and Beijing. In the default setting IVOCs was set 1.5 times of the original POA emission. However, according to the results of diluted emission experiments by Zhao et al. (2016), the IVOC emission was approximately 1.5 times of the POA emission from biomass burning, 3.0 times of industrial and coal combustion POA emissions and up to 30 times of gasoline vehicle POA emission. Therefore, IVOCs may have been significantly underestimated in the default setting that assumed IVOCs / POA = 1.5, and more source measures are needed to characterize the IVOC emissions for various source categories. According to the simulated SOA concentrations in urban Beijing in the P1 period (Table 3), accelerated increase of SOA was observed as the anthropogenic VOCs increased, while the SOA concentration increased almost linearly with the amount of IVOCs added to the inventory. Although the IVOC emission estimation showed a large uncertainty in literature reports, the near-linear dependence of SOA concentration on IVOCs would enable the estimation of SOA with different estimated IVOC emissions. In addition, in view of the overestimated original POA emission in inventory, we assumed 50% lower semi-volatile POA emission compared to the base case and no change of the amount of IVOC emission. The resulting average POA concentration decreased by 50.5%, while the average SOA concentration was only reduced by 9.1% (1.5 μg·m-3). While the POA emission appeared to significantly affect the atmospheric POA concentration, SOA was less affected since only a small fraction of the semi-volatile POA emission can be portioned into the gas phase and produce SOA, especially at low temperature and oxidant levels (Lin et al. 2011; Zheng et al. 2015). Besides, as the yield of SOA formation was a key parameter in the model and might be underestimated in chamber experiments (Zhang et al. 2014), the yields of the original aromatic precursors were doubled, which resulted in a 30.6% increase of modeled SOA.

It is worth noting that the sensitivity analysis on precursor emissions (anthropogenic VOCs, IVOCs, POA) represents an integrated effect of the first generation oxidation of adding precursor emissions and the subsequent multigenerational oxidation. To separate the impacts of the first generation oxidation of precursors and their chemical aging, the individual contributions of traditional VOCs, IVOCs, and semi-volatile POA as well as their chemical aging to SOA production are also shown in Table 3. When considering the traditional VOCs, IVOCs, and semi-volatile POA as the organic precursor only, the resulting SOA was 4.1, 6.8, and 3.9 μg·m-3 respectively, and the aging process increased the respective SOA production by 46.3, 11.8, and 10.3%. It appears that chemical aging affected the SOA production from traditional VOCs more significantly than from IVOCs or semi-volatile POA, probably because the traditional VOC precursors should undergo more oxidation steps than other low volatility organic precursors. Overall, compared to chemical aging, the first generation oxidation seemed to play a more important role in SOA production, and the higher the volatility of organic precursors was, the more obvious the aging effect.

To further investigate the overall uncertainty of aging, simulation tests were conducted by varying the aging rate constant with OH (Jo et al. 2013). As shown in Table 3, the average SOA concentration was increased by 3.9 and 12.8% respectively with the aging rate constant 2 times and 5 times of the base case. Besides, according to the spatial distribution of the absolute change of SOA concentration (Fig. 7), the effect of chemical aging was more significant around the rural areas. Therefore, while the continued aging reduced the volatility of oxidation products and increased the SOA concentration, it seemed to have limited effects on SOA production in urban Beijing by changing the aging rate constant with OH.

Table 3 also shows the effects of varying oxidants on SOA production. The average SOA concentration was increased by 75.6, 45.0, 13.9% with doubled OH concentration, halved NOx emission, and doubled HONO concentration, respectively. While the meteorological fields show profound impact on the secondary formation of oxidants such as OH and HONO, the atmospheric chemical complexity and reactivity can also affect the oxidant concentrations greatly (Wolfe et al. 2022). The modeled OH and HONO concentrations in this study were low compared to the observed data found in the literature, which could be due to several reasons such as underestimated precursor concentrations and reaction rates. To find out how such underestimation of oxidants could affect the model prediction of SOA without interfering with other factors, the OH and HONO concentrations were doubled directly in the subroutine of SOA simulation (VBS scheme) without changing the meteorological fields. Due to the strong solar radiation attenuation in the polluted period (Fig. 2), the OH radical concentration was low and the modeled daily averaged maximum OH concentration was approximately 0.5×106 cm-3 during the P1 period. In comparison, based on the wintertime radical measurement in the urban area of Beijing from November to December 2017 (Ma et al. 2019), the daily maximum OH radical concentration was on average 1.5×106 cm-3 during the polluted period, about 3 times of the modeled value in this study. As shown in Table 3, doubling the OH radical concentration would result in a 75.6% increase of the simulated SOA concentration (31.6 μg·m-3), approaching the value of estimated SOA concentration (35.1 μg·m-3) from measurement. Therefore, the underpredicted SOA in the base case could be largely attributed to the underestimated OH concentration by the model.

The modeled average NO2 concentration with original NOx emission was about 21% higher than that observed (Fig. S5). OH shows a strong non-linear relationship with NOx, with increased OH concentration along with NO2 in the low NOx range due to the enhanced reaction of HO2 + NO, and decreased OH concentration along with NO2 in the high NOx range due to the enhanced reaction of OH + NO2. The urban area of Beijing was NOx-rich, and in the “NOx/2” simulation scenario, the modeled daily averaged maximum OH concentration was nearly doubled during the P1 period, resulting in a substantial increase of the simulated SOA concentration. The overprediction of NOx can also lead to decreased O3 (Fig. S6) because of the dominance of HOx-NOx reactions over HOx-HOx reactions (Griffin et al., 2004). Given that O3 can further oxidize VOCs through formation of OH and NO3 radicals (Vutukuru et al. 2006), the underestimation of O3 may lead to underprediction of SOA. Besides, as shown in Table 1, the NOx levels have been shown to influence SOA yields and can lead to low SOA yields under high-NOx conditions, mainly due to the competition reactions of RO2 radical with NO and HO2 (Ng et al. 2007). Therefore, decreasing the NOx concentration can enhance the level of photochemical oxidants and promote the production of SOA. Photolysis of HONO is an important source of OH (Wang et al. 2017), and the HONO emission was widely estimated as 0.8% of NOx emission for modeling application (Czader et al. 2015). Such ratio may be underestimated and lead to underprediction of SOA concentration, especially in urban areas (Czader et al. 2015).

3.3.2 Optimization of SOA simulation

In order to substantially improve the simulation results to agree better with the measurements with regard to the magnitude of SOA concentration and POA-SOA split, an optimized simulation was conducted in which the IVOC emission and aging rate constant were tripled and doubled respectively and the semi-volatile POA emission was lowered by 50% compared to the base case. Figure 8 shows the spatial distributions of SOA, POA and SOA/OA during the P1 period based on the optimized simulation. In urban Beijing, the average SOA concentration (36.4 μg·m-3) increased by 102% and approached closely to the estimated value from observation (38.3 μg·m-3). The total OA concentration decreased by 8.5% (from 70.7 to 64.7 μg·m-3) and the ratio of SOA/OA increased to 53.2%. SOA was dominant throughout the modeled domain, contributing to 50-60% of total OA in southern Hebei where POA emission was remarkable, and more than 70% in rural areas in the west and northwest areas of the North China Plain.

Fig. 8
figure 8

Spatial distributions of SOA, POA and SOA/OA during the P1 period based on the optimized simulation

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3.4 Contributions of anthropogenic emissions to SOA in urban Beijing

Based on the optimized simulation scenario, the contributions of individual anthropogenic sources or source regions to the SOA concentration in urban Beijing during the haze period (P1) were investigated using the brute-force method on different scales. The average SOA concentration at BNU was obtained with only a single source category from one source region included in every simulation run, and then the relative proportion from each source category or source region was calculated.

Figure 9 shows the potential contribution ratio from different source regions and individual anthropogenic sources on different scales to SOA in urban Beijing during the P1 period. The contribution of local emissions to SOA in urban Beijing was only 12.4%, indicating that regional transport of SOA or SOA precursors dominated in the SOA pollution in urban Beijing. Previous observation study in urban Beijing also suggested that secondary aerosols were mainly formed over regional scales and SOA in urban Beijing was significantly influenced by the transport of pollutants from outside of the urban area (Sun et al. 2015). As shown in Fig. 9, the suburban emission showed the highest contribution of 32.7%, followed by Hebei with a contribution of 21.4%.

Fig. 9
figure 9

The potential contribution ratio from different source regions and individual anthropogenic sources on different scales to SOA in urban Beijing during the P1 period

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From the perspective of regional contribution, residential emission played a dominant role in the SOA formation in urban Beijing, with an average contribution of 74.6%. Previous simulation studies have also identified the significant contribution of residential emission to PM2.5 pollution in the NCP region (Liu et al., 2016; Li et al. 2018). Besides, the industry sector was also an important SOA source in NCP, with an average contribution of 15.6%. Compared with residential and industry emissions, the contributions of transportation and power sectors were smaller, with the average contributions less than 10%. As we zoomed into the suburban and urban areas, the contribution of residential emission decreased and all the contributions of industry, transportation and power increased. It should be noted that there were large uncertainties in the calculated contributions of different sources, because the above results were obtained using the same parameters for different sources. For example, if the IVOC emission was set as 30 times of the original POA emission from transportation, as suggested by Zhao et al. (2016), the transportation source would become the largest source in urban Beijing, with an average contribution of 34.1%. The contribution of the transportation source in the current study may have been considerably underestimated, especially in urban areas. Besides, the nonlinearities of source contributions overlooked by the brute-force method would also result in potential uncertainties of the calculated source contributions.

4 Conclusions

Based on the SOA simulation during the wintertime severe haze period in Beijing and the surrounding areas, it was found that the VBS scheme can produce higher predicted SOA concentration compared to the two-product scheme, which was also better correlated with the estimated SOA concentration from observation. However, there was still significant underestimation of the level of SOA, particularly during the peak time. According to the sensitivity tests, the VOC and IVOC emissions as well as the oxidant levels were the key factors that affected the predicted SOA concentration. The SOA concentration showed a roughly linear increase with the amount of IVOCs added to the inventory, and an accelerated increase with the amount of anthropogenic VOCs. While the average SOA concentration was increased by 75.6% with doubled OH concentration in the polluted period, decreasing the NOx concentration can also enhance the level of photochemical oxidants and promote the production of SOA. Comparatively, the predicted SOA was less affected by POA emission (given that IVOCs remain unchanged) and chemical aging during the winter time. Further studies with more accurate parameters and complex treatment processes regarding the model mechanism are needed to better improve the model performance.

Model simulation based on the brute-force method showed that regional transport dominated in the formation of SOA in urban Beijing. Over 80% of SOA were resulted from regional transport of SOA or its precursors from the surrounding areas during the polluted period. Residential emission in the North China Plain contributed to 74.6% of SOA in urban Beijing, followed by industry, transportation, and power. However, considering the high IVOC emission accompanying the POA emission of gasoline vehicles, the contribution of the transportation source in the current study may have been considerably underestimated, and transportation in urban Beijing would become the dominant local source of SOA. According to the source contributions from different source sectors in different areas, controlling residential and industry emissions in the suburban areas of Beijing and Hebei would sufficiently reduce the SOA pollution in the urban area of Beijing.

Heterogeneous aqueous-phase chemical reactions have been shown as an important pathway for SOA formation under haze conditions (Xu et al. 2017; Xing et al. 2019). In the WRF-CAMx model, the in-cloud SOA formation by the oxidation of aqueous SOA precursors (i.e. glyoxal, methylglyoxal and glycolaldehyde) was simulated in the RADM module, which partially accounted for the formation of biogenic SOA. However, the incorporation of aqueous formation processes of SOA in WRF-CAMx was inadequate compared to other models such as WRF-Chem and CMAQ. For example, the irreversible uptakes of glyoxal and methylglyoxal are incorporated in the WRF-Chem model (Xing et al. 2019) and CMAQ model (Li et al. 2019), and the CMAQ model also includes the isoprene-formed BSOA via aqueous uptake of isoprene epoxydiols (IEPOX) and subsequent addition of nucleophiles (Qin et al. 2018). These processes could be important and lead to changes in the simulated SOA concentration, but have large uncertainties (Matsui et al. 2014; Marais et al. 2016). Future research is needed regarding the role of aqueous reactions in SOA formation.