Measurement report: Size distributions of urban aerosols down to 1 nm from long-term measurements

. The size distributions of urban atmospheric aerosols convey important information on their origins and impacts. Their long-term characteristics, especially for sub-3 nm particles, are still limited. In this study, we examined the characteristics of atmospheric aerosol size distributions down to ∼ 1 nm based on 4-year measurements in urban Beijing. Using cluster analysis, three typical types of number size distributions were identiﬁed, i.e., daytime new particle formation (NPF) type, daytime non-NPF type, and nighttime type. Combining a power law distribution and multiple lognormal distributions can well represent the sharp concentration decrease of sub-3 nm particles with increasing size and the modal characteristics for those above 3 nm in the submicron size range. The daytime NPF type exhibits high concentrations of sub-3 nm aerosols together with other three modes. However, both the daytime non-NPF type and the nighttime type have a low abundance of sub-3 nm aerosol particles together with only two distinct modes. In urban Beijing, the concentration of H 2 SO 4 monomer during the daytime with NPF is similar to that during the daytime without NPF, while signiﬁcantly higher than that during the nighttime. The concentration of atmospheric sub-3 nm particles on NPF days has a strong seasonality while their seasonality on non-NPF days is less pronounced. In addition to NPF as the most important source, we show that vehicles can emit sub-3 nm particles as well, although their inﬂuence on the measured aerosol population strongly depends on the distance from the road.


Introduction
Atmospheric aerosol particles originate from both primary and secondary sources, spreading across a wide range of sizes from ∼ 1 nm to hundreds of micrometers. Primary sources directly emit particles over a broad size range, and these sources include natural ones such as windblown dust and sea spray, and anthropogenic ones such as coal com-bustion, traffic emissions, and biomass burning. Secondary sources produce mainly fine and ultrafine particles (Kumar et al., 2014). Atmospheric new particle formation (NPF), for example, generates a significant number of particles down to ∼ 1 nm, which has been shown to be ubiquitous in the atmosphere (Zhang et al., 2012). Traffic emissions can contain sub-3 nm particles and those particles are detected when measurements are made near the sources (Ronkko et al., Published by Copernicus Publications on behalf of the European Geosciences Union. 13570 C. Deng et al.: Size distributions of urban aerosols down to 1 nm 2017). In urban atmospheric environment mixed with various emissions, the size distributions of atmospheric aerosol particles are dynamic and complex, reflecting contributions from many primary and secondary sources.
For decades of development, size distributions of atmospheric particles larger than 3 nm have been well understood in contrast to limited information about sub-3 nm particles. Whitby tri-modal representation (Whitby, 1978) has been widely used to describe atmospheric aerosol size distributions, i.e., nuclei mode (∼ 5-100 nm), accumulation mode (∼ 100 nm-2 µm), and coarse mode (> 2 µm). These three modes reflect their origins. For instance, nuclei mode particles are considered to be mainly originated from gas-toparticle conversion. As the understanding of nucleation process extends, a number of studies proposed the presence of nucleation mode in the size range of 3-25 nm which overlaps with Whitby nuclei mode (Covert et al., 1996;Hoppel and Frick, 1990;McMurry et al., 2000). For instance, both modeling and experimental results showed that nucleation mode is present when NPF events occur in the atmosphere (McMurry et al., 2000;Dal Maso et al., 2005;Hussein et al., 2004).
Advancing measurement techniques enables the development of an improved picture of atmospheric aerosol size distributions. Prior to Whitby tri-modal representation, the prevailing size distribution of atmospheric aerosols was the power function model by Junge (1963), which was based on measurements using impactors with a large cut-off size (∼ 0.1 µm) and low size resolution. Developing electrical mobility-based techniques provided data for the tri-modal representation by achieving size distribution measurements down to tens of nanometers with high time resolution and high size resolution (Liu and Piu, 1975;Knutson and Whitby, 1975;Whitby and Clark, 1966). Electrical mobility size spectrometers are now widely used to measure atmospheric aerosol size distributions. During the last decade or so, advanced techniques were developed and improved towards measuring sub-3 nm atmospheric aerosols, such as diethylene glycol-based electrical mobility spectrometer (DEG SMPS) (Jiang et al., 2011a), particle size magnifier (PSM) (Vanhanen et al., 2011), neutral cluster and air ion spectrometer (NAIS) (Mirme and Mirme, 2013), half-mini differential mobility particle sizer (half-mini DMPS) , and differential mobility analyzer train (DMA train) (Stolzenburg et al., 2017). Among them, DEG SMPS, PSM, and NAIS have been used in a number of field measurements (Deng et al., 2021;Jiang et al., 2011b;Kontkanen et al., 2016Kontkanen et al., , 2017Sulo et al., 2021).
These developments and applications improve the understanding about size distributions of atmospheric sub-3 nm particles. Jiang et al. (2011b) first measured atmospheric size distributions down to ∼ 1 nm using DEG SMPS during a short-term campaign in Atlanta and showed the sharp concentration decrease of sub-3 nm particles. The measured aerosol size distribution was further verified by simulation and observation in chamber experiments with sulfuric acid and amine clustering conditions (Chen et al., 2012). Studies measured the concentration of sub-3 nm particles using the PSM at various sites from a boreal forest to polluted megacities (Kontkanen et al., , 2016. Despite these progresses, the characteristics of sub-3 nm particles are still limited. For instance, whether sub-2 nm aerosols always exist with high concentrations in the atmosphere is uncertain, although it is generally agreed that ion clusters in this size range are constantly present. DEG SMPS measurements report high concentrations of sub-2 nm aerosols only during NPF periods (Jiang et al., 2011b) while PSM measurements observe sub-2 nm signals all the time and with elevated concentrations during NPF periods (Kontkanen et al., 2016. This discrepancy can be partly attributed to different principles of these two instruments . Long-term measurements in various atmospheric environments together with improved understanding of their origins will help to better address this. Additionally, extending Whitby tri-modal representation down to sub-3 nm will provide a full picture of atmospheric aerosol size distributions . More importantly, it can provide information on nucleation processes where 1-3 nm is the critical size range, which can contribute to mechanistic, regional, and global atmospheric models.
To reveal the characteristics of atmospheric aerosol size distributions down to ∼ 1 nm, we started long-term atmospheric measurements in urban Beijing since 2018. Key gaseous precursors for the formation of sub-3 nm particles such as sulfuric acid and its clusters are also measured. This study aims to investigate the characteristics of typical aerosol size distributions together with gaseous precursors from the long-term perspective, the representation of the aerosol size distribution down to ∼ 1 nm, and the possible origins of sub-3 nm aerosols. Particularly, this study focuses on the sub-3 nm size range, including its origin and connection with the rest of the submicron size range, especially the nucleation mode and the nuclei mode.

Measurements
Atmospheric measurements were conducted at two urban sites in Beijing (Fig. 1). Long-term measurements were carried out on the west campus of Beijing University Chemical Technology (BUCT site) since January 2018. This site is situated ∼ 550 m to the west of the third ring road and ∼ 130 m to the southwest of a road, which is likely influenced by traffic emissions (Lu et al., 2019;Cai et al., 2021b;Deng et al., 2020). Due to instrument maintenance, the data used in this analysis included those from 16 January-17 May and 19 October-26 December 2018, 1 January-28 March 2019, and 19 July 2019-31 December 2021 (a total of 1009 available days). In addition, a short-term campaign was conducted on the campus of Tsinghua University (Tsinghua site) during 7 March-6 April 2016 (a total of 31 available days). Different from the BUCT site, the Tsinghua site is considered to be less influenced by traffic emissions because the closest major road is ∼ 1 km away from this site (Cai et al., 2017b;Cai and Jiang, 2017). There are no significant stationary emission sources nearby both two sites. Details about these two sites can be found in previous studies Cai et al., 2017b).
Size distributions of atmospheric aerosols in the range of 1 nm-10 µm (mobility diameter) were measured using a homemade DEG SMPS (1-6.5 nm) (Jiang et al., 2011a;Cai et al., 2017a) and a particle size distribution spectrometer (PSD; 3 nm-10 µm) (Liu et al., 2016). The schematics and pictures of the DEG SMPS and PSD are shown in Fig. S1 in the Supplement. The DEG SMPS is equipped with a core sampling inlet  for improving their sampling efficiency, a soft X-ray neutralizer (TSI Inc., model 3088), a specially designed miniature cylindrical differential mobility analyzer (Cai et al., 2017a for classifying sub-10 nm particles, and a two-stage condensation particle counter which includes a modified DEG-based ultrafine CPC and a conventional CPC (TSI Inc., 3772). The PSD consists of an aerodynamic particle sizer (APS; TSI Inc., model 3321) and two parallel SMPSs using a nano-DMA (model 3085, TSI Inc.) and a long-DMA (model 3081, TSI Inc.), respectively.
Concentrations of sulfuric acid and its clusters were measured using nitrate chemical ionization time-of-flight mass spectrometers (Aerodyne Research Inc.) (Zheng et al., 2015;Cai et al., 2017b;Lu et al., 2019). The sampling configu-rations and calibration procedures were reported previously (Lu et al., 2019;Zheng et al., 2015). The NO concentration was measured by a trace gas analyzer (42i-TL, Thermo Fisher). The meteorological data, including the temperature, relative humidity, and ambient pressure, were measured using local weather station data acquisition system (Vaisala, AWS310).

Data analysis
Cluster analysis was used to identify typical atmospheric aerosol number size distributions during the measurement period at both sites. Details about this methodology (Beddows et al., 2009;Wegner et al., 2012) are given in the Supplement. We identified three typical types of aerosol number size distributions in urban Beijing together with H 2 SO 4 and its clusters: C1, C2, and C3 types (Figs. S2 and S3). C1 type has high concentration of sub-3 nm aerosols and is mostly observed during NPF periods (e.g., 9-14) on NPF days. The other two types are mostly observed during non-NPF periods. Thus, they are referred to as daytime NPF type, daytime non-NPF type, and nighttime type, respectively. Their characteristics will be further discussed in the following section. The measurement days were classified into NPF days and non-NPF days according to the criteria and examples reported previously .
A combination of power law and multiple lognormal distribution functions was used to fit the measured H 2 SO 4 and its clusters and particle number size distributions. When focusing on number size distributions, we fitted only in the submicron size range, because number concentration of coarse mode particles (> 2 µm) is comparatively negligible. Note that to be consistent, we used mass diameter when combining size distributions of H 2 SO 4 clusters and particles, otherwise mobility diameter is used for particles. The relation between mobility diameter and mass diameter (Ku and De La Mora, 2009), i.e., mobility diameter is 0.3 nm larger than mass diameter, was used to convert mobility diameter for particles into mass diameter. It should be also noted that, in Figs. 2, 3, S3, S6, S7, and S9, the concentration of H 2 SO 4 monomers and dimers was converted into dN/dlogd p using the method by Jiang et al. (2011b).
For sub-3 nm particles, a power law function is used, where d p is the particle diameter, nm; dN dlogd p is the number size distribution function, cm −3 ; a and b are two fitting parameters for the power law function.
Note that the power law function was chosen to fit in the sub-3 nm because it can well capture the monotonic decrease from H 2 SO 4 monomer to dimer and then to the sizes representative of aerosol particles. The lognormal distribution function is not a good fit in the sub-3 nm size range (Fig. S4) Figure 2. Cases of three typical types of number size distributions from H 2 SO 4 monomer to dimer and then to larger aerosol size: the daytime NPF type (red), daytime non-NPF type (blue), and nighttime type (black). The daytime NPF, daytime non-NPF, and nighttime particle number size distribution (PNSD) is selected during the NPF period on a NPF day (16 February 2018, 11:10 LT), during the daytime on a non-NPF day (25 February 2018, 12:25) and during the nighttime (4 April 2018, 00:35). The diamonds, squares, and circles represent the distribution function (dN/dlogd p ) of H 2 SO 4 monomers, dimers, and aerosols, respectively. and especially a "mode" with a peak diameter of ∼ 0.4 nm resulting from such a fit seems not to be reasonable.
For particles above ∼ 3 nm, multiple lognormal distribution functions (Seinfeld and Pandis, 2006) are used: where d p is the particle diameter, nm; N i , d pg,i , and σ g,i represent total number concentration (cm −3 ), geometric mean diameter (nm), and geometric standard deviation (dimensionless) within the mode i. The intensity of NPF is characterized by the particle formation rate, which measures the growth flux through a certain particle size. A balance formula that enhances the evaluation of coagulation scavenging in the presence of high aerosol loadings was used in this study to evaluate the particle formation rate (Cai and Jiang, 2017), Here J k is the particle formation rate at size d k , cm 3 s −1 , where d k was 1.5 nm in this study, nm; d u is the upper size bound of the chosen aerosol population, nm; d min is the smallest particle size detected by particle size spectrometers, The x axis error bars of H 2 SO 4 monomers and dimers indicate the variation range of estimated H 2 SO 4 monomers and dimers diameters by assuming the bulk density to be 1000-1800 kg m 3 . The y axis error bars of H 2 SO 4 monomers and dimers indicate the 25th-75th range of concentrations. The black and red lines indicate the fitted size distribution in the whole size range and in sub-3 nm size range, respectively. The blue, magenta, and green lines present the fitted mode 1, mode 2, and mode 3, respectively. The diamonds, squares, and circles represent the distribution function (dN /dlogd p ) of H 2 SO 4 monomers, dimers, and aerosols, respectively. nm; N [d k ,d u ) is the number concentration of particles from size d k to d u , cm −3 ; d i denotes the lower bound of the ith size bin, nm; β (i,g) is the coagulation coefficient for the collision of two particles with size of d i and d g , cm 3 s −1 ; and GR u represents the particle growth rate at size d u , nm h −1 .
An indicator, I , represents the intensity of the NPF in atmospheric environment governed by H 2 SO 4 -amine nucleation, considering the effects of various parameters such as H 2 SO 4 concentration, amine concentration, the stability of H 2 SO 4 -amine clusters, and background aerosols (Cai et al., 2021a). This indicator has been used to reveal the governing factor for the seasonal variations of NPF in urban Beijing . It was calculated using the method by Cai et al. (2021a) (details can be found in the Supplement). Together with other evidence, it is used to explore whether the elevation of sub-3 nm aerosols on non-NPF days is due to nucleation process in Sect. 3.2.

Results and discussion
3.1 Typical number size distributions of sub-3 nm aerosols Figure 2 showed three cases of typical types of aerosol number size distributions. The number size distribution function (dN/dlogd p ) was at high levels in the sub-3 nm size range of the daytime NPF type size distribution, and the highest value in this case reached up to ∼ 1.1×10 6 cm −3 . The dN/dlogd p decreased from H 2 SO 4 monomer, H 2 SO 4 dimer to sub-3 nm aerosols, and reached a trough at ∼ 3 nm (note that H 2 SO 4 monomer and dimer are included in the size distribution to provide information about the precursors of nucleation process). This trough can be partly caused by aerosol dynamic processes, which have also been simulated by models (Chen et al., 2012;Li and Cai, 2020). After reaching the trough, the dN/dlogd p slightly increased but then dropped significantly. The dN/dlogd p showed no significant increase or decrease from ∼ 12 nm until it started to decrease substantially at ∼ 300 nm and reached a low level at 1000 nm. In contrast to the daytime NPF type size distributions, the values of dN /dlogd p in the sub-3 nm size range of the daytime non-NPF type and nighttime type size distributions were substantially low. The concentrations of sub-2 nm aerosol particles were near zero. In the 2-3 nm size range, the dN/dlogd p of both daytime non-NPF and nighttime types was low while the dN/dlogd p was high in the larger size range, and higher than that of the daytime NPF type at sizes larger than about 20 nm. Although the daytime non-NPF type and nighttime type showed similar characteristics in the size range above the H 2 SO 4 clusters, the H 2 SO 4 monomer concentration was higher during daytime than nighttime. From a long-term perspective, the characteristics of the median aerosol number size distributions for each type were similar in four seasons (Fig. S5). For the daytime NPF type, they showed a similarly sharp particle concentration decrease with increasing size in the sub-3 nm size range and local peaks above ∼ 3 nm in four seasons, although the concentration level showed seasonal variations. The seasonal variations of number concentrations of sub-3 nm aerosols will be discussed in the following section. For the daytime non-NPF and nighttime type, both the pattern and concentration level were similar in four seasons.
The median atmospheric aerosol size distributions for the whole measurement time period can be generally well fitted using a combination function of the power law and the lognormal distributions (Figs. 3 and S6-S7). Figure 3 showed that such combination function generally fitted the median daytime NPF type aerosol size distribution for the 4-year measurements well, both in logarithmic and linear scale of ordinate. In Fig. 3a, the power function depicted the characteristics that the concentrations decrease from H 2 SO 4 monomers to ∼ 3 nm particles. Meanwhile, the lognormal function agreed well with the raw distributions. Figure 3b showed the tri-modal lognormal distributions more clearly in the linear scale of ordinate. The daytime NPF type size distribution presented three modes, referred to as mode 1, mode 2, and mode 3, respectively. Unlike the daytime NPF type, the daytime non-NPF and nighttime types only showed two modes in the number size distributions (Figs. S6-S7). Table 1 summarized the fitted functions and their parameters of those median aerosol number size distributions for the 4 years of measurements in urban Beijing. The combination function consists of the power function and the lognormal distributions. For the power function, the parameters determining the fitting shape of sub-3 nm size distribution are a and b. With a larger b value, the concentrations decrease going from H 2 SO 4 monomer to small clusters and further to particles of a few nanometers is sharper, so b values were much larger for the daytime non-NPF and nighttime types than the daytime NPF type. For the daytime non-NPF and nighttime types, although their concentration in sub-3 nm size range were similarly low, the concentration decrease from H 2 SO 4 monomer to dimer was sharper for the nighttime type, so the b value was larger for the nighttime type than for the daytime non-NPF type. Concerning the lognormal distributions, the number concentration of mode 1 and mode 2 particles were much higher than that of mode 3 for the daytime NPF type. The modal diameters of mode 2 and mode 3 for the daytime non-NPF type and nighttime type were larger than those for the daytime NPF type.
Compared to the Whitby model, our results showed that in Beijing for the daytime NPF type number size distributions, there existed three modes (mode 1, mode 2, and mode 3) in the ultrafine size range. The first two modes are induced by atmospheric nucleation process and they are in the size range of nucleation mode. There was a trough between mode 1 and mode 2 in the daytime NPF type. This is because the nucleation process produces large numbers of small particles and only a fraction of them grows into larger sizes, together with a strong impact of coagulation in the small size range. Mode 3 in the daytime NPF type is mainly from primary emissions Ristovski et al., 1998), which is often called as Aitken mode.
In contrast to daytime NPF type, for the daytime non-NPF and nighttime type, there were only two modes (mode 2 and mode 3) in the ultrafine size range. The modal diameter in mode 2 for the daytime non-NPF and nighttime types was larger than the daytime NPF type. Also, for daytime non-NPF and nighttime types, the range of mode 2 was much broader and the number concentration in this mode was lower than that for the daytime NPF type. These characteristics indicate no influence of atmospheric nucleation process. Note that these fitting parameters are not presumed to be constant because atmospheric processes and emissions vary spatially and temporally.
The accumulation mode (100 nm-2 µm) was not shown for all the types of number size distributions in Figs. 3 and S6-S7 because their contribution in number concentrations was Table 1. The fitting parameters for the median daytime NPF, daytime non-NPF, and nighttime type aerosol size distributions of 4-year measurements in urban Beijing by the combination of the power law function and the lognormal distribution function. The power law function includes two parameters, a and b. The lognormal distribution function includes the number concentration within the mode (N), the geometric mean diameter within the mode (d pg ), and the standard deviation (σ g ) Fitting function Size range Sub-3 nm 3-1000 nm low. However, the accumulation mode obviously presented in the volume size distributions of all the types, and the concentration was lower for the daytime NPF type compared to other two types (Fig. S8). The accumulation mode particles showed high concentration in the surface area size distributions as well. This indicates their important role for scavenging smaller particles and condensing species. Additionally, we showed that this combination model performs well in the measured aerosol size distributions in Atlanta (Fig. S9). The combination model captured the sharp particle concentration decrease with an increasing size in the sub-3 nm size range and the modal characteristics above 3 nm size of the daytime NPF type aerosol size distribution in Atlanta.

Potential sources of sub-3 nm aerosols in urban Beijing
NPF process is the most important source of atmospheric sub-3 nm particles (N sub-3 ) in urban Beijing. As shown in Fig. 4a, N sub-3 showed a clear diurnal variation that reached its daily maximum in the noontime on NPF days. The median daily maximum N sub-3 was ∼ 1.1 × 10 4 cm −3 on NPF days in urban Beijing. The observed daytime maximum of N sub-3 results mainly from the formation of the H 2 SO 4 clusters driven by SO 2 oxidation through photochemical process during the daytime on NPF days (Figs. 4c, d and S10). When the NPF events occurred, N sub-3 was overwhelmingly higher than that when there were no NPF events (non-NPF daytime or nighttime). Similar diurnal cycles of N sub-3 and the dominant contribution of NPF process to the sub-3 nm aerosols were also observed in Shanghai, China (Xiao et al., 2015), Po Valley, Italy (Kontkanen et al., 2016), and Kent, US (Yu et al., 2014), which are relatively polluted atmospheric environments.
The concentrations of sub-3 nm aerosols showed a strong seasonality on NPF days but had no obvious seasonal variations on non-NPF days (Figs. 5 and S11), supporting that the elevated N sub-3 was introduced by the NPF process. N sub-3 was significantly higher in winter than those in summer on NPF days. The median daytime N sub-3 on NPF days was ∼ 1.2 × 10 4 cm −3 in winter in contrast to ∼ 200 cm −3 in summer. However, the more important reason is the much lower NPF intensity in summer because the seasonal variation of N sub-3 on NPF days was consistent with those of H 2 SO 4 dimer concentration and the formation rates of ∼ 1.5 nm aerosols (Fig. S12). This indicates that the seasonal variation of the formation process drives the seasonal variation of N sub-3 (Deng et al., , 2021. This seasonal variation is different from that observed in Hyytiälä, a boreal forest site in Finland, in which N sub-3 was the highest in summer or spring and the lowest in winter . The highest concentration of small particles in the size range of 1.1-1.7 nm in Hyytiälä was observed during summertime, coinciding with the high photochemical and biogenic activity in summer . In addition to atmospheric NPF, sub-3 nm aerosols can also be emitted by primary sources, such as traffic emissions. This is relatively easier to explore during non-NPF days. As shown in Fig. 4a, N sub-3 showed small morning (∼ 06:00-09:00) and evening (∼ 16:00-19:00) peaks on non-NPF days, roughly corresponding to the traffic rush hours in the morning and evening in urban Beijing. Although number concentrations of sub-2 nm aerosols were very low, those of 2-3 nm aerosols (N 2−3 ) showed diurnal patterns on non-NPF days (Fig. 4b), indicating that the morning and evening peaks are more likely due to primary emissions.
The obvious difference of the N 2−3 on non-NPF days between the Tsinghua site and the BUCT site, and between the COVID-19 lockdown period and normal period, further supports that vehicles emit 2-3 nm particles (Fig. 6). The morning and evening peaks of N 2−3 on non-NPF days were more prominent at the BUCT site (closer to traffic roads) than at the Tsinghua site that is considered to be less influenced by traffic emissions. In addition, we found that N 2−3 was much lower during the strict COVID-19 lockdown period at the BUCT site than normal time period. Traffic flows were extremely low during this strict lockdown period, such that traffic emissions were significantly reduced.
A non-NPF case (13 March 2018) was examined to further confirm that vehicles can emit 2-3 nm aerosols (Fig. 6b  and c). On this non-NPF day, N 2−3 started to increase at around 06:00 and reached the maximum at around 08:00 when the concentration of the gas tracer for the traffic emissions, NO, also showed a peak. Furthermore, the NPF indicator, I , had low values during this morning time, indicating that the increase of 2-3 nm aerosols was unlikely due to nucleation process (Fig. 6c). Previous studies reported that traffic can directly emit sub-3 nm aerosols and thus can be an important source for sub-3 nm aerosols (Ronkko et al., 2017). Our results in urban Beijing support that traffic can emit 2-3 nm particles, but their relative contribution to the total aerosol number is negligible on NPF days. Figure 6 also showed that, unlike secondary formation process, traffic emissions in terms of sub-3 nm aerosols is of local characteristic and its impact on the measured aerosol population strongly depends on the distance between the traffic road and the measurement site. Nucleation and subsequent growth processes exist not only in the atmosphere but also in the exit of pipelines of vehicles (Giechaskiel et al., 2014). In the large-scale atmosphere, the relative homogeneity of sufficient gaseous precursors for nucleation and growth processes enables the burst of sub-3 nm aerosols. The lifetime of sub-3 nm aerosols is extremely short due to strong coagulation effects in urban Beijing (Deng et al., 2021). Thus, sub-3 nm particles directly emitted from traffic are abundant only if one directly measures near the exhaust (Ronkko et al., 2017). This is supported by the fact that significantly less sub-2 aerosols were observed than 2-3 nm aerosols during the traffic rush hour both at the BUCT site and the Tsinghua site, i.e., due to the higher loss rate of sub-2 nm aerosols than 2-3 nm aerosols.

Implications
This study describes and interprets aerosol size distributions down to ∼ 1 nm in urban atmospheric environments. Based on the modified Whitby model, we introduce the simplification of aerosol size distributions in sub-3 nm sizes, i.e., the power function. This fitting function captures well the sharp concentration decrease of sub-3 nm particles with an increasing particle size. Although different nucleation mechanisms exist in different atmospheric environments (Sipilä et al., 2010;Jokinen et al., 2018;Lehtipalo et al., 2018;Yao et al., 2018;Yan et al., 2021;Beck et al., 2022), this simplified representation can be applied because concentrations often decrease with an increasing size when going from precursor molecules to small clusters and further to aerosol particle of a few nanometers (Jiang et al., 2011b;Chen et al., 2012;Kulmala et al., 2021).
The aerosol size distributions down to ∼ 1 nm and their representations are important parameters which can contribute to mechanistic, regional, and global atmospheric models. For instance, for large-scale or regional models, the aerosol size distributions are initial input parameters to estimate aerosol population or CCN budgets (Von Salzen et al., 2000;Adams, 2002). In some models, the aerosol module often takes the modal representation of aerosol size distributions as input to simulate the aerosol dynamics for better computational speed (Binkowski and Roselle, 2003;Vignati et al., 2004). In urban environments with great complexity of precursors and emission sources, the representation of aerosol size distributions could be adjusted according to our findings instead of using the traditional three lognormal modal aerosol size distributions. Another benefit is that size distributions ranging from molecular levels to the submicron size range can help to better simulate the NPF and growth mechanisms. For instance, Zhao and coworkers (2020) used a comprehensive model to investigate the NPF mechanisms in the Amazon free troposphere. They used measured aerosol size distributions with a lower size limit of ∼ 10 nm to compare to simulated ones. Since sub-3 nm is the critical size range where nucleation occurs, it is needed to cover this size range when comparing simulations with atmospheric measurements. This is more important for urban environment mixed with various processes and more complex than pristine environment. Additionally, the power law function can be readily incorporated in models. For instance, in the global climate models, the observed aerosol size distributions are used to compare with simulated ones (Bergman et al., 2012) and the sub-3 nm size range is the key to simulate nucleation process accurately. However, due to relative scarcity of measured particle size distributions in sub-3 nm around the world, the comparison between observed and simulated results is usually lacking this key size range. The power law function, as a simplified representation of sub-3 nm size distributions, can extend the observed particle size distributions above 3 nm to sub-3 nm, thus helping to constrain the aerosol module in the global models.
Based on long-term observational results, we addressed whether high concentrations of sub-2 nm aerosols are always present in the atmosphere. We show that concentrations of atmospheric sub-2 nm aerosols are high when NPF events occur. However, they are significantly lower during non-NPF periods (often not detected by DEG SMPS) compared to NPF periods even though the H 2 SO 4 monomer concentration is often similar. Different from results measured by DEG SMPS, previous studies reported that high concentrations of atmospheric sub-2 nm aerosols measured by PSM are con-stantly present in the daytime Kulmala et al., 2021). Although the higher noise-to-signal ratio and higher detection sensitivity of PSM may partly contribute , considering that there is always high concentration of ion clusters in the atmosphere, the high signal of PSM all the time may be because it measures both aerosol particles and ion clusters Kulmala et al., 2021).
Additionally, our study implies that although vehicles can be massive in megacities, their direct emissions of sub-3 nm aerosols only influence within the vicinities of traffic roads rather than the large-scale atmosphere. There are studies indicating that vehicles can emit high concentrations of sub-3 nm aerosols as detected by PSM (Ronkko et al., 2017;Okuljar et al., 2021). This is similar to previous studies showing that concentrations of ultrafine particles emitted by vehicles decrease significantly as the distance from the roads increases, due to the rapid dilution and strong aerosol dynamic processes such as coagulation and condensation in the atmosphere (Zhu et al., 2002). Our study indicates that the decreasing phenomenon is more significant with respect to sub-3 nm aerosols. Thus, though 2-3 nm aerosols emitted from vehicles were detected by DEG SMPS at both sites in urban Beijing, emissions of sub-2 nm aerosols were barely observed. Future studies measuring the size distributions of sub-3 nm aerosols simultaneously at sites with different distances from traffic roads can be performed to further investigate the impacts of vehicle emissions on atmospheric sub-3 nm aerosols without measurement interferences from ion clusters.

Conclusions
In this study, we identify three typical types of number size distributions of urban aerosols based on 4-year measurements using cluster analysis, i.e., daytime NPF type, daytime non-NPF type, and nighttime type, and investigate their characteristics. The daytime NPF type exhibits high concentrations of sub-3 nm aerosols together with other three modes. The first two modes are induced by atmospheric nucleation process and the third mode in the daytime NPF type is mainly from primary emissions. However, both the daytime non-NPF type and the nighttime type have a low abundance of sub-3 nm aerosol particles together with only two distinct modes because they have no influence of nucleation process. In urban Beijing, the concentration of H 2 SO 4 monomer during the daytime with NPF is similar to that during the daytime without NPF, while significantly higher than that during the nighttime. We use a power law distribution and multiple lognormal distributions to represent the sharp concentration decrease of sub-3 nm particles with increasing size and the modal characteristics for those above 3 nm in the submicron size range. This fitting function also performs well for aerosol size distributions measured in Atlanta. We show that NPF is the major source of sub-3 nm particles in urban Beijing. In addition to NPF, we find that vehicles can also emit sub-3 nm particles, although their influence on the measured aerosol population strongly depends on the distance from the road. The representation of aerosol size distributions in sub-3 nm can help to constrain the aerosol module in the global models.
Data availability. The datasets for this study can be accessed via https://doi.org/10.5281/zenodo.6654175 (Deng et al., 2022). The details are available upon request from the corresponding author.
Author contributions. CD and JJ designed the research; CD, YL, JW, CY, YL, MK, and JJ collected the data; CD and JJ analyzed data with the help from RC, DW, YC, VK, and MK; and CD and JJ wrote the paper with inputs from all co-authors.

Competing interests.
The contact author has declared that none of the authors has any competing interests.
Disclaimer. Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.