Introduction

New particle formation (NPF) refers to the process that gaseous vapors form stable molecular clusters and then undergo condensation and coagulation growth to become particles1,2. NPF can contribute greatly to particle number concentration (PNC)3, and the generation of ultrafine particles poses potential threats to human health4. When newly generated particles grow to a certain size (diameter >60 nm), they can be activated to become cloud condensation nuclei (CCN) under actual supersaturated conditions5, which affects the cloud properties, and thus indirectly influences the atmospheric radiation balance and climate change6,7,8. In addition, NPF and subsequent growth of particles can lead to severe air pollution9,10.

NPF has been recognized as a significant source of both PNC and CCN in various environments11,12,13,14,15. In regions like the Amazon rainforest, where anthropogenic pollution is minimal, organic nucleation plays a dominant role. During the rainy season, NPF within the boundary layer can contribute approximately 90% of PNC and 80% of CCN15. Yu et al.14 found that PNC and CCN concentrations increased rapidly during winter NPF events in the northeastern United States, with nucleation contributing up to 85% of PNC near the surface and 20–50% of CCN. Matsui et al.12 suggested that NPF contributed approximately 20–30% to PNC during the study period and significantly increased CCN concentrations at supersaturations greater than 0.2% in Beijing and its surrounding regions.

Nucleation is considered the first step in the process by which gaseous vapors are converted into stable molecular clusters, eventually leading to particle formation in NPF. Due to its extremely low saturation vapor pressure, gaseous sulfuric acid (H2SO4) is regarded as one of the most important precursors in the nucleation process16,17,18. Besides H2SO4, other precursors have been identified to play important roles in nucleation, including ammonia (NH3)19, nitric acid (HNO3)20, oxidized organic vapors21, iodine oxides22, and dimethylamine (DMA)23. In recent years, intense NPF events have been frequently observed in polluted urban areas. Research shows that H2SO4-DMA clusters can effectively explain the high frequency of NPF in such environments24, and growing evidence supports the role of the H2SO4-DMA nucleation mechanism in driving these intense NPF events25,26,27. Experimental studies have shown that compared to NH3, which is also an alkaline gas, DMA can increase the new particle formation rate by a factor of 1000 when concentrations exceed 3 ppt, even though NH3 emissions are much higher than those of DMA in the atmosphere28,29.

Early studies identified agricultural sources (primarily livestock) as the main contributors of DMA28. However, observations in suburban Nanjing have shown that industrial sources might be the primary contributors of DMA in that area30. Additionally, Mao et al.31 found that DMA emissions in the Yangtze River Delta primarily originate from agricultural and residential sources. A recent mobile observation studies32 suggest that average DMA concentrations in urban areas are higher than in rural regions, indicating that agricultural sources may no longer be the dominant contributors in cities. Therefore, emissions of non-agricultural DMA sources in urban areas require increased attention.

Despite the growing evidence that H2SO4-DMA nucleation is a key mechanism for NPF in urban environment and anthropogenic emissions are important DMA sources in urban environments, understanding about the impacts of DMA emissions on PNC and CCN remain limited. The objective of this study is to incorporate the H2SO4-DMA nucleation mechanism into regional chemical transport model to quantify its specific effects on PNC and CCN. In this study, we incorporated the DMA chemistry as well as the H2SO4-DMA nucleation mechanism into the WRF-Chem model with modifications in the MOSAIC aerosol module. We then applied the revised model to simulate NPF events during an observation episode from March 1 to March 18, 2017 in Beijing and its surrounding areas. We further analyzed the contributions of different DMA sources to PNC and CCN.

Results

Model validation

The modified WRF-Chem model incorporating the H2SO4-DMA nucleation mechanism was evaluated under three scenarios, with detailed explanations of each scenario provided in the Methods section. In the 8bin-modified model, a comparison between simulated and observed particle number size distribution (PNSD) showed that the results from the sim_no, sim_default, and sim_DMA scenarios were similar, all substantially overestimating particle number concentrations below 100 nm by more than 67% (Supplementary Fig. 1). The model also failed to accurately capture particle number concentrations across different size ranges, which may be attributed to the relatively coarse size resolution of the 8bin-modified model33. After increasing the number of size bins, Fig. 1a shows the comparison of simulated and observed PNC in different size ranges in the 12bin-modified model. The simulations from both the sim_no and sim_default scenarios were approximately an order of magnitude lower than the observed average PNSD in the 3–20 nm size range. Specifically, the observed average number concentration was 9859 cm−3, while the simulated average number concentrations from sim_no and sim_default were 1916 and 4060 cm⁻³, respectively, both exhibiting significant underprediction (Fig. 1b). After incorporating the H2SO4-DMA nucleation mechanism into the model, the simulated average PNSD in the 3–20 nm range exhibited improved agreement with observational data, resulting in an average number concentration of 9491 cm−3 within this size range. This adjustment reduced the normalized deviation to below 10%. The introduction of this mechanism brought the simulation results of PNSD in line with those of Li et al.34. The inclusion of the H2SO4-DMA nucleation mechanism significantly improved the model’s accuracy in simulating number concentrations for smaller particles, indicating the crucial role of DMA in the nucleation process.

Fig. 1: Comparison of simulation results under different nucleation scenarios with observations from March 1 to 18, 2017.
figure 1

Averaged particle number size distribution simulated and observations (a). Box plot showing a comparison of simulated and observed number concentrations for particles in the 3–20 nm size range (b). Time series of observed particle number size distributions (c). Simulated particle number size distributions using the default nucleation mechanism and the H2SO4-DMA nucleation mechanism on March 1, March 9, and March 14 (d).

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In the time series of PNSD, NPF events were identified based on a rapid increase in observed particle number concentration in the 3–10 nm size range, with concentrations exceeding 104 cm−3 35,36,37. As shown in Fig. 1c, a total of nine NPF events were recorded during the observation period, and days on which NPF events occurred were classified as NPF days. During these days, a characteristic burst in nanoparticle number concentrations followed by subsequent growth was observed. Fig. 1d shows that the model using the default binary nucleation mechanism failed to reproduce the explosive growth of particle number concentrations in the 3–10 nm size range on three selected NPF days (i.e., March 1, March 9, and March 14). Incorporating the H2SO4-DMA nucleation mechanism successfully captured the sharp increase in particle number concentrations in the 3–10 nm size range on these days. In contrast, for the remaining six NPF events, except for March 11, the incorporation of the H2SO4-DMA nucleation mechanism also successfully reproduced the rapid increase in particle number concentrations in the low size range, as well as the subsequent growth processes on the other five NPF days (Supplementary Figs. 2 and 3). This result suggests that the H2SO4-DMA nucleation mechanism may be the primary driver of NPF events during the observation period. The model did not reproduce the NPF events on March 11, likely due to that other nucleation mechanisms, such as organics involved nucleation processes, might contribute importantly on this day but were not considered in this study. A number of studies have revealed that organic compounds also play an important role in the nucleation process and the H2SO4-organic nucleation mechanism can explain certain NPF events in urban areas of China38,39,40,41.

Meteorological parameters and concentrations of other species were also validated. Meteorological factors play a role in NPF events, with wind speed, for example, affecting the concentration of precursor gases and the condensation sink1. The evaluation of simulated meteorological parameters for the period from March 1 to 18, 2017, is shown in Supplementary Table 1, where the mean bias (MB), mean error (ME), root mean square error (RMSE), and index of agreement (IOA) are calculated and summarized. The MB, RMSE, and IOA for simulated wind speed at 10 m (WS10) are 0.24 m s⁻¹, 1.52 m s⁻¹, and 0.76, respectively, while the MB, ME, and IOA for specific humidity are 0.03 g kg⁻¹, 0.43 g kg⁻¹, and 0.87, respectively. Both are within the benchmark recommended by Emery and Tai42 and Tesche43. Additionally, the model slightly underestimated the air temperature at 2 m (T2). Overall, the model performed well in capturing the variations in meteorological fields during the analysis period.

The model’s simulation results for SO2 and PM2.5 related to NPF were validated and analyzed. The results show that the model slightly underestimated the hourly concentrations of PM2.5 and SO2 compared to observations, with normalized mean biases (NMB) of −0.45 and −0.38, respectively (Supplementary Fig. 4). However, the correlation between the simulated and observed data was strong, with correlation coefficients of 0.75, both within the benchmark recommended by Emery et al.44. For the two key precursors of H2SO4-DMA nucleation, H2SO4 and DMA, although there were no observational data available for this period, the simulations showed an average H2SO4 concentration of 107 cm⁻³ and an average DMA concentration of 2.98 ppt. These simulated concentrations of H2SO4 and DMA are consistent with other studies using the WRF-Chem model and fall within reasonable simulation ranges31,34,36,45.

Contributions of H2SO4-DMA Nucleation to PNC and CCN

In the sim_all scenario, the contributions of different nucleation mechanisms and primary emissions to PNC and CCN were compared. The simulation result for number concentrations under this scenario is shown in Supplementary Fig. 5. Below approximately 300 m near the surface, the H2SO4-DMA nucleation mechanism dominates (Fig. 2a), primarily due to the higher concentration of DMA near the surface, which decreases with altitude (Supplementary Fig. 6), as well as the relatively short atmospheric lifetime of DMA46. Above 300 m, nucleation involving NH3 becomes the primary pathway. Studies at the urban Beijing site have similarly found that H2SO4-DMA nucleation is the dominant mechanism, contributing to more than 60% of PNC34. Recent research also indicates that in densely populated areas of eastern China, India, Europe, and parts of the United States, H2SO4-DMA nucleation plays a leading role near the surface47. Within the altitude range where H2SO4-DMA nucleation is dominant, this mechanism contributes 46–78% to PNC and 22–36% to CCN at 0.5% supersaturation (CCN0.5%). However, the relative importance of H2SO4-DMA nucleation and its contributions to PNC and CCN0.5% decrease as altitude increases. When considering the impact of primary emissions on PNC and CCN0.5%, primary emissions contribute up to 26% to PNC near the surface, but this influence weakens with altitude. For CCN0.5%, primary emissions dominate within the 1 km range near the surface, contributing 49-65%. Particles formed through H2SO4-DMA nucleation need to grow to reach the size required for activation as CCN0.5%. In contrast, particles from primary emissions are often already large enough to be activated. As a result, primary emissions have a greater influence on CCN0.5% near the surface. Overall, within the 300-meter altitude range near the surface, the H2SO4-DMA nucleation mechanism is the primary source of PNC compared to other nucleation mechanisms and primary emissions. Although its impact on CCN0.5% is smaller than that of primary emissions, it remains significant and should not be overlooked.

Fig. 2: Contributions of H2SO4-DMA nucleation-induced NPF to PNC and CCN0.5%.
figure 2

Comparison of different nucleation mechanisms and their relative contributions to PNC and CCN0.5% within the study area (a). Contributions of H2SO4-DMA nucleation to PNC and CCN0.5% at the Beijing site: overall contributions, and relative contributions on NPF and non-NPF days (b). Spatial distribution of the average PNC and CCN0.5% generated by H2SO4-DMA nucleation near the surface (c).

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Based on the results of the sim_all scenario, the average contributions of H2SO4-DMA nucleation to PNC and CCN0.5% were approximately 60% and 32% respectively (Fig. 2b) during the entire study period. The contributions of H2SO4-DMA nucleation to PNC and CCN on NPF days were 31% and 19% higher than on non-NPF days, respectively. On NPF days, the PNC driven by H2SO4-DMA nucleation was markedly higher than that on non-NPF days (Supplementary Fig. 7). On non-NPF days, the contributions of H2SO4-DMA nucleation to PNC and CCN0.5% were lower than the average levels observed throughout the study period, suggesting that the increase in PNC and CCN0.5% due to H2SO4-DMA nucleation primarily occurred on NPF days. Previous studies at the Beijing site have also noted that nucleation processes exert a more pronounced impact on PNC and CCN during NPF days12. Overall, H2SO4-DMA nucleation significantly contributed to both PNC and CCN0.5% on both NPF and non-NPF days, with its impact being particularly pronounced on NPF days.

Figure 2c shows the regional distributions of H2SO4-DMA contributed PNC and CCN0.5% in the modeling domain. High PNC regions generated by H2SO4-DMA nucleation closely correspond with the high CCN0.5% regions, primarily concentrated in southern Beijing, eastern Hebei, and areas to the west and south of Beijing. In these regions, the PNC and CCN0.5% values can reach 20,000 cm⁻³ and 2000 cm⁻³, respectively, and in some areas even as high as 50,000 cm⁻³ and 4000 cm⁻³. This suggests that particles generated by H2SO4-DMA nucleation may have contributed to the increase in CCN0.5%. The contributions of H2SO4-DMA nucleation to PNC and CCN0.5% can exceed 40% and 20%, respectively (Supplementary Fig. 8). Additionally, primary emissions in these areas also contributed significantly to PNC and CCN0.5% (Supplementary Fig. 9), as reflected in the sim_no scenario. While primary emissions contributed less to PNC than nucleation processes, they contributed more to CCN0.5%.

In regions where high PNC and CCN0.5% values are generated by H2SO4-DMA nucleation, higher concentrations of DMA are often observed (Supplementary Fig. 10a). In urban Beijing, although the highest DMA concentrations exceed 4 ppt, the corresponding concentrations of H2SO4 vapor and its precursor SO2 are lower compared to other high-value regions (Supplementary Fig. 10b, c), which inhibits the formation of larger and more stable clusters27. Moreover, when the H2SO4 concentration is ≤3 × 107 cm⁻³ (1.2 ppt), the threshold DMA concentration for nucleation rates is typically around 5 ppt, and further increases in DMA concentration do not significantly accelerate nucleation rates in the environment24,29. Due to these factors, the PNC and CCN0.5% produced by nucleation in urban Beijing are not higher than in the surrounding areas. In eastern Hebei, both DMA and H2SO4 vapor concentrations are high, which leads to higher PNC and CCN0.5% values from H2SO4-DMA nucleation compared to other simulated regions, with more significant contributions to both.

Contributions of different DMA sources in H2SO4-DMA nucleation

The emission inventory estimated for DMA in this study show that agricultural sources are the largest contributor to DMA in the study area, accounting for approximately 58%, while residential sources are another major contributor, with a share of around 37% (Supplementary Fig. 11a). This finding is consistent with the Yangtze River Delta region, where agriculture and residential sources are also the main contributors to amine emissions, contributing approximately 66% and 31% to the regional average amine levels, respectively31. Spatially, the simulation results show that agricultural DMA emissions are mainly distributed in eastern Hebei and areas south of Beijing during the study period, with an average concentration of approximately 2.2 ppt (Supplementary Fig. 11b). In contrast, residential DMA emissions are concentrated around urban Beijing, with an average concentration of approximately 2.7 ppt, and there are also higher residential DMA emissions south of Beijing (Supplementary Fig. 11c). Based on the dominance and spatial distribution of agricultural and residential sources of DMA, the specific impact of these two sources during H2SO4-DMA nucleation was further quantified.

Figure 3 shows the impact of agricultural and residential DMA emissions on PNC. In the entire study area, agricultural sources of DMA contribute approximately 52% of PNC in H2SO4-DMA nucleation, while residential sources contribute about 13%. In urban Beijing, where residential DMA emissions are concentrated, residential sources account for up to 78% of the PNC (Fig. 3a). High PNC values caused by agricultural DMA emissions spatially correspond to the high DMA concentration areas from agricultural sources (Supplementary Fig. 12a). In eastern Hebei, where both agricultural DMA emissions and nucleation precursor H2SO4 concentrations are high (Supplementary Fig. 10b), the PNC values resulting from agricultural DMA nucleation are the highest in the entire study area, averaging around 25,000 cm−3. In areas south of Beijing, although agricultural DMA emissions are comparable to those in eastern Hebei, the concentration of the nucleation precursor H2SO4 is significantly lower. As a result, the PNC values from agricultural DMA involved in H2SO4-DMA nucleation are lower in southern Beijing compared to eastern Hebei. In terms of spatial distribution, agricultural DMA contributes to over 40% of the total PNC generated by H2SO4-DMA nucleation, except in areas near urban Beijing (Fig. 3b). The spatial distribution of PNC changes driven by residential DMA emissions corresponds closely to the distribution of residential DMA itself (Supplementary Fig. 12b). The proportion of PNC generated by H2SO4-DMA nucleation involving residential DMA near urban Beijing is notably higher than in other areas, reaching around 70%. A similar situation is observed in urban Shanghai, where residential DMA emissions are the main driver of particle formation, accounting for 78% and 68% of total PNC in July and December, respectively32. Based on studies conducted in Beijing and Shanghai, two densely populated megacities, the impact of residential DMA emissions on particle number concentrations in urban areas has been revealed. Therefore, reducing residential DMA emissions may become an effective strategy for controlling ambient particle number concentrations in urban China, offering multiple benefits for air quality, human health, and climate change mitigation. The findings presented in the earlier sections of this study indicate that the spatial distribution of CCN0.5% corresponds to that of PNC, suggesting that the influence of DMA from different sources on CCN0.5% during nucleation may be consistent with its effect on PNC.

Fig. 3: Contributions of different DMA sources in H2SO4-DMA to PNC.
figure 3

Contributions of different DMA sources in the entire study area and urban Beijing (a). Spatial distribution of PNC proportion attributed to agricultural and residential sources relative to total PNC near the surface (b).

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Discussion

Incorporating the H2SO4-DMA nucleation mechanism into the model significantly improved its ability to simulate NPF and highlighted this mechanism as the primary driver of NPF events in the Beijing region. Consistent with previous studies that identified H2SO4-DMA nucleation as dominant in human-polluted environments34,48,49, we further quantified the impact of this mechanism on PNC and CCN. Based on the emission inventory and simulation results, we found that agriculture and residential sources are the main contributors to DMA, with residential sources playing a particularly significant role in urban areas. Moreover, DMA emissions from residential sources participating in H2SO4-DMA nucleation substantially contribute to urban PNC, providing a more reliable basis for attributing CCN and aerosol radiative forcing in urban areas to specific sources.

However, due to the lack of long-term and continuous observations of DMA and CCN, it is currently not possible to comprehensively evaluate the simulation performance of the model. We acknowledge that uncertainties remain in the representation of DMA sources and sinks, as well as in the nucleation parameterization when simulating H2SO4-DMA nucleation in the model. The lack of heterogeneous reactions associated with H2SO4 in MOSAIC aerosol module introduces corresponding uncertainties for H2SO4, another key precursor of nucleation. The absence of observational data further complicates the accurate evaluation of the simulation results for H2SO4. Additionally, aerosol particle size distribution is another source of uncertainty in the model. Although the size bins have been increased from 8 to 12, the resolution of the particle size remains insufficiently detailed. These uncertainties highlight the need for further research to address these limitations.

Methods

Model development

We employed the WRF-Chem model version 3.945,50,51 to investigate the impacts of DMA emissions on NPF events and contributions to PNC and CCN. DMA emissions and chemistry was added. DMA is primarily involved in gas-phase oxidation, wet deposition, and aerosol uptake46,52. The main oxidant for amines in the atmosphere is OH, with a reaction rate constant of 6.49 × 10−11 cm3 mol−1 s−1 for DMA and OH53. The impacts of O3 and NOx on DMA are minimal, so we only considered the OH oxidation in this study. The Henry’s law constant for wet deposition is set at 5.7 × 10−1 mol m−3 Pa−1, and the aerosol uptake coefficient for DMA is set at 0.00134.

We incorporated the H2SO4-DMA nucleation mechanism into the WRF-Chem model following the parameterization scheme in previous studies47,54. The parameterization scheme for the H2SO4-DMA nucleation mechanism incorporated into the model is based on results from the CLOUD (Cosmics Leaving Outdoor Droplets) chamber experiments, primarily involving the variables of H2SO4 and DMA. To account for the temperature dependence of the nucleation process, a temperature-dependent function is incorporated into the parameterization scheme. A more detailed explanation of this parameterization scheme can be found in previous studies and references therein47,54. We also added other nucleation mechanisms, including binary and ternary neutral and ion-induced nucleation and organic nucleation mechanisms38,54,55,56. The impact of different nucleation mechanisms on PNC and CCN is compared.

In the model, the default Model for Simulating Aerosol Interactions and Chemistry (MOSAIC) aerosol module uses eight size bins to simulate particle size distribution, ranging from 39 nm to 10 μm. The smallest size bin covers diameters from 39 to 78 nm, which is larger than the sizes reported for newly formed particles. As a result, the default eight-bin structure cannot effectively represent the nucleation mode (1–20 nm) and its early growth into larger particles57,58. Some studies have improved the capture of nucleation and particle growth processes by reducing the lowest size limit and increasing the number of size bins36,54,59. Therefore, this study adjusted the original eight-bin structure by expanding the particle size range from 39 nm – 10 µm to 1 nm – 10 µm and increasing the number of bins to twelve. Although adjusting the size lower limit and increasing the number of bins raises computational costs to some extent, it enhances simulation accuracy. Supplementary Table 2 summarizes the size ranges for each bin in the default 8-bin, adjusted 8-bin, and 12-bin structures. PNC is defined as particles within the size range of 3–1000 nm in this study.

Model applications

The simulation period spans from February 24 to March 18, 2017, with the first five days designated as a spin-up period to minimize the influence of initial conditions on the results, and thus not included in the analysis. The simulation domain is centered in Beijing, covering parts of the Beijing-Tianjin-Hebei region (Supplementary Fig. 13), with a horizontal resolution of 12 km and 44 vertical layers extending from the surface to 50 hPa. The Yonsei University (YSU) planetary boundary layer scheme was used60, a method commonly applied in NPF event analysis14,61,62. Further details on other physical parameters can be found in Cai et al.36. The gas phase chemistry was simulated using the Statewide Air Pollution Research Center (SAPRC-99) mechanism63, while aerosol chemistry were modeled using the MOSAIC module33.

The National Centers for Environmental Prediction Final (NCEP FNL) dataset with a resolution of 1.0° × 1.0° was used to provide initial and boundary conditions for the meteorological fields. Anthropogenic emissions data were taken from the Multiresolution Emission Inventory for China (MEIC) version 1.4, featuring a horizontal resolution of 0.25° × 0.25°64,65. Biogenic emissions were obtained from the Model of Emissions of Gases and Aerosols from Nature (MEGAN)66. Wildfire and biogenic emissions were sourced from the Fire INventory from NCAR (FINN) version 1.5, with a resolution of 1 km67.

Due to the lack of direct DMA emission inventory, this study established a DMA emission inventory based on the DMA/NH3 emission ratio source allocation factors proposed by Mao et al.31. Specifically, the emissions ratios for agricultural, residential, industrial, transportation, and power plant sources are 0.0015, 0.0100, 0.0018, 0.0009, and 0.0070, respectively. Several studies have confirmed that these ratios significantly improve the model’s performance in simulating DMA34,68,69.

In order to analyze the impact of the H2SO4-DMA nucleation mechanism on PNC and CCN, we conducted six simulation scenarios. Three of these scenarios were designed to validate the effects of incorporating the H2SO4-DMA nucleation mechanism: one scenario that does not consider any nucleation (sim_no), one that considers only the model’s default binary nucleation scenario (sim_default), and one that involves only the H2SO4-DMA nucleation mechanism (sim_DMA). The sim_no scenario focuses exclusively on primary emissions. The fourth scenario (sim_all) includes four types of nucleation mechanisms, comparing the influence of H2SO4-DMA nucleation with different nucleation mechanisms and primary emissions on PNC and CCN. The remaining two scenarios analyze the impact of DMA sources during the nucleation process, specifically considering agricultural source DMA (sim_agriDMA) and residential source DMA (sim_resiDMA) in the H2SO4-DMA nucleation process.

Observation data

The PNSD data from March 1 to 18, 2017, were collected at the Peking University Urban Atmosphere Environment Monitoring Station (PKUERS), located in the northwest of Beijing within the Peking University campus (39°59'21” N, 116°18'25” E). The measurement instruments were placed on the rooftop of a 20-meter-high building. The PNSD data, covering a particle size range from 3 nm to 10 µm, were obtained using a twin differential mobility particle sizer (TDMPS) and an aerodynamic particle sizer (APS, TSI Model 3321). Further details about the observation can be found in previous studies9,70. In addition to the PNSD data at the Beijing station, this study also collected air quality and meteorological data for Beijing. Hourly PM2.5 and SO2 concentrations from March 1 to 18, 2017, were downloaded from the website of the China National Environmental Monitoring Center (http://113.108.142.147:20035/emcpublish). Meteorological data were obtained from the National Centers for Environmental Prediction (ftp://ftp.ncdc.noaa.gov/pub/data/noaa/).