The measurements were conducted at Gucheng (GC) site (39∘09′01.1′′ N, 115∘44′02.6′′ E), situated at an Ecological and Agricultural Meteorology Station (39∘09′ N, 115∘44′ E) of the Chinese Academy of Meteorological Sciences from 12 November to 24 December 2018. The station is located in Dingxing county, Baoding city, Hebei province, China (as seen in Fig. 1), and surrounded by agricultural fields and sporadically distributed villages. Being far from the urban and industrial emission areas, this site can be treated as a representative regional site in the northern part of NCP. More details about this site can be found in Lin et al. (2009) and Shen et al. (2018a).

Figure 2 shows the time series of meteorological parameters (Fig. 2a shows the wind speed and direction; Fig. 2b shows the temperature and relative humidity) and aerosol properties (Fig. 2c shows the total surface and volume concentration; Fig. 2d and e show the PNSD in the size range of 10 to 800 nm and particle number concentration in the range of 1.3 to 2.4 nm) during this field campaign. During our study, wind speed was typically quite low, with an average of 1.18 m s-1, indicating stagnant meteorological conditions for the limited dilution of air pollutants at the current site. The temperature and relative humidity (RH) show opposite diurnal variations over the observational period, with the highest temperature and lowest RH during daytime and vice versa during nighttime. The observed time series of the concentration of different trace gases during current study is shown in Fig. S1 in the Supplement. To be specific, the campaign-averaged concentration of CO, O3, NOx, and SO2 was 1394, 7, 83, and 10 ppb, respectively.

According to the PNSD and PSM data, 5 d, with 4 d having a significant burst of sub-3 nm clusters (as shown in Fig. 2e), were classified as being NPF events occurring during the total experimental period. It has to be noted that, on the day of 18 November, though PSM data were not available due to technical issues, clear growth of nucleation mode particles with a typical banana-shaped PNSD was observed and lasted for more than 12 h. These particles under the growth of such a long time should not be from traffic emissions or transported particles. Therefore, it was also classified as an event day in our study. Considering all of these five NPF events, this corresponds to an NPF frequency of 12.8 %, which was lower than that at an urban site (i.e., Beijing) in the same region during the same season (Shen et al., 2018b found 25.8 %; Deng et al., 2020 found 51.4 %). Similar findings were also observed in Yue et al. (2009) and Wang et al. (2013) who found that NPF frequencies were higher at the Beijing urban site than at the corresponding regional background or rural site. Yue et al. (2009) and Wang et al. (2013) attributed this to the higher pollution level and correspondingly higher precursor content in the urban cities, leading to stronger NPF events there.

During our study, 6 d, with a slightly weak burst of sub-3 nm particles, were identified as being undefined days, as their formation and growth rate cannot be calculated accurately. For non-event days, we observed that, during many of them, some nucleation mode particles with sizes above 10 nm did appear. However, we did not observe the burst of sub-3 nm clusters from the PSM measurements, and moreover, no clear growth of these particles can be identified. This indicates that these small particles are probably not from the nucleation of H2SO4 with other species and their subsequent growth but more likely local emissions (traffic exhausts) or long-range transported particles.

Figure 3 shows a typical NPF event on 7 December as an example. Northwesterly wind prevailed, with elevated wind speed starting from around 08:00 LT, which was conducive to the diffusion of local pollutants, leading to a rapid decrease in CS concurrently. At the same time, an obvious rise in the H2SO4 concentration was observed, coinciding with a strong burst in the concentration of sub-3 nm clusters. Then, new particles with diameters larger than 10 nm, as shown in Fig. 3b, gradually formed by growth (exhibited as a visible banana shape in PNSD).

For all the identified NPF events, the formation rate of 1.3 nm (J1.3) particles ranged from 6.0 to about 30.4 cm-3 s-1, with an average value of 22.0 cm-3 s-1 at our GC site during the measurement period. Note that most atmospheric formation rates reported in China were based on the measured formation rates at relatively larger size, i.e., 3–10 nm, which are so-called “apparent” particle formation rates. In order to derive the formation rates of critical clusters from the apparent particle formation rates (Kulmala et al., 2017), the nuclei GR or GR at sub-3 nm is needed but usually remains unclear. Therefore, we focused more on the formation rate of particles at sizes below 3 nm in the following discussion. In principle, the particle formation rate is inversely proportional to the CS, as the nucleation precursors or clusters would be scavenged more rapidly under higher CS conditions, leading to a slower nanoparticle formation with a lower J. However, as shown in Table 1, in spite of the higher CS, the particle formation rates at our site appear to be higher than those in clean environments. This kind of intensive NPF becomes more noticeable for those Chinese megacities, such as Shanghai, Beijing, and Nanjing, which have an even higher J and CS compared to that at our GC site. The most plausible explanation could be the higher abundance of nucleating precursors for NPF in those polluted atmospheres, which is indicated by the SA concentration that is either measured in urban Shanghai and Nanjing or calculated in our study. To be specific, the mean SA proxy concentration during NPF at our GC site was around 1.4×107 cm-3, which is a factor of around 30 higher than that at Hyytiälä in Finland (Nieminen et al., 2014). The SA concentration during NPF at Shanghai (Xiao et al., 2015) and Nanjing (Herrmann et al., 2014) was even higher, at around 4×107 cm-3.

Although the formation rate of 1.3 nm particles is relatively high, the newly formed particles at our GC site usually cannot grow into very large particles within a short time, as indicated by their low GR. The average value of GR1.3–2.4 and GR9–15 at our site was 0.5 and 3.9 nm h-1, respectively, which is generally lower than many clean environments – GR1–3 of 0.9 nm h-1 for Hyytiälä (Kulmala, 2013) and of 5.1 nm h-1 for Jungfraujoch (Boulon et al., 2010) – but similar to those at urban Beijing (Chu et al., 2021) and rural Pingyuan (Fang et al., 2020). This could be attributed to the high CS or CoagS at those polluted environments, as the growth of small particles is limited, which are more vulnerable to the coagulation scavenging. However, despite the high CoagS, the observed GR at Shanghai and Nanjing was still exceptionally high. This discrepancy suggests that, besides the high concentration of precursors (mainly H2SO4) in polluted environments, including both rural and urban sites, other precursors with different efficiencies for nanoparticle growth and other involving mechanisms (for instance, multiphase reactions) may all contribute to the nanoparticle growth but have yet to be elucidated.

To further understand the dominating nucleation mechanism in the rural atmosphere of NCP in China, we plotted the measured formation rate of 1.3 nm particles (J1.3) against the simulated H2SO4 concentration and compared the results to previous studies conducted in different environments, as shown in Fig. 4. As illustrated by the significant correlation between the concentration of sulfuric acid and the particle formation rates, sulfuric acid is considered to be the driving species in the initial steps of NPF, as confirmed conventionally. However, the obtained J1.3–H2SO4 relationship for current environment appeared to deviate largely from those obtained by other studies. If only referring to the slope of the J1.3–H2SO4 relationship, our results seem to approximate most to the ones measured by these CLOUD (the Cosmics Leaving OUtdoor Droplets chamber) experiments, based on the mechanism of H2SO4-DMA (dimethylamine) nucleation. However, without the direct measurements of other potential precursors, the molecules stabilizing H2SO4 clustering still remain unclear.

Comparing the particle formation rates reported in different environments in China, our results were of a similar magnitude to that in Beijing (Cai et al., 2021b), an urban site in the NCP. It has to be noted that the Cai et al. (2021b) study was conducted during a much longer time and completely covered the measurement period of our study. More importantly, during the 5 d of events in our study, NPF concurrently occurred at their measurement site (Liu et al., 2020). Additionally, for these 5 event days, air masses arriving at our site followed similar transport paths to that in urban Beijing (see Fig. S2 in the Supplement for an example), as they both originated from Siberian areas, where the concentration of gaseous pollutants and particulate matter was typically quite low, through the northwest of the observational sites. Taking both sources of evidence, we hypothesize that NPF events during these days in this area might be a regional phenomenon that is sharing the same or a similar nucleation mechanism. Cai et al. (2021b) and Yan et al. (2021) further concluded that H2SO4-DMA was the dominating nucleation mechanism for urban Beijing, with additional support from the measured C2-amine concentration. Considering the similarities between these two sites, we speculated that the clustering of H2SO4 with DMA may also dominate the nucleation process at our site during winter, though future work is needed to verify the current hypothesis.

On the other hand, we noticed that our results deviate significantly from the measured formation rate at Pingyuan (Fang et al., 2020), which is another rural site in the NCP. They concluded that neither H2SO4-NH3 nor H2SO4-DMA mechanisms could fully explain their observed particle formation rate but suggested that gaseous dicarboxylic acids were the dominating species for the initial step of H2SO4 clustering under a diacid-rich environment. Being similar to the rural environment of NCP, we cannot completely rule out the contribution of dicarboxylic acids to the H2SO4 stabilization. However, as illustrated in Fig. S4, the concentration of these four dicarboxylic acids during NPF events was in general lower than that during non-event days. Furthermore, during the daytime of events days when NPF was typically initiated, the signals of these diacids obtained from the I-CIMS did not show a clear increase, unlike sulfuric acid, but were rather elevated during the nighttime (see Fig. S5), which is obviously different to the case of Pingyuan. Hence, the involvement of diacids during the initial steps of nucleation under the current rural atmosphere might not hold. This statement does not necessarily mean that our previous inference was incorrect but, on the other hand, provides some hints that although NPF events in the NCP are regional, there might be no uniform theory but multiple mechanisms coexisting to explain its features, with the dominating one varying according to different emission patterns or meteorological conditions.

The high concentration of SO2, NH3, NOx, and VOCs (Chu et al., 2019), as well as fine particles, makes the NCP of China a unique context for NPF compared to many other environments. In principle, the competition between how fast the newly formed clusters grow and how fast they are scavenged determines whether or not NPF will occur in the atmosphere. However, in the NCP, the concentration of SA was typically quite high, probably reaching its maximum rate to form clusters. Thus, CS or CoagS becomes the dominant factor controlling the occurrence of NPF. This was partly confirmed by existing observations; for instance, Cai et al. (2021b) found that H2SO4 was high enough in urban Beijing but did not necessarily lead to the occurrence of NPF there. Their research pointed out that as long as CS or CoagS was below a certain threshold (Cai et al., 2017), NPF is very likely to occur.

Was this also true for the rural atmosphere in the NCP? By comparing with non-event days at our site (see Fig. 5a), we noticed that the H2SO4 level was not significantly higher (but sometimes even lower) than that during non-event days. In other words, the abundance of H2SO4 did not always lead to NPF, and it was only when CS was significantly lowered that the event became more likely to occur. This strongly demonstrates the similarity between our site with that of urban Beijing in that CS would be the limiting factor for the occurrence of NPF. However, we noticed that there were a very few cases (two cases) in which the CS was somewhat low, with the levels being quite close to that under those event days, yet NPF still did not occur. The most plausible explanation for this could be, on the one hand, the lowered H2SO4 concentration on these days (as shown in Fig. 5a) and, on the other hand, that the other nucleating species rather than H2SO4 may not be always enough to initiate nucleation at this site.

As previously stated, the dimensionless criterion, I, is a good quantitative indicator to predict whether an NPF occurs or not during a certain day. Thus, we plotted I against the condensational sink for NPF days and other days under different H2SO4 levels. Cai et al. (2021a) found that the larger the I value, the higher frequency at which NPF events occurred for both urban Beijing and Shanghai, which was also clearly revealed by our results. On the one hand, as shown in Fig. 5b, the largest I values were mostly observed for NPF days, confirming its feasibility in predicting the occurrence of NPF events. On the other hand, the obtained I anti-correlated with CS quite well, while the influence from the available H2SO4 was not obvious. This strongly suggests that CS was the dominating factor governing the appearance of NPF events in the current environment, which is highly consistent with the feature observed in Beijing.

Moreover, we found that the RH level under event days was generally lower than that on non-event days (see Fig. 6). This is similar to the cases for which NPF was observed in Beijing by Yue et al. (2009), who suggested that photochemical reactions were faster on sunny days with low RH. In addition to this, the ambient temperature during NPF was relatively lower than that on non-event days (Kirkby et al., 2011; Riccobono et al., 2014). Yan et al. (2021) considered that temperature can affect the stability of H2SO4 clustering and thus influence NPF. Therefore, all of these factors could be the potential reasons increase or decrease the probability of NPF occurring in current rural areas. It has to be noted that all these features, including the reduced RH level in addition to ambient T during event days, could be coincidental, with reduced CS over clean days, for instance, being a consequence of air masses originating from the north and bringing drier, colder, and cleaner air to the site. Therefore, current discussion in this regard becomes ambiguous and may be inclusive but should still be considered separately when larger datasets are available. In addition, we observed that the O3 concentration was clearly higher during event days, implying that other condensable vapors, for instance, organics that involve O3, among others, in forming HOM, might also be important to NPF in this region. Although these organic compounds formed through O3 oxidation (Mohr et al., 2019) may not necessarily participate in H2SO4 clustering, they may contribute considerably to the growth of newly formed particles, which should not be ruled out in the study of NPF for this region and also need to be investigated in the future.